LMFDB - Embedded newform 756.2.bb.a.611.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.17
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.614155 + 1.27390i) q^{2} +(-1.24563 - 1.56474i) q^{4} +(3.69227 - 2.13173i) q^{5} +(-1.08153 - 2.41460i) q^{7} +(2.75833 - 0.625806i) q^{8} +O(q^{10})$	\(q+(-0.614155 + 1.27390i) q^{2} +(-1.24563 - 1.56474i) q^{4} +(3.69227 - 2.13173i) q^{5} +(-1.08153 - 2.41460i) q^{7} +(2.75833 - 0.625806i) q^{8} +(0.447980 + 6.01278i) q^{10} +(-0.425873 + 0.737633i) q^{11} +(-1.70346 + 2.95047i) q^{13} +(3.74018 + 0.105182i) q^{14} +(-0.896829 + 3.89817i) q^{16} +(2.96593 - 1.71238i) q^{17} +(-0.287188 - 0.165808i) q^{19} +(-7.93479 - 3.12210i) q^{20} +(-0.678117 - 0.995539i) q^{22} +(-2.12777 - 3.68541i) q^{23} +(6.58855 - 11.4117i) q^{25} +(-2.71241 - 3.98208i) q^{26} +(-2.43104 + 4.70000i) q^{28} +(3.76358 - 2.17290i) q^{29} -6.05964i q^{31} +(-4.41507 - 3.53655i) q^{32} +(0.359855 + 4.82996i) q^{34} +(-9.14057 - 6.60981i) q^{35} +(-0.964162 + 1.66998i) q^{37} +(0.387601 - 0.264016i) q^{38} +(8.85043 - 8.19065i) q^{40} +(-3.23608 - 1.86835i) q^{41} +(2.03904 - 1.17724i) q^{43} +(1.68468 - 0.252435i) q^{44} +(6.00161 - 0.447148i) q^{46} +5.34880 q^{47} +(-4.66059 + 5.22292i) q^{49} +(10.4909 + 15.4017i) q^{50} +(6.73860 - 1.00972i) q^{52} +(3.31113 - 1.91168i) q^{53} +3.63138i q^{55} +(-4.49428 - 5.98343i) q^{56} +(0.456633 + 6.12891i) q^{58} -2.42512 q^{59} -8.45286 q^{61} +(7.71935 + 3.72156i) q^{62} +(7.21673 - 3.45235i) q^{64} +14.5252i q^{65} +10.9500i q^{67} +(-6.37388 - 2.50793i) q^{68} +(14.0340 - 7.58469i) q^{70} +13.9538 q^{71} +(-4.39078 - 7.60506i) q^{73} +(-1.53523 - 2.25387i) q^{74} +(0.0982825 + 0.655911i) q^{76} +(2.24168 + 0.230540i) q^{77} -4.69272i q^{79} +(4.99851 + 16.3049i) q^{80} +(4.36754 - 2.97497i) q^{82} +(1.15741 + 2.00470i) q^{83} +(7.30067 - 12.6451i) q^{85} +(0.247395 + 3.32053i) q^{86} +(-0.713081 + 2.30115i) q^{88} +(7.69912 + 4.44509i) q^{89} +(8.96655 + 0.922141i) q^{91} +(-3.11630 + 7.92005i) q^{92} +(-3.28499 + 6.81382i) q^{94} -1.41383 q^{95} +(3.69412 + 6.39841i) q^{97} +(-3.79114 - 9.14479i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.614155	+	1.27390i	−0.434273	+	0.900781i
$2$	−0.614155	+	1.27390i	−0.434273	+	0.900781i
$3$		0			0
$3$		0			0
$4$	−1.24563	−	1.56474i	−0.622813	−	0.782371i
$5$	3.69227	−	2.13173i	1.65123	−	0.953339i	0.674664	−	0.738125i	$-0.264288\pi$
$5$	3.69227	−	2.13173i	1.65123	−	0.953339i	0.976567	−	0.215214i	$-0.0690449\pi$
$6$		0			0
$7$	−1.08153	−	2.41460i	−0.408780	−	0.912633i
$7$	−1.08153	−	2.41460i	−0.408780	−	0.912633i
$8$	2.75833	−	0.625806i	0.975216	−	0.221256i
$9$		0			0
$10$	0.447980	+	6.01278i	0.141664	+	1.90141i
$11$	−0.425873	+	0.737633i	−0.128405	+	0.222405i	−0.923059	−	0.384658i	$-0.874319\pi$
$11$	−0.425873	+	0.737633i	−0.128405	+	0.222405i	0.794654	+	0.607063i	$0.207653\pi$
$12$		0			0
$13$	−1.70346	+	2.95047i	−0.472454	+	0.818314i	−0.999503	−	0.0315208i	$-0.989965\pi$
$13$	−1.70346	+	2.95047i	−0.472454	+	0.818314i	0.527049	+	0.849835i	$0.323298\pi$
$14$	3.74018	+	0.105182i	0.999605	+	0.0281111i
$15$		0			0
$16$	−0.896829	+	3.89817i	−0.224207	+	0.974541i
$17$	2.96593	−	1.71238i	0.719344	−	0.415314i	−0.0951669	−	0.995461i	$-0.530338\pi$
$17$	2.96593	−	1.71238i	0.719344	−	0.415314i	0.814511	+	0.580148i	$0.197005\pi$
$18$		0			0
$19$	−0.287188	−	0.165808i	−0.0658856	−	0.0380390i	0.466695	−	0.884418i	$-0.345444\pi$
$19$	−0.287188	−	0.165808i	−0.0658856	−	0.0380390i	−0.532581	+	0.846379i	$0.678778\pi$
$20$	−7.93479	−	3.12210i	−1.77427	−	0.698123i
$21$		0			0
$22$	−0.678117	−	0.995539i	−0.144575	−	0.212250i
$23$	−2.12777	−	3.68541i	−0.443671	−	0.768461i	0.554288	−	0.832325i	$-0.312991\pi$
$23$	−2.12777	−	3.68541i	−0.443671	−	0.768461i	−0.997959	+	0.0638644i	$0.979657\pi$
$24$		0			0
$25$	6.58855	−	11.4117i	1.31771	−	2.28234i
$26$	−2.71241	−	3.98208i	−0.531948	−	0.780949i
$27$		0			0
$28$	−2.43104	+	4.70000i	−0.459424	+	0.888217i
$29$	3.76358	−	2.17290i	0.698879	−	0.403498i	−0.108051	−	0.994145i	$-0.534461\pi$
$29$	3.76358	−	2.17290i	0.698879	−	0.403498i	0.806930	+	0.590647i	$0.201128\pi$
$30$		0			0
$31$		−	6.05964i		−	1.08834i	−0.838974	−	0.544171i	$-0.816844\pi$
$31$		−	6.05964i		−	1.08834i	0.838974	−	0.544171i	$-0.183156\pi$
$32$	−4.41507	−	3.53655i	−0.780481	−	0.625179i
$33$		0			0
$34$	0.359855	+	4.82996i	0.0617146	+	0.828332i
$35$	−9.14057	−	6.60981i	−1.54504	−	1.11726i
$36$		0			0
$37$	−0.964162	+	1.66998i	−0.158507	+	0.274543i	−0.934331	−	0.356408i	$-0.884001\pi$
$37$	−0.964162	+	1.66998i	−0.158507	+	0.274543i	0.775823	+	0.630950i	$0.217335\pi$
$38$	0.387601	−	0.264016i	0.0628772	−	0.0428291i
$39$		0			0
$40$	8.85043	−	8.19065i	1.39938	−	1.29506i
$41$	−3.23608	−	1.86835i	−0.505391	−	0.291788i	0.225546	−	0.974232i	$-0.427583\pi$
$41$	−3.23608	−	1.86835i	−0.505391	−	0.291788i	−0.730937	+	0.682445i	$0.760917\pi$
$42$		0			0
$43$	2.03904	−	1.17724i	0.310950	−	0.179527i	−0.336401	−	0.941719i	$-0.609210\pi$
$43$	2.03904	−	1.17724i	0.310950	−	0.179527i	0.647352	+	0.762192i	$0.275877\pi$
$44$	1.68468	−	0.252435i	0.253976	−	0.0380560i
$45$		0			0
$46$	6.00161	−	0.447148i	0.884890	−	0.0659284i
$47$	5.34880			0.780202			0.390101	−	0.920772i	$-0.372440\pi$
$47$	5.34880			0.780202			0.390101	+	0.920772i	$0.372440\pi$
$48$		0			0
$49$	−4.66059	+	5.22292i	−0.665798	+	0.746132i
$50$	10.4909	+	15.4017i	1.48364	+	2.17813i
$51$		0			0
$52$	6.73860	−	1.00972i	0.934475	−	0.140023i
$53$	3.31113	−	1.91168i	0.454818	−	0.262589i	−0.255045	−	0.966929i	$-0.582090\pi$
$53$	3.31113	−	1.91168i	0.454818	−	0.262589i	0.709863	+	0.704340i	$0.248757\pi$
$54$		0			0
$55$			3.63138i			0.489656i
$56$	−4.49428	−	5.98343i	−0.600574	−	0.799569i
$57$		0			0
$58$	0.456633	+	6.12891i	0.0599588	+	0.804765i
$59$	−2.42512			−0.315724			−0.157862	−	0.987461i	$-0.550460\pi$
$59$	−2.42512			−0.315724			−0.157862	+	0.987461i	$0.550460\pi$
$60$		0			0
$61$	−8.45286			−1.08228			−0.541139	−	0.840933i	$-0.682007\pi$
$61$	−8.45286			−1.08228			−0.541139	+	0.840933i	$0.682007\pi$
$62$	7.71935	+	3.72156i	0.980359	+	0.472638i
$63$		0			0
$64$	7.21673	−	3.45235i	0.902092	−	0.431544i
$65$			14.5252i			1.80163i
$66$		0			0
$67$			10.9500i			1.33776i	0.743370	+	0.668880i	$0.233226\pi$
$67$			10.9500i			1.33776i	−0.743370	+	0.668880i	$0.766774\pi$
$68$	−6.37388	−	2.50793i	−0.772946	−	0.304131i
$69$		0			0
$70$	14.0340	−	7.58469i	1.67738	−	0.906544i
$71$	13.9538			1.65601			0.828003	−	0.560724i	$-0.189477\pi$
$71$	13.9538			1.65601			0.828003	+	0.560724i	$0.189477\pi$
$72$		0			0
$73$	−4.39078	−	7.60506i	−0.513902	−	0.890105i	−0.999870	−	0.0161279i	$-0.994866\pi$
$73$	−4.39078	−	7.60506i	−0.513902	−	0.890105i	0.485968	−	0.873977i	$-0.338467\pi$
$74$	−1.53523	−	2.25387i	−0.178467	−	0.262007i
$75$		0			0
$76$	0.0982825	+	0.655911i	0.0112738	+	0.0752381i
$77$	2.24168	+	0.230540i	0.255463	+	0.0262725i
$78$		0			0
$79$		−	4.69272i		−	0.527972i	−0.964526	−	0.263986i	$-0.914963\pi$
$79$		−	4.69272i		−	0.527972i	0.964526	−	0.263986i	$-0.0850373\pi$
$80$	4.99851	+	16.3049i	0.558850	+	1.82294i
$81$		0			0
$82$	4.36754	−	2.97497i	0.482314	−	0.328531i
$83$	1.15741	+	2.00470i	0.127043	+	0.220044i	0.922530	−	0.385926i	$-0.126118\pi$
$83$	1.15741	+	2.00470i	0.127043	+	0.220044i	−0.795487	+	0.605971i	$0.792785\pi$
$84$		0			0
$85$	7.30067	−	12.6451i	0.791869	−	1.37156i
$86$	0.247395	+	3.32053i	0.0266773	+	0.358062i
$87$		0			0
$88$	−0.713081	+	2.30115i	−0.0760147	+	0.245303i
$89$	7.69912	+	4.44509i	0.816105	+	0.471178i	0.849071	−	0.528278i	$-0.177162\pi$
$89$	7.69912	+	4.44509i	0.816105	+	0.471178i	−0.0329666	+	0.999456i	$0.510495\pi$
$90$		0			0
$91$	8.96655	+	0.922141i	0.939950	+	0.0966666i
$92$	−3.11630	+	7.92005i	−0.324897	+	0.825723i
$93$		0			0
$94$	−3.28499	+	6.81382i	−0.338821	+	0.702791i
$95$	−1.41383			−0.145056
$96$		0			0
$97$	3.69412	+	6.39841i	0.375081	+	0.649660i	0.990339	−	0.138666i	$-0.0442815\pi$
$97$	3.69412	+	6.39841i	0.375081	+	0.649660i	−0.615258	+	0.788326i	$0.710948\pi$
$98$	−3.79114	−	9.14479i	−0.382963	−	0.923764i
$99$		0			0
$100$	−26.0632	+	3.90534i	−2.60632	+	0.390534i
$101$	−5.67148	−	3.27443i	−0.564333	−	0.325818i	0.190550	−	0.981678i	$-0.438973\pi$
$101$	−5.67148	−	3.27443i	−0.564333	−	0.325818i	−0.754883	+	0.655860i	$0.772306\pi$
$102$		0			0
$103$	−7.01954	+	4.05273i	−0.691656	+	0.399328i	−0.804232	−	0.594316i	$-0.797423\pi$
$103$	−7.01954	+	4.05273i	−0.691656	+	0.399328i	0.112576	+	0.993643i	$0.464090\pi$
$104$	−2.85227	+	9.20440i	−0.279688	+	0.902566i
$105$		0			0
$106$	0.401737	+	5.39210i	0.0390201	+	0.523727i
$107$	−1.91800	+	3.32207i	−0.185420	+	0.321157i	−0.943718	−	0.330751i	$-0.892698\pi$
$107$	−1.91800	+	3.32207i	−0.185420	+	0.321157i	0.758298	+	0.651908i	$0.226031\pi$
$108$		0			0
$109$	−2.20783	−	3.82408i	−0.211472	−	0.366280i	0.740704	−	0.671832i	$-0.234492\pi$
$109$	−2.20783	−	3.82408i	−0.211472	−	0.366280i	−0.952175	+	0.305552i	$0.901159\pi$
$110$	−4.62601	−	2.23023i	−0.441072	−	0.212644i
$111$		0			0
$112$	10.3825	−	2.05050i	0.981050	−	0.193754i
$113$	0.130662	+	0.0754377i	0.0122916	+	0.00709658i	0.506133	−	0.862455i	$-0.331074\pi$
$113$	0.130662	+	0.0754377i	0.0122916	+	0.00709658i	−0.493842	+	0.869552i	$0.664408\pi$
$114$		0			0
$115$	−15.7126	−	9.07167i	−1.46521	−	0.845938i
$116$	−8.08804	−	3.18240i	−0.750956	−	0.295478i
$117$		0			0
$118$	1.48940	−	3.08935i	0.137110	−	0.284398i
$119$	−7.34246	−	5.30955i	−0.673082	−	0.486726i
$120$		0			0
$121$	5.13726	+	8.89800i	0.467024	+	0.808909i
$122$	5.19137	−	10.7681i	0.470005	−	0.974896i
$123$		0			0
$124$	−9.48176	+	7.54804i	−0.851487	+	0.677834i
$125$		−	34.8627i		−	3.11822i
$126$		0			0
$127$			18.6526i			1.65515i	0.561357	+	0.827573i	$0.310279\pi$
$127$			18.6526i			1.65515i	−0.561357	+	0.827573i	$0.689721\pi$
$128$	−0.0342542	+	11.3137i	−0.00302767	+	0.999995i
$129$		0			0
$130$	−18.5037	−	8.92075i	−1.62288	−	0.782402i
$131$	8.90019	+	15.4156i	0.777613	+	1.34687i	0.933314	+	0.359061i	$0.116903\pi$
$131$	8.90019	+	15.4156i	0.777613	+	1.34687i	−0.155701	+	0.987804i	$0.549764\pi$
$132$		0			0
$133$	−0.0897579	+	0.872772i	−0.00778300	+	0.0756789i
$134$	−13.9492	−	6.72503i	−1.20503	−	0.580954i
$135$		0			0
$136$	7.10939	−	6.57941i	0.609626	−	0.564180i
$137$	−6.73469	−	3.88827i	−0.575383	−	0.332198i	0.183913	−	0.982942i	$-0.441123\pi$
$137$	−6.73469	−	3.88827i	−0.575383	−	0.332198i	−0.759297	+	0.650745i	$0.774457\pi$
$138$		0			0
$139$	10.1853	+	5.88047i	0.863903	+	0.498775i	0.865317	−	0.501224i	$-0.167117\pi$
$139$	10.1853	+	5.88047i	0.863903	+	0.498775i	−0.00141439	+	0.999999i	$0.500450\pi$
$140$	1.04309	+	22.5360i	0.0881572	+	1.90464i
$141$		0			0
$142$	−8.56977	+	17.7756i	−0.719159	+	1.49170i
$143$	−1.45091	−	2.51305i	−0.121331	−	0.210152i
$144$		0			0
$145$	9.26408	−	16.0459i	0.769340	−	1.33254i
$146$	12.3847	−	0.922717i	1.02496	−	0.0763646i
$147$		0			0
$148$	3.81407	−	0.571505i	0.313515	−	0.0469774i
$149$	3.24952	−	1.87611i	0.266211	−	0.153697i	−0.360953	−	0.932584i	$-0.617549\pi$
$149$	3.24952	−	1.87611i	0.266211	−	0.153697i	0.627165	+	0.778887i	$0.284215\pi$
$150$		0			0
$151$	3.01746	+	1.74213i	0.245558	+	0.141773i	0.617728	−	0.786391i	$-0.288053\pi$
$151$	3.01746	+	1.74213i	0.245558	+	0.141773i	−0.372171	+	0.928164i	$0.621386\pi$
$152$	−0.895924	−	0.277629i	−0.0726690	−	0.0225187i
$153$		0			0
$154$	−1.67043	+	2.71409i	−0.134607	+	0.218707i
$155$	−12.9175	−	22.3738i	−1.03756	−	1.79711i
$156$		0			0
$157$	−2.90923			−0.232182			−0.116091	−	0.993239i	$-0.537036\pi$
$157$	−2.90923			−0.232182			−0.116091	+	0.993239i	$0.537036\pi$
$158$	5.97804	+	2.88206i	0.475588	+	0.229284i
$159$		0			0
$160$	−23.8406	−	3.64613i	−1.88476	−	0.288252i
$161$	−6.59754	+	9.12360i	−0.519959	+	0.719040i
$162$		0			0
$163$	−11.4224	−	6.59470i	−0.894668	−	0.516537i	−0.0192018	−	0.999816i	$-0.506112\pi$
$163$	−11.4224	−	6.59470i	−0.894668	−	0.516537i	−0.875467	+	0.483279i	$0.839446\pi$
$164$	1.10746	+	7.39090i	0.0864781	+	0.577132i
$165$		0			0
$166$	−3.26461	+	0.243229i	−0.253383	+	0.0188782i
$167$	−2.19364	+	3.79950i	−0.169749	+	0.294014i	−0.938332	−	0.345737i	$-0.887629\pi$
$167$	−2.19364	+	3.79950i	−0.169749	+	0.294014i	0.768582	+	0.639751i	$0.220962\pi$
$168$		0			0
$169$	0.696475	+	1.20633i	0.0535750	+	0.0927946i
$170$	11.6249	+	17.0664i	0.891586	+	1.30893i
$171$		0			0
$172$	−4.38195	−	1.72417i	−0.334121	−	0.131466i
$173$		−	14.1229i		−	1.07375i	−0.843663	−	0.536874i	$-0.819605\pi$
$173$		−	14.1229i		−	1.07375i	0.843663	−	0.536874i	$-0.180395\pi$
$174$		0			0
$175$	−34.6804	−	3.56661i	−2.62159	−	0.269611i
$176$	−2.49348	−	2.32165i	−0.187953	−	0.175001i
$177$		0			0
$178$	−10.3910	+	7.07791i	−0.778841	+	0.530512i
$179$	7.83236	+	13.5661i	0.585418	+	1.01397i	0.994823	+	0.101622i	$0.0324031\pi$
$179$	7.83236	+	13.5661i	0.585418	+	1.01397i	−0.409405	+	0.912353i	$0.634264\pi$
$180$		0			0
$181$	7.43944			0.552970			0.276485	−	0.961018i	$-0.410830\pi$
$181$	7.43944			0.552970			0.276485	+	0.961018i	$0.410830\pi$
$182$	−6.68157	+	10.8561i	−0.495271	+	0.804709i
$183$		0			0
$184$	−8.17544	−	8.83399i	−0.602701	−	0.651250i
$185$			8.22134i			0.604445i
$186$		0			0
$187$			2.91703i			0.213314i
$188$	−6.66260	−	8.36948i	−0.485920	−	0.610407i
$189$		0			0
$190$	0.868314	−	1.80108i	0.0629941	−	0.130664i
$191$	0.440702			0.0318881			0.0159441	−	0.999873i	$-0.494925\pi$
$191$	0.440702			0.0318881			0.0159441	+	0.999873i	$0.494925\pi$
$192$		0			0
$193$	1.76604			0.127122			0.0635610	−	0.997978i	$-0.479754\pi$
$193$	1.76604			0.127122			0.0635610	+	0.997978i	$0.479754\pi$
$194$	−10.4197	+	0.776315i	−0.748089	+	0.0557362i
$195$		0			0
$196$	13.9779	+	0.786799i	0.998420	+	0.0561999i
$197$			20.2138i			1.44017i	0.693884	+	0.720086i	$0.255898\pi$
$197$			20.2138i			1.44017i	−0.693884	+	0.720086i	$0.744102\pi$
$198$		0			0
$199$	11.8547	−	6.84431i	0.840357	−	0.485180i	−0.0170285	−	0.999855i	$-0.505421\pi$
$199$	11.8547	−	6.84431i	0.840357	−	0.485180i	0.857386	+	0.514675i	$0.172087\pi$
$200$	11.0319	−	35.6003i	0.780070	−	2.51732i
$201$		0			0
$202$	7.65446	−	5.21387i	0.538566	−	0.366847i
$203$	−9.31711	−	6.73748i	−0.653933	−	0.472878i
$204$		0			0
$205$	−15.9313			−1.11269
$206$	−0.851676	−	11.4312i	−0.0593391	−	0.796448i
$207$		0			0
$208$	−9.97372	−	9.28642i	−0.691553	−	0.643898i
$209$	0.244611	−	0.141227i	0.0169201	−	0.00976884i
$210$		0			0
$211$	−11.4244	−	6.59590i	−0.786491	−	0.454081i	0.0522349	−	0.998635i	$-0.483366\pi$
$211$	−11.4244	−	6.59590i	−0.786491	−	0.454081i	−0.838726	+	0.544554i	$0.816699\pi$
$212$	−7.11571	−	2.79982i	−0.488709	−	0.192292i
$213$		0			0
$214$	−3.05403	−	4.48360i	−0.208769	−	0.306493i
$215$	5.01911	−	8.69335i	0.342300	−	0.592882i
$216$		0			0
$217$	−14.6316	+	6.55368i	−0.993257	+	0.444893i
$218$	6.22743	−	0.463973i	0.421775	−	0.0314242i
$219$		0			0
$220$	5.68217	−	4.52335i	0.383092	−	0.304964i
$221$			11.6679i			0.784866i
$222$		0			0
$223$	21.8841	−	12.6348i	1.46547	−	0.846087i	0.466211	−	0.884673i	$-0.345619\pi$
$223$	21.8841	−	12.6348i	1.46547	−	0.846087i	0.999255	+	0.0385860i	$0.0122854\pi$
$224$	−3.76432	+	14.4855i	−0.251514	+	0.967854i
$225$		0			0
$226$	−0.176347	+	0.120119i	−0.0117304	+	0.00799022i
$227$	−3.96587	+	6.86909i	−0.263224	+	0.455917i	−0.967097	−	0.254409i	$-0.918119\pi$
$227$	−3.96587	+	6.86909i	−0.263224	+	0.455917i	0.703873	+	0.710326i	$0.251453\pi$
$228$		0			0
$229$	3.63237	+	6.29145i	0.240034	+	0.415751i	0.960724	−	0.277507i	$-0.0895081\pi$
$229$	3.63237	+	6.29145i	0.240034	+	0.415751i	−0.720690	+	0.693258i	$0.756175\pi$
$230$	21.2063	−	14.4448i	1.39831	−	0.952463i
$231$		0			0
$232$	9.02136	−	8.34884i	0.592282	−	0.548128i
$233$	−19.2592	−	11.1193i	−1.26171	−	0.728450i	−0.288307	−	0.957538i	$-0.593092\pi$
$233$	−19.2592	−	11.1193i	−1.26171	−	0.728450i	−0.973406	+	0.229088i	$0.926426\pi$
$234$		0			0
$235$	19.7492	−	11.4022i	1.28829	−	0.743797i
$236$	3.02079	+	3.79469i	0.196637	+	0.247013i
$237$		0			0
$238$	11.2732	−	6.09265i	0.730735	−	0.394928i
$239$	−8.54515	+	14.8006i	−0.552740	+	0.957374i	0.445335	+	0.895364i	$0.353084\pi$
$239$	−8.54515	+	14.8006i	−0.552740	+	0.957374i	−0.998076	+	0.0620101i	$0.980249\pi$
$240$		0			0
$241$	−2.82104	+	4.88618i	−0.181719	+	0.314747i	−0.942466	−	0.334302i	$-0.891500\pi$
$241$	−2.82104	+	4.88618i	−0.181719	+	0.314747i	0.760747	+	0.649049i	$0.224833\pi$
$242$	−14.4902	+	1.07959i	−0.931466	+	0.0693986i
$243$		0			0
$244$	10.5291	+	13.2265i	0.674057	+	0.846743i
$245$	−6.07426	+	29.2195i	−0.388070	+	1.86677i
$246$		0			0
$247$	0.978426	−	0.564894i	0.0622558	−	0.0359434i
$248$	−3.79215	−	16.7145i	−0.240802	−	1.06137i
$249$		0			0
$250$	44.4115	+	21.4111i	2.80883	+	1.35416i
$251$	4.80568			0.303332			0.151666	−	0.988432i	$-0.451536\pi$
$251$	4.80568			0.303332			0.151666	+	0.988432i	$0.451536\pi$
$252$		0			0
$253$	3.62464			0.227879
$254$	−23.7614	−	11.4556i	−1.49093	−	0.718786i
$255$		0			0
$256$	−14.3914	−	6.99198i	−0.899462	−	0.436999i
$257$	−4.21723	+	2.43482i	−0.263063	+	0.151880i	−0.625731	−	0.780039i	$-0.715199\pi$
$257$	−4.21723	+	2.43482i	−0.263063	+	0.151880i	0.362668	+	0.931918i	$0.381866\pi$
$258$		0			0
$259$	5.07510	+	0.521935i	0.315351	+	0.0324315i
$260$	22.7282	−	18.0930i	1.40955	−	1.12208i
$261$		0			0
$262$	−25.1040	+	1.87036i	−1.55093	+	0.115551i
$263$	−0.561213	+	0.972049i	−0.0346058	+	0.0599391i	−0.882810	−	0.469731i	$-0.844351\pi$
$263$	−0.561213	+	0.972049i	−0.0346058	+	0.0599391i	0.848204	+	0.529670i	$0.177684\pi$
$264$		0			0
$265$	8.15037	−	14.1169i	0.500673	−	0.867192i
$266$	−1.05670	−	0.650360i	−0.0647902	−	0.0398761i
$267$		0			0
$268$	17.1340	−	13.6397i	1.04662	−	0.833175i
$269$	10.0188	−	5.78433i	0.610854	−	0.352677i	−0.162446	−	0.986718i	$-0.551938\pi$
$269$	10.0188	−	5.78433i	0.610854	−	0.352677i	0.773300	+	0.634041i	$0.218605\pi$
$270$		0			0
$271$	−1.44803	−	0.836019i	−0.0879614	−	0.0507845i	0.455374	−	0.890300i	$-0.349506\pi$
$271$	−1.44803	−	0.836019i	−0.0879614	−	0.0507845i	−0.543336	+	0.839516i	$0.682839\pi$
$272$	4.01521	+	13.0974i	0.243458	+	0.794147i
$273$		0			0
$274$	9.08941	−	6.19129i	0.549111	−	0.374030i
$275$	5.61177	+	9.71986i	0.338402	+	0.586130i
$276$		0			0
$277$	−5.72341	+	9.91325i	−0.343887	+	0.595629i	−0.985151	−	0.171691i	$-0.945077\pi$
$277$	−5.72341	+	9.91325i	−0.343887	+	0.595629i	0.641264	+	0.767320i	$0.278410\pi$
$278$	−13.7464	+	9.36346i	−0.824457	+	0.561583i
$279$		0			0
$280$	−29.3491	−	12.5118i	−1.75395	−	0.747723i
$281$	6.49280	−	3.74862i	0.387328	−	0.223624i	−0.293674	−	0.955906i	$-0.594878\pi$
$281$	6.49280	−	3.74862i	0.387328	−	0.223624i	0.681002	+	0.732282i	$0.261545\pi$
$282$		0			0
$283$			29.9378i			1.77962i	0.456335	+	0.889808i	$0.349162\pi$
$283$			29.9378i			1.77962i	−0.456335	+	0.889808i	$0.650838\pi$
$284$	−17.3812	−	21.8340i	−1.03138	−	1.29561i
$285$		0			0
$286$	4.09245	−	0.304907i	0.241992	−	0.0180295i
$287$	−1.01140	+	9.83452i	−0.0597013	+	0.580513i
$288$		0			0
$289$	−2.63549	+	4.56481i	−0.155029	+	0.268518i
$290$	14.7512	+	21.6561i	0.866220	+	1.27169i
$291$		0			0
$292$	−6.43067	+	16.3435i	−0.376327	+	0.956431i
$293$	26.8301	+	15.4904i	1.56743	+	0.904958i	0.996467	+	0.0839853i	$0.0267649\pi$
$293$	26.8301	+	15.4904i	1.56743	+	0.904958i	0.570967	+	0.820973i	$0.306568\pi$
$294$		0			0
$295$	−8.95419	+	5.16970i	−0.521333	+	0.300992i
$296$	−1.61439	+	5.20972i	−0.0938347	+	0.302809i
$297$		0			0
$298$	0.394262	+	5.29178i	0.0228390	+	0.306544i
$299$	14.4983			0.838456
$300$		0			0
$301$	−5.04784	−	3.65024i	−0.290953	−	0.210396i
$302$	−4.07249	+	2.77400i	−0.234346	+	0.159626i
$303$		0			0
$304$	0.903908	−	0.970807i	0.0518427	−	0.0556796i
$305$	−31.2102	+	18.0192i	−1.78709	+	1.03178i
$306$		0			0
$307$			19.8714i			1.13412i	0.823677	+	0.567060i	$0.191919\pi$
$307$			19.8714i			1.13412i	−0.823677	+	0.567060i	$0.808081\pi$
$308$	−2.43156	−	3.79482i	−0.138551	−	0.216230i
$309$		0			0
$310$	36.4352	−	2.71460i	2.06938	−	0.154179i
$311$	30.0052			1.70144			0.850721	−	0.525618i	$-0.176166\pi$
$311$	30.0052			1.70144			0.850721	+	0.525618i	$0.176166\pi$
$312$		0			0
$313$	−27.9646			−1.58065			−0.790326	−	0.612686i	$-0.790089\pi$
$313$	−27.9646			−1.58065			−0.790326	+	0.612686i	$0.790089\pi$
$314$	1.78672	−	3.70606i	0.100830	−	0.209145i
$315$		0			0
$316$	−7.34289	+	5.84538i	−0.413070	+	0.328828i
$317$			3.77058i			0.211777i	0.994378	+	0.105888i	$0.0337686\pi$
$317$			3.77058i			0.211777i	−0.994378	+	0.105888i	$0.966231\pi$
$318$		0			0
$319$			3.70152i			0.207245i
$320$	19.2866	−	28.1311i	1.07815	−	1.57258i
$321$		0			0
$322$	−7.57061	−	14.0079i	−0.421893	−	0.780629i
$323$	−1.13571			−0.0631925
$324$		0			0
$325$	22.4466	+	38.8787i	1.24511	+	2.15660i
$326$	15.4161	−	10.5007i	0.853818	−	0.581582i
$327$		0			0
$328$	−10.0954	−	3.12837i	−0.557425	−	0.172735i
$329$	−5.78488	−	12.9152i	−0.318931	−	0.712038i
$330$		0			0
$331$		−	9.44739i		−	0.519276i	−0.965706	−	0.259638i	$-0.916397\pi$
$331$		−	9.44739i		−	0.519276i	0.965706	−	0.259638i	$-0.0836032\pi$
$332$	1.69513	−	4.30816i	0.0930324	−	0.236441i
$333$		0			0
$334$	−3.49293	−	5.12796i	−0.191125	−	0.280589i
$335$	23.3425	+	40.4305i	1.27534	+	2.20895i
$336$		0			0
$337$	−10.9656	+	18.9929i	−0.597333	+	1.03461i	0.395881	+	0.918302i	$0.370439\pi$
$337$	−10.9656	+	18.9929i	−0.597333	+	1.03461i	−0.993213	+	0.116308i	$0.962894\pi$
$338$	−1.96448	+	0.146363i	−0.106854	+	0.00796111i
$339$		0			0
$340$	−28.8803	+	4.32745i	−1.56625	+	0.234689i
$341$	4.46979	+	2.58063i	0.242053	+	0.139749i
$342$		0			0
$343$	17.6518	+	5.60470i	0.953110	+	0.302626i
$344$	4.88761	−	4.52325i	0.263522	−	0.243877i
$345$		0			0
$346$	17.9912	+	8.67368i	0.967211	+	0.466300i
$347$	−23.3765			−1.25491			−0.627457	−	0.778651i	$-0.715904\pi$
$347$	−23.3765			−1.25491			−0.627457	+	0.778651i	$0.715904\pi$
$348$		0			0
$349$	4.35929	+	7.55051i	0.233347	+	0.404169i	0.958791	−	0.284112i	$-0.0916988\pi$
$349$	4.35929	+	7.55051i	0.233347	+	0.404169i	−0.725444	+	0.688281i	$0.758365\pi$
$350$	25.8426	−	41.9888i	1.38135	−	2.24440i
$351$		0			0
$352$	4.48893	−	1.75058i	0.239261	−	0.0933063i
$353$	−17.9123	−	10.3417i	−0.953376	−	0.550432i	−0.0592482	−	0.998243i	$-0.518870\pi$
$353$	−17.9123	−	10.3417i	−0.953376	−	0.550432i	−0.894128	+	0.447811i	$0.852204\pi$
$354$		0			0
$355$	51.5210	−	29.7456i	2.73445	−	1.57873i
$356$	−2.63481	−	17.5840i	−0.139645	−	0.931953i
$357$		0			0
$358$	−22.0920	+	1.64596i	−1.16760	+	0.0869917i
$359$	−8.63068	+	14.9488i	−0.455510	+	0.788966i	−0.998717	−	0.0506324i	$-0.983876\pi$
$359$	−8.63068	+	14.9488i	−0.455510	+	0.788966i	0.543208	+	0.839598i	$0.317210\pi$
$360$		0			0
$361$	−9.44502	−	16.3592i	−0.497106	−	0.861013i
$362$	−4.56897	+	9.47708i	−0.240140	+	0.498104i
$363$		0			0
$364$	−9.72606	−	15.1790i	−0.509784	−	0.795594i
$365$	−32.4239	−	18.7199i	−1.69714	−	0.979846i
$366$		0			0
$367$	−7.75182	−	4.47552i	−0.404642	−	0.233620i	0.283843	−	0.958871i	$-0.408391\pi$
$367$	−7.75182	−	4.47552i	−0.404642	−	0.233620i	−0.688485	+	0.725251i	$0.741724\pi$
$368$	16.2746	−	4.98922i	0.848371	−	0.260081i
$369$		0			0
$370$	−10.4731	−	5.04918i	−0.544472	−	0.262494i
$371$	−8.19702	−	5.92751i	−0.425568	−	0.307741i
$372$		0			0
$373$	13.2643	+	22.9744i	0.686799	+	1.18957i	0.972868	+	0.231362i	$0.0743181\pi$
$373$	13.2643	+	22.9744i	0.686799	+	1.18957i	−0.286069	+	0.958209i	$0.592349\pi$
$374$	−3.71599	−	1.79151i	−0.192149	−	0.0926367i
$375$		0			0
$376$	14.7537	−	3.34731i	0.760866	−	0.172624i
$377$			14.8058i			0.762536i
$378$		0			0
$379$		−	31.0493i		−	1.59490i	−0.603387	−	0.797449i	$-0.706183\pi$
$379$		−	31.0493i		−	1.59490i	0.603387	−	0.797449i	$-0.293817\pi$
$380$	1.76111	+	2.21229i	0.0903430	+	0.113488i
$381$		0			0
$382$	−0.270660	+	0.561409i	−0.0138482	+	0.0287242i
$383$	−19.0825	−	33.0519i	−0.975070	−	1.68887i	−0.679704	−	0.733487i	$-0.737892\pi$
$383$	−19.0825	−	33.0519i	−0.975070	−	1.68887i	−0.295366	−	0.955384i	$-0.595442\pi$
$384$		0			0
$385$	8.76834	−	3.92745i	0.446876	−	0.200161i
$386$	−1.08462	+	2.24975i	−0.0552057	+	0.114509i
$387$		0			0
$388$	5.41035	−	13.7504i	0.274669	−	0.698069i
$389$	24.5349	+	14.1652i	1.24397	+	0.718206i	0.969900	−	0.243503i	$-0.0782967\pi$
$389$	24.5349	+	14.1652i	1.24397	+	0.718206i	0.274070	+	0.961710i	$0.411630\pi$
$390$		0			0
$391$	−12.6217	−	7.28712i	−0.638305	−	0.368525i
$392$	−9.58689	+	17.3232i	−0.484211	+	0.874951i
$393$		0			0
$394$	−25.7503	−	12.4144i	−1.29728	−	0.625429i
$395$	−10.0036	−	17.3268i	−0.503337	−	0.871805i
$396$		0			0
$397$	1.52318	−	2.63822i	0.0764461	−	0.132409i	−0.825268	−	0.564741i	$-0.808976\pi$
$397$	1.52318	−	2.63822i	0.0764461	−	0.132409i	0.901714	+	0.432333i	$0.142309\pi$
$398$	1.43832	+	19.3051i	0.0720966	+	0.967679i
$399$		0			0
$400$	38.5759	+	35.9176i	1.92879	+	1.79588i
$401$	20.2242	−	11.6764i	1.00995	−	0.583093i	0.0987709	−	0.995110i	$-0.468509\pi$
$401$	20.2242	−	11.6764i	1.00995	−	0.583093i	0.911176	+	0.412017i	$0.135176\pi$
$402$		0			0
$403$	17.8788	+	10.3223i	0.890606	+	0.514192i
$404$	1.94091	+	12.9531i	0.0965639	+	0.644442i
$405$		0			0
$406$	14.3050	−	7.73118i	0.709945	−	0.383692i
$407$	−0.821221	−	1.42240i	−0.0407064	−	0.0705056i
$408$		0			0
$409$	−11.8548			−0.586183			−0.293091	−	0.956084i	$-0.594684\pi$
$409$	−11.8548			−0.586183			−0.293091	+	0.956084i	$0.594684\pi$
$410$	9.78428	−	20.2948i	0.483211	−	1.00229i
$411$		0			0
$412$	15.0852	+	5.93557i	0.743194	+	0.292424i
$413$	2.62284	+	5.85570i	0.129062	+	0.288140i
$414$		0			0
$415$	8.54696	+	4.93459i	0.419554	+	0.242230i
$416$	17.9554	−	7.00219i	0.880334	−	0.343310i
$417$		0			0
$418$	0.0296786	+	0.398345i	0.00145163	+	0.0194837i
$419$	15.1361	−	26.2165i	0.739446	−	1.28076i	−0.213298	−	0.976987i	$-0.568421\pi$
$419$	15.1361	−	26.2165i	0.739446	−	1.28076i	0.952745	−	0.303772i	$-0.0982460\pi$
$420$		0			0
$421$	16.5898	+	28.7343i	0.808536	+	1.40043i	0.913878	+	0.405989i	$0.133073\pi$
$421$	16.5898	+	28.7343i	0.808536	+	1.40043i	−0.105342	+	0.994436i	$0.533594\pi$
$422$	15.4189	−	10.5026i	0.750579	−	0.511261i
$423$		0			0
$424$	7.93683	−	7.34516i	0.385446	−	0.356712i
$425$		−	45.1284i		−	2.18905i
$426$		0			0
$427$	9.14202	+	20.4103i	0.442414	+	0.987723i
$428$	7.58729	−	1.13689i	0.366746	−	0.0549536i
$429$		0			0
$430$	7.99192	+	11.7329i	0.385405	+	0.565811i
$431$	8.05650	+	13.9543i	0.388068	+	0.672154i	0.992190	−	0.124739i	$-0.0398092\pi$
$431$	8.05650	+	13.9543i	0.388068	+	0.672154i	−0.604122	+	0.796892i	$0.706476\pi$
$432$		0			0
$433$	19.4444			0.934438			0.467219	−	0.884142i	$-0.345256\pi$
$433$	19.4444			0.934438			0.467219	+	0.884142i	$0.345256\pi$
$434$	0.637364	−	22.6641i	0.0305945	−	1.08791i
$435$		0			0
$436$	−3.23355	+	8.21805i	−0.154859	+	0.393573i
$437$			1.41121i			0.0675073i
$438$		0			0
$439$		−	39.6685i		−	1.89327i	−0.322303	−	0.946636i	$-0.604457\pi$
$439$		−	39.6685i		−	1.89327i	0.322303	−	0.946636i	$-0.395543\pi$
$440$	2.27254	+	10.0165i	0.108339	+	0.477520i
$441$		0			0
$442$	−14.8637	−	7.16589i	−0.706992	−	0.340846i
$443$	−7.40095			−0.351630			−0.175815	−	0.984423i	$-0.556256\pi$
$443$	−7.40095			−0.351630			−0.175815	+	0.984423i	$0.556256\pi$
$444$		0			0
$445$	37.9029			1.79677
$446$	2.65518	+	35.6378i	0.125727	+	1.68750i
$447$		0			0
$448$	−16.1412	−	13.6917i	−0.762598	−	0.646872i
$449$			26.3471i			1.24340i	0.783257	+	0.621698i	$0.213557\pi$
$449$			26.3471i			1.24340i	−0.783257	+	0.621698i	$0.786443\pi$
$450$		0			0
$451$	2.75632	−	1.59136i	0.129790	−	0.0749342i
$452$	−0.0447155	−	0.298419i	−0.00210324	−	0.0140365i
$453$		0			0
$454$	−6.31485	−	9.27080i	−0.296371	−	0.435100i
$455$	35.0726	−	15.7095i	1.64423	−	0.736472i
$456$		0			0
$457$	7.88316			0.368759			0.184379	−	0.982855i	$-0.440973\pi$
$457$	7.88316			0.368759			0.184379	+	0.982855i	$0.440973\pi$
$458$	−10.2455	+	0.763338i	−0.478741	+	0.0356685i
$459$		0			0
$460$	5.37721	+	35.8861i	0.250714	+	1.67320i
$461$	3.46807	−	2.00229i	0.161524	−	0.0932560i	−0.417059	−	0.908879i	$-0.636939\pi$
$461$	3.46807	−	2.00229i	0.161524	−	0.0932560i	0.578583	+	0.815623i	$0.303606\pi$
$462$		0			0
$463$	−16.1624	−	9.33139i	−0.751133	−	0.433667i	0.0749704	−	0.997186i	$-0.476114\pi$
$463$	−16.1624	−	9.33139i	−0.751133	−	0.433667i	−0.826103	+	0.563519i	$0.809447\pi$
$464$	5.09505	+	16.6198i	0.236532	+	0.771554i
$465$		0			0
$466$	25.9930	−	17.7053i	1.20410	−	0.820181i
$467$	18.3541	−	31.7903i	0.849328	−	1.47108i	−0.0324813	−	0.999472i	$-0.510341\pi$
$467$	18.3541	−	31.7903i	0.849328	−	1.47108i	0.881809	−	0.471607i	$-0.156326\pi$
$468$		0			0
$469$	26.4400	−	11.8428i	1.22088	−	0.546850i
$470$	2.39616	+	32.1611i	0.110526	+	1.48348i
$471$		0			0
$472$	−6.68927	+	1.51765i	−0.307899	+	0.0698557i
$473$			2.00541i			0.0922091i
$474$		0			0
$475$	−3.78431	+	2.18487i	−0.173636	+	0.100249i
$476$	0.837897	+	18.1028i	0.0384049	+	0.829739i
$477$		0			0
$478$	−13.6064	−	19.9755i	−0.622344	−	0.913660i
$479$	5.36860	−	9.29868i	0.245297	−	0.424868i	−0.716918	−	0.697158i	$-0.754448\pi$
$479$	5.36860	−	9.29868i	0.245297	−	0.424868i	0.962215	+	0.272290i	$0.0877810\pi$
$480$		0			0
$481$	−3.28482	−	5.68947i	−0.149775	−	0.259417i
$482$	−4.49194	−	6.59459i	−0.204602	−	0.300375i
$483$		0			0
$484$	7.52396	−	19.1221i	0.341998	−	0.869185i
$485$	27.2794	+	15.7497i	1.23869	+	0.715159i
$486$		0			0
$487$	−20.1837	+	11.6531i	−0.914612	+	0.528051i	−0.881912	−	0.471414i	$-0.843744\pi$
$487$	−20.1837	+	11.6531i	−0.914612	+	0.528051i	−0.0326998	+	0.999465i	$0.510411\pi$
$488$	−23.3158	+	5.28985i	−1.05545	+	0.239460i
$489$		0			0
$490$	−33.4921	−	25.6833i	−1.51302	−	1.16025i
$491$	11.7342	−	20.3242i	0.529557	−	0.917220i	−0.469848	−	0.882747i	$-0.655691\pi$
$491$	11.7342	−	20.3242i	0.529557	−	0.917220i	0.999406	−	0.0344729i	$-0.0109752\pi$
$492$		0			0
$493$	7.44168	−	12.8894i	0.335156	−	0.580508i
$494$	0.118712	+	1.59335i	0.00534110	+	0.0716881i
$495$		0			0
$496$	23.6215	+	5.43446i	1.06064	+	0.244014i
$497$	−15.0914	−	33.6927i	−0.676942	−	1.51133i
$498$		0			0
$499$	−11.0247	+	6.36513i	−0.493535	+	0.284942i	−0.726040	−	0.687653i	$-0.758641\pi$
$499$	−11.0247	+	6.36513i	−0.493535	+	0.284942i	0.232505	+	0.972595i	$0.425308\pi$
$500$	−54.5511	+	43.4259i	−2.43960	+	1.94207i
$501$		0			0
$502$	−2.95143	+	6.12194i	−0.131729	+	0.273235i
$503$	−29.8656			−1.33164			−0.665822	−	0.746111i	$-0.731919\pi$
$503$	−29.8656			−1.33164			−0.665822	+	0.746111i	$0.731919\pi$
$504$		0			0
$505$	−27.9208			−1.24246
$506$	−2.22609	+	4.61742i	−0.0989618	+	0.205269i
$507$		0			0
$508$	29.1864	−	23.2341i	1.29494	−	1.03085i
$509$	−36.2754	+	20.9436i	−1.60788	+	0.928309i	−0.618035	+	0.786151i	$0.712071\pi$
$509$	−36.2754	+	20.9436i	−1.60788	+	0.928309i	−0.989844	+	0.142159i	$0.954596\pi$
$510$		0			0
$511$	−13.6144	+	18.8271i	−0.602266	+	0.832861i
$512$	17.7456	−	14.0390i	0.784253	−	0.620442i
$513$		0			0
$514$	−0.511673	−	6.86767i	−0.0225689	−	0.302920i
$515$	−17.2787	+	29.9275i	−0.761389	+	1.31876i
$516$		0			0
$517$	−2.27791	+	3.94545i	−0.100182	+	0.173521i
$518$	−3.78179	+	6.14461i	−0.166162	+	0.269978i
$519$		0			0
$520$	9.08997	+	40.0653i	0.398622	+	1.75698i
$521$	2.31281	−	1.33530i	0.101326	−	0.0585007i	−0.448481	−	0.893793i	$-0.648035\pi$
$521$	2.31281	−	1.33530i	0.101326	−	0.0585007i	0.549807	+	0.835292i	$0.314701\pi$
$522$		0			0
$523$	24.9885	+	14.4271i	1.09267	+	0.630855i	0.934287	−	0.356523i	$-0.116038\pi$
$523$	24.9885	+	14.4271i	1.09267	+	0.630855i	0.158386	+	0.987377i	$0.449371\pi$
$524$	13.0351	−	33.1285i	0.569440	−	1.44723i
$525$		0			0
$526$	−0.893618	−	1.31192i	−0.0389636	−	0.0572022i
$527$	−10.3764	−	17.9725i	−0.452004	−	0.782893i
$528$		0			0
$529$	2.44518	−	4.23517i	0.106312	−	0.184138i
$530$	12.9778	+	19.0527i	0.563721	+	0.827595i
$531$		0			0
$532$	1.47747	−	0.946700i	0.0640563	−	0.0410447i
$533$	11.0250	−	6.36531i	0.477547	−	0.275712i
$534$		0			0
$535$			16.3546i			0.707072i
$536$	6.85260	+	30.2038i	0.295987	+	1.30461i
$537$		0			0
$538$	1.21557	+	16.3153i	0.0524069	+	0.703404i
$539$	−1.86779	−	5.66210i	−0.0804512	−	0.243884i
$540$		0			0
$541$	−12.4775	+	21.6117i	−0.536450	+	0.929158i	0.462642	+	0.886545i	$0.346902\pi$
$541$	−12.4775	+	21.6117i	−0.536450	+	0.929158i	−0.999092	+	0.0426129i	$0.986432\pi$
$542$	1.95432	−	1.33119i	0.0839451	−	0.0571796i
$543$		0			0
$544$	−19.1507	−	2.92888i	−0.821080	−	0.125575i
$545$	−16.3038	−	9.41300i	−0.698378	−	0.403209i
$546$		0			0
$547$	−32.7756	+	18.9230i	−1.40138	+	0.809088i	−0.994535	−	0.104408i	$-0.966705\pi$
$547$	−32.7756	+	18.9230i	−1.40138	+	0.809088i	−0.406847	+	0.913496i	$0.633372\pi$
$548$	2.30476	+	15.3814i	0.0984546	+	0.657060i
$549$		0			0
$550$	−15.8286	+	1.17930i	−0.674934	+	0.0502857i
$551$	−1.44114			−0.0613947
$552$		0			0
$553$	−11.3310	+	5.07532i	−0.481845	+	0.215824i
$554$	−9.11339	−	13.3793i	−0.387191	−	0.568433i
$555$		0			0
$556$	−3.48563	−	23.2622i	−0.147824	−	0.986536i
$557$	16.9121	−	9.76419i	0.716588	−	0.413722i	−0.0969077	−	0.995293i	$-0.530895\pi$
$557$	16.9121	−	9.76419i	0.716588	−	0.413722i	0.813496	+	0.581571i	$0.197562\pi$
$558$		0			0
$559$			8.02150i			0.339273i
$560$	33.9637	−	29.7036i	1.43523	−	1.25521i
$561$		0			0
$562$	0.787768	+	10.5734i	0.0332300	+	0.446012i
$563$	2.71296			0.114337			0.0571687	−	0.998365i	$-0.481793\pi$
$563$	2.71296			0.114337			0.0571687	+	0.998365i	$0.481793\pi$
$564$		0			0
$565$	0.643252			0.0270618
$566$	−38.1376	−	18.3864i	−1.60304	−	0.772840i
$567$		0			0
$568$	38.4890	−	8.73234i	1.61496	−	0.366401i
$569$			11.0557i			0.463478i	0.972778	+	0.231739i	$0.0744415\pi$
$569$			11.0557i			0.463478i	−0.972778	+	0.231739i	$0.925559\pi$
$570$		0			0
$571$		−	11.8022i		−	0.493905i	−0.969028	−	0.246952i	$-0.920571\pi$
$571$		−	11.8022i		−	0.493905i	0.969028	−	0.246952i	$-0.0794291\pi$
$572$	−2.12498	+	5.40062i	−0.0888499	+	0.225811i
$573$		0			0
$574$	−11.9070	−	7.32835i	−0.496989	−	0.305879i
$575$	−56.0757			−2.33852
$576$		0			0
$577$	−9.48646	−	16.4310i	−0.394926	−	0.684033i	0.598165	−	0.801373i	$-0.295897\pi$
$577$	−9.48646	−	16.4310i	−0.394926	−	0.684033i	−0.993092	+	0.117340i	$0.962563\pi$
$578$	−4.19649	−	6.16085i	−0.174551	−	0.256258i
$579$		0			0
$580$	−36.6472	+	5.49126i	−1.52169	+	0.228012i
$581$	3.58877	−	4.96284i	0.148887	−	0.205893i
$582$		0			0
$583$			3.25653i			0.134872i
$584$	−16.8705	−	18.2295i	−0.698106	−	0.754340i
$585$		0			0
$586$	−36.2110	+	24.6653i	−1.49586	+	1.01892i
$587$	8.48640	+	14.6989i	0.350271	+	0.606688i	0.986297	−	0.164980i	$-0.0527560\pi$
$587$	8.48640	+	14.6989i	0.350271	+	0.606688i	−0.636025	+	0.771668i	$0.719423\pi$
$588$		0			0
$589$	−1.00474	+	1.74026i	−0.0413995	+	0.0717061i
$590$	−1.08641	−	14.5817i	−0.0447266	−	0.600320i
$591$		0			0
$592$	−5.64516	−	5.25615i	−0.232015	−	0.216026i
$593$	−26.9119	−	15.5376i	−1.10514	−	0.638051i	−0.167572	−	0.985860i	$-0.553593\pi$
$593$	−26.9119	−	15.5376i	−1.10514	−	0.638051i	−0.937566	+	0.347808i	$0.886926\pi$
$594$		0			0
$595$	−38.4288	−	3.95211i	−1.57543	−	0.162021i
$596$	−6.98332	−	2.74772i	−0.286048	−	0.112551i
$597$		0			0
$598$	−8.90418	+	18.4693i	−0.364119	+	0.755265i
$599$	−33.9428			−1.38686			−0.693432	−	0.720522i	$-0.743902\pi$
$599$	−33.9428			−1.38686			−0.693432	+	0.720522i	$0.743902\pi$
$600$		0			0
$601$	−15.1894	−	26.3088i	−0.619587	−	1.07316i	−0.989561	−	0.144115i	$-0.953967\pi$
$601$	−15.1894	−	26.3088i	−0.619587	−	1.07316i	0.369974	−	0.929042i	$-0.379367\pi$
$602$	7.75019	−	4.18861i	0.315874	−	0.170715i
$603$		0			0
$604$	−1.03265	−	6.89160i	−0.0420177	−	0.280415i
$605$	37.9363	+	21.9025i	1.54233	+	0.890464i
$606$		0			0
$607$	7.63211	−	4.40640i	0.309778	−	0.178850i	−0.337049	−	0.941487i	$-0.609429\pi$
$607$	7.63211	−	4.40640i	0.309778	−	0.178850i	0.646827	+	0.762637i	$0.276096\pi$
$608$	0.681568	+	1.74771i	0.0276412	+	0.0708790i
$609$		0			0
$610$	−3.78672	−	50.8252i	−0.153320	−	2.05785i
$611$	−9.11144	+	15.7815i	−0.368609	+	0.638450i
$612$		0			0
$613$	6.62528	+	11.4753i	0.267593	+	0.463484i	0.968240	−	0.250024i	$-0.0804385\pi$
$613$	6.62528	+	11.4753i	0.267593	+	0.463484i	−0.700647	+	0.713508i	$0.747105\pi$
$614$	−25.3141	−	12.2041i	−1.02159	−	0.492518i
$615$		0			0
$616$	6.32757	−	0.766953i	0.254945	−	0.0309014i
$617$	−5.95374	−	3.43739i	−0.239689	−	0.138384i	0.375345	−	0.926885i	$-0.377524\pi$
$617$	−5.95374	−	3.43739i	−0.239689	−	0.138384i	−0.615034	+	0.788501i	$0.710858\pi$
$618$		0			0
$619$	−3.91195	−	2.25857i	−0.157235	−	0.0907794i	0.419318	−	0.907839i	$-0.362269\pi$
$619$	−3.91195	−	2.25857i	−0.157235	−	0.0907794i	−0.576553	+	0.817060i	$0.695602\pi$
$620$	−18.9188	+	48.0819i	−0.759797	+	1.93102i
$621$		0			0
$622$	−18.4279	+	38.2236i	−0.738891	+	1.53263i
$623$	2.40628	−	23.3978i	0.0964057	−	0.937412i
$624$		0			0
$625$	−41.3752	−	71.6639i	−1.65501	−	2.86656i
$626$	17.1746	−	35.6240i	0.686435	−	1.42382i
$627$		0			0
$628$	3.62382	+	4.55220i	0.144606	+	0.181652i
$629$			6.60406i			0.263321i
$630$		0			0
$631$			9.52372i			0.379133i	0.981868	+	0.189567i	$0.0607083\pi$
$631$			9.52372i			0.379133i	−0.981868	+	0.189567i	$0.939292\pi$
$632$	−2.93673	−	12.9441i	−0.116817	−	0.514887i
$633$		0			0
$634$	−4.80333	−	2.31572i	−0.190764	−	0.0919690i
$635$	39.7622	+	68.8702i	1.57792	+	2.73303i
$636$		0			0
$637$	−7.47099	−	22.6480i	−0.296011	−	0.897345i
$638$	−4.71535	−	2.27331i	−0.186683	−	0.0900011i
$639$		0			0
$640$	23.9912	+	41.8460i	0.948335	+	1.65411i
$641$	19.6854	+	11.3654i	0.777527	+	0.448906i	0.835553	−	0.549410i	$-0.185147\pi$
$641$	19.6854	+	11.3654i	0.777527	+	0.448906i	−0.0580260	+	0.998315i	$0.518481\pi$
$642$		0			0
$643$	−28.4760	−	16.4406i	−1.12299	−	0.648356i	−0.180824	−	0.983515i	$-0.557876\pi$
$643$	−28.4760	−	16.4406i	−1.12299	−	0.648356i	−0.942161	+	0.335160i	$0.891210\pi$
$644$	22.4941	−	1.04115i	0.886393	−	0.0410272i
$645$		0			0
$646$	0.697502	−	1.44678i	0.0274428	−	0.0569226i
$647$	19.7354	+	34.1826i	0.775877	+	1.34386i	0.934300	+	0.356487i	$0.116025\pi$
$647$	19.7354	+	34.1826i	0.775877	+	1.34386i	−0.158424	+	0.987371i	$0.550641\pi$
$648$		0			0
$649$	1.03279	−	1.78885i	0.0405407	−	0.0702185i
$650$	−63.3131	+	4.71712i	−2.48334	+	0.185021i
$651$		0			0
$652$	3.90899	+	26.0876i	0.153088	+	1.02167i
$653$	−6.73103	+	3.88616i	−0.263406	+	0.152077i	−0.625887	−	0.779914i	$-0.715263\pi$
$653$	−6.73103	+	3.88616i	−0.263406	+	0.152077i	0.362481	+	0.931991i	$0.381930\pi$
$654$		0			0
$655$	65.7237	+	37.9456i	2.56804	+	1.48266i
$656$	10.1854	−	10.9392i	0.397671	−	0.427103i
$657$		0			0
$658$	20.0055	+	0.562597i	0.779894	+	0.0219323i
$659$	−5.26420	−	9.11786i	−0.205064	−	0.355181i	0.745089	−	0.666965i	$-0.232407\pi$
$659$	−5.26420	−	9.11786i	−0.205064	−	0.355181i	−0.950153	+	0.311784i	$0.899074\pi$
$660$		0			0
$661$	−3.66483			−0.142545			−0.0712727	−	0.997457i	$-0.522706\pi$
$661$	−3.66483			−0.142545			−0.0712727	+	0.997457i	$0.522706\pi$
$662$	12.0350	+	5.80217i	0.467754	+	0.225508i
$663$		0			0
$664$	4.44708	+	4.80530i	0.172580	+	0.186482i
$665$	1.52910	+	3.41385i	0.0592961	+	0.132383i
$666$		0			0
$667$	−16.0161	−	9.24688i	−0.620145	−	0.358041i
$668$	8.67769	−	1.30028i	0.335750	−	0.0503092i
$669$		0			0
$670$	−65.8402	+	4.90540i	−2.54363	+	0.189512i
$671$	3.59984	−	6.23511i	0.138970	−	0.240704i
$672$		0			0
$673$	−1.64613	−	2.85118i	−0.0634537	−	0.109905i	0.832553	−	0.553945i	$-0.186878\pi$
$673$	−1.64613	−	2.85118i	−0.0634537	−	0.109905i	−0.896007	+	0.444040i	$0.853545\pi$
$674$	−17.4605	−	25.6336i	−0.672552	−	0.987370i
$675$		0			0
$676$	1.02005	−	2.59244i	0.0392326	−	0.0997092i
$677$			28.3503i			1.08959i	0.838570	+	0.544794i	$0.183392\pi$
$677$			28.3503i			1.08959i	−0.838570	+	0.544794i	$0.816608\pi$
$678$		0			0
$679$	11.4543	−	15.8399i	0.439575	−	0.607879i
$680$	12.2242	−	39.4482i	0.468778	−	1.51277i
$681$		0			0
$682$	−6.03261	+	4.10914i	−0.231000	+	0.157347i
$683$	−6.78662	−	11.7548i	−0.259683	−	0.449784i	0.706474	−	0.707739i	$-0.250285\pi$
$683$	−6.78662	−	11.7548i	−0.259683	−	0.449784i	−0.966157	+	0.257955i	$0.916951\pi$
$684$		0			0
$685$	−33.1550			−1.26679
$686$	−17.9808	+	19.0445i	−0.686510	+	0.727121i
$687$		0			0
$688$	2.76040	+	9.00429i	0.105239	+	0.343285i
$689$			13.0258i			0.496245i
$690$		0			0
$691$			3.19917i			0.121702i	0.998147	+	0.0608510i	$0.0193815\pi$
$691$			3.19917i			0.121702i	−0.998147	+	0.0608510i	$0.980619\pi$
$692$	−22.0987	+	17.5919i	−0.840068	+	0.668744i
$693$		0			0
$694$	14.3568	−	29.7792i	0.544976	−	1.13040i
$695$	50.1423			1.90200
$696$		0			0
$697$	−12.7973			−0.484733
$698$	−12.2958	+	0.916098i	−0.465405	+	0.0346748i
$699$		0			0
$700$	37.6180	+	58.7085i	1.42183	+	2.21897i
$701$		−	28.8142i		−	1.08830i	−0.838989	−	0.544148i	$-0.816853\pi$
$701$		−	28.8142i		−	1.08830i	0.838989	−	0.544148i	$-0.183147\pi$
$702$		0			0
$703$	0.553793	−	0.319732i	0.0208867	−	0.0120589i
$704$	−0.526840	+	6.79357i	−0.0198560	+	0.256042i
$705$		0			0
$706$	24.1752	−	16.4670i	0.909845	−	0.619745i
$707$	−1.77257	+	17.2358i	−0.0666642	+	0.648217i
$708$		0			0
$709$	39.1530			1.47042			0.735210	−	0.677839i	$-0.237083\pi$
$709$	39.1530			1.47042			0.735210	+	0.677839i	$0.237083\pi$
$710$	6.25101	+	83.9008i	0.234596	+	3.14874i
$711$		0			0
$712$	24.0184	+	7.44285i	0.900129	+	0.278933i
$713$	−22.3322	+	12.8935i	−0.836349	+	0.482866i
$714$		0			0
$715$	−10.7143	−	6.18590i	−0.400692	−	0.231340i
$716$	11.4712	−	29.1539i	0.428697	−	1.08953i
$717$		0			0
$718$	−13.7426	−	20.1755i	−0.512870	−	0.752942i
$719$	8.20350	−	14.2089i	0.305939	−	0.529902i	−0.671531	−	0.740976i	$-0.734363\pi$
$719$	8.20350	−	14.2089i	0.305939	−	0.529902i	0.977470	+	0.211075i	$0.0676964\pi$
$720$		0			0
$721$	17.3776	+	12.5662i	0.647174	+	0.467991i
$722$	26.6407	−	1.98486i	0.991464	−	0.0738687i
$723$		0			0
$724$	−9.26677	−	11.6408i	−0.344397	−	0.432627i
$725$		−	57.2651i		−	2.12677i
$726$		0			0
$727$	2.31752	−	1.33802i	0.0859522	−	0.0496245i	−0.456408	−	0.889771i	$-0.650864\pi$
$727$	2.31752	−	1.33802i	0.0859522	−	0.0496245i	0.542360	+	0.840146i	$0.317531\pi$
$728$	25.3098	−	3.06775i	0.938042	−	0.113698i
$729$		0			0
$730$	43.7605	−	29.8077i	1.61965	−	1.10323i
$731$	4.03176	−	6.98322i	0.149120	−	0.258284i
$732$		0			0
$733$	−4.33386	−	7.50646i	−0.160075	−	0.277257i	0.774821	−	0.632181i	$-0.217840\pi$
$733$	−4.33386	−	7.50646i	−0.160075	−	0.277257i	−0.934895	+	0.354924i	$0.884507\pi$
$734$	10.4622	−	7.12636i	0.386166	−	0.263039i
$735$		0			0
$736$	−3.63936	+	23.7963i	−0.134149	+	0.877143i
$737$	−8.07712	−	4.66332i	−0.297524	−	0.171776i
$738$		0			0
$739$	−25.9736	+	14.9959i	−0.955454	+	0.551632i	−0.894771	−	0.446526i	$-0.852661\pi$
$739$	−25.9736	+	14.9959i	−0.955454	+	0.551632i	−0.0606830	+	0.998157i	$0.519328\pi$
$740$	12.8643	−	10.2407i	0.472900	−	0.376456i
$741$		0			0
$742$	12.5853	−	6.80175i	0.462020	−	0.249700i
$743$	−15.8135	+	27.3898i	−0.580141	+	1.00483i	0.415322	+	0.909675i	$0.363669\pi$
$743$	−15.8135	+	27.3898i	−0.580141	+	1.00483i	−0.995462	+	0.0951583i	$0.969664\pi$
$744$		0			0
$745$	7.99873	−	13.8542i	0.293051	−	0.507579i
$746$	−37.4134	+	2.78747i	−1.36980	+	0.102057i
$747$		0			0
$748$	4.56439	−	3.63353i	0.166891	−	0.132855i
$749$	10.0958	+	1.03828i	0.368894	+	0.0379379i
$750$		0			0
$751$	32.3064	−	18.6521i	1.17888	−	0.680626i	0.223124	−	0.974790i	$-0.428375\pi$
$751$	32.3064	−	18.6521i	1.17888	−	0.680626i	0.955755	+	0.294164i	$0.0950413\pi$
$752$	−4.79696	+	20.8505i	−0.174927	+	0.760339i
$753$		0			0
$754$	−18.8610	−	9.09305i	−0.686878	−	0.331149i
$755$	14.8550			0.540630
$756$		0			0
$757$	−22.0140			−0.800112			−0.400056	−	0.916491i	$-0.631009\pi$
$757$	−22.0140			−0.800112			−0.400056	+	0.916491i	$0.631009\pi$
$758$	39.5537	+	19.0691i	1.43665	+	0.692621i
$759$		0			0
$760$	−3.89982	+	0.884786i	−0.141461	+	0.0320946i
$761$	3.58320	−	2.06876i	0.129891	−	0.0749925i	−0.433647	−	0.901083i	$-0.642773\pi$
$761$	3.58320	−	2.06876i	0.129891	−	0.0749925i	0.563537	+	0.826090i	$0.309440\pi$
$762$		0			0
$763$	−6.84578	+	9.46688i	−0.247834	+	0.342724i
$764$	−0.548951	−	0.689585i	−0.0198603	−	0.0249483i
$765$		0			0
$766$	53.8243	−	4.01016i	1.94475	−	0.144893i
$767$	4.13109	−	7.15525i	0.149165	−	0.258361i
$768$		0			0
$769$	5.77384	−	10.0006i	0.208210	−	0.360630i	−0.742941	−	0.669357i	$-0.766570\pi$
$769$	5.77384	−	10.0006i	0.208210	−	0.360630i	0.951151	+	0.308727i	$0.0999029\pi$
$770$	−0.381956	+	13.5820i	−0.0137647	+	0.489462i
$771$		0			0
$772$	−2.19982	−	2.76339i	−0.0791733	−	0.0994566i
$773$	−4.09042	+	2.36160i	−0.147122	+	0.0849410i	−0.571754	−	0.820425i	$-0.693737\pi$
$773$	−4.09042	+	2.36160i	−0.147122	+	0.0849410i	0.424632	+	0.905366i	$0.360404\pi$
$774$		0			0
$775$	−69.1507	−	39.9242i	−2.48397	−	1.43412i
$776$	14.1938	+	15.3371i	0.509526	+	0.550570i
$777$		0			0
$778$	−33.1133	+	22.5553i	−1.18717	+	0.808647i
$779$	0.619577	+	1.07314i	0.0221986	+	0.0384492i
$780$		0			0
$781$	−5.94252	+	10.2928i	−0.212640	+	0.368304i
$782$	17.0347	−	11.6033i	0.609159	−	0.414932i
$783$		0			0
$784$	−16.1801	−	22.8518i	−0.577860	−	0.816136i
$785$	−10.7417	+	6.20170i	−0.383386	+	0.221348i
$786$		0			0
$787$		−	15.6262i		−	0.557013i	−0.960434	−	0.278507i	$-0.910161\pi$
$787$		−	15.6262i		−	0.557013i	0.960434	−	0.278507i	$-0.0898394\pi$
$788$	31.6293	−	25.1788i	1.12675	−	0.896959i
$789$		0			0
$790$	28.2163	−	2.10225i	1.00389	−	0.0747946i
$791$	0.0408371	−	0.397085i	0.00145200	−	0.0141187i
$792$		0			0
$793$	14.3991	−	24.9399i	0.511326	−	0.885643i
$794$	2.42535	+	3.56065i	0.0860726	+	0.126363i
$795$		0			0
$796$	−25.4761	−	10.0241i	−0.902976	−	0.355294i
$797$	36.4126	+	21.0228i	1.28980	+	0.744667i	0.978619	−	0.205683i	$-0.0659416\pi$
$797$	36.4126	+	21.0228i	1.28980	+	0.744667i	0.311183	+	0.950350i	$0.399275\pi$
$798$		0			0
$799$	15.8642	−	9.15919i	0.561234	−	0.324029i
$800$	−69.4469	+	27.0827i	−2.45532	+	0.957519i
$801$		0			0
$802$	2.45379	+	32.9347i	0.0866462	+	1.16296i
$803$	7.47966			0.263951
$804$		0			0
$805$	−4.91082	+	47.7509i	−0.173084	+	1.68300i
$806$	−24.1299	+	16.4362i	−0.849940	+	0.578941i
$807$		0			0
$808$	−17.6930	−	5.48271i	−0.622436	−	0.192881i
$809$	44.7898	−	25.8594i	1.57473	−	0.909169i	0.579149	−	0.815222i	$-0.303385\pi$
$809$	44.7898	−	25.8594i	1.57473	−	0.909169i	0.995577	−	0.0939467i	$-0.0299483\pi$
$810$		0			0
$811$		−	30.5623i		−	1.07319i	−0.843841	−	0.536593i	$-0.819711\pi$
$811$		−	30.5623i		−	1.07319i	0.843841	−	0.536593i	$-0.180289\pi$
$812$	1.06324	+	22.9712i	0.0373123	+	0.806133i
$813$		0			0
$814$	2.31634	−	0.172578i	0.0811878	−	0.00604887i
$815$	−56.2325			−1.96974
$816$		0			0
$817$	−0.780784			−0.0273162
$818$	7.28070	−	15.1018i	0.254564	−	0.528022i
$819$		0			0
$820$	19.8444	+	24.9283i	0.692998	+	0.870535i
$821$		−	31.5803i		−	1.10216i	−0.834452	−	0.551080i	$-0.814216\pi$
$821$		−	31.5803i		−	1.10216i	0.834452	−	0.551080i	$-0.185784\pi$
$822$		0			0
$823$			34.5707i			1.20506i	0.798096	+	0.602530i	$0.205840\pi$
$823$			34.5707i			1.20506i	−0.798096	+	0.602530i	$0.794160\pi$
$824$	−16.8260	+	15.5716i	−0.586160	+	0.542463i
$825$		0			0
$826$	−9.07038	−	0.255079i	−0.315599	−	0.00887533i
$827$	53.2997			1.85341			0.926705	−	0.375788i	$-0.122628\pi$
$827$	53.2997			1.85341			0.926705	+	0.375788i	$0.122628\pi$
$828$		0			0
$829$	19.6791	+	34.0853i	0.683485	+	1.18383i	0.973910	+	0.226933i	$0.0728697\pi$
$829$	19.6791	+	34.0853i	0.683485	+	1.18383i	−0.290426	+	0.956897i	$0.593797\pi$
$830$	−11.5353	+	7.85734i	−0.400397	+	0.272732i
$831$		0			0
$832$	−2.10732	+	27.1737i	−0.0730581	+	0.942079i
$833$	−4.87934	+	23.4715i	−0.169059	+	0.813241i
$834$		0			0
$835$			18.7050i			0.647314i
$836$	−0.525677	−	0.206838i	−0.0181809	−	0.00715365i
$837$		0			0
$838$	24.1012	+	35.3828i	0.832561	+	1.22228i
$839$	−12.4970	−	21.6454i	−0.431444	−	0.747282i	0.565554	−	0.824711i	$-0.308662\pi$
$839$	−12.4970	−	21.6454i	−0.431444	−	0.747282i	−0.996998	+	0.0774289i	$0.975329\pi$
$840$		0			0
$841$	−5.05699	+	8.75896i	−0.174379	+	0.302033i
$842$	−46.7933	+	3.48632i	−1.61260	+	0.120146i
$843$		0			0
$844$	3.90970	+	26.0923i	0.134578	+	0.898135i
$845$	5.14314	+	2.96939i	0.176929	+	0.102150i
$846$		0			0
$847$	15.9290	−	22.0279i	0.547327	−	0.756887i
$848$	4.48253	+	14.6218i	0.153931	+	0.502114i
$849$		0			0
$850$	57.4890	+	27.7159i	1.97186	+	0.950647i
$851$	8.20607			0.281300
$852$		0			0
$853$	−15.3129	−	26.5227i	−0.524303	−	0.908120i	−0.999600	−	0.0282939i	$-0.990993\pi$
$853$	−15.3129	−	26.5227i	−0.524303	−	0.908120i	0.475297	−	0.879826i	$-0.342341\pi$
$854$	−31.6152	−	0.889089i	−1.08185	−	0.0304240i
$855$		0			0
$856$	−3.21150	+	10.3637i	−0.109767	+	0.354222i
$857$	−17.5286	−	10.1202i	−0.598767	−	0.345698i	0.169789	−	0.985480i	$-0.445691\pi$
$857$	−17.5286	−	10.1202i	−0.598767	−	0.345698i	−0.768556	+	0.639782i	$0.779025\pi$
$858$		0			0
$859$	−18.1253	+	10.4646i	−0.618426	+	0.357049i	−0.776256	−	0.630418i	$-0.782884\pi$
$859$	−18.1253	+	10.4646i	−0.618426	+	0.357049i	0.157830	+	0.987466i	$0.449550\pi$
$860$	−19.8548	+	2.97506i	−0.677042	+	0.101449i
$861$		0			0
$862$	−22.7242	+	1.69306i	−0.773991	+	0.0576660i
$863$	3.24475	−	5.62008i	0.110453	−	0.191310i	−0.805500	−	0.592596i	$-0.798103\pi$
$863$	3.24475	−	5.62008i	0.110453	−	0.191310i	0.915953	+	0.401286i	$0.131437\pi$
$864$		0			0
$865$	−30.1063	−	52.1456i	−1.02364	−	1.77301i
$866$	−11.9419	+	24.7701i	−0.405801	+	0.841724i
$867$		0			0
$868$	28.4803	+	14.7312i	0.966685	+	0.500010i
$869$	3.46151	+	1.99850i	0.117424	+	0.0677945i
$870$		0			0
$871$	−32.3078	−	18.6529i	−1.09471	−	0.632030i
$872$	−8.48305	−	9.16638i	−0.287272	−	0.310413i
$873$		0			0
$874$	−1.79774	−	0.866702i	−0.0608093	−	0.0293166i
$875$	−84.1795	+	37.7051i	−2.84579	+	1.27466i
$876$		0			0
$877$	−19.0946	−	33.0728i	−0.644778	−	1.11679i	−0.984353	−	0.176209i	$-0.943617\pi$
$877$	−19.0946	−	33.0728i	−0.644778	−	1.11679i	0.339575	−	0.940579i	$-0.389717\pi$
$878$	50.5335	+	24.3626i	1.70542	+	0.822198i
$879$		0			0
$880$	−14.1557	−	3.25673i	−0.477190	−	0.109784i
$881$		−	8.90061i		−	0.299869i	−0.988696	−	0.149935i	$-0.952094\pi$
$881$		−	8.90061i		−	0.299869i	0.988696	−	0.149935i	$-0.0479063\pi$
$882$		0			0
$883$		−	4.49083i		−	0.151128i	−0.997141	−	0.0755642i	$-0.975924\pi$
$883$		−	4.49083i		−	0.151128i	0.997141	−	0.0755642i	$-0.0240758\pi$
$884$	18.2572	−	14.5338i	0.614056	−	0.488825i
$885$		0			0
$886$	4.54533	−	9.42804i	0.152703	−	0.316741i
$887$	−4.31989	−	7.48226i	−0.145048	−	0.251230i	0.784343	−	0.620327i	$-0.213000\pi$
$887$	−4.31989	−	7.48226i	−0.145048	−	0.251230i	−0.929391	+	0.369097i	$0.879667\pi$
$888$		0			0
$889$	45.0385	−	20.1733i	1.51054	−	0.676591i
$890$	−23.2783	+	48.2844i	−0.780290	+	1.61850i
$891$		0			0
$892$	−47.0295	−	18.5047i	−1.57467	−	0.619583i
$893$	−1.53611	−	0.886875i	−0.0514041	−	0.0296781i
$894$		0			0
$895$	57.8383	+	33.3930i	1.93332	+	1.11620i
$896$	27.3550	−	12.1533i	0.913866	−	0.406015i
$897$		0			0
$898$	−33.5635	−	16.1812i	−1.12003	−	0.539974i
$899$	−13.1670	−	22.8059i	−0.439144	−	0.760620i
$900$		0			0
$901$	6.54705	−	11.3398i	0.218114	−	0.377784i
$902$	0.334422	+	4.48860i	0.0111350	+	0.149454i
$903$		0			0
$904$	0.407618	+	0.126313i	0.0135572	+	0.00420111i
$905$	27.4684	−	15.8589i	0.913080	−	0.527167i
$906$		0			0
$907$	−28.2465	−	16.3081i	−0.937909	−	0.541502i	−0.0486050	−	0.998818i	$-0.515478\pi$
$907$	−28.2465	−	16.3081i	−0.937909	−	0.541502i	−0.889304	+	0.457316i	$0.848811\pi$
$908$	15.6883	−	2.35076i	0.520636	−	0.0780127i
$909$		0			0
$910$	−1.52779	+	54.3270i	−0.0506458	+	1.80092i
$911$	−6.60698	−	11.4436i	−0.218899	−	0.379144i	0.735573	−	0.677446i	$-0.236913\pi$
$911$	−6.60698	−	11.4436i	−0.218899	−	0.379144i	−0.954472	+	0.298302i	$0.903580\pi$
$912$		0			0
$913$	−1.97164			−0.0652519
$914$	−4.84148	+	10.0423i	−0.160142	+	0.332171i
$915$		0			0
$916$	5.31992	−	13.5205i	0.175775	−	0.446731i
$917$	27.5966	−	38.1628i	0.911321	−	1.26025i
$918$		0			0
$919$	30.5731	+	17.6514i	1.00851	+	0.582265i	0.910756	−	0.412945i	$-0.135500\pi$
$919$	30.5731	+	17.6514i	1.00851	+	0.582265i	0.0977572	+	0.995210i	$0.468833\pi$
$920$	−49.0176	−	15.1896i	−1.61606	−	0.500786i
$921$		0			0
$922$	0.420779	+	5.64768i	0.0138576	+	0.185996i
$923$	−23.7696	+	41.1702i	−0.782386	+	1.35513i
$924$		0			0
$925$	12.7049	+	22.0055i	0.417733	+	0.723535i
$926$	21.8135	−	14.8584i	0.716836	−	0.488276i
$927$		0			0
$928$	−24.3010	−	3.71656i	−0.797720	−	0.122002i
$929$			16.5478i			0.542916i	0.962450	+	0.271458i	$0.0875059\pi$
$929$			16.5478i			0.542916i	−0.962450	+	0.271458i	$0.912494\pi$
$930$		0			0
$931$	2.20447	−	0.727199i	0.0722486	−	0.0238330i
$932$	6.59094	+	43.9862i	0.215894	+	1.44082i
$933$		0			0
$934$	29.2253	+	42.9054i	0.956280	+	1.40391i
$935$	6.21832	+	10.7704i	0.203361	+	0.352231i
$936$		0			0
$937$	−42.2809			−1.38126			−0.690628	−	0.723211i	$-0.742666\pi$
$937$	−42.2809			−1.38126			−0.690628	+	0.723211i	$0.742666\pi$
$938$	−1.15175	+	40.9551i	−0.0376059	+	1.33723i
$939$		0			0
$940$	−42.4416	−	16.6995i	−1.38429	−	0.544677i
$941$		−	39.2228i		−	1.27863i	−0.768946	−	0.639314i	$-0.779219\pi$
$941$		−	39.2228i		−	1.27863i	0.768946	−	0.639314i	$-0.220781\pi$
$942$		0			0
$943$			15.9017i			0.517831i
$944$	2.17492	−	9.45352i	0.0707876	−	0.307686i
$945$		0			0
$946$	−2.55469	−	1.23164i	−0.0830602	−	0.0400439i
$947$	19.1031			0.620769			0.310384	−	0.950611i	$-0.399542\pi$
$947$	19.1031			0.620769			0.310384	+	0.950611i	$0.399542\pi$
$948$		0			0
$949$	29.9180			0.971180
$950$	−0.459148	−	6.16267i	−0.0148967	−	0.199943i
$951$		0			0
$952$	−23.5757	−	10.0505i	−0.764092	−	0.325739i
$953$		−	26.4380i		−	0.856410i	−0.903682	−	0.428205i	$-0.859146\pi$
$953$		−	26.4380i		−	0.856410i	0.903682	−	0.428205i	$-0.140854\pi$
$954$		0			0
$955$	1.62719	−	0.939459i	0.0526546	−	0.0304002i
$956$	33.8032	−	5.06512i	1.09328	−	0.163818i
$957$		0			0
$958$	8.54841	+	12.5499i	0.276187	+	0.405468i
$959$	−2.10486	+	20.4669i	−0.0679695	+	0.660910i
$960$		0			0
$961$	−5.71918			−0.184490
$962$	9.26519	−	0.690300i	0.298722	−	0.0222562i
$963$		0			0
$964$	11.1596	−	1.67216i	0.359426	−	0.0538568i
$965$	6.52067	−	3.76471i	0.209908	−	0.121190i
$966$		0			0
$967$	35.9050	+	20.7298i	1.15463	+	0.666625i	0.950011	−	0.312217i	$-0.101072\pi$
$967$	35.9050	+	20.7298i	1.15463	+	0.666625i	0.204617	+	0.978842i	$0.434405\pi$
$968$	19.7387	+	21.3287i	0.634425	+	0.685530i
$969$		0			0
$970$	−36.8173	+	25.0783i	−1.18213	+	0.805216i
$971$	−6.51503	+	11.2844i	−0.209077	+	0.362132i	−0.951424	−	0.307883i	$-0.900379\pi$
$971$	−6.51503	+	11.2844i	−0.209077	+	0.362132i	0.742347	+	0.670016i	$0.233713\pi$
$972$		0			0
$973$	3.18330	−	30.9532i	0.102052	−	0.992315i
$974$	−2.44888	−	32.8688i	−0.0784671	−	1.05318i
$975$		0			0
$976$	7.58078	−	32.9507i	0.242655	−	1.05473i
$977$			29.2391i			0.935440i	0.883877	+	0.467720i	$0.154925\pi$
$977$			29.2391i			0.935440i	−0.883877	+	0.467720i	$0.845075\pi$
$978$		0			0
$979$	−6.55769	+	3.78608i	−0.209585	+	0.121004i
$980$	53.2873	−	26.8920i	1.70220	−	0.859033i
$981$		0			0
$982$	18.6844	+	27.4304i	0.596242	+	0.875339i
$983$	21.4720	−	37.1906i	0.684851	−	1.18620i	−0.288633	−	0.957440i	$-0.593201\pi$
$983$	21.4720	−	37.1906i	0.684851	−	1.18620i	0.973484	−	0.228757i	$-0.0734660\pi$
$984$		0			0
$985$	43.0903	+	74.6347i	1.37297	+	2.37806i
$986$	11.8494	+	17.3960i	0.377361	+	0.554002i
$987$		0			0
$988$	−2.10267	−	0.827336i	−0.0668947	−	0.0263211i
$989$	−8.67721	−	5.00979i	−0.275919	−	0.159302i
$990$		0			0
$991$	−27.4338	+	15.8389i	−0.871463	+	0.503139i	−0.867834	−	0.496854i	$-0.834488\pi$
$991$	−27.4338	+	15.8389i	−0.871463	+	0.503139i	−0.00362864	+	0.999993i	$0.501155\pi$
$992$	−21.4302	+	26.7537i	−0.680409	+	0.849431i
$993$		0			0
$994$	52.1895	+	1.46768i	1.65535	+	0.0465521i
$995$	29.1805	−	50.5420i	0.925082	−	1.60229i
$996$		0			0
$997$	12.5646	−	21.7625i	0.397924	−	0.689224i	−0.595546	−	0.803321i	$-0.703064\pi$
$997$	12.5646	−	21.7625i	0.397924	−	0.689224i	0.993470	+	0.114097i	$0.0363975\pi$
$998$	−1.33762	−	17.9536i	−0.0423418	−	0.568310i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.17		88
3.2	odd	2		252.2.bb.a.23.28	yes	88
4.3	odd	2	inner	756.2.bb.a.611.28		88
7.4	even	3		756.2.o.a.179.13		88
9.2	odd	6		756.2.o.a.359.2		88
9.7	even	3		252.2.o.a.191.43	yes	88
12.11	even	2		252.2.bb.a.23.17	yes	88
21.11	odd	6		252.2.o.a.95.32	✓	88
28.11	odd	6		756.2.o.a.179.2		88
36.7	odd	6		252.2.o.a.191.32	yes	88
36.11	even	6		756.2.o.a.359.13		88
63.11	odd	6	inner	756.2.bb.a.683.28		88
63.25	even	3		252.2.bb.a.11.17	yes	88
84.11	even	6		252.2.o.a.95.43	yes	88
252.11	even	6	inner	756.2.bb.a.683.17		88
252.151	odd	6		252.2.bb.a.11.28	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.32	✓	88	21.11	odd	6
252.2.o.a.95.43	yes	88	84.11	even	6
252.2.o.a.191.32	yes	88	36.7	odd	6
252.2.o.a.191.43	yes	88	9.7	even	3
252.2.bb.a.11.17	yes	88	63.25	even	3
252.2.bb.a.11.28	yes	88	252.151	odd	6
252.2.bb.a.23.17	yes	88	12.11	even	2
252.2.bb.a.23.28	yes	88	3.2	odd	2
756.2.o.a.179.2		88	28.11	odd	6
756.2.o.a.179.13		88	7.4	even	3
756.2.o.a.359.2		88	9.2	odd	6
756.2.o.a.359.13		88	36.11	even	6
756.2.bb.a.611.17		88	1.1	even	1	trivial
756.2.bb.a.611.28		88	4.3	odd	2	inner
756.2.bb.a.683.17		88	252.11	even	6	inner
756.2.bb.a.683.28		88	63.11	odd	6	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.614155 + 1.27390i) q^{2} +(-1.24563 - 1.56474i) q^{4} +(3.69227 - 2.13173i) q^{5} +(-1.08153 - 2.41460i) q^{7} +(2.75833 - 0.625806i) q^{8} +O(q^{10})\)	\(q+(-0.614155 + 1.27390i) q^{2} +(-1.24563 - 1.56474i) q^{4} +(3.69227 - 2.13173i) q^{5} +(-1.08153 - 2.41460i) q^{7} +(2.75833 - 0.625806i) q^{8} +(0.447980 + 6.01278i) q^{10} +(-0.425873 + 0.737633i) q^{11} +(-1.70346 + 2.95047i) q^{13} +(3.74018 + 0.105182i) q^{14} +(-0.896829 + 3.89817i) q^{16} +(2.96593 - 1.71238i) q^{17} +(-0.287188 - 0.165808i) q^{19} +(-7.93479 - 3.12210i) q^{20} +(-0.678117 - 0.995539i) q^{22} +(-2.12777 - 3.68541i) q^{23} +(6.58855 - 11.4117i) q^{25} +(-2.71241 - 3.98208i) q^{26} +(-2.43104 + 4.70000i) q^{28} +(3.76358 - 2.17290i) q^{29} -6.05964i q^{31} +(-4.41507 - 3.53655i) q^{32} +(0.359855 + 4.82996i) q^{34} +(-9.14057 - 6.60981i) q^{35} +(-0.964162 + 1.66998i) q^{37} +(0.387601 - 0.264016i) q^{38} +(8.85043 - 8.19065i) q^{40} +(-3.23608 - 1.86835i) q^{41} +(2.03904 - 1.17724i) q^{43} +(1.68468 - 0.252435i) q^{44} +(6.00161 - 0.447148i) q^{46} +5.34880 q^{47} +(-4.66059 + 5.22292i) q^{49} +(10.4909 + 15.4017i) q^{50} +(6.73860 - 1.00972i) q^{52} +(3.31113 - 1.91168i) q^{53} +3.63138i q^{55} +(-4.49428 - 5.98343i) q^{56} +(0.456633 + 6.12891i) q^{58} -2.42512 q^{59} -8.45286 q^{61} +(7.71935 + 3.72156i) q^{62} +(7.21673 - 3.45235i) q^{64} +14.5252i q^{65} +10.9500i q^{67} +(-6.37388 - 2.50793i) q^{68} +(14.0340 - 7.58469i) q^{70} +13.9538 q^{71} +(-4.39078 - 7.60506i) q^{73} +(-1.53523 - 2.25387i) q^{74} +(0.0982825 + 0.655911i) q^{76} +(2.24168 + 0.230540i) q^{77} -4.69272i q^{79} +(4.99851 + 16.3049i) q^{80} +(4.36754 - 2.97497i) q^{82} +(1.15741 + 2.00470i) q^{83} +(7.30067 - 12.6451i) q^{85} +(0.247395 + 3.32053i) q^{86} +(-0.713081 + 2.30115i) q^{88} +(7.69912 + 4.44509i) q^{89} +(8.96655 + 0.922141i) q^{91} +(-3.11630 + 7.92005i) q^{92} +(-3.28499 + 6.81382i) q^{94} -1.41383 q^{95} +(3.69412 + 6.39841i) q^{97} +(-3.79114 - 9.14479i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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