LMFDB - Embedded newform 450.2.l.c.289.3

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			289.3
Root			$-2.79002 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	450.289
Dual form			450.2.l.c.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-2.03938 - 0.917020i) q^{5} -4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-2.03938 - 0.917020i) q^{5} -4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.456833 - 2.18890i) q^{10} +(-0.714027 + 0.518771i) q^{11} +(1.66061 - 2.28564i) q^{13} +(3.88890 - 2.82545i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.57666 - 0.512289i) q^{17} +(-1.66217 - 5.11563i) q^{19} +(1.50234 - 1.65619i) q^{20} +(-0.839389 - 0.272734i) q^{22} +(-3.44056 - 4.73553i) q^{23} +(3.31815 + 3.74031i) q^{25} +2.82520 q^{26} +(4.57167 + 1.48543i) q^{28} +(1.10574 - 3.40313i) q^{29} +(3.22681 + 9.93109i) q^{31} -1.00000i q^{32} +(1.34119 + 0.974432i) q^{34} +(-4.40806 + 9.80318i) q^{35} +(-1.02631 + 1.41260i) q^{37} +(3.16163 - 4.35161i) q^{38} +(2.22294 + 0.241934i) q^{40} +(-1.40381 - 1.01993i) q^{41} -2.27151i q^{43} +(-0.272734 - 0.839389i) q^{44} +(1.80881 - 5.56695i) q^{46} +(8.29746 + 2.69601i) q^{47} -16.1067 q^{49} +(-1.07561 + 4.88294i) q^{50} +(1.66061 + 2.28564i) q^{52} +(3.37565 + 1.09681i) q^{53} +(1.93190 - 0.403195i) q^{55} +(1.48543 + 4.57167i) q^{56} +(3.40313 - 1.10574i) q^{58} +(-8.37628 - 6.08572i) q^{59} +(0.0697810 - 0.0506988i) q^{61} +(-6.13775 + 8.44789i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-5.48259 + 3.13847i) q^{65} +(-11.3751 + 3.69601i) q^{67} +1.65780i q^{68} +(-10.5219 + 2.19597i) q^{70} +(1.08390 - 3.33591i) q^{71} +(4.24851 + 5.84757i) q^{73} -1.74607 q^{74} +5.37889 q^{76} +(2.49370 + 3.43228i) q^{77} +(3.88627 - 11.9607i) q^{79} +(1.11088 + 1.94060i) q^{80} -1.73520i q^{82} +(12.6244 - 4.10192i) q^{83} +(-3.68520 - 0.401079i) q^{85} +(1.83769 - 1.33516i) q^{86} +(0.518771 - 0.714027i) q^{88} +(-15.1178 + 10.9837i) q^{89} +(-10.9869 - 7.98246i) q^{91} +(5.56695 - 1.80881i) q^{92} +(2.69601 + 8.29746i) q^{94} +(-1.30134 + 11.9570i) q^{95} +(17.3764 + 5.64593i) q^{97} +(-9.46727 - 13.0306i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−2.03938	−	0.917020i	−0.912039	−	0.410104i
$5$	−2.03938	−	0.917020i	−0.912039	−	0.410104i
$6$		0			0
$7$		−	4.80694i		−	1.81685i	−0.418045	−	0.908426i	$-0.637284\pi$
$7$		−	4.80694i		−	1.81685i	0.418045	−	0.908426i	$-0.362716\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$		0			0
$10$	−0.456833	−	2.18890i	−0.144463	−	0.692192i
$11$	−0.714027	+	0.518771i	−0.215287	+	0.156415i	−0.690203	−	0.723616i	$-0.742479\pi$
$11$	−0.714027	+	0.518771i	−0.215287	+	0.156415i	0.474915	+	0.880031i	$0.342479\pi$
$12$		0			0
$13$	1.66061	−	2.28564i	0.460571	−	0.633921i	−0.514056	−	0.857756i	$-0.671858\pi$
$13$	1.66061	−	2.28564i	0.460571	−	0.633921i	0.974627	+	0.223835i	$0.0718578\pi$
$14$	3.88890	−	2.82545i	1.03935	−	0.755133i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.57666	−	0.512289i	0.382397	−	0.124248i	−0.111509	−	0.993763i	$-0.535568\pi$
$17$	1.57666	−	0.512289i	0.382397	−	0.124248i	0.493907	+	0.869515i	$0.335568\pi$
$18$		0			0
$19$	−1.66217	−	5.11563i	−0.381327	−	1.17361i	−0.939110	−	0.343618i	$-0.888348\pi$
$19$	−1.66217	−	5.11563i	−0.381327	−	1.17361i	0.557782	−	0.829987i	$-0.311652\pi$
$20$	1.50234	−	1.65619i	0.335934	−	0.370336i
$21$		0			0
$22$	−0.839389	−	0.272734i	−0.178958	−	0.0581471i
$23$	−3.44056	−	4.73553i	−0.717407	−	0.987426i	−0.999606	−	0.0280705i	$-0.991064\pi$
$23$	−3.44056	−	4.73553i	−0.717407	−	0.987426i	0.282199	−	0.959356i	$-0.408936\pi$
$24$		0			0
$25$	3.31815	+	3.74031i	0.663630	+	0.748061i
$26$	2.82520			0.554067
$27$		0			0
$28$	4.57167	+	1.48543i	0.863965	+	0.280719i
$29$	1.10574	−	3.40313i	0.205332	−	0.631946i	−0.794368	−	0.607437i	$-0.792198\pi$
$29$	1.10574	−	3.40313i	0.205332	−	0.631946i	0.999700	−	0.0245090i	$-0.00780223\pi$
$30$		0			0
$31$	3.22681	+	9.93109i	0.579551	+	1.78368i	0.620130	+	0.784499i	$0.287080\pi$
$31$	3.22681	+	9.93109i	0.579551	+	1.78368i	−0.0405785	+	0.999176i	$0.512920\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	1.34119	+	0.974432i	0.230012	+	0.167114i
$35$	−4.40806	+	9.80318i	−0.745098	+	1.65704i
$36$		0			0
$37$	−1.02631	+	1.41260i	−0.168725	+	0.232230i	−0.885003	−	0.465585i	$-0.845844\pi$
$37$	−1.02631	+	1.41260i	−0.168725	+	0.232230i	0.716278	+	0.697815i	$0.245844\pi$
$38$	3.16163	−	4.35161i	0.512884	−	0.705925i
$39$		0			0
$40$	2.22294	+	0.241934i	0.351478	+	0.0382532i
$41$	−1.40381	−	1.01993i	−0.219238	−	0.159286i	0.472746	−	0.881199i	$-0.343263\pi$
$41$	−1.40381	−	1.01993i	−0.219238	−	0.159286i	−0.691984	+	0.721913i	$0.743263\pi$
$42$		0			0
$43$		−	2.27151i		−	0.346403i	−0.984886	−	0.173201i	$-0.944589\pi$
$43$		−	2.27151i		−	0.346403i	0.984886	−	0.173201i	$-0.0554111\pi$
$44$	−0.272734	−	0.839389i	−0.0411162	−	0.126543i
$45$		0			0
$46$	1.80881	−	5.56695i	0.266695	−	0.820802i
$47$	8.29746	+	2.69601i	1.21031	+	0.393253i	0.843544	−	0.537060i	$-0.180465\pi$
$47$	8.29746	+	2.69601i	1.21031	+	0.393253i	0.366765	+	0.930314i	$0.380465\pi$
$48$		0			0
$49$	−16.1067			−2.30095
$50$	−1.07561	+	4.88294i	−0.152114	+	0.690551i
$51$		0			0
$52$	1.66061	+	2.28564i	0.230285	+	0.316961i
$53$	3.37565	+	1.09681i	0.463681	+	0.150659i	0.531535	−	0.847036i	$-0.321615\pi$
$53$	3.37565	+	1.09681i	0.463681	+	0.150659i	−0.0678545	+	0.997695i	$0.521615\pi$
$54$		0			0
$55$	1.93190	−	0.403195i	0.260497	−	0.0543667i
$56$	1.48543	+	4.57167i	0.198498	+	0.610915i
$57$		0			0
$58$	3.40313	−	1.10574i	0.446853	−	0.145191i
$59$	−8.37628	−	6.08572i	−1.09050	−	0.792293i	−0.111015	−	0.993819i	$-0.535410\pi$
$59$	−8.37628	−	6.08572i	−1.09050	−	0.792293i	−0.979483	+	0.201525i	$0.935410\pi$
$60$		0			0
$61$	0.0697810	−	0.0506988i	0.00893454	−	0.00649132i	−0.583309	−	0.812250i	$-0.698242\pi$
$61$	0.0697810	−	0.0506988i	0.00893454	−	0.00649132i	0.592244	+	0.805759i	$0.298242\pi$
$62$	−6.13775	+	8.44789i	−0.779495	+	1.07288i
$63$		0			0
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−5.48259	+	3.13847i	−0.680032	+	0.389279i
$66$		0			0
$67$	−11.3751	+	3.69601i	−1.38969	+	0.451539i	−0.905844	−	0.423611i	$-0.860762\pi$
$67$	−11.3751	+	3.69601i	−1.38969	+	0.451539i	−0.483851	+	0.875150i	$0.660762\pi$
$68$			1.65780i			0.201038i
$69$		0			0
$70$	−10.5219	+	2.19597i	−1.25761	+	0.262469i
$71$	1.08390	−	3.33591i	0.128636	−	0.395900i	−0.865910	−	0.500199i	$-0.833260\pi$
$71$	1.08390	−	3.33591i	0.128636	−	0.395900i	0.994546	+	0.104300i	$0.0332601\pi$
$72$		0			0
$73$	4.24851	+	5.84757i	0.497251	+	0.684407i	0.981705	−	0.190410i	$-0.0609817\pi$
$73$	4.24851	+	5.84757i	0.497251	+	0.684407i	−0.484454	+	0.874817i	$0.660982\pi$
$74$	−1.74607			−0.202977
$75$		0			0
$76$	5.37889			0.617001
$77$	2.49370	+	3.43228i	0.284184	+	0.391145i
$78$		0			0
$79$	3.88627	−	11.9607i	0.437240	−	1.34569i	−0.453533	−	0.891239i	$-0.649837\pi$
$79$	3.88627	−	11.9607i	0.437240	−	1.34569i	0.890774	−	0.454447i	$-0.150163\pi$
$80$	1.11088	+	1.94060i	0.124201	+	0.216966i
$81$		0			0
$82$		−	1.73520i		−	0.191621i
$83$	12.6244	−	4.10192i	1.38571	−	0.450244i	0.481166	−	0.876629i	$-0.340213\pi$
$83$	12.6244	−	4.10192i	1.38571	−	0.450244i	0.904541	+	0.426386i	$0.140213\pi$
$84$		0			0
$85$	−3.68520	−	0.401079i	−0.399716	−	0.0435032i
$86$	1.83769	−	1.33516i	0.198164	−	0.143974i
$87$		0			0
$88$	0.518771	−	0.714027i	0.0553011	−	0.0761155i
$89$	−15.1178	+	10.9837i	−1.60248	+	1.16427i	−0.719939	+	0.694037i	$0.755830\pi$
$89$	−15.1178	+	10.9837i	−1.60248	+	1.16427i	−0.882542	+	0.470233i	$0.844170\pi$
$90$		0			0
$91$	−10.9869	−	7.98246i	−1.15174	−	0.836789i
$92$	5.56695	−	1.80881i	0.580395	−	0.188582i
$93$		0			0
$94$	2.69601	+	8.29746i	0.278072	+	0.855818i
$95$	−1.30134	+	11.9570i	−0.133514	+	1.22676i
$96$		0			0
$97$	17.3764	+	5.64593i	1.76430	+	0.573257i	0.997632	−	0.0687822i	$-0.0219114\pi$
$97$	17.3764	+	5.64593i	1.76430	+	0.573257i	0.766672	+	0.642039i	$0.221911\pi$
$98$	−9.46727	−	13.0306i	−0.956339	−	1.31629i
$99$		0			0
$100$	−4.58261	+	1.99993i	−0.458261	+	0.199993i
$101$	5.46110			0.543400			0.271700	−	0.962382i	$-0.412414\pi$
$101$	5.46110			0.543400			0.271700	+	0.962382i	$0.412414\pi$
$102$		0			0
$103$	6.31725	+	2.05260i	0.622457	+	0.202248i	0.603231	−	0.797567i	$-0.293880\pi$
$103$	6.31725	+	2.05260i	0.622457	+	0.202248i	0.0192260	+	0.999815i	$0.493880\pi$
$104$	−0.873035	+	2.68693i	−0.0856081	+	0.263475i
$105$		0			0
$106$	1.09681	+	3.37565i	0.106532	+	0.327872i
$107$		−	14.5245i		−	1.40414i	−0.712108	−	0.702070i	$-0.752259\pi$
$107$		−	14.5245i		−	1.40414i	0.712108	−	0.702070i	$-0.247741\pi$
$108$		0			0
$109$	3.85954	+	2.80412i	0.369676	+	0.268586i	0.757077	−	0.653326i	$-0.226627\pi$
$109$	3.85954	+	2.80412i	0.369676	+	0.268586i	−0.387400	+	0.921912i	$0.626627\pi$
$110$	1.46173	+	1.32594i	0.139371	+	0.126424i
$111$		0			0
$112$	−2.82545	+	3.88890i	−0.266980	+	0.367466i
$113$	−2.84228	+	3.91206i	−0.267379	+	0.368016i	−0.921503	−	0.388372i	$-0.873038\pi$
$113$	−2.84228	+	3.91206i	−0.267379	+	0.368016i	0.654124	+	0.756388i	$0.273038\pi$
$114$		0			0
$115$	2.67405	+	12.8126i	0.249356	+	1.19478i
$116$	2.89488	+	2.10325i	0.268783	+	0.195282i
$117$		0			0
$118$		−	10.3536i		−	0.953131i
$119$	−2.46254	−	7.57893i	−0.225741	−	0.694759i
$120$		0			0
$121$	−3.15848	+	9.72079i	−0.287134	+	0.883708i
$122$	0.0820324	+	0.0266540i	0.00742687	+	0.00241314i
$123$		0			0
$124$	−10.4422			−0.937734
$125$	−3.33704	−	10.6707i	−0.298474	−	0.954418i
$126$		0			0
$127$	1.05908	+	1.45769i	0.0939779	+	0.129349i	0.853417	−	0.521229i	$-0.174526\pi$
$127$	1.05908	+	1.45769i	0.0939779	+	0.129349i	−0.759439	+	0.650579i	$0.774526\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$		0			0
$130$	−5.76166	−	2.59077i	−0.505331	−	0.227225i
$131$	4.95400	+	15.2468i	0.432833	+	1.33212i	0.895291	+	0.445481i	$0.146967\pi$
$131$	4.95400	+	15.2468i	0.432833	+	1.33212i	−0.462459	+	0.886641i	$0.653033\pi$
$132$		0			0
$133$	−24.5905	+	7.98994i	−2.13227	+	0.692816i
$134$	−9.67628	−	7.03023i	−0.835903	−	0.607319i
$135$		0			0
$136$	−1.34119	+	0.974432i	−0.115006	+	0.0835569i
$137$	1.03872	−	1.42968i	0.0887443	−	0.122146i	−0.762336	−	0.647181i	$-0.775948\pi$
$137$	1.03872	−	1.42968i	0.0887443	−	0.122146i	0.851081	+	0.525035i	$0.175948\pi$
$138$		0			0
$139$	8.89636	−	6.46359i	0.754580	−	0.548234i	−0.142663	−	0.989771i	$-0.545567\pi$
$139$	8.89636	−	6.46359i	0.754580	−	0.548234i	0.897243	+	0.441537i	$0.145567\pi$
$140$	−7.96122	−	7.22166i	−0.672846	−	0.610342i
$141$		0			0
$142$	3.33591	−	1.08390i	0.279943	−	0.0909591i
$143$			2.49348i			0.208515i
$144$		0			0
$145$	−5.37577	+	5.92629i	−0.446434	+	0.492152i
$146$	−2.23357	+	6.87424i	−0.184852	+	0.568916i
$147$		0			0
$148$	−1.02631	−	1.41260i	−0.0843625	−	0.116115i
$149$	2.90948			0.238354			0.119177	−	0.992873i	$-0.461974\pi$
$149$	2.90948			0.238354			0.119177	+	0.992873i	$0.461974\pi$
$150$		0			0
$151$	−1.34184			−0.109197			−0.0545986	−	0.998508i	$-0.517388\pi$
$151$	−1.34184			−0.109197			−0.0545986	+	0.998508i	$0.517388\pi$
$152$	3.16163	+	4.35161i	0.256442	+	0.352962i
$153$		0			0
$154$	−1.31102	+	4.03489i	−0.105645	+	0.325141i
$155$	2.52632	−	23.2123i	0.202919	−	1.86446i
$156$		0			0
$157$		−	8.31169i		−	0.663345i	−0.943395	−	0.331673i	$-0.892387\pi$
$157$		−	8.31169i		−	0.663345i	0.943395	−	0.331673i	$-0.107613\pi$
$158$	11.9607	−	3.88627i	0.951544	−	0.309175i
$159$		0			0
$160$	−0.917020	+	2.03938i	−0.0724968	+	0.161227i
$161$	−22.7634	+	16.5386i	−1.79401	+	1.30342i
$162$		0			0
$163$	3.66704	−	5.04724i	0.287225	−	0.395331i	−0.640886	−	0.767636i	$-0.721433\pi$
$163$	3.66704	−	5.04724i	0.287225	−	0.395331i	0.928110	+	0.372306i	$0.121433\pi$
$164$	1.40381	−	1.01993i	0.109619	−	0.0796429i
$165$		0			0
$166$	10.7390	+	7.80231i	0.833505	+	0.605576i
$167$	14.1107	−	4.58483i	1.09192	−	0.354785i	0.292929	−	0.956134i	$-0.405370\pi$
$167$	14.1107	−	4.58483i	1.09192	−	0.354785i	0.798986	+	0.601349i	$0.205370\pi$
$168$		0			0
$169$	1.55072	+	4.77263i	0.119286	+	0.367125i
$170$	−1.84163	−	3.21714i	−0.141246	−	0.246743i
$171$		0			0
$172$	2.16034	+	0.701936i	0.164724	+	0.0535221i
$173$	9.42623	+	12.9741i	0.716663	+	0.986402i	0.999628	+	0.0272719i	$0.00868201\pi$
$173$	9.42623	+	12.9741i	0.716663	+	0.986402i	−0.282965	+	0.959130i	$0.591318\pi$
$174$		0			0
$175$	17.9794	−	15.9501i	1.35912	−	1.20572i
$176$	0.882586			0.0665274
$177$		0			0
$178$	−17.7720	−	5.77448i	−1.33207	−	0.432815i
$179$	3.63061	−	11.1739i	0.271365	−	0.835174i	−0.718794	−	0.695223i	$-0.755306\pi$
$179$	3.63061	−	11.1739i	0.271365	−	0.835174i	0.990158	−	0.139951i	$-0.0446945\pi$
$180$		0			0
$181$	−1.24658	−	3.83658i	−0.0926577	−	0.285171i	0.893979	−	0.448110i	$-0.147903\pi$
$181$	−1.24658	−	3.83658i	−0.0926577	−	0.285171i	−0.986636	+	0.162939i	$0.947903\pi$
$182$		−	13.5806i		−	1.00666i
$183$		0			0
$184$	4.73553	+	3.44056i	0.349108	+	0.253642i
$185$	3.38843	−	1.93968i	0.249122	−	0.142608i
$186$		0			0
$187$	−0.860020	+	1.18372i	−0.0628909	+	0.0865618i
$188$	−5.12811	+	7.05824i	−0.374006	+	0.514775i
$189$		0			0
$190$	−10.4383	+	5.97532i	−0.757273	+	0.433495i
$191$	9.64472	+	7.00730i	0.697867	+	0.507030i	0.879237	−	0.476385i	$-0.158053\pi$
$191$	9.64472	+	7.00730i	0.697867	+	0.507030i	−0.181370	+	0.983415i	$0.558053\pi$
$192$		0			0
$193$		−	11.8088i		−	0.850019i	−0.905189	−	0.425009i	$-0.860271\pi$
$193$		−	11.8088i		−	0.850019i	0.905189	−	0.425009i	$-0.139729\pi$
$194$	5.64593	+	17.3764i	0.405354	+	1.24755i
$195$		0			0
$196$	4.97724	−	15.3184i	0.355517	−	1.09417i
$197$	6.92219	+	2.24916i	0.493186	+	0.160246i	0.545042	−	0.838409i	$-0.316514\pi$
$197$	6.92219	+	2.24916i	0.493186	+	0.160246i	−0.0518562	+	0.998655i	$0.516514\pi$
$198$		0			0
$199$	−2.27949			−0.161589			−0.0807944	−	0.996731i	$-0.525746\pi$
$199$	−2.27949			−0.161589			−0.0807944	+	0.996731i	$0.525746\pi$
$200$	−4.31157	−	2.53188i	−0.304874	−	0.179031i
$201$		0			0
$202$	3.20996	+	4.41813i	0.225852	+	0.310858i
$203$	−16.3587	−	5.31525i	−1.14815	−	0.373057i
$204$		0			0
$205$	1.92761	+	3.36734i	0.134630	+	0.235185i
$206$	2.05260	+	6.31725i	0.143011	+	0.440143i
$207$		0			0
$208$	−2.68693	+	0.873035i	−0.186305	+	0.0605341i
$209$	3.84067	+	2.79041i	0.265665	+	0.193017i
$210$		0			0
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	−0.552455	−	0.833543i	$-0.686309\pi$
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	0.622029	+	0.782994i	$0.286309\pi$
$212$	−2.08626	+	2.87150i	−0.143285	+	0.197215i
$213$		0			0
$214$	11.7506	−	8.53731i	0.803255	−	0.583599i
$215$	−2.08302	+	4.63248i	−0.142061	+	0.315933i
$216$		0			0
$217$	47.7381	−	15.5111i	3.24068	−	1.05296i
$218$			4.77065i			0.323109i
$219$		0			0
$220$	−0.213528	+	1.96194i	−0.0143960	+	0.132274i
$221$	1.44732	−	4.45439i	0.0973573	−	0.299635i
$222$		0			0
$223$	5.19727	+	7.15343i	0.348035	+	0.479029i	0.946767	−	0.321921i	$-0.104328\pi$
$223$	5.19727	+	7.15343i	0.348035	+	0.479029i	−0.598732	+	0.800950i	$0.704328\pi$
$224$	−4.80694			−0.321177
$225$		0			0
$226$	−4.83558			−0.321658
$227$	−10.4019	−	14.3170i	−0.690398	−	0.950251i	0.309602	−	0.950866i	$-0.399804\pi$
$227$	−10.4019	−	14.3170i	−0.690398	−	0.950251i	−1.00000		0.000615300i	$0.999804\pi$
$228$		0			0
$229$	2.75446	−	8.47737i	0.182020	−	0.560200i	−0.817864	−	0.575411i	$-0.804842\pi$
$229$	2.75446	−	8.47737i	0.182020	−	0.560200i	0.999884	+	0.0152110i	$0.00484200\pi$
$230$	−8.79386	+	9.69442i	−0.579850	+	0.639231i
$231$		0			0
$232$			3.57827i			0.234925i
$233$	9.12123	−	2.96367i	0.597551	−	0.194156i	0.00540335	−	0.999985i	$-0.498280\pi$
$233$	9.12123	−	2.96367i	0.597551	−	0.194156i	0.592148	+	0.805829i	$0.298280\pi$
$234$		0			0
$235$	−14.4494	−	13.1071i	−0.942574	−	0.855014i
$236$	8.37628	−	6.08572i	0.545249	−	0.396147i
$237$		0			0
$238$	4.68404	−	6.44702i	0.303621	−	0.417898i
$239$	7.41301	−	5.38587i	0.479508	−	0.348383i	−0.321627	−	0.946866i	$-0.604230\pi$
$239$	7.41301	−	5.38587i	0.479508	−	0.348383i	0.801135	+	0.598483i	$0.204230\pi$
$240$		0			0
$241$	2.01891	+	1.46682i	0.130049	+	0.0944864i	0.650908	−	0.759156i	$-0.274388\pi$
$241$	2.01891	+	1.46682i	0.130049	+	0.0944864i	−0.520859	+	0.853643i	$0.674388\pi$
$242$	−9.72079	+	3.15848i	−0.624876	+	0.203035i
$243$		0			0
$244$	0.0266540	+	0.0820324i	0.00170634	+	0.00525159i
$245$	32.8477	+	14.7701i	2.09856	+	0.943630i
$246$		0			0
$247$	−14.4527	−	4.69596i	−0.919601	−	0.298797i
$248$	−6.13775	−	8.44789i	−0.389747	−	0.536441i
$249$		0			0
$250$	6.67133	−	8.97181i	0.421932	−	0.567427i
$251$	−8.71262			−0.549936			−0.274968	−	0.961453i	$-0.588667\pi$
$251$	−8.71262			−0.549936			−0.274968	+	0.961453i	$0.588667\pi$
$252$		0			0
$253$	4.91331	+	1.59643i	0.308897	+	0.100367i
$254$	−0.556790	+	1.71362i	−0.0349361	+	0.107522i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			19.7871i			1.23429i	0.786851	+	0.617143i	$0.211710\pi$
$257$			19.7871i			1.23429i	−0.786851	+	0.617143i	$0.788290\pi$
$258$		0			0
$259$	6.79029	+	4.93343i	0.421928	+	0.306549i
$260$	−1.29065	−	6.18409i	−0.0800425	−	0.383521i
$261$		0			0
$262$	−9.42306	+	12.9697i	−0.582159	+	0.801272i
$263$	15.0258	−	20.6813i	0.926532	−	1.27526i	−0.0346651	−	0.999399i	$-0.511036\pi$
$263$	15.0258	−	20.6813i	0.926532	−	1.27526i	0.961197	−	0.275863i	$-0.0889636\pi$
$264$		0			0
$265$	−5.87843	−	5.33236i	−0.361109	−	0.327564i
$266$	−20.9179	−	15.1978i	−1.28256	−	0.931835i
$267$		0			0
$268$		−	11.9605i		−	0.730606i
$269$	7.54447	+	23.2195i	0.459994	+	1.41572i	0.865170	+	0.501478i	$0.167210\pi$
$269$	7.54447	+	23.2195i	0.459994	+	1.41572i	−0.405176	+	0.914239i	$0.632790\pi$
$270$		0			0
$271$	0.848720	−	2.61209i	0.0515561	−	0.158673i	−0.921964	−	0.387277i	$-0.873416\pi$
$271$	0.848720	−	2.61209i	0.0515561	−	0.158673i	0.973520	+	0.228603i	$0.0734159\pi$
$272$	−1.57666	−	0.512289i	−0.0955993	−	0.0310621i
$273$		0			0
$274$	1.76718			0.106760
$275$	−4.30961	−	0.949319i	−0.259879	−	0.0572461i
$276$		0			0
$277$	−1.75206	−	2.41151i	−0.105271	−	0.144893i	0.753131	−	0.657870i	$-0.228543\pi$
$277$	−1.75206	−	2.41151i	−0.105271	−	0.144893i	−0.858402	+	0.512977i	$0.828543\pi$
$278$	10.4583	+	3.39811i	0.627247	+	0.203805i
$279$		0			0
$280$	1.16296	−	10.6855i	0.0695004	−	0.638584i
$281$	−1.19334	−	3.67274i	−0.0711890	−	0.219097i	0.909132	−	0.416509i	$-0.136746\pi$
$281$	−1.19334	−	3.67274i	−0.0711890	−	0.219097i	−0.980321	+	0.197412i	$0.936746\pi$
$282$		0			0
$283$	−15.8844	+	5.16117i	−0.944232	+	0.306800i	−0.740370	−	0.672200i	$-0.765350\pi$
$283$	−15.8844	+	5.16117i	−0.944232	+	0.306800i	−0.203863	+	0.979000i	$0.565350\pi$
$284$	2.83769	+	2.06170i	0.168386	+	0.122340i
$285$		0			0
$286$	−2.01727	+	1.46563i	−0.119284	+	0.0866646i
$287$	−4.90273	+	6.74802i	−0.289399	+	0.398323i
$288$		0			0
$289$	−11.5299	+	8.37693i	−0.678227	+	0.492761i
$290$	−7.95427	−	0.865705i	−0.467091	−	0.0508360i
$291$		0			0
$292$	−6.87424	+	2.23357i	−0.402284	+	0.130710i
$293$		−	0.503153i		−	0.0293945i	−0.999892	−	0.0146972i	$-0.995322\pi$
$293$		−	0.503153i		−	0.0293945i	0.999892	−	0.0146972i	$-0.00467845\pi$
$294$		0			0
$295$	11.5017	+	20.0923i	0.669654	+	1.16982i
$296$	0.539565	−	1.66061i	0.0313616	−	0.0965211i
$297$		0			0
$298$	1.71015	+	2.35382i	0.0990664	+	0.136353i
$299$	−16.5371			−0.956367
$300$		0			0
$301$	−10.9190			−0.629363
$302$	−0.788713	−	1.08557i	−0.0453853	−	0.0624675i
$303$		0			0
$304$	−1.66217	+	5.11563i	−0.0953319	+	0.293401i
$305$	−0.188802	+	0.0394037i	−0.0108108	+	0.00225625i
$306$		0			0
$307$		−	8.63375i		−	0.492754i	−0.969174	−	0.246377i	$-0.920760\pi$
$307$		−	8.63375i		−	0.492754i	0.969174	−	0.246377i	$-0.0792402\pi$
$308$	−4.03489	+	1.31102i	−0.229909	+	0.0747021i
$309$		0			0
$310$	20.2641	−	11.6000i	1.15092	−	0.658837i
$311$	16.3967	−	11.9129i	0.929771	−	0.675518i	−0.0161660	−	0.999869i	$-0.505146\pi$
$311$	16.3967	−	11.9129i	0.929771	−	0.675518i	0.945937	+	0.324351i	$0.105146\pi$
$312$		0			0
$313$	10.0101	−	13.7777i	0.565805	−	0.778763i	−0.426245	−	0.904608i	$-0.640164\pi$
$313$	10.0101	−	13.7777i	0.565805	−	0.778763i	0.992050	+	0.125844i	$0.0401640\pi$
$314$	6.72430	−	4.88549i	0.379474	−	0.275704i
$315$		0			0
$316$	10.1744	+	7.39213i	0.572355	+	0.415840i
$317$	−2.68347	+	0.871912i	−0.150719	+	0.0489715i	−0.383405	−	0.923580i	$-0.625249\pi$
$317$	−2.68347	+	0.871912i	−0.150719	+	0.0489715i	0.232686	+	0.972552i	$0.425249\pi$
$318$		0			0
$319$	0.975914	+	3.00356i	0.0546407	+	0.168167i
$320$	−2.18890	+	0.456833i	−0.122363	+	0.0255378i
$321$		0			0
$322$	−26.7600	−	8.69485i	−1.49128	−	0.484545i
$323$	−5.24136	−	7.21411i	−0.291637	−	0.401404i
$324$		0			0
$325$	14.0591	−	1.37289i	0.779860	−	0.0761540i
$326$	6.23874			0.345532
$327$		0			0
$328$	1.65028	+	0.536207i	0.0911212	+	0.0296071i
$329$	12.9596	−	39.8854i	0.714483	−	2.19895i
$330$		0			0
$331$	−1.25862	−	3.87364i	−0.0691802	−	0.212915i	0.910489	−	0.413532i	$-0.135705\pi$
$331$	−1.25862	−	3.87364i	−0.0691802	−	0.212915i	−0.979670	+	0.200618i	$0.935705\pi$
$332$			13.2741i			0.728510i
$333$		0			0
$334$	12.0032	+	8.72086i	0.656788	+	0.477184i
$335$	26.5876	+	2.89366i	1.45263	+	0.158098i
$336$		0			0
$337$	−5.31818	+	7.31984i	−0.289700	+	0.398737i	−0.928917	−	0.370289i	$-0.879259\pi$
$337$	−5.31818	+	7.31984i	−0.289700	+	0.398737i	0.639217	+	0.769026i	$0.279259\pi$
$338$	−2.94965	+	4.05984i	−0.160440	+	0.220826i
$339$		0			0
$340$	1.52024	−	3.38089i	0.0824465	−	0.183355i
$341$	−7.45598	−	5.41709i	−0.403764	−	0.293352i
$342$		0			0
$343$			43.7753i			2.36364i
$344$	0.701936	+	2.16034i	0.0378459	+	0.116478i
$345$		0			0
$346$	−4.95566	+	15.2520i	−0.266418	+	0.819951i
$347$	−8.26141	−	2.68429i	−0.443495	−	0.144100i	0.0787523	−	0.996894i	$-0.474906\pi$
$347$	−8.26141	−	2.68429i	−0.443495	−	0.144100i	−0.522248	+	0.852794i	$0.674906\pi$
$348$		0			0
$349$	−26.8305			−1.43620			−0.718101	−	0.695938i	$-0.754989\pi$
$349$	−26.8305			−1.43620			−0.718101	+	0.695938i	$0.754989\pi$
$350$	23.4720	+	5.17040i	1.25463	+	0.276370i
$351$		0			0
$352$	0.518771	+	0.714027i	0.0276506	+	0.0380577i
$353$	−26.9623	−	8.76060i	−1.43506	−	0.466279i	−0.514707	−	0.857366i	$-0.672099\pi$
$353$	−26.9623	−	8.76060i	−1.43506	−	0.466279i	−0.920354	+	0.391087i	$0.872099\pi$
$354$		0			0
$355$	−5.26958	+	5.80923i	−0.279680	+	0.308322i
$356$	−5.77448	−	17.7720i	−0.306047	−	0.941915i
$357$		0			0
$358$	11.1739	−	3.63061i	0.590557	−	0.191884i
$359$	−7.02898	−	5.10686i	−0.370976	−	0.269530i	0.386640	−	0.922231i	$-0.373636\pi$
$359$	−7.02898	−	5.10686i	−0.370976	−	0.269530i	−0.757615	+	0.652701i	$0.773636\pi$
$360$		0			0
$361$	−8.03551	+	5.83814i	−0.422921	+	0.307270i
$362$	2.37114	−	3.26359i	0.124624	−	0.171531i
$363$		0			0
$364$	10.9869	−	7.98246i	0.575871	−	0.418395i
$365$	−3.30199	−	15.8214i	−0.172834	−	0.828130i
$366$		0			0
$367$	11.8609	−	3.85385i	0.619136	−	0.201170i	0.0173794	−	0.999849i	$-0.494468\pi$
$367$	11.8609	−	3.85385i	0.619136	−	0.201170i	0.601757	+	0.798679i	$0.294468\pi$
$368$			5.85344i			0.305132i
$369$		0			0
$370$	3.56090	+	1.60118i	0.185122	+	0.0832414i
$371$	5.27232	−	16.2265i	0.273725	−	0.842439i
$372$		0			0
$373$	−7.64048	−	10.5162i	−0.395609	−	0.544509i	0.564026	−	0.825757i	$-0.309252\pi$
$373$	−7.64048	−	10.5162i	−0.395609	−	0.544509i	−0.959635	+	0.281248i	$0.909252\pi$
$374$	−1.46315			−0.0756578
$375$		0			0
$376$	−8.72447			−0.449930
$377$	−5.94211	−	8.17861i	−0.306034	−	0.421220i
$378$		0			0
$379$	−0.541481	+	1.66651i	−0.0278140	+	0.0856027i	−0.964000	−	0.265903i	$-0.914330\pi$
$379$	−0.541481	+	1.66651i	−0.0278140	+	0.0856027i	0.936186	+	0.351505i	$0.114330\pi$
$380$	−10.9696	−	4.93255i	−0.562729	−	0.253034i
$381$		0			0
$382$			11.9215i			0.609958i
$383$	−32.4652	+	10.5486i	−1.65889	+	0.539007i	−0.980639	−	0.195822i	$-0.937262\pi$
$383$	−32.4652	+	10.5486i	−1.65889	+	0.539007i	−0.678252	+	0.734829i	$0.737262\pi$
$384$		0			0
$385$	−1.93813	−	9.28651i	−0.0987764	−	0.473284i
$386$	9.55355	−	6.94106i	0.486263	−	0.353291i
$387$		0			0
$388$	−10.7392	+	14.7812i	−0.545200	+	0.750403i
$389$	−5.54704	+	4.03016i	−0.281246	+	0.204337i	−0.719461	−	0.694533i	$-0.755611\pi$
$389$	−5.54704	+	4.03016i	−0.281246	+	0.204337i	0.438215	+	0.898870i	$0.355611\pi$
$390$		0			0
$391$	−7.85058	−	5.70378i	−0.397021	−	0.288452i
$392$	15.3184	−	4.97724i	0.773694	−	0.251388i
$393$		0			0
$394$	2.24916	+	6.92219i	0.113311	+	0.348735i
$395$	−18.8938	+	20.8287i	−0.950651	+	1.04800i
$396$		0			0
$397$	−31.5358	−	10.2466i	−1.58274	−	0.514262i	−0.619976	−	0.784621i	$-0.712858\pi$
$397$	−31.5358	−	10.2466i	−1.58274	−	0.514262i	−0.962760	+	0.270359i	$0.912858\pi$
$398$	−1.33985	−	1.84415i	−0.0671607	−	0.0924387i
$399$		0			0
$400$	−0.485943	−	4.97633i	−0.0242971	−	0.248816i
$401$	−3.51432			−0.175497			−0.0877483	−	0.996143i	$-0.527967\pi$
$401$	−3.51432			−0.175497			−0.0877483	+	0.996143i	$0.527967\pi$
$402$		0			0
$403$	28.0573	+	9.11637i	1.39763	+	0.454119i
$404$	−1.68757	+	5.19382i	−0.0839599	+	0.258402i
$405$		0			0
$406$	−5.31525	−	16.3587i	−0.263791	−	0.811866i
$407$		−	1.54106i		−	0.0763873i
$408$		0			0
$409$	−13.1746	−	9.57194i	−0.651444	−	0.473302i	0.212318	−	0.977201i	$-0.431899\pi$
$409$	−13.1746	−	9.57194i	−0.651444	−	0.473302i	−0.863763	+	0.503898i	$0.831899\pi$
$410$	−1.59122	+	3.53874i	−0.0785845	+	0.174766i
$411$		0			0
$412$	−3.90427	+	5.37377i	−0.192350	+	0.264747i
$413$	−29.2537	+	40.2643i	−1.43948	+	1.98128i
$414$		0			0
$415$	−29.5075	−	3.21146i	−1.44847	−	0.157644i
$416$	−2.28564	−	1.66061i	−0.112062	−	0.0814182i
$417$		0			0
$418$			4.74733i			0.232199i
$419$	8.18528	+	25.1917i	0.399877	+	1.23070i	0.925098	+	0.379730i	$0.123983\pi$
$419$	8.18528	+	25.1917i	0.399877	+	1.23070i	−0.525220	+	0.850966i	$0.676017\pi$
$420$		0			0
$421$	−9.56476	+	29.4373i	−0.466158	+	1.43469i	0.391362	+	0.920237i	$0.372004\pi$
$421$	−9.56476	+	29.4373i	−0.466158	+	1.43469i	−0.857520	+	0.514450i	$0.827996\pi$
$422$	1.18806	+	0.386023i	0.0578337	+	0.0187913i
$423$		0			0
$424$	−3.54936			−0.172372
$425$	7.14772	+	4.19735i	0.346716	+	0.203602i
$426$		0			0
$427$	−0.243706	−	0.335433i	−0.0117938	−	0.0162327i
$428$	13.8137	+	4.48833i	0.667708	+	0.216952i
$429$		0			0
$430$	−4.97213	+	1.03770i	−0.239777	+	0.0500425i
$431$	0.532381	+	1.63850i	0.0256439	+	0.0789238i	0.963059	−	0.269289i	$-0.0867887\pi$
$431$	0.532381	+	1.63850i	0.0256439	+	0.0789238i	−0.937416	+	0.348213i	$0.886789\pi$
$432$		0			0
$433$	22.9568	−	7.45911i	1.10323	−	0.358462i	0.299886	−	0.953975i	$-0.403051\pi$
$433$	22.9568	−	7.45911i	1.10323	−	0.358462i	0.803346	+	0.595513i	$0.203051\pi$
$434$	40.6085	+	29.5038i	1.94927	+	1.41623i
$435$		0			0
$436$	−3.85954	+	2.80412i	−0.184838	+	0.134293i
$437$	−18.5064	+	25.4719i	−0.885282	+	1.21849i
$438$		0			0
$439$	6.66899	−	4.84531i	0.318294	−	0.231254i	−0.417153	−	0.908836i	$-0.636972\pi$
$439$	6.66899	−	4.84531i	0.318294	−	0.231254i	0.735447	+	0.677582i	$0.236972\pi$
$440$	−1.71275	+	0.980449i	−0.0816520	+	0.0467411i
$441$		0			0
$442$	4.45439	−	1.44732i	0.211874	−	0.0688420i
$443$			22.4652i			1.06735i	0.845689	+	0.533676i	$0.179190\pi$
$443$			22.4652i			1.06735i	−0.845689	+	0.533676i	$0.820810\pi$
$444$		0			0
$445$	40.9032	−	8.53666i	1.93900	−	0.404677i
$446$	−2.73237	+	8.40936i	−0.129381	+	0.398195i
$447$		0			0
$448$	−2.82545	−	3.88890i	−0.133490	−	0.183733i
$449$	30.4988			1.43933			0.719663	−	0.694323i	$-0.244296\pi$
$449$	30.4988			1.43933			0.719663	+	0.694323i	$0.244296\pi$
$450$		0			0
$451$	1.53146			0.0721139
$452$	−2.84228	−	3.91206i	−0.133690	−	0.184008i
$453$		0			0
$454$	5.46860	−	16.8306i	0.256654	−	0.789900i
$455$	15.0864	+	26.3545i	0.707263	+	1.23552i
$456$		0			0
$457$		−	6.65272i		−	0.311201i	−0.987820	−	0.155601i	$-0.950269\pi$
$457$		−	6.65272i		−	0.311201i	0.987820	−	0.155601i	$-0.0497313\pi$
$458$	8.47737	−	2.75446i	0.396121	−	0.128708i
$459$		0			0
$460$	−13.0118	−	1.41615i	−0.606681	−	0.0660282i
$461$	−19.1479	+	13.9118i	−0.891808	+	0.647936i	−0.936349	−	0.351071i	$-0.885817\pi$
$461$	−19.1479	+	13.9118i	−0.891808	+	0.647936i	0.0445410	+	0.999008i	$0.485817\pi$
$462$		0			0
$463$	−15.3328	+	21.1038i	−0.712575	+	0.980775i	0.287163	+	0.957882i	$0.407288\pi$
$463$	−15.3328	+	21.1038i	−0.712575	+	0.980775i	−0.999738	+	0.0228935i	$0.992712\pi$
$464$	−2.89488	+	2.10325i	−0.134391	+	0.0976410i
$465$		0			0
$466$	7.75898	+	5.63723i	0.359428	+	0.261140i
$467$	−1.40340	+	0.455993i	−0.0649417	+	0.0211008i	−0.341308	−	0.939952i	$-0.610870\pi$
$467$	−1.40340	+	0.455993i	−0.0649417	+	0.0211008i	0.276366	+	0.961052i	$0.410870\pi$
$468$		0			0
$469$	17.7665	+	54.6796i	0.820380	+	2.52487i
$470$	2.11075	−	19.3940i	0.0973615	−	0.894577i
$471$		0			0
$472$	9.84690	+	3.19945i	0.453240	+	0.147267i
$473$	1.17839	+	1.62192i	0.0541827	+	0.0745760i
$474$		0			0
$475$	13.6187	−	23.1914i	0.624868	−	1.06410i
$476$	7.96896			0.365257
$477$		0			0
$478$	8.71452	+	2.83152i	0.398593	+	0.129511i
$479$	−4.14388	+	12.7536i	−0.189339	+	0.582725i	−0.999996	−	0.00279598i	$-0.999110\pi$
$479$	−4.14388	+	12.7536i	−0.189339	+	0.582725i	0.810657	+	0.585521i	$0.199110\pi$
$480$		0			0
$481$	1.52438	+	4.69156i	0.0695058	+	0.213917i
$482$			2.49551i			0.113667i
$483$		0			0
$484$	−8.26900	−	6.00778i	−0.375864	−	0.273081i
$485$	−30.2596	−	27.4487i	−1.37402	−	1.24638i
$486$		0			0
$487$	−1.24615	+	1.71518i	−0.0564686	+	0.0777224i	−0.836317	−	0.548246i	$-0.815296\pi$
$487$	−1.24615	+	1.71518i	−0.0564686	+	0.0777224i	0.779849	+	0.625968i	$0.215296\pi$
$488$	−0.0506988	+	0.0697810i	−0.00229503	+	0.00315884i
$489$		0			0
$490$	7.35807	+	35.2560i	0.332404	+	1.59270i
$491$	−1.79947	−	1.30739i	−0.0812091	−	0.0590019i	0.546440	−	0.837498i	$-0.315983\pi$
$491$	−1.79947	−	1.30739i	−0.0812091	−	0.0590019i	−0.627649	+	0.778496i	$0.715983\pi$
$492$		0			0
$493$		−	5.93206i		−	0.267166i
$494$	−4.69596	−	14.4527i	−0.211281	−	0.650256i
$495$		0			0
$496$	3.22681	−	9.93109i	0.144888	−	0.445919i
$497$	−16.0355	−	5.21025i	−0.719291	−	0.233712i
$498$		0			0
$499$	−14.5582			−0.651715			−0.325858	−	0.945419i	$-0.605653\pi$
$499$	−14.5582			−0.651715			−0.325858	+	0.945419i	$0.605653\pi$
$500$	11.1797	+	0.123723i	0.499969	+	0.00553307i
$501$		0			0
$502$	−5.12115	−	7.04866i	−0.228568	−	0.314597i
$503$	22.6744	+	7.36734i	1.01100	+	0.328494i	0.767252	−	0.641345i	$-0.221623\pi$
$503$	22.6744	+	7.36734i	1.01100	+	0.328494i	0.243747	+	0.969839i	$0.421623\pi$
$504$		0			0
$505$	−11.1373	−	5.00794i	−0.495602	−	0.222850i
$506$	1.59643	+	4.91331i	0.0709700	+	0.218423i
$507$		0			0
$508$	−1.71362	+	0.556790i	−0.0760297	+	0.0247035i
$509$	28.1543	+	20.4553i	1.24792	+	0.906664i	0.998099	−	0.0616289i	$-0.0196295\pi$
$509$	28.1543	+	20.4553i	1.24792	+	0.906664i	0.249817	+	0.968293i	$0.419630\pi$
$510$		0			0
$511$	28.1089	−	20.4223i	1.24347	−	0.903431i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$		0			0
$514$	−16.0081	+	11.6306i	−0.706088	+	0.513003i
$515$	−11.0010	−	9.97907i	−0.484762	−	0.439730i
$516$		0			0
$517$	−7.32322	+	2.37946i	−0.322075	+	0.104648i
$518$			8.39326i			0.368778i
$519$		0			0
$520$	4.24442	−	4.67907i	0.186130	−	0.205191i
$521$	2.68575	−	8.26589i	0.117665	−	0.362135i	−0.874829	−	0.484433i	$-0.839026\pi$
$521$	2.68575	−	8.26589i	0.117665	−	0.362135i	0.992494	+	0.122297i	$0.0390261\pi$
$522$		0			0
$523$	19.0655	+	26.2414i	0.833676	+	1.14746i	0.987228	+	0.159317i	$0.0509290\pi$
$523$	19.0655	+	26.2414i	0.833676	+	1.14746i	−0.153551	+	0.988141i	$0.549071\pi$
$524$	−16.0315			−0.700338
$525$		0			0
$526$	25.5635			1.11462
$527$	10.1752	+	14.0049i	0.443238	+	0.610064i
$528$		0			0
$529$	−3.48038	+	10.7115i	−0.151321	+	0.465717i
$530$	0.858713	−	7.89003i	0.0373001	−	0.342721i
$531$		0			0
$532$		−	25.8560i		−	1.12100i
$533$	−4.66236	+	1.51489i	−0.201949	+	0.0656173i
$534$		0			0
$535$	−13.3193	+	29.6211i	−0.575843	+	1.28063i
$536$	9.67628	−	7.03023i	0.417951	−	0.303659i
$537$		0			0
$538$	−14.3504	+	19.7517i	−0.618691	+	0.851555i
$539$	11.5006	−	8.35567i	0.495366	−	0.359904i
$540$		0			0
$541$	−25.0000	−	18.1636i	−1.07483	−	0.780913i	−0.0980596	−	0.995181i	$-0.531264\pi$
$541$	−25.0000	−	18.1636i	−1.07483	−	0.780913i	−0.976775	+	0.214268i	$0.931264\pi$
$542$	2.61209	−	0.848720i	0.112199	−	0.0364557i
$543$		0			0
$544$	−0.512289	−	1.57666i	−0.0219642	−	0.0675989i
$545$	−5.29963	−	9.25793i	−0.227011	−	0.396566i
$546$		0			0
$547$	−29.7315	−	9.66035i	−1.27123	−	0.413047i	−0.405745	−	0.913986i	$-0.632988\pi$
$547$	−29.7315	−	9.66035i	−1.27123	−	0.413047i	−0.865482	+	0.500940i	$0.832988\pi$
$548$	1.03872	+	1.42968i	0.0443721	+	0.0610730i
$549$		0			0
$550$	−1.76511	−	4.04454i	−0.0752645	−	0.172460i
$551$	−19.2471			−0.819953
$552$		0			0
$553$	−57.4945	−	18.6811i	−2.44491	−	0.794401i
$554$	0.921114	−	2.83490i	0.0391344	−	0.120443i
$555$		0			0
$556$	3.39811	+	10.4583i	0.144112	+	0.443531i
$557$		−	34.8113i		−	1.47500i	−0.675347	−	0.737500i	$-0.736006\pi$
$557$		−	34.8113i		−	1.47500i	0.675347	−	0.737500i	$-0.263994\pi$
$558$		0			0
$559$	−5.19185	−	3.77210i	−0.219592	−	0.159543i
$560$	9.32836	−	5.33995i	0.394195	−	0.225654i
$561$		0			0
$562$	2.26988	−	3.12422i	0.0957490	−	0.131787i
$563$	2.87518	−	3.95734i	0.121174	−	0.166782i	−0.744121	−	0.668045i	$-0.767131\pi$
$563$	2.87518	−	3.95734i	0.121174	−	0.166782i	0.865295	+	0.501263i	$0.167131\pi$
$564$		0			0
$565$	9.38393	−	5.37176i	0.394785	−	0.225992i
$566$	−13.5121	−	9.81713i	−0.567957	−	0.412645i
$567$		0			0
$568$			3.50758i			0.147175i
$569$	−0.906980	−	2.79140i	−0.0380226	−	0.117021i	0.930244	−	0.366942i	$-0.119595\pi$
$569$	−0.906980	−	2.79140i	−0.0380226	−	0.117021i	−0.968266	+	0.249921i	$0.919595\pi$
$570$		0			0
$571$	9.85310	−	30.3247i	0.412339	−	1.26905i	−0.502270	−	0.864711i	$-0.667501\pi$
$571$	9.85310	−	30.3247i	0.412339	−	1.26905i	0.914609	−	0.404339i	$-0.132499\pi$
$572$	−2.37144	−	0.770528i	−0.0991550	−	0.0322174i
$573$		0			0
$574$	−8.34102			−0.348147
$575$	6.29603	−	28.5820i	0.262562	−	1.19195i
$576$		0			0
$577$	21.7254	+	29.9024i	0.904439	+	1.24485i	0.969030	+	0.246942i	$0.0794256\pi$
$577$	21.7254	+	29.9024i	0.904439	+	1.24485i	−0.0645913	+	0.997912i	$0.520574\pi$
$578$	−13.5542	−	4.40401i	−0.563779	−	0.183183i
$579$		0			0
$580$	−3.97503	−	6.94399i	−0.165054	−	0.288334i
$581$	−19.7177	−	60.6847i	−0.818027	−	2.51763i
$582$		0			0
$583$	−2.97930	+	0.968032i	−0.123390	+	0.0400918i
$584$	−5.84757	−	4.24851i	−0.241974	−	0.175805i
$585$		0			0
$586$	0.407059	−	0.295746i	0.0168155	−	0.0122171i
$587$	−16.4935	+	22.7014i	−0.680761	+	0.936988i	−0.999943	−	0.0107059i	$-0.996592\pi$
$587$	−16.4935	+	22.7014i	−0.680761	+	0.936988i	0.319181	+	0.947694i	$0.396592\pi$
$588$		0			0
$589$	45.4402	−	33.0143i	1.87233	−	1.36033i
$590$	−9.49450	+	21.1150i	−0.390882	+	0.869292i
$591$		0			0
$592$	1.66061	−	0.539565i	0.0682507	−	0.0221760i
$593$		−	40.6263i		−	1.66832i	−0.551521	−	0.834161i	$-0.685952\pi$
$593$		−	40.6263i		−	1.66832i	0.551521	−	0.834161i	$-0.314048\pi$
$594$		0			0
$595$	−1.92796	+	17.7145i	−0.0790389	+	0.726225i
$596$	−0.899079	+	2.76708i	−0.0368277	+	0.113344i
$597$		0			0
$598$	−9.72029	−	13.3788i	−0.397492	−	0.547101i
$599$	−22.6989			−0.927451			−0.463725	−	0.885979i	$-0.653488\pi$
$599$	−22.6989			−0.927451			−0.463725	+	0.885979i	$0.653488\pi$
$600$		0			0
$601$	32.9640			1.34463			0.672316	−	0.740265i	$-0.265300\pi$
$601$	32.9640			1.34463			0.672316	+	0.740265i	$0.265300\pi$
$602$	−6.41805	−	8.83368i	−0.261580	−	0.360034i
$603$		0			0
$604$	0.414651	−	1.27616i	0.0168719	−	0.0519264i
$605$	15.3555	−	16.9280i	0.624290	−	0.688221i
$606$		0			0
$607$			8.32854i			0.338045i	0.985612	+	0.169023i	$0.0540611\pi$
$607$			8.32854i			0.338045i	−0.985612	+	0.169023i	$0.945939\pi$
$608$	−5.11563	+	1.66217i	−0.207466	+	0.0674098i
$609$		0			0
$610$	−0.142853	−	0.129583i	−0.00578396	−	0.00524666i
$611$	19.9409	−	14.4879i	0.806724	−	0.586120i
$612$		0			0
$613$	4.33351	−	5.96457i	0.175029	−	0.240907i	−0.712485	−	0.701687i	$-0.752430\pi$
$613$	4.33351	−	5.96457i	0.175029	−	0.240907i	0.887514	+	0.460780i	$0.152430\pi$
$614$	6.98485	−	5.07479i	0.281886	−	0.204802i
$615$		0			0
$616$	−3.43228	−	2.49370i	−0.138291	−	0.100474i
$617$	−8.43210	+	2.73975i	−0.339463	+	0.110298i	−0.473788	−	0.880639i	$-0.657114\pi$
$617$	−8.43210	+	2.73975i	−0.339463	+	0.110298i	0.134324	+	0.990937i	$0.457114\pi$
$618$		0			0
$619$	0.139486	+	0.429292i	0.00560640	+	0.0172547i	0.953821	−	0.300377i	$-0.0971125\pi$
$619$	0.139486	+	0.429292i	0.00560640	+	0.0172547i	−0.948214	+	0.317632i	$0.897112\pi$
$620$	21.2955	+	9.57567i	0.855250	+	0.384568i
$621$		0			0
$622$	19.2755	+	6.26298i	0.772875	+	0.251122i
$623$	52.7980	+	72.6703i	2.11531	+	2.91147i
$624$		0			0
$625$	−2.97977	+	24.8218i	−0.119191	+	0.992871i
$626$	17.0302			0.680664
$627$		0			0
$628$	7.90489	+	2.56845i	0.315439	+	0.102492i
$629$	−0.894493	+	2.75297i	−0.0356658	+	0.109768i
$630$		0			0
$631$	−9.74952	−	30.0059i	−0.388122	−	1.19452i	−0.934190	−	0.356776i	$-0.883876\pi$
$631$	−9.74952	−	30.0059i	−0.388122	−	1.19452i	0.546068	−	0.837741i	$-0.316124\pi$
$632$			12.5762i			0.500256i
$633$		0			0
$634$	−2.28270	−	1.65848i	−0.0906575	−	0.0658665i
$635$	−0.823127	−	3.94399i	−0.0326648	−	0.156512i
$636$		0			0
$637$	−26.7469	+	36.8140i	−1.05975	+	1.45862i
$638$	−1.85630	+	2.55498i	−0.0734916	+	0.101153i
$639$		0			0
$640$	−1.65619	−	1.50234i	−0.0654667	−	0.0593852i
$641$	15.1110	+	10.9788i	0.596848	+	0.433635i	0.844759	−	0.535147i	$-0.179744\pi$
$641$	15.1110	+	10.9788i	0.596848	+	0.433635i	−0.247911	+	0.968783i	$0.579744\pi$
$642$		0			0
$643$		−	15.5969i		−	0.615083i	−0.951535	−	0.307541i	$-0.900494\pi$
$643$		−	15.5969i		−	0.615083i	0.951535	−	0.307541i	$-0.0995063\pi$
$644$	−8.69485	−	26.7600i	−0.342625	−	1.05449i
$645$		0			0
$646$	2.75555	−	8.48070i	0.108416	−	0.333669i
$647$	−25.0683	−	8.14520i	−0.985538	−	0.320221i	−0.228466	−	0.973552i	$-0.573371\pi$
$647$	−25.0683	−	8.14520i	−0.985538	−	0.320221i	−0.757072	+	0.653331i	$0.773371\pi$
$648$		0			0
$649$	9.13798			0.358697
$650$	9.37444	+	10.5671i	0.367696	+	0.414476i
$651$		0			0
$652$	3.66704	+	5.04724i	0.143612	+	0.197665i
$653$	18.6583	+	6.06245i	0.730156	+	0.237242i	0.650421	−	0.759574i	$-0.274593\pi$
$653$	18.6583	+	6.06245i	0.730156	+	0.237242i	0.0797351	+	0.996816i	$0.474593\pi$
$654$		0			0
$655$	3.87856	−	35.6370i	0.151548	−	1.39245i
$656$	0.536207	+	1.65028i	0.0209354	+	0.0644324i
$657$		0			0
$658$	39.8854	−	12.9596i	1.55489	−	0.505216i
$659$	−18.7179	−	13.5993i	−0.729145	−	0.529755i	0.160148	−	0.987093i	$-0.448803\pi$
$659$	−18.7179	−	13.5993i	−0.729145	−	0.529755i	−0.889293	+	0.457338i	$0.848803\pi$
$660$		0			0
$661$	−14.1554	+	10.2845i	−0.550581	+	0.400021i	−0.828000	−	0.560729i	$-0.810521\pi$
$661$	−14.1554	+	10.2845i	−0.550581	+	0.400021i	0.277419	+	0.960749i	$0.410521\pi$
$662$	2.39404	−	3.29512i	0.0930472	−	0.128068i
$663$		0			0
$664$	−10.7390	+	7.80231i	−0.416752	+	0.302788i
$665$	57.4764	+	6.25545i	2.22884	+	0.242576i
$666$		0			0
$667$	−19.9200	+	6.47241i	−0.771306	+	0.250613i
$668$			14.8368i			0.574054i
$669$		0			0
$670$	13.2868	+	23.2106i	0.513312	+	0.896705i
$671$	−0.0235244	+	0.0724006i	−0.000908149	+	0.00279500i
$672$		0			0
$673$	0.608086	+	0.836959i	0.0234400	+	0.0322624i	0.820576	−	0.571537i	$-0.193653\pi$
$673$	0.608086	+	0.836959i	0.0234400	+	0.0322624i	−0.797136	+	0.603800i	$0.793653\pi$
$674$	−9.04782			−0.348509
$675$		0			0
$676$	−5.01824			−0.193009
$677$	−5.53353	−	7.61625i	−0.212671	−	0.292716i	0.689333	−	0.724445i	$-0.257904\pi$
$677$	−5.53353	−	7.61625i	−0.212671	−	0.292716i	−0.902004	+	0.431729i	$0.857904\pi$
$678$		0			0
$679$	27.1396	−	83.5272i	1.04152	−	3.20548i
$680$	3.62877	−	0.757340i	0.139157	−	0.0290427i
$681$		0			0
$682$		−	9.21610i		−	0.352903i
$683$	−13.1823	+	4.28318i	−0.504405	+	0.163891i	−0.550156	−	0.835062i	$-0.685432\pi$
$683$	−13.1823	+	4.28318i	−0.504405	+	0.163891i	0.0457510	+	0.998953i	$0.485432\pi$
$684$		0			0
$685$	−3.42940	+	1.96314i	−0.131031	+	0.0750075i
$686$	−35.4149	+	25.7305i	−1.35215	+	0.982394i
$687$		0			0
$688$	−1.33516	+	1.83769i	−0.0509026	+	0.0700614i
$689$	8.11255	−	5.89411i	0.309064	−	0.224548i
$690$		0			0
$691$	7.36726	+	5.35263i	0.280264	+	0.203624i	0.719032	−	0.694977i	$-0.244585\pi$
$691$	7.36726	+	5.35263i	0.280264	+	0.203624i	−0.438769	+	0.898600i	$0.644585\pi$
$692$	−15.2520	+	4.95566i	−0.579793	+	0.188386i
$693$		0			0
$694$	−2.68429	−	8.26141i	−0.101894	−	0.313599i
$695$	−24.0703	+	5.02357i	−0.913039	+	0.190555i
$696$		0			0
$697$	−2.73583	−	0.888926i	−0.103627	−	0.0336705i
$698$	−15.7706	−	21.7063i	−0.596925	−	0.821596i
$699$		0			0
$700$	9.61354	+	22.0283i	0.363358	+	0.832592i
$701$	22.6848			0.856791			0.428396	−	0.903591i	$-0.359079\pi$
$701$	22.6848			0.856791			0.428396	+	0.903591i	$0.359079\pi$
$702$		0			0
$703$	8.93224	+	2.90226i	0.336886	+	0.109461i
$704$	−0.272734	+	0.839389i	−0.0102790	+	0.0316357i
$705$		0			0
$706$	−8.76060	−	26.9623i	−0.329709	−	1.01474i
$707$		−	26.2512i		−	0.987278i
$708$		0			0
$709$	18.1615	+	13.1951i	0.682069	+	0.495552i	0.874043	−	0.485848i	$-0.161489\pi$
$709$	18.1615	+	13.1951i	0.682069	+	0.495552i	−0.191974	+	0.981400i	$0.561489\pi$
$710$	−7.79715	−	0.848604i	−0.292622	−	0.0318476i
$711$		0			0
$712$	10.9837	−	15.1178i	0.411632	−	0.566563i
$713$	35.9269	−	49.4492i	1.34547	−	1.85189i
$714$		0			0
$715$	2.28657	−	5.08516i	0.0855129	−	0.190174i
$716$	9.50506	+	6.90583i	0.355221	+	0.258083i
$717$		0			0
$718$		−	8.68830i		−	0.324245i
$719$	14.1238	+	43.4684i	0.526727	+	1.62110i	0.760875	+	0.648898i	$0.224770\pi$
$719$	14.1238	+	43.4684i	0.526727	+	1.62110i	−0.234148	+	0.972201i	$0.575230\pi$
$720$		0			0
$721$	9.86672	−	30.3666i	0.367456	−	1.13091i
$722$	−9.44630	−	3.06929i	−0.351555	−	0.114227i
$723$		0			0
$724$	4.03402			0.149923
$725$	16.3978	−	7.15628i	0.608998	−	0.265777i
$726$		0			0
$727$	−1.28973	−	1.77517i	−0.0478336	−	0.0658373i	0.784430	−	0.620217i	$-0.212956\pi$
$727$	−1.28973	−	1.77517i	−0.0478336	−	0.0658373i	−0.832264	+	0.554380i	$0.812956\pi$
$728$	12.9159	+	4.19663i	0.478695	+	0.155537i
$729$		0			0
$730$	10.8589	−	11.9710i	0.401907	−	0.443065i
$731$	−1.16367	−	3.58141i	−0.0430400	−	0.132463i
$732$		0			0
$733$	8.72887	−	2.83618i	0.322408	−	0.104757i	−0.143342	−	0.989673i	$-0.545785\pi$
$733$	8.72887	−	2.83618i	0.322408	−	0.104757i	0.465750	+	0.884917i	$0.345785\pi$
$734$	10.0895	+	7.33046i	0.372411	+	0.270572i
$735$		0			0
$736$	−4.73553	+	3.44056i	−0.174554	+	0.126821i
$737$	6.20478	−	8.54014i	0.228556	−	0.314580i
$738$		0			0
$739$	−35.2025	+	25.5761i	−1.29495	+	0.940833i	−0.999893	−	0.0146478i	$-0.995337\pi$
$739$	−35.2025	+	25.5761i	−1.29495	+	0.940833i	−0.295053	+	0.955481i	$0.595337\pi$
$740$	0.797663	+	3.82198i	0.0293227	+	0.140499i
$741$		0			0
$742$	16.2265	−	5.27232i	0.595695	−	0.193553i
$743$		−	8.61668i		−	0.316115i	−0.987430	−	0.158058i	$-0.949477\pi$
$743$		−	8.61668i		−	0.316115i	0.987430	−	0.158058i	$-0.0505232\pi$
$744$		0			0
$745$	−5.93354	−	2.66805i	−0.217388	−	0.0977499i
$746$	4.01684	−	12.3626i	0.147067	−	0.452625i
$747$		0			0
$748$	−0.860020	−	1.18372i	−0.0314454	−	0.0432809i
$749$	−69.8186			−2.55112
$750$		0			0
$751$	1.11603			0.0407245			0.0203623	−	0.999793i	$-0.493518\pi$
$751$	1.11603			0.0407245			0.0203623	+	0.999793i	$0.493518\pi$
$752$	−5.12811	−	7.05824i	−0.187003	−	0.257388i
$753$		0			0
$754$	3.12395	−	9.61453i	0.113768	−	0.350141i
$755$	2.73652	+	1.23049i	0.0995921	+	0.0447822i
$756$		0			0
$757$		−	37.2729i		−	1.35471i	−0.735658	−	0.677354i	$-0.763127\pi$
$757$		−	37.2729i		−	1.35471i	0.735658	−	0.677354i	$-0.236873\pi$
$758$	−1.66651	+	0.541481i	−0.0605302	+	0.0196675i
$759$		0			0
$760$	−2.45726	−	11.7739i	−0.0891340	−	0.427083i
$761$	−16.1999	+	11.7699i	−0.587245	+	0.426659i	−0.841329	−	0.540524i	$-0.818226\pi$
$761$	−16.1999	+	11.7699i	−0.587245	+	0.426659i	0.254084	+	0.967182i	$0.418226\pi$
$762$		0			0
$763$	13.4792	−	18.5526i	0.487981	−	0.671648i
$764$	−9.64472	+	7.00730i	−0.348934	+	0.253515i
$765$		0			0
$766$	−27.6165	−	20.0646i	−0.997825	−	0.724962i
$767$	−27.8195	+	9.03910i	−1.00450	+	0.326383i
$768$		0			0
$769$	4.78043	+	14.7126i	0.172387	+	0.530552i	0.999504	−	0.0314770i	$-0.0100211\pi$
$769$	4.78043	+	14.7126i	0.172387	+	0.530552i	−0.827118	+	0.562029i	$0.810021\pi$
$770$	6.37374	−	7.02645i	0.229694	−	0.253216i
$771$		0			0
$772$	11.2309	+	3.64913i	0.404208	+	0.131335i
$773$	14.1408	+	19.4632i	0.508610	+	0.700042i	0.983684	−	0.179904i	$-0.0575787\pi$
$773$	14.1408	+	19.4632i	0.508610	+	0.700042i	−0.475074	+	0.879946i	$0.657579\pi$
$774$		0			0
$775$	−26.4383	+	45.0221i	−0.949691	+	1.61724i
$776$	−18.2706			−0.655876
$777$		0			0
$778$	−6.52094	−	2.11878i	−0.233787	−	0.0759620i
$779$	−2.88420	+	8.87665i	−0.103337	+	0.318039i
$780$		0			0
$781$	0.956637	+	2.94422i	0.0342311	+	0.105353i
$782$		−	9.70385i		−	0.347009i
$783$		0			0
$784$	13.0306	+	9.46727i	0.465378	+	0.338117i
$785$	−7.62199	+	16.9507i	−0.272040	+	0.604997i
$786$		0			0
$787$	−19.6062	+	26.9857i	−0.698887	+	0.961935i	0.301079	+	0.953599i	$0.402653\pi$
$787$	−19.6062	+	26.9857i	−0.698887	+	0.961935i	−0.999965	+	0.00833555i	$0.997347\pi$
$788$	−4.27815	+	5.88837i	−0.152403	+	0.209764i
$789$		0			0
$790$	−27.9563	−	3.04263i	−0.994639	−	0.108252i
$791$	18.8051	+	13.6627i	0.668631	+	0.485789i
$792$		0			0
$793$		−	0.243685i		−	0.00865350i
$794$	−10.2466	−	31.5358i	−0.363638	−	1.11916i
$795$		0			0
$796$	0.704401	−	2.16792i	0.0249668	−	0.0768400i
$797$	31.0587	+	10.0916i	1.10016	+	0.357462i	0.802162	−	0.597106i	$-0.203683\pi$
$797$	31.0587	+	10.0916i	1.10016	+	0.357462i	0.297993	+	0.954568i	$0.403683\pi$
$798$		0			0
$799$	14.4634			0.511680
$800$	3.74031	−	3.31815i	0.132240	−	0.117314i
$801$		0			0
$802$	−2.06566	−	2.84314i	−0.0729411	−	0.100395i
$803$	−6.06710	−	1.97132i	−0.214103	−	0.0695664i
$804$		0			0
$805$	61.5895	−	12.8540i	2.17074	−	0.453043i
$806$	9.11637	+	28.0573i	0.321111	+	0.988277i
$807$		0			0
$808$	−5.19382	+	1.68757i	−0.182718	+	0.0593686i
$809$	−8.36995	−	6.08113i	−0.294272	−	0.213801i	0.430847	−	0.902425i	$-0.358215\pi$
$809$	−8.36995	−	6.08113i	−0.294272	−	0.213801i	−0.725118	+	0.688624i	$0.758215\pi$
$810$		0			0
$811$	30.7731	−	22.3580i	1.08059	−	0.785094i	0.102804	−	0.994702i	$-0.467219\pi$
$811$	30.7731	−	22.3580i	1.08059	−	0.785094i	0.977786	+	0.209607i	$0.0672186\pi$
$812$	10.1102	−	13.9155i	0.354799	−	0.488338i
$813$		0			0
$814$	1.24674	−	0.905810i	0.0436982	−	0.0317486i
$815$	−12.1069	+	6.93051i	−0.424087	+	0.242765i
$816$		0			0
$817$	−11.6202	+	3.77564i	−0.406540	+	0.132093i
$818$		−	16.2848i		−	0.569383i
$819$		0			0
$820$	−3.79819	+	0.792698i	−0.132639	+	0.0276822i
$821$	6.18062	−	19.0220i	0.215705	−	0.663872i	−0.783398	−	0.621521i	$-0.786515\pi$
$821$	6.18062	−	19.0220i	0.215705	−	0.663872i	0.999103	−	0.0423510i	$-0.0134848\pi$
$822$		0			0
$823$	−23.0591	−	31.7381i	−0.803790	−	1.10632i	−0.992252	−	0.124242i	$-0.960350\pi$
$823$	−23.0591	−	31.7381i	−0.803790	−	1.10632i	0.188462	−	0.982080i	$-0.439650\pi$
$824$	−6.64235			−0.231397
$825$		0			0
$826$	−49.7694			−1.73170
$827$	32.2736	+	44.4208i	1.12226	+	1.54466i	0.801991	+	0.597336i	$0.203774\pi$
$827$	32.2736	+	44.4208i	1.12226	+	1.54466i	0.320271	+	0.947326i	$0.396226\pi$
$828$		0			0
$829$	2.01553	−	6.20315i	0.0700021	−	0.215444i	−0.909935	−	0.414751i	$-0.863869\pi$
$829$	2.01553	−	6.20315i	0.0700021	−	0.215444i	0.979937	+	0.199306i	$0.0638689\pi$
$830$	−14.7459	−	25.7597i	−0.511839	−	0.894133i
$831$		0			0
$832$		−	2.82520i		−	0.0979462i
$833$	−25.3948	+	8.25128i	−0.879879	+	0.285890i
$834$		0			0
$835$	−32.9814	−	3.58954i	−1.14137	−	0.124221i
$836$	−3.84067	+	2.79041i	−0.132832	+	0.0965083i
$837$		0			0
$838$	−15.5693	+	21.4294i	−0.537834	+	0.740265i
$839$	35.1557	−	25.5421i	1.21371	−	0.881811i	0.218147	−	0.975916i	$-0.429999\pi$
$839$	35.1557	−	25.5421i	1.21371	−	0.881811i	0.995562	+	0.0941047i	$0.0299988\pi$
$840$		0			0
$841$	13.1029	+	9.51978i	0.451823	+	0.328268i
$842$	−29.4373	+	9.56476i	−1.01448	+	0.329624i
$843$		0			0
$844$	0.386023	+	1.18806i	0.0132875	+	0.0408946i
$845$	1.21408	−	11.1553i	0.0417658	−	0.383752i
$846$		0			0
$847$	46.7273	+	15.1826i	1.60557	+	0.521681i
$848$	−2.08626	−	2.87150i	−0.0716426	−	0.0986076i
$849$		0			0
$850$	0.805597	+	8.24977i	0.0276317	+	0.282965i
$851$	10.2205			0.350355
$852$		0			0
$853$	−19.8410	−	6.44673i	−0.679343	−	0.220732i	−0.0510350	−	0.998697i	$-0.516252\pi$
$853$	−19.8410	−	6.44673i	−0.679343	−	0.220732i	−0.628307	+	0.777965i	$0.716252\pi$
$854$	0.128124	−	0.394325i	0.00438431	−	0.0134935i
$855$		0			0
$856$	4.48833	+	13.8137i	0.153408	+	0.472141i
$857$			10.2125i			0.348854i	0.984670	+	0.174427i	$0.0558073\pi$
$857$			10.2125i			0.348854i	−0.984670	+	0.174427i	$0.944193\pi$
$858$		0			0
$859$	2.14672	+	1.55969i	0.0732453	+	0.0532158i	0.623805	−	0.781580i	$-0.285586\pi$
$859$	2.14672	+	1.55969i	0.0732453	+	0.0532158i	−0.550560	+	0.834796i	$0.685586\pi$
$860$	−3.76206	−	3.41259i	−0.128285	−	0.116368i
$861$		0			0
$862$	−1.01265	+	1.39379i	−0.0344910	+	0.0474727i
$863$	1.31766	−	1.81361i	0.0448538	−	0.0617360i	−0.786001	−	0.618225i	$-0.787852\pi$
$863$	1.31766	−	1.81361i	0.0448538	−	0.0617360i	0.830855	+	0.556489i	$0.187852\pi$
$864$		0			0
$865$	−7.32618	−	35.1032i	−0.249097	−	1.19354i
$866$	19.5282	+	14.1881i	0.663595	+	0.482130i
$867$		0			0
$868$			50.1948i			1.70372i
$869$	3.42997	+	10.5564i	0.116354	+	0.358100i
$870$		0			0
$871$	−10.4420	+	32.1371i	−0.353812	+	1.08892i
$872$	−4.53716	−	1.47421i	−0.153648	−	0.0499231i
$873$		0			0
$874$	−31.4850			−1.06500
$875$	−51.2935	+	16.0409i	−1.73404	+	0.542283i
$876$		0			0
$877$	30.0466	+	41.3556i	1.01460	+	1.39648i	0.915921	+	0.401359i	$0.131462\pi$
$877$	30.0466	+	41.3556i	1.01460	+	1.39648i	0.0986803	+	0.995119i	$0.468538\pi$
$878$	7.83987	+	2.54733i	0.264583	+	0.0859682i
$879$		0			0
$880$	−1.79993	−	0.809348i	−0.0606756	−	0.0272831i
$881$	14.5343	+	44.7321i	0.489674	+	1.50706i	0.825096	+	0.564993i	$0.191121\pi$
$881$	14.5343	+	44.7321i	0.489674	+	1.50706i	−0.335422	+	0.942068i	$0.608879\pi$
$882$		0			0
$883$	25.2883	−	8.21666i	0.851018	−	0.276513i	0.149146	−	0.988815i	$-0.452348\pi$
$883$	25.2883	−	8.21666i	0.851018	−	0.276513i	0.701873	+	0.712303i	$0.252348\pi$
$884$	3.78913	+	2.75297i	0.127442	+	0.0925923i
$885$		0			0
$886$	−18.1747	+	13.2047i	−0.610591	+	0.443621i
$887$	28.1751	−	38.7797i	0.946027	−	1.30209i	−0.00724276	−	0.999974i	$-0.502305\pi$
$887$	28.1751	−	38.7797i	0.946027	−	1.30209i	0.953270	−	0.302121i	$-0.0976945\pi$
$888$		0			0
$889$	7.00705	−	5.09092i	0.235009	−	0.170744i
$890$	30.9486	+	28.0736i	1.03740	+	0.941031i
$891$		0			0
$892$	−8.40936	+	2.73237i	−0.281566	+	0.0914864i
$893$		−	46.9279i		−	1.57038i
$894$		0			0
$895$	−17.6509	+	19.4584i	−0.590003	+	0.650424i
$896$	1.48543	−	4.57167i	0.0496246	−	0.152729i
$897$		0			0
$898$	17.9267	+	24.6740i	0.598223	+	0.823383i
$899$	37.3648			1.24619
$900$		0			0
$901$	5.88415			0.196029
$902$	0.900172	+	1.23898i	0.0299725	+	0.0412536i
$903$		0			0
$904$	1.49428	−	4.59891i	0.0496989	−	0.152957i
$905$	−0.975968	+	8.96739i	−0.0324423	+	0.298086i
$906$		0			0
$907$			5.35392i			0.177774i	0.996042	+	0.0888870i	$0.0283310\pi$
$907$			5.35392i			0.177774i	−0.996042	+	0.0888870i	$0.971669\pi$
$908$	16.8306	−	5.46860i	0.558543	−	0.181482i
$909$		0			0
$910$	−12.4537	+	27.6960i	−0.412835	+	0.918112i
$911$	−10.9464	+	7.95304i	−0.362671	+	0.263496i	−0.754165	−	0.656685i	$-0.771958\pi$
$911$	−10.9464	+	7.95304i	−0.362671	+	0.263496i	0.391494	+	0.920181i	$0.371958\pi$
$912$		0			0
$913$	−6.88620	+	9.47805i	−0.227900	+	0.313678i
$914$	5.38217	−	3.91037i	0.178026	−	0.129344i
$915$		0			0
$916$	7.21128	+	5.23930i	0.238267	+	0.173111i
$917$	73.2906	−	23.8136i	2.42027	−	0.786393i
$918$		0			0
$919$	17.2285	+	53.0240i	0.568317	+	1.74910i	0.657884	+	0.753119i	$0.271452\pi$
$919$	17.2285	+	53.0240i	0.568317	+	1.74910i	−0.0895666	+	0.995981i	$0.528548\pi$
$920$	−6.50249	−	11.3592i	−0.214381	−	0.374502i
$921$		0			0
$922$	−22.5097	−	7.31386i	−0.741319	−	0.240869i
$923$	−5.82473	−	8.01705i	−0.191723	−	0.263885i
$924$		0			0
$925$	−8.68902	+	0.848490i	−0.285693	+	0.0278982i
$926$	−26.0857			−0.857229
$927$		0			0
$928$	−3.40313	−	1.10574i	−0.111713	−	0.0362979i
$929$	−16.0123	+	49.2807i	−0.525346	+	1.61685i	0.238284	+	0.971195i	$0.423415\pi$
$929$	−16.0123	+	49.2807i	−0.525346	+	1.61685i	−0.763631	+	0.645653i	$0.776585\pi$
$930$		0			0
$931$	26.7720	+	82.3958i	0.877417	+	2.70041i
$932$			9.59063i			0.314151i
$933$		0			0
$934$	−1.19380	−	0.867350i	−0.0390625	−	0.0283805i
$935$	2.83940	−	1.62539i	0.0928582	−	0.0531560i
$936$		0			0
$937$	23.4907	−	32.3322i	0.767409	−	1.05625i	−0.229152	−	0.973391i	$-0.573595\pi$
$937$	23.4907	−	32.3322i	0.767409	−	1.05625i	0.996561	−	0.0828575i	$-0.0264046\pi$
$938$	−33.7939	+	46.5133i	−1.10341	+	1.51871i
$939$		0			0
$940$	16.9307	−	9.69186i	0.552219	−	0.316114i
$941$	−12.2262	−	8.88288i	−0.398564	−	0.289574i	0.370392	−	0.928876i	$-0.379223\pi$
$941$	−12.2262	−	8.88288i	−0.398564	−	0.289574i	−0.768956	+	0.639302i	$0.779223\pi$
$942$		0			0
$943$			10.1569i			0.330754i
$944$	3.19945	+	9.84690i	0.104133	+	0.320489i
$945$		0			0
$946$	−0.619519	+	1.90668i	−0.0201423	+	0.0619916i
$947$	−32.3992	−	10.5272i	−1.05283	−	0.342087i	−0.269054	−	0.963125i	$-0.586711\pi$
$947$	−32.3992	−	10.5272i	−1.05283	−	0.342087i	−0.783780	+	0.621039i	$0.786711\pi$
$948$		0			0
$949$	20.4205			0.662879
$950$	26.7671	−	2.61383i	0.868440	−	0.0848039i
$951$		0			0
$952$	4.68404	+	6.44702i	0.151811	+	0.208949i
$953$	−31.7376	−	10.3122i	−1.02808	−	0.334044i	−0.254050	−	0.967191i	$-0.581763\pi$
$953$	−31.7376	−	10.3122i	−1.02808	−	0.334044i	−0.774031	+	0.633147i	$0.781763\pi$
$954$		0			0
$955$	−13.2434	−	23.1349i	−0.428547	−	0.748629i
$956$	2.83152	+	8.71452i	0.0915779	+	0.281848i
$957$		0			0
$958$	−12.7536	+	4.14388i	−0.412049	+	0.133883i
$959$	−6.87240	−	4.99309i	−0.221921	−	0.161235i
$960$		0			0
$961$	−63.1347	+	45.8700i	−2.03660	+	1.47968i
$962$	−2.89954	+	3.99088i	−0.0934850	+	0.128671i
$963$		0			0
$964$	−2.01891	+	1.46682i	−0.0650247	+	0.0472432i
$965$	−10.8289	+	24.0827i	−0.348596	+	0.775250i
$966$		0			0
$967$	−25.1661	+	8.17697i	−0.809288	+	0.262954i	−0.684296	−	0.729204i	$-0.739890\pi$
$967$	−25.1661	+	8.17697i	−0.809288	+	0.262954i	−0.124992	+	0.992158i	$0.539890\pi$
$968$		−	10.2210i		−	0.328517i
$969$		0			0
$970$	4.42029	−	40.6145i	0.141927	−	1.30405i
$971$	−9.76352	+	30.0490i	−0.313326	+	0.964319i	0.663112	+	0.748520i	$0.269235\pi$
$971$	−9.76352	+	30.0490i	−0.313326	+	0.964319i	−0.976438	+	0.215798i	$0.930765\pi$
$972$		0			0
$973$	−31.0701	−	42.7643i	−0.996061	−	1.37096i
$974$	−2.12008			−0.0679318
$975$		0			0
$976$	−0.0862540			−0.00276092
$977$	−2.72764	−	3.75428i	−0.0872650	−	0.120110i	0.763152	−	0.646219i	$-0.223651\pi$
$977$	−2.72764	−	3.75428i	−0.0872650	−	0.120110i	−0.850417	+	0.526109i	$0.823651\pi$
$978$		0			0
$979$	5.09647	−	15.6853i	0.162884	−	0.501305i
$980$	−24.1977	+	26.6758i	−0.772968	+	0.852126i
$981$		0			0
$982$		−	2.22427i		−	0.0709793i
$983$	−32.3253	+	10.5031i	−1.03102	+	0.334998i	−0.775192	−	0.631725i	$-0.782347\pi$
$983$	−32.3253	+	10.5031i	−1.03102	+	0.334998i	−0.255825	+	0.966723i	$0.582347\pi$
$984$		0			0
$985$	−12.0545	−	10.9347i	−0.384087	−	0.348408i
$986$	4.79914	−	3.48678i	0.152836	−	0.111042i
$987$		0			0
$988$	8.93224	−	12.2942i	0.284172	−	0.391130i
$989$	−10.7568	+	7.81529i	−0.342047	+	0.248512i
$990$		0			0
$991$	44.5440	+	32.3631i	1.41499	+	1.02805i	0.992574	+	0.121643i	$0.0388162\pi$
$991$	44.5440	+	32.3631i	1.41499	+	1.02805i	0.422411	+	0.906404i	$0.361184\pi$
$992$	9.93109	−	3.22681i	0.315312	−	0.102451i
$993$		0			0
$994$	−5.21025	−	16.0355i	−0.165259	−	0.508616i
$995$	4.64875	+	2.09034i	0.147375	+	0.0662682i
$996$		0			0
$997$	−0.695101	−	0.225852i	−0.0220141	−	0.00715280i	0.297989	−	0.954569i	$-0.403684\pi$
$997$	−0.695101	−	0.225852i	−0.0220141	−	0.00715280i	−0.320003	+	0.947416i	$0.603684\pi$
$998$	−8.55710	−	11.7778i	−0.270870	−	0.372821i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.c.289.3		16
3.2	odd	2		150.2.h.b.139.2	yes	16
15.2	even	4		750.2.g.g.301.4		16
15.8	even	4		750.2.g.f.301.1		16
15.14	odd	2		750.2.h.d.199.4		16
25.9	even	10	inner	450.2.l.c.109.3		16
75.29	odd	10		3750.2.c.k.1249.8		16
75.38	even	20		750.2.g.f.451.1		16
75.41	odd	10		750.2.h.d.49.3		16
75.47	even	20		3750.2.a.u.1.8		8
75.53	even	20		3750.2.a.v.1.1		8
75.59	odd	10		150.2.h.b.109.2	✓	16
75.62	even	20		750.2.g.g.451.4		16
75.71	odd	10		3750.2.c.k.1249.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.2	✓	16	75.59	odd	10
150.2.h.b.139.2	yes	16	3.2	odd	2
450.2.l.c.109.3		16	25.9	even	10	inner
450.2.l.c.289.3		16	1.1	even	1	trivial
750.2.g.f.301.1		16	15.8	even	4
750.2.g.f.451.1		16	75.38	even	20
750.2.g.g.301.4		16	15.2	even	4
750.2.g.g.451.4		16	75.62	even	20
750.2.h.d.49.3		16	75.41	odd	10
750.2.h.d.199.4		16	15.14	odd	2
3750.2.a.u.1.8		8	75.47	even	20
3750.2.a.v.1.1		8	75.53	even	20
3750.2.c.k.1249.8		16	75.29	odd	10
3750.2.c.k.1249.9		16	75.71	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)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-2.03938 - 0.917020i) q^{5} -4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-2.03938 - 0.917020i) q^{5} -4.80694i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.456833 - 2.18890i) q^{10} +(-0.714027 + 0.518771i) q^{11} +(1.66061 - 2.28564i) q^{13} +(3.88890 - 2.82545i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.57666 - 0.512289i) q^{17} +(-1.66217 - 5.11563i) q^{19} +(1.50234 - 1.65619i) q^{20} +(-0.839389 - 0.272734i) q^{22} +(-3.44056 - 4.73553i) q^{23} +(3.31815 + 3.74031i) q^{25} +2.82520 q^{26} +(4.57167 + 1.48543i) q^{28} +(1.10574 - 3.40313i) q^{29} +(3.22681 + 9.93109i) q^{31} -1.00000i q^{32} +(1.34119 + 0.974432i) q^{34} +(-4.40806 + 9.80318i) q^{35} +(-1.02631 + 1.41260i) q^{37} +(3.16163 - 4.35161i) q^{38} +(2.22294 + 0.241934i) q^{40} +(-1.40381 - 1.01993i) q^{41} -2.27151i q^{43} +(-0.272734 - 0.839389i) q^{44} +(1.80881 - 5.56695i) q^{46} +(8.29746 + 2.69601i) q^{47} -16.1067 q^{49} +(-1.07561 + 4.88294i) q^{50} +(1.66061 + 2.28564i) q^{52} +(3.37565 + 1.09681i) q^{53} +(1.93190 - 0.403195i) q^{55} +(1.48543 + 4.57167i) q^{56} +(3.40313 - 1.10574i) q^{58} +(-8.37628 - 6.08572i) q^{59} +(0.0697810 - 0.0506988i) q^{61} +(-6.13775 + 8.44789i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-5.48259 + 3.13847i) q^{65} +(-11.3751 + 3.69601i) q^{67} +1.65780i q^{68} +(-10.5219 + 2.19597i) q^{70} +(1.08390 - 3.33591i) q^{71} +(4.24851 + 5.84757i) q^{73} -1.74607 q^{74} +5.37889 q^{76} +(2.49370 + 3.43228i) q^{77} +(3.88627 - 11.9607i) q^{79} +(1.11088 + 1.94060i) q^{80} -1.73520i q^{82} +(12.6244 - 4.10192i) q^{83} +(-3.68520 - 0.401079i) q^{85} +(1.83769 - 1.33516i) q^{86} +(0.518771 - 0.714027i) q^{88} +(-15.1178 + 10.9837i) q^{89} +(-10.9869 - 7.98246i) q^{91} +(5.56695 - 1.80881i) q^{92} +(2.69601 + 8.29746i) q^{94} +(-1.30134 + 11.9570i) q^{95} +(17.3764 + 5.64593i) q^{97} +(-9.46727 - 13.0306i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) 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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