LMFDB - Embedded newform 525.2.m.b.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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.1
Root			$-0.944649 - 1.05244i$ of defining polynomial
Character	$\chi$	$=$	525.118
Dual form			525.2.m.b.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48838 + 1.48838i) q^{2} +(-0.707107 + 0.707107i) q^{3} -2.43055i q^{4} -2.10489i q^{6} +(1.97552 - 1.75993i) q^{7} +(0.640825 + 0.640825i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.48838 + 1.48838i) q^{2} +(-0.707107 + 0.707107i) q^{3} -2.43055i q^{4} -2.10489i q^{6} +(1.97552 - 1.75993i) q^{7} +(0.640825 + 0.640825i) q^{8} -1.00000i q^{9} -2.67187 q^{11} +(1.71866 + 1.71866i) q^{12} +(-1.22714 + 1.22714i) q^{13} +(-0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(4.74624 + 4.74624i) q^{17} +(1.48838 + 1.48838i) q^{18} +6.01729 q^{19} +(-0.152445 + 2.64136i) q^{21} +(3.97676 - 3.97676i) q^{22} +(0.175684 + 0.175684i) q^{23} -0.906263 q^{24} -3.65291i q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.27759 - 4.80159i) q^{28} +0.304889i q^{29} +7.25379i q^{31} +(-5.67761 + 5.67761i) q^{32} +(1.88930 - 1.88930i) q^{33} -14.1284 q^{34} -2.43055 q^{36} +(0.735441 - 0.735441i) q^{37} +(-8.95602 + 8.95602i) q^{38} -1.73544i q^{39} +7.05736i q^{41} +(-3.70445 - 4.15824i) q^{42} +(-0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(-0.556866 - 0.556866i) q^{47} +(-2.08845 + 2.08845i) q^{48} +(0.805321 - 6.95352i) q^{49} -6.71220 q^{51} +(2.98263 + 2.98263i) q^{52} +(4.99031 + 4.99031i) q^{53} -2.10489 q^{54} +(2.39376 + 0.138155i) q^{56} +(-4.25487 + 4.25487i) q^{57} +(-0.453791 - 0.453791i) q^{58} -7.98837 q^{59} -5.53409i q^{61} +(-10.7964 - 10.7964i) q^{62} +(-1.75993 - 1.97552i) q^{63} -10.9939i q^{64} +5.62399i q^{66} +(3.43055 - 3.43055i) q^{67} +(11.5360 - 11.5360i) q^{68} -0.248455 q^{69} +15.3087 q^{71} +(0.640825 - 0.640825i) q^{72} +(-10.0208 + 10.0208i) q^{73} +2.18923i q^{74} -14.6253i q^{76} +(-5.27832 + 4.70230i) q^{77} +(2.58300 + 2.58300i) q^{78} +11.2973i q^{79} -1.00000 q^{81} +(-10.5040 - 10.5040i) q^{82} +(4.88941 - 4.88941i) q^{83} +(6.41995 + 0.370525i) q^{84} +0.907583 q^{86} +(-0.215589 - 0.215589i) q^{87} +(-1.71220 - 1.71220i) q^{88} +6.91251 q^{89} +(-0.264559 + 4.58392i) q^{91} +(0.427009 - 0.427009i) q^{92} +(-5.12921 - 5.12921i) q^{93} +1.65766 q^{94} -8.02936i q^{96} +(8.84137 + 8.84137i) q^{97} +(9.15086 + 11.5481i) q^{98} +2.67187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7} - 24 q^{8}+O(q^{10}) $ 16 * q + 8 * q^7 - 24 * q^8	$ 16 q + 8 q^{7} - 24 q^{8} - 16 q^{11} - 48 q^{16} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

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 $

$2$	−1.48838	+	1.48838i	−1.05244	+	1.05244i	−0.0538973	+	0.998546i	$0.517164\pi$
$2$	−1.48838	+	1.48838i	−1.05244	+	1.05244i	−0.998546	+	0.0538973i	$0.982836\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		−	2.43055i		−	1.21528i
$5$		0			0
$5$		0			0
$6$		−	2.10489i		−	0.859317i
$7$	1.97552	−	1.75993i	0.746675	−	0.665189i
$7$	1.97552	−	1.75993i	0.746675	−	0.665189i
$8$	0.640825	+	0.640825i	0.226566	+	0.226566i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−2.67187			−0.805600			−0.402800	−	0.915288i	$-0.631963\pi$
$11$	−2.67187			−0.805600			−0.402800	+	0.915288i	$0.631963\pi$
$12$	1.71866	+	1.71866i	0.496134	+	0.496134i
$13$	−1.22714	+	1.22714i	−0.340348	+	0.340348i	−0.856498	−	0.516150i	$-0.827365\pi$
$13$	−1.22714	+	1.22714i	−0.340348	+	0.340348i	0.516150	+	0.856498i	$0.327365\pi$
$14$	−0.320879	+	5.55976i	−0.0857585	+	1.48591i
$15$		0			0
$16$	2.95352			0.738380
$17$	4.74624	+	4.74624i	1.15113	+	1.15113i	0.986326	+	0.164807i	$0.0527002\pi$
$17$	4.74624	+	4.74624i	1.15113	+	1.15113i	0.164807	+	0.986326i	$0.447300\pi$
$18$	1.48838	+	1.48838i	0.350815	+	0.350815i
$19$	6.01729			1.38046			0.690231	−	0.723589i	$-0.257509\pi$
$19$	6.01729			1.38046			0.690231	+	0.723589i	$0.257509\pi$
$20$		0			0
$21$	−0.152445	+	2.64136i	−0.0332662	+	0.576391i
$22$	3.97676	−	3.97676i	0.847848	−	0.847848i
$23$	0.175684	+	0.175684i	0.0366327	+	0.0366327i	0.725186	−	0.688553i	$-0.241754\pi$
$23$	0.175684	+	0.175684i	0.0366327	+	0.0366327i	−0.688553	+	0.725186i	$0.741754\pi$
$24$	−0.906263			−0.184990
$25$		0			0
$26$		−	3.65291i		−	0.716394i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−4.27759	−	4.80159i	−0.808389	−	0.907416i
$29$			0.304889i			0.0566165i	0.999599	+	0.0283083i	$0.00901200\pi$
$29$			0.304889i			0.0566165i	−0.999599	+	0.0283083i	$0.990988\pi$
$30$		0			0
$31$			7.25379i			1.30282i	0.758726	+	0.651410i	$0.225822\pi$
$31$			7.25379i			1.30282i	−0.758726	+	0.651410i	$0.774178\pi$
$32$	−5.67761	+	5.67761i	−1.00367	+	1.00367i
$33$	1.88930	−	1.88930i	0.328885	−	0.328885i
$34$	−14.1284			−2.42301
$35$		0			0
$36$	−2.43055			−0.405092
$37$	0.735441	−	0.735441i	0.120906	−	0.120906i	−0.644065	−	0.764971i	$-0.722753\pi$
$37$	0.735441	−	0.735441i	0.120906	−	0.120906i	0.764971	+	0.644065i	$0.222753\pi$
$38$	−8.95602	+	8.95602i	−1.45286	+	1.45286i
$39$		−	1.73544i		−	0.277893i
$40$		0			0
$41$			7.05736i			1.10217i	0.834447	+	0.551087i	$0.185787\pi$
$41$			7.05736i			1.10217i	−0.834447	+	0.551087i	$0.814213\pi$
$42$	−3.70445	−	4.15824i	−0.571608	−	0.641630i
$43$	−0.304889	−	0.304889i	−0.0464952	−	0.0464952i	0.683477	−	0.729972i	$-0.260467\pi$
$43$	−0.304889	−	0.304889i	−0.0464952	−	0.0464952i	−0.729972	+	0.683477i	$0.760467\pi$
$44$			6.49412i			0.979026i
$45$		0			0
$46$	−0.522969			−0.0771076
$47$	−0.556866	−	0.556866i	−0.0812273	−	0.0812273i	0.665326	−	0.746553i	$-0.268293\pi$
$47$	−0.556866	−	0.556866i	−0.0812273	−	0.0812273i	−0.746553	+	0.665326i	$0.768293\pi$
$48$	−2.08845	+	2.08845i	−0.301442	+	0.301442i
$49$	0.805321	−	6.95352i	0.115046	−	0.993360i
$50$		0			0
$51$	−6.71220			−0.939896
$52$	2.98263	+	2.98263i	0.413617	+	0.413617i
$53$	4.99031	+	4.99031i	0.685472	+	0.685472i	0.961228	−	0.275756i	$-0.0889282\pi$
$53$	4.99031	+	4.99031i	0.685472	+	0.685472i	−0.275756	+	0.961228i	$0.588928\pi$
$54$	−2.10489			−0.286439
$55$		0			0
$56$	2.39376	+	0.138155i	0.319880	+	0.0184617i
$57$	−4.25487	+	4.25487i	−0.563571	+	0.563571i
$58$	−0.453791	−	0.453791i	−0.0595857	−	0.0595857i
$59$	−7.98837			−1.04000			−0.519999	−	0.854167i	$-0.674068\pi$
$59$	−7.98837			−1.04000			−0.519999	+	0.854167i	$0.674068\pi$
$60$		0			0
$61$		−	5.53409i		−	0.708567i	−0.935138	−	0.354284i	$-0.884725\pi$
$61$		−	5.53409i		−	0.708567i	0.935138	−	0.354284i	$-0.115275\pi$
$62$	−10.7964	−	10.7964i	−1.37114	−	1.37114i
$63$	−1.75993	−	1.97552i	−0.221730	−	0.248892i
$64$		−	10.9939i		−	1.37423i
$65$		0			0
$66$			5.62399i			0.692265i
$67$	3.43055	−	3.43055i	0.419109	−	0.419109i	−0.465788	−	0.884896i	$-0.654229\pi$
$67$	3.43055	−	3.43055i	0.419109	−	0.419109i	0.884896	+	0.465788i	$0.154229\pi$
$68$	11.5360	−	11.5360i	1.39894	−	1.39894i
$69$	−0.248455			−0.0299104
$70$		0			0
$71$	15.3087			1.81681			0.908407	−	0.418087i	$-0.137299\pi$
$71$	15.3087			1.81681			0.908407	+	0.418087i	$0.137299\pi$
$72$	0.640825	−	0.640825i	0.0755219	−	0.0755219i
$73$	−10.0208	+	10.0208i	−1.17285	+	1.17285i	−0.191323	+	0.981527i	$0.561278\pi$
$73$	−10.0208	+	10.0208i	−1.17285	+	1.17285i	−0.981527	+	0.191323i	$0.938722\pi$
$74$			2.18923i			0.254493i
$75$		0			0
$76$		−	14.6253i		−	1.67764i
$77$	−5.27832	+	4.70230i	−0.601521	+	0.535876i
$78$	2.58300	+	2.58300i	0.292467	+	0.292467i
$79$			11.2973i			1.27104i	0.772084	+	0.635521i	$0.219215\pi$
$79$			11.2973i			1.27104i	−0.772084	+	0.635521i	$0.780785\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−10.5040	−	10.5040i	−1.15998	−	1.15998i
$83$	4.88941	−	4.88941i	0.536682	−	0.536682i	−0.385871	−	0.922553i	$-0.626099\pi$
$83$	4.88941	−	4.88941i	0.536682	−	0.536682i	0.922553	+	0.385871i	$0.126099\pi$
$84$	6.41995	+	0.370525i	0.700474	+	0.0404276i
$85$		0			0
$86$	0.907583			0.0978671
$87$	−0.215589	−	0.215589i	−0.0231136	−	0.0231136i
$88$	−1.71220	−	1.71220i	−0.182521	−	0.182521i
$89$	6.91251			0.732725			0.366363	−	0.930472i	$-0.380603\pi$
$89$	6.91251			0.732725			0.366363	+	0.930472i	$0.380603\pi$
$90$		0			0
$91$	−0.264559	+	4.58392i	−0.0277333	+	0.480525i
$92$	0.427009	−	0.427009i	0.0445188	−	0.0445188i
$93$	−5.12921	−	5.12921i	−0.531874	−	0.531874i
$94$	1.65766			0.170974
$95$		0			0
$96$		−	8.02936i		−	0.819493i
$97$	8.84137	+	8.84137i	0.897705	+	0.897705i	0.995233	−	0.0975276i	$-0.0310934\pi$
$97$	8.84137	+	8.84137i	0.897705	+	0.897705i	−0.0975276	+	0.995233i	$0.531093\pi$
$98$	9.15086	+	11.5481i	0.924376	+	1.16654i
$99$			2.67187i			0.268533i
$100$		0			0
$101$			7.22962i			0.719374i	0.933073	+	0.359687i	$0.117117\pi$
$101$			7.22962i			0.719374i	−0.933073	+	0.359687i	$0.882883\pi$
$102$	9.99031	−	9.99031i	0.989188	−	0.989188i
$103$	6.94538	−	6.94538i	0.684349	−	0.684349i	−0.276628	−	0.960977i	$-0.589217\pi$
$103$	6.94538	−	6.94538i	0.684349	−	0.684349i	0.960977	+	0.276628i	$0.0892171\pi$
$104$	−1.57277			−0.154222
$105$		0			0
$106$	−14.8550			−1.44284
$107$	7.47295	−	7.47295i	0.722437	−	0.722437i	−0.246664	−	0.969101i	$-0.579334\pi$
$107$	7.47295	−	7.47295i	0.722437	−	0.722437i	0.969101	+	0.246664i	$0.0793344\pi$
$108$	1.71866	−	1.71866i	0.165378	−	0.165378i
$109$			5.95352i			0.570244i	0.958491	+	0.285122i	$0.0920341\pi$
$109$			5.95352i			0.570244i	−0.958491	+	0.285122i	$0.907966\pi$
$110$		0			0
$111$			1.04007i			0.0987192i
$112$	5.83473	−	5.19798i	0.551330	−	0.491163i
$113$	−6.99031	−	6.99031i	−0.657593	−	0.657593i	0.297217	−	0.954810i	$-0.403942\pi$
$113$	−6.99031	−	6.99031i	−0.657593	−	0.657593i	−0.954810	+	0.297217i	$0.903942\pi$
$114$		−	12.6657i		−	1.18625i
$115$		0			0
$116$	0.741049			0.0688047
$117$	1.22714	+	1.22714i	0.113449	+	0.113449i
$118$	11.8897	−	11.8897i	1.09454	−	1.09454i
$119$	17.7293	+	1.02324i	1.62524	+	0.0938002i
$120$		0			0
$121$	−3.86110			−0.351009
$122$	8.23683	+	8.23683i	0.745727	+	0.745727i
$123$	−4.99031	−	4.99031i	−0.449961	−	0.449961i
$124$	17.6307			1.58329
$125$		0			0
$126$	5.55976	+	0.320879i	0.495303	+	0.0285862i
$127$	−2.86110	+	2.86110i	−0.253882	+	0.253882i	−0.822560	−	0.568678i	$-0.807455\pi$
$127$	−2.86110	+	2.86110i	−0.253882	+	0.253882i	0.568678	+	0.822560i	$0.307455\pi$
$128$	5.00781	+	5.00781i	0.442632	+	0.442632i
$129$	0.431179			0.0379632
$130$		0			0
$131$		−	9.34764i		−	0.816707i	−0.912824	−	0.408353i	$-0.866103\pi$
$131$		−	9.34764i		−	0.816707i	0.912824	−	0.408353i	$-0.133897\pi$
$132$	−4.59204	−	4.59204i	−0.399686	−	0.399686i
$133$	11.8873	−	10.5900i	1.03076	−	0.918268i
$134$			10.2119i			0.882177i
$135$		0			0
$136$			6.08302i			0.521615i
$137$	−7.51943	+	7.51943i	−0.642428	+	0.642428i	−0.951152	−	0.308724i	$-0.900098\pi$
$137$	−7.51943	+	7.51943i	−0.642428	+	0.642428i	0.308724	+	0.951152i	$0.400098\pi$
$138$	0.369795	−	0.369795i	0.0314791	−	0.0314791i
$139$	7.78902			0.660656			0.330328	−	0.943866i	$-0.392841\pi$
$139$	7.78902			0.660656			0.330328	+	0.943866i	$0.392841\pi$
$140$		0			0
$141$	0.787528			0.0663218
$142$	−22.7852	+	22.7852i	−1.91209	+	1.91209i
$143$	3.27877	−	3.27877i	0.274184	−	0.274184i
$144$		−	2.95352i		−	0.246127i
$145$		0			0
$146$		−	29.8296i		−	2.46872i
$147$	4.34743	+	5.48633i	0.358570	+	0.452505i
$148$	−1.78753	−	1.78753i	−0.146934	−	0.146934i
$149$		−	14.2855i		−	1.17031i	−0.810920	−	0.585157i	$-0.801033\pi$
$149$		−	14.2855i		−	1.17031i	0.810920	−	0.585157i	$-0.198967\pi$
$150$		0			0
$151$	9.77990			0.795877			0.397939	−	0.917412i	$-0.369726\pi$
$151$	9.77990			0.795877			0.397939	+	0.917412i	$0.369726\pi$
$152$	3.85603	+	3.85603i	0.312765	+	0.312765i
$153$	4.74624	−	4.74624i	0.383711	−	0.383711i
$154$	0.857347	−	14.8550i	0.0690870	−	1.19705i
$155$		0			0
$156$	−4.21808			−0.337717
$157$	−2.17731	−	2.17731i	−0.173768	−	0.173768i	0.614864	−	0.788633i	$-0.289211\pi$
$157$	−2.17731	−	2.17731i	−0.173768	−	0.173768i	−0.788633	+	0.614864i	$0.789211\pi$
$158$	−16.8146	−	16.8146i	−1.33770	−	1.33770i
$159$	−7.05736			−0.559685
$160$		0			0
$161$	0.656257	+	0.0378756i	0.0517203	+	0.00298502i
$162$	1.48838	−	1.48838i	0.116938	−	0.116938i
$163$	13.6757	+	13.6757i	1.07117	+	1.07117i	0.997266	+	0.0739001i	$0.0235446\pi$
$163$	13.6757	+	13.6757i	1.07117	+	1.07117i	0.0739001	+	0.997266i	$0.476455\pi$
$164$	17.1533			1.33945
$165$		0			0
$166$			14.5546i			1.12966i
$167$	6.23288	+	6.23288i	0.482315	+	0.482315i	0.905870	−	0.423555i	$-0.139218\pi$
$167$	6.23288	+	6.23288i	0.482315	+	0.482315i	−0.423555	+	0.905870i	$0.639218\pi$
$168$	−1.79034	+	1.59496i	−0.138128	+	0.123054i
$169$			9.98824i			0.768326i
$170$		0			0
$171$		−	6.01729i		−	0.460154i
$172$	−0.741049	+	0.741049i	−0.0565045	+	0.0565045i
$173$	−6.76935	+	6.76935i	−0.514664	+	0.514664i	−0.915952	−	0.401288i	$-0.868563\pi$
$173$	−6.76935	+	6.76935i	−0.514664	+	0.514664i	0.401288	+	0.915952i	$0.368563\pi$
$174$	0.641758			0.0486515
$175$		0			0
$176$	−7.89143			−0.594839
$177$	5.64863	−	5.64863i	0.424577	−	0.424577i
$178$	−10.2885	+	10.2885i	−0.771152	+	0.771152i
$179$		−	1.30103i		−	0.0972437i	−0.998817	−	0.0486218i	$-0.984517\pi$
$179$		−	1.30103i		−	0.0972437i	0.998817	−	0.0486218i	$-0.0154829\pi$
$180$		0			0
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	−6.42885	−	7.21638i	−0.476538	−	0.534913i
$183$	3.91319	+	3.91319i	0.289271	+	0.289271i
$184$			0.225165i			0.0165994i
$185$		0			0
$186$	15.2684			1.11953
$187$	−12.6814	−	12.6814i	−0.927352	−	0.927352i
$188$	−1.35349	+	1.35349i	−0.0987136	+	0.0987136i
$189$	2.64136	+	0.152445i	0.192130	+	0.0110887i
$190$		0			0
$191$	1.93791			0.140222			0.0701110	−	0.997539i	$-0.477665\pi$
$191$	1.93791			0.140222			0.0701110	+	0.997539i	$0.477665\pi$
$192$	7.77383	+	7.77383i	0.561028	+	0.561028i
$193$	7.82786	+	7.82786i	0.563462	+	0.563462i	0.930289	−	0.366827i	$-0.119556\pi$
$193$	7.82786	+	7.82786i	0.563462	+	0.563462i	−0.366827	+	0.930289i	$0.619556\pi$
$194$	−26.3186			−1.88957
$195$		0			0
$196$	−16.9009	−	1.95738i	−1.20721	−	0.139813i
$197$	8.50767	−	8.50767i	0.606146	−	0.606146i	−0.335790	−	0.941937i	$-0.609003\pi$
$197$	8.50767	−	8.50767i	0.606146	−	0.606146i	0.941937	+	0.335790i	$0.109003\pi$
$198$	−3.97676	−	3.97676i	−0.282616	−	0.282616i
$199$	−3.25460			−0.230712			−0.115356	−	0.993324i	$-0.536801\pi$
$199$	−3.25460			−0.230712			−0.115356	+	0.993324i	$0.536801\pi$
$200$		0			0
$201$			4.85153i			0.342201i
$202$	−10.7604	−	10.7604i	−0.757101	−	0.757101i
$203$	0.536583	+	0.602314i	0.0376607	+	0.0422741i
$204$			16.3144i			1.14223i
$205$		0			0
$206$			20.6747i			1.44048i
$207$	0.175684	−	0.175684i	0.0122109	−	0.0122109i
$208$	−3.62439	+	3.62439i	−0.251306	+	0.251306i
$209$	−16.0774			−1.11210
$210$		0			0
$211$	−17.2508			−1.18759			−0.593797	−	0.804615i	$-0.702372\pi$
$211$	−17.2508			−1.18759			−0.593797	+	0.804615i	$0.702372\pi$
$212$	12.1292	−	12.1292i	0.833037	−	0.833037i
$213$	−10.8249	+	10.8249i	−0.741711	+	0.741711i
$214$			22.2452i			1.52065i
$215$		0			0
$216$			0.906263i			0.0616634i
$217$	12.7661	+	14.3300i	0.866622	+	0.972782i
$218$	−8.86110	−	8.86110i	−0.600150	−	0.600150i
$219$		−	14.1716i		−	0.957628i
$220$		0			0
$221$	−11.6486			−0.783572
$222$	−1.54802	−	1.54802i	−0.103896	−	0.103896i
$223$	4.58392	−	4.58392i	0.306962	−	0.306962i	−0.536768	−	0.843730i	$-0.680355\pi$
$223$	4.58392	−	4.58392i	0.306962	−	0.306962i	0.843730	+	0.536768i	$0.180355\pi$
$224$	−1.22403	+	21.2084i	−0.0817841	+	1.41705i
$225$		0			0
$226$	20.8085			1.38416
$227$	−14.1613	−	14.1613i	−0.939918	−	0.939918i	0.0583764	−	0.998295i	$-0.481408\pi$
$227$	−14.1613	−	14.1613i	−0.939918	−	0.939918i	−0.998295	+	0.0583764i	$0.981408\pi$
$228$	10.3417	+	10.3417i	0.684894	+	0.684894i
$229$	−28.9307			−1.91180			−0.955898	−	0.293699i	$-0.905114\pi$
$229$	−28.9307			−1.91180			−0.955898	+	0.293699i	$0.905114\pi$
$230$		0			0
$231$	0.407313	−	7.05736i	0.0267992	−	0.464340i
$232$	−0.195381	+	0.195381i	−0.0128274	+	0.0128274i
$233$	4.78546	+	4.78546i	0.313506	+	0.313506i	0.846266	−	0.532760i	$-0.178845\pi$
$233$	4.78546	+	4.78546i	0.313506	+	0.313506i	−0.532760	+	0.846266i	$0.678845\pi$
$234$	−3.65291			−0.238798
$235$		0			0
$236$			19.4162i			1.26388i
$237$	−7.98837	−	7.98837i	−0.518901	−	0.518901i
$238$	−27.9109	+	24.8650i	−1.80920	+	1.61176i
$239$		−	16.1769i		−	1.04640i	−0.852210	−	0.523200i	$-0.824738\pi$
$239$		−	16.1769i		−	1.04640i	0.852210	−	0.523200i	$-0.175262\pi$
$240$		0			0
$241$			11.3707i			0.732454i	0.930526	+	0.366227i	$0.119351\pi$
$241$			11.3707i			0.732454i	−0.930526	+	0.366227i	$0.880649\pi$
$242$	5.74679	−	5.74679i	0.369418	−	0.369418i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−13.4509			−0.861105
$245$		0			0
$246$	14.8550			0.947117
$247$	−7.38407	+	7.38407i	−0.469837	+	0.469837i
$248$	−4.64841	+	4.64841i	−0.295174	+	0.295174i
$249$			6.91467i			0.438199i
$250$		0			0
$251$		−	6.95039i		−	0.438705i	−0.975646	−	0.219352i	$-0.929606\pi$
$251$		−	6.95039i		−	0.438705i	0.975646	−	0.219352i	$-0.0703944\pi$
$252$	−4.80159	+	4.27759i	−0.302472	+	0.269463i
$253$	−0.469405	−	0.469405i	−0.0295112	−	0.0295112i
$254$		−	8.51682i		−	0.534393i
$255$		0			0
$256$	7.08066			0.442541
$257$	−10.0889	−	10.0889i	−0.629329	−	0.629329i	0.318570	−	0.947899i	$-0.396797\pi$
$257$	−10.0889	−	10.0889i	−0.629329	−	0.629329i	−0.947899	+	0.318570i	$0.896797\pi$
$258$	−0.641758	+	0.641758i	−0.0399541	+	0.0399541i
$259$	0.158553	−	2.74720i	0.00985202	−	0.170703i
$260$		0			0
$261$	0.304889			0.0188722
$262$	13.9128	+	13.9128i	0.859538	+	0.859538i
$263$	−18.1984	−	18.1984i	−1.12216	−	1.12216i	−0.991416	−	0.130744i	$-0.958263\pi$
$263$	−18.1984	−	18.1984i	−1.12216	−	1.12216i	−0.130744	−	0.991416i	$-0.541737\pi$
$264$	2.42142			0.149028
$265$		0			0
$266$	−1.93082	+	33.4547i	−0.118386	+	2.05124i
$267$	−4.88789	+	4.88789i	−0.299134	+	0.299134i
$268$	−8.33813	−	8.33813i	−0.509333	−	0.509333i
$269$	−15.5119			−0.945775			−0.472888	−	0.881123i	$-0.656788\pi$
$269$	−15.5119			−0.945775			−0.472888	+	0.881123i	$0.656788\pi$
$270$		0			0
$271$		−	13.3418i		−	0.810458i	−0.914215	−	0.405229i	$-0.867192\pi$
$271$		−	13.3418i		−	0.810458i	0.914215	−	0.405229i	$-0.132808\pi$
$272$	14.0181	+	14.0181i	0.849974	+	0.849974i
$273$	−3.05425	−	3.42839i	−0.184852	−	0.207496i
$274$		−	22.3835i		−	1.35224i
$275$		0			0
$276$			0.603882i			0.0363494i
$277$	2.00561	−	2.00561i	0.120505	−	0.120505i	−0.644282	−	0.764788i	$-0.722844\pi$
$277$	2.00561	−	2.00561i	0.120505	−	0.120505i	0.764788	+	0.644282i	$0.222844\pi$
$278$	−11.5930	+	11.5930i	−0.695304	+	0.695304i
$279$	7.25379			0.434273
$280$		0			0
$281$	13.5557			0.808664			0.404332	−	0.914612i	$-0.367504\pi$
$281$	13.5557			0.808664			0.404332	+	0.914612i	$0.367504\pi$
$282$	−1.17214	+	1.17214i	−0.0698000	+	0.0698000i
$283$	16.2444	−	16.2444i	0.965627	−	0.965627i	−0.0338017	−	0.999429i	$-0.510761\pi$
$283$	16.2444	−	16.2444i	0.965627	−	0.965627i	0.999429	+	0.0338017i	$0.0107615\pi$
$284$		−	37.2087i		−	2.20793i
$285$		0			0
$286$			9.76010i			0.577127i
$287$	12.4204	+	13.9419i	0.733155	+	0.822966i
$288$	5.67761	+	5.67761i	0.334557	+	0.334557i
$289$			28.0537i			1.65021i
$290$		0			0
$291$	−12.5036			−0.732973
$292$	24.3562	+	24.3562i	1.42534	+	1.42534i
$293$	2.41765	−	2.41765i	0.141240	−	0.141240i	−0.632951	−	0.774192i	$-0.718157\pi$
$293$	2.41765	−	2.41765i	0.141240	−	0.141240i	0.774192	+	0.632951i	$0.218157\pi$
$294$	−14.6364	−	1.69511i	−0.853611	−	0.0988609i
$295$		0			0
$296$	0.942578			0.0547862
$297$	−1.88930	−	1.88930i	−0.109628	−	0.109628i
$298$	21.2623	+	21.2623i	1.23169	+	1.23169i
$299$	−0.431179			−0.0249357
$300$		0			0
$301$	−1.13890	−	0.0657309i	−0.0656449	−	0.00378867i
$302$	−14.5562	+	14.5562i	−0.837616	+	0.837616i
$303$	−5.11211	−	5.11211i	−0.293683	−	0.293683i
$304$	17.7722			1.01931
$305$		0			0
$306$			14.1284i			0.807669i
$307$	−7.21300	−	7.21300i	−0.411667	−	0.411667i	0.470652	−	0.882319i	$-0.344019\pi$
$307$	−7.21300	−	7.21300i	−0.411667	−	0.411667i	−0.882319	+	0.470652i	$0.844019\pi$
$308$	11.4292	+	12.8292i	0.651238	+	0.731014i
$309$			9.82225i			0.558768i
$310$		0			0
$311$		−	10.2542i		−	0.581460i	−0.956805	−	0.290730i	$-0.906102\pi$
$311$		−	10.2542i		−	0.581460i	0.956805	−	0.290730i	$-0.0938981\pi$
$312$	1.11211	−	1.11211i	0.0629611	−	0.0629611i
$313$	−22.0904	+	22.0904i	−1.24862	+	1.24862i	−0.292293	+	0.956329i	$0.594418\pi$
$313$	−22.0904	+	22.0904i	−1.24862	+	1.24862i	−0.956329	+	0.292293i	$0.905582\pi$
$314$	6.48134			0.365763
$315$		0			0
$316$	27.4586			1.54467
$317$	12.2563	−	12.2563i	0.688385	−	0.688385i	−0.273490	−	0.961875i	$-0.588178\pi$
$317$	12.2563	−	12.2563i	0.688385	−	0.688385i	0.961875	+	0.273490i	$0.0881780\pi$
$318$	10.5040	−	10.5040i	0.589037	−	0.589037i
$319$		−	0.814625i		−	0.0456102i
$320$		0			0
$321$			10.5683i			0.589867i
$322$	−1.03313	+	0.920387i	−0.0575743	+	0.0512912i
$323$	28.5595	+	28.5595i	1.58909	+	1.58909i
$324$			2.43055i			0.135031i
$325$		0			0
$326$	−40.7094			−2.25468
$327$	−4.20978	−	4.20978i	−0.232801	−	0.232801i
$328$	−4.52253	+	4.52253i	−0.249715	+	0.249715i
$329$	−2.08014	−	0.120054i	−0.114682	−	0.00661882i
$330$		0			0
$331$	1.26308			0.0694252			0.0347126	−	0.999397i	$-0.488948\pi$
$331$	1.26308			0.0694252			0.0347126	+	0.999397i	$0.488948\pi$
$332$	−11.8840	−	11.8840i	−0.652217	−	0.652217i
$333$	−0.735441	−	0.735441i	−0.0403019	−	0.0403019i
$334$	−18.5538			−1.01522
$335$		0			0
$336$	−0.450249	+	7.80130i	−0.0245631	+	0.425596i
$337$	9.55621	−	9.55621i	0.520560	−	0.520560i	−0.397180	−	0.917741i	$-0.630011\pi$
$337$	9.55621	−	9.55621i	0.520560	−	0.520560i	0.917741	+	0.397180i	$0.130011\pi$
$338$	−14.8663	−	14.8663i	−0.808620	−	0.808620i
$339$	9.88579			0.536922
$340$		0			0
$341$		−	19.3812i		−	1.04955i
$342$	8.95602	+	8.95602i	0.484286	+	0.484286i
$343$	−10.6468	−	15.1541i	−0.574871	−	0.818244i
$344$		−	0.390761i		−	0.0210684i
$345$		0			0
$346$		−	20.1507i		−	1.08331i
$347$	−6.54975	+	6.54975i	−0.351609	+	0.351609i	−0.860708	−	0.509099i	$-0.829979\pi$
$347$	−6.54975	+	6.54975i	−0.351609	+	0.351609i	0.509099	+	0.860708i	$0.329979\pi$
$348$	−0.524001	+	0.524001i	−0.0280894	+	0.0280894i
$349$	−2.77139			−0.148349			−0.0741746	−	0.997245i	$-0.523632\pi$
$349$	−2.77139			−0.148349			−0.0741746	+	0.997245i	$0.523632\pi$
$350$		0			0
$351$	−1.73544			−0.0926310
$352$	15.1699	−	15.1699i	0.808556	−	0.808556i
$353$	0.970568	−	0.970568i	0.0516581	−	0.0516581i	−0.680806	−	0.732464i	$-0.738370\pi$
$353$	0.970568	−	0.970568i	0.0516581	−	0.0516581i	0.732464	+	0.680806i	$0.238370\pi$
$354$			16.8146i			0.893687i
$355$		0			0
$356$		−	16.8012i		−	0.890463i
$357$	−13.2601	+	11.8130i	−0.701797	+	0.625209i
$358$	1.93643	+	1.93643i	0.102344	+	0.102344i
$359$			9.32813i			0.492320i	0.969229	+	0.246160i	$0.0791688\pi$
$359$			9.32813i			0.492320i	−0.969229	+	0.246160i	$0.920831\pi$
$360$		0			0
$361$	17.2078			0.905674
$362$	12.6293	+	12.6293i	0.663783	+	0.663783i
$363$	2.73021	−	2.73021i	0.143299	−	0.143299i
$364$	11.1415	+	0.643024i	0.583971	+	0.0337036i
$365$		0			0
$366$	−11.6486			−0.608884
$367$	−13.0035	−	13.0035i	−0.678776	−	0.678776i	0.280948	−	0.959723i	$-0.409351\pi$
$367$	−13.0035	−	13.0035i	−0.678776	−	0.678776i	−0.959723	+	0.280948i	$0.909351\pi$
$368$	0.518887	+	0.518887i	0.0270488	+	0.0270488i
$369$	7.05736			0.367392
$370$		0			0
$371$	18.6410	+	1.07586i	0.967793	+	0.0558557i
$372$	−12.4668	+	12.4668i	−0.646373	+	0.646373i
$373$	−20.6757	−	20.6757i	−1.07055	−	1.07055i	−0.997315	−	0.0732339i	$-0.976668\pi$
$373$	−20.6757	−	20.6757i	−1.07055	−	1.07055i	−0.0732339	−	0.997315i	$-0.523332\pi$
$374$	37.7493			1.95197
$375$		0			0
$376$		−	0.713708i		−	0.0368067i
$377$	−0.374143	−	0.374143i	−0.0192693	−	0.0192693i
$378$	−4.15824	+	3.70445i	−0.213877	+	0.190536i
$379$		−	22.0077i		−	1.13046i	−0.824933	−	0.565230i	$-0.808787\pi$
$379$		−	22.0077i		−	1.13046i	0.824933	−	0.565230i	$-0.191213\pi$
$380$		0			0
$381$		−	4.04621i		−	0.207294i
$382$	−2.88434	+	2.88434i	−0.147576	+	0.147576i
$383$	0.390382	−	0.390382i	0.0199476	−	0.0199476i	−0.697063	−	0.717010i	$-0.745510\pi$
$383$	0.390382	−	0.390382i	0.0199476	−	0.0199476i	0.717010	+	0.697063i	$0.245510\pi$
$384$	−7.08211			−0.361407
$385$		0			0
$386$	−23.3017			−1.18602
$387$	−0.304889	+	0.304889i	−0.0154984	+	0.0154984i
$388$	21.4894	−	21.4894i	1.09096	−	1.09096i
$389$		−	25.9300i		−	1.31470i	−0.753584	−	0.657352i	$-0.771677\pi$
$389$		−	25.9300i		−	1.31470i	0.753584	−	0.657352i	$-0.228323\pi$
$390$		0			0
$391$			1.66768i			0.0843381i
$392$	4.97206	−	3.93992i	0.251127	−	0.198996i
$393$	6.60978	+	6.60978i	0.333419	+	0.333419i
$394$			25.3253i			1.27587i
$395$		0			0
$396$	6.49412			0.326342
$397$	17.1631	+	17.1631i	0.861391	+	0.861391i	0.991500	−	0.130109i	$-0.0415327\pi$
$397$	17.1631	+	17.1631i	0.861391	+	0.861391i	−0.130109	+	0.991500i	$0.541533\pi$
$398$	4.84408	−	4.84408i	0.242812	−	0.242812i
$399$	−0.917304	+	15.8938i	−0.0459226	+	0.795686i
$400$		0			0
$401$	−12.9418			−0.646281			−0.323140	−	0.946351i	$-0.604739\pi$
$401$	−12.9418			−0.646281			−0.323140	+	0.946351i	$0.604739\pi$
$402$	−7.22093	−	7.22093i	−0.360147	−	0.360147i
$403$	−8.90143	−	8.90143i	−0.443412	−	0.443412i
$404$	17.5720			0.874238
$405$		0			0
$406$	−1.69511	−	0.0978326i	−0.0841269	−	0.00485535i
$407$	−1.96500	+	1.96500i	−0.0974016	+	0.0974016i
$408$	−4.30135	−	4.30135i	−0.212948	−	0.212948i
$409$	−2.64278			−0.130677			−0.0653386	−	0.997863i	$-0.520813\pi$
$409$	−2.64278			−0.130677			−0.0653386	+	0.997863i	$0.520813\pi$
$410$		0			0
$411$		−	10.6341i		−	0.524540i
$412$	−16.8811	−	16.8811i	−0.831672	−	0.831672i
$413$	−15.7812	+	14.0589i	−0.776540	+	0.691795i
$414$			0.522969i			0.0257025i
$415$		0			0
$416$		−	13.9345i		−	0.683194i
$417$	−5.50767	+	5.50767i	−0.269712	+	0.269712i
$418$	23.9293	−	23.9293i	1.17042	−	1.17042i
$419$	10.0302			0.490007			0.245003	−	0.969522i	$-0.421211\pi$
$419$	10.0302			0.490007			0.245003	+	0.969522i	$0.421211\pi$
$420$		0			0
$421$	−26.6440			−1.29855			−0.649274	−	0.760555i	$-0.724927\pi$
$421$	−26.6440			−1.29855			−0.649274	+	0.760555i	$0.724927\pi$
$422$	25.6757	−	25.6757i	1.24987	−	1.24987i
$423$	−0.556866	+	0.556866i	−0.0270758	+	0.0270758i
$424$			6.39583i			0.310609i
$425$		0			0
$426$		−	32.2232i		−	1.56122i
$427$	−9.73958	−	10.9327i	−0.471332	−	0.529069i
$428$	−18.1634	−	18.1634i	−0.877960	−	0.877960i
$429$			4.63688i			0.223870i
$430$		0			0
$431$	22.3747			1.07775			0.538876	−	0.842385i	$-0.318849\pi$
$431$	22.3747			1.07775			0.538876	+	0.842385i	$0.318849\pi$
$432$	2.08845	+	2.08845i	0.100481	+	0.100481i
$433$	−13.4723	+	13.4723i	−0.647438	+	0.647438i	−0.952373	−	0.304935i	$-0.901365\pi$
$433$	−13.4723	+	13.4723i	−0.647438	+	0.647438i	0.304935	+	0.952373i	$0.401365\pi$
$434$	−40.3293	−	2.32759i	−1.93587	−	0.111728i
$435$		0			0
$436$	14.4703			0.693004
$437$	1.05714	+	1.05714i	0.0505700	+	0.0505700i
$438$	21.0927	+	21.0927i	1.00785	+	1.00785i
$439$	25.6790			1.22559			0.612795	−	0.790242i	$-0.290045\pi$
$439$	25.6790			1.22559			0.612795	+	0.790242i	$0.290045\pi$
$440$		0			0
$441$	−6.95352	−	0.805321i	−0.331120	−	0.0383486i
$442$	17.3376	−	17.3376i	0.824665	−	0.824665i
$443$	15.6351	+	15.6351i	0.742845	+	0.742845i	0.973125	−	0.230279i	$-0.0739640\pi$
$443$	15.6351	+	15.6351i	0.742845	+	0.742845i	−0.230279	+	0.973125i	$0.573964\pi$
$444$	2.52795			0.119971
$445$		0			0
$446$			13.6452i			0.646120i
$447$	10.1014	+	10.1014i	0.477779	+	0.477779i
$448$	−19.3484	−	21.7185i	−0.914124	−	1.02610i
$449$			7.01947i			0.331269i	0.986187	+	0.165635i	$0.0529673\pi$
$449$			7.01947i			0.331269i	−0.986187	+	0.165635i	$0.947033\pi$
$450$		0			0
$451$		−	18.8564i		−	0.887912i
$452$	−16.9903	+	16.9903i	−0.799157	+	0.799157i
$453$	−6.91544	+	6.91544i	−0.324916	+	0.324916i
$454$	42.1548			1.97842
$455$		0			0
$456$	−5.45325			−0.255372
$457$	−11.2119	+	11.2119i	−0.524472	+	0.524472i	−0.918919	−	0.394447i	$-0.870936\pi$
$457$	−11.2119	+	11.2119i	−0.524472	+	0.524472i	0.394447	+	0.918919i	$0.370936\pi$
$458$	43.0599	−	43.0599i	2.01206	−	2.01206i
$459$			6.71220i			0.313299i
$460$		0			0
$461$			29.9845i			1.39652i	0.715846	+	0.698259i	$0.246041\pi$
$461$			29.9845i			1.39652i	−0.715846	+	0.698259i	$0.753959\pi$
$462$	9.89780	+	11.1103i	0.460488	+	0.516897i
$463$	−7.70220	−	7.70220i	−0.357951	−	0.357951i	0.505106	−	0.863057i	$-0.331453\pi$
$463$	−7.70220	−	7.70220i	−0.357951	−	0.357951i	−0.863057	+	0.505106i	$0.831453\pi$
$464$			0.900497i			0.0418045i
$465$		0			0
$466$	−14.2452			−0.659895
$467$	−1.80961	−	1.80961i	−0.0837386	−	0.0837386i	0.663997	−	0.747735i	$-0.268859\pi$
$467$	−1.80961	−	1.80961i	−0.0837386	−	0.0837386i	−0.747735	+	0.663997i	$0.768859\pi$
$468$	2.98263	−	2.98263i	0.137872	−	0.137872i
$469$	0.739590	−	12.8146i	0.0341511	−	0.591724i
$470$		0			0
$471$	3.07918			0.141881
$472$	−5.11915	−	5.11915i	−0.235628	−	0.235628i
$473$	0.814625	+	0.814625i	0.0374565	+	0.0374565i
$474$	23.7795			1.09223
$475$		0			0
$476$	2.48704	−	43.0920i	0.113993	−	1.97512i
$477$	4.99031	−	4.99031i	0.228491	−	0.228491i
$478$	24.0774	+	24.0774i	1.10128	+	1.10128i
$479$	4.09455			0.187085			0.0935425	−	0.995615i	$-0.470181\pi$
$479$	4.09455			0.187085			0.0935425	+	0.995615i	$0.470181\pi$
$480$		0			0
$481$			1.80498i			0.0823001i
$482$	−16.9240	−	16.9240i	−0.770867	−	0.770867i
$483$	−0.490826	+	0.437262i	−0.0223334	+	0.0198961i
$484$			9.38461i			0.426573i
$485$		0			0
$486$			2.10489i			0.0954796i
$487$	10.3049	−	10.3049i	0.466959	−	0.466959i	−0.433969	−	0.900928i	$-0.642887\pi$
$487$	10.3049	−	10.3049i	0.466959	−	0.466959i	0.900928	+	0.433969i	$0.142887\pi$
$488$	3.54638	−	3.54638i	0.160537	−	0.160537i
$489$	−19.3404			−0.874603
$490$		0			0
$491$	−8.55953			−0.386286			−0.193143	−	0.981171i	$-0.561868\pi$
$491$	−8.55953			−0.386286			−0.193143	+	0.981171i	$0.561868\pi$
$492$	−12.1292	+	12.1292i	−0.546827	+	0.546827i
$493$	−1.44708	+	1.44708i	−0.0651732	+	0.0651732i
$494$		−	21.9806i		−	0.988955i
$495$		0			0
$496$			21.4242i			0.961976i
$497$	30.2427	−	26.9423i	1.35657	−	1.20853i
$498$	−10.2917	−	10.2917i	−0.461180	−	0.461180i
$499$		−	23.7564i		−	1.06348i	−0.846907	−	0.531741i	$-0.821538\pi$
$499$		−	23.7564i		−	1.06348i	0.846907	−	0.531741i	$-0.178462\pi$
$500$		0			0
$501$	−8.81463			−0.393808
$502$	10.3448	+	10.3448i	0.461712	+	0.461712i
$503$	17.9504	−	17.9504i	0.800367	−	0.800367i	−0.182786	−	0.983153i	$-0.558511\pi$
$503$	17.9504	−	17.9504i	0.800367	−	0.800367i	0.983153	+	0.182786i	$0.0585115\pi$
$504$	0.138155	−	2.39376i	0.00615391	−	0.106627i
$505$		0			0
$506$	1.39731			0.0621179
$507$	−7.06275	−	7.06275i	−0.313668	−	0.313668i
$508$	6.95406	+	6.95406i	0.308537	+	0.308537i
$509$	16.8977			0.748979			0.374489	−	0.927231i	$-0.377818\pi$
$509$	16.8977			0.748979			0.374489	+	0.927231i	$0.377818\pi$
$510$		0			0
$511$	−2.16039	+	37.4322i	−0.0955698	+	1.65590i
$512$	−20.5543	+	20.5543i	−0.908382	+	0.908382i
$513$	4.25487	+	4.25487i	0.187857	+	0.187857i
$514$	30.0323			1.32467
$515$		0			0
$516$		−	1.04800i		−	0.0461357i
$517$	1.48788	+	1.48788i	0.0654367	+	0.0654367i
$518$	3.85289	+	4.32486i	0.169286	+	0.190024i
$519$		−	9.57331i		−	0.420221i
$520$		0			0
$521$			7.88477i			0.345438i	0.984971	+	0.172719i	$0.0552552\pi$
$521$			7.88477i			0.345438i	−0.984971	+	0.172719i	$0.944745\pi$
$522$	−0.453791	+	0.453791i	−0.0198619	+	0.0198619i
$523$	1.23149	−	1.23149i	0.0538493	−	0.0538493i	−0.679669	−	0.733519i	$-0.737877\pi$
$523$	1.23149	−	1.23149i	0.0538493	−	0.0538493i	0.733519	+	0.679669i	$0.237877\pi$
$524$	−22.7199			−0.992524
$525$		0			0
$526$	54.1722			2.36202
$527$	−34.4283	+	34.4283i	−1.49972	+	1.49972i
$528$	5.58008	−	5.58008i	0.242842	−	0.242842i
$529$		−	22.9383i		−	0.997316i
$530$		0			0
$531$			7.98837i			0.346666i
$532$	−25.7395	−	28.8926i	−1.11595	−	1.25265i
$533$	−8.66039	−	8.66039i	−0.375123	−	0.375123i
$534$		−	14.5501i		−	0.629643i
$535$		0			0
$536$	4.39677			0.189911
$537$	0.919968	+	0.919968i	0.0396996	+	0.0396996i
$538$	23.0876	−	23.0876i	0.995375	−	0.995375i
$539$	−2.15171	+	18.5789i	−0.0926809	+	0.800250i
$540$		0			0
$541$	34.9495			1.50260			0.751298	−	0.659963i	$-0.229428\pi$
$541$	34.9495			1.50260			0.751298	+	0.659963i	$0.229428\pi$
$542$	19.8577	+	19.8577i	0.852962	+	0.852962i
$543$	6.00000	+	6.00000i	0.257485	+	0.257485i
$544$	−53.8947			−2.31071
$545$		0			0
$546$	9.64863	+	0.556866i	0.412923	+	0.0238317i
$547$	−3.83548	+	3.83548i	−0.163993	+	0.163993i	−0.784333	−	0.620340i	$-0.786995\pi$
$547$	−3.83548	+	3.83548i	−0.163993	+	0.163993i	0.620340	+	0.784333i	$0.286995\pi$
$548$	18.2764	+	18.2764i	0.780727	+	0.780727i
$549$	−5.53409			−0.236189
$550$		0			0
$551$			1.83461i			0.0781569i
$552$	−0.159216	−	0.159216i	−0.00677668	−	0.00677668i
$553$	19.8823	+	22.3179i	0.845483	+	0.949054i
$554$			5.97022i			0.253650i
$555$		0			0
$556$		−	18.9316i		−	0.802880i
$557$	16.3147	−	16.3147i	0.691275	−	0.691275i	−0.271238	−	0.962512i	$-0.587433\pi$
$557$	16.3147	−	16.3147i	0.691275	−	0.691275i	0.962512	+	0.271238i	$0.0874329\pi$
$558$	−10.7964	+	10.7964i	−0.457048	+	0.457048i
$559$	0.748285			0.0316491
$560$		0			0
$561$	17.9341			0.757180
$562$	−20.1760	+	20.1760i	−0.851073	+	0.851073i
$563$	−23.7521	+	23.7521i	−1.00103	+	1.00103i	−0.00103054	+	0.999999i	$0.500328\pi$
$563$	−23.7521	+	23.7521i	−1.00103	+	1.00103i	−0.999999	+	0.00103054i	$0.999672\pi$
$564$		−	1.91413i		−	0.0805993i
$565$		0			0
$566$			48.3556i			2.03254i
$567$	−1.97552	+	1.75993i	−0.0829638	+	0.0739099i
$568$	9.81023	+	9.81023i	0.411628	+	0.411628i
$569$			0.277792i			0.0116457i	0.999983	+	0.00582283i	$0.00185348\pi$
$569$			0.277792i			0.0116457i	−0.999983	+	0.00582283i	$0.998147\pi$
$570$		0			0
$571$	−3.11538			−0.130375			−0.0651874	−	0.997873i	$-0.520765\pi$
$571$	−3.11538			−0.130375			−0.0651874	+	0.997873i	$0.520765\pi$
$572$	−7.96921	−	7.96921i	−0.333209	−	0.333209i
$573$	−1.37031	+	1.37031i	−0.0572454	+	0.0572454i
$574$	−39.2372	−	2.26456i	−1.63773	−	0.0945209i
$575$		0			0
$576$	−10.9939			−0.458077
$577$	−29.5905	−	29.5905i	−1.23187	−	1.23187i	−0.963245	−	0.268625i	$-0.913431\pi$
$577$	−29.5905	−	29.5905i	−1.23187	−	1.23187i	−0.268625	−	0.963245i	$-0.586569\pi$
$578$	−41.7545	−	41.7545i	−1.73676	−	1.73676i
$579$	−11.0703			−0.460064
$580$		0			0
$581$	1.05410	−	18.2641i	0.0437316	−	0.757722i
$582$	18.6101	−	18.6101i	0.771413	−	0.771413i
$583$	−13.3335	−	13.3335i	−0.552216	−	0.552216i
$584$	−12.8432			−0.531456
$585$		0			0
$586$			7.19676i			0.297295i
$587$	−26.6462	−	26.6462i	−1.09981	−	1.09981i	−0.994433	−	0.105375i	$-0.966396\pi$
$587$	−26.6462	−	26.6462i	−1.09981	−	1.09981i	−0.105375	−	0.994433i	$-0.533604\pi$
$588$	13.3348	−	10.5667i	0.549918	−	0.435762i
$589$			43.6482i			1.79849i
$590$		0			0
$591$			12.0317i			0.494916i
$592$	2.17214	−	2.17214i	0.0892745	−	0.0892745i
$593$	−15.1889	+	15.1889i	−0.623733	+	0.623733i	−0.946484	−	0.322751i	$-0.895392\pi$
$593$	−15.1889	+	15.1889i	−0.623733	+	0.623733i	0.322751	+	0.946484i	$0.395392\pi$
$594$	5.62399			0.230755
$595$		0			0
$596$	−34.7217			−1.42225
$597$	2.30135	−	2.30135i	0.0941878	−	0.0941878i
$598$	0.641758	−	0.641758i	0.0262434	−	0.0262434i
$599$			22.2776i			0.910238i	0.890431	+	0.455119i	$0.150403\pi$
$599$			22.2776i			0.910238i	−0.890431	+	0.455119i	$0.849597\pi$
$600$		0			0
$601$		−	22.3458i		−	0.911503i	−0.890107	−	0.455752i	$-0.849371\pi$
$601$		−	22.3458i		−	0.911503i	0.890107	−	0.455752i	$-0.150629\pi$
$602$	1.79294	−	1.59728i	0.0730749	−	0.0651002i
$603$	−3.43055	−	3.43055i	−0.139703	−	0.139703i
$604$		−	23.7706i		−	0.967210i
$605$		0			0
$606$	15.2175			0.618170
$607$	0.576027	+	0.576027i	0.0233802	+	0.0233802i	0.718700	−	0.695320i	$-0.244737\pi$
$607$	0.576027	+	0.576027i	0.0233802	+	0.0233802i	−0.695320	+	0.718700i	$0.744737\pi$
$608$	−34.1639	+	34.1639i	−1.38553	+	1.38553i
$609$	−0.805321	−	0.0464788i	−0.0326333	−	0.00188341i
$610$		0			0
$611$	1.36671			0.0552911
$612$	−11.5360	−	11.5360i	−0.466315	−	0.466315i
$613$	16.4709	+	16.4709i	0.665253	+	0.665253i	0.956613	−	0.291361i	$-0.0941080\pi$
$613$	16.4709	+	16.4709i	0.665253	+	0.665253i	−0.291361	+	0.956613i	$0.594108\pi$
$614$	21.4714			0.866514
$615$		0			0
$616$	−6.39583	−	0.369132i	−0.257695	−	0.0148728i
$617$	3.70013	−	3.70013i	0.148962	−	0.148962i	−0.628692	−	0.777654i	$-0.716410\pi$
$617$	3.70013	−	3.70013i	0.148962	−	0.148962i	0.777654	+	0.628692i	$0.216410\pi$
$618$	−14.6192	−	14.6192i	−0.588072	−	0.588072i
$619$	−39.8840			−1.60307			−0.801536	−	0.597946i	$-0.795984\pi$
$619$	−39.8840			−1.60307			−0.801536	+	0.597946i	$0.795984\pi$
$620$		0			0
$621$			0.248455i			0.00997015i
$622$	15.2621	+	15.2621i	0.611954	+	0.611954i
$623$	13.6558	−	12.1655i	0.547107	−	0.487401i
$624$		−	5.12566i		−	0.205191i
$625$		0			0
$626$		−	65.7578i		−	2.62821i
$627$	11.3685	−	11.3685i	0.454013	−	0.454013i
$628$	−5.29207	+	5.29207i	−0.211177	+	0.211177i
$629$	6.98117			0.278357
$630$		0			0
$631$	−33.9725			−1.35242			−0.676211	−	0.736708i	$-0.736379\pi$
$631$	−33.9725			−1.35242			−0.676211	+	0.736708i	$0.736379\pi$
$632$	−7.23957	+	7.23957i	−0.287975	+	0.287975i
$633$	12.1981	−	12.1981i	0.484833	−	0.484833i
$634$			36.4842i			1.44897i
$635$		0			0
$636$			17.1533i			0.680172i
$637$	7.54472	+	9.52120i	0.298933	+	0.377244i
$638$	1.21247	+	1.21247i	0.0480022	+	0.0480022i
$639$		−	15.3087i		−	0.605605i
$640$		0			0
$641$	−18.1113			−0.715352			−0.357676	−	0.933846i	$-0.616431\pi$
$641$	−18.1113			−0.715352			−0.357676	+	0.933846i	$0.616431\pi$
$642$	−15.7297	−	15.7297i	−0.620802	−	0.620802i
$643$	−32.1062	+	32.1062i	−1.26614	+	1.26614i	−0.318082	+	0.948063i	$0.603039\pi$
$643$	−32.1062	+	32.1062i	−1.26614	+	1.26614i	−0.948063	+	0.318082i	$0.896961\pi$
$644$	0.0920586	−	1.59507i	0.00362762	−	0.0628545i
$645$		0			0
$646$	−85.0149			−3.34487
$647$	−12.9277	−	12.9277i	−0.508241	−	0.508241i	0.405745	−	0.913986i	$-0.367012\pi$
$647$	−12.9277	−	12.9277i	−0.508241	−	0.508241i	−0.913986	+	0.405745i	$0.867012\pi$
$648$	−0.640825	−	0.640825i	−0.0251740	−	0.0251740i
$649$	21.3439			0.837821
$650$		0			0
$651$	−19.1598	−	1.10580i	−0.750934	−	0.0433398i
$652$	33.2396	−	33.2396i	1.30176	−	1.30176i
$653$	9.39937	+	9.39937i	0.367826	+	0.367826i	0.866684	−	0.498858i	$-0.166247\pi$
$653$	9.39937	+	9.39937i	0.367826	+	0.367826i	−0.498858	+	0.866684i	$0.666247\pi$
$654$	12.5315			0.490020
$655$		0			0
$656$			20.8441i			0.813824i
$657$	10.0208	+	10.0208i	0.390950	+	0.390950i
$658$	3.27473	−	2.91736i	0.127662	−	0.113730i
$659$			9.13808i			0.355969i	0.984033	+	0.177985i	$0.0569577\pi$
$659$			9.13808i			0.355969i	−0.984033	+	0.177985i	$0.943042\pi$
$660$		0			0
$661$			28.4837i			1.10789i	0.832554	+	0.553943i	$0.186878\pi$
$661$			28.4837i			1.10789i	−0.832554	+	0.553943i	$0.813122\pi$
$662$	−1.87995	+	1.87995i	−0.0730662	+	0.0730662i
$663$	8.23683	−	8.23683i	0.319892	−	0.319892i
$664$	6.26651			0.243188
$665$		0			0
$666$	2.18923			0.0848310
$667$	−0.0535642	+	0.0535642i	−0.00207401	+	0.00207401i
$668$	15.1493	−	15.1493i	0.586146	−	0.586146i
$669$			6.48264i			0.250633i
$670$		0			0
$671$			14.7864i			0.570821i
$672$	−14.1311	−	15.8621i	−0.545118	−	0.611894i
$673$	−26.8815	−	26.8815i	−1.03621	−	1.03621i	−0.999319	−	0.0368867i	$-0.988256\pi$
$673$	−26.8815	−	26.8815i	−1.03621	−	1.03621i	−0.0368867	−	0.999319i	$-0.511744\pi$
$674$			28.4466i			1.09572i
$675$		0			0
$676$	24.2769			0.933729
$677$	1.19694	+	1.19694i	0.0460022	+	0.0460022i	0.729734	−	0.683731i	$-0.239644\pi$
$677$	1.19694	+	1.19694i	0.0460022	+	0.0460022i	−0.683731	+	0.729734i	$0.739644\pi$
$678$	−14.7138	+	14.7138i	−0.565081	+	0.565081i
$679$	33.0264	+	1.90611i	1.26744	+	0.0731496i
$680$		0			0
$681$	20.0271			0.767440
$682$	28.8466	+	28.8466i	1.10459	+	1.10459i
$683$	−2.41553	−	2.41553i	−0.0924275	−	0.0924275i	0.659381	−	0.751809i	$-0.270818\pi$
$683$	−2.41553	−	2.41553i	−0.0924275	−	0.0924275i	−0.751809	+	0.659381i	$0.770818\pi$
$684$	−14.6253			−0.559214
$685$		0			0
$686$	38.4015	+	6.70863i	1.46618	+	0.256137i
$687$	20.4571	−	20.4571i	0.780487	−	0.780487i
$688$	−0.900497	−	0.900497i	−0.0343311	−	0.0343311i
$689$	−12.2476			−0.466598
$690$		0			0
$691$		−	41.6703i		−	1.58521i	−0.609735	−	0.792606i	$-0.708724\pi$
$691$		−	41.6703i		−	1.58521i	0.609735	−	0.792606i	$-0.291276\pi$
$692$	16.4533	+	16.4533i	0.625459	+	0.625459i
$693$	4.70230	+	5.27832i	0.178625	+	0.200507i
$694$		−	19.4970i		−	0.740098i
$695$		0			0
$696$		−	0.276310i		−	0.0104735i
$697$	−33.4960	+	33.4960i	−1.26875	+	1.26875i
$698$	4.12488	−	4.12488i	0.156129	−	0.156129i
$699$	−6.76767			−0.255977
$700$		0			0
$701$	13.7870			0.520727			0.260364	−	0.965511i	$-0.416158\pi$
$701$	13.7870			0.520727			0.260364	+	0.965511i	$0.416158\pi$
$702$	2.58300	−	2.58300i	0.0974889	−	0.0974889i
$703$	4.42536	−	4.42536i	0.166906	−	0.166906i
$704$			29.3742i			1.10708i
$705$		0			0
$706$			2.88915i			0.108735i
$707$	12.7236	+	14.2822i	0.478520	+	0.537138i
$708$	−13.7293	−	13.7293i	−0.515978	−	0.515978i
$709$		−	24.6722i		−	0.926585i	−0.886205	−	0.463293i	$-0.846668\pi$
$709$		−	24.6722i		−	0.926585i	0.886205	−	0.463293i	$-0.153332\pi$
$710$		0			0
$711$	11.2973			0.423680
$712$	4.42971	+	4.42971i	0.166010	+	0.166010i
$713$	−1.27438	+	1.27438i	−0.0477257	+	0.0477257i
$714$	2.15380	−	37.3182i	0.0806041	−	1.39660i
$715$		0			0
$716$	−3.16223			−0.118178
$717$	11.4388	+	11.4388i	0.427191	+	0.427191i
$718$	−13.8838	−	13.8838i	−0.518139	−	0.518139i
$719$	−29.9117			−1.11552			−0.557758	−	0.830003i	$-0.688338\pi$
$719$	−29.9117			−1.11552			−0.557758	+	0.830003i	$0.688338\pi$
$720$		0			0
$721$	1.49735	−	25.9441i	0.0557642	−	0.966207i
$722$	−25.6118	+	25.6118i	−0.953171	+	0.953171i
$723$	−8.04033	−	8.04033i	−0.299023	−	0.299023i
$724$	−20.6239			−0.766482
$725$		0			0
$726$			8.12719i			0.301628i
$727$	29.8488	+	29.8488i	1.10703	+	1.10703i	0.993539	+	0.113491i	$0.0362034\pi$
$727$	29.8488	+	29.8488i	1.10703	+	1.10703i	0.113491	+	0.993539i	$0.463797\pi$
$728$	−3.10702	+	2.76795i	−0.115154	+	0.102587i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	2.89416i		−	0.107044i
$732$	9.51121	−	9.51121i	0.351545	−	0.351545i
$733$	3.86707	−	3.86707i	0.142834	−	0.142834i	−0.632074	−	0.774908i	$-0.717796\pi$
$733$	3.86707	−	3.86707i	0.142834	−	0.142834i	0.774908	+	0.632074i	$0.217796\pi$
$734$	38.7082			1.42875
$735$		0			0
$736$	−1.99493			−0.0735342
$737$	−9.16599	+	9.16599i	−0.337634	+	0.337634i
$738$	−10.5040	+	10.5040i	−0.386659	+	0.386659i
$739$			11.9735i			0.440454i	0.975449	+	0.220227i	$0.0706797\pi$
$739$			11.9735i			0.440454i	−0.975449	+	0.220227i	$0.929320\pi$
$740$		0			0
$741$		−	10.4427i		−	0.383621i
$742$	−29.3462	+	26.1436i	−1.07733	+	0.959763i
$743$	12.0406	+	12.0406i	0.441728	+	0.441728i	0.892593	−	0.450864i	$-0.148884\pi$
$743$	12.0406	+	12.0406i	0.441728	+	0.441728i	−0.450864	+	0.892593i	$0.648884\pi$
$744$		−	6.57385i		−	0.241009i
$745$		0			0
$746$	61.5467			2.25338
$747$	−4.88941	−	4.88941i	−0.178894	−	0.178894i
$748$	−30.8227	+	30.8227i	−1.12699	+	1.12699i
$749$	1.61109	−	27.9148i	0.0588679	−	1.01998i
$750$		0			0
$751$	−24.1119			−0.879855			−0.439928	−	0.898033i	$-0.644996\pi$
$751$	−24.1119			−0.879855			−0.439928	+	0.898033i	$0.644996\pi$
$752$	−1.64472	−	1.64472i	−0.0599767	−	0.0599767i
$753$	4.91467	+	4.91467i	0.179100	+	0.179100i
$754$	1.11373			0.0405598
$755$		0			0
$756$	0.370525	−	6.41995i	0.0134759	−	0.233491i
$757$	−29.2896	+	29.2896i	−1.06455	+	1.06455i	−0.0667825	+	0.997768i	$0.521273\pi$
$757$	−29.2896	+	29.2896i	−1.06455	+	1.06455i	−0.997768	+	0.0667825i	$0.978727\pi$
$758$	32.7558	+	32.7558i	1.18975	+	1.18975i
$759$	0.663839			0.0240958
$760$		0			0
$761$			32.3002i			1.17088i	0.810716	+	0.585440i	$0.199078\pi$
$761$			32.3002i			1.17088i	−0.810716	+	0.585440i	$0.800922\pi$
$762$	6.02230	+	6.02230i	0.218165	+	0.218165i
$763$	10.4778	+	11.7613i	0.379320	+	0.425787i
$764$		−	4.71018i		−	0.170408i
$765$		0			0
$766$			1.16207i			0.0419874i
$767$	9.80287	−	9.80287i	0.353961	−	0.353961i
$768$	−5.00678	+	5.00678i	−0.180667	+	0.180667i
$769$	18.4310			0.664640			0.332320	−	0.943167i	$-0.392169\pi$
$769$	18.4310			0.664640			0.332320	+	0.943167i	$0.392169\pi$
$770$		0			0
$771$	14.2679			0.513845
$772$	19.0260	−	19.0260i	0.684761	−	0.684761i
$773$	−17.7963	+	17.7963i	−0.640088	+	0.640088i	−0.950577	−	0.310489i	$-0.899507\pi$
$773$	−17.7963	+	17.7963i	−0.640088	+	0.640088i	0.310489	+	0.950577i	$0.399507\pi$
$774$		−	0.907583i		−	0.0326224i
$775$		0			0
$776$			11.3315i			0.406779i
$777$	1.83045	+	2.05468i	0.0656670	+	0.0737111i
$778$	38.5937	+	38.5937i	1.38365	+	1.38365i
$779$			42.4662i			1.52151i
$780$		0			0
$781$	−40.9030			−1.46362
$782$	−2.48214	−	2.48214i	−0.0887611	−	0.0887611i
$783$	−0.215589	+	0.215589i	−0.00770453	+	0.00770453i
$784$	2.37853	−	20.5374i	0.0849476	−	0.733478i
$785$		0			0
$786$	−19.6757			−0.701810
$787$	16.0671	+	16.0671i	0.572730	+	0.572730i	0.932890	−	0.360160i	$-0.117278\pi$
$787$	16.0671	+	16.0671i	0.572730	+	0.572730i	−0.360160	+	0.932890i	$0.617278\pi$
$788$	−20.6783	−	20.6783i	−0.736635	−	0.736635i
$789$	25.7364			0.916240
$790$		0			0
$791$	−26.1119	−	1.50704i	−0.928432	−	0.0535840i
$792$	−1.71220	+	1.71220i	−0.0608404	+	0.0608404i
$793$	6.79111	+	6.79111i	0.241159	+	0.241159i
$794$	−51.0904			−1.81313
$795$		0			0
$796$			7.91046i			0.280379i
$797$	25.5337	+	25.5337i	0.904451	+	0.904451i	0.995817	−	0.0913664i	$-0.0291235\pi$
$797$	25.5337	+	25.5337i	0.904451	+	0.904451i	−0.0913664	+	0.995817i	$0.529123\pi$
$798$	−22.2907	−	25.0213i	−0.789083	−	0.885745i
$799$		−	5.28605i		−	0.187007i
$800$		0			0
$801$		−	6.91251i		−	0.244242i
$802$	19.2623	−	19.2623i	0.680174	−	0.680174i
$803$	26.7744	−	26.7744i	0.944847	−	0.944847i
$804$	11.7919			0.415868
$805$		0			0
$806$	26.4974			0.933332
$807$	10.9685	−	10.9685i	0.386111	−	0.386111i
$808$	−4.63292	+	4.63292i	−0.162986	+	0.162986i
$809$		−	27.5404i		−	0.968270i	−0.874993	−	0.484135i	$-0.839134\pi$
$809$		−	27.5404i		−	0.968270i	0.874993	−	0.484135i	$-0.160866\pi$
$810$		0			0
$811$			34.2545i			1.20284i	0.798933	+	0.601420i	$0.205398\pi$
$811$			34.2545i			1.20284i	−0.798933	+	0.601420i	$0.794602\pi$
$812$	1.46395	−	1.30419i	0.0513747	−	0.0457682i
$813$	9.43409	+	9.43409i	0.330868	+	0.330868i
$814$		−	5.84935i		−	0.205020i
$815$		0			0
$816$	−19.8246			−0.694001
$817$	−1.83461	−	1.83461i	−0.0641848	−	0.0641848i
$818$	3.93347	−	3.93347i	0.137530	−	0.137530i
$819$	4.58392	+	0.264559i	0.160175	+	0.00924443i
$820$		0			0
$821$	49.7482			1.73623			0.868113	−	0.496367i	$-0.165333\pi$
$821$	49.7482			1.73623			0.868113	+	0.496367i	$0.165333\pi$
$822$	15.8275	+	15.8275i	0.552049	+	0.552049i
$823$	6.10417	+	6.10417i	0.212778	+	0.212778i	0.805447	−	0.592668i	$-0.201926\pi$
$823$	6.10417	+	6.10417i	0.212778	+	0.212778i	−0.592668	+	0.805447i	$0.701926\pi$
$824$	8.90155			0.310100
$825$		0			0
$826$	2.56330	−	44.4134i	0.0891886	−	1.54534i
$827$	4.96734	−	4.96734i	0.172731	−	0.172731i	−0.615447	−	0.788178i	$-0.711024\pi$
$827$	4.96734	−	4.96734i	0.172731	−	0.172731i	0.788178	+	0.615447i	$0.211024\pi$
$828$	−0.427009	−	0.427009i	−0.0148396	−	0.0148396i
$829$	−28.3500			−0.984636			−0.492318	−	0.870415i	$-0.663850\pi$
$829$	−28.3500			−0.984636			−0.492318	+	0.870415i	$0.663850\pi$
$830$		0			0
$831$			2.83636i			0.0983922i
$832$	13.4910	+	13.4910i	0.467717	+	0.467717i
$833$	36.8254	−	29.1809i	1.27592	−	1.01106i
$834$		−	16.3950i		−	0.567713i
$835$		0			0
$836$			39.0770i			1.35151i
$837$	−5.12921	+	5.12921i	−0.177291	+	0.177291i
$838$	−14.9287	+	14.9287i	−0.515705	+	0.515705i
$839$	32.8100			1.13273			0.566364	−	0.824156i	$-0.308350\pi$
$839$	32.8100			1.13273			0.566364	+	0.824156i	$0.308350\pi$
$840$		0			0
$841$	28.9070			0.996795
$842$	39.6563	−	39.6563i	1.36665	−	1.36665i
$843$	−9.58531	+	9.58531i	−0.330136	+	0.330136i
$844$			41.9289i			1.44325i
$845$		0			0
$846$		−	1.65766i		−	0.0569915i
$847$	−7.62767	+	6.79526i	−0.262090	+	0.233488i
$848$	14.7390	+	14.7390i	0.506139	+	0.506139i
$849$			22.9730i			0.788431i
$850$		0			0
$851$	0.258411			0.00885820
$852$	26.3105	+	26.3105i	0.901384	+	0.901384i
$853$	15.4954	−	15.4954i	0.530553	−	0.530553i	−0.390184	−	0.920737i	$-0.627589\pi$
$853$	15.4954	−	15.4954i	0.530553	−	0.530553i	0.920737	+	0.390184i	$0.127589\pi$
$854$	30.7682	+	1.77577i	1.05287	+	0.0607657i
$855$		0			0
$856$	9.57770			0.327359
$857$	17.8346	+	17.8346i	0.609218	+	0.609218i	0.942742	−	0.333523i	$-0.108238\pi$
$857$	17.8346	+	17.8346i	0.609218	+	0.609218i	−0.333523	+	0.942742i	$0.608238\pi$
$858$	−6.90143	−	6.90143i	−0.235611	−	0.235611i
$859$	17.2711			0.589283			0.294641	−	0.955608i	$-0.404800\pi$
$859$	17.2711			0.589283			0.294641	+	0.955608i	$0.404800\pi$
$860$		0			0
$861$	−18.6410	−	1.07586i	−0.635284	−	0.0366651i
$862$	−33.3021	+	33.3021i	−1.13427	+	1.13427i
$863$	−2.94383	−	2.94383i	−0.100209	−	0.100209i	0.655225	−	0.755434i	$-0.272574\pi$
$863$	−2.94383	−	2.94383i	−0.100209	−	0.100209i	−0.755434	+	0.655225i	$0.772574\pi$
$864$	−8.02936			−0.273164
$865$		0			0
$866$		−	40.1038i		−	1.36278i
$867$	−19.8369	−	19.8369i	−0.673697	−	0.673697i
$868$	34.8298	−	31.0288i	1.18220	−	1.05318i
$869$		−	30.1848i		−	1.02395i
$870$		0			0
$871$			8.41955i			0.285286i
$872$	−3.81517	+	3.81517i	−0.129198	+	0.129198i
$873$	8.84137	−	8.84137i	0.299235	−	0.299235i
$874$	−3.14686			−0.106444
$875$		0			0
$876$	−34.4448			−1.16378
$877$	8.49735	−	8.49735i	0.286935	−	0.286935i	−0.548932	−	0.835867i	$-0.684965\pi$
$877$	8.49735	−	8.49735i	0.286935	−	0.286935i	0.835867	+	0.548932i	$0.184965\pi$
$878$	−38.2201	+	38.2201i	−1.28987	+	1.28987i
$879$			3.41907i			0.115322i
$880$		0			0
$881$		−	35.7762i		−	1.20533i	−0.797994	−	0.602665i	$-0.794106\pi$
$881$		−	35.7762i		−	1.20533i	0.797994	−	0.602665i	$-0.205894\pi$
$882$	11.5481	−	9.15086i	0.388845	−	0.308125i
$883$	−24.6278	−	24.6278i	−0.828791	−	0.828791i	0.158559	−	0.987350i	$-0.449315\pi$
$883$	−24.6278	−	24.6278i	−0.828791	−	0.828791i	−0.987350	+	0.158559i	$0.949315\pi$
$884$			28.3126i			0.952256i
$885$		0			0
$886$	−46.5419			−1.56361
$887$	−0.732491	−	0.732491i	−0.0245946	−	0.0245946i	0.694703	−	0.719297i	$-0.255536\pi$
$887$	−0.732491	−	0.732491i	−0.0245946	−	0.0245946i	−0.719297	+	0.694703i	$0.755536\pi$
$888$	−0.666503	+	0.666503i	−0.0223664	+	0.0223664i
$889$	−0.616823	+	10.6875i	−0.0206876	+	0.358447i
$890$		0			0
$891$	2.67187			0.0895111
$892$	−11.1415	−	11.1415i	−0.373043	−	0.373043i
$893$	−3.35083	−	3.35083i	−0.112131	−	0.112131i
$894$	−30.0694			−1.00567
$895$		0			0
$896$	18.7064	+	1.07963i	0.624936	+	0.0360679i
$897$	0.304889	−	0.304889i	0.0101800	−	0.0101800i
$898$	−10.4476	−	10.4476i	−0.348642	−	0.348642i
$899$	−2.21160			−0.0737611
$900$		0			0
$901$			47.3704i			1.57814i
$902$	28.0654	+	28.0654i	0.934477	+	0.934477i
$903$	0.851800	−	0.758842i	0.0283461	−	0.0252527i
$904$		−	8.95913i		−	0.297976i
$905$		0			0
$906$		−	20.5856i		−	0.683911i
$907$	22.8743	−	22.8743i	0.759530	−	0.759530i	−0.216707	−	0.976237i	$-0.569532\pi$
$907$	22.8743	−	22.8743i	0.759530	−	0.759530i	0.976237	+	0.216707i	$0.0695316\pi$
$908$	−34.4198	+	34.4198i	−1.14226	+	1.14226i
$909$	7.22962			0.239791
$910$		0			0
$911$	24.7867			0.821220			0.410610	−	0.911811i	$-0.365316\pi$
$911$	24.7867			0.821220			0.410610	+	0.911811i	$0.365316\pi$
$912$	−12.5668	+	12.5668i	−0.416130	+	0.416130i
$913$	−13.0639	+	13.0639i	−0.432351	+	0.432351i
$914$		−	33.3752i		−	1.10395i
$915$		0			0
$916$			70.3176i			2.32336i
$917$	−16.4512	−	18.4664i	−0.543265	−	0.609814i
$918$	−9.99031	−	9.99031i	−0.329729	−	0.329729i
$919$		−	14.5898i		−	0.481272i	−0.970615	−	0.240636i	$-0.922644\pi$
$919$		−	14.5898i		−	0.481272i	0.970615	−	0.240636i	$-0.0773560\pi$
$920$		0			0
$921$	10.2007			0.336125
$922$	−44.6283	−	44.6283i	−1.46976	−	1.46976i
$923$	−18.7860	+	18.7860i	−0.618349	+	0.618349i
$924$	−17.1533	−	0.989994i	−0.564302	−	0.0325684i
$925$		0			0
$926$	22.9276			0.753447
$927$	−6.94538	−	6.94538i	−0.228116	−	0.228116i
$928$	−1.73104	−	1.73104i	−0.0568243	−	0.0568243i
$929$	−25.1526			−0.825229			−0.412615	−	0.910906i	$-0.635384\pi$
$929$	−25.1526			−0.825229			−0.412615	+	0.910906i	$0.635384\pi$
$930$		0			0
$931$	4.84585	−	41.8414i	0.158816	−	1.37130i
$932$	11.6313	−	11.6313i	0.380996	−	0.380996i
$933$	7.25079	+	7.25079i	0.237380	+	0.237380i
$934$	5.38676			0.176260
$935$		0			0
$936$			1.57277i			0.0514075i
$937$	−28.3540	−	28.3540i	−0.926286	−	0.926286i	0.0711778	−	0.997464i	$-0.477324\pi$
$937$	−28.3540	−	28.3540i	−0.926286	−	0.926286i	−0.997464	+	0.0711778i	$0.977324\pi$
$938$	17.9722	+	20.1738i	0.586815	+	0.658699i
$939$		−	31.2405i		−	1.01950i
$940$		0			0
$941$		−	0.106973i		−	0.00348721i	−0.999998	−	0.00174360i	$-0.999445\pi$
$941$		−	0.106973i		−	0.00348721i	0.999998	−	0.00174360i	$-0.000555007\pi$
$942$	−4.58300	+	4.58300i	−0.149322	+	0.149322i
$943$	−1.23987	+	1.23987i	−0.0403756	+	0.0403756i
$944$	−23.5938			−0.767914
$945$		0			0
$946$	−2.42494			−0.0788417
$947$	−17.9671	+	17.9671i	−0.583851	+	0.583851i	−0.935959	−	0.352108i	$-0.885465\pi$
$947$	−17.9671	+	17.9671i	−0.583851	+	0.583851i	0.352108	+	0.935959i	$0.385465\pi$
$948$	−19.4162	+	19.4162i	−0.630607	+	0.630607i
$949$		−	24.5940i		−	0.798354i
$950$		0			0
$951$			17.3331i			0.562064i
$952$	10.7057	+	12.0171i	0.346973	+	0.389477i
$953$	−31.8008	−	31.8008i	−1.03013	−	1.03013i	−0.999532	−	0.0305973i	$-0.990259\pi$
$953$	−31.8008	−	31.8008i	−1.03013	−	1.03013i	−0.0305973	−	0.999532i	$-0.509741\pi$
$954$			14.8550i			0.480947i
$955$		0			0
$956$	−39.3189			−1.27166
$957$	0.576027	+	0.576027i	0.0186203	+	0.0186203i
$958$	−6.09425	+	6.09425i	−0.196896	+	0.196896i
$959$	−1.62111	+	28.0884i	−0.0523483	+	0.907021i
$960$		0			0
$961$	−21.6175			−0.697339
$962$	−2.68650	−	2.68650i	−0.0866162	−	0.0866162i
$963$	−7.47295	−	7.47295i	−0.240812	−	0.240812i
$964$	27.6372			0.890134
$965$		0			0
$966$	0.0797239	−	1.38135i	0.00256507	−	0.0444441i
$967$	−0.210995	+	0.210995i	−0.00678513	+	0.00678513i	−0.710491	−	0.703706i	$-0.751527\pi$
$967$	−0.210995	+	0.210995i	−0.00678513	+	0.00678513i	0.703706	+	0.710491i	$0.251527\pi$
$968$	−2.47429	−	2.47429i	−0.0795267	−	0.0795267i
$969$	−40.3893			−1.29749
$970$		0			0
$971$		−	54.1165i		−	1.73668i	−0.495969	−	0.868340i	$-0.665187\pi$
$971$		−	54.1165i		−	1.73668i	0.495969	−	0.868340i	$-0.334813\pi$
$972$	−1.71866	−	1.71866i	−0.0551260	−	0.0551260i
$973$	15.3873	−	13.7081i	0.493295	−	0.439462i
$974$			30.6752i			0.982896i
$975$		0			0
$976$		−	16.3450i		−	0.523192i
$977$	−25.0981	+	25.0981i	−0.802958	+	0.802958i	−0.983557	−	0.180599i	$-0.942197\pi$
$977$	−25.0981	+	25.0981i	−0.802958	+	0.802958i	0.180599	+	0.983557i	$0.442197\pi$
$978$	28.7859	−	28.7859i	0.920471	−	0.920471i
$979$	−18.4693			−0.590283
$980$		0			0
$981$	5.95352			0.190081
$982$	12.7398	−	12.7398i	0.406545	−	0.406545i
$983$	1.23358	−	1.23358i	0.0393451	−	0.0393451i	−0.687161	−	0.726506i	$-0.741143\pi$
$983$	1.23358	−	1.23358i	0.0393451	−	0.0393451i	0.726506	+	0.687161i	$0.241143\pi$
$984$		−	6.39583i		−	0.203892i
$985$		0			0
$986$		−	4.30761i		−	0.137182i
$987$	1.55577	−	1.38599i	0.0495208	−	0.0441166i
$988$	17.9474	+	17.9474i	0.570982	+	0.570982i
$989$		−	0.107128i		−	0.00340648i
$990$		0			0
$991$	48.9637			1.55538			0.777691	−	0.628647i	$-0.216391\pi$
$991$	48.9637			1.55538			0.777691	+	0.628647i	$0.216391\pi$
$992$	−41.1842	−	41.1842i	−1.30760	−	1.30760i
$993$	−0.893133	+	0.893133i	−0.0283427	+	0.0283427i
$994$	−4.91225	+	85.1129i	−0.155807	+	2.69962i
$995$		0			0
$996$	16.8065			0.532533
$997$	−11.9844	−	11.9844i	−0.379551	−	0.379551i	0.491389	−	0.870940i	$-0.336489\pi$
$997$	−11.9844	−	11.9844i	−0.379551	−	0.379551i	−0.870940	+	0.491389i	$0.836489\pi$
$998$	35.3585	+	35.3585i	1.11926	+	1.11926i
$999$	1.04007			0.0329064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.m.b.118.1		16
5.2	odd	4	inner	525.2.m.b.307.2		16
5.3	odd	4		105.2.m.a.97.7	yes	16
5.4	even	2		105.2.m.a.13.8	yes	16
7.6	odd	2	inner	525.2.m.b.118.2		16
15.8	even	4		315.2.p.e.307.1		16
15.14	odd	2		315.2.p.e.118.2		16
20.3	even	4		1680.2.cz.d.97.8		16
20.19	odd	2		1680.2.cz.d.433.1		16
35.3	even	12		735.2.v.a.607.2		32
35.4	even	6		735.2.v.a.313.7		32
35.9	even	6		735.2.v.a.178.2		32
35.13	even	4		105.2.m.a.97.8	yes	16
35.18	odd	12		735.2.v.a.607.1		32
35.19	odd	6		735.2.v.a.178.1		32
35.23	odd	12		735.2.v.a.472.8		32
35.24	odd	6		735.2.v.a.313.8		32
35.27	even	4	inner	525.2.m.b.307.1		16
35.33	even	12		735.2.v.a.472.7		32
35.34	odd	2		105.2.m.a.13.7	✓	16
105.83	odd	4		315.2.p.e.307.2		16
105.104	even	2		315.2.p.e.118.1		16
140.83	odd	4		1680.2.cz.d.97.1		16
140.139	even	2		1680.2.cz.d.433.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	35.34	odd	2
105.2.m.a.13.8	yes	16	5.4	even	2
105.2.m.a.97.7	yes	16	5.3	odd	4
105.2.m.a.97.8	yes	16	35.13	even	4
315.2.p.e.118.1		16	105.104	even	2
315.2.p.e.118.2		16	15.14	odd	2
315.2.p.e.307.1		16	15.8	even	4
315.2.p.e.307.2		16	105.83	odd	4
525.2.m.b.118.1		16	1.1	even	1	trivial
525.2.m.b.118.2		16	7.6	odd	2	inner
525.2.m.b.307.1		16	35.27	even	4	inner
525.2.m.b.307.2		16	5.2	odd	4	inner
735.2.v.a.178.1		32	35.19	odd	6
735.2.v.a.178.2		32	35.9	even	6
735.2.v.a.313.7		32	35.4	even	6
735.2.v.a.313.8		32	35.24	odd	6
735.2.v.a.472.7		32	35.33	even	12
735.2.v.a.472.8		32	35.23	odd	12
735.2.v.a.607.1		32	35.18	odd	12
735.2.v.a.607.2		32	35.3	even	12
1680.2.cz.d.97.1		16	140.83	odd	4
1680.2.cz.d.97.8		16	20.3	even	4
1680.2.cz.d.433.1		16	20.19	odd	2
1680.2.cz.d.433.8		16	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.48838 + 1.48838i) q^{2} +(-0.707107 + 0.707107i) q^{3} -2.43055i q^{4} -2.10489i q^{6} +(1.97552 - 1.75993i) q^{7} +(0.640825 + 0.640825i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.48838 + 1.48838i) q^{2} +(-0.707107 + 0.707107i) q^{3} -2.43055i q^{4} -2.10489i q^{6} +(1.97552 - 1.75993i) q^{7} +(0.640825 + 0.640825i) q^{8} -1.00000i q^{9} -2.67187 q^{11} +(1.71866 + 1.71866i) q^{12} +(-1.22714 + 1.22714i) q^{13} +(-0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(4.74624 + 4.74624i) q^{17} +(1.48838 + 1.48838i) q^{18} +6.01729 q^{19} +(-0.152445 + 2.64136i) q^{21} +(3.97676 - 3.97676i) q^{22} +(0.175684 + 0.175684i) q^{23} -0.906263 q^{24} -3.65291i q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.27759 - 4.80159i) q^{28} +0.304889i q^{29} +7.25379i q^{31} +(-5.67761 + 5.67761i) q^{32} +(1.88930 - 1.88930i) q^{33} -14.1284 q^{34} -2.43055 q^{36} +(0.735441 - 0.735441i) q^{37} +(-8.95602 + 8.95602i) q^{38} -1.73544i q^{39} +7.05736i q^{41} +(-3.70445 - 4.15824i) q^{42} +(-0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(-0.556866 - 0.556866i) q^{47} +(-2.08845 + 2.08845i) q^{48} +(0.805321 - 6.95352i) q^{49} -6.71220 q^{51} +(2.98263 + 2.98263i) q^{52} +(4.99031 + 4.99031i) q^{53} -2.10489 q^{54} +(2.39376 + 0.138155i) q^{56} +(-4.25487 + 4.25487i) q^{57} +(-0.453791 - 0.453791i) q^{58} -7.98837 q^{59} -5.53409i q^{61} +(-10.7964 - 10.7964i) q^{62} +(-1.75993 - 1.97552i) q^{63} -10.9939i q^{64} +5.62399i q^{66} +(3.43055 - 3.43055i) q^{67} +(11.5360 - 11.5360i) q^{68} -0.248455 q^{69} +15.3087 q^{71} +(0.640825 - 0.640825i) q^{72} +(-10.0208 + 10.0208i) q^{73} +2.18923i q^{74} -14.6253i q^{76} +(-5.27832 + 4.70230i) q^{77} +(2.58300 + 2.58300i) q^{78} +11.2973i q^{79} -1.00000 q^{81} +(-10.5040 - 10.5040i) q^{82} +(4.88941 - 4.88941i) q^{83} +(6.41995 + 0.370525i) q^{84} +0.907583 q^{86} +(-0.215589 - 0.215589i) q^{87} +(-1.71220 - 1.71220i) q^{88} +6.91251 q^{89} +(-0.264559 + 4.58392i) q^{91} +(0.427009 - 0.427009i) q^{92} +(-5.12921 - 5.12921i) q^{93} +1.65766 q^{94} -8.02936i q^{96} +(8.84137 + 8.84137i) q^{97} +(9.15086 + 11.5481i) q^{98} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q + 8 * q^7 - 24 * q^8	\( 16 q + 8 q^{7} - 24 q^{8} - 16 q^{11} - 48 q^{16} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

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