LMFDB - Embedded newform 1470.2.m.c.1273.4

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} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 $ x^16 - 32x^13 + 2x^12 + 352x^10 - 288x^9 + 2x^8 - 1440x^7 + 8800x^6 + 1250x^4 - 100000*x^3 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1273.4
Root			$-2.01595 - 0.967451i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.c.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.49226 + 1.66528i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.49226 + 1.66528i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-2.23272 - 0.122339i) q^{10} -0.520689 q^{11} +(0.707107 + 0.707107i) q^{12} +(2.39217 - 2.39217i) q^{13} +(-2.23272 - 0.122339i) q^{15} -1.00000 q^{16} +(-0.110114 - 0.110114i) q^{17} +(0.707107 + 0.707107i) q^{18} +6.73985 q^{19} +(1.66528 - 1.49226i) q^{20} +(0.368182 - 0.368182i) q^{22} +(0.802483 + 0.802483i) q^{23} -1.00000 q^{24} +(-0.546298 + 4.97007i) q^{25} +3.38305i q^{26} +(0.707107 + 0.707107i) q^{27} +1.20346i q^{29} +(1.66528 - 1.49226i) q^{30} -7.18127i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.368182 - 0.368182i) q^{33} +0.155725 q^{34} -1.00000 q^{36} +(4.41428 - 4.41428i) q^{37} +(-4.76579 + 4.76579i) q^{38} +3.38305i q^{39} +(-0.122339 + 2.23272i) q^{40} -1.23303i q^{41} +(6.27475 + 6.27475i) q^{43} +0.520689i q^{44} +(1.66528 - 1.49226i) q^{45} -1.13488 q^{46} +(7.57888 + 7.57888i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-3.12808 - 3.90066i) q^{50} +0.155725 q^{51} +(-2.39217 - 2.39217i) q^{52} +(0.550357 + 0.550357i) q^{53} -1.00000 q^{54} +(-0.777005 - 0.867091i) q^{55} +(-4.76579 + 4.76579i) q^{57} +(-0.850978 - 0.850978i) q^{58} -8.93272 q^{59} +(-0.122339 + 2.23272i) q^{60} -15.4688i q^{61} +(5.07792 + 5.07792i) q^{62} +1.00000i q^{64} +(7.55339 + 0.413879i) q^{65} +0.520689i q^{66} +(-10.4060 + 10.4060i) q^{67} +(-0.110114 + 0.110114i) q^{68} -1.13488 q^{69} +3.05910 q^{71} +(0.707107 - 0.707107i) q^{72} +(3.22403 - 3.22403i) q^{73} +6.24274i q^{74} +(-3.12808 - 3.90066i) q^{75} -6.73985i q^{76} +(-2.39217 - 2.39217i) q^{78} +2.29777i q^{79} +(-1.49226 - 1.66528i) q^{80} -1.00000 q^{81} +(0.871887 + 0.871887i) q^{82} +(-3.43683 + 3.43683i) q^{83} +(0.0190513 - 0.347691i) q^{85} -8.87383 q^{86} +(-0.850978 - 0.850978i) q^{87} +(-0.368182 - 0.368182i) q^{88} +16.3024 q^{89} +(-0.122339 + 2.23272i) q^{90} +(0.802483 - 0.802483i) q^{92} +(5.07792 + 5.07792i) q^{93} -10.7182 q^{94} +(10.0576 + 11.2237i) q^{95} +1.00000i q^{96} +(9.40700 + 9.40700i) q^{97} +0.520689i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5}+O(q^{10}) $ 16 * q - 8 * q^5	$ 16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57} + 24 q^{58} - 48 q^{59} + 8 q^{62} + 72 q^{65} - 48 q^{67} + 8 q^{68} - 16 q^{73} + 8 q^{78} + 8 q^{80} - 16 q^{81} + 16 q^{82} - 72 q^{85} + 24 q^{87} + 8 q^{88} + 64 q^{89} - 8 q^{92} + 8 q^{93} - 64 q^{94} + 48 q^{95} + 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 - 8 * q^13 - 16 * q^16 + 8 * q^17 + 48 * q^19 - 8 * q^22 - 8 * q^23 - 16 * q^24 + 8 * q^25 - 8 * q^33 - 16 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^47 + 8 * q^52 + 8 * q^53 - 16 * q^54 + 8 * q^57 + 24 * q^58 - 48 * q^59 + 8 * q^62 + 72 * q^65 - 48 * q^67 + 8 * q^68 - 16 * q^73 + 8 * q^78 + 8 * q^80 - 16 * q^81 + 16 * q^82 - 72 * q^85 + 24 * q^87 + 8 * q^88 + 64 * q^89 - 8 * q^92 + 8 * q^93 - 64 * q^94 + 48 * q^95 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$5$	1.49226	+	1.66528i	0.667361	+	0.744735i
$5$	1.49226	+	1.66528i	0.667361	+	0.744735i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−2.23272	−	0.122339i	−0.706048	−	0.0386870i
$11$	−0.520689			−0.156994			−0.0784968	−	0.996914i	$-0.525012\pi$
$11$	−0.520689			−0.156994			−0.0784968	+	0.996914i	$0.525012\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	2.39217	−	2.39217i	0.663470	−	0.663470i	−0.292726	−	0.956196i	$-0.594563\pi$
$13$	2.39217	−	2.39217i	0.663470	−	0.663470i	0.956196	+	0.292726i	$0.0945625\pi$
$14$		0			0
$15$	−2.23272	−	0.122339i	−0.576486	−	0.0315878i
$16$	−1.00000			−0.250000
$17$	−0.110114	−	0.110114i	−0.0267067	−	0.0267067i	0.693627	−	0.720334i	$-0.256011\pi$
$17$	−0.110114	−	0.110114i	−0.0267067	−	0.0267067i	−0.720334	+	0.693627i	$0.756011\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	6.73985			1.54623			0.773114	−	0.634267i	$-0.218698\pi$
$19$	6.73985			1.54623			0.773114	+	0.634267i	$0.218698\pi$
$20$	1.66528	−	1.49226i	0.372367	−	0.333680i
$21$		0			0
$22$	0.368182	−	0.368182i	0.0784968	−	0.0784968i
$23$	0.802483	+	0.802483i	0.167329	+	0.167329i	0.785804	−	0.618475i	$-0.212249\pi$
$23$	0.802483	+	0.802483i	0.167329	+	0.167329i	−0.618475	+	0.785804i	$0.712249\pi$
$24$	−1.00000			−0.204124
$25$	−0.546298	+	4.97007i	−0.109260	+	0.994013i
$26$			3.38305i			0.663470i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			1.20346i			0.223478i	0.993738	+	0.111739i	$0.0356420\pi$
$29$			1.20346i			0.223478i	−0.993738	+	0.111739i	$0.964358\pi$
$30$	1.66528	−	1.49226i	0.304037	−	0.272449i
$31$		−	7.18127i		−	1.28979i	−0.764270	−	0.644897i	$-0.776900\pi$
$31$		−	7.18127i		−	1.28979i	0.764270	−	0.644897i	$-0.223100\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.368182	−	0.368182i	0.0640923	−	0.0640923i
$34$	0.155725			0.0267067
$35$		0			0
$36$	−1.00000			−0.166667
$37$	4.41428	−	4.41428i	0.725703	−	0.725703i	−0.244058	−	0.969761i	$-0.578479\pi$
$37$	4.41428	−	4.41428i	0.725703	−	0.725703i	0.969761	+	0.244058i	$0.0784786\pi$
$38$	−4.76579	+	4.76579i	−0.773114	+	0.773114i
$39$			3.38305i			0.541721i
$40$	−0.122339	+	2.23272i	−0.0193435	+	0.353024i
$41$		−	1.23303i		−	0.192568i	−0.995354	−	0.0962838i	$-0.969304\pi$
$41$		−	1.23303i		−	0.192568i	0.995354	−	0.0962838i	$-0.0306956\pi$
$42$		0			0
$43$	6.27475	+	6.27475i	0.956890	+	0.956890i	0.999108	−	0.0422185i	$-0.0134426\pi$
$43$	6.27475	+	6.27475i	0.956890	+	0.956890i	−0.0422185	+	0.999108i	$0.513443\pi$
$44$			0.520689i			0.0784968i
$45$	1.66528	−	1.49226i	0.248245	−	0.222454i
$46$	−1.13488			−0.167329
$47$	7.57888	+	7.57888i	1.10549	+	1.10549i	0.993736	+	0.111758i	$0.0356480\pi$
$47$	7.57888	+	7.57888i	1.10549	+	1.10549i	0.111758	+	0.993736i	$0.464352\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		0			0
$50$	−3.12808	−	3.90066i	−0.442377	−	0.551636i
$51$	0.155725			0.0218059
$52$	−2.39217	−	2.39217i	−0.331735	−	0.331735i
$53$	0.550357	+	0.550357i	0.0755974	+	0.0755974i	0.743894	−	0.668297i	$-0.232976\pi$
$53$	0.550357	+	0.550357i	0.0755974	+	0.0755974i	−0.668297	+	0.743894i	$0.732976\pi$
$54$	−1.00000			−0.136083
$55$	−0.777005	−	0.867091i	−0.104771	−	0.116919i
$56$		0			0
$57$	−4.76579	+	4.76579i	−0.631245	+	0.631245i
$58$	−0.850978	−	0.850978i	−0.111739	−	0.111739i
$59$	−8.93272			−1.16294			−0.581470	−	0.813568i	$-0.697522\pi$
$59$	−8.93272			−1.16294			−0.581470	+	0.813568i	$0.697522\pi$
$60$	−0.122339	+	2.23272i	−0.0157939	+	0.288243i
$61$		−	15.4688i		−	1.98058i	−0.139015	−	0.990290i	$-0.544394\pi$
$61$		−	15.4688i		−	1.98058i	0.139015	−	0.990290i	$-0.455606\pi$
$62$	5.07792	+	5.07792i	0.644897	+	0.644897i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	7.55339	+	0.413879i	0.936883	+	0.0513353i
$66$			0.520689i			0.0640923i
$67$	−10.4060	+	10.4060i	−1.27130	+	1.27130i	−0.325890	+	0.945408i	$0.605664\pi$
$67$	−10.4060	+	10.4060i	−1.27130	+	1.27130i	−0.945408	+	0.325890i	$0.894336\pi$
$68$	−0.110114	+	0.110114i	−0.0133533	+	0.0133533i
$69$	−1.13488			−0.136624
$70$		0			0
$71$	3.05910			0.363048			0.181524	−	0.983387i	$-0.441897\pi$
$71$	3.05910			0.363048			0.181524	+	0.983387i	$0.441897\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	3.22403	−	3.22403i	0.377345	−	0.377345i	−0.492799	−	0.870143i	$-0.664026\pi$
$73$	3.22403	−	3.22403i	0.377345	−	0.377345i	0.870143	+	0.492799i	$0.164026\pi$
$74$			6.24274i			0.725703i
$75$	−3.12808	−	3.90066i	−0.361199	−	0.450409i
$76$		−	6.73985i		−	0.773114i
$77$		0			0
$78$	−2.39217	−	2.39217i	−0.270860	−	0.270860i
$79$			2.29777i			0.258519i	0.991611	+	0.129260i	$0.0412601\pi$
$79$			2.29777i			0.258519i	−0.991611	+	0.129260i	$0.958740\pi$
$80$	−1.49226	−	1.66528i	−0.166840	−	0.186184i
$81$	−1.00000			−0.111111
$82$	0.871887	+	0.871887i	0.0962838	+	0.0962838i
$83$	−3.43683	+	3.43683i	−0.377241	+	0.377241i	−0.870106	−	0.492865i	$-0.835950\pi$
$83$	−3.43683	+	3.43683i	−0.377241	+	0.377241i	0.492865	+	0.870106i	$0.335950\pi$
$84$		0			0
$85$	0.0190513	−	0.347691i	0.00206640	−	0.0377124i
$86$	−8.87383			−0.956890
$87$	−0.850978	−	0.850978i	−0.0912344	−	0.0912344i
$88$	−0.368182	−	0.368182i	−0.0392484	−	0.0392484i
$89$	16.3024			1.72806			0.864028	−	0.503444i	$-0.167934\pi$
$89$	16.3024			1.72806			0.864028	+	0.503444i	$0.167934\pi$
$90$	−0.122339	+	2.23272i	−0.0128957	+	0.235349i
$91$		0			0
$92$	0.802483	−	0.802483i	0.0836647	−	0.0836647i
$93$	5.07792	+	5.07792i	0.526556	+	0.526556i
$94$	−10.7182			−1.10549
$95$	10.0576	+	11.2237i	1.03189	+	1.15153i
$96$			1.00000i			0.102062i
$97$	9.40700	+	9.40700i	0.955137	+	0.955137i	0.999036	−	0.0438993i	$-0.0139781\pi$
$97$	9.40700	+	9.40700i	0.955137	+	0.955137i	−0.0438993	+	0.999036i	$0.513978\pi$
$98$		0			0
$99$			0.520689i			0.0523312i
$100$	4.97007	+	0.546298i	0.497007	+	0.0546298i
$101$		−	3.60502i		−	0.358713i	−0.983784	−	0.179357i	$-0.942598\pi$
$101$		−	3.60502i		−	0.358713i	0.983784	−	0.179357i	$-0.0574016\pi$
$102$	−0.110114	+	0.110114i	−0.0109030	+	0.0109030i
$103$	−1.35152	+	1.35152i	−0.133169	+	0.133169i	−0.770549	−	0.637380i	$-0.780018\pi$
$103$	−1.35152	+	1.35152i	−0.133169	+	0.133169i	0.637380	+	0.770549i	$0.280018\pi$
$104$	3.38305			0.331735
$105$		0			0
$106$	−0.778323			−0.0755974
$107$	−8.81849	+	8.81849i	−0.852516	+	0.852516i	−0.990442	−	0.137927i	$-0.955956\pi$
$107$	−8.81849	+	8.81849i	−0.852516	+	0.852516i	0.137927	+	0.990442i	$0.455956\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$			4.51589i			0.432544i	0.976333	+	0.216272i	$0.0693898\pi$
$109$			4.51589i			0.432544i	−0.976333	+	0.216272i	$0.930610\pi$
$110$	1.16255	+	0.0637006i	0.110845	+	0.00607361i
$111$			6.24274i			0.592534i
$112$		0			0
$113$	10.1872	+	10.1872i	0.958330	+	0.958330i	0.999166	−	0.0408354i	$-0.0130019\pi$
$113$	10.1872	+	10.1872i	0.958330	+	0.958330i	−0.0408354	+	0.999166i	$0.513002\pi$
$114$		−	6.73985i		−	0.631245i
$115$	−0.138841	+	2.53387i	−0.0129469	+	0.236285i
$116$	1.20346			0.111739
$117$	−2.39217	−	2.39217i	−0.221157	−	0.221157i
$118$	6.31638	−	6.31638i	0.581470	−	0.581470i
$119$		0			0
$120$	−1.49226	−	1.66528i	−0.136224	−	0.152018i
$121$	−10.7289			−0.975353
$122$	10.9381	+	10.9381i	0.990290	+	0.990290i
$123$	0.871887	+	0.871887i	0.0786154	+	0.0786154i
$124$	−7.18127			−0.644897
$125$	−9.09176	+	6.50691i	−0.813192	+	0.581996i
$126$		0			0
$127$	−7.96610	+	7.96610i	−0.706877	+	0.706877i	−0.965877	−	0.259000i	$-0.916607\pi$
$127$	−7.96610	+	7.96610i	−0.706877	+	0.706877i	0.259000	+	0.965877i	$0.416607\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−8.87383			−0.781297
$130$	−5.63371	+	5.04840i	−0.494109	+	0.442774i
$131$			10.9412i			0.955939i	0.878376	+	0.477970i	$0.158627\pi$
$131$			10.9412i			0.955939i	−0.878376	+	0.477970i	$0.841373\pi$
$132$	−0.368182	−	0.368182i	−0.0320462	−	0.0320462i
$133$		0			0
$134$		−	14.7163i		−	1.27130i
$135$	−0.122339	+	2.23272i	−0.0105293	+	0.192162i
$136$		−	0.155725i		−	0.0133533i
$137$	13.4763	−	13.4763i	1.15136	−	1.15136i	0.165076	−	0.986281i	$-0.447213\pi$
$137$	13.4763	−	13.4763i	1.15136	−	1.15136i	0.986281	−	0.165076i	$-0.0527869\pi$
$138$	0.802483	−	0.802483i	0.0683119	−	0.0683119i
$139$	−14.6782			−1.24499			−0.622496	−	0.782623i	$-0.713881\pi$
$139$	−14.6782			−1.24499			−0.622496	+	0.782623i	$0.713881\pi$
$140$		0			0
$141$	−10.7182			−0.902631
$142$	−2.16311	+	2.16311i	−0.181524	+	0.181524i
$143$	−1.24558	+	1.24558i	−0.104160	+	0.104160i
$144$			1.00000i			0.0833333i
$145$	−2.00410	+	1.79589i	−0.166432	+	0.149140i
$146$			4.55947i			0.377345i
$147$		0			0
$148$	−4.41428	−	4.41428i	−0.362852	−	0.362852i
$149$			24.2631i			1.98771i	0.110704	+	0.993853i	$0.464689\pi$
$149$			24.2631i			1.98771i	−0.110704	+	0.993853i	$0.535311\pi$
$150$	4.97007	+	0.546298i	0.405804	+	0.0446050i
$151$	−4.41001			−0.358881			−0.179441	−	0.983769i	$-0.557429\pi$
$151$	−4.41001			−0.358881			−0.179441	+	0.983769i	$0.557429\pi$
$152$	4.76579	+	4.76579i	0.386557	+	0.386557i
$153$	−0.110114	+	0.110114i	−0.00890222	+	0.00890222i
$154$		0			0
$155$	11.9588	−	10.7163i	0.960554	−	0.860758i
$156$	3.38305			0.270860
$157$	6.41399	+	6.41399i	0.511892	+	0.511892i	0.915106	−	0.403214i	$-0.132107\pi$
$157$	6.41399	+	6.41399i	0.511892	+	0.511892i	−0.403214	+	0.915106i	$0.632107\pi$
$158$	−1.62477	−	1.62477i	−0.129260	−	0.129260i
$159$	−0.778323			−0.0617250
$160$	2.23272	+	0.122339i	0.176512	+	0.00967176i
$161$		0			0
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−2.77186	−	2.77186i	−0.217109	−	0.217109i	0.590170	−	0.807279i	$-0.299061\pi$
$163$	−2.77186	−	2.77186i	−0.217109	−	0.217109i	−0.807279	+	0.590170i	$0.799061\pi$
$164$	−1.23303			−0.0962838
$165$	1.16255	+	0.0637006i	0.0905045	+	0.00495908i
$166$		−	4.86041i		−	0.377241i
$167$	15.6204	+	15.6204i	1.20874	+	1.20874i	0.971435	+	0.237306i	$0.0762645\pi$
$167$	15.6204	+	15.6204i	1.20874	+	1.20874i	0.237306	+	0.971435i	$0.423736\pi$
$168$		0			0
$169$			1.55500i			0.119616i
$170$	0.232383	+	0.259326i	0.0178230	+	0.0198894i
$171$		−	6.73985i		−	0.515409i
$172$	6.27475	−	6.27475i	0.478445	−	0.478445i
$173$	2.59162	−	2.59162i	0.197037	−	0.197037i	−0.601691	−	0.798729i	$-0.705506\pi$
$173$	2.59162	−	2.59162i	0.197037	−	0.197037i	0.798729	+	0.601691i	$0.205506\pi$
$174$	1.20346			0.0912344
$175$		0			0
$176$	0.520689			0.0392484
$177$	6.31638	−	6.31638i	0.474768	−	0.474768i
$178$	−11.5276	+	11.5276i	−0.864028	+	0.864028i
$179$		−	6.58829i		−	0.492432i	−0.969215	−	0.246216i	$-0.920813\pi$
$179$		−	6.58829i		−	0.492432i	0.969215	−	0.246216i	$-0.0791872\pi$
$180$	−1.49226	−	1.66528i	−0.111227	−	0.124122i
$181$		−	19.4585i		−	1.44634i	−0.690670	−	0.723170i	$-0.742684\pi$
$181$		−	19.4585i		−	1.44634i	0.690670	−	0.723170i	$-0.257316\pi$
$182$		0			0
$183$	10.9381	+	10.9381i	0.808569	+	0.808569i
$184$			1.13488i			0.0836647i
$185$	13.9383	+	0.763731i	1.02476	+	0.0561506i
$186$	−7.18127			−0.526556
$187$	0.0573353	+	0.0573353i	0.00419277	+	0.00419277i
$188$	7.57888	−	7.57888i	0.552747	−	0.552747i
$189$		0			0
$190$	−15.0482	−	0.824547i	−1.09171	−	0.0598189i
$191$	−20.3636			−1.47346			−0.736730	−	0.676187i	$-0.763631\pi$
$191$	−20.3636			−1.47346			−0.736730	+	0.676187i	$0.763631\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−13.9167	−	13.9167i	−1.00175	−	1.00175i	−0.999998	−	0.00174987i	$-0.999443\pi$
$193$	−13.9167	−	13.9167i	−1.00175	−	1.00175i	−0.00174987	−	0.999998i	$-0.500557\pi$
$194$	−13.3035			−0.955137
$195$	−5.63371	+	5.04840i	−0.403438	+	0.361523i
$196$		0			0
$197$	1.01525	−	1.01525i	0.0723333	−	0.0723333i	−0.670015	−	0.742348i	$-0.733712\pi$
$197$	1.01525	−	1.01525i	0.0723333	−	0.0723333i	0.742348	+	0.670015i	$0.233712\pi$
$198$	−0.368182	−	0.368182i	−0.0261656	−	0.0261656i
$199$	14.0774			0.997922			0.498961	−	0.866624i	$-0.333715\pi$
$199$	14.0774			0.997922			0.498961	+	0.866624i	$0.333715\pi$
$200$	−3.90066	+	3.12808i	−0.275818	+	0.221188i
$201$		−	14.7163i		−	1.03801i
$202$	2.54914	+	2.54914i	0.179357	+	0.179357i
$203$		0			0
$204$		−	0.155725i		−	0.0109030i
$205$	2.05334	−	1.84001i	0.143412	−	0.128512i
$206$		−	1.91134i		−	0.133169i
$207$	0.802483	−	0.802483i	0.0557764	−	0.0557764i
$208$	−2.39217	+	2.39217i	−0.165867	+	0.165867i
$209$	−3.50936			−0.242748
$210$		0			0
$211$	5.66564			0.390039			0.195019	−	0.980799i	$-0.437523\pi$
$211$	5.66564			0.390039			0.195019	+	0.980799i	$0.437523\pi$
$212$	0.550357	−	0.550357i	0.0377987	−	0.0377987i
$213$	−2.16311	+	2.16311i	−0.148214	+	0.148214i
$214$		−	12.4712i		−	0.852516i
$215$	−1.08562	+	19.8128i	−0.0740385	+	1.35122i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	−3.19322	−	3.19322i	−0.216272	−	0.216272i
$219$			4.55947i			0.308101i
$220$	−0.867091	+	0.777005i	−0.0584593	+	0.0523857i
$221$	−0.526826			−0.0354381
$222$	−4.41428	−	4.41428i	−0.296267	−	0.296267i
$223$	5.13239	−	5.13239i	0.343691	−	0.343691i	−0.514062	−	0.857753i	$-0.671860\pi$
$223$	5.13239	−	5.13239i	0.343691	−	0.343691i	0.857753	+	0.514062i	$0.171860\pi$
$224$		0			0
$225$	4.97007	+	0.546298i	0.331338	+	0.0364198i
$226$	−14.4069			−0.958330
$227$	7.13182	+	7.13182i	0.473355	+	0.473355i	0.902999	−	0.429643i	$-0.141361\pi$
$227$	7.13182	+	7.13182i	0.473355	+	0.473355i	−0.429643	+	0.902999i	$0.641361\pi$
$228$	4.76579	+	4.76579i	0.315622	+	0.315622i
$229$	−10.8421			−0.716463			−0.358231	−	0.933633i	$-0.616620\pi$
$229$	−10.8421			−0.716463			−0.358231	+	0.933633i	$0.616620\pi$
$230$	−1.69354	−	1.88989i	−0.111669	−	0.124616i
$231$		0			0
$232$	−0.850978	+	0.850978i	−0.0558695	+	0.0558695i
$233$	−15.0490	−	15.0490i	−0.985893	−	0.985893i	0.0140088	−	0.999902i	$-0.495541\pi$
$233$	−15.0490	−	15.0490i	−0.985893	−	0.985893i	−0.999902	+	0.0140088i	$0.995541\pi$
$234$	3.38305			0.221157
$235$	−1.31125	+	23.9306i	−0.0855365	+	1.56106i
$236$			8.93272i			0.581470i
$237$	−1.62477	−	1.62477i	−0.105540	−	0.105540i
$238$		0			0
$239$		−	5.56033i		−	0.359668i	−0.983697	−	0.179834i	$-0.942444\pi$
$239$		−	5.56033i		−	0.359668i	0.983697	−	0.179834i	$-0.0575560\pi$
$240$	2.23272	+	0.122339i	0.144121	+	0.00789696i
$241$			11.1562i			0.718633i	0.933216	+	0.359317i	$0.116990\pi$
$241$			11.1562i			0.718633i	−0.933216	+	0.359317i	$0.883010\pi$
$242$	7.58647	−	7.58647i	0.487677	−	0.487677i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−15.4688			−0.990290
$245$		0			0
$246$	−1.23303			−0.0786154
$247$	16.1229	−	16.1229i	1.02588	−	1.02588i
$248$	5.07792	−	5.07792i	0.322448	−	0.322448i
$249$		−	4.86041i		−	0.308016i
$250$	1.82776	−	11.0299i	0.115598	−	0.697594i
$251$		−	12.6684i		−	0.799624i	−0.916597	−	0.399812i	$-0.869075\pi$
$251$		−	12.6684i		−	0.799624i	0.916597	−	0.399812i	$-0.130925\pi$
$252$		0			0
$253$	−0.417844	−	0.417844i	−0.0262696	−	0.0262696i
$254$		−	11.2658i		−	0.706877i
$255$	0.232383	+	0.259326i	0.0145524	+	0.0162396i
$256$	1.00000			0.0625000
$257$	−13.7801	−	13.7801i	−0.859580	−	0.859580i	0.131709	−	0.991288i	$-0.457954\pi$
$257$	−13.7801	−	13.7801i	−0.859580	−	0.859580i	−0.991288	+	0.131709i	$0.957954\pi$
$258$	6.27475	−	6.27475i	0.390649	−	0.390649i
$259$		0			0
$260$	0.413879	−	7.55339i	0.0256677	−	0.468441i
$261$	1.20346			0.0744926
$262$	−7.73662	−	7.73662i	−0.477970	−	0.477970i
$263$	−11.5451	−	11.5451i	−0.711900	−	0.711900i	0.255033	−	0.966932i	$-0.417914\pi$
$263$	−11.5451	−	11.5451i	−0.711900	−	0.711900i	−0.966932	+	0.255033i	$0.917914\pi$
$264$	0.520689			0.0320462
$265$	−0.0952193	+	1.73778i	−0.00584928	+	0.106751i
$266$		0			0
$267$	−11.5276	+	11.5276i	−0.705476	+	0.705476i
$268$	10.4060	+	10.4060i	0.635649	+	0.635649i
$269$	20.2777			1.23635			0.618175	−	0.786040i	$-0.287872\pi$
$269$	20.2777			1.23635			0.618175	+	0.786040i	$0.287872\pi$
$270$	−1.49226	−	1.66528i	−0.0908163	−	0.101346i
$271$		−	21.9453i		−	1.33308i	−0.745468	−	0.666541i	$-0.767774\pi$
$271$		−	21.9453i		−	1.33308i	0.745468	−	0.666541i	$-0.232226\pi$
$272$	0.110114	+	0.110114i	0.00667667	+	0.00667667i
$273$		0			0
$274$			19.0583i			1.15136i
$275$	0.284451	−	2.58786i	0.0171530	−	0.156054i
$276$			1.13488i			0.0683119i
$277$	15.2939	−	15.2939i	0.918922	−	0.918922i	−0.0780288	−	0.996951i	$-0.524863\pi$
$277$	15.2939	−	15.2939i	0.918922	−	0.918922i	0.996951	+	0.0780288i	$0.0248626\pi$
$278$	10.3791	−	10.3791i	0.622496	−	0.622496i
$279$	−7.18127			−0.429931
$280$		0			0
$281$	14.3335			0.855067			0.427534	−	0.904000i	$-0.359383\pi$
$281$	14.3335			0.855067			0.427534	+	0.904000i	$0.359383\pi$
$282$	7.57888	−	7.57888i	0.451316	−	0.451316i
$283$	16.8171	−	16.8171i	0.999674	−	0.999674i	−0.000325839	−	1.00000i	$-0.500104\pi$
$283$	16.8171	−	16.8171i	0.999674	−	0.999674i	1.00000		0.000325839i	$0.000103718\pi$
$284$		−	3.05910i		−	0.181524i
$285$	−15.0482	−	0.824547i	−0.891378	−	0.0488420i
$286$		−	1.76151i		−	0.104160i
$287$		0			0
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	16.9757i		−	0.998574i
$290$	0.147231	−	2.68700i	0.00864569	−	0.157786i
$291$	−13.3035			−0.779866
$292$	−3.22403	−	3.22403i	−0.188672	−	0.188672i
$293$	−2.72954	+	2.72954i	−0.159461	+	0.159461i	−0.782328	−	0.622867i	$-0.785968\pi$
$293$	−2.72954	+	2.72954i	−0.159461	+	0.159461i	0.622867	+	0.782328i	$0.285968\pi$
$294$		0			0
$295$	−13.3300	−	14.8754i	−0.776101	−	0.866082i
$296$	6.24274			0.362852
$297$	−0.368182	−	0.368182i	−0.0213641	−	0.0213641i
$298$	−17.1566	−	17.1566i	−0.993853	−	0.993853i
$299$	3.83936			0.222036
$300$	−3.90066	+	3.12808i	−0.225205	+	0.180600i
$301$		0			0
$302$	3.11835	−	3.11835i	0.179441	−	0.179441i
$303$	2.54914	+	2.54914i	0.146444	+	0.146444i
$304$	−6.73985			−0.386557
$305$	25.7599	−	23.0836i	1.47501	−	1.32176i
$306$		−	0.155725i		−	0.00890222i
$307$	10.8811	+	10.8811i	0.621015	+	0.621015i	0.945791	−	0.324776i	$-0.105289\pi$
$307$	10.8811	+	10.8811i	0.621015	+	0.621015i	−0.324776	+	0.945791i	$0.605289\pi$
$308$		0			0
$309$		−	1.91134i		−	0.108732i
$310$	−0.878550	+	16.0338i	−0.0498983	+	0.910656i
$311$		−	18.6832i		−	1.05943i	−0.848177	−	0.529714i	$-0.822299\pi$
$311$		−	18.6832i		−	1.05943i	0.848177	−	0.529714i	$-0.177701\pi$
$312$	−2.39217	+	2.39217i	−0.135430	+	0.135430i
$313$	−15.2868	+	15.2868i	−0.864061	+	0.864061i	−0.991807	−	0.127746i	$-0.959226\pi$
$313$	−15.2868	+	15.2868i	−0.864061	+	0.864061i	0.127746	+	0.991807i	$0.459226\pi$
$314$	−9.07075			−0.511892
$315$		0			0
$316$	2.29777			0.129260
$317$	11.9015	−	11.9015i	0.668456	−	0.668456i	−0.288902	−	0.957359i	$-0.593290\pi$
$317$	11.9015	−	11.9015i	0.668456	−	0.668456i	0.957359	+	0.288902i	$0.0932903\pi$
$318$	0.550357	−	0.550357i	0.0308625	−	0.0308625i
$319$		−	0.626630i		−	0.0350846i
$320$	−1.66528	+	1.49226i	−0.0930918	+	0.0834201i
$321$		−	12.4712i		−	0.696076i
$322$		0			0
$323$	−0.742155	−	0.742155i	−0.0412946	−	0.0412946i
$324$			1.00000i			0.0555556i
$325$	10.5824	+	13.1961i	0.587007	+	0.731988i
$326$	3.92000			0.217109
$327$	−3.19322	−	3.19322i	−0.176585	−	0.176585i
$328$	0.871887	−	0.871887i	0.0481419	−	0.0481419i
$329$		0			0
$330$	−0.867091	+	0.777005i	−0.0477318	+	0.0427727i
$331$	30.4989			1.67637			0.838187	−	0.545384i	$-0.183616\pi$
$331$	30.4989			1.67637			0.838187	+	0.545384i	$0.183616\pi$
$332$	3.43683	+	3.43683i	0.188621	+	0.188621i
$333$	−4.41428	−	4.41428i	−0.241901	−	0.241901i
$334$	−22.0906			−1.20874
$335$	−32.8574	−	1.80038i	−1.79519	−	0.0983655i
$336$		0			0
$337$	−3.07975	+	3.07975i	−0.167765	+	0.167765i	−0.785996	−	0.618231i	$-0.787849\pi$
$337$	−3.07975	+	3.07975i	−0.167765	+	0.167765i	0.618231	+	0.785996i	$0.287849\pi$
$338$	−1.09955	−	1.09955i	−0.0598079	−	0.0598079i
$339$	−14.4069			−0.782474
$340$	−0.347691	−	0.0190513i	−0.0188562	−	0.00103320i
$341$			3.73920i			0.202489i
$342$	4.76579	+	4.76579i	0.257705	+	0.257705i
$343$		0			0
$344$			8.87383i			0.478445i
$345$	−1.69354	−	1.88989i	−0.0911774	−	0.101749i
$346$			3.66511i			0.197037i
$347$	2.41587	−	2.41587i	0.129691	−	0.129691i	−0.639282	−	0.768972i	$-0.720768\pi$
$347$	2.41587	−	2.41587i	0.129691	−	0.129691i	0.768972	+	0.639282i	$0.220768\pi$
$348$	−0.850978	+	0.850978i	−0.0456172	+	0.0456172i
$349$	−23.4017			−1.25266			−0.626331	−	0.779557i	$-0.715444\pi$
$349$	−23.4017			−1.25266			−0.626331	+	0.779557i	$0.715444\pi$
$350$		0			0
$351$	3.38305			0.180574
$352$	−0.368182	+	0.368182i	−0.0196242	+	0.0196242i
$353$	−13.0484	+	13.0484i	−0.694495	+	0.694495i	−0.963218	−	0.268723i	$-0.913399\pi$
$353$	−13.0484	+	13.0484i	−0.694495	+	0.694495i	0.268723	+	0.963218i	$0.413399\pi$
$354$			8.93272i			0.474768i
$355$	4.56498	+	5.09425i	0.242284	+	0.270374i
$356$		−	16.3024i		−	0.864028i
$357$		0			0
$358$	4.65862	+	4.65862i	0.246216	+	0.246216i
$359$			27.0642i			1.42839i	0.699946	+	0.714196i	$0.253207\pi$
$359$			27.0642i			1.42839i	−0.699946	+	0.714196i	$0.746793\pi$
$360$	2.23272	+	0.122339i	0.117675	+	0.00644784i
$361$	26.4256			1.39082
$362$	13.7592	+	13.7592i	0.723170	+	0.723170i
$363$	7.58647	−	7.58647i	0.398186	−	0.398186i
$364$		0			0
$365$	10.1800	+	0.557802i	0.532847	+	0.0291967i
$366$	−15.4688			−0.808569
$367$	−10.2371	−	10.2371i	−0.534375	−	0.534375i	0.387496	−	0.921871i	$-0.373340\pi$
$367$	−10.2371	−	10.2371i	−0.534375	−	0.534375i	−0.921871	+	0.387496i	$0.873340\pi$
$368$	−0.802483	−	0.802483i	−0.0418323	−	0.0418323i
$369$	−1.23303			−0.0641892
$370$	−10.3959	+	9.31581i	−0.540456	+	0.484306i
$371$		0			0
$372$	5.07792	−	5.07792i	0.263278	−	0.263278i
$373$	−1.61493	−	1.61493i	−0.0836177	−	0.0836177i	0.664061	−	0.747679i	$-0.268832\pi$
$373$	−1.61493	−	1.61493i	−0.0836177	−	0.0836177i	−0.747679	+	0.664061i	$0.768832\pi$
$374$	−0.0810844			−0.00419277
$375$	1.82776	−	11.0299i	0.0943853	−	0.569583i
$376$			10.7182i			0.552747i
$377$	2.87890	+	2.87890i	0.148271	+	0.148271i
$378$		0			0
$379$		−	23.0995i		−	1.18654i	−0.805003	−	0.593271i	$-0.797836\pi$
$379$		−	23.0995i		−	1.18654i	0.805003	−	0.593271i	$-0.202164\pi$
$380$	11.2237	−	10.0576i	0.575765	−	0.515946i
$381$		−	11.2658i		−	0.577163i
$382$	14.3993	−	14.3993i	0.736730	−	0.736730i
$383$	−5.87675	+	5.87675i	−0.300288	+	0.300288i	−0.841126	−	0.540838i	$-0.818107\pi$
$383$	−5.87675	+	5.87675i	−0.300288	+	0.300288i	0.540838	+	0.841126i	$0.318107\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	19.6812			1.00175
$387$	6.27475	−	6.27475i	0.318963	−	0.318963i
$388$	9.40700	−	9.40700i	0.477568	−	0.477568i
$389$		−	3.50140i		−	0.177528i	−0.996053	−	0.0887641i	$-0.971708\pi$
$389$		−	3.50140i		−	0.177528i	0.996053	−	0.0887641i	$-0.0282917\pi$
$390$	0.413879	−	7.55339i	0.0209576	−	0.382481i
$391$		−	0.176730i		−	0.00893762i
$392$		0			0
$393$	−7.73662	−	7.73662i	−0.390261	−	0.390261i
$394$			1.43577i			0.0723333i
$395$	−3.82643	+	3.42888i	−0.192528	+	0.172526i
$396$	0.520689			0.0261656
$397$	4.03852	+	4.03852i	0.202687	+	0.202687i	0.801150	−	0.598463i	$-0.204222\pi$
$397$	4.03852	+	4.03852i	0.202687	+	0.202687i	−0.598463	+	0.801150i	$0.704222\pi$
$398$	−9.95424	+	9.95424i	−0.498961	+	0.498961i
$399$		0			0
$400$	0.546298	−	4.97007i	0.0273149	−	0.248503i
$401$	−10.4372			−0.521208			−0.260604	−	0.965446i	$-0.583922\pi$
$401$	−10.4372			−0.521208			−0.260604	+	0.965446i	$0.583922\pi$
$402$	10.4060	+	10.4060i	0.519005	+	0.519005i
$403$	−17.1788	−	17.1788i	−0.855739	−	0.855739i
$404$	−3.60502			−0.179357
$405$	−1.49226	−	1.66528i	−0.0741512	−	0.0827483i
$406$		0			0
$407$	−2.29847	+	2.29847i	−0.113931	+	0.113931i
$408$	0.110114	+	0.110114i	0.00545148	+	0.00545148i
$409$	26.7574			1.32307			0.661533	−	0.749916i	$-0.269906\pi$
$409$	26.7574			1.32307			0.661533	+	0.749916i	$0.269906\pi$
$410$	−0.150848	+	2.75302i	−0.00744987	+	0.135962i
$411$			19.0583i			0.940079i
$412$	1.35152	+	1.35152i	0.0665846	+	0.0665846i
$413$		0			0
$414$			1.13488i			0.0557764i
$415$	−10.8519	−	0.594619i	−0.532701	−	0.0291887i
$416$		−	3.38305i		−	0.165867i
$417$	10.3791	−	10.3791i	0.508266	−	0.508266i
$418$	2.48149	−	2.48149i	0.121374	−	0.121374i
$419$	18.8858			0.922634			0.461317	−	0.887235i	$-0.347377\pi$
$419$	18.8858			0.922634			0.461317	+	0.887235i	$0.347377\pi$
$420$		0			0
$421$	22.7291			1.10775			0.553873	−	0.832601i	$-0.313149\pi$
$421$	22.7291			1.10775			0.553873	+	0.832601i	$0.313149\pi$
$422$	−4.00621	+	4.00621i	−0.195019	+	0.195019i
$423$	7.57888	−	7.57888i	0.368498	−	0.368498i
$424$			0.778323i			0.0377987i
$425$	0.607431	−	0.487121i	0.0294647	−	0.0236288i
$426$		−	3.05910i		−	0.148214i
$427$		0			0
$428$	8.81849	+	8.81849i	0.426258	+	0.426258i
$429$		−	1.76151i		−	0.0850467i
$430$	−13.2421	−	14.7774i	−0.638591	−	0.712629i
$431$	−20.6568			−0.995002			−0.497501	−	0.867464i	$-0.665749\pi$
$431$	−20.6568			−0.995002			−0.497501	+	0.867464i	$0.665749\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−10.8821	+	10.8821i	−0.522960	+	0.522960i	−0.918464	−	0.395504i	$-0.870570\pi$
$433$	−10.8821	+	10.8821i	−0.522960	+	0.522960i	0.395504	+	0.918464i	$0.370570\pi$
$434$		0			0
$435$	0.147231	−	2.68700i	0.00705918	−	0.128832i
$436$	4.51589			0.216272
$437$	5.40862	+	5.40862i	0.258729	+	0.258729i
$438$	−3.22403	−	3.22403i	−0.154050	−	0.154050i
$439$	4.10589			0.195964			0.0979818	−	0.995188i	$-0.468761\pi$
$439$	4.10589			0.195964			0.0979818	+	0.995188i	$0.468761\pi$
$440$	0.0637006	−	1.16255i	0.00303681	−	0.0554225i
$441$		0			0
$442$	0.372522	−	0.372522i	0.0177191	−	0.0177191i
$443$	−8.62965	−	8.62965i	−0.410007	−	0.410007i	0.471734	−	0.881741i	$-0.343628\pi$
$443$	−8.62965	−	8.62965i	−0.410007	−	0.410007i	−0.881741	+	0.471734i	$0.843628\pi$
$444$	6.24274			0.296267
$445$	24.3275	+	27.1481i	1.15324	+	1.28694i
$446$			7.25830i			0.343691i
$447$	−17.1566	−	17.1566i	−0.811478	−	0.811478i
$448$		0			0
$449$		−	27.3827i		−	1.29227i	−0.763224	−	0.646135i	$-0.776384\pi$
$449$		−	27.3827i		−	1.29227i	0.763224	−	0.646135i	$-0.223616\pi$
$450$	−3.90066	+	3.12808i	−0.183879	+	0.147459i
$451$			0.642027i			0.0302319i
$452$	10.1872	−	10.1872i	0.479165	−	0.479165i
$453$	3.11835	−	3.11835i	0.146513	−	0.146513i
$454$	−10.0859			−0.473355
$455$		0			0
$456$	−6.73985			−0.315622
$457$	24.1968	−	24.1968i	1.13188	−	1.13188i	0.142015	−	0.989865i	$-0.454642\pi$
$457$	24.1968	−	24.1968i	1.13188	−	1.13188i	0.989865	−	0.142015i	$-0.0453581\pi$
$458$	7.66649	−	7.66649i	0.358231	−	0.358231i
$459$		−	0.155725i		−	0.00726864i
$460$	2.53387	+	0.138841i	0.118142	+	0.00647347i
$461$		−	33.4101i		−	1.55606i	−0.628224	−	0.778032i	$-0.716218\pi$
$461$		−	33.4101i		−	1.55606i	0.628224	−	0.778032i	$-0.283782\pi$
$462$		0			0
$463$	−12.4512	−	12.4512i	−0.578656	−	0.578656i	0.355877	−	0.934533i	$-0.384182\pi$
$463$	−12.4512	−	12.4512i	−0.578656	−	0.578656i	−0.934533	+	0.355877i	$0.884182\pi$
$464$		−	1.20346i		−	0.0558695i
$465$	−0.878550	+	16.0338i	−0.0407418	+	0.743547i
$466$	21.2825			0.985893
$467$	3.01728	+	3.01728i	0.139623	+	0.139623i	0.773464	−	0.633841i	$-0.218523\pi$
$467$	3.01728	+	3.01728i	0.139623	+	0.139623i	−0.633841	+	0.773464i	$0.718523\pi$
$468$	−2.39217	+	2.39217i	−0.110578	+	0.110578i
$469$		0			0
$470$	−15.9943	−	17.8487i	−0.737763	−	0.823299i
$471$	−9.07075			−0.417958
$472$	−6.31638	−	6.31638i	−0.290735	−	0.290735i
$473$	−3.26719	−	3.26719i	−0.150226	−	0.150226i
$474$	2.29777			0.105540
$475$	−3.68196	+	33.4975i	−0.168940	+	1.53697i
$476$		0			0
$477$	0.550357	−	0.550357i	0.0251991	−	0.0251991i
$478$	3.93175	+	3.93175i	0.179834	+	0.179834i
$479$	−20.4328			−0.933600			−0.466800	−	0.884363i	$-0.654593\pi$
$479$	−20.4328			−0.933600			−0.466800	+	0.884363i	$0.654593\pi$
$480$	−1.66528	+	1.49226i	−0.0760092	+	0.0681122i
$481$		−	21.1195i		−	0.962964i
$482$	−7.88862	−	7.88862i	−0.359317	−	0.359317i
$483$		0			0
$484$			10.7289i			0.487677i
$485$	−1.62754	+	29.7030i	−0.0739028	+	1.34874i
$486$			1.00000i			0.0453609i
$487$	−13.8180	+	13.8180i	−0.626154	+	0.626154i	−0.947098	−	0.320944i	$-0.896000\pi$
$487$	−13.8180	+	13.8180i	−0.626154	+	0.626154i	0.320944	+	0.947098i	$0.396000\pi$
$488$	10.9381	−	10.9381i	0.495145	−	0.495145i
$489$	3.92000			0.177269
$490$		0			0
$491$	−33.0270			−1.49049			−0.745245	−	0.666791i	$-0.767667\pi$
$491$	−33.0270			−1.49049			−0.745245	+	0.666791i	$0.767667\pi$
$492$	0.871887	−	0.871887i	0.0393077	−	0.0393077i
$493$	0.132519	−	0.132519i	0.00596835	−	0.00596835i
$494$			22.8012i			1.02588i
$495$	−0.867091	+	0.777005i	−0.0389728	+	0.0349238i
$496$			7.18127i			0.322448i
$497$		0			0
$498$	3.43683	+	3.43683i	0.154008	+	0.154008i
$499$			0.308432i			0.0138073i	0.999976	+	0.00690365i	$0.00219752\pi$
$499$			0.308432i			0.0138073i	−0.999976	+	0.00690365i	$0.997802\pi$
$500$	6.50691	+	9.09176i	0.290998	+	0.406596i
$501$	−22.0906			−0.986933
$502$	8.95793	+	8.95793i	0.399812	+	0.399812i
$503$	16.9253	−	16.9253i	0.754660	−	0.754660i	−0.220685	−	0.975345i	$-0.570829\pi$
$503$	16.9253	−	16.9253i	0.754660	−	0.754660i	0.975345	+	0.220685i	$0.0708292\pi$
$504$		0			0
$505$	6.00336	−	5.37965i	0.267146	−	0.239391i
$506$	0.590921			0.0262696
$507$	−1.09955	−	1.09955i	−0.0488329	−	0.0488329i
$508$	7.96610	+	7.96610i	0.353439	+	0.353439i
$509$	−36.1167			−1.60085			−0.800423	−	0.599436i	$-0.795392\pi$
$509$	−36.1167			−1.60085			−0.800423	+	0.599436i	$0.795392\pi$
$510$	−0.347691	−	0.0190513i	−0.0153960	−	0.000843606i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.76579	+	4.76579i	0.210415	+	0.210415i
$514$	19.4880			0.859580
$515$	−4.26748	−	0.233831i	−0.188048	−	0.0103038i
$516$			8.87383i			0.390649i
$517$	−3.94624	−	3.94624i	−0.173555	−	0.173555i
$518$		0			0
$519$			3.66511i			0.160880i
$520$	5.04840	+	5.63371i	0.221387	+	0.247054i
$521$			16.6972i			0.731520i	0.930709	+	0.365760i	$0.119191\pi$
$521$			16.6972i			0.731520i	−0.930709	+	0.365760i	$0.880809\pi$
$522$	−0.850978	+	0.850978i	−0.0372463	+	0.0372463i
$523$	−0.569211	+	0.569211i	−0.0248899	+	0.0248899i	−0.719442	−	0.694552i	$-0.755602\pi$
$523$	−0.569211	+	0.569211i	−0.0248899	+	0.0248899i	0.694552	+	0.719442i	$0.255602\pi$
$524$	10.9412			0.477970
$525$		0			0
$526$	16.3272			0.711900
$527$	−0.790761	+	0.790761i	−0.0344461	+	0.0344461i
$528$	−0.368182	+	0.368182i	−0.0160231	+	0.0160231i
$529$		−	21.7120i		−	0.944002i
$530$	−1.16146	−	1.29612i	−0.0504507	−	0.0563000i
$531$			8.93272i			0.387647i
$532$		0			0
$533$	−2.94963	−	2.94963i	−0.127763	−	0.127763i
$534$		−	16.3024i		−	0.705476i
$535$	−27.8448	−	1.52572i	−1.20383	−	0.0659626i
$536$	−14.7163			−0.635649
$537$	4.65862	+	4.65862i	0.201034	+	0.201034i
$538$	−14.3385	+	14.3385i	−0.618175	+	0.618175i
$539$		0			0
$540$	2.23272	+	0.122339i	0.0960809	+	0.00526464i
$541$	−1.10726			−0.0476046			−0.0238023	−	0.999717i	$-0.507577\pi$
$541$	−1.10726			−0.0476046			−0.0238023	+	0.999717i	$0.507577\pi$
$542$	15.5177	+	15.5177i	0.666541	+	0.666541i
$543$	13.7592	+	13.7592i	0.590466	+	0.590466i
$544$	−0.155725			−0.00667667
$545$	−7.52021	+	6.73890i	−0.322130	+	0.288663i
$546$		0			0
$547$	−29.2908	+	29.2908i	−1.25239	+	1.25239i	−0.297738	+	0.954648i	$0.596232\pi$
$547$	−29.2908	+	29.2908i	−1.25239	+	1.25239i	−0.954648	+	0.297738i	$0.903768\pi$
$548$	−13.4763	−	13.4763i	−0.575678	−	0.575678i
$549$	−15.4688			−0.660194
$550$	1.62875	+	2.03103i	0.0694503	+	0.0866033i
$551$			8.11117i			0.345548i
$552$	−0.802483	−	0.802483i	−0.0341560	−	0.0341560i
$553$		0			0
$554$			21.6289i			0.918922i
$555$	−10.3959	+	9.31581i	−0.441281	+	0.395434i
$556$			14.6782i			0.622496i
$557$	8.85186	−	8.85186i	0.375065	−	0.375065i	−0.494253	−	0.869318i	$-0.664558\pi$
$557$	8.85186	−	8.85186i	0.375065	−	0.375065i	0.869318	+	0.494253i	$0.164558\pi$
$558$	5.07792	−	5.07792i	0.214966	−	0.214966i
$559$	30.0206			1.26974
$560$		0			0
$561$	−0.0810844			−0.00342339
$562$	−10.1353	+	10.1353i	−0.427534	+	0.427534i
$563$	−27.9289	+	27.9289i	−1.17706	+	1.17706i	−0.196571	+	0.980490i	$0.562981\pi$
$563$	−27.9289	+	27.9289i	−1.17706	+	1.17706i	−0.980490	+	0.196571i	$0.937019\pi$
$564$			10.7182i			0.451316i
$565$	−1.76252	+	32.1665i	−0.0741499	+	1.35325i
$566$			23.7830i			0.999674i
$567$		0			0
$568$	2.16311	+	2.16311i	0.0907620	+	0.0907620i
$569$			6.99506i			0.293248i	0.989192	+	0.146624i	$0.0468408\pi$
$569$			6.99506i			0.293248i	−0.989192	+	0.146624i	$0.953159\pi$
$570$	11.2237	−	10.0576i	0.470110	−	0.421268i
$571$	−10.5916			−0.443243			−0.221622	−	0.975133i	$-0.571135\pi$
$571$	−10.5916			−0.443243			−0.221622	+	0.975133i	$0.571135\pi$
$572$	1.24558	+	1.24558i	0.0520802	+	0.0520802i
$573$	14.3993	−	14.3993i	0.601538	−	0.601538i
$574$		0			0
$575$	−4.42679	+	3.55000i	−0.184610	+	0.148045i
$576$	1.00000			0.0416667
$577$	−1.73829	−	1.73829i	−0.0723659	−	0.0723659i	0.669997	−	0.742363i	$-0.266295\pi$
$577$	−1.73829	−	1.73829i	−0.0723659	−	0.0723659i	−0.742363	+	0.669997i	$0.766295\pi$
$578$	12.0037	+	12.0037i	0.499287	+	0.499287i
$579$	19.6812			0.817924
$580$	1.79589	+	2.00410i	0.0745702	+	0.0832158i
$581$		0			0
$582$	9.40700	−	9.40700i	0.389933	−	0.389933i
$583$	−0.286565	−	0.286565i	−0.0118683	−	0.0118683i
$584$	4.55947			0.188672
$585$	0.413879	−	7.55339i	0.0171118	−	0.312294i
$586$		−	3.86015i		−	0.159461i
$587$	16.9754	+	16.9754i	0.700649	+	0.700649i	0.964550	−	0.263901i	$-0.0850091\pi$
$587$	16.9754	+	16.9754i	0.700649	+	0.700649i	−0.263901	+	0.964550i	$0.585009\pi$
$588$		0			0
$589$		−	48.4007i		−	1.99431i
$590$	19.9442	+	1.09282i	0.821091	+	0.0449907i
$591$			1.43577i			0.0590599i
$592$	−4.41428	+	4.41428i	−0.181426	+	0.181426i
$593$	30.4459	−	30.4459i	1.25026	−	1.25026i	0.294664	−	0.955601i	$-0.404792\pi$
$593$	30.4459	−	30.4459i	1.25026	−	1.25026i	0.955601	−	0.294664i	$-0.0952076\pi$
$594$	0.520689			0.0213641
$595$		0			0
$596$	24.2631			0.993853
$597$	−9.95424	+	9.95424i	−0.407400	+	0.407400i
$598$	−2.71484	+	2.71484i	−0.111018	+	0.111018i
$599$			30.2878i			1.23753i	0.785577	+	0.618764i	$0.212366\pi$
$599$			30.2878i			1.23753i	−0.785577	+	0.618764i	$0.787634\pi$
$600$	0.546298	−	4.97007i	0.0223025	−	0.202902i
$601$		−	15.5207i		−	0.633103i	−0.948575	−	0.316552i	$-0.897475\pi$
$601$		−	15.5207i		−	0.633103i	0.948575	−	0.316552i	$-0.102525\pi$
$602$		0			0
$603$	10.4060	+	10.4060i	0.423766	+	0.423766i
$604$			4.41001i			0.179441i
$605$	−16.0103	−	17.8666i	−0.650912	−	0.726379i
$606$	−3.60502			−0.146444
$607$	−2.40427	−	2.40427i	−0.0975864	−	0.0975864i	0.656628	−	0.754215i	$-0.271982\pi$
$607$	−2.40427	−	2.40427i	−0.0975864	−	0.0975864i	−0.754215	+	0.656628i	$0.771982\pi$
$608$	4.76579	−	4.76579i	0.193278	−	0.193278i
$609$		0			0
$610$	−1.89244	+	34.5375i	−0.0766228	+	1.39838i
$611$	36.2600			1.46692
$612$	0.110114	+	0.110114i	0.00445111	+	0.00445111i
$613$	33.2824	+	33.2824i	1.34427	+	1.34427i	0.891763	+	0.452502i	$0.149468\pi$
$613$	33.2824	+	33.2824i	1.34427	+	1.34427i	0.452502	+	0.891763i	$0.350532\pi$
$614$	−15.3881			−0.621015
$615$	−0.150848	+	2.75302i	−0.00608279	+	0.111012i
$616$		0			0
$617$	−29.8254	+	29.8254i	−1.20072	+	1.20072i	−0.226779	+	0.973946i	$0.572819\pi$
$617$	−29.8254	+	29.8254i	−1.20072	+	1.20072i	−0.973946	+	0.226779i	$0.927181\pi$
$618$	1.35152	+	1.35152i	0.0543661	+	0.0543661i
$619$	−3.30315			−0.132765			−0.0663824	−	0.997794i	$-0.521146\pi$
$619$	−3.30315			−0.132765			−0.0663824	+	0.997794i	$0.521146\pi$
$620$	−10.7163	−	11.9588i	−0.430379	−	0.480277i
$621$			1.13488i			0.0455413i
$622$	13.2110	+	13.2110i	0.529714	+	0.529714i
$623$		0			0
$624$		−	3.38305i		−	0.135430i
$625$	−24.4031	−	5.43027i	−0.976125	−	0.217211i
$626$		−	21.6188i		−	0.864061i
$627$	2.48149	−	2.48149i	0.0991013	−	0.0991013i
$628$	6.41399	−	6.41399i	0.255946	−	0.255946i
$629$	−0.972152			−0.0387622
$630$		0			0
$631$	−24.3148			−0.967957			−0.483979	−	0.875080i	$-0.660809\pi$
$631$	−24.3148			−0.967957			−0.483979	+	0.875080i	$0.660809\pi$
$632$	−1.62477	+	1.62477i	−0.0646299	+	0.0646299i
$633$	−4.00621	+	4.00621i	−0.159233	+	0.159233i
$634$			16.8313i			0.668456i
$635$	−25.1533	−	1.37824i	−0.998178	−	0.0546940i
$636$			0.778323i			0.0308625i
$637$		0			0
$638$	0.443095	+	0.443095i	0.0175423	+	0.0175423i
$639$		−	3.05910i		−	0.121016i
$640$	0.122339	−	2.23272i	0.00483588	−	0.0882560i
$641$	−42.0786			−1.66200			−0.831002	−	0.556269i	$-0.812232\pi$
$641$	−42.0786			−1.66200			−0.831002	+	0.556269i	$0.812232\pi$
$642$	8.81849	+	8.81849i	0.348038	+	0.348038i
$643$	10.7495	−	10.7495i	0.423918	−	0.423918i	−0.462632	−	0.886550i	$-0.653095\pi$
$643$	10.7495	−	10.7495i	0.423918	−	0.423918i	0.886550	+	0.462632i	$0.153095\pi$
$644$		0			0
$645$	−13.2421	−	14.7774i	−0.521407	−	0.581859i
$646$	1.04957			0.0412946
$647$	−26.2046	−	26.2046i	−1.03021	−	1.03021i	−0.999529	−	0.0306789i	$-0.990233\pi$
$647$	−26.2046	−	26.2046i	−1.03021	−	1.03021i	−0.0306789	−	0.999529i	$-0.509767\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	4.65116			0.182574
$650$	−16.8140	−	1.84815i	−0.659498	−	0.0724904i
$651$		0			0
$652$	−2.77186	+	2.77186i	−0.108554	+	0.108554i
$653$	−1.25509	−	1.25509i	−0.0491153	−	0.0491153i	0.682123	−	0.731238i	$-0.261057\pi$
$653$	−1.25509	−	1.25509i	−0.0491153	−	0.0491153i	−0.731238	+	0.682123i	$0.761057\pi$
$654$	4.51589			0.176585
$655$	−18.2202	+	16.3272i	−0.711921	+	0.637956i
$656$			1.23303i			0.0481419i
$657$	−3.22403	−	3.22403i	−0.125782	−	0.125782i
$658$		0			0
$659$			24.6311i			0.959491i	0.877408	+	0.479746i	$0.159271\pi$
$659$			24.6311i			0.959491i	−0.877408	+	0.479746i	$0.840729\pi$
$660$	0.0637006	−	1.16255i	0.00247954	−	0.0452522i
$661$			28.9577i			1.12632i	0.826347	+	0.563162i	$0.190415\pi$
$661$			28.9577i			1.12632i	−0.826347	+	0.563162i	$0.809585\pi$
$662$	−21.5660	+	21.5660i	−0.838187	+	0.838187i
$663$	0.372522	−	0.372522i	0.0144676	−	0.0144676i
$664$	−4.86041			−0.188621
$665$		0			0
$666$	6.24274			0.241901
$667$	−0.965760	+	0.965760i	−0.0373944	+	0.0373944i
$668$	15.6204	−	15.6204i	0.604371	−	0.604371i
$669$			7.25830i			0.280622i
$670$	24.5068	−	21.9607i	0.946780	−	0.848414i
$671$			8.05444i			0.310938i
$672$		0			0
$673$	3.98937	+	3.98937i	0.153779	+	0.153779i	0.779803	−	0.626025i	$-0.215319\pi$
$673$	3.98937	+	3.98937i	0.153779	+	0.153779i	−0.626025	+	0.779803i	$0.715319\pi$
$674$		−	4.35542i		−	0.167765i
$675$	−3.90066	+	3.12808i	−0.150136	+	0.120400i
$676$	1.55500			0.0598079
$677$	−25.9793	−	25.9793i	−0.998464	−	0.998464i	0.00153467	−	0.999999i	$-0.499511\pi$
$677$	−25.9793	−	25.9793i	−0.998464	−	0.998464i	−0.999999	+	0.00153467i	$0.999511\pi$
$678$	10.1872	−	10.1872i	0.391237	−	0.391237i
$679$		0			0
$680$	0.259326	−	0.232383i	0.00994469	−	0.00891149i
$681$	−10.0859			−0.386493
$682$	−2.64402	−	2.64402i	−0.101245	−	0.101245i
$683$	−12.8732	−	12.8732i	−0.492581	−	0.492581i	0.416538	−	0.909119i	$-0.363243\pi$
$683$	−12.8732	−	12.8732i	−0.492581	−	0.492581i	−0.909119	+	0.416538i	$0.863243\pi$
$684$	−6.73985			−0.257705
$685$	42.5519	+	2.33158i	1.62583	+	0.0890851i
$686$		0			0
$687$	7.66649	−	7.66649i	0.292495	−	0.292495i
$688$	−6.27475	−	6.27475i	−0.239222	−	0.239222i
$689$	2.63310			0.100313
$690$	2.53387	+	0.138841i	0.0964629	+	0.00528557i
$691$		−	16.3663i		−	0.622605i	−0.950311	−	0.311302i	$-0.899235\pi$
$691$		−	16.3663i		−	0.622605i	0.950311	−	0.311302i	$-0.100765\pi$
$692$	−2.59162	−	2.59162i	−0.0985187	−	0.0985187i
$693$		0			0
$694$			3.41655i			0.129691i
$695$	−21.9038	−	24.4434i	−0.830859	−	0.927189i
$696$		−	1.20346i		−	0.0456172i
$697$	−0.135775	+	0.135775i	−0.00514284	+	0.00514284i
$698$	16.5475	−	16.5475i	0.626331	−	0.626331i
$699$	21.2825			0.804978
$700$		0			0
$701$	−0.568822			−0.0214841			−0.0107421	−	0.999942i	$-0.503419\pi$
$701$	−0.568822			−0.0214841			−0.0107421	+	0.999942i	$0.503419\pi$
$702$	−2.39217	+	2.39217i	−0.0902868	+	0.0902868i
$703$	29.7516	−	29.7516i	1.12210	−	1.12210i
$704$		−	0.520689i		−	0.0196242i
$705$	−15.9943	−	17.8487i	−0.602381	−	0.672221i
$706$		−	18.4532i		−	0.694495i
$707$		0			0
$708$	−6.31638	−	6.31638i	−0.237384	−	0.237384i
$709$			38.1003i			1.43089i	0.698670	+	0.715444i	$0.253776\pi$
$709$			38.1003i			1.43089i	−0.698670	+	0.715444i	$0.746224\pi$
$710$	−6.83010	−	0.374247i	−0.256329	−	0.0140452i
$711$	2.29777			0.0861732
$712$	11.5276	+	11.5276i	0.432014	+	0.432014i
$713$	5.76285	−	5.76285i	0.215820	−	0.215820i
$714$		0			0
$715$	−3.93296	−	0.215502i	−0.147085	−	0.00805932i
$716$	−6.58829			−0.246216
$717$	3.93175	+	3.93175i	0.146834	+	0.146834i
$718$	−19.1372	−	19.1372i	−0.714196	−	0.714196i
$719$	43.4712			1.62120			0.810601	−	0.585600i	$-0.199141\pi$
$719$	43.4712			1.62120			0.810601	+	0.585600i	$0.199141\pi$
$720$	−1.66528	+	1.49226i	−0.0620612	+	0.0556134i
$721$		0			0
$722$	−18.6857	+	18.6857i	−0.695410	+	0.695410i
$723$	−7.88862	−	7.88862i	−0.293381	−	0.293381i
$724$	−19.4585			−0.723170
$725$	−5.98130	−	0.657450i	−0.222140	−	0.0244171i
$726$			10.7289i			0.398186i
$727$	13.7574	+	13.7574i	0.510235	+	0.510235i	0.914598	−	0.404364i	$-0.132507\pi$
$727$	13.7574	+	13.7574i	0.510235	+	0.510235i	−0.404364	+	0.914598i	$0.632507\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−7.59279	+	6.80394i	−0.281022	+	0.251825i
$731$		−	1.38188i		−	0.0511107i
$732$	10.9381	−	10.9381i	0.404284	−	0.404284i
$733$	−32.0037	+	32.0037i	−1.18208	+	1.18208i	−0.202880	+	0.979204i	$0.565030\pi$
$733$	−32.0037	+	32.0037i	−1.18208	+	1.18208i	−0.979204	+	0.202880i	$0.934970\pi$
$734$	14.4775			0.534375
$735$		0			0
$736$	1.13488			0.0418323
$737$	5.41830	−	5.41830i	0.199586	−	0.199586i
$738$	0.871887	−	0.871887i	0.0320946	−	0.0320946i
$739$			5.58520i			0.205455i	0.994710	+	0.102727i	$0.0327569\pi$
$739$			5.58520i			0.205455i	−0.994710	+	0.102727i	$0.967243\pi$
$740$	0.763731	−	13.9383i	0.0280753	−	0.512381i
$741$			22.8012i			0.837624i
$742$		0			0
$743$	6.87995	+	6.87995i	0.252401	+	0.252401i	0.821954	−	0.569554i	$-0.192884\pi$
$743$	6.87995	+	6.87995i	0.252401	+	0.252401i	−0.569554	+	0.821954i	$0.692884\pi$
$744$			7.18127i			0.263278i
$745$	−40.4047	+	36.2069i	−1.48031	+	1.32652i
$746$	2.28385			0.0836177
$747$	3.43683	+	3.43683i	0.125747	+	0.125747i
$748$	0.0573353	−	0.0573353i	0.00209639	−	0.00209639i
$749$		0			0
$750$	6.50691	+	9.09176i	0.237599	+	0.331984i
$751$	3.12662			0.114092			0.0570460	−	0.998372i	$-0.481832\pi$
$751$	3.12662			0.114092			0.0570460	+	0.998372i	$0.481832\pi$
$752$	−7.57888	−	7.57888i	−0.276373	−	0.276373i
$753$	8.95793	+	8.95793i	0.326445	+	0.326445i
$754$	−4.07138			−0.148271
$755$	−6.58090	−	7.34389i	−0.239503	−	0.267271i
$756$		0			0
$757$	9.34247	−	9.34247i	0.339558	−	0.339558i	−0.516643	−	0.856201i	$-0.672819\pi$
$757$	9.34247	−	9.34247i	0.339558	−	0.339558i	0.856201	+	0.516643i	$0.172819\pi$
$758$	16.3338	+	16.3338i	0.593271	+	0.593271i
$759$	0.590921			0.0214491
$760$	−0.824547	+	15.0482i	−0.0299095	+	0.545855i
$761$		−	17.5512i		−	0.636229i	−0.948052	−	0.318115i	$-0.896950\pi$
$761$		−	17.5512i		−	0.636229i	0.948052	−	0.318115i	$-0.103050\pi$
$762$	7.96610	+	7.96610i	0.288581	+	0.288581i
$763$		0			0
$764$			20.3636i			0.736730i
$765$	−0.347691	−	0.0190513i	−0.0125708	−	0.000688801i
$766$		−	8.31098i		−	0.300288i
$767$	−21.3686	+	21.3686i	−0.771576	+	0.771576i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	12.3991			0.447124			0.223562	−	0.974690i	$-0.428231\pi$
$769$	12.3991			0.447124			0.223562	+	0.974690i	$0.428231\pi$
$770$		0			0
$771$	19.4880			0.701844
$772$	−13.9167	+	13.9167i	−0.500874	+	0.500874i
$773$	−11.0543	+	11.0543i	−0.397595	+	0.397595i	−0.877384	−	0.479789i	$-0.840713\pi$
$773$	−11.0543	+	11.0543i	−0.397595	+	0.397595i	0.479789	+	0.877384i	$0.340713\pi$
$774$			8.87383i			0.318963i
$775$	35.6914	+	3.92311i	1.28207	+	0.140922i
$776$			13.3035i			0.477568i
$777$		0			0
$778$	2.47587	+	2.47587i	0.0887641	+	0.0887641i
$779$		−	8.31047i		−	0.297753i
$780$	5.04840	+	5.63371i	0.180762	+	0.201719i
$781$	−1.59284			−0.0569962
$782$	0.124967	+	0.124967i	0.00446881	+	0.00446881i
$783$	−0.850978	+	0.850978i	−0.0304115	+	0.0304115i
$784$		0			0
$785$	−1.10971	+	20.2524i	−0.0396071	+	0.722840i
$786$	10.9412			0.390261
$787$	5.45338	+	5.45338i	0.194392	+	0.194392i	0.797591	−	0.603199i	$-0.206107\pi$
$787$	5.45338	+	5.45338i	0.194392	+	0.194392i	−0.603199	+	0.797591i	$0.706107\pi$
$788$	−1.01525	−	1.01525i	−0.0361666	−	0.0361666i
$789$	16.3272			0.581264
$790$	0.281107	−	5.13028i	0.0100013	−	0.182527i
$791$		0			0
$792$	−0.368182	+	0.368182i	−0.0130828	+	0.0130828i
$793$	−37.0041	−	37.0041i	−1.31406	−	1.31406i
$794$	−5.71133			−0.202687
$795$	−1.16146	−	1.29612i	−0.0411928	−	0.0459688i
$796$		−	14.0774i		−	0.498961i
$797$	1.85423	+	1.85423i	0.0656804	+	0.0656804i	0.739184	−	0.673504i	$-0.235211\pi$
$797$	1.85423	+	1.85423i	0.0656804	+	0.0656804i	−0.673504	+	0.739184i	$0.735211\pi$
$798$		0			0
$799$		−	1.66909i		−	0.0590481i
$800$	3.12808	+	3.90066i	0.110594	+	0.137909i
$801$		−	16.3024i		−	0.576019i
$802$	7.38021	−	7.38021i	0.260604	−	0.260604i
$803$	−1.67872	+	1.67872i	−0.0592407	+	0.0592407i
$804$	−14.7163			−0.519005
$805$		0			0
$806$	24.2946			0.855739
$807$	−14.3385	+	14.3385i	−0.504738	+	0.504738i
$808$	2.54914	−	2.54914i	0.0896783	−	0.0896783i
$809$			27.6588i			0.972431i	0.873839	+	0.486216i	$0.161623\pi$
$809$			27.6588i			0.972431i	−0.873839	+	0.486216i	$0.838377\pi$
$810$	2.23272	+	0.122339i	0.0784497	+	0.00429856i
$811$		−	0.889404i		−	0.0312312i	−0.999878	−	0.0156156i	$-0.995029\pi$
$811$		−	0.889404i		−	0.0312312i	0.999878	−	0.0156156i	$-0.00497080\pi$
$812$		0			0
$813$	15.5177	+	15.5177i	0.544228	+	0.544228i
$814$		−	3.25052i		−	0.113931i
$815$	0.479570	−	8.75226i	0.0167986	−	0.306578i
$816$	−0.155725			−0.00545148
$817$	42.2908	+	42.2908i	1.47957	+	1.47957i
$818$	−18.9203	+	18.9203i	−0.661533	+	0.661533i
$819$		0			0
$820$	−1.84001	−	2.05334i	−0.0642560	−	0.0717059i
$821$	28.0880			0.980277			0.490139	−	0.871644i	$-0.336946\pi$
$821$	28.0880			0.980277			0.490139	+	0.871644i	$0.336946\pi$
$822$	−13.4763	−	13.4763i	−0.470039	−	0.470039i
$823$	−10.8863	−	10.8863i	−0.379471	−	0.379471i	0.491440	−	0.870911i	$-0.336471\pi$
$823$	−10.8863	−	10.8863i	−0.379471	−	0.379471i	−0.870911	+	0.491440i	$0.836471\pi$
$824$	−1.91134			−0.0665846
$825$	1.62875	+	2.03103i	0.0567059	+	0.0707113i
$826$		0			0
$827$	24.3451	−	24.3451i	0.846563	−	0.846563i	−0.143140	−	0.989702i	$-0.545720\pi$
$827$	24.3451	−	24.3451i	0.846563	−	0.846563i	0.989702	+	0.143140i	$0.0457198\pi$
$828$	−0.802483	−	0.802483i	−0.0278882	−	0.0278882i
$829$	8.78926			0.305264			0.152632	−	0.988283i	$-0.451225\pi$
$829$	8.78926			0.305264			0.152632	+	0.988283i	$0.451225\pi$
$830$	8.09394	−	7.25302i	0.280945	−	0.251756i
$831$			21.6289i			0.750297i
$832$	2.39217	+	2.39217i	0.0829337	+	0.0829337i
$833$		0			0
$834$			14.6782i			0.508266i
$835$	−2.70254	+	49.3220i	−0.0935252	+	1.70686i
$836$			3.50936i			0.121374i
$837$	5.07792	−	5.07792i	0.175519	−	0.175519i
$838$	−13.3543	+	13.3543i	−0.461317	+	0.461317i
$839$	30.7744			1.06245			0.531225	−	0.847231i	$-0.321732\pi$
$839$	30.7744			1.06245			0.531225	+	0.847231i	$0.321732\pi$
$840$		0			0
$841$	27.5517			0.950058
$842$	−16.0719	+	16.0719i	−0.553873	+	0.553873i
$843$	−10.1353	+	10.1353i	−0.349080	+	0.349080i
$844$		−	5.66564i		−	0.195019i
$845$	−2.58951	+	2.32048i	−0.0890820	+	0.0798268i
$846$			10.7182i			0.368498i
$847$		0			0
$848$	−0.550357	−	0.550357i	−0.0188994	−	0.0188994i
$849$			23.7830i			0.816230i
$850$	−0.0850724	+	0.773965i	−0.00291796	+	0.0265468i
$851$	7.08477			0.242863
$852$	2.16311	+	2.16311i	0.0741069	+	0.0741069i
$853$	−0.507425	+	0.507425i	−0.0173739	+	0.0173739i	−0.715740	−	0.698366i	$-0.753911\pi$
$853$	−0.507425	+	0.507425i	−0.0173739	+	0.0173739i	0.698366	+	0.715740i	$0.253911\pi$
$854$		0			0
$855$	11.2237	−	10.0576i	0.383843	−	0.343964i
$856$	−12.4712			−0.426258
$857$	−30.1460	−	30.1460i	−1.02977	−	1.02977i	−0.999543	−	0.0302232i	$-0.990378\pi$
$857$	−30.1460	−	30.1460i	−1.02977	−	1.02977i	−0.0302232	−	0.999543i	$-0.509622\pi$
$858$	1.24558	+	1.24558i	0.0425233	+	0.0425233i
$859$	31.9738			1.09093			0.545466	−	0.838133i	$-0.316353\pi$
$859$	31.9738			1.09093			0.545466	+	0.838133i	$0.316353\pi$
$860$	19.8128	+	1.08562i	0.675610	+	0.0370192i
$861$		0			0
$862$	14.6065	−	14.6065i	0.497501	−	0.497501i
$863$	−22.1192	−	22.1192i	−0.752946	−	0.752946i	0.222082	−	0.975028i	$-0.428715\pi$
$863$	−22.1192	−	22.1192i	−0.752946	−	0.752946i	−0.975028	+	0.222082i	$0.928715\pi$
$864$	1.00000			0.0340207
$865$	8.18315	+	0.448386i	0.278236	+	0.0152456i
$866$		−	15.3896i		−	0.522960i
$867$	12.0037	+	12.0037i	0.407666	+	0.407666i
$868$		0			0
$869$		−	1.19642i		−	0.0405859i
$870$	1.79589	+	2.00410i	0.0608863	+	0.0679455i
$871$			49.7860i			1.68694i
$872$	−3.19322	+	3.19322i	−0.108136	+	0.108136i
$873$	9.40700	−	9.40700i	0.318379	−	0.318379i
$874$	−7.64894			−0.258729
$875$		0			0
$876$	4.55947			0.154050
$877$	−18.6689	+	18.6689i	−0.630404	+	0.630404i	−0.948169	−	0.317765i	$-0.897068\pi$
$877$	−18.6689	+	18.6689i	−0.630404	+	0.630404i	0.317765	+	0.948169i	$0.397068\pi$
$878$	−2.90330	+	2.90330i	−0.0979818	+	0.0979818i
$879$		−	3.86015i		−	0.130200i
$880$	0.777005	+	0.867091i	0.0261928	+	0.0292296i
$881$			13.4845i			0.454306i	0.973859	+	0.227153i	$0.0729417\pi$
$881$			13.4845i			0.454306i	−0.973859	+	0.227153i	$0.927058\pi$
$882$		0			0
$883$	−11.6619	−	11.6619i	−0.392454	−	0.392454i	0.483107	−	0.875561i	$-0.339508\pi$
$883$	−11.6619	−	11.6619i	−0.392454	−	0.392454i	−0.875561	+	0.483107i	$0.839508\pi$
$884$			0.526826i			0.0177191i
$885$	19.9442	+	1.09282i	0.670418	+	0.0367348i
$886$	12.2042			0.410007
$887$	−19.4900	−	19.4900i	−0.654412	−	0.654412i	0.299641	−	0.954052i	$-0.403133\pi$
$887$	−19.4900	−	19.4900i	−0.654412	−	0.654412i	−0.954052	+	0.299641i	$0.903133\pi$
$888$	−4.41428	+	4.41428i	−0.148134	+	0.148134i
$889$		0			0
$890$	−36.3988	−	1.99443i	−1.22009	−	0.0668533i
$891$	0.520689			0.0174437
$892$	−5.13239	−	5.13239i	−0.171845	−	0.171845i
$893$	51.0805	+	51.0805i	1.70934	+	1.70934i
$894$	24.2631			0.811478
$895$	10.9713	−	9.83146i	0.366731	−	0.328630i
$896$		0			0
$897$	−2.71484	+	2.71484i	−0.0906458	+	0.0906458i
$898$	19.3625	+	19.3625i	0.646135	+	0.646135i
$899$	8.64240			0.288240
$900$	0.546298	−	4.97007i	0.0182099	−	0.165669i
$901$		−	0.121205i		−	0.00403791i
$902$	−0.453982	−	0.453982i	−0.0151159	−	0.0151159i
$903$		0			0
$904$			14.4069i			0.479165i
$905$	32.4038	−	29.0372i	1.07714	−	0.965230i
$906$			4.41001i			0.146513i
$907$	−31.1733	+	31.1733i	−1.03509	+	1.03509i	−0.0357317	+	0.999361i	$0.511376\pi$
$907$	−31.1733	+	31.1733i	−1.03509	+	1.03509i	−0.999361	+	0.0357317i	$0.988624\pi$
$908$	7.13182	−	7.13182i	0.236678	−	0.236678i
$909$	−3.60502			−0.119571
$910$		0			0
$911$	−49.8061			−1.65015			−0.825075	−	0.565023i	$-0.808867\pi$
$911$	−49.8061			−1.65015			−0.825075	+	0.565023i	$0.808867\pi$
$912$	4.76579	−	4.76579i	0.157811	−	0.157811i
$913$	1.78952	−	1.78952i	0.0592244	−	0.0592244i
$914$			34.2195i			1.13188i
$915$	−1.89244	+	34.5375i	−0.0625622	+	1.14178i
$916$			10.8421i			0.358231i
$917$		0			0
$918$	0.110114	+	0.110114i	0.00363432	+	0.00363432i
$919$		−	43.6834i		−	1.44098i	−0.693464	−	0.720491i	$-0.743917\pi$
$919$		−	43.6834i		−	1.44098i	0.693464	−	0.720491i	$-0.256083\pi$
$920$	−1.88989	+	1.69354i	−0.0623080	+	0.0558345i
$921$	−15.3881			−0.507057
$922$	23.6245	+	23.6245i	0.778032	+	0.778032i
$923$	7.31789	−	7.31789i	0.240871	−	0.240871i
$924$		0			0
$925$	19.5278	+	24.3508i	0.642069	+	0.800649i
$926$	17.6087			0.578656
$927$	1.35152	+	1.35152i	0.0443897	+	0.0443897i
$928$	0.850978	+	0.850978i	0.0279347	+	0.0279347i
$929$	13.1731			0.432195			0.216098	−	0.976372i	$-0.430667\pi$
$929$	13.1731			0.432195			0.216098	+	0.976372i	$0.430667\pi$
$930$	−10.7163	−	11.9588i	−0.351403	−	0.392145i
$931$		0			0
$932$	−15.0490	+	15.0490i	−0.492947	+	0.492947i
$933$	13.2110	+	13.2110i	0.432509	+	0.432509i
$934$	−4.26707			−0.139623
$935$	−0.00991979	+	0.181039i	−0.000324412	+	0.00592060i
$936$		−	3.38305i		−	0.110578i
$937$	−18.5202	−	18.5202i	−0.605028	−	0.605028i	0.336614	−	0.941643i	$-0.390718\pi$
$937$	−18.5202	−	18.5202i	−0.605028	−	0.605028i	−0.941643	+	0.336614i	$0.890718\pi$
$938$		0			0
$939$		−	21.6188i		−	0.705503i
$940$	23.9306	+	1.31125i	0.780531	+	0.0427682i
$941$		−	6.78475i		−	0.221176i	−0.993866	−	0.110588i	$-0.964727\pi$
$941$		−	6.78475i		−	0.221176i	0.993866	−	0.110588i	$-0.0352735\pi$
$942$	6.41399	−	6.41399i	0.208979	−	0.208979i
$943$	0.989490	−	0.989490i	0.0322222	−	0.0322222i
$944$	8.93272			0.290735
$945$		0			0
$946$	4.62050			0.150226
$947$	11.4669	−	11.4669i	0.372626	−	0.372626i	−0.495807	−	0.868433i	$-0.665128\pi$
$947$	11.4669	−	11.4669i	0.372626	−	0.372626i	0.868433	+	0.495807i	$0.165128\pi$
$948$	−1.62477	+	1.62477i	−0.0527701	+	0.0527701i
$949$		−	15.4249i		−	0.500714i
$950$	−21.0828	−	26.2898i	−0.684015	−	0.852955i
$951$			16.8313i			0.545792i
$952$		0			0
$953$	−32.0660	−	32.0660i	−1.03872	−	1.03872i	−0.999220	−	0.0395000i	$-0.987423\pi$
$953$	−32.0660	−	32.0660i	−1.03872	−	1.03872i	−0.0395000	−	0.999220i	$-0.512577\pi$
$954$			0.778323i			0.0251991i
$955$	−30.3879	−	33.9111i	−0.983330	−	1.09734i
$956$	−5.56033			−0.179834
$957$	0.443095	+	0.443095i	0.0143232	+	0.0143232i
$958$	14.4482	−	14.4482i	0.466800	−	0.466800i
$959$		0			0
$960$	0.122339	−	2.23272i	0.00394848	−	0.0720607i
$961$	−20.5706			−0.663568
$962$	14.9337	+	14.9337i	0.481482	+	0.481482i
$963$	8.81849	+	8.81849i	0.284172	+	0.284172i
$964$	11.1562			0.359317
$965$	2.40778	−	43.9427i	0.0775093	−	1.41456i
$966$		0			0
$967$	6.60036	−	6.60036i	0.212253	−	0.212253i	−0.592971	−	0.805224i	$-0.702045\pi$
$967$	6.60036	−	6.60036i	0.212253	−	0.212253i	0.805224	+	0.592971i	$0.202045\pi$
$968$	−7.58647	−	7.58647i	−0.243838	−	0.243838i
$969$	1.04957			0.0337169
$970$	−19.8524	−	22.1540i	−0.637421	−	0.711323i
$971$			35.0869i			1.12599i	0.826459	+	0.562996i	$0.190352\pi$
$971$			35.0869i			1.12599i	−0.826459	+	0.562996i	$0.809648\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$		0			0
$974$		−	19.5416i		−	0.626154i
$975$	−16.8140	−	1.84815i	−0.538478	−	0.0591882i
$976$			15.4688i			0.495145i
$977$	3.72737	−	3.72737i	0.119249	−	0.119249i	−0.644964	−	0.764213i	$-0.723128\pi$
$977$	3.72737	−	3.72737i	0.119249	−	0.119249i	0.764213	+	0.644964i	$0.223128\pi$
$978$	−2.77186	+	2.77186i	−0.0886343	+	0.0886343i
$979$	−8.48850			−0.271294
$980$		0			0
$981$	4.51589			0.144181
$982$	23.3536	−	23.3536i	0.745245	−	0.745245i
$983$	6.63843	−	6.63843i	0.211733	−	0.211733i	−0.593270	−	0.805003i	$-0.702163\pi$
$983$	6.63843	−	6.63843i	0.211733	−	0.211733i	0.805003	+	0.593270i	$0.202163\pi$
$984$			1.23303i			0.0393077i
$985$	3.20568	+	0.175651i	0.102141	+	0.00559672i
$986$			0.187410i			0.00596835i
$987$		0			0
$988$	−16.1229	−	16.1229i	−0.512938	−	0.512938i
$989$			10.0708i			0.320231i
$990$	0.0637006	−	1.16255i	0.00202454	−	0.0369483i
$991$	51.4831			1.63542			0.817708	−	0.575634i	$-0.195245\pi$
$991$	51.4831			1.63542			0.817708	+	0.575634i	$0.195245\pi$
$992$	−5.07792	−	5.07792i	−0.161224	−	0.161224i
$993$	−21.5660	+	21.5660i	−0.684377	+	0.684377i
$994$		0			0
$995$	21.0072	+	23.4428i	0.665974	+	0.743187i
$996$	−4.86041			−0.154008
$997$	3.32948	+	3.32948i	0.105446	+	0.105446i	0.757861	−	0.652416i	$-0.226244\pi$
$997$	3.32948	+	3.32948i	0.105446	+	0.105446i	−0.652416	+	0.757861i	$0.726244\pi$
$998$	−0.218094	−	0.218094i	−0.00690365	−	0.00690365i
$999$	6.24274			0.197511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.c.1273.4	yes	16
5.2	odd	4		1470.2.m.f.97.1	yes	16
7.6	odd	2		1470.2.m.f.1273.1	yes	16
35.27	even	4	inner	1470.2.m.c.97.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.4	✓	16	35.27	even	4	inner
1470.2.m.c.1273.4	yes	16	1.1	even	1	trivial
1470.2.m.f.97.1	yes	16	5.2	odd	4
1470.2.m.f.1273.1	yes	16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.49226 + 1.66528i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.49226 + 1.66528i) q^{5} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-2.23272 - 0.122339i) q^{10} -0.520689 q^{11} +(0.707107 + 0.707107i) q^{12} +(2.39217 - 2.39217i) q^{13} +(-2.23272 - 0.122339i) q^{15} -1.00000 q^{16} +(-0.110114 - 0.110114i) q^{17} +(0.707107 + 0.707107i) q^{18} +6.73985 q^{19} +(1.66528 - 1.49226i) q^{20} +(0.368182 - 0.368182i) q^{22} +(0.802483 + 0.802483i) q^{23} -1.00000 q^{24} +(-0.546298 + 4.97007i) q^{25} +3.38305i q^{26} +(0.707107 + 0.707107i) q^{27} +1.20346i q^{29} +(1.66528 - 1.49226i) q^{30} -7.18127i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.368182 - 0.368182i) q^{33} +0.155725 q^{34} -1.00000 q^{36} +(4.41428 - 4.41428i) q^{37} +(-4.76579 + 4.76579i) q^{38} +3.38305i q^{39} +(-0.122339 + 2.23272i) q^{40} -1.23303i q^{41} +(6.27475 + 6.27475i) q^{43} +0.520689i q^{44} +(1.66528 - 1.49226i) q^{45} -1.13488 q^{46} +(7.57888 + 7.57888i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-3.12808 - 3.90066i) q^{50} +0.155725 q^{51} +(-2.39217 - 2.39217i) q^{52} +(0.550357 + 0.550357i) q^{53} -1.00000 q^{54} +(-0.777005 - 0.867091i) q^{55} +(-4.76579 + 4.76579i) q^{57} +(-0.850978 - 0.850978i) q^{58} -8.93272 q^{59} +(-0.122339 + 2.23272i) q^{60} -15.4688i q^{61} +(5.07792 + 5.07792i) q^{62} +1.00000i q^{64} +(7.55339 + 0.413879i) q^{65} +0.520689i q^{66} +(-10.4060 + 10.4060i) q^{67} +(-0.110114 + 0.110114i) q^{68} -1.13488 q^{69} +3.05910 q^{71} +(0.707107 - 0.707107i) q^{72} +(3.22403 - 3.22403i) q^{73} +6.24274i q^{74} +(-3.12808 - 3.90066i) q^{75} -6.73985i q^{76} +(-2.39217 - 2.39217i) q^{78} +2.29777i q^{79} +(-1.49226 - 1.66528i) q^{80} -1.00000 q^{81} +(0.871887 + 0.871887i) q^{82} +(-3.43683 + 3.43683i) q^{83} +(0.0190513 - 0.347691i) q^{85} -8.87383 q^{86} +(-0.850978 - 0.850978i) q^{87} +(-0.368182 - 0.368182i) q^{88} +16.3024 q^{89} +(-0.122339 + 2.23272i) q^{90} +(0.802483 - 0.802483i) q^{92} +(5.07792 + 5.07792i) q^{93} -10.7182 q^{94} +(10.0576 + 11.2237i) q^{95} +1.00000i q^{96} +(9.40700 + 9.40700i) q^{97} +0.520689i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5}+O(q^{10}) \) 16 * q - 8 * q^5	\( 16 q - 8 q^{5} - 8 q^{13} - 16 q^{16} + 8 q^{17} + 48 q^{19} - 8 q^{22} - 8 q^{23} - 16 q^{24} + 8 q^{25} - 8 q^{33} - 16 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{47} + 8 q^{52} + 8 q^{53} - 16 q^{54} + 8 q^{57} + 24 q^{58} - 48 q^{59} + 8 q^{62} + 72 q^{65} - 48 q^{67} + 8 q^{68} - 16 q^{73} + 8 q^{78} + 8 q^{80} - 16 q^{81} + 16 q^{82} - 72 q^{85} + 24 q^{87} + 8 q^{88} + 64 q^{89} - 8 q^{92} + 8 q^{93} - 64 q^{94} + 48 q^{95} + 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 - 8 * q^13 - 16 * q^16 + 8 * q^17 + 48 * q^19 - 8 * q^22 - 8 * q^23 - 16 * q^24 + 8 * q^25 - 8 * q^33 - 16 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^47 + 8 * q^52 + 8 * q^53 - 16 * q^54 + 8 * q^57 + 24 * q^58 - 48 * q^59 + 8 * q^62 + 72 * q^65 - 48 * q^67 + 8 * q^68 - 16 * q^73 + 8 * q^78 + 8 * q^80 - 16 * q^81 + 16 * q^82 - 72 * q^85 + 24 * q^87 + 8 * q^88 + 64 * q^89 - 8 * q^92 + 8 * q^93 - 64 * q^94 + 48 * q^95 + 64 * q^97

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