LMFDB - Embedded newform 504.2.t.d.193.11

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			193.11
Character	$\chi$	$=$	504.193
Dual form			504.2.t.d.457.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70090 + 0.327002i) q^{3} +0.340200 q^{5} +(1.09748 - 2.40739i) q^{7} +(2.78614 + 1.11240i) q^{9} +O(q^{10})$	\(q+(1.70090 + 0.327002i) q^{3} +0.340200 q^{5} +(1.09748 - 2.40739i) q^{7} +(2.78614 + 1.11240i) q^{9} -0.671588 q^{11} +(1.62370 - 2.81233i) q^{13} +(0.578647 + 0.111246i) q^{15} +(-1.10014 + 1.90550i) q^{17} +(0.242085 + 0.419303i) q^{19} +(2.65393 - 3.73586i) q^{21} +4.18990 q^{23} -4.88426 q^{25} +(4.37520 + 2.80315i) q^{27} +(0.478868 + 0.829424i) q^{29} +(-1.04132 - 1.80361i) q^{31} +(-1.14231 - 0.219611i) q^{33} +(0.373363 - 0.818995i) q^{35} +(4.81613 + 8.34178i) q^{37} +(3.68139 - 4.25255i) q^{39} +(-3.90207 + 6.75858i) q^{41} +(-3.66119 - 6.34136i) q^{43} +(0.947845 + 0.378438i) q^{45} +(1.34951 - 2.33742i) q^{47} +(-4.59108 - 5.28413i) q^{49} +(-2.49434 + 2.88133i) q^{51} +(-6.12335 + 10.6059i) q^{53} -0.228474 q^{55} +(0.274649 + 0.792355i) q^{57} +(2.47148 + 4.28074i) q^{59} +(1.76059 - 3.04944i) q^{61} +(5.73571 - 5.48650i) q^{63} +(0.552383 - 0.956755i) q^{65} +(-6.16012 - 10.6696i) q^{67} +(7.12661 + 1.37011i) q^{69} -5.57304 q^{71} +(-3.71686 + 6.43779i) q^{73} +(-8.30766 - 1.59716i) q^{75} +(-0.737054 + 1.61677i) q^{77} +(5.00637 - 8.67128i) q^{79} +(6.52514 + 6.19859i) q^{81} +(2.47376 + 4.28468i) q^{83} +(-0.374269 + 0.648252i) q^{85} +(0.543284 + 1.56736i) q^{87} +(-8.52177 - 14.7601i) q^{89} +(-4.98840 - 6.99536i) q^{91} +(-1.18139 - 3.40828i) q^{93} +(0.0823572 + 0.142647i) q^{95} +(4.23657 + 7.33795i) q^{97} +(-1.87114 - 0.747072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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
$3$	1.70090	+	0.327002i	0.982017	+	0.188795i
$3$	1.70090	+	0.327002i	0.982017	+	0.188795i
$4$		0			0
$5$	0.340200			0.152142			0.0760711	−	0.997102i	$-0.475762\pi$
$5$	0.340200			0.152142			0.0760711	+	0.997102i	$0.475762\pi$
$6$		0			0
$7$	1.09748	−	2.40739i	0.414808	−	0.909909i
$7$	1.09748	−	2.40739i	0.414808	−	0.909909i
$8$		0			0
$9$	2.78614	+	1.11240i	0.928713	+	0.370799i
$10$		0			0
$11$	−0.671588			−0.202491			−0.101246	−	0.994861i	$-0.532283\pi$
$11$	−0.671588			−0.202491			−0.101246	+	0.994861i	$0.532283\pi$
$12$		0			0
$13$	1.62370	−	2.81233i	0.450333	−	0.780000i	−0.548073	−	0.836430i	$-0.684639\pi$
$13$	1.62370	−	2.81233i	0.450333	−	0.780000i	0.998407	+	0.0564303i	$0.0179719\pi$
$14$		0			0
$15$	0.578647	+	0.111246i	0.149406	+	0.0287236i
$16$		0			0
$17$	−1.10014	+	1.90550i	−0.266824	+	0.462152i	−0.968040	−	0.250796i	$-0.919308\pi$
$17$	−1.10014	+	1.90550i	−0.266824	+	0.462152i	0.701216	+	0.712949i	$0.252641\pi$
$18$		0			0
$19$	0.242085	+	0.419303i	0.0555380	+	0.0961946i	0.892458	−	0.451131i	$-0.148979\pi$
$19$	0.242085	+	0.419303i	0.0555380	+	0.0961946i	−0.836920	+	0.547326i	$0.815646\pi$
$20$		0			0
$21$	2.65393	−	3.73586i	0.579135	−	0.815232i
$22$		0			0
$23$	4.18990			0.873655			0.436827	−	0.899545i	$-0.356102\pi$
$23$	4.18990			0.873655			0.436827	+	0.899545i	$0.356102\pi$
$24$		0			0
$25$	−4.88426			−0.976853
$26$		0			0
$27$	4.37520	+	2.80315i	0.842007	+	0.539467i
$28$		0			0
$29$	0.478868	+	0.829424i	0.0889235	+	0.154020i	0.907056	−	0.421009i	$-0.138324\pi$
$29$	0.478868	+	0.829424i	0.0889235	+	0.154020i	−0.818133	+	0.575029i	$0.804991\pi$
$30$		0			0
$31$	−1.04132	−	1.80361i	−0.187026	−	0.323938i	0.757231	−	0.653147i	$-0.226551\pi$
$31$	−1.04132	−	1.80361i	−0.187026	−	0.323938i	−0.944257	+	0.329208i	$0.893218\pi$
$32$		0			0
$33$	−1.14231	−	0.219611i	−0.198850	−	0.0382293i
$34$		0			0
$35$	0.373363	−	0.818995i	0.0631098	−	0.138435i
$36$		0			0
$37$	4.81613	+	8.34178i	0.791767	+	1.37138i	0.924872	+	0.380278i	$0.124172\pi$
$37$	4.81613	+	8.34178i	0.791767	+	1.37138i	−0.133105	+	0.991102i	$0.542495\pi$
$38$		0			0
$39$	3.68139	−	4.25255i	0.589495	−	0.680952i
$40$		0			0
$41$	−3.90207	+	6.75858i	−0.609400	+	1.05551i	0.381939	+	0.924188i	$0.375256\pi$
$41$	−3.90207	+	6.75858i	−0.609400	+	1.05551i	−0.991339	+	0.131325i	$0.958077\pi$
$42$		0			0
$43$	−3.66119	−	6.34136i	−0.558326	−	0.967048i	−0.997636	−	0.0687132i	$-0.978111\pi$
$43$	−3.66119	−	6.34136i	−0.558326	−	0.967048i	0.439311	−	0.898335i	$-0.355223\pi$
$44$		0			0
$45$	0.947845	+	0.378438i	0.141296	+	0.0564142i
$46$		0			0
$47$	1.34951	−	2.33742i	0.196846	−	0.340947i	−0.750658	−	0.660691i	$-0.770263\pi$
$47$	1.34951	−	2.33742i	0.196846	−	0.340947i	0.947504	+	0.319744i	$0.103597\pi$
$48$		0			0
$49$	−4.59108	−	5.28413i	−0.655868	−	0.754876i
$50$		0			0
$51$	−2.49434	+	2.88133i	−0.349277	+	0.403466i
$52$		0			0
$53$	−6.12335	+	10.6059i	−0.841107	+	1.45684i	0.0478535	+	0.998854i	$0.484762\pi$
$53$	−6.12335	+	10.6059i	−0.841107	+	1.45684i	−0.888960	+	0.457985i	$0.848571\pi$
$54$		0			0
$55$	−0.228474			−0.0308075
$56$		0			0
$57$	0.274649	+	0.792355i	0.0363782	+	0.104950i
$58$		0			0
$59$	2.47148	+	4.28074i	0.321760	+	0.557304i	0.980851	−	0.194758i	$-0.0623923\pi$
$59$	2.47148	+	4.28074i	0.321760	+	0.557304i	−0.659091	+	0.752063i	$0.729059\pi$
$60$		0			0
$61$	1.76059	−	3.04944i	0.225421	−	0.390441i	−0.731025	−	0.682351i	$-0.760958\pi$
$61$	1.76059	−	3.04944i	0.225421	−	0.390441i	0.956446	+	0.291910i	$0.0942909\pi$
$62$		0			0
$63$	5.73571	−	5.48650i	0.722631	−	0.691234i
$64$		0			0
$65$	0.552383	−	0.956755i	0.0685147	−	0.118671i
$66$		0			0
$67$	−6.16012	−	10.6696i	−0.752579	−	1.30350i	−0.946569	−	0.322501i	$-0.895476\pi$
$67$	−6.16012	−	10.6696i	−0.752579	−	1.30350i	0.193990	−	0.981003i	$-0.437857\pi$
$68$		0			0
$69$	7.12661	+	1.37011i	0.857943	+	0.164941i
$70$		0			0
$71$	−5.57304			−0.661398			−0.330699	−	0.943736i	$-0.607285\pi$
$71$	−5.57304			−0.661398			−0.330699	+	0.943736i	$0.607285\pi$
$72$		0			0
$73$	−3.71686	+	6.43779i	−0.435026	+	0.753487i	−0.997298	−	0.0734657i	$-0.976594\pi$
$73$	−3.71686	+	6.43779i	−0.435026	+	0.753487i	0.562272	+	0.826952i	$0.309927\pi$
$74$		0			0
$75$	−8.30766	−	1.59716i	−0.959286	−	0.184425i
$76$		0			0
$77$	−0.737054	+	1.61677i	−0.0839951	+	0.184249i
$78$		0			0
$79$	5.00637	−	8.67128i	0.563260	−	0.975596i	−0.433949	−	0.900938i	$-0.642880\pi$
$79$	5.00637	−	8.67128i	0.563260	−	0.975596i	0.997209	−	0.0746582i	$-0.0237866\pi$
$80$		0			0
$81$	6.52514	+	6.19859i	0.725016	+	0.688732i
$82$		0			0
$83$	2.47376	+	4.28468i	0.271530	+	0.470305i	0.969254	−	0.246063i	$-0.0791369\pi$
$83$	2.47376	+	4.28468i	0.271530	+	0.470305i	−0.697723	+	0.716367i	$0.745804\pi$
$84$		0			0
$85$	−0.374269	+	0.648252i	−0.0405951	+	0.0703128i
$86$		0			0
$87$	0.543284	+	1.56736i	0.0582462	+	0.168039i
$88$		0			0
$89$	−8.52177	−	14.7601i	−0.903306	−	1.56457i	−0.823175	−	0.567788i	$-0.807799\pi$
$89$	−8.52177	−	14.7601i	−0.903306	−	1.56457i	−0.0801310	−	0.996784i	$-0.525534\pi$
$90$		0			0
$91$	−4.98840	−	6.99536i	−0.522927	−	0.733313i
$92$		0			0
$93$	−1.18139	−	3.40828i	−0.122505	−	0.353422i
$94$		0			0
$95$	0.0823572	+	0.142647i	0.00844967	+	0.0146353i
$96$		0			0
$97$	4.23657	+	7.33795i	0.430159	+	0.745056i	0.996887	−	0.0788485i	$-0.0251243\pi$
$97$	4.23657	+	7.33795i	0.430159	+	0.745056i	−0.566728	+	0.823905i	$0.691791\pi$
$98$		0			0
$99$	−1.87114	−	0.747072i	−0.188056	−	0.0750836i
$100$		0			0
$101$	−4.57385			−0.455115			−0.227558	−	0.973765i	$-0.573074\pi$
$101$	−4.57385			−0.455115			−0.227558	+	0.973765i	$0.573074\pi$
$102$		0			0
$103$	−1.80713			−0.178061			−0.0890307	−	0.996029i	$-0.528377\pi$
$103$	−1.80713			−0.178061			−0.0890307	+	0.996029i	$0.528377\pi$
$104$		0			0
$105$	0.902867	−	1.27094i	0.0881108	−	0.124031i
$106$		0			0
$107$	3.88188	+	6.72361i	0.375275	+	0.649996i	0.990368	−	0.138459i	$-0.0442149\pi$
$107$	3.88188	+	6.72361i	0.375275	+	0.649996i	−0.615093	+	0.788454i	$0.710882\pi$
$108$		0			0
$109$	−1.07178	+	1.85638i	−0.102658	+	0.177809i	−0.912779	−	0.408454i	$-0.866068\pi$
$109$	−1.07178	+	1.85638i	−0.102658	+	0.177809i	0.810121	+	0.586263i	$0.199401\pi$
$110$		0			0
$111$	5.46399	+	15.7634i	0.518619	+	1.49620i
$112$		0			0
$113$	−7.91006	+	13.7006i	−0.744116	+	1.28885i	0.206491	+	0.978449i	$0.433796\pi$
$113$	−7.91006	+	13.7006i	−0.744116	+	1.28885i	−0.950607	+	0.310398i	$0.899538\pi$
$114$		0			0
$115$	1.42540			0.132920
$116$		0			0
$117$	7.65228	−	6.02934i	0.707454	−	0.557413i
$118$		0			0
$119$	3.37991	+	4.73973i	0.309836	+	0.434490i
$120$		0			0
$121$	−10.5490			−0.958997
$122$		0			0
$123$	−8.84710	+	10.2197i	−0.797716	+	0.921479i
$124$		0			0
$125$	−3.36263			−0.300763
$126$		0			0
$127$	−13.8820			−1.23183			−0.615915	−	0.787812i	$-0.711214\pi$
$127$	−13.8820			−1.23183			−0.615915	+	0.787812i	$0.711214\pi$
$128$		0			0
$129$	−4.15368	−	11.9833i	−0.365711	−	1.05507i
$130$		0			0
$131$	−4.17538			−0.364805			−0.182402	−	0.983224i	$-0.558387\pi$
$131$	−4.17538			−0.364805			−0.182402	+	0.983224i	$0.558387\pi$
$132$		0			0
$133$	1.27511	−	0.122616i	0.110566	−	0.0106322i
$134$		0			0
$135$	1.48844	+	0.953633i	0.128105	+	0.0820757i
$136$		0			0
$137$	−12.7609			−1.09023			−0.545117	−	0.838360i	$-0.683515\pi$
$137$	−12.7609			−1.09023			−0.545117	+	0.838360i	$0.683515\pi$
$138$		0			0
$139$	5.95986	−	10.3228i	0.505509	−	0.875567i	−0.494471	−	0.869194i	$-0.664638\pi$
$139$	5.95986	−	10.3228i	0.505509	−	0.875567i	0.999980	−	0.00637264i	$-0.00202849\pi$
$140$		0			0
$141$	3.05972	−	3.53442i	0.257675	−	0.297652i
$142$		0			0
$143$	−1.09046	+	1.88873i	−0.0911885	+	0.157943i
$144$		0			0
$145$	0.162911	+	0.282170i	0.0135290	+	0.0234329i
$146$		0			0
$147$	−6.08105	−	10.4891i	−0.501557	−	0.865125i
$148$		0			0
$149$	−10.7510			−0.880753			−0.440376	−	0.897813i	$-0.645155\pi$
$149$	−10.7510			−0.880753			−0.440376	+	0.897813i	$0.645155\pi$
$150$		0			0
$151$	−2.58099			−0.210038			−0.105019	−	0.994470i	$-0.533490\pi$
$151$	−2.58099			−0.210038			−0.105019	+	0.994470i	$0.533490\pi$
$152$		0			0
$153$	−5.18483	+	4.08520i	−0.419168	+	0.330269i
$154$		0			0
$155$	−0.354256	−	0.613589i	−0.0284545	−	0.0492846i
$156$		0			0
$157$	−3.99846	−	6.92554i	−0.319112	−	0.552718i	0.661191	−	0.750218i	$-0.270051\pi$
$157$	−3.99846	−	6.92554i	−0.319112	−	0.552718i	−0.980303	+	0.197499i	$0.936718\pi$
$158$		0			0
$159$	−13.8834	+	16.0373i	−1.10102	+	1.27184i
$160$		0			0
$161$	4.59833	−	10.0867i	0.362399	−	0.794946i
$162$		0			0
$163$	4.13306	+	7.15868i	0.323727	+	0.560711i	0.981254	−	0.192720i	$-0.0617309\pi$
$163$	4.13306	+	7.15868i	0.323727	+	0.560711i	−0.657527	+	0.753431i	$0.728398\pi$
$164$		0			0
$165$	−0.388612	−	0.0747115i	−0.0302534	−	0.00581628i
$166$		0			0
$167$	8.99384	−	15.5778i	0.695964	−	1.20544i	−0.273891	−	0.961761i	$-0.588311\pi$
$167$	8.99384	−	15.5778i	0.695964	−	1.20544i	0.969855	−	0.243684i	$-0.0783560\pi$
$168$		0			0
$169$	1.22720	+	2.12557i	0.0944000	+	0.163506i
$170$		0			0
$171$	0.208050	+	1.43753i	0.0159100	+	0.109931i
$172$		0			0
$173$	8.49915	−	14.7210i	0.646179	−	1.11921i	−0.337849	−	0.941200i	$-0.609699\pi$
$173$	8.49915	−	14.7210i	0.646179	−	1.11921i	0.984028	−	0.178014i	$-0.0569672\pi$
$174$		0			0
$175$	−5.36038	+	11.7583i	−0.405207	+	0.888847i
$176$		0			0
$177$	2.80394	+	8.08930i	0.210757	+	0.608029i
$178$		0			0
$179$	−9.65073	+	16.7156i	−0.721329	+	1.24938i	0.239138	+	0.970986i	$0.423135\pi$
$179$	−9.65073	+	16.7156i	−0.721329	+	1.24938i	−0.960467	+	0.278393i	$0.910198\pi$
$180$		0			0
$181$	21.9640			1.63257			0.816287	−	0.577646i	$-0.196029\pi$
$181$	21.9640			1.63257			0.816287	+	0.577646i	$0.196029\pi$
$182$		0			0
$183$	3.99177	−	4.61108i	0.295080	−	0.340861i
$184$		0			0
$185$	1.63845	+	2.83788i	0.120461	+	0.208645i
$186$		0			0
$187$	0.738842	−	1.27971i	0.0540295	−	0.0935818i
$188$		0			0
$189$	11.5500	−	7.45641i	0.840137	−	0.542374i
$190$		0			0
$191$	−3.32872	+	5.76552i	−0.240858	+	0.417178i	−0.960959	−	0.276691i	$-0.910762\pi$
$191$	−3.32872	+	5.76552i	−0.240858	+	0.417178i	0.720101	+	0.693869i	$0.244095\pi$
$192$		0			0
$193$	−3.17453	−	5.49845i	−0.228508	−	0.395787i	0.728858	−	0.684665i	$-0.240051\pi$
$193$	−3.17453	−	5.49845i	−0.228508	−	0.395787i	−0.957366	+	0.288878i	$0.906718\pi$
$194$		0			0
$195$	1.25241	−	1.44672i	0.0896870	−	0.103602i
$196$		0			0
$197$	23.8112			1.69648			0.848239	−	0.529614i	$-0.177663\pi$
$197$	23.8112			1.69648			0.848239	+	0.529614i	$0.177663\pi$
$198$		0			0
$199$	−10.4771	+	18.1468i	−0.742701	+	1.28640i	0.208561	+	0.978009i	$0.433122\pi$
$199$	−10.4771	+	18.1468i	−0.742701	+	1.28640i	−0.951261	+	0.308386i	$0.900211\pi$
$200$		0			0
$201$	−6.98877	−	20.1624i	−0.492950	−	1.42215i
$202$		0			0
$203$	2.52230	−	0.242547i	0.177030	−	0.0170235i
$204$		0			0
$205$	−1.32748	+	2.29927i	−0.0927155	+	0.160588i
$206$		0			0
$207$	11.6736	+	4.66083i	0.811374	+	0.323950i
$208$		0			0
$209$	−0.162581	−	0.281599i	−0.0112460	−	0.0194786i
$210$		0			0
$211$	−6.32431	+	10.9540i	−0.435384	+	0.754106i	−0.997327	−	0.0730693i	$-0.976721\pi$
$211$	−6.32431	+	10.9540i	−0.435384	+	0.754106i	0.561943	+	0.827176i	$0.310054\pi$
$212$		0			0
$213$	−9.47920	−	1.82240i	−0.649504	−	0.124868i
$214$		0			0
$215$	−1.24554	−	2.15733i	−0.0849448	−	0.147129i
$216$		0			0
$217$	−5.48482	+	0.527427i	−0.372334	+	0.0358041i
$218$		0			0
$219$	−8.42719	+	9.73464i	−0.569457	+	0.657806i
$220$		0			0
$221$	3.57260	+	6.18793i	0.240319	+	0.416245i
$222$		0			0
$223$	−1.34432	−	2.32843i	−0.0900225	−	0.155924i	0.817498	−	0.575932i	$-0.195361\pi$
$223$	−1.34432	−	2.32843i	−0.0900225	−	0.155924i	−0.907520	+	0.420008i	$0.862027\pi$
$224$		0			0
$225$	−13.6082	−	5.43324i	−0.907216	−	0.362216i
$226$		0			0
$227$	27.9885			1.85766			0.928829	−	0.370508i	$-0.120816\pi$
$227$	27.9885			1.85766			0.928829	+	0.370508i	$0.120816\pi$
$228$		0			0
$229$	24.5390			1.62158			0.810790	−	0.585337i	$-0.199038\pi$
$229$	24.5390			1.62158			0.810790	+	0.585337i	$0.199038\pi$
$230$		0			0
$231$	−1.78235	+	2.50896i	−0.117270	+	0.165077i
$232$		0			0
$233$	−4.61844	−	7.99938i	−0.302564	−	0.524057i	0.674152	−	0.738593i	$-0.264509\pi$
$233$	−4.61844	−	7.99938i	−0.302564	−	0.524057i	−0.976716	+	0.214536i	$0.931176\pi$
$234$		0			0
$235$	0.459103	−	0.795189i	0.0299486	−	0.0518724i
$236$		0			0
$237$	11.3509	−	13.1119i	0.737318	−	0.851711i
$238$		0			0
$239$	14.0126	−	24.2706i	0.906403	−	1.56994i	0.0873796	−	0.996175i	$-0.472151\pi$
$239$	14.0126	−	24.2706i	0.906403	−	1.56994i	0.819023	−	0.573760i	$-0.194516\pi$
$240$		0			0
$241$	19.8282			1.27725			0.638624	−	0.769519i	$-0.279504\pi$
$241$	19.8282			1.27725			0.638624	+	0.769519i	$0.279504\pi$
$242$		0			0
$243$	9.07168	+	12.6769i	0.581949	+	0.813225i
$244$		0			0
$245$	−1.56188	−	1.79766i	−0.0997851	−	0.114848i
$246$		0			0
$247$	1.57229			0.100042
$248$		0			0
$249$	2.80653	+	8.09675i	0.177856	+	0.513110i
$250$		0			0
$251$	16.5759			1.04626			0.523132	−	0.852252i	$-0.324764\pi$
$251$	16.5759			1.04626			0.523132	+	0.852252i	$0.324764\pi$
$252$		0			0
$253$	−2.81389			−0.176907
$254$		0			0
$255$	−0.848574	+	0.980228i	−0.0531398	+	0.0613842i
$256$		0			0
$257$	7.29501			0.455050			0.227525	−	0.973772i	$-0.426937\pi$
$257$	7.29501			0.455050			0.227525	+	0.973772i	$0.426937\pi$
$258$		0			0
$259$	25.3675	−	2.43937i	1.57626	−	0.151575i
$260$		0			0
$261$	0.411544	+	2.84358i	0.0254739	+	0.176013i
$262$		0			0
$263$	−26.7798			−1.65131			−0.825657	−	0.564172i	$-0.809196\pi$
$263$	−26.7798			−1.65131			−0.825657	+	0.564172i	$0.809196\pi$
$264$		0			0
$265$	−2.08316	+	3.60815i	−0.127968	+	0.221647i
$266$		0			0
$267$	−9.66811	−	27.8922i	−0.591679	−	1.70698i
$268$		0			0
$269$	10.1791	−	17.6307i	0.620630	−	1.07496i	−0.368739	−	0.929533i	$-0.620210\pi$
$269$	10.1791	−	17.6307i	0.620630	−	1.07496i	0.989369	−	0.145429i	$-0.0464562\pi$
$270$		0			0
$271$	5.45842	+	9.45427i	0.331576	+	0.574306i	0.982821	−	0.184561i	$-0.0590864\pi$
$271$	5.45842	+	9.45427i	0.331576	+	0.574306i	−0.651245	+	0.758867i	$0.725753\pi$
$272$		0			0
$273$	−6.19729	−	13.5296i	−0.375077	−	0.818851i
$274$		0			0
$275$	3.28021			0.197804
$276$		0			0
$277$	17.6738			1.06191			0.530957	−	0.847399i	$-0.321832\pi$
$277$	17.6738			1.06191			0.530957	+	0.847399i	$0.321832\pi$
$278$		0			0
$279$	−0.894918	−	6.18347i	−0.0535773	−	0.370195i
$280$		0			0
$281$	7.17614	+	12.4294i	0.428092	+	0.741478i	0.996704	−	0.0811286i	$-0.0258524\pi$
$281$	7.17614	+	12.4294i	0.428092	+	0.741478i	−0.568611	+	0.822606i	$0.692519\pi$
$282$		0			0
$283$	−4.86420	−	8.42505i	−0.289147	−	0.500817i	0.684459	−	0.729051i	$-0.260038\pi$
$283$	−4.86420	−	8.42505i	−0.289147	−	0.500817i	−0.973606	+	0.228234i	$0.926705\pi$
$284$		0			0
$285$	0.0934358	+	0.269559i	0.00553466	+	0.0159673i
$286$		0			0
$287$	11.9881	+	16.8112i	0.707636	+	0.992334i
$288$		0			0
$289$	6.07937	+	10.5298i	0.357610	+	0.619399i
$290$		0			0
$291$	4.80647	+	13.8665i	0.281760	+	0.812869i
$292$		0			0
$293$	6.26345	−	10.8486i	0.365915	−	0.633783i	−0.623008	−	0.782216i	$-0.714089\pi$
$293$	6.26345	−	10.8486i	0.365915	−	0.633783i	0.988923	+	0.148433i	$0.0474228\pi$
$294$		0			0
$295$	0.840799	+	1.45631i	0.0489532	+	0.0847895i
$296$		0			0
$297$	−2.93833	−	1.88256i	−0.170499	−	0.109237i
$298$		0			0
$299$	6.80314	−	11.7834i	0.393436	−	0.681451i
$300$		0			0
$301$	−19.2842	+	1.85439i	−1.11152	+	0.106886i
$302$		0			0
$303$	−7.77968	−	1.49566i	−0.446931	−	0.0859233i
$304$		0			0
$305$	0.598954	−	1.03742i	0.0342960	−	0.0594025i
$306$		0			0
$307$	25.8747			1.47675			0.738375	−	0.674391i	$-0.235594\pi$
$307$	25.8747			1.47675			0.738375	+	0.674391i	$0.235594\pi$
$308$		0			0
$309$	−3.07375	−	0.590934i	−0.174859	−	0.0336171i
$310$		0			0
$311$	−14.2001	−	24.5952i	−0.805211	−	1.39467i	−0.916148	−	0.400840i	$-0.868718\pi$
$311$	−14.2001	−	24.5952i	−0.805211	−	1.39467i	0.110937	−	0.993827i	$-0.464615\pi$
$312$		0			0
$313$	6.10074	−	10.5668i	0.344834	−	0.597270i	−0.640490	−	0.767967i	$-0.721269\pi$
$313$	6.10074	−	10.5668i	0.344834	−	0.597270i	0.985324	+	0.170697i	$0.0546019\pi$
$314$		0			0
$315$	1.95129	−	1.86651i	0.109943	−	0.105166i
$316$		0			0
$317$	1.97609	−	3.42270i	0.110988	−	0.192238i	−0.805181	−	0.593030i	$-0.797932\pi$
$317$	1.97609	−	3.42270i	0.110988	−	0.192238i	0.916169	+	0.400792i	$0.131265\pi$
$318$		0			0
$319$	−0.321602	−	0.557031i	−0.0180062	−	0.0311877i
$320$		0			0
$321$	4.40406	+	12.7056i	0.245811	+	0.709156i
$322$		0			0
$323$	−1.06531			−0.0592754
$324$		0			0
$325$	−7.93058	+	13.7362i	−0.439909	+	0.761945i
$326$		0			0
$327$	−2.43004	+	2.80705i	−0.134382	+	0.155230i
$328$		0			0
$329$	−4.14602	−	5.81406i	−0.228577	−	0.320540i
$330$		0			0
$331$	4.44143	−	7.69278i	0.244123	−	0.422834i	−0.717762	−	0.696289i	$-0.754833\pi$
$331$	4.44143	−	7.69278i	0.244123	−	0.422834i	0.961885	+	0.273455i	$0.0881666\pi$
$332$		0			0
$333$	4.13903	+	28.5988i	0.226818	+	1.56721i
$334$		0			0
$335$	−2.09567	−	3.62981i	−0.114499	−	0.198318i
$336$		0			0
$337$	−11.9741	+	20.7397i	−0.652269	+	1.12976i	0.330302	+	0.943875i	$0.392849\pi$
$337$	−11.9741	+	20.7397i	−0.652269	+	1.12976i	−0.982571	+	0.185887i	$0.940484\pi$
$338$		0			0
$339$	−17.9344	+	20.7168i	−0.974062	+	1.12518i
$340$		0			0
$341$	0.699335	+	1.21128i	0.0378711	+	0.0655947i
$342$		0			0
$343$	−17.7596	+	5.25329i	−0.958928	+	0.283651i
$344$		0			0
$345$	2.42447	+	0.466110i	0.130529	+	0.0250945i
$346$		0			0
$347$	−4.74529	−	8.21909i	−0.254741	−	0.441224i	0.710084	−	0.704117i	$-0.248657\pi$
$347$	−4.74529	−	8.21909i	−0.254741	−	0.441224i	−0.964825	+	0.262893i	$0.915323\pi$
$348$		0			0
$349$	4.26145	+	7.38104i	0.228110	+	0.395098i	0.957248	−	0.289269i	$-0.0934121\pi$
$349$	4.26145	+	7.38104i	0.228110	+	0.395098i	−0.729138	+	0.684367i	$0.760079\pi$
$350$		0			0
$351$	14.9874	−	7.75302i	0.799968	−	0.413825i
$352$		0			0
$353$	−37.1744			−1.97859			−0.989297	−	0.145919i	$-0.953386\pi$
$353$	−37.1744			−1.97859			−0.989297	+	0.145919i	$0.953386\pi$
$354$		0			0
$355$	−1.89595			−0.100627
$356$		0			0
$357$	4.19900	+	9.16705i	0.222234	+	0.485172i
$358$		0			0
$359$	−5.30964	−	9.19657i	−0.280232	−	0.485376i	0.691210	−	0.722654i	$-0.257078\pi$
$359$	−5.30964	−	9.19657i	−0.280232	−	0.485376i	−0.971442	+	0.237278i	$0.923745\pi$
$360$		0			0
$361$	9.38279	−	16.2515i	0.493831	−	0.855340i
$362$		0			0
$363$	−17.9428	−	3.44953i	−0.941751	−	0.181054i
$364$		0			0
$365$	−1.26448	+	2.19014i	−0.0661857	+	0.114637i
$366$		0			0
$367$	22.3598			1.16717			0.583586	−	0.812051i	$-0.301649\pi$
$367$	22.3598			1.16717			0.583586	+	0.812051i	$0.301649\pi$
$368$		0			0
$369$	−18.3899	+	14.4897i	−0.957341	+	0.754303i
$370$		0			0
$371$	18.8124	+	26.3811i	0.976693	+	1.36964i
$372$		0			0
$373$	−17.5853			−0.910532			−0.455266	−	0.890356i	$-0.650456\pi$
$373$	−17.5853			−0.910532			−0.455266	+	0.890356i	$0.650456\pi$
$374$		0			0
$375$	−5.71950	−	1.09959i	−0.295354	−	0.0567824i
$376$		0			0
$377$	3.11015			0.160181
$378$		0			0
$379$	10.0443			0.515939			0.257969	−	0.966153i	$-0.416947\pi$
$379$	10.0443			0.515939			0.257969	+	0.966153i	$0.416947\pi$
$380$		0			0
$381$	−23.6120	−	4.53945i	−1.20968	−	0.232563i
$382$		0			0
$383$	−7.87238			−0.402260			−0.201130	−	0.979565i	$-0.564461\pi$
$383$	−7.87238			−0.402260			−0.201130	+	0.979565i	$0.564461\pi$
$384$		0			0
$385$	−0.250746	+	0.550027i	−0.0127792	+	0.0280320i
$386$		0			0
$387$	−3.14646	−	21.7406i	−0.159944	−	1.10514i
$388$		0			0
$389$	−3.64835			−0.184979			−0.0924893	−	0.995714i	$-0.529482\pi$
$389$	−3.64835			−0.184979			−0.0924893	+	0.995714i	$0.529482\pi$
$390$		0			0
$391$	−4.60949	+	7.98387i	−0.233112	+	0.403762i
$392$		0			0
$393$	−7.10192	−	1.36536i	−0.358244	−	0.0688732i
$394$		0			0
$395$	1.70317	−	2.94997i	0.0856956	−	0.148429i
$396$		0			0
$397$	6.56071	+	11.3635i	0.329272	+	0.570317i	0.982368	−	0.186959i	$-0.0598632\pi$
$397$	6.56071	+	11.3635i	0.329272	+	0.570317i	−0.653095	+	0.757276i	$0.726530\pi$
$398$		0			0
$399$	2.20893	+	0.208405i	0.110585	+	0.0104333i
$400$		0			0
$401$	11.4374			0.571159			0.285579	−	0.958355i	$-0.407814\pi$
$401$	11.4374			0.571159			0.285579	+	0.958355i	$0.407814\pi$
$402$		0			0
$403$	−6.76313			−0.336896
$404$		0			0
$405$	2.21986	+	2.10876i	0.110305	+	0.104785i
$406$		0			0
$407$	−3.23445	−	5.60224i	−0.160326	−	0.277693i
$408$		0			0
$409$	9.24106	+	16.0060i	0.456941	+	0.791445i	0.998797	−	0.0490262i	$-0.0156118\pi$
$409$	9.24106	+	16.0060i	0.456941	+	0.791445i	−0.541857	+	0.840471i	$0.682278\pi$
$410$		0			0
$411$	−21.7050	−	4.17283i	−1.07063	−	0.205830i
$412$		0			0
$413$	13.0178	−	1.25181i	0.640565	−	0.0615975i
$414$		0			0
$415$	0.841574	+	1.45765i	0.0413112	+	0.0715531i
$416$		0			0
$417$	13.5127	−	15.6092i	0.661720	−	0.764384i
$418$		0			0
$419$	−10.6290	+	18.4099i	−0.519260	+	0.899385i	0.480489	+	0.877001i	$0.340459\pi$
$419$	−10.6290	+	18.4099i	−0.519260	+	0.899385i	−0.999749	+	0.0223843i	$0.992874\pi$
$420$		0			0
$421$	−8.60478	−	14.9039i	−0.419371	−	0.726373i	0.576505	−	0.817094i	$-0.304416\pi$
$421$	−8.60478	−	14.9039i	−0.419371	−	0.726373i	−0.995876	+	0.0907211i	$0.971083\pi$
$422$		0			0
$423$	6.36005	−	5.01118i	0.309236	−	0.243652i
$424$		0			0
$425$	5.37339	−	9.30698i	0.260648	−	0.451455i
$426$		0			0
$427$	−5.40898	−	7.58514i	−0.261759	−	0.367071i
$428$		0			0
$429$	−2.47238	+	2.85596i	−0.119368	+	0.137887i
$430$		0			0
$431$	3.02962	−	5.24745i	0.145931	−	0.252761i	−0.783789	−	0.621028i	$-0.786715\pi$
$431$	3.02962	−	5.24745i	0.145931	−	0.252761i	0.929720	+	0.368267i	$0.120049\pi$
$432$		0			0
$433$	−17.6963			−0.850432			−0.425216	−	0.905092i	$-0.639802\pi$
$433$	−17.6963			−0.850432			−0.425216	+	0.905092i	$0.639802\pi$
$434$		0			0
$435$	0.184825	+	0.533216i	0.00886170	+	0.0255657i
$436$		0			0
$437$	1.01431	+	1.75684i	0.0485210	+	0.0840409i
$438$		0			0
$439$	−13.6687	+	23.6748i	−0.652370	+	1.12994i	0.330177	+	0.943919i	$0.392892\pi$
$439$	−13.6687	+	23.6748i	−0.652370	+	1.12994i	−0.982546	+	0.186018i	$0.940442\pi$
$440$		0			0
$441$	−6.91332	−	19.8294i	−0.329206	−	0.944258i
$442$		0			0
$443$	−0.958856	+	1.66079i	−0.0455566	+	0.0789064i	−0.887905	−	0.460028i	$-0.847839\pi$
$443$	−0.958856	+	1.66079i	−0.0455566	+	0.0789064i	0.842348	+	0.538934i	$0.181173\pi$
$444$		0			0
$445$	−2.89911	−	5.02140i	−0.137431	−	0.238037i
$446$		0			0
$447$	−18.2863	−	3.51559i	−0.864914	−	0.166281i
$448$		0			0
$449$	28.3249			1.33674			0.668368	−	0.743831i	$-0.266993\pi$
$449$	28.3249			1.33674			0.668368	+	0.743831i	$0.266993\pi$
$450$		0			0
$451$	2.62058	−	4.53898i	0.123398	−	0.213732i
$452$		0			0
$453$	−4.39002	−	0.843991i	−0.206261	−	0.0396541i
$454$		0			0
$455$	−1.69706	−	2.37982i	−0.0795592	−	0.111568i
$456$		0			0
$457$	−6.50427	+	11.2657i	−0.304257	+	0.526988i	−0.977096	−	0.212801i	$-0.931741\pi$
$457$	−6.50427	+	11.2657i	−0.304257	+	0.526988i	0.672839	+	0.739789i	$0.265075\pi$
$458$		0			0
$459$	−10.1548	+	5.25308i	−0.473983	+	0.245193i
$460$		0			0
$461$	−11.8278	−	20.4863i	−0.550875	−	0.954144i	−0.998212	−	0.0597782i	$-0.980961\pi$
$461$	−11.8278	−	20.4863i	−0.550875	−	0.954144i	0.447336	−	0.894366i	$-0.352373\pi$
$462$		0			0
$463$	−20.2403	+	35.0572i	−0.940647	+	1.62925i	−0.176406	+	0.984317i	$0.556447\pi$
$463$	−20.2403	+	35.0572i	−0.940647	+	1.62925i	−0.764241	+	0.644931i	$0.776886\pi$
$464$		0			0
$465$	−0.401910	−	1.15950i	−0.0186381	−	0.0537704i
$466$		0			0
$467$	−18.6010	−	32.2179i	−0.860753	−	1.49087i	−0.871203	−	0.490923i	$-0.836659\pi$
$467$	−18.6010	−	32.2179i	−0.860753	−	1.49087i	0.0104492	−	0.999945i	$-0.496674\pi$
$468$		0			0
$469$	−32.4466	+	3.12011i	−1.49825	+	0.144073i
$470$		0			0
$471$	−4.53633	−	13.0872i	−0.209023	−	0.603025i
$472$		0			0
$473$	2.45881	+	4.25878i	0.113056	+	0.195819i
$474$		0			0
$475$	−1.18240	−	2.04799i	−0.0542525	−	0.0939680i
$476$		0			0
$477$	−28.8585	+	22.7381i	−1.32134	+	1.04110i
$478$		0			0
$479$	40.5835			1.85431			0.927154	−	0.374681i	$-0.122248\pi$
$479$	40.5835			1.85431			0.927154	+	0.374681i	$0.122248\pi$
$480$		0			0
$481$	31.2798			1.42624
$482$		0			0
$483$	11.1197	−	15.6529i	0.505964	−	0.712231i
$484$		0			0
$485$	1.44128	+	2.49637i	0.0654452	+	0.113354i
$486$		0			0
$487$	10.5255	−	18.2307i	0.476956	−	0.826113i	−0.522695	−	0.852520i	$-0.675073\pi$
$487$	10.5255	−	18.2307i	0.476956	−	0.826113i	0.999651	+	0.0264072i	$0.00840666\pi$
$488$		0			0
$489$	4.68904	+	13.5277i	0.212046	+	0.611745i
$490$		0			0
$491$	−4.97925	+	8.62432i	−0.224711	+	0.389210i	−0.956233	−	0.292608i	$-0.905477\pi$
$491$	−4.97925	+	8.62432i	−0.224711	+	0.389210i	0.731522	+	0.681818i	$0.238810\pi$
$492$		0			0
$493$	−2.10729			−0.0949077
$494$		0			0
$495$	−0.636561	−	0.254154i	−0.0286113	−	0.0114234i
$496$		0			0
$497$	−6.11630	+	13.4165i	−0.274354	+	0.601812i
$498$		0			0
$499$	22.6301			1.01306			0.506531	−	0.862222i	$-0.330928\pi$
$499$	22.6301			1.01306			0.506531	+	0.862222i	$0.330928\pi$
$500$		0			0
$501$	20.3916	−	23.5553i	0.911030	−	1.05237i
$502$		0			0
$503$	−43.4520			−1.93743			−0.968714	−	0.248179i	$-0.920168\pi$
$503$	−43.4520			−1.93743			−0.968714	+	0.248179i	$0.920168\pi$
$504$		0			0
$505$	−1.55602			−0.0692422
$506$		0			0
$507$	1.39228	+	4.01669i	0.0618334	+	0.178387i
$508$		0			0
$509$	−9.55477			−0.423508			−0.211754	−	0.977323i	$-0.567918\pi$
$509$	−9.55477			−0.423508			−0.211754	+	0.977323i	$0.567918\pi$
$510$		0			0
$511$	11.4191	+	16.0133i	0.505152	+	0.708386i
$512$		0			0
$513$	−0.116202	+	2.51313i	−0.00513046	+	0.110957i
$514$		0			0
$515$	−0.614785			−0.0270906
$516$		0			0
$517$	−0.906312	+	1.56978i	−0.0398596	+	0.0690388i
$518$		0			0
$519$	19.2700	−	22.2597i	0.845860	−	0.977092i
$520$		0			0
$521$	0.581462	−	1.00712i	0.0254743	−	0.0441228i	−0.853007	−	0.521899i	$-0.825224\pi$
$521$	0.581462	−	1.00712i	0.0254743	−	0.0441228i	0.878482	+	0.477776i	$0.158557\pi$
$522$		0			0
$523$	−3.20567	−	5.55239i	−0.140174	−	0.242789i	0.787388	−	0.616458i	$-0.211433\pi$
$523$	−3.20567	−	5.55239i	−0.140174	−	0.242789i	−0.927562	+	0.373669i	$0.878100\pi$
$524$		0			0
$525$	−12.9625	+	18.2469i	−0.565729	+	0.796361i
$526$		0			0
$527$	4.58238			0.199612
$528$		0			0
$529$	−5.44474			−0.236728
$530$		0			0
$531$	2.12402	+	14.6760i	0.0921746	+	0.636884i
$532$		0			0
$533$	12.6716	+	21.9478i	0.548866	+	0.950665i
$534$		0			0
$535$	1.32061	+	2.28737i	0.0570952	+	0.0988917i
$536$		0			0
$537$	−21.8810	+	25.2757i	−0.944233	+	1.09073i
$538$		0			0
$539$	3.08331	+	3.54876i	0.132808	+	0.152856i
$540$		0			0
$541$	−7.37443	−	12.7729i	−0.317052	−	0.549150i	0.662820	−	0.748779i	$-0.269360\pi$
$541$	−7.37443	−	12.7729i	−0.317052	−	0.549150i	−0.979871	+	0.199629i	$0.936026\pi$
$542$		0			0
$543$	37.3587	+	7.18229i	1.60322	+	0.308221i
$544$		0			0
$545$	−0.364621	+	0.631542i	−0.0156187	+	0.0270523i
$546$		0			0
$547$	6.57905	+	11.3952i	0.281300	+	0.487226i	0.971705	−	0.236197i	$-0.0759011\pi$
$547$	6.57905	+	11.3952i	0.281300	+	0.487226i	−0.690405	+	0.723423i	$0.742568\pi$
$548$		0			0
$549$	8.29745	−	6.53768i	0.354126	−	0.279021i
$550$		0			0
$551$	−0.231853	+	0.401581i	−0.00987727	+	0.0171079i
$552$		0			0
$553$	−15.3808	−	21.5689i	−0.654058	−	0.917201i
$554$		0			0
$555$	1.85885	+	5.36273i	0.0789038	+	0.227635i
$556$		0			0
$557$	−12.1869	+	21.1083i	−0.516374	+	0.894385i	0.483446	+	0.875374i	$0.339385\pi$
$557$	−12.1869	+	21.1083i	−0.516374	+	0.894385i	−0.999819	+	0.0190111i	$0.993948\pi$
$558$		0			0
$559$	−23.7787			−1.00573
$560$		0			0
$561$	1.67517	−	1.93506i	0.0707256	−	0.0816984i
$562$		0			0
$563$	1.55982	+	2.70169i	0.0657388	+	0.113863i	0.897021	−	0.441987i	$-0.145726\pi$
$563$	1.55982	+	2.70169i	0.0657388	+	0.113863i	−0.831283	+	0.555850i	$0.812393\pi$
$564$		0			0
$565$	−2.69100	+	4.66096i	−0.113211	+	0.196088i
$566$		0			0
$567$	22.0836	−	8.90576i	0.927426	−	0.374007i
$568$		0			0
$569$	10.7384	−	18.5995i	0.450179	−	0.779733i	−0.548218	−	0.836336i	$-0.684693\pi$
$569$	10.7384	−	18.5995i	0.450179	−	0.779733i	0.998397	+	0.0566027i	$0.0180268\pi$
$570$		0			0
$571$	−16.5230	−	28.6187i	−0.691466	−	1.19765i	−0.971358	−	0.237623i	$-0.923632\pi$
$571$	−16.5230	−	28.6187i	−0.691466	−	1.19765i	0.279891	−	0.960032i	$-0.409702\pi$
$572$		0			0
$573$	−7.54717	+	8.71808i	−0.315287	+	0.364203i
$574$		0			0
$575$	−20.4646			−0.853432
$576$		0			0
$577$	0.904826	−	1.56720i	0.0376684	−	0.0652436i	−0.846577	−	0.532267i	$-0.821340\pi$
$577$	0.904826	−	1.56720i	0.0376684	−	0.0652436i	0.884245	+	0.467023i	$0.154674\pi$
$578$		0			0
$579$	−3.60156	−	10.3904i	−0.149676	−	0.431810i
$580$		0			0
$581$	13.0298	−	1.25296i	0.540567	−	0.0519816i
$582$		0			0
$583$	4.11236	−	7.12282i	0.170317	−	0.294997i
$584$		0			0
$585$	2.60331	−	2.05118i	0.107634	−	0.0848060i
$586$		0			0
$587$	1.65901	+	2.87349i	0.0684746	+	0.118601i	0.898230	−	0.439526i	$-0.144853\pi$
$587$	1.65901	+	2.87349i	0.0684746	+	0.118601i	−0.829755	+	0.558127i	$0.811520\pi$
$588$		0			0
$589$	0.504173	−	0.873253i	0.0207741	−	0.0359818i
$590$		0			0
$591$	40.5005	+	7.78631i	1.66597	+	0.320286i
$592$		0			0
$593$	15.3784	+	26.6362i	0.631516	+	1.09382i	0.987242	+	0.159228i	$0.0509005\pi$
$593$	15.3784	+	26.6362i	0.631516	+	1.09382i	−0.355726	+	0.934590i	$0.615766\pi$
$594$		0			0
$595$	1.14985	+	1.61246i	0.0471391	+	0.0661042i
$596$		0			0
$597$	−23.7545	+	27.4400i	−0.972209	+	1.12304i
$598$		0			0
$599$	−6.98523	−	12.0988i	−0.285409	−	0.494342i	0.687299	−	0.726374i	$-0.258796\pi$
$599$	−6.98523	−	12.0988i	−0.285409	−	0.494342i	−0.972708	+	0.232032i	$0.925463\pi$
$600$		0			0
$601$	−7.50432	−	12.9979i	−0.306108	−	0.530194i	0.671400	−	0.741096i	$-0.265693\pi$
$601$	−7.50432	−	12.9979i	−0.306108	−	0.530194i	−0.977507	+	0.210901i	$0.932360\pi$
$602$		0			0
$603$	−5.29408	−	36.5796i	−0.215591	−	1.48964i
$604$		0			0
$605$	−3.58876			−0.145904
$606$		0			0
$607$	23.3289			0.946889			0.473444	−	0.880824i	$-0.343010\pi$
$607$	23.3289			0.946889			0.473444	+	0.880824i	$0.343010\pi$
$608$		0			0
$609$	4.36949	+	0.412247i	0.177061	+	0.0167051i
$610$		0			0
$611$	−4.38239	−	7.59052i	−0.177292	−	0.307080i
$612$		0			0
$613$	22.3374	−	38.6895i	0.902198	−	1.56265i	0.0775635	−	0.996987i	$-0.475286\pi$
$613$	22.3374	−	38.6895i	0.902198	−	1.56265i	0.824635	−	0.565666i	$-0.191381\pi$
$614$		0			0
$615$	−3.00979	+	3.47674i	−0.121366	+	0.140196i
$616$		0			0
$617$	−1.18488	+	2.05227i	−0.0477013	+	0.0826212i	−0.888890	−	0.458120i	$-0.848523\pi$
$617$	−1.18488	+	2.05227i	−0.0477013	+	0.0826212i	0.841189	+	0.540741i	$0.181856\pi$
$618$		0			0
$619$	−22.7727			−0.915311			−0.457655	−	0.889130i	$-0.651311\pi$
$619$	−22.7727			−0.915311			−0.457655	+	0.889130i	$0.651311\pi$
$620$		0			0
$621$	18.3316	+	11.7449i	0.735623	+	0.471308i
$622$		0			0
$623$	−44.8859	+	4.31629i	−1.79832	+	0.172928i
$624$		0			0
$625$	23.2774			0.931094
$626$		0			0
$627$	−0.184451	−	0.532136i	−0.00736627	−	0.0212515i
$628$		0			0
$629$	−21.1937			−0.845049
$630$		0			0
$631$	17.8652			0.711201			0.355600	−	0.934638i	$-0.384276\pi$
$631$	17.8652			0.711201			0.355600	+	0.934638i	$0.384276\pi$
$632$		0			0
$633$	−14.3390	+	16.5637i	−0.569925	+	0.658347i
$634$		0			0
$635$	−4.72267			−0.187413
$636$		0			0
$637$	−22.3152	+	4.33178i	−0.884162	+	0.171631i
$638$		0			0
$639$	−15.5273	−	6.19943i	−0.614249	−	0.245246i
$640$		0			0
$641$	−25.5800			−1.01035			−0.505175	−	0.863017i	$-0.668572\pi$
$641$	−25.5800			−1.01035			−0.505175	+	0.863017i	$0.668572\pi$
$642$		0			0
$643$	7.99334	−	13.8449i	0.315227	−	0.545989i	−0.664259	−	0.747503i	$-0.731253\pi$
$643$	7.99334	−	13.8449i	0.315227	−	0.545989i	0.979486	+	0.201514i	$0.0645861\pi$
$644$		0			0
$645$	−1.41308	−	4.07670i	−0.0556401	−	0.160520i
$646$		0			0
$647$	7.47306	−	12.9437i	0.293796	−	0.508870i	−0.680908	−	0.732369i	$-0.738415\pi$
$647$	7.47306	−	12.9437i	0.293796	−	0.508870i	0.974704	+	0.223499i	$0.0717479\pi$
$648$		0			0
$649$	−1.65982	−	2.87489i	−0.0651536	−	0.112849i
$650$		0			0
$651$	−9.50162	−	0.896446i	−0.372398	−	0.0351345i
$652$		0			0
$653$	−9.65770			−0.377935			−0.188967	−	0.981983i	$-0.560514\pi$
$653$	−9.65770			−0.377935			−0.188967	+	0.981983i	$0.560514\pi$
$654$		0			0
$655$	−1.42047			−0.0555022
$656$		0			0
$657$	−17.5171	+	13.8020i	−0.683406	+	0.538466i
$658$		0			0
$659$	9.80353	+	16.9802i	0.381891	+	0.661455i	0.991333	−	0.131376i	$-0.0419396\pi$
$659$	9.80353	+	16.9802i	0.381891	+	0.661455i	−0.609441	+	0.792831i	$0.708606\pi$
$660$		0			0
$661$	5.13275	+	8.89018i	0.199641	+	0.345788i	0.948412	−	0.317041i	$-0.102689\pi$
$661$	5.13275	+	8.89018i	0.199641	+	0.345788i	−0.748771	+	0.662829i	$0.769356\pi$
$662$		0			0
$663$	4.05318	+	11.6933i	0.157413	+	0.454131i
$664$		0			0
$665$	0.433792	−	0.0417140i	0.0168217	−	0.00161760i
$666$		0			0
$667$	2.00641	+	3.47520i	0.0776885	+	0.134560i
$668$		0			0
$669$	−1.52516	−	4.40004i	−0.0589660	−	0.170115i
$670$		0			0
$671$	−1.18239	+	2.04797i	−0.0456458	+	0.0790608i
$672$		0			0
$673$	−17.1584	−	29.7191i	−0.661406	−	1.14559i	−0.980246	−	0.197780i	$-0.936627\pi$
$673$	−17.1584	−	29.7191i	−0.661406	−	1.14559i	0.318840	−	0.947808i	$-0.396707\pi$
$674$		0			0
$675$	−21.3696	−	13.6913i	−0.822517	−	0.526980i
$676$		0			0
$677$	−3.73709	+	6.47283i	−0.143628	+	0.248771i	−0.928860	−	0.370430i	$-0.879210\pi$
$677$	−3.73709	+	6.47283i	−0.143628	+	0.248771i	0.785232	+	0.619201i	$0.212544\pi$
$678$		0			0
$679$	22.3149	−	2.14583i	0.856367	−	0.0823493i
$680$		0			0
$681$	47.6056	+	9.15228i	1.82425	+	0.350716i
$682$		0			0
$683$	−18.1577	+	31.4501i	−0.694786	+	1.20340i	0.275467	+	0.961310i	$0.411167\pi$
$683$	−18.1577	+	31.4501i	−0.694786	+	1.20340i	−0.970253	+	0.242094i	$0.922166\pi$
$684$		0			0
$685$	−4.34125			−0.165871
$686$		0			0
$687$	41.7384	+	8.02429i	1.59242	+	0.306146i
$688$		0			0
$689$	19.8850	+	34.4417i	0.757556	+	1.31213i
$690$		0			0
$691$	−25.4812	+	44.1347i	−0.969350	+	1.67896i	−0.271906	+	0.962324i	$0.587654\pi$
$691$	−25.4812	+	44.1347i	−0.969350	+	1.67896i	−0.697444	+	0.716640i	$0.745679\pi$
$692$		0			0
$693$	−3.85203	+	3.68466i	−0.146327	+	0.139969i
$694$		0			0
$695$	2.02755	−	3.51181i	0.0769092	−	0.133211i
$696$		0			0
$697$	−8.58566	−	14.8708i	−0.325205	−	0.563272i
$698$		0			0
$699$	−5.23971	−	15.1164i	−0.198184	−	0.571755i
$700$		0			0
$701$	36.6075			1.38265			0.691324	−	0.722545i	$-0.257028\pi$
$701$	36.6075			1.38265			0.691324	+	0.722545i	$0.257028\pi$
$702$		0			0
$703$	−2.33182	+	4.03883i	−0.0879463	+	0.152327i
$704$		0			0
$705$	1.04092	−	1.20241i	0.0392032	−	0.0452854i
$706$		0			0
$707$	−5.01971	+	11.0111i	−0.188786	+	0.414113i
$708$		0			0
$709$	2.93789	−	5.08858i	0.110335	−	0.191106i	−0.805570	−	0.592500i	$-0.798141\pi$
$709$	2.93789	−	5.08858i	0.110335	−	0.191106i	0.915905	+	0.401394i	$0.131474\pi$
$710$		0			0
$711$	23.5944	−	18.5903i	0.884857	−	0.697192i
$712$		0			0
$713$	−4.36301	−	7.55695i	−0.163396	−	0.283010i
$714$		0			0
$715$	−0.370973	+	0.642545i	−0.0138736	+	0.0240298i
$716$		0			0
$717$	31.7707	−	36.6998i	1.18650	−	1.37058i
$718$		0			0
$719$	−8.09642	−	14.0234i	−0.301945	−	0.522985i	0.674631	−	0.738155i	$-0.264303\pi$
$719$	−8.09642	−	14.0234i	−0.301945	−	0.522985i	−0.976577	+	0.215170i	$0.930969\pi$
$720$		0			0
$721$	−1.98328	+	4.35046i	−0.0738614	+	0.162020i
$722$		0			0
$723$	33.7259	+	6.48387i	1.25428	+	0.241138i
$724$		0			0
$725$	−2.33892	−	4.05112i	−0.0868652	−	0.150455i
$726$		0			0
$727$	−22.8771	−	39.6243i	−0.848464	−	1.46958i	−0.882578	−	0.470166i	$-0.844194\pi$
$727$	−22.8771	−	39.6243i	−0.848464	−	1.46958i	0.0341138	−	0.999418i	$-0.489139\pi$
$728$		0			0
$729$	11.2847	+	24.5287i	0.417951	+	0.908470i
$730$		0			0
$731$	16.1113			0.595898
$732$		0			0
$733$	27.1833			1.00404			0.502019	−	0.864857i	$-0.332591\pi$
$733$	27.1833			1.00404			0.502019	+	0.864857i	$0.332591\pi$
$734$		0			0
$735$	−2.06877	−	3.56839i	−0.0763079	−	0.131622i
$736$		0			0
$737$	4.13706	+	7.16560i	0.152391	+	0.263948i
$738$		0			0
$739$	12.1738	−	21.0856i	0.447821	−	0.775648i	−0.550423	−	0.834886i	$-0.685534\pi$
$739$	12.1738	−	21.0856i	0.447821	−	0.775648i	0.998244	+	0.0592377i	$0.0188670\pi$
$740$		0			0
$741$	2.67431	+	0.514142i	0.0982433	+	0.0188875i
$742$		0			0
$743$	−0.0683178	+	0.118330i	−0.00250634	+	0.00434110i	−0.867276	−	0.497828i	$-0.834131\pi$
$743$	−0.0683178	+	0.118330i	−0.00250634	+	0.00434110i	0.864770	+	0.502169i	$0.167464\pi$
$744$		0			0
$745$	−3.65748			−0.134000
$746$		0			0
$747$	2.12598	+	14.6895i	0.0777854	+	0.537461i
$748$		0			0
$749$	20.4466	−	1.96617i	0.747104	−	0.0718424i
$750$		0			0
$751$	7.42893			0.271085			0.135543	−	0.990772i	$-0.456722\pi$
$751$	7.42893			0.271085			0.135543	+	0.990772i	$0.456722\pi$
$752$		0			0
$753$	28.1940	+	5.42036i	1.02745	+	0.197529i
$754$		0			0
$755$	−0.878055			−0.0319557
$756$		0			0
$757$	−14.0794			−0.511723			−0.255861	−	0.966713i	$-0.582359\pi$
$757$	−14.0794			−0.511723			−0.255861	+	0.966713i	$0.582359\pi$
$758$		0			0
$759$	−4.78614	−	0.920146i	−0.173726	−	0.0333992i
$760$		0			0
$761$	38.7232			1.40372			0.701858	−	0.712317i	$-0.252354\pi$
$761$	38.7232			1.40372			0.701858	+	0.712317i	$0.252354\pi$
$762$		0			0
$763$	3.29278	+	4.61755i	0.119207	+	0.167167i
$764$		0			0
$765$	−1.76388	+	1.38979i	−0.0637732	+	0.0502478i
$766$		0			0
$767$	16.0518			0.579597
$768$		0			0
$769$	5.14295	−	8.90786i	0.185460	−	0.321226i	−0.758272	−	0.651939i	$-0.773956\pi$
$769$	5.14295	−	8.90786i	0.185460	−	0.321226i	0.943731	+	0.330713i	$0.107289\pi$
$770$		0			0
$771$	12.4081	+	2.38548i	0.446867	+	0.0859111i
$772$		0			0
$773$	−22.6768	+	39.2773i	−0.815627	+	1.41271i	0.0932501	+	0.995643i	$0.470274\pi$
$773$	−22.6768	+	39.2773i	−0.815627	+	1.41271i	−0.908877	+	0.417064i	$0.863059\pi$
$774$		0			0
$775$	5.08606	+	8.80931i	0.182697	+	0.316440i
$776$		0			0
$777$	43.9454	+	4.14610i	1.57653	+	0.148741i
$778$		0			0
$779$	−3.77852			−0.135380
$780$		0			0
$781$	3.74279			0.133927
$782$		0			0
$783$	−0.229860	+	4.97123i	−0.00821453	+	0.177657i
$784$		0			0
$785$	−1.36028	−	2.35607i	−0.0485504	−	0.0840917i
$786$		0			0
$787$	−13.0543	−	22.6108i	−0.465337	−	0.805988i	0.533879	−	0.845561i	$-0.320734\pi$
$787$	−13.0543	−	22.6108i	−0.465337	−	0.805988i	−0.999217	+	0.0395728i	$0.987400\pi$
$788$		0			0
$789$	−45.5499	−	8.75706i	−1.62162	−	0.311759i
$790$		0			0
$791$	24.3017	+	34.0788i	0.864067	+	1.21170i
$792$		0			0
$793$	−5.71735	−	9.90274i	−0.203029	−	0.351657i
$794$		0			0
$795$	−4.72313	+	5.45591i	−0.167512	+	0.193501i
$796$		0			0
$797$	−16.1618	+	27.9931i	−0.572481	+	0.991567i	0.423829	+	0.905742i	$0.360686\pi$
$797$	−16.1618	+	27.9931i	−0.572481	+	0.991567i	−0.996310	+	0.0858244i	$0.972648\pi$
$798$		0			0
$799$	2.96930	+	5.14298i	0.105046	+	0.181946i
$800$		0			0
$801$	−7.32370	−	50.6034i	−0.258770	−	1.78798i
$802$		0			0
$803$	2.49620	−	4.32354i	0.0880889	−	0.152574i
$804$		0			0
$805$	1.56435	−	3.43151i	0.0551362	−	0.120945i
$806$		0			0
$807$	23.0789	−	26.6595i	0.812416	−	0.938459i
$808$		0			0
$809$	22.4553	−	38.8938i	0.789488	−	1.36743i	−0.136793	−	0.990600i	$-0.543680\pi$
$809$	22.4553	−	38.8938i	0.789488	−	1.36743i	0.926281	−	0.376833i	$-0.122987\pi$
$810$		0			0
$811$	42.8204			1.50363			0.751813	−	0.659376i	$-0.229180\pi$
$811$	42.8204			1.50363			0.751813	+	0.659376i	$0.229180\pi$
$812$		0			0
$813$	6.19268	+	17.8657i	0.217187	+	0.626578i
$814$		0			0
$815$	1.40607	+	2.43538i	0.0492524	+	0.0853077i
$816$		0			0
$817$	1.77263	−	3.07029i	0.0620166	−	0.107416i
$818$		0			0
$819$	−6.11677	−	25.0391i	−0.213737	−	0.874938i
$820$		0			0
$821$	16.1100	−	27.9033i	0.562242	−	0.973832i	−0.435058	−	0.900402i	$-0.643272\pi$
$821$	16.1100	−	27.9033i	0.562242	−	0.973832i	0.997300	−	0.0734300i	$-0.0233946\pi$
$822$		0			0
$823$	−2.19420	−	3.80047i	−0.0764851	−	0.132476i	0.825246	−	0.564773i	$-0.191036\pi$
$823$	−2.19420	−	3.80047i	−0.0764851	−	0.132476i	−0.901731	+	0.432297i	$0.857703\pi$
$824$		0			0
$825$	5.57932	+	1.07264i	0.194247	+	0.0373444i
$826$		0			0
$827$	−42.0996			−1.46395			−0.731973	−	0.681333i	$-0.761400\pi$
$827$	−42.0996			−1.46395			−0.731973	+	0.681333i	$0.761400\pi$
$828$		0			0
$829$	−5.55838	+	9.62739i	−0.193050	+	0.334373i	−0.946260	−	0.323408i	$-0.895171\pi$
$829$	−5.55838	+	9.62739i	−0.193050	+	0.334373i	0.753209	+	0.657781i	$0.228505\pi$
$830$		0			0
$831$	30.0614	+	5.77936i	1.04282	+	0.200484i
$832$		0			0
$833$	15.1198	−	2.93501i	0.523869	−	0.101692i
$834$		0			0
$835$	3.05970	−	5.29956i	0.105885	−	0.183399i
$836$		0			0
$837$	0.499839	−	10.8101i	0.0172770	−	0.373652i
$838$		0			0
$839$	−27.2669	−	47.2277i	−0.941360	−	1.63048i	−0.762881	−	0.646539i	$-0.776216\pi$
$839$	−27.2669	−	47.2277i	−0.941360	−	1.63048i	−0.178479	−	0.983944i	$-0.557118\pi$
$840$		0			0
$841$	14.0414	−	24.3204i	0.484185	−	0.838633i
$842$		0			0
$843$	8.14146	+	23.4879i	0.280407	+	0.808965i
$844$		0			0
$845$	0.417494	+	0.723120i	0.0143622	+	0.0248761i
$846$		0			0
$847$	−11.5773	+	25.3955i	−0.397800	+	0.872600i
$848$		0			0
$849$	−5.51853	−	15.9208i	−0.189395	−	0.546400i
$850$		0			0
$851$	20.1791	+	34.9512i	0.691731	+	1.19811i
$852$		0			0
$853$	−11.3669	−	19.6880i	−0.389194	−	0.674105i	0.603147	−	0.797630i	$-0.293913\pi$
$853$	−11.3669	−	19.6880i	−0.389194	−	0.674105i	−0.992341	+	0.123526i	$0.960580\pi$
$854$		0			0
$855$	0.0707787	+	0.489048i	0.00242058	+	0.0167251i
$856$		0			0
$857$	11.2386			0.383902			0.191951	−	0.981405i	$-0.438519\pi$
$857$	11.2386			0.383902			0.191951	+	0.981405i	$0.438519\pi$
$858$		0			0
$859$	50.8049			1.73344			0.866720	−	0.498795i	$-0.166224\pi$
$859$	50.8049			1.73344			0.866720	+	0.498795i	$0.166224\pi$
$860$		0			0
$861$	14.8933	+	32.5144i	0.507562	+	1.10809i
$862$		0			0
$863$	−0.340985	−	0.590603i	−0.0116073	−	0.0201044i	0.860163	−	0.510018i	$-0.170361\pi$
$863$	−0.340985	−	0.590603i	−0.0116073	−	0.0201044i	−0.871771	+	0.489914i	$0.837028\pi$
$864$		0			0
$865$	2.89141	−	5.00807i	0.0983110	−	0.170280i
$866$		0			0
$867$	6.89716	+	19.8981i	0.234240	+	0.675775i
$868$		0			0
$869$	−3.36222	+	5.82353i	−0.114055	+	0.197550i
$870$		0			0
$871$	−40.0087			−1.35564
$872$		0			0
$873$	3.64095	+	25.1573i	0.123228	+	0.851446i
$874$		0			0
$875$	−3.69042	+	8.09516i	−0.124759	+	0.273667i
$876$		0			0
$877$	−25.3190			−0.854961			−0.427480	−	0.904025i	$-0.640599\pi$
$877$	−25.3190			−0.854961			−0.427480	+	0.904025i	$0.640599\pi$
$878$		0			0
$879$	14.2010	−	16.4043i	0.478989	−	0.553303i
$880$		0			0
$881$	−30.9482			−1.04267			−0.521335	−	0.853352i	$-0.674566\pi$
$881$	−30.9482			−1.04267			−0.521335	+	0.853352i	$0.674566\pi$
$882$		0			0
$883$	9.48501			0.319196			0.159598	−	0.987182i	$-0.448980\pi$
$883$	9.48501			0.319196			0.159598	+	0.987182i	$0.448980\pi$
$884$		0			0
$885$	0.953902	+	2.75198i	0.0320651	+	0.0925068i
$886$		0			0
$887$	3.94938			0.132607			0.0663036	−	0.997799i	$-0.478879\pi$
$887$	3.94938			0.132607			0.0663036	+	0.997799i	$0.478879\pi$
$888$		0			0
$889$	−15.2352	+	33.4195i	−0.510974	+	1.12085i
$890$		0			0
$891$	−4.38221	−	4.16289i	−0.146809	−	0.139462i
$892$		0			0
$893$	1.30678			0.0437297
$894$		0			0
$895$	−3.28318	+	5.68663i	−0.109745	+	0.190083i
$896$		0			0
$897$	15.4247	−	17.8177i	0.515015	−	0.594917i
$898$		0			0
$899$	0.997305	−	1.72738i	0.0332620	−	0.0576115i
$900$		0			0
$901$	−13.4731	−	23.3361i	−0.448854	−	0.777439i
$902$		0			0
$903$	−33.4070	−	3.15183i	−1.11171	−	0.104886i
$904$		0			0
$905$	7.47217			0.248383
$906$		0			0
$907$	−33.5061			−1.11255			−0.556276	−	0.830998i	$-0.687770\pi$
$907$	−33.5061			−1.11255			−0.556276	+	0.830998i	$0.687770\pi$
$908$		0			0
$909$	−12.7434	−	5.08794i	−0.422671	−	0.168756i
$910$		0			0
$911$	5.26585	+	9.12072i	0.174465	+	0.302183i	0.939976	−	0.341240i	$-0.110847\pi$
$911$	5.26585	+	9.12072i	0.174465	+	0.302183i	−0.765511	+	0.643423i	$0.777514\pi$
$912$		0			0
$913$	−1.66135	−	2.87754i	−0.0549826	−	0.0952326i
$914$		0			0
$915$	1.35800	−	1.56869i	0.0448941	−	0.0518593i
$916$		0			0
$917$	−4.58240	+	10.0518i	−0.151324	+	0.331939i
$918$		0			0
$919$	1.81600	+	3.14540i	0.0599042	+	0.103757i	0.894422	−	0.447224i	$-0.147587\pi$
$919$	1.81600	+	3.14540i	0.0599042	+	0.103757i	−0.834518	+	0.550981i	$0.814254\pi$
$920$		0			0
$921$	44.0104	+	8.46109i	1.45019	+	0.278802i
$922$		0			0
$923$	−9.04894	+	15.6732i	−0.297850	+	0.515891i
$924$		0			0
$925$	−23.5232	−	40.7435i	−0.773440	−	1.33964i
$926$		0			0
$927$	−5.03491	−	2.01024i	−0.165368	−	0.0660250i
$928$		0			0
$929$	−6.80291	+	11.7830i	−0.223196	+	0.386587i	−0.955777	−	0.294093i	$-0.904982\pi$
$929$	−6.80291	+	11.7830i	−0.223196	+	0.386587i	0.732581	+	0.680680i	$0.238316\pi$
$930$		0			0
$931$	1.10422	−	3.20426i	0.0361894	−	0.105015i
$932$		0			0
$933$	−16.1102	−	46.4775i	−0.527425	−	1.52161i
$934$		0			0
$935$	0.251354	−	0.435358i	0.00822016	−	0.0142377i
$936$		0			0
$937$	9.98770			0.326284			0.163142	−	0.986603i	$-0.447837\pi$
$937$	9.98770			0.326284			0.163142	+	0.986603i	$0.447837\pi$
$938$		0			0
$939$	13.8321	−	15.9781i	0.451394	−	0.521426i
$940$		0			0
$941$	−17.3105	−	29.9826i	−0.564305	−	0.977405i	−0.997114	−	0.0759195i	$-0.975811\pi$
$941$	−17.3105	−	29.9826i	−0.564305	−	0.977405i	0.432809	−	0.901486i	$-0.357523\pi$
$942$		0			0
$943$	−16.3493	+	28.3178i	−0.532405	+	0.922153i
$944$		0			0
$945$	3.92930	−	2.53667i	0.127820	−	0.0825179i
$946$		0			0
$947$	−24.6085	+	42.6232i	−0.799670	+	1.38507i	0.120161	+	0.992754i	$0.461659\pi$
$947$	−24.6085	+	42.6232i	−0.799670	+	1.38507i	−0.919831	+	0.392315i	$0.871674\pi$
$948$		0			0
$949$	12.0701	+	20.9061i	0.391813	+	0.678640i
$950$		0			0
$951$	4.48037	−	5.17548i	0.145286	−	0.167827i
$952$		0			0
$953$	14.2310			0.460987			0.230494	−	0.973074i	$-0.425966\pi$
$953$	14.2310			0.460987			0.230494	+	0.973074i	$0.425966\pi$
$954$		0			0
$955$	−1.13243	+	1.96143i	−0.0366446	+	0.0634704i
$956$		0			0
$957$	−0.364863	−	1.05262i	−0.0117944	−	0.0340263i
$958$		0			0
$959$	−14.0048	+	30.7204i	−0.452238	+	0.992013i
$960$		0			0
$961$	13.3313	−	23.0905i	0.430043	−	0.744856i
$962$		0			0
$963$	3.33613	+	23.0511i	0.107505	+	0.742811i
$964$		0			0
$965$	−1.07998	−	1.87057i	−0.0347657	−	0.0602159i
$966$		0			0
$967$	−19.4246	+	33.6443i	−0.624652	+	1.08193i	0.363956	+	0.931416i	$0.381426\pi$
$967$	−19.4246	+	33.6443i	−0.624652	+	1.08193i	−0.988608	+	0.150513i	$0.951908\pi$
$968$		0			0
$969$	−1.81199	−	0.348359i	−0.0582095	−	0.0111909i
$970$		0			0
$971$	−4.13629	−	7.16427i	−0.132740	−	0.229912i	0.791992	−	0.610532i	$-0.209044\pi$
$971$	−4.13629	−	7.16427i	−0.132740	−	0.229912i	−0.924732	+	0.380619i	$0.875711\pi$
$972$		0			0
$973$	−18.3102	−	25.6768i	−0.586997	−	0.823159i
$974$		0			0
$975$	−17.9809	+	20.7706i	−0.575849	+	0.665190i
$976$		0			0
$977$	−3.68736	−	6.38670i	−0.117969	−	0.204329i	0.800994	−	0.598673i	$-0.204305\pi$
$977$	−3.68736	−	6.38670i	−0.117969	−	0.204329i	−0.918963	+	0.394344i	$0.870972\pi$
$978$		0			0
$979$	5.72312	+	9.91273i	0.182912	+	0.316812i
$980$		0			0
$981$	−5.05118	+	3.97990i	−0.161272	+	0.127068i
$982$		0			0
$983$	−4.78363			−0.152574			−0.0762870	−	0.997086i	$-0.524307\pi$
$983$	−4.78363			−0.152574			−0.0762870	+	0.997086i	$0.524307\pi$
$984$		0			0
$985$	8.10057			0.258106
$986$		0			0
$987$	−5.15076	−	11.2449i	−0.163951	−	0.357929i
$988$		0			0
$989$	−15.3400	−	26.5697i	−0.487784	−	0.844866i
$990$		0			0
$991$	18.4932	−	32.0312i	0.587456	−	1.01750i	−0.407108	−	0.913380i	$-0.633463\pi$
$991$	18.4932	−	32.0312i	0.587456	−	1.01750i	0.994564	−	0.104124i	$-0.0332038\pi$
$992$		0			0
$993$	10.0700	−	11.6323i	0.319562	−	0.369140i
$994$		0			0
$995$	−3.56430	+	6.17356i	−0.112996	+	0.195715i
$996$		0			0
$997$	48.6570			1.54098			0.770491	−	0.637451i	$-0.220011\pi$
$997$	48.6570			1.54098			0.770491	+	0.637451i	$0.220011\pi$
$998$		0			0
$999$	−2.31178	+	49.9973i	−0.0731414	+	1.58184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.d.193.11	yes	22
3.2	odd	2		1512.2.t.d.361.5		22
4.3	odd	2		1008.2.t.k.193.1		22
7.2	even	3		504.2.q.d.121.4	yes	22
9.2	odd	6		1512.2.q.c.1369.7		22
9.7	even	3		504.2.q.d.25.4	✓	22
12.11	even	2		3024.2.t.l.1873.5		22
21.2	odd	6		1512.2.q.c.793.7		22
28.23	odd	6		1008.2.q.k.625.8		22
36.7	odd	6		1008.2.q.k.529.8		22
36.11	even	6		3024.2.q.k.2881.7		22
63.2	odd	6		1512.2.t.d.289.5		22
63.16	even	3	inner	504.2.t.d.457.11	yes	22
84.23	even	6		3024.2.q.k.2305.7		22
252.79	odd	6		1008.2.t.k.961.1		22
252.191	even	6		3024.2.t.l.289.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.4	✓	22	9.7	even	3
504.2.q.d.121.4	yes	22	7.2	even	3
504.2.t.d.193.11	yes	22	1.1	even	1	trivial
504.2.t.d.457.11	yes	22	63.16	even	3	inner
1008.2.q.k.529.8		22	36.7	odd	6
1008.2.q.k.625.8		22	28.23	odd	6
1008.2.t.k.193.1		22	4.3	odd	2
1008.2.t.k.961.1		22	252.79	odd	6
1512.2.q.c.793.7		22	21.2	odd	6
1512.2.q.c.1369.7		22	9.2	odd	6
1512.2.t.d.289.5		22	63.2	odd	6
1512.2.t.d.361.5		22	3.2	odd	2
3024.2.q.k.2305.7		22	84.23	even	6
3024.2.q.k.2881.7		22	36.11	even	6
3024.2.t.l.289.5		22	252.191	even	6
3024.2.t.l.1873.5		22	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(1.70090 + 0.327002i) q^{3} +0.340200 q^{5} +(1.09748 - 2.40739i) q^{7} +(2.78614 + 1.11240i) q^{9} +O(q^{10})\)	\(q+(1.70090 + 0.327002i) q^{3} +0.340200 q^{5} +(1.09748 - 2.40739i) q^{7} +(2.78614 + 1.11240i) q^{9} -0.671588 q^{11} +(1.62370 - 2.81233i) q^{13} +(0.578647 + 0.111246i) q^{15} +(-1.10014 + 1.90550i) q^{17} +(0.242085 + 0.419303i) q^{19} +(2.65393 - 3.73586i) q^{21} +4.18990 q^{23} -4.88426 q^{25} +(4.37520 + 2.80315i) q^{27} +(0.478868 + 0.829424i) q^{29} +(-1.04132 - 1.80361i) q^{31} +(-1.14231 - 0.219611i) q^{33} +(0.373363 - 0.818995i) q^{35} +(4.81613 + 8.34178i) q^{37} +(3.68139 - 4.25255i) q^{39} +(-3.90207 + 6.75858i) q^{41} +(-3.66119 - 6.34136i) q^{43} +(0.947845 + 0.378438i) q^{45} +(1.34951 - 2.33742i) q^{47} +(-4.59108 - 5.28413i) q^{49} +(-2.49434 + 2.88133i) q^{51} +(-6.12335 + 10.6059i) q^{53} -0.228474 q^{55} +(0.274649 + 0.792355i) q^{57} +(2.47148 + 4.28074i) q^{59} +(1.76059 - 3.04944i) q^{61} +(5.73571 - 5.48650i) q^{63} +(0.552383 - 0.956755i) q^{65} +(-6.16012 - 10.6696i) q^{67} +(7.12661 + 1.37011i) q^{69} -5.57304 q^{71} +(-3.71686 + 6.43779i) q^{73} +(-8.30766 - 1.59716i) q^{75} +(-0.737054 + 1.61677i) q^{77} +(5.00637 - 8.67128i) q^{79} +(6.52514 + 6.19859i) q^{81} +(2.47376 + 4.28468i) q^{83} +(-0.374269 + 0.648252i) q^{85} +(0.543284 + 1.56736i) q^{87} +(-8.52177 - 14.7601i) q^{89} +(-4.98840 - 6.99536i) q^{91} +(-1.18139 - 3.40828i) q^{93} +(0.0823572 + 0.142647i) q^{95} +(4.23657 + 7.33795i) q^{97} +(-1.87114 - 0.747072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 6 q^{5} + 7 q^{7} - 8 q^{9}+O(q^{10}) \) 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

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