LMFDB - Embedded newform 525.2.m.c.118.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(118,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("525.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.m (of order $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.1
Character	$\chi$	$=$	525.118
Dual form			525.2.m.c.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68361 + 1.68361i) q^{2} +(-0.707107 + 0.707107i) q^{3} -3.66908i q^{4} -2.38098i q^{6} +(0.901937 + 2.48727i) q^{7} +(2.81008 + 2.81008i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.68361 + 1.68361i) q^{2} +(-0.707107 + 0.707107i) q^{3} -3.66908i q^{4} -2.38098i q^{6} +(0.901937 + 2.48727i) q^{7} +(2.81008 + 2.81008i) q^{8} -1.00000i q^{9} +1.54510 q^{11} +(2.59443 + 2.59443i) q^{12} +(4.16009 - 4.16009i) q^{13} +(-5.70610 - 2.66908i) q^{14} -2.12398 q^{16} +(-2.05755 - 2.05755i) q^{17} +(1.68361 + 1.68361i) q^{18} +5.70610 q^{19} +(-2.39653 - 1.12100i) q^{21} +(-2.60134 + 2.60134i) q^{22} +(3.72781 + 3.72781i) q^{23} -3.97405 q^{24} +14.0079i q^{26} +(0.707107 + 0.707107i) q^{27} +(9.12599 - 3.30928i) q^{28} +9.79306i q^{29} -3.81783i q^{31} +(-2.04420 + 2.04420i) q^{32} +(-1.09255 + 1.09255i) q^{33} +6.92820 q^{34} -3.66908 q^{36} +(-2.81008 + 2.81008i) q^{37} +(-9.60684 + 9.60684i) q^{38} +5.88325i q^{39} -6.92820i q^{41} +(5.92215 - 2.14750i) q^{42} +(-1.02819 - 1.02819i) q^{43} -5.66908i q^{44} -12.5523 q^{46} +(2.05755 + 2.05755i) q^{47} +(1.50188 - 1.50188i) q^{48} +(-5.37302 + 4.48672i) q^{49} +2.90981 q^{51} +(-15.2637 - 15.2637i) q^{52} +(-4.89898 - 4.89898i) q^{53} -2.38098 q^{54} +(-4.45490 + 9.52393i) q^{56} +(-4.03482 + 4.03482i) q^{57} +(-16.4877 - 16.4877i) q^{58} +7.07972 q^{59} +15.2300i q^{61} +(6.42774 + 6.42774i) q^{62} +(2.48727 - 0.901937i) q^{63} -11.1312i q^{64} -3.67885i q^{66} +(5.31314 - 5.31314i) q^{67} +(-7.54930 + 7.54930i) q^{68} -5.27191 q^{69} -4.45490 q^{71} +(2.81008 - 2.81008i) q^{72} +(0.770882 - 0.770882i) q^{73} -9.46214i q^{74} -20.9361i q^{76} +(1.39358 + 3.84307i) q^{77} +(-9.90510 - 9.90510i) q^{78} +11.1312i q^{79} -1.00000 q^{81} +(11.6644 + 11.6644i) q^{82} +(-9.60684 + 9.60684i) q^{83} +(-4.11303 + 8.79306i) q^{84} +3.46214 q^{86} +(-6.92474 - 6.92474i) q^{87} +(4.34184 + 4.34184i) q^{88} +9.52393 q^{89} +(14.0994 + 6.59512i) q^{91} +(13.6776 - 13.6776i) q^{92} +(2.69961 + 2.69961i) q^{93} -6.92820 q^{94} -2.89093i q^{96} +(5.09607 + 5.09607i) q^{97} +(1.49217 - 16.5999i) q^{98} -1.54510i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 48 q^{11} + 24 q^{16} + 12 q^{21} - 24 q^{36} - 120 q^{46} + 48 q^{51} - 96 q^{56} - 96 q^{71} - 24 q^{81} - 120 q^{86} + 108 q^{91}+O(q^{100}) $ 24 * q + 48 * q^11 + 24 * q^16 + 12 * q^21 - 24 * q^36 - 120 * q^46 + 48 * q^51 - 96 * q^56 - 96 * q^71 - 24 * q^81 - 120 * q^86 + 108 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−1.68361	+	1.68361i	−1.19049	+	1.19049i	−0.213562	+	0.976930i	$0.568506\pi$
$2$	−1.68361	+	1.68361i	−1.19049	+	1.19049i	−0.976930	+	0.213562i	$0.931494\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		−	3.66908i		−	1.83454i
$5$		0			0
$5$		0			0
$6$		−	2.38098i		−	0.972032i
$7$	0.901937	+	2.48727i	0.340900	+	0.940099i
$7$	0.901937	+	2.48727i	0.340900	+	0.940099i
$8$	2.81008	+	2.81008i	0.993512	+	0.993512i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.54510			0.465864			0.232932	−	0.972493i	$-0.425168\pi$
$11$	1.54510			0.465864			0.232932	+	0.972493i	$0.425168\pi$
$12$	2.59443	+	2.59443i	0.748948	+	0.748948i
$13$	4.16009	−	4.16009i	1.15380	−	1.15380i	0.168017	−	0.985784i	$-0.446264\pi$
$13$	4.16009	−	4.16009i	1.15380	−	1.15380i	0.985784	−	0.168017i	$-0.0537363\pi$
$14$	−5.70610	−	2.66908i	−1.52502	−	0.713341i
$15$		0			0
$16$	−2.12398			−0.530996
$17$	−2.05755	−	2.05755i	−0.499028	−	0.499028i	0.412107	−	0.911135i	$-0.364793\pi$
$17$	−2.05755	−	2.05755i	−0.499028	−	0.499028i	−0.911135	+	0.412107i	$0.864793\pi$
$18$	1.68361	+	1.68361i	0.396830	+	0.396830i
$19$	5.70610			1.30907			0.654534	−	0.756032i	$-0.272865\pi$
$19$	5.70610			1.30907			0.654534	+	0.756032i	$0.272865\pi$
$20$		0			0
$21$	−2.39653	−	1.12100i	−0.522966	−	0.244622i
$22$	−2.60134	+	2.60134i	−0.554607	+	0.554607i
$23$	3.72781	+	3.72781i	0.777301	+	0.777301i	0.979371	−	0.202070i	$-0.0647668\pi$
$23$	3.72781	+	3.72781i	0.777301	+	0.777301i	−0.202070	+	0.979371i	$0.564767\pi$
$24$	−3.97405			−0.811199
$25$		0			0
$26$			14.0079i			2.74718i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	9.12599	−	3.30928i	1.72465	−	0.625395i
$29$			9.79306i			1.81853i	0.416222	+	0.909263i	$0.363354\pi$
$29$			9.79306i			1.81853i	−0.416222	+	0.909263i	$0.636646\pi$
$30$		0			0
$31$		−	3.81783i		−	0.685703i	−0.939390	−	0.342851i	$-0.888607\pi$
$31$		−	3.81783i		−	0.685703i	0.939390	−	0.342851i	$-0.111393\pi$
$32$	−2.04420	+	2.04420i	−0.361366	+	0.361366i
$33$	−1.09255	+	1.09255i	−0.190188	+	0.190188i
$34$	6.92820			1.18818
$35$		0			0
$36$	−3.66908			−0.611513
$37$	−2.81008	+	2.81008i	−0.461974	+	0.461974i	−0.899302	−	0.437328i	$-0.855925\pi$
$37$	−2.81008	+	2.81008i	−0.461974	+	0.461974i	0.437328	+	0.899302i	$0.355925\pi$
$38$	−9.60684	+	9.60684i	−1.55844	+	1.55844i
$39$			5.88325i			0.942075i
$40$		0			0
$41$		−	6.92820i		−	1.08200i	−0.841021	−	0.541002i	$-0.818045\pi$
$41$		−	6.92820i		−	1.08200i	0.841021	−	0.541002i	$-0.181955\pi$
$42$	5.92215	−	2.14750i	0.913807	−	0.331366i
$43$	−1.02819	−	1.02819i	−0.156798	−	0.156798i	0.624348	−	0.781146i	$-0.285365\pi$
$43$	−1.02819	−	1.02819i	−0.156798	−	0.156798i	−0.781146	+	0.624348i	$0.785365\pi$
$44$		−	5.66908i		−	0.854646i
$45$		0			0
$46$	−12.5523			−1.85074
$47$	2.05755	+	2.05755i	0.300124	+	0.300124i	0.841062	−	0.540938i	$-0.181931\pi$
$47$	2.05755	+	2.05755i	0.300124	+	0.300124i	−0.540938	+	0.841062i	$0.681931\pi$
$48$	1.50188	−	1.50188i	0.216778	−	0.216778i
$49$	−5.37302	+	4.48672i	−0.767574	+	0.640960i
$50$		0			0
$51$	2.90981			0.407455
$52$	−15.2637	−	15.2637i	−2.11669	−	2.11669i
$53$	−4.89898	−	4.89898i	−0.672927	−	0.672927i	0.285463	−	0.958390i	$-0.407853\pi$
$53$	−4.89898	−	4.89898i	−0.672927	−	0.672927i	−0.958390	+	0.285463i	$0.907853\pi$
$54$	−2.38098			−0.324011
$55$		0			0
$56$	−4.45490	+	9.52393i	−0.595312	+	1.27269i
$57$	−4.03482	+	4.03482i	−0.534425	+	0.534425i
$58$	−16.4877	−	16.4877i	−2.16494	−	2.16494i
$59$	7.07972			0.921701			0.460851	−	0.887478i	$-0.347544\pi$
$59$	7.07972			0.921701			0.460851	+	0.887478i	$0.347544\pi$
$60$		0			0
$61$			15.2300i			1.95001i	0.222193	+	0.975003i	$0.428679\pi$
$61$			15.2300i			1.95001i	−0.222193	+	0.975003i	$0.571321\pi$
$62$	6.42774	+	6.42774i	0.816323	+	0.816323i
$63$	2.48727	−	0.901937i	0.313366	−	0.113633i
$64$		−	11.1312i		−	1.39140i
$65$		0			0
$66$		−	3.67885i		−	0.452835i
$67$	5.31314	−	5.31314i	0.649103	−	0.649103i	−0.303673	−	0.952776i	$-0.598213\pi$
$67$	5.31314	−	5.31314i	0.649103	−	0.649103i	0.952776	+	0.303673i	$0.0982131\pi$
$68$	−7.54930	+	7.54930i	−0.915487	+	0.915487i
$69$	−5.27191			−0.634664
$70$		0			0
$71$	−4.45490			−0.528700			−0.264350	−	0.964427i	$-0.585157\pi$
$71$	−4.45490			−0.528700			−0.264350	+	0.964427i	$0.585157\pi$
$72$	2.81008	−	2.81008i	0.331171	−	0.331171i
$73$	0.770882	−	0.770882i	0.0902249	−	0.0902249i	−0.660554	−	0.750779i	$-0.729678\pi$
$73$	0.770882	−	0.770882i	0.0902249	−	0.0902249i	0.750779	+	0.660554i	$0.229678\pi$
$74$		−	9.46214i		−	1.09995i
$75$		0			0
$76$		−	20.9361i		−	2.40154i
$77$	1.39358	+	3.84307i	0.158813	+	0.437958i
$78$	−9.90510	−	9.90510i	−1.12153	−	1.12153i
$79$			11.1312i			1.25236i	0.779678	+	0.626180i	$0.215383\pi$
$79$			11.1312i			1.25236i	−0.779678	+	0.626180i	$0.784617\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	11.6644	+	11.6644i	1.28812	+	1.28812i
$83$	−9.60684	+	9.60684i	−1.05449	+	1.05449i	−0.0560604	+	0.998427i	$0.517854\pi$
$83$	−9.60684	+	9.60684i	−1.05449	+	1.05449i	−0.998427	+	0.0560604i	$0.982146\pi$
$84$	−4.11303	+	8.79306i	−0.448769	+	0.959402i
$85$		0			0
$86$	3.46214			0.373332
$87$	−6.92474	−	6.92474i	−0.742410	−	0.742410i
$88$	4.34184	+	4.34184i	0.462841	+	0.462841i
$89$	9.52393			1.00953			0.504767	−	0.863255i	$-0.331578\pi$
$89$	9.52393			1.00953			0.504767	+	0.863255i	$0.331578\pi$
$90$		0			0
$91$	14.0994	+	6.59512i	1.47802	+	0.691357i
$92$	13.6776	−	13.6776i	1.42599	−	1.42599i
$93$	2.69961	+	2.69961i	0.279937	+	0.279937i
$94$	−6.92820			−0.714590
$95$		0			0
$96$		−	2.89093i		−	0.295054i
$97$	5.09607	+	5.09607i	0.517428	+	0.517428i	0.916792	−	0.399364i	$-0.130769\pi$
$97$	5.09607	+	5.09607i	0.517428	+	0.517428i	−0.399364	+	0.916792i	$0.630769\pi$
$98$	1.49217	−	16.5999i	0.150732	−	1.67685i
$99$		−	1.54510i		−	0.155288i
$100$		0			0
$101$		−	9.52393i		−	0.947667i	−0.880615	−	0.473833i	$-0.842870\pi$
$101$		−	9.52393i		−	0.947667i	0.880615	−	0.473833i	$-0.157130\pi$
$102$	−4.89898	+	4.89898i	−0.485071	+	0.485071i
$103$	8.83596	−	8.83596i	0.870633	−	0.870633i	−0.121908	−	0.992541i	$-0.538901\pi$
$103$	8.83596	−	8.83596i	0.870633	−	0.870633i	0.992541	+	0.121908i	$0.0389014\pi$
$104$	23.3803			2.29263
$105$		0			0
$106$	16.4959			1.60223
$107$	2.55663	−	2.55663i	0.247159	−	0.247159i	−0.572645	−	0.819804i	$-0.694083\pi$
$107$	2.55663	−	2.55663i	0.247159	−	0.247159i	0.819804	+	0.572645i	$0.194083\pi$
$108$	2.59443	−	2.59443i	0.249649	−	0.249649i
$109$			11.4959i			1.10111i	0.834799	+	0.550555i	$0.185584\pi$
$109$			11.4959i			1.10111i	−0.834799	+	0.550555i	$0.814416\pi$
$110$		0			0
$111$		−	3.97405i		−	0.377200i
$112$	−1.91570	−	5.28292i	−0.181017	−	0.499189i
$113$	14.0504	+	14.0504i	1.32175	+	1.32175i	0.912360	+	0.409389i	$0.134258\pi$
$113$	14.0504	+	14.0504i	1.32175	+	1.32175i	0.409389	+	0.912360i	$0.365742\pi$
$114$		−	13.5861i		−	1.27246i
$115$		0			0
$116$	35.9315			3.33616
$117$	−4.16009	−	4.16009i	−0.384600	−	0.384600i
$118$	−11.9195	+	11.9195i	−1.09728	+	1.09728i
$119$	3.26189	−	6.97345i	0.299017	−	0.639255i
$120$		0			0
$121$	−8.61268			−0.782971
$122$	−25.6414	−	25.6414i	−2.32146	−	2.32146i
$123$	4.89898	+	4.89898i	0.441726	+	0.441726i
$124$	−14.0079			−1.25795
$125$		0			0
$126$	−2.66908	+	5.70610i	−0.237780	+	0.508340i
$127$	5.56326	−	5.56326i	0.493660	−	0.493660i	−0.415798	−	0.909457i	$-0.636498\pi$
$127$	5.56326	−	5.56326i	0.493660	−	0.493660i	0.909457	+	0.415798i	$0.136498\pi$
$128$	14.6522	+	14.6522i	1.29509	+	1.29509i
$129$	1.45408			0.128025
$130$		0			0
$131$		−	6.37226i		−	0.556747i	−0.960473	−	0.278374i	$-0.910205\pi$
$131$		−	6.37226i		−	0.556747i	0.960473	−	0.278374i	$-0.0897953\pi$
$132$	4.00864	+	4.00864i	0.348908	+	0.348908i
$133$	5.14655	+	14.1926i	0.446262	+	1.23066i
$134$			17.8905i			1.54550i
$135$		0			0
$136$		−	11.5637i		−	0.991581i
$137$	1.72832	−	1.72832i	0.147660	−	0.147660i	−0.629412	−	0.777072i	$-0.716704\pi$
$137$	1.72832	−	1.72832i	0.147660	−	0.147660i	0.777072	+	0.629412i	$0.216704\pi$
$138$	8.87584	−	8.87584i	0.755562	−	0.755562i
$139$	−7.07972			−0.600494			−0.300247	−	0.953861i	$-0.597069\pi$
$139$	−7.07972			−0.600494			−0.300247	+	0.953861i	$0.597069\pi$
$140$		0			0
$141$	−2.90981			−0.245050
$142$	7.50032	−	7.50032i	0.629413	−	0.629413i
$143$	6.42774	−	6.42774i	0.537514	−	0.537514i
$144$			2.12398i			0.176999i
$145$		0			0
$146$			2.59573i			0.214824i
$147$	0.626705	−	6.97189i	0.0516897	−	0.575032i
$148$	10.3104	+	10.3104i	0.847509	+	0.847509i
$149$		−	9.79306i		−	0.802279i	−0.916017	−	0.401139i	$-0.868614\pi$
$149$		−	9.79306i		−	0.802279i	0.916017	−	0.401139i	$-0.131386\pi$
$150$		0			0
$151$	1.42835			0.116237			0.0581187	−	0.998310i	$-0.481490\pi$
$151$	1.42835			0.116237			0.0581187	+	0.998310i	$0.481490\pi$
$152$	16.0346	+	16.0346i	1.30058	+	1.30058i
$153$	−2.05755	+	2.05755i	−0.166343	+	0.166343i
$154$	−8.81647	−	4.12398i	−0.710451	−	0.332320i
$155$		0			0
$156$	21.5861			1.72827
$157$	2.10254	+	2.10254i	0.167801	+	0.167801i	0.786012	−	0.618211i	$-0.212142\pi$
$157$	2.10254	+	2.10254i	0.167801	+	0.167801i	−0.618211	+	0.786012i	$0.712142\pi$
$158$	−18.7406	−	18.7406i	−1.49092	−	1.49092i
$159$	6.92820			0.549442
$160$		0			0
$161$	−5.90981	+	12.6343i	−0.465758	+	0.995723i
$162$	1.68361	−	1.68361i	0.132277	−	0.132277i
$163$	−3.81390	−	3.81390i	−0.298728	−	0.298728i	0.541788	−	0.840515i	$-0.317748\pi$
$163$	−3.81390	−	3.81390i	−0.298728	−	0.298728i	−0.840515	+	0.541788i	$0.817748\pi$
$164$	−25.4201			−1.98498
$165$		0			0
$166$		−	32.3483i		−	2.51072i
$167$	−3.43421	−	3.43421i	−0.265747	−	0.265747i	0.561637	−	0.827384i	$-0.310172\pi$
$167$	−3.43421	−	3.43421i	−0.265747	−	0.265747i	−0.827384	+	0.561637i	$0.810172\pi$
$168$	−3.58434	−	9.88453i	−0.276538	−	0.762608i
$169$		−	21.6127i		−	1.66251i
$170$		0			0
$171$		−	5.70610i		−	0.436356i
$172$	−3.77251	+	3.77251i	−0.287651	+	0.287651i
$173$	17.1561	−	17.1561i	1.30436	−	1.30436i	0.378933	−	0.925424i	$-0.376291\pi$
$173$	17.1561	−	17.1561i	1.30436	−	1.30436i	0.925424	−	0.378933i	$-0.123709\pi$
$174$	23.3171			1.76767
$175$		0			0
$176$	−3.28176			−0.247372
$177$	−5.00612	+	5.00612i	−0.376283	+	0.376283i
$178$	−16.0346	+	16.0346i	−1.20184	+	1.20184i
$179$		−	7.76651i		−	0.580496i	−0.956951	−	0.290248i	$-0.906262\pi$
$179$		−	7.76651i		−	0.580496i	0.956951	−	0.290248i	$-0.0937378\pi$
$180$		0			0
$181$			7.74589i			0.575747i	0.957668	+	0.287874i	$0.0929483\pi$
$181$			7.74589i			0.575747i	−0.957668	+	0.287874i	$0.907052\pi$
$182$	−34.8415	+	12.6343i	−2.58262	+	0.936515i
$183$	−10.7693	−	10.7693i	−0.796086	−	0.796086i
$184$			20.9508i			1.54452i
$185$		0			0
$186$	−9.09019			−0.666525
$187$	−3.17910	−	3.17910i	−0.232479	−	0.232479i
$188$	7.54930	−	7.54930i	0.550589	−	0.550589i
$189$	−1.12100	+	2.39653i	−0.0815407	+	0.174322i
$190$		0			0
$191$	7.40574			0.535861			0.267930	−	0.963438i	$-0.413660\pi$
$191$	7.40574			0.535861			0.267930	+	0.963438i	$0.413660\pi$
$192$	7.87096	+	7.87096i	0.568038	+	0.568038i
$193$	−3.67423	−	3.67423i	−0.264477	−	0.264477i	0.562393	−	0.826870i	$-0.309881\pi$
$193$	−3.67423	−	3.67423i	−0.264477	−	0.264477i	−0.826870	+	0.562393i	$0.809881\pi$
$194$	−17.1596			−1.23199
$195$		0			0
$196$	16.4621	+	19.7140i	1.17587	+	1.40814i
$197$	4.14528	−	4.14528i	0.295339	−	0.295339i	−0.543846	−	0.839185i	$-0.683032\pi$
$197$	4.14528	−	4.14528i	0.295339	−	0.295339i	0.839185	+	0.543846i	$0.183032\pi$
$198$	2.60134	+	2.60134i	0.184869	+	0.184869i
$199$	−10.0386			−0.711616			−0.355808	−	0.934559i	$-0.615794\pi$
$199$	−10.0386			−0.711616			−0.355808	+	0.934559i	$0.615794\pi$
$200$		0			0
$201$			7.51391i			0.529990i
$202$	16.0346	+	16.0346i	1.12819	+	1.12819i
$203$	−24.3580	+	8.83273i	−1.70960	+	0.619936i
$204$		−	10.6763i		−	0.747492i
$205$		0			0
$206$			29.7526i			2.07296i
$207$	3.72781	−	3.72781i	0.259100	−	0.259100i
$208$	−8.83596	+	8.83596i	−0.612664	+	0.612664i
$209$	8.81647			0.609848
$210$		0			0
$211$	−1.38732			−0.0955071			−0.0477536	−	0.998859i	$-0.515206\pi$
$211$	−1.38732			−0.0955071			−0.0477536	+	0.998859i	$0.515206\pi$
$212$	−17.9747	+	17.9747i	−1.23451	+	1.23451i
$213$	3.15009	−	3.15009i	0.215841	−	0.215841i
$214$			8.60873i			0.588481i
$215$		0			0
$216$			3.97405i			0.270400i
$217$	9.49598	−	3.44345i	0.644629	−	0.233756i
$218$	−19.3547	−	19.3547i	−1.31086	−	1.31086i
$219$			1.09019i			0.0736683i
$220$		0			0
$221$	−17.1191			−1.15156
$222$	6.69074	+	6.69074i	0.449053	+	0.449053i
$223$	−8.27518	+	8.27518i	−0.554147	+	0.554147i	−0.927635	−	0.373488i	$-0.878162\pi$
$223$	−8.27518	+	8.27518i	−0.554147	+	0.554147i	0.373488	+	0.927635i	$0.378162\pi$
$224$	−6.92820	−	3.24073i	−0.462910	−	0.216530i
$225$		0			0
$226$	−47.3107			−3.14706
$227$	3.17910	+	3.17910i	0.211005	+	0.211005i	0.804694	−	0.593690i	$-0.202329\pi$
$227$	3.17910	+	3.17910i	0.211005	+	0.211005i	−0.593690	+	0.804694i	$0.702329\pi$
$228$	14.8041	+	14.8041i	0.980424	+	0.980424i
$229$	−0.666164			−0.0440213			−0.0220107	−	0.999758i	$-0.507007\pi$
$229$	−0.666164			−0.0440213			−0.0220107	+	0.999758i	$0.507007\pi$
$230$		0			0
$231$	−3.70287	−	1.73205i	−0.243631	−	0.113961i
$232$	−27.5193	+	27.5193i	−1.80673	+	1.80673i
$233$	4.31747	+	4.31747i	0.282847	+	0.282847i	0.834243	−	0.551397i	$-0.185905\pi$
$233$	4.31747	+	4.31747i	0.282847	+	0.282847i	−0.551397	+	0.834243i	$0.685905\pi$
$234$	14.0079			0.915727
$235$		0			0
$236$		−	25.9761i		−	1.69090i
$237$	−7.87096	−	7.87096i	−0.511274	−	0.511274i
$238$	6.24881	+	17.2323i	0.405050	+	1.11700i
$239$			5.81962i			0.376440i	0.982127	+	0.188220i	$0.0602717\pi$
$239$			5.81962i			0.376440i	−0.982127	+	0.188220i	$0.939728\pi$
$240$		0			0
$241$			10.8976i			0.701973i	0.936380	+	0.350987i	$0.114154\pi$
$241$			10.8976i			0.701973i	−0.936380	+	0.350987i	$0.885846\pi$
$242$	14.5004	−	14.5004i	0.932120	−	0.932120i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	55.8802			3.57736
$245$		0			0
$246$	−16.4959			−1.05174
$247$	23.7379	−	23.7379i	1.51041	−	1.51041i
$248$	10.7284	−	10.7284i	0.681254	−	0.681254i
$249$		−	13.5861i		−	0.860986i
$250$		0			0
$251$			6.37226i			0.402214i	0.979569	+	0.201107i	$0.0644538\pi$
$251$			6.37226i			0.402214i	−0.979569	+	0.201107i	$0.935546\pi$
$252$	−3.30928	−	9.12599i	−0.208465	−	0.574883i
$253$	5.75982	+	5.75982i	0.362117	+	0.362117i
$254$			18.7327i			1.17540i
$255$		0			0
$256$	−27.0748			−1.69218
$257$	−12.6004	−	12.6004i	−0.785990	−	0.785990i	0.194845	−	0.980834i	$-0.437580\pi$
$257$	−12.6004	−	12.6004i	−0.785990	−	0.785990i	−0.980834	+	0.194845i	$0.937580\pi$
$258$	−2.44810	+	2.44810i	−0.152412	+	0.152412i
$259$	−9.52393	−	4.45490i	−0.591788	−	0.276814i
$260$		0			0
$261$	9.79306			0.606175
$262$	10.7284	+	10.7284i	0.662803	+	0.662803i
$263$	6.89847	+	6.89847i	0.425378	+	0.425378i	0.887050	−	0.461673i	$-0.152750\pi$
$263$	6.89847	+	6.89847i	0.425378	+	0.425378i	−0.461673	+	0.887050i	$0.652750\pi$
$264$	−6.14029			−0.377908
$265$		0			0
$266$	−32.5596	−	15.2300i	−1.99636	−	0.933813i
$267$	−6.73444	+	6.73444i	−0.412141	+	0.412141i
$268$	−19.4943	−	19.4943i	−1.19081	−	1.19081i
$269$	−18.3404			−1.11823			−0.559117	−	0.829089i	$-0.688860\pi$
$269$	−18.3404			−1.11823			−0.559117	+	0.829089i	$0.688860\pi$
$270$		0			0
$271$			1.88827i			0.114704i	0.998354	+	0.0573520i	$0.0182657\pi$
$271$			1.88827i			0.114704i	−0.998354	+	0.0573520i	$0.981734\pi$
$272$	4.37019	+	4.37019i	0.264982	+	0.264982i
$273$	−14.6332	+	5.30633i	−0.885644	+	0.321154i
$274$			5.81962i			0.351576i
$275$		0			0
$276$			19.3431i			1.16432i
$277$	−17.1106	+	17.1106i	−1.02808	+	1.02808i	−0.0284811	+	0.999594i	$0.509067\pi$
$277$	−17.1106	+	17.1106i	−1.02808	+	1.02808i	−0.999594	+	0.0284811i	$0.990933\pi$
$278$	11.9195	−	11.9195i	0.714883	−	0.714883i
$279$	−3.81783			−0.228568
$280$		0			0
$281$	−22.2359			−1.32648			−0.663241	−	0.748406i	$-0.730820\pi$
$281$	−22.2359			−1.32648			−0.663241	+	0.748406i	$0.730820\pi$
$282$	4.89898	−	4.89898i	0.291730	−	0.291730i
$283$	18.8180	−	18.8180i	1.11861	−	1.11861i	0.126669	−	0.991945i	$-0.459571\pi$
$283$	18.8180	−	18.8180i	1.11861	−	1.11861i	0.991945	−	0.126669i	$-0.0404287\pi$
$284$			16.3454i			0.969921i
$285$		0			0
$286$			21.6436i			1.27981i
$287$	17.2323	−	6.24881i	1.01719	−	0.368855i
$288$	2.04420	+	2.04420i	0.120455	+	0.120455i
$289$		−	8.53302i		−	0.501942i
$290$		0			0
$291$	−7.20694			−0.422478
$292$	−2.82843	−	2.82843i	−0.165521	−	0.165521i
$293$	−6.42774	+	6.42774i	−0.375512	+	0.375512i	−0.869480	−	0.493968i	$-0.835546\pi$
$293$	−6.42774	+	6.42774i	−0.375512	+	0.375512i	0.493968	+	0.869480i	$0.335546\pi$
$294$	10.6828	+	12.7931i	0.623034	+	0.746107i
$295$		0			0
$296$	−15.7931			−0.917953
$297$	1.09255	+	1.09255i	0.0633961	+	0.0633961i
$298$	16.4877	+	16.4877i	0.955106	+	0.955106i
$299$	31.0160			1.79370
$300$		0			0
$301$	1.63002	−	3.48475i	0.0939530	−	0.200858i
$302$	−2.40478	+	2.40478i	−0.138380	+	0.138380i
$303$	6.73444	+	6.73444i	0.386883	+	0.386883i
$304$	−12.1197			−0.695110
$305$		0			0
$306$		−	6.92820i		−	0.396059i
$307$	5.44675	+	5.44675i	0.310863	+	0.310863i	0.845244	−	0.534381i	$-0.179455\pi$
$307$	5.44675	+	5.44675i	0.310863	+	0.310863i	−0.534381	+	0.845244i	$0.679455\pi$
$308$	14.1005	−	5.11315i	0.803452	−	0.291349i
$309$			12.4959i			0.710869i
$310$		0			0
$311$		−	17.7845i		−	1.00846i	−0.863568	−	0.504232i	$-0.831776\pi$
$311$		−	17.7845i		−	1.00846i	0.863568	−	0.504232i	$-0.168224\pi$
$312$	−16.5324	+	16.5324i	−0.935963	+	0.935963i
$313$	1.33166	−	1.33166i	0.0752700	−	0.0752700i	−0.668470	−	0.743740i	$-0.733050\pi$
$313$	1.33166	−	1.33166i	0.0752700	−	0.0752700i	0.743740	+	0.668470i	$0.233050\pi$
$314$	−7.07972			−0.399532
$315$		0			0
$316$	40.8413			2.29750
$317$	−16.6721	+	16.6721i	−0.936396	+	0.936396i	−0.998095	−	0.0616987i	$-0.980348\pi$
$317$	−16.6721	+	16.6721i	−0.936396	+	0.936396i	0.0616987	+	0.998095i	$0.480348\pi$
$318$	−11.6644	+	11.6644i	−0.654106	+	0.654106i
$319$			15.1312i			0.847186i
$320$		0			0
$321$			3.61562i			0.201804i
$322$	−11.3214	−	31.2210i	−0.630918	−	1.73988i
$323$	−11.7406	−	11.7406i	−0.653262	−	0.653262i
$324$			3.66908i			0.203838i
$325$		0			0
$326$	12.8422			0.711265
$327$	−8.12885	−	8.12885i	−0.449527	−	0.449527i
$328$	19.4688	−	19.4688i	1.07498	−	1.07498i
$329$	−3.26189	+	6.97345i	−0.179834	+	0.384459i
$330$		0			0
$331$	−3.18433			−0.175027			−0.0875133	−	0.996163i	$-0.527892\pi$
$331$	−3.18433			−0.175027			−0.0875133	+	0.996163i	$0.527892\pi$
$332$	35.2483	+	35.2483i	1.93450	+	1.93450i
$333$	2.81008	+	2.81008i	0.153991	+	0.153991i
$334$	11.5637			0.632739
$335$		0			0
$336$	5.09019	+	2.38098i	0.277693	+	0.129893i
$337$	−13.9399	+	13.9399i	−0.759356	+	0.759356i	−0.976205	−	0.216849i	$-0.930422\pi$
$337$	−13.9399	+	13.9399i	−0.759356	+	0.759356i	0.216849	+	0.976205i	$0.430422\pi$
$338$	36.3873	+	36.3873i	1.97921	+	1.97921i
$339$	−19.8702			−1.07920
$340$		0			0
$341$		−	5.89892i		−	0.319444i
$342$	9.60684	+	9.60684i	0.519478	+	0.519478i
$343$	−16.0058	−	9.31740i	−0.864233	−	0.503092i
$344$		−	5.77859i		−	0.311561i
$345$		0			0
$346$			57.7685i			3.10565i
$347$	16.5893	−	16.5893i	0.890560	−	0.890560i	−0.104016	−	0.994576i	$-0.533169\pi$
$347$	16.5893	−	16.5893i	0.890560	−	0.890560i	0.994576	+	0.104016i	$0.0331693\pi$
$348$	−25.4074	+	25.4074i	−1.36198	+	1.36198i
$349$	−30.6116			−1.63860			−0.819300	−	0.573365i	$-0.805638\pi$
$349$	−30.6116			−1.63860			−0.819300	+	0.573365i	$0.805638\pi$
$350$		0			0
$351$	5.88325			0.314025
$352$	−3.15848	+	3.15848i	−0.168347	+	0.168347i
$353$	13.7219	−	13.7219i	0.730345	−	0.730345i	−0.240343	−	0.970688i	$-0.577260\pi$
$353$	13.7219	−	13.7219i	0.730345	−	0.730345i	0.970688	+	0.240343i	$0.0772600\pi$
$354$		−	16.8567i		−	0.895923i
$355$		0			0
$356$		−	34.9441i		−	1.85203i
$357$	2.62447	+	7.23748i	0.138901	+	0.383048i
$358$	13.0758	+	13.0758i	0.691076	+	0.691076i
$359$		−	16.4549i		−	0.868457i	−0.900803	−	0.434228i	$-0.857021\pi$
$359$		−	16.4549i		−	0.868457i	0.900803	−	0.434228i	$-0.142979\pi$
$360$		0			0
$361$	13.5596			0.713662
$362$	−13.0410	−	13.0410i	−0.685422	−	0.685422i
$363$	6.09008	−	6.09008i	0.319646	−	0.319646i
$364$	24.1980	−	51.7318i	1.26832	−	2.71148i
$365$		0			0
$366$	36.2624			1.89547
$367$	−4.76587	−	4.76587i	−0.248776	−	0.248776i	0.571692	−	0.820468i	$-0.306287\pi$
$367$	−4.76587	−	4.76587i	−0.248776	−	0.248776i	−0.820468	+	0.571692i	$0.806287\pi$
$368$	−7.91780	−	7.91780i	−0.412744	−	0.412744i
$369$	−6.92820			−0.360668
$370$		0			0
$371$	7.76651	−	16.6037i	0.403217	−	0.862019i
$372$	9.90510	−	9.90510i	0.513556	−	0.513556i
$373$	−8.45943	−	8.45943i	−0.438013	−	0.438013i	0.453330	−	0.891343i	$-0.350236\pi$
$373$	−8.45943	−	8.45943i	−0.438013	−	0.438013i	−0.891343	+	0.453330i	$0.850236\pi$
$374$	10.7047			0.553529
$375$		0			0
$376$			11.5637i			0.596353i
$377$	40.7400	+	40.7400i	2.09822	+	2.09822i
$378$	−2.14750	−	5.92215i	−0.110455	−	0.304602i
$379$		−	19.7439i		−	1.01418i	−0.861894	−	0.507088i	$-0.830722\pi$
$379$		−	19.7439i		−	1.01418i	0.861894	−	0.507088i	$-0.169278\pi$
$380$		0			0
$381$			7.86764i			0.403071i
$382$	−12.4684	+	12.4684i	−0.637937	+	0.637937i
$383$	−20.4048	+	20.4048i	−1.04263	+	1.04263i	−0.0435852	+	0.999050i	$0.513878\pi$
$383$	−20.4048	+	20.4048i	−1.04263	+	1.04263i	−0.999050	+	0.0435852i	$0.986122\pi$
$384$	−20.7214			−1.05743
$385$		0			0
$386$	12.3719			0.629716
$387$	−1.02819	+	1.02819i	−0.0522659	+	0.0522659i
$388$	18.6979	−	18.6979i	0.949242	−	0.949242i
$389$		−	36.7849i		−	1.86507i	−0.361080	−	0.932535i	$-0.617592\pi$
$389$		−	36.7849i		−	1.86507i	0.361080	−	0.932535i	$-0.382408\pi$
$390$		0			0
$391$		−	15.3403i		−	0.775790i
$392$	−27.7066	−	2.49056i	−1.39940	−	0.125792i
$393$	4.50587	+	4.50587i	0.227291	+	0.227291i
$394$			13.9581i			0.703198i
$395$		0			0
$396$	−5.66908			−0.284882
$397$	−18.8180	−	18.8180i	−0.944449	−	0.944449i	0.0540876	−	0.998536i	$-0.482775\pi$
$397$	−18.8180	−	18.8180i	−0.944449	−	0.944449i	−0.998536	+	0.0540876i	$0.982775\pi$
$398$	16.9010	−	16.9010i	0.847172	−	0.847172i
$399$	−13.6748	−	6.39653i	−0.684599	−	0.320227i
$400$		0			0
$401$	−6.88325			−0.343733			−0.171867	−	0.985120i	$-0.554980\pi$
$401$	−6.88325			−0.343733			−0.171867	+	0.985120i	$0.554980\pi$
$402$	−12.6505	−	12.6505i	−0.630949	−	0.630949i
$403$	−15.8825	−	15.8825i	−0.791165	−	0.791165i
$404$	−34.9441			−1.73853
$405$		0			0
$406$	26.1385	−	55.8802i	1.29723	−	2.77329i
$407$	−4.34184	+	4.34184i	−0.215217	+	0.215217i
$408$	8.17678	+	8.17678i	0.404811	+	0.404811i
$409$	14.6741			0.725587			0.362794	−	0.931870i	$-0.381823\pi$
$409$	14.6741			0.725587			0.362794	+	0.931870i	$0.381823\pi$
$410$		0			0
$411$			2.44421i			0.120564i
$412$	−32.4198	−	32.4198i	−1.59721	−	1.59721i
$413$	6.38547	+	17.6092i	0.314208	+	0.866491i
$414$			12.5523i			0.616914i
$415$		0			0
$416$			17.0081i			0.833889i
$417$	5.00612	−	5.00612i	0.245151	−	0.245151i
$418$	−14.8435	+	14.8435i	−0.726019	+	0.726019i
$419$	−29.7526			−1.45351			−0.726755	−	0.686897i	$-0.758972\pi$
$419$	−29.7526			−1.45351			−0.726755	+	0.686897i	$0.758972\pi$
$420$		0			0
$421$	−0.936362			−0.0456355			−0.0228178	−	0.999740i	$-0.507264\pi$
$421$	−0.936362			−0.0456355			−0.0228178	+	0.999740i	$0.507264\pi$
$422$	2.33571	−	2.33571i	0.113700	−	0.113700i
$423$	2.05755	−	2.05755i	0.100041	−	0.100041i
$424$		−	27.5330i		−	1.33712i
$425$		0			0
$426$			10.6071i			0.513913i
$427$	−37.8812	+	13.7365i	−1.83320	+	0.664758i
$428$	−9.38048	−	9.38048i	−0.453423	−	0.453423i
$429$			9.09019i			0.438879i
$430$		0			0
$431$	31.4057			1.51276			0.756381	−	0.654132i	$-0.226966\pi$
$431$	31.4057			1.51276			0.756381	+	0.654132i	$0.226966\pi$
$432$	−1.50188	−	1.50188i	−0.0722594	−	0.0722594i
$433$	−12.8309	+	12.8309i	−0.616616	+	0.616616i	−0.944662	−	0.328046i	$-0.893610\pi$
$433$	−12.8309	+	12.8309i	−0.616616	+	0.616616i	0.328046	+	0.944662i	$0.393610\pi$
$434$	−10.1901	+	21.7849i	−0.489140	+	1.04571i
$435$		0			0
$436$	42.1795			2.02003
$437$	21.2712	+	21.2712i	1.01754	+	1.01754i
$438$	−1.83546	−	1.83546i	−0.0877015	−	0.0877015i
$439$	37.9029			1.80901			0.904504	−	0.426466i	$-0.140242\pi$
$439$	37.9029			1.80901			0.904504	+	0.426466i	$0.140242\pi$
$440$		0			0
$441$	4.48672	+	5.37302i	0.213653	+	0.255858i
$442$	28.8219	−	28.8219i	1.37092	−	1.37092i
$443$	−20.9245	−	20.9245i	−0.994152	−	0.994152i	0.00583081	−	0.999983i	$-0.498144\pi$
$443$	−20.9245	−	20.9245i	−0.994152	−	0.994152i	−0.999983	+	0.00583081i	$0.998144\pi$
$444$	−14.5811			−0.691988
$445$		0			0
$446$		−	27.8643i		−	1.31941i
$447$	6.92474	+	6.92474i	0.327529	+	0.327529i
$448$	27.6863	−	10.0397i	1.30806	−	0.474330i
$449$			5.11675i			0.241474i	0.992685	+	0.120737i	$0.0385258\pi$
$449$			5.11675i			0.241474i	−0.992685	+	0.120737i	$0.961474\pi$
$450$		0			0
$451$		−	10.7047i		−	0.504066i
$452$	51.5520	−	51.5520i	2.42480	−	2.42480i
$453$	−1.01000	+	1.01000i	−0.0474538	+	0.0474538i
$454$	−10.7047			−0.502398
$455$		0			0
$456$	−22.6763			−1.06192
$457$	−3.13814	+	3.13814i	−0.146796	+	0.146796i	−0.776685	−	0.629889i	$-0.783100\pi$
$457$	−3.13814	+	3.13814i	−0.146796	+	0.146796i	0.629889	+	0.776685i	$0.283100\pi$
$458$	1.12156	−	1.12156i	0.0524070	−	0.0524070i
$459$		−	2.90981i		−	0.135818i
$460$		0			0
$461$		−	27.4599i		−	1.27894i	−0.768818	−	0.639468i	$-0.779155\pi$
$461$		−	27.4599i		−	1.27894i	0.768818	−	0.639468i	$-0.220845\pi$
$462$	9.15028	−	3.31809i	0.425710	−	0.154372i
$463$	18.9819	+	18.9819i	0.882163	+	0.882163i	0.993754	−	0.111591i	$-0.0355947\pi$
$463$	18.9819	+	18.9819i	0.882163	+	0.882163i	−0.111591	+	0.993754i	$0.535595\pi$
$464$		−	20.8003i		−	0.965630i
$465$		0			0
$466$	−14.5379			−0.673453
$467$	−5.23665	−	5.23665i	−0.242323	−	0.242323i	0.575487	−	0.817811i	$-0.304812\pi$
$467$	−5.23665	−	5.23665i	−0.242323	−	0.242323i	−0.817811	+	0.575487i	$0.804812\pi$
$468$	−15.2637	+	15.2637i	−0.705565	+	0.705565i
$469$	18.0073	+	8.42309i	0.831501	+	0.388942i
$470$		0			0
$471$	−2.97345			−0.137009
$472$	19.8946	+	19.8946i	0.915722	+	0.915722i
$473$	−1.58865	−	1.58865i	−0.0730463	−	0.0730463i
$474$	26.5032			1.21733
$475$		0			0
$476$	−25.5861	−	11.9681i	−1.17274	−	0.548559i
$477$	−4.89898	+	4.89898i	−0.224309	+	0.224309i
$478$	−9.79796	−	9.79796i	−0.448148	−	0.448148i
$479$	29.9041			1.36635			0.683177	−	0.730253i	$-0.260598\pi$
$479$	29.9041			1.36635			0.683177	+	0.730253i	$0.260598\pi$
$480$		0			0
$481$			23.3803i			1.06605i
$482$	−18.3472	−	18.3472i	−0.835693	−	0.835693i
$483$	−4.75494	−	13.1127i	−0.216357	−	0.596647i
$484$			31.6006i			1.43639i
$485$		0			0
$486$			2.38098i			0.108004i
$487$	−11.2193	+	11.2193i	−0.508393	+	0.508393i	−0.914033	−	0.405640i	$-0.867049\pi$
$487$	−11.2193	+	11.2193i	−0.508393	+	0.508393i	0.405640	+	0.914033i	$0.367049\pi$
$488$	−42.7976	+	42.7976i	−1.93735	+	1.93735i
$489$	5.39367			0.243910
$490$		0			0
$491$	36.4839			1.64649			0.823247	−	0.567684i	$-0.192160\pi$
$491$	36.4839			1.64649			0.823247	+	0.567684i	$0.192160\pi$
$492$	17.9747	−	17.9747i	0.810364	−	0.810364i
$493$	20.1497	−	20.1497i	0.907495	−	0.907495i
$494$			79.9306i			3.59625i
$495$		0			0
$496$			8.10901i			0.364105i
$497$	−4.01805	−	11.0805i	−0.180234	−	0.497030i
$498$	22.8737	+	22.8737i	1.02500	+	1.02500i
$499$			10.9734i			0.491239i	0.969366	+	0.245619i	$0.0789914\pi$
$499$			10.9734i			0.491239i	−0.969366	+	0.245619i	$0.921009\pi$
$500$		0			0
$501$	4.85670			0.216981
$502$	−10.7284	−	10.7284i	−0.478832	−	0.478832i
$503$	12.8555	−	12.8555i	0.573197	−	0.573197i	−0.359823	−	0.933020i	$-0.617163\pi$
$503$	12.8555	−	12.8555i	0.573197	−	0.573197i	0.933020	+	0.359823i	$0.117163\pi$
$504$	9.52393	+	4.45490i	0.424230	+	0.198437i
$505$		0			0
$506$	−19.3946			−0.862193
$507$	15.2825	+	15.2825i	0.678718	+	0.678718i
$508$	−20.4120	−	20.4120i	−0.905638	−	0.905638i
$509$	7.07972			0.313803			0.156902	−	0.987614i	$-0.449849\pi$
$509$	7.07972			0.313803			0.156902	+	0.987614i	$0.449849\pi$
$510$		0			0
$511$	2.61268	+	1.22210i	0.115578	+	0.0540627i
$512$	16.2789	−	16.2789i	0.719435	−	0.719435i
$513$	4.03482	+	4.03482i	0.178142	+	0.178142i
$514$	42.4282			1.87143
$515$		0			0
$516$		−	5.33514i		−	0.234866i
$517$	3.17910	+	3.17910i	0.139817	+	0.139817i
$518$	23.5349	−	8.53426i	1.03406	−	0.374974i
$519$			24.2624i			1.06500i
$520$		0			0
$521$		−	2.44421i		−	0.107083i	−0.998566	−	0.0535413i	$-0.982949\pi$
$521$		−	2.44421i		−	0.107083i	0.998566	−	0.0535413i	$-0.0170509\pi$
$522$	−16.4877	+	16.4877i	−0.721647	+	0.721647i
$523$	−13.2511	+	13.2511i	−0.579432	+	0.579432i	−0.934747	−	0.355315i	$-0.884374\pi$
$523$	−13.2511	+	13.2511i	−0.579432	+	0.579432i	0.355315	+	0.934747i	$0.384374\pi$
$524$	−23.3803			−1.02137
$525$		0			0
$526$	−23.2286			−1.01282
$527$	−7.85536	+	7.85536i	−0.342185	+	0.342185i
$528$	2.32055	−	2.32055i	0.100989	−	0.100989i
$529$			4.79306i			0.208394i
$530$		0			0
$531$		−	7.07972i		−	0.307234i
$532$	52.0738	−	18.8831i	2.25769	−	0.818685i
$533$	−28.8219	−	28.8219i	−1.24842	−	1.24842i
$534$		−	22.6763i		−	0.981300i
$535$		0			0
$536$	29.8606			1.28978
$537$	5.49175	+	5.49175i	0.236987	+	0.236987i
$538$	30.8781	−	30.8781i	1.33125	−	1.33125i
$539$	−8.30183	+	6.93242i	−0.357585	+	0.298600i
$540$		0			0
$541$	−39.0289			−1.67799			−0.838993	−	0.544143i	$-0.816855\pi$
$541$	−39.0289			−1.67799			−0.838993	+	0.544143i	$0.816855\pi$
$542$	−3.17910	−	3.17910i	−0.136554	−	0.136554i
$543$	−5.47717	−	5.47717i	−0.235048	−	0.235048i
$544$	8.41205			0.360664
$545$		0			0
$546$	15.7029	−	33.5704i	0.672021	−	1.43668i
$547$	23.2099	−	23.2099i	0.992385	−	0.992385i	−0.00758585	−	0.999971i	$-0.502415\pi$
$547$	23.2099	−	23.2099i	0.992385	−	0.992385i	0.999971	+	0.00758585i	$0.00241467\pi$
$548$	−6.34133	−	6.34133i	−0.270888	−	0.270888i
$549$	15.2300			0.650002
$550$		0			0
$551$			55.8802i			2.38058i
$552$	−14.8145	−	14.8145i	−0.630546	−	0.630546i
$553$	−27.6863	+	10.0397i	−1.17734	+	0.426930i
$554$		−	57.6151i		−	2.44783i
$555$		0			0
$556$			25.9761i			1.10163i
$557$	−14.9437	+	14.9437i	−0.633187	+	0.633187i	−0.948866	−	0.315679i	$-0.897768\pi$
$557$	−14.9437	+	14.9437i	−0.633187	+	0.633187i	0.315679	+	0.948866i	$0.397768\pi$
$558$	6.42774	−	6.42774i	0.272108	−	0.272108i
$559$	−8.55473			−0.361826
$560$		0			0
$561$	4.49593			0.189818
$562$	37.4365	−	37.4365i	1.57917	−	1.57917i
$563$	−12.1051	+	12.1051i	−0.510167	+	0.510167i	−0.914578	−	0.404410i	$-0.867477\pi$
$563$	−12.1051	+	12.1051i	−0.510167	+	0.510167i	0.404410	+	0.914578i	$0.367477\pi$
$564$			10.6763i			0.449554i
$565$		0			0
$566$			63.3643i			2.66340i
$567$	−0.901937	−	2.48727i	−0.0378778	−	0.104455i
$568$	−12.5186	−	12.5186i	−0.525270	−	0.525270i
$569$			14.2890i			0.599026i	0.954092	+	0.299513i	$0.0968242\pi$
$569$			14.2890i			0.599026i	−0.954092	+	0.299513i	$0.903176\pi$
$570$		0			0
$571$	17.5635			0.735010			0.367505	−	0.930021i	$-0.380212\pi$
$571$	17.5635			0.735010			0.367505	+	0.930021i	$0.380212\pi$
$572$	−23.5839	−	23.5839i	−0.986091	−	0.986091i
$573$	−5.23665	+	5.23665i	−0.218764	+	0.218764i
$574$	−18.4919	+	39.5330i	−0.771838	+	1.65008i
$575$		0			0
$576$	−11.1312			−0.463801
$577$	1.33166	+	1.33166i	0.0554378	+	0.0554378i	0.734282	−	0.678844i	$-0.237519\pi$
$577$	1.33166	+	1.33166i	0.0554378	+	0.0554378i	−0.678844	+	0.734282i	$0.737519\pi$
$578$	14.3663	+	14.3663i	0.597558	+	0.597558i
$579$	5.19615			0.215945
$580$		0			0
$581$	−32.5596	−	15.2300i	−1.35080	−	0.631848i
$582$	12.1337	−	12.1337i	0.502957	−	0.502957i
$583$	−7.56939	−	7.56939i	−0.313492	−	0.313492i
$584$	4.33248			0.179279
$585$		0			0
$586$		−	21.6436i		−	0.894088i
$587$	−24.5199	−	24.5199i	−1.01204	−	1.01204i	−0.999927	−	0.0121163i	$-0.996143\pi$
$587$	−24.5199	−	24.5199i	−1.01204	−	1.01204i	−0.0121163	−	0.999927i	$-0.503857\pi$
$588$	−25.5804	−	2.29943i	−1.05492	−	0.0948269i
$589$		−	21.7849i		−	0.897632i
$590$		0			0
$591$			5.86232i			0.241143i
$592$	5.96856	−	5.96856i	0.245306	−	0.245306i
$593$	4.11509	−	4.11509i	0.168987	−	0.168987i	−0.617547	−	0.786534i	$-0.711874\pi$
$593$	4.11509	−	4.11509i	0.168987	−	0.168987i	0.786534	+	0.617547i	$0.211874\pi$
$594$	−3.67885			−0.150945
$595$		0			0
$596$	−35.9315			−1.47181
$597$	7.09834	−	7.09834i	0.290516	−	0.290516i
$598$	−52.2188	+	52.2188i	−2.13539	+	2.13539i
$599$			40.8977i			1.67104i	0.549463	+	0.835518i	$0.314832\pi$
$599$			40.8977i			1.67104i	−0.549463	+	0.835518i	$0.685168\pi$
$600$		0			0
$601$		−	24.6024i		−	1.00355i	−0.864997	−	0.501777i	$-0.832680\pi$
$601$		−	24.6024i		−	1.00355i	0.864997	−	0.501777i	$-0.167320\pi$
$602$	3.12264	+	8.61128i	0.127269	+	0.350969i
$603$	−5.31314	−	5.31314i	−0.216368	−	0.216368i
$604$		−	5.24073i		−	0.213242i
$605$		0			0
$606$	−22.6763			−0.921162
$607$	−9.09106	−	9.09106i	−0.368995	−	0.368995i	0.498116	−	0.867111i	$-0.334025\pi$
$607$	−9.09106	−	9.09106i	−0.368995	−	0.368995i	−0.867111	+	0.498116i	$0.834025\pi$
$608$	−11.6644	+	11.6644i	−0.473053	+	0.473053i
$609$	10.9780	−	23.4694i	0.444851	−	0.951027i
$610$		0			0
$611$	17.1191			0.692566
$612$	7.54930	+	7.54930i	0.305162	+	0.305162i
$613$	8.43023	+	8.43023i	0.340494	+	0.340494i	0.856553	−	0.516059i	$-0.172602\pi$
$613$	8.43023	+	8.43023i	0.340494	+	0.340494i	−0.516059	+	0.856553i	$0.672602\pi$
$614$	−18.3404			−0.740158
$615$		0			0
$616$	−6.88325	+	14.7154i	−0.277334	+	0.592900i
$617$	−24.0626	+	24.0626i	−0.968725	+	0.968725i	−0.999526	−	0.0308008i	$-0.990194\pi$
$617$	−24.0626	+	24.0626i	−0.968725	+	0.968725i	0.0308008	+	0.999526i	$0.490194\pi$
$618$	−21.0383	−	21.0383i	−0.846283	−	0.846283i
$619$	−43.3974			−1.74429			−0.872144	−	0.489248i	$-0.837271\pi$
$619$	−43.3974			−1.74429			−0.872144	+	0.489248i	$0.837271\pi$
$620$		0			0
$621$			5.27191i			0.211555i
$622$	29.9421	+	29.9421i	1.20057	+	1.20057i
$623$	8.58999	+	23.6886i	0.344151	+	0.949063i
$624$		−	12.4959i		−	0.500238i
$625$		0			0
$626$			4.48400i			0.179217i
$627$	−6.23419	+	6.23419i	−0.248969	+	0.248969i
$628$	7.71440	−	7.71440i	0.307838	−	0.307838i
$629$	11.5637			0.461076
$630$		0			0
$631$	−3.24797			−0.129299			−0.0646497	−	0.997908i	$-0.520593\pi$
$631$	−3.24797			−0.129299			−0.0646497	+	0.997908i	$0.520593\pi$
$632$	−31.2796	+	31.2796i	−1.24424	+	1.24424i
$633$	0.980984	−	0.980984i	0.0389906	−	0.0389906i
$634$		−	56.1385i		−	2.22954i
$635$		0			0
$636$		−	25.4201i		−	1.00797i
$637$	−3.68706	+	41.0174i	−0.146087	+	1.62517i
$638$	−25.4751	−	25.4751i	−1.00857	−	1.00857i
$639$			4.45490i			0.176233i
$640$		0			0
$641$	−0.342103			−0.0135123			−0.00675613	−	0.999977i	$-0.502151\pi$
$641$	−0.342103			−0.0135123			−0.00675613	+	0.999977i	$0.502151\pi$
$642$	−6.08729	−	6.08729i	−0.240246	−	0.240246i
$643$	−1.54176	+	1.54176i	−0.0608012	+	0.0608012i	−0.736854	−	0.676052i	$-0.763689\pi$
$643$	−1.54176	+	1.54176i	−0.0608012	+	0.0608012i	0.676052	+	0.736854i	$0.263689\pi$
$644$	46.3563	+	21.6836i	1.82669	+	0.854452i
$645$		0			0
$646$	39.5330			1.55541
$647$	−2.24312	−	2.24312i	−0.0881861	−	0.0881861i	0.661638	−	0.749824i	$-0.269862\pi$
$647$	−2.24312	−	2.24312i	−0.0881861	−	0.0881861i	−0.749824	+	0.661638i	$0.769862\pi$
$648$	−2.81008	−	2.81008i	−0.110390	−	0.110390i
$649$	10.9389			0.429387
$650$		0			0
$651$	−4.27979	+	9.14955i	−0.167738	+	0.358599i
$652$	−13.9935	+	13.9935i	−0.548027	+	0.548027i
$653$	−20.0962	−	20.0962i	−0.786424	−	0.786424i	0.194482	−	0.980906i	$-0.437697\pi$
$653$	−20.0962	−	20.0962i	−0.786424	−	0.786424i	−0.980906	+	0.194482i	$0.937697\pi$
$654$	27.3716			1.07031
$655$		0			0
$656$			14.7154i			0.574539i
$657$	−0.770882	−	0.770882i	−0.0300750	−	0.0300750i
$658$	−6.24881	−	17.2323i	−0.243604	−	0.671785i
$659$		−	9.35263i		−	0.364327i	−0.983268	−	0.182163i	$-0.941690\pi$
$659$		−	9.35263i		−	0.364327i	0.983268	−	0.182163i	$-0.0583100\pi$
$660$		0			0
$661$		−	39.2765i		−	1.52768i	−0.645406	−	0.763840i	$-0.723312\pi$
$661$		−	39.2765i		−	1.52768i	0.645406	−	0.763840i	$-0.276688\pi$
$662$	5.36116	−	5.36116i	0.208368	−	0.208368i
$663$	12.1051	−	12.1051i	0.470122	−	0.470122i
$664$	−53.9919			−2.09529
$665$		0			0
$666$	−9.46214			−0.366651
$667$	−36.5066	+	36.5066i	−1.41354	+	1.41354i
$668$	−12.6004	+	12.6004i	−0.487523	+	0.487523i
$669$		−	11.7029i		−	0.452459i
$670$		0			0
$671$			23.5319i			0.908437i
$672$	7.19052	−	2.60744i	0.277380	−	0.100584i
$673$	−3.45663	−	3.45663i	−0.133243	−	0.133243i	0.637340	−	0.770583i	$-0.280035\pi$
$673$	−3.45663	−	3.45663i	−0.133243	−	0.133243i	−0.770583	+	0.637340i	$0.780035\pi$
$674$		−	46.9388i		−	1.80801i
$675$		0			0
$676$	−79.2986			−3.04995
$677$	16.2202	+	16.2202i	0.623391	+	0.623391i	0.946397	−	0.323006i	$-0.104693\pi$
$677$	16.2202	+	16.2202i	0.623391	+	0.623391i	−0.323006	+	0.946397i	$0.604693\pi$
$678$	33.4537	−	33.4537i	1.28478	−	1.28478i
$679$	−8.07897	+	17.2717i	−0.310042	+	0.662825i
$680$		0			0
$681$	−4.49593			−0.172285
$682$	9.93147	+	9.93147i	0.380296	+	0.380296i
$683$	−0.950250	−	0.950250i	−0.0363603	−	0.0363603i	0.688693	−	0.725053i	$-0.258185\pi$
$683$	−0.950250	−	0.950250i	−0.0363603	−	0.0363603i	−0.725053	+	0.688693i	$0.758185\pi$
$684$	−20.9361			−0.800513
$685$		0			0
$686$	42.6344	−	11.2607i	1.62779	−	0.429935i
$687$	0.471049	−	0.471049i	0.0179716	−	0.0179716i
$688$	2.18386	+	2.18386i	0.0832588	+	0.0832588i
$689$	−40.7604			−1.55285
$690$		0			0
$691$		−	46.3563i		−	1.76348i	−0.471740	−	0.881738i	$-0.656374\pi$
$691$		−	46.3563i		−	1.76348i	0.471740	−	0.881738i	$-0.343626\pi$
$692$	−62.9472	−	62.9472i	−2.39289	−	2.39289i
$693$	3.84307	−	1.39358i	0.145986	−	0.0529377i
$694$			55.8597i			2.12041i
$695$		0			0
$696$		−	38.9181i		−	1.47519i
$697$	−14.2551	+	14.2551i	−0.539950	+	0.539950i
$698$	51.5379	−	51.5379i	1.95074	−	1.95074i
$699$	−6.10582			−0.230943
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−9.90510	+	9.90510i	−0.373844	+	0.373844i
$703$	−16.0346	+	16.0346i	−0.604756	+	0.604756i
$704$		−	17.1988i		−	0.648204i
$705$		0			0
$706$			46.2047i			1.73894i
$707$	23.6886	−	8.58999i	0.890901	−	0.323060i
$708$	18.3679	+	18.3679i	0.690306	+	0.690306i
$709$			10.9203i			0.410122i	0.978749	+	0.205061i	$0.0657393\pi$
$709$			10.9203i			0.410122i	−0.978749	+	0.205061i	$0.934261\pi$
$710$		0			0
$711$	11.1312			0.417453
$712$	26.7630	+	26.7630i	1.00298	+	1.00298i
$713$	14.2321	−	14.2321i	0.532998	−	0.532998i
$714$	−16.6037	−	7.76651i	−0.621376	−	0.290654i
$715$		0			0
$716$	−28.4959			−1.06494
$717$	−4.11509	−	4.11509i	−0.153681	−	0.153681i
$718$	27.7036	+	27.7036i	1.03389	+	1.03389i
$719$	27.3084			1.01843			0.509216	−	0.860639i	$-0.329936\pi$
$719$	27.3084			1.01843			0.509216	+	0.860639i	$0.329936\pi$
$720$		0			0
$721$	29.9469	+	14.0079i	1.11528	+	0.521682i
$722$	−22.8290	+	22.8290i	−0.849608	+	0.849608i
$723$	−7.70574	−	7.70574i	−0.286579	−	0.286579i
$724$	28.4203			1.05623
$725$		0			0
$726$			20.5066i			0.761073i
$727$	−20.8756	−	20.8756i	−0.774231	−	0.774231i	0.204612	−	0.978843i	$-0.434407\pi$
$727$	−20.8756	−	20.8756i	−0.774231	−	0.774231i	−0.978843	+	0.204612i	$0.934407\pi$
$728$	21.0876	+	58.1532i	0.781559	+	2.15530i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			4.23110i			0.156493i
$732$	−39.5133	+	39.5133i	−1.46045	+	1.46045i
$733$	−8.65039	+	8.65039i	−0.319509	+	0.319509i	−0.848579	−	0.529069i	$-0.822541\pi$
$733$	−8.65039	+	8.65039i	−0.319509	+	0.319509i	0.529069	+	0.848579i	$0.322541\pi$
$734$	16.0477			0.592332
$735$		0			0
$736$	−15.2407			−0.561781
$737$	8.20931	−	8.20931i	0.302394	−	0.302394i
$738$	11.6644	−	11.6644i	0.429372	−	0.429372i
$739$		−	3.98792i		−	0.146698i	−0.997306	−	0.0733490i	$-0.976631\pi$
$739$		−	3.98792i		−	0.146698i	0.997306	−	0.0733490i	$-0.0233687\pi$
$740$		0			0
$741$			33.5704i			1.23324i
$742$	14.8783	+	41.0298i	0.546200	+	1.50625i
$743$	34.8352	+	34.8352i	1.27798	+	1.27798i	0.941797	+	0.336183i	$0.109136\pi$
$743$	34.8352	+	34.8352i	1.27798	+	1.27798i	0.336183	+	0.941797i	$0.390864\pi$
$744$			15.1722i			0.556242i
$745$		0			0
$746$	28.4848			1.04290
$747$	9.60684	+	9.60684i	0.351496	+	0.351496i
$748$	−11.6644	+	11.6644i	−0.426492	+	0.426492i
$749$	8.66495	+	4.05311i	0.316610	+	0.148097i
$750$		0			0
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	−4.37019	−	4.37019i	−0.159364	−	0.159364i
$753$	−4.50587	−	4.50587i	−0.164203	−	0.164203i
$754$	−137.180			−4.99582
$755$		0			0
$756$	8.79306	+	4.11303i	0.319801	+	0.149590i
$757$	36.0599	−	36.0599i	1.31062	−	1.31062i	0.389664	−	0.920957i	$-0.372591\pi$
$757$	36.0599	−	36.0599i	1.31062	−	1.31062i	0.920957	−	0.389664i	$-0.127409\pi$
$758$	33.2410	+	33.2410i	1.20737	+	1.20737i
$759$	−8.14561			−0.295667
$760$		0			0
$761$			13.8564i			0.502294i	0.967949	+	0.251147i	$0.0808078\pi$
$761$			13.8564i			0.502294i	−0.967949	+	0.251147i	$0.919192\pi$
$762$	−13.2460	−	13.2460i	−0.479853	−	0.479853i
$763$	−28.5935	+	10.3686i	−1.03515	+	0.375369i
$764$		−	27.1722i		−	0.983057i
$765$		0			0
$766$		−	68.7073i		−	2.48250i
$767$	29.4523	−	29.4523i	1.06346	−	1.06346i
$768$	19.1448	−	19.1448i	0.690828	−	0.690828i
$769$	29.3895			1.05981			0.529906	−	0.848056i	$-0.322227\pi$
$769$	29.3895			1.05981			0.529906	+	0.848056i	$0.322227\pi$
$770$		0			0
$771$	17.8196			0.641758
$772$	−13.4811	+	13.4811i	−0.485194	+	0.485194i
$773$	19.4688	−	19.4688i	0.700243	−	0.700243i	−0.264219	−	0.964463i	$-0.585114\pi$
$773$	19.4688	−	19.4688i	0.700243	−	0.700243i	0.964463	+	0.264219i	$0.0851142\pi$
$774$		−	3.46214i		−	0.124444i
$775$		0			0
$776$			28.6407i			1.02814i
$777$	9.88453	−	3.58434i	0.354606	−	0.128588i
$778$	61.9314	+	61.9314i	2.22035	+	2.22035i
$779$		−	39.5330i		−	1.41642i
$780$		0			0
$781$	−6.88325			−0.246302
$782$	25.8270	+	25.8270i	0.923571	+	0.923571i
$783$	−6.92474	+	6.92474i	−0.247470	+	0.247470i
$784$	11.4122	−	9.52972i	0.407579	−	0.340347i
$785$		0			0
$786$	−15.1722			−0.541176
$787$	1.58676	+	1.58676i	0.0565620	+	0.0565620i	0.734822	−	0.678260i	$-0.237266\pi$
$787$	1.58676	+	1.58676i	0.0565620	+	0.0565620i	−0.678260	+	0.734822i	$0.737266\pi$
$788$	−15.2094	−	15.2094i	−0.541811	−	0.541811i
$789$	−9.75591			−0.347320
$790$		0			0
$791$	−22.2745	+	47.6197i	−0.791991	+	1.69316i
$792$	4.34184	−	4.34184i	0.154280	−	0.154280i
$793$	63.3583	+	63.3583i	2.24992	+	2.24992i
$794$	63.3643			2.24872
$795$		0			0
$796$			36.8323i			1.30549i
$797$	22.9030	+	22.9030i	0.811265	+	0.811265i	0.984824	−	0.173558i	$-0.0555265\pi$
$797$	22.9030	+	22.9030i	0.811265	+	0.811265i	−0.173558	+	0.984824i	$0.555526\pi$
$798$	33.7924	−	12.2538i	1.19624	−	0.433781i
$799$		−	8.46698i		−	0.299540i
$800$		0			0
$801$		−	9.52393i		−	0.336512i
$802$	11.5887	−	11.5887i	0.409212	−	0.409212i
$803$	1.19109	−	1.19109i	0.0420325	−	0.0420325i
$804$	27.5691			0.972288
$805$		0			0
$806$	53.4799			1.88375
$807$	12.9686	−	12.9686i	0.456517	−	0.456517i
$808$	26.7630	−	26.7630i	0.941518	−	0.941518i
$809$			2.10861i			0.0741348i	0.999313	+	0.0370674i	$0.0118016\pi$
$809$			2.10861i			0.0741348i	−0.999313	+	0.0370674i	$0.988198\pi$
$810$		0			0
$811$			7.99879i			0.280875i	0.990090	+	0.140438i	$0.0448510\pi$
$811$			7.99879i			0.280875i	−0.990090	+	0.140438i	$0.955149\pi$
$812$	32.4080	+	89.3714i	1.13730	+	3.13632i
$813$	−1.33521	−	1.33521i	−0.0468277	−	0.0468277i
$814$		−	14.6199i		−	0.512428i
$815$		0			0
$816$	−6.18038			−0.216357
$817$	−5.86696	−	5.86696i	−0.205259	−	0.205259i
$818$	−24.7054	+	24.7054i	−0.863805	+	0.863805i
$819$	6.59512	−	14.0994i	0.230452	−	0.492673i
$820$		0			0
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$	−4.11509	−	4.11509i	−0.143530	−	0.143530i
$823$	22.3458	+	22.3458i	0.778925	+	0.778925i	0.979648	−	0.200723i	$-0.0643291\pi$
$823$	22.3458	+	22.3458i	0.778925	+	0.778925i	−0.200723	+	0.979648i	$0.564329\pi$
$824$	49.6594			1.72997
$825$		0			0
$826$	−40.3976	−	18.8963i	−1.40561	−	0.657488i
$827$	−7.17779	+	7.17779i	−0.249596	+	0.249596i	−0.820805	−	0.571209i	$-0.806475\pi$
$827$	−7.17779	+	7.17779i	−0.249596	+	0.249596i	0.571209	+	0.820805i	$0.306475\pi$
$828$	−13.6776	−	13.6776i	−0.475330	−	0.475330i
$829$	−11.2607			−0.391100			−0.195550	−	0.980694i	$-0.562649\pi$
$829$	−11.2607			−0.391100			−0.195550	+	0.980694i	$0.562649\pi$
$830$		0			0
$831$		−	24.1980i		−	0.839420i
$832$	−46.3069	−	46.3069i	−1.60540	−	1.60540i
$833$	20.2869	+	1.82359i	0.702898	+	0.0631837i
$834$			16.8567i			0.583700i
$835$		0			0
$836$		−	32.3483i		−	1.11879i
$837$	2.69961	−	2.69961i	0.0933123	−	0.0933123i
$838$	50.0917	−	50.0917i	1.73039	−	1.73039i
$839$	−10.5532			−0.364338			−0.182169	−	0.983267i	$-0.558312\pi$
$839$	−10.5532			−0.364338			−0.182169	+	0.983267i	$0.558312\pi$
$840$		0			0
$841$	−66.9041			−2.30704
$842$	1.57647	−	1.57647i	0.0543287	−	0.0543287i
$843$	15.7231	−	15.7231i	0.541534	−	0.541534i
$844$			5.09019i			0.175212i
$845$		0			0
$846$			6.92820i			0.238197i
$847$	−7.76810	−	21.4221i	−0.266915	−	0.736070i
$848$	10.4054	+	10.4054i	0.357321	+	0.357321i
$849$			26.6127i			0.913345i
$850$		0			0
$851$	−20.9508			−0.718185
$852$	−11.5579	−	11.5579i	−0.395968	−	0.395968i
$853$	−2.26765	+	2.26765i	−0.0776428	+	0.0776428i	−0.744862	−	0.667219i	$-0.767485\pi$
$853$	−2.26765	+	2.26765i	−0.0776428	+	0.0776428i	0.667219	+	0.744862i	$0.267485\pi$
$854$	40.6502	−	86.9041i	1.39102	−	2.97380i
$855$		0			0
$856$	14.3687			0.491111
$857$	−25.8270	−	25.8270i	−0.882233	−	0.882233i	0.111528	−	0.993761i	$-0.464426\pi$
$857$	−25.8270	−	25.8270i	−0.882233	−	0.882233i	−0.993761	+	0.111528i	$0.964426\pi$
$858$	−15.3043	−	15.3043i	−0.522481	−	0.522481i
$859$	−25.5716			−0.872493			−0.436247	−	0.899827i	$-0.643692\pi$
$859$	−25.5716			−0.872493			−0.436247	+	0.899827i	$0.643692\pi$
$860$		0			0
$861$	−7.76651	+	16.6037i	−0.264682	+	0.565851i
$862$	−52.8750	+	52.8750i	−1.80093	+	1.80093i
$863$	−0.342859	−	0.342859i	−0.0116711	−	0.0116711i	0.701247	−	0.712918i	$-0.252627\pi$
$863$	−0.342859	−	0.342859i	−0.0116711	−	0.0116711i	−0.712918	+	0.701247i	$0.752627\pi$
$864$	−2.89093			−0.0983514
$865$		0			0
$866$		−	43.2046i		−	1.46815i
$867$	6.03375	+	6.03375i	0.204917	+	0.204917i
$868$	−12.6343	−	34.8415i	−0.428835	−	1.18260i
$869$			17.1988i			0.583429i
$870$		0			0
$871$		−	44.2062i		−	1.49787i
$872$	−32.3045	+	32.3045i	−1.09397	+	1.09397i
$873$	5.09607	−	5.09607i	0.172476	−	0.172476i
$874$	−71.6249			−2.42275
$875$		0			0
$876$	4.00000			0.135147
$877$	26.9085	−	26.9085i	0.908637	−	0.908637i	−0.0875253	−	0.996162i	$-0.527896\pi$
$877$	26.9085	−	26.9085i	0.908637	−	0.908637i	0.996162	+	0.0875253i	$0.0278959\pi$
$878$	−63.8137	+	63.8137i	−2.15361	+	2.15361i
$879$		−	9.09019i		−	0.306605i
$880$		0			0
$881$		−	25.9761i		−	0.875156i	−0.899180	−	0.437578i	$-0.855836\pi$
$881$		−	25.9761i		−	0.875156i	0.899180	−	0.437578i	$-0.144164\pi$
$882$	−16.5999	−	1.49217i	−0.558949	−	0.0502441i
$883$	−27.6379	−	27.6379i	−0.930088	−	0.930088i	0.0676226	−	0.997711i	$-0.478459\pi$
$883$	−27.6379	−	27.6379i	−0.930088	−	0.930088i	−0.997711	+	0.0676226i	$0.978459\pi$
$884$			62.8115i			2.11258i
$885$		0			0
$886$	70.4573			2.36706
$887$	15.5939	+	15.5939i	0.523592	+	0.523592i	0.918654	−	0.395062i	$-0.129277\pi$
$887$	15.5939	+	15.5939i	0.523592	+	0.523592i	−0.395062	+	0.918654i	$0.629277\pi$
$888$	11.1674	−	11.1674i	0.374753	−	0.374753i
$889$	18.8550	+	8.81962i	0.632378	+	0.295800i
$890$		0			0
$891$	−1.54510			−0.0517627
$892$	30.3623	+	30.3623i	1.01660	+	1.01660i
$893$	11.7406	+	11.7406i	0.392883	+	0.392883i
$894$	−23.3171			−0.779841
$895$		0			0
$896$	−23.2286	+	49.6594i	−0.776015	+	1.65901i
$897$	−21.9316	+	21.9316i	−0.732276	+	0.732276i
$898$	−8.61460	−	8.61460i	−0.287473	−	0.287473i
$899$	37.3883			1.24697
$900$		0			0
$901$			20.1597i			0.671618i
$902$	18.0226	+	18.0226i	0.600087	+	0.600087i
$903$	1.31149	+	3.61669i	0.0436437	+	0.120356i
$904$			78.9653i			2.62635i
$905$		0			0
$906$		−	3.40088i		−	0.112987i
$907$	10.4120	−	10.4120i	0.345725	−	0.345725i	−0.512790	−	0.858514i	$-0.671388\pi$
$907$	10.4120	−	10.4120i	0.345725	−	0.345725i	0.858514	+	0.512790i	$0.171388\pi$
$908$	11.6644	−	11.6644i	0.387096	−	0.387096i
$909$	−9.52393			−0.315889
$910$		0			0
$911$	−5.95897			−0.197430			−0.0987148	−	0.995116i	$-0.531473\pi$
$911$	−5.95897			−0.197430			−0.0987148	+	0.995116i	$0.531473\pi$
$912$	8.56989	−	8.56989i	0.283778	−	0.283778i
$913$	−14.8435	+	14.8435i	−0.491248	+	0.491248i
$914$		−	10.5668i		−	0.349519i
$915$		0			0
$916$			2.44421i			0.0807589i
$917$	15.8495	−	5.74738i	0.523398	−	0.189795i
$918$	4.89898	+	4.89898i	0.161690	+	0.161690i
$919$		−	26.1047i		−	0.861113i	−0.902564	−	0.430557i	$-0.858317\pi$
$919$		−	26.1047i		−	0.861113i	0.902564	−	0.430557i	$-0.141683\pi$
$920$		0			0
$921$	−7.70287			−0.253818
$922$	46.2318	+	46.2318i	1.52256	+	1.52256i
$923$	−18.5328	+	18.5328i	−0.610014	+	0.610014i
$924$	−6.35503	+	13.5861i	−0.209065	+	0.446951i
$925$		0			0
$926$	−63.9161			−2.10041
$927$	−8.83596	−	8.83596i	−0.290211	−	0.290211i
$928$	−20.0189	−	20.0189i	−0.657154	−	0.657154i
$929$	−46.2873			−1.51864			−0.759319	−	0.650719i	$-0.774468\pi$
$929$	−46.2873			−1.51864			−0.759319	+	0.650719i	$0.774468\pi$
$930$		0			0
$931$	−30.6590	+	25.6017i	−1.00481	+	0.839061i
$932$	15.8411	−	15.8411i	0.518894	−	0.518894i
$933$	12.5755	+	12.5755i	0.411704	+	0.411704i
$934$	17.6329			0.576967
$935$		0			0
$936$		−	23.3803i		−	0.764210i
$937$	−25.8515	−	25.8515i	−0.844532	−	0.844532i	0.144912	−	0.989445i	$-0.453710\pi$
$937$	−25.8515	−	25.8515i	−0.844532	−	0.844532i	−0.989445	+	0.144912i	$0.953710\pi$
$938$	−44.4985	+	16.1361i	−1.45293	+	0.526863i
$939$			1.88325i			0.0614577i
$940$		0			0
$941$		−	24.6437i		−	0.803363i	−0.915779	−	0.401681i	$-0.868426\pi$
$941$		−	24.6437i		−	0.803363i	0.915779	−	0.401681i	$-0.131574\pi$
$942$	5.00612	−	5.00612i	0.163108	−	0.163108i
$943$	25.8270	−	25.8270i	0.841043	−	0.841043i
$944$	−15.0372			−0.489420
$945$		0			0
$946$	5.34934			0.173922
$947$	−27.5518	+	27.5518i	−0.895312	+	0.895312i	−0.995017	−	0.0997046i	$-0.968210\pi$
$947$	−27.5518	+	27.5518i	−0.895312	+	0.895312i	0.0997046	+	0.995017i	$0.468210\pi$
$948$	−28.8792	+	28.8792i	−0.937952	+	0.937952i
$949$		−	6.41388i		−	0.208203i
$950$		0			0
$951$		−	23.5779i		−	0.764564i
$952$	28.7621	−	10.4298i	0.932184	−	0.338030i
$953$	−12.6080	−	12.6080i	−0.408414	−	0.408414i	0.472771	−	0.881185i	$-0.343254\pi$
$953$	−12.6080	−	12.6080i	−0.408414	−	0.408414i	−0.881185	+	0.472771i	$0.843254\pi$
$954$		−	16.4959i		−	0.534076i
$955$		0			0
$956$	21.3526			0.690593
$957$	−10.6994	−	10.6994i	−0.345862	−	0.345862i
$958$	−50.3469	+	50.3469i	−1.62663	+	1.62663i
$959$	5.85762	+	2.73995i	0.189152	+	0.0884777i
$960$		0			0
$961$	16.4242			0.529812
$962$	−39.3633	−	39.3633i	−1.26913	−	1.26913i
$963$	−2.55663	−	2.55663i	−0.0823863	−	0.0823863i
$964$	39.9840			1.28780
$965$		0			0
$966$	30.0821	+	14.0712i	0.967874	+	0.452732i
$967$	19.9824	−	19.9824i	0.642590	−	0.642590i	−0.308601	−	0.951191i	$-0.599861\pi$
$967$	19.9824	−	19.9824i	0.642590	−	0.642590i	0.951191	+	0.308601i	$0.0998609\pi$
$968$	−24.2023	−	24.2023i	−0.777891	−	0.777891i
$969$	16.6037			0.533386
$970$		0			0
$971$		−	3.62501i		−	0.116332i	−0.998307	−	0.0581661i	$-0.981475\pi$
$971$		−	3.62501i		−	0.116332i	0.998307	−	0.0581661i	$-0.0185253\pi$
$972$	−2.59443	−	2.59443i	−0.0832164	−	0.0832164i
$973$	−6.38547	−	17.6092i	−0.204709	−	0.564524i
$974$		−	37.7777i		−	1.21048i
$975$		0			0
$976$		−	32.3483i		−	1.03544i
$977$	4.75267	−	4.75267i	0.152052	−	0.152052i	−0.626982	−	0.779034i	$-0.715710\pi$
$977$	4.75267	−	4.75267i	0.152052	−	0.152052i	0.779034	+	0.626982i	$0.215710\pi$
$978$	−9.08082	+	9.08082i	−0.290373	+	0.290373i
$979$	14.7154			0.470306
$980$		0			0
$981$	11.4959			0.367037
$982$	−61.4245	+	61.4245i	−1.96014	+	1.96014i
$983$	32.3243	−	32.3243i	1.03098	−	1.03098i	0.0314792	−	0.999504i	$-0.489978\pi$
$983$	32.3243	−	32.3243i	1.03098	−	1.03098i	0.999504	−	0.0314792i	$-0.0100218\pi$
$984$			27.5330i			0.877721i
$985$		0			0
$986$			67.8483i			2.16073i
$987$	−2.62447	−	7.23748i	−0.0835376	−	0.230371i
$988$	−87.0962	−	87.0962i	−2.77090	−	2.77090i
$989$		−	7.66579i		−	0.243758i
$990$		0			0
$991$	−33.1949			−1.05447			−0.527235	−	0.849720i	$-0.676771\pi$
$991$	−33.1949			−1.05447			−0.527235	+	0.849720i	$0.676771\pi$
$992$	7.80440	+	7.80440i	0.247790	+	0.247790i
$993$	2.25166	−	2.25166i	0.0714543	−	0.0714543i
$994$	25.4201	+	11.8905i	0.806277	+	0.377143i
$995$		0			0
$996$	−49.8486			−1.57951
$997$	−26.5979	−	26.5979i	−0.842363	−	0.842363i	0.146803	−	0.989166i	$-0.453102\pi$
$997$	−26.5979	−	26.5979i	−0.842363	−	0.842363i	−0.989166	+	0.146803i	$0.953102\pi$
$998$	−18.4750	−	18.4750i	−0.584816	−	0.584816i
$999$	−3.97405			−0.125733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.m.c.118.1	✓	24
5.2	odd	4	inner	525.2.m.c.307.2	yes	24
5.3	odd	4	inner	525.2.m.c.307.11	yes	24
5.4	even	2	inner	525.2.m.c.118.12	yes	24
7.6	odd	2	inner	525.2.m.c.118.2	yes	24
35.13	even	4	inner	525.2.m.c.307.12	yes	24
35.27	even	4	inner	525.2.m.c.307.1	yes	24
35.34	odd	2	inner	525.2.m.c.118.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.m.c.118.1	✓	24	1.1	even	1	trivial
525.2.m.c.118.2	yes	24	7.6	odd	2	inner
525.2.m.c.118.11	yes	24	35.34	odd	2	inner
525.2.m.c.118.12	yes	24	5.4	even	2	inner
525.2.m.c.307.1	yes	24	35.27	even	4	inner
525.2.m.c.307.2	yes	24	5.2	odd	4	inner
525.2.m.c.307.11	yes	24	5.3	odd	4	inner
525.2.m.c.307.12	yes	24	35.13	even	4	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68361 + 1.68361i) q^{2} +(-0.707107 + 0.707107i) q^{3} -3.66908i q^{4} -2.38098i q^{6} +(0.901937 + 2.48727i) q^{7} +(2.81008 + 2.81008i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.68361 + 1.68361i) q^{2} +(-0.707107 + 0.707107i) q^{3} -3.66908i q^{4} -2.38098i q^{6} +(0.901937 + 2.48727i) q^{7} +(2.81008 + 2.81008i) q^{8} -1.00000i q^{9} +1.54510 q^{11} +(2.59443 + 2.59443i) q^{12} +(4.16009 - 4.16009i) q^{13} +(-5.70610 - 2.66908i) q^{14} -2.12398 q^{16} +(-2.05755 - 2.05755i) q^{17} +(1.68361 + 1.68361i) q^{18} +5.70610 q^{19} +(-2.39653 - 1.12100i) q^{21} +(-2.60134 + 2.60134i) q^{22} +(3.72781 + 3.72781i) q^{23} -3.97405 q^{24} +14.0079i q^{26} +(0.707107 + 0.707107i) q^{27} +(9.12599 - 3.30928i) q^{28} +9.79306i q^{29} -3.81783i q^{31} +(-2.04420 + 2.04420i) q^{32} +(-1.09255 + 1.09255i) q^{33} +6.92820 q^{34} -3.66908 q^{36} +(-2.81008 + 2.81008i) q^{37} +(-9.60684 + 9.60684i) q^{38} +5.88325i q^{39} -6.92820i q^{41} +(5.92215 - 2.14750i) q^{42} +(-1.02819 - 1.02819i) q^{43} -5.66908i q^{44} -12.5523 q^{46} +(2.05755 + 2.05755i) q^{47} +(1.50188 - 1.50188i) q^{48} +(-5.37302 + 4.48672i) q^{49} +2.90981 q^{51} +(-15.2637 - 15.2637i) q^{52} +(-4.89898 - 4.89898i) q^{53} -2.38098 q^{54} +(-4.45490 + 9.52393i) q^{56} +(-4.03482 + 4.03482i) q^{57} +(-16.4877 - 16.4877i) q^{58} +7.07972 q^{59} +15.2300i q^{61} +(6.42774 + 6.42774i) q^{62} +(2.48727 - 0.901937i) q^{63} -11.1312i q^{64} -3.67885i q^{66} +(5.31314 - 5.31314i) q^{67} +(-7.54930 + 7.54930i) q^{68} -5.27191 q^{69} -4.45490 q^{71} +(2.81008 - 2.81008i) q^{72} +(0.770882 - 0.770882i) q^{73} -9.46214i q^{74} -20.9361i q^{76} +(1.39358 + 3.84307i) q^{77} +(-9.90510 - 9.90510i) q^{78} +11.1312i q^{79} -1.00000 q^{81} +(11.6644 + 11.6644i) q^{82} +(-9.60684 + 9.60684i) q^{83} +(-4.11303 + 8.79306i) q^{84} +3.46214 q^{86} +(-6.92474 - 6.92474i) q^{87} +(4.34184 + 4.34184i) q^{88} +9.52393 q^{89} +(14.0994 + 6.59512i) q^{91} +(13.6776 - 13.6776i) q^{92} +(2.69961 + 2.69961i) q^{93} -6.92820 q^{94} -2.89093i q^{96} +(5.09607 + 5.09607i) q^{97} +(1.49217 - 16.5999i) q^{98} -1.54510i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 48 q^{11} + 24 q^{16} + 12 q^{21} - 24 q^{36} - 120 q^{46} + 48 q^{51} - 96 q^{56} - 96 q^{71} - 24 q^{81} - 120 q^{86} + 108 q^{91}+O(q^{100}) \) 24 * q + 48 * q^11 + 24 * q^16 + 12 * q^21 - 24 * q^36 - 120 * q^46 + 48 * q^51 - 96 * q^56 - 96 * q^71 - 24 * q^81 - 120 * q^86 + 108 * q^91

Introduction

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