LMFDB - Embedded newform 1470.2.m.d.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.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:	$11.7380090971$
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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.2
Root			$0.339278 - 0.0446668i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.d.1273.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.03078 + 1.98431i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.03078 + 1.98431i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.13199 - 0.674247i) q^{10} +2.62544 q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.21865 + 1.21865i) q^{13} +(-2.13199 + 0.674247i) q^{15} -1.00000 q^{16} +(5.35303 - 5.35303i) q^{17} +(0.707107 - 0.707107i) q^{18} +4.65232 q^{19} +(-1.98431 - 1.03078i) q^{20} +(-1.85647 - 1.85647i) q^{22} +(-3.62926 + 3.62926i) q^{23} +1.00000 q^{24} +(-2.87498 - 4.09078i) q^{25} -1.72343i q^{26} +(-0.707107 + 0.707107i) q^{27} -5.99410i q^{29} +(1.98431 + 1.03078i) q^{30} +10.0018i q^{31} +(0.707107 + 0.707107i) q^{32} +(1.85647 + 1.85647i) q^{33} -7.57033 q^{34} -1.00000 q^{36} +(2.79841 + 2.79841i) q^{37} +(-3.28969 - 3.28969i) q^{38} +1.72343i q^{39} +(0.674247 + 2.13199i) q^{40} +5.59423i q^{41} +(-0.545731 + 0.545731i) q^{43} +2.62544i q^{44} +(-1.98431 - 1.03078i) q^{45} +5.13255 q^{46} +(4.48288 - 4.48288i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-0.859701 + 4.92554i) q^{50} +7.57033 q^{51} +(-1.21865 + 1.21865i) q^{52} +(-6.06671 + 6.06671i) q^{53} +1.00000 q^{54} +(-2.70626 + 5.20970i) q^{55} +(3.28969 + 3.28969i) q^{57} +(-4.23847 + 4.23847i) q^{58} +7.72043 q^{59} +(-0.674247 - 2.13199i) q^{60} +4.80982i q^{61} +(7.07231 - 7.07231i) q^{62} -1.00000i q^{64} +(-3.67435 + 1.16202i) q^{65} -2.62544i q^{66} +(-1.81260 - 1.81260i) q^{67} +(5.35303 + 5.35303i) q^{68} -5.13255 q^{69} -8.36973 q^{71} +(0.707107 + 0.707107i) q^{72} +(9.65407 + 9.65407i) q^{73} -3.95756i q^{74} +(0.859701 - 4.92554i) q^{75} +4.65232i q^{76} +(1.21865 - 1.21865i) q^{78} +8.99488i q^{79} +(1.03078 - 1.98431i) q^{80} -1.00000 q^{81} +(3.95571 - 3.95571i) q^{82} +(-7.99504 - 7.99504i) q^{83} +(5.10428 + 16.1399i) q^{85} +0.771781 q^{86} +(4.23847 - 4.23847i) q^{87} +(1.85647 - 1.85647i) q^{88} +0.162532 q^{89} +(0.674247 + 2.13199i) q^{90} +(-3.62926 - 3.62926i) q^{92} +(-7.07231 + 7.07231i) q^{93} -6.33974 q^{94} +(-4.79552 + 9.23165i) q^{95} +1.00000i q^{96} +(-4.35278 + 4.35278i) q^{97} +2.62544i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{10} - 8 q^{11} - 16 q^{13} + 4 q^{15} - 16 q^{16} + 24 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{25} + 8 q^{30} - 4 q^{33} + 16 q^{34} - 16 q^{36} + 16 q^{37} + 8 q^{38} - 24 q^{43} - 8 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 16 q^{54} - 56 q^{55} - 8 q^{57} - 36 q^{58} - 16 q^{59} + 8 q^{62} - 32 q^{65} + 48 q^{67} + 24 q^{68} - 8 q^{69} - 32 q^{71} + 56 q^{73} - 16 q^{78} - 16 q^{81} + 24 q^{82} - 16 q^{83} + 8 q^{85} + 16 q^{86} + 36 q^{87} - 4 q^{88} + 32 q^{89} + 8 q^{92} - 8 q^{93} - 16 q^{94} - 24 q^{95} + 44 q^{97}+O(q^{100}) $ 16 * q - 4 * q^10 - 8 * q^11 - 16 * q^13 + 4 * q^15 - 16 * q^16 + 24 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^25 + 8 * q^30 - 4 * q^33 + 16 * q^34 - 16 * q^36 + 16 * q^37 + 8 * q^38 - 24 * q^43 - 8 * q^45 + 8 * q^46 + 24 * q^47 - 16 * q^51 + 16 * q^52 - 16 * q^53 + 16 * q^54 - 56 * q^55 - 8 * q^57 - 36 * q^58 - 16 * q^59 + 8 * q^62 - 32 * q^65 + 48 * q^67 + 24 * q^68 - 8 * q^69 - 32 * q^71 + 56 * q^73 - 16 * q^78 - 16 * q^81 + 24 * q^82 - 16 * q^83 + 8 * q^85 + 16 * q^86 + 36 * q^87 - 4 * q^88 + 32 * q^89 + 8 * q^92 - 8 * q^93 - 16 * q^94 - 24 * q^95 + 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	−1.03078	+	1.98431i	−0.460979	+	0.887411i
$5$	−1.03078	+	1.98431i	−0.460979	+	0.887411i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	2.13199	−	0.674247i	0.674195	−	0.213216i
$11$	2.62544			0.791601			0.395800	−	0.918337i	$-0.370467\pi$
$11$	2.62544			0.791601			0.395800	+	0.918337i	$0.370467\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	1.21865	+	1.21865i	0.337993	+	0.337993i	0.855612	−	0.517618i	$-0.173181\pi$
$13$	1.21865	+	1.21865i	0.337993	+	0.337993i	−0.517618	+	0.855612i	$0.673181\pi$
$14$		0			0
$15$	−2.13199	+	0.674247i	−0.550478	+	0.174090i
$16$	−1.00000			−0.250000
$17$	5.35303	−	5.35303i	1.29830	−	1.29830i	0.368788	−	0.929514i	$-0.379773\pi$
$17$	5.35303	−	5.35303i	1.29830	−	1.29830i	0.929514	−	0.368788i	$-0.120227\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	4.65232			1.06732			0.533658	−	0.845701i	$-0.320817\pi$
$19$	4.65232			1.06732			0.533658	+	0.845701i	$0.320817\pi$
$20$	−1.98431	−	1.03078i	−0.443705	−	0.230490i
$21$		0			0
$22$	−1.85647	−	1.85647i	−0.395800	−	0.395800i
$23$	−3.62926	+	3.62926i	−0.756753	+	0.756753i	−0.975730	−	0.218977i	$-0.929728\pi$
$23$	−3.62926	+	3.62926i	−0.756753	+	0.756753i	0.218977	+	0.975730i	$0.429728\pi$
$24$	1.00000			0.204124
$25$	−2.87498	−	4.09078i	−0.574996	−	0.818156i
$26$		−	1.72343i		−	0.337993i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	5.99410i		−	1.11308i	−0.830822	−	0.556538i	$-0.812129\pi$
$29$		−	5.99410i		−	1.11308i	0.830822	−	0.556538i	$-0.187871\pi$
$30$	1.98431	+	1.03078i	0.362284	+	0.188194i
$31$			10.0018i			1.79637i	0.439620	+	0.898184i	$0.355113\pi$
$31$			10.0018i			1.79637i	−0.439620	+	0.898184i	$0.644887\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.85647	+	1.85647i	0.323170	+	0.323170i
$34$	−7.57033			−1.29830
$35$		0			0
$36$	−1.00000			−0.166667
$37$	2.79841	+	2.79841i	0.460057	+	0.460057i	0.898674	−	0.438617i	$-0.144532\pi$
$37$	2.79841	+	2.79841i	0.460057	+	0.460057i	−0.438617	+	0.898674i	$0.644532\pi$
$38$	−3.28969	−	3.28969i	−0.533658	−	0.533658i
$39$			1.72343i			0.275970i
$40$	0.674247	+	2.13199i	0.106608	+	0.337098i
$41$			5.59423i			0.873671i	0.899541	+	0.436836i	$0.143901\pi$
$41$			5.59423i			0.873671i	−0.899541	+	0.436836i	$0.856099\pi$
$42$		0			0
$43$	−0.545731	+	0.545731i	−0.0832233	+	0.0832233i	−0.747493	−	0.664270i	$-0.768743\pi$
$43$	−0.545731	+	0.545731i	−0.0832233	+	0.0832233i	0.664270	+	0.747493i	$0.268743\pi$
$44$			2.62544i			0.395800i
$45$	−1.98431	−	1.03078i	−0.295804	−	0.153660i
$46$	5.13255			0.756753
$47$	4.48288	−	4.48288i	0.653895	−	0.653895i	−0.300034	−	0.953929i	$-0.596998\pi$
$47$	4.48288	−	4.48288i	0.653895	−	0.653895i	0.953929	+	0.300034i	$0.0969980\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		0			0
$50$	−0.859701	+	4.92554i	−0.121580	+	0.696576i
$51$	7.57033			1.06006
$52$	−1.21865	+	1.21865i	−0.168997	+	0.168997i
$53$	−6.06671	+	6.06671i	−0.833327	+	0.833327i	−0.987970	−	0.154643i	$-0.950577\pi$
$53$	−6.06671	+	6.06671i	−0.833327	+	0.833327i	0.154643	+	0.987970i	$0.450577\pi$
$54$	1.00000			0.136083
$55$	−2.70626	+	5.20970i	−0.364912	+	0.702475i
$56$		0			0
$57$	3.28969	+	3.28969i	0.435730	+	0.435730i
$58$	−4.23847	+	4.23847i	−0.556538	+	0.556538i
$59$	7.72043			1.00511			0.502557	−	0.864544i	$-0.332393\pi$
$59$	7.72043			1.00511			0.502557	+	0.864544i	$0.332393\pi$
$60$	−0.674247	−	2.13199i	−0.0870450	−	0.275239i
$61$			4.80982i			0.615835i	0.951413	+	0.307917i	$0.0996320\pi$
$61$			4.80982i			0.615835i	−0.951413	+	0.307917i	$0.900368\pi$
$62$	7.07231	−	7.07231i	0.898184	−	0.898184i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−3.67435	+	1.16202i	−0.455747	+	0.144131i
$66$		−	2.62544i		−	0.323170i
$67$	−1.81260	−	1.81260i	−0.221444	−	0.221444i	0.587662	−	0.809106i	$-0.300048\pi$
$67$	−1.81260	−	1.81260i	−0.221444	−	0.221444i	−0.809106	+	0.587662i	$0.800048\pi$
$68$	5.35303	+	5.35303i	0.649151	+	0.649151i
$69$	−5.13255			−0.617886
$70$		0			0
$71$	−8.36973			−0.993304			−0.496652	−	0.867950i	$-0.665437\pi$
$71$	−8.36973			−0.993304			−0.496652	+	0.867950i	$0.665437\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	9.65407	+	9.65407i	1.12992	+	1.12992i	0.990189	+	0.139734i	$0.0446247\pi$
$73$	9.65407	+	9.65407i	1.12992	+	1.12992i	0.139734	+	0.990189i	$0.455375\pi$
$74$		−	3.95756i		−	0.460057i
$75$	0.859701	−	4.92554i	0.0992697	−	0.568752i
$76$			4.65232i			0.533658i
$77$		0			0
$78$	1.21865	−	1.21865i	0.137985	−	0.137985i
$79$			8.99488i			1.01200i	0.862532	+	0.506002i	$0.168877\pi$
$79$			8.99488i			1.01200i	−0.862532	+	0.506002i	$0.831123\pi$
$80$	1.03078	−	1.98431i	0.115245	−	0.221853i
$81$	−1.00000			−0.111111
$82$	3.95571	−	3.95571i	0.436836	−	0.436836i
$83$	−7.99504	−	7.99504i	−0.877570	−	0.877570i	0.115713	−	0.993283i	$-0.463085\pi$
$83$	−7.99504	−	7.99504i	−0.877570	−	0.877570i	−0.993283	+	0.115713i	$0.963085\pi$
$84$		0			0
$85$	5.10428	+	16.1399i	0.553637	+	1.75062i
$86$	0.771781			0.0832233
$87$	4.23847	−	4.23847i	0.454411	−	0.454411i
$88$	1.85647	−	1.85647i	0.197900	−	0.197900i
$89$	0.162532			0.0172284			0.00861419	−	0.999963i	$-0.497258\pi$
$89$	0.162532			0.0172284			0.00861419	+	0.999963i	$0.497258\pi$
$90$	0.674247	+	2.13199i	0.0710719	+	0.224732i
$91$		0			0
$92$	−3.62926	−	3.62926i	−0.378376	−	0.378376i
$93$	−7.07231	+	7.07231i	−0.733364	+	0.733364i
$94$	−6.33974			−0.653895
$95$	−4.79552	+	9.23165i	−0.492010	+	0.947147i
$96$			1.00000i			0.102062i
$97$	−4.35278	+	4.35278i	−0.441958	+	0.441958i	−0.892670	−	0.450711i	$-0.851170\pi$
$97$	−4.35278	+	4.35278i	−0.441958	+	0.441958i	0.450711	+	0.892670i	$0.351170\pi$
$98$		0			0
$99$			2.62544i			0.263867i
$100$	4.09078	−	2.87498i	0.409078	−	0.287498i
$101$			7.67397i			0.763589i	0.924247	+	0.381795i	$0.124694\pi$
$101$			7.67397i			0.763589i	−0.924247	+	0.381795i	$0.875306\pi$
$102$	−5.35303	−	5.35303i	−0.530029	−	0.530029i
$103$	−2.87646	−	2.87646i	−0.283426	−	0.283426i	0.551048	−	0.834474i	$-0.314228\pi$
$103$	−2.87646	−	2.87646i	−0.283426	−	0.283426i	−0.834474	+	0.551048i	$0.814228\pi$
$104$	1.72343			0.168997
$105$		0			0
$106$	8.57963			0.833327
$107$	−1.99197	−	1.99197i	−0.192571	−	0.192571i	0.604235	−	0.796806i	$-0.293479\pi$
$107$	−1.99197	−	1.99197i	−0.192571	−	0.192571i	−0.796806	+	0.604235i	$0.793479\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			12.1606i			1.16478i	0.812911	+	0.582388i	$0.197881\pi$
$109$			12.1606i			1.16478i	−0.812911	+	0.582388i	$0.802119\pi$
$110$	5.59742	−	1.77020i	0.533693	−	0.168782i
$111$			3.95756i			0.375635i
$112$		0			0
$113$	1.63875	−	1.63875i	0.154161	−	0.154161i	−0.625813	−	0.779973i	$-0.715233\pi$
$113$	1.63875	−	1.63875i	0.154161	−	0.154161i	0.779973	+	0.625813i	$0.215233\pi$
$114$		−	4.65232i		−	0.435730i
$115$	−3.46061	−	10.9425i	−0.322703	−	1.02040i
$116$	5.99410			0.556538
$117$	−1.21865	+	1.21865i	−0.112664	+	0.112664i
$118$	−5.45917	−	5.45917i	−0.502557	−	0.502557i
$119$		0			0
$120$	−1.03078	+	1.98431i	−0.0940970	+	0.181142i
$121$	−4.10705			−0.373368
$122$	3.40106	−	3.40106i	0.307917	−	0.307917i
$123$	−3.95571	+	3.95571i	−0.356675	+	0.356675i
$124$	−10.0018			−0.898184
$125$	11.0809	−	1.48815i	0.991102	−	0.133105i
$126$		0			0
$127$	6.79622	+	6.79622i	0.603067	+	0.603067i	0.941125	−	0.338058i	$-0.109770\pi$
$127$	6.79622	+	6.79622i	0.603067	+	0.603067i	−0.338058	+	0.941125i	$0.609770\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.771781			−0.0679515
$130$	3.41983	+	1.77648i	0.299939	+	0.155808i
$131$		−	4.23598i		−	0.370099i	−0.982729	−	0.185050i	$-0.940755\pi$
$131$		−	4.23598i		−	0.370099i	0.982729	−	0.185050i	$-0.0592446\pi$
$132$	−1.85647	+	1.85647i	−0.161585	+	0.161585i
$133$		0			0
$134$			2.56340i			0.221444i
$135$	−0.674247	−	2.13199i	−0.0580300	−	0.183493i
$136$		−	7.57033i		−	0.649151i
$137$	−5.84256	−	5.84256i	−0.499163	−	0.499163i	0.412014	−	0.911177i	$-0.364825\pi$
$137$	−5.84256	−	5.84256i	−0.499163	−	0.499163i	−0.911177	+	0.412014i	$0.864825\pi$
$138$	3.62926	+	3.62926i	0.308943	+	0.308943i
$139$	9.35059			0.793106			0.396553	−	0.918012i	$-0.370206\pi$
$139$	9.35059			0.793106			0.396553	+	0.918012i	$0.370206\pi$
$140$		0			0
$141$	6.33974			0.533903
$142$	5.91829	+	5.91829i	0.496652	+	0.496652i
$143$	3.19950	+	3.19950i	0.267556	+	0.267556i
$144$		−	1.00000i		−	0.0833333i
$145$	11.8942	+	6.17860i	0.987756	+	0.513105i
$146$		−	13.6529i		−	1.12992i
$147$		0			0
$148$	−2.79841	+	2.79841i	−0.230028	+	0.230028i
$149$		−	4.75815i		−	0.389803i	−0.980823	−	0.194902i	$-0.937561\pi$
$149$		−	4.75815i		−	0.389803i	0.980823	−	0.194902i	$-0.0624387\pi$
$150$	−4.09078	+	2.87498i	−0.334011	+	0.234741i
$151$	2.15114			0.175057			0.0875286	−	0.996162i	$-0.472103\pi$
$151$	2.15114			0.175057			0.0875286	+	0.996162i	$0.472103\pi$
$152$	3.28969	−	3.28969i	0.266829	−	0.266829i
$153$	5.35303	+	5.35303i	0.432767	+	0.432767i
$154$		0			0
$155$	−19.8466	−	10.3096i	−1.59412	−	0.828089i
$156$	−1.72343			−0.137985
$157$	2.69007	−	2.69007i	0.214691	−	0.214691i	−0.591566	−	0.806257i	$-0.701490\pi$
$157$	2.69007	−	2.69007i	0.214691	−	0.214691i	0.806257	+	0.591566i	$0.201490\pi$
$158$	6.36034	−	6.36034i	0.506002	−	0.506002i
$159$	−8.57963			−0.680409
$160$	−2.13199	+	0.674247i	−0.168549	+	0.0533039i
$161$		0			0
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	3.15459	−	3.15459i	0.247086	−	0.247086i	−0.572687	−	0.819774i	$-0.694099\pi$
$163$	3.15459	−	3.15459i	0.247086	−	0.247086i	0.819774	+	0.572687i	$0.194099\pi$
$164$	−5.59423			−0.436836
$165$	−5.59742	+	1.77020i	−0.435759	+	0.137810i
$166$			11.3067i			0.877570i
$167$	16.1327	−	16.1327i	1.24839	−	1.24839i	0.291956	−	0.956432i	$-0.405694\pi$
$167$	16.1327	−	16.1327i	1.24839	−	1.24839i	0.956432	−	0.291956i	$-0.0943062\pi$
$168$		0			0
$169$		−	10.0298i		−	0.771521i
$170$	7.80336	−	15.0219i	0.598490	−	1.15213i
$171$			4.65232i			0.355772i
$172$	−0.545731	−	0.545731i	−0.0416116	−	0.0416116i
$173$	−8.75557	−	8.75557i	−0.665673	−	0.665673i	0.291038	−	0.956711i	$-0.405999\pi$
$173$	−8.75557	−	8.75557i	−0.665673	−	0.665673i	−0.956711	+	0.291038i	$0.905999\pi$
$174$	−5.99410			−0.454411
$175$		0			0
$176$	−2.62544			−0.197900
$177$	5.45917	+	5.45917i	0.410336	+	0.410336i
$178$	−0.114928	−	0.114928i	−0.00861419	−	0.00861419i
$179$			20.2701i			1.51506i	0.652803	+	0.757528i	$0.273593\pi$
$179$			20.2701i			1.51506i	−0.652803	+	0.757528i	$0.726407\pi$
$180$	1.03078	−	1.98431i	0.0768299	−	0.147902i
$181$		−	7.52637i		−	0.559431i	−0.960083	−	0.279715i	$-0.909760\pi$
$181$		−	7.52637i		−	0.559431i	0.960083	−	0.279715i	$-0.0902401\pi$
$182$		0			0
$183$	−3.40106	+	3.40106i	−0.251413	+	0.251413i
$184$			5.13255i			0.378376i
$185$	−8.43748	+	2.66837i	−0.620336	+	0.196183i
$186$	10.0018			0.733364
$187$	14.0541	−	14.0541i	1.02774	−	1.02774i
$188$	4.48288	+	4.48288i	0.326947	+	0.326947i
$189$		0			0
$190$	9.91871	−	3.13681i	0.719579	−	0.227568i
$191$	4.32789			0.313155			0.156578	−	0.987666i	$-0.449954\pi$
$191$	4.32789			0.313155			0.156578	+	0.987666i	$0.449954\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	15.0388	−	15.0388i	1.08252	−	1.08252i	0.0862422	−	0.996274i	$-0.472514\pi$
$193$	15.0388	−	15.0388i	1.08252	−	1.08252i	0.996274	−	0.0862422i	$-0.0274859\pi$
$194$	6.15577			0.441958
$195$	−3.41983	−	1.77648i	−0.244899	−	0.127217i
$196$		0			0
$197$	−14.1314	−	14.1314i	−1.00682	−	1.00682i	−0.999977	−	0.00684089i	$-0.997822\pi$
$197$	−14.1314	−	14.1314i	−1.00682	−	1.00682i	−0.00684089	−	0.999977i	$-0.502178\pi$
$198$	1.85647	−	1.85647i	0.131933	−	0.131933i
$199$	−0.844069			−0.0598345			−0.0299172	−	0.999552i	$-0.509524\pi$
$199$	−0.844069			−0.0598345			−0.0299172	+	0.999552i	$0.509524\pi$
$200$	−4.92554	−	0.859701i	−0.348288	−	0.0607901i
$201$		−	2.56340i		−	0.180808i
$202$	5.42632	−	5.42632i	0.381795	−	0.381795i
$203$		0			0
$204$			7.57033i			0.530029i
$205$	−11.1007	−	5.76642i	−0.775305	−	0.402744i
$206$			4.06792i			0.283426i
$207$	−3.62926	−	3.62926i	−0.252251	−	0.252251i
$208$	−1.21865	−	1.21865i	−0.0844983	−	0.0844983i
$209$	12.2144			0.844888
$210$		0			0
$211$	22.1844			1.52724			0.763619	−	0.645667i	$-0.223421\pi$
$211$	22.1844			1.52724			0.763619	+	0.645667i	$0.223421\pi$
$212$	−6.06671	−	6.06671i	−0.416664	−	0.416664i
$213$	−5.91829	−	5.91829i	−0.405515	−	0.405515i
$214$			2.81707i			0.192571i
$215$	−0.520371	−	1.64543i	−0.0354890	−	0.112217i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	8.59885	−	8.59885i	0.582388	−	0.582388i
$219$			13.6529i			0.922578i
$220$	−5.20970	−	2.70626i	−0.351238	−	0.182456i
$221$	13.0470			0.877634
$222$	2.79841	−	2.79841i	0.187817	−	0.187817i
$223$	10.7632	+	10.7632i	0.720757	+	0.720757i	0.968759	−	0.248002i	$-0.0797741\pi$
$223$	10.7632	+	10.7632i	0.720757	+	0.720757i	−0.248002	+	0.968759i	$0.579774\pi$
$224$		0			0
$225$	4.09078	−	2.87498i	0.272719	−	0.191665i
$226$	−2.31755			−0.154161
$227$	2.64357	−	2.64357i	0.175460	−	0.175460i	−0.613913	−	0.789373i	$-0.710406\pi$
$227$	2.64357	−	2.64357i	0.175460	−	0.175460i	0.789373	+	0.613913i	$0.210406\pi$
$228$	−3.28969	+	3.28969i	−0.217865	+	0.217865i
$229$	−15.1818			−1.00324			−0.501619	−	0.865089i	$-0.667262\pi$
$229$	−15.1818			−1.00324			−0.501619	+	0.865089i	$0.667262\pi$
$230$	−5.29053	+	10.1846i	−0.348847	+	0.671551i
$231$		0			0
$232$	−4.23847	−	4.23847i	−0.278269	−	0.278269i
$233$	−0.857745	+	0.857745i	−0.0561928	+	0.0561928i	−0.734645	−	0.678452i	$-0.762651\pi$
$233$	−0.857745	+	0.857745i	−0.0561928	+	0.0561928i	0.678452	+	0.734645i	$0.262651\pi$
$234$	1.72343			0.112664
$235$	4.27456	+	13.5163i	0.278841	+	0.881705i
$236$			7.72043i			0.502557i
$237$	−6.36034	+	6.36034i	−0.413149	+	0.413149i
$238$		0			0
$239$			16.1593i			1.04526i	0.852560	+	0.522630i	$0.175049\pi$
$239$			16.1593i			1.04526i	−0.852560	+	0.522630i	$0.824951\pi$
$240$	2.13199	−	0.674247i	0.137620	−	0.0435225i
$241$			25.2169i			1.62436i	0.583407	+	0.812180i	$0.301719\pi$
$241$			25.2169i			1.62436i	−0.583407	+	0.812180i	$0.698281\pi$
$242$	2.90412	+	2.90412i	0.186684	+	0.186684i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−4.80982			−0.307917
$245$		0			0
$246$	5.59423			0.356675
$247$	5.66956	+	5.66956i	0.360745	+	0.360745i
$248$	7.07231	+	7.07231i	0.449092	+	0.449092i
$249$		−	11.3067i		−	0.716533i
$250$	−8.88763	−	6.78307i	−0.562103	−	0.428999i
$251$			2.07559i			0.131010i	0.997852	+	0.0655051i	$0.0208659\pi$
$251$			2.07559i			0.131010i	−0.997852	+	0.0655051i	$0.979134\pi$
$252$		0			0
$253$	−9.52841	+	9.52841i	−0.599046	+	0.599046i
$254$		−	9.61130i		−	0.603067i
$255$	−7.80336	+	15.0219i	−0.488665	+	0.940707i
$256$	1.00000			0.0625000
$257$	−3.18355	+	3.18355i	−0.198584	+	0.198584i	−0.799393	−	0.600809i	$-0.794845\pi$
$257$	−3.18355	+	3.18355i	−0.198584	+	0.198584i	0.600809	+	0.799393i	$0.294845\pi$
$258$	0.545731	+	0.545731i	0.0339757	+	0.0339757i
$259$		0			0
$260$	−1.16202	−	3.67435i	−0.0720655	−	0.227873i
$261$	5.99410			0.371025
$262$	−2.99529	+	2.99529i	−0.185050	+	0.185050i
$263$	15.8389	−	15.8389i	0.976669	−	0.976669i	−0.0230649	−	0.999734i	$-0.507342\pi$
$263$	15.8389	−	15.8389i	0.976669	−	0.976669i	0.999734	+	0.0230649i	$0.00734243\pi$
$264$	2.62544			0.161585
$265$	−5.78479	−	18.2917i	−0.355357	−	1.12365i
$266$		0			0
$267$	0.114928	+	0.114928i	0.00703346	+	0.00703346i
$268$	1.81260	−	1.81260i	0.110722	−	0.110722i
$269$	−11.7242			−0.714838			−0.357419	−	0.933944i	$-0.616343\pi$
$269$	−11.7242			−0.714838			−0.357419	+	0.933944i	$0.616343\pi$
$270$	−1.03078	+	1.98431i	−0.0627313	+	0.120761i
$271$			24.0471i			1.46075i	0.683044	+	0.730377i	$0.260656\pi$
$271$			24.0471i			1.46075i	−0.683044	+	0.730377i	$0.739344\pi$
$272$	−5.35303	+	5.35303i	−0.324575	+	0.324575i
$273$		0			0
$274$			8.26262i			0.499163i
$275$	−7.54810	−	10.7401i	−0.455167	−	0.647653i
$276$		−	5.13255i		−	0.308943i
$277$	−19.2314	−	19.2314i	−1.15550	−	1.15550i	−0.985432	−	0.170068i	$-0.945601\pi$
$277$	−19.2314	−	19.2314i	−1.15550	−	1.15550i	−0.170068	−	0.985432i	$-0.554399\pi$
$278$	−6.61186	−	6.61186i	−0.396553	−	0.396553i
$279$	−10.0018			−0.598789
$280$		0			0
$281$	22.1913			1.32382			0.661910	−	0.749583i	$-0.269746\pi$
$281$	22.1913			1.32382			0.661910	+	0.749583i	$0.269746\pi$
$282$	−4.48288	−	4.48288i	−0.266951	−	0.266951i
$283$	−7.85084	−	7.85084i	−0.466684	−	0.466684i	0.434155	−	0.900838i	$-0.357047\pi$
$283$	−7.85084	−	7.85084i	−0.466684	−	0.466684i	−0.900838	+	0.434155i	$0.857047\pi$
$284$		−	8.36973i		−	0.496652i
$285$	−9.91871	+	3.13681i	−0.587534	+	0.185809i
$286$		−	4.52478i		−	0.267556i
$287$		0			0
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$		−	40.3099i		−	2.37117i
$290$	−4.04150	−	12.7794i	−0.237325	−	0.750430i
$291$	−6.15577			−0.360857
$292$	−9.65407	+	9.65407i	−0.564961	+	0.564961i
$293$	6.51580	+	6.51580i	0.380657	+	0.380657i	0.871339	−	0.490682i	$-0.163252\pi$
$293$	6.51580	+	6.51580i	0.380657	+	0.380657i	−0.490682	+	0.871339i	$0.663252\pi$
$294$		0			0
$295$	−7.95808	+	15.3197i	−0.463337	+	0.891950i
$296$	3.95756			0.230028
$297$	−1.85647	+	1.85647i	−0.107723	+	0.107723i
$298$	−3.36452	+	3.36452i	−0.194902	+	0.194902i
$299$	−8.84561			−0.511555
$300$	4.92554	+	0.859701i	0.284376	+	0.0496349i
$301$		0			0
$302$	−1.52108	−	1.52108i	−0.0875286	−	0.0875286i
$303$	−5.42632	+	5.42632i	−0.311734	+	0.311734i
$304$	−4.65232			−0.266829
$305$	−9.54418	−	4.95787i	−0.546498	−	0.283887i
$306$		−	7.57033i		−	0.432767i
$307$	−20.6010	+	20.6010i	−1.17576	+	1.17576i	−0.194947	+	0.980814i	$0.562454\pi$
$307$	−20.6010	+	20.6010i	−1.17576	+	1.17576i	−0.980814	+	0.194947i	$0.937546\pi$
$308$		0			0
$309$		−	4.06792i		−	0.231416i
$310$	6.74366	+	21.3237i	0.383014	+	1.21110i
$311$		−	32.8663i		−	1.86368i	−0.362870	−	0.931840i	$-0.618203\pi$
$311$		−	32.8663i		−	1.86368i	0.362870	−	0.931840i	$-0.381797\pi$
$312$	1.21865	+	1.21865i	0.0689926	+	0.0689926i
$313$	−15.6858	−	15.6858i	−0.886615	−	0.886615i	0.107582	−	0.994196i	$-0.465689\pi$
$313$	−15.6858	−	15.6858i	−0.886615	−	0.886615i	−0.994196	+	0.107582i	$0.965689\pi$
$314$	−3.80434			−0.214691
$315$		0			0
$316$	−8.99488			−0.506002
$317$	−10.1572	−	10.1572i	−0.570488	−	0.570488i	0.361777	−	0.932265i	$-0.382170\pi$
$317$	−10.1572	−	10.1572i	−0.570488	−	0.570488i	−0.932265	+	0.361777i	$0.882170\pi$
$318$	6.06671	+	6.06671i	0.340204	+	0.340204i
$319$		−	15.7372i		−	0.881112i
$320$	1.98431	+	1.03078i	0.110926	+	0.0576224i
$321$		−	2.81707i		−	0.157234i
$322$		0			0
$323$	24.9040	−	24.9040i	1.38570	−	1.38570i
$324$		−	1.00000i		−	0.0555556i
$325$	1.48164	−	8.48884i	0.0821865	−	0.470876i
$326$	−4.46126			−0.247086
$327$	−8.59885	+	8.59885i	−0.475518	+	0.475518i
$328$	3.95571	+	3.95571i	0.218418	+	0.218418i
$329$		0			0
$330$	5.20970	+	2.70626i	0.286784	+	0.148975i
$331$	−2.89067			−0.158885			−0.0794427	−	0.996839i	$-0.525314\pi$
$331$	−2.89067			−0.158885			−0.0794427	+	0.996839i	$0.525314\pi$
$332$	7.99504	−	7.99504i	0.438785	−	0.438785i
$333$	−2.79841	+	2.79841i	−0.153352	+	0.153352i
$334$	−22.8151			−1.24839
$335$	5.46514	−	1.72836i	0.298593	−	0.0944306i
$336$		0			0
$337$	−23.4453	−	23.4453i	−1.27715	−	1.27715i	−0.942257	−	0.334891i	$-0.891301\pi$
$337$	−23.4453	−	23.4453i	−1.27715	−	1.27715i	−0.334891	−	0.942257i	$-0.608699\pi$
$338$	−7.09212	+	7.09212i	−0.385761	+	0.385761i
$339$	2.31755			0.125872
$340$	−16.1399	+	5.10428i	−0.875308	+	0.276818i
$341$			26.2590i			1.42201i
$342$	3.28969	−	3.28969i	0.177886	−	0.177886i
$343$		0			0
$344$			0.771781i			0.0416116i
$345$	5.29053	−	10.1846i	0.284833	−	0.548319i
$346$			12.3822i			0.665673i
$347$	−8.01712	−	8.01712i	−0.430382	−	0.430382i	0.458376	−	0.888758i	$-0.348431\pi$
$347$	−8.01712	−	8.01712i	−0.430382	−	0.430382i	−0.888758	+	0.458376i	$0.848431\pi$
$348$	4.23847	+	4.23847i	0.227206	+	0.227206i
$349$	6.80786			0.364417			0.182208	−	0.983260i	$-0.441675\pi$
$349$	6.80786			0.364417			0.182208	+	0.983260i	$0.441675\pi$
$350$		0			0
$351$	−1.72343			−0.0919901
$352$	1.85647	+	1.85647i	0.0989501	+	0.0989501i
$353$	19.6750	+	19.6750i	1.04719	+	1.04719i	0.998830	+	0.0483634i	$0.0154005\pi$
$353$	19.6750	+	19.6750i	1.04719	+	1.04719i	0.0483634	+	0.998830i	$0.484599\pi$
$354$		−	7.72043i		−	0.410336i
$355$	8.62736	−	16.6081i	0.457893	−	0.881469i
$356$			0.162532i			0.00861419i
$357$		0			0
$358$	14.3331	−	14.3331i	0.757528	−	0.757528i
$359$		−	13.7385i		−	0.725092i	−0.931966	−	0.362546i	$-0.881908\pi$
$359$		−	13.7385i		−	0.725092i	0.931966	−	0.362546i	$-0.118092\pi$
$360$	−2.13199	+	0.674247i	−0.112366	+	0.0355360i
$361$	2.64408			0.139162
$362$	−5.32195	+	5.32195i	−0.279715	+	0.279715i
$363$	−2.90412	−	2.90412i	−0.152427	−	0.152427i
$364$		0			0
$365$	−29.1079	+	9.20544i	−1.52358	+	0.481835i
$366$	4.80982			0.251413
$367$	17.8318	−	17.8318i	0.930812	−	0.930812i	−0.0669445	−	0.997757i	$-0.521325\pi$
$367$	17.8318	−	17.8318i	0.930812	−	0.930812i	0.997757	+	0.0669445i	$0.0213250\pi$
$368$	3.62926	−	3.62926i	0.189188	−	0.189188i
$369$	−5.59423			−0.291224
$370$	7.85302	+	4.07937i	0.408259	+	0.212077i
$371$		0			0
$372$	−7.07231	−	7.07231i	−0.366682	−	0.366682i
$373$	18.9888	−	18.9888i	0.983201	−	0.983201i	−0.0166605	−	0.999861i	$-0.505303\pi$
$373$	18.9888	−	18.9888i	0.983201	−	0.983201i	0.999861	+	0.0166605i	$0.00530346\pi$
$374$	−19.8755			−1.02774
$375$	8.88763	+	6.78307i	0.458955	+	0.350276i
$376$		−	6.33974i		−	0.326947i
$377$	7.30472	−	7.30472i	0.376212	−	0.376212i
$378$		0			0
$379$		−	3.51982i		−	0.180801i	−0.995905	−	0.0904005i	$-0.971185\pi$
$379$		−	3.51982i		−	0.180801i	0.995905	−	0.0904005i	$-0.0288147\pi$
$380$	−9.23165	−	4.79552i	−0.473574	−	0.246005i
$381$			9.61130i			0.492402i
$382$	−3.06028	−	3.06028i	−0.156578	−	0.156578i
$383$	6.33781	+	6.33781i	0.323847	+	0.323847i	0.850241	−	0.526394i	$-0.176456\pi$
$383$	6.33781	+	6.33781i	0.323847	+	0.323847i	−0.526394	+	0.850241i	$0.676456\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−21.2681			−1.08252
$387$	−0.545731	−	0.545731i	−0.0277411	−	0.0277411i
$388$	−4.35278	−	4.35278i	−0.220979	−	0.220979i
$389$			31.5371i			1.59899i	0.600670	+	0.799497i	$0.294900\pi$
$389$			31.5371i			1.59899i	−0.600670	+	0.799497i	$0.705100\pi$
$390$	1.16202	+	3.67435i	0.0588412	+	0.186058i
$391$			38.8551i			1.96499i
$392$		0			0
$393$	2.99529	−	2.99529i	0.151092	−	0.151092i
$394$			19.9848i			1.00682i
$395$	−17.8486	−	9.27176i	−0.898063	−	0.466513i
$396$	−2.62544			−0.131933
$397$	4.39711	−	4.39711i	0.220685	−	0.220685i	−0.588102	−	0.808787i	$-0.700125\pi$
$397$	4.39711	−	4.39711i	0.220685	−	0.220685i	0.808787	+	0.588102i	$0.200125\pi$
$398$	0.596847	+	0.596847i	0.0299172	+	0.0299172i
$399$		0			0
$400$	2.87498	+	4.09078i	0.143749	+	0.204539i
$401$	−20.5141			−1.02442			−0.512211	−	0.858859i	$-0.671174\pi$
$401$	−20.5141			−1.02442			−0.512211	+	0.858859i	$0.671174\pi$
$402$	−1.81260	+	1.81260i	−0.0904041	+	0.0904041i
$403$	−12.1887	+	12.1887i	−0.607160	+	0.607160i
$404$	−7.67397			−0.381795
$405$	1.03078	−	1.98431i	0.0512199	−	0.0986012i
$406$		0			0
$407$	7.34708	+	7.34708i	0.364181	+	0.364181i
$408$	5.35303	−	5.35303i	0.265015	−	0.265015i
$409$	−25.6511			−1.26837			−0.634184	−	0.773182i	$-0.718664\pi$
$409$	−25.6511			−1.26837			−0.634184	+	0.773182i	$0.718664\pi$
$410$	3.77189	+	11.9268i	0.186280	+	0.589025i
$411$		−	8.26262i		−	0.407565i
$412$	2.87646	−	2.87646i	0.141713	−	0.141713i
$413$		0			0
$414$			5.13255i			0.252251i
$415$	24.1058	−	7.62351i	1.18331	−	0.374223i
$416$			1.72343i			0.0844983i
$417$	6.61186	+	6.61186i	0.323784	+	0.323784i
$418$	−8.63688	−	8.63688i	−0.422444	−	0.422444i
$419$	1.54146			0.0753054			0.0376527	−	0.999291i	$-0.488012\pi$
$419$	1.54146			0.0753054			0.0376527	+	0.999291i	$0.488012\pi$
$420$		0			0
$421$	−20.0850			−0.978884			−0.489442	−	0.872036i	$-0.662800\pi$
$421$	−20.0850			−0.978884			−0.489442	+	0.872036i	$0.662800\pi$
$422$	−15.6867	−	15.6867i	−0.763619	−	0.763619i
$423$	4.48288	+	4.48288i	0.217965	+	0.217965i
$424$			8.57963i			0.416664i
$425$	−37.2880	−	6.50822i	−1.80873	−	0.315695i
$426$			8.36973i			0.405515i
$427$		0			0
$428$	1.99197	−	1.99197i	0.0962855	−	0.0962855i
$429$			4.52478i			0.218458i
$430$	−0.795537	+	1.53145i	−0.0383642	+	0.0738532i
$431$	21.9006			1.05491			0.527457	−	0.849581i	$-0.323145\pi$
$431$	21.9006			1.05491			0.527457	+	0.849581i	$0.323145\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−5.51584	−	5.51584i	−0.265074	−	0.265074i	0.562038	−	0.827112i	$-0.310018\pi$
$433$	−5.51584	−	5.51584i	−0.265074	−	0.265074i	−0.827112	+	0.562038i	$0.810018\pi$
$434$		0			0
$435$	4.04150	+	12.7794i	0.193775	+	0.612724i
$436$	−12.1606			−0.582388
$437$	−16.8845	+	16.8845i	−0.807694	+	0.807694i
$438$	9.65407	−	9.65407i	0.461289	−	0.461289i
$439$	−5.24407			−0.250286			−0.125143	−	0.992139i	$-0.539939\pi$
$439$	−5.24407			−0.250286			−0.125143	+	0.992139i	$0.539939\pi$
$440$	1.77020	+	5.59742i	0.0843909	+	0.266847i
$441$		0			0
$442$	−9.22560	−	9.22560i	−0.438817	−	0.438817i
$443$	0.919519	−	0.919519i	0.0436877	−	0.0436877i	−0.684925	−	0.728613i	$-0.740165\pi$
$443$	0.919519	−	0.919519i	0.0436877	−	0.0436877i	0.728613	+	0.684925i	$0.240165\pi$
$444$	−3.95756			−0.187817
$445$	−0.167535	+	0.322515i	−0.00794193	+	0.0152887i
$446$		−	15.2215i		−	0.720757i
$447$	3.36452	−	3.36452i	0.159136	−	0.159136i
$448$		0			0
$449$		−	22.3625i		−	1.05535i	−0.849445	−	0.527676i	$-0.823063\pi$
$449$		−	22.3625i		−	1.05535i	0.849445	−	0.527676i	$-0.176937\pi$
$450$	−4.92554	−	0.859701i	−0.232192	−	0.0405267i
$451$			14.6873i			0.691599i
$452$	1.63875	+	1.63875i	0.0770804	+	0.0770804i
$453$	1.52108	+	1.52108i	0.0714668	+	0.0714668i
$454$	−3.73858			−0.175460
$455$		0			0
$456$	4.65232			0.217865
$457$	2.33309	+	2.33309i	0.109137	+	0.109137i	0.759567	−	0.650429i	$-0.225411\pi$
$457$	2.33309	+	2.33309i	0.109137	+	0.109137i	−0.650429	+	0.759567i	$0.725411\pi$
$458$	10.7351	+	10.7351i	0.501619	+	0.501619i
$459$			7.57033i			0.353353i
$460$	10.9425	−	3.46061i	0.510199	−	0.161352i
$461$			6.97417i			0.324819i	0.986723	+	0.162410i	$0.0519266\pi$
$461$			6.97417i			0.324819i	−0.986723	+	0.162410i	$0.948073\pi$
$462$		0			0
$463$	16.6658	−	16.6658i	0.774527	−	0.774527i	−0.204367	−	0.978894i	$-0.565514\pi$
$463$	16.6658	−	16.6658i	0.774527	−	0.774527i	0.978894	+	0.204367i	$0.0655136\pi$
$464$			5.99410i			0.278269i
$465$	−6.74366	−	21.3237i	−0.312730	−	0.988861i
$466$	1.21304			0.0561928
$467$	8.10351	−	8.10351i	0.374986	−	0.374986i	−0.494304	−	0.869289i	$-0.664577\pi$
$467$	8.10351	−	8.10351i	0.374986	−	0.374986i	0.869289	+	0.494304i	$0.164577\pi$
$468$	−1.21865	−	1.21865i	−0.0563322	−	0.0563322i
$469$		0			0
$470$	6.53489	−	12.5800i	0.301432	−	0.580273i
$471$	3.80434			0.175295
$472$	5.45917	−	5.45917i	0.251279	−	0.251279i
$473$	−1.43279	+	1.43279i	−0.0658796	+	0.0658796i
$474$	8.99488			0.413149
$475$	−13.3753	−	19.0316i	−0.613702	−	0.873231i
$476$		0			0
$477$	−6.06671	−	6.06671i	−0.277776	−	0.277776i
$478$	11.4264	−	11.4264i	0.522630	−	0.522630i
$479$	10.1172			0.462266			0.231133	−	0.972922i	$-0.425757\pi$
$479$	10.1172			0.462266			0.231133	+	0.972922i	$0.425757\pi$
$480$	−1.98431	−	1.03078i	−0.0905710	−	0.0470485i
$481$			6.82059i			0.310992i
$482$	17.8310	−	17.8310i	0.812180	−	0.812180i
$483$		0			0
$484$		−	4.10705i		−	0.186684i
$485$	−4.15051	−	13.1240i	−0.188465	−	0.595932i
$486$			1.00000i			0.0453609i
$487$	−26.1275	−	26.1275i	−1.18395	−	1.18395i	−0.978713	−	0.205235i	$-0.934204\pi$
$487$	−26.1275	−	26.1275i	−1.18395	−	1.18395i	−0.205235	−	0.978713i	$-0.565796\pi$
$488$	3.40106	+	3.40106i	0.153959	+	0.153959i
$489$	4.46126			0.201745
$490$		0			0
$491$	−8.00737			−0.361368			−0.180684	−	0.983541i	$-0.557831\pi$
$491$	−8.00737			−0.361368			−0.180684	+	0.983541i	$0.557831\pi$
$492$	−3.95571	−	3.95571i	−0.178337	−	0.178337i
$493$	−32.0866	−	32.0866i	−1.44511	−	1.44511i
$494$		−	8.01797i		−	0.360745i
$495$	−5.20970	−	2.70626i	−0.234158	−	0.121637i
$496$		−	10.0018i		−	0.449092i
$497$		0			0
$498$	−7.99504	+	7.99504i	−0.358266	+	0.358266i
$499$		−	11.9668i		−	0.535708i	−0.963459	−	0.267854i	$-0.913685\pi$
$499$		−	11.9668i		−	0.535708i	0.963459	−	0.267854i	$-0.0863146\pi$
$500$	1.48815	+	11.0809i	0.0665523	+	0.495551i
$501$	22.8151			1.01930
$502$	1.46767	−	1.46767i	0.0655051	−	0.0655051i
$503$	−20.3121	−	20.3121i	−0.905670	−	0.905670i	0.0902493	−	0.995919i	$-0.471234\pi$
$503$	−20.3121	−	20.3121i	−0.905670	−	0.905670i	−0.995919	+	0.0902493i	$0.971234\pi$
$504$		0			0
$505$	−15.2276	−	7.91019i	−0.677617	−	0.351999i
$506$	13.4752			0.599046
$507$	7.09212	−	7.09212i	0.314972	−	0.314972i
$508$	−6.79622	+	6.79622i	−0.301533	+	0.301533i
$509$	29.5594			1.31020			0.655098	−	0.755544i	$-0.272627\pi$
$509$	29.5594			1.31020			0.655098	+	0.755544i	$0.272627\pi$
$510$	16.1399	−	5.10428i	0.714686	−	0.226021i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.28969	+	3.28969i	−0.145243	+	0.145243i
$514$	4.50222			0.198584
$515$	8.67278	−	2.74279i	0.382168	−	0.120862i
$516$		−	0.771781i		−	0.0339757i
$517$	11.7695	−	11.7695i	0.517624	−	0.517624i
$518$		0			0
$519$		−	12.3822i		−	0.543520i
$520$	−1.77648	+	3.41983i	−0.0779040	+	0.149969i
$521$			8.82958i			0.386831i	0.981117	+	0.193415i	$0.0619565\pi$
$521$			8.82958i			0.386831i	−0.981117	+	0.193415i	$0.938043\pi$
$522$	−4.23847	−	4.23847i	−0.185513	−	0.185513i
$523$	29.1936	+	29.1936i	1.27655	+	1.27655i	0.942587	+	0.333960i	$0.108385\pi$
$523$	29.1936	+	29.1936i	1.27655	+	1.27655i	0.333960	+	0.942587i	$0.391615\pi$
$524$	4.23598			0.185050
$525$		0			0
$526$	−22.3996			−0.976669
$527$	53.5397	+	53.5397i	2.33223	+	2.33223i
$528$	−1.85647	−	1.85647i	−0.0807924	−	0.0807924i
$529$		−	3.34303i		−	0.145349i
$530$	−8.84372	+	17.0247i	−0.384147	+	0.739504i
$531$			7.72043i			0.335038i
$532$		0			0
$533$	−6.81741	+	6.81741i	−0.295295	+	0.295295i
$534$		−	0.162532i		−	0.00703346i
$535$	6.00597	−	1.89940i	0.259661	−	0.0821183i
$536$	−2.56340			−0.110722
$537$	−14.3331	+	14.3331i	−0.618519	+	0.618519i
$538$	8.29027	+	8.29027i	0.357419	+	0.357419i
$539$		0			0
$540$	2.13199	−	0.674247i	0.0917463	−	0.0290150i
$541$	−25.5347			−1.09782			−0.548911	−	0.835881i	$-0.684958\pi$
$541$	−25.5347			−1.09782			−0.548911	+	0.835881i	$0.684958\pi$
$542$	17.0038	−	17.0038i	0.730377	−	0.730377i
$543$	5.32195	−	5.32195i	0.228387	−	0.228387i
$544$	7.57033			0.324575
$545$	−24.1304	−	12.5349i	−1.03363	−	0.536937i
$546$		0			0
$547$	22.6183	+	22.6183i	0.967087	+	0.967087i	0.999475	−	0.0323883i	$-0.0103113\pi$
$547$	22.6183	+	22.6183i	0.967087	+	0.967087i	−0.0323883	+	0.999475i	$0.510311\pi$
$548$	5.84256	−	5.84256i	0.249582	−	0.249582i
$549$	−4.80982			−0.205278
$550$	−2.25710	+	12.9317i	−0.0962429	+	0.551410i
$551$		−	27.8865i		−	1.18800i
$552$	−3.62926	+	3.62926i	−0.154471	+	0.154471i
$553$		0			0
$554$			27.1973i			1.15550i
$555$	−7.85302	−	4.07937i	−0.333342	−	0.173160i
$556$			9.35059i			0.396553i
$557$	−12.4024	−	12.4024i	−0.525507	−	0.525507i	0.393722	−	0.919229i	$-0.371187\pi$
$557$	−12.4024	−	12.4024i	−0.525507	−	0.525507i	−0.919229	+	0.393722i	$0.871187\pi$
$558$	7.07231	+	7.07231i	0.299395	+	0.299395i
$559$	−1.33011			−0.0562578
$560$		0			0
$561$	19.8755			0.839143
$562$	−15.6916	−	15.6916i	−0.661910	−	0.661910i
$563$	−11.0433	−	11.0433i	−0.465418	−	0.465418i	0.435009	−	0.900426i	$-0.356745\pi$
$563$	−11.0433	−	11.0433i	−0.465418	−	0.465418i	−0.900426	+	0.435009i	$0.856745\pi$
$564$			6.33974i			0.266951i
$565$	1.56260	+	4.94099i	0.0657390	+	0.207869i
$566$			11.1028i			0.466684i
$567$		0			0
$568$	−5.91829	+	5.91829i	−0.248326	+	0.248326i
$569$			17.9102i			0.750835i	0.926856	+	0.375418i	$0.122501\pi$
$569$			17.9102i			0.750835i	−0.926856	+	0.375418i	$0.877499\pi$
$570$	9.23165	+	4.79552i	0.386671	+	0.200862i
$571$	−20.4679			−0.856557			−0.428278	−	0.903647i	$-0.640880\pi$
$571$	−20.4679			−0.856557			−0.428278	+	0.903647i	$0.640880\pi$
$572$	−3.19950	+	3.19950i	−0.133778	+	0.133778i
$573$	3.06028	+	3.06028i	0.127845	+	0.127845i
$574$		0			0
$575$	25.2805	+	4.41246i	1.05427	+	0.184012i
$576$	1.00000			0.0416667
$577$	18.1035	−	18.1035i	0.753658	−	0.753658i	−0.221502	−	0.975160i	$-0.571096\pi$
$577$	18.1035	−	18.1035i	0.753658	−	0.753658i	0.975160	+	0.221502i	$0.0710958\pi$
$578$	−28.5034	+	28.5034i	−1.18559	+	1.18559i
$579$	21.2681			0.883871
$580$	−6.17860	+	11.8942i	−0.256553	+	0.493878i
$581$		0			0
$582$	4.35278	+	4.35278i	0.180429	+	0.180429i
$583$	−15.9278	+	15.9278i	−0.659663	+	0.659663i
$584$	13.6529			0.564961
$585$	−1.16202	−	3.67435i	−0.0480436	−	0.151916i
$586$		−	9.21473i		−	0.380657i
$587$	−26.2627	+	26.2627i	−1.08398	+	1.08398i	−0.0878438	+	0.996134i	$0.527998\pi$
$587$	−26.2627	+	26.2627i	−1.08398	+	1.08398i	−0.996134	+	0.0878438i	$0.972002\pi$
$588$		0			0
$589$			46.5313i			1.91729i
$590$	16.4599	−	5.20548i	0.677643	−	0.214306i
$591$		−	19.9848i		−	0.822063i
$592$	−2.79841	−	2.79841i	−0.115014	−	0.115014i
$593$	−6.80591	−	6.80591i	−0.279485	−	0.279485i	0.553418	−	0.832903i	$-0.313323\pi$
$593$	−6.80591	−	6.80591i	−0.279485	−	0.279485i	−0.832903	+	0.553418i	$0.813323\pi$
$594$	2.62544			0.107723
$595$		0			0
$596$	4.75815			0.194902
$597$	−0.596847	−	0.596847i	−0.0244273	−	0.0244273i
$598$	6.25479	+	6.25479i	0.255777	+	0.255777i
$599$		−	3.88788i		−	0.158855i	−0.996841	−	0.0794273i	$-0.974691\pi$
$599$		−	3.88788i		−	0.158855i	0.996841	−	0.0794273i	$-0.0253091\pi$
$600$	−2.87498	−	4.09078i	−0.117371	−	0.167005i
$601$		−	36.4068i		−	1.48506i	−0.669811	−	0.742531i	$-0.733625\pi$
$601$		−	36.4068i		−	1.48506i	0.669811	−	0.742531i	$-0.266375\pi$
$602$		0			0
$603$	1.81260	−	1.81260i	0.0738146	−	0.0738146i
$604$			2.15114i			0.0875286i
$605$	4.23347	−	8.14966i	0.172115	−	0.331331i
$606$	7.67397			0.311734
$607$	−4.89302	+	4.89302i	−0.198601	+	0.198601i	−0.799400	−	0.600799i	$-0.794849\pi$
$607$	−4.89302	+	4.89302i	−0.198601	+	0.198601i	0.600799	+	0.799400i	$0.294849\pi$
$608$	3.28969	+	3.28969i	0.133414	+	0.133414i
$609$		0			0
$610$	3.24301	+	10.2545i	0.131306	+	0.415193i
$611$	10.9261			0.442024
$612$	−5.35303	+	5.35303i	−0.216384	+	0.216384i
$613$	31.5132	−	31.5132i	1.27281	−	1.27281i	0.328198	−	0.944609i	$-0.393559\pi$
$613$	31.5132	−	31.5132i	1.27281	−	1.27281i	0.944609	−	0.328198i	$-0.106441\pi$
$614$	29.1342			1.17576
$615$	−3.77189	−	11.9268i	−0.152097	−	0.480937i
$616$		0			0
$617$	8.27627	+	8.27627i	0.333190	+	0.333190i	0.853797	−	0.520607i	$-0.174294\pi$
$617$	8.27627	+	8.27627i	0.333190	+	0.333190i	−0.520607	+	0.853797i	$0.674294\pi$
$618$	−2.87646	+	2.87646i	−0.115708	+	0.115708i
$619$	11.5952			0.466052			0.233026	−	0.972471i	$-0.425137\pi$
$619$	11.5952			0.466052			0.233026	+	0.972471i	$0.425137\pi$
$620$	10.3096	−	19.8466i	0.414044	−	0.797058i
$621$		−	5.13255i		−	0.205962i
$622$	−23.2400	+	23.2400i	−0.931840	+	0.931840i
$623$		0			0
$624$		−	1.72343i		−	0.0689926i
$625$	−8.46898	+	23.5218i	−0.338759	+	0.940873i
$626$			22.1831i			0.886615i
$627$	8.63688	+	8.63688i	0.344924	+	0.344924i
$628$	2.69007	+	2.69007i	0.107346	+	0.107346i
$629$	29.9600			1.19458
$630$		0			0
$631$	2.25813			0.0898949			0.0449474	−	0.998989i	$-0.485688\pi$
$631$	2.25813			0.0898949			0.0449474	+	0.998989i	$0.485688\pi$
$632$	6.36034	+	6.36034i	0.253001	+	0.253001i
$633$	15.6867	+	15.6867i	0.623492	+	0.623492i
$634$			14.3645i			0.570488i
$635$	−20.4912	+	6.48040i	−0.813169	+	0.257167i
$636$		−	8.57963i		−	0.340204i
$637$		0			0
$638$	−11.1279	+	11.1279i	−0.440556	+	0.440556i
$639$		−	8.36973i		−	0.331101i
$640$	−0.674247	−	2.13199i	−0.0266520	−	0.0842744i
$641$	19.2249			0.759339			0.379669	−	0.925122i	$-0.376038\pi$
$641$	19.2249			0.759339			0.379669	+	0.925122i	$0.376038\pi$
$642$	−1.99197	+	1.99197i	−0.0786168	+	0.0786168i
$643$	15.5634	+	15.5634i	0.613760	+	0.613760i	0.943924	−	0.330163i	$-0.107104\pi$
$643$	15.5634	+	15.5634i	0.613760	+	0.613760i	−0.330163	+	0.943924i	$0.607104\pi$
$644$		0			0
$645$	0.795537	−	1.53145i	0.0313242	−	0.0603009i
$646$	−35.2196			−1.38570
$647$	−6.98936	+	6.98936i	−0.274780	+	0.274780i	−0.831021	−	0.556241i	$-0.812243\pi$
$647$	−6.98936	+	6.98936i	−0.274780	+	0.274780i	0.556241	+	0.831021i	$0.312243\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	20.2696			0.795650
$650$	−7.05019	+	4.95484i	−0.276531	+	0.194345i
$651$		0			0
$652$	3.15459	+	3.15459i	0.123543	+	0.123543i
$653$	−7.03748	+	7.03748i	−0.275398	+	0.275398i	−0.831269	−	0.555871i	$-0.812385\pi$
$653$	−7.03748	+	7.03748i	−0.275398	+	0.275398i	0.555871	+	0.831269i	$0.312385\pi$
$654$	12.1606			0.475518
$655$	8.40550	+	4.36637i	0.328430	+	0.170608i
$656$		−	5.59423i		−	0.218418i
$657$	−9.65407	+	9.65407i	−0.376641	+	0.376641i
$658$		0			0
$659$			16.2333i			0.632360i	0.948699	+	0.316180i	$0.102400\pi$
$659$			16.2333i			0.632360i	−0.948699	+	0.316180i	$0.897600\pi$
$660$	−1.77020	−	5.59742i	−0.0689049	−	0.217879i
$661$			10.1278i			0.393928i	0.980411	+	0.196964i	$0.0631081\pi$
$661$			10.1278i			0.393928i	−0.980411	+	0.196964i	$0.936892\pi$
$662$	2.04401	+	2.04401i	0.0794427	+	0.0794427i
$663$	9.22560	+	9.22560i	0.358293	+	0.358293i
$664$	−11.3067			−0.438785
$665$		0			0
$666$	3.95756			0.153352
$667$	21.7541	+	21.7541i	0.842323	+	0.842323i
$668$	16.1327	+	16.1327i	0.624194	+	0.624194i
$669$			15.2215i			0.588496i
$670$	−5.08658	−	2.64230i	−0.196512	−	0.102081i
$671$			12.6279i			0.487495i
$672$		0			0
$673$	15.2038	−	15.2038i	0.586062	−	0.586062i	−0.350501	−	0.936563i	$-0.613989\pi$
$673$	15.2038	−	15.2038i	0.586062	−	0.586062i	0.936563	+	0.350501i	$0.113989\pi$
$674$			33.1567i			1.27715i
$675$	4.92554	+	0.859701i	0.189584	+	0.0330899i
$676$	10.0298			0.385761
$677$	−8.52782	+	8.52782i	−0.327751	+	0.327751i	−0.851731	−	0.523980i	$-0.824447\pi$
$677$	−8.52782	+	8.52782i	−0.327751	+	0.327751i	0.523980	+	0.851731i	$0.324447\pi$
$678$	−1.63875	−	1.63875i	−0.0629359	−	0.0629359i
$679$		0			0
$680$	15.0219	+	7.80336i	0.576063	+	0.299245i
$681$	3.73858			0.143263
$682$	18.5679	−	18.5679i	0.711003	−	0.711003i
$683$	8.28510	−	8.28510i	0.317020	−	0.317020i	−0.530601	−	0.847622i	$-0.678034\pi$
$683$	8.28510	−	8.28510i	0.317020	−	0.317020i	0.847622	+	0.530601i	$0.178034\pi$
$684$	−4.65232			−0.177886
$685$	17.6158	−	5.57105i	0.673067	−	0.212859i
$686$		0			0
$687$	−10.7351	−	10.7351i	−0.409570	−	0.409570i
$688$	0.545731	−	0.545731i	0.0208058	−	0.0208058i
$689$	−14.7864			−0.563318
$690$	−10.9425	+	3.46061i	−0.416576	+	0.131743i
$691$		−	28.7034i		−	1.09193i	−0.837808	−	0.545965i	$-0.816163\pi$
$691$		−	28.7034i		−	1.09193i	0.837808	−	0.545965i	$-0.183837\pi$
$692$	8.75557	−	8.75557i	0.332837	−	0.332837i
$693$		0			0
$694$			11.3379i			0.430382i
$695$	−9.63841	+	18.5545i	−0.365606	+	0.703811i
$696$		−	5.99410i		−	0.227206i
$697$	29.9461	+	29.9461i	1.13429	+	1.13429i
$698$	−4.81389	−	4.81389i	−0.182208	−	0.182208i
$699$	−1.21304			−0.0458812
$700$		0			0
$701$	47.8761			1.80825			0.904127	−	0.427264i	$-0.140523\pi$
$701$	47.8761			1.80825			0.904127	+	0.427264i	$0.140523\pi$
$702$	1.21865	+	1.21865i	0.0459951	+	0.0459951i
$703$	13.0191	+	13.0191i	0.491025	+	0.491025i
$704$		−	2.62544i		−	0.0989501i
$705$	−6.53489	+	12.5800i	−0.246118	+	0.473791i
$706$		−	27.8246i		−	1.04719i
$707$		0			0
$708$	−5.45917	+	5.45917i	−0.205168	+	0.205168i
$709$		−	25.4992i		−	0.957643i	−0.877912	−	0.478822i	$-0.841064\pi$
$709$		−	25.4992i		−	0.957643i	0.877912	−	0.478822i	$-0.158936\pi$
$710$	−17.8442	+	5.64327i	−0.669681	+	0.211788i
$711$	−8.99488			−0.337334
$712$	0.114928	−	0.114928i	0.00430710	−	0.00430710i
$713$	−36.2989	−	36.2989i	−1.35941	−	1.35941i
$714$		0			0
$715$	−9.64679	+	3.05082i	−0.360770	+	0.114094i
$716$	−20.2701			−0.757528
$717$	−11.4264	+	11.4264i	−0.426726	+	0.426726i
$718$	−9.71461	+	9.71461i	−0.362546	+	0.362546i
$719$	32.0876			1.19667			0.598333	−	0.801248i	$-0.295830\pi$
$719$	32.0876			1.19667			0.598333	+	0.801248i	$0.295830\pi$
$720$	1.98431	+	1.03078i	0.0739509	+	0.0384149i
$721$		0			0
$722$	−1.86964	−	1.86964i	−0.0695809	−	0.0695809i
$723$	−17.8310	+	17.8310i	−0.663142	+	0.663142i
$724$	7.52637			0.279715
$725$	−24.5205	+	17.2329i	−0.910670	+	0.640014i
$726$			4.10705i			0.152427i
$727$	11.3772	−	11.3772i	0.421956	−	0.421956i	−0.463921	−	0.885877i	$-0.653558\pi$
$727$	11.3772	−	11.3772i	0.421956	−	0.421956i	0.885877	+	0.463921i	$0.153558\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	27.0916	+	14.0732i	1.00271	+	0.520871i
$731$			5.84264i			0.216098i
$732$	−3.40106	−	3.40106i	−0.125707	−	0.125707i
$733$	14.8516	+	14.8516i	0.548557	+	0.548557i	0.926023	−	0.377466i	$-0.123205\pi$
$733$	14.8516	+	14.8516i	0.548557	+	0.548557i	−0.377466	+	0.926023i	$0.623205\pi$
$734$	−25.2180			−0.930812
$735$		0			0
$736$	−5.13255			−0.189188
$737$	−4.75887	−	4.75887i	−0.175295	−	0.175295i
$738$	3.95571	+	3.95571i	0.145612	+	0.145612i
$739$		−	36.7595i		−	1.35222i	−0.736801	−	0.676110i	$-0.763664\pi$
$739$		−	36.7595i		−	1.35222i	0.736801	−	0.676110i	$-0.236336\pi$
$740$	−2.66837	−	8.43748i	−0.0980913	−	0.310168i
$741$			8.01797i			0.294547i
$742$		0			0
$743$	−17.1637	+	17.1637i	−0.629676	+	0.629676i	−0.947987	−	0.318310i	$-0.896885\pi$
$743$	−17.1637	+	17.1637i	−0.629676	+	0.629676i	0.318310	+	0.947987i	$0.396885\pi$
$744$			10.0018i			0.366682i
$745$	9.44166	+	4.90462i	0.345916	+	0.179691i
$746$	−26.8542			−0.983201
$747$	7.99504	−	7.99504i	0.292523	−	0.292523i
$748$	14.0541	+	14.0541i	0.513868	+	0.513868i
$749$		0			0
$750$	−1.48815	−	11.0809i	−0.0543397	−	0.404616i
$751$	30.2637			1.10434			0.552168	−	0.833733i	$-0.313801\pi$
$751$	30.2637			1.10434			0.552168	+	0.833733i	$0.313801\pi$
$752$	−4.48288	+	4.48288i	−0.163474	+	0.163474i
$753$	−1.46767	+	1.46767i	−0.0534847	+	0.0534847i
$754$	−10.3304			−0.376212
$755$	−2.21735	+	4.26853i	−0.0806978	+	0.155348i
$756$		0			0
$757$	−1.48321	−	1.48321i	−0.0539082	−	0.0539082i	0.679639	−	0.733547i	$-0.262137\pi$
$757$	−1.48321	−	1.48321i	−0.0539082	−	0.0539082i	−0.733547	+	0.679639i	$0.762137\pi$
$758$	−2.48889	+	2.48889i	−0.0904005	+	0.0904005i
$759$	−13.4752			−0.489119
$760$	3.13681	+	9.91871i	0.113784	+	0.359789i
$761$			6.91949i			0.250831i	0.992104	+	0.125416i	$0.0400265\pi$
$761$			6.91949i			0.250831i	−0.992104	+	0.125416i	$0.959974\pi$
$762$	6.79622	−	6.79622i	0.246201	−	0.246201i
$763$		0			0
$764$			4.32789i			0.156578i
$765$	−16.1399	+	5.10428i	−0.583539	+	0.184546i
$766$		−	8.96302i		−	0.323847i
$767$	9.40852	+	9.40852i	0.339722	+	0.339722i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	16.5757			0.597736			0.298868	−	0.954294i	$-0.403391\pi$
$769$	16.5757			0.597736			0.298868	+	0.954294i	$0.403391\pi$
$770$		0			0
$771$	−4.50222			−0.162143
$772$	15.0388	+	15.0388i	0.541258	+	0.541258i
$773$	4.74612	+	4.74612i	0.170706	+	0.170706i	0.787289	−	0.616584i	$-0.211484\pi$
$773$	4.74612	+	4.74612i	0.170706	+	0.170706i	−0.616584	+	0.787289i	$0.711484\pi$
$774$			0.771781i			0.0277411i
$775$	40.9150	−	28.7548i	1.46971	−	1.03290i
$776$			6.15577i			0.220979i
$777$		0			0
$778$	22.3001	−	22.3001i	0.799497	−	0.799497i
$779$			26.0261i			0.932483i
$780$	1.77648	−	3.41983i	0.0636083	−	0.122450i
$781$	−21.9742			−0.786300
$782$	27.4747	−	27.4747i	0.982493	−	0.982493i
$783$	4.23847	+	4.23847i	0.151470	+	0.151470i
$784$		0			0
$785$	2.56506	+	8.11082i	0.0915511	+	0.289488i
$786$	−4.23598			−0.151092
$787$	10.6060	−	10.6060i	0.378063	−	0.378063i	−0.492340	−	0.870403i	$-0.663858\pi$
$787$	10.6060	−	10.6060i	0.378063	−	0.378063i	0.870403	+	0.492340i	$0.163858\pi$
$788$	14.1314	−	14.1314i	0.503409	−	0.503409i
$789$	22.3996			0.797447
$790$	6.06478	+	19.1770i	0.215775	+	0.682288i
$791$		0			0
$792$	1.85647	+	1.85647i	0.0659667	+	0.0659667i
$793$	−5.86150	+	5.86150i	−0.208148	+	0.208148i
$794$	−6.21845			−0.220685
$795$	8.84372	−	17.0247i	0.313654	−	0.603802i
$796$		−	0.844069i		−	0.0299172i
$797$	−29.9616	+	29.9616i	−1.06130	+	1.06130i	−0.0633012	+	0.997994i	$0.520163\pi$
$797$	−29.9616	+	29.9616i	−1.06130	+	1.06130i	−0.997994	+	0.0633012i	$0.979837\pi$
$798$		0			0
$799$		−	47.9940i		−	1.69790i
$800$	0.859701	−	4.92554i	0.0303950	−	0.174144i
$801$			0.162532i			0.00574280i
$802$	14.5056	+	14.5056i	0.512211	+	0.512211i
$803$	25.3462	+	25.3462i	0.894448	+	0.894448i
$804$	2.56340			0.0904041
$805$		0			0
$806$	17.2374			0.607160
$807$	−8.29027	−	8.29027i	−0.291831	−	0.291831i
$808$	5.42632	+	5.42632i	0.190897	+	0.190897i
$809$		−	8.67329i		−	0.304937i	−0.988308	−	0.152468i	$-0.951278\pi$
$809$		−	8.67329i		−	0.304937i	0.988308	−	0.152468i	$-0.0487222\pi$
$810$	−2.13199	+	0.674247i	−0.0749106	+	0.0236906i
$811$		−	21.4366i		−	0.752741i	−0.926469	−	0.376370i	$-0.877172\pi$
$811$		−	21.4366i		−	0.752741i	0.926469	−	0.376370i	$-0.122828\pi$
$812$		0			0
$813$	−17.0038	+	17.0038i	−0.596351	+	0.596351i
$814$		−	10.3903i		−	0.364181i
$815$	3.00799	+	9.51137i	0.105365	+	0.333169i
$816$	−7.57033			−0.265015
$817$	−2.53892	+	2.53892i	−0.0888254	+	0.0888254i
$818$	18.1381	+	18.1381i	0.634184	+	0.634184i
$819$		0			0
$820$	5.76642	−	11.1007i	0.201372	−	0.387653i
$821$	19.1999			0.670082			0.335041	−	0.942204i	$-0.391250\pi$
$821$	19.1999			0.670082			0.335041	+	0.942204i	$0.391250\pi$
$822$	−5.84256	+	5.84256i	−0.203783	+	0.203783i
$823$	7.13593	−	7.13593i	0.248743	−	0.248743i	−0.571712	−	0.820455i	$-0.693720\pi$
$823$	7.13593	−	7.13593i	0.248743	−	0.248743i	0.820455	+	0.571712i	$0.193720\pi$
$824$	−4.06792			−0.141713
$825$	2.25710	−	12.9317i	0.0785820	−	0.450225i
$826$		0			0
$827$	−2.93550	−	2.93550i	−0.102077	−	0.102077i	0.654224	−	0.756301i	$-0.272995\pi$
$827$	−2.93550	−	2.93550i	−0.102077	−	0.102077i	−0.756301	+	0.654224i	$0.772995\pi$
$828$	3.62926	−	3.62926i	0.126125	−	0.126125i
$829$	−0.632225			−0.0219581			−0.0109790	−	0.999940i	$-0.503495\pi$
$829$	−0.632225			−0.0219581			−0.0109790	+	0.999940i	$0.503495\pi$
$830$	−22.4360	−	11.6547i	−0.778765	−	0.404542i
$831$		−	27.1973i		−	0.943462i
$832$	1.21865	−	1.21865i	0.0422492	−	0.0422492i
$833$		0			0
$834$		−	9.35059i		−	0.323784i
$835$	15.3830	+	48.6417i	0.532352	+	1.68331i
$836$			12.2144i			0.422444i
$837$	−7.07231	−	7.07231i	−0.244455	−	0.244455i
$838$	−1.08998	−	1.08998i	−0.0376527	−	0.0376527i
$839$	−7.93406			−0.273914			−0.136957	−	0.990577i	$-0.543732\pi$
$839$	−7.93406			−0.273914			−0.136957	+	0.990577i	$0.543732\pi$
$840$		0			0
$841$	−6.92921			−0.238938
$842$	14.2023	+	14.2023i	0.489442	+	0.489442i
$843$	15.6916	+	15.6916i	0.540447	+	0.540447i
$844$			22.1844i			0.763619i
$845$	19.9022	+	10.3385i	0.684656	+	0.355655i
$846$		−	6.33974i		−	0.217965i
$847$		0			0
$848$	6.06671	−	6.06671i	0.208332	−	0.208332i
$849$		−	11.1028i		−	0.381046i
$850$	21.7646	+	30.9686i	0.746518	+	1.06221i
$851$	−20.3123			−0.696298
$852$	5.91829	−	5.91829i	0.202757	−	0.202757i
$853$	−13.0203	−	13.0203i	−0.445806	−	0.445806i	0.448152	−	0.893957i	$-0.352082\pi$
$853$	−13.0203	−	13.0203i	−0.445806	−	0.445806i	−0.893957	+	0.448152i	$0.852082\pi$
$854$		0			0
$855$	−9.23165	−	4.79552i	−0.315716	−	0.164003i
$856$	−2.81707			−0.0962855
$857$	−8.06970	+	8.06970i	−0.275656	+	0.275656i	−0.831372	−	0.555716i	$-0.812444\pi$
$857$	−8.06970	+	8.06970i	−0.275656	+	0.275656i	0.555716	+	0.831372i	$0.312444\pi$
$858$	3.19950	−	3.19950i	0.109229	−	0.109229i
$859$	12.8977			0.440063			0.220031	−	0.975493i	$-0.429384\pi$
$859$	12.8977			0.440063			0.220031	+	0.975493i	$0.429384\pi$
$860$	1.64543	−	0.520371i	0.0561087	−	0.0177445i
$861$		0			0
$862$	−15.4861	−	15.4861i	−0.527457	−	0.527457i
$863$	−8.97306	+	8.97306i	−0.305447	+	0.305447i	−0.843140	−	0.537694i	$-0.819296\pi$
$863$	−8.97306	+	8.97306i	−0.305447	+	0.305447i	0.537694	+	0.843140i	$0.319296\pi$
$864$	−1.00000			−0.0340207
$865$	26.3988	−	8.34869i	0.897588	−	0.283864i
$866$			7.80057i			0.265074i
$867$	28.5034	−	28.5034i	0.968027	−	0.968027i
$868$		0			0
$869$			23.6156i			0.801103i
$870$	6.17860	−	11.8942i	0.209474	−	0.403250i
$871$		−	4.41785i		−	0.149693i
$872$	8.59885	+	8.59885i	0.291194	+	0.291194i
$873$	−4.35278	−	4.35278i	−0.147319	−	0.147319i
$874$	23.8782			0.807694
$875$		0			0
$876$	−13.6529			−0.461289
$877$	−18.4582	−	18.4582i	−0.623289	−	0.623289i	0.323082	−	0.946371i	$-0.395281\pi$
$877$	−18.4582	−	18.4582i	−0.623289	−	0.623289i	−0.946371	+	0.323082i	$0.895281\pi$
$878$	3.70812	+	3.70812i	0.125143	+	0.125143i
$879$			9.21473i			0.310805i
$880$	2.70626	−	5.20970i	0.0912279	−	0.175619i
$881$			34.2689i			1.15455i	0.816551	+	0.577274i	$0.195884\pi$
$881$			34.2689i			1.15455i	−0.816551	+	0.577274i	$0.804116\pi$
$882$		0			0
$883$	−33.0880	+	33.0880i	−1.11350	+	1.11350i	−0.120827	+	0.992674i	$0.538555\pi$
$883$	−33.0880	+	33.0880i	−1.11350	+	1.11350i	−0.992674	+	0.120827i	$0.961445\pi$
$884$			13.0470i			0.438817i
$885$	−16.4599	+	5.20548i	−0.553293	+	0.174980i
$886$	−1.30040			−0.0436877
$887$	13.4304	−	13.4304i	0.450949	−	0.450949i	−0.444720	−	0.895670i	$-0.646697\pi$
$887$	13.4304	−	13.4304i	0.450949	−	0.450949i	0.895670	+	0.444720i	$0.146697\pi$
$888$	2.79841	+	2.79841i	0.0939087	+	0.0939087i
$889$		0			0
$890$	0.346518	−	0.109587i	0.0116153	−	0.00367336i
$891$	−2.62544			−0.0879557
$892$	−10.7632	+	10.7632i	−0.360378	+	0.360378i
$893$	20.8558	−	20.8558i	0.697912	−	0.697912i
$894$	−4.75815			−0.159136
$895$	−40.2221	−	20.8940i	−1.34448	−	0.698410i
$896$		0			0
$897$	−6.25479	−	6.25479i	−0.208841	−	0.208841i
$898$	−15.8127	+	15.8127i	−0.527676	+	0.527676i
$899$	59.9515			1.99949
$900$	2.87498	+	4.09078i	0.0958327	+	0.136359i
$901$			64.9506i			2.16382i
$902$	10.3855	−	10.3855i	0.345799	−	0.345799i
$903$		0			0
$904$		−	2.31755i		−	0.0770804i
$905$	14.9347	+	7.75804i	0.496445	+	0.257886i
$906$		−	2.15114i		−	0.0714668i
$907$	39.9835	+	39.9835i	1.32763	+	1.32763i	0.907432	+	0.420200i	$0.138040\pi$
$907$	39.9835	+	39.9835i	1.32763	+	1.32763i	0.420200	+	0.907432i	$0.361960\pi$
$908$	2.64357	+	2.64357i	0.0877301	+	0.0877301i
$909$	−7.67397			−0.254530
$910$		0			0
$911$	−18.6286			−0.617193			−0.308596	−	0.951193i	$-0.599859\pi$
$911$	−18.6286			−0.617193			−0.308596	+	0.951193i	$0.599859\pi$
$912$	−3.28969	−	3.28969i	−0.108932	−	0.108932i
$913$	−20.9905	−	20.9905i	−0.694685	−	0.694685i
$914$		−	3.29949i		−	0.109137i
$915$	−3.24301	−	10.2545i	−0.107211	−	0.339003i
$916$		−	15.1818i		−	0.501619i
$917$		0			0
$918$	5.35303	−	5.35303i	0.176676	−	0.176676i
$919$		−	44.3232i		−	1.46209i	−0.682331	−	0.731043i	$-0.739034\pi$
$919$		−	44.3232i		−	1.46209i	0.682331	−	0.731043i	$-0.260966\pi$
$920$	−10.1846	−	5.29053i	−0.335775	−	0.174424i
$921$	−29.1342			−0.960005
$922$	4.93148	−	4.93148i	0.162410	−	0.162410i
$923$	−10.1998	−	10.1998i	−0.335730	−	0.335730i
$924$		0			0
$925$	3.40232	−	19.4931i	0.111867	−	0.640929i
$926$	−23.5691			−0.774527
$927$	2.87646	−	2.87646i	0.0944752	−	0.0944752i
$928$	4.23847	−	4.23847i	0.139135	−	0.139135i
$929$	−14.0476			−0.460886			−0.230443	−	0.973086i	$-0.574018\pi$
$929$	−14.0476			−0.460886			−0.230443	+	0.973086i	$0.574018\pi$
$930$	−10.3096	+	19.8466i	−0.338066	+	0.650795i
$931$		0			0
$932$	−0.857745	−	0.857745i	−0.0280964	−	0.0280964i
$933$	23.2400	−	23.2400i	0.760844	−	0.760844i
$934$	−11.4601			−0.374986
$935$	13.4010	+	42.3744i	0.438259	+	1.38579i
$936$			1.72343i			0.0563322i
$937$	24.1561	−	24.1561i	0.789145	−	0.789145i	−0.192209	−	0.981354i	$-0.561565\pi$
$937$	24.1561	−	24.1561i	0.789145	−	0.789145i	0.981354	+	0.192209i	$0.0615652\pi$
$938$		0			0
$939$		−	22.1831i		−	0.723918i
$940$	−13.5163	+	4.27456i	−0.440853	+	0.139421i
$941$		−	52.3393i		−	1.70621i	−0.521738	−	0.853106i	$-0.674716\pi$
$941$		−	52.3393i		−	1.70621i	0.521738	−	0.853106i	$-0.325284\pi$
$942$	−2.69007	−	2.69007i	−0.0876473	−	0.0876473i
$943$	−20.3029	−	20.3029i	−0.661153	−	0.661153i
$944$	−7.72043			−0.251279
$945$		0			0
$946$	2.02627			0.0658796
$947$	−27.5701	−	27.5701i	−0.895908	−	0.895908i	0.0991635	−	0.995071i	$-0.468383\pi$
$947$	−27.5701	−	27.5701i	−0.895908	−	0.895908i	−0.995071	+	0.0991635i	$0.968383\pi$
$948$	−6.36034	−	6.36034i	−0.206574	−	0.206574i
$949$			23.5299i			0.763813i
$950$	−3.99960	+	22.9152i	−0.129764	+	0.743466i
$951$		−	14.3645i		−	0.465801i
$952$		0			0
$953$	1.45944	−	1.45944i	0.0472759	−	0.0472759i	−0.683074	−	0.730350i	$-0.739357\pi$
$953$	1.45944	−	1.45944i	0.0472759	−	0.0472759i	0.730350	+	0.683074i	$0.239357\pi$
$954$			8.57963i			0.277776i
$955$	−4.46111	+	8.58789i	−0.144358	+	0.277898i
$956$	−16.1593			−0.522630
$957$	11.1279	−	11.1279i	0.359712	−	0.359712i
$958$	−7.15393	−	7.15393i	−0.231133	−	0.231133i
$959$		0			0
$960$	0.674247	+	2.13199i	0.0217612	+	0.0688098i
$961$	−69.0351			−2.22694
$962$	4.82288	−	4.82288i	0.155496	−	0.155496i
$963$	1.99197	−	1.99197i	0.0641903	−	0.0641903i
$964$	−25.2169			−0.812180
$965$	14.3399	+	45.3434i	0.461619	+	1.45965i
$966$		0			0
$967$	11.2656	+	11.2656i	0.362279	+	0.362279i	0.864651	−	0.502373i	$-0.167539\pi$
$967$	11.2656	+	11.2656i	0.362279	+	0.362279i	−0.502373	+	0.864651i	$0.667539\pi$
$968$	−2.90412	+	2.90412i	−0.0933420	+	0.0933420i
$969$	35.2196			1.13142
$970$	−6.34525	+	12.2150i	−0.203734	+	0.392199i
$971$		−	9.80195i		−	0.314559i	−0.987554	−	0.157280i	$-0.949728\pi$
$971$		−	9.80195i		−	0.314559i	0.987554	−	0.157280i	$-0.0502724\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$		0			0
$974$			36.9498i			1.18395i
$975$	7.05019	−	4.95484i	0.225787	−	0.158682i
$976$		−	4.80982i		−	0.153959i
$977$	−34.8727	−	34.8727i	−1.11568	−	1.11568i	−0.992368	−	0.123309i	$-0.960649\pi$
$977$	−34.8727	−	34.8727i	−1.11568	−	1.11568i	−0.123309	−	0.992368i	$-0.539351\pi$
$978$	−3.15459	−	3.15459i	−0.100873	−	0.100873i
$979$	0.426719			0.0136380
$980$		0			0
$981$	−12.1606			−0.388258
$982$	5.66207	+	5.66207i	0.180684	+	0.180684i
$983$	4.22505	+	4.22505i	0.134758	+	0.134758i	0.771268	−	0.636510i	$-0.219623\pi$
$983$	4.22505	+	4.22505i	0.134758	+	0.134758i	−0.636510	+	0.771268i	$0.719623\pi$
$984$			5.59423i			0.178337i
$985$	42.6073	−	13.4747i	1.35758	−	0.429339i
$986$			45.3773i			1.44511i
$987$		0			0
$988$	−5.66956	+	5.66956i	−0.180373	+	0.180373i
$989$		−	3.96120i		−	0.125959i
$990$	1.77020	+	5.59742i	0.0562606	+	0.177898i
$991$	13.0417			0.414284			0.207142	−	0.978311i	$-0.433584\pi$
$991$	13.0417			0.414284			0.207142	+	0.978311i	$0.433584\pi$
$992$	−7.07231	+	7.07231i	−0.224546	+	0.224546i
$993$	−2.04401	−	2.04401i	−0.0648647	−	0.0648647i
$994$		0			0
$995$	0.870050	−	1.67490i	0.0275824	−	0.0530977i
$996$	11.3067			0.358266
$997$	15.0223	−	15.0223i	0.475761	−	0.475761i	−0.428012	−	0.903773i	$-0.640786\pi$
$997$	15.0223	−	15.0223i	0.475761	−	0.475761i	0.903773	+	0.428012i	$0.140786\pi$
$998$	−8.46182	+	8.46182i	−0.267854	+	0.267854i
$999$	−3.95756			−0.125212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.d.97.2		16
5.3	odd	4		1470.2.m.e.1273.3		16
7.2	even	3		210.2.u.a.157.2	yes	16
7.3	odd	6		210.2.u.b.187.3	yes	16
7.6	odd	2		1470.2.m.e.97.3		16
21.2	odd	6		630.2.bv.a.577.3		16
21.17	even	6		630.2.bv.b.397.2		16
35.2	odd	12		1050.2.bc.g.493.1		16
35.3	even	12		210.2.u.a.103.2	✓	16
35.9	even	6		1050.2.bc.h.157.3		16
35.13	even	4	inner	1470.2.m.d.1273.2		16
35.17	even	12		1050.2.bc.h.943.3		16
35.23	odd	12		210.2.u.b.73.3	yes	16
35.24	odd	6		1050.2.bc.g.607.1		16
105.23	even	12		630.2.bv.b.73.2		16
105.38	odd	12		630.2.bv.a.523.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.2	✓	16	35.3	even	12
210.2.u.a.157.2	yes	16	7.2	even	3
210.2.u.b.73.3	yes	16	35.23	odd	12
210.2.u.b.187.3	yes	16	7.3	odd	6
630.2.bv.a.523.3		16	105.38	odd	12
630.2.bv.a.577.3		16	21.2	odd	6
630.2.bv.b.73.2		16	105.23	even	12
630.2.bv.b.397.2		16	21.17	even	6
1050.2.bc.g.493.1		16	35.2	odd	12
1050.2.bc.g.607.1		16	35.24	odd	6
1050.2.bc.h.157.3		16	35.9	even	6
1050.2.bc.h.943.3		16	35.17	even	12
1470.2.m.d.97.2		16	1.1	even	1	trivial
1470.2.m.d.1273.2		16	35.13	even	4	inner
1470.2.m.e.97.3		16	7.6	odd	2
1470.2.m.e.1273.3		16	5.3	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.03078 + 1.98431i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.03078 + 1.98431i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.13199 - 0.674247i) q^{10} +2.62544 q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.21865 + 1.21865i) q^{13} +(-2.13199 + 0.674247i) q^{15} -1.00000 q^{16} +(5.35303 - 5.35303i) q^{17} +(0.707107 - 0.707107i) q^{18} +4.65232 q^{19} +(-1.98431 - 1.03078i) q^{20} +(-1.85647 - 1.85647i) q^{22} +(-3.62926 + 3.62926i) q^{23} +1.00000 q^{24} +(-2.87498 - 4.09078i) q^{25} -1.72343i q^{26} +(-0.707107 + 0.707107i) q^{27} -5.99410i q^{29} +(1.98431 + 1.03078i) q^{30} +10.0018i q^{31} +(0.707107 + 0.707107i) q^{32} +(1.85647 + 1.85647i) q^{33} -7.57033 q^{34} -1.00000 q^{36} +(2.79841 + 2.79841i) q^{37} +(-3.28969 - 3.28969i) q^{38} +1.72343i q^{39} +(0.674247 + 2.13199i) q^{40} +5.59423i q^{41} +(-0.545731 + 0.545731i) q^{43} +2.62544i q^{44} +(-1.98431 - 1.03078i) q^{45} +5.13255 q^{46} +(4.48288 - 4.48288i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-0.859701 + 4.92554i) q^{50} +7.57033 q^{51} +(-1.21865 + 1.21865i) q^{52} +(-6.06671 + 6.06671i) q^{53} +1.00000 q^{54} +(-2.70626 + 5.20970i) q^{55} +(3.28969 + 3.28969i) q^{57} +(-4.23847 + 4.23847i) q^{58} +7.72043 q^{59} +(-0.674247 - 2.13199i) q^{60} +4.80982i q^{61} +(7.07231 - 7.07231i) q^{62} -1.00000i q^{64} +(-3.67435 + 1.16202i) q^{65} -2.62544i q^{66} +(-1.81260 - 1.81260i) q^{67} +(5.35303 + 5.35303i) q^{68} -5.13255 q^{69} -8.36973 q^{71} +(0.707107 + 0.707107i) q^{72} +(9.65407 + 9.65407i) q^{73} -3.95756i q^{74} +(0.859701 - 4.92554i) q^{75} +4.65232i q^{76} +(1.21865 - 1.21865i) q^{78} +8.99488i q^{79} +(1.03078 - 1.98431i) q^{80} -1.00000 q^{81} +(3.95571 - 3.95571i) q^{82} +(-7.99504 - 7.99504i) q^{83} +(5.10428 + 16.1399i) q^{85} +0.771781 q^{86} +(4.23847 - 4.23847i) q^{87} +(1.85647 - 1.85647i) q^{88} +0.162532 q^{89} +(0.674247 + 2.13199i) q^{90} +(-3.62926 - 3.62926i) q^{92} +(-7.07231 + 7.07231i) q^{93} -6.33974 q^{94} +(-4.79552 + 9.23165i) q^{95} +1.00000i q^{96} +(-4.35278 + 4.35278i) q^{97} +2.62544i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{10} - 8 q^{11} - 16 q^{13} + 4 q^{15} - 16 q^{16} + 24 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{25} + 8 q^{30} - 4 q^{33} + 16 q^{34} - 16 q^{36} + 16 q^{37} + 8 q^{38} - 24 q^{43} - 8 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 16 q^{54} - 56 q^{55} - 8 q^{57} - 36 q^{58} - 16 q^{59} + 8 q^{62} - 32 q^{65} + 48 q^{67} + 24 q^{68} - 8 q^{69} - 32 q^{71} + 56 q^{73} - 16 q^{78} - 16 q^{81} + 24 q^{82} - 16 q^{83} + 8 q^{85} + 16 q^{86} + 36 q^{87} - 4 q^{88} + 32 q^{89} + 8 q^{92} - 8 q^{93} - 16 q^{94} - 24 q^{95} + 44 q^{97}+O(q^{100}) \) 16 * q - 4 * q^10 - 8 * q^11 - 16 * q^13 + 4 * q^15 - 16 * q^16 + 24 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^25 + 8 * q^30 - 4 * q^33 + 16 * q^34 - 16 * q^36 + 16 * q^37 + 8 * q^38 - 24 * q^43 - 8 * q^45 + 8 * q^46 + 24 * q^47 - 16 * q^51 + 16 * q^52 - 16 * q^53 + 16 * q^54 - 56 * q^55 - 8 * q^57 - 36 * q^58 - 16 * q^59 + 8 * q^62 - 32 * q^65 + 48 * q^67 + 24 * q^68 - 8 * q^69 - 32 * q^71 + 56 * q^73 - 16 * q^78 - 16 * q^81 + 24 * q^82 - 16 * q^83 + 8 * q^85 + 16 * q^86 + 36 * q^87 - 4 * q^88 + 32 * q^89 + 8 * q^92 - 8 * q^93 - 16 * q^94 - 24 * q^95 + 44 * q^97

Introduction

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