LMFDB - Embedded newform 1014.2.i.h.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(361,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("1014.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.i (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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$1.07992 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	1014.361
Dual form			1014.2.i.h.823.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.13706i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.0423637 + 0.0244587i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.13706i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.0423637 + 0.0244587i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.06853 + 1.85075i) q^{10} +(5.45241 - 3.14795i) q^{11} +1.00000 q^{12} -0.0489173 q^{14} +(1.85075 - 1.06853i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.44504 + 2.50289i) q^{17} -1.00000i q^{18} +(-6.24210 - 3.60388i) q^{19} +(-1.85075 - 1.06853i) q^{20} +0.0489173i q^{21} +(-3.14795 + 5.45241i) q^{22} +(1.35690 + 2.35021i) q^{23} +(-0.866025 + 0.500000i) q^{24} +0.432960 q^{25} -1.00000 q^{27} +(0.0423637 - 0.0244587i) q^{28} +(-2.45593 - 4.25379i) q^{29} +(-1.06853 + 1.85075i) q^{30} -9.00969i q^{31} +(0.866025 + 0.500000i) q^{32} +(5.45241 + 3.14795i) q^{33} -2.89008i q^{34} +(0.0522697 - 0.0905338i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.152673 + 0.0881460i) q^{37} +7.20775 q^{38} +2.13706 q^{40} +(7.44071 - 4.29590i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(3.35690 - 5.81431i) q^{43} -6.29590i q^{44} +(1.85075 + 1.06853i) q^{45} +(-2.35021 - 1.35690i) q^{46} +7.20775i q^{47} +(0.500000 - 0.866025i) q^{48} +(-3.49880 - 6.06011i) q^{49} +(-0.374955 + 0.216480i) q^{50} -2.89008 q^{51} +9.34481 q^{53} +(0.866025 - 0.500000i) q^{54} +(-6.72737 - 11.6521i) q^{55} +(-0.0244587 + 0.0423637i) q^{56} -7.20775i q^{57} +(4.25379 + 2.45593i) q^{58} +(3.69685 + 2.13437i) q^{59} -2.13706i q^{60} +(-3.55496 + 6.15737i) q^{61} +(4.50484 + 7.80262i) q^{62} +(-0.0423637 + 0.0244587i) q^{63} -1.00000 q^{64} -6.29590 q^{66} +(-4.66272 + 2.69202i) q^{67} +(1.44504 + 2.50289i) q^{68} +(-1.35690 + 2.35021i) q^{69} +0.104539i q^{70} +(-7.54637 - 4.35690i) q^{71} +(-0.866025 - 0.500000i) q^{72} -14.9487i q^{73} +(0.0881460 - 0.152673i) q^{74} +(0.216480 + 0.374955i) q^{75} +(-6.24210 + 3.60388i) q^{76} +0.307979 q^{77} +13.8291 q^{79} +(-1.85075 + 1.06853i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.29590 + 7.44071i) q^{82} +11.1347i q^{83} +(0.0423637 + 0.0244587i) q^{84} +(5.34883 + 3.08815i) q^{85} +6.71379i q^{86} +(2.45593 - 4.25379i) q^{87} +(3.14795 + 5.45241i) q^{88} +(3.39616 - 1.96077i) q^{89} -2.13706 q^{90} +2.71379 q^{92} +(7.80262 - 4.50484i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(-7.70171 + 13.3398i) q^{95} +1.00000i q^{96} +(-2.14678 - 1.23945i) q^{97} +(6.06011 + 3.49880i) q^{98} +6.29590i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9	$ 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9} + 2 q^{10} + 12 q^{12} + 36 q^{14} - 6 q^{16} - 16 q^{17} - 10 q^{22} - 72 q^{25} - 12 q^{27} - 22 q^{29} - 2 q^{30} + 8 q^{35} + 6 q^{36} + 16 q^{38} + 4 q^{40} + 18 q^{42} + 24 q^{43} + 6 q^{48} + 40 q^{49} - 32 q^{51} + 20 q^{53} - 36 q^{55} + 18 q^{56} - 44 q^{61} + 10 q^{62} - 12 q^{64} - 20 q^{66} + 16 q^{68} + 16 q^{74} - 36 q^{75} + 24 q^{77} + 124 q^{79} - 6 q^{81} + 4 q^{82} + 22 q^{87} + 10 q^{88} - 4 q^{90} - 8 q^{94} + 16 q^{95}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9 + 2 * q^10 + 12 * q^12 + 36 * q^14 - 6 * q^16 - 16 * q^17 - 10 * q^22 - 72 * q^25 - 12 * q^27 - 22 * q^29 - 2 * q^30 + 8 * q^35 + 6 * q^36 + 16 * q^38 + 4 * q^40 + 18 * q^42 + 24 * q^43 + 6 * q^48 + 40 * q^49 - 32 * q^51 + 20 * q^53 - 36 * q^55 + 18 * q^56 - 44 * q^61 + 10 * q^62 - 12 * q^64 - 20 * q^66 + 16 * q^68 + 16 * q^74 - 36 * q^75 + 24 * q^77 + 124 * q^79 - 6 * q^81 + 4 * q^82 + 22 * q^87 + 10 * q^88 - 4 * q^90 - 8 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	2.13706i		−	0.955724i	−0.878435	−	0.477862i	$-0.841412\pi$
$5$		−	2.13706i		−	0.955724i	0.878435	−	0.477862i	$-0.158588\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	0.0423637	+	0.0244587i	0.0160120	+	0.00924451i	0.507985	−	0.861366i	$-0.330391\pi$
$7$	0.0423637	+	0.0244587i	0.0160120	+	0.00924451i	−0.491973	+	0.870611i	$0.663724\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.06853	+	1.85075i	0.337899	+	0.585259i
$11$	5.45241	−	3.14795i	1.64396	−	0.949142i	0.664557	−	0.747237i	$-0.268620\pi$
$11$	5.45241	−	3.14795i	1.64396	−	0.949142i	0.979405	−	0.201905i	$-0.0647132\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	−0.0489173			−0.0130737
$15$	1.85075	−	1.06853i	0.477862	−	0.275894i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.44504	+	2.50289i	−0.350474	+	0.607039i	−0.986333	−	0.164767i	$-0.947313\pi$
$17$	−1.44504	+	2.50289i	−0.350474	+	0.607039i	0.635858	+	0.771806i	$0.280646\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−6.24210	−	3.60388i	−1.43203	−	0.826786i	−0.434759	−	0.900547i	$-0.643166\pi$
$19$	−6.24210	−	3.60388i	−1.43203	−	0.826786i	−0.997276	+	0.0737611i	$0.976500\pi$
$20$	−1.85075	−	1.06853i	−0.413841	−	0.238931i
$21$			0.0489173i			0.0106746i
$22$	−3.14795	+	5.45241i	−0.671145	+	1.16246i
$23$	1.35690	+	2.35021i	0.282932	+	0.490053i	0.972106	−	0.234543i	$-0.0753595\pi$
$23$	1.35690	+	2.35021i	0.282932	+	0.490053i	−0.689173	+	0.724597i	$0.742026\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.432960			0.0865921
$26$		0			0
$27$	−1.00000			−0.192450
$28$	0.0423637	−	0.0244587i	0.00800598	−	0.00462225i
$29$	−2.45593	−	4.25379i	−0.456054	−	0.789909i	0.542694	−	0.839931i	$-0.317404\pi$
$29$	−2.45593	−	4.25379i	−0.456054	−	0.789909i	−0.998748	+	0.0500215i	$0.984071\pi$
$30$	−1.06853	+	1.85075i	−0.195086	+	0.337899i
$31$		−	9.00969i		−	1.61819i	−0.587679	−	0.809094i	$-0.699958\pi$
$31$		−	9.00969i		−	1.61819i	0.587679	−	0.809094i	$-0.300042\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	5.45241	+	3.14795i	0.949142	+	0.547987i
$34$		−	2.89008i		−	0.495645i
$35$	0.0522697	−	0.0905338i	0.00883520	−	0.0153030i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−0.152673	+	0.0881460i	−0.0250993	+	0.0144911i	−0.512497	−	0.858689i	$-0.671279\pi$
$37$	−0.152673	+	0.0881460i	−0.0250993	+	0.0144911i	0.487398	+	0.873180i	$0.337946\pi$
$38$	7.20775			1.16925
$39$		0			0
$40$	2.13706			0.337899
$41$	7.44071	−	4.29590i	1.16204	−	0.670906i	0.210251	−	0.977647i	$-0.432572\pi$
$41$	7.44071	−	4.29590i	1.16204	−	0.670906i	0.951793	+	0.306741i	$0.0992386\pi$
$42$	−0.0244587	−	0.0423637i	−0.00377405	−	0.00653685i
$43$	3.35690	−	5.81431i	0.511922	−	0.886675i	−0.487983	−	0.872853i	$-0.662267\pi$
$43$	3.35690	−	5.81431i	0.511922	−	0.886675i	0.999904	−	0.0138213i	$-0.00439959\pi$
$44$		−	6.29590i		−	0.949142i
$45$	1.85075	+	1.06853i	0.275894	+	0.159287i
$46$	−2.35021	−	1.35690i	−0.346520	−	0.200063i
$47$			7.20775i			1.05136i	0.850683	+	0.525679i	$0.176189\pi$
$47$			7.20775i			1.05136i	−0.850683	+	0.525679i	$0.823811\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−3.49880	−	6.06011i	−0.499829	−	0.865729i
$50$	−0.374955	+	0.216480i	−0.0530266	+	0.0306149i
$51$	−2.89008			−0.404693
$52$		0			0
$53$	9.34481			1.28361			0.641804	−	0.766868i	$-0.278186\pi$
$53$	9.34481			1.28361			0.641804	+	0.766868i	$0.278186\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−6.72737	−	11.6521i	−0.907118	−	1.57117i
$56$	−0.0244587	+	0.0423637i	−0.00326843	+	0.00566108i
$57$		−	7.20775i		−	0.954690i
$58$	4.25379	+	2.45593i	0.558550	+	0.322479i
$59$	3.69685	+	2.13437i	0.481288	+	0.277872i	0.720953	−	0.692984i	$-0.243704\pi$
$59$	3.69685	+	2.13437i	0.481288	+	0.277872i	−0.239665	+	0.970856i	$0.577038\pi$
$60$		−	2.13706i		−	0.275894i
$61$	−3.55496	+	6.15737i	−0.455166	+	0.788370i	−0.998698	−	0.0510183i	$-0.983753\pi$
$61$	−3.55496	+	6.15737i	−0.455166	+	0.788370i	0.543532	+	0.839388i	$0.317087\pi$
$62$	4.50484	+	7.80262i	0.572116	+	0.990934i
$63$	−0.0423637	+	0.0244587i	−0.00533732	+	0.00308150i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.29590			−0.774971
$67$	−4.66272	+	2.69202i	−0.569642	+	0.328883i	−0.757006	−	0.653408i	$-0.773339\pi$
$67$	−4.66272	+	2.69202i	−0.569642	+	0.328883i	0.187365	+	0.982290i	$0.440005\pi$
$68$	1.44504	+	2.50289i	0.175237	+	0.303520i
$69$	−1.35690	+	2.35021i	−0.163351	+	0.282932i
$70$			0.104539i			0.0124949i
$71$	−7.54637	−	4.35690i	−0.895589	−	0.517068i	−0.0198223	−	0.999804i	$-0.506310\pi$
$71$	−7.54637	−	4.35690i	−0.895589	−	0.517068i	−0.875766	+	0.482735i	$0.839643\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	14.9487i		−	1.74961i	−0.484474	−	0.874806i	$-0.660989\pi$
$73$		−	14.9487i		−	1.74961i	0.484474	−	0.874806i	$-0.339011\pi$
$74$	0.0881460	−	0.152673i	0.0102468	−	0.0177479i
$75$	0.216480	+	0.374955i	0.0249970	+	0.0432960i
$76$	−6.24210	+	3.60388i	−0.716017	+	0.413393i
$77$	0.307979			0.0350974
$78$		0			0
$79$	13.8291			1.55589			0.777947	−	0.628330i	$-0.216261\pi$
$79$	13.8291			1.55589			0.777947	+	0.628330i	$0.216261\pi$
$80$	−1.85075	+	1.06853i	−0.206920	+	0.119465i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.29590	+	7.44071i	−0.474402	+	0.821689i
$83$			11.1347i			1.22219i	0.791558	+	0.611094i	$0.209270\pi$
$83$			11.1347i			1.22219i	−0.791558	+	0.611094i	$0.790730\pi$
$84$	0.0423637	+	0.0244587i	0.00462225	+	0.00266866i
$85$	5.34883	+	3.08815i	0.580162	+	0.334956i
$86$			6.71379i			0.723967i
$87$	2.45593	−	4.25379i	0.263303	−	0.456054i
$88$	3.14795	+	5.45241i	0.335572	+	0.581229i
$89$	3.39616	−	1.96077i	0.359992	−	0.207841i	−0.309085	−	0.951034i	$-0.600023\pi$
$89$	3.39616	−	1.96077i	0.359992	−	0.207841i	0.669077	+	0.743193i	$0.266690\pi$
$90$	−2.13706			−0.225266
$91$		0			0
$92$	2.71379			0.282932
$93$	7.80262	−	4.50484i	0.809094	−	0.467131i
$94$	−3.60388	−	6.24210i	−0.371711	−	0.643823i
$95$	−7.70171	+	13.3398i	−0.790179	+	1.36863i
$96$			1.00000i			0.102062i
$97$	−2.14678	−	1.23945i	−0.217973	−	0.125847i	0.387038	−	0.922064i	$-0.373498\pi$
$97$	−2.14678	−	1.23945i	−0.217973	−	0.125847i	−0.605011	+	0.796217i	$0.706831\pi$
$98$	6.06011	+	3.49880i	0.612163	+	0.353433i
$99$			6.29590i			0.632761i
$100$	0.216480	−	0.374955i	0.0216480	−	0.0374955i
$101$	0.826396	+	1.43136i	0.0822295	+	0.142426i	0.904207	−	0.427094i	$-0.140463\pi$
$101$	0.826396	+	1.43136i	0.0822295	+	0.142426i	−0.821978	+	0.569520i	$0.807129\pi$
$102$	2.50289	−	1.44504i	0.247823	−	0.143080i
$103$	8.23490			0.811409			0.405704	−	0.914004i	$-0.367026\pi$
$103$	8.23490			0.811409			0.405704	+	0.914004i	$0.367026\pi$
$104$		0			0
$105$	0.104539			0.0102020
$106$	−8.09285	+	4.67241i	−0.786047	+	0.453824i
$107$	4.18329	+	7.24567i	0.404414	+	0.700466i	0.994253	−	0.107055i	$-0.0341421\pi$
$107$	4.18329	+	7.24567i	0.404414	+	0.700466i	−0.589839	+	0.807521i	$0.700809\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			17.4276i			1.66926i	0.550811	+	0.834630i	$0.314318\pi$
$109$			17.4276i			1.66926i	−0.550811	+	0.834630i	$0.685682\pi$
$110$	11.6521	+	6.72737i	1.11099	+	0.641429i
$111$	−0.152673	−	0.0881460i	−0.0144911	−	0.00836645i
$112$		−	0.0489173i		−	0.00462225i
$113$	6.98792	−	12.1034i	0.657368	−	1.13859i	−0.323926	−	0.946082i	$-0.605003\pi$
$113$	6.98792	−	12.1034i	0.657368	−	1.13859i	0.981294	−	0.192513i	$-0.0616636\pi$
$114$	3.60388	+	6.24210i	0.337534	+	0.584626i
$115$	5.02255	−	2.89977i	0.468355	−	0.270405i
$116$	−4.91185			−0.456054
$117$		0			0
$118$	−4.26875			−0.392970
$119$	−0.122435	+	0.0706876i	−0.0112236	+	0.00647992i
$120$	1.06853	+	1.85075i	0.0975431	+	0.168950i
$121$	14.3192	−	24.8015i	1.30174	−	2.25468i
$122$		−	7.10992i		−	0.643702i
$123$	7.44071	+	4.29590i	0.670906	+	0.387348i
$124$	−7.80262	−	4.50484i	−0.700696	−	0.404547i
$125$		−	11.6106i		−	1.03848i
$126$	0.0244587	−	0.0423637i	0.00217895	−	0.00377405i
$127$	−3.76055	−	6.51347i	−0.333695	−	0.577977i	0.649538	−	0.760329i	$-0.274962\pi$
$127$	−3.76055	−	6.51347i	−0.333695	−	0.577977i	−0.983233	+	0.182352i	$0.941629\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	6.71379			0.591116
$130$		0			0
$131$	5.12498			0.447772			0.223886	−	0.974615i	$-0.428126\pi$
$131$	5.12498			0.447772			0.223886	+	0.974615i	$0.428126\pi$
$132$	5.45241	−	3.14795i	0.474571	−	0.273994i
$133$	−0.176292	−	0.305347i	−0.0152865	−	0.0264769i
$134$	2.69202	−	4.66272i	0.232555	−	0.402797i
$135$			2.13706i			0.183929i
$136$	−2.50289	−	1.44504i	−0.214621	−	0.123911i
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	0.640626	−	0.767853i	$-0.278675\pi$
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	−0.344668	+	0.938725i	$0.612008\pi$
$138$		−	2.71379i		−	0.231013i
$139$	−4.34481	+	7.52544i	−0.368522	+	0.638299i	−0.989335	−	0.145660i	$-0.953470\pi$
$139$	−4.34481	+	7.52544i	−0.368522	+	0.638299i	0.620812	+	0.783959i	$0.286803\pi$
$140$	−0.0522697	−	0.0905338i	−0.00441760	−	0.00765150i
$141$	−6.24210	+	3.60388i	−0.525679	+	0.303501i
$142$	8.71379			0.731245
$143$		0			0
$144$	1.00000			0.0833333
$145$	−9.09062	+	5.24847i	−0.754935	+	0.435862i
$146$	7.47434	+	12.9459i	0.618581	+	1.07141i
$147$	3.49880	−	6.06011i	0.288576	−	0.499829i
$148$			0.176292i			0.0144911i
$149$	−4.21608	−	2.43416i	−0.345395	−	0.199414i	0.317260	−	0.948339i	$-0.397237\pi$
$149$	−4.21608	−	2.43416i	−0.345395	−	0.199414i	−0.662655	+	0.748925i	$0.730570\pi$
$150$	−0.374955	−	0.216480i	−0.0306149	−	0.0176755i
$151$			14.7463i			1.20004i	0.799986	+	0.600019i	$0.204840\pi$
$151$			14.7463i			1.20004i	−0.799986	+	0.600019i	$0.795160\pi$
$152$	3.60388	−	6.24210i	0.292313	−	0.506301i
$153$	−1.44504	−	2.50289i	−0.116825	−	0.202346i
$154$	−0.266717	+	0.153989i	−0.0214927	+	0.0124088i
$155$	−19.2543			−1.54654
$156$		0			0
$157$	−16.7138			−1.33391			−0.666953	−	0.745100i	$-0.732402\pi$
$157$	−16.7138			−1.33391			−0.666953	+	0.745100i	$0.732402\pi$
$158$	−11.9763	+	6.91454i	−0.952786	+	0.550091i
$159$	4.67241	+	8.09285i	0.370546	+	0.641804i
$160$	1.06853	−	1.85075i	0.0844748	−	0.146315i
$161$			0.132751i			0.0104623i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−4.80608	−	2.77479i	−0.376441	−	0.217338i	0.299828	−	0.953993i	$-0.403071\pi$
$163$	−4.80608	−	2.77479i	−0.376441	−	0.217338i	−0.676269	+	0.736655i	$0.736404\pi$
$164$		−	8.59179i		−	0.670906i
$165$	6.72737	−	11.6521i	0.523725	−	0.907118i
$166$	−5.56734	−	9.64291i	−0.432109	−	0.748435i
$167$	−3.39616	+	1.96077i	−0.262802	+	0.151729i	−0.625612	−	0.780134i	$-0.715151\pi$
$167$	−3.39616	+	1.96077i	−0.262802	+	0.151729i	0.362810	+	0.931863i	$0.381817\pi$
$168$	−0.0489173			−0.00377405
$169$		0			0
$170$	−6.17629			−0.473700
$171$	6.24210	−	3.60388i	0.477345	−	0.275595i
$172$	−3.35690	−	5.81431i	−0.255961	−	0.443337i
$173$	−1.74214	+	3.01747i	−0.132452	+	0.229414i	−0.924621	−	0.380888i	$-0.875618\pi$
$173$	−1.74214	+	3.01747i	−0.132452	+	0.229414i	0.792169	+	0.610302i	$0.208952\pi$
$174$			4.91185i			0.372367i
$175$	0.0183418	+	0.0105896i	0.00138651	+	0.000800501i
$176$	−5.45241	−	3.14795i	−0.410991	−	0.237286i
$177$			4.26875i			0.320859i
$178$	−1.96077	+	3.39616i	−0.146966	+	0.254553i
$179$	1.79440	+	3.10800i	0.134120	+	0.232303i	0.925261	−	0.379331i	$-0.123846\pi$
$179$	1.79440	+	3.10800i	0.134120	+	0.232303i	−0.791141	+	0.611634i	$0.790513\pi$
$180$	1.85075	−	1.06853i	0.137947	−	0.0796436i
$181$	−5.50604			−0.409261			−0.204630	−	0.978839i	$-0.565599\pi$
$181$	−5.50604			−0.409261			−0.204630	+	0.978839i	$0.565599\pi$
$182$		0			0
$183$	−7.10992			−0.525580
$184$	−2.35021	+	1.35690i	−0.173260	+	0.100032i
$185$	0.188374	+	0.326273i	0.0138495	+	0.0239880i
$186$	−4.50484	+	7.80262i	−0.330311	+	0.572116i
$187$			18.1957i			1.33060i
$188$	6.24210	+	3.60388i	0.455252	+	0.262840i
$189$	−0.0423637	−	0.0244587i	−0.00308150	−	0.00177911i
$190$		−	15.4034i		−	1.11748i
$191$	2.82908	−	4.90012i	0.204705	−	0.354560i	−0.745333	−	0.666692i	$-0.767710\pi$
$191$	2.82908	−	4.90012i	0.204705	−	0.354560i	0.950039	+	0.312132i	$0.101043\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−11.6077	+	6.70171i	−0.835541	+	0.482400i	−0.855746	−	0.517396i	$-0.826901\pi$
$193$	−11.6077	+	6.70171i	−0.835541	+	0.482400i	0.0202053	+	0.999796i	$0.493568\pi$
$194$	2.47889			0.177974
$195$		0			0
$196$	−6.99761			−0.499829
$197$	17.3042	−	9.99061i	1.23288	−	0.711801i	0.265248	−	0.964180i	$-0.414546\pi$
$197$	17.3042	−	9.99061i	1.23288	−	0.711801i	0.967628	+	0.252379i	$0.0812130\pi$
$198$	−3.14795	−	5.45241i	−0.223715	−	0.387486i
$199$	−3.12080	+	5.40539i	−0.221228	+	0.383178i	−0.955181	−	0.296022i	$-0.904340\pi$
$199$	−3.12080	+	5.40539i	−0.221228	+	0.383178i	0.733953	+	0.679200i	$0.237673\pi$
$200$			0.432960i			0.0306149i
$201$	−4.66272	−	2.69202i	−0.328883	−	0.189881i
$202$	−1.43136	−	0.826396i	−0.100710	−	0.0581450i
$203$		−	0.240275i		−	0.0168640i
$204$	−1.44504	+	2.50289i	−0.101173	+	0.175237i
$205$	−9.18060	−	15.9013i	−0.641201	−	1.11059i
$206$	−7.13163	+	4.11745i	−0.496884	+	0.286876i
$207$	−2.71379			−0.188622
$208$		0			0
$209$	−45.3793			−3.13895
$210$	−0.0905338	+	0.0522697i	−0.00624743	+	0.00360695i
$211$	2.54288	+	4.40439i	0.175059	+	0.303211i	0.940182	−	0.340674i	$-0.110655\pi$
$211$	2.54288	+	4.40439i	0.175059	+	0.303211i	−0.765123	+	0.643884i	$0.777322\pi$
$212$	4.67241	−	8.09285i	0.320902	−	0.555819i
$213$		−	8.71379i		−	0.597059i
$214$	−7.24567	−	4.18329i	−0.495304	−	0.285964i
$215$	−12.4256	−	7.17390i	−0.847416	−	0.489256i
$216$		−	1.00000i		−	0.0680414i
$217$	0.220365	−	0.381683i	0.0149594	−	0.0259104i
$218$	−8.71379	−	15.0927i	−0.590172	−	1.02221i
$219$	12.9459	−	7.47434i	0.874806	−	0.505069i
$220$	−13.4547			−0.907118
$221$		0			0
$222$	0.176292			0.0118319
$223$	−17.7953	+	10.2741i	−1.19166	+	0.688006i	−0.958683	−	0.284475i	$-0.908181\pi$
$223$	−17.7953	+	10.2741i	−1.19166	+	0.688006i	−0.232979	+	0.972482i	$0.574847\pi$
$224$	0.0244587	+	0.0423637i	0.00163421	+	0.00283054i
$225$	−0.216480	+	0.374955i	−0.0144320	+	0.0249970i
$226$			13.9758i			0.929659i
$227$	−3.82020	−	2.20560i	−0.253556	−	0.146390i	0.367836	−	0.929891i	$-0.380099\pi$
$227$	−3.82020	−	2.20560i	−0.253556	−	0.146390i	−0.621391	+	0.783500i	$0.713432\pi$
$228$	−6.24210	−	3.60388i	−0.413393	−	0.238672i
$229$		−	0.230586i		−	0.0152376i	−0.999971	−	0.00761878i	$-0.997575\pi$
$229$		−	0.230586i		−	0.0152376i	0.999971	−	0.00761878i	$-0.00242516\pi$
$230$	−2.89977	+	5.02255i	−0.191205	+	0.331177i
$231$	0.153989	+	0.266717i	0.0101317	+	0.0175487i
$232$	4.25379	−	2.45593i	0.279275	−	0.161240i
$233$	7.82371			0.512548			0.256274	−	0.966604i	$-0.417505\pi$
$233$	7.82371			0.512548			0.256274	+	0.966604i	$0.417505\pi$
$234$		0			0
$235$	15.4034			1.00481
$236$	3.69685	−	2.13437i	0.240644	−	0.138936i
$237$	6.91454	+	11.9763i	0.449148	+	0.777947i
$238$	0.0706876	−	0.122435i	0.00458200	−	0.00793625i
$239$			11.1535i			0.721457i	0.932671	+	0.360729i	$0.117472\pi$
$239$			11.1535i			0.721457i	−0.932671	+	0.360729i	$0.882528\pi$
$240$	−1.85075	−	1.06853i	−0.119465	−	0.0689734i
$241$	−3.07029	−	1.77263i	−0.197775	−	0.114185i	0.397842	−	0.917454i	$-0.369759\pi$
$241$	−3.07029	−	1.77263i	−0.197775	−	0.114185i	−0.595617	+	0.803268i	$0.703092\pi$
$242$			28.6383i			1.84094i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	3.55496	+	6.15737i	0.227583	+	0.394185i
$245$	−12.9508	+	7.47716i	−0.827398	+	0.477699i
$246$	−8.59179			−0.547793
$247$		0			0
$248$	9.00969			0.572116
$249$	−9.64291	+	5.56734i	−0.611094	+	0.352816i
$250$	5.80529	+	10.0551i	0.367159	+	0.635938i
$251$	−2.08546	+	3.61212i	−0.131633	+	0.227995i	−0.924306	−	0.381652i	$-0.875355\pi$
$251$	−2.08546	+	3.61212i	−0.131633	+	0.227995i	0.792673	+	0.609647i	$0.208689\pi$
$252$			0.0489173i			0.00308150i
$253$	14.7967	+	8.54288i	0.930260	+	0.537086i
$254$	6.51347	+	3.76055i	0.408691	+	0.235958i
$255$			6.17629i			0.386774i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.44504	−	9.43109i	−0.339652	−	0.588295i	0.644715	−	0.764423i	$-0.276976\pi$
$257$	−5.44504	−	9.43109i	−0.339652	−	0.588295i	−0.984367	+	0.176128i	$0.943643\pi$
$258$	−5.81431	+	3.35690i	−0.361983	+	0.208991i
$259$	−0.00862374			−0.000535853
$260$		0			0
$261$	4.91185			0.304036
$262$	−4.43836	+	2.56249i	−0.274203	+	0.158311i
$263$	15.6136	+	27.0435i	0.962774	+	1.66757i	0.715481	+	0.698632i	$0.246207\pi$
$263$	15.6136	+	27.0435i	0.962774	+	1.66757i	0.247292	+	0.968941i	$0.420459\pi$
$264$	−3.14795	+	5.45241i	−0.193743	+	0.335572i
$265$		−	19.9705i		−	1.22678i
$266$	0.305347	+	0.176292i	0.0187220	+	0.0108092i
$267$	3.39616	+	1.96077i	0.207841	+	0.119997i
$268$			5.38404i			0.328883i
$269$	−7.95862	+	13.7847i	−0.485245	+	0.840470i	−0.999856	−	0.0169542i	$-0.994603\pi$
$269$	−7.95862	+	13.7847i	−0.485245	+	0.840470i	0.514611	+	0.857424i	$0.327936\pi$
$270$	−1.06853	−	1.85075i	−0.0650288	−	0.112633i
$271$	−3.04937	+	1.76055i	−0.185236	+	0.106946i	−0.589750	−	0.807586i	$-0.700774\pi$
$271$	−3.04937	+	1.76055i	−0.185236	+	0.106946i	0.404514	+	0.914532i	$0.367441\pi$
$272$	2.89008			0.175237
$273$		0			0
$274$	−4.00000			−0.241649
$275$	2.36068	−	1.36294i	0.142354	−	0.0821882i
$276$	1.35690	+	2.35021i	0.0816755	+	0.141466i
$277$	−4.29052	+	7.43140i	−0.257792	+	0.446509i	−0.965650	−	0.259845i	$-0.916328\pi$
$277$	−4.29052	+	7.43140i	−0.257792	+	0.446509i	0.707858	+	0.706355i	$0.249662\pi$
$278$		−	8.68963i		−	0.521169i
$279$	7.80262	+	4.50484i	0.467131	+	0.269698i
$280$	0.0905338	+	0.0522697i	0.00541043	+	0.00312371i
$281$			8.07846i			0.481920i	0.970535	+	0.240960i	$0.0774623\pi$
$281$			8.07846i			0.481920i	−0.970535	+	0.240960i	$0.922538\pi$
$282$	3.60388	−	6.24210i	0.214608	−	0.371711i
$283$	−8.70171	−	15.0718i	−0.517263	−	0.895926i	−0.999799	−	0.0200496i	$-0.993618\pi$
$283$	−8.70171	−	15.0718i	−0.517263	−	0.895926i	0.482536	−	0.875876i	$-0.339716\pi$
$284$	−7.54637	+	4.35690i	−0.447794	+	0.258534i
$285$	−15.4034			−0.912420
$286$		0			0
$287$	0.420288			0.0248088
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	4.32371	+	7.48888i	0.254336	+	0.440522i
$290$	5.24847	−	9.09062i	0.308201	−	0.533820i
$291$		−	2.47889i		−	0.145315i
$292$	−12.9459	−	7.47434i	−0.757604	−	0.437403i
$293$	−16.7757	−	9.68545i	−0.980046	−	0.565830i	−0.0777621	−	0.996972i	$-0.524777\pi$
$293$	−16.7757	−	9.68545i	−0.980046	−	0.565830i	−0.902284	+	0.431142i	$0.858111\pi$
$294$			6.99761i			0.408109i
$295$	4.56129	−	7.90039i	0.265569	−	0.459979i
$296$	−0.0881460	−	0.152673i	−0.00512338	−	0.00887396i
$297$	−5.45241	+	3.14795i	−0.316381	+	0.182662i
$298$	4.86831			0.282014
$299$		0			0
$300$	0.432960			0.0249970
$301$	0.284421	−	0.164210i	0.0163937	−	0.00946493i
$302$	−7.37316	−	12.7707i	−0.424278	−	0.734870i
$303$	−0.826396	+	1.43136i	−0.0474752	+	0.0822295i
$304$			7.20775i			0.413393i
$305$	13.1587	+	7.59717i	0.753464	+	0.435013i
$306$	2.50289	+	1.44504i	0.143080	+	0.0826075i
$307$			12.4263i			0.709204i	0.935017	+	0.354602i	$0.115384\pi$
$307$			12.4263i			0.709204i	−0.935017	+	0.354602i	$0.884616\pi$
$308$	0.153989	−	0.266717i	0.00877435	−	0.0151976i
$309$	4.11745	+	7.13163i	0.234233	+	0.405704i
$310$	16.6747	−	9.62714i	0.947059	−	0.546785i
$311$	−2.71379			−0.153885			−0.0769425	−	0.997036i	$-0.524516\pi$
$311$	−2.71379			−0.153885			−0.0769425	+	0.997036i	$0.524516\pi$
$312$		0			0
$313$	15.3884			0.869801			0.434901	−	0.900478i	$-0.356783\pi$
$313$	15.3884			0.869801			0.434901	+	0.900478i	$0.356783\pi$
$314$	14.4746	−	8.35690i	0.816847	−	0.471607i
$315$	0.0522697	+	0.0905338i	0.00294507	+	0.00510100i
$316$	6.91454	−	11.9763i	0.388973	−	0.673722i
$317$			25.6528i			1.44080i	0.693557	+	0.720402i	$0.256043\pi$
$317$			25.6528i			1.44080i	−0.693557	+	0.720402i	$0.743957\pi$
$318$	−8.09285	−	4.67241i	−0.453824	−	0.262016i
$319$	−26.7814	−	15.4623i	−1.49947	−	0.865721i
$320$			2.13706i			0.119465i
$321$	−4.18329	+	7.24567i	−0.233489	+	0.404414i
$322$	−0.0663757	−	0.114966i	−0.00369898	−	0.00640681i
$323$	18.0402	−	10.4155i	1.00378	−	0.579534i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	5.54958			0.307363
$327$	−15.0927	+	8.71379i	−0.834630	+	0.481874i
$328$	4.29590	+	7.44071i	0.237201	+	0.410845i
$329$	−0.176292	+	0.305347i	−0.00971929	+	0.0168343i
$330$			13.4547i			0.740659i
$331$	3.31143	+	1.91185i	0.182013	+	0.105085i	0.588238	−	0.808688i	$-0.299822\pi$
$331$	3.31143	+	1.91185i	0.182013	+	0.105085i	−0.406225	+	0.913773i	$0.633155\pi$
$332$	9.64291	+	5.56734i	0.529223	+	0.305547i
$333$		−	0.176292i		−	0.00966074i
$334$	1.96077	−	3.39616i	0.107289	−	0.185829i
$335$	5.75302	+	9.96452i	0.314321	+	0.544420i
$336$	0.0423637	−	0.0244587i	0.00231113	−	0.00133433i
$337$	−20.1304			−1.09657			−0.548285	−	0.836291i	$-0.684719\pi$
$337$	−20.1304			−1.09657			−0.548285	+	0.836291i	$0.684719\pi$
$338$		0			0
$339$	13.9758			0.759063
$340$	5.34883	−	3.08815i	0.290081	−	0.167478i
$341$	−28.3620	−	49.1245i	−1.53589	−	2.66024i
$342$	−3.60388	+	6.24210i	−0.194875	+	0.337534i
$343$		−	0.684726i		−	0.0369717i
$344$	5.81431	+	3.35690i	0.313487	+	0.180992i
$345$	5.02255	+	2.89977i	0.270405	+	0.156118i
$346$		−	3.48427i		−	0.187316i
$347$	−1.46950	+	2.54525i	−0.0788869	+	0.136636i	−0.902770	−	0.430124i	$-0.858470\pi$
$347$	−1.46950	+	2.54525i	−0.0788869	+	0.136636i	0.823883	+	0.566760i	$0.191803\pi$
$348$	−2.45593	−	4.25379i	−0.131652	−	0.228027i
$349$	−6.38546	+	3.68664i	−0.341806	+	0.197342i	−0.661070	−	0.750324i	$-0.729897\pi$
$349$	−6.38546	+	3.68664i	−0.341806	+	0.197342i	0.319265	+	0.947666i	$0.396564\pi$
$350$	−0.0211793			−0.00113208
$351$		0			0
$352$	6.29590			0.335572
$353$	−1.74136	+	1.00538i	−0.0926834	+	0.0535108i	−0.545625	−	0.838029i	$-0.683708\pi$
$353$	−1.74136	+	1.00538i	−0.0926834	+	0.0535108i	0.452942	+	0.891540i	$0.350374\pi$
$354$	−2.13437	−	3.69685i	−0.113441	−	0.196485i
$355$	−9.31096	+	16.1271i	−0.494175	+	0.855935i
$356$		−	3.92154i		−	0.207841i
$357$	−0.122435	−	0.0706876i	−0.00647992	−	0.00374118i
$358$	−3.10800	−	1.79440i	−0.164263	−	0.0948373i
$359$		−	31.4577i		−	1.66027i	−0.557559	−	0.830137i	$-0.688262\pi$
$359$		−	31.4577i		−	1.66027i	0.557559	−	0.830137i	$-0.311738\pi$
$360$	−1.06853	+	1.85075i	−0.0563166	+	0.0975431i
$361$	16.4758	+	28.5370i	0.867149	+	1.50195i
$362$	4.76837	−	2.75302i	0.250620	−	0.144696i
$363$	28.6383			1.50312
$364$		0			0
$365$	−31.9463			−1.67215
$366$	6.15737	−	3.55496i	0.321851	−	0.185821i
$367$	2.24967	+	3.89654i	0.117432	+	0.203398i	0.918749	−	0.394842i	$-0.129201\pi$
$367$	2.24967	+	3.89654i	0.117432	+	0.203398i	−0.801317	+	0.598239i	$0.795867\pi$
$368$	1.35690	−	2.35021i	0.0707331	−	0.122513i
$369$			8.59179i			0.447271i
$370$	−0.326273	−	0.188374i	−0.0169621	−	0.00979308i
$371$	0.395881	+	0.228562i	0.0205531	+	0.0118663i
$372$		−	9.00969i		−	0.467131i
$373$	−18.9148	+	32.7615i	−0.979373	+	1.69632i	−0.314698	+	0.949192i	$0.601903\pi$
$373$	−18.9148	+	32.7615i	−0.979373	+	1.69632i	−0.664676	+	0.747132i	$0.731430\pi$
$374$	−9.09783	−	15.7579i	−0.470438	−	0.814822i
$375$	10.0551	−	5.80529i	0.519241	−	0.299784i
$376$	−7.20775			−0.371711
$377$		0			0
$378$	0.0489173			0.00251604
$379$	−7.30896	+	4.21983i	−0.375436	+	0.216758i	−0.675831	−	0.737057i	$-0.736215\pi$
$379$	−7.30896	+	4.21983i	−0.375436	+	0.216758i	0.300395	+	0.953815i	$0.402882\pi$
$380$	7.70171	+	13.3398i	0.395089	+	0.684315i
$381$	3.76055	−	6.51347i	0.192659	−	0.333695i
$382$			5.65817i			0.289497i
$383$	−1.11389	−	0.643104i	−0.0569171	−	0.0328611i	0.471271	−	0.881988i	$-0.343795\pi$
$383$	−1.11389	−	0.643104i	−0.0569171	−	0.0328611i	−0.528188	+	0.849127i	$0.677129\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		−	0.658170i		−	0.0335434i
$386$	6.70171	−	11.6077i	0.341108	−	0.590817i
$387$	3.35690	+	5.81431i	0.170641	+	0.295558i
$388$	−2.14678	+	1.23945i	−0.108986	+	0.0629234i
$389$	−23.3924			−1.18604			−0.593021	−	0.805187i	$-0.702065\pi$
$389$	−23.3924			−1.18604			−0.593021	+	0.805187i	$0.702065\pi$
$390$		0			0
$391$	−7.84309			−0.396642
$392$	6.06011	−	3.49880i	0.306082	−	0.176716i
$393$	2.56249	+	4.43836i	0.129261	+	0.223886i
$394$	−9.99061	+	17.3042i	−0.503320	+	0.871775i
$395$		−	29.5536i		−	1.48700i
$396$	5.45241	+	3.14795i	0.273994	+	0.158190i
$397$	32.1172	+	18.5429i	1.61192	+	0.930640i	0.988926	+	0.148411i	$0.0474158\pi$
$397$	32.1172	+	18.5429i	1.61192	+	0.930640i	0.622990	+	0.782229i	$0.285918\pi$
$398$		−	6.24160i		−	0.312863i
$399$	0.176292	−	0.305347i	0.00882564	−	0.0152865i
$400$	−0.216480	−	0.374955i	−0.0108240	−	0.0187477i
$401$	−4.21401	+	2.43296i	−0.210438	+	0.121496i	−0.601515	−	0.798862i	$-0.705436\pi$
$401$	−4.21401	+	2.43296i	−0.210438	+	0.121496i	0.391077	+	0.920358i	$0.372103\pi$
$402$	5.38404			0.268532
$403$		0			0
$404$	1.65279			0.0822295
$405$	−1.85075	+	1.06853i	−0.0919646	+	0.0530958i
$406$	0.120137	+	0.208084i	0.00596232	+	0.0103270i
$407$	−0.554958	+	0.961216i	−0.0275083	+	0.0476457i
$408$		−	2.89008i		−	0.143080i
$409$	0.385418	+	0.222521i	0.0190577	+	0.0110030i	0.509499	−	0.860472i	$-0.329831\pi$
$409$	0.385418	+	0.222521i	0.0190577	+	0.0110030i	−0.490441	+	0.871474i	$0.663164\pi$
$410$	15.9013	+	9.18060i	0.785308	+	0.453398i
$411$			4.00000i			0.197305i
$412$	4.11745	−	7.13163i	0.202852	−	0.351350i
$413$	0.104408	+	0.180840i	0.00513758	+	0.00889855i
$414$	2.35021	−	1.35690i	0.115507	−	0.0666878i
$415$	23.7955			1.16807
$416$		0			0
$417$	−8.68963			−0.425533
$418$	39.2996	−	22.6896i	1.92221	−	1.10979i
$419$	−8.99343	−	15.5771i	−0.439358	−	0.760990i	0.558282	−	0.829651i	$-0.311461\pi$
$419$	−8.99343	−	15.5771i	−0.439358	−	0.760990i	−0.997640	+	0.0686612i	$0.978127\pi$
$420$	0.0522697	−	0.0905338i	0.00255050	−	0.00441760i
$421$		−	21.2814i		−	1.03719i	−0.855019	−	0.518597i	$-0.826455\pi$
$421$		−	21.2814i		−	1.03719i	0.855019	−	0.518597i	$-0.173545\pi$
$422$	−4.40439	−	2.54288i	−0.214402	−	0.123785i
$423$	−6.24210	−	3.60388i	−0.303501	−	0.175226i
$424$			9.34481i			0.453824i
$425$	−0.625646	+	1.08365i	−0.0303483	+	0.0525648i
$426$	4.35690	+	7.54637i	0.211092	+	0.365623i
$427$	−0.301202	+	0.173899i	−0.0145762	+	0.00841557i
$428$	8.36658			0.404414
$429$		0			0
$430$	14.3478			0.691912
$431$	−21.4028	+	12.3569i	−1.03094	+	0.595211i	−0.917252	−	0.398306i	$-0.869598\pi$
$431$	−21.4028	+	12.3569i	−1.03094	+	0.595211i	−0.113683	+	0.993517i	$0.536265\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	16.1087	−	27.9011i	0.774136	−	1.34084i	−0.161143	−	0.986931i	$-0.551518\pi$
$433$	16.1087	−	27.9011i	0.774136	−	1.34084i	0.935279	−	0.353911i	$-0.115149\pi$
$434$			0.440730i			0.0211557i
$435$	−9.09062	−	5.24847i	−0.435862	−	0.251645i
$436$	15.0927	+	8.71379i	0.722811	+	0.417315i
$437$		−	19.5603i		−	0.935698i
$438$	−7.47434	+	12.9459i	−0.357138	+	0.618581i
$439$	16.0438	+	27.7887i	0.765731	+	1.32628i	0.939859	+	0.341561i	$0.110956\pi$
$439$	16.0438	+	27.7887i	0.765731	+	1.32628i	−0.174129	+	0.984723i	$0.555711\pi$
$440$	11.6521	−	6.72737i	0.555494	−	0.320715i
$441$	6.99761			0.333219
$442$		0			0
$443$	20.5109			0.974504			0.487252	−	0.873261i	$-0.337999\pi$
$443$	20.5109			0.974504			0.487252	+	0.873261i	$0.337999\pi$
$444$	−0.152673	+	0.0881460i	−0.00724556	+	0.00418322i
$445$	−4.19029	−	7.25780i	−0.198639	−	0.344053i
$446$	10.2741	−	17.7953i	0.486494	−	0.842632i
$447$		−	4.86831i		−	0.230263i
$448$	−0.0423637	−	0.0244587i	−0.00200149	−	0.00115556i
$449$	13.2643	+	7.65817i	0.625983	+	0.361411i	0.779195	−	0.626782i	$-0.215628\pi$
$449$	13.2643	+	7.65817i	0.625983	+	0.361411i	−0.153212	+	0.988193i	$0.548962\pi$
$450$		−	0.432960i		−	0.0204099i
$451$	27.0465	−	46.8460i	1.27357	−	2.20589i
$452$	−6.98792	−	12.1034i	−0.328684	−	0.569297i
$453$	−12.7707	+	7.37316i	−0.600019	+	0.346421i
$454$	4.41119			0.207027
$455$		0			0
$456$	7.20775			0.337534
$457$	16.6155	−	9.59299i	0.777242	−	0.448741i	−0.0582096	−	0.998304i	$-0.518539\pi$
$457$	16.6155	−	9.59299i	0.777242	−	0.448741i	0.835452	+	0.549563i	$0.185206\pi$
$458$	0.115293	+	0.199693i	0.00538729	+	0.00933106i
$459$	1.44504	−	2.50289i	0.0674488	−	0.116825i
$460$		−	5.79954i		−	0.270405i
$461$	7.19865	+	4.15615i	0.335275	+	0.193571i	0.658181	−	0.752860i	$-0.271326\pi$
$461$	7.19865	+	4.15615i	0.335275	+	0.193571i	−0.322906	+	0.946431i	$0.604660\pi$
$462$	−0.266717	−	0.153989i	−0.0124088	−	0.00716423i
$463$		−	6.32842i		−	0.294107i	−0.989129	−	0.147053i	$-0.953021\pi$
$463$		−	6.32842i		−	0.294107i	0.989129	−	0.147053i	$-0.0469789\pi$
$464$	−2.45593	+	4.25379i	−0.114014	+	0.197477i
$465$	−9.62714	−	16.6747i	−0.446448	−	0.773270i
$466$	−6.77553	+	3.91185i	−0.313870	+	0.181213i
$467$	31.1879			1.44320			0.721602	−	0.692308i	$-0.243406\pi$
$467$	31.1879			1.44320			0.721602	+	0.692308i	$0.243406\pi$
$468$		0			0
$469$	−0.263373			−0.0121614
$470$	−13.3398	+	7.70171i	−0.615317	+	0.355253i
$471$	−8.35690	−	14.4746i	−0.385065	−	0.666953i
$472$	−2.13437	+	3.69685i	−0.0982426	+	0.170161i
$473$		−	42.2693i		−	1.94355i
$474$	−11.9763	−	6.91454i	−0.550091	−	0.317595i
$475$	−2.70258	−	1.56033i	−0.124003	−	0.0715931i
$476$			0.141375i			0.00647992i
$477$	−4.67241	+	8.09285i	−0.213935	+	0.370546i
$478$	−5.57673	−	9.65918i	−0.255074	−	0.441800i
$479$	−15.5298	+	8.96615i	−0.709576	+	0.409674i	−0.810904	−	0.585179i	$-0.801024\pi$
$479$	−15.5298	+	8.96615i	−0.709576	+	0.409674i	0.101328	+	0.994853i	$0.467691\pi$
$480$	2.13706			0.0975431
$481$		0			0
$482$	3.54527			0.161483
$483$	−0.114966	+	0.0663757i	−0.00523114	+	0.00302020i
$484$	−14.3192	−	24.8015i	−0.650871	−	1.12734i
$485$	−2.64878	+	4.58782i	−0.120275	+	0.208322i
$486$			1.00000i			0.0453609i
$487$	26.2648	+	15.1640i	1.19017	+	0.687145i	0.958345	−	0.285612i	$-0.0921969\pi$
$487$	26.2648	+	15.1640i	1.19017	+	0.687145i	0.231825	+	0.972757i	$0.425530\pi$
$488$	−6.15737	−	3.55496i	−0.278731	−	0.160925i
$489$		−	5.54958i		−	0.250961i
$490$	7.47716	−	12.9508i	0.337784	−	0.585059i
$491$	15.0477	+	26.0634i	0.679094	+	1.17623i	0.975254	+	0.221087i	$0.0709605\pi$
$491$	15.0477	+	26.0634i	0.679094	+	1.17623i	−0.296160	+	0.955138i	$0.595706\pi$
$492$	7.44071	−	4.29590i	0.335453	−	0.193674i
$493$	14.1957			0.639341
$494$		0			0
$495$	13.4547			0.604745
$496$	−7.80262	+	4.50484i	−0.350348	+	0.202273i
$497$	−0.213128	−	0.369148i	−0.00956009	−	0.0165586i
$498$	5.56734	−	9.64291i	0.249478	−	0.432109i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	−10.0551	−	5.80529i	−0.449676	−	0.259620i
$501$	−3.39616	−	1.96077i	−0.151729	−	0.0876008i
$502$		−	4.17092i		−	0.186157i
$503$	−16.8756	+	29.2294i	−0.752446	+	1.30328i	0.194188	+	0.980964i	$0.437793\pi$
$503$	−16.8756	+	29.2294i	−0.752446	+	1.30328i	−0.946634	+	0.322311i	$0.895540\pi$
$504$	−0.0244587	−	0.0423637i	−0.00108948	−	0.00188703i
$505$	3.05891	−	1.76606i	0.136120	−	0.0785887i
$506$	−17.0858			−0.759554
$507$		0			0
$508$	−7.52111			−0.333695
$509$	12.7686	−	7.37196i	0.565959	−	0.326756i	−0.189575	−	0.981866i	$-0.560711\pi$
$509$	12.7686	−	7.37196i	0.565959	−	0.326756i	0.755534	+	0.655110i	$0.227378\pi$
$510$	−3.08815	−	5.34883i	−0.136745	−	0.236850i
$511$	0.365625	−	0.633281i	0.0161743	−	0.0280147i
$512$		−	1.00000i		−	0.0441942i
$513$	6.24210	+	3.60388i	0.275595	+	0.159115i
$514$	9.43109	+	5.44504i	0.415988	+	0.240171i
$515$		−	17.5985i		−	0.775483i
$516$	3.35690	−	5.81431i	0.147779	−	0.255961i
$517$	22.6896	+	39.2996i	0.997889	+	1.72839i
$518$	0.00746837	−	0.00431187i	0.000328142	−	0.000189453i
$519$	−3.48427			−0.152943
$520$		0			0
$521$	22.1086			0.968595			0.484297	−	0.874903i	$-0.339075\pi$
$521$	22.1086			0.968595			0.484297	+	0.874903i	$0.339075\pi$
$522$	−4.25379	+	2.45593i	−0.186183	+	0.107493i
$523$	8.67994	+	15.0341i	0.379547	+	0.657395i	0.990996	−	0.133889i	$-0.0427464\pi$
$523$	8.67994	+	15.0341i	0.379547	+	0.657395i	−0.611449	+	0.791284i	$0.709413\pi$
$524$	2.56249	−	4.43836i	0.111943	−	0.193891i
$525$			0.0211793i			0.000924339i
$526$	−27.0435	−	15.6136i	−1.17915	−	0.680784i
$527$	22.5502	+	13.0194i	0.982303	+	0.567133i
$528$		−	6.29590i		−	0.273994i
$529$	7.81767	−	13.5406i	0.339899	−	0.588722i
$530$	9.98523	+	17.2949i	0.433731	+	0.751244i
$531$	−3.69685	+	2.13437i	−0.160429	+	0.0926240i
$532$	−0.352584			−0.0152865
$533$		0			0
$534$	−3.92154			−0.169702
$535$	15.4845	−	8.93996i	0.669452	−	0.386508i
$536$	−2.69202	−	4.66272i	−0.116278	−	0.201399i
$537$	−1.79440	+	3.10800i	−0.0774343	+	0.134120i
$538$		−	15.9172i		−	0.686241i
$539$	−38.1538	−	22.0281i	−1.64340	−	0.948818i
$540$	1.85075	+	1.06853i	0.0796436	+	0.0459823i
$541$		−	8.83579i		−	0.379880i	−0.981796	−	0.189940i	$-0.939171\pi$
$541$		−	8.83579i		−	0.379880i	0.981796	−	0.189940i	$-0.0608294\pi$
$542$	1.76055	−	3.04937i	0.0756222	−	0.130982i
$543$	−2.75302	−	4.76837i	−0.118143	−	0.204630i
$544$	−2.50289	+	1.44504i	−0.107310	+	0.0619557i
$545$	37.2438			1.59535
$546$		0			0
$547$	−8.10859			−0.346698			−0.173349	−	0.984860i	$-0.555459\pi$
$547$	−8.10859			−0.346698			−0.173349	+	0.984860i	$0.555459\pi$
$548$	3.46410	−	2.00000i	0.147979	−	0.0854358i
$549$	−3.55496	−	6.15737i	−0.151722	−	0.262790i
$550$	−1.36294	+	2.36068i	−0.0581158	+	0.100660i
$551$			35.4034i			1.50824i
$552$	−2.35021	−	1.35690i	−0.100032	−	0.0577533i
$553$	0.585851	+	0.338241i	0.0249129	+	0.0143835i
$554$		−	8.58104i		−	0.364573i
$555$	−0.188374	+	0.326273i	−0.00799601	+	0.0138495i
$556$	4.34481	+	7.52544i	0.184261	+	0.319150i
$557$	−8.27949	+	4.78017i	−0.350813	+	0.202542i	−0.665043	−	0.746805i	$-0.731587\pi$
$557$	−8.27949	+	4.78017i	−0.350813	+	0.202542i	0.314230	+	0.949347i	$0.398254\pi$
$558$	−9.00969			−0.381411
$559$		0			0
$560$	−0.104539			−0.00441760
$561$	−15.7579	+	9.09783i	−0.665300	+	0.384111i
$562$	−4.03923	−	6.99615i	−0.170385	−	0.295115i
$563$	−22.5819	+	39.1129i	−0.951712	+	1.64841i	−0.209994	+	0.977703i	$0.567344\pi$
$563$	−22.5819	+	39.1129i	−0.951712	+	1.64841i	−0.741719	+	0.670711i	$0.765989\pi$
$564$			7.20775i			0.303501i
$565$	−25.8658	−	14.9336i	−1.08818	−	0.628262i
$566$	15.0718	+	8.70171i	0.633515	+	0.365760i
$567$		−	0.0489173i		−	0.00205434i
$568$	4.35690	−	7.54637i	0.182811	−	0.316638i
$569$	−1.60388	−	2.77799i	−0.0672380	−	0.116460i	0.830447	−	0.557098i	$-0.188085\pi$
$569$	−1.60388	−	2.77799i	−0.0672380	−	0.116460i	−0.897685	+	0.440639i	$0.854752\pi$
$570$	13.3398	−	7.70171i	0.558741	−	0.322589i
$571$	−0.0241632			−0.00101120			−0.000505599	−	1.00000i	$-0.500161\pi$
$571$	−0.0241632			−0.00101120			−0.000505599		1.00000i	$0.500161\pi$
$572$		0			0
$573$	5.65817			0.236373
$574$	−0.363980	+	0.210144i	−0.0151922	+	0.00877123i
$575$	0.587482	+	1.01755i	0.0244997	+	0.0424347i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	46.0200i		−	1.91584i	−0.287041	−	0.957918i	$-0.592672\pi$
$577$		−	46.0200i		−	1.91584i	0.287041	−	0.957918i	$-0.407328\pi$
$578$	−7.48888	−	4.32371i	−0.311496	−	0.179843i
$579$	−11.6077	−	6.70171i	−0.482400	−	0.278514i
$580$			10.4969i			0.435862i
$581$	−0.272339	+	0.471705i	−0.0112985	+	0.0195696i
$582$	1.23945	+	2.14678i	0.0513767	+	0.0889871i
$583$	50.9517	−	29.4170i	2.11020	−	1.21833i
$584$	14.9487			0.618581
$585$		0			0
$586$	19.3709			0.800204
$587$	−22.4634	+	12.9693i	−0.927165	+	0.535299i	−0.885914	−	0.463850i	$-0.846468\pi$
$587$	−22.4634	+	12.9693i	−0.927165	+	0.535299i	−0.0412510	+	0.999149i	$0.513134\pi$
$588$	−3.49880	−	6.06011i	−0.144288	−	0.249915i
$589$	−32.4698	+	56.2393i	−1.33789	+	2.31730i
$590$			9.12259i			0.375571i
$591$	17.3042	+	9.99061i	0.711801	+	0.410959i
$592$	0.152673	+	0.0881460i	0.00627484	+	0.00362278i
$593$			8.30691i			0.341124i	0.985347	+	0.170562i	$0.0545583\pi$
$593$			8.30691i			0.341124i	−0.985347	+	0.170562i	$0.945442\pi$
$594$	3.14795	−	5.45241i	0.129162	−	0.223715i
$595$	0.151064	+	0.261650i	0.00619302	+	0.0107266i
$596$	−4.21608	+	2.43416i	−0.172697	+	0.0997069i
$597$	−6.24160			−0.255452
$598$		0			0
$599$	37.1702			1.51873			0.759366	−	0.650664i	$-0.225509\pi$
$599$	37.1702			1.51873			0.759366	+	0.650664i	$0.225509\pi$
$600$	−0.374955	+	0.216480i	−0.0153075	+	0.00883776i
$601$	6.28501	+	10.8860i	0.256371	+	0.444048i	0.965267	−	0.261265i	$-0.0841398\pi$
$601$	6.28501	+	10.8860i	0.256371	+	0.444048i	−0.708896	+	0.705313i	$0.750806\pi$
$602$	−0.164210	+	0.284421i	−0.00669272	+	0.0115921i
$603$		−	5.38404i		−	0.219255i
$604$	12.7707	+	7.37316i	0.519632	+	0.300010i
$605$	−53.0024	−	30.6010i	−2.15485	−	1.24411i
$606$		−	1.65279i		−	0.0671401i
$607$	−4.02446	+	6.97057i	−0.163348	+	0.282927i	−0.936067	−	0.351821i	$-0.885563\pi$
$607$	−4.02446	+	6.97057i	−0.163348	+	0.282927i	0.772720	+	0.634748i	$0.218896\pi$
$608$	−3.60388	−	6.24210i	−0.146156	−	0.253150i
$609$	0.208084	−	0.120137i	0.00843199	−	0.00486821i
$610$	−15.1943			−0.615201
$611$		0			0
$612$	−2.89008			−0.116825
$613$	26.3783	−	15.2295i	1.06541	−	0.615115i	0.138486	−	0.990364i	$-0.455776\pi$
$613$	26.3783	−	15.2295i	1.06541	−	0.615115i	0.926924	+	0.375250i	$0.122443\pi$
$614$	−6.21313	−	10.7615i	−0.250741	−	0.434297i
$615$	9.18060	−	15.9013i	0.370198	−	0.641201i
$616$			0.307979i			0.0124088i
$617$	−4.09904	−	2.36658i	−0.165021	−	0.0952751i	0.415215	−	0.909723i	$-0.363706\pi$
$617$	−4.09904	−	2.36658i	−0.165021	−	0.0952751i	−0.580236	+	0.814448i	$0.697040\pi$
$618$	−7.13163	−	4.11745i	−0.286876	−	0.165628i
$619$			24.9095i			1.00120i	0.865680	+	0.500598i	$0.166886\pi$
$619$			24.9095i			1.00120i	−0.865680	+	0.500598i	$0.833114\pi$
$620$	−9.62714	+	16.6747i	−0.386635	+	0.669672i
$621$	−1.35690	−	2.35021i	−0.0544504	−	0.0943108i
$622$	2.35021	−	1.35690i	0.0942349	−	0.0544066i
$623$	0.191831			0.00768556
$624$		0			0
$625$	−22.6477			−0.905910
$626$	−13.3267	+	7.69418i	−0.532642	+	0.307521i
$627$	−22.6896	−	39.2996i	−0.906136	−	1.56947i
$628$	−8.35690	+	14.4746i	−0.333476	+	0.577598i
$629$		−	0.509499i		−	0.0203150i
$630$	−0.0905338	−	0.0522697i	−0.00360695	−	0.00208248i
$631$	21.1566	+	12.2148i	0.842230	+	0.486262i	0.858022	−	0.513614i	$-0.171694\pi$
$631$	21.1566	+	12.2148i	0.842230	+	0.486262i	−0.0157918	+	0.999875i	$0.505027\pi$
$632$			13.8291i			0.550091i
$633$	−2.54288	+	4.40439i	−0.101070	+	0.175059i
$634$	−12.8264	−	22.2160i	−0.509401	−	0.882309i
$635$	−13.9197	+	8.03654i	−0.552386	+	0.318920i
$636$	9.34481			0.370546
$637$		0			0
$638$	30.9245			1.22431
$639$	7.54637	−	4.35690i	0.298530	−	0.172356i
$640$	−1.06853	−	1.85075i	−0.0422374	−	0.0731574i
$641$	24.3991	−	42.2605i	0.963707	−	1.66919i	0.250657	−	0.968076i	$-0.419353\pi$
$641$	24.3991	−	42.2605i	0.963707	−	1.66919i	0.713050	−	0.701113i	$-0.247313\pi$
$642$		−	8.36658i		−	0.330203i
$643$	24.4820	+	14.1347i	0.965475	+	0.557417i	0.897854	−	0.440294i	$-0.145126\pi$
$643$	24.4820	+	14.1347i	0.965475	+	0.557417i	0.0676209	+	0.997711i	$0.478459\pi$
$644$	0.114966	+	0.0663757i	0.00453030	+	0.00261557i
$645$		−	14.3478i		−	0.564944i
$646$	−10.4155	+	18.0402i	−0.409792	+	0.709781i
$647$	17.4480	+	30.2209i	0.685953	+	1.18810i	0.973136	+	0.230229i	$0.0739476\pi$
$647$	17.4480	+	30.2209i	0.685953	+	1.18810i	−0.287184	+	0.957876i	$0.592719\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	26.8756			1.05496
$650$		0			0
$651$	0.440730			0.0172736
$652$	−4.80608	+	2.77479i	−0.188221	+	0.108669i
$653$	5.85786	+	10.1461i	0.229236	+	0.397048i	0.957582	−	0.288162i	$-0.0930440\pi$
$653$	5.85786	+	10.1461i	0.229236	+	0.397048i	−0.728346	+	0.685209i	$0.759711\pi$
$654$	8.71379	−	15.0927i	0.340736	−	0.590172i
$655$		−	10.9524i		−	0.427946i
$656$	−7.44071	−	4.29590i	−0.290511	−	0.167727i
$657$	12.9459	+	7.47434i	0.505069	+	0.291602i
$658$		−	0.352584i		−	0.0137452i
$659$	3.56734	−	6.17881i	0.138964	−	0.240692i	−0.788141	−	0.615495i	$-0.788956\pi$
$659$	3.56734	−	6.17881i	0.138964	−	0.240692i	0.927105	+	0.374803i	$0.122290\pi$
$660$	−6.72737	−	11.6521i	−0.261862	−	0.453559i
$661$	7.38622	−	4.26444i	0.287291	−	0.165867i	−0.349429	−	0.936963i	$-0.613624\pi$
$661$	7.38622	−	4.26444i	0.287291	−	0.165867i	0.636719	+	0.771096i	$0.280291\pi$
$662$	−3.82371			−0.148613
$663$		0			0
$664$	−11.1347			−0.432109
$665$	−0.652545	+	0.376747i	−0.0253046	+	0.0146096i
$666$	0.0881460	+	0.152673i	0.00341559	+	0.00591597i
$667$	6.66487	−	11.5439i	0.258065	−	0.446982i
$668$			3.92154i			0.151729i
$669$	−17.7953	−	10.2741i	−0.688006	−	0.397221i
$670$	−9.96452	−	5.75302i	−0.384963	−	0.222259i
$671$			44.7633i			1.72807i
$672$	−0.0244587	+	0.0423637i	−0.000943514	+	0.00163421i
$673$	−15.7969	−	27.3610i	−0.608924	−	1.05469i	−0.991418	−	0.130729i	$-0.958268\pi$
$673$	−15.7969	−	27.3610i	−0.608924	−	1.05469i	0.382494	−	0.923958i	$-0.375065\pi$
$674$	17.4334	−	10.0652i	0.671510	−	0.387696i
$675$	−0.432960			−0.0166646
$676$		0			0
$677$	−17.3002			−0.664901			−0.332451	−	0.943121i	$-0.607875\pi$
$677$	−17.3002			−0.664901			−0.332451	+	0.943121i	$0.607875\pi$
$678$	−12.1034	+	6.98792i	−0.464829	+	0.268369i
$679$	−0.0606304	−	0.105015i	−0.00232678	−	0.00403011i
$680$	−3.08815	+	5.34883i	−0.118425	+	0.205118i
$681$		−	4.41119i		−	0.169037i
$682$	49.1245	+	28.3620i	1.88107	+	1.08604i
$683$	26.3234	+	15.1978i	1.00724	+	0.581529i	0.910382	−	0.413770i	$-0.135788\pi$
$683$	26.3234	+	15.1978i	1.00724	+	0.581529i	0.0968556	+	0.995298i	$0.469122\pi$
$684$		−	7.20775i		−	0.275595i
$685$	4.27413	−	7.40300i	0.163306	−	0.282854i
$686$	0.342363	+	0.592990i	0.0130715	+	0.0226405i
$687$	0.199693	−	0.115293i	0.00761878	−	0.00439871i
$688$	−6.71379			−0.255961
$689$		0			0
$690$	−5.79954			−0.220785
$691$	30.9447	−	17.8659i	1.17719	−	0.679652i	0.221828	−	0.975086i	$-0.428798\pi$
$691$	30.9447	−	17.8659i	1.17719	−	0.679652i	0.955363	+	0.295434i	$0.0954643\pi$
$692$	1.74214	+	3.01747i	0.0662260	+	0.114707i
$693$	−0.153989	+	0.266717i	−0.00584957	+	0.0101317i
$694$		−	2.93900i		−	0.111563i
$695$	16.0823	+	9.28514i	0.610038	+	0.352206i
$696$	4.25379	+	2.45593i	0.161240	+	0.0930917i
$697$			24.8310i			0.940541i
$698$	3.68664	−	6.38546i	0.139542	−	0.241693i
$699$	3.91185	+	6.77553i	0.147960	+	0.256274i
$700$	0.0183418	−	0.0105896i	0.000693254	−	0.000400250i
$701$	−20.1328			−0.760404			−0.380202	−	0.924904i	$-0.624145\pi$
$701$	−20.1328			−0.760404			−0.380202	+	0.924904i	$0.624145\pi$
$702$		0			0
$703$	1.27067			0.0479242
$704$	−5.45241	+	3.14795i	−0.205495	+	0.118643i
$705$	7.70171	+	13.3398i	0.290063	+	0.502404i
$706$	1.00538	−	1.74136i	0.0378379	−	0.0655371i
$707$			0.0808502i			0.00304069i
$708$	3.69685	+	2.13437i	0.138936	+	0.0802147i
$709$	14.3898	+	8.30798i	0.540422	+	0.312013i	0.745250	−	0.666785i	$-0.232330\pi$
$709$	14.3898	+	8.30798i	0.540422	+	0.312013i	−0.204828	+	0.978798i	$0.565664\pi$
$710$		−	18.6219i		−	0.698868i
$711$	−6.91454	+	11.9763i	−0.259316	+	0.449148i
$712$	1.96077	+	3.39616i	0.0734830	+	0.127276i
$713$	21.1747	−	12.2252i	0.792998	−	0.457838i
$714$	0.141375			0.00529083
$715$		0			0
$716$	3.58881			0.134120
$717$	−9.65918	+	5.57673i	−0.360729	+	0.208267i
$718$	15.7289	+	27.2432i	0.586996	+	1.01671i
$719$	1.02416	−	1.77390i	0.0381948	−	0.0661554i	−0.846296	−	0.532713i	$-0.821173\pi$
$719$	1.02416	−	1.77390i	0.0381948	−	0.0661554i	0.884491	+	0.466557i	$0.154506\pi$
$720$		−	2.13706i		−	0.0796436i
$721$	0.348860	+	0.201415i	0.0129922	+	0.00750107i
$722$	−28.5370	−	16.4758i	−1.06204	−	0.613167i
$723$		−	3.54527i		−	0.131850i
$724$	−2.75302	+	4.76837i	−0.102315	+	0.177215i
$725$	−1.06332	−	1.84172i	−0.0394907	−	0.0683998i
$726$	−24.8015	+	14.3192i	−0.920470	+	0.531434i
$727$	−29.9377			−1.11033			−0.555163	−	0.831741i	$-0.687344\pi$
$727$	−29.9377			−1.11033			−0.555163	+	0.831741i	$0.687344\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	27.6663	−	15.9731i	1.02398	−	0.591193i
$731$	9.70171	+	16.8039i	0.358831	+	0.621513i
$732$	−3.55496	+	6.15737i	−0.131395	+	0.227583i
$733$		−	1.46250i		−	0.0540187i	−0.999635	−	0.0270093i	$-0.991402\pi$
$733$		−	1.46250i		−	0.0540187i	0.999635	−	0.0270093i	$-0.00859839\pi$
$734$	−3.89654	−	2.24967i	−0.143824	−	0.0830368i
$735$	−12.9508	−	7.47716i	−0.477699	−	0.275799i
$736$			2.71379i			0.100032i
$737$	−16.9487	+	29.3560i	−0.624313	+	1.08134i
$738$	−4.29590	−	7.44071i	−0.158134	−	0.273896i
$739$	−34.9758	+	20.1933i	−1.28660	+	0.742822i	−0.978047	−	0.208384i	$-0.933180\pi$
$739$	−34.9758	+	20.1933i	−1.28660	+	0.742822i	−0.308558	+	0.951206i	$0.599846\pi$
$740$	0.376747			0.0138495
$741$		0			0
$742$	−0.457123			−0.0167815
$743$	−8.46573	+	4.88769i	−0.310577	+	0.179312i	−0.647185	−	0.762333i	$-0.724054\pi$
$743$	−8.46573	+	4.88769i	−0.310577	+	0.179312i	0.336607	+	0.941645i	$0.390720\pi$
$744$	4.50484	+	7.80262i	0.165156	+	0.286058i
$745$	−5.20195	+	9.01004i	−0.190585	+	0.330102i
$746$		−	37.8297i		−	1.38504i
$747$	−9.64291	−	5.56734i	−0.352816	−	0.203698i
$748$	15.7579	+	9.09783i	0.576166	+	0.332650i
$749$			0.409271i			0.0149544i
$750$	−5.80529	+	10.0551i	−0.211979	+	0.367159i
$751$	17.2729	+	29.9176i	0.630298	+	1.09171i	0.987491	+	0.157678i	$0.0504007\pi$
$751$	17.2729	+	29.9176i	0.630298	+	1.09171i	−0.357192	+	0.934031i	$0.616266\pi$
$752$	6.24210	−	3.60388i	0.227626	−	0.131420i
$753$	−4.17092			−0.151997
$754$		0			0
$755$	31.5138			1.14690
$756$	−0.0423637	+	0.0244587i	−0.00154075	+	0.000889553i
$757$	2.57242	+	4.45556i	0.0934961	+	0.161940i	0.908980	−	0.416840i	$-0.136862\pi$
$757$	2.57242	+	4.45556i	0.0934961	+	0.161940i	−0.815484	+	0.578780i	$0.803529\pi$
$758$	4.21983	−	7.30896i	0.153271	−	0.265474i
$759$			17.0858i			0.620174i
$760$	−13.3398	−	7.70171i	−0.483884	−	0.279370i
$761$	−16.8979	−	9.75600i	−0.612548	−	0.353655i	0.161414	−	0.986887i	$-0.448395\pi$
$761$	−16.8979	−	9.75600i	−0.612548	−	0.353655i	−0.773962	+	0.633232i	$0.781728\pi$
$762$			7.52111i			0.272461i
$763$	−0.426256	+	0.738296i	−0.0154315	+	0.0267281i
$764$	−2.82908	−	4.90012i	−0.102353	−	0.177280i
$765$	−5.34883	+	3.08815i	−0.193387	+	0.111652i
$766$	1.28621			0.0464726
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	4.98485	−	2.87800i	0.179758	−	0.103783i	−0.407421	−	0.913241i	$-0.633572\pi$
$769$	4.98485	−	2.87800i	0.179758	−	0.103783i	0.587179	+	0.809457i	$0.300238\pi$
$770$	0.329085	+	0.569992i	0.0118594	+	0.0205411i
$771$	5.44504	−	9.43109i	0.196098	−	0.339652i
$772$			13.4034i			0.482400i
$773$	3.57441	+	2.06369i	0.128563	+	0.0742257i	0.562902	−	0.826524i	$-0.309685\pi$
$773$	3.57441	+	2.06369i	0.128563	+	0.0742257i	−0.434339	+	0.900749i	$0.643018\pi$
$774$	−5.81431	−	3.35690i	−0.208991	−	0.120661i
$775$		−	3.90084i		−	0.140122i
$776$	1.23945	−	2.14678i	0.0444935	−	0.0770651i
$777$	−0.00431187	−	0.00746837i	−0.000154687	−	0.000267926i
$778$	20.2584	−	11.6962i	0.726299	−	0.419329i
$779$	−61.9275			−2.21878
$780$		0			0
$781$	−54.8611			−1.96309
$782$	6.79231	−	3.92154i	0.242893	−	0.140234i
$783$	2.45593	+	4.25379i	0.0877677	+	0.152018i
$784$	−3.49880	+	6.06011i	−0.124957	+	0.216432i
$785$			35.7184i			1.27485i
$786$	−4.43836	−	2.56249i	−0.158311	−	0.0914010i
$787$	−14.0636	−	8.11960i	−0.501312	−	0.289433i	0.227943	−	0.973674i	$-0.426800\pi$
$787$	−14.0636	−	8.11960i	−0.501312	−	0.289433i	−0.729255	+	0.684242i	$0.760133\pi$
$788$		−	19.9812i		−	0.711801i
$789$	−15.6136	+	27.0435i	−0.555858	+	0.962774i
$790$	14.7768	+	25.5942i	0.525735	+	0.910601i
$791$	0.592068	−	0.341830i	0.0210515	−	0.0121541i
$792$	−6.29590			−0.223715
$793$		0			0
$794$	−37.0858			−1.31612
$795$	17.2949	−	9.98523i	0.613388	−	0.354140i
$796$	3.12080	+	5.40539i	0.110614	+	0.191589i
$797$	8.05741	−	13.9558i	0.285408	−	0.494341i	−0.687300	−	0.726374i	$-0.741204\pi$
$797$	8.05741	−	13.9558i	0.285408	−	0.494341i	0.972708	+	0.232032i	$0.0745375\pi$
$798$			0.352584i			0.0124813i
$799$	−18.0402	−	10.4155i	−0.638216	−	0.368474i
$800$	0.374955	+	0.216480i	0.0132566	+	0.00765373i
$801$			3.92154i			0.138561i
$802$	2.43296	−	4.21401i	0.0859108	−	0.148802i
$803$	−47.0577	−	81.5063i	−1.66063	−	2.87630i
$804$	−4.66272	+	2.69202i	−0.164441	+	0.0949403i
$805$	0.283698			0.00999905
$806$		0			0
$807$	−15.9172			−0.560313
$808$	−1.43136	+	0.826396i	−0.0503551	+	0.0290725i
$809$	−20.0761	−	34.7728i	−0.705837	−	1.22255i	−0.966389	−	0.257085i	$-0.917238\pi$
$809$	−20.0761	−	34.7728i	−0.705837	−	1.22255i	0.260552	−	0.965460i	$-0.416096\pi$
$810$	1.06853	−	1.85075i	0.0375444	−	0.0650288i
$811$			39.8646i			1.39984i	0.714224	+	0.699918i	$0.246780\pi$
$811$			39.8646i			1.39984i	−0.714224	+	0.699918i	$0.753220\pi$
$812$	−0.208084	−	0.120137i	−0.00730232	−	0.00421600i
$813$	−3.04937	−	1.76055i	−0.106946	−	0.0617453i
$814$		−	1.10992i		−	0.0389025i
$815$	−5.92990	+	10.2709i	−0.207715	+	0.359774i
$816$	1.44504	+	2.50289i	0.0505866	+	0.0876185i
$817$	−41.9081	+	24.1957i	−1.46618	+	0.846499i
$818$	−0.445042			−0.0155605
$819$		0			0
$820$	−18.3612			−0.641201
$821$	−5.41636	+	3.12714i	−0.189032	+	0.109138i	−0.591529	−	0.806283i	$-0.701476\pi$
$821$	−5.41636	+	3.12714i	−0.189032	+	0.109138i	0.402497	+	0.915421i	$0.368142\pi$
$822$	−2.00000	−	3.46410i	−0.0697580	−	0.120824i
$823$	−2.37167	+	4.10785i	−0.0826711	+	0.143191i	−0.904396	−	0.426693i	$-0.859678\pi$
$823$	−2.37167	+	4.10785i	−0.0826711	+	0.143191i	0.821725	+	0.569884i	$0.193012\pi$
$824$			8.23490i			0.286876i
$825$	2.36068	+	1.36294i	0.0821882	+	0.0474514i
$826$	−0.180840	−	0.104408i	−0.00629222	−	0.00363282i
$827$			0.716185i			0.0249042i	0.999922	+	0.0124521i	$0.00396373\pi$
$827$			0.716185i			0.0249042i	−0.999922	+	0.0124521i	$0.996036\pi$
$828$	−1.35690	+	2.35021i	−0.0471554	+	0.0816755i
$829$	−18.0030	−	31.1821i	−0.625269	−	1.08300i	−0.988489	−	0.151295i	$-0.951656\pi$
$829$	−18.0030	−	31.1821i	−0.625269	−	1.08300i	0.363219	−	0.931704i	$-0.381678\pi$
$830$	−20.6075	+	11.8977i	−0.715297	+	0.412977i
$831$	−8.58104			−0.297673
$832$		0			0
$833$	20.2237			0.700709
$834$	7.52544	−	4.34481i	0.260585	−	0.150449i
$835$	4.19029	+	7.25780i	0.145011	+	0.251167i
$836$	−22.6896	+	39.2996i	−0.784737	+	1.35920i
$837$			9.00969i			0.311420i
$838$	15.5771	+	8.99343i	0.538101	+	0.310673i
$839$	−18.6677	−	10.7778i	−0.644479	−	0.372090i	0.141859	−	0.989887i	$-0.454692\pi$
$839$	−18.6677	−	10.7778i	−0.644479	−	0.372090i	−0.786338	+	0.617797i	$0.788025\pi$
$840$			0.104539i			0.00360695i
$841$	2.43685	−	4.22074i	0.0840291	−	0.145543i
$842$	10.6407	+	18.4303i	0.366703	+	0.635148i
$843$	−6.99615	+	4.03923i	−0.240960	+	0.139118i
$844$	5.08575			0.175059
$845$		0			0
$846$	7.20775			0.247808
$847$	1.21322	−	0.700455i	0.0416869	−	0.0240679i
$848$	−4.67241	−	8.09285i	−0.160451	−	0.277909i
$849$	8.70171	−	15.0718i	0.298642	−	0.517263i
$850$		−	1.25129i		−	0.0429189i
$851$	−0.414324	−	0.239210i	−0.0142028	−	0.00820001i
$852$	−7.54637	−	4.35690i	−0.258534	−	0.149265i
$853$		−	37.8237i		−	1.29506i	−0.762040	−	0.647530i	$-0.775802\pi$
$853$		−	37.8237i		−	1.29506i	0.762040	−	0.647530i	$-0.224198\pi$
$854$	0.173899	−	0.301202i	0.00595070	−	0.0103069i
$855$	−7.70171	−	13.3398i	−0.263393	−	0.456210i
$856$	−7.24567	+	4.18329i	−0.247652	+	0.142982i
$857$	6.58317			0.224877			0.112438	−	0.993659i	$-0.464134\pi$
$857$	6.58317			0.224877			0.112438	+	0.993659i	$0.464134\pi$
$858$		0			0
$859$	−20.6246			−0.703702			−0.351851	−	0.936056i	$-0.614448\pi$
$859$	−20.6246			−0.703702			−0.351851	+	0.936056i	$0.614448\pi$
$860$	−12.4256	+	7.17390i	−0.423708	+	0.244628i
$861$	0.210144	+	0.363980i	0.00716168	+	0.0124044i
$862$	12.3569	−	21.4028i	0.420878	−	0.728981i
$863$		−	15.9081i		−	0.541519i	−0.962647	−	0.270760i	$-0.912725\pi$
$863$		−	15.9081i		−	0.541519i	0.962647	−	0.270760i	$-0.0872748\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	6.44852	+	3.72305i	0.219256	+	0.126588i
$866$			32.2174i			1.09479i
$867$	−4.32371	+	7.48888i	−0.146841	+	0.254336i
$868$	−0.220365	−	0.381683i	−0.00747968	−	0.0129552i
$869$	75.4018	−	43.5332i	2.55783	−	1.47676i
$870$	10.4969			0.355880
$871$		0			0
$872$	−17.4276			−0.590172
$873$	2.14678	−	1.23945i	0.0726577	−	0.0419489i
$874$	9.78017	+	16.9397i	0.330819	+	0.572995i
$875$	0.283979	−	0.491867i	0.00960025	−	0.0166281i
$876$		−	14.9487i		−	0.505069i
$877$	−13.5134	−	7.80194i	−0.456313	−	0.263453i	0.254179	−	0.967157i	$-0.418195\pi$
$877$	−13.5134	−	7.80194i	−0.456313	−	0.263453i	−0.710493	+	0.703704i	$0.751528\pi$
$878$	−27.7887	−	16.0438i	−0.937825	−	0.541453i
$879$		−	19.3709i		−	0.653364i
$880$	−6.72737	+	11.6521i	−0.226779	+	0.392794i
$881$	−7.12737	−	12.3450i	−0.240127	−	0.415913i	0.720623	−	0.693327i	$-0.243856\pi$
$881$	−7.12737	−	12.3450i	−0.240127	−	0.415913i	−0.960750	+	0.277414i	$0.910523\pi$
$882$	−6.06011	+	3.49880i	−0.204054	+	0.117811i
$883$	−1.65817			−0.0558019			−0.0279009	−	0.999611i	$-0.508882\pi$
$883$	−1.65817			−0.0558019			−0.0279009	+	0.999611i	$0.508882\pi$
$884$		0			0
$885$	9.12259			0.306652
$886$	−17.7630	+	10.2555i	−0.596760	+	0.344539i
$887$	9.60148	+	16.6303i	0.322386	+	0.558389i	0.980980	−	0.194109i	$-0.0621817\pi$
$887$	9.60148	+	16.6303i	0.322386	+	0.558389i	−0.658594	+	0.752499i	$0.728848\pi$
$888$	0.0881460	−	0.152673i	0.00295799	−	0.00512338i
$889$		−	0.367913i		−	0.0123394i
$890$	7.25780	+	4.19029i	0.243282	+	0.140459i
$891$	−5.45241	−	3.14795i	−0.182662	−	0.105460i
$892$			20.5483i			0.688006i
$893$	25.9758	−	44.9915i	0.869248	−	1.50558i
$894$	2.43416	+	4.21608i	0.0814104	+	0.141007i
$895$	6.64199	−	3.83476i	0.222017	−	0.128182i
$896$	0.0489173			0.00163421
$897$		0			0
$898$	−15.3163			−0.511113
$899$	−38.3253	+	22.1271i	−1.27822	+	0.737981i
$900$	0.216480	+	0.374955i	0.00721600	+	0.0124985i
$901$	−13.5036	+	23.3890i	−0.449872	+	0.779201i
$902$			54.0930i			1.80110i
$903$	0.284421	+	0.164210i	0.00946493	+	0.00546458i
$904$	12.1034	+	6.98792i	0.402554	+	0.232415i
$905$			11.7668i			0.391140i
$906$	7.37316	−	12.7707i	0.244957	−	0.424278i
$907$	−16.1836	−	28.0308i	−0.537367	−	0.930747i	−0.999045	−	0.0436995i	$-0.986086\pi$
$907$	−16.1836	−	28.0308i	−0.537367	−	0.930747i	0.461678	−	0.887048i	$-0.347248\pi$
$908$	−3.82020	+	2.20560i	−0.126778	+	0.0731952i
$909$	−1.65279			−0.0548197
$910$		0			0
$911$	−33.9624			−1.12523			−0.562613	−	0.826721i	$-0.690204\pi$
$911$	−33.9624			−1.12523			−0.562613	+	0.826721i	$0.690204\pi$
$912$	−6.24210	+	3.60388i	−0.206696	+	0.119336i
$913$	35.0514	+	60.7108i	1.16003	+	2.00923i
$914$	−9.59299	+	16.6155i	−0.317308	+	0.549593i
$915$			15.1943i			0.502309i
$916$	−0.199693	−	0.115293i	−0.00659806	−	0.00380939i
$917$	0.217113	+	0.125350i	0.00716970	+	0.00413943i
$918$			2.89008i			0.0953870i
$919$	10.0390	−	17.3880i	0.331156	−	0.573579i	−0.651583	−	0.758577i	$-0.725895\pi$
$919$	10.0390	−	17.3880i	0.331156	−	0.573579i	0.982739	+	0.184999i	$0.0592281\pi$
$920$	2.89977	+	5.02255i	0.0956027	+	0.165589i
$921$	−10.7615	+	6.21313i	−0.354602	+	0.204730i
$922$	−8.31229			−0.273751
$923$		0			0
$924$	0.307979			0.0101317
$925$	−0.0661015	+	0.0381637i	−0.00217340	+	0.00125482i
$926$	3.16421	+	5.48057i	0.103982	+	0.180103i
$927$	−4.11745	+	7.13163i	−0.135235	+	0.234233i
$928$		−	4.91185i		−	0.161240i
$929$	48.6082	+	28.0640i	1.59478	+	0.920749i	0.992470	+	0.122491i	$0.0390883\pi$
$929$	48.6082	+	28.0640i	1.59478	+	0.920749i	0.602315	+	0.798258i	$0.294245\pi$
$930$	16.6747	+	9.62714i	0.546785	+	0.315686i
$931$			50.4370i			1.65301i
$932$	3.91185	−	6.77553i	0.128137	−	0.221940i
$933$	−1.35690	−	2.35021i	−0.0444228	−	0.0769425i
$934$	−27.0095	+	15.5939i	−0.883778	+	0.510250i
$935$	38.8853			1.27169
$936$		0			0
$937$	27.0291			0.883001			0.441501	−	0.897261i	$-0.354446\pi$
$937$	27.0291			0.883001			0.441501	+	0.897261i	$0.354446\pi$
$938$	0.228088	−	0.131687i	0.00744733	−	0.00429972i
$939$	7.69418	+	13.3267i	0.251090	+	0.434901i
$940$	7.70171	−	13.3398i	0.251202	−	0.435095i
$941$			24.0277i			0.783282i	0.920118	+	0.391641i	$0.128092\pi$
$941$			24.0277i			0.783282i	−0.920118	+	0.391641i	$0.871908\pi$
$942$	14.4746	+	8.35690i	0.471607	+	0.272282i
$943$	20.1925	+	11.6582i	0.657560	+	0.379642i
$944$		−	4.26875i		−	0.138936i
$945$	−0.0522697	+	0.0905338i	−0.00170033	+	0.00294507i
$946$	21.1347	+	36.6063i	0.687147	+	1.19017i
$947$	−23.2065	+	13.3983i	−0.754110	+	0.435386i	−0.827177	−	0.561941i	$-0.810055\pi$
$947$	−23.2065	+	13.3983i	−0.754110	+	0.435386i	0.0730670	+	0.997327i	$0.476721\pi$
$948$	13.8291			0.449148
$949$		0			0
$950$	3.12067			0.101248
$951$	−22.2160	+	12.8264i	−0.720402	+	0.415924i
$952$	−0.0706876	−	0.122435i	−0.00229100	−	0.00396813i
$953$	17.2107	−	29.8099i	0.557510	−	0.965636i	−0.440193	−	0.897903i	$-0.645090\pi$
$953$	17.2107	−	29.8099i	0.557510	−	0.965636i	0.997703	−	0.0677332i	$-0.0215767\pi$
$954$		−	9.34481i		−	0.302550i
$955$	−10.4719	−	6.04593i	−0.338862	−	0.195642i
$956$	9.65918	+	5.57673i	0.312400	+	0.180364i
$957$		−	30.9245i		−	0.999648i
$958$	8.96615	−	15.5298i	0.289683	−	0.501746i
$959$	0.0978347	+	0.169455i	0.00315925	+	0.00547198i
$960$	−1.85075	+	1.06853i	−0.0597327	+	0.0344867i
$961$	−50.1745			−1.61853
$962$		0			0
$963$	−8.36658			−0.269609
$964$	−3.07029	+	1.77263i	−0.0988875	+	0.0570927i
$965$	14.3220	+	24.8064i	0.461041	+	0.798546i
$966$	0.0663757	−	0.114966i	0.00213560	−	0.00369898i
$967$		−	26.2631i		−	0.844565i	−0.906464	−	0.422282i	$-0.861229\pi$
$967$		−	26.2631i		−	0.844565i	0.906464	−	0.422282i	$-0.138771\pi$
$968$	24.8015	+	14.3192i	0.797151	+	0.460235i
$969$	18.0402	+	10.4155i	0.579534	+	0.334594i
$970$		−	5.29755i		−	0.170094i
$971$	19.9921	−	34.6273i	0.641577	−	1.11124i	−0.343504	−	0.939151i	$-0.611614\pi$
$971$	19.9921	−	34.6273i	0.641577	−	1.11124i	0.985081	−	0.172093i	$-0.0550528\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−0.368124	+	0.212537i	−0.0118015	+	0.00681362i
$974$	−30.3279			−0.971770
$975$		0			0
$976$	7.10992			0.227583
$977$	−3.96914	+	2.29159i	−0.126984	+	0.0733143i	−0.562146	−	0.827038i	$-0.690024\pi$
$977$	−3.96914	+	2.29159i	−0.126984	+	0.0733143i	0.435162	+	0.900352i	$0.356691\pi$
$978$	2.77479	+	4.80608i	0.0887280	+	0.153681i
$979$	12.3448	−	21.3818i	0.394542	−	0.683367i
$980$			14.9543i			0.477699i
$981$	−15.0927	−	8.71379i	−0.481874	−	0.278210i
$982$	−26.0634	−	15.0477i	−0.831717	−	0.480192i
$983$		−	10.6848i		−	0.340794i	−0.985376	−	0.170397i	$-0.945495\pi$
$983$		−	10.6848i		−	0.340794i	0.985376	−	0.170397i	$-0.0545049\pi$
$984$	−4.29590	+	7.44071i	−0.136948	+	0.237201i
$985$	−21.3506	−	36.9803i	−0.680285	−	1.17829i
$986$	−12.2938	+	7.09783i	−0.391515	+	0.226041i
$987$	−0.352584			−0.0112229
$988$		0			0
$989$	18.2198			0.579357
$990$	−11.6521	+	6.72737i	−0.370329	+	0.213810i
$991$	−25.3010	−	43.8227i	−0.803714	−	1.39207i	−0.917156	−	0.398529i	$-0.869521\pi$
$991$	−25.3010	−	43.8227i	−0.803714	−	1.39207i	0.113442	−	0.993545i	$-0.463812\pi$
$992$	4.50484	−	7.80262i	0.143029	−	0.247733i
$993$			3.82371i			0.121342i
$994$	0.369148	+	0.213128i	0.0117087	+	0.00676000i
$995$	11.5517	+	6.66935i	0.366212	+	0.211433i
$996$			11.1347i			0.352816i
$997$	17.9801	−	31.1425i	0.569437	−	0.986294i	−0.427185	−	0.904164i	$-0.640495\pi$
$997$	17.9801	−	31.1425i	0.569437	−	0.986294i	0.996622	−	0.0821294i	$-0.0261721\pi$
$998$		0			0
$999$	0.152673	−	0.0881460i	0.00483037	−	0.00278882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.h.361.2		12
13.2	odd	12		1014.2.a.l.1.2	✓	3
13.3	even	3		1014.2.b.f.337.2		6
13.4	even	6	inner	1014.2.i.h.823.2		12
13.5	odd	4		1014.2.e.n.991.2		6
13.6	odd	12		1014.2.e.n.529.2		6
13.7	odd	12		1014.2.e.l.529.2		6
13.8	odd	4		1014.2.e.l.991.2		6
13.9	even	3	inner	1014.2.i.h.823.5		12
13.10	even	6		1014.2.b.f.337.5		6
13.11	odd	12		1014.2.a.n.1.2	yes	3
13.12	even	2	inner	1014.2.i.h.361.5		12
39.2	even	12		3042.2.a.bh.1.2		3
39.11	even	12		3042.2.a.ba.1.2		3
39.23	odd	6		3042.2.b.o.1351.2		6
39.29	odd	6		3042.2.b.o.1351.5		6
52.11	even	12		8112.2.a.cm.1.2		3
52.15	even	12		8112.2.a.cj.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.2	✓	3	13.2	odd	12
1014.2.a.n.1.2	yes	3	13.11	odd	12
1014.2.b.f.337.2		6	13.3	even	3
1014.2.b.f.337.5		6	13.10	even	6
1014.2.e.l.529.2		6	13.7	odd	12
1014.2.e.l.991.2		6	13.8	odd	4
1014.2.e.n.529.2		6	13.6	odd	12
1014.2.e.n.991.2		6	13.5	odd	4
1014.2.i.h.361.2		12	1.1	even	1	trivial
1014.2.i.h.361.5		12	13.12	even	2	inner
1014.2.i.h.823.2		12	13.4	even	6	inner
1014.2.i.h.823.5		12	13.9	even	3	inner
3042.2.a.ba.1.2		3	39.11	even	12
3042.2.a.bh.1.2		3	39.2	even	12
3042.2.b.o.1351.2		6	39.23	odd	6
3042.2.b.o.1351.5		6	39.29	odd	6
8112.2.a.cj.1.2		3	52.15	even	12
8112.2.a.cm.1.2		3	52.11	even	12

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.13706i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.0423637 + 0.0244587i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.13706i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.0423637 + 0.0244587i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.06853 + 1.85075i) q^{10} +(5.45241 - 3.14795i) q^{11} +1.00000 q^{12} -0.0489173 q^{14} +(1.85075 - 1.06853i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.44504 + 2.50289i) q^{17} -1.00000i q^{18} +(-6.24210 - 3.60388i) q^{19} +(-1.85075 - 1.06853i) q^{20} +0.0489173i q^{21} +(-3.14795 + 5.45241i) q^{22} +(1.35690 + 2.35021i) q^{23} +(-0.866025 + 0.500000i) q^{24} +0.432960 q^{25} -1.00000 q^{27} +(0.0423637 - 0.0244587i) q^{28} +(-2.45593 - 4.25379i) q^{29} +(-1.06853 + 1.85075i) q^{30} -9.00969i q^{31} +(0.866025 + 0.500000i) q^{32} +(5.45241 + 3.14795i) q^{33} -2.89008i q^{34} +(0.0522697 - 0.0905338i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.152673 + 0.0881460i) q^{37} +7.20775 q^{38} +2.13706 q^{40} +(7.44071 - 4.29590i) q^{41} +(-0.0244587 - 0.0423637i) q^{42} +(3.35690 - 5.81431i) q^{43} -6.29590i q^{44} +(1.85075 + 1.06853i) q^{45} +(-2.35021 - 1.35690i) q^{46} +7.20775i q^{47} +(0.500000 - 0.866025i) q^{48} +(-3.49880 - 6.06011i) q^{49} +(-0.374955 + 0.216480i) q^{50} -2.89008 q^{51} +9.34481 q^{53} +(0.866025 - 0.500000i) q^{54} +(-6.72737 - 11.6521i) q^{55} +(-0.0244587 + 0.0423637i) q^{56} -7.20775i q^{57} +(4.25379 + 2.45593i) q^{58} +(3.69685 + 2.13437i) q^{59} -2.13706i q^{60} +(-3.55496 + 6.15737i) q^{61} +(4.50484 + 7.80262i) q^{62} +(-0.0423637 + 0.0244587i) q^{63} -1.00000 q^{64} -6.29590 q^{66} +(-4.66272 + 2.69202i) q^{67} +(1.44504 + 2.50289i) q^{68} +(-1.35690 + 2.35021i) q^{69} +0.104539i q^{70} +(-7.54637 - 4.35690i) q^{71} +(-0.866025 - 0.500000i) q^{72} -14.9487i q^{73} +(0.0881460 - 0.152673i) q^{74} +(0.216480 + 0.374955i) q^{75} +(-6.24210 + 3.60388i) q^{76} +0.307979 q^{77} +13.8291 q^{79} +(-1.85075 + 1.06853i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.29590 + 7.44071i) q^{82} +11.1347i q^{83} +(0.0423637 + 0.0244587i) q^{84} +(5.34883 + 3.08815i) q^{85} +6.71379i q^{86} +(2.45593 - 4.25379i) q^{87} +(3.14795 + 5.45241i) q^{88} +(3.39616 - 1.96077i) q^{89} -2.13706 q^{90} +2.71379 q^{92} +(7.80262 - 4.50484i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(-7.70171 + 13.3398i) q^{95} +1.00000i q^{96} +(-2.14678 - 1.23945i) q^{97} +(6.06011 + 3.49880i) q^{98} +6.29590i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9	\( 12 q + 6 q^{3} + 6 q^{4} - 6 q^{9} + 2 q^{10} + 12 q^{12} + 36 q^{14} - 6 q^{16} - 16 q^{17} - 10 q^{22} - 72 q^{25} - 12 q^{27} - 22 q^{29} - 2 q^{30} + 8 q^{35} + 6 q^{36} + 16 q^{38} + 4 q^{40} + 18 q^{42} + 24 q^{43} + 6 q^{48} + 40 q^{49} - 32 q^{51} + 20 q^{53} - 36 q^{55} + 18 q^{56} - 44 q^{61} + 10 q^{62} - 12 q^{64} - 20 q^{66} + 16 q^{68} + 16 q^{74} - 36 q^{75} + 24 q^{77} + 124 q^{79} - 6 q^{81} + 4 q^{82} + 22 q^{87} + 10 q^{88} - 4 q^{90} - 8 q^{94} + 16 q^{95}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 6 * q^9 + 2 * q^10 + 12 * q^12 + 36 * q^14 - 6 * q^16 - 16 * q^17 - 10 * q^22 - 72 * q^25 - 12 * q^27 - 22 * q^29 - 2 * q^30 + 8 * q^35 + 6 * q^36 + 16 * q^38 + 4 * q^40 + 18 * q^42 + 24 * q^43 + 6 * q^48 + 40 * q^49 - 32 * q^51 + 20 * q^53 - 36 * q^55 + 18 * q^56 - 44 * q^61 + 10 * q^62 - 12 * q^64 - 20 * q^66 + 16 * q^68 + 16 * q^74 - 36 * q^75 + 24 * q^77 + 124 * q^79 - 6 * q^81 + 4 * q^82 + 22 * q^87 + 10 * q^88 - 4 * q^90 - 8 * q^94 + 16 * q^95

Introduction

L-functions

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