LMFDB - Embedded newform 504.2.t.c.457.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			457.4
Character	$\chi$	$=$	504.457
Dual form			504.2.t.c.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04208 + 1.38350i) q^{3} -0.0619693 q^{5} +(-1.63689 + 2.07860i) q^{7} +(-0.828124 - 2.88344i) q^{9} +O(q^{10})$	\(q+(-1.04208 + 1.38350i) q^{3} -0.0619693 q^{5} +(-1.63689 + 2.07860i) q^{7} +(-0.828124 - 2.88344i) q^{9} -3.18053 q^{11} +(-0.252417 - 0.437198i) q^{13} +(0.0645772 - 0.0857342i) q^{15} +(-0.554700 - 0.960769i) q^{17} +(0.933573 - 1.61700i) q^{19} +(-1.16996 - 4.43071i) q^{21} -6.20496 q^{23} -4.99616 q^{25} +(4.85220 + 1.85908i) q^{27} +(2.39645 - 4.15077i) q^{29} +(1.26858 - 2.19724i) q^{31} +(3.31438 - 4.40026i) q^{33} +(0.101437 - 0.128809i) q^{35} +(-4.26085 + 7.38001i) q^{37} +(0.867902 + 0.106380i) q^{39} +(-4.94516 - 8.56527i) q^{41} +(-3.95574 + 6.85154i) q^{43} +(0.0513182 + 0.178684i) q^{45} +(-3.29168 - 5.70136i) q^{47} +(-1.64116 - 6.80489i) q^{49} +(1.90726 + 0.233776i) q^{51} +(-1.58258 - 2.74112i) q^{53} +0.197095 q^{55} +(1.26425 + 2.97664i) q^{57} +(-4.50652 + 7.80552i) q^{59} +(6.94094 + 12.0221i) q^{61} +(7.34906 + 2.99854i) q^{63} +(0.0156421 + 0.0270929i) q^{65} +(-1.66642 + 2.88632i) q^{67} +(6.46609 - 8.58454i) q^{69} +2.25651 q^{71} +(2.07503 + 3.59406i) q^{73} +(5.20642 - 6.91217i) q^{75} +(5.20619 - 6.61106i) q^{77} +(1.48925 + 2.57946i) q^{79} +(-7.62842 + 4.77569i) q^{81} +(2.17289 - 3.76355i) q^{83} +(0.0343744 + 0.0595381i) q^{85} +(3.24528 + 7.64093i) q^{87} +(-4.30077 + 7.44915i) q^{89} +(1.32194 + 0.190974i) q^{91} +(1.71791 + 4.04478i) q^{93} +(-0.0578528 + 0.100204i) q^{95} +(-3.27671 + 5.67542i) q^{97} +(2.63388 + 9.17087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.04208	+	1.38350i	−0.601647	+	0.798762i
$3$	−1.04208	+	1.38350i	−0.601647	+	0.798762i
$4$		0			0
$5$	−0.0619693			−0.0277135			−0.0138567	−	0.999904i	$-0.504411\pi$
$5$	−0.0619693			−0.0277135			−0.0138567	+	0.999904i	$0.504411\pi$
$6$		0			0
$7$	−1.63689	+	2.07860i	−0.618688	+	0.785637i
$7$	−1.63689	+	2.07860i	−0.618688	+	0.785637i
$8$		0			0
$9$	−0.828124	−	2.88344i	−0.276041	−	0.961146i
$10$		0			0
$11$	−3.18053			−0.958967			−0.479483	−	0.877551i	$-0.659176\pi$
$11$	−3.18053			−0.958967			−0.479483	+	0.877551i	$0.659176\pi$
$12$		0			0
$13$	−0.252417	−	0.437198i	−0.0700078	−	0.121257i	0.828897	−	0.559402i	$-0.188969\pi$
$13$	−0.252417	−	0.437198i	−0.0700078	−	0.121257i	−0.898904	+	0.438145i	$0.855636\pi$
$14$		0			0
$15$	0.0645772	−	0.0857342i	0.0166737	−	0.0221365i
$16$		0			0
$17$	−0.554700	−	0.960769i	−0.134535	−	0.233021i	0.790885	−	0.611965i	$-0.209621\pi$
$17$	−0.554700	−	0.960769i	−0.134535	−	0.233021i	−0.925420	+	0.378944i	$0.876287\pi$
$18$		0			0
$19$	0.933573	−	1.61700i	0.214176	−	0.370964i	−0.738841	−	0.673880i	$-0.764627\pi$
$19$	0.933573	−	1.61700i	0.214176	−	0.370964i	0.953017	+	0.302915i	$0.0979599\pi$
$20$		0			0
$21$	−1.16996	−	4.43071i	−0.255305	−	0.966860i
$22$		0			0
$23$	−6.20496			−1.29382			−0.646912	−	0.762565i	$-0.723940\pi$
$23$	−6.20496			−1.29382			−0.646912	+	0.762565i	$0.723940\pi$
$24$		0			0
$25$	−4.99616			−0.999232
$26$		0			0
$27$	4.85220	+	1.85908i	0.933806	+	0.357779i
$28$		0			0
$29$	2.39645	−	4.15077i	0.445010	−	0.770779i	−0.553043	−	0.833153i	$-0.686534\pi$
$29$	2.39645	−	4.15077i	0.445010	−	0.770779i	0.998053	+	0.0623731i	$0.0198669\pi$
$30$		0			0
$31$	1.26858	−	2.19724i	0.227843	−	0.394636i	−0.729325	−	0.684167i	$-0.760166\pi$
$31$	1.26858	−	2.19724i	0.227843	−	0.394636i	0.957169	+	0.289531i	$0.0934993\pi$
$32$		0			0
$33$	3.31438	−	4.40026i	0.576960	−	0.765986i
$34$		0			0
$35$	0.101437	−	0.128809i	0.0171460	−	0.0217728i
$36$		0			0
$37$	−4.26085	+	7.38001i	−0.700479	+	1.21327i	0.267819	+	0.963469i	$0.413697\pi$
$37$	−4.26085	+	7.38001i	−0.700479	+	1.21327i	−0.968298	+	0.249797i	$0.919636\pi$
$38$		0			0
$39$	0.867902	+	0.106380i	0.138976	+	0.0170344i
$40$		0			0
$41$	−4.94516	−	8.56527i	−0.772305	−	1.33767i	−0.936297	−	0.351210i	$-0.885770\pi$
$41$	−4.94516	−	8.56527i	−0.772305	−	1.33767i	0.163992	−	0.986462i	$-0.447563\pi$
$42$		0			0
$43$	−3.95574	+	6.85154i	−0.603244	+	1.04485i	0.389082	+	0.921203i	$0.372792\pi$
$43$	−3.95574	+	6.85154i	−0.603244	+	1.04485i	−0.992326	+	0.123646i	$0.960541\pi$
$44$		0			0
$45$	0.0513182	+	0.178684i	0.00765007	+	0.0266367i
$46$		0			0
$47$	−3.29168	−	5.70136i	−0.480141	−	0.831628i	0.519600	−	0.854410i	$-0.326081\pi$
$47$	−3.29168	−	5.70136i	−0.480141	−	0.831628i	−0.999740	+	0.0227816i	$0.992748\pi$
$48$		0			0
$49$	−1.64116	−	6.80489i	−0.234451	−	0.972128i
$50$		0			0
$51$	1.90726	+	0.233776i	0.267070	+	0.0327352i
$52$		0			0
$53$	−1.58258	−	2.74112i	−0.217385	−	0.376521i	0.736623	−	0.676304i	$-0.236419\pi$
$53$	−1.58258	−	2.74112i	−0.217385	−	0.376521i	−0.954008	+	0.299782i	$0.903086\pi$
$54$		0			0
$55$	0.197095			0.0265763
$56$		0			0
$57$	1.26425	+	2.97664i	0.167454	+	0.394266i
$58$		0			0
$59$	−4.50652	+	7.80552i	−0.586699	+	1.01619i	0.407962	+	0.912999i	$0.366240\pi$
$59$	−4.50652	+	7.80552i	−0.586699	+	1.01619i	−0.994661	+	0.103194i	$0.967094\pi$
$60$		0			0
$61$	6.94094	+	12.0221i	0.888697	+	1.53927i	0.841417	+	0.540386i	$0.181722\pi$
$61$	6.94094	+	12.0221i	0.888697	+	1.53927i	0.0472794	+	0.998882i	$0.484945\pi$
$62$		0			0
$63$	7.34906	+	2.99854i	0.925895	+	0.377781i
$64$		0			0
$65$	0.0156421	+	0.0270929i	0.00194016	+	0.00336046i
$66$		0			0
$67$	−1.66642	+	2.88632i	−0.203585	+	0.352620i	−0.949681	−	0.313219i	$-0.898593\pi$
$67$	−1.66642	+	2.88632i	−0.203585	+	0.352620i	0.746096	+	0.665839i	$0.231926\pi$
$68$		0			0
$69$	6.46609	−	8.58454i	0.778425	−	1.03346i
$70$		0			0
$71$	2.25651			0.267798			0.133899	−	0.990995i	$-0.457250\pi$
$71$	2.25651			0.267798			0.133899	+	0.990995i	$0.457250\pi$
$72$		0			0
$73$	2.07503	+	3.59406i	0.242864	+	0.420652i	0.961529	−	0.274704i	$-0.0885799\pi$
$73$	2.07503	+	3.59406i	0.242864	+	0.420652i	−0.718665	+	0.695356i	$0.755247\pi$
$74$		0			0
$75$	5.20642	−	6.91217i	0.601185	−	0.798148i
$76$		0			0
$77$	5.20619	−	6.61106i	0.593301	−	0.753400i
$78$		0			0
$79$	1.48925	+	2.57946i	0.167554	+	0.290211i	0.937559	−	0.347826i	$-0.113080\pi$
$79$	1.48925	+	2.57946i	0.167554	+	0.290211i	−0.770006	+	0.638037i	$0.779747\pi$
$80$		0			0
$81$	−7.62842	+	4.77569i	−0.847602	+	0.530632i
$82$		0			0
$83$	2.17289	−	3.76355i	0.238506	−	0.413104i	−0.721780	−	0.692122i	$-0.756676\pi$
$83$	2.17289	−	3.76355i	0.238506	−	0.413104i	0.960286	+	0.279019i	$0.0900092\pi$
$84$		0			0
$85$	0.0343744	+	0.0595381i	0.00372842	+	0.00645782i
$86$		0			0
$87$	3.24528	+	7.64093i	0.347930	+	0.819194i
$88$		0			0
$89$	−4.30077	+	7.44915i	−0.455880	+	0.789608i	−0.998738	−	0.0502166i	$-0.984009\pi$
$89$	−4.30077	+	7.44915i	−0.455880	+	0.789608i	0.542858	+	0.839824i	$0.317342\pi$
$90$		0			0
$91$	1.32194	+	0.190974i	0.138577	+	0.0200195i
$92$		0			0
$93$	1.71791	+	4.04478i	0.178139	+	0.419424i
$94$		0			0
$95$	−0.0578528	+	0.100204i	−0.00593558	+	0.0102807i
$96$		0			0
$97$	−3.27671	+	5.67542i	−0.332699	+	0.576252i	−0.983040	−	0.183391i	$-0.941293\pi$
$97$	−3.27671	+	5.67542i	−0.332699	+	0.576252i	0.650341	+	0.759642i	$0.274626\pi$
$98$		0			0
$99$	2.63388	+	9.17087i	0.264714	+	0.921707i
$100$		0			0
$101$	6.51654			0.648420			0.324210	−	0.945985i	$-0.394902\pi$
$101$	6.51654			0.648420			0.324210	+	0.945985i	$0.394902\pi$
$102$		0			0
$103$	17.0196			1.67699			0.838494	−	0.544911i	$-0.183437\pi$
$103$	17.0196			1.67699			0.838494	+	0.544911i	$0.183437\pi$
$104$		0			0
$105$	0.0725013	+	0.274568i	0.00707540	+	0.0267951i
$106$		0			0
$107$	−8.86075	+	15.3473i	−0.856601	+	1.48368i	0.0185508	+	0.999828i	$0.494095\pi$
$107$	−8.86075	+	15.3473i	−0.856601	+	1.48368i	−0.875152	+	0.483848i	$0.839239\pi$
$108$		0			0
$109$	6.62928	+	11.4822i	0.634970	+	1.09980i	0.986522	+	0.163631i	$0.0523208\pi$
$109$	6.62928	+	11.4822i	0.634970	+	1.09980i	−0.351552	+	0.936168i	$0.614346\pi$
$110$		0			0
$111$	−5.77005	−	13.5855i	−0.547669	−	1.28947i
$112$		0			0
$113$	1.10094	+	1.90689i	0.103568	+	0.179385i	0.913152	−	0.407619i	$-0.133641\pi$
$113$	1.10094	+	1.90689i	0.103568	+	0.179385i	−0.809584	+	0.587004i	$0.800307\pi$
$114$		0			0
$115$	0.384517			0.0358564
$116$		0			0
$117$	−1.05160	+	1.08988i	−0.0972207	+	0.100760i
$118$		0			0
$119$	2.90504	+	0.419676i	0.266305	+	0.0384717i
$120$		0			0
$121$	−0.884207			−0.0803825
$122$		0			0
$123$	17.0033	+	2.08412i	1.53314	+	0.187918i
$124$		0			0
$125$	0.619455			0.0554057
$126$		0			0
$127$	−4.61290			−0.409329			−0.204664	−	0.978832i	$-0.565610\pi$
$127$	−4.61290			−0.409329			−0.204664	+	0.978832i	$0.565610\pi$
$128$		0			0
$129$	−5.35687	−	12.6126i	−0.471646	−	1.11048i
$130$		0			0
$131$	−0.152139			−0.0132925			−0.00664623	−	0.999978i	$-0.502116\pi$
$131$	−0.152139			−0.0132925			−0.00664623	+	0.999978i	$0.502116\pi$
$132$		0			0
$133$	1.83293	+	4.58738i	0.158935	+	0.397776i
$134$		0			0
$135$	−0.300687	−	0.115206i	−0.0258790	−	0.00991532i
$136$		0			0
$137$	−3.55540			−0.303759			−0.151879	−	0.988399i	$-0.548533\pi$
$137$	−3.55540			−0.303759			−0.151879	+	0.988399i	$0.548533\pi$
$138$		0			0
$139$	−7.60945	−	13.1800i	−0.645425	−	1.11791i	−0.984203	−	0.177043i	$-0.943347\pi$
$139$	−7.60945	−	13.1800i	−0.645425	−	1.11791i	0.338778	−	0.940866i	$-0.389987\pi$
$140$		0			0
$141$	11.3180	+	1.38726i	0.953148	+	0.116829i
$142$		0			0
$143$	0.802820	+	1.39052i	0.0671352	+	0.116281i
$144$		0			0
$145$	−0.148506	+	0.257220i	−0.0123328	+	0.0213610i
$146$		0			0
$147$	11.1248	+	4.82073i	0.917556	+	0.397607i
$148$		0			0
$149$	0.366914			0.0300588			0.0150294	−	0.999887i	$-0.495216\pi$
$149$	0.366914			0.0300588			0.0150294	+	0.999887i	$0.495216\pi$
$150$		0			0
$151$	−12.5832			−1.02401			−0.512005	−	0.858983i	$-0.671097\pi$
$151$	−12.5832			−1.02401			−0.512005	+	0.858983i	$0.671097\pi$
$152$		0			0
$153$	−2.31096	+	2.39508i	−0.186830	+	0.193631i
$154$		0			0
$155$	−0.0786128	+	0.136161i	−0.00631434	+	0.0109368i
$156$		0			0
$157$	2.72734	−	4.72389i	0.217666	−	0.377008i	−0.736428	−	0.676516i	$-0.763489\pi$
$157$	2.72734	−	4.72389i	0.217666	−	0.377008i	0.954094	+	0.299508i	$0.0968225\pi$
$158$		0			0
$159$	5.44151	+	0.666973i	0.431540	+	0.0528944i
$160$		0			0
$161$	10.1569	−	12.8976i	0.800473	−	1.01648i
$162$		0			0
$163$	3.83559	−	6.64343i	0.300426	−	0.520354i	−0.675806	−	0.737079i	$-0.736204\pi$
$163$	3.83559	−	6.64343i	0.300426	−	0.520354i	0.976233	+	0.216726i	$0.0695377\pi$
$164$		0			0
$165$	−0.205390	+	0.272681i	−0.0159896	+	0.0212282i
$166$		0			0
$167$	−9.47493	−	16.4111i	−0.733192	−	1.26993i	−0.955512	−	0.294952i	$-0.904696\pi$
$167$	−9.47493	−	16.4111i	−0.733192	−	1.26993i	0.222320	−	0.974974i	$-0.428637\pi$
$168$		0			0
$169$	6.37257	−	11.0376i	0.490198	−	0.849048i
$170$		0			0
$171$	−5.43562	−	1.35283i	−0.415672	−	0.103453i
$172$		0			0
$173$	11.9959	+	20.7776i	0.912034	+	1.57969i	0.811187	+	0.584787i	$0.198822\pi$
$173$	11.9959	+	20.7776i	0.912034	+	1.57969i	0.100846	+	0.994902i	$0.467845\pi$
$174$		0			0
$175$	8.17818	−	10.3850i	0.618212	−	0.785034i
$176$		0			0
$177$	−6.10274	−	14.3688i	−0.458710	−	1.08002i
$178$		0			0
$179$	−4.27901	−	7.41146i	−0.319828	−	0.553959i	0.660624	−	0.750717i	$-0.270292\pi$
$179$	−4.27901	−	7.41146i	−0.319828	−	0.553959i	−0.980452	+	0.196758i	$0.936959\pi$
$180$		0			0
$181$	0.632669			0.0470259			0.0235130	−	0.999724i	$-0.492515\pi$
$181$	0.632669			0.0470259			0.0235130	+	0.999724i	$0.492515\pi$
$182$		0			0
$183$	−23.8655	−	2.92523i	−1.76419	−	0.216239i
$184$		0			0
$185$	0.264042	−	0.457334i	0.0194127	−	0.0336238i
$186$		0			0
$187$	1.76424	+	3.05576i	0.129014	+	0.223459i
$188$		0			0
$189$	−11.8068	+	7.04267i	−0.858819	+	0.512279i
$190$		0			0
$191$	−11.7915	−	20.4235i	−0.853205	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$191$	−11.7915	−	20.4235i	−0.853205	−	1.47780i	0.0250944	−	0.999685i	$-0.492011\pi$
$192$		0			0
$193$	−12.8030	+	22.1754i	−0.921577	+	1.59622i	−0.124600	+	0.992207i	$0.539765\pi$
$193$	−12.8030	+	22.1754i	−0.921577	+	1.59622i	−0.796976	+	0.604011i	$0.793568\pi$
$194$		0			0
$195$	−0.0537832	−	0.00659228i	−0.00385150	−	0.000472083i
$196$		0			0
$197$	9.45810			0.673862			0.336931	−	0.941529i	$-0.390611\pi$
$197$	9.45810			0.673862			0.336931	+	0.941529i	$0.390611\pi$
$198$		0			0
$199$	4.15133	+	7.19032i	0.294280	+	0.509708i	0.974817	−	0.223005i	$-0.0715868\pi$
$199$	4.15133	+	7.19032i	0.294280	+	0.509708i	−0.680537	+	0.732714i	$0.738253\pi$
$200$		0			0
$201$	−2.25666	−	5.31327i	−0.159173	−	0.374769i
$202$		0			0
$203$	4.70507	+	11.7756i	0.330231	+	0.826488i
$204$		0			0
$205$	0.306448	+	0.530784i	0.0214033	+	0.0370715i
$206$		0			0
$207$	5.13848	+	17.8916i	0.357149	+	1.24355i
$208$		0			0
$209$	−2.96926	+	5.14291i	−0.205388	+	0.355742i
$210$		0			0
$211$	−10.1164	−	17.5222i	−0.696444	−	1.20628i	−0.969691	−	0.244333i	$-0.921431\pi$
$211$	−10.1164	−	17.5222i	−0.696444	−	1.20628i	0.273247	−	0.961944i	$-0.411902\pi$
$212$		0			0
$213$	−2.35147	+	3.12187i	−0.161120	+	0.213907i
$214$		0			0
$215$	0.245134	−	0.424585i	0.0167180	−	0.0289564i
$216$		0			0
$217$	2.49066	+	6.23352i	0.169077	+	0.423159i
$218$		0			0
$219$	−7.13472	−	0.874512i	−0.482120	−	0.0590940i
$220$		0			0
$221$	−0.280031	+	0.485028i	−0.0188369	+	0.0326265i
$222$		0			0
$223$	−2.41918	+	4.19014i	−0.162000	+	0.280593i	−0.935586	−	0.353099i	$-0.885128\pi$
$223$	−2.41918	+	4.19014i	−0.162000	+	0.280593i	0.773586	+	0.633692i	$0.218461\pi$
$224$		0			0
$225$	4.13744	+	14.4061i	0.275829	+	0.960408i
$226$		0			0
$227$	0.672213			0.0446163			0.0223082	−	0.999751i	$-0.492899\pi$
$227$	0.672213			0.0446163			0.0223082	+	0.999751i	$0.492899\pi$
$228$		0			0
$229$	−6.13553			−0.405447			−0.202724	−	0.979236i	$-0.564979\pi$
$229$	−6.13553			−0.405447			−0.202724	+	0.979236i	$0.564979\pi$
$230$		0			0
$231$	3.72108	+	14.0920i	0.244829	+	0.927187i
$232$		0			0
$233$	12.1492	−	21.0431i	0.795922	−	1.37858i	−0.126330	−	0.991988i	$-0.540320\pi$
$233$	12.1492	−	21.0431i	0.795922	−	1.37858i	0.922252	−	0.386589i	$-0.126347\pi$
$234$		0			0
$235$	0.203983	+	0.353309i	0.0133064	+	0.0230473i
$236$		0			0
$237$	−5.12059	−	0.627637i	−0.332618	−	0.0407694i
$238$		0			0
$239$	13.5978	+	23.5521i	0.879569	+	1.52346i	0.851815	+	0.523843i	$0.175502\pi$
$239$	13.5978	+	23.5521i	0.879569	+	1.52346i	0.0277545	+	0.999615i	$0.491164\pi$
$240$		0			0
$241$	−25.8054			−1.66227			−0.831135	−	0.556070i	$-0.812309\pi$
$241$	−25.8054			−1.66227			−0.831135	+	0.556070i	$0.812309\pi$
$242$		0			0
$243$	1.34231	−	15.5306i	0.0861092	−	0.996286i
$244$		0			0
$245$	0.101701	+	0.421694i	0.00649747	+	0.0269411i
$246$		0			0
$247$	−0.942598			−0.0599760
$248$		0			0
$249$	2.94253	+	6.92812i	0.186475	+	0.439052i
$250$		0			0
$251$	−27.0741			−1.70890			−0.854450	−	0.519533i	$-0.826106\pi$
$251$	−27.0741			−1.70890			−0.854450	+	0.519533i	$0.826106\pi$
$252$		0			0
$253$	19.7351			1.24073
$254$		0			0
$255$	−0.118192	−	0.0144869i	−0.00740146	−	0.000907206i
$256$		0			0
$257$	−13.5215			−0.843445			−0.421723	−	0.906725i	$-0.638574\pi$
$257$	−13.5215			−0.843445			−0.421723	+	0.906725i	$0.638574\pi$
$258$		0			0
$259$	−8.36553	−	20.9369i	−0.519809	−	1.30096i
$260$		0			0
$261$	−13.9531	−	3.47266i	−0.863672	−	0.214952i
$262$		0			0
$263$	−13.3745			−0.824710			−0.412355	−	0.911023i	$-0.635294\pi$
$263$	−13.3745			−0.824710			−0.412355	+	0.911023i	$0.635294\pi$
$264$		0			0
$265$	0.0980716	+	0.169865i	0.00602449	+	0.0104347i
$266$		0			0
$267$	−5.82411	−	13.7127i	−0.356430	−	0.839205i
$268$		0			0
$269$	3.91594	+	6.78261i	0.238759	+	0.413543i	0.960359	−	0.278768i	$-0.0899260\pi$
$269$	3.91594	+	6.78261i	0.238759	+	0.413543i	−0.721599	+	0.692311i	$0.756593\pi$
$270$		0			0
$271$	15.1737	−	26.2816i	0.921735	−	1.59649i	0.125005	−	0.992156i	$-0.460105\pi$
$271$	15.1737	−	26.2816i	0.921735	−	1.59649i	0.796730	−	0.604335i	$-0.206561\pi$
$272$		0			0
$273$	−1.64178	+	1.62989i	−0.0993653	+	0.0986453i
$274$		0			0
$275$	15.8905			0.958230
$276$		0			0
$277$	−22.6924			−1.36346			−0.681728	−	0.731606i	$-0.738771\pi$
$277$	−22.6924			−1.36346			−0.681728	+	0.731606i	$0.738771\pi$
$278$		0			0
$279$	−7.38615	−	1.83828i	−0.442197	−	0.110055i
$280$		0			0
$281$	−10.0826	+	17.4635i	−0.601475	+	1.04179i	0.391122	+	0.920339i	$0.372087\pi$
$281$	−10.0826	+	17.4635i	−0.601475	+	1.04179i	−0.992598	+	0.121447i	$0.961246\pi$
$282$		0			0
$283$	8.45297	−	14.6410i	0.502477	−	0.870316i	−0.497519	−	0.867453i	$-0.665755\pi$
$283$	8.45297	−	14.6410i	0.502477	−	0.870316i	0.999996	−	0.00286255i	$-0.000911181\pi$
$284$		0			0
$285$	−0.0783444	−	0.184460i	−0.00464072	−	0.0109265i
$286$		0			0
$287$	25.8985	+	3.74142i	1.52874	+	0.220849i
$288$		0			0
$289$	7.88462	−	13.6566i	0.463801	−	0.803327i
$290$		0			0
$291$	−4.43732	−	10.4476i	−0.260120	−	0.612448i
$292$		0			0
$293$	2.40597	+	4.16727i	0.140558	+	0.243454i	0.927707	−	0.373309i	$-0.121777\pi$
$293$	2.40597	+	4.16727i	0.140558	+	0.243454i	−0.787149	+	0.616763i	$0.788444\pi$
$294$		0			0
$295$	0.279266	−	0.483703i	0.0162595	−	0.0281623i
$296$		0			0
$297$	−15.4326	−	5.91286i	−0.895489	−	0.343099i
$298$		0			0
$299$	1.56624	+	2.71280i	0.0905777	+	0.156885i
$300$		0			0
$301$	−7.76649	−	19.4376i	−0.447653	−	1.12037i
$302$		0			0
$303$	−6.79078	+	9.01561i	−0.390120	+	0.517933i
$304$		0			0
$305$	−0.430125	−	0.744999i	−0.0246289	−	0.0426585i
$306$		0			0
$307$	15.9188			0.908534			0.454267	−	0.890866i	$-0.349901\pi$
$307$	15.9188			0.908534			0.454267	+	0.890866i	$0.349901\pi$
$308$		0			0
$309$	−17.7358	+	23.5465i	−1.00896	+	1.33951i
$310$		0			0
$311$	0.131435	−	0.227651i	0.00745297	−	0.0129089i	−0.862275	−	0.506441i	$-0.830961\pi$
$311$	0.131435	−	0.227651i	0.00745297	−	0.0129089i	0.869728	+	0.493532i	$0.164294\pi$
$312$		0			0
$313$	3.12534	+	5.41325i	0.176655	+	0.305975i	0.940733	−	0.339149i	$-0.110139\pi$
$313$	3.12534	+	5.41325i	0.176655	+	0.305975i	−0.764078	+	0.645124i	$0.776806\pi$
$314$		0			0
$315$	−0.455416	−	0.185817i	−0.0256598	−	0.0104696i
$316$		0			0
$317$	9.83961	+	17.0427i	0.552648	+	0.957214i	0.998082	+	0.0618994i	$0.0197158\pi$
$317$	9.83961	+	17.0427i	0.552648	+	0.957214i	−0.445435	+	0.895314i	$0.646951\pi$
$318$		0			0
$319$	−7.62199	+	13.2017i	−0.426750	+	0.739152i
$320$		0			0
$321$	−11.9992	−	28.2519i	−0.669733	−	1.57687i
$322$		0			0
$323$	−2.07141			−0.115256
$324$		0			0
$325$	1.26111	+	2.18431i	0.0699540	+	0.121164i
$326$		0			0
$327$	−22.7939	−	2.79388i	−1.26051	−	0.154502i
$328$		0			0
$329$	17.2390	+	2.49043i	0.950415	+	0.137302i
$330$		0			0
$331$	−12.2669	−	21.2469i	−0.674249	−	1.16783i	−0.976688	−	0.214665i	$-0.931134\pi$
$331$	−12.2669	−	21.2469i	−0.674249	−	1.16783i	0.302439	−	0.953169i	$-0.402199\pi$
$332$		0			0
$333$	24.8083	+	6.17433i	1.35949	+	0.338351i
$334$		0			0
$335$	0.103267	−	0.178863i	0.00564206	−	0.00977233i
$336$		0			0
$337$	−6.89471	−	11.9420i	−0.375579	−	0.650521i	0.614835	−	0.788656i	$-0.289223\pi$
$337$	−6.89471	−	11.9420i	−0.375579	−	0.650521i	−0.990413	+	0.138135i	$0.955889\pi$
$338$		0			0
$339$	−3.78545	−	0.463988i	−0.205598	−	0.0252004i
$340$		0			0
$341$	−4.03475	+	6.98840i	−0.218494	+	0.378443i
$342$		0			0
$343$	16.8311	+	7.72757i	0.908792	+	0.417250i
$344$		0			0
$345$	−0.400699	+	0.531978i	−0.0215729	+	0.0286407i
$346$		0			0
$347$	9.84786	−	17.0570i	0.528661	−	0.915667i	−0.470781	−	0.882250i	$-0.656028\pi$
$347$	9.84786	−	17.0570i	0.528661	−	0.915667i	0.999441	−	0.0334170i	$-0.0106389\pi$
$348$		0			0
$349$	5.34712	−	9.26149i	0.286225	−	0.495756i	−0.686681	−	0.726959i	$-0.740933\pi$
$349$	5.34712	−	9.26149i	0.286225	−	0.495756i	0.972905	+	0.231203i	$0.0742662\pi$
$350$		0			0
$351$	−0.411990	−	2.59064i	−0.0219904	−	0.138278i
$352$		0			0
$353$	−11.6615			−0.620677			−0.310338	−	0.950626i	$-0.600442\pi$
$353$	−11.6615			−0.620677			−0.310338	+	0.950626i	$0.600442\pi$
$354$		0			0
$355$	−0.139834			−0.00742162
$356$		0			0
$357$	−3.60792	+	3.58177i	−0.190951	+	0.189568i
$358$		0			0
$359$	−8.82159	+	15.2794i	−0.465586	+	0.806418i	−0.999228	−	0.0392925i	$-0.987490\pi$
$359$	−8.82159	+	15.2794i	−0.465586	+	0.806418i	0.533642	+	0.845710i	$0.320823\pi$
$360$		0			0
$361$	7.75688	+	13.4353i	0.408257	+	0.707122i
$362$		0			0
$363$	0.921418	−	1.22330i	0.0483619	−	0.0642064i
$364$		0			0
$365$	−0.128588	−	0.222721i	−0.00673061	−	0.0116578i
$366$		0			0
$367$	3.38292			0.176587			0.0882934	−	0.996095i	$-0.471859\pi$
$367$	3.38292			0.176587			0.0882934	+	0.996095i	$0.471859\pi$
$368$		0			0
$369$	−20.6022	+	21.3522i	−1.07251	+	1.11155i
$370$		0			0
$371$	8.28821	+	1.19736i	0.430302	+	0.0621636i
$372$		0			0
$373$	13.3902			0.693320			0.346660	−	0.937991i	$-0.387316\pi$
$373$	13.3902			0.693320			0.346660	+	0.937991i	$0.387316\pi$
$374$		0			0
$375$	−0.645524	+	0.857013i	−0.0333347	+	0.0442560i
$376$		0			0
$377$	−2.41962			−0.124617
$378$		0			0
$379$	−27.6131			−1.41839			−0.709194	−	0.705013i	$-0.750941\pi$
$379$	−27.6131			−1.41839			−0.709194	+	0.705013i	$0.750941\pi$
$380$		0			0
$381$	4.80703	−	6.38193i	0.246271	−	0.326956i
$382$		0			0
$383$	25.0040			1.27764			0.638822	−	0.769354i	$-0.279422\pi$
$383$	25.0040			1.27764			0.638822	+	0.769354i	$0.279422\pi$
$384$		0			0
$385$	−0.322624	+	0.409682i	−0.0164424	+	0.0208793i
$386$		0			0
$387$	23.0318	+	5.73220i	1.17077	+	0.291384i
$388$		0			0
$389$	−0.136646			−0.00692821			−0.00346411	−	0.999994i	$-0.501103\pi$
$389$	−0.136646			−0.00692821			−0.00346411	+	0.999994i	$0.501103\pi$
$390$		0			0
$391$	3.44189	+	5.96153i	0.174064	+	0.301488i
$392$		0			0
$393$	0.158542	−	0.210484i	0.00799737	−	0.0106175i
$394$		0			0
$395$	−0.0922877	−	0.159847i	−0.00464350	−	0.00804277i
$396$		0			0
$397$	7.91030	−	13.7010i	0.397006	−	0.687635i	−0.596349	−	0.802726i	$-0.703382\pi$
$397$	7.91030	−	13.7010i	0.397006	−	0.687635i	0.993355	+	0.115090i	$0.0367157\pi$
$398$		0			0
$399$	−8.25668	−	2.24458i	−0.413351	−	0.112369i
$400$		0			0
$401$	−11.0549			−0.552055			−0.276028	−	0.961150i	$-0.589018\pi$
$401$	−11.0549			−0.552055			−0.276028	+	0.961150i	$0.589018\pi$
$402$		0			0
$403$	−1.28084			−0.0638032
$404$		0			0
$405$	0.472728	−	0.295946i	0.0234900	−	0.0147057i
$406$		0			0
$407$	13.5518	−	23.4724i	0.671737	−	1.16348i
$408$		0			0
$409$	18.0064	−	31.1880i	0.890358	−	1.54215i	0.0509122	−	0.998703i	$-0.483787\pi$
$409$	18.0064	−	31.1880i	0.890358	−	1.54215i	0.839446	−	0.543443i	$-0.182880\pi$
$410$		0			0
$411$	3.70503	−	4.91889i	0.182756	−	0.242631i
$412$		0			0
$413$	−8.84787	−	22.1441i	−0.435375	−	1.08964i
$414$		0			0
$415$	−0.134652	+	0.233225i	−0.00660982	+	0.0114485i
$416$		0			0
$417$	26.1641	+	3.20697i	1.28126	+	0.157046i
$418$		0			0
$419$	16.4877	+	28.5576i	0.805477	+	1.39513i	0.915968	+	0.401251i	$0.131424\pi$
$419$	16.4877	+	28.5576i	0.805477	+	1.39513i	−0.110491	+	0.993877i	$0.535242\pi$
$420$		0			0
$421$	14.9800	−	25.9461i	0.730080	−	1.26454i	−0.226769	−	0.973949i	$-0.572816\pi$
$421$	14.9800	−	25.9461i	0.730080	−	1.26454i	0.956849	−	0.290587i	$-0.0938505\pi$
$422$		0			0
$423$	−13.7136	+	14.2128i	−0.666777	+	0.691049i
$424$		0			0
$425$	2.77137	+	4.80016i	0.134431	+	0.232842i
$426$		0			0
$427$	−36.3507	−	5.25139i	−1.75913	−	0.254133i
$428$		0			0
$429$	−2.76039	−	0.338345i	−0.133273	−	0.0163354i
$430$		0			0
$431$	−12.4021	−	21.4811i	−0.597389	−	1.03471i	−0.993205	−	0.116379i	$-0.962871\pi$
$431$	−12.4021	−	21.4811i	−0.597389	−	1.03471i	0.395816	−	0.918330i	$-0.370462\pi$
$432$		0			0
$433$	−5.00906			−0.240720			−0.120360	−	0.992730i	$-0.538405\pi$
$433$	−5.00906			−0.240720			−0.120360	+	0.992730i	$0.538405\pi$
$434$		0			0
$435$	−0.201108	−	0.473503i	−0.00964237	−	0.0227027i
$436$		0			0
$437$	−5.79278	+	10.0334i	−0.277106	+	0.479962i
$438$		0			0
$439$	20.2918	+	35.1464i	0.968475	+	1.67745i	0.699973	+	0.714169i	$0.253195\pi$
$439$	20.2918	+	35.1464i	0.968475	+	1.67745i	0.268502	+	0.963279i	$0.413471\pi$
$440$		0			0
$441$	−18.2624	+	10.3675i	−0.869638	+	0.493689i
$442$		0			0
$443$	14.1332	+	24.4795i	0.671490	+	1.16305i	0.977482	+	0.211021i	$0.0676787\pi$
$443$	14.1332	+	24.4795i	0.671490	+	1.16305i	−0.305992	+	0.952034i	$0.598988\pi$
$444$		0			0
$445$	0.266515	−	0.461618i	0.0126340	−	0.0218828i
$446$		0			0
$447$	−0.382355	+	0.507624i	−0.0180848	+	0.0240098i
$448$		0			0
$449$	36.6443			1.72935			0.864676	−	0.502329i	$-0.167523\pi$
$449$	36.6443			1.72935			0.864676	+	0.502329i	$0.167523\pi$
$450$		0			0
$451$	15.7283	+	27.2421i	0.740615	+	1.28278i
$452$		0			0
$453$	13.1128	−	17.4089i	0.616092	−	0.817939i
$454$		0			0
$455$	−0.0819197	−	0.0118345i	−0.00384045	−	0.000554811i
$456$		0			0
$457$	3.19154	+	5.52791i	0.149294	+	0.258585i	0.930967	−	0.365104i	$-0.118967\pi$
$457$	3.19154	+	5.52791i	0.149294	+	0.258585i	−0.781673	+	0.623689i	$0.785633\pi$
$458$		0			0
$459$	−0.905373	−	5.69307i	−0.0422592	−	0.265730i
$460$		0			0
$461$	7.24366	−	12.5464i	0.337371	−	0.584343i	−0.646567	−	0.762858i	$-0.723796\pi$
$461$	7.24366	−	12.5464i	0.337371	−	0.584343i	0.983937	+	0.178514i	$0.0571291\pi$
$462$		0			0
$463$	13.2527	+	22.9544i	0.615907	+	1.06678i	0.990225	+	0.139482i	$0.0445438\pi$
$463$	13.2527	+	22.9544i	0.615907	+	1.06678i	−0.374317	+	0.927301i	$0.622123\pi$
$464$		0			0
$465$	−0.106458	−	0.250652i	−0.00493686	−	0.0116237i
$466$		0			0
$467$	−11.6879	+	20.2440i	−0.540851	+	0.936782i	0.458004	+	0.888950i	$0.348564\pi$
$467$	−11.6879	+	20.2440i	−0.540851	+	0.936782i	−0.998855	+	0.0478318i	$0.984769\pi$
$468$		0			0
$469$	−3.27176	−	8.18841i	−0.151076	−	0.378106i
$470$		0			0
$471$	3.69337	+	8.69596i	0.170182	+	0.400689i
$472$		0			0
$473$	12.5814	−	21.7915i	0.578491	−	1.00198i
$474$		0			0
$475$	−4.66428	+	8.07877i	−0.214012	+	0.370679i
$476$		0			0
$477$	−6.59326	+	6.83327i	−0.301885	+	0.312874i
$478$		0			0
$479$	9.29606			0.424748			0.212374	−	0.977188i	$-0.431881\pi$
$479$	9.29606			0.424748			0.212374	+	0.977188i	$0.431881\pi$
$480$		0			0
$481$	4.30204			0.196156
$482$		0			0
$483$	7.25953	+	27.4924i	0.330320	+	1.25095i
$484$		0			0
$485$	0.203055	−	0.351702i	0.00922026	−	0.0159700i
$486$		0			0
$487$	2.04947	+	3.54979i	0.0928704	+	0.160856i	0.908718	−	0.417411i	$-0.137062\pi$
$487$	2.04947	+	3.54979i	0.0928704	+	0.160856i	−0.815847	+	0.578267i	$0.803729\pi$
$488$		0			0
$489$	5.19416	+	12.2295i	0.234888	+	0.553038i
$490$		0			0
$491$	4.98703	+	8.63778i	0.225061	+	0.389818i	0.956338	−	0.292264i	$-0.0944084\pi$
$491$	4.98703	+	8.63778i	0.225061	+	0.389818i	−0.731277	+	0.682081i	$0.761075\pi$
$492$		0			0
$493$	−5.31725			−0.239477
$494$		0			0
$495$	−0.163219	−	0.568312i	−0.00733616	−	0.0255437i
$496$		0			0
$497$	−3.69366	+	4.69037i	−0.165683	+	0.210392i
$498$		0			0
$499$	−11.2083			−0.501752			−0.250876	−	0.968019i	$-0.580719\pi$
$499$	−11.2083			−0.501752			−0.250876	+	0.968019i	$0.580719\pi$
$500$		0			0
$501$	32.5783	+	3.99317i	1.45549	+	0.178402i
$502$		0			0
$503$	−1.69350			−0.0755094			−0.0377547	−	0.999287i	$-0.512021\pi$
$503$	−1.69350			−0.0755094			−0.0377547	+	0.999287i	$0.512021\pi$
$504$		0			0
$505$	−0.403825			−0.0179700
$506$		0			0
$507$	8.62975	+	20.3185i	0.383261	+	0.902378i
$508$		0			0
$509$	−40.9555			−1.81532			−0.907659	−	0.419707i	$-0.862133\pi$
$509$	−40.9555			−1.81532			−0.907659	+	0.419707i	$0.862133\pi$
$510$		0			0
$511$	−10.8672	−	1.56993i	−0.480737	−	0.0694496i
$512$		0			0
$513$	7.53600	−	6.11040i	0.332723	−	0.269781i
$514$		0			0
$515$	−1.05469			−0.0464752
$516$		0			0
$517$	10.4693	+	18.1334i	0.460439	+	0.797504i
$518$		0			0
$519$	−41.2464	−	5.05563i	−1.81052	−	0.221918i
$520$		0			0
$521$	15.5075	+	26.8598i	0.679396	+	1.17675i	0.975163	+	0.221488i	$0.0710914\pi$
$521$	15.5075	+	26.8598i	0.679396	+	1.17675i	−0.295767	+	0.955260i	$0.595575\pi$
$522$		0			0
$523$	−3.67840	+	6.37117i	−0.160845	+	0.278592i	−0.935172	−	0.354194i	$-0.884755\pi$
$523$	−3.67840	+	6.37117i	−0.160845	+	0.278592i	0.774327	+	0.632786i	$0.218089\pi$
$524$		0			0
$525$	5.84529	+	22.1365i	0.255109	+	0.966118i
$526$		0			0
$527$	−2.81472			−0.122611
$528$		0			0
$529$	15.5015			0.673980
$530$		0			0
$531$	26.2387	+	6.53033i	1.13866	+	0.283392i
$532$		0			0
$533$	−2.49648	+	4.32404i	−0.108135	+	0.187295i
$534$		0			0
$535$	0.549094	−	0.951059i	0.0237394	−	0.0411179i
$536$		0			0
$537$	14.7128	+	1.80337i	0.634905	+	0.0778211i
$538$		0			0
$539$	5.21976	+	21.6432i	0.224831	+	0.932238i
$540$		0			0
$541$	−14.4735	+	25.0688i	−0.622262	+	1.07779i	0.366801	+	0.930299i	$0.380453\pi$
$541$	−14.4735	+	25.0688i	−0.622262	+	1.07779i	−0.989063	+	0.147491i	$0.952880\pi$
$542$		0			0
$543$	−0.659294	+	0.875295i	−0.0282930	+	0.0375625i
$544$		0			0
$545$	−0.410812	−	0.711546i	−0.0175972	−	0.0304793i
$546$		0			0
$547$	9.34891	−	16.1928i	0.399731	−	0.692354i	−0.593962	−	0.804493i	$-0.702437\pi$
$547$	9.34891	−	16.1928i	0.399731	−	0.692354i	0.993692	+	0.112140i	$0.0357704\pi$
$548$		0			0
$549$	28.9169	−	29.9695i	1.23414	−	1.27907i
$550$		0			0
$551$	−4.47452	−	7.75010i	−0.190621	−	0.330165i
$552$		0			0
$553$	−7.79940	−	1.12674i	−0.331664	−	0.0479138i
$554$		0			0
$555$	0.357566	+	0.841881i	0.0151778	+	0.0357358i
$556$		0			0
$557$	−17.1787	−	29.7544i	−0.727886	−	1.26074i	−0.957775	−	0.287519i	$-0.907170\pi$
$557$	−17.1787	−	29.7544i	−0.727886	−	1.26074i	0.229889	−	0.973217i	$-0.426164\pi$
$558$		0			0
$559$	3.99397			0.168927
$560$		0			0
$561$	−6.06612	−	0.743532i	−0.256112	−	0.0313919i
$562$		0			0
$563$	7.37355	−	12.7714i	0.310758	−	0.538249i	−0.667769	−	0.744369i	$-0.732750\pi$
$563$	7.37355	−	12.7714i	0.310758	−	0.538249i	0.978527	+	0.206120i	$0.0660838\pi$
$564$		0			0
$565$	−0.0682247	−	0.118169i	−0.00287024	−	0.00497139i
$566$		0			0
$567$	2.56017	−	23.6737i	0.107517	−	0.994203i
$568$		0			0
$569$	−1.66821	−	2.88942i	−0.0699349	−	0.121131i	0.828938	−	0.559341i	$-0.188946\pi$
$569$	−1.66821	−	2.88942i	−0.0699349	−	0.121131i	−0.898872	+	0.438210i	$0.855613\pi$
$570$		0			0
$571$	−9.40360	+	16.2875i	−0.393528	+	0.681611i	−0.992912	−	0.118851i	$-0.962079\pi$
$571$	−9.40360	+	16.2875i	−0.393528	+	0.681611i	0.599384	+	0.800462i	$0.295412\pi$
$572$		0			0
$573$	40.5437	+	4.96949i	1.69374	+	0.207603i
$574$		0			0
$575$	31.0010			1.29283
$576$		0			0
$577$	−17.6961	−	30.6505i	−0.736697	−	1.27600i	−0.953975	−	0.299887i	$-0.903051\pi$
$577$	−17.6961	−	30.6505i	−0.736697	−	1.27600i	0.217277	−	0.976110i	$-0.430282\pi$
$578$		0			0
$579$	−17.3378	−	40.8214i	−0.720534	−	1.69648i
$580$		0			0
$581$	4.26614	+	10.6771i	0.176989	+	0.442961i
$582$		0			0
$583$	5.03346	+	8.71821i	0.208465	+	0.361072i
$584$		0			0
$585$	0.0651670	−	0.0675392i	0.00269432	−	0.00279240i
$586$		0			0
$587$	−17.2921	+	29.9508i	−0.713722	+	1.23620i	0.249728	+	0.968316i	$0.419659\pi$
$587$	−17.2921	+	29.9508i	−0.713722	+	1.23620i	−0.963450	+	0.267887i	$0.913674\pi$
$588$		0			0
$589$	−2.36862	−	4.10257i	−0.0975973	−	0.169043i
$590$		0			0
$591$	−9.85613	+	13.0852i	−0.405427	+	0.538255i
$592$		0			0
$593$	−15.9787	+	27.6759i	−0.656166	+	1.13651i	0.325434	+	0.945565i	$0.394490\pi$
$593$	−15.9787	+	27.6759i	−0.656166	+	1.13651i	−0.981600	+	0.190949i	$0.938844\pi$
$594$		0			0
$595$	−0.180023	−	0.0260070i	−0.00738023	−	0.00106618i
$596$		0			0
$597$	−14.2738	−	1.74956i	−0.584188	−	0.0716047i
$598$		0			0
$599$	4.92476	−	8.52993i	0.201220	−	0.348524i	−0.747702	−	0.664035i	$-0.768843\pi$
$599$	4.92476	−	8.52993i	0.201220	−	0.348524i	0.948922	+	0.315511i	$0.102176\pi$
$600$		0			0
$601$	−3.77340	+	6.53572i	−0.153920	+	0.266598i	−0.932665	−	0.360743i	$-0.882523\pi$
$601$	−3.77340	+	6.53572i	−0.153920	+	0.266598i	0.778745	+	0.627340i	$0.215857\pi$
$602$		0			0
$603$	9.70252	+	2.41478i	0.395117	+	0.0983374i
$604$		0			0
$605$	0.0547937			0.00222768
$606$		0			0
$607$	10.8584			0.440730			0.220365	−	0.975417i	$-0.429275\pi$
$607$	10.8584			0.440730			0.220365	+	0.975417i	$0.429275\pi$
$608$		0			0
$609$	−21.1946	−	5.76176i	−0.858850	−	0.233478i
$610$		0			0
$611$	−1.66175	+	2.87823i	−0.0672272	+	0.116441i
$612$		0			0
$613$	−23.8823	−	41.3653i	−0.964596	−	1.67073i	−0.710697	−	0.703499i	$-0.751620\pi$
$613$	−23.8823	−	41.3653i	−0.964596	−	1.67073i	−0.253899	−	0.967231i	$-0.581713\pi$
$614$		0			0
$615$	−1.05368	−	0.129151i	−0.0424886	−	0.00520788i
$616$		0			0
$617$	−18.7769	−	32.5225i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$617$	−18.7769	−	32.5225i	−0.755929	−	1.30931i	0.188982	−	0.981980i	$-0.439481\pi$
$618$		0			0
$619$	35.9657			1.44558			0.722792	−	0.691065i	$-0.242858\pi$
$619$	35.9657			1.44558			0.722792	+	0.691065i	$0.242858\pi$
$620$		0			0
$621$	−30.1077	−	11.5355i	−1.20818	−	0.462904i
$622$		0			0
$623$	−8.44390	−	21.1330i	−0.338298	−	0.846677i
$624$		0			0
$625$	24.9424			0.997696
$626$		0			0
$627$	−4.02098	−	9.46730i	−0.160582	−	0.378088i
$628$		0			0
$629$	9.45398			0.376955
$630$		0			0
$631$	−31.8848			−1.26931			−0.634656	−	0.772794i	$-0.718858\pi$
$631$	−31.8848			−1.26931			−0.634656	+	0.772794i	$0.718858\pi$
$632$		0			0
$633$	34.7840	+	4.26353i	1.38254	+	0.169460i
$634$		0			0
$635$	0.285858			0.0113439
$636$		0			0
$637$	−2.56083	+	2.43518i	−0.101464	+	0.0964854i
$638$		0			0
$639$	−1.86867	−	6.50649i	−0.0739233	−	0.257393i
$640$		0			0
$641$	16.6788			0.658772			0.329386	−	0.944195i	$-0.393158\pi$
$641$	16.6788			0.658772			0.329386	+	0.944195i	$0.393158\pi$
$642$		0			0
$643$	23.5295	+	40.7544i	0.927915	+	1.60720i	0.786805	+	0.617201i	$0.211734\pi$
$643$	23.5295	+	40.7544i	0.927915	+	1.60720i	0.141109	+	0.989994i	$0.454933\pi$
$644$		0			0
$645$	0.331961	+	0.781595i	0.0130710	+	0.0307753i
$646$		0			0
$647$	−12.2324	−	21.1872i	−0.480906	−	0.832954i	0.518854	−	0.854863i	$-0.326359\pi$
$647$	−12.2324	−	21.1872i	−0.480906	−	0.832954i	−0.999760	+	0.0219091i	$0.993026\pi$
$648$		0			0
$649$	14.3331	−	24.8257i	0.562625	−	0.974495i
$650$		0			0
$651$	−11.2195	−	3.05003i	−0.439728	−	0.119540i
$652$		0			0
$653$	−11.8261			−0.462792			−0.231396	−	0.972860i	$-0.574329\pi$
$653$	−11.8261			−0.462792			−0.231396	+	0.972860i	$0.574329\pi$
$654$		0			0
$655$	0.00942795			0.000368380
$656$		0			0
$657$	8.64486	−	8.95954i	0.337268	−	0.349545i
$658$		0			0
$659$	3.51539	−	6.08883i	0.136940	−	0.237187i	−0.789397	−	0.613883i	$-0.789607\pi$
$659$	3.51539	−	6.08883i	0.136940	−	0.237187i	0.926337	+	0.376696i	$0.122940\pi$
$660$		0			0
$661$	−7.43024	+	12.8696i	−0.289003	+	0.500568i	−0.973572	−	0.228380i	$-0.926657\pi$
$661$	−7.43024	+	12.8696i	−0.289003	+	0.500568i	0.684569	+	0.728948i	$0.259990\pi$
$662$		0			0
$663$	−0.379219	−	0.892862i	−0.0147276	−	0.0346759i
$664$		0			0
$665$	−0.113585	−	0.284276i	−0.00440465	−	0.0110238i
$666$		0			0
$667$	−14.8699	+	25.7554i	−0.575764	+	0.997253i
$668$		0			0
$669$	−3.27606	−	7.71341i	−0.126660	−	0.298218i
$670$		0			0
$671$	−22.0759	−	38.2366i	−0.852231	−	1.47611i
$672$		0			0
$673$	7.81679	−	13.5391i	0.301315	−	0.521893i	−0.675119	−	0.737709i	$-0.735908\pi$
$673$	7.81679	−	13.5391i	0.301315	−	0.521893i	0.976434	+	0.215816i	$0.0692411\pi$
$674$		0			0
$675$	−24.2424	−	9.28824i	−0.933089	−	0.357505i
$676$		0			0
$677$	−12.3561	−	21.4014i	−0.474883	−	0.822522i	0.524703	−	0.851285i	$-0.324176\pi$
$677$	−12.3561	−	21.4014i	−0.474883	−	0.822522i	−0.999586	+	0.0287634i	$0.990843\pi$
$678$		0			0
$679$	−6.43332	−	16.1010i	−0.246888	−	0.617901i
$680$		0			0
$681$	−0.700502	+	0.930004i	−0.0268433	+	0.0356378i
$682$		0			0
$683$	−16.7467	−	29.0061i	−0.640794	−	1.10989i	−0.985256	−	0.171087i	$-0.945272\pi$
$683$	−16.7467	−	29.0061i	−0.640794	−	1.10989i	0.344462	−	0.938800i	$-0.388061\pi$
$684$		0			0
$685$	0.220326			0.00841821
$686$		0			0
$687$	6.39373	−	8.48848i	0.243936	−	0.323856i
$688$		0			0
$689$	−0.798941	+	1.38381i	−0.0304372	+	0.0527189i
$690$		0			0
$691$	1.33836	+	2.31811i	0.0509137	+	0.0881851i	0.890359	−	0.455259i	$-0.150453\pi$
$691$	1.33836	+	2.31811i	0.0509137	+	0.0881851i	−0.839445	+	0.543444i	$0.817120\pi$
$692$		0			0
$693$	−23.3739	−	9.53696i	−0.887903	−	0.362279i
$694$		0			0
$695$	0.471552	+	0.816752i	0.0178870	+	0.0309812i
$696$		0			0
$697$	−5.48617	+	9.50232i	−0.207803	+	0.359926i
$698$		0			0
$699$	16.4525	+	38.7370i	0.622291	+	1.46517i
$700$		0			0
$701$	−36.3715			−1.37373			−0.686866	−	0.726784i	$-0.741014\pi$
$701$	−36.3715			−1.37373			−0.686866	+	0.726784i	$0.741014\pi$
$702$		0			0
$703$	7.95563	+	13.7796i	0.300052	+	0.519706i
$704$		0			0
$705$	−0.701369	−	0.0859677i	−0.0264151	−	0.00323773i
$706$		0			0
$707$	−10.6669	+	13.5453i	−0.401169	+	0.509423i
$708$		0			0
$709$	5.95369	+	10.3121i	0.223596	+	0.387279i	0.955897	−	0.293702i	$-0.0948872\pi$
$709$	5.95369	+	10.3121i	0.223596	+	0.387279i	−0.732302	+	0.680980i	$0.761554\pi$
$710$		0			0
$711$	6.20442	−	6.43027i	0.232684	−	0.241154i
$712$		0			0
$713$	−7.87148	+	13.6338i	−0.294789	+	0.510590i
$714$		0			0
$715$	−0.0497501	−	0.0861698i	−0.00186055	−	0.00322257i
$716$		0			0
$717$	−46.7543	−	5.73073i	−1.74607	−	0.214018i
$718$		0			0
$719$	8.44050	−	14.6194i	0.314778	−	0.545211i	−0.664613	−	0.747188i	$-0.731403\pi$
$719$	8.44050	−	14.6194i	0.314778	−	0.545211i	0.979390	+	0.201977i	$0.0647367\pi$
$720$		0			0
$721$	−27.8592	+	35.3769i	−1.03753	+	1.31750i
$722$		0			0
$723$	26.8914	−	35.7016i	1.00010	−	1.32776i
$724$		0			0
$725$	−11.9731	+	20.7379i	−0.444668	+	0.770187i
$726$		0			0
$727$	1.24570	−	2.15762i	0.0462006	−	0.0800218i	−0.842000	−	0.539477i	$-0.818622\pi$
$727$	1.24570	−	2.15762i	0.0462006	−	0.0800218i	0.888201	+	0.459455i	$0.151955\pi$
$728$		0			0
$729$	20.0877	+	18.0412i	0.743988	+	0.668193i
$730$		0			0
$731$	8.77699			0.324629
$732$		0			0
$733$	−12.5131			−0.462181			−0.231090	−	0.972932i	$-0.574229\pi$
$733$	−12.5131			−0.462181			−0.231090	+	0.972932i	$0.574229\pi$
$734$		0			0
$735$	−0.689394	−	0.298737i	−0.0254287	−	0.0110191i
$736$		0			0
$737$	5.30009	−	9.18003i	0.195231	−	0.338151i
$738$		0			0
$739$	−10.0051	−	17.3294i	−0.368044	−	0.637472i	0.621215	−	0.783640i	$-0.286639\pi$
$739$	−10.0051	−	17.3294i	−0.368044	−	0.637472i	−0.989260	+	0.146168i	$0.953306\pi$
$740$		0			0
$741$	0.982265	−	1.30408i	0.0360844	−	0.0479066i
$742$		0			0
$743$	5.49879	+	9.52419i	0.201731	+	0.349408i	0.949086	−	0.315016i	$-0.102010\pi$
$743$	5.49879	+	9.52419i	0.201731	+	0.349408i	−0.747355	+	0.664425i	$0.768677\pi$
$744$		0			0
$745$	−0.0227374			−0.000833034
$746$		0			0
$747$	−12.6514	−	3.14870i	−0.462890	−	0.115205i
$748$		0			0
$749$	−17.3967	−	43.5398i	−0.635663	−	1.59091i
$750$		0			0
$751$	28.8670			1.05337			0.526686	−	0.850060i	$-0.323434\pi$
$751$	28.8670			1.05337			0.526686	+	0.850060i	$0.323434\pi$
$752$		0			0
$753$	28.2135	−	37.4569i	1.02816	−	1.36500i
$754$		0			0
$755$	0.779774			0.0283789
$756$		0			0
$757$	−17.3626			−0.631053			−0.315527	−	0.948917i	$-0.602181\pi$
$757$	−17.3626			−0.631053			−0.315527	+	0.948917i	$0.602181\pi$
$758$		0			0
$759$	−20.5656	+	27.3034i	−0.746484	+	0.991051i
$760$		0			0
$761$	−52.0039			−1.88514			−0.942571	−	0.334006i	$-0.891599\pi$
$761$	−52.0039			−1.88514			−0.942571	+	0.334006i	$0.891599\pi$
$762$		0			0
$763$	−34.7184	−	5.01559i	−1.25689	−	0.181577i
$764$		0			0
$765$	0.143208	−	0.148421i	0.00517771	−	0.00536618i
$766$		0			0
$767$	4.55008			0.164294
$768$		0			0
$769$	13.5839	+	23.5280i	0.489849	+	0.848443i	0.999932	−	0.0116822i	$-0.00371865\pi$
$769$	13.5839	+	23.5280i	0.489849	+	0.848443i	−0.510083	+	0.860125i	$0.670385\pi$
$770$		0			0
$771$	14.0905	−	18.7069i	0.507457	−	0.673712i
$772$		0			0
$773$	12.2452	+	21.2093i	0.440428	+	0.762845i	0.997721	−	0.0674716i	$-0.0214932\pi$
$773$	12.2452	+	21.2093i	0.440428	+	0.762845i	−0.557293	+	0.830316i	$0.688160\pi$
$774$		0			0
$775$	−6.33802	+	10.9778i	−0.227668	+	0.394333i
$776$		0			0
$777$	37.6837	+	10.2443i	1.35189	+	0.367513i
$778$		0			0
$779$	−18.4667			−0.661638
$780$		0			0
$781$	−7.17689			−0.256809
$782$		0			0
$783$	19.3447	−	15.6852i	0.691322	−	0.560543i
$784$		0			0
$785$	−0.169011	+	0.292736i	−0.00603227	+	0.0104482i
$786$		0			0
$787$	−0.939312	+	1.62694i	−0.0334828	+	0.0579940i	−0.882281	−	0.470723i	$-0.843993\pi$
$787$	−0.939312	+	1.62694i	−0.0334828	+	0.0579940i	0.848798	+	0.528717i	$0.177327\pi$
$788$		0			0
$789$	13.9374	−	18.5036i	0.496184	−	0.658747i
$790$		0			0
$791$	−5.76579	−	0.832955i	−0.205008	−	0.0296165i
$792$		0			0
$793$	3.50402	−	6.06914i	0.124431	−	0.215521i
$794$		0			0
$795$	−0.337206	−	0.0413318i	−0.0119595	−	0.00146589i
$796$		0			0
$797$	17.6067	+	30.4957i	0.623662	+	1.08021i	0.988798	+	0.149259i	$0.0476890\pi$
$797$	17.6067	+	30.4957i	0.623662	+	1.08021i	−0.365137	+	0.930954i	$0.618978\pi$
$798$		0			0
$799$	−3.65179	+	6.32509i	−0.129191	+	0.223765i
$800$		0			0
$801$	25.0407	+	6.23218i	0.884770	+	0.220203i
$802$		0			0
$803$	−6.59970	−	11.4310i	−0.232898	−	0.403392i
$804$		0			0
$805$	−0.629413	+	0.799257i	−0.0221839	+	0.0281701i
$806$		0			0
$807$	−13.4645	−	1.65036i	−0.473971	−	0.0580953i
$808$		0			0
$809$	1.53614	+	2.66067i	0.0540077	+	0.0935441i	0.891765	−	0.452498i	$-0.149467\pi$
$809$	1.53614	+	2.66067i	0.0540077	+	0.0935441i	−0.837758	+	0.546042i	$0.816134\pi$
$810$		0			0
$811$	−14.8034			−0.519818			−0.259909	−	0.965633i	$-0.583693\pi$
$811$	−14.8034			−0.519818			−0.259909	+	0.965633i	$0.583693\pi$
$812$		0			0
$813$	20.5482	+	48.3803i	0.720657	+	1.69677i
$814$		0			0
$815$	−0.237688	+	0.411689i	−0.00832586	+	0.0144208i
$816$		0			0
$817$	7.38594	+	12.7928i	0.258401	+	0.447564i
$818$		0			0
$819$	−0.544069	−	3.96988i	−0.0190113	−	0.138719i
$820$		0			0
$821$	−12.5061	−	21.6612i	−0.436467	−	0.755982i	0.560947	−	0.827851i	$-0.310437\pi$
$821$	−12.5061	−	21.6612i	−0.436467	−	0.755982i	−0.997414	+	0.0718690i	$0.977104\pi$
$822$		0			0
$823$	−19.7480	+	34.2046i	−0.688374	+	1.19230i	0.283990	+	0.958827i	$0.408342\pi$
$823$	−19.7480	+	34.2046i	−0.688374	+	1.19230i	−0.972364	+	0.233471i	$0.924992\pi$
$824$		0			0
$825$	−16.5592	+	21.9844i	−0.576517	+	0.765398i
$826$		0			0
$827$	12.4528			0.433026			0.216513	−	0.976280i	$-0.430532\pi$
$827$	12.4528			0.433026			0.216513	+	0.976280i	$0.430532\pi$
$828$		0			0
$829$	−14.2995	−	24.7675i	−0.496643	−	0.860211i	0.503350	−	0.864083i	$-0.332101\pi$
$829$	−14.2995	−	24.7675i	−0.496643	−	0.860211i	−0.999993	+	0.00387209i	$0.998767\pi$
$830$		0			0
$831$	23.6474	−	31.3949i	0.820320	−	1.08908i
$832$		0			0
$833$	−5.62758	+	5.35145i	−0.194984	+	0.185417i
$834$		0			0
$835$	0.587154	+	1.01698i	0.0203193	+	0.0351941i
$836$		0			0
$837$	10.2402	−	8.30307i	0.353954	−	0.286996i
$838$		0			0
$839$	21.0794	−	36.5107i	0.727743	−	1.26049i	−0.230092	−	0.973169i	$-0.573903\pi$
$839$	21.0794	−	36.5107i	0.727743	−	1.26049i	0.957835	−	0.287319i	$-0.0927641\pi$
$840$		0			0
$841$	3.01405	+	5.22048i	0.103933	+	0.180017i
$842$		0			0
$843$	−13.6538	−	32.1476i	−0.470263	−	1.10722i
$844$		0			0
$845$	−0.394904	+	0.683993i	−0.0135851	+	0.0235301i
$846$		0			0
$847$	1.44735	−	1.83791i	0.0497316	−	0.0631514i
$848$		0			0
$849$	11.4470	+	26.9518i	0.392861	+	0.924983i
$850$		0			0
$851$	26.4384	−	45.7927i	0.906297	−	1.56975i
$852$		0			0
$853$	−25.6206	+	44.3761i	−0.877232	+	1.51941i	−0.0228654	+	0.999739i	$0.507279\pi$
$853$	−25.6206	+	44.3761i	−0.877232	+	1.51941i	−0.854366	+	0.519671i	$0.826054\pi$
$854$		0			0
$855$	0.336841	+	0.0838337i	0.0115197	+	0.00286705i
$856$		0			0
$857$	−37.8058			−1.29142			−0.645710	−	0.763582i	$-0.723439\pi$
$857$	−37.8058			−1.29142			−0.645710	+	0.763582i	$0.723439\pi$
$858$		0			0
$859$	−44.6224			−1.52250			−0.761249	−	0.648460i	$-0.775413\pi$
$859$	−44.6224			−1.52250			−0.761249	+	0.648460i	$0.775413\pi$
$860$		0			0
$861$	−32.1646	+	31.9316i	−1.09617	+	1.08823i
$862$		0			0
$863$	−15.4848	+	26.8205i	−0.527109	+	0.912980i	0.472392	+	0.881389i	$0.343391\pi$
$863$	−15.4848	+	26.8205i	−0.527109	+	0.912980i	−0.999501	+	0.0315912i	$0.989943\pi$
$864$		0			0
$865$	−0.743379	−	1.28757i	−0.0252756	−	0.0437787i
$866$		0			0
$867$	10.6774	+	25.1396i	0.362622	+	0.853786i
$868$		0			0
$869$	−4.73661	−	8.20405i	−0.160678	−	0.278303i
$870$		0			0
$871$	1.68253			0.0570102
$872$		0			0
$873$	19.0782	+	4.74823i	0.645701	+	0.160703i
$874$		0			0
$875$	−1.01398	+	1.28760i	−0.0342788	+	0.0435288i
$876$		0			0
$877$	23.1686			0.782347			0.391174	−	0.920317i	$-0.372069\pi$
$877$	23.1686			0.782347			0.391174	+	0.920317i	$0.372069\pi$
$878$		0			0
$879$	−8.27263	−	1.01399i	−0.279029	−	0.0342009i
$880$		0			0
$881$	14.0143			0.472155			0.236077	−	0.971734i	$-0.424138\pi$
$881$	14.0143			0.472155			0.236077	+	0.971734i	$0.424138\pi$
$882$		0			0
$883$	−39.9269			−1.34365			−0.671824	−	0.740711i	$-0.734489\pi$
$883$	−39.9269			−1.34365			−0.671824	+	0.740711i	$0.734489\pi$
$884$		0			0
$885$	0.378182	+	0.890422i	0.0127125	+	0.0299312i
$886$		0			0
$887$	−26.8441			−0.901338			−0.450669	−	0.892691i	$-0.648814\pi$
$887$	−26.8441			−0.901338			−0.450669	+	0.892691i	$0.648814\pi$
$888$		0			0
$889$	7.55082	−	9.58837i	0.253246	−	0.321584i
$890$		0			0
$891$	24.2625	−	15.1892i	0.812823	−	0.508858i
$892$		0			0
$893$	−12.2921			−0.411339
$894$		0			0
$895$	0.265167	+	0.459283i	0.00886356	+	0.0153521i
$896$		0			0
$897$	−5.38530	−	0.660083i	−0.179810	−	0.0220395i
$898$		0			0
$899$	−6.08017	−	10.5312i	−0.202785	−	0.351234i
$900$		0			0
$901$	−1.75572	+	3.04100i	−0.0584915	+	0.101310i
$902$		0			0
$903$	34.9852	+	9.51073i	1.16424	+	0.316497i
$904$		0			0
$905$	−0.0392060			−0.00130325
$906$		0			0
$907$	37.7617			1.25386			0.626928	−	0.779077i	$-0.284312\pi$
$907$	37.7617			1.25386			0.626928	+	0.779077i	$0.284312\pi$
$908$		0			0
$909$	−5.39650	−	18.7900i	−0.178991	−	0.623226i
$910$		0			0
$911$	7.93650	−	13.7464i	0.262948	−	0.455439i	−0.704076	−	0.710125i	$-0.748639\pi$
$911$	7.93650	−	13.7464i	0.262948	−	0.455439i	0.967024	+	0.254685i	$0.0819719\pi$
$912$		0			0
$913$	−6.91094	+	11.9701i	−0.228719	+	0.396153i
$914$		0			0
$915$	1.47893	+	0.181274i	0.0488919	+	0.00599274i
$916$		0			0
$917$	0.249035	−	0.316236i	0.00822388	−	0.0104430i
$918$		0			0
$919$	5.22203	−	9.04482i	0.172259	−	0.298361i	−0.766950	−	0.641706i	$-0.778227\pi$
$919$	5.22203	−	9.04482i	0.172259	−	0.298361i	0.939209	+	0.343345i	$0.111560\pi$
$920$		0			0
$921$	−16.5887	+	22.0236i	−0.546617	+	0.725702i
$922$		0			0
$923$	−0.569580	−	0.986541i	−0.0187479	−	0.0324724i
$924$		0			0
$925$	21.2879	−	36.8717i	0.699941	−	1.21233i
$926$		0			0
$927$	−14.0943	−	49.0749i	−0.462918	−	1.61183i
$928$		0			0
$929$	9.58169	+	16.5960i	0.314365	+	0.544496i	0.979302	−	0.202403i	$-0.0648751\pi$
$929$	9.58169	+	16.5960i	0.314365	+	0.544496i	−0.664937	+	0.746899i	$0.731542\pi$
$930$		0			0
$931$	−12.5356	−	3.69912i	−0.410839	−	0.121234i
$932$		0			0
$933$	0.177989	+	0.419071i	0.00582710	+	0.0137198i
$934$		0			0
$935$	−0.109329	−	0.189363i	−0.00357543	−	0.00619283i
$936$		0			0
$937$	3.09451			0.101093			0.0505467	−	0.998722i	$-0.483904\pi$
$937$	3.09451			0.101093			0.0505467	+	0.998722i	$0.483904\pi$
$938$		0			0
$939$	−10.7461	−	1.31716i	−0.350685	−	0.0429839i
$940$		0			0
$941$	−7.65564	+	13.2600i	−0.249567	+	0.432262i	−0.963406	−	0.268048i	$-0.913622\pi$
$941$	−7.65564	+	13.2600i	−0.249567	+	0.432262i	0.713839	+	0.700310i	$0.246955\pi$
$942$		0			0
$943$	30.6845	+	53.1472i	0.999226	+	1.73071i
$944$		0			0
$945$	0.731659	−	0.436429i	0.0238009	−	0.0141970i
$946$		0			0
$947$	−0.507747	−	0.879443i	−0.0164995	−	0.0285781i	0.857658	−	0.514221i	$-0.171919\pi$
$947$	−0.507747	−	0.879443i	−0.0164995	−	0.0285781i	−0.874157	+	0.485643i	$0.838586\pi$
$948$		0			0
$949$	1.04754	−	1.81440i	0.0340047	−	0.0588979i
$950$		0			0
$951$	−33.8322	−	4.14686i	−1.09708	−	0.134471i
$952$		0			0
$953$	−35.4930			−1.14973			−0.574865	−	0.818248i	$-0.694945\pi$
$953$	−35.4930			−1.14973			−0.574865	+	0.818248i	$0.694945\pi$
$954$		0			0
$955$	0.730713	+	1.26563i	0.0236453	+	0.0409549i
$956$		0			0
$957$	−10.3217	−	24.3022i	−0.333654	−	0.785580i
$958$		0			0
$959$	5.81982	−	7.39026i	0.187932	−	0.238644i
$960$		0			0
$961$	12.2814	+	21.2720i	0.396175	+	0.686195i
$962$		0			0
$963$	51.5907	+	12.8400i	1.66249	+	0.413763i
$964$		0			0
$965$	0.793390	−	1.37419i	0.0255401	−	0.0442368i
$966$		0			0
$967$	6.87762	+	11.9124i	0.221169	+	0.383077i	0.955163	−	0.296079i	$-0.0956793\pi$
$967$	6.87762	+	11.9124i	0.221169	+	0.383077i	−0.733994	+	0.679156i	$0.762346\pi$
$968$		0			0
$969$	2.15859	−	2.86579i	0.0693437	−	0.0920625i
$970$		0			0
$971$	−21.6567	+	37.5104i	−0.694995	+	1.20377i	0.275187	+	0.961391i	$0.411260\pi$
$971$	−21.6567	+	37.5104i	−0.694995	+	1.20377i	−0.970182	+	0.242376i	$0.922073\pi$
$972$		0			0
$973$	39.8517	+	5.75718i	1.27759	+	0.184567i
$974$		0			0
$975$	−4.33618	−	0.531491i	−0.138869	−	0.0170213i
$976$		0			0
$977$	4.78420	−	8.28648i	0.153060	−	0.265108i	−0.779291	−	0.626662i	$-0.784421\pi$
$977$	4.78420	−	8.28648i	0.153060	−	0.265108i	0.932351	+	0.361554i	$0.117754\pi$
$978$		0			0
$979$	13.6787	−	23.6923i	0.437174	−	0.757208i
$980$		0			0
$981$	27.6185	−	28.6238i	0.881790	−	0.913889i
$982$		0			0
$983$	17.1329			0.546454			0.273227	−	0.961950i	$-0.411909\pi$
$983$	17.1329			0.546454			0.273227	+	0.961950i	$0.411909\pi$
$984$		0			0
$985$	−0.586111			−0.0186751
$986$		0			0
$987$	−21.4099	+	21.2548i	−0.681486	+	0.676548i
$988$		0			0
$989$	24.5452	−	42.5135i	0.780492	−	1.35185i
$990$		0			0
$991$	6.32891	+	10.9620i	0.201044	+	0.348219i	0.948865	−	0.315682i	$-0.102233\pi$
$991$	6.32891	+	10.9620i	0.201044	+	0.348219i	−0.747821	+	0.663901i	$0.768900\pi$
$992$		0			0
$993$	42.1781	+	5.16982i	1.33848	+	0.164059i
$994$		0			0
$995$	−0.257255	−	0.445579i	−0.00815553	−	0.0141258i
$996$		0			0
$997$	−25.6704			−0.812989			−0.406495	−	0.913653i	$-0.633249\pi$
$997$	−25.6704			−0.812989			−0.406495	+	0.913653i	$0.633249\pi$
$998$		0			0
$999$	−34.3945	+	27.8880i	−1.08819	+	0.882338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.457.4	yes	22
3.2	odd	2		1512.2.t.c.289.6		22
4.3	odd	2		1008.2.t.l.961.8		22
7.4	even	3		504.2.q.c.25.11	✓	22
9.4	even	3		504.2.q.c.121.11	yes	22
9.5	odd	6		1512.2.q.d.793.6		22
12.11	even	2		3024.2.t.k.289.6		22
21.11	odd	6		1512.2.q.d.1369.6		22
28.11	odd	6		1008.2.q.l.529.1		22
36.23	even	6		3024.2.q.l.2305.6		22
36.31	odd	6		1008.2.q.l.625.1		22
63.4	even	3	inner	504.2.t.c.193.4	yes	22
63.32	odd	6		1512.2.t.c.361.6		22
84.11	even	6		3024.2.q.l.2881.6		22
252.67	odd	6		1008.2.t.l.193.8		22
252.95	even	6		3024.2.t.k.1873.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.11	✓	22	7.4	even	3
504.2.q.c.121.11	yes	22	9.4	even	3
504.2.t.c.193.4	yes	22	63.4	even	3	inner
504.2.t.c.457.4	yes	22	1.1	even	1	trivial
1008.2.q.l.529.1		22	28.11	odd	6
1008.2.q.l.625.1		22	36.31	odd	6
1008.2.t.l.193.8		22	252.67	odd	6
1008.2.t.l.961.8		22	4.3	odd	2
1512.2.q.d.793.6		22	9.5	odd	6
1512.2.q.d.1369.6		22	21.11	odd	6
1512.2.t.c.289.6		22	3.2	odd	2
1512.2.t.c.361.6		22	63.32	odd	6
3024.2.q.l.2305.6		22	36.23	even	6
3024.2.q.l.2881.6		22	84.11	even	6
3024.2.t.k.289.6		22	12.11	even	2
3024.2.t.k.1873.6		22	252.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.04208 + 1.38350i) q^{3} -0.0619693 q^{5} +(-1.63689 + 2.07860i) q^{7} +(-0.828124 - 2.88344i) q^{9} +O(q^{10})\)	\(q+(-1.04208 + 1.38350i) q^{3} -0.0619693 q^{5} +(-1.63689 + 2.07860i) q^{7} +(-0.828124 - 2.88344i) q^{9} -3.18053 q^{11} +(-0.252417 - 0.437198i) q^{13} +(0.0645772 - 0.0857342i) q^{15} +(-0.554700 - 0.960769i) q^{17} +(0.933573 - 1.61700i) q^{19} +(-1.16996 - 4.43071i) q^{21} -6.20496 q^{23} -4.99616 q^{25} +(4.85220 + 1.85908i) q^{27} +(2.39645 - 4.15077i) q^{29} +(1.26858 - 2.19724i) q^{31} +(3.31438 - 4.40026i) q^{33} +(0.101437 - 0.128809i) q^{35} +(-4.26085 + 7.38001i) q^{37} +(0.867902 + 0.106380i) q^{39} +(-4.94516 - 8.56527i) q^{41} +(-3.95574 + 6.85154i) q^{43} +(0.0513182 + 0.178684i) q^{45} +(-3.29168 - 5.70136i) q^{47} +(-1.64116 - 6.80489i) q^{49} +(1.90726 + 0.233776i) q^{51} +(-1.58258 - 2.74112i) q^{53} +0.197095 q^{55} +(1.26425 + 2.97664i) q^{57} +(-4.50652 + 7.80552i) q^{59} +(6.94094 + 12.0221i) q^{61} +(7.34906 + 2.99854i) q^{63} +(0.0156421 + 0.0270929i) q^{65} +(-1.66642 + 2.88632i) q^{67} +(6.46609 - 8.58454i) q^{69} +2.25651 q^{71} +(2.07503 + 3.59406i) q^{73} +(5.20642 - 6.91217i) q^{75} +(5.20619 - 6.61106i) q^{77} +(1.48925 + 2.57946i) q^{79} +(-7.62842 + 4.77569i) q^{81} +(2.17289 - 3.76355i) q^{83} +(0.0343744 + 0.0595381i) q^{85} +(3.24528 + 7.64093i) q^{87} +(-4.30077 + 7.44915i) q^{89} +(1.32194 + 0.190974i) q^{91} +(1.71791 + 4.04478i) q^{93} +(-0.0578528 + 0.100204i) q^{95} +(-3.27671 + 5.67542i) q^{97} +(2.63388 + 9.17087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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