LMFDB - Embedded newform 135.3.g.a.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(28,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("135.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.g (of order $4$, degree $2$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 217x^{12} + 9264x^{8} + 59497x^{4} + 28561 $ x^16 + 217x^12 + 9264x^8 + 59497*x^4 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			82.2
Root			$-1.85358 - 1.85358i$ of defining polynomial
Character	$\chi$	$=$	135.82
Dual form			135.3.g.a.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85358 - 1.85358i) q^{2} +2.87153i q^{4} +(-4.93699 - 0.791263i) q^{5} +(1.80972 + 1.80972i) q^{7} +(-2.09171 + 2.09171i) q^{8} +O(q^{10})$	\(q+(-1.85358 - 1.85358i) q^{2} +2.87153i q^{4} +(-4.93699 - 0.791263i) q^{5} +(1.80972 + 1.80972i) q^{7} +(-2.09171 + 2.09171i) q^{8} +(7.68445 + 10.6178i) q^{10} +2.05878 q^{11} +(-16.3641 + 16.3641i) q^{13} -6.70894i q^{14} +19.2404 q^{16} +(14.0526 + 14.0526i) q^{17} -7.13001i q^{19} +(2.27214 - 14.1767i) q^{20} +(-3.81612 - 3.81612i) q^{22} +(-12.5675 + 12.5675i) q^{23} +(23.7478 + 7.81292i) q^{25} +60.6642 q^{26} +(-5.19667 + 5.19667i) q^{28} +36.5390i q^{29} -22.1056 q^{31} +(-27.2969 - 27.2969i) q^{32} -52.0955i q^{34} +(-7.50262 - 10.3666i) q^{35} +(-39.3412 - 39.3412i) q^{37} +(-13.2161 + 13.2161i) q^{38} +(11.9818 - 8.67166i) q^{40} -14.6864 q^{41} +(-46.9899 + 46.9899i) q^{43} +5.91185i q^{44} +46.5899 q^{46} +(-56.2870 - 56.2870i) q^{47} -42.4498i q^{49} +(-29.5366 - 58.5004i) q^{50} +(-46.9899 - 46.9899i) q^{52} +(-21.4083 + 21.4083i) q^{53} +(-10.1642 - 1.62904i) q^{55} -7.57082 q^{56} +(67.7281 - 67.7281i) q^{58} +36.9457i q^{59} -46.3359 q^{61} +(40.9745 + 40.9745i) q^{62} +24.2323i q^{64} +(93.7375 - 67.8409i) q^{65} +(76.9734 + 76.9734i) q^{67} +(-40.3526 + 40.3526i) q^{68} +(-5.30853 + 33.1220i) q^{70} +102.118 q^{71} +(-10.4292 + 10.4292i) q^{73} +145.844i q^{74} +20.4741 q^{76} +(3.72582 + 3.72582i) q^{77} +73.5321i q^{79} +(-94.9899 - 15.2242i) q^{80} +(27.2224 + 27.2224i) q^{82} +(56.6893 - 56.6893i) q^{83} +(-58.2585 - 80.4972i) q^{85} +174.199 q^{86} +(-4.30637 + 4.30637i) q^{88} -73.0044i q^{89} -59.2288 q^{91} +(-36.0881 - 36.0881i) q^{92} +208.665i q^{94} +(-5.64172 + 35.2008i) q^{95} +(78.3975 + 78.3975i) q^{97} +(-78.6842 + 78.6842i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 32 q^{10} + 28 q^{13} - 20 q^{16} + 176 q^{22} + 64 q^{25} + 80 q^{28} - 208 q^{31} - 176 q^{37} - 252 q^{40} - 188 q^{43} + 188 q^{46} - 188 q^{52} - 136 q^{55} + 504 q^{58} + 296 q^{61} + 304 q^{67} + 684 q^{70} - 56 q^{73} - 732 q^{76} - 76 q^{82} - 788 q^{85} - 1128 q^{88} + 200 q^{91} - 284 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 32 * q^10 + 28 * q^13 - 20 * q^16 + 176 * q^22 + 64 * q^25 + 80 * q^28 - 208 * q^31 - 176 * q^37 - 252 * q^40 - 188 * q^43 + 188 * q^46 - 188 * q^52 - 136 * q^55 + 504 * q^58 + 296 * q^61 + 304 * q^67 + 684 * q^70 - 56 * q^73 - 732 * q^76 - 76 * q^82 - 788 * q^85 - 1128 * q^88 + 200 * q^91 - 284 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.85358	−	1.85358i	−0.926791	−	0.926791i	0.0707062	−	0.997497i	$-0.477475\pi$
$2$	−1.85358	−	1.85358i	−0.926791	−	0.926791i	−0.997497	+	0.0707062i	$0.977475\pi$
$3$		0			0
$3$		0			0
$4$			2.87153i			0.717883i
$5$	−4.93699	−	0.791263i	−0.987399	−	0.158253i
$5$	−4.93699	−	0.791263i	−0.987399	−	0.158253i
$6$		0			0
$7$	1.80972	+	1.80972i	0.258532	+	0.258532i	0.824457	−	0.565925i	$-0.191481\pi$
$7$	1.80972	+	1.80972i	0.258532	+	0.258532i	−0.565925	+	0.824457i	$0.691481\pi$
$8$	−2.09171	+	2.09171i	−0.261464	+	0.261464i
$9$		0			0
$10$	7.68445	+	10.6178i	0.768445	+	1.06178i
$11$	2.05878			0.187162			0.0935809	−	0.995612i	$-0.470169\pi$
$11$	2.05878			0.187162			0.0935809	+	0.995612i	$0.470169\pi$
$12$		0			0
$13$	−16.3641	+	16.3641i	−1.25877	+	1.25877i	−0.307094	+	0.951679i	$0.599357\pi$
$13$	−16.3641	+	16.3641i	−1.25877	+	1.25877i	−0.951679	+	0.307094i	$0.900643\pi$
$14$		−	6.70894i		−	0.479210i
$15$		0			0
$16$	19.2404			1.20253
$17$	14.0526	+	14.0526i	0.826626	+	0.826626i	0.987048	−	0.160422i	$-0.0512856\pi$
$17$	14.0526	+	14.0526i	0.826626	+	0.826626i	−0.160422	+	0.987048i	$0.551286\pi$
$18$		0			0
$19$		−	7.13001i		−	0.375264i	−0.982239	−	0.187632i	$-0.939919\pi$
$19$		−	7.13001i		−	0.375264i	0.982239	−	0.187632i	$-0.0600812\pi$
$20$	2.27214	−	14.1767i	0.113607	−	0.708837i
$21$		0			0
$22$	−3.81612	−	3.81612i	−0.173460	−	0.173460i
$23$	−12.5675	+	12.5675i	−0.546415	+	0.546415i	−0.925402	−	0.378987i	$-0.876272\pi$
$23$	−12.5675	+	12.5675i	−0.546415	+	0.546415i	0.378987	+	0.925402i	$0.376272\pi$
$24$		0			0
$25$	23.7478	+	7.81292i	0.949912	+	0.312517i
$26$	60.6642			2.33324
$27$		0			0
$28$	−5.19667	+	5.19667i	−0.185595	+	0.185595i
$29$			36.5390i			1.25997i	0.776609	+	0.629983i	$0.216938\pi$
$29$			36.5390i			1.25997i	−0.776609	+	0.629983i	$0.783062\pi$
$30$		0			0
$31$	−22.1056			−0.713083			−0.356541	−	0.934280i	$-0.616044\pi$
$31$	−22.1056			−0.713083			−0.356541	+	0.934280i	$0.616044\pi$
$32$	−27.2969	−	27.2969i	−0.853028	−	0.853028i
$33$		0			0
$34$		−	52.0955i		−	1.53222i
$35$	−7.50262	−	10.3666i	−0.214361	−	0.296187i
$36$		0			0
$37$	−39.3412	−	39.3412i	−1.06327	−	1.06327i	−0.997858	−	0.0654164i	$-0.979162\pi$
$37$	−39.3412	−	39.3412i	−1.06327	−	1.06327i	−0.0654164	−	0.997858i	$-0.520838\pi$
$38$	−13.2161	+	13.2161i	−0.347791	+	0.347791i
$39$		0			0
$40$	11.9818	−	8.67166i	0.299546	−	0.216792i
$41$	−14.6864			−0.358204			−0.179102	−	0.983831i	$-0.557319\pi$
$41$	−14.6864			−0.358204			−0.179102	+	0.983831i	$0.557319\pi$
$42$		0			0
$43$	−46.9899	+	46.9899i	−1.09279	+	1.09279i	−0.0975584	+	0.995230i	$0.531103\pi$
$43$	−46.9899	+	46.9899i	−1.09279	+	1.09279i	−0.995230	+	0.0975584i	$0.968897\pi$
$44$			5.91185i			0.134360i
$45$		0			0
$46$	46.5899			1.01282
$47$	−56.2870	−	56.2870i	−1.19760	−	1.19760i	−0.974884	−	0.222712i	$-0.928509\pi$
$47$	−56.2870	−	56.2870i	−1.19760	−	1.19760i	−0.222712	−	0.974884i	$-0.571491\pi$
$48$		0			0
$49$		−	42.4498i		−	0.866323i
$50$	−29.5366	−	58.5004i	−0.590732	−	1.17001i
$51$		0			0
$52$	−46.9899	−	46.9899i	−0.903652	−	0.903652i
$53$	−21.4083	+	21.4083i	−0.403930	+	0.403930i	−0.879615	−	0.475685i	$-0.842200\pi$
$53$	−21.4083	+	21.4083i	−0.403930	+	0.403930i	0.475685	+	0.879615i	$0.342200\pi$
$54$		0			0
$55$	−10.1642	−	1.62904i	−0.184803	−	0.0296188i
$56$	−7.57082			−0.135193
$57$		0			0
$58$	67.7281	−	67.7281i	1.16773	−	1.16773i
$59$			36.9457i			0.626197i	0.949721	+	0.313099i	$0.101367\pi$
$59$			36.9457i			0.626197i	−0.949721	+	0.313099i	$0.898633\pi$
$60$		0			0
$61$	−46.3359			−0.759605			−0.379802	−	0.925068i	$-0.624008\pi$
$61$	−46.3359			−0.759605			−0.379802	+	0.925068i	$0.624008\pi$
$62$	40.9745	+	40.9745i	0.660879	+	0.660879i
$63$		0			0
$64$			24.2323i			0.378629i
$65$	93.7375	−	67.8409i	1.44212	−	1.04371i
$66$		0			0
$67$	76.9734	+	76.9734i	1.14886	+	1.14886i	0.986778	+	0.162079i	$0.0518198\pi$
$67$	76.9734	+	76.9734i	1.14886	+	1.14886i	0.162079	+	0.986778i	$0.448180\pi$
$68$	−40.3526	+	40.3526i	−0.593421	+	0.593421i
$69$		0			0
$70$	−5.30853	+	33.1220i	−0.0758362	+	0.473171i
$71$	102.118			1.43828			0.719140	−	0.694865i	$-0.244536\pi$
$71$	102.118			1.43828			0.719140	+	0.694865i	$0.244536\pi$
$72$		0			0
$73$	−10.4292	+	10.4292i	−0.142865	+	0.142865i	−0.774922	−	0.632057i	$-0.782211\pi$
$73$	−10.4292	+	10.4292i	−0.142865	+	0.142865i	0.632057	+	0.774922i	$0.282211\pi$
$74$			145.844i			1.97087i
$75$		0			0
$76$	20.4741			0.269396
$77$	3.72582	+	3.72582i	0.0483873	+	0.0483873i
$78$		0			0
$79$			73.5321i			0.930786i	0.885104	+	0.465393i	$0.154087\pi$
$79$			73.5321i			0.930786i	−0.885104	+	0.465393i	$0.845913\pi$
$80$	−94.9899	−	15.2242i	−1.18737	−	0.190303i
$81$		0			0
$82$	27.2224	+	27.2224i	0.331980	+	0.331980i
$83$	56.6893	−	56.6893i	0.683003	−	0.683003i	−0.277673	−	0.960676i	$-0.589563\pi$
$83$	56.6893	−	56.6893i	0.683003	−	0.683003i	0.960676	+	0.277673i	$0.0895631\pi$
$84$		0			0
$85$	−58.2585	−	80.4972i	−0.685394	−	0.947025i
$86$	174.199			2.02557
$87$		0			0
$88$	−4.30637	+	4.30637i	−0.0489360	+	0.0489360i
$89$		−	73.0044i		−	0.820274i	−0.912024	−	0.410137i	$-0.865481\pi$
$89$		−	73.0044i		−	0.820274i	0.912024	−	0.410137i	$-0.134519\pi$
$90$		0			0
$91$	−59.2288			−0.650866
$92$	−36.0881	−	36.0881i	−0.392262	−	0.392262i
$93$		0			0
$94$			208.665i			2.21984i
$95$	−5.64172	+	35.2008i	−0.0593865	+	0.370535i
$96$		0			0
$97$	78.3975	+	78.3975i	0.808222	+	0.808222i	0.984365	−	0.176143i	$-0.0563621\pi$
$97$	78.3975	+	78.3975i	0.808222	+	0.808222i	−0.176143	+	0.984365i	$0.556362\pi$
$98$	−78.6842	+	78.6842i	−0.802900	+	0.802900i
$99$		0			0
$100$	−22.4350	+	68.1926i	−0.224350	+	0.681926i
$101$	−60.3120			−0.597148			−0.298574	−	0.954386i	$-0.596511\pi$
$101$	−60.3120			−0.597148			−0.298574	+	0.954386i	$0.596511\pi$
$102$		0			0
$103$	66.9105	−	66.9105i	0.649617	−	0.649617i	−0.303284	−	0.952900i	$-0.598083\pi$
$103$	66.9105	−	66.9105i	0.649617	−	0.649617i	0.952900	+	0.303284i	$0.0980830\pi$
$104$		−	68.4577i		−	0.658247i
$105$		0			0
$106$	79.3641			0.748717
$107$	−49.2226	−	49.2226i	−0.460024	−	0.460024i	0.438639	−	0.898663i	$-0.355461\pi$
$107$	−49.2226	−	49.2226i	−0.460024	−	0.460024i	−0.898663	+	0.438639i	$0.855461\pi$
$108$		0			0
$109$		−	33.0939i		−	0.303614i	−0.988410	−	0.151807i	$-0.951491\pi$
$109$		−	33.0939i		−	0.303614i	0.988410	−	0.151807i	$-0.0485092\pi$
$110$	15.8206	+	21.8597i	0.143824	+	0.198724i
$111$		0			0
$112$	34.8198	+	34.8198i	0.310891	+	0.310891i
$113$	6.79790	−	6.79790i	0.0601584	−	0.0601584i	−0.676388	−	0.736546i	$-0.736456\pi$
$113$	6.79790	−	6.79790i	0.0601584	−	0.0601584i	0.736546	+	0.676388i	$0.236456\pi$
$114$		0			0
$115$	71.9901	−	52.1016i	0.626001	−	0.453058i
$116$	−104.923			−0.904509
$117$		0			0
$118$	68.4818	−	68.4818i	0.580354	−	0.580354i
$119$			50.8628i			0.427418i
$120$		0			0
$121$	−116.761			−0.964970
$122$	85.8874	+	85.8874i	0.703995	+	0.703995i
$123$		0			0
$124$		−	63.4768i		−	0.511910i
$125$	−111.061	−	57.3631i	−0.888485	−	0.458905i
$126$		0			0
$127$	111.358	+	111.358i	0.876835	+	0.876835i	0.993206	−	0.116371i	$-0.0371260\pi$
$127$	111.358	+	111.358i	0.876835	+	0.876835i	−0.116371	+	0.993206i	$0.537126\pi$
$128$	−64.2710	+	64.2710i	−0.502117	+	0.502117i
$129$		0			0
$130$	−299.499	−	48.0013i	−2.30384	−	0.369241i
$131$	−53.1896			−0.406028			−0.203014	−	0.979176i	$-0.565074\pi$
$131$	−53.1896			−0.406028			−0.203014	+	0.979176i	$0.565074\pi$
$132$		0			0
$133$	12.9033	−	12.9033i	0.0970176	−	0.0970176i
$134$		−	285.353i		−	2.12950i
$135$		0			0
$136$	−58.7881			−0.432265
$137$	−20.0488	−	20.0488i	−0.146341	−	0.146341i	0.630140	−	0.776482i	$-0.282997\pi$
$137$	−20.0488	−	20.0488i	−0.146341	−	0.146341i	−0.776482	+	0.630140i	$0.782997\pi$
$138$		0			0
$139$			130.488i			0.938762i	0.882996	+	0.469381i	$0.155523\pi$
$139$			130.488i			0.938762i	−0.882996	+	0.469381i	$0.844477\pi$
$140$	29.7679	−	21.5440i	0.212628	−	0.153886i
$141$		0			0
$142$	−189.284	−	189.284i	−1.33299	−	1.33299i
$143$	−33.6900	+	33.6900i	−0.235594	+	0.235594i
$144$		0			0
$145$	28.9120	−	180.393i	0.199393	−	1.24409i
$146$	38.6626			0.264812
$147$		0			0
$148$	112.969	−	112.969i	0.763306	−	0.763306i
$149$			165.939i			1.11369i	0.830617	+	0.556844i	$0.187988\pi$
$149$			165.939i			1.11369i	−0.830617	+	0.556844i	$0.812012\pi$
$150$		0			0
$151$	89.5470			0.593027			0.296513	−	0.955029i	$-0.404176\pi$
$151$	89.5470			0.593027			0.296513	+	0.955029i	$0.404176\pi$
$152$	14.9139	+	14.9139i	0.0981179	+	0.0981179i
$153$		0			0
$154$		−	13.8122i		−	0.0896897i
$155$	109.135	+	17.4913i	0.704097	+	0.112847i
$156$		0			0
$157$	−58.5049	−	58.5049i	−0.372643	−	0.372643i	0.495796	−	0.868439i	$-0.334876\pi$
$157$	−58.5049	−	58.5049i	−0.372643	−	0.372643i	−0.868439	+	0.495796i	$0.834876\pi$
$158$	136.298	−	136.298i	0.862644	−	0.862644i
$159$		0			0
$160$	113.166	+	156.364i	0.707284	+	0.977272i
$161$	−45.4875			−0.282531
$162$		0			0
$163$	−32.4956	+	32.4956i	−0.199360	+	0.199360i	−0.799725	−	0.600366i	$-0.795022\pi$
$163$	−32.4956	+	32.4956i	−0.199360	+	0.199360i	0.600366	+	0.799725i	$0.295022\pi$
$164$		−	42.1724i		−	0.257149i
$165$		0			0
$166$	−210.156			−1.26600
$167$	78.6216	+	78.6216i	0.470788	+	0.470788i	0.902170	−	0.431382i	$-0.141974\pi$
$167$	78.6216	+	78.6216i	0.470788	+	0.470788i	−0.431382	+	0.902170i	$0.641974\pi$
$168$		0			0
$169$		−	366.564i		−	2.16902i
$170$	−41.2212	+	257.195i	−0.242478	+	1.51291i
$171$		0			0
$172$	−134.933	−	134.933i	−0.784494	−	0.784494i
$173$	197.965	−	197.965i	1.14431	−	1.14431i	0.156654	−	0.987654i	$-0.449929\pi$
$173$	197.965	−	197.965i	1.14431	−	1.14431i	0.987654	−	0.156654i	$-0.0500707\pi$
$174$		0			0
$175$	28.8377	+	57.1161i	0.164787	+	0.326378i
$176$	39.6118			0.225067
$177$		0			0
$178$	−135.320	+	135.320i	−0.760222	+	0.760222i
$179$			264.555i			1.47796i	0.673727	+	0.738981i	$0.264692\pi$
$179$			264.555i			1.47796i	−0.673727	+	0.738981i	$0.735308\pi$
$180$		0			0
$181$	114.827			0.634403			0.317201	−	0.948358i	$-0.397257\pi$
$181$	114.827			0.634403			0.317201	+	0.948358i	$0.397257\pi$
$182$	109.785	+	109.785i	0.603216	+	0.603216i
$183$		0			0
$184$		−	52.5753i		−	0.285735i
$185$	163.098	+	225.356i	0.881610	+	1.21814i
$186$		0			0
$187$	28.9313	+	28.9313i	0.154713	+	0.154713i
$188$	161.630	−	161.630i	0.859734	−	0.859734i
$189$		0			0
$190$	75.7050	−	54.7902i	0.398447	−	0.288370i
$191$	−194.636			−1.01904			−0.509518	−	0.860460i	$-0.670176\pi$
$191$	−194.636			−1.01904			−0.509518	+	0.860460i	$0.670176\pi$
$192$		0			0
$193$	141.848	−	141.848i	0.734966	−	0.734966i	−0.236633	−	0.971599i	$-0.576044\pi$
$193$	141.848	−	141.848i	0.734966	−	0.734966i	0.971599	+	0.236633i	$0.0760440\pi$
$194$		−	290.632i		−	1.49810i
$195$		0			0
$196$	121.896			0.621918
$197$	−66.5728	−	66.5728i	−0.337933	−	0.337933i	0.517656	−	0.855589i	$-0.326805\pi$
$197$	−66.5728	−	66.5728i	−0.337933	−	0.337933i	−0.855589	+	0.517656i	$0.826805\pi$
$198$		0			0
$199$		−	50.9462i		−	0.256011i	−0.991773	−	0.128006i	$-0.959142\pi$
$199$		−	50.9462i		−	0.256011i	0.991773	−	0.128006i	$-0.0408575\pi$
$200$	−66.0158	+	33.3311i	−0.330079	+	0.166656i
$201$		0			0
$202$	111.793	+	111.793i	0.553432	+	0.553432i
$203$	−66.1255	+	66.1255i	−0.325741	+	0.325741i
$204$		0			0
$205$	72.5065	+	11.6208i	0.353690	+	0.0566867i
$206$	−248.048			−1.20412
$207$		0			0
$208$	−314.851	+	314.851i	−1.51371	+	1.51371i
$209$		−	14.6791i		−	0.0702351i
$210$		0			0
$211$	182.712			0.865932			0.432966	−	0.901410i	$-0.357467\pi$
$211$	182.712			0.865932			0.432966	+	0.901410i	$0.357467\pi$
$212$	−61.4746	−	61.4746i	−0.289974	−	0.289974i
$213$		0			0
$214$			182.476i			0.852692i
$215$	269.170	−	194.807i	1.25195	−	0.906081i
$216$		0			0
$217$	−40.0049	−	40.0049i	−0.184355	−	0.184355i
$218$	−61.3423	+	61.3423i	−0.281387	+	0.281387i
$219$		0			0
$220$	4.67783	−	29.1868i	0.0212629	−	0.132667i
$221$	−459.916			−2.08107
$222$		0			0
$223$	−271.161	+	271.161i	−1.21597	+	1.21597i	−0.246940	+	0.969031i	$0.579425\pi$
$223$	−271.161	+	271.161i	−1.21597	+	1.21597i	−0.969031	+	0.246940i	$0.920575\pi$
$224$		−	98.7995i		−	0.441069i
$225$		0			0
$226$	−25.2009			−0.111508
$227$	−118.724	−	118.724i	−0.523012	−	0.523012i	0.395468	−	0.918480i	$-0.370582\pi$
$227$	−118.724	−	118.724i	−0.523012	−	0.523012i	−0.918480	+	0.395468i	$0.870582\pi$
$228$		0			0
$229$			96.1274i			0.419771i	0.977726	+	0.209885i	$0.0673090\pi$
$229$			96.1274i			0.419771i	−0.977726	+	0.209885i	$0.932691\pi$
$230$	−230.014	−	36.8649i	−1.00006	−	0.160282i
$231$		0			0
$232$	−76.4290	−	76.4290i	−0.329435	−	0.329435i
$233$	20.3322	−	20.3322i	0.0872627	−	0.0872627i	−0.662128	−	0.749391i	$-0.730347\pi$
$233$	20.3322	−	20.3322i	0.0872627	−	0.0872627i	0.749391	+	0.662128i	$0.230347\pi$
$234$		0			0
$235$	233.351	+	322.426i	0.992982	+	1.37203i
$236$	−106.091			−0.449536
$237$		0			0
$238$	94.2783	−	94.2783i	0.396127	−	0.396127i
$239$		−	88.5788i		−	0.370622i	−0.982680	−	0.185311i	$-0.940671\pi$
$239$		−	88.5788i		−	0.370622i	0.982680	−	0.185311i	$-0.0593293\pi$
$240$		0			0
$241$	−141.038			−0.585220			−0.292610	−	0.956232i	$-0.594524\pi$
$241$	−141.038			−0.585220			−0.292610	+	0.956232i	$0.594524\pi$
$242$	216.427	+	216.427i	0.894326	+	0.894326i
$243$		0			0
$244$		−	133.055i		−	0.545307i
$245$	−33.5890	+	209.574i	−0.137098	+	0.855406i
$246$		0			0
$247$	116.676	+	116.676i	0.472372	+	0.472372i
$248$	46.2384	−	46.2384i	0.186445	−	0.186445i
$249$		0			0
$250$	99.5329	+	312.187i	0.398132	+	1.24875i
$251$	77.6528			0.309374			0.154687	−	0.987964i	$-0.450563\pi$
$251$	77.6528			0.309374			0.154687	+	0.987964i	$0.450563\pi$
$252$		0			0
$253$	−25.8738	+	25.8738i	−0.102268	+	0.102268i
$254$		−	412.823i		−	1.62529i
$255$		0			0
$256$	335.192			1.30934
$257$	−98.4646	−	98.4646i	−0.383131	−	0.383131i	0.489098	−	0.872229i	$-0.337326\pi$
$257$	−98.4646	−	98.4646i	−0.383131	−	0.383131i	−0.872229	+	0.489098i	$0.837326\pi$
$258$		0			0
$259$		−	142.393i		−	0.549780i
$260$	194.807	+	269.170i	0.749259	+	1.03527i
$261$		0			0
$262$	98.5914	+	98.5914i	0.376303	+	0.376303i
$263$	−126.086	+	126.086i	−0.479416	+	0.479416i	−0.904945	−	0.425529i	$-0.860088\pi$
$263$	−126.086	+	126.086i	−0.479416	+	0.479416i	0.425529	+	0.904945i	$0.360088\pi$
$264$		0			0
$265$	122.632	−	88.7530i	0.462763	−	0.334917i
$266$	−47.8348			−0.179830
$267$		0			0
$268$	−221.032	+	221.032i	−0.824744	+	0.824744i
$269$			175.683i			0.653096i	0.945181	+	0.326548i	$0.105885\pi$
$269$			175.683i			0.653096i	−0.945181	+	0.326548i	$0.894115\pi$
$270$		0			0
$271$	79.8046			0.294482			0.147241	−	0.989101i	$-0.452961\pi$
$271$	79.8046			0.294482			0.147241	+	0.989101i	$0.452961\pi$
$272$	270.379	+	270.379i	0.994040	+	0.994040i
$273$		0			0
$274$			74.3241i			0.271256i
$275$	48.8915	+	16.0851i	0.177787	+	0.0584912i
$276$		0			0
$277$	−204.250	−	204.250i	−0.737364	−	0.737364i	0.234703	−	0.972067i	$-0.424588\pi$
$277$	−204.250	−	204.250i	−0.737364	−	0.737364i	−0.972067	+	0.234703i	$0.924588\pi$
$278$	241.870	−	241.870i	0.870036	−	0.870036i
$279$		0			0
$280$	37.3771	+	5.99051i	0.133490	+	0.0213947i
$281$	291.935			1.03891			0.519457	−	0.854497i	$-0.326134\pi$
$281$	291.935			1.03891			0.519457	+	0.854497i	$0.326134\pi$
$282$		0			0
$283$	−98.4389	+	98.4389i	−0.347841	+	0.347841i	−0.859305	−	0.511464i	$-0.829103\pi$
$283$	−98.4389	+	98.4389i	−0.347841	+	0.347841i	0.511464	+	0.859305i	$0.329103\pi$
$284$			293.235i			1.03252i
$285$		0			0
$286$	124.894			0.436693
$287$	−26.5782	−	26.5782i	−0.0926071	−	0.0926071i
$288$		0			0
$289$			105.954i			0.366622i
$290$	−387.964	+	280.782i	−1.33781	+	0.968215i
$291$		0			0
$292$	−29.9477	−	29.9477i	−0.102561	−	0.102561i
$293$	253.598	−	253.598i	0.865522	−	0.865522i	−0.126451	−	0.991973i	$-0.540359\pi$
$293$	253.598	−	253.598i	0.865522	−	0.865522i	0.991973	+	0.126451i	$0.0403586\pi$
$294$		0			0
$295$	29.2337	−	182.400i	0.0990974	−	0.618307i
$296$	164.580			0.556015
$297$		0			0
$298$	307.582	−	307.582i	1.03216	−	1.03216i
$299$		−	411.312i		−	1.37562i
$300$		0			0
$301$	−170.077			−0.565041
$302$	−165.983	−	165.983i	−0.549612	−	0.549612i
$303$		0			0
$304$		−	137.185i		−	0.451265i
$305$	228.760	+	36.6639i	0.750033	+	0.120209i
$306$		0			0
$307$	−135.946	−	135.946i	−0.442822	−	0.442822i	0.450137	−	0.892959i	$-0.351375\pi$
$307$	−135.946	−	135.946i	−0.442822	−	0.442822i	−0.892959	+	0.450137i	$0.851375\pi$
$308$	−10.6988	+	10.6988i	−0.0347364	+	0.0347364i
$309$		0			0
$310$	−169.869	−	234.712i	−0.547965	−	0.757137i
$311$	−104.078			−0.334657			−0.167329	−	0.985901i	$-0.553514\pi$
$311$	−104.078			−0.334657			−0.167329	+	0.985901i	$0.553514\pi$
$312$		0			0
$313$	40.9560	−	40.9560i	0.130850	−	0.130850i	−0.638649	−	0.769498i	$-0.720506\pi$
$313$	40.9560	−	40.9560i	0.130850	−	0.130850i	0.769498	+	0.638649i	$0.220506\pi$
$314$			216.887i			0.690724i
$315$		0			0
$316$	−211.150			−0.668195
$317$	347.406	+	347.406i	1.09592	+	1.09592i	0.994883	+	0.101037i	$0.0322160\pi$
$317$	347.406	+	347.406i	1.09592	+	1.09592i	0.101037	+	0.994883i	$0.467784\pi$
$318$		0			0
$319$			75.2258i			0.235818i
$320$	19.1741	−	119.635i	0.0599191	−	0.373858i
$321$		0			0
$322$	84.3148	+	84.3148i	0.261847	+	0.261847i
$323$	100.196	−	100.196i	0.310203	−	0.310203i
$324$		0			0
$325$	−516.461	+	260.759i	−1.58911	+	0.802336i
$326$	120.467			0.369529
$327$		0			0
$328$	30.7196	−	30.7196i	0.0936573	−	0.0936573i
$329$		−	203.728i		−	0.619233i
$330$		0			0
$331$	25.0983			0.0758256			0.0379128	−	0.999281i	$-0.487929\pi$
$331$	25.0983			0.0758256			0.0379128	+	0.999281i	$0.487929\pi$
$332$	162.785	+	162.785i	0.490316	+	0.490316i
$333$		0			0
$334$		−	291.463i		−	0.872644i
$335$	−319.111	−	440.923i	−0.952570	−	1.31619i
$336$		0			0
$337$	−73.3287	−	73.3287i	−0.217593	−	0.217593i	0.589891	−	0.807483i	$-0.299171\pi$
$337$	−73.3287	−	73.3287i	−0.217593	−	0.217593i	−0.807483	+	0.589891i	$0.799171\pi$
$338$	−679.457	+	679.457i	−2.01023	+	2.01023i
$339$		0			0
$340$	231.150	−	167.291i	0.679853	−	0.492033i
$341$	−45.5105			−0.133462
$342$		0			0
$343$	165.499	−	165.499i	0.482504	−	0.482504i
$344$		−	196.578i		−	0.571449i
$345$		0			0
$346$	−733.889			−2.12107
$347$	−25.1989	−	25.1989i	−0.0726192	−	0.0726192i	0.669864	−	0.742484i	$-0.266352\pi$
$347$	−25.1989	−	25.1989i	−0.0726192	−	0.0726192i	−0.742484	+	0.669864i	$0.766352\pi$
$348$		0			0
$349$		−	112.522i		−	0.322412i	−0.986921	−	0.161206i	$-0.948462\pi$
$349$		−	112.522i		−	0.322412i	0.986921	−	0.161206i	$-0.0515384\pi$
$350$	52.4164	−	159.322i	0.149761	−	0.455207i
$351$		0			0
$352$	−56.1983	−	56.1983i	−0.159654	−	0.159654i
$353$	−6.07002	+	6.07002i	−0.0171955	+	0.0171955i	−0.715652	−	0.698457i	$-0.753870\pi$
$353$	−6.07002	+	6.07002i	−0.0171955	+	0.0171955i	0.698457	+	0.715652i	$0.253870\pi$
$354$		0			0
$355$	−504.155	−	80.8021i	−1.42016	−	0.227612i
$356$	209.634			0.588861
$357$		0			0
$358$	490.374	−	490.374i	1.36976	−	1.36976i
$359$			576.227i			1.60509i	0.596592	+	0.802544i	$0.296521\pi$
$359$			576.227i			1.60509i	−0.596592	+	0.802544i	$0.703479\pi$
$360$		0			0
$361$	310.163			0.859177
$362$	−212.841	−	212.841i	−0.587958	−	0.587958i
$363$		0			0
$364$		−	170.077i		−	0.467245i
$365$	59.7409	−	43.2365i	0.163674	−	0.118456i
$366$		0			0
$367$	110.722	+	110.722i	0.301695	+	0.301695i	0.841677	−	0.539982i	$-0.181569\pi$
$367$	110.722	+	110.722i	0.301695	+	0.301695i	−0.539982	+	0.841677i	$0.681569\pi$
$368$	−241.805	+	241.805i	−0.657079	+	0.657079i
$369$		0			0
$370$	115.401	−	720.031i	0.311895	−	1.94603i
$371$	−77.4861			−0.208857
$372$		0			0
$373$	−70.1819	+	70.1819i	−0.188155	+	0.188155i	−0.794898	−	0.606743i	$-0.792476\pi$
$373$	−70.1819	+	70.1819i	−0.188155	+	0.188155i	0.606743	+	0.794898i	$0.292476\pi$
$374$		−	107.253i		−	0.286773i
$375$		0			0
$376$	235.472			0.626256
$377$	−597.927	−	597.927i	−1.58601	−	1.58601i
$378$		0			0
$379$			648.160i			1.71018i	0.518476	+	0.855092i	$0.326500\pi$
$379$			648.160i			1.71018i	−0.518476	+	0.855092i	$0.673500\pi$
$380$	−101.080	−	16.2004i	−0.266001	−	0.0426325i
$381$		0			0
$382$	360.774	+	360.774i	0.944434	+	0.944434i
$383$	377.891	−	377.891i	0.986659	−	0.986659i	−0.0132527	−	0.999912i	$-0.504219\pi$
$383$	377.891	−	377.891i	0.986659	−	0.986659i	0.999912	+	0.0132527i	$0.00421860\pi$
$384$		0			0
$385$	−15.4462	−	21.3424i	−0.0401201	−	0.0554349i
$386$	−525.855			−1.36232
$387$		0			0
$388$	−225.121	+	225.121i	−0.580208	+	0.580208i
$389$			139.022i			0.357382i	0.983905	+	0.178691i	$0.0571863\pi$
$389$			139.022i			0.357382i	−0.983905	+	0.178691i	$0.942814\pi$
$390$		0			0
$391$	−353.214			−0.903362
$392$	88.7927	+	88.7927i	0.226512	+	0.226512i
$393$		0			0
$394$			246.796i			0.626386i
$395$	58.1832	−	363.027i	0.147299	−	0.919057i
$396$		0			0
$397$	−291.864	−	291.864i	−0.735175	−	0.735175i	0.236465	−	0.971640i	$-0.424011\pi$
$397$	−291.864	−	291.864i	−0.735175	−	0.735175i	−0.971640	+	0.236465i	$0.924011\pi$
$398$	−94.4330	+	94.4330i	−0.237269	+	0.237269i
$399$		0			0
$400$	456.918	+	150.324i	1.14230	+	0.375810i
$401$	−231.602			−0.577562			−0.288781	−	0.957395i	$-0.593250\pi$
$401$	−231.602			−0.577562			−0.288781	+	0.957395i	$0.593250\pi$
$402$		0			0
$403$	361.737	−	361.737i	0.897610	−	0.897610i
$404$		−	173.188i		−	0.428683i
$405$		0			0
$406$	245.138			0.603788
$407$	−80.9948	−	80.9948i	−0.199004	−	0.199004i
$408$		0			0
$409$		−	5.56023i		−	0.0135947i	−0.999977	−	0.00679735i	$-0.997836\pi$
$409$		−	5.56023i		−	0.0135947i	0.999977	−	0.00679735i	$-0.00216368\pi$
$410$	−112.857	−	155.937i	−0.275260	−	0.380334i
$411$		0			0
$412$	192.136	+	192.136i	0.466349	+	0.466349i
$413$	−66.8614	+	66.8614i	−0.161892	+	0.161892i
$414$		0			0
$415$	−324.731	+	235.018i	−0.782483	+	0.566309i
$416$	893.375			2.14754
$417$		0			0
$418$	−27.2090	+	27.2090i	−0.0650932	+	0.0650932i
$419$			556.456i			1.32806i	0.747707	+	0.664028i	$0.231155\pi$
$419$			556.456i			1.32806i	−0.747707	+	0.664028i	$0.768845\pi$
$420$		0			0
$421$	−593.997			−1.41092			−0.705459	−	0.708751i	$-0.749259\pi$
$421$	−593.997			−1.41092			−0.705459	+	0.708751i	$0.749259\pi$
$422$	−338.671	−	338.671i	−0.802537	−	0.802537i
$423$		0			0
$424$		−	89.5598i		−	0.211226i
$425$	223.927	+	443.512i	0.526888	+	1.04356i
$426$		0			0
$427$	−83.8551	−	83.8551i	−0.196382	−	0.196382i
$428$	141.344	−	141.344i	0.330243	−	0.330243i
$429$		0			0
$430$	−860.020	−	137.837i	−2.00005	−	0.320552i
$431$	566.825			1.31514			0.657569	−	0.753394i	$-0.271585\pi$
$431$	566.825			1.31514			0.657569	+	0.753394i	$0.271585\pi$
$432$		0			0
$433$	347.506	−	347.506i	0.802555	−	0.802555i	−0.180940	−	0.983494i	$-0.557914\pi$
$433$	347.506	−	347.506i	0.802555	−	0.802555i	0.983494	+	0.180940i	$0.0579138\pi$
$434$			148.305i			0.341716i
$435$		0			0
$436$	95.0302			0.217959
$437$	89.6068	+	89.6068i	0.205050	+	0.205050i
$438$		0			0
$439$			805.424i			1.83468i	0.398106	+	0.917340i	$0.369668\pi$
$439$			805.424i			1.83468i	−0.398106	+	0.917340i	$0.630332\pi$
$440$	24.6680	−	17.8530i	0.0560636	−	0.0405751i
$441$		0			0
$442$	852.493	+	852.493i	1.92872	+	1.92872i
$443$	−524.532	+	524.532i	−1.18405	+	1.18405i	−0.205359	+	0.978687i	$0.565836\pi$
$443$	−524.532	+	524.532i	−1.18405	+	1.18405i	−0.978687	+	0.205359i	$0.934164\pi$
$444$		0			0
$445$	−57.7657	+	360.422i	−0.129810	+	0.809937i
$446$	1005.24			2.25390
$447$		0			0
$448$	−43.8537	+	43.8537i	−0.0978877	+	0.0978877i
$449$			345.404i			0.769273i	0.923068	+	0.384637i	$0.125673\pi$
$449$			345.404i			0.769273i	−0.923068	+	0.384637i	$0.874327\pi$
$450$		0			0
$451$	−30.2360			−0.0670421
$452$	19.5204	+	19.5204i	0.0431867	+	0.0431867i
$453$		0			0
$454$			440.128i			0.969445i
$455$	292.412	+	46.8655i	0.642664	+	0.103001i
$456$		0			0
$457$	331.219	+	331.219i	0.724769	+	0.724769i	0.969573	−	0.244804i	$-0.0787235\pi$
$457$	331.219	+	331.219i	0.724769	+	0.724769i	−0.244804	+	0.969573i	$0.578724\pi$
$458$	178.180	−	178.180i	0.389040	−	0.389040i
$459$		0			0
$460$	149.612	+	206.722i	0.325242	+	0.449395i
$461$	−69.3667			−0.150470			−0.0752351	−	0.997166i	$-0.523971\pi$
$461$	−69.3667			−0.150470			−0.0752351	+	0.997166i	$0.523971\pi$
$462$		0			0
$463$	162.327	−	162.327i	0.350598	−	0.350598i	−0.509734	−	0.860332i	$-0.670256\pi$
$463$	162.327	−	162.327i	0.350598	−	0.350598i	0.860332	+	0.509734i	$0.170256\pi$
$464$			703.027i			1.51514i
$465$		0			0
$466$	−75.3748			−0.161749
$467$	104.749	+	104.749i	0.224303	+	0.224303i	0.810308	−	0.586005i	$-0.199300\pi$
$467$	104.749	+	104.749i	0.224303	+	0.224303i	−0.586005	+	0.810308i	$0.699300\pi$
$468$		0			0
$469$			278.601i			0.594032i
$470$	165.109	−	1030.18i	0.351296	−	2.19187i
$471$		0			0
$472$	−77.2795	−	77.2795i	−0.163728	−	0.163728i
$473$	−96.7418	+	96.7418i	−0.204528	+	0.204528i
$474$		0			0
$475$	55.7062	−	169.322i	0.117276	−	0.356468i
$476$	−146.054			−0.306836
$477$		0			0
$478$	−164.188	+	164.188i	−0.343489	+	0.343489i
$479$			504.447i			1.05313i	0.850136	+	0.526563i	$0.176519\pi$
$479$			504.447i			1.05313i	−0.850136	+	0.526563i	$0.823481\pi$
$480$		0			0
$481$	1287.56			2.67684
$482$	261.425	+	261.425i	0.542376	+	0.542376i
$483$		0			0
$484$		−	335.284i		−	0.692736i
$485$	−325.015	−	449.081i	−0.670134	−	0.925940i
$486$		0			0
$487$	−435.576	−	435.576i	−0.894407	−	0.894407i	0.100527	−	0.994934i	$-0.467947\pi$
$487$	−435.576	−	435.576i	−0.894407	−	0.894407i	−0.994934	+	0.100527i	$0.967947\pi$
$488$	96.9212	−	96.9212i	0.198609	−	0.198609i
$489$		0			0
$490$	450.723	−	326.204i	0.919843	−	0.665721i
$491$	488.734			0.995386			0.497693	−	0.867353i	$-0.334181\pi$
$491$	488.734			0.995386			0.497693	+	0.867353i	$0.334181\pi$
$492$		0			0
$493$	−513.470	+	513.470i	−1.04152	+	1.04152i
$494$		−	432.537i		−	0.875580i
$495$		0			0
$496$	−425.321			−0.857501
$497$	184.805	+	184.805i	0.371841	+	0.371841i
$498$		0			0
$499$		−	521.418i		−	1.04493i	−0.852662	−	0.522463i	$-0.825013\pi$
$499$		−	521.418i		−	1.04493i	0.852662	−	0.522463i	$-0.174987\pi$
$500$	164.720	−	318.914i	0.329440	−	0.637829i
$501$		0			0
$502$	−143.936	−	143.936i	−0.286725	−	0.286725i
$503$	−638.392	+	638.392i	−1.26917	+	1.26917i	−0.322650	+	0.946518i	$0.604574\pi$
$503$	−638.392	+	638.392i	−1.26917	+	1.26917i	−0.946518	+	0.322650i	$0.895426\pi$
$504$		0			0
$505$	297.760	+	47.7226i	0.589624	+	0.0945003i
$506$	95.9184			0.189562
$507$		0			0
$508$	−319.768	+	319.768i	−0.629465	+	0.629465i
$509$		−	862.426i		−	1.69435i	−0.531311	−	0.847177i	$-0.678300\pi$
$509$		−	862.426i		−	1.69435i	0.531311	−	0.847177i	$-0.321700\pi$
$510$		0			0
$511$	−37.7478			−0.0738704
$512$	−364.222	−	364.222i	−0.711372	−	0.711372i
$513$		0			0
$514$			365.024i			0.710164i
$515$	−383.281	+	277.393i	−0.744234	+	0.538627i
$516$		0			0
$517$	−115.883	−	115.883i	−0.224144	−	0.224144i
$518$	−263.937	+	263.937i	−0.509531	+	0.509531i
$519$		0			0
$520$	−54.1680	+	337.975i	−0.104169	+	0.649952i
$521$	−810.812			−1.55626			−0.778130	−	0.628103i	$-0.783832\pi$
$521$	−810.812			−1.55626			−0.778130	+	0.628103i	$0.783832\pi$
$522$		0			0
$523$	81.0491	−	81.0491i	0.154970	−	0.154970i	−0.625364	−	0.780333i	$-0.715049\pi$
$523$	81.0491	−	81.0491i	0.154970	−	0.154970i	0.780333	+	0.625364i	$0.215049\pi$
$524$		−	152.736i		−	0.291480i
$525$		0			0
$526$	467.423			0.888637
$527$	−310.642	−	310.642i	−0.589453	−	0.589453i
$528$		0			0
$529$			213.114i			0.402862i
$530$	−391.820	−	62.7978i	−0.739283	−	0.118486i
$531$		0			0
$532$	37.0524	+	37.0524i	0.0696473	+	0.0696473i
$533$	240.328	−	240.328i	0.450898	−	0.450898i
$534$		0			0
$535$	204.064	+	281.960i	0.381427	+	0.527027i
$536$	−322.012			−0.600768
$537$		0			0
$538$	325.642	−	325.642i	0.605283	−	0.605283i
$539$		−	87.3948i		−	0.162143i
$540$		0			0
$541$	−473.428			−0.875098			−0.437549	−	0.899195i	$-0.644153\pi$
$541$	−473.428			−0.875098			−0.437549	+	0.899195i	$0.644153\pi$
$542$	−147.924	−	147.924i	−0.272923	−	0.272923i
$543$		0			0
$544$		−	767.187i		−	1.41027i
$545$	−26.1860	+	163.384i	−0.0480477	+	0.299788i
$546$		0			0
$547$	44.8918	+	44.8918i	0.0820691	+	0.0820691i	0.746950	−	0.664881i	$-0.231518\pi$
$547$	44.8918	+	44.8918i	0.0820691	+	0.0820691i	−0.664881	+	0.746950i	$0.731518\pi$
$548$	57.5707	−	57.5707i	0.105056	−	0.105056i
$549$		0			0
$550$	−60.8094	−	120.439i	−0.110563	−	0.218981i
$551$	260.524			0.472820
$552$		0			0
$553$	−133.073	+	133.073i	−0.240638	+	0.240638i
$554$			757.188i			1.36676i
$555$		0			0
$556$	−374.700			−0.673921
$557$	245.069	+	245.069i	0.439981	+	0.439981i	0.892005	−	0.452025i	$-0.149298\pi$
$557$	245.069	+	245.069i	0.439981	+	0.439981i	−0.452025	+	0.892005i	$0.649298\pi$
$558$		0			0
$559$		−	1537.89i		−	2.75114i
$560$	−144.354	−	199.457i	−0.257774	−	0.356173i
$561$		0			0
$562$	−541.125	−	541.125i	−0.962856	−	0.962856i
$563$	92.1197	−	92.1197i	0.163623	−	0.163623i	−0.620547	−	0.784170i	$-0.713089\pi$
$563$	92.1197	−	92.1197i	0.163623	−	0.163623i	0.784170	+	0.620547i	$0.213089\pi$
$564$		0			0
$565$	−38.9401	+	28.1822i	−0.0689205	+	0.0498801i
$566$	364.929			0.644751
$567$		0			0
$568$	−213.601	+	213.601i	−0.376058	+	0.376058i
$569$		−	52.7798i		−	0.0927589i	−0.998924	−	0.0463794i	$-0.985232\pi$
$569$		−	52.7798i		−	0.0927589i	0.998924	−	0.0463794i	$-0.0147683\pi$
$570$		0			0
$571$	187.813			0.328919			0.164459	−	0.986384i	$-0.447412\pi$
$571$	187.813			0.328919			0.164459	+	0.986384i	$0.447412\pi$
$572$	−96.7418	−	96.7418i	−0.169129	−	0.169129i
$573$		0			0
$574$			98.5299i			0.171655i
$575$	−396.641	+	200.262i	−0.689810	+	0.348282i
$576$		0			0
$577$	115.526	+	115.526i	0.200218	+	0.200218i	0.800093	−	0.599875i	$-0.204783\pi$
$577$	115.526	+	115.526i	0.200218	+	0.200218i	−0.599875	+	0.800093i	$0.704783\pi$
$578$	196.394	−	196.394i	0.339782	−	0.339782i
$579$		0			0
$580$	518.004	+	83.0217i	0.893111	+	0.143141i
$581$	205.184			0.353156
$582$		0			0
$583$	−44.0750	+	44.0750i	−0.0756003	+	0.0756003i
$584$		−	43.6296i		−	0.0747081i
$585$		0			0
$586$	−940.129			−1.60432
$587$	−572.894	−	572.894i	−0.975969	−	0.975969i	0.0237494	−	0.999718i	$-0.492440\pi$
$587$	−572.894	−	572.894i	−0.975969	−	0.975969i	−0.999718	+	0.0237494i	$0.992440\pi$
$588$		0			0
$589$			157.613i			0.267594i
$590$	−392.281	+	283.907i	−0.664883	+	0.481198i
$591$		0			0
$592$	−756.941	−	756.941i	−1.27862	−	1.27862i
$593$	−374.017	+	374.017i	−0.630721	+	0.630721i	−0.948249	−	0.317528i	$-0.897147\pi$
$593$	−374.017	+	374.017i	−0.630721	+	0.630721i	0.317528	+	0.948249i	$0.397147\pi$
$594$		0			0
$595$	40.2458	−	251.109i	0.0676400	−	0.422032i
$596$	−476.500			−0.799497
$597$		0			0
$598$	−762.400	+	762.400i	−1.27492	+	1.27492i
$599$		−	541.163i		−	0.903443i	−0.892159	−	0.451722i	$-0.850810\pi$
$599$		−	541.163i		−	0.903443i	0.892159	−	0.451722i	$-0.149190\pi$
$600$		0			0
$601$	915.778			1.52376			0.761878	−	0.647720i	$-0.224277\pi$
$601$	915.778			1.52376			0.761878	+	0.647720i	$0.224277\pi$
$602$	315.252	+	315.252i	0.523675	+	0.523675i
$603$		0			0
$604$			257.137i			0.425724i
$605$	576.450	+	92.3890i	0.952811	+	0.152709i
$606$		0			0
$607$	−789.819	−	789.819i	−1.30118	−	1.30118i	−0.927594	−	0.373591i	$-0.878127\pi$
$607$	−789.819	−	789.819i	−1.30118	−	1.30118i	−0.373591	−	0.927594i	$-0.621873\pi$
$608$	−194.627	+	194.627i	−0.320110	+	0.320110i
$609$		0			0
$610$	−356.066	−	491.985i	−0.583715	−	0.806533i
$611$	1842.17			3.01500
$612$		0			0
$613$	54.2959	−	54.2959i	0.0885741	−	0.0885741i	−0.661432	−	0.750006i	$-0.730051\pi$
$613$	54.2959	−	54.2959i	0.0885741	−	0.0885741i	0.750006	+	0.661432i	$0.230051\pi$
$614$			503.976i			0.820807i
$615$		0			0
$616$	−15.5867			−0.0253030
$617$	546.520	+	546.520i	0.885770	+	0.885770i	0.994114	−	0.108343i	$-0.0345546\pi$
$617$	546.520	+	546.520i	0.885770	+	0.885770i	−0.108343	+	0.994114i	$0.534555\pi$
$618$		0			0
$619$		−	770.649i		−	1.24499i	−0.782623	−	0.622495i	$-0.786119\pi$
$619$		−	770.649i		−	1.24499i	0.782623	−	0.622495i	$-0.213881\pi$
$620$	−50.2269	+	313.385i	−0.0810111	+	0.505459i
$621$		0			0
$622$	192.918	+	192.918i	0.310157	+	0.310157i
$623$	132.118	−	132.118i	0.212067	−	0.212067i
$624$		0			0
$625$	502.917	+	371.079i	0.804667	+	0.593727i
$626$	−151.830			−0.242541
$627$		0			0
$628$	167.999	−	167.999i	0.267514	−	0.267514i
$629$		−	1105.69i		−	1.75786i
$630$		0			0
$631$	1187.77			1.88236			0.941181	−	0.337903i	$-0.109718\pi$
$631$	1187.77			1.88236			0.941181	+	0.337903i	$0.109718\pi$
$632$	−153.808	−	153.808i	−0.243367	−	0.243367i
$633$		0			0
$634$		−	1287.89i		−	2.03138i
$635$	−461.661	−	637.888i	−0.727025	−	1.00455i
$636$		0			0
$637$	694.651	+	694.651i	1.09050	+	1.09050i
$638$	139.437	−	139.437i	0.218554	−	0.218554i
$639$		0			0
$640$	368.161	−	266.450i	0.575251	−	0.416329i
$641$	−684.175			−1.06736			−0.533678	−	0.845688i	$-0.679190\pi$
$641$	−684.175			−1.06736			−0.533678	+	0.845688i	$0.679190\pi$
$642$		0			0
$643$	5.98402	−	5.98402i	0.00930640	−	0.00930640i	−0.702438	−	0.711745i	$-0.747905\pi$
$643$	5.98402	−	5.98402i	0.00930640	−	0.00930640i	0.711745	+	0.702438i	$0.247905\pi$
$644$		−	130.619i		−	0.202824i
$645$		0			0
$646$	−371.441			−0.574987
$647$	425.885	+	425.885i	0.658246	+	0.658246i	0.954965	−	0.296719i	$-0.0958925\pi$
$647$	425.885	+	425.885i	0.658246	+	0.658246i	−0.296719	+	0.954965i	$0.595893\pi$
$648$		0			0
$649$			76.0630i			0.117200i
$650$	1440.64	+	473.965i	2.21637	+	0.729176i
$651$		0			0
$652$	−93.3122	−	93.3122i	−0.143117	−	0.143117i
$653$	285.832	−	285.832i	0.437721	−	0.437721i	−0.453523	−	0.891245i	$-0.649833\pi$
$653$	285.832	−	285.832i	0.437721	−	0.437721i	0.891245	+	0.453523i	$0.149833\pi$
$654$		0			0
$655$	262.597	+	42.0870i	0.400911	+	0.0642550i
$656$	−282.572			−0.430750
$657$		0			0
$658$	−377.626	+	377.626i	−0.573900	+	0.573900i
$659$			968.254i			1.46928i	0.678458	+	0.734639i	$0.262648\pi$
$659$			968.254i			1.46928i	−0.678458	+	0.734639i	$0.737352\pi$
$660$		0			0
$661$	−552.045			−0.835166			−0.417583	−	0.908639i	$-0.637123\pi$
$661$	−552.045			−0.835166			−0.417583	+	0.908639i	$0.637123\pi$
$662$	−46.5217	−	46.5217i	−0.0702745	−	0.0702745i
$663$		0			0
$664$			237.155i			0.357161i
$665$	−73.9137	+	53.4938i	−0.111148	+	0.0804418i
$666$		0			0
$667$	−459.206	−	459.206i	−0.688465	−	0.688465i
$668$	−225.764	+	225.764i	−0.337971	+	0.337971i
$669$		0			0
$670$	−225.789	+	1408.79i	−0.336999	+	2.10267i
$671$	−95.3954			−0.142169
$672$		0			0
$673$	480.638	−	480.638i	0.714172	−	0.714172i	−0.253233	−	0.967405i	$-0.581494\pi$
$673$	480.638	−	480.638i	0.714172	−	0.714172i	0.967405	+	0.253233i	$0.0814940\pi$
$674$			271.841i			0.403326i
$675$		0			0
$676$	1052.60			1.55710
$677$	480.020	+	480.020i	0.709040	+	0.709040i	0.966333	−	0.257294i	$-0.0828307\pi$
$677$	480.020	+	480.020i	0.709040	+	0.709040i	−0.257294	+	0.966333i	$0.582831\pi$
$678$		0			0
$679$			283.755i			0.417902i
$680$	290.236	+	46.5168i	0.426818	+	0.0684071i
$681$		0			0
$682$	84.3574	+	84.3574i	0.123691	+	0.123691i
$683$	641.686	−	641.686i	0.939511	−	0.939511i	−0.0587612	−	0.998272i	$-0.518715\pi$
$683$	641.686	−	641.686i	0.939511	−	0.939511i	0.998272	+	0.0587612i	$0.0187150\pi$
$684$		0			0
$685$	83.1169	+	114.845i	0.121338	+	0.167656i
$686$	−613.531			−0.894360
$687$		0			0
$688$	−904.106	+	904.106i	−1.31411	+	1.31411i
$689$		−	700.653i		−	1.01691i
$690$		0			0
$691$	−849.132			−1.22885			−0.614423	−	0.788977i	$-0.710611\pi$
$691$	−849.132			−1.22885			−0.614423	+	0.788977i	$0.710611\pi$
$692$	568.463	+	568.463i	0.821479	+	0.821479i
$693$		0			0
$694$			93.4164i			0.134606i
$695$	103.250	−	644.218i	0.148561	−	0.926932i
$696$		0			0
$697$	−206.382	−	206.382i	−0.296101	−	0.296101i
$698$	−208.568	+	208.568i	−0.298809	+	0.298809i
$699$		0			0
$700$	−164.011	+	82.8084i	−0.234301	+	0.118298i
$701$	−295.917			−0.422136			−0.211068	−	0.977471i	$-0.567694\pi$
$701$	−295.917			−0.422136			−0.211068	+	0.977471i	$0.567694\pi$
$702$		0			0
$703$	−280.503	+	280.503i	−0.399009	+	0.399009i
$704$			49.8889i			0.0708650i
$705$		0			0
$706$	22.5026			0.0318733
$707$	−109.148	−	109.148i	−0.154382	−	0.154382i
$708$		0			0
$709$			634.567i			0.895018i	0.894280	+	0.447509i	$0.147689\pi$
$709$			634.567i			0.895018i	−0.894280	+	0.447509i	$0.852311\pi$
$710$	784.720	+	1084.27i	1.10524	+	1.52714i
$711$		0			0
$712$	152.704	+	152.704i	0.214472	+	0.214472i
$713$	277.813	−	277.813i	0.389639	−	0.389639i
$714$		0			0
$715$	192.985	−	139.670i	0.269909	−	0.195342i
$716$	−759.678			−1.06100
$717$		0			0
$718$	1068.08	−	1068.08i	1.48758	−	1.48758i
$719$		−	200.698i		−	0.279135i	−0.990213	−	0.139568i	$-0.955429\pi$
$719$		−	200.698i		−	0.279135i	0.990213	−	0.139568i	$-0.0445712\pi$
$720$		0			0
$721$	242.179			0.335893
$722$	−574.912	−	574.912i	−0.796277	−	0.796277i
$723$		0			0
$724$			329.729i			0.455427i
$725$	−285.477	+	867.722i	−0.393761	+	1.19686i
$726$		0			0
$727$	566.268	+	566.268i	0.778910	+	0.778910i	0.979646	−	0.200735i	$-0.0643331\pi$
$727$	566.268	+	566.268i	0.778910	+	0.778910i	−0.200735	+	0.979646i	$0.564333\pi$
$728$	123.889	−	123.889i	0.170178	−	0.170178i
$729$		0			0
$730$	−190.877	−	30.5923i	−0.261476	−	0.0419073i
$731$	−1320.66			−1.80665
$732$		0			0
$733$	−452.422	+	452.422i	−0.617219	+	0.617219i	−0.944817	−	0.327598i	$-0.893761\pi$
$733$	−452.422	+	452.422i	−0.617219	+	0.617219i	0.327598	+	0.944817i	$0.393761\pi$
$734$		−	410.465i		−	0.559216i
$735$		0			0
$736$	686.109			0.932214
$737$	158.471	+	158.471i	0.215022	+	0.215022i
$738$		0			0
$739$			831.653i			1.12538i	0.826669	+	0.562688i	$0.190233\pi$
$739$			831.653i			1.12538i	−0.826669	+	0.562688i	$0.809767\pi$
$740$	−647.117	+	468.341i	−0.874483	+	0.632893i
$741$		0			0
$742$	143.627	+	143.627i	0.193567	+	0.193567i
$743$	−314.358	+	314.358i	−0.423093	+	0.423093i	−0.886267	−	0.463174i	$-0.846710\pi$
$743$	−314.358	+	314.358i	−0.423093	+	0.423093i	0.463174	+	0.886267i	$0.346710\pi$
$744$		0			0
$745$	131.302	−	819.242i	0.176244	−	1.09965i
$746$	260.176			0.348761
$747$		0			0
$748$	−83.0771	+	83.0771i	−0.111066	+	0.111066i
$749$		−	178.158i		−	0.237862i
$750$		0			0
$751$	227.368			0.302754			0.151377	−	0.988476i	$-0.451629\pi$
$751$	227.368			0.302754			0.151377	+	0.988476i	$0.451629\pi$
$752$	−1082.99	−	1082.99i	−1.44014	−	1.44014i
$753$		0			0
$754$			2216.61i			2.93980i
$755$	−442.093	−	70.8552i	−0.585554	−	0.0938480i
$756$		0			0
$757$	453.799	+	453.799i	0.599470	+	0.599470i	0.940171	−	0.340702i	$-0.110665\pi$
$757$	453.799	+	453.799i	0.599470	+	0.599470i	−0.340702	+	0.940171i	$0.610665\pi$
$758$	1201.42	−	1201.42i	1.58498	−	1.58498i
$759$		0			0
$760$	−61.8291	−	85.4307i	−0.0813540	−	0.112409i
$761$	−819.267			−1.07657			−0.538283	−	0.842764i	$-0.680927\pi$
$761$	−819.267			−1.07657			−0.538283	+	0.842764i	$0.680927\pi$
$762$		0			0
$763$	59.8908	−	59.8908i	0.0784938	−	0.0784938i
$764$		−	558.903i		−	0.731549i
$765$		0			0
$766$	−1400.90			−1.82885
$767$	−604.581	−	604.581i	−0.788241	−	0.788241i
$768$		0			0
$769$		−	194.732i		−	0.253227i	−0.991952	−	0.126614i	$-0.959589\pi$
$769$		−	194.732i		−	0.253227i	0.991952	−	0.126614i	$-0.0404108\pi$
$770$	−10.9291	+	68.1908i	−0.0141936	+	0.0885595i
$771$		0			0
$772$	407.322	+	407.322i	0.527619	+	0.527619i
$773$	57.3776	−	57.3776i	0.0742271	−	0.0742271i	−0.669019	−	0.743246i	$-0.733285\pi$
$773$	57.3776	−	57.3776i	0.0742271	−	0.0742271i	0.743246	+	0.669019i	$0.233285\pi$
$774$		0			0
$775$	−524.959	−	172.709i	−0.677366	−	0.222850i
$776$	−327.969			−0.422641
$777$		0			0
$778$	257.688	−	257.688i	0.331219	−	0.331219i
$779$			104.714i			0.134421i
$780$		0			0
$781$	210.238			0.269191
$782$	654.712	+	654.712i	0.837228	+	0.837228i
$783$		0			0
$784$		−	816.753i		−	1.04178i
$785$	242.546	+	335.131i	0.308975	+	0.426919i
$786$		0			0
$787$	650.541	+	650.541i	0.826609	+	0.826609i	0.987046	−	0.160437i	$-0.0512904\pi$
$787$	650.541	+	650.541i	0.826609	+	0.826609i	−0.160437	+	0.987046i	$0.551290\pi$
$788$	191.166	−	191.166i	0.242596	−	0.242596i
$789$		0			0
$790$	−780.748	+	565.054i	−0.988289	+	0.715258i
$791$	24.6046			0.0311057
$792$		0			0
$793$	758.243	−	758.243i	0.956170	−	0.956170i
$794$			1081.99i			1.36271i
$795$		0			0
$796$	146.294			0.183786
$797$	−304.474	−	304.474i	−0.382025	−	0.382025i	0.489806	−	0.871831i	$-0.337068\pi$
$797$	−304.474	−	304.474i	−0.382025	−	0.382025i	−0.871831	+	0.489806i	$0.837068\pi$
$798$		0			0
$799$		−	1581.96i		−	1.97993i
$800$	−434.973	−	861.509i	−0.543716	−	1.07689i
$801$		0			0
$802$	429.294	+	429.294i	0.535279	+	0.535279i
$803$	−21.4714	+	21.4714i	−0.0267389	+	0.0267389i
$804$		0			0
$805$	224.572	+	35.9926i	0.278971	+	0.0447113i
$806$	−1341.02			−1.66379
$807$		0			0
$808$	126.155	−	126.155i	0.156133	−	0.156133i
$809$		−	324.798i		−	0.401480i	−0.979645	−	0.200740i	$-0.935665\pi$
$809$		−	324.798i		−	0.401480i	0.979645	−	0.200740i	$-0.0643347\pi$
$810$		0			0
$811$	−341.672			−0.421297			−0.210649	−	0.977562i	$-0.567558\pi$
$811$	−341.672			−0.421297			−0.210649	+	0.977562i	$0.567558\pi$
$812$	−189.881	−	189.881i	−0.233844	−	0.233844i
$813$		0			0
$814$			300.261i			0.368871i
$815$	186.143	−	134.718i	0.228397	−	0.165298i
$816$		0			0
$817$	335.039	+	335.039i	0.410084	+	0.410084i
$818$	−10.3063	+	10.3063i	−0.0125994	+	0.0125994i
$819$		0			0
$820$	−33.3694	+	208.205i	−0.0406944	+	0.253908i
$821$	1063.72			1.29564			0.647821	−	0.761793i	$-0.275681\pi$
$821$	1063.72			1.29564			0.647821	+	0.761793i	$0.275681\pi$
$822$		0			0
$823$	384.927	−	384.927i	0.467712	−	0.467712i	−0.433461	−	0.901173i	$-0.642708\pi$
$823$	384.927	−	384.927i	0.467712	−	0.467712i	0.901173	+	0.433461i	$0.142708\pi$
$824$			279.915i			0.339702i
$825$		0			0
$826$	247.866			0.300080
$827$	464.647	+	464.647i	0.561846	+	0.561846i	0.929832	−	0.367985i	$-0.119952\pi$
$827$	464.647	+	464.647i	0.561846	+	0.561846i	−0.367985	+	0.929832i	$0.619952\pi$
$828$		0			0
$829$			1169.96i			1.41130i	0.708563	+	0.705648i	$0.249344\pi$
$829$			1169.96i			1.41130i	−0.708563	+	0.705648i	$0.750656\pi$
$830$	1037.54	+	166.289i	1.25005	+	0.200348i
$831$		0			0
$832$	−396.538	−	396.538i	−0.476609	−	0.476609i
$833$	596.532	−	596.532i	0.716125	−	0.716125i
$834$		0			0
$835$	−325.944	−	450.365i	−0.390352	−	0.539359i
$836$	42.1516			0.0504205
$837$		0			0
$838$	1031.44	−	1031.44i	1.23083	−	1.23083i
$839$		−	1023.15i		−	1.21949i	−0.792598	−	0.609745i	$-0.791272\pi$
$839$		−	1023.15i		−	1.21949i	0.792598	−	0.609745i	$-0.208728\pi$
$840$		0			0
$841$	−494.102			−0.587517
$842$	1101.02	+	1101.02i	1.30763	+	1.30763i
$843$		0			0
$844$			524.662i			0.621637i
$845$	−290.049	+	1809.73i	−0.343253	+	2.14169i
$846$		0			0
$847$	−211.306	−	211.306i	−0.249475	−	0.249475i
$848$	−411.905	+	411.905i	−0.485737	+	0.485737i
$849$		0			0
$850$	407.018	−	1237.15i	0.478844	−	1.45547i
$851$	988.843			1.16198
$852$		0			0
$853$	−1074.01	+	1074.01i	−1.25909	+	1.25909i	−0.307565	+	0.951527i	$0.599514\pi$
$853$	−1074.01	+	1074.01i	−1.25909	+	1.25909i	−0.951527	+	0.307565i	$0.900486\pi$
$854$			310.864i			0.364010i
$855$		0			0
$856$	205.919			0.240559
$857$	969.340	+	969.340i	1.13109	+	1.13109i	0.989997	+	0.141088i	$0.0450602\pi$
$857$	969.340	+	969.340i	1.13109	+	1.13109i	0.141088	+	0.989997i	$0.454940\pi$
$858$		0			0
$859$		−	615.624i		−	0.716675i	−0.933592	−	0.358338i	$-0.883344\pi$
$859$		−	615.624i		−	0.716675i	0.933592	−	0.358338i	$-0.116656\pi$
$860$	559.396	+	772.931i	0.650460	+	0.898756i
$861$		0			0
$862$	−1050.66	−	1050.66i	−1.21886	−	1.21886i
$863$	−691.930	+	691.930i	−0.801773	+	0.801773i	−0.983373	−	0.181600i	$-0.941872\pi$
$863$	−691.930	+	691.930i	−0.801773	+	0.801773i	0.181600	+	0.983373i	$0.441872\pi$
$864$		0			0
$865$	−1134.00	+	820.710i	−1.31098	+	0.948798i
$866$	−1288.26			−1.48760
$867$		0			0
$868$	114.875	−	114.875i	0.132345	−	0.132345i
$869$			151.386i			0.174208i
$870$		0			0
$871$	−2519.19			−2.89230
$872$	69.2228	+	69.2228i	0.0793840	+	0.0793840i
$873$		0			0
$874$		−	332.187i		−	0.380077i
$875$	−97.1777	−	304.800i	−0.111060	−	0.348343i
$876$		0			0
$877$	332.120	+	332.120i	0.378700	+	0.378700i	0.870633	−	0.491933i	$-0.163709\pi$
$877$	332.120	+	332.120i	0.378700	+	0.378700i	−0.491933	+	0.870633i	$0.663709\pi$
$878$	1492.92	−	1492.92i	1.70036	−	1.70036i
$879$		0			0
$880$	−195.563	−	31.3434i	−0.222231	−	0.0356175i
$881$	−239.224			−0.271537			−0.135768	−	0.990741i	$-0.543350\pi$
$881$	−239.224			−0.271537			−0.135768	+	0.990741i	$0.543350\pi$
$882$		0			0
$883$	2.33713	−	2.33713i	0.00264681	−	0.00264681i	−0.705782	−	0.708429i	$-0.749404\pi$
$883$	2.33713	−	2.33713i	0.00264681	−	0.00264681i	0.708429	+	0.705782i	$0.249404\pi$
$884$		−	1320.66i		−	1.49396i
$885$		0			0
$886$	1944.53			2.19473
$887$	980.906	+	980.906i	1.10587	+	1.10587i	0.993688	+	0.112182i	$0.0357840\pi$
$887$	980.906	+	980.906i	1.10587	+	1.10587i	0.112182	+	0.993688i	$0.464216\pi$
$888$		0			0
$889$			403.054i			0.453379i
$890$	775.145	−	560.999i	0.870950	−	0.630335i
$891$		0			0
$892$	−778.648	−	778.648i	−0.872924	−	0.872924i
$893$	−401.327	+	401.327i	−0.449415	+	0.449415i
$894$		0			0
$895$	209.333	−	1306.11i	0.233891	−	1.45934i
$896$	−232.625			−0.259626
$897$		0			0
$898$	640.234	−	640.234i	0.712955	−	0.712955i
$899$		−	807.716i		−	0.898461i
$900$		0			0
$901$	−601.686			−0.667798
$902$	56.0449	+	56.0449i	0.0621340	+	0.0621340i
$903$		0			0
$904$			28.4384i			0.0314585i
$905$	−566.899	−	90.8582i	−0.626408	−	0.100396i
$906$		0			0
$907$	167.419	+	167.419i	0.184586	+	0.184586i	0.793351	−	0.608765i	$-0.208335\pi$
$907$	167.419	+	167.419i	0.184586	+	0.184586i	−0.608765	+	0.793351i	$0.708335\pi$
$908$	340.919	−	340.919i	0.375461	−	0.375461i
$909$		0			0
$910$	−455.141	−	628.879i	−0.500154	−	0.691075i
$911$	954.706			1.04798			0.523988	−	0.851726i	$-0.324444\pi$
$911$	954.706			1.04798			0.523988	+	0.851726i	$0.324444\pi$
$912$		0			0
$913$	116.711	−	116.711i	0.127832	−	0.127832i
$914$		−	1227.88i		−	1.34342i
$915$		0			0
$916$	−276.033			−0.301346
$917$	−96.2585	−	96.2585i	−0.104971	−	0.104971i
$918$		0			0
$919$			549.663i			0.598110i	0.954236	+	0.299055i	$0.0966714\pi$
$919$			549.663i			0.598110i	−0.954236	+	0.299055i	$0.903329\pi$
$920$	−41.6009	+	259.564i	−0.0452183	+	0.282135i
$921$		0			0
$922$	128.577	+	128.577i	0.139454	+	0.139454i
$923$	−1671.06	+	1671.06i	−1.81047	+	1.81047i
$924$		0			0
$925$	−626.897	−	1241.64i	−0.677726	−	1.34231i
$926$	−601.772			−0.649861
$927$		0			0
$928$	997.402	−	997.402i	1.07479	−	1.07479i
$929$			338.546i			0.364419i	0.983260	+	0.182210i	$0.0583250\pi$
$929$			338.546i			0.364419i	−0.983260	+	0.182210i	$0.941675\pi$
$930$		0			0
$931$	−302.668			−0.325100
$932$	58.3846	+	58.3846i	0.0626444	+	0.0626444i
$933$		0			0
$934$		−	388.323i		−	0.415763i
$935$	−119.941	−	165.726i	−0.128280	−	0.177247i
$936$		0			0
$937$	721.149	+	721.149i	0.769636	+	0.769636i	0.978042	−	0.208406i	$-0.0668277\pi$
$937$	721.149	+	721.149i	0.769636	+	0.769636i	−0.208406	+	0.978042i	$0.566828\pi$
$938$	516.409	−	516.409i	0.550543	−	0.550543i
$939$		0			0
$940$	−925.858	+	670.074i	−0.984955	+	0.712845i
$941$	18.0797			0.0192133			0.00960663	−	0.999954i	$-0.496942\pi$
$941$	18.0797			0.0192133			0.00960663	+	0.999954i	$0.496942\pi$
$942$		0			0
$943$	184.572	−	184.572i	0.195728	−	0.195728i
$944$			710.850i			0.753019i
$945$		0			0
$946$	358.638			0.379110
$947$	−126.473	−	126.473i	−0.133551	−	0.133551i	0.637171	−	0.770722i	$-0.280104\pi$
$947$	−126.473	−	126.473i	−0.133551	−	0.133551i	−0.770722	+	0.637171i	$0.780104\pi$
$948$		0			0
$949$		−	341.327i		−	0.359670i
$950$	−417.109	+	210.597i	−0.439062	+	0.221681i
$951$		0			0
$952$	−106.390	−	106.390i	−0.111754	−	0.111754i
$953$	1120.28	−	1120.28i	1.17553	−	1.17553i	0.194656	−	0.980872i	$-0.437641\pi$
$953$	1120.28	−	1120.28i	1.17553	−	1.17553i	0.980872	−	0.194656i	$-0.0623591\pi$
$954$		0			0
$955$	960.916	+	154.008i	1.00620	+	0.161265i
$956$	254.357			0.266063
$957$		0			0
$958$	935.034	−	935.034i	0.976027	−	0.976027i
$959$		−	72.5654i		−	0.0756678i
$960$		0			0
$961$	−472.344			−0.491513
$962$	−2386.60	−	2386.60i	−2.48087	−	2.48087i
$963$		0			0
$964$		−	404.995i		−	0.420119i
$965$	−812.544	+	588.065i	−0.842014	+	0.609394i
$966$		0			0
$967$	265.571	+	265.571i	0.274634	+	0.274634i	0.830962	−	0.556329i	$-0.187790\pi$
$967$	265.571	+	265.571i	0.274634	+	0.274634i	−0.556329	+	0.830962i	$0.687790\pi$
$968$	244.231	−	244.231i	0.252305	−	0.252305i
$969$		0			0
$970$	−229.967	+	1434.85i	−0.237079	+	1.47923i
$971$	−416.272			−0.428704			−0.214352	−	0.976756i	$-0.568764\pi$
$971$	−416.272			−0.428704			−0.214352	+	0.976756i	$0.568764\pi$
$972$		0			0
$973$	−236.147	+	236.147i	−0.242700	+	0.242700i
$974$			1614.75i			1.65786i
$975$		0			0
$976$	−891.523			−0.913445
$977$	−446.115	−	446.115i	−0.456617	−	0.456617i	0.440926	−	0.897543i	$-0.354650\pi$
$977$	−446.115	−	446.115i	−0.456617	−	0.456617i	−0.897543	+	0.440926i	$0.854650\pi$
$978$		0			0
$979$		−	150.300i		−	0.153524i
$980$	−601.800	−	96.4518i	−0.614081	−	0.0984202i
$981$		0			0
$982$	−905.909	−	905.909i	−0.922515	−	0.922515i
$983$	−783.072	+	783.072i	−0.796615	+	0.796615i	−0.982560	−	0.185945i	$-0.940465\pi$
$983$	−783.072	+	783.072i	−0.796615	+	0.796615i	0.185945	+	0.982560i	$0.440465\pi$
$984$		0			0
$985$	275.993	+	381.346i	0.280196	+	0.387153i
$986$	1903.52			1.93055
$987$		0			0
$988$	−335.039	+	335.039i	−0.339108	+	0.339108i
$989$		−	1181.09i		−	1.19423i
$990$		0			0
$991$	416.020			0.419798			0.209899	−	0.977723i	$-0.432686\pi$
$991$	416.020			0.419798			0.209899	+	0.977723i	$0.432686\pi$
$992$	603.413	+	603.413i	0.608279	+	0.608279i
$993$		0			0
$994$		−	685.102i		−	0.689238i
$995$	−40.3118	+	251.521i	−0.0405144	+	0.252785i
$996$		0			0
$997$	−268.813	−	268.813i	−0.269621	−	0.269621i	0.559326	−	0.828948i	$-0.311060\pi$
$997$	−268.813	−	268.813i	−0.269621	−	0.269621i	−0.828948	+	0.559326i	$0.811060\pi$
$998$	−966.491	+	966.491i	−0.968427	+	0.968427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.g.a.82.2	yes	16
3.2	odd	2	inner	135.3.g.a.82.7	yes	16
5.2	odd	4		675.3.g.k.568.7		16
5.3	odd	4	inner	135.3.g.a.28.2	✓	16
5.4	even	2		675.3.g.k.82.7		16
9.2	odd	6		405.3.l.o.352.7		32
9.4	even	3		405.3.l.o.217.7		32
9.5	odd	6		405.3.l.o.217.2		32
9.7	even	3		405.3.l.o.352.2		32
15.2	even	4		675.3.g.k.568.2		16
15.8	even	4	inner	135.3.g.a.28.7	yes	16
15.14	odd	2		675.3.g.k.82.2		16
45.13	odd	12		405.3.l.o.298.2		32
45.23	even	12		405.3.l.o.298.7		32
45.38	even	12		405.3.l.o.28.2		32
45.43	odd	12		405.3.l.o.28.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.2	✓	16	5.3	odd	4	inner
135.3.g.a.28.7	yes	16	15.8	even	4	inner
135.3.g.a.82.2	yes	16	1.1	even	1	trivial
135.3.g.a.82.7	yes	16	3.2	odd	2	inner
405.3.l.o.28.2		32	45.38	even	12
405.3.l.o.28.7		32	45.43	odd	12
405.3.l.o.217.2		32	9.5	odd	6
405.3.l.o.217.7		32	9.4	even	3
405.3.l.o.298.2		32	45.13	odd	12
405.3.l.o.298.7		32	45.23	even	12
405.3.l.o.352.2		32	9.7	even	3
405.3.l.o.352.7		32	9.2	odd	6
675.3.g.k.82.2		16	15.14	odd	2
675.3.g.k.82.7		16	5.4	even	2
675.3.g.k.568.2		16	15.2	even	4
675.3.g.k.568.7		16	5.2	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85358 - 1.85358i) q^{2} +2.87153i q^{4} +(-4.93699 - 0.791263i) q^{5} +(1.80972 + 1.80972i) q^{7} +(-2.09171 + 2.09171i) q^{8} +O(q^{10})\)	\(q+(-1.85358 - 1.85358i) q^{2} +2.87153i q^{4} +(-4.93699 - 0.791263i) q^{5} +(1.80972 + 1.80972i) q^{7} +(-2.09171 + 2.09171i) q^{8} +(7.68445 + 10.6178i) q^{10} +2.05878 q^{11} +(-16.3641 + 16.3641i) q^{13} -6.70894i q^{14} +19.2404 q^{16} +(14.0526 + 14.0526i) q^{17} -7.13001i q^{19} +(2.27214 - 14.1767i) q^{20} +(-3.81612 - 3.81612i) q^{22} +(-12.5675 + 12.5675i) q^{23} +(23.7478 + 7.81292i) q^{25} +60.6642 q^{26} +(-5.19667 + 5.19667i) q^{28} +36.5390i q^{29} -22.1056 q^{31} +(-27.2969 - 27.2969i) q^{32} -52.0955i q^{34} +(-7.50262 - 10.3666i) q^{35} +(-39.3412 - 39.3412i) q^{37} +(-13.2161 + 13.2161i) q^{38} +(11.9818 - 8.67166i) q^{40} -14.6864 q^{41} +(-46.9899 + 46.9899i) q^{43} +5.91185i q^{44} +46.5899 q^{46} +(-56.2870 - 56.2870i) q^{47} -42.4498i q^{49} +(-29.5366 - 58.5004i) q^{50} +(-46.9899 - 46.9899i) q^{52} +(-21.4083 + 21.4083i) q^{53} +(-10.1642 - 1.62904i) q^{55} -7.57082 q^{56} +(67.7281 - 67.7281i) q^{58} +36.9457i q^{59} -46.3359 q^{61} +(40.9745 + 40.9745i) q^{62} +24.2323i q^{64} +(93.7375 - 67.8409i) q^{65} +(76.9734 + 76.9734i) q^{67} +(-40.3526 + 40.3526i) q^{68} +(-5.30853 + 33.1220i) q^{70} +102.118 q^{71} +(-10.4292 + 10.4292i) q^{73} +145.844i q^{74} +20.4741 q^{76} +(3.72582 + 3.72582i) q^{77} +73.5321i q^{79} +(-94.9899 - 15.2242i) q^{80} +(27.2224 + 27.2224i) q^{82} +(56.6893 - 56.6893i) q^{83} +(-58.2585 - 80.4972i) q^{85} +174.199 q^{86} +(-4.30637 + 4.30637i) q^{88} -73.0044i q^{89} -59.2288 q^{91} +(-36.0881 - 36.0881i) q^{92} +208.665i q^{94} +(-5.64172 + 35.2008i) q^{95} +(78.3975 + 78.3975i) q^{97} +(-78.6842 + 78.6842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 32 q^{10} + 28 q^{13} - 20 q^{16} + 176 q^{22} + 64 q^{25} + 80 q^{28} - 208 q^{31} - 176 q^{37} - 252 q^{40} - 188 q^{43} + 188 q^{46} - 188 q^{52} - 136 q^{55} + 504 q^{58} + 296 q^{61} + 304 q^{67} + 684 q^{70} - 56 q^{73} - 732 q^{76} - 76 q^{82} - 788 q^{85} - 1128 q^{88} + 200 q^{91} - 284 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 32 * q^10 + 28 * q^13 - 20 * q^16 + 176 * q^22 + 64 * q^25 + 80 * q^28 - 208 * q^31 - 176 * q^37 - 252 * q^40 - 188 * q^43 + 188 * q^46 - 188 * q^52 - 136 * q^55 + 504 * q^58 + 296 * q^61 + 304 * q^67 + 684 * q^70 - 56 * q^73 - 732 * q^76 - 76 * q^82 - 788 * q^85 - 1128 * q^88 + 200 * q^91 - 284 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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