LMFDB - Embedded newform 1386.2.bu.b.827.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.6
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.b.1205.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.599043 + 0.194641i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.599043 + 0.194641i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -0.629871i q^{10} +(3.04975 - 1.30348i) q^{11} +(-2.38667 - 0.775477i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.701620 - 2.15936i) q^{17} +(0.0702465 + 0.0966860i) q^{19} +(0.599043 + 0.194641i) q^{20} +(0.297258 + 3.30328i) q^{22} -6.23072i q^{23} +(-3.72412 + 2.70573i) q^{25} +(1.47504 - 2.03022i) q^{26} +(0.951057 - 0.309017i) q^{28} +(-1.61483 - 1.17324i) q^{29} +(0.811560 - 2.49773i) q^{31} -1.00000 q^{32} +2.27049 q^{34} +(0.194641 - 0.599043i) q^{35} +(-0.0380106 - 0.0276163i) q^{37} +(-0.113661 + 0.0369308i) q^{38} +(-0.370229 + 0.509576i) q^{40} +(5.70843 - 4.14742i) q^{41} +1.49648i q^{43} +(-3.23346 - 0.738060i) q^{44} +(5.92577 + 1.92540i) q^{46} +(-4.12845 - 5.68232i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-1.42249 - 4.37796i) q^{50} +(1.47504 + 2.03022i) q^{52} +(10.3106 + 3.35013i) q^{53} +(-1.57322 + 1.37444i) q^{55} +1.00000i q^{56} +(1.61483 - 1.17324i) q^{58} +(7.91768 - 10.8978i) q^{59} +(-3.30272 + 1.07312i) q^{61} +(2.12469 + 1.54368i) q^{62} +(0.309017 - 0.951057i) q^{64} +1.58066 q^{65} +0.558084 q^{67} +(-0.701620 + 2.15936i) q^{68} +(0.509576 + 0.370229i) q^{70} +(0.452895 - 0.147154i) q^{71} +(8.88539 - 12.2297i) q^{73} +(0.0380106 - 0.0276163i) q^{74} -0.119511i q^{76} +(-0.738060 + 3.23346i) q^{77} +(8.26641 + 2.68592i) q^{79} +(-0.370229 - 0.509576i) q^{80} +(2.18043 + 6.71066i) q^{82} +(-1.75860 - 5.41240i) q^{83} +(0.840600 + 1.15699i) q^{85} +(-1.42324 - 0.462439i) q^{86} +(1.70113 - 2.84713i) q^{88} -11.4637i q^{89} +(2.03022 - 1.47504i) q^{91} +(-3.66232 + 5.04076i) q^{92} +(6.67997 - 2.17045i) q^{94} +(-0.0608997 - 0.0442462i) q^{95} +(-0.681563 + 2.09763i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.599043	+	0.194641i	−0.267900	+	0.0870460i	−0.439887	−	0.898053i	$-0.644981\pi$
$5$	−0.599043	+	0.194641i	−0.267900	+	0.0870460i	0.171987	+	0.985099i	$0.444981\pi$
$6$		0			0
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$		−	0.629871i		−	0.199183i
$11$	3.04975	−	1.30348i	0.919533	−	0.393013i
$11$	3.04975	−	1.30348i	0.919533	−	0.393013i
$12$		0			0
$13$	−2.38667	−	0.775477i	−0.661944	−	0.215079i	−0.0412706	−	0.999148i	$-0.513141\pi$
$13$	−2.38667	−	0.775477i	−0.661944	−	0.215079i	−0.620673	+	0.784069i	$0.713141\pi$
$14$	−0.587785	−	0.809017i	−0.157092	−	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.701620	−	2.15936i	−0.170168	−	0.523722i	0.829212	−	0.558934i	$-0.188789\pi$
$17$	−0.701620	−	2.15936i	−0.170168	−	0.523722i	−0.999380	+	0.0352116i	$0.988789\pi$
$18$		0			0
$19$	0.0702465	+	0.0966860i	0.0161157	+	0.0221813i	0.816999	−	0.576639i	$-0.195636\pi$
$19$	0.0702465	+	0.0966860i	0.0161157	+	0.0221813i	−0.800883	+	0.598821i	$0.795636\pi$
$20$	0.599043	+	0.194641i	0.133950	+	0.0435230i
$21$		0			0
$22$	0.297258	+	3.30328i	0.0633756	+	0.704261i
$23$		−	6.23072i		−	1.29919i	−0.760278	−	0.649597i	$-0.774938\pi$
$23$		−	6.23072i		−	1.29919i	0.760278	−	0.649597i	$-0.225062\pi$
$24$		0			0
$25$	−3.72412	+	2.70573i	−0.744824	+	0.541146i
$26$	1.47504	−	2.03022i	0.289280	−	0.398160i
$27$		0			0
$28$	0.951057	−	0.309017i	0.179733	−	0.0583987i
$29$	−1.61483	−	1.17324i	−0.299867	−	0.217866i	0.427670	−	0.903935i	$-0.359335\pi$
$29$	−1.61483	−	1.17324i	−0.299867	−	0.217866i	−0.727536	+	0.686069i	$0.759335\pi$
$30$		0			0
$31$	0.811560	−	2.49773i	0.145761	−	0.448605i	−0.851348	−	0.524602i	$-0.824214\pi$
$31$	0.811560	−	2.49773i	0.145761	−	0.448605i	0.997108	+	0.0759974i	$0.0242141\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	2.27049			0.389386
$35$	0.194641	−	0.599043i	0.0329003	−	0.101257i
$36$		0			0
$37$	−0.0380106	−	0.0276163i	−0.00624891	−	0.00454010i	0.584656	−	0.811281i	$-0.301229\pi$
$37$	−0.0380106	−	0.0276163i	−0.00624891	−	0.00454010i	−0.590905	+	0.806741i	$0.701229\pi$
$38$	−0.113661	+	0.0369308i	−0.0184383	+	0.00599096i
$39$		0			0
$40$	−0.370229	+	0.509576i	−0.0585383	+	0.0805711i
$41$	5.70843	−	4.14742i	0.891507	−	0.647718i	−0.0447637	−	0.998998i	$-0.514253\pi$
$41$	5.70843	−	4.14742i	0.891507	−	0.647718i	0.936270	+	0.351280i	$0.114253\pi$
$42$		0			0
$43$			1.49648i			0.228212i	0.993469	+	0.114106i	$0.0364003\pi$
$43$			1.49648i			0.228212i	−0.993469	+	0.114106i	$0.963600\pi$
$44$	−3.23346	−	0.738060i	−0.487463	−	0.111267i
$45$		0			0
$46$	5.92577	+	1.92540i	0.873706	+	0.283884i
$47$	−4.12845	−	5.68232i	−0.602196	−	0.828852i	0.393711	−	0.919234i	$-0.371191\pi$
$47$	−4.12845	−	5.68232i	−0.602196	−	0.828852i	−0.995907	+	0.0903826i	$0.971191\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	−1.42249	−	4.37796i	−0.201170	−	0.619137i
$51$		0			0
$52$	1.47504	+	2.03022i	0.204552	+	0.281541i
$53$	10.3106	+	3.35013i	1.41628	+	0.460176i	0.914417	−	0.404774i	$-0.132650\pi$
$53$	10.3106	+	3.35013i	1.41628	+	0.460176i	0.501858	+	0.864950i	$0.332650\pi$
$54$		0			0
$55$	−1.57322	+	1.37444i	−0.212133	+	0.185330i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	1.61483	−	1.17324i	0.212038	−	0.154054i
$59$	7.91768	−	10.8978i	1.03079	−	1.41877i	0.126445	−	0.991974i	$-0.459643\pi$
$59$	7.91768	−	10.8978i	1.03079	−	1.41877i	0.904349	−	0.426793i	$-0.140357\pi$
$60$		0			0
$61$	−3.30272	+	1.07312i	−0.422870	+	0.137399i	−0.512719	−	0.858557i	$-0.671362\pi$
$61$	−3.30272	+	1.07312i	−0.422870	+	0.137399i	0.0898486	+	0.995955i	$0.471362\pi$
$62$	2.12469	+	1.54368i	0.269836	+	0.196047i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.58066			0.196057
$66$		0			0
$67$	0.558084			0.0681808			0.0340904	−	0.999419i	$-0.489147\pi$
$67$	0.558084			0.0681808			0.0340904	+	0.999419i	$0.489147\pi$
$68$	−0.701620	+	2.15936i	−0.0850839	+	0.261861i
$69$		0			0
$70$	0.509576	+	0.370229i	0.0609060	+	0.0442508i
$71$	0.452895	−	0.147154i	0.0537487	−	0.0174640i	−0.282019	−	0.959409i	$-0.591004\pi$
$71$	0.452895	−	0.147154i	0.0537487	−	0.0174640i	0.335768	+	0.941945i	$0.391004\pi$
$72$		0			0
$73$	8.88539	−	12.2297i	1.03996	−	1.43138i	0.142753	−	0.989758i	$-0.454404\pi$
$73$	8.88539	−	12.2297i	1.03996	−	1.43138i	0.897203	−	0.441619i	$-0.145596\pi$
$74$	0.0380106	−	0.0276163i	0.00441864	−	0.00321033i
$75$		0			0
$76$		−	0.119511i		−	0.0137088i
$77$	−0.738060	+	3.23346i	−0.0841097	+	0.368487i
$78$		0			0
$79$	8.26641	+	2.68592i	0.930044	+	0.302190i	0.734581	−	0.678521i	$-0.237379\pi$
$79$	8.26641	+	2.68592i	0.930044	+	0.302190i	0.195463	+	0.980711i	$0.437379\pi$
$80$	−0.370229	−	0.509576i	−0.0413928	−	0.0569724i
$81$		0			0
$82$	2.18043	+	6.71066i	0.240788	+	0.741068i
$83$	−1.75860	−	5.41240i	−0.193031	−	0.594088i	−0.999994	−	0.00348625i	$-0.998890\pi$
$83$	−1.75860	−	5.41240i	−0.193031	−	0.594088i	0.806963	−	0.590602i	$-0.201110\pi$
$84$		0			0
$85$	0.840600	+	1.15699i	0.0911759	+	0.125493i
$86$	−1.42324	−	0.462439i	−0.153472	−	0.0498661i
$87$		0			0
$88$	1.70113	−	2.84713i	0.181341	−	0.303505i
$89$		−	11.4637i		−	1.21515i	−0.794263	−	0.607574i	$-0.792143\pi$
$89$		−	11.4637i		−	1.21515i	0.794263	−	0.607574i	$-0.207857\pi$
$90$		0			0
$91$	2.03022	−	1.47504i	0.212825	−	0.154627i
$92$	−3.66232	+	5.04076i	−0.381824	+	0.525535i
$93$		0			0
$94$	6.67997	−	2.17045i	0.688986	−	0.223865i
$95$	−0.0608997	−	0.0442462i	−0.00624818	−	0.00453957i
$96$		0			0
$97$	−0.681563	+	2.09763i	−0.0692022	+	0.212983i	−0.979677	−	0.200582i	$-0.935717\pi$
$97$	−0.681563	+	2.09763i	−0.0692022	+	0.212983i	0.910475	+	0.413565i	$0.135717\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	4.60326			0.460326
$101$	0.960191	−	2.95516i	0.0955425	−	0.294050i	−0.891852	−	0.452327i	$-0.850594\pi$
$101$	0.960191	−	2.95516i	0.0955425	−	0.294050i	0.987395	+	0.158277i	$0.0505940\pi$
$102$		0			0
$103$	−0.465431	−	0.338156i	−0.0458603	−	0.0333195i	0.564619	−	0.825352i	$-0.309023\pi$
$103$	−0.465431	−	0.338156i	−0.0458603	−	0.0333195i	−0.610479	+	0.792032i	$0.709023\pi$
$104$	−2.38667	+	0.775477i	−0.234032	+	0.0760418i
$105$		0			0
$106$	−6.37232	+	8.77075i	−0.618935	+	0.851891i
$107$	−1.75574	+	1.27562i	−0.169734	+	0.123319i	−0.669409	−	0.742894i	$-0.733453\pi$
$107$	−1.75574	+	1.27562i	−0.169734	+	0.123319i	0.499675	+	0.866213i	$0.333453\pi$
$108$		0			0
$109$		−	13.7150i		−	1.31365i	−0.754041	−	0.656827i	$-0.771898\pi$
$109$		−	13.7150i		−	1.31365i	0.754041	−	0.656827i	$-0.228102\pi$
$110$	−0.821023	−	1.92095i	−0.0782814	−	0.183155i
$111$		0			0
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	0.0122513	+	0.0168624i	0.00115250	+	0.00158628i	0.809593	−	0.586992i	$-0.199688\pi$
$113$	0.0122513	+	0.0168624i	0.00115250	+	0.00158628i	−0.808440	+	0.588578i	$0.799688\pi$
$114$		0			0
$115$	1.21275	+	3.73247i	0.113090	+	0.348054i
$116$	0.616811	+	1.89835i	0.0572694	+	0.176257i
$117$		0			0
$118$	7.91768	+	10.8978i	0.728882	+	1.00322i
$119$	2.15936	+	0.701620i	0.197948	+	0.0643174i
$120$		0			0
$121$	7.60189	−	7.95055i	0.691081	−	0.722777i
$122$		−	3.47269i		−	0.314402i
$123$		0			0
$124$	−2.12469	+	1.54368i	−0.190803	+	0.138626i
$125$	3.55540	−	4.89359i	0.318005	−	0.437696i
$126$		0			0
$127$	−8.48218	+	2.75603i	−0.752672	+	0.244558i	−0.660131	−	0.751151i	$-0.729499\pi$
$127$	−8.48218	+	2.75603i	−0.752672	+	0.244558i	−0.0925415	+	0.995709i	$0.529499\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−0.488450	+	1.50330i	−0.0428399	+	0.131848i
$131$	−7.76303			−0.678259			−0.339130	−	0.940740i	$-0.610132\pi$
$131$	−7.76303			−0.678259			−0.339130	+	0.940740i	$0.610132\pi$
$132$		0			0
$133$	−0.119511			−0.0103629
$134$	−0.172457	+	0.530770i	−0.0148981	+	0.0458515i
$135$		0			0
$136$	−1.83686	−	1.33456i	−0.157510	−	0.114438i
$137$	2.85014	−	0.926068i	0.243504	−	0.0791193i	−0.184722	−	0.982791i	$-0.559139\pi$
$137$	2.85014	−	0.926068i	0.243504	−	0.0791193i	0.428226	+	0.903671i	$0.359139\pi$
$138$		0			0
$139$	−9.57205	+	13.1748i	−0.811890	+	1.11747i	0.179139	+	0.983824i	$0.442669\pi$
$139$	−9.57205	+	13.1748i	−0.811890	+	1.11747i	−0.991029	+	0.133647i	$0.957331\pi$
$140$	−0.509576	+	0.370229i	−0.0430671	+	0.0312900i
$141$		0			0
$142$			0.476202i			0.0399620i
$143$	−8.28956	+	0.745967i	−0.693208	+	0.0623809i
$144$		0			0
$145$	1.19571	+	0.388511i	0.0992986	+	0.0322641i
$146$	8.88539	+	12.2297i	0.735360	+	1.01214i
$147$		0			0
$148$	0.0145188	+	0.0446841i	0.00119343	+	0.00367301i
$149$	−0.734580	−	2.26081i	−0.0601792	−	0.185212i	0.916448	−	0.400155i	$-0.131044\pi$
$149$	−0.734580	−	2.26081i	−0.0601792	−	0.185212i	−0.976627	+	0.214942i	$0.931044\pi$
$150$		0			0
$151$	9.10170	+	12.5274i	0.740686	+	1.01947i	0.998579	+	0.0532935i	$0.0169719\pi$
$151$	9.10170	+	12.5274i	0.740686	+	1.01947i	−0.257893	+	0.966174i	$0.583028\pi$
$152$	0.113661	+	0.0369308i	0.00921914	+	0.00299548i
$153$		0			0
$154$	−2.84713	−	1.70113i	−0.229428	−	0.137081i
$155$			1.65421i			0.132869i
$156$		0			0
$157$	−5.21273	+	3.78727i	−0.416021	+	0.302257i	−0.776035	−	0.630690i	$-0.782772\pi$
$157$	−5.21273	+	3.78727i	−0.416021	+	0.302257i	0.360014	+	0.932947i	$0.382772\pi$
$158$	−5.10892	+	7.03183i	−0.406444	+	0.559422i
$159$		0			0
$160$	0.599043	−	0.194641i	0.0473585	−	0.0153877i
$161$	5.04076	+	3.66232i	0.397267	+	0.288632i
$162$		0			0
$163$	6.00137	−	18.4703i	0.470064	−	1.44671i	−0.382437	−	0.923982i	$-0.624915\pi$
$163$	6.00137	−	18.4703i	0.470064	−	1.44671i	0.852501	−	0.522726i	$-0.175085\pi$
$164$	−7.05601			−0.550981
$165$		0			0
$166$	5.69094			0.441702
$167$	−7.22686	+	22.2420i	−0.559231	+	1.72114i	0.125269	+	0.992123i	$0.460021\pi$
$167$	−7.22686	+	22.2420i	−0.559231	+	1.72114i	−0.684500	+	0.729013i	$0.739979\pi$
$168$		0			0
$169$	−5.42238	−	3.93959i	−0.417106	−	0.303045i
$170$	−1.36012	+	0.441930i	−0.104316	+	0.0338945i
$171$		0			0
$172$	0.879612	−	1.21068i	0.0670698	−	0.0923136i
$173$	−0.822523	+	0.597598i	−0.0625353	+	0.0454346i	−0.618614	−	0.785695i	$-0.712305\pi$
$173$	−0.822523	+	0.597598i	−0.0625353	+	0.0454346i	0.556078	+	0.831130i	$0.312305\pi$
$174$		0			0
$175$		−	4.60326i		−	0.347974i
$176$	2.18210	+	2.49768i	0.164482	+	0.188270i
$177$		0			0
$178$	10.9026	+	3.54247i	0.817185	+	0.265519i
$179$	6.96958	+	9.59280i	0.520931	+	0.716999i	0.985715	−	0.168425i	$-0.0538680\pi$
$179$	6.96958	+	9.59280i	0.520931	+	0.716999i	−0.464784	+	0.885424i	$0.653868\pi$
$180$		0			0
$181$	−1.86955	−	5.75388i	−0.138962	−	0.427682i	0.857223	−	0.514946i	$-0.172188\pi$
$181$	−1.86955	−	5.75388i	−0.138962	−	0.427682i	−0.996185	+	0.0872632i	$0.972188\pi$
$182$	0.775477	+	2.38667i	0.0574822	+	0.176912i
$183$		0			0
$184$	−3.66232	−	5.04076i	−0.269990	−	0.371610i
$185$	0.0281452	+	0.00914494i	0.00206928	+	0.000672350i
$186$		0			0
$187$	−4.95444	−	5.67096i	−0.362305	−	0.414702i
$188$			7.02373i			0.512258i
$189$		0			0
$190$	0.0608997	−	0.0442462i	0.00441813	−	0.00320996i
$191$	3.63415	−	5.00198i	0.262958	−	0.361931i	−0.657039	−	0.753857i	$-0.728191\pi$
$191$	3.63415	−	5.00198i	0.262958	−	0.361931i	0.919997	+	0.391926i	$0.128191\pi$
$192$		0			0
$193$	−14.1611	+	4.60121i	−1.01934	+	0.331202i	−0.770566	−	0.637361i	$-0.780026\pi$
$193$	−14.1611	+	4.60121i	−1.01934	+	0.331202i	−0.248770	+	0.968563i	$0.580026\pi$
$194$	−1.78435	−	1.29641i	−0.128109	−	0.0930768i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	14.6043			1.04051			0.520256	−	0.854010i	$-0.325837\pi$
$197$	14.6043			1.04051			0.520256	+	0.854010i	$0.325837\pi$
$198$		0			0
$199$	8.60494			0.609988			0.304994	−	0.952354i	$-0.401346\pi$
$199$	8.60494			0.609988			0.304994	+	0.952354i	$0.401346\pi$
$200$	−1.42249	+	4.37796i	−0.100585	+	0.309569i
$201$		0			0
$202$	2.51381	+	1.82639i	0.176871	+	0.128504i
$203$	1.89835	−	0.616811i	0.133238	−	0.0432916i
$204$		0			0
$205$	−2.61234	+	3.59557i	−0.182454	+	0.251126i
$206$	0.465431	−	0.338156i	0.0324281	−	0.0235604i
$207$		0			0
$208$		−	2.50950i		−	0.174002i
$209$	0.340262	+	0.203303i	0.0235364	+	0.0140628i
$210$		0			0
$211$	4.60479	+	1.49619i	0.317007	+	0.103002i	0.463199	−	0.886255i	$-0.346702\pi$
$211$	4.60479	+	1.49619i	0.317007	+	0.103002i	−0.146192	+	0.989256i	$0.546702\pi$
$212$	−6.37232	−	8.77075i	−0.437653	−	0.602378i
$213$		0			0
$214$	−0.670632	−	2.06399i	−0.0458435	−	0.141092i
$215$	−0.291277	−	0.896458i	−0.0198649	−	0.0611380i
$216$		0			0
$217$	1.54368	+	2.12469i	0.104792	+	0.144233i
$218$	13.0437	+	4.23816i	0.883431	+	0.287044i
$219$		0			0
$220$	2.08064	−	0.187234i	0.140277	−	0.0126233i
$221$			5.69778i			0.383274i
$222$		0			0
$223$	−21.7644	+	15.8128i	−1.45745	+	1.05890i	−0.473433	+	0.880830i	$0.656986\pi$
$223$	−21.7644	+	15.8128i	−1.45745	+	1.05890i	−0.984018	+	0.178071i	$0.943014\pi$
$224$	0.587785	−	0.809017i	0.0392731	−	0.0540547i
$225$		0			0
$226$	−0.0198230	+	0.00644088i	−0.00131861	+	0.000428441i
$227$	−6.77267	−	4.92063i	−0.449518	−	0.326594i	0.339888	−	0.940466i	$-0.389611\pi$
$227$	−6.77267	−	4.92063i	−0.449518	−	0.326594i	−0.789405	+	0.613872i	$0.789611\pi$
$228$		0			0
$229$	0.0621325	−	0.191224i	0.00410583	−	0.0126365i	−0.948983	−	0.315328i	$-0.897885\pi$
$229$	0.0621325	−	0.191224i	0.00410583	−	0.0126365i	0.953088	+	0.302692i	$0.0978853\pi$
$230$	−3.92455			−0.258777
$231$		0			0
$232$	−1.99604			−0.131047
$233$	−2.12554	+	6.54175i	−0.139249	+	0.428564i	−0.996227	−	0.0867891i	$-0.972339\pi$
$233$	−2.12554	+	6.54175i	−0.139249	+	0.428564i	0.856978	+	0.515353i	$0.172339\pi$
$234$		0			0
$235$	3.57913	+	2.60039i	0.233477	+	0.169631i
$236$	−12.8111	+	4.16257i	−0.833930	+	0.270960i
$237$		0			0
$238$	−1.33456	+	1.83686i	−0.0865067	+	0.119066i
$239$	−13.5806	+	9.86691i	−0.878459	+	0.638238i	−0.932843	−	0.360283i	$-0.882680\pi$
$239$	−13.5806	+	9.86691i	−0.878459	+	0.638238i	0.0543846	+	0.998520i	$0.482680\pi$
$240$		0			0
$241$		−	21.3749i		−	1.37688i	−0.725295	−	0.688438i	$-0.758297\pi$
$241$		−	21.3749i		−	1.37688i	0.725295	−	0.688438i	$-0.241703\pi$
$242$	5.21231	+	9.68668i	0.335060	+	0.622684i
$243$		0			0
$244$	3.30272	+	1.07312i	0.211435	+	0.0686994i
$245$	0.370229	+	0.509576i	0.0236531	+	0.0325556i
$246$		0			0
$247$	−0.0926776	−	0.285232i	−0.00589694	−	0.0181489i
$248$	−0.811560	−	2.49773i	−0.0515341	−	0.158606i
$249$		0			0
$250$	3.55540	+	4.89359i	0.224864	+	0.309498i
$251$	20.6079	+	6.69592i	1.30076	+	0.422643i	0.875846	−	0.482590i	$-0.160304\pi$
$251$	20.6079	+	6.69592i	1.30076	+	0.422643i	0.424915	+	0.905233i	$0.360304\pi$
$252$		0			0
$253$	−8.12160	−	19.0021i	−0.510601	−	1.19465i
$254$		−	8.91870i		−	0.559609i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	4.37238	−	6.01806i	0.272742	−	0.375397i	−0.650571	−	0.759445i	$-0.725470\pi$
$257$	4.37238	−	6.01806i	0.272742	−	0.375397i	0.923313	+	0.384049i	$0.125470\pi$
$258$		0			0
$259$	0.0446841	−	0.0145188i	0.00277654	−	0.000902152i
$260$	−1.27878	−	0.929087i	−0.0793065	−	0.0576196i
$261$		0			0
$262$	2.39891	−	7.38308i	0.148205	−	0.456128i
$263$	−1.91211			−0.117906			−0.0589528	−	0.998261i	$-0.518776\pi$
$263$	−1.91211			−0.117906			−0.0589528	+	0.998261i	$0.518776\pi$
$264$		0			0
$265$	−6.82858			−0.419477
$266$	0.0369308	−	0.113661i	0.00226437	−	0.00696902i
$267$		0			0
$268$	−0.451500	−	0.328034i	−0.0275797	−	0.0200378i
$269$	−19.5656	+	6.35725i	−1.19294	+	0.387608i	−0.837157	−	0.546962i	$-0.815784\pi$
$269$	−19.5656	+	6.35725i	−1.19294	+	0.387608i	−0.355778	+	0.934570i	$0.615784\pi$
$270$		0			0
$271$	−6.32019	+	8.69900i	−0.383924	+	0.528427i	−0.956619	−	0.291342i	$-0.905898\pi$
$271$	−6.32019	+	8.69900i	−0.383924	+	0.528427i	0.572694	+	0.819769i	$0.305898\pi$
$272$	1.83686	−	1.33456i	0.111376	−	0.0809196i
$273$		0			0
$274$			2.99682i			0.181044i
$275$	−7.83075	+	13.1061i	−0.472212	+	0.790327i
$276$		0			0
$277$	−24.1343	−	7.84171i	−1.45009	−	0.471163i	−0.525063	−	0.851064i	$-0.675958\pi$
$277$	−24.1343	−	7.84171i	−1.45009	−	0.471163i	−0.925027	+	0.379901i	$0.875958\pi$
$278$	−9.57205	−	13.1748i	−0.574093	−	0.790171i
$279$		0			0
$280$	−0.194641	−	0.599043i	−0.0116320	−	0.0357997i
$281$	9.48319	+	29.1862i	0.565719	+	1.74111i	0.665804	+	0.746127i	$0.268089\pi$
$281$	9.48319	+	29.1862i	0.565719	+	1.74111i	−0.100085	+	0.994979i	$0.531911\pi$
$282$		0			0
$283$	−0.535799	−	0.737464i	−0.0318500	−	0.0438377i	0.792795	−	0.609488i	$-0.208625\pi$
$283$	−0.535799	−	0.737464i	−0.0318500	−	0.0438377i	−0.824645	+	0.565651i	$0.808625\pi$
$284$	−0.452895	−	0.147154i	−0.0268744	−	0.00873201i
$285$		0			0
$286$	1.85216	−	8.11435i	0.109520	−	0.479812i
$287$			7.05601i			0.416503i
$288$		0			0
$289$	9.58271	−	6.96225i	0.563689	−	0.409544i
$290$	−0.738992	+	1.01714i	−0.0433951	+	0.0597282i
$291$		0			0
$292$	−14.3769	+	4.67133i	−0.841342	+	0.273369i
$293$	−21.9467	−	15.9452i	−1.28214	−	0.931529i	−0.282524	−	0.959260i	$-0.591172\pi$
$293$	−21.9467	−	15.9452i	−1.28214	−	0.931529i	−0.999615	+	0.0277310i	$0.991172\pi$
$294$		0			0
$295$	−2.62188	+	8.06932i	−0.152652	+	0.469814i
$296$	−0.0469837			−0.00273087
$297$		0			0
$298$	2.37715			0.137705
$299$	−4.83178	+	14.8707i	−0.279429	+	0.859994i
$300$		0			0
$301$	−1.21068	−	0.879612i	−0.0697825	−	0.0507000i
$302$	−14.7269	+	4.78505i	−0.847436	+	0.275349i
$303$		0			0
$304$	−0.0702465	+	0.0966860i	−0.00402891	+	0.00554532i
$305$	1.76960	−	1.28569i	0.101327	−	0.0736183i
$306$		0			0
$307$		−	6.64121i		−	0.379034i	−0.981877	−	0.189517i	$-0.939308\pi$
$307$		−	6.64121i		−	0.379034i	0.981877	−	0.189517i	$-0.0606922\pi$
$308$	2.49768	−	2.18210i	0.142319	−	0.124337i
$309$		0			0
$310$	−1.57324	−	0.511178i	−0.0893543	−	0.0290330i
$311$	−18.7936	−	25.8671i	−1.06568	−	1.46679i	−0.874370	−	0.485260i	$-0.838725\pi$
$311$	−18.7936	−	25.8671i	−1.06568	−	1.46679i	−0.191315	−	0.981529i	$-0.561275\pi$
$312$		0			0
$313$	4.02670	+	12.3929i	0.227603	+	0.700489i	0.998017	+	0.0629454i	$0.0200494\pi$
$313$	4.02670	+	12.3929i	0.227603	+	0.700489i	−0.770414	+	0.637544i	$0.779951\pi$
$314$	−1.99109	−	6.12793i	−0.112363	−	0.345819i
$315$		0			0
$316$	−5.10892	−	7.03183i	−0.287399	−	0.395571i
$317$	6.68600	+	2.17241i	0.375523	+	0.122015i	0.490697	−	0.871331i	$-0.336742\pi$
$317$	6.68600	+	2.17241i	0.375523	+	0.122015i	−0.115173	+	0.993345i	$0.536742\pi$
$318$		0			0
$319$	−6.45412	−	1.47320i	−0.361361	−	0.0824832i
$320$			0.629871i			0.0352109i
$321$		0			0
$322$	−5.04076	+	3.66232i	−0.280910	+	0.204093i
$323$	0.159494	−	0.219525i	0.00887448	−	0.0122147i
$324$		0			0
$325$	10.9865	−	3.56972i	0.609420	−	0.198013i
$326$	15.7118	+	11.4153i	0.870196	+	0.632235i
$327$		0			0
$328$	2.18043	−	6.71066i	0.120394	−	0.370534i
$329$	7.02373			0.387231
$330$		0			0
$331$	−0.839284			−0.0461312			−0.0230656	−	0.999734i	$-0.507343\pi$
$331$	−0.839284			−0.0461312			−0.0230656	+	0.999734i	$0.507343\pi$
$332$	−1.75860	+	5.41240i	−0.0965155	+	0.297044i
$333$		0			0
$334$	−18.9202	−	13.7463i	−1.03526	−	0.752164i
$335$	−0.334316	+	0.108626i	−0.0182656	+	0.00593487i
$336$		0			0
$337$	−18.9542	+	26.0882i	−1.03250	+	1.42112i	−0.129447	+	0.991586i	$0.541320\pi$
$337$	−18.9542	+	26.0882i	−1.03250	+	1.42112i	−0.903053	+	0.429529i	$0.858680\pi$
$338$	5.42238	−	3.93959i	0.294939	−	0.214286i
$339$		0			0
$340$		−	1.43011i		−	0.0775589i
$341$	−0.780677	−	8.67528i	−0.0422760	−	0.469793i
$342$		0			0
$343$	0.951057	+	0.309017i	0.0513522	+	0.0166853i
$344$	0.879612	+	1.21068i	0.0474255	+	0.0652756i
$345$		0			0
$346$	−0.314176	−	0.966934i	−0.0168902	−	0.0519827i
$347$	8.28697	+	25.5047i	0.444868	+	1.36916i	0.882628	+	0.470071i	$0.155772\pi$
$347$	8.28697	+	25.5047i	0.444868	+	1.36916i	−0.437761	+	0.899092i	$0.644228\pi$
$348$		0			0
$349$	−5.11915	−	7.04590i	−0.274022	−	0.377159i	0.649721	−	0.760173i	$-0.274886\pi$
$349$	−5.11915	−	7.04590i	−0.274022	−	0.377159i	−0.923742	+	0.383015i	$0.874886\pi$
$350$	4.37796	+	1.42249i	0.234012	+	0.0760351i
$351$		0			0
$352$	−3.04975	+	1.30348i	−0.162552	+	0.0694756i
$353$		−	30.1191i		−	1.60308i	−0.597942	−	0.801540i	$-0.704015\pi$
$353$		−	30.1191i		−	1.60308i	0.597942	−	0.801540i	$-0.295985\pi$
$354$		0			0
$355$	−0.242661	+	0.176304i	−0.0128791	+	0.00935723i
$356$	−6.73818	+	9.27431i	−0.357123	+	0.491538i
$357$		0			0
$358$	−11.2770	+	3.66412i	−0.596008	+	0.193655i
$359$	−0.720523	−	0.523491i	−0.0380278	−	0.0276288i	0.568609	−	0.822608i	$-0.307482\pi$
$359$	−0.720523	−	0.523491i	−0.0380278	−	0.0276288i	−0.606637	+	0.794979i	$0.707482\pi$
$360$		0			0
$361$	5.86691	−	18.0565i	0.308785	−	0.950342i
$362$	6.04999			0.317980
$363$		0			0
$364$	−2.50950			−0.131533
$365$	−2.94233	+	9.05557i	−0.154009	+	0.473990i
$366$		0			0
$367$	−7.84196	−	5.69752i	−0.409347	−	0.297408i	0.363990	−	0.931403i	$-0.381414\pi$
$367$	−7.84196	−	5.69752i	−0.409347	−	0.297408i	−0.773337	+	0.633995i	$0.781414\pi$
$368$	5.92577	−	1.92540i	0.308902	−	0.100368i
$369$		0			0
$370$	−0.0173947	+	0.0239418i	−0.000904308	+	0.00124467i
$371$	−8.77075	+	6.37232i	−0.455355	+	0.330835i
$372$		0			0
$373$		−	27.4932i		−	1.42355i	−0.702410	−	0.711773i	$-0.747893\pi$
$373$		−	27.4932i		−	1.42355i	0.702410	−	0.711773i	$-0.252107\pi$
$374$	6.92441	−	2.95953i	0.358053	−	0.153034i
$375$		0			0
$376$	−6.67997	−	2.17045i	−0.344493	−	0.111933i
$377$	2.94425	+	4.05241i	0.151637	+	0.208710i
$378$		0			0
$379$	2.34368	+	7.21309i	0.120387	+	0.370512i	0.993032	−	0.117842i	$-0.0375976\pi$
$379$	2.34368	+	7.21309i	0.120387	+	0.370512i	−0.872646	+	0.488354i	$0.837598\pi$
$380$	0.0232616	+	0.0715919i	0.00119330	+	0.00367259i
$381$		0			0
$382$	3.63415	+	5.00198i	0.185939	+	0.255924i
$383$	−13.9907	−	4.54586i	−0.714892	−	0.232283i	−0.0710849	−	0.997470i	$-0.522646\pi$
$383$	−13.9907	−	4.54586i	−0.714892	−	0.232283i	−0.643807	+	0.765188i	$0.722646\pi$
$384$		0			0
$385$	−0.187234	−	2.08064i	−0.00954233	−	0.106039i
$386$		−	14.8898i		−	0.757872i
$387$		0			0
$388$	1.78435	−	1.29641i	0.0905869	−	0.0658152i
$389$	7.94704	−	10.9382i	0.402931	−	0.554587i	−0.558546	−	0.829474i	$-0.688640\pi$
$389$	7.94704	−	10.9382i	0.402931	−	0.554587i	0.961477	+	0.274887i	$0.0886404\pi$
$390$		0			0
$391$	−13.4544	+	4.37159i	−0.680417	+	0.221081i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$		0			0
$394$	−4.51297	+	13.8895i	−0.227360	+	0.699743i
$395$	−5.47472			−0.275463
$396$		0			0
$397$	−2.34572			−0.117729			−0.0588643	−	0.998266i	$-0.518748\pi$
$397$	−2.34572			−0.117729			−0.0588643	+	0.998266i	$0.518748\pi$
$398$	−2.65907	+	8.18379i	−0.133287	+	0.410216i
$399$		0			0
$400$	−3.72412	−	2.70573i	−0.186206	−	0.135286i
$401$	2.28745	−	0.743238i	0.114230	−	0.0371156i	−0.251344	−	0.967898i	$-0.580873\pi$
$401$	2.28745	−	0.743238i	0.114230	−	0.0371156i	0.365574	+	0.930782i	$0.380873\pi$
$402$		0			0
$403$	−3.87386	+	5.33191i	−0.192971	+	0.265601i
$404$	−2.51381	+	1.82639i	−0.125067	+	0.0908664i
$405$		0			0
$406$			1.99604i			0.0990619i
$407$	−0.151920	−	0.0346768i	−0.00753039	−	0.00171886i
$408$		0			0
$409$	32.5407	+	10.5731i	1.60903	+	0.522806i	0.969319	−	0.245807i	$-0.0790530\pi$
$409$	32.5407	+	10.5731i	1.60903	+	0.522806i	0.639714	+	0.768613i	$0.279053\pi$
$410$	−2.61234	−	3.59557i	−0.129014	−	0.177573i
$411$		0			0
$412$	0.177779	+	0.547147i	0.00875854	+	0.0269560i
$413$	4.16257	+	12.8111i	0.204827	+	0.630392i
$414$		0			0
$415$	2.10695	+	2.89997i	0.103426	+	0.142354i
$416$	2.38667	+	0.775477i	0.117016	+	0.0380209i
$417$		0			0
$418$	−0.298499	+	0.260784i	−0.0146001	+	0.0127554i
$419$		−	16.1713i		−	0.790019i	−0.918677	−	0.395009i	$-0.870741\pi$
$419$		−	16.1713i		−	0.790019i	0.918677	−	0.395009i	$-0.129259\pi$
$420$		0			0
$421$	−12.6478	+	9.18915i	−0.616415	+	0.447852i	−0.851668	−	0.524082i	$-0.824408\pi$
$421$	−12.6478	+	9.18915i	−0.616415	+	0.447852i	0.235252	+	0.971934i	$0.424408\pi$
$422$	−2.84592	+	3.91707i	−0.138537	+	0.190680i
$423$		0			0
$424$	10.3106	−	3.35013i	0.500729	−	0.162697i
$425$	8.45557	+	6.14333i	0.410155	+	0.297995i
$426$		0			0
$427$	1.07312	−	3.30272i	0.0519319	−	0.159830i
$428$	2.17021			0.104901
$429$		0			0
$430$	0.942592			0.0454558
$431$	−8.29602	+	25.5325i	−0.399605	+	1.22986i	0.525711	+	0.850663i	$0.323799\pi$
$431$	−8.29602	+	25.5325i	−0.399605	+	1.22986i	−0.925317	+	0.379195i	$0.876201\pi$
$432$		0			0
$433$	−9.68358	−	7.03554i	−0.465363	−	0.338106i	0.330268	−	0.943887i	$-0.392861\pi$
$433$	−9.68358	−	7.03554i	−0.465363	−	0.338106i	−0.795632	+	0.605781i	$0.792861\pi$
$434$	−2.49773	+	0.811560i	−0.119895	+	0.0389561i
$435$		0			0
$436$	−8.06145	+	11.0956i	−0.386073	+	0.531385i
$437$	0.602423	−	0.437686i	0.0288178	−	0.0209374i
$438$		0			0
$439$			26.0501i			1.24330i	0.783293	+	0.621652i	$0.213538\pi$
$439$			26.0501i			1.24330i	−0.783293	+	0.621652i	$0.786462\pi$
$440$	−0.464882	+	2.03666i	−0.0221624	+	0.0970941i
$441$		0			0
$442$	−5.41891	−	1.76071i	−0.257751	−	0.0837485i
$443$	−13.4650	−	18.5330i	−0.639742	−	0.880530i	0.358859	−	0.933392i	$-0.383166\pi$
$443$	−13.4650	−	18.5330i	−0.639742	−	0.880530i	−0.998602	+	0.0528617i	$0.983166\pi$
$444$		0			0
$445$	2.23130	+	6.86723i	0.105774	+	0.325538i
$446$	−8.31326	−	25.5856i	−0.393644	−	1.21151i
$447$		0			0
$448$	0.587785	+	0.809017i	0.0277702	+	0.0382225i
$449$	18.6126	+	6.04759i	0.878382	+	0.285404i	0.713285	−	0.700874i	$-0.247206\pi$
$449$	18.6126	+	6.04759i	0.878382	+	0.285404i	0.165097	+	0.986277i	$0.447206\pi$
$450$		0			0
$451$	12.0032	−	20.0894i	0.565208	−	0.945972i
$452$		−	0.0208431i		−	0.000980378i
$453$		0			0
$454$	6.77267	−	4.92063i	0.317857	−	0.230937i
$455$	−0.929087	+	1.27878i	−0.0435563	+	0.0599501i
$456$		0			0
$457$	−2.64697	+	0.860053i	−0.123820	+	0.0402316i	−0.370272	−	0.928924i	$-0.620735\pi$
$457$	−2.64697	+	0.860053i	−0.123820	+	0.0402316i	0.246452	+	0.969155i	$0.420735\pi$
$458$	0.162665	+	0.118183i	0.00760084	+	0.00552233i
$459$		0			0
$460$	1.21275	−	3.73247i	0.0565449	−	0.174027i
$461$	3.16951			0.147619			0.0738095	−	0.997272i	$-0.476484\pi$
$461$	3.16951			0.147619			0.0738095	+	0.997272i	$0.476484\pi$
$462$		0			0
$463$	5.38147			0.250098			0.125049	−	0.992151i	$-0.460091\pi$
$463$	5.38147			0.250098			0.125049	+	0.992151i	$0.460091\pi$
$464$	0.616811	−	1.89835i	0.0286347	−	0.0881286i
$465$		0			0
$466$	−5.56475	−	4.04302i	−0.257782	−	0.187289i
$467$	−13.7409	+	4.46469i	−0.635853	+	0.206601i	−0.609166	−	0.793043i	$-0.708496\pi$
$467$	−13.7409	+	4.46469i	−0.635853	+	0.206601i	−0.0266870	+	0.999644i	$0.508496\pi$
$468$		0			0
$469$	−0.328034	+	0.451500i	−0.0151472	+	0.0208483i
$470$	−3.57913	+	2.60039i	−0.165093	+	0.119947i
$471$		0			0
$472$		−	13.4704i		−	0.620024i
$473$	1.95063	+	4.56390i	0.0896903	+	0.209848i
$474$		0			0
$475$	−0.523213	−	0.170002i	−0.0240066	−	0.00780023i
$476$	−1.33456	−	1.83686i	−0.0611694	−	0.0841925i
$477$		0			0
$478$	−5.18734	−	15.9650i	−0.237264	−	0.730222i
$479$	−9.75363	−	30.0186i	−0.445655	−	1.37158i	−0.881764	−	0.471690i	$-0.843644\pi$
$479$	−9.75363	−	30.0186i	−0.445655	−	1.37158i	0.436110	−	0.899894i	$-0.356356\pi$
$480$		0			0
$481$	0.0693030	+	0.0953874i	0.00315995	+	0.00434929i
$482$	20.3287	+	6.60520i	0.925947	+	0.300858i
$483$		0			0
$484$	−10.8233	+	1.96385i	−0.491967	+	0.0892659i
$485$		−	1.38923i		−	0.0630818i
$486$		0			0
$487$	−26.5056	+	19.2575i	−1.20108	+	0.872639i	−0.994391	−	0.105766i	$-0.966270\pi$
$487$	−26.5056	+	19.2575i	−1.20108	+	0.872639i	−0.206694	+	0.978406i	$0.566270\pi$
$488$	−2.04119	+	2.80946i	−0.0924005	+	0.127178i
$489$		0			0
$490$	−0.599043	+	0.194641i	−0.0270620	+	0.00879298i
$491$	17.8538	+	12.9715i	0.805729	+	0.585397i	0.912589	−	0.408877i	$-0.134080\pi$
$491$	17.8538	+	12.9715i	0.805729	+	0.585397i	−0.106860	+	0.994274i	$0.534080\pi$
$492$		0			0
$493$	−1.40046	+	4.31018i	−0.0630736	+	0.194121i
$494$	0.299911			0.0134936
$495$		0			0
$496$	2.62626			0.117923
$497$	−0.147154	+	0.452895i	−0.00660078	+	0.0203151i
$498$		0			0
$499$	19.6615	+	14.2849i	0.880168	+	0.639480i	0.933296	−	0.359108i	$-0.116919\pi$
$499$	19.6615	+	14.2849i	0.880168	+	0.639480i	−0.0531278	+	0.998588i	$0.516919\pi$
$500$	−5.75277	+	1.86919i	−0.257271	+	0.0835926i
$501$		0			0
$502$	−12.7364	+	17.5302i	−0.568454	+	0.782409i
$503$	−9.94247	+	7.22363i	−0.443313	+	0.322086i	−0.786950	−	0.617017i	$-0.788341\pi$
$503$	−9.94247	+	7.22363i	−0.443313	+	0.322086i	0.343637	+	0.939103i	$0.388341\pi$
$504$		0			0
$505$			1.95716i			0.0870925i
$506$	20.5818	−	1.85213i	0.914972	−	0.0823372i
$507$		0			0
$508$	8.48218	+	2.75603i	0.376336	+	0.122279i
$509$	9.98221	+	13.7393i	0.442453	+	0.608985i	0.970755	−	0.240072i	$-0.0771710\pi$
$509$	9.98221	+	13.7393i	0.442453	+	0.608985i	−0.528302	+	0.849057i	$0.677171\pi$
$510$		0			0
$511$	4.67133	+	14.3769i	0.206647	+	0.635995i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	4.37238	+	6.01806i	0.192857	+	0.265445i
$515$	0.344632	+	0.111978i	0.0151863	+	0.00493433i
$516$		0			0
$517$	−19.9975	−	11.9483i	−0.879489	−	0.525485i
$518$			0.0469837i			0.00206434i
$519$		0			0
$520$	1.27878	−	0.929087i	0.0560782	−	0.0407432i
$521$	0.0231379	−	0.0318466i	0.00101369	−	0.00139523i	−0.808510	−	0.588483i	$-0.799726\pi$
$521$	0.0231379	−	0.0318466i	0.00101369	−	0.00139523i	0.809524	+	0.587087i	$0.199726\pi$
$522$		0			0
$523$	26.7680	−	8.69746i	1.17048	−	0.380313i	0.341660	−	0.939823i	$-0.389011\pi$
$523$	26.7680	−	8.69746i	1.17048	−	0.380313i	0.828823	+	0.559510i	$0.189011\pi$
$524$	6.28042	+	4.56299i	0.274362	+	0.199335i
$525$		0			0
$526$	0.590874	−	1.81852i	0.0257633	−	0.0792913i
$527$	−5.96290			−0.259748
$528$		0			0
$529$	−15.8218			−0.687906
$530$	2.11015	−	6.49437i	0.0916590	−	0.282097i
$531$		0			0
$532$	0.0966860	+	0.0702465i	0.00419187	+	0.00304557i
$533$	−16.8404	+	5.47177i	−0.729437	+	0.237009i
$534$		0			0
$535$	0.803475	−	1.10589i	0.0347372	−	0.0478117i
$536$	0.451500	−	0.328034i	0.0195018	−	0.0141689i
$537$		0			0
$538$		−	20.5725i		−	0.886943i
$539$	−2.18210	−	2.49768i	−0.0939899	−	0.107583i
$540$		0			0
$541$	39.5989	+	12.8665i	1.70249	+	0.553172i	0.989054	−	0.147551i	$-0.0471390\pi$
$541$	39.5989	+	12.8665i	1.70249	+	0.553172i	0.713434	+	0.700723i	$0.247139\pi$
$542$	−6.32019	−	8.69900i	−0.271476	−	0.373654i
$543$		0			0
$544$	0.701620	+	2.15936i	0.0300817	+	0.0925819i
$545$	2.66949	+	8.21585i	0.114348	+	0.351928i
$546$		0			0
$547$	7.98466	+	10.9899i	0.341399	+	0.469896i	0.944850	−	0.327505i	$-0.106208\pi$
$547$	7.98466	+	10.9899i	0.341399	+	0.469896i	−0.603450	+	0.797401i	$0.706208\pi$
$548$	−2.85014	−	0.926068i	−0.121752	−	0.0395597i
$549$		0			0
$550$	−10.0448	−	11.4975i	−0.428312	−	0.490255i
$551$		−	0.238548i		−	0.0101625i
$552$		0			0
$553$	−7.03183	+	5.10892i	−0.299024	+	0.217253i
$554$	14.9158	−	20.5299i	0.633713	−	0.872231i
$555$		0			0
$556$	15.4879	−	5.03232i	0.656833	−	0.213418i
$557$	−7.62925	−	5.54297i	−0.323262	−	0.234863i	0.414304	−	0.910138i	$-0.364025\pi$
$557$	−7.62925	−	5.54297i	−0.323262	−	0.234863i	−0.737566	+	0.675275i	$0.764025\pi$
$558$		0			0
$559$	1.16049	−	3.57162i	0.0490835	−	0.151063i
$560$	0.629871			0.0266169
$561$		0			0
$562$	−30.6882			−1.29451
$563$	1.50504	−	4.63202i	0.0634297	−	0.195216i	−0.914320	−	0.404993i	$-0.867274\pi$
$563$	1.50504	−	4.63202i	0.0634297	−	0.195216i	0.977749	+	0.209777i	$0.0672738\pi$
$564$		0			0
$565$	−0.0106212	−	0.00771672i	−0.000446835	−	0.000324645i
$566$	0.866941	−	0.281686i	0.0364403	−	0.0118402i
$567$		0			0
$568$	0.279904	−	0.385255i	0.0117445	−	0.0161650i
$569$	−12.4572	+	9.05067i	−0.522232	+	0.379424i	−0.817444	−	0.576008i	$-0.804610\pi$
$569$	−12.4572	+	9.05067i	−0.522232	+	0.379424i	0.295212	+	0.955432i	$0.404610\pi$
$570$		0			0
$571$		−	6.05643i		−	0.253454i	−0.991938	−	0.126727i	$-0.959553\pi$
$571$		−	6.05643i		−	0.253454i	0.991938	−	0.126727i	$-0.0404472\pi$
$572$	7.14486	+	4.26898i	0.298742	+	0.178495i
$573$		0			0
$574$	−6.71066	−	2.18043i	−0.280098	−	0.0910092i
$575$	16.8586	+	23.2039i	0.703054	+	0.967671i
$576$		0			0
$577$	−3.01317	−	9.27358i	−0.125440	−	0.386064i	0.868541	−	0.495617i	$-0.165058\pi$
$577$	−3.01317	−	9.27358i	−0.125440	−	0.386064i	−0.993981	+	0.109553i	$0.965058\pi$
$578$	3.66027	+	11.2652i	0.152247	+	0.468569i
$579$		0			0
$580$	−0.738992	−	1.01714i	−0.0306850	−	0.0422342i
$581$	5.41240	+	1.75860i	0.224544	+	0.0729589i
$582$		0			0
$583$	35.8116	−	3.22264i	1.48317	−	0.133468i
$584$		−	15.1167i		−	0.625535i
$585$		0			0
$586$	21.9467	−	15.9452i	0.906610	−	0.658691i
$587$	7.16460	−	9.86123i	0.295715	−	0.407016i	−0.635145	−	0.772393i	$-0.719060\pi$
$587$	7.16460	−	9.86123i	0.295715	−	0.407016i	0.930860	+	0.365376i	$0.119060\pi$
$588$		0			0
$589$	0.298504	−	0.0969900i	0.0122997	−	0.00399640i
$590$	−6.86418	−	4.98712i	−0.282594	−	0.205316i
$591$		0			0
$592$	0.0145188	−	0.0446841i	0.000596717	−	0.00183651i
$593$	3.24966			0.133448			0.0667238	−	0.997771i	$-0.478745\pi$
$593$	3.24966			0.133448			0.0667238	+	0.997771i	$0.478745\pi$
$594$		0			0
$595$	−1.43011			−0.0586290
$596$	−0.734580	+	2.26081i	−0.0300896	+	0.0926062i
$597$		0			0
$598$	−12.6498	−	9.19059i	−0.517287	−	0.375831i
$599$	−3.78373	+	1.22941i	−0.154599	+	0.0502323i	−0.385294	−	0.922794i	$-0.625900\pi$
$599$	−3.78373	+	1.22941i	−0.154599	+	0.0502323i	0.230695	+	0.973026i	$0.425900\pi$
$600$		0			0
$601$	6.60161	−	9.08634i	0.269285	−	0.370639i	−0.652863	−	0.757476i	$-0.726432\pi$
$601$	6.60161	−	9.08634i	0.269285	−	0.370639i	0.922148	+	0.386837i	$0.126432\pi$
$602$	1.21068	−	0.879612i	0.0493437	−	0.0358503i
$603$		0			0
$604$		−	15.4847i		−	0.630065i
$605$	−3.00636	+	6.24236i	−0.122226	+	0.253788i
$606$		0			0
$607$	40.5857	+	13.1871i	1.64732	+	0.535247i	0.978157	−	0.207868i	$-0.0666523\pi$
$607$	40.5857	+	13.1871i	1.64732	+	0.535247i	0.669164	+	0.743115i	$0.266652\pi$
$608$	−0.0702465	−	0.0966860i	−0.00284887	−	0.00392114i
$609$		0			0
$610$	0.675927	+	2.08029i	0.0273675	+	0.0842284i
$611$	5.44674	+	16.7633i	0.220352	+	0.678173i
$612$		0			0
$613$	21.2156	+	29.2007i	0.856889	+	1.17941i	0.982302	+	0.187302i	$0.0599743\pi$
$613$	21.2156	+	29.2007i	0.856889	+	1.17941i	−0.125413	+	0.992105i	$0.540026\pi$
$614$	6.31616	+	2.05225i	0.254900	+	0.0828219i
$615$		0			0
$616$	1.30348	+	3.04975i	0.0525186	+	0.122878i
$617$			1.92267i			0.0774037i	0.999251	+	0.0387019i	$0.0123223\pi$
$617$			1.92267i			0.0774037i	−0.999251	+	0.0387019i	$0.987678\pi$
$618$		0			0
$619$	−5.70941	+	4.14813i	−0.229481	+	0.166728i	−0.696584	−	0.717475i	$-0.745298\pi$
$619$	−5.70941	+	4.14813i	−0.229481	+	0.166728i	0.467103	+	0.884203i	$0.345298\pi$
$620$	0.972319	−	1.33828i	0.0390493	−	0.0537467i
$621$		0			0
$622$	30.4086	−	9.88035i	1.21927	−	0.396166i
$623$	9.27431	+	6.73818i	0.371567	+	0.269960i
$624$		0			0
$625$	5.93509	−	18.2663i	0.237403	−	0.730653i
$626$	−13.0307			−0.520811
$627$		0			0
$628$	6.44329			0.257115
$629$	−0.0329647	+	0.101455i	−0.00131439	+	0.00404527i
$630$		0			0
$631$	28.7824	+	20.9116i	1.14581	+	0.832479i	0.987918	−	0.154977i	$-0.0495304\pi$
$631$	28.7824	+	20.9116i	1.14581	+	0.832479i	0.157892	+	0.987456i	$0.449530\pi$
$632$	8.26641	−	2.68592i	0.328820	−	0.106840i
$633$		0			0
$634$	−4.13218	+	5.68745i	−0.164110	+	0.225878i
$635$	4.54476	−	3.30196i	0.180353	−	0.131034i
$636$		0			0
$637$			2.50950i			0.0994298i
$638$	3.39553	−	5.68299i	0.134430	−	0.224992i
$639$		0			0
$640$	−0.599043	−	0.194641i	−0.0236792	−	0.00769385i
$641$	−10.5688	−	14.5467i	−0.417443	−	0.574561i	0.547571	−	0.836759i	$-0.315553\pi$
$641$	−10.5688	−	14.5467i	−0.417443	−	0.574561i	−0.965014	+	0.262198i	$0.915553\pi$
$642$		0			0
$643$	15.0786	+	46.4072i	0.594643	+	1.83012i	0.556497	+	0.830850i	$0.312145\pi$
$643$	15.0786	+	46.4072i	0.594643	+	1.83012i	0.0381457	+	0.999272i	$0.487855\pi$
$644$	−1.92540	−	5.92577i	−0.0758713	−	0.233508i
$645$		0			0
$646$	0.159494	+	0.219525i	0.00627520	+	0.00863708i
$647$	−13.6512	−	4.43555i	−0.536685	−	0.174379i	0.0281193	−	0.999605i	$-0.491048\pi$
$647$	−13.6512	−	4.43555i	−0.536685	−	0.174379i	−0.564804	+	0.825225i	$0.691048\pi$
$648$		0			0
$649$	9.94193	−	43.5559i	0.390255	−	1.70972i
$650$			11.5519i			0.453101i
$651$		0			0
$652$	−15.7118	+	11.4153i	−0.615322	+	0.447057i
$653$	19.8747	−	27.3552i	0.777759	−	1.07049i	−0.217767	−	0.976001i	$-0.569877\pi$
$653$	19.8747	−	27.3552i	0.777759	−	1.07049i	0.995526	−	0.0944925i	$-0.0301228\pi$
$654$		0			0
$655$	4.65039	−	1.51100i	0.181706	−	0.0590397i
$656$	5.70843	+	4.14742i	0.222877	+	0.161929i
$657$		0			0
$658$	−2.17045	+	6.67997i	−0.0846131	+	0.260412i
$659$	−5.40624			−0.210597			−0.105299	−	0.994441i	$-0.533580\pi$
$659$	−5.40624			−0.210597			−0.105299	+	0.994441i	$0.533580\pi$
$660$		0			0
$661$	32.7593			1.27419			0.637094	−	0.770786i	$-0.280136\pi$
$661$	32.7593			1.27419			0.637094	+	0.770786i	$0.280136\pi$
$662$	0.259353	−	0.798206i	0.0100800	−	0.0310232i
$663$		0			0
$664$	−4.60406	−	3.34505i	−0.178672	−	0.129813i
$665$	0.0715919	−	0.0232616i	0.00277622	−	0.000902047i
$666$		0			0
$667$	−7.31015	+	10.0616i	−0.283050	+	0.389585i
$668$	18.9202	−	13.7463i	0.732043	−	0.531860i
$669$		0			0
$670$		−	0.351521i		−	0.0135804i
$671$	−8.67367	+	7.57777i	−0.334843	+	0.292536i
$672$		0			0
$673$	31.5866	+	10.2631i	1.21757	+	0.395614i	0.846198	−	0.532868i	$-0.178886\pi$
$673$	31.5866	+	10.2631i	1.21757	+	0.395614i	0.371376	+	0.928482i	$0.378886\pi$
$674$	−18.9542	−	26.0882i	−0.730088	−	1.00488i
$675$		0			0
$676$	2.07117	+	6.37439i	0.0796602	+	0.245169i
$677$	2.36161	+	7.26828i	0.0907640	+	0.279343i	0.986127	−	0.165995i	$-0.0530836\pi$
$677$	2.36161	+	7.26828i	0.0907640	+	0.279343i	−0.895363	+	0.445338i	$0.853084\pi$
$678$		0			0
$679$	−1.29641	−	1.78435i	−0.0497516	−	0.0684773i
$680$	1.36012	+	0.441930i	0.0521582	+	0.0169472i
$681$		0			0
$682$	8.49192	+	1.93834i	0.325172	+	0.0742229i
$683$		−	40.5429i		−	1.55133i	−0.631145	−	0.775665i	$-0.717415\pi$
$683$		−	40.5429i		−	1.55133i	0.631145	−	0.775665i	$-0.282585\pi$
$684$		0			0
$685$	−1.52711	+	1.10951i	−0.0583478	+	0.0423921i
$686$	−0.587785	+	0.809017i	−0.0224417	+	0.0308884i
$687$		0			0
$688$	−1.42324	+	0.462439i	−0.0542606	+	0.0176303i
$689$	−22.0102	−	15.9913i	−0.838520	−	0.609221i
$690$		0			0
$691$	3.82850	−	11.7829i	0.145643	−	0.448243i	−0.851450	−	0.524435i	$-0.824276\pi$
$691$	3.82850	−	11.7829i	0.145643	−	0.448243i	0.997093	+	0.0761928i	$0.0242764\pi$
$692$	1.01669			0.0386489
$693$		0			0
$694$	−26.8172			−1.01797
$695$	3.16971	−	9.75537i	0.120234	−	0.370042i
$696$		0			0
$697$	−12.9609	−	9.41666i	−0.490930	−	0.356681i
$698$	8.28296	−	2.69130i	0.313515	−	0.101867i
$699$		0			0
$700$	−2.70573	+	3.72412i	−0.102267	+	0.140758i
$701$	27.3419	−	19.8651i	1.03269	−	0.750294i	0.0638456	−	0.997960i	$-0.479663\pi$
$701$	27.3419	−	19.8651i	1.03269	−	0.750294i	0.968846	+	0.247666i	$0.0796635\pi$
$702$		0			0
$703$		−	0.00561505i		−	0.000211775i
$704$	−0.297258	−	3.30328i	−0.0112033	−	0.124497i
$705$		0			0
$706$	28.6450	+	9.30732i	1.07807	+	0.350286i
$707$	1.82639	+	2.51381i	0.0686885	+	0.0945416i
$708$		0			0
$709$	1.26075	+	3.88020i	0.0473486	+	0.145724i	0.971936	−	0.235247i	$-0.0755898\pi$
$709$	1.26075	+	3.88020i	0.0473486	+	0.145724i	−0.924587	+	0.380971i	$0.875590\pi$
$710$	−0.0926883	−	0.285265i	−0.00347853	−	0.0107058i
$711$		0			0
$712$	−6.73818	−	9.27431i	−0.252524	−	0.347570i
$713$	−15.5626	−	5.05660i	−0.582825	−	0.189371i
$714$		0			0
$715$	4.82060	−	2.06035i	0.180280	−	0.0770528i
$716$		−	11.8573i		−	0.443130i
$717$		0			0
$718$	0.720523	−	0.523491i	0.0268897	−	0.0195365i
$719$	15.5031	−	21.3382i	0.578167	−	0.795779i	−0.415325	−	0.909673i	$-0.636332\pi$
$719$	15.5031	−	21.3382i	0.578167	−	0.795779i	0.993493	+	0.113894i	$0.0363323\pi$
$720$		0			0
$721$	0.547147	−	0.177779i	0.0203768	−	0.00662083i
$722$	15.3598	+	11.1595i	0.571631	+	0.415315i
$723$		0			0
$724$	−1.86955	+	5.75388i	−0.0694812	+	0.213841i
$725$	9.18830			0.341245
$726$		0			0
$727$	−14.4864			−0.537272			−0.268636	−	0.963242i	$-0.586573\pi$
$727$	−14.4864			−0.537272			−0.268636	+	0.963242i	$0.586573\pi$
$728$	0.775477	−	2.38667i	0.0287411	−	0.0884559i
$729$		0			0
$730$	−7.70313	−	5.59665i	−0.285105	−	0.207141i
$731$	3.23145	−	1.04996i	0.119520	−	0.0388343i
$732$		0			0
$733$	5.35440	−	7.36969i	0.197769	−	0.272206i	−0.698602	−	0.715511i	$-0.746194\pi$
$733$	5.35440	−	7.36969i	0.197769	−	0.272206i	0.896371	+	0.443305i	$0.146194\pi$
$734$	7.84196	−	5.69752i	0.289452	−	0.210299i
$735$		0			0
$736$			6.23072i			0.229667i
$737$	1.70201	−	0.727450i	0.0626945	−	0.0267960i
$738$		0			0
$739$	31.4635	+	10.2231i	1.15740	+	0.376063i	0.823927	−	0.566695i	$-0.191778\pi$
$739$	31.4635	+	10.2231i	1.15740	+	0.376063i	0.333476	+	0.942759i	$0.391778\pi$
$740$	−0.0173947	−	0.0239418i	−0.000639443	−	0.000880117i
$741$		0			0
$742$	−3.35013	−	10.3106i	−0.122987	−	0.378515i
$743$	6.43639	+	19.8092i	0.236128	+	0.726729i	0.996970	+	0.0777905i	$0.0247865\pi$
$743$	6.43639	+	19.8092i	0.236128	+	0.726729i	−0.760841	+	0.648938i	$0.775213\pi$
$744$		0			0
$745$	0.880090	+	1.21134i	0.0322440	+	0.0443801i
$746$	26.1476	+	8.49587i	0.957332	+	0.311056i
$747$		0			0
$748$	0.674920	+	7.50005i	0.0246775	+	0.274229i
$749$		−	2.17021i		−	0.0792978i
$750$		0			0
$751$	−32.8228	+	23.8472i	−1.19772	+	0.870195i	−0.994059	−	0.108846i	$-0.965284\pi$
$751$	−32.8228	+	23.8472i	−1.19772	+	0.870195i	−0.203662	+	0.979041i	$0.565284\pi$
$752$	4.12845	−	5.68232i	0.150549	−	0.207213i
$753$		0			0
$754$	−4.76390	+	1.54788i	−0.173491	+	0.0563706i
$755$	−7.89066	−	5.73290i	−0.287170	−	0.208642i
$756$		0			0
$757$	16.6217	−	51.1564i	0.604126	−	1.85931i	0.101437	−	0.994842i	$-0.467656\pi$
$757$	16.6217	−	51.1564i	0.604126	−	1.85931i	0.502689	−	0.864467i	$-0.332344\pi$
$758$	−7.58429			−0.275474
$759$		0			0
$760$	−0.0752762			−0.00273055
$761$	−9.47802	+	29.1703i	−0.343578	+	1.05742i	0.618763	+	0.785578i	$0.287634\pi$
$761$	−9.47802	+	29.1703i	−0.343578	+	1.05742i	−0.962341	+	0.271846i	$0.912366\pi$
$762$		0			0
$763$	11.0956	+	8.06145i	0.401689	+	0.291844i
$764$	−5.88018	+	1.91059i	−0.212737	+	0.0691226i
$765$		0			0
$766$	8.64674	−	11.9012i	0.312419	−	0.430008i
$767$	−27.3479	+	19.8694i	−0.987474	+	0.717442i
$768$		0			0
$769$			51.3621i			1.85216i	0.377322	+	0.926082i	$0.376845\pi$
$769$			51.3621i			1.85216i	−0.377322	+	0.926082i	$0.623155\pi$
$770$	2.03666	+	0.464882i	0.0733962	+	0.0167532i
$771$		0			0
$772$	14.1611	+	4.60121i	0.509668	+	0.165601i
$773$	−13.1210	−	18.0594i	−0.471928	−	0.649553i	0.505001	−	0.863119i	$-0.331492\pi$
$773$	−13.1210	−	18.0594i	−0.471928	−	0.649553i	−0.976929	+	0.213566i	$0.931492\pi$
$774$		0			0
$775$	3.73582	+	11.4977i	0.134195	+	0.413009i
$776$	0.681563	+	2.09763i	0.0244667	+	0.0753007i
$777$		0			0
$778$	7.94704	+	10.9382i	0.284915	+	0.392152i
$779$	0.801994	+	0.260584i	0.0287344	+	0.00933638i
$780$		0			0
$781$	1.18940	−	1.03912i	0.0425601	−	0.0371827i
$782$		−	14.1468i		−	0.505888i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	2.38549	−	3.28335i	0.0851418	−	0.117188i
$786$		0			0
$787$	−18.4577	+	5.99728i	−0.657947	+	0.213780i	−0.618915	−	0.785458i	$-0.712427\pi$
$787$	−18.4577	+	5.99728i	−0.657947	+	0.213780i	−0.0390319	+	0.999238i	$0.512427\pi$
$788$	−11.8151	−	8.58418i	−0.420896	−	0.305799i
$789$		0			0
$790$	1.69178	−	5.20677i	0.0601909	−	0.185249i
$791$	−0.0208431			−0.000741096
$792$		0			0
$793$	8.71469			0.309468
$794$	0.724869	−	2.23092i	0.0257246	−	0.0791723i
$795$		0			0
$796$	−6.96154	−	5.05786i	−0.246745	−	0.179271i
$797$	37.2675	−	12.1089i	1.32008	−	0.428921i	0.437559	−	0.899190i	$-0.355843\pi$
$797$	37.2675	−	12.1089i	1.32008	−	0.428921i	0.882523	+	0.470269i	$0.155843\pi$
$798$		0			0
$799$	−9.37359	+	12.9016i	−0.331614	+	0.456427i
$800$	3.72412	−	2.70573i	0.131667	−	0.0956620i
$801$		0			0
$802$			2.40517i			0.0849295i
$803$	11.1570	−	48.8793i	0.393724	−	1.72491i
$804$		0			0
$805$	−3.73247	−	1.21275i	−0.131552	−	0.0427439i
$806$	−3.87386	−	5.33191i	−0.136451	−	0.187808i
$807$		0			0
$808$	−0.960191	−	2.95516i	−0.0337794	−	0.103962i
$809$	−2.18407	−	6.72187i	−0.0767877	−	0.236328i	0.905293	−	0.424787i	$-0.139651\pi$
$809$	−2.18407	−	6.72187i	−0.0767877	−	0.236328i	−0.982081	+	0.188458i	$0.939651\pi$
$810$		0			0
$811$	9.03625	+	12.4373i	0.317306	+	0.436734i	0.937642	−	0.347602i	$-0.113004\pi$
$811$	9.03625	+	12.4373i	0.317306	+	0.436734i	−0.620337	+	0.784336i	$0.713004\pi$
$812$	−1.89835	−	0.616811i	−0.0666189	−	0.0216458i
$813$		0			0
$814$	0.0799254	−	0.133769i	0.00280138	−	0.00468859i
$815$			12.2326i			0.428490i
$816$		0			0
$817$	−0.144689	+	0.105123i	−0.00506203	+	0.00367778i
$818$	−20.1112	+	27.6807i	−0.703173	+	0.967834i
$819$		0			0
$820$	4.22685	−	1.37339i	0.147608	−	0.0479607i
$821$	−9.82416	−	7.13767i	−0.342866	−	0.249106i	0.403004	−	0.915198i	$-0.367966\pi$
$821$	−9.82416	−	7.13767i	−0.342866	−	0.249106i	−0.745870	+	0.666092i	$0.767966\pi$
$822$		0			0
$823$	−5.62802	+	17.3213i	−0.196180	+	0.603781i	0.803780	+	0.594926i	$0.202819\pi$
$823$	−5.62802	+	17.3213i	−0.196180	+	0.603781i	−0.999961	+	0.00885504i	$0.997181\pi$
$824$	−0.575305			−0.0200417
$825$		0			0
$826$	−13.4704			−0.468694
$827$	−9.09953	+	28.0055i	−0.316422	+	0.973846i	0.658744	+	0.752368i	$0.271088\pi$
$827$	−9.09953	+	28.0055i	−0.316422	+	0.973846i	−0.975165	+	0.221478i	$0.928912\pi$
$828$		0			0
$829$	32.8469	+	23.8647i	1.14082	+	0.828854i	0.987233	−	0.159282i	$-0.0509178\pi$
$829$	32.8469	+	23.8647i	1.14082	+	0.828854i	0.153586	+	0.988135i	$0.450918\pi$
$830$	−3.40911	+	1.10769i	−0.118332	+	0.0384484i
$831$		0			0
$832$	−1.47504	+	2.03022i	−0.0511380	+	0.0703854i
$833$	−1.83686	+	1.33456i	−0.0636436	+	0.0462398i
$834$		0			0
$835$		−	14.7305i		−	0.509771i
$836$	−0.155779	−	0.364477i	−0.00538774	−	0.0126057i
$837$		0			0
$838$	15.3798	+	4.99720i	0.531286	+	0.172625i
$839$	−20.7992	−	28.6276i	−0.718068	−	0.988336i	−0.999586	−	0.0287798i	$-0.990838\pi$
$839$	−20.7992	−	28.6276i	−0.718068	−	0.988336i	0.281518	−	0.959556i	$-0.409162\pi$
$840$		0			0
$841$	−7.73031	−	23.7915i	−0.266563	−	0.820395i
$842$	−4.83102	−	14.8684i	−0.166488	−	0.512398i
$843$		0			0
$844$	−2.84592	−	3.91707i	−0.0979604	−	0.134831i
$845$	4.01504	+	1.30457i	0.138122	+	0.0448785i
$846$		0			0
$847$	1.96385	+	10.8233i	0.0674787	+	0.371892i
$848$			10.8412i			0.372290i
$849$		0			0
$850$	−8.45557	+	6.14333i	−0.290024	+	0.210714i
$851$	−0.172070	+	0.236833i	−0.00589847	+	0.00811854i
$852$		0			0
$853$	−13.3234	+	4.32904i	−0.456185	+	0.148223i	−0.528091	−	0.849188i	$-0.677092\pi$
$853$	−13.3234	+	4.32904i	−0.456185	+	0.148223i	0.0719058	+	0.997411i	$0.477092\pi$
$854$	2.80946	+	2.04119i	0.0961378	+	0.0698482i
$855$		0			0
$856$	−0.670632	+	2.06399i	−0.0229217	+	0.0705458i
$857$	55.7802			1.90541			0.952707	−	0.303890i	$-0.0982855\pi$
$857$	55.7802			1.90541			0.952707	+	0.303890i	$0.0982855\pi$
$858$		0			0
$859$	18.4377			0.629086			0.314543	−	0.949243i	$-0.398149\pi$
$859$	18.4377			0.629086			0.314543	+	0.949243i	$0.398149\pi$
$860$	−0.291277	+	0.896458i	−0.00993246	+	0.0305690i
$861$		0			0
$862$	−21.7193	−	15.7800i	−0.739761	−	0.537468i
$863$	−9.67335	+	3.14306i	−0.329285	+	0.106991i	−0.468994	−	0.883202i	$-0.655383\pi$
$863$	−9.67335	+	3.14306i	−0.329285	+	0.106991i	0.139709	+	0.990193i	$0.455383\pi$
$864$		0			0
$865$	0.376410	−	0.518084i	0.0127983	−	0.0176154i
$866$	9.68358	−	7.03554i	0.329062	−	0.239077i
$867$		0			0
$868$		−	2.62626i		−	0.0891412i
$869$	28.7115	−	2.58371i	0.973970	−	0.0876464i
$870$		0			0
$871$	−1.33196	−	0.432781i	−0.0451319	−	0.0146642i
$872$	−8.06145	−	11.0956i	−0.272995	−	0.375746i
$873$		0			0
$874$	0.230105	+	0.708191i	0.00778343	+	0.0239549i
$875$	1.86919	+	5.75277i	0.0631900	+	0.194479i
$876$		0			0
$877$	2.67990	+	3.68857i	0.0904939	+	0.124554i	0.851863	−	0.523764i	$-0.175473\pi$
$877$	2.67990	+	3.68857i	0.0904939	+	0.124554i	−0.761369	+	0.648318i	$0.775473\pi$
$878$	−24.7751	−	8.04993i	−0.836120	−	0.271672i
$879$		0			0
$880$	−1.79332	−	1.07149i	−0.0604530	−	0.0361200i
$881$		−	40.6879i		−	1.37081i	−0.728161	−	0.685406i	$-0.759625\pi$
$881$		−	40.6879i		−	1.37081i	0.728161	−	0.685406i	$-0.240375\pi$
$882$		0			0
$883$	25.7718	−	18.7243i	0.867291	−	0.630124i	−0.0625679	−	0.998041i	$-0.519929\pi$
$883$	25.7718	−	18.7243i	0.867291	−	0.630124i	0.929859	+	0.367917i	$0.119929\pi$
$884$	3.34907	−	4.60960i	0.112641	−	0.155038i
$885$		0			0
$886$	21.7869	−	7.07898i	0.731944	−	0.237823i
$887$	−11.5175	−	8.36796i	−0.386720	−	0.280969i	0.377390	−	0.926054i	$-0.376822\pi$
$887$	−11.5175	−	8.36796i	−0.386720	−	0.280969i	−0.764110	+	0.645086i	$0.776822\pi$
$888$		0			0
$889$	2.75603	−	8.48218i	0.0924342	−	0.284483i
$890$	−7.22064			−0.242036
$891$		0			0
$892$	26.9023			0.900754
$893$	0.259392	−	0.798326i	0.00868022	−	0.0267150i
$894$		0			0
$895$	−6.04222	−	4.38993i	−0.201969	−	0.146739i
$896$	−0.951057	+	0.309017i	−0.0317726	+	0.0103235i
$897$		0			0
$898$	−11.5032	+	15.8328i	−0.383867	+	0.528347i
$899$	−4.24097	+	3.08125i	−0.141444	+	0.102765i
$900$		0			0
$901$		−	24.6149i		−	0.820042i
$902$	15.3969	+	17.6237i	0.512662	+	0.586804i
$903$		0			0
$904$	0.0198230	+	0.00644088i	0.000659303	+	0.000214220i
$905$	2.23988	+	3.08293i	0.0744561	+	0.102480i
$906$		0			0
$907$	3.15693	+	9.71602i	0.104824	+	0.322615i	0.989689	−	0.143232i	$-0.0457496\pi$
$907$	3.15693	+	9.71602i	0.104824	+	0.322615i	−0.884865	+	0.465847i	$0.845750\pi$
$908$	2.58693	+	7.96175i	0.0858503	+	0.264220i
$909$		0			0
$910$	−0.929087	−	1.27878i	−0.0307990	−	0.0423911i
$911$	−12.0133	−	3.90337i	−0.398020	−	0.129324i	0.103166	−	0.994664i	$-0.467103\pi$
$911$	−12.0133	−	3.90337i	−0.398020	−	0.129324i	−0.501186	+	0.865340i	$0.667103\pi$
$912$		0			0
$913$	−12.4182	−	14.2142i	−0.410983	−	0.470420i
$914$		−	2.78319i		−	0.0920597i
$915$		0			0
$916$	−0.162665	+	0.118183i	−0.00537460	+	0.00390488i
$917$	4.56299	−	6.28042i	0.150683	−	0.207398i
$918$		0			0
$919$	25.8842	−	8.41028i	0.853840	−	0.277429i	0.150786	−	0.988566i	$-0.451819\pi$
$919$	25.8842	−	8.41028i	0.853840	−	0.277429i	0.703054	+	0.711137i	$0.251819\pi$
$920$	3.17503	+	2.30679i	0.104678	+	0.0760527i
$921$		0			0
$922$	−0.979434	+	3.01439i	−0.0322559	+	0.0992736i
$923$	−1.19503			−0.0393348
$924$		0			0
$925$	0.216278			0.00711119
$926$	−1.66297	+	5.11808i	−0.0546484	+	0.168191i
$927$		0			0
$928$	1.61483	+	1.17324i	0.0530094	+	0.0385136i
$929$	−24.1582	+	7.84947i	−0.792605	+	0.257533i	−0.677213	−	0.735787i	$-0.736812\pi$
$929$	−24.1582	+	7.84947i	−0.792605	+	0.257533i	−0.115392	+	0.993320i	$0.536812\pi$
$930$		0			0
$931$	0.0702465	−	0.0966860i	0.00230224	−	0.00316876i
$932$	5.56475	−	4.04302i	0.182279	−	0.132434i
$933$		0			0
$934$		−	14.4480i		−	0.472754i
$935$	4.07172	+	2.43281i	0.133160	+	0.0795615i
$936$		0			0
$937$	−31.7625	−	10.3203i	−1.03764	−	0.337149i	−0.259832	−	0.965654i	$-0.583667\pi$
$937$	−31.7625	−	10.3203i	−1.03764	−	0.337149i	−0.777805	+	0.628505i	$0.783667\pi$
$938$	−0.328034	−	0.451500i	−0.0107107	−	0.0147420i
$939$		0			0
$940$	−1.36711	−	4.20752i	−0.0445901	−	0.137234i
$941$	1.56108	+	4.80451i	0.0508898	+	0.156623i	0.973272	−	0.229656i	$-0.0737602\pi$
$941$	1.56108	+	4.80451i	0.0508898	+	0.156623i	−0.922382	+	0.386279i	$0.873760\pi$
$942$		0			0
$943$	−25.8414	−	35.5676i	−0.841511	−	1.15824i
$944$	12.8111	+	4.16257i	0.416965	+	0.135480i
$945$		0			0
$946$	−4.94330	+	0.444842i	−0.160721	+	0.0144631i
$947$			27.4330i			0.891454i	0.895169	+	0.445727i	$0.147055\pi$
$947$			27.4330i			0.891454i	−0.895169	+	0.445727i	$0.852945\pi$
$948$		0			0
$949$	−30.6904	+	22.2978i	−0.996251	+	0.723819i
$950$	0.323363	−	0.445071i	0.0104913	−	0.0144400i
$951$		0			0
$952$	2.15936	−	0.701620i	0.0699854	−	0.0227396i
$953$	−16.7567	−	12.1745i	−0.542803	−	0.394370i	0.282322	−	0.959320i	$-0.408895\pi$
$953$	−16.7567	−	12.1745i	−0.542803	−	0.394370i	−0.825125	+	0.564950i	$0.808895\pi$
$954$		0			0
$955$	−1.20342	+	3.70375i	−0.0389418	+	0.119851i
$956$	16.7866			0.542917
$957$		0			0
$958$	31.5634			1.01977
$959$	−0.926068	+	2.85014i	−0.0299043	+	0.0920359i
$960$		0			0
$961$	19.4995	+	14.1672i	0.629017	+	0.457008i
$962$	−0.112135	+	0.0364348i	−0.00361537	+	0.00117470i
$963$		0			0
$964$	−12.5638	+	17.2926i	−0.404654	+	0.556958i
$965$	7.58750	−	5.51264i	0.244250	−	0.177458i
$966$		0			0
$967$			17.5452i			0.564217i	0.959382	+	0.282109i	$0.0910338\pi$
$967$			17.5452i			0.564217i	−0.959382	+	0.282109i	$0.908966\pi$
$968$	1.47684	−	10.9004i	0.0474676	−	0.350352i
$969$		0			0
$970$	1.32124	+	0.429297i	0.0424224	+	0.0137839i
$971$	24.5102	+	33.7354i	0.786569	+	1.08262i	0.994527	+	0.104482i	$0.0333183\pi$
$971$	24.5102	+	33.7354i	0.786569	+	1.08262i	−0.207958	+	0.978138i	$0.566682\pi$
$972$		0			0
$973$	−5.03232	−	15.4879i	−0.161329	−	0.496519i
$974$	−10.1243	−	31.1592i	−0.324402	−	0.998407i
$975$		0			0
$976$	−2.04119	−	2.80946i	−0.0653370	−	0.0899287i
$977$	26.9977	+	8.77208i	0.863733	+	0.280644i	0.707187	−	0.707027i	$-0.249964\pi$
$977$	26.9977	+	8.77208i	0.863733	+	0.280644i	0.156546	+	0.987671i	$0.449964\pi$
$978$		0			0
$979$	−14.9426	−	34.9613i	−0.477569	−	1.11737i
$980$		−	0.629871i		−	0.0201205i
$981$		0			0
$982$	−17.8538	+	12.9715i	−0.569737	+	0.413938i
$983$	26.8818	−	36.9996i	0.857395	−	1.18010i	−0.124789	−	0.992183i	$-0.539825\pi$
$983$	26.8818	−	36.9996i	0.857395	−	1.18010i	0.982184	−	0.187920i	$-0.0601746\pi$
$984$		0			0
$985$	−8.74859	+	2.84259i	−0.278753	+	0.0905724i
$986$	−3.66646	−	2.66384i	−0.116764	−	0.0848338i
$987$		0			0
$988$	−0.0926776	+	0.285232i	−0.00294847	+	0.00907445i
$989$	9.32418			0.296492
$990$		0			0
$991$	−43.2114			−1.37265			−0.686327	−	0.727293i	$-0.740778\pi$
$991$	−43.2114			−1.37265			−0.686327	+	0.727293i	$0.740778\pi$
$992$	−0.811560	+	2.49773i	−0.0257671	+	0.0793029i
$993$		0			0
$994$	−0.385255	−	0.279904i	−0.0122196	−	0.00887803i
$995$	−5.15473	+	1.67487i	−0.163416	+	0.0530970i
$996$		0			0
$997$	−3.47760	+	4.78650i	−0.110137	+	0.151590i	−0.860527	−	0.509405i	$-0.829866\pi$
$997$	−3.47760	+	4.78650i	−0.110137	+	0.151590i	0.750390	+	0.660995i	$0.229866\pi$
$998$	−19.6615	+	14.2849i	−0.622373	+	0.452180i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.b.827.6	yes	48
3.2	odd	2		1386.2.bu.a.827.7	✓	48
11.6	odd	10		1386.2.bu.a.1205.7	yes	48
33.17	even	10	inner	1386.2.bu.b.1205.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.7	✓	48	3.2	odd	2
1386.2.bu.a.1205.7	yes	48	11.6	odd	10
1386.2.bu.b.827.6	yes	48	1.1	even	1	trivial
1386.2.bu.b.1205.6	yes	48	33.17	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.599043 + 0.194641i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.599043 + 0.194641i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} -0.629871i q^{10} +(3.04975 - 1.30348i) q^{11} +(-2.38667 - 0.775477i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.701620 - 2.15936i) q^{17} +(0.0702465 + 0.0966860i) q^{19} +(0.599043 + 0.194641i) q^{20} +(0.297258 + 3.30328i) q^{22} -6.23072i q^{23} +(-3.72412 + 2.70573i) q^{25} +(1.47504 - 2.03022i) q^{26} +(0.951057 - 0.309017i) q^{28} +(-1.61483 - 1.17324i) q^{29} +(0.811560 - 2.49773i) q^{31} -1.00000 q^{32} +2.27049 q^{34} +(0.194641 - 0.599043i) q^{35} +(-0.0380106 - 0.0276163i) q^{37} +(-0.113661 + 0.0369308i) q^{38} +(-0.370229 + 0.509576i) q^{40} +(5.70843 - 4.14742i) q^{41} +1.49648i q^{43} +(-3.23346 - 0.738060i) q^{44} +(5.92577 + 1.92540i) q^{46} +(-4.12845 - 5.68232i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-1.42249 - 4.37796i) q^{50} +(1.47504 + 2.03022i) q^{52} +(10.3106 + 3.35013i) q^{53} +(-1.57322 + 1.37444i) q^{55} +1.00000i q^{56} +(1.61483 - 1.17324i) q^{58} +(7.91768 - 10.8978i) q^{59} +(-3.30272 + 1.07312i) q^{61} +(2.12469 + 1.54368i) q^{62} +(0.309017 - 0.951057i) q^{64} +1.58066 q^{65} +0.558084 q^{67} +(-0.701620 + 2.15936i) q^{68} +(0.509576 + 0.370229i) q^{70} +(0.452895 - 0.147154i) q^{71} +(8.88539 - 12.2297i) q^{73} +(0.0380106 - 0.0276163i) q^{74} -0.119511i q^{76} +(-0.738060 + 3.23346i) q^{77} +(8.26641 + 2.68592i) q^{79} +(-0.370229 - 0.509576i) q^{80} +(2.18043 + 6.71066i) q^{82} +(-1.75860 - 5.41240i) q^{83} +(0.840600 + 1.15699i) q^{85} +(-1.42324 - 0.462439i) q^{86} +(1.70113 - 2.84713i) q^{88} -11.4637i q^{89} +(2.03022 - 1.47504i) q^{91} +(-3.66232 + 5.04076i) q^{92} +(6.67997 - 2.17045i) q^{94} +(-0.0608997 - 0.0442462i) q^{95} +(-0.681563 + 2.09763i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

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