LMFDB - Embedded newform 637.2.e.h.79.1

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			79.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.h.508.1

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	0.190983	−	0.330792i	0.135045	−	0.233905i	0.925615	+	0.378467i	$0.123549\pi$
$3$	1.11803	+	1.93649i	0.645497	+	1.11803i	0.984186	+	0.177136i	$0.0566831\pi$
$3$	1.11803	+	1.93649i	0.645497	+	1.11803i	−0.338689	+	0.940898i	$0.609984\pi$
$4$	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	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	−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	−0.819394	−	0.573231i	$-0.805690\pi$
$17$	−3.73607	−	6.47106i	−0.906130	−	1.56946i	−0.0867359	−	0.996231i	$-0.527644\pi$
$18$	0.381966	+	0.661585i	0.0900303	+	0.155937i
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$	−4.14590			−0.927051
$21$		0			0
$22$	1.14590			0.244306
$23$	1.88197	−	3.25966i	0.392417	−	0.679686i	−0.600351	−	0.799737i	$-0.704972\pi$
$23$	1.88197	−	3.25966i	0.392417	−	0.679686i	0.992768	+	0.120051i	$0.0383057\pi$
$24$	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	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$	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	−0.246836	−	0.969057i	$-0.579391\pi$
$37$	4.35410	−	7.54153i	0.715810	−	1.23982i	0.962646	−	0.270762i	$-0.0872757\pi$
$38$	−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	−0.807336	−	0.590092i	$-0.799091\pi$
$47$	0.736068	−	1.27491i	0.107367	−	0.185964i	0.914703	+	0.404128i	$0.132425\pi$
$48$	−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	0.811034	−	0.584999i	$-0.198905\pi$
$53$	−0.736068	−	1.27491i	−0.101107	−	0.175122i	−0.912141	+	0.409877i	$0.865572\pi$
$54$	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	0.999878	−	0.0156395i	$-0.00497842\pi$
$59$	3.73607	+	6.47106i	0.486395	+	0.842460i	−0.513483	+	0.858100i	$0.671645\pi$
$60$	−4.63525	−	8.02850i	−0.598409	−	1.03647i
$61$	1.50000	−	2.59808i	0.192055	−	0.332650i	−0.753876	−	0.657017i	$-0.771818\pi$
$61$	1.50000	−	2.59808i	0.192055	−	0.332650i	0.945931	+	0.324367i	$0.105151\pi$
$62$	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	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$	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	0.988219	+	0.153045i	$0.0489079\pi$
$73$	5.35410	+	9.27358i	0.626650	+	1.08539i	−0.361569	+	0.932345i	$0.617759\pi$
$74$	−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	0.390076	+	0.920783i	$0.372449\pi$
$79$	−5.35410	+	9.27358i	−0.602384	+	1.04336i	−0.992459	+	0.122576i	$0.960884\pi$
$80$	−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	−0.919178	−	0.393842i	$-0.871146\pi$
$89$	−1.11803	+	1.93649i	−0.118511	+	0.205268i	0.800667	+	0.599110i	$0.204479\pi$
$90$	−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	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−3.19098	−	5.52694i	−0.315954	−	0.547249i
$103$	5.35410	−	9.27358i	0.527555	−	0.913753i	−0.471929	−	0.881637i	$-0.656442\pi$
$103$	5.35410	−	9.27358i	0.527555	−	0.913753i	0.999484	−	0.0321160i	$-0.0102246\pi$
$104$	1.47214			0.144355
$105$		0			0
$106$	−0.562306			−0.0546160
$107$	7.11803	−	12.3288i	0.688126	−	1.19187i	−0.284317	−	0.958730i	$-0.591767\pi$
$107$	7.11803	−	12.3288i	0.688126	−	1.19187i	0.972443	−	0.233139i	$-0.0748999\pi$
$108$	2.07295	+	3.59045i	0.199470	+	0.345492i
$109$	−5.35410	−	9.27358i	−0.512830	−	0.888248i	−0.999889	−	0.0148787i	$-0.995264\pi$
$109$	−5.35410	−	9.27358i	−0.512830	−	0.888248i	0.487059	−	0.873369i	$-0.338070\pi$
$110$	−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	−0.936452	−	0.350796i	$-0.885911\pi$
$131$	−1.88197	+	3.25966i	−0.164428	+	0.284798i	0.772024	+	0.635593i	$0.219245\pi$
$132$	−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	0.935151	−	0.354249i	$-0.115263\pi$
$137$	1.88197	+	3.25966i	0.160787	+	0.278492i	−0.774364	+	0.632740i	$0.781930\pi$
$138$	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	−0.479166	−	0.877724i	$-0.659061\pi$
$149$	6.35410	−	11.0056i	0.520548	−	0.901616i	0.999715	−	0.0238920i	$-0.00760577\pi$
$150$		0			0
$151$	3.20820	+	5.55677i	0.261080	+	0.452204i	0.966529	−	0.256557i	$-0.0825880\pi$
$151$	3.20820	+	5.55677i	0.261080	+	0.452204i	−0.705449	+	0.708760i	$0.749255\pi$
$152$	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	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$	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	−0.994659	−	0.103220i	$-0.967085\pi$
$163$	−5.20820	+	9.02087i	−0.407938	+	0.706569i	0.586721	+	0.809789i	$0.300419\pi$
$164$	−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	−0.597252	−	0.802053i	$-0.703741\pi$
$173$	5.20820	−	9.02087i	0.395972	−	0.685844i	0.993225	+	0.116209i	$0.0370743\pi$
$174$	−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	−0.946807	−	0.321802i	$-0.895712\pi$
$179$	−10.0623	−	17.4284i	−0.752092	−	1.30266i	0.194715	−	0.980860i	$-0.437622\pi$
$180$	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	−0.589772	−	0.807570i	$-0.700782\pi$
$191$	5.59017	−	9.68246i	0.404491	−	0.700598i	0.994262	+	0.106972i	$0.0341155\pi$
$192$	−5.26393	−	9.11740i	−0.379892	−	0.657992i
$193$	6.35410	+	11.0056i	0.457378	+	0.792202i	0.998821	−	0.0485349i	$-0.0154552\pi$
$193$	6.35410	+	11.0056i	0.457378	+	0.792202i	−0.541443	+	0.840737i	$0.682122\pi$
$194$	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	0.707376	−	0.706837i	$-0.249879\pi$
$199$	−3.64590	−	6.31488i	−0.258451	−	0.447650i	−0.965827	+	0.259187i	$0.916545\pi$
$200$		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	0.596892	−	0.802321i	$-0.296402\pi$
$227$	−5.97214	−	10.3440i	−0.396385	−	0.686558i	−0.993277	+	0.115763i	$0.963069\pi$
$228$	6.21885	+	10.7714i	0.411853	+	0.713351i
$229$	−8.06231	+	13.9643i	−0.532772	+	0.922788i	0.466495	+	0.884524i	$0.345516\pi$
$229$	−8.06231	+	13.9643i	−0.532772	+	0.922788i	−0.999268	+	0.0382649i	$0.987817\pi$
$230$	3.21478			0.211976
$231$		0			0
$232$	−6.58359			−0.432234
$233$	2.97214	−	5.14789i	0.194711	−	0.337250i	−0.752095	−	0.659055i	$-0.770956\pi$
$233$	2.97214	−	5.14789i	0.194711	−	0.337250i	0.946806	+	0.321806i	$0.104290\pi$
$234$	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	0.691029	−	0.722827i	$-0.257158\pi$
$241$	−4.35410	−	7.54153i	−0.280472	−	0.485792i	−0.971501	+	0.237035i	$0.923824\pi$
$242$	−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	0.437858	+	0.899044i	$0.355737\pi$
$257$	−8.97214	+	15.5402i	−0.559666	+	0.969371i	−0.997524	+	0.0703264i	$0.977596\pi$
$258$	−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	0.997335	−	0.0729620i	$-0.0232452\pi$
$263$	7.06231	+	12.2323i	0.435480	+	0.754274i	−0.561854	+	0.827236i	$0.689912\pi$
$264$	−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	0.926753	−	0.375672i	$-0.122588\pi$
$269$	2.26393	+	3.92125i	0.138034	+	0.239083i	−0.788718	+	0.614755i	$0.789255\pi$
$270$	0.954915	+	1.65396i	0.0581143	+	0.100657i
$271$	3.20820	−	5.55677i	0.194885	−	0.337550i	−0.751978	−	0.659188i	$-0.770900\pi$
$271$	3.20820	−	5.55677i	0.194885	−	0.337550i	0.946863	+	0.321638i	$0.104233\pi$
$272$	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	−0.923722	−	0.383064i	$-0.874869\pi$
$277$	−13.2082	−	22.8773i	−0.793604	−	1.37456i	0.130118	−	0.991499i	$-0.458464\pi$
$278$	−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	0.576110	−	0.817372i	$-0.304570\pi$
$283$	−7.06231	−	12.2323i	−0.419811	−	0.727133i	−0.995920	+	0.0902393i	$0.971237\pi$
$284$	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	−0.808403	−	0.588630i	$-0.799667\pi$
$311$	−16.1180	−	27.9173i	−0.913970	−	1.58304i	−0.105567	−	0.994412i	$-0.533666\pi$
$312$	1.64590	+	2.85078i	0.0931806	+	0.161394i
$313$	−16.2082	+	28.0734i	−0.916142	+	1.58680i	−0.110921	+	0.993829i	$0.535380\pi$
$313$	−16.2082	+	28.0734i	−0.916142	+	1.58680i	−0.805221	+	0.592975i	$0.797953\pi$
$314$	2.67376			0.150889
$315$		0			0
$316$	−19.8541			−1.11688
$317$	1.88197	−	3.25966i	0.105702	−	0.183081i	−0.808323	−	0.588739i	$-0.799624\pi$
$317$	1.88197	−	3.25966i	0.105702	−	0.183081i	0.914025	+	0.405659i	$0.132958\pi$
$318$	−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	−0.150433	−	0.988620i	$-0.548067\pi$
$331$	14.2082	−	24.6093i	0.780954	−	1.35265i	0.931387	−	0.364031i	$-0.118600\pi$
$332$		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	0.762999	+	0.646400i	$0.223726\pi$
$347$	17.5344	+	30.3705i	0.941298	+	1.63038i	0.178299	+	0.983976i	$0.442940\pi$
$348$	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	0.907725	+	0.419565i	$0.137817\pi$
$353$	15.3541	+	26.5941i	0.817216	+	1.41546i	−0.0905091	+	0.995896i	$0.528849\pi$
$354$	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	−0.776873	−	0.629658i	$-0.783195\pi$
$359$	2.97214	−	5.14789i	0.156863	−	0.271695i	0.933736	+	0.357963i	$0.116528\pi$
$360$	−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	0.875119	−	0.483907i	$-0.160783\pi$
$367$	0.354102	+	0.613323i	0.0184840	+	0.0320152i	−0.856635	+	0.515922i	$0.827449\pi$
$368$	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	−0.218755	−	0.975780i	$-0.570199\pi$
$373$	14.2082	−	24.6093i	0.735673	−	1.27422i	0.954427	−	0.298443i	$-0.0964673\pi$
$374$	−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	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$	−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	0.945059	−	0.326900i	$-0.106004\pi$
$389$	3.73607	+	6.47106i	0.189426	+	0.328096i	−0.755633	+	0.654995i	$0.772671\pi$
$390$	−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	−0.632576	−	0.774498i	$-0.718002\pi$
$397$	7.06231	−	12.2323i	0.354447	−	0.613920i	0.987023	+	0.160578i	$0.0513358\pi$
$398$	−2.78522			−0.139610
$399$		0			0
$400$		0			0
$401$	−4.88197	+	8.45581i	−0.243794	+	0.422263i	−0.961792	−	0.273782i	$-0.911725\pi$
$401$	−4.88197	+	8.45581i	−0.243794	+	0.422263i	0.717998	+	0.696045i	$0.245059\pi$
$402$	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	0.801937	−	0.597409i	$-0.203803\pi$
$409$	−2.35410	−	4.07742i	−0.116403	−	0.201616i	−0.918340	+	0.395793i	$0.870470\pi$
$410$	−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	0.659075	−	0.752077i	$-0.270948\pi$
$431$	−6.68034	−	11.5707i	−0.321781	−	0.557340i	−0.980856	+	0.194737i	$0.937615\pi$
$432$	−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	−0.991740	−	0.128261i	$-0.959060\pi$
$439$	−8.06231	+	13.9643i	−0.384793	+	0.666481i	0.606948	+	0.794742i	$0.292394\pi$
$440$	−9.87539			−0.470791
$441$		0			0
$442$	−2.85410			−0.135756
$443$	1.11803	−	1.93649i	0.0531194	−	0.0920055i	−0.838243	−	0.545297i	$-0.816417\pi$
$443$	1.11803	−	1.93649i	0.0531194	−	0.0920055i	0.891362	+	0.453291i	$0.149750\pi$
$444$	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	0.122684	+	0.992446i	$0.460850\pi$
$457$	−17.0623	+	29.5528i	−0.798141	+	1.38242i	−0.920825	+	0.389975i	$0.872484\pi$
$458$	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	0.499021	+	0.866590i	$0.333693\pi$
$467$	−10.8262	+	18.7516i	−0.500979	+	0.867720i	−0.999999	+	0.00113029i	$0.999640\pi$
$468$	−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	−0.974508	−	0.224351i	$-0.927974\pi$
$479$	−14.9164	−	25.8360i	−0.681548	−	1.18048i	0.292960	−	0.956125i	$-0.405360\pi$
$480$	−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	−0.960503	−	0.278271i	$-0.910239\pi$
$487$	−15.9164	−	27.5680i	−0.721241	−	1.24923i	0.239261	−	0.970955i	$-0.423095\pi$
$488$	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	−0.861328	−	0.508050i	$-0.830366\pi$
$499$	0.208204	−	0.360620i	0.00932049	−	0.0161436i	0.870648	+	0.491907i	$0.163700\pi$
$500$	−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	−0.986136	−	0.165938i	$-0.946935\pi$
$509$	−7.88197	+	13.6520i	−0.349362	+	0.605113i	0.636774	+	0.771050i	$0.280268\pi$
$510$	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	0.865414	−	0.501057i	$-0.167055\pi$
$521$	−0.0278640	−	0.0482619i	−0.00122075	−	0.00211439i	−0.866635	+	0.498942i	$0.833722\pi$
$522$	−1.70820	−	2.95870i	−0.0747661	−	0.129499i
$523$	9.64590	−	16.7072i	0.421786	−	0.730554i	−0.574329	−	0.818625i	$-0.694737\pi$
$523$	9.64590	−	16.7072i	0.421786	−	0.730554i	0.996114	+	0.0880707i	$0.0280701\pi$
$524$	−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	−0.979687	−	0.200532i	$-0.935733\pi$
$541$	−7.35410	+	12.7377i	−0.316178	+	0.547636i	0.663510	+	0.748168i	$0.269066\pi$
$542$	−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	0.916621	−	0.399758i	$-0.130906\pi$
$557$	2.64590	+	4.58283i	0.112110	+	0.194181i	−0.804511	+	0.593938i	$0.797572\pi$
$558$	−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	−0.936914	−	0.349560i	$-0.886331\pi$
$563$	−18.2984	−	31.6937i	−0.771185	−	1.33573i	0.165730	−	0.986171i	$-0.447002\pi$
$564$	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	−0.985615	−	0.169008i	$-0.945944\pi$
$569$	−8.26393	+	14.3136i	−0.346442	+	0.600055i	0.639173	+	0.769063i	$0.279277\pi$
$570$	2.86475	+	4.96188i	0.119991	+	0.207830i
$571$	−2.06231	−	3.57202i	−0.0863048	−	0.149484i	0.819642	−	0.572877i	$-0.194173\pi$
$571$	−2.06231	−	3.57202i	−0.0863048	−	0.149484i	−0.905946	+	0.423392i	$0.860839\pi$
$572$	−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	−0.974728	−	0.223396i	$-0.928286\pi$
$577$	−16.3541	−	28.3261i	−0.680830	−	1.17923i	0.293898	−	0.955837i	$-0.405047\pi$
$578$	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	−0.318231	−	0.948013i	$-0.603089\pi$
$593$	16.1180	−	27.9173i	0.661888	−	1.14642i	0.980119	−	0.198411i	$-0.0635780\pi$
$594$	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	−0.890719	−	0.454553i	$-0.849799\pi$
$599$	−20.5344	−	35.5667i	−0.839015	−	1.45322i	0.0517049	−	0.998662i	$-0.483534\pi$
$600$		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	−0.981963	−	0.189074i	$-0.939452\pi$
$607$	−8.06231	+	13.9643i	−0.327239	+	0.566794i	0.654724	+	0.755868i	$0.272785\pi$
$608$	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	0.551373	−	0.834259i	$-0.314104\pi$
$613$	−11.0623	−	19.1605i	−0.446802	−	0.773884i	−0.998176	+	0.0603742i	$0.980771\pi$
$614$	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	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	−0.643094	+	0.765787i	$0.722350\pi$
$620$	−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	0.918734	−	0.394878i	$-0.129213\pi$
$641$	2.97214	+	5.14789i	0.117392	+	0.203329i	−0.801341	+	0.598208i	$0.795880\pi$
$642$	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	0.978334	−	0.207032i	$-0.0663804\pi$
$647$	7.88197	+	13.6520i	0.309872	+	0.536714i	−0.668462	+	0.743746i	$0.733047\pi$
$648$	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	−0.967197	−	0.254029i	$-0.918244\pi$
$653$	−6.73607	+	11.6672i	−0.263603	+	0.456573i	0.703594	+	0.710602i	$0.251577\pi$
$654$	−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	0.923854	−	0.382746i	$-0.125021\pi$
$661$	3.35410	+	5.80948i	0.130459	+	0.225962i	−0.793394	+	0.608708i	$0.791688\pi$
$662$	−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	−0.355137	−	0.934814i	$-0.615566\pi$
$677$	16.4443	−	28.4823i	0.632005	−	1.09466i	0.987141	−	0.159850i	$-0.0511010\pi$
$678$	−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	0.906083	−	0.423099i	$-0.139058\pi$
$683$	2.26393	+	3.92125i	0.0866270	+	0.150042i	−0.819456	+	0.573142i	$0.805725\pi$
$684$	−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	−0.848068	−	0.529887i	$-0.822234\pi$
$691$	0.916408	−	1.58726i	0.0348618	−	0.0603824i	0.882930	+	0.469505i	$0.155568\pi$
$692$	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	−0.758285	−	0.651923i	$-0.773963\pi$
$709$	4.93769	−	8.55234i	0.185439	−	0.321190i	0.943724	+	0.330733i	$0.107296\pi$
$710$	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	−0.741332	−	0.671138i	$-0.765806\pi$
$719$	5.64590	−	9.77898i	0.210556	−	0.364694i	0.951889	+	0.306444i	$0.0991391\pi$
$720$	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	−0.689570	−	0.724219i	$-0.742200\pi$
$733$	7.64590	−	13.2431i	0.282408	−	0.489144i	0.971977	+	0.235075i	$0.0755336\pi$
$734$	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	−0.980858	−	0.194725i	$-0.937619\pi$
$739$	−17.9164	−	31.0321i	−0.659066	−	1.14154i	0.321792	−	0.946810i	$-0.395715\pi$
$740$	−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	0.448668	+	0.893698i	$0.351898\pi$
$751$	−15.0623	+	26.0887i	−0.549631	+	0.951989i	−0.998300	+	0.0582911i	$0.981435\pi$
$752$	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	−0.383650	−	0.923478i	$-0.625333\pi$
$761$	16.7705	−	29.0474i	0.607931	−	1.05297i	0.991581	−	0.129488i	$-0.0413334\pi$
$762$	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	0.948224	−	0.317603i	$-0.102878\pi$
$773$	5.53444	+	9.58593i	0.199060	+	0.344782i	−0.749164	+	0.662385i	$0.769544\pi$
$774$	−3.05573	−	5.29268i	−0.109836	−	0.190241i
$775$		0			0
$776$	25.6393			0.920398
$777$

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

Introduction

L-functions

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