LMFDB - Embedded newform 450.2.l.c.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.4
Root			$-1.80334 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	450.19
Dual form			450.2.l.c.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.73558 - 1.40988i) q^{5} +2.61995i q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.73558 - 1.40988i) q^{5} +2.61995i q^{7} +(0.587785 - 0.809017i) q^{8} +(1.21496 - 1.87720i) q^{10} +(0.0883198 + 0.271820i) q^{11} +(2.66799 + 0.866884i) q^{13} +(0.809610 + 2.49172i) q^{14} +(0.309017 - 0.951057i) q^{16} +(3.81615 - 5.25248i) q^{17} +(-0.358647 - 0.260572i) q^{19} +(0.575410 - 2.16076i) q^{20} +(0.167994 + 0.231224i) q^{22} +(-6.20562 + 2.01633i) q^{23} +(1.02449 - 4.89392i) q^{25} +2.80530 q^{26} +(1.53997 + 2.11959i) q^{28} +(-5.87052 + 4.26518i) q^{29} +(-2.93409 - 2.13174i) q^{31} -1.00000i q^{32} +(2.00627 - 6.17466i) q^{34} +(3.69381 + 4.54714i) q^{35} +(4.31691 + 1.40265i) q^{37} +(-0.421615 - 0.136991i) q^{38} +(-0.120465 - 2.23282i) q^{40} +(-1.64523 + 5.06349i) q^{41} -8.05390i q^{43} +(0.231224 + 0.167994i) q^{44} +(-5.27882 + 3.83529i) q^{46} +(5.28799 + 7.27829i) q^{47} +0.135854 q^{49} +(-0.537954 - 4.97098i) q^{50} +(2.66799 - 0.866884i) q^{52} +(-8.17947 - 11.2581i) q^{53} +(0.536520 + 0.347247i) q^{55} +(2.11959 + 1.53997i) q^{56} +(-4.26518 + 5.87052i) q^{58} +(-1.15784 + 3.56347i) q^{59} +(4.02308 + 12.3818i) q^{61} +(-3.44923 - 1.12072i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(5.85272 - 2.25700i) q^{65} +(-6.01453 + 8.27829i) q^{67} -6.49242i q^{68} +(4.91817 + 3.18314i) q^{70} +(-3.89771 + 2.83185i) q^{71} +(-11.2098 + 3.64230i) q^{73} +4.53906 q^{74} -0.443312 q^{76} +(-0.712156 + 0.231394i) q^{77} +(-6.32216 + 4.59332i) q^{79} +(-0.804549 - 2.08631i) q^{80} +5.32407i q^{82} +(-3.03407 + 4.17604i) q^{83} +(-0.782111 - 14.4964i) q^{85} +(-2.48879 - 7.65972i) q^{86} +(0.271820 + 0.0883198i) q^{88} +(-1.90527 - 5.86383i) q^{89} +(-2.27119 + 6.99002i) q^{91} +(-3.83529 + 5.27882i) q^{92} +(7.27829 + 5.28799i) q^{94} +(-0.989836 + 0.0534036i) q^{95} +(-3.20367 - 4.40947i) q^{97} +(0.129205 - 0.0419811i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 - 4 * q^5	$ 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	1.73558	−	1.40988i	0.776176	−	0.630516i
$5$	1.73558	−	1.40988i	0.776176	−	0.630516i
$6$		0			0
$7$			2.61995i			0.990249i	0.868822	+	0.495124i	$0.164877\pi$
$7$			2.61995i			0.990249i	−0.868822	+	0.495124i	$0.835123\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$		0			0
$10$	1.21496	−	1.87720i	0.384204	−	0.593622i
$11$	0.0883198	+	0.271820i	0.0266294	+	0.0819569i	0.963488	−	0.267752i	$-0.0862806\pi$
$11$	0.0883198	+	0.271820i	0.0266294	+	0.0819569i	−0.936859	+	0.349708i	$0.886281\pi$
$12$		0			0
$13$	2.66799	+	0.866884i	0.739968	+	0.240430i	0.654659	−	0.755924i	$-0.272812\pi$
$13$	2.66799	+	0.866884i	0.739968	+	0.240430i	0.0853093	+	0.996355i	$0.472812\pi$
$14$	0.809610	+	2.49172i	0.216377	+	0.665941i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.81615	−	5.25248i	0.925553	−	1.27391i	−0.0360165	−	0.999351i	$-0.511467\pi$
$17$	3.81615	−	5.25248i	0.925553	−	1.27391i	0.961569	−	0.274563i	$-0.0885331\pi$
$18$		0			0
$19$	−0.358647	−	0.260572i	−0.0822792	−	0.0597794i	0.545885	−	0.837860i	$-0.316193\pi$
$19$	−0.358647	−	0.260572i	−0.0822792	−	0.0597794i	−0.628164	+	0.778081i	$0.716193\pi$
$20$	0.575410	−	2.16076i	0.128666	−	0.483162i
$21$		0			0
$22$	0.167994	+	0.231224i	0.0358165	+	0.0492972i
$23$	−6.20562	+	2.01633i	−1.29396	+	0.420434i	−0.873477	−	0.486866i	$-0.838140\pi$
$23$	−6.20562	+	2.01633i	−1.29396	+	0.420434i	−0.420485	+	0.907299i	$0.638140\pi$
$24$		0			0
$25$	1.02449	−	4.89392i	0.204898	−	0.978783i
$26$	2.80530			0.550164
$27$		0			0
$28$	1.53997	+	2.11959i	0.291027	+	0.400564i
$29$	−5.87052	+	4.26518i	−1.09013	+	0.792024i	−0.979421	−	0.201829i	$-0.935311\pi$
$29$	−5.87052	+	4.26518i	−1.09013	+	0.792024i	−0.110707	+	0.993853i	$0.535311\pi$
$30$		0			0
$31$	−2.93409	−	2.13174i	−0.526979	−	0.382872i	0.292248	−	0.956343i	$-0.405597\pi$
$31$	−2.93409	−	2.13174i	−0.526979	−	0.382872i	−0.819226	+	0.573470i	$0.805597\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	2.00627	−	6.17466i	0.344072	−	1.05895i
$35$	3.69381	+	4.54714i	0.624368	+	0.768607i
$36$		0			0
$37$	4.31691	+	1.40265i	0.709695	+	0.230594i	0.641550	−	0.767082i	$-0.278292\pi$
$37$	4.31691	+	1.40265i	0.709695	+	0.230594i	0.0681453	+	0.997675i	$0.478292\pi$
$38$	−0.421615	−	0.136991i	−0.0683949	−	0.0222229i
$39$		0			0
$40$	−0.120465	−	2.23282i	−0.0190472	−	0.353040i
$41$	−1.64523	+	5.06349i	−0.256941	+	0.790784i	0.736500	+	0.676438i	$0.236477\pi$
$41$	−1.64523	+	5.06349i	−0.256941	+	0.790784i	−0.993441	+	0.114346i	$0.963523\pi$
$42$		0			0
$43$		−	8.05390i		−	1.22821i	−0.789225	−	0.614104i	$-0.789517\pi$
$43$		−	8.05390i		−	1.22821i	0.789225	−	0.614104i	$-0.210483\pi$
$44$	0.231224	+	0.167994i	0.0348584	+	0.0253261i
$45$		0			0
$46$	−5.27882	+	3.83529i	−0.778319	+	0.565482i
$47$	5.28799	+	7.27829i	0.771332	+	1.06165i	0.996186	+	0.0872549i	$0.0278095\pi$
$47$	5.28799	+	7.27829i	0.771332	+	1.06165i	−0.224854	+	0.974392i	$0.572191\pi$
$48$		0			0
$49$	0.135854			0.0194077
$50$	−0.537954	−	4.97098i	−0.0760782	−	0.703002i
$51$		0			0
$52$	2.66799	−	0.866884i	0.369984	−	0.120215i
$53$	−8.17947	−	11.2581i	−1.12354	−	1.54642i	−0.799797	−	0.600270i	$-0.795060\pi$
$53$	−8.17947	−	11.2581i	−1.12354	−	1.54642i	−0.323740	−	0.946146i	$-0.604940\pi$
$54$		0			0
$55$	0.536520	+	0.347247i	0.0723443	+	0.0468227i
$56$	2.11959	+	1.53997i	0.283242	+	0.205787i
$57$		0			0
$58$	−4.26518	+	5.87052i	−0.560046	+	0.770837i
$59$	−1.15784	+	3.56347i	−0.150738	+	0.463924i	−0.997704	−	0.0677230i	$-0.978427\pi$
$59$	−1.15784	+	3.56347i	−0.150738	+	0.463924i	0.846966	+	0.531647i	$0.178427\pi$
$60$		0			0
$61$	4.02308	+	12.3818i	0.515102	+	1.58532i	0.783096	+	0.621901i	$0.213639\pi$
$61$	4.02308	+	12.3818i	0.515102	+	1.58532i	−0.267994	+	0.963421i	$0.586361\pi$
$62$	−3.44923	−	1.12072i	−0.438053	−	0.142332i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	5.85272	−	2.25700i	0.725941	−	0.279946i
$66$		0			0
$67$	−6.01453	+	8.27829i	−0.734792	+	1.01135i	0.264110	+	0.964493i	$0.414922\pi$
$67$	−6.01453	+	8.27829i	−0.734792	+	1.01135i	−0.998901	+	0.0468612i	$0.985078\pi$
$68$		−	6.49242i		−	0.787322i
$69$		0			0
$70$	4.91817	+	3.18314i	0.587833	+	0.380458i
$71$	−3.89771	+	2.83185i	−0.462573	+	0.336079i	−0.794540	−	0.607212i	$-0.792288\pi$
$71$	−3.89771	+	2.83185i	−0.462573	+	0.336079i	0.331967	+	0.943291i	$0.392288\pi$
$72$		0			0
$73$	−11.2098	+	3.64230i	−1.31201	+	0.426298i	−0.879744	−	0.475447i	$-0.842286\pi$
$73$	−11.2098	+	3.64230i	−1.31201	+	0.426298i	−0.432267	+	0.901745i	$0.642286\pi$
$74$	4.53906			0.527655
$75$		0			0
$76$	−0.443312			−0.0508514
$77$	−0.712156	+	0.231394i	−0.0811577	+	0.0263698i
$78$		0			0
$79$	−6.32216	+	4.59332i	−0.711299	+	0.516789i	−0.883592	−	0.468257i	$-0.844882\pi$
$79$	−6.32216	+	4.59332i	−0.711299	+	0.516789i	0.172294	+	0.985046i	$0.444882\pi$
$80$	−0.804549	−	2.08631i	−0.0899513	−	0.233257i
$81$		0			0
$82$			5.32407i			0.587945i
$83$	−3.03407	+	4.17604i	−0.333032	+	0.458380i	−0.942390	−	0.334516i	$-0.891427\pi$
$83$	−3.03407	+	4.17604i	−0.333032	+	0.458380i	0.609358	+	0.792895i	$0.291427\pi$
$84$		0			0
$85$	−0.782111	−	14.4964i	−0.0848318	−	1.57236i
$86$	−2.48879	−	7.65972i	−0.268373	−	0.825968i
$87$		0			0
$88$	0.271820	+	0.0883198i	0.0289762	+	0.00941492i
$89$	−1.90527	−	5.86383i	−0.201959	−	0.621565i	−0.999825	−	0.0187300i	$-0.994038\pi$
$89$	−1.90527	−	5.86383i	−0.201959	−	0.621565i	0.797866	−	0.602835i	$-0.205962\pi$
$90$		0			0
$91$	−2.27119	+	6.99002i	−0.238086	+	0.732753i
$92$	−3.83529	+	5.27882i	−0.399856	+	0.550355i
$93$		0			0
$94$	7.27829	+	5.28799i	0.750698	+	0.545414i
$95$	−0.989836	+	0.0534036i	−0.101555	+	0.00547910i
$96$		0			0
$97$	−3.20367	−	4.40947i	−0.325283	−	0.447714i	0.614788	−	0.788692i	$-0.289242\pi$
$97$	−3.20367	−	4.40947i	−0.325283	−	0.447714i	−0.940071	+	0.340979i	$0.889242\pi$
$98$	0.129205	−	0.0419811i	0.0130516	−	0.00424073i
$99$		0			0
$100$	−2.04774	−	4.56144i	−0.204774	−	0.456144i
$101$	−10.7765			−1.07230			−0.536152	−	0.844121i	$-0.680123\pi$
$101$	−10.7765			−1.07230			−0.536152	+	0.844121i	$0.680123\pi$
$102$		0			0
$103$	−10.5308	−	14.4945i	−1.03763	−	1.42818i	−0.899058	−	0.437829i	$-0.855748\pi$
$103$	−10.5308	−	14.4945i	−1.03763	−	1.42818i	−0.138576	−	0.990352i	$-0.544252\pi$
$104$	2.26953	−	1.64891i	0.222546	−	0.161689i
$105$		0			0
$106$	−11.2581	−	8.17947i	−1.09348	−	0.794461i
$107$		−	3.81291i		−	0.368608i	−0.982869	−	0.184304i	$-0.940997\pi$
$107$		−	3.81291i		−	0.368608i	0.982869	−	0.184304i	$-0.0590030\pi$
$108$		0			0
$109$	−2.46160	+	7.57602i	−0.235778	+	0.725651i	0.761239	+	0.648472i	$0.224591\pi$
$109$	−2.46160	+	7.57602i	−0.235778	+	0.725651i	−0.997017	+	0.0771796i	$0.975409\pi$
$110$	0.617566	+	0.164457i	0.0588826	+	0.0156804i
$111$		0			0
$112$	2.49172	+	0.809610i	0.235446	+	0.0765009i
$113$	4.99319	+	1.62239i	0.469720	+	0.152621i	0.534306	−	0.845291i	$-0.320573\pi$
$113$	4.99319	+	1.62239i	0.469720	+	0.152621i	−0.0645865	+	0.997912i	$0.520573\pi$
$114$		0			0
$115$	−7.92759	+	12.2487i	−0.739252	+	1.14219i
$116$	−2.24234	+	6.90121i	−0.208196	+	0.640761i
$117$		0			0
$118$			3.74685i			0.344926i
$119$	13.7612	+	9.99813i	1.26149	+	0.916527i
$120$		0			0
$121$	8.83310	−	6.41762i	0.803009	−	0.583420i
$122$	7.65235	+	10.5326i	0.692811	+	0.953572i
$123$		0			0
$124$	−3.62674			−0.325691
$125$	−5.12173	−	9.93820i	−0.458102	−	0.888900i
$126$		0			0
$127$	17.7838	−	5.77832i	1.57806	−	0.512743i	0.616505	−	0.787351i	$-0.288548\pi$
$127$	17.7838	−	5.77832i	1.57806	−	0.512743i	0.961556	+	0.274608i	$0.0885481\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$		0			0
$130$	4.86882	−	3.95512i	0.427024	−	0.346887i
$131$	3.68219	+	2.67527i	0.321714	+	0.233739i	0.736907	−	0.675995i	$-0.236286\pi$
$131$	3.68219	+	2.67527i	0.321714	+	0.233739i	−0.415192	+	0.909734i	$0.636286\pi$
$132$		0			0
$133$	0.682687	−	0.939637i	0.0591964	−	0.0814769i
$134$	−3.16202	+	9.73171i	−0.273157	+	0.840692i
$135$		0			0
$136$	−2.00627	−	6.17466i	−0.172036	−	0.529473i
$137$	14.7832	+	4.80334i	1.26301	+	0.410377i	0.862566	−	0.505944i	$-0.168856\pi$
$137$	14.7832	+	4.80334i	1.26301	+	0.410377i	0.400444	+	0.916321i	$0.368856\pi$
$138$		0			0
$139$	2.78145	+	8.56041i	0.235919	+	0.726085i	0.996998	+	0.0774254i	$0.0246700\pi$
$139$	2.78145	+	8.56041i	0.235919	+	0.726085i	−0.761079	+	0.648659i	$0.775330\pi$
$140$	5.66110	+	1.50755i	0.478450	+	0.127411i
$141$		0			0
$142$	−2.83185	+	3.89771i	−0.237644	+	0.327089i
$143$			0.801778i			0.0670481i
$144$		0			0
$145$	−4.17538	+	15.6793i	−0.346747	+	1.30209i
$146$	−9.53565	+	6.92806i	−0.789176	+	0.573370i
$147$		0			0
$148$	4.31691	−	1.40265i	0.354847	−	0.115297i
$149$	−7.87441			−0.645097			−0.322548	−	0.946553i	$-0.604540\pi$
$149$	−7.87441			−0.645097			−0.322548	+	0.946553i	$0.604540\pi$
$150$		0			0
$151$	17.7660			1.44578			0.722888	−	0.690965i	$-0.242814\pi$
$151$	17.7660			1.44578			0.722888	+	0.690965i	$0.242814\pi$
$152$	−0.421615	+	0.136991i	−0.0341975	+	0.0111114i
$153$		0			0
$154$	−0.605796	+	0.440137i	−0.0488165	+	0.0354672i
$155$	−8.09786	+	0.436896i	−0.650435	+	0.0350923i
$156$		0			0
$157$		−	20.1191i		−	1.60568i	−0.596194	−	0.802840i	$-0.703321\pi$
$157$		−	20.1191i		−	1.60568i	0.596194	−	0.802840i	$-0.296679\pi$
$158$	−4.59332	+	6.32216i	−0.365425	+	0.502964i
$159$		0			0
$160$	−1.40988	−	1.73558i	−0.111461	−	0.137210i
$161$	−5.28269	−	16.2584i	−0.416334	−	1.28134i
$162$		0			0
$163$	−2.01084	−	0.653363i	−0.157501	−	0.0511753i	0.229205	−	0.973378i	$-0.426387\pi$
$163$	−2.01084	−	0.653363i	−0.157501	−	0.0511753i	−0.386707	+	0.922203i	$0.626387\pi$
$164$	1.64523	+	5.06349i	0.128471	+	0.395392i
$165$		0			0
$166$	−1.59510	+	4.90923i	−0.123804	+	0.381030i
$167$	11.4476	−	15.7563i	0.885844	−	1.21926i	−0.0889243	−	0.996038i	$-0.528343\pi$
$167$	11.4476	−	15.7563i	0.885844	−	1.21926i	0.974768	−	0.223221i	$-0.0716571\pi$
$168$		0			0
$169$	−4.15052	−	3.01553i	−0.319270	−	0.231964i
$170$	−5.22347	−	13.5452i	−0.400622	−	1.03887i
$171$		0			0
$172$	−4.73397	−	6.51574i	−0.360961	−	0.496821i
$173$	3.14874	−	1.02309i	0.239394	−	0.0777838i	−0.186863	−	0.982386i	$-0.559832\pi$
$173$	3.14874	−	1.02309i	0.239394	−	0.0777838i	0.426257	+	0.904602i	$0.359832\pi$
$174$		0			0
$175$	12.8218	+	2.68412i	0.969239	+	0.202900i
$176$	0.285809			0.0215437
$177$		0			0
$178$	−3.62405	−	4.98807i	−0.271634	−	0.373872i
$179$	10.0806	−	7.32398i	0.753459	−	0.547420i	−0.143438	−	0.989659i	$-0.545816\pi$
$179$	10.0806	−	7.32398i	0.753459	−	0.547420i	0.896897	+	0.442239i	$0.145816\pi$
$180$		0			0
$181$	−4.90060	−	3.56050i	−0.364259	−	0.264650i	0.390567	−	0.920574i	$-0.372279\pi$
$181$	−4.90060	−	3.56050i	−0.364259	−	0.264650i	−0.754826	+	0.655925i	$0.772279\pi$
$182$			7.34974i			0.544799i
$183$		0			0
$184$	−2.01633	+	6.20562i	−0.148646	+	0.457485i
$185$	9.46991	−	3.65190i	0.696241	−	0.268493i
$186$		0			0
$187$	1.76477	+	0.573410i	0.129053	+	0.0419319i
$188$	8.55614	+	2.78006i	0.624021	+	0.202757i
$189$		0			0
$190$	−0.924887	+	0.356666i	−0.0670984	+	0.0258753i
$191$	−7.22123	+	22.2247i	−0.522510	+	1.60812i	0.246678	+	0.969098i	$0.420661\pi$
$191$	−7.22123	+	22.2247i	−0.522510	+	1.60812i	−0.769188	+	0.639023i	$0.779339\pi$
$192$		0			0
$193$			2.13291i			0.153530i	0.997049	+	0.0767650i	$0.0244591\pi$
$193$			2.13291i			0.153530i	−0.997049	+	0.0767650i	$0.975541\pi$
$194$	−4.40947	−	3.20367i	−0.316581	−	0.230010i
$195$		0			0
$196$	0.109908	−	0.0798529i	0.00785057	−	0.00570378i
$197$	9.67275	+	13.3134i	0.689155	+	0.948540i	0.999998	−	0.00192101i	$-0.000611477\pi$
$197$	9.67275	+	13.3134i	0.689155	+	0.948540i	−0.310843	+	0.950461i	$0.600611\pi$
$198$		0			0
$199$	−1.66552			−0.118065			−0.0590327	−	0.998256i	$-0.518802\pi$
$199$	−1.66552			−0.118065			−0.0590327	+	0.998256i	$0.518802\pi$
$200$	−3.35708	−	3.70540i	−0.237381	−	0.262012i
$201$		0			0
$202$	−10.2491	+	3.33013i	−0.721123	+	0.234307i
$203$	−11.1746	−	15.3805i	−0.784301	−	1.07950i
$204$		0			0
$205$	4.28347	+	11.1077i	0.299171	+	0.775794i
$206$	−14.4945	−	10.5308i	−1.00988	−	0.733718i
$207$		0			0
$208$	1.64891	−	2.26953i	0.114331	−	0.157364i
$209$	0.0391532	−	0.120501i	0.00270829	−	0.00833525i
$210$		0			0
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	−0.994727	−	0.102559i	$-0.967297\pi$
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	0.744468	−	0.667658i	$-0.232703\pi$
$212$	−13.2347	−	4.30020i	−0.908961	−	0.295339i
$213$		0			0
$214$	−1.17825	−	3.62629i	−0.0805437	−	0.247888i
$215$	−11.3550	−	13.9782i	−0.774406	−	0.953306i
$216$		0			0
$217$	5.58506	−	7.68718i	0.379139	−	0.521840i
$218$			7.96590i			0.539519i
$219$		0			0
$220$	0.638160	−	0.0344300i	0.0430247	−	0.00232127i
$221$	14.7348	−	10.7054i	0.991167	−	0.720125i
$222$		0			0
$223$	9.05554	−	2.94232i	0.606404	−	0.197033i	0.0103094	−	0.999947i	$-0.496718\pi$
$223$	9.05554	−	2.94232i	0.606404	−	0.197033i	0.596095	+	0.802914i	$0.296718\pi$
$224$	2.61995			0.175053
$225$		0			0
$226$	5.25015			0.349235
$227$	−15.5187	+	5.04232i	−1.03001	+	0.334671i	−0.774794	−	0.632213i	$-0.782147\pi$
$227$	−15.5187	+	5.04232i	−1.03001	+	0.334671i	−0.255216	+	0.966884i	$0.582147\pi$
$228$		0			0
$229$	−0.431759	+	0.313691i	−0.0285314	+	0.0207293i	−0.601960	−	0.798527i	$-0.705613\pi$
$229$	−0.431759	+	0.313691i	−0.0285314	+	0.0207293i	0.573428	+	0.819256i	$0.305613\pi$
$230$	−3.75454	+	14.0989i	−0.247567	+	0.929657i
$231$		0			0
$232$			7.25636i			0.476403i
$233$	6.43141	−	8.85208i	0.421336	−	0.579919i	−0.544602	−	0.838695i	$-0.683319\pi$
$233$	6.43141	−	8.85208i	0.421336	−	0.579919i	0.965937	+	0.258776i	$0.0833191\pi$
$234$		0			0
$235$	19.4392	+	5.17666i	1.26808	+	0.337688i
$236$	1.15784	+	3.56347i	0.0753690	+	0.231962i
$237$		0			0
$238$	16.1773	+	5.25633i	1.04862	+	0.340717i
$239$	1.86591	+	5.74268i	0.120696	+	0.371463i	0.993092	−	0.117336i	$-0.0374353\pi$
$239$	1.86591	+	5.74268i	0.120696	+	0.371463i	−0.872397	+	0.488798i	$0.837435\pi$
$240$		0			0
$241$	0.682003	−	2.09899i	0.0439317	−	0.135208i	−0.926685	−	0.375839i	$-0.877354\pi$
$241$	0.682003	−	2.09899i	0.0439317	−	0.135208i	0.970617	+	0.240631i	$0.0773545\pi$
$242$	6.41762	−	8.83310i	0.412540	−	0.567813i
$243$		0			0
$244$	10.5326	+	7.65235i	0.674277	+	0.489891i
$245$	0.235785	−	0.191537i	0.0150638	−	0.0122369i
$246$		0			0
$247$	−0.730982	−	1.00611i	−0.0465113	−	0.0640173i
$248$	−3.44923	+	1.12072i	−0.219027	+	0.0711660i
$249$		0			0
$250$	−7.94213	−	7.86909i	−0.502304	−	0.497685i
$251$	0.151651			0.00957211			0.00478606	−	0.999989i	$-0.498477\pi$
$251$	0.151651			0.00957211			0.00478606	+	0.999989i	$0.498477\pi$
$252$		0			0
$253$	−1.09616	−	1.50873i	−0.0689149	−	0.0948533i
$254$	15.1278	−	10.9910i	0.949205	−	0.689638i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$		−	10.4462i		−	0.651614i	−0.945436	−	0.325807i	$-0.894364\pi$
$257$		−	10.4462i		−	0.651614i	0.945436	−	0.325807i	$-0.105636\pi$
$258$		0			0
$259$	−3.67487	+	11.3101i	−0.228345	+	0.702774i
$260$	3.40832	−	5.26609i	0.211375	−	0.326589i
$261$		0			0
$262$	4.32867	+	1.40647i	0.267426	+	0.0868920i
$263$	20.8854	+	6.78608i	1.28785	+	0.418448i	0.871338	−	0.490683i	$-0.163253\pi$
$263$	20.8854	+	6.78608i	1.28785	+	0.418448i	0.416511	+	0.909131i	$0.363253\pi$
$264$		0			0
$265$	−30.0687	−	8.00727i	−1.84710	−	0.491883i
$266$	0.358910	−	1.10461i	0.0220062	−	0.0677280i
$267$		0			0
$268$			10.2325i			0.625051i
$269$	11.4313	+	8.30535i	0.696981	+	0.506386i	0.878948	−	0.476918i	$-0.158246\pi$
$269$	11.4313	+	8.30535i	0.696981	+	0.506386i	−0.181967	+	0.983305i	$0.558246\pi$
$270$		0			0
$271$	−22.2714	+	16.1811i	−1.35289	+	0.982934i	−0.354031	+	0.935234i	$0.615189\pi$
$271$	−22.2714	+	16.1811i	−1.35289	+	0.982934i	−0.998862	+	0.0477007i	$0.984811\pi$
$272$	−3.81615	−	5.25248i	−0.231388	−	0.318478i
$273$		0			0
$274$	15.5439			0.939043
$275$	1.42075	−	0.153752i	0.0856744	−	0.00927160i
$276$		0			0
$277$	22.4411	−	7.29155i	1.34835	−	0.438107i	0.456216	−	0.889869i	$-0.349205\pi$
$277$	22.4411	−	7.29155i	1.34835	−	0.438107i	0.892138	+	0.451763i	$0.149205\pi$
$278$	5.29063	+	7.28192i	0.317311	+	0.436741i
$279$		0			0
$280$	5.84988	−	0.315613i	0.349597	−	0.0188615i
$281$	5.80174	+	4.21521i	0.346103	+	0.251458i	0.747232	−	0.664563i	$-0.231382\pi$
$281$	5.80174	+	4.21521i	0.346103	+	0.251458i	−0.401130	+	0.916021i	$0.631382\pi$
$282$		0			0
$283$	13.5380	−	18.6334i	0.804748	−	1.10764i	−0.187365	−	0.982290i	$-0.559995\pi$
$283$	13.5380	−	18.6334i	0.804748	−	1.10764i	0.992113	−	0.125350i	$-0.0400054\pi$
$284$	−1.48879	+	4.58203i	−0.0883436	+	0.271894i
$285$		0			0
$286$	0.247763	+	0.762537i	0.0146505	+	0.0450897i
$287$	−13.2661	−	4.31042i	−0.783073	−	0.254436i
$288$		0			0
$289$	−7.77227	−	23.9206i	−0.457192	−	1.40709i
$290$	0.874138	+	16.2021i	0.0513312	+	0.951423i
$291$		0			0
$292$	−6.92806	+	9.53565i	−0.405434	+	0.558032i
$293$		−	16.3851i		−	0.957230i	−0.878025	−	0.478615i	$-0.841139\pi$
$293$		−	16.3851i		−	0.957230i	0.878025	−	0.478615i	$-0.158861\pi$
$294$		0			0
$295$	3.01452	+	7.81710i	0.175512	+	0.455129i
$296$	3.67218	−	2.66799i	0.213441	−	0.155074i
$297$		0			0
$298$	−7.48901	+	2.43333i	−0.433827	+	0.140959i
$299$	−18.3045			−1.05858
$300$		0			0
$301$	21.1008			1.21623
$302$	16.8965	−	5.48999i	0.972282	−	0.315914i
$303$		0			0
$304$	−0.358647	+	0.260572i	−0.0205698	+	0.0149448i
$305$	24.4391	+	15.8175i	1.39938	+	0.905708i
$306$		0			0
$307$		−	18.6027i		−	1.06171i	−0.847461	−	0.530857i	$-0.821870\pi$
$307$		−	18.6027i		−	1.06171i	0.847461	−	0.530857i	$-0.178130\pi$
$308$	−0.440137	+	0.605796i	−0.0250791	+	0.0345185i
$309$		0			0
$310$	−7.56651	+	2.91789i	−0.429749	+	0.165725i
$311$	4.30073	+	13.2363i	0.243872	+	0.750561i	0.995820	+	0.0913384i	$0.0291145\pi$
$311$	4.30073	+	13.2363i	0.243872	+	0.750561i	−0.751948	+	0.659223i	$0.770886\pi$
$312$		0			0
$313$	14.6277	+	4.75282i	0.826805	+	0.268645i	0.691699	−	0.722186i	$-0.256863\pi$
$313$	14.6277	+	4.75282i	0.826805	+	0.268645i	0.135106	+	0.990831i	$0.456863\pi$
$314$	−6.21715	−	19.1344i	−0.350854	−	1.07982i
$315$		0			0
$316$	−2.41485	+	7.43215i	−0.135846	+	0.418091i
$317$	−3.77620	+	5.19749i	−0.212092	+	0.291920i	−0.901787	−	0.432180i	$-0.857745\pi$
$317$	−3.77620	+	5.19749i	−0.212092	+	0.291920i	0.689695	+	0.724100i	$0.257745\pi$
$318$		0			0
$319$	−1.67785	−	1.21903i	−0.0939413	−	0.0682524i
$320$	−1.87720	−	1.21496i	−0.104939	−	0.0679184i
$321$		0			0
$322$	−10.0483	−	13.8303i	−0.559968	−	0.770730i
$323$	−2.73730	+	0.889403i	−0.152308	+	0.0494877i
$324$		0			0
$325$	6.97579	−	12.1688i	0.386947	−	0.675005i
$326$	−2.11433			−0.117102
$327$		0			0
$328$	3.12941	+	4.30726i	0.172793	+	0.237829i
$329$	−19.0688	+	13.8543i	−1.05129	+	0.763810i
$330$		0			0
$331$	−14.6979	−	10.6786i	−0.807868	−	0.586951i	0.105344	−	0.994436i	$-0.466406\pi$
$331$	−14.6979	−	10.6786i	−0.807868	−	0.586951i	−0.913212	+	0.407485i	$0.866406\pi$
$332$			5.16187i			0.283294i
$333$		0			0
$334$	6.01837	−	18.5226i	0.329311	−	1.01351i
$335$	1.23266	+	22.8474i	0.0673476	+	1.24829i
$336$		0			0
$337$	−2.26995	−	0.737552i	−0.123652	−	0.0401770i	0.246537	−	0.969133i	$-0.420707\pi$
$337$	−2.26995	−	0.737552i	−0.123652	−	0.0401770i	−0.370189	+	0.928956i	$0.620707\pi$
$338$	−4.87922	−	1.58536i	−0.265395	−	0.0862320i
$339$		0			0
$340$	−9.15352	−	11.2681i	−0.496419	−	0.611101i
$341$	0.320313	−	0.985821i	0.0173459	−	0.0533852i
$342$		0			0
$343$			18.6956i			1.00947i
$344$	−6.51574	−	4.73397i	−0.351305	−	0.255238i
$345$		0			0
$346$	2.67848	−	1.94603i	0.143996	−	0.104619i
$347$	−15.2463	−	20.9848i	−0.818466	−	1.12652i	−0.989961	−	0.141337i	$-0.954860\pi$
$347$	−15.2463	−	20.9848i	−0.818466	−	1.12652i	0.171495	−	0.985185i	$-0.445140\pi$
$348$		0			0
$349$	−0.246770			−0.0132093			−0.00660463	−	0.999978i	$-0.502102\pi$
$349$	−0.246770			−0.0132093			−0.00660463	+	0.999978i	$0.502102\pi$
$350$	13.0237	−	1.40941i	0.696147	−	0.0753363i
$351$		0			0
$352$	0.271820	−	0.0883198i	0.0144881	−	0.00470746i
$353$	11.2868	+	15.5350i	0.600738	+	0.826844i	0.995776	−	0.0918205i	$-0.0292686\pi$
$353$	11.2868	+	15.5350i	0.600738	+	0.826844i	−0.395038	+	0.918665i	$0.629269\pi$
$354$		0			0
$355$	−2.77223	+	10.4102i	−0.147135	+	0.552516i
$356$	−4.98807	−	3.62405i	−0.264367	−	0.192074i
$357$		0			0
$358$	7.32398	−	10.0806i	0.387084	−	0.532776i
$359$	4.77188	−	14.6863i	0.251850	−	0.775116i	−0.742584	−	0.669753i	$-0.766400\pi$
$359$	4.77188	−	14.6863i	0.251850	−	0.775116i	0.994434	−	0.105362i	$-0.0336002\pi$
$360$		0			0
$361$	−5.81059	−	17.8832i	−0.305821	−	0.941219i
$362$	−5.76100	−	1.87186i	−0.302792	−	0.0983830i
$363$		0			0
$364$	2.27119	+	6.99002i	0.119043	+	0.366376i
$365$	−14.3204	+	22.1260i	−0.749564	+	1.15813i
$366$		0			0
$367$	−14.6775	+	20.2019i	−0.766160	+	1.05453i	0.230516	+	0.973068i	$0.425959\pi$
$367$	−14.6775	+	20.2019i	−0.766160	+	1.05453i	−0.996677	+	0.0814607i	$0.974041\pi$
$368$			6.52498i			0.340138i
$369$		0			0
$370$	7.87792	−	6.39952i	0.409553	−	0.332695i
$371$	29.4956	−	21.4298i	1.53134	−	1.11258i
$372$		0			0
$373$	−17.7509	+	5.76763i	−0.919109	+	0.298637i	−0.730101	−	0.683339i	$-0.760527\pi$
$373$	−17.7509	+	5.76763i	−0.919109	+	0.298637i	−0.189008	+	0.981976i	$0.560527\pi$
$374$	1.85559			0.0959504
$375$		0			0
$376$	8.99646			0.463957
$377$	−19.3599	+	6.29042i	−0.997087	+	0.323973i
$378$		0			0
$379$	23.6622	−	17.1916i	1.21545	−	0.883073i	0.219732	−	0.975560i	$-0.429482\pi$
$379$	23.6622	−	17.1916i	1.21545	−	0.883073i	0.995714	+	0.0924869i	$0.0294816\pi$
$380$	−0.769404	+	0.625015i	−0.0394696	+	0.0320626i
$381$		0			0
$382$			23.3684i			1.19563i
$383$	−6.09627	+	8.39079i	−0.311505	+	0.428750i	−0.935850	−	0.352399i	$-0.885366\pi$
$383$	−6.09627	+	8.39079i	−0.311505	+	0.428750i	0.624345	+	0.781149i	$0.285366\pi$
$384$		0			0
$385$	−0.909769	+	1.40566i	−0.0463661	+	0.0716389i
$386$	0.659104	+	2.02851i	0.0335475	+	0.103249i
$387$		0			0
$388$	−5.18364	−	1.68427i	−0.263160	−	0.0855057i
$389$	−2.82831	−	8.70463i	−0.143401	−	0.441342i	0.853401	−	0.521255i	$-0.174536\pi$
$389$	−2.82831	−	8.70463i	−0.143401	−	0.441342i	−0.996802	+	0.0799126i	$0.974536\pi$
$390$		0			0
$391$	−13.0909	+	40.2895i	−0.662034	+	2.03753i
$392$	0.0798529	−	0.109908i	0.00403318	−	0.00555119i
$393$		0			0
$394$	13.3134	+	9.67275i	0.670719	+	0.487306i
$395$	−4.49662	+	16.8856i	−0.226249	+	0.849605i
$396$		0			0
$397$	9.48983	+	13.0616i	0.476281	+	0.655544i	0.977785	−	0.209611i	$-0.0672198\pi$
$397$	9.48983	+	13.0616i	0.476281	+	0.655544i	−0.501504	+	0.865155i	$0.667220\pi$
$398$	−1.58400	+	0.514674i	−0.0793989	+	0.0257983i
$399$		0			0
$400$	−4.33781	−	2.48665i	−0.216890	−	0.124333i
$401$	25.9388			1.29532			0.647662	−	0.761928i	$-0.275747\pi$
$401$	25.9388			1.29532			0.647662	+	0.761928i	$0.275747\pi$
$402$		0			0
$403$	−5.98017	−	8.23100i	−0.297893	−	0.410015i
$404$	−8.71839	+	6.33428i	−0.433756	+	0.315142i
$405$		0			0
$406$	−15.3805	−	11.1746i	−0.763320	−	0.554584i
$407$			1.29730i			0.0643050i
$408$		0			0
$409$	−5.27338	+	16.2298i	−0.260752	+	0.802512i	0.731890	+	0.681423i	$0.238639\pi$
$409$	−5.27338	+	16.2298i	−0.260752	+	0.802512i	−0.992642	+	0.121089i	$0.961361\pi$
$410$	7.50629	+	9.24036i	0.370709	+	0.456349i
$411$		0			0
$412$	−17.0392	−	5.53639i	−0.839464	−	0.272758i
$413$	−9.33611	−	3.03349i	−0.459400	−	0.149268i
$414$		0			0
$415$	0.621825	+	11.5255i	0.0305242	+	0.565766i
$416$	0.866884	−	2.66799i	0.0425025	−	0.130809i
$417$		0			0
$418$		−	0.126703i		−	0.00619722i
$419$	−11.1748	−	8.11899i	−0.545926	−	0.396639i	0.280355	−	0.959896i	$-0.409548\pi$
$419$	−11.1748	−	8.11899i	−0.545926	−	0.396639i	−0.826281	+	0.563258i	$0.809548\pi$
$420$		0			0
$421$	1.68679	−	1.22553i	0.0822093	−	0.0597286i	−0.545921	−	0.837836i	$-0.683820\pi$
$421$	1.68679	−	1.22553i	0.0822093	−	0.0597286i	0.628131	+	0.778108i	$0.283820\pi$
$422$	−6.91460	−	9.51713i	−0.336597	−	0.463287i
$423$		0			0
$424$	−13.9158			−0.675809
$425$	−21.7956	−	24.0570i	−1.05724	−	1.16694i
$426$		0			0
$427$	−32.4396	+	10.5403i	−1.56986	+	0.510079i
$428$	−2.24117	−	3.08471i	−0.108331	−	0.149105i
$429$		0			0
$430$	−15.1188	−	9.78517i	−0.729092	−	0.471883i
$431$	7.55310	+	5.48765i	0.363820	+	0.264331i	0.754644	−	0.656135i	$-0.227810\pi$
$431$	7.55310	+	5.48765i	0.363820	+	0.264331i	−0.390824	+	0.920466i	$0.627810\pi$
$432$		0			0
$433$	−6.88534	+	9.47685i	−0.330888	+	0.455429i	−0.941752	−	0.336307i	$-0.890822\pi$
$433$	−6.88534	+	9.47685i	−0.330888	+	0.455429i	0.610864	+	0.791735i	$0.290822\pi$
$434$	2.93624	−	9.03682i	0.140944	−	0.433781i
$435$		0			0
$436$	2.46160	+	7.57602i	0.117889	+	0.362826i
$437$	2.75103	+	0.893863i	0.131599	+	0.0427593i
$438$		0			0
$439$	−0.952391	−	2.93116i	−0.0454552	−	0.139897i	0.925753	−	0.378128i	$-0.123432\pi$
$439$	−0.952391	−	2.93116i	−0.0454552	−	0.139897i	−0.971208	+	0.238232i	$0.923432\pi$
$440$	0.596287	−	0.229947i	0.0284269	−	0.0109623i
$441$		0			0
$442$	10.7054	−	14.7348i	0.509205	−	0.700861i
$443$			10.6355i			0.505309i	0.967557	+	0.252654i	$0.0813035\pi$
$443$			10.6355i			0.505309i	−0.967557	+	0.252654i	$0.918696\pi$
$444$		0			0
$445$	−11.5740	−	7.49096i	−0.548662	−	0.355106i
$446$	7.70310	−	5.59663i	0.364753	−	0.265008i
$447$		0			0
$448$	2.49172	−	0.809610i	0.117723	−	0.0382505i
$449$	−22.8276			−1.07730			−0.538651	−	0.842529i	$-0.681066\pi$
$449$	−22.8276			−1.07730			−0.538651	+	0.842529i	$0.681066\pi$
$450$		0			0
$451$	−1.52167			−0.0716525
$452$	4.99319	−	1.62239i	0.234860	−	0.0763106i
$453$		0			0
$454$	−13.2010	+	9.59107i	−0.619552	+	0.450131i
$455$	5.91322	+	15.3339i	0.277216	+	0.718862i
$456$		0			0
$457$			25.7628i			1.20513i	0.798068	+	0.602567i	$0.205855\pi$
$457$			25.7628i			1.20513i	−0.798068	+	0.602567i	$0.794145\pi$
$458$	−0.313691	+	0.431759i	−0.0146578	+	0.0201748i
$459$		0			0
$460$	0.786033	+	14.5691i	0.0366490	+	0.679288i
$461$	−10.0189	−	30.8349i	−0.466626	−	1.43613i	−0.856926	−	0.515439i	$-0.827629\pi$
$461$	−10.0189	−	30.8349i	−0.466626	−	1.43613i	0.390301	−	0.920688i	$-0.372371\pi$
$462$		0			0
$463$	17.8584	+	5.80256i	0.829952	+	0.269668i	0.693025	−	0.720914i	$-0.256278\pi$
$463$	17.8584	+	5.80256i	0.829952	+	0.269668i	0.136927	+	0.990581i	$0.456278\pi$
$464$	2.24234	+	6.90121i	0.104098	+	0.320380i
$465$		0			0
$466$	3.38119	−	10.4062i	0.156631	−	0.482060i
$467$	1.15330	−	1.58739i	0.0533686	−	0.0734555i	−0.781499	−	0.623907i	$-0.785544\pi$
$467$	1.15330	−	1.58739i	0.0533686	−	0.0734555i	0.834867	+	0.550451i	$0.185544\pi$
$468$		0			0
$469$	−21.6887	−	15.7578i	−1.00149	−	0.727626i
$470$	20.0875	−	1.08376i	0.926566	−	0.0499901i
$471$		0			0
$472$	2.20234	+	3.03127i	0.101371	+	0.139525i
$473$	2.18922	−	0.711319i	0.100660	−	0.0327065i
$474$		0			0
$475$	−1.64265	+	1.48823i	−0.0753699	+	0.0682849i
$476$	17.0098			0.779645
$477$		0			0
$478$	3.54917	+	4.88501i	0.162335	+	0.223435i
$479$	5.45583	−	3.96389i	0.249283	−	0.181115i	−0.456126	−	0.889915i	$-0.650763\pi$
$479$	5.45583	−	3.96389i	0.249283	−	0.181115i	0.705409	+	0.708800i	$0.250763\pi$
$480$		0			0
$481$	10.3015	+	7.48451i	0.469710	+	0.341264i
$482$		−	2.20701i		−	0.100526i
$483$		0			0
$484$	3.37394	−	10.3839i	0.153361	−	0.471997i
$485$	−11.7770	−	3.13622i	−0.534768	−	0.142408i
$486$		0			0
$487$	1.10709	+	0.359717i	0.0501672	+	0.0163003i	0.333993	−	0.942576i	$-0.391604\pi$
$487$	1.10709	+	0.359717i	0.0501672	+	0.0163003i	−0.283826	+	0.958876i	$0.591604\pi$
$488$	12.3818	+	4.02308i	0.560496	+	0.182116i
$489$		0			0
$490$	0.165057	−	0.255024i	0.00745652	−	0.0115208i
$491$	2.59179	−	7.97671i	0.116966	−	0.359984i	−0.875386	−	0.483424i	$-0.839393\pi$
$491$	2.59179	−	7.97671i	0.116966	−	0.359984i	0.992352	+	0.123441i	$0.0393928\pi$
$492$		0			0
$493$			47.1113i			2.12179i
$494$	−1.00611	−	0.730982i	−0.0452670	−	0.0328884i
$495$		0			0
$496$	−2.93409	+	2.13174i	−0.131745	+	0.0957181i
$497$	−7.41931	−	10.2118i	−0.332802	−	0.458062i
$498$		0			0
$499$	−17.2590			−0.772620			−0.386310	−	0.922369i	$-0.626251\pi$
$499$	−17.2590			−0.772620			−0.386310	+	0.922369i	$0.626251\pi$
$500$	−9.98510	−	5.02969i	−0.446547	−	0.224935i
$501$		0			0
$502$	0.144228	−	0.0468627i	0.00643723	−	0.00209158i
$503$	−5.18659	−	7.13873i	−0.231259	−	0.318300i	0.677579	−	0.735450i	$-0.263029\pi$
$503$	−5.18659	−	7.13873i	−0.231259	−	0.318300i	−0.908838	+	0.417150i	$0.863029\pi$
$504$		0			0
$505$	−18.7035	+	15.1936i	−0.832297	+	0.676105i
$506$	−1.50873	−	1.09616i	−0.0670714	−	0.0487302i
$507$		0			0
$508$	10.9910	−	15.1278i	0.487648	−	0.671189i
$509$	−4.21361	+	12.9682i	−0.186765	+	0.574804i	−0.999974	−	0.00716772i	$-0.997718\pi$
$509$	−4.21361	+	12.9682i	−0.186765	+	0.574804i	0.813209	+	0.581971i	$0.197718\pi$
$510$		0			0
$511$	−9.54264	−	29.3692i	−0.422141	−	1.29922i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$		0			0
$514$	−3.22805	−	9.93490i	−0.142383	−	0.438210i
$515$	−38.7125	−	10.3091i	−1.70588	−	0.454274i
$516$		0			0
$517$	−1.51135	+	2.08020i	−0.0664692	+	0.0914871i
$518$			11.8921i			0.522510i
$519$		0			0
$520$	1.61420	−	6.06158i	0.0707872	−	0.265818i
$521$	−10.9134	+	7.92905i	−0.478125	+	0.347378i	−0.800599	−	0.599200i	$-0.795485\pi$
$521$	−10.9134	+	7.92905i	−0.478125	+	0.347378i	0.322474	+	0.946578i	$0.395485\pi$
$522$		0			0
$523$	−9.68125	+	3.14563i	−0.423332	+	0.137549i	−0.512932	−	0.858429i	$-0.671441\pi$
$523$	−9.68125	+	3.14563i	−0.423332	+	0.137549i	0.0896008	+	0.995978i	$0.471441\pi$
$524$	4.55143			0.198830
$525$		0			0
$526$	21.9602			0.957511
$527$	−22.3939	+	7.27621i	−0.975493	+	0.316957i
$528$		0			0
$529$	15.8368	−	11.5061i	0.688556	−	0.500266i
$530$	−31.0714	+	1.67636i	−1.34965	+	0.0728166i
$531$		0			0
$532$		−	1.16146i		−	0.0503555i
$533$	−8.77892	+	12.0831i	−0.380257	+	0.523379i
$534$		0			0
$535$	−5.37573	−	6.61761i	−0.232413	−	0.286104i
$536$	3.16202	+	9.73171i	0.136579	+	0.420346i
$537$		0			0
$538$	13.4383	+	4.36638i	0.579368	+	0.188248i
$539$	0.0119986	+	0.0369278i	0.000516816	+	0.00159059i
$540$		0			0
$541$	−3.58842	+	11.0440i	−0.154278	+	0.474819i	−0.998087	−	0.0618246i	$-0.980308\pi$
$541$	−3.58842	+	11.0440i	−0.154278	+	0.474819i	0.843809	+	0.536644i	$0.180308\pi$
$542$	−16.1811	+	22.2714i	−0.695039	+	0.956640i
$543$		0			0
$544$	−5.25248	−	3.81615i	−0.225198	−	0.163616i
$545$	6.40896	+	16.6194i	0.274529	+	0.711895i
$546$		0			0
$547$	−11.8352	−	16.2897i	−0.506035	−	0.696497i	0.477210	−	0.878789i	$-0.341648\pi$
$547$	−11.8352	−	16.2897i	−0.506035	−	0.696497i	−0.983244	+	0.182293i	$0.941648\pi$
$548$	14.7832	−	4.80334i	0.631505	−	0.205188i
$549$		0			0
$550$	1.30370	−	0.585263i	0.0555900	−	0.0249557i
$551$	3.21683			0.137042
$552$		0			0
$553$	−12.0343	−	16.5638i	−0.511750	−	0.704363i
$554$	19.0895	−	13.8693i	0.811036	−	0.589252i
$555$		0			0
$556$	7.28192	+	5.29063i	0.308822	+	0.224373i
$557$			8.99374i			0.381077i	0.981680	+	0.190539i	$0.0610234\pi$
$557$			8.99374i			0.381077i	−0.981680	+	0.190539i	$0.938977\pi$
$558$		0			0
$559$	6.98180	−	21.4878i	0.295299	−	0.908836i
$560$	5.46604	−	2.10788i	0.230982	−	0.0890741i
$561$		0			0
$562$	6.82035	+	2.21607i	0.287699	+	0.0934791i
$563$	0.442435	+	0.143756i	0.0186464	+	0.00605858i	0.318325	−	0.947982i	$-0.396880\pi$
$563$	0.442435	+	0.143756i	0.0186464	+	0.00605858i	−0.299679	+	0.954040i	$0.596880\pi$
$564$		0			0
$565$	10.9535	−	4.22400i	0.460815	−	0.177705i
$566$	7.11732	−	21.9049i	0.299163	−	0.920730i
$567$		0			0
$568$			4.81783i			0.202152i
$569$	4.12851	+	2.99954i	0.173076	+	0.125747i	0.670951	−	0.741502i	$-0.265886\pi$
$569$	4.12851	+	2.99954i	0.173076	+	0.125747i	−0.497875	+	0.867249i	$0.665886\pi$
$570$		0			0
$571$	34.9562	−	25.3971i	1.46287	−	1.06284i	0.480266	−	0.877123i	$-0.340540\pi$
$571$	34.9562	−	25.3971i	1.46287	−	1.06284i	0.982604	−	0.185714i	$-0.0594597\pi$
$572$	0.471274	+	0.648652i	0.0197049	+	0.0271215i
$573$		0			0
$574$	−13.9488			−0.582212
$575$	3.51014	+	32.4355i	0.146383	+	1.35265i
$576$		0			0
$577$	−14.6870	+	4.77209i	−0.611427	+	0.198665i	−0.598330	−	0.801249i	$-0.704169\pi$
$577$	−14.6870	+	4.77209i	−0.611427	+	0.198665i	−0.0130969	+	0.999914i	$0.504169\pi$
$578$	−14.7837	−	20.3481i	−0.614922	−	0.846367i
$579$		0			0
$580$	5.83809	+	15.1390i	0.242414	+	0.628614i
$581$	−10.9410	−	7.94911i	−0.453910	−	0.329785i
$582$		0			0
$583$	2.33777	−	3.21766i	0.0968204	−	0.133262i
$584$	−3.64230	+	11.2098i	−0.150719	+	0.463866i
$585$		0			0
$586$	−5.06328	−	15.5832i	−0.209162	−	0.643735i
$587$	27.1662	+	8.82684i	1.12127	+	0.364323i	0.810252	−	0.586081i	$-0.199330\pi$
$587$	27.1662	+	8.82684i	1.12127	+	0.364323i	0.311018	+	0.950404i	$0.399330\pi$
$588$		0			0
$589$	0.496830	+	1.52909i	0.0204715	+	0.0630049i
$590$	5.28260	+	6.50297i	0.217481	+	0.267723i
$591$		0			0
$592$	2.66799	−	3.67218i	0.109654	−	0.150926i
$593$			31.6123i			1.29816i	0.760720	+	0.649080i	$0.224846\pi$
$593$			31.6123i			1.29816i	−0.760720	+	0.649080i	$0.775154\pi$
$594$		0			0
$595$	37.9799	−	2.04909i	1.55702	−	0.0840046i
$596$	−6.37053	+	4.62846i	−0.260947	+	0.189589i
$597$		0			0
$598$	−17.4086	+	5.65640i	−0.711891	+	0.231307i
$599$	36.7361			1.50099			0.750497	−	0.660873i	$-0.229814\pi$
$599$	36.7361			1.50099			0.750497	+	0.660873i	$0.229814\pi$
$600$		0			0
$601$	45.3145			1.84842			0.924209	−	0.381887i	$-0.124726\pi$
$601$	45.3145			1.84842			0.924209	+	0.381887i	$0.124726\pi$
$602$	20.0681	−	6.52052i	0.817914	−	0.265756i
$603$		0			0
$604$	14.3730	−	10.4426i	0.584829	−	0.424903i
$605$	6.28251	−	23.5919i	0.255420	−	0.959147i
$606$		0			0
$607$		−	3.15730i		−	0.128151i	−0.997945	−	0.0640754i	$-0.979590\pi$
$607$		−	3.15730i		−	0.128151i	0.997945	−	0.0640754i	$-0.0204098\pi$
$608$	−0.260572	+	0.358647i	−0.0105676	+	0.0145451i
$609$		0			0
$610$	28.1309	+	7.49124i	1.13899	+	0.303311i
$611$	7.79888	+	24.0025i	0.315509	+	0.971037i
$612$		0			0
$613$	19.9336	+	6.47683i	0.805111	+	0.261596i	0.682526	−	0.730861i	$-0.260881\pi$
$613$	19.9336	+	6.47683i	0.805111	+	0.261596i	0.122585	+	0.992458i	$0.460881\pi$
$614$	−5.74856	−	17.6923i	−0.231993	−	0.714002i
$615$		0			0
$616$	−0.231394	+	0.712156i	−0.00932311	+	0.0286936i
$617$	−21.5952	+	29.7233i	−0.869391	+	1.19661i	0.109856	+	0.993947i	$0.464961\pi$
$617$	−21.5952	+	29.7233i	−0.869391	+	1.19661i	−0.979248	+	0.202667i	$0.935039\pi$
$618$		0			0
$619$	−9.41595	−	6.84109i	−0.378459	−	0.274967i	0.382251	−	0.924059i	$-0.375149\pi$
$619$	−9.41595	−	6.84109i	−0.378459	−	0.274967i	−0.760710	+	0.649092i	$0.775149\pi$
$620$	−6.29450	+	5.11326i	−0.252793	+	0.205353i
$621$		0			0
$622$	8.18047	+	11.2595i	0.328007	+	0.451463i
$623$	15.3630	−	4.99173i	0.615504	−	0.199989i
$624$		0			0
$625$	−22.9008	−	10.0275i	−0.916033	−	0.401102i
$626$	15.3804			0.614726
$627$		0			0
$628$	−11.8257	−	16.2767i	−0.471898	−	0.649511i
$629$	23.8413	−	17.3218i	0.950617	−	0.690663i
$630$		0			0
$631$	−3.73919	−	2.71668i	−0.148855	−	0.108149i	0.510865	−	0.859661i	$-0.329325\pi$
$631$	−3.73919	−	2.71668i	−0.148855	−	0.108149i	−0.659720	+	0.751511i	$0.729325\pi$
$632$			7.81462i			0.310849i
$633$		0			0
$634$	−1.98526	+	6.11001i	−0.0788449	+	0.242660i
$635$	22.7186	−	35.1018i	0.901560	−	1.39297i
$636$		0			0
$637$	0.362457	+	0.117769i	0.0143611	+	0.00466620i
$638$	−1.97243	−	0.640880i	−0.0780891	−	0.0253727i
$639$		0			0
$640$	−2.16076	−	0.575410i	−0.0854117	−	0.0227451i
$641$	−7.85079	+	24.1623i	−0.310088	+	0.954352i	0.667642	+	0.744483i	$0.267304\pi$
$641$	−7.85079	+	24.1623i	−0.310088	+	0.954352i	−0.977730	+	0.209869i	$0.932696\pi$
$642$		0			0
$643$		−	41.3338i		−	1.63005i	−0.579429	−	0.815023i	$-0.696724\pi$
$643$		−	41.3338i		−	1.63005i	0.579429	−	0.815023i	$-0.303276\pi$
$644$	−13.8303	−	10.0483i	−0.544988	−	0.395957i
$645$		0			0
$646$	−2.32849	+	1.69175i	−0.0916131	+	0.0665608i
$647$	3.20446	+	4.41055i	0.125980	+	0.173397i	0.867348	−	0.497702i	$-0.165823\pi$
$647$	3.20446	+	4.41055i	0.125980	+	0.173397i	−0.741368	+	0.671099i	$0.765823\pi$
$648$		0			0
$649$	−1.07088			−0.0420358
$650$	2.87400	−	13.7289i	0.112728	−	0.538491i
$651$		0			0
$652$	−2.01084	+	0.653363i	−0.0787507	+	0.0255877i
$653$	16.1526	+	22.2322i	0.632101	+	0.870013i	0.998163	−	0.0605775i	$-0.0192942\pi$
$653$	16.1526	+	22.2322i	0.632101	+	0.870013i	−0.366062	+	0.930590i	$0.619294\pi$
$654$		0			0
$655$	10.1625	−	0.548289i	0.397083	−	0.0214234i
$656$	4.30726	+	3.12941i	0.168170	+	0.122183i
$657$		0			0
$658$	−13.8543	+	19.0688i	−0.540096	+	0.743378i
$659$	13.0534	−	40.1743i	0.508489	−	1.56497i	−0.286336	−	0.958129i	$-0.592437\pi$
$659$	13.0534	−	40.1743i	0.508489	−	1.56497i	0.794825	−	0.606839i	$-0.207563\pi$
$660$		0			0
$661$	1.96478	+	6.04696i	0.0764210	+	0.235200i	0.981968	−	0.189046i	$-0.0605394\pi$
$661$	1.96478	+	6.04696i	0.0764210	+	0.235200i	−0.905547	+	0.424245i	$0.860539\pi$
$662$	−17.2784	−	5.61409i	−0.671544	−	0.218198i
$663$		0			0
$664$	1.59510	+	4.90923i	0.0619021	+	0.190515i
$665$	−0.139915	−	2.59332i	−0.00542567	−	0.100565i
$666$		0			0
$667$	27.8302	−	38.3050i	1.07759	−	1.48318i
$668$		−	19.4759i		−	0.753544i
$669$		0			0
$670$	8.23257	+	21.3483i	0.318052	+	0.824755i
$671$	−3.01030	+	2.18711i	−0.116211	+	0.0844324i
$672$		0			0
$673$	−19.3775	+	6.29612i	−0.746947	+	0.242698i	−0.657667	−	0.753309i	$-0.728457\pi$
$673$	−19.3775	+	6.29612i	−0.746947	+	0.242698i	−0.0892798	+	0.996007i	$0.528457\pi$
$674$	−2.38677			−0.0919349
$675$		0			0
$676$	−5.13032			−0.197320
$677$	5.99042	−	1.94641i	0.230231	−	0.0748065i	−0.191630	−	0.981467i	$-0.561377\pi$
$677$	5.99042	−	1.94641i	0.230231	−	0.0748065i	0.421860	+	0.906661i	$0.361377\pi$
$678$		0			0
$679$	11.5526	−	8.39345i	0.443348	−	0.322111i
$680$	−12.1876	−	7.88804i	−0.467372	−	0.302493i
$681$		0			0
$682$		−	1.03655i		−	0.0396917i
$683$	11.5797	−	15.9381i	0.443085	−	0.609855i	−0.527809	−	0.849363i	$-0.676986\pi$
$683$	11.5797	−	15.9381i	0.443085	−	0.609855i	0.970894	+	0.239508i	$0.0769862\pi$
$684$		0			0
$685$	32.4295	−	12.5058i	1.23907	−	0.477824i
$686$	5.77726	+	17.7806i	0.220577	+	0.678865i
$687$		0			0
$688$	−7.65972	−	2.48879i	−0.292024	−	0.0948843i
$689$	−12.0633	−	37.1272i	−0.459577	−	1.41443i
$690$		0			0
$691$	−15.0733	+	46.3909i	−0.573416	+	1.76479i	0.0680955	+	0.997679i	$0.478308\pi$
$691$	−15.0733	+	46.3909i	−0.573416	+	1.76479i	−0.641511	+	0.767114i	$0.721692\pi$
$692$	1.94603	−	2.67848i	0.0739768	−	0.101820i
$693$		0			0
$694$	−20.9848	−	15.2463i	−0.796572	−	0.578743i
$695$	16.8966	+	10.9358i	0.640923	+	0.414819i
$696$		0			0
$697$	20.3175	+	27.9646i	0.769578	+	1.05923i
$698$	−0.234692	+	0.0762560i	−0.00888321	+	0.00288633i
$699$		0			0
$700$	11.9508	−	5.36498i	0.451696	−	0.202777i
$701$	43.3213			1.63622			0.818111	−	0.575061i	$-0.195022\pi$
$701$	43.3213			1.63622			0.818111	+	0.575061i	$0.195022\pi$
$702$		0			0
$703$	−1.18275	−	1.62792i	−0.0446084	−	0.0613982i
$704$	0.231224	−	0.167994i	0.00871459	−	0.00633152i
$705$		0			0
$706$	15.5350	+	11.2868i	0.584667	+	0.424786i
$707$		−	28.2340i		−	1.06185i
$708$		0			0
$709$	−4.95136	+	15.2387i	−0.185952	+	0.572302i	−0.999963	−	0.00854727i	$-0.997279\pi$
$709$	−4.95136	+	15.2387i	−0.185952	+	0.572302i	0.814011	+	0.580849i	$0.197279\pi$
$710$	0.580381	+	10.7574i	0.0217813	+	0.403717i
$711$		0			0
$712$	−5.86383	−	1.90527i	−0.219756	−	0.0714032i
$713$	22.5062	+	7.31270i	0.842863	+	0.273863i
$714$		0			0
$715$	1.13041	+	1.39155i	0.0422749	+	0.0520411i
$716$	3.85044	−	11.8504i	0.143898	−	0.442872i
$717$		0			0
$718$		−	15.4421i		−	0.576296i
$719$	−22.4469	−	16.3087i	−0.837130	−	0.608210i	0.0844377	−	0.996429i	$-0.473091\pi$
$719$	−22.4469	−	16.3087i	−0.837130	−	0.608210i	−0.921567	+	0.388218i	$0.873091\pi$
$720$		0			0
$721$	37.9748	−	27.5903i	1.41425	−	1.02752i
$722$	−11.0524	−	15.2123i	−0.411328	−	0.566144i
$723$		0			0
$724$	−6.05748			−0.225124
$725$	14.8591	+	33.0995i	0.551855	+	1.22928i
$726$		0			0
$727$	−43.2427	+	14.0504i	−1.60378	+	0.521101i	−0.968039	−	0.250799i	$-0.919307\pi$
$727$	−43.2427	+	14.0504i	−1.60378	+	0.521101i	−0.635744	+	0.771900i	$0.719307\pi$
$728$	4.32007	+	5.94606i	0.160112	+	0.220376i
$729$		0			0
$730$	−6.78220	+	25.4683i	−0.251020	+	0.942625i
$731$	−42.3030	−	30.7349i	−1.56463	−	1.13677i
$732$		0			0
$733$	18.4749	−	25.4285i	0.682385	−	0.939223i	−0.317574	−	0.948233i	$-0.602868\pi$
$733$	18.4749	−	25.4285i	0.682385	−	0.939223i	0.999959	+	0.00901080i	$0.00286826\pi$
$734$	−7.71643	+	23.7487i	−0.284819	+	0.876581i
$735$		0			0
$736$	2.01633	+	6.20562i	0.0743229	+	0.228742i
$737$	−2.78141	−	0.903735i	−0.102455	−	0.0332895i
$738$		0			0
$739$	5.26372	+	16.2001i	0.193629	+	0.595929i	0.999990	+	0.00450517i	$0.00143405\pi$
$739$	5.26372	+	16.2001i	0.193629	+	0.595929i	−0.806361	+	0.591424i	$0.798566\pi$
$740$	5.51478	−	8.52072i	0.202727	−	0.313228i
$741$		0			0
$742$	21.4298	−	29.4956i	0.786714	−	1.08282i
$743$			1.44429i			0.0529858i	0.999649	+	0.0264929i	$0.00843393\pi$
$743$			1.44429i			0.0529858i	−0.999649	+	0.0264929i	$0.991566\pi$
$744$		0			0
$745$	−13.6667	+	11.1020i	−0.500709	+	0.406744i
$746$	−15.0999	+	10.9707i	−0.552845	+	0.401665i
$747$		0			0
$748$	1.76477	−	0.573410i	0.0645265	−	0.0209659i
$749$	9.98963			0.365013
$750$		0			0
$751$	22.1167			0.807051			0.403526	−	0.914968i	$-0.367785\pi$
$751$	22.1167			0.807051			0.403526	+	0.914968i	$0.367785\pi$
$752$	8.55614	−	2.78006i	0.312010	−	0.101378i
$753$		0			0
$754$	−16.4685	+	11.9651i	−0.599748	+	0.435743i
$755$	30.8343	−	25.0479i	1.12218	−	0.911585i
$756$		0			0
$757$		−	18.0645i		−	0.656565i	−0.944580	−	0.328283i	$-0.893530\pi$
$757$		−	18.0645i		−	0.656565i	0.944580	−	0.328283i	$-0.106470\pi$
$758$	17.1916	−	23.6622i	0.624427	−	0.859450i
$759$		0			0
$760$	−0.538607	+	0.832184i	−0.0195373	+	0.0301865i
$761$	−4.42227	−	13.6103i	−0.160307	−	0.493375i	0.838353	−	0.545128i	$-0.183519\pi$
$761$	−4.42227	−	13.6103i	−0.160307	−	0.493375i	−0.998660	+	0.0517535i	$0.983519\pi$
$762$		0			0
$763$	−19.8488	−	6.44927i	−0.718575	−	0.233479i
$764$	7.22123	+	22.2247i	0.261255	+	0.804060i
$765$		0			0
$766$	−3.20500	+	9.86397i	−0.115801	+	0.356400i
$767$	−6.17822	+	8.50359i	−0.223083	+	0.307047i
$768$		0			0
$769$	27.8453	+	20.2308i	1.00413	+	0.729541i	0.962969	−	0.269612i	$-0.0868954\pi$
$769$	27.8453	+	20.2308i	1.00413	+	0.729541i	0.0411578	+	0.999153i	$0.486895\pi$
$770$	−0.430870	+	1.61799i	−0.0155275	+	0.0583084i
$771$		0			0
$772$	1.25369	+	1.72556i	0.0451213	+	0.0621042i
$773$	−30.5888	+	9.93889i	−1.10020	+	0.357477i	−0.802180	−	0.597082i	$-0.796327\pi$
$773$	−30.5888	+	9.93889i	−1.10020	+	0.357477i	−0.298021	+	0.954559i	$0.596327\pi$
$774$		0			0
$775$	−13.4385	+	12.1753i	−0.482726	+	0.437348i
$776$	−5.45040			−0.195658
$777$		0			0
$778$	−5.37976	−	7.40460i	−0.192874	−	0.265468i
$779$	1.90946	−	1.38730i	0.0684135	−	0.0497053i
$780$		0			0
$781$	−1.11400	−	0.809369i	−0.0398621	−	0.0289615i
$782$			42.3629i			1.51490i
$783$		0			0
$784$	0.0419811	−	0.129205i	0.00149933	−	0.00461445i
$785$	−28.3655	−	34.9184i	−1.01241	−	1.24629i
$786$		0			0
$787$	−30.0132	−	9.75188i	−1.06985	−	0.347617i	−0.279424	−	0.960168i	$-0.590143\pi$
$787$	−30.0132	−	9.75188i	−1.06985	−	0.347617i	−0.790431	+	0.612551i	$0.790143\pi$
$788$	15.6508	+	5.08526i	0.557538	+	0.181155i
$789$		0			0
$790$	0.941390	+	17.4487i	0.0334931	+	0.620795i
$791$	−4.25057	+	13.0819i	−0.151133	+	0.465139i
$792$		0			0
$793$			36.5220i			1.29693i
$794$	13.0616	+	9.48983i	0.463540	+	0.336781i
$795$		0			0
$796$	−1.34743	+	0.978967i	−0.0477585	+	0.0346986i
$797$	16.0150	+	22.0428i	0.567281	+	0.780796i	0.992229	−	0.124422i	$-0.0397077\pi$
$797$	16.0150	+	22.0428i	0.567281	+	0.780796i	−0.424948	+	0.905218i	$0.639708\pi$
$798$		0			0
$799$	58.4088			2.06636
$800$	−4.89392	−	1.02449i	−0.173026	−	0.0362212i
$801$		0			0
$802$	24.6693	−	8.01554i	0.871103	−	0.283039i
$803$	−1.98010	−	2.72537i	−0.0698762	−	0.0961764i
$804$		0			0
$805$	−32.0909	−	20.7699i	−1.13106	−	0.732043i
$806$	−8.23100	−	5.98017i	−0.289924	−	0.210642i
$807$		0			0
$808$	−6.33428	+	8.71839i	−0.222839	+	0.306712i
$809$	4.84894	−	14.9235i	0.170480	−	0.524682i	−0.828919	−	0.559369i	$-0.811043\pi$
$809$	4.84894	−	14.9235i	0.170480	−	0.524682i	0.999398	+	0.0346871i	$0.0110434\pi$
$810$		0			0
$811$	−7.11528	−	21.8986i	−0.249851	−	0.768963i	−0.994801	−	0.101842i	$-0.967526\pi$
$811$	−7.11528	−	21.8986i	−0.249851	−	0.768963i	0.744949	−	0.667121i	$-0.232474\pi$
$812$	−18.0808	−	5.87482i	−0.634513	−	0.206166i
$813$		0			0
$814$	0.400889	+	1.23381i	0.0140512	+	0.0432450i
$815$	−4.41115	+	1.70108i	−0.154516	+	0.0595862i
$816$		0			0
$817$	−2.09862	+	2.88851i	−0.0734215	+	0.101056i
$818$			17.0650i			0.596665i
$819$		0			0
$820$	9.99433	+	6.46854i	0.349017	+	0.225891i
$821$	−8.97939	+	6.52391i	−0.313383	+	0.227686i	−0.733347	−	0.679855i	$-0.762043\pi$
$821$	−8.97939	+	6.52391i	−0.313383	+	0.227686i	0.419964	+	0.907541i	$0.362043\pi$
$822$		0			0
$823$	42.1285	−	13.6884i	1.46851	−	0.477146i	0.537849	−	0.843041i	$-0.319237\pi$
$823$	42.1285	−	13.6884i	1.46851	−	0.477146i	0.930656	+	0.365894i	$0.119237\pi$
$824$	−17.9161			−0.624138
$825$		0			0
$826$	−9.81657			−0.341562
$827$	−9.82358	+	3.19188i	−0.341599	+	0.110992i	−0.474793	−	0.880098i	$-0.657477\pi$
$827$	−9.82358	+	3.19188i	−0.341599	+	0.110992i	0.133193	+	0.991090i	$0.457477\pi$
$828$		0			0
$829$	−38.9949	+	28.3315i	−1.35435	+	0.983992i	−0.355567	+	0.934651i	$0.615712\pi$
$829$	−38.9949	+	28.3315i	−1.35435	+	0.983992i	−0.998782	+	0.0493418i	$0.984288\pi$
$830$	4.15297	+	10.7693i	0.144152	+	0.373807i
$831$		0			0
$832$		−	2.80530i		−	0.0972561i
$833$	0.518439	−	0.713570i	0.0179628	−	0.0247237i
$834$		0			0
$835$	−2.34616	−	43.4861i	−0.0811923	−	1.50490i
$836$	−0.0391532	−	0.120501i	−0.00135414	−	0.00416762i
$837$		0			0
$838$	−13.1368	−	4.26840i	−0.453803	−	0.147450i
$839$	0.808745	+	2.48906i	0.0279210	+	0.0859320i	0.964046	−	0.265736i	$-0.0856148\pi$
$839$	0.808745	+	2.48906i	0.0279210	+	0.0859320i	−0.936125	+	0.351667i	$0.885615\pi$
$840$		0			0
$841$	7.30971	−	22.4970i	0.252059	−	0.775758i
$842$	1.22553	−	1.68679i	0.0422345	−	0.0581308i
$843$		0			0
$844$	−9.51713	−	6.91460i	−0.327593	−	0.238010i
$845$	−11.4551	+	0.618025i	−0.394067	+	0.0212607i
$846$		0			0
$847$	16.8139	+	23.1423i	0.577731	+	0.795179i
$848$	−13.2347	+	4.30020i	−0.454480	+	0.147670i
$849$		0			0
$850$	−28.1629	−	16.1444i	−0.965979	−	0.553748i
$851$	−29.6173			−1.01527
$852$		0			0
$853$	8.93777	+	12.3018i	0.306023	+	0.421205i	0.934136	−	0.356917i	$-0.116172\pi$
$853$	8.93777	+	12.3018i	0.306023	+	0.421205i	−0.628113	+	0.778123i	$0.716172\pi$
$854$	−27.5948	+	20.0488i	−0.944274	+	0.686055i
$855$		0			0
$856$	−3.08471	−	2.24117i	−0.105433	−	0.0766016i
$857$		−	26.1596i		−	0.893595i	−0.894635	−	0.446797i	$-0.852564\pi$
$857$		−	26.1596i		−	0.893595i	0.894635	−	0.446797i	$-0.147436\pi$
$858$		0			0
$859$	−2.21938	+	6.83054i	−0.0757241	+	0.233055i	−0.981753	−	0.190161i	$-0.939099\pi$
$859$	−2.21938	+	6.83054i	−0.0757241	+	0.233055i	0.906029	+	0.423216i	$0.139099\pi$
$860$	−17.4026	−	4.63430i	−0.593423	−	0.158028i
$861$		0			0
$862$	8.87920	+	2.88503i	0.302427	+	0.0982644i
$863$	34.9141	+	11.3443i	1.18849	+	0.386164i	0.835515	−	0.549468i	$-0.185170\pi$
$863$	34.9141	+	11.3443i	1.18849	+	0.386164i	0.352977	+	0.935632i	$0.385170\pi$
$864$		0			0
$865$	4.02246	−	6.21498i	0.136768	−	0.211316i
$866$	−3.61984	+	11.1407i	−0.123007	+	0.378577i
$867$		0			0
$868$		−	9.50188i		−	0.322515i
$869$	−1.80693	−	1.31281i	−0.0612959	−	0.0445341i
$870$		0			0
$871$	−23.2230	+	16.8725i	−0.786883	+	0.571704i
$872$	4.68224	+	6.44455i	0.158561	+	0.218240i
$873$		0			0
$874$	2.89260			0.0978437
$875$	26.0376	−	13.4187i	0.880232	−	0.453635i
$876$		0			0
$877$	−17.1289	+	5.56551i	−0.578401	+	0.187934i	−0.583584	−	0.812053i	$-0.698350\pi$
$877$	−17.1289	+	5.56551i	−0.578401	+	0.187934i	0.00518298	+	0.999987i	$0.498350\pi$
$878$	−1.81156	−	2.49339i	−0.0611371	−	0.0841479i
$879$		0			0
$880$	0.496045	−	0.402956i	0.0167217	−	0.0135836i
$881$	−2.31663	−	1.68313i	−0.0780491	−	0.0567060i	0.548076	−	0.836428i	$-0.315360\pi$
$881$	−2.31663	−	1.68313i	−0.0780491	−	0.0567060i	−0.626126	+	0.779722i	$0.715360\pi$
$882$		0			0
$883$	−26.9383	+	37.0773i	−0.906545	+	1.24775i	0.0617883	+	0.998089i	$0.480320\pi$
$883$	−26.9383	+	37.0773i	−0.906545	+	1.24775i	−0.968333	+	0.249662i	$0.919680\pi$
$884$	5.62818	−	17.3218i	0.189296	−	0.582594i
$885$		0			0
$886$	3.28656	+	10.1150i	0.110414	+	0.339819i
$887$	14.1264	+	4.58995i	0.474319	+	0.154116i	0.536414	−	0.843955i	$-0.319778\pi$
$887$	14.1264	+	4.58995i	0.474319	+	0.154116i	−0.0620957	+	0.998070i	$0.519778\pi$
$888$		0			0
$889$	15.1389	+	46.5928i	0.507743	+	1.56267i
$890$	−13.3224	−	3.54775i	−0.446568	−	0.118921i
$891$		0			0
$892$	5.59663	−	7.70310i	0.187389	−	0.257919i
$893$		−	3.98824i		−	0.133461i
$894$		0			0
$895$	7.16978	−	26.9238i	0.239659	−	0.899962i
$896$	2.11959	−	1.53997i	0.0708104	−	0.0514467i
$897$		0			0
$898$	−21.7104	+	7.05412i	−0.724484	+	0.235399i
$899$	26.3169			0.877718
$900$		0			0
$901$	−90.3470			−3.00989
$902$	−1.44719	+	0.470221i	−0.0481862	+	0.0156566i
$903$		0			0
$904$	4.24746	−	3.08596i	0.141268	−	0.102638i
$905$	−13.5253	+	0.729715i	−0.449595	+	0.0242565i
$906$		0			0
$907$		−	38.6577i		−	1.28361i	−0.766869	−	0.641804i	$-0.778186\pi$
$907$		−	38.6577i		−	1.28361i	0.766869	−	0.641804i	$-0.221814\pi$
$908$	−9.59107	+	13.2010i	−0.318291	+	0.438090i
$909$		0			0
$910$	10.3622	+	12.7561i	0.343505	+	0.422860i
$911$	−15.0057	−	46.1829i	−0.497162	−	1.53011i	−0.813560	−	0.581481i	$-0.802474\pi$
$911$	−15.0057	−	46.1829i	−0.497162	−	1.53011i	0.316398	−	0.948627i	$-0.397526\pi$
$912$		0			0
$913$	−1.40310	−	0.455895i	−0.0464359	−	0.0150879i
$914$	7.96115	+	24.5019i	0.263331	+	0.810451i
$915$		0			0
$916$	−0.164917	+	0.507563i	−0.00544902	+	0.0167704i
$917$	−7.00907	+	9.64715i	−0.231460	+	0.318577i
$918$		0			0
$919$	−23.7760	−	17.2743i	−0.784298	−	0.569826i	0.121968	−	0.992534i	$-0.461080\pi$
$919$	−23.7760	−	17.2743i	−0.784298	−	0.569826i	−0.906266	+	0.422708i	$0.861080\pi$
$920$	5.24966	+	13.6131i	0.173076	+	0.448812i
$921$		0			0
$922$	−19.0570	−	26.2298i	−0.627610	−	0.863831i
$923$	−12.8540	+	4.17650i	−0.423093	+	0.137471i
$924$		0			0
$925$	11.2871	−	19.6896i	0.371117	−	0.647389i
$926$	18.7775			0.617066
$927$		0			0
$928$	4.26518	+	5.87052i	0.140011	+	0.192709i
$929$	−38.3191	+	27.8405i	−1.25721	+	0.913416i	−0.998617	−	0.0525705i	$-0.983259\pi$
$929$	−38.3191	+	27.8405i	−1.25721	+	0.913416i	−0.258592	+	0.965987i	$0.583259\pi$
$930$		0			0
$931$	−0.0487235	−	0.0353997i	−0.00159685	−	0.00116018i
$932$		−	10.9418i		−	0.358410i
$933$		0			0
$934$	0.606328	−	1.86609i	0.0198397	−	0.0610602i
$935$	3.87135	−	1.49291i	0.126607	−	0.0488235i
$936$		0			0
$937$	23.1496	+	7.52176i	0.756264	+	0.245725i	0.661675	−	0.749791i	$-0.269846\pi$
$937$	23.1496	+	7.52176i	0.756264	+	0.245725i	0.0945898	+	0.995516i	$0.469846\pi$
$938$	−25.4966	−	8.28435i	−0.832494	−	0.270494i
$939$		0			0
$940$	18.7694	−	7.23809i	0.612191	−	0.236080i
$941$	−6.04638	+	18.6088i	−0.197106	+	0.606631i	0.802839	+	0.596196i	$0.203322\pi$
$941$	−6.04638	+	18.6088i	−0.197106	+	0.606631i	−0.999946	+	0.0104355i	$0.996678\pi$
$942$		0			0
$943$		−	34.7394i		−	1.13127i
$944$	3.03127	+	2.20234i	0.0986593	+	0.0716802i
$945$		0			0
$946$	1.86226	−	1.35301i	0.0605472	−	0.0439901i
$947$	−26.9916	−	37.1508i	−0.877110	−	1.20724i	−0.977213	−	0.212261i	$-0.931917\pi$
$947$	−26.9916	−	37.1508i	−0.877110	−	1.20724i	0.100103	−	0.994977i	$-0.468083\pi$
$948$		0			0
$949$	−33.0652			−1.07334
$950$	−1.10236	+	1.92300i	−0.0357654	+	0.0623904i
$951$		0			0
$952$	16.1773	−	5.25633i	0.524310	−	0.170359i
$953$	11.6259	+	16.0017i	0.376600	+	0.518346i	0.954680	−	0.297635i	$-0.0961977\pi$
$953$	11.6259	+	16.0017i	0.376600	+	0.518346i	−0.578080	+	0.815980i	$0.696198\pi$
$954$		0			0
$955$	18.8010	+	48.7538i	0.608386	+	1.57764i
$956$	4.88501	+	3.54917i	0.157993	+	0.114788i
$957$		0			0
$958$	3.96389	−	5.45583i	0.128068	−	0.176270i
$959$	−12.5845	+	38.7311i	−0.406375	+	1.25069i
$960$		0			0
$961$	−5.51496	−	16.9733i	−0.177902	−	0.547525i
$962$	12.1102	+	3.93484i	0.390448	+	0.126864i
$963$		0			0
$964$	−0.682003	−	2.09899i	−0.0219658	−	0.0676039i
$965$	3.00714	+	3.70183i	0.0968031	+	0.119166i
$966$		0			0
$967$	−12.4205	+	17.0954i	−0.399417	+	0.549750i	−0.960598	−	0.277943i	$-0.910347\pi$
$967$	−12.4205	+	17.0954i	−0.399417	+	0.549750i	0.561181	+	0.827693i	$0.310347\pi$
$968$		−	10.9183i		−	0.350928i
$969$		0			0
$970$	−12.1698	+	0.656584i	−0.390748	+	0.0210816i
$971$	−38.9629	+	28.3082i	−1.25038	+	0.908454i	−0.998244	−	0.0592379i	$-0.981133\pi$
$971$	−38.9629	+	28.3082i	−1.25038	+	0.908454i	−0.252136	+	0.967692i	$0.581133\pi$
$972$		0			0
$973$	−22.4279	+	7.28726i	−0.719004	+	0.233619i
$974$	1.16407			0.0372991
$975$		0			0
$976$	13.0189			0.416726
$977$	48.0847	−	15.6237i	1.53837	−	0.499846i	0.587441	−	0.809267i	$-0.300135\pi$
$977$	48.0847	−	15.6237i	1.53837	−	0.499846i	0.950925	+	0.309421i	$0.100135\pi$
$978$		0			0
$979$	1.42564	−	1.03579i	0.0455635	−	0.0331038i
$980$	0.0781717	−	0.293548i	0.00249710	−	0.00937705i
$981$		0			0
$982$		−	8.38720i		−	0.267646i
$983$	19.9304	−	27.4319i	0.635683	−	0.874942i	−0.362693	−	0.931908i	$-0.618143\pi$
$983$	19.9304	−	27.4319i	0.635683	−	0.874942i	0.998376	+	0.0569664i	$0.0181428\pi$
$984$		0			0
$985$	35.5581	+	9.46910i	1.13298	+	0.301711i
$986$	14.5582	+	44.8056i	0.463628	+	1.42690i
$987$		0			0
$988$	−1.18275	−	0.384300i	−0.0376284	−	0.0122262i
$989$	16.2393	+	49.9795i	0.516380	+	1.58926i
$990$		0			0
$991$	−15.9403	+	49.0592i	−0.506360	+	1.55842i	0.292111	+	0.956384i	$0.405642\pi$
$991$	−15.9403	+	49.0592i	−0.506360	+	1.55842i	−0.798472	+	0.602033i	$0.794358\pi$
$992$	−2.13174	+	2.93409i	−0.0676829	+	0.0931575i
$993$		0			0
$994$	−10.2118	−	7.41931i	−0.323899	−	0.235326i
$995$	−2.89064	+	2.34818i	−0.0916396	+	0.0744422i
$996$		0			0
$997$	20.1177	+	27.6896i	0.637134	+	0.876940i	0.998459	−	0.0555003i	$-0.0176754\pi$
$997$	20.1177	+	27.6896i	0.637134	+	0.876940i	−0.361325	+	0.932440i	$0.617675\pi$
$998$	−16.4143	+	5.33333i	−0.519586	+	0.168824i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.c.19.4		16
3.2	odd	2		150.2.h.b.19.1	✓	16
15.2	even	4		750.2.g.g.151.2		16
15.8	even	4		750.2.g.f.151.3		16
15.14	odd	2		750.2.h.d.349.3		16
25.4	even	10	inner	450.2.l.c.379.4		16
75.2	even	20		3750.2.a.u.1.4		8
75.11	odd	10		3750.2.c.k.1249.13		16
75.14	odd	10		3750.2.c.k.1249.4		16
75.23	even	20		3750.2.a.v.1.5		8
75.29	odd	10		150.2.h.b.79.1	yes	16
75.47	even	20		750.2.g.g.601.2		16
75.53	even	20		750.2.g.f.601.3		16
75.71	odd	10		750.2.h.d.649.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.1	✓	16	3.2	odd	2
150.2.h.b.79.1	yes	16	75.29	odd	10
450.2.l.c.19.4		16	1.1	even	1	trivial
450.2.l.c.379.4		16	25.4	even	10	inner
750.2.g.f.151.3		16	15.8	even	4
750.2.g.f.601.3		16	75.53	even	20
750.2.g.g.151.2		16	15.2	even	4
750.2.g.g.601.2		16	75.47	even	20
750.2.h.d.349.3		16	15.14	odd	2
750.2.h.d.649.4		16	75.71	odd	10
3750.2.a.u.1.4		8	75.2	even	20
3750.2.a.v.1.5		8	75.23	even	20
3750.2.c.k.1249.4		16	75.14	odd	10
3750.2.c.k.1249.13		16	75.11	odd	10

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.73558 - 1.40988i) q^{5} +2.61995i q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.73558 - 1.40988i) q^{5} +2.61995i q^{7} +(0.587785 - 0.809017i) q^{8} +(1.21496 - 1.87720i) q^{10} +(0.0883198 + 0.271820i) q^{11} +(2.66799 + 0.866884i) q^{13} +(0.809610 + 2.49172i) q^{14} +(0.309017 - 0.951057i) q^{16} +(3.81615 - 5.25248i) q^{17} +(-0.358647 - 0.260572i) q^{19} +(0.575410 - 2.16076i) q^{20} +(0.167994 + 0.231224i) q^{22} +(-6.20562 + 2.01633i) q^{23} +(1.02449 - 4.89392i) q^{25} +2.80530 q^{26} +(1.53997 + 2.11959i) q^{28} +(-5.87052 + 4.26518i) q^{29} +(-2.93409 - 2.13174i) q^{31} -1.00000i q^{32} +(2.00627 - 6.17466i) q^{34} +(3.69381 + 4.54714i) q^{35} +(4.31691 + 1.40265i) q^{37} +(-0.421615 - 0.136991i) q^{38} +(-0.120465 - 2.23282i) q^{40} +(-1.64523 + 5.06349i) q^{41} -8.05390i q^{43} +(0.231224 + 0.167994i) q^{44} +(-5.27882 + 3.83529i) q^{46} +(5.28799 + 7.27829i) q^{47} +0.135854 q^{49} +(-0.537954 - 4.97098i) q^{50} +(2.66799 - 0.866884i) q^{52} +(-8.17947 - 11.2581i) q^{53} +(0.536520 + 0.347247i) q^{55} +(2.11959 + 1.53997i) q^{56} +(-4.26518 + 5.87052i) q^{58} +(-1.15784 + 3.56347i) q^{59} +(4.02308 + 12.3818i) q^{61} +(-3.44923 - 1.12072i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(5.85272 - 2.25700i) q^{65} +(-6.01453 + 8.27829i) q^{67} -6.49242i q^{68} +(4.91817 + 3.18314i) q^{70} +(-3.89771 + 2.83185i) q^{71} +(-11.2098 + 3.64230i) q^{73} +4.53906 q^{74} -0.443312 q^{76} +(-0.712156 + 0.231394i) q^{77} +(-6.32216 + 4.59332i) q^{79} +(-0.804549 - 2.08631i) q^{80} +5.32407i q^{82} +(-3.03407 + 4.17604i) q^{83} +(-0.782111 - 14.4964i) q^{85} +(-2.48879 - 7.65972i) q^{86} +(0.271820 + 0.0883198i) q^{88} +(-1.90527 - 5.86383i) q^{89} +(-2.27119 + 6.99002i) q^{91} +(-3.83529 + 5.27882i) q^{92} +(7.27829 + 5.28799i) q^{94} +(-0.989836 + 0.0534036i) q^{95} +(-3.20367 - 4.40947i) q^{97} +(0.129205 - 0.0419811i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 - 4 * q^5	\( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^5 + 2 * q^10 - 2 * q^11 + 20 * q^13 - 2 * q^14 - 4 * q^16 + 30 * q^17 + 4 * q^20 - 20 * q^22 + 10 * q^23 + 24 * q^25 - 4 * q^26 + 10 * q^29 - 18 * q^31 + 12 * q^34 + 34 * q^35 + 20 * q^37 - 10 * q^38 - 2 * q^40 - 22 * q^41 - 8 * q^44 - 6 * q^46 + 50 * q^47 - 52 * q^49 - 12 * q^50 + 20 * q^52 - 30 * q^53 + 18 * q^55 + 2 * q^56 - 30 * q^58 - 20 * q^59 + 12 * q^61 - 50 * q^62 + 4 * q^64 + 8 * q^65 - 50 * q^67 - 12 * q^70 + 28 * q^71 + 20 * q^73 - 12 * q^74 + 20 * q^76 - 100 * q^77 - 20 * q^79 - 4 * q^80 + 30 * q^83 - 4 * q^85 + 6 * q^86 - 70 * q^89 + 12 * q^91 + 30 * q^92 + 2 * q^94 + 30 * q^95 - 10 * q^97 - 60 * q^98

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