LMFDB - Embedded newform 2646.2.f.m.883.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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([4, 0]))

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (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			883.3
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2646.883
Dual form			2646.2.f.m.1765.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.59097 + 2.75564i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.59097 + 2.75564i) q^{5} +1.00000 q^{8} -3.18194 q^{10} +(1.59097 - 2.75564i) q^{11} +(-2.85185 - 4.93955i) q^{13} +(-0.500000 + 0.866025i) q^{16} +1.52175 q^{17} -1.28263 q^{19} +(1.59097 - 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} +(1.11956 + 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} +5.70370 q^{26} +(3.54063 - 6.13255i) q^{29} +(-4.71053 - 8.15888i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.760877 + 1.31788i) q^{34} -1.00000 q^{37} +(0.641315 - 1.11079i) q^{38} +(1.59097 + 2.75564i) q^{40} +(-2.80150 - 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} -3.18194 q^{44} -2.23912 q^{46} +(2.91423 - 5.04759i) q^{47} +(-2.56238 - 4.43818i) q^{50} +(-2.85185 + 4.93955i) q^{52} +2.05718 q^{53} +10.1248 q^{55} +(3.54063 + 6.13255i) q^{58} +(0.562382 + 0.974074i) q^{59} +(1.56238 - 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(9.07442 - 15.7174i) q^{65} +(-5.48345 - 9.49761i) q^{67} +(-0.760877 - 1.31788i) q^{68} -8.69002 q^{71} -4.96690 q^{73} +(0.500000 - 0.866025i) q^{74} +(0.641315 + 1.11079i) q^{76} +(2.06922 - 3.58399i) q^{79} -3.18194 q^{80} +5.60301 q^{82} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(3.41423 + 5.91362i) q^{86} +(1.59097 - 2.75564i) q^{88} -0.225450 q^{89} +(1.11956 - 1.93914i) q^{92} +(2.91423 + 5.04759i) q^{94} +(-2.04063 - 3.53447i) q^{95} +(-7.42107 + 12.8537i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + q^5 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + q^{5} + 6 q^{8} - 2 q^{10} + q^{11} - 8 q^{13} - 3 q^{16} + 8 q^{17} - 6 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} + 16 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} - 6 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} - 2 q^{44} - 14 q^{46} - 9 q^{47} + 2 q^{50} - 8 q^{52} + 30 q^{53} + 26 q^{55} + 5 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} - 4 q^{68} - 14 q^{71} + 38 q^{73} + 3 q^{74} + 3 q^{76} + 5 q^{79} - 2 q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} + 18 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + q^5 + 6 * q^8 - 2 * q^10 + q^11 - 8 * q^13 - 3 * q^16 + 8 * q^17 - 6 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 + 16 * q^26 + 5 * q^29 - 20 * q^31 - 3 * q^32 - 4 * q^34 - 6 * q^37 + 3 * q^38 + q^40 - 6 * q^43 - 2 * q^44 - 14 * q^46 - 9 * q^47 + 2 * q^50 - 8 * q^52 + 30 * q^53 + 26 * q^55 + 5 * q^58 - 14 * q^59 - 8 * q^61 + 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 - 4 * q^68 - 14 * q^71 + 38 * q^73 + 3 * q^74 + 3 * q^76 + 5 * q^79 - 2 * q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 + 18 * q^89 + 7 * q^92 - 9 * q^94 + 4 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	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
$5$	1.59097	+	2.75564i	0.711504	+	1.23236i	0.964292	+	0.264840i	$0.0853191\pi$
$5$	1.59097	+	2.75564i	0.711504	+	1.23236i	−0.252788	+	0.967522i	$0.581348\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.18194			−1.00622
$11$	1.59097	−	2.75564i	0.479696	−	0.830858i	−0.520033	−	0.854146i	$-0.674080\pi$
$11$	1.59097	−	2.75564i	0.479696	−	0.830858i	0.999729	+	0.0232884i	$0.00741361\pi$
$12$		0			0
$13$	−2.85185	−	4.93955i	−0.790960	−	1.36998i	−0.925373	−	0.379058i	$-0.876248\pi$
$13$	−2.85185	−	4.93955i	−0.790960	−	1.36998i	0.134412	−	0.990925i	$-0.457085\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.52175			0.369079			0.184540	−	0.982825i	$-0.440921\pi$
$17$	1.52175			0.369079			0.184540	+	0.982825i	$0.440921\pi$
$18$		0			0
$19$	−1.28263			−0.294256			−0.147128	−	0.989117i	$-0.547003\pi$
$19$	−1.28263			−0.294256			−0.147128	+	0.989117i	$0.547003\pi$
$20$	1.59097	−	2.75564i	0.355752	−	0.616181i
$21$		0			0
$22$	1.59097	+	2.75564i	0.339196	+	0.587505i
$23$	1.11956	+	1.93914i	0.233445	+	0.404338i	0.958820	−	0.284016i	$-0.0916669\pi$
$23$	1.11956	+	1.93914i	0.233445	+	0.404338i	−0.725375	+	0.688354i	$0.758334\pi$
$24$		0			0
$25$	−2.56238	+	4.43818i	−0.512476	+	0.887635i
$26$	5.70370			1.11859
$27$		0			0
$28$		0			0
$29$	3.54063	−	6.13255i	0.657478	−	1.13879i	−0.323788	−	0.946130i	$-0.604957\pi$
$29$	3.54063	−	6.13255i	0.657478	−	1.13879i	0.981266	−	0.192656i	$-0.0617101\pi$
$30$		0			0
$31$	−4.71053	−	8.15888i	−0.846037	−	1.46538i	−0.884718	−	0.466127i	$-0.845649\pi$
$31$	−4.71053	−	8.15888i	−0.846037	−	1.46538i	0.0386810	−	0.999252i	$-0.487684\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−0.760877	+	1.31788i	−0.130489	+	0.226014i
$35$		0			0
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	0.641315	−	1.11079i	0.104035	−	0.180194i
$39$		0			0
$40$	1.59097	+	2.75564i	0.251555	+	0.435706i
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	0.559976	−	0.828509i	$-0.310810\pi$
$41$	−2.80150	−	4.85235i	−0.437522	−	0.757810i	−0.997498	+	0.0706992i	$0.977477\pi$
$42$		0			0
$43$	3.41423	−	5.91362i	0.520665	−	0.901819i	−0.479046	−	0.877790i	$-0.659017\pi$
$43$	3.41423	−	5.91362i	0.520665	−	0.901819i	0.999711	−	0.0240288i	$-0.00764935\pi$
$44$	−3.18194			−0.479696
$45$		0			0
$46$	−2.23912			−0.330141
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	−0.571344	−	0.820711i	$-0.693578\pi$
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	0.996428	+	0.0844432i	$0.0269112\pi$
$48$		0			0
$49$		0			0
$50$	−2.56238	−	4.43818i	−0.362375	−	0.627653i
$51$		0			0
$52$	−2.85185	+	4.93955i	−0.395480	+	0.684992i
$53$	2.05718			0.282575			0.141288	−	0.989969i	$-0.454876\pi$
$53$	2.05718			0.282575			0.141288	+	0.989969i	$0.454876\pi$
$54$		0			0
$55$	10.1248			1.36522
$56$		0			0
$57$		0			0
$58$	3.54063	+	6.13255i	0.464907	+	0.805243i
$59$	0.562382	+	0.974074i	0.0732159	+	0.126814i	0.900309	−	0.435251i	$-0.143340\pi$
$59$	0.562382	+	0.974074i	0.0732159	+	0.126814i	−0.827093	+	0.562065i	$0.810007\pi$
$60$		0			0
$61$	1.56238	−	2.70612i	0.200042	−	0.346484i	−0.748499	−	0.663135i	$-0.769225\pi$
$61$	1.56238	−	2.70612i	0.200042	−	0.346484i	0.948542	+	0.316652i	$0.102559\pi$
$62$	9.42107			1.19648
$63$		0			0
$64$	1.00000			0.125000
$65$	9.07442	−	15.7174i	1.12554	−	1.94950i
$66$		0			0
$67$	−5.48345	−	9.49761i	−0.669910	−	1.16032i	−0.977929	−	0.208938i	$-0.932999\pi$
$67$	−5.48345	−	9.49761i	−0.669910	−	1.16032i	0.308019	−	0.951380i	$-0.400334\pi$
$68$	−0.760877	−	1.31788i	−0.0922699	−	0.159816i
$69$		0			0
$70$		0			0
$71$	−8.69002			−1.03132			−0.515658	−	0.856794i	$-0.672452\pi$
$71$	−8.69002			−1.03132			−0.515658	+	0.856794i	$0.672452\pi$
$72$		0			0
$73$	−4.96690			−0.581331			−0.290666	−	0.956825i	$-0.593877\pi$
$73$	−4.96690			−0.581331			−0.290666	+	0.956825i	$0.593877\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	0.641315	+	1.11079i	0.0735639	+	0.127416i
$77$		0			0
$78$		0			0
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	−0.725827	−	0.687877i	$-0.758543\pi$
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	0.958633	+	0.284646i	$0.0918762\pi$
$80$	−3.18194			−0.355752
$81$		0			0
$82$	5.60301			0.618749
$83$	−4.03379	+	6.98673i	−0.442766	+	0.766893i	−0.997894	−	0.0648718i	$-0.979336\pi$
$83$	−4.03379	+	6.98673i	−0.442766	+	0.766893i	0.555127	+	0.831765i	$0.312669\pi$
$84$		0			0
$85$	2.42107	+	4.19341i	0.262602	+	0.454839i
$86$	3.41423	+	5.91362i	0.368166	+	0.637682i
$87$		0			0
$88$	1.59097	−	2.75564i	0.169598	−	0.293753i
$89$	−0.225450			−0.0238977			−0.0119488	−	0.999929i	$-0.503804\pi$
$89$	−0.225450			−0.0238977			−0.0119488	+	0.999929i	$0.503804\pi$
$90$		0			0
$91$		0			0
$92$	1.11956	−	1.93914i	0.116722	−	0.202169i
$93$		0			0
$94$	2.91423	+	5.04759i	0.300580	+	0.520620i
$95$	−2.04063	−	3.53447i	−0.209364	−	0.362629i
$96$		0			0
$97$	−7.42107	+	12.8537i	−0.753495	+	1.30509i	0.192624	+	0.981273i	$0.438300\pi$
$97$	−7.42107	+	12.8537i	−0.753495	+	1.30509i	−0.946119	+	0.323819i	$0.895033\pi$
$98$		0			0
$99$		0			0
$100$	5.12476			0.512476
$101$	−9.29467	+	16.0988i	−0.924854	+	1.60189i	−0.133058	+	0.991108i	$0.542480\pi$
$101$	−9.29467	+	16.0988i	−0.924854	+	1.60189i	−0.791796	+	0.610786i	$0.790854\pi$
$102$		0			0
$103$	−0.141315	−	0.244765i	−0.0139242	−	0.0241174i	0.858979	−	0.512010i	$-0.171099\pi$
$103$	−0.141315	−	0.244765i	−0.0139242	−	0.0241174i	−0.872904	+	0.487893i	$0.837766\pi$
$104$	−2.85185	−	4.93955i	−0.279647	−	0.484362i
$105$		0			0
$106$	−1.02859	+	1.78157i	−0.0999055	+	0.173041i
$107$	11.3776			1.09991			0.549955	−	0.835194i	$-0.314645\pi$
$107$	11.3776			1.09991			0.549955	+	0.835194i	$0.314645\pi$
$108$		0			0
$109$	4.42107			0.423461			0.211731	−	0.977328i	$-0.432090\pi$
$109$	4.42107			0.423461			0.211731	+	0.977328i	$0.432090\pi$
$110$	−5.06238	+	8.76830i	−0.482679	+	0.836025i
$111$		0			0
$112$		0			0
$113$	1.60752	+	2.78431i	0.151223	+	0.261926i	0.931677	−	0.363287i	$-0.118345\pi$
$113$	1.60752	+	2.78431i	0.151223	+	0.261926i	−0.780454	+	0.625213i	$0.785012\pi$
$114$		0			0
$115$	−3.56238	+	6.17023i	−0.332194	+	0.575377i
$116$	−7.08126			−0.657478
$117$		0			0
$118$	−1.12476			−0.103543
$119$		0			0
$120$		0			0
$121$	0.437618	+	0.757977i	0.0397835	+	0.0689070i
$122$	1.56238	+	2.70612i	0.141451	+	0.245001i
$123$		0			0
$124$	−4.71053	+	8.15888i	−0.423018	+	0.732689i
$125$	−0.396990			−0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	9.07442	+	15.7174i	0.795879	+	1.37850i
$131$	−3.18194	−	5.51129i	−0.278008	−	0.481523i	0.692882	−	0.721051i	$-0.256341\pi$
$131$	−3.18194	−	5.51129i	−0.278008	−	0.481523i	−0.970890	+	0.239528i	$0.923007\pi$
$132$		0			0
$133$		0			0
$134$	10.9669			0.947396
$135$		0			0
$136$	1.52175			0.130489
$137$	1.37072	−	2.37416i	0.117109	−	0.202838i	−0.801512	−	0.597979i	$-0.795971\pi$
$137$	1.37072	−	2.37416i	0.117109	−	0.202838i	0.918621	+	0.395140i	$0.129304\pi$
$138$		0			0
$139$	3.98345	+	6.89953i	0.337872	+	0.585211i	0.984032	−	0.177991i	$-0.0569597\pi$
$139$	3.98345	+	6.89953i	0.337872	+	0.585211i	−0.646161	+	0.763202i	$0.723626\pi$
$140$		0			0
$141$		0			0
$142$	4.34501	−	7.52578i	0.364625	−	0.631550i
$143$	−18.1488			−1.51768
$144$		0			0
$145$	22.5322			1.87119
$146$	2.48345	−	4.30146i	0.205532	−	0.355991i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−11.6300	−	20.1437i	−0.952764	−	1.65024i	−0.739404	−	0.673262i	$-0.764893\pi$
$149$	−11.6300	−	20.1437i	−0.952764	−	1.65024i	−0.213360	−	0.976974i	$-0.568441\pi$
$150$		0			0
$151$	4.06238	−	7.03625i	0.330592	−	0.572602i	−0.652036	−	0.758188i	$-0.726085\pi$
$151$	4.06238	−	7.03625i	0.330592	−	0.572602i	0.982628	+	0.185586i	$0.0594183\pi$
$152$	−1.28263			−0.104035
$153$		0			0
$154$		0			0
$155$	14.9887	−	25.9611i	1.20392	−	2.08525i
$156$		0			0
$157$	−5.63160	−	9.75422i	−0.449451	−	0.778471i	0.548900	−	0.835888i	$-0.315047\pi$
$157$	−5.63160	−	9.75422i	−0.449451	−	0.778471i	−0.998350	+	0.0574170i	$0.981714\pi$
$158$	2.06922	+	3.58399i	0.164618	+	0.285127i
$159$		0			0
$160$	1.59097	−	2.75564i	0.125777	−	0.217853i
$161$		0			0
$162$		0			0
$163$	3.98057			0.311782			0.155891	−	0.987774i	$-0.450175\pi$
$163$	3.98057			0.311782			0.155891	+	0.987774i	$0.450175\pi$
$164$	−2.80150	+	4.85235i	−0.218761	+	0.378905i
$165$		0			0
$166$	−4.03379	−	6.98673i	−0.313083	−	0.542276i
$167$	2.61956	+	4.53721i	0.202708	+	0.351100i	0.949400	−	0.314070i	$-0.101693\pi$
$167$	2.61956	+	4.53721i	0.202708	+	0.351100i	−0.746692	+	0.665170i	$0.768359\pi$
$168$		0			0
$169$	−9.76608	+	16.9153i	−0.751237	+	1.30118i
$170$	−4.84213			−0.371375
$171$		0			0
$172$	−6.82846			−0.520665
$173$	−1.27579	+	2.20974i	−0.0969968	+	0.168003i	−0.910440	−	0.413641i	$-0.864257\pi$
$173$	−1.27579	+	2.20974i	−0.0969968	+	0.168003i	0.813443	+	0.581644i	$0.197590\pi$
$174$		0			0
$175$		0			0
$176$	1.59097	+	2.75564i	0.119924	+	0.207714i
$177$		0			0
$178$	0.112725	−	0.195246i	0.00844910	−	0.0146343i
$179$	7.03775			0.526026			0.263013	−	0.964792i	$-0.415284\pi$
$179$	7.03775			0.526026			0.263013	+	0.964792i	$0.415284\pi$
$180$		0			0
$181$	12.9669			0.963822			0.481911	−	0.876220i	$-0.339943\pi$
$181$	12.9669			0.963822			0.481911	+	0.876220i	$0.339943\pi$
$182$		0			0
$183$		0			0
$184$	1.11956	+	1.93914i	0.0825352	+	0.142955i
$185$	−1.59097	−	2.75564i	−0.116971	−	0.202599i
$186$		0			0
$187$	2.42107	−	4.19341i	0.177046	−	0.306653i
$188$	−5.82846			−0.425084
$189$		0			0
$190$	4.08126			0.296085
$191$	0.990285	−	1.71522i	0.0716545	−	0.124109i	−0.827972	−	0.560769i	$-0.810505\pi$
$191$	0.990285	−	1.71522i	0.0716545	−	0.124109i	0.899627	+	0.436660i	$0.143839\pi$
$192$		0			0
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	0.936160	−	0.351574i	$-0.114353\pi$
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	−0.772552	+	0.634951i	$0.781020\pi$
$194$	−7.42107	−	12.8537i	−0.532802	−	0.922839i
$195$		0			0
$196$		0			0
$197$	21.8148			1.55424			0.777120	−	0.629353i	$-0.216680\pi$
$197$	21.8148			1.55424			0.777120	+	0.629353i	$0.216680\pi$
$198$		0			0
$199$	12.2826			0.870693			0.435346	−	0.900263i	$-0.356626\pi$
$199$	12.2826			0.870693			0.435346	+	0.900263i	$0.356626\pi$
$200$	−2.56238	+	4.43818i	−0.181188	+	0.313826i
$201$		0			0
$202$	−9.29467	−	16.0988i	−0.653971	−	1.13271i
$203$		0			0
$204$		0			0
$205$	8.91423	−	15.4399i	0.622597	−	1.07837i
$206$	0.282630			0.0196918
$207$		0			0
$208$	5.70370			0.395480
$209$	−2.04063	+	3.53447i	−0.141153	+	0.244485i
$210$		0			0
$211$	−8.32846	−	14.4253i	−0.573355	−	0.993080i	−0.996218	−	0.0868863i	$-0.972308\pi$
$211$	−8.32846	−	14.4253i	−0.573355	−	0.993080i	0.422863	−	0.906193i	$-0.361025\pi$
$212$	−1.02859	−	1.78157i	−0.0706438	−	0.122359i
$213$		0			0
$214$	−5.68878	+	9.85326i	−0.388877	+	0.673555i
$215$	21.7278			1.48182
$216$		0			0
$217$		0			0
$218$	−2.21053	+	3.82876i	−0.149716	+	0.259316i
$219$		0			0
$220$	−5.06238	−	8.76830i	−0.341306	−	0.591159i
$221$	−4.33981	−	7.51677i	−0.291927	−	0.505633i
$222$		0			0
$223$	5.32846	−	9.22916i	0.356820	−	0.618031i	−0.630608	−	0.776102i	$-0.717194\pi$
$223$	5.32846	−	9.22916i	0.356820	−	0.618031i	0.987428	+	0.158071i	$0.0505276\pi$
$224$		0			0
$225$		0			0
$226$	−3.21505			−0.213862
$227$	7.25404	−	12.5644i	0.481468	−	0.833926i	−0.518306	−	0.855195i	$-0.673437\pi$
$227$	7.25404	−	12.5644i	0.481468	−	0.833926i	0.999774	+	0.0212688i	$0.00677059\pi$
$228$		0			0
$229$	5.12476	+	8.87635i	0.338654	+	0.586566i	0.984180	−	0.177173i	$-0.0566951\pi$
$229$	5.12476	+	8.87635i	0.338654	+	0.586566i	−0.645526	+	0.763738i	$0.723362\pi$
$230$	−3.56238	−	6.17023i	−0.234896	−	0.406853i
$231$		0			0
$232$	3.54063	−	6.13255i	0.232454	−	0.402622i
$233$	1.08126			0.0708355			0.0354177	−	0.999373i	$-0.488724\pi$
$233$	1.08126			0.0708355			0.0354177	+	0.999373i	$0.488724\pi$
$234$		0			0
$235$	18.5458			1.20980
$236$	0.562382	−	0.974074i	0.0366079	−	0.0634068i
$237$		0			0
$238$		0			0
$239$	6.16019	+	10.6698i	0.398470	+	0.690170i	0.993537	−	0.113506i	$-0.0362081\pi$
$239$	6.16019	+	10.6698i	0.398470	+	0.690170i	−0.595068	+	0.803676i	$0.702875\pi$
$240$		0			0
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	−0.995809	−	0.0914555i	$-0.970848\pi$
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	0.577107	+	0.816668i	$0.304181\pi$
$242$	−0.875237			−0.0562623
$243$		0			0
$244$	−3.12476			−0.200042
$245$		0			0
$246$		0			0
$247$	3.65787	+	6.33561i	0.232744	+	0.403125i
$248$	−4.71053	−	8.15888i	−0.299119	−	0.518090i
$249$		0			0
$250$	0.198495	−	0.343803i	0.0125539	−	0.0217440i
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$	−10.0527	+	17.4117i	−0.630760	+	1.09251i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.83009	−	6.63392i	−0.238915	−	0.413813i	0.721488	−	0.692427i	$-0.243458\pi$
$257$	−3.83009	−	6.63392i	−0.238915	−	0.413813i	−0.960403	+	0.278614i	$0.910125\pi$
$258$		0			0
$259$		0			0
$260$	−18.1488			−1.12554
$261$		0			0
$262$	6.36389			0.393162
$263$	−1.54746	+	2.68029i	−0.0954208	+	0.165274i	−0.909784	−	0.415082i	$-0.863753\pi$
$263$	−1.54746	+	2.68029i	−0.0954208	+	0.165274i	0.814363	+	0.580355i	$0.197086\pi$
$264$		0			0
$265$	3.27292	+	5.66886i	0.201054	+	0.348235i
$266$		0			0
$267$		0			0
$268$	−5.48345	+	9.49761i	−0.334955	+	0.580159i
$269$	26.8903			1.63953			0.819765	−	0.572700i	$-0.194104\pi$
$269$	26.8903			1.63953			0.819765	+	0.572700i	$0.194104\pi$
$270$		0			0
$271$	−22.2164			−1.34955			−0.674776	−	0.738023i	$-0.735760\pi$
$271$	−22.2164			−1.34955			−0.674776	+	0.738023i	$0.735760\pi$
$272$	−0.760877	+	1.31788i	−0.0461349	+	0.0799080i
$273$		0			0
$274$	1.37072	+	2.37416i	0.0828084	+	0.143428i
$275$	8.15335	+	14.1220i	0.491666	+	0.851590i
$276$		0			0
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	−0.557928	−	0.829889i	$-0.688404\pi$
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	0.997669	+	0.0682357i	$0.0217370\pi$
$278$	−7.96690			−0.477823
$279$		0			0
$280$		0			0
$281$	−11.6992	+	20.2636i	−0.697915	+	1.20882i	0.271273	+	0.962502i	$0.412555\pi$
$281$	−11.6992	+	20.2636i	−0.697915	+	1.20882i	−0.969188	+	0.246322i	$0.920778\pi$
$282$		0			0
$283$	−13.0624	−	22.6247i	−0.776478	−	1.34490i	−0.933960	−	0.357377i	$-0.883671\pi$
$283$	−13.0624	−	22.6247i	−0.776478	−	1.34490i	0.157482	−	0.987522i	$-0.449662\pi$
$284$	4.34501	+	7.52578i	0.257829	+	0.446573i
$285$		0			0
$286$	9.07442	−	15.7174i	0.536582	−	0.929387i
$287$		0			0
$288$		0			0
$289$	−14.6843			−0.863780
$290$	−11.2661	+	19.5134i	−0.661567	+	1.14587i
$291$		0			0
$292$	2.48345	+	4.30146i	0.145333	+	0.251724i
$293$	12.9315	+	22.3980i	0.755465	+	1.30850i	0.945143	+	0.326657i	$0.105922\pi$
$293$	12.9315	+	22.3980i	0.755465	+	1.30850i	−0.189678	+	0.981846i	$0.560745\pi$
$294$		0			0
$295$	−1.78947	+	3.09945i	−0.104187	+	0.180457i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$	23.2599			1.34741
$299$	6.38564	−	11.0603i	0.369291	−	0.639631i
$300$		0			0
$301$		0			0
$302$	4.06238	+	7.03625i	0.233764	+	0.404891i
$303$		0			0
$304$	0.641315	−	1.11079i	0.0367819	−	0.0637082i
$305$	9.94282			0.569324
$306$		0			0
$307$	−3.53216			−0.201591			−0.100795	−	0.994907i	$-0.532139\pi$
$307$	−3.53216			−0.201591			−0.100795	+	0.994907i	$0.532139\pi$
$308$		0			0
$309$		0			0
$310$	14.9887	+	25.9611i	0.851298	+	1.47449i
$311$	−0.851848	−	1.47544i	−0.0483039	−	0.0836648i	0.840863	−	0.541249i	$-0.182048\pi$
$311$	−0.851848	−	1.47544i	−0.0483039	−	0.0836648i	−0.889166	+	0.457584i	$0.848715\pi$
$312$		0			0
$313$	−1.42107	+	2.46136i	−0.0803234	+	0.139124i	−0.903389	−	0.428822i	$-0.858929\pi$
$313$	−1.42107	+	2.46136i	−0.0803234	+	0.139124i	0.823065	+	0.567947i	$0.192262\pi$
$314$	11.2632			0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	−12.4601	+	21.5815i	−0.699827	+	1.21214i	0.268700	+	0.963224i	$0.413406\pi$
$317$	−12.4601	+	21.5815i	−0.699827	+	1.21214i	−0.968526	+	0.248911i	$0.919927\pi$
$318$		0			0
$319$	−11.2661	−	19.5134i	−0.630779	−	1.09254i
$320$	1.59097	+	2.75564i	0.0889380	+	0.154045i
$321$		0			0
$322$		0			0
$323$	−1.95185			−0.108604
$324$		0			0
$325$	29.2301			1.62139
$326$	−1.99028	+	3.44727i	−0.110232	+	0.190927i
$327$		0			0
$328$	−2.80150	−	4.85235i	−0.154687	−	0.267926i
$329$		0			0
$330$		0			0
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	−0.750492	−	0.660879i	$-0.770184\pi$
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	0.947584	+	0.319506i	$0.103517\pi$
$332$	8.06758			0.442766
$333$		0			0
$334$	−5.23912			−0.286672
$335$	17.4480	−	30.2209i	0.953287	−	1.65114i
$336$		0			0
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	−0.993560	−	0.113309i	$-0.963855\pi$
$337$	−10.9211	−	18.9158i	−0.594908	−	1.03041i	0.398651	−	0.917103i	$-0.369478\pi$
$338$	−9.76608	−	16.9153i	−0.531205	−	0.920073i
$339$		0			0
$340$	2.42107	−	4.19341i	0.131301	−	0.227420i
$341$	−29.9773			−1.62336
$342$		0			0
$343$		0			0
$344$	3.41423	−	5.91362i	0.184083	−	0.318841i
$345$		0			0
$346$	−1.27579	−	2.20974i	−0.0685871	−	0.118796i
$347$	−1.05555	−	1.82826i	−0.0566646	−	0.0981460i	0.836302	−	0.548270i	$-0.184713\pi$
$347$	−1.05555	−	1.82826i	−0.0566646	−	0.0981460i	−0.892966	+	0.450124i	$0.851380\pi$
$348$		0			0
$349$	−18.1082	+	31.3643i	−0.969310	+	1.67889i	−0.271751	+	0.962368i	$0.587603\pi$
$349$	−18.1082	+	31.3643i	−0.969310	+	1.67889i	−0.697559	+	0.716527i	$0.745731\pi$
$350$		0			0
$351$		0			0
$352$	−3.18194			−0.169598
$353$	5.24433	−	9.08344i	0.279127	−	0.483463i	−0.692041	−	0.721858i	$-0.743288\pi$
$353$	5.24433	−	9.08344i	0.279127	−	0.483463i	0.971168	+	0.238396i	$0.0766215\pi$
$354$		0			0
$355$	−13.8256	−	23.9466i	−0.733786	−	1.27095i
$356$	0.112725	+	0.195246i	0.00597442	+	0.0103480i
$357$		0			0
$358$	−3.51887	+	6.09487i	−0.185978	+	0.322124i
$359$	32.4419			1.71222			0.856108	−	0.516796i	$-0.172876\pi$
$359$	32.4419			1.71222			0.856108	+	0.516796i	$0.172876\pi$
$360$		0			0
$361$	−17.3549			−0.913414
$362$	−6.48345	+	11.2297i	−0.340762	+	0.590218i
$363$		0			0
$364$		0			0
$365$	−7.90219	−	13.6870i	−0.413620	−	0.716410i
$366$		0			0
$367$	−9.05555	+	15.6847i	−0.472696	+	0.818733i	−0.999512	−	0.0312465i	$-0.990052\pi$
$367$	−9.05555	+	15.6847i	−0.472696	+	0.818733i	0.526816	+	0.849979i	$0.323386\pi$
$368$	−2.23912			−0.116722
$369$		0			0
$370$	3.18194			0.165421
$371$		0			0
$372$		0			0
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	0.976621	−	0.214971i	$-0.0689656\pi$
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	−0.674480	+	0.738293i	$0.735632\pi$
$374$	2.42107	+	4.19341i	0.125190	+	0.216836i
$375$		0			0
$376$	2.91423	−	5.04759i	0.150290	−	0.260310i
$377$	−40.3893			−2.08016
$378$		0			0
$379$	14.2690			0.732947			0.366474	−	0.930428i	$-0.380565\pi$
$379$	14.2690			0.732947			0.366474	+	0.930428i	$0.380565\pi$
$380$	−2.04063	+	3.53447i	−0.104682	+	0.181315i
$381$		0			0
$382$	0.990285	+	1.71522i	0.0506674	+	0.0877585i
$383$	0.824893	+	1.42876i	0.0421501	+	0.0730061i	0.886331	−	0.463053i	$-0.153246\pi$
$383$	0.824893	+	1.42876i	0.0421501	+	0.0730061i	−0.844181	+	0.536059i	$0.819913\pi$
$384$		0			0
$385$		0			0
$386$	−4.54583			−0.231377
$387$		0			0
$388$	14.8421			0.753495
$389$	−16.0338	+	27.7713i	−0.812946	+	1.40806i	0.0978483	+	0.995201i	$0.468804\pi$
$389$	−16.0338	+	27.7713i	−0.812946	+	1.40806i	−0.910794	+	0.412862i	$0.864529\pi$
$390$		0			0
$391$	1.70370	+	2.95089i	0.0861596	+	0.149233i
$392$		0			0
$393$		0			0
$394$	−10.9074	+	18.8922i	−0.549507	+	0.951773i
$395$	13.1683			0.662568
$396$		0			0
$397$	−37.9338			−1.90384			−0.951921	−	0.306343i	$-0.900895\pi$
$397$	−37.9338			−1.90384			−0.951921	+	0.306343i	$0.900895\pi$
$398$	−6.14132	+	10.6371i	−0.307836	+	0.533188i
$399$		0			0
$400$	−2.56238	−	4.43818i	−0.128119	−	0.221909i
$401$	5.30959	+	9.19647i	0.265148	+	0.459250i	0.967602	−	0.252479i	$-0.0812458\pi$
$401$	5.30959	+	9.19647i	0.265148	+	0.459250i	−0.702454	+	0.711729i	$0.747913\pi$
$402$		0			0
$403$	−26.8675	+	46.5358i	−1.33836	+	2.31811i
$404$	18.5893			0.924854
$405$		0			0
$406$		0			0
$407$	−1.59097	+	2.75564i	−0.0788615	+	0.136592i
$408$		0			0
$409$	2.77292	+	4.80283i	0.137112	+	0.237485i	0.926402	−	0.376535i	$-0.122885\pi$
$409$	2.77292	+	4.80283i	0.137112	+	0.237485i	−0.789290	+	0.614020i	$0.789551\pi$
$410$	8.91423	+	15.4399i	0.440242	+	0.762522i
$411$		0			0
$412$	−0.141315	+	0.244765i	−0.00696209	+	0.0120587i
$413$		0			0
$414$		0			0
$415$	−25.6706			−1.26012
$416$	−2.85185	+	4.93955i	−0.139823	+	0.242181i
$417$		0			0
$418$	−2.04063	−	3.53447i	−0.0998104	−	0.172877i
$419$	2.77455	+	4.80566i	0.135546	+	0.234772i	0.925806	−	0.378000i	$-0.123388\pi$
$419$	2.77455	+	4.80566i	0.135546	+	0.234772i	−0.790260	+	0.612772i	$0.790055\pi$
$420$		0			0
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	−0.937269	−	0.348606i	$-0.886655\pi$
$421$	−3.42107	+	5.92546i	−0.166733	+	0.288789i	0.770537	+	0.637396i	$0.219988\pi$
$422$	16.6569			0.810846
$423$		0			0
$424$	2.05718			0.0999055
$425$	−3.89931	+	6.75381i	−0.189144	+	0.327608i
$426$		0			0
$427$		0			0
$428$	−5.68878	−	9.85326i	−0.274978	−	0.476275i
$429$		0			0
$430$	−10.8639	+	18.8168i	−0.523903	+	0.907427i
$431$	33.1078			1.59475			0.797374	−	0.603486i	$-0.206222\pi$
$431$	33.1078			1.59475			0.797374	+	0.603486i	$0.206222\pi$
$432$		0			0
$433$	12.1111			0.582022			0.291011	−	0.956720i	$-0.406008\pi$
$433$	12.1111			0.582022			0.291011	+	0.956720i	$0.406008\pi$
$434$		0			0
$435$		0			0
$436$	−2.21053	−	3.82876i	−0.105865	−	0.183364i
$437$	−1.43598	−	2.48720i	−0.0686924	−	0.118979i
$438$		0			0
$439$	−4.41711	+	7.65066i	−0.210817	+	0.365146i	−0.951970	−	0.306190i	$-0.900946\pi$
$439$	−4.41711	+	7.65066i	−0.210817	+	0.365146i	0.741153	+	0.671336i	$0.234279\pi$
$440$	10.1248			0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	8.75924	−	15.1715i	0.416164	−	0.720817i	−0.579386	−	0.815053i	$-0.696708\pi$
$443$	8.75924	−	15.1715i	0.416164	−	0.720817i	0.995550	+	0.0942360i	$0.0300408\pi$
$444$		0			0
$445$	−0.358685	−	0.621261i	−0.0170033	−	0.0294506i
$446$	5.32846	+	9.22916i	0.252310	+	0.437014i
$447$		0			0
$448$		0			0
$449$	−31.2301			−1.47384			−0.736920	−	0.675980i	$-0.763720\pi$
$449$	−31.2301			−1.47384			−0.736920	+	0.675980i	$0.763720\pi$
$450$		0			0
$451$	−17.8285			−0.839509
$452$	1.60752	−	2.78431i	0.0756115	−	0.130963i
$453$		0			0
$454$	7.25404	+	12.5644i	0.340449	+	0.589675i
$455$		0			0
$456$		0			0
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	−0.195794	−	0.980645i	$-0.562728\pi$
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	0.947161	−	0.320760i	$-0.103938\pi$
$458$	−10.2495			−0.478929
$459$		0			0
$460$	7.12476			0.332194
$461$	1.23229	−	2.13438i	0.0573933	−	0.0994081i	−0.835901	−	0.548880i	$-0.815054\pi$
$461$	1.23229	−	2.13438i	0.0573933	−	0.0994081i	0.893295	+	0.449472i	$0.148388\pi$
$462$		0			0
$463$	15.1735	+	26.2812i	0.705171	+	1.22139i	0.966630	+	0.256177i	$0.0824631\pi$
$463$	15.1735	+	26.2812i	0.705171	+	1.22139i	−0.261459	+	0.965215i	$0.584204\pi$
$464$	3.54063	+	6.13255i	0.164370	+	0.284696i
$465$		0			0
$466$	−0.540628	+	0.936396i	−0.0250441	+	0.0433777i
$467$	15.9636			0.738709			0.369354	−	0.929289i	$-0.379579\pi$
$467$	15.9636			0.738709			0.369354	+	0.929289i	$0.379579\pi$
$468$		0			0
$469$		0			0
$470$	−9.27292	+	16.0612i	−0.427728	+	0.740846i
$471$		0			0
$472$	0.562382	+	0.974074i	0.0258857	+	0.0448354i
$473$	−10.8639	−	18.8168i	−0.499522	−	0.865198i
$474$		0			0
$475$	3.28659	−	5.69254i	0.150799	−	0.261192i
$476$		0			0
$477$		0			0
$478$	−12.3204			−0.563521
$479$	11.5865	−	20.0683i	0.529399	−	0.916946i	−0.470013	−	0.882659i	$-0.655751\pi$
$479$	11.5865	−	20.0683i	0.529399	−	0.916946i	0.999412	−	0.0342863i	$-0.0109158\pi$
$480$		0			0
$481$	2.85185	+	4.93955i	0.130033	+	0.225224i
$482$	−6.50000	−	11.2583i	−0.296067	−	0.512803i
$483$		0			0
$484$	0.437618	−	0.757977i	0.0198917	−	0.0344535i
$485$	−47.2268			−2.14446
$486$		0			0
$487$	−3.41315			−0.154665			−0.0773323	−	0.997005i	$-0.524640\pi$
$487$	−3.41315			−0.154665			−0.0773323	+	0.997005i	$0.524640\pi$
$488$	1.56238	−	2.70612i	0.0707257	−	0.122500i
$489$		0			0
$490$		0			0
$491$	9.58414	+	16.6002i	0.432526	+	0.749157i	0.997090	−	0.0762323i	$-0.0242890\pi$
$491$	9.58414	+	16.6002i	0.432526	+	0.749157i	−0.564564	+	0.825389i	$0.690956\pi$
$492$		0			0
$493$	5.38796	−	9.33223i	0.242662	−	0.420302i
$494$	−7.31573			−0.329150
$495$		0			0
$496$	9.42107			0.423018
$497$		0			0
$498$		0			0
$499$	−20.5848	−	35.6540i	−0.921503	−	1.59609i	−0.797090	−	0.603860i	$-0.793629\pi$
$499$	−20.5848	−	35.6540i	−0.921503	−	1.59609i	−0.124413	−	0.992231i	$-0.539705\pi$
$500$	0.198495	+	0.343803i	0.00887697	+	0.0153754i
$501$		0			0
$502$	−2.55555	+	4.42633i	−0.114060	+	0.197557i
$503$	−26.4542			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$503$	−26.4542			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$	−3.56238	+	6.17023i	−0.158367	+	0.274300i
$507$		0			0
$508$	−10.0527	−	17.4117i	−0.446015	−	0.772521i
$509$	−6.38564	−	11.0603i	−0.283039	−	0.490237i	0.689093	−	0.724673i	$-0.258009\pi$
$509$	−6.38564	−	11.0603i	−0.283039	−	0.490237i	−0.972132	+	0.234436i	$0.924676\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	7.66019			0.337876
$515$	0.449657	−	0.778828i	0.0198142	−	0.0343193i
$516$		0			0
$517$	−9.27292	−	16.0612i	−0.407822	−	0.706369i
$518$		0			0
$519$		0			0
$520$	9.07442	−	15.7174i	0.397940	−	0.689252i
$521$	6.81230			0.298452			0.149226	−	0.988803i	$-0.452322\pi$
$521$	6.81230			0.298452			0.149226	+	0.988803i	$0.452322\pi$
$522$		0			0
$523$	29.5070			1.29025			0.645125	−	0.764077i	$-0.276805\pi$
$523$	29.5070			1.29025			0.645125	+	0.764077i	$0.276805\pi$
$524$	−3.18194	+	5.51129i	−0.139004	+	0.240762i
$525$		0			0
$526$	−1.54746	−	2.68029i	−0.0674727	−	0.116866i
$527$	−7.16827	−	12.4158i	−0.312255	−	0.540841i
$528$		0			0
$529$	8.99316	−	15.5766i	0.391007	−	0.677244i
$530$	−6.54583			−0.284333
$531$		0			0
$532$		0			0
$533$	−15.9789	+	27.6763i	−0.692125	+	1.19879i
$534$		0			0
$535$	18.1014	+	31.3525i	0.782591	+	1.35549i
$536$	−5.48345	−	9.49761i	−0.236849	−	0.410234i
$537$		0			0
$538$	−13.4451	+	23.2877i	−0.579661	+	1.00400i
$539$		0			0
$540$		0			0
$541$	−29.4016			−1.26408			−0.632038	−	0.774938i	$-0.717781\pi$
$541$	−29.4016			−1.26408			−0.632038	+	0.774938i	$0.717781\pi$
$542$	11.1082	−	19.2400i	0.477139	−	0.826428i
$543$		0			0
$544$	−0.760877	−	1.31788i	−0.0326223	−	0.0565035i
$545$	7.03379	+	12.1829i	0.301295	+	0.521857i
$546$		0			0
$547$	17.6150	−	30.5102i	0.753165	−	1.30452i	−0.193116	−	0.981176i	$-0.561859\pi$
$547$	17.6150	−	30.5102i	0.753165	−	1.30452i	0.946281	−	0.323344i	$-0.104807\pi$
$548$	−2.74145			−0.117109
$549$		0			0
$550$	−16.3067			−0.695320
$551$	−4.54132	+	7.86579i	−0.193467	+	0.335094i
$552$		0			0
$553$		0			0
$554$	7.31875	+	12.6764i	0.310944	+	0.538570i
$555$		0			0
$556$	3.98345	−	6.89953i	0.168936	−	0.292605i
$557$	−6.73818			−0.285506			−0.142753	−	0.989758i	$-0.545595\pi$
$557$	−6.73818			−0.285506			−0.142753	+	0.989758i	$0.545595\pi$
$558$		0			0
$559$	−38.9475			−1.64730
$560$		0			0
$561$		0			0
$562$	−11.6992	−	20.2636i	−0.493500	−	0.854768i
$563$	0.729964	+	1.26433i	0.0307643	+	0.0532853i	0.880998	−	0.473121i	$-0.156873\pi$
$563$	0.729964	+	1.26433i	0.0307643	+	0.0532853i	−0.850233	+	0.526406i	$0.823539\pi$
$564$		0			0
$565$	−5.11505	+	8.85952i	−0.215192	+	0.372723i
$566$	26.1248			1.09811
$567$		0			0
$568$	−8.69002			−0.364625
$569$	9.78263	−	16.9440i	0.410109	−	0.710330i	−0.584792	−	0.811183i	$-0.698824\pi$
$569$	9.78263	−	16.9440i	0.410109	−	0.710330i	0.994901	+	0.100853i	$0.0321573\pi$
$570$		0			0
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	0.998897	−	0.0469545i	$-0.0149516\pi$
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	−0.540112	+	0.841593i	$0.681618\pi$
$572$	9.07442	+	15.7174i	0.379421	+	0.657176i
$573$		0			0
$574$		0			0
$575$	−11.4750			−0.478540
$576$		0			0
$577$	24.7310			1.02957			0.514783	−	0.857320i	$-0.327872\pi$
$577$	24.7310			1.02957			0.514783	+	0.857320i	$0.327872\pi$
$578$	7.34213	−	12.7169i	0.305392	−	0.528955i
$579$		0			0
$580$	−11.2661	−	19.5134i	−0.467798	−	0.810251i
$581$		0			0
$582$		0			0
$583$	3.27292	−	5.66886i	0.135550	−	0.234780i
$584$	−4.96690			−0.205532
$585$		0			0
$586$	−25.8629			−1.06839
$587$	−18.0796	+	31.3148i	−0.746226	+	1.29250i	0.203394	+	0.979097i	$0.434803\pi$
$587$	−18.0796	+	31.3148i	−0.746226	+	1.29250i	−0.949620	+	0.313404i	$0.898531\pi$
$588$		0			0
$589$	6.04187	+	10.4648i	0.248951	+	0.431196i
$590$	−1.78947	−	3.09945i	−0.0736712	−	0.127602i
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	15.1078			0.620404			0.310202	−	0.950671i	$-0.399603\pi$
$593$	15.1078			0.620404			0.310202	+	0.950671i	$0.399603\pi$
$594$		0			0
$595$		0			0
$596$	−11.6300	+	20.1437i	−0.476382	+	0.825118i
$597$		0			0
$598$	6.38564	+	11.0603i	0.261128	+	0.452287i
$599$	−2.72708	−	4.72345i	−0.111426	−	0.192995i	0.804920	−	0.593384i	$-0.202208\pi$
$599$	−2.72708	−	4.72345i	−0.111426	−	0.192995i	−0.916345	+	0.400389i	$0.868875\pi$
$600$		0			0
$601$	3.36840	−	5.83424i	0.137400	−	0.237984i	−0.789112	−	0.614250i	$-0.789459\pi$
$601$	3.36840	−	5.83424i	0.137400	−	0.237984i	0.926512	+	0.376266i	$0.122792\pi$
$602$		0			0
$603$		0			0
$604$	−8.12476			−0.330592
$605$	−1.39248	+	2.41184i	−0.0566122	+	0.0980553i
$606$		0			0
$607$	3.33530	+	5.77690i	0.135376	+	0.234477i	0.925741	−	0.378159i	$-0.123443\pi$
$607$	3.33530	+	5.77690i	0.135376	+	0.234477i	−0.790365	+	0.612636i	$0.790109\pi$
$608$	0.641315	+	1.11079i	0.0260088	+	0.0450485i
$609$		0			0
$610$	−4.97141	+	8.61073i	−0.201287	+	0.348638i
$611$	−33.2438			−1.34490
$612$		0			0
$613$	−1.30998			−0.0529094			−0.0264547	−	0.999650i	$-0.508422\pi$
$613$	−1.30998			−0.0529094			−0.0264547	+	0.999650i	$0.508422\pi$
$614$	1.76608	−	3.05894i	0.0712731	−	0.123449i
$615$		0			0
$616$		0			0
$617$	−17.2483	−	29.8749i	−0.694390	−	1.20272i	−0.970386	−	0.241560i	$-0.922341\pi$
$617$	−17.2483	−	29.8749i	−0.694390	−	1.20272i	0.275996	−	0.961159i	$-0.410992\pi$
$618$		0			0
$619$	−8.22421	+	14.2447i	−0.330559	+	0.572545i	−0.982622	−	0.185620i	$-0.940571\pi$
$619$	−8.22421	+	14.2447i	−0.330559	+	0.572545i	0.652063	+	0.758165i	$0.273904\pi$
$620$	−29.9773			−1.20392
$621$		0			0
$622$	1.70370			0.0683120
$623$		0			0
$624$		0			0
$625$	12.1803	+	21.0969i	0.487212	+	0.843877i
$626$	−1.42107	−	2.46136i	−0.0567972	−	0.0983757i
$627$		0			0
$628$	−5.63160	+	9.75422i	−0.224725	+	0.389236i
$629$	−1.52175			−0.0606763
$630$		0			0
$631$	−30.0118			−1.19475			−0.597375	−	0.801962i	$-0.703790\pi$
$631$	−30.0118			−1.19475			−0.597375	+	0.801962i	$0.703790\pi$
$632$	2.06922	−	3.58399i	0.0823091	−	0.142564i
$633$		0			0
$634$	−12.4601	−	21.5815i	−0.494852	−	0.857109i
$635$	31.9870	+	55.4031i	1.26937	+	2.19861i
$636$		0			0
$637$		0			0
$638$	22.5322			0.892057
$639$		0			0
$640$	−3.18194			−0.125777
$641$	13.9497	−	24.1615i	0.550978	−	0.954322i	−0.447226	−	0.894421i	$-0.647588\pi$
$641$	13.9497	−	24.1615i	0.550978	−	0.954322i	0.998204	−	0.0599014i	$-0.0190786\pi$
$642$		0			0
$643$	−14.2524	−	24.6859i	−0.562060	−	0.973516i	−0.997317	−	0.0732100i	$-0.976676\pi$
$643$	−14.2524	−	24.6859i	−0.562060	−	0.973516i	0.435257	−	0.900306i	$-0.356658\pi$
$644$		0			0
$645$		0			0
$646$	0.975923	−	1.69035i	0.0383972	−	0.0665059i
$647$	−16.7141			−0.657099			−0.328550	−	0.944487i	$-0.606560\pi$
$647$	−16.7141			−0.657099			−0.328550	+	0.944487i	$0.606560\pi$
$648$		0			0
$649$	3.57893			0.140485
$650$	−14.6150	+	25.3140i	−0.573249	+	0.992897i
$651$		0			0
$652$	−1.99028	−	3.44727i	−0.0779456	−	0.135006i
$653$	19.0825	+	33.0519i	0.746756	+	1.29342i	0.949370	+	0.314161i	$0.101723\pi$
$653$	19.0825	+	33.0519i	0.746756	+	1.29342i	−0.202614	+	0.979259i	$0.564944\pi$
$654$		0			0
$655$	10.1248	−	17.5366i	0.395607	−	0.685212i
$656$	5.60301			0.218761
$657$		0			0
$658$		0			0
$659$	−4.37072	+	7.57031i	−0.170259	+	0.294898i	−0.938510	−	0.345251i	$-0.887794\pi$
$659$	−4.37072	+	7.57031i	−0.170259	+	0.294898i	0.768251	+	0.640148i	$0.221127\pi$
$660$		0			0
$661$	−10.0419	−	17.3930i	−0.390584	−	0.676511i	0.601943	−	0.798539i	$-0.294393\pi$
$661$	−10.0419	−	17.3930i	−0.390584	−	0.676511i	−0.992527	+	0.122028i	$0.961060\pi$
$662$	3.58577	+	6.21074i	0.139365	+	0.241387i
$663$		0			0
$664$	−4.03379	+	6.98673i	−0.156541	+	0.271138i
$665$		0			0
$666$		0			0
$667$	15.8558			0.613939
$668$	2.61956	−	4.53721i	0.101354	−	0.175550i
$669$		0			0
$670$	17.4480	+	30.2209i	0.674076	+	1.16753i
$671$	−4.97141	−	8.61073i	−0.191919	−	0.332414i
$672$		0			0
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	0.325242	+	0.945631i	$0.394554\pi$
$673$	−17.0264	+	29.4906i	−0.656319	+	1.13678i	−0.981561	+	0.191148i	$0.938779\pi$
$674$	21.8421			0.841328
$675$		0			0
$676$	19.5322			0.751237
$677$	0.358685	−	0.621261i	0.0137854	−	0.0238770i	−0.859050	−	0.511891i	$-0.828945\pi$
$677$	0.358685	−	0.621261i	0.0137854	−	0.0238770i	0.872836	+	0.488014i	$0.162279\pi$
$678$		0			0
$679$		0			0
$680$	2.42107	+	4.19341i	0.0928437	+	0.160810i
$681$		0			0
$682$	14.9887	−	25.9611i	0.573945	−	0.994102i
$683$	−21.0539			−0.805605			−0.402803	−	0.915287i	$-0.631964\pi$
$683$	−21.0539			−0.805605			−0.402803	+	0.915287i	$0.631964\pi$
$684$		0			0
$685$	8.72313			0.333294
$686$		0			0
$687$		0			0
$688$	3.41423	+	5.91362i	0.130166	+	0.225455i
$689$	−5.86677	−	10.1615i	−0.223506	−	0.387124i
$690$		0			0
$691$	2.92395	−	5.06442i	0.111232	−	0.192660i	−0.805035	−	0.593227i	$-0.797854\pi$
$691$	2.92395	−	5.06442i	0.111232	−	0.192660i	0.916267	+	0.400567i	$0.131187\pi$
$692$	2.55159			0.0969968
$693$		0			0
$694$	2.11109			0.0801359
$695$	−12.6751	+	21.9539i	−0.480794	+	0.832760i
$696$		0			0
$697$	−4.26320	−	7.38408i	−0.161480	−	0.279692i
$698$	−18.1082	−	31.3643i	−0.685406	−	1.18716i
$699$		0			0
$700$		0			0
$701$	−10.2711			−0.387935			−0.193967	−	0.981008i	$-0.562136\pi$
$701$	−10.2711			−0.387935			−0.193967	+	0.981008i	$0.562136\pi$
$702$		0			0
$703$	1.28263			0.0483753
$704$	1.59097	−	2.75564i	0.0599620	−	0.103857i
$705$		0			0
$706$	5.24433	+	9.08344i	0.197373	+	0.341860i
$707$		0			0
$708$		0			0
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	0.0916356	+	0.995793i	$0.470790\pi$
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	−0.908200	+	0.418538i	$0.862543\pi$
$710$	27.6512			1.03773
$711$		0			0
$712$	−0.225450			−0.00844910
$713$	10.5475	−	18.2687i	0.395006	−	0.684170i
$714$		0			0
$715$	−28.8743	−	50.0117i	−1.07984	−	1.87033i
$716$	−3.51887	−	6.09487i	−0.131507	−	0.227776i
$717$		0			0
$718$	−16.2209	+	28.0955i	−0.605360	+	1.04851i
$719$	−50.8824			−1.89759			−0.948796	−	0.315889i	$-0.897697\pi$
$719$	−50.8824			−1.89759			−0.948796	+	0.315889i	$0.897697\pi$
$720$		0			0
$721$		0			0
$722$	8.67743	−	15.0297i	0.322941	−	0.559349i
$723$		0			0
$724$	−6.48345	−	11.2297i	−0.240955	−	0.417347i
$725$	18.1449	+	31.4279i	0.673884	+	1.16720i
$726$		0			0
$727$	−6.07210	+	10.5172i	−0.225202	+	0.390061i	−0.956380	−	0.292126i	$-0.905637\pi$
$727$	−6.07210	+	10.5172i	−0.225202	+	0.390061i	0.731178	+	0.682186i	$0.238971\pi$
$728$		0			0
$729$		0			0
$730$	15.8044			0.584946
$731$	5.19562	−	8.99907i	0.192167	−	0.332843i
$732$		0			0
$733$	−23.0848	−	39.9841i	−0.852657	−	1.47685i	−0.878801	−	0.477188i	$-0.841656\pi$
$733$	−23.0848	−	39.9841i	−0.852657	−	1.47685i	0.0261440	−	0.999658i	$-0.491677\pi$
$734$	−9.05555	−	15.6847i	−0.334246	−	0.578932i
$735$		0			0
$736$	1.11956	−	1.93914i	0.0412676	−	0.0714776i
$737$	−34.8960			−1.28541
$738$		0			0
$739$	4.99208			0.183637			0.0918184	−	0.995776i	$-0.470732\pi$
$739$	4.99208			0.183637			0.0918184	+	0.995776i	$0.470732\pi$
$740$	−1.59097	+	2.75564i	−0.0584853	+	0.101299i
$741$		0			0
$742$		0			0
$743$	15.7060	+	27.2036i	0.576198	+	0.998004i	0.995910	+	0.0903470i	$0.0287976\pi$
$743$	15.7060	+	27.2036i	0.576198	+	0.998004i	−0.419712	+	0.907657i	$0.637869\pi$
$744$		0			0
$745$	37.0059	−	64.0961i	1.35579	−	2.34830i
$746$	−11.6706			−0.427291
$747$		0			0
$748$	−4.84213			−0.177046
$749$		0			0
$750$		0			0
$751$	−1.64815	−	2.85468i	−0.0601419	−	0.104169i	0.834387	−	0.551179i	$-0.185822\pi$
$751$	−1.64815	−	2.85468i	−0.0601419	−	0.104169i	−0.894529	+	0.447010i	$0.852489\pi$
$752$	2.91423	+	5.04759i	0.106271	+	0.184067i
$753$		0			0
$754$	20.1947	−	34.9782i	0.735447	−	1.27383i
$755$	25.8525			0.940870
$756$		0			0
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$	−7.13448	+	12.3573i	−0.259136	+	0.448837i
$759$		0			0
$760$	−2.04063	−	3.53447i	−0.0740214	−	0.128209i
$761$	−7.03379	−	12.1829i	−0.254975	−	0.441629i	0.709914	−	0.704288i	$-0.248734\pi$
$761$	−7.03379	−	12.1829i	−0.254975	−	0.441629i	−0.964889	+	0.262659i	$0.915400\pi$
$762$		0			0
$763$		0			0
$764$	−1.98057			−0.0716545
$765$		0			0
$766$	−1.64979			−0.0596092
$767$	3.20765	−	5.55582i	0.115822	−	0.200609i
$768$		0			0
$769$	−11.3461	−	19.6520i	−0.409151	−	0.708669i	0.585644	−	0.810568i	$-0.300842\pi$
$769$	−11.3461	−	19.6520i	−0.409151	−	0.708669i	−0.994795	+	0.101899i	$0.967508\pi$
$770$		0			0
$771$		0			0
$772$	2.27292	−	3.93680i	0.0818040	−	0.141689i
$773$	−0.655544			−0.0235783			−0.0117891	−	0.999931i	$-0.503753\pi$
$773$	−0.655544			−0.0235783			−0.0117891	+	0.999931i	$0.503753\pi$
$774$		0			0
$775$	48.2807			1.73430
$776$	−7.42107	+	12.8537i	−0.266401	+	0.461420i
$777$		0			0
$778$	−16.0338	−	27.7713i	−0.574839	−	0.995651i
$779$	3.59329	+	6.22377i	0.128743	+	0.222990i
$780$		0			0
$781$	−13.8256	+	23.9466i	−0.494718	+	0.856877i
$782$	−3.40739			−0.121848
$783$		0			0
$784$		0			0
$785$	17.9194	−	31.0374i	0.639572	−	1.10777i
$786$		0			0
$787$	0.270036	+	0.467717i	0.00962576	+	0.0166723i	0.870798	−	0.491641i	$-0.163603\pi$
$787$	0.270036	+	0.467717i	0.00962576	+	0.0166723i	−0.861172	+	0.508313i	$0.830269\pi$
$788$	−10.9074	−	18.8922i	−0.388560	−	0.673005i
$789$		0			0
$790$	−6.58414	+	11.4041i	−0.234253	+	0.405738i
$791$		0			0
$792$		0			0
$793$	−17.8227			−0.632903
$794$	18.9669	−	32.8516i	0.673110	−	1.16586i
$795$		0			0
$796$	−6.14132	−	10.6371i	−0.217673	−	0.377021i
$797$	−12.5550	−	21.7459i	−0.444721	−	0.770279i	0.553312	−	0.832974i	$-0.313364\pi$
$797$	−12.5550	−	21.7459i	−0.444721	−	0.770279i	−0.998033	+	0.0626954i	$0.980030\pi$
$798$		0			0
$799$	4.43474	−	7.68119i	0.156890	−	0.271741i
$800$	5.12476			0.181188
$801$		0			0
$802$	−10.6192			−0.374976
$803$	−7.90219	+	13.6870i	−0.278862	+	0.483004i
$804$		0			0
$805$		0			0
$806$	−26.8675	−	46.5358i	−0.946366	−	1.63915i
$807$		0			0
$808$	−9.29467	+	16.0988i	−0.326985	+	0.566355i
$809$	−29.1729			−1.02567			−0.512833	−	0.858489i	$-0.671404\pi$
$809$	−29.1729			−1.02567			−0.512833	+	0.858489i	$0.671404\pi$
$810$		0			0
$811$	15.4290			0.541785			0.270892	−	0.962610i	$-0.412681\pi$
$811$	15.4290			0.541785			0.270892	+	0.962610i	$0.412681\pi$
$812$		0			0
$813$		0			0
$814$	−1.59097	−	2.75564i	−0.0557635	−	0.0965853i
$815$	6.33297	+	10.9690i	0.221834	+	0.384228i
$816$		0			0
$817$	−4.37919	+	7.58499i	−0.153209	+	0.265365i
$818$	−5.54583			−0.193905
$819$		0			0
$820$	−17.8285			−0.622597
$821$	4.24364	−	7.35019i	0.148104	−	0.256524i	−0.782423	−	0.622748i	$-0.786016\pi$
$821$	4.24364	−	7.35019i	0.148104	−	0.256524i	0.930527	+	0.366224i	$0.119350\pi$
$822$		0			0
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	−0.999966	−	0.00825976i	$-0.997371\pi$
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	0.492830	−	0.870126i	$-0.335963\pi$
$824$	−0.141315	−	0.244765i	−0.00492294	−	0.00852679i
$825$		0			0
$826$		0			0
$827$	25.9396			0.902007			0.451003	−	0.892522i	$-0.351066\pi$
$827$	25.9396			0.902007			0.451003	+	0.892522i	$0.351066\pi$
$828$		0			0
$829$	6.21642			0.215905			0.107953	−	0.994156i	$-0.465571\pi$
$829$	6.21642			0.215905			0.107953	+	0.994156i	$0.465571\pi$
$830$	12.8353	−	22.2314i	0.445520	−	0.771663i
$831$		0			0
$832$	−2.85185	−	4.93955i	−0.0988701	−	0.171248i
$833$		0			0
$834$		0			0
$835$	−8.33530	+	14.4372i	−0.288455	+	0.499618i
$836$	4.08126			0.141153
$837$		0			0
$838$	−5.54910			−0.191690
$839$	21.2947	−	36.8834i	0.735174	−	1.27336i	−0.219474	−	0.975618i	$-0.570434\pi$
$839$	21.2947	−	36.8834i	0.735174	−	1.27336i	0.954647	−	0.297740i	$-0.0962327\pi$
$840$		0			0
$841$	−10.5721	−	18.3114i	−0.364555	−	0.631428i
$842$	−3.42107	−	5.92546i	−0.117898	−	0.204205i
$843$		0			0
$844$	−8.32846	+	14.4253i	−0.286677	+	0.496540i
$845$	−62.1502			−2.13803
$846$		0			0
$847$		0			0
$848$	−1.02859	+	1.78157i	−0.0353219	+	0.0611794i
$849$		0			0
$850$	−3.89931	−	6.75381i	−0.133745	−	0.231654i
$851$	−1.11956	−	1.93914i	−0.0383781	−	0.0664728i
$852$		0			0
$853$	10.6969	−	18.5275i	0.366254	−	0.634370i	−0.622723	−	0.782442i	$-0.713974\pi$
$853$	10.6969	−	18.5275i	0.366254	−	0.634370i	0.988976	+	0.148073i	$0.0473070\pi$
$854$		0			0
$855$		0			0
$856$	11.3776			0.388877
$857$	18.4218	−	31.9074i	0.629275	−	1.08994i	−0.358422	−	0.933560i	$-0.616685\pi$
$857$	18.4218	−	31.9074i	0.629275	−	1.08994i	0.987697	−	0.156377i	$-0.0499815\pi$
$858$		0			0
$859$	−8.81875	−	15.2745i	−0.300892	−	0.521160i	0.675446	−	0.737409i	$-0.263951\pi$
$859$	−8.81875	−	15.2745i	−0.300892	−	0.521160i	−0.976338	+	0.216249i	$0.930618\pi$
$860$	−10.8639	−	18.8168i	−0.370455	−	0.641648i
$861$		0			0
$862$	−16.5539	+	28.6722i	−0.563828	+	0.976579i
$863$	−0.760877			−0.0259005			−0.0129503	−	0.999916i	$-0.504122\pi$
$863$	−0.760877			−0.0259005			−0.0129503	+	0.999916i	$0.504122\pi$
$864$		0			0
$865$	−8.11901			−0.276054
$866$	−6.05555	+	10.4885i	−0.205776	+	0.356414i
$867$		0			0
$868$		0			0
$869$	−6.58414	−	11.4041i	−0.223351	−	0.386856i
$870$		0			0
$871$	−31.2759	+	54.1715i	−1.05974	+	1.83553i
$872$	4.42107			0.149716
$873$		0			0
$874$	2.87197			0.0971457
$875$		0			0
$876$		0			0
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	0.968234	+	0.250044i	$0.0804451\pi$
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	−0.267573	+	0.963538i	$0.586222\pi$
$878$	−4.41711	−	7.65066i	−0.149070	−	0.258197i
$879$		0			0
$880$	−5.06238	+	8.76830i	−0.170653	+	0.295579i
$881$	8.35486			0.281482			0.140741	−	0.990046i	$-0.455051\pi$
$881$	8.35486			0.281482			0.140741	+	0.990046i	$0.455051\pi$
$882$		0			0
$883$	35.6181			1.19864			0.599322	−	0.800508i	$-0.295437\pi$
$883$	35.6181			1.19864			0.599322	+	0.800508i	$0.295437\pi$
$884$	−4.33981	+	7.51677i	−0.145964	+	0.252816i
$885$		0			0
$886$	8.75924	+	15.1715i	0.294272	+	0.509695i
$887$	18.5550	+	32.1382i	0.623016	+	1.07909i	0.988921	+	0.148443i	$0.0474260\pi$
$887$	18.5550	+	32.1382i	0.623016	+	1.07909i	−0.365905	+	0.930652i	$0.619241\pi$
$888$		0			0
$889$		0			0
$890$	0.717370			0.0240463
$891$		0			0
$892$	−10.6569			−0.356820
$893$	−3.73788	+	6.47420i	−0.125083	+	0.216651i
$894$		0			0
$895$	11.1969	+	19.3935i	0.374270	+	0.648254i
$896$		0			0
$897$		0			0
$898$	15.6150	−	27.0461i	0.521081	−	0.902539i
$899$	−66.7130			−2.22500
$900$		0			0
$901$	3.13052			0.104293
$902$	8.91423	−	15.4399i	0.296811	−	0.514092i
$903$		0			0
$904$	1.60752	+	2.78431i	0.0534654	+	0.0926048i
$905$	20.6300	+	35.7321i	0.685763	+	1.18778i
$906$		0			0
$907$	24.0751	−	41.6993i	0.799401	−	1.38460i	−0.120606	−	0.992700i	$-0.538484\pi$
$907$	24.0751	−	41.6993i	0.799401	−	1.38460i	0.920007	−	0.391902i	$-0.128183\pi$
$908$	−14.5081			−0.481468
$909$		0			0
$910$		0			0
$911$	−17.4428	+	30.2119i	−0.577906	+	1.00096i	0.417813	+	0.908533i	$0.362797\pi$
$911$	−17.4428	+	30.2119i	−0.577906	+	1.00096i	−0.995719	+	0.0924301i	$0.970537\pi$
$912$		0			0
$913$	12.8353	+	22.2314i	0.424786	+	0.735751i
$914$	16.0624	+	27.8209i	0.531296	+	0.920232i
$915$		0			0
$916$	5.12476	−	8.87635i	0.169327	−	0.293283i
$917$		0			0
$918$		0			0
$919$	51.7349			1.70658			0.853289	−	0.521439i	$-0.174605\pi$
$919$	51.7349			1.70658			0.853289	+	0.521439i	$0.174605\pi$
$920$	−3.56238	+	6.17023i	−0.117448	+	0.203426i
$921$		0			0
$922$	1.23229	+	2.13438i	0.0405832	+	0.0702922i
$923$	24.7826	+	42.9248i	0.815730	+	1.41289i
$924$		0			0
$925$	2.56238	−	4.43818i	0.0842506	−	0.145926i
$926$	−30.3469			−0.997262
$927$		0			0
$928$	−7.08126			−0.232454
$929$	25.4142	−	44.0187i	0.833814	−	1.44421i	−0.0611787	−	0.998127i	$-0.519486\pi$
$929$	25.4142	−	44.0187i	0.833814	−	1.44421i	0.894993	−	0.446081i	$-0.147181\pi$
$930$		0			0
$931$		0			0
$932$	−0.540628	−	0.936396i	−0.0177089	−	0.0306727i
$933$		0			0
$934$	−7.98181	+	13.8249i	−0.261173	+	0.452365i
$935$	15.4074			0.503876
$936$		0			0
$937$	−2.54583			−0.0831686			−0.0415843	−	0.999135i	$-0.513241\pi$
$937$	−2.54583			−0.0831686			−0.0415843	+	0.999135i	$0.513241\pi$
$938$		0			0
$939$		0			0
$940$	−9.27292	−	16.0612i	−0.302449	−	0.523857i
$941$	−0.578933	−	1.00274i	−0.0188727	−	0.0326885i	0.856435	−	0.516255i	$-0.172674\pi$
$941$	−0.578933	−	1.00274i	−0.0188727	−	0.0326885i	−0.875308	+	0.483567i	$0.839341\pi$
$942$		0			0
$943$	6.27292	−	10.8650i	0.204274	−	0.353813i
$944$	−1.12476			−0.0366079
$945$		0			0
$946$	21.7278			0.706431
$947$	4.90739	−	8.49985i	0.159469	−	0.276208i	−0.775208	−	0.631706i	$-0.782355\pi$
$947$	4.90739	−	8.49985i	0.159469	−	0.276208i	0.934677	+	0.355497i	$0.115689\pi$
$948$		0			0
$949$	14.1648	+	24.5342i	0.459810	+	0.796414i
$950$	3.28659	+	5.69254i	0.106631	+	0.184690i
$951$		0			0
$952$		0			0
$953$	−6.53791			−0.211784			−0.105892	−	0.994378i	$-0.533770\pi$
$953$	−6.53791			−0.211784			−0.105892	+	0.994378i	$0.533770\pi$
$954$		0			0
$955$	6.30206			0.203930
$956$	6.16019	−	10.6698i	0.199235	−	0.345085i
$957$		0			0
$958$	11.5865	+	20.0683i	0.374341	+	0.648378i
$959$		0			0
$960$		0			0
$961$	−28.8782	+	50.0186i	−0.931556	+	1.61350i
$962$	−5.70370			−0.183895
$963$		0			0
$964$	13.0000			0.418702
$965$	−7.23229	+	12.5267i	−0.232816	+	0.403248i
$966$		0			0
$967$	14.4445	+	25.0185i	0.464502	+	0.804542i	0.999179	−	0.0405151i	$-0.0128999\pi$
$967$	14.4445	+	25.0185i	0.464502	+	0.804542i	−0.534677	+	0.845057i	$0.679567\pi$
$968$	0.437618	+	0.757977i	0.0140656	+	0.0243623i
$969$		0			0
$970$	23.6134	−	40.8996i	0.758181	−	1.31321i
$971$	−5.33654			−0.171258			−0.0856289	−	0.996327i	$-0.527290\pi$
$971$	−5.33654			−0.171258			−0.0856289	+	0.996327i	$0.527290\pi$
$972$		0			0
$973$		0			0
$974$	1.70658	−	2.95588i	0.0546822	−	0.0947124i
$975$		0			0
$976$	1.56238	+	2.70612i	0.0500106	+	0.0866209i
$977$	−24.0361	−	41.6318i	−0.768983	−	1.33192i	−0.938115	−	0.346325i	$-0.887429\pi$
$977$	−24.0361	−	41.6318i	−0.768983	−	1.33192i	0.169131	−	0.985594i	$-0.445904\pi$
$978$		0			0
$979$	−0.358685	+	0.621261i	−0.0114636	+	0.0198556i
$980$		0			0
$981$		0			0
$982$	−19.1683			−0.611684
$983$	−14.7313	+	25.5154i	−0.469857	+	0.813816i	−0.999406	−	0.0344634i	$-0.989028\pi$
$983$	−14.7313	+	25.5154i	−0.469857	+	0.813816i	0.529549	+	0.848279i	$0.322361\pi$
$984$		0			0
$985$	34.7067	+	60.1138i	1.10585	+	1.91538i
$986$	5.38796	+	9.33223i	0.171588	+	0.297199i
$987$		0			0
$988$	3.65787	−	6.33561i	0.116372	−	0.201563i
$989$	15.2898			0.486186
$990$		0			0
$991$	−30.8285			−0.979298			−0.489649	−	0.871920i	$-0.662875\pi$
$991$	−30.8285			−0.979298			−0.489649	+	0.871920i	$0.662875\pi$
$992$	−4.71053	+	8.15888i	−0.149560	+	0.259045i
$993$		0			0
$994$		0			0
$995$	19.5413	+	33.8466i	0.619501	+	1.07301i
$996$		0			0
$997$	2.77292	−	4.80283i	0.0878191	−	0.152107i	−0.818770	−	0.574122i	$-0.805344\pi$
$997$	2.77292	−	4.80283i	0.0878191	−	0.152107i	0.906589	+	0.422015i	$0.138677\pi$
$998$	41.1696			1.30320
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.m.883.3		6
3.2	odd	2		882.2.f.o.295.2		6
7.2	even	3		2646.2.e.p.2125.3		6
7.3	odd	6		378.2.h.c.289.3		6
7.4	even	3		2646.2.h.o.667.1		6
7.5	odd	6		378.2.e.d.235.1		6
7.6	odd	2		2646.2.f.l.883.1		6
9.2	odd	6		7938.2.a.bw.1.3		3
9.4	even	3	inner	2646.2.f.m.1765.3		6
9.5	odd	6		882.2.f.o.589.2		6
9.7	even	3		7938.2.a.bz.1.1		3
21.2	odd	6		882.2.e.o.655.1		6
21.5	even	6		126.2.e.c.25.3	✓	6
21.11	odd	6		882.2.h.p.79.3		6
21.17	even	6		126.2.h.d.79.1	yes	6
21.20	even	2		882.2.f.n.295.2		6
28.3	even	6		3024.2.t.h.289.3		6
28.19	even	6		3024.2.q.g.2881.1		6
63.4	even	3		2646.2.e.p.1549.3		6
63.5	even	6		126.2.h.d.67.1	yes	6
63.13	odd	6		2646.2.f.l.1765.1		6
63.20	even	6		7938.2.a.bv.1.1		3
63.23	odd	6		882.2.h.p.67.3		6
63.31	odd	6		378.2.e.d.37.1		6
63.32	odd	6		882.2.e.o.373.1		6
63.34	odd	6		7938.2.a.ca.1.3		3
63.38	even	6		1134.2.g.m.163.3		6
63.40	odd	6		378.2.h.c.361.3		6
63.41	even	6		882.2.f.n.589.2		6
63.47	even	6		1134.2.g.m.487.3		6
63.52	odd	6		1134.2.g.l.163.1		6
63.58	even	3		2646.2.h.o.361.1		6
63.59	even	6		126.2.e.c.121.3	yes	6
63.61	odd	6		1134.2.g.l.487.1		6
84.47	odd	6		1008.2.q.g.529.1		6
84.59	odd	6		1008.2.t.h.961.3		6
252.31	even	6		3024.2.q.g.2305.1		6
252.59	odd	6		1008.2.q.g.625.1		6
252.103	even	6		3024.2.t.h.1873.3		6
252.131	odd	6		1008.2.t.h.193.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	21.5	even	6
126.2.e.c.121.3	yes	6	63.59	even	6
126.2.h.d.67.1	yes	6	63.5	even	6
126.2.h.d.79.1	yes	6	21.17	even	6
378.2.e.d.37.1		6	63.31	odd	6
378.2.e.d.235.1		6	7.5	odd	6
378.2.h.c.289.3		6	7.3	odd	6
378.2.h.c.361.3		6	63.40	odd	6
882.2.e.o.373.1		6	63.32	odd	6
882.2.e.o.655.1		6	21.2	odd	6
882.2.f.n.295.2		6	21.20	even	2
882.2.f.n.589.2		6	63.41	even	6
882.2.f.o.295.2		6	3.2	odd	2
882.2.f.o.589.2		6	9.5	odd	6
882.2.h.p.67.3		6	63.23	odd	6
882.2.h.p.79.3		6	21.11	odd	6
1008.2.q.g.529.1		6	84.47	odd	6
1008.2.q.g.625.1		6	252.59	odd	6
1008.2.t.h.193.3		6	252.131	odd	6
1008.2.t.h.961.3		6	84.59	odd	6
1134.2.g.l.163.1		6	63.52	odd	6
1134.2.g.l.487.1		6	63.61	odd	6
1134.2.g.m.163.3		6	63.38	even	6
1134.2.g.m.487.3		6	63.47	even	6
2646.2.e.p.1549.3		6	63.4	even	3
2646.2.e.p.2125.3		6	7.2	even	3
2646.2.f.l.883.1		6	7.6	odd	2
2646.2.f.l.1765.1		6	63.13	odd	6
2646.2.f.m.883.3		6	1.1	even	1	trivial
2646.2.f.m.1765.3		6	9.4	even	3	inner
2646.2.h.o.361.1		6	63.58	even	3
2646.2.h.o.667.1		6	7.4	even	3
3024.2.q.g.2305.1		6	252.31	even	6
3024.2.q.g.2881.1		6	28.19	even	6
3024.2.t.h.289.3		6	28.3	even	6
3024.2.t.h.1873.3		6	252.103	even	6
7938.2.a.bv.1.1		3	63.20	even	6
7938.2.a.bw.1.3		3	9.2	odd	6
7938.2.a.bz.1.1		3	9.7	even	3
7938.2.a.ca.1.3		3	63.34	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.59097 + 2.75564i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.59097 + 2.75564i) q^{5} +1.00000 q^{8} -3.18194 q^{10} +(1.59097 - 2.75564i) q^{11} +(-2.85185 - 4.93955i) q^{13} +(-0.500000 + 0.866025i) q^{16} +1.52175 q^{17} -1.28263 q^{19} +(1.59097 - 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} +(1.11956 + 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} +5.70370 q^{26} +(3.54063 - 6.13255i) q^{29} +(-4.71053 - 8.15888i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.760877 + 1.31788i) q^{34} -1.00000 q^{37} +(0.641315 - 1.11079i) q^{38} +(1.59097 + 2.75564i) q^{40} +(-2.80150 - 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} -3.18194 q^{44} -2.23912 q^{46} +(2.91423 - 5.04759i) q^{47} +(-2.56238 - 4.43818i) q^{50} +(-2.85185 + 4.93955i) q^{52} +2.05718 q^{53} +10.1248 q^{55} +(3.54063 + 6.13255i) q^{58} +(0.562382 + 0.974074i) q^{59} +(1.56238 - 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(9.07442 - 15.7174i) q^{65} +(-5.48345 - 9.49761i) q^{67} +(-0.760877 - 1.31788i) q^{68} -8.69002 q^{71} -4.96690 q^{73} +(0.500000 - 0.866025i) q^{74} +(0.641315 + 1.11079i) q^{76} +(2.06922 - 3.58399i) q^{79} -3.18194 q^{80} +5.60301 q^{82} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(3.41423 + 5.91362i) q^{86} +(1.59097 - 2.75564i) q^{88} -0.225450 q^{89} +(1.11956 - 1.93914i) q^{92} +(2.91423 + 5.04759i) q^{94} +(-2.04063 - 3.53447i) q^{95} +(-7.42107 + 12.8537i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + q^5 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + q^{5} + 6 q^{8} - 2 q^{10} + q^{11} - 8 q^{13} - 3 q^{16} + 8 q^{17} - 6 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} + 16 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} - 6 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} - 2 q^{44} - 14 q^{46} - 9 q^{47} + 2 q^{50} - 8 q^{52} + 30 q^{53} + 26 q^{55} + 5 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} - 4 q^{68} - 14 q^{71} + 38 q^{73} + 3 q^{74} + 3 q^{76} + 5 q^{79} - 2 q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} + 18 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + q^5 + 6 * q^8 - 2 * q^10 + q^11 - 8 * q^13 - 3 * q^16 + 8 * q^17 - 6 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 + 16 * q^26 + 5 * q^29 - 20 * q^31 - 3 * q^32 - 4 * q^34 - 6 * q^37 + 3 * q^38 + q^40 - 6 * q^43 - 2 * q^44 - 14 * q^46 - 9 * q^47 + 2 * q^50 - 8 * q^52 + 30 * q^53 + 26 * q^55 + 5 * q^58 - 14 * q^59 - 8 * q^61 + 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 - 4 * q^68 - 14 * q^71 + 38 * q^73 + 3 * q^74 + 3 * q^76 + 5 * q^79 - 2 * q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 + 18 * q^89 + 7 * q^92 - 9 * q^94 + 4 * q^95 - 28 * q^97

Introduction

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