LMFDB - Embedded newform 1008.2.q.k.625.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, 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("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.4
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.k.529.4

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			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	0.926433	+	0.376459i	$0.122858\pi$
$5$	1.76479	+	3.05671i	0.789239	+	1.36700i	−0.137194	+	0.990544i	$0.543808\pi$
$6$		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	$-0.947105\pi$
$11$	−1.16036	+	2.00981i	−0.349863	+	0.605981i	0.636362	+	0.771391i	$0.280439\pi$
$12$		0			0
$13$	−2.35884	+	4.08563i	−0.654224	+	1.13315i	0.327864	+	0.944725i	$0.393671\pi$
$13$	−2.35884	+	4.08563i	−0.654224	+	1.13315i	−0.982088	+	0.188424i	$0.939662\pi$
$14$		0			0
$15$	1.56880	−	5.90871i	0.405062	−	1.52562i
$16$		0			0
$17$	−0.636946	−	1.10322i	−0.154482	−	0.267571i	0.778388	−	0.627783i	$-0.216038\pi$
$17$	−0.636946	−	1.10322i	−0.154482	−	0.267571i	−0.932870	+	0.360212i	$0.882704\pi$
$18$		0			0
$19$	−2.78386	+	4.82178i	−0.638661	+	1.10619i	0.347066	+	0.937841i	$0.387178\pi$
$19$	−2.78386	+	4.82178i	−0.638661	+	1.10619i	−0.985727	+	0.168352i	$0.946155\pi$
$20$		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	$-0.278363\pi$
$23$	−1.64855	−	2.85537i	−0.343746	−	0.595386i	−0.985125	+	0.171838i	$0.945029\pi$
$24$		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	−0.918020	−	0.396535i	$-0.870213\pi$
$29$	−4.32116	−	7.48447i	−0.802419	−	1.38983i	0.115601	−	0.993296i	$-0.463121\pi$
$30$		0			0
$31$	−8.51642			−1.52959			−0.764797	−	0.644272i	$-0.777161\pi$
$31$	−8.51642			−1.52959			−0.764797	+	0.644272i	$0.777161\pi$
$32$		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	−0.999286	−	0.0377716i	$-0.987974\pi$
$37$	−2.84024	+	4.91943i	−0.466932	+	0.808750i	0.532354	+	0.846522i	$0.321307\pi$
$38$		0			0
$39$	7.88798	−	2.13287i	1.26309	−	0.341533i
$40$		0			0
$41$	1.66553	−	2.88478i	0.260112	−	0.450528i	−0.706159	−	0.708053i	$-0.749574\pi$
$41$	1.66553	−	2.88478i	0.260112	−	0.450528i	0.966272	+	0.257525i	$0.0829071\pi$
$42$		0			0
$43$	−0.0444165	−	0.0769317i	−0.00677346	−	0.0117320i	0.862619	−	0.505855i	$-0.168823\pi$
$43$	−0.0444165	−	0.0769317i	−0.00677346	−	0.0117320i	−0.869392	+	0.494123i	$0.835489\pi$
$44$		0			0
$45$	−9.14589	+	5.33615i	−1.36339	+	0.795466i
$46$		0			0
$47$	−7.05213			−1.02866			−0.514330	−	0.857593i	$-0.671959\pi$
$47$	−7.05213			−1.02866			−0.514330	+	0.857593i	$0.671959\pi$
$48$		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	0.999393	−	0.0348444i	$-0.0110936\pi$
$53$	3.41816	+	5.92042i	0.469520	+	0.813233i	−0.529873	+	0.848077i	$0.677760\pi$
$54$		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	$-0.325774\pi$
$59$	7.99490			1.04085			0.520423	+	0.853908i	$0.325774\pi$
$60$		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	$-0.622127\pi$
$67$	−6.12804			−0.748660			−0.374330	+	0.927296i	$0.622127\pi$
$68$		0			0
$69$	−1.46546	+	5.51951i	−0.176421	+	0.664471i
$70$		0			0
$71$	−1.30202			−0.154522			−0.0772609	−	0.997011i	$-0.524617\pi$
$71$	−1.30202			−0.154522			−0.0772609	+	0.997011i	$0.524617\pi$
$72$		0			0
$73$	6.64529	+	11.5100i	0.777772	+	1.34714i	0.933223	+	0.359297i	$0.116984\pi$
$73$	6.64529	+	11.5100i	0.777772	+	1.34714i	−0.155451	+	0.987844i	$0.549683\pi$
$74$		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	$-0.309215\pi$
$79$	10.0281			1.12824			0.564122	+	0.825691i	$0.309215\pi$
$80$		0			0
$81$	−8.99963	+	0.0820978i	−0.999958	+	0.00912197i
$82$		0			0
$83$	5.90243	+	10.2233i	0.647876	+	1.12215i	0.983629	+	0.180204i	$0.0576758\pi$
$83$	5.90243	+	10.2233i	0.647876	+	1.12215i	−0.335753	+	0.941950i	$0.608991\pi$
$84$		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	−0.834731	−	0.550658i	$-0.814377\pi$
$89$	0.561496	−	0.972540i	0.0595185	−	0.103089i	0.894249	+	0.447569i	$0.147710\pi$
$90$		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	0.631121	−	0.775685i	$-0.282595\pi$
$97$	−3.50818	−	6.07635i	−0.356202	−	0.616960i	−0.987323	+	0.158724i	$0.949262\pi$
$98$		0			0
$99$	−6.04525	−	3.45356i	−0.607570	−	0.347096i
$100$		0			0
$101$	4.87055	−	8.43605i	0.484638	−	0.839418i	−0.515206	−	0.857066i	$-0.672285\pi$
$101$	4.87055	−	8.43605i	0.484638	−	0.839418i	0.999844	+	0.0176482i	$0.00561789\pi$
$102$		0			0
$103$	5.14279	+	8.90757i	0.506734	+	0.877689i	0.999970	+	0.00779301i	$0.00248062\pi$
$103$	5.14279	+	8.90757i	0.506734	+	0.877689i	−0.493236	+	0.869896i	$0.664186\pi$
$104$		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	$-0.918094\pi$
$107$	−2.72201	+	4.71465i	−0.263146	+	0.455783i	0.703930	+	0.710269i	$0.251427\pi$
$108$		0			0
$109$	0.417404	+	0.722965i	0.0399800	+	0.0692475i	0.885323	−	0.464977i	$-0.153937\pi$
$109$	0.417404	+	0.722965i	0.0399800	+	0.0692475i	−0.845343	+	0.534224i	$0.820604\pi$
$110$		0			0
$111$	9.49778	−	2.56815i	0.901490	−	0.243758i
$112$		0			0
$113$	5.44881	−	9.43761i	0.512581	−	0.887815i	−0.487313	−	0.873227i	$-0.662023\pi$
$113$	5.44881	−	9.43761i	0.512581	−	0.887815i	0.999894	−	0.0145882i	$-0.00464372\pi$
$114$		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	$-0.355192\pi$
$127$	9.90354			0.878797			0.439399	+	0.898292i	$0.355192\pi$
$128$		0			0
$129$	−0.0394837	+	0.148711i	−0.00347635	+	0.0130933i
$130$		0			0
$131$	8.59220	+	14.8821i	0.750704	+	1.30026i	0.947482	+	0.319809i	$0.103619\pi$
$131$	8.59220	+	14.8821i	0.750704	+	1.30026i	−0.196778	+	0.980448i	$0.563048\pi$
$132$		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	−0.285147	−	0.958484i	$-0.592042\pi$
$137$	8.04696	−	13.9377i	0.687498	−	1.19078i	0.972645	−	0.232298i	$-0.0746243\pi$
$138$		0			0
$139$	−1.11151	+	1.92519i	−0.0942768	+	0.163292i	−0.909307	−	0.416127i	$-0.863387\pi$
$139$	−1.11151	+	1.92519i	−0.0942768	+	0.163292i	0.815030	+	0.579419i	$0.196721\pi$
$140$		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	0.688255	−	0.725469i	$-0.258377\pi$
$149$	−3.46846	−	6.00755i	−0.284147	−	0.492158i	−0.972402	+	0.233312i	$0.925044\pi$
$150$		0			0
$151$	7.75834	−	13.4378i	0.631365	−	1.09356i	−0.355908	−	0.934521i	$-0.615828\pi$
$151$	7.75834	−	13.4378i	0.631365	−	1.09356i	0.987273	−	0.159035i	$-0.0508383\pi$
$152$		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	$-0.877731\pi$
$163$	−1.77500	+	3.07438i	−0.139028	+	0.240804i	0.788101	+	0.615546i	$0.211065\pi$
$164$		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	$-0.854659\pi$
$167$	−0.865131	+	1.49845i	−0.0669459	+	0.115954i	0.830610	+	0.556855i	$0.187992\pi$
$168$		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	$-0.158329\pi$
$179$	0.350412	+	0.606931i	0.0261910	+	0.0453641i	−0.852633	+	0.522511i	$0.824996\pi$
$180$		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	$-0.697715\pi$
$191$	−16.0858			−1.16393			−0.581963	+	0.813215i	$0.697715\pi$
$192$		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	0.866369	+	0.499404i	$0.166448\pi$
$199$	12.2119	+	21.1517i	0.865681	+	1.49940i	−0.000687656		1.00000i	$0.500219\pi$
$200$		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	$-0.707656\pi$
$211$	5.58733	−	9.67754i	0.384648	−	0.666230i	0.991720	+	0.128417i	$0.0409895\pi$
$212$		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	$-0.138290\pi$
$223$	1.32951	+	2.30277i	0.0890303	+	0.154205i	−0.818071	+	0.575117i	$0.804957\pi$
$224$		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	$-0.703927\pi$
$227$	5.95786	−	10.3193i	0.395437	−	0.684917i	0.993157	+	0.116788i	$0.0372598\pi$
$228$		0			0
$229$	14.8064	+	25.6454i	0.978434	+	1.69470i	0.668104	+	0.744068i	$0.267106\pi$
$229$	14.8064	+	25.6454i	0.978434	+	1.69470i	0.310330	+	0.950629i	$0.399561\pi$
$230$		0			0
$231$	10.4285	−	2.08522i	0.686144	−	0.137197i
$232$		0			0
$233$	1.84417	−	3.19420i	0.120816	−	0.209259i	−0.799274	−	0.600967i	$-0.794782\pi$
$233$	1.84417	−	3.19420i	0.120816	−	0.209259i	0.920090	+	0.391708i	$0.128116\pi$
$234$		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	0.479936	+	0.877304i	$0.340660\pi$
$239$	−8.03590	+	13.9186i	−0.519799	+	0.900319i	−0.999735	+	0.0230153i	$0.992673\pi$
$240$		0			0
$241$	−2.24933	+	3.89596i	−0.144892	+	0.250961i	−0.929333	−	0.369243i	$-0.879617\pi$
$241$	−2.24933	+	3.89596i	−0.144892	+	0.250961i	0.784440	+	0.620204i	$0.212950\pi$
$242$		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	$-0.316521\pi$
$251$	17.2696			1.09005			0.545023	+	0.838421i	$0.316521\pi$
$252$		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	0.780984	−	0.624552i	$-0.214718\pi$
$257$	−2.41087	−	4.17574i	−0.150386	−	0.260476i	−0.931369	+	0.364076i	$0.881385\pi$
$258$		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	7.41948e−5	−	1.00000i	$-0.499976\pi$
$263$	14.0452	−	24.3270i	0.866062	−	1.50006i	0.865988	−	0.500064i	$-0.166690\pi$
$264$		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	0.944469	+	0.328599i	$0.106577\pi$
$269$	12.4126	+	21.4993i	0.756810	+	1.31083i	−0.187659	+	0.982234i	$0.560090\pi$
$270$		0			0
$271$	4.79671	−	8.30815i	0.291379	−	0.504684i	−0.682757	−	0.730646i	$-0.739219\pi$
$271$	4.79671	−	8.30815i	0.291379	−	0.504684i	0.974136	+	0.225962i	$0.0725524\pi$
$272$		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	0.491086	+	0.871111i	$0.336600\pi$
$277$	−8.46914	+	14.6690i	−0.508862	+	0.881374i	−0.999947	+	0.0102629i	$0.996733\pi$
$278$		0			0
$279$	−0.116531	−	25.5490i	−0.00697653	−	1.52958i
$280$		0			0
$281$	11.4291	+	19.7958i	0.681805	+	1.18092i	0.974430	+	0.224693i	$0.0721379\pi$
$281$	11.4291	+	19.7958i	0.681805	+	1.18092i	−0.292625	+	0.956227i	$0.594529\pi$
$282$		0			0
$283$	−8.35621			−0.496725			−0.248363	−	0.968667i	$-0.579892\pi$
$283$	−8.35621			−0.496725			−0.248363	+	0.968667i	$0.579892\pi$
$284$		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	−0.922229	−	0.386644i	$-0.873634\pi$
$293$	−2.16141	+	3.74368i	−0.126271	+	0.218708i	0.795958	+	0.605352i	$0.206968\pi$
$294$		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	$-0.415169\pi$
$307$	9.22888			0.526720			0.263360	+	0.964698i	$0.415169\pi$
$308$		0			0
$309$	4.57164	−	17.2186i	0.260072	−	0.979530i
$310$		0			0
$311$	19.1073			1.08348			0.541738	−	0.840548i	$-0.317767\pi$
$311$	19.1073			1.08348			0.541738	+	0.840548i	$0.317767\pi$
$312$		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	$-0.441222\pi$
$331$	6.68091			0.367216			0.183608	+	0.983000i	$0.441222\pi$
$332$		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	−0.945363	−	0.326018i	$-0.894293\pi$
$337$	−3.49421	+	6.05215i	−0.190342	+	0.329681i	0.755022	+	0.655700i	$0.227626\pi$
$338$		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	$-0.571411\pi$
$347$	−8.28821			−0.444934			−0.222467	+	0.974940i	$0.571411\pi$
$348$		0			0
$349$	3.05373	+	5.28921i	0.163462	+	0.283125i	0.936108	−	0.351712i	$-0.114400\pi$
$349$	3.05373	+	5.28921i	0.163462	+	0.283125i	−0.772646	+	0.634837i	$0.781067\pi$
$350$		0			0
$351$	6.50648	+	23.6345i	0.347290	+	1.26152i
$352$		0			0
$353$	13.3604	−	23.1409i	0.711104	−	1.23167i	−0.253340	−	0.967377i	$-0.581529\pi$
$353$	13.3604	−	23.1409i	0.711104	−	1.23167i	0.964443	−	0.264290i	$-0.0851377\pi$
$354$		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	$-0.874711\pi$
$359$	−2.45603	+	4.25397i	−0.129624	+	0.224516i	0.793907	+	0.608040i	$0.208044\pi$
$360$		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	0.117245	+	0.993103i	$0.462594\pi$
$367$	−15.3532	+	26.5925i	−0.801430	+	1.38812i	−0.918675	+	0.395015i	$0.870740\pi$
$368$		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	0.567477	−	0.823390i	$-0.307920\pi$
$373$	−8.29190	−	14.3620i	−0.429338	−	0.743635i	−0.996815	+	0.0797543i	$0.974586\pi$
$374$		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	$-0.533487\pi$
$379$	−4.08857			−0.210016			−0.105008	+	0.994471i	$0.533487\pi$
$380$		0			0
$381$	−12.1569	−	12.1016i	−0.622819	−	0.619985i
$382$		0			0
$383$	15.1769	+	26.2871i	0.775503	+	1.34321i	0.934511	+	0.355933i	$0.115837\pi$
$383$	15.1769	+	26.2871i	0.775503	+	1.34321i	−0.159009	+	0.987277i	$0.550830\pi$
$384$		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	−0.818719	−	0.574195i	$-0.805315\pi$
$389$	1.73382	−	3.00307i	0.0879082	−	0.152261i	0.906627	+	0.421934i	$0.138648\pi$
$390$		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	−0.986851	−	0.161630i	$-0.948325\pi$
$397$	−7.04243	+	12.1979i	−0.353450	+	0.612193i	0.633402	+	0.773823i	$0.281658\pi$
$398$		0			0
$399$	25.0192	−	5.00269i	1.25253	−	0.250448i
$400$		0			0
$401$	5.46593	+	9.46726i	0.272955	+	0.472772i	0.969617	−	0.244627i	$-0.0786656\pi$
$401$	5.46593	+	9.46726i	0.272955	+	0.472772i	−0.696662	+	0.717400i	$0.745332\pi$
$402$		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	$-0.777660\pi$
$419$	3.56197	−	6.16951i	0.174014	−	0.301400i	0.939819	+	0.341671i	$0.110993\pi$
$420$		0			0
$421$	−16.6326	−	28.8086i	−0.810625	−	1.40404i	−0.912427	−	0.409239i	$-0.865794\pi$
$421$	−16.6326	−	28.8086i	−0.810625	−	1.40404i	0.101802	−	0.994805i	$-0.467539\pi$
$422$		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	$-0.126329\pi$
$431$	2.62382	+	4.54459i	0.126385	+	0.218905i	−0.795889	+	0.605443i	$0.792996\pi$
$432$		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	$-0.809433\pi$
$439$	−34.6165			−1.65216			−0.826079	+	0.563555i	$0.809433\pi$
$440$		0			0
$441$	−2.69934	+	20.8258i	−0.128540	+	0.991704i
$442$		0			0
$443$	4.40923			0.209489			0.104744	−	0.994499i	$-0.466598\pi$
$443$	4.40923			0.209489			0.104744	+	0.994499i	$0.466598\pi$
$444$		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	−0.986557	−	0.163415i	$-0.947749\pi$
$461$	−13.6297	−	23.6074i	−0.634800	−	1.09951i	0.351757	−	0.936091i	$-0.385584\pi$
$462$		0			0
$463$	0.959750	−	1.66234i	0.0446034	−	0.0772553i	−0.842862	−	0.538130i	$-0.819131\pi$
$463$	0.959750	−	1.66234i	0.0446034	−	0.0772553i	0.887465	+	0.460875i	$0.152464\pi$
$464$		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	$-0.905938\pi$
$467$	−4.88655	+	8.46376i	−0.226123	+	0.391656i	0.730533	+	0.682877i	$0.239272\pi$
$468$		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	$-0.719081\pi$
$479$	7.68809	−	13.3162i	0.351278	−	0.608431i	0.986474	+	0.163920i	$0.0524139\pi$
$480$		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	$-0.242137\pi$
$487$	−5.18342	−	8.97794i	−0.234883	−	0.406829i	−0.959239	+	0.282597i	$0.908804\pi$
$488$		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	$-0.731825\pi$
$491$	6.94718	−	12.0329i	0.313522	−	0.543035i	0.979122	+	0.203273i	$0.0651578\pi$
$492$		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	$-0.190984\pi$
$499$	−1.70488	−	2.95294i	−0.0763210	−	0.132192i	−0.901660	+	0.432446i	$0.857651\pi$
$500$		0			0
$501$	2.89301	−	0.782255i	0.129250	−	0.0349486i
$502$		0			0
$503$	−43.8911			−1.95701			−0.978504	−	0.206227i	$-0.933881\pi$
$503$	−43.8911			−1.95701			−0.978504	+	0.206227i	$0.933881\pi$
$504$		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	−0.860193	−	0.509968i	$-0.829657\pi$
$509$	−19.6674	−	34.0649i	−0.871742	−	1.50990i	−0.0115483	−	0.999933i	$-0.503676\pi$
$510$		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	0.998500	+	0.0547547i	$0.0174377\pi$
$521$	12.4779	+	21.6124i	0.546669	+	0.946858i	−0.451831	+	0.892104i	$0.649229\pi$
$522$		0			0
$523$	15.1575	−	26.2536i	0.662792	−	1.14799i	−0.317086	−	0.948397i	$-0.602704\pi$
$523$	15.1575	−	26.2536i	0.662792	−	1.14799i	0.979879	−	0.199594i	$-0.0639622\pi$
$524$		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	0.376563	+	0.926391i	$0.377106\pi$
$541$	−14.2812	+	24.7357i	−0.613996	+	1.06347i	−0.990560	+	0.137082i	$0.956228\pi$
$542$		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	$-0.219889\pi$
$547$	−3.89233	−	6.74171i	−0.166424	−	0.288255i	−0.937160	+	0.348900i	$0.886555\pi$
$548$		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	−0.641900	−	0.766788i	$-0.721854\pi$
$557$	−23.2470	−	40.2650i	−0.985008	−	1.70608i	−0.343108	−	0.939296i	$-0.611480\pi$
$558$		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	$-0.700739\pi$
$563$	−27.9826			−1.17933			−0.589663	+	0.807650i	$0.700739\pi$
$564$		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	$-0.263500\pi$
$571$	32.3304			1.35298			0.676492	+	0.736450i	$0.263500\pi$
$572$		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	−0.968075	−	0.250659i	$-0.919353\pi$
$577$	−16.8414	−	29.1701i	−0.701115	−	1.21437i	0.266960	−	0.963707i	$-0.413981\pi$
$578$		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	$-0.150358\pi$
$587$	1.24076	+	2.14907i	0.0512118	+	0.0887015i	−0.839283	+	0.543695i	$0.817025\pi$
$588$		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	0.369859	+	0.929088i	$0.379406\pi$
$593$	−15.0903	+	26.1371i	−0.619684	+	1.07332i	−0.989543	+	0.144236i	$0.953928\pi$
$594$		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	$-0.391192\pi$
$599$	16.4083			0.670424			0.335212	+	0.942143i	$0.391192\pi$
$600$		0			0
$601$	−2.96998	−	5.14416i	−0.121148	−	0.209835i	0.799073	−	0.601235i	$-0.205324\pi$
$601$	−2.96998	−	5.14416i	−0.121148	−	0.209835i	−0.920221	+	0.391400i	$0.871991\pi$
$602$		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	$-0.205207\pi$
$607$	−2.97573	−	5.15412i	−0.120781	−	0.209199i	−0.920076	+	0.391740i	$0.871873\pi$
$608$		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	0.987601	+	0.156988i	$0.0501783\pi$
$613$	15.5920	+	27.0062i	0.629756	+	1.09077i	−0.357845	+	0.933781i	$0.616488\pi$
$614$		0			0
$615$	−14.4325	−	14.3668i	−0.581973	−	0.579325i
$616$		0			0
$617$	−11.1437	+	19.3014i	−0.448627	+	0.777045i	−0.998297	−	0.0583367i	$-0.981420\pi$
$617$	−11.1437	+	19.3014i	−0.448627	+	0.777045i	0.549670	+	0.835382i	$0.314754\pi$
$618$		0			0
$619$	17.2943	−	29.9547i	0.695118	−	1.20398i	−0.275022	−	0.961438i	$-0.588685\pi$
$619$	17.2943	−	29.9547i	0.695118	−	1.20398i	0.970141	−	0.242543i	$-0.0779814\pi$
$620$		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	$-0.324678\pi$
$631$	26.2933			1.04672			0.523360	+	0.852112i	$0.324678\pi$
$632$		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	−0.342349	−	0.939573i	$-0.611223\pi$
$641$	16.2673	−	28.1758i	0.642519	−	1.11288i	0.984869	−	0.173303i	$-0.0554441\pi$
$642$		0			0
$643$	−5.21987	+	9.04107i	−0.205851	+	0.356545i	−0.950404	−	0.311019i	$-0.899330\pi$
$643$	−5.21987	+	9.04107i	−0.205851	+	0.356545i	0.744552	+	0.667564i	$0.232663\pi$
$644$		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	$-0.175250\pi$
$647$	−0.685824	−	1.18788i	−0.0269625	−	0.0467005i	−0.879192	+	0.476468i	$0.841917\pi$
$648$		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	0.928206	−	0.372067i	$-0.121351\pi$
$653$	3.62567	+	6.27985i	0.141883	+	0.245749i	−0.786322	+	0.617816i	$0.788018\pi$
$654$		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	0.999761	+	0.0218722i	$0.00696268\pi$
$659$	13.3187	+	23.0686i	0.518822	+	0.898626i	−0.480939	+	0.876754i	$0.659704\pi$
$660$		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	0.979980	−	0.199096i	$-0.0638007\pi$
$673$	8.23841	+	14.2693i	0.317567	+	0.550043i	−0.662412	+	0.749139i	$0.730467\pi$
$674$		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	−0.998980	−	0.0451447i	$-0.985625\pi$
$683$	−14.0756	−	24.3796i	−0.538587	−	0.932859i	0.460394	−	0.887715i	$-0.347708\pi$
$684$		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	$-0.618217\pi$
$691$	−19.0796			−0.725822			−0.362911	+	0.931824i	$0.618217\pi$
$692$		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	$-0.794150\pi$
$719$	3.29246	−	5.70270i	0.122788	−	0.212675i	0.920866	+	0.389879i	$0.127483\pi$
$720$		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	−0.976096	−	0.217339i	$-0.930262\pi$
$727$	−18.2342	−	31.5826i	−0.676269	−	1.17133i	0.299827	−	0.953994i	$-0.403071\pi$
$728$		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	0.565504	−	0.824745i	$-0.308682\pi$
$733$	−11.6824	−	20.2345i	−0.431498	−	0.747377i	−0.997003	+	0.0773684i	$0.975348\pi$
$734$		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	−0.999306	−	0.0372422i	$-0.988143\pi$
$739$	−14.4596	−	25.0448i	−0.531906	−	0.921288i	0.467400	−	0.884046i	$-0.345191\pi$
$740$		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	$-0.974282\pi$
$743$	−11.6794	+	20.2292i	−0.428474	+	0.742139i	0.568264	+	0.822847i	$0.307615\pi$
$744$		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	$-0.176618\pi$
$751$	−0.856616	−	1.48370i	−0.0312584	−	0.0541411i	−0.881231	+	0.472685i	$0.843285\pi$
$752$		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	0.989822	+	0.142308i	$0.0454524\pi$
$761$	17.0525	+	29.5358i	0.618154	+	1.07067i	−0.371669	+	0.928365i	$0.621214\pi$
$762$		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	−0.817742	−	0.575584i	$-0.804775\pi$
$769$	2.48467	−	4.30357i	0.0895995	−	0.155191i	0.907342	+	0.420394i	$0.138108\pi$
$770$		0			0
$771$	−2.14312	+	8.07183i	−0.0771826	+	0.290700i
$772$		0			0
$773$	−5.74814	−	9.95607i	−0.206746	−	0.358095i	0.743941	−	0.668245i	$-0.232954\pi$
$773$	−5.74814	−	9.95607i	−0.206746	−	0.358095i	−0.950688	+	0.310150i	$0.899621\pi$
$774$		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	$-0.833458\pi$
$787$	−48.6011			−1.73244			−0.866221	+	0.499661i	$0.833458\pi$
$788$		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	−0.396198	−	0.918165i	$-0.629670\pi$
$797$	16.8556	−	29.1947i	0.597056	−	1.03413i	0.993253	−	0.115965i	$-0.0369962\pi$
$798$		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	0.692121	−	0.721782i	$-0.256677\pi$
$809$	−7.93617	−	13.7459i	−0.279021	−	0.483278i	−0.971142	+	0.238503i	$0.923343\pi$
$810$		0			0
$811$	−27.2524			−0.956963			−0.478481	−	0.878098i	$-0.658813\pi$
$811$	−27.2524			−0.956963			−0.478481	+	0.878098i	$0.658813\pi$
$812$		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	$-0.435550\pi$
$823$	11.5380			0.402188			0.201094	+	0.979572i	$0.435550\pi$
$824$		0			0
$825$	−7.69289	+	28.9744i	−0.267832	+	1.00876i
$826$		0			0
$827$	34.8582			1.21214			0.606069	−	0.795412i	$-0.292745\pi$
$827$	34.8582			1.21214			0.606069	+	0.795412i	$0.292745\pi$
$828$		0			0
$829$	−7.64018	−	13.2332i	−0.265354	−	0.459607i	0.702302	−	0.711879i	$-0.252156\pi$
$829$	−7.64018	−	13.2332i	−0.265354	−	0.459607i	−0.967656	+	0.252272i	$0.918822\pi$
$830$		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	$-0.0730125\pi$
$839$	8.39990	+	14.5490i	0.289997	+	0.502289i	−0.683812	+	0.729658i	$0.739679\pi$
$840$		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	0.601362	−	0.798977i	$-0.294625\pi$
$853$	−11.4270	−	19.7921i	−0.391253	−	0.677670i	−0.992615	+	0.121306i	$0.961292\pi$
$854$		0			0
$855$	−0.268897	−	58.9546i	−0.00919607	−	2.01620i
$856$		0			0
$857$	17.5871	−	30.4618i	0.600765	−	1.04056i	−0.391940	−	0.919991i	$-0.628196\pi$
$857$	17.5871	−	30.4618i	0.600765	−	1.04056i	0.992705	−	0.120565i	$-0.0384706\pi$
$858$		0			0
$859$	5.28520	+	9.15424i	0.180329	+	0.312339i	0.941993	−	0.335634i	$-0.108950\pi$
$859$	5.28520	+	9.15424i	0.180329	+	0.312339i	−0.761664	+	0.647973i	$0.775617\pi$
$860$		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	$-0.753473\pi$
$863$	7.29326	−	12.6323i	0.248265	−	0.430008i	0.963045	+	0.269342i	$0.0868061\pi$
$864$		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	0.754518	−	0.656279i	$-0.227871\pi$
$877$	−5.65914	−	9.80192i	−0.191096	−	0.330987i	−0.945614	+	0.325292i	$0.894537\pi$
$878$		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	$-0.423353\pi$
$883$	14.1726			0.476944			0.238472	+	0.971149i	$0.423353\pi$
$884$		0			0
$885$	12.5424	−	47.2395i	0.421608	−	1.58794i
$886$		0			0
$887$	−16.8162	−	29.1266i	−0.564634	−	0.977975i	−0.997084	−	0.0763170i	$-0.975684\pi$
$887$	−16.8162	−	29.1266i	−0.564634	−	0.977975i	0.432449	−	0.901658i	$-0.357649\pi$
$888$		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	$-0.782463\pi$
$907$	4.79255	−	8.30094i	0.159134	−	0.275628i	0.934557	+	0.355814i	$0.115796\pi$
$908$		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	$-0.0661342\pi$
$911$	9.37499	+	16.2380i	0.310607	+	0.537988i	−0.667887	+	0.744263i	$0.732801\pi$
$912$		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	0.265390	+	0.964141i	$0.414499\pi$
$919$	−21.2895	+	36.8745i	−0.702276	+	1.21638i	−0.967666	+	0.252236i	$0.918834\pi$
$920$		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	$-0.421038\pi$
$947$	15.1115			0.491058			0.245529	+	0.969389i	$0.421038\pi$
$948$		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	$-0.925004\pi$
$967$	−8.83228	+	15.2980i	−0.284027	+	0.491949i	0.688346	+	0.725383i	$0.258337\pi$
$968$		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	$-0.710238\pi$
$971$	11.7523	−	20.3555i	0.377148	−	0.653240i	0.990646	+	0.136456i	$0.0435713\pi$
$972$		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	$-0.844031\pi$
$983$	−1.05345	+	1.82463i	−0.0335998	+	0.0581966i	0.848736	+	0.528816i	$0.177364\pi$
$984$		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	$-0.258026\pi$
$991$	−8.91172	−	15.4356i	−0.283090	−	0.490327i	−0.972144	+	0.234383i	$0.924693\pi$
$992$		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	−0.417807	−	0.908536i	$-0.637201\pi$
$997$	18.2477	−	31.6060i	0.577911	−	1.00097i	0.995719	−	0.0924360i	$-0.0294653\pi$
$998$		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	1008.2.q.k.625.4		22
3.2	odd	2		3024.2.q.k.2305.1		22
4.3	odd	2		504.2.q.d.121.8	yes	22
7.4	even	3		1008.2.t.k.193.5		22
9.2	odd	6		3024.2.t.l.289.11		22
9.7	even	3		1008.2.t.k.961.5		22
12.11	even	2		1512.2.q.c.793.1		22
21.11	odd	6		3024.2.t.l.1873.11		22
28.11	odd	6		504.2.t.d.193.7	yes	22
36.7	odd	6		504.2.t.d.457.7	yes	22
36.11	even	6		1512.2.t.d.289.11		22
63.11	odd	6		3024.2.q.k.2881.1		22
63.25	even	3	inner	1008.2.q.k.529.4		22
84.11	even	6		1512.2.t.d.361.11		22
252.11	even	6		1512.2.q.c.1369.1		22
252.151	odd	6		504.2.q.d.25.8	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.8	✓	22	252.151	odd	6
504.2.q.d.121.8	yes	22	4.3	odd	2
504.2.t.d.193.7	yes	22	28.11	odd	6
504.2.t.d.457.7	yes	22	36.7	odd	6
1008.2.q.k.529.4		22	63.25	even	3	inner
1008.2.q.k.625.4		22	1.1	even	1	trivial
1008.2.t.k.193.5		22	7.4	even	3
1008.2.t.k.961.5		22	9.7	even	3
1512.2.q.c.793.1		22	12.11	even	2
1512.2.q.c.1369.1		22	252.11	even	6
1512.2.t.d.289.11		22	36.11	even	6
1512.2.t.d.361.11		22	84.11	even	6
3024.2.q.k.2305.1		22	3.2	odd	2
3024.2.q.k.2881.1		22	63.11	odd	6
3024.2.t.l.289.11		22	9.2	odd	6
3024.2.t.l.1873.11		22	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not 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

L-functions

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