LMFDB - Embedded newform 666.2.x.g.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(127,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("666.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.x (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			127.2
Root			$-2.00752 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	666.127
Dual form			666.2.x.g.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{5} +(0.598489 - 3.39420i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{5} +(0.598489 - 3.39420i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.939693 - 1.62760i) q^{10} +(-1.40483 - 2.43324i) q^{11} +(-2.65877 - 2.23097i) q^{13} +(1.72328 - 2.98481i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.37417 - 1.99217i) q^{17} +(-6.99748 + 2.54687i) q^{19} +(1.43969 - 1.20805i) q^{20} +(-0.487893 - 2.76698i) q^{22} +(-0.321769 + 0.557320i) q^{23} +(1.37939 + 0.502055i) q^{25} +(-1.73539 - 3.00578i) q^{26} +(2.64022 - 2.21541i) q^{28} +(1.08449 + 1.87840i) q^{29} +9.90716 q^{31} +(-0.173648 + 0.984808i) q^{32} +(2.91235 - 1.06001i) q^{34} +(-6.08678 - 2.21541i) q^{35} +(-2.56368 - 5.51612i) q^{37} -7.44656 q^{38} +(1.76604 - 0.642788i) q^{40} +(8.13803 + 6.82862i) q^{41} +8.30465 q^{43} +(0.487893 - 2.76698i) q^{44} +(-0.492978 + 0.413658i) q^{46} +(-3.92821 + 6.80387i) q^{47} +(-4.58455 - 1.66864i) q^{49} +(1.12449 + 0.943555i) q^{50} +(-0.602694 - 3.41805i) q^{52} +(-0.839394 - 4.76044i) q^{53} +(-4.96199 + 1.80602i) q^{55} +(3.23871 - 1.17879i) q^{56} +(0.376641 + 2.13604i) q^{58} +(-0.0961039 - 0.545032i) q^{59} +(5.37102 + 4.50682i) q^{61} +(9.30969 + 3.38845i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-4.99685 + 4.19285i) q^{65} +(0.0366435 - 0.207815i) q^{67} +3.09926 q^{68} +(-4.96199 - 4.16360i) q^{70} +(4.75197 - 1.72957i) q^{71} +10.2297 q^{73} +(-0.522449 - 6.06028i) q^{74} +(-6.99748 - 2.54687i) q^{76} +(-9.09967 + 3.31201i) q^{77} +(-0.330775 + 1.87592i) q^{79} +1.87939 q^{80} +(5.31172 + 9.20017i) q^{82} +(-5.21650 + 4.37717i) q^{83} +(-2.91235 - 5.04435i) q^{85} +(7.80382 + 2.84036i) q^{86} +(1.40483 - 2.43324i) q^{88} +(1.68226 + 9.54055i) q^{89} +(-9.16360 + 7.68917i) q^{91} +(-0.604727 + 0.220103i) q^{92} +(-6.01837 + 5.05001i) q^{94} +(2.43020 + 13.7823i) q^{95} +(-8.52990 + 14.7742i) q^{97} +(-3.73736 - 3.13602i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.326352	−	1.85083i	0.145949	−	0.827718i	−0.820651	−	0.571429i	$-0.806389\pi$
$5$	0.326352	−	1.85083i	0.145949	−	0.827718i	0.966600	−	0.256289i	$-0.0824997\pi$
$6$		0			0
$7$	0.598489	−	3.39420i	0.226208	−	1.28289i	−0.634156	−	0.773205i	$-0.718652\pi$
$7$	0.598489	−	3.39420i	0.226208	−	1.28289i	0.860363	−	0.509681i	$-0.170237\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	0.939693	−	1.62760i	0.297157	−	0.514691i
$11$	−1.40483	−	2.43324i	−0.423572	−	0.733649i	0.572714	−	0.819756i	$-0.305891\pi$
$11$	−1.40483	−	2.43324i	−0.423572	−	0.733649i	−0.996286	+	0.0861067i	$0.972557\pi$
$12$		0			0
$13$	−2.65877	−	2.23097i	−0.737409	−	0.618760i	0.194731	−	0.980857i	$-0.437617\pi$
$13$	−2.65877	−	2.23097i	−0.737409	−	0.618760i	−0.932141	+	0.362097i	$0.882061\pi$
$14$	1.72328	−	2.98481i	0.460566	−	0.797724i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.37417	−	1.99217i	0.575822	−	0.483172i	−0.307750	−	0.951467i	$-0.599576\pi$
$17$	2.37417	−	1.99217i	0.575822	−	0.483172i	0.883572	+	0.468295i	$0.155132\pi$
$18$		0			0
$19$	−6.99748	+	2.54687i	−1.60533	+	0.584293i	−0.980509	−	0.196474i	$-0.937051\pi$
$19$	−6.99748	+	2.54687i	−1.60533	+	0.584293i	−0.624822	+	0.780767i	$0.714829\pi$
$20$	1.43969	−	1.20805i	0.321925	−	0.270127i
$21$		0			0
$22$	−0.487893	−	2.76698i	−0.104019	−	0.589921i
$23$	−0.321769	+	0.557320i	−0.0670934	+	0.116209i	−0.897621	−	0.440769i	$-0.854706\pi$
$23$	−0.321769	+	0.557320i	−0.0670934	+	0.116209i	0.830527	+	0.556978i	$0.188039\pi$
$24$		0			0
$25$	1.37939	+	0.502055i	0.275877	+	0.100411i
$26$	−1.73539	−	3.00578i	−0.340337	−	0.589482i
$27$		0			0
$28$	2.64022	−	2.21541i	0.498954	−	0.418672i
$29$	1.08449	+	1.87840i	0.201385	+	0.348810i	0.948975	−	0.315351i	$-0.102122\pi$
$29$	1.08449	+	1.87840i	0.201385	+	0.348810i	−0.747590	+	0.664161i	$0.768789\pi$
$30$		0			0
$31$	9.90716			1.77938			0.889690	−	0.456566i	$-0.150921\pi$
$31$	9.90716			1.77938			0.889690	+	0.456566i	$0.150921\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$		0			0
$34$	2.91235	−	1.06001i	0.499465	−	0.181790i
$35$	−6.08678	−	2.21541i	−1.02885	−	0.374472i
$36$		0			0
$37$	−2.56368	−	5.51612i	−0.421466	−	0.906844i
$37$	−2.56368	−	5.51612i	−0.421466	−	0.906844i
$38$	−7.44656			−1.20799
$39$		0			0
$40$	1.76604	−	0.642788i	0.279236	−	0.101634i
$41$	8.13803	+	6.82862i	1.27095	+	1.06645i	0.994425	+	0.105443i	$0.0336261\pi$
$41$	8.13803	+	6.82862i	1.27095	+	1.06645i	0.276521	+	0.961008i	$0.410818\pi$
$42$		0			0
$43$	8.30465			1.26645			0.633224	−	0.773969i	$-0.281731\pi$
$43$	8.30465			1.26645			0.633224	+	0.773969i	$0.281731\pi$
$44$	0.487893	−	2.76698i	0.0735526	−	0.417137i
$45$		0			0
$46$	−0.492978	+	0.413658i	−0.0726857	+	0.0609905i
$47$	−3.92821	+	6.80387i	−0.572989	+	0.992446i	0.423268	+	0.906004i	$0.360883\pi$
$47$	−3.92821	+	6.80387i	−0.572989	+	0.992446i	−0.996257	+	0.0864413i	$0.972450\pi$
$48$		0			0
$49$	−4.58455	−	1.66864i	−0.654935	−	0.238377i
$50$	1.12449	+	0.943555i	0.159026	+	0.133439i
$51$		0			0
$52$	−0.602694	−	3.41805i	−0.0835786	−	0.473998i
$53$	−0.839394	−	4.76044i	−0.115300	−	0.653897i	−0.986601	−	0.163149i	$-0.947835\pi$
$53$	−0.839394	−	4.76044i	−0.115300	−	0.653897i	0.871302	−	0.490748i	$-0.163276\pi$
$54$		0			0
$55$	−4.96199	+	1.80602i	−0.669074	+	0.243523i
$56$	3.23871	−	1.17879i	0.432790	−	0.157523i
$57$		0			0
$58$	0.376641	+	2.13604i	0.0494553	+	0.280475i
$59$	−0.0961039	−	0.545032i	−0.0125117	−	0.0709572i	0.977913	−	0.209014i	$-0.0670254\pi$
$59$	−0.0961039	−	0.545032i	−0.0125117	−	0.0709572i	−0.990424	+	0.138057i	$0.955914\pi$
$60$		0			0
$61$	5.37102	+	4.50682i	0.687689	+	0.577039i	0.918242	−	0.396020i	$-0.129609\pi$
$61$	5.37102	+	4.50682i	0.687689	+	0.577039i	−0.230553	+	0.973060i	$0.574053\pi$
$62$	9.30969	+	3.38845i	1.18233	+	0.430333i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.99685	+	4.19285i	−0.619783	+	0.520060i
$66$		0			0
$67$	0.0366435	−	0.207815i	0.00447671	−	0.0253887i	−0.982488	−	0.186328i	$-0.940341\pi$
$67$	0.0366435	−	0.207815i	0.00447671	−	0.0253887i	0.986964	+	0.160939i	$0.0514524\pi$
$68$	3.09926			0.375841
$69$		0			0
$70$	−4.96199	−	4.16360i	−0.593071	−	0.497646i
$71$	4.75197	−	1.72957i	0.563955	−	0.205263i	−0.0442811	−	0.999019i	$-0.514100\pi$
$71$	4.75197	−	1.72957i	0.563955	−	0.205263i	0.608236	+	0.793756i	$0.291877\pi$
$72$		0			0
$73$	10.2297			1.19730			0.598648	−	0.801012i	$-0.295705\pi$
$73$	10.2297			1.19730			0.598648	+	0.801012i	$0.295705\pi$
$74$	−0.522449	−	6.06028i	−0.0607334	−	0.704494i
$75$		0			0
$76$	−6.99748	−	2.54687i	−0.802666	−	0.292146i
$77$	−9.09967	+	3.31201i	−1.03700	+	0.377438i
$78$		0			0
$79$	−0.330775	+	1.87592i	−0.0372151	+	0.211057i	−0.997745	−	0.0671197i	$-0.978619\pi$
$79$	−0.330775	+	1.87592i	−0.0372151	+	0.211057i	0.960530	+	0.278177i	$0.0897302\pi$
$80$	1.87939			0.210122
$81$		0			0
$82$	5.31172	+	9.20017i	0.586582	+	1.01599i
$83$	−5.21650	+	4.37717i	−0.572586	+	0.480456i	−0.882503	−	0.470307i	$-0.844143\pi$
$83$	−5.21650	+	4.37717i	−0.572586	+	0.480456i	0.309917	+	0.950764i	$0.399699\pi$
$84$		0			0
$85$	−2.91235	−	5.04435i	−0.315889	−	0.547136i
$86$	7.80382	+	2.84036i	0.841507	+	0.306284i
$87$		0			0
$88$	1.40483	−	2.43324i	0.149755	−	0.259384i
$89$	1.68226	+	9.54055i	0.178319	+	1.01130i	0.934243	+	0.356637i	$0.116077\pi$
$89$	1.68226	+	9.54055i	0.178319	+	1.01130i	−0.755924	+	0.654659i	$0.772812\pi$
$90$		0			0
$91$	−9.16360	+	7.68917i	−0.960606	+	0.806044i
$92$	−0.604727	+	0.220103i	−0.0630472	+	0.0229473i
$93$		0			0
$94$	−6.01837	+	5.05001i	−0.620748	+	0.520869i
$95$	2.43020	+	13.7823i	0.249333	+	1.41404i
$96$		0			0
$97$	−8.52990	+	14.7742i	−0.866080	+	1.50009i	−0.000109562		1.00000i	$0.500035\pi$
$97$	−8.52990	+	14.7742i	−0.866080	+	1.50009i	−0.865971	+	0.500095i	$0.833298\pi$
$98$	−3.73736	−	3.13602i	−0.377530	−	0.316785i
$99$		0			0
$100$	0.733956	+	1.27125i	0.0733956	+	0.127125i
$101$	5.98911	−	10.3734i	0.595938	−	1.03220i	−0.397475	−	0.917613i	$-0.630114\pi$
$101$	5.98911	−	10.3734i	0.595938	−	1.03220i	0.993414	−	0.114583i	$-0.0365531\pi$
$102$		0			0
$103$	−6.47233	−	11.2104i	−0.637737	−	1.10459i	−0.985928	−	0.167170i	$-0.946537\pi$
$103$	−6.47233	−	11.2104i	−0.637737	−	1.10459i	0.348191	−	0.937424i	$-0.386796\pi$
$104$	0.602694	−	3.41805i	0.0590990	−	0.335167i
$105$		0			0
$106$	0.839394	−	4.76044i	0.0815291	−	0.462375i
$107$	−11.9706	−	10.0445i	−1.15724	−	0.971037i	−0.157374	−	0.987539i	$-0.550303\pi$
$107$	−11.9706	−	10.0445i	−1.15724	−	0.971037i	−0.999864	+	0.0165017i	$0.994747\pi$
$108$		0			0
$109$	−1.45663	−	0.530170i	−0.139520	−	0.0507810i	0.271317	−	0.962490i	$-0.412541\pi$
$109$	−1.45663	−	0.530170i	−0.139520	−	0.0507810i	−0.410836	+	0.911709i	$0.634763\pi$
$110$	−5.28044			−0.503470
$111$		0			0
$112$	3.44656			0.325669
$113$	−4.80629	−	1.74935i	−0.452138	−	0.164565i	0.105906	−	0.994376i	$-0.466226\pi$
$113$	−4.80629	−	1.74935i	−0.452138	−	0.164565i	−0.558044	+	0.829811i	$0.688448\pi$
$114$		0			0
$115$	0.926496	+	0.777422i	0.0863962	+	0.0724950i
$116$	−0.376641	+	2.13604i	−0.0349702	+	0.198326i
$117$		0			0
$118$	0.0961039	−	0.545032i	0.00884708	−	0.0501743i
$119$	−5.34090	−	9.25071i	−0.489599	−	0.848011i
$120$		0			0
$121$	1.55290	−	2.68971i	0.141173	−	0.244519i
$122$	3.50569	+	6.07203i	0.317390	+	0.549735i
$123$		0			0
$124$	7.58933	+	6.36820i	0.681542	+	0.571881i
$125$	6.07785	−	10.5271i	0.543619	−	0.941576i
$126$		0			0
$127$	−1.23207	−	6.98740i	−0.109328	−	0.620032i	−0.989403	−	0.145196i	$-0.953619\pi$
$127$	−1.23207	−	6.98740i	−0.109328	−	0.620032i	0.880075	−	0.474836i	$-0.157492\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$		0			0
$130$	−6.12954	+	2.23097i	−0.537596	+	0.195669i
$131$	−13.3781	+	11.2256i	−1.16885	+	0.980781i	−0.999988	−	0.00485874i	$-0.998453\pi$
$131$	−13.3781	+	11.2256i	−1.16885	+	0.980781i	−0.168861	+	0.985640i	$0.554009\pi$
$132$		0			0
$133$	4.45668	+	25.2751i	0.386443	+	2.19163i
$134$	0.105511	−	0.182750i	0.00911473	−	0.0157872i
$135$		0			0
$136$	2.91235	+	1.06001i	0.249732	+	0.0908951i
$137$	4.92852	+	8.53645i	0.421072	+	0.729318i	0.996045	−	0.0888546i	$-0.0283206\pi$
$137$	4.92852	+	8.53645i	0.421072	+	0.729318i	−0.574973	+	0.818173i	$0.694987\pi$
$138$		0			0
$139$	−6.89049	+	5.78181i	−0.584444	+	0.490407i	−0.886403	−	0.462914i	$-0.846804\pi$
$139$	−6.89049	+	5.78181i	−0.584444	+	0.490407i	0.301959	+	0.953321i	$0.402359\pi$
$140$	−3.23871	−	5.60960i	−0.273721	−	0.474098i
$141$		0			0
$142$	5.05694			0.424369
$143$	−1.69337	+	9.60355i	−0.141606	+	0.803089i
$144$		0			0
$145$	3.83053	−	1.39420i	0.318108	−	0.115782i
$146$	9.61277	+	3.49876i	0.795559	+	0.289560i
$147$		0			0
$148$	1.58180	−	5.87349i	0.130023	−	0.482798i
$149$	9.97301			0.817021			0.408511	−	0.912754i	$-0.366048\pi$
$149$	9.97301			0.817021			0.408511	+	0.912754i	$0.366048\pi$
$150$		0			0
$151$	−9.07997	+	3.30484i	−0.738918	+	0.268944i	−0.683935	−	0.729543i	$-0.739733\pi$
$151$	−9.07997	+	3.30484i	−0.738918	+	0.268944i	−0.0549831	+	0.998487i	$0.517510\pi$
$152$	−5.70440	−	4.78656i	−0.462688	−	0.388241i
$153$		0			0
$154$	−9.68366			−0.780332
$155$	3.23322	−	18.3365i	0.259699	−	1.47282i
$156$		0			0
$157$	−6.73320	+	5.64982i	−0.537368	+	0.450905i	−0.870637	−	0.491927i	$-0.836293\pi$
$157$	−6.73320	+	5.64982i	−0.537368	+	0.450905i	0.333269	+	0.942832i	$0.391848\pi$
$158$	−0.952429	+	1.64965i	−0.0757712	+	0.131239i
$159$		0			0
$160$	1.76604	+	0.642788i	0.139618	+	0.0508168i
$161$	1.69908	+	1.42570i	0.133906	+	0.112361i
$162$		0			0
$163$	−0.331175	−	1.87819i	−0.0259397	−	0.147111i	0.969087	−	0.246719i	$-0.0793524\pi$
$163$	−0.331175	−	1.87819i	−0.0259397	−	0.147111i	−0.995027	+	0.0996076i	$0.968241\pi$
$164$	1.84474	+	10.4620i	0.144050	+	0.816949i
$165$		0			0
$166$	−6.39899	+	2.32904i	−0.496658	+	0.180769i
$167$	6.22793	−	2.26678i	0.481932	−	0.175409i	−0.0896181	−	0.995976i	$-0.528565\pi$
$167$	6.22793	−	2.26678i	0.481932	−	0.175409i	0.571550	+	0.820567i	$0.306342\pi$
$168$		0			0
$169$	−0.165612	−	0.939235i	−0.0127394	−	0.0722488i
$170$	−1.01145	−	5.73622i	−0.0775747	−	0.439948i
$171$		0			0
$172$	6.36173	+	5.33813i	0.485077	+	0.407028i
$173$	23.8769	+	8.69049i	1.81533	+	0.660725i	0.996198	+	0.0871179i	$0.0277657\pi$
$173$	23.8769	+	8.69049i	1.81533	+	0.660725i	0.819130	+	0.573608i	$0.194457\pi$
$174$		0			0
$175$	2.52962	−	4.38143i	0.191221	−	0.331205i
$176$	2.15233	−	1.80602i	0.162238	−	0.136134i
$177$		0			0
$178$	−1.68226	+	9.54055i	−0.126090	+	0.715095i
$179$	−8.12492			−0.607285			−0.303643	−	0.952786i	$-0.598203\pi$
$179$	−8.12492			−0.607285			−0.303643	+	0.952786i	$0.598203\pi$
$180$		0			0
$181$	9.12118	+	7.65358i	0.677972	+	0.568886i	0.915413	−	0.402516i	$-0.131864\pi$
$181$	9.12118	+	7.65358i	0.677972	+	0.568886i	−0.237441	+	0.971402i	$0.576309\pi$
$182$	−11.2408	+	4.09132i	−0.833225	+	0.303269i
$183$		0			0
$184$	−0.643537			−0.0474422
$185$	−11.0461	+	2.94475i	−0.812123	+	0.216502i
$186$		0			0
$187$	−8.18273	−	2.97827i	−0.598381	−	0.217793i
$188$	−7.38263	+	2.68706i	−0.538433	+	0.195974i
$189$		0			0
$190$	−2.43020	+	13.7823i	−0.176305	+	0.999876i
$191$	−0.266722			−0.0192993			−0.00964965	−	0.999953i	$-0.503072\pi$
$191$	−0.266722			−0.0192993			−0.00964965	+	0.999953i	$0.503072\pi$
$192$		0			0
$193$	−3.96417	−	6.86615i	−0.285348	−	0.494236i	0.687346	−	0.726330i	$-0.258776\pi$
$193$	−3.96417	−	6.86615i	−0.285348	−	0.494236i	−0.972693	+	0.232094i	$0.925442\pi$
$194$	−13.0686	+	10.9658i	−0.938268	+	0.787301i
$195$		0			0
$196$	−2.43939	−	4.22514i	−0.174242	−	0.301796i
$197$	−0.386805	−	0.140786i	−0.0275587	−	0.0100306i	0.328204	−	0.944607i	$-0.393557\pi$
$197$	−0.386805	−	0.140786i	−0.0275587	−	0.0100306i	−0.355763	+	0.934576i	$0.615779\pi$
$198$		0			0
$199$	1.01751	−	1.76239i	0.0721297	−	0.124932i	−0.827705	−	0.561164i	$-0.810354\pi$
$199$	1.01751	−	1.76239i	0.0721297	−	0.124932i	0.899834	+	0.436232i	$0.143687\pi$
$200$	0.254900	+	1.44561i	0.0180242	+	0.102220i
$201$		0			0
$202$	9.17584	−	7.69945i	0.645610	−	0.541731i
$203$	7.02471	−	2.55679i	0.493038	−	0.179451i
$204$		0			0
$205$	15.2945	−	12.8336i	1.06821	−	0.896338i
$206$	−2.24782	−	12.7480i	−0.156613	−	0.888195i
$207$		0			0
$208$	1.73539	−	3.00578i	0.120327	−	0.208413i
$209$	16.0274	+	13.4486i	1.10864	+	0.930259i
$210$		0			0
$211$	7.87052	+	13.6321i	0.541829	+	0.938475i	0.998799	+	0.0489932i	$0.0156013\pi$
$211$	7.87052	+	13.6321i	0.541829	+	0.938475i	−0.456970	+	0.889482i	$0.651065\pi$
$212$	2.41694	−	4.18626i	0.165996	−	0.287513i
$213$		0			0
$214$	−7.81323	−	13.5329i	−0.534101	−	0.925090i
$215$	2.71024	−	15.3705i	0.184837	−	1.04826i
$216$		0			0
$217$	5.92933	−	33.6269i	0.402509	−	2.28274i
$218$	−1.18745	−	0.996393i	−0.0804246	−	0.0674842i
$219$		0			0
$220$	−4.96199	−	1.80602i	−0.334537	−	0.121762i
$221$	−10.7568			−0.723584
$222$		0			0
$223$	−3.43531			−0.230045			−0.115023	−	0.993363i	$-0.536694\pi$
$223$	−3.43531			−0.230045			−0.115023	+	0.993363i	$0.536694\pi$
$224$	3.23871	+	1.17879i	0.216395	+	0.0787614i
$225$		0			0
$226$	−3.91812	−	3.28770i	−0.260630	−	0.218694i
$227$	0.401614	−	2.27767i	0.0266561	−	0.151174i	−0.968575	−	0.248723i	$-0.919989\pi$
$227$	0.401614	−	2.27767i	0.0266561	−	0.151174i	0.995231	+	0.0975489i	$0.0311002\pi$
$228$		0			0
$229$	−1.02642	+	5.82114i	−0.0678280	+	0.384672i	0.931929	+	0.362640i	$0.118125\pi$
$229$	−1.02642	+	5.82114i	−0.0678280	+	0.384672i	−0.999757	+	0.0220316i	$0.992987\pi$
$230$	0.604727	+	1.04742i	0.0398745	+	0.0690647i
$231$		0			0
$232$	−1.08449	+	1.87840i	−0.0712005	+	0.123323i
$233$	−14.1679	−	24.5395i	−0.928168	−	1.60763i	−0.786386	−	0.617736i	$-0.788050\pi$
$233$	−14.1679	−	24.5395i	−0.928168	−	1.60763i	−0.141782	−	0.989898i	$-0.545283\pi$
$234$		0			0
$235$	11.3108	+	9.49092i	0.737838	+	0.619120i
$236$	0.276720	−	0.479293i	0.0180129	−	0.0311993i
$237$		0			0
$238$	−1.85487	−	10.5195i	−0.120234	−	0.681879i
$239$	−18.5674	+	15.5799i	−1.20103	+	1.00778i	−0.201427	+	0.979504i	$0.564558\pi$
$239$	−18.5674	+	15.5799i	−1.20103	+	1.00778i	−0.999600	+	0.0282780i	$0.990998\pi$
$240$		0			0
$241$	−8.31692	+	3.02711i	−0.535740	+	0.194993i	−0.595700	−	0.803207i	$-0.703125\pi$
$241$	−8.31692	+	3.02711i	−0.535740	+	0.194993i	0.0599594	+	0.998201i	$0.480903\pi$
$242$	2.37918	−	1.99637i	0.152940	−	0.128332i
$243$		0			0
$244$	1.21751	+	6.90485i	0.0779432	+	0.442038i
$245$	−4.58455	+	7.94067i	−0.292896	+	0.507311i
$246$		0			0
$247$	24.2867	+	8.83962i	1.54532	+	0.562452i
$248$	4.95358	+	8.57985i	0.314553	+	0.544821i
$249$		0			0
$250$	9.31180	−	7.81353i	0.588930	−	0.494171i
$251$	3.29525	+	5.70754i	0.207994	+	0.360257i	0.951083	−	0.308937i	$-0.0999731\pi$
$251$	3.29525	+	5.70754i	0.207994	+	0.360257i	−0.743088	+	0.669193i	$0.766640\pi$
$252$		0			0
$253$	1.80812			0.113676
$254$	1.23207	−	6.98740i	0.0773068	−	0.438429i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	9.04522	+	3.29219i	0.564225	+	0.205361i	0.608356	−	0.793665i	$-0.291829\pi$
$257$	9.04522	+	3.29219i	0.564225	+	0.205361i	−0.0441304	+	0.999026i	$0.514052\pi$
$258$		0			0
$259$	−20.2571	+	5.40031i	−1.25872	+	0.335559i
$260$	−6.52292			−0.404534
$261$		0			0
$262$	−16.4107	+	5.97299i	−1.01385	+	0.369013i
$263$	1.21898	+	1.02284i	0.0751654	+	0.0630712i	0.679596	−	0.733586i	$-0.262155\pi$
$263$	1.21898	+	1.02284i	0.0751654	+	0.0630712i	−0.604431	+	0.796658i	$0.706599\pi$
$264$		0			0
$265$	−9.08472			−0.558070
$266$	−4.45668	+	25.2751i	−0.273257	+	1.54972i
$267$		0			0
$268$	0.161652	−	0.135642i	0.00987445	−	0.00828565i
$269$	11.5599	−	20.0223i	0.704819	−	1.22078i	−0.261938	−	0.965085i	$-0.584362\pi$
$269$	11.5599	−	20.0223i	0.704819	−	1.22078i	0.966757	−	0.255697i	$-0.0823051\pi$
$270$		0			0
$271$	−0.172362	−	0.0627348i	−0.0104703	−	0.00381087i	0.336780	−	0.941583i	$-0.390662\pi$
$271$	−0.172362	−	0.0627348i	−0.0104703	−	0.00381087i	−0.347250	+	0.937773i	$0.612884\pi$
$272$	2.37417	+	1.99217i	0.143955	+	0.120793i
$273$		0			0
$274$	1.71166	+	9.70729i	0.103405	+	0.586439i
$275$	−0.716183	−	4.06167i	−0.0431875	−	0.244928i
$276$		0			0
$277$	11.9260	−	4.34070i	0.716562	−	0.260807i	0.0420965	−	0.999114i	$-0.486596\pi$
$277$	11.9260	−	4.34070i	0.716562	−	0.260807i	0.674466	+	0.738306i	$0.264374\pi$
$278$	−8.45244	+	3.07644i	−0.506944	+	0.184512i
$279$		0			0
$280$	−1.12479	−	6.37901i	−0.0672191	−	0.381219i
$281$	−3.02774	−	17.1712i	−0.180620	−	1.02435i	−0.931455	−	0.363857i	$-0.881460\pi$
$281$	−3.02774	−	17.1712i	−0.180620	−	1.02435i	0.750835	−	0.660490i	$-0.229651\pi$
$282$		0			0
$283$	−10.0612	−	8.44232i	−0.598074	−	0.501844i	0.292752	−	0.956188i	$-0.405429\pi$
$283$	−10.0612	−	8.44232i	−0.598074	−	0.501844i	−0.890826	+	0.454345i	$0.849873\pi$
$284$	4.75197	+	1.72957i	0.281977	+	0.102631i
$285$		0			0
$286$	−4.87585	+	8.44522i	−0.288315	+	0.499376i
$287$	28.0482	−	23.5352i	1.65563	−	1.38924i
$288$		0			0
$289$	−1.28405	+	7.28223i	−0.0755325	+	0.428366i
$290$	4.07636			0.239372
$291$		0			0
$292$	7.83641	+	6.57552i	0.458591	+	0.384803i
$293$	6.37791	−	2.32137i	0.372602	−	0.135616i	−0.148930	−	0.988848i	$-0.547583\pi$
$293$	6.37791	−	2.32137i	0.372602	−	0.135616i	0.521532	+	0.853232i	$0.325361\pi$
$294$		0			0
$295$	−1.04013			−0.0605586
$296$	3.49526	−	4.97827i	0.203158	−	0.289356i
$297$		0			0
$298$	9.37157	+	3.41097i	0.542880	+	0.197592i
$299$	2.09887	−	0.763927i	0.121381	−	0.0441790i
$300$		0			0
$301$	4.97024	−	28.1876i	0.286480	−	1.62471i
$302$	−9.66271			−0.556026
$303$		0			0
$304$	−3.72328	−	6.44891i	−0.213545	−	0.369870i
$305$	10.0942	−	8.47006i	0.577993	−	0.484994i
$306$		0			0
$307$	−4.10242	−	7.10560i	−0.234138	−	0.405538i	0.724884	−	0.688871i	$-0.241893\pi$
$307$	−4.10242	−	7.10560i	−0.234138	−	0.405538i	−0.959022	+	0.283333i	$0.908560\pi$
$308$	−9.09967	−	3.31201i	−0.518502	−	0.188719i
$309$		0			0
$310$	9.30969	−	16.1249i	0.528755	−	0.915830i
$311$	1.88461	+	10.6882i	0.106867	+	0.606070i	0.990458	+	0.137812i	$0.0440071\pi$
$311$	1.88461	+	10.6882i	0.106867	+	0.606070i	−0.883592	+	0.468258i	$0.844882\pi$
$312$		0			0
$313$	−6.63058	+	5.56372i	−0.374783	+	0.314480i	−0.810650	−	0.585531i	$-0.800886\pi$
$313$	−6.63058	+	5.56372i	−0.374783	+	0.314480i	0.435867	+	0.900011i	$0.356442\pi$
$314$	−8.25949	+	3.00621i	−0.466110	+	0.169650i
$315$		0			0
$316$	−1.45921	+	1.22442i	−0.0820867	+	0.0688789i
$317$	4.41505	+	25.0390i	0.247974	+	1.40633i	0.813484	+	0.581587i	$0.197568\pi$
$317$	4.41505	+	25.0390i	0.247974	+	1.40633i	−0.565510	+	0.824741i	$0.691321\pi$
$318$		0			0
$319$	3.04706	−	5.27766i	0.170603	−	0.295492i
$320$	1.43969	+	1.20805i	0.0804813	+	0.0675318i
$321$		0			0
$322$	1.10899	+	1.92084i	0.0618019	+	0.107044i
$323$	−11.5394	+	19.9869i	−0.642071	+	1.11210i
$324$		0			0
$325$	−2.54739	−	4.41222i	−0.141304	−	0.244746i
$326$	0.331175	−	1.87819i	0.0183421	−	0.104023i
$327$		0			0
$328$	−1.84474	+	10.4620i	−0.101859	+	0.577670i
$329$	20.7427	+	17.4052i	1.14358	+	0.959578i
$330$		0			0
$331$	19.5470	+	7.11454i	1.07440	+	0.391050i	0.817821	−	0.575473i	$-0.195182\pi$
$331$	19.5470	+	7.11454i	1.07440	+	0.391050i	0.256581	+	0.966523i	$0.417404\pi$
$332$	−6.80966			−0.373729
$333$		0			0
$334$	6.62762			0.362647
$335$	−0.372673	−	0.135642i	−0.0203613	−	0.00741091i
$336$		0			0
$337$	−1.89385	−	1.58913i	−0.103165	−	0.0865653i	0.589746	−	0.807588i	$-0.299228\pi$
$337$	−1.89385	−	1.58913i	−0.103165	−	0.0865653i	−0.692911	+	0.721023i	$0.743672\pi$
$338$	0.165612	−	0.939235i	0.00900813	−	0.0510876i
$339$		0			0
$340$	1.01145	−	5.73622i	0.0548536	−	0.311090i
$341$	−13.9179	−	24.1065i	−0.753696	−	1.30544i
$342$		0			0
$343$	3.65547	−	6.33145i	0.197377	−	0.341866i
$344$	4.15233	+	7.19204i	0.223878	+	0.387769i
$345$		0			0
$346$	19.4646	+	16.3328i	1.04643	+	0.878055i
$347$	−2.92690	+	5.06953i	−0.157124	+	0.272147i	−0.933830	−	0.357716i	$-0.883556\pi$
$347$	−2.92690	+	5.06953i	−0.157124	+	0.272147i	0.776706	+	0.629863i	$0.216889\pi$
$348$		0			0
$349$	0.545283	+	3.09246i	0.0291883	+	0.165535i	0.995918	−	0.0902661i	$-0.0287718\pi$
$349$	0.545283	+	3.09246i	0.0291883	+	0.165535i	−0.966729	+	0.255801i	$0.917661\pi$
$350$	3.87561	−	3.25202i	0.207160	−	0.173828i
$351$		0			0
$352$	2.64022	−	0.960961i	0.140724	−	0.0512194i
$353$	8.61667	−	7.23024i	0.458619	−	0.384827i	−0.384004	−	0.923332i	$-0.625455\pi$
$353$	8.61667	−	7.23024i	0.458619	−	0.384827i	0.842623	+	0.538505i	$0.181011\pi$
$354$		0			0
$355$	−1.65034	−	9.35955i	−0.0875910	−	0.496753i
$356$	−4.84387	+	8.38982i	−0.256724	+	0.444660i
$357$		0			0
$358$	−7.63493	−	2.77889i	−0.403518	−	0.146869i
$359$	−11.5467	−	19.9994i	−0.609410	−	1.05553i	−0.991338	−	0.131337i	$-0.958073\pi$
$359$	−11.5467	−	19.9994i	−0.609410	−	1.05553i	0.381927	−	0.924192i	$-0.375260\pi$
$360$		0			0
$361$	27.9233	−	23.4304i	1.46965	−	1.23318i
$362$	5.95343	+	10.3116i	0.312905	+	0.541968i
$363$		0			0
$364$	−11.9622			−0.626991
$365$	3.33848	−	18.9335i	0.174744	−	0.991023i
$366$		0			0
$367$	−1.47673	+	0.537487i	−0.0770848	+	0.0280566i	−0.380275	−	0.924874i	$-0.624171\pi$
$367$	−1.47673	+	0.537487i	−0.0770848	+	0.0280566i	0.303190	+	0.952930i	$0.401948\pi$
$368$	−0.604727	−	0.220103i	−0.0315236	−	0.0114736i
$369$		0			0
$370$	−11.3871	−	1.01082i	−0.591986	−	0.0525500i
$371$	−16.6602			−0.864957
$372$		0			0
$373$	−6.28835	+	2.28877i	−0.325599	+	0.118508i	−0.499647	−	0.866229i	$-0.666537\pi$
$373$	−6.28835	+	2.28877i	−0.325599	+	0.118508i	0.174049	+	0.984737i	$0.444315\pi$
$374$	−6.67062	−	5.59732i	−0.344930	−	0.289430i
$375$		0			0
$376$	−7.85643			−0.405164
$377$	1.30723	−	7.41370i	0.0673260	−	0.381825i
$378$		0			0
$379$	−8.40501	+	7.05264i	−0.431737	+	0.362270i	−0.832606	−	0.553865i	$-0.813152\pi$
$379$	−8.40501	+	7.05264i	−0.431737	+	0.362270i	0.400870	+	0.916135i	$0.368708\pi$
$380$	−6.99748	+	12.1200i	−0.358963	+	0.621742i
$381$		0			0
$382$	−0.250636	−	0.0912241i	−0.0128237	−	0.00466743i
$383$	19.3480	+	16.2349i	0.988638	+	0.829566i	0.985370	−	0.170429i	$-0.0545152\pi$
$383$	19.3480	+	16.2349i	0.988638	+	0.829566i	0.00326840	+	0.999995i	$0.498960\pi$
$384$		0			0
$385$	3.16028	+	17.9228i	0.161063	+	0.913433i
$386$	−1.37674	−	7.80790i	−0.0700744	−	0.397412i
$387$		0			0
$388$	−16.0310	+	5.83480i	−0.813849	+	0.296217i
$389$	−10.1599	+	3.69792i	−0.515130	+	0.187492i	−0.586487	−	0.809959i	$-0.699489\pi$
$389$	−10.1599	+	3.69792i	−0.515130	+	0.187492i	0.0713568	+	0.997451i	$0.477267\pi$
$390$		0			0
$391$	0.346340	+	1.96419i	0.0175152	+	0.0993334i
$392$	−0.847190	−	4.80465i	−0.0427896	−	0.242672i
$393$		0			0
$394$	−0.315326	−	0.264590i	−0.0158859	−	0.0133299i
$395$	3.36406	+	1.22442i	0.169264	+	0.0616072i
$396$		0			0
$397$	5.40570	−	9.36295i	0.271304	−	0.469913i	−0.697892	−	0.716203i	$-0.745878\pi$
$397$	5.40570	−	9.36295i	0.271304	−	0.469913i	0.969196	+	0.246290i	$0.0792117\pi$
$398$	1.55892	−	1.30809i	0.0781417	−	0.0655687i
$399$		0			0
$400$	−0.254900	+	1.44561i	−0.0127450	+	0.0722805i
$401$	34.6974			1.73271			0.866353	−	0.499432i	$-0.166458\pi$
$401$	34.6974			1.73271			0.866353	+	0.499432i	$0.166458\pi$
$402$		0			0
$403$	−26.3408	−	22.1026i	−1.31213	−	1.10101i
$404$	11.2558	−	4.09679i	0.559999	−	0.203823i
$405$		0			0
$406$	7.47554			0.371005
$407$	−9.82049	+	13.9873i	−0.486783	+	0.693322i
$408$		0			0
$409$	−1.77330	−	0.645428i	−0.0876840	−	0.0319144i	0.297806	−	0.954627i	$-0.403745\pi$
$409$	−1.77330	−	0.645428i	−0.0876840	−	0.0319144i	−0.385490	+	0.922712i	$0.625967\pi$
$410$	18.7615	−	6.82862i	0.926563	−	0.337241i
$411$		0			0
$412$	2.24782	−	12.7480i	0.110742	−	0.628049i
$413$	−1.90747			−0.0938602
$414$		0			0
$415$	6.39899	+	11.0834i	0.314114	+	0.544061i
$416$	2.65877	−	2.23097i	0.130357	−	0.109382i
$417$		0			0
$418$	10.4612	+	18.1193i	0.511672	+	0.886242i
$419$	−16.3766	−	5.96059i	−0.800048	−	0.291194i	−0.0905419	−	0.995893i	$-0.528860\pi$
$419$	−16.3766	−	5.96059i	−0.800048	−	0.291194i	−0.709507	+	0.704699i	$0.751082\pi$
$420$		0			0
$421$	9.07719	−	15.7222i	0.442395	−	0.766251i	−0.555471	−	0.831536i	$-0.687462\pi$
$421$	9.07719	−	15.7222i	0.442395	−	0.766251i	0.997867	+	0.0652845i	$0.0207955\pi$
$422$	2.73340	+	15.5019i	0.133060	+	0.754621i
$423$		0			0
$424$	3.70296	−	3.10716i	0.179832	−	0.150897i
$425$	4.27508	−	1.55600i	0.207372	−	0.0754771i
$426$		0			0
$427$	18.5115	−	15.5330i	0.895837	−	0.751696i
$428$	−2.71350	−	15.3891i	−0.131162	−	0.743858i
$429$		0			0
$430$	7.80382	−	13.5166i	0.376334	−	0.651829i
$431$	−21.7480	−	18.2487i	−1.04756	−	0.879011i	−0.0547286	−	0.998501i	$-0.517429\pi$
$431$	−21.7480	−	18.2487i	−1.04756	−	0.879011i	−0.992835	+	0.119491i	$0.961874\pi$
$432$		0			0
$433$	3.73468	+	6.46865i	0.179477	+	0.310864i	0.941702	−	0.336449i	$-0.109226\pi$
$433$	3.73468	+	6.46865i	0.179477	+	0.310864i	−0.762224	+	0.647313i	$0.775893\pi$
$434$	17.0728	−	29.5710i	0.819521	−	1.41945i
$435$		0			0
$436$	−0.775056	−	1.34244i	−0.0371185	−	0.0642910i
$437$	0.832146	−	4.71934i	0.0398069	−	0.225756i
$438$		0			0
$439$	−5.99873	+	34.0205i	−0.286304	+	1.62371i	0.414287	+	0.910146i	$0.364031\pi$
$439$	−5.99873	+	34.0205i	−0.286304	+	1.62371i	−0.700590	+	0.713564i	$0.747080\pi$
$440$	−4.04505	−	3.39420i	−0.192840	−	0.161812i
$441$		0			0
$442$	−10.1081	−	3.67906i	−0.480795	−	0.174995i
$443$	2.89849			0.137712			0.0688558	−	0.997627i	$-0.478065\pi$
$443$	2.89849			0.137712			0.0688558	+	0.997627i	$0.478065\pi$
$444$		0			0
$445$	18.2070			0.863094
$446$	−3.22814	−	1.17495i	−0.152857	−	0.0556353i
$447$		0			0
$448$	2.64022	+	2.21541i	0.124739	+	0.104668i
$449$	−4.84053	+	27.4520i	−0.228439	+	1.29554i	0.627563	+	0.778566i	$0.284052\pi$
$449$	−4.84053	+	27.4520i	−0.228439	+	1.29554i	−0.856002	+	0.516973i	$0.827059\pi$
$450$		0			0
$451$	5.18310	−	29.3948i	0.244063	−	1.38415i
$452$	−2.55737	−	4.42950i	−0.120289	−	0.208346i
$453$		0			0
$454$	1.15640	−	2.00295i	0.0542726	−	0.0940029i
$455$	11.2408	+	19.4697i	0.526978	+	0.912752i
$456$		0			0
$457$	7.48390	+	6.27974i	0.350082	+	0.293754i	0.800823	−	0.598901i	$-0.204396\pi$
$457$	7.48390	+	6.27974i	0.350082	+	0.293754i	−0.450741	+	0.892655i	$0.648840\pi$
$458$	−2.95547	+	5.11902i	−0.138100	+	0.239196i
$459$		0			0
$460$	0.210020	+	1.19108i	0.00979221	+	0.0555344i
$461$	−11.8337	+	9.92965i	−0.551150	+	0.462470i	−0.875330	−	0.483525i	$-0.839356\pi$
$461$	−11.8337	+	9.92965i	−0.551150	+	0.462470i	0.324180	+	0.945995i	$0.394912\pi$
$462$		0			0
$463$	−17.2009	+	6.26063i	−0.799395	+	0.290956i	−0.709236	−	0.704971i	$-0.750960\pi$
$463$	−17.2009	+	6.26063i	−0.799395	+	0.290956i	−0.0901595	+	0.995927i	$0.528738\pi$
$464$	−1.66154	+	1.39420i	−0.0771351	+	0.0647240i
$465$		0			0
$466$	−4.92045	−	27.9053i	−0.227935	−	1.29269i
$467$	11.8035	−	20.4443i	0.546201	−	0.946048i	−0.452329	−	0.891851i	$-0.649407\pi$
$467$	11.8035	−	20.4443i	0.546201	−	0.946048i	0.998530	−	0.0541966i	$-0.0172598\pi$
$468$		0			0
$469$	−0.683436	−	0.248750i	−0.0315581	−	0.0114862i
$470$	7.38263	+	12.7871i	0.340535	+	0.589824i
$471$		0			0
$472$	0.423960	−	0.355745i	0.0195143	−	0.0163745i
$473$	−11.6666	−	20.2072i	−0.536432	−	0.929128i
$474$		0			0
$475$	−10.9309			−0.501544
$476$	1.85487	−	10.5195i	0.0850180	−	0.482161i
$477$		0			0
$478$	−22.7763	+	8.28990i	−1.04176	+	0.379171i
$479$	−8.16238	−	2.97086i	−0.372949	−	0.135742i	0.148744	−	0.988876i	$-0.452477\pi$
$479$	−8.16238	−	2.97086i	−0.372949	−	0.135742i	−0.521693	+	0.853134i	$0.674699\pi$
$480$		0			0
$481$	−5.49006	+	20.3856i	−0.250325	+	0.929502i
$482$	−8.85069			−0.403138
$483$		0			0
$484$	2.91850	−	1.06225i	0.132659	−	0.0482840i
$485$	24.5609	+	20.6090i	1.11525	+	0.935807i
$486$		0			0
$487$	20.9350			0.948654			0.474327	−	0.880349i	$-0.342691\pi$
$487$	20.9350			0.948654			0.474327	+	0.880349i	$0.342691\pi$
$488$	−1.21751	+	6.90485i	−0.0551142	+	0.312568i
$489$		0			0
$490$	−7.02393	+	5.89378i	−0.317309	+	0.266254i
$491$	21.6055	−	37.4219i	0.975044	−	1.68883i	0.295253	−	0.955419i	$-0.404596\pi$
$491$	21.6055	−	37.4219i	0.975044	−	1.68883i	0.679791	−	0.733406i	$-0.262070\pi$
$492$		0			0
$493$	6.31686	+	2.29915i	0.284497	+	0.103548i
$494$	19.7987	+	16.6131i	0.890784	+	0.747457i
$495$		0			0
$496$	1.72036	+	9.75665i	0.0772465	+	0.438087i
$497$	−3.02652	−	17.1643i	−0.135758	−	0.769922i
$498$		0			0
$499$	6.35892	−	2.31446i	0.284664	−	0.103609i	−0.195742	−	0.980655i	$-0.562711\pi$
$499$	6.35892	−	2.31446i	0.284664	−	0.103609i	0.480406	+	0.877046i	$0.340489\pi$
$500$	11.4226	−	4.15749i	0.510835	−	0.185929i
$501$		0			0
$502$	1.14443	+	6.49037i	0.0510783	+	0.289679i
$503$	4.76565	+	27.0274i	0.212490	+	1.20509i	0.885209	+	0.465193i	$0.154015\pi$
$503$	4.76565	+	27.0274i	0.212490	+	1.20509i	−0.672719	+	0.739898i	$0.734874\pi$
$504$		0			0
$505$	−17.2449	−	14.4702i	−0.767390	−	0.643917i
$506$	1.69908	+	0.618414i	0.0755333	+	0.0274919i
$507$		0			0
$508$	3.54760	−	6.14462i	0.157399	−	0.272623i
$509$	−16.0780	+	13.4910i	−0.712643	+	0.597978i	−0.925339	−	0.379140i	$-0.876220\pi$
$509$	−16.0780	+	13.4910i	−0.712643	+	0.597978i	0.212696	+	0.977118i	$0.431775\pi$
$510$		0			0
$511$	6.12236	−	34.7216i	0.270837	−	1.53599i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.37373	+	6.18729i	0.325241	+	0.272910i
$515$	−22.8608	+	8.32066i	−1.00737	+	0.366652i
$516$		0			0
$517$	22.0739			0.970809
$518$	−20.8825	−	1.85372i	−0.917524	−	0.0814477i
$519$		0			0
$520$	−6.12954	−	2.23097i	−0.268798	−	0.0978345i
$521$	−35.3011	+	12.8486i	−1.54657	+	0.562906i	−0.967610	−	0.252449i	$-0.918764\pi$
$521$	−35.3011	+	12.8486i	−1.54657	+	0.562906i	−0.578961	+	0.815355i	$0.696542\pi$
$522$		0			0
$523$	3.28508	−	18.6306i	0.143647	−	0.814660i	−0.824797	−	0.565428i	$-0.808711\pi$
$523$	3.28508	−	18.6306i	0.143647	−	0.814660i	0.968444	−	0.249232i	$-0.0801781\pi$
$524$	−17.4639			−0.762912
$525$		0			0
$526$	0.795631	+	1.37807i	0.0346912	+	0.0600869i
$527$	23.5213	−	19.7367i	1.02460	−	0.859746i
$528$		0			0
$529$	11.2929	+	19.5599i	0.490997	+	0.850432i
$530$	−8.53684	−	3.10716i	−0.370817	−	0.134966i
$531$		0			0
$532$	−12.8325	+	22.2266i	−0.556360	+	0.963643i
$533$	−6.40268	−	36.3114i	−0.277331	−	1.57282i
$534$		0			0
$535$	−22.4973	+	18.8775i	−0.972643	+	0.816144i
$536$	0.198295	−	0.0721735i	0.00856505	−	0.00311742i
$537$		0			0
$538$	17.7108	−	14.8611i	0.763566	−	0.640708i
$539$	2.38032	+	13.4994i	0.102528	+	0.581462i
$540$		0			0
$541$	−8.23739	+	14.2676i	−0.354153	+	0.613411i	−0.986973	−	0.160888i	$-0.948564\pi$
$541$	−8.23739	+	14.2676i	−0.354153	+	0.613411i	0.632820	+	0.774299i	$0.281897\pi$
$542$	−0.140511	−	0.117903i	−0.00603547	−	0.00506436i
$543$		0			0
$544$	1.54963	+	2.68404i	0.0664399	+	0.115077i
$545$	−1.45663	+	2.52296i	−0.0623951	+	0.108072i
$546$		0			0
$547$	6.00067	+	10.3935i	0.256570	+	0.444392i	0.965321	−	0.261067i	$-0.0840742\pi$
$547$	6.00067	+	10.3935i	0.256570	+	0.444392i	−0.708751	+	0.705459i	$0.750741\pi$
$548$	−1.71166	+	9.70729i	−0.0731184	+	0.414675i
$549$		0			0
$550$	0.716183	−	4.06167i	0.0305381	−	0.173190i
$551$	−12.3728	−	10.3820i	−0.527097	−	0.442287i
$552$		0			0
$553$	6.16927	+	2.24543i	0.262344	+	0.0954855i
$554$	12.6914			0.539204
$555$		0			0
$556$	−8.99490			−0.381469
$557$	−40.2026	−	14.6325i	−1.70344	−	0.620001i	−0.707229	−	0.706985i	$-0.750055\pi$
$557$	−40.2026	−	14.6325i	−1.70344	−	0.620001i	−0.996210	+	0.0869842i	$0.972277\pi$
$558$		0			0
$559$	−22.0801	−	18.5274i	−0.933890	−	0.783627i
$560$	1.12479	−	6.37901i	0.0475311	−	0.269562i
$561$		0			0
$562$	3.02774	−	17.1712i	0.127718	−	0.724323i
$563$	11.8738	+	20.5660i	0.500421	+	0.866754i	1.00000		0.000486132i	$0.000154741\pi$
$563$	11.8738	+	20.5660i	0.500421	+	0.866754i	−0.499579	+	0.866268i	$0.666512\pi$
$564$		0			0
$565$	−4.80629	+	8.32474i	−0.202202	+	0.350224i
$566$	−6.56696	−	11.3743i	−0.276030	−	0.478098i
$567$		0			0
$568$	3.87384	+	3.25054i	0.162543	+	0.136389i
$569$	−2.64332	+	4.57837i	−0.110814	+	0.191935i	−0.916099	−	0.400953i	$-0.868679\pi$
$569$	−2.64332	+	4.57837i	−0.110814	+	0.191935i	0.805285	+	0.592888i	$0.202012\pi$
$570$		0			0
$571$	−4.21057	−	23.8793i	−0.176207	−	0.999318i	−0.936742	−	0.350021i	$-0.886174\pi$
$571$	−4.21057	−	23.8793i	−0.176207	−	0.999318i	0.760535	−	0.649297i	$-0.224937\pi$
$572$	−7.47024	+	6.26827i	−0.312346	+	0.262090i
$573$		0			0
$574$	34.4062	−	12.5228i	1.43609	−	0.522693i
$575$	−0.723648	+	0.607213i	−0.0301782	+	0.0253225i
$576$		0			0
$577$	−0.296836	−	1.68344i	−0.0123574	−	0.0700825i	0.978005	−	0.208579i	$-0.0668840\pi$
$577$	−0.296836	−	1.68344i	−0.0123574	−	0.0700825i	−0.990363	+	0.138497i	$0.955773\pi$
$578$	−3.69728	+	6.40388i	−0.153787	+	0.266366i
$579$		0			0
$580$	3.83053	+	1.39420i	0.159054	+	0.0578909i
$581$	11.7350	+	20.3255i	0.486848	+	0.843245i
$582$		0			0
$583$	−10.4041	+	8.73005i	−0.430893	+	0.361562i
$584$	5.11485	+	8.85918i	0.211654	+	0.366595i
$585$		0			0
$586$	6.78723			0.280378
$587$	−4.51530	+	25.6076i	−0.186366	+	1.05694i	0.737821	+	0.674997i	$0.235855\pi$
$587$	−4.51530	+	25.6076i	−0.186366	+	1.05694i	−0.924187	+	0.381940i	$0.875256\pi$
$588$		0			0
$589$	−69.3251	+	25.2323i	−2.85649	+	1.03968i
$590$	−0.977400	−	0.355745i	−0.0402389	−	0.0146458i
$591$		0			0
$592$	4.98714	−	3.48260i	0.204970	−	0.143134i
$593$	−19.5933			−0.804601			−0.402300	−	0.915508i	$-0.631789\pi$
$593$	−19.5933			−0.804601			−0.402300	+	0.915508i	$0.631789\pi$
$594$		0			0
$595$	−18.8645	+	6.86613i	−0.773370	+	0.281484i
$596$	7.63977	+	6.41053i	0.312937	+	0.262586i
$597$		0			0
$598$	2.23357			0.0913376
$599$	−6.43804	+	36.5119i	−0.263051	+	1.49184i	0.511477	+	0.859297i	$0.329099\pi$
$599$	−6.43804	+	36.5119i	−0.263051	+	1.49184i	−0.774528	+	0.632540i	$0.782012\pi$
$600$		0			0
$601$	−14.1667	+	11.8873i	−0.577871	+	0.484892i	−0.884247	−	0.467019i	$-0.845328\pi$
$601$	−14.1667	+	11.8873i	−0.577871	+	0.484892i	0.306376	+	0.951911i	$0.400884\pi$
$602$	14.3112	−	24.7878i	0.583282	−	1.01027i
$603$		0			0
$604$	−9.07997	−	3.30484i	−0.369459	−	0.134472i
$605$	−4.47140	−	3.75195i	−0.181788	−	0.152539i
$606$		0			0
$607$	0.923385	+	5.23678i	0.0374791	+	0.212554i	0.997796	−	0.0663569i	$-0.0211376\pi$
$607$	0.923385	+	5.23678i	0.0374791	+	0.212554i	−0.960317	+	0.278911i	$0.910026\pi$
$608$	−1.29308	−	7.33343i	−0.0524414	−	0.297410i
$609$		0			0
$610$	12.3824	−	4.50682i	0.501348	−	0.182476i
$611$	25.6234	−	9.32617i	1.03661	−	0.377296i
$612$		0			0
$613$	7.01848	+	39.8038i	0.283474	+	1.60766i	0.710687	+	0.703508i	$0.248384\pi$
$613$	7.01848	+	39.8038i	0.283474	+	1.60766i	−0.427213	+	0.904151i	$0.640505\pi$
$614$	−1.42476	−	8.08020i	−0.0574985	−	0.326090i
$615$		0			0
$616$	−7.41812	−	6.22454i	−0.298884	−	0.250794i
$617$	−30.8191	−	11.2172i	−1.24073	−	0.451589i	−0.363470	−	0.931606i	$-0.618408\pi$
$617$	−30.8191	−	11.2172i	−1.24073	−	0.451589i	−0.877259	+	0.480017i	$0.840630\pi$
$618$		0			0
$619$	2.07537	−	3.59465i	0.0834163	−	0.144481i	−0.821299	−	0.570498i	$-0.806750\pi$
$619$	2.07537	−	3.59465i	0.0834163	−	0.144481i	0.904715	+	0.426017i	$0.140084\pi$
$620$	14.2633	−	11.9683i	0.572827	−	0.480659i
$621$		0			0
$622$	−1.88461	+	10.6882i	−0.0755660	+	0.428556i
$623$	33.3893			1.33772
$624$		0			0
$625$	−11.8780	−	9.96686i	−0.475122	−	0.398674i
$626$	−8.13361	+	2.96039i	−0.325085	+	0.118321i
$627$		0			0
$628$	−8.78957			−0.350742
$629$	−17.0757	−	7.98893i	−0.680851	−	0.318540i
$630$		0			0
$631$	−28.1162	−	10.2335i	−1.11929	−	0.407387i	−0.284896	−	0.958559i	$-0.591959\pi$
$631$	−28.1162	−	10.2335i	−1.11929	−	0.407387i	−0.834392	+	0.551171i	$0.814181\pi$
$632$	−1.78998	+	0.651500i	−0.0712016	+	0.0259153i
$633$		0			0
$634$	−4.41505	+	25.0390i	−0.175344	+	0.994425i
$635$	−13.3346			−0.529168
$636$		0			0
$637$	8.46656	+	14.6645i	0.335457	+	0.581029i
$638$	4.66837	−	3.91722i	0.184822	−	0.155084i
$639$		0			0
$640$	0.939693	+	1.62760i	0.0371446	+	0.0643364i
$641$	6.42331	+	2.33789i	0.253705	+	0.0923412i	0.465742	−	0.884920i	$-0.345787\pi$
$641$	6.42331	+	2.33789i	0.253705	+	0.0923412i	−0.212037	+	0.977262i	$0.568010\pi$
$642$		0			0
$643$	−18.7592	+	32.4920i	−0.739792	+	1.28136i	0.212796	+	0.977097i	$0.431743\pi$
$643$	−18.7592	+	32.4920i	−0.739792	+	1.28136i	−0.952589	+	0.304262i	$0.901590\pi$
$644$	0.385150	+	2.18429i	0.0151770	+	0.0860732i
$645$		0			0
$646$	−17.6794	+	14.8348i	−0.695588	+	0.583667i
$647$	2.48480	−	0.904395i	0.0976877	−	0.0355554i	−0.292714	−	0.956200i	$-0.594558\pi$
$647$	2.48480	−	0.904395i	0.0976877	−	0.0355554i	0.390402	+	0.920645i	$0.372336\pi$
$648$		0			0
$649$	−1.19118	+	0.999522i	−0.0467580	+	0.0392347i
$650$	−0.884701	−	5.01739i	−0.0347008	−	0.196798i
$651$		0			0
$652$	0.953582	−	1.65165i	0.0373451	−	0.0646837i
$653$	34.2792	+	28.7636i	1.34145	+	1.12561i	0.981251	+	0.192732i	$0.0617348\pi$
$653$	34.2792	+	28.7636i	1.34145	+	1.12561i	0.360197	+	0.932876i	$0.382710\pi$
$654$		0			0
$655$	16.4107	+	28.4241i	0.641218	+	1.11062i
$656$	−5.31172	+	9.20017i	−0.207388	+	0.359206i
$657$		0			0
$658$	13.5388	+	23.4499i	0.527798	+	0.914173i
$659$	0.790306	−	4.48205i	0.0307859	−	0.174596i	−0.965538	−	0.260262i	$-0.916191\pi$
$659$	0.790306	−	4.48205i	0.0307859	−	0.174596i	0.996324	+	0.0856667i	$0.0273020\pi$
$660$		0			0
$661$	−7.56467	+	42.9014i	−0.294231	+	1.66867i	0.376078	+	0.926588i	$0.377272\pi$
$661$	−7.56467	+	42.9014i	−0.294231	+	1.66867i	−0.670310	+	0.742082i	$0.733839\pi$
$662$	15.9349	+	13.3710i	0.619327	+	0.519677i
$663$		0			0
$664$	−6.39899	−	2.32904i	−0.248329	−	0.0903843i
$665$	48.2344			1.87045
$666$		0			0
$667$	−1.39582			−0.0540465
$668$	6.22793	+	2.26678i	0.240966	+	0.0877044i
$669$		0			0
$670$	−0.303806	−	0.254923i	−0.0117370	−	0.00984855i
$671$	3.42080	−	19.4003i	0.132058	−	0.748940i
$672$		0			0
$673$	6.60813	−	37.4766i	0.254725	−	1.44462i	−0.542053	−	0.840344i	$-0.682353\pi$
$673$	6.60813	−	37.4766i	0.254725	−	1.44462i	0.796778	−	0.604272i	$-0.206536\pi$
$674$	−1.23612	−	2.14103i	−0.0476136	−	0.0824693i
$675$		0			0
$676$	0.476862	−	0.825949i	0.0183408	−	0.0317673i
$677$	22.0131	+	38.1278i	0.846032	+	1.46537i	0.884722	+	0.466120i	$0.154348\pi$
$677$	22.0131	+	38.1278i	0.846032	+	1.46537i	−0.0386894	+	0.999251i	$0.512318\pi$
$678$		0			0
$679$	45.0416	+	37.7944i	1.72854	+	1.45042i
$680$	2.91235	−	5.04435i	0.111684	−	0.193442i
$681$		0			0
$682$	−4.83363	−	27.4129i	−0.185089	−	1.04969i
$683$	−14.4021	+	12.0848i	−0.551081	+	0.462412i	−0.875307	−	0.483568i	$-0.839341\pi$
$683$	−14.4021	+	12.0848i	−0.551081	+	0.462412i	0.324226	+	0.945980i	$0.394896\pi$
$684$		0			0
$685$	17.4080	−	6.33598i	0.665125	−	0.242086i
$686$	5.60050	−	4.69938i	0.213828	−	0.179423i
$687$		0			0
$688$	1.44209	+	8.17848i	0.0549791	+	0.311802i
$689$	−8.38865	+	14.5296i	−0.319582	+	0.553532i
$690$		0			0
$691$	−25.3128	−	9.21310i	−0.962944	−	0.350483i	−0.187757	−	0.982215i	$-0.560122\pi$
$691$	−25.3128	−	9.21310i	−0.962944	−	0.350483i	−0.775186	+	0.631733i	$0.782344\pi$
$692$	12.7046	+	22.0051i	0.482958	+	0.836508i
$693$		0			0
$694$	−4.48427	+	3.76275i	−0.170220	+	0.142832i
$695$	8.45244	+	14.6401i	0.320619	+	0.555329i
$696$		0			0
$697$	32.9248			1.24712
$698$	−0.545283	+	3.09246i	−0.0206393	+	0.117051i
$699$		0			0
$700$	4.75413	−	1.73036i	0.179689	−	0.0654016i
$701$	6.98332	+	2.54172i	0.263756	+	0.0959995i	0.470513	−	0.882393i	$-0.344069\pi$
$701$	6.98332	+	2.54172i	0.263756	+	0.0959995i	−0.206757	+	0.978392i	$0.566291\pi$
$702$		0			0
$703$	31.9881	+	32.0695i	1.20646	+	1.20953i
$704$	2.80966			0.105893
$705$		0			0
$706$	10.5699	−	3.84713i	0.397804	−	0.144789i
$707$	−31.6251	−	26.5366i	−1.18938	−	0.998012i
$708$		0			0
$709$	0.834473			0.0313393			0.0156697	−	0.999877i	$-0.495012\pi$
$709$	0.834473			0.0313393			0.0156697	+	0.999877i	$0.495012\pi$
$710$	1.65034	−	9.35955i	0.0619362	−	0.351258i
$711$		0			0
$712$	−7.42123	+	6.22715i	−0.278122	+	0.233372i
$713$	−3.18781	+	5.52146i	−0.119385	+	0.206780i
$714$		0			0
$715$	17.2219	+	6.26827i	0.644064	+	0.234420i
$716$	−6.22405	−	5.22260i	−0.232604	−	0.195178i
$717$		0			0
$718$	−4.01012	−	22.7425i	−0.149656	−	0.848743i
$719$	0.874879	+	4.96169i	0.0326275	+	0.185040i	0.996766	−	0.0803603i	$-0.0256071\pi$
$719$	0.874879	+	4.96169i	0.0326275	+	0.185040i	−0.964138	+	0.265400i	$0.914496\pi$
$720$		0			0
$721$	−41.9239	+	15.2591i	−1.56133	+	0.568277i
$722$	34.2530	−	12.4671i	1.27476	−	0.463976i
$723$		0			0
$724$	2.06760	+	11.7260i	0.0768419	+	0.435792i
$725$	0.552875	+	3.13551i	0.0205333	+	0.116450i
$726$		0			0
$727$	14.2591	+	11.9648i	0.528842	+	0.443751i	0.867701	−	0.497086i	$-0.165597\pi$
$727$	14.2591	+	11.9648i	0.528842	+	0.443751i	−0.338860	+	0.940837i	$0.610041\pi$
$728$	−11.2408	−	4.09132i	−0.416613	−	0.151635i
$729$		0			0
$730$	9.61277	−	16.6498i	0.355785	−	0.616237i
$731$	19.7167	−	16.5443i	0.729248	−	0.611912i
$732$		0			0
$733$	0.797139	−	4.52080i	0.0294430	−	0.166980i	−0.966541	−	0.256513i	$-0.917426\pi$
$733$	0.797139	−	4.52080i	0.0294430	−	0.166980i	0.995984	+	0.0895332i	$0.0285375\pi$
$734$	−1.57151			−0.0580054
$735$		0			0
$736$	−0.492978	−	0.413658i	−0.0181714	−	0.0152476i
$737$	−0.557142	+	0.202783i	−0.0205226	+	0.00746961i
$738$		0			0
$739$	−46.9098			−1.72560			−0.862802	−	0.505542i	$-0.831292\pi$
$739$	−46.9098			−1.72560			−0.862802	+	0.505542i	$0.831292\pi$
$740$	−10.3546	−	4.84447i	−0.380644	−	0.178086i
$741$		0			0
$742$	−15.6555	−	5.69814i	−0.574732	−	0.209185i
$743$	4.69037	−	1.70716i	0.172073	−	0.0626295i	−0.254547	−	0.967060i	$-0.581926\pi$
$743$	4.69037	−	1.70716i	0.172073	−	0.0626295i	0.426620	+	0.904431i	$0.359704\pi$
$744$		0			0
$745$	3.25471	−	18.4584i	0.119243	−	0.676263i
$746$	−6.69192			−0.245009
$747$		0			0
$748$	−4.35394	−	7.54125i	−0.159196	−	0.275735i
$749$	−41.2572	+	34.6189i	−1.50751	+	1.26495i
$750$		0			0
$751$	−9.41422	−	16.3059i	−0.343530	−	0.595011i	0.641556	−	0.767077i	$-0.278289\pi$
$751$	−9.41422	−	16.3059i	−0.343530	−	0.595011i	−0.985086	+	0.172065i	$0.944956\pi$
$752$	−7.38263	−	2.68706i	−0.269217	−	0.0979869i
$753$		0			0
$754$	3.76403	−	6.51950i	0.137078	−	0.237426i
$755$	3.15344	+	17.8841i	0.114766	+	0.650867i
$756$		0			0
$757$	0.598778	−	0.502435i	0.0217630	−	0.0182613i	−0.631841	−	0.775098i	$-0.717701\pi$
$757$	0.598778	−	0.502435i	0.0217630	−	0.0182613i	0.653604	+	0.756837i	$0.273256\pi$
$758$	−10.3103	+	3.75263i	−0.374486	+	0.136302i
$759$		0			0
$760$	−10.7208	+	8.99578i	−0.388883	+	0.326311i
$761$	5.27399	+	29.9103i	0.191182	+	1.08425i	0.917752	+	0.397154i	$0.130002\pi$
$761$	5.27399	+	29.9103i	0.191182	+	1.08425i	−0.726570	+	0.687092i	$0.758887\pi$
$762$		0			0
$763$	−2.67128	+	4.62679i	−0.0967067	+	0.167501i
$764$	−0.204321	−	0.171445i	−0.00739206	−	0.00620267i
$765$		0			0
$766$	12.6285	+	21.8733i	0.456287	+	0.790313i
$767$	−0.960433	+	1.66352i	−0.0346792	+	0.0600662i
$768$		0			0
$769$	7.98228	+	13.8257i	0.287848	+	0.498568i	0.973296	−	0.229554i	$-0.0737268\pi$
$769$	7.98228	+	13.8257i	0.287848	+	0.498568i	−0.685448	+	0.728122i	$0.740393\pi$
$770$	−3.16028	+	17.9228i	−0.113889	+	0.645895i
$771$		0			0
$772$	1.37674	−	7.80790i	0.0495501	−	0.281012i
$773$	−20.2985	−	17.0324i	−0.730086	−	0.612615i	0.200069	−	0.979782i	$-0.435883\pi$
$773$	−20.2985	−	17.0324i	−0.730086	−	0.612615i	−0.930155	+	0.367167i	$0.880328\pi$
$774$		0			0
$775$	13.6658	+	4.97394i	0.490890	+	0.178669i
$776$	−17.0598			−0.612411
$777$		0			0
$778$	−10.8120			−0.387629
$779$	−74.3373	−	27.0566i	−2.66341	−	0.969402i
$780$		0			0
$781$	−10.8842	−	9.13291i	−0.389466	−	0.326801i
$782$	−0.346340	+	1.96419i	−0.0123851	+	0.0702393i
$783$		0			0
$784$	0.847190	−	4.80465i	0.0302568	−	0.171595i
$785$	8.25949	+	14.3059i	0.294794	+	0.510598i
$786$		0			0
$787$	24.1869	−	41.8930i	0.862171	−	1.49332i	−0.00765866	−	0.999971i	$-0.502438\pi$
$787$	24.1869	−	41.8930i	0.862171	−	1.49332i	0.869829	−	0.493353i	$-0.164229\pi$
$788$	−0.205815	−	0.356481i	−0.00733184	−	0.0126991i
$789$		0			0
$790$	2.74241	+	2.30115i	0.0975705	+	0.0818714i
$791$	−8.81414	+	15.2665i	−0.313395	+	0.542816i
$792$		0			0
$793$	−4.22571	−	23.9652i	−0.150059	−	0.851029i
$794$	8.28202	−	6.94944i	0.293918	−	0.246626i
$795$		0			0
$796$	1.91230	−	0.696021i	0.0677797	−	0.0246698i
$797$	−18.1488	+	15.2286i	−0.642863	+	0.539426i	−0.904896	−	0.425633i	$-0.860052\pi$
$797$	−18.1488	+	15.2286i	−0.642863	+	0.539426i	0.262033	+	0.965059i	$0.415607\pi$
$798$		0			0
$799$	4.22818	+	23.9792i	0.149582	+	0.848324i
$800$	−0.733956	+	1.27125i	−0.0259492	+	0.0449454i
$801$		0			0
$802$	32.6049	+	11.8672i	1.15132	+	0.419046i
$803$	−14.3710	−	24.8913i	−0.507141	−	0.878395i
$804$		0			0
$805$	3.19322	−	2.67943i	0.112546	−	0.0944376i
$806$	−17.1928	−	29.7787i	−0.605589	−	1.04891i
$807$		0			0
$808$	11.9782			0.421392
$809$	−0.138317	+	0.784433i	−0.00486295	+	0.0275792i	−0.987143	−	0.159842i	$-0.948902\pi$
$809$	−0.138317	+	0.784433i	−0.00486295	+	0.0275792i	0.982280	+	0.187421i	$0.0600128\pi$
$810$		0			0
$811$	−13.0191	+	4.73855i	−0.457161	+	0.166393i	−0.560328	−	0.828271i	$-0.689325\pi$
$811$	−13.0191	+	4.73855i	−0.457161	+	0.166393i	0.103166	+	0.994664i	$0.467103\pi$
$812$	7.02471	+	2.55679i	0.246519	+	0.0897256i
$813$		0			0
$814$	−14.0122	+	9.78491i	−0.491126	+	0.342961i
$815$	−3.58429			−0.125552
$816$		0			0
$817$	−58.1116	+	21.1509i	−2.03307	+	0.739976i
$818$	−1.44561	−	1.21301i	−0.0505445	−	0.0424118i
$819$		0			0
$820$	19.9655			0.697227
$821$	3.79631	−	21.5300i	0.132492	−	0.751401i	−0.844081	−	0.536216i	$-0.819853\pi$
$821$	3.79631	−	21.5300i	0.132492	−	0.751401i	0.976573	−	0.215185i	$-0.0690355\pi$
$822$		0			0
$823$	26.4467	−	22.1914i	0.921873	−	0.773544i	−0.0524672	−	0.998623i	$-0.516708\pi$
$823$	26.4467	−	22.1914i	0.921873	−	0.773544i	0.974341	+	0.225079i	$0.0722640\pi$
$824$	6.47233	−	11.2104i	0.225474	−	0.390533i
$825$		0			0
$826$	−1.79243	−	0.652392i	−0.0623666	−	0.0226996i
$827$	−3.04336	−	2.55369i	−0.105828	−	0.0888003i	0.588338	−	0.808615i	$-0.299782\pi$
$827$	−3.04336	−	2.55369i	−0.105828	−	0.0888003i	−0.694166	+	0.719815i	$0.744227\pi$
$828$		0			0
$829$	−2.91749	−	16.5459i	−0.101329	−	0.574664i	−0.992623	−	0.121239i	$-0.961313\pi$
$829$	−2.91749	−	16.5459i	−0.101329	−	0.574664i	0.891295	−	0.453425i	$-0.149798\pi$
$830$	2.22235	+	12.6035i	0.0771387	+	0.437475i
$831$		0			0
$832$	3.26146	−	1.18707i	0.113071	−	0.0411544i
$833$	−14.2087	+	5.17155i	−0.492303	+	0.179184i
$834$		0			0
$835$	−2.16294	−	12.2666i	−0.0748515	−	0.424504i
$836$	3.63312	+	20.6045i	0.125654	+	0.712620i
$837$		0			0
$838$	−13.3503	−	11.2022i	−0.461179	−	0.386975i
$839$	6.33057	+	2.30414i	0.218556	+	0.0795478i	0.448977	−	0.893543i	$-0.351788\pi$
$839$	6.33057	+	2.30414i	0.218556	+	0.0795478i	−0.230422	+	0.973091i	$0.574011\pi$
$840$		0			0
$841$	12.1477	−	21.0405i	0.418888	−	0.725535i
$842$	13.9071	−	11.6694i	0.479269	−	0.402155i
$843$		0			0
$844$	−2.73340	+	15.5019i	−0.0940876	+	0.533597i
$845$	−1.79241			−0.0616609
$846$		0			0
$847$	−8.20000	−	6.88062i	−0.281755	−	0.236421i
$848$	4.54236	−	1.65328i	0.155985	−	0.0567740i
$849$		0			0
$850$	4.54944			0.156045
$851$	3.89915	+	0.346124i	0.133661	+	0.0118650i
$852$		0			0
$853$	−40.3273	−	14.6779i	−1.38078	−	0.502563i	−0.458365	−	0.888764i	$-0.651565\pi$
$853$	−40.3273	−	14.6779i	−1.38078	−	0.502563i	−0.922415	+	0.386201i	$0.873787\pi$
$854$	22.7078	−	8.26495i	0.777044	−	0.282821i
$855$		0			0
$856$	2.71350	−	15.3891i	0.0927457	−	0.525987i
$857$	27.6910			0.945906			0.472953	−	0.881088i	$-0.343188\pi$
$857$	27.6910			0.945906			0.472953	+	0.881088i	$0.343188\pi$
$858$		0			0
$859$	−9.42711	−	16.3282i	−0.321649	−	0.557112i	0.659179	−	0.751986i	$-0.270904\pi$
$859$	−9.42711	−	16.3282i	−0.321649	−	0.557112i	−0.980828	+	0.194873i	$0.937570\pi$
$860$	11.9561	−	10.0324i	0.407701	−	0.342102i
$861$		0			0
$862$	−14.1950	−	24.5865i	−0.483483	−	0.837418i
$863$	28.0177	+	10.1976i	0.953734	+	0.347131i	0.771575	−	0.636138i	$-0.219469\pi$
$863$	28.0177	+	10.1976i	0.953734	+	0.347131i	0.182159	+	0.983269i	$0.441691\pi$
$864$		0			0
$865$	23.8769	−	41.3560i	0.811839	−	1.40615i
$866$	1.29704	+	7.35588i	0.0440752	+	0.249963i
$867$		0			0
$868$	26.1571	−	21.9484i	0.887829	−	0.744977i
$869$	5.02924	−	1.83049i	0.170605	−	0.0620952i
$870$		0			0
$871$	−0.561057	+	0.470782i	−0.0190107	+	0.0159519i
$872$	−0.269174	−	1.52656i	−0.00911539	−	0.0516959i
$873$		0			0
$874$	2.39607	−	4.15011i	0.0810483	−	0.140380i
$875$	−32.0937	−	26.9298i	−1.08496	−	0.910393i
$876$		0			0
$877$	−2.11792	−	3.66834i	−0.0715170	−	0.123871i	0.828049	−	0.560655i	$-0.189451\pi$
$877$	−2.11792	−	3.66834i	−0.0715170	−	0.123871i	−0.899566	+	0.436784i	$0.856117\pi$
$878$	−17.2727	+	29.9171i	−0.582924	+	1.00965i
$879$		0			0
$880$	−2.64022	−	4.57299i	−0.0890017	−	0.154156i
$881$	−1.14459	+	6.49127i	−0.0385621	+	0.218697i	−0.997999	−	0.0632261i	$-0.979861\pi$
$881$	−1.14459	+	6.49127i	−0.0385621	+	0.218697i	0.959437	+	0.281923i	$0.0909722\pi$
$882$		0			0
$883$	−2.14960	+	12.1910i	−0.0723397	+	0.410259i	0.927037	+	0.374969i	$0.122347\pi$
$883$	−2.14960	+	12.1910i	−0.0723397	+	0.410259i	−0.999377	+	0.0352901i	$0.988764\pi$
$884$	−8.24022	−	6.91437i	−0.277149	−	0.232555i
$885$		0			0
$886$	2.72369	+	0.991344i	0.0915043	+	0.0333048i
$887$	25.0422			0.840833			0.420417	−	0.907331i	$-0.361884\pi$
$887$	25.0422			0.840833			0.420417	+	0.907331i	$0.361884\pi$
$888$		0			0
$889$	−24.4540			−0.820161
$890$	17.1090	+	6.22715i	0.573494	+	0.208735i
$891$		0			0
$892$	−2.63160	−	2.20817i	−0.0881125	−	0.0739351i
$893$	10.1590	−	57.6146i	0.339958	−	1.92800i
$894$		0			0
$895$	−2.65158	+	15.0379i	−0.0886326	+	0.502661i
$896$	1.72328	+	2.98481i	0.0575707	+	0.0997154i
$897$		0			0
$898$	−13.9377	+	24.1409i	−0.465108	+	0.805591i
$899$	10.7443	+	18.6096i	0.358341	+	0.620665i
$900$		0			0
$901$	−11.4765	−	9.62989i	−0.382336	−	0.320818i
$902$	14.9241	−	25.8494i	0.496919	−	0.860690i
$903$		0			0
$904$	−0.888167	−	5.03704i	−0.0295400	−	0.167530i
$905$	17.1422	−	14.3840i	0.569826	−	0.478141i
$906$		0			0
$907$	54.3968	−	19.7988i	1.80622	−	0.657409i	0.808602	−	0.588355i	$-0.200224\pi$
$907$	54.3968	−	19.7988i	1.80622	−	0.657409i	0.997613	−	0.0690533i	$-0.0219979\pi$
$908$	1.77171	−	1.48664i	0.0587963	−	0.0493359i
$909$		0			0
$910$	3.90390	+	22.1401i	0.129413	+	0.733937i
$911$	−4.18373	+	7.24644i	−0.138613	+	0.240085i	−0.926972	−	0.375131i	$-0.877598\pi$
$911$	−4.18373	+	7.24644i	−0.138613	+	0.240085i	0.788359	+	0.615216i	$0.210931\pi$
$912$		0			0
$913$	17.9790	+	6.54382i	0.595018	+	0.216569i
$914$	4.88477	+	8.46066i	0.161574	+	0.279854i
$915$		0			0
$916$	−4.52804	+	3.79948i	−0.149611	+	0.125538i
$917$	30.0951	+	52.1263i	0.993828	+	1.72136i
$918$		0			0
$919$	3.64798			0.120336			0.0601678	−	0.998188i	$-0.480836\pi$
$919$	3.64798			0.120336			0.0601678	+	0.998188i	$0.480836\pi$
$920$	−0.210020	+	1.19108i	−0.00692414	+	0.0392687i
$921$		0			0
$922$	−14.5162	+	5.28346i	−0.478065	+	0.174001i
$923$	−16.4930	−	6.00296i	−0.542874	−	0.197590i
$924$		0			0
$925$	−0.766908	−	8.89596i	−0.0252158	−	0.292497i
$926$	−18.3049			−0.601535
$927$		0			0
$928$	−2.03818	+	0.741837i	−0.0669066	+	0.0243520i
$929$	−40.7198	−	34.1679i	−1.33597	−	1.12101i	−0.982641	−	0.185516i	$-0.940604\pi$
$929$	−40.7198	−	34.1679i	−1.33597	−	1.12101i	−0.353331	−	0.935498i	$-0.614951\pi$
$930$		0			0
$931$	36.3301			1.19067
$932$	4.92045	−	27.9053i	0.161175	−	0.914067i
$933$		0			0
$934$	18.0840	−	15.1743i	0.591727	−	0.496518i
$935$	−8.18273	+	14.1729i	−0.267604	+	0.463504i
$936$		0			0
$937$	−0.433752	−	0.157873i	−0.0141701	−	0.00515748i	0.334925	−	0.942245i	$-0.391289\pi$
$937$	−0.433752	−	0.157873i	−0.0141701	−	0.00515748i	−0.349095	+	0.937087i	$0.613511\pi$
$938$	−0.557142	−	0.467498i	−0.0181913	−	0.0152643i
$939$		0			0
$940$	2.56396	+	14.5409i	0.0836271	+	0.474273i
$941$	−7.83670	−	44.4441i	−0.255469	−	1.44884i	−0.794865	−	0.606786i	$-0.792459\pi$
$941$	−7.83670	−	44.4441i	−0.255469	−	1.44884i	0.539396	−	0.842052i	$-0.318653\pi$
$942$		0			0
$943$	−6.42429	+	2.33825i	−0.209204	+	0.0761439i
$944$	0.520064	−	0.189288i	0.0169266	−	0.00616079i
$945$		0			0
$946$	−4.05178	−	22.9788i	−0.131735	−	0.747104i
$947$	0.192264	+	1.09038i	0.00624773	+	0.0354326i	0.987772	−	0.155904i	$-0.0498290\pi$
$947$	0.192264	+	1.09038i	0.00624773	+	0.0354326i	−0.981525	+	0.191336i	$0.938718\pi$
$948$		0			0
$949$	−27.1984	−	22.8222i	−0.882897	−	0.740839i
$950$	−10.2717	−	3.73858i	−0.333257	−	0.121296i
$951$		0			0
$952$	5.34090	−	9.25071i	0.173099	−	0.299817i
$953$	3.46116	−	2.90426i	0.112118	−	0.0940782i	−0.585005	−	0.811030i	$-0.698908\pi$
$953$	3.46116	−	2.90426i	0.112118	−	0.0940782i	0.697123	+	0.716951i	$0.254463\pi$
$954$		0			0
$955$	−0.0870451	+	0.493657i	−0.00281671	+	0.0159744i
$956$	−24.2381			−0.783915
$957$		0			0
$958$	−6.65403	−	5.58340i	−0.214982	−	0.180391i
$959$	31.9241	−	11.6194i	1.03088	−	0.375210i
$960$		0			0
$961$	67.1519			2.16619
$962$	−12.1312	+	17.2785i	−0.391127	+	0.557080i
$963$		0			0
$964$	−8.31692	−	3.02711i	−0.267870	−	0.0974967i
$965$	−14.0018	+	5.09624i	−0.450734	+	0.164054i
$966$		0			0
$967$	−5.99944	+	34.0245i	−0.192929	+	1.09415i	0.722409	+	0.691466i	$0.243035\pi$
$967$	−5.99944	+	34.0245i	−0.192929	+	1.09415i	−0.915338	+	0.402688i	$0.868076\pi$
$968$	3.10580			0.0998243
$969$		0			0
$970$	16.0310	+	27.7665i	0.514723	+	0.891527i
$971$	7.54292	−	6.32926i	0.242064	−	0.203116i	−0.513682	−	0.857981i	$-0.671719\pi$
$971$	7.54292	−	6.32926i	0.242064	−	0.203116i	0.755746	+	0.654865i	$0.227274\pi$
$972$		0			0
$973$	15.5007	+	26.8481i	0.496931	+	0.860709i
$974$	19.6724	+	7.16018i	0.630345	+	0.229427i
$975$		0			0
$976$	−3.50569	+	6.07203i	−0.112214	+	0.194361i
$977$	−6.85364	−	38.8689i	−0.219267	−	1.24353i	−0.873346	−	0.487100i	$-0.838055\pi$
$977$	−6.85364	−	38.8689i	−0.219267	−	1.24353i	0.654079	−	0.756427i	$-0.273057\pi$
$978$		0			0
$979$	20.8512	−	17.4962i	0.666406	−	0.559181i
$980$	−8.61613	+	3.13602i	−0.275232	+	0.100176i
$981$		0			0
$982$	33.1016	−	27.7755i	1.05631	−	0.886353i
$983$	−2.68903	−	15.2502i	−0.0857666	−	0.486407i	−0.997189	−	0.0749336i	$-0.976126\pi$
$983$	−2.68903	−	15.2502i	−0.0857666	−	0.486407i	0.911422	−	0.411473i	$-0.134986\pi$
$984$		0			0
$985$	−0.386805	+	0.669966i	−0.0123246	+	0.0213469i
$986$	5.14955	+	4.32099i	0.163995	+	0.137608i
$987$		0			0
$988$	12.9227	+	22.3827i	0.411125	+	0.712089i
$989$	−2.67218	+	4.62834i	−0.0849703	+	0.147173i
$990$		0			0
$991$	−2.60235	−	4.50740i	−0.0826663	−	0.143182i	0.821728	−	0.569880i	$-0.193010\pi$
$991$	−2.60235	−	4.50740i	−0.0826663	−	0.143182i	−0.904394	+	0.426698i	$0.859677\pi$
$992$	−1.72036	+	9.75665i	−0.0546215	+	0.309774i
$993$		0			0
$994$	3.02652	−	17.1643i	0.0959954	−	0.544417i
$995$	−2.92982	−	2.45841i	−0.0928814	−	0.0779367i
$996$		0			0
$997$	−35.0496	−	12.7570i	−1.11003	−	0.404018i	−0.279026	−	0.960284i	$-0.590012\pi$
$997$	−35.0496	−	12.7570i	−1.11003	−	0.404018i	−0.831005	+	0.556265i	$0.812234\pi$
$998$	6.76702			0.214206
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.x.g.127.2		12
3.2	odd	2		74.2.f.b.53.2	yes	12
12.11	even	2		592.2.bc.d.497.1		12
37.7	even	9	inner	666.2.x.g.451.2		12
111.44	odd	18		74.2.f.b.7.2	✓	12
111.65	odd	18		2738.2.a.q.1.2		6
111.83	odd	18		2738.2.a.t.1.2		6
444.155	even	18		592.2.bc.d.81.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.7.2	✓	12	111.44	odd	18
74.2.f.b.53.2	yes	12	3.2	odd	2
592.2.bc.d.81.1		12	444.155	even	18
592.2.bc.d.497.1		12	12.11	even	2
666.2.x.g.127.2		12	1.1	even	1	trivial
666.2.x.g.451.2		12	37.7	even	9	inner
2738.2.a.q.1.2		6	111.65	odd	18
2738.2.a.t.1.2		6	111.83	odd	18

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.x (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{5} +(0.598489 - 3.39420i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.326352 - 1.85083i) q^{5} +(0.598489 - 3.39420i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.939693 - 1.62760i) q^{10} +(-1.40483 - 2.43324i) q^{11} +(-2.65877 - 2.23097i) q^{13} +(1.72328 - 2.98481i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.37417 - 1.99217i) q^{17} +(-6.99748 + 2.54687i) q^{19} +(1.43969 - 1.20805i) q^{20} +(-0.487893 - 2.76698i) q^{22} +(-0.321769 + 0.557320i) q^{23} +(1.37939 + 0.502055i) q^{25} +(-1.73539 - 3.00578i) q^{26} +(2.64022 - 2.21541i) q^{28} +(1.08449 + 1.87840i) q^{29} +9.90716 q^{31} +(-0.173648 + 0.984808i) q^{32} +(2.91235 - 1.06001i) q^{34} +(-6.08678 - 2.21541i) q^{35} +(-2.56368 - 5.51612i) q^{37} -7.44656 q^{38} +(1.76604 - 0.642788i) q^{40} +(8.13803 + 6.82862i) q^{41} +8.30465 q^{43} +(0.487893 - 2.76698i) q^{44} +(-0.492978 + 0.413658i) q^{46} +(-3.92821 + 6.80387i) q^{47} +(-4.58455 - 1.66864i) q^{49} +(1.12449 + 0.943555i) q^{50} +(-0.602694 - 3.41805i) q^{52} +(-0.839394 - 4.76044i) q^{53} +(-4.96199 + 1.80602i) q^{55} +(3.23871 - 1.17879i) q^{56} +(0.376641 + 2.13604i) q^{58} +(-0.0961039 - 0.545032i) q^{59} +(5.37102 + 4.50682i) q^{61} +(9.30969 + 3.38845i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-4.99685 + 4.19285i) q^{65} +(0.0366435 - 0.207815i) q^{67} +3.09926 q^{68} +(-4.96199 - 4.16360i) q^{70} +(4.75197 - 1.72957i) q^{71} +10.2297 q^{73} +(-0.522449 - 6.06028i) q^{74} +(-6.99748 - 2.54687i) q^{76} +(-9.09967 + 3.31201i) q^{77} +(-0.330775 + 1.87592i) q^{79} +1.87939 q^{80} +(5.31172 + 9.20017i) q^{82} +(-5.21650 + 4.37717i) q^{83} +(-2.91235 - 5.04435i) q^{85} +(7.80382 + 2.84036i) q^{86} +(1.40483 - 2.43324i) q^{88} +(1.68226 + 9.54055i) q^{89} +(-9.16360 + 7.68917i) q^{91} +(-0.604727 + 0.220103i) q^{92} +(-6.01837 + 5.05001i) q^{94} +(2.43020 + 13.7823i) q^{95} +(-8.52990 + 14.7742i) q^{97} +(-3.73736 - 3.13602i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

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