LMFDB - Embedded newform 1014.2.e.f.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.f.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(2.00000 + 3.46410i) q^{11} -1.00000 q^{12} -4.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(4.00000 - 6.92820i) q^{19} +(-1.00000 + 1.73205i) q^{20} -4.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{25} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-1.00000 + 1.73205i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} -2.00000 q^{34} +(-4.00000 + 6.92820i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} +8.00000 q^{38} -2.00000 q^{40} +(5.00000 + 8.66025i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(-2.00000 + 3.46410i) q^{43} -4.00000 q^{44} +(-1.00000 + 1.73205i) q^{45} +8.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} -2.00000 q^{51} -10.0000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.00000 + 6.92820i) q^{55} +(2.00000 - 3.46410i) q^{56} +8.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(-2.00000 + 3.46410i) q^{59} -2.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} -4.00000 q^{66} +(8.00000 + 13.8564i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{70} +(4.00000 - 6.92820i) q^{71} +(0.500000 - 0.866025i) q^{72} +2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(4.00000 + 6.92820i) q^{76} -16.0000 q^{77} +8.00000 q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} +12.0000 q^{83} +(2.00000 - 3.46410i) q^{84} +(-2.00000 + 3.46410i) q^{85} -4.00000 q^{86} +(3.00000 - 5.19615i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-7.00000 - 12.1244i) q^{89} -2.00000 q^{90} +(-2.00000 - 3.46410i) q^{93} +(4.00000 + 6.92820i) q^{94} +(8.00000 - 13.8564i) q^{95} +1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(4.50000 - 7.79423i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 8 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 2 q^{18} + 8 q^{19} - 2 q^{20} - 8 q^{21} - 4 q^{22}+ \cdots - 8 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 4 * q^5 - q^6 - 4 * q^7 - 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 - 8 * q^14 + 2 * q^15 - q^16 - 2 * q^17 - 2 * q^18 + 8 * q^19 - 2 * q^20 - 8 * q^21 - 4 * q^22 - q^24 - 2 * q^25 - 2 * q^27 - 4 * q^28 - 6 * q^29 - 2 * q^30 - 8 * q^31 + q^32 - 4 * q^33 - 4 * q^34 - 8 * q^35 - q^36 + 2 * q^37 + 16 * q^38 - 4 * q^40 + 10 * q^41 - 4 * q^42 - 4 * q^43 - 8 * q^44 - 2 * q^45 + 16 * q^47 + q^48 - 9 * q^49 - q^50 - 4 * q^51 - 20 * q^53 - q^54 + 8 * q^55 + 4 * q^56 + 16 * q^57 + 6 * q^58 - 4 * q^59 - 4 * q^60 + 2 * q^61 - 4 * q^62 - 4 * q^63 + 2 * q^64 - 8 * q^66 + 16 * q^67 - 2 * q^68 - 16 * q^70 + 8 * q^71 + q^72 + 4 * q^73 - 2 * q^74 - q^75 + 8 * q^76 - 32 * q^77 + 16 * q^79 - 2 * q^80 - q^81 - 10 * q^82 + 24 * q^83 + 4 * q^84 - 4 * q^85 - 8 * q^86 + 6 * q^87 - 4 * q^88 - 14 * q^89 - 4 * q^90 - 4 * q^93 + 8 * q^94 + 16 * q^95 + 2 * q^96 - 10 * q^97 + 9 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−4.00000			−1.06904
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−1.00000			−0.235702
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	4.00000	−	6.92820i	0.917663	−	1.58944i	0.802955	−	0.596040i	$-0.203260\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$	−4.00000			−0.872872
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−2.00000	−	3.46410i	−0.377964	−	0.654654i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.00000	+	3.46410i	−0.348155	+	0.603023i
$34$	−2.00000			−0.342997
$35$	−4.00000	+	6.92820i	−0.676123	+	1.17108i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	8.00000			1.29777
$39$		0			0
$40$	−2.00000			−0.316228
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	0.931436	+	0.363905i	$0.118557\pi$
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	−0.150567	+	0.988600i	$0.548110\pi$
$42$	−2.00000	−	3.46410i	−0.308607	−	0.534522i
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$	−4.00000			−0.603023
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$		0			0
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−2.00000			−0.280056
$52$		0			0
$53$	−10.0000			−1.37361			−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000			−1.37361			−0.686803	+	0.726844i	$0.740986\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	4.00000	+	6.92820i	0.539360	+	0.934199i
$56$	2.00000	−	3.46410i	0.267261	−	0.462910i
$57$	8.00000			1.05963
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	−2.00000			−0.258199
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−2.00000	−	3.46410i	−0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.00000			−0.492366
$67$	8.00000	+	13.8564i	0.977356	+	1.69283i	0.671932	+	0.740613i	$0.265465\pi$
$67$	8.00000	+	13.8564i	0.977356	+	1.69283i	0.305424	+	0.952217i	$0.401202\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$	−8.00000			−0.956183
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	−0.524868	−	0.851184i	$-0.675885\pi$
$71$	4.00000	−	6.92820i	0.474713	−	0.822226i	0.999581	+	0.0289572i	$0.00921865\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	4.00000	+	6.92820i	0.458831	+	0.794719i
$77$	−16.0000			−1.82337
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.00000	+	8.66025i	−0.552158	+	0.956365i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$	−2.00000	+	3.46410i	−0.216930	+	0.375735i
$86$	−4.00000			−0.431331
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$	−2.00000			−0.210819
$91$		0			0
$92$		0			0
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$	8.00000	−	13.8564i	0.820783	−	1.42164i
$96$	1.00000			0.102062
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	0.492287	+	0.870433i	$0.336161\pi$
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	−0.999961	+	0.00888289i	$0.997172\pi$
$98$	4.50000	−	7.79423i	0.454569	−	0.787336i
$99$	−4.00000			−0.402015
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	16.0000			1.57653			0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000			1.57653			0.788263	+	0.615338i	$0.210980\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$	−5.00000	−	8.66025i	−0.485643	−	0.841158i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−4.00000	+	6.92820i	−0.381385	+	0.660578i
$111$	−1.00000	+	1.73205i	−0.0949158	+	0.164399i
$112$	4.00000			0.377964
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	4.00000	+	6.92820i	0.374634	+	0.648886i
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$	−4.00000			−0.368230
$119$	−4.00000	−	6.92820i	−0.366679	−	0.635107i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	2.00000			0.181071
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−12.0000			−1.07331
$126$	2.00000	−	3.46410i	0.178174	−	0.308607i
$127$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$127$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.00000			−0.352180
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	−2.00000	−	3.46410i	−0.174078	−	0.301511i
$133$	16.0000	+	27.7128i	1.38738	+	2.40301i
$134$	−8.00000	+	13.8564i	−0.691095	+	1.19701i
$135$	−2.00000			−0.172133
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	−0.569442	−	0.822031i	$-0.692841\pi$
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	0.996621	+	0.0821359i	$0.0261741\pi$
$138$		0			0
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$	4.00000	+	6.92820i	0.336861	+	0.583460i
$142$	8.00000			0.671345
$143$		0			0
$144$	1.00000			0.0833333
$145$	−6.00000	−	10.3923i	−0.498273	−	0.863034i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	4.50000	−	7.79423i	0.371154	−	0.642857i
$148$	−2.00000			−0.164399
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	−4.00000	+	6.92820i	−0.324443	+	0.561951i
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$	−8.00000	−	13.8564i	−0.644658	−	1.11658i
$155$	−8.00000			−0.642575
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$	−5.00000	−	8.66025i	−0.396526	−	0.686803i
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$		0			0
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	−10.0000			−0.780869
$165$	−4.00000	+	6.92820i	−0.311400	+	0.539360i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	4.00000			0.308607
$169$		0			0
$170$	−4.00000			−0.306786
$171$	4.00000	+	6.92820i	0.305888	+	0.529813i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	−0.610939	−	0.791677i	$-0.709208\pi$
$173$	5.00000	−	8.66025i	0.380143	−	0.658427i	0.991082	+	0.133250i	$0.0425415\pi$
$174$	6.00000			0.454859
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	2.00000	−	3.46410i	0.150756	−	0.261116i
$177$	−4.00000			−0.300658
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	−8.00000			−0.585018
$188$	−4.00000	+	6.92820i	−0.291730	+	0.505291i
$189$	2.00000	−	3.46410i	0.145479	−	0.251976i
$190$	16.0000			1.16076
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	9.00000			0.642857
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	−0.985160	−	0.171639i	$-0.945094\pi$
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	0.343937	−	0.938993i	$-0.388239\pi$
$198$	−2.00000	−	3.46410i	−0.142134	−	0.246183i
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$	1.00000			0.0707107
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$	−1.00000	+	1.73205i	−0.0703598	+	0.121867i
$203$	24.0000			1.68447
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	10.0000	+	17.3205i	0.698430	+	1.20972i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$		0			0
$208$		0			0
$209$	32.0000			2.21349
$210$	−4.00000	−	6.92820i	−0.276026	−	0.478091i
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	5.00000	−	8.66025i	0.343401	−	0.594789i
$213$	8.00000			0.548151
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$	1.00000			0.0680414
$217$	8.00000	−	13.8564i	0.543075	−	0.940634i
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$	1.00000	+	1.73205i	0.0675737	+	0.117041i
$220$	−8.00000			−0.539360
$221$		0			0
$222$	−2.00000			−0.134231
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	0.925188	−	0.379509i	$-0.123907\pi$
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	−0.791258	+	0.611482i	$0.790574\pi$
$224$	2.00000	+	3.46410i	0.133631	+	0.231455i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	6.00000			0.399114
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$	−4.00000	+	6.92820i	−0.264906	+	0.458831i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−8.00000	−	13.8564i	−0.526361	−	0.911685i
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	16.0000			1.04372
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	4.00000	−	6.92820i	0.259281	−	0.449089i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	−5.00000			−0.321412
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	−9.00000	−	15.5885i	−0.574989	−	0.995910i
$246$	−10.0000			−0.637577
$247$		0			0
$248$	4.00000			0.254000
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	−0.922217	−	0.386674i	$-0.873624\pi$
$251$	−2.00000	+	3.46410i	−0.126239	+	0.218652i	0.795978	+	0.605326i	$0.206957\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$		0			0
$255$	−4.00000			−0.250490
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	−2.00000	−	3.46410i	−0.124515	−	0.215666i
$259$	−8.00000			−0.497096
$260$		0			0
$261$	6.00000			0.371391
$262$	2.00000	+	3.46410i	0.123560	+	0.214013i
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	−20.0000			−1.22859
$266$	−16.0000	+	27.7128i	−0.981023	+	1.69918i
$267$	7.00000	−	12.1244i	0.428393	−	0.741999i
$268$	−16.0000			−0.977356
$269$	13.0000	−	22.5167i	0.792624	−	1.37287i	−0.131713	−	0.991288i	$-0.542048\pi$
$269$	13.0000	−	22.5167i	0.792624	−	1.37287i	0.924337	−	0.381577i	$-0.124619\pi$
$270$	−1.00000	−	1.73205i	−0.0608581	−	0.105409i
$271$	2.00000	+	3.46410i	0.121491	+	0.210429i	0.920356	−	0.391082i	$-0.127899\pi$
$271$	2.00000	+	3.46410i	0.121491	+	0.210429i	−0.798865	+	0.601511i	$0.794566\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		0			0
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	−12.0000			−0.719712
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	4.00000	−	6.92820i	0.239046	−	0.414039i
$281$	−26.0000			−1.55103			−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000			−1.55103			−0.775515	+	0.631329i	$0.782510\pi$
$282$	−4.00000	+	6.92820i	−0.238197	+	0.412568i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$	16.0000			0.947758
$286$		0			0
$287$	−40.0000			−2.36113
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	6.00000	−	10.3923i	0.352332	−	0.610257i
$291$	−10.0000			−0.586210
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−13.0000	+	22.5167i	−0.759468	+	1.31544i	0.183654	+	0.982991i	$0.441207\pi$
$293$	−13.0000	+	22.5167i	−0.759468	+	1.31544i	−0.943122	+	0.332446i	$0.892126\pi$
$294$	9.00000			0.524891
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$	6.00000			0.347571
$299$		0			0
$300$	1.00000			0.0577350
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$	−8.00000			−0.458831
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$	1.00000	−	1.73205i	0.0571662	−	0.0990148i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$	8.00000	−	13.8564i	0.455842	−	0.789542i
$309$	8.00000	+	13.8564i	0.455104	+	0.788263i
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	7.00000	+	12.1244i	0.395033	+	0.684217i
$315$	−4.00000	−	6.92820i	−0.225374	−	0.390360i
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	5.00000	−	8.66025i	0.280386	−	0.485643i
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$	2.00000			0.111803
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$	8.00000	+	13.8564i	0.445132	+	0.770991i
$324$	1.00000			0.0555556
$325$		0			0
$326$	16.0000			0.886158
$327$	−1.00000	−	1.73205i	−0.0553001	−	0.0957826i
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	−16.0000	+	27.7128i	−0.882109	+	1.52786i
$330$	−8.00000			−0.440386
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	−2.00000			−0.109599
$334$		0			0
$335$	16.0000	+	27.7128i	0.874173	+	1.51411i
$336$	2.00000	+	3.46410i	0.109109	+	0.188982i
$337$	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			0
$339$	6.00000			0.325875
$340$	−2.00000	−	3.46410i	−0.108465	−	0.187867i
$341$	−8.00000	−	13.8564i	−0.433224	−	0.750366i
$342$	−4.00000	+	6.92820i	−0.216295	+	0.374634i
$343$	8.00000			0.431959
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$		0			0
$346$	10.0000			0.537603
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	0.774493	−	0.632583i	$-0.218005\pi$
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	−0.935079	+	0.354439i	$0.884672\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	4.00000			0.213201
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	0.617388	−	0.786659i	$-0.288191\pi$
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	−0.989960	+	0.141344i	$0.954858\pi$
$354$	−2.00000	−	3.46410i	−0.106299	−	0.184115i
$355$	8.00000	−	13.8564i	0.424596	−	0.735422i
$356$	14.0000			0.741999
$357$	4.00000	−	6.92820i	0.211702	−	0.366679i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	−22.5000	−	38.9711i	−1.18421	−	2.05111i
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$	−5.00000			−0.262432
$364$		0			0
$365$	4.00000			0.209370
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$		0			0
$369$	−10.0000			−0.520579
$370$	−2.00000	+	3.46410i	−0.103975	+	0.180090i
$371$	20.0000	−	34.6410i	1.03835	−	1.79847i
$372$	4.00000			0.207390
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$	−8.00000			−0.412568
$377$		0			0
$378$	4.00000			0.205738
$379$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$379$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$380$	8.00000	+	13.8564i	0.410391	+	0.710819i
$381$		0			0
$382$	8.00000			0.409316
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−32.0000			−1.63087
$386$	−7.00000	+	12.1244i	−0.356291	+	0.617113i
$387$	−2.00000	−	3.46410i	−0.101666	−	0.176090i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−26.0000			−1.31825			−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000			−1.31825			−0.659126	+	0.752032i	$0.729074\pi$
$390$		0			0
$391$		0			0
$392$	4.50000	+	7.79423i	0.227284	+	0.393668i
$393$	2.00000	+	3.46410i	0.100887	+	0.174741i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	16.0000			0.805047
$396$	2.00000	−	3.46410i	0.100504	−	0.174078i
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	−0.931436	−	0.363906i	$-0.881443\pi$
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	0.780870	+	0.624694i	$0.214776\pi$
$398$	8.00000			0.401004
$399$	−16.0000	+	27.7128i	−0.801002	+	1.38738i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$	−16.0000			−0.798007
$403$		0			0
$404$	−2.00000			−0.0995037
$405$	−1.00000	−	1.73205i	−0.0496904	−	0.0860663i
$406$	12.0000	+	20.7846i	0.595550	+	1.03152i
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$	2.00000			0.0990148
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$	−10.0000	+	17.3205i	−0.493865	+	0.855399i
$411$	10.0000			0.493264
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$	−8.00000	−	13.8564i	−0.393654	−	0.681829i
$414$		0			0
$415$	24.0000			1.17811
$416$		0			0
$417$	−12.0000			−0.587643
$418$	16.0000	+	27.7128i	0.782586	+	1.35548i
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	0.813029	−	0.582224i	$-0.197817\pi$
$419$	−2.00000	−	3.46410i	−0.0977064	−	0.169232i	−0.910735	+	0.412991i	$0.864484\pi$
$420$	4.00000	−	6.92820i	0.195180	−	0.338062i
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	6.00000	−	10.3923i	0.292075	−	0.505889i
$423$	−4.00000	+	6.92820i	−0.194487	+	0.336861i
$424$	10.0000			0.485643
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$	4.00000	+	6.92820i	0.193801	+	0.335673i
$427$	4.00000	+	6.92820i	0.193574	+	0.335279i
$428$	12.0000			0.580042
$429$		0			0
$430$	−8.00000			−0.385794
$431$	4.00000	+	6.92820i	0.192673	+	0.333720i	0.946135	−	0.323772i	$-0.104951\pi$
$431$	4.00000	+	6.92820i	0.192673	+	0.333720i	−0.753462	+	0.657491i	$0.771618\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	15.0000	−	25.9808i	0.720854	−	1.24856i	−0.239804	−	0.970821i	$-0.577083\pi$
$433$	15.0000	−	25.9808i	0.720854	−	1.24856i	0.960658	−	0.277734i	$-0.0895835\pi$
$434$	16.0000			0.768025
$435$	6.00000	−	10.3923i	0.287678	−	0.498273i
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$	−1.00000	+	1.73205i	−0.0477818	+	0.0827606i
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	0.609503	−	0.792784i	$-0.291369\pi$
$439$	−8.00000	−	13.8564i	−0.381819	−	0.661330i	−0.991322	+	0.131453i	$0.958036\pi$
$440$	−4.00000	−	6.92820i	−0.190693	−	0.330289i
$441$	9.00000			0.428571
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$	6.00000			0.283790
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	−0.928091	−	0.372353i	$-0.878551\pi$
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	0.786513	+	0.617574i	$0.211885\pi$
$450$	1.00000			0.0471405
$451$	−20.0000	+	34.6410i	−0.941763	+	1.63118i
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	6.00000	+	10.3923i	0.281905	+	0.488273i
$454$	−20.0000			−0.938647
$455$		0			0
$456$	−8.00000			−0.374634
$457$	15.0000	+	25.9808i	0.701670	+	1.21533i	0.967880	+	0.251414i	$0.0808954\pi$
$457$	15.0000	+	25.9808i	0.701670	+	1.21533i	−0.266209	+	0.963915i	$0.585771\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$		0			0
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	−0.787668	−	0.616100i	$-0.788712\pi$
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	0.927392	+	0.374091i	$0.122045\pi$
$462$	8.00000	−	13.8564i	0.372194	−	0.644658i
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$	−4.00000			−0.185098			−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000			−0.185098			−0.0925490	+	0.995708i	$0.529501\pi$
$468$		0			0
$469$	−64.0000			−2.95525
$470$	8.00000	+	13.8564i	0.369012	+	0.639148i
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	−16.0000			−0.735681
$474$	−4.00000	+	6.92820i	−0.183726	+	0.318223i
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	8.00000			0.366679
$477$	5.00000	−	8.66025i	0.228934	−	0.396526i
$478$		0			0
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	0.988861	−	0.148842i	$-0.0475547\pi$
$479$	8.00000	+	13.8564i	0.365529	+	0.633115i	−0.623332	+	0.781958i	$0.714221\pi$
$480$	2.00000			0.0912871
$481$		0			0
$482$	−10.0000			−0.455488
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−10.0000	+	17.3205i	−0.454077	+	0.786484i
$486$	1.00000			0.0453609
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	−0.907776	−	0.419456i	$-0.862221\pi$
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	0.817147	+	0.576429i	$0.195554\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$	16.0000			0.723545
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	−18.0000	−	31.1769i	−0.812329	−	1.40699i	−0.911230	−	0.411897i	$-0.864866\pi$
$491$	−18.0000	−	31.1769i	−0.812329	−	1.40699i	0.0989017	−	0.995097i	$-0.468467\pi$
$492$	−5.00000	−	8.66025i	−0.225417	−	0.390434i
$493$	12.0000			0.540453
$494$		0			0
$495$	−8.00000			−0.359573
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	16.0000	+	27.7128i	0.717698	+	1.24309i
$498$	−6.00000	+	10.3923i	−0.268866	+	0.465690i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$	−4.00000			−0.178529
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.0539870	+	0.998542i	$0.517193\pi$
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.837769	+	0.546025i	$0.816140\pi$
$504$	2.00000	+	3.46410i	0.0890871	+	0.154303i
$505$	2.00000	+	3.46410i	0.0889988	+	0.154150i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−21.0000	−	36.3731i	−0.930809	−	1.61221i	−0.781943	−	0.623350i	$-0.785771\pi$
$509$	−21.0000	−	36.3731i	−0.930809	−	1.61221i	−0.148866	−	0.988857i	$-0.547562\pi$
$510$	−2.00000	−	3.46410i	−0.0885615	−	0.153393i
$511$	−4.00000	+	6.92820i	−0.176950	+	0.306486i
$512$	−1.00000			−0.0441942
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$	32.0000			1.41009
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	16.0000	+	27.7128i	0.703679	+	1.21881i
$518$	−4.00000	−	6.92820i	−0.175750	−	0.304408i
$519$	10.0000			0.438951
$520$		0			0
$521$	−14.0000			−0.613351			−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000			−0.613351			−0.306676	+	0.951814i	$0.599217\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$	4.00000			0.174574
$526$	4.00000	−	6.92820i	0.174408	−	0.302084i
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$	4.00000			0.174078
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−10.0000	−	17.3205i	−0.434372	−	0.752355i
$531$	−2.00000	−	3.46410i	−0.0867926	−	0.150329i
$532$	−32.0000			−1.38738
$533$		0			0
$534$	14.0000			0.605839
$535$	−12.0000	−	20.7846i	−0.518805	−	0.898597i
$536$	−8.00000	−	13.8564i	−0.345547	−	0.598506i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	26.0000			1.12094
$539$	18.0000	−	31.1769i	0.775315	−	1.34288i
$540$	1.00000	−	1.73205i	0.0430331	−	0.0745356i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	−2.00000	+	3.46410i	−0.0859074	+	0.148796i
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	5.00000	+	8.66025i	0.213589	+	0.369948i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	2.00000	−	3.46410i	0.0852803	−	0.147710i
$551$	−48.0000			−2.04487
$552$		0			0
$553$	−16.0000	+	27.7128i	−0.680389	+	1.17847i
$554$	−22.0000			−0.934690
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	8.00000			0.338062
$561$	−4.00000	−	6.92820i	−0.168880	−	0.292509i
$562$	−13.0000	−	22.5167i	−0.548372	−	0.949808i
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	−0.905088	−	0.425223i	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$	−8.00000			−0.336861
$565$	6.00000	−	10.3923i	0.252422	−	0.437208i
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$	4.00000			0.167984
$568$	−4.00000	+	6.92820i	−0.167836	+	0.290701i
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$	8.00000	+	13.8564i	0.335083	+	0.580381i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$		0			0
$573$	8.00000			0.334205
$574$	−20.0000	−	34.6410i	−0.834784	−	1.44589i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	−6.50000	+	11.2583i	−0.270364	+	0.468285i
$579$	−7.00000	+	12.1244i	−0.290910	+	0.503871i
$580$	12.0000			0.498273
$581$	−24.0000	+	41.5692i	−0.995688	+	1.72458i
$582$	−5.00000	−	8.66025i	−0.207257	−	0.358979i
$583$	−20.0000	−	34.6410i	−0.828315	−	1.43468i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−26.0000			−1.07405
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	0.821795	−	0.569783i	$-0.192973\pi$
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	−0.904344	+	0.426804i	$0.859639\pi$
$588$	4.50000	+	7.79423i	0.185577	+	0.321429i
$589$	−16.0000	+	27.7128i	−0.659269	+	1.14189i
$590$	−8.00000			−0.329355
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	−42.0000			−1.72473			−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000			−1.72473			−0.862367	+	0.506284i	$0.831019\pi$
$594$	2.00000	−	3.46410i	0.0820610	−	0.142134i
$595$	−8.00000	−	13.8564i	−0.327968	−	0.568057i
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	8.00000			0.327418
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	8.00000	−	13.8564i	0.326056	−	0.564745i
$603$	−16.0000			−0.651570
$604$	−6.00000	+	10.3923i	−0.244137	+	0.422857i
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$	−2.00000			−0.0812444
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	−4.00000	−	6.92820i	−0.162221	−	0.280976i
$609$	12.0000	+	20.7846i	0.486265	+	0.842235i
$610$	4.00000			0.161955
$611$		0			0
$612$	2.00000			0.0808452
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	0.885514	−	0.464614i	$-0.153807\pi$
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	−0.845124	+	0.534570i	$0.820473\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$	−10.0000	+	17.3205i	−0.403239	+	0.698430i
$616$	16.0000			0.644658
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$	−8.00000	+	13.8564i	−0.321807	+	0.557386i
$619$	32.0000			1.28619			0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000			1.28619			0.643094	+	0.765787i	$0.277650\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$		0			0
$622$		0			0
$623$	56.0000			2.24359
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	16.0000	+	27.7128i	0.638978	+	1.10674i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	−4.00000			−0.159490
$630$	4.00000	−	6.92820i	0.159364	−	0.276026i
$631$	18.0000	−	31.1769i	0.716569	−	1.24113i	−0.245783	−	0.969325i	$-0.579045\pi$
$631$	18.0000	−	31.1769i	0.716569	−	1.24113i	0.962351	−	0.271808i	$-0.0876217\pi$
$632$	−8.00000			−0.318223
$633$	6.00000	−	10.3923i	0.238479	−	0.413057i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$		0			0
$636$	10.0000			0.396526
$637$		0			0
$638$	24.0000			0.950169
$639$	4.00000	+	6.92820i	0.158238	+	0.274075i
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$	12.0000			0.473602
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$	−8.00000	+	13.8564i	−0.314756	+	0.545173i
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	0.527710	−	0.849425i	$-0.323051\pi$
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	−0.999478	+	0.0322975i	$0.989718\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−16.0000			−0.628055
$650$		0			0
$651$	16.0000			0.627089
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	0.947118	−	0.320884i	$-0.103980\pi$
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	−0.751453	+	0.659786i	$0.770647\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$	8.00000			0.312586
$656$	5.00000	−	8.66025i	0.195217	−	0.338126i
$657$	−1.00000	+	1.73205i	−0.0390137	+	0.0675737i
$658$	−32.0000			−1.24749
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	−4.00000	−	6.92820i	−0.155700	−	0.269680i
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	0.884818	−	0.465937i	$-0.154283\pi$
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	−0.845922	+	0.533306i	$0.820949\pi$
$662$	−8.00000			−0.310929
$663$		0			0
$664$	−12.0000			−0.465690
$665$	32.0000	+	55.4256i	1.24091	+	2.14931i
$666$	−1.00000	−	1.73205i	−0.0387492	−	0.0671156i
$667$		0			0
$668$		0			0
$669$	−2.00000	+	3.46410i	−0.0773245	+	0.133930i
$670$	−16.0000	+	27.7128i	−0.618134	+	1.07064i
$671$	8.00000			0.308837
$672$	−2.00000	+	3.46410i	−0.0771517	+	0.133631i
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	0.968818	−	0.247774i	$-0.0796991\pi$
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	−0.698988	+	0.715134i	$0.746366\pi$
$674$	9.00000	+	15.5885i	0.346667	+	0.600445i
$675$	1.00000			0.0384900
$676$		0			0
$677$	38.0000			1.46046			0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000			1.46046			0.730229	+	0.683202i	$0.239413\pi$
$678$	3.00000	+	5.19615i	0.115214	+	0.199557i
$679$	−20.0000	−	34.6410i	−0.767530	−	1.32940i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$	−20.0000			−0.766402
$682$	8.00000	−	13.8564i	0.306336	−	0.530589i
$683$	−22.0000	+	38.1051i	−0.841807	+	1.45805i	0.0465592	+	0.998916i	$0.485174\pi$
$683$	−22.0000	+	38.1051i	−0.841807	+	1.45805i	−0.888366	+	0.459136i	$0.848159\pi$
$684$	−8.00000			−0.305888
$685$	10.0000	−	17.3205i	0.382080	−	0.661783i
$686$	4.00000	+	6.92820i	0.152721	+	0.264520i
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$	4.00000			0.152499
$689$		0			0
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$	5.00000	+	8.66025i	0.190071	+	0.329213i
$693$	8.00000	−	13.8564i	0.303895	−	0.526361i
$694$	12.0000			0.455514
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$	−20.0000			−0.757554
$698$	3.00000	−	5.19615i	0.113552	−	0.196677i
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	−50.0000			−1.88847			−0.944237	−	0.329267i	$-0.893198\pi$
$701$	−50.0000			−1.88847			−0.944237	+	0.329267i	$0.893198\pi$
$702$		0			0
$703$	16.0000			0.603451
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$	8.00000	+	13.8564i	0.301297	+	0.521862i
$706$	7.00000	−	12.1244i	0.263448	−	0.456306i
$707$	−8.00000			−0.300871
$708$	2.00000	−	3.46410i	0.0751646	−	0.130189i
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$	16.0000			0.600469
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	7.00000	+	12.1244i	0.262336	+	0.454379i
$713$		0			0
$714$	8.00000			0.299392
$715$		0			0
$716$	−12.0000			−0.448461
$717$		0			0
$718$		0			0
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	−0.550700	−	0.834703i	$-0.685639\pi$
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	0.998224	+	0.0595683i	$0.0189724\pi$
$720$	2.00000			0.0745356
$721$	−32.0000	+	55.4256i	−1.19174	+	2.06416i
$722$	22.5000	−	38.9711i	0.837363	−	1.45036i
$723$	−10.0000			−0.371904
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	−2.50000	−	4.33013i	−0.0927837	−	0.160706i
$727$	−40.0000			−1.48352			−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000			−1.48352			−0.741759	+	0.670667i	$0.766008\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	2.00000	+	3.46410i	0.0740233	+	0.128212i
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−2.00000			−0.0738717			−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000			−0.0738717			−0.0369358	+	0.999318i	$0.511760\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$	9.00000	−	15.5885i	0.331970	−	0.574989i
$736$		0			0
$737$	−32.0000	+	55.4256i	−1.17874	+	2.04163i
$738$	−5.00000	−	8.66025i	−0.184053	−	0.318788i
$739$	−20.0000	−	34.6410i	−0.735712	−	1.27429i	−0.954410	−	0.298498i	$-0.903514\pi$
$739$	−20.0000	−	34.6410i	−0.735712	−	1.27429i	0.218698	−	0.975793i	$-0.429819\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	40.0000			1.46845
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	0.997707	−	0.0676840i	$-0.0215610\pi$
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	−0.557470	+	0.830197i	$0.688228\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	6.00000	−	10.3923i	0.219823	−	0.380745i
$746$	−6.00000			−0.219676
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	4.00000	−	6.92820i	0.146254	−	0.253320i
$749$	48.0000			1.75388
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	−4.00000			−0.145768
$754$		0			0
$755$	24.0000			0.873449
$756$	2.00000	+	3.46410i	0.0727393	+	0.125988i
$757$	−27.0000	−	46.7654i	−0.981332	−	1.69972i	−0.657222	−	0.753697i	$-0.728269\pi$
$757$	−27.0000	−	46.7654i	−0.981332	−	1.69972i	−0.324109	−	0.946020i	$-0.605065\pi$
$758$		0			0
$759$		0			0
$760$	−8.00000	+	13.8564i	−0.290191	+	0.502625i
$761$	13.0000	−	22.5167i	0.471250	−	0.816228i	−0.528209	−	0.849114i	$-0.677136\pi$
$761$	13.0000	−	22.5167i	0.471250	−	0.816228i	0.999459	+	0.0328858i	$0.0104698\pi$
$762$		0			0
$763$	4.00000	−	6.92820i	0.144810	−	0.250818i
$764$	4.00000	+	6.92820i	0.144715	+	0.250654i
$765$	−2.00000	−	3.46410i	−0.0723102	−	0.125245i
$766$	24.0000			0.867155
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$	−16.0000	−	27.7128i	−0.576600	−	0.998700i
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$	−14.0000			−0.503871
$773$	27.0000	−	46.7654i	0.971123	−	1.68203i	0.278944	−	0.960307i	$-0.410016\pi$
$773$	27.0000	−	46.7654i	0.971123	−	1.68203i	0.692179	−	0.721726i	$-0.256651\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$	4.00000			0.143684
$776$	5.00000	−	8.66025i	0.179490	−	0.310885i
$777$	−4.00000	−	6.92820i	−0.143499	−	0.248548i
$778$	−13.0000	−	22.5167i	−0.466073	−	0.807261i
$779$	80.0000			2.86630
$780$		0			0
$781$	32.0000			1.14505
$782$		0			0
$783$	3.00000	+	5.19615i	0.107211	+	0.185695i
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	28.0000			0.999363
$786$	−2.00000	+	3.46410i	−0.0713376	+	0.123560i
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	0.250832	+	0.968031i	$0.419296\pi$
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	−0.963755	+	0.266788i	$0.914038\pi$
$788$	18.0000			0.641223
$789$	4.00000	−	6.92820i	0.142404	−	0.246651i
$790$	8.00000	+	13.8564i	0.284627	+	0.492989i
$791$	12.0000	+	20.7846i	0.426671	+	0.739016i
$792$	4.00000			0.142134
$793$		0			0
$794$	−6.00000			−0.212932
$795$	−10.0000	−	17.3205i	−0.354663	−	0.614295i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	−0.847771	−	0.530362i	$-0.822056\pi$
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	0.883193	+	0.469010i	$0.155389\pi$
$798$	−32.0000			−1.13279
$799$	−8.00000	+	13.8564i	−0.283020	+	0.490204i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	14.0000			0.494666
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$	−8.00000	−	13.8564i	−0.282138	−	0.488678i
$805$		0			0
$806$		0			0
$807$	26.0000			0.915243
$808$	−1.00000	−	1.73205i	−0.0351799	−	0.0609333i
$809$	−1.00000	−	1.73205i	−0.0351581	−	0.0608957i	0.847911	−	0.530139i	$-0.177860\pi$
$809$	−1.00000	−	1.73205i	−0.0351581	−	0.0608957i	−0.883069	+	0.469243i	$0.844527\pi$
$810$	1.00000	−	1.73205i	0.0351364	−	0.0608581i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	−12.0000	+	20.7846i	−0.421117	+	0.729397i
$813$	−2.00000	+	3.46410i	−0.0701431	+	0.121491i
$814$	−8.00000			−0.280400
$815$	16.0000	−	27.7128i	0.560456	−	0.970737i
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	−2.00000			−0.0699284
$819$		0			0
$820$	−20.0000			−0.698430
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	−0.955636	−	0.294549i	$-0.904831\pi$
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	0.222731	−	0.974880i	$-0.428503\pi$
$822$	5.00000	+	8.66025i	0.174395	+	0.302061i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−16.0000			−0.557386
$825$	2.00000	−	3.46410i	0.0696311	−	0.120605i
$826$	8.00000	−	13.8564i	0.278356	−	0.482126i
$827$	28.0000			0.973655			0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000			0.973655			0.486828	+	0.873498i	$0.338154\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$	12.0000	+	20.7846i	0.416526	+	0.721444i
$831$	−22.0000			−0.763172
$832$		0			0
$833$	18.0000			0.623663
$834$	−6.00000	−	10.3923i	−0.207763	−	0.359856i
$835$		0			0
$836$	−16.0000	+	27.7128i	−0.553372	+	0.958468i
$837$	4.00000			0.138260
$838$	2.00000	−	3.46410i	0.0690889	−	0.119665i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$	8.00000			0.276026
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	11.0000	+	19.0526i	0.379085	+	0.656595i
$843$	−13.0000	−	22.5167i	−0.447744	−	0.775515i
$844$	12.0000			0.413057
$845$		0			0
$846$	−8.00000			−0.275046
$847$	−10.0000	−	17.3205i	−0.343604	−	0.595140i
$848$	5.00000	+	8.66025i	0.171701	+	0.297394i
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$	2.00000			0.0685994
$851$		0			0
$852$	−4.00000	+	6.92820i	−0.137038	+	0.237356i
$853$	−2.00000			−0.0684787			−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000			−0.0684787			−0.0342393	+	0.999414i	$0.510901\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$	8.00000	+	13.8564i	0.273594	+	0.473879i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	−44.0000			−1.50126			−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000			−1.50126			−0.750630	+	0.660722i	$0.770250\pi$
$860$	−4.00000	−	6.92820i	−0.136399	−	0.236250i
$861$	−20.0000	−	34.6410i	−0.681598	−	1.18056i
$862$	−4.00000	+	6.92820i	−0.136241	+	0.235976i
$863$	40.0000			1.36162			0.680808	−	0.732462i	$-0.261629\pi$
$863$	40.0000			1.36162			0.680808	+	0.732462i	$0.261629\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	10.0000	−	17.3205i	0.340010	−	0.588915i
$866$	30.0000			1.01944
$867$	−6.50000	+	11.2583i	−0.220752	+	0.382353i
$868$	8.00000	+	13.8564i	0.271538	+	0.470317i
$869$	16.0000	+	27.7128i	0.542763	+	0.940093i
$870$	12.0000			0.406838
$871$		0			0
$872$	2.00000			0.0677285
$873$	−5.00000	−	8.66025i	−0.169224	−	0.293105i
$874$		0			0
$875$	24.0000	−	41.5692i	0.811348	−	1.40530i
$876$	−2.00000			−0.0675737
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$	8.00000	−	13.8564i	0.269987	−	0.467631i
$879$	−26.0000			−0.876958
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$	−13.0000	−	22.5167i	−0.437981	−	0.758606i	0.559553	−	0.828795i	$-0.310973\pi$
$881$	−13.0000	−	22.5167i	−0.437981	−	0.758606i	−0.997534	+	0.0701893i	$0.977640\pi$
$882$	4.50000	+	7.79423i	0.151523	+	0.262445i
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$	−8.00000			−0.268917
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	1.00000	−	1.73205i	0.0335578	−	0.0581238i
$889$		0			0
$890$	14.0000	−	24.2487i	0.469281	−	0.812819i
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	−4.00000			−0.133930
$893$	32.0000	−	55.4256i	1.07084	−	1.85475i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$	12.0000	+	20.7846i	0.401116	+	0.694753i
$896$	−4.00000			−0.133631
$897$		0			0
$898$	−6.00000			−0.200223
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	10.0000	−	17.3205i	0.333148	−	0.577030i
$902$	−40.0000			−1.33185
$903$	8.00000	−	13.8564i	0.266223	−	0.461112i
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	−20.0000			−0.664822
$906$	−6.00000	+	10.3923i	−0.199337	+	0.345261i
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	−10.0000	−	17.3205i	−0.331862	−	0.574801i
$909$	−2.00000			−0.0663358
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$	−4.00000	−	6.92820i	−0.132453	−	0.229416i
$913$	24.0000	+	41.5692i	0.794284	+	1.37574i
$914$	−15.0000	+	25.9808i	−0.496156	+	0.859367i
$915$	4.00000			0.132236
$916$	−11.0000	+	19.0526i	−0.363450	+	0.629514i
$917$	−8.00000	+	13.8564i	−0.264183	+	0.457579i
$918$	2.00000			0.0660098
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−4.00000	−	6.92820i	−0.131804	−	0.228292i
$922$	6.00000			0.197599
$923$		0			0
$924$	16.0000			0.526361
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$	−10.0000	−	17.3205i	−0.328620	−	0.569187i
$927$	−8.00000	+	13.8564i	−0.262754	+	0.455104i
$928$	−6.00000			−0.196960
$929$	−23.0000	+	39.8372i	−0.754606	+	1.30702i	0.190965	+	0.981597i	$0.438838\pi$
$929$	−23.0000	+	39.8372i	−0.754606	+	1.30702i	−0.945570	+	0.325418i	$0.894495\pi$
$930$	4.00000	−	6.92820i	0.131165	−	0.227185i
$931$	−72.0000			−2.35970
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$		0			0
$934$	−2.00000	−	3.46410i	−0.0654420	−	0.113349i
$935$	−16.0000			−0.523256
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	−32.0000	−	55.4256i	−1.04484	−	1.80971i
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$	−8.00000	+	13.8564i	−0.260931	+	0.451946i
$941$	−46.0000			−1.49956			−0.749779	−	0.661689i	$-0.769840\pi$
$941$	−46.0000			−1.49956			−0.749779	+	0.661689i	$0.769840\pi$
$942$	−7.00000	+	12.1244i	−0.228072	+	0.395033i
$943$		0			0
$944$	4.00000			0.130189
$945$	4.00000	−	6.92820i	0.130120	−	0.225374i
$946$	−8.00000	−	13.8564i	−0.260102	−	0.450511i
$947$	2.00000	+	3.46410i	0.0649913	+	0.112568i	0.896690	−	0.442659i	$-0.145965\pi$
$947$	2.00000	+	3.46410i	0.0649913	+	0.112568i	−0.831699	+	0.555227i	$0.812631\pi$
$948$	−8.00000			−0.259828
$949$		0			0
$950$	−8.00000			−0.259554
$951$	−3.00000	−	5.19615i	−0.0972817	−	0.168497i
$952$	4.00000	+	6.92820i	0.129641	+	0.224544i
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	−0.513971	−	0.857808i	$-0.671826\pi$
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	0.999869	+	0.0162081i	$0.00515944\pi$
$954$	10.0000			0.323762
$955$	8.00000	−	13.8564i	0.258874	−	0.448383i
$956$		0			0
$957$	24.0000			0.775810
$958$	−8.00000	+	13.8564i	−0.258468	+	0.447680i
$959$	20.0000	+	34.6410i	0.645834	+	1.11862i
$960$	1.00000	+	1.73205i	0.0322749	+	0.0559017i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	12.0000			0.386695
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	14.0000	+	24.2487i	0.450676	+	0.780594i
$966$		0			0
$967$	4.00000			0.128631			0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000			0.128631			0.0643157	+	0.997930i	$0.479514\pi$
$968$	2.50000	−	4.33013i	0.0803530	−	0.139176i
$969$	−8.00000	+	13.8564i	−0.256997	+	0.445132i
$970$	−20.0000			−0.642161
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	−0.549058	−	0.835784i	$-0.685013\pi$
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	0.998339	+	0.0576061i	$0.0183467\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−24.0000	−	41.5692i	−0.769405	−	1.33265i
$974$	−4.00000			−0.128168
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	0.814038	−	0.580812i	$-0.197265\pi$
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	−0.910017	+	0.414572i	$0.863931\pi$
$978$	8.00000	+	13.8564i	0.255812	+	0.443079i
$979$	28.0000	−	48.4974i	0.894884	−	1.54998i
$980$	18.0000			0.574989
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	18.0000	−	31.1769i	0.574403	−	0.994895i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$	5.00000	−	8.66025i	0.159394	−	0.276079i
$985$	−18.0000	−	31.1769i	−0.573528	−	0.993379i
$986$	6.00000	+	10.3923i	0.191079	+	0.330958i
$987$	−32.0000			−1.01857
$988$		0			0
$989$		0			0
$990$	−4.00000	−	6.92820i	−0.127128	−	0.220193i
$991$	24.0000	+	41.5692i	0.762385	+	1.32049i	0.941618	+	0.336683i	$0.109305\pi$
$991$	24.0000	+	41.5692i	0.762385	+	1.32049i	−0.179233	+	0.983807i	$0.557362\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−8.00000			−0.253872
$994$	−16.0000	+	27.7128i	−0.507489	+	0.878997i
$995$	8.00000	−	13.8564i	0.253617	−	0.439278i
$996$	−12.0000			−0.380235
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$		0			0
$999$	−1.00000	−	1.73205i	−0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.f.991.1		2
13.2	odd	12		1014.2.b.b.337.2		2
13.3	even	3		78.2.a.a.1.1	✓	1
13.4	even	6		1014.2.e.c.529.1		2
13.5	odd	4		1014.2.i.d.361.2		4
13.6	odd	12		1014.2.i.d.823.1		4
13.7	odd	12		1014.2.i.d.823.2		4
13.8	odd	4		1014.2.i.d.361.1		4
13.9	even	3	inner	1014.2.e.f.529.1		2
13.10	even	6		1014.2.a.d.1.1		1
13.11	odd	12		1014.2.b.b.337.1		2
13.12	even	2		1014.2.e.c.991.1		2
39.2	even	12		3042.2.b.g.1351.1		2
39.11	even	12		3042.2.b.g.1351.2		2
39.23	odd	6		3042.2.a.f.1.1		1
39.29	odd	6		234.2.a.c.1.1		1
52.3	odd	6		624.2.a.h.1.1		1
52.23	odd	6		8112.2.a.v.1.1		1
65.3	odd	12		1950.2.e.i.1249.2		2
65.29	even	6		1950.2.a.w.1.1		1
65.42	odd	12		1950.2.e.i.1249.1		2
91.55	odd	6		3822.2.a.j.1.1		1
104.3	odd	6		2496.2.a.b.1.1		1
104.29	even	6		2496.2.a.t.1.1		1
117.16	even	3		2106.2.e.q.1405.1		2
117.29	odd	6		2106.2.e.j.1405.1		2
117.68	odd	6		2106.2.e.j.703.1		2
117.94	even	3		2106.2.e.q.703.1		2
143.120	odd	6		9438.2.a.t.1.1		1
156.107	even	6		1872.2.a.c.1.1		1
195.29	odd	6		5850.2.a.d.1.1		1
195.68	even	12		5850.2.e.bb.5149.1		2
195.107	even	12		5850.2.e.bb.5149.2		2
312.29	odd	6		7488.2.a.bz.1.1		1
312.107	even	6		7488.2.a.bk.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.a.a.1.1	✓	1	13.3	even	3
234.2.a.c.1.1		1	39.29	odd	6
624.2.a.h.1.1		1	52.3	odd	6
1014.2.a.d.1.1		1	13.10	even	6
1014.2.b.b.337.1		2	13.11	odd	12
1014.2.b.b.337.2		2	13.2	odd	12
1014.2.e.c.529.1		2	13.4	even	6
1014.2.e.c.991.1		2	13.12	even	2
1014.2.e.f.529.1		2	13.9	even	3	inner
1014.2.e.f.991.1		2	1.1	even	1	trivial
1014.2.i.d.361.1		4	13.8	odd	4
1014.2.i.d.361.2		4	13.5	odd	4
1014.2.i.d.823.1		4	13.6	odd	12
1014.2.i.d.823.2		4	13.7	odd	12
1872.2.a.c.1.1		1	156.107	even	6
1950.2.a.w.1.1		1	65.29	even	6
1950.2.e.i.1249.1		2	65.42	odd	12
1950.2.e.i.1249.2		2	65.3	odd	12
2106.2.e.j.703.1		2	117.68	odd	6
2106.2.e.j.1405.1		2	117.29	odd	6
2106.2.e.q.703.1		2	117.94	even	3
2106.2.e.q.1405.1		2	117.16	even	3
2496.2.a.b.1.1		1	104.3	odd	6
2496.2.a.t.1.1		1	104.29	even	6
3042.2.a.f.1.1		1	39.23	odd	6
3042.2.b.g.1351.1		2	39.2	even	12
3042.2.b.g.1351.2		2	39.11	even	12
3822.2.a.j.1.1		1	91.55	odd	6
5850.2.a.d.1.1		1	195.29	odd	6
5850.2.e.bb.5149.1		2	195.68	even	12
5850.2.e.bb.5149.2		2	195.107	even	12
7488.2.a.bk.1.1		1	312.107	even	6
7488.2.a.bz.1.1		1	312.29	odd	6
8112.2.a.v.1.1		1	52.23	odd	6
9438.2.a.t.1.1		1	143.120	odd	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(2.00000 + 3.46410i) q^{11} -1.00000 q^{12} -4.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(4.00000 - 6.92820i) q^{19} +(-1.00000 + 1.73205i) q^{20} -4.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{25} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-1.00000 + 1.73205i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} -2.00000 q^{34} +(-4.00000 + 6.92820i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} +8.00000 q^{38} -2.00000 q^{40} +(5.00000 + 8.66025i) q^{41} +(-2.00000 - 3.46410i) q^{42} +(-2.00000 + 3.46410i) q^{43} -4.00000 q^{44} +(-1.00000 + 1.73205i) q^{45} +8.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} -2.00000 q^{51} -10.0000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.00000 + 6.92820i) q^{55} +(2.00000 - 3.46410i) q^{56} +8.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(-2.00000 + 3.46410i) q^{59} -2.00000 q^{60} +(1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-2.00000 - 3.46410i) q^{63} +1.00000 q^{64} -4.00000 q^{66} +(8.00000 + 13.8564i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{70} +(4.00000 - 6.92820i) q^{71} +(0.500000 - 0.866025i) q^{72} +2.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(4.00000 + 6.92820i) q^{76} -16.0000 q^{77} +8.00000 q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} +12.0000 q^{83} +(2.00000 - 3.46410i) q^{84} +(-2.00000 + 3.46410i) q^{85} -4.00000 q^{86} +(3.00000 - 5.19615i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-7.00000 - 12.1244i) q^{89} -2.00000 q^{90} +(-2.00000 - 3.46410i) q^{93} +(4.00000 + 6.92820i) q^{94} +(8.00000 - 13.8564i) q^{95} +1.00000 q^{96} +(-5.00000 + 8.66025i) q^{97} +(4.50000 - 7.79423i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 4 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 8 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 2 q^{18} + 8 q^{19} - 2 q^{20} - 8 q^{21} - 4 q^{22}+ \cdots - 8 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 4 * q^5 - q^6 - 4 * q^7 - 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 - 8 * q^14 + 2 * q^15 - q^16 - 2 * q^17 - 2 * q^18 + 8 * q^19 - 2 * q^20 - 8 * q^21 - 4 * q^22 - q^24 - 2 * q^25 - 2 * q^27 - 4 * q^28 - 6 * q^29 - 2 * q^30 - 8 * q^31 + q^32 - 4 * q^33 - 4 * q^34 - 8 * q^35 - q^36 + 2 * q^37 + 16 * q^38 - 4 * q^40 + 10 * q^41 - 4 * q^42 - 4 * q^43 - 8 * q^44 - 2 * q^45 + 16 * q^47 + q^48 - 9 * q^49 - q^50 - 4 * q^51 - 20 * q^53 - q^54 + 8 * q^55 + 4 * q^56 + 16 * q^57 + 6 * q^58 - 4 * q^59 - 4 * q^60 + 2 * q^61 - 4 * q^62 - 4 * q^63 + 2 * q^64 - 8 * q^66 + 16 * q^67 - 2 * q^68 - 16 * q^70 + 8 * q^71 + q^72 + 4 * q^73 - 2 * q^74 - q^75 + 8 * q^76 - 32 * q^77 + 16 * q^79 - 2 * q^80 - q^81 - 10 * q^82 + 24 * q^83 + 4 * q^84 - 4 * q^85 - 8 * q^86 + 6 * q^87 - 4 * q^88 - 14 * q^89 - 4 * q^90 - 4 * q^93 + 8 * q^94 + 16 * q^95 + 2 * q^96 - 10 * q^97 + 9 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more