LMFDB - Embedded newform 525.2.m.b.307.2

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			307.2
Root			$0.944649 - 1.05244i$ of defining polynomial
Character	$\chi$	$=$	525.307
Dual form			525.2.m.b.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48838 - 1.48838i) q^{2} +(0.707107 + 0.707107i) q^{3} +2.43055i q^{4} -2.10489i q^{6} +(1.75993 + 1.97552i) q^{7} +(0.640825 - 0.640825i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.48838 - 1.48838i) q^{2} +(0.707107 + 0.707107i) q^{3} +2.43055i q^{4} -2.10489i q^{6} +(1.75993 + 1.97552i) q^{7} +(0.640825 - 0.640825i) q^{8} +1.00000i q^{9} -2.67187 q^{11} +(-1.71866 + 1.71866i) q^{12} +(1.22714 + 1.22714i) q^{13} +(0.320879 - 5.55976i) q^{14} +2.95352 q^{16} +(-4.74624 + 4.74624i) q^{17} +(1.48838 - 1.48838i) q^{18} -6.01729 q^{19} +(-0.152445 + 2.64136i) q^{21} +(3.97676 + 3.97676i) q^{22} +(0.175684 - 0.175684i) q^{23} +0.906263 q^{24} -3.65291i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.80159 + 4.27759i) q^{28} -0.304889i q^{29} +7.25379i q^{31} +(-5.67761 - 5.67761i) q^{32} +(-1.88930 - 1.88930i) q^{33} +14.1284 q^{34} -2.43055 q^{36} +(0.735441 + 0.735441i) q^{37} +(8.95602 + 8.95602i) q^{38} +1.73544i q^{39} +7.05736i q^{41} +(4.15824 - 3.70445i) q^{42} +(-0.304889 + 0.304889i) q^{43} -6.49412i q^{44} -0.522969 q^{46} +(0.556866 - 0.556866i) q^{47} +(2.08845 + 2.08845i) q^{48} +(-0.805321 + 6.95352i) q^{49} -6.71220 q^{51} +(-2.98263 + 2.98263i) q^{52} +(4.99031 - 4.99031i) q^{53} +2.10489 q^{54} +(2.39376 + 0.138155i) q^{56} +(-4.25487 - 4.25487i) q^{57} +(-0.453791 + 0.453791i) q^{58} +7.98837 q^{59} -5.53409i q^{61} +(10.7964 - 10.7964i) q^{62} +(-1.97552 + 1.75993i) q^{63} +10.9939i q^{64} +5.62399i q^{66} +(3.43055 + 3.43055i) q^{67} +(-11.5360 - 11.5360i) q^{68} +0.248455 q^{69} +15.3087 q^{71} +(0.640825 + 0.640825i) q^{72} +(10.0208 + 10.0208i) q^{73} -2.18923i q^{74} -14.6253i q^{76} +(-4.70230 - 5.27832i) q^{77} +(2.58300 - 2.58300i) q^{78} -11.2973i q^{79} -1.00000 q^{81} +(10.5040 - 10.5040i) q^{82} +(-4.88941 - 4.88941i) q^{83} +(-6.41995 - 0.370525i) q^{84} +0.907583 q^{86} +(0.215589 - 0.215589i) q^{87} +(-1.71220 + 1.71220i) q^{88} -6.91251 q^{89} +(-0.264559 + 4.58392i) q^{91} +(0.427009 + 0.427009i) q^{92} +(-5.12921 + 5.12921i) q^{93} -1.65766 q^{94} -8.02936i q^{96} +(-8.84137 + 8.84137i) q^{97} +(11.5481 - 9.15086i) q^{98} -2.67187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	−0.998546	−	0.0538973i	$-0.982836\pi$
$2$	−1.48838	−	1.48838i	−1.05244	−	1.05244i	−0.0538973	−	0.998546i	$-0.517164\pi$
$3$	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
$7$	1.75993	+	1.97552i	0.665189	+	0.746675i
$7$	1.75993	+	1.97552i	0.665189	+	0.746675i
$8$	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	$-0.172635\pi$
$13$	1.22714	+	1.22714i	0.340348	+	0.340348i	−0.516150	+	0.856498i	$0.672635\pi$
$14$	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	−0.164807	+	0.986326i	$0.552700\pi$
$17$	−4.74624	+	4.74624i	−1.15113	+	1.15113i	−0.986326	+	0.164807i	$0.947300\pi$
$18$	1.48838	−	1.48838i	0.350815	−	0.350815i
$19$	−6.01729			−1.38046			−0.690231	−	0.723589i	$-0.742491\pi$
$19$	−6.01729			−1.38046			−0.690231	+	0.723589i	$0.742491\pi$
$20$		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	−0.688553	−	0.725186i	$-0.741754\pi$
$23$	0.175684	−	0.175684i	0.0366327	−	0.0366327i	0.725186	+	0.688553i	$0.241754\pi$
$24$	0.906263			0.184990
$25$		0			0
$26$		−	3.65291i		−	0.716394i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−4.80159	+	4.27759i	−0.907416	+	0.808389i
$29$		−	0.304889i		−	0.0566165i	−0.999599	−	0.0283083i	$-0.990988\pi$
$29$		−	0.304889i		−	0.0566165i	0.999599	−	0.0283083i	$-0.00901200\pi$
$30$		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	0.764971	−	0.644065i	$-0.222753\pi$
$37$	0.735441	+	0.735441i	0.120906	+	0.120906i	−0.644065	+	0.764971i	$0.722753\pi$
$38$	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	$0.814213\pi$
$42$	4.15824	−	3.70445i	0.641630	−	0.571608i
$43$	−0.304889	+	0.304889i	−0.0464952	+	0.0464952i	−0.729972	−	0.683477i	$-0.760467\pi$
$43$	−0.304889	+	0.304889i	−0.0464952	+	0.0464952i	0.683477	+	0.729972i	$0.260467\pi$
$44$		−	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	$-0.731707\pi$
$47$	0.556866	−	0.556866i	0.0812273	−	0.0812273i	0.746553	+	0.665326i	$0.231707\pi$
$48$	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	−0.275756	−	0.961228i	$-0.588928\pi$
$53$	4.99031	−	4.99031i	0.685472	−	0.685472i	0.961228	+	0.275756i	$0.0889282\pi$
$54$	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	$-0.325932\pi$
$59$	7.98837			1.04000			0.519999	+	0.854167i	$0.325932\pi$
$60$		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
$63$	−1.97552	+	1.75993i	−0.248892	+	0.221730i
$64$			10.9939i			1.37423i
$65$		0			0
$66$			5.62399i			0.692265i
$67$	3.43055	+	3.43055i	0.419109	+	0.419109i	0.884896	−	0.465788i	$-0.154229\pi$
$67$	3.43055	+	3.43055i	0.419109	+	0.419109i	−0.465788	+	0.884896i	$0.654229\pi$
$68$	−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	0.981527	+	0.191323i	$0.0612778\pi$
$73$	10.0208	+	10.0208i	1.17285	+	1.17285i	0.191323	+	0.981527i	$0.438722\pi$
$74$		−	2.18923i		−	0.254493i
$75$		0			0
$76$		−	14.6253i		−	1.67764i
$77$	−4.70230	−	5.27832i	−0.535876	−	0.601521i
$78$	2.58300	−	2.58300i	0.292467	−	0.292467i
$79$		−	11.2973i		−	1.27104i	−0.772084	−	0.635521i	$-0.780785\pi$
$79$		−	11.2973i		−	1.27104i	0.772084	−	0.635521i	$-0.219215\pi$
$80$		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	$-0.373901\pi$
$83$	−4.88941	−	4.88941i	−0.536682	−	0.536682i	−0.922553	+	0.385871i	$0.873901\pi$
$84$	−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	$-0.619397\pi$
$89$	−6.91251			−0.732725			−0.366363	+	0.930472i	$0.619397\pi$
$90$		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	$-0.968907\pi$
$97$	−8.84137	+	8.84137i	−0.897705	+	0.897705i	0.0975276	+	0.995233i	$0.468907\pi$
$98$	11.5481	−	9.15086i	1.16654	−	0.924376i
$99$		−	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	$-0.410783\pi$
$103$	−6.94538	−	6.94538i	−0.684349	−	0.684349i	−0.960977	+	0.276628i	$0.910783\pi$
$104$	1.57277			0.154222
$105$		0			0
$106$	−14.8550			−1.44284
$107$	7.47295	+	7.47295i	0.722437	+	0.722437i	0.969101	−	0.246664i	$-0.0793344\pi$
$107$	7.47295	+	7.47295i	0.722437	+	0.722437i	−0.246664	+	0.969101i	$0.579334\pi$
$108$	−1.71866	−	1.71866i	−0.165378	−	0.165378i
$109$		−	5.95352i		−	0.570244i	−0.958491	−	0.285122i	$-0.907966\pi$
$109$		−	5.95352i		−	0.570244i	0.958491	−	0.285122i	$-0.0920341\pi$
$110$		0			0
$111$			1.04007i			0.0987192i
$112$	5.19798	+	5.83473i	0.491163	+	0.551330i
$113$	−6.99031	+	6.99031i	−0.657593	+	0.657593i	−0.954810	−	0.297217i	$-0.903942\pi$
$113$	−6.99031	+	6.99031i	−0.657593	+	0.657593i	0.297217	+	0.954810i	$0.403942\pi$
$114$			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	0.568678	−	0.822560i	$-0.307455\pi$
$127$	−2.86110	−	2.86110i	−0.253882	−	0.253882i	−0.822560	+	0.568678i	$0.807455\pi$
$128$	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
$133$	−10.5900	−	11.8873i	−0.918268	−	1.03076i
$134$		−	10.2119i		−	0.882177i
$135$		0			0
$136$			6.08302i			0.521615i
$137$	−7.51943	−	7.51943i	−0.642428	−	0.642428i	0.308724	−	0.951152i	$-0.400098\pi$
$137$	−7.51943	−	7.51943i	−0.642428	−	0.642428i	−0.951152	+	0.308724i	$0.900098\pi$
$138$	−0.369795	−	0.369795i	−0.0314791	−	0.0314791i
$139$	−7.78902			−0.660656			−0.330328	−	0.943866i	$-0.607159\pi$
$139$	−7.78902			−0.660656			−0.330328	+	0.943866i	$0.607159\pi$
$140$		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
$147$	−5.48633	+	4.34743i	−0.452505	+	0.358570i
$148$	−1.78753	+	1.78753i	−0.146934	+	0.146934i
$149$			14.2855i			1.17031i	0.810920	+	0.585157i	$0.198967\pi$
$149$			14.2855i			1.17031i	−0.810920	+	0.585157i	$0.801033\pi$
$150$		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	$-0.710789\pi$
$157$	2.17731	−	2.17731i	0.173768	−	0.173768i	0.788633	+	0.614864i	$0.210789\pi$
$158$	−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	0.0739001	−	0.997266i	$-0.476455\pi$
$163$	13.6757	−	13.6757i	1.07117	−	1.07117i	0.997266	−	0.0739001i	$-0.0235446\pi$
$164$	−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	$-0.860782\pi$
$167$	−6.23288	+	6.23288i	−0.482315	+	0.482315i	0.423555	+	0.905870i	$0.360782\pi$
$168$	1.59496	+	1.79034i	0.123054	+	0.138128i
$169$		−	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	$-0.131437\pi$
$173$	6.76935	+	6.76935i	0.514664	+	0.514664i	−0.401288	+	0.915952i	$0.631437\pi$
$174$	−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	$0.0154829\pi$
$179$			1.30103i			0.0972437i	−0.998817	+	0.0486218i	$0.984517\pi$
$180$		0			0
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	7.21638	−	6.42885i	0.534913	−	0.476538i
$183$	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	−0.366827	−	0.930289i	$-0.619556\pi$
$193$	7.82786	−	7.82786i	0.563462	−	0.563462i	0.930289	+	0.366827i	$0.119556\pi$
$194$	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	0.941937	−	0.335790i	$-0.109003\pi$
$197$	8.50767	+	8.50767i	0.606146	+	0.606146i	−0.335790	+	0.941937i	$0.609003\pi$
$198$	−3.97676	+	3.97676i	−0.282616	+	0.282616i
$199$	3.25460			0.230712			0.115356	−	0.993324i	$-0.463199\pi$
$199$	3.25460			0.230712			0.115356	+	0.993324i	$0.463199\pi$
$200$		0			0
$201$			4.85153i			0.342201i
$202$	10.7604	−	10.7604i	0.757101	−	0.757101i
$203$	0.602314	−	0.536583i	0.0422741	−	0.0376607i
$204$		−	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
$217$	−14.3300	+	12.7661i	−0.972782	+	0.866622i
$218$	−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	$-0.319645\pi$
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	−0.843730	+	0.536768i	$0.819645\pi$
$224$	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	$-0.518592\pi$
$227$	14.1613	−	14.1613i	0.939918	−	0.939918i	0.998295	+	0.0583764i	$0.0185924\pi$
$228$	10.3417	−	10.3417i	0.684894	−	0.684894i
$229$	28.9307			1.91180			0.955898	−	0.293699i	$-0.0948864\pi$
$229$	28.9307			1.91180			0.955898	+	0.293699i	$0.0948864\pi$
$230$		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	−0.532760	−	0.846266i	$-0.678845\pi$
$233$	4.78546	−	4.78546i	0.313506	−	0.313506i	0.846266	+	0.532760i	$0.178845\pi$
$234$	3.65291			0.238798
$235$		0			0
$236$			19.4162i			1.26388i
$237$	7.98837	−	7.98837i	0.518901	−	0.518901i
$238$	24.8650	+	27.9109i	1.61176	+	1.80920i
$239$			16.1769i			1.04640i	0.852210	+	0.523200i	$0.175262\pi$
$239$			16.1769i			1.04640i	−0.852210	+	0.523200i	$0.824738\pi$
$240$		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	$-0.0703944\pi$
$252$	−4.27759	−	4.80159i	−0.269463	−	0.302472i
$253$	−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	$-0.603203\pi$
$257$	10.0889	−	10.0889i	0.629329	−	0.629329i	0.947899	+	0.318570i	$0.103203\pi$
$258$	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	−0.130744	+	0.991416i	$0.541737\pi$
$263$	−18.1984	+	18.1984i	−1.12216	+	1.12216i	−0.991416	+	0.130744i	$0.958263\pi$
$264$	−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	$-0.343212\pi$
$269$	15.5119			0.945775			0.472888	+	0.881123i	$0.343212\pi$
$270$		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
$273$	−3.42839	+	3.05425i	−0.207496	+	0.184852i
$274$			22.3835i			1.35224i
$275$		0			0
$276$			0.603882i			0.0363494i
$277$	2.00561	+	2.00561i	0.120505	+	0.120505i	0.764788	−	0.644282i	$-0.222844\pi$
$277$	2.00561	+	2.00561i	0.120505	+	0.120505i	−0.644282	+	0.764788i	$0.722844\pi$
$278$	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	$-0.489239\pi$
$283$	−16.2444	−	16.2444i	−0.965627	−	0.965627i	−0.999429	+	0.0338017i	$0.989239\pi$
$284$			37.2087i			2.20793i
$285$		0			0
$286$			9.76010i			0.577127i
$287$	−13.9419	+	12.4204i	−0.822966	+	0.733155i
$288$	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	$-0.281843\pi$
$293$	−2.41765	−	2.41765i	−0.141240	−	0.141240i	−0.774192	+	0.632951i	$0.781843\pi$
$294$	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	$-0.655981\pi$
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	0.882319	+	0.470652i	$0.155981\pi$
$308$	12.8292	−	11.4292i	0.731014	−	0.651238i
$309$		−	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	0.956329	+	0.292293i	$0.0944182\pi$
$313$	22.0904	+	22.0904i	1.24862	+	1.24862i	0.292293	+	0.956329i	$0.405582\pi$
$314$	−6.48134			−0.365763
$315$		0			0
$316$	27.4586			1.54467
$317$	12.2563	+	12.2563i	0.688385	+	0.688385i	0.961875	−	0.273490i	$-0.0881780\pi$
$317$	12.2563	+	12.2563i	0.688385	+	0.688385i	−0.273490	+	0.961875i	$0.588178\pi$
$318$	−10.5040	−	10.5040i	−0.589037	−	0.589037i
$319$			0.814625i			0.0456102i
$320$		0			0
$321$			10.5683i			0.589867i
$322$	−0.920387	−	1.03313i	−0.0512912	−	0.0575743i
$323$	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	0.917741	−	0.397180i	$-0.130011\pi$
$337$	9.55621	+	9.55621i	0.520560	+	0.520560i	−0.397180	+	0.917741i	$0.630011\pi$
$338$	−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
$343$	−15.1541	+	10.6468i	−0.818244	+	0.574871i
$344$			0.390761i			0.0210684i
$345$		0			0
$346$		−	20.1507i		−	1.08331i
$347$	−6.54975	−	6.54975i	−0.351609	−	0.351609i	0.509099	−	0.860708i	$-0.329979\pi$
$347$	−6.54975	−	6.54975i	−0.351609	−	0.351609i	−0.860708	+	0.509099i	$0.829979\pi$
$348$	0.524001	+	0.524001i	0.0280894	+	0.0280894i
$349$	2.77139			0.148349			0.0741746	−	0.997245i	$-0.476368\pi$
$349$	2.77139			0.148349			0.0741746	+	0.997245i	$0.476368\pi$
$350$		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	$-0.261630\pi$
$353$	−0.970568	−	0.970568i	−0.0516581	−	0.0516581i	−0.732464	+	0.680806i	$0.761630\pi$
$354$		−	16.8146i		−	0.893687i
$355$		0			0
$356$		−	16.8012i		−	0.890463i
$357$	−11.8130	−	13.2601i	−0.625209	−	0.701797i
$358$	1.93643	−	1.93643i	0.102344	−	0.102344i
$359$		−	9.32813i		−	0.492320i	−0.969229	−	0.246160i	$-0.920831\pi$
$359$		−	9.32813i		−	0.492320i	0.969229	−	0.246160i	$-0.0791688\pi$
$360$		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	$-0.590649\pi$
$367$	13.0035	−	13.0035i	0.678776	−	0.678776i	0.959723	+	0.280948i	$0.0906487\pi$
$368$	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	−0.0732339	+	0.997315i	$0.523332\pi$
$373$	−20.6757	+	20.6757i	−1.07055	+	1.07055i	−0.997315	+	0.0732339i	$0.976668\pi$
$374$	−37.7493			−1.95197
$375$		0			0
$376$		−	0.713708i		−	0.0368067i
$377$	0.374143	−	0.374143i	0.0192693	−	0.0192693i
$378$	3.70445	+	4.15824i	0.190536	+	0.213877i
$379$			22.0077i			1.13046i	0.824933	+	0.565230i	$0.191213\pi$
$379$			22.0077i			1.13046i	−0.824933	+	0.565230i	$0.808787\pi$
$380$		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	$-0.254490\pi$
$383$	−0.390382	−	0.390382i	−0.0199476	−	0.0199476i	−0.717010	+	0.697063i	$0.754490\pi$
$384$	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	$0.228323\pi$
$389$			25.9300i			1.31470i	−0.753584	+	0.657352i	$0.771677\pi$
$390$		0			0
$391$			1.66768i			0.0843381i
$392$	3.93992	+	4.97206i	0.198996	+	0.251127i
$393$	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	$-0.958467\pi$
$397$	−17.1631	+	17.1631i	−0.861391	+	0.861391i	0.130109	+	0.991500i	$0.458467\pi$
$398$	−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	$-0.479187\pi$
$409$	2.64278			0.130677			0.0653386	+	0.997863i	$0.479187\pi$
$410$		0			0
$411$		−	10.6341i		−	0.524540i
$412$	16.8811	−	16.8811i	0.831672	−	0.831672i
$413$	14.0589	+	15.7812i	0.691795	+	0.776540i
$414$		−	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	$-0.578789\pi$
$419$	−10.0302			−0.490007			−0.245003	+	0.969522i	$0.578789\pi$
$420$		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
$427$	10.9327	−	9.73958i	0.529069	−	0.471332i
$428$	−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	$-0.0986349\pi$
$433$	13.4723	+	13.4723i	0.647438	+	0.647438i	−0.304935	+	0.952373i	$0.598635\pi$
$434$	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	$-0.709955\pi$
$439$	−25.6790			−1.22559			−0.612795	+	0.790242i	$0.709955\pi$
$440$		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	−0.230279	−	0.973125i	$-0.573964\pi$
$443$	15.6351	−	15.6351i	0.742845	−	0.742845i	0.973125	+	0.230279i	$0.0739640\pi$
$444$	−2.52795			−0.119971
$445$		0			0
$446$			13.6452i			0.646120i
$447$	−10.1014	+	10.1014i	−0.477779	+	0.477779i
$448$	−21.7185	+	19.3484i	−1.02610	+	0.914124i
$449$		−	7.01947i		−	0.331269i	−0.986187	−	0.165635i	$-0.947033\pi$
$449$		−	7.01947i		−	0.331269i	0.986187	−	0.165635i	$-0.0529673\pi$
$450$		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	0.394447	−	0.918919i	$-0.370936\pi$
$457$	−11.2119	−	11.2119i	−0.524472	−	0.524472i	−0.918919	+	0.394447i	$0.870936\pi$
$458$	−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	$0.753959\pi$
$462$	−11.1103	+	9.89780i	−0.516897	+	0.460488i
$463$	−7.70220	+	7.70220i	−0.357951	+	0.357951i	−0.863057	−	0.505106i	$-0.831453\pi$
$463$	−7.70220	+	7.70220i	−0.357951	+	0.357951i	0.505106	+	0.863057i	$0.331453\pi$
$464$		−	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	$-0.731141\pi$
$467$	1.80961	−	1.80961i	0.0837386	−	0.0837386i	0.747735	+	0.663997i	$0.231141\pi$
$468$	−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	$-0.529819\pi$
$479$	−4.09455			−0.187085			−0.0935425	+	0.995615i	$0.529819\pi$
$480$		0			0
$481$			1.80498i			0.0823001i
$482$	16.9240	−	16.9240i	0.770867	−	0.770867i
$483$	0.437262	+	0.490826i	0.0198961	+	0.0223334i
$484$		−	9.38461i		−	0.426573i
$485$		0			0
$486$			2.10489i			0.0954796i
$487$	10.3049	+	10.3049i	0.466959	+	0.466959i	0.900928	−	0.433969i	$-0.142887\pi$
$487$	10.3049	+	10.3049i	0.466959	+	0.466959i	−0.433969	+	0.900928i	$0.642887\pi$
$488$	−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
$497$	26.9423	+	30.2427i	1.20853	+	1.35657i
$498$	−10.2917	+	10.2917i	−0.461180	+	0.461180i
$499$			23.7564i			1.06348i	0.846907	+	0.531741i	$0.178462\pi$
$499$			23.7564i			1.06348i	−0.846907	+	0.531741i	$0.821538\pi$
$500$		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	$-0.441489\pi$
$503$	−17.9504	−	17.9504i	−0.800367	−	0.800367i	−0.983153	+	0.182786i	$0.941489\pi$
$504$	−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	$-0.622182\pi$
$509$	−16.8977			−0.748979			−0.374489	+	0.927231i	$0.622182\pi$
$510$		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
$518$	4.32486	−	3.85289i	0.190024	−	0.169286i
$519$			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	$-0.262123\pi$
$523$	−1.23149	−	1.23149i	−0.0538493	−	0.0538493i	−0.733519	+	0.679669i	$0.762123\pi$
$524$	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
$532$	28.8926	−	25.7395i	1.25265	−	1.11595i
$533$	−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	0.620340	−	0.784333i	$-0.286995\pi$
$547$	−3.83548	−	3.83548i	−0.163993	−	0.163993i	−0.784333	+	0.620340i	$0.786995\pi$
$548$	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
$553$	22.3179	−	19.8823i	0.949054	−	0.845483i
$554$		−	5.97022i		−	0.253650i
$555$		0			0
$556$		−	18.9316i		−	0.802880i
$557$	16.3147	+	16.3147i	0.691275	+	0.691275i	0.962512	−	0.271238i	$-0.0874329\pi$
$557$	16.3147	+	16.3147i	0.691275	+	0.691275i	−0.271238	+	0.962512i	$0.587433\pi$
$558$	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	0.999999	+	0.00103054i	$0.000328032\pi$
$563$	23.7521	+	23.7521i	1.00103	+	1.00103i	0.00103054	+	0.999999i	$0.499672\pi$
$564$			1.91413i			0.0805993i
$565$		0			0
$566$			48.3556i			2.03254i
$567$	−1.75993	−	1.97552i	−0.0739099	−	0.0829638i
$568$	9.81023	−	9.81023i	0.411628	−	0.411628i
$569$		−	0.277792i		−	0.0116457i	−0.999983	−	0.00582283i	$-0.998147\pi$
$569$		−	0.277792i		−	0.0116457i	0.999983	−	0.00582283i	$-0.00185348\pi$
$570$		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	0.268625	−	0.963245i	$-0.413431\pi$
$577$	29.5905	−	29.5905i	1.23187	−	1.23187i	0.963245	−	0.268625i	$-0.0865693\pi$
$578$	−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	0.105375	−	0.994433i	$-0.466396\pi$
$587$	26.6462	−	26.6462i	1.09981	−	1.09981i	0.994433	−	0.105375i	$-0.0336041\pi$
$588$	−10.5667	−	13.3348i	−0.435762	−	0.549918i
$589$		−	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	$-0.104608\pi$
$593$	15.1889	+	15.1889i	0.623733	+	0.623733i	−0.322751	+	0.946484i	$0.604608\pi$
$594$	−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	$-0.849597\pi$
$599$		−	22.2776i		−	0.910238i	0.890431	−	0.455119i	$-0.150403\pi$
$600$		0			0
$601$		−	22.3458i		−	0.911503i	−0.890107	−	0.455752i	$-0.849371\pi$
$601$		−	22.3458i		−	0.911503i	0.890107	−	0.455752i	$-0.150629\pi$
$602$	1.59728	+	1.79294i	0.0651002	+	0.0730749i
$603$	−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	$-0.755263\pi$
$607$	−0.576027	+	0.576027i	−0.0233802	+	0.0233802i	0.695320	+	0.718700i	$0.255263\pi$
$608$	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	−0.291361	−	0.956613i	$-0.594108\pi$
$613$	16.4709	−	16.4709i	0.665253	−	0.665253i	0.956613	+	0.291361i	$0.0941080\pi$
$614$	−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	0.777654	−	0.628692i	$-0.216410\pi$
$617$	3.70013	+	3.70013i	0.148962	+	0.148962i	−0.628692	+	0.777654i	$0.716410\pi$
$618$	−14.6192	+	14.6192i	−0.588072	+	0.588072i
$619$	39.8840			1.60307			0.801536	−	0.597946i	$-0.204016\pi$
$619$	39.8840			1.60307			0.801536	+	0.597946i	$0.204016\pi$
$620$		0			0
$621$			0.248455i			0.00997015i
$622$	−15.2621	+	15.2621i	−0.611954	+	0.611954i
$623$	−12.1655	−	13.6558i	−0.487401	−	0.547107i
$624$			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
$637$	−9.52120	+	7.54472i	−0.377244	+	0.298933i
$638$	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	0.948063	+	0.318082i	$0.103039\pi$
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.318082	+	0.948063i	$0.396961\pi$
$644$	−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	$-0.632988\pi$
$647$	12.9277	−	12.9277i	0.508241	−	0.508241i	0.913986	+	0.405745i	$0.132988\pi$
$648$	−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	−0.498858	−	0.866684i	$-0.666247\pi$
$653$	9.39937	−	9.39937i	0.367826	−	0.367826i	0.866684	+	0.498858i	$0.166247\pi$
$654$	−12.5315			−0.490020
$655$		0			0
$656$			20.8441i			0.813824i
$657$	−10.0208	+	10.0208i	−0.390950	+	0.390950i
$658$	−2.91736	−	3.27473i	−0.113730	−	0.127662i
$659$		−	9.13808i		−	0.355969i	−0.984033	−	0.177985i	$-0.943042\pi$
$659$		−	9.13808i		−	0.355969i	0.984033	−	0.177985i	$-0.0569577\pi$
$660$		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
$672$	15.8621	−	14.1311i	0.611894	−	0.545118i
$673$	−26.8815	+	26.8815i	−1.03621	+	1.03621i	−0.0368867	+	0.999319i	$0.511744\pi$
$673$	−26.8815	+	26.8815i	−1.03621	+	1.03621i	−0.999319	+	0.0368867i	$0.988256\pi$
$674$		−	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	$-0.760356\pi$
$677$	−1.19694	+	1.19694i	−0.0460022	+	0.0460022i	0.683731	+	0.729734i	$0.260356\pi$
$678$	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	−0.751809	−	0.659381i	$-0.770818\pi$
$683$	−2.41553	+	2.41553i	−0.0924275	+	0.0924275i	0.659381	+	0.751809i	$0.270818\pi$
$684$	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
$693$	5.27832	−	4.70230i	0.200507	−	0.178625i
$694$			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
$707$	−14.2822	+	12.7236i	−0.537138	+	0.478520i
$708$	−13.7293	+	13.7293i	−0.515978	+	0.515978i
$709$			24.6722i			0.926585i	0.886205	+	0.463293i	$0.153332\pi$
$709$			24.6722i			0.926585i	−0.886205	+	0.463293i	$0.846668\pi$
$710$		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	$-0.311662\pi$
$719$	29.9117			1.11552			0.557758	+	0.830003i	$0.311662\pi$
$720$		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	−0.113491	+	0.993539i	$0.536203\pi$
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.993539	+	0.113491i	$0.963797\pi$
$728$	2.76795	+	3.10702i	0.102587	+	0.115154i
$729$		−	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	$-0.282204\pi$
$733$	−3.86707	−	3.86707i	−0.142834	−	0.142834i	−0.774908	+	0.632074i	$0.782204\pi$
$734$	−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	$-0.929320\pi$
$739$		−	11.9735i		−	0.440454i	0.975449	−	0.220227i	$-0.0706797\pi$
$740$		0			0
$741$		−	10.4427i		−	0.383621i
$742$	−26.1436	−	29.3462i	−0.959763	−	1.07733i
$743$	12.0406	−	12.0406i	0.441728	−	0.441728i	−0.450864	−	0.892593i	$-0.648884\pi$
$743$	12.0406	−	12.0406i	0.441728	−	0.441728i	0.892593	+	0.450864i	$0.148884\pi$
$744$			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	−0.997768	−	0.0667825i	$-0.978727\pi$
$757$	−29.2896	−	29.2896i	−1.06455	−	1.06455i	−0.0667825	−	0.997768i	$-0.521273\pi$
$758$	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
$763$	11.7613	−	10.4778i	0.425787	−	0.379320i
$764$			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	$-0.607831\pi$
$769$	−18.4310			−0.664640			−0.332320	+	0.943167i	$0.607831\pi$
$770$		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	$-0.100493\pi$
$773$	17.7963	+	17.7963i	0.640088	+	0.640088i	−0.310489	+	0.950577i	$0.600493\pi$
$774$			0.907583i			0.0326224i
$775$		0			0
$776$			11.3315i			0.406779i
$777$	−2.05468	+	1.83045i	−0.0737111	+	0.0656670i
$778$	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	$-0.882722\pi$
$787$	−16.0671	+	16.0671i	−0.572730	+	0.572730i	0.360160	+	0.932890i	$0.382722\pi$
$788$	−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	$-0.970877\pi$
$797$	−25.5337	+	25.5337i	−0.904451	+	0.904451i	0.0913664	+	0.995817i	$0.470877\pi$
$798$	−25.0213	+	22.2907i	−0.885745	+	0.789083i
$799$			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	$0.160866\pi$
$809$			27.5404i			0.968270i	−0.874993	+	0.484135i	$0.839134\pi$
$810$		0			0
$811$			34.2545i			1.20284i	0.798933	+	0.601420i	$0.205398\pi$
$811$			34.2545i			1.20284i	−0.798933	+	0.601420i	$0.794602\pi$
$812$	1.30419	+	1.46395i	0.0457682	+	0.0513747i
$813$	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	−0.592668	−	0.805447i	$-0.701926\pi$
$823$	6.10417	−	6.10417i	0.212778	−	0.212778i	0.805447	+	0.592668i	$0.201926\pi$
$824$	−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	0.788178	−	0.615447i	$-0.211024\pi$
$827$	4.96734	+	4.96734i	0.172731	+	0.172731i	−0.615447	+	0.788178i	$0.711024\pi$
$828$	−0.427009	+	0.427009i	−0.0148396	+	0.0148396i
$829$	28.3500			0.984636			0.492318	−	0.870415i	$-0.336150\pi$
$829$	28.3500			0.984636			0.492318	+	0.870415i	$0.336150\pi$
$830$		0			0
$831$			2.83636i			0.0983922i
$832$	−13.4910	+	13.4910i	−0.467717	+	0.467717i
$833$	−29.1809	−	36.8254i	−1.01106	−	1.27592i
$834$			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	$-0.691650\pi$
$839$	−32.8100			−1.13273			−0.566364	+	0.824156i	$0.691650\pi$
$840$		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
$847$	−6.79526	−	7.62767i	−0.233488	−	0.262090i
$848$	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	$-0.372411\pi$
$853$	−15.4954	−	15.4954i	−0.530553	−	0.530553i	−0.920737	+	0.390184i	$0.872411\pi$
$854$	−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	$-0.891762\pi$
$857$	−17.8346	+	17.8346i	−0.609218	+	0.609218i	0.333523	+	0.942742i	$0.391762\pi$
$858$	−6.90143	+	6.90143i	−0.235611	+	0.235611i
$859$	−17.2711			−0.589283			−0.294641	−	0.955608i	$-0.595200\pi$
$859$	−17.2711			−0.589283			−0.294641	+	0.955608i	$0.595200\pi$
$860$		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	−0.755434	−	0.655225i	$-0.772574\pi$
$863$	−2.94383	+	2.94383i	−0.100209	+	0.100209i	0.655225	+	0.755434i	$0.272574\pi$
$864$	8.02936			0.273164
$865$		0			0
$866$		−	40.1038i		−	1.36278i
$867$	19.8369	−	19.8369i	0.673697	−	0.673697i
$868$	−31.0288	−	34.8298i	−1.05318	−	1.18220i
$869$			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	0.835867	−	0.548932i	$-0.184965\pi$
$877$	8.49735	+	8.49735i	0.286935	+	0.286935i	−0.548932	+	0.835867i	$0.684965\pi$
$878$	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	$-0.205894\pi$
$882$	9.15086	+	11.5481i	0.308125	+	0.388845i
$883$	−24.6278	+	24.6278i	−0.828791	+	0.828791i	−0.987350	−	0.158559i	$-0.949315\pi$
$883$	−24.6278	+	24.6278i	−0.828791	+	0.828791i	0.158559	+	0.987350i	$0.449315\pi$
$884$		−	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	$-0.744464\pi$
$887$	0.732491	−	0.732491i	0.0245946	−	0.0245946i	0.719297	+	0.694703i	$0.244464\pi$
$888$	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
$903$	−0.758842	−	0.851800i	−0.0252527	−	0.0283461i
$904$			8.95913i			0.297976i
$905$		0			0
$906$		−	20.5856i		−	0.683911i
$907$	22.8743	+	22.8743i	0.759530	+	0.759530i	0.976237	−	0.216707i	$-0.0695316\pi$
$907$	22.8743	+	22.8743i	0.759530	+	0.759530i	−0.216707	+	0.976237i	$0.569532\pi$
$908$	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
$917$	18.4664	−	16.4512i	0.609814	−	0.543265i
$918$	−9.99031	+	9.99031i	−0.329729	+	0.329729i
$919$			14.5898i			0.481272i	0.970615	+	0.240636i	$0.0773560\pi$
$919$			14.5898i			0.481272i	−0.970615	+	0.240636i	$0.922644\pi$
$920$		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	$-0.364616\pi$
$929$	25.1526			0.825229			0.412615	+	0.910906i	$0.364616\pi$
$930$		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	$-0.522676\pi$
$937$	28.3540	−	28.3540i	0.926286	−	0.926286i	0.997464	+	0.0711778i	$0.0226758\pi$
$938$	20.1738	−	17.9722i	0.658699	−	0.586815i
$939$			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	0.352108	−	0.935959i	$-0.385465\pi$
$947$	−17.9671	−	17.9671i	−0.583851	−	0.583851i	−0.935959	+	0.352108i	$0.885465\pi$
$948$	19.4162	+	19.4162i	0.630607	+	0.630607i
$949$			24.5940i			0.798354i
$950$		0			0
$951$			17.3331i			0.562064i
$952$	−12.0171	+	10.7057i	−0.389477	+	0.346973i
$953$	−31.8008	+	31.8008i	−1.03013	+	1.03013i	−0.0305973	+	0.999532i	$0.509741\pi$
$953$	−31.8008	+	31.8008i	−1.03013	+	1.03013i	−0.999532	+	0.0305973i	$0.990259\pi$
$954$		−	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	0.703706	−	0.710491i	$-0.251527\pi$
$967$	−0.210995	−	0.210995i	−0.00678513	−	0.00678513i	−0.710491	+	0.703706i	$0.751527\pi$
$968$	−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
$973$	−13.7081	−	15.3873i	−0.439462	−	0.493295i
$974$		−	30.6752i		−	0.982896i
$975$		0			0
$976$		−	16.3450i		−	0.523192i
$977$	−25.0981	−	25.0981i	−0.802958	−	0.802958i	0.180599	−	0.983557i	$-0.442197\pi$
$977$	−25.0981	−	25.0981i	−0.802958	−	0.802958i	−0.983557	+	0.180599i	$0.942197\pi$
$978$	−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	$-0.258857\pi$
$983$	−1.23358	−	1.23358i	−0.0393451	−	0.0393451i	−0.726506	+	0.687161i	$0.758857\pi$
$984$			6.39583i			0.203892i
$985$		0			0
$986$		−	4.30761i		−	0.137182i
$987$	1.38599	+	1.55577i	0.0441166	+	0.0495208i
$988$	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	$-0.663511\pi$
$997$	11.9844	−	11.9844i	0.379551	−	0.379551i	0.870940	+	0.491389i	$0.163511\pi$
$998$	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.307.2		16
5.2	odd	4		105.2.m.a.13.8	yes	16
5.3	odd	4	inner	525.2.m.b.118.1		16
5.4	even	2		105.2.m.a.97.7	yes	16
7.6	odd	2	inner	525.2.m.b.307.1		16
15.2	even	4		315.2.p.e.118.2		16
15.14	odd	2		315.2.p.e.307.1		16
20.7	even	4		1680.2.cz.d.433.1		16
20.19	odd	2		1680.2.cz.d.97.8		16
35.2	odd	12		735.2.v.a.178.2		32
35.4	even	6		735.2.v.a.607.1		32
35.9	even	6		735.2.v.a.472.8		32
35.12	even	12		735.2.v.a.178.1		32
35.13	even	4	inner	525.2.m.b.118.2		16
35.17	even	12		735.2.v.a.313.8		32
35.19	odd	6		735.2.v.a.472.7		32
35.24	odd	6		735.2.v.a.607.2		32
35.27	even	4		105.2.m.a.13.7	✓	16
35.32	odd	12		735.2.v.a.313.7		32
35.34	odd	2		105.2.m.a.97.8	yes	16
105.62	odd	4		315.2.p.e.118.1		16
105.104	even	2		315.2.p.e.307.2		16
140.27	odd	4		1680.2.cz.d.433.8		16
140.139	even	2		1680.2.cz.d.97.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	35.27	even	4
105.2.m.a.13.8	yes	16	5.2	odd	4
105.2.m.a.97.7	yes	16	5.4	even	2
105.2.m.a.97.8	yes	16	35.34	odd	2
315.2.p.e.118.1		16	105.62	odd	4
315.2.p.e.118.2		16	15.2	even	4
315.2.p.e.307.1		16	15.14	odd	2
315.2.p.e.307.2		16	105.104	even	2
525.2.m.b.118.1		16	5.3	odd	4	inner
525.2.m.b.118.2		16	35.13	even	4	inner
525.2.m.b.307.1		16	7.6	odd	2	inner
525.2.m.b.307.2		16	1.1	even	1	trivial
735.2.v.a.178.1		32	35.12	even	12
735.2.v.a.178.2		32	35.2	odd	12
735.2.v.a.313.7		32	35.32	odd	12
735.2.v.a.313.8		32	35.17	even	12
735.2.v.a.472.7		32	35.19	odd	6
735.2.v.a.472.8		32	35.9	even	6
735.2.v.a.607.1		32	35.4	even	6
735.2.v.a.607.2		32	35.24	odd	6
1680.2.cz.d.97.1		16	140.139	even	2
1680.2.cz.d.97.8		16	20.19	odd	2
1680.2.cz.d.433.1		16	20.7	even	4
1680.2.cz.d.433.8		16	140.27	odd	4

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)

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