LMFDB - Embedded newform 650.2.e.b.451.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(451,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.451"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,-1,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.19027613138$
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 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	650.451
Dual form			650.2.e.b.601.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +(3.50000 - 0.866025i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +3.00000 q^{18} +(-3.50000 - 6.06218i) q^{19} +(-1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.00000 - 3.46410i) q^{26} +(-1.50000 + 2.59808i) q^{28} +(4.00000 - 6.92820i) q^{29} -10.0000 q^{31} +(0.500000 + 0.866025i) q^{32} -4.00000 q^{34} +(1.50000 - 2.59808i) q^{36} +(1.50000 - 2.59808i) q^{37} -7.00000 q^{38} +(1.00000 - 1.73205i) q^{41} +(3.00000 + 5.19615i) q^{43} -3.00000 q^{44} +(2.00000 + 3.46410i) q^{46} +1.00000 q^{47} +(-1.00000 + 1.73205i) q^{49} +(-2.50000 - 2.59808i) q^{52} +9.00000 q^{53} +(1.50000 + 2.59808i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(2.00000 + 3.46410i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-5.00000 + 8.66025i) q^{62} +(4.50000 - 7.79423i) q^{63} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -4.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} +(-3.50000 + 6.06218i) q^{76} -9.00000 q^{77} +10.0000 q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.00000 - 1.73205i) q^{82} +6.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(-7.50000 - 7.79423i) q^{91} +4.00000 q^{92} +(0.500000 - 0.866025i) q^{94} +(8.00000 + 13.8564i) q^{97} +(1.00000 + 1.73205i) q^{98} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 3 q^{7} - 2 q^{8} + 3 q^{9} + 3 q^{11} + 7 q^{13} - 6 q^{14} - q^{16} - 4 q^{17} + 6 q^{18} - 7 q^{19} - 3 q^{22} - 4 q^{23} + 2 q^{26} - 3 q^{28} + 8 q^{29} - 20 q^{31} + q^{32}+ \cdots + 18 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^4 - 3 * q^7 - 2 * q^8 + 3 * q^9 + 3 * q^11 + 7 * q^13 - 6 * q^14 - q^16 - 4 * q^17 + 6 * q^18 - 7 * q^19 - 3 * q^22 - 4 * q^23 + 2 * q^26 - 3 * q^28 + 8 * q^29 - 20 * q^31 + q^32 - 8 * q^34 + 3 * q^36 + 3 * q^37 - 14 * q^38 + 2 * q^41 + 6 * q^43 - 6 * q^44 + 4 * q^46 + 2 * q^47 - 2 * q^49 - 5 * q^52 + 18 * q^53 + 3 * q^56 - 8 * q^58 + 4 * q^59 + 14 * q^61 - 10 * q^62 + 9 * q^63 + 2 * q^64 + 4 * q^67 - 4 * q^68 - 6 * q^71 - 3 * q^72 - 8 * q^73 - 3 * q^74 - 7 * q^76 - 18 * q^77 + 20 * q^79 - 9 * q^81 - 2 * q^82 + 12 * q^86 - 3 * q^88 - q^89 - 15 * q^91 + 8 * q^92 + q^94 + 16 * q^97 + 2 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$		0			0
$6$		0			0
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	−3.00000			−0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	3.00000			0.707107
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		0			0
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$		0			0
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$		0			0
$28$	−1.50000	+	2.59808i	−0.283473	+	0.490990i
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	−0.208443	−	0.978035i	$-0.566840\pi$
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	0.951224	−	0.308500i	$-0.0998271\pi$
$30$		0			0
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−4.00000			−0.685994
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	−0.715981	−	0.698119i	$-0.754020\pi$
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	0.962580	+	0.270998i	$0.0873538\pi$
$38$	−7.00000			−1.13555
$39$		0			0
$40$		0			0
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$		0			0
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	0.998828	−	0.0484030i	$-0.0154132\pi$
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	−0.541332	+	0.840809i	$0.682080\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	1.00000			0.145865			0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000			0.145865			0.0729325	+	0.997337i	$0.476764\pi$
$48$		0			0
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$		0			0
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$		0			0
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$		0			0
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−5.00000	+	8.66025i	−0.635001	+	1.09985i
$63$	4.50000	−	7.79423i	0.566947	−	0.981981i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$		0			0
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$		0			0
$76$	−3.50000	+	6.06218i	−0.401478	+	0.695379i
$77$	−9.00000			−1.02565
$78$		0			0
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$	6.00000			0.646997
$87$		0			0
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$		0			0
$91$	−7.50000	−	7.79423i	−0.786214	−	0.817057i
$92$	4.00000			0.417029
$93$		0			0
$94$	0.500000	−	0.866025i	0.0515711	−	0.0893237i
$95$		0			0
$96$		0			0
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	0.911267	+	0.411816i	$0.135106\pi$
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	−0.0989899	+	0.995088i	$0.531561\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$	9.00000			0.904534
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	1.00000			0.0985329			0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000			0.0985329			0.0492665	+	0.998786i	$0.484312\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$		0			0
$106$	4.50000	−	7.79423i	0.437079	−	0.757042i
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$	3.00000			0.283473
$113$	−4.00000	−	6.92820i	−0.376288	−	0.651751i	0.614231	−	0.789127i	$-0.289466\pi$
$113$	−4.00000	−	6.92820i	−0.376288	−	0.651751i	−0.990519	+	0.137376i	$0.956133\pi$
$114$		0			0
$115$		0			0
$116$	−8.00000			−0.742781
$117$	7.50000	+	7.79423i	0.693375	+	0.720577i
$118$	4.00000			0.368230
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	14.0000			1.26750
$123$		0			0
$124$	5.00000	+	8.66025i	0.449013	+	0.777714i
$125$		0			0
$126$	−4.50000	−	7.79423i	−0.400892	−	0.694365i
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	−0.419064	−	0.907957i	$-0.637642\pi$
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	0.995846	−	0.0910585i	$-0.0290250\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	13.0000			1.13582			0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000			1.13582			0.567908	+	0.823092i	$0.307753\pi$
$132$		0			0
$133$	−10.5000	+	18.1865i	−0.910465	+	1.57697i
$134$	−2.00000	−	3.46410i	−0.172774	−	0.299253i
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$	−6.00000			−0.503509
$143$	3.00000	−	10.3923i	0.250873	−	0.869048i
$144$	−3.00000			−0.250000
$145$		0			0
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$		0			0
$148$	−3.00000			−0.246598
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	3.50000	+	6.06218i	0.283887	+	0.491708i
$153$	6.00000	−	10.3923i	0.485071	−	0.840168i
$154$	−4.50000	+	7.79423i	−0.362620	+	0.628077i
$155$		0			0
$156$		0			0
$157$	3.00000			0.239426			0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000			0.239426			0.119713	+	0.992809i	$0.461803\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$		0			0
$160$		0			0
$161$	12.0000			0.945732
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$		0			0
$167$	9.50000	−	16.4545i	0.735132	−	1.27329i	−0.219533	−	0.975605i	$-0.570453\pi$
$167$	9.50000	−	16.4545i	0.735132	−	1.27329i	0.954665	−	0.297681i	$-0.0962132\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	10.5000	−	18.1865i	0.802955	−	1.39076i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	−0.920722	−	0.390218i	$-0.872399\pi$
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	0.122422	−	0.992478i	$-0.460934\pi$
$174$		0			0
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	0.500000	+	0.866025i	0.0374766	+	0.0649113i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	−10.5000	+	2.59808i	−0.778312	+	0.192582i
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$		0			0
$186$		0			0
$187$	−12.0000			−0.877527
$188$	−0.500000	−	0.866025i	−0.0364662	−	0.0631614i
$189$		0			0
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	−12.0000	+	20.7846i	−0.863779	+	1.49611i	0.00447566	+	0.999990i	$0.498575\pi$
$193$	−12.0000	+	20.7846i	−0.863779	+	1.49611i	−0.868255	+	0.496119i	$0.834758\pi$
$194$	16.0000			1.14873
$195$		0			0
$196$	2.00000			0.142857
$197$	6.50000	−	11.2583i	0.463106	−	0.802123i	−0.536008	−	0.844213i	$-0.680068\pi$
$197$	6.50000	−	11.2583i	0.463106	−	0.802123i	0.999114	+	0.0420901i	$0.0134016\pi$
$198$	4.50000	−	7.79423i	0.319801	−	0.553912i
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	0.985873	+	0.167497i	$0.0535685\pi$
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	−0.347879	+	0.937539i	$0.613098\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−24.0000			−1.68447
$204$		0			0
$205$		0			0
$206$	0.500000	−	0.866025i	0.0348367	−	0.0603388i
$207$	−12.0000			−0.834058
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	−21.0000			−1.45260
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$		0			0
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$		0			0
$216$		0			0
$217$	15.0000	+	25.9808i	1.01827	+	1.76369i
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$		0			0
$220$		0			0
$221$	−10.0000	−	10.3923i	−0.672673	−	0.699062i
$222$		0			0
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$		0			0
$226$	−8.00000			−0.532152
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	0.791989	−	0.610535i	$-0.209046\pi$
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	−0.924734	+	0.380615i	$0.875712\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$		0			0
$232$	−4.00000	+	6.92820i	−0.262613	+	0.454859i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	10.5000	−	2.59808i	0.686406	−	0.169842i
$235$		0			0
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$		0			0
$238$	6.00000	+	10.3923i	0.388922	+	0.673633i
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$		0			0
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	2.00000			0.128565
$243$		0			0
$244$	7.00000	−	12.1244i	0.448129	−	0.776182i
$245$		0			0
$246$		0			0
$247$	−17.5000	−	18.1865i	−1.11350	−	1.15718i
$248$	10.0000			0.635001
$249$		0			0
$250$		0			0
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	−0.958613	−	0.284711i	$-0.908102\pi$
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	0.232740	−	0.972539i	$-0.425231\pi$
$252$	−9.00000			−0.566947
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	−6.50000	−	11.2583i	−0.407846	−	0.706410i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	−0.713878	−	0.700270i	$-0.753063\pi$
$257$	4.00000	−	6.92820i	0.249513	−	0.432169i	0.963391	+	0.268101i	$0.0863961\pi$
$258$		0			0
$259$	−9.00000			−0.559233
$260$		0			0
$261$	24.0000			1.48556
$262$	6.50000	−	11.2583i	0.401571	−	0.695542i
$263$	5.50000	−	9.52628i	0.339145	−	0.587416i	−0.645128	−	0.764075i	$-0.723196\pi$
$263$	5.50000	−	9.52628i	0.339145	−	0.587416i	0.984272	+	0.176659i	$0.0565291\pi$
$264$		0			0
$265$		0			0
$266$	10.5000	+	18.1865i	0.643796	+	1.11509i
$267$		0			0
$268$	−4.00000			−0.244339
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	12.0000			0.724947
$275$		0			0
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$	5.00000			0.299880
$279$	−15.0000	−	25.9808i	−0.898027	−	1.55543i
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$		0			0
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−7.50000	−	7.79423i	−0.443484	−	0.460882i
$287$	−6.00000			−0.354169
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$		0			0
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	0.967009	−	0.254741i	$-0.0819901\pi$
$293$	4.50000	+	7.79423i	0.262893	+	0.455344i	−0.704117	+	0.710084i	$0.748657\pi$
$294$		0			0
$295$		0			0
$296$	−1.50000	+	2.59808i	−0.0871857	+	0.151010i
$297$		0			0
$298$	6.00000			0.347571
$299$	−4.00000	+	13.8564i	−0.231326	+	0.801337i
$300$		0			0
$301$	9.00000	−	15.5885i	0.518751	−	0.898504i
$302$	−1.00000	+	1.73205i	−0.0575435	+	0.0996683i
$303$		0			0
$304$	7.00000			0.401478
$305$		0			0
$306$	−6.00000	−	10.3923i	−0.342997	−	0.594089i
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$	4.50000	+	7.79423i	0.256411	+	0.444117i
$309$		0			0
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	1.50000	−	2.59808i	0.0846499	−	0.146618i
$315$		0			0
$316$	−5.00000	−	8.66025i	−0.281272	−	0.487177i
$317$	−31.0000			−1.74113			−0.870567	−	0.492050i	$-0.836248\pi$
$317$	−31.0000			−1.74113			−0.870567	+	0.492050i	$0.836248\pi$
$318$		0			0
$319$	−12.0000	−	20.7846i	−0.671871	−	1.16371i
$320$		0			0
$321$		0			0
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$	−14.0000	+	24.2487i	−0.778981	+	1.34923i
$324$	9.00000			0.500000
$325$		0			0
$326$	8.00000			0.443079
$327$		0			0
$328$	−1.00000	+	1.73205i	−0.0552158	+	0.0956365i
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$	9.00000			0.493197
$334$	−9.50000	−	16.4545i	−0.519817	−	0.900349i
$335$		0			0
$336$		0			0
$337$	−30.0000			−1.63420			−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000			−1.63420			−0.817102	+	0.576493i	$0.804421\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$		0			0
$340$		0			0
$341$	−15.0000	+	25.9808i	−0.812296	+	1.40694i
$342$	−10.5000	−	18.1865i	−0.567775	−	0.983415i
$343$	−15.0000			−0.809924
$344$	−3.00000	−	5.19615i	−0.161749	−	0.280158i
$345$		0			0
$346$	−21.0000			−1.12897
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$		0			0
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	−0.568486	−	0.822693i	$-0.692471\pi$
$349$	8.00000	−	13.8564i	0.428230	−	0.741716i	0.996716	+	0.0809766i	$0.0258039\pi$
$350$		0			0
$351$		0			0
$352$	3.00000			0.159901
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$		0			0
$356$	1.00000			0.0529999
$357$		0			0
$358$	2.00000	+	3.46410i	0.105703	+	0.183083i
$359$	10.0000			0.527780			0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000			0.527780			0.263890	+	0.964553i	$0.414994\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−7.00000	+	12.1244i	−0.367912	+	0.637242i
$363$		0			0
$364$	−3.00000	+	10.3923i	−0.157243	+	0.544705i
$365$		0			0
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$	6.00000			0.312348
$370$		0			0
$371$	−13.5000	−	23.3827i	−0.700885	−	1.21397i
$372$		0			0
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	0.777847	−	0.628454i	$-0.216312\pi$
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	−0.933181	+	0.359408i	$0.882979\pi$
$374$	−6.00000	+	10.3923i	−0.310253	+	0.537373i
$375$		0			0
$376$	−1.00000			−0.0515711
$377$	8.00000	−	27.7128i	0.412021	−	1.42728i
$378$		0			0
$379$	−13.5000	+	23.3827i	−0.693448	+	1.20109i	0.277253	+	0.960797i	$0.410576\pi$
$379$	−13.5000	+	23.3827i	−0.693448	+	1.20109i	−0.970701	+	0.240291i	$0.922757\pi$
$380$		0			0
$381$		0			0
$382$	6.00000			0.306987
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	−0.962818	−	0.270151i	$-0.912926\pi$
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	0.247451	−	0.968900i	$-0.420407\pi$
$384$		0			0
$385$		0			0
$386$	12.0000	+	20.7846i	0.610784	+	1.05791i
$387$	−9.00000	+	15.5885i	−0.457496	+	0.792406i
$388$	8.00000	−	13.8564i	0.406138	−	0.703452i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	1.00000	−	1.73205i	0.0505076	−	0.0874818i
$393$		0			0
$394$	−6.50000	−	11.2583i	−0.327465	−	0.567186i
$395$		0			0
$396$	−4.50000	−	7.79423i	−0.226134	−	0.391675i
$397$	−10.5000	−	18.1865i	−0.526980	−	0.912756i	−0.999506	−	0.0314391i	$-0.989991\pi$
$397$	−10.5000	−	18.1865i	−0.526980	−	0.912756i	0.472526	−	0.881317i	$-0.343342\pi$
$398$	18.0000			0.902258
$399$		0			0
$400$		0			0
$401$	19.5000	−	33.7750i	0.973784	−	1.68664i	0.289891	−	0.957060i	$-0.406381\pi$
$401$	19.5000	−	33.7750i	0.973784	−	1.68664i	0.683892	−	0.729583i	$-0.260286\pi$
$402$		0			0
$403$	−35.0000	+	8.66025i	−1.74347	+	0.431398i
$404$		0			0
$405$		0			0
$406$	−12.0000	+	20.7846i	−0.595550	+	1.03152i
$407$	−4.50000	−	7.79423i	−0.223057	−	0.386346i
$408$		0			0
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	0.575670	−	0.817682i	$-0.304741\pi$
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	−0.995968	+	0.0897044i	$0.971408\pi$
$410$		0			0
$411$		0			0
$412$	−0.500000	−	0.866025i	−0.0246332	−	0.0426660i
$413$	6.00000	−	10.3923i	0.295241	−	0.511372i
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$		0			0
$416$	2.50000	+	2.59808i	0.122573	+	0.127381i
$417$		0			0
$418$	−10.5000	+	18.1865i	−0.513572	+	0.889532i
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	6.50000	+	11.2583i	0.316415	+	0.548047i
$423$	1.50000	+	2.59808i	0.0729325	+	0.126323i
$424$	−9.00000			−0.437079
$425$		0			0
$426$		0			0
$427$	21.0000	−	36.3731i	1.01626	−	1.76022i
$428$	18.0000			0.870063
$429$		0			0
$430$		0			0
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$		0			0
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	0.991693	−	0.128624i	$-0.0410559\pi$
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	−0.607238	+	0.794520i	$0.707723\pi$
$434$	30.0000			1.44005
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	28.0000			1.33942
$438$		0			0
$439$	3.00000	−	5.19615i	0.143182	−	0.247999i	−0.785511	−	0.618848i	$-0.787600\pi$
$439$	3.00000	−	5.19615i	0.143182	−	0.247999i	0.928693	+	0.370849i	$0.120933\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	−14.0000	+	3.46410i	−0.665912	+	0.164771i
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$		0			0
$445$		0			0
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$		0			0
$448$	−1.50000	−	2.59808i	−0.0708683	−	0.122748i
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	0.986937	−	0.161106i	$-0.0515060\pi$
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	−0.632990	+	0.774160i	$0.718173\pi$
$450$		0			0
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	−4.00000	+	6.92820i	−0.188144	+	0.325875i
$453$		0			0
$454$	−4.00000			−0.187729
$455$		0			0
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−11.0000	+	19.0526i	−0.513996	+	0.890268i
$459$		0			0
$460$		0			0
$461$	20.0000	+	34.6410i	0.931493	+	1.61339i	0.780771	+	0.624817i	$0.214826\pi$
$461$	20.0000	+	34.6410i	0.931493	+	1.61339i	0.150721	+	0.988576i	$0.451840\pi$
$462$		0			0
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$	4.00000	+	6.92820i	0.185695	+	0.321634i
$465$		0			0
$466$	9.00000	−	15.5885i	0.416917	−	0.722121i
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$	3.00000	−	10.3923i	0.138675	−	0.480384i
$469$	−12.0000			−0.554109
$470$		0			0
$471$		0			0
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	18.0000			0.827641
$474$		0			0
$475$		0			0
$476$	12.0000			0.550019
$477$	13.5000	+	23.3827i	0.618123	+	1.07062i
$478$	1.00000	−	1.73205i	0.0457389	−	0.0792222i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	3.00000	−	10.3923i	0.136788	−	0.473848i
$482$	25.0000			1.13872
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$		0			0
$487$	9.50000	+	16.4545i	0.430486	+	0.745624i	0.996915	−	0.0784867i	$-0.0250088\pi$
$487$	9.50000	+	16.4545i	0.430486	+	0.745624i	−0.566429	+	0.824110i	$0.691675\pi$
$488$	−7.00000	−	12.1244i	−0.316875	−	0.548844i
$489$		0			0
$490$		0			0
$491$	21.5000	−	37.2391i	0.970281	−	1.68058i	0.275581	−	0.961278i	$-0.411130\pi$
$491$	21.5000	−	37.2391i	0.970281	−	1.68058i	0.694701	−	0.719299i	$-0.255537\pi$
$492$		0			0
$493$	−32.0000			−1.44121
$494$	−24.5000	+	6.06218i	−1.10231	+	0.272750i
$495$		0			0
$496$	5.00000	−	8.66025i	0.224507	−	0.388857i
$497$	−9.00000	+	15.5885i	−0.403705	+	0.699238i
$498$		0			0
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$		0			0
$502$	−23.0000			−1.02654
$503$	11.5000	+	19.9186i	0.512760	+	0.888126i	0.999891	+	0.0147968i	$0.00471014\pi$
$503$	11.5000	+	19.9186i	0.512760	+	0.888126i	−0.487131	+	0.873329i	$0.661957\pi$
$504$	−4.50000	+	7.79423i	−0.200446	+	0.347183i
$505$		0			0
$506$	12.0000			0.533465
$507$		0			0
$508$	−13.0000			−0.576782
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−4.00000	−	6.92820i	−0.176432	−	0.305590i
$515$		0			0
$516$		0			0
$517$	1.50000	−	2.59808i	0.0659699	−	0.114263i
$518$	−4.50000	+	7.79423i	−0.197719	+	0.342459i
$519$		0			0
$520$		0			0
$521$	−31.0000			−1.35813			−0.679067	−	0.734076i	$-0.737616\pi$
$521$	−31.0000			−1.35813			−0.679067	+	0.734076i	$0.737616\pi$
$522$	12.0000	−	20.7846i	0.525226	−	0.909718i
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	−0.518766	−	0.854916i	$-0.673608\pi$
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	0.999762	+	0.0218062i	$0.00694167\pi$
$524$	−6.50000	−	11.2583i	−0.283954	−	0.491822i
$525$		0			0
$526$	−5.50000	−	9.52628i	−0.239811	−	0.415366i
$527$	20.0000	+	34.6410i	0.871214	+	1.50899i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	−6.00000	+	10.3923i	−0.260378	+	0.450988i
$532$	21.0000			0.910465
$533$	2.00000	−	6.92820i	0.0866296	−	0.300094i
$534$		0			0
$535$		0			0
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$		0			0
$538$	−24.0000			−1.03471
$539$	3.00000	+	5.19615i	0.129219	+	0.223814i
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$	4.00000	+	6.92820i	0.171815	+	0.297592i
$543$		0			0
$544$	2.00000	−	3.46410i	0.0857493	−	0.148522i
$545$		0			0
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	−21.0000	+	36.3731i	−0.896258	+	1.55236i
$550$		0			0
$551$	−56.0000			−2.38568
$552$		0			0
$553$	−15.0000	−	25.9808i	−0.637865	−	1.10481i
$554$	19.0000			0.807233
$555$		0			0
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	−15.5000	+	26.8468i	−0.656756	+	1.13753i	0.324694	+	0.945819i	$0.394739\pi$
$557$	−15.5000	+	26.8468i	−0.656756	+	1.13753i	−0.981450	+	0.191716i	$0.938595\pi$
$558$	−30.0000			−1.27000
$559$	15.0000	+	15.5885i	0.634432	+	0.659321i
$560$		0			0
$561$		0			0
$562$	1.00000	−	1.73205i	0.0421825	−	0.0730622i
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$		0			0
$565$		0			0
$566$	7.00000	+	12.1244i	0.294232	+	0.509625i
$567$	27.0000			1.13389
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	−0.727405	−	0.686209i	$-0.759274\pi$
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	0.957977	+	0.286846i	$0.0926069\pi$
$570$		0			0
$571$	−37.0000			−1.54840			−0.774201	−	0.632940i	$-0.781848\pi$
$571$	−37.0000			−1.54840			−0.774201	+	0.632940i	$0.781848\pi$
$572$	−10.5000	+	2.59808i	−0.439027	+	0.108631i
$573$		0			0
$574$	−3.00000	+	5.19615i	−0.125218	+	0.216883i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	13.5000	−	23.3827i	0.559113	−	0.968412i
$584$	4.00000			0.165521
$585$		0			0
$586$	9.00000			0.371787
$587$	−1.00000	+	1.73205i	−0.0412744	+	0.0714894i	−0.885925	−	0.463829i	$-0.846475\pi$
$587$	−1.00000	+	1.73205i	−0.0412744	+	0.0714894i	0.844650	+	0.535319i	$0.179808\pi$
$588$		0			0
$589$	35.0000	+	60.6218i	1.44215	+	2.49788i
$590$		0			0
$591$		0			0
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	−20.0000			−0.821302			−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000			−0.821302			−0.410651	+	0.911793i	$0.634698\pi$
$594$		0			0
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$	10.0000	+	10.3923i	0.408930	+	0.424973i
$599$	26.0000			1.06233			0.531166	−	0.847268i	$-0.321754\pi$
$599$	26.0000			1.06233			0.531166	+	0.847268i	$0.321754\pi$
$600$		0			0
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	−0.912499	−	0.409079i	$-0.865850\pi$
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	0.810522	+	0.585708i	$0.199184\pi$
$602$	−9.00000	−	15.5885i	−0.366813	−	0.635338i
$603$	12.0000			0.488678
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$		0			0
$606$		0			0
$607$	10.5000	+	18.1865i	0.426182	+	0.738169i	0.996530	−	0.0832344i	$-0.0265250\pi$
$607$	10.5000	+	18.1865i	0.426182	+	0.738169i	−0.570348	+	0.821403i	$0.693192\pi$
$608$	3.50000	−	6.06218i	0.141944	−	0.245854i
$609$		0			0
$610$		0			0
$611$	3.50000	−	0.866025i	0.141595	−	0.0350356i
$612$	−12.0000			−0.485071
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	−0.733316	−	0.679888i	$-0.762028\pi$
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	0.955458	+	0.295126i	$0.0953615\pi$
$614$	7.00000	−	12.1244i	0.282497	−	0.489299i
$615$		0			0
$616$	9.00000			0.362620
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	0.555056	−	0.831813i	$-0.312697\pi$
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	−0.997899	+	0.0647859i	$0.979364\pi$
$618$		0			0
$619$	−3.00000			−0.120580			−0.0602901	−	0.998181i	$-0.519203\pi$
$619$	−3.00000			−0.120580			−0.0602901	+	0.998181i	$0.519203\pi$
$620$		0			0
$621$		0			0
$622$	−12.0000	+	20.7846i	−0.481156	+	0.833387i
$623$	3.00000			0.120192
$624$		0			0
$625$		0			0
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	−1.50000	−	2.59808i	−0.0598565	−	0.103675i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	18.0000	+	31.1769i	0.716569	+	1.24113i	0.962351	+	0.271808i	$0.0876217\pi$
$631$	18.0000	+	31.1769i	0.716569	+	1.24113i	−0.245783	+	0.969325i	$0.579045\pi$
$632$	−10.0000			−0.397779
$633$		0			0
$634$	−15.5000	+	26.8468i	−0.615584	+	1.06622i
$635$		0			0
$636$		0			0
$637$	−2.00000	+	6.92820i	−0.0792429	+	0.274505i
$638$	−24.0000			−0.950169
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$		0			0
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	0.941106	−	0.338112i	$-0.109788\pi$
$641$	4.50000	+	7.79423i	0.177739	+	0.307854i	−0.763367	+	0.645966i	$0.776455\pi$
$642$		0			0
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	0.979541	−	0.201243i	$-0.0644981\pi$
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	−0.664052	+	0.747686i	$0.731165\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$		0			0
$646$	14.0000	+	24.2487i	0.550823	+	0.954053i
$647$	−3.50000	+	6.06218i	−0.137599	+	0.238329i	−0.926587	−	0.376080i	$-0.877272\pi$
$647$	−3.50000	+	6.06218i	−0.137599	+	0.238329i	0.788988	+	0.614408i	$0.210605\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	12.0000			0.471041
$650$		0			0
$651$		0			0
$652$	4.00000	−	6.92820i	0.156652	−	0.271329i
$653$	−5.50000	+	9.52628i	−0.215232	+	0.372792i	−0.953344	−	0.301885i	$-0.902384\pi$
$653$	−5.50000	+	9.52628i	−0.215232	+	0.372792i	0.738113	+	0.674678i	$0.235717\pi$
$654$		0			0
$655$		0			0
$656$	1.00000	+	1.73205i	0.0390434	+	0.0676252i
$657$	−6.00000	−	10.3923i	−0.234082	−	0.405442i
$658$	−3.00000			−0.116952
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$		0			0
$665$		0			0
$666$	4.50000	−	7.79423i	0.174371	−	0.302020i
$667$	16.0000	+	27.7128i	0.619522	+	1.07304i
$668$	−19.0000			−0.735132
$669$		0			0
$670$		0			0
$671$	42.0000			1.62139
$672$		0			0
$673$	−4.00000	+	6.92820i	−0.154189	+	0.267063i	−0.932763	−	0.360489i	$-0.882610\pi$
$673$	−4.00000	+	6.92820i	−0.154189	+	0.267063i	0.778575	+	0.627552i	$0.215943\pi$
$674$	−15.0000	+	25.9808i	−0.577778	+	1.00074i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	50.0000			1.92166			0.960828	−	0.277145i	$-0.0893883\pi$
$677$	50.0000			1.92166			0.960828	+	0.277145i	$0.0893883\pi$
$678$		0			0
$679$	24.0000	−	41.5692i	0.921035	−	1.59528i
$680$		0			0
$681$		0			0
$682$	15.0000	+	25.9808i	0.574380	+	0.994855i
$683$	−1.00000	−	1.73205i	−0.0382639	−	0.0662751i	0.846259	−	0.532771i	$-0.178849\pi$
$683$	−1.00000	−	1.73205i	−0.0382639	−	0.0662751i	−0.884523	+	0.466496i	$0.845516\pi$
$684$	−21.0000			−0.802955
$685$		0			0
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$		0			0
$688$	−6.00000			−0.228748
$689$	31.5000	−	7.79423i	1.20005	−	0.296936i
$690$		0			0
$691$	−14.5000	+	25.1147i	−0.551606	+	0.955410i	0.446553	+	0.894757i	$0.352651\pi$
$691$	−14.5000	+	25.1147i	−0.551606	+	0.955410i	−0.998159	+	0.0606524i	$0.980682\pi$
$692$	−10.5000	+	18.1865i	−0.399150	+	0.691348i
$693$	−13.5000	−	23.3827i	−0.512823	−	0.888235i
$694$	−16.0000			−0.607352
$695$		0			0
$696$		0			0
$697$	−8.00000			−0.303022
$698$	−8.00000	−	13.8564i	−0.302804	−	0.524473i
$699$		0			0
$700$		0			0
$701$	−40.0000			−1.51078			−0.755390	−	0.655276i	$-0.772552\pi$
$701$	−40.0000			−1.51078			−0.755390	+	0.655276i	$0.772552\pi$
$702$		0			0
$703$	−21.0000			−0.792030
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	0.781086	−	0.624423i	$-0.214666\pi$
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	−0.931309	+	0.364229i	$0.881333\pi$
$710$		0			0
$711$	15.0000	+	25.9808i	0.562544	+	0.974355i
$712$	0.500000	−	0.866025i	0.0187383	−	0.0324557i
$713$	20.0000	−	34.6410i	0.749006	−	1.29732i
$714$		0			0
$715$		0			0
$716$	4.00000			0.149487
$717$		0			0
$718$	5.00000	−	8.66025i	0.186598	−	0.323198i
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	−0.999669	−	0.0257237i	$-0.991811\pi$
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	0.477557	−	0.878601i	$-0.341522\pi$
$720$		0			0
$721$	−1.50000	−	2.59808i	−0.0558629	−	0.0967574i
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$		0			0
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$		0			0
$726$		0			0
$727$	−35.0000			−1.29808			−0.649039	−	0.760755i	$-0.724829\pi$
$727$	−35.0000			−1.29808			−0.649039	+	0.760755i	$0.724829\pi$
$728$	7.50000	+	7.79423i	0.277968	+	0.288873i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	1.00000			0.0369358			0.0184679	−	0.999829i	$-0.494121\pi$
$733$	1.00000			0.0369358			0.0184679	+	0.999829i	$0.494121\pi$
$734$		0			0
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	3.00000	−	5.19615i	0.110432	−	0.191273i
$739$	−19.5000	+	33.7750i	−0.717319	+	1.24243i	0.244739	+	0.969589i	$0.421298\pi$
$739$	−19.5000	+	33.7750i	−0.717319	+	1.24243i	−0.962058	+	0.272844i	$0.912036\pi$
$740$		0			0
$741$		0			0
$742$	−27.0000			−0.991201
$743$	−4.00000	+	6.92820i	−0.146746	+	0.254171i	−0.930023	−	0.367502i	$-0.880213\pi$
$743$	−4.00000	+	6.92820i	−0.146746	+	0.254171i	0.783277	+	0.621673i	$0.213547\pi$
$744$		0			0
$745$		0			0
$746$	−6.00000			−0.219676
$747$		0			0
$748$	6.00000	+	10.3923i	0.219382	+	0.379980i
$749$	54.0000			1.97312
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	−0.500000	+	0.866025i	−0.0182331	+	0.0315807i
$753$		0			0
$754$	−20.0000	−	20.7846i	−0.728357	−	0.756931i
$755$		0			0
$756$		0			0
$757$	−14.5000	+	25.1147i	−0.527011	+	0.912811i	0.472493	+	0.881334i	$0.343354\pi$
$757$	−14.5000	+	25.1147i	−0.527011	+	0.912811i	−0.999505	+	0.0314762i	$0.989979\pi$
$758$	13.5000	+	23.3827i	0.490342	+	0.849297i
$759$		0			0
$760$		0			0
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	0.610527	−	0.791995i	$-0.290958\pi$
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	−0.991152	+	0.132734i	$0.957624\pi$
$762$		0			0
$763$	3.00000	+	5.19615i	0.108607	+	0.188113i
$764$	3.00000	−	5.19615i	0.108536	−	0.187990i
$765$		0			0
$766$	−28.0000			−1.01168
$767$	10.0000	+	10.3923i	0.361079	+	0.375244i
$768$		0			0
$769$	1.00000	−	1.73205i	0.0360609	−	0.0624593i	−0.847432	−	0.530904i	$-0.821852\pi$
$769$	1.00000	−	1.73205i	0.0360609	−	0.0624593i	0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$		0			0
$772$	24.0000			0.863779
$773$	15.5000	+	26.8468i	0.557496	+	0.965612i	0.997705	+	0.0677162i	$0.0215712\pi$
$773$	15.5000	+	26.8468i	0.557496	+	0.965612i	−0.440208	+	0.897896i	$0.645095\pi$
$774$	9.00000	+	15.5885i	0.323498	+	0.560316i
$775$		0			0
$776$	−8.00000	−	13.8564i	−0.287183	−	0.497416i
$777$		0			0
$778$	6.00000	−	10.3923i	0.215110	−	0.372582i
$779$	−14.0000			−0.501602
$780$		0			0
$781$	−18.0000			−0.644091
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$		0			0
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$		0			0
$786$		0			0
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	−13.0000			−0.463106
$789$		0			0
$790$		0			0
$791$	−12.0000	+	20.7846i	−0.426671	+	0.739016i
$792$	−9.00000			−0.319801
$793$	35.0000	+	36.3731i	1.24289	+	1.29165i
$794$	−21.0000			−0.745262
$795$		0			0
$796$	9.00000	−	15.5885i	0.318997	−	0.552518i
$797$	1.00000	+	1.73205i	0.0354218	+	0.0613524i	0.883193	−	0.469010i	$-0.155389\pi$
$797$	1.00000	+	1.73205i	0.0354218	+	0.0613524i	−0.847771	+	0.530362i	$0.822056\pi$
$798$		0			0
$799$	−2.00000	−	3.46410i	−0.0707549	−	0.122551i
$800$		0			0
$801$	−3.00000			−0.106000
$802$	−19.5000	−	33.7750i	−0.688569	−	1.19264i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$		0			0
$806$	−10.0000	+	34.6410i	−0.352235	+	1.22018i
$807$		0			0
$808$		0			0
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	−0.764644	−	0.644453i	$-0.777085\pi$
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	0.940435	+	0.339975i	$0.110418\pi$
$810$		0			0
$811$	21.0000			0.737410			0.368705	−	0.929547i	$-0.379801\pi$
$811$	21.0000			0.737410			0.368705	+	0.929547i	$0.379801\pi$
$812$	12.0000	+	20.7846i	0.421117	+	0.729397i
$813$		0			0
$814$	−9.00000			−0.315450
$815$		0			0
$816$		0			0
$817$	21.0000	−	36.3731i	0.734697	−	1.27253i
$818$	−17.0000			−0.594391
$819$	9.00000	−	31.1769i	0.314485	−	1.08941i
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$		0			0
$823$	−18.5000	−	32.0429i	−0.644869	−	1.11695i	−0.984332	−	0.176327i	$-0.943578\pi$
$823$	−18.5000	−	32.0429i	−0.644869	−	1.11695i	0.339462	−	0.940620i	$-0.389755\pi$
$824$	−1.00000			−0.0348367
$825$		0			0
$826$	−6.00000	−	10.3923i	−0.208767	−	0.361595i
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$	6.00000	+	10.3923i	0.208514	+	0.361158i
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	−0.513635	−	0.858009i	$-0.671701\pi$
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	0.999875	+	0.0158163i	$0.00503471\pi$
$830$		0			0
$831$		0			0
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	8.00000			0.277184
$834$		0			0
$835$		0			0
$836$	10.5000	+	18.1865i	0.363150	+	0.628994i
$837$		0			0
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	13.0000	+	22.5167i	0.448810	+	0.777361i	0.998309	−	0.0581329i	$-0.0185147\pi$
$839$	13.0000	+	22.5167i	0.448810	+	0.777361i	−0.549499	+	0.835494i	$0.685181\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	8.00000	−	13.8564i	0.275698	−	0.477523i
$843$		0			0
$844$	13.0000			0.447478
$845$		0			0
$846$	3.00000			0.103142
$847$	3.00000	−	5.19615i	0.103081	−	0.178542i
$848$	−4.50000	+	7.79423i	−0.154531	+	0.267655i
$849$		0			0
$850$		0			0
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	−21.0000	−	36.3731i	−0.718605	−	1.24466i
$855$		0			0
$856$	9.00000	−	15.5885i	0.307614	−	0.532803i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	−1.00000			−0.0341196			−0.0170598	−	0.999854i	$-0.505431\pi$
$859$	−1.00000			−0.0341196			−0.0170598	+	0.999854i	$0.505431\pi$
$860$		0			0
$861$		0			0
$862$	−12.0000	−	20.7846i	−0.408722	−	0.707927i
$863$	32.0000			1.08929			0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000			1.08929			0.544646	+	0.838666i	$0.316664\pi$
$864$		0			0
$865$		0			0
$866$	16.0000			0.543702
$867$		0			0
$868$	15.0000	−	25.9808i	0.509133	−	0.881845i
$869$	15.0000	−	25.9808i	0.508840	−	0.881337i
$870$		0			0
$871$	4.00000	−	13.8564i	0.135535	−	0.469506i
$872$	2.00000			0.0677285
$873$	−24.0000	+	41.5692i	−0.812277	+	1.40690i
$874$	14.0000	−	24.2487i	0.473557	−	0.820225i
$875$		0			0
$876$		0			0
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	−0.996144	−	0.0877308i	$-0.972038\pi$
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	0.422095	−	0.906552i	$-0.361295\pi$
$878$	−3.00000	−	5.19615i	−0.101245	−	0.175362i
$879$		0			0
$880$		0			0
$881$	−2.50000	+	4.33013i	−0.0842271	+	0.145886i	−0.905062	−	0.425280i	$-0.860175\pi$
$881$	−2.50000	+	4.33013i	−0.0842271	+	0.145886i	0.820834	+	0.571166i	$0.193509\pi$
$882$	−3.00000	+	5.19615i	−0.101015	+	0.174964i
$883$	26.0000			0.874970			0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000			0.874970			0.437485	+	0.899226i	$0.355869\pi$
$884$	−4.00000	+	13.8564i	−0.134535	+	0.466041i
$885$		0			0
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	−6.50000	+	11.2583i	−0.218249	+	0.378018i	−0.954273	−	0.298938i	$-0.903368\pi$
$887$	−6.50000	+	11.2583i	−0.218249	+	0.378018i	0.736024	+	0.676955i	$0.236701\pi$
$888$		0			0
$889$	−39.0000			−1.30802
$890$		0			0
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	−19.0000			−0.636167
$893$	−3.50000	−	6.06218i	−0.117123	−	0.202863i
$894$		0			0
$895$		0			0
$896$	−3.00000			−0.100223
$897$		0			0
$898$	15.0000			0.500556
$899$	−40.0000	+	69.2820i	−1.33407	+	2.31069i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$	−6.00000			−0.199778
$903$		0			0
$904$	4.00000	+	6.92820i	0.133038	+	0.230429i
$905$		0			0
$906$		0			0
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$	−2.00000	+	3.46410i	−0.0663723	+	0.114960i
$909$		0			0
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$		0			0
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$	−19.5000	−	33.7750i	−0.643947	−	1.11535i
$918$		0			0
$919$	−25.0000	−	43.3013i	−0.824674	−	1.42838i	−0.902168	−	0.431384i	$-0.858025\pi$
$919$	−25.0000	−	43.3013i	−0.824674	−	1.42838i	0.0774944	−	0.996993i	$-0.475308\pi$
$920$		0			0
$921$		0			0
$922$	40.0000			1.31733
$923$	−15.0000	−	15.5885i	−0.493731	−	0.513100i
$924$		0			0
$925$		0			0
$926$	20.0000	−	34.6410i	0.657241	−	1.13837i
$927$	1.50000	+	2.59808i	0.0492665	+	0.0853320i
$928$	8.00000			0.262613
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$	14.0000			0.458831
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$		0			0
$934$	−10.0000	+	17.3205i	−0.327210	+	0.566744i
$935$		0			0
$936$	−7.50000	−	7.79423i	−0.245145	−	0.254762i
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$	−6.00000	+	10.3923i	−0.195907	+	0.339321i
$939$		0			0
$940$		0			0
$941$	−24.0000			−0.782378			−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000			−0.782378			−0.391189	+	0.920310i	$0.627936\pi$
$942$		0			0
$943$	4.00000	+	6.92820i	0.130258	+	0.225613i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	9.00000	−	15.5885i	0.292615	−	0.506824i
$947$	19.0000	−	32.9090i	0.617417	−	1.06940i	−0.372538	−	0.928017i	$-0.621512\pi$
$947$	19.0000	−	32.9090i	0.617417	−	1.06940i	0.989955	−	0.141381i	$-0.0451542\pi$
$948$		0			0
$949$	−14.0000	+	3.46410i	−0.454459	+	0.112449i
$950$		0			0
$951$		0			0
$952$	6.00000	−	10.3923i	0.194461	−	0.336817i
$953$	−11.0000	−	19.0526i	−0.356325	−	0.617173i	0.631019	−	0.775768i	$-0.282637\pi$
$953$	−11.0000	−	19.0526i	−0.356325	−	0.617173i	−0.987344	+	0.158595i	$0.949304\pi$
$954$	27.0000			0.874157
$955$		0			0
$956$	−1.00000	−	1.73205i	−0.0323423	−	0.0560185i
$957$		0			0
$958$	−14.0000	−	24.2487i	−0.452319	−	0.783440i
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$		0			0
$961$	69.0000			2.22581
$962$	−7.50000	−	7.79423i	−0.241810	−	0.251296i
$963$	−54.0000			−1.74013
$964$	12.5000	−	21.6506i	0.402598	−	0.697320i
$965$		0			0
$966$		0			0
$967$	33.0000			1.06121			0.530604	−	0.847620i	$-0.321965\pi$
$967$	33.0000			1.06121			0.530604	+	0.847620i	$0.321965\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$		0			0
$970$		0			0
$971$	24.5000	+	42.4352i	0.786242	+	1.36181i	0.928254	+	0.371947i	$0.121310\pi$
$971$	24.5000	+	42.4352i	0.786242	+	1.36181i	−0.142012	+	0.989865i	$0.545357\pi$
$972$		0			0
$973$	7.50000	−	12.9904i	0.240439	−	0.416452i
$974$	19.0000			0.608799
$975$		0			0
$976$	−14.0000			−0.448129
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	−0.991618	−	0.129205i	$-0.958757\pi$
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	0.607704	+	0.794164i	$0.292091\pi$
$978$		0			0
$979$	1.50000	+	2.59808i	0.0479402	+	0.0830349i
$980$		0			0
$981$	−3.00000	−	5.19615i	−0.0957826	−	0.165900i
$982$	−21.5000	−	37.2391i	−0.686093	−	1.18835i
$983$	3.00000			0.0956851			0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000			0.0956851			0.0478426	+	0.998855i	$0.484765\pi$
$984$		0			0
$985$		0			0
$986$	−16.0000	+	27.7128i	−0.509544	+	0.882556i
$987$		0			0
$988$	−7.00000	+	24.2487i	−0.222700	+	0.771454i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	5.00000	−	8.66025i	0.158830	−	0.275102i	−0.775617	−	0.631204i	$-0.782561\pi$
$991$	5.00000	−	8.66025i	0.158830	−	0.275102i	0.934447	+	0.356102i	$0.115894\pi$
$992$	−5.00000	−	8.66025i	−0.158750	−	0.274963i
$993$		0			0
$994$	9.00000	+	15.5885i	0.285463	+	0.494436i
$995$		0			0
$996$		0			0
$997$	−5.50000	−	9.52628i	−0.174187	−	0.301700i	0.765693	−	0.643206i	$-0.222396\pi$
$997$	−5.50000	−	9.52628i	−0.174187	−	0.301700i	−0.939880	+	0.341506i	$0.889063\pi$
$998$	−2.00000	+	3.46410i	−0.0633089	+	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.e.b.451.1		2
5.2	odd	4		650.2.o.d.399.2		4
5.3	odd	4		650.2.o.d.399.1		4
5.4	even	2		130.2.e.a.61.1	✓	2
13.3	even	3	inner	650.2.e.b.601.1		2
13.4	even	6		8450.2.a.q.1.1		1
13.9	even	3		8450.2.a.g.1.1		1
15.14	odd	2		1170.2.i.i.451.1		2
20.19	odd	2		1040.2.q.h.321.1		2
65.3	odd	12		650.2.o.d.549.2		4
65.4	even	6		1690.2.a.c.1.1		1
65.9	even	6		1690.2.a.h.1.1		1
65.19	odd	12		1690.2.d.c.1351.1		2
65.24	odd	12		1690.2.l.e.361.2		4
65.29	even	6		130.2.e.a.81.1	yes	2
65.34	odd	4		1690.2.l.e.1161.1		4
65.42	odd	12		650.2.o.d.549.1		4
65.44	odd	4		1690.2.l.e.1161.2		4
65.49	even	6		1690.2.e.h.991.1		2
65.54	odd	12		1690.2.l.e.361.1		4
65.59	odd	12		1690.2.d.c.1351.2		2
65.64	even	2		1690.2.e.h.191.1		2
195.29	odd	6		1170.2.i.i.991.1		2
260.159	odd	6		1040.2.q.h.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.a.61.1	✓	2	5.4	even	2
130.2.e.a.81.1	yes	2	65.29	even	6
650.2.e.b.451.1		2	1.1	even	1	trivial
650.2.e.b.601.1		2	13.3	even	3	inner
650.2.o.d.399.1		4	5.3	odd	4
650.2.o.d.399.2		4	5.2	odd	4
650.2.o.d.549.1		4	65.42	odd	12
650.2.o.d.549.2		4	65.3	odd	12
1040.2.q.h.81.1		2	260.159	odd	6
1040.2.q.h.321.1		2	20.19	odd	2
1170.2.i.i.451.1		2	15.14	odd	2
1170.2.i.i.991.1		2	195.29	odd	6
1690.2.a.c.1.1		1	65.4	even	6
1690.2.a.h.1.1		1	65.9	even	6
1690.2.d.c.1351.1		2	65.19	odd	12
1690.2.d.c.1351.2		2	65.59	odd	12
1690.2.e.h.191.1		2	65.64	even	2
1690.2.e.h.991.1		2	65.49	even	6
1690.2.l.e.361.1		4	65.54	odd	12
1690.2.l.e.361.2		4	65.24	odd	12
1690.2.l.e.1161.1		4	65.34	odd	4
1690.2.l.e.1161.2		4	65.44	odd	4
8450.2.a.g.1.1		1	13.9	even	3
8450.2.a.q.1.1		1	13.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +(3.50000 - 0.866025i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +3.00000 q^{18} +(-3.50000 - 6.06218i) q^{19} +(-1.50000 - 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.00000 - 3.46410i) q^{26} +(-1.50000 + 2.59808i) q^{28} +(4.00000 - 6.92820i) q^{29} -10.0000 q^{31} +(0.500000 + 0.866025i) q^{32} -4.00000 q^{34} +(1.50000 - 2.59808i) q^{36} +(1.50000 - 2.59808i) q^{37} -7.00000 q^{38} +(1.00000 - 1.73205i) q^{41} +(3.00000 + 5.19615i) q^{43} -3.00000 q^{44} +(2.00000 + 3.46410i) q^{46} +1.00000 q^{47} +(-1.00000 + 1.73205i) q^{49} +(-2.50000 - 2.59808i) q^{52} +9.00000 q^{53} +(1.50000 + 2.59808i) q^{56} +(-4.00000 - 6.92820i) q^{58} +(2.00000 + 3.46410i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-5.00000 + 8.66025i) q^{62} +(4.50000 - 7.79423i) q^{63} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -4.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} +(-3.50000 + 6.06218i) q^{76} -9.00000 q^{77} +10.0000 q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.00000 - 1.73205i) q^{82} +6.00000 q^{86} +(-1.50000 + 2.59808i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(-7.50000 - 7.79423i) q^{91} +4.00000 q^{92} +(0.500000 - 0.866025i) q^{94} +(8.00000 + 13.8564i) q^{97} +(1.00000 + 1.73205i) q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 3 q^{7} - 2 q^{8} + 3 q^{9} + 3 q^{11} + 7 q^{13} - 6 q^{14} - q^{16} - 4 q^{17} + 6 q^{18} - 7 q^{19} - 3 q^{22} - 4 q^{23} + 2 q^{26} - 3 q^{28} + 8 q^{29} - 20 q^{31} + q^{32}+ \cdots + 18 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^4 - 3 * q^7 - 2 * q^8 + 3 * q^9 + 3 * q^11 + 7 * q^13 - 6 * q^14 - q^16 - 4 * q^17 + 6 * q^18 - 7 * q^19 - 3 * q^22 - 4 * q^23 + 2 * q^26 - 3 * q^28 + 8 * q^29 - 20 * q^31 + q^32 - 8 * q^34 + 3 * q^36 + 3 * q^37 - 14 * q^38 + 2 * q^41 + 6 * q^43 - 6 * q^44 + 4 * q^46 + 2 * q^47 - 2 * q^49 - 5 * q^52 + 18 * q^53 + 3 * q^56 - 8 * q^58 + 4 * q^59 + 14 * q^61 - 10 * q^62 + 9 * q^63 + 2 * q^64 + 4 * q^67 - 4 * q^68 - 6 * q^71 - 3 * q^72 - 8 * q^73 - 3 * q^74 - 7 * q^76 - 18 * q^77 + 20 * q^79 - 9 * q^81 - 2 * q^82 + 12 * q^86 - 3 * q^88 - q^89 - 15 * q^91 + 8 * q^92 + q^94 + 16 * q^97 + 2 * q^98 + 18 * q^99

Introduction

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