LMFDB - Embedded newform 637.2.e.h.508.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.h.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 + 0.330792i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +0.854102 q^{6} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.190983 + 0.330792i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +0.854102 q^{6} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.427051 - 0.739674i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-2.07295 - 3.59045i) q^{12} +1.00000 q^{13} -5.00000 q^{15} +(-1.57295 - 2.72443i) q^{16} +(-3.73607 + 6.47106i) q^{17} +(0.381966 - 0.661585i) q^{18} +(1.50000 + 2.59808i) q^{19} -4.14590 q^{20} +1.14590 q^{22} +(1.88197 + 3.25966i) q^{23} +(1.64590 - 2.85078i) q^{24} +(0.190983 + 0.330792i) q^{26} +2.23607 q^{27} -4.47214 q^{29} +(-0.954915 - 1.65396i) q^{30} +(2.50000 - 4.33013i) q^{31} +(2.07295 - 3.59045i) q^{32} +(-3.35410 - 5.80948i) q^{33} -2.85410 q^{34} -3.70820 q^{36} +(4.35410 + 7.54153i) q^{37} +(-0.572949 + 0.992377i) q^{38} +(1.11803 - 1.93649i) q^{39} +(-1.64590 - 2.85078i) q^{40} -4.47214 q^{41} -8.00000 q^{43} +(-2.78115 - 4.81710i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(-0.718847 + 1.24508i) q^{46} +(0.736068 + 1.27491i) q^{47} -7.03444 q^{48} +(8.35410 + 14.4697i) q^{51} +(0.927051 - 1.60570i) q^{52} +(-0.736068 + 1.27491i) q^{53} +(0.427051 + 0.739674i) q^{54} -6.70820 q^{55} +6.70820 q^{57} +(-0.854102 - 1.47935i) q^{58} +(3.73607 - 6.47106i) q^{59} +(-4.63525 + 8.02850i) q^{60} +(1.50000 + 2.59808i) q^{61} +1.90983 q^{62} -4.70820 q^{64} +(-1.11803 - 1.93649i) q^{65} +(1.28115 - 2.21902i) q^{66} +(1.50000 - 2.59808i) q^{67} +(6.92705 + 11.9980i) q^{68} +8.41641 q^{69} +8.94427 q^{71} +(-1.47214 - 2.54981i) q^{72} +(5.35410 - 9.27358i) q^{73} +(-1.66312 + 2.88061i) q^{74} +5.56231 q^{76} +0.854102 q^{78} +(-5.35410 - 9.27358i) q^{79} +(-3.51722 + 6.09201i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-0.854102 - 1.47935i) q^{82} +16.7082 q^{85} +(-1.52786 - 2.64634i) q^{86} +(-5.00000 + 8.66025i) q^{87} +(2.20820 - 3.82472i) q^{88} +(-1.11803 - 1.93649i) q^{89} -1.70820 q^{90} +6.97871 q^{92} +(-5.59017 - 9.68246i) q^{93} +(-0.281153 + 0.486971i) q^{94} +(3.35410 - 5.80948i) q^{95} +(-4.63525 - 8.02850i) q^{96} +17.4164 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 3 q^{4} - 10 q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 3 * q^4 - 10 * q^6 - 12 * q^8 - 4 * q^9	$ 4 q + 3 q^{2} - 3 q^{4} - 10 q^{6} - 12 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - 15 q^{12} + 4 q^{13} - 20 q^{15} - 13 q^{16} - 6 q^{17} + 6 q^{18} + 6 q^{19} - 30 q^{20} + 18 q^{22} + 12 q^{23} + 20 q^{24} + 3 q^{26} - 15 q^{30} + 10 q^{31} + 15 q^{32} + 2 q^{34} + 12 q^{36} + 4 q^{37} - 9 q^{38} - 20 q^{40} - 32 q^{43} + 9 q^{44} - 23 q^{46} - 6 q^{47} + 30 q^{48} + 20 q^{51} - 3 q^{52} + 6 q^{53} - 5 q^{54} + 10 q^{58} + 6 q^{59} + 15 q^{60} + 6 q^{61} + 30 q^{62} + 8 q^{64} - 15 q^{66} + 6 q^{67} + 21 q^{68} - 20 q^{69} + 12 q^{72} + 8 q^{73} + 9 q^{74} - 18 q^{76} - 10 q^{78} - 8 q^{79} + 15 q^{80} + 22 q^{81} + 10 q^{82} + 40 q^{85} - 24 q^{86} - 20 q^{87} - 18 q^{88} + 20 q^{90} - 66 q^{92} + 19 q^{94} + 15 q^{96} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 3 * q^4 - 10 * q^6 - 12 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - 15 * q^12 + 4 * q^13 - 20 * q^15 - 13 * q^16 - 6 * q^17 + 6 * q^18 + 6 * q^19 - 30 * q^20 + 18 * q^22 + 12 * q^23 + 20 * q^24 + 3 * q^26 - 15 * q^30 + 10 * q^31 + 15 * q^32 + 2 * q^34 + 12 * q^36 + 4 * q^37 - 9 * q^38 - 20 * q^40 - 32 * q^43 + 9 * q^44 - 23 * q^46 - 6 * q^47 + 30 * q^48 + 20 * q^51 - 3 * q^52 + 6 * q^53 - 5 * q^54 + 10 * q^58 + 6 * q^59 + 15 * q^60 + 6 * q^61 + 30 * q^62 + 8 * q^64 - 15 * q^66 + 6 * q^67 + 21 * q^68 - 20 * q^69 + 12 * q^72 + 8 * q^73 + 9 * q^74 - 18 * q^76 - 10 * q^78 - 8 * q^79 + 15 * q^80 + 22 * q^81 + 10 * q^82 + 40 * q^85 - 24 * q^86 - 20 * q^87 - 18 * q^88 + 20 * q^90 - 66 * q^92 + 19 * q^94 + 15 * q^96 + 16 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.190983	+	0.330792i	0.135045	+	0.233905i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	0.190983	+	0.330792i	0.135045	+	0.233905i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	−0.338689	−	0.940898i	$-0.609984\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	0.984186	−	0.177136i	$-0.0566831\pi$
$4$	0.927051	−	1.60570i	0.463525	−	0.802850i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i	−1.00000			$\pi$
$6$	0.854102			0.348686
$7$		0			0
$7$		0			0
$8$	1.47214			0.520479
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	0.427051	−	0.739674i	0.135045	−	0.233905i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−2.07295	−	3.59045i	−0.598409	−	1.03647i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−5.00000			−1.29099
$16$	−1.57295	−	2.72443i	−0.393237	−	0.681107i
$17$	−3.73607	+	6.47106i	−0.906130	+	1.56946i	−0.0867359	+	0.996231i	$0.527644\pi$
$17$	−3.73607	+	6.47106i	−0.906130	+	1.56946i	−0.819394	+	0.573231i	$0.805690\pi$
$18$	0.381966	−	0.661585i	0.0900303	−	0.155937i
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	0.985194	−	0.171442i	$-0.0548427\pi$
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	−0.641071	+	0.767482i	$0.721509\pi$
$20$	−4.14590			−0.927051
$21$		0			0
$22$	1.14590			0.244306
$23$	1.88197	+	3.25966i	0.392417	+	0.679686i	0.992768	−	0.120051i	$-0.0383057\pi$
$23$	1.88197	+	3.25966i	0.392417	+	0.679686i	−0.600351	+	0.799737i	$0.704972\pi$
$24$	1.64590	−	2.85078i	0.335968	−	0.581913i
$25$		0			0
$26$	0.190983	+	0.330792i	0.0374548	+	0.0648737i
$27$	2.23607			0.430331
$28$		0			0
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$	−0.954915	−	1.65396i	−0.174343	−	0.301971i
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$	2.07295	−	3.59045i	0.366449	−	0.634708i
$33$	−3.35410	−	5.80948i	−0.583874	−	1.01130i
$34$	−2.85410			−0.489474
$35$		0			0
$36$	−3.70820			−0.618034
$37$	4.35410	+	7.54153i	0.715810	+	1.23982i	0.962646	+	0.270762i	$0.0872757\pi$
$37$	4.35410	+	7.54153i	0.715810	+	1.23982i	−0.246836	+	0.969057i	$0.579391\pi$
$38$	−0.572949	+	0.992377i	−0.0929446	+	0.160985i
$39$	1.11803	−	1.93649i	0.179029	−	0.310087i
$40$	−1.64590	−	2.85078i	−0.260239	−	0.450748i
$41$	−4.47214			−0.698430			−0.349215	−	0.937043i	$-0.613552\pi$
$41$	−4.47214			−0.698430			−0.349215	+	0.937043i	$0.613552\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.78115	−	4.81710i	−0.419275	−	0.726205i
$45$	−2.23607	+	3.87298i	−0.333333	+	0.577350i
$46$	−0.718847	+	1.24508i	−0.105988	+	0.183577i
$47$	0.736068	+	1.27491i	0.107367	+	0.185964i	0.914703	−	0.404128i	$-0.132425\pi$
$47$	0.736068	+	1.27491i	0.107367	+	0.185964i	−0.807336	+	0.590092i	$0.799091\pi$
$48$	−7.03444			−1.01533
$49$		0			0
$50$		0			0
$51$	8.35410	+	14.4697i	1.16981	+	2.02617i
$52$	0.927051	−	1.60570i	0.128559	−	0.222670i
$53$	−0.736068	+	1.27491i	−0.101107	+	0.175122i	−0.912141	−	0.409877i	$-0.865572\pi$
$53$	−0.736068	+	1.27491i	−0.101107	+	0.175122i	0.811034	+	0.584999i	$0.198905\pi$
$54$	0.427051	+	0.739674i	0.0581143	+	0.100657i
$55$	−6.70820			−0.904534
$56$		0			0
$57$	6.70820			0.888523
$58$	−0.854102	−	1.47935i	−0.112149	−	0.194248i
$59$	3.73607	−	6.47106i	0.486395	−	0.842460i	−0.513483	−	0.858100i	$-0.671645\pi$
$59$	3.73607	−	6.47106i	0.486395	−	0.842460i	0.999878	+	0.0156395i	$0.00497842\pi$
$60$	−4.63525	+	8.02850i	−0.598409	+	1.03647i
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	0.945931	−	0.324367i	$-0.105151\pi$
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	−0.753876	+	0.657017i	$0.771818\pi$
$62$	1.90983			0.242549
$63$		0			0
$64$	−4.70820			−0.588525
$65$	−1.11803	−	1.93649i	−0.138675	−	0.240192i
$66$	1.28115	−	2.21902i	0.157699	−	0.273143i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	6.92705	+	11.9980i	0.840028	+	1.45497i
$69$	8.41641			1.01322
$70$		0			0
$71$	8.94427			1.06149			0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427			1.06149			0.530745	+	0.847532i	$0.321912\pi$
$72$	−1.47214	−	2.54981i	−0.173493	−	0.300498i
$73$	5.35410	−	9.27358i	0.626650	−	1.08539i	−0.361569	−	0.932345i	$-0.617759\pi$
$73$	5.35410	−	9.27358i	0.626650	−	1.08539i	0.988219	−	0.153045i	$-0.0489079\pi$
$74$	−1.66312	+	2.88061i	−0.193334	+	0.334864i
$75$		0			0
$76$	5.56231			0.638040
$77$		0			0
$78$	0.854102			0.0967080
$79$	−5.35410	−	9.27358i	−0.602384	−	1.04336i	−0.992459	−	0.122576i	$-0.960884\pi$
$79$	−5.35410	−	9.27358i	−0.602384	−	1.04336i	0.390076	−	0.920783i	$-0.372449\pi$
$80$	−3.51722	+	6.09201i	−0.393237	+	0.681107i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−0.854102	−	1.47935i	−0.0943198	−	0.163367i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	16.7082			1.81226
$86$	−1.52786	−	2.64634i	−0.164754	−	0.285362i
$87$	−5.00000	+	8.66025i	−0.536056	+	0.928477i
$88$	2.20820	−	3.82472i	0.235395	−	0.407717i
$89$	−1.11803	−	1.93649i	−0.118511	−	0.205268i	0.800667	−	0.599110i	$-0.204479\pi$
$89$	−1.11803	−	1.93649i	−0.118511	−	0.205268i	−0.919178	+	0.393842i	$0.871146\pi$
$90$	−1.70820			−0.180061
$91$		0			0
$92$	6.97871			0.727581
$93$	−5.59017	−	9.68246i	−0.579674	−	1.00402i
$94$	−0.281153	+	0.486971i	−0.0289987	+	0.0502272i
$95$	3.35410	−	5.80948i	0.344124	−	0.596040i
$96$	−4.63525	−	8.02850i	−0.473084	−	0.819405i
$97$	17.4164			1.76837			0.884184	−	0.467139i	$-0.154715\pi$
$97$	17.4164			1.76837			0.884184	+	0.467139i	$0.154715\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$	−3.19098	+	5.52694i	−0.315954	+	0.547249i
$103$	5.35410	+	9.27358i	0.527555	+	0.913753i	0.999484	+	0.0321160i	$0.0102246\pi$
$103$	5.35410	+	9.27358i	0.527555	+	0.913753i	−0.471929	+	0.881637i	$0.656442\pi$
$104$	1.47214			0.144355
$105$		0			0
$106$	−0.562306			−0.0546160
$107$	7.11803	+	12.3288i	0.688126	+	1.19187i	0.972443	+	0.233139i	$0.0748999\pi$
$107$	7.11803	+	12.3288i	0.688126	+	1.19187i	−0.284317	+	0.958730i	$0.591767\pi$
$108$	2.07295	−	3.59045i	0.199470	−	0.345492i
$109$	−5.35410	+	9.27358i	−0.512830	+	0.888248i	0.487059	+	0.873369i	$0.338070\pi$
$109$	−5.35410	+	9.27358i	−0.512830	+	0.888248i	−0.999889	+	0.0148787i	$0.995264\pi$
$110$	−1.28115	−	2.21902i	−0.122153	−	0.211575i
$111$	19.4721			1.84821
$112$		0			0
$113$	−14.9443			−1.40584			−0.702919	−	0.711269i	$-0.748121\pi$
$113$	−14.9443			−1.40584			−0.702919	+	0.711269i	$0.748121\pi$
$114$	1.28115	+	2.21902i	0.119991	+	0.207830i
$115$	4.20820	−	7.28882i	0.392417	−	0.679686i
$116$	−4.14590	+	7.18091i	−0.384937	+	0.666730i
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$	2.85410			0.262741
$119$		0			0
$120$	−7.36068			−0.671935
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−0.572949	+	0.992377i	−0.0518724	+	0.0898456i
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	−4.63525	−	8.02850i	−0.416258	−	0.720980i
$125$	−11.1803			−1.00000
$126$		0			0
$127$	15.4164			1.36798			0.683992	−	0.729489i	$-0.260242\pi$
$127$	15.4164			1.36798			0.683992	+	0.729489i	$0.260242\pi$
$128$	−5.04508	−	8.73834i	−0.445927	−	0.772368i
$129$	−8.94427	+	15.4919i	−0.787499	+	1.36399i
$130$	0.427051	−	0.739674i	0.0374548	−	0.0648737i
$131$	−1.88197	−	3.25966i	−0.164428	−	0.284798i	0.772024	−	0.635593i	$-0.219245\pi$
$131$	−1.88197	−	3.25966i	−0.164428	−	0.284798i	−0.936452	+	0.350796i	$0.885911\pi$
$132$	−12.4377			−1.08256
$133$		0			0
$134$	1.14590			0.0989905
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$	−5.50000	+	9.52628i	−0.471621	+	0.816872i
$137$	1.88197	−	3.25966i	0.160787	−	0.278492i	−0.774364	−	0.632740i	$-0.781930\pi$
$137$	1.88197	−	3.25966i	0.160787	−	0.278492i	0.935151	+	0.354249i	$0.115263\pi$
$138$	1.60739	+	2.78408i	0.136830	+	0.236997i
$139$	−3.41641			−0.289776			−0.144888	−	0.989448i	$-0.546282\pi$
$139$	−3.41641			−0.289776			−0.144888	+	0.989448i	$0.546282\pi$
$140$		0			0
$141$	3.29180			0.277219
$142$	1.70820	+	2.95870i	0.143349	+	0.248288i
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$	−3.14590	+	5.44886i	−0.262158	+	0.454071i
$145$	5.00000	+	8.66025i	0.415227	+	0.719195i
$146$	4.09017			0.338505
$147$		0			0
$148$	16.1459			1.32718
$149$	6.35410	+	11.0056i	0.520548	+	0.901616i	0.999715	+	0.0238920i	$0.00760577\pi$
$149$	6.35410	+	11.0056i	0.520548	+	0.901616i	−0.479166	+	0.877724i	$0.659061\pi$
$150$		0			0
$151$	3.20820	−	5.55677i	0.261080	−	0.452204i	−0.705449	−	0.708760i	$-0.749255\pi$
$151$	3.20820	−	5.55677i	0.261080	−	0.452204i	0.966529	+	0.256557i	$0.0825880\pi$
$152$	2.20820	+	3.82472i	0.179109	+	0.310226i
$153$	14.9443			1.20817
$154$		0			0
$155$	−11.1803			−0.898027
$156$	−2.07295	−	3.59045i	−0.165969	−	0.287466i
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$	2.04508	−	3.54219i	0.162698	−	0.281802i
$159$	1.64590	+	2.85078i	0.130528	+	0.226081i
$160$	−9.27051			−0.732898
$161$		0			0
$162$	4.20163			0.330111
$163$	−5.20820	−	9.02087i	−0.407938	−	0.706569i	0.586721	−	0.809789i	$-0.300419\pi$
$163$	−5.20820	−	9.02087i	−0.407938	−	0.706569i	−0.994659	+	0.103220i	$0.967085\pi$
$164$	−4.14590	+	7.18091i	−0.323740	+	0.560735i
$165$	−7.50000	+	12.9904i	−0.583874	+	1.01130i
$166$		0			0
$167$	−13.5279			−1.04682			−0.523409	−	0.852082i	$-0.675340\pi$
$167$	−13.5279			−1.04682			−0.523409	+	0.852082i	$0.675340\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	3.19098	+	5.52694i	0.244737	+	0.423897i
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	−7.41641	+	12.8456i	−0.565496	+	0.979467i
$173$	5.20820	+	9.02087i	0.395972	+	0.685844i	0.993225	−	0.116209i	$-0.0370743\pi$
$173$	5.20820	+	9.02087i	0.395972	+	0.685844i	−0.597252	+	0.802053i	$0.703741\pi$
$174$	−3.81966			−0.289568
$175$		0			0
$176$	−9.43769			−0.711393
$177$	−8.35410	−	14.4697i	−0.627933	−	1.08761i
$178$	0.427051	−	0.739674i	0.0320088	−	0.0554409i
$179$	−10.0623	+	17.4284i	−0.752092	+	1.30266i	0.194715	+	0.980860i	$0.437622\pi$
$179$	−10.0623	+	17.4284i	−0.752092	+	1.30266i	−0.946807	+	0.321802i	$0.895712\pi$
$180$	4.14590	+	7.18091i	0.309017	+	0.535233i
$181$	−1.41641			−0.105281			−0.0526404	−	0.998614i	$-0.516764\pi$
$181$	−1.41641			−0.105281			−0.0526404	+	0.998614i	$0.516764\pi$
$182$		0			0
$183$	6.70820			0.495885
$184$	2.77051	+	4.79866i	0.204245	+	0.353762i
$185$	9.73607	−	16.8634i	0.715810	−	1.23982i
$186$	2.13525	−	3.69837i	0.156564	−	0.271178i
$187$	11.2082	+	19.4132i	0.819625	+	1.41963i
$188$	2.72949			0.199069
$189$		0			0
$190$	2.56231			0.185889
$191$	5.59017	+	9.68246i	0.404491	+	0.700598i	0.994262	−	0.106972i	$-0.0341155\pi$
$191$	5.59017	+	9.68246i	0.404491	+	0.700598i	−0.589772	+	0.807570i	$0.700782\pi$
$192$	−5.26393	+	9.11740i	−0.379892	+	0.657992i
$193$	6.35410	−	11.0056i	0.457378	−	0.792202i	−0.541443	−	0.840737i	$-0.682122\pi$
$193$	6.35410	−	11.0056i	0.457378	−	0.792202i	0.998821	+	0.0485349i	$0.0154552\pi$
$194$	3.32624	+	5.76121i	0.238810	+	0.413631i
$195$	−5.00000			−0.358057
$196$		0			0
$197$	−26.9443			−1.91970			−0.959850	−	0.280514i	$-0.909495\pi$
$197$	−26.9443			−1.91970			−0.959850	+	0.280514i	$0.909495\pi$
$198$	−1.14590	−	1.98475i	−0.0814354	−	0.141050i
$199$	−3.64590	+	6.31488i	−0.258451	+	0.447650i	−0.965827	−	0.259187i	$-0.916545\pi$
$199$	−3.64590	+	6.31488i	−0.258451	+	0.447650i	0.707376	+	0.706837i	$0.249879\pi$
$200$		0			0
$201$	−3.35410	−	5.80948i	−0.236580	−	0.409769i
$202$	−3.43769			−0.241875
$203$		0			0
$204$	30.9787			2.16894
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$	−2.04508	+	3.54219i	−0.142488	+	0.246796i
$207$	3.76393	−	6.51932i	0.261611	−	0.453124i
$208$	−1.57295	−	2.72443i	−0.109064	−	0.188905i
$209$	9.00000			0.622543
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	1.36475	+	2.36381i	0.0937311	+	0.162347i
$213$	10.0000	−	17.3205i	0.685189	−	1.18678i
$214$	−2.71885	+	4.70918i	−0.185857	+	0.321913i
$215$	8.94427	+	15.4919i	0.609994	+	1.05654i
$216$	3.29180			0.223978
$217$		0			0
$218$	−4.09017			−0.277021
$219$	−11.9721	−	20.7363i	−0.809002	−	1.40123i
$220$	−6.21885	+	10.7714i	−0.419275	+	0.726205i
$221$	−3.73607	+	6.47106i	−0.251315	+	0.435291i
$222$	3.71885	+	6.44123i	0.249593	+	0.432307i
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$		0			0
$226$	−2.85410	−	4.94345i	−0.189852	−	0.328833i
$227$	−5.97214	+	10.3440i	−0.396385	+	0.686558i	−0.993277	−	0.115763i	$-0.963069\pi$
$227$	−5.97214	+	10.3440i	−0.396385	+	0.686558i	0.596892	+	0.802321i	$0.296402\pi$
$228$	6.21885	−	10.7714i	0.411853	−	0.713351i
$229$	−8.06231	−	13.9643i	−0.532772	−	0.922788i	−0.999268	−	0.0382649i	$-0.987817\pi$
$229$	−8.06231	−	13.9643i	−0.532772	−	0.922788i	0.466495	−	0.884524i	$-0.345516\pi$
$230$	3.21478			0.211976
$231$		0			0
$232$	−6.58359			−0.432234
$233$	2.97214	+	5.14789i	0.194711	+	0.337250i	0.946806	−	0.321806i	$-0.104290\pi$
$233$	2.97214	+	5.14789i	0.194711	+	0.337250i	−0.752095	+	0.659055i	$0.770956\pi$
$234$	0.381966	−	0.661585i	0.0249699	−	0.0432491i
$235$	1.64590	−	2.85078i	0.107367	−	0.185964i
$236$	−6.92705	−	11.9980i	−0.450913	−	0.781004i
$237$	−23.9443			−1.55535
$238$		0			0
$239$	−7.41641			−0.479728			−0.239864	−	0.970807i	$-0.577103\pi$
$239$	−7.41641			−0.479728			−0.239864	+	0.970807i	$0.577103\pi$
$240$	7.86475	+	13.6221i	0.507667	+	0.879305i
$241$	−4.35410	+	7.54153i	−0.280472	+	0.485792i	−0.971501	−	0.237035i	$-0.923824\pi$
$241$	−4.35410	+	7.54153i	−0.280472	+	0.485792i	0.691029	+	0.722827i	$0.257158\pi$
$242$	−0.381966	+	0.661585i	−0.0245537	+	0.0425283i
$243$	−8.94427	−	15.4919i	−0.573775	−	0.993808i
$244$	5.56231			0.356090
$245$		0			0
$246$	−3.81966			−0.243533
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$	3.68034	−	6.37454i	0.233702	−	0.404783i
$249$		0			0
$250$	−2.13525	−	3.69837i	−0.135045	−	0.233905i
$251$	−10.4721			−0.660995			−0.330498	−	0.943807i	$-0.607217\pi$
$251$	−10.4721			−0.660995			−0.330498	+	0.943807i	$0.607217\pi$
$252$		0			0
$253$	11.2918			0.709909
$254$	2.94427	+	5.09963i	0.184740	+	0.319979i
$255$	18.6803	−	32.3553i	1.16981	−	2.02617i
$256$	−2.78115	+	4.81710i	−0.173822	+	0.301069i
$257$	−8.97214	−	15.5402i	−0.559666	−	0.969371i	−0.997524	−	0.0703264i	$-0.977596\pi$
$257$	−8.97214	−	15.5402i	−0.559666	−	0.969371i	0.437858	−	0.899044i	$-0.355737\pi$
$258$	−6.83282			−0.425393
$259$		0			0
$260$	−4.14590			−0.257118
$261$	4.47214	+	7.74597i	0.276818	+	0.479463i
$262$	0.718847	−	1.24508i	0.0444105	−	0.0769213i
$263$	7.06231	−	12.2323i	0.435480	−	0.754274i	−0.561854	−	0.827236i	$-0.689912\pi$
$263$	7.06231	−	12.2323i	0.435480	−	0.754274i	0.997335	+	0.0729620i	$0.0232452\pi$
$264$	−4.93769	−	8.55234i	−0.303894	−	0.526360i
$265$	3.29180			0.202213
$266$		0			0
$267$	−5.00000			−0.305995
$268$	−2.78115	−	4.81710i	−0.169886	−	0.294251i
$269$	2.26393	−	3.92125i	0.138034	−	0.239083i	−0.788718	−	0.614755i	$-0.789255\pi$
$269$	2.26393	−	3.92125i	0.138034	−	0.239083i	0.926753	+	0.375672i	$0.122588\pi$
$270$	0.954915	−	1.65396i	0.0581143	−	0.100657i
$271$	3.20820	+	5.55677i	0.194885	+	0.337550i	0.946863	−	0.321638i	$-0.104233\pi$
$271$	3.20820	+	5.55677i	0.194885	+	0.337550i	−0.751978	+	0.659188i	$0.770900\pi$
$272$	23.5066			1.42530
$273$		0			0
$274$	1.43769			0.0868543
$275$		0			0
$276$	7.80244	−	13.5142i	0.469652	−	0.813461i
$277$	−13.2082	+	22.8773i	−0.793604	+	1.37456i	0.130118	+	0.991499i	$0.458464\pi$
$277$	−13.2082	+	22.8773i	−0.793604	+	1.37456i	−0.923722	+	0.383064i	$0.874869\pi$
$278$	−0.652476	−	1.13012i	−0.0391329	−	0.0677802i
$279$	−10.0000			−0.598684
$280$		0			0
$281$	9.05573			0.540219			0.270110	−	0.962830i	$-0.412940\pi$
$281$	9.05573			0.540219			0.270110	+	0.962830i	$0.412940\pi$
$282$	0.628677	+	1.08890i	0.0374372	+	0.0648431i
$283$	−7.06231	+	12.2323i	−0.419811	+	0.727133i	−0.995920	−	0.0902393i	$-0.971237\pi$
$283$	−7.06231	+	12.2323i	−0.419811	+	0.727133i	0.576110	+	0.817372i	$0.304570\pi$
$284$	8.29180	−	14.3618i	0.492028	−	0.852217i
$285$	−7.50000	−	12.9904i	−0.444262	−	0.769484i
$286$	1.14590			0.0677584
$287$		0			0
$288$	−8.29180			−0.488599
$289$	−19.4164	−	33.6302i	−1.14214	−	1.97825i
$290$	−1.90983	+	3.30792i	−0.112149	+	0.194248i
$291$	19.4721	−	33.7267i	1.14148	−	1.97710i
$292$	−9.92705	−	17.1942i	−0.580937	−	1.00621i
$293$	−2.94427			−0.172006			−0.0860031	−	0.996295i	$-0.527409\pi$
$293$	−2.94427			−0.172006			−0.0860031	+	0.996295i	$0.527409\pi$
$294$		0			0
$295$	−16.7082			−0.972789
$296$	6.40983	+	11.1022i	0.372564	+	0.645299i
$297$	3.35410	−	5.80948i	0.194625	−	0.337100i
$298$	−2.42705	+	4.20378i	−0.140595	+	0.243518i
$299$	1.88197	+	3.25966i	0.108837	+	0.188511i
$300$		0			0
$301$		0			0
$302$	2.45085			0.141031
$303$	10.0623	+	17.4284i	0.578064	+	1.00124i
$304$	4.71885	−	8.17328i	0.270644	−	0.468770i
$305$	3.35410	−	5.80948i	0.192055	−	0.332650i
$306$	2.85410	+	4.94345i	0.163158	+	0.282598i
$307$	7.41641			0.423277			0.211638	−	0.977348i	$-0.432120\pi$
$307$	7.41641			0.423277			0.211638	+	0.977348i	$0.432120\pi$
$308$		0			0
$309$	23.9443			1.36214
$310$	−2.13525	−	3.69837i	−0.121274	−	0.210053i
$311$	−16.1180	+	27.9173i	−0.913970	+	1.58304i	−0.105567	+	0.994412i	$0.533666\pi$
$311$	−16.1180	+	27.9173i	−0.913970	+	1.58304i	−0.808403	+	0.588630i	$0.799667\pi$
$312$	1.64590	−	2.85078i	0.0931806	−	0.161394i
$313$	−16.2082	−	28.0734i	−0.916142	−	1.58680i	−0.805221	−	0.592975i	$-0.797953\pi$
$313$	−16.2082	−	28.0734i	−0.916142	−	1.58680i	−0.110921	−	0.993829i	$-0.535380\pi$
$314$	2.67376			0.150889
$315$		0			0
$316$	−19.8541			−1.11688
$317$	1.88197	+	3.25966i	0.105702	+	0.183081i	0.914025	−	0.405659i	$-0.132958\pi$
$317$	1.88197	+	3.25966i	0.105702	+	0.183081i	−0.808323	+	0.588739i	$0.799624\pi$
$318$	−0.628677	+	1.08890i	−0.0352545	+	0.0610625i
$319$	−6.70820	+	11.6190i	−0.375587	+	0.650536i
$320$	5.26393	+	9.11740i	0.294263	+	0.509678i
$321$	31.8328			1.77673
$322$		0			0
$323$	−22.4164			−1.24728
$324$	−10.1976	−	17.6627i	−0.566531	−	0.981261i
$325$		0			0
$326$	1.98936	−	3.44567i	0.110180	−	0.190838i
$327$	11.9721	+	20.7363i	0.662061	+	1.14672i
$328$	−6.58359			−0.363518
$329$		0			0
$330$	−5.72949			−0.315398
$331$	14.2082	+	24.6093i	0.780954	+	1.35265i	0.931387	+	0.364031i	$0.118600\pi$
$331$	14.2082	+	24.6093i	0.780954	+	1.35265i	−0.150433	+	0.988620i	$0.548067\pi$
$332$		0			0
$333$	8.70820	−	15.0831i	0.477207	−	0.826546i
$334$	−2.58359	−	4.47491i	−0.141368	−	0.244856i
$335$	−6.70820			−0.366508
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	0.190983	+	0.330792i	0.0103881	+	0.0179927i
$339$	−16.7082	+	28.9395i	−0.907465	+	1.57178i
$340$	15.4894	−	26.8284i	0.840028	−	1.45497i
$341$	−7.50000	−	12.9904i	−0.406148	−	0.703469i
$342$	2.29180			0.123926
$343$		0			0
$344$	−11.7771			−0.634978
$345$	−9.40983	−	16.2983i	−0.506608	−	0.877471i
$346$	−1.98936	+	3.44567i	−0.106948	+	0.185240i
$347$	17.5344	−	30.3705i	0.941298	−	1.63038i	0.178299	−	0.983976i	$-0.442940\pi$
$347$	17.5344	−	30.3705i	0.941298	−	1.63038i	0.762999	−	0.646400i	$-0.223726\pi$
$348$	9.27051	+	16.0570i	0.496951	+	0.860745i
$349$	2.58359			0.138297			0.0691483	−	0.997606i	$-0.477972\pi$
$349$	2.58359			0.138297			0.0691483	+	0.997606i	$0.477972\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$	−6.21885	−	10.7714i	−0.331466	−	0.574115i
$353$	15.3541	−	26.5941i	0.817216	−	1.41546i	−0.0905091	−	0.995896i	$-0.528849\pi$
$353$	15.3541	−	26.5941i	0.817216	−	1.41546i	0.907725	−	0.419565i	$-0.137817\pi$
$354$	3.19098	−	5.52694i	0.169599	−	0.293754i
$355$	−10.0000	−	17.3205i	−0.530745	−	0.919277i
$356$	−4.14590			−0.219732
$357$		0			0
$358$	−7.68692			−0.406266
$359$	2.97214	+	5.14789i	0.156863	+	0.271695i	0.933736	−	0.357963i	$-0.116528\pi$
$359$	2.97214	+	5.14789i	0.156863	+	0.271695i	−0.776873	+	0.629658i	$0.783195\pi$
$360$	−3.29180	+	5.70156i	−0.173493	+	0.300498i
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	−0.270510	−	0.468537i	−0.0142177	−	0.0246257i
$363$	4.47214			0.234726
$364$		0			0
$365$	−23.9443			−1.25330
$366$	1.28115	+	2.21902i	0.0669669	+	0.115990i
$367$	0.354102	−	0.613323i	0.0184840	−	0.0320152i	−0.856635	−	0.515922i	$-0.827449\pi$
$367$	0.354102	−	0.613323i	0.0184840	−	0.0320152i	0.875119	+	0.483907i	$0.160783\pi$
$368$	5.92047	−	10.2546i	0.308626	−	0.534556i
$369$	4.47214	+	7.74597i	0.232810	+	0.403239i
$370$	7.43769			0.386667
$371$		0			0
$372$	−20.7295			−1.07477
$373$	14.2082	+	24.6093i	0.735673	+	1.27422i	0.954427	+	0.298443i	$0.0964673\pi$
$373$	14.2082	+	24.6093i	0.735673	+	1.27422i	−0.218755	+	0.975780i	$0.570199\pi$
$374$	−4.28115	+	7.41517i	−0.221373	+	0.383430i
$375$	−12.5000	+	21.6506i	−0.645497	+	1.11803i
$376$	1.08359	+	1.87684i	0.0558820	+	0.0967905i
$377$	−4.47214			−0.230327
$378$		0			0
$379$	11.4164			0.586421			0.293211	−	0.956048i	$-0.405276\pi$
$379$	11.4164			0.586421			0.293211	+	0.956048i	$0.405276\pi$
$380$	−6.21885	−	10.7714i	−0.319020	−	0.552559i
$381$	17.2361	−	29.8537i	0.883031	−	1.52945i
$382$	−2.13525	+	3.69837i	−0.109249	+	0.189225i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	−22.5623			−1.15138
$385$		0			0
$386$	4.85410			0.247067
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	16.1459	−	27.9655i	0.819684	−	1.41973i
$389$	3.73607	−	6.47106i	0.189426	−	0.328096i	−0.755633	−	0.654995i	$-0.772671\pi$
$389$	3.73607	−	6.47106i	0.189426	−	0.328096i	0.945059	+	0.326900i	$0.106004\pi$
$390$	−0.954915	−	1.65396i	−0.0483540	−	0.0837516i
$391$	−28.1246			−1.42232
$392$		0			0
$393$	−8.41641			−0.424552
$394$	−5.14590	−	8.91296i	−0.259247	−	0.449028i
$395$	−11.9721	+	20.7363i	−0.602384	+	1.04336i
$396$	−5.56231	+	9.63420i	−0.279516	+	0.484137i
$397$	7.06231	+	12.2323i	0.354447	+	0.613920i	0.987023	−	0.160578i	$-0.0513358\pi$
$397$	7.06231	+	12.2323i	0.354447	+	0.613920i	−0.632576	+	0.774498i	$0.718002\pi$
$398$	−2.78522			−0.139610
$399$		0			0
$400$		0			0
$401$	−4.88197	−	8.45581i	−0.243794	−	0.422263i	0.717998	−	0.696045i	$-0.245059\pi$
$401$	−4.88197	−	8.45581i	−0.243794	−	0.422263i	−0.961792	+	0.273782i	$0.911725\pi$
$402$	1.28115	−	2.21902i	0.0638981	−	0.110675i
$403$	2.50000	−	4.33013i	0.124534	−	0.215699i
$404$	8.34346	+	14.4513i	0.415103	+	0.718979i
$405$	−24.5967			−1.22222
$406$		0			0
$407$	26.1246			1.29495
$408$	12.2984	+	21.3014i	0.608860	+	1.05458i
$409$	−2.35410	+	4.07742i	−0.116403	+	0.201616i	−0.918340	−	0.395793i	$-0.870470\pi$
$409$	−2.35410	+	4.07742i	−0.116403	+	0.201616i	0.801937	+	0.597409i	$0.203803\pi$
$410$	−1.90983	+	3.30792i	−0.0943198	+	0.163367i
$411$	−4.20820	−	7.28882i	−0.207575	−	0.359531i
$412$	19.8541			0.978141
$413$		0			0
$414$	2.87539			0.141318
$415$		0			0
$416$	2.07295	−	3.59045i	0.101635	−	0.176036i
$417$	−3.81966	+	6.61585i	−0.187050	+	0.323979i
$418$	1.71885	+	2.97713i	0.0840716	+	0.145616i
$419$	−15.0557			−0.735520			−0.367760	−	0.929921i	$-0.619875\pi$
$419$	−15.0557			−0.735520			−0.367760	+	0.929921i	$0.619875\pi$
$420$		0			0
$421$	−13.4164			−0.653876			−0.326938	−	0.945046i	$-0.606017\pi$
$421$	−13.4164			−0.653876			−0.326938	+	0.945046i	$0.606017\pi$
$422$	0.763932	+	1.32317i	0.0371876	+	0.0644109i
$423$	1.47214	−	2.54981i	0.0715777	−	0.123976i
$424$	−1.08359	+	1.87684i	−0.0526239	+	0.0911472i
$425$		0			0
$426$	7.63932			0.370126
$427$		0			0
$428$	26.3951			1.27586
$429$	−3.35410	−	5.80948i	−0.161938	−	0.280484i
$430$	−3.41641	+	5.91739i	−0.164754	+	0.285362i
$431$	−6.68034	+	11.5707i	−0.321781	+	0.557340i	−0.980856	−	0.194737i	$-0.937615\pi$
$431$	−6.68034	+	11.5707i	−0.321781	+	0.557340i	0.659075	+	0.752077i	$0.270948\pi$
$432$	−3.51722	−	6.09201i	−0.169222	−	0.293102i
$433$	−2.58359			−0.124160			−0.0620798	−	0.998071i	$-0.519773\pi$
$433$	−2.58359			−0.124160			−0.0620798	+	0.998071i	$0.519773\pi$
$434$		0			0
$435$	22.3607			1.07211
$436$	9.92705	+	17.1942i	0.475420	+	0.823451i
$437$	−5.64590	+	9.77898i	−0.270080	+	0.467792i
$438$	4.57295	−	7.92058i	0.218504	−	0.378460i
$439$	−8.06231	−	13.9643i	−0.384793	−	0.666481i	0.606948	−	0.794742i	$-0.292394\pi$
$439$	−8.06231	−	13.9643i	−0.384793	−	0.666481i	−0.991740	+	0.128261i	$0.959060\pi$
$440$	−9.87539			−0.470791
$441$		0			0
$442$	−2.85410			−0.135756
$443$	1.11803	+	1.93649i	0.0531194	+	0.0920055i	0.891362	−	0.453291i	$-0.149750\pi$
$443$	1.11803	+	1.93649i	0.0531194	+	0.0920055i	−0.838243	+	0.545297i	$0.816417\pi$
$444$	18.0517	−	31.2664i	0.856694	−	1.48384i
$445$	−2.50000	+	4.33013i	−0.118511	+	0.205268i
$446$	0.763932	+	1.32317i	0.0361732	+	0.0626539i
$447$	28.4164			1.34405
$448$		0			0
$449$	10.3607			0.488951			0.244475	−	0.969656i	$-0.421384\pi$
$449$	10.3607			0.488951			0.244475	+	0.969656i	$0.421384\pi$
$450$		0			0
$451$	−6.70820	+	11.6190i	−0.315877	+	0.547115i
$452$	−13.8541	+	23.9960i	−0.651642	+	1.12868i
$453$	−7.17376	−	12.4253i	−0.337053	−	0.583792i
$454$	−4.56231			−0.214120
$455$		0			0
$456$	9.87539			0.462457
$457$	−17.0623	−	29.5528i	−0.798141	−	1.38242i	−0.920825	−	0.389975i	$-0.872484\pi$
$457$	−17.0623	−	29.5528i	−0.798141	−	1.38242i	0.122684	−	0.992446i	$-0.460850\pi$
$458$	3.07953	−	5.33390i	0.143897	−	0.249237i
$459$	−8.35410	+	14.4697i	−0.389936	+	0.675389i
$460$	−7.80244	−	13.5142i	−0.363791	−	0.630104i
$461$	10.3607			0.482545			0.241272	−	0.970457i	$-0.422435\pi$
$461$	10.3607			0.482545			0.241272	+	0.970457i	$0.422435\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	7.03444	+	12.1840i	0.326566	+	0.565628i
$465$	−12.5000	+	21.6506i	−0.579674	+	1.00402i
$466$	−1.13525	+	1.96632i	−0.0525897	+	0.0910880i
$467$	−10.8262	−	18.7516i	−0.500979	−	0.867720i	−0.999999	−	0.00113029i	$-0.999640\pi$
$467$	−10.8262	−	18.7516i	−0.500979	−	0.867720i	0.499021	−	0.866590i	$-0.333693\pi$
$468$	−3.70820			−0.171412
$469$		0			0
$470$	1.25735			0.0579974
$471$	−7.82624	−	13.5554i	−0.360614	−	0.624602i
$472$	5.50000	−	9.52628i	0.253158	−	0.438483i
$473$	−12.0000	+	20.7846i	−0.551761	+	0.955677i
$474$	−4.57295	−	7.92058i	−0.210043	−	0.363804i
$475$		0			0
$476$		0			0
$477$	2.94427			0.134809
$478$	−1.41641	−	2.45329i	−0.0647850	−	0.112211i
$479$	−14.9164	+	25.8360i	−0.681548	+	1.18048i	0.292960	+	0.956125i	$0.405360\pi$
$479$	−14.9164	+	25.8360i	−0.681548	+	1.18048i	−0.974508	+	0.224351i	$0.927974\pi$
$480$	−10.3647	+	17.9523i	−0.473084	+	0.819405i
$481$	4.35410	+	7.54153i	0.198530	+	0.343864i
$482$	−3.32624			−0.151506
$483$		0			0
$484$	3.70820			0.168555
$485$	−19.4721	−	33.7267i	−0.884184	−	1.53145i
$486$	3.41641	−	5.91739i	0.154971	−	0.268418i
$487$	−15.9164	+	27.5680i	−0.721241	+	1.24923i	0.239261	+	0.970955i	$0.423095\pi$
$487$	−15.9164	+	27.5680i	−0.721241	+	1.24923i	−0.960503	+	0.278271i	$0.910239\pi$
$488$	2.20820	+	3.82472i	0.0999607	+	0.173137i
$489$	−23.2918			−1.05329
$490$		0			0
$491$	−34.4721			−1.55571			−0.777853	−	0.628446i	$-0.783691\pi$
$491$	−34.4721			−1.55571			−0.777853	+	0.628446i	$0.783691\pi$
$492$	9.27051	+	16.0570i	0.417947	+	0.723905i
$493$	16.7082	−	28.9395i	0.752500	−	1.30337i
$494$	−0.572949	+	0.992377i	−0.0257782	+	0.0446491i
$495$	6.70820	+	11.6190i	0.301511	+	0.522233i
$496$	−15.7295			−0.706275
$497$		0			0
$498$		0			0
$499$	0.208204	+	0.360620i	0.00932049	+	0.0161436i	0.870648	−	0.491907i	$-0.163700\pi$
$499$	0.208204	+	0.360620i	0.00932049	+	0.0161436i	−0.861328	+	0.508050i	$0.830366\pi$
$500$	−10.3647	+	17.9523i	−0.463525	+	0.802850i
$501$	−15.1246	+	26.1966i	−0.675718	+	1.17038i
$502$	−2.00000	−	3.46410i	−0.0892644	−	0.154610i
$503$	−3.05573			−0.136248			−0.0681241	−	0.997677i	$-0.521701\pi$
$503$	−3.05573			−0.136248			−0.0681241	+	0.997677i	$0.521701\pi$
$504$		0			0
$505$	20.1246			0.895533
$506$	2.15654	+	3.73524i	0.0958699	+	0.166052i
$507$	1.11803	−	1.93649i	0.0496536	−	0.0860026i
$508$	14.2918	−	24.7541i	0.634096	−	1.09829i
$509$	−7.88197	−	13.6520i	−0.349362	−	0.605113i	0.636774	−	0.771050i	$-0.280268\pi$
$509$	−7.88197	−	13.6520i	−0.349362	−	0.605113i	−0.986136	+	0.165938i	$0.946935\pi$
$510$	14.2705			0.631909
$511$		0			0
$512$	−22.3050			−0.985749
$513$	3.35410	+	5.80948i	0.148087	+	0.256495i
$514$	3.42705	−	5.93583i	0.151161	−	0.261818i
$515$	11.9721	−	20.7363i	0.527555	−	0.913753i
$516$	16.5836	+	28.7236i	0.730052	+	1.26449i
$517$	4.41641			0.194233
$518$		0			0
$519$	23.2918			1.02240
$520$	−1.64590	−	2.85078i	−0.0721774	−	0.125015i
$521$	−0.0278640	+	0.0482619i	−0.00122075	+	0.00211439i	−0.866635	−	0.498942i	$-0.833722\pi$
$521$	−0.0278640	+	0.0482619i	−0.00122075	+	0.00211439i	0.865414	+	0.501057i	$0.167055\pi$
$522$	−1.70820	+	2.95870i	−0.0747661	+	0.129499i
$523$	9.64590	+	16.7072i	0.421786	+	0.730554i	0.996114	−	0.0880707i	$-0.0280701\pi$
$523$	9.64590	+	16.7072i	0.421786	+	0.730554i	−0.574329	+	0.818625i	$0.694737\pi$
$524$	−6.97871			−0.304867
$525$		0			0
$526$	5.39512			0.235238
$527$	18.6803	+	32.3553i	0.813728	+	1.40942i
$528$	−10.5517	+	18.2760i	−0.459202	+	0.795362i
$529$	4.41641	−	7.64944i	0.192018	−	0.332584i
$530$	0.628677	+	1.08890i	0.0273080	+	0.0472988i
$531$	−14.9443			−0.648526
$532$		0			0
$533$	−4.47214			−0.193710
$534$	−0.954915	−	1.65396i	−0.0413232	−	0.0715739i
$535$	15.9164	−	27.5680i	0.688126	−	1.19187i
$536$	2.20820	−	3.82472i	0.0953799	−	0.165203i
$537$	22.5000	+	38.9711i	0.970947	+	1.68173i
$538$	1.72949			0.0745636
$539$		0			0
$540$	−9.27051			−0.398939
$541$	−7.35410	−	12.7377i	−0.316178	−	0.547636i	0.663510	−	0.748168i	$-0.269066\pi$
$541$	−7.35410	−	12.7377i	−0.316178	−	0.547636i	−0.979687	+	0.200532i	$0.935733\pi$
$542$	−1.22542	+	2.12250i	−0.0526365	+	0.0911691i
$543$	−1.58359	+	2.74286i	−0.0679584	+	0.117707i
$544$	15.4894	+	26.8284i	0.664101	+	1.15026i
$545$	23.9443			1.02566
$546$		0			0
$547$	−31.4164			−1.34327			−0.671634	−	0.740883i	$-0.734407\pi$
$547$	−31.4164			−1.34327			−0.671634	+	0.740883i	$0.734407\pi$
$548$	−3.48936	−	6.04374i	−0.149058	−	0.258176i
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$		0			0
$551$	−6.70820	−	11.6190i	−0.285779	−	0.494984i
$552$	12.3901			0.527358
$553$		0			0
$554$	−10.0902			−0.428690
$555$	−21.7705	−	37.7076i	−0.924107	−	1.60060i
$556$	−3.16718	+	5.48572i	−0.134319	+	0.232647i
$557$	2.64590	−	4.58283i	0.112110	−	0.194181i	−0.804511	−	0.593938i	$-0.797572\pi$
$557$	2.64590	−	4.58283i	0.112110	−	0.194181i	0.916621	+	0.399758i	$0.130906\pi$
$558$	−1.90983	−	3.30792i	−0.0808496	−	0.140036i
$559$	−8.00000			−0.338364
$560$		0			0
$561$	50.1246			2.11626
$562$	1.72949	+	2.99556i	0.0729541	+	0.126360i
$563$	−18.2984	+	31.6937i	−0.771185	+	1.33573i	0.165730	+	0.986171i	$0.447002\pi$
$563$	−18.2984	+	31.6937i	−0.771185	+	1.33573i	−0.936914	+	0.349560i	$0.886331\pi$
$564$	3.05166	−	5.28563i	0.128498	−	0.222565i
$565$	16.7082	+	28.9395i	0.702919	+	1.21749i
$566$	−5.39512			−0.226774
$567$		0			0
$568$	13.1672			0.552483
$569$	−8.26393	−	14.3136i	−0.346442	−	0.600055i	0.639173	−	0.769063i	$-0.279277\pi$
$569$	−8.26393	−	14.3136i	−0.346442	−	0.600055i	−0.985615	+	0.169008i	$0.945944\pi$
$570$	2.86475	−	4.96188i	0.119991	−	0.207830i
$571$	−2.06231	+	3.57202i	−0.0863048	+	0.149484i	−0.905946	−	0.423392i	$-0.860839\pi$
$571$	−2.06231	+	3.57202i	−0.0863048	+	0.149484i	0.819642	+	0.572877i	$0.194173\pi$
$572$	−2.78115	−	4.81710i	−0.116286	−	0.201413i
$573$	25.0000			1.04439
$574$		0			0
$575$		0			0
$576$	4.70820	+	8.15485i	0.196175	+	0.339785i
$577$	−16.3541	+	28.3261i	−0.680830	+	1.17923i	0.293898	+	0.955837i	$0.405047\pi$
$577$	−16.3541	+	28.3261i	−0.680830	+	1.17923i	−0.974728	+	0.223396i	$0.928286\pi$
$578$	7.41641	−	12.8456i	0.308482	−	0.534306i
$579$	−14.2082	−	24.6093i	−0.590473	−	1.02273i
$580$	18.5410			0.769874
$581$		0			0
$582$	14.8754			0.616605
$583$	2.20820	+	3.82472i	0.0914545	+	0.158404i
$584$	7.88197	−	13.6520i	0.326158	−	0.564922i
$585$	−2.23607	+	3.87298i	−0.0924500	+	0.160128i
$586$	−0.562306	−	0.973942i	−0.0232286	−	0.0402332i
$587$	41.8885			1.72893			0.864463	−	0.502697i	$-0.167659\pi$
$587$	41.8885			1.72893			0.864463	+	0.502697i	$0.167659\pi$
$588$		0			0
$589$	15.0000			0.618064
$590$	−3.19098	−	5.52694i	−0.131371	−	0.227541i
$591$	−30.1246	+	52.1774i	−1.23916	+	2.14629i
$592$	13.6976	−	23.7249i	0.562966	−	0.975086i
$593$	16.1180	+	27.9173i	0.661888	+	1.14642i	0.980119	+	0.198411i	$0.0635780\pi$
$593$	16.1180	+	27.9173i	0.661888	+	1.14642i	−0.318231	+	0.948013i	$0.603089\pi$
$594$	2.56231			0.105133
$595$		0			0
$596$	23.5623			0.965150
$597$	8.15248	+	14.1205i	0.333659	+	0.577914i
$598$	−0.718847	+	1.24508i	−0.0293958	+	0.0509151i
$599$	−20.5344	+	35.5667i	−0.839015	+	1.45322i	0.0517049	+	0.998662i	$0.483534\pi$
$599$	−20.5344	+	35.5667i	−0.839015	+	1.45322i	−0.890719	+	0.454553i	$0.849799\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$	−6.00000			−0.244339
$604$	−5.94834	−	10.3028i	−0.242034	−	0.419216i
$605$	2.23607	−	3.87298i	0.0909091	−	0.157459i
$606$	−3.84346	+	6.65707i	−0.156130	+	0.270425i
$607$	−8.06231	−	13.9643i	−0.327239	−	0.566794i	0.654724	−	0.755868i	$-0.272785\pi$
$607$	−8.06231	−	13.9643i	−0.327239	−	0.566794i	−0.981963	+	0.189074i	$0.939452\pi$
$608$	12.4377			0.504415
$609$		0			0
$610$	2.56231			0.103745
$611$	0.736068	+	1.27491i	0.0297781	+	0.0515772i
$612$	13.8541	−	23.9960i	0.560019	−	0.969981i
$613$	−11.0623	+	19.1605i	−0.446802	+	0.773884i	−0.998176	−	0.0603742i	$-0.980771\pi$
$613$	−11.0623	+	19.1605i	−0.446802	+	0.773884i	0.551373	+	0.834259i	$0.314104\pi$
$614$	1.41641	+	2.45329i	0.0571616	+	0.0990067i
$615$	22.3607			0.901670
$616$		0			0
$617$	4.47214			0.180041			0.0900207	−	0.995940i	$-0.471307\pi$
$617$	4.47214			0.180041			0.0900207	+	0.995940i	$0.471307\pi$
$618$	4.57295	+	7.92058i	0.183951	+	0.318612i
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	−0.643094	−	0.765787i	$-0.722350\pi$
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	0.984738	+	0.174042i	$0.0556830\pi$
$620$	−10.3647	+	17.9523i	−0.416258	+	0.720980i
$621$	4.20820	+	7.28882i	0.168869	+	0.292490i
$622$	−12.3131			−0.493710
$623$		0			0
$624$	−7.03444			−0.281603
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	6.19098	−	10.7231i	0.247441	−	0.428581i
$627$	10.0623	−	17.4284i	0.401850	−	0.696024i
$628$	−6.48936	−	11.2399i	−0.258954	−	0.448521i
$629$	−65.0689			−2.59447
$630$		0			0
$631$	−30.8328			−1.22744			−0.613718	−	0.789526i	$-0.710327\pi$
$631$	−30.8328			−1.22744			−0.613718	+	0.789526i	$0.710327\pi$
$632$	−7.88197	−	13.6520i	−0.313528	−	0.543046i
$633$	4.47214	−	7.74597i	0.177751	−	0.307875i
$634$	−0.718847	+	1.24508i	−0.0285491	+	0.0494484i
$635$	−17.2361	−	29.8537i	−0.683992	−	1.18471i
$636$	6.10333			0.242013
$637$		0			0
$638$	−5.12461			−0.202885
$639$	−8.94427	−	15.4919i	−0.353830	−	0.612851i
$640$	−11.2812	+	19.5395i	−0.445927	+	0.772368i
$641$	2.97214	−	5.14789i	0.117392	−	0.203329i	−0.801341	−	0.598208i	$-0.795880\pi$
$641$	2.97214	−	5.14789i	0.117392	−	0.203329i	0.918734	+	0.394878i	$0.129213\pi$
$642$	6.07953	+	10.5300i	0.239940	+	0.415588i
$643$	18.8328			0.742694			0.371347	−	0.928494i	$-0.378896\pi$
$643$	18.8328			0.742694			0.371347	+	0.928494i	$0.378896\pi$
$644$		0			0
$645$	40.0000			1.57500
$646$	−4.28115	−	7.41517i	−0.168440	−	0.291746i
$647$	7.88197	−	13.6520i	0.309872	−	0.536714i	−0.668462	−	0.743746i	$-0.733047\pi$
$647$	7.88197	−	13.6520i	0.309872	−	0.536714i	0.978334	+	0.207032i	$0.0663804\pi$
$648$	8.09675	−	14.0240i	0.318070	−	0.550914i
$649$	−11.2082	−	19.4132i	−0.439960	−	0.762034i
$650$		0			0
$651$		0			0
$652$	−19.3131			−0.756359
$653$	−6.73607	−	11.6672i	−0.263603	−	0.456573i	0.703594	−	0.710602i	$-0.251577\pi$
$653$	−6.73607	−	11.6672i	−0.263603	−	0.456573i	−0.967197	+	0.254029i	$0.918244\pi$
$654$	−4.57295	+	7.92058i	−0.178816	+	0.309719i
$655$	−4.20820	+	7.28882i	−0.164428	+	0.284798i
$656$	7.03444	+	12.1840i	0.274649	+	0.475706i
$657$	−21.4164			−0.835534
$658$		0			0
$659$	8.94427			0.348419			0.174210	−	0.984709i	$-0.444263\pi$
$659$	8.94427			0.348419			0.174210	+	0.984709i	$0.444263\pi$
$660$	13.9058	+	24.0855i	0.541281	+	0.937526i
$661$	3.35410	−	5.80948i	0.130459	−	0.225962i	−0.793394	−	0.608708i	$-0.791688\pi$
$661$	3.35410	−	5.80948i	0.130459	−	0.225962i	0.923854	+	0.382746i	$0.125021\pi$
$662$	−5.42705	+	9.39993i	−0.210928	+	0.365339i
$663$	8.35410	+	14.4697i	0.324446	+	0.561958i
$664$		0			0
$665$		0			0
$666$	6.65248			0.257778
$667$	−8.41641	−	14.5776i	−0.325885	−	0.564449i
$668$	−12.5410	+	21.7217i	−0.485227	+	0.840437i
$669$	4.47214	−	7.74597i	0.172903	−	0.299476i
$670$	−1.28115	−	2.21902i	−0.0494953	−	0.0857283i
$671$	9.00000			0.347441
$672$		0			0
$673$	17.4164			0.671353			0.335677	−	0.941977i	$-0.391035\pi$
$673$	17.4164			0.671353			0.335677	+	0.941977i	$0.391035\pi$
$674$	3.43769	+	5.95426i	0.132415	+	0.229350i
$675$		0			0
$676$	0.927051	−	1.60570i	0.0356558	−	0.0617577i
$677$	16.4443	+	28.4823i	0.632005	+	1.09466i	0.987141	+	0.159850i	$0.0511010\pi$
$677$	16.4443	+	28.4823i	0.632005	+	1.09466i	−0.355137	+	0.934814i	$0.615566\pi$
$678$	−12.7639			−0.490196
$679$		0			0
$680$	24.5967			0.943242
$681$	13.3541	+	23.1300i	0.511730	+	0.886343i
$682$	2.86475	−	4.96188i	0.109697	−	0.190000i
$683$	2.26393	−	3.92125i	0.0866270	−	0.150042i	−0.819456	−	0.573142i	$-0.805725\pi$
$683$	2.26393	−	3.92125i	0.0866270	−	0.150042i	0.906083	+	0.423099i	$0.139058\pi$
$684$	−5.56231	−	9.63420i	−0.212680	−	0.368373i
$685$	−8.41641			−0.321574
$686$		0			0
$687$	−36.0557			−1.37561
$688$	12.5836	+	21.7954i	0.479745	+	0.830943i
$689$	−0.736068	+	1.27491i	−0.0280420	+	0.0485701i
$690$	3.59424	−	6.22540i	0.136830	−	0.236997i
$691$	0.916408	+	1.58726i	0.0348618	+	0.0603824i	0.882930	−	0.469505i	$-0.155568\pi$
$691$	0.916408	+	1.58726i	0.0348618	+	0.0603824i	−0.848068	+	0.529887i	$0.822234\pi$
$692$	19.3131			0.734173
$693$		0			0
$694$	13.3951			0.508472
$695$	3.81966	+	6.61585i	0.144888	+	0.250953i
$696$	−7.36068	+	12.7491i	−0.279006	+	0.483252i
$697$	16.7082	−	28.9395i	0.632868	−	1.09616i
$698$	0.493422	+	0.854632i	0.0186763	+	0.0323483i
$699$	13.2918			0.502742
$700$		0			0
$701$	22.3607			0.844551			0.422276	−	0.906467i	$-0.361231\pi$
$701$	22.3607			0.844551			0.422276	+	0.906467i	$0.361231\pi$
$702$	0.427051	+	0.739674i	0.0161180	+	0.0279172i
$703$	−13.0623	+	22.6246i	−0.492654	+	0.853302i
$704$	−7.06231	+	12.2323i	−0.266171	+	0.461021i
$705$	−3.68034	−	6.37454i	−0.138610	−	0.240079i
$706$	11.7295			0.441445
$707$		0			0
$708$	−30.9787			−1.16425
$709$	4.93769	+	8.55234i	0.185439	+	0.321190i	0.943724	−	0.330733i	$-0.107296\pi$
$709$	4.93769	+	8.55234i	0.185439	+	0.321190i	−0.758285	+	0.651923i	$0.773963\pi$
$710$	3.81966	−	6.61585i	0.143349	−	0.248288i
$711$	−10.7082	+	18.5472i	−0.401589	+	0.695573i
$712$	−1.64590	−	2.85078i	−0.0616826	−	0.106837i
$713$	18.8197			0.704802
$714$		0			0
$715$	−6.70820			−0.250873
$716$	18.6565	+	32.3141i	0.697228	+	1.20763i
$717$	−8.29180	+	14.3618i	−0.309663	+	0.536352i
$718$	−1.13525	+	1.96632i	−0.0423673	+	0.0733824i
$719$	5.64590	+	9.77898i	0.210556	+	0.364694i	0.951889	−	0.306444i	$-0.0991391\pi$
$719$	5.64590	+	9.77898i	0.210556	+	0.364694i	−0.741332	+	0.671138i	$0.765806\pi$
$720$	14.0689			0.524316
$721$		0			0
$722$	3.81966			0.142153
$723$	9.73607	+	16.8634i	0.362088	+	0.627155i
$724$	−1.31308	+	2.27433i	−0.0488003	+	0.0845246i
$725$		0			0
$726$	0.854102	+	1.47935i	0.0316987	+	0.0549038i
$727$	−14.8328			−0.550119			−0.275059	−	0.961427i	$-0.588698\pi$
$727$	−14.8328			−0.550119			−0.275059	+	0.961427i	$0.588698\pi$
$728$		0			0
$729$	−7.00000			−0.259259
$730$	−4.57295	−	7.92058i	−0.169252	−	0.293154i
$731$	29.8885	−	51.7685i	1.10547	−	1.91473i
$732$	6.21885	−	10.7714i	0.229855	−	0.398121i
$733$	7.64590	+	13.2431i	0.282408	+	0.489144i	0.971977	−	0.235075i	$-0.0755336\pi$
$733$	7.64590	+	13.2431i	0.282408	+	0.489144i	−0.689570	+	0.724219i	$0.742200\pi$
$734$	0.270510			0.00998470
$735$		0			0
$736$	15.6049			0.575203
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$	−1.70820	+	2.95870i	−0.0628799	+	0.108911i
$739$	−17.9164	+	31.0321i	−0.659066	+	1.14154i	0.321792	+	0.946810i	$0.395715\pi$
$739$	−17.9164	+	31.0321i	−0.659066	+	1.14154i	−0.980858	+	0.194725i	$0.937619\pi$
$740$	−18.0517	−	31.2664i	−0.663592	−	1.14938i
$741$	6.70820			0.246432
$742$		0			0
$743$	15.0557			0.552341			0.276171	−	0.961109i	$-0.410935\pi$
$743$	15.0557			0.552341			0.276171	+	0.961109i	$0.410935\pi$
$744$	−8.22949	−	14.2539i	−0.301708	−	0.522573i
$745$	14.2082	−	24.6093i	0.520548	−	0.901616i
$746$	−5.42705	+	9.39993i	−0.198698	+	0.344156i
$747$		0			0
$748$	41.5623			1.51967
$749$		0			0
$750$	−9.54915			−0.348686
$751$	−15.0623	−	26.0887i	−0.549631	−	0.951989i	−0.998300	−	0.0582911i	$-0.981435\pi$
$751$	−15.0623	−	26.0887i	−0.549631	−	0.951989i	0.448668	−	0.893698i	$-0.351898\pi$
$752$	2.31559	−	4.01073i	0.0844411	−	0.146256i
$753$	−11.7082	+	20.2792i	−0.426671	+	0.739015i
$754$	−0.854102	−	1.47935i	−0.0311046	−	0.0538747i
$755$	−14.3475			−0.522160
$756$		0			0
$757$	0.832816			0.0302692			0.0151346	−	0.999885i	$-0.495182\pi$
$757$	0.832816			0.0302692			0.0151346	+	0.999885i	$0.495182\pi$
$758$	2.18034	+	3.77646i	0.0791935	+	0.137167i
$759$	12.6246	−	21.8665i	0.458244	−	0.793703i
$760$	4.93769	−	8.55234i	0.179109	−	0.310226i
$761$	16.7705	+	29.0474i	0.607931	+	1.05297i	0.991581	+	0.129488i	$0.0413334\pi$
$761$	16.7705	+	29.0474i	0.607931	+	1.05297i	−0.383650	+	0.923478i	$0.625333\pi$
$762$	13.1672			0.476997
$763$		0			0
$764$	20.7295			0.749967
$765$	−16.7082	−	28.9395i	−0.604086	−	1.04631i
$766$	−2.86475	+	4.96188i	−0.103507	+	0.179280i
$767$	3.73607	−	6.47106i	0.134902	−	0.233656i
$768$	6.21885	+	10.7714i	0.224403	+	0.388678i
$769$	−46.0000			−1.65880			−0.829401	−	0.558653i	$-0.811318\pi$
$769$	−46.0000			−1.65880			−0.829401	+	0.558653i	$0.811318\pi$
$770$		0			0
$771$	−40.1246			−1.44505
$772$	−11.7812	−	20.4056i	−0.424013	−	0.734412i
$773$	5.53444	−	9.58593i	0.199060	−	0.344782i	−0.749164	−	0.662385i	$-0.769544\pi$
$773$	5.53444	−	9.58593i	0.199060	−	0.344782i	0.948224	+	0.317603i	$0.102878\pi$
$774$	−3.05573	+	5.29268i	−0.109836	+	0.190241i
$775$		0			0
$776$	25.6393			0.920398
$777$		0			0
$778$	2.85410			0.102325
$779$	−6.70820	−	11.6190i	−0.240346	−	0.416292i
$780$	−4.63525	+	8.02850i	−0.165969	+	0.287466i
$781$	13.4164	−	23.2379i	0.480077	−	0.831517i
$782$	−5.37132	−	9.30340i	−0.192078	−	0.332689i
$783$	−10.0000			−0.357371
$784$		0			0
$785$	−15.6525			−0.558661
$786$	−1.60739	−	2.78408i	−0.0573337	−	0.0993049i
$787$	−3.20820	+	5.55677i	−0.114360	+	0.198078i	−0.917524	−	0.397681i	$-0.869815\pi$
$787$	−3.20820	+	5.55677i	−0.114360	+	0.198078i	0.803164	+	0.595758i	$0.203148\pi$
$788$	−24.9787	+	43.2644i	−0.889830	+	1.54123i
$789$	−15.7918	−	27.3522i	−0.562203	−	0.973764i
$790$	−9.14590			−0.325396
$791$		0			0
$792$	−8.83282			−0.313860
$793$	1.50000	+	2.59808i	0.0532666	+	0.0922604i
$794$	−2.69756	+	4.67231i	−0.0957329	+	0.165814i
$795$	3.68034	−	6.37454i	0.130528	−	0.226081i
$796$	6.75987	+	11.7084i	0.239597	+	0.414994i
$797$	−26.9443			−0.954415			−0.477208	−	0.878791i	$-0.658351\pi$
$797$	−26.9443			−0.954415			−0.477208	+	0.878791i	$0.658351\pi$
$798$		0			0
$799$	−11.0000			−0.389152
$800$		0			0
$801$	−2.23607	+	3.87298i	−0.0790076	+	0.136845i
$802$	1.86475	−	3.22983i	0.0658464	−	0.114049i
$803$	−16.0623	−	27.8207i	−0.566826	−	0.981772i
$804$	−12.4377			−0.438644
$805$		0			0
$806$	1.90983			0.0672709
$807$	−5.06231	−	8.76817i	−0.178202	−	0.308654i
$808$	−6.62461	+	11.4742i	−0.233053	+	0.403660i
$809$	2.20820	−	3.82472i	0.0776363	−	0.134470i	−0.824593	−	0.565726i	$-0.808596\pi$
$809$	2.20820	−	3.82472i	0.0776363	−	0.134470i	0.902230	+	0.431256i	$0.141929\pi$
$810$	−4.69756	−	8.13641i	−0.165055	−	0.285884i
$811$	−38.8328			−1.36360			−0.681802	−	0.731536i	$-0.738804\pi$
$811$	−38.8328			−1.36360			−0.681802	+	0.731536i	$0.738804\pi$
$812$		0			0
$813$	14.3475			0.503190
$814$	4.98936	+	8.64182i	0.174877	+	0.302896i
$815$	−11.6459	+	20.1713i	−0.407938	+	0.706569i
$816$	26.2812	−	45.5203i	0.920024	−	1.59353i
$817$	−12.0000	−	20.7846i	−0.419827	−	0.727161i
$818$	−1.79837			−0.0628787
$819$		0			0
$820$	18.5410			0.647480
$821$	−16.8820	−	29.2404i	−0.589185	−	1.02050i	−0.994339	−	0.106250i	$-0.966116\pi$
$821$	−16.8820	−	29.2404i	−0.589185	−	1.02050i	0.405155	−	0.914248i	$-0.367218\pi$
$822$	1.60739	−	2.78408i	0.0560642	−	0.0971060i
$823$	3.06231	−	5.30407i	0.106745	−	0.184888i	−0.807705	−	0.589587i	$-0.799290\pi$
$823$	3.06231	−	5.30407i	0.106745	−	0.184888i	0.914450	+	0.404699i	$0.132624\pi$
$824$	7.88197	+	13.6520i	0.274581	+	0.475589i
$825$		0			0
$826$		0			0
$827$	−26.8328			−0.933068			−0.466534	−	0.884503i	$-0.654498\pi$
$827$	−26.8328			−0.933068			−0.466534	+	0.884503i	$0.654498\pi$
$828$	−6.97871	−	12.0875i	−0.242527	−	0.420069i
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	−0.997225	−	0.0744432i	$-0.976282\pi$
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	0.563082	+	0.826401i	$0.309615\pi$
$830$		0			0
$831$	29.5344	+	51.1552i	1.02454	+	1.77455i
$832$	−4.70820			−0.163228
$833$		0			0
$834$	−2.91796			−0.101041
$835$	15.1246	+	26.1966i	0.523409	+	0.906571i
$836$	8.34346	−	14.4513i	0.288565	−	0.499808i
$837$	5.59017	−	9.68246i	0.193225	−	0.334675i
$838$	−2.87539	−	4.98032i	−0.0993286	−	0.172042i
$839$	−29.8885			−1.03187			−0.515934	−	0.856629i	$-0.672555\pi$
$839$	−29.8885			−1.03187			−0.515934	+	0.856629i	$0.672555\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$	−2.56231	−	4.43804i	−0.0883029	−	0.152945i
$843$	10.1246	−	17.5363i	0.348710	−	0.603984i
$844$	3.70820	−	6.42280i	0.127642	−	0.221082i
$845$	−1.11803	−	1.93649i	−0.0384615	−	0.0666173i
$846$	1.12461			0.0386650
$847$		0			0
$848$	4.63119			0.159036
$849$	15.7918	+	27.3522i	0.541973	+	0.938725i
$850$		0			0
$851$	−16.3885	+	28.3858i	−0.561792	+	0.973052i
$852$	−18.5410	−	32.1140i	−0.635205	−	1.10021i
$853$	−28.2492			−0.967235			−0.483617	−	0.875279i	$-0.660677\pi$
$853$	−28.2492			−0.967235			−0.483617	+	0.875279i	$0.660677\pi$
$854$		0			0
$855$	−13.4164			−0.458831
$856$	10.4787	+	18.1497i	0.358155	+	0.620343i
$857$	21.6803	−	37.5515i	0.740586	−	1.28273i	−0.211642	−	0.977347i	$-0.567881\pi$
$857$	21.6803	−	37.5515i	0.740586	−	1.28273i	0.952229	−	0.305386i	$-0.0987855\pi$
$858$	1.28115	−	2.21902i	0.0437378	−	0.0757562i
$859$	3.64590	+	6.31488i	0.124396	+	0.215461i	0.921497	−	0.388386i	$-0.126967\pi$
$859$	3.64590	+	6.31488i	0.124396	+	0.215461i	−0.797100	+	0.603847i	$0.793634\pi$
$860$	33.1672			1.13099
$861$		0			0
$862$	−5.10333			−0.173820
$863$	−3.02786	−	5.24441i	−0.103070	−	0.178522i	0.809878	−	0.586598i	$-0.199533\pi$
$863$	−3.02786	−	5.24441i	−0.103070	−	0.178522i	−0.912948	+	0.408076i	$0.866200\pi$
$864$	4.63525	−	8.02850i	0.157695	−	0.273135i
$865$	11.6459	−	20.1713i	0.395972	−	0.685844i
$866$	−0.493422	−	0.854632i	−0.0167672	−	0.0290416i
$867$	−86.8328			−2.94900
$868$		0			0
$869$	−32.1246			−1.08975
$870$	4.27051	+	7.39674i	0.144784	+	0.250773i
$871$	1.50000	−	2.59808i	0.0508256	−	0.0880325i
$872$	−7.88197	+	13.6520i	−0.266917	+	0.462314i
$873$	−17.4164	−	30.1661i	−0.589456	−	1.02097i
$874$	−4.31308			−0.145892
$875$		0			0
$876$	−44.3951			−1.49997
$877$	4.06231	+	7.03612i	0.137174	+	0.237593i	0.926426	−	0.376477i	$-0.122865\pi$
$877$	4.06231	+	7.03612i	0.137174	+	0.237593i	−0.789252	+	0.614070i	$0.789531\pi$
$878$	3.07953	−	5.33390i	0.103929	−	0.180010i
$879$	−3.29180	+	5.70156i	−0.111030	+	0.192309i
$880$	10.5517	+	18.2760i	0.355696	+	0.616084i
$881$	19.3050			0.650400			0.325200	−	0.945645i	$-0.394568\pi$
$881$	19.3050			0.650400			0.325200	+	0.945645i	$0.394568\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	6.92705	+	11.9980i	0.232982	+	0.403537i
$885$	−18.6803	+	32.3553i	−0.627933	+	1.08761i
$886$	−0.427051	+	0.739674i	−0.0143471	+	0.0248498i
$887$	−7.88197	−	13.6520i	−0.264651	−	0.458388i	0.702821	−	0.711366i	$-0.251923\pi$
$887$	−7.88197	−	13.6520i	−0.264651	−	0.458388i	−0.967472	+	0.252978i	$0.918590\pi$
$888$	28.6656			0.961956
$889$		0			0
$890$	−1.90983			−0.0640176
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$	3.70820	−	6.42280i	0.124160	−	0.215051i
$893$	−2.20820	+	3.82472i	−0.0738947	+	0.127989i
$894$	5.42705	+	9.39993i	0.181508	+	0.314381i
$895$	45.0000			1.50418
$896$		0			0
$897$	8.41641			0.281016
$898$	1.97871	+	3.42723i	0.0660305	+	0.114368i
$899$	−11.1803	+	19.3649i	−0.372885	+	0.645856i
$900$		0			0
$901$	−5.50000	−	9.52628i	−0.183232	−	0.317366i
$902$	−5.12461			−0.170631
$903$		0			0
$904$	−22.0000			−0.731709
$905$	1.58359	+	2.74286i	0.0526404	+	0.0911758i
$906$	2.74013	−	4.74605i	0.0910348	−	0.157677i
$907$	−2.64590	+	4.58283i	−0.0878556	+	0.152170i	−0.906604	−	0.421981i	$-0.861335\pi$
$907$	−2.64590	+	4.58283i	−0.0878556	+	0.152170i	0.818749	+	0.574152i	$0.194668\pi$
$908$	11.0729	+	19.1789i	0.367469	+	0.636474i
$909$	18.0000			0.597022
$910$		0			0
$911$	46.2492			1.53231			0.766153	−	0.642659i	$-0.222169\pi$
$911$	46.2492			1.53231			0.766153	+	0.642659i	$0.222169\pi$
$912$	−10.5517	−	18.2760i	−0.349400	−	0.605179i
$913$		0			0
$914$	6.51722	−	11.2882i	0.215571	−	0.373379i
$915$	−7.50000	−	12.9904i	−0.247942	−	0.429449i
$916$	−29.8967			−0.987814
$917$		0			0
$918$	−6.38197			−0.210636
$919$	10.0623	+	17.4284i	0.331925	+	0.574911i	0.982889	−	0.184198i	$-0.0589686\pi$
$919$	10.0623	+	17.4284i	0.331925	+	0.574911i	−0.650964	+	0.759108i	$0.725635\pi$
$920$	6.19505	−	10.7301i	0.204245	−	0.353762i
$921$	8.29180	−	14.3618i	0.273224	−	0.473238i
$922$	1.97871	+	3.42723i	0.0651655	+	0.112870i
$923$	8.94427			0.294404
$924$		0			0
$925$		0			0
$926$	−4.58359	−	7.93901i	−0.150626	−	0.260892i
$927$	10.7082	−	18.5472i	0.351704	−	0.609168i
$928$	−9.27051	+	16.0570i	−0.304319	+	0.527097i
$929$	−23.5902	−	40.8594i	−0.773968	−	1.34055i	−0.935372	−	0.353664i	$-0.884936\pi$
$929$	−23.5902	−	40.8594i	−0.773968	−	1.34055i	0.161404	−	0.986888i	$-0.448398\pi$
$930$	−9.54915			−0.313129
$931$		0			0
$932$	11.0213			0.361014
$933$	36.0410	+	62.4249i	1.17993	+	2.04370i
$934$	4.13525	−	7.16247i	0.135310	−	0.234363i
$935$	25.0623	−	43.4092i	0.819625	−	1.41963i
$936$	−1.47214	−	2.54981i	−0.0481183	−	0.0833433i
$937$	1.41641			0.0462720			0.0231360	−	0.999732i	$-0.492635\pi$
$937$	1.41641			0.0462720			0.0231360	+	0.999732i	$0.492635\pi$
$938$		0			0
$939$	−72.4853			−2.36547
$940$	−3.05166	−	5.28563i	−0.0995343	−	0.172398i
$941$	22.8820	−	39.6327i	0.745931	−	1.29199i	−0.203828	−	0.979007i	$-0.565338\pi$
$941$	22.8820	−	39.6327i	0.745931	−	1.29199i	0.949759	−	0.312983i	$-0.101328\pi$
$942$	2.98936	−	5.17772i	0.0973985	−	0.168699i
$943$	−8.41641	−	14.5776i	−0.274076	−	0.474713i
$944$	−23.5066			−0.765074
$945$		0			0
$946$	−9.16718			−0.298051
$947$	15.7361	+	27.2557i	0.511354	+	0.885690i	0.999913	+	0.0131599i	$0.00418904\pi$
$947$	15.7361	+	27.2557i	0.511354	+	0.885690i	−0.488560	+	0.872530i	$0.662478\pi$
$948$	−22.1976	+	38.4473i	−0.720943	+	1.24871i
$949$	5.35410	−	9.27358i	0.173802	−	0.301033i
$950$		0			0
$951$	8.41641			0.272921
$952$		0			0
$953$	29.7771			0.964574			0.482287	−	0.876013i	$-0.339806\pi$
$953$	29.7771			0.964574			0.482287	+	0.876013i	$0.339806\pi$
$954$	0.562306	+	0.973942i	0.0182053	+	0.0315325i
$955$	12.5000	−	21.6506i	0.404491	−	0.700598i
$956$	−6.87539	+	11.9085i	−0.222366	+	0.385149i
$957$	15.0000	+	25.9808i	0.484881	+	0.839839i
$958$	−11.3951			−0.368160
$959$		0			0
$960$	23.5410			0.759783
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	−1.66312	+	2.88061i	−0.0536211	+	0.0928745i
$963$	14.2361	−	24.6576i	0.458751	−	0.794580i
$964$	8.07295	+	13.9828i	0.260012	+	0.450354i
$965$	−28.4164			−0.914757
$966$		0			0
$967$	43.4164			1.39618			0.698089	−	0.716011i	$-0.254034\pi$
$967$	43.4164			1.39618			0.698089	+	0.716011i	$0.254034\pi$
$968$	1.47214	+	2.54981i	0.0473162	+	0.0819541i
$969$	−25.0623	+	43.4092i	−0.805117	+	1.39450i
$970$	7.43769	−	12.8825i	0.238810	−	0.413631i
$971$	−12.3541	−	21.3979i	−0.396462	−	0.686692i	0.596825	−	0.802372i	$-0.296429\pi$
$971$	−12.3541	−	21.3979i	−0.396462	−	0.686692i	−0.993287	+	0.115679i	$0.963095\pi$
$972$	−33.1672			−1.06384
$973$		0			0
$974$	−12.1591			−0.389601
$975$		0			0
$976$	4.71885	−	8.17328i	0.151047	−	0.261620i
$977$	16.8262	−	29.1439i	0.538319	−	0.932396i	−0.460676	−	0.887569i	$-0.652393\pi$
$977$	16.8262	−	29.1439i	0.538319	−	0.932396i	0.998995	−	0.0448274i	$-0.0142738\pi$
$978$	−4.44834	−	7.70475i	−0.142242	−	0.246371i
$979$	−6.70820			−0.214395
$980$		0			0
$981$	21.4164			0.683773
$982$	−6.58359	−	11.4031i	−0.210091	−	0.363888i
$983$	−0.736068	+	1.27491i	−0.0234769	+	0.0406632i	−0.877525	−	0.479531i	$-0.840807\pi$
$983$	−0.736068	+	1.27491i	−0.0234769	+	0.0406632i	0.854048	+	0.520194i	$0.174140\pi$
$984$	−7.36068	+	12.7491i	−0.234650	+	0.406426i
$985$	30.1246	+	52.1774i	0.959850	+	1.66251i
$986$	12.7639			0.406486
$987$		0			0
$988$	5.56231			0.176961
$989$	−15.0557	−	26.0773i	−0.478744	−	0.829209i
$990$	−2.56231	+	4.43804i	−0.0814354	+	0.141050i
$991$	−8.64590	+	14.9751i	−0.274646	+	0.475701i	−0.970046	−	0.242922i	$-0.921894\pi$
$991$	−8.64590	+	14.9751i	−0.274646	+	0.475701i	0.695400	+	0.718623i	$0.255227\pi$
$992$	−10.3647	−	17.9523i	−0.329081	−	0.569985i
$993$	63.5410			2.01641
$994$		0			0
$995$	16.3050			0.516902
$996$		0			0
$997$	−0.208204	+	0.360620i	−0.00659388	+	0.0114209i	−0.869304	−	0.494279i	$-0.835432\pi$
$997$	−0.208204	+	0.360620i	−0.00659388	+	0.0114209i	0.862710	+	0.505700i	$0.168766\pi$
$998$	−0.0795268	+	0.137745i	−0.00251738	+	0.00436023i
$999$	9.73607	+	16.8634i	0.308036	+	0.533533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.h.508.1		4
7.2	even	3	inner	637.2.e.h.79.1		4
7.3	odd	6		637.2.a.f.1.2		2
7.4	even	3		637.2.a.e.1.2		2
7.5	odd	6		91.2.e.b.79.1	yes	4
7.6	odd	2		91.2.e.b.53.1	✓	4
21.5	even	6		819.2.j.c.352.2		4
21.11	odd	6		5733.2.a.w.1.1		2
21.17	even	6		5733.2.a.v.1.1		2
21.20	even	2		819.2.j.c.235.2		4
28.19	even	6		1456.2.r.j.625.2		4
28.27	even	2		1456.2.r.j.417.2		4
91.12	odd	6		1183.2.e.d.170.2		4
91.25	even	6		8281.2.a.ba.1.1		2
91.38	odd	6		8281.2.a.z.1.1		2
91.90	odd	2		1183.2.e.d.508.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.b.53.1	✓	4	7.6	odd	2
91.2.e.b.79.1	yes	4	7.5	odd	6
637.2.a.e.1.2		2	7.4	even	3
637.2.a.f.1.2		2	7.3	odd	6
637.2.e.h.79.1		4	7.2	even	3	inner
637.2.e.h.508.1		4	1.1	even	1	trivial
819.2.j.c.235.2		4	21.20	even	2
819.2.j.c.352.2		4	21.5	even	6
1183.2.e.d.170.2		4	91.12	odd	6
1183.2.e.d.508.2		4	91.90	odd	2
1456.2.r.j.417.2		4	28.27	even	2
1456.2.r.j.625.2		4	28.19	even	6
5733.2.a.v.1.1		2	21.17	even	6
5733.2.a.w.1.1		2	21.11	odd	6
8281.2.a.z.1.1		2	91.38	odd	6
8281.2.a.ba.1.1		2	91.25	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 + 0.330792i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +0.854102 q^{6} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.190983 + 0.330792i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +0.854102 q^{6} +1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.427051 - 0.739674i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-2.07295 - 3.59045i) q^{12} +1.00000 q^{13} -5.00000 q^{15} +(-1.57295 - 2.72443i) q^{16} +(-3.73607 + 6.47106i) q^{17} +(0.381966 - 0.661585i) q^{18} +(1.50000 + 2.59808i) q^{19} -4.14590 q^{20} +1.14590 q^{22} +(1.88197 + 3.25966i) q^{23} +(1.64590 - 2.85078i) q^{24} +(0.190983 + 0.330792i) q^{26} +2.23607 q^{27} -4.47214 q^{29} +(-0.954915 - 1.65396i) q^{30} +(2.50000 - 4.33013i) q^{31} +(2.07295 - 3.59045i) q^{32} +(-3.35410 - 5.80948i) q^{33} -2.85410 q^{34} -3.70820 q^{36} +(4.35410 + 7.54153i) q^{37} +(-0.572949 + 0.992377i) q^{38} +(1.11803 - 1.93649i) q^{39} +(-1.64590 - 2.85078i) q^{40} -4.47214 q^{41} -8.00000 q^{43} +(-2.78115 - 4.81710i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(-0.718847 + 1.24508i) q^{46} +(0.736068 + 1.27491i) q^{47} -7.03444 q^{48} +(8.35410 + 14.4697i) q^{51} +(0.927051 - 1.60570i) q^{52} +(-0.736068 + 1.27491i) q^{53} +(0.427051 + 0.739674i) q^{54} -6.70820 q^{55} +6.70820 q^{57} +(-0.854102 - 1.47935i) q^{58} +(3.73607 - 6.47106i) q^{59} +(-4.63525 + 8.02850i) q^{60} +(1.50000 + 2.59808i) q^{61} +1.90983 q^{62} -4.70820 q^{64} +(-1.11803 - 1.93649i) q^{65} +(1.28115 - 2.21902i) q^{66} +(1.50000 - 2.59808i) q^{67} +(6.92705 + 11.9980i) q^{68} +8.41641 q^{69} +8.94427 q^{71} +(-1.47214 - 2.54981i) q^{72} +(5.35410 - 9.27358i) q^{73} +(-1.66312 + 2.88061i) q^{74} +5.56231 q^{76} +0.854102 q^{78} +(-5.35410 - 9.27358i) q^{79} +(-3.51722 + 6.09201i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-0.854102 - 1.47935i) q^{82} +16.7082 q^{85} +(-1.52786 - 2.64634i) q^{86} +(-5.00000 + 8.66025i) q^{87} +(2.20820 - 3.82472i) q^{88} +(-1.11803 - 1.93649i) q^{89} -1.70820 q^{90} +6.97871 q^{92} +(-5.59017 - 9.68246i) q^{93} +(-0.281153 + 0.486971i) q^{94} +(3.35410 - 5.80948i) q^{95} +(-4.63525 - 8.02850i) q^{96} +17.4164 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 3 q^{4} - 10 q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 3 * q^4 - 10 * q^6 - 12 * q^8 - 4 * q^9	\( 4 q + 3 q^{2} - 3 q^{4} - 10 q^{6} - 12 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - 15 q^{12} + 4 q^{13} - 20 q^{15} - 13 q^{16} - 6 q^{17} + 6 q^{18} + 6 q^{19} - 30 q^{20} + 18 q^{22} + 12 q^{23} + 20 q^{24} + 3 q^{26} - 15 q^{30} + 10 q^{31} + 15 q^{32} + 2 q^{34} + 12 q^{36} + 4 q^{37} - 9 q^{38} - 20 q^{40} - 32 q^{43} + 9 q^{44} - 23 q^{46} - 6 q^{47} + 30 q^{48} + 20 q^{51} - 3 q^{52} + 6 q^{53} - 5 q^{54} + 10 q^{58} + 6 q^{59} + 15 q^{60} + 6 q^{61} + 30 q^{62} + 8 q^{64} - 15 q^{66} + 6 q^{67} + 21 q^{68} - 20 q^{69} + 12 q^{72} + 8 q^{73} + 9 q^{74} - 18 q^{76} - 10 q^{78} - 8 q^{79} + 15 q^{80} + 22 q^{81} + 10 q^{82} + 40 q^{85} - 24 q^{86} - 20 q^{87} - 18 q^{88} + 20 q^{90} - 66 q^{92} + 19 q^{94} + 15 q^{96} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 3 * q^4 - 10 * q^6 - 12 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - 15 * q^12 + 4 * q^13 - 20 * q^15 - 13 * q^16 - 6 * q^17 + 6 * q^18 + 6 * q^19 - 30 * q^20 + 18 * q^22 + 12 * q^23 + 20 * q^24 + 3 * q^26 - 15 * q^30 + 10 * q^31 + 15 * q^32 + 2 * q^34 + 12 * q^36 + 4 * q^37 - 9 * q^38 - 20 * q^40 - 32 * q^43 + 9 * q^44 - 23 * q^46 - 6 * q^47 + 30 * q^48 + 20 * q^51 - 3 * q^52 + 6 * q^53 - 5 * q^54 + 10 * q^58 + 6 * q^59 + 15 * q^60 + 6 * q^61 + 30 * q^62 + 8 * q^64 - 15 * q^66 + 6 * q^67 + 21 * q^68 - 20 * q^69 + 12 * q^72 + 8 * q^73 + 9 * q^74 - 18 * q^76 - 10 * q^78 - 8 * q^79 + 15 * q^80 + 22 * q^81 + 10 * q^82 + 40 * q^85 - 24 * q^86 - 20 * q^87 - 18 * q^88 + 20 * q^90 - 66 * q^92 + 19 * q^94 + 15 * q^96 + 16 * q^97 - 24 * q^99

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