LMFDB - Embedded newform 2646.2.h.o.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.1
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.o.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +1.00000 q^{8} +(1.59097 + 2.75564i) q^{10} -3.18194 q^{11} +(-2.85185 - 4.93955i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.760877 - 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} -2.23912 q^{23} +5.12476 q^{25} +(-2.85185 + 4.93955i) q^{26} +(3.54063 - 6.13255i) q^{29} +(-4.71053 + 8.15888i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.760877 + 1.31788i) q^{34} +(0.500000 - 0.866025i) q^{37} -1.28263 q^{38} -3.18194 q^{40} +(-2.80150 - 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} +(1.59097 - 2.75564i) q^{44} +(1.11956 + 1.93914i) q^{46} +(2.91423 + 5.04759i) q^{47} +(-2.56238 - 4.43818i) q^{50} +5.70370 q^{52} +(-1.02859 - 1.78157i) q^{53} +10.1248 q^{55} -7.08126 q^{58} +(0.562382 - 0.974074i) q^{59} +(1.56238 + 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(9.07442 + 15.7174i) q^{65} +(-5.48345 + 9.49761i) q^{67} +1.52175 q^{68} -8.69002 q^{71} +(2.48345 + 4.30146i) q^{73} -1.00000 q^{74} +(0.641315 + 1.11079i) q^{76} +(2.06922 + 3.58399i) q^{79} +(1.59097 + 2.75564i) q^{80} +(-2.80150 + 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} -6.82846 q^{86} -3.18194 q^{88} +(0.112725 - 0.195246i) q^{89} +(1.11956 - 1.93914i) q^{92} +(2.91423 - 5.04759i) q^{94} +(-2.04063 + 3.53447i) q^{95} +(-7.42107 + 12.8537i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + q^{10} - 2 q^{11} - 8 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} - 14 q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} + 3 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} - 9 q^{47} + 2 q^{50} + 16 q^{52} - 15 q^{53} + 26 q^{55} - 10 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 8 q^{68} - 14 q^{71} - 19 q^{73} - 6 q^{74} + 3 q^{76} + 5 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} - 9 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 - 2 * q^5 + 6 * q^8 + q^10 - 2 * q^11 - 8 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 - 14 * q^23 - 4 * q^25 - 8 * q^26 + 5 * q^29 - 20 * q^31 - 3 * q^32 - 4 * q^34 + 3 * q^37 - 6 * q^38 - 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 - 9 * q^47 + 2 * q^50 + 16 * q^52 - 15 * q^53 + 26 * q^55 - 10 * q^58 - 14 * q^59 - 8 * q^61 + 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 + 8 * q^68 - 14 * q^71 - 19 * q^73 - 6 * q^74 + 3 * q^76 + 5 * q^79 + q^80 + 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 - 9 * 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 $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.18194			−1.42301			−0.711504	−	0.702682i	$-0.751986\pi$
$5$	−3.18194			−1.42301			−0.711504	+	0.702682i	$0.751986\pi$
$6$		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
$11$	−3.18194			−0.959392			−0.479696	−	0.877435i	$-0.659253\pi$
$11$	−3.18194			−0.959392			−0.479696	+	0.877435i	$0.659253\pi$
$12$		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
$17$	−0.760877	−	1.31788i	−0.184540	−	0.319632i	0.758882	−	0.651229i	$-0.225746\pi$
$17$	−0.760877	−	1.31788i	−0.184540	−	0.319632i	−0.943421	+	0.331596i	$0.892413\pi$
$18$		0			0
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	−0.783037	−	0.621975i	$-0.786330\pi$
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	0.930165	+	0.367142i	$0.119664\pi$
$20$	1.59097	−	2.75564i	0.355752	−	0.616181i
$21$		0			0
$22$	1.59097	+	2.75564i	0.339196	+	0.587505i
$23$	−2.23912			−0.466889			−0.233445	−	0.972370i	$-0.575000\pi$
$23$	−2.23912			−0.466889			−0.233445	+	0.972370i	$0.575000\pi$
$24$		0			0
$25$	5.12476			1.02495
$26$	−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
$31$	−4.71053	+	8.15888i	−0.846037	+	1.46538i	0.0386810	+	0.999252i	$0.487684\pi$
$31$	−4.71053	+	8.15888i	−0.846037	+	1.46538i	−0.884718	+	0.466127i	$0.845649\pi$
$32$	−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
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−1.28263			−0.208070
$39$		0			0
$40$	−3.18194			−0.503109
$41$	−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
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	0.996428	−	0.0844432i	$-0.0269112\pi$
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	−0.571344	+	0.820711i	$0.693578\pi$
$48$		0			0
$49$		0			0
$50$	−2.56238	−	4.43818i	−0.362375	−	0.627653i
$51$		0			0
$52$	5.70370			0.790960
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	0.786694	−	0.617343i	$-0.211791\pi$
$53$	−1.02859	−	1.78157i	−0.141288	−	0.244717i	−0.927982	+	0.372626i	$0.878458\pi$
$54$		0			0
$55$	10.1248			1.36522
$56$		0			0
$57$		0			0
$58$	−7.08126			−0.929815
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	−0.827093	−	0.562065i	$-0.810007\pi$
$59$	0.562382	−	0.974074i	0.0732159	−	0.126814i	0.900309	+	0.435251i	$0.143340\pi$
$60$		0			0
$61$	1.56238	+	2.70612i	0.200042	+	0.346484i	0.948542	−	0.316652i	$-0.102559\pi$
$61$	1.56238	+	2.70612i	0.200042	+	0.346484i	−0.748499	+	0.663135i	$0.769225\pi$
$62$	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	0.308019	+	0.951380i	$0.400334\pi$
$67$	−5.48345	+	9.49761i	−0.669910	+	1.16032i	−0.977929	+	0.208938i	$0.932999\pi$
$68$	1.52175			0.184540
$69$		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	0.973967	−	0.226689i	$-0.0727899\pi$
$73$	2.48345	+	4.30146i	0.290666	+	0.503448i	−0.683302	+	0.730136i	$0.739457\pi$
$74$	−1.00000			−0.116248
$75$		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	0.958633	−	0.284646i	$-0.0918762\pi$
$79$	2.06922	+	3.58399i	0.232805	+	0.403231i	−0.725827	+	0.687877i	$0.758543\pi$
$80$	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
$86$	−6.82846			−0.736332
$87$		0			0
$88$	−3.18194			−0.339196
$89$	0.112725	−	0.195246i	0.0119488	−	0.0206960i	−0.859989	−	0.510312i	$-0.829530\pi$
$89$	0.112725	−	0.195246i	0.0119488	−	0.0206960i	0.871938	+	0.489616i	$0.162863\pi$
$90$		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
$100$	−2.56238	+	4.43818i	−0.256238	+	0.443818i
$101$	18.5893			1.84971			0.924854	−	0.380322i	$-0.124187\pi$
$101$	18.5893			1.84971			0.924854	+	0.380322i	$0.124187\pi$
$102$		0			0
$103$	0.282630			0.0278484			0.0139242	−	0.999903i	$-0.495568\pi$
$103$	0.282630			0.0278484			0.0139242	+	0.999903i	$0.495568\pi$
$104$	−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	0.448322	+	0.893872i	$0.352022\pi$
$107$	−5.68878	+	9.85326i	−0.549955	+	0.952550i	−0.998277	+	0.0586780i	$0.981311\pi$
$108$		0			0
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	0.740526	−	0.672028i	$-0.234577\pi$
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	−0.952256	+	0.305300i	$0.901243\pi$
$110$	−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
$115$	7.12476			0.664388
$116$	3.54063	+	6.13255i	0.328739	+	0.569393i
$117$		0			0
$118$	−1.12476			−0.103543
$119$		0			0
$120$		0			0
$121$	−0.875237			−0.0795670
$122$	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
$131$	6.36389			0.556015			0.278008	−	0.960579i	$-0.410326\pi$
$131$	6.36389			0.556015			0.278008	+	0.960579i	$0.410326\pi$
$132$		0			0
$133$		0			0
$134$	10.9669			0.947396
$135$		0			0
$136$	−0.760877	−	1.31788i	−0.0652446	−	0.113007i
$137$	−2.74145			−0.234218			−0.117109	−	0.993119i	$-0.537363\pi$
$137$	−2.74145			−0.234218			−0.117109	+	0.993119i	$0.537363\pi$
$138$		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
$143$	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
$149$	23.2599			1.90553			0.952764	−	0.303712i	$-0.0982261\pi$
$149$	23.2599			1.90553			0.952764	+	0.303712i	$0.0982261\pi$
$150$		0			0
$151$	−8.12476			−0.661184			−0.330592	−	0.943774i	$-0.607248\pi$
$151$	−8.12476			−0.661184			−0.330592	+	0.943774i	$0.607248\pi$
$152$	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
$157$	−5.63160	+	9.75422i	−0.449451	+	0.778471i	−0.998350	−	0.0574170i	$-0.981714\pi$
$157$	−5.63160	+	9.75422i	−0.449451	+	0.778471i	0.548900	+	0.835888i	$0.315047\pi$
$158$	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
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	−0.933383	−	0.358881i	$-0.883158\pi$
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	0.777492	+	0.628893i	$0.216492\pi$
$164$	5.60301			0.437522
$165$		0			0
$166$	8.06758			0.626166
$167$	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
$173$	−1.27579	−	2.20974i	−0.0969968	−	0.168003i	0.813443	−	0.581644i	$-0.197590\pi$
$173$	−1.27579	−	2.20974i	−0.0969968	−	0.168003i	−0.910440	+	0.413641i	$0.864257\pi$
$174$		0			0
$175$		0			0
$176$	1.59097	+	2.75564i	0.119924	+	0.207714i
$177$		0			0
$178$	−0.225450			−0.0168982
$179$	−3.51887	−	6.09487i	−0.263013	−	0.455552i	0.704028	−	0.710172i	$-0.251383\pi$
$179$	−3.51887	−	6.09487i	−0.263013	−	0.455552i	−0.967041	+	0.254620i	$0.918050\pi$
$180$		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
$184$	−2.23912			−0.165070
$185$	−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	0.899627	−	0.436660i	$-0.143839\pi$
$191$	0.990285	+	1.71522i	0.0716545	+	0.124109i	−0.827972	+	0.560769i	$0.810505\pi$
$192$		0			0
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	−0.772552	−	0.634951i	$-0.781020\pi$
$193$	2.27292	−	3.93680i	0.163608	−	0.283377i	0.936160	+	0.351574i	$0.114353\pi$
$194$	14.8421			1.06560
$195$		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	0.561978	−	0.827152i	$-0.310041\pi$
$199$	−6.14132	−	10.6371i	−0.435346	−	0.754042i	−0.997324	+	0.0731106i	$0.976707\pi$
$200$	5.12476			0.362375
$201$		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
$206$	−0.141315	−	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	$-0.361025\pi$
$212$	2.05718			0.141288
$213$		0			0
$214$	11.3776			0.777754
$215$	−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
$220$	−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
$226$	1.60752	−	2.78431i	0.106931	−	0.185210i
$227$	−14.5081			−0.962935			−0.481468	−	0.876464i	$-0.659896\pi$
$227$	−14.5081			−0.962935			−0.481468	+	0.876464i	$0.659896\pi$
$228$		0			0
$229$	−10.2495			−0.677308			−0.338654	−	0.940911i	$-0.609972\pi$
$229$	−10.2495			−0.677308			−0.338654	+	0.940911i	$0.609972\pi$
$230$	−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	−0.883191	−	0.469014i	$-0.844610\pi$
$233$	−0.540628	+	0.936396i	−0.0354177	+	0.0613453i	0.847773	+	0.530359i	$0.177943\pi$
$234$		0			0
$235$	−9.27292	−	16.0612i	−0.604898	−	1.04771i
$236$	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
$241$	13.0000			0.837404			0.418702	−	0.908124i	$-0.362485\pi$
$241$	13.0000			0.837404			0.418702	+	0.908124i	$0.362485\pi$
$242$	0.437618	+	0.757977i	0.0281312	+	0.0487246i
$243$		0			0
$244$	−3.12476			−0.200042
$245$		0			0
$246$		0			0
$247$	−7.31573			−0.465489
$248$	−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
$257$	7.66019			0.477830			0.238915	−	0.971041i	$-0.423208\pi$
$257$	7.66019			0.477830			0.238915	+	0.971041i	$0.423208\pi$
$258$		0			0
$259$		0			0
$260$	−18.1488			−1.12554
$261$		0			0
$262$	−3.18194	−	5.51129i	−0.196581	−	0.340488i
$263$	3.09493			0.190842			0.0954208	−	0.995437i	$-0.469580\pi$
$263$	3.09493			0.190842			0.0954208	+	0.995437i	$0.469580\pi$
$264$		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
$269$	−13.4451	−	23.2877i	−0.819765	−	1.41987i	−0.905855	−	0.423587i	$-0.860771\pi$
$269$	−13.4451	−	23.2877i	−0.819765	−	1.41987i	0.0860906	−	0.996287i	$-0.472563\pi$
$270$		0			0
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	−0.301759	−	0.953384i	$-0.597574\pi$
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	0.976534	−	0.215362i	$-0.0690930\pi$
$272$	−0.760877	+	1.31788i	−0.0461349	+	0.0799080i
$273$		0			0
$274$	1.37072	+	2.37416i	0.0828084	+	0.143428i
$275$	−16.3067			−0.983331
$276$		0			0
$277$	−14.6375			−0.879482			−0.439741	−	0.898125i	$-0.644930\pi$
$277$	−14.6375			−0.879482			−0.439741	+	0.898125i	$0.644930\pi$
$278$	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
$283$	−13.0624	+	22.6247i	−0.776478	+	1.34490i	0.157482	+	0.987522i	$0.449662\pi$
$283$	−13.0624	+	22.6247i	−0.776478	+	1.34490i	−0.933960	+	0.357377i	$0.883671\pi$
$284$	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
$289$	7.34213	−	12.7169i	0.431890	−	0.748056i
$290$	22.5322			1.32313
$291$		0			0
$292$	−4.96690			−0.290666
$293$	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
$299$	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
$304$	−1.28263			−0.0735639
$305$	−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
$310$	−29.9773			−1.70260
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	−0.889166	−	0.457584i	$-0.848715\pi$
$311$	−0.851848	+	1.47544i	−0.0483039	+	0.0836648i	0.840863	+	0.541249i	$0.182048\pi$
$312$		0			0
$313$	−1.42107	−	2.46136i	−0.0803234	−	0.139124i	0.823065	−	0.567947i	$-0.192262\pi$
$313$	−1.42107	−	2.46136i	−0.0803234	−	0.139124i	−0.903389	+	0.428822i	$0.858929\pi$
$314$	11.2632			0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	−12.4601	−	21.5815i	−0.699827	−	1.21214i	−0.968526	−	0.248911i	$-0.919927\pi$
$317$	−12.4601	−	21.5815i	−0.699827	−	1.21214i	0.268700	−	0.963224i	$-0.413406\pi$
$318$		0			0
$319$	−11.2661	+	19.5134i	−0.630779	+	1.09254i
$320$	−3.18194			−0.177876
$321$		0			0
$322$		0			0
$323$	−1.95185			−0.108604
$324$		0			0
$325$	−14.6150	−	25.3140i	−0.810697	−	1.40417i
$326$	3.98057			0.220463
$327$		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	0.947584	−	0.319506i	$-0.103517\pi$
$331$	3.58577	+	6.21074i	0.197092	+	0.341373i	−0.750492	+	0.660879i	$0.770184\pi$
$332$	−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	$-0.369478\pi$
$338$	19.5322			1.06241
$339$		0			0
$340$	−4.84213			−0.262602
$341$	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
$346$	−1.27579	+	2.20974i	−0.0685871	+	0.118796i
$347$	−1.05555	+	1.82826i	−0.0566646	+	0.0981460i	−0.892966	−	0.450124i	$-0.851380\pi$
$347$	−1.05555	+	1.82826i	−0.0566646	+	0.0981460i	0.836302	+	0.548270i	$0.184713\pi$
$348$		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
$353$	−10.4887			−0.558255			−0.279127	−	0.960254i	$-0.590045\pi$
$353$	−10.4887			−0.558255			−0.279127	+	0.960254i	$0.590045\pi$
$354$		0			0
$355$	27.6512			1.46757
$356$	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	0.0195047	+	0.999810i	$0.493791\pi$
$359$	−16.2209	+	28.0955i	−0.856108	+	1.48282i	−0.875613	+	0.483013i	$0.839542\pi$
$360$		0			0
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$	−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
$367$	18.1111			0.945391			0.472696	−	0.881226i	$-0.343281\pi$
$367$	18.1111			0.945391			0.472696	+	0.881226i	$0.343281\pi$
$368$	1.11956	+	1.93914i	0.0583612	+	0.101085i
$369$		0			0
$370$	3.18194			0.165421
$371$		0			0
$372$		0			0
$373$	−11.6706			−0.604280			−0.302140	−	0.953263i	$-0.597701\pi$
$373$	−11.6706			−0.604280			−0.302140	+	0.953263i	$0.597701\pi$
$374$	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
$383$	−1.64979			−0.0843001			−0.0421501	−	0.999111i	$-0.513421\pi$
$383$	−1.64979			−0.0843001			−0.0421501	+	0.999111i	$0.513421\pi$
$384$		0			0
$385$		0			0
$386$	−4.54583			−0.231377
$387$		0			0
$388$	−7.42107	−	12.8537i	−0.376748	−	0.652546i
$389$	32.0676			1.62589			0.812946	−	0.582340i	$-0.197863\pi$
$389$	32.0676			1.62589			0.812946	+	0.582340i	$0.197863\pi$
$390$		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
$395$	−6.58414	−	11.4041i	−0.331284	−	0.573800i
$396$		0			0
$397$	18.9669	−	32.8516i	0.951921	−	1.64878i	0.210660	−	0.977559i	$-0.432439\pi$
$397$	18.9669	−	32.8516i	0.951921	−	1.64878i	0.741261	−	0.671217i	$-0.234228\pi$
$398$	−6.14132	+	10.6371i	−0.307836	+	0.533188i
$399$		0			0
$400$	−2.56238	−	4.43818i	−0.128119	−	0.221909i
$401$	−10.6192			−0.530296			−0.265148	−	0.964208i	$-0.585421\pi$
$401$	−10.6192			−0.530296			−0.265148	+	0.964208i	$0.585421\pi$
$402$		0			0
$403$	53.7349			2.67673
$404$	−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
$409$	2.77292	−	4.80283i	0.137112	−	0.237485i	−0.789290	−	0.614020i	$-0.789551\pi$
$409$	2.77292	−	4.80283i	0.137112	−	0.237485i	0.926402	+	0.376535i	$0.122885\pi$
$410$	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
$415$	12.8353	−	22.2314i	0.630060	−	1.09130i
$416$	5.70370			0.279647
$417$		0			0
$418$	4.08126			0.199621
$419$	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
$425$	−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
$430$	21.7278			1.04781
$431$	−16.5539	−	28.6722i	−0.797374	−	1.38109i	−0.921321	−	0.388803i	$-0.872889\pi$
$431$	−16.5539	−	28.6722i	−0.797374	−	1.38109i	0.123947	−	0.992289i	$-0.460445\pi$
$432$		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
$436$	4.42107			0.211731
$437$	−1.43598	+	2.48720i	−0.0686924	+	0.118979i
$438$		0			0
$439$	−4.41711	−	7.65066i	−0.210817	−	0.365146i	0.741153	−	0.671336i	$-0.234279\pi$
$439$	−4.41711	−	7.65066i	−0.210817	−	0.365146i	−0.951970	+	0.306190i	$0.900946\pi$
$440$	10.1248			0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	8.75924	+	15.1715i	0.416164	+	0.720817i	0.995550	−	0.0942360i	$-0.0300408\pi$
$443$	8.75924	+	15.1715i	0.416164	+	0.720817i	−0.579386	+	0.815053i	$0.696708\pi$
$444$		0			0
$445$	−0.358685	+	0.621261i	−0.0170033	+	0.0294506i
$446$	−10.6569			−0.504620
$447$		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
$452$	−3.21505			−0.151223
$453$		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	0.947161	+	0.320760i	$0.103938\pi$
$457$	16.0624	+	27.8209i	0.751367	+	1.30140i	−0.195794	+	0.980645i	$0.562728\pi$
$458$	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	$0.584204\pi$
$464$	−7.08126			−0.328739
$465$		0			0
$466$	1.08126			0.0500882
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	−0.989465	−	0.144774i	$-0.953754\pi$
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	0.620110	+	0.784515i	$0.287088\pi$
$468$		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
$478$	6.16019	−	10.6698i	0.281761	−	0.488024i
$479$	−23.1729			−1.05880			−0.529399	−	0.848373i	$-0.677582\pi$
$479$	−23.1729			−1.05880			−0.529399	+	0.848373i	$0.677582\pi$
$480$		0			0
$481$	−5.70370			−0.260066
$482$	−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	0.902098	−	0.431531i	$-0.142026\pi$
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	−0.824766	+	0.565474i	$0.808693\pi$
$488$	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
$493$	−10.7759			−0.485323
$494$	3.65787	+	6.33561i	0.164575	+	0.285053i
$495$		0			0
$496$	9.42107			0.423018
$497$		0			0
$498$		0			0
$499$	41.1696			1.84301			0.921503	−	0.388371i	$-0.126962\pi$
$499$	41.1696			1.84301			0.921503	+	0.388371i	$0.126962\pi$
$500$	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
$509$	12.7713			0.566077			0.283039	−	0.959109i	$-0.408658\pi$
$509$	12.7713			0.566077			0.283039	+	0.959109i	$0.408658\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.83009	−	6.63392i	−0.168938	−	0.292610i
$515$	−0.899313			−0.0396285
$516$		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
$521$	−3.40615	−	5.89962i	−0.149226	−	0.258467i	0.781716	−	0.623635i	$-0.214345\pi$
$521$	−3.40615	−	5.89962i	−0.149226	−	0.258467i	−0.930942	+	0.365168i	$0.881012\pi$
$522$		0			0
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	0.339148	+	0.940733i	$0.389861\pi$
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	−0.984273	+	0.176656i	$0.943472\pi$
$524$	−3.18194	+	5.51129i	−0.139004	+	0.240762i
$525$		0			0
$526$	−1.54746	−	2.68029i	−0.0674727	−	0.116866i
$527$	14.3365			0.624510
$528$		0			0
$529$	−17.9863			−0.782014
$530$	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
$535$	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
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	−0.355097	−	0.934829i	$-0.615552\pi$
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	0.987135	−	0.159892i	$-0.0511145\pi$
$542$	−22.2164			−0.954277
$543$		0			0
$544$	1.52175			0.0652446
$545$	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
$551$	−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
$556$	−7.96690			−0.337872
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	0.928532	−	0.371252i	$-0.121071\pi$
$557$	3.36909	+	5.83543i	0.142753	+	0.247255i	−0.785779	+	0.618507i	$0.787738\pi$
$558$		0			0
$559$	−38.9475			−1.64730
$560$		0			0
$561$		0			0
$562$	23.3984			0.987001
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	−0.850233	−	0.526406i	$-0.823539\pi$
$563$	0.729964	−	1.26433i	0.0307643	−	0.0532853i	0.880998	+	0.473121i	$0.156873\pi$
$564$		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	0.994901	−	0.100853i	$-0.0321573\pi$
$569$	9.78263	+	16.9440i	0.410109	+	0.710330i	−0.584792	+	0.811183i	$0.698824\pi$
$570$		0			0
$571$	10.9629	−	18.9884i	0.458785	−	0.794638i	−0.540112	−	0.841593i	$-0.681618\pi$
$571$	10.9629	−	18.9884i	0.458785	−	0.794638i	0.998897	+	0.0469545i	$0.0149516\pi$
$572$	−18.1488			−0.758841
$573$		0			0
$574$		0			0
$575$	−11.4750			−0.478540
$576$		0			0
$577$	−12.3655	−	21.4177i	−0.514783	−	0.891631i	−0.999853	−	0.0171554i	$-0.994539\pi$
$577$	−12.3655	−	21.4177i	−0.514783	−	0.891631i	0.485069	−	0.874476i	$-0.338794\pi$
$578$	−14.6843			−0.610785
$579$		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
$584$	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
$590$	3.57893			0.147342
$591$		0			0
$592$	−1.00000			−0.0410997
$593$	−7.55391	+	13.0838i	−0.310202	+	0.537285i	−0.978406	−	0.206693i	$-0.933730\pi$
$593$	−7.55391	+	13.0838i	−0.310202	+	0.537285i	0.668204	+	0.743978i	$0.267063\pi$
$594$		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	−0.916345	−	0.400389i	$-0.868875\pi$
$599$	−2.72708	+	4.72345i	−0.111426	+	0.192995i	0.804920	+	0.593384i	$0.202208\pi$
$600$		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
$605$	2.78495			0.113224
$606$		0			0
$607$	−6.67059			−0.270751			−0.135376	−	0.990794i	$-0.543224\pi$
$607$	−6.67059			−0.270751			−0.135376	+	0.990794i	$0.543224\pi$
$608$	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	0.878950	−	0.476915i	$-0.158245\pi$
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	−0.852495	+	0.522735i	$0.824912\pi$
$614$	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
$619$	16.4484			0.661118			0.330559	−	0.943785i	$-0.392763\pi$
$619$	16.4484			0.661118			0.330559	+	0.943785i	$0.392763\pi$
$620$	14.9887	+	25.9611i	0.601959	+	1.04262i
$621$		0			0
$622$	1.70370			0.0683120
$623$		0			0
$624$		0			0
$625$	−24.3606			−0.974425
$626$	−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
$635$	−63.9740			−2.53873
$636$		0			0
$637$		0			0
$638$	22.5322			0.892057
$639$		0			0
$640$	1.59097	+	2.75564i	0.0628887	+	0.108926i
$641$	−27.8993			−1.10196			−0.550978	−	0.834520i	$-0.685745\pi$
$641$	−27.8993			−1.10196			−0.550978	+	0.834520i	$0.685745\pi$
$642$		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
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	0.982224	−	0.187711i	$-0.0601069\pi$
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	−0.653675	+	0.756776i	$0.726774\pi$
$648$		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
$653$	−38.1650			−1.49351			−0.746756	−	0.665098i	$-0.768390\pi$
$653$	−38.1650			−1.49351			−0.746756	+	0.665098i	$0.768390\pi$
$654$		0			0
$655$	−20.2495			−0.791214
$656$	−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
$661$	−10.0419	+	17.3930i	−0.390584	+	0.676511i	−0.992527	−	0.122028i	$-0.961060\pi$
$661$	−10.0419	+	17.3930i	−0.390584	+	0.676511i	0.601943	+	0.798539i	$0.294393\pi$
$662$	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
$667$	−7.92790	+	13.7315i	−0.306970	+	0.531687i
$668$	−5.23912			−0.202708
$669$		0			0
$670$	−34.8960			−1.34815
$671$	−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
$677$	0.358685	+	0.621261i	0.0137854	+	0.0238770i	0.872836	−	0.488014i	$-0.162279\pi$
$677$	0.358685	+	0.621261i	0.0137854	+	0.0238770i	−0.859050	+	0.511891i	$0.828945\pi$
$678$		0			0
$679$		0			0
$680$	2.42107	+	4.19341i	0.0928437	+	0.160810i
$681$		0			0
$682$	−29.9773			−1.14789
$683$	10.5270	+	18.2332i	0.402803	+	0.697675i	0.994063	−	0.108806i	$-0.0347027\pi$
$683$	10.5270	+	18.2332i	0.402803	+	0.697675i	−0.591260	+	0.806481i	$0.701369\pi$
$684$		0			0
$685$	8.72313			0.333294
$686$		0			0
$687$		0			0
$688$	−6.82846			−0.260333
$689$	−5.86677	+	10.1615i	−0.223506	+	0.387124i
$690$		0			0
$691$	2.92395	+	5.06442i	0.111232	+	0.192660i	0.916267	−	0.400567i	$-0.131187\pi$
$691$	2.92395	+	5.06442i	0.111232	+	0.192660i	−0.805035	+	0.593227i	$0.797854\pi$
$692$	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
$698$	36.2164			1.37081
$699$		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
$704$	−3.18194			−0.119924
$705$		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	−0.908200	−	0.418538i	$-0.862543\pi$
$709$	−21.7427	−	37.6594i	−0.816564	−	1.41433i	0.0916356	−	0.995793i	$-0.470790\pi$
$710$	−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
$716$	7.03775			0.263013
$717$		0			0
$718$	32.4419			1.21072
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.200830	−	0.979626i	$-0.435636\pi$
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.747966	−	0.663737i	$-0.231031\pi$
$720$		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
$730$	−7.90219	+	13.6870i	−0.292473	+	0.506579i
$731$	−10.3912			−0.384334
$732$		0			0
$733$	46.1696			1.70531			0.852657	−	0.522470i	$-0.174989\pi$
$733$	46.1696			1.70531			0.852657	+	0.522470i	$0.174989\pi$
$734$	−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	0.816458	−	0.577405i	$-0.195935\pi$
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	−0.908276	+	0.418371i	$0.862601\pi$
$740$	−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
$745$	−74.0118			−2.71158
$746$	5.83530	+	10.1070i	0.213645	+	0.370045i
$747$		0			0
$748$	−4.84213			−0.177046
$749$		0			0
$750$		0			0
$751$	3.29630			0.120284			0.0601419	−	0.998190i	$-0.480845\pi$
$751$	3.29630			0.120284			0.0601419	+	0.998190i	$0.480845\pi$
$752$	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
$761$	14.0676			0.509950			0.254975	−	0.966948i	$-0.417933\pi$
$761$	14.0676			0.509950			0.254975	+	0.966948i	$0.417933\pi$
$762$		0			0
$763$		0			0
$764$	−1.98057			−0.0716545
$765$		0			0
$766$	0.824893	+	1.42876i	0.0298046	+	0.0516231i
$767$	−6.41531			−0.231643
$768$		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
$773$	0.327772	+	0.567717i	0.0117891	+	0.0204194i	0.871860	−	0.489756i	$-0.162914\pi$
$773$	0.327772	+	0.567717i	0.0117891	+	0.0204194i	−0.860071	+	0.510175i	$0.829581\pi$
$774$		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
$779$	−7.18659			−0.257486
$780$		0			0
$781$	27.6512			0.989436
$782$	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
$787$	0.270036	−	0.467717i	0.00962576	−	0.0166723i	−0.861172	−	0.508313i	$-0.830269\pi$
$787$	0.270036	−	0.467717i	0.00962576	−	0.0166723i	0.870798	+	0.491641i	$0.163603\pi$
$788$	−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
$793$	8.91135	−	15.4349i	0.316451	−	0.548110i
$794$	−37.9338			−1.34622
$795$		0			0
$796$	12.2826			0.435346
$797$	−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
$803$	−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
$808$	18.5893			0.653971
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	0.999889	+	0.0148817i	$0.00473717\pi$
$809$	14.5865	+	25.2645i	0.512833	+	0.888252i	−0.487057	+	0.873370i	$0.661929\pi$
$810$		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
$814$	3.18194			0.111527
$815$	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	0.930527	−	0.366224i	$-0.119350\pi$
$821$	4.24364	+	7.35019i	0.148104	+	0.256524i	−0.782423	+	0.622748i	$0.786016\pi$
$822$		0			0
$823$	−14.5487	+	25.1991i	−0.507136	+	0.878385i	0.492830	+	0.870126i	$0.335963\pi$
$823$	−14.5487	+	25.1991i	−0.507136	+	0.878385i	−0.999966	+	0.00825976i	$0.997371\pi$
$824$	0.282630			0.00984589
$825$		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	0.806988	−	0.590568i	$-0.201096\pi$
$829$	−3.10821	−	5.38358i	−0.107953	−	0.186979i	−0.914941	+	0.403588i	$0.867763\pi$
$830$	−25.6706			−0.891039
$831$		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
$836$	−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
$842$	6.84213			0.235795
$843$		0			0
$844$	16.6569			0.573355
$845$	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
$850$	−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
$856$	−5.68878	+	9.85326i	−0.194438	+	0.336777i
$857$	−36.8435			−1.25855			−0.629275	−	0.777183i	$-0.716648\pi$
$857$	−36.8435			−1.25855			−0.629275	+	0.777183i	$0.716648\pi$
$858$		0			0
$859$	17.6375			0.601783			0.300892	−	0.953658i	$-0.402716\pi$
$859$	17.6375			0.601783			0.300892	+	0.953658i	$0.402716\pi$
$860$	−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	−0.859478	−	0.511173i	$-0.829211\pi$
$863$	0.380438	−	0.658939i	0.0129503	−	0.0224305i	0.872428	+	0.488743i	$0.162544\pi$
$864$		0			0
$865$	4.05950	+	7.03127i	0.138027	+	0.239070i
$866$	−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
$871$	62.5519			2.11949
$872$	−2.21053	−	3.82876i	−0.0748581	−	0.129658i
$873$		0			0
$874$	2.87197			0.0971457
$875$		0			0
$876$		0			0
$877$	−41.4991			−1.40132			−0.700662	−	0.713494i	$-0.747112\pi$
$877$	−41.4991			−1.40132			−0.700662	+	0.713494i	$0.747112\pi$
$878$	−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
$887$	−37.1100			−1.24603			−0.623016	−	0.782209i	$-0.714093\pi$
$887$	−37.1100			−1.24603			−0.623016	+	0.782209i	$0.714093\pi$
$888$		0			0
$889$		0			0
$890$	0.717370			0.0240463
$891$		0			0
$892$	5.32846	+	9.22916i	0.178410	+	0.309015i
$893$	7.47576			0.250167
$894$		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
$899$	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
$905$	−41.2599			−1.37153
$906$		0			0
$907$	−48.1502			−1.59880			−0.799401	−	0.600798i	$-0.794850\pi$
$907$	−48.1502			−1.59880			−0.799401	+	0.600798i	$0.794850\pi$
$908$	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
$913$	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
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	0.0249351	+	0.999689i	$0.492062\pi$
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	−0.878224	+	0.478250i	$0.841271\pi$
$920$	7.12476			0.234896
$921$		0			0
$922$	−2.46457			−0.0811664
$923$	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
$929$	25.4142	+	44.0187i	0.833814	+	1.44421i	0.894993	+	0.446081i	$0.147181\pi$
$929$	25.4142	+	44.0187i	0.833814	+	1.44421i	−0.0611787	+	0.998127i	$0.519486\pi$
$930$		0			0
$931$		0			0
$932$	−0.540628	−	0.936396i	−0.0177089	−	0.0306727i
$933$		0			0
$934$	15.9636			0.522346
$935$	−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
$940$	18.5458			0.604898
$941$	−0.578933	+	1.00274i	−0.0188727	+	0.0326885i	−0.875308	−	0.483567i	$-0.839341\pi$
$941$	−0.578933	+	1.00274i	−0.0188727	+	0.0326885i	0.856435	+	0.516255i	$0.172674\pi$
$942$		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	0.934677	−	0.355497i	$-0.115689\pi$
$947$	4.90739	+	8.49985i	0.159469	+	0.276208i	−0.775208	+	0.631706i	$0.782355\pi$
$948$		0			0
$949$	14.1648	−	24.5342i	0.459810	−	0.796414i
$950$	−6.57318			−0.213262
$951$		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
$956$	−12.3204			−0.398470
$957$		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
$962$	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	$0.679567\pi$
$968$	−0.875237			−0.0281312
$969$		0			0
$970$	−47.2268			−1.51636
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	−0.820030	−	0.572320i	$-0.806043\pi$
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	0.905659	+	0.424007i	$0.139377\pi$
$972$		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	0.169131	+	0.985594i	$0.445904\pi$
$977$	−24.0361	+	41.6318i	−0.768983	+	1.33192i	−0.938115	+	0.346325i	$0.887429\pi$
$978$		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
$983$	29.4627			0.939714			0.469857	−	0.882743i	$-0.344306\pi$
$983$	29.4627			0.939714			0.469857	+	0.882743i	$0.344306\pi$
$984$		0			0
$985$	−69.4134			−2.21170
$986$	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	0.999929	−	0.0119112i	$-0.00379153\pi$
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	−0.510280	+	0.860008i	$0.670458\pi$
$992$	−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
$997$	−5.54583			−0.175638			−0.0878191	−	0.996136i	$-0.527990\pi$
$997$	−5.54583			−0.175638			−0.0878191	+	0.996136i	$0.527990\pi$
$998$	−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.h.o.667.1		6
3.2	odd	2		882.2.h.p.79.3		6
7.2	even	3		2646.2.f.m.883.3		6
7.3	odd	6		378.2.e.d.235.1		6
7.4	even	3		2646.2.e.p.2125.3		6
7.5	odd	6		2646.2.f.l.883.1		6
7.6	odd	2		378.2.h.c.289.3		6
9.4	even	3		2646.2.e.p.1549.3		6
9.5	odd	6		882.2.e.o.373.1		6
21.2	odd	6		882.2.f.o.295.2		6
21.5	even	6		882.2.f.n.295.2		6
21.11	odd	6		882.2.e.o.655.1		6
21.17	even	6		126.2.e.c.25.3	✓	6
21.20	even	2		126.2.h.d.79.1	yes	6
28.3	even	6		3024.2.q.g.2881.1		6
28.27	even	2		3024.2.t.h.289.3		6
63.2	odd	6		7938.2.a.bw.1.3		3
63.4	even	3	inner	2646.2.h.o.361.1		6
63.5	even	6		882.2.f.n.589.2		6
63.13	odd	6		378.2.e.d.37.1		6
63.16	even	3		7938.2.a.bz.1.1		3
63.20	even	6		1134.2.g.m.163.3		6
63.23	odd	6		882.2.f.o.589.2		6
63.31	odd	6		378.2.h.c.361.3		6
63.32	odd	6		882.2.h.p.67.3		6
63.34	odd	6		1134.2.g.l.163.1		6
63.38	even	6		1134.2.g.m.487.3		6
63.40	odd	6		2646.2.f.l.1765.1		6
63.41	even	6		126.2.e.c.121.3	yes	6
63.47	even	6		7938.2.a.bv.1.1		3
63.52	odd	6		1134.2.g.l.487.1		6
63.58	even	3		2646.2.f.m.1765.3		6
63.59	even	6		126.2.h.d.67.1	yes	6
63.61	odd	6		7938.2.a.ca.1.3		3
84.59	odd	6		1008.2.q.g.529.1		6
84.83	odd	2		1008.2.t.h.961.3		6
252.31	even	6		3024.2.t.h.1873.3		6
252.59	odd	6		1008.2.t.h.193.3		6
252.139	even	6		3024.2.q.g.2305.1		6
252.167	odd	6		1008.2.q.g.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	21.17	even	6
126.2.e.c.121.3	yes	6	63.41	even	6
126.2.h.d.67.1	yes	6	63.59	even	6
126.2.h.d.79.1	yes	6	21.20	even	2
378.2.e.d.37.1		6	63.13	odd	6
378.2.e.d.235.1		6	7.3	odd	6
378.2.h.c.289.3		6	7.6	odd	2
378.2.h.c.361.3		6	63.31	odd	6
882.2.e.o.373.1		6	9.5	odd	6
882.2.e.o.655.1		6	21.11	odd	6
882.2.f.n.295.2		6	21.5	even	6
882.2.f.n.589.2		6	63.5	even	6
882.2.f.o.295.2		6	21.2	odd	6
882.2.f.o.589.2		6	63.23	odd	6
882.2.h.p.67.3		6	63.32	odd	6
882.2.h.p.79.3		6	3.2	odd	2
1008.2.q.g.529.1		6	84.59	odd	6
1008.2.q.g.625.1		6	252.167	odd	6
1008.2.t.h.193.3		6	252.59	odd	6
1008.2.t.h.961.3		6	84.83	odd	2
1134.2.g.l.163.1		6	63.34	odd	6
1134.2.g.l.487.1		6	63.52	odd	6
1134.2.g.m.163.3		6	63.20	even	6
1134.2.g.m.487.3		6	63.38	even	6
2646.2.e.p.1549.3		6	9.4	even	3
2646.2.e.p.2125.3		6	7.4	even	3
2646.2.f.l.883.1		6	7.5	odd	6
2646.2.f.l.1765.1		6	63.40	odd	6
2646.2.f.m.883.3		6	7.2	even	3
2646.2.f.m.1765.3		6	63.58	even	3
2646.2.h.o.361.1		6	63.4	even	3	inner
2646.2.h.o.667.1		6	1.1	even	1	trivial
3024.2.q.g.2305.1		6	252.139	even	6
3024.2.q.g.2881.1		6	28.3	even	6
3024.2.t.h.289.3		6	28.27	even	2
3024.2.t.h.1873.3		6	252.31	even	6
7938.2.a.bv.1.1		3	63.47	even	6
7938.2.a.bw.1.3		3	63.2	odd	6
7938.2.a.bz.1.1		3	63.16	even	3
7938.2.a.ca.1.3		3	63.61	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.18194 q^{5} +1.00000 q^{8} +(1.59097 + 2.75564i) q^{10} -3.18194 q^{11} +(-2.85185 - 4.93955i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.760877 - 1.31788i) q^{17} +(0.641315 - 1.11079i) q^{19} +(1.59097 - 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} -2.23912 q^{23} +5.12476 q^{25} +(-2.85185 + 4.93955i) q^{26} +(3.54063 - 6.13255i) q^{29} +(-4.71053 + 8.15888i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.760877 + 1.31788i) q^{34} +(0.500000 - 0.866025i) q^{37} -1.28263 q^{38} -3.18194 q^{40} +(-2.80150 - 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} +(1.59097 - 2.75564i) q^{44} +(1.11956 + 1.93914i) q^{46} +(2.91423 + 5.04759i) q^{47} +(-2.56238 - 4.43818i) q^{50} +5.70370 q^{52} +(-1.02859 - 1.78157i) q^{53} +10.1248 q^{55} -7.08126 q^{58} +(0.562382 - 0.974074i) q^{59} +(1.56238 + 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(9.07442 + 15.7174i) q^{65} +(-5.48345 + 9.49761i) q^{67} +1.52175 q^{68} -8.69002 q^{71} +(2.48345 + 4.30146i) q^{73} -1.00000 q^{74} +(0.641315 + 1.11079i) q^{76} +(2.06922 + 3.58399i) q^{79} +(1.59097 + 2.75564i) q^{80} +(-2.80150 + 4.85235i) q^{82} +(-4.03379 + 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} -6.82846 q^{86} -3.18194 q^{88} +(0.112725 - 0.195246i) q^{89} +(1.11956 - 1.93914i) q^{92} +(2.91423 - 5.04759i) q^{94} +(-2.04063 + 3.53447i) q^{95} +(-7.42107 + 12.8537i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 6 q^{8} + q^{10} - 2 q^{11} - 8 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} - 14 q^{23} - 4 q^{25} - 8 q^{26} + 5 q^{29} - 20 q^{31} - 3 q^{32} - 4 q^{34} + 3 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{43} + q^{44} + 7 q^{46} - 9 q^{47} + 2 q^{50} + 16 q^{52} - 15 q^{53} + 26 q^{55} - 10 q^{58} - 14 q^{59} - 8 q^{61} + 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 8 q^{68} - 14 q^{71} - 19 q^{73} - 6 q^{74} + 3 q^{76} + 5 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} + 12 q^{86} - 2 q^{88} - 9 q^{89} + 7 q^{92} - 9 q^{94} + 4 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 6 * q^8 + q^10 - 2 * q^11 - 8 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 - 14 * q^23 - 4 * q^25 - 8 * q^26 + 5 * q^29 - 20 * q^31 - 3 * q^32 - 4 * q^34 + 3 * q^37 - 6 * q^38 - 2 * q^40 - 6 * q^43 + q^44 + 7 * q^46 - 9 * q^47 + 2 * q^50 + 16 * q^52 - 15 * q^53 + 26 * q^55 - 10 * q^58 - 14 * q^59 - 8 * q^61 + 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 + 8 * q^68 - 14 * q^71 - 19 * q^73 - 6 * q^74 + 3 * q^76 + 5 * q^79 + q^80 + 2 * q^83 - 2 * q^85 + 12 * q^86 - 2 * q^88 - 9 * q^89 + 7 * q^92 - 9 * q^94 + 4 * q^95 - 28 * q^97

Introduction

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