LMFDB - Embedded newform 2646.2.e.p.2125.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$6$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2125.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2646.2125
Dual form			2646.2.e.p.1549.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(1.59097 - 2.75564i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.59097 - 2.75564i) q^{5} +1.00000 q^{8} +(1.59097 - 2.75564i) q^{10} +(1.59097 + 2.75564i) q^{11} +(-2.85185 - 4.93955i) q^{13} +1.00000 q^{16} +(-0.760877 + 1.31788i) q^{17} +(0.641315 + 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} +(1.11956 - 1.93914i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(-2.85185 - 4.93955i) q^{26} +(3.54063 - 6.13255i) q^{29} +9.42107 q^{31} +1.00000 q^{32} +(-0.760877 + 1.31788i) q^{34} +(0.500000 + 0.866025i) q^{37} +(0.641315 + 1.11079i) q^{38} +(1.59097 - 2.75564i) q^{40} +(-2.80150 - 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} +(1.59097 + 2.75564i) q^{44} +(1.11956 - 1.93914i) q^{46} -5.82846 q^{47} +(-2.56238 - 4.43818i) q^{50} +(-2.85185 - 4.93955i) q^{52} +(-1.02859 + 1.78157i) q^{53} +10.1248 q^{55} +(3.54063 - 6.13255i) q^{58} -1.12476 q^{59} -3.12476 q^{61} +9.42107 q^{62} +1.00000 q^{64} -18.1488 q^{65} +10.9669 q^{67} +(-0.760877 + 1.31788i) q^{68} -8.69002 q^{71} +(2.48345 - 4.30146i) q^{73} +(0.500000 + 0.866025i) q^{74} +(0.641315 + 1.11079i) q^{76} -4.13844 q^{79} +(1.59097 - 2.75564i) q^{80} +(-2.80150 - 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(3.41423 - 5.91362i) q^{86} +(1.59097 + 2.75564i) q^{88} +(0.112725 + 0.195246i) q^{89} +(1.11956 - 1.93914i) q^{92} -5.82846 q^{94} +4.08126 q^{95} +(-7.42107 + 12.8537i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8	$ 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8} + q^{10} + q^{11} - 8 q^{13} + 6 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 8 q^{26} + 5 q^{29} + 40 q^{31} + 6 q^{32} - 4 q^{34} + 3 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 18 q^{47} + 2 q^{50} - 8 q^{52} - 15 q^{53} + 26 q^{55} + 5 q^{58} + 28 q^{59} + 16 q^{61} + 40 q^{62} + 6 q^{64} - 24 q^{65} - 2 q^{67} - 4 q^{68} - 14 q^{71} - 19 q^{73} + 3 q^{74} + 3 q^{76} - 10 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 9 q^{89} + 7 q^{92} + 18 q^{94} - 8 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8 + q^10 + q^11 - 8 * q^13 + 6 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 - 8 * q^26 + 5 * q^29 + 40 * q^31 + 6 * q^32 - 4 * q^34 + 3 * q^37 + 3 * q^38 + q^40 - 6 * q^43 + q^44 + 7 * q^46 + 18 * q^47 + 2 * q^50 - 8 * q^52 - 15 * q^53 + 26 * q^55 + 5 * q^58 + 28 * q^59 + 16 * q^61 + 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 - 4 * q^68 - 14 * q^71 - 19 * q^73 + 3 * q^74 + 3 * q^76 - 10 * q^79 + q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 9 * q^89 + 7 * q^92 + 18 * q^94 - 8 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	−0.252788	−	0.967522i	$-0.581348\pi$
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	0.964292	−	0.264840i	$-0.0853191\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	1.59097	−	2.75564i	0.503109	−	0.871411i
$11$	1.59097	+	2.75564i	0.479696	+	0.830858i	0.999729	−	0.0232884i	$-0.00741361\pi$
$11$	1.59097	+	2.75564i	0.479696	+	0.830858i	−0.520033	+	0.854146i	$0.674080\pi$
$12$		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
$16$	1.00000			0.250000
$17$	−0.760877	+	1.31788i	−0.184540	+	0.319632i	−0.943421	−	0.331596i	$-0.892413\pi$
$17$	−0.760877	+	1.31788i	−0.184540	+	0.319632i	0.758882	+	0.651229i	$0.225746\pi$
$18$		0			0
$19$	0.641315	+	1.11079i	0.147128	+	0.254833i	0.930165	−	0.367142i	$-0.119664\pi$
$19$	0.641315	+	1.11079i	0.147128	+	0.254833i	−0.783037	+	0.621975i	$0.786330\pi$
$20$	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	−0.725375	−	0.688354i	$-0.758334\pi$
$23$	1.11956	−	1.93914i	0.233445	−	0.404338i	0.958820	+	0.284016i	$0.0916669\pi$
$24$		0			0
$25$	−2.56238	−	4.43818i	−0.512476	−	0.887635i
$26$	−2.85185	−	4.93955i	−0.559293	−	0.968725i
$27$		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
$31$	9.42107			1.69207			0.846037	−	0.533125i	$-0.178982\pi$
$31$	9.42107			1.69207			0.846037	+	0.533125i	$0.178982\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.760877	+	1.31788i	−0.130489	+	0.226014i
$35$		0			0
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	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	$-0.00764935\pi$
$44$	1.59097	+	2.75564i	0.239848	+	0.415429i
$45$		0			0
$46$	1.11956	−	1.93914i	0.165070	−	0.285910i
$47$	−5.82846			−0.850168			−0.425084	−	0.905154i	$-0.639755\pi$
$47$	−5.82846			−0.850168			−0.425084	+	0.905154i	$0.639755\pi$
$48$		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
$53$	−1.02859	+	1.78157i	−0.141288	+	0.244717i	−0.927982	−	0.372626i	$-0.878458\pi$
$53$	−1.02859	+	1.78157i	−0.141288	+	0.244717i	0.786694	+	0.617343i	$0.211791\pi$
$54$		0			0
$55$	10.1248			1.36522
$56$		0			0
$57$		0			0
$58$	3.54063	−	6.13255i	0.464907	−	0.805243i
$59$	−1.12476			−0.146432			−0.0732159	−	0.997316i	$-0.523326\pi$
$59$	−1.12476			−0.146432			−0.0732159	+	0.997316i	$0.523326\pi$
$60$		0			0
$61$	−3.12476			−0.400085			−0.200042	−	0.979787i	$-0.564108\pi$
$61$	−3.12476			−0.400085			−0.200042	+	0.979787i	$0.564108\pi$
$62$	9.42107			1.19648
$63$		0			0
$64$	1.00000			0.125000
$65$	−18.1488			−2.25109
$66$		0			0
$67$	10.9669			1.33982			0.669910	−	0.742442i	$-0.266333\pi$
$67$	10.9669			1.33982			0.669910	+	0.742442i	$0.266333\pi$
$68$	−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
$73$	2.48345	−	4.30146i	0.290666	−	0.503448i	−0.683302	−	0.730136i	$-0.739457\pi$
$73$	2.48345	−	4.30146i	0.290666	−	0.503448i	0.973967	+	0.226689i	$0.0727899\pi$
$74$	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
$79$	−4.13844			−0.465610			−0.232805	−	0.972523i	$-0.574790\pi$
$79$	−4.13844			−0.465610			−0.232805	+	0.972523i	$0.574790\pi$
$80$	1.59097	−	2.75564i	0.177876	−	0.308090i
$81$		0			0
$82$	−2.80150	−	4.85235i	−0.309374	−	0.535852i
$83$	−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
$89$	0.112725	+	0.195246i	0.0119488	+	0.0206960i	0.871938	−	0.489616i	$-0.162863\pi$
$89$	0.112725	+	0.195246i	0.0119488	+	0.0206960i	−0.859989	+	0.510312i	$0.829530\pi$
$90$		0			0
$91$		0			0
$92$	1.11956	−	1.93914i	0.116722	−	0.202169i
$93$		0			0
$94$	−5.82846			−0.601160
$95$	4.08126			0.418728
$96$		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
$100$	−2.56238	−	4.43818i	−0.256238	−	0.443818i
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.791796	−	0.610786i	$-0.790854\pi$
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.133058	−	0.991108i	$-0.542480\pi$
$102$		0			0
$103$	−0.141315	+	0.244765i	−0.0139242	+	0.0241174i	−0.872904	−	0.487893i	$-0.837766\pi$
$103$	−0.141315	+	0.244765i	−0.0139242	+	0.0241174i	0.858979	+	0.512010i	$0.171099\pi$
$104$	−2.85185	−	4.93955i	−0.279647	−	0.484362i
$105$		0			0
$106$	−1.02859	+	1.78157i	−0.0999055	+	0.173041i
$107$	−5.68878	−	9.85326i	−0.549955	−	0.952550i	−0.998277	−	0.0586780i	$-0.981311\pi$
$107$	−5.68878	−	9.85326i	−0.549955	−	0.952550i	0.448322	−	0.893872i	$-0.352022\pi$
$108$		0			0
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	−0.952256	−	0.305300i	$-0.901243\pi$
$109$	−2.21053	+	3.82876i	−0.211731	+	0.366728i	0.740526	+	0.672028i	$0.234577\pi$
$110$	10.1248			0.965358
$111$		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
$116$	3.54063	−	6.13255i	0.328739	−	0.569393i
$117$		0			0
$118$	−1.12476			−0.103543
$119$		0			0
$120$		0			0
$121$	0.437618	−	0.757977i	0.0397835	−	0.0689070i
$122$	−3.12476			−0.282903
$123$		0			0
$124$	9.42107			0.846037
$125$	−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	$0.149281\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−18.1488			−1.59176
$131$	−3.18194	+	5.51129i	−0.278008	+	0.481523i	−0.970890	−	0.239528i	$-0.923007\pi$
$131$	−3.18194	+	5.51129i	−0.278008	+	0.481523i	0.692882	+	0.721051i	$0.256341\pi$
$132$		0			0
$133$		0			0
$134$	10.9669			0.947396
$135$		0			0
$136$	−0.760877	+	1.31788i	−0.0652446	+	0.113007i
$137$	1.37072	+	2.37416i	0.117109	+	0.202838i	0.918621	−	0.395140i	$-0.129304\pi$
$137$	1.37072	+	2.37416i	0.117109	+	0.202838i	−0.801512	+	0.597979i	$0.795971\pi$
$138$		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
$142$	−8.69002			−0.729251
$143$	9.07442	−	15.7174i	0.758841	−	1.31435i
$144$		0			0
$145$	−11.2661	−	19.5134i	−0.935597	−	1.62050i
$146$	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	−0.213360	+	0.976974i	$0.568441\pi$
$149$	−11.6300	+	20.1437i	−0.952764	+	1.65024i	−0.739404	+	0.673262i	$0.764893\pi$
$150$		0			0
$151$	4.06238	+	7.03625i	0.330592	+	0.572602i	0.982628	−	0.185586i	$-0.0594183\pi$
$151$	4.06238	+	7.03625i	0.330592	+	0.572602i	−0.652036	+	0.758188i	$0.726085\pi$
$152$	0.641315	+	1.11079i	0.0520175	+	0.0900970i
$153$		0			0
$154$		0			0
$155$	14.9887	−	25.9611i	1.20392	−	2.08525i
$156$		0			0
$157$	11.2632			0.898901			0.449451	−	0.893305i	$-0.351620\pi$
$157$	11.2632			0.898901			0.449451	+	0.893305i	$0.351620\pi$
$158$	−4.13844			−0.329236
$159$		0			0
$160$	1.59097	−	2.75564i	0.125777	−	0.217853i
$161$		0			0
$162$		0			0
$163$	−1.99028	−	3.44727i	−0.155891	−	0.270011i	0.777492	−	0.628893i	$-0.216492\pi$
$163$	−1.99028	−	3.44727i	−0.155891	−	0.270011i	−0.933383	+	0.358881i	$0.883158\pi$
$164$	−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
$170$	2.42107	+	4.19341i	0.185687	+	0.321620i
$171$		0			0
$172$	3.41423	−	5.91362i	0.260333	−	0.450909i
$173$	2.55159			0.193994			0.0969968	−	0.995285i	$-0.469076\pi$
$173$	2.55159			0.193994			0.0969968	+	0.995285i	$0.469076\pi$
$174$		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
$179$	−3.51887	+	6.09487i	−0.263013	+	0.455552i	−0.967041	−	0.254620i	$-0.918050\pi$
$179$	−3.51887	+	6.09487i	−0.263013	+	0.455552i	0.704028	+	0.710172i	$0.251383\pi$
$180$		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
$185$	3.18194			0.233941
$186$		0			0
$187$	−4.84213			−0.354092
$188$	−5.82846			−0.425084
$189$		0			0
$190$	4.08126			0.296085
$191$	−1.98057			−0.143309			−0.0716545	−	0.997430i	$-0.522828\pi$
$191$	−1.98057			−0.143309			−0.0716545	+	0.997430i	$0.522828\pi$
$192$		0			0
$193$	−4.54583			−0.327216			−0.163608	−	0.986525i	$-0.552313\pi$
$193$	−4.54583			−0.327216			−0.163608	+	0.986525i	$0.552313\pi$
$194$	−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
$199$	−6.14132	+	10.6371i	−0.435346	+	0.754042i	−0.997324	−	0.0731106i	$-0.976707\pi$
$199$	−6.14132	+	10.6371i	−0.435346	+	0.754042i	0.561978	+	0.827152i	$0.310041\pi$
$200$	−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
$205$	−17.8285			−1.24519
$206$	−0.141315	+	0.244765i	−0.00984589	+	0.0170536i
$207$		0			0
$208$	−2.85185	−	4.93955i	−0.197740	−	0.342496i
$209$	−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
$215$	−10.8639	−	18.8168i	−0.740911	−	1.28330i
$216$		0			0
$217$		0			0
$218$	−2.21053	+	3.82876i	−0.149716	+	0.259316i
$219$		0			0
$220$	10.1248			0.682611
$221$	8.67962			0.583854
$222$		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
$226$	1.60752	+	2.78431i	0.106931	+	0.185210i
$227$	7.25404	+	12.5644i	0.481468	+	0.833926i	0.999774	−	0.0212688i	$-0.00677059\pi$
$227$	7.25404	+	12.5644i	0.481468	+	0.833926i	−0.518306	+	0.855195i	$0.673437\pi$
$228$		0			0
$229$	5.12476	−	8.87635i	0.338654	−	0.586566i	−0.645526	−	0.763738i	$-0.723362\pi$
$229$	5.12476	−	8.87635i	0.338654	−	0.586566i	0.984180	+	0.177173i	$0.0566951\pi$
$230$	−3.56238	−	6.17023i	−0.234896	−	0.406853i
$231$		0			0
$232$	3.54063	−	6.13255i	0.232454	−	0.402622i
$233$	−0.540628	−	0.936396i	−0.0354177	−	0.0613453i	0.847773	−	0.530359i	$-0.177943\pi$
$233$	−0.540628	−	0.936396i	−0.0354177	−	0.0613453i	−0.883191	+	0.469014i	$0.844610\pi$
$234$		0			0
$235$	−9.27292	+	16.0612i	−0.604898	+	1.04771i
$236$	−1.12476			−0.0732159
$237$		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	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$	0.437618	−	0.757977i	0.0281312	−	0.0487246i
$243$		0			0
$244$	−3.12476			−0.200042
$245$		0			0
$246$		0			0
$247$	3.65787	−	6.33561i	0.232744	−	0.403125i
$248$	9.42107			0.598238
$249$		0			0
$250$	−0.396990			−0.0251079
$251$	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
$254$	20.1053			1.26152
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	−0.960403	−	0.278614i	$-0.910125\pi$
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	0.721488	+	0.692427i	$0.243458\pi$
$258$		0			0
$259$		0			0
$260$	−18.1488			−1.12554
$261$		0			0
$262$	−3.18194	+	5.51129i	−0.196581	+	0.340488i
$263$	−1.54746	−	2.68029i	−0.0954208	−	0.165274i	0.814363	−	0.580355i	$-0.197086\pi$
$263$	−1.54746	−	2.68029i	−0.0954208	−	0.165274i	−0.909784	+	0.415082i	$0.863753\pi$
$264$		0			0
$265$	3.27292	+	5.66886i	0.201054	+	0.348235i
$266$		0			0
$267$		0			0
$268$	10.9669			0.669910
$269$	−13.4451	+	23.2877i	−0.819765	+	1.41987i	0.0860906	+	0.996287i	$0.472563\pi$
$269$	−13.4451	+	23.2877i	−0.819765	+	1.41987i	−0.905855	+	0.423587i	$0.860771\pi$
$270$		0			0
$271$	11.1082	+	19.2400i	0.674776	+	1.16875i	0.976534	+	0.215362i	$0.0690930\pi$
$271$	11.1082	+	19.2400i	0.674776	+	1.16875i	−0.301759	+	0.953384i	$0.597574\pi$
$272$	−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	0.997669	−	0.0682357i	$-0.0217370\pi$
$277$	7.31875	+	12.6764i	0.439741	+	0.761653i	−0.557928	+	0.829889i	$0.688404\pi$
$278$	3.98345	+	6.89953i	0.238911	+	0.413807i
$279$		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
$283$	26.1248			1.55296			0.776478	−	0.630144i	$-0.217004\pi$
$283$	26.1248			1.55296			0.776478	+	0.630144i	$0.217004\pi$
$284$	−8.69002			−0.515658
$285$		0			0
$286$	9.07442	−	15.7174i	0.536582	−	0.929387i
$287$		0			0
$288$		0			0
$289$	7.34213	+	12.7169i	0.431890	+	0.748056i
$290$	−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
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$		0			0
$298$	−11.6300	+	20.1437i	−0.673706	+	1.16689i
$299$	−12.7713			−0.738582
$300$		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
$305$	−4.97141	+	8.61073i	−0.284662	+	0.493049i
$306$		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
$311$	1.70370			0.0966078			0.0483039	−	0.998833i	$-0.484618\pi$
$311$	1.70370			0.0966078			0.0483039	+	0.998833i	$0.484618\pi$
$312$		0			0
$313$	2.84213			0.160647			0.0803234	−	0.996769i	$-0.474405\pi$
$313$	2.84213			0.160647			0.0803234	+	0.996769i	$0.474405\pi$
$314$	11.2632			0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	24.9201			1.39965			0.699827	−	0.714313i	$-0.253261\pi$
$317$	24.9201			1.39965			0.699827	+	0.714313i	$0.253261\pi$
$318$		0			0
$319$	22.5322			1.26156
$320$	1.59097	−	2.75564i	0.0889380	−	0.154045i
$321$		0			0
$322$		0			0
$323$	−1.95185			−0.108604
$324$		0			0
$325$	−14.6150	+	25.3140i	−0.810697	+	1.40417i
$326$	−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
$331$	−7.17154			−0.394183			−0.197092	−	0.980385i	$-0.563150\pi$
$331$	−7.17154			−0.394183			−0.197092	+	0.980385i	$0.563150\pi$
$332$	−4.03379	+	6.98673i	−0.221383	+	0.383447i
$333$		0			0
$334$	2.61956	+	4.53721i	0.143336	+	0.248265i
$335$	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
$341$	14.9887	+	25.9611i	0.811681	+	1.40587i
$342$		0			0
$343$		0			0
$344$	3.41423	−	5.91362i	0.184083	−	0.318841i
$345$		0			0
$346$	2.55159			0.137174
$347$	2.11109			0.113329			0.0566646	−	0.998393i	$-0.481953\pi$
$347$	2.11109			0.113329			0.0566646	+	0.998393i	$0.481953\pi$
$348$		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
$352$	1.59097	+	2.75564i	0.0847991	+	0.146876i
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	0.971168	−	0.238396i	$-0.0766215\pi$
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	−0.692041	+	0.721858i	$0.743288\pi$
$354$		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
$359$	−16.2209	−	28.0955i	−0.856108	−	1.48282i	−0.875613	−	0.483013i	$-0.839542\pi$
$359$	−16.2209	−	28.0955i	−0.856108	−	1.48282i	0.0195047	−	0.999810i	$-0.493791\pi$
$360$		0			0
$361$	8.67743	−	15.0297i	0.456707	−	0.791039i
$362$	12.9669			0.681525
$363$		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	0.526816	−	0.849979i	$-0.323386\pi$
$367$	−9.05555	−	15.6847i	−0.472696	−	0.818733i	−0.999512	+	0.0312465i	$0.990052\pi$
$368$	1.11956	−	1.93914i	0.0583612	−	0.101085i
$369$		0			0
$370$	3.18194			0.165421
$371$		0			0
$372$		0			0
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	−0.674480	−	0.738293i	$-0.735632\pi$
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	0.976621	+	0.214971i	$0.0689656\pi$
$374$	−4.84213			−0.250381
$375$		0			0
$376$	−5.82846			−0.300580
$377$	−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	$0.380565\pi$
$380$	4.08126			0.209364
$381$		0			0
$382$	−1.98057			−0.101335
$383$	0.824893	−	1.42876i	0.0421501	−	0.0730061i	−0.844181	−	0.536059i	$-0.819913\pi$
$383$	0.824893	−	1.42876i	0.0421501	−	0.0730061i	0.886331	+	0.463053i	$0.153246\pi$
$384$		0			0
$385$		0			0
$386$	−4.54583			−0.231377
$387$		0			0
$388$	−7.42107	+	12.8537i	−0.376748	+	0.652546i
$389$	−16.0338	−	27.7713i	−0.812946	−	1.40806i	−0.910794	−	0.412862i	$-0.864529\pi$
$389$	−16.0338	−	27.7713i	−0.812946	−	1.40806i	0.0978483	−	0.995201i	$-0.468804\pi$
$390$		0			0
$391$	1.70370	+	2.95089i	0.0861596	+	0.149233i
$392$		0			0
$393$		0			0
$394$	21.8148			1.09901
$395$	−6.58414	+	11.4041i	−0.331284	+	0.573800i
$396$		0			0
$397$	18.9669	+	32.8516i	0.951921	+	1.64878i	0.741261	+	0.671217i	$0.234228\pi$
$397$	18.9669	+	32.8516i	0.951921	+	1.64878i	0.210660	+	0.977559i	$0.432439\pi$
$398$	−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	−0.702454	−	0.711729i	$-0.747913\pi$
$401$	5.30959	−	9.19647i	0.265148	−	0.459250i	0.967602	+	0.252479i	$0.0812458\pi$
$402$		0			0
$403$	−26.8675	−	46.5358i	−1.33836	−	2.31811i
$404$	−9.29467	−	16.0988i	−0.462427	−	0.800947i
$405$		0			0
$406$		0			0
$407$	−1.59097	+	2.75564i	−0.0788615	+	0.136592i
$408$		0			0
$409$	−5.54583			−0.274224			−0.137112	−	0.990556i	$-0.543782\pi$
$409$	−5.54583			−0.274224			−0.137112	+	0.990556i	$0.543782\pi$
$410$	−17.8285			−0.880485
$411$		0			0
$412$	−0.141315	+	0.244765i	−0.00696209	+	0.0120587i
$413$		0			0
$414$		0			0
$415$	12.8353	+	22.2314i	0.630060	+	1.09130i
$416$	−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	$0.219988\pi$
$422$	−8.32846	−	14.4253i	−0.405423	−	0.702213i
$423$		0			0
$424$	−1.02859	+	1.78157i	−0.0499527	+	0.0865207i
$425$	7.79863			0.378289
$426$		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
$431$	−16.5539	+	28.6722i	−0.797374	+	1.38109i	0.123947	+	0.992289i	$0.460445\pi$
$431$	−16.5539	+	28.6722i	−0.797374	+	1.38109i	−0.921321	+	0.388803i	$0.872889\pi$
$432$		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
$437$	2.87197			0.137385
$438$		0			0
$439$	8.83422			0.421634			0.210817	−	0.977526i	$-0.432388\pi$
$439$	8.83422			0.421634			0.210817	+	0.977526i	$0.432388\pi$
$440$	10.1248			0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	−17.5185			−0.832328			−0.416164	−	0.909290i	$-0.636626\pi$
$443$	−17.5185			−0.832328			−0.416164	+	0.909290i	$0.636626\pi$
$444$		0			0
$445$	0.717370			0.0340066
$446$	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
$451$	8.91423	−	15.4399i	0.419755	−	0.727036i
$452$	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
$457$	−32.1248			−1.50273			−0.751367	−	0.659885i	$-0.770605\pi$
$457$	−32.1248			−1.50273			−0.751367	+	0.659885i	$0.770605\pi$
$458$	5.12476	−	8.87635i	0.239464	−	0.414765i
$459$		0			0
$460$	−3.56238	−	6.17023i	−0.166097	−	0.287688i
$461$	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
$467$	−7.98181	−	13.8249i	−0.369354	−	0.639740i	0.620110	−	0.784515i	$-0.287088\pi$
$467$	−7.98181	−	13.8249i	−0.369354	−	0.639740i	−0.989465	+	0.144774i	$0.953754\pi$
$468$		0			0
$469$		0			0
$470$	−9.27292	+	16.0612i	−0.427728	+	0.740846i
$471$		0			0
$472$	−1.12476			−0.0517714
$473$	21.7278			0.999044
$474$		0			0
$475$	3.28659	−	5.69254i	0.150799	−	0.261192i
$476$		0			0
$477$		0			0
$478$	6.16019	+	10.6698i	0.281761	+	0.488024i
$479$	11.5865	+	20.0683i	0.529399	+	0.916946i	0.999412	+	0.0342863i	$0.0109158\pi$
$479$	11.5865	+	20.0683i	0.529399	+	0.916946i	−0.470013	+	0.882659i	$0.655751\pi$
$480$		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
$485$	23.6134	+	40.8996i	1.07223	+	1.85716i
$486$		0			0
$487$	1.70658	−	2.95588i	0.0773323	−	0.133943i	−0.824766	−	0.565474i	$-0.808693\pi$
$487$	1.70658	−	2.95588i	0.0773323	−	0.133943i	0.902098	+	0.431531i	$0.142026\pi$
$488$	−3.12476			−0.141451
$489$		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
$494$	3.65787	−	6.33561i	0.164575	−	0.285053i
$495$		0			0
$496$	9.42107			0.423018
$497$		0			0
$498$		0			0
$499$	−20.5848	+	35.6540i	−0.921503	+	1.59609i	−0.124413	+	0.992231i	$0.539705\pi$
$499$	−20.5848	+	35.6540i	−0.921503	+	1.59609i	−0.797090	+	0.603860i	$0.793629\pi$
$500$	−0.396990			−0.0177539
$501$		0			0
$502$	5.11109			0.228119
$503$	−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
$506$	7.12476			0.316734
$507$		0			0
$508$	20.1053			0.892030
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	−0.972132	−	0.234436i	$-0.924676\pi$
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	0.689093	+	0.724673i	$0.258009\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.83009	+	6.63392i	−0.168938	+	0.292610i
$515$	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
$520$	−18.1488			−0.795879
$521$	−3.40615	+	5.89962i	−0.149226	+	0.258467i	−0.930942	−	0.365168i	$-0.881012\pi$
$521$	−3.40615	+	5.89962i	−0.149226	+	0.258467i	0.781716	+	0.623635i	$0.214345\pi$
$522$		0			0
$523$	−14.7535	−	25.5538i	−0.645125	−	1.11739i	−0.984273	−	0.176656i	$-0.943472\pi$
$523$	−14.7535	−	25.5538i	−0.645125	−	1.11739i	0.339148	−	0.940733i	$-0.389861\pi$
$524$	−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
$530$	3.27292	+	5.66886i	0.142166	+	0.246239i
$531$		0			0
$532$		0			0
$533$	−15.9789	+	27.6763i	−0.692125	+	1.19879i
$534$		0			0
$535$	−36.2028			−1.56518
$536$	10.9669			0.473698
$537$		0			0
$538$	−13.4451	+	23.2877i	−0.579661	+	1.00400i
$539$		0			0
$540$		0			0
$541$	14.7008	+	25.4626i	0.632038	+	1.09472i	0.987135	+	0.159892i	$0.0511145\pi$
$541$	14.7008	+	25.4626i	0.632038	+	1.09472i	−0.355097	+	0.934829i	$0.615552\pi$
$542$	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	$-0.104807\pi$
$548$	1.37072	+	2.37416i	0.0585544	+	0.101419i
$549$		0			0
$550$	8.15335	−	14.1220i	0.347660	−	0.602165i
$551$	9.08263			0.386933
$552$		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
$557$	3.36909	−	5.83543i	0.142753	−	0.247255i	−0.785779	−	0.618507i	$-0.787738\pi$
$557$	3.36909	−	5.83543i	0.142753	−	0.247255i	0.928532	+	0.371252i	$0.121071\pi$
$558$		0			0
$559$	−38.9475			−1.64730
$560$		0			0
$561$		0			0
$562$	−11.6992	+	20.2636i	−0.493500	+	0.854768i
$563$	−1.45993			−0.0615286			−0.0307643	−	0.999527i	$-0.509794\pi$
$563$	−1.45993			−0.0615286			−0.0307643	+	0.999527i	$0.509794\pi$
$564$		0			0
$565$	10.2301			0.430383
$566$	26.1248			1.09811
$567$		0			0
$568$	−8.69002			−0.364625
$569$	−19.5653			−0.820218			−0.410109	−	0.912036i	$-0.634509\pi$
$569$	−19.5653			−0.820218			−0.410109	+	0.912036i	$0.634509\pi$
$570$		0			0
$571$	−21.9259			−0.917569			−0.458785	−	0.888547i	$-0.651715\pi$
$571$	−21.9259			−0.917569			−0.458785	+	0.888547i	$0.651715\pi$
$572$	9.07442	−	15.7174i	0.379421	−	0.657176i
$573$		0			0
$574$		0			0
$575$	−11.4750			−0.478540
$576$		0			0
$577$	−12.3655	+	21.4177i	−0.514783	+	0.891631i	0.485069	+	0.874476i	$0.338794\pi$
$577$	−12.3655	+	21.4177i	−0.514783	+	0.891631i	−0.999853	+	0.0171554i	$0.994539\pi$
$578$	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
$583$	−6.54583			−0.271101
$584$	2.48345	−	4.30146i	0.102766	−	0.177996i
$585$		0			0
$586$	12.9315	+	22.3980i	0.534194	+	0.925251i
$587$	−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
$593$	−7.55391	−	13.0838i	−0.310202	−	0.537285i	0.668204	−	0.743978i	$-0.267063\pi$
$593$	−7.55391	−	13.0838i	−0.310202	−	0.537285i	−0.978406	+	0.206693i	$0.933730\pi$
$594$		0			0
$595$		0			0
$596$	−11.6300	+	20.1437i	−0.476382	+	0.825118i
$597$		0			0
$598$	−12.7713			−0.522256
$599$	5.45417			0.222851			0.111426	−	0.993773i	$-0.464458\pi$
$599$	5.45417			0.222851			0.111426	+	0.993773i	$0.464458\pi$
$600$		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
$604$	4.06238	+	7.03625i	0.165296	+	0.286301i
$605$	−1.39248	−	2.41184i	−0.0566122	−	0.0980553i
$606$		0			0
$607$	3.33530	−	5.77690i	0.135376	−	0.234477i	−0.790365	−	0.612636i	$-0.790109\pi$
$607$	3.33530	−	5.77690i	0.135376	−	0.234477i	0.925741	+	0.378159i	$0.123443\pi$
$608$	0.641315	+	1.11079i	0.0260088	+	0.0450485i
$609$		0			0
$610$	−4.97141	+	8.61073i	−0.201287	+	0.348638i
$611$	16.6219	+	28.7899i	0.672449	+	1.16472i
$612$		0			0
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	−0.852495	−	0.522735i	$-0.824912\pi$
$613$	0.654988	−	1.13447i	0.0264547	−	0.0458209i	0.878950	+	0.476915i	$0.158245\pi$
$614$	−3.53216			−0.142546
$615$		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	0.652063	−	0.758165i	$-0.273904\pi$
$619$	−8.22421	−	14.2447i	−0.330559	−	0.572545i	−0.982622	+	0.185620i	$0.940571\pi$
$620$	14.9887	−	25.9611i	0.601959	−	1.04262i
$621$		0			0
$622$	1.70370			0.0683120
$623$		0			0
$624$		0			0
$625$	12.1803	−	21.0969i	0.487212	−	0.843877i
$626$	2.84213			0.113594
$627$		0			0
$628$	11.2632			0.449451
$629$	−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	$0.703790\pi$
$632$	−4.13844			−0.164618
$633$		0			0
$634$	24.9201			0.989704
$635$	31.9870	−	55.4031i	1.26937	−	2.19861i
$636$		0			0
$637$		0			0
$638$	22.5322			0.892057
$639$		0			0
$640$	1.59097	−	2.75564i	0.0628887	−	0.108926i
$641$	13.9497	+	24.1615i	0.550978	+	0.954322i	0.998204	+	0.0599014i	$0.0190786\pi$
$641$	13.9497	+	24.1615i	0.550978	+	0.954322i	−0.447226	+	0.894421i	$0.647588\pi$
$642$		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
$646$	−1.95185			−0.0767944
$647$	8.35705	−	14.4748i	0.328550	−	0.569065i	−0.653675	−	0.756776i	$-0.726774\pi$
$647$	8.35705	−	14.4748i	0.328550	−	0.569065i	0.982224	+	0.187711i	$0.0601069\pi$
$648$		0			0
$649$	−1.78947	−	3.09945i	−0.0702427	−	0.121664i
$650$	−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	−0.202614	−	0.979259i	$-0.564944\pi$
$653$	19.0825	−	33.0519i	0.746756	−	1.29342i	0.949370	−	0.314161i	$-0.101723\pi$
$654$		0			0
$655$	10.1248	+	17.5366i	0.395607	+	0.685212i
$656$	−2.80150	−	4.85235i	−0.109380	−	0.189452i
$657$		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
$661$	20.0837			0.781167			0.390584	−	0.920567i	$-0.372273\pi$
$661$	20.0837			0.781167			0.390584	+	0.920567i	$0.372273\pi$
$662$	−7.17154			−0.278730
$663$		0			0
$664$	−4.03379	+	6.98673i	−0.156541	+	0.271138i
$665$		0			0
$666$		0			0
$667$	−7.92790	−	13.7315i	−0.306970	−	0.531687i
$668$	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	$0.938779\pi$
$674$	−10.9211	−	18.9158i	−0.420664	−	0.728611i
$675$		0			0
$676$	−9.76608	+	16.9153i	−0.375618	+	0.650590i
$677$	−0.717370			−0.0275708			−0.0137854	−	0.999905i	$-0.504388\pi$
$677$	−0.717370			−0.0275708			−0.0137854	+	0.999905i	$0.504388\pi$
$678$		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
$683$	10.5270	−	18.2332i	0.402803	−	0.697675i	−0.591260	−	0.806481i	$-0.701369\pi$
$683$	10.5270	−	18.2332i	0.402803	−	0.697675i	0.994063	+	0.108806i	$0.0347027\pi$
$684$		0			0
$685$	8.72313			0.333294
$686$		0			0
$687$		0			0
$688$	3.41423	−	5.91362i	0.130166	−	0.225455i
$689$	11.7335			0.447012
$690$		0			0
$691$	−5.84789			−0.222464			−0.111232	−	0.993794i	$-0.535480\pi$
$691$	−5.84789			−0.222464			−0.111232	+	0.993794i	$0.535480\pi$
$692$	2.55159			0.0969968
$693$		0			0
$694$	2.11109			0.0801359
$695$	25.3502			0.961588
$696$		0			0
$697$	8.52640			0.322960
$698$	−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
$703$	−0.641315	+	1.11079i	−0.0241877	+	0.0418942i
$704$	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
$709$	43.4854			1.63313			0.816564	−	0.577255i	$-0.195876\pi$
$709$	43.4854			1.63313			0.816564	+	0.577255i	$0.195876\pi$
$710$	−13.8256	+	23.9466i	−0.518865	+	0.898700i
$711$		0			0
$712$	0.112725	+	0.195246i	0.00422455	+	0.00731714i
$713$	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
$719$	25.4412	+	44.0654i	0.948796	+	1.64336i	0.747966	+	0.663737i	$0.231031\pi$
$719$	25.4412	+	44.0654i	0.948796	+	1.64336i	0.200830	+	0.979626i	$0.435636\pi$
$720$		0			0
$721$		0			0
$722$	8.67743	−	15.0297i	0.322941	−	0.559349i
$723$		0			0
$724$	12.9669			0.481911
$725$	−36.2898			−1.34777
$726$		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
$730$	−7.90219	−	13.6870i	−0.292473	−	0.506579i
$731$	5.19562	+	8.99907i	0.192167	+	0.332843i
$732$		0			0
$733$	−23.0848	+	39.9841i	−0.852657	+	1.47685i	0.0261440	+	0.999658i	$0.491677\pi$
$733$	−23.0848	+	39.9841i	−0.852657	+	1.47685i	−0.878801	+	0.477188i	$0.841656\pi$
$734$	−9.05555	−	15.6847i	−0.334246	−	0.578932i
$735$		0			0
$736$	1.11956	−	1.93914i	0.0412676	−	0.0714776i
$737$	17.4480	+	30.2209i	0.642706	+	1.11320i
$738$		0			0
$739$	−2.49604	+	4.32327i	−0.0918184	+	0.159034i	−0.908276	−	0.418371i	$-0.862601\pi$
$739$	−2.49604	+	4.32327i	−0.0918184	+	0.159034i	0.816458	+	0.577405i	$0.195935\pi$
$740$	3.18194			0.116971
$741$		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
$746$	5.83530	−	10.1070i	0.213645	−	0.370045i
$747$		0			0
$748$	−4.84213			−0.177046
$749$		0			0
$750$		0			0
$751$	−1.64815	+	2.85468i	−0.0601419	+	0.104169i	−0.894529	−	0.447010i	$-0.852489\pi$
$751$	−1.64815	+	2.85468i	−0.0601419	+	0.104169i	0.834387	+	0.551179i	$0.185822\pi$
$752$	−5.82846			−0.212542
$753$		0			0
$754$	−40.3893			−1.47089
$755$	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	$0.558984\pi$
$758$	14.2690			0.518272
$759$		0			0
$760$	4.08126			0.148043
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	−0.964889	−	0.262659i	$-0.915400\pi$
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	0.709914	+	0.704288i	$0.248734\pi$
$762$		0			0
$763$		0			0
$764$	−1.98057			−0.0716545
$765$		0			0
$766$	0.824893	−	1.42876i	0.0298046	−	0.0516231i
$767$	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
$772$	−4.54583			−0.163608
$773$	0.327772	−	0.567717i	0.0117891	−	0.0204194i	−0.860071	−	0.510175i	$-0.829581\pi$
$773$	0.327772	−	0.567717i	0.0117891	−	0.0204194i	0.871860	+	0.489756i	$0.162914\pi$
$774$		0			0
$775$	−24.1404	−	41.8123i	−0.867148	−	1.50194i
$776$	−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
$782$	1.70370	+	2.95089i	0.0609241	+	0.105524i
$783$		0			0
$784$		0			0
$785$	17.9194	−	31.0374i	0.639572	−	1.10777i
$786$		0			0
$787$	−0.540073			−0.0192515			−0.00962576	−	0.999954i	$-0.503064\pi$
$787$	−0.540073			−0.0192515			−0.00962576	+	0.999954i	$0.503064\pi$
$788$	21.8148			0.777120
$789$		0			0
$790$	−6.58414	+	11.4041i	−0.234253	+	0.405738i
$791$		0			0
$792$		0			0
$793$	8.91135	+	15.4349i	0.316451	+	0.548110i
$794$	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
$800$	−2.56238	−	4.43818i	−0.0905939	−	0.156913i
$801$		0			0
$802$	5.30959	−	9.19647i	0.187488	−	0.324739i
$803$	15.8044			0.557725
$804$		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
$809$	14.5865	−	25.2645i	0.512833	−	0.888252i	−0.487057	−	0.873370i	$-0.661929\pi$
$809$	14.5865	−	25.2645i	0.512833	−	0.888252i	0.999889	−	0.0148817i	$-0.00473717\pi$
$810$		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
$815$	−12.6659			−0.443669
$816$		0			0
$817$	8.75839			0.306417
$818$	−5.54583			−0.193905
$819$		0			0
$820$	−17.8285			−0.622597
$821$	−8.48727			−0.296208			−0.148104	−	0.988972i	$-0.547317\pi$
$821$	−8.48727			−0.296208			−0.148104	+	0.988972i	$0.547317\pi$
$822$		0			0
$823$	29.0974			1.01427			0.507136	−	0.861866i	$-0.330704\pi$
$823$	29.0974			1.01427			0.507136	+	0.861866i	$0.330704\pi$
$824$	−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
$829$	−3.10821	+	5.38358i	−0.107953	+	0.186979i	−0.914941	−	0.403588i	$-0.867763\pi$
$829$	−3.10821	+	5.38358i	−0.107953	+	0.186979i	0.806988	+	0.590568i	$0.201096\pi$
$830$	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
$835$	16.6706			0.576910
$836$	−2.04063	+	3.53447i	−0.0705766	+	0.122242i
$837$		0			0
$838$	2.77455	+	4.80566i	0.0958452	+	0.166009i
$839$	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
$845$	31.0751	+	53.8237i	1.06902	+	1.85159i
$846$		0			0
$847$		0			0
$848$	−1.02859	+	1.78157i	−0.0353219	+	0.0611794i
$849$		0			0
$850$	7.79863			0.267491
$851$	2.23912			0.0767562
$852$		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
$856$	−5.68878	−	9.85326i	−0.194438	−	0.336777i
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	0.987697	+	0.156377i	$0.0499815\pi$
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	−0.358422	+	0.933560i	$0.616685\pi$
$858$		0			0
$859$	−8.81875	+	15.2745i	−0.300892	+	0.521160i	−0.976338	−	0.216249i	$-0.930618\pi$
$859$	−8.81875	+	15.2745i	−0.300892	+	0.521160i	0.675446	+	0.737409i	$0.263951\pi$
$860$	−10.8639	−	18.8168i	−0.370455	−	0.641648i
$861$		0			0
$862$	−16.5539	+	28.6722i	−0.563828	+	0.976579i
$863$	0.380438	+	0.658939i	0.0129503	+	0.0224305i	0.872428	−	0.488743i	$-0.162544\pi$
$863$	0.380438	+	0.658939i	0.0129503	+	0.0224305i	−0.859478	+	0.511173i	$0.829211\pi$
$864$		0			0
$865$	4.05950	−	7.03127i	0.138027	−	0.239070i
$866$	12.1111			0.411552
$867$		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
$872$	−2.21053	+	3.82876i	−0.0748581	+	0.129658i
$873$		0			0
$874$	2.87197			0.0971457
$875$		0			0
$876$		0			0
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	−0.267573	−	0.963538i	$-0.586222\pi$
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	0.968234	−	0.250044i	$-0.0804451\pi$
$878$	8.83422			0.298140
$879$		0			0
$880$	10.1248			0.341306
$881$	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	$0.295437\pi$
$884$	8.67962			0.291927
$885$		0			0
$886$	−17.5185			−0.588545
$887$	18.5550	−	32.1382i	0.623016	−	1.07909i	−0.365905	−	0.930652i	$-0.619241\pi$
$887$	18.5550	−	32.1382i	0.623016	−	1.07909i	0.988921	−	0.148443i	$-0.0474260\pi$
$888$		0			0
$889$		0			0
$890$	0.717370			0.0240463
$891$		0			0
$892$	5.32846	−	9.22916i	0.178410	−	0.309015i
$893$	−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
$898$	−31.2301			−1.04216
$899$	33.3565	−	57.7751i	1.11250	−	1.92691i
$900$		0			0
$901$	−1.56526	−	2.71111i	−0.0521464	−	0.0903202i
$902$	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	0.920007	+	0.391902i	$0.128183\pi$
$907$	24.0751	+	41.6993i	0.799401	+	1.38460i	−0.120606	+	0.992700i	$0.538484\pi$
$908$	7.25404	+	12.5644i	0.240734	+	0.416963i
$909$		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
$913$	−25.6706			−0.849573
$914$	−32.1248			−1.06259
$915$		0			0
$916$	5.12476	−	8.87635i	0.169327	−	0.293283i
$917$		0			0
$918$		0			0
$919$	−25.8675	−	44.8037i	−0.853289	−	1.47794i	−0.878224	−	0.478250i	$-0.841271\pi$
$919$	−25.8675	−	44.8037i	−0.853289	−	1.47794i	0.0249351	−	0.999689i	$-0.492062\pi$
$920$	−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
$926$	15.1735	+	26.2812i	0.498631	+	0.863655i
$927$		0			0
$928$	3.54063	−	6.13255i	0.116227	−	0.201311i
$929$	−50.8285			−1.66763			−0.833814	−	0.552046i	$-0.813847\pi$
$929$	−50.8285			−1.66763			−0.833814	+	0.552046i	$0.813847\pi$
$930$		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
$935$	−7.70370	+	13.3432i	−0.251938	+	0.436369i
$936$		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
$941$	1.15787			0.0377454			0.0188727	−	0.999822i	$-0.493992\pi$
$941$	1.15787			0.0377454			0.0188727	+	0.999822i	$0.493992\pi$
$942$		0			0
$943$	−12.5458			−0.408548
$944$	−1.12476			−0.0366079
$945$		0			0
$946$	21.7278			0.706431
$947$	−9.81479			−0.318938			−0.159469	−	0.987203i	$-0.550978\pi$
$947$	−9.81479			−0.318938			−0.159469	+	0.987203i	$0.550978\pi$
$948$		0			0
$949$	−28.3297			−0.919620
$950$	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
$955$	−3.15103	+	5.45774i	−0.101965	+	0.176608i
$956$	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
$961$	57.7565			1.86311
$962$	2.85185	−	4.93955i	0.0919473	−	0.159257i
$963$		0			0
$964$	−6.50000	−	11.2583i	−0.209351	−	0.362606i
$965$	−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
$971$	2.66827	+	4.62158i	0.0856289	+	0.148314i	0.905659	−	0.424007i	$-0.139377\pi$
$971$	2.66827	+	4.62158i	0.0856289	+	0.148314i	−0.820030	+	0.572320i	$0.806043\pi$
$972$		0			0
$973$		0			0
$974$	1.70658	−	2.95588i	0.0546822	−	0.0947124i
$975$		0			0
$976$	−3.12476			−0.100021
$977$	48.0722			1.53797			0.768983	−	0.639269i	$-0.220763\pi$
$977$	48.0722			1.53797			0.768983	+	0.639269i	$0.220763\pi$
$978$		0			0
$979$	−0.358685	+	0.621261i	−0.0114636	+	0.0198556i
$980$		0			0
$981$		0			0
$982$	9.58414	+	16.6002i	0.305842	+	0.529734i
$983$	−14.7313	−	25.5154i	−0.469857	−	0.813816i	0.529549	−	0.848279i	$-0.322361\pi$
$983$	−14.7313	−	25.5154i	−0.469857	−	0.813816i	−0.999406	+	0.0344634i	$0.989028\pi$
$984$		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
$989$	−7.64488	−	13.2413i	−0.243093	−	0.421050i
$990$		0			0
$991$	15.4142	−	26.6982i	0.489649	−	0.848097i	−0.510280	−	0.860008i	$-0.670458\pi$
$991$	15.4142	−	26.6982i	0.489649	−	0.848097i	0.999929	+	0.0119112i	$0.00379153\pi$
$992$	9.42107			0.299119
$993$		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	0.906589	−	0.422015i	$-0.138677\pi$
$997$	2.77292	+	4.80283i	0.0878191	+	0.152107i	−0.818770	+	0.574122i	$0.805344\pi$
$998$	−20.5848	+	35.6540i	−0.651601	+	1.12861i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.p.2125.3		6
3.2	odd	2		882.2.e.o.655.1		6
7.2	even	3		2646.2.h.o.667.1		6
7.3	odd	6		2646.2.f.l.883.1		6
7.4	even	3		2646.2.f.m.883.3		6
7.5	odd	6		378.2.h.c.289.3		6
7.6	odd	2		378.2.e.d.235.1		6
9.4	even	3		2646.2.h.o.361.1		6
9.5	odd	6		882.2.h.p.67.3		6
21.2	odd	6		882.2.h.p.79.3		6
21.5	even	6		126.2.h.d.79.1	yes	6
21.11	odd	6		882.2.f.o.295.2		6
21.17	even	6		882.2.f.n.295.2		6
21.20	even	2		126.2.e.c.25.3	✓	6
28.19	even	6		3024.2.t.h.289.3		6
28.27	even	2		3024.2.q.g.2881.1		6
63.4	even	3		2646.2.f.m.1765.3		6
63.5	even	6		126.2.e.c.121.3	yes	6
63.11	odd	6		7938.2.a.bw.1.3		3
63.13	odd	6		378.2.h.c.361.3		6
63.20	even	6		1134.2.g.m.487.3		6
63.23	odd	6		882.2.e.o.373.1		6
63.25	even	3		7938.2.a.bz.1.1		3
63.31	odd	6		2646.2.f.l.1765.1		6
63.32	odd	6		882.2.f.o.589.2		6
63.34	odd	6		1134.2.g.l.487.1		6
63.38	even	6		7938.2.a.bv.1.1		3
63.40	odd	6		378.2.e.d.37.1		6
63.41	even	6		126.2.h.d.67.1	yes	6
63.47	even	6		1134.2.g.m.163.3		6
63.52	odd	6		7938.2.a.ca.1.3		3
63.58	even	3	inner	2646.2.e.p.1549.3		6
63.59	even	6		882.2.f.n.589.2		6
63.61	odd	6		1134.2.g.l.163.1		6
84.47	odd	6		1008.2.t.h.961.3		6
84.83	odd	2		1008.2.q.g.529.1		6
252.103	even	6		3024.2.q.g.2305.1		6
252.131	odd	6		1008.2.q.g.625.1		6
252.139	even	6		3024.2.t.h.1873.3		6
252.167	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	21.20	even	2
126.2.e.c.121.3	yes	6	63.5	even	6
126.2.h.d.67.1	yes	6	63.41	even	6
126.2.h.d.79.1	yes	6	21.5	even	6
378.2.e.d.37.1		6	63.40	odd	6
378.2.e.d.235.1		6	7.6	odd	2
378.2.h.c.289.3		6	7.5	odd	6
378.2.h.c.361.3		6	63.13	odd	6
882.2.e.o.373.1		6	63.23	odd	6
882.2.e.o.655.1		6	3.2	odd	2
882.2.f.n.295.2		6	21.17	even	6
882.2.f.n.589.2		6	63.59	even	6
882.2.f.o.295.2		6	21.11	odd	6
882.2.f.o.589.2		6	63.32	odd	6
882.2.h.p.67.3		6	9.5	odd	6
882.2.h.p.79.3		6	21.2	odd	6
1008.2.q.g.529.1		6	84.83	odd	2
1008.2.q.g.625.1		6	252.131	odd	6
1008.2.t.h.193.3		6	252.167	odd	6
1008.2.t.h.961.3		6	84.47	odd	6
1134.2.g.l.163.1		6	63.61	odd	6
1134.2.g.l.487.1		6	63.34	odd	6
1134.2.g.m.163.3		6	63.47	even	6
1134.2.g.m.487.3		6	63.20	even	6
2646.2.e.p.1549.3		6	63.58	even	3	inner
2646.2.e.p.2125.3		6	1.1	even	1	trivial
2646.2.f.l.883.1		6	7.3	odd	6
2646.2.f.l.1765.1		6	63.31	odd	6
2646.2.f.m.883.3		6	7.4	even	3
2646.2.f.m.1765.3		6	63.4	even	3
2646.2.h.o.361.1		6	9.4	even	3
2646.2.h.o.667.1		6	7.2	even	3
3024.2.q.g.2305.1		6	252.103	even	6
3024.2.q.g.2881.1		6	28.27	even	2
3024.2.t.h.289.3		6	28.19	even	6
3024.2.t.h.1873.3		6	252.139	even	6
7938.2.a.bv.1.1		3	63.38	even	6
7938.2.a.bw.1.3		3	63.11	odd	6
7938.2.a.bz.1.1		3	63.25	even	3
7938.2.a.ca.1.3		3	63.52	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.59097 - 2.75564i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.59097 - 2.75564i) q^{5} +1.00000 q^{8} +(1.59097 - 2.75564i) q^{10} +(1.59097 + 2.75564i) q^{11} +(-2.85185 - 4.93955i) q^{13} +1.00000 q^{16} +(-0.760877 + 1.31788i) q^{17} +(0.641315 + 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} +(1.11956 - 1.93914i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(-2.85185 - 4.93955i) q^{26} +(3.54063 - 6.13255i) q^{29} +9.42107 q^{31} +1.00000 q^{32} +(-0.760877 + 1.31788i) q^{34} +(0.500000 + 0.866025i) q^{37} +(0.641315 + 1.11079i) q^{38} +(1.59097 - 2.75564i) q^{40} +(-2.80150 - 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} +(1.59097 + 2.75564i) q^{44} +(1.11956 - 1.93914i) q^{46} -5.82846 q^{47} +(-2.56238 - 4.43818i) q^{50} +(-2.85185 - 4.93955i) q^{52} +(-1.02859 + 1.78157i) q^{53} +10.1248 q^{55} +(3.54063 - 6.13255i) q^{58} -1.12476 q^{59} -3.12476 q^{61} +9.42107 q^{62} +1.00000 q^{64} -18.1488 q^{65} +10.9669 q^{67} +(-0.760877 + 1.31788i) q^{68} -8.69002 q^{71} +(2.48345 - 4.30146i) q^{73} +(0.500000 + 0.866025i) q^{74} +(0.641315 + 1.11079i) q^{76} -4.13844 q^{79} +(1.59097 - 2.75564i) q^{80} +(-2.80150 - 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(3.41423 - 5.91362i) q^{86} +(1.59097 + 2.75564i) q^{88} +(0.112725 + 0.195246i) q^{89} +(1.11956 - 1.93914i) q^{92} -5.82846 q^{94} +4.08126 q^{95} +(-7.42107 + 12.8537i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8	\( 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8} + q^{10} + q^{11} - 8 q^{13} + 6 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 8 q^{26} + 5 q^{29} + 40 q^{31} + 6 q^{32} - 4 q^{34} + 3 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 18 q^{47} + 2 q^{50} - 8 q^{52} - 15 q^{53} + 26 q^{55} + 5 q^{58} + 28 q^{59} + 16 q^{61} + 40 q^{62} + 6 q^{64} - 24 q^{65} - 2 q^{67} - 4 q^{68} - 14 q^{71} - 19 q^{73} + 3 q^{74} + 3 q^{76} - 10 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 9 q^{89} + 7 q^{92} + 18 q^{94} - 8 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8 + q^10 + q^11 - 8 * q^13 + 6 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 - 8 * q^26 + 5 * q^29 + 40 * q^31 + 6 * q^32 - 4 * q^34 + 3 * q^37 + 3 * q^38 + q^40 - 6 * q^43 + q^44 + 7 * q^46 + 18 * q^47 + 2 * q^50 - 8 * q^52 - 15 * q^53 + 26 * q^55 + 5 * q^58 + 28 * q^59 + 16 * q^61 + 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 - 4 * q^68 - 14 * q^71 - 19 * q^73 + 3 * q^74 + 3 * q^76 - 10 * q^79 + q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 9 * q^89 + 7 * q^92 + 18 * q^94 - 8 * q^95 - 28 * q^97

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