LMFDB - Embedded newform 950.2.j.c.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.00000i q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.00000i q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} -1.00000 q^{11} +(1.73205 + 1.00000i) q^{13} +(2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 1.50000i) q^{17} +3.00000i q^{18} +(-4.00000 + 1.73205i) q^{19} +(-0.866025 + 0.500000i) q^{22} +(3.46410 + 2.00000i) q^{23} +2.00000 q^{26} +(3.46410 + 2.00000i) q^{28} +(-3.00000 + 5.19615i) q^{29} -2.00000 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(1.50000 + 2.59808i) q^{36} -2.00000i q^{37} +(-2.59808 + 3.50000i) q^{38} +(1.50000 + 2.59808i) q^{41} +(10.3923 - 6.00000i) q^{43} +(-0.500000 + 0.866025i) q^{44} +4.00000 q^{46} +(5.19615 + 3.00000i) q^{47} -9.00000 q^{49} +(1.73205 - 1.00000i) q^{52} +(-3.46410 - 2.00000i) q^{53} +4.00000 q^{56} +6.00000i q^{58} +(4.50000 + 7.79423i) q^{59} +(6.00000 - 10.3923i) q^{61} +(-1.73205 + 1.00000i) q^{62} +(-10.3923 - 6.00000i) q^{63} -1.00000 q^{64} +(12.9904 + 7.50000i) q^{67} +3.00000i q^{68} +(-3.00000 - 5.19615i) q^{71} +(2.59808 + 1.50000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 4.33013i) q^{76} -4.00000i q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 1.50000i) q^{82} +4.00000i q^{83} +(6.00000 - 10.3923i) q^{86} +1.00000i q^{88} +(-0.500000 + 0.866025i) q^{89} +(-4.00000 + 6.92820i) q^{91} +(3.46410 - 2.00000i) q^{92} +6.00000 q^{94} +(0.866025 - 0.500000i) q^{97} +(-7.79423 + 4.50000i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 6 * q^9	$ 4 q + 2 q^{4} - 6 q^{9} - 4 q^{11} + 8 q^{14} - 2 q^{16} - 16 q^{19} + 8 q^{26} - 12 q^{29} - 8 q^{31} - 6 q^{34} + 6 q^{36} + 6 q^{41} - 2 q^{44} + 16 q^{46} - 36 q^{49} + 16 q^{56} + 18 q^{59} + 24 q^{61} - 4 q^{64} - 12 q^{71} - 4 q^{74} - 2 q^{76} - 28 q^{79} - 18 q^{81} + 24 q^{86} - 2 q^{89} - 16 q^{91} + 24 q^{94} + 6 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^9 - 4 * q^11 + 8 * q^14 - 2 * q^16 - 16 * q^19 + 8 * q^26 - 12 * q^29 - 8 * q^31 - 6 * q^34 + 6 * q^36 + 6 * q^41 - 2 * q^44 + 16 * q^46 - 36 * q^49 + 16 * q^56 + 18 * q^59 + 24 * q^61 - 4 * q^64 - 12 * q^71 - 4 * q^74 - 2 * q^76 - 28 * q^79 - 18 * q^81 + 24 * q^86 - 2 * q^89 - 16 * q^91 + 24 * q^94 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$3$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			4.00000i			1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$			4.00000i			1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$		0			0
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	0.720577	−	0.693375i	$-0.243877\pi$
$13$	1.73205	+	1.00000i	0.480384	+	0.277350i	−0.240192	+	0.970725i	$0.577210\pi$
$14$	2.00000	+	3.46410i	0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	−0.780801	−	0.624780i	$-0.785189\pi$
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	0.150675	+	0.988583i	$0.451855\pi$
$18$			3.00000i			0.707107i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$		0			0
$21$		0			0
$22$	−0.866025	+	0.500000i	−0.184637	+	0.106600i
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	0.815604	−	0.578610i	$-0.196405\pi$
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	−0.0932891	+	0.995639i	$0.529738\pi$
$24$		0			0
$25$		0			0
$26$	2.00000			0.392232
$27$		0			0
$28$	3.46410	+	2.00000i	0.654654	+	0.377964i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	−2.59808	+	3.50000i	−0.421464	+	0.567775i
$39$		0			0
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	10.3923	−	6.00000i	1.58481	−	0.914991i	0.590669	−	0.806914i	$-0.298864\pi$
$43$	10.3923	−	6.00000i	1.58481	−	0.914991i	0.994142	−	0.108078i	$-0.0344695\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	4.00000			0.589768
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	0.828554	−	0.559908i	$-0.189164\pi$
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	−0.0706177	+	0.997503i	$0.522497\pi$
$48$		0			0
$49$	−9.00000			−1.28571
$50$		0			0
$51$		0			0
$52$	1.73205	−	1.00000i	0.240192	−	0.138675i
$53$	−3.46410	−	2.00000i	−0.475831	−	0.274721i	0.242846	−	0.970065i	$-0.421919\pi$
$53$	−3.46410	−	2.00000i	−0.475831	−	0.274721i	−0.718677	+	0.695344i	$0.755252\pi$
$54$		0			0
$55$		0			0
$56$	4.00000			0.534522
$57$		0			0
$58$			6.00000i			0.787839i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		0			0
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	−0.170305	−	0.985391i	$-0.554475\pi$
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	0.938527	−	0.345207i	$-0.112191\pi$
$62$	−1.73205	+	1.00000i	−0.219971	+	0.127000i
$63$	−10.3923	−	6.00000i	−1.30931	−	0.755929i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	12.9904	+	7.50000i	1.58703	+	0.916271i	0.993793	+	0.111241i	$0.0354825\pi$
$67$	12.9904	+	7.50000i	1.58703	+	0.916271i	0.593234	+	0.805030i	$0.297851\pi$
$68$			3.00000i			0.363803i
$69$		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	$0.949205\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.101361	−	0.994850i	$-0.467680\pi$
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.912245	+	0.409644i	$0.134347\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$	−0.500000	+	4.33013i	−0.0573539	+	0.496700i
$77$		−	4.00000i		−	0.455842i
$78$		0			0
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	−0.927457	−	0.373930i	$-0.878010\pi$
$79$	−7.00000	−	12.1244i	−0.787562	−	1.36410i	0.139895	−	0.990166i	$-0.455323\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.59808	+	1.50000i	0.286910	+	0.165647i
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$		0			0
$86$	6.00000	−	10.3923i	0.646997	−	1.12063i
$87$		0			0
$88$			1.00000i			0.106600i
$89$	−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
$91$	−4.00000	+	6.92820i	−0.419314	+	0.726273i
$92$	3.46410	−	2.00000i	0.361158	−	0.208514i
$93$		0			0
$94$	6.00000			0.618853
$95$		0			0
$96$		0			0
$97$	0.866025	−	0.500000i	0.0879316	−	0.0507673i	−0.455389	−	0.890292i	$-0.650500\pi$
$97$	0.866025	−	0.500000i	0.0879316	−	0.0507673i	0.543321	+	0.839525i	$0.317167\pi$
$98$	−7.79423	+	4.50000i	−0.787336	+	0.454569i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$		−	4.00000i		−	0.394132i	−0.980390	−	0.197066i	$-0.936859\pi$
$103$		−	4.00000i		−	0.394132i	0.980390	−	0.197066i	$-0.0631413\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	−4.00000			−0.388514
$107$			5.00000i			0.483368i	0.970355	+	0.241684i	$0.0776998\pi$
$107$			5.00000i			0.483368i	−0.970355	+	0.241684i	$0.922300\pi$
$108$		0			0
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$		0			0
$111$		0			0
$112$	3.46410	−	2.00000i	0.327327	−	0.188982i
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$		0			0
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−5.19615	+	3.00000i	−0.480384	+	0.277350i
$118$	7.79423	+	4.50000i	0.717517	+	0.414259i
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	−10.0000			−0.909091
$122$		−	12.0000i		−	1.08643i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$	−12.0000			−1.06904
$127$	−5.19615	−	3.00000i	−0.461084	−	0.266207i	0.251416	−	0.967879i	$-0.419104\pi$
$127$	−5.19615	−	3.00000i	−0.461084	−	0.266207i	−0.712500	+	0.701672i	$0.752437\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	−3.50000	−	6.06218i	−0.305796	−	0.529655i	0.671642	−	0.740876i	$-0.265589\pi$
$131$	−3.50000	−	6.06218i	−0.305796	−	0.529655i	−0.977438	+	0.211221i	$0.932256\pi$
$132$		0			0
$133$	−6.92820	−	16.0000i	−0.600751	−	1.38738i
$134$	15.0000			1.29580
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.985577	+	0.169226i	$0.945873\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$	−5.19615	−	3.00000i	−0.436051	−	0.251754i
$143$	−1.73205	−	1.00000i	−0.144841	−	0.0836242i
$144$	3.00000			0.250000
$145$		0			0
$146$	5.00000	−	8.66025i	0.413803	−	0.716728i
$147$		0			0
$148$	−1.73205	−	1.00000i	−0.142374	−	0.0821995i
$149$	−8.00000	−	13.8564i	−0.655386	−	1.13516i	−0.981797	−	0.189933i	$-0.939173\pi$
$149$	−8.00000	−	13.8564i	−0.655386	−	1.13516i	0.326411	−	0.945228i	$-0.394160\pi$
$150$		0			0
$151$	14.0000			1.13930			0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000			1.13930			0.569652	+	0.821886i	$0.307078\pi$
$152$	1.73205	+	4.00000i	0.140488	+	0.324443i
$153$		−	9.00000i		−	0.727607i
$154$	−2.00000	−	3.46410i	−0.161165	−	0.279145i
$155$		0			0
$156$		0			0
$157$	5.19615	−	3.00000i	0.414698	−	0.239426i	−0.278108	−	0.960550i	$-0.589707\pi$
$157$	5.19615	−	3.00000i	0.414698	−	0.239426i	0.692806	+	0.721124i	$0.256374\pi$
$158$	−12.1244	−	7.00000i	−0.964562	−	0.556890i
$159$		0			0
$160$		0			0
$161$	−8.00000	+	13.8564i	−0.630488	+	1.09204i
$162$	−7.79423	−	4.50000i	−0.612372	−	0.353553i
$163$		−	1.00000i		−	0.0783260i	−0.999233	−	0.0391630i	$-0.987531\pi$
$163$		−	1.00000i		−	0.0783260i	0.999233	−	0.0391630i	$-0.0124692\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	2.00000	+	3.46410i	0.155230	+	0.268866i
$167$	6.92820	+	4.00000i	0.536120	+	0.309529i	0.743505	−	0.668730i	$-0.233162\pi$
$167$	6.92820	+	4.00000i	0.536120	+	0.309529i	−0.207385	+	0.978259i	$0.566495\pi$
$168$		0			0
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$	1.50000	−	12.9904i	0.114708	−	0.993399i
$172$		−	12.0000i		−	0.914991i
$173$	−3.46410	+	2.00000i	−0.263371	+	0.152057i	−0.625871	−	0.779926i	$-0.715256\pi$
$173$	−3.46410	+	2.00000i	−0.263371	+	0.152057i	0.362500	+	0.931984i	$0.381923\pi$
$174$		0			0
$175$		0			0
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		0			0
$178$			1.00000i			0.0749532i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$		0			0
$181$	−7.00000	+	12.1244i	−0.520306	+	0.901196i	0.479415	+	0.877588i	$0.340849\pi$
$181$	−7.00000	+	12.1244i	−0.520306	+	0.901196i	−0.999721	+	0.0236082i	$0.992485\pi$
$182$			8.00000i			0.592999i
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$		0			0
$186$		0			0
$187$	2.59808	−	1.50000i	0.189990	−	0.109691i
$188$	5.19615	−	3.00000i	0.378968	−	0.218797i
$189$		0			0
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	−0.116289	−	0.993215i	$-0.537100\pi$
$193$	9.52628	−	5.50000i	0.685717	−	0.395899i	0.802005	+	0.597317i	$0.203766\pi$
$194$	0.500000	−	0.866025i	0.0358979	−	0.0621770i
$195$		0			0
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$		−	3.00000i		−	0.213201i
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	−0.347879	−	0.937539i	$-0.613098\pi$
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	0.985873	−	0.167497i	$-0.0535685\pi$
$200$		0			0
$201$		0			0
$202$			10.0000i			0.703598i
$203$	−20.7846	−	12.0000i	−1.45879	−	0.842235i
$204$		0			0
$205$		0			0
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$	−10.3923	+	6.00000i	−0.722315	+	0.417029i
$208$		−	2.00000i		−	0.138675i
$209$	4.00000	−	1.73205i	0.276686	−	0.119808i
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	−3.46410	+	2.00000i	−0.237915	+	0.137361i
$213$		0			0
$214$	2.50000	+	4.33013i	0.170896	+	0.296001i
$215$		0			0
$216$		0			0
$217$		−	8.00000i		−	0.543075i
$218$	8.66025	+	5.00000i	0.586546	+	0.338643i
$219$		0			0
$220$		0			0
$221$	−6.00000			−0.403604
$222$		0			0
$223$	−19.0526	+	11.0000i	−1.27585	+	0.736614i	−0.976083	−	0.217397i	$-0.930243\pi$
$223$	−19.0526	+	11.0000i	−1.27585	+	0.736614i	−0.299770	+	0.954011i	$0.596910\pi$
$224$	2.00000	−	3.46410i	0.133631	−	0.231455i
$225$		0			0
$226$	9.00000	+	15.5885i	0.598671	+	1.03693i
$227$		−	19.0000i		−	1.26107i	−0.776159	−	0.630537i	$-0.782835\pi$
$227$		−	19.0000i		−	1.26107i	0.776159	−	0.630537i	$-0.217165\pi$
$228$		0			0
$229$	18.0000			1.18947			0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000			1.18947			0.594737	+	0.803921i	$0.297256\pi$
$230$		0			0
$231$		0			0
$232$	5.19615	+	3.00000i	0.341144	+	0.196960i
$233$	14.7224	−	8.50000i	0.964499	−	0.556854i	0.0669439	−	0.997757i	$-0.478675\pi$
$233$	14.7224	−	8.50000i	0.964499	−	0.556854i	0.897555	+	0.440903i	$0.145342\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$		0			0
$236$	9.00000			0.585850
$237$		0			0
$238$	−10.3923	−	6.00000i	−0.673633	−	0.388922i
$239$	14.0000			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$240$		0			0
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	0.299704	+	0.954032i	$0.403112\pi$
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	−0.976068	+	0.217465i	$0.930221\pi$
$242$	−8.66025	+	5.00000i	−0.556702	+	0.321412i
$243$		0			0
$244$	−6.00000	−	10.3923i	−0.384111	−	0.665299i
$245$		0			0
$246$		0			0
$247$	−8.66025	−	1.00000i	−0.551039	−	0.0636285i
$248$			2.00000i			0.127000i
$249$		0			0
$250$		0			0
$251$	13.5000	−	23.3827i	0.852112	−	1.47590i	−0.0271858	−	0.999630i	$-0.508655\pi$
$251$	13.5000	−	23.3827i	0.852112	−	1.47590i	0.879298	−	0.476272i	$-0.158012\pi$
$252$	−10.3923	+	6.00000i	−0.654654	+	0.377964i
$253$	−3.46410	−	2.00000i	−0.217786	−	0.125739i
$254$	−6.00000			−0.376473
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−26.8468	−	15.5000i	−1.67466	−	0.966863i	−0.964975	−	0.262341i	$-0.915506\pi$
$257$	−26.8468	−	15.5000i	−1.67466	−	0.966863i	−0.709681	−	0.704523i	$-0.751161\pi$
$258$		0			0
$259$	8.00000			0.497096
$260$		0			0
$261$	−9.00000	−	15.5885i	−0.557086	−	0.964901i
$262$	−6.06218	−	3.50000i	−0.374523	−	0.216231i
$263$	8.66025	−	5.00000i	0.534014	−	0.308313i	−0.208635	−	0.977993i	$-0.566902\pi$
$263$	8.66025	−	5.00000i	0.534014	−	0.308313i	0.742650	+	0.669680i	$0.233569\pi$
$264$		0			0
$265$		0			0
$266$	−14.0000	−	10.3923i	−0.858395	−	0.637193i
$267$		0			0
$268$	12.9904	−	7.50000i	0.793514	−	0.458135i
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	0.961817	−	0.273692i	$-0.0882449\pi$
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	−0.717933	+	0.696112i	$0.754912\pi$
$270$		0			0
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479155\pi$
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	−0.624218	+	0.781251i	$0.714582\pi$
$272$	2.59808	+	1.50000i	0.157532	+	0.0909509i
$273$		0			0
$274$	−18.0000			−1.08742
$275$		0			0
$276$		0			0
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$			5.00000i			0.299880i
$279$	3.00000	−	5.19615i	0.179605	−	0.311086i
$280$		0			0
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$		0			0
$283$	−0.866025	+	0.500000i	−0.0514799	+	0.0297219i	−0.525519	−	0.850782i	$-0.676129\pi$
$283$	−0.866025	+	0.500000i	−0.0514799	+	0.0297219i	0.474039	+	0.880504i	$0.342796\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−2.00000			−0.118262
$287$	−10.3923	+	6.00000i	−0.613438	+	0.354169i
$288$	2.59808	−	1.50000i	0.153093	−	0.0883883i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		−	10.0000i		−	0.585206i
$293$			24.0000i			1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$293$			24.0000i			1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$		0			0
$295$		0			0
$296$	−2.00000			−0.116248
$297$		0			0
$298$	−13.8564	−	8.00000i	−0.802680	−	0.463428i
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$		0			0
$301$	24.0000	+	41.5692i	1.38334	+	2.39601i
$302$	12.1244	−	7.00000i	0.697678	−	0.402805i
$303$		0			0
$304$	3.50000	+	2.59808i	0.200739	+	0.149010i
$305$		0			0
$306$	−4.50000	−	7.79423i	−0.257248	−	0.445566i
$307$	3.46410	−	2.00000i	0.197707	−	0.114146i	−0.397879	−	0.917438i	$-0.630253\pi$
$307$	3.46410	−	2.00000i	0.197707	−	0.114146i	0.595585	+	0.803292i	$0.296920\pi$
$308$	−3.46410	−	2.00000i	−0.197386	−	0.113961i
$309$		0			0
$310$		0			0
$311$	−20.0000			−1.13410			−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000			−1.13410			−0.567048	+	0.823685i	$0.691915\pi$
$312$		0			0
$313$	4.33013	+	2.50000i	0.244753	+	0.141308i	0.617359	−	0.786681i	$-0.288202\pi$
$313$	4.33013	+	2.50000i	0.244753	+	0.141308i	−0.372606	+	0.927990i	$0.621536\pi$
$314$	3.00000	−	5.19615i	0.169300	−	0.293236i
$315$		0			0
$316$	−14.0000			−0.787562
$317$	−10.3923	−	6.00000i	−0.583690	−	0.336994i	0.178908	−	0.983866i	$-0.442743\pi$
$317$	−10.3923	−	6.00000i	−0.583690	−	0.336994i	−0.762598	+	0.646872i	$0.776077\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$		0			0
$321$		0			0
$322$			16.0000i			0.891645i
$323$	7.79423	−	10.5000i	0.433682	−	0.584236i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	−0.500000	−	0.866025i	−0.0276924	−	0.0479647i
$327$		0			0
$328$	2.59808	−	1.50000i	0.143455	−	0.0828236i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	3.46410	+	2.00000i	0.190117	+	0.109764i
$333$	5.19615	+	3.00000i	0.284747	+	0.164399i
$334$	8.00000			0.437741
$335$		0			0
$336$		0			0
$337$	−7.79423	+	4.50000i	−0.424579	+	0.245131i	−0.697034	−	0.717038i	$-0.745498\pi$
$337$	−7.79423	+	4.50000i	−0.424579	+	0.245131i	0.272456	+	0.962168i	$0.412164\pi$
$338$	−7.79423	−	4.50000i	−0.423950	−	0.244768i
$339$		0			0
$340$		0			0
$341$	2.00000			0.108306
$342$	−5.19615	−	12.0000i	−0.280976	−	0.648886i
$343$		−	8.00000i		−	0.431959i
$344$	−6.00000	−	10.3923i	−0.323498	−	0.560316i
$345$		0			0
$346$	−2.00000	+	3.46410i	−0.107521	+	0.186231i
$347$	23.3827	−	13.5000i	1.25525	−	0.724718i	0.283101	−	0.959090i	$-0.408637\pi$
$347$	23.3827	−	13.5000i	1.25525	−	0.724718i	0.972147	+	0.234372i	$0.0753034\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$	0.866025	+	0.500000i	0.0461593	+	0.0266501i
$353$			17.0000i			0.904819i	0.891810	+	0.452409i	$0.149435\pi$
$353$			17.0000i			0.904819i	−0.891810	+	0.452409i	$0.850565\pi$
$354$		0			0
$355$		0			0
$356$	0.500000	+	0.866025i	0.0264999	+	0.0458993i
$357$		0			0
$358$	17.3205	−	10.0000i	0.915417	−	0.528516i
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$			14.0000i			0.735824i
$363$		0			0
$364$	4.00000	+	6.92820i	0.209657	+	0.363137i
$365$		0			0
$366$		0			0
$367$	29.4449	+	17.0000i	1.53701	+	0.887393i	0.999012	+	0.0444464i	$0.0141524\pi$
$367$	29.4449	+	17.0000i	1.53701	+	0.887393i	0.537998	+	0.842946i	$0.319181\pi$
$368$		−	4.00000i		−	0.208514i
$369$	−9.00000			−0.468521
$370$		0			0
$371$	8.00000	−	13.8564i	0.415339	−	0.719389i
$372$		0			0
$373$			38.0000i			1.96757i	0.179364	+	0.983783i	$0.442596\pi$
$373$			38.0000i			1.96757i	−0.179364	+	0.983783i	$0.557404\pi$
$374$	1.50000	−	2.59808i	0.0775632	−	0.134343i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	−10.3923	+	6.00000i	−0.535231	+	0.309016i
$378$		0			0
$379$	9.00000			0.462299			0.231149	−	0.972918i	$-0.425751\pi$
$379$	9.00000			0.462299			0.231149	+	0.972918i	$0.425751\pi$
$380$		0			0
$381$		0			0
$382$	10.3923	−	6.00000i	0.531717	−	0.306987i
$383$	−12.1244	+	7.00000i	−0.619526	+	0.357683i	−0.776684	−	0.629890i	$-0.783100\pi$
$383$	−12.1244	+	7.00000i	−0.619526	+	0.357683i	0.157159	+	0.987573i	$0.449767\pi$
$384$		0			0
$385$		0			0
$386$	5.50000	−	9.52628i	0.279943	−	0.484875i
$387$			36.0000i			1.82998i
$388$		−	1.00000i		−	0.0507673i
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	−0.839561	−	0.543266i	$-0.817187\pi$
$389$	1.00000	−	1.73205i	0.0507020	−	0.0878185i	0.890263	+	0.455448i	$0.150521\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$			9.00000i			0.454569i
$393$		0			0
$394$	4.00000	+	6.92820i	0.201517	+	0.349038i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	32.9090	−	19.0000i	1.65165	−	0.953583i	0.675261	−	0.737579i	$-0.264031\pi$
$397$	32.9090	−	19.0000i	1.65165	−	0.953583i	0.976392	−	0.216004i	$-0.0693024\pi$
$398$		−	18.0000i		−	0.902258i
$399$		0			0
$400$		0			0
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	−0.902703	−	0.430263i	$-0.858421\pi$
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	0.0787327	−	0.996896i	$-0.474913\pi$
$402$		0			0
$403$	−3.46410	−	2.00000i	−0.172559	−	0.0996271i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	−24.0000			−1.19110
$407$			2.00000i			0.0991363i
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$		0			0
$412$	−3.46410	−	2.00000i	−0.170664	−	0.0985329i
$413$	−31.1769	+	18.0000i	−1.53412	+	0.885722i
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	2.59808	−	3.50000i	0.127076	−	0.171191i
$419$	−29.0000			−1.41674			−0.708371	−	0.705840i	$-0.750570\pi$
$419$	−29.0000			−1.41674			−0.708371	+	0.705840i	$0.750570\pi$
$420$		0			0
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	0.718076	−	0.695965i	$-0.245023\pi$
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	−0.961761	+	0.273890i	$0.911690\pi$
$422$	4.33013	+	2.50000i	0.210787	+	0.121698i
$423$	−15.5885	+	9.00000i	−0.757937	+	0.437595i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$		0			0
$426$		0			0
$427$	41.5692	+	24.0000i	2.01168	+	1.16144i
$428$	4.33013	+	2.50000i	0.209305	+	0.120842i
$429$		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
$433$	25.1147	+	14.5000i	1.20694	+	0.696826i	0.962089	−	0.272736i	$-0.0879285\pi$
$433$	25.1147	+	14.5000i	1.20694	+	0.696826i	0.244848	+	0.969561i	$0.421262\pi$
$434$	−4.00000	−	6.92820i	−0.192006	−	0.332564i
$435$		0			0
$436$	10.0000			0.478913
$437$	−17.3205	−	2.00000i	−0.828552	−	0.0956730i
$438$		0			0
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$	−5.19615	+	3.00000i	−0.247156	+	0.142695i
$443$	18.1865	+	10.5000i	0.864068	+	0.498870i	0.865373	−	0.501129i	$-0.167082\pi$
$443$	18.1865	+	10.5000i	0.864068	+	0.498870i	−0.00130426	+	0.999999i	$0.500415\pi$
$444$		0			0
$445$		0			0
$446$	−11.0000	+	19.0526i	−0.520865	+	0.902165i
$447$		0			0
$448$		−	4.00000i		−	0.188982i
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$		0			0
$451$	−1.50000	−	2.59808i	−0.0706322	−	0.122339i
$452$	15.5885	+	9.00000i	0.733219	+	0.423324i
$453$		0			0
$454$	−9.50000	−	16.4545i	−0.445857	−	0.772247i
$455$		0			0
$456$		0			0
$457$		−	14.0000i		−	0.654892i	−0.944870	−	0.327446i	$-0.893812\pi$
$457$		−	14.0000i		−	0.654892i	0.944870	−	0.327446i	$-0.106188\pi$
$458$	15.5885	−	9.00000i	0.728401	−	0.420542i
$459$		0			0
$460$		0			0
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	8.50000	−	14.7224i	0.393755	−	0.682003i
$467$		−	5.00000i		−	0.231372i	−0.993286	−	0.115686i	$-0.963093\pi$
$467$		−	5.00000i		−	0.231372i	0.993286	−	0.115686i	$-0.0369067\pi$
$468$			6.00000i			0.277350i
$469$	−30.0000	+	51.9615i	−1.38527	+	2.39936i
$470$		0			0
$471$		0			0
$472$	7.79423	−	4.50000i	0.358758	−	0.207129i
$473$	−10.3923	+	6.00000i	−0.477839	+	0.275880i
$474$		0			0
$475$		0			0
$476$	−12.0000			−0.550019
$477$	10.3923	−	6.00000i	0.475831	−	0.274721i
$478$	12.1244	−	7.00000i	0.554555	−	0.320173i
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$		0			0
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$			21.0000i			0.956524i
$483$		0			0
$484$	−5.00000	+	8.66025i	−0.227273	+	0.393648i
$485$		0			0
$486$		0			0
$487$		−	2.00000i		−	0.0906287i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$		−	2.00000i		−	0.0906287i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$	−10.3923	−	6.00000i	−0.470438	−	0.271607i
$489$		0			0
$490$		0			0
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$		0			0
$493$		−	18.0000i		−	0.810679i
$494$	−8.00000	+	3.46410i	−0.359937	+	0.155857i
$495$		0			0
$496$	1.00000	+	1.73205i	0.0449013	+	0.0777714i
$497$	20.7846	−	12.0000i	0.932317	−	0.538274i
$498$		0			0
$499$	−13.5000	−	23.3827i	−0.604343	−	1.04675i	−0.992155	−	0.125014i	$-0.960102\pi$
$499$	−13.5000	−	23.3827i	−0.604343	−	1.04675i	0.387812	−	0.921739i	$-0.373231\pi$
$500$		0			0
$501$		0			0
$502$		−	27.0000i		−	1.20507i
$503$	31.1769	+	18.0000i	1.39011	+	0.802580i	0.993327	−	0.115332i	$-0.0367932\pi$
$503$	31.1769	+	18.0000i	1.39011	+	0.802580i	0.396783	+	0.917912i	$0.370127\pi$
$504$	−6.00000	+	10.3923i	−0.267261	+	0.462910i
$505$		0			0
$506$	−4.00000			−0.177822
$507$		0			0
$508$	−5.19615	+	3.00000i	−0.230542	+	0.133103i
$509$	−11.0000	+	19.0526i	−0.487566	+	0.844490i	−0.999898	−	0.0142980i	$-0.995449\pi$
$509$	−11.0000	+	19.0526i	−0.487566	+	0.844490i	0.512331	+	0.858788i	$0.328782\pi$
$510$		0			0
$511$	20.0000	+	34.6410i	0.884748	+	1.53243i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−31.0000			−1.36735
$515$		0			0
$516$		0			0
$517$	−5.19615	−	3.00000i	−0.228527	−	0.131940i
$518$	6.92820	−	4.00000i	0.304408	−	0.175750i
$519$		0			0
$520$		0			0
$521$	45.0000			1.97149			0.985743	−	0.168259i	$-0.0538144\pi$
$521$	45.0000			1.97149			0.985743	+	0.168259i	$0.0538144\pi$
$522$	−15.5885	−	9.00000i	−0.682288	−	0.393919i
$523$	7.79423	+	4.50000i	0.340818	+	0.196771i	0.660634	−	0.750708i	$-0.270288\pi$
$523$	7.79423	+	4.50000i	0.340818	+	0.196771i	−0.319816	+	0.947480i	$0.603621\pi$
$524$	−7.00000			−0.305796
$525$		0			0
$526$	5.00000	−	8.66025i	0.218010	−	0.377605i
$527$	5.19615	−	3.00000i	0.226348	−	0.130682i
$528$		0			0
$529$	−3.50000	−	6.06218i	−0.152174	−	0.263573i
$530$		0			0
$531$	−27.0000			−1.17170
$532$	−17.3205	−	2.00000i	−0.750939	−	0.0867110i
$533$			6.00000i			0.259889i
$534$		0			0
$535$		0			0
$536$	7.50000	−	12.9904i	0.323951	−	0.561099i
$537$		0			0
$538$	6.92820	+	4.00000i	0.298696	+	0.172452i
$539$	9.00000			0.387657
$540$		0			0
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	−0.843728	−	0.536771i	$-0.819644\pi$
$541$	1.00000	−	1.73205i	0.0429934	−	0.0744667i	0.886721	+	0.462304i	$0.152977\pi$
$542$	10.3923	+	6.00000i	0.446388	+	0.257722i
$543$		0			0
$544$	3.00000			0.128624
$545$		0			0
$546$		0			0
$547$	6.06218	+	3.50000i	0.259200	+	0.149649i	0.623970	−	0.781449i	$-0.285519\pi$
$547$	6.06218	+	3.50000i	0.259200	+	0.149649i	−0.364770	+	0.931098i	$0.618852\pi$
$548$	−15.5885	+	9.00000i	−0.665906	+	0.384461i
$549$	18.0000	+	31.1769i	0.768221	+	1.33060i
$550$		0			0
$551$	3.00000	−	25.9808i	0.127804	−	1.10682i
$552$		0			0
$553$	48.4974	−	28.0000i	2.06232	−	1.19068i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	2.50000	+	4.33013i	0.106024	+	0.183638i
$557$	−31.1769	−	18.0000i	−1.32101	−	0.762684i	−0.337119	−	0.941462i	$-0.609452\pi$
$557$	−31.1769	−	18.0000i	−1.32101	−	0.762684i	−0.983890	+	0.178778i	$0.942786\pi$
$558$		−	6.00000i		−	0.254000i
$559$	24.0000			1.01509
$560$		0			0
$561$		0			0
$562$			15.0000i			0.632737i
$563$			31.0000i			1.30649i	0.757145	+	0.653247i	$0.226594\pi$
$563$			31.0000i			1.30649i	−0.757145	+	0.653247i	$0.773406\pi$
$564$		0			0
$565$		0			0
$566$	−0.500000	+	0.866025i	−0.0210166	+	0.0364018i
$567$	31.1769	−	18.0000i	1.30931	−	0.755929i
$568$	−5.19615	+	3.00000i	−0.218026	+	0.125877i
$569$	−45.0000			−1.88650			−0.943249	−	0.332086i	$-0.892248\pi$
$569$	−45.0000			−1.88650			−0.943249	+	0.332086i	$0.892248\pi$
$570$		0			0
$571$	3.00000			0.125546			0.0627730	−	0.998028i	$-0.480006\pi$
$571$	3.00000			0.125546			0.0627730	+	0.998028i	$0.480006\pi$
$572$	−1.73205	+	1.00000i	−0.0724207	+	0.0418121i
$573$		0			0
$574$	−6.00000	+	10.3923i	−0.250435	+	0.433766i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$		−	1.00000i		−	0.0416305i	−0.999783	−	0.0208153i	$-0.993374\pi$
$577$		−	1.00000i		−	0.0416305i	0.999783	−	0.0208153i	$-0.00662619\pi$
$578$			8.00000i			0.332756i
$579$		0			0
$580$		0			0
$581$	−16.0000			−0.663792
$582$		0			0
$583$	3.46410	+	2.00000i	0.143468	+	0.0828315i
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$		0			0
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$	−18.1865	+	10.5000i	−0.750639	+	0.433381i	−0.825925	−	0.563781i	$-0.809346\pi$
$587$	−18.1865	+	10.5000i	−0.750639	+	0.433381i	0.0752860	+	0.997162i	$0.476013\pi$
$588$		0			0
$589$	8.00000	−	3.46410i	0.329634	−	0.142736i
$590$		0			0
$591$		0			0
$592$	−1.73205	+	1.00000i	−0.0711868	+	0.0410997i
$593$	−28.5788	−	16.5000i	−1.17359	−	0.677574i	−0.219069	−	0.975709i	$-0.570302\pi$
$593$	−28.5788	−	16.5000i	−1.17359	−	0.677574i	−0.954524	+	0.298136i	$0.903635\pi$
$594$		0			0
$595$		0			0
$596$	−16.0000			−0.655386
$597$		0			0
$598$	6.92820	+	4.00000i	0.283315	+	0.163572i
$599$	−16.0000	+	27.7128i	−0.653742	+	1.13231i	0.328465	+	0.944516i	$0.393469\pi$
$599$	−16.0000	+	27.7128i	−0.653742	+	1.13231i	−0.982208	+	0.187799i	$0.939865\pi$
$600$		0			0
$601$	−18.0000			−0.734235			−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000			−0.734235			−0.367118	+	0.930175i	$0.619655\pi$
$602$	41.5692	+	24.0000i	1.69423	+	0.978167i
$603$	−38.9711	+	22.5000i	−1.58703	+	0.916271i
$604$	7.00000	−	12.1244i	0.284826	−	0.493333i
$605$		0			0
$606$		0			0
$607$			4.00000i			0.162355i	0.996700	+	0.0811775i	$0.0258681\pi$
$607$			4.00000i			0.162355i	−0.996700	+	0.0811775i	$0.974132\pi$
$608$	4.33013	+	0.500000i	0.175610	+	0.0202777i
$609$		0			0
$610$		0			0
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$	−7.79423	−	4.50000i	−0.315063	−	0.181902i
$613$	−13.8564	+	8.00000i	−0.559655	+	0.323117i	−0.753007	−	0.658012i	$-0.771397\pi$
$613$	−13.8564	+	8.00000i	−0.559655	+	0.323117i	0.193352	+	0.981129i	$0.438064\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		0			0
$616$	−4.00000			−0.161165
$617$	11.2583	+	6.50000i	0.453243	+	0.261680i	0.709199	−	0.705008i	$-0.249057\pi$
$617$	11.2583	+	6.50000i	0.453243	+	0.261680i	−0.255956	+	0.966689i	$0.582390\pi$
$618$		0			0
$619$	36.0000			1.44696			0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000			1.44696			0.723481	+	0.690344i	$0.242541\pi$
$620$		0			0
$621$		0			0
$622$	−17.3205	+	10.0000i	−0.694489	+	0.400963i
$623$	−3.46410	−	2.00000i	−0.138786	−	0.0801283i
$624$		0			0
$625$		0			0
$626$	5.00000			0.199840
$627$		0			0
$628$		−	6.00000i		−	0.239426i
$629$	3.00000	+	5.19615i	0.119618	+	0.207184i
$630$		0			0
$631$	2.00000	−	3.46410i	0.0796187	−	0.137904i	−0.823467	−	0.567365i	$-0.807963\pi$
$631$	2.00000	−	3.46410i	0.0796187	−	0.137904i	0.903085	+	0.429461i	$0.141296\pi$
$632$	−12.1244	+	7.00000i	−0.482281	+	0.278445i
$633$		0			0
$634$	−12.0000			−0.476581
$635$		0			0
$636$		0			0
$637$	−15.5885	−	9.00000i	−0.617637	−	0.356593i
$638$		−	6.00000i		−	0.237542i
$639$	18.0000			0.712069
$640$		0			0
$641$	−20.5000	−	35.5070i	−0.809701	−	1.40244i	−0.913071	−	0.407801i	$-0.866296\pi$
$641$	−20.5000	−	35.5070i	−0.809701	−	1.40244i	0.103370	−	0.994643i	$-0.467038\pi$
$642$		0			0
$643$	42.4352	−	24.5000i	1.67348	−	0.966186i	0.707818	−	0.706395i	$-0.249680\pi$
$643$	42.4352	−	24.5000i	1.67348	−	0.966186i	0.965665	−	0.259791i	$-0.0836535\pi$
$644$	8.00000	+	13.8564i	0.315244	+	0.546019i
$645$		0			0
$646$	1.50000	−	12.9904i	0.0590167	−	0.511100i
$647$			36.0000i			1.41531i	0.706560	+	0.707653i	$0.250246\pi$
$647$			36.0000i			1.41531i	−0.706560	+	0.707653i	$0.749754\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$		0			0
$651$		0			0
$652$	−0.866025	−	0.500000i	−0.0339162	−	0.0195815i
$653$		−	20.0000i		−	0.782660i	−0.920250	−	0.391330i	$-0.872015\pi$
$653$		−	20.0000i		−	0.782660i	0.920250	−	0.391330i	$-0.127985\pi$
$654$		0			0
$655$		0			0
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$			30.0000i			1.17041i
$658$			24.0000i			0.935617i
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$		0			0
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	0.411636	+	0.911348i	$0.364957\pi$
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	−0.995069	+	0.0991864i	$0.968376\pi$
$662$	17.3205	−	10.0000i	0.673181	−	0.388661i
$663$		0			0
$664$	4.00000			0.155230
$665$		0			0
$666$	6.00000			0.232495
$667$	−20.7846	+	12.0000i	−0.804783	+	0.464642i
$668$	6.92820	−	4.00000i	0.268060	−	0.154765i
$669$		0			0
$670$		0			0
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$		0			0
$673$		−	10.0000i		−	0.385472i	−0.981251	−	0.192736i	$-0.938264\pi$
$673$		−	10.0000i		−	0.385472i	0.981251	−	0.192736i	$-0.0617360\pi$
$674$	−4.50000	+	7.79423i	−0.173334	+	0.300222i
$675$		0			0
$676$	−9.00000			−0.346154
$677$			30.0000i			1.15299i	0.817099	+	0.576497i	$0.195581\pi$
$677$			30.0000i			1.15299i	−0.817099	+	0.576497i	$0.804419\pi$
$678$		0			0
$679$	2.00000	+	3.46410i	0.0767530	+	0.132940i
$680$		0			0
$681$		0			0
$682$	1.73205	−	1.00000i	0.0663237	−	0.0382920i
$683$		−	25.0000i		−	0.956598i	−0.878197	−	0.478299i	$-0.841253\pi$
$683$		−	25.0000i		−	0.956598i	0.878197	−	0.478299i	$-0.158747\pi$
$684$	−10.5000	−	7.79423i	−0.401478	−	0.298020i
$685$		0			0
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$		0			0
$688$	−10.3923	−	6.00000i	−0.396203	−	0.228748i
$689$	−4.00000	−	6.92820i	−0.152388	−	0.263944i
$690$		0			0
$691$	−27.0000			−1.02713			−0.513564	−	0.858051i	$-0.671675\pi$
$691$	−27.0000			−1.02713			−0.513564	+	0.858051i	$0.671675\pi$
$692$			4.00000i			0.152057i
$693$	10.3923	+	6.00000i	0.394771	+	0.227921i
$694$	13.5000	−	23.3827i	0.512453	−	0.887595i
$695$		0			0
$696$		0			0
$697$	−7.79423	−	4.50000i	−0.295227	−	0.170450i
$698$	−12.1244	+	7.00000i	−0.458914	+	0.264954i
$699$		0			0
$700$		0			0
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	0.998585	−	0.0531839i	$-0.0169370\pi$
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	−0.545351	+	0.838208i	$0.683604\pi$
$702$		0			0
$703$	3.46410	+	8.00000i	0.130651	+	0.301726i
$704$	1.00000			0.0376889
$705$		0			0
$706$	8.50000	+	14.7224i	0.319902	+	0.554086i
$707$	−34.6410	−	20.0000i	−1.30281	−	0.752177i
$708$		0			0
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	−0.614852	−	0.788642i	$-0.710784\pi$
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	0.990410	+	0.138157i	$0.0441178\pi$
$710$		0			0
$711$	42.0000			1.57512
$712$	0.866025	+	0.500000i	0.0324557	+	0.0187383i
$713$	−6.92820	−	4.00000i	−0.259463	−	0.149801i
$714$		0			0
$715$		0			0
$716$	10.0000	−	17.3205i	0.373718	−	0.647298i
$717$		0			0
$718$	8.66025	+	5.00000i	0.323198	+	0.186598i
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	0.998224	−	0.0595683i	$-0.0189724\pi$
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	−0.550700	+	0.834703i	$0.685639\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	4.33013	−	18.5000i	0.161151	−	0.688499i
$723$		0			0
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$		0			0
$726$		0			0
$727$	27.7128	−	16.0000i	1.02781	−	0.593407i	0.111454	−	0.993770i	$-0.464449\pi$
$727$	27.7128	−	16.0000i	1.02781	−	0.593407i	0.916357	+	0.400362i	$0.131116\pi$
$728$	6.92820	+	4.00000i	0.256776	+	0.148250i
$729$	27.0000			1.00000
$730$		0			0
$731$	−18.0000	+	31.1769i	−0.665754	+	1.15312i
$732$		0			0
$733$			24.0000i			0.886460i	0.896408	+	0.443230i	$0.146168\pi$
$733$			24.0000i			0.886460i	−0.896408	+	0.443230i	$0.853832\pi$
$734$	34.0000			1.25496
$735$		0			0
$736$	−2.00000	−	3.46410i	−0.0737210	−	0.127688i
$737$	−12.9904	−	7.50000i	−0.478507	−	0.276266i
$738$	−7.79423	+	4.50000i	−0.286910	+	0.165647i
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$		0			0
$741$		0			0
$742$		−	16.0000i		−	0.587378i
$743$	25.9808	−	15.0000i	0.953142	−	0.550297i	0.0590862	−	0.998253i	$-0.481181\pi$
$743$	25.9808	−	15.0000i	0.953142	−	0.550297i	0.894055	+	0.447956i	$0.147848\pi$
$744$		0			0
$745$		0			0
$746$	19.0000	+	32.9090i	0.695639	+	1.20488i
$747$	−10.3923	−	6.00000i	−0.380235	−	0.219529i
$748$		−	3.00000i		−	0.109691i
$749$	−20.0000			−0.730784
$750$		0			0
$751$	22.0000	−	38.1051i	0.802791	−	1.39048i	−0.114981	−	0.993368i	$-0.536681\pi$
$751$	22.0000	−	38.1051i	0.802791	−	1.39048i	0.917772	−	0.397108i	$-0.129986\pi$
$752$		−	6.00000i		−	0.218797i
$753$		0			0
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$		0			0
$756$		0			0
$757$	−5.19615	+	3.00000i	−0.188857	+	0.109037i	−0.591448	−	0.806343i	$-0.701443\pi$
$757$	−5.19615	+	3.00000i	−0.188857	+	0.109037i	0.402590	+	0.915380i	$0.368110\pi$
$758$	7.79423	−	4.50000i	0.283099	−	0.163447i
$759$		0			0
$760$		0			0
$761$	17.0000			0.616250			0.308125	−	0.951346i	$-0.400299\pi$
$761$	17.0000			0.616250			0.308125	+	0.951346i	$0.400299\pi$
$762$		0			0
$763$	−34.6410	+	20.0000i	−1.25409	+	0.724049i
$764$	6.00000	−	10.3923i	0.217072	−	0.375980i
$765$		0			0
$766$	−7.00000	+	12.1244i	−0.252920	+	0.438071i
$767$			18.0000i			0.649942i
$768$		0			0
$769$	12.5000	−	21.6506i	0.450762	−	0.780742i	−0.547672	−	0.836693i	$-0.684486\pi$
$769$	12.5000	−	21.6506i	0.450762	−	0.780742i	0.998434	+	0.0559513i	$0.0178191\pi$
$770$		0			0
$771$		0			0
$772$		−	11.0000i		−	0.395899i
$773$	−20.7846	−	12.0000i	−0.747570	−	0.431610i	0.0772449	−	0.997012i	$-0.475388\pi$
$773$	−20.7846	−	12.0000i	−0.747570	−	0.431610i	−0.824815	+	0.565402i	$0.808721\pi$
$774$	18.0000	+	31.1769i	0.646997	+	1.12063i
$775$		0			0
$776$	−0.500000	−	0.866025i	−0.0179490	−	0.0310885i
$777$		0			0
$778$		−	2.00000i		−	0.0717035i
$779$	−10.5000	−	7.79423i	−0.376202	−	0.279257i
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	−10.3923	+	6.00000i	−0.371628	+	0.214560i
$783$		0			0
$784$	4.50000	+	7.79423i	0.160714	+	0.278365i
$785$		0			0
$786$		0			0
$787$			3.00000i			0.106938i	0.998569	+	0.0534692i	$0.0170279\pi$
$787$			3.00000i			0.106938i	−0.998569	+	0.0534692i	$0.982972\pi$
$788$	6.92820	+	4.00000i	0.246807	+	0.142494i
$789$		0			0
$790$		0			0
$791$	−72.0000			−2.56003
$792$	−2.59808	−	1.50000i	−0.0923186	−	0.0533002i
$793$	20.7846	−	12.0000i	0.738083	−	0.426132i
$794$	19.0000	−	32.9090i	0.674285	−	1.16790i
$795$		0			0
$796$	−9.00000	−	15.5885i	−0.318997	−	0.552518i
$797$		−	44.0000i		−	1.55856i	−0.626676	−	0.779280i	$-0.715585\pi$
$797$		−	44.0000i		−	1.55856i	0.626676	−	0.779280i	$-0.284415\pi$
$798$		0			0
$799$	−18.0000			−0.636794
$800$		0			0
$801$	−1.50000	−	2.59808i	−0.0529999	−	0.0917985i
$802$	−28.5788	−	16.5000i	−1.00915	−	0.582635i
$803$	−8.66025	+	5.00000i	−0.305614	+	0.176446i
$804$		0			0
$805$		0			0
$806$	−4.00000			−0.140894
$807$		0			0
$808$	8.66025	+	5.00000i	0.304667	+	0.175899i
$809$	−37.0000			−1.30085			−0.650425	−	0.759570i	$-0.725409\pi$
$809$	−37.0000			−1.30085			−0.650425	+	0.759570i	$0.725409\pi$
$810$		0			0
$811$	−2.00000	+	3.46410i	−0.0702295	+	0.121641i	−0.899002	−	0.437945i	$-0.855706\pi$
$811$	−2.00000	+	3.46410i	−0.0702295	+	0.121641i	0.828772	+	0.559586i	$0.189040\pi$
$812$	−20.7846	+	12.0000i	−0.729397	+	0.421117i
$813$		0			0
$814$	1.00000	+	1.73205i	0.0350500	+	0.0607083i
$815$		0			0
$816$		0			0
$817$	−31.1769	+	42.0000i	−1.09074	+	1.46939i
$818$		−	25.0000i		−	0.874105i
$819$	−12.0000	−	20.7846i	−0.419314	−	0.726273i
$820$		0			0
$821$	−13.0000	+	22.5167i	−0.453703	+	0.785837i	−0.998613	−	0.0526580i	$-0.983231\pi$
$821$	−13.0000	+	22.5167i	−0.453703	+	0.785837i	0.544909	+	0.838495i	$0.316564\pi$
$822$		0			0
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.245295	−	0.969448i	$-0.578885\pi$
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.962215	+	0.272292i	$0.912218\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$	−18.0000	+	31.1769i	−0.626300	+	1.08478i
$827$	−7.79423	−	4.50000i	−0.271032	−	0.156480i	0.358325	−	0.933597i	$-0.383348\pi$
$827$	−7.79423	−	4.50000i	−0.271032	−	0.156480i	−0.629356	+	0.777117i	$0.716681\pi$
$828$			12.0000i			0.417029i
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$		0			0
$831$		0			0
$832$	−1.73205	−	1.00000i	−0.0600481	−	0.0346688i
$833$	23.3827	−	13.5000i	0.810162	−	0.467747i
$834$		0			0
$835$		0			0
$836$	0.500000	−	4.33013i	0.0172929	−	0.149761i
$837$		0			0
$838$	−25.1147	+	14.5000i	−0.867574	+	0.500894i
$839$	4.00000	+	6.92820i	0.138095	+	0.239188i	0.926776	−	0.375615i	$-0.122569\pi$
$839$	4.00000	+	6.92820i	0.138095	+	0.239188i	−0.788680	+	0.614804i	$0.789235\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−8.66025	−	5.00000i	−0.298452	−	0.172311i
$843$		0			0
$844$	5.00000			0.172107
$845$		0			0
$846$	−9.00000	+	15.5885i	−0.309426	+	0.535942i
$847$		−	40.0000i		−	1.37442i
$848$			4.00000i			0.137361i
$849$		0			0
$850$		0			0
$851$	4.00000	−	6.92820i	0.137118	−	0.237496i
$852$		0			0
$853$	−5.19615	+	3.00000i	−0.177913	+	0.102718i	−0.586312	−	0.810086i	$-0.699421\pi$
$853$	−5.19615	+	3.00000i	−0.177913	+	0.102718i	0.408399	+	0.912804i	$0.366087\pi$
$854$	48.0000			1.64253
$855$		0			0
$856$	5.00000			0.170896
$857$	−6.06218	+	3.50000i	−0.207080	+	0.119558i	−0.599954	−	0.800035i	$-0.704814\pi$
$857$	−6.06218	+	3.50000i	−0.207080	+	0.119558i	0.392874	+	0.919592i	$0.371481\pi$
$858$		0			0
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$		0			0
$861$		0			0
$862$		−	24.0000i		−	0.817443i
$863$		−	50.0000i		−	1.70202i	−0.525150	−	0.851010i	$-0.675991\pi$
$863$		−	50.0000i		−	1.70202i	0.525150	−	0.851010i	$-0.324009\pi$
$864$		0			0
$865$		0			0
$866$	29.0000			0.985460
$867$		0			0
$868$	−6.92820	−	4.00000i	−0.235159	−	0.135769i
$869$	7.00000	+	12.1244i	0.237459	+	0.411291i
$870$		0			0
$871$	15.0000	+	25.9808i	0.508256	+	0.880325i
$872$	8.66025	−	5.00000i	0.293273	−	0.169321i
$873$			3.00000i			0.101535i
$874$	−16.0000	+	6.92820i	−0.541208	+	0.234350i
$875$		0			0
$876$		0			0
$877$	15.5885	−	9.00000i	0.526385	−	0.303908i	−0.213158	−	0.977018i	$-0.568375\pi$
$877$	15.5885	−	9.00000i	0.526385	−	0.303908i	0.739543	+	0.673109i	$0.235042\pi$
$878$	−24.2487	−	14.0000i	−0.818354	−	0.472477i
$879$		0			0
$880$		0			0
$881$	−53.0000			−1.78562			−0.892808	−	0.450438i	$-0.851268\pi$
$881$	−53.0000			−1.78562			−0.892808	+	0.450438i	$0.851268\pi$
$882$		−	27.0000i		−	0.909137i
$883$	−10.3923	−	6.00000i	−0.349729	−	0.201916i	0.314837	−	0.949146i	$-0.398050\pi$
$883$	−10.3923	−	6.00000i	−0.349729	−	0.201916i	−0.664566	+	0.747230i	$0.731383\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$		0			0
$886$	21.0000			0.705509
$887$	−48.4974	−	28.0000i	−1.62838	−	0.940148i	−0.984575	−	0.174962i	$-0.944020\pi$
$887$	−48.4974	−	28.0000i	−1.62838	−	0.940148i	−0.643809	−	0.765186i	$-0.722647\pi$
$888$		0			0
$889$	12.0000	−	20.7846i	0.402467	−	0.697093i
$890$		0			0
$891$	4.50000	+	7.79423i	0.150756	+	0.261116i
$892$			22.0000i			0.736614i
$893$	−25.9808	−	3.00000i	−0.869413	−	0.100391i
$894$		0			0
$895$		0			0
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$		0			0
$898$	29.4449	−	17.0000i	0.982588	−	0.567297i
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$		0			0
$901$	12.0000			0.399778
$902$	−2.59808	−	1.50000i	−0.0865065	−	0.0499445i
$903$		0			0
$904$	18.0000			0.598671
$905$		0			0
$906$		0			0
$907$	−32.0429	+	18.5000i	−1.06397	+	0.614282i	−0.926527	−	0.376228i	$-0.877221\pi$
$907$	−32.0429	+	18.5000i	−1.06397	+	0.614282i	−0.137441	+	0.990510i	$0.543888\pi$
$908$	−16.4545	−	9.50000i	−0.546061	−	0.315269i
$909$	−15.0000	−	25.9808i	−0.497519	−	0.861727i
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$		−	4.00000i		−	0.132381i
$914$	−7.00000	−	12.1244i	−0.231539	−	0.401038i
$915$		0			0
$916$	9.00000	−	15.5885i	0.297368	−	0.515057i
$917$	24.2487	−	14.0000i	0.800763	−	0.462321i
$918$		0			0
$919$	14.0000			0.461817			0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000			0.461817			0.230909	+	0.972975i	$0.425830\pi$
$920$		0			0
$921$		0			0
$922$	25.9808	+	15.0000i	0.855631	+	0.493999i
$923$		−	12.0000i		−	0.394985i
$924$		0			0
$925$		0			0
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$	10.3923	+	6.00000i	0.341328	+	0.197066i
$928$	5.19615	−	3.00000i	0.170572	−	0.0984798i
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	−0.985482	−	0.169779i	$-0.945695\pi$
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	0.345708	−	0.938342i	$-0.387639\pi$
$930$		0			0
$931$	36.0000	−	15.5885i	1.17985	−	0.510891i
$932$		−	17.0000i		−	0.556854i
$933$		0			0
$934$	−2.50000	−	4.33013i	−0.0818025	−	0.141686i
$935$		0			0
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	29.4449	+	17.0000i	0.961922	+	0.555366i	0.896764	−	0.442509i	$-0.145912\pi$
$937$	29.4449	+	17.0000i	0.961922	+	0.555366i	0.0651578	+	0.997875i	$0.479245\pi$
$938$			60.0000i			1.95907i
$939$		0			0
$940$		0			0
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$			12.0000i			0.390774i
$944$	4.50000	−	7.79423i	0.146463	−	0.253681i
$945$		0			0
$946$	−6.00000	+	10.3923i	−0.195077	+	0.337883i
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$		0			0
$949$	20.0000			0.649227
$950$		0			0
$951$		0			0
$952$	−10.3923	+	6.00000i	−0.336817	+	0.194461i
$953$	44.1673	−	25.5000i	1.43072	−	0.826026i	0.433544	−	0.901133i	$-0.357263\pi$
$953$	44.1673	−	25.5000i	1.43072	−	0.826026i	0.997176	+	0.0751066i	$0.0239297\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$		0			0
$956$	7.00000	−	12.1244i	0.226396	−	0.392130i
$957$		0			0
$958$			30.0000i			0.969256i
$959$	36.0000	−	62.3538i	1.16250	−	2.01351i
$960$		0			0
$961$	−27.0000			−0.870968
$962$		−	4.00000i		−	0.128965i
$963$	−12.9904	−	7.50000i	−0.418609	−	0.241684i
$964$	10.5000	+	18.1865i	0.338182	+	0.585749i
$965$		0			0
$966$		0			0
$967$	24.2487	−	14.0000i	0.779786	−	0.450210i	−0.0565684	−	0.998399i	$-0.518016\pi$
$967$	24.2487	−	14.0000i	0.779786	−	0.450210i	0.836354	+	0.548189i	$0.184683\pi$
$968$			10.0000i			0.321412i
$969$		0			0
$970$		0			0
$971$	22.0000	+	38.1051i	0.706014	+	1.22285i	0.966324	+	0.257327i	$0.0828416\pi$
$971$	22.0000	+	38.1051i	0.706014	+	1.22285i	−0.260311	+	0.965525i	$0.583825\pi$
$972$		0			0
$973$	−17.3205	−	10.0000i	−0.555270	−	0.320585i
$974$	−1.00000	−	1.73205i	−0.0320421	−	0.0554985i
$975$		0			0
$976$	−12.0000			−0.384111
$977$		−	11.0000i		−	0.351921i	−0.984397	−	0.175961i	$-0.943697\pi$
$977$		−	11.0000i		−	0.351921i	0.984397	−	0.175961i	$-0.0563031\pi$
$978$		0			0
$979$	0.500000	−	0.866025i	0.0159801	−	0.0276783i
$980$		0			0
$981$	−30.0000			−0.957826
$982$	10.3923	+	6.00000i	0.331632	+	0.191468i
$983$	5.19615	−	3.00000i	0.165732	−	0.0956851i	−0.414840	−	0.909894i	$-0.636162\pi$
$983$	5.19615	−	3.00000i	0.165732	−	0.0956851i	0.580572	+	0.814209i	$0.302829\pi$
$984$		0			0
$985$		0			0
$986$	−9.00000	−	15.5885i	−0.286618	−	0.496438i
$987$		0			0
$988$	−5.19615	+	7.00000i	−0.165312	+	0.222700i
$989$	48.0000			1.52631
$990$		0			0
$991$	−12.0000	−	20.7846i	−0.381193	−	0.660245i	0.610040	−	0.792370i	$-0.291153\pi$
$991$	−12.0000	−	20.7846i	−0.381193	−	0.660245i	−0.991233	+	0.132125i	$0.957820\pi$
$992$	1.73205	+	1.00000i	0.0549927	+	0.0317500i
$993$		0			0
$994$	12.0000	−	20.7846i	0.380617	−	0.659248i
$995$		0			0
$996$		0			0
$997$	48.4974	+	28.0000i	1.53593	+	0.886769i	0.999071	+	0.0430962i	$0.0137222\pi$
$997$	48.4974	+	28.0000i	1.53593	+	0.886769i	0.536858	+	0.843673i	$0.319611\pi$
$998$	−23.3827	−	13.5000i	−0.740166	−	0.427335i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.c.349.2		4
5.2	odd	4		950.2.e.e.501.1	yes	2
5.3	odd	4		950.2.e.c.501.1	yes	2
5.4	even	2	inner	950.2.j.c.349.1		4
19.11	even	3	inner	950.2.j.c.49.1		4
95.49	even	6	inner	950.2.j.c.49.2		4
95.68	odd	12		950.2.e.c.201.1	✓	2
95.87	odd	12		950.2.e.e.201.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.c.201.1	✓	2	95.68	odd	12
950.2.e.c.501.1	yes	2	5.3	odd	4
950.2.e.e.201.1	yes	2	95.87	odd	12
950.2.e.e.501.1	yes	2	5.2	odd	4
950.2.j.c.49.1		4	19.11	even	3	inner
950.2.j.c.49.2		4	95.49	even	6	inner
950.2.j.c.349.1		4	5.4	even	2	inner
950.2.j.c.349.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.00000i q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +4.00000i q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} -1.00000 q^{11} +(1.73205 + 1.00000i) q^{13} +(2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 1.50000i) q^{17} +3.00000i q^{18} +(-4.00000 + 1.73205i) q^{19} +(-0.866025 + 0.500000i) q^{22} +(3.46410 + 2.00000i) q^{23} +2.00000 q^{26} +(3.46410 + 2.00000i) q^{28} +(-3.00000 + 5.19615i) q^{29} -2.00000 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(1.50000 + 2.59808i) q^{36} -2.00000i q^{37} +(-2.59808 + 3.50000i) q^{38} +(1.50000 + 2.59808i) q^{41} +(10.3923 - 6.00000i) q^{43} +(-0.500000 + 0.866025i) q^{44} +4.00000 q^{46} +(5.19615 + 3.00000i) q^{47} -9.00000 q^{49} +(1.73205 - 1.00000i) q^{52} +(-3.46410 - 2.00000i) q^{53} +4.00000 q^{56} +6.00000i q^{58} +(4.50000 + 7.79423i) q^{59} +(6.00000 - 10.3923i) q^{61} +(-1.73205 + 1.00000i) q^{62} +(-10.3923 - 6.00000i) q^{63} -1.00000 q^{64} +(12.9904 + 7.50000i) q^{67} +3.00000i q^{68} +(-3.00000 - 5.19615i) q^{71} +(2.59808 + 1.50000i) q^{72} +(8.66025 - 5.00000i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 4.33013i) q^{76} -4.00000i q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 1.50000i) q^{82} +4.00000i q^{83} +(6.00000 - 10.3923i) q^{86} +1.00000i q^{88} +(-0.500000 + 0.866025i) q^{89} +(-4.00000 + 6.92820i) q^{91} +(3.46410 - 2.00000i) q^{92} +6.00000 q^{94} +(0.866025 - 0.500000i) q^{97} +(-7.79423 + 4.50000i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 6 * q^9	\( 4 q + 2 q^{4} - 6 q^{9} - 4 q^{11} + 8 q^{14} - 2 q^{16} - 16 q^{19} + 8 q^{26} - 12 q^{29} - 8 q^{31} - 6 q^{34} + 6 q^{36} + 6 q^{41} - 2 q^{44} + 16 q^{46} - 36 q^{49} + 16 q^{56} + 18 q^{59} + 24 q^{61} - 4 q^{64} - 12 q^{71} - 4 q^{74} - 2 q^{76} - 28 q^{79} - 18 q^{81} + 24 q^{86} - 2 q^{89} - 16 q^{91} + 24 q^{94} + 6 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^9 - 4 * q^11 + 8 * q^14 - 2 * q^16 - 16 * q^19 + 8 * q^26 - 12 * q^29 - 8 * q^31 - 6 * q^34 + 6 * q^36 + 6 * q^41 - 2 * q^44 + 16 * q^46 - 36 * q^49 + 16 * q^56 + 18 * q^59 + 24 * q^61 - 4 * q^64 - 12 * q^71 - 4 * q^74 - 2 * q^76 - 28 * q^79 - 18 * q^81 + 24 * q^86 - 2 * q^89 - 16 * q^91 + 24 * q^94 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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