LMFDB - Embedded newform 504.2.q.d.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	504.121
Dual form			504.2.q.d.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56287 - 0.746620i) q^{3} +(1.71796 + 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +(1.88512 + 2.33374i) q^{9} +O(q^{10})$	\(q+(-1.56287 - 0.746620i) q^{3} +(1.71796 + 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +(1.88512 + 2.33374i) q^{9} +(-2.20469 + 3.81863i) q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.463308 - 5.93312i) q^{15} +(0.542270 + 0.939239i) q^{17} +(-3.74273 + 6.48261i) q^{19} +(-0.761471 + 4.51887i) q^{21} +(2.16279 + 3.74606i) q^{23} +(-3.40276 + 5.89375i) q^{25} +(-1.20378 - 5.05479i) q^{27} +(1.68485 + 2.91825i) q^{29} +9.37469 q^{31} +(6.29671 - 4.32196i) q^{33} +(6.31828 - 6.53590i) q^{35} +(-2.50767 + 4.34341i) q^{37} +(-4.26698 + 2.92879i) q^{39} +(-1.20160 + 2.08122i) q^{41} +(3.31412 + 5.74023i) q^{43} +(-3.70569 + 9.61860i) q^{45} +3.00831 q^{47} +(-5.94023 + 3.70320i) q^{49} +(-0.146242 - 1.87278i) q^{51} +(-0.530699 - 0.919198i) q^{53} -15.1502 q^{55} +(10.6894 - 7.33706i) q^{57} +12.4094 q^{59} -5.42668 q^{61} +(4.56396 - 6.49387i) q^{63} +10.2666 q^{65} +3.33998 q^{67} +(-0.583272 - 7.46938i) q^{69} -12.9064 q^{71} +(-8.21382 - 14.2267i) q^{73} +(9.71846 - 6.67059i) q^{75} +(11.3181 + 2.82823i) q^{77} -2.35031 q^{79} +(-1.89266 + 8.79874i) q^{81} +(-1.60602 - 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-0.454380 - 5.81879i) q^{87} +(5.67524 - 9.82981i) q^{89} +(-7.66974 - 1.91656i) q^{91} +(-14.6514 - 6.99933i) q^{93} -25.7194 q^{95} +(-6.40321 - 11.0907i) q^{97} +(-13.0678 + 2.05341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.56287	−	0.746620i	−0.902323	−	0.431061i
$3$	−1.56287	−	0.746620i	−0.902323	−	0.431061i
$4$		0			0
$5$	1.71796	+	2.97559i	0.768294	+	1.33072i	0.938487	+	0.345314i	$0.112227\pi$
$5$	1.71796	+	2.97559i	0.768294	+	1.33072i	−0.170193	+	0.985411i	$0.554439\pi$
$6$		0			0
$7$	−0.727932	−	2.54364i	−0.275132	−	0.961406i
$7$	−0.727932	−	2.54364i	−0.275132	−	0.961406i
$8$		0			0
$9$	1.88512	+	2.33374i	0.628373	+	0.777913i
$10$		0			0
$11$	−2.20469	+	3.81863i	−0.664739	+	1.15136i	0.314618	+	0.949219i	$0.398124\pi$
$11$	−2.20469	+	3.81863i	−0.664739	+	1.15136i	−0.979356	+	0.202143i	$0.935210\pi$
$12$		0			0
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	−0.580997	−	0.813906i	$-0.697337\pi$
$13$	1.49401	−	2.58771i	0.414365	−	0.717701i	0.995362	+	0.0962048i	$0.0306704\pi$
$14$		0			0
$15$	−0.463308	−	5.93312i	−0.119626	−	1.53192i
$16$		0			0
$17$	0.542270	+	0.939239i	0.131520	+	0.227799i	0.924263	−	0.381757i	$-0.124681\pi$
$17$	0.542270	+	0.939239i	0.131520	+	0.227799i	−0.792743	+	0.609556i	$0.791348\pi$
$18$		0			0
$19$	−3.74273	+	6.48261i	−0.858642	+	1.48721i	0.0145824	+	0.999894i	$0.495358\pi$
$19$	−3.74273	+	6.48261i	−0.858642	+	1.48721i	−0.873225	+	0.487318i	$0.837975\pi$
$20$		0			0
$21$	−0.761471	+	4.51887i	−0.166167	+	0.986098i
$22$		0			0
$23$	2.16279	+	3.74606i	0.450972	+	0.781107i	0.998447	−	0.0557153i	$-0.0177439\pi$
$23$	2.16279	+	3.74606i	0.450972	+	0.781107i	−0.547474	+	0.836823i	$0.684411\pi$
$24$		0			0
$25$	−3.40276	+	5.89375i	−0.680552	+	1.17875i
$26$		0			0
$27$	−1.20378	−	5.05479i	−0.231667	−	0.972795i
$28$		0			0
$29$	1.68485	+	2.91825i	0.312870	+	0.541906i	0.978982	−	0.203945i	$-0.0653764\pi$
$29$	1.68485	+	2.91825i	0.312870	+	0.541906i	−0.666113	+	0.745851i	$0.732043\pi$
$30$		0			0
$31$	9.37469			1.68374			0.841872	−	0.539678i	$-0.181454\pi$
$31$	9.37469			1.68374			0.841872	+	0.539678i	$0.181454\pi$
$32$		0			0
$33$	6.29671	−	4.32196i	1.09612	−	0.752356i
$34$		0			0
$35$	6.31828	−	6.53590i	1.06798	−	1.10477i
$36$		0			0
$37$	−2.50767	+	4.34341i	−0.412258	+	0.714052i	−0.995136	−	0.0985079i	$-0.968593\pi$
$37$	−2.50767	+	4.34341i	−0.412258	+	0.714052i	0.582878	+	0.812559i	$0.301926\pi$
$38$		0			0
$39$	−4.26698	+	2.92879i	−0.683264	+	0.468981i
$40$		0			0
$41$	−1.20160	+	2.08122i	−0.187658	+	0.325033i	−0.944469	−	0.328601i	$-0.893423\pi$
$41$	−1.20160	+	2.08122i	−0.187658	+	0.325033i	0.756811	+	0.653634i	$0.226756\pi$
$42$		0			0
$43$	3.31412	+	5.74023i	0.505399	+	0.875377i	0.999980	+	0.00624563i	$0.00198806\pi$
$43$	3.31412	+	5.74023i	0.505399	+	0.875377i	−0.494581	+	0.869131i	$0.664679\pi$
$44$		0			0
$45$	−3.70569	+	9.61860i	−0.552412	+	1.43386i
$46$		0			0
$47$	3.00831			0.438807			0.219403	−	0.975634i	$-0.429589\pi$
$47$	3.00831			0.438807			0.219403	+	0.975634i	$0.429589\pi$
$48$		0			0
$49$	−5.94023	+	3.70320i	−0.848604	+	0.529028i
$50$		0			0
$51$	−0.146242	−	1.87278i	−0.0204780	−	0.262241i
$52$		0			0
$53$	−0.530699	−	0.919198i	−0.0728971	−	0.126262i	0.827273	−	0.561801i	$-0.189891\pi$
$53$	−0.530699	−	0.919198i	−0.0728971	−	0.126262i	−0.900170	+	0.435539i	$0.856558\pi$
$54$		0			0
$55$	−15.1502			−2.04286
$56$		0			0
$57$	10.6894	−	7.33706i	1.41585	−	0.971818i
$58$		0			0
$59$	12.4094			1.61557			0.807783	−	0.589480i	$-0.200668\pi$
$59$	12.4094			1.61557			0.807783	+	0.589480i	$0.200668\pi$
$60$		0			0
$61$	−5.42668			−0.694816			−0.347408	−	0.937714i	$-0.612938\pi$
$61$	−5.42668			−0.694816			−0.347408	+	0.937714i	$0.612938\pi$
$62$		0			0
$63$	4.56396	−	6.49387i	0.575004	−	0.818150i
$64$		0			0
$65$	10.2666			1.27342
$66$		0			0
$67$	3.33998			0.408043			0.204022	−	0.978966i	$-0.434599\pi$
$67$	3.33998			0.408043			0.204022	+	0.978966i	$0.434599\pi$
$68$		0			0
$69$	−0.583272	−	7.46938i	−0.0702177	−	0.899208i
$70$		0			0
$71$	−12.9064			−1.53171			−0.765857	−	0.643011i	$-0.777685\pi$
$71$	−12.9064			−1.53171			−0.765857	+	0.643011i	$0.777685\pi$
$72$		0			0
$73$	−8.21382	−	14.2267i	−0.961355	−	1.66511i	−0.719106	−	0.694901i	$-0.755448\pi$
$73$	−8.21382	−	14.2267i	−0.961355	−	1.66511i	−0.242249	−	0.970214i	$-0.577885\pi$
$74$		0			0
$75$	9.71846	−	6.67059i	1.12219	−	0.770254i
$76$		0			0
$77$	11.3181	+	2.82823i	1.28982	+	0.322307i
$78$		0			0
$79$	−2.35031			−0.264431			−0.132216	−	0.991221i	$-0.542209\pi$
$79$	−2.35031			−0.264431			−0.132216	+	0.991221i	$0.542209\pi$
$80$		0			0
$81$	−1.89266	+	8.79874i	−0.210296	+	0.977638i
$82$		0			0
$83$	−1.60602	−	2.78171i	−0.176283	−	0.305332i	0.764321	−	0.644836i	$-0.223074\pi$
$83$	−1.60602	−	2.78171i	−0.176283	−	0.305332i	−0.940605	+	0.339504i	$0.889741\pi$
$84$		0			0
$85$	−1.86319	+	3.22715i	−0.202092	+	0.350033i
$86$		0			0
$87$	−0.454380	−	5.81879i	−0.0487147	−	0.623840i
$88$		0			0
$89$	5.67524	−	9.82981i	0.601575	−	1.04196i	−0.391008	−	0.920387i	$-0.627874\pi$
$89$	5.67524	−	9.82981i	0.601575	−	1.04196i	0.992583	−	0.121570i	$-0.0387930\pi$
$90$		0			0
$91$	−7.66974	−	1.91656i	−0.804008	−	0.200910i
$92$		0			0
$93$	−14.6514	−	6.99933i	−1.51928	−	0.725796i
$94$		0			0
$95$	−25.7194			−2.63876
$96$		0			0
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	−0.983087	−	0.183140i	$-0.941374\pi$
$97$	−6.40321	−	11.0907i	−0.650148	−	1.12609i	0.332939	−	0.942948i	$-0.391960\pi$
$98$		0			0
$99$	−13.0678	+	2.05341i	−1.31336	+	0.206375i
$100$		0			0
$101$	0.388110	−	0.672227i	0.0386184	−	0.0668891i	−0.846070	−	0.533072i	$-0.821038\pi$
$101$	0.388110	−	0.672227i	0.0386184	−	0.0668891i	0.884689	+	0.466182i	$0.154371\pi$
$102$		0			0
$103$	−1.14131	−	1.97681i	−0.112457	−	0.194781i	0.804304	−	0.594219i	$-0.202539\pi$
$103$	−1.14131	−	1.97681i	−0.112457	−	0.194781i	−0.916760	+	0.399438i	$0.869205\pi$
$104$		0			0
$105$	−14.7545	+	5.49740i	−1.43989	+	0.536491i
$106$		0			0
$107$	−2.27468	+	3.93986i	−0.219901	+	0.380880i	−0.954778	−	0.297321i	$-0.903907\pi$
$107$	−2.27468	+	3.93986i	−0.219901	+	0.380880i	0.734876	+	0.678201i	$0.237240\pi$
$108$		0			0
$109$	2.36710	+	4.09994i	0.226727	+	0.392703i	0.956836	−	0.290627i	$-0.0938640\pi$
$109$	2.36710	+	4.09994i	0.226727	+	0.392703i	−0.730109	+	0.683331i	$0.760531\pi$
$110$		0			0
$111$	7.16203	−	4.91590i	0.679789	−	0.466597i
$112$		0			0
$113$	0.175367	−	0.303745i	0.0164972	−	0.0285740i	−0.857659	−	0.514219i	$-0.828082\pi$
$113$	0.175367	−	0.303745i	0.0164972	−	0.0285740i	0.874156	+	0.485645i	$0.161415\pi$
$114$		0			0
$115$	−7.43116	+	12.8711i	−0.692959	+	1.20024i
$116$		0			0
$117$	8.85542	−	1.39150i	0.818684	−	0.128644i
$118$		0			0
$119$	1.99435	−	2.06304i	0.182822	−	0.189119i
$120$		0			0
$121$	−4.22130	−	7.31151i	−0.383755	−	0.664683i
$122$		0			0
$123$	3.43182	−	2.35554i	0.309437	−	0.212392i
$124$		0			0
$125$	−6.20360			−0.554867
$126$		0			0
$127$	12.4175			1.10187			0.550935	−	0.834548i	$-0.314271\pi$
$127$	12.4175			1.10187			0.550935	+	0.834548i	$0.314271\pi$
$128$		0			0
$129$	−0.893770	−	11.4456i	−0.0786921	−	1.00773i
$130$		0			0
$131$	−7.87152	−	13.6339i	−0.687738	−	1.19120i	−0.972568	−	0.232619i	$-0.925270\pi$
$131$	−7.87152	−	13.6339i	−0.687738	−	1.19120i	0.284830	−	0.958578i	$-0.408063\pi$
$132$		0			0
$133$	19.2139	+	4.80128i	1.66606	+	0.416324i
$134$		0			0
$135$	12.9730	−	12.2659i	1.11653	−	1.05568i
$136$		0			0
$137$	2.11510	−	3.66346i	0.180705	−	0.312990i	−0.761416	−	0.648264i	$-0.775495\pi$
$137$	2.11510	−	3.66346i	0.180705	−	0.312990i	0.942121	+	0.335274i	$0.108829\pi$
$138$		0			0
$139$	9.80367	−	16.9805i	0.831537	−	1.44026i	−0.0652824	−	0.997867i	$-0.520795\pi$
$139$	9.80367	−	16.9805i	0.831537	−	1.44026i	0.896819	−	0.442397i	$-0.145872\pi$
$140$		0			0
$141$	−4.70159	−	2.24606i	−0.395945	−	0.189152i
$142$		0			0
$143$	6.58767	+	11.4102i	0.550889	+	0.954167i
$144$		0			0
$145$	−5.78902	+	10.0269i	−0.480752	+	0.832686i
$146$		0			0
$147$	12.0487	−	1.35252i	0.993758	−	0.111554i
$148$		0			0
$149$	4.86326	+	8.42341i	0.398414	+	0.690073i	0.993530	−	0.113567i	$-0.0362276\pi$
$149$	4.86326	+	8.42341i	0.398414	+	0.690073i	−0.595117	+	0.803639i	$0.702894\pi$
$150$		0			0
$151$	4.91074	−	8.50565i	0.399630	−	0.692180i	−0.594050	−	0.804428i	$-0.702472\pi$
$151$	4.91074	−	8.50565i	0.399630	−	0.692180i	0.993680	+	0.112248i	$0.0358051\pi$
$152$		0			0
$153$	−1.16969	+	3.03609i	−0.0945642	+	0.245453i
$154$		0			0
$155$	16.1053	+	27.8952i	1.29361	+	2.24060i
$156$		0			0
$157$	−12.0408			−0.960962			−0.480481	−	0.877005i	$-0.659538\pi$
$157$	−12.0408			−0.960962			−0.480481	+	0.877005i	$0.659538\pi$
$158$		0			0
$159$	0.143122	+	1.83282i	0.0113503	+	0.145352i
$160$		0			0
$161$	7.95427	−	8.22824i	0.626884	−	0.648476i
$162$		0			0
$163$	0.885601	−	1.53391i	0.0693656	−	0.120145i	−0.829257	−	0.558868i	$-0.811236\pi$
$163$	0.885601	−	1.53391i	0.0693656	−	0.120145i	0.898622	+	0.438723i	$0.144569\pi$
$164$		0			0
$165$	23.6778	+	11.3115i	1.84332	+	0.880597i
$166$		0			0
$167$	−7.86350	+	13.6200i	−0.608496	+	1.05395i	0.382993	+	0.923751i	$0.374893\pi$
$167$	−7.86350	+	13.6200i	−0.608496	+	1.05395i	−0.991489	+	0.130194i	$0.958440\pi$
$168$		0			0
$169$	2.03584	+	3.52618i	0.156603	+	0.271245i
$170$		0			0
$171$	−22.1842	+	3.48591i	−1.69647	+	0.266575i
$172$		0			0
$173$	18.8063			1.42981			0.714907	−	0.699220i	$-0.246469\pi$
$173$	18.8063			1.42981			0.714907	+	0.699220i	$0.246469\pi$
$174$		0			0
$175$	17.4686	+	4.36515i	1.32050	+	0.329974i
$176$		0			0
$177$	−19.3943	−	9.26510i	−1.45776	−	0.696407i
$178$		0			0
$179$	3.34201	+	5.78853i	0.249794	+	0.432655i	0.963468	−	0.267822i	$-0.0863039\pi$
$179$	3.34201	+	5.78853i	0.249794	+	0.432655i	−0.713675	+	0.700477i	$0.752971\pi$
$180$		0			0
$181$	4.73726			0.352117			0.176059	−	0.984380i	$-0.443665\pi$
$181$	4.73726			0.352117			0.176059	+	0.984380i	$0.443665\pi$
$182$		0			0
$183$	8.48119	+	4.05167i	0.626948	+	0.299508i
$184$		0			0
$185$	−17.2323			−1.26694
$186$		0			0
$187$	−4.78214			−0.349705
$188$		0			0
$189$	−11.9813	+	6.74152i	−0.871512	+	0.490374i
$190$		0			0
$191$	−23.0693			−1.66924			−0.834618	−	0.550829i	$-0.814312\pi$
$191$	−23.0693			−1.66924			−0.834618	+	0.550829i	$0.814312\pi$
$192$		0			0
$193$	18.3070			1.31777			0.658885	−	0.752244i	$-0.271028\pi$
$193$	18.3070			1.31777			0.658885	+	0.752244i	$0.271028\pi$
$194$		0			0
$195$	−16.0454	−	7.66526i	−1.14903	−	0.548920i
$196$		0			0
$197$	14.5866			1.03925			0.519625	−	0.854395i	$-0.326072\pi$
$197$	14.5866			1.03925			0.519625	+	0.854395i	$0.326072\pi$
$198$		0			0
$199$	−0.912102	−	1.57981i	−0.0646572	−	0.111990i	0.831885	−	0.554949i	$-0.187262\pi$
$199$	−0.912102	−	1.57981i	−0.0646572	−	0.111990i	−0.896542	+	0.442959i	$0.853929\pi$
$200$		0			0
$201$	−5.21995	−	2.49369i	−0.368187	−	0.175892i
$202$		0			0
$203$	6.19653	−	6.40996i	0.434911	−	0.449891i
$204$		0			0
$205$	−8.25716			−0.576705
$206$		0			0
$207$	−4.66521	+	12.1091i	−0.324254	+	0.841644i
$208$		0			0
$209$	−16.5031	−	28.5843i	−1.14155	−	1.97721i
$210$		0			0
$211$	−2.77359	+	4.80400i	−0.190942	+	0.330721i	−0.945563	−	0.325440i	$-0.894488\pi$
$211$	−2.77359	+	4.80400i	−0.190942	+	0.330721i	0.754621	+	0.656161i	$0.227821\pi$
$212$		0			0
$213$	20.1711	+	9.63621i	1.38210	+	0.660262i
$214$		0			0
$215$	−11.3870	+	19.7229i	−0.776590	+	1.34509i
$216$		0			0
$217$	−6.82413	−	23.8458i	−0.463252	−	1.61876i
$218$		0			0
$219$	2.21515	+	28.3671i	0.149686	+	1.91687i
$220$		0			0
$221$	3.24064			0.217989
$222$		0			0
$223$	6.01726	+	10.4222i	0.402946	+	0.697922i	0.994080	−	0.108651i	$-0.0346530\pi$
$223$	6.01726	+	10.4222i	0.402946	+	0.697922i	−0.591134	+	0.806573i	$0.701320\pi$
$224$		0			0
$225$	−20.1691	+	3.16927i	−1.34460	+	0.211284i
$226$		0			0
$227$	6.57834	−	11.3940i	0.436620	−	0.756248i	−0.560806	−	0.827947i	$-0.689509\pi$
$227$	6.57834	−	11.3940i	0.436620	−	0.756248i	0.997426	+	0.0716991i	$0.0228421\pi$
$228$		0			0
$229$	−6.24159	−	10.8108i	−0.412456	−	0.714395i	0.582702	−	0.812686i	$-0.301996\pi$
$229$	−6.24159	−	10.8108i	−0.412456	−	0.714395i	−0.995158	+	0.0982915i	$0.968662\pi$
$230$		0			0
$231$	−15.5771	−	12.8705i	−1.02490	−	0.846815i
$232$		0			0
$233$	−2.01687	+	3.49332i	−0.132130	+	0.228855i	−0.924497	−	0.381189i	$-0.875515\pi$
$233$	−2.01687	+	3.49332i	−0.132130	+	0.228855i	0.792368	+	0.610044i	$0.208848\pi$
$234$		0			0
$235$	5.16814	+	8.95149i	0.337133	+	0.583931i
$236$		0			0
$237$	3.67323	+	1.75479i	0.238602	+	0.113986i
$238$		0			0
$239$	13.8679	−	24.0200i	0.897043	−	1.55372i	0.0657873	−	0.997834i	$-0.479044\pi$
$239$	13.8679	−	24.0200i	0.897043	−	1.55372i	0.831256	−	0.555890i	$-0.187623\pi$
$240$		0			0
$241$	−11.9567	+	20.7096i	−0.770199	+	1.33402i	0.167254	+	0.985914i	$0.446510\pi$
$241$	−11.9567	+	20.7096i	−0.770199	+	1.33402i	−0.937453	+	0.348111i	$0.886823\pi$
$242$		0			0
$243$	9.52730	−	12.3382i	0.611176	−	0.791494i
$244$		0			0
$245$	−21.2243	−	11.3138i	−1.35597	−	0.722809i
$246$		0			0
$247$	11.1834	+	19.3702i	0.711582	+	1.23250i
$248$		0			0
$249$	0.433119	+	5.54653i	0.0274478	+	0.351497i
$250$		0			0
$251$	−3.33510			−0.210509			−0.105255	−	0.994445i	$-0.533566\pi$
$251$	−3.33510			−0.210509			−0.105255	+	0.994445i	$0.533566\pi$
$252$		0			0
$253$	−19.0731			−1.19912
$254$		0			0
$255$	5.32138	−	3.65251i	0.333238	−	0.228729i
$256$		0			0
$257$	10.9345	+	18.9392i	0.682078	+	1.18139i	0.974346	+	0.225057i	$0.0722567\pi$
$257$	10.9345	+	18.9392i	0.682078	+	1.18139i	−0.292268	+	0.956336i	$0.594410\pi$
$258$		0			0
$259$	12.8735	+	3.21690i	0.799919	+	0.199889i
$260$		0			0
$261$	−3.63429	+	9.43326i	−0.224957	+	0.583904i
$262$		0			0
$263$	−2.75522	+	4.77218i	−0.169894	+	0.294265i	−0.938382	−	0.345599i	$-0.887676\pi$
$263$	−2.75522	+	4.77218i	−0.169894	+	0.294265i	0.768488	+	0.639864i	$0.221009\pi$
$264$		0			0
$265$	1.82344	−	3.15829i	0.112013	−	0.194012i
$266$		0			0
$267$	−16.2088	+	11.1255i	−0.991962	+	0.680867i
$268$		0			0
$269$	3.37393	+	5.84382i	0.205712	+	0.356304i	0.950359	−	0.311154i	$-0.100716\pi$
$269$	3.37393	+	5.84382i	0.205712	+	0.356304i	−0.744647	+	0.667458i	$0.767382\pi$
$270$		0			0
$271$	6.21944	−	10.7724i	0.377804	−	0.654376i	−0.612938	−	0.790131i	$-0.710013\pi$
$271$	6.21944	−	10.7724i	0.377804	−	0.654376i	0.990742	+	0.135755i	$0.0433459\pi$
$272$		0			0
$273$	10.5559	+	8.72172i	0.638870	+	0.527862i
$274$		0			0
$275$	−15.0040	−	25.9878i	−0.904778	−	1.56712i
$276$		0			0
$277$	4.85945	−	8.41681i	0.291976	−	0.505717i	−0.682301	−	0.731071i	$-0.739021\pi$
$277$	4.85945	−	8.41681i	0.291976	−	0.505717i	0.974277	+	0.225354i	$0.0723539\pi$
$278$		0			0
$279$	17.6724	+	21.8781i	1.05802	+	1.30981i
$280$		0			0
$281$	−9.66772	−	16.7450i	−0.576728	−	0.998922i	−0.995852	−	0.0909928i	$-0.970996\pi$
$281$	−9.66772	−	16.7450i	−0.576728	−	0.998922i	0.419124	−	0.907929i	$-0.362337\pi$
$282$		0			0
$283$	8.30900			0.493919			0.246959	−	0.969026i	$-0.420569\pi$
$283$	8.30900			0.493919			0.246959	+	0.969026i	$0.420569\pi$
$284$		0			0
$285$	40.1961	+	19.2026i	2.38101	+	1.13747i
$286$		0			0
$287$	6.16857	+	1.54144i	0.364119	+	0.0909882i
$288$		0			0
$289$	7.91189	−	13.7038i	0.465405	−	0.806105i
$290$		0			0
$291$	1.72685	+	22.1141i	0.101230	+	1.29635i
$292$		0			0
$293$	−3.97318	+	6.88175i	−0.232116	+	0.402036i	−0.958430	−	0.285326i	$-0.907898\pi$
$293$	−3.97318	+	6.88175i	−0.232116	+	0.402036i	0.726315	+	0.687362i	$0.241231\pi$
$294$		0			0
$295$	21.3188	+	36.9253i	1.24123	+	2.14987i
$296$		0			0
$297$	21.9563	+	6.54746i	1.27404	+	0.379922i
$298$		0			0
$299$	12.9249			0.747469
$300$		0			0
$301$	12.1886	−	12.6084i	0.702541	−	0.726739i
$302$		0			0
$303$	−1.10846	+	0.760832i	−0.0636796	+	0.0437086i
$304$		0			0
$305$	−9.32281	−	16.1476i	−0.533823	−	0.924608i
$306$		0			0
$307$	−26.9180			−1.53629			−0.768145	−	0.640276i	$-0.778820\pi$
$307$	−26.9180			−1.53629			−0.768145	+	0.640276i	$0.778820\pi$
$308$		0			0
$309$	0.307795	+	3.94162i	0.0175098	+	0.224231i
$310$		0			0
$311$	9.34917			0.530143			0.265071	−	0.964229i	$-0.414604\pi$
$311$	9.34917			0.530143			0.265071	+	0.964229i	$0.414604\pi$
$312$		0			0
$313$	15.8380			0.895219			0.447610	−	0.894229i	$-0.352275\pi$
$313$	15.8380			0.895219			0.447610	+	0.894229i	$0.352275\pi$
$314$		0			0
$315$	27.1638	+	2.42427i	1.53051	+	0.136592i
$316$		0			0
$317$	−28.4591			−1.59843			−0.799213	−	0.601049i	$-0.794750\pi$
$317$	−28.4591			−1.59843			−0.799213	+	0.601049i	$0.794750\pi$
$318$		0			0
$319$	−14.8583			−0.831906
$320$		0			0
$321$	6.49660	−	4.45916i	0.362605	−	0.248886i
$322$		0			0
$323$	−8.11829			−0.451714
$324$		0			0
$325$	10.1675	+	17.6107i	0.563994	+	0.976865i
$326$		0			0
$327$	−0.638373	−	8.17500i	−0.0353021	−	0.452078i
$328$		0			0
$329$	−2.18984	−	7.65205i	−0.120730	−	0.421871i
$330$		0			0
$331$	−19.5904			−1.07679			−0.538393	−	0.842694i	$-0.680968\pi$
$331$	−19.5904			−1.07679			−0.538393	+	0.842694i	$0.680968\pi$
$332$		0			0
$333$	−14.8636	+	2.33559i	−0.814521	+	0.127990i
$334$		0			0
$335$	5.73794	+	9.93841i	0.313497	+	0.542993i
$336$		0			0
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	−0.524023	−	0.851704i	$-0.675569\pi$
$337$	8.73059	−	15.1218i	0.475586	−	0.823739i	0.999609	+	0.0279654i	$0.00890283\pi$
$338$		0			0
$339$	−0.500859	+	0.343781i	−0.0272029	+	0.0186716i
$340$		0			0
$341$	−20.6683	+	35.7985i	−1.11925	+	1.93860i
$342$		0			0
$343$	13.7437	+	12.4141i	0.742090	+	0.670301i
$344$		0			0
$345$	21.2238	−	14.5677i	1.14265	−	0.784296i
$346$		0			0
$347$	−19.4502			−1.04414			−0.522070	−	0.852903i	$-0.674840\pi$
$347$	−19.4502			−1.04414			−0.522070	+	0.852903i	$0.674840\pi$
$348$		0			0
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	0.989582	−	0.143971i	$-0.0459872\pi$
$349$	6.91419	+	11.9757i	0.370108	+	0.641046i	−0.619474	+	0.785018i	$0.712654\pi$
$350$		0			0
$351$	−14.8788	−	4.43691i	−0.794171	−	0.236825i
$352$		0			0
$353$	−5.92295	+	10.2588i	−0.315247	+	0.546023i	−0.979490	−	0.201493i	$-0.935421\pi$
$353$	−5.92295	+	10.2588i	−0.315247	+	0.546023i	0.664243	+	0.747517i	$0.268754\pi$
$354$		0			0
$355$	−22.1727	−	38.4043i	−1.17681	−	2.03829i
$356$		0			0
$357$	−4.65722	+	1.73524i	−0.246486	+	0.0918388i
$358$		0			0
$359$	−0.628489	+	1.08858i	−0.0331704	+	0.0574528i	−0.882134	−	0.470998i	$-0.843894\pi$
$359$	−0.628489	+	1.08858i	−0.0331704	+	0.0574528i	0.848964	+	0.528451i	$0.177227\pi$
$360$		0			0
$361$	−18.5161	−	32.0709i	−0.974533	−	1.68794i
$362$		0			0
$363$	1.13842	+	14.5786i	0.0597517	+	0.765180i
$364$		0			0
$365$	28.2220	−	48.8819i	1.47721	−	2.55860i
$366$		0			0
$367$	7.61928	−	13.1970i	0.397723	−	0.688877i	−0.595721	−	0.803191i	$-0.703134\pi$
$367$	7.61928	−	13.1970i	0.397723	−	0.688877i	0.993445	+	0.114314i	$0.0364671\pi$
$368$		0			0
$369$	−7.12218	+	1.11914i	−0.370766	+	0.0582603i
$370$		0			0
$371$	−1.95180	+	2.01902i	−0.101332	+	0.104822i
$372$		0			0
$373$	−8.66756	−	15.0127i	−0.448789	−	0.777326i	0.549518	−	0.835482i	$-0.314811\pi$
$373$	−8.66756	−	15.0127i	−0.448789	−	0.777326i	−0.998308	+	0.0581556i	$0.981478\pi$
$374$		0			0
$375$	9.69542	+	4.63173i	0.500669	+	0.239182i
$376$		0			0
$377$	10.0688			0.518569
$378$		0			0
$379$	15.6319			0.802955			0.401478	−	0.915869i	$-0.368497\pi$
$379$	15.6319			0.802955			0.401478	+	0.915869i	$0.368497\pi$
$380$		0			0
$381$	−19.4068	−	9.27112i	−0.994243	−	0.474974i
$382$		0			0
$383$	8.90615	+	15.4259i	0.455083	+	0.788227i	0.998693	−	0.0511113i	$-0.0162763\pi$
$383$	8.90615	+	15.4259i	0.455083	+	0.788227i	−0.543610	+	0.839338i	$0.682943\pi$
$384$		0			0
$385$	11.0284	+	38.5368i	0.562057	+	1.96402i
$386$		0			0
$387$	−7.14868	+	18.5553i	−0.363388	+	0.943219i
$388$		0			0
$389$	−14.7074	+	25.4740i	−0.745695	+	1.29158i	0.204175	+	0.978934i	$0.434549\pi$
$389$	−14.7074	+	25.4740i	−0.745695	+	1.29158i	−0.949869	+	0.312647i	$0.898784\pi$
$390$		0			0
$391$	−2.34563	+	4.06275i	−0.118624	+	0.205462i
$392$		0			0
$393$	2.12283	+	27.1850i	0.107083	+	1.37130i
$394$		0			0
$395$	−4.03774	−	6.99357i	−0.203161	−	0.351885i
$396$		0			0
$397$	−1.55930	+	2.70079i	−0.0782592	+	0.135549i	−0.902499	−	0.430692i	$-0.858270\pi$
$397$	−1.55930	+	2.70079i	−0.0782592	+	0.135549i	0.824240	+	0.566241i	$0.191603\pi$
$398$		0			0
$399$	−26.4441	−	21.8492i	−1.32386	−	1.09383i
$400$		0			0
$401$	17.8613	+	30.9367i	0.891950	+	1.54490i	0.837534	+	0.546385i	$0.183996\pi$
$401$	17.8613	+	30.9367i	0.891950	+	1.54490i	0.0544157	+	0.998518i	$0.482670\pi$
$402$		0			0
$403$	14.0059	−	24.2590i	0.697684	−	1.20842i
$404$		0			0
$405$	−29.4330	+	9.48407i	−1.46254	+	0.471267i
$406$		0			0
$407$	−11.0572	−	19.1517i	−0.548087	−	0.949315i
$408$		0			0
$409$	9.81652			0.485396			0.242698	−	0.970102i	$-0.421968\pi$
$409$	9.81652			0.485396			0.242698	+	0.970102i	$0.421968\pi$
$410$		0			0
$411$	−6.04083	+	4.14633i	−0.297972	+	0.204523i
$412$		0			0
$413$	−9.03320	−	31.5651i	−0.444494	−	1.55321i
$414$		0			0
$415$	5.51814	−	9.55771i	0.270875	−	0.469169i
$416$		0			0
$417$	−27.9998	+	19.2186i	−1.37116	+	0.941140i
$418$		0			0
$419$	6.09812	−	10.5623i	0.297913	−	0.516000i	−0.677746	−	0.735297i	$-0.737043\pi$
$419$	6.09812	−	10.5623i	0.297913	−	0.516000i	0.975658	+	0.219297i	$0.0703762\pi$
$420$		0			0
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	0.714562	−	0.699572i	$-0.246626\pi$
$421$	−5.10015	−	8.83373i	−0.248566	−	0.430529i	−0.963128	+	0.269043i	$0.913293\pi$
$422$		0			0
$423$	5.67101	+	7.02060i	0.275734	+	0.341353i
$424$		0			0
$425$	−7.38085			−0.358024
$426$		0			0
$427$	3.95026	+	13.8035i	0.191166	+	0.668000i
$428$		0			0
$429$	−1.77660	−	22.7511i	−0.0857750	−	1.09843i
$430$		0			0
$431$	−5.70254	−	9.87710i	−0.274682	−	0.475763i	0.695373	−	0.718649i	$-0.255239\pi$
$431$	−5.70254	−	9.87710i	−0.274682	−	0.475763i	−0.970055	+	0.242886i	$0.921906\pi$
$432$		0			0
$433$	26.2391			1.26097			0.630486	−	0.776201i	$-0.282856\pi$
$433$	26.2391			1.26097			0.630486	+	0.776201i	$0.282856\pi$
$434$		0			0
$435$	16.5337	−	11.3485i	0.792732	−	0.544118i
$436$		0			0
$437$	−32.3790			−1.54890
$438$		0			0
$439$	22.9554			1.09560			0.547801	−	0.836609i	$-0.315465\pi$
$439$	22.9554			1.09560			0.547801	+	0.836609i	$0.315465\pi$
$440$		0			0
$441$	−19.8403	−	6.88197i	−0.944777	−	0.327713i
$442$		0			0
$443$	22.4025			1.06438			0.532188	−	0.846626i	$-0.321370\pi$
$443$	22.4025			1.06438			0.532188	+	0.846626i	$0.321370\pi$
$444$		0			0
$445$	38.9993			1.84874
$446$		0			0
$447$	−1.31155	−	16.7957i	−0.0620341	−	0.794409i
$448$		0			0
$449$	17.0576			0.805000			0.402500	−	0.915420i	$-0.368141\pi$
$449$	17.0576			0.805000			0.402500	+	0.915420i	$0.368141\pi$
$450$		0			0
$451$	−5.29829	−	9.17690i	−0.249487	−	0.432123i
$452$		0			0
$453$	−14.0253	+	9.62676i	−0.658968	+	0.452305i
$454$		0			0
$455$	−7.47340	−	26.1146i	−0.350358	−	1.22427i
$456$		0			0
$457$	9.54729			0.446604			0.223302	−	0.974749i	$-0.428316\pi$
$457$	9.54729			0.446604			0.223302	+	0.974749i	$0.428316\pi$
$458$		0			0
$459$	4.09489	−	3.87170i	0.191133	−	0.180715i
$460$		0			0
$461$	10.1213	+	17.5305i	0.471394	+	0.816478i	0.999464	−	0.0327222i	$-0.0104177\pi$
$461$	10.1213	+	17.5305i	0.471394	+	0.816478i	−0.528070	+	0.849201i	$0.677084\pi$
$462$		0			0
$463$	−7.81948	+	13.5437i	−0.363402	+	0.629431i	−0.988518	−	0.151101i	$-0.951718\pi$
$463$	−7.81948	+	13.5437i	−0.363402	+	0.629431i	0.625116	+	0.780532i	$0.285052\pi$
$464$		0			0
$465$	−4.34337	−	55.6211i	−0.201419	−	2.57937i
$466$		0			0
$467$	−2.96638	+	5.13793i	−0.137268	+	0.237755i	−0.926461	−	0.376390i	$-0.877165\pi$
$467$	−2.96638	+	5.13793i	−0.137268	+	0.237755i	0.789194	+	0.614144i	$0.210499\pi$
$468$		0			0
$469$	−2.43128	−	8.49571i	−0.112266	−	0.392295i
$470$		0			0
$471$	18.8182	+	8.98992i	0.867098	+	0.414234i
$472$		0			0
$473$	−29.2264			−1.34383
$474$		0			0
$475$	−25.4712	−	44.1175i	−1.16870	−	2.02425i
$476$		0			0
$477$	1.14474	−	2.97131i	0.0524139	−	0.136047i
$478$		0			0
$479$	8.69708	−	15.0638i	0.397380	−	0.688282i	−0.596022	−	0.802968i	$-0.703253\pi$
$479$	8.69708	−	15.0638i	0.397380	−	0.688282i	0.993402	+	0.114686i	$0.0365862\pi$
$480$		0			0
$481$	7.49298	+	12.9782i	0.341650	+	0.591756i
$482$		0			0
$483$	−18.5748	+	6.92084i	−0.845185	+	0.314909i
$484$		0			0
$485$	22.0009	−	38.1067i	0.999009	−	1.73033i
$486$		0			0
$487$	−9.76967	−	16.9216i	−0.442706	−	0.766790i	0.555183	−	0.831728i	$-0.312648\pi$
$487$	−9.76967	−	16.9216i	−0.442706	−	0.766790i	−0.997889	+	0.0649386i	$0.979315\pi$
$488$		0			0
$489$	−2.52932	+	1.73609i	−0.114380	+	0.0785086i
$490$		0			0
$491$	−6.16702	+	10.6816i	−0.278314	+	0.482054i	−0.970966	−	0.239218i	$-0.923109\pi$
$491$	−6.16702	+	10.6816i	−0.278314	+	0.482054i	0.692652	+	0.721272i	$0.256442\pi$
$492$		0			0
$493$	−1.82729	+	3.16496i	−0.0822971	+	0.142543i
$494$		0			0
$495$	−28.5600	−	35.3567i	−1.28368	−	1.58917i
$496$		0			0
$497$	9.39502	+	32.8294i	0.421424	+	1.47260i
$498$		0			0
$499$	−9.27308	−	16.0614i	−0.415120	−	0.719009i	0.580321	−	0.814388i	$-0.302927\pi$
$499$	−9.27308	−	16.0614i	−0.415120	−	0.719009i	−0.995441	+	0.0953788i	$0.969594\pi$
$500$		0			0
$501$	22.4586	−	15.4152i	1.00337	−	0.688700i
$502$		0			0
$503$	−14.3264			−0.638782			−0.319391	−	0.947623i	$-0.603478\pi$
$503$	−14.3264			−0.638782			−0.319391	+	0.947623i	$0.603478\pi$
$504$		0			0
$505$	2.66703			0.118681
$506$		0			0
$507$	−0.549037	−	7.03097i	−0.0243836	−	0.312256i
$508$		0			0
$509$	8.43056	+	14.6022i	0.373678	+	0.647229i	0.990128	−	0.140165i	$-0.0447632\pi$
$509$	8.43056	+	14.6022i	0.373678	+	0.647229i	−0.616450	+	0.787394i	$0.711430\pi$
$510$		0			0
$511$	−30.2087	+	31.2491i	−1.33635	+	1.38238i
$512$		0			0
$513$	37.2736	+	11.1151i	1.64567	+	0.490745i
$514$		0			0
$515$	3.92145	−	6.79215i	0.172800	−	0.299298i
$516$		0			0
$517$	−6.63238	+	11.4876i	−0.291692	+	0.505225i
$518$		0			0
$519$	−29.3917	−	14.0411i	−1.29015	−	0.616337i
$520$		0			0
$521$	10.8132	+	18.7291i	0.473737	+	0.820536i	0.999548	−	0.0300652i	$-0.00957151\pi$
$521$	10.8132	+	18.7291i	0.473737	+	0.820536i	−0.525811	+	0.850601i	$0.676238\pi$
$522$		0			0
$523$	8.27472	−	14.3322i	0.361828	−	0.626705i	−0.626433	−	0.779475i	$-0.715486\pi$
$523$	8.27472	−	14.3322i	0.361828	−	0.626705i	0.988262	+	0.152770i	$0.0488193\pi$
$524$		0			0
$525$	−24.0420	−	19.8645i	−1.04928	−	0.866959i
$526$		0			0
$527$	5.08361	+	8.80507i	0.221446	+	0.383555i
$528$		0			0
$529$	2.14470	−	3.71472i	0.0932476	−	0.161510i
$530$		0			0
$531$	23.3932	+	28.9603i	1.01518	+	1.25677i
$532$		0			0
$533$	3.59040	+	6.21876i	0.155517	+	0.269364i
$534$		0			0
$535$	−15.6312			−0.675796
$536$		0			0
$537$	−0.901291	−	11.5419i	−0.0388936	−	0.498071i
$538$		0			0
$539$	−1.04479	−	30.8480i	−0.0450025	−	1.32872i
$540$		0			0
$541$	−11.9542	+	20.7053i	−0.513952	+	0.890191i	0.485917	+	0.874005i	$0.338486\pi$
$541$	−11.9542	+	20.7053i	−0.513952	+	0.890191i	−0.999869	+	0.0161861i	$0.994848\pi$
$542$		0			0
$543$	−7.40371	−	3.53693i	−0.317724	−	0.151784i
$544$		0			0
$545$	−8.13317	+	14.0871i	−0.348387	+	0.603423i
$546$		0			0
$547$	−14.8193	−	25.6678i	−0.633627	−	1.09747i	−0.986804	−	0.161918i	$-0.948232\pi$
$547$	−14.8193	−	25.6678i	−0.633627	−	1.09747i	0.353177	−	0.935556i	$-0.385101\pi$
$548$		0			0
$549$	−10.2299	−	12.6645i	−0.436603	−	0.540506i
$550$		0			0
$551$	−25.2238			−1.07457
$552$		0			0
$553$	1.71087	+	5.97836i	0.0727536	+	0.254226i
$554$		0			0
$555$	26.9318	+	12.8659i	1.14319	+	0.546129i
$556$		0			0
$557$	−10.8366	−	18.7695i	−0.459160	−	0.795288i	0.539757	−	0.841821i	$-0.318516\pi$
$557$	−10.8366	−	18.7695i	−0.459160	−	0.795288i	−0.998917	+	0.0465330i	$0.985183\pi$
$558$		0			0
$559$	19.8054			0.837679
$560$		0			0
$561$	7.47387	+	3.57044i	0.315547	+	0.150744i
$562$		0			0
$563$	14.1556			0.596589			0.298294	−	0.954474i	$-0.403582\pi$
$563$	14.1556			0.596589			0.298294	+	0.954474i	$0.403582\pi$
$564$		0			0
$565$	1.20510			0.0506988
$566$		0			0
$567$	23.7586	−	1.59063i	0.997766	−	0.0668001i
$568$		0			0
$569$	−34.0356			−1.42684			−0.713422	−	0.700734i	$-0.752856\pi$
$569$	−34.0356			−1.42684			−0.713422	+	0.700734i	$0.752856\pi$
$570$		0			0
$571$	−5.34970			−0.223878			−0.111939	−	0.993715i	$-0.535706\pi$
$571$	−5.34970			−0.223878			−0.111939	+	0.993715i	$0.535706\pi$
$572$		0			0
$573$	36.0543	+	17.2240i	1.50619	+	0.719543i
$574$		0			0
$575$	−29.4378			−1.22764
$576$		0			0
$577$	11.1865	+	19.3756i	0.465699	+	0.806615i	0.999233	−	0.0391640i	$-0.0124695\pi$
$577$	11.1865	+	19.3756i	0.465699	+	0.806615i	−0.533533	+	0.845779i	$0.679136\pi$
$578$		0			0
$579$	−28.6115	−	13.6684i	−1.18905	−	0.568039i
$580$		0			0
$581$	−5.90659	+	6.11003i	−0.245047	+	0.253487i
$582$		0			0
$583$	4.68011			0.193830
$584$		0			0
$585$	19.3538	+	23.9596i	0.800180	+	0.990607i
$586$		0			0
$587$	−2.49899	−	4.32839i	−0.103145	−	0.178652i	0.809834	−	0.586659i	$-0.199557\pi$
$587$	−2.49899	−	4.32839i	−0.103145	−	0.178652i	−0.912979	+	0.408007i	$0.866224\pi$
$588$		0			0
$589$	−35.0870	+	60.7724i	−1.44573	+	2.50408i
$590$		0			0
$591$	−22.7969	−	10.8906i	−0.937739	−	0.447980i
$592$		0			0
$593$	12.1698	−	21.0788i	0.499755	−	0.865601i	−0.500245	−	0.865884i	$-0.666757\pi$
$593$	12.1698	−	21.0788i	0.499755	−	0.865601i	1.00000		0.000282582i	$8.99487e-5\pi$
$594$		0			0
$595$	9.56498	+	2.39015i	0.392126	+	0.0979868i
$596$		0			0
$597$	0.245981	+	3.15003i	0.0100673	+	0.128922i
$598$		0			0
$599$	46.2145			1.88827			0.944137	−	0.329552i	$-0.106898\pi$
$599$	46.2145			1.88827			0.944137	+	0.329552i	$0.106898\pi$
$600$		0			0
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	−0.975644	−	0.219359i	$-0.929603\pi$
$601$	−16.6163	−	28.7803i	−0.677792	−	1.17397i	0.297852	−	0.954612i	$-0.403730\pi$
$602$		0			0
$603$	6.29625	+	7.79463i	0.256403	+	0.317422i
$604$		0			0
$605$	14.5040	−	25.1217i	0.589673	−	1.02134i
$606$		0			0
$607$	−21.9318	−	37.9869i	−0.890182	−	1.54184i	−0.839656	−	0.543118i	$-0.817244\pi$
$607$	−21.9318	−	37.9869i	−0.890182	−	1.54184i	−0.0505262	−	0.998723i	$-0.516090\pi$
$608$		0			0
$609$	−14.4702	+	5.39147i	−0.586361	+	0.218473i
$610$		0			0
$611$	4.49445	−	7.78462i	0.181826	−	0.314932i
$612$		0			0
$613$	1.81569	+	3.14487i	0.0733351	+	0.127020i	0.900361	−	0.435144i	$-0.143302\pi$
$613$	1.81569	+	3.14487i	0.0733351	+	0.127020i	−0.827026	+	0.562164i	$0.809969\pi$
$614$		0			0
$615$	12.9049	+	6.16496i	0.520374	+	0.248595i
$616$		0			0
$617$	10.4542	−	18.1073i	0.420872	−	0.728971i	−0.575153	−	0.818046i	$-0.695058\pi$
$617$	10.4542	−	18.1073i	0.420872	−	0.728971i	0.996025	+	0.0890744i	$0.0283909\pi$
$618$		0			0
$619$	−11.9745	+	20.7405i	−0.481296	+	0.833629i	−0.999770	−	0.0214645i	$-0.993167\pi$
$619$	−11.9745	+	20.7405i	−0.481296	+	0.833629i	0.518474	+	0.855094i	$0.326500\pi$
$620$		0			0
$621$	16.3320	−	15.4419i	0.655382	−	0.619661i
$622$		0			0
$623$	−29.1347	−	7.28035i	−1.16726	−	0.291681i
$624$		0			0
$625$	6.35626	+	11.0094i	0.254251	+	0.440375i
$626$		0			0
$627$	4.45065	+	56.9950i	0.177742	+	2.27616i
$628$		0			0
$629$	−5.43933			−0.216880
$630$		0			0
$631$	−6.06918			−0.241610			−0.120805	−	0.992676i	$-0.538548\pi$
$631$	−6.06918			−0.241610			−0.120805	+	0.992676i	$0.538548\pi$
$632$		0			0
$633$	7.92152	−	5.43720i	0.314852	−	0.216109i
$634$		0			0
$635$	21.3327	+	36.9492i	0.846561	+	1.46629i
$636$		0			0
$637$	0.708008	+	20.9042i	0.0280523	+	0.828255i
$638$		0			0
$639$	−24.3302	−	30.1203i	−0.962487	−	1.19154i
$640$		0			0
$641$	8.69407	−	15.0586i	0.343395	−	0.594778i	−0.641666	−	0.766984i	$-0.721756\pi$
$641$	8.69407	−	15.0586i	0.343395	−	0.594778i	0.985061	+	0.172207i	$0.0550897\pi$
$642$		0			0
$643$	9.66411	−	16.7387i	0.381115	−	0.660111i	−0.610107	−	0.792319i	$-0.708873\pi$
$643$	9.66411	−	16.7387i	0.381115	−	0.660111i	0.991222	+	0.132208i	$0.0422068\pi$
$644$		0			0
$645$	32.5220	−	22.3226i	1.28055	−	0.878951i
$646$		0			0
$647$	12.7041	+	22.0042i	0.499451	+	0.865075i	1.00000		0.000633482i	$-0.000201644\pi$
$647$	12.7041	+	22.0042i	0.499451	+	0.865075i	−0.500549	+	0.865708i	$0.666868\pi$
$648$		0			0
$649$	−27.3588	+	47.3869i	−1.07393	+	1.86010i
$650$		0			0
$651$	−7.13855	+	42.3630i	−0.279782	+	1.66034i
$652$		0			0
$653$	12.9064	+	22.3545i	0.505065	+	0.874799i	0.999983	+	0.00585902i	$0.00186499\pi$
$653$	12.9064	+	22.3545i	0.505065	+	0.874799i	−0.494917	+	0.868940i	$0.664802\pi$
$654$		0			0
$655$	27.0459	−	46.8449i	1.05677	−	1.83038i
$656$		0			0
$657$	17.7175	−	45.9880i	0.691225	−	1.79416i
$658$		0			0
$659$	8.62598	+	14.9406i	0.336020	+	0.582004i	0.983680	−	0.179925i	$-0.0575856\pi$
$659$	8.62598	+	14.9406i	0.336020	+	0.582004i	−0.647660	+	0.761930i	$0.724252\pi$
$660$		0			0
$661$	12.9635			0.504222			0.252111	−	0.967698i	$-0.418875\pi$
$661$	12.9635			0.504222			0.252111	+	0.967698i	$0.418875\pi$
$662$		0			0
$663$	−5.06469	−	2.41952i	−0.196696	−	0.0939665i
$664$		0			0
$665$	18.7220	+	65.4210i	0.726008	+	2.53692i
$666$		0			0
$667$	−7.28797	+	12.6231i	−0.282191	+	0.488769i
$668$		0			0
$669$	−1.62277	−	20.7811i	−0.0627398	−	0.803445i
$670$		0			0
$671$	11.9641	−	20.7225i	0.461871	−	0.799984i
$672$		0			0
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	−0.918289	−	0.395910i	$-0.870429\pi$
$673$	−20.8060	−	36.0371i	−0.802013	−	1.38913i	0.116277	−	0.993217i	$-0.462904\pi$
$674$		0			0
$675$	33.8878	+	10.1055i	1.30434	+	0.388960i
$676$		0			0
$677$	−22.1998			−0.853209			−0.426605	−	0.904438i	$-0.640290\pi$
$677$	−22.1998			−0.853209			−0.426605	+	0.904438i	$0.640290\pi$
$678$		0			0
$679$	−23.5496	+	24.3607i	−0.903752	+	0.934879i
$680$		0			0
$681$	−18.7881	+	12.8958i	−0.719961	+	0.494170i
$682$		0			0
$683$	−4.60315	−	7.97289i	−0.176135	−	0.305074i	0.764419	−	0.644720i	$-0.223026\pi$
$683$	−4.60315	−	7.97289i	−0.176135	−	0.305074i	−0.940553	+	0.339646i	$0.889693\pi$
$684$		0			0
$685$	14.5346			0.555338
$686$		0			0
$687$	1.68326	+	21.5559i	0.0642206	+	0.822408i
$688$		0			0
$689$	−3.17149			−0.120824
$690$		0			0
$691$	−40.0585			−1.52390			−0.761949	−	0.647636i	$-0.775758\pi$
$691$	−40.0585			−1.52390			−0.761949	+	0.647636i	$0.775758\pi$
$692$		0			0
$693$	14.7356	+	31.7450i	0.559759	+	1.20589i
$694$		0			0
$695$	67.3692			2.55546
$696$		0			0
$697$	−2.60636			−0.0987228
$698$		0			0
$699$	5.76029	−	3.95377i	0.217874	−	0.149545i
$700$		0			0
$701$	34.3868			1.29877			0.649385	−	0.760459i	$-0.275026\pi$
$701$	34.3868			1.29877			0.649385	+	0.760459i	$0.275026\pi$
$702$		0			0
$703$	−18.7711	−	32.5124i	−0.707964	−	1.22623i
$704$		0			0
$705$	−1.39377	−	17.8486i	−0.0524925	−	0.672219i
$706$		0			0
$707$	−1.99242	−	0.497878i	−0.0749328	−	0.0187246i
$708$		0			0
$709$	21.1840			0.795582			0.397791	−	0.917476i	$-0.369777\pi$
$709$	21.1840			0.795582			0.397791	+	0.917476i	$0.369777\pi$
$710$		0			0
$711$	−4.43062	−	5.48502i	−0.166161	−	0.205704i
$712$		0			0
$713$	20.2755	+	35.1181i	0.759322	+	1.31518i
$714$		0			0
$715$	−22.6347	+	39.2044i	−0.846489	+	1.46616i
$716$		0			0
$717$	−39.6076	+	27.1860i	−1.47917	+	1.01528i
$718$		0			0
$719$	−21.5994	+	37.4113i	−0.805523	+	1.39521i	0.110414	+	0.993886i	$0.464782\pi$
$719$	−21.5994	+	37.4113i	−0.805523	+	1.39521i	−0.915937	+	0.401321i	$0.868551\pi$
$720$		0			0
$721$	−4.19750	+	4.34207i	−0.156323	+	0.161707i
$722$		0			0
$723$	34.1490	−	23.4393i	1.27001	−	0.871718i
$724$		0			0
$725$	−22.9326			−0.851696
$726$		0			0
$727$	20.5571	+	35.6059i	0.762420	+	1.32055i	0.941600	+	0.336734i	$0.109322\pi$
$727$	20.5571	+	35.6059i	0.762420	+	1.32055i	−0.179180	+	0.983816i	$0.557344\pi$
$728$		0			0
$729$	−24.1018	+	12.1697i	−0.892661	+	0.450729i
$730$		0			0
$731$	−3.59430	+	6.22551i	−0.132940	+	0.230259i
$732$		0			0
$733$	−26.0425	−	45.1070i	−0.961903	−	1.66607i	−0.717715	−	0.696337i	$-0.754812\pi$
$733$	−26.0425	−	45.1070i	−0.961903	−	1.66607i	−0.244189	−	0.969728i	$-0.578522\pi$
$734$		0			0
$735$	24.7237	+	33.5284i	0.911946	+	1.23671i
$736$		0			0
$737$	−7.36361	+	12.7541i	−0.271242	+	0.469805i
$738$		0			0
$739$	7.18624	+	12.4469i	0.264350	+	0.457868i	0.967393	−	0.253279i	$-0.0815092\pi$
$739$	7.18624	+	12.4469i	0.264350	+	0.457868i	−0.703043	+	0.711147i	$0.748176\pi$
$740$		0			0
$741$	−3.01600	−	38.6228i	−0.110795	−	1.41885i
$742$		0			0
$743$	−21.3167	+	36.9216i	−0.782034	+	1.35452i	0.148721	+	0.988879i	$0.452484\pi$
$743$	−21.3167	+	36.9216i	−0.782034	+	1.35452i	−0.930755	+	0.365643i	$0.880849\pi$
$744$		0			0
$745$	−16.7097	+	28.9421i	−0.612198	+	1.06036i
$746$		0			0
$747$	3.46424	−	8.99187i	0.126750	−	0.328995i
$748$		0			0
$749$	11.6774	+	2.91802i	0.426683	+	0.106622i
$750$		0			0
$751$	18.9846	+	32.8823i	0.692758	+	1.19989i	0.970931	+	0.239360i	$0.0769378\pi$
$751$	18.9846	+	32.8823i	0.692758	+	1.19989i	−0.278173	+	0.960531i	$0.589729\pi$
$752$		0			0
$753$	5.21232	+	2.49005i	0.189947	+	0.0907424i
$754$		0			0
$755$	33.7458			1.22813
$756$		0			0
$757$	27.6692			1.00565			0.502827	−	0.864387i	$-0.332293\pi$
$757$	27.6692			1.00565			0.502827	+	0.864387i	$0.332293\pi$
$758$		0			0
$759$	29.8087	+	14.2404i	1.08199	+	0.516892i
$760$		0			0
$761$	−5.97210	−	10.3440i	−0.216488	−	0.374969i	0.737244	−	0.675627i	$-0.236127\pi$
$761$	−5.97210	−	10.3440i	−0.216488	−	0.374969i	−0.953732	+	0.300658i	$0.902794\pi$
$762$		0			0
$763$	8.70570	−	9.00554i	0.315167	−	0.326023i
$764$		0			0
$765$	−11.0437	+	1.73534i	−0.399284	+	0.0627415i
$766$		0			0
$767$	18.5398	−	32.1119i	0.669434	−	1.15949i
$768$		0			0
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	0.360487	+	0.932764i	$0.382610\pi$
$769$	−17.4026	+	30.1422i	−0.627554	+	1.08695i	−0.988041	+	0.154191i	$0.950723\pi$
$770$		0			0
$771$	−2.94888	−	37.7634i	−0.106201	−	1.36002i
$772$		0			0
$773$	−13.5014	−	23.3851i	−0.485611	−	0.841103i	0.514253	−	0.857639i	$-0.328069\pi$
$773$	−13.5014	−	23.3851i	−0.485611	−	0.841103i	−0.999863	+	0.0165363i	$0.994736\pi$
$774$		0			0
$775$	−31.8998	+	55.2521i	−1.14587	+	1.98471i
$776$		0			0
$777$	−17.7178	−	14.6392i	−0.635621	−	0.525178i
$778$		0			0
$779$	−8.99450	−	15.5789i	−0.322261	−	0.558173i
$780$		0			0
$781$	28.4547	−	49.2850i	1.01819	−	1.76356i
$782$		0			0
$783$	12.7230	−	12.0295i	0.454682	−	0.429900i
$784$		0			0
$785$	−20.6856	−	35.8286i	−0.738302	−	1.27878i
$786$		0			0
$787$	21.2840			0.758693			0.379347	−	0.925255i	$-0.376149\pi$
$787$	21.2840			0.758693			0.379347	+	0.925255i	$0.376149\pi$
$788$		0			0
$789$	7.86905	−	5.40119i	0.280146	−	0.192287i
$790$		0			0
$791$	−0.900275	−	0.224966i	−0.0320101	−	0.00799887i
$792$		0			0
$793$	−8.10754	+	14.0427i	−0.287907	+	0.498670i
$794$		0			0
$795$	−5.20783	+	3.57457i	−0.184703	+	0.126777i
$796$		0			0
$797$	−10.3062	+	17.8508i	−0.365064	+	0.632309i	−0.988786	−	0.149337i	$-0.952286\pi$
$797$	−10.3062	+	17.8508i	−0.365064	+	0.632309i	0.623723	+	0.781646i	$0.285619\pi$
$798$		0			0
$799$	1.63131	+	2.82552i	0.0577117	+	0.0999597i
$800$		0			0
$801$	33.6387	−	5.28582i	1.18856	−	0.186765i
$802$		0			0
$803$	72.4356			2.55620
$804$		0			0
$805$	38.1490	+	9.53289i	1.34457	+	0.335990i
$806$		0			0
$807$	−0.909900	−	11.6522i	−0.0320300	−	0.410176i
$808$		0			0
$809$	2.54223	+	4.40328i	0.0893802	+	0.154811i	0.907249	−	0.420593i	$-0.138178\pi$
$809$	2.54223	+	4.40328i	0.0893802	+	0.154811i	−0.817869	+	0.575404i	$0.804845\pi$
$810$		0			0
$811$	−7.58775			−0.266442			−0.133221	−	0.991086i	$-0.542532\pi$
$811$	−7.58775			−0.266442			−0.133221	+	0.991086i	$0.542532\pi$
$812$		0			0
$813$	−17.7631	+	12.1923i	−0.622977	+	0.427602i
$814$		0			0
$815$	6.08570			0.213173
$816$		0			0
$817$	−49.6155			−1.73583
$818$		0			0
$819$	−9.98562	−	21.5121i	−0.348926	−	0.751694i
$820$		0			0
$821$	20.2696			0.707413			0.353706	−	0.935357i	$-0.384921\pi$
$821$	20.2696			0.707413			0.353706	+	0.935357i	$0.384921\pi$
$822$		0			0
$823$	21.7911			0.759588			0.379794	−	0.925071i	$-0.375995\pi$
$823$	21.7911			0.759588			0.379794	+	0.925071i	$0.375995\pi$
$824$		0			0
$825$	4.04637	+	51.8178i	0.140877	+	1.80406i
$826$		0			0
$827$	26.3796			0.917307			0.458654	−	0.888615i	$-0.348332\pi$
$827$	26.3796			0.917307			0.458654	+	0.888615i	$0.348332\pi$
$828$		0			0
$829$	9.33400	+	16.1670i	0.324183	+	0.561502i	0.981347	−	0.192246i	$-0.0615773\pi$
$829$	9.33400	+	16.1670i	0.324183	+	0.561502i	−0.657164	+	0.753748i	$0.728244\pi$
$830$		0			0
$831$	−13.8788	+	9.52621i	−0.481452	+	0.330461i
$832$		0			0
$833$	−6.69940	−	3.57116i	−0.232120	−	0.123733i
$834$		0			0
$835$	−54.0366			−1.87001
$836$		0			0
$837$	−11.2850	−	47.3871i	−0.390068	−	1.63794i
$838$		0			0
$839$	12.5265	+	21.6966i	0.432464	+	0.749050i	0.997085	−	0.0763004i	$-0.0243108\pi$
$839$	12.5265	+	21.6966i	0.432464	+	0.749050i	−0.564621	+	0.825351i	$0.690977\pi$
$840$		0			0
$841$	8.82253	−	15.2811i	0.304225	−	0.526934i
$842$		0			0
$843$	2.60724	+	33.3883i	0.0897982	+	1.14995i
$844$		0			0
$845$	−6.99499	+	12.1157i	−0.240635	+	0.416792i
$846$		0			0
$847$	−15.5250	+	16.0598i	−0.533447	+	0.551820i
$848$		0			0
$849$	−12.9859	−	6.20367i	−0.445674	−	0.212909i
$850$		0			0
$851$	−21.6942			−0.743668
$852$		0			0
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	−0.981095	−	0.193526i	$-0.938008\pi$
$853$	−19.2219	−	33.2933i	−0.658146	−	1.13994i	0.322949	−	0.946416i	$-0.395326\pi$
$854$		0			0
$855$	−48.4842	−	60.0224i	−1.65812	−	2.05272i
$856$		0			0
$857$	6.00299	−	10.3975i	0.205058	−	0.355172i	−0.745093	−	0.666961i	$-0.767595\pi$
$857$	6.00299	−	10.3975i	0.205058	−	0.355172i	0.950151	+	0.311789i	$0.100928\pi$
$858$		0			0
$859$	6.30154	+	10.9146i	0.215006	+	0.372401i	0.953274	−	0.302106i	$-0.0976896\pi$
$859$	6.30154	+	10.9146i	0.215006	+	0.372401i	−0.738269	+	0.674507i	$0.764356\pi$
$860$		0			0
$861$	−8.48979	−	7.01464i	−0.289331	−	0.239058i
$862$		0			0
$863$	−0.210643	+	0.364845i	−0.00717038	+	0.0124195i	−0.869588	−	0.493777i	$-0.835616\pi$
$863$	−0.210643	+	0.364845i	−0.00717038	+	0.0124195i	0.862418	+	0.506197i	$0.168949\pi$
$864$		0			0
$865$	32.3084	+	55.9597i	1.09852	+	1.90269i
$866$		0			0
$867$	−22.5968	+	15.5101i	−0.767426	+	0.526749i
$868$		0			0
$869$	5.18171	−	8.97499i	0.175778	−	0.304456i
$870$		0			0
$871$	4.98997	−	8.64289i	0.169079	−	0.292853i
$872$		0			0
$873$	13.8119	−	35.8507i	0.467464	−	1.21336i
$874$		0			0
$875$	4.51580	+	15.7797i	0.152662	+	0.533453i
$876$		0			0
$877$	−0.893424	−	1.54746i	−0.0301688	−	0.0522539i	0.850547	−	0.525899i	$-0.176271\pi$
$877$	−0.893424	−	1.54746i	−0.0301688	−	0.0522539i	−0.880716	+	0.473645i	$0.842938\pi$
$878$		0			0
$879$	11.3476	−	7.78881i	0.382745	−	0.262710i
$880$		0			0
$881$	−49.8891			−1.68081			−0.840403	−	0.541962i	$-0.817682\pi$
$881$	−49.8891			−1.68081			−0.840403	+	0.541962i	$0.817682\pi$
$882$		0			0
$883$	34.7935			1.17090			0.585448	−	0.810710i	$-0.300919\pi$
$883$	34.7935			1.17090			0.585448	+	0.810710i	$0.300919\pi$
$884$		0			0
$885$	−5.74937	−	73.6264i	−0.193263	−	2.47492i
$886$		0			0
$887$	−11.9040	−	20.6184i	−0.399698	−	0.692297i	0.593991	−	0.804472i	$-0.297552\pi$
$887$	−11.9040	−	20.6184i	−0.399698	−	0.692297i	−0.993688	+	0.112175i	$0.964218\pi$
$888$		0			0
$889$	−9.03906	−	31.5855i	−0.303160	−	1.05935i
$890$		0			0
$891$	−29.4264	−	26.6259i	−0.985822	−	0.892000i
$892$		0			0
$893$	−11.2593	+	19.5017i	−0.376778	+	0.652598i
$894$		0			0
$895$	−11.4829	+	19.8889i	−0.383830	+	0.664813i
$896$		0			0
$897$	−20.2000	−	9.65002i	−0.674458	−	0.322205i
$898$		0			0
$899$	15.7950	+	27.3577i	0.526792	+	0.912431i
$900$		0			0
$901$	0.575564	−	0.996907i	0.0191748	−	0.0332118i
$902$		0			0
$903$	−28.4630	+	10.6051i	−0.947188	+	0.352914i
$904$		0			0
$905$	8.13841	+	14.0961i	0.270530	+	0.468571i
$906$		0			0
$907$	−17.1406	+	29.6885i	−0.569146	+	0.985789i	0.427505	+	0.904013i	$0.359393\pi$
$907$	−17.1406	+	29.6885i	−0.569146	+	0.985789i	−0.996651	+	0.0817761i	$0.973941\pi$
$908$		0			0
$909$	2.30044	−	0.361479i	0.0763006	−	0.0119895i
$910$		0			0
$911$	14.9839	+	25.9529i	0.496438	+	0.859857i	0.999992	−	0.00410771i	$-0.00130753\pi$
$911$	14.9839	+	25.9529i	0.496438	+	0.859857i	−0.503553	+	0.863964i	$0.667974\pi$
$912$		0			0
$913$	14.1631			0.468730
$914$		0			0
$915$	2.51423	+	32.1972i	0.0831177	+	1.06441i
$916$		0			0
$917$	−28.9498	+	29.9469i	−0.956006	+	0.988933i
$918$		0			0
$919$	−0.391037	+	0.677296i	−0.0128991	+	0.0223419i	−0.872403	−	0.488787i	$-0.837439\pi$
$919$	−0.391037	+	0.677296i	−0.0128991	+	0.0223419i	0.859504	+	0.511129i	$0.170773\pi$
$920$		0			0
$921$	42.0693	+	20.0975i	1.38623	+	0.662235i
$922$		0			0
$923$	−19.2824	+	33.3981i	−0.634688	+	1.09931i
$924$		0			0
$925$	−17.0660	−	29.5591i	−0.561126	−	0.971898i
$926$		0			0
$927$	2.46185	−	6.39004i	0.0808577	−	0.209876i
$928$		0			0
$929$	−13.5324			−0.443983			−0.221992	−	0.975049i	$-0.571256\pi$
$929$	−13.5324			−0.443983			−0.221992	+	0.975049i	$0.571256\pi$
$930$		0			0
$931$	−1.77367	−	52.3683i	−0.0581297	−	1.71630i
$932$		0			0
$933$	−14.6115	−	6.98028i	−0.478360	−	0.228524i
$934$		0			0
$935$	−8.21552	−	14.2297i	−0.268676	−	0.465361i
$936$		0			0
$937$	−2.27674			−0.0743777			−0.0371889	−	0.999308i	$-0.511840\pi$
$937$	−2.27674			−0.0743777			−0.0371889	+	0.999308i	$0.511840\pi$
$938$		0			0
$939$	−24.7528	−	11.8250i	−0.807776	−	0.385894i
$940$		0			0
$941$	−8.15440			−0.265826			−0.132913	−	0.991128i	$-0.542433\pi$
$941$	−8.15440			−0.265826			−0.132913	+	0.991128i	$0.542433\pi$
$942$		0			0
$943$	−10.3952			−0.338514
$944$		0			0
$945$	−40.6434	−	24.0698i	−1.32213	−	0.782992i
$946$		0			0
$947$	7.87106			0.255775			0.127888	−	0.991789i	$-0.459180\pi$
$947$	7.87106			0.255775			0.127888	+	0.991789i	$0.459180\pi$
$948$		0			0
$949$	−49.0862			−1.59341
$950$		0			0
$951$	44.4779	+	21.2482i	1.44230	+	0.689019i
$952$		0			0
$953$	43.1097			1.39646			0.698230	−	0.715873i	$-0.253971\pi$
$953$	43.1097			1.39646			0.698230	+	0.715873i	$0.253971\pi$
$954$		0			0
$955$	−39.6321	−	68.6448i	−1.28246	−	2.22129i
$956$		0			0
$957$	23.2216	+	11.0935i	0.750648	+	0.358602i
$958$		0			0
$959$	−10.8582	−	2.71330i	−0.350629	−	0.0876172i
$960$		0			0
$961$	56.8847			1.83499
$962$		0			0
$963$	−13.4826	+	2.11859i	−0.434472	+	0.0682707i
$964$		0			0
$965$	31.4507	+	54.4742i	1.01243	+	1.75359i
$966$		0			0
$967$	13.9537	−	24.1684i	0.448719	−	0.777205i	−0.549584	−	0.835439i	$-0.685214\pi$
$967$	13.9537	−	24.1684i	0.448719	−	0.777205i	0.998303	+	0.0582340i	$0.0185470\pi$
$968$		0			0
$969$	12.6878	+	6.06128i	0.407591	+	0.194716i
$970$		0			0
$971$	21.0705	−	36.4952i	0.676185	−	1.17119i	−0.299936	−	0.953959i	$-0.596965\pi$
$971$	21.0705	−	36.4952i	0.676185	−	1.17119i	0.976121	−	0.217228i	$-0.0697015\pi$
$972$		0			0
$973$	−50.3286	−	12.5764i	−1.61346	−	0.403181i
$974$		0			0
$975$	−2.74204	−	35.1145i	−0.0878154	−	1.12456i
$976$		0			0
$977$	−13.8549			−0.443259			−0.221629	−	0.975131i	$-0.571137\pi$
$977$	−13.8549			−0.443259			−0.221629	+	0.975131i	$0.571137\pi$
$978$		0			0
$979$	25.0243	+	43.3433i	0.799780	+	1.38526i
$980$		0			0
$981$	−5.10592	+	13.2531i	−0.163020	+	0.423138i
$982$		0			0
$983$	−3.97938	+	6.89249i	−0.126923	+	0.219836i	−0.922483	−	0.386038i	$-0.873843\pi$
$983$	−3.97938	+	6.89249i	−0.126923	+	0.219836i	0.795560	+	0.605874i	$0.207177\pi$
$984$		0			0
$985$	25.0591	+	43.4036i	0.798449	+	1.38296i
$986$		0			0
$987$	−2.29074	+	13.5941i	−0.0729150	+	0.432706i
$988$		0			0
$989$	−14.3355	+	24.8298i	−0.455842	+	0.789542i
$990$		0			0
$991$	4.36428	+	7.55916i	0.138636	+	0.240125i	0.926981	−	0.375109i	$-0.122395\pi$
$991$	4.36428	+	7.55916i	0.138636	+	0.240125i	−0.788345	+	0.615234i	$0.789062\pi$
$992$		0			0
$993$	30.6172	+	14.6266i	0.971609	+	0.464161i
$994$		0			0
$995$	3.13391	−	5.42809i	0.0993515	−	0.172082i
$996$		0			0
$997$	1.15190	−	1.99514i	0.0364810	−	0.0631869i	−0.847208	−	0.531261i	$-0.821719\pi$
$997$	1.15190	−	1.99514i	0.0364810	−	0.0631869i	0.883689	+	0.468074i	$0.155052\pi$
$998$		0			0
$999$	24.9737	+	7.44724i	0.790132	+	0.235620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.121.2	yes	22
3.2	odd	2		1512.2.q.c.793.2		22
4.3	odd	2		1008.2.q.k.625.10		22
7.4	even	3		504.2.t.d.193.5	yes	22
9.2	odd	6		1512.2.t.d.289.10		22
9.7	even	3		504.2.t.d.457.5	yes	22
12.11	even	2		3024.2.q.k.2305.2		22
21.11	odd	6		1512.2.t.d.361.10		22
28.11	odd	6		1008.2.t.k.193.7		22
36.7	odd	6		1008.2.t.k.961.7		22
36.11	even	6		3024.2.t.l.289.10		22
63.11	odd	6		1512.2.q.c.1369.2		22
63.25	even	3	inner	504.2.q.d.25.2	✓	22
84.11	even	6		3024.2.t.l.1873.10		22
252.11	even	6		3024.2.q.k.2881.2		22
252.151	odd	6		1008.2.q.k.529.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.2	✓	22	63.25	even	3	inner
504.2.q.d.121.2	yes	22	1.1	even	1	trivial
504.2.t.d.193.5	yes	22	7.4	even	3
504.2.t.d.457.5	yes	22	9.7	even	3
1008.2.q.k.529.10		22	252.151	odd	6
1008.2.q.k.625.10		22	4.3	odd	2
1008.2.t.k.193.7		22	28.11	odd	6
1008.2.t.k.961.7		22	36.7	odd	6
1512.2.q.c.793.2		22	3.2	odd	2
1512.2.q.c.1369.2		22	63.11	odd	6
1512.2.t.d.289.10		22	9.2	odd	6
1512.2.t.d.361.10		22	21.11	odd	6
3024.2.q.k.2305.2		22	12.11	even	2
3024.2.q.k.2881.2		22	252.11	even	6
3024.2.t.l.289.10		22	36.11	even	6
3024.2.t.l.1873.10		22	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56287 - 0.746620i) q^{3} +(1.71796 + 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +(1.88512 + 2.33374i) q^{9} +O(q^{10})\)	\(q+(-1.56287 - 0.746620i) q^{3} +(1.71796 + 2.97559i) q^{5} +(-0.727932 - 2.54364i) q^{7} +(1.88512 + 2.33374i) q^{9} +(-2.20469 + 3.81863i) q^{11} +(1.49401 - 2.58771i) q^{13} +(-0.463308 - 5.93312i) q^{15} +(0.542270 + 0.939239i) q^{17} +(-3.74273 + 6.48261i) q^{19} +(-0.761471 + 4.51887i) q^{21} +(2.16279 + 3.74606i) q^{23} +(-3.40276 + 5.89375i) q^{25} +(-1.20378 - 5.05479i) q^{27} +(1.68485 + 2.91825i) q^{29} +9.37469 q^{31} +(6.29671 - 4.32196i) q^{33} +(6.31828 - 6.53590i) q^{35} +(-2.50767 + 4.34341i) q^{37} +(-4.26698 + 2.92879i) q^{39} +(-1.20160 + 2.08122i) q^{41} +(3.31412 + 5.74023i) q^{43} +(-3.70569 + 9.61860i) q^{45} +3.00831 q^{47} +(-5.94023 + 3.70320i) q^{49} +(-0.146242 - 1.87278i) q^{51} +(-0.530699 - 0.919198i) q^{53} -15.1502 q^{55} +(10.6894 - 7.33706i) q^{57} +12.4094 q^{59} -5.42668 q^{61} +(4.56396 - 6.49387i) q^{63} +10.2666 q^{65} +3.33998 q^{67} +(-0.583272 - 7.46938i) q^{69} -12.9064 q^{71} +(-8.21382 - 14.2267i) q^{73} +(9.71846 - 6.67059i) q^{75} +(11.3181 + 2.82823i) q^{77} -2.35031 q^{79} +(-1.89266 + 8.79874i) q^{81} +(-1.60602 - 2.78171i) q^{83} +(-1.86319 + 3.22715i) q^{85} +(-0.454380 - 5.81879i) q^{87} +(5.67524 - 9.82981i) q^{89} +(-7.66974 - 1.91656i) q^{91} +(-14.6514 - 6.99933i) q^{93} -25.7194 q^{95} +(-6.40321 - 11.0907i) q^{97} +(-13.0678 + 2.05341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Introduction

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