LMFDB - Embedded newform 315.2.bz.d.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(73,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("315.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	315.73
Dual form			315.2.bz.d.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.17399 - 0.582519i) q^{2} +(2.65485 + 1.53278i) q^{4} +(1.96540 + 1.06640i) q^{5} +(-0.660211 + 2.56205i) q^{7} +(-1.69581 - 1.69581i) q^{8} +O(q^{10})$	\(q+(-2.17399 - 0.582519i) q^{2} +(2.65485 + 1.53278i) q^{4} +(1.96540 + 1.06640i) q^{5} +(-0.660211 + 2.56205i) q^{7} +(-1.69581 - 1.69581i) q^{8} +(-3.65156 - 3.46322i) q^{10} +(-0.329757 + 0.571155i) q^{11} +(-2.55836 + 2.55836i) q^{13} +(2.92774 - 5.18530i) q^{14} +(-0.366726 - 0.635189i) q^{16} +(-5.43281 + 1.45572i) q^{17} +(-1.48115 - 2.56543i) q^{19} +(3.58330 + 5.84366i) q^{20} +(1.04960 - 1.04960i) q^{22} +(-0.0726580 + 0.271163i) q^{23} +(2.72560 + 4.19179i) q^{25} +(7.05213 - 4.07155i) q^{26} +(-5.67983 + 5.78992i) q^{28} +5.03568i q^{29} +(6.53164 + 3.77104i) q^{31} +(1.66867 + 6.22756i) q^{32} +12.6589 q^{34} +(-4.02974 + 4.33141i) q^{35} +(-7.79682 - 2.08915i) q^{37} +(1.72560 + 6.44003i) q^{38} +(-1.52454 - 5.14136i) q^{40} +7.07821i q^{41} +(8.53242 + 8.53242i) q^{43} +(-1.75091 + 1.01089i) q^{44} +(0.315915 - 0.547181i) q^{46} +(3.11986 - 11.6435i) q^{47} +(-6.12824 - 3.38299i) q^{49} +(-3.48362 - 10.7006i) q^{50} +(-10.7135 + 2.87066i) q^{52} +(4.65369 - 1.24695i) q^{53} +(-1.25718 + 0.770897i) q^{55} +(5.46435 - 3.22517i) q^{56} +(2.93338 - 10.9475i) q^{58} +(0.782440 - 1.35522i) q^{59} +(-1.02074 + 0.589324i) q^{61} +(-12.0030 - 12.0030i) q^{62} -13.0438i q^{64} +(-7.75641 + 2.29997i) q^{65} +(0.762962 + 2.84741i) q^{67} +(-16.6546 - 4.46259i) q^{68} +(11.2838 - 7.06905i) q^{70} -3.13175 q^{71} +(0.417656 + 1.55871i) q^{73} +(15.7332 + 9.08359i) q^{74} -9.08114i q^{76} +(-1.24562 - 1.22194i) q^{77} +(6.17258 - 3.56374i) q^{79} +(-0.0434010 - 1.63948i) q^{80} +(4.12319 - 15.3880i) q^{82} +(2.14992 - 2.14992i) q^{83} +(-12.2300 - 2.93246i) q^{85} +(-13.5791 - 23.5197i) q^{86} +(1.52778 - 0.409367i) q^{88} +(2.24332 + 3.88554i) q^{89} +(-4.86559 - 8.24370i) q^{91} +(-0.608530 + 0.608530i) q^{92} +(-13.5651 + 23.4954i) q^{94} +(-0.175290 - 6.62160i) q^{95} +(-3.33893 - 3.33893i) q^{97} +(11.3521 + 10.9244i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8}+O(q^{10}) $ 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8	$ 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8} - 12 q^{10} + 8 q^{11} - 8 q^{22} + 8 q^{23} + 12 q^{25} - 24 q^{26} - 24 q^{28} + 24 q^{31} - 24 q^{32} - 44 q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 40 q^{43} - 40 q^{46} + 60 q^{47} - 72 q^{50} - 108 q^{52} + 24 q^{53} + 48 q^{56} + 4 q^{58} - 24 q^{61} + 4 q^{65} + 8 q^{67} - 132 q^{68} + 4 q^{70} + 16 q^{71} + 36 q^{73} - 60 q^{77} + 12 q^{80} + 12 q^{82} - 72 q^{85} + 16 q^{86} - 32 q^{88} - 24 q^{91} + 56 q^{92} + 12 q^{95} + 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8 - 12 * q^10 + 8 * q^11 - 8 * q^22 + 8 * q^23 + 12 * q^25 - 24 * q^26 - 24 * q^28 + 24 * q^31 - 24 * q^32 - 44 * q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 40 * q^43 - 40 * q^46 + 60 * q^47 - 72 * q^50 - 108 * q^52 + 24 * q^53 + 48 * q^56 + 4 * q^58 - 24 * q^61 + 4 * q^65 + 8 * q^67 - 132 * q^68 + 4 * q^70 + 16 * q^71 + 36 * q^73 - 60 * q^77 + 12 * q^80 + 12 * q^82 - 72 * q^85 + 16 * q^86 - 32 * q^88 - 24 * q^91 + 56 * q^92 + 12 * q^95 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.17399	−	0.582519i	−1.53724	−	0.411903i	−0.611869	−	0.790959i	$-0.709582\pi$
$2$	−2.17399	−	0.582519i	−1.53724	−	0.411903i	−0.925374	+	0.379056i	$0.876249\pi$
$3$		0			0
$3$		0			0
$4$	2.65485	+	1.53278i	1.32743	+	0.766391i
$5$	1.96540	+	1.06640i	0.878954	+	0.476907i
$5$	1.96540	+	1.06640i	0.878954	+	0.476907i
$6$		0			0
$7$	−0.660211	+	2.56205i	−0.249536	+	0.968365i
$7$	−0.660211	+	2.56205i	−0.249536	+	0.968365i
$8$	−1.69581	−	1.69581i	−0.599560	−	0.599560i
$9$		0			0
$10$	−3.65156	−	3.46322i	−1.15473	−	1.09517i
$11$	−0.329757	+	0.571155i	−0.0994253	+	0.172210i	−0.911447	−	0.411418i	$-0.865034\pi$
$11$	−0.329757	+	0.571155i	−0.0994253	+	0.172210i	0.812022	+	0.583627i	$0.198367\pi$
$12$		0			0
$13$	−2.55836	+	2.55836i	−0.709560	+	0.709560i	−0.966443	−	0.256882i	$-0.917305\pi$
$13$	−2.55836	+	2.55836i	−0.709560	+	0.709560i	0.256882	+	0.966443i	$0.417305\pi$
$14$	2.92774	−	5.18530i	0.782471	−	1.38583i
$15$		0			0
$16$	−0.366726	−	0.635189i	−0.0916816	−	0.158797i
$17$	−5.43281	+	1.45572i	−1.31765	+	0.353063i	−0.848097	−	0.529842i	$-0.822251\pi$
$17$	−5.43281	+	1.45572i	−1.31765	+	0.353063i	−0.469552	+	0.882905i	$0.655585\pi$
$18$		0			0
$19$	−1.48115	−	2.56543i	−0.339800	−	0.588551i	0.644595	−	0.764524i	$-0.277026\pi$
$19$	−1.48115	−	2.56543i	−0.339800	−	0.588551i	−0.984395	+	0.175973i	$0.943693\pi$
$20$	3.58330	+	5.84366i	0.801250	+	1.30668i
$21$		0			0
$22$	1.04960	−	1.04960i	0.223775	−	0.223775i
$23$	−0.0726580	+	0.271163i	−0.0151502	+	0.0565414i	−0.973087	−	0.230437i	$-0.925984\pi$
$23$	−0.0726580	+	0.271163i	−0.0151502	+	0.0565414i	0.957937	+	0.286979i	$0.0926510\pi$
$24$		0			0
$25$	2.72560	+	4.19179i	0.545119	+	0.838358i
$26$	7.05213	−	4.07155i	1.38304	−	0.798497i
$27$		0			0
$28$	−5.67983	+	5.78992i	−1.07339	+	1.09419i
$29$			5.03568i			0.935102i	0.883966	+	0.467551i	$0.154864\pi$
$29$			5.03568i			0.935102i	−0.883966	+	0.467551i	$0.845136\pi$
$30$		0			0
$31$	6.53164	+	3.77104i	1.17312	+	0.677299i	0.954412	−	0.298492i	$-0.0964835\pi$
$31$	6.53164	+	3.77104i	1.17312	+	0.677299i	0.218705	+	0.975791i	$0.429817\pi$
$32$	1.66867	+	6.22756i	0.294982	+	1.10089i
$33$		0			0
$34$	12.6589			2.17097
$35$	−4.02974	+	4.33141i	−0.681151	+	0.732143i
$36$		0			0
$37$	−7.79682	−	2.08915i	−1.28179	−	0.343454i	−0.447253	−	0.894408i	$-0.647598\pi$
$37$	−7.79682	−	2.08915i	−1.28179	−	0.343454i	−0.834536	+	0.550953i	$0.814264\pi$
$38$	1.72560	+	6.44003i	0.279929	+	1.04471i
$39$		0			0
$40$	−1.52454	−	5.14136i	−0.241051	−	0.812920i
$41$			7.07821i			1.10543i	0.833370	+	0.552715i	$0.186408\pi$
$41$			7.07821i			1.10543i	−0.833370	+	0.552715i	$0.813592\pi$
$42$		0			0
$43$	8.53242	+	8.53242i	1.30118	+	1.30118i	0.927595	+	0.373586i	$0.121872\pi$
$43$	8.53242	+	8.53242i	1.30118	+	1.30118i	0.373586	+	0.927595i	$0.378128\pi$
$44$	−1.75091	+	1.01089i	−0.263960	+	0.152397i
$45$		0			0
$46$	0.315915	−	0.547181i	0.0465792	−	0.0806775i
$47$	3.11986	−	11.6435i	0.455078	−	1.69838i	−0.232779	−	0.972530i	$-0.574782\pi$
$47$	3.11986	−	11.6435i	0.455078	−	1.69838i	0.687857	−	0.725846i	$-0.258551\pi$
$48$		0			0
$49$	−6.12824	−	3.38299i	−0.875463	−	0.483285i
$50$	−3.48362	−	10.7006i	−0.492659	−	1.51330i
$51$		0			0
$52$	−10.7135	+	2.87066i	−1.48569	+	0.398089i
$53$	4.65369	−	1.24695i	0.639233	−	0.171282i	0.0753771	−	0.997155i	$-0.475984\pi$
$53$	4.65369	−	1.24695i	0.639233	−	0.171282i	0.563856	+	0.825873i	$0.309317\pi$
$54$		0			0
$55$	−1.25718	+	0.770897i	−0.169518	+	0.103948i
$56$	5.46435	−	3.22517i	0.730205	−	0.430981i
$57$		0			0
$58$	2.93338	−	10.9475i	0.385171	−	1.43748i
$59$	0.782440	−	1.35522i	0.101865	−	0.176435i	−0.810588	−	0.585617i	$-0.800852\pi$
$59$	0.782440	−	1.35522i	0.101865	−	0.176435i	0.912453	+	0.409181i	$0.134186\pi$
$60$		0			0
$61$	−1.02074	+	0.589324i	−0.130692	+	0.0754553i	−0.563921	−	0.825829i	$-0.690708\pi$
$61$	−1.02074	+	0.589324i	−0.130692	+	0.0754553i	0.433228	+	0.901284i	$0.357374\pi$
$62$	−12.0030	−	12.0030i	−1.52438	−	1.52438i
$63$		0			0
$64$		−	13.0438i		−	1.63047i
$65$	−7.75641	+	2.29997i	−0.962065	+	0.285276i
$66$		0			0
$67$	0.762962	+	2.84741i	0.0932107	+	0.347867i	0.996742	−	0.0806549i	$-0.0257012\pi$
$67$	0.762962	+	2.84741i	0.0932107	+	0.347867i	−0.903531	+	0.428522i	$0.859034\pi$
$68$	−16.6546	−	4.46259i	−2.01967	−	0.541168i
$69$		0			0
$70$	11.2838	−	7.06905i	1.34867	−	0.844913i
$71$	−3.13175			−0.371671			−0.185835	−	0.982581i	$-0.559499\pi$
$71$	−3.13175			−0.371671			−0.185835	+	0.982581i	$0.559499\pi$
$72$		0			0
$73$	0.417656	+	1.55871i	0.0488830	+	0.182434i	0.986051	−	0.166446i	$-0.0532290\pi$
$73$	0.417656	+	1.55871i	0.0488830	+	0.182434i	−0.937168	+	0.348879i	$0.886562\pi$
$74$	15.7332	+	9.08359i	1.82895	+	1.05595i
$75$		0			0
$76$		−	9.08114i		−	1.04168i
$77$	−1.24562	−	1.22194i	−0.141952	−	0.139253i
$78$		0			0
$79$	6.17258	−	3.56374i	0.694469	−	0.400952i	−0.110815	−	0.993841i	$-0.535346\pi$
$79$	6.17258	−	3.56374i	0.694469	−	0.400952i	0.805284	+	0.592889i	$0.202013\pi$
$80$	−0.0434010	−	1.63948i	−0.00485238	−	0.183299i
$81$		0			0
$82$	4.12319	−	15.3880i	0.455330	−	1.69932i
$83$	2.14992	−	2.14992i	0.235985	−	0.235985i	−0.579200	−	0.815185i	$-0.696635\pi$
$83$	2.14992	−	2.14992i	0.235985	−	0.235985i	0.815185	+	0.579200i	$0.196635\pi$
$84$		0			0
$85$	−12.2300	−	2.93246i	−1.32653	−	0.318070i
$86$	−13.5791	−	23.5197i	−1.46427	−	2.53619i
$87$		0			0
$88$	1.52778	−	0.409367i	0.162862	−	0.0436386i
$89$	2.24332	+	3.88554i	0.237791	+	0.411867i	0.960080	−	0.279725i	$-0.0902432\pi$
$89$	2.24332	+	3.88554i	0.237791	+	0.411867i	−0.722289	+	0.691592i	$0.756910\pi$
$90$		0			0
$91$	−4.86559	−	8.24370i	−0.510052	−	0.864175i
$92$	−0.608530	+	0.608530i	−0.0634436	+	0.0634436i
$93$		0			0
$94$	−13.5651	+	23.4954i	−1.39913	+	2.42337i
$95$	−0.175290	−	6.62160i	−0.0179844	−	0.679362i
$96$		0			0
$97$	−3.33893	−	3.33893i	−0.339017	−	0.339017i	0.516980	−	0.855997i	$-0.327056\pi$
$97$	−3.33893	−	3.33893i	−0.339017	−	0.339017i	−0.855997	+	0.516980i	$0.827056\pi$
$98$	11.3521	+	10.9244i	1.14673	+	1.10353i
$99$		0			0
$100$	0.810963	+	15.3063i	0.0810963	+	1.53063i
$101$	2.24112	+	1.29391i	0.222999	+	0.128749i	0.607338	−	0.794443i	$-0.292237\pi$
$101$	2.24112	+	1.29391i	0.222999	+	0.128749i	−0.384339	+	0.923192i	$0.625571\pi$
$102$		0			0
$103$	−6.53180	−	1.75019i	−0.643597	−	0.172451i	−0.0777649	−	0.996972i	$-0.524778\pi$
$103$	−6.53180	−	1.75019i	−0.643597	−	0.172451i	−0.565832	+	0.824520i	$0.691445\pi$
$104$	8.67698			0.850848
$105$		0			0
$106$	−10.8434			−1.05321
$107$	16.3680	+	4.38579i	1.58235	+	0.423990i	0.939654	−	0.342128i	$-0.111147\pi$
$107$	16.3680	+	4.38579i	1.58235	+	0.423990i	0.642700	+	0.766118i	$0.277814\pi$
$108$		0			0
$109$	−4.90678	−	2.83293i	−0.469984	−	0.271346i	0.246249	−	0.969207i	$-0.420802\pi$
$109$	−4.90678	−	2.83293i	−0.469984	−	0.271346i	−0.716233	+	0.697861i	$0.754135\pi$
$110$	3.18216	−	0.943591i	0.303407	−	0.0899679i
$111$		0			0
$112$	1.86951	−	0.520214i	0.176652	−	0.0491556i
$113$	3.42048	+	3.42048i	0.321771	+	0.321771i	0.849446	−	0.527675i	$-0.176936\pi$
$113$	3.42048	+	3.42048i	0.321771	+	0.321771i	−0.527675	+	0.849446i	$0.676936\pi$
$114$		0			0
$115$	−0.431969	+	0.455462i	−0.0402814	+	0.0424720i
$116$	−7.71859	+	13.3690i	−0.716653	+	1.24128i
$117$		0			0
$118$	−2.49046	+	2.49046i	−0.229265	+	0.229265i
$119$	−0.142824	−	14.8802i	−0.0130927	−	1.36407i
$120$		0			0
$121$	5.28252	+	9.14960i	0.480229	+	0.831781i
$122$	2.56237	−	0.686585i	0.231986	−	0.0621605i
$123$		0			0
$124$	11.5604	+	20.0231i	1.03815	+	1.79813i
$125$	0.886775	+	11.1451i	0.0793156	+	0.996850i
$126$		0			0
$127$	7.59890	−	7.59890i	0.674294	−	0.674294i	−0.284409	−	0.958703i	$-0.591797\pi$
$127$	7.59890	−	7.59890i	0.674294	−	0.674294i	0.958703	+	0.284409i	$0.0917975\pi$
$128$	−4.26091	+	15.9019i	−0.376615	+	1.40555i
$129$		0			0
$130$	18.2021	−	0.481856i	1.59643	−	0.0422616i
$131$	−2.18517	+	1.26161i	−0.190919	+	0.110227i	−0.592413	−	0.805635i	$-0.701824\pi$
$131$	−2.18517	+	1.26161i	−0.190919	+	0.110227i	0.401494	+	0.915862i	$0.368491\pi$
$132$		0			0
$133$	7.55066	−	2.10107i	0.654725	−	0.182186i
$134$		−	6.63469i		−	0.573150i
$135$		0			0
$136$	11.6816	+	6.74440i	1.00169	+	0.578327i
$137$	0.385322	+	1.43804i	0.0329203	+	0.122860i	0.980431	−	0.196865i	$-0.0630761\pi$
$137$	0.385322	+	1.43804i	0.0329203	+	0.122860i	−0.947510	+	0.319725i	$0.896409\pi$
$138$		0			0
$139$	0.596354			0.0505821			0.0252910	−	0.999680i	$-0.491949\pi$
$139$	0.596354			0.0505821			0.0252910	+	0.999680i	$0.491949\pi$
$140$	−17.3375	+	5.32256i	−1.46529	+	0.449838i
$141$		0			0
$142$	6.80840	+	1.82430i	0.571348	+	0.153092i
$143$	−0.617583	−	2.30485i	−0.0516449	−	0.192741i
$144$		0			0
$145$	−5.37003	+	9.89712i	−0.445957	+	0.821911i
$146$		−	3.63192i		−	0.300580i
$147$		0			0
$148$	−17.4972	−	17.4972i	−1.43826	−	1.43826i
$149$	9.59905	−	5.54201i	0.786385	−	0.454020i	−0.0523034	−	0.998631i	$-0.516656\pi$
$149$	9.59905	−	5.54201i	0.786385	−	0.454020i	0.838688	+	0.544612i	$0.183323\pi$
$150$		0			0
$151$	−5.29957	+	9.17912i	−0.431273	+	0.746986i	−0.996983	−	0.0776177i	$-0.975269\pi$
$151$	−5.29957	+	9.17912i	−0.431273	+	0.746986i	0.565710	+	0.824604i	$0.308602\pi$
$152$	−1.83873	+	6.86225i	−0.149141	+	0.556602i
$153$		0			0
$154$	1.99617	+	3.38208i	0.160856	+	0.272536i
$155$	8.81586	+	14.3769i	0.708107	+	1.15478i
$156$		0			0
$157$	14.4473	−	3.87114i	1.15302	−	0.308950i	0.368844	−	0.929491i	$-0.379754\pi$
$157$	14.4473	−	3.87114i	1.15302	−	0.308950i	0.784174	+	0.620541i	$0.213087\pi$
$158$	−15.4951	+	4.15189i	−1.23272	+	0.330307i
$159$		0			0
$160$	−3.36145	+	14.0191i	−0.265746	+	1.10831i
$161$	−0.646765	−	0.365179i	−0.0509722	−	0.0287801i
$162$		0			0
$163$	3.22643	−	12.0412i	0.252714	−	0.943140i	−0.716635	−	0.697449i	$-0.754318\pi$
$163$	3.22643	−	12.0412i	0.252714	−	0.943140i	0.969348	−	0.245691i	$-0.0790149\pi$
$164$	−10.8493	+	18.7916i	−0.847191	+	1.46738i
$165$		0			0
$166$	−5.92629	+	3.42154i	−0.459969	+	0.265563i
$167$	−6.09391	−	6.09391i	−0.471561	−	0.471561i	0.430859	−	0.902419i	$-0.358211\pi$
$167$	−6.09391	−	6.09391i	−0.471561	−	0.471561i	−0.902419	+	0.430859i	$0.858211\pi$
$168$		0			0
$169$		−	0.0903667i		−	0.00695128i
$170$	24.8797	+	13.4994i	1.90819	+	1.03535i
$171$		0			0
$172$	9.57400	+	35.7307i	0.730011	+	2.72444i
$173$	−19.1602	−	5.13396i	−1.45672	−	0.390328i	−0.558366	−	0.829594i	$-0.688572\pi$
$173$	−19.1602	−	5.13396i	−1.45672	−	0.390328i	−0.898357	+	0.439267i	$0.855238\pi$
$174$		0			0
$175$	−12.5391	+	4.21566i	−0.947864	+	0.318674i
$176$	0.483722			0.0364619
$177$		0			0
$178$	−2.61355	−	9.75391i	−0.195894	−	0.731087i
$179$	−14.5197	−	8.38294i	−1.08525	−	0.626571i	−0.152944	−	0.988235i	$-0.548875\pi$
$179$	−14.5197	−	8.38294i	−1.08525	−	0.626571i	−0.932308	+	0.361664i	$0.882209\pi$
$180$		0			0
$181$		−	3.85987i		−	0.286902i	−0.989657	−	0.143451i	$-0.954180\pi$
$181$		−	3.85987i		−	0.286902i	0.989657	−	0.143451i	$-0.0458200\pi$
$182$	5.77564	+	20.7560i	0.428119	+	1.53854i
$183$		0			0
$184$	0.583056	−	0.336627i	0.0429835	−	0.0248165i
$185$	−13.0960	−	12.4205i	−0.962837	−	0.913175i
$186$		0			0
$187$	0.960064	−	3.58301i	0.0702068	−	0.262015i
$188$	26.1297	−	26.1297i	1.90570	−	1.90570i
$189$		0			0
$190$	−3.47613	+	14.4974i	−0.252185	+	1.05175i
$191$	−0.668876	−	1.15853i	−0.0483982	−	0.0838281i	0.840811	−	0.541328i	$-0.182078\pi$
$191$	−0.668876	−	1.15853i	−0.0483982	−	0.0838281i	−0.889210	+	0.457500i	$0.848745\pi$
$192$		0			0
$193$	23.8973	−	6.40325i	1.72016	−	0.460916i	0.742283	−	0.670087i	$-0.233743\pi$
$193$	23.8973	−	6.40325i	1.72016	−	0.460916i	0.977879	+	0.209171i	$0.0670764\pi$
$194$	5.31381	+	9.20379i	0.381509	+	0.660794i
$195$		0			0
$196$	−11.0842	−	18.3746i	−0.791729	−	1.31247i
$197$	4.58820	−	4.58820i	0.326896	−	0.326896i	−0.524509	−	0.851405i	$-0.675751\pi$
$197$	4.58820	−	4.58820i	0.326896	−	0.326896i	0.851405	+	0.524509i	$0.175751\pi$
$198$		0			0
$199$	2.40686	−	4.16881i	0.170618	−	0.295519i	−0.768018	−	0.640428i	$-0.778757\pi$
$199$	2.40686	−	4.16881i	0.170618	−	0.295519i	0.938636	+	0.344909i	$0.112090\pi$
$200$	2.48639	−	11.7306i	0.175814	−	0.829478i
$201$		0			0
$202$	−4.11844	−	4.11844i	−0.289772	−	0.289772i
$203$	−12.9017	−	3.32461i	−0.905520	−	0.233342i
$204$		0			0
$205$	−7.54818	+	13.9115i	−0.527188	+	0.971622i
$206$	13.1805	+	7.60979i	0.918332	+	0.530199i
$207$		0			0
$208$	2.56326	+	0.686822i	0.177730	+	0.0476226i
$209$	1.95368			0.135139
$210$		0			0
$211$	16.1407			1.11117			0.555586	−	0.831459i	$-0.312494\pi$
$211$	16.1407			1.11117			0.555586	+	0.831459i	$0.312494\pi$
$212$	14.2662	+	3.82261i	0.979804	+	0.262538i
$213$		0			0
$214$	−33.0291	−	19.0693i	−2.25782	−	1.30355i
$215$	7.67068	+	25.8686i	0.523136	+	1.76422i
$216$		0			0
$217$	−13.9739	+	14.2447i	−0.948609	+	0.966995i
$218$	9.01706	+	9.01706i	0.610712	+	0.610712i
$219$		0			0
$220$	−4.51925	+	0.119636i	−0.304688	+	0.00806585i
$221$	10.1748	−	17.6233i	0.684432	−	1.18547i
$222$		0			0
$223$	−8.13715	+	8.13715i	−0.544904	+	0.544904i	−0.924962	−	0.380059i	$-0.875904\pi$
$223$	−8.13715	+	8.13715i	−0.544904	+	0.544904i	0.380059	+	0.924962i	$0.375904\pi$
$224$	−17.0570	+	0.163718i	−1.13967	+	0.0109389i
$225$		0			0
$226$	−5.44359	−	9.42858i	−0.362102	−	0.627180i
$227$	−2.28305	+	0.611740i	−0.151531	+	0.0406026i	−0.333787	−	0.942648i	$-0.608327\pi$
$227$	−2.28305	+	0.611740i	−0.151531	+	0.0406026i	0.182256	+	0.983251i	$0.441660\pi$
$228$		0			0
$229$	4.10206	+	7.10498i	0.271072	+	0.469511i	0.969137	−	0.246524i	$-0.0792885\pi$
$229$	4.10206	+	7.10498i	0.271072	+	0.469511i	−0.698065	+	0.716035i	$0.745955\pi$
$230$	1.20441	−	0.738540i	0.0794166	−	0.0486979i
$231$		0			0
$232$	8.53956	−	8.53956i	0.560650	−	0.560650i
$233$	6.76568	−	25.2499i	0.443234	−	1.65417i	−0.277322	−	0.960777i	$-0.589447\pi$
$233$	6.76568	−	25.2499i	0.443234	−	1.65417i	0.720557	−	0.693396i	$-0.243886\pi$
$234$		0			0
$235$	18.5483	−	19.5571i	1.20996	−	1.27576i
$236$	4.15453	−	2.39862i	0.270437	−	0.156137i
$237$		0			0
$238$	−8.35751	+	32.4327i	−0.541737	+	2.10230i
$239$		−	11.3000i		−	0.730938i	−0.930824	−	0.365469i	$-0.880909\pi$
$239$		−	11.3000i		−	0.730938i	0.930824	−	0.365469i	$-0.119091\pi$
$240$		0			0
$241$	−20.3500	−	11.7491i	−1.31086	−	0.756825i	−0.328621	−	0.944462i	$-0.606584\pi$
$241$	−20.3500	−	11.7491i	−1.31086	−	0.756825i	−0.982239	+	0.187636i	$0.939917\pi$
$242$	−6.15434	−	22.9683i	−0.395616	−	1.47646i
$243$		0			0
$244$	−3.61322			−0.231313
$245$	−8.43684	−	13.1841i	−0.539010	−	0.842300i
$246$		0			0
$247$	10.3526	+	2.77397i	0.658721	+	0.176504i
$248$	−4.68145	−	17.4714i	−0.297272	−	1.10944i
$249$		0			0
$250$	4.56440	−	24.7459i	0.288678	−	1.56507i
$251$			2.83197i			0.178752i	0.995998	+	0.0893761i	$0.0284873\pi$
$251$			2.83197i			0.178752i	−0.995998	+	0.0893761i	$0.971513\pi$
$252$		0			0
$253$	−0.130917	−	0.130917i	−0.00823067	−	0.00823067i
$254$	−20.9464	+	12.0934i	−1.31430	+	0.758810i
$255$		0			0
$256$	5.48258	−	9.49610i	0.342661	−	0.593506i
$257$	−5.50524	+	20.5458i	−0.343407	+	1.28161i	0.551055	+	0.834469i	$0.314226\pi$
$257$	−5.50524	+	20.5458i	−0.343407	+	1.28161i	−0.894462	+	0.447144i	$0.852441\pi$
$258$		0			0
$259$	10.5001	−	18.5966i	0.652442	−	1.15554i
$260$	−24.1175	−	5.78280i	−1.49570	−	0.358634i
$261$		0			0
$262$	5.48544	−	1.46982i	0.338892	−	0.0908058i
$263$	30.2454	−	8.10423i	1.86501	−	0.499728i	0.865013	−	0.501750i	$-0.167310\pi$
$263$	30.2454	−	8.10423i	1.86501	−	0.499728i	0.999998	+	0.00202161i	$0.000643499\pi$
$264$		0			0
$265$	10.4761	+	2.51192i	0.643542	+	0.154306i
$266$	−17.6390	+	0.169303i	−1.08151	+	0.0103807i
$267$		0			0
$268$	−2.33891	+	8.72892i	−0.142872	+	0.533204i
$269$	−3.19483	+	5.53361i	−0.194792	+	0.337390i	−0.946832	−	0.321727i	$-0.895737\pi$
$269$	−3.19483	+	5.53361i	−0.194792	+	0.337390i	0.752040	+	0.659117i	$0.229070\pi$
$270$		0			0
$271$	0.769821	−	0.444456i	0.0467633	−	0.0269988i	−0.476436	−	0.879209i	$-0.658072\pi$
$271$	0.769821	−	0.444456i	0.0467633	−	0.0269988i	0.523199	+	0.852210i	$0.324738\pi$
$272$	2.91701	+	2.91701i	0.176870	+	0.176870i
$273$		0			0
$274$		−	3.35074i		−	0.202426i
$275$	−3.29295	+	0.174467i	−0.198572	+	0.0105208i
$276$		0			0
$277$	−3.82551	−	14.2770i	−0.229852	−	0.857821i	−0.980402	−	0.197007i	$-0.936878\pi$
$277$	−3.82551	−	14.2770i	−0.229852	−	0.857821i	0.750550	−	0.660814i	$-0.229789\pi$
$278$	−1.29647	−	0.347387i	−0.0777569	−	0.0208349i
$279$		0			0
$280$	14.1790	−	0.511576i	0.847354	−	0.0305725i
$281$	13.9226			0.830552			0.415276	−	0.909695i	$-0.363685\pi$
$281$	13.9226			0.830552			0.415276	+	0.909695i	$0.363685\pi$
$282$		0			0
$283$	−0.391632	−	1.46159i	−0.0232801	−	0.0868825i	0.953308	−	0.301998i	$-0.0976537\pi$
$283$	−0.391632	−	1.46159i	−0.0232801	−	0.0868825i	−0.976589	+	0.215116i	$0.930987\pi$
$284$	−8.31435	−	4.80029i	−0.493366	−	0.284845i
$285$		0			0
$286$			5.37048i			0.317563i
$287$	−18.1348	−	4.67311i	−1.07046	−	0.275845i
$288$		0			0
$289$	12.6738	−	7.31725i	0.745520	−	0.430426i
$290$	17.4397	−	18.3881i	1.02409	−	1.07979i
$291$		0			0
$292$	−1.28035	+	4.77834i	−0.0749269	+	0.279631i
$293$	−22.9823	+	22.9823i	−1.34264	+	1.34264i	−0.449222	+	0.893420i	$0.648299\pi$
$293$	−22.9823	+	22.9823i	−1.34264	+	1.34264i	−0.893420	+	0.449222i	$0.851701\pi$
$294$		0			0
$295$	2.98301	−	1.82917i	0.173678	−	0.106498i
$296$	9.67913	+	16.7647i	0.562588	+	0.974431i
$297$		0			0
$298$	−24.0966	+	6.45666i	−1.39588	+	0.374024i
$299$	−0.507847	−	0.879617i	−0.0293695	−	0.0508695i
$300$		0			0
$301$	−27.4937	+	16.2273i	−1.58471	+	0.935327i
$302$	16.8682	−	16.8682i	0.970657	−	0.970657i
$303$		0			0
$304$	−1.08636	+	1.88163i	−0.0623068	+	0.107919i
$305$	−2.63462	+	0.0697449i	−0.150858	+	0.00399358i
$306$		0			0
$307$	−11.9575	−	11.9575i	−0.682451	−	0.682451i	0.278101	−	0.960552i	$-0.410295\pi$
$307$	−11.9575	−	11.9575i	−0.682451	−	0.682451i	−0.960552	+	0.278101i	$0.910295\pi$
$308$	−1.43398	−	5.15333i	−0.0817087	−	0.293638i
$309$		0			0
$310$	−10.7908	−	36.3907i	−0.612874	−	2.06685i
$311$	12.7204	+	7.34413i	0.721308	+	0.416448i	0.815234	−	0.579132i	$-0.196608\pi$
$311$	12.7204	+	7.34413i	0.721308	+	0.416448i	−0.0939257	+	0.995579i	$0.529942\pi$
$312$		0			0
$313$	2.64092	+	0.707633i	0.149274	+	0.0399978i	0.332682	−	0.943039i	$-0.392046\pi$
$313$	2.64092	+	0.707633i	0.149274	+	0.0399978i	−0.183408	+	0.983037i	$0.558713\pi$
$314$	−33.6633			−1.89973
$315$		0			0
$316$	21.8497			1.22914
$317$	−1.92350	−	0.515400i	−0.108034	−	0.0289477i	0.204397	−	0.978888i	$-0.434477\pi$
$317$	−1.92350	−	0.515400i	−0.108034	−	0.0289477i	−0.312431	+	0.949940i	$0.601143\pi$
$318$		0			0
$319$	−2.87615	−	1.66055i	−0.161034	−	0.0929728i
$320$	13.9099	−	25.6363i	0.777584	−	1.43311i
$321$		0			0
$322$	1.19334	+	1.17065i	0.0665021	+	0.0652376i
$323$	11.7814	+	11.7814i	0.655533	+	0.655533i
$324$		0			0
$325$	−17.6971	−	3.75105i	−0.981661	−	0.208071i
$326$	−14.0285	+	24.2980i	−0.776965	+	1.34574i
$327$		0			0
$328$	12.0033	−	12.0033i	0.662772	−	0.662772i
$329$	27.7715	+	15.6804i	1.53109	+	0.864489i
$330$		0			0
$331$	6.64077	+	11.5022i	0.365010	+	0.632215i	0.988778	−	0.149394i	$-0.0477323\pi$
$331$	6.64077	+	11.5022i	0.365010	+	0.632215i	−0.623768	+	0.781610i	$0.714399\pi$
$332$	9.00310	−	2.41237i	0.494109	−	0.132396i
$333$		0			0
$334$	9.69828	+	16.7979i	0.530666	+	0.919141i
$335$	−1.53695	+	6.40993i	−0.0839724	+	0.350212i
$336$		0			0
$337$	−5.32066	+	5.32066i	−0.289835	+	0.289835i	−0.837015	−	0.547180i	$-0.815701\pi$
$337$	−5.32066	+	5.32066i	−0.289835	+	0.289835i	0.547180	+	0.837015i	$0.315701\pi$
$338$	−0.0526403	+	0.196456i	−0.00286325	+	0.0106858i
$339$		0			0
$340$	−27.9741	−	26.5312i	−1.51711	−	1.43886i
$341$	−4.30770	+	2.48705i	−0.233275	+	0.134681i
$342$		0			0
$343$	12.7133	−	13.4674i	0.686456	−	0.727171i
$344$		−	28.9388i		−	1.56027i
$345$		0			0
$346$	38.6635	+	22.3224i	2.07856	+	1.20006i
$347$	5.24264	+	19.5658i	0.281439	+	1.05035i	0.951402	+	0.307952i	$0.0996435\pi$
$347$	5.24264	+	19.5658i	0.281439	+	1.05035i	−0.669963	+	0.742395i	$0.733690\pi$
$348$		0			0
$349$	−3.47123			−0.185811			−0.0929054	−	0.995675i	$-0.529615\pi$
$349$	−3.47123			−0.185811			−0.0929054	+	0.995675i	$0.529615\pi$
$350$	29.7155	−	1.86055i	1.58836	−	0.0994508i
$351$		0			0
$352$	−4.10716	−	1.10051i	−0.218912	−	0.0586574i
$353$	0.624808	+	2.33182i	0.0332552	+	0.124110i	0.980558	−	0.196229i	$-0.0628697\pi$
$353$	0.624808	+	2.33182i	0.0332552	+	0.124110i	−0.947303	+	0.320339i	$0.896203\pi$
$354$		0			0
$355$	−6.15515	−	3.33969i	−0.326681	−	0.177252i
$356$			13.7541i			0.728965i
$357$		0			0
$358$	26.6824	+	26.6824i	1.41021	+	1.41021i
$359$	−6.84204	+	3.95025i	−0.361109	+	0.208486i	−0.669567	−	0.742752i	$-0.733520\pi$
$359$	−6.84204	+	3.95025i	−0.361109	+	0.208486i	0.308458	+	0.951238i	$0.400187\pi$
$360$		0			0
$361$	5.11237	−	8.85488i	0.269072	−	0.466046i
$362$	−2.24845	+	8.39133i	−0.118176	+	0.441039i
$363$		0			0
$364$	−0.281649	−	29.3437i	−0.0147624	−	1.53803i
$365$	−0.841346	+	3.50889i	−0.0440381	+	0.183663i
$366$		0			0
$367$	19.2082	−	5.14683i	1.00266	−	0.268662i	0.280102	−	0.959970i	$-0.409632\pi$
$367$	19.2082	−	5.14683i	1.00266	−	0.268662i	0.722560	+	0.691308i	$0.242965\pi$
$368$	0.198885	−	0.0532912i	0.0103676	−	0.00277800i
$369$		0			0
$370$	21.2354	+	34.6308i	1.10398	+	1.80037i
$371$	0.122342	+	12.7463i	0.00635167	+	0.661752i
$372$		0			0
$373$	−4.91241	+	18.3334i	−0.254355	+	0.949266i	0.714093	+	0.700051i	$0.246839\pi$
$373$	−4.91241	+	18.3334i	−0.254355	+	0.949266i	−0.968448	+	0.249215i	$0.919827\pi$
$374$	−4.17434	+	7.23017i	−0.215850	+	0.373863i
$375$		0			0
$376$	−25.0358	+	14.4544i	−1.29112	+	0.745431i
$377$	−12.8831	−	12.8831i	−0.663511	−	0.663511i
$378$		0			0
$379$			19.5011i			1.00171i	0.865533	+	0.500853i	$0.166980\pi$
$379$			19.5011i			1.00171i	−0.865533	+	0.500853i	$0.833020\pi$
$380$	9.68410	−	17.8481i	0.496784	−	0.915587i
$381$		0			0
$382$	0.779266	+	2.90826i	0.0398707	+	0.148800i
$383$	17.1955	+	4.60753i	0.878651	+	0.235434i	0.669825	−	0.742519i	$-0.266369\pi$
$383$	17.1955	+	4.60753i	0.878651	+	0.235434i	0.208826	+	0.977953i	$0.433036\pi$
$384$		0			0
$385$	−1.14508	−	3.72992i	−0.0583584	−	0.190094i
$386$	−55.6824			−2.83416
$387$		0			0
$388$	−3.74652	−	13.9822i	−0.190201	−	0.709840i
$389$	−9.12743	−	5.26972i	−0.462779	−	0.267186i	0.250433	−	0.968134i	$-0.419427\pi$
$389$	−9.12743	−	5.26972i	−0.462779	−	0.267186i	−0.713212	+	0.700948i	$0.752760\pi$
$390$		0			0
$391$		−	1.57895i		−	0.0798507i
$392$	4.65543	+	16.1293i	0.235135	+	0.814651i
$393$		0			0
$394$	−12.6474	+	7.30199i	−0.637168	+	0.367869i
$395$	15.9319	−	0.421758i	0.801623	−	0.0212210i
$396$		0			0
$397$	−5.17474	+	19.3124i	−0.259713	+	0.969261i	0.705695	+	0.708516i	$0.250635\pi$
$397$	−5.17474	+	19.3124i	−0.259713	+	0.969261i	−0.965408	+	0.260745i	$0.916032\pi$
$398$	−7.66091	+	7.66091i	−0.384007	+	0.384007i
$399$		0			0
$400$	1.66303	−	3.26851i	0.0831516	−	0.163425i
$401$	9.36197	+	16.2154i	0.467515	+	0.809759i	0.999311	−	0.0371131i	$-0.0118162\pi$
$401$	9.36197	+	16.2154i	0.467515	+	0.809759i	−0.531796	+	0.846872i	$0.678483\pi$
$402$		0			0
$403$	−26.3579	+	7.06259i	−1.31298	+	0.351812i
$404$	3.96656	+	6.87028i	0.197344	+	0.341809i
$405$		0			0
$406$	26.1115	+	14.7431i	1.29589	+	0.731690i
$407$	3.76428	−	3.76428i	0.186588	−	0.186588i
$408$		0			0
$409$	−17.2861	+	29.9403i	−0.854741	+	1.48045i	0.0221442	+	0.999755i	$0.492951\pi$
$409$	−17.2861	+	29.9403i	−0.854741	+	1.48045i	−0.876885	+	0.480700i	$0.840383\pi$
$410$	24.5134	−	25.8465i	1.21063	−	1.27647i
$411$		0			0
$412$	−14.6583	−	14.6583i	−0.722163	−	0.722163i
$413$	2.95558	+	2.89939i	0.145435	+	0.142670i
$414$		0			0
$415$	6.51813	−	1.93279i	0.319963	−	0.0948769i
$416$	−20.2014	−	11.6633i	−0.990454	−	0.571839i
$417$		0			0
$418$	−4.24728	−	1.13806i	−0.207741	−	0.0556642i
$419$	1.14439			0.0559069			0.0279535	−	0.999609i	$-0.491101\pi$
$419$	1.14439			0.0559069			0.0279535	+	0.999609i	$0.491101\pi$
$420$		0			0
$421$	17.3376			0.844984			0.422492	−	0.906367i	$-0.361155\pi$
$421$	17.3376			0.844984			0.422492	+	0.906367i	$0.361155\pi$
$422$	−35.0897	−	9.40226i	−1.70814	−	0.457695i
$423$		0			0
$424$	−10.0064	−	5.77718i	−0.485952	−	0.280565i
$425$	−20.9097	−	18.8055i	−1.01427	−	0.912201i
$426$		0			0
$427$	−0.835977	−	3.00427i	−0.0404558	−	0.145387i
$428$	36.7322	+	36.7322i	1.77552	+	1.77552i
$429$		0			0
$430$	−1.60705	−	60.7063i	−0.0774987	−	2.92752i
$431$	−10.4011	+	18.0153i	−0.501005	+	0.867766i	0.498995	+	0.866605i	$0.333703\pi$
$431$	−10.4011	+	18.0153i	−0.501005	+	0.867766i	−0.999999	+	0.00116059i	$0.999631\pi$
$432$		0			0
$433$	23.2262	−	23.2262i	1.11618	−	1.11618i	0.123883	−	0.992297i	$-0.460465\pi$
$433$	23.2262	−	23.2262i	1.11618	−	1.11618i	0.992297	−	0.123883i	$-0.0395349\pi$
$434$	38.6769	−	22.8279i	1.85655	−	1.09577i
$435$		0			0
$436$	−8.68453	−	15.0420i	−0.415913	−	0.720383i
$437$	0.803269	−	0.215235i	0.0384256	−	0.0102961i
$438$		0			0
$439$	−3.87326	−	6.70868i	−0.184861	−	0.320188i	0.758669	−	0.651476i	$-0.225850\pi$
$439$	−3.87326	−	6.70868i	−0.184861	−	0.320188i	−0.943530	+	0.331288i	$0.892517\pi$
$440$	3.43924	+	0.824647i	0.163959	+	0.0393135i
$441$		0			0
$442$	−32.3858	+	32.3858i	−1.54044	+	1.54044i
$443$	1.80076	−	6.72052i	0.0855566	−	0.319302i	−0.909862	−	0.414910i	$-0.863813\pi$
$443$	1.80076	−	6.72052i	0.0855566	−	0.319302i	0.995419	+	0.0956084i	$0.0304797\pi$
$444$		0			0
$445$	0.265491	+	10.0289i	0.0125855	+	0.475416i
$446$	22.4301	−	12.9500i	1.06210	−	0.613202i
$447$		0			0
$448$	33.4189	+	8.61165i	1.57889	+	0.406862i
$449$			5.42872i			0.256197i	0.991761	+	0.128099i	$0.0408874\pi$
$449$			5.42872i			0.256197i	−0.991761	+	0.128099i	$0.959113\pi$
$450$		0			0
$451$	−4.04276	−	2.33409i	−0.190366	−	0.109908i
$452$	3.83803	+	14.3237i	0.180526	+	0.673731i
$453$		0			0
$454$	5.31967			0.249664
$455$	−0.771779	−	21.3908i	−0.0361816	−	1.00282i
$456$		0			0
$457$	−28.6586	−	7.67904i	−1.34059	−	0.359211i	−0.483938	−	0.875102i	$-0.660794\pi$
$457$	−28.6586	−	7.67904i	−1.34059	−	0.359211i	−0.856654	+	0.515892i	$0.827461\pi$
$458$	−4.77906	−	17.8357i	−0.223311	−	0.833407i
$459$		0			0
$460$	−1.84494	+	0.547071i	−0.0860208	+	0.0255073i
$461$		−	19.9799i		−	0.930558i	−0.885164	−	0.465279i	$-0.845954\pi$
$461$		−	19.9799i		−	0.930558i	0.885164	−	0.465279i	$-0.154046\pi$
$462$		0			0
$463$	−9.88604	−	9.88604i	−0.459443	−	0.459443i	0.439029	−	0.898473i	$-0.355322\pi$
$463$	−9.88604	−	9.88604i	−0.459443	−	0.459443i	−0.898473	+	0.439029i	$0.855322\pi$
$464$	3.19861	−	1.84672i	0.148492	−	0.0857317i
$465$		0			0
$466$	−29.4170	+	50.9518i	−1.36272	+	2.36030i
$467$	−3.28895	+	12.2745i	−0.152194	+	0.567997i	0.847135	+	0.531378i	$0.178326\pi$
$467$	−3.28895	+	12.2745i	−0.152194	+	0.567997i	−0.999329	+	0.0366194i	$0.988341\pi$
$468$		0			0
$469$	−7.79894	+	0.0748563i	−0.360122	+	0.00345654i
$470$	−51.7163	+	31.7122i	−2.38549	+	1.46277i
$471$		0			0
$472$	−3.62508	+	0.971336i	−0.166858	+	0.0447094i
$473$	−7.68696	+	2.05971i	−0.353447	+	0.0947057i
$474$		0			0
$475$	6.71674	−	13.2010i	0.308185	−	0.605705i
$476$	22.4289	−	39.7237i	1.02803	−	1.82074i
$477$		0			0
$478$	−6.58248	+	24.5661i	−0.301075	+	1.12363i
$479$	3.94391	−	6.83105i	0.180202	−	0.312119i	−0.761747	−	0.647874i	$-0.775658\pi$
$479$	3.94391	−	6.83105i	0.180202	−	0.312119i	0.941949	+	0.335755i	$0.108992\pi$
$480$		0			0
$481$	25.2918	−	14.6022i	1.15321	−	0.665805i
$482$	37.3967	+	37.3967i	1.70337	+	1.70337i
$483$		0			0
$484$			32.3878i			1.47217i
$485$	−3.00171	−	10.1230i	−0.136301	−	0.459660i
$486$		0			0
$487$	1.91775	+	7.15715i	0.0869016	+	0.324321i	0.995668	−	0.0929851i	$-0.0296409\pi$
$487$	1.91775	+	7.15715i	0.0869016	+	0.324321i	−0.908766	+	0.417306i	$0.862974\pi$
$488$	2.73037	+	0.731599i	0.123598	+	0.0331179i
$489$		0			0
$490$	10.6616	+	33.5767i	0.481643	+	1.51684i
$491$	−4.11130			−0.185541			−0.0927703	−	0.995688i	$-0.529572\pi$
$491$	−4.11130			−0.185541			−0.0927703	+	0.995688i	$0.529572\pi$
$492$		0			0
$493$	−7.33052	−	27.3579i	−0.330150	−	1.23214i
$494$	−20.8906	−	12.0612i	−0.939912	−	0.542658i
$495$		0			0
$496$		−	5.53177i		−	0.248384i
$497$	2.06762	−	8.02372i	0.0927453	−	0.359913i
$498$		0			0
$499$	28.3458	−	16.3655i	1.26893	−	0.732619i	0.294147	−	0.955760i	$-0.404964\pi$
$499$	28.3458	−	16.3655i	1.26893	−	0.732619i	0.974786	+	0.223141i	$0.0716311\pi$
$500$	−14.7288	+	30.9479i	−0.658690	+	1.38403i
$501$		0			0
$502$	1.64967	−	6.15667i	0.0736285	−	0.274785i
$503$	17.7907	−	17.7907i	0.793246	−	0.793246i	−0.188774	−	0.982021i	$-0.560451\pi$
$503$	17.7907	−	17.7907i	0.793246	−	0.793246i	0.982021	+	0.188774i	$0.0604514\pi$
$504$		0			0
$505$	3.02487	+	4.93297i	0.134605	+	0.219514i
$506$	0.208350	+	0.360873i	0.00926230	+	0.0160428i
$507$		0			0
$508$	31.8214	−	8.52653i	1.41185	−	0.378303i
$509$	−7.18464	−	12.4442i	−0.318454	−	0.551578i	0.661712	−	0.749758i	$-0.269830\pi$
$509$	−7.18464	−	12.4442i	−0.318454	−	0.551578i	−0.980166	+	0.198180i	$0.936497\pi$
$510$		0			0
$511$	−4.26925	+	0.0409774i	−0.188861	+	0.00181273i
$512$	5.83133	−	5.83133i	0.257711	−	0.257711i
$513$		0			0
$514$	23.9367	−	41.4595i	1.05580	−	1.82870i
$515$	−10.9712	−	10.4053i	−0.483449	−	0.458513i
$516$		0			0
$517$	5.62144	+	5.62144i	0.247231	+	0.247231i
$518$	−33.6599	+	34.3123i	−1.47893	+	1.50760i
$519$		0			0
$520$	17.0537	+	9.25310i	0.747856	+	0.405775i
$521$	18.7050	+	10.7993i	0.819480	+	0.473127i	0.850237	−	0.526400i	$-0.176458\pi$
$521$	18.7050	+	10.7993i	0.819480	+	0.473127i	−0.0307570	+	0.999527i	$0.509792\pi$
$522$		0			0
$523$	−36.7310	−	9.84203i	−1.60613	−	0.430362i	−0.659245	−	0.751928i	$-0.729124\pi$
$523$	−36.7310	−	9.84203i	−1.60613	−	0.430362i	−0.946887	+	0.321566i	$0.895791\pi$
$524$	−7.73507			−0.337908
$525$		0			0
$526$	−70.4741			−3.07281
$527$	−40.9747	−	10.9791i	−1.78489	−	0.478259i
$528$		0			0
$529$	19.8503	+	11.4606i	0.863058	+	0.498287i
$530$	−21.3117	−	11.5634i	−0.925721	−	0.502283i
$531$		0			0
$532$	23.2664	+	5.99547i	1.00873	+	0.259937i
$533$	−18.1086	−	18.1086i	−0.784369	−	0.784369i
$534$		0			0
$535$	27.4927	+	26.0746i	1.18861	+	1.12730i
$536$	3.53484	−	6.12252i	0.152682	−	0.264453i
$537$		0			0
$538$	10.1690	−	10.1690i	0.438415	−	0.438415i
$539$	3.95304	−	2.38461i	0.170270	−	0.102713i
$540$		0			0
$541$	17.5252	+	30.3545i	0.753466	+	1.30504i	0.946133	+	0.323777i	$0.104953\pi$
$541$	17.5252	+	30.3545i	0.753466	+	1.30504i	−0.192667	+	0.981264i	$0.561714\pi$
$542$	−1.93249	+	0.517808i	−0.0830074	+	0.0222418i
$543$		0			0
$544$	−18.1311	−	31.4040i	−0.777366	−	1.34644i
$545$	−6.62276	−	10.8004i	−0.283688	−	0.462639i
$546$		0			0
$547$	−8.10599	+	8.10599i	−0.346587	+	0.346587i	−0.858837	−	0.512250i	$-0.828812\pi$
$547$	−8.10599	+	8.10599i	−0.346587	+	0.346587i	0.512250	+	0.858837i	$0.328812\pi$
$548$	−1.18123	+	4.40840i	−0.0504596	+	0.188318i
$549$		0			0
$550$	7.26047	+	1.53891i	0.309587	+	0.0656195i
$551$	12.9187	−	7.45862i	0.550355	−	0.317748i
$552$		0			0
$553$	5.05529	+	18.1673i	0.214973	+	0.772552i
$554$			33.2665i			1.41336i
$555$		0			0
$556$	1.58323	+	0.914080i	0.0671440	+	0.0387656i
$557$	10.5129	+	39.2348i	0.445447	+	1.66243i	0.714753	+	0.699377i	$0.246539\pi$
$557$	10.5129	+	39.2348i	0.445447	+	1.66243i	−0.269306	+	0.963055i	$0.586794\pi$
$558$		0			0
$559$	−43.6579			−1.84653
$560$	4.22908	+	0.971205i	0.178711	+	0.0410409i
$561$		0			0
$562$	−30.2676	−	8.11018i	−1.27676	−	0.342107i
$563$	−3.30381	−	12.3300i	−0.139239	−	0.519647i	−0.999944	−	0.0105435i	$-0.996644\pi$
$563$	−3.30381	−	12.3300i	−0.139239	−	0.519647i	0.860706	−	0.509103i	$-0.170023\pi$
$564$		0			0
$565$	3.07502	+	10.3702i	0.129367	+	0.436277i
$566$			3.40561i			0.143149i
$567$		0			0
$568$	5.31086	+	5.31086i	0.222839	+	0.222839i
$569$	−13.3195	+	7.69000i	−0.558381	+	0.322382i	−0.752496	−	0.658597i	$-0.771150\pi$
$569$	−13.3195	+	7.69000i	−0.558381	+	0.322382i	0.194114	+	0.980979i	$0.437817\pi$
$570$		0			0
$571$	15.5986	−	27.0176i	0.652782	−	1.13065i	−0.329663	−	0.944099i	$-0.606935\pi$
$571$	15.5986	−	27.0176i	0.652782	−	1.13065i	0.982445	−	0.186552i	$-0.0597314\pi$
$572$	1.89324	−	7.06567i	0.0791604	−	0.295430i
$573$		0			0
$574$	36.7026	+	20.7231i	1.53194	+	0.864967i
$575$	−1.33470	+	0.434514i	−0.0556607	+	0.0181205i
$576$		0			0
$577$	31.1456	−	8.34542i	1.29661	−	0.347425i	0.456440	−	0.889754i	$-0.349124\pi$
$577$	31.1456	−	8.34542i	1.29661	−	0.347425i	0.840166	+	0.542329i	$0.182458\pi$
$578$	−31.8152	+	8.52487i	−1.32334	+	0.354588i
$579$		0			0
$580$	−29.4268	+	18.0443i	−1.22188	+	0.749251i
$581$	4.08882	+	6.92763i	0.169633	+	0.287406i
$582$		0			0
$583$	−0.822381	+	3.06917i	−0.0340595	+	0.127112i
$584$	1.93502	−	3.35155i	0.0800717	−	0.138688i
$585$		0			0
$586$	63.3510	−	36.5757i	2.61701	−	1.51093i
$587$	−3.73477	−	3.73477i	−0.154150	−	0.154150i	0.625818	−	0.779969i	$-0.284765\pi$
$587$	−3.73477	−	3.73477i	−0.154150	−	0.154150i	−0.779969	+	0.625818i	$0.784765\pi$
$588$		0			0
$589$		−	22.3420i		−	0.920586i
$590$	−7.55057	+	2.23893i	−0.310852	+	0.0921754i
$591$		0			0
$592$	1.53229	+	5.71860i	0.0629769	+	0.235033i
$593$	−16.9028	−	4.52910i	−0.694116	−	0.185988i	−0.105523	−	0.994417i	$-0.533652\pi$
$593$	−16.9028	−	4.52910i	−0.694116	−	0.185988i	−0.588594	+	0.808429i	$0.700318\pi$
$594$		0			0
$595$	15.5875	−	29.3979i	0.639026	−	1.20520i
$596$	33.9788			1.39183
$597$		0			0
$598$	0.591661	+	2.20811i	0.0241948	+	0.0902963i
$599$	5.44301	+	3.14253i	0.222396	+	0.128400i	0.607059	−	0.794657i	$-0.292349\pi$
$599$	5.44301	+	3.14253i	0.222396	+	0.128400i	−0.384663	+	0.923057i	$0.625682\pi$
$600$		0			0
$601$			16.3147i			0.665492i	0.943017	+	0.332746i	$0.107975\pi$
$601$			16.3147i			0.665492i	−0.943017	+	0.332746i	$0.892025\pi$
$602$	69.2238	−	19.2624i	2.82135	−	0.785078i
$603$		0			0
$604$	−28.1392	+	16.2462i	−1.14497	+	0.661047i
$605$	0.625171	+	23.6159i	0.0254168	+	0.960122i
$606$		0			0
$607$	−11.6579	+	43.5077i	−0.473178	+	1.76592i	0.155061	+	0.987905i	$0.450442\pi$
$607$	−11.6579	+	43.5077i	−0.473178	+	1.76592i	−0.628240	+	0.778020i	$0.716224\pi$
$608$	13.5048	−	13.5048i	0.547694	−	0.547694i
$609$		0			0
$610$	5.76826	+	1.38309i	0.233550	+	0.0559996i
$611$	21.8064	+	37.7699i	0.882194	+	1.52801i
$612$		0			0
$613$	−40.1334	+	10.7537i	−1.62097	+	0.434338i	−0.951287	−	0.308306i	$-0.900238\pi$
$613$	−40.1334	+	10.7537i	−1.62097	+	0.434338i	−0.669686	+	0.742645i	$0.733571\pi$
$614$	19.0300	+	32.9610i	0.767989	+	1.33020i
$615$		0			0
$616$	0.0401641	+	4.18451i	0.00161826	+	0.168599i
$617$	6.92260	−	6.92260i	0.278693	−	0.278693i	−0.553894	−	0.832587i	$-0.686859\pi$
$617$	6.92260	−	6.92260i	0.278693	−	0.278693i	0.832587	+	0.553894i	$0.186859\pi$
$618$		0			0
$619$	−6.42457	+	11.1277i	−0.258225	+	0.447260i	−0.965767	−	0.259413i	$-0.916471\pi$
$619$	−6.42457	+	11.1277i	−0.258225	+	0.447260i	0.707541	+	0.706672i	$0.249804\pi$
$620$	1.36814	+	51.6814i	0.0549457	+	2.07558i
$621$		0			0
$622$	−23.3760	−	23.3760i	−0.937290	−	0.937290i
$623$	−11.4360	+	3.18223i	−0.458175	+	0.127493i
$624$		0			0
$625$	−10.1422	+	22.8503i	−0.405690	+	0.914011i
$626$	−5.32913	−	3.07677i	−0.212995	−	0.122973i
$627$		0			0
$628$	44.2890	+	11.8672i	1.76732	+	0.473553i
$629$	45.3998			1.81021
$630$		0			0
$631$	−16.2517			−0.646971			−0.323485	−	0.946233i	$-0.604855\pi$
$631$	−16.2517			−0.646971			−0.323485	+	0.946233i	$0.604855\pi$
$632$	−16.5110	−	4.42410i	−0.656771	−	0.175981i
$633$		0			0
$634$	3.88144	+	2.24095i	0.154151	+	0.0889994i
$635$	23.0383	−	6.83144i	0.914248	−	0.271097i
$636$		0			0
$637$	24.3331	−	7.02332i	0.964113	−	0.278274i
$638$	5.28543	+	5.28543i	0.209252	+	0.209252i
$639$		0			0
$640$	−25.3322	+	26.7099i	−1.00134	+	1.05580i
$641$	16.4363	−	28.4685i	0.649194	−	1.12444i	−0.334122	−	0.942530i	$-0.608440\pi$
$641$	16.4363	−	28.4685i	0.649194	−	1.12444i	0.983316	−	0.181907i	$-0.0582269\pi$
$642$		0			0
$643$	−14.6822	+	14.6822i	−0.579009	+	0.579009i	−0.934630	−	0.355621i	$-0.884269\pi$
$643$	−14.6822	+	14.6822i	−0.579009	+	0.579009i	0.355621	+	0.934630i	$0.384269\pi$
$644$	−1.15733	−	1.96085i	−0.0456051	−	0.0772681i
$645$		0			0
$646$	−18.7497	−	32.4754i	−0.737697	−	1.27773i
$647$	14.0379	−	3.76144i	0.551887	−	0.147878i	0.0279104	−	0.999610i	$-0.491115\pi$
$647$	14.0379	−	3.76144i	0.551887	−	0.147878i	0.523976	+	0.851733i	$0.324448\pi$
$648$		0			0
$649$	0.516029	+	0.893789i	0.0202559	+	0.0350843i
$650$	36.2884	+	18.4637i	1.42335	+	0.724205i
$651$		0			0
$652$	27.0222	−	27.0222i	1.05827	−	1.05827i
$653$	−7.14961	+	26.6827i	−0.279786	+	1.04417i	0.672780	+	0.739842i	$0.265100\pi$
$653$	−7.14961	+	26.6827i	−0.279786	+	1.04417i	−0.952566	+	0.304332i	$0.901567\pi$
$654$		0			0
$655$	−5.64010	+	0.149308i	−0.220377	+	0.00583393i
$656$	4.49600	−	2.59577i	0.175539	−	0.101348i
$657$		0			0
$658$	−51.2407	−	50.2664i	−1.99757	−	1.95959i
$659$		−	28.4761i		−	1.10927i	−0.832094	−	0.554635i	$-0.812858\pi$
$659$		−	28.4761i		−	1.10927i	0.832094	−	0.554635i	$-0.187142\pi$
$660$		0			0
$661$	−16.5474	−	9.55364i	−0.643619	−	0.371593i	0.142388	−	0.989811i	$-0.454522\pi$
$661$	−16.5474	−	9.55364i	−0.643619	−	0.371593i	−0.786007	+	0.618217i	$0.787855\pi$
$662$	−7.73675	−	28.8739i	−0.300697	−	1.12222i
$663$		0			0
$664$	−7.29173			−0.282974
$665$	17.0806	+	3.92255i	0.662359	+	0.152110i
$666$		0			0
$667$	−1.36549	−	0.365882i	−0.0528720	−	0.0141670i
$668$	−6.83781	−	25.5191i	−0.264563	−	0.987363i
$669$		0			0
$670$	7.07521	−	13.0398i	0.273339	−	0.503772i
$671$		−	0.777334i		−	0.0300087i
$672$		0			0
$673$	−4.27499	−	4.27499i	−0.164789	−	0.164789i	0.619896	−	0.784684i	$-0.287175\pi$
$673$	−4.27499	−	4.27499i	−0.164789	−	0.164789i	−0.784684	+	0.619896i	$0.787175\pi$
$674$	14.6664	−	8.46768i	0.564930	−	0.326163i
$675$		0			0
$676$	0.138512	−	0.239910i	0.00532740	−	0.00922732i
$677$	7.49968	−	27.9892i	0.288236	−	1.07571i	−0.658206	−	0.752838i	$-0.728684\pi$
$677$	7.49968	−	27.9892i	0.288236	−	1.07571i	0.946442	−	0.322874i	$-0.104649\pi$
$678$		0			0
$679$	10.7589	−	6.35012i	0.412889	−	0.243695i
$680$	15.7669	+	25.7127i	0.604633	+	0.986037i
$681$		0			0
$682$	10.8137	−	2.89751i	0.414076	−	0.110951i
$683$	−1.34238	+	0.359690i	−0.0513647	+	0.0137631i	−0.284410	−	0.958703i	$-0.591798\pi$
$683$	−1.34238	+	0.359690i	−0.0513647	+	0.0137631i	0.233045	+	0.972466i	$0.425131\pi$
$684$		0			0
$685$	−0.776210	+	3.23723i	−0.0296575	+	0.123688i
$686$	−35.4837	+	21.8722i	−1.35477	+	0.835086i
$687$		0			0
$688$	2.29063	−	8.54876i	0.0873296	−	0.325919i
$689$	−8.71564	+	15.0959i	−0.332039	+	0.575109i
$690$		0			0
$691$	10.9802	−	6.33940i	0.417705	−	0.241162i	−0.276390	−	0.961046i	$-0.589138\pi$
$691$	10.9802	−	6.33940i	0.417705	−	0.241162i	0.694095	+	0.719884i	$0.255805\pi$
$692$	−42.9983	−	42.9983i	−1.63455	−	1.63455i
$693$		0			0
$694$		−	45.5898i		−	1.73056i
$695$	1.17207	+	0.635950i	0.0444593	+	0.0241229i
$696$		0			0
$697$	−10.3039	−	38.4545i	−0.390287	−	1.45657i
$698$	7.54643	+	2.02206i	0.285637	+	0.0765361i
$699$		0			0
$700$	−39.7511	−	8.02769i	−1.50245	−	0.303418i
$701$	−42.9975			−1.62399			−0.811997	−	0.583661i	$-0.801620\pi$
$701$	−42.9975			−1.62399			−0.811997	+	0.583661i	$0.801620\pi$
$702$		0			0
$703$	6.18871	+	23.0966i	0.233412	+	0.871104i
$704$	7.45003	+	4.30128i	0.280783	+	0.162110i
$705$		0			0
$706$		−	5.43331i		−	0.204485i
$707$	−4.79468	+	4.88761i	−0.180322	+	0.183817i
$708$		0			0
$709$	−29.9264	+	17.2780i	−1.12391	+	0.648889i	−0.942396	−	0.334500i	$-0.891433\pi$
$709$	−29.9264	+	17.2780i	−1.12391	+	0.648889i	−0.181513	+	0.983389i	$0.558099\pi$
$710$	11.4358	+	10.8459i	0.429178	+	0.407041i
$711$		0			0
$712$	2.78490	−	10.3934i	0.104369	−	0.389509i
$713$	−1.49714	+	1.49714i	−0.0560685	+	0.0560685i
$714$		0			0
$715$	1.24409	−	5.18855i	0.0465263	−	0.194041i
$716$	−25.6984	−	44.5110i	−0.960396	−	1.66345i
$717$		0			0
$718$	17.1756	−	4.60219i	0.640988	−	0.171752i
$719$	−17.2872	−	29.9423i	−0.644703	−	1.11666i	−0.984370	−	0.176112i	$-0.943648\pi$
$719$	−17.2872	−	29.9423i	−0.644703	−	1.11666i	0.339667	−	0.940546i	$-0.389685\pi$
$720$		0			0
$721$	8.79645	−	15.5793i	0.327597	−	0.580204i
$722$	−16.2724	+	16.2724i	−0.605595	+	0.605595i
$723$		0			0
$724$	5.91634	−	10.2474i	0.219879	−	0.380842i
$725$	−21.1085	+	13.7252i	−0.783951	+	0.509742i
$726$		0			0
$727$	27.4042	+	27.4042i	1.01637	+	1.01637i	0.999864	+	0.0165022i	$0.00525306\pi$
$727$	27.4042	+	27.4042i	1.01637	+	1.01637i	0.0165022	+	0.999864i	$0.494747\pi$
$728$	−5.72864	+	22.2309i	−0.212317	+	0.823932i
$729$		0			0
$730$	3.87307	−	7.13818i	0.143349	−	0.264196i
$731$	−58.7758	−	33.9342i	−2.17390	−	1.25510i
$732$		0			0
$733$	−41.4261	−	11.1001i	−1.53011	−	0.409991i	−0.607054	−	0.794661i	$-0.707649\pi$
$733$	−41.4261	−	11.1001i	−1.53011	−	0.409991i	−0.923054	+	0.384670i	$0.874315\pi$
$734$	−44.7567			−1.65200
$735$		0			0
$736$	−1.80993			−0.0667148
$737$	−1.87791	−	0.503184i	−0.0691736	−	0.0185350i
$738$		0			0
$739$	−9.46751	−	5.46607i	−0.348268	−	0.201073i	0.315654	−	0.948874i	$-0.397776\pi$
$739$	−9.46751	−	5.46607i	−0.348268	−	0.201073i	−0.663922	+	0.747802i	$0.731109\pi$
$740$	−15.7301	−	53.0480i	−0.578248	−	1.95008i
$741$		0			0
$742$	7.15896	−	27.7815i	0.262814	−	1.01989i
$743$	5.63096	+	5.63096i	0.206580	+	0.206580i	0.802812	−	0.596232i	$-0.203336\pi$
$743$	5.63096	+	5.63096i	0.206580	+	0.206580i	−0.596232	+	0.802812i	$0.703336\pi$
$744$		0			0
$745$	24.7760	−	0.655882i	0.907721	−	0.0240296i
$746$	21.3591	−	36.9950i	0.782011	−	1.35448i
$747$		0			0
$748$	8.04080	−	8.04080i	0.294001	−	0.294001i
$749$	−22.0430	+	39.0401i	−0.805432	+	1.42650i
$750$		0			0
$751$	−12.4387	−	21.5445i	−0.453895	−	0.786168i	0.544729	−	0.838612i	$-0.316632\pi$
$751$	−12.4387	−	21.5445i	−0.453895	−	0.786168i	−0.998624	+	0.0524435i	$0.983299\pi$
$752$	−8.53994	+	2.28827i	−0.311420	+	0.0834446i
$753$		0			0
$754$	20.5030	+	35.5123i	0.746676	+	1.29328i
$755$	−20.2044	+	12.3892i	−0.735312	+	0.450889i
$756$		0			0
$757$	27.5480	−	27.5480i	1.00125	−	1.00125i	0.00124921	−	0.999999i	$-0.499602\pi$
$757$	27.5480	−	27.5480i	1.00125	−	1.00125i	0.999999	−	0.00124921i	$-0.000397635\pi$
$758$	11.3598	−	42.3952i	0.412605	−	1.53986i
$759$		0			0
$760$	−10.9317	+	11.5263i	−0.396536	+	0.418101i
$761$	9.56982	−	5.52514i	0.346906	−	0.200286i	−0.316416	−	0.948621i	$-0.602479\pi$
$761$	9.56982	−	5.52514i	0.346906	−	0.200286i	0.663322	+	0.748334i	$0.269146\pi$
$762$		0			0
$763$	10.4976	−	10.7011i	0.380040	−	0.387406i
$764$		−	4.10096i		−	0.148368i
$765$		0			0
$766$	−34.6990	−	20.0335i	−1.25372	−	0.723838i
$767$	1.46539	+	5.46891i	0.0529121	+	0.197471i
$768$		0			0
$769$	49.5135			1.78550			0.892751	−	0.450550i	$-0.148772\pi$
$769$	49.5135			1.78550			0.892751	+	0.450550i	$0.148772\pi$
$770$	0.316632	+	8.77584i	0.0114106	+	0.316259i
$771$		0			0
$772$	73.2585	+	19.6296i	2.63663	+	0.706483i
$773$	−7.61853	−	28.4327i	−0.274019	−	1.02265i	−0.956496	−	0.291747i	$-0.905764\pi$
$773$	−7.61853	−	28.4327i	−0.274019	−	1.02265i	0.682476	−	0.730908i	$-0.260903\pi$
$774$		0			0
$775$	1.99518	+	37.6576i	0.0716690	+	1.35270i
$776$			11.3244i			0.406522i
$777$		0			0
$778$	16.7732	+	16.7732i	0.601349	+	0.601349i
$779$	18.1587	−	10.4839i	0.650602	−	0.375625i
$780$		0			0
$781$	1.03272	−	1.78872i	0.0369535	−	0.0640053i
$782$	−0.919766	+	3.43261i	−0.0328908	+	0.122750i
$783$		0			0
$784$	0.0985491	+	5.13322i	0.00351961	+	0.183329i
$785$	32.5228	+	7.79820i	1.16079	+	0.278330i
$786$		0			0
$787$	−44.3313	+	11.8785i	−1.58024	+	0.423424i	−0.939000	−	0.343917i	$-0.888246\pi$
$787$	−44.3313	+	11.8785i	−1.58024	+	0.423424i	−0.641239	+	0.767341i	$0.721579\pi$
$788$	19.2137	−	5.14830i	0.684460	−	0.183401i
$789$		0			0
$790$	−34.8816	−	8.36376i	−1.24103	−	0.297569i
$791$	−11.0217	+	6.50521i	−0.391886	+	0.231299i
$792$		0			0
$793$	1.10371	−	4.11912i	0.0391940	−	0.146274i
$794$	22.4997	−	38.9706i	0.798483	−	1.38301i
$795$		0			0
$796$	12.7797	−	7.37839i	0.452966	−	0.261520i
$797$	−2.95840	−	2.95840i	−0.104792	−	0.104792i	0.652767	−	0.757559i	$-0.273608\pi$
$797$	−2.95840	−	2.95840i	−0.104792	−	0.104792i	−0.757559	+	0.652767i	$0.773608\pi$
$798$		0			0
$799$			67.7984i			2.39853i
$800$	−21.5565	+	23.9685i	−0.762138	+	0.847416i
$801$		0			0
$802$	−10.9071	−	40.7057i	−0.385141	−	1.43737i
$803$	−1.02799	−	0.275450i	−0.0362771	−	0.00972041i
$804$		0			0
$805$	−0.881727	−	1.40743i	−0.0310768	−	0.0496054i
$806$	61.4160			2.16329
$807$		0			0
$808$	−1.60629	−	5.99474i	−0.0565089	−	0.210894i
$809$	22.7389	+	13.1283i	0.799459	+	0.461568i	0.843282	−	0.537472i	$-0.180620\pi$
$809$	22.7389	+	13.1283i	0.799459	+	0.461568i	−0.0438232	+	0.999039i	$0.513954\pi$
$810$		0			0
$811$			35.6672i			1.25245i	0.779644	+	0.626223i	$0.215400\pi$
$811$			35.6672i			1.25245i	−0.779644	+	0.626223i	$0.784600\pi$
$812$	−29.1562	−	28.6018i	−1.02318	−	1.00373i
$813$		0			0
$814$	−10.3763	+	5.99075i	−0.363688	+	0.209976i
$815$	19.1819	−	20.2251i	0.671914	−	0.708455i
$816$		0			0
$817$	9.25153	−	34.5272i	0.323670	−	1.20795i
$818$	55.0206	−	55.0206i	1.92375	−	1.92375i
$819$		0			0
$820$	−41.3626	+	25.3633i	−1.44445	+	0.885726i
$821$	2.87764	+	4.98422i	0.100430	+	0.173951i	0.911862	−	0.410497i	$-0.134645\pi$
$821$	2.87764	+	4.98422i	0.100430	+	0.173951i	−0.811432	+	0.584447i	$0.801311\pi$
$822$		0			0
$823$	36.1401	−	9.68371i	1.25977	−	0.337553i	0.433664	−	0.901075i	$-0.357221\pi$
$823$	36.1401	−	9.68371i	1.25977	−	0.337553i	0.826101	+	0.563522i	$0.190554\pi$
$824$	8.10871	+	14.0447i	0.282480	+	0.489270i
$825$		0			0
$826$	−4.73646	−	8.02492i	−0.164803	−	0.279223i
$827$	−19.9746	+	19.9746i	−0.694585	+	0.694585i	−0.963237	−	0.268653i	$-0.913422\pi$
$827$	−19.9746	+	19.9746i	−0.694585	+	0.694585i	0.268653	+	0.963237i	$0.413422\pi$
$828$		0			0
$829$	−6.38582	+	11.0606i	−0.221789	+	0.384149i	−0.955351	−	0.295473i	$-0.904523\pi$
$829$	−6.38582	+	11.0606i	−0.221789	+	0.384149i	0.733563	+	0.679622i	$0.237856\pi$
$830$	−15.2962	+	0.404930i	−0.530940	+	0.0140553i
$831$		0			0
$832$	33.3706	+	33.3706i	1.15692	+	1.15692i
$833$	38.2182	+	9.45817i	1.32418	+	0.327706i
$834$		0			0
$835$	−5.47845	−	18.4755i	−0.189589	−	0.639371i
$836$	5.18674	+	2.99457i	0.179387	+	0.103569i
$837$		0			0
$838$	−2.48788	−	0.666627i	−0.0859426	−	0.0230282i
$839$	−26.8449			−0.926790			−0.463395	−	0.886152i	$-0.653369\pi$
$839$	−26.8449			−0.926790			−0.463395	+	0.886152i	$0.653369\pi$
$840$		0			0
$841$	3.64194			0.125584
$842$	−37.6918	−	10.0995i	−1.29895	−	0.348051i
$843$		0			0
$844$	42.8512	+	24.7402i	1.47500	+	0.851591i
$845$	0.0963667	−	0.177607i	0.00331512	−	0.00610985i
$846$		0			0
$847$	−26.9293	+	7.49344i	−0.925303	+	0.257478i
$848$	−2.49868	−	2.49868i	−0.0858050	−	0.0858050i
$849$		0			0
$850$	34.5029	+	53.0633i	1.18344	+	1.82006i
$851$	1.13300	−	1.96242i	0.0388388	−	0.0672708i
$852$		0			0
$853$	0.887080	−	0.887080i	0.0303730	−	0.0303730i	−0.691757	−	0.722130i	$-0.743163\pi$
$853$	0.887080	−	0.887080i	0.0303730	−	0.0303730i	0.722130	+	0.691757i	$0.243163\pi$
$854$	0.0673627	+	7.01823i	0.00230511	+	0.240159i
$855$		0			0
$856$	−20.3196	−	35.1945i	−0.694508	−	1.20292i
$857$	54.2324	−	14.5315i	1.85254	−	0.496387i	0.852873	−	0.522118i	$-0.174858\pi$
$857$	54.2324	−	14.5315i	1.85254	−	0.496387i	0.999669	+	0.0257309i	$0.00819132\pi$
$858$		0			0
$859$	−2.37642	−	4.11608i	−0.0810824	−	0.140439i	0.822633	−	0.568573i	$-0.192504\pi$
$859$	−2.37642	−	4.11608i	−0.0810824	−	0.140439i	−0.903715	+	0.428134i	$0.859171\pi$
$860$	−19.2863	+	80.4347i	−0.657658	+	2.74280i
$861$		0			0
$862$	33.1062	−	33.1062i	1.12760	−	1.12760i
$863$	−13.2188	+	49.3332i	−0.449973	+	1.67932i	0.252489	+	0.967600i	$0.418751\pi$
$863$	−13.2188	+	49.3332i	−0.449973	+	1.67932i	−0.702462	+	0.711721i	$0.747916\pi$
$864$		0			0
$865$	−32.1826	−	30.5227i	−1.09424	−	1.03780i
$866$	−64.0233	+	36.9638i	−2.17560	+	1.25608i
$867$		0			0
$868$	−58.9327	+	16.3988i	−2.00031	+	0.556611i
$869$			4.70067i			0.159459i
$870$		0			0
$871$	−9.23663	−	5.33277i	−0.312971	−	0.180694i
$872$	3.51686	+	13.1251i	0.119096	+	0.444472i
$873$		0			0
$874$	−1.87168			−0.0633104
$875$	−29.1399	−	5.08616i	−0.985107	−	0.171944i
$876$		0			0
$877$	−5.91642	−	1.58530i	−0.199783	−	0.0535317i	0.157540	−	0.987513i	$-0.449644\pi$
$877$	−5.91642	−	1.58530i	−0.199783	−	0.0535317i	−0.357323	+	0.933981i	$0.616310\pi$
$878$	4.51250	+	16.8409i	0.152289	+	0.568352i
$879$		0			0
$880$	0.950707	+	0.515839i	0.0320483	+	0.0173889i
$881$		−	16.2995i		−	0.549144i	−0.961567	−	0.274572i	$-0.911464\pi$
$881$		−	16.2995i		−	0.549144i	0.961567	−	0.274572i	$-0.0885362\pi$
$882$		0			0
$883$	21.9970	+	21.9970i	0.740259	+	0.740259i	0.972628	−	0.232368i	$-0.0746475\pi$
$883$	21.9970	+	21.9970i	0.740259	+	0.740259i	−0.232368	+	0.972628i	$0.574647\pi$
$884$	54.0253	−	31.1915i	1.81707	−	1.04908i
$885$		0			0
$886$	−7.82967	+	13.5614i	−0.263043	+	0.455603i
$887$	−10.9632	+	40.9152i	−0.368108	+	1.37380i	0.495051	+	0.868864i	$0.335149\pi$
$887$	−10.9632	+	40.9152i	−0.368108	+	1.37380i	−0.863159	+	0.504933i	$0.831517\pi$
$888$		0			0
$889$	14.4519	+	24.4857i	0.484702	+	0.821223i
$890$	5.26486	−	21.9574i	0.176479	−	0.736015i
$891$		0			0
$892$	−34.0754	+	9.13048i	−1.14093	+	0.305711i
$893$	−34.4916	+	9.24199i	−1.15422	+	0.309271i
$894$		0			0
$895$	−19.5975	−	31.9596i	−0.655071	−	1.06829i
$896$	−37.9285	−	21.4153i	−1.26710	−	0.715436i
$897$		0			0
$898$	3.16233	−	11.8020i	0.105528	−	0.393837i
$899$	−18.9898	+	32.8912i	−0.633344	+	1.09698i
$900$		0			0
$901$	−23.4674	+	13.5489i	−0.781812	+	0.451379i
$902$	7.42926	+	7.42926i	0.247367	+	0.247367i
$903$		0			0
$904$		−	11.6010i		−	0.385843i
$905$	4.11616	−	7.58620i	0.136826	−	0.252174i
$906$		0			0
$907$	9.14255	+	34.1204i	0.303573	+	1.13295i	0.934167	+	0.356837i	$0.116145\pi$
$907$	9.14255	+	34.1204i	0.303573	+	1.13295i	−0.630593	+	0.776113i	$0.717188\pi$
$908$	−6.99882	−	1.87533i	−0.232264	−	0.0622349i
$909$		0			0
$910$	−10.7827	+	46.9530i	−0.357444	+	1.55648i
$911$	−16.8101			−0.556943			−0.278471	−	0.960445i	$-0.589828\pi$
$911$	−16.8101			−0.556943			−0.278471	+	0.960445i	$0.589828\pi$
$912$		0			0
$913$	0.518989	+	1.93689i	0.0171760	+	0.0641018i
$914$	57.8303	+	33.3883i	1.91286	+	1.10439i
$915$		0			0
$916$			25.1503i			0.830988i
$917$	−1.78963	−	6.43144i	−0.0590989	−	0.212385i
$918$		0			0
$919$	23.5888	−	13.6190i	0.778124	−	0.449250i	−0.0576411	−	0.998337i	$-0.518358\pi$
$919$	23.5888	−	13.6190i	0.778124	−	0.449250i	0.835765	+	0.549087i	$0.185025\pi$
$920$	1.50492	−	0.0398389i	0.0496156	−	0.00131345i
$921$		0			0
$922$	−11.6387	+	43.4362i	−0.383300	+	1.43049i
$923$	8.01213	−	8.01213i	0.263723	−	0.263723i
$924$		0			0
$925$	−12.4937	−	38.3768i	−0.410790	−	1.26182i
$926$	15.7334	+	27.2510i	0.517030	+	0.895522i
$927$		0			0
$928$	−31.3600	+	8.40289i	−1.02944	+	0.275838i
$929$	28.8600	+	49.9870i	0.946865	+	1.64002i	0.751973	+	0.659194i	$0.229102\pi$
$929$	28.8600	+	49.9870i	0.946865	+	1.64002i	0.194892	+	0.980825i	$0.437564\pi$
$930$		0			0
$931$	0.398025	+	20.7323i	0.0130448	+	0.679475i
$932$	56.6644	−	56.6644i	1.85610	−	1.85610i
$933$		0			0
$934$	14.3003	−	24.7688i	0.467920	−	0.810461i
$935$	5.70782	−	6.01823i	0.186666	−	0.196817i
$936$		0			0
$937$	34.1373	+	34.1373i	1.11522	+	1.11522i	0.992433	+	0.122785i	$0.0391825\pi$
$937$	34.1373	+	34.1373i	1.11522	+	1.11522i	0.122785	+	0.992433i	$0.460817\pi$
$938$	16.9984	+	4.38030i	0.555019	+	0.143022i
$939$		0			0
$940$	79.2199	−	23.4907i	2.58387	−	0.766181i
$941$	20.8767	+	12.0532i	0.680562	+	0.392923i	0.800067	−	0.599911i	$-0.204797\pi$
$941$	20.8767	+	12.0532i	0.680562	+	0.392923i	−0.119504	+	0.992834i	$0.538131\pi$
$942$		0			0
$943$	−1.91935	−	0.514288i	−0.0625026	−	0.0167475i
$944$	−1.14777			−0.0373566
$945$		0			0
$946$	17.9112			0.582343
$947$	48.6797	+	13.0437i	1.58188	+	0.423863i	0.939506	−	0.342532i	$-0.111284\pi$
$947$	48.6797	+	13.0437i	1.58188	+	0.423863i	0.642370	+	0.766394i	$0.277951\pi$
$948$		0			0
$949$	−5.05626	−	2.91923i	−0.164133	−	0.0947623i
$950$	−22.2920	+	24.7863i	−0.723247	+	0.804173i
$951$		0			0
$952$	−24.9919	+	25.4763i	−0.809991	+	0.825690i
$953$	−7.43135	−	7.43135i	−0.240725	−	0.240725i	0.576425	−	0.817150i	$-0.304447\pi$
$953$	−7.43135	−	7.43135i	−0.240725	−	0.240725i	−0.817150	+	0.576425i	$0.804447\pi$
$954$		0			0
$955$	−0.0791596	−	2.99026i	−0.00256154	−	0.0967625i
$956$	17.3205	−	29.9999i	0.560184	−	0.970267i
$957$		0			0
$958$	−12.5532	+	12.5532i	−0.405577	+	0.405577i
$959$	−3.93873	+	0.0378050i	−0.127188	+	0.00122079i
$960$		0			0
$961$	12.9415	+	22.4154i	0.417469	+	0.723078i
$962$	−63.4903	+	17.0122i	−2.04701	+	0.548494i
$963$		0			0
$964$	−36.0176	−	62.3842i	−1.16005	−	2.00926i
$965$	53.7961	+	12.8990i	1.73176	+	0.415234i
$966$		0			0
$967$	−1.61362	+	1.61362i	−0.0518906	+	0.0518906i	−0.732576	−	0.680685i	$-0.761682\pi$
$967$	−1.61362	+	1.61362i	−0.0518906	+	0.0518906i	0.680685	+	0.732576i	$0.261682\pi$
$968$	6.55783	−	24.4742i	0.210777	−	0.786629i
$969$		0			0
$970$	0.628874	+	23.7558i	0.0201919	+	0.762751i
$971$	16.4540	−	9.49972i	0.528034	−	0.304860i	−0.212182	−	0.977230i	$-0.568057\pi$
$971$	16.4540	−	9.49972i	0.528034	−	0.304860i	0.740215	+	0.672370i	$0.234724\pi$
$972$		0			0
$973$	−0.393719	+	1.52789i	−0.0126221	+	0.0489819i
$974$		−	16.6767i		−	0.534356i
$975$		0			0
$976$	0.748665	+	0.432242i	0.0239642	+	0.0138357i
$977$	−9.10702	−	33.9879i	−0.291359	−	1.08737i	−0.944066	−	0.329757i	$-0.893033\pi$
$977$	−9.10702	−	33.9879i	−0.291359	−	1.08737i	0.652706	−	0.757611i	$-0.273634\pi$
$978$		0			0
$979$	−2.95900			−0.0945700
$980$	−2.19028	−	47.9336i	−0.0699659	−	1.53118i
$981$		0			0
$982$	8.93793	+	2.39491i	0.285221	+	0.0764247i
$983$	9.27190	+	34.6032i	0.295728	+	1.10367i	0.940638	+	0.339412i	$0.110228\pi$
$983$	9.27190	+	34.6032i	0.295728	+	1.10367i	−0.644910	+	0.764259i	$0.723105\pi$
$984$		0			0
$985$	13.9105	−	4.12481i	0.443225	−	0.131427i
$986$			63.7459i			2.03008i
$987$		0			0
$988$	23.2328	+	23.2328i	0.739133	+	0.739133i
$989$	−2.93363	+	1.69373i	−0.0932839	+	0.0538575i
$990$		0			0
$991$	16.3163	−	28.2606i	0.518303	−	0.897727i	−0.481471	−	0.876462i	$-0.659897\pi$
$991$	16.3163	−	28.2606i	0.518303	−	0.897727i	0.999774	−	0.0212648i	$-0.00676930\pi$
$992$	−12.5853	+	46.9688i	−0.399582	+	1.49126i
$993$		0			0
$994$	−9.16895	+	16.2391i	−0.290821	+	0.515072i
$995$	9.17606	−	5.62671i	0.290901	−	0.178379i
$996$		0			0
$997$	−34.5910	+	9.26864i	−1.09551	+	0.293541i	−0.760934	−	0.648829i	$-0.775259\pi$
$997$	−34.5910	+	9.26864i	−1.09551	+	0.293541i	−0.334574	+	0.942369i	$0.608592\pi$
$998$	−71.1567	+	19.0664i	−2.25243	+	0.603536i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bz.d.73.1		32
3.2	odd	2		105.2.u.a.73.8	yes	32
5.2	odd	4	inner	315.2.bz.d.262.8		32
7.5	odd	6	inner	315.2.bz.d.208.8		32
15.2	even	4		105.2.u.a.52.1	✓	32
15.8	even	4		525.2.bc.e.157.8		32
15.14	odd	2		525.2.bc.e.493.1		32
21.2	odd	6		735.2.v.b.313.1		32
21.5	even	6		105.2.u.a.103.1	yes	32
21.11	odd	6		735.2.m.c.538.1		32
21.17	even	6		735.2.m.c.538.2		32
21.20	even	2		735.2.v.b.178.8		32
35.12	even	12	inner	315.2.bz.d.82.1		32
105.2	even	12		735.2.v.b.607.8		32
105.17	odd	12		735.2.m.c.97.1		32
105.32	even	12		735.2.m.c.97.2		32
105.47	odd	12		105.2.u.a.82.8	yes	32
105.62	odd	4		735.2.v.b.472.1		32
105.68	odd	12		525.2.bc.e.82.1		32
105.89	even	6		525.2.bc.e.418.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.1	✓	32	15.2	even	4
105.2.u.a.73.8	yes	32	3.2	odd	2
105.2.u.a.82.8	yes	32	105.47	odd	12
105.2.u.a.103.1	yes	32	21.5	even	6
315.2.bz.d.73.1		32	1.1	even	1	trivial
315.2.bz.d.82.1		32	35.12	even	12	inner
315.2.bz.d.208.8		32	7.5	odd	6	inner
315.2.bz.d.262.8		32	5.2	odd	4	inner
525.2.bc.e.82.1		32	105.68	odd	12
525.2.bc.e.157.8		32	15.8	even	4
525.2.bc.e.418.8		32	105.89	even	6
525.2.bc.e.493.1		32	15.14	odd	2
735.2.m.c.97.1		32	105.17	odd	12
735.2.m.c.97.2		32	105.32	even	12
735.2.m.c.538.1		32	21.11	odd	6
735.2.m.c.538.2		32	21.17	even	6
735.2.v.b.178.8		32	21.20	even	2
735.2.v.b.313.1		32	21.2	odd	6
735.2.v.b.472.1		32	105.62	odd	4
735.2.v.b.607.8		32	105.2	even	12

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.17399 - 0.582519i) q^{2} +(2.65485 + 1.53278i) q^{4} +(1.96540 + 1.06640i) q^{5} +(-0.660211 + 2.56205i) q^{7} +(-1.69581 - 1.69581i) q^{8} +O(q^{10})\)	\(q+(-2.17399 - 0.582519i) q^{2} +(2.65485 + 1.53278i) q^{4} +(1.96540 + 1.06640i) q^{5} +(-0.660211 + 2.56205i) q^{7} +(-1.69581 - 1.69581i) q^{8} +(-3.65156 - 3.46322i) q^{10} +(-0.329757 + 0.571155i) q^{11} +(-2.55836 + 2.55836i) q^{13} +(2.92774 - 5.18530i) q^{14} +(-0.366726 - 0.635189i) q^{16} +(-5.43281 + 1.45572i) q^{17} +(-1.48115 - 2.56543i) q^{19} +(3.58330 + 5.84366i) q^{20} +(1.04960 - 1.04960i) q^{22} +(-0.0726580 + 0.271163i) q^{23} +(2.72560 + 4.19179i) q^{25} +(7.05213 - 4.07155i) q^{26} +(-5.67983 + 5.78992i) q^{28} +5.03568i q^{29} +(6.53164 + 3.77104i) q^{31} +(1.66867 + 6.22756i) q^{32} +12.6589 q^{34} +(-4.02974 + 4.33141i) q^{35} +(-7.79682 - 2.08915i) q^{37} +(1.72560 + 6.44003i) q^{38} +(-1.52454 - 5.14136i) q^{40} +7.07821i q^{41} +(8.53242 + 8.53242i) q^{43} +(-1.75091 + 1.01089i) q^{44} +(0.315915 - 0.547181i) q^{46} +(3.11986 - 11.6435i) q^{47} +(-6.12824 - 3.38299i) q^{49} +(-3.48362 - 10.7006i) q^{50} +(-10.7135 + 2.87066i) q^{52} +(4.65369 - 1.24695i) q^{53} +(-1.25718 + 0.770897i) q^{55} +(5.46435 - 3.22517i) q^{56} +(2.93338 - 10.9475i) q^{58} +(0.782440 - 1.35522i) q^{59} +(-1.02074 + 0.589324i) q^{61} +(-12.0030 - 12.0030i) q^{62} -13.0438i q^{64} +(-7.75641 + 2.29997i) q^{65} +(0.762962 + 2.84741i) q^{67} +(-16.6546 - 4.46259i) q^{68} +(11.2838 - 7.06905i) q^{70} -3.13175 q^{71} +(0.417656 + 1.55871i) q^{73} +(15.7332 + 9.08359i) q^{74} -9.08114i q^{76} +(-1.24562 - 1.22194i) q^{77} +(6.17258 - 3.56374i) q^{79} +(-0.0434010 - 1.63948i) q^{80} +(4.12319 - 15.3880i) q^{82} +(2.14992 - 2.14992i) q^{83} +(-12.2300 - 2.93246i) q^{85} +(-13.5791 - 23.5197i) q^{86} +(1.52778 - 0.409367i) q^{88} +(2.24332 + 3.88554i) q^{89} +(-4.86559 - 8.24370i) q^{91} +(-0.608530 + 0.608530i) q^{92} +(-13.5651 + 23.4954i) q^{94} +(-0.175290 - 6.62160i) q^{95} +(-3.33893 - 3.33893i) q^{97} +(11.3521 + 10.9244i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8}+O(q^{10}) \) 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8	\( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8} - 12 q^{10} + 8 q^{11} - 8 q^{22} + 8 q^{23} + 12 q^{25} - 24 q^{26} - 24 q^{28} + 24 q^{31} - 24 q^{32} - 44 q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 40 q^{43} - 40 q^{46} + 60 q^{47} - 72 q^{50} - 108 q^{52} + 24 q^{53} + 48 q^{56} + 4 q^{58} - 24 q^{61} + 4 q^{65} + 8 q^{67} - 132 q^{68} + 4 q^{70} + 16 q^{71} + 36 q^{73} - 60 q^{77} + 12 q^{80} + 12 q^{82} - 72 q^{85} + 16 q^{86} - 32 q^{88} - 24 q^{91} + 56 q^{92} + 12 q^{95} + 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8 - 12 * q^10 + 8 * q^11 - 8 * q^22 + 8 * q^23 + 12 * q^25 - 24 * q^26 - 24 * q^28 + 24 * q^31 - 24 * q^32 - 44 * q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 40 * q^43 - 40 * q^46 + 60 * q^47 - 72 * q^50 - 108 * q^52 + 24 * q^53 + 48 * q^56 + 4 * q^58 - 24 * q^61 + 4 * q^65 + 8 * q^67 - 132 * q^68 + 4 * q^70 + 16 * q^71 + 36 * q^73 - 60 * q^77 + 12 * q^80 + 12 * q^82 - 72 * q^85 + 16 * q^86 - 32 * q^88 - 24 * q^91 + 56 * q^92 + 12 * q^95 + 72 * q^98

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