LMFDB - Embedded newform 1274.2.f.u.1145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(79,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1274.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.f (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:	$10.1729412175$
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 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1145.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.1145
Dual form			1274.2.f.u.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +(1.50000 + 2.59808i) q^{12} +1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.00000 - 5.19615i) q^{18} +(1.00000 + 1.73205i) q^{19} +5.00000 q^{22} +(-2.50000 - 4.33013i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} -9.00000 q^{27} +4.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.50000 - 12.9904i) q^{33} -4.00000 q^{34} +6.00000 q^{36} +(-3.50000 - 6.06218i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.50000 - 2.59808i) q^{39} +9.00000 q^{41} -12.0000 q^{43} +(2.50000 + 4.33013i) q^{44} +(2.50000 - 4.33013i) q^{46} +(-3.50000 - 6.06218i) q^{47} -3.00000 q^{48} +5.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(2.00000 - 3.46410i) q^{53} +(-4.50000 - 7.79423i) q^{54} +6.00000 q^{57} +(2.00000 + 3.46410i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(7.50000 - 12.9904i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(-2.00000 - 3.46410i) q^{68} -15.0000 q^{69} +(3.00000 + 5.19615i) q^{72} +(3.50000 - 6.06218i) q^{73} +(3.50000 - 6.06218i) q^{74} +(-7.50000 - 12.9904i) q^{75} -2.00000 q^{76} +3.00000 q^{78} +(8.50000 + 14.7224i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(4.50000 + 7.79423i) q^{82} -4.00000 q^{83} +(-6.00000 - 10.3923i) q^{86} +(6.00000 - 10.3923i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(7.00000 + 12.1244i) q^{89} +5.00000 q^{92} +(-1.50000 - 2.59808i) q^{93} +(3.50000 - 6.06218i) q^{94} +(-1.50000 - 2.59808i) q^{96} -5.00000 q^{97} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - 2 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 2 q^{13} - q^{16} - 4 q^{17} + 6 q^{18} + 2 q^{19} + 10 q^{22} - 5 q^{23} - 3 q^{24} + 5 q^{25} + q^{26} - 18 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 6 * q^6 - 2 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 2 * q^13 - q^16 - 4 * q^17 + 6 * q^18 + 2 * q^19 + 10 * q^22 - 5 * q^23 - 3 * q^24 + 5 * q^25 + q^26 - 18 * q^27 + 8 * q^29 + q^31 + q^32 - 15 * q^33 - 8 * q^34 + 12 * q^36 - 7 * q^37 - 2 * q^38 + 3 * q^39 + 18 * q^41 - 24 * q^43 + 5 * q^44 + 5 * q^46 - 7 * q^47 - 6 * q^48 + 10 * q^50 + 12 * q^51 - q^52 + 4 * q^53 - 9 * q^54 + 12 * q^57 + 4 * q^58 - 6 * q^59 + 13 * q^61 + 2 * q^62 + 2 * q^64 + 15 * q^66 - 11 * q^67 - 4 * q^68 - 30 * q^69 + 6 * q^72 + 7 * q^73 + 7 * q^74 - 15 * q^75 - 4 * q^76 + 6 * q^78 + 17 * q^79 - 9 * q^81 + 9 * q^82 - 8 * q^83 - 12 * q^86 + 12 * q^87 - 5 * q^88 + 14 * q^89 + 10 * q^92 - 3 * q^93 + 7 * q^94 - 3 * q^96 - 10 * q^97 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	3.00000			1.22474
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$	3.00000	−	5.19615i	0.707107	−	1.22474i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$	5.00000			1.06600
$23$	−2.50000	−	4.33013i	−0.521286	−	0.902894i	−0.999694	−	0.0247559i	$-0.992119\pi$
$23$	−2.50000	−	4.33013i	−0.521286	−	0.902894i	0.478407	−	0.878138i	$-0.341214\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	−9.00000			−1.73205
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−7.50000	−	12.9904i	−1.30558	−	2.26134i
$34$	−4.00000			−0.685994
$35$		0			0
$36$	6.00000			1.00000
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$		0			0
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$		0			0
$43$	−12.0000			−1.82998			−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000			−1.82998			−0.914991	+	0.403473i	$0.867803\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$		0			0
$46$	2.50000	−	4.33013i	0.368605	−	0.638442i
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$	−3.00000			−0.433013
$49$		0			0
$50$	5.00000			0.707107
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$	−4.50000	−	7.79423i	−0.612372	−	1.06066i
$55$		0			0
$56$		0			0
$57$	6.00000			0.794719
$58$	2.00000	+	3.46410i	0.262613	+	0.454859i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	1.00000			0.127000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	7.50000	−	12.9904i	0.923186	−	1.59901i
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	−15.0000			−1.80579
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	3.00000	+	5.19615i	0.353553	+	0.612372i
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	3.50000	−	6.06218i	0.406867	−	0.704714i
$75$	−7.50000	−	12.9904i	−0.866025	−	1.50000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	3.00000			0.339683
$79$	8.50000	+	14.7224i	0.956325	+	1.65640i	0.731307	+	0.682048i	$0.238911\pi$
$79$	8.50000	+	14.7224i	0.956325	+	1.65640i	0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$		0			0
$86$	−6.00000	−	10.3923i	−0.646997	−	1.12063i
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$		0			0
$91$		0			0
$92$	5.00000			0.521286
$93$	−1.50000	−	2.59808i	−0.155543	−	0.269408i
$94$	3.50000	−	6.06218i	0.360997	−	0.625266i
$95$		0			0
$96$	−1.50000	−	2.59808i	−0.153093	−	0.265165i
$97$	−5.00000			−0.507673			−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000			−0.507673			−0.253837	+	0.967247i	$0.581693\pi$
$98$		0			0
$99$	−30.0000			−3.01511
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$	−6.00000	+	10.3923i	−0.594089	+	1.02899i
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	0.975124	−	0.221660i	$-0.0711475\pi$
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	−0.679525	+	0.733652i	$0.737814\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	4.00000			0.388514
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$	4.50000	−	7.79423i	0.433013	−	0.750000i
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	0.869953	−	0.493135i	$-0.164149\pi$
$110$		0			0
$111$	−21.0000			−1.99323
$112$		0			0
$113$	1.00000			0.0940721			0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000			0.0940721			0.0470360	+	0.998893i	$0.485022\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$		0			0
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	−6.00000			−0.552345
$119$		0			0
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−6.50000	+	11.2583i	−0.588482	+	1.01928i
$123$	13.5000	−	23.3827i	1.21725	−	2.10835i
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$		0			0
$126$		0			0
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−18.0000	+	31.1769i	−1.58481	+	2.74497i
$130$		0			0
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$	15.0000			1.30558
$133$		0			0
$134$	−11.0000			−0.950255
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$	−7.50000	−	12.9904i	−0.638442	−	1.10581i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	−21.0000			−1.76852
$142$		0			0
$143$	2.50000	−	4.33013i	0.209061	−	0.362103i
$144$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$145$		0			0
$146$	7.00000			0.579324
$147$		0			0
$148$	7.00000			0.575396
$149$	−3.50000	−	6.06218i	−0.286731	−	0.496633i	0.686296	−	0.727322i	$-0.259235\pi$
$149$	−3.50000	−	6.06218i	−0.286731	−	0.496633i	−0.973028	+	0.230689i	$0.925902\pi$
$150$	7.50000	−	12.9904i	0.612372	−	1.06066i
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	−0.511636	−	0.859202i	$-0.670960\pi$
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	0.999909	+	0.0134886i	$0.00429367\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$	24.0000			1.94029
$154$		0			0
$155$		0			0
$156$	1.50000	+	2.59808i	0.120096	+	0.208013i
$157$	0.500000	−	0.866025i	0.0399043	−	0.0691164i	−0.845383	−	0.534160i	$-0.820628\pi$
$157$	0.500000	−	0.866025i	0.0399043	−	0.0691164i	0.885288	+	0.465044i	$0.153961\pi$
$158$	−8.50000	+	14.7224i	−0.676224	+	1.17125i
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$		0			0
$162$	−9.00000			−0.707107
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	6.00000	−	10.3923i	0.458831	−	0.794719i
$172$	6.00000	−	10.3923i	0.457496	−	0.792406i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$	12.0000			0.909718
$175$		0			0
$176$	−5.00000			−0.376889
$177$	9.00000	+	15.5885i	0.676481	+	1.17170i
$178$	−7.00000	+	12.1244i	−0.524672	+	0.908759i
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	−0.826231	−	0.563331i	$-0.809520\pi$
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	0.900975	+	0.433872i	$0.142853\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		0			0
$183$	39.0000			2.88296
$184$	2.50000	+	4.33013i	0.184302	+	0.319221i
$185$		0			0
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	10.0000	+	17.3205i	0.731272	+	1.26660i
$188$	7.00000			0.510527
$189$		0			0
$190$		0			0
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$	1.50000	−	2.59808i	0.108253	−	0.187500i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	−2.50000	−	4.33013i	−0.179490	−	0.310885i
$195$		0			0
$196$		0			0
$197$	27.0000			1.92367			0.961835	−	0.273629i	$-0.0882242\pi$
$197$	27.0000			1.92367			0.961835	+	0.273629i	$0.0882242\pi$
$198$	−15.0000	−	25.9808i	−1.06600	−	1.84637i
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$	16.5000	+	28.5788i	1.16382	+	2.01580i
$202$	15.0000			1.05540
$203$		0			0
$204$	−12.0000			−0.840168
$205$		0			0
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$	−15.0000	+	25.9808i	−1.04257	+	1.80579i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	10.0000			0.691714
$210$		0			0
$211$	−14.0000			−0.963800			−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000			−0.963800			−0.481900	+	0.876226i	$0.660053\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$		0			0
$216$	9.00000			0.612372
$217$		0			0
$218$	18.0000			1.21911
$219$	−10.5000	−	18.1865i	−0.709524	−	1.22893i
$220$		0			0
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$	−10.5000	−	18.1865i	−0.704714	−	1.22060i
$223$	−3.00000			−0.200895			−0.100447	−	0.994942i	$-0.532027\pi$
$223$	−3.00000			−0.200895			−0.100447	+	0.994942i	$0.532027\pi$
$224$		0			0
$225$	−30.0000			−2.00000
$226$	0.500000	+	0.866025i	0.0332595	+	0.0576072i
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$	−3.00000	+	5.19615i	−0.198680	+	0.344124i
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$		0			0
$231$		0			0
$232$	−4.00000			−0.262613
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$		0			0
$236$	−3.00000	−	5.19615i	−0.195283	−	0.338241i
$237$	51.0000			3.31281
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−15.0000	+	25.9808i	−0.966235	+	1.67357i	−0.259975	+	0.965615i	$0.583714\pi$
$241$	−15.0000	+	25.9808i	−0.966235	+	1.67357i	−0.706260	+	0.707953i	$0.749619\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$		0			0
$244$	−13.0000			−0.832240
$245$		0			0
$246$	27.0000			1.72146
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$	−0.500000	+	0.866025i	−0.0317500	+	0.0549927i
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	13.0000			0.820553			0.410276	−	0.911961i	$-0.365432\pi$
$251$	13.0000			0.820553			0.410276	+	0.911961i	$0.365432\pi$
$252$		0			0
$253$	−25.0000			−1.57174
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.858567	+	0.512702i	$0.171355\pi$
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.0147291	+	0.999892i	$0.495311\pi$
$258$	−36.0000			−2.24126
$259$		0			0
$260$		0			0
$261$	−12.0000	−	20.7846i	−0.742781	−	1.28654i
$262$	−4.00000	+	6.92820i	−0.247121	+	0.428026i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	7.50000	+	12.9904i	0.461593	+	0.799503i
$265$		0			0
$266$		0			0
$267$	42.0000			2.57036
$268$	−5.50000	−	9.52628i	−0.335966	−	0.581910i
$269$	6.50000	−	11.2583i	0.396312	−	0.686433i	−0.596956	−	0.802274i	$-0.703623\pi$
$269$	6.50000	−	11.2583i	0.396312	−	0.686433i	0.993268	+	0.115842i	$0.0369565\pi$
$270$		0			0
$271$	−0.500000	−	0.866025i	−0.0303728	−	0.0526073i	0.850439	−	0.526073i	$-0.176336\pi$
$271$	−0.500000	−	0.866025i	−0.0303728	−	0.0526073i	−0.880812	+	0.473466i	$0.843003\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−18.0000			−1.08742
$275$	−12.5000	−	21.6506i	−0.753778	−	1.30558i
$276$	7.50000	−	12.9904i	0.451447	−	0.781929i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$	−6.00000			−0.359211
$280$		0			0
$281$	−16.0000			−0.954480			−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000			−0.954480			−0.477240	+	0.878773i	$0.658363\pi$
$282$	−10.5000	−	18.1865i	−0.625266	−	1.08299i
$283$	1.50000	−	2.59808i	0.0891657	−	0.154440i	−0.817993	−	0.575228i	$-0.804913\pi$
$283$	1.50000	−	2.59808i	0.0891657	−	0.154440i	0.907159	+	0.420789i	$0.138247\pi$
$284$		0			0
$285$		0			0
$286$	5.00000			0.295656
$287$		0			0
$288$	−6.00000			−0.353553
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	−7.50000	+	12.9904i	−0.439658	+	0.761510i
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$		0			0
$296$	3.50000	+	6.06218i	0.203433	+	0.352357i
$297$	−22.5000	+	38.9711i	−1.30558	+	2.26134i
$298$	3.50000	−	6.06218i	0.202750	−	0.351173i
$299$	−2.50000	−	4.33013i	−0.144579	−	0.250418i
$300$	15.0000			0.866025
$301$		0			0
$302$	12.0000			0.690522
$303$	−22.5000	−	38.9711i	−1.29259	−	2.23883i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$		0			0
$306$	12.0000	+	20.7846i	0.685994	+	1.18818i
$307$	−32.0000			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$308$		0			0
$309$	18.0000			1.02398
$310$		0			0
$311$	13.0000	−	22.5167i	0.737162	−	1.27680i	−0.216606	−	0.976259i	$-0.569499\pi$
$311$	13.0000	−	22.5167i	0.737162	−	1.27680i	0.953768	−	0.300544i	$-0.0971681\pi$
$312$	−1.50000	+	2.59808i	−0.0849208	+	0.147087i
$313$	−15.0000	−	25.9808i	−0.847850	−	1.46852i	−0.883123	−	0.469142i	$-0.844563\pi$
$313$	−15.0000	−	25.9808i	−0.847850	−	1.46852i	0.0352727	−	0.999378i	$-0.488770\pi$
$314$	1.00000			0.0564333
$315$		0			0
$316$	−17.0000			−0.956325
$317$	−5.50000	−	9.52628i	−0.308911	−	0.535049i	0.669214	−	0.743070i	$-0.266631\pi$
$317$	−5.50000	−	9.52628i	−0.308911	−	0.535049i	−0.978124	+	0.208021i	$0.933298\pi$
$318$	6.00000	−	10.3923i	0.336463	−	0.582772i
$319$	10.0000	−	17.3205i	0.559893	−	0.969762i
$320$		0			0
$321$	24.0000			1.33955
$322$		0			0
$323$	−8.00000			−0.445132
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	2.50000	−	4.33013i	0.138675	−	0.240192i
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−27.0000	−	46.7654i	−1.49310	−	2.58613i
$328$	−9.00000			−0.496942
$329$		0			0
$330$		0			0
$331$	−1.50000	−	2.59808i	−0.0824475	−	0.142803i	0.821853	−	0.569699i	$-0.192940\pi$
$331$	−1.50000	−	2.59808i	−0.0824475	−	0.142803i	−0.904301	+	0.426896i	$0.859607\pi$
$332$	2.00000	−	3.46410i	0.109764	−	0.190117i
$333$	−21.0000	+	36.3731i	−1.15079	+	1.99323i
$334$	−4.00000	−	6.92820i	−0.218870	−	0.379094i
$335$		0			0
$336$		0			0
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$	1.50000	−	2.59808i	0.0814688	−	0.141108i
$340$		0			0
$341$	−2.50000	−	4.33013i	−0.135383	−	0.234490i
$342$	12.0000			0.648886
$343$		0			0
$344$	12.0000			0.646997
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	−0.996826	−	0.0796169i	$-0.974630\pi$
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	0.567363	+	0.823468i	$0.307964\pi$
$348$	6.00000	+	10.3923i	0.321634	+	0.557086i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−9.00000			−0.480384
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$	−9.00000	+	15.5885i	−0.478345	+	0.828517i
$355$		0			0
$356$	−14.0000			−0.741999
$357$		0			0
$358$	2.00000			0.105703
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	2.50000	+	4.33013i	0.131397	+	0.227586i
$363$	−42.0000			−2.20443
$364$		0			0
$365$		0			0
$366$	19.5000	+	33.7750i	1.01928	+	1.76545i
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$	−2.50000	+	4.33013i	−0.130322	+	0.225723i
$369$	−27.0000	−	46.7654i	−1.40556	−	2.43451i
$370$		0			0
$371$		0			0
$372$	3.00000			0.155543
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	−10.0000	+	17.3205i	−0.517088	+	0.895622i
$375$		0			0
$376$	3.50000	+	6.06218i	0.180499	+	0.312633i
$377$	4.00000			0.206010
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	13.5000	−	23.3827i	0.691626	−	1.19793i
$382$	−8.00000	+	13.8564i	−0.409316	+	0.708955i
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	0.727851	−	0.685736i	$-0.240519\pi$
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	−0.957790	+	0.287469i	$0.907186\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	−4.00000			−0.203595
$387$	36.0000	+	62.3538i	1.82998	+	3.16962i
$388$	2.50000	−	4.33013i	0.126918	−	0.219829i
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	−0.949432	−	0.313972i	$-0.898340\pi$
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	0.746624	+	0.665246i	$0.231673\pi$
$390$		0			0
$391$	20.0000			1.01144
$392$		0			0
$393$	24.0000			1.21064
$394$	13.5000	+	23.3827i	0.680120	+	1.17800i
$395$		0			0
$396$	15.0000	−	25.9808i	0.753778	−	1.30558i
$397$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$397$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$398$	−20.0000			−1.00251
$399$		0			0
$400$	−5.00000			−0.250000
$401$	14.0000	+	24.2487i	0.699127	+	1.21092i	0.968770	+	0.247962i	$0.0797610\pi$
$401$	14.0000	+	24.2487i	0.699127	+	1.21092i	−0.269643	+	0.962960i	$0.586906\pi$
$402$	−16.5000	+	28.5788i	−0.822945	+	1.42538i
$403$	0.500000	−	0.866025i	0.0249068	−	0.0431398i
$404$	7.50000	+	12.9904i	0.373139	+	0.646296i
$405$		0			0
$406$		0			0
$407$	−35.0000			−1.73489
$408$	−6.00000	−	10.3923i	−0.297044	−	0.514496i
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	−0.930614	−	0.366002i	$-0.880726\pi$
$409$	−3.00000	+	5.19615i	−0.148340	+	0.256933i	0.782274	+	0.622935i	$0.214060\pi$
$410$		0			0
$411$	27.0000	+	46.7654i	1.33181	+	2.30677i
$412$	−6.00000			−0.295599
$413$		0			0
$414$	−30.0000			−1.47442
$415$		0			0
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	−6.00000	+	10.3923i	−0.293821	+	0.508913i
$418$	5.00000	+	8.66025i	0.244558	+	0.423587i
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	−35.0000			−1.70580			−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000			−1.70580			−0.852898	+	0.522078i	$0.825157\pi$
$422$	−7.00000	−	12.1244i	−0.340755	−	0.590204i
$423$	−21.0000	+	36.3731i	−1.02105	+	1.76852i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	10.0000	+	17.3205i	0.485071	+	0.840168i
$426$		0			0
$427$		0			0
$428$	−8.00000			−0.386695
$429$	−7.50000	−	12.9904i	−0.362103	−	0.627182i
$430$		0			0
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	−0.784683	−	0.619897i	$-0.787174\pi$
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	0.929188	+	0.369607i	$0.120508\pi$
$432$	4.50000	+	7.79423i	0.216506	+	0.375000i
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$		0			0
$435$		0			0
$436$	9.00000	+	15.5885i	0.431022	+	0.746552i
$437$	5.00000	−	8.66025i	0.239182	−	0.414276i
$438$	10.5000	−	18.1865i	0.501709	−	0.868986i
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	0.841175	−	0.540763i	$-0.181865\pi$
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	−0.888902	+	0.458097i	$0.848531\pi$
$440$		0			0
$441$		0			0
$442$	−4.00000			−0.190261
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$	10.5000	−	18.1865i	0.498308	−	0.863095i
$445$		0			0
$446$	−1.50000	−	2.59808i	−0.0710271	−	0.123022i
$447$	−21.0000			−0.993266
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$	−15.0000	−	25.9808i	−0.707107	−	1.22474i
$451$	22.5000	−	38.9711i	1.05948	−	1.83508i
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$	−18.0000	−	31.1769i	−0.845714	−	1.46482i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	−6.00000			−0.280976
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−8.00000	+	13.8564i	−0.373815	+	0.647467i
$459$	18.0000	−	31.1769i	0.840168	−	1.45521i
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	12.0000			0.557687			0.278844	−	0.960337i	$-0.410049\pi$
$463$	12.0000			0.557687			0.278844	+	0.960337i	$0.410049\pi$
$464$	−2.00000	−	3.46410i	−0.0928477	−	0.160817i
$465$		0			0
$466$	−10.5000	+	18.1865i	−0.486403	+	0.842475i
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	−0.895696	−	0.444667i	$-0.853322\pi$
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	0.0627555	−	0.998029i	$-0.480011\pi$
$468$	6.00000			0.277350
$469$		0			0
$470$		0			0
$471$	−1.50000	−	2.59808i	−0.0691164	−	0.119713i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	−30.0000	+	51.9615i	−1.37940	+	2.38919i
$474$	25.5000	+	44.1673i	1.17125	+	2.02867i
$475$	10.0000			0.458831
$476$		0			0
$477$	−24.0000			−1.09888
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$		0			0
$481$	−3.50000	−	6.06218i	−0.159586	−	0.276412i
$482$	−30.0000			−1.36646
$483$		0			0
$484$	14.0000			0.636364
$485$		0			0
$486$		0			0
$487$	13.0000	−	22.5167i	0.589086	−	1.02033i	−0.405266	−	0.914199i	$-0.632821\pi$
$487$	13.0000	−	22.5167i	0.589086	−	1.02033i	0.994352	−	0.106129i	$-0.0338455\pi$
$488$	−6.50000	−	11.2583i	−0.294241	−	0.509641i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$	13.5000	+	23.3827i	0.608627	+	1.05417i
$493$	−8.00000	+	13.8564i	−0.360302	+	0.624061i
$494$	−1.00000	+	1.73205i	−0.0449921	+	0.0779287i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$		0			0
$498$	−12.0000			−0.537733
$499$	−0.500000	−	0.866025i	−0.0223831	−	0.0387686i	0.854617	−	0.519259i	$-0.173792\pi$
$499$	−0.500000	−	0.866025i	−0.0223831	−	0.0387686i	−0.877000	+	0.480490i	$0.840459\pi$
$500$		0			0
$501$	−12.0000	+	20.7846i	−0.536120	+	0.928588i
$502$	6.50000	+	11.2583i	0.290109	+	0.502484i
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$		0			0
$505$		0			0
$506$	−12.5000	−	21.6506i	−0.555693	−	0.962488i
$507$	1.50000	−	2.59808i	0.0666173	−	0.115385i
$508$	−4.50000	+	7.79423i	−0.199655	+	0.345813i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−9.00000	−	15.5885i	−0.397360	−	0.688247i
$514$	−14.0000	+	24.2487i	−0.617514	+	1.06956i
$515$		0			0
$516$	−18.0000	−	31.1769i	−0.792406	−	1.37249i
$517$	−35.0000			−1.53930
$518$		0			0
$519$	54.0000			2.37034
$520$		0			0
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$	12.0000	−	20.7846i	0.525226	−	0.909718i
$523$	−6.50000	−	11.2583i	−0.284225	−	0.492292i	0.688196	−	0.725525i	$-0.258403\pi$
$523$	−6.50000	−	11.2583i	−0.284225	−	0.492292i	−0.972421	+	0.233233i	$0.925070\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$		0			0
$527$	2.00000	+	3.46410i	0.0871214	+	0.150899i
$528$	−7.50000	+	12.9904i	−0.326396	+	0.565334i
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	36.0000			1.56227
$532$		0			0
$533$	9.00000			0.389833
$534$	21.0000	+	36.3731i	0.908759	+	1.57402i
$535$		0			0
$536$	5.50000	−	9.52628i	0.237564	−	0.411473i
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$	13.0000			0.560470
$539$		0			0
$540$		0			0
$541$	−9.00000	−	15.5885i	−0.386940	−	0.670200i	0.605096	−	0.796152i	$-0.293135\pi$
$541$	−9.00000	−	15.5885i	−0.386940	−	0.670200i	−0.992036	+	0.125952i	$0.959801\pi$
$542$	0.500000	−	0.866025i	0.0214768	−	0.0371990i
$543$	7.50000	−	12.9904i	0.321856	−	0.557471i
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$		0			0
$546$		0			0
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$	39.0000	−	67.5500i	1.66448	−	2.88296i
$550$	12.5000	−	21.6506i	0.533002	−	0.923186i
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$	15.0000			0.638442
$553$		0			0
$554$	10.0000			0.424859
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$	−3.00000	−	5.19615i	−0.127000	−	0.219971i
$559$	−12.0000			−0.507546
$560$		0			0
$561$	60.0000			2.53320
$562$	−8.00000	−	13.8564i	−0.337460	−	0.584497i
$563$	17.5000	−	30.3109i	0.737537	−	1.27745i	−0.216064	−	0.976379i	$-0.569322\pi$
$563$	17.5000	−	30.3109i	0.737537	−	1.27745i	0.953601	−	0.301073i	$-0.0973446\pi$
$564$	10.5000	−	18.1865i	0.442130	−	0.765791i
$565$		0			0
$566$	3.00000			0.126099
$567$		0			0
$568$		0			0
$569$	−10.5000	−	18.1865i	−0.440183	−	0.762419i	0.557520	−	0.830164i	$-0.311753\pi$
$569$	−10.5000	−	18.1865i	−0.440183	−	0.762419i	−0.997703	+	0.0677445i	$0.978420\pi$
$570$		0			0
$571$	−11.0000	+	19.0526i	−0.460336	+	0.797325i	−0.998978	−	0.0452101i	$-0.985604\pi$
$571$	−11.0000	+	19.0526i	−0.460336	+	0.797325i	0.538642	+	0.842535i	$0.318938\pi$
$572$	2.50000	+	4.33013i	0.104530	+	0.181052i
$573$	48.0000			2.00523
$574$		0			0
$575$	−25.0000			−1.04257
$576$	−3.00000	−	5.19615i	−0.125000	−	0.216506i
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	6.00000	+	10.3923i	0.249351	+	0.431889i
$580$		0			0
$581$		0			0
$582$	−15.0000			−0.621770
$583$	−10.0000	−	17.3205i	−0.414158	−	0.717342i
$584$	−3.50000	+	6.06218i	−0.144831	+	0.250855i
$585$		0			0
$586$	3.00000	+	5.19615i	0.123929	+	0.214651i
$587$	−18.0000			−0.742940			−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000			−0.742940			−0.371470	+	0.928445i	$0.621146\pi$
$588$		0			0
$589$	2.00000			0.0824086
$590$		0			0
$591$	40.5000	−	70.1481i	1.66595	−	2.88551i
$592$	−3.50000	+	6.06218i	−0.143849	+	0.249154i
$593$	−23.0000	−	39.8372i	−0.944497	−	1.63592i	−0.756756	−	0.653698i	$-0.773217\pi$
$593$	−23.0000	−	39.8372i	−0.944497	−	1.63592i	−0.187741	−	0.982219i	$-0.560117\pi$
$594$	−45.0000			−1.84637
$595$		0			0
$596$	7.00000			0.286731
$597$	30.0000	+	51.9615i	1.22782	+	2.12664i
$598$	2.50000	−	4.33013i	0.102233	−	0.177072i
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$	7.50000	+	12.9904i	0.306186	+	0.530330i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	66.0000			2.68773
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$		0			0
$606$	22.5000	−	38.9711i	0.914000	−	1.58309i
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$		0			0
$611$	−3.50000	−	6.06218i	−0.141595	−	0.245249i
$612$	−12.0000	+	20.7846i	−0.485071	+	0.840168i
$613$	11.5000	−	19.9186i	0.464481	−	0.804504i	−0.534697	−	0.845044i	$-0.679574\pi$
$613$	11.5000	−	19.9186i	0.464481	−	0.804504i	0.999178	+	0.0405396i	$0.0129077\pi$
$614$	−16.0000	−	27.7128i	−0.645707	−	1.11840i
$615$		0			0
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	9.00000	+	15.5885i	0.362033	+	0.627060i
$619$	3.00000	−	5.19615i	0.120580	−	0.208851i	−0.799416	−	0.600777i	$-0.794858\pi$
$619$	3.00000	−	5.19615i	0.120580	−	0.208851i	0.919997	+	0.391926i	$0.128191\pi$
$620$		0			0
$621$	22.5000	+	38.9711i	0.902894	+	1.56386i
$622$	26.0000			1.04251
$623$		0			0
$624$	−3.00000			−0.120096
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	15.0000	−	25.9808i	0.599521	−	1.03840i
$627$	15.0000	−	25.9808i	0.599042	−	1.03757i
$628$	0.500000	+	0.866025i	0.0199522	+	0.0345582i
$629$	28.0000			1.11643
$630$		0			0
$631$	−26.0000			−1.03504			−0.517522	−	0.855670i	$-0.673145\pi$
$631$	−26.0000			−1.03504			−0.517522	+	0.855670i	$0.673145\pi$
$632$	−8.50000	−	14.7224i	−0.338112	−	0.585627i
$633$	−21.0000	+	36.3731i	−0.834675	+	1.44570i
$634$	5.50000	−	9.52628i	0.218433	−	0.378337i
$635$		0			0
$636$	12.0000			0.475831
$637$		0			0
$638$	20.0000			0.791808
$639$		0			0
$640$		0			0
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$	12.0000	+	20.7846i	0.473602	+	0.820303i
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$		0			0
$645$		0			0
$646$	−4.00000	−	6.92820i	−0.157378	−	0.272587i
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	15.0000	+	25.9808i	0.588802	+	1.01983i
$650$	5.00000			0.196116
$651$		0			0
$652$	4.00000			0.156652
$653$	6.00000	+	10.3923i	0.234798	+	0.406682i	0.959214	−	0.282681i	$-0.0912238\pi$
$653$	6.00000	+	10.3923i	0.234798	+	0.406682i	−0.724416	+	0.689363i	$0.757890\pi$
$654$	27.0000	−	46.7654i	1.05578	−	1.82867i
$655$		0			0
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$	−42.0000			−1.63858
$658$		0			0
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$		0			0
$661$	−10.0000	+	17.3205i	−0.388955	+	0.673690i	−0.992309	−	0.123784i	$-0.960497\pi$
$661$	−10.0000	+	17.3205i	−0.388955	+	0.673690i	0.603354	+	0.797473i	$0.293830\pi$
$662$	1.50000	−	2.59808i	0.0582992	−	0.100977i
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$	4.00000			0.155230
$665$		0			0
$666$	−42.0000			−1.62747
$667$	−10.0000	−	17.3205i	−0.387202	−	0.670653i
$668$	4.00000	−	6.92820i	0.154765	−	0.268060i
$669$	−4.50000	+	7.79423i	−0.173980	+	0.301342i
$670$		0			0
$671$	65.0000			2.50930
$672$		0			0
$673$	−9.00000			−0.346925			−0.173462	−	0.984841i	$-0.555495\pi$
$673$	−9.00000			−0.346925			−0.173462	+	0.984841i	$0.555495\pi$
$674$	4.50000	+	7.79423i	0.173334	+	0.300222i
$675$	−22.5000	+	38.9711i	−0.866025	+	1.50000i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	0.893410	−	0.449242i	$-0.148306\pi$
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	−0.835760	+	0.549095i	$0.814973\pi$
$678$	3.00000			0.115214
$679$		0			0
$680$		0			0
$681$	18.0000	+	31.1769i	0.689761	+	1.19470i
$682$	2.50000	−	4.33013i	0.0957299	−	0.165809i
$683$	−1.50000	+	2.59808i	−0.0573959	+	0.0994126i	−0.893296	−	0.449469i	$-0.851613\pi$
$683$	−1.50000	+	2.59808i	−0.0573959	+	0.0994126i	0.835900	+	0.548882i	$0.184946\pi$
$684$	6.00000	+	10.3923i	0.229416	+	0.397360i
$685$		0			0
$686$		0			0
$687$	48.0000			1.83131
$688$	6.00000	+	10.3923i	0.228748	+	0.396203i
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		0			0
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	−0.973515	−	0.228625i	$-0.926577\pi$
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	0.288762	−	0.957401i	$-0.406756\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	−16.0000			−0.607352
$695$		0			0
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$	−1.00000	−	1.73205i	−0.0378506	−	0.0655591i
$699$	63.0000			2.38288
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$	−4.50000	−	7.79423i	−0.169842	−	0.294174i
$703$	7.00000	−	12.1244i	0.264010	−	0.457279i
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$		0			0
$706$	3.00000			0.112906
$707$		0			0
$708$	−18.0000			−0.676481
$709$	−14.5000	−	25.1147i	−0.544559	−	0.943204i	−0.998635	−	0.0522406i	$-0.983364\pi$
$709$	−14.5000	−	25.1147i	−0.544559	−	0.943204i	0.454076	−	0.890963i	$-0.349970\pi$
$710$		0			0
$711$	51.0000	−	88.3346i	1.91265	−	3.31281i
$712$	−7.00000	−	12.1244i	−0.262336	−	0.454379i
$713$	−5.00000			−0.187251
$714$		0			0
$715$		0			0
$716$	1.00000	+	1.73205i	0.0373718	+	0.0647298i
$717$	−9.00000	+	15.5885i	−0.336111	+	0.582162i
$718$	−2.00000	+	3.46410i	−0.0746393	+	0.129279i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$		0			0
$722$	15.0000			0.558242
$723$	45.0000	+	77.9423i	1.67357	+	2.89870i
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$	10.0000	−	17.3205i	0.371391	−	0.643268i
$726$	−21.0000	−	36.3731i	−0.779383	−	1.34993i
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$	−19.5000	+	33.7750i	−0.720741	+	1.24836i
$733$	10.0000	+	17.3205i	0.369358	+	0.639748i	0.989465	−	0.144770i	$-0.0462441\pi$
$733$	10.0000	+	17.3205i	0.369358	+	0.639748i	−0.620107	+	0.784517i	$0.712911\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	−5.00000			−0.184302
$737$	27.5000	+	47.6314i	1.01298	+	1.75453i
$738$	27.0000	−	46.7654i	0.993884	−	1.72146i
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$		0			0
$741$	6.00000			0.220416
$742$		0			0
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$	1.50000	+	2.59808i	0.0549927	+	0.0952501i
$745$		0			0
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	12.0000	+	20.7846i	0.439057	+	0.760469i
$748$	−20.0000			−0.731272
$749$		0			0
$750$		0			0
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	0.542621	−	0.839978i	$-0.317432\pi$
$751$	−12.5000	−	21.6506i	−0.456131	−	0.790043i	−0.998752	+	0.0499348i	$0.984099\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$	19.5000	−	33.7750i	0.710620	−	1.23083i
$754$	2.00000	+	3.46410i	0.0728357	+	0.126155i
$755$		0			0
$756$		0			0
$757$	−18.0000			−0.654221			−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000			−0.654221			−0.327111	+	0.944986i	$0.606075\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$	−37.5000	+	64.9519i	−1.36116	+	2.35760i
$760$		0			0
$761$	−16.5000	−	28.5788i	−0.598125	−	1.03598i	−0.993098	−	0.117289i	$-0.962579\pi$
$761$	−16.5000	−	28.5788i	−0.598125	−	1.03598i	0.394973	−	0.918693i	$-0.370754\pi$
$762$	27.0000			0.978107
$763$		0			0
$764$	−16.0000			−0.578860
$765$		0			0
$766$	4.50000	−	7.79423i	0.162592	−	0.281617i
$767$	−3.00000	+	5.19615i	−0.108324	+	0.187622i
$768$	1.50000	+	2.59808i	0.0541266	+	0.0937500i
$769$	1.00000			0.0360609			0.0180305	−	0.999837i	$-0.494260\pi$
$769$	1.00000			0.0360609			0.0180305	+	0.999837i	$0.494260\pi$
$770$		0			0
$771$	84.0000			3.02519
$772$	−2.00000	−	3.46410i	−0.0719816	−	0.124676i
$773$	17.0000	−	29.4449i	0.611448	−	1.05906i	−0.379549	−	0.925172i	$-0.623921\pi$
$773$	17.0000	−	29.4449i	0.611448	−	1.05906i	0.990997	−	0.133887i	$-0.0427458\pi$
$774$	−36.0000	+	62.3538i	−1.29399	+	2.24126i
$775$	−2.50000	−	4.33013i	−0.0898027	−	0.155543i
$776$	5.00000			0.179490
$777$		0			0
$778$	−8.00000			−0.286814
$779$	9.00000	+	15.5885i	0.322458	+	0.558514i
$780$		0			0
$781$		0			0
$782$	10.0000	+	17.3205i	0.357599	+	0.619380i
$783$	−36.0000			−1.28654
$784$		0			0
$785$		0			0
$786$	12.0000	+	20.7846i	0.428026	+	0.741362i
$787$	4.00000	−	6.92820i	0.142585	−	0.246964i	−0.785885	−	0.618373i	$-0.787792\pi$
$787$	4.00000	−	6.92820i	0.142585	−	0.246964i	0.928469	+	0.371409i	$0.121125\pi$
$788$	−13.5000	+	23.3827i	−0.480918	+	0.832974i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	30.0000			1.06600
$793$	6.50000	+	11.2583i	0.230822	+	0.399795i
$794$		0			0
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	−3.00000			−0.106265			−0.0531327	−	0.998587i	$-0.516921\pi$
$797$	−3.00000			−0.106265			−0.0531327	+	0.998587i	$0.516921\pi$
$798$		0			0
$799$	28.0000			0.990569
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	42.0000	−	72.7461i	1.48400	−	2.57036i
$802$	−14.0000	+	24.2487i	−0.494357	+	0.856252i
$803$	−17.5000	−	30.3109i	−0.617562	−	1.06965i
$804$	−33.0000			−1.16382
$805$		0			0
$806$	1.00000			0.0352235
$807$	−19.5000	−	33.7750i	−0.686433	−	1.18894i
$808$	−7.50000	+	12.9904i	−0.263849	+	0.457000i
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	−52.0000			−1.82597			−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000			−1.82597			−0.912983	+	0.407997i	$0.866228\pi$
$812$		0			0
$813$	−3.00000			−0.105215
$814$	−17.5000	−	30.3109i	−0.613375	−	1.06240i
$815$		0			0
$816$	6.00000	−	10.3923i	0.210042	−	0.363803i
$817$	−12.0000	−	20.7846i	−0.419827	−	0.727161i
$818$	−6.00000			−0.209785
$819$		0			0
$820$		0			0
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$	−27.0000	+	46.7654i	−0.941733	+	1.63113i
$823$	7.50000	−	12.9904i	0.261434	−	0.452816i	−0.705190	−	0.709019i	$-0.749138\pi$
$823$	7.50000	−	12.9904i	0.261434	−	0.452816i	0.966623	+	0.256203i	$0.0824714\pi$
$824$	−3.00000	−	5.19615i	−0.104510	−	0.181017i
$825$	−75.0000			−2.61116
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	−15.0000	−	25.9808i	−0.521286	−	0.902894i
$829$	−27.0000	+	46.7654i	−0.937749	+	1.62423i	−0.168091	+	0.985771i	$0.553760\pi$
$829$	−27.0000	+	46.7654i	−0.937749	+	1.62423i	−0.769657	+	0.638457i	$0.779573\pi$
$830$		0			0
$831$	−15.0000	−	25.9808i	−0.520344	−	0.901263i
$832$	1.00000			0.0346688
$833$		0			0
$834$	−12.0000			−0.415526
$835$		0			0
$836$	−5.00000	+	8.66025i	−0.172929	+	0.299521i
$837$	−4.50000	+	7.79423i	−0.155543	+	0.269408i
$838$	4.50000	+	7.79423i	0.155450	+	0.269247i
$839$	−47.0000			−1.62262			−0.811310	−	0.584616i	$-0.801245\pi$
$839$	−47.0000			−1.62262			−0.811310	+	0.584616i	$0.801245\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−17.5000	−	30.3109i	−0.603090	−	1.04458i
$843$	−24.0000	+	41.5692i	−0.826604	+	1.43172i
$844$	7.00000	−	12.1244i	0.240950	−	0.417338i
$845$		0			0
$846$	−42.0000			−1.44399
$847$		0			0
$848$	−4.00000			−0.137361
$849$	−4.50000	−	7.79423i	−0.154440	−	0.267497i
$850$	−10.0000	+	17.3205i	−0.342997	+	0.594089i
$851$	−17.5000	+	30.3109i	−0.599892	+	1.03904i
$852$		0			0
$853$	16.0000			0.547830			0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000			0.547830			0.273915	+	0.961754i	$0.411681\pi$
$854$		0			0
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	1.00000	−	1.73205i	0.0341593	−	0.0591657i	−0.848440	−	0.529291i	$-0.822458\pi$
$857$	1.00000	−	1.73205i	0.0341593	−	0.0591657i	0.882600	+	0.470125i	$0.155791\pi$
$858$	7.50000	−	12.9904i	0.256046	−	0.443484i
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	0.999982	−	0.00607046i	$-0.00193230\pi$
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	−0.505248	+	0.862974i	$0.668599\pi$
$860$		0			0
$861$		0			0
$862$	6.00000			0.204361
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	0.994720	−	0.102624i	$-0.0327240\pi$
$863$	12.0000	+	20.7846i	0.408485	+	0.707516i	−0.586235	+	0.810141i	$0.699391\pi$
$864$	−4.50000	+	7.79423i	−0.153093	+	0.265165i
$865$		0			0
$866$	−13.0000	−	22.5167i	−0.441758	−	0.765147i
$867$	3.00000			0.101885
$868$		0			0
$869$	85.0000			2.88343
$870$		0			0
$871$	−5.50000	+	9.52628i	−0.186360	+	0.322786i
$872$	−9.00000	+	15.5885i	−0.304778	+	0.527892i
$873$	15.0000	+	25.9808i	0.507673	+	0.879316i
$874$	10.0000			0.338255
$875$		0			0
$876$	21.0000			0.709524
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	0.735163	−	0.677891i	$-0.237106\pi$
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	−0.954652	+	0.297724i	$0.903772\pi$
$878$	1.00000	−	1.73205i	0.0337484	−	0.0584539i
$879$	9.00000	−	15.5885i	0.303562	−	0.525786i
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	30.0000			1.00958			0.504790	−	0.863242i	$-0.331570\pi$
$883$	30.0000			1.00958			0.504790	+	0.863242i	$0.331570\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	27.0000	+	46.7654i	0.906571	+	1.57023i	0.818794	+	0.574087i	$0.194643\pi$
$887$	27.0000	+	46.7654i	0.906571	+	1.57023i	0.0877772	+	0.996140i	$0.472024\pi$
$888$	21.0000			0.704714
$889$		0			0
$890$		0			0
$891$	22.5000	+	38.9711i	0.753778	+	1.30558i
$892$	1.50000	−	2.59808i	0.0502237	−	0.0869900i
$893$	7.00000	−	12.1244i	0.234246	−	0.405726i
$894$	−10.5000	−	18.1865i	−0.351173	−	0.608249i
$895$		0			0
$896$		0			0
$897$	−15.0000			−0.500835
$898$	9.00000	+	15.5885i	0.300334	+	0.520194i
$899$	2.00000	−	3.46410i	0.0667037	−	0.115534i
$900$	15.0000	−	25.9808i	0.500000	−	0.866025i
$901$	8.00000	+	13.8564i	0.266519	+	0.461624i
$902$	45.0000			1.49834
$903$		0			0
$904$	−1.00000			−0.0332595
$905$		0			0
$906$	18.0000	−	31.1769i	0.598010	−	1.03578i
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	−0.958523	−	0.285015i	$-0.908001\pi$
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	0.726092	+	0.687598i	$0.241335\pi$
$908$	−6.00000	−	10.3923i	−0.199117	−	0.344881i
$909$	−90.0000			−2.98511
$910$		0			0
$911$	28.0000			0.927681			0.463841	−	0.885919i	$-0.346471\pi$
$911$	28.0000			0.927681			0.463841	+	0.885919i	$0.346471\pi$
$912$	−3.00000	−	5.19615i	−0.0993399	−	0.172062i
$913$	−10.0000	+	17.3205i	−0.330952	+	0.573225i
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		0			0
$916$	−16.0000			−0.528655
$917$		0			0
$918$	36.0000			1.18818
$919$	−15.5000	−	26.8468i	−0.511298	−	0.885594i	−0.999914	−	0.0130951i	$-0.995832\pi$
$919$	−15.5000	−	26.8468i	−0.511298	−	0.885594i	0.488616	−	0.872499i	$-0.337502\pi$
$920$		0			0
$921$	−48.0000	+	83.1384i	−1.58165	+	2.73950i
$922$	−6.00000	−	10.3923i	−0.197599	−	0.342252i
$923$		0			0
$924$		0			0
$925$	−35.0000			−1.15079
$926$	6.00000	+	10.3923i	0.197172	+	0.341512i
$927$	18.0000	−	31.1769i	0.591198	−	1.02398i
$928$	2.00000	−	3.46410i	0.0656532	−	0.113715i
$929$	−14.5000	−	25.1147i	−0.475730	−	0.823988i	0.523884	−	0.851790i	$-0.324483\pi$
$929$	−14.5000	−	25.1147i	−0.475730	−	0.823988i	−0.999613	+	0.0278019i	$0.991149\pi$
$930$		0			0
$931$		0			0
$932$	−21.0000			−0.687878
$933$	−39.0000	−	67.5500i	−1.27680	−	2.21149i
$934$	18.0000	−	31.1769i	0.588978	−	1.02014i
$935$		0			0
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$		0			0
$939$	−90.0000			−2.93704
$940$		0			0
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	−0.812975	−	0.582298i	$-0.802154\pi$
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	0.910773	+	0.412908i	$0.135487\pi$
$942$	1.50000	−	2.59808i	0.0488726	−	0.0846499i
$943$	−22.5000	−	38.9711i	−0.732701	−	1.26908i
$944$	6.00000			0.195283
$945$		0			0
$946$	−60.0000			−1.95077
$947$	8.00000	+	13.8564i	0.259965	+	0.450273i	0.966232	−	0.257673i	$-0.0829556\pi$
$947$	8.00000	+	13.8564i	0.259965	+	0.450273i	−0.706267	+	0.707945i	$0.749622\pi$
$948$	−25.5000	+	44.1673i	−0.828201	+	1.43449i
$949$	3.50000	−	6.06218i	0.113615	−	0.196787i
$950$	5.00000	+	8.66025i	0.162221	+	0.280976i
$951$	−33.0000			−1.07010
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−12.0000	−	20.7846i	−0.388514	−	0.672927i
$955$		0			0
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$	−30.0000	−	51.9615i	−0.969762	−	1.67968i
$958$	−16.0000			−0.516937
$959$		0			0
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	3.50000	−	6.06218i	0.112845	−	0.195452i
$963$	24.0000	−	41.5692i	0.773389	−	1.33955i
$964$	−15.0000	−	25.9808i	−0.483117	−	0.836784i
$965$		0			0
$966$		0			0
$967$	2.00000			0.0643157			0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000			0.0643157			0.0321578	+	0.999483i	$0.489762\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$	−12.0000	+	20.7846i	−0.385496	+	0.667698i
$970$		0			0
$971$	4.50000	+	7.79423i	0.144412	+	0.250129i	0.929153	−	0.369694i	$-0.120538\pi$
$971$	4.50000	+	7.79423i	0.144412	+	0.250129i	−0.784741	+	0.619823i	$0.787204\pi$
$972$		0			0
$973$		0			0
$974$	26.0000			0.833094
$975$	−7.50000	−	12.9904i	−0.240192	−	0.416025i
$976$	6.50000	−	11.2583i	0.208060	−	0.360370i
$977$	13.0000	−	22.5167i	0.415907	−	0.720372i	−0.579616	−	0.814890i	$-0.696798\pi$
$977$	13.0000	−	22.5167i	0.415907	−	0.720372i	0.995523	+	0.0945177i	$0.0301309\pi$
$978$	−6.00000	−	10.3923i	−0.191859	−	0.332309i
$979$	70.0000			2.23721
$980$		0			0
$981$	−108.000			−3.44817
$982$	14.0000	+	24.2487i	0.446758	+	0.773807i
$983$	−28.0000	+	48.4974i	−0.893061	+	1.54683i	−0.0568755	+	0.998381i	$0.518114\pi$
$983$	−28.0000	+	48.4974i	−0.893061	+	1.54683i	−0.836186	+	0.548446i	$0.815220\pi$
$984$	−13.5000	+	23.3827i	−0.430364	+	0.745413i
$985$		0			0
$986$	−16.0000			−0.509544
$987$		0			0
$988$	−2.00000			−0.0636285
$989$	30.0000	+	51.9615i	0.953945	+	1.65228i
$990$		0			0
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.166250	+	0.986084i	$0.553166\pi$
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.770849	+	0.637018i	$0.780168\pi$
$992$	−0.500000	−	0.866025i	−0.0158750	−	0.0274963i
$993$	−9.00000			−0.285606
$994$		0			0
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	16.5000	−	28.5788i	0.522560	−	0.905101i	−0.477095	−	0.878852i	$-0.658310\pi$
$997$	16.5000	−	28.5788i	0.522560	−	0.905101i	0.999655	−	0.0262493i	$-0.00835636\pi$
$998$	0.500000	−	0.866025i	0.0158272	−	0.0274136i
$999$	31.5000	+	54.5596i	0.996616	+	1.72619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.f.u.1145.1		2
7.2	even	3	inner	1274.2.f.u.79.1		2
7.3	odd	6		182.2.a.b.1.1	✓	1
7.4	even	3		1274.2.a.a.1.1		1
7.5	odd	6		1274.2.f.m.79.1		2
7.6	odd	2		1274.2.f.m.1145.1		2
21.17	even	6		1638.2.a.q.1.1		1
28.3	even	6		1456.2.a.b.1.1		1
35.24	odd	6		4550.2.a.o.1.1		1
56.3	even	6		5824.2.a.be.1.1		1
56.45	odd	6		5824.2.a.a.1.1		1
91.31	even	12		2366.2.d.i.337.2		2
91.38	odd	6		2366.2.a.o.1.1		1
91.73	even	12		2366.2.d.i.337.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.a.b.1.1	✓	1	7.3	odd	6
1274.2.a.a.1.1		1	7.4	even	3
1274.2.f.m.79.1		2	7.5	odd	6
1274.2.f.m.1145.1		2	7.6	odd	2
1274.2.f.u.79.1		2	7.2	even	3	inner
1274.2.f.u.1145.1		2	1.1	even	1	trivial
1456.2.a.b.1.1		1	28.3	even	6
1638.2.a.q.1.1		1	21.17	even	6
2366.2.a.o.1.1		1	91.38	odd	6
2366.2.d.i.337.1		2	91.73	even	12
2366.2.d.i.337.2		2	91.31	even	12
4550.2.a.o.1.1		1	35.24	odd	6
5824.2.a.a.1.1		1	56.45	odd	6
5824.2.a.be.1.1		1	56.3	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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(2.50000 - 4.33013i) q^{11} +(1.50000 + 2.59808i) q^{12} +1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(3.00000 - 5.19615i) q^{18} +(1.00000 + 1.73205i) q^{19} +5.00000 q^{22} +(-2.50000 - 4.33013i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} -9.00000 q^{27} +4.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-7.50000 - 12.9904i) q^{33} -4.00000 q^{34} +6.00000 q^{36} +(-3.50000 - 6.06218i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.50000 - 2.59808i) q^{39} +9.00000 q^{41} -12.0000 q^{43} +(2.50000 + 4.33013i) q^{44} +(2.50000 - 4.33013i) q^{46} +(-3.50000 - 6.06218i) q^{47} -3.00000 q^{48} +5.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(2.00000 - 3.46410i) q^{53} +(-4.50000 - 7.79423i) q^{54} +6.00000 q^{57} +(2.00000 + 3.46410i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(7.50000 - 12.9904i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(-2.00000 - 3.46410i) q^{68} -15.0000 q^{69} +(3.00000 + 5.19615i) q^{72} +(3.50000 - 6.06218i) q^{73} +(3.50000 - 6.06218i) q^{74} +(-7.50000 - 12.9904i) q^{75} -2.00000 q^{76} +3.00000 q^{78} +(8.50000 + 14.7224i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(4.50000 + 7.79423i) q^{82} -4.00000 q^{83} +(-6.00000 - 10.3923i) q^{86} +(6.00000 - 10.3923i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(7.00000 + 12.1244i) q^{89} +5.00000 q^{92} +(-1.50000 - 2.59808i) q^{93} +(3.50000 - 6.06218i) q^{94} +(-1.50000 - 2.59808i) q^{96} -5.00000 q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - 2 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 2 q^{13} - q^{16} - 4 q^{17} + 6 q^{18} + 2 q^{19} + 10 q^{22} - 5 q^{23} - 3 q^{24} + 5 q^{25} + q^{26} - 18 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 6 * q^6 - 2 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 2 * q^13 - q^16 - 4 * q^17 + 6 * q^18 + 2 * q^19 + 10 * q^22 - 5 * q^23 - 3 * q^24 + 5 * q^25 + q^26 - 18 * q^27 + 8 * q^29 + q^31 + q^32 - 15 * q^33 - 8 * q^34 + 12 * q^36 - 7 * q^37 - 2 * q^38 + 3 * q^39 + 18 * q^41 - 24 * q^43 + 5 * q^44 + 5 * q^46 - 7 * q^47 - 6 * q^48 + 10 * q^50 + 12 * q^51 - q^52 + 4 * q^53 - 9 * q^54 + 12 * q^57 + 4 * q^58 - 6 * q^59 + 13 * q^61 + 2 * q^62 + 2 * q^64 + 15 * q^66 - 11 * q^67 - 4 * q^68 - 30 * q^69 + 6 * q^72 + 7 * q^73 + 7 * q^74 - 15 * q^75 - 4 * q^76 + 6 * q^78 + 17 * q^79 - 9 * q^81 + 9 * q^82 - 8 * q^83 - 12 * q^86 + 12 * q^87 - 5 * q^88 + 14 * q^89 + 10 * q^92 - 3 * q^93 + 7 * q^94 - 3 * q^96 - 10 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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