LMFDB - Embedded newform 168.2.c.b.85.2

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			85.2
Root			$1.40961 + 0.114062i$ of defining polynomial
Character	$\chi$	$=$	168.85
Dual form			168.2.c.b.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40961 + 0.114062i) q^{2} -1.00000i q^{3} +(1.97398 - 0.321565i) q^{4} -1.12875i q^{5} +(0.114062 + 1.40961i) q^{6} +1.00000 q^{7} +(-2.74586 + 0.678435i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.40961 + 0.114062i) q^{2} -1.00000i q^{3} +(1.97398 - 0.321565i) q^{4} -1.12875i q^{5} +(0.114062 + 1.40961i) q^{6} +1.00000 q^{7} +(-2.74586 + 0.678435i) q^{8} -1.00000 q^{9} +(0.128747 + 1.59109i) q^{10} -4.76717i q^{11} +(-0.321565 - 1.97398i) q^{12} +0.456247i q^{13} +(-1.40961 + 0.114062i) q^{14} -1.12875 q^{15} +(3.79319 - 1.26952i) q^{16} +0.415006 q^{17} +(1.40961 - 0.114062i) q^{18} -7.63843i q^{19} +(-0.362965 - 2.22812i) q^{20} -1.00000i q^{21} +(0.543753 + 6.71984i) q^{22} +1.58499 q^{23} +(0.678435 + 2.74586i) q^{24} +3.72593 q^{25} +(-0.0520404 - 0.643129i) q^{26} +1.00000i q^{27} +(1.97398 - 0.321565i) q^{28} +6.72593i q^{29} +(1.59109 - 0.128747i) q^{30} -5.89592 q^{31} +(-5.20210 + 2.22219i) q^{32} -4.76717 q^{33} +(-0.584994 + 0.0473363i) q^{34} -1.12875i q^{35} +(-1.97398 + 0.321565i) q^{36} +5.89592i q^{37} +(0.871253 + 10.7672i) q^{38} +0.456247 q^{39} +(0.765782 + 3.09938i) q^{40} -0.415006 q^{41} +(0.114062 + 1.40961i) q^{42} +9.43967i q^{43} +(-1.53295 - 9.41030i) q^{44} +1.12875i q^{45} +(-2.23422 + 0.180787i) q^{46} +11.2769 q^{47} +(-1.26952 - 3.79319i) q^{48} +1.00000 q^{49} +(-5.25209 + 0.424987i) q^{50} -0.415006i q^{51} +(0.146713 + 0.900623i) q^{52} +7.63843i q^{53} +(-0.114062 - 1.40961i) q^{54} -5.38093 q^{55} +(-2.74586 + 0.678435i) q^{56} -7.63843 q^{57} +(-0.767172 - 9.48091i) q^{58} +4.00000i q^{59} +(-2.22812 + 0.362965i) q^{60} -1.80125i q^{61} +(8.31092 - 0.672500i) q^{62} -1.00000 q^{63} +(7.07945 - 3.72577i) q^{64} +0.514988 q^{65} +(6.71984 - 0.543753i) q^{66} -8.09467i q^{67} +(0.819213 - 0.133451i) q^{68} -1.58499i q^{69} +(0.128747 + 1.59109i) q^{70} +10.2068 q^{71} +(2.74586 - 0.678435i) q^{72} -3.34500 q^{73} +(-0.672500 - 8.31092i) q^{74} -3.72593i q^{75} +(-2.45625 - 15.0781i) q^{76} -4.76717i q^{77} +(-0.643129 + 0.0520404i) q^{78} -4.83001 q^{79} +(-1.43297 - 4.28155i) q^{80} +1.00000 q^{81} +(0.584994 - 0.0473363i) q^{82} +5.53434i q^{83} +(-0.321565 - 1.97398i) q^{84} -0.468436i q^{85} +(-1.07671 - 13.3062i) q^{86} +6.72593 q^{87} +(3.23422 + 13.0900i) q^{88} +4.92999 q^{89} +(-0.128747 - 1.59109i) q^{90} +0.456247i q^{91} +(3.12875 - 0.509678i) q^{92} +5.89592i q^{93} +(-15.8959 + 1.28626i) q^{94} -8.62185 q^{95} +(2.22219 + 5.20210i) q^{96} +16.4468 q^{97} +(-1.40961 + 0.114062i) q^{98} +4.76717i 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 $

$2$	−1.40961	+	0.114062i	−0.996742	+	0.0806539i
$2$	−1.40961	+	0.114062i	−0.996742	+	0.0806539i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.97398	−	0.321565i	0.986990	−	0.160782i
$5$		−	1.12875i		−	0.504791i	−0.967624	−	0.252395i	$-0.918782\pi$
$5$		−	1.12875i		−	0.504791i	0.967624	−	0.252395i	$-0.0812184\pi$
$6$	0.114062	+	1.40961i	0.0465656	+	0.575469i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.74586	+	0.678435i	−0.970807	+	0.239863i
$9$	−1.00000			−0.333333
$10$	0.128747	+	1.59109i	0.0407134	+	0.503146i
$11$		−	4.76717i		−	1.43736i	−0.695343	−	0.718678i	$-0.744747\pi$
$11$		−	4.76717i		−	1.43736i	0.695343	−	0.718678i	$-0.255253\pi$
$12$	−0.321565	−	1.97398i	−0.0928277	−	0.569839i
$13$			0.456247i			0.126540i	0.997996	+	0.0632701i	$0.0201530\pi$
$13$			0.456247i			0.126540i	−0.997996	+	0.0632701i	$0.979847\pi$
$14$	−1.40961	+	0.114062i	−0.376733	+	0.0304843i
$15$	−1.12875			−0.291441
$16$	3.79319	−	1.26952i	0.948298	−	0.317381i
$17$	0.415006			0.100654			0.0503268	−	0.998733i	$-0.483974\pi$
$17$	0.415006			0.100654			0.0503268	+	0.998733i	$0.483974\pi$
$18$	1.40961	−	0.114062i	0.332247	−	0.0268846i
$19$		−	7.63843i		−	1.75237i	−0.481970	−	0.876187i	$-0.660079\pi$
$19$		−	7.63843i		−	1.75237i	0.481970	−	0.876187i	$-0.339921\pi$
$20$	−0.362965	−	2.22812i	−0.0811615	−	0.498224i
$21$		−	1.00000i		−	0.218218i
$22$	0.543753	+	6.71984i	0.115928	+	1.43267i
$23$	1.58499			0.330494			0.165247	−	0.986252i	$-0.447158\pi$
$23$	1.58499			0.330494			0.165247	+	0.986252i	$0.447158\pi$
$24$	0.678435	+	2.74586i	0.138485	+	0.560496i
$25$	3.72593			0.745186
$26$	−0.0520404	−	0.643129i	−0.0102060	−	0.126128i
$27$			1.00000i			0.192450i
$28$	1.97398	−	0.321565i	0.373047	−	0.0607700i
$29$			6.72593i			1.24897i	0.781035	+	0.624487i	$0.214692\pi$
$29$			6.72593i			1.24897i	−0.781035	+	0.624487i	$0.785308\pi$
$30$	1.59109	−	0.128747i	0.290492	−	0.0235059i
$31$	−5.89592			−1.05894			−0.529469	−	0.848329i	$-0.677609\pi$
$31$	−5.89592			−1.05894			−0.529469	+	0.848329i	$0.677609\pi$
$32$	−5.20210	+	2.22219i	−0.919611	+	0.392831i
$33$	−4.76717			−0.829858
$34$	−0.584994	+	0.0473363i	−0.100326	+	0.00811811i
$35$		−	1.12875i		−	0.190793i
$36$	−1.97398	+	0.321565i	−0.328997	+	0.0535941i
$37$			5.89592i			0.969283i	0.874713	+	0.484642i	$0.161050\pi$
$37$			5.89592i			0.969283i	−0.874713	+	0.484642i	$0.838950\pi$
$38$	0.871253	+	10.7672i	0.141336	+	1.74667i
$39$	0.456247			0.0730581
$40$	0.765782	+	3.09938i	0.121081	+	0.490054i
$41$	−0.415006			−0.0648130			−0.0324065	−	0.999475i	$-0.510317\pi$
$41$	−0.415006			−0.0648130			−0.0324065	+	0.999475i	$0.510317\pi$
$42$	0.114062	+	1.40961i	0.0176001	+	0.217507i
$43$			9.43967i			1.43954i	0.694214	+	0.719768i	$0.255752\pi$
$43$			9.43967i			1.43954i	−0.694214	+	0.719768i	$0.744248\pi$
$44$	−1.53295	−	9.41030i	−0.231102	−	1.41866i
$45$			1.12875i			0.168264i
$46$	−2.23422	+	0.180787i	−0.329417	+	0.0266557i
$47$	11.2769			1.64490			0.822449	−	0.568839i	$-0.192607\pi$
$47$	11.2769			1.64490			0.822449	+	0.568839i	$0.192607\pi$
$48$	−1.26952	−	3.79319i	−0.183240	−	0.547500i
$49$	1.00000			0.142857
$50$	−5.25209	+	0.424987i	−0.742758	+	0.0601022i
$51$		−	0.415006i		−	0.0581124i
$52$	0.146713	+	0.900623i	0.0203454	+	0.124894i
$53$			7.63843i			1.04922i	0.851343	+	0.524609i	$0.175789\pi$
$53$			7.63843i			1.04922i	−0.851343	+	0.524609i	$0.824211\pi$
$54$	−0.114062	−	1.40961i	−0.0155219	−	0.191823i
$55$	−5.38093			−0.725565
$56$	−2.74586	+	0.678435i	−0.366930	+	0.0906597i
$57$	−7.63843			−1.01173
$58$	−0.767172	−	9.48091i	−0.100735	−	1.24490i
$59$			4.00000i			0.520756i	0.965507	+	0.260378i	$0.0838471\pi$
$59$			4.00000i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$60$	−2.22812	+	0.362965i	−0.287650	+	0.0468586i
$61$		−	1.80125i		−	0.230626i	−0.993329	−	0.115313i	$-0.963213\pi$
$61$		−	1.80125i		−	0.230626i	0.993329	−	0.115313i	$-0.0367871\pi$
$62$	8.31092	−	0.672500i	1.05549	−	0.0854075i
$63$	−1.00000			−0.125988
$64$	7.07945	−	3.72577i	0.884931	−	0.465721i
$65$	0.514988			0.0638764
$66$	6.71984	−	0.543753i	0.827155	−	0.0669313i
$67$		−	8.09467i		−	0.988922i	−0.869200	−	0.494461i	$-0.835366\pi$
$67$		−	8.09467i		−	0.988922i	0.869200	−	0.494461i	$-0.164634\pi$
$68$	0.819213	−	0.133451i	0.0993441	−	0.0161833i
$69$		−	1.58499i		−	0.190811i
$70$	0.128747	+	1.59109i	0.0153882	+	0.190171i
$71$	10.2068			1.21133			0.605665	−	0.795720i	$-0.292907\pi$
$71$	10.2068			1.21133			0.605665	+	0.795720i	$0.292907\pi$
$72$	2.74586	−	0.678435i	0.323602	−	0.0799544i
$73$	−3.34500			−0.391503			−0.195751	−	0.980654i	$-0.562715\pi$
$73$	−3.34500			−0.391503			−0.195751	+	0.980654i	$0.562715\pi$
$74$	−0.672500	−	8.31092i	−0.0781765	−	0.966125i
$75$		−	3.72593i		−	0.430233i
$76$	−2.45625	−	15.0781i	−0.281751	−	1.72958i
$77$		−	4.76717i		−	0.543270i
$78$	−0.643129	+	0.0520404i	−0.0728201	+	0.00589242i
$79$	−4.83001			−0.543419			−0.271709	−	0.962379i	$-0.587589\pi$
$79$	−4.83001			−0.543419			−0.271709	+	0.962379i	$0.587589\pi$
$80$	−1.43297	−	4.28155i	−0.160211	−	0.478692i
$81$	1.00000			0.111111
$82$	0.584994	−	0.0473363i	0.0646018	−	0.00522742i
$83$			5.53434i			0.607473i	0.952756	+	0.303737i	$0.0982343\pi$
$83$			5.53434i			0.607473i	−0.952756	+	0.303737i	$0.901766\pi$
$84$	−0.321565	−	1.97398i	−0.0350856	−	0.215379i
$85$		−	0.468436i		−	0.0508090i
$86$	−1.07671	−	13.3062i	−0.116104	−	1.43485i
$87$	6.72593			0.721095
$88$	3.23422	+	13.0900i	0.344769	+	1.39540i
$89$	4.92999			0.522578			0.261289	−	0.965261i	$-0.415852\pi$
$89$	4.92999			0.522578			0.261289	+	0.965261i	$0.415852\pi$
$90$	−0.128747	−	1.59109i	−0.0135711	−	0.167715i
$91$			0.456247i			0.0478277i
$92$	3.12875	−	0.509678i	0.326194	−	0.0531376i
$93$			5.89592i			0.611378i
$94$	−15.8959	+	1.28626i	−1.63954	+	0.132667i
$95$	−8.62185			−0.884583
$96$	2.22219	+	5.20210i	0.226801	+	0.530937i
$97$	16.4468			1.66992			0.834962	−	0.550308i	$-0.185490\pi$
$97$	16.4468			1.66992			0.834962	+	0.550308i	$0.185490\pi$
$98$	−1.40961	+	0.114062i	−0.142392	+	0.0115220i
$99$			4.76717i			0.479119i
$100$	7.35491	−	1.19813i	0.735491	−	0.119813i
$101$		−	16.4056i		−	1.63242i	−0.577757	−	0.816209i	$-0.696072\pi$
$101$		−	16.4056i		−	1.63242i	0.577757	−	0.816209i	$-0.303928\pi$
$102$	0.0473363	+	0.584994i	0.00468699	+	0.0579231i
$103$	−17.1728			−1.69208			−0.846042	−	0.533117i	$-0.821021\pi$
$103$	−17.1728			−1.69208			−0.846042	+	0.533117i	$0.821021\pi$
$104$	−0.309534	−	1.25279i	−0.0303523	−	0.122846i
$105$	−1.12875			−0.110154
$106$	−0.871253	−	10.7672i	−0.0846236	−	1.04580i
$107$			12.7672i			1.23425i	0.786865	+	0.617125i	$0.211703\pi$
$107$			12.7672i			1.23425i	−0.786865	+	0.617125i	$0.788297\pi$
$108$	0.321565	+	1.97398i	0.0309426	+	0.189946i
$109$			7.27685i			0.696996i	0.937310	+	0.348498i	$0.113308\pi$
$109$			7.27685i			0.696996i	−0.937310	+	0.348498i	$0.886692\pi$
$110$	7.58499	−	0.613759i	0.723201	−	0.0585196i
$111$	5.89592			0.559616
$112$	3.79319	−	1.26952i	0.358423	−	0.119959i
$113$	−3.34500			−0.314671			−0.157336	−	0.987545i	$-0.550290\pi$
$113$	−3.34500			−0.314671			−0.157336	+	0.987545i	$0.550290\pi$
$114$	10.7672	−	0.871253i	1.00844	−	0.0816003i
$115$		−	1.78906i		−	0.166830i
$116$	2.16282	+	13.2769i	0.200813	+	1.23272i
$117$		−	0.456247i		−	0.0421801i
$118$	−0.456247	−	5.63843i	−0.0420010	−	0.519059i
$119$	0.415006			0.0380435
$120$	3.09938	−	0.765782i	0.282933	−	0.0699060i
$121$	−11.7259			−1.06599
$122$	0.205454	+	2.53905i	0.0186009	+	0.229875i
$123$			0.415006i			0.0374198i
$124$	−11.6384	+	1.89592i	−1.04516	+	0.170259i
$125$		−	9.84937i		−	0.880954i
$126$	1.40961	−	0.114062i	0.125578	−	0.0101614i
$127$	−10.4468			−0.927007			−0.463504	−	0.886095i	$-0.653408\pi$
$127$	−10.4468			−0.927007			−0.463504	+	0.886095i	$0.653408\pi$
$128$	−9.55427	+	6.05937i	−0.844486	+	0.535577i
$129$	9.43967			0.831117
$130$	−0.725930	+	0.0587405i	−0.0636683	+	0.00515188i
$131$		−	6.25749i		−	0.546720i	−0.961912	−	0.273360i	$-0.911865\pi$
$131$		−	6.25749i		−	0.546720i	0.961912	−	0.273360i	$-0.0881350\pi$
$132$	−9.41030	+	1.53295i	−0.819062	+	0.133427i
$133$		−	7.63843i		−	0.662335i
$134$	0.923293	+	11.4103i	0.0797604	+	0.985700i
$135$	1.12875			0.0971471
$136$	−1.13955	+	0.281554i	−0.0977152	+	0.0241431i
$137$	−12.9618			−1.10740			−0.553702	−	0.832715i	$-0.686785\pi$
$137$	−12.9618			−1.10740			−0.553702	+	0.832715i	$0.686785\pi$
$138$	0.180787	+	2.23422i	0.0153896	+	0.190189i
$139$			18.3644i			1.55764i	0.627245	+	0.778822i	$0.284183\pi$
$139$			18.3644i			1.55764i	−0.627245	+	0.778822i	$0.715817\pi$
$140$	−0.362965	−	2.22812i	−0.0306762	−	0.188311i
$141$		−	11.2769i		−	0.949682i
$142$	−14.3876	+	1.16421i	−1.20738	+	0.0976985i
$143$	2.17501			0.181883
$144$	−3.79319	+	1.26952i	−0.316099	+	0.105794i
$145$	7.59187			0.630471
$146$	4.71513	−	0.381537i	0.390227	−	0.0315762i
$147$		−	1.00000i		−	0.0824786i
$148$	1.89592	+	11.6384i	0.155844	+	0.956673i
$149$			15.6384i			1.28115i	0.767896	+	0.640575i	$0.221304\pi$
$149$			15.6384i			1.28115i	−0.767896	+	0.640575i	$0.778696\pi$
$150$	0.424987	+	5.25209i	0.0347000	+	0.428832i
$151$	15.2769			1.24321			0.621606	−	0.783330i	$-0.286480\pi$
$151$	15.2769			1.24321			0.621606	+	0.783330i	$0.286480\pi$
$152$	5.18218	+	20.9740i	0.420330	+	1.70122i
$153$	−0.415006			−0.0335512
$154$	0.543753	+	6.71984i	0.0438168	+	0.541500i
$155$			6.65500i			0.534543i
$156$	0.900623	−	0.146713i	0.0721076	−	0.0117464i
$157$		−	21.7824i		−	1.73843i	−0.494437	−	0.869214i	$-0.664626\pi$
$157$		−	21.7824i		−	1.73843i	0.494437	−	0.869214i	$-0.335374\pi$
$158$	6.80841	−	0.550920i	0.541648	−	0.0438288i
$159$	7.63843			0.605767
$160$	2.50829	+	5.87186i	0.198298	+	0.464211i
$161$	1.58499			0.124915
$162$	−1.40961	+	0.114062i	−0.110749	+	0.00896155i
$163$			4.60966i			0.361056i	0.983570	+	0.180528i	$0.0577807\pi$
$163$			4.60966i			0.361056i	−0.983570	+	0.180528i	$0.942219\pi$
$164$	−0.819213	+	0.133451i	−0.0639698	+	0.0104208i
$165$			5.38093i			0.418905i
$166$	−0.631258	−	7.80125i	−0.0489951	−	0.605494i
$167$	−22.9618			−1.77684			−0.888420	−	0.459032i	$-0.848196\pi$
$167$	−22.9618			−1.77684			−0.888420	+	0.459032i	$0.848196\pi$
$168$	0.678435	+	2.74586i	0.0523424	+	0.211847i
$169$	12.7918			0.983988
$170$	0.0534307	+	0.660311i	0.00409795	+	0.0506435i
$171$			7.63843i			0.584125i
$172$	3.03546	+	18.6337i	0.231452	+	1.42081i
$173$			0.216252i			0.0164413i	0.999966	+	0.00822067i	$0.00261675\pi$
$173$			0.216252i			0.0164413i	−0.999966	+	0.00822067i	$0.997383\pi$
$174$	−9.48091	+	0.767172i	−0.718746	+	0.0581592i
$175$	3.72593			0.281654
$176$	−6.05204	−	18.0828i	−0.456190	−	1.36304i
$177$	4.00000			0.300658
$178$	−6.94935	+	0.562324i	−0.520876	+	0.0421480i
$179$		−	22.6165i		−	1.69044i	−0.534419	−	0.845220i	$-0.679470\pi$
$179$		−	22.6165i		−	1.69044i	0.534419	−	0.845220i	$-0.320530\pi$
$180$	0.362965	+	2.22812i	0.0270538	+	0.166075i
$181$		−	7.73310i		−	0.574797i	−0.957811	−	0.287398i	$-0.907210\pi$
$181$		−	7.73310i		−	0.574797i	0.957811	−	0.287398i	$-0.0927903\pi$
$182$	−0.0520404	−	0.643129i	−0.00385749	−	0.0476719i
$183$	−1.80125			−0.133152
$184$	−4.35217	+	1.07532i	−0.320846	+	0.0792734i
$185$	6.65500			0.489285
$186$	−0.672500	−	8.31092i	−0.0493101	−	0.609387i
$187$		−	1.97840i		−	0.144675i
$188$	22.2603	−	3.62624i	1.62350	−	0.264470i
$189$			1.00000i			0.0727393i
$190$	12.1534	−	0.983424i	0.881701	−	0.0713451i
$191$	10.2068			0.738541			0.369271	−	0.929322i	$-0.379608\pi$
$191$	10.2068			0.738541			0.369271	+	0.929322i	$0.379608\pi$
$192$	−3.72577	−	7.07945i	−0.268884	−	0.510915i
$193$	5.96407			0.429303			0.214651	−	0.976691i	$-0.431138\pi$
$193$	5.96407			0.429303			0.214651	+	0.976691i	$0.431138\pi$
$194$	−23.1836	+	1.87596i	−1.66448	+	0.134686i
$195$		−	0.514988i		−	0.0368791i
$196$	1.97398	−	0.321565i	0.140999	−	0.0229689i
$197$		−	18.8084i		−	1.34004i	−0.742341	−	0.670022i	$-0.766285\pi$
$197$		−	18.8084i		−	1.34004i	0.742341	−	0.670022i	$-0.233715\pi$
$198$	−0.543753	−	6.71984i	−0.0386428	−	0.477558i
$199$	3.27685			0.232290			0.116145	−	0.993232i	$-0.462946\pi$
$199$	3.27685			0.232290			0.116145	+	0.993232i	$0.462946\pi$
$200$	−10.2309	+	2.52780i	−0.723432	+	0.178743i
$201$	−8.09467			−0.570954
$202$	1.87125	+	23.1254i	0.131661	+	1.62710i
$203$			6.72593i			0.472068i
$204$	−0.133451	−	0.819213i	−0.00934345	−	0.0573564i
$205$			0.468436i			0.0327170i
$206$	24.2068	−	1.95876i	1.68657	−	0.136473i
$207$	−1.58499			−0.110165
$208$	0.579217	+	1.73063i	0.0401615	+	0.119998i
$209$	−36.4137			−2.51879
$210$	1.59109	−	0.128747i	0.109796	−	0.00888439i
$211$		−	10.1628i		−	0.699637i	−0.936817	−	0.349819i	$-0.886243\pi$
$211$		−	10.1628i		−	0.699637i	0.936817	−	0.349819i	$-0.113757\pi$
$212$	2.45625	+	15.0781i	0.168696	+	1.03557i
$213$		−	10.2068i		−	0.699361i
$214$	−1.45625	−	17.9967i	−0.0995470	−	1.23023i
$215$	10.6550			0.726665
$216$	−0.678435	−	2.74586i	−0.0461617	−	0.186832i
$217$	−5.89592			−0.400241
$218$	−0.830011	−	10.2575i	−0.0562154	−	0.694725i
$219$			3.34500i			0.226034i
$220$	−10.6218	+	1.73032i	−0.716125	+	0.116658i
$221$			0.189345i			0.0127367i
$222$	−8.31092	+	0.672500i	−0.557793	+	0.0451352i
$223$	21.9668			1.47101			0.735504	−	0.677520i	$-0.236945\pi$
$223$	21.9668			1.47101			0.735504	+	0.677520i	$0.236945\pi$
$224$	−5.20210	+	2.22219i	−0.347580	+	0.148476i
$225$	−3.72593			−0.248395
$226$	4.71513	−	0.381537i	0.313646	−	0.0253795i
$227$		−	7.91752i		−	0.525504i	−0.964863	−	0.262752i	$-0.915370\pi$
$227$		−	7.91752i		−	0.525504i	0.964863	−	0.262752i	$-0.0846301\pi$
$228$	−15.0781	+	2.45625i	−0.998571	+	0.162669i
$229$			13.1606i			0.869676i	0.900509	+	0.434838i	$0.143194\pi$
$229$			13.1606i			0.869676i	−0.900509	+	0.434838i	$0.856806\pi$
$230$	0.204063	+	2.52187i	0.0134555	+	0.166287i
$231$	−4.76717			−0.313657
$232$	−4.56311	−	18.4684i	−0.299583	−	1.21251i
$233$	17.2769			1.13184			0.565922	−	0.824459i	$-0.308520\pi$
$233$	17.2769			1.13184			0.565922	+	0.824459i	$0.308520\pi$
$234$	0.0520404	+	0.643129i	0.00340199	+	0.0420427i
$235$		−	12.7287i		−	0.830330i
$236$	1.28626	+	7.89592i	0.0837283	+	0.513981i
$237$			4.83001i			0.313743i
$238$	−0.584994	+	0.0473363i	−0.0379196	+	0.00306836i
$239$	−10.5219			−0.680603			−0.340301	−	0.940316i	$-0.610529\pi$
$239$	−10.5219			−0.680603			−0.340301	+	0.940316i	$0.610529\pi$
$240$	−4.28155	+	1.43297i	−0.276373	+	0.0924979i
$241$	−6.10686			−0.393378			−0.196689	−	0.980466i	$-0.563019\pi$
$241$	−6.10686			−0.393378			−0.196689	+	0.980466i	$0.563019\pi$
$242$	16.5289	−	1.33748i	1.06252	−	0.0859766i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.579217	−	3.55562i	−0.0370806	−	0.227626i
$245$		−	1.12875i		−	0.0721130i
$246$	−0.0473363	−	0.584994i	−0.00301805	−	0.0372979i
$247$	3.48501			0.221746
$248$	16.1893	−	4.00000i	1.02802	−	0.254000i
$249$	5.53434			0.350725
$250$	1.12344	+	13.8837i	0.0710524	+	0.878084i
$251$			19.8743i			1.25446i	0.778836	+	0.627228i	$0.215811\pi$
$251$			19.8743i			1.25446i	−0.778836	+	0.627228i	$0.784189\pi$
$252$	−1.97398	+	0.321565i	−0.124349	+	0.0202567i
$253$		−	7.55594i		−	0.475038i
$254$	14.7259	−	1.19159i	0.923987	−	0.0747668i
$255$	−0.468436			−0.0293346
$256$	12.7766	−	9.63110i	0.798539	−	0.601944i
$257$	−14.7550			−0.920391			−0.460195	−	0.887818i	$-0.652221\pi$
$257$	−14.7550			−0.920391			−0.460195	+	0.887818i	$0.652221\pi$
$258$	−13.3062	+	1.07671i	−0.828409	+	0.0670328i
$259$			5.89592i			0.366355i
$260$	1.01658	−	0.165602i	0.0630454	−	0.0102702i
$261$		−	6.72593i		−	0.416325i
$262$	0.713741	+	8.82060i	0.0440951	+	0.544939i
$263$	−15.7600			−0.971804			−0.485902	−	0.874013i	$-0.661509\pi$
$263$	−15.7600			−0.971804			−0.485902	+	0.874013i	$0.661509\pi$
$264$	13.0900	−	3.23422i	0.805632	−	0.199052i
$265$	8.62185			0.529636
$266$	0.871253	+	10.7672i	0.0534199	+	0.660178i
$267$		−	4.92999i		−	0.301711i
$268$	−2.60296	−	15.9787i	−0.159001	−	0.976056i
$269$			21.8331i			1.33119i	0.746315	+	0.665593i	$0.231821\pi$
$269$			21.8331i			1.33119i	−0.746315	+	0.665593i	$0.768179\pi$
$270$	−1.59109	+	0.128747i	−0.0968306	+	0.00783529i
$271$	−18.8328			−1.14401			−0.572005	−	0.820250i	$-0.693834\pi$
$271$	−18.8328			−1.14401			−0.572005	+	0.820250i	$0.693834\pi$
$272$	1.57420	−	0.526860i	0.0954496	−	0.0319456i
$273$	0.456247			0.0276134
$274$	18.2711	−	1.47845i	1.10380	−	0.0893164i
$275$		−	17.7622i		−	1.07110i
$276$	−0.509678	−	3.12875i	−0.0306790	−	0.188328i
$277$			24.4684i			1.47017i	0.677977	+	0.735083i	$0.262857\pi$
$277$			24.4684i			1.47017i	−0.677977	+	0.735083i	$0.737143\pi$
$278$	−2.09467	−	25.8865i	−0.125630	−	1.55257i
$279$	5.89592			0.352979
$280$	0.765782	+	3.09938i	0.0457642	+	0.185223i
$281$	14.5150			0.865892			0.432946	−	0.901420i	$-0.357474\pi$
$281$	14.5150			0.865892			0.432946	+	0.901420i	$0.357474\pi$
$282$	1.28626	+	15.8959i	0.0765956	+	0.946588i
$283$			16.5509i			0.983850i	0.870638	+	0.491925i	$0.163707\pi$
$283$			16.5509i			0.983850i	−0.870638	+	0.491925i	$0.836293\pi$
$284$	20.1481	−	3.28216i	1.19557	−	0.194760i
$285$			8.62185i			0.510714i
$286$	−3.06591	+	0.248086i	−0.181291	+	0.0146696i
$287$	−0.415006			−0.0244970
$288$	5.20210	−	2.22219i	0.306537	−	0.130944i
$289$	−16.8278			−0.989869
$290$	−10.7016	+	0.865943i	−0.628417	+	0.0508499i
$291$		−	16.4468i		−	0.964131i
$292$	−6.60296	+	1.07563i	−0.386409	+	0.0629467i
$293$		−	9.44377i		−	0.551711i	−0.961199	−	0.275855i	$-0.911039\pi$
$293$		−	9.44377i		−	0.551711i	0.961199	−	0.275855i	$-0.0889611\pi$
$294$	0.114062	+	1.40961i	0.00665222	+	0.0822099i
$295$	4.51499			0.262873
$296$	−4.00000	−	16.1893i	−0.232495	−	0.940987i
$297$	4.76717			0.276619
$298$	−1.78375	−	22.0440i	−0.103330	−	1.27698i
$299$			0.723150i			0.0418208i
$300$	−1.19813	−	7.35491i	−0.0691739	−	0.424636i
$301$			9.43967i			0.544094i
$302$	−21.5343	+	1.74251i	−1.23916	+	0.100270i
$303$	−16.4056			−0.942477
$304$	−9.69717	−	28.9740i	−0.556171	−	1.66177i
$305$	−2.03315			−0.116418
$306$	0.584994	−	0.0473363i	0.0334419	−	0.00270604i
$307$		−	0.361575i		−	0.0206362i	−0.999947	−	0.0103181i	$-0.996716\pi$
$307$		−	0.361575i		−	0.0206362i	0.999947	−	0.0103181i	$-0.00328441\pi$
$308$	−1.53295	−	9.41030i	−0.0873482	−	0.536202i
$309$			17.1728i			0.976925i
$310$	−0.759082	−	9.38093i	−0.0431130	−	0.532801i
$311$	−11.2769			−0.639452			−0.319726	−	0.947510i	$-0.603591\pi$
$311$	−11.2769			−0.639452			−0.319726	+	0.947510i	$0.603591\pi$
$312$	−1.25279	+	0.309534i	−0.0709253	+	0.0175239i
$313$	25.5837			1.44607			0.723037	−	0.690809i	$-0.242745\pi$
$313$	25.5837			1.44607			0.723037	+	0.690809i	$0.242745\pi$
$314$	2.48454	+	30.7047i	0.140211	+	1.73276i
$315$			1.12875i			0.0635977i
$316$	−9.53434	+	1.55316i	−0.536349	+	0.0873721i
$317$		−	0.361575i		−	0.0203081i	−0.999948	−	0.0101540i	$-0.996768\pi$
$317$		−	0.361575i		−	0.0203081i	0.999948	−	0.0101540i	$-0.00323218\pi$
$318$	−10.7672	+	0.871253i	−0.603793	+	0.0488574i
$319$	32.0637			1.79522
$320$	−4.20545	−	7.99091i	−0.235092	−	0.446705i
$321$	12.7672			0.712594
$322$	−2.23422	+	0.180787i	−0.124508	+	0.0100749i
$323$		−	3.16999i		−	0.176383i
$324$	1.97398	−	0.321565i	0.109666	−	0.0178647i
$325$			1.69995i			0.0942960i
$326$	−0.525786	−	6.49781i	−0.0291206	−	0.359880i
$327$	7.27685			0.402411
$328$	1.13955	−	0.281554i	0.0629209	−	0.0155462i
$329$	11.2769			0.621713
$330$	−0.613759	−	7.58499i	−0.0337863	−	0.417540i
$331$		−	7.80403i		−	0.428948i	−0.976730	−	0.214474i	$-0.931196\pi$
$331$		−	7.80403i		−	0.428948i	0.976730	−	0.214474i	$-0.0688037\pi$
$332$	1.77965	+	10.9247i	0.0976710	+	0.599570i
$333$		−	5.89592i		−	0.323094i
$334$	32.3671	−	2.61907i	1.77105	−	0.143309i
$335$	−9.13684			−0.499199
$336$	−1.26952	−	3.79319i	−0.0692582	−	0.206936i
$337$	8.76186			0.477289			0.238645	−	0.971107i	$-0.423297\pi$
$337$	8.76186			0.477289			0.238645	+	0.971107i	$0.423297\pi$
$338$	−18.0315	+	1.45906i	−0.980782	+	0.0793625i
$339$			3.34500i			0.181675i
$340$	−0.150633	−	0.924684i	−0.00816920	−	0.0501480i
$341$			28.1069i			1.52207i
$342$	−0.871253	−	10.7672i	−0.0471120	−	0.582222i
$343$	1.00000			0.0539949
$344$	−6.40421	−	25.9200i	−0.345292	−	1.39751i
$345$	−1.78906			−0.0963196
$346$	−0.0246661	−	0.304830i	−0.00132606	−	0.0163878i
$347$		−	2.07717i		−	0.111509i	−0.998445	−	0.0557543i	$-0.982244\pi$
$347$		−	2.07717i		−	0.111509i	0.998445	−	0.0557543i	$-0.0177563\pi$
$348$	13.2769	−	2.16282i	0.711714	−	0.115939i
$349$			18.7381i			1.00303i	0.865149	+	0.501514i	$0.167224\pi$
$349$			18.7381i			1.00303i	−0.865149	+	0.501514i	$0.832776\pi$
$350$	−5.25209	+	0.424987i	−0.280736	+	0.0227165i
$351$	−0.456247			−0.0243527
$352$	10.5936	+	24.7993i	0.564638	+	1.32181i
$353$	−13.2450			−0.704961			−0.352481	−	0.935819i	$-0.614662\pi$
$353$	−13.2450			−0.704961			−0.352481	+	0.935819i	$0.614662\pi$
$354$	−5.63843	+	0.456247i	−0.299679	+	0.0242493i
$355$		−	11.5209i		−	0.611468i
$356$	9.73171	−	1.58531i	0.515779	−	0.0840213i
$357$		−	0.415006i		−	0.0219644i
$358$	2.57968	+	31.8804i	0.136341	+	1.68493i
$359$	−5.69186			−0.300405			−0.150202	−	0.988655i	$-0.547993\pi$
$359$	−5.69186			−0.300405			−0.150202	+	0.988655i	$0.547993\pi$
$360$	−0.765782	−	3.09938i	−0.0403602	−	0.163351i
$361$	−39.3455			−2.07082
$362$	0.882052	+	10.9006i	0.0463596	+	0.572924i
$363$			11.7259i			0.615452i
$364$	0.146713	+	0.900623i	0.00768985	+	0.0472055i
$365$			3.77566i			0.197627i
$366$	2.53905	−	0.205454i	0.132718	−	0.0107392i
$367$	11.2769			0.588647			0.294323	−	0.955706i	$-0.404906\pi$
$367$	11.2769			0.588647			0.294323	+	0.955706i	$0.404906\pi$
$368$	6.01219	−	2.01219i	0.313407	−	0.104893i
$369$	0.415006			0.0216043
$370$	−9.38093	+	0.759082i	−0.487691	+	0.0394628i
$371$			7.63843i			0.396567i
$372$	1.89592	+	11.6384i	0.0982988	+	0.603424i
$373$			7.08751i			0.366977i	0.983022	+	0.183489i	$0.0587390\pi$
$373$			7.08751i			0.366977i	−0.983022	+	0.183489i	$0.941261\pi$
$374$	0.225660	+	2.78877i	0.0116686	+	0.144204i
$375$	−9.84937			−0.508619
$376$	−30.9646	+	7.65061i	−1.59688	+	0.394550i
$377$	−3.06869			−0.158046
$378$	−0.114062	−	1.40961i	−0.00586671	−	0.0725023i
$379$			6.67781i			0.343016i	0.985183	+	0.171508i	$0.0548639\pi$
$379$			6.67781i			0.343016i	−0.985183	+	0.171508i	$0.945136\pi$
$380$	−17.0194	+	2.77248i	−0.873075	+	0.142225i
$381$			10.4468i			0.535208i
$382$	−14.3876	+	1.16421i	−0.736135	+	0.0595662i
$383$	−18.6550			−0.953226			−0.476613	−	0.879113i	$-0.658136\pi$
$383$	−18.6550			−0.953226			−0.476613	+	0.879113i	$0.658136\pi$
$384$	6.05937	+	9.55427i	0.309216	+	0.487564i
$385$	−5.38093			−0.274238
$386$	−8.40699	+	0.680273i	−0.427904	+	0.0346250i
$387$		−	9.43967i		−	0.479845i
$388$	32.4657	−	5.28872i	1.64820	−	0.268494i
$389$			20.3428i			1.03142i	0.856764	+	0.515709i	$0.172472\pi$
$389$			20.3428i			1.03142i	−0.856764	+	0.515709i	$0.827528\pi$
$390$	0.0587405	+	0.725930i	0.00297444	+	0.0367589i
$391$	0.657782			0.0332654
$392$	−2.74586	+	0.678435i	−0.138687	+	0.0342662i
$393$	−6.25749			−0.315649
$394$	2.14532	+	26.5125i	0.108080	+	1.33568i
$395$			5.45186i			0.274313i
$396$	1.53295	+	9.41030i	0.0770338	+	0.472885i
$397$			10.9031i			0.547210i	0.961842	+	0.273605i	$0.0882161\pi$
$397$			10.9031i			0.547210i	−0.961842	+	0.273605i	$0.911784\pi$
$398$	−4.61907	+	0.373764i	−0.231533	+	0.0187351i
$399$	−7.63843			−0.382400
$400$	14.1332	−	4.73016i	0.706659	−	0.236508i
$401$	29.1756			1.45696			0.728479	−	0.685068i	$-0.240228\pi$
$401$	29.1756			1.45696			0.728479	+	0.685068i	$0.240228\pi$
$402$	11.4103	−	0.923293i	0.569094	−	0.0460497i
$403$		−	2.69000i		−	0.133998i
$404$	−5.27546	−	32.3843i	−0.262464	−	1.61118i
$405$		−	1.12875i		−	0.0560879i
$406$	−0.767172	−	9.48091i	−0.0380741	−	0.470530i
$407$	28.1069			1.39321
$408$	0.281554	+	1.13955i	0.0139390	+	0.0564159i
$409$	−31.7237			−1.56864			−0.784318	−	0.620359i	$-0.786987\pi$
$409$	−31.7237			−1.56864			−0.784318	+	0.620359i	$0.786987\pi$
$410$	−0.0534307	−	0.660311i	−0.00263875	−	0.0326104i
$411$			12.9618i			0.639360i
$412$	−33.8987	+	5.52216i	−1.67007	+	0.272057i
$413$			4.00000i			0.196827i
$414$	2.23422	−	0.180787i	0.109806	−	0.00888522i
$415$	6.24687			0.306647
$416$	−1.01387	−	2.37345i	−0.0497089	−	0.116368i
$417$	18.3644			0.899306
$418$	51.3290	−	4.15341i	2.51058	−	0.203150i
$419$		−	19.2769i		−	0.941736i	−0.882204	−	0.470868i	$-0.843941\pi$
$419$		−	19.2769i		−	0.941736i	0.882204	−	0.470868i	$-0.156059\pi$
$420$	−2.22812	+	0.362965i	−0.108721	+	0.0177109i
$421$		−	19.3234i		−	0.941765i	−0.882196	−	0.470882i	$-0.843936\pi$
$421$		−	19.3234i		−	0.941765i	0.882196	−	0.470882i	$-0.156064\pi$
$422$	1.15919	+	14.3256i	0.0564285	+	0.697358i
$423$	−11.2769			−0.548299
$424$	−5.18218	−	20.9740i	−0.251669	−	1.01859i
$425$	1.54628			0.0750057
$426$	1.16421	+	14.3876i	0.0564062	+	0.697083i
$427$		−	1.80125i		−	0.0871684i
$428$	4.10547	+	25.2021i	0.198445	+	1.21819i
$429$		−	2.17501i		−	0.105010i
$430$	−15.0194	+	1.21533i	−0.724298	+	0.0586084i
$431$	14.4150			0.694346			0.347173	−	0.937801i	$-0.387142\pi$
$431$	14.4150			0.694346			0.347173	+	0.937801i	$0.387142\pi$
$432$	1.26952	+	3.79319i	0.0610800	+	0.182500i
$433$	−9.27685			−0.445817			−0.222908	−	0.974839i	$-0.571555\pi$
$433$	−9.27685			−0.445817			−0.222908	+	0.974839i	$0.571555\pi$
$434$	8.31092	−	0.672500i	0.398937	−	0.0322810i
$435$		−	7.59187i		−	0.364002i
$436$	2.33998	+	14.3644i	0.112065	+	0.687928i
$437$		−	12.1069i		−	0.579150i
$438$	−0.381537	−	4.71513i	−0.0182305	−	0.225298i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	14.7753	−	3.65061i	0.704383	−	0.174036i
$441$	−1.00000			−0.0476190
$442$	−0.0215971	−	0.266902i	−0.00102727	−	0.0126952i
$443$		−	15.6465i		−	0.743388i	−0.928355	−	0.371694i	$-0.878777\pi$
$443$		−	15.6465i		−	0.743388i	0.928355	−	0.371694i	$-0.121223\pi$
$444$	11.6384	−	1.89592i	0.552335	−	0.0899763i
$445$		−	5.56472i		−	0.263793i
$446$	−30.9646	+	2.50558i	−1.46622	+	0.118643i
$447$	15.6384			0.739672
$448$	7.07945	−	3.72577i	0.334473	−	0.176026i
$449$	−12.6550			−0.597226			−0.298613	−	0.954374i	$-0.596524\pi$
$449$	−12.6550			−0.597226			−0.298613	+	0.954374i	$0.596524\pi$
$450$	5.25209	−	0.424987i	0.247586	−	0.0200341i
$451$			1.97840i			0.0931594i
$452$	−6.60296	+	1.07563i	−0.310577	+	0.0505935i
$453$		−	15.2769i		−	0.717769i
$454$	0.903087	+	11.1606i	0.0423840	+	0.523792i
$455$	0.514988			0.0241430
$456$	20.9740	−	5.18218i	0.982198	−	0.242678i
$457$	−23.9237			−1.11910			−0.559551	−	0.828796i	$-0.689026\pi$
$457$	−23.9237			−1.11910			−0.559551	+	0.828796i	$0.689026\pi$
$458$	−1.50112	−	18.5512i	−0.0701427	−	0.866842i
$459$			0.415006i			0.0193708i
$460$	−0.575298	−	3.53156i	−0.0268234	−	0.164660i
$461$		−	6.74558i		−	0.314173i	−0.987585	−	0.157086i	$-0.949790\pi$
$461$		−	6.74558i		−	0.314173i	0.987585	−	0.157086i	$-0.0502101\pi$
$462$	6.71984	−	0.543753i	0.312635	−	0.0252977i
$463$	−11.1700			−0.519113			−0.259557	−	0.965728i	$-0.583576\pi$
$463$	−11.1700			−0.519113			−0.259557	+	0.965728i	$0.583576\pi$
$464$	8.53873	+	25.5127i	0.396401	+	1.18440i
$465$	6.65500			0.308618
$466$	−24.3536	+	1.97063i	−1.12816	+	0.0912877i
$467$		−	3.70935i		−	0.171648i	−0.996310	−	0.0858242i	$-0.972648\pi$
$467$		−	3.70935i		−	0.171648i	0.996310	−	0.0858242i	$-0.0273523\pi$
$468$	−0.146713	−	0.900623i	−0.00678181	−	0.0416313i
$469$		−	8.09467i		−	0.373777i
$470$	1.45186	+	17.9425i	0.0669693	+	0.827624i
$471$	−21.7824			−1.00368
$472$	−2.71374	−	10.9834i	−0.124910	−	0.505553i
$473$	45.0005			2.06913
$474$	−0.550920	−	6.80841i	−0.0253046	−	0.312721i
$475$		−	28.4602i		−	1.30585i
$476$	0.819213	−	0.133451i	0.0375485	−	0.00611672i
$477$		−	7.63843i		−	0.349739i
$478$	14.8317	−	1.20014i	0.678386	−	0.0548933i
$479$	−2.17501			−0.0993788			−0.0496894	−	0.998765i	$-0.515823\pi$
$479$	−2.17501			−0.0993788			−0.0496894	+	0.998765i	$0.515823\pi$
$480$	5.87186	−	2.50829i	0.268012	−	0.114487i
$481$	−2.69000			−0.122653
$482$	8.60827	−	0.696560i	0.392096	−	0.0317274i
$483$		−	1.58499i		−	0.0721197i
$484$	−23.1467	+	3.77064i	−1.05212	+	0.171393i
$485$		−	18.5643i		−	0.842962i
$486$	0.114062	+	1.40961i	0.00517395	+	0.0639410i
$487$	−4.51499			−0.204594			−0.102297	−	0.994754i	$-0.532619\pi$
$487$	−4.51499			−0.204594			−0.102297	+	0.994754i	$0.532619\pi$
$488$	1.22203	+	4.94596i	0.0553187	+	0.223893i
$489$	4.60966			0.208456
$490$	0.128747	+	1.59109i	0.00581620	+	0.0718781i
$491$			1.91221i			0.0862967i	0.999069	+	0.0431483i	$0.0137388\pi$
$491$			1.91221i			0.0862967i	−0.999069	+	0.0431483i	$0.986261\pi$
$492$	0.133451	+	0.819213i	0.00601644	+	0.0369330i
$493$			2.79130i			0.125714i
$494$	−4.91249	+	0.397507i	−0.221024	+	0.0178847i
$495$	5.38093			0.241855
$496$	−22.3644	+	7.48501i	−1.00419	+	0.336087i
$497$	10.2068			0.457840
$498$	−7.80125	+	0.631258i	−0.349582	+	0.0282873i
$499$		−	27.4065i		−	1.22688i	−0.789740	−	0.613442i	$-0.789784\pi$
$499$		−	27.4065i		−	1.22688i	0.789740	−	0.613442i	$-0.210216\pi$
$500$	−3.16721	−	19.4425i	−0.141642	−	0.869493i
$501$			22.9618i			1.02586i
$502$	−2.26690	−	28.0150i	−0.101177	−	1.25037i
$503$	17.1368			0.764094			0.382047	−	0.924143i	$-0.375219\pi$
$503$	17.1368			0.764094			0.382047	+	0.924143i	$0.375219\pi$
$504$	2.74586	−	0.678435i	0.122310	−	0.0302199i
$505$	−18.5178			−0.824030
$506$	0.861845	+	10.6509i	0.0383137	+	0.473490i
$507$		−	12.7918i		−	0.568105i
$508$	−20.6218	+	3.35933i	−0.914947	+	0.149046i
$509$		−	21.6437i		−	0.959342i	−0.877449	−	0.479671i	$-0.840756\pi$
$509$		−	21.6437i		−	0.959342i	0.877449	−	0.479671i	$-0.159244\pi$
$510$	0.660311	−	0.0534307i	0.0292390	−	0.00236595i
$511$	−3.34500			−0.147974
$512$	−16.9115	+	15.0334i	−0.747388	+	0.664388i
$513$	7.63843			0.337245
$514$	20.7987	−	1.68298i	0.917392	−	0.0742331i
$515$			19.3837i			0.854148i
$516$	18.6337	−	3.03546i	0.820304	−	0.133629i
$517$		−	53.7587i		−	2.36430i
$518$	−0.672500	−	8.31092i	−0.0295479	−	0.365161i
$519$	0.216252			0.00949241
$520$	−1.41408	+	0.349386i	−0.0620116	+	0.0153216i
$521$	28.3137			1.24045			0.620223	−	0.784426i	$-0.287042\pi$
$521$	28.3137			1.24045			0.620223	+	0.784426i	$0.287042\pi$
$522$	0.767172	+	9.48091i	0.0335782	+	0.414968i
$523$			15.0687i			0.658908i	0.944172	+	0.329454i	$0.106865\pi$
$523$			15.0687i			0.658908i	−0.944172	+	0.329454i	$0.893135\pi$
$524$	−2.01219	−	12.3522i	−0.0879029	−	0.539607i
$525$		−	3.72593i		−	0.162613i
$526$	22.2154	−	1.79762i	0.968638	−	0.0783798i
$527$	−2.44684			−0.106586
$528$	−18.0828	+	6.05204i	−0.786953	+	0.263381i
$529$	−20.4878			−0.890774
$530$	−12.1534	+	0.983424i	−0.527911	+	0.0427172i
$531$		−	4.00000i		−	0.173585i
$532$	−2.45625	−	15.0781i	−0.106492	−	0.653718i
$533$		−	0.189345i		−	0.00820145i
$534$	0.562324	+	6.94935i	0.0243342	+	0.300728i
$535$	14.4109			0.623038
$536$	5.49171	+	22.2268i	0.237206	+	0.960052i
$537$	−22.6165			−0.975976
$538$	−2.49032	−	30.7760i	−0.107365	−	1.32685i
$539$		−	4.76717i		−	0.205337i
$540$	2.22812	−	0.362965i	0.0958832	−	0.0156195i
$541$		−	46.2990i		−	1.99055i	−0.0971017	−	0.995274i	$-0.530957\pi$
$541$		−	46.2990i		−	1.99055i	0.0971017	−	0.995274i	$-0.469043\pi$
$542$	26.5468	−	2.14810i	1.14028	−	0.0922689i
$543$	−7.73310			−0.331859
$544$	−2.15890	+	0.922220i	−0.0925622	+	0.0395399i
$545$	8.21372			0.351837
$546$	−0.643129	+	0.0520404i	−0.0275234	+	0.00222713i
$547$		−	2.03714i		−	0.0871020i	−0.999051	−	0.0435510i	$-0.986133\pi$
$547$		−	2.03714i		−	0.0871020i	0.999051	−	0.0435510i	$-0.0138671\pi$
$548$	−25.5864	+	4.16807i	−1.09300	+	0.178051i
$549$			1.80125i			0.0768753i
$550$	2.02598	+	25.0376i	0.0863882	+	1.06761i
$551$	51.3755			2.18867
$552$	1.07532	+	4.35217i	0.0457685	+	0.185241i
$553$	−4.83001			−0.205393
$554$	−2.79092	−	34.4909i	−0.118575	−	1.46538i
$555$		−	6.65500i		−	0.282489i
$556$	5.90533	+	36.2509i	0.250442	+	1.53738i
$557$		−	11.1234i		−	0.471315i	−0.971836	−	0.235658i	$-0.924276\pi$
$557$		−	11.1234i		−	0.471315i	0.971836	−	0.235658i	$-0.0757244\pi$
$558$	−8.31092	+	0.672500i	−0.351829	+	0.0284692i
$559$	−4.30683			−0.182159
$560$	−1.43297	−	4.28155i	−0.0605541	−	0.180929i
$561$	−1.97840			−0.0835282
$562$	−20.4604	+	1.65561i	−0.863071	+	0.0698375i
$563$			37.2437i			1.56963i	0.619727	+	0.784817i	$0.287243\pi$
$563$			37.2437i			1.56963i	−0.619727	+	0.784817i	$0.712757\pi$
$564$	−3.62624	−	22.2603i	−0.152692	−	0.937327i
$565$			3.77566i			0.158843i
$566$	−1.88783	−	23.3303i	−0.0793514	−	0.980645i
$567$	1.00000			0.0419961
$568$	−28.0265	+	6.92468i	−1.17597	+	0.290553i
$569$	22.9369			0.961564			0.480782	−	0.876840i	$-0.340353\pi$
$569$	22.9369			0.961564			0.480782	+	0.876840i	$0.340353\pi$
$570$	−0.983424	−	12.1534i	−0.0411911	−	0.509050i
$571$			35.1634i			1.47154i	0.677231	+	0.735770i	$0.263180\pi$
$571$			35.1634i			1.47154i	−0.677231	+	0.735770i	$0.736820\pi$
$572$	4.29343	−	0.699406i	0.179517	−	0.0292436i
$573$		−	10.2068i		−	0.426397i
$574$	0.584994	−	0.0473363i	0.0244172	−	0.00197578i
$575$	5.90558			0.246280
$576$	−7.07945	+	3.72577i	−0.294977	+	0.155240i
$577$	13.7918			0.574162			0.287081	−	0.957906i	$-0.407315\pi$
$577$	13.7918			0.574162			0.287081	+	0.957906i	$0.407315\pi$
$578$	23.7205	−	1.91941i	0.986644	−	0.0798368i
$579$		−	5.96407i		−	0.247858i
$580$	14.9862	−	2.44128i	0.622268	−	0.101369i
$581$			5.53434i			0.229603i
$582$	1.87596	+	23.1836i	0.0777609	+	0.960990i
$583$	36.4137			1.50810
$584$	9.18489	−	2.26937i	0.380073	−	0.0939070i
$585$	−0.514988			−0.0212921
$586$	1.07717	+	13.3120i	0.0444976	+	0.549914i
$587$		−	26.9862i		−	1.11384i	−0.830566	−	0.556920i	$-0.811983\pi$
$587$		−	26.9862i		−	1.11384i	0.830566	−	0.556920i	$-0.188017\pi$
$588$	−0.321565	−	1.97398i	−0.0132611	−	0.0814056i
$589$			45.0355i			1.85566i
$590$	−6.36436	+	0.514988i	−0.262016	+	0.0212017i
$591$	−18.8084			−0.773675
$592$	7.48501	+	22.3644i	0.307632	+	0.919169i
$593$	−31.8337			−1.30725			−0.653627	−	0.756817i	$-0.726753\pi$
$593$	−31.8337			−1.30725			−0.653627	+	0.756817i	$0.726753\pi$
$594$	−6.71984	+	0.543753i	−0.275718	+	0.0223104i
$595$		−	0.468436i		−	0.0192040i
$596$	5.02876	+	30.8699i	0.205986	+	1.26448i
$597$		−	3.27685i		−	0.134113i
$598$	−0.0824838	−	1.01936i	−0.00337301	−	0.0416846i
$599$	−34.9006			−1.42600			−0.712999	−	0.701165i	$-0.752664\pi$
$599$	−34.9006			−1.42600			−0.712999	+	0.701165i	$0.752664\pi$
$600$	2.52780	+	10.2309i	0.103197	+	0.417673i
$601$	−0.175010			−0.00713881			−0.00356941	−	0.999994i	$-0.501136\pi$
$601$	−0.175010			−0.00713881			−0.00356941	+	0.999994i	$0.501136\pi$
$602$	−1.07671	−	13.3062i	−0.0438833	−	0.542321i
$603$			8.09467i			0.329641i
$604$	30.1562	−	4.91249i	1.22704	−	0.199887i
$605$			13.2356i			0.538104i
$606$	23.1254	−	1.87125i	0.939407	−	0.0760145i
$607$	−32.1705			−1.30576			−0.652881	−	0.757461i	$-0.726440\pi$
$607$	−32.1705			−1.30576			−0.652881	+	0.757461i	$0.726440\pi$
$608$	16.9740	+	39.7359i	0.688387	+	1.61150i
$609$	6.72593			0.272548
$610$	2.86594	−	0.231905i	0.116039	−	0.00938956i
$611$			5.14503i			0.208146i
$612$	−0.819213	+	0.133451i	−0.0331147	+	0.00539444i
$613$		−	8.37869i		−	0.338412i	−0.985581	−	0.169206i	$-0.945880\pi$
$613$		−	8.37869i		−	0.338412i	0.985581	−	0.169206i	$-0.0541203\pi$
$614$	0.0412419	+	0.509678i	0.00166439	+	0.0205689i
$615$	0.468436			0.0188892
$616$	3.23422	+	13.0900i	0.130310	+	0.527410i
$617$	28.9618			1.16596			0.582980	−	0.812487i	$-0.301887\pi$
$617$	28.9618			1.16596			0.582980	+	0.812487i	$0.301887\pi$
$618$	−1.95876	−	24.2068i	−0.0787928	−	0.973742i
$619$			6.85497i			0.275524i	0.990465	+	0.137762i	$0.0439910\pi$
$619$			6.85497i			0.275524i	−0.990465	+	0.137762i	$0.956009\pi$
$620$	2.14001	+	13.1368i	0.0859450	+	0.527588i
$621$			1.58499i			0.0636036i
$622$	15.8959	−	1.28626i	0.637368	−	0.0515743i
$623$	4.92999			0.197516
$624$	1.73063	−	0.579217i	0.0692808	−	0.0231872i
$625$	7.51221			0.300488
$626$	−36.0629	+	2.91812i	−1.44136	+	0.116632i
$627$			36.4137i			1.45422i
$628$	−7.00446	−	42.9981i	−0.279508	−	1.71581i
$629$			2.44684i			0.0975619i
$630$	−0.128747	−	1.59109i	−0.00512940	−	0.0633905i
$631$	−40.2055			−1.60056			−0.800278	−	0.599629i	$-0.795315\pi$
$631$	−40.2055			−1.60056			−0.800278	+	0.599629i	$0.795315\pi$
$632$	13.2625	−	3.27685i	0.527555	−	0.130346i
$633$	−10.1628			−0.403936
$634$	0.0412419	+	0.509678i	0.00163793	+	0.0202419i
$635$			11.7918i			0.467945i
$636$	15.0781	−	2.45625i	0.597885	−	0.0973965i
$637$			0.456247i			0.0180772i
$638$	−45.1971	+	3.65724i	−1.78937	+	0.144792i
$639$	−10.2068			−0.403777
$640$	6.83949	+	10.7844i	0.270355	+	0.426289i
$641$	−24.0737			−0.950854			−0.475427	−	0.879755i	$-0.657706\pi$
$641$	−24.0737			−0.950854			−0.475427	+	0.879755i	$0.657706\pi$
$642$	−17.9967	+	1.45625i	−0.710273	+	0.0574735i
$643$			23.7559i			0.936841i	0.883506	+	0.468421i	$0.155177\pi$
$643$			23.7559i			0.936841i	−0.883506	+	0.468421i	$0.844823\pi$
$644$	3.12875	−	0.509678i	0.123290	−	0.0200841i
$645$		−	10.6550i		−	0.419540i
$646$	0.361575	+	4.46844i	0.0142260	+	0.175808i
$647$	−32.6218			−1.28250			−0.641249	−	0.767333i	$-0.721583\pi$
$647$	−32.6218			−1.28250			−0.641249	+	0.767333i	$0.721583\pi$
$648$	−2.74586	+	0.678435i	−0.107867	+	0.0266515i
$649$	19.0687			0.748512
$650$	−0.193899	−	2.39625i	−0.00760535	−	0.0939888i
$651$			5.89592i			0.231079i
$652$	1.48230	+	9.09938i	0.0580515	+	0.356359i
$653$		−	14.4109i		−	0.563942i	−0.959423	−	0.281971i	$-0.909012\pi$
$653$		−	14.4109i		−	0.563942i	0.959423	−	0.281971i	$-0.0909883\pi$
$654$	−10.2575	+	0.830011i	−0.401100	+	0.0324560i
$655$	−7.06313			−0.275979
$656$	−1.57420	+	0.526860i	−0.0614620	+	0.0205704i
$657$	3.34500			0.130501
$658$	−15.8959	+	1.28626i	−0.619687	+	0.0501436i
$659$			23.3315i			0.908866i	0.890781	+	0.454433i	$0.150158\pi$
$659$			23.3315i			0.908866i	−0.890781	+	0.454433i	$0.849842\pi$
$660$	1.73032	+	10.6218i	0.0673525	+	0.413455i
$661$			44.1468i			1.71711i	0.512721	+	0.858555i	$0.328638\pi$
$661$			44.1468i			1.71711i	−0.512721	+	0.858555i	$0.671362\pi$
$662$	0.890142	+	11.0006i	0.0345963	+	0.427551i
$663$	0.189345			0.00735356
$664$	−3.75469	−	15.1965i	−0.145710	−	0.589739i
$665$	−8.62185			−0.334341
$666$	0.672500	+	8.31092i	0.0260588	+	0.322042i
$667$			10.6606i			0.412779i
$668$	−45.3262	+	7.38371i	−1.75372	+	0.285684i
$669$		−	21.9668i		−	0.849287i
$670$	12.8793	−	1.04216i	0.497572	−	0.0402623i
$671$	−8.58685			−0.331492
$672$	2.22219	+	5.20210i	0.0857228	+	0.200675i
$673$	11.6960			0.450846			0.225423	−	0.974261i	$-0.427624\pi$
$673$	11.6960			0.450846			0.225423	+	0.974261i	$0.427624\pi$
$674$	−12.3508	+	0.999394i	−0.475734	+	0.0384952i
$675$			3.72593i			0.143411i
$676$	25.2508	−	4.11340i	0.971186	−	0.158208i
$677$			0.648756i			0.0249337i	0.999922	+	0.0124669i	$0.00396843\pi$
$677$			0.648756i			0.0249337i	−0.999922	+	0.0124669i	$0.996032\pi$
$678$	−0.381537	−	4.71513i	−0.0146528	−	0.181084i
$679$	16.4468			0.631172
$680$	0.317804	+	1.28626i	0.0121872	+	0.0493258i
$681$	−7.91752			−0.303400
$682$	−3.20592	−	39.6196i	−0.122761	−	1.51711i
$683$			22.4909i			0.860589i	0.902689	+	0.430294i	$0.141590\pi$
$683$			22.4909i			0.860589i	−0.902689	+	0.430294i	$0.858410\pi$
$684$	2.45625	+	15.0781i	0.0939170	+	0.576525i
$685$			14.6306i			0.559007i
$686$	−1.40961	+	0.114062i	−0.0538190	+	0.00435490i
$687$	13.1606			0.502107
$688$	11.9839	+	35.8065i	0.456882	+	1.36511i
$689$	−3.48501			−0.132768
$690$	2.52187	−	0.204063i	0.0960058	−	0.00776856i
$691$			45.2681i			1.72208i	0.508538	+	0.861039i	$0.330186\pi$
$691$			45.2681i			1.72208i	−0.508538	+	0.861039i	$0.669814\pi$
$692$	0.0695390	+	0.426877i	0.00264348	+	0.0162274i
$693$			4.76717i			0.181090i
$694$	0.236926	+	2.92800i	0.00899360	+	0.111145i
$695$	20.7287			0.786285
$696$	−18.4684	+	4.56311i	−0.700044	+	0.172964i
$697$	−0.172230			−0.00652366
$698$	−2.13730	−	26.4134i	−0.0808982	−	0.999761i
$699$		−	17.2769i		−	0.653470i
$700$	7.35491	−	1.19813i	0.277990	−	0.0452850i
$701$		−	1.03091i		−	0.0389370i	−0.999810	−	0.0194685i	$-0.993803\pi$
$701$		−	1.03091i		−	0.0389370i	0.999810	−	0.0194685i	$-0.00619740\pi$
$702$	0.643129	−	0.0520404i	0.0242734	−	0.00196414i
$703$	45.0355			1.69855
$704$	−17.7614	−	33.7490i	−0.669408	−	1.27196i
$705$	−12.7287			−0.479391
$706$	18.6703	−	1.51075i	0.702664	−	0.0568579i
$707$		−	16.4056i		−	0.616996i
$708$	7.89592	−	1.28626i	0.296747	−	0.0483406i
$709$		−	10.5481i		−	0.396144i	−0.980188	−	0.198072i	$-0.936532\pi$
$709$		−	10.5481i		−	0.396144i	0.980188	−	0.198072i	$-0.0634679\pi$
$710$	1.31410	+	16.2400i	0.0493173	+	0.609476i
$711$	4.83001			0.181140
$712$	−13.5371	+	3.34468i	−0.507322	+	0.125347i
$713$	−9.34500			−0.349973
$714$	0.0473363	+	0.584994i	0.00177152	+	0.0218929i
$715$		−	2.45504i		−	0.0918131i
$716$	−7.27268	−	44.6446i	−0.271793	−	1.66845i
$717$			10.5219i			0.392946i
$718$	8.02328	−	0.649224i	0.299426	−	0.0242288i
$719$	−7.00502			−0.261243			−0.130622	−	0.991432i	$-0.541697\pi$
$719$	−7.00502			−0.261243			−0.130622	+	0.991432i	$0.541697\pi$
$720$	1.43297	+	4.28155i	0.0534037	+	0.159564i
$721$	−17.1728			−0.639547
$722$	55.4617	−	4.48783i	2.06407	−	0.167020i
$723$			6.10686i			0.227117i
$724$	−2.48669	−	15.2650i	−0.0924171	−	0.567318i
$725$			25.0603i			0.930718i
$726$	−1.33748	−	16.5289i	−0.0496386	−	0.613447i
$727$	−17.8028			−0.660270			−0.330135	−	0.943934i	$-0.607094\pi$
$727$	−17.8028			−0.660270			−0.330135	+	0.943934i	$0.607094\pi$
$728$	−0.309534	−	1.25279i	−0.0114721	−	0.0464315i
$729$	−1.00000			−0.0370370
$730$	−0.430659	−	5.32219i	−0.0159394	−	0.196983i
$731$			3.91752i			0.144895i
$732$	−3.55562	+	0.579217i	−0.131420	+	0.0214085i
$733$		−	34.3300i		−	1.26801i	−0.773330	−	0.634004i	$-0.781410\pi$
$733$		−	34.3300i		−	1.26801i	0.773330	−	0.634004i	$-0.218590\pi$
$734$	−15.8959	+	1.28626i	−0.586729	+	0.0474767i
$735$	−1.12875			−0.0416345
$736$	−8.24531	+	3.52216i	−0.303926	+	0.129828i
$737$	−38.5887			−1.42143
$738$	−0.584994	+	0.0473363i	−0.0215339	+	0.00174247i
$739$			0.0946726i			0.00348259i	0.999998	+	0.00174129i	$0.000554271\pi$
$739$			0.0946726i			0.00348259i	−0.999998	+	0.00174129i	$0.999446\pi$
$740$	13.1368	−	2.14001i	0.482920	−	0.0786684i
$741$		−	3.48501i		−	0.128025i
$742$	−0.871253	−	10.7672i	−0.0319847	−	0.395275i
$743$	−13.2755			−0.487032			−0.243516	−	0.969897i	$-0.578301\pi$
$743$	−13.2755			−0.487032			−0.243516	+	0.969897i	$0.578301\pi$
$744$	−4.00000	−	16.1893i	−0.146647	−	0.593530i
$745$	17.6518			0.646713
$746$	−0.808414	−	9.99059i	−0.0295981	−	0.365782i
$747$		−	5.53434i		−	0.202491i
$748$	−0.636184	−	3.90533i	−0.0232612	−	0.142793i
$749$			12.7672i			0.466502i
$750$	13.8837	−	1.12344i	0.506962	−	0.0410221i
$751$	15.4187			0.562637			0.281318	−	0.959615i	$-0.409228\pi$
$751$	15.4187			0.562637			0.281318	+	0.959615i	$0.409228\pi$
$752$	42.7753	−	14.3162i	1.55985	−	0.522059i
$753$	19.8743			0.724261
$754$	4.32564	−	0.350020i	0.157531	−	0.0127470i
$755$		−	17.2437i		−	0.627562i
$756$	0.321565	+	1.97398i	0.0116952	+	0.0717930i
$757$		−	9.96685i		−	0.362251i	−0.983460	−	0.181126i	$-0.942026\pi$
$757$		−	9.96685i		−	0.362251i	0.983460	−	0.181126i	$-0.0579741\pi$
$758$	−0.761683	−	9.41308i	−0.0276656	−	0.341899i
$759$	−7.55594			−0.274263
$760$	23.6744	−	5.84937i	0.858759	−	0.212179i
$761$	23.4837			0.851283			0.425642	−	0.904892i	$-0.360048\pi$
$761$	23.4837			0.851283			0.425642	+	0.904892i	$0.360048\pi$
$762$	−1.19159	−	14.7259i	−0.0431666	−	0.533464i
$763$			7.27685i			0.263440i
$764$	20.1481	−	3.28216i	0.728933	−	0.118744i
$765$			0.468436i			0.0169363i
$766$	26.2962	−	2.12782i	0.950121	−	0.0768814i
$767$	−1.82499			−0.0658966
$768$	−9.63110	−	12.7766i	−0.347532	−	0.461036i
$769$	22.9369			0.827125			0.413562	−	0.910476i	$-0.364284\pi$
$769$	22.9369			0.827125			0.413562	+	0.910476i	$0.364284\pi$
$770$	7.58499	−	0.613759i	0.273344	−	0.0221183i
$771$			14.7550i			0.531388i
$772$	11.7729	−	1.91783i	0.423718	−	0.0690243i
$773$		−	35.0956i		−	1.26230i	−0.775660	−	0.631150i	$-0.782583\pi$
$773$		−	35.0956i		−	1.26230i	0.775660	−	0.631150i	$-0.217417\pi$
$774$	1.07671	+	13.3062i	0.0387014	+	0.478282i
$775$	−21.9678			−0.789106
$776$	−45.1607	+	11.1581i	−1.62117	+	0.400553i
$777$	5.89592			0.211515
$778$	−2.32033	−	28.6753i	−0.0831880	−	1.02806i
$779$			3.16999i			0.113577i
$780$	−0.165602	−	1.01658i	−0.00592950	−	0.0363993i
$781$		−	48.6578i		−	1.74111i
$782$	−0.927213	+	0.0750278i	−0.0331571	+	0.00268299i
$783$	−6.72593			−0.240365
$784$	3.79319	−	1.26952i	0.135471	−	0.0453402i
$785$	−24.5869			−0.877542
$786$	8.82060	−	0.713741i	0.314620	−	0.0254583i
$787$		−	17.9480i		−	0.639778i	−0.947455	−	0.319889i	$-0.896354\pi$
$787$		−	17.9480i		−	0.639778i	0.947455	−	0.319889i	$-0.103646\pi$
$788$	−6.04812	−	37.1274i	−0.215455	−	1.32261i
$789$			15.7600i			0.561071i
$790$	−0.621849	−	7.68498i	−0.0221244	−	0.273419i
$791$	−3.34500			−0.118934
$792$	−3.23422	−	13.0900i	−0.114923	−	0.465132i
$793$	0.821814			0.0291835
$794$	−1.24363	−	15.3691i	−0.0441346	−	0.545428i
$795$		−	8.62185i		−	0.305785i
$796$	6.46844	−	1.05372i	0.229268	−	0.0373481i
$797$			34.4199i			1.21922i	0.792703	+	0.609608i	$0.208673\pi$
$797$			34.4199i			1.21922i	−0.792703	+	0.609608i	$0.791327\pi$
$798$	10.7672	−	0.871253i	0.381154	−	0.0308420i
$799$	4.67996			0.165565
$800$	−19.3827	+	8.27972i	−0.685281	+	0.292732i
$801$	−4.92999			−0.174193
$802$	−41.1260	+	3.32782i	−1.45221	+	0.117509i
$803$			15.9462i			0.562729i
$804$	−15.9787	+	2.60296i	−0.563526	+	0.0917993i
$805$		−	1.78906i		−	0.0630560i
$806$	0.306826	+	3.79184i	0.0108075	+	0.133562i
$807$	21.8331			0.768561
$808$	11.1301	+	45.0474i	0.391557	+	1.58476i
$809$	1.89314			0.0665592			0.0332796	−	0.999446i	$-0.489405\pi$
$809$	1.89314			0.0665592			0.0332796	+	0.999446i	$0.489405\pi$
$810$	0.128747	+	1.59109i	0.00452371	+	0.0559052i
$811$		−	10.3400i		−	0.363086i	−0.983383	−	0.181543i	$-0.941891\pi$
$811$		−	10.3400i		−	0.363086i	0.983383	−	0.181543i	$-0.0581091\pi$
$812$	2.16282	+	13.2769i	0.0759002	+	0.465926i
$813$			18.8328i			0.660495i
$814$	−39.6196	+	3.20592i	−1.38867	+	0.112367i
$815$	5.20314			0.182258
$816$	−0.526860	−	1.57420i	−0.0184438	−	0.0551079i
$817$	72.1042			2.52261
$818$	44.7179	−	3.61846i	1.56353	−	0.126517i
$819$		−	0.456247i		−	0.0159426i
$820$	0.150633	+	0.924684i	0.00526032	+	0.0322914i
$821$		−	2.40029i		−	0.0837706i	−0.999122	−	0.0418853i	$-0.986664\pi$
$821$		−	2.40029i		−	0.0837706i	0.999122	−	0.0418853i	$-0.0133364\pi$
$822$	−1.47845	−	18.2711i	−0.0515669	−	0.637277i
$823$	25.8655			0.901616			0.450808	−	0.892621i	$-0.351136\pi$
$823$	25.8655			0.901616			0.450808	+	0.892621i	$0.351136\pi$
$824$	47.1540	−	11.6506i	1.64269	−	0.405868i
$825$	−17.7622			−0.618399
$826$	−0.456247	−	5.63843i	−0.0158749	−	0.196186i
$827$		−	17.0928i		−	0.594375i	−0.954819	−	0.297188i	$-0.903951\pi$
$827$		−	17.0928i		−	0.594375i	0.954819	−	0.297188i	$-0.0960487\pi$
$828$	−3.12875	+	0.509678i	−0.108731	+	0.0177125i
$829$			41.8893i			1.45488i	0.686174	+	0.727438i	$0.259289\pi$
$829$			41.8893i			1.45488i	−0.686174	+	0.727438i	$0.740711\pi$
$830$	−8.80563	+	0.712530i	−0.305648	+	0.0247323i
$831$	24.4684			0.848801
$832$	1.69987	+	3.22998i	0.0589325	+	0.111979i
$833$	0.415006			0.0143791
$834$	−25.8865	+	2.09467i	−0.896377	+	0.0725326i
$835$			25.9181i			0.896933i
$836$	−71.8799	+	11.7094i	−2.48602	+	0.404976i
$837$		−	5.89592i		−	0.203793i
$838$	2.19875	+	27.1728i	0.0759547	+	0.938668i
$839$	−24.5500			−0.847560			−0.423780	−	0.905765i	$-0.639297\pi$
$839$	−24.5500			−0.847560			−0.423780	+	0.905765i	$0.639297\pi$
$840$	3.09938	−	0.765782i	0.106939	−	0.0264220i
$841$	−16.2381			−0.559936
$842$	2.20406	+	27.2384i	0.0759570	+	0.938697i
$843$		−	14.5150i		−	0.499923i
$844$	−3.26800	−	20.0612i	−0.112489	−	0.690535i
$845$		−	14.4387i		−	0.496708i
$846$	15.8959	−	1.28626i	0.546513	−	0.0442225i
$847$	−11.7259			−0.402908
$848$	9.69717	+	28.9740i	0.333002	+	0.994972i
$849$	16.5509			0.568026
$850$	−2.17965	+	0.176372i	−0.0747613	+	0.00604950i
$851$			9.34500i			0.320342i
$852$	−3.28216	−	20.1481i	−0.112445	−	0.690263i
$853$			38.7193i			1.32572i	0.748742	+	0.662862i	$0.230658\pi$
$853$			38.7193i			1.32572i	−0.748742	+	0.662862i	$0.769342\pi$
$854$	0.205454	+	2.53905i	0.00703048	+	0.0868844i
$855$	8.62185			0.294861
$856$	−8.66170	−	35.0568i	−0.296051	−	1.19822i
$857$	−45.2074			−1.54425			−0.772127	−	0.635468i	$-0.780807\pi$
$857$	−45.2074			−1.54425			−0.772127	+	0.635468i	$0.780807\pi$
$858$	0.248086	+	3.06591i	0.00846951	+	0.104668i
$859$		−	57.1890i		−	1.95126i	−0.219418	−	0.975631i	$-0.570416\pi$
$859$		−	57.1890i		−	1.95126i	0.219418	−	0.975631i	$-0.429584\pi$
$860$	21.0328	−	3.42627i	0.717211	−	0.116835i
$861$			0.415006i			0.0141434i
$862$	−20.3195	+	1.64420i	−0.692084	+	0.0560018i
$863$	−45.1106			−1.53558			−0.767791	−	0.640701i	$-0.778644\pi$
$863$	−45.1106			−1.53558			−0.767791	+	0.640701i	$0.778644\pi$
$864$	−2.22219	−	5.20210i	−0.0756004	−	0.176979i
$865$	0.244094			0.00829944
$866$	13.0767	−	1.05813i	0.444365	−	0.0359569i
$867$			16.8278i			0.571501i
$868$	−11.6384	+	1.89592i	−0.395034	+	0.0643517i
$869$			23.0255i			0.781086i
$870$	0.865943	+	10.7016i	0.0293582	+	0.362817i
$871$	3.69317			0.125138
$872$	−4.93687	−	19.9812i	−0.167184	−	0.676648i
$873$	−16.4468			−0.556641
$874$	1.38093	+	17.0659i	0.0467107	+	0.577263i
$875$		−	9.84937i		−	0.332969i
$876$	1.07563	+	6.60296i	0.0363423	+	0.223093i
$877$			17.6600i			0.596337i	0.954513	+	0.298168i	$0.0963757\pi$
$877$			17.6600i			0.596337i	−0.954513	+	0.298168i	$0.903624\pi$
$878$		0			0
$879$	−9.44377			−0.318530
$880$	−20.4109	+	6.83122i	−0.688052	+	0.230280i
$881$	6.78998			0.228760			0.114380	−	0.993437i	$-0.463512\pi$
$881$	6.78998			0.228760			0.114380	+	0.993437i	$0.463512\pi$
$882$	1.40961	−	0.114062i	0.0474639	−	0.00384066i
$883$		−	28.6015i		−	0.962516i	−0.876579	−	0.481258i	$-0.840180\pi$
$883$		−	28.6015i		−	0.962516i	0.876579	−	0.481258i	$-0.159820\pi$
$884$	0.0608867	+	0.373764i	0.00204784	+	0.0125710i
$885$		−	4.51499i		−	0.151770i
$886$	1.78467	+	22.0554i	0.0599572	+	0.740967i
$887$	23.5919			0.792138			0.396069	−	0.918221i	$-0.370374\pi$
$887$	23.5919			0.792138			0.396069	+	0.918221i	$0.370374\pi$
$888$	−16.1893	+	4.00000i	−0.543279	+	0.134231i
$889$	−10.4468			−0.350376
$890$	0.634722	+	7.84406i	0.0212759	+	0.262933i
$891$		−	4.76717i		−	0.159706i
$892$	43.3621	−	7.06376i	1.45187	−	0.236512i
$893$		−	86.1374i		−	2.88248i
$894$	−22.0440	+	1.78375i	−0.737262	+	0.0596575i
$895$	−25.5284			−0.853319
$896$	−9.55427	+	6.05937i	−0.319186	+	0.202429i
$897$	0.723150			0.0241453
$898$	17.8386	−	1.44345i	0.595281	−	0.0481687i
$899$		−	39.6555i		−	1.32259i
$900$	−7.35491	+	1.19813i	−0.245164	+	0.0399376i
$901$			3.16999i			0.105608i
$902$	−0.225660	−	2.78877i	−0.00751367	−	0.0928559i
$903$	9.43967			0.314133
$904$	9.18489	−	2.26937i	0.305485	−	0.0754780i
$905$	−8.72871			−0.290152
$906$	1.74251	+	21.5343i	0.0578909	+	0.715431i
$907$		−	2.02096i		−	0.0671050i	−0.999437	−	0.0335525i	$-0.989318\pi$
$907$		−	2.02096i		−	0.0671050i	0.999437	−	0.0335525i	$-0.0106821\pi$
$908$	−2.54599	−	15.6290i	−0.0844918	−	0.518667i
$909$			16.4056i			0.544139i
$910$	−0.725930	+	0.0587405i	−0.0240644	+	0.00194723i
$911$	52.5524			1.74114			0.870569	−	0.492046i	$-0.163751\pi$
$911$	52.5524			1.74114			0.870569	+	0.492046i	$0.163751\pi$
$912$	−28.9740	+	9.69717i	−0.959426	+	0.321105i
$913$	26.3832			0.873156
$914$	33.7229	−	2.72878i	1.11546	−	0.0902599i
$915$			2.03315i			0.0672139i
$916$	4.23198	+	25.9787i	0.139828	+	0.858361i
$917$		−	6.25749i		−	0.206641i
$918$	−0.0473363	−	0.584994i	−0.00156233	−	0.0193077i
$919$	21.5237			0.710002			0.355001	−	0.934866i	$-0.384480\pi$
$919$	21.5237			0.710002			0.355001	+	0.934866i	$0.384480\pi$
$920$	1.21376	+	4.91249i	0.0400165	+	0.161960i
$921$	−0.361575			−0.0119143
$922$	0.769413	+	9.50861i	0.0253393	+	0.313149i
$923$			4.65685i			0.153282i
$924$	−9.41030	+	1.53295i	−0.309576	+	0.0504305i
$925$			21.9678i			0.722296i
$926$	15.7453	−	1.27407i	0.517422	−	0.0418685i
$927$	17.1728			0.564028
$928$	−14.9463	−	34.9890i	−0.490636	−	1.14857i
$929$	−15.7500			−0.516739			−0.258370	−	0.966046i	$-0.583185\pi$
$929$	−15.7500			−0.516739			−0.258370	+	0.966046i	$0.583185\pi$
$930$	−9.38093	+	0.759082i	−0.307613	+	0.0248913i
$931$		−	7.63843i		−	0.250339i
$932$	34.1042	−	5.55562i	1.11712	−	0.181981i
$933$			11.2769i			0.369188i
$934$	0.423096	+	5.22873i	0.0138441	+	0.171089i
$935$	−2.23312			−0.0730307
$936$	0.309534	+	1.25279i	0.0101174	+	0.0409487i
$937$	17.0687			0.557610			0.278805	−	0.960348i	$-0.410062\pi$
$937$	17.0687			0.557610			0.278805	+	0.960348i	$0.410062\pi$
$938$	0.923293	+	11.4103i	0.0301466	+	0.372560i
$939$		−	25.5837i		−	0.834892i
$940$	−4.09310	−	25.1262i	−0.133502	−	0.819527i
$941$			26.5456i			0.865362i	0.901547	+	0.432681i	$0.142432\pi$
$941$			26.5456i			0.865362i	−0.901547	+	0.432681i	$0.857568\pi$
$942$	30.7047	−	2.48454i	1.00041	−	0.0809508i
$943$	−0.657782			−0.0214203
$944$	5.07810	+	15.1728i	0.165278	+	0.493832i
$945$	1.12875			0.0367181
$946$	−63.4330	+	5.13285i	−2.06239	+	0.166883i
$947$			20.3265i			0.660522i	0.943890	+	0.330261i	$0.107137\pi$
$947$			20.3265i			0.660522i	−0.943890	+	0.330261i	$0.892863\pi$
$948$	1.55316	+	9.53434i	0.0504443	+	0.309661i
$949$		−	1.52615i		−	0.0495408i
$950$	3.24623	+	40.1177i	0.105322	+	1.30159i
$951$	−0.361575			−0.0117249
$952$	−1.13955	+	0.281554i	−0.0369329	+	0.00912523i
$953$	−38.6855			−1.25315			−0.626573	−	0.779362i	$-0.715543\pi$
$953$	−38.6855			−1.25315			−0.626573	+	0.779362i	$0.715543\pi$
$954$	0.871253	+	10.7672i	0.0282079	+	0.348600i
$955$		−	11.5209i		−	0.372809i
$956$	−20.7700	+	3.38346i	−0.671748	+	0.109429i
$957$		−	32.0637i		−	1.03647i
$958$	3.06591	−	0.248086i	0.0990550	−	0.00801529i
$959$	−12.9618			−0.418559
$960$	−7.99091	+	4.20545i	−0.257905	+	0.135730i
$961$	3.76186			0.121350
$962$	3.79184	−	0.306826i	0.122254	−	0.00989247i
$963$		−	12.7672i		−	0.411416i
$964$	−12.0548	+	1.96375i	−0.388260	+	0.0632482i
$965$		−	6.73192i		−	0.216708i
$966$	0.180787	+	2.23422i	0.00581674	+	0.0718848i
$967$	−26.6606			−0.857346			−0.428673	−	0.903460i	$-0.641019\pi$
$967$	−26.6606			−0.857346			−0.428673	+	0.903460i	$0.641019\pi$
$968$	32.1977	−	7.95529i	1.03487	−	0.255693i
$969$	−3.16999			−0.101835
$970$	2.11748	+	26.1684i	0.0679882	+	0.840216i
$971$			3.27685i			0.105159i	0.998617	+	0.0525796i	$0.0167443\pi$
$971$			3.27685i			0.105159i	−0.998617	+	0.0525796i	$0.983256\pi$
$972$	−0.321565	−	1.97398i	−0.0103142	−	0.0633154i
$973$			18.3644i			0.588734i
$974$	6.36436	−	0.514988i	0.203927	−	0.0165013i
$975$	1.69995			0.0544418
$976$	−2.28673	−	6.83247i	−0.0731963	−	0.218702i
$977$	12.0387			0.385153			0.192576	−	0.981282i	$-0.438316\pi$
$977$	12.0387			0.385153			0.192576	+	0.981282i	$0.438316\pi$
$978$	−6.49781	+	0.525786i	−0.207777	+	0.0168128i
$979$		−	23.5021i		−	0.751131i
$980$	−0.362965	−	2.22812i	−0.0115945	−	0.0711748i
$981$		−	7.27685i		−	0.232332i
$982$	−0.218110	−	2.69546i	−0.00696016	−	0.0860155i
$983$	4.42188			0.141036			0.0705181	−	0.997510i	$-0.477535\pi$
$983$	4.42188			0.141036			0.0705181	+	0.997510i	$0.477535\pi$
$984$	−0.281554	−	1.13955i	−0.00897563	−	0.0363274i
$985$	−21.2299			−0.676442
$986$	−0.318381	−	3.93463i	−0.0101393	−	0.125304i
$987$		−	11.2769i		−	0.358946i
$988$	6.87934	−	1.12066i	0.218861	−	0.0356528i
$989$			14.9618i			0.475758i
$990$	−7.58499	+	0.613759i	−0.241067	+	0.0195065i
$991$	−9.10184			−0.289129			−0.144565	−	0.989495i	$-0.546178\pi$
$991$	−9.10184			−0.289129			−0.144565	+	0.989495i	$0.546178\pi$
$992$	30.6712	−	13.1018i	0.973811	−	0.415984i
$993$	−7.80403			−0.247653
$994$	−14.3876	+	1.16421i	−0.456348	+	0.0369266i
$995$		−	3.69873i		−	0.117258i
$996$	10.9247	−	1.77965i	0.346162	−	0.0563904i
$997$		−	42.8556i		−	1.35725i	−0.734485	−	0.678625i	$-0.762576\pi$
$997$		−	42.8556i		−	1.35725i	0.734485	−	0.678625i	$-0.237424\pi$
$998$	3.12604	+	38.6324i	0.0989530	+	1.22289i
$999$	−5.89592			−0.186539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.c.b.85.2	yes	8
3.2	odd	2		504.2.c.f.253.7		8
4.3	odd	2		672.2.c.b.337.6		8
7.6	odd	2		1176.2.c.c.589.2		8
8.3	odd	2		672.2.c.b.337.3		8
8.5	even	2	inner	168.2.c.b.85.1	✓	8
12.11	even	2		2016.2.c.e.1009.6		8
16.3	odd	4		5376.2.a.bl.1.2		4
16.5	even	4		5376.2.a.bm.1.3		4
16.11	odd	4		5376.2.a.bq.1.3		4
16.13	even	4		5376.2.a.bp.1.2		4
24.5	odd	2		504.2.c.f.253.8		8
24.11	even	2		2016.2.c.e.1009.3		8
28.27	even	2		4704.2.c.c.2353.3		8
56.13	odd	2		1176.2.c.c.589.1		8
56.27	even	2		4704.2.c.c.2353.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.c.b.85.1	✓	8	8.5	even	2	inner
168.2.c.b.85.2	yes	8	1.1	even	1	trivial
504.2.c.f.253.7		8	3.2	odd	2
504.2.c.f.253.8		8	24.5	odd	2
672.2.c.b.337.3		8	8.3	odd	2
672.2.c.b.337.6		8	4.3	odd	2
1176.2.c.c.589.1		8	56.13	odd	2
1176.2.c.c.589.2		8	7.6	odd	2
2016.2.c.e.1009.3		8	24.11	even	2
2016.2.c.e.1009.6		8	12.11	even	2
4704.2.c.c.2353.3		8	28.27	even	2
4704.2.c.c.2353.6		8	56.27	even	2
5376.2.a.bl.1.2		4	16.3	odd	4
5376.2.a.bm.1.3		4	16.5	even	4
5376.2.a.bp.1.2		4	16.13	even	4
5376.2.a.bq.1.3		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)

\(f(q)\)	\(=\)	\(q+(-1.40961 + 0.114062i) q^{2} -1.00000i q^{3} +(1.97398 - 0.321565i) q^{4} -1.12875i q^{5} +(0.114062 + 1.40961i) q^{6} +1.00000 q^{7} +(-2.74586 + 0.678435i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.40961 + 0.114062i) q^{2} -1.00000i q^{3} +(1.97398 - 0.321565i) q^{4} -1.12875i q^{5} +(0.114062 + 1.40961i) q^{6} +1.00000 q^{7} +(-2.74586 + 0.678435i) q^{8} -1.00000 q^{9} +(0.128747 + 1.59109i) q^{10} -4.76717i q^{11} +(-0.321565 - 1.97398i) q^{12} +0.456247i q^{13} +(-1.40961 + 0.114062i) q^{14} -1.12875 q^{15} +(3.79319 - 1.26952i) q^{16} +0.415006 q^{17} +(1.40961 - 0.114062i) q^{18} -7.63843i q^{19} +(-0.362965 - 2.22812i) q^{20} -1.00000i q^{21} +(0.543753 + 6.71984i) q^{22} +1.58499 q^{23} +(0.678435 + 2.74586i) q^{24} +3.72593 q^{25} +(-0.0520404 - 0.643129i) q^{26} +1.00000i q^{27} +(1.97398 - 0.321565i) q^{28} +6.72593i q^{29} +(1.59109 - 0.128747i) q^{30} -5.89592 q^{31} +(-5.20210 + 2.22219i) q^{32} -4.76717 q^{33} +(-0.584994 + 0.0473363i) q^{34} -1.12875i q^{35} +(-1.97398 + 0.321565i) q^{36} +5.89592i q^{37} +(0.871253 + 10.7672i) q^{38} +0.456247 q^{39} +(0.765782 + 3.09938i) q^{40} -0.415006 q^{41} +(0.114062 + 1.40961i) q^{42} +9.43967i q^{43} +(-1.53295 - 9.41030i) q^{44} +1.12875i q^{45} +(-2.23422 + 0.180787i) q^{46} +11.2769 q^{47} +(-1.26952 - 3.79319i) q^{48} +1.00000 q^{49} +(-5.25209 + 0.424987i) q^{50} -0.415006i q^{51} +(0.146713 + 0.900623i) q^{52} +7.63843i q^{53} +(-0.114062 - 1.40961i) q^{54} -5.38093 q^{55} +(-2.74586 + 0.678435i) q^{56} -7.63843 q^{57} +(-0.767172 - 9.48091i) q^{58} +4.00000i q^{59} +(-2.22812 + 0.362965i) q^{60} -1.80125i q^{61} +(8.31092 - 0.672500i) q^{62} -1.00000 q^{63} +(7.07945 - 3.72577i) q^{64} +0.514988 q^{65} +(6.71984 - 0.543753i) q^{66} -8.09467i q^{67} +(0.819213 - 0.133451i) q^{68} -1.58499i q^{69} +(0.128747 + 1.59109i) q^{70} +10.2068 q^{71} +(2.74586 - 0.678435i) q^{72} -3.34500 q^{73} +(-0.672500 - 8.31092i) q^{74} -3.72593i q^{75} +(-2.45625 - 15.0781i) q^{76} -4.76717i q^{77} +(-0.643129 + 0.0520404i) q^{78} -4.83001 q^{79} +(-1.43297 - 4.28155i) q^{80} +1.00000 q^{81} +(0.584994 - 0.0473363i) q^{82} +5.53434i q^{83} +(-0.321565 - 1.97398i) q^{84} -0.468436i q^{85} +(-1.07671 - 13.3062i) q^{86} +6.72593 q^{87} +(3.23422 + 13.0900i) q^{88} +4.92999 q^{89} +(-0.128747 - 1.59109i) q^{90} +0.456247i q^{91} +(3.12875 - 0.509678i) q^{92} +5.89592i q^{93} +(-15.8959 + 1.28626i) q^{94} -8.62185 q^{95} +(2.22219 + 5.20210i) q^{96} +16.4468 q^{97} +(-1.40961 + 0.114062i) q^{98} +4.76717i 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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