LMFDB - Embedded newform 1274.2.f.q.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.q.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} -1.00000 q^{22} +(-1.00000 - 1.73205i) q^{23} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} -5.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.00000 q^{34} -3.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(-2.50000 + 4.33013i) q^{38} -6.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{46} +(5.50000 + 9.52628i) q^{47} +5.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-2.50000 - 4.33013i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(0.500000 + 0.866025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(3.50000 - 6.06218i) q^{67} +(-0.500000 - 0.866025i) q^{68} -9.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} -5.00000 q^{76} +(7.00000 + 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} +8.00000 q^{83} +(-3.00000 - 5.19615i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-8.00000 - 13.8564i) q^{89} +2.00000 q^{92} +(-5.50000 + 9.52628i) q^{94} -2.00000 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 2 q^{8} + 3 q^{9} - q^{11} + 2 q^{13} - q^{16} - q^{17} - 3 q^{18} + 5 q^{19} - 2 q^{22} - 2 q^{23} + 5 q^{25} + q^{26} - 10 q^{29} - 8 q^{31} + q^{32} - 2 q^{34} - 6 q^{36}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^4 - 2 * q^8 + 3 * q^9 - q^11 + 2 * q^13 - q^16 - q^17 - 3 * q^18 + 5 * q^19 - 2 * q^22 - 2 * q^23 + 5 * q^25 + q^26 - 10 * q^29 - 8 * q^31 + q^32 - 2 * q^34 - 6 * q^36 + 8 * q^37 - 5 * q^38 - 12 * q^43 - q^44 + 2 * q^46 + 11 * q^47 + 10 * q^50 - q^52 - 5 * q^53 - 5 * q^58 - 3 * q^59 + q^61 - 16 * q^62 + 2 * q^64 + 7 * q^67 - q^68 - 18 * q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 10 * q^76 + 14 * q^79 - 9 * q^81 + 16 * q^83 - 6 * q^86 + q^88 - 16 * q^89 + 4 * q^92 - 11 * q^94 - 4 * q^97 - 6 * 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
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		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	$0.833333\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		0			0
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.00000			−0.171499
$35$		0			0
$36$	−3.00000			−0.500000
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	−2.50000	+	4.33013i	−0.405554	+	0.702439i
$39$		0			0
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	1.00000	−	1.73205i	0.147442	−	0.255377i
$47$	5.50000	+	9.52628i	0.802257	+	1.38955i	0.918127	+	0.396286i	$0.129701\pi$
$47$	5.50000	+	9.52628i	0.802257	+	1.38955i	−0.115870	+	0.993264i	$0.536965\pi$
$48$		0			0
$49$		0			0
$50$	5.00000			0.707107
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	−0.985062	−	0.172200i	$-0.944912\pi$
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	0.641661	+	0.766989i	$0.278246\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−2.50000	−	4.33013i	−0.328266	−	0.568574i
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$		0			0
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	−5.00000			−0.573539
$77$		0			0
$78$		0			0
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	0.927457	+	0.373930i	$0.121990\pi$
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	−0.139895	+	0.990166i	$0.544677\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$		0			0
$85$		0			0
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	0.0349934	−	0.999388i	$-0.488859\pi$
$90$		0			0
$91$		0			0
$92$	2.00000			0.208514
$93$		0			0
$94$	−5.50000	+	9.52628i	−0.567282	+	0.982561i
$95$		0			0
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$		0			0
$103$	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
$106$	−5.00000			−0.485643
$107$	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	$0.706950\pi$
$108$		0			0
$109$	6.00000	−	10.3923i	0.574696	−	0.995402i	−0.421379	−	0.906885i	$-0.638454\pi$
$109$	6.00000	−	10.3923i	0.574696	−	0.995402i	0.996075	−	0.0885176i	$-0.0282129\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.00000			0.0940721			0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000			0.0940721			0.0470360	+	0.998893i	$0.485022\pi$
$114$		0			0
$115$		0			0
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$	−3.00000			−0.276172
$119$		0			0
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−0.500000	+	0.866025i	−0.0452679	+	0.0784063i
$123$		0			0
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$		0			0
$126$		0			0
$127$	−6.00000			−0.532414			−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000			−0.532414			−0.266207	+	0.963916i	$0.585770\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−5.00000	−	8.66025i	−0.436852	−	0.756650i	0.560593	−	0.828092i	$-0.310573\pi$
$131$	−5.00000	−	8.66025i	−0.436852	−	0.756650i	−0.997445	+	0.0714417i	$0.977240\pi$
$132$		0			0
$133$		0			0
$134$	7.00000			0.604708
$135$		0			0
$136$	0.500000	−	0.866025i	0.0428746	−	0.0742611i
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$		0			0
$142$	−4.50000	−	7.79423i	−0.377632	−	0.654077i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$		0			0
$146$	−2.00000			−0.165521
$147$		0			0
$148$	−8.00000			−0.657596
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$		0			0
$151$	7.50000	−	12.9904i	0.610341	−	1.05714i	−0.380841	−	0.924640i	$-0.624366\pi$
$151$	7.50000	−	12.9904i	0.610341	−	1.05714i	0.991183	−	0.132502i	$-0.0423010\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	−3.00000			−0.242536
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$	−7.00000	+	12.1244i	−0.556890	+	0.964562i
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−9.00000			−0.707107
$163$	−3.50000	−	6.06218i	−0.274141	−	0.474826i	0.695777	−	0.718258i	$-0.255060\pi$
$163$	−3.50000	−	6.06218i	−0.274141	−	0.474826i	−0.969918	+	0.243432i	$0.921727\pi$
$164$		0			0
$165$		0			0
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	19.0000			1.47026			0.735132	−	0.677924i	$-0.237120\pi$
$167$	19.0000			1.47026			0.735132	+	0.677924i	$0.237120\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−7.50000	+	12.9904i	−0.573539	+	0.993399i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$		0			0
$175$		0			0
$176$	1.00000			0.0753778
$177$		0			0
$178$	8.00000	−	13.8564i	0.599625	−	1.03858i
$179$	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
$181$	23.0000			1.70958			0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000			1.70958			0.854788	+	0.518977i	$0.173687\pi$
$182$		0			0
$183$		0			0
$184$	1.00000	+	1.73205i	0.0737210	+	0.127688i
$185$		0			0
$186$		0			0
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	−11.0000			−0.802257
$189$		0			0
$190$		0			0
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	0.929267	−	0.369410i	$-0.120440\pi$
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	−0.784552	+	0.620063i	$0.787107\pi$
$192$		0			0
$193$	−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	$0.212651\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		0			0
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$		0			0
$202$	18.0000			1.26648
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$	3.00000	−	5.19615i	0.208514	−	0.361158i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−5.00000			−0.345857
$210$		0			0
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$	−2.50000	−	4.33013i	−0.171701	−	0.297394i
$213$		0			0
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	12.0000			0.812743
$219$		0			0
$220$		0			0
$221$	−0.500000	+	0.866025i	−0.0336336	+	0.0582552i
$222$		0			0
$223$	15.0000			1.00447			0.502237	−	0.864730i	$-0.332510\pi$
$223$	15.0000			1.00447			0.502237	+	0.864730i	$0.332510\pi$
$224$		0			0
$225$	15.0000			1.00000
$226$	0.500000	+	0.866025i	0.0332595	+	0.0576072i
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$		0			0
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$		0			0
$231$		0			0
$232$	5.00000			0.328266
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	−0.972523	−	0.232806i	$-0.925209\pi$
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	0.284645	−	0.958633i	$-0.408124\pi$
$234$	−1.50000	+	2.59808i	−0.0980581	+	0.169842i
$235$		0			0
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		0			0
$238$		0			0
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	−0.605481	−	0.795860i	$-0.707019\pi$
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	0.991975	+	0.126432i	$0.0403527\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$		0			0
$244$	−1.00000			−0.0640184
$245$		0			0
$246$		0			0
$247$	2.50000	+	4.33013i	0.159071	+	0.275519i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$		0			0
$250$		0			0
$251$	−26.0000			−1.64111			−0.820553	−	0.571571i	$-0.806334\pi$
$251$	−26.0000			−1.64111			−0.820553	+	0.571571i	$0.806334\pi$
$252$		0			0
$253$	2.00000			0.125739
$254$	−3.00000	−	5.19615i	−0.188237	−	0.326036i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−7.50000	−	12.9904i	−0.464238	−	0.804084i
$262$	5.00000	−	8.66025i	0.308901	−	0.535032i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$	−2.50000	+	4.33013i	−0.152428	+	0.264013i	−0.932119	−	0.362151i	$-0.882042\pi$
$269$	−2.50000	+	4.33013i	−0.152428	+	0.264013i	0.779692	+	0.626164i	$0.215376\pi$
$270$		0			0
$271$	−9.50000	−	16.4545i	−0.577084	−	0.999539i	−0.995812	−	0.0914269i	$-0.970857\pi$
$271$	−9.50000	−	16.4545i	−0.577084	−	0.999539i	0.418728	−	0.908112i	$-0.362476\pi$
$272$	1.00000			0.0606339
$273$		0			0
$274$	12.0000			0.724947
$275$	2.50000	+	4.33013i	0.150756	+	0.261116i
$276$		0			0
$277$	−11.5000	+	19.9186i	−0.690968	+	1.19679i	0.280553	+	0.959839i	$0.409482\pi$
$277$	−11.5000	+	19.9186i	−0.690968	+	1.19679i	−0.971521	+	0.236953i	$0.923851\pi$
$278$	−8.00000	−	13.8564i	−0.479808	−	0.831052i
$279$	−24.0000			−1.43684
$280$		0			0
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$		0			0
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	−0.941309	−	0.337546i	$-0.890403\pi$
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	0.762978	+	0.646425i	$0.223737\pi$
$284$	4.50000	−	7.79423i	0.267026	−	0.462502i
$285$		0			0
$286$	−1.00000			−0.0591312
$287$		0			0
$288$	3.00000			0.176777
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		0			0
$295$		0			0
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$	5.00000	−	8.66025i	0.289642	−	0.501675i
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$		0			0
$302$	15.0000			0.863153
$303$		0			0
$304$	2.50000	−	4.33013i	0.143385	−	0.248350i
$305$		0			0
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.0894452	−	0.995992i	$-0.471491\pi$
$311$	16.0000	−	27.7128i	0.907277	−	1.57145i	0.817832	−	0.575458i	$-0.195176\pi$
$312$		0			0
$313$	9.00000	+	15.5885i	0.508710	+	0.881112i	0.999949	+	0.0100869i	$0.00321082\pi$
$313$	9.00000	+	15.5885i	0.508710	+	0.881112i	−0.491239	+	0.871025i	$0.663456\pi$
$314$	7.00000			0.395033
$315$		0			0
$316$	−14.0000			−0.787562
$317$	−13.0000	−	22.5167i	−0.730153	−	1.26466i	−0.956818	−	0.290689i	$-0.906116\pi$
$317$	−13.0000	−	22.5167i	−0.730153	−	1.26466i	0.226665	−	0.973973i	$-0.427218\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.00000			−0.278207
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	2.50000	−	4.33013i	0.138675	−	0.240192i
$326$	3.50000	−	6.06218i	0.193847	−	0.335753i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	0.982470	−	0.186421i	$-0.0596888\pi$
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	−0.652680	+	0.757634i	$0.726355\pi$
$332$	−4.00000	+	6.92820i	−0.219529	+	0.380235i
$333$	−12.0000	+	20.7846i	−0.657596	+	1.13899i
$334$	9.50000	+	16.4545i	0.519817	+	0.900349i
$335$		0			0
$336$		0			0
$337$	15.0000			0.817102			0.408551	−	0.912735i	$-0.366034\pi$
$337$	15.0000			0.817102			0.408551	+	0.912735i	$0.366034\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$		0			0
$340$		0			0
$341$	−4.00000	−	6.92820i	−0.216612	−	0.375183i
$342$	−15.0000			−0.811107
$343$		0			0
$344$	6.00000			0.323498
$345$		0			0
$346$	−7.50000	+	12.9904i	−0.403202	+	0.698367i
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	−0.914702	−	0.404128i	$-0.867575\pi$
$347$	−2.00000	+	3.46410i	−0.107366	+	0.185963i	0.807337	+	0.590091i	$0.200908\pi$
$348$		0			0
$349$	34.0000			1.81998			0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000			1.81998			0.909989	+	0.414632i	$0.136090\pi$
$350$		0			0
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$		0			0
$356$	16.0000			0.847998
$357$		0			0
$358$	2.00000			0.105703
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	0.996157	−	0.0875892i	$-0.0279163\pi$
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	11.5000	+	19.9186i	0.604427	+	1.04690i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	−0.966507	−	0.256639i	$-0.917385\pi$
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	0.705509	+	0.708700i	$0.250718\pi$
$368$	−1.00000	+	1.73205i	−0.0521286	+	0.0902894i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−15.5000	−	26.8468i	−0.802560	−	1.39007i	−0.917926	−	0.396751i	$-0.870138\pi$
$373$	−15.5000	−	26.8468i	−0.802560	−	1.39007i	0.115367	−	0.993323i	$-0.463196\pi$
$374$	0.500000	−	0.866025i	0.0258544	−	0.0447811i
$375$		0			0
$376$	−5.50000	−	9.52628i	−0.283641	−	0.491280i
$377$	−5.00000			−0.257513
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$		0			0
$381$		0			0
$382$	−2.00000	+	3.46410i	−0.102329	+	0.177239i
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$		0			0
$385$		0			0
$386$	−4.00000			−0.203595
$387$	−9.00000	−	15.5885i	−0.457496	−	0.792406i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	9.50000	−	16.4545i	0.481669	−	0.834275i	−0.518110	−	0.855314i	$-0.673364\pi$
$389$	9.50000	−	16.4545i	0.481669	−	0.834275i	0.999779	+	0.0210389i	$0.00669738\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$		0			0
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$		0			0
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	0.546795	−	0.837267i	$-0.315848\pi$
$397$	−9.00000	−	15.5885i	−0.451697	−	0.782362i	−0.998492	+	0.0549046i	$0.982515\pi$
$398$	10.0000			0.501255
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−19.0000	−	32.9090i	−0.948815	−	1.64340i	−0.747927	−	0.663781i	$-0.768951\pi$
$401$	−19.0000	−	32.9090i	−0.948815	−	1.64340i	−0.200888	−	0.979614i	$-0.564383\pi$
$402$		0			0
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	9.00000	+	15.5885i	0.447767	+	0.775555i
$405$		0			0
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	18.0000	−	31.1769i	0.890043	−	1.54160i	0.0502202	−	0.998738i	$-0.484008\pi$
$409$	18.0000	−	31.1769i	0.890043	−	1.54160i	0.839823	−	0.542861i	$-0.182659\pi$
$410$		0			0
$411$		0			0
$412$	−6.00000			−0.295599
$413$		0			0
$414$	6.00000			0.294884
$415$		0			0
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$	−2.50000	−	4.33013i	−0.122279	−	0.211793i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−1.00000	−	1.73205i	−0.0486792	−	0.0843149i
$423$	−16.5000	+	28.5788i	−0.802257	+	1.38955i
$424$	2.50000	−	4.33013i	0.121411	−	0.210290i
$425$	2.50000	+	4.33013i	0.121268	+	0.210042i
$426$		0			0
$427$		0			0
$428$	−8.00000			−0.386695
$429$		0			0
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	−5.00000			−0.240285			−0.120142	−	0.992757i	$-0.538335\pi$
$433$	−5.00000			−0.240285			−0.120142	+	0.992757i	$0.538335\pi$
$434$		0			0
$435$		0			0
$436$	6.00000	+	10.3923i	0.287348	+	0.497701i
$437$	5.00000	−	8.66025i	0.239182	−	0.414276i
$438$		0			0
$439$	11.0000	+	19.0526i	0.525001	+	0.909329i	0.999576	+	0.0291138i	$0.00926853\pi$
$439$	11.0000	+	19.0526i	0.525001	+	0.909329i	−0.474575	+	0.880215i	$0.657398\pi$
$440$		0			0
$441$		0			0
$442$	−1.00000			−0.0475651
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$		0			0
$446$	7.50000	+	12.9904i	0.355135	+	0.615112i
$447$		0			0
$448$		0			0
$449$	36.0000			1.69895			0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000			1.69895			0.849473	+	0.527633i	$0.176920\pi$
$450$	7.50000	+	12.9904i	0.353553	+	0.612372i
$451$		0			0
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$		0			0
$454$	12.0000			0.563188
$455$		0			0
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$	1.00000	−	1.73205i	0.0467269	−	0.0809334i
$459$		0			0
$460$		0			0
$461$	−36.0000			−1.67669			−0.838344	−	0.545142i	$-0.816476\pi$
$461$	−36.0000			−1.67669			−0.838344	+	0.545142i	$0.816476\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$	−21.0000	−	36.3731i	−0.971764	−	1.68314i	−0.690225	−	0.723595i	$-0.742488\pi$
$467$	−21.0000	−	36.3731i	−0.971764	−	1.68314i	−0.281539	−	0.959550i	$-0.590845\pi$
$468$	−3.00000			−0.138675
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	25.0000			1.14708
$476$		0			0
$477$	−15.0000			−0.686803
$478$	4.50000	+	7.79423i	0.205825	+	0.356500i
$479$	−18.5000	+	32.0429i	−0.845287	+	1.46408i	0.0400855	+	0.999196i	$0.487237\pi$
$479$	−18.5000	+	32.0429i	−0.845287	+	1.46408i	−0.885372	+	0.464883i	$0.846096\pi$
$480$		0			0
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	12.0000			0.546585
$483$		0			0
$484$	−10.0000			−0.454545
$485$		0			0
$486$		0			0
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	0.0529875	+	0.998595i	$0.483126\pi$
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	−0.891303	+	0.453409i	$0.850208\pi$
$488$	−0.500000	−	0.866025i	−0.0226339	−	0.0392031i
$489$		0			0
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$		0			0
$493$	2.50000	−	4.33013i	0.112594	−	0.195019i
$494$	−2.50000	+	4.33013i	−0.112480	+	0.194822i
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$		0			0
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$		0			0
$501$		0			0
$502$	−13.0000	−	22.5167i	−0.580218	−	1.00497i
$503$	−20.0000			−0.891756			−0.445878	−	0.895094i	$-0.647108\pi$
$503$	−20.0000			−0.891756			−0.445878	+	0.895094i	$0.647108\pi$
$504$		0			0
$505$		0			0
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$		0			0
$508$	3.00000	−	5.19615i	0.133103	−	0.230542i
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	0.701866	−	0.712309i	$-0.252351\pi$
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	−0.967811	+	0.251679i	$0.919017\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.00000	−	12.1244i	0.308757	−	0.534782i
$515$		0			0
$516$		0			0
$517$	−11.0000			−0.483779
$518$		0			0
$519$		0			0
$520$		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	$0.265883\pi$
$522$	7.50000	−	12.9904i	0.328266	−	0.568574i
$523$	13.0000	+	22.5167i	0.568450	+	0.984585i	0.996719	+	0.0809336i	$0.0257902\pi$
$523$	13.0000	+	22.5167i	0.568450	+	0.984585i	−0.428269	+	0.903651i	$0.640876\pi$
$524$	10.0000			0.436852
$525$		0			0
$526$	−24.0000			−1.04645
$527$	−4.00000	−	6.92820i	−0.174243	−	0.301797i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	−9.00000			−0.390567
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−3.50000	+	6.06218i	−0.151177	+	0.261846i
$537$		0			0
$538$	−5.00000			−0.215565
$539$		0			0
$540$		0			0
$541$	12.0000	+	20.7846i	0.515920	+	0.893600i	0.999829	+	0.0184818i	$0.00588327\pi$
$541$	12.0000	+	20.7846i	0.515920	+	0.893600i	−0.483909	+	0.875118i	$0.660783\pi$
$542$	9.50000	−	16.4545i	0.408060	−	0.706781i
$543$		0			0
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$		0			0
$546$		0			0
$547$	−38.0000			−1.62476			−0.812381	−	0.583127i	$-0.801829\pi$
$547$	−38.0000			−1.62476			−0.812381	+	0.583127i	$0.801829\pi$
$548$	6.00000	+	10.3923i	0.256307	+	0.443937i
$549$	−1.50000	+	2.59808i	−0.0640184	+	0.110883i
$550$	−2.50000	+	4.33013i	−0.106600	+	0.184637i
$551$	−12.5000	−	21.6506i	−0.532518	−	0.922348i
$552$		0			0
$553$		0			0
$554$	−23.0000			−0.977176
$555$		0			0
$556$	8.00000	−	13.8564i	0.339276	−	0.587643i
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	−0.350824	−	0.936442i	$-0.614098\pi$
$557$	15.0000	−	25.9808i	0.635570	−	1.10084i	0.986394	−	0.164399i	$-0.0525683\pi$
$558$	−12.0000	−	20.7846i	−0.508001	−	0.879883i
$559$	−6.00000			−0.253773
$560$		0			0
$561$		0			0
$562$	10.0000	+	17.3205i	0.421825	+	0.730622i
$563$	−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	$0.193529\pi$
$564$		0			0
$565$		0			0
$566$	−6.00000			−0.252199
$567$		0			0
$568$	9.00000			0.377632
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$		0			0
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.122292	−	0.992494i	$-0.460975\pi$
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.798379	−	0.602155i	$-0.205691\pi$
$572$	−0.500000	−	0.866025i	−0.0209061	−	0.0362103i
$573$		0			0
$574$		0			0
$575$	−10.0000			−0.417029
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	−0.682730	−	0.730670i	$-0.739208\pi$
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	0.974144	+	0.225927i	$0.0725410\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.50000	−	4.33013i	−0.103539	−	0.179336i
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$		0			0
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$	−33.0000			−1.36206			−0.681028	−	0.732257i	$-0.738467\pi$
$587$	−33.0000			−1.36206			−0.681028	+	0.732257i	$0.738467\pi$
$588$		0			0
$589$	−40.0000			−1.64817
$590$		0			0
$591$		0			0
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	−8.00000	−	13.8564i	−0.328521	−	0.569014i	0.653698	−	0.756756i	$-0.273217\pi$
$593$	−8.00000	−	13.8564i	−0.328521	−	0.569014i	−0.982219	+	0.187741i	$0.939883\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$	1.00000	−	1.73205i	0.0408930	−	0.0708288i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−17.0000			−0.693444			−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000			−0.693444			−0.346722	+	0.937968i	$0.612705\pi$
$602$		0			0
$603$	21.0000			0.855186
$604$	7.50000	+	12.9904i	0.305171	+	0.528571i
$605$		0			0
$606$		0			0
$607$	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	$0.686012\pi$
$608$	5.00000			0.202777
$609$		0			0
$610$		0			0
$611$	5.50000	+	9.52628i	0.222506	+	0.385392i
$612$	1.50000	−	2.59808i	0.0606339	−	0.105021i
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	−0.981129	−	0.193352i	$-0.938064\pi$
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	0.658012	+	0.753007i	$0.271397\pi$
$614$	3.50000	+	6.06218i	0.141249	+	0.244650i
$615$		0			0
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$		0			0
$619$	−18.0000	+	31.1769i	−0.723481	+	1.25311i	0.236115	+	0.971725i	$0.424126\pi$
$619$	−18.0000	+	31.1769i	−0.723481	+	1.25311i	−0.959596	+	0.281381i	$0.909208\pi$
$620$		0			0
$621$		0			0
$622$	32.0000			1.28308
$623$		0			0
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−9.00000	+	15.5885i	−0.359712	+	0.623040i
$627$		0			0
$628$	3.50000	+	6.06218i	0.139665	+	0.241907i
$629$	−8.00000			−0.318981
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−7.00000	−	12.1244i	−0.278445	−	0.482281i
$633$		0			0
$634$	13.0000	−	22.5167i	0.516296	−	0.894251i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	5.00000			0.197952
$639$	−13.5000	−	23.3827i	−0.534052	−	0.925005i
$640$		0			0
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$		0			0
$643$	−21.0000			−0.828159			−0.414080	−	0.910241i	$-0.635896\pi$
$643$	−21.0000			−0.828159			−0.414080	+	0.910241i	$0.635896\pi$
$644$		0			0
$645$		0			0
$646$	−2.50000	−	4.33013i	−0.0983612	−	0.170367i
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	−0.986916	−	0.161233i	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−1.50000	−	2.59808i	−0.0588802	−	0.101983i
$650$	5.00000			0.196116
$651$		0			0
$652$	7.00000			0.274141
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−6.00000			−0.234082
$658$		0			0
$659$	−40.0000			−1.55818			−0.779089	−	0.626913i	$-0.784318\pi$
$659$	−40.0000			−1.55818			−0.779089	+	0.626913i	$0.784318\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$	−6.00000	+	10.3923i	−0.233197	+	0.403908i
$663$		0			0
$664$	−8.00000			−0.310460
$665$		0			0
$666$	−24.0000			−0.929981
$667$	5.00000	+	8.66025i	0.193601	+	0.335326i
$668$	−9.50000	+	16.4545i	−0.367566	+	0.636643i
$669$		0			0
$670$		0			0
$671$	−1.00000			−0.0386046
$672$		0			0
$673$	6.00000			0.231283			0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000			0.231283			0.115642	+	0.993291i	$0.463108\pi$
$674$	7.50000	+	12.9904i	0.288889	+	0.500371i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	24.0000	−	41.5692i	0.918334	−	1.59060i	0.116390	−	0.993204i	$-0.462868\pi$
$683$	24.0000	−	41.5692i	0.918334	−	1.59060i	0.801945	−	0.597398i	$-0.203799\pi$
$684$	−7.50000	−	12.9904i	−0.286770	−	0.496700i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	3.00000	+	5.19615i	0.114374	+	0.198101i
$689$	−2.50000	+	4.33013i	−0.0952424	+	0.164965i
$690$		0			0
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	0.972685	−	0.232128i	$-0.0745690\pi$
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	−0.687372	+	0.726306i	$0.741236\pi$
$692$	−15.0000			−0.570214
$693$		0			0
$694$	−4.00000			−0.151838
$695$		0			0
$696$		0			0
$697$		0			0
$698$	17.0000	+	29.4449i	0.643459	+	1.11450i
$699$		0			0
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	−20.0000	+	34.6410i	−0.754314	+	1.30651i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−18.0000			−0.677439
$707$		0			0
$708$		0			0
$709$	−1.00000	−	1.73205i	−0.0375558	−	0.0650485i	0.846637	−	0.532172i	$-0.178624\pi$
$709$	−1.00000	−	1.73205i	−0.0375558	−	0.0650485i	−0.884192	+	0.467123i	$0.845291\pi$
$710$		0			0
$711$	−21.0000	+	36.3731i	−0.787562	+	1.36410i
$712$	8.00000	+	13.8564i	0.299813	+	0.519291i
$713$	16.0000			0.599205
$714$		0			0
$715$		0			0
$716$	1.00000	+	1.73205i	0.0373718	+	0.0647298i
$717$		0			0
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	0.997546	+	0.0700124i	$0.0223039\pi$
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	−0.438141	+	0.898906i	$0.644363\pi$
$720$		0			0
$721$		0			0
$722$	−6.00000			−0.223297
$723$		0			0
$724$	−11.5000	+	19.9186i	−0.427394	+	0.740268i
$725$	−12.5000	+	21.6506i	−0.464238	+	0.804084i
$726$		0			0
$727$	4.00000			0.148352			0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000			0.148352			0.0741759	+	0.997245i	$0.476367\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$		0			0
$733$	13.0000	+	22.5167i	0.480166	+	0.831672i	0.999741	−	0.0227529i	$-0.00724310\pi$
$733$	13.0000	+	22.5167i	0.480166	+	0.831672i	−0.519575	+	0.854425i	$0.673910\pi$
$734$	−10.0000			−0.369107
$735$		0			0
$736$	−2.00000			−0.0737210
$737$	3.50000	+	6.06218i	0.128924	+	0.223303i
$738$		0			0
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	−0.826893	−	0.562360i	$-0.809894\pi$
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	0.900464	+	0.434930i	$0.143227\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−27.0000			−0.990534			−0.495267	−	0.868741i	$-0.664930\pi$
$743$	−27.0000			−0.990534			−0.495267	+	0.868741i	$0.664930\pi$
$744$		0			0
$745$		0			0
$746$	15.5000	−	26.8468i	0.567495	−	0.982931i
$747$	12.0000	+	20.7846i	0.439057	+	0.760469i
$748$	1.00000			0.0365636
$749$		0			0
$750$		0			0
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	−0.999921	−	0.0125942i	$-0.995991\pi$
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	0.489053	−	0.872254i	$-0.337342\pi$
$752$	5.50000	−	9.52628i	0.200564	−	0.347388i
$753$		0			0
$754$	−2.50000	−	4.33013i	−0.0910446	−	0.157694i
$755$		0			0
$756$		0			0
$757$	33.0000			1.19941			0.599703	−	0.800223i	$-0.295286\pi$
$757$	33.0000			1.19941			0.599703	+	0.800223i	$0.295286\pi$
$758$	−2.00000	−	3.46410i	−0.0726433	−	0.125822i
$759$		0			0
$760$		0			0
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.00800331	−	0.999968i	$-0.502548\pi$
$762$		0			0
$763$		0			0
$764$	−4.00000			−0.144715
$765$		0			0
$766$	−12.0000	+	20.7846i	−0.433578	+	0.750978i
$767$	−1.50000	+	2.59808i	−0.0541619	+	0.0938111i
$768$		0			0
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$		0			0
$771$		0			0
$772$	−2.00000	−	3.46410i	−0.0719816	−	0.124676i
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	−0.761987	−	0.647592i	$-0.775776\pi$
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	0.941825	+	0.336104i	$0.109109\pi$
$774$	9.00000	−	15.5885i	0.323498	−	0.560316i
$775$	20.0000	+	34.6410i	0.718421	+	1.24434i
$776$	2.00000			0.0717958
$777$		0			0
$778$	19.0000			0.681183
$779$		0			0
$780$		0			0
$781$	4.50000	−	7.79423i	0.161023	−	0.278899i
$782$	1.00000	+	1.73205i	0.0357599	+	0.0619380i
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	5.50000	−	9.52628i	0.196054	−	0.339575i	−0.751192	−	0.660084i	$-0.770521\pi$
$787$	5.50000	−	9.52628i	0.196054	−	0.339575i	0.947245	+	0.320509i	$0.103854\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	3.00000			0.106600
$793$	0.500000	+	0.866025i	0.0177555	+	0.0307535i
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−54.0000			−1.91278			−0.956389	−	0.292096i	$-0.905647\pi$
$797$	−54.0000			−1.91278			−0.956389	+	0.292096i	$0.905647\pi$
$798$		0			0
$799$	−11.0000			−0.389152
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	24.0000	−	41.5692i	0.847998	−	1.46878i
$802$	19.0000	−	32.9090i	0.670913	−	1.16206i
$803$	−1.00000	−	1.73205i	−0.0352892	−	0.0611227i
$804$		0			0
$805$		0			0
$806$	−8.00000			−0.281788
$807$		0			0
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$		0			0
$813$		0			0
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$		0			0
$816$		0			0
$817$	−15.0000	−	25.9808i	−0.524784	−	0.908952i
$818$	36.0000			1.25871
$819$		0			0
$820$		0			0
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	0.951526	−	0.307568i	$-0.0995151\pi$
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	−0.742125	+	0.670262i	$0.766182\pi$
$822$		0			0
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	0.360623	+	0.932712i	$0.382564\pi$
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	−0.988063	+	0.154047i	$0.950769\pi$
$824$	−3.00000	−	5.19615i	−0.104510	−	0.181017i
$825$		0			0
$826$		0			0
$827$	−33.0000			−1.14752			−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000			−1.14752			−0.573761	+	0.819023i	$0.694516\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	13.5000	−	23.3827i	0.468874	−	0.812114i	−0.530493	−	0.847690i	$-0.677993\pi$
$829$	13.5000	−	23.3827i	0.468874	−	0.812114i	0.999367	+	0.0355753i	$0.0113264\pi$
$830$		0			0
$831$		0			0
$832$	1.00000			0.0346688
$833$		0			0
$834$		0			0
$835$		0			0
$836$	2.50000	−	4.33013i	0.0864643	−	0.149761i
$837$		0			0
$838$	−3.00000	−	5.19615i	−0.103633	−	0.179498i
$839$	37.0000			1.27738			0.638691	−	0.769463i	$-0.279476\pi$
$839$	37.0000			1.27738			0.638691	+	0.769463i	$0.279476\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−1.00000	−	1.73205i	−0.0344623	−	0.0596904i
$843$		0			0
$844$	1.00000	−	1.73205i	0.0344214	−	0.0596196i
$845$		0			0
$846$	−33.0000			−1.13456
$847$		0			0
$848$	5.00000			0.171701
$849$		0			0
$850$	−2.50000	+	4.33013i	−0.0857493	+	0.148522i
$851$	8.00000	−	13.8564i	0.274236	−	0.474991i
$852$		0			0
$853$	−38.0000			−1.30110			−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000			−1.30110			−0.650548	+	0.759465i	$0.725461\pi$
$854$		0			0
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	−21.5000	+	37.2391i	−0.734426	+	1.27206i	0.220549	+	0.975376i	$0.429215\pi$
$857$	−21.5000	+	37.2391i	−0.734426	+	1.27206i	−0.954975	+	0.296687i	$0.904118\pi$
$858$		0			0
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.00000	+	10.3923i	0.204242	+	0.353758i	0.949891	−	0.312581i	$-0.101194\pi$
$863$	6.00000	+	10.3923i	0.204242	+	0.353758i	−0.745649	+	0.666339i	$0.767860\pi$
$864$		0			0
$865$		0			0
$866$	−2.50000	−	4.33013i	−0.0849535	−	0.147144i
$867$		0			0
$868$		0			0
$869$	−14.0000			−0.474917
$870$		0			0
$871$	3.50000	−	6.06218i	0.118593	−	0.205409i
$872$	−6.00000	+	10.3923i	−0.203186	+	0.351928i
$873$	−3.00000	−	5.19615i	−0.101535	−	0.175863i
$874$	10.0000			0.338255
$875$		0			0
$876$		0			0
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	−11.0000	+	19.0526i	−0.371232	+	0.642993i
$879$		0			0
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	24.0000			0.807664			0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000			0.807664			0.403832	+	0.914833i	$0.367678\pi$
$884$	−0.500000	−	0.866025i	−0.0168168	−	0.0291276i
$885$		0			0
$886$	6.00000	−	10.3923i	0.201574	−	0.349136i
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$	−7.50000	+	12.9904i	−0.251119	+	0.434950i
$893$	−27.5000	+	47.6314i	−0.920252	+	1.59392i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	18.0000	+	31.1769i	0.600668	+	1.04039i
$899$	20.0000	−	34.6410i	0.667037	−	1.15534i
$900$	−7.50000	+	12.9904i	−0.250000	+	0.433013i
$901$	−2.50000	−	4.33013i	−0.0832871	−	0.144257i
$902$		0			0
$903$		0			0
$904$	−1.00000			−0.0332595
$905$		0			0
$906$		0			0
$907$	23.0000	−	39.8372i	0.763702	−	1.32277i	−0.177227	−	0.984170i	$-0.556713\pi$
$907$	23.0000	−	39.8372i	0.763702	−	1.32277i	0.940930	−	0.338602i	$-0.109954\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	54.0000			1.79107
$910$		0			0
$911$	34.0000			1.12647			0.563235	−	0.826297i	$-0.309557\pi$
$911$	34.0000			1.12647			0.563235	+	0.826297i	$0.309557\pi$
$912$		0			0
$913$	−4.00000	+	6.92820i	−0.132381	+	0.229290i
$914$	−11.0000	+	19.0526i	−0.363848	+	0.630203i
$915$		0			0
$916$	2.00000			0.0660819
$917$		0			0
$918$		0			0
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	0.988199	+	0.153174i	$0.0489495\pi$
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	−0.361447	+	0.932393i	$0.617717\pi$
$920$		0			0
$921$		0			0
$922$	−18.0000	−	31.1769i	−0.592798	−	1.02676i
$923$	−9.00000			−0.296239
$924$		0			0
$925$	40.0000			1.31519
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	−9.00000	+	15.5885i	−0.295599	+	0.511992i
$928$	−2.50000	+	4.33013i	−0.0820665	+	0.142143i
$929$	23.0000	+	39.8372i	0.754606	+	1.30702i	0.945570	+	0.325418i	$0.105505\pi$
$929$	23.0000	+	39.8372i	0.754606	+	1.30702i	−0.190965	+	0.981597i	$0.561162\pi$
$930$		0			0
$931$		0			0
$932$	21.0000			0.687878
$933$		0			0
$934$	21.0000	−	36.3731i	0.687141	−	1.19016i
$935$		0			0
$936$	−1.50000	−	2.59808i	−0.0490290	−	0.0849208i
$937$	41.0000			1.33941			0.669706	−	0.742627i	$-0.266420\pi$
$937$	41.0000			1.33941			0.669706	+	0.742627i	$0.266420\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.00000	−	10.3923i	0.195594	−	0.338779i	−0.751501	−	0.659732i	$-0.770670\pi$
$941$	6.00000	−	10.3923i	0.195594	−	0.338779i	0.947095	+	0.320953i	$0.104003\pi$
$942$		0			0
$943$		0			0
$944$	3.00000			0.0976417
$945$		0			0
$946$	6.00000			0.195077
$947$	3.50000	+	6.06218i	0.113735	+	0.196994i	0.917273	−	0.398258i	$-0.130385\pi$
$947$	3.50000	+	6.06218i	0.113735	+	0.196994i	−0.803539	+	0.595253i	$0.797052\pi$
$948$		0			0
$949$	−1.00000	+	1.73205i	−0.0324614	+	0.0562247i
$950$	12.5000	+	21.6506i	0.405554	+	0.702439i
$951$		0			0
$952$		0			0
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$	−7.50000	−	12.9904i	−0.242821	−	0.420579i
$955$		0			0
$956$	−4.50000	+	7.79423i	−0.145540	+	0.252083i
$957$		0			0
$958$	−37.0000			−1.19542
$959$		0			0
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−4.00000	+	6.92820i	−0.128965	+	0.223374i
$963$	−12.0000	+	20.7846i	−0.386695	+	0.669775i
$964$	6.00000	+	10.3923i	0.193247	+	0.334714i
$965$		0			0
$966$		0			0
$967$	23.0000			0.739630			0.369815	−	0.929105i	$-0.379421\pi$
$967$	23.0000			0.739630			0.369815	+	0.929105i	$0.379421\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$		0			0
$970$		0			0
$971$	−30.0000	−	51.9615i	−0.962746	−	1.66752i	−0.715553	−	0.698558i	$-0.753825\pi$
$971$	−30.0000	−	51.9615i	−0.962746	−	1.66752i	−0.247193	−	0.968966i	$-0.579508\pi$
$972$		0			0
$973$		0			0
$974$	−37.0000			−1.18556
$975$		0			0
$976$	0.500000	−	0.866025i	0.0160046	−	0.0277208i
$977$	−5.00000	+	8.66025i	−0.159964	+	0.277066i	−0.934856	−	0.355028i	$-0.884471\pi$
$977$	−5.00000	+	8.66025i	−0.159964	+	0.277066i	0.774891	+	0.632094i	$0.217805\pi$
$978$		0			0
$979$	16.0000			0.511362
$980$		0			0
$981$	36.0000			1.14939
$982$	−13.0000	−	22.5167i	−0.414847	−	0.718536i
$983$	6.50000	−	11.2583i	0.207318	−	0.359085i	−0.743551	−	0.668679i	$-0.766860\pi$
$983$	6.50000	−	11.2583i	0.207318	−	0.359085i	0.950869	+	0.309594i	$0.100193\pi$
$984$		0			0
$985$		0			0
$986$	5.00000			0.159232
$987$		0			0
$988$	−5.00000			−0.159071
$989$	6.00000	+	10.3923i	0.190789	+	0.330456i
$990$		0			0
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	−0.553308	−	0.832977i	$-0.686635\pi$
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	0.998033	+	0.0626908i	$0.0199682\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.50000	+	12.9904i	−0.237527	+	0.411409i	−0.960004	−	0.279986i	$-0.909670\pi$
$997$	−7.50000	+	12.9904i	−0.237527	+	0.411409i	0.722477	+	0.691395i	$0.243004\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.f.q.1145.1		2
7.2	even	3	inner	1274.2.f.q.79.1		2
7.3	odd	6		1274.2.a.e.1.1		1
7.4	even	3		1274.2.a.f.1.1		1
7.5	odd	6		182.2.f.a.79.1	yes	2
7.6	odd	2		182.2.f.a.53.1	✓	2
21.5	even	6		1638.2.j.c.1171.1		2
21.20	even	2		1638.2.j.c.235.1		2
28.19	even	6		1456.2.r.f.625.1		2
28.27	even	2		1456.2.r.f.417.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.f.a.53.1	✓	2	7.6	odd	2
182.2.f.a.79.1	yes	2	7.5	odd	6
1274.2.a.e.1.1		1	7.3	odd	6
1274.2.a.f.1.1		1	7.4	even	3
1274.2.f.q.79.1		2	7.2	even	3	inner
1274.2.f.q.1145.1		2	1.1	even	1	trivial
1456.2.r.f.417.1		2	28.27	even	2
1456.2.r.f.625.1		2	28.19	even	6
1638.2.j.c.235.1		2	21.20	even	2
1638.2.j.c.1171.1		2	21.5	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} -1.00000 q^{22} +(-1.00000 - 1.73205i) q^{23} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} -5.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.00000 q^{34} -3.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(-2.50000 + 4.33013i) q^{38} -6.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{46} +(5.50000 + 9.52628i) q^{47} +5.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-2.50000 - 4.33013i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(0.500000 + 0.866025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(3.50000 - 6.06218i) q^{67} +(-0.500000 - 0.866025i) q^{68} -9.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} -5.00000 q^{76} +(7.00000 + 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} +8.00000 q^{83} +(-3.00000 - 5.19615i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-8.00000 - 13.8564i) q^{89} +2.00000 q^{92} +(-5.50000 + 9.52628i) q^{94} -2.00000 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 2 q^{8} + 3 q^{9} - q^{11} + 2 q^{13} - q^{16} - q^{17} - 3 q^{18} + 5 q^{19} - 2 q^{22} - 2 q^{23} + 5 q^{25} + q^{26} - 10 q^{29} - 8 q^{31} + q^{32} - 2 q^{34} - 6 q^{36}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^4 - 2 * q^8 + 3 * q^9 - q^11 + 2 * q^13 - q^16 - q^17 - 3 * q^18 + 5 * q^19 - 2 * q^22 - 2 * q^23 + 5 * q^25 + q^26 - 10 * q^29 - 8 * q^31 + q^32 - 2 * q^34 - 6 * q^36 + 8 * q^37 - 5 * q^38 - 12 * q^43 - q^44 + 2 * q^46 + 11 * q^47 + 10 * q^50 - q^52 - 5 * q^53 - 5 * q^58 - 3 * q^59 + q^61 - 16 * q^62 + 2 * q^64 + 7 * q^67 - q^68 - 18 * q^71 - 3 * q^72 - 2 * q^73 - 8 * q^74 - 10 * q^76 + 14 * q^79 - 9 * q^81 + 16 * q^83 - 6 * q^86 + q^88 - 16 * q^89 + 4 * q^92 - 11 * q^94 - 4 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

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