LMFDB - Embedded newform 504.2.q.d.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.8
Character	$\chi$	$=$	504.25
Dual form			504.2.q.d.121.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22753 - 1.22195i) q^{3} +(1.76479 - 3.05671i) q^{5} +(-2.63986 + 0.176417i) q^{7} +(0.0136831 - 2.99997i) q^{9} +O(q^{10})$	\(q+(1.22753 - 1.22195i) q^{3} +(1.76479 - 3.05671i) q^{5} +(-2.63986 + 0.176417i) q^{7} +(0.0136831 - 2.99997i) q^{9} +(1.16036 + 2.00981i) q^{11} +(-2.35884 - 4.08563i) q^{13} +(-1.56880 - 5.90871i) q^{15} +(-0.636946 + 1.10322i) q^{17} +(2.78386 + 4.82178i) q^{19} +(-3.02495 + 3.44233i) q^{21} +(1.64855 - 2.85537i) q^{23} +(-3.72899 - 6.45880i) q^{25} +(-3.64901 - 3.69929i) q^{27} +(-4.32116 + 7.48447i) q^{29} +8.51642 q^{31} +(3.88027 + 1.04921i) q^{33} +(-4.11956 + 8.38064i) q^{35} +(-2.84024 - 4.91943i) q^{37} +(-7.88798 - 2.13287i) q^{39} +(1.66553 + 2.88478i) q^{41} +(0.0444165 - 0.0769317i) q^{43} +(-9.14589 - 5.33615i) q^{45} +7.05213 q^{47} +(6.93775 - 0.931432i) q^{49} +(0.566208 + 2.13256i) q^{51} +(3.41816 - 5.92042i) q^{53} +8.19121 q^{55} +(9.30925 + 2.51717i) q^{57} -7.99490 q^{59} +13.3553 q^{61} +(0.493123 + 7.92192i) q^{63} -16.6514 q^{65} +6.12804 q^{67} +(-1.46546 - 5.51951i) q^{69} +1.30202 q^{71} +(6.64529 - 11.5100i) q^{73} +(-12.4698 - 3.37177i) q^{75} +(-3.41777 - 5.10092i) q^{77} -10.0281 q^{79} +(-8.99963 - 0.0820978i) q^{81} +(-5.90243 + 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(3.84126 + 14.4677i) q^{87} +(0.561496 + 0.972540i) q^{89} +(6.94778 + 10.3694i) q^{91} +(10.4542 - 10.4066i) q^{93} +19.6517 q^{95} +(-3.50818 + 6.07635i) q^{97} +(6.04525 - 3.45356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.22753	−	1.22195i	0.708718	−	0.705492i
$3$	1.22753	−	1.22195i	0.708718	−	0.705492i
$4$		0			0
$5$	1.76479	−	3.05671i	0.789239	−	1.36700i	−0.137194	−	0.990544i	$-0.543808\pi$
$5$	1.76479	−	3.05671i	0.789239	−	1.36700i	0.926433	−	0.376459i	$-0.122858\pi$
$6$		0			0
$7$	−2.63986	+	0.176417i	−0.997774	+	0.0666792i
$7$	−2.63986	+	0.176417i	−0.997774	+	0.0666792i
$8$		0			0
$9$	0.0136831	−	2.99997i	0.00456103	−	0.999990i
$10$		0			0
$11$	1.16036	+	2.00981i	0.349863	+	0.605981i	0.986225	−	0.165410i	$-0.0528948\pi$
$11$	1.16036	+	2.00981i	0.349863	+	0.605981i	−0.636362	+	0.771391i	$0.719561\pi$
$12$		0			0
$13$	−2.35884	−	4.08563i	−0.654224	−	1.13315i	−0.982088	−	0.188424i	$-0.939662\pi$
$13$	−2.35884	−	4.08563i	−0.654224	−	1.13315i	0.327864	−	0.944725i	$-0.393671\pi$
$14$		0			0
$15$	−1.56880	−	5.90871i	−0.405062	−	1.52562i
$16$		0			0
$17$	−0.636946	+	1.10322i	−0.154482	+	0.267571i	−0.932870	−	0.360212i	$-0.882704\pi$
$17$	−0.636946	+	1.10322i	−0.154482	+	0.267571i	0.778388	+	0.627783i	$0.216038\pi$
$18$		0			0
$19$	2.78386	+	4.82178i	0.638661	+	1.10619i	0.985727	+	0.168352i	$0.0538445\pi$
$19$	2.78386	+	4.82178i	0.638661	+	1.10619i	−0.347066	+	0.937841i	$0.612822\pi$
$20$		0			0
$21$	−3.02495	+	3.44233i	−0.660099	+	0.751179i
$22$		0			0
$23$	1.64855	−	2.85537i	0.343746	−	0.595386i	−0.641379	−	0.767224i	$-0.721637\pi$
$23$	1.64855	−	2.85537i	0.343746	−	0.595386i	0.985125	+	0.171838i	$0.0549707\pi$
$24$		0			0
$25$	−3.72899	−	6.45880i	−0.745798	−	1.29176i
$26$		0			0
$27$	−3.64901	−	3.69929i	−0.702253	−	0.711928i
$28$		0			0
$29$	−4.32116	+	7.48447i	−0.802419	+	1.38983i	0.115601	+	0.993296i	$0.463121\pi$
$29$	−4.32116	+	7.48447i	−0.802419	+	1.38983i	−0.918020	+	0.396535i	$0.870213\pi$
$30$		0			0
$31$	8.51642			1.52959			0.764797	−	0.644272i	$-0.222839\pi$
$31$	8.51642			1.52959			0.764797	+	0.644272i	$0.222839\pi$
$32$		0			0
$33$	3.88027	+	1.04921i	0.675469	+	0.182643i
$34$		0			0
$35$	−4.11956	+	8.38064i	−0.696332	+	1.41659i
$36$		0			0
$37$	−2.84024	−	4.91943i	−0.466932	−	0.808750i	0.532354	−	0.846522i	$-0.321307\pi$
$37$	−2.84024	−	4.91943i	−0.466932	−	0.808750i	−0.999286	+	0.0377716i	$0.987974\pi$
$38$		0			0
$39$	−7.88798	−	2.13287i	−1.26309	−	0.341533i
$40$		0			0
$41$	1.66553	+	2.88478i	0.260112	+	0.450528i	0.966272	−	0.257525i	$-0.0829071\pi$
$41$	1.66553	+	2.88478i	0.260112	+	0.450528i	−0.706159	+	0.708053i	$0.749574\pi$
$42$		0			0
$43$	0.0444165	−	0.0769317i	0.00677346	−	0.0117320i	−0.862619	−	0.505855i	$-0.831177\pi$
$43$	0.0444165	−	0.0769317i	0.00677346	−	0.0117320i	0.869392	+	0.494123i	$0.164511\pi$
$44$		0			0
$45$	−9.14589	−	5.33615i	−1.36339	−	0.795466i
$46$		0			0
$47$	7.05213			1.02866			0.514330	−	0.857593i	$-0.328041\pi$
$47$	7.05213			1.02866			0.514330	+	0.857593i	$0.328041\pi$
$48$		0			0
$49$	6.93775	−	0.931432i	0.991108	−	0.133062i
$50$		0			0
$51$	0.566208	+	2.13256i	0.0792850	+	0.298618i
$52$		0			0
$53$	3.41816	−	5.92042i	0.469520	−	0.813233i	−0.529873	−	0.848077i	$-0.677760\pi$
$53$	3.41816	−	5.92042i	0.469520	−	0.813233i	0.999393	+	0.0348444i	$0.0110936\pi$
$54$		0			0
$55$	8.19121			1.10450
$56$		0			0
$57$	9.30925	+	2.51717i	1.23304	+	0.333408i
$58$		0			0
$59$	−7.99490			−1.04085			−0.520423	−	0.853908i	$-0.674226\pi$
$59$	−7.99490			−1.04085			−0.520423	+	0.853908i	$0.674226\pi$
$60$		0			0
$61$	13.3553			1.70997			0.854985	−	0.518653i	$-0.173566\pi$
$61$	13.3553			1.70997			0.854985	+	0.518653i	$0.173566\pi$
$62$		0			0
$63$	0.493123	+	7.92192i	0.0621277	+	0.998068i
$64$		0			0
$65$	−16.6514			−2.06536
$66$		0			0
$67$	6.12804			0.748660			0.374330	−	0.927296i	$-0.377873\pi$
$67$	6.12804			0.748660			0.374330	+	0.927296i	$0.377873\pi$
$68$		0			0
$69$	−1.46546	−	5.51951i	−0.176421	−	0.664471i
$70$		0			0
$71$	1.30202			0.154522			0.0772609	−	0.997011i	$-0.475383\pi$
$71$	1.30202			0.154522			0.0772609	+	0.997011i	$0.475383\pi$
$72$		0			0
$73$	6.64529	−	11.5100i	0.777772	−	1.34714i	−0.155451	−	0.987844i	$-0.549683\pi$
$73$	6.64529	−	11.5100i	0.777772	−	1.34714i	0.933223	−	0.359297i	$-0.116984\pi$
$74$		0			0
$75$	−12.4698	−	3.37177i	−1.43989	−	0.389338i
$76$		0			0
$77$	−3.41777	−	5.10092i	−0.389491	−	0.581303i
$78$		0			0
$79$	−10.0281			−1.12824			−0.564122	−	0.825691i	$-0.690785\pi$
$79$	−10.0281			−1.12824			−0.564122	+	0.825691i	$0.690785\pi$
$80$		0			0
$81$	−8.99963	−	0.0820978i	−0.999958	−	0.00912197i
$82$		0			0
$83$	−5.90243	+	10.2233i	−0.647876	+	1.12215i	0.335753	+	0.941950i	$0.391009\pi$
$83$	−5.90243	+	10.2233i	−0.647876	+	1.12215i	−0.983629	+	0.180204i	$0.942324\pi$
$84$		0			0
$85$	2.24815	+	3.89392i	0.243847	+	0.422355i
$86$		0			0
$87$	3.84126	+	14.4677i	0.411826	+	1.55110i
$88$		0			0
$89$	0.561496	+	0.972540i	0.0595185	+	0.103089i	0.894249	−	0.447569i	$-0.147710\pi$
$89$	0.561496	+	0.972540i	0.0595185	+	0.103089i	−0.834731	+	0.550658i	$0.814377\pi$
$90$		0			0
$91$	6.94778	+	10.3694i	0.728325	+	1.08700i
$92$		0			0
$93$	10.4542	−	10.4066i	1.08405	−	1.07912i
$94$		0			0
$95$	19.6517			2.01622
$96$		0			0
$97$	−3.50818	+	6.07635i	−0.356202	+	0.616960i	−0.987323	−	0.158724i	$-0.949262\pi$
$97$	−3.50818	+	6.07635i	−0.356202	+	0.616960i	0.631121	+	0.775685i	$0.282595\pi$
$98$		0			0
$99$	6.04525	−	3.45356i	0.607570	−	0.347096i
$100$		0			0
$101$	4.87055	+	8.43605i	0.484638	+	0.839418i	0.999844	−	0.0176482i	$-0.00561789\pi$
$101$	4.87055	+	8.43605i	0.484638	+	0.839418i	−0.515206	+	0.857066i	$0.672285\pi$
$102$		0			0
$103$	−5.14279	+	8.90757i	−0.506734	+	0.877689i	0.493236	+	0.869896i	$0.335814\pi$
$103$	−5.14279	+	8.90757i	−0.506734	+	0.877689i	−0.999970	+	0.00779301i	$0.997519\pi$
$104$		0			0
$105$	5.18381	+	15.3214i	0.505888	+	1.49522i
$106$		0			0
$107$	2.72201	+	4.71465i	0.263146	+	0.455783i	0.967076	−	0.254487i	$-0.0819065\pi$
$107$	2.72201	+	4.71465i	0.263146	+	0.455783i	−0.703930	+	0.710269i	$0.748573\pi$
$108$		0			0
$109$	0.417404	−	0.722965i	0.0399800	−	0.0692475i	−0.845343	−	0.534224i	$-0.820604\pi$
$109$	0.417404	−	0.722965i	0.0399800	−	0.0692475i	0.885323	+	0.464977i	$0.153937\pi$
$110$		0			0
$111$	−9.49778	−	2.56815i	−0.901490	−	0.243758i
$112$		0			0
$113$	5.44881	+	9.43761i	0.512581	+	0.887815i	0.999894	+	0.0145882i	$0.00464372\pi$
$113$	5.44881	+	9.43761i	0.512581	+	0.887815i	−0.487313	+	0.873227i	$0.662023\pi$
$114$		0			0
$115$	−5.81870	−	10.0783i	−0.542596	−	0.939804i
$116$		0			0
$117$	−12.2890	+	7.02054i	−1.13612	+	0.649049i
$118$		0			0
$119$	1.48682	−	3.02472i	0.136297	−	0.277276i
$120$		0			0
$121$	2.80711	−	4.86205i	0.255192	−	0.442005i
$122$		0			0
$123$	5.56956	+	1.50598i	0.502190	+	0.135790i
$124$		0			0
$125$	−8.67565			−0.775974
$126$		0			0
$127$	−9.90354			−0.878797			−0.439399	−	0.898292i	$-0.644808\pi$
$127$	−9.90354			−0.878797			−0.439399	+	0.898292i	$0.644808\pi$
$128$		0			0
$129$	−0.0394837	−	0.148711i	−0.00347635	−	0.0130933i
$130$		0			0
$131$	−8.59220	+	14.8821i	−0.750704	+	1.30026i	0.196778	+	0.980448i	$0.436952\pi$
$131$	−8.59220	+	14.8821i	−0.750704	+	1.30026i	−0.947482	+	0.319809i	$0.896381\pi$
$132$		0			0
$133$	−8.19964	−	12.2377i	−0.710999	−	1.06115i
$134$		0			0
$135$	−17.7474	+	4.62550i	−1.52745	+	0.398100i
$136$		0			0
$137$	8.04696	+	13.9377i	0.687498	+	1.19078i	0.972645	+	0.232298i	$0.0746243\pi$
$137$	8.04696	+	13.9377i	0.687498	+	1.19078i	−0.285147	+	0.958484i	$0.592042\pi$
$138$		0			0
$139$	1.11151	+	1.92519i	0.0942768	+	0.163292i	0.909307	−	0.416127i	$-0.136613\pi$
$139$	1.11151	+	1.92519i	0.0942768	+	0.163292i	−0.815030	+	0.579419i	$0.803279\pi$
$140$		0			0
$141$	8.65674	−	8.61735i	0.729029	−	0.725711i
$142$		0			0
$143$	5.47422	−	9.48163i	0.457778	−	0.792894i
$144$		0			0
$145$	15.2519	+	26.4171i	1.26660	+	2.19382i
$146$		0			0
$147$	7.37817	−	9.62094i	0.608541	−	0.793522i
$148$		0			0
$149$	−3.46846	+	6.00755i	−0.284147	+	0.492158i	−0.972402	−	0.233312i	$-0.925044\pi$
$149$	−3.46846	+	6.00755i	−0.284147	+	0.492158i	0.688255	+	0.725469i	$0.258377\pi$
$150$		0			0
$151$	−7.75834	−	13.4378i	−0.631365	−	1.09356i	−0.987273	−	0.159035i	$-0.949162\pi$
$151$	−7.75834	−	13.4378i	−0.631365	−	1.09356i	0.355908	−	0.934521i	$-0.384172\pi$
$152$		0			0
$153$	3.30092	+	1.92591i	0.266863	+	0.155701i
$154$		0			0
$155$	15.0297	−	26.0322i	1.20722	−	2.09096i
$156$		0			0
$157$	0.802110			0.0640154			0.0320077	−	0.999488i	$-0.489810\pi$
$157$	0.802110			0.0640154			0.0320077	+	0.999488i	$0.489810\pi$
$158$		0			0
$159$	−3.03855	−	11.4443i	−0.240972	−	0.907595i
$160$		0			0
$161$	−3.84821	+	7.82862i	−0.303281	+	0.616982i
$162$		0			0
$163$	1.77500	+	3.07438i	0.139028	+	0.240804i	0.927129	−	0.374742i	$-0.122269\pi$
$163$	1.77500	+	3.07438i	0.139028	+	0.240804i	−0.788101	+	0.615546i	$0.788935\pi$
$164$		0			0
$165$	10.0550	−	10.0092i	0.782781	−	0.779219i
$166$		0			0
$167$	0.865131	+	1.49845i	0.0669459	+	0.115954i	0.897556	−	0.440901i	$-0.145341\pi$
$167$	0.865131	+	1.49845i	0.0669459	+	0.115954i	−0.830610	+	0.556855i	$0.812008\pi$
$168$		0			0
$169$	−4.62823	+	8.01633i	−0.356018	+	0.616641i
$170$		0			0
$171$	14.5033	−	8.28551i	1.10909	−	0.633609i
$172$		0			0
$173$	2.23458			0.169892			0.0849462	−	0.996386i	$-0.472928\pi$
$173$	2.23458			0.169892			0.0849462	+	0.996386i	$0.472928\pi$
$174$		0			0
$175$	10.9835	+	16.3925i	0.830272	+	1.23916i
$176$		0			0
$177$	−9.81401	+	9.76935i	−0.737666	+	0.734309i
$178$		0			0
$179$	−0.350412	+	0.606931i	−0.0261910	+	0.0453641i	−0.878824	−	0.477146i	$-0.841671\pi$
$179$	−0.350412	+	0.606931i	−0.0261910	+	0.0453641i	0.852633	+	0.522511i	$0.175004\pi$
$180$		0			0
$181$	−19.6339			−1.45938			−0.729688	−	0.683780i	$-0.760335\pi$
$181$	−19.6339			−1.45938			−0.729688	+	0.683780i	$0.760335\pi$
$182$		0			0
$183$	16.3941	−	16.3195i	1.21189	−	1.20637i
$184$		0			0
$185$	−20.0497			−1.47408
$186$		0			0
$187$	−2.95636			−0.216190
$188$		0			0
$189$	10.2855	+	9.12186i	0.748160	+	0.663518i
$190$		0			0
$191$	16.0858			1.16393			0.581963	−	0.813215i	$-0.302285\pi$
$191$	16.0858			1.16393			0.581963	+	0.813215i	$0.302285\pi$
$192$		0			0
$193$	−0.585463			−0.0421426			−0.0210713	−	0.999778i	$-0.506708\pi$
$193$	−0.585463			−0.0421426			−0.0210713	+	0.999778i	$0.506708\pi$
$194$		0			0
$195$	−20.4402	+	20.3472i	−1.46375	+	1.45709i
$196$		0			0
$197$	−17.2923			−1.23203			−0.616014	−	0.787735i	$-0.711254\pi$
$197$	−17.2923			−1.23203			−0.616014	+	0.787735i	$0.711254\pi$
$198$		0			0
$199$	−12.2119	+	21.1517i	−0.865681	+	1.49940i	0.000687656		1.00000i	$0.499781\pi$
$199$	−12.2119	+	21.1517i	−0.865681	+	1.49940i	−0.866369	+	0.499404i	$0.833552\pi$
$200$		0			0
$201$	7.52239	−	7.48815i	0.530588	−	0.528174i
$202$		0			0
$203$	10.0869	−	20.5203i	0.707960	−	1.44024i
$204$		0			0
$205$	11.7573			0.821164
$206$		0			0
$207$	−8.54347	−	4.98467i	−0.593812	−	0.346458i
$208$		0			0
$209$	−6.46058	+	11.1900i	−0.446888	+	0.774032i
$210$		0			0
$211$	−5.58733	−	9.67754i	−0.384648	−	0.666230i	0.607072	−	0.794647i	$-0.292344\pi$
$211$	−5.58733	−	9.67754i	−0.384648	−	0.666230i	−0.991720	+	0.128417i	$0.959010\pi$
$212$		0			0
$213$	1.59828	−	1.59101i	0.109512	−	0.109014i
$214$		0			0
$215$	−0.156772	−	0.271537i	−0.0106918	−	0.0185187i
$216$		0			0
$217$	−22.4822	+	1.50244i	−1.52619	+	0.101992i
$218$		0			0
$219$	−5.90728	−	22.2491i	−0.399177	−	1.50345i
$220$		0			0
$221$	6.00981			0.404263
$222$		0			0
$223$	−1.32951	+	2.30277i	−0.0890303	+	0.154205i	−0.907101	−	0.420912i	$-0.861710\pi$
$223$	−1.32951	+	2.30277i	−0.0890303	+	0.154205i	0.818071	+	0.575117i	$0.195043\pi$
$224$		0			0
$225$	−19.4272	+	11.0985i	−1.29515	+	0.739898i
$226$		0			0
$227$	−5.95786	−	10.3193i	−0.395437	−	0.684917i	0.597720	−	0.801705i	$-0.296073\pi$
$227$	−5.95786	−	10.3193i	−0.395437	−	0.684917i	−0.993157	+	0.116788i	$0.962740\pi$
$228$		0			0
$229$	14.8064	−	25.6454i	0.978434	−	1.69470i	0.310330	−	0.950629i	$-0.399561\pi$
$229$	14.8064	−	25.6454i	0.978434	−	1.69470i	0.668104	−	0.744068i	$-0.267106\pi$
$230$		0			0
$231$	−10.4285	−	2.08522i	−0.686144	−	0.137197i
$232$		0			0
$233$	1.84417	+	3.19420i	0.120816	+	0.209259i	0.920090	−	0.391708i	$-0.128116\pi$
$233$	1.84417	+	3.19420i	0.120816	+	0.209259i	−0.799274	+	0.600967i	$0.794782\pi$
$234$		0			0
$235$	12.4456	−	21.5563i	0.811859	−	1.40618i
$236$		0			0
$237$	−12.3098	+	12.2538i	−0.799607	+	0.795968i
$238$		0			0
$239$	8.03590	+	13.9186i	0.519799	+	0.900319i	0.999735	+	0.0230153i	$0.00732663\pi$
$239$	8.03590	+	13.9186i	0.519799	+	0.900319i	−0.479936	+	0.877304i	$0.659340\pi$
$240$		0			0
$241$	−2.24933	−	3.89596i	−0.144892	−	0.250961i	0.784440	−	0.620204i	$-0.212950\pi$
$241$	−2.24933	−	3.89596i	−0.144892	−	0.250961i	−0.929333	+	0.369243i	$0.879617\pi$
$242$		0			0
$243$	−11.1477	+	10.8963i	−0.715124	+	0.698998i
$244$		0			0
$245$	9.39658	−	22.8505i	0.600326	−	1.45986i
$246$		0			0
$247$	13.1333	−	22.7476i	0.835654	−	1.44740i
$248$		0			0
$249$	5.24692	+	19.7619i	0.332510	+	1.25236i
$250$		0			0
$251$	−17.2696			−1.09005			−0.545023	−	0.838421i	$-0.683479\pi$
$251$	−17.2696			−1.09005			−0.545023	+	0.838421i	$0.683479\pi$
$252$		0			0
$253$	7.65167			0.481057
$254$		0			0
$255$	7.51786	+	2.03279i	0.470786	+	0.127298i
$256$		0			0
$257$	−2.41087	+	4.17574i	−0.150386	+	0.260476i	−0.931369	−	0.364076i	$-0.881385\pi$
$257$	−2.41087	+	4.17574i	−0.150386	+	0.260476i	0.780984	+	0.624552i	$0.214718\pi$
$258$		0			0
$259$	8.36571	+	12.4856i	0.519820	+	0.775815i
$260$		0			0
$261$	22.3940	+	13.0658i	1.38616	+	0.808750i
$262$		0			0
$263$	−14.0452	−	24.3270i	−0.866062	−	1.50006i	−0.865988	−	0.500064i	$-0.833310\pi$
$263$	−14.0452	−	24.3270i	−0.866062	−	1.50006i	−7.41948e−5	−	1.00000i	$-0.500024\pi$
$264$		0			0
$265$	−12.0647	−	20.8966i	−0.741128	−	1.28367i
$266$		0			0
$267$	1.87765	+	0.507707i	0.114910	+	0.0310712i
$268$		0			0
$269$	12.4126	−	21.4993i	0.756810	−	1.31083i	−0.187659	−	0.982234i	$-0.560090\pi$
$269$	12.4126	−	21.4993i	0.756810	−	1.31083i	0.944469	−	0.328599i	$-0.106577\pi$
$270$		0			0
$271$	−4.79671	−	8.30815i	−0.291379	−	0.504684i	0.682757	−	0.730646i	$-0.260781\pi$
$271$	−4.79671	−	8.30815i	−0.291379	−	0.504684i	−0.974136	+	0.225962i	$0.927448\pi$
$272$		0			0
$273$	21.1995	+	4.23891i	1.28305	+	0.256551i
$274$		0			0
$275$	8.65398	−	14.9891i	0.521854	−	0.903878i
$276$		0			0
$277$	−8.46914	−	14.6690i	−0.508862	−	0.881374i	−0.999947	−	0.0102629i	$-0.996733\pi$
$277$	−8.46914	−	14.6690i	−0.508862	−	0.881374i	0.491086	−	0.871111i	$-0.336600\pi$
$278$		0			0
$279$	0.116531	−	25.5490i	0.00697653	−	1.52958i
$280$		0			0
$281$	11.4291	−	19.7958i	0.681805	−	1.18092i	−0.292625	−	0.956227i	$-0.594529\pi$
$281$	11.4291	−	19.7958i	0.681805	−	1.18092i	0.974430	−	0.224693i	$-0.0721379\pi$
$282$		0			0
$283$	8.35621			0.496725			0.248363	−	0.968667i	$-0.420108\pi$
$283$	8.35621			0.496725			0.248363	+	0.968667i	$0.420108\pi$
$284$		0			0
$285$	24.1232	−	24.0134i	1.42893	−	1.42243i
$286$		0			0
$287$	−4.90570	−	7.32161i	−0.289574	−	0.432181i
$288$		0			0
$289$	7.68860	+	13.3170i	0.452271	+	0.783356i
$290$		0			0
$291$	3.11857	+	11.7458i	0.182814	+	0.688549i
$292$		0			0
$293$	−2.16141	−	3.74368i	−0.126271	−	0.218708i	0.795958	−	0.605352i	$-0.206968\pi$
$293$	−2.16141	−	3.74368i	−0.126271	−	0.218708i	−0.922229	+	0.386644i	$0.873634\pi$
$294$		0			0
$295$	−14.1093	+	24.4381i	−0.821477	+	1.42284i
$296$		0			0
$297$	3.20068	−	11.6263i	0.185722	−	0.674629i
$298$		0			0
$299$	−15.5546			−0.899548
$300$		0			0
$301$	−0.103682	+	0.210925i	−0.00597610	+	0.0121575i
$302$		0			0
$303$	16.2872	+	4.40397i	0.935675	+	0.253002i
$304$		0			0
$305$	23.5693	−	40.8233i	1.34958	−	2.33753i
$306$		0			0
$307$	−9.22888			−0.526720			−0.263360	−	0.964698i	$-0.584831\pi$
$307$	−9.22888			−0.526720			−0.263360	+	0.964698i	$0.584831\pi$
$308$		0			0
$309$	4.57164	+	17.2186i	0.260072	+	0.979530i
$310$		0			0
$311$	−19.1073			−1.08348			−0.541738	−	0.840548i	$-0.682233\pi$
$311$	−19.1073			−1.08348			−0.541738	+	0.840548i	$0.682233\pi$
$312$		0			0
$313$	5.67903			0.320997			0.160499	−	0.987036i	$-0.448690\pi$
$313$	5.67903			0.320997			0.160499	+	0.987036i	$0.448690\pi$
$314$		0			0
$315$	25.0853	+	12.4732i	1.41340	+	0.702786i
$316$		0			0
$317$	−28.2681			−1.58770			−0.793848	−	0.608116i	$-0.791925\pi$
$317$	−28.2681			−1.58770			−0.793848	+	0.608116i	$0.791925\pi$
$318$		0			0
$319$	−20.0565			−1.12295
$320$		0			0
$321$	9.10242	+	2.46125i	0.508048	+	0.137373i
$322$		0			0
$323$	−7.09266			−0.394646
$324$		0			0
$325$	−17.5922	+	30.4705i	−0.975838	+	1.69020i
$326$		0			0
$327$	−0.371048	−	1.39751i	−0.0205190	−	0.0772825i
$328$		0			0
$329$	−18.6167	+	1.24411i	−1.02637	+	0.0685902i
$330$		0			0
$331$	−6.68091			−0.367216			−0.183608	−	0.983000i	$-0.558778\pi$
$331$	−6.68091			−0.367216			−0.183608	+	0.983000i	$0.558778\pi$
$332$		0			0
$333$	−14.7970	+	8.45331i	−0.810871	+	0.463238i
$334$		0			0
$335$	10.8147	−	18.7317i	0.590872	−	1.02342i
$336$		0			0
$337$	−3.49421	−	6.05215i	−0.190342	−	0.329681i	0.755022	−	0.655700i	$-0.227626\pi$
$337$	−3.49421	−	6.05215i	−0.190342	−	0.329681i	−0.945363	+	0.326018i	$0.894293\pi$
$338$		0			0
$339$	18.2209	+	4.92683i	0.989622	+	0.267589i
$340$		0			0
$341$	9.88215	+	17.1164i	0.535148	+	0.926904i
$342$		0			0
$343$	−18.1504	+	3.68279i	−0.980030	+	0.198852i
$344$		0			0
$345$	−19.4578	−	5.26129i	−1.04757	−	0.283258i
$346$		0			0
$347$	8.28821			0.444934			0.222467	−	0.974940i	$-0.428589\pi$
$347$	8.28821			0.444934			0.222467	+	0.974940i	$0.428589\pi$
$348$		0			0
$349$	3.05373	−	5.28921i	0.163462	−	0.283125i	−0.772646	−	0.634837i	$-0.781067\pi$
$349$	3.05373	−	5.28921i	0.163462	−	0.283125i	0.936108	+	0.351712i	$0.114400\pi$
$350$		0			0
$351$	−6.50648	+	23.6345i	−0.347290	+	1.26152i
$352$		0			0
$353$	13.3604	+	23.1409i	0.711104	+	1.23167i	0.964443	+	0.264290i	$0.0851377\pi$
$353$	13.3604	+	23.1409i	0.711104	+	1.23167i	−0.253340	+	0.967377i	$0.581529\pi$
$354$		0			0
$355$	2.29780	−	3.97991i	0.121955	−	0.211232i
$356$		0			0
$357$	−1.87093	−	5.52977i	−0.0990201	−	0.292667i
$358$		0			0
$359$	2.45603	+	4.25397i	0.129624	+	0.224516i	0.923531	−	0.383523i	$-0.125289\pi$
$359$	2.45603	+	4.25397i	0.129624	+	0.224516i	−0.793907	+	0.608040i	$0.791956\pi$
$360$		0			0
$361$	−5.99972	+	10.3918i	−0.315775	+	0.546938i
$362$		0			0
$363$	−2.49536	−	9.39848i	−0.130972	−	0.493292i
$364$		0			0
$365$	−23.4551	−	40.6255i	−1.22770	−	2.12643i
$366$		0			0
$367$	15.3532	+	26.5925i	0.801430	+	1.38812i	0.918675	+	0.395015i	$0.129260\pi$
$367$	15.3532	+	26.5925i	0.801430	+	1.38812i	−0.117245	+	0.993103i	$0.537406\pi$
$368$		0			0
$369$	8.67705	−	4.95707i	0.451709	−	0.258055i
$370$		0			0
$371$	−7.97901	+	16.2321i	−0.414250	+	0.842730i
$372$		0			0
$373$	−8.29190	+	14.3620i	−0.429338	+	0.743635i	−0.996815	−	0.0797543i	$-0.974586\pi$
$373$	−8.29190	+	14.3620i	−0.429338	+	0.743635i	0.567477	+	0.823390i	$0.307920\pi$
$374$		0			0
$375$	−10.6497	+	10.6012i	−0.549946	+	0.547443i
$376$		0			0
$377$	40.7716			2.09985
$378$		0			0
$379$	4.08857			0.210016			0.105008	−	0.994471i	$-0.466513\pi$
$379$	4.08857			0.210016			0.105008	+	0.994471i	$0.466513\pi$
$380$		0			0
$381$	−12.1569	+	12.1016i	−0.622819	+	0.619985i
$382$		0			0
$383$	−15.1769	+	26.2871i	−0.775503	+	1.34321i	0.159009	+	0.987277i	$0.449170\pi$
$383$	−15.1769	+	26.2871i	−0.775503	+	1.34321i	−0.934511	+	0.355933i	$0.884163\pi$
$384$		0			0
$385$	−21.6237	+	1.44507i	−1.10205	+	0.0736474i
$386$		0			0
$387$	−0.230185	−	0.134301i	−0.0117010	−	0.00682690i
$388$		0			0
$389$	1.73382	+	3.00307i	0.0879082	+	0.152261i	0.906627	−	0.421934i	$-0.138648\pi$
$389$	1.73382	+	3.00307i	0.0879082	+	0.152261i	−0.818719	+	0.574195i	$0.805315\pi$
$390$		0			0
$391$	2.10007	+	3.63743i	0.106205	+	0.183953i
$392$		0			0
$393$	7.63797	+	28.7675i	0.385285	+	1.45113i
$394$		0			0
$395$	−17.6974	+	30.6529i	−0.890455	+	1.54231i
$396$		0			0
$397$	−7.04243	−	12.1979i	−0.353450	−	0.612193i	0.633402	−	0.773823i	$-0.281658\pi$
$397$	−7.04243	−	12.1979i	−0.353450	−	0.612193i	−0.986851	+	0.161630i	$0.948325\pi$
$398$		0			0
$399$	−25.0192	−	5.00269i	−1.25253	−	0.250448i
$400$		0			0
$401$	5.46593	−	9.46726i	0.272955	−	0.472772i	−0.696662	−	0.717400i	$-0.745332\pi$
$401$	5.46593	−	9.46726i	0.272955	−	0.472772i	0.969617	+	0.244627i	$0.0786656\pi$
$402$		0			0
$403$	−20.0888	−	34.7949i	−1.00070	−	1.73326i
$404$		0			0
$405$	−16.1334	+	27.3644i	−0.801676	+	1.35975i
$406$		0			0
$407$	6.59142	−	11.4167i	0.326725	−	0.565904i
$408$		0			0
$409$	15.9879			0.790553			0.395276	−	0.918562i	$-0.370649\pi$
$409$	15.9879			0.790553			0.395276	+	0.918562i	$0.370649\pi$
$410$		0			0
$411$	26.9091	+	7.27609i	1.32733	+	0.358903i
$412$		0			0
$413$	21.1054	−	1.41043i	1.03853	−	0.0694029i
$414$		0			0
$415$	20.8331	+	36.0841i	1.02266	+	1.77130i
$416$		0			0
$417$	3.71689	+	1.00503i	0.182017	+	0.0492165i
$418$		0			0
$419$	−3.56197	−	6.16951i	−0.174014	−	0.301400i	0.765806	−	0.643072i	$-0.222340\pi$
$419$	−3.56197	−	6.16951i	−0.174014	−	0.301400i	−0.939819	+	0.341671i	$0.889007\pi$
$420$		0			0
$421$	−16.6326	+	28.8086i	−0.810625	+	1.40404i	0.101802	+	0.994805i	$0.467539\pi$
$421$	−16.6326	+	28.8086i	−0.810625	+	1.40404i	−0.912427	+	0.409239i	$0.865794\pi$
$422$		0			0
$423$	0.0964951	−	21.1562i	0.00469175	−	1.02865i
$424$		0			0
$425$	9.50066			0.460849
$426$		0			0
$427$	−35.2561	+	2.35610i	−1.70616	+	0.114019i
$428$		0			0
$429$	−4.86627	−	18.3283i	−0.234946	−	0.884897i
$430$		0			0
$431$	−2.62382	+	4.54459i	−0.126385	+	0.218905i	−0.922273	−	0.386538i	$-0.873671\pi$
$431$	−2.62382	+	4.54459i	−0.126385	+	0.218905i	0.795889	+	0.605443i	$0.207004\pi$
$432$		0			0
$433$	22.1053			1.06231			0.531156	−	0.847274i	$-0.321758\pi$
$433$	22.1053			1.06231			0.531156	+	0.847274i	$0.321758\pi$
$434$		0			0
$435$	51.0025	+	13.7908i	2.44538	+	0.661220i
$436$		0			0
$437$	18.3573			0.878149
$438$		0			0
$439$	34.6165			1.65216			0.826079	−	0.563555i	$-0.190567\pi$
$439$	34.6165			1.65216			0.826079	+	0.563555i	$0.190567\pi$
$440$		0			0
$441$	−2.69934	−	20.8258i	−0.128540	−	0.991704i
$442$		0			0
$443$	−4.40923			−0.209489			−0.104744	−	0.994499i	$-0.533402\pi$
$443$	−4.40923			−0.209489			−0.104744	+	0.994499i	$0.533402\pi$
$444$		0			0
$445$	3.96370			0.187897
$446$		0			0
$447$	3.08326	+	11.6128i	0.145833	+	0.549265i
$448$		0			0
$449$	−19.6336			−0.926568			−0.463284	−	0.886210i	$-0.653329\pi$
$449$	−19.6336			−0.926568			−0.463284	+	0.886210i	$0.653329\pi$
$450$		0			0
$451$	−3.86525	+	6.69481i	−0.182007	+	0.315246i
$452$		0			0
$453$	−25.9440	−	7.01512i	−1.21895	−	0.329599i
$454$		0			0
$455$	43.9575	−	2.93759i	2.06076	−	0.137716i
$456$		0			0
$457$	−30.8392			−1.44259			−0.721297	−	0.692626i	$-0.756454\pi$
$457$	−30.8392			−1.44259			−0.721297	+	0.692626i	$0.756454\pi$
$458$		0			0
$459$	6.40536	−	1.66943i	0.298976	−	0.0779221i
$460$		0			0
$461$	−13.6297	+	23.6074i	−0.634800	+	1.09951i	0.351757	+	0.936091i	$0.385584\pi$
$461$	−13.6297	+	23.6074i	−0.634800	+	1.09951i	−0.986557	+	0.163415i	$0.947749\pi$
$462$		0			0
$463$	−0.959750	−	1.66234i	−0.0446034	−	0.0772553i	0.842862	−	0.538130i	$-0.180869\pi$
$463$	−0.959750	−	1.66234i	−0.0446034	−	0.0772553i	−0.887465	+	0.460875i	$0.847536\pi$
$464$		0			0
$465$	−13.3605	−	50.3210i	−0.619581	−	2.33358i
$466$		0			0
$467$	4.88655	+	8.46376i	0.226123	+	0.391656i	0.956656	−	0.291221i	$-0.0940616\pi$
$467$	4.88655	+	8.46376i	0.226123	+	0.391656i	−0.730533	+	0.682877i	$0.760728\pi$
$468$		0			0
$469$	−16.1772	+	1.08109i	−0.746994	+	0.0499201i
$470$		0			0
$471$	0.984618	−	0.980138i	0.0453688	−	0.0451624i
$472$		0			0
$473$	0.206158			0.00947913
$474$		0			0
$475$	20.7619	−	35.9607i	0.952623	−	1.64999i
$476$		0			0
$477$	−17.7143	−	10.3354i	−0.811083	−	0.473225i
$478$		0			0
$479$	−7.68809	−	13.3162i	−0.351278	−	0.608431i	0.635196	−	0.772351i	$-0.280919\pi$
$479$	−7.68809	−	13.3162i	−0.351278	−	0.608431i	−0.986474	+	0.163920i	$0.947586\pi$
$480$		0			0
$481$	−13.3993	+	23.2083i	−0.610956	+	1.05821i
$482$		0			0
$483$	4.84236	+	14.3122i	0.220335	+	0.651228i
$484$		0			0
$485$	12.3824	+	21.4470i	0.562258	+	0.973859i
$486$		0			0
$487$	5.18342	−	8.97794i	0.234883	−	0.406829i	−0.724356	−	0.689427i	$-0.757863\pi$
$487$	5.18342	−	8.97794i	0.234883	−	0.406829i	0.959239	+	0.282597i	$0.0911959\pi$
$488$		0			0
$489$	5.93561	+	1.60496i	0.268418	+	0.0725788i
$490$		0			0
$491$	−6.94718	−	12.0329i	−0.313522	−	0.543035i	0.665600	−	0.746308i	$-0.268175\pi$
$491$	−6.94718	−	12.0329i	−0.313522	−	0.543035i	−0.979122	+	0.203273i	$0.934842\pi$
$492$		0			0
$493$	−5.50469	−	9.53440i	−0.247919	−	0.429408i
$494$		0			0
$495$	0.112081	−	24.5734i	0.00503768	−	1.10449i
$496$		0			0
$497$	−3.43717	+	0.229699i	−0.154178	+	0.0103034i
$498$		0			0
$499$	1.70488	−	2.95294i	0.0763210	−	0.132192i	−0.825339	−	0.564638i	$-0.809016\pi$
$499$	1.70488	−	2.95294i	0.0763210	−	0.132192i	0.901660	+	0.432446i	$0.142349\pi$
$500$		0			0
$501$	2.89301	+	0.782255i	0.129250	+	0.0349486i
$502$		0			0
$503$	43.8911			1.95701			0.978504	−	0.206227i	$-0.0661185\pi$
$503$	43.8911			1.95701			0.978504	+	0.206227i	$0.0661185\pi$
$504$		0			0
$505$	34.3821			1.52998
$506$		0			0
$507$	4.11423	+	15.4958i	0.182719	+	0.688192i
$508$		0			0
$509$	−19.6674	+	34.0649i	−0.871742	+	1.50990i	−0.0115483	+	0.999933i	$0.503676\pi$
$509$	−19.6674	+	34.0649i	−0.871742	+	1.50990i	−0.860193	+	0.509968i	$0.829657\pi$
$510$		0			0
$511$	−15.5121	+	31.5571i	−0.686215	+	1.39600i
$512$		0			0
$513$	7.67882	−	27.8930i	0.339028	−	1.23151i
$514$		0			0
$515$	18.1519	+	31.4400i	0.799869	+	1.38541i
$516$		0			0
$517$	8.18305	+	14.1735i	0.359890	+	0.623348i
$518$		0			0
$519$	2.74303	−	2.73055i	0.120406	−	0.119858i
$520$		0			0
$521$	12.4779	−	21.6124i	0.546669	−	0.946858i	−0.451831	−	0.892104i	$-0.649229\pi$
$521$	12.4779	−	21.6124i	0.546669	−	0.946858i	0.998500	−	0.0547547i	$-0.0174377\pi$
$522$		0			0
$523$	−15.1575	−	26.2536i	−0.662792	−	1.14799i	−0.979879	−	0.199594i	$-0.936038\pi$
$523$	−15.1575	−	26.2536i	−0.662792	−	1.14799i	0.317086	−	0.948397i	$-0.397296\pi$
$524$		0			0
$525$	33.5134	+	6.70112i	1.46264	+	0.292461i
$526$		0			0
$527$	−5.42449	+	9.39550i	−0.236295	+	0.409274i
$528$		0			0
$529$	6.06457	+	10.5041i	0.263677	+	0.456702i
$530$		0			0
$531$	−0.109395	+	23.9844i	−0.00474734	+	1.04084i
$532$		0			0
$533$	7.85744	−	13.6095i	0.340343	−	0.589492i
$534$		0			0
$535$	19.2151			0.830742
$536$		0			0
$537$	0.311496	+	1.17321i	0.0134420	+	0.0506279i
$538$		0			0
$539$	9.92233	+	12.8628i	0.427385	+	0.554039i
$540$		0			0
$541$	−14.2812	−	24.7357i	−0.613996	−	1.06347i	−0.990560	−	0.137082i	$-0.956228\pi$
$541$	−14.2812	−	24.7357i	−0.613996	−	1.06347i	0.376563	−	0.926391i	$-0.377106\pi$
$542$		0			0
$543$	−24.1013	+	23.9916i	−1.03429	+	1.02958i
$544$		0			0
$545$	−1.47326	−	2.55177i	−0.0631077	−	0.109306i
$546$		0			0
$547$	3.89233	−	6.74171i	0.166424	−	0.288255i	−0.770736	−	0.637154i	$-0.780111\pi$
$547$	3.89233	−	6.74171i	0.166424	−	0.288255i	0.937160	+	0.348900i	$0.113445\pi$
$548$		0			0
$549$	0.182742	−	40.0654i	0.00779923	−	1.70995i
$550$		0			0
$551$	−48.1179			−2.04989
$552$		0			0
$553$	26.4727	−	1.76912i	1.12573	−	0.0752305i
$554$		0			0
$555$	−24.6117	+	24.4997i	−1.04471	+	1.03996i
$556$		0			0
$557$	−23.2470	+	40.2650i	−0.985008	+	1.70608i	−0.343108	+	0.939296i	$0.611480\pi$
$557$	−23.2470	+	40.2650i	−0.985008	+	1.70608i	−0.641900	+	0.766788i	$0.721854\pi$
$558$		0			0
$559$	−0.419086			−0.0177254
$560$		0			0
$561$	−3.62903	+	3.61252i	−0.153218	+	0.152521i
$562$		0			0
$563$	27.9826			1.17933			0.589663	−	0.807650i	$-0.299261\pi$
$563$	27.9826			1.17933			0.589663	+	0.807650i	$0.299261\pi$
$564$		0			0
$565$	38.4641			1.61820
$566$		0			0
$567$	23.7723	−	1.37096i	0.998341	−	0.0575748i
$568$		0			0
$569$	8.89957			0.373090			0.186545	−	0.982446i	$-0.440271\pi$
$569$	8.89957			0.373090			0.186545	+	0.982446i	$0.440271\pi$
$570$		0			0
$571$	−32.3304			−1.35298			−0.676492	−	0.736450i	$-0.736500\pi$
$571$	−32.3304			−1.35298			−0.676492	+	0.736450i	$0.736500\pi$
$572$		0			0
$573$	19.7459	−	19.6560i	0.824895	−	0.821141i
$574$		0			0
$575$	−24.5897			−1.02546
$576$		0			0
$577$	−16.8414	+	29.1701i	−0.701115	+	1.21437i	0.266960	+	0.963707i	$0.413981\pi$
$577$	−16.8414	+	29.1701i	−0.701115	+	1.21437i	−0.968075	+	0.250659i	$0.919353\pi$
$578$		0			0
$579$	−0.718676	+	0.715406i	−0.0298672	+	0.0297313i
$580$		0			0
$581$	13.7780	−	28.0294i	0.571610	−	1.16286i
$582$		0			0
$583$	15.8652			0.657071
$584$		0			0
$585$	−0.227843	+	49.9538i	−0.00942016	+	2.06534i
$586$		0			0
$587$	−1.24076	+	2.14907i	−0.0512118	+	0.0887015i	−0.890495	−	0.454993i	$-0.849642\pi$
$587$	−1.24076	+	2.14907i	−0.0512118	+	0.0887015i	0.839283	+	0.543695i	$0.182975\pi$
$588$		0			0
$589$	23.7085	+	41.0643i	0.976891	+	1.69202i
$590$		0			0
$591$	−21.2270	+	21.1304i	−0.873160	+	0.869187i
$592$		0			0
$593$	−15.0903	−	26.1371i	−0.619684	−	1.07332i	−0.989543	−	0.144236i	$-0.953928\pi$
$593$	−15.0903	−	26.1371i	−0.619684	−	1.07332i	0.369859	−	0.929088i	$-0.379406\pi$
$594$		0			0
$595$	−6.62177	−	9.88280i	−0.271466	−	0.405155i
$596$		0			0
$597$	10.8557	+	40.8868i	0.444295	+	1.67339i
$598$		0			0
$599$	−16.4083			−0.670424			−0.335212	−	0.942143i	$-0.608808\pi$
$599$	−16.4083			−0.670424			−0.335212	+	0.942143i	$0.608808\pi$
$600$		0			0
$601$	−2.96998	+	5.14416i	−0.121148	+	0.209835i	−0.920221	−	0.391400i	$-0.871991\pi$
$601$	−2.96998	+	5.14416i	−0.121148	+	0.209835i	0.799073	+	0.601235i	$0.205324\pi$
$602$		0			0
$603$	0.0838506	−	18.3839i	0.00341466	−	0.748652i
$604$		0			0
$605$	−9.90793	−	17.1610i	−0.402815	−	0.697695i
$606$		0			0
$607$	2.97573	−	5.15412i	0.120781	−	0.209199i	−0.799295	−	0.600939i	$-0.794793\pi$
$607$	2.97573	−	5.15412i	0.120781	−	0.209199i	0.920076	+	0.391740i	$0.128127\pi$
$608$		0			0
$609$	−12.6927	−	37.5150i	−0.514336	−	1.52019i
$610$		0			0
$611$	−16.6348	−	28.8124i	−0.672974	−	1.16562i
$612$		0			0
$613$	15.5920	−	27.0062i	0.629756	−	1.09077i	−0.357845	−	0.933781i	$-0.616488\pi$
$613$	15.5920	−	27.0062i	0.629756	−	1.09077i	0.987601	−	0.156988i	$-0.0501783\pi$
$614$		0			0
$615$	14.4325	−	14.3668i	0.581973	−	0.579325i
$616$		0			0
$617$	−11.1437	−	19.3014i	−0.448627	−	0.777045i	0.549670	−	0.835382i	$-0.314754\pi$
$617$	−11.1437	−	19.3014i	−0.448627	−	0.777045i	−0.998297	+	0.0583367i	$0.981420\pi$
$618$		0			0
$619$	−17.2943	−	29.9547i	−0.695118	−	1.20398i	−0.970141	−	0.242543i	$-0.922019\pi$
$619$	−17.2943	−	29.9547i	−0.695118	−	1.20398i	0.275022	−	0.961438i	$-0.411315\pi$
$620$		0			0
$621$	−16.5784	+	4.32083i	−0.665269	+	0.173389i
$622$		0			0
$623$	−1.65384	−	2.46831i	−0.0662599	−	0.0988909i
$624$		0			0
$625$	3.33422	−	5.77504i	0.133369	−	0.231002i
$626$		0			0
$627$	5.74308	+	21.6307i	0.229357	+	0.863846i
$628$		0			0
$629$	7.23631			0.288530
$630$		0			0
$631$	−26.2933			−1.04672			−0.523360	−	0.852112i	$-0.675322\pi$
$631$	−26.2933			−1.04672			−0.523360	+	0.852112i	$0.675322\pi$
$632$		0			0
$633$	−18.6841	−	5.05209i	−0.742627	−	0.200802i
$634$		0			0
$635$	−17.4777	+	30.2723i	−0.693582	+	1.20132i
$636$		0			0
$637$	−20.1705	−	26.1480i	−0.799185	−	1.03602i
$638$		0			0
$639$	0.0178157	−	3.90603i	0.000704779	−	0.154520i
$640$		0			0
$641$	16.2673	+	28.1758i	0.642519	+	1.11288i	0.984869	+	0.173303i	$0.0554441\pi$
$641$	16.2673	+	28.1758i	0.642519	+	1.11288i	−0.342349	+	0.939573i	$0.611223\pi$
$642$		0			0
$643$	5.21987	+	9.04107i	0.205851	+	0.356545i	0.950404	−	0.311019i	$-0.100670\pi$
$643$	5.21987	+	9.04107i	0.205851	+	0.356545i	−0.744552	+	0.667564i	$0.767337\pi$
$644$		0			0
$645$	−0.524247	−	0.141754i	−0.0206422	−	0.00558155i
$646$		0			0
$647$	0.685824	−	1.18788i	0.0269625	−	0.0467005i	−0.852229	−	0.523168i	$-0.824750\pi$
$647$	0.685824	−	1.18788i	0.0269625	−	0.0467005i	0.879192	+	0.476468i	$0.158083\pi$
$648$		0			0
$649$	−9.27699	−	16.0682i	−0.364154	−	0.630733i
$650$		0			0
$651$	−25.7617	+	29.3164i	−1.00968	+	1.14900i
$652$		0			0
$653$	3.62567	−	6.27985i	0.141883	−	0.245749i	−0.786322	−	0.617816i	$-0.788018\pi$
$653$	3.62567	−	6.27985i	0.141883	−	0.245749i	0.928206	+	0.372067i	$0.121351\pi$
$654$		0			0
$655$	30.3269	+	52.5277i	1.18497	+	2.05243i
$656$		0			0
$657$	−34.4386	−	20.0931i	−1.34358	−	0.783908i
$658$		0			0
$659$	−13.3187	+	23.0686i	−0.518822	+	0.898626i	0.480939	+	0.876754i	$0.340296\pi$
$659$	−13.3187	+	23.0686i	−0.518822	+	0.898626i	−0.999761	+	0.0218722i	$0.993037\pi$
$660$		0			0
$661$	−34.8199			−1.35434			−0.677168	−	0.735828i	$-0.736793\pi$
$661$	−34.8199			−1.35434			−0.677168	+	0.735828i	$0.736793\pi$
$662$		0			0
$663$	7.37725	−	7.34367i	0.286508	−	0.285205i
$664$		0			0
$665$	−51.8779	+	3.46689i	−2.01174	+	0.134440i
$666$		0			0
$667$	14.2473	+	24.6770i	0.551657	+	0.955498i
$668$		0			0
$669$	1.18185	+	4.45132i	0.0456931	+	0.172098i
$670$		0			0
$671$	15.4970	+	26.8416i	0.598255	+	1.03621i
$672$		0			0
$673$	8.23841	−	14.2693i	0.317567	−	0.550043i	−0.662412	−	0.749139i	$-0.730467\pi$
$673$	8.23841	−	14.2693i	0.317567	−	0.550043i	0.979980	+	0.199096i	$0.0638007\pi$
$674$		0			0
$675$	−10.2858	+	37.3628i	−0.395901	+	1.43810i
$676$		0			0
$677$	−21.1654			−0.813450			−0.406725	−	0.913551i	$-0.633329\pi$
$677$	−21.1654			−0.813450			−0.406725	+	0.913551i	$0.633329\pi$
$678$		0			0
$679$	8.18916	−	16.6596i	0.314271	−	0.639339i
$680$		0			0
$681$	−19.9231	−	5.38712i	−0.763457	−	0.206435i
$682$		0			0
$683$	14.0756	−	24.3796i	0.538587	−	0.932859i	−0.460394	−	0.887715i	$-0.652292\pi$
$683$	14.0756	−	24.3796i	0.538587	−	0.932859i	0.998980	−	0.0451447i	$-0.0143749\pi$
$684$		0			0
$685$	56.8049			2.17040
$686$		0			0
$687$	−13.1620	−	49.5733i	−0.502163	−	1.89134i
$688$		0			0
$689$	−32.2515			−1.22869
$690$		0			0
$691$	19.0796			0.725822			0.362911	−	0.931824i	$-0.381783\pi$
$691$	19.0796			0.725822			0.362911	+	0.931824i	$0.381783\pi$
$692$		0			0
$693$	−15.3494	+	10.1834i	−0.583074	+	0.386835i
$694$		0			0
$695$	7.84632			0.297628
$696$		0			0
$697$	−4.24341			−0.160731
$698$		0			0
$699$	6.16694	+	1.66751i	0.233255	+	0.0630710i
$700$		0			0
$701$	23.8508			0.900834			0.450417	−	0.892818i	$-0.351275\pi$
$701$	23.8508			0.900834			0.450417	+	0.892818i	$0.351275\pi$
$702$		0			0
$703$	15.8136	−	27.3900i	0.596422	−	1.03303i
$704$		0			0
$705$	−11.0634	−	41.6690i	−0.416671	−	1.56934i
$706$		0			0
$707$	−14.3459	−	21.4108i	−0.539532	−	0.805235i
$708$		0			0
$709$	20.0986			0.754817			0.377409	−	0.926047i	$-0.376815\pi$
$709$	20.0986			0.754817			0.377409	+	0.926047i	$0.376815\pi$
$710$		0			0
$711$	−0.137215	+	30.0839i	−0.00514596	+	1.12823i
$712$		0			0
$713$	14.0397	−	24.3175i	0.525792	−	0.910698i
$714$		0			0
$715$	−19.3217	−	33.4662i	−0.722592	−	1.25157i
$716$		0			0
$717$	26.8722	+	7.26610i	1.00356	+	0.271357i
$718$		0			0
$719$	−3.29246	−	5.70270i	−0.122788	−	0.212675i	0.798078	−	0.602554i	$-0.205850\pi$
$719$	−3.29246	−	5.70270i	−0.122788	−	0.212675i	−0.920866	+	0.389879i	$0.872517\pi$
$720$		0			0
$721$	12.0048	−	24.4220i	0.447082	−	0.909524i
$722$		0			0
$723$	−7.52180	−	2.03386i	−0.279739	−	0.0756399i
$724$		0			0
$725$	64.4542			2.39377
$726$		0			0
$727$	18.2342	−	31.5826i	0.676269	−	1.17133i	−0.299827	−	0.953994i	$-0.596929\pi$
$727$	18.2342	−	31.5826i	0.676269	−	1.17133i	0.976096	−	0.217339i	$-0.0697376\pi$
$728$		0			0
$729$	−0.369433	+	26.9975i	−0.0136827	+	0.999906i
$730$		0			0
$731$	0.0565818	+	0.0980026i	0.00209276	+	0.00362476i
$732$		0			0
$733$	−11.6824	+	20.2345i	−0.431498	+	0.747377i	−0.997003	−	0.0773684i	$-0.975348\pi$
$733$	−11.6824	+	20.2345i	−0.431498	+	0.747377i	0.565504	+	0.824745i	$0.308682\pi$
$734$		0			0
$735$	−16.3875	−	39.5319i	−0.604462	−	1.45816i
$736$		0			0
$737$	7.11077	+	12.3162i	0.261928	+	0.453673i
$738$		0			0
$739$	14.4596	−	25.0448i	0.531906	−	0.921288i	−0.467400	−	0.884046i	$-0.654809\pi$
$739$	14.4596	−	25.0448i	0.531906	−	0.921288i	0.999306	−	0.0372422i	$-0.0118573\pi$
$740$		0			0
$741$	−11.6748	−	43.9717i	−0.428884	−	1.61534i
$742$		0			0
$743$	11.6794	+	20.2292i	0.428474	+	0.742139i	0.996738	−	0.0807074i	$-0.0257179\pi$
$743$	11.6794	+	20.2292i	0.428474	+	0.742139i	−0.568264	+	0.822847i	$0.692385\pi$
$744$		0			0
$745$	12.2422	+	21.2042i	0.448521	+	0.776860i
$746$		0			0
$747$	30.5888	+	17.8470i	1.11919	+	0.652987i
$748$		0			0
$749$	−8.01747	−	11.9658i	−0.292952	−	0.437222i
$750$		0			0
$751$	0.856616	−	1.48370i	0.0312584	−	0.0541411i	−0.849973	−	0.526826i	$-0.823382\pi$
$751$	0.856616	−	1.48370i	0.0312584	−	0.0541411i	0.881231	+	0.472685i	$0.156715\pi$
$752$		0			0
$753$	−21.1990	+	21.1025i	−0.772535	+	0.769019i
$754$		0			0
$755$	−54.7675			−1.99319
$756$		0			0
$757$	28.4587			1.03435			0.517175	−	0.855880i	$-0.326984\pi$
$757$	28.4587			1.03435			0.517175	+	0.855880i	$0.326984\pi$
$758$		0			0
$759$	9.39269	−	9.34995i	0.340933	−	0.339382i
$760$		0			0
$761$	17.0525	−	29.5358i	0.618154	−	1.07067i	−0.371669	−	0.928365i	$-0.621214\pi$
$761$	17.0525	−	29.5358i	0.618154	−	1.07067i	0.989822	−	0.142308i	$-0.0454524\pi$
$762$		0			0
$763$	−0.974346	+	1.98216i	−0.0352737	+	0.0717592i
$764$		0			0
$765$	11.7124	−	6.69111i	0.423463	−	0.241918i
$766$		0			0
$767$	18.8587	+	32.6642i	0.680947	+	1.17943i
$768$		0			0
$769$	2.48467	+	4.30357i	0.0895995	+	0.155191i	0.907342	−	0.420394i	$-0.138108\pi$
$769$	2.48467	+	4.30357i	0.0895995	+	0.155191i	−0.817742	+	0.575584i	$0.804775\pi$
$770$		0			0
$771$	2.14312	+	8.07183i	0.0771826	+	0.290700i
$772$		0			0
$773$	−5.74814	+	9.95607i	−0.206746	+	0.358095i	−0.950688	−	0.310150i	$-0.899621\pi$
$773$	−5.74814	+	9.95607i	−0.206746	+	0.358095i	0.743941	+	0.668245i	$0.232954\pi$
$774$		0			0
$775$	−31.7576	−	55.0058i	−1.14077	−	1.97587i
$776$		0			0
$777$	25.5259	+	5.10400i	0.915737	+	0.183105i
$778$		0			0
$779$	−9.27320	+	16.0617i	−0.332247	+	0.575469i
$780$		0			0
$781$	1.51082	+	2.61682i	0.0540615	+	0.0936373i
$782$		0			0
$783$	43.4551	−	11.3257i	1.55296	−	0.404748i
$784$		0			0
$785$	1.41556	−	2.45182i	0.0505235	−	0.0875092i
$786$		0			0
$787$	48.6011			1.73244			0.866221	−	0.499661i	$-0.166542\pi$
$787$	48.6011			1.73244			0.866221	+	0.499661i	$0.166542\pi$
$788$		0			0
$789$	−46.9672	−	12.6997i	−1.67208	−	0.452121i
$790$		0			0
$791$	−16.0491	−	23.9527i	−0.570639	−	0.851661i
$792$		0			0
$793$	−31.5030	−	54.5647i	−1.11870	−	1.93765i
$794$		0			0
$795$	−40.3445	−	10.9089i	−1.43087	−	0.386900i
$796$		0			0
$797$	16.8556	+	29.1947i	0.597056	+	1.03413i	0.993253	+	0.115965i	$0.0369962\pi$
$797$	16.8556	+	29.1947i	0.597056	+	1.03413i	−0.396198	+	0.918165i	$0.629670\pi$
$798$		0			0
$799$	−4.49183	+	7.78007i	−0.158909	+	0.275239i
$800$		0			0
$801$	2.92527	−	1.67116i	0.103359	−	0.0590476i
$802$		0			0
$803$	30.8438			1.08846
$804$		0			0
$805$	17.1385	+	25.5788i	0.604054	+	0.901533i
$806$		0			0
$807$	−11.0341	−	41.5587i	−0.388418	−	1.46293i
$808$		0			0
$809$	−7.93617	+	13.7459i	−0.279021	+	0.483278i	−0.971142	−	0.238503i	$-0.923343\pi$
$809$	−7.93617	+	13.7459i	−0.279021	+	0.483278i	0.692121	+	0.721782i	$0.256677\pi$
$810$		0			0
$811$	27.2524			0.956963			0.478481	−	0.878098i	$-0.341187\pi$
$811$	27.2524			0.956963			0.478481	+	0.878098i	$0.341187\pi$
$812$		0			0
$813$	−16.0403	−	4.33720i	−0.562556	−	0.152112i
$814$		0			0
$815$	12.5300			0.438907
$816$		0			0
$817$	0.494597			0.0173038
$818$		0			0
$819$	31.2028	−	20.7012i	1.09031	−	0.723360i
$820$		0			0
$821$	24.3389			0.849433			0.424717	−	0.905326i	$-0.360374\pi$
$821$	24.3389			0.849433			0.424717	+	0.905326i	$0.360374\pi$
$822$		0			0
$823$	−11.5380			−0.402188			−0.201094	−	0.979572i	$-0.564450\pi$
$823$	−11.5380			−0.402188			−0.201094	+	0.979572i	$0.564450\pi$
$824$		0			0
$825$	−7.69289	−	28.9744i	−0.267832	−	1.00876i
$826$		0			0
$827$	−34.8582			−1.21214			−0.606069	−	0.795412i	$-0.707255\pi$
$827$	−34.8582			−1.21214			−0.606069	+	0.795412i	$0.707255\pi$
$828$		0			0
$829$	−7.64018	+	13.2332i	−0.265354	+	0.459607i	−0.967656	−	0.252272i	$-0.918822\pi$
$829$	−7.64018	+	13.2332i	−0.265354	+	0.459607i	0.702302	+	0.711879i	$0.252156\pi$
$830$		0			0
$831$	−28.3209	−	7.65783i	−0.982442	−	0.265647i
$832$		0			0
$833$	−3.39140	+	8.24716i	−0.117505	+	0.285747i
$834$		0			0
$835$	6.10711			0.211345
$836$		0			0
$837$	−31.0765	−	31.5047i	−1.07416	−	1.08896i
$838$		0			0
$839$	−8.39990	+	14.5490i	−0.289997	+	0.502289i	−0.973809	−	0.227369i	$-0.926988\pi$
$839$	−8.39990	+	14.5490i	−0.289997	+	0.502289i	0.683812	+	0.729658i	$0.260321\pi$
$840$		0			0
$841$	−22.8448	−	39.5684i	−0.787753	−	1.36443i
$842$		0			0
$843$	−10.1598	−	38.2659i	−0.349923	−	1.31795i
$844$		0			0
$845$	16.3357	+	28.2943i	0.561967	+	0.973355i
$846$		0			0
$847$	−6.55263	+	13.3304i	−0.225151	+	0.458037i
$848$		0			0
$849$	10.2575	−	10.2109i	0.352038	−	0.350436i
$850$		0			0
$851$	−18.7291			−0.642024
$852$		0			0
$853$	−11.4270	+	19.7921i	−0.391253	+	0.677670i	−0.992615	−	0.121306i	$-0.961292\pi$
$853$	−11.4270	+	19.7921i	−0.391253	+	0.677670i	0.601362	+	0.798977i	$0.294625\pi$
$854$		0			0
$855$	0.268897	−	58.9546i	0.00919607	−	2.01620i
$856$		0			0
$857$	17.5871	+	30.4618i	0.600765	+	1.04056i	0.992705	+	0.120565i	$0.0384706\pi$
$857$	17.5871	+	30.4618i	0.600765	+	1.04056i	−0.391940	+	0.919991i	$0.628196\pi$
$858$		0			0
$859$	−5.28520	+	9.15424i	−0.180329	+	0.312339i	−0.941993	−	0.335634i	$-0.891050\pi$
$859$	−5.28520	+	9.15424i	−0.180329	+	0.312339i	0.761664	+	0.647973i	$0.224383\pi$
$860$		0			0
$861$	−14.9685	−	2.99302i	−0.510127	−	0.102002i
$862$		0			0
$863$	−7.29326	−	12.6323i	−0.248265	−	0.430008i	0.714779	−	0.699350i	$-0.246527\pi$
$863$	−7.29326	−	12.6323i	−0.248265	−	0.430008i	−0.963045	+	0.269342i	$0.913194\pi$
$864$		0			0
$865$	3.94358	−	6.83048i	0.134086	−	0.232243i
$866$		0			0
$867$	25.7108	+	6.95206i	0.873184	+	0.236104i
$868$		0			0
$869$	−11.6362	−	20.1545i	−0.394731	−	0.683694i
$870$		0			0
$871$	−14.4551	−	25.0369i	−0.489791	−	0.848343i
$872$		0			0
$873$	18.1809	+	10.6076i	0.615329	+	0.359012i
$874$		0			0
$875$	22.9025	−	1.53053i	0.774247	−	0.0517413i
$876$		0			0
$877$	−5.65914	+	9.80192i	−0.191096	+	0.330987i	−0.945614	−	0.325292i	$-0.894537\pi$
$877$	−5.65914	+	9.80192i	−0.191096	+	0.330987i	0.754518	+	0.656279i	$0.227871\pi$
$878$		0			0
$879$	−7.22779	−	1.95436i	−0.243787	−	0.0659188i
$880$		0			0
$881$	−0.733220			−0.0247028			−0.0123514	−	0.999924i	$-0.503932\pi$
$881$	−0.733220			−0.0247028			−0.0123514	+	0.999924i	$0.503932\pi$
$882$		0			0
$883$	−14.1726			−0.476944			−0.238472	−	0.971149i	$-0.576647\pi$
$883$	−14.1726			−0.476944			−0.238472	+	0.971149i	$0.576647\pi$
$884$		0			0
$885$	12.5424	+	47.2395i	0.421608	+	1.58794i
$886$		0			0
$887$	16.8162	−	29.1266i	0.564634	−	0.977975i	−0.432449	−	0.901658i	$-0.642351\pi$
$887$	16.8162	−	29.1266i	0.564634	−	0.977975i	0.997084	−	0.0763170i	$-0.0243161\pi$
$888$		0			0
$889$	26.1440	−	1.74715i	0.876842	−	0.0585975i
$890$		0			0
$891$	−10.2778	−	18.1828i	−0.344321	−	0.609147i
$892$		0			0
$893$	19.6321	+	34.0038i	0.656964	+	1.13790i
$894$		0			0
$895$	1.23681	+	2.14221i	0.0413419	+	0.0716063i
$896$		0			0
$897$	−19.0939	+	19.0070i	−0.637525	+	0.634624i
$898$		0			0
$899$	−36.8008	+	63.7408i	−1.22737	+	2.12588i
$900$		0			0
$901$	4.35436	+	7.54198i	0.145065	+	0.251260i
$902$		0			0
$903$	0.130467	+	0.385611i	0.00434166	+	0.0128323i
$904$		0			0
$905$	−34.6498	+	60.0152i	−1.15180	+	1.99497i
$906$		0			0
$907$	−4.79255	−	8.30094i	−0.159134	−	0.275628i	0.775423	−	0.631443i	$-0.217537\pi$
$907$	−4.79255	−	8.30094i	−0.159134	−	0.275628i	−0.934557	+	0.355814i	$0.884204\pi$
$908$		0			0
$909$	25.3745	−	14.4961i	0.841620	−	0.480805i
$910$		0			0
$911$	−9.37499	+	16.2380i	−0.310607	+	0.537988i	−0.978494	−	0.206275i	$-0.933866\pi$
$911$	−9.37499	+	16.2380i	−0.310607	+	0.537988i	0.667887	+	0.744263i	$0.267199\pi$
$912$		0			0
$913$	−27.3959			−0.906672
$914$		0			0
$915$	−20.9518	−	78.9125i	−0.692644	−	2.60877i
$916$		0			0
$917$	20.0568	−	40.8026i	0.662333	−	1.34742i
$918$		0			0
$919$	21.2895	+	36.8745i	0.702276	+	1.21638i	0.967666	+	0.252236i	$0.0811661\pi$
$919$	21.2895	+	36.8745i	0.702276	+	1.21638i	−0.265390	+	0.964141i	$0.585501\pi$
$920$		0			0
$921$	−11.3288	+	11.2772i	−0.373296	+	0.371597i
$922$		0			0
$923$	−3.07126	−	5.31958i	−0.101092	−	0.175096i
$924$		0			0
$925$	−21.1824	+	36.6890i	−0.696474	+	1.20633i
$926$		0			0
$927$	26.6521	+	15.5501i	0.875368	+	0.510732i
$928$		0			0
$929$	38.1524			1.25174			0.625869	−	0.779928i	$-0.284744\pi$
$929$	38.1524			1.25174			0.625869	+	0.779928i	$0.284744\pi$
$930$		0			0
$931$	23.8049	+	30.8594i	0.780173	+	1.01137i
$932$		0			0
$933$	−23.4549	+	23.3481i	−0.767878	+	0.764383i
$934$		0			0
$935$	−5.21736	+	9.03673i	−0.170626	+	0.295533i
$936$		0			0
$937$	6.48960			0.212006			0.106003	−	0.994366i	$-0.466195\pi$
$937$	6.48960			0.212006			0.106003	+	0.994366i	$0.466195\pi$
$938$		0			0
$939$	6.97120	−	6.93948i	0.227497	−	0.226461i
$940$		0			0
$941$	−0.466471			−0.0152065			−0.00760326	−	0.999971i	$-0.502420\pi$
$941$	−0.466471			−0.0152065			−0.00760326	+	0.999971i	$0.502420\pi$
$942$		0			0
$943$	10.9828			0.357650
$944$		0			0
$945$	46.0347	−	15.3416i	1.49751	−	0.499063i
$946$		0			0
$947$	−15.1115			−0.491058			−0.245529	−	0.969389i	$-0.578962\pi$
$947$	−15.1115			−0.491058			−0.245529	+	0.969389i	$0.578962\pi$
$948$		0			0
$949$	−62.7006			−2.03535
$950$		0			0
$951$	−34.7001	+	34.5422i	−1.12523	+	1.12011i
$952$		0			0
$953$	19.6802			0.637503			0.318751	−	0.947838i	$-0.396736\pi$
$953$	19.6802			0.637503			0.318751	+	0.947838i	$0.396736\pi$
$954$		0			0
$955$	28.3881	−	49.1696i	0.918616	−	1.59109i
$956$		0			0
$957$	−24.6200	+	24.5080i	−0.795852	+	0.792231i
$958$		0			0
$959$	−23.7017	−	35.3741i	−0.765368	−	1.14229i
$960$		0			0
$961$	41.5293			1.33966
$962$		0			0
$963$	14.1811	−	8.10142i	0.456978	−	0.261065i
$964$		0			0
$965$	−1.03322	+	1.78959i	−0.0332606	+	0.0576090i
$966$		0			0
$967$	8.83228	+	15.2980i	0.284027	+	0.491949i	0.972373	−	0.233433i	$-0.0749961\pi$
$967$	8.83228	+	15.2980i	0.284027	+	0.491949i	−0.688346	+	0.725383i	$0.741663\pi$
$968$		0			0
$969$	−8.70649	+	8.66687i	−0.279693	+	0.278420i
$970$		0			0
$971$	−11.7523	−	20.3555i	−0.377148	−	0.653240i	0.613498	−	0.789697i	$-0.289762\pi$
$971$	−11.7523	−	20.3555i	−0.377148	−	0.653240i	−0.990646	+	0.136456i	$0.956429\pi$
$972$		0			0
$973$	−3.27386	−	4.88614i	−0.104955	−	0.156642i
$974$		0			0
$975$	15.6384	+	58.9003i	0.500830	+	1.88632i
$976$		0			0
$977$	−5.43379			−0.173842			−0.0869211	−	0.996215i	$-0.527703\pi$
$977$	−5.43379			−0.173842			−0.0869211	+	0.996215i	$0.527703\pi$
$978$		0			0
$979$	−1.30308	+	2.25700i	−0.0416466	+	0.0721341i
$980$		0			0
$981$	−2.16316	−	1.26209i	−0.0690644	−	0.0402955i
$982$		0			0
$983$	1.05345	+	1.82463i	0.0335998	+	0.0581966i	0.882336	−	0.470619i	$-0.155969\pi$
$983$	1.05345	+	1.82463i	0.0335998	+	0.0581966i	−0.848736	+	0.528816i	$0.822636\pi$
$984$		0			0
$985$	−30.5174	+	52.8577i	−0.972366	+	1.68419i
$986$		0			0
$987$	−21.3324	+	24.2758i	−0.679017	+	0.772707i
$988$		0			0
$989$	−0.146446	−	0.253651i	−0.00465670	−	0.00806564i
$990$		0			0
$991$	8.91172	−	15.4356i	0.283090	−	0.490327i	−0.689054	−	0.724710i	$-0.741974\pi$
$991$	8.91172	−	15.4356i	0.283090	−	0.490327i	0.972144	+	0.234383i	$0.0753071\pi$
$992$		0			0
$993$	−8.20105	+	8.16373i	−0.260252	+	0.259068i
$994$		0			0
$995$	43.1031	+	74.6567i	1.36646	+	2.36678i
$996$		0			0
$997$	18.2477	+	31.6060i	0.577911	+	1.00097i	0.995719	+	0.0924360i	$0.0294653\pi$
$997$	18.2477	+	31.6060i	0.577911	+	1.00097i	−0.417807	+	0.908536i	$0.637201\pi$
$998$		0			0
$999$	−7.83434	+	28.4579i	−0.247867	+	0.900369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.25.8	✓	22
3.2	odd	2		1512.2.q.c.1369.1		22
4.3	odd	2		1008.2.q.k.529.4		22
7.2	even	3		504.2.t.d.457.7	yes	22
9.4	even	3		504.2.t.d.193.7	yes	22
9.5	odd	6		1512.2.t.d.361.11		22
12.11	even	2		3024.2.q.k.2881.1		22
21.2	odd	6		1512.2.t.d.289.11		22
28.23	odd	6		1008.2.t.k.961.5		22
36.23	even	6		3024.2.t.l.1873.11		22
36.31	odd	6		1008.2.t.k.193.5		22
63.23	odd	6		1512.2.q.c.793.1		22
63.58	even	3	inner	504.2.q.d.121.8	yes	22
84.23	even	6		3024.2.t.l.289.11		22
252.23	even	6		3024.2.q.k.2305.1		22
252.247	odd	6		1008.2.q.k.625.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.8	✓	22	1.1	even	1	trivial
504.2.q.d.121.8	yes	22	63.58	even	3	inner
504.2.t.d.193.7	yes	22	9.4	even	3
504.2.t.d.457.7	yes	22	7.2	even	3
1008.2.q.k.529.4		22	4.3	odd	2
1008.2.q.k.625.4		22	252.247	odd	6
1008.2.t.k.193.5		22	36.31	odd	6
1008.2.t.k.961.5		22	28.23	odd	6
1512.2.q.c.793.1		22	63.23	odd	6
1512.2.q.c.1369.1		22	3.2	odd	2
1512.2.t.d.289.11		22	21.2	odd	6
1512.2.t.d.361.11		22	9.5	odd	6
3024.2.q.k.2305.1		22	252.23	even	6
3024.2.q.k.2881.1		22	12.11	even	2
3024.2.t.l.289.11		22	84.23	even	6
3024.2.t.l.1873.11		22	36.23	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22753 - 1.22195i) q^{3} +(1.76479 - 3.05671i) q^{5} +(-2.63986 + 0.176417i) q^{7} +(0.0136831 - 2.99997i) q^{9} +O(q^{10})\)	\(q+(1.22753 - 1.22195i) q^{3} +(1.76479 - 3.05671i) q^{5} +(-2.63986 + 0.176417i) q^{7} +(0.0136831 - 2.99997i) q^{9} +(1.16036 + 2.00981i) q^{11} +(-2.35884 - 4.08563i) q^{13} +(-1.56880 - 5.90871i) q^{15} +(-0.636946 + 1.10322i) q^{17} +(2.78386 + 4.82178i) q^{19} +(-3.02495 + 3.44233i) q^{21} +(1.64855 - 2.85537i) q^{23} +(-3.72899 - 6.45880i) q^{25} +(-3.64901 - 3.69929i) q^{27} +(-4.32116 + 7.48447i) q^{29} +8.51642 q^{31} +(3.88027 + 1.04921i) q^{33} +(-4.11956 + 8.38064i) q^{35} +(-2.84024 - 4.91943i) q^{37} +(-7.88798 - 2.13287i) q^{39} +(1.66553 + 2.88478i) q^{41} +(0.0444165 - 0.0769317i) q^{43} +(-9.14589 - 5.33615i) q^{45} +7.05213 q^{47} +(6.93775 - 0.931432i) q^{49} +(0.566208 + 2.13256i) q^{51} +(3.41816 - 5.92042i) q^{53} +8.19121 q^{55} +(9.30925 + 2.51717i) q^{57} -7.99490 q^{59} +13.3553 q^{61} +(0.493123 + 7.92192i) q^{63} -16.6514 q^{65} +6.12804 q^{67} +(-1.46546 - 5.51951i) q^{69} +1.30202 q^{71} +(6.64529 - 11.5100i) q^{73} +(-12.4698 - 3.37177i) q^{75} +(-3.41777 - 5.10092i) q^{77} -10.0281 q^{79} +(-8.99963 - 0.0820978i) q^{81} +(-5.90243 + 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(3.84126 + 14.4677i) q^{87} +(0.561496 + 0.972540i) q^{89} +(6.94778 + 10.3694i) q^{91} +(10.4542 - 10.4066i) q^{93} +19.6517 q^{95} +(-3.50818 + 6.07635i) q^{97} +(6.04525 - 3.45356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Introduction

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