LMFDB - Embedded newform 1014.2.i.a.823.2

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:	$4$
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:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			823.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.823
Dual form			1014.2.i.a.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.86603 - 3.23205i) q^{10} +(-1.09808 - 0.633975i) q^{11} -1.00000 q^{12} -2.73205 q^{14} +(3.23205 + 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} -1.00000i q^{18} +(-4.09808 + 2.36603i) q^{19} +(3.23205 - 1.86603i) q^{20} -2.73205i q^{21} +(-0.633975 - 1.09808i) q^{22} +(2.09808 - 3.63397i) q^{23} +(-0.866025 - 0.500000i) q^{24} -8.92820 q^{25} +1.00000 q^{27} +(-2.36603 - 1.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(1.86603 + 3.23205i) q^{30} -1.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.09808 - 0.633975i) q^{33} -5.73205i q^{34} +(5.09808 + 8.83013i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-3.06218 - 1.76795i) q^{37} -4.73205 q^{38} +3.73205 q^{40} +(-8.13397 - 4.69615i) q^{41} +(1.36603 - 2.36603i) q^{42} +(-4.83013 - 8.36603i) q^{43} -1.26795i q^{44} +(-3.23205 + 1.86603i) q^{45} +(3.63397 - 2.09808i) q^{46} +2.19615i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.232051 - 0.401924i) q^{49} +(-7.73205 - 4.46410i) q^{50} +5.73205 q^{51} -6.46410 q^{53} +(0.866025 + 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(-1.36603 - 2.36603i) q^{56} -4.73205i q^{57} +(3.86603 - 2.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +3.73205i q^{60} +(4.59808 + 7.96410i) q^{61} +(0.732051 - 1.26795i) q^{62} +(2.36603 + 1.36603i) q^{63} -1.00000 q^{64} +1.26795 q^{66} +(11.3660 + 6.56218i) q^{67} +(2.86603 - 4.96410i) q^{68} +(2.09808 + 3.63397i) q^{69} +10.1962i q^{70} +(-4.09808 + 2.36603i) q^{71} +(0.866025 - 0.500000i) q^{72} -6.26795i q^{73} +(-1.76795 - 3.06218i) q^{74} +(4.46410 - 7.73205i) q^{75} +(-4.09808 - 2.36603i) q^{76} +3.46410 q^{77} -2.53590 q^{79} +(3.23205 + 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.69615 - 8.13397i) q^{82} +0.196152i q^{83} +(2.36603 - 1.36603i) q^{84} +(-18.5263 + 10.6962i) q^{85} -9.66025i q^{86} +(2.23205 + 3.86603i) q^{87} +(0.633975 - 1.09808i) q^{88} +(8.19615 + 4.73205i) q^{89} -3.73205 q^{90} +4.19615 q^{92} +(1.26795 + 0.732051i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(8.83013 + 15.2942i) q^{95} -1.00000i q^{96} +(5.19615 - 3.00000i) q^{97} +(0.401924 - 0.232051i) q^{98} +1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{14} + 6 q^{15} - 2 q^{16} - 8 q^{17} - 6 q^{19} + 6 q^{20} - 6 q^{22} - 2 q^{23} - 8 q^{25} + 4 q^{27} - 6 q^{28} + 2 q^{29} + 4 q^{30} - 6 q^{33} + 10 q^{35} + 2 q^{36} + 12 q^{37} - 12 q^{38} + 8 q^{40} - 36 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 18 q^{46} - 2 q^{48} - 6 q^{49} - 24 q^{50} + 16 q^{51} - 12 q^{53} - 6 q^{55} - 2 q^{56} + 12 q^{58} + 8 q^{61} - 4 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{66} + 42 q^{67} + 8 q^{68} - 2 q^{69} - 6 q^{71} - 14 q^{74} + 4 q^{75} - 6 q^{76} - 24 q^{79} + 6 q^{80} - 2 q^{81} + 2 q^{82} + 6 q^{84} - 36 q^{85} + 2 q^{87} + 6 q^{88} + 12 q^{89} - 8 q^{90} - 4 q^{92} + 12 q^{93} + 6 q^{94} + 18 q^{95} + 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^14 + 6 * q^15 - 2 * q^16 - 8 * q^17 - 6 * q^19 + 6 * q^20 - 6 * q^22 - 2 * q^23 - 8 * q^25 + 4 * q^27 - 6 * q^28 + 2 * q^29 + 4 * q^30 - 6 * q^33 + 10 * q^35 + 2 * q^36 + 12 * q^37 - 12 * q^38 + 8 * q^40 - 36 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 18 * q^46 - 2 * q^48 - 6 * q^49 - 24 * q^50 + 16 * q^51 - 12 * q^53 - 6 * q^55 - 2 * q^56 + 12 * q^58 + 8 * q^61 - 4 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^66 + 42 * q^67 + 8 * q^68 - 2 * q^69 - 6 * q^71 - 14 * q^74 + 4 * q^75 - 6 * q^76 - 24 * q^79 + 6 * q^80 - 2 * q^81 + 2 * q^82 + 6 * q^84 - 36 * q^85 + 2 * q^87 + 6 * q^88 + 12 * q^89 - 8 * q^90 - 4 * q^92 + 12 * q^93 + 6 * q^94 + 18 * q^95 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$		−	3.73205i		−	1.66902i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$		−	3.73205i		−	1.66902i	0.550990	−	0.834512i	$-0.314250\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−2.36603	+	1.36603i	−0.894274	+	0.516309i	−0.875338	−	0.483512i	$-0.839361\pi$
$7$	−2.36603	+	1.36603i	−0.894274	+	0.516309i	−0.0189356	+	0.999821i	$0.506028\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.86603	−	3.23205i	0.590089	−	1.02206i
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	0.325239	−	0.945632i	$-0.394555\pi$
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	−0.656322	+	0.754481i	$0.727889\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−2.73205			−0.730171
$15$	3.23205	+	1.86603i	0.834512	+	0.481806i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.86603	−	4.96410i	−0.695113	−	1.20397i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−2.86603	−	4.96410i	−0.695113	−	1.20397i	0.275029	−	0.961436i	$-0.411312\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.890011	−	0.455938i	$-0.849304\pi$
$19$	−4.09808	+	2.36603i	−0.940163	+	0.542803i	−0.0501517	+	0.998742i	$0.515970\pi$
$20$	3.23205	−	1.86603i	0.722709	−	0.417256i
$21$		−	2.73205i		−	0.596182i
$22$	−0.633975	−	1.09808i	−0.135164	−	0.234111i
$23$	2.09808	−	3.63397i	0.437479	−	0.757736i	−0.560015	−	0.828482i	$-0.689205\pi$
$23$	2.09808	−	3.63397i	0.437479	−	0.757736i	0.997494	+	0.0707462i	$0.0225381\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−8.92820			−1.78564
$26$		0			0
$27$	1.00000			0.192450
$28$	−2.36603	−	1.36603i	−0.447137	−	0.258155i
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	−0.580892	−	0.813980i	$-0.697296\pi$
$29$	2.23205	−	3.86603i	0.414481	−	0.717903i	0.995374	+	0.0960774i	$0.0306296\pi$
$30$	1.86603	+	3.23205i	0.340688	+	0.590089i
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.09808	−	0.633975i	0.191151	−	0.110361i
$34$		−	5.73205i		−	0.983039i
$35$	5.09808	+	8.83013i	0.861732	+	1.49256i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−3.06218	−	1.76795i	−0.503419	−	0.290649i	0.226705	−	0.973963i	$-0.427205\pi$
$37$	−3.06218	−	1.76795i	−0.503419	−	0.290649i	−0.730124	+	0.683314i	$0.760538\pi$
$38$	−4.73205			−0.767640
$39$		0			0
$40$	3.73205			0.590089
$41$	−8.13397	−	4.69615i	−1.27031	−	0.733416i	−0.295267	−	0.955415i	$-0.595408\pi$
$41$	−8.13397	−	4.69615i	−1.27031	−	0.733416i	−0.975047	+	0.221999i	$0.928742\pi$
$42$	1.36603	−	2.36603i	0.210782	−	0.365086i
$43$	−4.83013	−	8.36603i	−0.736587	−	1.27581i	−0.954023	−	0.299732i	$-0.903103\pi$
$43$	−4.83013	−	8.36603i	−0.736587	−	1.27581i	0.217436	−	0.976075i	$-0.430231\pi$
$44$		−	1.26795i		−	0.191151i
$45$	−3.23205	+	1.86603i	−0.481806	+	0.278171i
$46$	3.63397	−	2.09808i	0.535800	−	0.309344i
$47$			2.19615i			0.320342i	0.987089	+	0.160171i	$0.0512045\pi$
$47$			2.19615i			0.320342i	−0.987089	+	0.160171i	$0.948795\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	0.232051	−	0.401924i	0.0331501	−	0.0574177i
$50$	−7.73205	−	4.46410i	−1.09348	−	0.631319i
$51$	5.73205			0.802648
$52$		0			0
$53$	−6.46410			−0.887913			−0.443956	−	0.896048i	$-0.646425\pi$
$53$	−6.46410			−0.887913			−0.443956	+	0.896048i	$0.646425\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−2.36603	+	4.09808i	−0.319035	+	0.552584i
$56$	−1.36603	−	2.36603i	−0.182543	−	0.316173i
$57$		−	4.73205i		−	0.626775i
$58$	3.86603	−	2.23205i	0.507634	−	0.293083i
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.0241347	−	0.999709i	$-0.492317\pi$
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.877841	+	0.478953i	$0.158984\pi$
$60$			3.73205i			0.481806i
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	0.994400	+	0.105682i	$0.0337026\pi$
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	−0.405677	+	0.914017i	$0.632964\pi$
$62$	0.732051	−	1.26795i	0.0929705	−	0.161030i
$63$	2.36603	+	1.36603i	0.298091	+	0.172103i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.26795			0.156074
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.993155	−	0.116800i	$-0.0372638\pi$
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.395426	+	0.918498i	$0.370597\pi$
$68$	2.86603	−	4.96410i	0.347557	−	0.601986i
$69$	2.09808	+	3.63397i	0.252579	+	0.437479i
$70$			10.1962i			1.21867i
$71$	−4.09808	+	2.36603i	−0.486352	+	0.280796i	−0.723060	−	0.690785i	$-0.757265\pi$
$71$	−4.09808	+	2.36603i	−0.486352	+	0.280796i	0.236708	+	0.971581i	$0.423932\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	6.26795i		−	0.733608i	−0.930298	−	0.366804i	$-0.880452\pi$
$73$		−	6.26795i		−	0.733608i	0.930298	−	0.366804i	$-0.119548\pi$
$74$	−1.76795	−	3.06218i	−0.205520	−	0.355971i
$75$	4.46410	−	7.73205i	0.515470	−	0.892820i
$76$	−4.09808	−	2.36603i	−0.470082	−	0.271402i
$77$	3.46410			0.394771
$78$		0			0
$79$	−2.53590			−0.285311			−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590			−0.285311			−0.142655	+	0.989772i	$0.545564\pi$
$80$	3.23205	+	1.86603i	0.361354	+	0.208628i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.69615	−	8.13397i	−0.518603	−	0.898247i
$83$			0.196152i			0.0215305i	0.999942	+	0.0107653i	$0.00342676\pi$
$83$			0.196152i			0.0215305i	−0.999942	+	0.0107653i	$0.996573\pi$
$84$	2.36603	−	1.36603i	0.258155	−	0.149046i
$85$	−18.5263	+	10.6962i	−2.00946	+	1.16016i
$86$		−	9.66025i		−	1.04169i
$87$	2.23205	+	3.86603i	0.239301	+	0.414481i
$88$	0.633975	−	1.09808i	0.0675819	−	0.117055i
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.866946	−	0.498402i	$-0.166080\pi$
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.00184433	+	0.999998i	$0.499413\pi$
$90$	−3.73205			−0.393393
$91$		0			0
$92$	4.19615			0.437479
$93$	1.26795	+	0.732051i	0.131480	+	0.0759101i
$94$	−1.09808	+	1.90192i	−0.113258	+	0.196168i
$95$	8.83013	+	15.2942i	0.905952	+	1.56915i
$96$		−	1.00000i		−	0.102062i
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$	0.401924	−	0.232051i	0.0406004	−	0.0234407i
$99$			1.26795i			0.127434i
$100$	−4.46410	−	7.73205i	−0.446410	−	0.773205i
$101$	0.964102	−	1.66987i	0.0959317	−	0.166159i	−0.814065	−	0.580773i	$-0.802750\pi$
$101$	0.964102	−	1.66987i	0.0959317	−	0.166159i	0.909997	+	0.414615i	$0.136084\pi$
$102$	4.96410	+	2.86603i	0.491519	+	0.283779i
$103$	15.2679			1.50440			0.752198	−	0.658937i	$-0.228994\pi$
$103$	15.2679			1.50440			0.752198	+	0.658937i	$0.228994\pi$
$104$		0			0
$105$	−10.1962			−0.995043
$106$	−5.59808	−	3.23205i	−0.543733	−	0.313925i
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	−0.999966	−	0.00823695i	$-0.997378\pi$
$107$	−5.09808	+	8.83013i	−0.492850	+	0.853641i	0.507116	+	0.861878i	$0.330711\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$		−	1.46410i		−	0.140236i	−0.997539	−	0.0701178i	$-0.977662\pi$
$109$		−	1.46410i		−	0.140236i	0.997539	−	0.0701178i	$-0.0223375\pi$
$110$	−4.09808	+	2.36603i	−0.390736	+	0.225592i
$111$	3.06218	−	1.76795i	0.290649	−	0.167806i
$112$		−	2.73205i		−	0.258155i
$113$	0.669873	+	1.16025i	0.0630163	+	0.109148i	0.895812	−	0.444432i	$-0.146595\pi$
$113$	0.669873	+	1.16025i	0.0630163	+	0.109148i	−0.832796	+	0.553580i	$0.813261\pi$
$114$	2.36603	−	4.09808i	0.221599	−	0.383820i
$115$	−13.5622	−	7.83013i	−1.26468	−	0.730163i
$116$	4.46410			0.414481
$117$		0			0
$118$	8.00000			0.736460
$119$	13.5622	+	7.83013i	1.24324	+	0.717787i
$120$	−1.86603	+	3.23205i	−0.170344	+	0.295045i
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$			9.19615i			0.832581i
$123$	8.13397	−	4.69615i	0.733416	−	0.423438i
$124$	1.26795	−	0.732051i	0.113865	−	0.0657401i
$125$			14.6603i			1.31125i
$126$	1.36603	+	2.36603i	0.121695	+	0.210782i
$127$	−4.92820	+	8.53590i	−0.437307	+	0.757438i	−0.997481	−	0.0709368i	$-0.977401\pi$
$127$	−4.92820	+	8.53590i	−0.437307	+	0.757438i	0.560173	+	0.828375i	$0.310734\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	9.66025			0.850538
$130$		0			0
$131$	6.53590			0.571044			0.285522	−	0.958372i	$-0.407833\pi$
$131$	6.53590			0.571044			0.285522	+	0.958372i	$0.407833\pi$
$132$	1.09808	+	0.633975i	0.0955753	+	0.0551804i
$133$	6.46410	−	11.1962i	0.560509	−	0.970830i
$134$	6.56218	+	11.3660i	0.566886	+	0.981875i
$135$		−	3.73205i		−	0.321204i
$136$	4.96410	−	2.86603i	0.425668	−	0.245760i
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.0110599	−	0.999939i	$-0.496479\pi$
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.871502	+	0.490391i	$0.163146\pi$
$138$			4.19615i			0.357200i
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	−0.944233	−	0.329279i	$-0.893194\pi$
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	0.186952	−	0.982369i	$-0.440139\pi$
$140$	−5.09808	+	8.83013i	−0.430866	+	0.746282i
$141$	−1.90192	−	1.09808i	−0.160171	−	0.0924747i
$142$	−4.73205			−0.397105
$143$		0			0
$144$	1.00000			0.0833333
$145$	−14.4282	−	8.33013i	−1.19820	−	0.691779i
$146$	3.13397	−	5.42820i	0.259370	−	0.449241i
$147$	0.232051	+	0.401924i	0.0191392	+	0.0331501i
$148$		−	3.53590i		−	0.290649i
$149$	−11.4282	+	6.59808i	−0.936235	+	0.540535i	−0.888778	−	0.458338i	$-0.848445\pi$
$149$	−11.4282	+	6.59808i	−0.936235	+	0.540535i	−0.0474568	+	0.998873i	$0.515112\pi$
$150$	7.73205	−	4.46410i	0.631319	−	0.364492i
$151$			6.73205i			0.547847i	0.961752	+	0.273923i	$0.0883214\pi$
$151$			6.73205i			0.547847i	−0.961752	+	0.273923i	$0.911679\pi$
$152$	−2.36603	−	4.09808i	−0.191910	−	0.332398i
$153$	−2.86603	+	4.96410i	−0.231704	+	0.401324i
$154$	3.00000	+	1.73205i	0.241747	+	0.139573i
$155$	−5.46410			−0.438887
$156$		0			0
$157$	7.58846			0.605625			0.302812	−	0.953050i	$-0.402074\pi$
$157$	7.58846			0.605625			0.302812	+	0.953050i	$0.402074\pi$
$158$	−2.19615	−	1.26795i	−0.174717	−	0.100873i
$159$	3.23205	−	5.59808i	0.256318	−	0.443956i
$160$	1.86603	+	3.23205i	0.147522	+	0.255516i
$161$			11.4641i			0.903498i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	−11.6603	+	6.73205i	−0.913302	+	0.527295i	−0.881492	−	0.472199i	$-0.843460\pi$
$163$	−11.6603	+	6.73205i	−0.913302	+	0.527295i	−0.0318096	+	0.999494i	$0.510127\pi$
$164$		−	9.39230i		−	0.733416i
$165$	−2.36603	−	4.09808i	−0.184195	−	0.319035i
$166$	−0.0980762	+	0.169873i	−0.00761219	+	0.0131847i
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	0.782391	−	0.622787i	$-0.214000\pi$
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	−0.148154	+	0.988964i	$0.547333\pi$
$168$	2.73205			0.210782
$169$		0			0
$170$	−21.3923			−1.64071
$171$	4.09808	+	2.36603i	0.313388	+	0.180934i
$172$	4.83013	−	8.36603i	0.368294	−	0.637903i
$173$	2.19615	+	3.80385i	0.166970	+	0.289201i	0.937353	−	0.348380i	$-0.113268\pi$
$173$	2.19615	+	3.80385i	0.166970	+	0.289201i	−0.770383	+	0.637582i	$0.779935\pi$
$174$			4.46410i			0.338423i
$175$	21.1244	−	12.1962i	1.59685	−	0.921942i
$176$	1.09808	−	0.633975i	0.0827706	−	0.0477876i
$177$			8.00000i			0.601317i
$178$	4.73205	+	8.19615i	0.354682	+	0.614328i
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	0.392921	+	0.919572i	$0.371465\pi$
$179$	−8.02628	+	13.9019i	−0.599912	+	1.03908i	−0.992833	+	0.119506i	$0.961869\pi$
$180$	−3.23205	−	1.86603i	−0.240903	−	0.139085i
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$		0			0
$183$	−9.19615			−0.679799
$184$	3.63397	+	2.09808i	0.267900	+	0.154672i
$185$	−6.59808	+	11.4282i	−0.485100	+	0.840218i
$186$	0.732051	+	1.26795i	0.0536766	+	0.0929705i
$187$			7.26795i			0.531485i
$188$	−1.90192	+	1.09808i	−0.138712	+	0.0800854i
$189$	−2.36603	+	1.36603i	−0.172103	+	0.0993637i
$190$			17.6603i			1.28121i
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	0.963706	−	0.266966i	$-0.0860212\pi$
$191$	3.46410	+	6.00000i	0.250654	+	0.434145i	−0.713052	+	0.701111i	$0.752688\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	10.1603	+	5.86603i	0.731351	+	0.422246i	0.818916	−	0.573913i	$-0.194575\pi$
$193$	10.1603	+	5.86603i	0.731351	+	0.422246i	−0.0875652	+	0.996159i	$0.527909\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	0.464102			0.0331501
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.165086	−	0.986279i	$-0.552790\pi$
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.936686	+	0.350171i	$0.886123\pi$
$198$	−0.633975	+	1.09808i	−0.0450546	+	0.0780369i
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	−0.999993	−	0.00366345i	$-0.998834\pi$
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	0.496824	−	0.867851i	$-0.334499\pi$
$200$		−	8.92820i		−	0.631319i
$201$	−11.3660	+	6.56218i	−0.801698	+	0.462860i
$202$	1.66987	−	0.964102i	0.117492	−	0.0678340i
$203$			12.1962i			0.856002i
$204$	2.86603	+	4.96410i	0.200662	+	0.347557i
$205$	−17.5263	+	30.3564i	−1.22409	+	2.12018i
$206$	13.2224	+	7.63397i	0.921250	+	0.531884i
$207$	−4.19615			−0.291653
$208$		0			0
$209$	6.00000			0.415029
$210$	−8.83013	−	5.09808i	−0.609337	−	0.351801i
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	0.432873	+	0.901455i	$0.357500\pi$
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	−0.997119	+	0.0758485i	$0.975833\pi$
$212$	−3.23205	−	5.59808i	−0.221978	−	0.384477i
$213$		−	4.73205i		−	0.324235i
$214$	−8.83013	+	5.09808i	−0.603615	+	0.348497i
$215$	−31.2224	+	18.0263i	−2.12935	+	1.22938i
$216$			1.00000i			0.0680414i
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	0.732051	−	1.26795i	0.0495807	−	0.0858764i
$219$	5.42820	+	3.13397i	0.366804	+	0.211774i
$220$	−4.73205			−0.319035
$221$		0			0
$222$	3.53590			0.237314
$223$	−23.3205	−	13.4641i	−1.56166	−	0.901623i	−0.997090	−	0.0762356i	$-0.975710\pi$
$223$	−23.3205	−	13.4641i	−1.56166	−	0.901623i	−0.564567	−	0.825387i	$-0.690957\pi$
$224$	1.36603	−	2.36603i	0.0912714	−	0.158087i
$225$	4.46410	+	7.73205i	0.297607	+	0.515470i
$226$			1.33975i			0.0891186i
$227$	10.5622	−	6.09808i	0.701036	−	0.404744i	−0.106697	−	0.994292i	$-0.534027\pi$
$227$	10.5622	−	6.09808i	0.701036	−	0.404744i	0.807733	+	0.589548i	$0.200694\pi$
$228$	4.09808	−	2.36603i	0.271402	−	0.156694i
$229$		−	11.8564i		−	0.783493i	−0.920073	−	0.391747i	$-0.871871\pi$
$229$		−	11.8564i		−	0.783493i	0.920073	−	0.391747i	$-0.128129\pi$
$230$	−7.83013	−	13.5622i	−0.516303	−	0.894264i
$231$	−1.73205	+	3.00000i	−0.113961	+	0.197386i
$232$	3.86603	+	2.23205i	0.253817	+	0.146541i
$233$	7.85641			0.514690			0.257345	−	0.966320i	$-0.417152\pi$
$233$	7.85641			0.514690			0.257345	+	0.966320i	$0.417152\pi$
$234$		0			0
$235$	8.19615			0.534658
$236$	6.92820	+	4.00000i	0.450988	+	0.260378i
$237$	1.26795	−	2.19615i	0.0823622	−	0.142655i
$238$	7.83013	+	13.5622i	0.507552	+	0.879105i
$239$		−	7.66025i		−	0.495501i	−0.968824	−	0.247750i	$-0.920309\pi$
$239$		−	7.66025i		−	0.495501i	0.968824	−	0.247750i	$-0.0796913\pi$
$240$	−3.23205	+	1.86603i	−0.208628	+	0.120451i
$241$	11.7679	−	6.79423i	0.758040	−	0.437655i	−0.0705514	−	0.997508i	$-0.522476\pi$
$241$	11.7679	−	6.79423i	0.758040	−	0.437655i	0.828592	+	0.559853i	$0.189143\pi$
$242$		−	9.39230i		−	0.603760i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.59808	+	7.96410i	−0.294362	+	0.509849i
$245$	−1.50000	−	0.866025i	−0.0958315	−	0.0553283i
$246$	9.39230			0.598831
$247$		0			0
$248$	1.46410			0.0929705
$249$	−0.169873	−	0.0980762i	−0.0107653	−	0.00621533i
$250$	−7.33013	+	12.6962i	−0.463598	+	0.802975i
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	0.996413	−	0.0846203i	$-0.0269677\pi$
$251$	6.73205	+	11.6603i	0.424923	+	0.735989i	−0.571490	+	0.820609i	$0.693634\pi$
$252$			2.73205i			0.172103i
$253$	−4.60770	+	2.66025i	−0.289683	+	0.167249i
$254$	−8.53590	+	4.92820i	−0.535590	+	0.309223i
$255$		−	21.3923i		−	1.33964i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.66987	−	8.08846i	0.291299	−	0.504544i	−0.682818	−	0.730588i	$-0.739246\pi$
$257$	4.66987	−	8.08846i	0.291299	−	0.504544i	0.974117	+	0.226044i	$0.0725793\pi$
$258$	8.36603	+	4.83013i	0.520846	+	0.300711i
$259$	9.66025			0.600259
$260$		0			0
$261$	−4.46410			−0.276321
$262$	5.66025	+	3.26795i	0.349692	+	0.201895i
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	−0.668414	−	0.743790i	$-0.733026\pi$
$263$	5.02628	−	8.70577i	0.309934	−	0.536821i	0.978348	+	0.206969i	$0.0663598\pi$
$264$	0.633975	+	1.09808i	0.0390184	+	0.0675819i
$265$			24.1244i			1.48195i
$266$	11.1962	−	6.46410i	0.686480	−	0.396339i
$267$	−8.19615	+	4.73205i	−0.501596	+	0.289597i
$268$			13.1244i			0.801698i
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	0.770638	−	0.637273i	$-0.219938\pi$
$269$	−2.73205	−	4.73205i	−0.166576	−	0.288518i	−0.937214	+	0.348755i	$0.886604\pi$
$270$	1.86603	−	3.23205i	0.113563	−	0.196696i
$271$	18.9282	+	10.9282i	1.14981	+	0.663841i	0.948840	−	0.315757i	$-0.102258\pi$
$271$	18.9282	+	10.9282i	1.14981	+	0.663841i	0.200966	+	0.979598i	$0.435592\pi$
$272$	5.73205			0.347557
$273$		0			0
$274$	11.9282			0.720609
$275$	9.80385	+	5.66025i	0.591194	+	0.341326i
$276$	−2.09808	+	3.63397i	−0.126289	+	0.218740i
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	0.766987	−	0.641663i	$-0.221755\pi$
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	−0.939190	+	0.343399i	$0.888422\pi$
$278$		−	17.8564i		−	1.07096i
$279$	−1.26795	+	0.732051i	−0.0759101	+	0.0438267i
$280$	−8.83013	+	5.09808i	−0.527701	+	0.304668i
$281$			12.3205i			0.734980i	0.930027	+	0.367490i	$0.119783\pi$
$281$			12.3205i			0.734980i	−0.930027	+	0.367490i	$0.880217\pi$
$282$	−1.09808	−	1.90192i	−0.0653895	−	0.113258i
$283$	12.8301	−	22.2224i	0.762672	−	1.32099i	−0.178797	−	0.983886i	$-0.557220\pi$
$283$	12.8301	−	22.2224i	0.762672	−	1.32099i	0.941469	−	0.337100i	$-0.109446\pi$
$284$	−4.09808	−	2.36603i	−0.243176	−	0.140398i
$285$	−17.6603			−1.04610
$286$		0			0
$287$	25.6603			1.51468
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−7.92820	+	13.7321i	−0.466365	+	0.807768i
$290$	−8.33013	−	14.4282i	−0.489162	−	0.847253i
$291$			6.00000i			0.351726i
$292$	5.42820	−	3.13397i	0.317662	−	0.183402i
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.545368	−	0.838196i	$-0.316390\pi$
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.998584	−	0.0532048i	$-0.0169436\pi$
$294$			0.464102i			0.0270670i
$295$	−14.9282	−	25.8564i	−0.869154	−	1.50542i
$296$	1.76795	−	3.06218i	0.102760	−	0.177985i
$297$	−1.09808	−	0.633975i	−0.0637168	−	0.0367869i
$298$	−13.1962			−0.764433
$299$		0			0
$300$	8.92820			0.515470
$301$	22.8564	+	13.1962i	1.31742	+	0.760614i
$302$	−3.36603	+	5.83013i	−0.193693	+	0.335486i
$303$	0.964102	+	1.66987i	0.0553862	+	0.0959317i
$304$		−	4.73205i		−	0.271402i
$305$	29.7224	−	17.1603i	1.70190	−	0.982593i
$306$	−4.96410	+	2.86603i	−0.283779	+	0.163840i
$307$		−	22.5885i		−	1.28919i	−0.764524	−	0.644596i	$-0.777026\pi$
$307$		−	22.5885i		−	1.28919i	0.764524	−	0.644596i	$-0.222974\pi$
$308$	1.73205	+	3.00000i	0.0986928	+	0.170941i
$309$	−7.63397	+	13.2224i	−0.434282	+	0.752198i
$310$	−4.73205	−	2.73205i	−0.268762	−	0.155170i
$311$	1.66025			0.0941444			0.0470722	−	0.998891i	$-0.485011\pi$
$311$	1.66025			0.0941444			0.0470722	+	0.998891i	$0.485011\pi$
$312$		0			0
$313$	6.53590			0.369431			0.184715	−	0.982792i	$-0.440864\pi$
$313$	6.53590			0.369431			0.184715	+	0.982792i	$0.440864\pi$
$314$	6.57180	+	3.79423i	0.370868	+	0.214121i
$315$	5.09808	−	8.83013i	0.287244	−	0.497521i
$316$	−1.26795	−	2.19615i	−0.0713277	−	0.123543i
$317$		−	20.6603i		−	1.16040i	−0.814476	−	0.580198i	$-0.802975\pi$
$317$		−	20.6603i		−	1.16040i	0.814476	−	0.580198i	$-0.197025\pi$
$318$	5.59808	−	3.23205i	0.313925	−	0.181244i
$319$	−4.90192	+	2.83013i	−0.274455	+	0.158457i
$320$			3.73205i			0.208628i
$321$	−5.09808	−	8.83013i	−0.284547	−	0.492850i
$322$	−5.73205	+	9.92820i	−0.319435	+	0.553277i
$323$	23.4904	+	13.5622i	1.30704	+	0.754620i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−13.4641			−0.745708
$327$	1.26795	+	0.732051i	0.0701178	+	0.0404825i
$328$	4.69615	−	8.13397i	0.259302	−	0.449124i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		−	4.73205i		−	0.260491i
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.893708	−	0.448649i	$-0.851905\pi$
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.0583130	+	0.998298i	$0.518572\pi$
$332$	−0.169873	+	0.0980762i	−0.00932299	+	0.00538263i
$333$			3.53590i			0.193766i
$334$	4.73205	+	8.19615i	0.258926	+	0.448474i
$335$	24.4904	−	42.4186i	1.33805	−	2.31757i
$336$	2.36603	+	1.36603i	0.129077	+	0.0745228i
$337$	20.8564			1.13612			0.568060	−	0.822987i	$-0.307694\pi$
$337$	20.8564			1.13612			0.568060	+	0.822987i	$0.307694\pi$
$338$		0			0
$339$	−1.33975			−0.0727650
$340$	−18.5263	−	10.6962i	−1.00473	−	0.580080i
$341$	−0.928203	+	1.60770i	−0.0502650	+	0.0870616i
$342$	2.36603	+	4.09808i	0.127940	+	0.221599i
$343$		−	17.8564i		−	0.964155i
$344$	8.36603	−	4.83013i	0.451066	−	0.260423i
$345$	13.5622	−	7.83013i	0.730163	−	0.421560i
$346$			4.39230i			0.236132i
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.840936	−	0.541135i	$-0.817995\pi$
$347$	−16.5622	−	28.6865i	−0.889104	−	1.53997i	−0.0481683	−	0.998839i	$-0.515338\pi$
$348$	−2.23205	+	3.86603i	−0.119650	+	0.207241i
$349$	−13.2679	−	7.66025i	−0.710217	−	0.410044i	0.100924	−	0.994894i	$-0.467820\pi$
$349$	−13.2679	−	7.66025i	−0.710217	−	0.410044i	−0.811141	+	0.584850i	$0.801153\pi$
$350$	24.3923			1.30382
$351$		0			0
$352$	1.26795			0.0675819
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.0946674	−	0.995509i	$-0.530179\pi$
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.909470	+	0.415770i	$0.863512\pi$
$354$	−4.00000	+	6.92820i	−0.212598	+	0.368230i
$355$	8.83013	+	15.2942i	0.468654	+	0.811733i
$356$			9.46410i			0.501596i
$357$	−13.5622	+	7.83013i	−0.717787	+	0.414414i
$358$	−13.9019	+	8.02628i	−0.734740	+	0.424202i
$359$		−	1.12436i		−	0.0593412i	−0.999560	−	0.0296706i	$-0.990554\pi$
$359$		−	1.12436i		−	0.0593412i	0.999560	−	0.0296706i	$-0.00944584\pi$
$360$	−1.86603	−	3.23205i	−0.0983482	−	0.170344i
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	−16.6244	−	9.59808i	−0.873757	−	0.504464i
$363$	9.39230			0.492968
$364$		0			0
$365$	−23.3923			−1.22441
$366$	−7.96410	−	4.59808i	−0.416290	−	0.240345i
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	−0.680682	−	0.732579i	$-0.738316\pi$
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	0.974773	+	0.223198i	$0.0716498\pi$
$368$	2.09808	+	3.63397i	0.109370	+	0.189434i
$369$			9.39230i			0.488944i
$370$	−11.4282	+	6.59808i	−0.594124	+	0.343018i
$371$	15.2942	−	8.83013i	0.794037	−	0.458437i
$372$			1.46410i			0.0759101i
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	0.987205	−	0.159456i	$-0.0509741\pi$
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	−0.631696	+	0.775216i	$0.717641\pi$
$374$	−3.63397	+	6.29423i	−0.187908	+	0.325467i
$375$	−12.6962	−	7.33013i	−0.655626	−	0.378526i
$376$	−2.19615			−0.113258
$377$		0			0
$378$	−2.73205			−0.140522
$379$	−4.73205	−	2.73205i	−0.243069	−	0.140336i	0.373517	−	0.927623i	$-0.378152\pi$
$379$	−4.73205	−	2.73205i	−0.243069	−	0.140336i	−0.616587	+	0.787287i	$0.711485\pi$
$380$	−8.83013	+	15.2942i	−0.452976	+	0.784577i
$381$	−4.92820	−	8.53590i	−0.252479	−	0.437307i
$382$			6.92820i			0.354478i
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	−0.467255	−	0.884122i	$-0.654757\pi$
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	0.532045	+	0.846716i	$0.321424\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		−	12.9282i		−	0.658882i
$386$	5.86603	+	10.1603i	0.298573	+	0.517143i
$387$	−4.83013	+	8.36603i	−0.245529	+	0.425269i
$388$	5.19615	+	3.00000i	0.263795	+	0.152302i
$389$	−11.7846			−0.597503			−0.298752	−	0.954331i	$-0.596570\pi$
$389$	−11.7846			−0.597503			−0.298752	+	0.954331i	$0.596570\pi$
$390$		0			0
$391$	−24.0526			−1.21639
$392$	0.401924	+	0.232051i	0.0203002	+	0.0117203i
$393$	−3.26795	+	5.66025i	−0.164846	+	0.285522i
$394$	−8.92820	−	15.4641i	−0.449796	−	0.779070i
$395$			9.46410i			0.476191i
$396$	−1.09808	+	0.633975i	−0.0551804	+	0.0318584i
$397$	17.6603	−	10.1962i	0.886343	−	0.511730i	0.0135983	−	0.999908i	$-0.495671\pi$
$397$	17.6603	−	10.1962i	0.886343	−	0.511730i	0.872744	+	0.488177i	$0.162338\pi$
$398$		−	14.1962i		−	0.711589i
$399$	6.46410	+	11.1962i	0.323610	+	0.560509i
$400$	4.46410	−	7.73205i	0.223205	−	0.386603i
$401$	−6.99038	−	4.03590i	−0.349083	−	0.201543i	0.315198	−	0.949026i	$-0.397929\pi$
$401$	−6.99038	−	4.03590i	−0.349083	−	0.201543i	−0.664281	+	0.747483i	$0.731262\pi$
$402$	−13.1244			−0.654583
$403$		0			0
$404$	1.92820			0.0959317
$405$	3.23205	+	1.86603i	0.160602	+	0.0927235i
$406$	−6.09808	+	10.5622i	−0.302642	+	0.524192i
$407$	2.24167	+	3.88269i	0.111115	+	0.192458i
$408$			5.73205i			0.283779i
$409$	−15.3564	+	8.86603i	−0.759325	+	0.438397i	−0.829053	−	0.559169i	$-0.811120\pi$
$409$	−15.3564	+	8.86603i	−0.759325	+	0.438397i	0.0697281	+	0.997566i	$0.477787\pi$
$410$	−30.3564	+	17.5263i	−1.49920	+	0.865561i
$411$			11.9282i			0.588375i
$412$	7.63397	+	13.2224i	0.376099	+	0.651422i
$413$	−10.9282	+	18.9282i	−0.537742	+	0.931396i
$414$	−3.63397	−	2.09808i	−0.178600	−	0.103115i
$415$	0.732051			0.0359350
$416$		0			0
$417$	17.8564			0.874432
$418$	5.19615	+	3.00000i	0.254152	+	0.146735i
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	−0.569979	−	0.821659i	$-0.693049\pi$
$419$	8.73205	−	15.1244i	0.426589	−	0.738873i	0.996567	+	0.0827863i	$0.0263819\pi$
$420$	−5.09808	−	8.83013i	−0.248761	−	0.430866i
$421$			22.7128i			1.10695i	0.832864	+	0.553477i	$0.186699\pi$
$421$			22.7128i			1.10695i	−0.832864	+	0.553477i	$0.813301\pi$
$422$	−14.1962	+	8.19615i	−0.691058	+	0.398982i
$423$	1.90192	−	1.09808i	0.0924747	−	0.0533903i
$424$		−	6.46410i		−	0.313925i
$425$	25.5885	+	44.3205i	1.24122	+	2.14986i
$426$	2.36603	−	4.09808i	0.114634	−	0.198552i
$427$	−21.7583	−	12.5622i	−1.05296	−	0.607926i
$428$	−10.1962			−0.492850
$429$		0			0
$430$	−36.0526			−1.73861
$431$	11.3660	+	6.56218i	0.547482	+	0.316089i	0.748106	−	0.663579i	$-0.230964\pi$
$431$	11.3660	+	6.56218i	0.547482	+	0.316089i	−0.200624	+	0.979668i	$0.564297\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	0.978126	−	0.208012i	$-0.0666992\pi$
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	−0.669207	+	0.743076i	$0.733366\pi$
$434$			4.00000i			0.192006i
$435$	14.4282	−	8.33013i	0.691779	−	0.399399i
$436$	1.26795	−	0.732051i	0.0607238	−	0.0350589i
$437$			19.8564i			0.949861i
$438$	3.13397	+	5.42820i	0.149747	+	0.259370i
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	−0.870051	−	0.492962i	$-0.835914\pi$
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	0.861943	+	0.507005i	$0.169247\pi$
$440$	−4.09808	−	2.36603i	−0.195368	−	0.112796i
$441$	−0.464102			−0.0221001
$442$		0			0
$443$	15.6077			0.741544			0.370772	−	0.928724i	$-0.379093\pi$
$443$	15.6077			0.741544			0.370772	+	0.928724i	$0.379093\pi$
$444$	3.06218	+	1.76795i	0.145325	+	0.0839032i
$445$	17.6603	−	30.5885i	0.837176	−	1.45003i
$446$	−13.4641	−	23.3205i	−0.637544	−	1.10426i
$447$		−	13.1962i		−	0.624157i
$448$	2.36603	−	1.36603i	0.111784	−	0.0645386i
$449$	9.80385	−	5.66025i	0.462672	−	0.267124i	−0.250495	−	0.968118i	$-0.580593\pi$
$449$	9.80385	−	5.66025i	0.462672	−	0.267124i	0.713167	+	0.700994i	$0.247260\pi$
$450$			8.92820i			0.420880i
$451$	5.95448	+	10.3135i	0.280386	+	0.485642i
$452$	−0.669873	+	1.16025i	−0.0315082	+	0.0545738i
$453$	−5.83013	−	3.36603i	−0.273923	−	0.158150i
$454$	12.1962			0.572394
$455$		0			0
$456$	4.73205			0.221599
$457$	1.16025	+	0.669873i	0.0542744	+	0.0313353i	0.526892	−	0.849932i	$-0.323357\pi$
$457$	1.16025	+	0.669873i	0.0542744	+	0.0313353i	−0.472617	+	0.881268i	$0.656691\pi$
$458$	5.92820	−	10.2679i	0.277007	−	0.479790i
$459$	−2.86603	−	4.96410i	−0.133775	−	0.231704i
$460$		−	15.6603i		−	0.730163i
$461$	−19.2846	+	11.1340i	−0.898174	+	0.518561i	−0.876607	−	0.481207i	$-0.840199\pi$
$461$	−19.2846	+	11.1340i	−0.898174	+	0.518561i	−0.0215666	+	0.999767i	$0.506865\pi$
$462$	−3.00000	+	1.73205i	−0.139573	+	0.0805823i
$463$			10.0526i			0.467182i	0.972335	+	0.233591i	$0.0750477\pi$
$463$			10.0526i			0.467182i	−0.972335	+	0.233591i	$0.924952\pi$
$464$	2.23205	+	3.86603i	0.103620	+	0.179476i
$465$	2.73205	−	4.73205i	0.126696	−	0.219444i
$466$	6.80385	+	3.92820i	0.315182	+	0.181971i
$467$	−18.5885			−0.860171			−0.430086	−	0.902788i	$-0.641517\pi$
$467$	−18.5885			−0.860171			−0.430086	+	0.902788i	$0.641517\pi$
$468$		0			0
$469$	−35.8564			−1.65570
$470$	7.09808	+	4.09808i	0.327410	+	0.189030i
$471$	−3.79423	+	6.57180i	−0.174829	+	0.302812i
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$			12.2487i			0.563196i
$474$	2.19615	−	1.26795i	0.100873	−	0.0582388i
$475$	36.5885	−	21.1244i	1.67879	−	0.969252i
$476$			15.6603i			0.717787i
$477$	3.23205	+	5.59808i	0.147985	+	0.256318i
$478$	3.83013	−	6.63397i	0.175186	−	0.303431i
$479$	−28.9808	−	16.7321i	−1.32416	−	0.764507i	−0.339775	−	0.940507i	$-0.610351\pi$
$479$	−28.9808	−	16.7321i	−1.32416	−	0.764507i	−0.984390	+	0.176000i	$0.943684\pi$
$480$	−3.73205			−0.170344
$481$		0			0
$482$	13.5885			0.618937
$483$	−9.92820	−	5.73205i	−0.451749	−	0.260817i
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	−11.1962	−	19.3923i	−0.508391	−	0.880559i
$486$		−	1.00000i		−	0.0453609i
$487$	2.70577	−	1.56218i	0.122610	−	0.0707890i	−0.437441	−	0.899247i	$-0.644115\pi$
$487$	2.70577	−	1.56218i	0.122610	−	0.0707890i	0.560051	+	0.828458i	$0.310782\pi$
$488$	−7.96410	+	4.59808i	−0.360518	+	0.208145i
$489$		−	13.4641i		−	0.608868i
$490$	−0.866025	−	1.50000i	−0.0391230	−	0.0677631i
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	−0.750530	−	0.660836i	$-0.770202\pi$
$491$	4.36603	−	7.56218i	0.197036	−	0.341276i	0.947566	+	0.319560i	$0.103535\pi$
$492$	8.13397	+	4.69615i	0.366708	+	0.211719i
$493$	−25.5885			−1.15245
$494$		0			0
$495$	4.73205			0.212690
$496$	1.26795	+	0.732051i	0.0569326	+	0.0328701i
$497$	6.46410	−	11.1962i	0.289955	−	0.502216i
$498$	−0.0980762	−	0.169873i	−0.00439490	−	0.00761219i
$499$		−	32.0000i		−	1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$	−12.6962	+	7.33013i	−0.567789	+	0.327813i
$501$	−8.19615	+	4.73205i	−0.366177	+	0.211412i
$502$			13.4641i			0.600932i
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.808908	−	0.587935i	$-0.799941\pi$
$503$	−20.4904	−	35.4904i	−0.913621	−	1.58244i	−0.104713	−	0.994502i	$-0.533392\pi$
$504$	−1.36603	+	2.36603i	−0.0608476	+	0.105391i
$505$	−6.23205	−	3.59808i	−0.277323	−	0.160112i
$506$	−5.32051			−0.236525
$507$		0			0
$508$	−9.85641			−0.437307
$509$	11.8923	+	6.86603i	0.527117	+	0.304331i	0.739842	−	0.672781i	$-0.234900\pi$
$509$	11.8923	+	6.86603i	0.527117	+	0.304331i	−0.212725	+	0.977112i	$0.568234\pi$
$510$	10.6962	−	18.5263i	0.473634	−	0.820357i
$511$	8.56218	+	14.8301i	0.378768	+	0.656046i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.09808	+	2.36603i	−0.180934	+	0.104463i
$514$	8.08846	−	4.66987i	0.356767	−	0.205979i
$515$		−	56.9808i		−	2.51087i
$516$	4.83013	+	8.36603i	0.212634	+	0.368294i
$517$	1.39230	−	2.41154i	0.0612335	−	0.106060i
$518$	8.36603	+	4.83013i	0.367582	+	0.212224i
$519$	−4.39230			−0.192801
$520$		0			0
$521$	41.4449			1.81573			0.907866	−	0.419260i	$-0.137710\pi$
$521$	41.4449			1.81573			0.907866	+	0.419260i	$0.137710\pi$
$522$	−3.86603	−	2.23205i	−0.169211	−	0.0976942i
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	−0.509220	−	0.860636i	$-0.670066\pi$
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	0.999943	+	0.0106796i	$0.00339949\pi$
$524$	3.26795	+	5.66025i	0.142761	+	0.247269i
$525$			24.3923i			1.06457i
$526$	8.70577	−	5.02628i	0.379590	−	0.219156i
$527$	−7.26795	+	4.19615i	−0.316597	+	0.182787i
$528$			1.26795i			0.0551804i
$529$	2.69615	+	4.66987i	0.117224	+	0.203038i
$530$	−12.0622	+	20.8923i	−0.523948	+	0.907504i
$531$	−6.92820	−	4.00000i	−0.300658	−	0.173585i
$532$	12.9282			0.560509
$533$		0			0
$534$	−9.46410			−0.409552
$535$	32.9545	+	19.0263i	1.42475	+	0.822578i
$536$	−6.56218	+	11.3660i	−0.283443	+	0.490938i
$537$	−8.02628	−	13.9019i	−0.346360	−	0.599912i
$538$		−	5.46410i		−	0.235574i
$539$	−0.509619	+	0.294229i	−0.0219508	+	0.0126733i
$540$	3.23205	−	1.86603i	0.139085	−	0.0803009i
$541$			5.67949i			0.244180i	0.992519	+	0.122090i	$0.0389597\pi$
$541$			5.67949i			0.244180i	−0.992519	+	0.122090i	$0.961040\pi$
$542$	10.9282	+	18.9282i	0.469407	+	0.813036i
$543$	9.59808	−	16.6244i	0.411893	−	0.713419i
$544$	4.96410	+	2.86603i	0.212834	+	0.122880i
$545$	−5.46410			−0.234056
$546$		0			0
$547$	−4.19615			−0.179415			−0.0897073	−	0.995968i	$-0.528593\pi$
$547$	−4.19615			−0.179415			−0.0897073	+	0.995968i	$0.528593\pi$
$548$	10.3301	+	5.96410i	0.441281	+	0.254774i
$549$	4.59808	−	7.96410i	0.196241	−	0.339900i
$550$	5.66025	+	9.80385i	0.241354	+	0.418037i
$551$			21.1244i			0.899928i
$552$	−3.63397	+	2.09808i	−0.154672	+	0.0893001i
$553$	6.00000	−	3.46410i	0.255146	−	0.147309i
$554$		−	5.73205i		−	0.243532i
$555$	−6.59808	−	11.4282i	−0.280073	−	0.485100i
$556$	8.92820	−	15.4641i	0.378640	−	0.655824i
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.997734	−	0.0672780i	$-0.978569\pi$
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.557132	−	0.830424i	$-0.688098\pi$
$558$	−1.46410			−0.0619804
$559$		0			0
$560$	−10.1962			−0.430866
$561$	−6.29423	−	3.63397i	−0.265743	−	0.153427i
$562$	−6.16025	+	10.6699i	−0.259855	+	0.450081i
$563$	17.4641	+	30.2487i	0.736024	+	1.27483i	0.954273	+	0.298938i	$0.0966324\pi$
$563$	17.4641	+	30.2487i	0.736024	+	1.27483i	−0.218248	+	0.975893i	$0.570034\pi$
$564$		−	2.19615i		−	0.0924747i
$565$	4.33013	−	2.50000i	0.182170	−	0.105176i
$566$	22.2224	−	12.8301i	0.934078	−	0.539290i
$567$		−	2.73205i		−	0.114735i
$568$	−2.36603	−	4.09808i	−0.0992762	−	0.171951i
$569$	15.3205	−	26.5359i	0.642269	−	1.11244i	−0.342656	−	0.939461i	$-0.611326\pi$
$569$	15.3205	−	26.5359i	0.642269	−	1.11244i	0.984925	−	0.172982i	$-0.0553402\pi$
$570$	−15.2942	−	8.83013i	−0.640605	−	0.369853i
$571$	−14.0526			−0.588081			−0.294041	−	0.955793i	$-0.595000\pi$
$571$	−14.0526			−0.588081			−0.294041	+	0.955793i	$0.595000\pi$
$572$		0			0
$573$	−6.92820			−0.289430
$574$	22.2224	+	12.8301i	0.927546	+	0.535519i
$575$	−18.7321	+	32.4449i	−0.781181	+	1.35304i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	3.73205i		−	0.155367i	−0.996978	−	0.0776837i	$-0.975248\pi$
$577$		−	3.73205i		−	0.155367i	0.996978	−	0.0776837i	$-0.0247524\pi$
$578$	−13.7321	+	7.92820i	−0.571178	+	0.329770i
$579$	−10.1603	+	5.86603i	−0.422246	+	0.243784i
$580$		−	16.6603i		−	0.691779i
$581$	−0.267949	−	0.464102i	−0.0111164	−	0.0192542i
$582$	−3.00000	+	5.19615i	−0.124354	+	0.215387i
$583$	7.09808	+	4.09808i	0.293972	+	0.169725i
$584$	6.26795			0.259370
$585$		0			0
$586$	30.5167			1.26063
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	0.757914	−	0.652355i	$-0.226219\pi$
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	−0.185999	+	0.982550i	$0.559552\pi$
$588$	−0.232051	+	0.401924i	−0.00956961	+	0.0165751i
$589$	3.46410	+	6.00000i	0.142736	+	0.247226i
$590$		−	29.8564i		−	1.22917i
$591$	15.4641	−	8.92820i	0.636108	−	0.367257i
$592$	3.06218	−	1.76795i	0.125855	−	0.0726623i
$593$		−	9.14359i		−	0.375482i	−0.982219	−	0.187741i	$-0.939883\pi$
$593$		−	9.14359i		−	0.375482i	0.982219	−	0.187741i	$-0.0601166\pi$
$594$	−0.633975	−	1.09808i	−0.0260123	−	0.0450546i
$595$	29.2224	−	50.6147i	1.19800	−	2.07500i
$596$	−11.4282	−	6.59808i	−0.468117	−	0.270268i
$597$	14.1962			0.581010
$598$		0			0
$599$	−2.53590			−0.103614			−0.0518070	−	0.998657i	$-0.516498\pi$
$599$	−2.53590			−0.103614			−0.0518070	+	0.998657i	$0.516498\pi$
$600$	7.73205	+	4.46410i	0.315660	+	0.182246i
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	−0.935478	−	0.353385i	$-0.885031\pi$
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	0.773779	+	0.633456i	$0.218364\pi$
$602$	13.1962	+	22.8564i	0.537835	+	0.931558i
$603$		−	13.1244i		−	0.534465i
$604$	−5.83013	+	3.36603i	−0.237225	+	0.136962i
$605$	−30.3564	+	17.5263i	−1.23416	+	0.712545i
$606$			1.92820i			0.0783279i
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	0.899840	+	0.436221i	$0.143683\pi$
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	−0.0721415	+	0.997394i	$0.522983\pi$
$608$	2.36603	−	4.09808i	0.0959550	−	0.166199i
$609$	−10.5622	−	6.09808i	−0.428001	−	0.247107i
$610$	34.3205			1.38960
$611$		0			0
$612$	−5.73205			−0.231704
$613$	−8.13397	−	4.69615i	−0.328528	−	0.189676i	0.326659	−	0.945142i	$-0.394077\pi$
$613$	−8.13397	−	4.69615i	−0.328528	−	0.189676i	−0.655187	+	0.755466i	$0.727410\pi$
$614$	11.2942	−	19.5622i	0.455798	−	0.789465i
$615$	−17.5263	−	30.3564i	−0.706728	−	1.22409i
$616$			3.46410i			0.139573i
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	−0.250934	−	0.968004i	$-0.580738\pi$
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	0.712849	+	0.701318i	$0.247404\pi$
$618$	−13.2224	+	7.63397i	−0.531884	+	0.307083i
$619$			17.4641i			0.701942i	0.936386	+	0.350971i	$0.114148\pi$
$619$			17.4641i			0.701942i	−0.936386	+	0.350971i	$0.885852\pi$
$620$	−2.73205	−	4.73205i	−0.109722	−	0.190044i
$621$	2.09808	−	3.63397i	0.0841929	−	0.145826i
$622$	1.43782	+	0.830127i	0.0576514	+	0.0332851i
$623$	−25.8564			−1.03592
$624$		0			0
$625$	10.0718			0.402872
$626$	5.66025	+	3.26795i	0.226229	+	0.130614i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	3.79423	+	6.57180i	0.151406	+	0.262243i
$629$			20.2679i			0.808136i
$630$	8.83013	−	5.09808i	0.351801	−	0.203112i
$631$	−6.67949	+	3.85641i	−0.265906	+	0.153521i	−0.627026	−	0.778998i	$-0.715728\pi$
$631$	−6.67949	+	3.85641i	−0.265906	+	0.153521i	0.361119	+	0.932520i	$0.382395\pi$
$632$		−	2.53590i		−	0.100873i
$633$	−8.19615	−	14.1962i	−0.325768	−	0.564246i
$634$	10.3301	−	17.8923i	0.410262	−	0.710594i
$635$	31.8564	+	18.3923i	1.26418	+	0.729876i
$636$	6.46410			0.256318
$637$		0			0
$638$	−5.66025			−0.224092
$639$	4.09808	+	2.36603i	0.162117	+	0.0935985i
$640$	−1.86603	+	3.23205i	−0.0737611	+	0.127758i
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	−0.999885	−	0.0151806i	$-0.995168\pi$
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	0.486796	−	0.873516i	$-0.338166\pi$
$642$		−	10.1962i		−	0.402410i
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	−0.244359	−	0.969685i	$-0.578577\pi$
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	0.717592	+	0.696463i	$0.245244\pi$
$644$	−9.92820	+	5.73205i	−0.391226	+	0.225874i
$645$		−	36.0526i		−	1.41957i
$646$	13.5622	+	23.4904i	0.533597	+	0.924217i
$647$	−11.1244	+	19.2679i	−0.437344	+	0.757501i	−0.997484	−	0.0708966i	$-0.977414\pi$
$647$	−11.1244	+	19.2679i	−0.437344	+	0.757501i	0.560140	+	0.828398i	$0.310747\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−10.1436			−0.398171
$650$		0			0
$651$	−4.00000			−0.156772
$652$	−11.6603	−	6.73205i	−0.456651	−	0.263647i
$653$	8.73205	−	15.1244i	0.341712	−	0.591862i	−0.643039	−	0.765833i	$-0.722327\pi$
$653$	8.73205	−	15.1244i	0.341712	−	0.591862i	0.984751	+	0.173972i	$0.0556601\pi$
$654$	0.732051	+	1.26795i	0.0286255	+	0.0495807i
$655$		−	24.3923i		−	0.953086i
$656$	8.13397	−	4.69615i	0.317578	−	0.183354i
$657$	−5.42820	+	3.13397i	−0.211774	+	0.122268i
$658$		−	6.00000i		−	0.233904i
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	0.948404	−	0.317064i	$-0.102697\pi$
$659$	5.12436	+	8.87564i	0.199617	+	0.345746i	−0.748788	+	0.662810i	$0.769364\pi$
$660$	2.36603	−	4.09808i	0.0920974	−	0.159517i
$661$	−9.86603	−	5.69615i	−0.383744	−	0.221555i	0.295702	−	0.955280i	$-0.404446\pi$
$661$	−9.86603	−	5.69615i	−0.383744	−	0.221555i	−0.679446	+	0.733726i	$0.737780\pi$
$662$	−20.0000			−0.777322
$663$		0			0
$664$	−0.196152			−0.00761219
$665$	−41.7846	−	24.1244i	−1.62034	−	0.935502i
$666$	−1.76795	+	3.06218i	−0.0685066	+	0.118657i
$667$	−9.36603	−	16.2224i	−0.362654	−	0.628135i
$668$			9.46410i			0.366177i
$669$	23.3205	−	13.4641i	0.901623	−	0.520552i
$670$	42.4186	−	24.4904i	1.63877	−	0.946146i
$671$		−	11.6603i		−	0.450139i
$672$	1.36603	+	2.36603i	0.0526956	+	0.0912714i
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	−0.460720	−	0.887545i	$-0.652409\pi$
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	0.998997	−	0.0447770i	$-0.0142577\pi$
$674$	18.0622	+	10.4282i	0.695729	+	0.401679i
$675$	−8.92820			−0.343647
$676$		0			0
$677$	−45.4641			−1.74733			−0.873664	−	0.486530i	$-0.838262\pi$
$677$	−45.4641			−1.74733			−0.873664	+	0.486530i	$0.838262\pi$
$678$	−1.16025	−	0.669873i	−0.0445593	−	0.0257263i
$679$	−8.19615	+	14.1962i	−0.314539	+	0.544798i
$680$	−10.6962	−	18.5263i	−0.410179	−	0.710450i
$681$			12.1962i			0.467358i
$682$	−1.60770	+	0.928203i	−0.0615618	+	0.0355427i
$683$	−8.78461	+	5.07180i	−0.336134	+	0.194067i	−0.658561	−	0.752527i	$-0.728835\pi$
$683$	−8.78461	+	5.07180i	−0.336134	+	0.194067i	0.322427	+	0.946594i	$0.395501\pi$
$684$			4.73205i			0.180934i
$685$	−22.2583	−	38.5526i	−0.850447	−	1.47302i
$686$	8.92820	−	15.4641i	0.340880	−	0.590422i
$687$	10.2679	+	5.92820i	0.391747	+	0.226175i
$688$	9.66025			0.368294
$689$		0			0
$690$	15.6603			0.596176
$691$	37.8109	+	21.8301i	1.43839	+	0.830457i	0.997738	−	0.0672190i	$-0.0214126\pi$
$691$	37.8109	+	21.8301i	1.43839	+	0.830457i	0.440656	+	0.897676i	$0.354746\pi$
$692$	−2.19615	+	3.80385i	−0.0834852	+	0.144601i
$693$	−1.73205	−	3.00000i	−0.0657952	−	0.113961i
$694$		−	33.1244i		−	1.25738i
$695$	−57.7128	+	33.3205i	−2.18917	+	1.26392i
$696$	−3.86603	+	2.23205i	−0.146541	+	0.0846057i
$697$			53.8372i			2.03923i
$698$	−7.66025	−	13.2679i	−0.289945	−	0.502199i
$699$	−3.92820	+	6.80385i	−0.148578	+	0.257345i
$700$	21.1244	+	12.1962i	0.798426	+	0.460971i
$701$	3.32051			0.125414			0.0627069	−	0.998032i	$-0.480027\pi$
$701$	3.32051			0.125414			0.0627069	+	0.998032i	$0.480027\pi$
$702$		0			0
$703$	16.7321			0.631061
$704$	1.09808	+	0.633975i	0.0413853	+	0.0238938i
$705$	−4.09808	+	7.09808i	−0.154342	+	0.267329i
$706$	−10.8923	−	18.8660i	−0.409937	−	0.710032i
$707$			5.26795i			0.198122i
$708$	−6.92820	+	4.00000i	−0.260378	+	0.150329i
$709$	11.3827	−	6.57180i	0.427486	−	0.246809i	−0.270789	−	0.962639i	$-0.587285\pi$
$709$	11.3827	−	6.57180i	0.427486	−	0.246809i	0.698275	+	0.715830i	$0.253951\pi$
$710$			17.6603i			0.662778i
$711$	1.26795	+	2.19615i	0.0475518	+	0.0823622i
$712$	−4.73205	+	8.19615i	−0.177341	+	0.307164i
$713$	−5.32051	−	3.07180i	−0.199255	−	0.115040i
$714$	−15.6603			−0.586070
$715$		0			0
$716$	−16.0526			−0.599912
$717$	6.63397	+	3.83013i	0.247750	+	0.143039i
$718$	0.562178	−	0.973721i	0.0209803	−	0.0363389i
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	−0.998315	−	0.0580299i	$-0.981518\pi$
$719$	−14.7321	−	25.5167i	−0.549413	−	0.951611i	0.448902	−	0.893581i	$-0.351815\pi$
$720$		−	3.73205i		−	0.139085i
$721$	−36.1244	+	20.8564i	−1.34534	+	0.776733i
$722$	2.93782	−	1.69615i	0.109334	−	0.0631243i
$723$			13.5885i			0.505360i
$724$	−9.59808	−	16.6244i	−0.356710	−	0.617839i
$725$	−19.9282	+	34.5167i	−0.740115	+	1.28192i
$726$	8.13397	+	4.69615i	0.301880	+	0.174291i
$727$	30.9808			1.14901			0.574506	−	0.818500i	$-0.305194\pi$
$727$	30.9808			1.14901			0.574506	+	0.818500i	$0.305194\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−20.2583	−	11.6962i	−0.749794	−	0.432894i
$731$	−27.6865	+	47.9545i	−1.02402	+	1.77366i
$732$	−4.59808	−	7.96410i	−0.169950	−	0.294362i
$733$		−	19.0000i		−	0.701781i	−0.936416	−	0.350891i	$-0.885879\pi$
$733$		−	19.0000i		−	0.701781i	0.936416	−	0.350891i	$-0.114121\pi$
$734$	9.75833	−	5.63397i	0.360187	−	0.207954i
$735$	1.50000	−	0.866025i	0.0553283	−	0.0319438i
$736$			4.19615i			0.154672i
$737$	−8.32051	−	14.4115i	−0.306490	−	0.530856i
$738$	−4.69615	+	8.13397i	−0.172868	+	0.299416i
$739$	−2.53590	−	1.46410i	−0.0932845	−	0.0538578i	0.452632	−	0.891697i	$-0.350485\pi$
$739$	−2.53590	−	1.46410i	−0.0932845	−	0.0538578i	−0.545917	+	0.837840i	$0.683818\pi$
$740$	−13.1962			−0.485100
$741$		0			0
$742$	17.6603			0.648328
$743$	−41.9090	−	24.1962i	−1.53749	−	0.887671i	−0.998985	−	0.0450491i	$-0.985656\pi$
$743$	−41.9090	−	24.1962i	−1.53749	−	0.887671i	−0.538506	−	0.842622i	$-0.681011\pi$
$744$	−0.732051	+	1.26795i	−0.0268383	+	0.0464853i
$745$	24.6244	+	42.6506i	0.902167	+	1.56260i
$746$			13.7321i			0.502766i
$747$	0.169873	−	0.0980762i	0.00621533	−	0.00358842i
$748$	−6.29423	+	3.63397i	−0.230140	+	0.132871i
$749$		−	27.8564i		−	1.01785i
$750$	−7.33013	−	12.6962i	−0.267658	−	0.463598i
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.0973862	+	0.995247i	$0.531048\pi$
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.813216	+	0.581962i	$0.802285\pi$
$752$	−1.90192	−	1.09808i	−0.0693560	−	0.0400427i
$753$	−13.4641			−0.490659
$754$		0			0
$755$	25.1244			0.914369
$756$	−2.36603	−	1.36603i	−0.0860515	−	0.0496819i
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	−0.991109	−	0.133056i	$-0.957521\pi$
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	0.610784	+	0.791797i	$0.290854\pi$
$758$	−2.73205	−	4.73205i	−0.0992326	−	0.171876i
$759$		−	5.32051i		−	0.193122i
$760$	−15.2942	+	8.83013i	−0.554780	+	0.320302i
$761$	9.80385	−	5.66025i	0.355389	−	0.205184i	−0.311667	−	0.950191i	$-0.600887\pi$
$761$	9.80385	−	5.66025i	0.355389	−	0.205184i	0.667056	+	0.745007i	$0.267554\pi$
$762$		−	9.85641i		−	0.357060i
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	−3.46410	+	6.00000i	−0.125327	+	0.217072i
$765$	18.5263	+	10.6962i	0.669819	+	0.386720i
$766$	1.46410			0.0529001
$767$		0			0
$768$	1.00000			0.0360844
$769$	−37.9808	−	21.9282i	−1.36962	−	0.790751i	−0.378742	−	0.925502i	$-0.623643\pi$
$769$	−37.9808	−	21.9282i	−1.36962	−	0.790751i	−0.990879	+	0.134751i	$0.956977\pi$
$770$	6.46410	−	11.1962i	0.232950	−	0.403481i
$771$	4.66987	+	8.08846i	0.168181	+	0.291299i
$772$			11.7321i			0.422246i
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.524459	−	0.851436i	$-0.324268\pi$
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.999594	−	0.0284768i	$-0.00906566\pi$
$774$	−8.36603	+	4.83013i	−0.300711	+	0.173615i
$775$			13.0718i			0.469553i
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	−4.83013	+	8.36603i	−0.173280	+	0.300129i
$778$	−10.2058	−	5.89230i	−0.365895	−	0.211249i
$779$	44.4449			1.59240
$780$		0			0
$781$	6.00000			0.214697
$782$	−20.8301	−	12.0263i	−0.744884	−	0.430059i
$783$	2.23205	−	3.86603i	0.0797670	−	0.138160i
$784$	0.232051	+	0.401924i	0.00828753	+	0.0143544i
$785$		−	28.3205i		−	1.01080i
$786$	−5.66025	+	3.26795i	−0.201895	+	0.116564i
$787$	4.05256	−	2.33975i	0.144458	−	0.0834029i	−0.426029	−	0.904710i	$-0.640088\pi$
$787$	4.05256	−	2.33975i	0.144458	−	0.0834029i	0.570487	+	0.821307i	$0.306754\pi$
$788$		−	17.8564i		−	0.636108i
$789$	5.02628	+	8.70577i	0.178940	+	0.309934i
$790$	−4.73205	+	8.19615i	−0.168359	+	0.291606i
$791$	−3.16987	−	1.83013i	−0.112708	−	0.0650718i
$792$	−1.26795			−0.0450546
$793$		0			0
$794$	20.3923			0.723696
$795$	−20.8923	−	12.0622i	−0.740974	−	0.427801i
$796$	7.09808	−	12.2942i	0.251585	−	0.435757i
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	−0.992492	−	0.122312i	$-0.960969\pi$
$797$	−17.0000	−	29.4449i	−0.602171	−	1.04299i	0.390321	−	0.920679i	$-0.372364\pi$
$798$			12.9282i			0.457653i
$799$	10.9019	−	6.29423i	0.385682	−	0.222674i
$800$	7.73205	−	4.46410i	0.273369	−	0.157830i
$801$		−	9.46410i		−	0.334398i
$802$	−4.03590	−	6.99038i	−0.142513	−	0.246839i
$803$	−3.97372	+	6.88269i	−0.140230	+	0.242885i
$804$	−11.3660	−	6.56218i	−0.400849	−	0.231430i
$805$	42.7846			1.50796
$806$		0			0
$807$	5.46410			0.192345
$808$	1.66987	+	0.964102i	0.0587459	+	0.0339170i
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.180453	−	0.983584i	$-0.442244\pi$
$809$	26.7942	−	46.4090i	0.942035	−	1.63165i	0.761582	−	0.648069i	$-0.224423\pi$
$810$	1.86603	+	3.23205i	0.0655654	+	0.113563i
$811$		−	17.1769i		−	0.603163i	−0.953440	−	0.301582i	$-0.902485\pi$
$811$		−	17.1769i		−	0.603163i	0.953440	−	0.301582i	$-0.0975145\pi$
$812$	−10.5622	+	6.09808i	−0.370660	+	0.214001i
$813$	−18.9282	+	10.9282i	−0.663841	+	0.383269i
$814$			4.48334i			0.157141i
$815$	25.1244	+	43.5167i	0.880068	+	1.52432i
$816$	−2.86603	+	4.96410i	−0.100331	+	0.173778i
$817$	39.5885	+	22.8564i	1.38502	+	0.799644i
$818$	−17.7321			−0.619987
$819$		0			0
$820$	−35.0526			−1.22409
$821$	−0.803848	−	0.464102i	−0.0280545	−	0.0161973i	0.485907	−	0.874010i	$-0.338489\pi$
$821$	−0.803848	−	0.464102i	−0.0280545	−	0.0161973i	−0.513962	+	0.857813i	$0.671823\pi$
$822$	−5.96410	+	10.3301i	−0.208022	+	0.360305i
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	0.959177	+	0.282806i	$0.0912654\pi$
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	−0.234671	+	0.972075i	$0.575401\pi$
$824$			15.2679i			0.531884i
$825$	−9.80385	+	5.66025i	−0.341326	+	0.197065i
$826$	−18.9282	+	10.9282i	−0.658596	+	0.380241i
$827$			26.5359i			0.922744i	0.887207	+	0.461372i	$0.152643\pi$
$827$			26.5359i			0.922744i	−0.887207	+	0.461372i	$0.847357\pi$
$828$	−2.09808	−	3.63397i	−0.0729132	−	0.126289i
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	−0.951886	−	0.306452i	$-0.900858\pi$
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	0.741338	+	0.671132i	$0.234192\pi$
$830$	0.633975	+	0.366025i	0.0220056	+	0.0127049i
$831$	5.73205			0.198843
$832$		0			0
$833$	−2.66025			−0.0921723
$834$	15.4641	+	8.92820i	0.535478	+	0.309158i
$835$	17.6603	−	30.5885i	0.611158	−	1.05856i
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$		−	1.46410i		−	0.0506068i
$838$	15.1244	−	8.73205i	0.522462	−	0.301644i
$839$	36.2487	−	20.9282i	1.25144	−	0.722522i	0.280048	−	0.959986i	$-0.409650\pi$
$839$	36.2487	−	20.9282i	1.25144	−	0.722522i	0.971396	+	0.237464i	$0.0763162\pi$
$840$		−	10.1962i		−	0.351801i
$841$	4.53590	+	7.85641i	0.156410	+	0.270911i
$842$	−11.3564	+	19.6699i	−0.391368	+	0.677869i
$843$	−10.6699	−	6.16025i	−0.367490	−	0.212170i
$844$	−16.3923			−0.564246
$845$		0			0
$846$	2.19615			0.0755053
$847$	22.2224	+	12.8301i	0.763572	+	0.440848i
$848$	3.23205	−	5.59808i	0.110989	−	0.192239i
$849$	12.8301	+	22.2224i	0.440329	+	0.762672i
$850$			51.1769i			1.75535i
$851$	−12.8494	+	7.41858i	−0.440471	+	0.254306i
$852$	4.09808	−	2.36603i	0.140398	−	0.0810587i
$853$		−	54.1769i		−	1.85498i	−0.373845	−	0.927491i	$-0.621961\pi$
$853$		−	54.1769i		−	1.85498i	0.373845	−	0.927491i	$-0.378039\pi$
$854$	−12.5622	−	21.7583i	−0.429869	−	0.744555i
$855$	8.83013	−	15.2942i	0.301984	−	0.523052i
$856$	−8.83013	−	5.09808i	−0.301808	−	0.174249i
$857$	−39.4449			−1.34741			−0.673705	−	0.739000i	$-0.735298\pi$
$857$	−39.4449			−1.34741			−0.673705	+	0.739000i	$0.735298\pi$
$858$		0			0
$859$	−47.1244			−1.60786			−0.803931	−	0.594722i	$-0.797262\pi$
$859$	−47.1244			−1.60786			−0.803931	+	0.594722i	$0.797262\pi$
$860$	−31.2224	−	18.0263i	−1.06468	−	0.614691i
$861$	−12.8301	+	22.2224i	−0.437250	+	0.757338i
$862$	6.56218	+	11.3660i	0.223509	+	0.387128i
$863$			17.1244i			0.582920i	0.956583	+	0.291460i	$0.0941410\pi$
$863$			17.1244i			0.582920i	−0.956583	+	0.291460i	$0.905859\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	14.1962	−	8.19615i	0.482684	−	0.278678i
$866$			12.8564i			0.436878i
$867$	−7.92820	−	13.7321i	−0.269256	−	0.466365i
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	2.78461	+	1.60770i	0.0944614	+	0.0545373i
$870$	16.6603			0.564836
$871$		0			0
$872$	1.46410			0.0495807
$873$	−5.19615	−	3.00000i	−0.175863	−	0.101535i
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$	−20.0263	−	34.6865i	−0.677012	−	1.17262i
$876$			6.26795i			0.211774i
$877$	−20.7224	+	11.9641i	−0.699747	+	0.403999i	−0.807253	−	0.590205i	$-0.799047\pi$
$877$	−20.7224	+	11.9641i	−0.699747	+	0.403999i	0.107506	+	0.994204i	$0.465713\pi$
$878$	−0.294229	+	0.169873i	−0.00992974	+	0.00573294i
$879$			30.5167i			1.02930i
$880$	−2.36603	−	4.09808i	−0.0797587	−	0.138146i
$881$	−13.9186	+	24.1077i	−0.468929	+	0.812209i	−0.999369	−	0.0355135i	$-0.988693\pi$
$881$	−13.9186	+	24.1077i	−0.468929	+	0.812209i	0.530440	+	0.847722i	$0.322027\pi$
$882$	−0.401924	−	0.232051i	−0.0135335	−	0.00781356i
$883$	−42.9282			−1.44465			−0.722325	−	0.691554i	$-0.756926\pi$
$883$	−42.9282			−1.44465			−0.722325	+	0.691554i	$0.756926\pi$
$884$		0			0
$885$	29.8564			1.00361
$886$	13.5167	+	7.80385i	0.454101	+	0.262175i
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	0.350852	+	0.936431i	$0.385892\pi$
$887$	−18.9282	+	32.7846i	−0.635547	+	1.10080i	−0.986399	+	0.164369i	$0.947441\pi$
$888$	1.76795	+	3.06218i	0.0593285	+	0.102760i
$889$		−	26.9282i		−	0.903143i
$890$	30.5885	−	17.6603i	1.02533	−	0.591973i
$891$	1.09808	−	0.633975i	0.0367869	−	0.0212389i
$892$		−	26.9282i		−	0.901623i
$893$	−5.19615	−	9.00000i	−0.173883	−	0.301174i
$894$	6.59808	−	11.4282i	0.220673	−	0.382216i
$895$	51.8827	+	29.9545i	1.73425	+	1.00127i
$896$	2.73205			0.0912714
$897$		0			0
$898$	11.3205			0.377770
$899$	−5.66025	−	3.26795i	−0.188780	−	0.108992i
$900$	−4.46410	+	7.73205i	−0.148803	+	0.257735i
$901$	18.5263	+	32.0885i	0.617200	+	1.06902i
$902$			11.9090i			0.396525i
$903$	−22.8564	+	13.1962i	−0.760614	+	0.439140i
$904$	−1.16025	+	0.669873i	−0.0385895	+	0.0222796i
$905$			71.6410i			2.38143i
$906$	−3.36603	−	5.83013i	−0.111829	−	0.193693i
$907$	18.1962	−	31.5167i	0.604193	−	1.04649i	−0.387985	−	0.921666i	$-0.626829\pi$
$907$	18.1962	−	31.5167i	0.604193	−	1.04649i	0.992178	−	0.124828i	$-0.0398379\pi$
$908$	10.5622	+	6.09808i	0.350518	+	0.202372i
$909$	−1.92820			−0.0639545
$910$		0			0
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$	4.09808	+	2.36603i	0.135701	+	0.0783469i
$913$	0.124356	−	0.215390i	0.00411557	−	0.00712838i
$914$	0.669873	+	1.16025i	0.0221574	+	0.0383778i
$915$			34.3205i			1.13460i
$916$	10.2679	−	5.92820i	0.339263	−	0.195873i
$917$	−15.4641	+	8.92820i	−0.510670	+	0.294835i
$918$		−	5.73205i		−	0.189186i
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	−0.943836	−	0.330415i	$-0.892811\pi$
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	0.185770	−	0.982593i	$-0.440522\pi$
$920$	7.83013	−	13.5622i	0.258152	−	0.447132i
$921$	19.5622	+	11.2942i	0.644596	+	0.372157i
$922$	−22.2679			−0.733356
$923$		0			0
$924$	−3.46410			−0.113961
$925$	27.3397	+	15.7846i	0.898925	+	0.518995i
$926$	−5.02628	+	8.70577i	−0.165174	+	0.286089i
$927$	−7.63397	−	13.2224i	−0.250733	−	0.434282i
$928$			4.46410i			0.146541i
$929$	33.9904	−	19.6244i	1.11519	−	0.643854i	0.175020	−	0.984565i	$-0.444001\pi$
$929$	33.9904	−	19.6244i	1.11519	−	0.643854i	0.940168	+	0.340711i	$0.110668\pi$
$930$	4.73205	−	2.73205i	0.155170	−	0.0895875i
$931$			2.19615i			0.0719760i
$932$	3.92820	+	6.80385i	0.128673	+	0.222867i
$933$	−0.830127	+	1.43782i	−0.0271771	+	0.0470722i
$934$	−16.0981	−	9.29423i	−0.526745	−	0.304116i
$935$	27.1244			0.887061
$936$		0			0
$937$	−5.24871			−0.171468			−0.0857340	−	0.996318i	$-0.527324\pi$
$937$	−5.24871			−0.171468			−0.0857340	+	0.996318i	$0.527324\pi$
$938$	−31.0526	−	17.9282i	−1.01390	−	0.585377i
$939$	−3.26795	+	5.66025i	−0.106645	+	0.184715i
$940$	4.09808	+	7.09808i	0.133665	+	0.231514i
$941$		−	12.6410i		−	0.412085i	−0.978543	−	0.206043i	$-0.933941\pi$
$941$		−	12.6410i		−	0.412085i	0.978543	−	0.206043i	$-0.0660586\pi$
$942$	−6.57180	+	3.79423i	−0.214121	+	0.123623i
$943$	−34.1314	+	19.7058i	−1.11147	+	0.641708i
$944$			8.00000i			0.260378i
$945$	5.09808	+	8.83013i	0.165840	+	0.287244i
$946$	−6.12436	+	10.6077i	−0.199120	+	0.344886i
$947$	−18.2487	−	10.5359i	−0.593003	−	0.342371i	0.173281	−	0.984872i	$-0.444563\pi$
$947$	−18.2487	−	10.5359i	−0.593003	−	0.342371i	−0.766284	+	0.642502i	$0.777897\pi$
$948$	2.53590			0.0823622
$949$		0			0
$950$	42.2487			1.37073
$951$	17.8923	+	10.3301i	0.580198	+	0.334977i
$952$	−7.83013	+	13.5622i	−0.253776	+	0.439553i
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	0.976969	+	0.213383i	$0.0684483\pi$
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	−0.303689	+	0.952771i	$0.598218\pi$
$954$			6.46410i			0.209283i
$955$	22.3923	−	12.9282i	0.724598	−	0.418347i
$956$	6.63397	−	3.83013i	0.214558	−	0.123875i
$957$		−	5.66025i		−	0.182970i
$958$	−16.7321	−	28.9808i	−0.540588	−	0.936326i
$959$	−16.2942	+	28.2224i	−0.526168	+	0.911350i
$960$	−3.23205	−	1.86603i	−0.104314	−	0.0602257i
$961$	28.8564			0.930852
$962$		0			0
$963$	10.1962			0.328566
$964$	11.7679	+	6.79423i	0.379020	+	0.218827i
$965$	21.8923	−	37.9186i	0.704738	−	1.22064i
$966$	−5.73205	−	9.92820i	−0.184426	−	0.319435i
$967$			43.1244i			1.38679i	0.720560	+	0.693393i	$0.243885\pi$
$967$			43.1244i			1.38679i	−0.720560	+	0.693393i	$0.756115\pi$
$968$	8.13397	−	4.69615i	0.261436	−	0.150940i
$969$	−23.4904	+	13.5622i	−0.754620	+	0.435680i
$970$		−	22.3923i		−	0.718974i
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	0.514495	−	0.857493i	$-0.327979\pi$
$971$	−15.1244	−	26.1962i	−0.485364	−	0.840675i	−0.999859	+	0.0168189i	$0.994646\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	42.2487	+	24.3923i	1.35443	+	0.781981i
$974$	3.12436			0.100111
$975$		0			0
$976$	−9.19615			−0.294362
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.975461	−	0.220174i	$-0.0706625\pi$
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.297054	+	0.954861i	$0.403996\pi$
$978$	6.73205	−	11.6603i	0.215267	−	0.372854i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		−	1.73205i		−	0.0553283i
$981$	−1.26795	+	0.732051i	−0.0404825	+	0.0233726i
$982$	7.56218	−	4.36603i	0.241319	−	0.139325i
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$	4.69615	+	8.13397i	0.149708	+	0.259302i
$985$	−33.3205	+	57.7128i	−1.06168	+	1.83888i
$986$	−22.1603	−	12.7942i	−0.705726	−	0.407451i
$987$	6.00000			0.190982
$988$		0			0
$989$	−40.5359			−1.28897
$990$	4.09808	+	2.36603i	0.130245	+	0.0751972i
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	−0.987756	−	0.156006i	$-0.950138\pi$
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	0.628983	+	0.777419i	$0.283471\pi$
$992$	0.732051	+	1.26795i	0.0232426	+	0.0402574i
$993$		−	20.0000i		−	0.634681i
$994$	11.1962	−	6.46410i	0.355120	−	0.205029i
$995$	−45.8827	+	26.4904i	−1.45458	+	0.839802i
$996$		−	0.196152i		−	0.00621533i
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	0.646123	−	0.763234i	$-0.276389\pi$
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	−0.984041	+	0.177942i	$0.943056\pi$
$998$	16.0000	−	27.7128i	0.506471	−	0.877234i
$999$	−3.06218	−	1.76795i	−0.0968830	−	0.0559354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.a.823.2		4
13.2	odd	12		1014.2.e.i.991.1		4
13.3	even	3		78.2.i.a.49.1	yes	4
13.4	even	6		1014.2.b.e.337.4		4
13.5	odd	4		1014.2.e.i.529.1		4
13.6	odd	12		1014.2.a.i.1.1		2
13.7	odd	12		1014.2.a.k.1.2		2
13.8	odd	4		1014.2.e.g.529.2		4
13.9	even	3		1014.2.b.e.337.1		4
13.10	even	6	inner	1014.2.i.a.361.2		4
13.11	odd	12		1014.2.e.g.991.2		4
13.12	even	2		78.2.i.a.43.1	✓	4
39.17	odd	6		3042.2.b.i.1351.1		4
39.20	even	12		3042.2.a.p.1.1		2
39.29	odd	6		234.2.l.c.127.2		4
39.32	even	12		3042.2.a.y.1.2		2
39.35	odd	6		3042.2.b.i.1351.4		4
39.38	odd	2		234.2.l.c.199.2		4
52.3	odd	6		624.2.bv.e.49.1		4
52.7	even	12		8112.2.a.bp.1.2		2
52.19	even	12		8112.2.a.bj.1.1		2
52.51	odd	2		624.2.bv.e.433.2		4
65.3	odd	12		1950.2.y.g.49.2		4
65.12	odd	4		1950.2.y.g.199.2		4
65.29	even	6		1950.2.bc.d.751.2		4
65.38	odd	4		1950.2.y.b.199.1		4
65.42	odd	12		1950.2.y.b.49.1		4
65.64	even	2		1950.2.bc.d.901.2		4
156.107	even	6		1872.2.by.h.1297.2		4
156.155	even	2		1872.2.by.h.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	13.12	even	2
78.2.i.a.49.1	yes	4	13.3	even	3
234.2.l.c.127.2		4	39.29	odd	6
234.2.l.c.199.2		4	39.38	odd	2
624.2.bv.e.49.1		4	52.3	odd	6
624.2.bv.e.433.2		4	52.51	odd	2
1014.2.a.i.1.1		2	13.6	odd	12
1014.2.a.k.1.2		2	13.7	odd	12
1014.2.b.e.337.1		4	13.9	even	3
1014.2.b.e.337.4		4	13.4	even	6
1014.2.e.g.529.2		4	13.8	odd	4
1014.2.e.g.991.2		4	13.11	odd	12
1014.2.e.i.529.1		4	13.5	odd	4
1014.2.e.i.991.1		4	13.2	odd	12
1014.2.i.a.361.2		4	13.10	even	6	inner
1014.2.i.a.823.2		4	1.1	even	1	trivial
1872.2.by.h.433.1		4	156.155	even	2
1872.2.by.h.1297.2		4	156.107	even	6
1950.2.y.b.49.1		4	65.42	odd	12
1950.2.y.b.199.1		4	65.38	odd	4
1950.2.y.g.49.2		4	65.3	odd	12
1950.2.y.g.199.2		4	65.12	odd	4
1950.2.bc.d.751.2		4	65.29	even	6
1950.2.bc.d.901.2		4	65.64	even	2
3042.2.a.p.1.1		2	39.20	even	12
3042.2.a.y.1.2		2	39.32	even	12
3042.2.b.i.1351.1		4	39.17	odd	6
3042.2.b.i.1351.4		4	39.35	odd	6
8112.2.a.bj.1.1		2	52.19	even	12
8112.2.a.bp.1.2		2	52.7	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-2.36603 + 1.36603i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.86603 - 3.23205i) q^{10} +(-1.09808 - 0.633975i) q^{11} -1.00000 q^{12} -2.73205 q^{14} +(3.23205 + 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} -1.00000i q^{18} +(-4.09808 + 2.36603i) q^{19} +(3.23205 - 1.86603i) q^{20} -2.73205i q^{21} +(-0.633975 - 1.09808i) q^{22} +(2.09808 - 3.63397i) q^{23} +(-0.866025 - 0.500000i) q^{24} -8.92820 q^{25} +1.00000 q^{27} +(-2.36603 - 1.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(1.86603 + 3.23205i) q^{30} -1.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.09808 - 0.633975i) q^{33} -5.73205i q^{34} +(5.09808 + 8.83013i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-3.06218 - 1.76795i) q^{37} -4.73205 q^{38} +3.73205 q^{40} +(-8.13397 - 4.69615i) q^{41} +(1.36603 - 2.36603i) q^{42} +(-4.83013 - 8.36603i) q^{43} -1.26795i q^{44} +(-3.23205 + 1.86603i) q^{45} +(3.63397 - 2.09808i) q^{46} +2.19615i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.232051 - 0.401924i) q^{49} +(-7.73205 - 4.46410i) q^{50} +5.73205 q^{51} -6.46410 q^{53} +(0.866025 + 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(-1.36603 - 2.36603i) q^{56} -4.73205i q^{57} +(3.86603 - 2.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +3.73205i q^{60} +(4.59808 + 7.96410i) q^{61} +(0.732051 - 1.26795i) q^{62} +(2.36603 + 1.36603i) q^{63} -1.00000 q^{64} +1.26795 q^{66} +(11.3660 + 6.56218i) q^{67} +(2.86603 - 4.96410i) q^{68} +(2.09808 + 3.63397i) q^{69} +10.1962i q^{70} +(-4.09808 + 2.36603i) q^{71} +(0.866025 - 0.500000i) q^{72} -6.26795i q^{73} +(-1.76795 - 3.06218i) q^{74} +(4.46410 - 7.73205i) q^{75} +(-4.09808 - 2.36603i) q^{76} +3.46410 q^{77} -2.53590 q^{79} +(3.23205 + 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.69615 - 8.13397i) q^{82} +0.196152i q^{83} +(2.36603 - 1.36603i) q^{84} +(-18.5263 + 10.6962i) q^{85} -9.66025i q^{86} +(2.23205 + 3.86603i) q^{87} +(0.633975 - 1.09808i) q^{88} +(8.19615 + 4.73205i) q^{89} -3.73205 q^{90} +4.19615 q^{92} +(1.26795 + 0.732051i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(8.83013 + 15.2942i) q^{95} -1.00000i q^{96} +(5.19615 - 3.00000i) q^{97} +(0.401924 - 0.232051i) q^{98} +1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} + 4 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{14} + 6 q^{15} - 2 q^{16} - 8 q^{17} - 6 q^{19} + 6 q^{20} - 6 q^{22} - 2 q^{23} - 8 q^{25} + 4 q^{27} - 6 q^{28} + 2 q^{29} + 4 q^{30} - 6 q^{33} + 10 q^{35} + 2 q^{36} + 12 q^{37} - 12 q^{38} + 8 q^{40} - 36 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 18 q^{46} - 2 q^{48} - 6 q^{49} - 24 q^{50} + 16 q^{51} - 12 q^{53} - 6 q^{55} - 2 q^{56} + 12 q^{58} + 8 q^{61} - 4 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{66} + 42 q^{67} + 8 q^{68} - 2 q^{69} - 6 q^{71} - 14 q^{74} + 4 q^{75} - 6 q^{76} - 24 q^{79} + 6 q^{80} - 2 q^{81} + 2 q^{82} + 6 q^{84} - 36 q^{85} + 2 q^{87} + 6 q^{88} + 12 q^{89} - 8 q^{90} - 4 q^{92} + 12 q^{93} + 6 q^{94} + 18 q^{95} + 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 + 4 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^14 + 6 * q^15 - 2 * q^16 - 8 * q^17 - 6 * q^19 + 6 * q^20 - 6 * q^22 - 2 * q^23 - 8 * q^25 + 4 * q^27 - 6 * q^28 + 2 * q^29 + 4 * q^30 - 6 * q^33 + 10 * q^35 + 2 * q^36 + 12 * q^37 - 12 * q^38 + 8 * q^40 - 36 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 18 * q^46 - 2 * q^48 - 6 * q^49 - 24 * q^50 + 16 * q^51 - 12 * q^53 - 6 * q^55 - 2 * q^56 + 12 * q^58 + 8 * q^61 - 4 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^66 + 42 * q^67 + 8 * q^68 - 2 * q^69 - 6 * q^71 - 14 * q^74 + 4 * q^75 - 6 * q^76 - 24 * q^79 + 6 * q^80 - 2 * q^81 + 2 * q^82 + 6 * q^84 - 36 * q^85 + 2 * q^87 + 6 * q^88 + 12 * q^89 - 8 * q^90 - 4 * q^92 + 12 * q^93 + 6 * q^94 + 18 * q^95 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more