LMFDB - Embedded newform 2646.2.e.m.1549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
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			1549.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.m.2125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-2.18614 - 3.78651i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.18614 - 3.78651i) q^{5} +1.00000 q^{8} +(-2.18614 - 3.78651i) q^{10} +(-0.686141 + 1.18843i) q^{11} +(1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(-0.686141 - 1.18843i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-2.18614 - 3.78651i) q^{20} +(-0.686141 + 1.18843i) q^{22} +(-0.813859 - 1.40965i) q^{23} +(-7.05842 + 12.2255i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.37228 - 7.57301i) q^{29} -2.00000 q^{31} +1.00000 q^{32} +(-0.686141 - 1.18843i) q^{34} +(-1.00000 + 1.73205i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-2.18614 - 3.78651i) q^{40} +(-2.31386 + 4.00772i) q^{41} +(4.05842 + 7.02939i) q^{43} +(-0.686141 + 1.18843i) q^{44} +(-0.813859 - 1.40965i) q^{46} +(-7.05842 + 12.2255i) q^{50} +(1.00000 - 1.73205i) q^{52} +(-4.37228 - 7.57301i) q^{53} +6.00000 q^{55} +(-4.37228 - 7.57301i) q^{58} -10.1168 q^{59} -3.11684 q^{61} -2.00000 q^{62} +1.00000 q^{64} -8.74456 q^{65} -2.11684 q^{67} +(-0.686141 - 1.18843i) q^{68} +7.11684 q^{71} +(6.05842 + 10.4935i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{76} -5.11684 q^{79} +(-2.18614 - 3.78651i) q^{80} +(-2.31386 + 4.00772i) q^{82} +(-8.74456 - 15.1460i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(4.05842 + 7.02939i) q^{86} +(-0.686141 + 1.18843i) q^{88} +(-7.37228 + 12.7692i) q^{89} +(-0.813859 - 1.40965i) q^{92} -21.8614 q^{95} +(-4.05842 - 7.02939i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} + 4 q^{8} - 3 q^{10} + 3 q^{11} + 4 q^{13} + 4 q^{16} + 3 q^{17} + 10 q^{19} - 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} + 4 q^{26} - 6 q^{29} - 8 q^{31} + 4 q^{32} + 3 q^{34} - 4 q^{37} + 10 q^{38} - 3 q^{40} - 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} + 4 q^{52} - 6 q^{53} + 24 q^{55} - 6 q^{58} - 6 q^{59} + 22 q^{61} - 8 q^{62} + 4 q^{64} - 12 q^{65} + 26 q^{67} + 3 q^{68} - 6 q^{71} + 7 q^{73} - 4 q^{74} + 10 q^{76} + 14 q^{79} - 3 q^{80} - 15 q^{82} - 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} - 18 q^{89} - 9 q^{92} - 30 q^{95} + q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 + 4 * q^8 - 3 * q^10 + 3 * q^11 + 4 * q^13 + 4 * q^16 + 3 * q^17 + 10 * q^19 - 3 * q^20 + 3 * q^22 - 9 * q^23 - 11 * q^25 + 4 * q^26 - 6 * q^29 - 8 * q^31 + 4 * q^32 + 3 * q^34 - 4 * q^37 + 10 * q^38 - 3 * q^40 - 15 * q^41 - q^43 + 3 * q^44 - 9 * q^46 - 11 * q^50 + 4 * q^52 - 6 * q^53 + 24 * q^55 - 6 * q^58 - 6 * q^59 + 22 * q^61 - 8 * q^62 + 4 * q^64 - 12 * q^65 + 26 * q^67 + 3 * q^68 - 6 * q^71 + 7 * q^73 - 4 * q^74 + 10 * q^76 + 14 * q^79 - 3 * q^80 - 15 * q^82 - 12 * q^83 - 12 * q^85 - q^86 + 3 * q^88 - 18 * q^89 - 9 * q^92 - 30 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.18614	−	3.78651i	−0.977672	−	1.69338i	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−2.18614	−	3.78651i	−0.977672	−	1.69338i	−0.306851	−	0.951757i	$-0.599275\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.18614	−	3.78651i	−0.691318	−	1.19740i
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	−0.950730	−	0.310021i	$-0.899664\pi$
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	0.743851	+	0.668346i	$0.232997\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.686141	−	1.18843i	−0.166414	−	0.288237i	0.770743	−	0.637146i	$-0.219885\pi$
$17$	−0.686141	−	1.18843i	−0.166414	−	0.288237i	−0.937156	+	0.348910i	$0.886552\pi$
$18$		0			0
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$	−2.18614	−	3.78651i	−0.488836	−	0.846689i
$21$		0			0
$22$	−0.686141	+	1.18843i	−0.146286	+	0.253374i
$23$	−0.813859	−	1.40965i	−0.169701	−	0.293931i	0.768613	−	0.639713i	$-0.220947\pi$
$23$	−0.813859	−	1.40965i	−0.169701	−	0.293931i	−0.938315	+	0.345782i	$0.887614\pi$
$24$		0			0
$25$	−7.05842	+	12.2255i	−1.41168	+	2.44511i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$		0			0
$28$		0			0
$29$	−4.37228	−	7.57301i	−0.811912	−	1.40627i	−0.911524	−	0.411247i	$-0.865093\pi$
$29$	−4.37228	−	7.57301i	−0.811912	−	1.40627i	0.0996117	−	0.995026i	$-0.468240\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.686141	−	1.18843i	−0.117672	−	0.203814i
$35$		0			0
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	2.50000	−	4.33013i	0.405554	−	0.702439i
$39$		0			0
$40$	−2.18614	−	3.78651i	−0.345659	−	0.598699i
$41$	−2.31386	+	4.00772i	−0.361364	+	0.625901i	−0.988186	−	0.153262i	$-0.951022\pi$
$41$	−2.31386	+	4.00772i	−0.361364	+	0.625901i	0.626821	+	0.779163i	$0.284356\pi$
$42$		0			0
$43$	4.05842	+	7.02939i	0.618904	+	1.07197i	0.989686	+	0.143253i	$0.0457562\pi$
$43$	4.05842	+	7.02939i	0.618904	+	1.07197i	−0.370783	+	0.928720i	$0.620910\pi$
$44$	−0.686141	+	1.18843i	−0.103440	+	0.179163i
$45$		0			0
$46$	−0.813859	−	1.40965i	−0.119997	−	0.207841i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$		0			0
$50$	−7.05842	+	12.2255i	−0.998212	+	1.72895i
$51$		0			0
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−4.37228	−	7.57301i	−0.600579	−	1.04023i	−0.992733	−	0.120334i	$-0.961603\pi$
$53$	−4.37228	−	7.57301i	−0.600579	−	1.04023i	0.392154	−	0.919899i	$-0.371730\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$		0			0
$57$		0			0
$58$	−4.37228	−	7.57301i	−0.574109	−	0.994385i
$59$	−10.1168			−1.31710			−0.658550	−	0.752537i	$-0.728830\pi$
$59$	−10.1168			−1.31710			−0.658550	+	0.752537i	$0.728830\pi$
$60$		0			0
$61$	−3.11684			−0.399071			−0.199535	−	0.979891i	$-0.563943\pi$
$61$	−3.11684			−0.399071			−0.199535	+	0.979891i	$0.563943\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.74456			−1.08463
$66$		0			0
$67$	−2.11684			−0.258614			−0.129307	−	0.991605i	$-0.541275\pi$
$67$	−2.11684			−0.258614			−0.129307	+	0.991605i	$0.541275\pi$
$68$	−0.686141	−	1.18843i	−0.0832068	−	0.144118i
$69$		0			0
$70$		0			0
$71$	7.11684			0.844614			0.422307	−	0.906453i	$-0.361220\pi$
$71$	7.11684			0.844614			0.422307	+	0.906453i	$0.361220\pi$
$72$		0			0
$73$	6.05842	+	10.4935i	0.709085	+	1.22817i	0.965197	+	0.261524i	$0.0842249\pi$
$73$	6.05842	+	10.4935i	0.709085	+	1.22817i	−0.256112	+	0.966647i	$0.582442\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$		0			0
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$		0			0
$78$		0			0
$79$	−5.11684			−0.575690			−0.287845	−	0.957677i	$-0.592939\pi$
$79$	−5.11684			−0.575690			−0.287845	+	0.957677i	$0.592939\pi$
$80$	−2.18614	−	3.78651i	−0.244418	−	0.423344i
$81$		0			0
$82$	−2.31386	+	4.00772i	−0.255523	+	0.442579i
$83$	−8.74456	−	15.1460i	−0.959840	−	1.66249i	−0.722881	−	0.690973i	$-0.757182\pi$
$83$	−8.74456	−	15.1460i	−0.959840	−	1.66249i	−0.236960	−	0.971519i	$-0.576151\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$	4.05842	+	7.02939i	0.437631	+	0.757999i
$87$		0			0
$88$	−0.686141	+	1.18843i	−0.0731428	+	0.126687i
$89$	−7.37228	+	12.7692i	−0.781460	+	1.35353i	0.149631	+	0.988742i	$0.452192\pi$
$89$	−7.37228	+	12.7692i	−0.781460	+	1.35353i	−0.931091	+	0.364787i	$0.881142\pi$
$90$		0			0
$91$		0			0
$92$	−0.813859	−	1.40965i	−0.0848507	−	0.146966i
$93$		0			0
$94$		0			0
$95$	−21.8614			−2.24293
$96$		0			0
$97$	−4.05842	−	7.02939i	−0.412070	−	0.713727i	0.583046	−	0.812439i	$-0.301861\pi$
$97$	−4.05842	−	7.02939i	−0.412070	−	0.713727i	−0.995116	+	0.0987127i	$0.968528\pi$
$98$		0			0
$99$		0			0
$100$	−7.05842	+	12.2255i	−0.705842	+	1.22255i
$101$	−0.813859	+	1.40965i	−0.0809820	+	0.140265i	−0.903672	−	0.428225i	$-0.859139\pi$
$101$	−0.813859	+	1.40965i	−0.0809820	+	0.140265i	0.822690	+	0.568490i	$0.192472\pi$
$102$		0			0
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	0.507300	−	0.861770i	$-0.330644\pi$
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	−0.999964	+	0.00844953i	$0.997310\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	−4.37228	−	7.57301i	−0.424674	−	0.735556i
$107$	−3.68614	+	6.38458i	−0.356353	+	0.617221i	−0.987348	−	0.158565i	$-0.949313\pi$
$107$	−3.68614	+	6.38458i	−0.356353	+	0.617221i	0.630996	+	0.775786i	$0.282646\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	6.00000			0.572078
$111$		0			0
$112$		0			0
$113$	−2.18614	+	3.78651i	−0.205655	+	0.356205i	−0.950341	−	0.311210i	$-0.899266\pi$
$113$	−2.18614	+	3.78651i	−0.205655	+	0.356205i	0.744686	+	0.667415i	$0.232599\pi$
$114$		0			0
$115$	−3.55842	+	6.16337i	−0.331825	+	0.574737i
$116$	−4.37228	−	7.57301i	−0.405956	−	0.703137i
$117$		0			0
$118$	−10.1168			−0.931331
$119$		0			0
$120$		0			0
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$	−3.11684			−0.282186
$123$		0			0
$124$	−2.00000			−0.179605
$125$	39.8614			3.56531
$126$		0			0
$127$	3.11684			0.276575			0.138288	−	0.990392i	$-0.455840\pi$
$127$	3.11684			0.276575			0.138288	+	0.990392i	$0.455840\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−8.74456			−0.766949
$131$	0.813859	+	1.40965i	0.0711072	+	0.123161i	0.899387	−	0.437154i	$-0.144013\pi$
$131$	0.813859	+	1.40965i	0.0711072	+	0.123161i	−0.828280	+	0.560315i	$0.810680\pi$
$132$		0			0
$133$		0			0
$134$	−2.11684			−0.182867
$135$		0			0
$136$	−0.686141	−	1.18843i	−0.0588361	−	0.101907i
$137$	5.31386	−	9.20387i	0.453994	−	0.786340i	−0.544636	−	0.838672i	$-0.683332\pi$
$137$	5.31386	−	9.20387i	0.453994	−	0.786340i	0.998630	+	0.0523324i	$0.0166655\pi$
$138$		0			0
$139$	6.61684	−	11.4607i	0.561233	−	0.972085i	−0.436156	−	0.899871i	$-0.643660\pi$
$139$	6.61684	−	11.4607i	0.561233	−	0.972085i	0.997389	−	0.0722136i	$-0.0230063\pi$
$140$		0			0
$141$		0			0
$142$	7.11684			0.597232
$143$	1.37228	+	2.37686i	0.114756	+	0.198763i
$144$		0			0
$145$	−19.1168	+	33.1113i	−1.58757	+	2.74975i
$146$	6.05842	+	10.4935i	0.501399	+	0.868448i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	1.62772	+	2.81929i	0.133348	+	0.230965i	0.924965	−	0.380052i	$-0.124094\pi$
$149$	1.62772	+	2.81929i	0.133348	+	0.230965i	−0.791617	+	0.611017i	$0.790761\pi$
$150$		0			0
$151$	−4.55842	+	7.89542i	−0.370959	+	0.642520i	−0.989713	−	0.143065i	$-0.954304\pi$
$151$	−4.55842	+	7.89542i	−0.370959	+	0.642520i	0.618754	+	0.785585i	$0.287638\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$		0			0
$154$		0			0
$155$	4.37228	+	7.57301i	0.351190	+	0.608279i
$156$		0			0
$157$	−9.11684			−0.727603			−0.363802	−	0.931476i	$-0.618521\pi$
$157$	−9.11684			−0.727603			−0.363802	+	0.931476i	$0.618521\pi$
$158$	−5.11684			−0.407074
$159$		0			0
$160$	−2.18614	−	3.78651i	−0.172830	−	0.299350i
$161$		0			0
$162$		0			0
$163$	9.11684	−	15.7908i	0.714086	−	1.23683i	−0.249225	−	0.968446i	$-0.580176\pi$
$163$	9.11684	−	15.7908i	0.714086	−	1.23683i	0.963311	−	0.268388i	$-0.0864909\pi$
$164$	−2.31386	+	4.00772i	−0.180682	+	0.312951i
$165$		0			0
$166$	−8.74456	−	15.1460i	−0.678710	−	1.17556i
$167$	2.74456	−	4.75372i	0.212381	−	0.367854i	−0.740078	−	0.672521i	$-0.765212\pi$
$167$	2.74456	−	4.75372i	0.212381	−	0.367854i	0.952459	+	0.304666i	$0.0985450\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$		0			0
$172$	4.05842	+	7.02939i	0.309452	+	0.535986i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$		0			0
$176$	−0.686141	+	1.18843i	−0.0517198	+	0.0895813i
$177$		0			0
$178$	−7.37228	+	12.7692i	−0.552576	+	0.957089i
$179$	1.62772	+	2.81929i	0.121661	+	0.210724i	0.920423	−	0.390924i	$-0.127844\pi$
$179$	1.62772	+	2.81929i	0.121661	+	0.210724i	−0.798762	+	0.601648i	$0.794511\pi$
$180$		0			0
$181$	−0.883156			−0.0656445			−0.0328222	−	0.999461i	$-0.510450\pi$
$181$	−0.883156			−0.0656445			−0.0328222	+	0.999461i	$0.510450\pi$
$182$		0			0
$183$		0			0
$184$	−0.813859	−	1.40965i	−0.0599985	−	0.103920i
$185$	8.74456			0.642913
$186$		0			0
$187$	1.88316			0.137710
$188$		0			0
$189$		0			0
$190$	−21.8614			−1.58599
$191$	19.1168			1.38325			0.691623	−	0.722259i	$-0.256896\pi$
$191$	19.1168			1.38325			0.691623	+	0.722259i	$0.256896\pi$
$192$		0			0
$193$	−7.00000			−0.503871			−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000			−0.503871			−0.251936	+	0.967744i	$0.581067\pi$
$194$	−4.05842	−	7.02939i	−0.291378	−	0.504681i
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$	−7.05842	+	12.2255i	−0.499106	+	0.864477i
$201$		0			0
$202$	−0.813859	+	1.40965i	−0.0572629	+	0.0991823i
$203$		0			0
$204$		0			0
$205$	20.2337			1.41318
$206$	−5.00000	−	8.66025i	−0.348367	−	0.603388i
$207$		0			0
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	3.43070	+	5.94215i	0.237307	+	0.411027i
$210$		0			0
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$	−4.37228	−	7.57301i	−0.300290	−	0.520117i
$213$		0			0
$214$	−3.68614	+	6.38458i	−0.251979	+	0.436441i
$215$	17.7446	−	30.7345i	1.21017	−	2.09607i
$216$		0			0
$217$		0			0
$218$	−7.00000	−	12.1244i	−0.474100	−	0.821165i
$219$		0			0
$220$	6.00000			0.404520
$221$	−2.74456			−0.184619
$222$		0			0
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$		0			0
$225$		0			0
$226$	−2.18614	+	3.78651i	−0.145420	+	0.251875i
$227$	6.12772	−	10.6135i	0.406711	−	0.704444i	−0.587808	−	0.809000i	$-0.700009\pi$
$227$	6.12772	−	10.6135i	0.406711	−	0.704444i	0.994519	+	0.104556i	$0.0333423\pi$
$228$		0			0
$229$	−1.44158	−	2.49689i	−0.0952622	−	0.164999i	0.814456	−	0.580226i	$-0.197036\pi$
$229$	−1.44158	−	2.49689i	−0.0952622	−	0.164999i	−0.909718	+	0.415227i	$0.863702\pi$
$230$	−3.55842	+	6.16337i	−0.234635	+	0.406400i
$231$		0			0
$232$	−4.37228	−	7.57301i	−0.287054	−	0.497193i
$233$	−0.127719	+	0.221215i	−0.00836713	+	0.0144923i	−0.870179	−	0.492736i	$-0.835997\pi$
$233$	−0.127719	+	0.221215i	−0.00836713	+	0.0144923i	0.861812	+	0.507229i	$0.169330\pi$
$234$		0			0
$235$		0			0
$236$	−10.1168			−0.658550
$237$		0			0
$238$		0			0
$239$	4.93070	−	8.54023i	0.318941	−	0.552421i	−0.661327	−	0.750098i	$-0.730006\pi$
$239$	4.93070	−	8.54023i	0.318941	−	0.552421i	0.980267	+	0.197677i	$0.0633396\pi$
$240$		0			0
$241$	9.05842	−	15.6896i	0.583504	−	1.01066i	−0.411556	−	0.911385i	$-0.635014\pi$
$241$	9.05842	−	15.6896i	0.583504	−	1.01066i	0.995060	−	0.0992745i	$-0.0316522\pi$
$242$	4.55842	+	7.89542i	0.293026	+	0.507537i
$243$		0			0
$244$	−3.11684			−0.199535
$245$		0			0
$246$		0			0
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	−2.00000			−0.127000
$249$		0			0
$250$	39.8614			2.52106
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$	2.23369			0.140431
$254$	3.11684			0.195568
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.43070	+	5.94215i	0.214001	+	0.370661i	0.952963	−	0.303086i	$-0.0980170\pi$
$257$	3.43070	+	5.94215i	0.214001	+	0.370661i	−0.738962	+	0.673747i	$0.764684\pi$
$258$		0			0
$259$		0			0
$260$	−8.74456			−0.542315
$261$		0			0
$262$	0.813859	+	1.40965i	0.0502804	+	0.0870882i
$263$	3.81386	−	6.60580i	0.235173	−	0.407331i	−0.724150	−	0.689642i	$-0.757768\pi$
$263$	3.81386	−	6.60580i	0.235173	−	0.407331i	0.959323	+	0.282311i	$0.0911011\pi$
$264$		0			0
$265$	−19.1168	+	33.1113i	−1.17434	+	2.03401i
$266$		0			0
$267$		0			0
$268$	−2.11684			−0.129307
$269$	0.813859	+	1.40965i	0.0496219	+	0.0859476i	0.889769	−	0.456410i	$-0.150865\pi$
$269$	0.813859	+	1.40965i	0.0496219	+	0.0859476i	−0.840148	+	0.542358i	$0.817532\pi$
$270$		0			0
$271$	8.11684	−	14.0588i	0.493063	−	0.854010i	−0.506905	−	0.862002i	$-0.669210\pi$
$271$	8.11684	−	14.0588i	0.493063	−	0.854010i	0.999968	+	0.00799154i	$0.00254381\pi$
$272$	−0.686141	−	1.18843i	−0.0416034	−	0.0720592i
$273$		0			0
$274$	5.31386	−	9.20387i	0.321022	−	0.556026i
$275$	−9.68614	−	16.7769i	−0.584096	−	1.01168i
$276$		0			0
$277$	6.11684	−	10.5947i	0.367526	−	0.636573i	−0.621652	−	0.783293i	$-0.713538\pi$
$277$	6.11684	−	10.5947i	0.367526	−	0.636573i	0.989178	+	0.146720i	$0.0468717\pi$
$278$	6.61684	−	11.4607i	0.396852	−	0.687368i
$279$		0			0
$280$		0			0
$281$	8.18614	+	14.1788i	0.488344	+	0.845837i	0.999910	−	0.0134071i	$-0.00426773\pi$
$281$	8.18614	+	14.1788i	0.488344	+	0.845837i	−0.511566	+	0.859244i	$0.670934\pi$
$282$		0			0
$283$	−27.1168			−1.61193			−0.805965	−	0.591964i	$-0.798353\pi$
$283$	−27.1168			−1.61193			−0.805965	+	0.591964i	$0.798353\pi$
$284$	7.11684			0.422307
$285$		0			0
$286$	1.37228	+	2.37686i	0.0811447	+	0.140547i
$287$		0			0
$288$		0			0
$289$	7.55842	−	13.0916i	0.444613	−	0.770092i
$290$	−19.1168	+	33.1113i	−1.12258	+	1.94437i
$291$		0			0
$292$	6.05842	+	10.4935i	0.354542	+	0.614085i
$293$	5.18614	−	8.98266i	0.302978	−	0.524773i	−0.673831	−	0.738885i	$-0.735353\pi$
$293$	5.18614	−	8.98266i	0.302978	−	0.524773i	0.976809	+	0.214113i	$0.0686859\pi$
$294$		0			0
$295$	22.1168	+	38.3075i	1.28769	+	2.23035i
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$		0			0
$298$	1.62772	+	2.81929i	0.0942912	+	0.163317i
$299$	−3.25544			−0.188267
$300$		0			0
$301$		0			0
$302$	−4.55842	+	7.89542i	−0.262308	+	0.454330i
$303$		0			0
$304$	2.50000	−	4.33013i	0.143385	−	0.248350i
$305$	6.81386	+	11.8020i	0.390160	+	0.675778i
$306$		0			0
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$		0			0
$310$	4.37228	+	7.57301i	0.248329	+	0.430118i
$311$	8.23369			0.466890			0.233445	−	0.972370i	$-0.425000\pi$
$311$	8.23369			0.466890			0.233445	+	0.972370i	$0.425000\pi$
$312$		0			0
$313$	20.1168			1.13707			0.568536	−	0.822659i	$-0.307510\pi$
$313$	20.1168			1.13707			0.568536	+	0.822659i	$0.307510\pi$
$314$	−9.11684			−0.514493
$315$		0			0
$316$	−5.11684			−0.287845
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	12.0000			0.671871
$320$	−2.18614	−	3.78651i	−0.122209	−	0.211672i
$321$		0			0
$322$		0			0
$323$	−6.86141			−0.381779
$324$		0			0
$325$	14.1168	+	24.4511i	0.783062	+	1.35630i
$326$	9.11684	−	15.7908i	0.504935	−	0.874574i
$327$		0			0
$328$	−2.31386	+	4.00772i	−0.127762	+	0.221289i
$329$		0			0
$330$		0			0
$331$	22.2337			1.22207			0.611037	−	0.791602i	$-0.290753\pi$
$331$	22.2337			1.22207			0.611037	+	0.791602i	$0.290753\pi$
$332$	−8.74456	−	15.1460i	−0.479920	−	0.831246i
$333$		0			0
$334$	2.74456	−	4.75372i	0.150176	−	0.260112i
$335$	4.62772	+	8.01544i	0.252839	+	0.437930i
$336$		0			0
$337$	4.05842	−	7.02939i	0.221076	−	0.382915i	−0.734059	−	0.679086i	$-0.762376\pi$
$337$	4.05842	−	7.02939i	0.221076	−	0.382915i	0.955135	+	0.296171i	$0.0957097\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	1.37228	−	2.37686i	0.0743132	−	0.128714i
$342$		0			0
$343$		0			0
$344$	4.05842	+	7.02939i	0.218815	+	0.378999i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	10.1168			0.543101			0.271550	−	0.962424i	$-0.412464\pi$
$347$	10.1168			0.543101			0.271550	+	0.962424i	$0.412464\pi$
$348$		0			0
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	−0.994388	−	0.105797i	$-0.966261\pi$
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	0.405571	−	0.914063i	$-0.367073\pi$
$350$		0			0
$351$		0			0
$352$	−0.686141	+	1.18843i	−0.0365714	+	0.0633436i
$353$	6.68614	−	11.5807i	0.355867	−	0.616380i	−0.631399	−	0.775458i	$-0.717519\pi$
$353$	6.68614	−	11.5807i	0.355867	−	0.616380i	0.987266	+	0.159078i	$0.0508522\pi$
$354$		0			0
$355$	−15.5584	−	26.9480i	−0.825755	−	1.43025i
$356$	−7.37228	+	12.7692i	−0.390730	+	0.676764i
$357$		0			0
$358$	1.62772	+	2.81929i	0.0860276	+	0.149004i
$359$	10.9307	−	18.9325i	0.576900	−	0.999221i	−0.418932	−	0.908018i	$-0.637595\pi$
$359$	10.9307	−	18.9325i	0.576900	−	0.999221i	0.995832	−	0.0912032i	$-0.0290713\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−0.883156			−0.0464177
$363$		0			0
$364$		0			0
$365$	26.4891	−	45.8805i	1.38650	−	2.40150i
$366$		0			0
$367$	−6.11684	+	10.5947i	−0.319297	+	0.553038i	−0.980341	−	0.197308i	$-0.936780\pi$
$367$	−6.11684	+	10.5947i	−0.319297	+	0.553038i	0.661045	+	0.750346i	$0.270113\pi$
$368$	−0.813859	−	1.40965i	−0.0424254	−	0.0734829i
$369$		0			0
$370$	8.74456			0.454608
$371$		0			0
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	1.88316			0.0973757
$375$		0			0
$376$		0			0
$377$	−17.4891			−0.900736
$378$		0			0
$379$	−8.11684			−0.416934			−0.208467	−	0.978029i	$-0.566847\pi$
$379$	−8.11684			−0.416934			−0.208467	+	0.978029i	$0.566847\pi$
$380$	−21.8614			−1.12147
$381$		0			0
$382$	19.1168			0.978103
$383$	16.3723	+	28.3576i	0.836584	+	1.44901i	0.892734	+	0.450584i	$0.148784\pi$
$383$	16.3723	+	28.3576i	0.836584	+	1.44901i	−0.0561493	+	0.998422i	$0.517882\pi$
$384$		0			0
$385$		0			0
$386$	−7.00000			−0.356291
$387$		0			0
$388$	−4.05842	−	7.02939i	−0.206035	−	0.356863i
$389$	5.48913	−	9.50744i	0.278310	−	0.482047i	−0.692655	−	0.721269i	$-0.743559\pi$
$389$	5.48913	−	9.50744i	0.278310	−	0.482047i	0.970965	+	0.239222i	$0.0768925\pi$
$390$		0			0
$391$	−1.11684	+	1.93443i	−0.0564812	+	0.0978284i
$392$		0			0
$393$		0			0
$394$	6.00000			0.302276
$395$	11.1861	+	19.3750i	0.562836	+	0.974860i
$396$		0			0
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$	−5.00000	−	8.66025i	−0.250627	−	0.434099i
$399$		0			0
$400$	−7.05842	+	12.2255i	−0.352921	+	0.611277i
$401$	−5.87228	−	10.1711i	−0.293248	−	0.507920i	0.681328	−	0.731978i	$-0.261403\pi$
$401$	−5.87228	−	10.1711i	−0.293248	−	0.507920i	−0.974576	+	0.224058i	$0.928069\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−0.813859	+	1.40965i	−0.0404910	+	0.0701325i
$405$		0			0
$406$		0			0
$407$	−1.37228	−	2.37686i	−0.0680215	−	0.117817i
$408$		0			0
$409$	22.3505			1.10516			0.552581	−	0.833459i	$-0.313643\pi$
$409$	22.3505			1.10516			0.552581	+	0.833459i	$0.313643\pi$
$410$	20.2337			0.999271
$411$		0			0
$412$	−5.00000	−	8.66025i	−0.246332	−	0.426660i
$413$		0			0
$414$		0			0
$415$	−38.2337	+	66.2227i	−1.87682	+	3.25074i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$		0			0
$418$	3.43070	+	5.94215i	0.167801	+	0.290640i
$419$	6.30298	−	10.9171i	0.307921	−	0.533335i	−0.669986	−	0.742373i	$-0.733700\pi$
$419$	6.30298	−	10.9171i	0.307921	−	0.533335i	0.977907	+	0.209039i	$0.0670334\pi$
$420$		0			0
$421$	−17.1168	−	29.6472i	−0.834224	−	1.44492i	−0.894661	−	0.446746i	$-0.852583\pi$
$421$	−17.1168	−	29.6472i	−0.834224	−	1.44492i	0.0604368	−	0.998172i	$-0.480751\pi$
$422$	8.00000	−	13.8564i	0.389434	−	0.674519i
$423$		0			0
$424$	−4.37228	−	7.57301i	−0.212337	−	0.367778i
$425$	19.3723			0.939694
$426$		0			0
$427$		0			0
$428$	−3.68614	+	6.38458i	−0.178176	+	0.308610i
$429$		0			0
$430$	17.7446	−	30.7345i	0.855719	−	1.48215i
$431$	−3.25544	−	5.63858i	−0.156809	−	0.271601i	0.776907	−	0.629615i	$-0.216787\pi$
$431$	−3.25544	−	5.63858i	−0.156809	−	0.271601i	−0.933716	+	0.358014i	$0.883454\pi$
$432$		0			0
$433$	20.1168			0.966754			0.483377	−	0.875412i	$-0.339410\pi$
$433$	20.1168			0.966754			0.483377	+	0.875412i	$0.339410\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	−8.13859			−0.389322
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	−2.74456			−0.130546
$443$	40.1168			1.90601			0.953004	−	0.302956i	$-0.0979737\pi$
$443$	40.1168			1.90601			0.953004	+	0.302956i	$0.0979737\pi$
$444$		0			0
$445$	64.4674			3.05605
$446$	−2.00000	−	3.46410i	−0.0947027	−	0.164030i
$447$		0			0
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$	−3.17527	−	5.49972i	−0.149517	−	0.258972i
$452$	−2.18614	+	3.78651i	−0.102827	+	0.178102i
$453$		0			0
$454$	6.12772	−	10.6135i	0.287588	−	0.498117i
$455$		0			0
$456$		0			0
$457$	−35.4674			−1.65909			−0.829547	−	0.558437i	$-0.811401\pi$
$457$	−35.4674			−1.65909			−0.829547	+	0.558437i	$0.811401\pi$
$458$	−1.44158	−	2.49689i	−0.0673605	−	0.116672i
$459$		0			0
$460$	−3.55842	+	6.16337i	−0.165912	+	0.287368i
$461$	−1.06930	−	1.85208i	−0.0498021	−	0.0862598i	0.840050	−	0.542509i	$-0.182526\pi$
$461$	−1.06930	−	1.85208i	−0.0498021	−	0.0862598i	−0.889852	+	0.456250i	$0.849192\pi$
$462$		0			0
$463$	11.5584	−	20.0198i	0.537165	−	0.930398i	−0.461890	−	0.886937i	$-0.652828\pi$
$463$	11.5584	−	20.0198i	0.537165	−	0.930398i	0.999055	−	0.0434604i	$-0.0138382\pi$
$464$	−4.37228	−	7.57301i	−0.202978	−	0.351568i
$465$		0			0
$466$	−0.127719	+	0.221215i	−0.00591645	+	0.0102476i
$467$	−16.5475	+	28.6612i	−0.765729	+	1.32628i	0.174131	+	0.984722i	$0.444288\pi$
$467$	−16.5475	+	28.6612i	−0.765729	+	1.32628i	−0.939860	+	0.341559i	$0.889045\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−10.1168			−0.465665
$473$	−11.1386			−0.512153
$474$		0			0
$475$	35.2921	+	61.1277i	1.61931	+	2.80473i
$476$		0			0
$477$		0			0
$478$	4.93070	−	8.54023i	0.225525	−	0.390621i
$479$	−16.3723	+	28.3576i	−0.748069	+	1.29569i	0.200679	+	0.979657i	$0.435685\pi$
$479$	−16.3723	+	28.3576i	−0.748069	+	1.29569i	−0.948747	+	0.316036i	$0.897648\pi$
$480$		0			0
$481$	2.00000	+	3.46410i	0.0911922	+	0.157949i
$482$	9.05842	−	15.6896i	0.412600	−	0.714644i
$483$		0			0
$484$	4.55842	+	7.89542i	0.207201	+	0.358883i
$485$	−17.7446	+	30.7345i	−0.805739	+	1.39558i
$486$		0			0
$487$	−17.6753	−	30.6145i	−0.800943	−	1.38727i	−0.918996	−	0.394266i	$-0.870999\pi$
$487$	−17.6753	−	30.6145i	−0.800943	−	1.38727i	0.118053	−	0.993007i	$-0.462335\pi$
$488$	−3.11684			−0.141093
$489$		0			0
$490$		0			0
$491$	−12.6861	+	21.9730i	−0.572518	+	0.991629i	0.423789	+	0.905761i	$0.360700\pi$
$491$	−12.6861	+	21.9730i	−0.572518	+	0.991629i	−0.996306	+	0.0858685i	$0.972634\pi$
$492$		0			0
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$	−5.00000	−	8.66025i	−0.224961	−	0.389643i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$		0			0
$498$		0			0
$499$	−9.05842	−	15.6896i	−0.405511	−	0.702365i	0.588870	−	0.808228i	$-0.299573\pi$
$499$	−9.05842	−	15.6896i	−0.405511	−	0.702365i	−0.994381	+	0.105863i	$0.966240\pi$
$500$	39.8614			1.78266
$501$		0			0
$502$	−9.00000			−0.401690
$503$	−32.2337			−1.43723			−0.718615	−	0.695409i	$-0.755223\pi$
$503$	−32.2337			−1.43723			−0.718615	+	0.695409i	$0.755223\pi$
$504$		0			0
$505$	7.11684			0.316695
$506$	2.23369			0.0992995
$507$		0			0
$508$	3.11684			0.138288
$509$	14.4891	+	25.0959i	0.642219	+	1.11236i	0.984936	+	0.172918i	$0.0553194\pi$
$509$	14.4891	+	25.0959i	0.642219	+	1.11236i	−0.342717	+	0.939439i	$0.611347\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.43070	+	5.94215i	0.151322	+	0.262097i
$515$	−21.8614	+	37.8651i	−0.963329	+	1.66853i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−8.74456			−0.383474
$521$	12.4307	+	21.5306i	0.544599	+	0.943273i	0.998632	+	0.0522883i	$0.0166515\pi$
$521$	12.4307	+	21.5306i	0.544599	+	0.943273i	−0.454033	+	0.890985i	$0.650015\pi$
$522$		0			0
$523$	−17.5584	+	30.4121i	−0.767776	+	1.32983i	0.170990	+	0.985273i	$0.445303\pi$
$523$	−17.5584	+	30.4121i	−0.767776	+	1.32983i	−0.938766	+	0.344555i	$0.888030\pi$
$524$	0.813859	+	1.40965i	0.0355536	+	0.0615807i
$525$		0			0
$526$	3.81386	−	6.60580i	0.166292	−	0.288026i
$527$	1.37228	+	2.37686i	0.0597775	+	0.103538i
$528$		0			0
$529$	10.1753	−	17.6241i	0.442403	−	0.766264i
$530$	−19.1168	+	33.1113i	−0.830383	+	1.43826i
$531$		0			0
$532$		0			0
$533$	4.62772	+	8.01544i	0.200449	+	0.347187i
$534$		0			0
$535$	32.2337			1.39358
$536$	−2.11684			−0.0914337
$537$		0			0
$538$	0.813859	+	1.40965i	0.0350880	+	0.0607741i
$539$		0			0
$540$		0			0
$541$	3.11684	−	5.39853i	0.134004	−	0.232101i	−0.791213	−	0.611541i	$-0.790550\pi$
$541$	3.11684	−	5.39853i	0.134004	−	0.232101i	0.925216	+	0.379440i	$0.123883\pi$
$542$	8.11684	−	14.0588i	0.348648	−	0.603877i
$543$		0			0
$544$	−0.686141	−	1.18843i	−0.0294180	−	0.0509535i
$545$	−30.6060	+	53.0111i	−1.31102	+	2.27075i
$546$		0			0
$547$	−9.05842	−	15.6896i	−0.387310	−	0.670841i	0.604777	−	0.796395i	$-0.293262\pi$
$547$	−9.05842	−	15.6896i	−0.387310	−	0.670841i	−0.992087	+	0.125554i	$0.959929\pi$
$548$	5.31386	−	9.20387i	0.226997	−	0.393170i
$549$		0			0
$550$	−9.68614	−	16.7769i	−0.413018	−	0.715369i
$551$	−43.7228			−1.86265
$552$		0			0
$553$		0			0
$554$	6.11684	−	10.5947i	0.259880	−	0.450125i
$555$		0			0
$556$	6.61684	−	11.4607i	0.280617	−	0.486042i
$557$	14.7446	+	25.5383i	0.624747	+	1.08209i	0.988590	+	0.150633i	$0.0481313\pi$
$557$	14.7446	+	25.5383i	0.624747	+	1.08209i	−0.363843	+	0.931460i	$0.618535\pi$
$558$		0			0
$559$	16.2337			0.686612
$560$		0			0
$561$		0			0
$562$	8.18614	+	14.1788i	0.345312	+	0.598097i
$563$	3.00000			0.126435			0.0632175	−	0.998000i	$-0.479864\pi$
$563$	3.00000			0.126435			0.0632175	+	0.998000i	$0.479864\pi$
$564$		0			0
$565$	19.1168			0.804252
$566$	−27.1168			−1.13981
$567$		0			0
$568$	7.11684			0.298616
$569$	−16.1168			−0.675653			−0.337827	−	0.941208i	$-0.609692\pi$
$569$	−16.1168			−0.675653			−0.337827	+	0.941208i	$0.609692\pi$
$570$		0			0
$571$	−22.3505			−0.935341			−0.467670	−	0.883903i	$-0.654907\pi$
$571$	−22.3505			−0.935341			−0.467670	+	0.883903i	$0.654907\pi$
$572$	1.37228	+	2.37686i	0.0573780	+	0.0993815i
$573$		0			0
$574$		0			0
$575$	22.9783			0.958259
$576$		0			0
$577$	4.94158	+	8.55906i	0.205721	+	0.356319i	0.950362	−	0.311146i	$-0.100713\pi$
$577$	4.94158	+	8.55906i	0.205721	+	0.356319i	−0.744641	+	0.667465i	$0.767380\pi$
$578$	7.55842	−	13.0916i	0.314389	−	0.544538i
$579$		0			0
$580$	−19.1168	+	33.1113i	−0.793784	+	1.37487i
$581$		0			0
$582$		0			0
$583$	12.0000			0.496989
$584$	6.05842	+	10.4935i	0.250699	+	0.434224i
$585$		0			0
$586$	5.18614	−	8.98266i	0.214237	−	0.371070i
$587$	−7.24456	−	12.5480i	−0.299015	−	0.517909i	0.676896	−	0.736079i	$-0.263325\pi$
$587$	−7.24456	−	12.5480i	−0.299015	−	0.517909i	−0.975911	+	0.218170i	$0.929991\pi$
$588$		0			0
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$	22.1168	+	38.3075i	0.910536	+	1.57709i
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−7.37228	+	12.7692i	−0.302743	+	0.524367i	−0.976756	−	0.214353i	$-0.931236\pi$
$593$	−7.37228	+	12.7692i	−0.302743	+	0.524367i	0.674013	+	0.738719i	$0.264569\pi$
$594$		0			0
$595$		0			0
$596$	1.62772	+	2.81929i	0.0666740	+	0.115483i
$597$		0			0
$598$	−3.25544			−0.133125
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	12.0584	+	20.8858i	0.491873	+	0.851950i	0.999956	−	0.00935863i	$-0.00297899\pi$
$601$	12.0584	+	20.8858i	0.491873	+	0.851950i	−0.508083	+	0.861308i	$0.669646\pi$
$602$		0			0
$603$		0			0
$604$	−4.55842	+	7.89542i	−0.185480	+	0.321260i
$605$	19.9307	−	34.5210i	0.810298	−	1.40348i
$606$		0			0
$607$	11.1168	+	19.2549i	0.451219	+	0.781534i	0.998462	−	0.0554398i	$-0.0176561\pi$
$607$	11.1168	+	19.2549i	0.451219	+	0.781534i	−0.547243	+	0.836974i	$0.684323\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	6.81386	+	11.8020i	0.275885	+	0.477847i
$611$		0			0
$612$		0			0
$613$	18.1168	+	31.3793i	0.731732	+	1.26740i	0.956142	+	0.292903i	$0.0946213\pi$
$613$	18.1168	+	31.3793i	0.731732	+	1.26740i	−0.224410	+	0.974495i	$0.572045\pi$
$614$	13.0000			0.524637
$615$		0			0
$616$		0			0
$617$	9.43070	−	16.3345i	0.379666	−	0.657600i	−0.611348	−	0.791362i	$-0.709372\pi$
$617$	9.43070	−	16.3345i	0.379666	−	0.657600i	0.991014	+	0.133762i	$0.0427056\pi$
$618$		0			0
$619$	22.7337	−	39.3759i	0.913744	−	1.58265i	0.105014	−	0.994471i	$-0.466511\pi$
$619$	22.7337	−	39.3759i	0.913744	−	1.58265i	0.808730	−	0.588180i	$-0.200156\pi$
$620$	4.37228	+	7.57301i	0.175595	+	0.304140i
$621$		0			0
$622$	8.23369			0.330141
$623$		0			0
$624$		0			0
$625$	−51.8505	−	89.8078i	−2.07402	−	3.59231i
$626$	20.1168			0.804031
$627$		0			0
$628$	−9.11684			−0.363802
$629$	2.74456			0.109433
$630$		0			0
$631$	−37.3505			−1.48690			−0.743451	−	0.668791i	$-0.766812\pi$
$631$	−37.3505			−1.48690			−0.743451	+	0.668791i	$0.766812\pi$
$632$	−5.11684			−0.203537
$633$		0			0
$634$	6.00000			0.238290
$635$	−6.81386	−	11.8020i	−0.270400	−	0.468346i
$636$		0			0
$637$		0			0
$638$	12.0000			0.475085
$639$		0			0
$640$	−2.18614	−	3.78651i	−0.0864148	−	0.149675i
$641$	17.1060	−	29.6284i	0.675645	−	1.17025i	−0.300635	−	0.953739i	$-0.597198\pi$
$641$	17.1060	−	29.6284i	0.675645	−	1.17025i	0.976280	−	0.216512i	$-0.0694682\pi$
$642$		0			0
$643$	13.1753	−	22.8202i	0.519582	−	0.899942i	−0.480159	−	0.877181i	$-0.659421\pi$
$643$	13.1753	−	22.8202i	0.519582	−	0.899942i	0.999741	−	0.0227606i	$-0.00724556\pi$
$644$		0			0
$645$		0			0
$646$	−6.86141			−0.269958
$647$	−2.74456	−	4.75372i	−0.107900	−	0.186888i	0.807019	−	0.590525i	$-0.201079\pi$
$647$	−2.74456	−	4.75372i	−0.107900	−	0.186888i	−0.914919	+	0.403637i	$0.867746\pi$
$648$		0			0
$649$	6.94158	−	12.0232i	0.272481	−	0.471951i
$650$	14.1168	+	24.4511i	0.553708	+	0.959051i
$651$		0			0
$652$	9.11684	−	15.7908i	0.357043	−	0.618417i
$653$	−13.3723	−	23.1615i	−0.523298	−	0.906378i	−0.999632	−	0.0271143i	$-0.991368\pi$
$653$	−13.3723	−	23.1615i	−0.523298	−	0.906378i	0.476335	−	0.879264i	$-0.341965\pi$
$654$		0			0
$655$	3.55842	−	6.16337i	0.139039	−	0.240823i
$656$	−2.31386	+	4.00772i	−0.0903410	+	0.156475i
$657$		0			0
$658$		0			0
$659$	−10.3723	−	17.9653i	−0.404047	−	0.699829i	0.590163	−	0.807284i	$-0.299063\pi$
$659$	−10.3723	−	17.9653i	−0.404047	−	0.699829i	−0.994210	+	0.107454i	$0.965730\pi$
$660$		0			0
$661$	−27.1168			−1.05472			−0.527361	−	0.849641i	$-0.676819\pi$
$661$	−27.1168			−1.05472			−0.527361	+	0.849641i	$0.676819\pi$
$662$	22.2337			0.864137
$663$		0			0
$664$	−8.74456	−	15.1460i	−0.339355	−	0.587780i
$665$		0			0
$666$		0			0
$667$	−7.11684	+	12.3267i	−0.275565	+	0.477293i
$668$	2.74456	−	4.75372i	0.106190	−	0.183927i
$669$		0			0
$670$	4.62772	+	8.01544i	0.178784	+	0.309664i
$671$	2.13859	−	3.70415i	0.0825595	−	0.142997i
$672$		0			0
$673$	1.44158	+	2.49689i	0.0555687	+	0.0962479i	0.892472	−	0.451103i	$-0.148969\pi$
$673$	1.44158	+	2.49689i	0.0555687	+	0.0962479i	−0.836903	+	0.547351i	$0.815636\pi$
$674$	4.05842	−	7.02939i	0.156325	−	0.270762i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	34.4674			1.32469			0.662344	−	0.749199i	$-0.269562\pi$
$677$	34.4674			1.32469			0.662344	+	0.749199i	$0.269562\pi$
$678$		0			0
$679$		0			0
$680$	−3.00000	+	5.19615i	−0.115045	+	0.199263i
$681$		0			0
$682$	1.37228	−	2.37686i	0.0525474	−	0.0910147i
$683$	14.9198	+	25.8419i	0.570891	+	0.988813i	0.996475	+	0.0838936i	$0.0267356\pi$
$683$	14.9198	+	25.8419i	0.570891	+	0.988813i	−0.425583	+	0.904919i	$0.639931\pi$
$684$		0			0
$685$	−46.4674			−1.77543
$686$		0			0
$687$		0			0
$688$	4.05842	+	7.02939i	0.154726	+	0.267993i
$689$	−17.4891			−0.666283
$690$		0			0
$691$	23.1168			0.879406			0.439703	−	0.898143i	$-0.355084\pi$
$691$	23.1168			0.879406			0.439703	+	0.898143i	$0.355084\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	10.1168			0.384030
$695$	−57.8614			−2.19481
$696$		0			0
$697$	6.35053			0.240544
$698$	−11.0000	−	19.0526i	−0.416356	−	0.721150i
$699$		0			0
$700$		0			0
$701$	38.2337			1.44407			0.722033	−	0.691858i	$-0.243208\pi$
$701$	38.2337			1.44407			0.722033	+	0.691858i	$0.243208\pi$
$702$		0			0
$703$	5.00000	+	8.66025i	0.188579	+	0.326628i
$704$	−0.686141	+	1.18843i	−0.0258599	+	0.0447907i
$705$		0			0
$706$	6.68614	−	11.5807i	0.251636	−	0.435847i
$707$		0			0
$708$		0			0
$709$	44.0000			1.65245			0.826227	−	0.563337i	$-0.190483\pi$
$709$	44.0000			1.65245			0.826227	+	0.563337i	$0.190483\pi$
$710$	−15.5584	−	26.9480i	−0.583897	−	1.01134i
$711$		0			0
$712$	−7.37228	+	12.7692i	−0.276288	+	0.478545i
$713$	1.62772	+	2.81929i	0.0609585	+	0.105583i
$714$		0			0
$715$	6.00000	−	10.3923i	0.224387	−	0.388650i
$716$	1.62772	+	2.81929i	0.0608307	+	0.105362i
$717$		0			0
$718$	10.9307	−	18.9325i	0.407930	−	0.706556i
$719$	−1.37228	+	2.37686i	−0.0511775	+	0.0886420i	−0.890479	−	0.455024i	$-0.849631\pi$
$719$	−1.37228	+	2.37686i	−0.0511775	+	0.0886420i	0.839302	+	0.543666i	$0.182964\pi$
$720$		0			0
$721$		0			0
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$		0			0
$724$	−0.883156			−0.0328222
$725$	123.446			4.58466
$726$		0			0
$727$	−18.1168	−	31.3793i	−0.671917	−	1.16379i	−0.977360	−	0.211583i	$-0.932138\pi$
$727$	−18.1168	−	31.3793i	−0.671917	−	1.16379i	0.305443	−	0.952210i	$-0.401195\pi$
$728$		0			0
$729$		0			0
$730$	26.4891	−	45.8805i	0.980407	−	1.69811i
$731$	5.56930	−	9.64630i	0.205988	−	0.356781i
$732$		0			0
$733$	−20.5584	−	35.6082i	−0.759343	−	1.31522i	−0.943186	−	0.332265i	$-0.892187\pi$
$733$	−20.5584	−	35.6082i	−0.759343	−	1.31522i	0.183844	−	0.982956i	$-0.441146\pi$
$734$	−6.11684	+	10.5947i	−0.225777	+	0.391057i
$735$		0			0
$736$	−0.813859	−	1.40965i	−0.0299993	−	0.0519602i
$737$	1.45245	−	2.51572i	0.0535018	−	0.0926678i
$738$		0			0
$739$	4.05842	+	7.02939i	0.149291	+	0.258580i	0.930966	−	0.365106i	$-0.118967\pi$
$739$	4.05842	+	7.02939i	0.149291	+	0.258580i	−0.781674	+	0.623687i	$0.785634\pi$
$740$	8.74456			0.321457
$741$		0			0
$742$		0			0
$743$	−6.86141	+	11.8843i	−0.251721	+	0.435993i	−0.964000	−	0.265904i	$-0.914330\pi$
$743$	−6.86141	+	11.8843i	−0.251721	+	0.435993i	0.712279	+	0.701896i	$0.247663\pi$
$744$		0			0
$745$	7.11684	−	12.3267i	0.260741	−	0.451617i
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$		0			0
$748$	1.88316			0.0688550
$749$		0			0
$750$		0			0
$751$	8.55842	+	14.8236i	0.312301	+	0.540922i	0.978860	−	0.204531i	$-0.0655668\pi$
$751$	8.55842	+	14.8236i	0.312301	+	0.540922i	−0.666559	+	0.745452i	$0.732234\pi$
$752$		0			0
$753$		0			0
$754$	−17.4891			−0.636916
$755$	39.8614			1.45071
$756$		0			0
$757$	46.2337			1.68039			0.840196	−	0.542283i	$-0.182440\pi$
$757$	46.2337			1.68039			0.840196	+	0.542283i	$0.182440\pi$
$758$	−8.11684			−0.294817
$759$		0			0
$760$	−21.8614			−0.792997
$761$	−17.7446	−	30.7345i	−0.643240	−	1.11412i	−0.984705	−	0.174230i	$-0.944256\pi$
$761$	−17.7446	−	30.7345i	−0.643240	−	1.11412i	0.341465	−	0.939894i	$-0.389077\pi$
$762$		0			0
$763$		0			0
$764$	19.1168			0.691623
$765$		0			0
$766$	16.3723	+	28.3576i	0.591555	+	1.02460i
$767$	−10.1168	+	17.5229i	−0.365298	+	0.632715i
$768$		0			0
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	−0.941984	−	0.335657i	$-0.891042\pi$
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	0.761680	+	0.647954i	$0.224375\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000			−0.251936
$773$	19.9307	+	34.5210i	0.716858	+	1.24163i	0.962239	+	0.272207i	$0.0877536\pi$
$773$	19.9307	+	34.5210i	0.716858	+	1.24163i	−0.245381	+	0.969427i	$0.578913\pi$
$774$		0			0
$775$	14.1168	−	24.4511i	0.507092	−	0.878309i
$776$	−4.05842	−	7.02939i	−0.145689	−	0.252341i
$777$		0			0
$778$	5.48913	−	9.50744i	0.196795	−	0.340858i
$779$	11.5693	+	20.0386i	0.414513	+	0.717958i
$780$		0			0
$781$	−4.88316	+	8.45787i	−0.174733	+	0.302647i
$782$	−1.11684	+	1.93443i	−0.0399383	+	0.0691751i
$783$		0			0
$784$		0			0
$785$	19.9307	+	34.5210i	0.711357	+	1.23211i
$786$		0			0
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	6.00000			0.213741
$789$		0			0
$790$	11.1861	+	19.3750i	0.397985	+	0.689330i
$791$		0			0
$792$		0			0
$793$	−3.11684	+	5.39853i	−0.110682	+	0.191707i
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$		0			0
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	4.06930	−	7.04823i	0.144142	−	0.249661i	−0.784911	−	0.619609i	$-0.787291\pi$
$797$	4.06930	−	7.04823i	0.144142	−	0.249661i	0.929052	+	0.369948i	$0.120624\pi$
$798$		0			0
$799$		0			0
$800$	−7.05842	+	12.2255i	−0.249553	+	0.432238i
$801$		0			0
$802$	−5.87228	−	10.1711i	−0.207357	−	0.359154i
$803$	−16.6277			−0.586779
$804$		0			0
$805$		0			0
$806$	−2.00000	+	3.46410i	−0.0704470	+	0.122018i
$807$		0			0
$808$	−0.813859	+	1.40965i	−0.0286315	+	0.0495912i
$809$	−3.43070	−	5.94215i	−0.120617	−	0.208915i	0.799394	−	0.600807i	$-0.205154\pi$
$809$	−3.43070	−	5.94215i	−0.120617	−	0.208915i	−0.920011	+	0.391892i	$0.871821\pi$
$810$		0			0
$811$	−42.1168			−1.47892			−0.739461	−	0.673199i	$-0.764920\pi$
$811$	−42.1168			−1.47892			−0.739461	+	0.673199i	$0.764920\pi$
$812$		0			0
$813$		0			0
$814$	−1.37228	−	2.37686i	−0.0480984	−	0.0833089i
$815$	−79.7228			−2.79257
$816$		0			0
$817$	40.5842			1.41986
$818$	22.3505			0.781468
$819$		0			0
$820$	20.2337			0.706591
$821$	3.76631			0.131445			0.0657226	−	0.997838i	$-0.479065\pi$
$821$	3.76631			0.131445			0.0657226	+	0.997838i	$0.479065\pi$
$822$		0			0
$823$	−12.2337			−0.426440			−0.213220	−	0.977004i	$-0.568395\pi$
$823$	−12.2337			−0.426440			−0.213220	+	0.977004i	$0.568395\pi$
$824$	−5.00000	−	8.66025i	−0.174183	−	0.301694i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	−6.88316	−	11.9220i	−0.239062	−	0.414067i	0.721383	−	0.692536i	$-0.243507\pi$
$829$	−6.88316	−	11.9220i	−0.239062	−	0.414067i	−0.960445	+	0.278468i	$0.910173\pi$
$830$	−38.2337	+	66.2227i	−1.32711	+	2.29862i
$831$		0			0
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	−24.0000			−0.830554
$836$	3.43070	+	5.94215i	0.118653	+	0.205514i
$837$		0			0
$838$	6.30298	−	10.9171i	0.217733	−	0.377125i
$839$	−2.74456	−	4.75372i	−0.0947528	−	0.164117i	0.814753	−	0.579809i	$-0.196873\pi$
$839$	−2.74456	−	4.75372i	−0.0947528	−	0.164117i	−0.909505	+	0.415692i	$0.863539\pi$
$840$		0			0
$841$	−23.7337	+	41.1080i	−0.818403	+	1.41752i
$842$	−17.1168	−	29.6472i	−0.589885	−	1.02171i
$843$		0			0
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	19.6753	−	34.0786i	0.676850	−	1.17234i
$846$		0			0
$847$		0			0
$848$	−4.37228	−	7.57301i	−0.150145	−	0.260058i
$849$		0			0
$850$	19.3723			0.664464
$851$	3.25544			0.111595
$852$		0			0
$853$	−17.5584	−	30.4121i	−0.601189	−	1.04129i	−0.992641	−	0.121091i	$-0.961361\pi$
$853$	−17.5584	−	30.4121i	−0.601189	−	1.04129i	0.391452	−	0.920198i	$-0.371973\pi$
$854$		0			0
$855$		0			0
$856$	−3.68614	+	6.38458i	−0.125990	+	0.218221i
$857$	19.9783	−	34.6033i	0.682444	−	1.18203i	−0.291789	−	0.956483i	$-0.594250\pi$
$857$	19.9783	−	34.6033i	0.682444	−	1.18203i	0.974233	−	0.225545i	$-0.0724163\pi$
$858$		0			0
$859$	16.9416	+	29.3437i	0.578039	+	1.00119i	0.995704	+	0.0925921i	$0.0295153\pi$
$859$	16.9416	+	29.3437i	0.578039	+	1.00119i	−0.417665	+	0.908601i	$0.637151\pi$
$860$	17.7446	−	30.7345i	0.605085	−	1.04804i
$861$		0			0
$862$	−3.25544	−	5.63858i	−0.110881	−	0.192051i
$863$	4.93070	−	8.54023i	0.167843	−	0.290713i	−0.769818	−	0.638263i	$-0.779653\pi$
$863$	4.93070	−	8.54023i	0.167843	−	0.290713i	0.937661	+	0.347550i	$0.112986\pi$
$864$		0			0
$865$	13.1168	+	22.7190i	0.445986	+	0.772471i
$866$	20.1168			0.683598
$867$		0			0
$868$		0			0
$869$	3.51087	−	6.08101i	0.119098	−	0.206284i
$870$		0			0
$871$	−2.11684	+	3.66648i	−0.0717265	+	0.124234i
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$		0			0
$874$	−8.13859			−0.275292
$875$		0			0
$876$		0			0
$877$	29.3505	+	50.8366i	0.991097	+	1.71663i	0.610852	+	0.791744i	$0.290827\pi$
$877$	29.3505	+	50.8366i	0.991097	+	1.71663i	0.380245	+	0.924886i	$0.375840\pi$
$878$	−8.00000			−0.269987
$879$		0			0
$880$	6.00000			0.202260
$881$	−20.2337			−0.681690			−0.340845	−	0.940119i	$-0.610713\pi$
$881$	−20.2337			−0.681690			−0.340845	+	0.940119i	$0.610713\pi$
$882$		0			0
$883$	−40.3505			−1.35790			−0.678952	−	0.734183i	$-0.737565\pi$
$883$	−40.3505			−1.35790			−0.678952	+	0.734183i	$0.737565\pi$
$884$	−2.74456			−0.0923096
$885$		0			0
$886$	40.1168			1.34775
$887$	−12.8614	−	22.2766i	−0.431844	−	0.747975i	0.565188	−	0.824962i	$-0.308803\pi$
$887$	−12.8614	−	22.2766i	−0.431844	−	0.747975i	−0.997032	+	0.0769865i	$0.975470\pi$
$888$		0			0
$889$		0			0
$890$	64.4674			2.16095
$891$		0			0
$892$	−2.00000	−	3.46410i	−0.0669650	−	0.115987i
$893$		0			0
$894$		0			0
$895$	7.11684	−	12.3267i	0.237890	−	0.412037i
$896$		0			0
$897$		0			0
$898$	−33.0000			−1.10122
$899$	8.74456	+	15.1460i	0.291647	+	0.505148i
$900$		0			0
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$	−3.17527	−	5.49972i	−0.105725	−	0.183121i
$903$		0			0
$904$	−2.18614	+	3.78651i	−0.0727100	+	0.125937i
$905$	1.93070	+	3.34408i	0.0641787	+	0.111161i
$906$		0			0
$907$	13.0584	−	22.6179i	0.433598	−	0.751013i	−0.563582	−	0.826060i	$-0.690577\pi$
$907$	13.0584	−	22.6179i	0.433598	−	0.751013i	0.997180	+	0.0750466i	$0.0239105\pi$
$908$	6.12772	−	10.6135i	0.203355	−	0.352222i
$909$		0			0
$910$		0			0
$911$	−18.8139	−	32.5866i	−0.623331	−	1.07964i	−0.988861	−	0.148841i	$-0.952446\pi$
$911$	−18.8139	−	32.5866i	−0.623331	−	1.07964i	0.365530	−	0.930800i	$-0.380888\pi$
$912$		0			0
$913$	24.0000			0.794284
$914$	−35.4674			−1.17316
$915$		0			0
$916$	−1.44158	−	2.49689i	−0.0476311	−	0.0824994i
$917$		0			0
$918$		0			0
$919$	23.5584	−	40.8044i	0.777121	−	1.34601i	−0.156474	−	0.987682i	$-0.550013\pi$
$919$	23.5584	−	40.8044i	0.777121	−	1.34601i	0.933595	−	0.358330i	$-0.116654\pi$
$920$	−3.55842	+	6.16337i	−0.117318	+	0.203200i
$921$		0			0
$922$	−1.06930	−	1.85208i	−0.0352154	−	0.0609949i
$923$	7.11684	−	12.3267i	0.234254	−	0.405739i
$924$		0			0
$925$	−14.1168	−	24.4511i	−0.464159	−	0.803947i
$926$	11.5584	−	20.0198i	0.379833	−	0.657891i
$927$		0			0
$928$	−4.37228	−	7.57301i	−0.143527	−	0.248596i
$929$	44.2337			1.45126			0.725630	−	0.688085i	$-0.241548\pi$
$929$	44.2337			1.45126			0.725630	+	0.688085i	$0.241548\pi$
$930$		0			0
$931$		0			0
$932$	−0.127719	+	0.221215i	−0.00418356	+	0.00724615i
$933$		0			0
$934$	−16.5475	+	28.6612i	−0.541452	+	0.937823i
$935$	−4.11684	−	7.13058i	−0.134635	−	0.233195i
$936$		0			0
$937$	−30.4674			−0.995326			−0.497663	−	0.867371i	$-0.665808\pi$
$937$	−30.4674			−0.995326			−0.497663	+	0.867371i	$0.665808\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.1168			0.623191			0.311596	−	0.950215i	$-0.399137\pi$
$941$	19.1168			0.623191			0.311596	+	0.950215i	$0.399137\pi$
$942$		0			0
$943$	7.53262			0.245296
$944$	−10.1168			−0.329275
$945$		0			0
$946$	−11.1386			−0.362147
$947$	−34.1168			−1.10865			−0.554324	−	0.832301i	$-0.687023\pi$
$947$	−34.1168			−1.10865			−0.554324	+	0.832301i	$0.687023\pi$
$948$		0			0
$949$	24.2337			0.786659
$950$	35.2921	+	61.1277i	1.14503	+	1.98325i
$951$		0			0
$952$		0			0
$953$	−28.1168			−0.910794			−0.455397	−	0.890288i	$-0.650503\pi$
$953$	−28.1168			−0.910794			−0.455397	+	0.890288i	$0.650503\pi$
$954$		0			0
$955$	−41.7921	−	72.3861i	−1.35236	−	2.34236i
$956$	4.93070	−	8.54023i	0.159470	−	0.276211i
$957$		0			0
$958$	−16.3723	+	28.3576i	−0.528964	+	0.916193i
$959$		0			0
$960$		0			0
$961$	−27.0000			−0.870968
$962$	2.00000	+	3.46410i	0.0644826	+	0.111687i
$963$		0			0
$964$	9.05842	−	15.6896i	0.291752	−	0.505330i
$965$	15.3030	+	26.5055i	0.492621	+	0.853244i
$966$		0			0
$967$	−15.4416	+	26.7456i	−0.496568	+	0.860080i	−0.999992	−	0.00395879i	$-0.998740\pi$
$967$	−15.4416	+	26.7456i	−0.496568	+	0.860080i	0.503424	+	0.864039i	$0.332073\pi$
$968$	4.55842	+	7.89542i	0.146513	+	0.253768i
$969$		0			0
$970$	−17.7446	+	30.7345i	−0.569744	+	0.986825i
$971$	−0.813859	+	1.40965i	−0.0261180	+	0.0452377i	−0.878789	−	0.477211i	$-0.841648\pi$
$971$	−0.813859	+	1.40965i	−0.0261180	+	0.0452377i	0.852671	+	0.522448i	$0.174981\pi$
$972$		0			0
$973$		0			0
$974$	−17.6753	−	30.6145i	−0.566352	−	0.980951i
$975$		0			0
$976$	−3.11684			−0.0997677
$977$	−40.1168			−1.28345			−0.641726	−	0.766934i	$-0.721781\pi$
$977$	−40.1168			−1.28345			−0.641726	+	0.766934i	$0.721781\pi$
$978$		0			0
$979$	−10.1168	−	17.5229i	−0.323336	−	0.560034i
$980$		0			0
$981$		0			0
$982$	−12.6861	+	21.9730i	−0.404831	+	0.701188i
$983$	19.6277	−	33.9962i	0.626027	−	1.08431i	−0.362314	−	0.932056i	$-0.618013\pi$
$983$	19.6277	−	33.9962i	0.626027	−	1.08431i	0.988341	−	0.152255i	$-0.0486534\pi$
$984$		0			0
$985$	−13.1168	−	22.7190i	−0.417937	−	0.723889i
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$		0			0
$988$	−5.00000	−	8.66025i	−0.159071	−	0.275519i
$989$	6.60597	−	11.4419i	0.210058	−	0.363830i
$990$		0			0
$991$	−24.2337	−	41.9740i	−0.769808	−	1.33335i	−0.937667	−	0.347536i	$-0.887018\pi$
$991$	−24.2337	−	41.9740i	−0.769808	−	1.33335i	0.167858	−	0.985811i	$-0.446315\pi$
$992$	−2.00000			−0.0635001
$993$		0			0
$994$		0			0
$995$	−21.8614	+	37.8651i	−0.693053	+	1.20040i
$996$		0			0
$997$	−2.55842	+	4.43132i	−0.0810260	+	0.140341i	−0.903691	−	0.428185i	$-0.859153\pi$
$997$	−2.55842	+	4.43132i	−0.0810260	+	0.140341i	0.822665	+	0.568527i	$0.192486\pi$
$998$	−9.05842	−	15.6896i	−0.286739	−	0.496647i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.m.1549.1		4
3.2	odd	2		882.2.e.k.373.1		4
7.2	even	3		2646.2.f.j.1765.1		4
7.3	odd	6		2646.2.h.k.361.1		4
7.4	even	3		2646.2.h.l.361.2		4
7.5	odd	6		378.2.f.c.253.2		4
7.6	odd	2		2646.2.e.n.1549.2		4
9.2	odd	6		882.2.h.n.79.1		4
9.7	even	3		2646.2.h.l.667.2		4
21.2	odd	6		882.2.f.k.589.2		4
21.5	even	6		126.2.f.d.85.1	yes	4
21.11	odd	6		882.2.h.n.67.1		4
21.17	even	6		882.2.h.m.67.2		4
21.20	even	2		882.2.e.l.373.2		4
28.19	even	6		3024.2.r.f.1009.2		4
63.2	odd	6		882.2.f.k.295.2		4
63.5	even	6		1134.2.a.k.1.2		2
63.11	odd	6		882.2.e.k.655.2		4
63.16	even	3		2646.2.f.j.883.1		4
63.20	even	6		882.2.h.m.79.2		4
63.23	odd	6		7938.2.a.bh.1.1		2
63.25	even	3	inner	2646.2.e.m.2125.1		4
63.34	odd	6		2646.2.h.k.667.1		4
63.38	even	6		882.2.e.l.655.1		4
63.40	odd	6		1134.2.a.n.1.1		2
63.47	even	6		126.2.f.d.43.1	✓	4
63.52	odd	6		2646.2.e.n.2125.2		4
63.58	even	3		7938.2.a.bs.1.2		2
63.61	odd	6		378.2.f.c.127.2		4
84.47	odd	6		1008.2.r.f.337.2		4
252.47	odd	6		1008.2.r.f.673.2		4
252.103	even	6		9072.2.a.bb.1.1		2
252.131	odd	6		9072.2.a.bm.1.2		2
252.187	even	6		3024.2.r.f.2017.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.1	✓	4	63.47	even	6
126.2.f.d.85.1	yes	4	21.5	even	6
378.2.f.c.127.2		4	63.61	odd	6
378.2.f.c.253.2		4	7.5	odd	6
882.2.e.k.373.1		4	3.2	odd	2
882.2.e.k.655.2		4	63.11	odd	6
882.2.e.l.373.2		4	21.20	even	2
882.2.e.l.655.1		4	63.38	even	6
882.2.f.k.295.2		4	63.2	odd	6
882.2.f.k.589.2		4	21.2	odd	6
882.2.h.m.67.2		4	21.17	even	6
882.2.h.m.79.2		4	63.20	even	6
882.2.h.n.67.1		4	21.11	odd	6
882.2.h.n.79.1		4	9.2	odd	6
1008.2.r.f.337.2		4	84.47	odd	6
1008.2.r.f.673.2		4	252.47	odd	6
1134.2.a.k.1.2		2	63.5	even	6
1134.2.a.n.1.1		2	63.40	odd	6
2646.2.e.m.1549.1		4	1.1	even	1	trivial
2646.2.e.m.2125.1		4	63.25	even	3	inner
2646.2.e.n.1549.2		4	7.6	odd	2
2646.2.e.n.2125.2		4	63.52	odd	6
2646.2.f.j.883.1		4	63.16	even	3
2646.2.f.j.1765.1		4	7.2	even	3
2646.2.h.k.361.1		4	7.3	odd	6
2646.2.h.k.667.1		4	63.34	odd	6
2646.2.h.l.361.2		4	7.4	even	3
2646.2.h.l.667.2		4	9.7	even	3
3024.2.r.f.1009.2		4	28.19	even	6
3024.2.r.f.2017.2		4	252.187	even	6
7938.2.a.bh.1.1		2	63.23	odd	6
7938.2.a.bs.1.2		2	63.58	even	3
9072.2.a.bb.1.1		2	252.103	even	6
9072.2.a.bm.1.2		2	252.131	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.18614 - 3.78651i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-2.18614 - 3.78651i) q^{5} +1.00000 q^{8} +(-2.18614 - 3.78651i) q^{10} +(-0.686141 + 1.18843i) q^{11} +(1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(-0.686141 - 1.18843i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-2.18614 - 3.78651i) q^{20} +(-0.686141 + 1.18843i) q^{22} +(-0.813859 - 1.40965i) q^{23} +(-7.05842 + 12.2255i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.37228 - 7.57301i) q^{29} -2.00000 q^{31} +1.00000 q^{32} +(-0.686141 - 1.18843i) q^{34} +(-1.00000 + 1.73205i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-2.18614 - 3.78651i) q^{40} +(-2.31386 + 4.00772i) q^{41} +(4.05842 + 7.02939i) q^{43} +(-0.686141 + 1.18843i) q^{44} +(-0.813859 - 1.40965i) q^{46} +(-7.05842 + 12.2255i) q^{50} +(1.00000 - 1.73205i) q^{52} +(-4.37228 - 7.57301i) q^{53} +6.00000 q^{55} +(-4.37228 - 7.57301i) q^{58} -10.1168 q^{59} -3.11684 q^{61} -2.00000 q^{62} +1.00000 q^{64} -8.74456 q^{65} -2.11684 q^{67} +(-0.686141 - 1.18843i) q^{68} +7.11684 q^{71} +(6.05842 + 10.4935i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{76} -5.11684 q^{79} +(-2.18614 - 3.78651i) q^{80} +(-2.31386 + 4.00772i) q^{82} +(-8.74456 - 15.1460i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(4.05842 + 7.02939i) q^{86} +(-0.686141 + 1.18843i) q^{88} +(-7.37228 + 12.7692i) q^{89} +(-0.813859 - 1.40965i) q^{92} -21.8614 q^{95} +(-4.05842 - 7.02939i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} - 3 q^{5} + 4 q^{8} - 3 q^{10} + 3 q^{11} + 4 q^{13} + 4 q^{16} + 3 q^{17} + 10 q^{19} - 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} + 4 q^{26} - 6 q^{29} - 8 q^{31} + 4 q^{32} + 3 q^{34} - 4 q^{37} + 10 q^{38} - 3 q^{40} - 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} + 4 q^{52} - 6 q^{53} + 24 q^{55} - 6 q^{58} - 6 q^{59} + 22 q^{61} - 8 q^{62} + 4 q^{64} - 12 q^{65} + 26 q^{67} + 3 q^{68} - 6 q^{71} + 7 q^{73} - 4 q^{74} + 10 q^{76} + 14 q^{79} - 3 q^{80} - 15 q^{82} - 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} - 18 q^{89} - 9 q^{92} - 30 q^{95} + q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 - 3 * q^5 + 4 * q^8 - 3 * q^10 + 3 * q^11 + 4 * q^13 + 4 * q^16 + 3 * q^17 + 10 * q^19 - 3 * q^20 + 3 * q^22 - 9 * q^23 - 11 * q^25 + 4 * q^26 - 6 * q^29 - 8 * q^31 + 4 * q^32 + 3 * q^34 - 4 * q^37 + 10 * q^38 - 3 * q^40 - 15 * q^41 - q^43 + 3 * q^44 - 9 * q^46 - 11 * q^50 + 4 * q^52 - 6 * q^53 + 24 * q^55 - 6 * q^58 - 6 * q^59 + 22 * q^61 - 8 * q^62 + 4 * q^64 - 12 * q^65 + 26 * q^67 + 3 * q^68 - 6 * q^71 + 7 * q^73 - 4 * q^74 + 10 * q^76 + 14 * q^79 - 3 * q^80 - 15 * q^82 - 12 * q^83 - 12 * q^85 - q^86 + 3 * q^88 - 18 * q^89 - 9 * q^92 - 30 * q^95 + q^97

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