LMFDB - Embedded newform 504.2.t.d.457.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (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			457.7
Character	$\chi$	$=$	504.457
Dual form			504.2.t.d.193.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.444471 + 1.67405i) q^{3} -3.52959 q^{5} +(1.16715 + 2.37440i) q^{7} +(-2.60489 + 1.48813i) q^{9} +O(q^{10})$	\(q+(0.444471 + 1.67405i) q^{3} -3.52959 q^{5} +(1.16715 + 2.37440i) q^{7} +(-2.60489 + 1.48813i) q^{9} -2.32073 q^{11} +(-2.35884 - 4.08563i) q^{13} +(-1.56880 - 5.90871i) q^{15} +(-0.636946 - 1.10322i) q^{17} +(2.78386 - 4.82178i) q^{19} +(-3.45610 + 3.00922i) q^{21} -3.29710 q^{23} +7.45798 q^{25} +(-3.64901 - 3.69929i) q^{27} +(-4.32116 + 7.48447i) q^{29} +(-4.25821 + 7.37543i) q^{31} +(-1.03150 - 3.88502i) q^{33} +(-4.11956 - 8.38064i) q^{35} +(-2.84024 + 4.91943i) q^{37} +(5.79111 - 5.76476i) q^{39} +(1.66553 + 2.88478i) q^{41} +(0.0444165 - 0.0769317i) q^{43} +(9.19419 - 5.25250i) q^{45} +(-3.52607 - 6.10733i) q^{47} +(-4.27552 + 5.54256i) q^{49} +(1.56375 - 1.55663i) q^{51} +(3.41816 + 5.92042i) q^{53} +8.19121 q^{55} +(9.30925 + 2.51717i) q^{57} +(3.99745 - 6.92378i) q^{59} +(-6.67764 - 11.5660i) q^{61} +(-6.57372 - 4.44817i) q^{63} +(8.32572 + 14.4206i) q^{65} +(-3.06402 + 5.30704i) q^{67} +(-1.46546 - 5.51951i) q^{69} +1.30202 q^{71} +(6.64529 + 11.5100i) q^{73} +(3.31486 + 12.4850i) q^{75} +(-2.70864 - 5.51033i) q^{77} +(5.01403 + 8.68455i) q^{79} +(4.57091 - 7.75286i) q^{81} +(-5.90243 + 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(-14.4500 - 3.90721i) q^{87} +(0.561496 - 0.972540i) q^{89} +(6.94778 - 10.3694i) q^{91} +(-14.2395 - 3.85029i) q^{93} +(-9.82586 + 17.0189i) q^{95} +(-3.50818 + 6.07635i) q^{97} +(6.04525 - 3.45356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9	$ 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39} + 16 q^{41} + 22 q^{45} + 5 q^{47} - 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} - 19 q^{59} - 13 q^{61} + 21 q^{63} + 13 q^{65} + 26 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 8 q^{75} - 4 q^{77} + 10 q^{79} - 8 q^{81} - 28 q^{83} - 20 q^{85} + 9 q^{87} + 6 q^{89} - 37 q^{91} - 32 q^{93} + 12 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.444471	+	1.67405i	0.256616	+	0.966514i
$3$	0.444471	+	1.67405i	0.256616	+	0.966514i
$4$		0			0
$5$	−3.52959			−1.57848			−0.789239	−	0.614086i	$-0.789525\pi$
$5$	−3.52959			−1.57848			−0.789239	+	0.614086i	$0.789525\pi$
$6$		0			0
$7$	1.16715	+	2.37440i	0.441141	+	0.897438i
$7$	1.16715	+	2.37440i	0.441141	+	0.897438i
$8$		0			0
$9$	−2.60489	+	1.48813i	−0.868297	+	0.496045i
$10$		0			0
$11$	−2.32073			−0.699726			−0.349863	−	0.936801i	$-0.613772\pi$
$11$	−2.32073			−0.699726			−0.349863	+	0.936801i	$0.613772\pi$
$12$		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	0.778388	−	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	$-0.612822\pi$
$19$	2.78386	−	4.82178i	0.638661	−	1.10619i	0.985727	−	0.168352i	$-0.0538445\pi$
$20$		0			0
$21$	−3.45610	+	3.00922i	−0.754182	+	0.656666i
$22$		0			0
$23$	−3.29710			−0.687492			−0.343746	−	0.939063i	$-0.611696\pi$
$23$	−3.29710			−0.687492			−0.343746	+	0.939063i	$0.611696\pi$
$24$		0			0
$25$	7.45798			1.49160
$26$		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
$31$	−4.25821	+	7.37543i	−0.764797	+	1.32467i	0.175557	+	0.984469i	$0.443827\pi$
$31$	−4.25821	+	7.37543i	−0.764797	+	1.32467i	−0.940354	+	0.340197i	$0.889506\pi$
$32$		0			0
$33$	−1.03150	−	3.88502i	−0.179561	−	0.676295i
$34$		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
$39$	5.79111	−	5.76476i	0.927320	−	0.923100i
$40$		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
$45$	9.19419	−	5.25250i	1.37059	−	0.782996i
$46$		0			0
$47$	−3.52607	−	6.10733i	−0.514330	−	0.890845i	−0.999862	−	0.0166264i	$-0.994707\pi$
$47$	−3.52607	−	6.10733i	−0.514330	−	0.890845i	0.485532	−	0.874219i	$-0.338626\pi$
$48$		0			0
$49$	−4.27552	+	5.54256i	−0.610789	+	0.791794i
$50$		0			0
$51$	1.56375	−	1.55663i	0.218968	−	0.217972i
$52$		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
$59$	3.99745	−	6.92378i	0.520423	−	0.901400i	−0.479295	−	0.877654i	$-0.659107\pi$
$59$	3.99745	−	6.92378i	0.520423	−	0.901400i	0.999718	−	0.0237457i	$-0.00755920\pi$
$60$		0			0
$61$	−6.67764	−	11.5660i	−0.854985	−	1.48088i	−0.876659	−	0.481112i	$-0.840233\pi$
$61$	−6.67764	−	11.5660i	−0.854985	−	1.48088i	0.0216747	−	0.999765i	$-0.493100\pi$
$62$		0			0
$63$	−6.57372	−	4.44817i	−0.828211	−	0.560416i
$64$		0			0
$65$	8.32572	+	14.4206i	1.03268	+	1.78865i
$66$		0			0
$67$	−3.06402	+	5.30704i	−0.374330	+	0.648358i	−0.990226	−	0.139469i	$-0.955461\pi$
$67$	−3.06402	+	5.30704i	−0.374330	+	0.648358i	0.615897	+	0.787827i	$0.288794\pi$
$68$		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	0.933223	+	0.359297i	$0.116984\pi$
$73$	6.64529	+	11.5100i	0.777772	+	1.34714i	−0.155451	+	0.987844i	$0.549683\pi$
$74$		0			0
$75$	3.31486	+	12.4850i	0.382767	+	1.44165i
$76$		0			0
$77$	−2.70864	−	5.51033i	−0.308678	−	0.627961i
$78$		0			0
$79$	5.01403	+	8.68455i	0.564122	+	0.977088i	0.997131	+	0.0756985i	$0.0241187\pi$
$79$	5.01403	+	8.68455i	0.564122	+	0.977088i	−0.433009	+	0.901390i	$0.642548\pi$
$80$		0			0
$81$	4.57091	−	7.75286i	0.507879	−	0.861428i
$82$		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
$87$	−14.4500	−	3.90721i	−1.54920	−	0.418897i
$88$		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
$93$	−14.2395	−	3.85029i	−1.47657	−	0.399256i
$94$		0			0
$95$	−9.82586	+	17.0189i	−1.00811	+	1.74610i
$96$		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
$101$	−9.74111			−0.969277			−0.484638	−	0.874715i	$-0.661049\pi$
$101$	−9.74111			−0.969277			−0.484638	+	0.874715i	$0.661049\pi$
$102$		0			0
$103$	10.2856			1.01347			0.506734	−	0.862103i	$-0.330853\pi$
$103$	10.2856			1.01347			0.506734	+	0.862103i	$0.330853\pi$
$104$		0			0
$105$	12.1986	−	10.6213i	1.19046	−	1.03653i
$106$		0			0
$107$	2.72201	−	4.71465i	0.263146	−	0.455783i	−0.703930	−	0.710269i	$-0.748573\pi$
$107$	2.72201	−	4.71465i	0.263146	−	0.455783i	0.967076	+	0.254487i	$0.0819065\pi$
$108$		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	0.999894	+	0.0145882i	$0.00464372\pi$
$113$	5.44881	+	9.43761i	0.512581	+	0.887815i	−0.487313	+	0.873227i	$0.662023\pi$
$114$		0			0
$115$	11.6374			1.08519
$116$		0			0
$117$	12.2245	+	7.13234i	1.13015	+	0.659385i
$118$		0			0
$119$	1.87608	−	2.79999i	0.171980	−	0.256674i
$120$		0			0
$121$	−5.61421			−0.510383
$122$		0			0
$123$	−4.08900	+	4.07039i	−0.368692	+	0.367014i
$124$		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
$129$	0.148529	+	0.0401616i	0.0130773	+	0.00353603i
$130$		0			0
$131$	17.1844			1.50141			0.750704	−	0.660639i	$-0.229715\pi$
$131$	17.1844			1.50141			0.750704	+	0.660639i	$0.229715\pi$
$132$		0			0
$133$	14.6980	+	0.982238i	1.27448	+	0.0851708i
$134$		0			0
$135$	12.8795	+	13.0569i	1.10849	+	1.12376i
$136$		0			0
$137$	−16.0939			−1.37500			−0.687498	−	0.726186i	$-0.741291\pi$
$137$	−16.0939			−1.37500			−0.687498	+	0.726186i	$0.741291\pi$
$138$		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
$147$	−11.1789	−	4.69393i	−0.922017	−	0.387149i
$148$		0			0
$149$	6.93692			0.568295			0.284147	−	0.958781i	$-0.408290\pi$
$149$	6.93692			0.568295			0.284147	+	0.958781i	$0.408290\pi$
$150$		0			0
$151$	15.5167			1.26273			0.631365	−	0.775486i	$-0.282495\pi$
$151$	15.5167			1.26273			0.631365	+	0.775486i	$0.282495\pi$
$152$		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
$157$	−0.401055	+	0.694648i	−0.0320077	+	0.0554389i	−0.881586	−	0.472024i	$-0.843523\pi$
$157$	−0.401055	+	0.694648i	−0.0320077	+	0.0554389i	0.849578	+	0.527463i	$0.176857\pi$
$158$		0			0
$159$	−8.39182	+	8.35363i	−0.665514	+	0.662486i
$160$		0			0
$161$	−3.84821	−	7.82862i	−0.303281	−	0.616982i
$162$		0			0
$163$	1.77500	−	3.07438i	0.139028	−	0.240804i	−0.788101	−	0.615546i	$-0.788935\pi$
$163$	1.77500	−	3.07438i	0.139028	−	0.240804i	0.927129	+	0.374742i	$0.122269\pi$
$164$		0			0
$165$	3.64076	+	13.7125i	0.283433	+	1.06752i
$166$		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
$171$	−0.0761836	+	16.7030i	−0.00582590	+	1.27731i
$172$		0			0
$173$	−1.11729	−	1.93521i	−0.0849462	−	0.147131i	0.820422	−	0.571758i	$-0.193738\pi$
$173$	−1.11729	−	1.93521i	−0.0849462	−	0.147131i	−0.905368	+	0.424627i	$0.860405\pi$
$174$		0			0
$175$	8.70458	+	17.7082i	0.658005	+	1.33861i
$176$		0			0
$177$	13.3675	+	3.61451i	1.00476	+	0.271683i
$178$		0			0
$179$	−0.350412	−	0.606931i	−0.0261910	−	0.0453641i	0.852633	−	0.522511i	$-0.175004\pi$
$179$	−0.350412	−	0.606931i	−0.0261910	−	0.0453641i	−0.878824	+	0.477146i	$0.841671\pi$
$180$		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
$185$	10.0249	−	17.3636i	0.737042	−	1.27659i
$186$		0			0
$187$	1.47818	+	2.56028i	0.108095	+	0.187226i
$188$		0			0
$189$	4.52463	−	12.9818i	0.329118	−	0.944289i
$190$		0			0
$191$	−8.04289	−	13.9307i	−0.581963	−	1.00799i	−0.995247	−	0.0973872i	$-0.968951\pi$
$191$	−8.04289	−	13.9307i	−0.581963	−	1.00799i	0.413284	−	0.910602i	$-0.364382\pi$
$192$		0			0
$193$	0.292732	−	0.507026i	0.0210713	−	0.0364965i	−0.855297	−	0.518137i	$-0.826626\pi$
$193$	0.292732	−	0.507026i	0.0210713	−	0.0364965i	0.876369	+	0.481641i	$0.159959\pi$
$194$		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	$-0.833552\pi$
$199$	−12.2119	−	21.1517i	−0.865681	−	1.49940i	0.000687656	−	1.00000i	$-0.499781\pi$
$200$		0			0
$201$	−10.2461	−	2.77050i	−0.722706	−	0.195416i
$202$		0			0
$203$	−22.8145	−	1.52465i	−1.60127	−	0.107009i
$204$		0			0
$205$	−5.87864	−	10.1821i	−0.410582	−	0.711149i
$206$		0			0
$207$	8.58858	−	4.90653i	0.596948	−	0.341027i
$208$		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
$213$	0.578712	+	2.17965i	0.0396527	+	0.149347i
$214$		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
$219$	−16.3146	+	16.2404i	−1.10244	+	1.09742i
$220$		0			0
$221$	−3.00490	+	5.20464i	−0.202132	+	0.350102i
$222$		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
$227$	11.9157			0.790874			0.395437	−	0.918493i	$-0.370593\pi$
$227$	11.9157			0.790874			0.395437	+	0.918493i	$0.370593\pi$
$228$		0			0
$229$	−29.6128			−1.95687			−0.978434	−	0.206561i	$-0.933773\pi$
$229$	−29.6128			−1.95687			−0.978434	+	0.206561i	$0.933773\pi$
$230$		0			0
$231$	8.02066	−	6.98358i	0.527721	−	0.459486i
$232$		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	0.999735	+	0.0230153i	$0.00732663\pi$
$239$	8.03590	+	13.9186i	0.519799	+	0.900319i	−0.479936	+	0.877304i	$0.659340\pi$
$240$		0			0
$241$	4.49867			0.289785			0.144892	−	0.989447i	$-0.453716\pi$
$241$	4.49867			0.289785			0.144892	+	0.989447i	$0.453716\pi$
$242$		0			0
$243$	15.0103	+	4.20602i	0.962912	+	0.269816i
$244$		0			0
$245$	15.0908	−	19.5629i	0.964117	−	1.24983i
$246$		0			0
$247$	−26.2667			−1.67131
$248$		0			0
$249$	−19.7378	−	5.33700i	−1.25083	−	0.338219i
$250$		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
$255$	−5.51938	+	5.49426i	−0.345637	+	0.344064i
$256$		0			0
$257$	4.82173			0.300771			0.150386	−	0.988627i	$-0.451948\pi$
$257$	4.82173			0.300771			0.150386	+	0.988627i	$0.451948\pi$
$258$		0			0
$259$	−14.9957	−	1.00213i	−0.931786	−	0.0622693i
$260$		0			0
$261$	0.118254	−	25.9267i	0.00731972	−	1.60482i
$262$		0			0
$263$	28.0903			1.73212			0.866062	−	0.499936i	$-0.166643\pi$
$263$	28.0903			1.73212			0.866062	+	0.499936i	$0.166643\pi$
$264$		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	−0.974136	−	0.225962i	$-0.927448\pi$
$271$	−4.79671	+	8.30815i	−0.291379	+	0.504684i	0.682757	+	0.730646i	$0.260781\pi$
$272$		0			0
$273$	20.4469	+	7.02206i	1.23750	+	0.424994i
$274$		0			0
$275$	−17.3080			−1.04371
$276$		0			0
$277$	16.9383			1.01772			0.508862	−	0.860848i	$-0.330067\pi$
$277$	16.9383			1.01772			0.508862	+	0.860848i	$0.330067\pi$
$278$		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
$283$	−4.17811	+	7.23669i	−0.248363	+	0.430177i	−0.963072	−	0.269245i	$-0.913226\pi$
$283$	−4.17811	+	7.23669i	−0.248363	+	0.430177i	0.714709	+	0.699422i	$0.246559\pi$
$284$		0			0
$285$	−32.8578	−	8.88458i	−1.94633	−	0.526277i
$286$		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
$291$	−11.7314	−	3.17211i	−0.687708	−	0.185953i
$292$		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
$297$	8.46837	+	8.58504i	0.491385	+	0.498155i
$298$		0			0
$299$	7.77732	+	13.4707i	0.449774	+	0.779031i
$300$		0			0
$301$	0.234507	+	0.0156716i	0.0135168	+	0.000903298i
$302$		0			0
$303$	−4.32964	−	16.3071i	−0.248731	−	0.936819i
$304$		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
$311$	9.55365	−	16.5474i	0.541738	−	0.938317i	−0.457067	−	0.889432i	$-0.651100\pi$
$311$	9.55365	−	16.5474i	0.541738	−	0.938317i	0.998804	−	0.0488847i	$-0.0155667\pi$
$312$		0			0
$313$	−2.83951	−	4.91818i	−0.160499	−	0.277992i	0.774549	−	0.632514i	$-0.217977\pi$
$313$	−2.83951	−	4.91818i	−0.160499	−	0.277992i	−0.935048	+	0.354522i	$0.884644\pi$
$314$		0			0
$315$	23.2025	+	15.7002i	1.30731	+	0.884606i
$316$		0			0
$317$	14.1341	+	24.4809i	0.793848	+	1.37499i	0.923568	+	0.383434i	$0.125259\pi$
$317$	14.1341	+	24.4809i	0.793848	+	1.37499i	−0.129720	+	0.991551i	$0.541408\pi$
$318$		0			0
$319$	10.0282	−	17.3694i	0.561474	−	0.972501i
$320$		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
$327$	−1.02476	+	1.02009i	−0.0566691	+	0.0564112i
$328$		0			0
$329$	10.3858	−	15.5005i	0.572586	−	0.854568i
$330$		0			0
$331$	3.34045	+	5.78584i	0.183608	+	0.318018i	0.943107	−	0.332491i	$-0.107889\pi$
$331$	3.34045	+	5.78584i	0.183608	+	0.318018i	−0.759499	+	0.650509i	$0.774556\pi$
$332$		0			0
$333$	0.0777265	−	17.0412i	0.00425938	−	0.933854i
$334$		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
$339$	−13.3772	+	13.3163i	−0.726550	+	0.723243i
$340$		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
$345$	5.17249	+	19.4816i	0.278477	+	1.04885i
$346$		0			0
$347$	−4.14410	+	7.17780i	−0.222467	+	0.385324i	−0.955557	−	0.294808i	$-0.904744\pi$
$347$	−4.14410	+	7.17780i	−0.222467	+	0.385324i	0.733089	+	0.680132i	$0.238078\pi$
$348$		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
$353$	−26.7208			−1.42221			−0.711104	−	0.703087i	$-0.751804\pi$
$353$	−26.7208			−1.42221			−0.711104	+	0.703087i	$0.751804\pi$
$354$		0			0
$355$	−4.59561			−0.243909
$356$		0			0
$357$	5.52118	+	1.89613i	0.292212	+	0.100354i
$358$		0			0
$359$	2.45603	−	4.25397i	0.129624	−	0.224516i	−0.793907	−	0.608040i	$-0.791956\pi$
$359$	2.45603	−	4.25397i	0.129624	−	0.224516i	0.923531	+	0.383523i	$0.125289\pi$
$360$		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
$367$	−30.7064			−1.60286			−0.801430	−	0.598089i	$-0.795927\pi$
$367$	−30.7064			−1.60286			−0.801430	+	0.598089i	$0.795927\pi$
$368$		0			0
$369$	−8.63147	−	5.03601i	−0.449337	−	0.262164i
$370$		0			0
$371$	−10.0679	+	15.0261i	−0.522701	+	0.780116i
$372$		0			0
$373$	16.5838			0.858676			0.429338	−	0.903144i	$-0.358747\pi$
$373$	16.5838			0.858676			0.429338	+	0.903144i	$0.358747\pi$
$374$		0			0
$375$	−3.85608	−	14.5235i	−0.199127	−	0.749989i
$376$		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
$381$	−4.40184	−	16.5790i	−0.225513	−	0.849370i
$382$		0			0
$383$	30.3538			1.55101			0.775503	−	0.631344i	$-0.217496\pi$
$383$	30.3538			1.55101			0.775503	+	0.631344i	$0.217496\pi$
$384$		0			0
$385$	9.56038	+	19.4492i	0.487242	+	0.991223i
$386$		0			0
$387$	−0.00121551	+	0.266496i	−6.17879e−5	+	0.0135468i
$388$		0			0
$389$	−3.46764			−0.175816			−0.0879082	−	0.996129i	$-0.528018\pi$
$389$	−3.46764			−0.175816			−0.0879082	+	0.996129i	$0.528018\pi$
$390$		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
$399$	4.88852	+	25.0418i	0.244732	+	1.25366i
$400$		0			0
$401$	−10.9319			−0.545911			−0.272955	−	0.962027i	$-0.588001\pi$
$401$	−10.9319			−0.545911			−0.272955	+	0.962027i	$0.588001\pi$
$402$		0			0
$403$	40.1777			2.00139
$404$		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
$409$	−7.99397	+	13.8460i	−0.395276	+	0.684639i	−0.993136	−	0.116962i	$-0.962685\pi$
$409$	−7.99397	+	13.8460i	−0.395276	+	0.684639i	0.597860	+	0.801600i	$0.296018\pi$
$410$		0			0
$411$	−7.15328	−	26.9420i	−0.352845	−	1.32895i
$412$		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
$417$	−2.72883	+	2.71641i	−0.133631	+	0.133023i
$418$		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
$423$	18.2735	+	10.6617i	0.888490	+	0.518388i
$424$		0			0
$425$	−4.75033	−	8.22781i	−0.230425	−	0.399107i
$426$		0			0
$427$	19.6685	−	29.3547i	0.951826	−	1.42057i
$428$		0			0
$429$	−13.4396	+	13.3784i	−0.648870	+	0.645917i
$430$		0			0
$431$	−2.62382	−	4.54459i	−0.126385	−	0.218905i	0.795889	−	0.605443i	$-0.207004\pi$
$431$	−2.62382	−	4.54459i	−0.126385	−	0.218905i	−0.922273	+	0.386538i	$0.873671\pi$
$432$		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
$437$	−9.17865	+	15.8979i	−0.439074	+	0.760499i
$438$		0			0
$439$	−17.3083	−	29.9788i	−0.826079	−	1.43081i	−0.901092	−	0.433628i	$-0.857233\pi$
$439$	−17.3083	−	29.9788i	−0.826079	−	1.43081i	0.0750132	−	0.997183i	$-0.476100\pi$
$440$		0			0
$441$	2.88920	−	20.8003i	0.137581	−	0.990491i
$442$		0			0
$443$	2.20461	+	3.81850i	0.104744	+	0.181423i	0.913634	−	0.406538i	$-0.133264\pi$
$443$	2.20461	+	3.81850i	0.104744	+	0.181423i	−0.808889	+	0.587961i	$0.799931\pi$
$444$		0			0
$445$	−1.98185	+	3.43266i	−0.0939486	+	0.162724i
$446$		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
$453$	6.89672	+	25.9757i	0.324036	+	1.22045i
$454$		0			0
$455$	−24.5228	+	36.5995i	−1.14965	+	1.71581i
$456$		0			0
$457$	15.4196	+	26.7075i	0.721297	+	1.24932i	0.960480	+	0.278349i	$0.0897872\pi$
$457$	15.4196	+	26.7075i	0.721297	+	1.24932i	−0.239183	+	0.970975i	$0.576879\pi$
$458$		0			0
$459$	−1.75691	+	6.38191i	−0.0820057	+	0.297882i
$460$		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
$465$	50.2595	+	13.5899i	2.33073	+	0.630218i
$466$		0			0
$467$	4.88655	−	8.46376i	0.226123	−	0.391656i	−0.730533	−	0.682877i	$-0.760728\pi$
$467$	4.88655	−	8.46376i	0.226123	−	0.391656i	0.956656	+	0.291221i	$0.0940616\pi$
$468$		0			0
$469$	−16.1772	−	1.08109i	−0.746994	−	0.0499201i
$470$		0			0
$471$	−1.34113	−	0.362636i	−0.0617962	−	0.0167094i
$472$		0			0
$473$	−0.103079	+	0.178538i	−0.00473957	+	0.00820917i
$474$		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
$479$	15.3762			0.702556			0.351278	−	0.936271i	$-0.385747\pi$
$479$	15.3762			0.702556			0.351278	+	0.936271i	$0.385747\pi$
$480$		0			0
$481$	26.7986			1.22191
$482$		0			0
$483$	11.3951	−	9.92169i	0.518494	−	0.451453i
$484$		0			0
$485$	12.3824	−	21.4470i	0.562258	−	0.973859i
$486$		0			0
$487$	5.18342	+	8.97794i	0.234883	+	0.406829i	0.959239	−	0.282597i	$-0.0911959\pi$
$487$	5.18342	+	8.97794i	0.234883	+	0.406829i	−0.724356	+	0.689427i	$0.757863\pi$
$488$		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
$493$	11.0094			0.495837
$494$		0			0
$495$	−21.3372	+	12.1896i	−0.959037	+	0.547883i
$496$		0			0
$497$	1.51966	+	3.09152i	0.0681660	+	0.138674i
$498$		0			0
$499$	−3.40977			−0.152642			−0.0763210	−	0.997083i	$-0.524317\pi$
$499$	−3.40977			−0.152642			−0.0763210	+	0.997083i	$0.524317\pi$
$500$		0			0
$501$	−2.12396	+	2.11429i	−0.0948914	+	0.0944596i
$502$		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
$507$	−15.4769	−	4.18486i	−0.687351	−	0.185856i
$508$		0			0
$509$	39.3348			1.74348			0.871742	−	0.489966i	$-0.162991\pi$
$509$	39.3348			1.74348			0.871742	+	0.489966i	$0.162991\pi$
$510$		0			0
$511$	−19.5732	+	29.2124i	−0.865868	+	1.29228i
$512$		0			0
$513$	−27.9955	+	7.29645i	−1.23603	+	0.322146i
$514$		0			0
$515$	−36.3038			−1.59974
$516$		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	$0.397296\pi$
$523$	−15.1575	+	26.2536i	−0.662792	+	1.14799i	−0.979879	+	0.199594i	$0.936038\pi$
$524$		0			0
$525$	−25.7755	+	22.4427i	−1.12493	+	0.979480i
$526$		0			0
$527$	10.8490			0.472589
$528$		0			0
$529$	−12.1291			−0.527354
$530$		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
$535$	−9.60755	+	16.6408i	−0.415371	+	0.719443i
$536$		0			0
$537$	0.860285	−	0.856370i	0.0371240	−	0.0369551i
$538$		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
$543$	−8.72671	−	32.8682i	−0.374499	−	1.41051i
$544$		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
$549$	34.6063	+	20.1910i	1.47696	+	0.861730i
$550$		0			0
$551$	24.0590	+	41.6714i	1.02495	+	1.77526i
$552$		0			0
$553$	−14.7684	+	22.0415i	−0.628018	+	0.937299i
$554$		0			0
$555$	33.5232	+	9.06452i	1.42298	+	0.384767i
$556$		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
$563$	−13.9913	+	24.2336i	−0.589663	+	1.02133i	0.404614	+	0.914488i	$0.367406\pi$
$563$	−13.9913	+	24.2336i	−0.589663	+	1.02133i	−0.994276	+	0.106838i	$0.965927\pi$
$564$		0			0
$565$	−19.2320	−	33.3109i	−0.809098	−	1.40140i
$566$		0			0
$567$	23.7433	+	1.80441i	0.997125	+	0.0757781i
$568$		0			0
$569$	−4.44979	−	7.70726i	−0.186545	−	0.323105i	0.757551	−	0.652776i	$-0.226396\pi$
$569$	−4.44979	−	7.70726i	−0.186545	−	0.323105i	−0.944096	+	0.329671i	$0.893062\pi$
$570$		0			0
$571$	16.1652	−	27.9989i	0.676492	−	1.17172i	−0.299539	−	0.954084i	$-0.596833\pi$
$571$	16.1652	−	27.9989i	0.676492	−	1.17172i	0.976031	−	0.217634i	$-0.0698338\pi$
$572$		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
$579$	0.978898	+	0.264689i	0.0406816	+	0.0110001i
$580$		0			0
$581$	−31.1632	−	2.08257i	−1.29287	−	0.0863997i
$582$		0			0
$583$	−7.93262	−	13.7397i	−0.328536	−	0.569040i
$584$		0			0
$585$	−43.1473	−	25.1742i	−1.78392	−	1.04083i
$586$		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
$591$	−7.68595	−	28.9483i	−0.316158	−	1.19077i
$592$		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
$597$	29.9812	−	29.8447i	1.22705	−	1.22146i
$598$		0			0
$599$	8.20414	−	14.2100i	0.335212	−	0.580604i	−0.648314	−	0.761373i	$-0.724525\pi$
$599$	8.20414	−	14.2100i	0.335212	−	0.580604i	0.983526	+	0.180769i	$0.0578588\pi$
$600$		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
$605$	19.8159			0.805629
$606$		0			0
$607$	−5.95146			−0.241563			−0.120781	−	0.992679i	$-0.538540\pi$
$607$	−5.95146			−0.241563			−0.120781	+	0.992679i	$0.538540\pi$
$608$		0			0
$609$	−7.58806	−	38.8703i	−0.307484	−	1.57511i
$610$		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	0.549670	−	0.835382i	$-0.314754\pi$
$617$	−11.1437	−	19.3014i	−0.448627	−	0.777045i	−0.998297	+	0.0583367i	$0.981420\pi$
$618$		0			0
$619$	34.5887			1.39024			0.695118	−	0.718895i	$-0.255352\pi$
$619$	34.5887			1.39024			0.695118	+	0.718895i	$0.255352\pi$
$620$		0			0
$621$	12.0311	+	12.1969i	0.482793	+	0.489445i
$622$		0			0
$623$	2.96454	+	0.198115i	0.118772	+	0.00793729i
$624$		0			0
$625$	−6.66844			−0.266738
$626$		0			0
$627$	−21.6043	−	5.84168i	−0.862791	−	0.233294i
$628$		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
$633$	13.7173	−	13.6549i	0.545213	−	0.542732i
$634$		0			0
$635$	34.9554			1.38716
$636$		0			0
$637$	32.7301	+	4.39419i	1.29681	+	0.174104i
$638$		0			0
$639$	−3.39163	+	1.93759i	−0.134171	+	0.0766498i
$640$		0			0
$641$	−32.5346			−1.28504			−0.642519	−	0.766269i	$-0.722111\pi$
$641$	−32.5346			−1.28504			−0.642519	+	0.766269i	$0.722111\pi$
$642$		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	0.879192	−	0.476468i	$-0.158083\pi$
$647$	0.685824	+	1.18788i	0.0269625	+	0.0467005i	−0.852229	+	0.523168i	$0.824750\pi$
$648$		0			0
$649$	−9.27699	+	16.0682i	−0.364154	+	0.630733i
$650$		0			0
$651$	−7.47752	−	38.3041i	−0.293067	−	1.50126i
$652$		0			0
$653$	−7.25134			−0.283767			−0.141883	−	0.989883i	$-0.545316\pi$
$653$	−7.25134			−0.283767			−0.141883	+	0.989883i	$0.545316\pi$
$654$		0			0
$655$	−60.6538			−2.36994
$656$		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
$661$	17.4099	−	30.1549i	0.677168	−	1.17289i	−0.298662	−	0.954359i	$-0.596540\pi$
$661$	17.4099	−	30.1549i	0.677168	−	1.17289i	0.975830	−	0.218531i	$-0.0701265\pi$
$662$		0			0
$663$	−10.0484	−	2.71705i	−0.390249	−	0.105521i
$664$		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
$669$	−4.44588	−	1.20214i	−0.171888	−	0.0464776i
$670$		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
$675$	−27.2142	−	27.5892i	−1.04748	−	1.06191i
$676$		0			0
$677$	10.5827	+	18.3297i	0.406725	+	0.704469i	0.994521	−	0.104541i	$-0.0333373\pi$
$677$	10.5827	+	18.3297i	0.406725	+	0.704469i	−0.587795	+	0.809010i	$0.700004\pi$
$678$		0			0
$679$	−18.5223	−	1.23780i	−0.710819	−	0.0475026i
$680$		0			0
$681$	5.29619	+	19.9475i	0.202951	+	0.764390i
$682$		0			0
$683$	14.0756	+	24.3796i	0.538587	+	0.932859i	0.998980	+	0.0451447i	$0.0143749\pi$
$683$	14.0756	+	24.3796i	0.538587	+	0.932859i	−0.460394	+	0.887715i	$0.652292\pi$
$684$		0			0
$685$	56.8049			2.17040
$686$		0			0
$687$	−13.1620	−	49.5733i	−0.502163	−	1.89134i
$688$		0			0
$689$	16.1258	−	27.9306i	0.614343	−	1.06407i
$690$		0			0
$691$	−9.53980	−	16.5234i	−0.362911	−	0.628580i	0.625528	−	0.780202i	$-0.284884\pi$
$691$	−9.53980	−	16.5234i	−0.362911	−	0.628580i	−0.988439	+	0.151622i	$0.951550\pi$
$692$		0			0
$693$	15.2558	+	10.3230i	0.579521	+	0.392138i
$694$		0			0
$695$	−3.92316	−	6.79511i	−0.148814	−	0.257753i
$696$		0			0
$697$	2.12171	−	3.67490i	0.0803653	−	0.139197i
$698$		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
$705$	−30.5547	+	30.4157i	−1.15076	+	1.14552i
$706$		0			0
$707$	−11.3693	−	23.1293i	−0.427588	−	0.869865i
$708$		0			0
$709$	−10.0493	−	17.4059i	−0.377409	−	0.653691i	0.613276	−	0.789869i	$-0.289851\pi$
$709$	−10.0493	−	17.4059i	−0.377409	−	0.653691i	−0.990684	+	0.136178i	$0.956518\pi$
$710$		0			0
$711$	−25.9848	−	15.1608i	−0.974505	−	0.568573i
$712$		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
$717$	−19.7287	+	19.6389i	−0.736782	+	0.733429i
$718$		0			0
$719$	−3.29246	+	5.70270i	−0.122788	+	0.212675i	−0.920866	−	0.389879i	$-0.872517\pi$
$719$	−3.29246	+	5.70270i	−0.122788	+	0.212675i	0.798078	+	0.602554i	$0.205850\pi$
$720$		0			0
$721$	12.0048	+	24.4220i	0.447082	+	0.909524i
$722$		0			0
$723$	1.99953	+	7.53100i	0.0743632	+	0.280081i
$724$		0			0
$725$	−32.2271	+	55.8190i	−1.19688	+	2.07307i
$726$		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
$731$	−0.113164			−0.00418551
$732$		0			0
$733$	23.3647			0.862997			0.431498	−	0.902114i	$-0.357985\pi$
$733$	23.3647			0.862997			0.431498	+	0.902114i	$0.357985\pi$
$734$		0			0
$735$	39.4568	+	16.5676i	1.45538	+	0.611106i
$736$		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	$0.0118573\pi$
$739$	14.4596	+	25.0448i	0.531906	+	0.921288i	−0.467400	+	0.884046i	$0.654809\pi$
$740$		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
$745$	−24.4845			−0.897041
$746$		0			0
$747$	0.161527	−	35.4142i	0.00590997	−	1.29574i
$748$		0			0
$749$	14.3714	+	0.960415i	0.525121	+	0.0350928i
$750$		0			0
$751$	−1.71323			−0.0625167			−0.0312584	−	0.999511i	$-0.509951\pi$
$751$	−1.71323			−0.0625167			−0.0312584	+	0.999511i	$0.509951\pi$
$752$		0			0
$753$	−7.67583	−	28.9101i	−0.279723	−	1.05354i
$754$		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
$759$	3.40095	+	12.8093i	0.123447	+	0.464948i
$760$		0			0
$761$	−34.1051			−1.23631			−0.618154	−	0.786057i	$-0.712119\pi$
$761$	−34.1051			−1.23631			−0.618154	+	0.786057i	$0.712119\pi$
$762$		0			0
$763$	−1.22943	+	1.83489i	−0.0445084	+	0.0664275i
$764$		0			0
$765$	−11.6509	−	6.79768i	−0.421238	−	0.245770i
$766$		0			0
$767$	−37.7173			−1.36189
$768$		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	0.743941	−	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
$777$	−4.98753	−	25.5489i	−0.178927	−	0.916563i
$778$		0			0
$779$	18.5464			0.664494
$780$		0			0
$781$	−3.02165			−0.108123
$782$		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
$787$	−24.3005	+	42.0898i	−0.866221	+	1.50034i	−0.000391003		1.00000i	$0.500124\pi$
$787$	−24.3005	+	42.0898i	−0.866221	+	1.50034i	−0.865830	+	0.500339i	$0.833209\pi$
$788$		0			0
$789$	12.4853	+	47.0247i	0.444490	+	1.67412i
$790$		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
$795$	29.6196	−	29.4849i	1.05050	−	1.04572i
$796$		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
$801$	−0.0153660	+	3.36894i	−0.000542931	+	0.119036i
$802$		0			0
$803$	−15.4219	−	26.7115i	−0.544228	−	0.942630i
$804$		0			0
$805$	13.5826	+	27.6318i	0.478723	+	0.973892i
$806$		0			0
$807$	−30.4738	+	30.3351i	−1.07273	+	1.06785i
$808$		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	$-0.341187\pi$
$811$	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
$815$	−6.26500	+	10.8513i	−0.219454	+	0.380105i
$816$		0			0
$817$	−0.247299	−	0.428334i	−0.00865188	−	0.0149855i
$818$		0			0
$819$	−2.66721	+	37.3503i	−0.0932000	+	1.30512i
$820$		0			0
$821$	−12.1694	−	21.0781i	−0.424717	−	0.735631i	0.571677	−	0.820479i	$-0.306293\pi$
$821$	−12.1694	−	21.0781i	−0.424717	−	0.735631i	−0.996394	+	0.0848477i	$0.972960\pi$
$822$		0			0
$823$	5.76898	−	9.99217i	0.201094	−	0.348305i	−0.747787	−	0.663939i	$-0.768884\pi$
$823$	5.76898	−	9.99217i	0.201094	−	0.348305i	0.948881	+	0.315633i	$0.102217\pi$
$824$		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	0.702302	−	0.711879i	$-0.252156\pi$
$829$	−7.64018	−	13.2332i	−0.265354	−	0.459607i	−0.967656	+	0.252272i	$0.918822\pi$
$830$		0			0
$831$	7.52858	+	28.3556i	0.261164	+	0.983643i
$832$		0			0
$833$	8.83795	+	1.18654i	0.306217	+	0.0411113i
$834$		0			0
$835$	−3.05356	−	5.28891i	−0.105673	−	0.183030i
$836$		0			0
$837$	42.8221	−	11.1607i	1.48015	−	0.385770i
$838$		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
$843$	38.2191	+	10.3343i	1.31634	+	0.355931i
$844$		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
$849$	−13.9716	−	3.77786i	−0.479505	−	0.129656i
$850$		0			0
$851$	9.36454	−	16.2199i	0.321012	−	0.556009i
$852$		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
$857$	−35.1743			−1.20153			−0.600765	−	0.799426i	$-0.705137\pi$
$857$	−35.1743			−1.20153			−0.600765	+	0.799426i	$0.705137\pi$
$858$		0			0
$859$	10.5704			0.360658			0.180329	−	0.983606i	$-0.442284\pi$
$859$	10.5704			0.360658			0.180329	+	0.983606i	$0.442284\pi$
$860$		0			0
$861$	−14.4372	−	4.95814i	−0.492018	−	0.168973i
$862$		0			0
$863$	−7.29326	+	12.6323i	−0.248265	+	0.430008i	−0.963045	−	0.269342i	$-0.913194\pi$
$863$	−7.29326	+	12.6323i	−0.248265	+	0.430008i	0.714779	+	0.699350i	$0.246527\pi$
$864$		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
$871$	28.9101			0.979582
$872$		0			0
$873$	0.0960057	−	21.0489i	0.00324930	−	0.712397i
$874$		0			0
$875$	−10.1258	−	20.5994i	−0.342314	−	0.696388i
$876$		0			0
$877$	11.3183			0.382191			0.191096	−	0.981571i	$-0.438796\pi$
$877$	11.3183			0.382191			0.191096	+	0.981571i	$0.438796\pi$
$878$		0			0
$879$	5.30642	−	5.28227i	0.178981	−	0.178167i
$880$		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
$885$	−47.1818	−	12.7577i	−1.58600	−	0.428846i
$886$		0			0
$887$	−33.6325			−1.12927			−0.564634	−	0.825341i	$-0.690983\pi$
$887$	−33.6325			−1.12927			−0.564634	+	0.825341i	$0.690983\pi$
$888$		0			0
$889$	−11.5589	−	23.5149i	−0.387674	−	0.788666i
$890$		0			0
$891$	−10.6078	+	17.9923i	−0.355376	+	0.602764i
$892$		0			0
$893$	−39.2643			−1.31393
$894$		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
$903$	0.0779966	+	0.399542i	0.00259556	+	0.0132959i
$904$		0			0
$905$	69.2996			2.30360
$906$		0			0
$907$	9.58510			0.318268			0.159134	−	0.987257i	$-0.449130\pi$
$907$	9.58510			0.318268			0.159134	+	0.987257i	$0.449130\pi$
$908$		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
$913$	13.6979	−	23.7255i	0.453336	−	0.785201i
$914$		0			0
$915$	−57.8643	+	57.6010i	−1.91294	+	1.90423i
$916$		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	$-0.585501\pi$
$919$	21.2895	−	36.8745i	0.702276	−	1.21638i	0.967666	−	0.252236i	$-0.0811661\pi$
$920$		0			0
$921$	−4.10197	−	15.4496i	−0.135165	−	0.509082i
$922$		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
$927$	−26.7928	+	15.3063i	−0.879991	+	0.502725i
$928$		0			0
$929$	−19.0762	−	33.0409i	−0.625869	−	1.08404i	−0.988372	−	0.152054i	$-0.951411\pi$
$929$	−19.0762	−	33.0409i	−0.625869	−	1.08404i	0.362503	−	0.931983i	$-0.381922\pi$
$930$		0			0
$931$	14.8226	+	36.0453i	0.485790	+	1.18134i
$932$		0			0
$933$	31.9475	+	8.63844i	1.04591	+	0.282810i
$934$		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
$941$	0.233235	−	0.403976i	0.00760326	−	0.0131692i	−0.862199	−	0.506570i	$-0.830913\pi$
$941$	0.233235	−	0.403976i	0.00760326	−	0.0131692i	0.869802	+	0.493401i	$0.164246\pi$
$942$		0			0
$943$	−5.49142	−	9.51142i	−0.178825	−	0.309734i
$944$		0			0
$945$	−15.9701	+	45.8205i	−0.519506	+	1.49054i
$946$		0			0
$947$	7.55575	+	13.0869i	0.245529	+	0.425268i	0.962280	−	0.272060i	$-0.0877051\pi$
$947$	7.55575	+	13.0869i	0.245529	+	0.425268i	−0.716751	+	0.697329i	$0.754372\pi$
$948$		0			0
$949$	31.3503	−	54.3003i	1.01767	−	1.76266i
$950$		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
$957$	33.5346	+	9.06757i	1.08402	+	0.293113i
$958$		0			0
$959$	−18.7840	−	38.2133i	−0.606568	−	1.23397i
$960$		0			0
$961$	−20.7647	−	35.9655i	−0.669828	−	1.16018i
$962$		0			0
$963$	−0.0744910	+	16.3319i	−0.00240044	+	0.526287i
$964$		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
$969$	−3.15248	−	11.8735i	−0.101272	−	0.381431i
$970$		0			0
$971$	−11.7523	+	20.3555i	−0.377148	+	0.653240i	−0.990646	−	0.136456i	$-0.956429\pi$
$971$	−11.7523	+	20.3555i	−0.377148	+	0.653240i	0.613498	+	0.789697i	$0.289762\pi$
$972$		0			0
$973$	−3.27386	+	4.88614i	−0.104955	+	0.156642i
$974$		0			0
$975$	43.1900	−	42.9934i	1.38319	−	1.37689i
$976$		0			0
$977$	2.71689	−	4.70580i	0.0869211	−	0.150552i	−0.819287	−	0.573384i	$-0.805631\pi$
$977$	2.71689	−	4.70580i	0.0869211	−	0.150552i	0.906208	+	0.422832i	$0.138964\pi$
$978$		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
$983$	−2.10690			−0.0671997			−0.0335998	−	0.999435i	$-0.510697\pi$
$983$	−2.10690			−0.0671997			−0.0335998	+	0.999435i	$0.510697\pi$
$984$		0			0
$985$	61.0348			1.94473
$986$		0			0
$987$	30.5647	+	10.4968i	0.972886	+	0.334117i
$988$		0			0
$989$	−0.146446	+	0.253651i	−0.00465670	+	0.00806564i
$990$		0			0
$991$	8.91172	+	15.4356i	0.283090	+	0.490327i	0.972144	−	0.234383i	$-0.0753071\pi$
$991$	8.91172	+	15.4356i	0.283090	+	0.490327i	−0.689054	+	0.724710i	$0.741974\pi$
$992$		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
$997$	−36.4954			−1.15582			−0.577911	−	0.816100i	$-0.696132\pi$
$997$	−36.4954			−1.15582			−0.577911	+	0.816100i	$0.696132\pi$
$998$		0			0
$999$	28.5624	−	7.44422i	0.903676	−	0.235525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.d.457.7	yes	22
3.2	odd	2		1512.2.t.d.289.11		22
4.3	odd	2		1008.2.t.k.961.5		22
7.4	even	3		504.2.q.d.25.8	✓	22
9.4	even	3		504.2.q.d.121.8	yes	22
9.5	odd	6		1512.2.q.c.793.1		22
12.11	even	2		3024.2.t.l.289.11		22
21.11	odd	6		1512.2.q.c.1369.1		22
28.11	odd	6		1008.2.q.k.529.4		22
36.23	even	6		3024.2.q.k.2305.1		22
36.31	odd	6		1008.2.q.k.625.4		22
63.4	even	3	inner	504.2.t.d.193.7	yes	22
63.32	odd	6		1512.2.t.d.361.11		22
84.11	even	6		3024.2.q.k.2881.1		22
252.67	odd	6		1008.2.t.k.193.5		22
252.95	even	6		3024.2.t.l.1873.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.8	✓	22	7.4	even	3
504.2.q.d.121.8	yes	22	9.4	even	3
504.2.t.d.193.7	yes	22	63.4	even	3	inner
504.2.t.d.457.7	yes	22	1.1	even	1	trivial
1008.2.q.k.529.4		22	28.11	odd	6
1008.2.q.k.625.4		22	36.31	odd	6
1008.2.t.k.193.5		22	252.67	odd	6
1008.2.t.k.961.5		22	4.3	odd	2
1512.2.q.c.793.1		22	9.5	odd	6
1512.2.q.c.1369.1		22	21.11	odd	6
1512.2.t.d.289.11		22	3.2	odd	2
1512.2.t.d.361.11		22	63.32	odd	6
3024.2.q.k.2305.1		22	36.23	even	6
3024.2.q.k.2881.1		22	84.11	even	6
3024.2.t.l.289.11		22	12.11	even	2
3024.2.t.l.1873.11		22	252.95	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.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.444471 + 1.67405i) q^{3} -3.52959 q^{5} +(1.16715 + 2.37440i) q^{7} +(-2.60489 + 1.48813i) q^{9} +O(q^{10})\)	\(q+(0.444471 + 1.67405i) q^{3} -3.52959 q^{5} +(1.16715 + 2.37440i) q^{7} +(-2.60489 + 1.48813i) q^{9} -2.32073 q^{11} +(-2.35884 - 4.08563i) q^{13} +(-1.56880 - 5.90871i) q^{15} +(-0.636946 - 1.10322i) q^{17} +(2.78386 - 4.82178i) q^{19} +(-3.45610 + 3.00922i) q^{21} -3.29710 q^{23} +7.45798 q^{25} +(-3.64901 - 3.69929i) q^{27} +(-4.32116 + 7.48447i) q^{29} +(-4.25821 + 7.37543i) q^{31} +(-1.03150 - 3.88502i) q^{33} +(-4.11956 - 8.38064i) q^{35} +(-2.84024 + 4.91943i) q^{37} +(5.79111 - 5.76476i) q^{39} +(1.66553 + 2.88478i) q^{41} +(0.0444165 - 0.0769317i) q^{43} +(9.19419 - 5.25250i) q^{45} +(-3.52607 - 6.10733i) q^{47} +(-4.27552 + 5.54256i) q^{49} +(1.56375 - 1.55663i) q^{51} +(3.41816 + 5.92042i) q^{53} +8.19121 q^{55} +(9.30925 + 2.51717i) q^{57} +(3.99745 - 6.92378i) q^{59} +(-6.67764 - 11.5660i) q^{61} +(-6.57372 - 4.44817i) q^{63} +(8.32572 + 14.4206i) q^{65} +(-3.06402 + 5.30704i) q^{67} +(-1.46546 - 5.51951i) q^{69} +1.30202 q^{71} +(6.64529 + 11.5100i) q^{73} +(3.31486 + 12.4850i) q^{75} +(-2.70864 - 5.51033i) q^{77} +(5.01403 + 8.68455i) q^{79} +(4.57091 - 7.75286i) q^{81} +(-5.90243 + 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(-14.4500 - 3.90721i) q^{87} +(0.561496 - 0.972540i) q^{89} +(6.94778 - 10.3694i) q^{91} +(-14.2395 - 3.85029i) q^{93} +(-9.82586 + 17.0189i) q^{95} +(-3.50818 + 6.07635i) q^{97} +(6.04525 - 3.45356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9} + 6 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} - 15 q^{21} - 4 q^{23} + 20 q^{25} - 4 q^{27} + 9 q^{29} - 4 q^{31} - 31 q^{33} + 14 q^{35} + 2 q^{37} + 8 q^{39} + 16 q^{41} + 22 q^{45} + 5 q^{47} - 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} - 19 q^{59} - 13 q^{61} + 21 q^{63} + 13 q^{65} + 26 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 8 q^{75} - 4 q^{77} + 10 q^{79} - 8 q^{81} - 28 q^{83} - 20 q^{85} + 9 q^{87} + 6 q^{89} - 37 q^{91} - 32 q^{93} + 12 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 6 * q^5 + 7 * q^7 - 8 * q^9 + 6 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 - 15 * q^21 - 4 * q^23 + 20 * q^25 - 4 * q^27 + 9 * q^29 - 4 * q^31 - 31 * q^33 + 14 * q^35 + 2 * q^37 + 8 * q^39 + 16 * q^41 + 22 * q^45 + 5 * q^47 - 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 - 19 * q^59 - 13 * q^61 + 21 * q^63 + 13 * q^65 + 26 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 8 * q^75 - 4 * q^77 + 10 * q^79 - 8 * q^81 - 28 * q^83 - 20 * q^85 + 9 * q^87 + 6 * q^89 - 37 * q^91 - 32 * q^93 + 12 * q^95 - 29 * q^97 - 56 * q^99

Introduction

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