LMFDB - Embedded newform 2646.2.h.l.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.l.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.37228 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.37228 q^{5} +1.00000 q^{8} +(-2.18614 - 3.78651i) q^{10} +1.37228 q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.686141 - 1.18843i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-2.18614 + 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} +1.62772 q^{23} +14.1168 q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.37228 + 7.57301i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.686141 + 1.18843i) q^{34} +(-1.00000 + 1.73205i) q^{37} -5.00000 q^{38} +4.37228 q^{40} +(-2.31386 - 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +(-0.686141 + 1.18843i) q^{44} +(-0.813859 - 1.40965i) q^{46} +(-7.05842 - 12.2255i) q^{50} -2.00000 q^{52} +(-4.37228 - 7.57301i) q^{53} +6.00000 q^{55} +8.74456 q^{58} +(5.05842 - 8.76144i) q^{59} +(1.55842 + 2.69927i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(4.37228 + 7.57301i) q^{65} +(1.05842 - 1.83324i) q^{67} +1.37228 q^{68} +7.11684 q^{71} +(6.05842 + 10.4935i) q^{73} +2.00000 q^{74} +(2.50000 + 4.33013i) q^{76} +(2.55842 + 4.43132i) q^{79} +(-2.18614 - 3.78651i) q^{80} +(-2.31386 + 4.00772i) q^{82} +(-8.74456 + 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} -8.11684 q^{86} +1.37228 q^{88} +(-7.37228 + 12.7692i) q^{89} +(-0.813859 + 1.40965i) q^{92} +(10.9307 - 18.9325i) q^{95} +(-4.05842 + 7.02939i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 6 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 6 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 6 q^{5} + 4 q^{8} - 3 q^{10} - 6 q^{11} + 4 q^{13} - 2 q^{16} + 3 q^{17} + 10 q^{19} - 3 q^{20} + 3 q^{22} + 18 q^{23} + 22 q^{25} + 4 q^{26} - 6 q^{29} + 4 q^{31} - 2 q^{32} + 3 q^{34} - 4 q^{37} - 20 q^{38} + 6 q^{40} - 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} - 8 q^{52} - 6 q^{53} + 24 q^{55} + 12 q^{58} + 3 q^{59} - 11 q^{61} - 8 q^{62} + 4 q^{64} + 6 q^{65} - 13 q^{67} - 6 q^{68} - 6 q^{71} + 7 q^{73} + 8 q^{74} + 10 q^{76} - 7 q^{79} - 3 q^{80} - 15 q^{82} - 12 q^{83} - 12 q^{85} + 2 q^{86} - 6 q^{88} - 18 q^{89} - 9 q^{92} + 15 q^{95} + q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 6 * q^5 + 4 * q^8 - 3 * q^10 - 6 * q^11 + 4 * q^13 - 2 * q^16 + 3 * q^17 + 10 * q^19 - 3 * q^20 + 3 * q^22 + 18 * q^23 + 22 * q^25 + 4 * q^26 - 6 * q^29 + 4 * q^31 - 2 * q^32 + 3 * q^34 - 4 * q^37 - 20 * q^38 + 6 * q^40 - 15 * q^41 - q^43 + 3 * q^44 - 9 * q^46 - 11 * q^50 - 8 * q^52 - 6 * q^53 + 24 * q^55 + 12 * q^58 + 3 * q^59 - 11 * q^61 - 8 * q^62 + 4 * q^64 + 6 * q^65 - 13 * q^67 - 6 * q^68 - 6 * q^71 + 7 * q^73 + 8 * q^74 + 10 * q^76 - 7 * q^79 - 3 * q^80 - 15 * q^82 - 12 * q^83 - 12 * q^85 + 2 * q^86 - 6 * q^88 - 18 * q^89 - 9 * q^92 + 15 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	4.37228			1.95534			0.977672	−	0.210138i	$-0.0673912\pi$
$5$	4.37228			1.95534			0.977672	+	0.210138i	$0.0673912\pi$
$6$		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
$11$	1.37228			0.413758			0.206879	−	0.978366i	$-0.433669\pi$
$11$	1.37228			0.413758			0.206879	+	0.978366i	$0.433669\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−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
$23$	1.62772			0.339403			0.169701	−	0.985496i	$-0.445720\pi$
$23$	1.62772			0.339403			0.169701	+	0.985496i	$0.445720\pi$
$24$		0			0
$25$	14.1168			2.82337
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$		0			0
$28$		0			0
$29$	−4.37228	+	7.57301i	−0.811912	+	1.40627i	0.0996117	+	0.995026i	$0.468240\pi$
$29$	−4.37228	+	7.57301i	−0.811912	+	1.40627i	−0.911524	+	0.411247i	$0.865093\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		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	$0.219235\pi$
$38$	−5.00000			−0.811107
$39$		0			0
$40$	4.37228			0.691318
$41$	−2.31386	−	4.00772i	−0.361364	−	0.625901i	0.626821	−	0.779163i	$-0.284356\pi$
$41$	−2.31386	−	4.00772i	−0.361364	−	0.625901i	−0.988186	+	0.153262i	$0.951022\pi$
$42$		0			0
$43$	4.05842	−	7.02939i	0.618904	−	1.07197i	−0.370783	−	0.928720i	$-0.620910\pi$
$43$	4.05842	−	7.02939i	0.618904	−	1.07197i	0.989686	−	0.143253i	$-0.0457562\pi$
$44$	−0.686141	+	1.18843i	−0.103440	+	0.179163i
$45$		0			0
$46$	−0.813859	−	1.40965i	−0.119997	−	0.207841i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$	−7.05842	−	12.2255i	−0.998212	−	1.72895i
$51$		0			0
$52$	−2.00000			−0.277350
$53$	−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
$58$	8.74456			1.14822
$59$	5.05842	−	8.76144i	0.658550	−	1.14064i	−0.322441	−	0.946590i	$-0.604503\pi$
$59$	5.05842	−	8.76144i	0.658550	−	1.14064i	0.980991	−	0.194053i	$-0.0621634\pi$
$60$		0			0
$61$	1.55842	+	2.69927i	0.199535	+	0.345606i	0.948378	−	0.317142i	$-0.102723\pi$
$61$	1.55842	+	2.69927i	0.199535	+	0.345606i	−0.748842	+	0.662748i	$0.769390\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	4.37228	+	7.57301i	0.542315	+	0.939317i
$66$		0			0
$67$	1.05842	−	1.83324i	0.129307	−	0.223966i	−0.794101	−	0.607785i	$-0.792058\pi$
$67$	1.05842	−	1.83324i	0.129307	−	0.223966i	0.923408	+	0.383819i	$0.125391\pi$
$68$	1.37228			0.166414
$69$		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	$0.582442\pi$
$74$	2.00000			0.232495
$75$		0			0
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$		0			0
$78$		0			0
$79$	2.55842	+	4.43132i	0.287845	+	0.498562i	0.973295	−	0.229557i	$-0.0737279\pi$
$79$	2.55842	+	4.43132i	0.287845	+	0.498562i	−0.685450	+	0.728120i	$0.740395\pi$
$80$	−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	−0.236960	+	0.971519i	$0.576151\pi$
$83$	−8.74456	+	15.1460i	−0.959840	+	1.66249i	−0.722881	+	0.690973i	$0.757182\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$	−8.11684			−0.875262
$87$		0			0
$88$	1.37228			0.146286
$89$	−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
$95$	10.9307	−	18.9325i	1.12147	−	1.94244i
$96$		0			0
$97$	−4.05842	+	7.02939i	−0.412070	+	0.713727i	−0.995116	−	0.0987127i	$-0.968528\pi$
$97$	−4.05842	+	7.02939i	−0.412070	+	0.713727i	0.583046	+	0.812439i	$0.301861\pi$
$98$		0			0
$99$		0			0
$100$	−7.05842	+	12.2255i	−0.705842	+	1.22255i
$101$	1.62772			0.161964			0.0809820	−	0.996716i	$-0.474194\pi$
$101$	1.62772			0.161964			0.0809820	+	0.996716i	$0.474194\pi$
$102$		0			0
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$	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	$-0.400578\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$		0			0
$112$		0			0
$113$	−2.18614	−	3.78651i	−0.205655	−	0.356205i	0.744686	−	0.667415i	$-0.232599\pi$
$113$	−2.18614	−	3.78651i	−0.205655	−	0.356205i	−0.950341	+	0.311210i	$0.899266\pi$
$114$		0			0
$115$	7.11684			0.663649
$116$	−4.37228	−	7.57301i	−0.405956	−	0.703137i
$117$		0			0
$118$	−10.1168			−0.931331
$119$		0			0
$120$		0			0
$121$	−9.11684			−0.828804
$122$	1.55842	−	2.69927i	0.141093	−	0.244380i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	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	$0.455840\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	4.37228	−	7.57301i	0.383474	−	0.664197i
$131$	−1.62772			−0.142214			−0.0711072	−	0.997469i	$-0.522653\pi$
$131$	−1.62772			−0.142214			−0.0711072	+	0.997469i	$0.522653\pi$
$132$		0			0
$133$		0			0
$134$	−2.11684			−0.182867
$135$		0			0
$136$	−0.686141	−	1.18843i	−0.0588361	−	0.101907i
$137$	−10.6277			−0.907987			−0.453994	−	0.891005i	$-0.650001\pi$
$137$	−10.6277			−0.907987			−0.453994	+	0.891005i	$0.650001\pi$
$138$		0			0
$139$	6.61684	+	11.4607i	0.561233	+	0.972085i	0.997389	+	0.0722136i	$0.0230063\pi$
$139$	6.61684	+	11.4607i	0.561233	+	0.972085i	−0.436156	+	0.899871i	$0.643660\pi$
$140$		0			0
$141$		0			0
$142$	−3.55842	−	6.16337i	−0.298616	−	0.517218i
$143$	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
$149$	−3.25544			−0.266696			−0.133348	−	0.991069i	$-0.542573\pi$
$149$	−3.25544			−0.266696			−0.133348	+	0.991069i	$0.542573\pi$
$150$		0			0
$151$	9.11684			0.741918			0.370959	−	0.928649i	$-0.379029\pi$
$151$	9.11684			0.741918			0.370959	+	0.928649i	$0.379029\pi$
$152$	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
$157$	4.55842	−	7.89542i	0.363802	−	0.630123i	−0.624781	−	0.780800i	$-0.714812\pi$
$157$	4.55842	−	7.89542i	0.363802	−	0.630123i	0.988583	+	0.150677i	$0.0481453\pi$
$158$	2.55842	−	4.43132i	0.203537	−	0.352537i
$159$		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	$-0.0864909\pi$
$164$	4.62772			0.361364
$165$		0			0
$166$	17.4891			1.35742
$167$	2.74456	+	4.75372i	0.212381	+	0.367854i	0.952459	−	0.304666i	$-0.0985450\pi$
$167$	2.74456	+	4.75372i	0.212381	+	0.367854i	−0.740078	+	0.672521i	$0.765212\pi$
$168$		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
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$	−0.686141	−	1.18843i	−0.0517198	−	0.0895813i
$177$		0			0
$178$	14.7446			1.10515
$179$	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
$184$	1.62772			0.119997
$185$	−4.37228	+	7.57301i	−0.321457	+	0.556779i
$186$		0			0
$187$	−0.941578	−	1.63086i	−0.0688550	−	0.119260i
$188$		0			0
$189$		0			0
$190$	−21.8614			−1.58599
$191$	−9.55842	−	16.5557i	−0.691623	−	1.19793i	−0.971306	−	0.237834i	$-0.923563\pi$
$191$	−9.55842	−	16.5557i	−0.691623	−	1.19793i	0.279683	−	0.960092i	$-0.409771\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	8.11684			0.582755
$195$		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	$0.948662\pi$
$200$	14.1168			0.998212
$201$		0			0
$202$	−0.813859	−	1.40965i	−0.0572629	−	0.0991823i
$203$		0			0
$204$		0			0
$205$	−10.1168	−	17.5229i	−0.706591	−	1.22385i
$206$	−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	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	8.74456			0.600579
$213$		0			0
$214$	7.37228			0.503959
$215$	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
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	1.37228	−	2.37686i	0.0923096	−	0.159885i
$222$		0			0
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$		0			0
$225$		0			0
$226$	−2.18614	+	3.78651i	−0.145420	+	0.251875i
$227$	−12.2554			−0.813422			−0.406711	−	0.913557i	$-0.633324\pi$
$227$	−12.2554			−0.813422			−0.406711	+	0.913557i	$0.633324\pi$
$228$		0			0
$229$	2.88316			0.190524			0.0952622	−	0.995452i	$-0.469631\pi$
$229$	2.88316			0.190524			0.0952622	+	0.995452i	$0.469631\pi$
$230$	−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
$236$	5.05842	+	8.76144i	0.329275	+	0.570321i
$237$		0			0
$238$		0			0
$239$	4.93070	+	8.54023i	0.318941	+	0.552421i	0.980267	−	0.197677i	$-0.0633396\pi$
$239$	4.93070	+	8.54023i	0.318941	+	0.552421i	−0.661327	+	0.750098i	$0.730006\pi$
$240$		0			0
$241$	−18.1168			−1.16701			−0.583504	−	0.812110i	$-0.698319\pi$
$241$	−18.1168			−1.16701			−0.583504	+	0.812110i	$0.698319\pi$
$242$	4.55842	+	7.89542i	0.293026	+	0.507537i
$243$		0			0
$244$	−3.11684			−0.199535
$245$		0			0
$246$		0			0
$247$	10.0000			0.636285
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$		0			0
$250$	−19.9307	−	34.5210i	−1.26053	−	2.18330i
$251$	−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
$254$	−1.55842	−	2.69927i	−0.0977841	−	0.169367i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.86141			−0.428003			−0.214001	−	0.976833i	$-0.568650\pi$
$257$	−6.86141			−0.428003			−0.214001	+	0.976833i	$0.568650\pi$
$258$		0			0
$259$		0			0
$260$	−8.74456			−0.542315
$261$		0			0
$262$	0.813859	+	1.40965i	0.0502804	+	0.0870882i
$263$	−7.62772			−0.470345			−0.235173	−	0.971954i	$-0.575566\pi$
$263$	−7.62772			−0.470345			−0.235173	+	0.971954i	$0.575566\pi$
$264$		0			0
$265$	−19.1168	−	33.1113i	−1.17434	−	2.03401i
$266$		0			0
$267$		0			0
$268$	1.05842	+	1.83324i	0.0646534	+	0.111983i
$269$	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
$275$	19.3723			1.16819
$276$		0			0
$277$	−12.2337			−0.735051			−0.367526	−	0.930013i	$-0.619795\pi$
$277$	−12.2337			−0.735051			−0.367526	+	0.930013i	$0.619795\pi$
$278$	6.61684	−	11.4607i	0.396852	−	0.687368i
$279$		0			0
$280$		0			0
$281$	8.18614	−	14.1788i	0.488344	−	0.845837i	−0.511566	−	0.859244i	$-0.670934\pi$
$281$	8.18614	−	14.1788i	0.488344	−	0.845837i	0.999910	+	0.0134071i	$0.00426773\pi$
$282$		0			0
$283$	13.5584	−	23.4839i	0.805965	−	1.39597i	−0.109673	−	0.993968i	$-0.534981\pi$
$283$	13.5584	−	23.4839i	0.805965	−	1.39597i	0.915638	−	0.402004i	$-0.131686\pi$
$284$	−3.55842	+	6.16337i	−0.211153	+	0.365729i
$285$		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
$290$	38.2337			2.24516
$291$		0			0
$292$	−12.1168			−0.709085
$293$	5.18614	+	8.98266i	0.302978	+	0.524773i	0.976809	−	0.214113i	$-0.0686859\pi$
$293$	5.18614	+	8.98266i	0.302978	+	0.524773i	−0.673831	+	0.738885i	$0.735353\pi$
$294$		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
$299$	1.62772	+	2.81929i	0.0941334	+	0.163044i
$300$		0			0
$301$		0			0
$302$	−4.55842	−	7.89542i	−0.262308	−	0.454330i
$303$		0			0
$304$	−5.00000			−0.286770
$305$	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
$310$	−8.74456			−0.496658
$311$	−4.11684	+	7.13058i	−0.233445	+	0.404338i	−0.958820	−	0.284016i	$-0.908333\pi$
$311$	−4.11684	+	7.13058i	−0.233445	+	0.404338i	0.725375	+	0.688354i	$0.241666\pi$
$312$		0			0
$313$	−10.0584	−	17.4217i	−0.568536	−	0.984733i	−0.996711	−	0.0810370i	$-0.974177\pi$
$313$	−10.0584	−	17.4217i	−0.568536	−	0.984733i	0.428175	−	0.903696i	$-0.359157\pi$
$314$	−9.11684			−0.514493
$315$		0			0
$316$	−5.11684			−0.287845
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	4.37228			0.244418
$321$		0			0
$322$		0			0
$323$	−6.86141			−0.381779
$324$		0			0
$325$	14.1168	+	24.4511i	0.783062	+	1.35630i
$326$	−18.2337			−1.00987
$327$		0			0
$328$	−2.31386	−	4.00772i	−0.127762	−	0.221289i
$329$		0			0
$330$		0			0
$331$	−11.1168	−	19.2549i	−0.611037	−	1.05835i	−0.991066	−	0.133373i	$-0.957419\pi$
$331$	−11.1168	−	19.2549i	−0.611037	−	1.05835i	0.380029	−	0.924975i	$-0.375914\pi$
$332$	−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	0.955135	−	0.296171i	$-0.0957097\pi$
$337$	4.05842	+	7.02939i	0.221076	+	0.382915i	−0.734059	+	0.679086i	$0.762376\pi$
$338$	−9.00000			−0.489535
$339$		0			0
$340$	6.00000			0.325396
$341$	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
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−5.05842	+	8.76144i	−0.271550	+	0.470339i	−0.969259	−	0.246043i	$-0.920870\pi$
$347$	−5.05842	+	8.76144i	−0.271550	+	0.470339i	0.697709	+	0.716382i	$0.254203\pi$
$348$		0			0
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	0.405571	+	0.914063i	$0.367073\pi$
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	−0.994388	+	0.105797i	$0.966261\pi$
$350$		0			0
$351$		0			0
$352$	−0.686141	+	1.18843i	−0.0365714	+	0.0633436i
$353$	−13.3723			−0.711735			−0.355867	−	0.934536i	$-0.615815\pi$
$353$	−13.3723			−0.711735			−0.355867	+	0.934536i	$0.615815\pi$
$354$		0			0
$355$	31.1168			1.65151
$356$	−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
$362$	0.441578	+	0.764836i	0.0232088	+	0.0401989i
$363$		0			0
$364$		0			0
$365$	26.4891	+	45.8805i	1.38650	+	2.40150i
$366$		0			0
$367$	12.2337			0.638593			0.319297	−	0.947655i	$-0.396553\pi$
$367$	12.2337			0.638593			0.319297	+	0.947655i	$0.396553\pi$
$368$	−0.813859	−	1.40965i	−0.0424254	−	0.0734829i
$369$		0			0
$370$	8.74456			0.454608
$371$		0			0
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	−0.941578	+	1.63086i	−0.0486878	+	0.0843298i
$375$		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	$0.566847\pi$
$380$	10.9307	+	18.9325i	0.560733	+	0.971218i
$381$		0			0
$382$	−9.55842	+	16.5557i	−0.489051	+	0.847062i
$383$	−32.7446			−1.67317			−0.836584	−	0.547838i	$-0.815451\pi$
$383$	−32.7446			−1.67317			−0.836584	+	0.547838i	$0.815451\pi$
$384$		0			0
$385$		0			0
$386$	−7.00000			−0.356291
$387$		0			0
$388$	−4.05842	−	7.02939i	−0.206035	−	0.356863i
$389$	−10.9783			−0.556619			−0.278310	−	0.960491i	$-0.589774\pi$
$389$	−10.9783			−0.556619			−0.278310	+	0.960491i	$0.589774\pi$
$390$		0			0
$391$	−1.11684	−	1.93443i	−0.0564812	−	0.0978284i
$392$		0			0
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	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
$401$	11.7446			0.586495			0.293248	−	0.956036i	$-0.405264\pi$
$401$	11.7446			0.586495			0.293248	+	0.956036i	$0.405264\pi$
$402$		0			0
$403$	4.00000			0.199254
$404$	−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
$409$	−11.1753	+	19.3561i	−0.552581	+	0.957099i	0.445506	+	0.895279i	$0.353024\pi$
$409$	−11.1753	+	19.3561i	−0.552581	+	0.957099i	−0.998087	+	0.0618200i	$0.980310\pi$
$410$	−10.1168	+	17.5229i	−0.499635	+	0.865394i
$411$		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
$416$	−2.00000			−0.0980581
$417$		0			0
$418$	−6.86141			−0.335602
$419$	6.30298	+	10.9171i	0.307921	+	0.533335i	0.977907	−	0.209039i	$-0.0670334\pi$
$419$	6.30298	+	10.9171i	0.307921	+	0.533335i	−0.669986	+	0.742373i	$0.733700\pi$
$420$		0			0
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	0.0604368	+	0.998172i	$0.480751\pi$
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	−0.894661	+	0.446746i	$0.852583\pi$
$422$	8.00000	−	13.8564i	0.389434	−	0.674519i
$423$		0			0
$424$	−4.37228	−	7.57301i	−0.212337	−	0.367778i
$425$	−9.68614	−	16.7769i	−0.469847	−	0.813799i
$426$		0			0
$427$		0			0
$428$	−3.68614	−	6.38458i	−0.178176	−	0.308610i
$429$		0			0
$430$	−35.4891			−1.71144
$431$	−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
$436$	14.0000			0.670478
$437$	4.06930	−	7.04823i	0.194661	−	0.337162i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	−2.74456			−0.130546
$443$	−20.0584	−	34.7422i	−0.953004	−	1.65065i	−0.738870	−	0.673848i	$-0.764640\pi$
$443$	−20.0584	−	34.7422i	−0.953004	−	1.65065i	−0.214134	−	0.976804i	$-0.568693\pi$
$444$		0			0
$445$	−32.2337	+	55.8304i	−1.52802	+	2.64661i
$446$	4.00000			0.189405
$447$		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
$452$	4.37228			0.205655
$453$		0			0
$454$	6.12772	+	10.6135i	0.287588	+	0.498117i
$455$		0			0
$456$		0			0
$457$	17.7337	+	30.7156i	0.829547	+	1.43682i	0.898394	+	0.439190i	$0.144735\pi$
$457$	17.7337	+	30.7156i	0.829547	+	1.43682i	−0.0688472	+	0.997627i	$0.521932\pi$
$458$	−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	−0.889852	−	0.456250i	$-0.849192\pi$
$461$	−1.06930	+	1.85208i	−0.0498021	+	0.0862598i	0.840050	+	0.542509i	$0.182526\pi$
$462$		0			0
$463$	11.5584	+	20.0198i	0.537165	+	0.930398i	0.999055	+	0.0434604i	$0.0138382\pi$
$463$	11.5584	+	20.0198i	0.537165	+	0.930398i	−0.461890	+	0.886937i	$0.652828\pi$
$464$	8.74456			0.405956
$465$		0			0
$466$	0.255437			0.0118329
$467$	−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
$472$	5.05842	−	8.76144i	0.232833	−	0.403278i
$473$	5.56930	−	9.64630i	0.256077	−	0.443538i
$474$		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
$479$	32.7446			1.49614			0.748069	−	0.663621i	$-0.230981\pi$
$479$	32.7446			1.49614			0.748069	+	0.663621i	$0.230981\pi$
$480$		0			0
$481$	−4.00000			−0.182384
$482$	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	$-0.462335\pi$
$488$	1.55842	+	2.69927i	0.0705464	+	0.122190i
$489$		0			0
$490$		0			0
$491$	−12.6861	−	21.9730i	−0.572518	−	0.991629i	−0.996306	−	0.0858685i	$-0.972634\pi$
$491$	−12.6861	−	21.9730i	−0.572518	−	0.991629i	0.423789	−	0.905761i	$-0.360700\pi$
$492$		0			0
$493$	12.0000			0.540453
$494$	−5.00000	−	8.66025i	−0.224961	−	0.389643i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$		0			0
$498$		0			0
$499$	18.1168			0.811021			0.405511	−	0.914090i	$-0.367094\pi$
$499$	18.1168			0.811021			0.405511	+	0.914090i	$0.367094\pi$
$500$	−19.9307	+	34.5210i	−0.891328	+	1.54383i
$501$		0			0
$502$	4.50000	+	7.79423i	0.200845	+	0.347873i
$503$	−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
$506$	−1.11684	−	1.93443i	−0.0496498	−	0.0859959i
$507$		0			0
$508$	−1.55842	+	2.69927i	−0.0691438	+	0.119761i
$509$	−28.9783			−1.28444			−0.642219	−	0.766521i	$-0.721986\pi$
$509$	−28.9783			−1.28444			−0.642219	+	0.766521i	$0.721986\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.43070	+	5.94215i	0.151322	+	0.262097i
$515$	43.7228			1.92666
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	4.37228	+	7.57301i	0.191737	+	0.332099i
$521$	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
$527$	−2.74456			−0.119555
$528$		0			0
$529$	−20.3505			−0.884806
$530$	−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
$535$	−16.1168	+	27.9152i	−0.696792	+	1.20688i
$536$	1.05842	−	1.83324i	0.0457169	−	0.0791839i
$537$		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	$0.123883\pi$
$542$	−16.2337			−0.697297
$543$		0			0
$544$	1.37228			0.0588361
$545$	−30.6060	−	53.0111i	−1.31102	−	2.27075i
$546$		0			0
$547$	−9.05842	+	15.6896i	−0.387310	+	0.670841i	−0.992087	−	0.125554i	$-0.959929\pi$
$547$	−9.05842	+	15.6896i	−0.387310	+	0.670841i	0.604777	+	0.796395i	$0.293262\pi$
$548$	5.31386	−	9.20387i	0.226997	−	0.393170i
$549$		0			0
$550$	−9.68614	−	16.7769i	−0.413018	−	0.715369i
$551$	21.8614	+	37.8651i	0.931327	+	1.61311i
$552$		0			0
$553$		0			0
$554$	6.11684	+	10.5947i	0.259880	+	0.450125i
$555$		0			0
$556$	−13.2337			−0.561233
$557$	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
$562$	−16.3723			−0.690623
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	−0.895902	−	0.444252i	$-0.853470\pi$
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	0.832684	+	0.553748i	$0.186803\pi$
$564$		0			0
$565$	−9.55842	−	16.5557i	−0.402126	−	0.696502i
$566$	−27.1168			−1.13981
$567$		0			0
$568$	7.11684			0.298616
$569$	8.05842	+	13.9576i	0.337827	+	0.585133i	0.984024	−	0.178038i	$-0.0569749\pi$
$569$	8.05842	+	13.9576i	0.337827	+	0.585133i	−0.646197	+	0.763171i	$0.723642\pi$
$570$		0			0
$571$	11.1753	−	19.3561i	0.467670	−	0.810029i	−0.531647	−	0.846966i	$-0.678427\pi$
$571$	11.1753	−	19.3561i	0.467670	−	0.810029i	0.999318	+	0.0369371i	$0.0117601\pi$
$572$	−2.74456			−0.114756
$573$		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	$0.767380\pi$
$578$	−15.1168			−0.628778
$579$		0			0
$580$	−19.1168	−	33.1113i	−0.793784	−	1.37487i
$581$		0			0
$582$		0			0
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$	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	−0.975911	−	0.218170i	$-0.929991\pi$
$587$	−7.24456	+	12.5480i	−0.299015	+	0.517909i	0.676896	+	0.736079i	$0.263325\pi$
$588$		0			0
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	−44.2337			−1.82107
$591$		0			0
$592$	2.00000			0.0821995
$593$	−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
$598$	1.62772	−	2.81929i	0.0665624	−	0.115289i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	12.0584	−	20.8858i	0.491873	−	0.851950i	−0.508083	−	0.861308i	$-0.669646\pi$
$601$	12.0584	−	20.8858i	0.491873	−	0.851950i	0.999956	+	0.00935863i	$0.00297899\pi$
$602$		0			0
$603$		0			0
$604$	−4.55842	+	7.89542i	−0.185480	+	0.321260i
$605$	−39.8614			−1.62060
$606$		0			0
$607$	−22.2337			−0.902438			−0.451219	−	0.892413i	$-0.649011\pi$
$607$	−22.2337			−0.902438			−0.451219	+	0.892413i	$0.649011\pi$
$608$	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	$0.572045\pi$
$614$	−6.50000	−	11.2583i	−0.262319	−	0.454349i
$615$		0			0
$616$		0			0
$617$	9.43070	+	16.3345i	0.379666	+	0.657600i	0.991014	−	0.133762i	$-0.0427056\pi$
$617$	9.43070	+	16.3345i	0.379666	+	0.657600i	−0.611348	+	0.791362i	$0.709372\pi$
$618$		0			0
$619$	−45.4674			−1.82749			−0.913744	−	0.406290i	$-0.866822\pi$
$619$	−45.4674			−1.82749			−0.913744	+	0.406290i	$0.866822\pi$
$620$	4.37228	+	7.57301i	0.175595	+	0.304140i
$621$		0			0
$622$	8.23369			0.330141
$623$		0			0
$624$		0			0
$625$	103.701			4.14804
$626$	−10.0584	+	17.4217i	−0.402015	+	0.696311i
$627$		0			0
$628$	4.55842	+	7.89542i	0.181901	+	0.315061i
$629$	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	$0.766812\pi$
$632$	2.55842	+	4.43132i	0.101769	+	0.176268i
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	13.6277			0.540800
$636$		0			0
$637$		0			0
$638$	12.0000			0.475085
$639$		0			0
$640$	−2.18614	−	3.78651i	−0.0864148	−	0.149675i
$641$	−34.2119			−1.35129			−0.675645	−	0.737227i	$-0.736135\pi$
$641$	−34.2119			−1.35129			−0.675645	+	0.737227i	$0.736135\pi$
$642$		0			0
$643$	13.1753	+	22.8202i	0.519582	+	0.899942i	0.999741	+	0.0227606i	$0.00724556\pi$
$643$	13.1753	+	22.8202i	0.519582	+	0.899942i	−0.480159	+	0.877181i	$0.659421\pi$
$644$		0			0
$645$		0			0
$646$	3.43070	+	5.94215i	0.134979	+	0.233791i
$647$	−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
$653$	26.7446			1.04660			0.523298	−	0.852150i	$-0.324702\pi$
$653$	26.7446			1.04660			0.523298	+	0.852150i	$0.324702\pi$
$654$		0			0
$655$	−7.11684			−0.278078
$656$	−2.31386	+	4.00772i	−0.0903410	+	0.156475i
$657$		0			0
$658$		0			0
$659$	−10.3723	+	17.9653i	−0.404047	+	0.699829i	−0.994210	−	0.107454i	$-0.965730\pi$
$659$	−10.3723	+	17.9653i	−0.404047	+	0.699829i	0.590163	+	0.807284i	$0.299063\pi$
$660$		0			0
$661$	13.5584	−	23.4839i	0.527361	−	0.913417i	−0.472130	−	0.881529i	$-0.656515\pi$
$661$	13.5584	−	23.4839i	0.527361	−	0.913417i	0.999491	−	0.0318879i	$-0.0101520\pi$
$662$	−11.1168	+	19.2549i	−0.432068	+	0.748364i
$663$		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
$668$	−5.48913			−0.212381
$669$		0			0
$670$	−9.25544			−0.357569
$671$	2.13859	+	3.70415i	0.0825595	+	0.142997i
$672$		0			0
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	−0.836903	−	0.547351i	$-0.815636\pi$
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	0.892472	+	0.451103i	$0.148969\pi$
$674$	4.05842	−	7.02939i	0.156325	−	0.270762i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−17.2337	−	29.8496i	−0.662344	−	1.14721i	−0.979998	−	0.199007i	$-0.936228\pi$
$677$	−17.2337	−	29.8496i	−0.662344	−	1.14721i	0.317654	−	0.948207i	$-0.397105\pi$
$678$		0			0
$679$		0			0
$680$	−3.00000	−	5.19615i	−0.115045	−	0.199263i
$681$		0			0
$682$	−2.74456			−0.105095
$683$	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
$688$	−8.11684			−0.309452
$689$	8.74456	−	15.1460i	0.333141	−	0.577018i
$690$		0			0
$691$	−11.5584	−	20.0198i	−0.439703	−	0.761588i	0.557963	−	0.829866i	$-0.311583\pi$
$691$	−11.5584	−	20.0198i	−0.439703	−	0.761588i	−0.997666	+	0.0682775i	$0.978250\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	10.1168			0.384030
$695$	28.9307	+	50.1094i	1.09740	+	1.90076i
$696$		0			0
$697$	−3.17527	+	5.49972i	−0.120272	+	0.208317i
$698$	22.0000			0.832712
$699$		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
$704$	1.37228			0.0517198
$705$		0			0
$706$	6.68614	+	11.5807i	0.251636	+	0.435847i
$707$		0			0
$708$		0			0
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$	−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
$716$	−3.25544			−0.121661
$717$		0			0
$718$	−21.8614			−0.815860
$719$	−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
$724$	0.441578	−	0.764836i	0.0164111	−	0.0284249i
$725$	−61.7228	+	106.907i	−2.29233	+	3.97043i
$726$		0			0
$727$	−18.1168	+	31.3793i	−0.671917	+	1.16379i	0.305443	+	0.952210i	$0.401195\pi$
$727$	−18.1168	+	31.3793i	−0.671917	+	1.16379i	−0.977360	+	0.211583i	$0.932138\pi$
$728$		0			0
$729$		0			0
$730$	26.4891	−	45.8805i	0.980407	−	1.69811i
$731$	−11.1386			−0.411976
$732$		0			0
$733$	41.1168			1.51869			0.759343	−	0.650691i	$-0.225521\pi$
$733$	41.1168			1.51869			0.759343	+	0.650691i	$0.225521\pi$
$734$	−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	$0.785634\pi$
$740$	−4.37228	−	7.57301i	−0.160728	−	0.278390i
$741$		0			0
$742$		0			0
$743$	−6.86141	−	11.8843i	−0.251721	−	0.435993i	0.712279	−	0.701896i	$-0.247663\pi$
$743$	−6.86141	−	11.8843i	−0.251721	−	0.435993i	−0.964000	+	0.265904i	$0.914330\pi$
$744$		0			0
$745$	−14.2337			−0.521482
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$		0			0
$748$	1.88316			0.0688550
$749$		0			0
$750$		0			0
$751$	−17.1168			−0.624603			−0.312301	−	0.949983i	$-0.601100\pi$
$751$	−17.1168			−0.624603			−0.312301	+	0.949983i	$0.601100\pi$
$752$		0			0
$753$		0			0
$754$	8.74456	+	15.1460i	0.318458	+	0.551586i
$755$	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	$0.182440\pi$
$758$	4.05842	+	7.02939i	0.147409	+	0.255319i
$759$		0			0
$760$	10.9307	−	18.9325i	0.396498	−	0.686755i
$761$	35.4891			1.28648			0.643240	−	0.765665i	$-0.277590\pi$
$761$	35.4891			1.28648			0.643240	+	0.765665i	$0.277590\pi$
$762$		0			0
$763$		0			0
$764$	19.1168			0.691623
$765$		0			0
$766$	16.3723	+	28.3576i	0.591555	+	1.02460i
$767$	20.2337			0.730596
$768$		0			0
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	0.761680	−	0.647954i	$-0.224375\pi$
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	−0.941984	+	0.335657i	$0.891042\pi$
$770$		0			0
$771$		0			0
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	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
$779$	−23.1386			−0.829026
$780$		0			0
$781$	9.76631			0.349466
$782$	−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
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		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
$794$	22.0000			0.780751
$795$		0			0
$796$	10.0000			0.354441
$797$	4.06930	+	7.04823i	0.144142	+	0.249661i	0.929052	−	0.369948i	$-0.120624\pi$
$797$	4.06930	+	7.04823i	0.144142	+	0.249661i	−0.784911	+	0.619609i	$0.787291\pi$
$798$		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
$803$	8.31386	+	14.4000i	0.293390	+	0.508166i
$804$		0			0
$805$		0			0
$806$	−2.00000	−	3.46410i	−0.0704470	−	0.122018i
$807$		0			0
$808$	1.62772			0.0572629
$809$	−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
$814$	2.74456			0.0961969
$815$	39.8614	−	69.0420i	1.39628	−	2.41844i
$816$		0			0
$817$	−20.2921	−	35.1470i	−0.709931	−	1.22964i
$818$	22.3505			0.781468
$819$		0			0
$820$	20.2337			0.706591
$821$	−1.88316	−	3.26172i	−0.0657226	−	0.113835i	0.831292	−	0.555836i	$-0.187602\pi$
$821$	−1.88316	−	3.26172i	−0.0657226	−	0.113835i	−0.897014	+	0.442002i	$0.854269\pi$
$822$		0			0
$823$	6.11684	−	10.5947i	0.213220	−	0.369307i	−0.739501	−	0.673156i	$-0.764938\pi$
$823$	6.11684	−	10.5947i	0.213220	−	0.369307i	0.952720	+	0.303848i	$0.0982716\pi$
$824$	10.0000			0.348367
$825$		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	$0.910173\pi$
$830$	76.4674			2.65422
$831$		0			0
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$		0			0
$834$		0			0
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	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	−0.909505	−	0.415692i	$-0.863539\pi$
$839$	−2.74456	+	4.75372i	−0.0947528	+	0.164117i	0.814753	+	0.579809i	$0.196873\pi$
$840$		0			0
$841$	−23.7337	−	41.1080i	−0.818403	−	1.41752i
$842$	34.2337			1.17977
$843$		0			0
$844$	−16.0000			−0.550743
$845$	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
$850$	−9.68614	+	16.7769i	−0.332232	+	0.575443i
$851$	−1.62772	+	2.81929i	−0.0557975	+	0.0966441i
$852$		0			0
$853$	−17.5584	+	30.4121i	−0.601189	+	1.04129i	0.391452	+	0.920198i	$0.371973\pi$
$853$	−17.5584	+	30.4121i	−0.601189	+	1.04129i	−0.992641	+	0.121091i	$0.961361\pi$
$854$		0			0
$855$		0			0
$856$	−3.68614	+	6.38458i	−0.125990	+	0.218221i
$857$	−39.9565			−1.36489			−0.682444	−	0.730938i	$-0.739083\pi$
$857$	−39.9565			−1.36489			−0.682444	+	0.730938i	$0.739083\pi$
$858$		0			0
$859$	−33.8832			−1.15608			−0.578039	−	0.816009i	$-0.696182\pi$
$859$	−33.8832			−1.15608			−0.578039	+	0.816009i	$0.696182\pi$
$860$	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
$866$	−10.0584	−	17.4217i	−0.341799	−	0.592013i
$867$		0			0
$868$		0			0
$869$	3.51087	+	6.08101i	0.119098	+	0.206284i
$870$		0			0
$871$	4.23369			0.143453
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$		0			0
$874$	−8.13859			−0.275292
$875$		0			0
$876$		0			0
$877$	−58.7011			−1.98219			−0.991097	−	0.133141i	$-0.957494\pi$
$877$	−58.7011			−1.98219			−0.991097	+	0.133141i	$0.957494\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$		0			0
$880$	−3.00000	−	5.19615i	−0.101130	−	0.175162i
$881$	−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	$0.737565\pi$
$884$	1.37228	+	2.37686i	0.0461548	+	0.0799425i
$885$		0			0
$886$	−20.0584	+	34.7422i	−0.673876	+	1.16719i
$887$	25.7228			0.863688			0.431844	−	0.901948i	$-0.357863\pi$
$887$	25.7228			0.863688			0.431844	+	0.901948i	$0.357863\pi$
$888$		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
$898$	16.5000	+	28.5788i	0.550612	+	0.953688i
$899$	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
$905$	−3.86141			−0.128357
$906$		0			0
$907$	−26.1168			−0.867196			−0.433598	−	0.901107i	$-0.642756\pi$
$907$	−26.1168			−0.867196			−0.433598	+	0.901107i	$0.642756\pi$
$908$	6.12772	−	10.6135i	0.203355	−	0.352222i
$909$		0			0
$910$		0			0
$911$	−18.8139	+	32.5866i	−0.623331	+	1.07964i	0.365530	+	0.930800i	$0.380888\pi$
$911$	−18.8139	+	32.5866i	−0.623331	+	1.07964i	−0.988861	+	0.148841i	$0.952446\pi$
$912$		0			0
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$	17.7337	−	30.7156i	0.586578	−	1.01598i
$915$		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	$-0.116654\pi$
$920$	7.11684			0.234635
$921$		0			0
$922$	2.13859			0.0704308
$923$	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
$929$	−22.1168	−	38.3075i	−0.725630	−	1.25683i	−0.958714	−	0.284372i	$-0.908215\pi$
$929$	−22.1168	−	38.3075i	−0.725630	−	1.25683i	0.233084	−	0.972457i	$-0.425118\pi$
$930$		0			0
$931$		0			0
$932$	−0.127719	−	0.221215i	−0.00418356	−	0.00724615i
$933$		0			0
$934$	33.0951			1.08290
$935$	−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
$941$	−9.55842	+	16.5557i	−0.311596	+	0.539699i	−0.978708	−	0.205258i	$-0.934197\pi$
$941$	−9.55842	+	16.5557i	−0.311596	+	0.539699i	0.667112	+	0.744957i	$0.267530\pi$
$942$		0			0
$943$	−3.76631	−	6.52344i	−0.122648	−	0.212433i
$944$	−10.1168			−0.329275
$945$		0			0
$946$	−11.1386			−0.362147
$947$	17.0584	+	29.5461i	0.554324	+	0.960118i	0.997956	+	0.0639085i	$0.0203566\pi$
$947$	17.0584	+	29.5461i	0.554324	+	0.960118i	−0.443632	+	0.896209i	$0.646310\pi$
$948$		0			0
$949$	−12.1168	+	20.9870i	−0.393329	+	0.681267i
$950$	−70.5842			−2.29005
$951$		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
$956$	−9.86141			−0.318941
$957$		0			0
$958$	−16.3723	−	28.3576i	−0.528964	−	0.916193i
$959$		0			0
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	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	0.503424	−	0.864039i	$-0.332073\pi$
$967$	−15.4416	−	26.7456i	−0.496568	−	0.860080i	−0.999992	+	0.00395879i	$0.998740\pi$
$968$	−9.11684			−0.293026
$969$		0			0
$970$	35.4891			1.13949
$971$	−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
$976$	1.55842	−	2.69927i	0.0498839	−	0.0864014i
$977$	20.0584	−	34.7422i	0.641726	−	1.11150i	−0.343322	−	0.939218i	$-0.611552\pi$
$977$	20.0584	−	34.7422i	0.641726	−	1.11150i	0.985047	−	0.172284i	$-0.0551146\pi$
$978$		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
$983$	−39.2554			−1.25205			−0.626027	−	0.779801i	$-0.715320\pi$
$983$	−39.2554			−1.25205			−0.626027	+	0.779801i	$0.715320\pi$
$984$		0			0
$985$	26.2337			0.835875
$986$	−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	$-0.446315\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$		0			0
$994$		0			0
$995$	−21.8614	−	37.8651i	−0.693053	−	1.20040i
$996$		0			0
$997$	5.11684			0.162052			0.0810260	−	0.996712i	$-0.474180\pi$
$997$	5.11684			0.162052			0.0810260	+	0.996712i	$0.474180\pi$
$998$	−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.h.l.667.2		4
3.2	odd	2		882.2.h.n.79.1		4
7.2	even	3		2646.2.f.j.883.1		4
7.3	odd	6		2646.2.e.n.2125.2		4
7.4	even	3		2646.2.e.m.2125.1		4
7.5	odd	6		378.2.f.c.127.2		4
7.6	odd	2		2646.2.h.k.667.1		4
9.4	even	3		2646.2.e.m.1549.1		4
9.5	odd	6		882.2.e.k.373.1		4
21.2	odd	6		882.2.f.k.295.2		4
21.5	even	6		126.2.f.d.43.1	✓	4
21.11	odd	6		882.2.e.k.655.2		4
21.17	even	6		882.2.e.l.655.1		4
21.20	even	2		882.2.h.m.79.2		4
28.19	even	6		3024.2.r.f.2017.2		4
63.2	odd	6		7938.2.a.bh.1.1		2
63.4	even	3	inner	2646.2.h.l.361.2		4
63.5	even	6		126.2.f.d.85.1	yes	4
63.13	odd	6		2646.2.e.n.1549.2		4
63.16	even	3		7938.2.a.bs.1.2		2
63.23	odd	6		882.2.f.k.589.2		4
63.31	odd	6		2646.2.h.k.361.1		4
63.32	odd	6		882.2.h.n.67.1		4
63.40	odd	6		378.2.f.c.253.2		4
63.41	even	6		882.2.e.l.373.2		4
63.47	even	6		1134.2.a.k.1.2		2
63.58	even	3		2646.2.f.j.1765.1		4
63.59	even	6		882.2.h.m.67.2		4
63.61	odd	6		1134.2.a.n.1.1		2
84.47	odd	6		1008.2.r.f.673.2		4
252.47	odd	6		9072.2.a.bm.1.2		2
252.103	even	6		3024.2.r.f.1009.2		4
252.131	odd	6		1008.2.r.f.337.2		4
252.187	even	6		9072.2.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.1	✓	4	21.5	even	6
126.2.f.d.85.1	yes	4	63.5	even	6
378.2.f.c.127.2		4	7.5	odd	6
378.2.f.c.253.2		4	63.40	odd	6
882.2.e.k.373.1		4	9.5	odd	6
882.2.e.k.655.2		4	21.11	odd	6
882.2.e.l.373.2		4	63.41	even	6
882.2.e.l.655.1		4	21.17	even	6
882.2.f.k.295.2		4	21.2	odd	6
882.2.f.k.589.2		4	63.23	odd	6
882.2.h.m.67.2		4	63.59	even	6
882.2.h.m.79.2		4	21.20	even	2
882.2.h.n.67.1		4	63.32	odd	6
882.2.h.n.79.1		4	3.2	odd	2
1008.2.r.f.337.2		4	252.131	odd	6
1008.2.r.f.673.2		4	84.47	odd	6
1134.2.a.k.1.2		2	63.47	even	6
1134.2.a.n.1.1		2	63.61	odd	6
2646.2.e.m.1549.1		4	9.4	even	3
2646.2.e.m.2125.1		4	7.4	even	3
2646.2.e.n.1549.2		4	63.13	odd	6
2646.2.e.n.2125.2		4	7.3	odd	6
2646.2.f.j.883.1		4	7.2	even	3
2646.2.f.j.1765.1		4	63.58	even	3
2646.2.h.k.361.1		4	63.31	odd	6
2646.2.h.k.667.1		4	7.6	odd	2
2646.2.h.l.361.2		4	63.4	even	3	inner
2646.2.h.l.667.2		4	1.1	even	1	trivial
3024.2.r.f.1009.2		4	252.103	even	6
3024.2.r.f.2017.2		4	28.19	even	6
7938.2.a.bh.1.1		2	63.2	odd	6
7938.2.a.bs.1.2		2	63.16	even	3
9072.2.a.bb.1.1		2	252.187	even	6
9072.2.a.bm.1.2		2	252.47	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.37228 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.37228 q^{5} +1.00000 q^{8} +(-2.18614 - 3.78651i) q^{10} +1.37228 q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.686141 - 1.18843i) q^{17} +(2.50000 - 4.33013i) q^{19} +(-2.18614 + 3.78651i) q^{20} +(-0.686141 - 1.18843i) q^{22} +1.62772 q^{23} +14.1168 q^{25} +(1.00000 - 1.73205i) q^{26} +(-4.37228 + 7.57301i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.686141 + 1.18843i) q^{34} +(-1.00000 + 1.73205i) q^{37} -5.00000 q^{38} +4.37228 q^{40} +(-2.31386 - 4.00772i) q^{41} +(4.05842 - 7.02939i) q^{43} +(-0.686141 + 1.18843i) q^{44} +(-0.813859 - 1.40965i) q^{46} +(-7.05842 - 12.2255i) q^{50} -2.00000 q^{52} +(-4.37228 - 7.57301i) q^{53} +6.00000 q^{55} +8.74456 q^{58} +(5.05842 - 8.76144i) q^{59} +(1.55842 + 2.69927i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(4.37228 + 7.57301i) q^{65} +(1.05842 - 1.83324i) q^{67} +1.37228 q^{68} +7.11684 q^{71} +(6.05842 + 10.4935i) q^{73} +2.00000 q^{74} +(2.50000 + 4.33013i) q^{76} +(2.55842 + 4.43132i) q^{79} +(-2.18614 - 3.78651i) q^{80} +(-2.31386 + 4.00772i) q^{82} +(-8.74456 + 15.1460i) q^{83} +(-3.00000 - 5.19615i) q^{85} -8.11684 q^{86} +1.37228 q^{88} +(-7.37228 + 12.7692i) q^{89} +(-0.813859 + 1.40965i) q^{92} +(10.9307 - 18.9325i) q^{95} +(-4.05842 + 7.02939i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 6 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 6 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 6 q^{5} + 4 q^{8} - 3 q^{10} - 6 q^{11} + 4 q^{13} - 2 q^{16} + 3 q^{17} + 10 q^{19} - 3 q^{20} + 3 q^{22} + 18 q^{23} + 22 q^{25} + 4 q^{26} - 6 q^{29} + 4 q^{31} - 2 q^{32} + 3 q^{34} - 4 q^{37} - 20 q^{38} + 6 q^{40} - 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} - 8 q^{52} - 6 q^{53} + 24 q^{55} + 12 q^{58} + 3 q^{59} - 11 q^{61} - 8 q^{62} + 4 q^{64} + 6 q^{65} - 13 q^{67} - 6 q^{68} - 6 q^{71} + 7 q^{73} + 8 q^{74} + 10 q^{76} - 7 q^{79} - 3 q^{80} - 15 q^{82} - 12 q^{83} - 12 q^{85} + 2 q^{86} - 6 q^{88} - 18 q^{89} - 9 q^{92} + 15 q^{95} + q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 6 * q^5 + 4 * q^8 - 3 * q^10 - 6 * q^11 + 4 * q^13 - 2 * q^16 + 3 * q^17 + 10 * q^19 - 3 * q^20 + 3 * q^22 + 18 * q^23 + 22 * q^25 + 4 * q^26 - 6 * q^29 + 4 * q^31 - 2 * q^32 + 3 * q^34 - 4 * q^37 - 20 * q^38 + 6 * q^40 - 15 * q^41 - q^43 + 3 * q^44 - 9 * q^46 - 11 * q^50 - 8 * q^52 - 6 * q^53 + 24 * q^55 + 12 * q^58 + 3 * q^59 - 11 * q^61 - 8 * q^62 + 4 * q^64 + 6 * q^65 - 13 * q^67 - 6 * q^68 - 6 * q^71 + 7 * q^73 + 8 * q^74 + 10 * q^76 - 7 * q^79 - 3 * q^80 - 15 * q^82 - 12 * q^83 - 12 * q^85 + 2 * q^86 - 6 * q^88 - 18 * q^89 - 9 * q^92 + 15 * q^95 + q^97

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