LMFDB - Embedded newform 168.2.c.b.85.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(85,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("168.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.c (of order $2$, degree $1$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.386672896.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			85.8
Root			$-1.19503 + 0.756243i$ of defining polynomial
Character	$\chi$	$=$	168.85
Dual form			168.2.c.b.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19503 + 0.756243i) q^{2} -1.00000i q^{3} +(0.856193 + 1.80747i) q^{4} -4.10245i q^{5} +(0.756243 - 1.19503i) q^{6} +1.00000 q^{7} +(-0.343707 + 2.80747i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.19503 + 0.756243i) q^{2} -1.00000i q^{3} +(0.856193 + 1.80747i) q^{4} -4.10245i q^{5} +(0.756243 - 1.19503i) q^{6} +1.00000 q^{7} +(-0.343707 + 2.80747i) q^{8} -1.00000 q^{9} +(3.10245 - 4.90255i) q^{10} +2.67767i q^{11} +(1.80747 - 0.856193i) q^{12} +3.02497i q^{13} +(1.19503 + 0.756243i) q^{14} -4.10245 q^{15} +(-2.53387 + 3.09508i) q^{16} -5.12742 q^{17} +(-1.19503 - 0.756243i) q^{18} +2.78012i q^{19} +(7.41503 - 3.51249i) q^{20} -1.00000i q^{21} +(-2.02497 + 3.19990i) q^{22} +7.12742 q^{23} +(2.80747 + 0.343707i) q^{24} -11.8301 q^{25} +(-2.28761 + 3.61493i) q^{26} +1.00000i q^{27} +(0.856193 + 1.80747i) q^{28} -8.83006i q^{29} +(-4.90255 - 3.10245i) q^{30} -1.42477 q^{31} +(-5.36868 + 1.78249i) q^{32} +2.67767 q^{33} +(-6.12742 - 3.87757i) q^{34} -4.10245i q^{35} +(-0.856193 - 1.80747i) q^{36} +1.42477i q^{37} +(-2.10245 + 3.32233i) q^{38} +3.02497 q^{39} +(11.5175 + 1.41004i) q^{40} +5.12742 q^{41} +(0.756243 - 1.19503i) q^{42} +2.39980i q^{43} +(-4.83980 + 2.29261i) q^{44} +4.10245i q^{45} +(8.51748 + 5.39006i) q^{46} -9.56024 q^{47} +(3.09508 + 2.53387i) q^{48} +1.00000 q^{49} +(-14.1373 - 8.94640i) q^{50} +5.12742i q^{51} +(-5.46753 + 2.58996i) q^{52} -2.78012i q^{53} +(-0.756243 + 1.19503i) q^{54} +10.9850 q^{55} +(-0.343707 + 2.80747i) q^{56} +2.78012 q^{57} +(6.67767 - 10.5522i) q^{58} +4.00000i q^{59} +(-3.51249 - 7.41503i) q^{60} -5.17992i q^{61} +(-1.70265 - 1.07747i) q^{62} -1.00000 q^{63} +(-7.76373 - 1.92989i) q^{64} +12.4098 q^{65} +(3.19990 + 2.02497i) q^{66} -0.244852i q^{67} +(-4.39006 - 9.26763i) q^{68} -7.12742i q^{69} +(3.10245 - 4.90255i) q^{70} -4.27787 q^{71} +(0.343707 - 2.80747i) q^{72} -4.15495 q^{73} +(-1.07747 + 1.70265i) q^{74} +11.8301i q^{75} +(-5.02497 + 2.38032i) q^{76} +2.67767i q^{77} +(3.61493 + 2.28761i) q^{78} +6.25484 q^{79} +(12.6974 + 10.3951i) q^{80} +1.00000 q^{81} +(6.12742 + 3.87757i) q^{82} -9.35535i q^{83} +(1.80747 - 0.856193i) q^{84} +21.0350i q^{85} +(-1.81483 + 2.86783i) q^{86} -8.83006 q^{87} +(-7.51748 - 0.920336i) q^{88} +11.2824 q^{89} +(-3.10245 + 4.90255i) q^{90} +3.02497i q^{91} +(6.10245 + 12.8826i) q^{92} +1.42477i q^{93} +(-11.4248 - 7.22986i) q^{94} +11.4053 q^{95} +(1.78249 + 5.36868i) q^{96} +6.69460 q^{97} +(1.19503 + 0.756243i) q^{98} -2.67767i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 8 * q^9	$ 8 q + 2 q^{4} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 8 q^{9} - 4 q^{10} - 4 q^{12} - 4 q^{15} - 6 q^{16} + 4 q^{17} + 24 q^{20} + 12 q^{23} + 4 q^{24} - 24 q^{25} - 28 q^{26} + 2 q^{28} - 12 q^{30} + 8 q^{31} - 30 q^{32} + 12 q^{33} - 4 q^{34} - 2 q^{36} + 12 q^{38} + 8 q^{39} + 28 q^{40} - 4 q^{41} + 2 q^{42} + 16 q^{44} + 4 q^{46} + 16 q^{48} + 8 q^{49} - 20 q^{50} - 12 q^{52} - 2 q^{54} - 8 q^{55} - 6 q^{56} - 16 q^{57} + 44 q^{58} - 20 q^{60} + 12 q^{62} - 8 q^{63} + 26 q^{64} - 16 q^{65} + 24 q^{66} - 16 q^{68} - 4 q^{70} - 28 q^{71} + 6 q^{72} - 8 q^{73} + 4 q^{74} - 24 q^{76} - 8 q^{78} - 40 q^{79} - 4 q^{80} + 8 q^{81} + 4 q^{82} - 4 q^{84} + 24 q^{86} + 4 q^{88} + 20 q^{89} + 4 q^{90} + 20 q^{92} - 72 q^{94} + 40 q^{95} + 12 q^{96} + 40 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 8 * q^9 - 4 * q^10 - 4 * q^12 - 4 * q^15 - 6 * q^16 + 4 * q^17 + 24 * q^20 + 12 * q^23 + 4 * q^24 - 24 * q^25 - 28 * q^26 + 2 * q^28 - 12 * q^30 + 8 * q^31 - 30 * q^32 + 12 * q^33 - 4 * q^34 - 2 * q^36 + 12 * q^38 + 8 * q^39 + 28 * q^40 - 4 * q^41 + 2 * q^42 + 16 * q^44 + 4 * q^46 + 16 * q^48 + 8 * q^49 - 20 * q^50 - 12 * q^52 - 2 * q^54 - 8 * q^55 - 6 * q^56 - 16 * q^57 + 44 * q^58 - 20 * q^60 + 12 * q^62 - 8 * q^63 + 26 * q^64 - 16 * q^65 + 24 * q^66 - 16 * q^68 - 4 * q^70 - 28 * q^71 + 6 * q^72 - 8 * q^73 + 4 * q^74 - 24 * q^76 - 8 * q^78 - 40 * q^79 - 4 * q^80 + 8 * q^81 + 4 * q^82 - 4 * q^84 + 24 * q^86 + 4 * q^88 + 20 * q^89 + 4 * q^90 + 20 * q^92 - 72 * q^94 + 40 * q^95 + 12 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	1.19503	+	0.756243i	0.845014	+	0.534745i
$2$	1.19503	+	0.756243i	0.845014	+	0.534745i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.856193	+	1.80747i	0.428097	+	0.903733i
$5$		−	4.10245i		−	1.83467i	−0.398117	−	0.917335i	$-0.630336\pi$
$5$		−	4.10245i		−	1.83467i	0.398117	−	0.917335i	$-0.369664\pi$
$6$	0.756243	−	1.19503i	0.308735	−	0.487869i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.343707	+	2.80747i	−0.121519	+	0.992589i
$9$	−1.00000			−0.333333
$10$	3.10245	−	4.90255i	0.981080	−	1.55032i
$11$			2.67767i			0.807349i	0.914903	+	0.403674i	$0.132267\pi$
$11$			2.67767i			0.807349i	−0.914903	+	0.403674i	$0.867733\pi$
$12$	1.80747	−	0.856193i	0.521770	−	0.247162i
$13$			3.02497i			0.838976i	0.907761	+	0.419488i	$0.137790\pi$
$13$			3.02497i			0.838976i	−0.907761	+	0.419488i	$0.862210\pi$
$14$	1.19503	+	0.756243i	0.319385	+	0.202114i
$15$	−4.10245			−1.05925
$16$	−2.53387	+	3.09508i	−0.633467	+	0.773770i
$17$	−5.12742			−1.24358			−0.621791	−	0.783183i	$-0.713595\pi$
$17$	−5.12742			−1.24358			−0.621791	+	0.783183i	$0.713595\pi$
$18$	−1.19503	−	0.756243i	−0.281671	−	0.178248i
$19$			2.78012i			0.637803i	0.947788	+	0.318902i	$0.103314\pi$
$19$			2.78012i			0.637803i	−0.947788	+	0.318902i	$0.896686\pi$
$20$	7.41503	−	3.51249i	1.65805	−	0.785416i
$21$		−	1.00000i		−	0.218218i
$22$	−2.02497	+	3.19990i	−0.431725	+	0.682221i
$23$	7.12742			1.48617			0.743085	−	0.669197i	$-0.233362\pi$
$23$	7.12742			1.48617			0.743085	+	0.669197i	$0.233362\pi$
$24$	2.80747	+	0.343707i	0.573072	+	0.0701589i
$25$	−11.8301			−2.36601
$26$	−2.28761	+	3.61493i	−0.448638	+	0.708946i
$27$			1.00000i			0.192450i
$28$	0.856193	+	1.80747i	0.161805	+	0.341579i
$29$		−	8.83006i		−	1.63970i	−0.572577	−	0.819851i	$-0.694056\pi$
$29$		−	8.83006i		−	1.63970i	0.572577	−	0.819851i	$-0.305944\pi$
$30$	−4.90255	−	3.10245i	−0.895078	−	0.566427i
$31$	−1.42477			−0.255897			−0.127948	−	0.991781i	$-0.540839\pi$
$31$	−1.42477			−0.255897			−0.127948	+	0.991781i	$0.540839\pi$
$32$	−5.36868	+	1.78249i	−0.949057	+	0.315103i
$33$	2.67767			0.466123
$34$	−6.12742	−	3.87757i	−1.05084	−	0.664998i
$35$		−	4.10245i		−	0.693440i
$36$	−0.856193	−	1.80747i	−0.142699	−	0.301244i
$37$			1.42477i			0.234231i	0.993118	+	0.117116i	$0.0373648\pi$
$37$			1.42477i			0.234231i	−0.993118	+	0.117116i	$0.962635\pi$
$38$	−2.10245	+	3.32233i	−0.341062	+	0.538952i
$39$	3.02497			0.484383
$40$	11.5175	+	1.41004i	1.82107	+	0.222947i
$41$	5.12742			0.800768			0.400384	−	0.916347i	$-0.368877\pi$
$41$	5.12742			0.800768			0.400384	+	0.916347i	$0.368877\pi$
$42$	0.756243	−	1.19503i	0.116691	−	0.184397i
$43$			2.39980i			0.365966i	0.983116	+	0.182983i	$0.0585754\pi$
$43$			2.39980i			0.365966i	−0.983116	+	0.182983i	$0.941425\pi$
$44$	−4.83980	+	2.29261i	−0.729628	+	0.345623i
$45$			4.10245i			0.611557i
$46$	8.51748	+	5.39006i	1.25583	+	0.794721i
$47$	−9.56024			−1.39450			−0.697252	−	0.716826i	$-0.745594\pi$
$47$	−9.56024			−1.39450			−0.697252	+	0.716826i	$0.745594\pi$
$48$	3.09508	+	2.53387i	0.446736	+	0.365732i
$49$	1.00000			0.142857
$50$	−14.1373	−	8.94640i	−1.99931	−	1.26521i
$51$			5.12742i			0.717982i
$52$	−5.46753	+	2.58996i	−0.758211	+	0.359163i
$53$		−	2.78012i		−	0.381879i	−0.981602	−	0.190939i	$-0.938847\pi$
$53$		−	2.78012i		−	0.381879i	0.981602	−	0.190939i	$-0.0611534\pi$
$54$	−0.756243	+	1.19503i	−0.102912	+	0.162623i
$55$	10.9850			1.48122
$56$	−0.343707	+	2.80747i	−0.0459298	+	0.375163i
$57$	2.78012			0.368236
$58$	6.67767	−	10.5522i	0.876822	−	1.38557i
$59$			4.00000i			0.520756i	0.965507	+	0.260378i	$0.0838471\pi$
$59$			4.00000i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$60$	−3.51249	−	7.41503i	−0.453460	−	0.957276i
$61$		−	5.17992i		−	0.663221i	−0.943416	−	0.331610i	$-0.892408\pi$
$61$		−	5.17992i		−	0.663221i	0.943416	−	0.331610i	$-0.107592\pi$
$62$	−1.70265	−	1.07747i	−0.216236	−	0.136839i
$63$	−1.00000			−0.125988
$64$	−7.76373	−	1.92989i	−0.970466	−	0.241237i
$65$	12.4098			1.53924
$66$	3.19990	+	2.02497i	0.393880	+	0.249257i
$67$		−	0.244852i		−	0.0299135i	−0.999888	−	0.0149567i	$-0.995239\pi$
$67$		−	0.244852i		−	0.0299135i	0.999888	−	0.0149567i	$-0.00476105\pi$
$68$	−4.39006	−	9.26763i	−0.532373	−	1.12387i
$69$		−	7.12742i		−	0.858040i
$70$	3.10245	−	4.90255i	0.370813	−	0.585966i
$71$	−4.27787			−0.507690			−0.253845	−	0.967245i	$-0.581695\pi$
$71$	−4.27787			−0.507690			−0.253845	+	0.967245i	$0.581695\pi$
$72$	0.343707	−	2.80747i	0.0405063	−	0.330863i
$73$	−4.15495			−0.486300			−0.243150	−	0.969989i	$-0.578181\pi$
$73$	−4.15495			−0.486300			−0.243150	+	0.969989i	$0.578181\pi$
$74$	−1.07747	+	1.70265i	−0.125254	+	0.197929i
$75$			11.8301i			1.36602i
$76$	−5.02497	+	2.38032i	−0.576404	+	0.273041i
$77$			2.67767i			0.305149i
$78$	3.61493	+	2.28761i	0.409310	+	0.259021i
$79$	6.25484			0.703724			0.351862	−	0.936052i	$-0.385549\pi$
$79$	6.25484			0.703724			0.351862	+	0.936052i	$0.385549\pi$
$80$	12.6974	+	10.3951i	1.41961	+	1.16220i
$81$	1.00000			0.111111
$82$	6.12742	+	3.87757i	0.676660	+	0.428206i
$83$		−	9.35535i		−	1.02688i	−0.858125	−	0.513441i	$-0.828370\pi$
$83$		−	9.35535i		−	1.02688i	0.858125	−	0.513441i	$-0.171630\pi$
$84$	1.80747	−	0.856193i	0.197211	−	0.0934183i
$85$			21.0350i			2.28156i
$86$	−1.81483	+	2.86783i	−0.195698	+	0.309246i
$87$	−8.83006			−0.946682
$88$	−7.51748	−	0.920336i	−0.801366	−	0.0981081i
$89$	11.2824			1.19593			0.597964	−	0.801523i	$-0.295976\pi$
$89$	11.2824			1.19593			0.597964	+	0.801523i	$0.295976\pi$
$90$	−3.10245	+	4.90255i	−0.327027	+	0.516774i
$91$			3.02497i			0.317103i
$92$	6.10245	+	12.8826i	0.636224	+	1.34310i
$93$			1.42477i			0.147742i
$94$	−11.4248	−	7.22986i	−1.17838	−	0.745704i
$95$	11.4053			1.17016
$96$	1.78249	+	5.36868i	0.181925	+	0.547939i
$97$	6.69460			0.679733			0.339867	−	0.940474i	$-0.389618\pi$
$97$	6.69460			0.679733			0.339867	+	0.940474i	$0.389618\pi$
$98$	1.19503	+	0.756243i	0.120716	+	0.0763921i
$99$		−	2.67767i		−	0.269116i
$100$	−10.1288	−	21.3824i	−1.01288	−	2.13824i
$101$			1.45779i			0.145056i	0.997366	+	0.0725279i	$0.0231066\pi$
$101$			1.45779i			0.145056i	−0.997366	+	0.0725279i	$0.976893\pi$
$102$	−3.87757	+	6.12742i	−0.383937	+	0.606705i
$103$	8.13547			0.801611			0.400806	−	0.916163i	$-0.368730\pi$
$103$	8.13547			0.801611			0.400806	+	0.916163i	$0.368730\pi$
$104$	−8.49251	−	1.03970i	−0.832759	−	0.101951i
$105$	−4.10245			−0.400358
$106$	2.10245	−	3.32233i	0.204208	−	0.322693i
$107$			5.32233i			0.514529i	0.966341	+	0.257264i	$0.0828211\pi$
$107$			5.32233i			0.514529i	−0.966341	+	0.257264i	$0.917179\pi$
$108$	−1.80747	+	0.856193i	−0.173923	+	0.0823872i
$109$		−	13.5602i		−	1.29884i	−0.760432	−	0.649418i	$-0.775013\pi$
$109$		−	13.5602i		−	1.29884i	0.760432	−	0.649418i	$-0.224987\pi$
$110$	13.1274	+	8.30734i	1.25165	+	0.792074i
$111$	1.42477			0.135233
$112$	−2.53387	+	3.09508i	−0.239428	+	0.292458i
$113$	−4.15495			−0.390865			−0.195432	−	0.980717i	$-0.562611\pi$
$113$	−4.15495			−0.390865			−0.195432	+	0.980717i	$0.562611\pi$
$114$	3.32233	+	2.10245i	0.311164	+	0.196912i
$115$		−	29.2398i		−	2.72663i
$116$	15.9600	−	7.56024i	1.48185	−	0.701951i
$117$		−	3.02497i		−	0.279659i
$118$	−3.02497	+	4.78012i	−0.278471	+	0.440046i
$119$	−5.12742			−0.470030
$120$	1.41004	−	11.5175i	0.128718	−	1.05140i
$121$	3.83006			0.348188
$122$	3.91728	−	6.19016i	0.354654	−	0.560431i
$123$		−	5.12742i		−	0.462324i
$124$	−1.21988	−	2.57523i	−0.109548	−	0.231262i
$125$			28.0200i			2.50618i
$126$	−1.19503	−	0.756243i	−0.106462	−	0.0673715i
$127$	−0.694597			−0.0616355			−0.0308177	−	0.999525i	$-0.509811\pi$
$127$	−0.694597			−0.0616355			−0.0308177	+	0.999525i	$0.509811\pi$
$128$	−7.81842	−	8.17755i	−0.691058	−	0.722800i
$129$	2.39980			0.211291
$130$	14.8301	+	9.38481i	1.30068	+	0.823102i
$131$		−	12.2049i		−	1.06635i	−0.846006	−	0.533173i	$-0.820999\pi$
$131$		−	12.2049i		−	1.06635i	0.846006	−	0.533173i	$-0.179001\pi$
$132$	2.29261	+	4.83980i	0.199546	+	0.421251i
$133$			2.78012i			0.241067i
$134$	0.185168	−	0.292606i	0.0159961	−	0.0252773i
$135$	4.10245			0.353082
$136$	1.76233	−	14.3951i	0.151119	−	1.23437i
$137$	−15.1044			−1.29045			−0.645227	−	0.763991i	$-0.723237\pi$
$137$	−15.1044			−1.29045			−0.645227	+	0.763991i	$0.723237\pi$
$138$	5.39006	−	8.51748i	0.458832	−	0.725056i
$139$		−	7.61018i		−	0.645487i	−0.946486	−	0.322744i	$-0.895395\pi$
$139$		−	7.61018i		−	0.645487i	0.946486	−	0.322744i	$-0.104605\pi$
$140$	7.41503	−	3.51249i	0.626685	−	0.296859i
$141$			9.56024i			0.805117i
$142$	−5.11219	−	3.23511i	−0.429005	−	0.271485i
$143$	−8.09989			−0.677347
$144$	2.53387	−	3.09508i	0.211156	−	0.257923i
$145$	−36.2249			−3.00831
$146$	−4.96529	−	3.14215i	−0.410930	−	0.260046i
$147$		−	1.00000i		−	0.0824786i
$148$	−2.57523	+	1.21988i	−0.211682	+	0.100274i
$149$			5.21988i			0.427629i	0.976874	+	0.213815i	$0.0685889\pi$
$149$			5.21988i			0.427629i	−0.976874	+	0.213815i	$0.931411\pi$
$150$	−8.94640	+	14.1373i	−0.730471	+	1.15430i
$151$	−5.56024			−0.452486			−0.226243	−	0.974071i	$-0.572644\pi$
$151$	−5.56024			−0.452486			−0.226243	+	0.974071i	$0.572644\pi$
$152$	−7.80509	−	0.955547i	−0.633077	−	0.0775051i
$153$	5.12742			0.414527
$154$	−2.02497	+	3.19990i	−0.163177	+	0.257855i
$155$			5.84505i			0.469486i
$156$	2.58996	+	5.46753i	0.207363	+	0.437753i
$157$		−	0.519169i		−	0.0414342i	−0.999785	−	0.0207171i	$-0.993405\pi$
$157$		−	0.519169i		−	0.0414342i	0.999785	−	0.0207171i	$-0.00659493\pi$
$158$	7.47472	+	4.73018i	0.594656	+	0.376313i
$159$	−2.78012			−0.220478
$160$	7.31259	+	22.0247i	0.578111	+	1.74121i
$161$	7.12742			0.561719
$162$	1.19503	+	0.756243i	0.0938904	+	0.0594161i
$163$			8.65464i			0.677883i	0.940807	+	0.338942i	$0.110069\pi$
$163$			8.65464i			0.677883i	−0.940807	+	0.338942i	$0.889931\pi$
$164$	4.39006	+	9.26763i	0.342806	+	0.723681i
$165$		−	10.9850i		−	0.855182i
$166$	7.07492	−	11.1799i	0.549120	−	0.867730i
$167$	−25.1044			−1.94264			−0.971318	−	0.237786i	$-0.923578\pi$
$167$	−25.1044			−1.94264			−0.971318	+	0.237786i	$0.923578\pi$
$168$	2.80747	+	0.343707i	0.216601	+	0.0265176i
$169$	3.84954			0.296119
$170$	−15.9075	+	25.1374i	−1.22005	+	1.92795i
$171$		−	2.78012i		−	0.212601i
$172$	−4.33756	+	2.05469i	−0.330736	+	0.156669i
$173$		−	1.94750i		−	0.148066i	−0.997256	−	0.0740328i	$-0.976413\pi$
$173$		−	1.94750i		−	0.148066i	0.997256	−	0.0740328i	$-0.0235869\pi$
$174$	−10.5522	−	6.67767i	−0.799959	−	0.506233i
$175$	−11.8301			−0.894269
$176$	−8.28761	−	6.78487i	−0.624702	−	0.511429i
$177$	4.00000			0.300658
$178$	13.4828	+	8.53221i	1.01058	+	0.639516i
$179$			22.6976i			1.69650i	0.529595	+	0.848251i	$0.322344\pi$
$179$			22.6976i			1.69650i	−0.529595	+	0.848251i	$0.677656\pi$
$180$	−7.41503	+	3.51249i	−0.552684	+	0.261805i
$181$			10.5353i			0.783080i	0.920161	+	0.391540i	$0.128058\pi$
$181$			10.5353i			0.783080i	−0.920161	+	0.391540i	$0.871942\pi$
$182$	−2.28761	+	3.61493i	−0.169569	+	0.267957i
$183$	−5.17992			−0.382911
$184$	−2.44974	+	20.0100i	−0.180598	+	1.47516i
$185$	5.84505			0.429737
$186$	−1.07747	+	1.70265i	−0.0790042	+	0.124844i
$187$		−	13.7296i		−	1.00400i
$188$	−8.18541	−	17.2798i	−0.596982	−	1.26026i
$189$			1.00000i			0.0727393i
$190$	13.6297	+	8.62517i	0.988800	+	0.625736i
$191$	−4.27787			−0.309536			−0.154768	−	0.987951i	$-0.549463\pi$
$191$	−4.27787			−0.309536			−0.154768	+	0.987951i	$0.549463\pi$
$192$	−1.92989	+	7.76373i	−0.139278	+	0.560299i
$193$	23.1400			1.66565			0.832825	−	0.553536i	$-0.186722\pi$
$193$	23.1400			1.66565			0.832825	+	0.553536i	$0.186722\pi$
$194$	8.00024	+	5.06274i	0.574384	+	0.363484i
$195$		−	12.4098i		−	0.888683i
$196$	0.856193	+	1.80747i	0.0611566	+	0.129105i
$197$		−	19.4747i		−	1.38752i	−0.720208	−	0.693758i	$-0.755954\pi$
$197$		−	19.4747i		−	1.38752i	0.720208	−	0.693758i	$-0.244046\pi$
$198$	2.02497	−	3.19990i	0.143908	−	0.227407i
$199$	−17.5602			−1.24481			−0.622406	−	0.782694i	$-0.713845\pi$
$199$	−17.5602			−1.24481			−0.622406	+	0.782694i	$0.713845\pi$
$200$	4.06608	−	33.2125i	0.287515	−	2.34848i
$201$	−0.244852			−0.0172705
$202$	−1.10245	+	1.74211i	−0.0775678	+	0.122574i
$203$		−	8.83006i		−	0.619749i
$204$	−9.26763	+	4.39006i	−0.648864	+	0.307366i
$205$		−	21.0350i		−	1.46915i
$206$	9.72213	+	6.15239i	0.677373	+	0.428657i
$207$	−7.12742			−0.495390
$208$	−9.36253	−	7.66488i	−0.649175	−	0.531464i
$209$	−7.44425			−0.514930
$210$	−4.90255	−	3.10245i	−0.338308	−	0.214089i
$211$		−	23.9600i		−	1.64948i	−0.565514	−	0.824739i	$-0.691322\pi$
$211$		−	23.9600i		−	1.64948i	0.565514	−	0.824739i	$-0.308678\pi$
$212$	5.02497	−	2.38032i	0.345116	−	0.163481i
$213$			4.27787i			0.293115i
$214$	−4.02497	+	6.36034i	−0.275141	+	0.434784i
$215$	9.84505			0.671427
$216$	−2.80747	−	0.343707i	−0.191024	−	0.0233863i
$217$	−1.42477			−0.0967199
$218$	10.2548	−	16.2049i	0.694545	−	1.09753i
$219$			4.15495i			0.280765i
$220$	9.40529	+	19.8550i	0.634105	+	1.33863i
$221$		−	15.5103i		−	1.04334i
$222$	1.70265	+	1.07747i	0.114274	+	0.0723153i
$223$	2.74966			0.184131			0.0920653	−	0.995753i	$-0.470653\pi$
$223$	2.74966			0.184131			0.0920653	+	0.995753i	$0.470653\pi$
$224$	−5.36868	+	1.78249i	−0.358710	+	0.119098i
$225$	11.8301			0.788671
$226$	−4.96529	−	3.14215i	−0.330286	−	0.209013i
$227$			8.30478i			0.551208i	0.961271	+	0.275604i	$0.0888778\pi$
$227$			8.30478i			0.551208i	−0.961271	+	0.275604i	$0.911122\pi$
$228$	2.38032	+	5.02497i	0.157640	+	0.332787i
$229$			11.9245i			0.787991i	0.919112	+	0.393995i	$0.128907\pi$
$229$			11.9245i			0.787991i	−0.919112	+	0.393995i	$0.871093\pi$
$230$	22.1124	−	34.9425i	1.45805	−	2.30404i
$231$	2.67767			0.176178
$232$	24.7901	+	3.03496i	1.62755	+	0.199255i
$233$	−3.56024			−0.233239			−0.116620	−	0.993177i	$-0.537206\pi$
$233$	−3.56024			−0.233239			−0.116620	+	0.993177i	$0.537206\pi$
$234$	2.28761	−	3.61493i	0.149546	−	0.236315i
$235$			39.2204i			2.55845i
$236$	−7.22986	+	3.42477i	−0.470624	+	0.222934i
$237$		−	6.25484i		−	0.406295i
$238$	−6.12742	−	3.87757i	−0.397182	−	0.251346i
$239$	26.9425			1.74277			0.871383	−	0.490604i	$-0.163224\pi$
$239$	26.9425			1.74277			0.871383	+	0.490604i	$0.163224\pi$
$240$	10.3951	−	12.6974i	0.670998	−	0.819614i
$241$	25.8151			1.66290			0.831448	−	0.555603i	$-0.187513\pi$
$241$	25.8151			1.66290			0.831448	+	0.555603i	$0.187513\pi$
$242$	4.57704	+	2.89646i	0.294223	+	0.186191i
$243$		−	1.00000i		−	0.0641500i
$244$	9.36253	−	4.43501i	0.599375	−	0.283923i
$245$		−	4.10245i		−	0.262096i
$246$	3.87757	−	6.12742i	0.247225	−	0.390670i
$247$	−8.40978			−0.535102
$248$	0.489704	−	4.00000i	0.0310963	−	0.254000i
$249$	−9.35535			−0.592871
$250$	−21.1899	+	33.4847i	−1.34017	+	2.11776i
$251$			27.1543i			1.71397i	0.515345	+	0.856983i	$0.327664\pi$
$251$			27.1543i			1.71397i	−0.515345	+	0.856983i	$0.672336\pi$
$252$	−0.856193	−	1.80747i	−0.0539351	−	0.113860i
$253$			19.0849i			1.19986i
$254$	−0.830064	−	0.525284i	−0.0520828	−	0.0329592i
$255$	21.0350			1.31726
$256$	−3.15904	−	15.6850i	−0.197440	−	0.980315i
$257$	−31.3823			−1.95757			−0.978786	−	0.204887i	$-0.934317\pi$
$257$	−31.3823			−1.95757			−0.978786	+	0.204887i	$0.934317\pi$
$258$	2.86783	+	1.81483i	0.178544	+	0.112987i
$259$			1.42477i			0.0885310i
$260$	10.6252	+	22.4303i	0.658945	+	1.39107i
$261$			8.83006i			0.546567i
$262$	9.22986	−	14.5852i	0.570223	−	0.901077i
$263$	−11.0275			−0.679987			−0.339993	−	0.940428i	$-0.610425\pi$
$263$	−11.0275			−0.679987			−0.339993	+	0.940428i	$0.610425\pi$
$264$	−0.920336	+	7.51748i	−0.0566427	+	0.462669i
$265$	−11.4053			−0.700621
$266$	−2.10245	+	3.32233i	−0.128909	+	0.203705i
$267$		−	11.2824i		−	0.690470i
$268$	0.442562	−	0.209641i	0.0270338	−	0.0128058i
$269$			21.0019i			1.28051i	0.768162	+	0.640255i	$0.221171\pi$
$269$			21.0019i			1.28051i	−0.768162	+	0.640255i	$0.778829\pi$
$270$	4.90255	+	3.10245i	0.298359	+	0.188809i
$271$	28.6451			1.74007			0.870034	−	0.492991i	$-0.164097\pi$
$271$	28.6451			1.74007			0.870034	+	0.492991i	$0.164097\pi$
$272$	12.9922	−	15.8698i	0.787767	−	0.962246i
$273$	3.02497			0.183080
$274$	−18.0502	−	11.4226i	−1.09045	−	0.690063i
$275$		−	31.6771i		−	1.91020i
$276$	12.8826	−	6.10245i	0.775439	−	0.367324i
$277$			2.96504i			0.178152i	0.996025	+	0.0890761i	$0.0283914\pi$
$277$			2.96504i			0.178152i	−0.996025	+	0.0890761i	$0.971609\pi$
$278$	5.75515	−	9.09440i	0.345171	−	0.545446i
$279$	1.42477			0.0852989
$280$	11.5175	+	1.41004i	0.688301	+	0.0842660i
$281$	26.4098			1.57548			0.787738	−	0.616011i	$-0.211252\pi$
$281$	26.4098			1.57548			0.787738	+	0.616011i	$0.211252\pi$
$282$	−7.22986	+	11.4248i	−0.430532	+	0.680335i
$283$			11.2698i			0.669922i	0.942232	+	0.334961i	$0.108723\pi$
$283$			11.2698i			0.669922i	−0.942232	+	0.334961i	$0.891277\pi$
$284$	−3.66269	−	7.73211i	−0.217340	−	0.458816i
$285$		−	11.4053i		−	0.675591i
$286$	−9.67961	−	6.12548i	−0.572367	−	0.362207i
$287$	5.12742			0.302662
$288$	5.36868	−	1.78249i	0.316352	−	0.105034i
$289$	9.29042			0.546495
$290$	−43.2898	−	27.3948i	−2.54206	−	1.60868i
$291$		−	6.69460i		−	0.392444i
$292$	−3.55744	−	7.50993i	−0.208183	−	0.439485i
$293$			10.5622i			0.617049i	0.951216	+	0.308524i	$0.0998351\pi$
$293$			10.5622i			0.617049i	−0.951216	+	0.308524i	$0.900165\pi$
$294$	0.756243	−	1.19503i	0.0441050	−	0.0696956i
$295$	16.4098			0.955415
$296$	−4.00000	−	0.489704i	−0.232495	−	0.0284635i
$297$	−2.67767			−0.155374
$298$	−3.94750	+	6.23791i	−0.228672	+	0.361353i
$299$			21.5602i			1.24686i
$300$	−21.3824	+	10.1288i	−1.23452	+	0.584788i
$301$			2.39980i			0.138322i
$302$	−6.64465	−	4.20489i	−0.382357	−	0.241964i
$303$	1.45779			0.0837480
$304$	−8.60469	−	7.04445i	−0.493513	−	0.404027i
$305$	−21.2503			−1.21679
$306$	6.12742	+	3.87757i	0.350281	+	0.221666i
$307$		−	10.7801i		−	0.615254i	−0.951507	−	0.307627i	$-0.900465\pi$
$307$		−	10.7801i		−	0.615254i	0.951507	−	0.307627i	$-0.0995349\pi$
$308$	−4.83980	+	2.29261i	−0.275773	+	0.130633i
$309$		−	8.13547i		−	0.462811i
$310$	−4.42028	+	6.98501i	−0.251055	+	0.396722i
$311$	9.56024			0.542111			0.271056	−	0.962564i	$-0.412627\pi$
$311$	9.56024			0.542111			0.271056	+	0.962564i	$0.412627\pi$
$312$	−1.03970	+	8.49251i	−0.0588617	+	0.480793i
$313$	7.69909			0.435178			0.217589	−	0.976040i	$-0.430181\pi$
$313$	7.69909			0.435178			0.217589	+	0.976040i	$0.430181\pi$
$314$	0.392618	−	0.620423i	0.0221567	−	0.0350125i
$315$			4.10245i			0.231147i
$316$	5.35535	+	11.3054i	0.301262	+	0.635979i
$317$		−	10.7801i		−	0.605472i	−0.953074	−	0.302736i	$-0.902100\pi$
$317$		−	10.7801i		−	0.605472i	0.953074	−	0.302736i	$-0.0979000\pi$
$318$	−3.32233	−	2.10245i	−0.186307	−	0.117899i
$319$	23.6440			1.32381
$320$	−7.91728	+	31.8503i	−0.442589	+	1.78049i
$321$	5.32233			0.297063
$322$	8.51748	+	5.39006i	0.474660	+	0.300376i
$323$		−	14.2548i		−	0.793160i
$324$	0.856193	+	1.80747i	0.0475663	+	0.100415i
$325$		−	35.7856i		−	1.98503i
$326$	−6.54501	+	10.3425i	−0.362494	+	0.572821i
$327$	−13.5602			−0.749883
$328$	−1.76233	+	14.3951i	−0.0973084	+	0.794834i
$329$	−9.56024			−0.527073
$330$	8.30734	−	13.1274i	0.457304	−	0.722641i
$331$			25.2104i			1.38569i	0.721088	+	0.692844i	$0.243643\pi$
$331$			25.2104i			1.38569i	−0.721088	+	0.692844i	$0.756357\pi$
$332$	16.9095	−	8.00998i	0.928028	−	0.439605i
$333$		−	1.42477i		−	0.0780770i
$334$	−30.0005	−	18.9850i	−1.64155	−	1.03881i
$335$	−1.00449			−0.0548813
$336$	3.09508	+	2.53387i	0.168850	+	0.138234i
$337$	−23.9700			−1.30573			−0.652865	−	0.757474i	$-0.726433\pi$
$337$	−23.9700			−1.30573			−0.652865	+	0.757474i	$0.726433\pi$
$338$	4.60032	+	2.91119i	0.250224	+	0.158348i
$339$			4.15495i			0.225666i
$340$	−38.0200	+	18.0100i	−2.06192	+	0.976729i
$341$		−	3.81508i		−	0.206598i
$342$	2.10245	−	3.32233i	0.113687	−	0.179651i
$343$	1.00000			0.0539949
$344$	−6.73736	−	0.824828i	−0.363254	−	0.0444718i
$345$	−29.2398			−1.57422
$346$	1.47278	−	2.32732i	0.0791772	−	0.125117i
$347$			6.98757i			0.375112i	0.982254	+	0.187556i	$0.0600567\pi$
$347$			6.98757i			0.375112i	−0.982254	+	0.187556i	$0.939943\pi$
$348$	−7.56024	−	15.9600i	−0.405271	−	0.855548i
$349$		−	20.8900i		−	1.11822i	−0.829095	−	0.559108i	$-0.811144\pi$
$349$		−	20.8900i		−	1.11822i	0.829095	−	0.559108i	$-0.188856\pi$
$350$	−14.1373	−	8.94640i	−0.755669	−	0.478205i
$351$	−3.02497			−0.161461
$352$	−4.77294	−	14.3756i	−0.254398	−	0.766220i
$353$	3.38225			0.180019			0.0900096	−	0.995941i	$-0.471310\pi$
$353$	3.38225			0.180019			0.0900096	+	0.995941i	$0.471310\pi$
$354$	4.78012	+	3.02497i	0.254060	+	0.160775i
$355$			17.5497i			0.931444i
$356$	9.65988	+	20.3925i	0.511973	+	1.08080i
$357$			5.12742i			0.271372i
$358$	−17.1649	+	27.1244i	−0.907195	+	1.43357i
$359$	20.6877			1.09185			0.545926	−	0.837833i	$-0.316178\pi$
$359$	20.6877			1.09185			0.545926	+	0.837833i	$0.316178\pi$
$360$	−11.5175	−	1.41004i	−0.607024	−	0.0743156i
$361$	11.2709			0.593207
$362$	−7.96722	+	12.5900i	−0.418748	+	0.661714i
$363$		−	3.83006i		−	0.201026i
$364$	−5.46753	+	2.58996i	−0.286577	+	0.135751i
$365$			17.0455i			0.892200i
$366$	−6.19016	−	3.91728i	−0.323565	−	0.204759i
$367$	−9.56024			−0.499040			−0.249520	−	0.968370i	$-0.580273\pi$
$367$	−9.56024			−0.499040			−0.249520	+	0.968370i	$0.580273\pi$
$368$	−18.0599	+	22.0599i	−0.941439	+	1.14995i
$369$	−5.12742			−0.266923
$370$	6.98501	+	4.42028i	0.363133	+	0.229799i
$371$		−	2.78012i		−	0.144337i
$372$	−2.57523	+	1.21988i	−0.133519	+	0.0632478i
$373$			1.95006i			0.100970i	0.998725	+	0.0504850i	$0.0160767\pi$
$373$			1.95006i			0.100970i	−0.998725	+	0.0504850i	$0.983923\pi$
$374$	10.3829	−	16.4072i	0.536886	−	0.848397i
$375$	28.0200			1.44694
$376$	3.28592	−	26.8400i	0.169459	−	1.38417i
$377$	26.7107			1.37567
$378$	−0.756243	+	1.19503i	−0.0388969	+	0.0614657i
$379$			32.3698i			1.66273i	0.555730	+	0.831363i	$0.312439\pi$
$379$			32.3698i			1.66273i	−0.555730	+	0.831363i	$0.687561\pi$
$380$	9.76513	+	20.6147i	0.500941	+	1.05751i
$381$			0.694597i			0.0355853i
$382$	−5.11219	−	3.23511i	−0.261562	−	0.165523i
$383$	−17.8451			−0.911840			−0.455920	−	0.890021i	$-0.650690\pi$
$383$	−17.8451			−0.911840			−0.455920	+	0.890021i	$0.650690\pi$
$384$	−8.17755	+	7.81842i	−0.417309	+	0.398982i
$385$	10.9850			0.559848
$386$	27.6529	+	17.4994i	1.40750	+	0.890698i
$387$		−	2.39980i		−	0.121989i
$388$	5.73187	+	12.1003i	0.290991	+	0.614297i
$389$			6.11937i			0.310264i	0.987894	+	0.155132i	$0.0495803\pi$
$389$			6.11937i			0.310264i	−0.987894	+	0.155132i	$0.950420\pi$
$390$	9.38481	−	14.8301i	0.475218	−	0.750949i
$391$	−36.5453			−1.84817
$392$	−0.343707	+	2.80747i	−0.0173598	+	0.141798i
$393$	−12.2049			−0.615655
$394$	14.7276	−	23.2729i	0.741967	−	1.17247i
$395$		−	25.6601i		−	1.29110i
$396$	4.83980	−	2.29261i	0.243209	−	0.115208i
$397$			3.71957i			0.186680i	0.995634	+	0.0933399i	$0.0297543\pi$
$397$			3.71957i			0.186680i	−0.995634	+	0.0933399i	$0.970246\pi$
$398$	−20.9850	−	13.2798i	−1.05188	−	0.665657i
$399$	2.78012			0.139180
$400$	29.9758	−	36.6150i	1.49879	−	1.83075i
$401$	−32.5258			−1.62426			−0.812130	−	0.583477i	$-0.801692\pi$
$401$	−32.5258			−1.62426			−0.812130	+	0.583477i	$0.801692\pi$
$402$	−0.292606	−	0.185168i	−0.0145938	−	0.00923533i
$403$		−	4.30990i		−	0.214691i
$404$	−2.63491	+	1.24815i	−0.131092	+	0.0620979i
$405$		−	4.10245i		−	0.203852i
$406$	6.67767	−	10.5522i	0.331407	−	0.523696i
$407$	−3.81508			−0.189106
$408$	−14.3951	−	1.76233i	−0.712661	−	0.0872483i
$409$	−1.13436			−0.0560903			−0.0280452	−	0.999607i	$-0.508928\pi$
$409$	−1.13436			−0.0560903			−0.0280452	+	0.999607i	$0.508928\pi$
$410$	15.9075	−	25.1374i	0.785617	−	1.24145i
$411$			15.1044i			0.745044i
$412$	6.96553	+	14.7046i	0.343167	+	0.724443i
$413$			4.00000i			0.196827i
$414$	−8.51748	−	5.39006i	−0.418611	−	0.264907i
$415$	−38.3798			−1.88399
$416$	−5.39199	−	16.2401i	−0.264364	−	0.796237i
$417$	−7.61018			−0.372672
$418$	−8.89611	−	5.62966i	−0.435123	−	0.275356i
$419$			1.56024i			0.0762227i	0.999273	+	0.0381113i	$0.0121342\pi$
$419$			1.56024i			0.0762227i	−0.999273	+	0.0381113i	$0.987866\pi$
$420$	−3.51249	−	7.41503i	−0.171392	−	0.361817i
$421$		−	31.8845i		−	1.55396i	−0.629528	−	0.776978i	$-0.716752\pi$
$421$		−	31.8845i		−	1.55396i	0.629528	−	0.776978i	$-0.283248\pi$
$422$	18.1196	−	28.6330i	0.882049	−	1.39383i
$423$	9.56024			0.464835
$424$	7.80509	+	0.955547i	0.379049	+	0.0464055i
$425$	60.6577			2.94233
$426$	−3.23511	+	5.11219i	−0.156742	+	0.247686i
$427$		−	5.17992i		−	0.250674i
$428$	−9.61992	+	4.55694i	−0.464997	+	0.220268i
$429$			8.09989i			0.391066i
$430$	11.7651	+	7.44525i	0.567365	+	0.359042i
$431$	8.87258			0.427377			0.213689	−	0.976902i	$-0.431452\pi$
$431$	8.87258			0.427377			0.213689	+	0.976902i	$0.431452\pi$
$432$	−3.09508	−	2.53387i	−0.148912	−	0.121911i
$433$	11.5602			0.555550			0.277775	−	0.960646i	$-0.410403\pi$
$433$	11.5602			0.555550			0.277775	+	0.960646i	$0.410403\pi$
$434$	−1.70265	−	1.07747i	−0.0817296	−	0.0517204i
$435$			36.2249i			1.73685i
$436$	24.5097	−	11.6102i	1.17380	−	0.556027i
$437$			19.8151i			0.947884i
$438$	−3.14215	+	4.96529i	−0.150138	+	0.237251i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	−3.77563	+	30.8400i	−0.179996	+	1.47024i
$441$	−1.00000			−0.0476190
$442$	11.7296	−	18.5353i	0.557918	−	0.881633i
$443$			5.87807i			0.279276i	0.990203	+	0.139638i	$0.0445938\pi$
$443$			5.87807i			0.279276i	−0.990203	+	0.139638i	$0.955406\pi$
$444$	1.21988	+	2.57523i	0.0578930	+	0.122215i
$445$		−	46.2853i		−	2.19413i
$446$	3.28592	+	2.07941i	0.155593	+	0.0984629i
$447$	5.21988			0.246892
$448$	−7.76373	−	1.92989i	−0.366802	−	0.0911788i
$449$	−11.8451			−0.559003			−0.279501	−	0.960145i	$-0.590169\pi$
$449$	−11.8451			−0.559003			−0.279501	+	0.960145i	$0.590169\pi$
$450$	14.1373	+	8.94640i	0.666438	+	0.421737i
$451$			13.7296i			0.646499i
$452$	−3.55744	−	7.50993i	−0.167328	−	0.353237i
$453$			5.56024i			0.261243i
$454$	−6.28043	+	9.92446i	−0.294755	+	0.465778i
$455$	12.4098			0.581780
$456$	−0.955547	+	7.80509i	−0.0447476	+	0.365507i
$457$	−28.2088			−1.31955			−0.659775	−	0.751463i	$-0.729348\pi$
$457$	−28.2088			−1.31955			−0.659775	+	0.751463i	$0.729348\pi$
$458$	−9.01779	+	14.2501i	−0.421374	+	0.665863i
$459$		−	5.12742i		−	0.239327i
$460$	52.8500	−	25.0350i	2.46415	−	1.16726i
$461$		−	11.0519i		−	0.514737i	−0.966313	−	0.257369i	$-0.917145\pi$
$461$		−	11.0519i		−	0.514737i	0.966313	−	0.257369i	$-0.0828555\pi$
$462$	3.19990	+	2.02497i	0.148873	+	0.0942102i
$463$	−22.2548			−1.03427			−0.517135	−	0.855904i	$-0.673001\pi$
$463$	−22.2548			−1.03427			−0.517135	+	0.855904i	$0.673001\pi$
$464$	27.3298	+	22.3742i	1.26875	+	1.03870i
$465$	5.84505			0.271058
$466$	−4.25459	−	2.69241i	−0.197090	−	0.124723i
$467$			21.4552i			0.992830i	0.868085	+	0.496415i	$0.165351\pi$
$467$			21.4552i			0.992830i	−0.868085	+	0.496415i	$0.834649\pi$
$468$	5.46753	−	2.58996i	0.252737	−	0.119721i
$469$		−	0.244852i		−	0.0113062i
$470$	−29.6601	+	46.8695i	−1.36812	+	2.16193i
$471$	−0.519169			−0.0239221
$472$	−11.2299	−	1.37483i	−0.516896	−	0.0632816i
$473$	−6.42588			−0.295462
$474$	4.73018	−	7.47472i	0.217264	−	0.343325i
$475$		−	32.8890i		−	1.50905i
$476$	−4.39006	−	9.26763i	−0.201218	−	0.424781i
$477$			2.78012i			0.127293i
$478$	32.1971	+	20.3751i	1.47266	+	0.931934i
$479$	8.09989			0.370093			0.185047	−	0.982730i	$-0.440756\pi$
$479$	8.09989			0.370093			0.185047	+	0.982730i	$0.440756\pi$
$480$	22.0247	−	7.31259i	1.00529	−	0.333772i
$481$	−4.30990			−0.196514
$482$	30.8498	+	19.5225i	1.40517	+	0.889224i
$483$		−	7.12742i		−	0.324309i
$484$	3.27927	+	6.92271i	0.149058	+	0.314669i
$485$		−	27.4642i		−	1.24709i
$486$	0.756243	−	1.19503i	0.0343039	−	0.0542077i
$487$	−16.4098			−0.743598			−0.371799	−	0.928313i	$-0.621259\pi$
$487$	−16.4098			−0.743598			−0.371799	+	0.928313i	$0.621259\pi$
$488$	14.5424	+	1.78038i	0.658306	+	0.0805938i
$489$	8.65464			0.391376
$490$	3.10245	−	4.90255i	0.140154	−	0.221474i
$491$		−	39.5971i		−	1.78699i	−0.449070	−	0.893497i	$-0.648245\pi$
$491$		−	39.5971i		−	1.78699i	0.449070	−	0.893497i	$-0.351755\pi$
$492$	9.26763	−	4.39006i	0.417817	−	0.197919i
$493$			45.2754i			2.03910i
$494$	−10.0499	−	6.35984i	−0.452168	−	0.286143i
$495$	−10.9850			−0.493740
$496$	3.61018	−	4.40978i	0.162102	−	0.198005i
$497$	−4.27787			−0.191889
$498$	−11.1799	−	7.07492i	−0.500984	−	0.317035i
$499$		−	1.14946i		−	0.0514568i	−0.999669	−	0.0257284i	$-0.991809\pi$
$499$		−	1.14946i		−	0.0514568i	0.999669	−	0.0257284i	$-0.00819050\pi$
$500$	−50.6451	+	23.9905i	−2.26492	+	1.07289i
$501$			25.1044i			1.12158i
$502$	−20.5353	+	32.4502i	−0.916534	+	1.44832i
$503$	9.00449			0.401490			0.200745	−	0.979643i	$-0.435664\pi$
$503$	9.00449			0.401490			0.200745	+	0.979643i	$0.435664\pi$
$504$	0.343707	−	2.80747i	0.0153099	−	0.125054i
$505$	5.98052			0.266130
$506$	−14.4328	+	22.8070i	−0.641617	+	1.01390i
$507$		−	3.84954i		−	0.170964i
$508$	−0.594709	−	1.25546i	−0.0263859	−	0.0557020i
$509$		−	36.5122i		−	1.61838i	−0.587550	−	0.809188i	$-0.699907\pi$
$509$		−	36.5122i		−	1.61838i	0.587550	−	0.809188i	$-0.300093\pi$
$510$	25.1374	+	15.9075i	1.11310	+	0.704398i
$511$	−4.15495			−0.183804
$512$	8.08656	−	21.1331i	0.357379	−	0.933960i
$513$	−2.78012			−0.122745
$514$	−37.5027	−	23.7326i	−1.65417	−	1.04680i
$515$		−	33.3753i		−	1.47069i
$516$	2.05469	+	4.33756i	0.0904528	+	0.190950i
$517$		−	25.5992i		−	1.12585i
$518$	−1.07747	+	1.70265i	−0.0473415	+	0.0748100i
$519$	−1.94750			−0.0854857
$520$	−4.26533	+	34.8400i	−0.187047	+	1.52784i
$521$	−18.0929			−0.792666			−0.396333	−	0.918107i	$-0.629718\pi$
$521$	−18.0929			−0.792666			−0.396333	+	0.918107i	$0.629718\pi$
$522$	−6.67767	+	10.5522i	−0.292274	+	0.461857i
$523$		−	14.7107i		−	0.643254i	−0.946866	−	0.321627i	$-0.895770\pi$
$523$		−	14.7107i		−	0.643254i	0.946866	−	0.321627i	$-0.104230\pi$
$524$	22.0599	−	10.4497i	0.963692	−	0.456499i
$525$			11.8301i			0.516306i
$526$	−13.1782	−	8.33949i	−0.574598	−	0.363619i
$527$	7.30540			0.318228
$528$	−6.78487	+	8.28761i	−0.295273	+	0.360672i
$529$	27.8001			1.20870
$530$	−13.6297	−	8.62517i	−0.592035	−	0.374654i
$531$		−	4.00000i		−	0.173585i
$532$	−5.02497	+	2.38032i	−0.217860	+	0.103200i
$533$			15.5103i			0.671825i
$534$	8.53221	−	13.4828i	0.369225	−	0.583456i
$535$	21.8346			0.943990
$536$	0.687414	+	0.0841574i	0.0296918	+	0.00363505i
$537$	22.6976			0.979476
$538$	−15.8826	+	25.0979i	−0.684746	+	1.08205i
$539$			2.67767i			0.115336i
$540$	3.51249	+	7.41503i	0.151153	+	0.319092i
$541$			37.7157i			1.62152i	0.585376	+	0.810762i	$0.300947\pi$
$541$			37.7157i			1.62152i	−0.585376	+	0.810762i	$0.699053\pi$
$542$	34.2318	+	21.6627i	1.47038	+	0.930492i
$543$	10.5353			0.452112
$544$	27.5275	−	9.13959i	1.18023	−	0.391857i
$545$	−55.6302			−2.38293
$546$	3.61493	+	2.28761i	0.154705	+	0.0979008i
$547$		−	23.1144i		−	0.988299i	−0.869377	−	0.494149i	$-0.835480\pi$
$547$		−	23.1144i		−	0.988299i	0.869377	−	0.494149i	$-0.164520\pi$
$548$	−12.9323	−	27.3007i	−0.552439	−	1.16623i
$549$			5.17992i			0.221074i
$550$	23.9555	−	37.8550i	1.02147	−	1.61414i
$551$	24.5486			1.04581
$552$	20.0100	+	2.44974i	0.851681	+	0.104268i
$553$	6.25484			0.265983
$554$	−2.24229	+	3.54332i	−0.0952659	+	0.150541i
$555$		−	5.84505i		−	0.248109i
$556$	13.7551	−	6.51579i	0.583348	−	0.276331i
$557$			11.1899i			0.474131i	0.971494	+	0.237066i	$0.0761857\pi$
$557$			11.1899i			0.474131i	−0.971494	+	0.237066i	$0.923814\pi$
$558$	1.70265	+	1.07747i	0.0720787	+	0.0456131i
$559$	−7.25933			−0.307037
$560$	12.6974	+	10.3951i	0.536563	+	0.439271i
$561$	−13.7296			−0.579662
$562$	31.5605	+	19.9722i	1.33130	+	0.842477i
$563$		−	2.81058i		−	0.118452i	−0.998245	−	0.0592260i	$-0.981137\pi$
$563$		−	2.81058i		−	0.118452i	0.998245	−	0.0592260i	$-0.0188632\pi$
$564$	−17.2798	+	8.18541i	−0.727611	+	0.344668i
$565$			17.0455i			0.717108i
$566$	−8.52273	+	13.4678i	−0.358237	+	0.566093i
$567$	1.00000			0.0419961
$568$	1.47034	−	12.0100i	0.0616939	−	0.503928i
$569$	−20.0699			−0.841374			−0.420687	−	0.907206i	$-0.638211\pi$
$569$	−20.0699			−0.841374			−0.420687	+	0.907206i	$0.638211\pi$
$570$	8.62517	−	13.6297i	0.361269	−	0.570884i
$571$		−	2.46584i		−	0.103192i	−0.998668	−	0.0515961i	$-0.983569\pi$
$571$		−	2.46584i		−	0.103192i	0.998668	−	0.0515961i	$-0.0164309\pi$
$572$	−6.93507	−	14.6403i	−0.289970	−	0.612141i
$573$			4.27787i			0.178711i
$574$	6.12742	+	3.87757i	0.255753	+	0.161847i
$575$	−84.3178			−3.51630
$576$	7.76373	+	1.92989i	0.323489	+	0.0804122i
$577$	4.84954			0.201889			0.100945	−	0.994892i	$-0.467814\pi$
$577$	4.84954			0.201889			0.100945	+	0.994892i	$0.467814\pi$
$578$	11.1023	+	7.02581i	0.461796	+	0.292235i
$579$		−	23.1400i		−	0.961664i
$580$	−31.0155	−	65.4752i	−1.28785	−	2.71871i
$581$		−	9.35535i		−	0.388125i
$582$	5.06274	−	8.00024i	0.209857	−	0.331621i
$583$	7.44425			0.308309
$584$	1.42809	−	11.6649i	0.0590946	−	0.482696i
$585$	−12.4098			−0.513081
$586$	−7.98757	+	12.6221i	−0.329963	+	0.521415i
$587$			19.0155i			0.784853i	0.919783	+	0.392426i	$0.128364\pi$
$587$			19.0155i			0.784853i	−0.919783	+	0.392426i	$0.871636\pi$
$588$	1.80747	−	0.856193i	0.0745386	−	0.0353088i
$589$		−	3.96104i		−	0.163212i
$590$	19.6102	+	12.4098i	0.807338	+	0.510903i
$591$	−19.4747			−0.801083
$592$	−4.40978	−	3.61018i	−0.181241	−	0.148378i
$593$	24.0379			0.987118			0.493559	−	0.869712i	$-0.335696\pi$
$593$	24.0379			0.987118			0.493559	+	0.869712i	$0.335696\pi$
$594$	−3.19990	−	2.02497i	−0.131293	−	0.0830856i
$595$			21.0350i			0.862349i
$596$	−9.43476	+	4.46923i	−0.386463	+	0.183067i
$597$			17.5602i			0.718693i
$598$	−16.3048	+	25.7651i	−0.666752	+	1.05361i
$599$	33.9631			1.38769			0.693847	−	0.720122i	$-0.255914\pi$
$599$	33.9631			1.38769			0.693847	+	0.720122i	$0.255914\pi$
$600$	−33.2125	−	4.06608i	−1.35589	−	0.165997i
$601$	10.0999			0.411983			0.205992	−	0.978554i	$-0.433958\pi$
$601$	10.0999			0.411983			0.205992	+	0.978554i	$0.433958\pi$
$602$	−1.81483	+	2.86783i	−0.0739670	+	0.116884i
$603$			0.244852i			0.00997115i
$604$	−4.76064	−	10.0499i	−0.193708	−	0.408926i
$605$		−	15.7126i		−	0.638809i
$606$	1.74211	+	1.10245i	0.0707683	+	0.0447838i
$607$	8.17105			0.331653			0.165826	−	0.986155i	$-0.446971\pi$
$607$	8.17105			0.331653			0.165826	+	0.986155i	$0.446971\pi$
$608$	−4.95555	−	14.9256i	−0.200974	−	0.605312i
$609$	−8.83006			−0.357812
$610$	−25.3948	−	16.0704i	−1.02821	−	0.650672i
$611$		−	28.9195i		−	1.16996i
$612$	4.39006	+	9.26763i	0.177458	+	0.374622i
$613$			23.0206i			0.929793i	0.885365	+	0.464896i	$0.153908\pi$
$613$			23.0206i			0.929793i	−0.885365	+	0.464896i	$0.846092\pi$
$614$	8.15239	−	12.8826i	0.329004	−	0.519898i
$615$	−21.0350			−0.848211
$616$	−7.51748	−	0.920336i	−0.302888	−	0.0370814i
$617$	31.1044			1.25222			0.626108	−	0.779737i	$-0.284647\pi$
$617$	31.1044			1.25222			0.626108	+	0.779737i	$0.284647\pi$
$618$	6.15239	−	9.72213i	0.247485	−	0.391081i
$619$			40.9195i			1.64469i	0.568988	+	0.822346i	$0.307335\pi$
$619$			40.9195i			1.64469i	−0.568988	+	0.822346i	$0.692665\pi$
$620$	−10.5647	+	5.00449i	−0.424290	+	0.200985i
$621$			7.12742i			0.286013i
$622$	11.4248	+	7.22986i	0.458092	+	0.289891i
$623$	11.2824			0.452018
$624$	−7.66488	+	9.36253i	−0.306841	+	0.374801i
$625$	55.8001			2.23200
$626$	9.20064	+	5.82238i	0.367732	+	0.232709i
$627$			7.44425i			0.297295i
$628$	0.938381	−	0.444509i	0.0374455	−	0.0177378i
$629$		−	7.30540i		−	0.291286i
$630$	−3.10245	+	4.90255i	−0.123604	+	0.195322i
$631$	−2.29380			−0.0913147			−0.0456573	−	0.998957i	$-0.514538\pi$
$631$	−2.29380			−0.0913147			−0.0456573	+	0.998957i	$0.514538\pi$
$632$	−2.14983	+	17.5602i	−0.0855157	+	0.698509i
$633$	−23.9600			−0.952326
$634$	8.15239	−	12.8826i	0.323773	−	0.511632i
$635$			2.84954i			0.113081i
$636$	−2.38032	−	5.02497i	−0.0943858	−	0.199253i
$637$			3.02497i			0.119854i
$638$	28.2553	+	17.8806i	1.11864	+	0.707901i
$639$	4.27787			0.169230
$640$	−33.5479	+	32.0747i	−1.32610	+	1.26786i
$641$	27.0654			1.06902			0.534510	−	0.845162i	$-0.320496\pi$
$641$	27.0654			1.06902			0.534510	+	0.845162i	$0.320496\pi$
$642$	6.36034	+	4.02497i	0.251023	+	0.158853i
$643$			31.9895i			1.26154i	0.775969	+	0.630771i	$0.217261\pi$
$643$			31.9895i			1.26154i	−0.775969	+	0.630771i	$0.782739\pi$
$644$	6.10245	+	12.8826i	0.240470	+	0.507644i
$645$		−	9.84505i		−	0.387649i
$646$	10.7801	−	17.0350i	0.424138	−	0.670231i
$647$	−12.5947			−0.495149			−0.247575	−	0.968869i	$-0.579634\pi$
$647$	−12.5947			−0.495149			−0.247575	+	0.968869i	$0.579634\pi$
$648$	−0.343707	+	2.80747i	−0.0135021	+	0.110288i
$649$	−10.7107			−0.420432
$650$	27.0626	−	42.7649i	1.06148	−	1.67738i
$651$			1.42477i			0.0558412i
$652$	−15.6430	+	7.41004i	−0.612626	+	0.290200i
$653$		−	21.8346i		−	0.854452i	−0.904145	−	0.427226i	$-0.859491\pi$
$653$		−	21.8346i		−	0.854452i	0.904145	−	0.427226i	$-0.140509\pi$
$654$	−16.2049	−	10.2548i	−0.633661	−	0.400996i
$655$	−50.0699			−1.95639
$656$	−12.9922	+	15.8698i	−0.507260	+	0.619610i
$657$	4.15495			0.162100
$658$	−11.4248	−	7.22986i	−0.445384	−	0.281849i
$659$			24.7865i			0.965547i	0.875745	+	0.482773i	$0.160371\pi$
$659$			24.7865i			0.965547i	−0.875745	+	0.482773i	$0.839629\pi$
$660$	19.8550	−	9.40529i	0.772856	−	0.366100i
$661$		−	3.09101i		−	0.120227i	−0.998192	−	0.0601133i	$-0.980854\pi$
$661$		−	3.09101i		−	0.120227i	0.998192	−	0.0601133i	$-0.0191462\pi$
$662$	−19.0652	+	30.1272i	−0.740989	+	1.17093i
$663$	−15.5103			−0.602370
$664$	26.2648	+	3.21550i	1.01927	+	0.124786i
$665$	11.4053			0.442278
$666$	1.07747	−	1.70265i	0.0417513	−	0.0659762i
$667$		−	62.9356i		−	2.43687i
$668$	−21.4942	−	45.3753i	−0.831635	−	1.75562i
$669$		−	2.74966i		−	0.106308i
$670$	−1.20040	−	0.759641i	−0.0463755	−	0.0293475i
$671$	13.8701			0.535451
$672$	1.78249	+	5.36868i	0.0687612	+	0.207101i
$673$	−27.6496			−1.06581			−0.532907	−	0.846174i	$-0.678901\pi$
$673$	−27.6496			−1.06581			−0.532907	+	0.846174i	$0.678901\pi$
$674$	−28.6449	−	18.1272i	−1.10336	−	0.698232i
$675$		−	11.8301i		−	0.455339i
$676$	3.29595	+	6.95792i	0.126767	+	0.267612i
$677$		−	5.84249i		−	0.224545i	−0.993677	−	0.112273i	$-0.964187\pi$
$677$		−	5.84249i		−	0.224545i	0.993677	−	0.112273i	$-0.0358130\pi$
$678$	−3.14215	+	4.96529i	−0.120674	+	0.190691i
$679$	6.69460			0.256915
$680$	−59.0549	−	7.22986i	−2.26465	−	0.277253i
$681$	8.30478			0.318240
$682$	2.88512	−	4.55913i	0.110477	−	0.174578i
$683$		−	15.5433i		−	0.594748i	−0.954761	−	0.297374i	$-0.903889\pi$
$683$		−	15.5433i		−	0.594748i	0.954761	−	0.297374i	$-0.0961109\pi$
$684$	5.02497	−	2.38032i	0.192135	−	0.0910138i
$685$			61.9649i			2.36756i
$686$	1.19503	+	0.756243i	0.0456265	+	0.0288735i
$687$	11.9245			0.454947
$688$	−7.42757	−	6.08077i	−0.283174	−	0.231827i
$689$	8.40978			0.320387
$690$	−34.9425	−	22.1124i	−1.33024	−	0.841806i
$691$		−	42.9304i		−	1.63315i	−0.577239	−	0.816575i	$-0.695870\pi$
$691$		−	42.9304i		−	1.63315i	0.577239	−	0.816575i	$-0.304130\pi$
$692$	3.52004	−	1.66743i	0.133812	−	0.0633863i
$693$		−	2.67767i		−	0.101716i
$694$	−5.28430	+	8.35036i	−0.200589	+	0.316975i
$695$	−31.2204			−1.18426
$696$	3.03496	−	24.7901i	0.115040	−	0.939666i
$697$	−26.2904			−0.995820
$698$	15.7979	−	24.9642i	0.597960	−	0.944908i
$699$			3.56024i			0.134661i
$700$	−10.1288	−	21.3824i	−0.382833	−	0.808180i
$701$		−	5.21476i		−	0.196959i	−0.995139	−	0.0984795i	$-0.968602\pi$
$701$		−	5.21476i		−	0.196959i	0.995139	−	0.0984795i	$-0.0313979\pi$
$702$	−3.61493	−	2.28761i	−0.136437	−	0.0863404i
$703$	−3.96104			−0.149393
$704$	5.16762	−	20.7887i	0.194762	−	0.783505i
$705$	39.2204			1.47712
$706$	4.04189	+	2.55781i	0.152119	+	0.0962643i
$707$			1.45779i			0.0548260i
$708$	3.42477	+	7.22986i	0.128711	+	0.271715i
$709$		−	41.6601i		−	1.56458i	−0.622915	−	0.782289i	$-0.714052\pi$
$709$		−	41.6601i		−	1.56458i	0.622915	−	0.782289i	$-0.285948\pi$
$710$	−13.2719	+	20.9725i	−0.498084	+	0.787083i
$711$	−6.25484			−0.234575
$712$	−3.87783	+	31.6749i	−0.145328	+	1.18707i
$713$	−10.1549			−0.380306
$714$	−3.87757	+	6.12742i	−0.145115	+	0.229313i
$715$			33.2294i			1.24271i
$716$	−41.0252	+	19.4336i	−1.53318	+	0.726266i
$717$		−	26.9425i		−	1.00619i
$718$	24.7224	+	15.6449i	0.922631	+	0.583862i
$719$	14.3547			0.535341			0.267670	−	0.963511i	$-0.413746\pi$
$719$	14.3547			0.535341			0.267670	+	0.963511i	$0.413746\pi$
$720$	−12.6974	−	10.3951i	−0.473204	−	0.387401i
$721$	8.13547			0.302981
$722$	13.4691	+	8.52356i	0.501268	+	0.317214i
$723$		−	25.8151i		−	0.960073i
$724$	−19.0421	+	9.02022i	−0.707695	+	0.335234i
$725$			104.460i			3.87955i
$726$	2.89646	−	4.57704i	0.107498	−	0.169870i
$727$	53.4647			1.98290			0.991448	−	0.130501i	$-0.0416587\pi$
$727$	53.4647			1.98290			0.991448	+	0.130501i	$0.0416587\pi$
$728$	−8.49251	−	1.03970i	−0.314753	−	0.0385340i
$729$	−1.00000			−0.0370370
$730$	−12.8905	+	20.3698i	−0.477099	+	0.753921i
$731$		−	12.3048i		−	0.455109i
$732$	−4.43501	−	9.36253i	−0.163923	−	0.346049i
$733$			49.1149i			1.81410i	0.421025	+	0.907049i	$0.361671\pi$
$733$			49.1149i			1.81410i	−0.421025	+	0.907049i	$0.638329\pi$
$734$	−11.4248	−	7.22986i	−0.421696	−	0.266859i
$735$	−4.10245			−0.151321
$736$	−38.2648	+	12.7046i	−1.41046	+	0.468297i
$737$	0.655634			0.0241506
$738$	−6.12742	−	3.87757i	−0.225553	−	0.142735i
$739$		−	7.75515i		−	0.285278i	−0.989775	−	0.142639i	$-0.954441\pi$
$739$		−	7.75515i		−	0.285278i	0.989775	−	0.142639i	$-0.0455587\pi$
$740$	5.00449	+	10.5647i	0.183969	+	0.388367i
$741$			8.40978i			0.308941i
$742$	2.10245	−	3.32233i	0.0771832	−	0.121966i
$743$	30.9886			1.13686			0.568430	−	0.822732i	$-0.307551\pi$
$743$	30.9886			1.13686			0.568430	+	0.822732i	$0.307551\pi$
$744$	−4.00000	−	0.489704i	−0.146647	−	0.0179534i
$745$	21.4143			0.784558
$746$	−1.47472	+	2.33038i	−0.0539932	+	0.0853211i
$747$			9.35535i			0.342294i
$748$	24.8157	−	11.7551i	0.907352	−	0.429811i
$749$			5.32233i			0.194474i
$750$	33.4847	+	21.1899i	1.22269	+	0.773746i
$751$	−34.9105			−1.27390			−0.636951	−	0.770905i	$-0.719804\pi$
$751$	−34.9105			−1.27390			−0.636951	+	0.770905i	$0.719804\pi$
$752$	24.2244	−	29.5897i	0.883372	−	1.07903i
$753$	27.1543			0.989559
$754$	31.9201	+	20.1998i	1.16246	+	0.735632i
$755$			22.8106i			0.830162i
$756$	−1.80747	+	0.856193i	−0.0657369	+	0.0311394i
$757$			9.25034i			0.336209i	0.985769	+	0.168105i	$0.0537647\pi$
$757$			9.25034i			0.336209i	−0.985769	+	0.168105i	$0.946235\pi$
$758$	−24.4795	+	38.6829i	−0.889134	+	1.40503i
$759$	19.0849			0.692738
$760$	−3.92008	+	32.0200i	−0.142196	+	1.16149i
$761$	−11.8381			−0.429131			−0.214566	−	0.976710i	$-0.568834\pi$
$761$	−11.8381			−0.429131			−0.214566	+	0.976710i	$0.568834\pi$
$762$	−0.525284	+	0.830064i	−0.0190290	+	0.0300700i
$763$		−	13.5602i		−	0.490914i
$764$	−3.66269	−	7.73211i	−0.132511	−	0.279738i
$765$		−	21.0350i		−	0.760520i
$766$	−21.3254	−	13.4952i	−0.770517	−	0.487601i
$767$	−12.0999			−0.436902
$768$	−15.6850	+	3.15904i	−0.565985	+	0.113992i
$769$	−20.0699			−0.723740			−0.361870	−	0.932229i	$-0.617861\pi$
$769$	−20.0699			−0.723740			−0.361870	+	0.932229i	$0.617861\pi$
$770$	13.1274	+	8.30734i	0.473079	+	0.299376i
$771$			31.3823i			1.13020i
$772$	19.8123	+	41.8247i	0.713059	+	1.50530i
$773$		−	18.8521i		−	0.678063i	−0.940775	−	0.339032i	$-0.889901\pi$
$773$		−	18.8521i		−	0.678063i	0.940775	−	0.339032i	$-0.110099\pi$
$774$	1.81483	−	2.86783i	0.0652328	−	0.103082i
$775$	16.8551			0.605455
$776$	−2.30098	+	18.7949i	−0.0826004	+	0.674696i
$777$	1.42477			0.0511134
$778$	−4.62773	+	7.31283i	−0.165912	+	0.262178i
$779$			14.2548i			0.510733i
$780$	22.4303	−	10.6252i	0.803132	−	0.380442i
$781$		−	11.4547i		−	0.409883i
$782$	−43.6727	−	27.6371i	−1.56173	−	0.988300i
$783$	8.83006			0.315561
$784$	−2.53387	+	3.09508i	−0.0904952	+	0.110539i
$785$	−2.12986			−0.0760181
$786$	−14.5852	−	9.22986i	−0.520237	−	0.329218i
$787$			25.9111i			0.923631i	0.886976	+	0.461815i	$0.152802\pi$
$787$			25.9111i			0.923631i	−0.886976	+	0.461815i	$0.847198\pi$
$788$	35.1999	−	16.6741i	1.25394	−	0.593991i
$789$			11.0275i			0.392590i
$790$	19.4053	−	30.6646i	0.690409	−	1.09100i
$791$	−4.15495			−0.147733
$792$	7.51748	+	0.920336i	0.267122	+	0.0327027i
$793$	15.6691			0.556427
$794$	−2.81290	+	4.44500i	−0.0998260	+	0.157747i
$795$			11.4053i			0.404504i
$796$	−15.0350	−	31.7395i	−0.532900	−	1.12498i
$797$			11.1318i			0.394309i	0.980372	+	0.197154i	$0.0631700\pi$
$797$			11.1318i			0.394309i	−0.980372	+	0.197154i	$0.936830\pi$
$798$	3.32233	+	2.10245i	0.117609	+	0.0744258i
$799$	49.0193			1.73418
$800$	63.5118	−	21.0870i	2.24548	−	0.745539i
$801$	−11.2824			−0.398643
$802$	−38.8693	−	24.5974i	−1.37252	−	0.868564i
$803$		−	11.1256i		−	0.392614i
$804$	−0.209641	−	0.442562i	−0.00739346	−	0.0156080i
$805$		−	29.2398i		−	1.03057i
$806$	3.25933	−	5.15046i	0.114805	−	0.181417i
$807$	21.0019			0.739303
$808$	−4.09271	−	0.501054i	−0.143981	−	0.0176270i
$809$	33.8151			1.18887			0.594437	−	0.804142i	$-0.297375\pi$
$809$	33.8151			1.18887			0.594437	+	0.804142i	$0.297375\pi$
$810$	3.10245	−	4.90255i	0.109009	−	0.172258i
$811$		−	32.5097i		−	1.14157i	−0.821100	−	0.570784i	$-0.806639\pi$
$811$		−	32.5097i		−	1.14157i	0.821100	−	0.570784i	$-0.193361\pi$
$812$	15.9600	−	7.56024i	0.560088	−	0.265312i
$813$		−	28.6451i		−	1.00463i
$814$	−4.55913	−	2.88512i	−0.159797	−	0.101124i
$815$	35.5052			1.24369
$816$	−15.8698	−	12.9922i	−0.555553	−	0.454818i
$817$	−6.67173			−0.233414
$818$	−1.35559	−	0.857850i	−0.0473971	−	0.0299940i
$819$		−	3.02497i		−	0.105701i
$820$	38.0200	−	18.0100i	1.32771	−	0.628936i
$821$			40.7501i			1.42219i	0.703096	+	0.711095i	$0.251800\pi$
$821$			40.7501i			1.42219i	−0.703096	+	0.711095i	$0.748200\pi$
$822$	−11.4226	+	18.0502i	−0.398408	+	0.629573i
$823$	−34.2159			−1.19269			−0.596345	−	0.802728i	$-0.703381\pi$
$823$	−34.2159			−1.19269			−0.596345	+	0.802728i	$0.703381\pi$
$824$	−2.79622	+	22.8400i	−0.0974109	+	0.795671i
$825$	−31.6771			−1.10285
$826$	−3.02497	+	4.78012i	−0.105252	+	0.166322i
$827$		−	37.2424i		−	1.29505i	−0.762046	−	0.647523i	$-0.775805\pi$
$827$		−	37.2424i		−	1.29505i	0.762046	−	0.647523i	$-0.224195\pi$
$828$	−6.10245	−	12.8826i	−0.212075	−	0.447700i
$829$		−	11.2959i		−	0.392323i	−0.980572	−	0.196162i	$-0.937152\pi$
$829$		−	11.2959i		−	0.392323i	0.980572	−	0.196162i	$-0.0628477\pi$
$830$	−45.8650	−	29.0245i	−1.59200	−	1.00745i
$831$	2.96504			0.102856
$832$	5.83787	−	23.4851i	0.202392	−	0.814198i
$833$	−5.12742			−0.177655
$834$	−9.09440	−	5.75515i	−0.314913	−	0.199284i
$835$			102.989i			3.56409i
$836$	−6.37372	−	13.4552i	−0.220440	−	0.465359i
$837$		−	1.42477i		−	0.0492473i
$838$	−1.17992	+	1.86453i	−0.0407597	+	0.0644092i
$839$	−38.8746			−1.34210			−0.671051	−	0.741412i	$-0.734157\pi$
$839$	−38.8746			−1.34210			−0.671051	+	0.741412i	$0.734157\pi$
$840$	1.41004	−	11.5175i	0.0486510	−	0.397391i
$841$	−48.9700			−1.68862
$842$	24.1124	−	38.1029i	0.830969	−	1.31311i
$843$		−	26.4098i		−	0.909601i
$844$	43.3070	−	20.5144i	1.49069	−	0.706135i
$845$		−	15.7925i		−	0.543280i
$846$	11.4248	+	7.22986i	0.392792	+	0.248568i
$847$	3.83006			0.131603
$848$	8.60469	+	7.04445i	0.295486	+	0.241908i
$849$	11.2698			0.386779
$850$	72.4877	+	45.8719i	2.48631	+	1.57339i
$851$			10.1549i			0.348107i
$852$	−7.73211	+	3.66269i	−0.264898	+	0.125482i
$853$		−	25.5507i		−	0.874841i	−0.899257	−	0.437420i	$-0.855892\pi$
$853$		−	25.5507i		−	0.874841i	0.899257	−	0.437420i	$-0.144108\pi$
$854$	3.91728	−	6.19016i	0.134047	−	0.211823i
$855$	−11.4053			−0.390053
$856$	−14.9423	−	1.82932i	−0.510716	−	0.0625249i
$857$	20.7038			0.707227			0.353613	−	0.935392i	$-0.384953\pi$
$857$	20.7038			0.707227			0.353613	+	0.935392i	$0.384953\pi$
$858$	−6.12548	+	9.67961i	−0.209121	+	0.330456i
$859$		−	9.66863i		−	0.329889i	−0.986303	−	0.164945i	$-0.947255\pi$
$859$		−	9.66863i		−	0.329889i	0.986303	−	0.164945i	$-0.0527445\pi$
$860$	8.42927	+	17.7946i	0.287436	+	0.606791i
$861$		−	5.12742i		−	0.174742i
$862$	10.6030	+	6.70983i	0.361140	+	0.228538i
$863$	31.5981			1.07561			0.537806	−	0.843068i	$-0.319253\pi$
$863$	31.5981			1.07561			0.537806	+	0.843068i	$0.319253\pi$
$864$	−1.78249	−	5.36868i	−0.0606417	−	0.182646i
$865$	−7.98950			−0.271651
$866$	13.8148	+	8.74235i	0.469447	+	0.297077i
$867$		−	9.29042i		−	0.315519i
$868$	−1.21988	−	2.57523i	−0.0414054	−	0.0874089i
$869$			16.7484i			0.568151i
$870$	−27.3948	+	43.2898i	−0.928771	+	1.46766i
$871$	0.740671			0.0250967
$872$	38.0699	+	4.66075i	1.28921	+	0.157833i
$873$	−6.69460			−0.226578
$874$	−14.9850	+	23.6796i	−0.506876	+	0.800975i
$875$			28.0200i			0.947248i
$876$	−7.50993	+	3.55744i	−0.253737	+	0.120195i
$877$		−	4.50967i		−	0.152281i	−0.997097	−	0.0761404i	$-0.975740\pi$
$877$		−	4.50967i		−	0.152281i	0.997097	−	0.0761404i	$-0.0242597\pi$
$878$		0			0
$879$	10.5622			0.356253
$880$	−27.8346	+	33.9995i	−0.938303	+	1.14612i
$881$	25.8471			0.870811			0.435405	−	0.900234i	$-0.356605\pi$
$881$	25.8471			0.870811			0.435405	+	0.900234i	$0.356605\pi$
$882$	−1.19503	−	0.756243i	−0.0402388	−	0.0254640i
$883$		−	58.5786i		−	1.97133i	−0.168725	−	0.985663i	$-0.553965\pi$
$883$		−	58.5786i		−	1.97133i	0.168725	−	0.985663i	$-0.446035\pi$
$884$	28.0343	−	13.2798i	0.942897	−	0.446648i
$885$		−	16.4098i		−	0.551609i
$886$	−4.44525	+	7.02447i	−0.149341	+	0.235992i
$887$	−20.2249			−0.679084			−0.339542	−	0.940591i	$-0.610272\pi$
$887$	−20.2249			−0.679084			−0.339542	+	0.940591i	$0.610272\pi$
$888$	−0.489704	+	4.00000i	−0.0164334	+	0.134231i
$889$	−0.694597			−0.0232960
$890$	35.0029	−	55.3123i	1.17330	−	1.85407i
$891$			2.67767i			0.0897054i
$892$	2.35424	+	4.96991i	0.0788257	+	0.166405i
$893$		−	26.5786i		−	0.889419i
$894$	6.23791	+	3.94750i	0.208627	+	0.132024i
$895$	93.1158			3.11252
$896$	−7.81842	−	8.17755i	−0.261195	−	0.273193i
$897$	21.5602			0.719875
$898$	−14.1552	−	8.95774i	−0.472365	−	0.298924i
$899$			12.5808i			0.419594i
$900$	10.1288	+	21.3824i	0.337627	+	0.712748i
$901$			14.2548i			0.474897i
$902$	−10.3829	+	16.4072i	−0.345712	+	0.546301i
$903$	2.39980			0.0798604
$904$	1.42809	−	11.6649i	0.0474974	−	0.387968i
$905$	43.2204			1.43669
$906$	−4.20489	+	6.64465i	−0.139698	+	0.220754i
$907$		−	45.3103i		−	1.50450i	−0.658876	−	0.752251i	$-0.728968\pi$
$907$		−	45.3103i		−	1.50450i	0.658876	−	0.752251i	$-0.271032\pi$
$908$	−15.0106	+	7.11050i	−0.498145	+	0.235970i
$909$		−	1.45779i		−	0.0483520i
$910$	14.8301	+	9.38481i	0.491612	+	0.311103i
$911$	−12.5488			−0.415761			−0.207880	−	0.978154i	$-0.566656\pi$
$911$	−12.5488			−0.415761			−0.207880	+	0.978154i	$0.566656\pi$
$912$	−7.04445	+	8.60469i	−0.233265	+	0.284930i
$913$	25.0506			0.829053
$914$	−33.7103	−	21.3327i	−1.11504	−	0.705622i
$915$			21.2503i			0.702515i
$916$	−21.5531	+	10.2096i	−0.712133	+	0.337336i
$917$		−	12.2049i		−	0.403041i
$918$	3.87757	−	6.12742i	0.127979	−	0.202235i
$919$	−43.9400			−1.44945			−0.724724	−	0.689039i	$-0.758033\pi$
$919$	−43.9400			−1.44945			−0.724724	+	0.689039i	$0.758033\pi$
$920$	82.0899	+	10.0499i	2.70642	+	0.331337i
$921$	−10.7801			−0.355217
$922$	8.35791	−	13.2073i	0.275253	−	0.434960i
$923$		−	12.9404i		−	0.425940i
$924$	2.29261	+	4.83980i	0.0754212	+	0.159218i
$925$		−	16.8551i		−	0.554194i
$926$	−26.5952	−	16.8301i	−0.873972	−	0.553070i
$927$	−8.13547			−0.267204
$928$	15.7395	+	47.4058i	0.516676	+	1.55617i
$929$	−53.7370			−1.76305			−0.881527	−	0.472134i	$-0.843484\pi$
$929$	−53.7370			−1.76305			−0.881527	+	0.472134i	$0.843484\pi$
$930$	6.98501	+	4.42028i	0.229048	+	0.144947i
$931$			2.78012i			0.0911147i
$932$	−3.04825	−	6.43501i	−0.0998488	−	0.210786i
$933$		−	9.56024i		−	0.312988i
$934$	−16.2254	+	25.6396i	−0.530910	+	0.838955i
$935$	−56.3247			−1.84202
$936$	8.49251	+	1.03970i	0.277586	+	0.0339838i
$937$	−12.7107			−0.415240			−0.207620	−	0.978210i	$-0.566572\pi$
$937$	−12.7107			−0.415240			−0.207620	+	0.978210i	$0.566572\pi$
$938$	0.185168	−	0.292606i	0.00604594	−	0.00955392i
$939$		−	7.69909i		−	0.251250i
$940$	−70.8895	+	33.5802i	−2.31216	+	1.09527i
$941$		−	4.02253i		−	0.131131i	−0.997848	−	0.0655653i	$-0.979115\pi$
$941$		−	4.02253i		−	0.131131i	0.997848	−	0.0655653i	$-0.0208851\pi$
$942$	−0.620423	−	0.392618i	−0.0202145	−	0.0127922i
$943$	36.5453			1.19008
$944$	−12.3803	−	10.1355i	−0.402945	−	0.329881i
$945$	4.10245			0.133453
$946$	−7.67912	−	4.85953i	−0.249670	−	0.157997i
$947$			43.1413i			1.40190i	0.713209	+	0.700951i	$0.247241\pi$
$947$			43.1413i			1.40190i	−0.713209	+	0.700951i	$0.752759\pi$
$948$	11.3054	−	5.35535i	0.367182	−	0.173934i
$949$		−	12.5686i		−	0.407994i
$950$	24.8721	−	39.3033i	0.806957	−	1.27517i
$951$	−10.7801			−0.349569
$952$	1.76233	−	14.3951i	0.0571174	−	0.466546i
$953$	−10.2387			−0.331665			−0.165833	−	0.986154i	$-0.553031\pi$
$953$	−10.2387			−0.331665			−0.165833	+	0.986154i	$0.553031\pi$
$954$	−2.10245	+	3.32233i	−0.0680692	+	0.107564i
$955$			17.5497i			0.567896i
$956$	23.0680	+	48.6976i	0.746072	+	1.57499i
$957$		−	23.6440i		−	0.764303i
$958$	9.67961	+	6.12548i	0.312734	+	0.197905i
$959$	−15.1044			−0.487746
$960$	31.8503	+	7.91728i	1.02796	+	0.255529i
$961$	−28.9700			−0.934517
$962$	−5.15046	−	3.25933i	−0.166057	−	0.105085i
$963$		−	5.32233i		−	0.171510i
$964$	22.1027	+	46.6599i	0.711880	+	1.50281i
$965$		−	94.9304i		−	3.05592i
$966$	5.39006	−	8.51748i	0.173422	−	0.274045i
$967$	46.9356			1.50935			0.754673	−	0.656101i	$-0.227796\pi$
$967$	46.9356			1.50935			0.754673	+	0.656101i	$0.227796\pi$
$968$	−1.31642	+	10.7528i	−0.0423113	+	0.345607i
$969$	−14.2548			−0.457931
$970$	20.7696	−	32.8206i	0.666872	−	1.05380i
$971$		−	17.5602i		−	0.563535i	−0.959483	−	0.281767i	$-0.909079\pi$
$971$		−	17.5602i		−	0.563535i	0.959483	−	0.281767i	$-0.0909207\pi$
$972$	1.80747	−	0.856193i	0.0579745	−	0.0274624i
$973$		−	7.61018i		−	0.243971i
$974$	−19.6102	−	12.4098i	−0.628351	−	0.397635i
$975$	−35.7856			−1.14606
$976$	16.0323	+	13.1252i	0.513180	+	0.420128i
$977$	−41.5303			−1.32867			−0.664335	−	0.747435i	$-0.731285\pi$
$977$	−41.5303			−1.32867			−0.664335	+	0.747435i	$0.731285\pi$
$978$	10.3425	+	6.54501i	0.330718	+	0.209286i
$979$			30.2105i			0.965532i
$980$	7.41503	−	3.51249i	0.236865	−	0.112202i
$981$			13.5602i			0.432945i
$982$	29.9451	−	47.3198i	0.955585	−	1.51003i
$983$	−50.4797			−1.61005			−0.805026	−	0.593239i	$-0.797849\pi$
$983$	−50.4797			−1.61005			−0.805026	+	0.593239i	$0.797849\pi$
$984$	14.3951	+	1.76233i	0.458897	+	0.0561810i
$985$	−79.8940			−2.54563
$986$	−34.2392	+	54.1055i	−1.09040	+	1.72307i
$987$			9.56024i			0.304306i
$988$	−7.20040	−	15.2004i	−0.229075	−	0.483589i
$989$			17.1044i			0.543888i
$990$	−13.1274	−	8.30734i	−0.417217	−	0.264025i
$991$	1.46035			0.0463896			0.0231948	−	0.999731i	$-0.492616\pi$
$991$	1.46035			0.0463896			0.0231948	+	0.999731i	$0.492616\pi$
$992$	7.64915	−	2.53965i	0.242861	−	0.0806339i
$993$	25.2104			0.800027
$994$	−5.11219	−	3.23511i	−0.162149	−	0.102612i
$995$			72.0399i			2.28382i
$996$	−8.00998	−	16.9095i	−0.253806	−	0.535797i
$997$		−	21.8796i		−	0.692935i	−0.938062	−	0.346467i	$-0.887381\pi$
$997$		−	21.8796i		−	0.692935i	0.938062	−	0.346467i	$-0.112619\pi$
$998$	0.869269	−	1.37364i	0.0275162	−	0.0434817i
$999$	−1.42477			−0.0450778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.c.b.85.8	yes	8
3.2	odd	2		504.2.c.f.253.1		8
4.3	odd	2		672.2.c.b.337.5		8
7.6	odd	2		1176.2.c.c.589.8		8
8.3	odd	2		672.2.c.b.337.4		8
8.5	even	2	inner	168.2.c.b.85.7	✓	8
12.11	even	2		2016.2.c.e.1009.8		8
16.3	odd	4		5376.2.a.bl.1.1		4
16.5	even	4		5376.2.a.bm.1.4		4
16.11	odd	4		5376.2.a.bq.1.4		4
16.13	even	4		5376.2.a.bp.1.1		4
24.5	odd	2		504.2.c.f.253.2		8
24.11	even	2		2016.2.c.e.1009.1		8
28.27	even	2		4704.2.c.c.2353.4		8
56.13	odd	2		1176.2.c.c.589.7		8
56.27	even	2		4704.2.c.c.2353.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.c.b.85.7	✓	8	8.5	even	2	inner
168.2.c.b.85.8	yes	8	1.1	even	1	trivial
504.2.c.f.253.1		8	3.2	odd	2
504.2.c.f.253.2		8	24.5	odd	2
672.2.c.b.337.4		8	8.3	odd	2
672.2.c.b.337.5		8	4.3	odd	2
1176.2.c.c.589.7		8	56.13	odd	2
1176.2.c.c.589.8		8	7.6	odd	2
2016.2.c.e.1009.1		8	24.11	even	2
2016.2.c.e.1009.8		8	12.11	even	2
4704.2.c.c.2353.4		8	28.27	even	2
4704.2.c.c.2353.5		8	56.27	even	2
5376.2.a.bl.1.1		4	16.3	odd	4
5376.2.a.bm.1.4		4	16.5	even	4
5376.2.a.bp.1.1		4	16.13	even	4
5376.2.a.bq.1.4		4	16.11	odd	4

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19503 + 0.756243i) q^{2} -1.00000i q^{3} +(0.856193 + 1.80747i) q^{4} -4.10245i q^{5} +(0.756243 - 1.19503i) q^{6} +1.00000 q^{7} +(-0.343707 + 2.80747i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.19503 + 0.756243i) q^{2} -1.00000i q^{3} +(0.856193 + 1.80747i) q^{4} -4.10245i q^{5} +(0.756243 - 1.19503i) q^{6} +1.00000 q^{7} +(-0.343707 + 2.80747i) q^{8} -1.00000 q^{9} +(3.10245 - 4.90255i) q^{10} +2.67767i q^{11} +(1.80747 - 0.856193i) q^{12} +3.02497i q^{13} +(1.19503 + 0.756243i) q^{14} -4.10245 q^{15} +(-2.53387 + 3.09508i) q^{16} -5.12742 q^{17} +(-1.19503 - 0.756243i) q^{18} +2.78012i q^{19} +(7.41503 - 3.51249i) q^{20} -1.00000i q^{21} +(-2.02497 + 3.19990i) q^{22} +7.12742 q^{23} +(2.80747 + 0.343707i) q^{24} -11.8301 q^{25} +(-2.28761 + 3.61493i) q^{26} +1.00000i q^{27} +(0.856193 + 1.80747i) q^{28} -8.83006i q^{29} +(-4.90255 - 3.10245i) q^{30} -1.42477 q^{31} +(-5.36868 + 1.78249i) q^{32} +2.67767 q^{33} +(-6.12742 - 3.87757i) q^{34} -4.10245i q^{35} +(-0.856193 - 1.80747i) q^{36} +1.42477i q^{37} +(-2.10245 + 3.32233i) q^{38} +3.02497 q^{39} +(11.5175 + 1.41004i) q^{40} +5.12742 q^{41} +(0.756243 - 1.19503i) q^{42} +2.39980i q^{43} +(-4.83980 + 2.29261i) q^{44} +4.10245i q^{45} +(8.51748 + 5.39006i) q^{46} -9.56024 q^{47} +(3.09508 + 2.53387i) q^{48} +1.00000 q^{49} +(-14.1373 - 8.94640i) q^{50} +5.12742i q^{51} +(-5.46753 + 2.58996i) q^{52} -2.78012i q^{53} +(-0.756243 + 1.19503i) q^{54} +10.9850 q^{55} +(-0.343707 + 2.80747i) q^{56} +2.78012 q^{57} +(6.67767 - 10.5522i) q^{58} +4.00000i q^{59} +(-3.51249 - 7.41503i) q^{60} -5.17992i q^{61} +(-1.70265 - 1.07747i) q^{62} -1.00000 q^{63} +(-7.76373 - 1.92989i) q^{64} +12.4098 q^{65} +(3.19990 + 2.02497i) q^{66} -0.244852i q^{67} +(-4.39006 - 9.26763i) q^{68} -7.12742i q^{69} +(3.10245 - 4.90255i) q^{70} -4.27787 q^{71} +(0.343707 - 2.80747i) q^{72} -4.15495 q^{73} +(-1.07747 + 1.70265i) q^{74} +11.8301i q^{75} +(-5.02497 + 2.38032i) q^{76} +2.67767i q^{77} +(3.61493 + 2.28761i) q^{78} +6.25484 q^{79} +(12.6974 + 10.3951i) q^{80} +1.00000 q^{81} +(6.12742 + 3.87757i) q^{82} -9.35535i q^{83} +(1.80747 - 0.856193i) q^{84} +21.0350i q^{85} +(-1.81483 + 2.86783i) q^{86} -8.83006 q^{87} +(-7.51748 - 0.920336i) q^{88} +11.2824 q^{89} +(-3.10245 + 4.90255i) q^{90} +3.02497i q^{91} +(6.10245 + 12.8826i) q^{92} +1.42477i q^{93} +(-11.4248 - 7.22986i) q^{94} +11.4053 q^{95} +(1.78249 + 5.36868i) q^{96} +6.69460 q^{97} +(1.19503 + 0.756243i) q^{98} -2.67767i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 8 * q^9	\( 8 q + 2 q^{4} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 8 q^{9} - 4 q^{10} - 4 q^{12} - 4 q^{15} - 6 q^{16} + 4 q^{17} + 24 q^{20} + 12 q^{23} + 4 q^{24} - 24 q^{25} - 28 q^{26} + 2 q^{28} - 12 q^{30} + 8 q^{31} - 30 q^{32} + 12 q^{33} - 4 q^{34} - 2 q^{36} + 12 q^{38} + 8 q^{39} + 28 q^{40} - 4 q^{41} + 2 q^{42} + 16 q^{44} + 4 q^{46} + 16 q^{48} + 8 q^{49} - 20 q^{50} - 12 q^{52} - 2 q^{54} - 8 q^{55} - 6 q^{56} - 16 q^{57} + 44 q^{58} - 20 q^{60} + 12 q^{62} - 8 q^{63} + 26 q^{64} - 16 q^{65} + 24 q^{66} - 16 q^{68} - 4 q^{70} - 28 q^{71} + 6 q^{72} - 8 q^{73} + 4 q^{74} - 24 q^{76} - 8 q^{78} - 40 q^{79} - 4 q^{80} + 8 q^{81} + 4 q^{82} - 4 q^{84} + 24 q^{86} + 4 q^{88} + 20 q^{89} + 4 q^{90} + 20 q^{92} - 72 q^{94} + 40 q^{95} + 12 q^{96} + 40 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 8 * q^7 - 6 * q^8 - 8 * q^9 - 4 * q^10 - 4 * q^12 - 4 * q^15 - 6 * q^16 + 4 * q^17 + 24 * q^20 + 12 * q^23 + 4 * q^24 - 24 * q^25 - 28 * q^26 + 2 * q^28 - 12 * q^30 + 8 * q^31 - 30 * q^32 + 12 * q^33 - 4 * q^34 - 2 * q^36 + 12 * q^38 + 8 * q^39 + 28 * q^40 - 4 * q^41 + 2 * q^42 + 16 * q^44 + 4 * q^46 + 16 * q^48 + 8 * q^49 - 20 * q^50 - 12 * q^52 - 2 * q^54 - 8 * q^55 - 6 * q^56 - 16 * q^57 + 44 * q^58 - 20 * q^60 + 12 * q^62 - 8 * q^63 + 26 * q^64 - 16 * q^65 + 24 * q^66 - 16 * q^68 - 4 * q^70 - 28 * q^71 + 6 * q^72 - 8 * q^73 + 4 * q^74 - 24 * q^76 - 8 * q^78 - 40 * q^79 - 4 * q^80 + 8 * q^81 + 4 * q^82 - 4 * q^84 + 24 * q^86 + 4 * q^88 + 20 * q^89 + 4 * q^90 + 20 * q^92 - 72 * q^94 + 40 * q^95 + 12 * q^96 + 40 * q^97

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