LMFDB - Embedded newform 819.2.j.c.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(235,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("819.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.j (of order $3$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.2
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	819.235
Dual form			819.2.j.c.352.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 - 0.330792i) q^{2} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.47214 q^{8} +O(q^{10})$	\(q+(-0.190983 - 0.330792i) q^{2} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.47214 q^{8} +(-0.427051 + 0.739674i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(0.954915 + 0.330792i) q^{14} +(-1.57295 - 2.72443i) q^{16} +(-3.73607 + 6.47106i) q^{17} +(-1.50000 - 2.59808i) q^{19} -4.14590 q^{20} +1.14590 q^{22} +(-1.88197 - 3.25966i) q^{23} +(0.190983 + 0.330792i) q^{26} +(0.927051 + 4.81710i) q^{28} +4.47214 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-2.07295 + 3.59045i) q^{32} +2.85410 q^{34} +(5.59017 + 1.93649i) q^{35} +(4.35410 + 7.54153i) q^{37} +(-0.572949 + 0.992377i) q^{38} +(1.64590 + 2.85078i) q^{40} -4.47214 q^{41} -8.00000 q^{43} +(2.78115 + 4.81710i) q^{44} +(-0.718847 + 1.24508i) q^{46} +(0.736068 + 1.27491i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-0.927051 + 1.60570i) q^{52} +(0.736068 - 1.27491i) q^{53} +6.70820 q^{55} +(2.94427 - 2.54981i) q^{56} +(-0.854102 - 1.47935i) q^{58} +(3.73607 - 6.47106i) q^{59} +(-1.50000 - 2.59808i) q^{61} +1.90983 q^{62} -4.70820 q^{64} +(1.11803 + 1.93649i) q^{65} +(1.50000 - 2.59808i) q^{67} +(6.92705 + 11.9980i) q^{68} +(-0.427051 - 2.21902i) q^{70} -8.94427 q^{71} +(-5.35410 + 9.27358i) q^{73} +(1.66312 - 2.88061i) q^{74} -5.56231 q^{76} +(-1.50000 - 7.79423i) q^{77} +(-5.35410 - 9.27358i) q^{79} +(-3.51722 + 6.09201i) q^{80} +(0.854102 + 1.47935i) q^{82} +16.7082 q^{85} +(1.52786 + 2.64634i) q^{86} +(2.20820 - 3.82472i) q^{88} +(-1.11803 - 1.93649i) q^{89} +(2.00000 - 1.73205i) q^{91} -6.97871 q^{92} +(0.281153 - 0.486971i) q^{94} +(-3.35410 + 5.80948i) q^{95} -17.4164 q^{97} +(-2.48278 + 0.992377i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q - 3 * q^2 - 3 * q^4 - 8 * q^7 + 12 * q^8	$ 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + 5 q^{10} - 6 q^{11} - 4 q^{13} + 15 q^{14} - 13 q^{16} - 6 q^{17} - 6 q^{19} - 30 q^{20} + 18 q^{22} - 12 q^{23} + 3 q^{26} - 3 q^{28} - 10 q^{31} - 15 q^{32} - 2 q^{34} + 4 q^{37} - 9 q^{38} + 20 q^{40} - 32 q^{43} - 9 q^{44} - 23 q^{46} - 6 q^{47} + 4 q^{49} + 3 q^{52} - 6 q^{53} - 24 q^{56} + 10 q^{58} + 6 q^{59} - 6 q^{61} + 30 q^{62} + 8 q^{64} + 6 q^{67} + 21 q^{68} + 5 q^{70} - 8 q^{73} - 9 q^{74} + 18 q^{76} - 6 q^{77} - 8 q^{79} + 15 q^{80} - 10 q^{82} + 40 q^{85} + 24 q^{86} - 18 q^{88} + 8 q^{91} + 66 q^{92} - 19 q^{94} - 16 q^{97} - 39 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 - 3 * q^4 - 8 * q^7 + 12 * q^8 + 5 * q^10 - 6 * q^11 - 4 * q^13 + 15 * q^14 - 13 * q^16 - 6 * q^17 - 6 * q^19 - 30 * q^20 + 18 * q^22 - 12 * q^23 + 3 * q^26 - 3 * q^28 - 10 * q^31 - 15 * q^32 - 2 * q^34 + 4 * q^37 - 9 * q^38 + 20 * q^40 - 32 * q^43 - 9 * q^44 - 23 * q^46 - 6 * q^47 + 4 * q^49 + 3 * q^52 - 6 * q^53 - 24 * q^56 + 10 * q^58 + 6 * q^59 - 6 * q^61 + 30 * q^62 + 8 * q^64 + 6 * q^67 + 21 * q^68 + 5 * q^70 - 8 * q^73 - 9 * q^74 + 18 * q^76 - 6 * q^77 - 8 * q^79 + 15 * q^80 - 10 * q^82 + 40 * q^85 + 24 * q^86 - 18 * q^88 + 8 * q^91 + 66 * q^92 - 19 * q^94 - 16 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	0.790569	−	0.612372i	$-0.209785\pi$
$2$	−0.190983	−	0.330792i	−0.135045	−	0.233905i	−0.925615	+	0.378467i	$0.876451\pi$
$3$		0			0
$3$		0			0
$4$	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			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−1.47214			−0.520479
$9$		0			0
$10$	−0.427051	+	0.739674i	−0.135045	+	0.233905i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	0.954915	+	0.330792i	0.255212	+	0.0884080i
$15$		0			0
$16$	−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			0
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$	−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	$-0.295028\pi$
$23$	−1.88197	−	3.25966i	−0.392417	−	0.679686i	−0.992768	+	0.120051i	$0.961694\pi$
$24$		0			0
$25$		0			0
$26$	0.190983	+	0.330792i	0.0374548	+	0.0648737i
$27$		0			0
$28$	0.927051	+	4.81710i	0.175196	+	0.910346i
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	−2.07295	+	3.59045i	−0.366449	+	0.634708i
$33$		0			0
$34$	2.85410			0.489474
$35$	5.59017	+	1.93649i	0.944911	+	0.327327i
$36$		0			0
$37$	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
$39$		0			0
$40$	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
$45$		0			0
$46$	−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	$0.799091\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		0			0
$52$	−0.927051	+	1.60570i	−0.128559	+	0.222670i
$53$	0.736068	−	1.27491i	0.101107	−	0.175122i	−0.811034	−	0.584999i	$-0.801095\pi$
$53$	0.736068	−	1.27491i	0.101107	−	0.175122i	0.912141	+	0.409877i	$0.134428\pi$
$54$		0			0
$55$	6.70820			0.904534
$56$	2.94427	−	2.54981i	0.393445	−	0.340733i
$57$		0			0
$58$	−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	$0.00497842\pi$
$60$		0			0
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	0.753876	−	0.657017i	$-0.228182\pi$
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	−0.945931	+	0.324367i	$0.894849\pi$
$62$	1.90983			0.242549
$63$		0			0
$64$	−4.70820			−0.588525
$65$	1.11803	+	1.93649i	0.138675	+	0.240192i
$66$		0			0
$67$	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
$69$		0			0
$70$	−0.427051	−	2.21902i	−0.0510424	−	0.265224i
$71$	−8.94427			−1.06149			−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427			−1.06149			−0.530745	+	0.847532i	$0.678088\pi$
$72$		0			0
$73$	−5.35410	+	9.27358i	−0.626650	+	1.08539i	0.361569	+	0.932345i	$0.382241\pi$
$73$	−5.35410	+	9.27358i	−0.626650	+	1.08539i	−0.988219	+	0.153045i	$0.951092\pi$
$74$	1.66312	−	2.88061i	0.193334	−	0.334864i
$75$		0			0
$76$	−5.56231			−0.638040
$77$	−1.50000	−	7.79423i	−0.170941	−	0.888235i
$78$		0			0
$79$	−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
$81$		0			0
$82$	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
$87$		0			0
$88$	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	$0.871146\pi$
$90$		0			0
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	−6.97871			−0.727581
$93$		0			0
$94$	0.281153	−	0.486971i	0.0289987	−	0.0502272i
$95$	−3.35410	+	5.80948i	−0.344124	+	0.596040i
$96$		0			0
$97$	−17.4164			−1.76837			−0.884184	−	0.467139i	$-0.845285\pi$
$97$	−17.4164			−1.76837			−0.884184	+	0.467139i	$0.845285\pi$
$98$	−2.48278	+	0.992377i	−0.250799	+	0.100245i
$99$		0			0
$100$		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	$0.314447\pi$
$102$		0			0
$103$	−5.35410	−	9.27358i	−0.527555	−	0.913753i	−0.999484	−	0.0321160i	$-0.989775\pi$
$103$	−5.35410	−	9.27358i	−0.527555	−	0.913753i	0.471929	−	0.881637i	$-0.343558\pi$
$104$	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	$-0.925100\pi$
$107$	−7.11803	−	12.3288i	−0.688126	−	1.19187i	0.284317	−	0.958730i	$-0.408233\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	7.86475	+	2.72443i	0.743149	+	0.257434i
$113$	14.9443			1.40584			0.702919	−	0.711269i	$-0.251879\pi$
$113$	14.9443			1.40584			0.702919	+	0.711269i	$0.251879\pi$
$114$		0			0
$115$	−4.20820	+	7.28882i	−0.392417	+	0.679686i
$116$	4.14590	−	7.18091i	0.384937	−	0.666730i
$117$		0			0
$118$	−2.85410			−0.262741
$119$	−3.73607	−	19.4132i	−0.342485	−	1.77960i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−0.572949	+	0.992377i	−0.0518724	+	0.0898456i
$123$		0			0
$124$	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
$129$		0			0
$130$	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	$0.885911\pi$
$132$		0			0
$133$	7.50000	+	2.59808i	0.650332	+	0.225282i
$134$	−1.14590			−0.0989905
$135$		0			0
$136$	5.50000	−	9.52628i	0.471621	−	0.816872i
$137$	−1.88197	+	3.25966i	−0.160787	+	0.278492i	−0.935151	−	0.354249i	$-0.884737\pi$
$137$	−1.88197	+	3.25966i	−0.160787	+	0.278492i	0.774364	+	0.632740i	$0.218070\pi$
$138$		0			0
$139$	3.41641			0.289776			0.144888	−	0.989448i	$-0.453718\pi$
$139$	3.41641			0.289776			0.144888	+	0.989448i	$0.453718\pi$
$140$	8.29180	−	7.18091i	0.700785	−	0.606897i
$141$		0			0
$142$	1.70820	+	2.95870i	0.143349	+	0.248288i
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$		0			0
$145$	−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	$-0.992394\pi$
$149$	−6.35410	−	11.0056i	−0.520548	−	0.901616i	0.479166	−	0.877724i	$-0.340939\pi$
$150$		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
$153$		0			0
$154$	−2.29180	+	1.98475i	−0.184678	+	0.159936i
$155$	11.1803			0.898027
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	−2.04508	+	3.54219i	−0.162698	+	0.281802i
$159$		0			0
$160$	9.27051			0.732898
$161$	9.40983	+	3.25966i	0.741598	+	0.256897i
$162$		0			0
$163$	−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
$165$		0			0
$166$		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
$171$		0			0
$172$	−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	$0.703741\pi$
$174$		0			0
$175$		0			0
$176$	9.43769			0.711393
$177$		0			0
$178$	−0.427051	+	0.739674i	−0.0320088	+	0.0554409i
$179$	10.0623	−	17.4284i	0.752092	−	1.30266i	−0.194715	−	0.980860i	$-0.562378\pi$
$179$	10.0623	−	17.4284i	0.752092	−	1.30266i	0.946807	−	0.321802i	$-0.104288\pi$
$180$		0			0
$181$	1.41641			0.105281			0.0526404	−	0.998614i	$-0.483236\pi$
$181$	1.41641			0.105281			0.0526404	+	0.998614i	$0.483236\pi$
$182$	−0.954915	−	0.330792i	−0.0707830	−	0.0245200i
$183$		0			0
$184$	2.77051	+	4.79866i	0.204245	+	0.353762i
$185$	9.73607	−	16.8634i	0.715810	−	1.23982i
$186$		0			0
$187$	−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	$-0.299218\pi$
$191$	−5.59017	−	9.68246i	−0.404491	−	0.700598i	−0.994262	+	0.106972i	$0.965884\pi$
$192$		0			0
$193$	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
$195$		0			0
$196$	−10.1976	−	8.02850i	−0.728397	−	0.573464i
$197$	26.9443			1.91970			0.959850	−	0.280514i	$-0.0905049\pi$
$197$	26.9443			1.91970			0.959850	+	0.280514i	$0.0905049\pi$
$198$		0			0
$199$	3.64590	−	6.31488i	0.258451	−	0.447650i	−0.707376	−	0.706837i	$-0.750121\pi$
$199$	3.64590	−	6.31488i	0.258451	−	0.447650i	0.965827	+	0.259187i	$0.0834547\pi$
$200$		0			0
$201$		0			0
$202$	3.43769			0.241875
$203$	−8.94427	+	7.74597i	−0.627765	+	0.543660i
$204$		0			0
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$	−2.04508	+	3.54219i	−0.142488	+	0.246796i
$207$		0			0
$208$	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
$213$		0			0
$214$	−2.71885	+	4.70918i	−0.185857	+	0.321913i
$215$	8.94427	+	15.4919i	0.609994	+	1.05654i
$216$		0			0
$217$	−2.50000	−	12.9904i	−0.169711	−	0.881845i
$218$	4.09017			0.277021
$219$		0			0
$220$	6.21885	−	10.7714i	0.419275	−	0.726205i
$221$	3.73607	−	6.47106i	0.251315	−	0.435291i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	−2.07295	−	10.7714i	−0.138505	−	0.719692i
$225$		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	$0.296402\pi$
$228$		0			0
$229$	8.06231	+	13.9643i	0.532772	+	0.922788i	0.999268	+	0.0382649i	$0.0121831\pi$
$229$	8.06231	+	13.9643i	0.532772	+	0.922788i	−0.466495	+	0.884524i	$0.654484\pi$
$230$	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	$-0.229044\pi$
$233$	−2.97214	−	5.14789i	−0.194711	−	0.337250i	−0.946806	+	0.321806i	$0.895710\pi$
$234$		0			0
$235$	1.64590	−	2.85078i	0.107367	−	0.185964i
$236$	−6.92705	−	11.9980i	−0.450913	−	0.781004i
$237$		0			0
$238$	−5.70820	+	4.94345i	−0.370008	+	0.320436i
$239$	7.41641			0.479728			0.239864	−	0.970807i	$-0.422897\pi$
$239$	7.41641			0.479728			0.239864	+	0.970807i	$0.422897\pi$
$240$		0			0
$241$	4.35410	−	7.54153i	0.280472	−	0.485792i	−0.691029	−	0.722827i	$-0.742842\pi$
$241$	4.35410	−	7.54153i	0.280472	−	0.485792i	0.971501	+	0.237035i	$0.0761756\pi$
$242$	0.381966	−	0.661585i	0.0245537	−	0.0425283i
$243$		0			0
$244$	−5.56231			−0.356090
$245$	−14.5344	+	5.80948i	−0.928571	+	0.371154i
$246$		0			0
$247$	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
$255$		0			0
$256$	−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	$-0.355737\pi$
$258$		0			0
$259$	−21.7705	−	7.54153i	−1.35275	−	0.468608i
$260$	4.14590			0.257118
$261$		0			0
$262$	−0.718847	+	1.24508i	−0.0444105	+	0.0769213i
$263$	−7.06231	+	12.2323i	−0.435480	+	0.754274i	−0.997335	−	0.0729620i	$-0.976755\pi$
$263$	−7.06231	+	12.2323i	−0.435480	+	0.754274i	0.561854	+	0.827236i	$0.310088\pi$
$264$		0			0
$265$	−3.29180			−0.202213
$266$	−0.572949	−	2.97713i	−0.0351298	−	0.182540i
$267$		0			0
$268$	−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			0
$271$	−3.20820	−	5.55677i	−0.194885	−	0.337550i	0.751978	−	0.659188i	$-0.229100\pi$
$271$	−3.20820	−	5.55677i	−0.194885	−	0.337550i	−0.946863	+	0.321638i	$0.895767\pi$
$272$	23.5066			1.42530
$273$		0			0
$274$	1.43769			0.0868543
$275$		0			0
$276$		0			0
$277$	−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
$279$		0			0
$280$	−8.22949	−	2.85078i	−0.491806	−	0.170367i
$281$	−9.05573			−0.540219			−0.270110	−	0.962830i	$-0.587060\pi$
$281$	−9.05573			−0.540219			−0.270110	+	0.962830i	$0.587060\pi$
$282$		0			0
$283$	7.06231	−	12.2323i	0.419811	−	0.727133i	−0.576110	−	0.817372i	$-0.695430\pi$
$283$	7.06231	−	12.2323i	0.419811	−	0.727133i	0.995920	+	0.0902393i	$0.0287632\pi$
$284$	−8.29180	+	14.3618i	−0.492028	+	0.852217i
$285$		0			0
$286$	−1.14590			−0.0677584
$287$	8.94427	−	7.74597i	0.527964	−	0.457230i
$288$		0			0
$289$	−19.4164	−	33.6302i	−1.14214	−	1.97825i
$290$	−1.90983	+	3.30792i	−0.112149	+	0.194248i
$291$		0			0
$292$	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
$297$		0			0
$298$	−2.42705	+	4.20378i	−0.140595	+	0.243518i
$299$	1.88197	+	3.25966i	0.108837	+	0.188511i
$300$		0			0
$301$	16.0000	−	13.8564i	0.922225	−	0.798670i
$302$	−2.45085			−0.141031
$303$		0			0
$304$	−4.71885	+	8.17328i	−0.270644	+	0.468770i
$305$	−3.35410	+	5.80948i	−0.192055	+	0.332650i
$306$		0			0
$307$	−7.41641			−0.423277			−0.211638	−	0.977348i	$-0.567880\pi$
$307$	−7.41641			−0.423277			−0.211638	+	0.977348i	$0.567880\pi$
$308$	−13.9058	−	4.81710i	−0.792354	−	0.274480i
$309$		0			0
$310$	−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	$0.799667\pi$
$312$		0			0
$313$	16.2082	+	28.0734i	0.916142	+	1.58680i	0.805221	+	0.592975i	$0.202047\pi$
$313$	16.2082	+	28.0734i	0.916142	+	1.58680i	0.110921	+	0.993829i	$0.464620\pi$
$314$	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	$-0.200376\pi$
$317$	−1.88197	−	3.25966i	−0.105702	−	0.183081i	−0.914025	+	0.405659i	$0.867042\pi$
$318$		0			0
$319$	−6.70820	+	11.6190i	−0.375587	+	0.650536i
$320$	5.26393	+	9.11740i	0.294263	+	0.509678i
$321$		0			0
$322$	−0.718847	−	3.73524i	−0.0400598	−	0.208157i
$323$	22.4164			1.24728
$324$		0			0
$325$		0			0
$326$	−1.98936	+	3.44567i	−0.110180	+	0.190838i
$327$		0			0
$328$	6.58359			0.363518
$329$	−3.68034	−	1.27491i	−0.202904	−	0.0702879i
$330$		0			0
$331$	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
$333$		0			0
$334$	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
$339$		0			0
$340$	15.4894	−	26.8284i	0.840028	−	1.45497i
$341$	−7.50000	−	12.9904i	−0.406148	−	0.703469i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	11.7771			0.634978
$345$		0			0
$346$	1.98936	−	3.44567i	0.106948	−	0.185240i
$347$	−17.5344	+	30.3705i	−0.941298	+	1.63038i	−0.178299	+	0.983976i	$0.557060\pi$
$347$	−17.5344	+	30.3705i	−0.941298	+	1.63038i	−0.762999	+	0.646400i	$0.776274\pi$
$348$		0			0
$349$	−2.58359			−0.138297			−0.0691483	−	0.997606i	$-0.522028\pi$
$349$	−2.58359			−0.138297			−0.0691483	+	0.997606i	$0.522028\pi$
$350$		0			0
$351$		0			0
$352$	−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	$-0.137817\pi$
$354$		0			0
$355$	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	$-0.216805\pi$
$359$	−2.97214	−	5.14789i	−0.156863	−	0.271695i	−0.933736	+	0.357963i	$0.883472\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	−0.270510	−	0.468537i	−0.0142177	−	0.0246257i
$363$		0			0
$364$	−0.927051	−	4.81710i	−0.0485907	−	0.252485i
$365$	23.9443			1.25330
$366$		0			0
$367$	−0.354102	+	0.613323i	−0.0184840	+	0.0320152i	−0.875119	−	0.483907i	$-0.839217\pi$
$367$	−0.354102	+	0.613323i	−0.0184840	+	0.0320152i	0.856635	+	0.515922i	$0.172551\pi$
$368$	−5.92047	+	10.2546i	−0.308626	+	0.534556i
$369$		0			0
$370$	−7.43769			−0.386667
$371$	0.736068	+	3.82472i	0.0382147	+	0.198570i
$372$		0			0
$373$	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
$375$		0			0
$376$	−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
$381$		0			0
$382$	−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	$0.708144\pi$
$384$		0			0
$385$	−13.4164	+	11.6190i	−0.683763	+	0.592157i
$386$	−4.85410			−0.247067
$387$		0			0
$388$	−16.1459	+	27.9655i	−0.819684	+	1.41973i
$389$	−3.73607	+	6.47106i	−0.189426	+	0.328096i	−0.945059	−	0.326900i	$-0.893996\pi$
$389$	−3.73607	+	6.47106i	−0.189426	+	0.328096i	0.755633	+	0.654995i	$0.227329\pi$
$390$		0			0
$391$	28.1246			1.42232
$392$	−1.47214	+	10.1993i	−0.0743541	+	0.515140i
$393$		0			0
$394$	−5.14590	−	8.91296i	−0.259247	−	0.449028i
$395$	−11.9721	+	20.7363i	−0.602384	+	1.04336i
$396$		0			0
$397$	−7.06231	−	12.2323i	−0.354447	−	0.613920i	0.632576	−	0.774498i	$-0.281998\pi$
$397$	−7.06231	−	12.2323i	−0.354447	−	0.613920i	−0.987023	+	0.160578i	$0.948664\pi$
$398$	−2.78522			−0.139610
$399$		0			0
$400$		0			0
$401$	4.88197	+	8.45581i	0.243794	+	0.422263i	0.961792	−	0.273782i	$-0.0882747\pi$
$401$	4.88197	+	8.45581i	0.243794	+	0.422263i	−0.717998	+	0.696045i	$0.754941\pi$
$402$		0			0
$403$	2.50000	−	4.33013i	0.124534	−	0.215699i
$404$	8.34346	+	14.4513i	0.415103	+	0.718979i
$405$		0			0
$406$	4.27051	+	1.47935i	0.211942	+	0.0734188i
$407$	−26.1246			−1.29495
$408$		0			0
$409$	2.35410	−	4.07742i	0.116403	−	0.201616i	−0.801937	−	0.597409i	$-0.796197\pi$
$409$	2.35410	−	4.07742i	0.116403	−	0.201616i	0.918340	+	0.395793i	$0.129530\pi$
$410$	1.90983	−	3.30792i	0.0943198	−	0.163367i
$411$		0			0
$412$	−19.8541			−0.978141
$413$	3.73607	+	19.4132i	0.183840	+	0.955260i
$414$		0			0
$415$		0			0
$416$	2.07295	−	3.59045i	0.101635	−	0.176036i
$417$		0			0
$418$	−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
$423$		0			0
$424$	−1.08359	+	1.87684i	−0.0526239	+	0.0911472i
$425$		0			0
$426$		0			0
$427$	7.50000	+	2.59808i	0.362950	+	0.125730i
$428$	−26.3951			−1.27586
$429$		0			0
$430$	3.41641	−	5.91739i	0.164754	−	0.285362i
$431$	6.68034	−	11.5707i	0.321781	−	0.557340i	−0.659075	−	0.752077i	$-0.729052\pi$
$431$	6.68034	−	11.5707i	0.321781	−	0.557340i	0.980856	+	0.194737i	$0.0623853\pi$
$432$		0			0
$433$	2.58359			0.124160			0.0620798	−	0.998071i	$-0.480227\pi$
$433$	2.58359			0.124160			0.0620798	+	0.998071i	$0.480227\pi$
$434$	−3.81966	+	3.30792i	−0.183350	+	0.158785i
$435$		0			0
$436$	9.92705	+	17.1942i	0.475420	+	0.823451i
$437$	−5.64590	+	9.77898i	−0.270080	+	0.467792i
$438$		0			0
$439$	8.06231	+	13.9643i	0.384793	+	0.666481i	0.991740	−	0.128261i	$-0.0409395\pi$
$439$	8.06231	+	13.9643i	0.384793	+	0.666481i	−0.606948	+	0.794742i	$0.707606\pi$
$440$	−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	$-0.183583\pi$
$443$	−1.11803	−	1.93649i	−0.0531194	−	0.0920055i	−0.891362	+	0.453291i	$0.850250\pi$
$444$		0			0
$445$	−2.50000	+	4.33013i	−0.118511	+	0.205268i
$446$	0.763932	+	1.32317i	0.0361732	+	0.0626539i
$447$		0			0
$448$	9.41641	−	8.15485i	0.444883	−	0.385280i
$449$	−10.3607			−0.488951			−0.244475	−	0.969656i	$-0.578616\pi$
$449$	−10.3607			−0.488951			−0.244475	+	0.969656i	$0.578616\pi$
$450$		0			0
$451$	6.70820	−	11.6190i	0.315877	−	0.547115i
$452$	13.8541	−	23.9960i	0.651642	−	1.12868i
$453$		0			0
$454$	4.56231			0.214120
$455$	−5.59017	−	1.93649i	−0.262071	−	0.0907841i
$456$		0			0
$457$	−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
$459$		0			0
$460$	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
$465$		0			0
$466$	−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	$-0.333693\pi$
$468$		0			0
$469$	1.50000	+	7.79423i	0.0692636	+	0.359904i
$470$	−1.25735			−0.0579974
$471$		0			0
$472$	−5.50000	+	9.52628i	−0.253158	+	0.438483i
$473$	12.0000	−	20.7846i	0.551761	−	0.955677i
$474$		0			0
$475$		0			0
$476$	−34.6353	−	11.9980i	−1.58750	−	0.549928i
$477$		0			0
$478$	−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	$0.927974\pi$
$480$		0			0
$481$	−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
$486$		0			0
$487$	−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
$489$		0			0
$490$	4.69756	+	3.69837i	0.212214	+	0.167075i
$491$	34.4721			1.55571			0.777853	−	0.628446i	$-0.216309\pi$
$491$	34.4721			1.55571			0.777853	+	0.628446i	$0.216309\pi$
$492$		0			0
$493$	−16.7082	+	28.9395i	−0.752500	+	1.30337i
$494$	0.572949	−	0.992377i	0.0257782	−	0.0446491i
$495$		0			0
$496$	15.7295			0.706275
$497$	17.8885	−	15.4919i	0.802411	−	0.694908i
$498$		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
$501$		0			0
$502$	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
$507$		0			0
$508$	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	$0.946935\pi$
$510$		0			0
$511$	−5.35410	−	27.8207i	−0.236852	−	1.23072i
$512$	22.3050			0.985749
$513$		0			0
$514$	−3.42705	+	5.93583i	−0.151161	+	0.261818i
$515$	−11.9721	+	20.7363i	−0.527555	+	0.913753i
$516$		0			0
$517$	−4.41641			−0.194233
$518$	1.66312	+	8.64182i	0.0730733	+	0.379700i
$519$		0			0
$520$	−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	$0.167055\pi$
$522$		0			0
$523$	−9.64590	−	16.7072i	−0.421786	−	0.730554i	0.574329	−	0.818625i	$-0.305263\pi$
$523$	−9.64590	−	16.7072i	−0.421786	−	0.730554i	−0.996114	+	0.0880707i	$0.971930\pi$
$524$	−6.97871			−0.304867
$525$		0			0
$526$	5.39512			0.235238
$527$	−18.6803	−	32.3553i	−0.813728	−	1.40942i
$528$		0			0
$529$	4.41641	−	7.64944i	0.192018	−	0.332584i
$530$	0.628677	+	1.08890i	0.0273080	+	0.0472988i
$531$		0			0
$532$	11.1246	−	9.63420i	0.482313	−	0.417695i
$533$	4.47214			0.193710
$534$		0			0
$535$	−15.9164	+	27.5680i	−0.688126	+	1.19187i
$536$	−2.20820	+	3.82472i	−0.0953799	+	0.165203i
$537$		0			0
$538$	−1.72949			−0.0745636
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−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
$549$		0			0
$550$		0			0
$551$	−6.70820	−	11.6190i	−0.285779	−	0.494984i
$552$		0			0
$553$	26.7705	+	9.27358i	1.13840	+	0.394353i
$554$	10.0902			0.428690
$555$		0			0
$556$	3.16718	−	5.48572i	0.134319	−	0.232647i
$557$	−2.64590	+	4.58283i	−0.112110	+	0.194181i	−0.916621	−	0.399758i	$-0.869094\pi$
$557$	−2.64590	+	4.58283i	−0.112110	+	0.194181i	0.804511	+	0.593938i	$0.202428\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	−3.51722	−	18.2760i	−0.148630	−	0.772303i
$561$		0			0
$562$	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	$0.886331\pi$
$564$		0			0
$565$	−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	$-0.0540564\pi$
$569$	8.26393	+	14.3136i	0.346442	+	0.600055i	−0.639173	+	0.769063i	$0.720723\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−4.27051	−	1.47935i	−0.178248	−	0.0617468i
$575$		0			0
$576$		0			0
$577$	16.3541	−	28.3261i	0.680830	−	1.17923i	−0.293898	−	0.955837i	$-0.594953\pi$
$577$	16.3541	−	28.3261i	0.680830	−	1.17923i	0.974728	−	0.223396i	$-0.0717142\pi$
$578$	−7.41641	+	12.8456i	−0.308482	+	0.534306i
$579$		0			0
$580$	−18.5410			−0.769874
$581$		0			0
$582$		0			0
$583$	2.20820	+	3.82472i	0.0914545	+	0.158404i
$584$	7.88197	−	13.6520i	0.326158	−	0.564922i
$585$		0			0
$586$	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
$591$		0			0
$592$	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	$0.603089\pi$
$594$		0			0
$595$	−33.4164	+	28.9395i	−1.36994	+	1.18640i
$596$	−23.5623			−0.965150
$597$		0			0
$598$	0.718847	−	1.24508i	0.0293958	−	0.0509151i
$599$	20.5344	−	35.5667i	0.839015	−	1.45322i	−0.0517049	−	0.998662i	$-0.516466\pi$
$599$	20.5344	−	35.5667i	0.839015	−	1.45322i	0.890719	−	0.454553i	$-0.150201\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−7.63932	−	2.64634i	−0.311355	−	0.107857i
$603$		0			0
$604$	−5.94834	−	10.3028i	−0.242034	−	0.419216i
$605$	2.23607	−	3.87298i	0.0909091	−	0.157459i
$606$		0			0
$607$	8.06231	+	13.9643i	0.327239	+	0.566794i	0.981963	−	0.189074i	$-0.0605485\pi$
$607$	8.06231	+	13.9643i	0.327239	+	0.566794i	−0.654724	+	0.755868i	$0.727215\pi$
$608$	12.4377			0.504415
$609$		0			0
$610$	2.56231			0.103745
$611$	−0.736068	−	1.27491i	−0.0297781	−	0.0515772i
$612$		0			0
$613$	−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
$615$		0			0
$616$	2.20820	+	11.4742i	0.0889711	+	0.462307i
$617$	−4.47214			−0.180041			−0.0900207	−	0.995940i	$-0.528693\pi$
$617$	−4.47214			−0.180041			−0.0900207	+	0.995940i	$0.528693\pi$
$618$		0			0
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	0.643094	+	0.765787i	$0.277650\pi$
$620$	10.3647	−	17.9523i	0.416258	−	0.720980i
$621$		0			0
$622$	12.3131			0.493710
$623$	5.59017	+	1.93649i	0.223965	+	0.0775839i
$624$		0			0
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	6.19098	−	10.7231i	0.247441	−	0.428581i
$627$		0			0
$628$	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
$633$		0			0
$634$	−0.718847	+	1.24508i	−0.0285491	+	0.0494484i
$635$	−17.2361	−	29.8537i	−0.683992	−	1.18471i
$636$		0			0
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$	5.12461			0.202885
$639$		0			0
$640$	11.2812	−	19.5395i	0.445927	−	0.772368i
$641$	−2.97214	+	5.14789i	−0.117392	+	0.203329i	−0.918734	−	0.394878i	$-0.870787\pi$
$641$	−2.97214	+	5.14789i	−0.117392	+	0.203329i	0.801341	+	0.598208i	$0.204120\pi$
$642$		0			0
$643$	−18.8328			−0.742694			−0.371347	−	0.928494i	$-0.621104\pi$
$643$	−18.8328			−0.742694			−0.371347	+	0.928494i	$0.621104\pi$
$644$	13.9574	−	12.0875i	0.550000	−	0.476314i
$645$		0			0
$646$	−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	$0.0663804\pi$
$648$		0			0
$649$	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	$-0.0817559\pi$
$653$	6.73607	+	11.6672i	0.263603	+	0.456573i	−0.703594	+	0.710602i	$0.748423\pi$
$654$		0			0
$655$	−4.20820	+	7.28882i	−0.164428	+	0.284798i
$656$	7.03444	+	12.1840i	0.274649	+	0.475706i
$657$		0			0
$658$	0.281153	+	1.46091i	0.0109605	+	0.0569523i
$659$	−8.94427			−0.348419			−0.174210	−	0.984709i	$-0.555737\pi$
$659$	−8.94427			−0.348419			−0.174210	+	0.984709i	$0.555737\pi$
$660$		0			0
$661$	−3.35410	+	5.80948i	−0.130459	+	0.225962i	−0.923854	−	0.382746i	$-0.874979\pi$
$661$	−3.35410	+	5.80948i	−0.130459	+	0.225962i	0.793394	+	0.608708i	$0.208312\pi$
$662$	5.42705	−	9.39993i	0.210928	−	0.365339i
$663$		0			0
$664$		0			0
$665$	−3.35410	−	17.4284i	−0.130066	−	0.675845i
$666$		0			0
$667$	−8.41641	−	14.5776i	−0.325885	−	0.564449i
$668$	−12.5410	+	21.7217i	−0.485227	+	0.840437i
$669$		0			0
$670$	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	$0.615566\pi$
$678$		0			0
$679$	34.8328	−	30.1661i	1.33676	−	1.15767i
$680$	−24.5967			−0.943242
$681$		0			0
$682$	−2.86475	+	4.96188i	−0.109697	+	0.190000i
$683$	−2.26393	+	3.92125i	−0.0866270	+	0.150042i	−0.906083	−	0.423099i	$-0.860942\pi$
$683$	−2.26393	+	3.92125i	−0.0866270	+	0.150042i	0.819456	+	0.573142i	$0.194275\pi$
$684$		0			0
$685$	8.41641			0.321574
$686$	3.24671	−	6.28505i	0.123960	−	0.239964i
$687$		0			0
$688$	12.5836	+	21.7954i	0.479745	+	0.830943i
$689$	−0.736068	+	1.27491i	−0.0280420	+	0.0485701i
$690$		0			0
$691$	−0.916408	−	1.58726i	−0.0348618	−	0.0603824i	0.848068	−	0.529887i	$-0.177766\pi$
$691$	−0.916408	−	1.58726i	−0.0348618	−	0.0603824i	−0.882930	+	0.469505i	$0.844432\pi$
$692$	19.3131			0.734173
$693$		0			0
$694$	13.3951			0.508472
$695$	−3.81966	−	6.61585i	−0.144888	−	0.250953i
$696$		0			0
$697$	16.7082	−	28.9395i	0.632868	−	1.09616i
$698$	0.493422	+	0.854632i	0.0186763	+	0.0323483i
$699$		0			0
$700$		0			0
$701$	−22.3607			−0.844551			−0.422276	−	0.906467i	$-0.638769\pi$
$701$	−22.3607			−0.844551			−0.422276	+	0.906467i	$0.638769\pi$
$702$		0			0
$703$	13.0623	−	22.6246i	0.492654	−	0.853302i
$704$	7.06231	−	12.2323i	0.266171	−	0.461021i
$705$		0			0
$706$	−11.7295			−0.441445
$707$	−4.50000	−	23.3827i	−0.169240	−	0.879396i
$708$		0			0
$709$	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
$711$		0			0
$712$	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
$717$		0			0
$718$	−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	$0.765806\pi$
$720$		0			0
$721$	26.7705	+	9.27358i	0.996986	+	0.345366i
$722$	−3.81966			−0.142153
$723$		0			0
$724$	1.31308	−	2.27433i	0.0488003	−	0.0845246i
$725$		0			0
$726$		0			0
$727$	14.8328			0.550119			0.275059	−	0.961427i	$-0.411302\pi$
$727$	14.8328			0.550119			0.275059	+	0.961427i	$0.411302\pi$
$728$	−2.94427	+	2.54981i	−0.109122	+	0.0945024i
$729$		0			0
$730$	−4.57295	−	7.92058i	−0.169252	−	0.293154i
$731$	29.8885	−	51.7685i	1.10547	−	1.91473i
$732$		0			0
$733$	−7.64590	−	13.2431i	−0.282408	−	0.489144i	0.689570	−	0.724219i	$-0.257800\pi$
$733$	−7.64590	−	13.2431i	−0.282408	−	0.489144i	−0.971977	+	0.235075i	$0.924466\pi$
$734$	0.270510			0.00998470
$735$		0			0
$736$	15.6049			0.575203
$737$	4.50000	+	7.79423i	0.165760	+	0.287104i
$738$		0			0
$739$	−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
$741$		0			0
$742$	1.12461	−	0.973942i	0.0412858	−	0.0357545i
$743$	−15.0557			−0.552341			−0.276171	−	0.961109i	$-0.589065\pi$
$743$	−15.0557			−0.552341			−0.276171	+	0.961109i	$0.589065\pi$
$744$		0			0
$745$	−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
$749$	35.5902	+	12.3288i	1.30044	+	0.450484i
$750$		0			0
$751$	−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
$753$		0			0
$754$	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
$759$		0			0
$760$	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	$0.625333\pi$
$762$		0			0
$763$	−5.35410	−	27.8207i	−0.193832	−	1.00718i
$764$	−20.7295			−0.749967
$765$		0			0
$766$	2.86475	−	4.96188i	0.103507	−	0.179280i
$767$	−3.73607	+	6.47106i	−0.134902	+	0.233656i
$768$		0			0
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$	6.40576	+	2.21902i	0.230848	+	0.0799680i
$771$		0			0
$772$	−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	$0.102878\pi$
$774$		0			0
$775$		0			0
$776$	25.6393			0.920398
$777$		0			0
$778$	2.85410			0.102325
$779$	6.70820	+	11.6190i	0.240346	+	0.416292i
$780$		0			0
$781$	13.4164	−	23.2379i	0.480077	−	0.831517i
$782$	−5.37132	−	9.30340i	−0.192078	−	0.332689i
$783$		0			0
$784$	−20.4483	+	8.17328i	−0.730298	+	0.291903i
$785$	15.6525			0.558661
$786$		0			0
$787$	3.20820	−	5.55677i	0.114360	−	0.198078i	−0.803164	−	0.595758i	$-0.796852\pi$
$787$	3.20820	−	5.55677i	0.114360	−	0.198078i	0.917524	+	0.397681i	$0.130185\pi$
$788$	24.9787	−	43.2644i	0.889830	−	1.54123i
$789$		0			0
$790$	9.14590			0.325396
$791$	−29.8885	+	25.8842i	−1.06271	+	0.920338i
$792$		0			0
$793$	1.50000	+	2.59808i	0.0532666	+	0.0922604i
$794$	−2.69756	+	4.67231i	−0.0957329	+	0.165814i
$795$		0			0
$796$	−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
$801$		0			0
$802$	1.86475	−	3.22983i	0.0658464	−	0.114049i
$803$	−16.0623	−	27.8207i	−0.566826	−	0.981772i
$804$		0			0
$805$	−4.20820	−	21.8665i	−0.148320	−	0.770692i
$806$	−1.90983			−0.0672709
$807$		0			0
$808$	6.62461	−	11.4742i	0.233053	−	0.403660i
$809$	−2.20820	+	3.82472i	−0.0776363	+	0.134470i	−0.902230	−	0.431256i	$-0.858071\pi$
$809$	−2.20820	+	3.82472i	−0.0776363	+	0.134470i	0.824593	+	0.565726i	$0.191404\pi$
$810$		0			0
$811$	38.8328			1.36360			0.681802	−	0.731536i	$-0.261196\pi$
$811$	38.8328			1.36360			0.681802	+	0.731536i	$0.261196\pi$
$812$	4.14590	+	21.5427i	0.145492	+	0.756001i
$813$		0			0
$814$	4.98936	+	8.64182i	0.174877	+	0.302896i
$815$	−11.6459	+	20.1713i	−0.407938	+	0.706569i
$816$		0			0
$817$	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	$0.0338843\pi$
$821$	16.8820	+	29.2404i	0.589185	+	1.02050i	−0.405155	+	0.914248i	$0.632782\pi$
$822$		0			0
$823$	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
$826$	5.70820	−	4.94345i	0.198614	−	0.172005i
$827$	26.8328			0.933068			0.466534	−	0.884503i	$-0.345502\pi$
$827$	26.8328			0.933068			0.466534	+	0.884503i	$0.345502\pi$
$828$		0			0
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$		0			0
$831$		0			0
$832$	4.70820			0.163228
$833$	41.0967	+	32.3553i	1.42392	+	1.12104i
$834$		0			0
$835$	15.1246	+	26.1966i	0.523409	+	0.906571i
$836$	8.34346	−	14.4513i	0.288565	−	0.499808i
$837$		0			0
$838$	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
$843$		0			0
$844$	3.70820	−	6.42280i	0.127642	−	0.221082i
$845$	−1.11803	−	1.93649i	−0.0384615	−	0.0666173i
$846$		0			0
$847$	−5.00000	−	1.73205i	−0.171802	−	0.0595140i
$848$	−4.63119			−0.159036
$849$		0			0
$850$		0			0
$851$	16.3885	−	28.3858i	0.561792	−	0.973052i
$852$		0			0
$853$	28.2492			0.967235			0.483617	−	0.875279i	$-0.339323\pi$
$853$	28.2492			0.967235			0.483617	+	0.875279i	$0.339323\pi$
$854$	−0.572949	−	2.97713i	−0.0196059	−	0.101875i
$855$		0			0
$856$	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	$-0.0987855\pi$
$858$		0			0
$859$	−3.64590	−	6.31488i	−0.124396	−	0.215461i	0.797100	−	0.603847i	$-0.206366\pi$
$859$	−3.64590	−	6.31488i	−0.124396	−	0.215461i	−0.921497	+	0.388386i	$0.873033\pi$
$860$	33.1672			1.13099
$861$		0			0
$862$	−5.10333			−0.173820
$863$	3.02786	+	5.24441i	0.103070	+	0.178522i	0.912948	−	0.408076i	$-0.133800\pi$
$863$	3.02786	+	5.24441i	0.103070	+	0.178522i	−0.809878	+	0.586598i	$0.800467\pi$
$864$		0			0
$865$	11.6459	−	20.1713i	0.395972	−	0.685844i
$866$	−0.493422	−	0.854632i	−0.0167672	−	0.0290416i
$867$		0			0
$868$	−23.1763	−	8.02850i	−0.786654	−	0.272505i
$869$	32.1246			1.08975
$870$		0			0
$871$	−1.50000	+	2.59808i	−0.0508256	+	0.0880325i
$872$	7.88197	−	13.6520i	0.266917	−	0.462314i
$873$		0			0
$874$	4.31308			0.145892
$875$	22.3607	−	19.3649i	0.755929	−	0.654654i
$876$		0			0
$877$	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
$879$		0			0
$880$	−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
$885$		0			0
$886$	−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	$0.918590\pi$
$888$		0			0
$889$	−30.8328	+	26.7020i	−1.03410	+	0.895556i
$890$	1.90983			0.0640176
$891$		0			0
$892$	−3.70820	+	6.42280i	−0.124160	+	0.215051i
$893$	2.20820	−	3.82472i	0.0738947	−	0.127989i
$894$		0			0
$895$	−45.0000			−1.50418
$896$	−25.2254	−	8.73834i	−0.842722	−	0.291928i
$897$		0			0
$898$	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
$906$		0			0
$907$	−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
$909$		0			0
$910$	0.427051	+	2.21902i	0.0141566	+	0.0735599i
$911$	−46.2492			−1.53231			−0.766153	−	0.642659i	$-0.777831\pi$
$911$	−46.2492			−1.53231			−0.766153	+	0.642659i	$0.777831\pi$
$912$		0			0
$913$		0			0
$914$	−6.51722	+	11.2882i	−0.215571	+	0.373379i
$915$		0			0
$916$	29.8967			0.987814
$917$	9.40983	+	3.25966i	0.310740	+	0.107643i
$918$		0			0
$919$	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
$921$		0			0
$922$	−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
$927$		0			0
$928$	−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	$-0.448398\pi$
$930$		0			0
$931$	−19.5000	+	7.79423i	−0.639087	+	0.255446i
$932$	−11.0213			−0.361014
$933$		0			0
$934$	−4.13525	+	7.16247i	−0.135310	+	0.234363i
$935$	−25.0623	+	43.4092i	−0.819625	+	1.41963i
$936$		0			0
$937$	−1.41641			−0.0462720			−0.0231360	−	0.999732i	$-0.507365\pi$
$937$	−1.41641			−0.0462720			−0.0231360	+	0.999732i	$0.507365\pi$
$938$	2.29180	−	1.98475i	0.0748298	−	0.0648045i
$939$		0			0
$940$	−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	$-0.101328\pi$
$942$		0			0
$943$	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	$-0.995811\pi$
$947$	−15.7361	−	27.2557i	−0.511354	−	0.885690i	0.488560	−	0.872530i	$-0.337522\pi$
$948$		0			0
$949$	5.35410	−	9.27358i	0.173802	−	0.301033i
$950$		0			0
$951$		0			0
$952$	5.50000	+	28.5788i	0.178256	+	0.926245i
$953$	−29.7771			−0.964574			−0.482287	−	0.876013i	$-0.660194\pi$
$953$	−29.7771			−0.964574			−0.482287	+	0.876013i	$0.660194\pi$
$954$		0			0
$955$	−12.5000	+	21.6506i	−0.404491	+	0.700598i
$956$	6.87539	−	11.9085i	0.222366	−	0.385149i
$957$		0			0
$958$	11.3951			0.368160
$959$	−1.88197	−	9.77898i	−0.0607719	−	0.315780i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	−1.66312	+	2.88061i	−0.0536211	+	0.0928745i
$963$		0			0
$964$	−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
$969$		0			0
$970$	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	$0.963095\pi$
$972$		0			0
$973$	−6.83282	+	5.91739i	−0.219050	+	0.189703i
$974$	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	$0.347607\pi$
$977$	−16.8262	+	29.1439i	−0.538319	+	0.932396i	−0.998995	+	0.0448274i	$0.985726\pi$
$978$		0			0
$979$	6.70820			0.214395
$980$	−4.14590	+	28.7236i	−0.132436	+	0.917543i
$981$		0			0
$982$	−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	$0.174140\pi$
$984$		0			0
$985$	−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
$990$		0			0
$991$	−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
$993$		0			0
$994$	−8.54102	−	2.95870i	−0.270905	−	0.0938441i
$995$	−16.3050			−0.516902
$996$		0			0
$997$	0.208204	−	0.360620i	0.00659388	−	0.0114209i	−0.862710	−	0.505700i	$-0.831234\pi$
$997$	0.208204	−	0.360620i	0.00659388	−	0.0114209i	0.869304	+	0.494279i	$0.164568\pi$
$998$	0.0795268	−	0.137745i	0.00251738	−	0.00436023i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.c.235.2		4
3.2	odd	2		91.2.e.b.53.1	✓	4
7.2	even	3	inner	819.2.j.c.352.2		4
7.3	odd	6		5733.2.a.w.1.1		2
7.4	even	3		5733.2.a.v.1.1		2
12.11	even	2		1456.2.r.j.417.2		4
21.2	odd	6		91.2.e.b.79.1	yes	4
21.5	even	6		637.2.e.h.79.1		4
21.11	odd	6		637.2.a.f.1.2		2
21.17	even	6		637.2.a.e.1.2		2
21.20	even	2		637.2.e.h.508.1		4
39.38	odd	2		1183.2.e.d.508.2		4
84.23	even	6		1456.2.r.j.625.2		4
273.38	even	6		8281.2.a.ba.1.1		2
273.116	odd	6		8281.2.a.z.1.1		2
273.233	odd	6		1183.2.e.d.170.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.b.53.1	✓	4	3.2	odd	2
91.2.e.b.79.1	yes	4	21.2	odd	6
637.2.a.e.1.2		2	21.17	even	6
637.2.a.f.1.2		2	21.11	odd	6
637.2.e.h.79.1		4	21.5	even	6
637.2.e.h.508.1		4	21.20	even	2
819.2.j.c.235.2		4	1.1	even	1	trivial
819.2.j.c.352.2		4	7.2	even	3	inner
1183.2.e.d.170.2		4	273.233	odd	6
1183.2.e.d.508.2		4	39.38	odd	2
1456.2.r.j.417.2		4	12.11	even	2
1456.2.r.j.625.2		4	84.23	even	6
5733.2.a.v.1.1		2	7.4	even	3
5733.2.a.w.1.1		2	7.3	odd	6
8281.2.a.z.1.1		2	273.116	odd	6
8281.2.a.ba.1.1		2	273.38	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 - 0.330792i) q^{2} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.47214 q^{8} +O(q^{10})\)	\(q+(-0.190983 - 0.330792i) q^{2} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.47214 q^{8} +(-0.427051 + 0.739674i) q^{10} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(0.954915 + 0.330792i) q^{14} +(-1.57295 - 2.72443i) q^{16} +(-3.73607 + 6.47106i) q^{17} +(-1.50000 - 2.59808i) q^{19} -4.14590 q^{20} +1.14590 q^{22} +(-1.88197 - 3.25966i) q^{23} +(0.190983 + 0.330792i) q^{26} +(0.927051 + 4.81710i) q^{28} +4.47214 q^{29} +(-2.50000 + 4.33013i) q^{31} +(-2.07295 + 3.59045i) q^{32} +2.85410 q^{34} +(5.59017 + 1.93649i) q^{35} +(4.35410 + 7.54153i) q^{37} +(-0.572949 + 0.992377i) q^{38} +(1.64590 + 2.85078i) q^{40} -4.47214 q^{41} -8.00000 q^{43} +(2.78115 + 4.81710i) q^{44} +(-0.718847 + 1.24508i) q^{46} +(0.736068 + 1.27491i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-0.927051 + 1.60570i) q^{52} +(0.736068 - 1.27491i) q^{53} +6.70820 q^{55} +(2.94427 - 2.54981i) q^{56} +(-0.854102 - 1.47935i) q^{58} +(3.73607 - 6.47106i) q^{59} +(-1.50000 - 2.59808i) q^{61} +1.90983 q^{62} -4.70820 q^{64} +(1.11803 + 1.93649i) q^{65} +(1.50000 - 2.59808i) q^{67} +(6.92705 + 11.9980i) q^{68} +(-0.427051 - 2.21902i) q^{70} -8.94427 q^{71} +(-5.35410 + 9.27358i) q^{73} +(1.66312 - 2.88061i) q^{74} -5.56231 q^{76} +(-1.50000 - 7.79423i) q^{77} +(-5.35410 - 9.27358i) q^{79} +(-3.51722 + 6.09201i) q^{80} +(0.854102 + 1.47935i) q^{82} +16.7082 q^{85} +(1.52786 + 2.64634i) q^{86} +(2.20820 - 3.82472i) q^{88} +(-1.11803 - 1.93649i) q^{89} +(2.00000 - 1.73205i) q^{91} -6.97871 q^{92} +(0.281153 - 0.486971i) q^{94} +(-3.35410 + 5.80948i) q^{95} -17.4164 q^{97} +(-2.48278 + 0.992377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q - 3 * q^2 - 3 * q^4 - 8 * q^7 + 12 * q^8	\( 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + 5 q^{10} - 6 q^{11} - 4 q^{13} + 15 q^{14} - 13 q^{16} - 6 q^{17} - 6 q^{19} - 30 q^{20} + 18 q^{22} - 12 q^{23} + 3 q^{26} - 3 q^{28} - 10 q^{31} - 15 q^{32} - 2 q^{34} + 4 q^{37} - 9 q^{38} + 20 q^{40} - 32 q^{43} - 9 q^{44} - 23 q^{46} - 6 q^{47} + 4 q^{49} + 3 q^{52} - 6 q^{53} - 24 q^{56} + 10 q^{58} + 6 q^{59} - 6 q^{61} + 30 q^{62} + 8 q^{64} + 6 q^{67} + 21 q^{68} + 5 q^{70} - 8 q^{73} - 9 q^{74} + 18 q^{76} - 6 q^{77} - 8 q^{79} + 15 q^{80} - 10 q^{82} + 40 q^{85} + 24 q^{86} - 18 q^{88} + 8 q^{91} + 66 q^{92} - 19 q^{94} - 16 q^{97} - 39 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^4 - 8 * q^7 + 12 * q^8 + 5 * q^10 - 6 * q^11 - 4 * q^13 + 15 * q^14 - 13 * q^16 - 6 * q^17 - 6 * q^19 - 30 * q^20 + 18 * q^22 - 12 * q^23 + 3 * q^26 - 3 * q^28 - 10 * q^31 - 15 * q^32 - 2 * q^34 + 4 * q^37 - 9 * q^38 + 20 * q^40 - 32 * q^43 - 9 * q^44 - 23 * q^46 - 6 * q^47 + 4 * q^49 + 3 * q^52 - 6 * q^53 - 24 * q^56 + 10 * q^58 + 6 * q^59 - 6 * q^61 + 30 * q^62 + 8 * q^64 + 6 * q^67 + 21 * q^68 + 5 * q^70 - 8 * q^73 - 9 * q^74 + 18 * q^76 - 6 * q^77 - 8 * q^79 + 15 * q^80 - 10 * q^82 + 40 * q^85 + 24 * q^86 - 18 * q^88 + 8 * q^91 + 66 * q^92 - 19 * q^94 - 16 * q^97 - 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more