LMFDB - Embedded newform 1470.2.m.f.97.1

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			97.1
Root			$-2.01595 + 0.967451i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.f.1273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-1.49226 + 1.66528i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

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

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
$5$	−1.49226	+	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	$-0.405437\pi$
$13$	−2.39217	−	2.39217i	−0.663470	−	0.663470i	−0.956196	+	0.292726i	$0.905437\pi$
$14$		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	$-0.743989\pi$
$17$	0.110114	−	0.110114i	0.0267067	−	0.0267067i	0.720334	+	0.693627i	$0.243989\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−6.73985			−1.54623			−0.773114	−	0.634267i	$-0.781302\pi$
$19$	−6.73985			−1.54623			−0.773114	+	0.634267i	$0.781302\pi$
$20$	−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	−0.618475	−	0.785804i	$-0.712249\pi$
$23$	0.802483	−	0.802483i	0.167329	−	0.167329i	0.785804	+	0.618475i	$0.212249\pi$
$24$	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	$-0.964358\pi$
$29$		−	1.20346i		−	0.223478i	0.993738	−	0.111739i	$-0.0356420\pi$
$30$	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	0.969761	−	0.244058i	$-0.0784786\pi$
$37$	4.41428	+	4.41428i	0.725703	+	0.725703i	−0.244058	+	0.969761i	$0.578479\pi$
$38$	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	−0.0422185	−	0.999108i	$-0.513443\pi$
$43$	6.27475	−	6.27475i	0.956890	−	0.956890i	0.999108	+	0.0422185i	$0.0134426\pi$
$44$		−	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	−0.111758	+	0.993736i	$0.535648\pi$
$47$	−7.57888	+	7.57888i	−1.10549	+	1.10549i	−0.993736	+	0.111758i	$0.964352\pi$
$48$	−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	−0.668297	−	0.743894i	$-0.732976\pi$
$53$	0.550357	−	0.550357i	0.0755974	−	0.0755974i	0.743894	+	0.668297i	$0.232976\pi$
$54$	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	$-0.302478\pi$
$59$	8.93272			1.16294			0.581470	+	0.813568i	$0.302478\pi$
$60$	−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	−0.945408	−	0.325890i	$-0.894336\pi$
$67$	−10.4060	−	10.4060i	−1.27130	−	1.27130i	−0.325890	−	0.945408i	$-0.605664\pi$
$68$	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	$-0.335974\pi$
$73$	−3.22403	−	3.22403i	−0.377345	−	0.377345i	−0.870143	+	0.492799i	$0.835974\pi$
$74$		−	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	$-0.958740\pi$
$79$		−	2.29777i		−	0.258519i	0.991611	−	0.129260i	$-0.0412601\pi$
$80$	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	$-0.164050\pi$
$83$	3.43683	+	3.43683i	0.377241	+	0.377241i	−0.492865	+	0.870106i	$0.664050\pi$
$84$		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	$-0.832066\pi$
$89$	−16.3024			−1.72806			−0.864028	+	0.503444i	$0.832066\pi$
$90$	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	$-0.986022\pi$
$97$	−9.40700	+	9.40700i	−0.955137	+	0.955137i	0.0438993	+	0.999036i	$0.486022\pi$
$98$		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	$-0.219982\pi$
$103$	1.35152	+	1.35152i	0.133169	+	0.133169i	−0.637380	+	0.770549i	$0.719982\pi$
$104$	−3.38305			−0.331735
$105$		0			0
$106$	−0.778323			−0.0755974
$107$	−8.81849	−	8.81849i	−0.852516	−	0.852516i	0.137927	−	0.990442i	$-0.455956\pi$
$107$	−8.81849	−	8.81849i	−0.852516	−	0.852516i	−0.990442	+	0.137927i	$0.955956\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	4.51589i		−	0.432544i	−0.976333	−	0.216272i	$-0.930610\pi$
$109$		−	4.51589i		−	0.432544i	0.976333	−	0.216272i	$-0.0693898\pi$
$110$	−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	−0.0408354	−	0.999166i	$-0.513002\pi$
$113$	10.1872	−	10.1872i	0.958330	−	0.958330i	0.999166	+	0.0408354i	$0.0130019\pi$
$114$			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	0.259000	−	0.965877i	$-0.416607\pi$
$127$	−7.96610	−	7.96610i	−0.706877	−	0.706877i	−0.965877	+	0.259000i	$0.916607\pi$
$128$	−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	0.986281	+	0.165076i	$0.0527869\pi$
$137$	13.4763	+	13.4763i	1.15136	+	1.15136i	0.165076	+	0.986281i	$0.447213\pi$
$138$	−0.802483	−	0.802483i	−0.0683119	−	0.0683119i
$139$	14.6782			1.24499			0.622496	−	0.782623i	$-0.286119\pi$
$139$	14.6782			1.24499			0.622496	+	0.782623i	$0.286119\pi$
$140$		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	$-0.535311\pi$
$149$		−	24.2631i		−	1.98771i	0.110704	−	0.993853i	$-0.464689\pi$
$150$	−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	$-0.867893\pi$
$157$	−6.41399	+	6.41399i	−0.511892	+	0.511892i	0.403214	+	0.915106i	$0.367893\pi$
$158$	−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	−0.807279	−	0.590170i	$-0.799061\pi$
$163$	−2.77186	+	2.77186i	−0.217109	+	0.217109i	0.590170	+	0.807279i	$0.299061\pi$
$164$	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	−0.237306	+	0.971435i	$0.576264\pi$
$167$	−15.6204	+	15.6204i	−1.20874	+	1.20874i	−0.971435	+	0.237306i	$0.923736\pi$
$168$		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	$-0.294494\pi$
$173$	−2.59162	−	2.59162i	−0.197037	−	0.197037i	−0.798729	+	0.601691i	$0.794494\pi$
$174$	−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	$0.0791872\pi$
$179$			6.58829i			0.492432i	−0.969215	+	0.246216i	$0.920813\pi$
$180$	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	−0.00174987	+	0.999998i	$0.500557\pi$
$193$	−13.9167	+	13.9167i	−1.00175	+	1.00175i	−0.999998	+	0.00174987i	$0.999443\pi$
$194$	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	0.742348	−	0.670015i	$-0.233712\pi$
$197$	1.01525	+	1.01525i	0.0723333	+	0.0723333i	−0.670015	+	0.742348i	$0.733712\pi$
$198$	−0.368182	+	0.368182i	−0.0261656	+	0.0261656i
$199$	−14.0774			−0.997922			−0.498961	−	0.866624i	$-0.666285\pi$
$199$	−14.0774			−0.997922			−0.498961	+	0.866624i	$0.666285\pi$
$200$	−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	$-0.328140\pi$
$223$	−5.13239	−	5.13239i	−0.343691	−	0.343691i	−0.857753	+	0.514062i	$0.828140\pi$
$224$		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	$-0.858639\pi$
$227$	−7.13182	+	7.13182i	−0.473355	+	0.473355i	0.429643	+	0.902999i	$0.358639\pi$
$228$	4.76579	−	4.76579i	0.315622	−	0.315622i
$229$	10.8421			0.716463			0.358231	−	0.933633i	$-0.383380\pi$
$229$	10.8421			0.716463			0.358231	+	0.933633i	$0.383380\pi$
$230$	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	−0.999902	−	0.0140088i	$-0.995541\pi$
$233$	−15.0490	+	15.0490i	−0.985893	+	0.985893i	0.0140088	+	0.999902i	$0.495541\pi$
$234$	−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	$0.0575560\pi$
$239$			5.56033i			0.359668i	−0.983697	+	0.179834i	$0.942444\pi$
$240$	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	$-0.542046\pi$
$257$	13.7801	−	13.7801i	0.859580	−	0.859580i	0.991288	+	0.131709i	$0.0420463\pi$
$258$	−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	−0.966932	−	0.255033i	$-0.917914\pi$
$263$	−11.5451	+	11.5451i	−0.711900	+	0.711900i	0.255033	+	0.966932i	$0.417914\pi$
$264$	−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	$-0.712128\pi$
$269$	−20.2777			−1.23635			−0.618175	+	0.786040i	$0.712128\pi$
$270$	−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	0.996951	−	0.0780288i	$-0.0248626\pi$
$277$	15.2939	+	15.2939i	0.918922	+	0.918922i	−0.0780288	+	0.996951i	$0.524863\pi$
$278$	−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	$-0.499896\pi$
$283$	−16.8171	−	16.8171i	−0.999674	−	0.999674i	−1.00000		0.000325839i	$0.999896\pi$
$284$			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	$-0.214032\pi$
$293$	2.72954	+	2.72954i	0.159461	+	0.159461i	−0.622867	+	0.782328i	$0.714032\pi$
$294$		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	$-0.894711\pi$
$307$	−10.8811	+	10.8811i	−0.621015	+	0.621015i	0.324776	+	0.945791i	$0.394711\pi$
$308$		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	$-0.0407743\pi$
$313$	15.2868	+	15.2868i	0.864061	+	0.864061i	−0.127746	+	0.991807i	$0.540774\pi$
$314$	9.07075			0.511892
$315$		0			0
$316$	2.29777			0.129260
$317$	11.9015	+	11.9015i	0.668456	+	0.668456i	0.957359	−	0.288902i	$-0.0932903\pi$
$317$	11.9015	+	11.9015i	0.668456	+	0.668456i	−0.288902	+	0.957359i	$0.593290\pi$
$318$	−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	0.618231	−	0.785996i	$-0.287849\pi$
$337$	−3.07975	−	3.07975i	−0.167765	−	0.167765i	−0.785996	+	0.618231i	$0.787849\pi$
$338$	−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	0.768972	−	0.639282i	$-0.220768\pi$
$347$	2.41587	+	2.41587i	0.129691	+	0.129691i	−0.639282	+	0.768972i	$0.720768\pi$
$348$	0.850978	+	0.850978i	0.0456172	+	0.0456172i
$349$	23.4017			1.25266			0.626331	−	0.779557i	$-0.284556\pi$
$349$	23.4017			1.25266			0.626331	+	0.779557i	$0.284556\pi$
$350$		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	$-0.0866015\pi$
$353$	13.0484	+	13.0484i	0.694495	+	0.694495i	−0.268723	+	0.963218i	$0.586601\pi$
$354$		−	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	$-0.746793\pi$
$359$		−	27.0642i		−	1.42839i	0.699946	−	0.714196i	$-0.253207\pi$
$360$	−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	$-0.626660\pi$
$367$	10.2371	−	10.2371i	0.534375	−	0.534375i	0.921871	+	0.387496i	$0.126660\pi$
$368$	−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	−0.747679	−	0.664061i	$-0.768832\pi$
$373$	−1.61493	+	1.61493i	−0.0836177	+	0.0836177i	0.664061	+	0.747679i	$0.268832\pi$
$374$	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	$0.202164\pi$
$379$			23.0995i			1.18654i	−0.805003	+	0.593271i	$0.797836\pi$
$380$	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	$-0.181893\pi$
$383$	5.87675	+	5.87675i	0.300288	+	0.300288i	−0.540838	+	0.841126i	$0.681893\pi$
$384$	−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	$0.0282917\pi$
$389$			3.50140i			0.177528i	−0.996053	+	0.0887641i	$0.971708\pi$
$390$	−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	$-0.795778\pi$
$397$	−4.03852	+	4.03852i	−0.202687	+	0.202687i	0.598463	+	0.801150i	$0.295778\pi$
$398$	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	$-0.730094\pi$
$409$	−26.7574			−1.32307			−0.661533	+	0.749916i	$0.730094\pi$
$410$	−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	$-0.652623\pi$
$419$	−18.8858			−0.922634			−0.461317	+	0.887235i	$0.652623\pi$
$420$		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	$-0.129430\pi$
$433$	10.8821	+	10.8821i	0.522960	+	0.522960i	−0.395504	+	0.918464i	$0.629430\pi$
$434$		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	$-0.531239\pi$
$439$	−4.10589			−0.195964			−0.0979818	+	0.995188i	$0.531239\pi$
$440$	−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	−0.881741	−	0.471734i	$-0.843628\pi$
$443$	−8.62965	+	8.62965i	−0.410007	+	0.410007i	0.471734	+	0.881741i	$0.343628\pi$
$444$	−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	$0.223616\pi$
$449$			27.3827i			1.29227i	−0.763224	+	0.646135i	$0.776384\pi$
$450$	−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	0.989865	+	0.142015i	$0.0453581\pi$
$457$	24.1968	+	24.1968i	1.13188	+	1.13188i	0.142015	+	0.989865i	$0.454642\pi$
$458$	−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	−0.934533	−	0.355877i	$-0.884182\pi$
$463$	−12.4512	+	12.4512i	−0.578656	+	0.578656i	0.355877	+	0.934533i	$0.384182\pi$
$464$			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	$-0.781477\pi$
$467$	−3.01728	+	3.01728i	−0.139623	+	0.139623i	0.633841	+	0.773464i	$0.281477\pi$
$468$	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	$-0.345407\pi$
$479$	20.4328			0.933600			0.466800	+	0.884363i	$0.345407\pi$
$480$	−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	0.320944	−	0.947098i	$-0.396000\pi$
$487$	−13.8180	−	13.8180i	−0.626154	−	0.626154i	−0.947098	+	0.320944i	$0.896000\pi$
$488$	−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	$-0.997802\pi$
$499$		−	0.308432i		−	0.0138073i	0.999976	−	0.00690365i	$-0.00219752\pi$
$500$	−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	$-0.429171\pi$
$503$	−16.9253	−	16.9253i	−0.754660	−	0.754660i	−0.975345	+	0.220685i	$0.929171\pi$
$504$		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	$-0.204608\pi$
$509$	36.1167			1.60085			0.800423	+	0.599436i	$0.204608\pi$
$510$	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	$-0.244398\pi$
$523$	0.569211	+	0.569211i	0.0248899	+	0.0248899i	−0.694552	+	0.719442i	$0.744398\pi$
$524$	−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	−0.954648	−	0.297738i	$-0.903768\pi$
$547$	−29.2908	−	29.2908i	−1.25239	−	1.25239i	−0.297738	−	0.954648i	$-0.596232\pi$
$548$	−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	0.869318	−	0.494253i	$-0.164558\pi$
$557$	8.85186	+	8.85186i	0.375065	+	0.375065i	−0.494253	+	0.869318i	$0.664558\pi$
$558$	−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	0.980490	+	0.196571i	$0.0629807\pi$
$563$	27.9289	+	27.9289i	1.17706	+	1.17706i	0.196571	+	0.980490i	$0.437019\pi$
$564$		−	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	$-0.953159\pi$
$569$		−	6.99506i		−	0.293248i	0.989192	−	0.146624i	$-0.0468408\pi$
$570$	−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	$-0.733705\pi$
$577$	1.73829	−	1.73829i	0.0723659	−	0.0723659i	0.742363	+	0.669997i	$0.233705\pi$
$578$	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	$-0.914991\pi$
$587$	−16.9754	+	16.9754i	−0.700649	+	0.700649i	0.263901	+	0.964550i	$0.414991\pi$
$588$		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	−0.955601	−	0.294664i	$-0.904792\pi$
$593$	−30.4459	−	30.4459i	−1.25026	−	1.25026i	−0.294664	−	0.955601i	$-0.595208\pi$
$594$	−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	$-0.787634\pi$
$599$		−	30.2878i		−	1.23753i	0.785577	−	0.618764i	$-0.212366\pi$
$600$	−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	$-0.728018\pi$
$607$	2.40427	−	2.40427i	0.0975864	−	0.0975864i	0.754215	+	0.656628i	$0.228018\pi$
$608$	−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	0.452502	−	0.891763i	$-0.350532\pi$
$613$	33.2824	−	33.2824i	1.34427	−	1.34427i	0.891763	−	0.452502i	$-0.149468\pi$
$614$	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	−0.973946	−	0.226779i	$-0.927181\pi$
$617$	−29.8254	−	29.8254i	−1.20072	−	1.20072i	−0.226779	−	0.973946i	$-0.572819\pi$
$618$	1.35152	−	1.35152i	0.0543661	−	0.0543661i
$619$	3.30315			0.132765			0.0663824	−	0.997794i	$-0.478854\pi$
$619$	3.30315			0.132765			0.0663824	+	0.997794i	$0.478854\pi$
$620$	−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	$-0.346905\pi$
$643$	−10.7495	−	10.7495i	−0.423918	−	0.423918i	−0.886550	+	0.462632i	$0.846905\pi$
$644$		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	0.0306789	−	0.999529i	$-0.490233\pi$
$647$	26.2046	−	26.2046i	1.03021	−	1.03021i	0.999529	−	0.0306789i	$-0.00976694\pi$
$648$	−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	−0.731238	−	0.682123i	$-0.761057\pi$
$653$	−1.25509	+	1.25509i	−0.0491153	+	0.0491153i	0.682123	+	0.731238i	$0.261057\pi$
$654$	−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	$-0.840729\pi$
$659$		−	24.6311i		−	0.959491i	0.877408	−	0.479746i	$-0.159271\pi$
$660$	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	−0.626025	−	0.779803i	$-0.715319\pi$
$673$	3.98937	−	3.98937i	0.153779	−	0.153779i	0.779803	+	0.626025i	$0.215319\pi$
$674$			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	$-0.500489\pi$
$677$	25.9793	−	25.9793i	0.998464	−	0.998464i	0.999999	+	0.00153467i	$0.000488500\pi$
$678$	−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	−0.909119	−	0.416538i	$-0.863243\pi$
$683$	−12.8732	+	12.8732i	−0.492581	+	0.492581i	0.416538	+	0.909119i	$0.363243\pi$
$684$	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	$-0.746224\pi$
$709$		−	38.1003i		−	1.43089i	0.698670	−	0.715444i	$-0.253776\pi$
$710$	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	$-0.800859\pi$
$719$	−43.4712			−1.62120			−0.810601	+	0.585600i	$0.800859\pi$
$720$	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	$-0.867493\pi$
$727$	−13.7574	+	13.7574i	−0.510235	+	0.510235i	0.404364	+	0.914598i	$0.367493\pi$
$728$		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	0.979204	+	0.202880i	$0.0650302\pi$
$733$	32.0037	+	32.0037i	1.18208	+	1.18208i	0.202880	+	0.979204i	$0.434970\pi$
$734$	−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	$-0.967243\pi$
$739$		−	5.58520i		−	0.205455i	0.994710	−	0.102727i	$-0.0327569\pi$
$740$	−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	−0.569554	−	0.821954i	$-0.692884\pi$
$743$	6.87995	−	6.87995i	0.252401	−	0.252401i	0.821954	+	0.569554i	$0.192884\pi$
$744$		−	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	0.856201	−	0.516643i	$-0.172819\pi$
$757$	9.34247	+	9.34247i	0.339558	+	0.339558i	−0.516643	+	0.856201i	$0.672819\pi$
$758$	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	$-0.571769\pi$
$769$	−12.3991			−0.447124			−0.223562	+	0.974690i	$0.571769\pi$
$770$		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	$-0.159287\pi$
$773$	11.0543	+	11.0543i	0.397595	+	0.397595i	−0.479789	+	0.877384i	$0.659287\pi$
$774$		−	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	$-0.793893\pi$
$787$	−5.45338	+	5.45338i	−0.194392	+	0.194392i	0.603199	+	0.797591i	$0.293893\pi$
$788$	−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	$-0.764789\pi$
$797$	−1.85423	+	1.85423i	−0.0656804	+	0.0656804i	0.673504	+	0.739184i	$0.264789\pi$
$798$		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	$-0.838377\pi$
$809$		−	27.6588i		−	0.972431i	0.873839	−	0.486216i	$-0.161623\pi$
$810$	−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	−0.870911	−	0.491440i	$-0.836471\pi$
$823$	−10.8863	+	10.8863i	−0.379471	+	0.379471i	0.491440	+	0.870911i	$0.336471\pi$
$824$	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	0.989702	−	0.143140i	$-0.0457198\pi$
$827$	24.3451	+	24.3451i	0.846563	+	0.846563i	−0.143140	+	0.989702i	$0.545720\pi$
$828$	−0.802483	+	0.802483i	−0.0278882	+	0.0278882i
$829$	−8.78926			−0.305264			−0.152632	−	0.988283i	$-0.548775\pi$
$829$	−8.78926			−0.305264			−0.152632	+	0.988283i	$0.548775\pi$
$830$	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	$-0.678268\pi$
$839$	−30.7744			−1.06245			−0.531225	+	0.847231i	$0.678268\pi$
$840$		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	$-0.246089\pi$
$853$	0.507425	+	0.507425i	0.0173739	+	0.0173739i	−0.698366	+	0.715740i	$0.746089\pi$
$854$		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	0.0302232	−	0.999543i	$-0.490378\pi$
$857$	30.1460	−	30.1460i	1.02977	−	1.02977i	0.999543	−	0.0302232i	$-0.00962181\pi$
$858$	1.24558	−	1.24558i	0.0425233	−	0.0425233i
$859$	−31.9738			−1.09093			−0.545466	−	0.838133i	$-0.683647\pi$
$859$	−31.9738			−1.09093			−0.545466	+	0.838133i	$0.683647\pi$
$860$	−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	−0.975028	−	0.222082i	$-0.928715\pi$
$863$	−22.1192	+	22.1192i	−0.752946	+	0.752946i	0.222082	+	0.975028i	$0.428715\pi$
$864$	−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	0.317765	−	0.948169i	$-0.397068\pi$
$877$	−18.6689	−	18.6689i	−0.630404	−	0.630404i	−0.948169	+	0.317765i	$0.897068\pi$
$878$	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	−0.875561	−	0.483107i	$-0.839508\pi$
$883$	−11.6619	+	11.6619i	−0.392454	+	0.392454i	0.483107	+	0.875561i	$0.339508\pi$
$884$		−	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	$-0.596867\pi$
$887$	19.4900	−	19.4900i	0.654412	−	0.654412i	0.954052	+	0.299641i	$0.0968667\pi$
$888$	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	−0.999361	−	0.0357317i	$-0.988624\pi$
$907$	−31.1733	−	31.1733i	−1.03509	−	1.03509i	−0.0357317	−	0.999361i	$-0.511376\pi$
$908$	−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	$0.256083\pi$
$919$			43.6834i			1.44098i	−0.693464	+	0.720491i	$0.743917\pi$
$920$	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	$-0.569333\pi$
$929$	−13.1731			−0.432195			−0.216098	+	0.976372i	$0.569333\pi$
$930$	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	$-0.609282\pi$
$937$	18.5202	−	18.5202i	0.605028	−	0.605028i	0.941643	+	0.336614i	$0.109282\pi$
$938$		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	0.868433	−	0.495807i	$-0.165128\pi$
$947$	11.4669	+	11.4669i	0.372626	+	0.372626i	−0.495807	+	0.868433i	$0.665128\pi$
$948$	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	−0.0395000	+	0.999220i	$0.512577\pi$
$953$	−32.0660	+	32.0660i	−1.03872	+	1.03872i	−0.999220	+	0.0395000i	$0.987423\pi$
$954$		−	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	0.805224	−	0.592971i	$-0.202045\pi$
$967$	6.60036	+	6.60036i	0.212253	+	0.212253i	−0.592971	+	0.805224i	$0.702045\pi$
$968$	−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	0.764213	−	0.644964i	$-0.223128\pi$
$977$	3.72737	+	3.72737i	0.119249	+	0.119249i	−0.644964	+	0.764213i	$0.723128\pi$
$978$	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	$-0.297837\pi$
$983$	−6.63843	−	6.63843i	−0.211733	−	0.211733i	−0.805003	+	0.593270i	$0.797837\pi$
$984$		−	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	$-0.773756\pi$
$997$	−3.32948	+	3.32948i	−0.105446	+	0.105446i	0.652416	+	0.757861i	$0.273756\pi$
$998$	−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.f.97.1	yes	16
5.3	odd	4		1470.2.m.c.1273.4	yes	16
7.6	odd	2		1470.2.m.c.97.4	✓	16
35.13	even	4	inner	1470.2.m.f.1273.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.m.c.97.4	✓	16	7.6	odd	2
1470.2.m.c.1273.4	yes	16	5.3	odd	4
1470.2.m.f.97.1	yes	16	1.1	even	1	trivial
1470.2.m.f.1273.1	yes	16	35.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
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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