LMFDB - Embedded newform 693.2.m.i.379.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.4
Root			$0.751051 + 2.31150i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.i.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.751051 + 2.31150i) q^{2} +(-3.16091 + 2.29654i) q^{4} +(-0.388938 + 1.19703i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-3.74989 - 2.72445i) q^{8} +O(q^{10})$	\(q+(0.751051 + 2.31150i) q^{2} +(-3.16091 + 2.29654i) q^{4} +(-0.388938 + 1.19703i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-3.74989 - 2.72445i) q^{8} -3.05904 q^{10} +(-3.18332 - 0.930846i) q^{11} +(-0.982152 - 3.02275i) q^{13} +(-1.96628 - 1.42858i) q^{14} +(1.06649 - 3.28231i) q^{16} +(-1.83067 + 5.63423i) q^{17} +(-2.31558 - 1.68237i) q^{19} +(-1.51962 - 4.67691i) q^{20} +(-0.239188 - 8.05735i) q^{22} -6.76343 q^{23} +(2.76348 + 2.00778i) q^{25} +(6.24944 - 4.54048i) q^{26} +(1.20736 - 3.71587i) q^{28} +(3.63693 - 2.64238i) q^{29} +(3.00597 + 9.25141i) q^{31} -0.882184 q^{32} -14.3984 q^{34} +(-0.388938 - 1.19703i) q^{35} +(4.41315 - 3.20634i) q^{37} +(2.14967 - 6.61601i) q^{38} +(4.71972 - 3.42908i) q^{40} +(-0.254423 - 0.184849i) q^{41} -0.132562 q^{43} +(12.1999 - 4.36829i) q^{44} +(-5.07968 - 15.6337i) q^{46} +(7.58458 + 5.51052i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-2.56548 + 7.89572i) q^{50} +(10.0463 + 7.29910i) q^{52} +(-1.34482 - 4.13893i) q^{53} +(2.35237 - 3.44849i) q^{55} +4.63512 q^{56} +(8.83939 + 6.42219i) q^{58} +(-5.62012 + 4.08326i) q^{59} +(-0.757757 + 2.33214i) q^{61} +(-19.1270 + 13.8966i) q^{62} +(-2.79554 - 8.60379i) q^{64} +4.00032 q^{65} -9.41987 q^{67} +(-7.15262 - 22.0135i) q^{68} +(2.47482 - 1.79806i) q^{70} +(0.0360345 - 0.110903i) q^{71} +(-0.497571 + 0.361506i) q^{73} +(10.7260 + 7.79286i) q^{74} +11.1830 q^{76} +(3.12250 - 1.11804i) q^{77} +(2.63569 + 8.11183i) q^{79} +(3.51423 + 2.55324i) q^{80} +(0.236194 - 0.726930i) q^{82} +(-0.293731 + 0.904010i) q^{83} +(-6.03232 - 4.38274i) q^{85} +(-0.0995608 - 0.306417i) q^{86} +(9.40104 + 12.1634i) q^{88} -10.0552 q^{89} +(2.57131 + 1.86816i) q^{91} +(21.3786 - 15.5325i) q^{92} +(-7.04114 + 21.6704i) q^{94} +(2.91446 - 2.11748i) q^{95} +(5.43159 + 16.7167i) q^{97} +2.43045 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.751051	+	2.31150i	0.531073	+	1.63448i	0.751984	+	0.659182i	$0.229097\pi$
$2$	0.751051	+	2.31150i	0.531073	+	1.63448i	−0.220910	+	0.975294i	$0.570903\pi$
$3$		0			0
$3$		0			0
$4$	−3.16091	+	2.29654i	−1.58046	+	1.14827i
$5$	−0.388938	+	1.19703i	−0.173939	+	0.535328i	−0.999583	−	0.0288624i	$-0.990812\pi$
$5$	−0.388938	+	1.19703i	−0.173939	+	0.535328i	0.825645	+	0.564190i	$0.190812\pi$
$6$		0			0
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$7$	−0.809017	+	0.587785i	−0.305780	+	0.222162i
$8$	−3.74989	−	2.72445i	−1.32579	−	0.963239i
$9$		0			0
$10$	−3.05904			−0.967354
$11$	−3.18332	−	0.930846i	−0.959807	−	0.280661i
$11$	−3.18332	−	0.930846i	−0.959807	−	0.280661i
$12$		0			0
$13$	−0.982152	−	3.02275i	−0.272400	−	0.838361i	−0.989896	−	0.141798i	$-0.954712\pi$
$13$	−0.982152	−	3.02275i	−0.272400	−	0.838361i	0.717496	−	0.696563i	$-0.245288\pi$
$14$	−1.96628	−	1.42858i	−0.525510	−	0.381805i
$15$		0			0
$16$	1.06649	−	3.28231i	0.266622	−	0.820578i
$17$	−1.83067	+	5.63423i	−0.444003	+	1.36650i	0.439570	+	0.898208i	$0.355131\pi$
$17$	−1.83067	+	5.63423i	−0.444003	+	1.36650i	−0.883573	+	0.468293i	$0.844869\pi$
$18$		0			0
$19$	−2.31558	−	1.68237i	−0.531231	−	0.385962i	0.289587	−	0.957152i	$-0.406482\pi$
$19$	−2.31558	−	1.68237i	−0.531231	−	0.385962i	−0.820818	+	0.571190i	$0.806482\pi$
$20$	−1.51962	−	4.67691i	−0.339798	−	1.04579i
$21$		0			0
$22$	−0.239188	−	8.05735i	−0.0509950	−	1.71783i
$23$	−6.76343			−1.41027			−0.705136	−	0.709072i	$-0.749114\pi$
$23$	−6.76343			−1.41027			−0.705136	+	0.709072i	$0.749114\pi$
$24$		0			0
$25$	2.76348	+	2.00778i	0.552696	+	0.401557i
$26$	6.24944	−	4.54048i	1.22562	−	0.890462i
$27$		0			0
$28$	1.20736	−	3.71587i	0.228170	−	0.702234i
$29$	3.63693	−	2.64238i	0.675361	−	0.490678i	−0.196454	−	0.980513i	$-0.562943\pi$
$29$	3.63693	−	2.64238i	0.675361	−	0.490678i	0.871815	+	0.489834i	$0.162943\pi$
$30$		0			0
$31$	3.00597	+	9.25141i	0.539888	+	1.66160i	0.732845	+	0.680396i	$0.238192\pi$
$31$	3.00597	+	9.25141i	0.539888	+	1.66160i	−0.192957	+	0.981207i	$0.561808\pi$
$32$	−0.882184			−0.155950
$33$		0			0
$34$	−14.3984			−2.46931
$35$	−0.388938	−	1.19703i	−0.0657426	−	0.202335i
$36$		0			0
$37$	4.41315	−	3.20634i	0.725517	−	0.527119i	−0.162625	−	0.986688i	$-0.551996\pi$
$37$	4.41315	−	3.20634i	0.725517	−	0.527119i	0.888142	+	0.459569i	$0.151996\pi$
$38$	2.14967	−	6.61601i	0.348723	−	1.07326i
$39$		0			0
$40$	4.71972	−	3.42908i	0.746254	−	0.542185i
$41$	−0.254423	−	0.184849i	−0.0397342	−	0.0288686i	0.567741	−	0.823207i	$-0.307818\pi$
$41$	−0.254423	−	0.184849i	−0.0397342	−	0.0288686i	−0.607475	+	0.794339i	$0.707818\pi$
$42$		0			0
$43$	−0.132562			−0.0202155			−0.0101078	−	0.999949i	$-0.503217\pi$
$43$	−0.132562			−0.0202155			−0.0101078	+	0.999949i	$0.503217\pi$
$44$	12.1999	−	4.36829i	1.83921	−	0.658544i
$45$		0			0
$46$	−5.07968	−	15.6337i	−0.748958	−	2.30506i
$47$	7.58458	+	5.51052i	1.10632	+	0.803791i	0.982081	−	0.188460i	$-0.0603497\pi$
$47$	7.58458	+	5.51052i	1.10632	+	0.803791i	0.124243	+	0.992252i	$0.460350\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−2.56548	+	7.89572i	−0.362813	+	1.11662i
$51$		0			0
$52$	10.0463	+	7.29910i	1.39318	+	1.01220i
$53$	−1.34482	−	4.13893i	−0.184725	−	0.568525i	0.815219	−	0.579153i	$-0.196617\pi$
$53$	−1.34482	−	4.13893i	−0.184725	−	0.568525i	−0.999944	+	0.0106284i	$0.996617\pi$
$54$		0			0
$55$	2.35237	−	3.44849i	0.317193	−	0.464994i
$56$	4.63512			0.619393
$57$		0			0
$58$	8.83939	+	6.42219i	1.16067	+	0.843275i
$59$	−5.62012	+	4.08326i	−0.731678	+	0.531595i	−0.890094	−	0.455778i	$-0.849361\pi$
$59$	−5.62012	+	4.08326i	−0.731678	+	0.531595i	0.158416	+	0.987372i	$0.449361\pi$
$60$		0			0
$61$	−0.757757	+	2.33214i	−0.0970209	+	0.298600i	−0.987775	−	0.155886i	$-0.950177\pi$
$61$	−0.757757	+	2.33214i	−0.0970209	+	0.298600i	0.890754	+	0.454485i	$0.150177\pi$
$62$	−19.1270	+	13.8966i	−2.42913	+	1.76487i
$63$		0			0
$64$	−2.79554	−	8.60379i	−0.349443	−	1.07547i
$65$	4.00032			0.496179
$66$		0			0
$67$	−9.41987			−1.15082			−0.575410	−	0.817865i	$-0.695158\pi$
$67$	−9.41987			−1.15082			−0.575410	+	0.817865i	$0.695158\pi$
$68$	−7.15262	−	22.0135i	−0.867383	−	2.66953i
$69$		0			0
$70$	2.47482	−	1.79806i	0.295797	−	0.214909i
$71$	0.0360345	−	0.110903i	0.00427651	−	0.0131617i	−0.948895	−	0.315590i	$-0.897797\pi$
$71$	0.0360345	−	0.110903i	0.00427651	−	0.0131617i	0.953172	+	0.302429i	$0.0977974\pi$
$72$		0			0
$73$	−0.497571	+	0.361506i	−0.0582363	+	0.0423111i	−0.616523	−	0.787337i	$-0.711459\pi$
$73$	−0.497571	+	0.361506i	−0.0582363	+	0.0423111i	0.558286	+	0.829648i	$0.311459\pi$
$74$	10.7260	+	7.79286i	1.24687	+	0.905902i
$75$		0			0
$76$	11.1830			1.28277
$77$	3.12250	−	1.11804i	0.355842	−	0.127412i
$78$		0			0
$79$	2.63569	+	8.11183i	0.296539	+	0.912652i	0.982700	+	0.185203i	$0.0592943\pi$
$79$	2.63569	+	8.11183i	0.296539	+	0.912652i	−0.686162	+	0.727449i	$0.740706\pi$
$80$	3.51423	+	2.55324i	0.392903	+	0.285460i
$81$		0			0
$82$	0.236194	−	0.726930i	0.0260832	−	0.0802760i
$83$	−0.293731	+	0.904010i	−0.0322411	+	0.0992280i	−0.965882	−	0.258982i	$-0.916613\pi$
$83$	−0.293731	+	0.904010i	−0.0322411	+	0.0992280i	0.933641	+	0.358210i	$0.116613\pi$
$84$		0			0
$85$	−6.03232	−	4.38274i	−0.654297	−	0.475375i
$86$	−0.0995608	−	0.306417i	−0.0107359	−	0.0330418i
$87$		0			0
$88$	9.40104	+	12.1634i	1.00215	+	1.29662i
$89$	−10.0552			−1.06585			−0.532923	−	0.846164i	$-0.678906\pi$
$89$	−10.0552			−1.06585			−0.532923	+	0.846164i	$0.678906\pi$
$90$		0			0
$91$	2.57131	+	1.86816i	0.269546	+	0.195837i
$92$	21.3786	−	15.5325i	2.22887	−	1.61937i
$93$		0			0
$94$	−7.04114	+	21.6704i	−0.726238	+	2.23513i
$95$	2.91446	−	2.11748i	0.299018	−	0.217249i
$96$		0			0
$97$	5.43159	+	16.7167i	0.551495	+	1.69733i	0.705025	+	0.709182i	$0.250936\pi$
$97$	5.43159	+	16.7167i	0.551495	+	1.69733i	−0.153530	+	0.988144i	$0.549064\pi$
$98$	2.43045			0.245513
$99$		0			0
$100$	−13.3461			−1.33461
$101$	3.85534	+	11.8655i	0.383621	+	1.18066i	0.937476	+	0.348050i	$0.113156\pi$
$101$	3.85534	+	11.8655i	0.383621	+	1.18066i	−0.553855	+	0.832613i	$0.686844\pi$
$102$		0			0
$103$	−6.64852	+	4.83043i	−0.655098	+	0.475957i	−0.865004	−	0.501765i	$-0.832684\pi$
$103$	−6.64852	+	4.83043i	−0.655098	+	0.475957i	0.209906	+	0.977722i	$0.432684\pi$
$104$	−4.55239	+	14.0108i	−0.446398	+	1.37387i
$105$		0			0
$106$	8.55709	−	6.21709i	0.831138	−	0.603857i
$107$	9.86072	+	7.16423i	0.953272	+	0.692593i	0.951578	−	0.307406i	$-0.0994610\pi$
$107$	9.86072	+	7.16423i	0.953272	+	0.692593i	0.00169340	+	0.999999i	$0.499461\pi$
$108$		0			0
$109$	0.886088			0.0848718			0.0424359	−	0.999099i	$-0.486488\pi$
$109$	0.886088			0.0848718			0.0424359	+	0.999099i	$0.486488\pi$
$110$	9.73791	+	2.84750i	0.928474	+	0.271498i
$111$		0			0
$112$	1.06649	+	3.28231i	0.100774	+	0.310149i
$113$	3.67700	+	2.67149i	0.345903	+	0.251313i	0.747148	−	0.664658i	$-0.231423\pi$
$113$	3.67700	+	2.67149i	0.345903	+	0.251313i	−0.401245	+	0.915971i	$0.631423\pi$
$114$		0			0
$115$	2.63056	−	8.09602i	0.245301	−	0.754958i
$116$	−5.42768	+	16.7047i	−0.503947	+	1.55099i
$117$		0			0
$118$	−13.6594	−	9.92416i	−1.25745	−	0.913593i
$119$	−1.83067	−	5.63423i	−0.167817	−	0.516489i
$120$		0			0
$121$	9.26705	+	5.92636i	0.842459	+	0.538760i
$122$	−5.95984			−0.539579
$123$		0			0
$124$	−30.7478	−	22.3396i	−2.76123	−	2.00615i
$125$	−8.56947	+	6.22608i	−0.766477	+	0.556878i
$126$		0			0
$127$	−2.48072	+	7.63488i	−0.220129	+	0.677486i	0.778621	+	0.627494i	$0.215919\pi$
$127$	−2.48072	+	7.63488i	−0.220129	+	0.677486i	−0.998750	+	0.0499916i	$0.984081\pi$
$128$	16.3606	−	11.8867i	1.44609	−	1.05065i
$129$		0			0
$130$	3.00444	+	9.24673i	0.263507	+	0.810992i
$131$	−0.101461			−0.00886466			−0.00443233	−	0.999990i	$-0.501411\pi$
$131$	−0.101461			−0.00886466			−0.00443233	+	0.999990i	$0.501411\pi$
$132$		0			0
$133$	2.86222			0.248186
$134$	−7.07480	−	21.7740i	−0.611170	−	1.88099i
$135$		0			0
$136$	22.2150	−	16.1401i	1.90492	−	1.38401i
$137$	1.41038	−	4.34071i	0.120497	−	0.370852i	−0.872557	−	0.488513i	$-0.837540\pi$
$137$	1.41038	−	4.34071i	0.120497	−	0.370852i	0.993054	+	0.117661i	$0.0375396\pi$
$138$		0			0
$139$	3.09475	−	2.24847i	0.262494	−	0.190713i	−0.448752	−	0.893656i	$-0.648131\pi$
$139$	3.09475	−	2.24847i	0.262494	−	0.190713i	0.711246	+	0.702944i	$0.248131\pi$
$140$	3.97842	+	2.89049i	0.336238	+	0.244291i
$141$		0			0
$142$	0.283415			0.0237837
$143$	0.312786	+	10.5366i	0.0261565	+	0.881116i
$144$		0			0
$145$	1.74847	+	5.38124i	0.145203	+	0.446887i
$146$	−1.20932	−	0.878624i	−0.100084	−	0.0727155i
$147$		0			0
$148$	−6.58609	+	20.2699i	−0.541374	+	1.66618i
$149$	1.50560	−	4.63377i	0.123344	−	0.379613i	−0.870252	−	0.492607i	$-0.836044\pi$
$149$	1.50560	−	4.63377i	0.123344	−	0.379613i	0.993596	+	0.112994i	$0.0360440\pi$
$150$		0			0
$151$	13.7321	+	9.97699i	1.11751	+	0.811916i	0.983829	−	0.179109i	$-0.0573215\pi$
$151$	13.7321	+	9.97699i	1.11751	+	0.811916i	0.133677	+	0.991025i	$0.457322\pi$
$152$	4.09964	+	12.6174i	0.332525	+	1.02341i
$153$		0			0
$154$	4.92950	+	6.37794i	0.397230	+	0.513949i
$155$	−12.2434			−0.983410
$156$		0			0
$157$	−1.81611	−	1.31948i	−0.144941	−	0.105306i	0.512952	−	0.858417i	$-0.328552\pi$
$157$	−1.81611	−	1.31948i	−0.144941	−	0.105306i	−0.657893	+	0.753112i	$0.728552\pi$
$158$	−16.7709	+	12.1848i	−1.33422	+	0.969371i
$159$		0			0
$160$	0.343115	−	1.05600i	0.0271256	−	0.0834841i
$161$	5.47173	−	3.97544i	0.431233	−	0.313309i
$162$		0			0
$163$	−4.89398	−	15.0621i	−0.383326	−	1.17976i	−0.937687	−	0.347480i	$-0.887037\pi$
$163$	−4.89398	−	15.0621i	−0.383326	−	1.17976i	0.554361	−	0.832276i	$-0.312963\pi$
$164$	1.22872			0.0959470
$165$		0			0
$166$	−2.31022			−0.179308
$167$	−6.40950	−	19.7264i	−0.495982	−	1.52647i	−0.815421	−	0.578868i	$-0.803495\pi$
$167$	−6.40950	−	19.7264i	−0.495982	−	1.52647i	0.319440	−	0.947607i	$-0.396505\pi$
$168$		0			0
$169$	2.34481	−	1.70361i	0.180370	−	0.131047i
$170$	5.60011	−	17.2354i	0.429509	−	1.32189i
$171$		0			0
$172$	0.419017	−	0.304433i	0.0319497	−	0.0232128i
$173$	−17.4387	−	12.6700i	−1.32584	−	0.963279i	−0.999840	−	0.0179090i	$-0.994299\pi$
$173$	−17.4387	−	12.6700i	−1.32584	−	0.963279i	−0.326000	−	0.945370i	$-0.605701\pi$
$174$		0			0
$175$	−3.41585			−0.258214
$176$	−6.45030	+	9.45592i	−0.486210	+	0.712767i
$177$		0			0
$178$	−7.55194	−	23.2425i	−0.566042	−	1.74210i
$179$	3.86840	+	2.81056i	0.289138	+	0.210071i	0.722893	−	0.690960i	$-0.242812\pi$
$179$	3.86840	+	2.81056i	0.289138	+	0.210071i	−0.433755	+	0.901031i	$0.642812\pi$
$180$		0			0
$181$	−2.42666	+	7.46850i	−0.180372	+	0.555129i	−0.999838	−	0.0179992i	$-0.994270\pi$
$181$	−2.42666	+	7.46850i	−0.180372	+	0.555129i	0.819466	+	0.573128i	$0.194270\pi$
$182$	−2.38707	+	7.34665i	−0.176942	+	0.544570i
$183$		0			0
$184$	25.3621	+	18.4266i	1.86972	+	1.35843i
$185$	2.12164	+	6.52974i	0.155986	+	0.480076i
$186$		0			0
$187$	11.0722	−	16.2315i	0.809681	−	1.18696i
$188$	−36.6293			−2.67146
$189$		0			0
$190$	7.08347	+	5.14644i	0.513889	+	0.373362i
$191$	−7.14385	+	5.19031i	−0.516911	+	0.375558i	−0.815439	−	0.578843i	$-0.803504\pi$
$191$	−7.14385	+	5.19031i	−0.516911	+	0.375558i	0.298528	+	0.954401i	$0.403504\pi$
$192$		0			0
$193$	7.91153	−	24.3492i	0.569485	−	1.75269i	−0.0847500	−	0.996402i	$-0.527009\pi$
$193$	7.91153	−	24.3492i	0.569485	−	1.75269i	0.654235	−	0.756292i	$-0.272991\pi$
$194$	−34.5613	+	25.1102i	−2.48135	+	1.80281i
$195$		0			0
$196$	1.20736	+	3.71587i	0.0862400	+	0.265419i
$197$	11.1977			0.797802			0.398901	−	0.916994i	$-0.369392\pi$
$197$	11.1977			0.797802			0.398901	+	0.916994i	$0.369392\pi$
$198$		0			0
$199$	−12.2503			−0.868400			−0.434200	−	0.900817i	$-0.642969\pi$
$199$	−12.2503			−0.868400			−0.434200	+	0.900817i	$0.642969\pi$
$200$	−4.89262	−	15.0579i	−0.345960	−	1.06476i
$201$		0			0
$202$	−24.5316	+	17.8232i	−1.72603	+	1.25404i
$203$	−1.38918	+	4.27547i	−0.0975016	+	0.300079i
$204$		0			0
$205$	0.320225	−	0.232657i	0.0223655	−	0.0162495i
$206$	−16.1589	−	11.7401i	−1.12585	−	0.817974i
$207$		0			0
$208$	−10.9691			−0.760568
$209$	5.80521	+	7.51097i	0.401555	+	0.519545i
$210$		0			0
$211$	−4.40769	−	13.5655i	−0.303438	−	0.933887i	−0.980255	−	0.197736i	$-0.936641\pi$
$211$	−4.40769	−	13.5655i	−0.303438	−	0.933887i	0.676817	−	0.736151i	$-0.263359\pi$
$212$	13.7560	+	9.99435i	0.944769	+	0.686415i
$213$		0			0
$214$	−9.15420	+	28.1737i	−0.625768	+	1.92592i
$215$	0.0515585	−	0.158681i	0.00351626	−	0.0108219i
$216$		0			0
$217$	−7.86972	−	5.71769i	−0.534232	−	0.388142i
$218$	0.665497	+	2.04819i	0.0450732	+	0.138721i
$219$		0			0
$220$	0.483955	+	16.3026i	0.0326282	+	1.09912i
$221$	18.8289			1.26657
$222$		0			0
$223$	2.39793	+	1.74220i	0.160577	+	0.116666i	0.665172	−	0.746690i	$-0.268358\pi$
$223$	2.39793	+	1.74220i	0.160577	+	0.116666i	−0.504595	+	0.863356i	$0.668358\pi$
$224$	0.713702	−	0.518535i	0.0476862	−	0.0346460i
$225$		0			0
$226$	−3.41354	+	10.5058i	−0.227065	+	0.698835i
$227$	6.67929	−	4.85279i	0.443320	−	0.322091i	−0.343633	−	0.939104i	$-0.611658\pi$
$227$	6.67929	−	4.85279i	0.443320	−	0.322091i	0.786953	+	0.617013i	$0.211658\pi$
$228$		0			0
$229$	4.05063	+	12.4666i	0.267673	+	0.823813i	0.991066	+	0.133376i	$0.0425818\pi$
$229$	4.05063	+	12.4666i	0.267673	+	0.823813i	−0.723392	+	0.690437i	$0.757418\pi$
$230$	20.6896			1.36423
$231$		0			0
$232$	−20.8371			−1.36802
$233$	3.96397	+	12.1998i	0.259688	+	0.799239i	0.992870	+	0.119205i	$0.0380347\pi$
$233$	3.96397	+	12.1998i	0.259688	+	0.799239i	−0.733181	+	0.680033i	$0.761965\pi$
$234$		0			0
$235$	−9.54618	+	6.93571i	−0.622724	+	0.452436i
$236$	8.38735	−	25.8136i	0.545970	−	1.68032i
$237$		0			0
$238$	11.6486	−	8.46319i	0.755065	−	0.548587i
$239$	−4.02979	−	2.92781i	−0.260665	−	0.189384i	0.449775	−	0.893142i	$-0.351504\pi$
$239$	−4.02979	−	2.92781i	−0.260665	−	0.189384i	−0.710440	+	0.703758i	$0.751504\pi$
$240$		0			0
$241$	−2.62686			−0.169211			−0.0846053	−	0.996415i	$-0.526963\pi$
$241$	−2.62686			−0.169211			−0.0846053	+	0.996415i	$0.526963\pi$
$242$	−6.73874	+	25.8718i	−0.433183	+	1.66310i
$243$		0			0
$244$	−2.96063	−	9.11189i	−0.189535	−	0.583329i
$245$	1.01825	+	0.739805i	0.0650539	+	0.0472644i
$246$		0			0
$247$	−2.81113	+	8.65177i	−0.178868	+	0.550499i
$248$	13.9330	−	42.8814i	0.884747	−	2.72297i
$249$		0			0
$250$	−20.8277	−	15.1322i	−1.31726	−	0.957045i
$251$	8.10332	+	24.9395i	0.511477	+	1.57417i	0.789601	+	0.613620i	$0.210287\pi$
$251$	8.10332	+	24.9395i	0.511477	+	1.57417i	−0.278124	+	0.960545i	$0.589713\pi$
$252$		0			0
$253$	21.5302	+	6.29571i	1.35359	+	0.395808i
$254$	−19.5112			−1.22424
$255$		0			0
$256$	25.1261	+	18.2552i	1.57038	+	1.14095i
$257$	24.2315	−	17.6052i	1.51152	−	1.09818i	0.546022	−	0.837771i	$-0.316141\pi$
$257$	24.2315	−	17.6052i	1.51152	−	1.09818i	0.965497	−	0.260413i	$-0.0838586\pi$
$258$		0			0
$259$	−1.68567	+	5.18797i	−0.104743	+	0.322365i
$260$	−12.6446	+	9.18688i	−0.784188	+	0.569746i
$261$		0			0
$262$	−0.0762022	−	0.234526i	−0.00470779	−	0.0144891i
$263$	−3.33709			−0.205774			−0.102887	−	0.994693i	$-0.532808\pi$
$263$	−3.33709			−0.205774			−0.102887	+	0.994693i	$0.532808\pi$
$264$		0			0
$265$	5.47747			0.336478
$266$	2.14967	+	6.61601i	0.131805	+	0.405654i
$267$		0			0
$268$	29.7754	−	21.6331i	1.81882	−	1.32145i
$269$	0.536395	−	1.65086i	0.0327046	−	0.100654i	−0.933372	−	0.358911i	$-0.883148\pi$
$269$	0.536395	−	1.65086i	0.0327046	−	0.100654i	0.966076	+	0.258257i	$0.0831481\pi$
$270$		0			0
$271$	2.00309	−	1.45533i	0.121679	−	0.0884051i	−0.525281	−	0.850929i	$-0.676040\pi$
$271$	2.00309	−	1.45533i	0.121679	−	0.0884051i	0.646960	+	0.762524i	$0.276040\pi$
$272$	16.5409	+	12.0177i	1.00294	+	0.728679i
$273$		0			0
$274$	11.0928			0.670141
$275$	−6.92810	−	8.96379i	−0.417780	−	0.540537i
$276$		0			0
$277$	1.59320	+	4.90337i	0.0957262	+	0.294615i	0.987442	−	0.157980i	$-0.0504983\pi$
$277$	1.59320	+	4.90337i	0.0957262	+	0.294615i	−0.891716	+	0.452595i	$0.850498\pi$
$278$	7.52165	+	5.46480i	0.451119	+	0.327757i
$279$		0			0
$280$	−1.80277	+	5.54837i	−0.107736	+	0.331578i
$281$	6.97467	−	21.4658i	0.416074	−	1.28054i	−0.495213	−	0.868772i	$-0.664910\pi$
$281$	6.97467	−	21.4658i	0.416074	−	1.28054i	0.911287	−	0.411772i	$-0.135090\pi$
$282$		0			0
$283$	6.86659	+	4.98887i	0.408176	+	0.296557i	0.772863	−	0.634573i	$-0.218824\pi$
$283$	6.86659	+	4.98887i	0.408176	+	0.296557i	−0.364687	+	0.931130i	$0.618824\pi$
$284$	0.140790	+	0.433309i	0.00835438	+	0.0257121i
$285$		0			0
$286$	−24.1205	+	8.63654i	−1.42627	+	0.510690i
$287$	0.314484			0.0185634
$288$		0			0
$289$	−14.6399	−	10.6365i	−0.861171	−	0.625677i
$290$	−11.1255	+	8.08317i	−0.653313	+	0.474660i
$291$		0			0
$292$	0.742565	−	2.28538i	0.0434553	−	0.133742i
$293$	19.9229	−	14.4749i	1.16391	−	0.845630i	0.173643	−	0.984809i	$-0.444446\pi$
$293$	19.9229	−	14.4749i	1.16391	−	0.845630i	0.990267	+	0.139178i	$0.0444462\pi$
$294$		0			0
$295$	−2.70190	−	8.31559i	−0.157311	−	0.484152i
$296$	−25.2843			−1.46962
$297$		0			0
$298$	11.8417			0.685973
$299$	6.64271	+	20.4442i	0.384158	+	1.18232i
$300$		0			0
$301$	0.107245	−	0.0779180i	0.00618149	−	0.00449112i
$302$	−12.7482	+	39.2351i	−0.733579	+	2.25772i
$303$		0			0
$304$	−7.99160	+	5.80624i	−0.458350	+	0.333011i
$305$	−2.49692	−	1.81412i	−0.142973	−	0.103876i
$306$		0			0
$307$	4.59391			0.262188			0.131094	−	0.991370i	$-0.458151\pi$
$307$	4.59391			0.262188			0.131094	+	0.991370i	$0.458151\pi$
$308$	−7.30232	+	10.7049i	−0.416088	+	0.609971i
$309$		0			0
$310$	−9.19538	−	28.3005i	−0.522263	−	1.60736i
$311$	−1.78852	−	1.29944i	−0.101418	−	0.0736843i	0.535921	−	0.844268i	$-0.319965\pi$
$311$	−1.78852	−	1.29944i	−0.101418	−	0.0736843i	−0.637338	+	0.770584i	$0.719965\pi$
$312$		0			0
$313$	−2.99724	+	9.22457i	−0.169414	+	0.521403i	−0.999334	−	0.0364788i	$-0.988386\pi$
$313$	−2.99724	+	9.22457i	−0.169414	+	0.521403i	0.829920	+	0.557882i	$0.188386\pi$
$314$	1.68598	−	5.18892i	0.0951455	−	0.292828i
$315$		0			0
$316$	−26.9603	−	19.5878i	−1.51664	−	1.10190i
$317$	−1.99483	−	6.13944i	−0.112041	−	0.344826i	0.879278	−	0.476310i	$-0.158026\pi$
$317$	−1.99483	−	6.13944i	−0.112041	−	0.344826i	−0.991318	+	0.131484i	$0.958026\pi$
$318$		0			0
$319$	−14.0372	+	5.02613i	−0.785930	+	0.281409i
$320$	11.3863			0.636513
$321$		0			0
$322$	13.2988	+	9.66213i	0.741112	+	0.538449i
$323$	13.7179	−	9.96666i	0.763286	−	0.554560i
$324$		0			0
$325$	3.35488	−	10.3253i	0.186095	−	0.572742i
$326$	31.1404	−	22.6248i	1.72471	−	1.25307i
$327$		0			0
$328$	0.450445	+	1.38633i	0.0248717	+	0.0765471i
$329$	−9.37505			−0.516863
$330$		0			0
$331$	3.62076			0.199015			0.0995075	−	0.995037i	$-0.468273\pi$
$331$	3.62076			0.199015			0.0995075	+	0.995037i	$0.468273\pi$
$332$	−1.14763	−	3.53206i	−0.0629846	−	0.193847i
$333$		0			0
$334$	40.7837	−	29.6311i	2.23158	−	1.62134i
$335$	3.66375	−	11.2759i	0.200172	−	0.616066i
$336$		0			0
$337$	5.18183	−	3.76482i	0.282272	−	0.205083i	−0.437636	−	0.899152i	$-0.644184\pi$
$337$	5.18183	−	3.76482i	0.282272	−	0.205083i	0.719908	+	0.694070i	$0.244184\pi$
$338$	5.69896	+	4.14054i	0.309983	+	0.225215i
$339$		0			0
$340$	29.1327			1.57994
$341$	−0.957312	−	32.2483i	−0.0518414	−	1.74634i
$342$		0			0
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	0.497093	+	0.361159i	0.0268014	+	0.0194724i
$345$		0			0
$346$	16.1892	−	49.8253i	0.870338	−	2.67862i
$347$	5.39544	−	16.6054i	0.289642	−	0.891427i	−0.695327	−	0.718694i	$-0.744740\pi$
$347$	5.39544	−	16.6054i	0.289642	−	0.891427i	0.984969	−	0.172733i	$-0.0552598\pi$
$348$		0			0
$349$	17.4949	+	12.7108i	0.936481	+	0.680393i	0.947571	−	0.319545i	$-0.103530\pi$
$349$	17.4949	+	12.7108i	0.936481	+	0.680393i	−0.0110900	+	0.999939i	$0.503530\pi$
$350$	−2.56548	−	7.89572i	−0.137130	−	0.422044i
$351$		0			0
$352$	2.80827	+	0.821177i	0.149681	+	0.0437689i
$353$	−4.40150			−0.234268			−0.117134	−	0.993116i	$-0.537371\pi$
$353$	−4.40150			−0.234268			−0.117134	+	0.993116i	$0.537371\pi$
$354$		0			0
$355$	0.118739	+	0.0862688i	0.00630200	+	0.00457867i
$356$	31.7835	−	23.0920i	1.68452	−	1.22388i
$357$		0			0
$358$	−3.59123	+	11.0527i	−0.189802	+	0.584152i
$359$	−8.64170	+	6.27857i	−0.456092	+	0.331370i	−0.791996	−	0.610526i	$-0.790958\pi$
$359$	−8.64170	+	6.27857i	−0.456092	+	0.331370i	0.335904	+	0.941896i	$0.390958\pi$
$360$		0			0
$361$	−3.33977	−	10.2787i	−0.175777	−	0.540986i
$362$	−19.0860			−1.00314
$363$		0			0
$364$	−12.4180			−0.650879
$365$	−0.239209	−	0.736211i	−0.0125208	−	0.0385350i
$366$		0			0
$367$	−8.26552	+	6.00525i	−0.431456	+	0.313471i	−0.782231	−	0.622988i	$-0.785918\pi$
$367$	−8.26552	+	6.00525i	−0.431456	+	0.313471i	0.350775	+	0.936460i	$0.385918\pi$
$368$	−7.21312	+	22.1997i	−0.376010	+	1.15724i
$369$		0			0
$370$	−13.5000	+	9.80834i	−0.701833	+	0.509911i
$371$	3.52078	+	2.55800i	0.182790	+	0.132805i
$372$		0			0
$373$	−27.8851			−1.44383			−0.721917	−	0.691980i	$-0.756739\pi$
$373$	−27.8851			−1.44383			−0.721917	+	0.691980i	$0.756739\pi$
$374$	45.8348	+	13.4027i	2.37006	+	0.693039i
$375$		0			0
$376$	−13.4282	−	41.3276i	−0.692504	−	2.13131i
$377$	−11.5593	−	8.39832i	−0.595334	−	0.432535i
$378$		0			0
$379$	0.354761	−	1.09184i	0.0182228	−	0.0560841i	−0.941532	−	0.336925i	$-0.890613\pi$
$379$	0.354761	−	1.09184i	0.0182228	−	0.0560841i	0.959754	+	0.280841i	$0.0906132\pi$
$380$	−4.34949	+	13.3863i	−0.223124	+	0.686705i
$381$		0			0
$382$	−17.3628	−	12.6148i	−0.888358	−	0.645430i
$383$	6.16539	+	18.9751i	0.315037	+	0.969583i	0.975739	+	0.218936i	$0.0702584\pi$
$383$	6.16539	+	18.9751i	0.315037	+	0.969583i	−0.660703	+	0.750648i	$0.729742\pi$
$384$		0			0
$385$	0.123865	+	4.17257i	0.00631277	+	0.212654i
$386$	62.2251			3.16717
$387$		0			0
$388$	−55.5593	−	40.3662i	−2.82060	−	2.04928i
$389$	2.10345	−	1.52824i	0.106649	−	0.0774850i	−0.533183	−	0.846000i	$-0.679004\pi$
$389$	2.10345	−	1.52824i	0.106649	−	0.0774850i	0.639832	+	0.768515i	$0.279004\pi$
$390$		0			0
$391$	12.3816	−	38.1067i	0.626166	−	1.92714i
$392$	−3.74989	+	2.72445i	−0.189398	+	0.137606i
$393$		0			0
$394$	8.41003	+	25.8834i	0.423691	+	1.30399i
$395$	−10.7352			−0.540148
$396$		0			0
$397$	8.77237			0.440272			0.220136	−	0.975469i	$-0.429350\pi$
$397$	8.77237			0.440272			0.220136	+	0.975469i	$0.429350\pi$
$398$	−9.20059	−	28.3165i	−0.461184	−	1.41938i
$399$		0			0
$400$	9.53740	−	6.92932i	0.476870	−	0.346466i
$401$	−8.76171	+	26.9658i	−0.437539	+	1.34661i	0.452923	+	0.891549i	$0.350381\pi$
$401$	−8.76171	+	26.9658i	−0.437539	+	1.34661i	−0.890462	+	0.455057i	$0.849619\pi$
$402$		0			0
$403$	25.0124	−	18.1726i	1.24596	−	0.905241i
$404$	−39.4360	−	28.6519i	−1.96201	−	1.42549i
$405$		0			0
$406$	−10.9261			−0.542252
$407$	−17.0331	+	6.09885i	−0.844298	+	0.302309i
$408$		0			0
$409$	6.15114	+	18.9313i	0.304154	+	0.936091i	0.979991	+	0.199040i	$0.0637823\pi$
$409$	6.15114	+	18.9313i	0.304154	+	0.936091i	−0.675837	+	0.737051i	$0.736218\pi$
$410$	0.778292	+	0.565462i	0.0384371	+	0.0279262i
$411$		0			0
$412$	9.92212	−	30.5371i	0.488828	−	1.50446i
$413$	2.14670	−	6.60685i	0.105632	−	0.325102i
$414$		0			0
$415$	−0.967883	−	0.703208i	−0.0475115	−	0.0345191i
$416$	0.866438	+	2.66662i	0.0424806	+	0.130742i
$417$		0			0
$418$	−13.0016	+	19.0599i	−0.635928	+	0.932248i
$419$	30.8957			1.50935			0.754676	−	0.656097i	$-0.227794\pi$
$419$	30.8957			1.50935			0.754676	+	0.656097i	$0.227794\pi$
$420$		0			0
$421$	19.5727	+	14.2204i	0.953913	+	0.693058i	0.951729	−	0.306939i	$-0.0993049\pi$
$421$	19.5727	+	14.2204i	0.953913	+	0.693058i	0.00218371	+	0.999998i	$0.499305\pi$
$422$	28.0462	−	20.3767i	1.36527	−	0.991925i
$423$		0			0
$424$	−6.23339	+	19.1844i	−0.302720	+	0.931677i
$425$	−16.3713	+	11.8945i	−0.794127	+	0.576967i
$426$		0			0
$427$	−0.757757	−	2.33214i	−0.0366704	−	0.112860i
$428$	−47.6218			−2.30188
$429$		0			0
$430$	0.405513			0.0195556
$431$	−5.99495	−	18.4506i	−0.288766	−	0.888732i	−0.985244	−	0.171154i	$-0.945251\pi$
$431$	−5.99495	−	18.4506i	−0.288766	−	0.888732i	0.696478	−	0.717578i	$-0.254749\pi$
$432$		0			0
$433$	17.3030	−	12.5714i	0.831530	−	0.604142i	−0.0884616	−	0.996080i	$-0.528195\pi$
$433$	17.3030	−	12.5714i	0.831530	−	0.604142i	0.919992	+	0.391937i	$0.128195\pi$
$434$	7.30586	−	22.4851i	0.350692	−	1.07932i
$435$		0			0
$436$	−2.80084	+	2.03493i	−0.134136	+	0.0974556i
$437$	15.6613	+	11.3786i	0.749181	+	0.544312i
$438$		0			0
$439$	−31.7315			−1.51446			−0.757232	−	0.653146i	$-0.773449\pi$
$439$	−31.7315			−1.51446			−0.757232	+	0.653146i	$0.773449\pi$
$440$	−18.2163	+	6.52252i	−0.868430	+	0.310949i
$441$		0			0
$442$	14.1415	+	43.5229i	0.672640	+	2.07017i
$443$	−1.34791	−	0.979312i	−0.0640410	−	0.0465285i	0.555304	−	0.831647i	$-0.312602\pi$
$443$	−1.34791	−	0.979312i	−0.0640410	−	0.0465285i	−0.619345	+	0.785119i	$0.712602\pi$
$444$		0			0
$445$	3.91084	−	12.0363i	0.185392	−	0.570577i
$446$	−2.22612	+	6.85128i	−0.105410	+	0.324417i
$447$		0			0
$448$	7.31882	+	5.31744i	0.345782	+	0.251225i
$449$	5.31070	+	16.3447i	0.250627	+	0.771352i	0.994660	+	0.103208i	$0.0329108\pi$
$449$	5.31070	+	16.3447i	0.250627	+	0.771352i	−0.744032	+	0.668144i	$0.767089\pi$
$450$		0			0
$451$	0.637844	+	0.825263i	0.0300349	+	0.0388601i
$452$	−17.7578			−0.835258
$453$		0			0
$454$	16.2337	+	11.7945i	0.761885	+	0.553542i
$455$	−3.23633	+	2.35133i	−0.151721	+	0.110232i
$456$		0			0
$457$	3.15835	−	9.72041i	0.147741	−	0.454701i	−0.849612	−	0.527408i	$-0.823164\pi$
$457$	3.15835	−	9.72041i	0.147741	−	0.454701i	0.997353	+	0.0727070i	$0.0231638\pi$
$458$	−25.7742	+	18.7260i	−1.20435	+	0.875010i
$459$		0			0
$460$	10.2779	+	31.6320i	0.479207	+	1.47485i
$461$	22.1160			1.03004			0.515022	−	0.857177i	$-0.327784\pi$
$461$	22.1160			1.03004			0.515022	+	0.857177i	$0.327784\pi$
$462$		0			0
$463$	−30.3717			−1.41149			−0.705747	−	0.708464i	$-0.749389\pi$
$463$	−30.3717			−1.41149			−0.705747	+	0.708464i	$0.749389\pi$
$464$	−4.79439	−	14.7556i	−0.222574	−	0.685012i
$465$		0			0
$466$	−25.2228	+	18.3254i	−1.16842	+	0.848909i
$467$	−7.78441	+	23.9580i	−0.360220	+	1.10864i	0.592701	+	0.805422i	$0.298062\pi$
$467$	−7.78441	+	23.9580i	−0.360220	+	1.10864i	−0.952921	+	0.303220i	$0.901938\pi$
$468$		0			0
$469$	7.62083	−	5.53686i	0.351897	−	0.255668i
$470$	−23.2015	−	16.8569i	−1.07021	−	0.777551i
$471$		0			0
$472$	32.1995			1.48210
$473$	0.421987	+	0.123395i	0.0194030	+	0.00567370i
$474$		0			0
$475$	−3.02123	−	9.29838i	−0.138623	−	0.426639i
$476$	18.7258	+	13.6051i	0.858296	+	0.623588i
$477$		0			0
$478$	3.74105	−	11.5138i	0.171112	−	0.526628i
$479$	6.55239	−	20.1662i	0.299386	−	0.921417i	−0.682326	−	0.731048i	$-0.739032\pi$
$479$	6.55239	−	20.1662i	0.299386	−	0.921417i	0.981713	−	0.190369i	$-0.0609684\pi$
$480$		0			0
$481$	−14.0264	−	10.1907i	−0.639547	−	0.464658i
$482$	−1.97290	−	6.07197i	−0.0898633	−	0.276571i
$483$		0			0
$484$	−42.9024	+	2.54942i	−1.95011	+	0.115883i
$485$	−22.1230			−1.00455
$486$		0			0
$487$	13.6075	+	9.88641i	0.616613	+	0.447996i	0.851737	−	0.523970i	$-0.175549\pi$
$487$	13.6075	+	9.88641i	0.616613	+	0.447996i	−0.235123	+	0.971966i	$0.575549\pi$
$488$	9.19530	−	6.68078i	0.416252	−	0.302425i
$489$		0			0
$490$	−0.945296	+	2.90932i	−0.0427041	+	0.131430i
$491$	3.91406	−	2.84373i	0.176639	−	0.128336i	−0.495953	−	0.868350i	$-0.665181\pi$
$491$	3.91406	−	2.84373i	0.176639	−	0.128336i	0.672592	+	0.740014i	$0.265181\pi$
$492$		0			0
$493$	8.22978	+	25.3286i	0.370650	+	1.14074i
$494$	−22.1099			−0.994770
$495$		0			0
$496$	33.5719			1.50742
$497$	0.0360345	+	0.110903i	0.00161637	+	0.00497467i
$498$		0			0
$499$	−24.7426	+	17.9766i	−1.10763	+	0.804742i	−0.982289	−	0.187372i	$-0.940003\pi$
$499$	−24.7426	+	17.9766i	−1.10763	+	0.804742i	−0.125343	+	0.992114i	$0.540003\pi$
$500$	12.7889	−	39.3602i	0.571937	−	1.76024i
$501$		0			0
$502$	−51.5615	+	37.4616i	−2.30130	+	1.67199i
$503$	−22.8472	−	16.5994i	−1.01871	−	0.740133i	−0.0526880	−	0.998611i	$-0.516779\pi$
$503$	−22.8472	−	16.5994i	−1.01871	−	0.740133i	−0.966017	+	0.258478i	$0.916779\pi$
$504$		0			0
$505$	−15.7029			−0.698768
$506$	1.61773	+	54.4953i	0.0719168	+	2.42261i
$507$		0			0
$508$	−9.69243	−	29.8302i	−0.430032	−	1.32350i
$509$	−3.39839	−	2.46908i	−0.150631	−	0.109440i	0.509917	−	0.860224i	$-0.329676\pi$
$509$	−3.39839	−	2.46908i	−0.150631	−	0.109440i	−0.660548	+	0.750784i	$0.729676\pi$
$510$		0			0
$511$	0.190055	−	0.584930i	0.00840755	−	0.0258758i
$512$	−10.8274	+	33.3234i	−0.478509	+	1.47270i
$513$		0			0
$514$	58.8935	+	42.7886i	2.59768	+	1.88733i
$515$	−3.19631	−	9.83722i	−0.140846	−	0.433480i
$516$		0			0
$517$	−19.0147	−	24.6018i	−0.836265	−	1.08199i
$518$	−13.2580			−0.582523
$519$		0			0
$520$	−15.0007	−	10.8987i	−0.657826	−	0.477939i
$521$	−16.7037	+	12.1360i	−0.731804	+	0.531687i	−0.890134	−	0.455700i	$-0.849389\pi$
$521$	−16.7037	+	12.1360i	−0.731804	+	0.531687i	0.158330	+	0.987386i	$0.449389\pi$
$522$		0			0
$523$	−6.99431	+	21.5263i	−0.305840	+	0.941278i	0.673523	+	0.739167i	$0.264780\pi$
$523$	−6.99431	+	21.5263i	−0.305840	+	0.941278i	−0.979362	+	0.202112i	$0.935220\pi$
$524$	0.320708	−	0.233008i	0.0140102	−	0.0101790i
$525$		0			0
$526$	−2.50632	−	7.71367i	−0.109281	−	0.336332i
$527$	−57.6275			−2.51030
$528$		0			0
$529$	22.7440			0.988869
$530$	4.11386	+	12.6612i	0.178695	+	0.549965i
$531$		0			0
$532$	−9.04721	+	6.57318i	−0.392246	+	0.284984i
$533$	−0.308871	+	0.950608i	−0.0133787	+	0.0411754i
$534$		0			0
$535$	−12.4110	+	9.01713i	−0.536575	+	0.389844i
$536$	35.3234	+	25.6640i	1.52574	+	1.10852i
$537$		0			0
$538$	4.21881			0.181886
$539$	−1.86899	+	2.73987i	−0.0805030	+	0.118015i
$540$		0			0
$541$	13.2001	+	40.6256i	0.567515	+	1.74663i	0.660359	+	0.750950i	$0.270404\pi$
$541$	13.2001	+	40.6256i	0.567515	+	1.74663i	−0.0928437	+	0.995681i	$0.529596\pi$
$542$	4.86842	+	3.53711i	0.209117	+	0.151932i
$543$		0			0
$544$	1.61499	−	4.97043i	0.0692421	−	0.213105i
$545$	−0.344634	+	1.06067i	−0.0147625	+	0.0454343i
$546$		0			0
$547$	−35.9873	−	26.1463i	−1.53870	−	1.11793i	−0.951141	−	0.308756i	$-0.900087\pi$
$547$	−35.9873	−	26.1463i	−1.53870	−	1.11793i	−0.587563	−	0.809178i	$-0.699913\pi$
$548$	5.51050	+	16.9596i	0.235397	+	0.724477i
$549$		0			0
$550$	15.5164	−	22.7466i	0.661623	−	0.969916i
$551$	−12.8671			−0.548156
$552$		0			0
$553$	−6.90033	−	5.01339i	−0.293432	−	0.213191i
$554$	−10.1376	+	7.36536i	−0.430703	+	0.312924i
$555$		0			0
$556$	−4.61855	+	14.2144i	−0.195870	+	0.602826i
$557$	−20.2182	+	14.6894i	−0.856674	+	0.622410i	−0.926978	−	0.375116i	$-0.877603\pi$
$557$	−20.2182	+	14.6894i	−0.856674	+	0.622410i	0.0703041	+	0.997526i	$0.477603\pi$
$558$		0			0
$559$	0.130196	+	0.400702i	0.00550670	+	0.0169479i
$560$	−4.34382			−0.183560
$561$		0			0
$562$	54.8565			2.31398
$563$	−2.78426	−	8.56907i	−0.117343	−	0.361143i	0.875086	−	0.483968i	$-0.160805\pi$
$563$	−2.78426	−	8.56907i	−0.117343	−	0.361143i	−0.992428	+	0.122824i	$0.960805\pi$
$564$		0			0
$565$	−4.62798	+	3.36243i	−0.194701	+	0.141458i
$566$	−6.37460	+	19.6190i	−0.267944	+	0.824648i
$567$		0			0
$568$	−0.437275	+	0.317699i	−0.0183476	+	0.0133303i
$569$	23.6021	+	17.1480i	0.989453	+	0.718880i	0.959801	−	0.280681i	$-0.0905601\pi$
$569$	23.6021	+	17.1480i	0.989453	+	0.718880i	0.0296519	+	0.999560i	$0.490560\pi$
$570$		0			0
$571$	1.78994			0.0749067			0.0374533	−	0.999298i	$-0.488075\pi$
$571$	1.78994			0.0749067			0.0374533	+	0.999298i	$0.488075\pi$
$572$	−25.1864	−	32.5870i	−1.05310	−	1.36253i
$573$		0			0
$574$	0.236194	+	0.726930i	0.00985854	+	0.0303415i
$575$	−18.6906	−	13.5795i	−0.779452	−	0.566305i
$576$		0			0
$577$	−6.67012	+	20.5285i	−0.277681	+	0.854614i	0.710817	+	0.703377i	$0.248325\pi$
$577$	−6.67012	+	20.5285i	−0.277681	+	0.854614i	−0.988498	+	0.151236i	$0.951675\pi$
$578$	13.5910	−	41.8287i	0.565309	−	1.73984i
$579$		0			0
$580$	−17.8850	−	12.9942i	−0.742633	−	0.539554i
$581$	−0.293731	−	0.904010i	−0.0121860	−	0.0375046i
$582$		0			0
$583$	0.428285	+	14.4273i	0.0177378	+	0.597519i
$584$	2.85074			0.117965
$585$		0			0
$586$	48.4217	+	35.1805i	2.00028	+	1.45329i
$587$	4.46865	−	3.24666i	0.184441	−	0.134004i	−0.491734	−	0.870746i	$-0.663637\pi$
$587$	4.46865	−	3.24666i	0.184441	−	0.134004i	0.676174	+	0.736742i	$0.263637\pi$
$588$		0			0
$589$	8.60373	−	26.4796i	0.354511	−	1.09107i
$590$	17.1922	−	12.4909i	0.707792	−	0.514241i
$591$		0			0
$592$	−5.81764	−	17.9049i	−0.239104	−	0.735886i
$593$	40.7867			1.67491			0.837454	−	0.546508i	$-0.184043\pi$
$593$	40.7867			1.67491			0.837454	+	0.546508i	$0.184043\pi$
$594$		0			0
$595$	7.45636			0.305681
$596$	5.88254	+	18.1046i	0.240958	+	0.741593i
$597$		0			0
$598$	−42.2676	+	30.7092i	−1.72845	+	1.25579i
$599$	8.19356	−	25.2172i	0.334780	−	1.03035i	−0.632051	−	0.774927i	$-0.717787\pi$
$599$	8.19356	−	25.2172i	0.334780	−	1.03035i	0.966830	−	0.255419i	$-0.0822134\pi$
$600$		0			0
$601$	30.5565	−	22.2006i	1.24643	−	0.905581i	0.248417	−	0.968653i	$-0.420090\pi$
$601$	30.5565	−	22.2006i	1.24643	−	0.905581i	0.998009	+	0.0630720i	$0.0200898\pi$
$602$	0.260654	+	0.189376i	0.0106235	+	0.00771839i
$603$		0			0
$604$	−66.3186			−2.69847
$605$	−10.6983	+	8.78794i	−0.434949	+	0.357281i
$606$		0			0
$607$	−8.56730	−	26.3674i	−0.347736	−	1.07022i	−0.960103	−	0.279647i	$-0.909782\pi$
$607$	−8.56730	−	26.3674i	−0.347736	−	1.07022i	0.612367	−	0.790574i	$-0.290218\pi$
$608$	2.04277	+	1.48416i	0.0828452	+	0.0601906i
$609$		0			0
$610$	2.31801	−	7.13411i	0.0938536	−	0.288852i
$611$	9.20772	−	28.3385i	0.372505	−	1.14645i
$612$		0			0
$613$	−29.3078	−	21.2934i	−1.18373	−	0.860031i	−0.191144	−	0.981562i	$-0.561220\pi$
$613$	−29.3078	−	21.2934i	−1.18373	−	0.860031i	−0.992588	+	0.121531i	$0.961220\pi$
$614$	3.45026	+	10.6188i	0.139241	+	0.428540i
$615$		0			0
$616$	−14.7551	−	4.31458i	−0.594498	−	0.173839i
$617$	−41.1920			−1.65833			−0.829163	−	0.559007i	$-0.811183\pi$
$617$	−41.1920			−1.65833			−0.829163	+	0.559007i	$0.811183\pi$
$618$		0			0
$619$	28.9139	+	21.0072i	1.16215	+	0.844349i	0.990048	−	0.140730i	$-0.0449450\pi$
$619$	28.9139	+	21.0072i	1.16215	+	0.844349i	0.172099	+	0.985080i	$0.444945\pi$
$620$	38.7001	−	28.1173i	1.55423	−	1.12922i
$621$		0			0
$622$	1.66037	−	5.11010i	0.0665749	−	0.204897i
$623$	8.13480	−	5.91028i	0.325914	−	0.236790i
$624$		0			0
$625$	1.15796	+	3.56385i	0.0463186	+	0.142554i
$626$	−23.5736			−0.942192
$627$		0			0
$628$	8.77077			0.349992
$629$	9.98623	+	30.7345i	0.398177	+	1.22546i
$630$		0			0
$631$	−2.23700	+	1.62527i	−0.0890534	+	0.0647011i	−0.631421	−	0.775440i	$-0.717528\pi$
$631$	−2.23700	+	1.62527i	−0.0890534	+	0.0647011i	0.542368	+	0.840141i	$0.317528\pi$
$632$	12.2167	−	37.5993i	0.485956	−	1.49562i
$633$		0			0
$634$	12.6931	−	9.22207i	0.504107	−	0.366255i
$635$	−8.17433	−	5.93900i	−0.324388	−	0.235682i
$636$		0			0
$637$	−3.17831			−0.125929
$638$	−22.1605	−	28.6720i	−0.877344	−	1.13514i
$639$		0			0
$640$	7.86545	+	24.2074i	0.310909	+	0.956880i
$641$	31.1362	+	22.6218i	1.22981	+	0.893506i	0.996876	−	0.0789878i	$-0.0251688\pi$
$641$	31.1362	+	22.6218i	1.22981	+	0.893506i	0.232930	+	0.972494i	$0.425169\pi$
$642$		0			0
$643$	−8.15130	+	25.0871i	−0.321456	+	0.989339i	0.651559	+	0.758598i	$0.274115\pi$
$643$	−8.15130	+	25.0871i	−0.321456	+	0.989339i	−0.973015	+	0.230741i	$0.925885\pi$
$644$	−8.16590	+	25.1320i	−0.321781	+	0.990341i
$645$		0			0
$646$	33.3408	+	24.2235i	1.31178	+	0.953061i
$647$	8.44268	+	25.9839i	0.331916	+	1.02153i	0.968221	+	0.250095i	$0.0804619\pi$
$647$	8.44268	+	25.9839i	0.331916	+	1.02153i	−0.636305	+	0.771437i	$0.719538\pi$
$648$		0			0
$649$	21.6915	−	7.76685i	0.851467	−	0.304875i
$650$	26.3865			1.03496
$651$		0			0
$652$	50.0601	+	36.3708i	1.96051	+	1.42439i
$653$	−6.84562	+	4.97364i	−0.267890	+	0.194633i	−0.713618	−	0.700535i	$-0.752945\pi$
$653$	−6.84562	+	4.97364i	−0.267890	+	0.194633i	0.445728	+	0.895168i	$0.352945\pi$
$654$		0			0
$655$	0.0394620	−	0.121451i	0.00154191	−	0.00474550i
$656$	−0.878073	+	0.637957i	−0.0342830	+	0.0249080i
$657$		0			0
$658$	−7.04114	−	21.6704i	−0.274492	−	0.844800i
$659$	5.29247			0.206165			0.103083	−	0.994673i	$-0.467129\pi$
$659$	5.29247			0.206165			0.103083	+	0.994673i	$0.467129\pi$
$660$		0			0
$661$	−19.2700			−0.749517			−0.374759	−	0.927122i	$-0.622274\pi$
$661$	−19.2700			−0.749517			−0.374759	+	0.927122i	$0.622274\pi$
$662$	2.71938	+	8.36938i	0.105692	+	0.325285i
$663$		0			0
$664$	3.56439	−	2.58968i	0.138325	−	0.100499i
$665$	−1.11323	+	3.42616i	−0.0431691	+	0.132861i
$666$		0			0
$667$	−24.5981	+	17.8716i	−0.952443	+	0.691990i
$668$	65.5622	+	47.6337i	2.53668	+	1.84300i
$669$		0			0
$670$	28.8158			1.11325
$671$	4.58304	−	6.71858i	0.176926	−	0.259368i
$672$		0			0
$673$	−5.86892	−	18.0627i	−0.226230	−	0.696265i	−0.998164	−	0.0605625i	$-0.980711\pi$
$673$	−5.86892	−	18.0627i	−0.226230	−	0.696265i	0.771934	−	0.635702i	$-0.219289\pi$
$674$	12.5942	+	9.15022i	0.485110	+	0.352453i
$675$		0			0
$676$	−3.49935	+	10.7699i	−0.134590	+	0.414227i
$677$	−10.0189	+	30.8350i	−0.385058	+	1.18509i	0.551380	+	0.834254i	$0.314101\pi$
$677$	−10.0189	+	30.8350i	−0.385058	+	1.18509i	−0.936438	+	0.350833i	$0.885899\pi$
$678$		0			0
$679$	−14.2201	−	10.3315i	−0.545717	−	0.396487i
$680$	10.6800	+	32.8695i	0.409558	+	1.26049i
$681$		0			0
$682$	73.8229	−	26.4330i	2.82682	−	1.01217i
$683$	−15.1260			−0.578779			−0.289389	−	0.957211i	$-0.593452\pi$
$683$	−15.1260			−0.578779			−0.289389	+	0.957211i	$0.593452\pi$
$684$		0			0
$685$	4.64740	+	3.37654i	0.177568	+	0.129011i
$686$	−1.96628	+	1.42858i	−0.0750728	+	0.0545436i
$687$		0			0
$688$	−0.141376	+	0.435110i	−0.00538990	+	0.0165884i
$689$	−11.1901	+	8.13010i	−0.426310	+	0.309732i
$690$		0			0
$691$	−9.70646	−	29.8734i	−0.369251	−	1.13644i	−0.947276	−	0.320419i	$-0.896176\pi$
$691$	−9.70646	−	29.8734i	−0.369251	−	1.13644i	0.578025	−	0.816019i	$-0.303824\pi$
$692$	84.2192			3.20153
$693$		0			0
$694$	42.4357			1.61084
$695$	1.48782	+	4.57903i	0.0564361	+	0.173692i
$696$		0			0
$697$	1.50725	−	1.09508i	0.0570911	−	0.0414791i
$698$	−16.2414	+	49.9859i	−0.614746	+	1.89199i
$699$		0			0
$700$	10.7972	−	7.84462i	0.408095	−	0.296499i
$701$	−12.9966	−	9.44259i	−0.490875	−	0.356642i	0.314646	−	0.949209i	$-0.398114\pi$
$701$	−12.9966	−	9.44259i	−0.490875	−	0.356642i	−0.805521	+	0.592568i	$0.798114\pi$
$702$		0			0
$703$	−15.6133			−0.588865
$704$	0.890298	+	29.9908i	0.0335544	+	1.13032i
$705$		0			0
$706$	−3.30575	−	10.1741i	−0.124414	−	0.382906i
$707$	−10.0934	−	7.33330i	−0.379602	−	0.275797i
$708$		0			0
$709$	12.2673	−	37.7548i	0.460708	−	1.41791i	−0.403594	−	0.914938i	$-0.632239\pi$
$709$	12.2673	−	37.7548i	0.460708	−	1.41791i	0.864301	−	0.502974i	$-0.167761\pi$
$710$	−0.110231	+	0.339257i	−0.00413690	+	0.0127321i
$711$		0			0
$712$	37.7057	+	27.3948i	1.41308	+	1.02666i
$713$	−20.3306	−	62.5713i	−0.761389	−	2.34331i
$714$		0			0
$715$	−12.7343	−	3.72368i	−0.476236	−	0.139258i
$716$	−18.6822			−0.698187
$717$		0			0
$718$	−21.0033	−	15.2598i	−0.783834	−	0.569489i
$719$	−7.97885	+	5.79698i	−0.297561	+	0.216191i	−0.726541	−	0.687123i	$-0.758873\pi$
$719$	−7.97885	+	5.79698i	−0.297561	+	0.216191i	0.428980	+	0.903314i	$0.358873\pi$
$720$		0			0
$721$	2.53951	−	7.81581i	0.0945763	−	0.291076i
$722$	21.2510	−	15.4397i	0.790879	−	0.574607i
$723$		0			0
$724$	−9.48121	−	29.1802i	−0.352366	−	1.08447i
$725$	15.3559			0.570305
$726$		0			0
$727$	−31.5764			−1.17111			−0.585553	−	0.810634i	$-0.699122\pi$
$727$	−31.5764			−1.17111			−0.585553	+	0.810634i	$0.699122\pi$
$728$	−4.55239	−	14.0108i	−0.168723	−	0.519275i
$729$		0			0
$730$	1.52209	−	1.10586i	0.0563351	−	0.0409299i
$731$	0.242678	−	0.746885i	0.00897576	−	0.0276245i
$732$		0			0
$733$	−33.4064	+	24.2712i	−1.23389	+	0.896476i	−0.997176	−	0.0751027i	$-0.976072\pi$
$733$	−33.4064	+	24.2712i	−1.23389	+	0.896476i	−0.236717	+	0.971579i	$0.576072\pi$
$734$	−20.0889	−	14.5955i	−0.741496	−	0.538729i
$735$		0			0
$736$	5.96659			0.219931
$737$	29.9865	+	8.76845i	1.10457	+	0.322990i
$738$		0			0
$739$	10.9422	+	33.6765i	0.402514	+	1.23881i	0.922954	+	0.384911i	$0.125768\pi$
$739$	10.9422	+	33.6765i	0.402514	+	1.23881i	−0.520440	+	0.853898i	$0.674232\pi$
$740$	−21.7021	−	15.7675i	−0.797785	−	0.579625i
$741$		0			0
$742$	−3.26852	+	10.0595i	−0.119991	+	0.369294i
$743$	1.24351	−	3.82713i	0.0456200	−	0.140404i	−0.925652	−	0.378376i	$-0.876483\pi$
$743$	1.24351	−	3.82713i	0.0456200	−	0.140404i	0.971272	+	0.237972i	$0.0764827\pi$
$744$		0			0
$745$	4.96117	+	3.60450i	0.181763	+	0.132059i
$746$	−20.9431	−	64.4562i	−0.766781	−	2.35991i
$747$		0			0
$748$	2.27790	+	76.7340i	0.0832882	+	2.80567i
$749$	−12.1885			−0.445359
$750$		0			0
$751$	−19.7554	−	14.3531i	−0.720884	−	0.523753i	0.165783	−	0.986162i	$-0.446985\pi$
$751$	−19.7554	−	14.3531i	−0.720884	−	0.523753i	−0.886666	+	0.462410i	$0.846985\pi$
$752$	26.1761	−	19.0181i	0.954544	−	0.693517i
$753$		0			0
$754$	10.7311	−	33.0268i	0.390803	−	1.20277i
$755$	−17.2837	+	12.5573i	−0.629019	+	0.457009i
$756$		0			0
$757$	−0.407046	−	1.25276i	−0.0147943	−	0.0455323i	0.943387	−	0.331695i	$-0.107620\pi$
$757$	−0.407046	−	1.25276i	−0.0147943	−	0.0455323i	−0.958181	+	0.286162i	$0.907620\pi$
$758$	2.79023			0.101346
$759$		0			0
$760$	−16.6979			−0.605696
$761$	2.23853	+	6.88949i	0.0811467	+	0.249744i	0.983397	−	0.181470i	$-0.0580855\pi$
$761$	2.23853	+	6.88949i	0.0811467	+	0.249744i	−0.902250	+	0.431214i	$0.858085\pi$
$762$		0			0
$763$	−0.716860	+	0.520829i	−0.0259521	+	0.0188553i
$764$	10.6613	−	32.8122i	0.385714	−	1.18710i
$765$		0			0
$766$	−39.2304	+	28.5026i	−1.41745	+	1.02984i
$767$	17.8625	+	12.9779i	0.644977	+	0.468603i
$768$		0			0
$769$	44.3139			1.59800			0.798999	−	0.601332i	$-0.205363\pi$
$769$	44.3139			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$770$	−9.55186	+	3.42013i	−0.344225	+	0.123253i
$771$		0			0
$772$	30.9112	+	95.1348i	1.11252	+	3.42397i
$773$	15.4166	+	11.2008i	0.554496	+	0.402865i	0.829440	−	0.558595i	$-0.188659\pi$
$773$	15.4166	+	11.2008i	0.554496	+	0.402865i	−0.274944	+	0.961460i	$0.588659\pi$
$774$		0			0
$775$	−10.2679	+	31.6014i	−0.368835	+	1.13516i
$776$	25.1761	−	77.4839i	0.903768	−	2.78151i
$777$		0			0
$778$	5.11232	+	3.71432i	0.183286	+	0.133165i
$779$	0.278153	+	0.856068i	0.00996587	+	0.0306718i
$780$		0			0
$781$	−0.217943	+	0.319497i	−0.00779861	+	0.0114325i
$782$	97.3828			3.48240
$783$		0			0
$784$	−2.79210	−	2.02858i	−0.0997179	−	0.0724493i
$785$	2.28581	−	1.66074i	0.0815840	−	0.0592742i
$786$		0			0
$787$	9.72168	−	29.9203i	0.346540	−	1.06654i	−0.614213	−	0.789140i	$-0.710527\pi$
$787$	9.72168	−	29.9203i	0.346540	−	1.06654i	0.960754	−	0.277402i	$-0.0894734\pi$
$788$	−35.3949	+	25.7159i	−1.26089	+	0.916090i
$789$		0			0
$790$	−8.06270	−	24.8144i	−0.286858	−	0.882858i
$791$	−4.54502			−0.161602
$792$		0			0
$793$	7.79370			0.276763
$794$	6.58850	+	20.2773i	0.233817	+	0.719615i
$795$		0			0
$796$	38.7220	−	28.1332i	1.37247	−	0.997155i
$797$	3.87670	−	11.9313i	0.137320	−	0.422627i	−0.858624	−	0.512606i	$-0.828680\pi$
$797$	3.87670	−	11.9313i	0.137320	−	0.422627i	0.995944	+	0.0899793i	$0.0286801\pi$
$798$		0			0
$799$	−44.9324	+	32.6453i	−1.58959	+	1.15491i
$800$	−2.43790	−	1.77123i	−0.0861926	−	0.0626226i
$801$		0			0
$802$	−68.9118			−2.43336
$803$	1.92043	−	0.687629i	0.0677707	−	0.0242659i
$804$		0			0
$805$	2.63056	+	8.09602i	0.0927150	+	0.285347i
$806$	60.7915	+	44.1676i	2.14129	+	1.55574i
$807$		0			0
$808$	17.8700	−	54.9981i	0.628663	−	1.93482i
$809$	1.66259	−	5.11691i	0.0584534	−	0.179901i	−0.917567	−	0.397582i	$-0.869849\pi$
$809$	1.66259	−	5.11691i	0.0584534	−	0.179901i	0.976020	+	0.217681i	$0.0698493\pi$
$810$		0			0
$811$	−11.0835	−	8.05262i	−0.389194	−	0.282766i	0.375931	−	0.926647i	$-0.377323\pi$
$811$	−11.0835	−	8.05262i	−0.389194	−	0.282766i	−0.765125	+	0.643882i	$0.777323\pi$
$812$	−5.42768	−	16.7047i	−0.190474	−	0.586219i
$813$		0			0
$814$	−26.8902	−	34.7914i	−0.942501	−	1.21944i
$815$	19.9333			0.698231
$816$		0			0
$817$	0.306958	+	0.223018i	0.0107391	+	0.00780242i
$818$	−39.1398	+	28.4367i	−1.36849	+	0.994266i
$819$		0			0
$820$	−0.477897	+	1.47082i	−0.0166889	+	0.0513631i
$821$	−7.46816	+	5.42594i	−0.260641	+	0.189367i	−0.710429	−	0.703768i	$-0.751499\pi$
$821$	−7.46816	+	5.42594i	−0.260641	+	0.189367i	0.449789	+	0.893135i	$0.351499\pi$
$822$		0			0
$823$	−3.84500	−	11.8337i	−0.134028	−	0.412496i	0.861409	−	0.507911i	$-0.169582\pi$
$823$	−3.84500	−	11.8337i	−0.134028	−	0.412496i	−0.995438	+	0.0954150i	$0.969582\pi$
$824$	38.0915			1.32698
$825$		0			0
$826$	16.8840			0.587469
$827$	1.38559	+	4.26441i	0.0481817	+	0.148288i	0.972253	−	0.233932i	$-0.0751595\pi$
$827$	1.38559	+	4.26441i	0.0481817	+	0.148288i	−0.924071	+	0.382221i	$0.875159\pi$
$828$		0			0
$829$	29.8346	−	21.6761i	1.03620	−	0.752842i	0.0666578	−	0.997776i	$-0.478766\pi$
$829$	29.8346	−	21.6761i	1.03620	−	0.752842i	0.969540	+	0.244934i	$0.0787664\pi$
$830$	0.898534	−	2.76540i	0.0311886	−	0.0959886i
$831$		0			0
$832$	−23.2615	+	16.9005i	−0.806447	+	0.585918i
$833$	4.79276	+	3.48215i	0.166059	+	0.120649i
$834$		0			0
$835$	26.1060			0.903435
$836$	−35.5990	−	10.4096i	−1.23122	−	0.360024i
$837$		0			0
$838$	23.2042	+	71.4153i	0.801577	+	2.46700i
$839$	7.41389	+	5.38651i	0.255956	+	0.185963i	0.708362	−	0.705849i	$-0.249434\pi$
$839$	7.41389	+	5.38651i	0.255956	+	0.185963i	−0.452406	+	0.891812i	$0.649434\pi$
$840$		0			0
$841$	−2.71643	+	8.36030i	−0.0936699	+	0.288286i
$842$	−18.1703	+	55.9224i	−0.626189	+	1.92721i
$843$		0			0
$844$	45.0859	+	32.7569i	1.55192	+	1.12754i
$845$	1.12728	+	3.46941i	0.0387796	+	0.119351i
$846$		0			0
$847$	−10.9806	+	0.652509i	−0.377299	+	0.0224205i
$848$	−15.0195			−0.515771
$849$		0			0
$850$	−39.7898	−	28.9090i	−1.36478	−	0.991570i
$851$	−29.8480	+	21.6859i	−1.02318	+	0.743382i
$852$		0			0
$853$	2.01494	−	6.20135i	0.0689903	−	0.212330i	−0.910617	−	0.413251i	$-0.864393\pi$
$853$	2.01494	−	6.20135i	0.0689903	−	0.212330i	0.979608	+	0.200921i	$0.0643933\pi$
$854$	4.82162	−	3.50311i	0.164992	−	0.119874i
$855$		0			0
$856$	−17.4580	−	53.7301i	−0.596701	−	1.83646i
$857$	−48.0736			−1.64216			−0.821082	−	0.570810i	$-0.806629\pi$
$857$	−48.0736			−1.64216			−0.821082	+	0.570810i	$0.806629\pi$
$858$		0			0
$859$	−0.316298			−0.0107920			−0.00539598	−	0.999985i	$-0.501718\pi$
$859$	−0.316298			−0.0107920			−0.00539598	+	0.999985i	$0.501718\pi$
$860$	0.201444	+	0.619981i	0.00686918	+	0.0211412i
$861$		0			0
$862$	38.1459	−	27.7146i	1.29925	−	0.943963i
$863$	−1.12078	+	3.44942i	−0.0381519	+	0.117419i	−0.968319	−	0.249718i	$-0.919662\pi$
$863$	−1.12078	+	3.44942i	−0.0381519	+	0.117419i	0.930167	+	0.367137i	$0.119662\pi$
$864$		0			0
$865$	21.9489	−	15.9468i	0.746285	−	0.542207i
$866$	42.0542	+	30.5542i	1.42906	+	1.03827i
$867$		0			0
$868$	38.0064			1.29002
$869$	−0.839391	−	28.2760i	−0.0284744	−	0.959197i
$870$		0			0
$871$	9.25174	+	28.4739i	0.313483	+	0.964802i
$872$	−3.32273	−	2.41410i	−0.112522	−	0.0817519i
$873$		0			0
$874$	−14.5392	+	44.7469i	−0.491794	+	1.51359i
$875$	3.27325	−	10.0740i	0.110656	−	0.340564i
$876$		0			0
$877$	−21.6069	−	15.6983i	−0.729614	−	0.530095i	0.159828	−	0.987145i	$-0.448906\pi$
$877$	−21.6069	−	15.6983i	−0.729614	−	0.530095i	−0.889441	+	0.457050i	$0.848906\pi$
$878$	−23.8320	−	73.3474i	−0.804291	−	2.47535i
$879$		0			0
$880$	−8.81024	−	11.3990i	−0.296993	−	0.384259i
$881$	−2.91937			−0.0983560			−0.0491780	−	0.998790i	$-0.515660\pi$
$881$	−2.91937			−0.0983560			−0.0491780	+	0.998790i	$0.515660\pi$
$882$		0			0
$883$	36.5331	+	26.5429i	1.22944	+	0.893238i	0.996848	−	0.0793369i	$-0.0252803\pi$
$883$	36.5331	+	26.5429i	1.22944	+	0.893238i	0.232589	+	0.972575i	$0.425280\pi$
$884$	−59.5164	+	43.2412i	−2.00175	+	1.45436i
$885$		0			0
$886$	1.25133	−	3.85120i	0.0420392	−	0.129383i
$887$	−19.4365	+	14.1215i	−0.652614	+	0.474152i	−0.864161	−	0.503216i	$-0.832150\pi$
$887$	−19.4365	+	14.1215i	−0.652614	+	0.474152i	0.211546	+	0.977368i	$0.432150\pi$
$888$		0			0
$889$	−2.48072	−	7.63488i	−0.0832008	−	0.256066i
$890$	30.7592			1.03105
$891$		0			0
$892$	−11.5806			−0.387749
$893$	−8.29199	−	25.5201i	−0.277481	−	0.853998i
$894$		0			0
$895$	−4.86889	+	3.53746i	−0.162749	+	0.118244i
$896$	−6.24921	+	19.2331i	−0.208772	+	0.642533i
$897$		0			0
$898$	−33.7920	+	24.5513i	−1.12765	+	0.819289i
$899$	35.3783	+	25.7038i	1.17993	+	0.857271i
$900$		0			0
$901$	25.7816			0.858909
$902$	−1.42854	+	2.09419i	−0.0475652	+	0.0697289i
$903$		0			0
$904$	−6.50996	−	20.0356i	−0.216518	−	0.666374i
$905$	−7.99619	−	5.80957i	−0.265802	−	0.193117i
$906$		0			0
$907$	−4.95260	+	15.2425i	−0.164448	+	0.506120i	−0.998995	−	0.0448168i	$-0.985730\pi$
$907$	−4.95260	+	15.2425i	−0.164448	+	0.506120i	0.834547	+	0.550937i	$0.185730\pi$
$908$	−9.96803	+	30.6784i	−0.330801	+	1.01810i
$909$		0			0
$910$	−7.86574	−	5.71479i	−0.260747	−	0.189444i
$911$	5.06922	+	15.6014i	0.167951	+	0.516899i	0.999242	−	0.0389385i	$-0.0123976\pi$
$911$	5.06922	+	15.6014i	0.167951	+	0.516899i	−0.831291	+	0.555838i	$0.812398\pi$
$912$		0			0
$913$	1.77653	−	2.60433i	0.0587946	−	0.0861909i
$914$	24.8408			0.821660
$915$		0			0
$916$	−41.4336	−	30.1032i	−1.36900	−	0.994639i
$917$	0.0820834	−	0.0596371i	0.00271063	−	0.00196939i
$918$		0			0
$919$	9.98747	−	30.7383i	0.329456	−	1.01396i	−0.639933	−	0.768431i	$-0.721038\pi$
$919$	9.98747	−	30.7383i	0.329456	−	1.01396i	0.969389	−	0.245531i	$-0.0789623\pi$
$920$	−31.9215	+	23.1923i	−1.05242	+	0.764629i
$921$		0			0
$922$	16.6102	+	51.1210i	0.547029	+	1.68358i
$923$	−0.370623			−0.0121992
$924$		0			0
$925$	18.6333			0.612659
$926$	−22.8107	−	70.2042i	−0.749607	−	2.30705i
$927$		0			0
$928$	−3.20844	+	2.33107i	−0.105322	+	0.0765211i
$929$	2.53249	−	7.79420i	0.0830883	−	0.255720i	−0.900878	−	0.434071i	$-0.857077\pi$
$929$	2.53249	−	7.79420i	0.0830883	−	0.255720i	0.983967	+	0.178352i	$0.0570765\pi$
$930$		0			0
$931$	−2.31558	+	1.68237i	−0.0758902	+	0.0551374i
$932$	−40.5471	−	29.4592i	−1.32817	−	0.964969i
$933$		0			0
$934$	−61.2253			−2.00335
$935$	15.1232	+	19.5668i	0.494580	+	0.639903i
$936$		0			0
$937$	10.5490	+	32.4666i	0.344622	+	1.06064i	0.961786	+	0.273803i	$0.0882817\pi$
$937$	10.5490	+	32.4666i	0.344622	+	1.06064i	−0.617164	+	0.786835i	$0.711718\pi$
$938$	18.5221	+	13.4571i	0.604767	+	0.439389i
$939$		0			0
$940$	14.2465	−	43.8463i	0.464670	−	1.43011i
$941$	−0.302642	+	0.931437i	−0.00986585	+	0.0303640i	−0.955868	−	0.293796i	$-0.905081\pi$
$941$	−0.302642	+	0.931437i	−0.00986585	+	0.0303640i	0.946002	+	0.324160i	$0.105081\pi$
$942$		0			0
$943$	1.72077	+	1.25022i	0.0560361	+	0.0407126i
$944$	7.40874	+	22.8017i	0.241134	+	0.742134i
$945$		0			0
$946$	0.0317072	+	1.06810i	0.00103089	+	0.0347269i
$947$	−0.935599			−0.0304029			−0.0152014	−	0.999884i	$-0.504839\pi$
$947$	−0.935599			−0.0304029			−0.0152014	+	0.999884i	$0.504839\pi$
$948$		0			0
$949$	1.58143	+	1.14898i	0.0513355	+	0.0372974i
$950$	19.2241	−	13.9671i	0.623712	−	0.453153i
$951$		0			0
$952$	−8.48538	+	26.1153i	−0.275013	+	0.846402i
$953$	13.5365	−	9.83486i	0.438491	−	0.318582i	−0.346544	−	0.938034i	$-0.612645\pi$
$953$	13.5365	−	9.83486i	0.438491	−	0.318582i	0.785035	+	0.619451i	$0.212645\pi$
$954$		0			0
$955$	−3.43444	−	10.5701i	−0.111136	−	0.342041i
$956$	19.4616			0.629434
$957$		0			0
$958$	51.5353			1.66503
$959$	1.41038	+	4.34071i	0.0455436	+	0.140169i
$960$		0			0
$961$	−51.4733	+	37.3975i	−1.66043	+	1.20637i
$962$	13.0214	−	40.0757i	0.419826	−	1.29209i
$963$		0			0
$964$	8.30326	−	6.03267i	0.267430	−	0.194299i
$965$	26.0696	+	18.9407i	0.839210	+	0.609722i
$966$		0			0
$967$	36.4439			1.17196			0.585978	−	0.810327i	$-0.300710\pi$
$967$	36.4439			1.17196			0.585978	+	0.810327i	$0.300710\pi$
$968$	−18.6043	−	47.4708i	−0.597965	−	1.52577i
$969$		0			0
$970$	−16.6155	−	51.1372i	−0.533491	−	1.64192i
$971$	−26.8931	−	19.5390i	−0.863042	−	0.627036i	0.0656691	−	0.997841i	$-0.479082\pi$
$971$	−26.8931	−	19.5390i	−0.863042	−	0.627036i	−0.928711	+	0.370805i	$0.879082\pi$
$972$		0			0
$973$	−1.18209	+	3.63810i	−0.0378961	+	0.116632i
$974$	−12.6325	+	38.8788i	−0.404771	+	1.24576i
$975$		0			0
$976$	6.84667	+	4.97439i	0.219156	+	0.159226i
$977$	−6.97347	−	21.4621i	−0.223101	−	0.686634i	−0.998479	−	0.0551366i	$-0.982441\pi$
$977$	−6.97347	−	21.4621i	−0.223101	−	0.686634i	0.775378	−	0.631498i	$-0.217559\pi$
$978$		0			0
$979$	32.0088	+	9.35981i	1.02301	+	0.299141i
$980$	−4.91760			−0.157087
$981$		0			0
$982$	9.51294	+	6.91155i	0.303570	+	0.220557i
$983$	−12.2200	+	8.87836i	−0.389758	+	0.283176i	−0.765356	−	0.643607i	$-0.777437\pi$
$983$	−12.2200	+	8.87836i	−0.389758	+	0.283176i	0.375598	+	0.926783i	$0.377437\pi$
$984$		0			0
$985$	−4.35521	+	13.4040i	−0.138769	+	0.427086i
$986$	−52.3661	+	38.0462i	−1.66768	+	1.21164i
$987$		0			0
$988$	−10.9834	−	33.8033i	−0.349428	−	1.07543i
$989$	0.896574			0.0285094
$990$		0			0
$991$	−55.1534			−1.75201			−0.876003	−	0.482305i	$-0.839800\pi$
$991$	−55.1534			−1.75201			−0.876003	+	0.482305i	$0.839800\pi$
$992$	−2.65181	−	8.16145i	−0.0841952	−	0.259126i
$993$		0			0
$994$	−0.229288	+	0.166587i	−0.00727257	+	0.00528383i
$995$	4.76461	−	14.6639i	0.151048	−	0.464878i
$996$		0			0
$997$	−40.2120	+	29.2157i	−1.27353	+	0.925272i	−0.999337	−	0.0364038i	$-0.988410\pi$
$997$	−40.2120	+	29.2157i	−1.27353	+	0.925272i	−0.274190	+	0.961676i	$0.588410\pi$
$998$	−60.1358	−	43.6912i	−1.90356	−	1.38302i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.i.379.4		16
3.2	odd	2		77.2.f.b.71.1	yes	16
11.3	even	5		7623.2.a.ct.1.8		8
11.8	odd	10		7623.2.a.cw.1.1		8
11.9	even	5	inner	693.2.m.i.64.4		16
21.2	odd	6		539.2.q.g.214.1		32
21.5	even	6		539.2.q.f.214.1		32
21.11	odd	6		539.2.q.g.324.4		32
21.17	even	6		539.2.q.f.324.4		32
21.20	even	2		539.2.f.e.148.1		16
33.2	even	10		847.2.f.x.372.4		16
33.5	odd	10		847.2.f.w.323.4		16
33.8	even	10		847.2.a.o.1.8		8
33.14	odd	10		847.2.a.p.1.1		8
33.17	even	10		847.2.f.v.323.1		16
33.20	odd	10		77.2.f.b.64.1	✓	16
33.26	odd	10		847.2.f.w.729.4		16
33.29	even	10		847.2.f.v.729.1		16
33.32	even	2		847.2.f.x.148.4		16
231.20	even	10		539.2.f.e.295.1		16
231.41	odd	10		5929.2.a.bs.1.8		8
231.53	odd	30		539.2.q.g.471.1		32
231.86	odd	30		539.2.q.g.361.4		32
231.146	even	10		5929.2.a.bt.1.1		8
231.152	even	30		539.2.q.f.361.4		32
231.185	even	30		539.2.q.f.471.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.1	✓	16	33.20	odd	10
77.2.f.b.71.1	yes	16	3.2	odd	2
539.2.f.e.148.1		16	21.20	even	2
539.2.f.e.295.1		16	231.20	even	10
539.2.q.f.214.1		32	21.5	even	6
539.2.q.f.324.4		32	21.17	even	6
539.2.q.f.361.4		32	231.152	even	30
539.2.q.f.471.1		32	231.185	even	30
539.2.q.g.214.1		32	21.2	odd	6
539.2.q.g.324.4		32	21.11	odd	6
539.2.q.g.361.4		32	231.86	odd	30
539.2.q.g.471.1		32	231.53	odd	30
693.2.m.i.64.4		16	11.9	even	5	inner
693.2.m.i.379.4		16	1.1	even	1	trivial
847.2.a.o.1.8		8	33.8	even	10
847.2.a.p.1.1		8	33.14	odd	10
847.2.f.v.323.1		16	33.17	even	10
847.2.f.v.729.1		16	33.29	even	10
847.2.f.w.323.4		16	33.5	odd	10
847.2.f.w.729.4		16	33.26	odd	10
847.2.f.x.148.4		16	33.32	even	2
847.2.f.x.372.4		16	33.2	even	10
5929.2.a.bs.1.8		8	231.41	odd	10
5929.2.a.bt.1.1		8	231.146	even	10
7623.2.a.ct.1.8		8	11.3	even	5
7623.2.a.cw.1.1		8	11.8	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.751051 + 2.31150i) q^{2} +(-3.16091 + 2.29654i) q^{4} +(-0.388938 + 1.19703i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-3.74989 - 2.72445i) q^{8} +O(q^{10})\)	\(q+(0.751051 + 2.31150i) q^{2} +(-3.16091 + 2.29654i) q^{4} +(-0.388938 + 1.19703i) q^{5} +(-0.809017 + 0.587785i) q^{7} +(-3.74989 - 2.72445i) q^{8} -3.05904 q^{10} +(-3.18332 - 0.930846i) q^{11} +(-0.982152 - 3.02275i) q^{13} +(-1.96628 - 1.42858i) q^{14} +(1.06649 - 3.28231i) q^{16} +(-1.83067 + 5.63423i) q^{17} +(-2.31558 - 1.68237i) q^{19} +(-1.51962 - 4.67691i) q^{20} +(-0.239188 - 8.05735i) q^{22} -6.76343 q^{23} +(2.76348 + 2.00778i) q^{25} +(6.24944 - 4.54048i) q^{26} +(1.20736 - 3.71587i) q^{28} +(3.63693 - 2.64238i) q^{29} +(3.00597 + 9.25141i) q^{31} -0.882184 q^{32} -14.3984 q^{34} +(-0.388938 - 1.19703i) q^{35} +(4.41315 - 3.20634i) q^{37} +(2.14967 - 6.61601i) q^{38} +(4.71972 - 3.42908i) q^{40} +(-0.254423 - 0.184849i) q^{41} -0.132562 q^{43} +(12.1999 - 4.36829i) q^{44} +(-5.07968 - 15.6337i) q^{46} +(7.58458 + 5.51052i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-2.56548 + 7.89572i) q^{50} +(10.0463 + 7.29910i) q^{52} +(-1.34482 - 4.13893i) q^{53} +(2.35237 - 3.44849i) q^{55} +4.63512 q^{56} +(8.83939 + 6.42219i) q^{58} +(-5.62012 + 4.08326i) q^{59} +(-0.757757 + 2.33214i) q^{61} +(-19.1270 + 13.8966i) q^{62} +(-2.79554 - 8.60379i) q^{64} +4.00032 q^{65} -9.41987 q^{67} +(-7.15262 - 22.0135i) q^{68} +(2.47482 - 1.79806i) q^{70} +(0.0360345 - 0.110903i) q^{71} +(-0.497571 + 0.361506i) q^{73} +(10.7260 + 7.79286i) q^{74} +11.1830 q^{76} +(3.12250 - 1.11804i) q^{77} +(2.63569 + 8.11183i) q^{79} +(3.51423 + 2.55324i) q^{80} +(0.236194 - 0.726930i) q^{82} +(-0.293731 + 0.904010i) q^{83} +(-6.03232 - 4.38274i) q^{85} +(-0.0995608 - 0.306417i) q^{86} +(9.40104 + 12.1634i) q^{88} -10.0552 q^{89} +(2.57131 + 1.86816i) q^{91} +(21.3786 - 15.5325i) q^{92} +(-7.04114 + 21.6704i) q^{94} +(2.91446 - 2.11748i) q^{95} +(5.43159 + 16.7167i) q^{97} +2.43045 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

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