LMFDB - Embedded newform 950.2.j.b.49.1

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			49.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	950.49
Dual form			950.2.j.b.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000i q^{7} -1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000i q^{7} -1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +1.00000i q^{12} +(-5.19615 + 3.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-6.06218 - 3.50000i) q^{17} +2.00000i q^{18} +(-3.50000 + 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(-1.73205 + 1.00000i) q^{23} +(0.500000 - 0.866025i) q^{24} +6.00000 q^{26} -5.00000i q^{27} +(1.73205 - 1.00000i) q^{28} +(5.00000 + 8.66025i) q^{29} -2.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(3.50000 + 6.06218i) q^{34} +(1.00000 - 1.73205i) q^{36} +4.00000i q^{37} +(4.33013 - 0.500000i) q^{38} -6.00000 q^{39} +(-1.00000 + 1.73205i) q^{41} +(-1.73205 + 1.00000i) q^{42} +(-10.3923 - 6.00000i) q^{43} +2.00000 q^{46} +(-0.866025 + 0.500000i) q^{48} +3.00000 q^{49} +(-3.50000 - 6.06218i) q^{51} +(-5.19615 - 3.00000i) q^{52} +(-2.50000 + 4.33013i) q^{54} -2.00000 q^{56} +(-4.33013 + 0.500000i) q^{57} -10.0000i q^{58} +(-0.500000 + 0.866025i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(1.73205 + 1.00000i) q^{62} +(-3.46410 + 2.00000i) q^{63} -1.00000 q^{64} +(6.92820 - 4.00000i) q^{67} -7.00000i q^{68} -2.00000 q^{69} +(6.00000 - 10.3923i) q^{71} +(-1.73205 + 1.00000i) q^{72} +(-2.59808 - 1.50000i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.00000 - 1.73205i) q^{76} +(5.19615 + 3.00000i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.73205 - 1.00000i) q^{82} +13.0000i q^{83} +2.00000 q^{84} +(6.00000 + 10.3923i) q^{86} +10.0000i q^{87} +(-6.50000 - 11.2583i) q^{89} +(6.00000 + 10.3923i) q^{91} +(-1.73205 - 1.00000i) q^{92} +(-1.73205 - 1.00000i) q^{93} +1.00000 q^{96} +(-12.9904 - 7.50000i) q^{97} +(-2.59808 - 1.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9	$ 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9} - 4 q^{14} - 2 q^{16} - 14 q^{19} + 4 q^{21} + 2 q^{24} + 24 q^{26} + 20 q^{29} - 8 q^{31} + 14 q^{34} + 4 q^{36} - 24 q^{39} - 4 q^{41} + 8 q^{46} + 12 q^{49} - 14 q^{51} - 10 q^{54} - 8 q^{56} - 2 q^{59} - 16 q^{61} - 4 q^{64} - 8 q^{69} + 24 q^{71} + 8 q^{74} - 16 q^{76} - 8 q^{79} - 2 q^{81} + 8 q^{84} + 24 q^{86} - 26 q^{89} + 24 q^{91} + 4 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9 - 4 * q^14 - 2 * q^16 - 14 * q^19 + 4 * q^21 + 2 * q^24 + 24 * q^26 + 20 * q^29 - 8 * q^31 + 14 * q^34 + 4 * q^36 - 24 * q^39 - 4 * q^41 + 8 * q^46 + 12 * q^49 - 14 * q^51 - 10 * q^54 - 8 * q^56 - 2 * q^59 - 16 * q^61 - 4 * q^64 - 8 * q^69 + 24 * q^71 + 8 * q^74 - 16 * q^76 - 8 * q^79 - 2 * q^81 + 8 * q^84 + 24 * q^86 - 26 * q^89 + 24 * q^91 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	0.728714	−	0.684819i	$-0.240119\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	−0.228714	+	0.973494i	$0.573452\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$			1.00000i			0.288675i
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−1.00000	+	1.73205i	−0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.06218	−	3.50000i	−1.47029	−	0.848875i	−0.470850	−	0.882213i	$-0.656053\pi$
$17$	−6.06218	−	3.50000i	−1.47029	−	0.848875i	−0.999444	+	0.0333386i	$0.989386\pi$
$18$			2.00000i			0.471405i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$		0			0
$21$	1.00000	−	1.73205i	0.218218	−	0.377964i
$22$		0			0
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	−0.669588	−	0.742732i	$-0.733529\pi$
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	0.308431	+	0.951247i	$0.400196\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	6.00000			1.17670
$27$		−	5.00000i		−	0.962250i
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.785872	+	0.618389i	$0.212214\pi$
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.142605	+	0.989780i	$0.454452\pi$
$30$		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
$34$	3.50000	+	6.06218i	0.600245	+	1.03965i
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	4.33013	−	0.500000i	0.702439	−	0.0811107i
$39$	−6.00000			−0.960769
$40$		0			0
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	−0.933486	−	0.358614i	$-0.883249\pi$
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	0.777312	+	0.629115i	$0.216583\pi$
$42$	−1.73205	+	1.00000i	−0.267261	+	0.154303i
$43$	−10.3923	−	6.00000i	−1.58481	−	0.914991i	−0.994142	−	0.108078i	$-0.965531\pi$
$43$	−10.3923	−	6.00000i	−1.58481	−	0.914991i	−0.590669	−	0.806914i	$-0.701136\pi$
$44$		0			0
$45$		0			0
$46$	2.00000			0.294884
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	3.00000			0.428571
$50$		0			0
$51$	−3.50000	−	6.06218i	−0.490098	−	0.848875i
$52$	−5.19615	−	3.00000i	−0.720577	−	0.416025i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$	−2.00000			−0.267261
$57$	−4.33013	+	0.500000i	−0.573539	+	0.0662266i
$58$		−	10.0000i		−	1.31306i
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	−0.896736	−	0.442566i	$-0.854068\pi$
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	0.831641	+	0.555313i	$0.187402\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	1.73205	+	1.00000i	0.219971	+	0.127000i
$63$	−3.46410	+	2.00000i	−0.436436	+	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	−0.0130248	−	0.999915i	$-0.504146\pi$
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	0.859440	+	0.511237i	$0.170813\pi$
$68$		−	7.00000i		−	0.848875i
$69$	−2.00000			−0.240772
$70$		0			0
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	−0.252010	−	0.967725i	$-0.581092\pi$
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	0.964079	−	0.265615i	$-0.0855750\pi$
$72$	−1.73205	+	1.00000i	−0.204124	+	0.117851i
$73$	−2.59808	−	1.50000i	−0.304082	−	0.175562i	0.340193	−	0.940356i	$-0.389507\pi$
$73$	−2.59808	−	1.50000i	−0.304082	−	0.175562i	−0.644275	+	0.764794i	$0.722841\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	−4.00000	−	1.73205i	−0.458831	−	0.198680i
$77$		0			0
$78$	5.19615	+	3.00000i	0.588348	+	0.339683i
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.73205	−	1.00000i	0.191273	−	0.110432i
$83$			13.0000i			1.42694i	0.700688	+	0.713468i	$0.252876\pi$
$83$			13.0000i			1.42694i	−0.700688	+	0.713468i	$0.747124\pi$
$84$	2.00000			0.218218
$85$		0			0
$86$	6.00000	+	10.3923i	0.646997	+	1.12063i
$87$			10.0000i			1.07211i
$88$		0			0
$89$	−6.50000	−	11.2583i	−0.688999	−	1.19338i	−0.972162	−	0.234309i	$-0.924717\pi$
$89$	−6.50000	−	11.2583i	−0.688999	−	1.19338i	0.283164	−	0.959072i	$-0.408616\pi$
$90$		0			0
$91$	6.00000	+	10.3923i	0.628971	+	1.08941i
$92$	−1.73205	−	1.00000i	−0.180579	−	0.104257i
$93$	−1.73205	−	1.00000i	−0.179605	−	0.103695i
$94$		0			0
$95$		0			0
$96$	1.00000			0.102062
$97$	−12.9904	−	7.50000i	−1.31897	−	0.761510i	−0.335410	−	0.942072i	$-0.608875\pi$
$97$	−12.9904	−	7.50000i	−1.31897	−	0.761510i	−0.983563	+	0.180563i	$0.942208\pi$
$98$	−2.59808	−	1.50000i	−0.262445	−	0.151523i
$99$		0			0
$100$		0			0
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$			7.00000i			0.693103i
$103$		−	12.0000i		−	1.18240i	−0.806527	−	0.591198i	$-0.798655\pi$
$103$		−	12.0000i		−	1.18240i	0.806527	−	0.591198i	$-0.201345\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$		0			0
$106$		0			0
$107$			15.0000i			1.45010i	0.688694	+	0.725052i	$0.258184\pi$
$107$			15.0000i			1.45010i	−0.688694	+	0.725052i	$0.741816\pi$
$108$	4.33013	−	2.50000i	0.416667	−	0.240563i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	−2.00000	+	3.46410i	−0.189832	+	0.328798i
$112$	1.73205	+	1.00000i	0.163663	+	0.0944911i
$113$		−	1.00000i		−	0.0940721i	−0.998893	−	0.0470360i	$-0.985022\pi$
$113$		−	1.00000i		−	0.0940721i	0.998893	−	0.0470360i	$-0.0149776\pi$
$114$	4.00000	+	1.73205i	0.374634	+	0.162221i
$115$		0			0
$116$	−5.00000	+	8.66025i	−0.464238	+	0.804084i
$117$	10.3923	+	6.00000i	0.960769	+	0.554700i
$118$	0.866025	−	0.500000i	0.0797241	−	0.0460287i
$119$	−7.00000	+	12.1244i	−0.641689	+	1.11144i
$120$		0			0
$121$	−11.0000			−1.00000
$122$			8.00000i			0.724286i
$123$	−1.73205	+	1.00000i	−0.156174	+	0.0901670i
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$		0			0
$126$	4.00000			0.356348
$127$	10.3923	−	6.00000i	0.922168	−	0.532414i	0.0378419	−	0.999284i	$-0.487952\pi$
$127$	10.3923	−	6.00000i	0.922168	−	0.532414i	0.884326	+	0.466870i	$0.154618\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−6.00000	−	10.3923i	−0.528271	−	0.914991i
$130$		0			0
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	5.19615	+	7.00000i	0.450564	+	0.606977i
$134$	−8.00000			−0.691095
$135$		0			0
$136$	−3.50000	+	6.06218i	−0.300123	+	0.519827i
$137$	12.9904	−	7.50000i	1.10984	−	0.640768i	0.171054	−	0.985262i	$-0.445283\pi$
$137$	12.9904	−	7.50000i	1.10984	−	0.640768i	0.938789	+	0.344493i	$0.111949\pi$
$138$	1.73205	+	1.00000i	0.147442	+	0.0851257i
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$		0			0
$142$	−10.3923	+	6.00000i	−0.872103	+	0.503509i
$143$		0			0
$144$	2.00000			0.166667
$145$		0			0
$146$	1.50000	+	2.59808i	0.124141	+	0.215018i
$147$	2.59808	+	1.50000i	0.214286	+	0.123718i
$148$	−3.46410	+	2.00000i	−0.284747	+	0.164399i
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	−0.326411	−	0.945228i	$-0.605840\pi$
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	0.981797	−	0.189933i	$-0.0608272\pi$
$150$		0			0
$151$	−12.0000			−0.976546			−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000			−0.976546			−0.488273	+	0.872691i	$0.662373\pi$
$152$	2.59808	+	3.50000i	0.210732	+	0.283887i
$153$			14.0000i			1.13183i
$154$		0			0
$155$		0			0
$156$	−3.00000	−	5.19615i	−0.240192	−	0.416025i
$157$	−5.19615	−	3.00000i	−0.414698	−	0.239426i	0.278108	−	0.960550i	$-0.410293\pi$
$157$	−5.19615	−	3.00000i	−0.414698	−	0.239426i	−0.692806	+	0.721124i	$0.743626\pi$
$158$	3.46410	−	2.00000i	0.275589	−	0.159111i
$159$		0			0
$160$		0			0
$161$	2.00000	+	3.46410i	0.157622	+	0.273009i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$			12.0000i			0.939913i	0.882690	+	0.469956i	$0.155730\pi$
$163$			12.0000i			0.939913i	−0.882690	+	0.469956i	$0.844270\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	6.50000	−	11.2583i	0.504498	−	0.873816i
$167$	8.66025	−	5.00000i	0.670151	−	0.386912i	−0.125983	−	0.992032i	$-0.540209\pi$
$167$	8.66025	−	5.00000i	0.670151	−	0.386912i	0.796134	+	0.605121i	$0.206875\pi$
$168$	−1.73205	−	1.00000i	−0.133631	−	0.0771517i
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$		0			0
$171$	8.00000	+	3.46410i	0.611775	+	0.264906i
$172$		−	12.0000i		−	0.914991i
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	0.684349	−	0.729155i	$-0.260087\pi$
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	−0.289292	+	0.957241i	$0.593420\pi$
$174$	5.00000	−	8.66025i	0.379049	−	0.656532i
$175$		0			0
$176$		0			0
$177$	−0.866025	+	0.500000i	−0.0650945	+	0.0375823i
$178$			13.0000i			0.974391i
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−10.0000	−	17.3205i	−0.743294	−	1.28742i	−0.950988	−	0.309229i	$-0.899929\pi$
$181$	−10.0000	−	17.3205i	−0.743294	−	1.28742i	0.207693	−	0.978194i	$-0.433404\pi$
$182$		−	12.0000i		−	0.889499i
$183$		−	8.00000i		−	0.591377i
$184$	1.00000	+	1.73205i	0.0737210	+	0.127688i
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$		0			0
$188$		0			0
$189$	−10.0000			−0.727393
$190$		0			0
$191$	−10.0000			−0.723575			−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000			−0.723575			−0.361787	+	0.932261i	$0.617833\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	9.52628	+	5.50000i	0.685717	+	0.395899i	0.802005	−	0.597317i	$-0.203766\pi$
$193$	9.52628	+	5.50000i	0.685717	+	0.395899i	−0.116289	+	0.993215i	$0.537100\pi$
$194$	7.50000	+	12.9904i	0.538469	+	0.932655i
$195$		0			0
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$			4.00000i			0.284988i	0.989796	+	0.142494i	$0.0455122\pi$
$197$			4.00000i			0.284988i	−0.989796	+	0.142494i	$0.954488\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$		0			0
$201$	8.00000			0.564276
$202$			2.00000i			0.140720i
$203$	17.3205	−	10.0000i	1.21566	−	0.701862i
$204$	3.50000	−	6.06218i	0.245049	−	0.424437i
$205$		0			0
$206$	−6.00000	+	10.3923i	−0.418040	+	0.724066i
$207$	3.46410	+	2.00000i	0.240772	+	0.139010i
$208$		−	6.00000i		−	0.416025i
$209$		0			0
$210$		0			0
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	0.133226	+	0.991086i	$0.457467\pi$
$211$	−11.5000	+	19.9186i	−0.791693	+	1.37125i	−0.924918	+	0.380166i	$0.875867\pi$
$212$		0			0
$213$	10.3923	−	6.00000i	0.712069	−	0.411113i
$214$	7.50000	−	12.9904i	0.512689	−	0.888004i
$215$		0			0
$216$	−5.00000			−0.340207
$217$			4.00000i			0.271538i
$218$	1.73205	−	1.00000i	0.117309	−	0.0677285i
$219$	−1.50000	−	2.59808i	−0.101361	−	0.175562i
$220$		0			0
$221$	42.0000			2.82523
$222$	3.46410	−	2.00000i	0.232495	−	0.134231i
$223$	−1.73205	−	1.00000i	−0.115987	−	0.0669650i	0.440884	−	0.897564i	$-0.354665\pi$
$223$	−1.73205	−	1.00000i	−0.115987	−	0.0669650i	−0.556871	+	0.830599i	$0.687998\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$		0			0
$226$	−0.500000	+	0.866025i	−0.0332595	+	0.0576072i
$227$			13.0000i			0.862840i	0.902151	+	0.431420i	$0.141987\pi$
$227$			13.0000i			0.862840i	−0.902151	+	0.431420i	$0.858013\pi$
$228$	−2.59808	−	3.50000i	−0.172062	−	0.231793i
$229$	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
$232$	8.66025	−	5.00000i	0.568574	−	0.328266i
$233$	11.2583	+	6.50000i	0.737558	+	0.425829i	0.821181	−	0.570668i	$-0.193316\pi$
$233$	11.2583	+	6.50000i	0.737558	+	0.425829i	−0.0836229	+	0.996497i	$0.526649\pi$
$234$	−6.00000	−	10.3923i	−0.392232	−	0.679366i
$235$		0			0
$236$	−1.00000			−0.0650945
$237$	−3.46410	+	2.00000i	−0.225018	+	0.129914i
$238$	12.1244	−	7.00000i	0.785905	−	0.453743i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	9.52628	+	5.50000i	0.612372	+	0.353553i
$243$	−13.8564	+	8.00000i	−0.888889	+	0.513200i
$244$	4.00000	−	6.92820i	0.256074	−	0.443533i
$245$		0			0
$246$	2.00000			0.127515
$247$	10.3923	−	24.0000i	0.661247	−	1.52708i
$248$			2.00000i			0.127000i
$249$	−6.50000	+	11.2583i	−0.411921	+	0.713468i
$250$		0			0
$251$	10.0000	+	17.3205i	0.631194	+	1.09326i	0.987308	+	0.158818i	$0.0507683\pi$
$251$	10.0000	+	17.3205i	0.631194	+	1.09326i	−0.356113	+	0.934443i	$0.615898\pi$
$252$	−3.46410	−	2.00000i	−0.218218	−	0.125988i
$253$		0			0
$254$	−12.0000			−0.752947
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.9904	+	7.50000i	−0.810318	+	0.467837i	−0.847066	−	0.531487i	$-0.821633\pi$
$257$	−12.9904	+	7.50000i	−0.810318	+	0.467837i	0.0367485	+	0.999325i	$0.488300\pi$
$258$			12.0000i			0.747087i
$259$	8.00000			0.497096
$260$		0			0
$261$	10.0000	−	17.3205i	0.618984	−	1.07211i
$262$	0.866025	−	0.500000i	0.0535032	−	0.0308901i
$263$	12.1244	+	7.00000i	0.747620	+	0.431638i	0.824833	−	0.565376i	$-0.191269\pi$
$263$	12.1244	+	7.00000i	0.747620	+	0.431638i	−0.0772134	+	0.997015i	$0.524602\pi$
$264$		0			0
$265$		0			0
$266$	−1.00000	−	8.66025i	−0.0613139	−	0.530994i
$267$		−	13.0000i		−	0.795587i
$268$	6.92820	+	4.00000i	0.423207	+	0.244339i
$269$	13.0000	−	22.5167i	0.792624	−	1.37287i	−0.131713	−	0.991288i	$-0.542048\pi$
$269$	13.0000	−	22.5167i	0.792624	−	1.37287i	0.924337	−	0.381577i	$-0.124619\pi$
$270$		0			0
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	0.136461	+	0.990645i	$0.456427\pi$
$271$	−13.0000	+	22.5167i	−0.789694	+	1.36779i	−0.926155	+	0.377144i	$0.876906\pi$
$272$	6.06218	−	3.50000i	0.367574	−	0.212219i
$273$			12.0000i			0.726273i
$274$	−15.0000			−0.906183
$275$		0			0
$276$	−1.00000	−	1.73205i	−0.0601929	−	0.104257i
$277$		−	22.0000i		−	1.32185i	−0.750451	−	0.660926i	$-0.770164\pi$
$277$		−	22.0000i		−	1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$		0			0
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$		0			0
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	0.742542	−	0.669800i	$-0.233620\pi$
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	−0.951334	+	0.308160i	$0.900287\pi$
$282$		0			0
$283$	−24.2487	−	14.0000i	−1.44144	−	0.832214i	−0.443491	−	0.896279i	$-0.646260\pi$
$283$	−24.2487	−	14.0000i	−1.44144	−	0.832214i	−0.997946	+	0.0640654i	$0.979593\pi$
$284$	12.0000			0.712069
$285$		0			0
$286$		0			0
$287$	3.46410	+	2.00000i	0.204479	+	0.118056i
$288$	−1.73205	−	1.00000i	−0.102062	−	0.0589256i
$289$	16.0000	+	27.7128i	0.941176	+	1.63017i
$290$		0			0
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$		−	3.00000i		−	0.175562i
$293$		−	32.0000i		−	1.86946i	−0.355359	−	0.934730i	$-0.615641\pi$
$293$		−	32.0000i		−	1.86946i	0.355359	−	0.934730i	$-0.384359\pi$
$294$	−1.50000	−	2.59808i	−0.0874818	−	0.151523i
$295$		0			0
$296$	4.00000			0.232495
$297$		0			0
$298$	−13.8564	+	8.00000i	−0.802680	+	0.463428i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$		0			0
$301$	−12.0000	+	20.7846i	−0.691669	+	1.19800i
$302$	10.3923	+	6.00000i	0.598010	+	0.345261i
$303$		−	2.00000i		−	0.114897i
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$		0			0
$306$	7.00000	−	12.1244i	0.400163	−	0.693103i
$307$	16.4545	+	9.50000i	0.939107	+	0.542194i	0.889680	−	0.456584i	$-0.150927\pi$
$307$	16.4545	+	9.50000i	0.939107	+	0.542194i	0.0494267	+	0.998778i	$0.484261\pi$
$308$		0			0
$309$	6.00000	−	10.3923i	0.341328	−	0.591198i
$310$		0			0
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$			6.00000i			0.339683i
$313$	−9.52628	+	5.50000i	−0.538457	+	0.310878i	−0.744453	−	0.667674i	$-0.767290\pi$
$313$	−9.52628	+	5.50000i	−0.538457	+	0.310878i	0.205996	+	0.978553i	$0.433957\pi$
$314$	3.00000	+	5.19615i	0.169300	+	0.293236i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−20.7846	+	12.0000i	−1.16738	+	0.673987i	−0.953062	−	0.302777i	$-0.902086\pi$
$317$	−20.7846	+	12.0000i	−1.16738	+	0.673987i	−0.214318	+	0.976764i	$0.568753\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−7.50000	+	12.9904i	−0.418609	+	0.725052i
$322$		−	4.00000i		−	0.222911i
$323$	30.3109	−	3.50000i	1.68654	−	0.194745i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$	1.73205	+	1.00000i	0.0956365	+	0.0552158i
$329$		0			0
$330$		0			0
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	−11.2583	+	6.50000i	−0.617881	+	0.356734i
$333$	6.92820	−	4.00000i	0.379663	−	0.219199i
$334$	−10.0000			−0.547176
$335$		0			0
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	19.0526	+	11.0000i	1.03786	+	0.599208i	0.919226	−	0.393730i	$-0.128816\pi$
$337$	19.0526	+	11.0000i	1.03786	+	0.599208i	0.118633	+	0.992938i	$0.462149\pi$
$338$	−19.9186	+	11.5000i	−1.08343	+	0.625518i
$339$	0.500000	−	0.866025i	0.0271563	−	0.0470360i
$340$		0			0
$341$		0			0
$342$	−5.19615	−	7.00000i	−0.280976	−	0.378517i
$343$		−	20.0000i		−	1.07990i
$344$	−6.00000	+	10.3923i	−0.323498	+	0.560316i
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$	−8.66025	+	5.00000i	−0.464238	+	0.268028i
$349$	−16.0000			−0.856460			−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000			−0.856460			−0.428230	+	0.903670i	$0.640863\pi$
$350$		0			0
$351$	15.0000	+	25.9808i	0.800641	+	1.38675i
$352$		0			0
$353$			3.00000i			0.159674i	0.996808	+	0.0798369i	$0.0254400\pi$
$353$			3.00000i			0.159674i	−0.996808	+	0.0798369i	$0.974560\pi$
$354$	1.00000			0.0531494
$355$		0			0
$356$	6.50000	−	11.2583i	0.344499	−	0.596690i
$357$	−12.1244	+	7.00000i	−0.641689	+	0.370479i
$358$	−7.79423	−	4.50000i	−0.411938	−	0.237832i
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$			20.0000i			1.05118i
$363$	−9.52628	−	5.50000i	−0.500000	−	0.288675i
$364$	−6.00000	+	10.3923i	−0.314485	+	0.544705i
$365$		0			0
$366$	−4.00000	+	6.92820i	−0.209083	+	0.362143i
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	−0.669804	−	0.742538i	$-0.733622\pi$
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	0.308155	+	0.951336i	$0.400289\pi$
$368$		−	2.00000i		−	0.104257i
$369$	4.00000			0.208232
$370$		0			0
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$			6.00000i			0.310668i	0.987862	+	0.155334i	$0.0496454\pi$
$373$			6.00000i			0.310668i	−0.987862	+	0.155334i	$0.950355\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−51.9615	−	30.0000i	−2.67615	−	1.54508i
$378$	8.66025	+	5.00000i	0.445435	+	0.257172i
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$		0			0
$381$	12.0000			0.614779
$382$	8.66025	+	5.00000i	0.443097	+	0.255822i
$383$	−10.3923	−	6.00000i	−0.531022	−	0.306586i	0.210411	−	0.977613i	$-0.432520\pi$
$383$	−10.3923	−	6.00000i	−0.531022	−	0.306586i	−0.741433	+	0.671027i	$0.765853\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	−5.50000	−	9.52628i	−0.279943	−	0.484875i
$387$			24.0000i			1.21999i
$388$		−	15.0000i		−	0.761510i
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$		−	3.00000i		−	0.151523i
$393$	−0.866025	+	0.500000i	−0.0436852	+	0.0252217i
$394$	2.00000	−	3.46410i	0.100759	−	0.174519i
$395$		0			0
$396$		0			0
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	0.163876	−	0.986481i	$-0.447600\pi$
$397$	−12.1244	−	7.00000i	−0.608504	−	0.351320i	−0.772380	+	0.635161i	$0.780934\pi$
$398$			16.0000i			0.802008i
$399$	1.00000	+	8.66025i	0.0500626	+	0.433555i
$400$		0			0
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	−6.92820	−	4.00000i	−0.345547	−	0.199502i
$403$	10.3923	−	6.00000i	0.517678	−	0.298881i
$404$	1.00000	−	1.73205i	0.0497519	−	0.0861727i
$405$		0			0
$406$	−20.0000			−0.992583
$407$		0			0
$408$	−6.06218	+	3.50000i	−0.300123	+	0.173276i
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	0.889689	−	0.456566i	$-0.150921\pi$
$409$	1.00000	+	1.73205i	0.0494468	+	0.0856444i	−0.840243	+	0.542211i	$0.817588\pi$
$410$		0			0
$411$	15.0000			0.739895
$412$	10.3923	−	6.00000i	0.511992	−	0.295599i
$413$	1.73205	+	1.00000i	0.0852286	+	0.0492068i
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$		0			0
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$		0			0
$418$		0			0
$419$	−13.0000			−0.635092			−0.317546	−	0.948243i	$-0.602859\pi$
$419$	−13.0000			−0.635092			−0.317546	+	0.948243i	$0.602859\pi$
$420$		0			0
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	0.0706626	+	0.997500i	$0.477489\pi$
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	−0.899192	+	0.437555i	$0.855845\pi$
$422$	19.9186	−	11.5000i	0.969622	−	0.559811i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	−13.8564	+	8.00000i	−0.670559	+	0.387147i
$428$	−12.9904	+	7.50000i	−0.627914	+	0.362526i
$429$		0			0
$430$		0			0
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$	4.33013	+	2.50000i	0.208333	+	0.120281i
$433$	18.1865	−	10.5000i	0.873989	−	0.504598i	0.00531724	−	0.999986i	$-0.498307\pi$
$433$	18.1865	−	10.5000i	0.873989	−	0.504598i	0.868672	+	0.495388i	$0.164974\pi$
$434$	2.00000	−	3.46410i	0.0960031	−	0.166282i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	3.46410	−	8.00000i	0.165710	−	0.382692i
$438$			3.00000i			0.143346i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$	−3.00000	−	5.19615i	−0.142857	−	0.247436i
$442$	−36.3731	−	21.0000i	−1.73009	−	0.998868i
$443$	−31.1769	+	18.0000i	−1.48126	+	0.855206i	−0.999774	−	0.0212481i	$-0.993236\pi$
$443$	−31.1769	+	18.0000i	−1.48126	+	0.855206i	−0.481486	+	0.876454i	$0.659903\pi$
$444$	−4.00000			−0.189832
$445$		0			0
$446$	1.00000	+	1.73205i	0.0473514	+	0.0820150i
$447$	13.8564	−	8.00000i	0.655386	−	0.378387i
$448$			2.00000i			0.0944911i
$449$	−41.0000			−1.93491			−0.967455	−	0.253044i	$-0.918568\pi$
$449$	−41.0000			−1.93491			−0.967455	+	0.253044i	$0.918568\pi$
$450$		0			0
$451$		0			0
$452$	0.866025	−	0.500000i	0.0407344	−	0.0235180i
$453$	−10.3923	−	6.00000i	−0.488273	−	0.281905i
$454$	6.50000	−	11.2583i	0.305060	−	0.528380i
$455$		0			0
$456$	0.500000	+	4.33013i	0.0234146	+	0.202777i
$457$			11.0000i			0.514558i	0.966337	+	0.257279i	$0.0828260\pi$
$457$			11.0000i			0.514558i	−0.966337	+	0.257279i	$0.917174\pi$
$458$	−15.5885	−	9.00000i	−0.728401	−	0.420542i
$459$	−17.5000	+	30.3109i	−0.816830	+	1.41479i
$460$		0			0
$461$	−1.00000	+	1.73205i	−0.0465746	+	0.0806696i	−0.888373	−	0.459123i	$-0.848164\pi$
$461$	−1.00000	+	1.73205i	−0.0465746	+	0.0806696i	0.841798	+	0.539792i	$0.181497\pi$
$462$		0			0
$463$			22.0000i			1.02243i	0.859454	+	0.511213i	$0.170804\pi$
$463$			22.0000i			1.02243i	−0.859454	+	0.511213i	$0.829196\pi$
$464$	−10.0000			−0.464238
$465$		0			0
$466$	−6.50000	−	11.2583i	−0.301107	−	0.521532i
$467$			23.0000i			1.06431i	0.846646	+	0.532157i	$0.178618\pi$
$467$			23.0000i			1.06431i	−0.846646	+	0.532157i	$0.821382\pi$
$468$			12.0000i			0.554700i
$469$	−8.00000	−	13.8564i	−0.369406	−	0.639829i
$470$		0			0
$471$	−3.00000	−	5.19615i	−0.138233	−	0.239426i
$472$	0.866025	+	0.500000i	0.0398621	+	0.0230144i
$473$		0			0
$474$	4.00000			0.183726
$475$		0			0
$476$	−14.0000			−0.641689
$477$		0			0
$478$	−5.19615	−	3.00000i	−0.237666	−	0.137217i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−12.0000	−	20.7846i	−0.547153	−	0.947697i
$482$			14.0000i			0.637683i
$483$			4.00000i			0.182006i
$484$	−5.50000	−	9.52628i	−0.250000	−	0.433013i
$485$		0			0
$486$	16.0000			0.725775
$487$			20.0000i			0.906287i	0.891438	+	0.453143i	$0.149697\pi$
$487$			20.0000i			0.906287i	−0.891438	+	0.453143i	$0.850303\pi$
$488$	−6.92820	+	4.00000i	−0.313625	+	0.181071i
$489$	−6.00000	+	10.3923i	−0.271329	+	0.469956i
$490$		0			0
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	−0.942057	−	0.335453i	$-0.891111\pi$
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	0.761539	+	0.648119i	$0.224444\pi$
$492$	−1.73205	−	1.00000i	−0.0780869	−	0.0450835i
$493$		−	70.0000i		−	3.15264i
$494$	−21.0000	+	15.5885i	−0.944835	+	0.701358i
$495$		0			0
$496$	1.00000	−	1.73205i	0.0449013	−	0.0777714i
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$	11.2583	−	6.50000i	0.504498	−	0.291272i
$499$	−16.5000	+	28.5788i	−0.738641	+	1.27936i	0.214466	+	0.976732i	$0.431199\pi$
$499$	−16.5000	+	28.5788i	−0.738641	+	1.27936i	−0.953107	+	0.302633i	$0.902134\pi$
$500$		0			0
$501$	10.0000			0.446767
$502$		−	20.0000i		−	0.892644i
$503$	−6.92820	+	4.00000i	−0.308913	+	0.178351i	−0.646440	−	0.762965i	$-0.723743\pi$
$503$	−6.92820	+	4.00000i	−0.308913	+	0.178351i	0.337527	+	0.941316i	$0.390410\pi$
$504$	2.00000	+	3.46410i	0.0890871	+	0.154303i
$505$		0			0
$506$		0			0
$507$	19.9186	−	11.5000i	0.884615	−	0.510733i
$508$	10.3923	+	6.00000i	0.461084	+	0.266207i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	−3.00000	+	5.19615i	−0.132712	+	0.229864i
$512$			1.00000i			0.0441942i
$513$	12.9904	+	17.5000i	0.573539	+	0.772644i
$514$	15.0000			0.661622
$515$		0			0
$516$	6.00000	−	10.3923i	0.264135	−	0.457496i
$517$		0			0
$518$	−6.92820	−	4.00000i	−0.304408	−	0.175750i
$519$	3.00000	+	5.19615i	0.131685	+	0.228086i
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	−17.3205	+	10.0000i	−0.758098	+	0.437688i
$523$	25.1147	−	14.5000i	1.09819	−	0.634041i	0.162446	−	0.986718i	$-0.448062\pi$
$523$	25.1147	−	14.5000i	1.09819	−	0.634041i	0.935745	+	0.352677i	$0.114728\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$	−7.00000	−	12.1244i	−0.305215	−	0.528647i
$527$	12.1244	+	7.00000i	0.528145	+	0.304925i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	2.00000			0.0867926
$532$	−3.46410	+	8.00000i	−0.150188	+	0.346844i
$533$		−	12.0000i		−	0.519778i
$534$	−6.50000	+	11.2583i	−0.281283	+	0.487196i
$535$		0			0
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	7.79423	+	4.50000i	0.336346	+	0.194189i
$538$	−22.5167	+	13.0000i	−0.970762	+	0.560470i
$539$		0			0
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	22.5167	−	13.0000i	0.967173	−	0.558398i
$543$		−	20.0000i		−	0.858282i
$544$	−7.00000			−0.300123
$545$		0			0
$546$	6.00000	−	10.3923i	0.256776	−	0.444750i
$547$	−0.866025	+	0.500000i	−0.0370286	+	0.0213785i	−0.518400	−	0.855138i	$-0.673472\pi$
$547$	−0.866025	+	0.500000i	−0.0370286	+	0.0213785i	0.481371	+	0.876517i	$0.340139\pi$
$548$	12.9904	+	7.50000i	0.554922	+	0.320384i
$549$	−8.00000	+	13.8564i	−0.341432	+	0.591377i
$550$		0			0
$551$	−40.0000	−	17.3205i	−1.70406	−	0.737878i
$552$			2.00000i			0.0851257i
$553$	6.92820	+	4.00000i	0.294617	+	0.170097i
$554$	−11.0000	+	19.0526i	−0.467345	+	0.809466i
$555$		0			0
$556$		0			0
$557$	−1.73205	+	1.00000i	−0.0733893	+	0.0423714i	−0.536246	−	0.844062i	$-0.680158\pi$
$557$	−1.73205	+	1.00000i	−0.0733893	+	0.0423714i	0.462856	+	0.886433i	$0.346825\pi$
$558$		−	4.00000i		−	0.169334i
$559$	72.0000			3.04528
$560$		0			0
$561$		0			0
$562$			7.00000i			0.295277i
$563$			43.0000i			1.81223i	0.423027	+	0.906117i	$0.360967\pi$
$563$			43.0000i			1.81223i	−0.423027	+	0.906117i	$0.639033\pi$
$564$		0			0
$565$		0			0
$566$	14.0000	+	24.2487i	0.588464	+	1.01925i
$567$	1.73205	+	1.00000i	0.0727393	+	0.0419961i
$568$	−10.3923	−	6.00000i	−0.436051	−	0.251754i
$569$	−1.00000			−0.0419222			−0.0209611	−	0.999780i	$-0.506673\pi$
$569$	−1.00000			−0.0419222			−0.0209611	+	0.999780i	$0.506673\pi$
$570$		0			0
$571$	1.00000			0.0418487			0.0209243	−	0.999781i	$-0.493339\pi$
$571$	1.00000			0.0418487			0.0209243	+	0.999781i	$0.493339\pi$
$572$		0			0
$573$	−8.66025	−	5.00000i	−0.361787	−	0.208878i
$574$	−2.00000	−	3.46410i	−0.0834784	−	0.144589i
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$		−	34.0000i		−	1.41544i	−0.706494	−	0.707719i	$-0.749724\pi$
$577$		−	34.0000i		−	1.41544i	0.706494	−	0.707719i	$-0.250276\pi$
$578$		−	32.0000i		−	1.33102i
$579$	5.50000	+	9.52628i	0.228572	+	0.395899i
$580$		0			0
$581$	26.0000			1.07866
$582$			15.0000i			0.621770i
$583$		0			0
$584$	−1.50000	+	2.59808i	−0.0620704	+	0.107509i
$585$		0			0
$586$	−16.0000	+	27.7128i	−0.660954	+	1.14481i
$587$	−38.9711	−	22.5000i	−1.60851	−	0.928674i	−0.989704	−	0.143132i	$-0.954283\pi$
$587$	−38.9711	−	22.5000i	−1.60851	−	0.928674i	−0.618808	−	0.785543i	$-0.712384\pi$
$588$			3.00000i			0.123718i
$589$	7.00000	−	5.19615i	0.288430	−	0.214104i
$590$		0			0
$591$	−2.00000	+	3.46410i	−0.0822690	+	0.142494i
$592$	−3.46410	−	2.00000i	−0.142374	−	0.0821995i
$593$	12.1244	−	7.00000i	0.497888	−	0.287456i	−0.229953	−	0.973202i	$-0.573857\pi$
$593$	12.1244	−	7.00000i	0.497888	−	0.287456i	0.727841	+	0.685746i	$0.240524\pi$
$594$		0			0
$595$		0			0
$596$	16.0000			0.655386
$597$		−	16.0000i		−	0.654836i
$598$	−10.3923	+	6.00000i	−0.424973	+	0.245358i
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	0.717021	−	0.697051i	$-0.245505\pi$
$599$	−6.00000	−	10.3923i	−0.245153	−	0.424618i	−0.962175	+	0.272433i	$0.912172\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	20.7846	−	12.0000i	0.847117	−	0.489083i
$603$	−13.8564	−	8.00000i	−0.564276	−	0.325785i
$604$	−6.00000	−	10.3923i	−0.244137	−	0.422857i
$605$		0			0
$606$	−1.00000	+	1.73205i	−0.0406222	+	0.0703598i
$607$			14.0000i			0.568242i	0.958788	+	0.284121i	$0.0917018\pi$
$607$			14.0000i			0.568242i	−0.958788	+	0.284121i	$0.908298\pi$
$608$	−1.73205	+	4.00000i	−0.0702439	+	0.162221i
$609$	20.0000			0.810441
$610$		0			0
$611$		0			0
$612$	−12.1244	+	7.00000i	−0.490098	+	0.282958i
$613$	−12.1244	−	7.00000i	−0.489698	−	0.282727i	0.234751	−	0.972056i	$-0.424572\pi$
$613$	−12.1244	−	7.00000i	−0.489698	−	0.282727i	−0.724449	+	0.689328i	$0.757906\pi$
$614$	−9.50000	−	16.4545i	−0.383389	−	0.664049i
$615$		0			0
$616$		0			0
$617$	−6.06218	+	3.50000i	−0.244054	+	0.140905i	−0.617039	−	0.786933i	$-0.711668\pi$
$617$	−6.06218	+	3.50000i	−0.244054	+	0.140905i	0.372985	+	0.927838i	$0.378334\pi$
$618$	−10.3923	+	6.00000i	−0.418040	+	0.241355i
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$	5.00000	+	8.66025i	0.200643	+	0.347524i
$622$	−25.9808	−	15.0000i	−1.04173	−	0.601445i
$623$	−22.5167	+	13.0000i	−0.902111	+	0.520834i
$624$	3.00000	−	5.19615i	0.120096	−	0.208013i
$625$		0			0
$626$	11.0000			0.439648
$627$		0			0
$628$		−	6.00000i		−	0.239426i
$629$	14.0000	−	24.2487i	0.558217	−	0.966859i
$630$		0			0
$631$	−24.0000	−	41.5692i	−0.955425	−	1.65484i	−0.733393	−	0.679805i	$-0.762064\pi$
$631$	−24.0000	−	41.5692i	−0.955425	−	1.65484i	−0.222032	−	0.975039i	$-0.571269\pi$
$632$	3.46410	+	2.00000i	0.137795	+	0.0795557i
$633$	−19.9186	+	11.5000i	−0.791693	+	0.457084i
$634$	24.0000			0.953162
$635$		0			0
$636$		0			0
$637$	−15.5885	+	9.00000i	−0.617637	+	0.356593i
$638$		0			0
$639$	−24.0000			−0.949425
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$	12.9904	−	7.50000i	0.512689	−	0.296001i
$643$	−21.6506	−	12.5000i	−0.853818	−	0.492952i	0.00811944	−	0.999967i	$-0.497415\pi$
$643$	−21.6506	−	12.5000i	−0.853818	−	0.492952i	−0.861937	+	0.507015i	$0.830749\pi$
$644$	−2.00000	+	3.46410i	−0.0788110	+	0.136505i
$645$		0			0
$646$	−28.0000	−	12.1244i	−1.10165	−	0.477026i
$647$		−	12.0000i		−	0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$		0			0
$650$		0			0
$651$	−2.00000	+	3.46410i	−0.0783862	+	0.135769i
$652$	−10.3923	+	6.00000i	−0.406994	+	0.234978i
$653$			12.0000i			0.469596i	0.972044	+	0.234798i	$0.0754429\pi$
$653$			12.0000i			0.469596i	−0.972044	+	0.234798i	$0.924557\pi$
$654$	2.00000			0.0782062
$655$		0			0
$656$	−1.00000	−	1.73205i	−0.0390434	−	0.0676252i
$657$			6.00000i			0.234082i
$658$		0			0
$659$	1.50000	+	2.59808i	0.0584317	+	0.101207i	0.893762	−	0.448542i	$-0.148057\pi$
$659$	1.50000	+	2.59808i	0.0584317	+	0.101207i	−0.835330	+	0.549749i	$0.814723\pi$
$660$		0			0
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	0.902297	−	0.431116i	$-0.141880\pi$
$661$	2.00000	+	3.46410i	0.0777910	+	0.134738i	−0.824506	+	0.565854i	$0.808547\pi$
$662$	14.7224	+	8.50000i	0.572204	+	0.330362i
$663$	36.3731	+	21.0000i	1.41261	+	0.815572i
$664$	13.0000			0.504498
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−17.3205	−	10.0000i	−0.670653	−	0.387202i
$668$	8.66025	+	5.00000i	0.335075	+	0.193456i
$669$	−1.00000	−	1.73205i	−0.0386622	−	0.0669650i
$670$		0			0
$671$		0			0
$672$		−	2.00000i		−	0.0771517i
$673$			26.0000i			1.00223i	0.865382	+	0.501113i	$0.167076\pi$
$673$			26.0000i			1.00223i	−0.865382	+	0.501113i	$0.832924\pi$
$674$	−11.0000	−	19.0526i	−0.423704	−	0.733877i
$675$		0			0
$676$	23.0000			0.884615
$677$			26.0000i			0.999261i	0.866239	+	0.499631i	$0.166531\pi$
$677$			26.0000i			0.999261i	−0.866239	+	0.499631i	$0.833469\pi$
$678$	−0.866025	+	0.500000i	−0.0332595	+	0.0192024i
$679$	−15.0000	+	25.9808i	−0.575647	+	0.997050i
$680$		0			0
$681$	−6.50000	+	11.2583i	−0.249081	+	0.431420i
$682$		0			0
$683$		−	15.0000i		−	0.573959i	−0.957937	−	0.286980i	$-0.907349\pi$
$683$		−	15.0000i		−	0.573959i	0.957937	−	0.286980i	$-0.0926512\pi$
$684$	1.00000	+	8.66025i	0.0382360	+	0.331133i
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	15.5885	+	9.00000i	0.594737	+	0.343371i
$688$	10.3923	−	6.00000i	0.396203	−	0.228748i
$689$		0			0
$690$		0			0
$691$	37.0000			1.40755			0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000			1.40755			0.703773	+	0.710425i	$0.251497\pi$
$692$			6.00000i			0.228086i
$693$		0			0
$694$	−6.00000	−	10.3923i	−0.227757	−	0.394486i
$695$		0			0
$696$	10.0000			0.379049
$697$	12.1244	−	7.00000i	0.459243	−	0.265144i
$698$	13.8564	+	8.00000i	0.524473	+	0.302804i
$699$	6.50000	+	11.2583i	0.245853	+	0.425829i
$700$		0			0
$701$	12.0000	−	20.7846i	0.453234	−	0.785024i	−0.545351	−	0.838208i	$-0.683604\pi$
$701$	12.0000	−	20.7846i	0.453234	−	0.785024i	0.998585	+	0.0531839i	$0.0169370\pi$
$702$		−	30.0000i		−	1.13228i
$703$	−10.3923	−	14.0000i	−0.391953	−	0.528020i
$704$		0			0
$705$		0			0
$706$	1.50000	−	2.59808i	0.0564532	−	0.0977799i
$707$	−3.46410	+	2.00000i	−0.130281	+	0.0752177i
$708$	−0.866025	−	0.500000i	−0.0325472	−	0.0187912i
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	−0.999549	−	0.0300298i	$-0.990440\pi$
$709$	−14.0000	−	24.2487i	−0.525781	−	0.910679i	0.473768	−	0.880650i	$-0.342894\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	−11.2583	+	6.50000i	−0.421924	+	0.243598i
$713$	3.46410	−	2.00000i	0.129732	−	0.0749006i
$714$	14.0000			0.523937
$715$		0			0
$716$	4.50000	+	7.79423i	0.168173	+	0.291284i
$717$	5.19615	+	3.00000i	0.194054	+	0.112037i
$718$	20.7846	−	12.0000i	0.775675	−	0.447836i
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	−0.396605	−	0.917989i	$-0.629812\pi$
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	0.993305	−	0.115524i	$-0.0368548\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	−13.8564	+	13.0000i	−0.515682	+	0.483810i
$723$		−	14.0000i		−	0.520666i
$724$	10.0000	−	17.3205i	0.371647	−	0.643712i
$725$		0			0
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$	12.1244	+	7.00000i	0.449667	+	0.259616i	0.707690	−	0.706523i	$-0.249737\pi$
$727$	12.1244	+	7.00000i	0.449667	+	0.259616i	−0.258022	+	0.966139i	$0.583071\pi$
$728$	10.3923	−	6.00000i	0.385164	−	0.222375i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	42.0000	+	72.7461i	1.55343	+	2.69061i
$732$	6.92820	−	4.00000i	0.256074	−	0.147844i
$733$			6.00000i			0.221615i	0.993842	+	0.110808i	$0.0353437\pi$
$733$			6.00000i			0.221615i	−0.993842	+	0.110808i	$0.964656\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	−1.00000	+	1.73205i	−0.0368605	+	0.0638442i
$737$		0			0
$738$	−3.46410	−	2.00000i	−0.127515	−	0.0736210i
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	−0.00311943	−	0.999995i	$-0.500993\pi$
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	0.867581	−	0.497296i	$-0.165674\pi$
$740$		0			0
$741$	21.0000	−	15.5885i	0.771454	−	0.572656i
$742$		0			0
$743$	22.5167	+	13.0000i	0.826056	+	0.476924i	0.852500	−	0.522727i	$-0.175085\pi$
$743$	22.5167	+	13.0000i	0.826056	+	0.476924i	−0.0264443	+	0.999650i	$0.508418\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$		0			0
$746$	3.00000	−	5.19615i	0.109838	−	0.190245i
$747$	22.5167	−	13.0000i	0.823842	−	0.475645i
$748$		0			0
$749$	30.0000			1.09618
$750$		0			0
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	0.999570	−	0.0293387i	$-0.00934013\pi$
$751$	13.0000	+	22.5167i	0.474377	+	0.821645i	−0.525193	+	0.850983i	$0.676007\pi$
$752$		0			0
$753$			20.0000i			0.728841i
$754$	30.0000	+	51.9615i	1.09254	+	1.89233i
$755$		0			0
$756$	−5.00000	−	8.66025i	−0.181848	−	0.314970i
$757$	−27.7128	−	16.0000i	−1.00724	−	0.581530i	−0.0968571	−	0.995298i	$-0.530879\pi$
$757$	−27.7128	−	16.0000i	−1.00724	−	0.581530i	−0.910382	+	0.413768i	$0.864212\pi$
$758$	−0.866025	−	0.500000i	−0.0314555	−	0.0181608i
$759$		0			0
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$	−10.3923	−	6.00000i	−0.376473	−	0.217357i
$763$	3.46410	+	2.00000i	0.125409	+	0.0724049i
$764$	−5.00000	−	8.66025i	−0.180894	−	0.313317i
$765$		0			0
$766$	6.00000	+	10.3923i	0.216789	+	0.375489i
$767$		−	6.00000i		−	0.216647i
$768$		−	1.00000i		−	0.0360844i
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$		0			0
$771$	−15.0000			−0.540212
$772$			11.0000i			0.395899i
$773$	−5.19615	+	3.00000i	−0.186893	+	0.107903i	−0.590527	−	0.807018i	$-0.701080\pi$
$773$	−5.19615	+	3.00000i	−0.186893	+	0.107903i	0.403634	+	0.914920i	$0.367747\pi$
$774$	12.0000	−	20.7846i	0.431331	−	0.747087i
$775$		0			0
$776$	−7.50000	+	12.9904i	−0.269234	+	0.466328i
$777$	6.92820	+	4.00000i	0.248548	+	0.143499i
$778$		−	18.0000i		−	0.645331i
$779$	−1.00000	−	8.66025i	−0.0358287	−	0.310286i
$780$		0			0
$781$		0			0
$782$	−12.1244	−	7.00000i	−0.433566	−	0.250319i
$783$	43.3013	−	25.0000i	1.54746	−	0.893427i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		0			0
$786$	1.00000			0.0356688
$787$		−	29.0000i		−	1.03374i	−0.856064	−	0.516869i	$-0.827097\pi$
$787$		−	29.0000i		−	1.03374i	0.856064	−	0.516869i	$-0.172903\pi$
$788$	−3.46410	+	2.00000i	−0.123404	+	0.0712470i
$789$	7.00000	+	12.1244i	0.249207	+	0.431638i
$790$		0			0
$791$	−2.00000			−0.0711118
$792$		0			0
$793$	41.5692	+	24.0000i	1.47617	+	0.852265i
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$	3.46410	−	8.00000i	0.122628	−	0.283197i
$799$		0			0
$800$		0			0
$801$	−13.0000	+	22.5167i	−0.459332	+	0.795587i
$802$	−5.19615	+	3.00000i	−0.183483	+	0.105934i
$803$		0			0
$804$	4.00000	+	6.92820i	0.141069	+	0.244339i
$805$		0			0
$806$	−12.0000			−0.422682
$807$	22.5167	−	13.0000i	0.792624	−	0.457622i
$808$	−1.73205	+	1.00000i	−0.0609333	+	0.0351799i
$809$	−45.0000			−1.58212			−0.791058	−	0.611741i	$-0.790469\pi$
$809$	−45.0000			−1.58212			−0.791058	+	0.611741i	$0.790469\pi$
$810$		0			0
$811$	−22.0000	−	38.1051i	−0.772524	−	1.33805i	−0.936175	−	0.351533i	$-0.885660\pi$
$811$	−22.0000	−	38.1051i	−0.772524	−	1.33805i	0.163651	−	0.986518i	$-0.447673\pi$
$812$	17.3205	+	10.0000i	0.607831	+	0.350931i
$813$	−22.5167	+	13.0000i	−0.789694	+	0.455930i
$814$		0			0
$815$		0			0
$816$	7.00000			0.245049
$817$	51.9615	−	6.00000i	1.81790	−	0.209913i
$818$		−	2.00000i		−	0.0699284i
$819$	12.0000	−	20.7846i	0.419314	−	0.726273i
$820$		0			0
$821$	−23.0000	−	39.8372i	−0.802706	−	1.39033i	−0.917829	−	0.396976i	$-0.870060\pi$
$821$	−23.0000	−	39.8372i	−0.802706	−	1.39033i	0.115124	−	0.993351i	$-0.463274\pi$
$822$	−12.9904	−	7.50000i	−0.453092	−	0.261593i
$823$	6.92820	−	4.00000i	0.241502	−	0.139431i	−0.374365	−	0.927281i	$-0.622139\pi$
$823$	6.92820	−	4.00000i	0.241502	−	0.139431i	0.615867	+	0.787850i	$0.288806\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$	−1.00000	−	1.73205i	−0.0347945	−	0.0602658i
$827$	31.1769	−	18.0000i	1.08413	−	0.625921i	0.152121	−	0.988362i	$-0.451390\pi$
$827$	31.1769	−	18.0000i	1.08413	−	0.625921i	0.932007	+	0.362441i	$0.118056\pi$
$828$			4.00000i			0.139010i
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$		0			0
$831$	11.0000	−	19.0526i	0.381586	−	0.660926i
$832$	5.19615	−	3.00000i	0.180144	−	0.104006i
$833$	−18.1865	−	10.5000i	−0.630126	−	0.363803i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			10.0000i			0.345651i
$838$	11.2583	+	6.50000i	0.388913	+	0.224539i
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	−0.581067	−	0.813856i	$-0.697365\pi$
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	0.995353	+	0.0962912i	$0.0306980\pi$
$840$		0			0
$841$	−35.5000	+	61.4878i	−1.22414	+	2.12027i
$842$	29.4449	−	17.0000i	1.01474	−	0.585859i
$843$		−	7.00000i		−	0.241093i
$844$	−23.0000			−0.791693
$845$		0			0
$846$		0			0
$847$			22.0000i			0.755929i
$848$		0			0
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$		0			0
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$	10.3923	+	6.00000i	0.356034	+	0.205557i
$853$	−38.1051	−	22.0000i	−1.30469	−	0.753266i	−0.323489	−	0.946232i	$-0.604856\pi$
$853$	−38.1051	−	22.0000i	−1.30469	−	0.753266i	−0.981205	+	0.192966i	$0.938189\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$	15.0000			0.512689
$857$	15.5885	+	9.00000i	0.532492	+	0.307434i	0.742030	−	0.670366i	$-0.233863\pi$
$857$	15.5885	+	9.00000i	0.532492	+	0.307434i	−0.209539	+	0.977800i	$0.567196\pi$
$858$		0			0
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	0.570064	−	0.821600i	$-0.306918\pi$
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	−0.996559	+	0.0828900i	$0.973585\pi$
$860$		0			0
$861$	2.00000	+	3.46410i	0.0681598	+	0.118056i
$862$			30.0000i			1.02180i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$		0			0
$866$	−21.0000			−0.713609
$867$			32.0000i			1.08678i
$868$	−3.46410	+	2.00000i	−0.117579	+	0.0678844i
$869$		0			0
$870$		0			0
$871$	−24.0000	+	41.5692i	−0.813209	+	1.40852i
$872$	1.73205	+	1.00000i	0.0586546	+	0.0338643i
$873$			30.0000i			1.01535i
$874$	−7.00000	+	5.19615i	−0.236779	+	0.175762i
$875$		0			0
$876$	1.50000	−	2.59808i	0.0506803	−	0.0877809i
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	0.639040	−	0.769174i	$-0.279332\pi$
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	−0.346604	+	0.938012i	$0.612665\pi$
$878$	6.92820	−	4.00000i	0.233816	−	0.134993i
$879$	16.0000	−	27.7128i	0.539667	−	0.934730i
$880$		0			0
$881$	−37.0000			−1.24656			−0.623281	−	0.781998i	$-0.714201\pi$
$881$	−37.0000			−1.24656			−0.623281	+	0.781998i	$0.714201\pi$
$882$			6.00000i			0.202031i
$883$	−11.2583	+	6.50000i	−0.378873	+	0.218742i	−0.677328	−	0.735681i	$-0.736862\pi$
$883$	−11.2583	+	6.50000i	−0.378873	+	0.218742i	0.298455	+	0.954424i	$0.403529\pi$
$884$	21.0000	+	36.3731i	0.706306	+	1.22336i
$885$		0			0
$886$	36.0000			1.20944
$887$	−24.2487	+	14.0000i	−0.814192	+	0.470074i	−0.848410	−	0.529340i	$-0.822439\pi$
$887$	−24.2487	+	14.0000i	−0.814192	+	0.470074i	0.0342175	+	0.999414i	$0.489106\pi$
$888$	3.46410	+	2.00000i	0.116248	+	0.0671156i
$889$	−12.0000	−	20.7846i	−0.402467	−	0.697093i
$890$		0			0
$891$		0			0
$892$		−	2.00000i		−	0.0669650i
$893$		0			0
$894$	−16.0000			−0.535120
$895$		0			0
$896$	1.00000	−	1.73205i	0.0334077	−	0.0578638i
$897$	10.3923	−	6.00000i	0.346989	−	0.200334i
$898$	35.5070	+	20.5000i	1.18489	+	0.684094i
$899$	−10.0000	−	17.3205i	−0.333519	−	0.577671i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−20.7846	+	12.0000i	−0.691669	+	0.399335i
$904$	−1.00000			−0.0332595
$905$		0			0
$906$	6.00000	+	10.3923i	0.199337	+	0.345261i
$907$	45.8993	+	26.5000i	1.52406	+	0.879918i	0.999594	+	0.0284883i	$0.00906934\pi$
$907$	45.8993	+	26.5000i	1.52406	+	0.879918i	0.524469	+	0.851430i	$0.324264\pi$
$908$	−11.2583	+	6.50000i	−0.373621	+	0.215710i
$909$	−2.00000	+	3.46410i	−0.0663358	+	0.114897i
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$	1.73205	−	4.00000i	0.0573539	−	0.132453i
$913$		0			0
$914$	5.50000	−	9.52628i	0.181924	−	0.315101i
$915$		0			0
$916$	9.00000	+	15.5885i	0.297368	+	0.515057i
$917$	1.73205	+	1.00000i	0.0571974	+	0.0330229i
$918$	30.3109	−	17.5000i	1.00041	−	0.577586i
$919$	−56.0000			−1.84727			−0.923635	−	0.383274i	$-0.874797\pi$
$919$	−56.0000			−1.84727			−0.923635	+	0.383274i	$0.874797\pi$
$920$		0			0
$921$	9.50000	+	16.4545i	0.313036	+	0.542194i
$922$	1.73205	−	1.00000i	0.0570421	−	0.0329332i
$923$			72.0000i			2.36991i
$924$		0			0
$925$		0			0
$926$	11.0000	−	19.0526i	0.361482	−	0.626106i
$927$	−20.7846	+	12.0000i	−0.682656	+	0.394132i
$928$	8.66025	+	5.00000i	0.284287	+	0.164133i
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	−0.889583	−	0.456774i	$-0.849005\pi$
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	0.840369	+	0.542014i	$0.182338\pi$
$930$		0			0
$931$	−10.5000	+	7.79423i	−0.344124	+	0.255446i
$932$			13.0000i			0.425829i
$933$	25.9808	+	15.0000i	0.850572	+	0.491078i
$934$	11.5000	−	19.9186i	0.376291	−	0.651756i
$935$		0			0
$936$	6.00000	−	10.3923i	0.196116	−	0.339683i
$937$	0.866025	−	0.500000i	0.0282918	−	0.0163343i	−0.485787	−	0.874077i	$-0.661467\pi$
$937$	0.866025	−	0.500000i	0.0282918	−	0.0163343i	0.514079	+	0.857743i	$0.328134\pi$
$938$			16.0000i			0.522419i
$939$	−11.0000			−0.358971
$940$		0			0
$941$	−22.0000	−	38.1051i	−0.717180	−	1.24219i	−0.962113	−	0.272651i	$-0.912099\pi$
$941$	−22.0000	−	38.1051i	−0.717180	−	1.24219i	0.244933	−	0.969540i	$-0.421234\pi$
$942$			6.00000i			0.195491i
$943$		−	4.00000i		−	0.130258i
$944$	−0.500000	−	0.866025i	−0.0162736	−	0.0281867i
$945$		0			0
$946$		0			0
$947$	−45.0333	−	26.0000i	−1.46339	−	0.844886i	−0.464220	−	0.885720i	$-0.653665\pi$
$947$	−45.0333	−	26.0000i	−1.46339	−	0.844886i	−0.999166	+	0.0408333i	$0.986999\pi$
$948$	−3.46410	−	2.00000i	−0.112509	−	0.0649570i
$949$	18.0000			0.584305
$950$		0			0
$951$	−24.0000			−0.778253
$952$	12.1244	+	7.00000i	0.392953	+	0.226871i
$953$	−1.73205	−	1.00000i	−0.0561066	−	0.0323932i	0.471684	−	0.881768i	$-0.343646\pi$
$953$	−1.73205	−	1.00000i	−0.0561066	−	0.0323932i	−0.527791	+	0.849374i	$0.676980\pi$
$954$		0			0
$955$		0			0
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$		0			0
$958$		−	24.0000i		−	0.775405i
$959$	−15.0000	−	25.9808i	−0.484375	−	0.838963i
$960$		0			0
$961$	−27.0000			−0.870968
$962$			24.0000i			0.773791i
$963$	25.9808	−	15.0000i	0.837218	−	0.483368i
$964$	7.00000	−	12.1244i	0.225455	−	0.390499i
$965$		0			0
$966$	2.00000	−	3.46410i	0.0643489	−	0.111456i
$967$	−10.3923	−	6.00000i	−0.334194	−	0.192947i	0.323508	−	0.946226i	$-0.395138\pi$
$967$	−10.3923	−	6.00000i	−0.334194	−	0.192947i	−0.657702	+	0.753279i	$0.728471\pi$
$968$			11.0000i			0.353553i
$969$	28.0000	+	12.1244i	0.899490	+	0.389490i
$970$		0			0
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	−0.238114	−	0.971237i	$-0.576529\pi$
$971$	22.5000	−	38.9711i	0.722059	−	1.25064i	0.960173	−	0.279406i	$-0.0901376\pi$
$972$	−13.8564	−	8.00000i	−0.444444	−	0.256600i
$973$		0			0
$974$	10.0000	−	17.3205i	0.320421	−	0.554985i
$975$		0			0
$976$	8.00000			0.256074
$977$		−	42.0000i		−	1.34370i	−0.740688	−	0.671850i	$-0.765500\pi$
$977$		−	42.0000i		−	1.34370i	0.740688	−	0.671850i	$-0.234500\pi$
$978$	10.3923	−	6.00000i	0.332309	−	0.191859i
$979$		0			0
$980$		0			0
$981$	4.00000			0.127710
$982$	6.92820	−	4.00000i	0.221088	−	0.127645i
$983$	−20.7846	−	12.0000i	−0.662926	−	0.382741i	0.130465	−	0.991453i	$-0.458353\pi$
$983$	−20.7846	−	12.0000i	−0.662926	−	0.382741i	−0.793391	+	0.608712i	$0.791686\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$		0			0
$986$	−35.0000	+	60.6218i	−1.11463	+	1.93059i
$987$		0			0
$988$	25.9808	−	3.00000i	0.826558	−	0.0954427i
$989$	24.0000			0.763156
$990$		0			0
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$	−1.73205	+	1.00000i	−0.0549927	+	0.0317500i
$993$	−14.7224	−	8.50000i	−0.467202	−	0.269739i
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$		0			0
$996$	−13.0000			−0.411921
$997$	19.0526	−	11.0000i	0.603401	−	0.348373i	−0.166978	−	0.985961i	$-0.553401\pi$
$997$	19.0526	−	11.0000i	0.603401	−	0.348373i	0.770378	+	0.637587i	$0.220067\pi$
$998$	28.5788	−	16.5000i	0.904647	−	0.522298i
$999$	20.0000			0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.b.49.1		4
5.2	odd	4		950.2.e.g.201.1	yes	2
5.3	odd	4		950.2.e.b.201.1	✓	2
5.4	even	2	inner	950.2.j.b.49.2		4
19.7	even	3	inner	950.2.j.b.349.2		4
95.7	odd	12		950.2.e.g.501.1	yes	2
95.64	even	6	inner	950.2.j.b.349.1		4
95.83	odd	12		950.2.e.b.501.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.b.201.1	✓	2	5.3	odd	4
950.2.e.b.501.1	yes	2	95.83	odd	12
950.2.e.g.201.1	yes	2	5.2	odd	4
950.2.e.g.501.1	yes	2	95.7	odd	12
950.2.j.b.49.1		4	1.1	even	1	trivial
950.2.j.b.49.2		4	5.4	even	2	inner
950.2.j.b.349.1		4	95.64	even	6	inner
950.2.j.b.349.2		4	19.7	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000i q^{7} -1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -2.00000i q^{7} -1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +1.00000i q^{12} +(-5.19615 + 3.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-6.06218 - 3.50000i) q^{17} +2.00000i q^{18} +(-3.50000 + 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(-1.73205 + 1.00000i) q^{23} +(0.500000 - 0.866025i) q^{24} +6.00000 q^{26} -5.00000i q^{27} +(1.73205 - 1.00000i) q^{28} +(5.00000 + 8.66025i) q^{29} -2.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(3.50000 + 6.06218i) q^{34} +(1.00000 - 1.73205i) q^{36} +4.00000i q^{37} +(4.33013 - 0.500000i) q^{38} -6.00000 q^{39} +(-1.00000 + 1.73205i) q^{41} +(-1.73205 + 1.00000i) q^{42} +(-10.3923 - 6.00000i) q^{43} +2.00000 q^{46} +(-0.866025 + 0.500000i) q^{48} +3.00000 q^{49} +(-3.50000 - 6.06218i) q^{51} +(-5.19615 - 3.00000i) q^{52} +(-2.50000 + 4.33013i) q^{54} -2.00000 q^{56} +(-4.33013 + 0.500000i) q^{57} -10.0000i q^{58} +(-0.500000 + 0.866025i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(1.73205 + 1.00000i) q^{62} +(-3.46410 + 2.00000i) q^{63} -1.00000 q^{64} +(6.92820 - 4.00000i) q^{67} -7.00000i q^{68} -2.00000 q^{69} +(6.00000 - 10.3923i) q^{71} +(-1.73205 + 1.00000i) q^{72} +(-2.59808 - 1.50000i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.00000 - 1.73205i) q^{76} +(5.19615 + 3.00000i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.73205 - 1.00000i) q^{82} +13.0000i q^{83} +2.00000 q^{84} +(6.00000 + 10.3923i) q^{86} +10.0000i q^{87} +(-6.50000 - 11.2583i) q^{89} +(6.00000 + 10.3923i) q^{91} +(-1.73205 - 1.00000i) q^{92} +(-1.73205 - 1.00000i) q^{93} +1.00000 q^{96} +(-12.9904 - 7.50000i) q^{97} +(-2.59808 - 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9	\( 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9} - 4 q^{14} - 2 q^{16} - 14 q^{19} + 4 q^{21} + 2 q^{24} + 24 q^{26} + 20 q^{29} - 8 q^{31} + 14 q^{34} + 4 q^{36} - 24 q^{39} - 4 q^{41} + 8 q^{46} + 12 q^{49} - 14 q^{51} - 10 q^{54} - 8 q^{56} - 2 q^{59} - 16 q^{61} - 4 q^{64} - 8 q^{69} + 24 q^{71} + 8 q^{74} - 16 q^{76} - 8 q^{79} - 2 q^{81} + 8 q^{84} + 24 q^{86} - 26 q^{89} + 24 q^{91} + 4 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9 - 4 * q^14 - 2 * q^16 - 14 * q^19 + 4 * q^21 + 2 * q^24 + 24 * q^26 + 20 * q^29 - 8 * q^31 + 14 * q^34 + 4 * q^36 - 24 * q^39 - 4 * q^41 + 8 * q^46 + 12 * q^49 - 14 * q^51 - 10 * q^54 - 8 * q^56 - 2 * q^59 - 16 * q^61 - 4 * q^64 - 8 * q^69 + 24 * q^71 + 8 * q^74 - 16 * q^76 - 8 * q^79 - 2 * q^81 + 8 * q^84 + 24 * q^86 - 26 * q^89 + 24 * q^91 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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