LMFDB - Embedded newform 784.2.x.p.557.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.21
Character	$\chi$	$=$	784.557
Dual form			784.2.x.p.373.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18937 + 0.765113i) q^{2} +(-3.19528 + 0.856173i) q^{3} +(0.829204 + 1.82001i) q^{4} +(0.890122 + 0.238507i) q^{5} +(-4.45544 - 1.42644i) q^{6} +(-0.406279 + 2.79910i) q^{8} +(6.87872 - 3.97143i) q^{9} +O(q^{10})$	\(q+(1.18937 + 0.765113i) q^{2} +(-3.19528 + 0.856173i) q^{3} +(0.829204 + 1.82001i) q^{4} +(0.890122 + 0.238507i) q^{5} +(-4.45544 - 1.42644i) q^{6} +(-0.406279 + 2.79910i) q^{8} +(6.87872 - 3.97143i) q^{9} +(0.876200 + 0.964717i) q^{10} +(0.873930 + 3.26155i) q^{11} +(-4.20778 - 5.10549i) q^{12} +(3.39380 + 3.39380i) q^{13} -3.04839 q^{15} +(-2.62484 + 3.01831i) q^{16} +(-1.40768 + 2.43817i) q^{17} +(11.2199 + 0.539495i) q^{18} +(0.392879 - 1.46625i) q^{19} +(0.304008 + 1.81780i) q^{20} +(-1.45603 + 4.54785i) q^{22} +(-3.94180 + 2.27580i) q^{23} +(-1.09834 - 9.29175i) q^{24} +(-3.59470 - 2.07540i) q^{25} +(1.43985 + 6.63313i) q^{26} +(-11.5619 + 11.5619i) q^{27} +(-5.76129 - 5.76129i) q^{29} +(-3.62567 - 2.33237i) q^{30} +(0.611172 - 1.05858i) q^{31} +(-5.43126 + 1.58159i) q^{32} +(-5.58490 - 9.67334i) q^{33} +(-3.53972 + 1.82285i) q^{34} +(12.9319 + 9.22618i) q^{36} +(9.40318 + 2.51957i) q^{37} +(1.58912 - 1.44331i) q^{38} +(-13.7498 - 7.93848i) q^{39} +(-1.02924 + 2.39464i) q^{40} -5.10326i q^{41} +(-2.53146 + 2.53146i) q^{43} +(-5.21137 + 4.29505i) q^{44} +(7.07011 - 1.89443i) q^{45} +(-6.42951 - 0.309154i) q^{46} +(-1.77664 - 3.07723i) q^{47} +(5.80291 - 11.8917i) q^{48} +(-2.68751 - 5.21877i) q^{50} +(2.41043 - 8.99584i) q^{51} +(-3.36258 + 8.99090i) q^{52} +(1.48464 + 5.54077i) q^{53} +(-22.5975 + 4.90522i) q^{54} +3.11162i q^{55} +5.02144i q^{57} +(-2.44427 - 11.2603i) q^{58} +(0.724612 + 2.70429i) q^{59} +(-2.52774 - 5.54809i) q^{60} +(-3.53690 + 13.1999i) q^{61} +(1.53684 - 0.791429i) q^{62} +(-7.66988 - 2.27443i) q^{64} +(2.21145 + 3.83035i) q^{65} +(0.758676 - 15.7783i) q^{66} +(-1.30397 + 0.349397i) q^{67} +(-5.60473 - 0.540240i) q^{68} +(10.6467 - 10.6467i) q^{69} -0.695700i q^{71} +(8.32173 + 20.8677i) q^{72} +(0.275624 + 0.159132i) q^{73} +(9.25610 + 10.1912i) q^{74} +(13.2630 + 3.55380i) q^{75} +(2.99435 - 0.500775i) q^{76} +(-10.2798 - 19.9620i) q^{78} +(-1.32165 - 2.28916i) q^{79} +(-3.05632 + 2.06062i) q^{80} +(15.1302 - 26.2063i) q^{81} +(3.90457 - 6.06967i) q^{82} +(6.22648 + 6.22648i) q^{83} +(-1.83452 + 1.83452i) q^{85} +(-4.94770 + 1.07399i) q^{86} +(23.3416 + 13.4763i) q^{87} +(-9.48445 + 1.12111i) q^{88} +(-5.18733 + 2.99491i) q^{89} +(9.85844 + 3.15625i) q^{90} +(-7.41053 - 5.28700i) q^{92} +(-1.04654 + 3.90573i) q^{93} +(0.241346 - 5.01929i) q^{94} +(0.699421 - 1.21143i) q^{95} +(16.0003 - 9.70373i) q^{96} +11.0724 q^{97} +(18.9645 + 18.9645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.18937	+	0.765113i	0.841012	+	0.541017i
$2$	1.18937	+	0.765113i	0.841012	+	0.541017i
$3$	−3.19528	+	0.856173i	−1.84480	+	0.494312i	−0.999218	−	0.0395388i	$-0.987411\pi$
$3$	−3.19528	+	0.856173i	−1.84480	+	0.494312i	−0.845579	+	0.533851i	$0.820744\pi$
$4$	0.829204	+	1.82001i	0.414602	+	0.910003i
$5$	0.890122	+	0.238507i	0.398075	+	0.106664i	0.452302	−	0.891865i	$-0.350603\pi$
$5$	0.890122	+	0.238507i	0.398075	+	0.106664i	−0.0542274	+	0.998529i	$0.517270\pi$
$6$	−4.45544	−	1.42644i	−1.81893	−	0.582344i
$7$		0			0
$7$		0			0
$8$	−0.406279	+	2.79910i	−0.143641	+	0.989630i
$9$	6.87872	−	3.97143i	2.29291	−	1.32381i
$10$	0.876200	+	0.964717i	0.277079	+	0.305070i
$11$	0.873930	+	3.26155i	0.263500	+	0.983394i	0.963162	+	0.268921i	$0.0866670\pi$
$11$	0.873930	+	3.26155i	0.263500	+	0.983394i	−0.699663	+	0.714473i	$0.746666\pi$
$12$	−4.20778	−	5.10549i	−1.21468	−	1.47383i
$13$	3.39380	+	3.39380i	0.941272	+	0.941272i	0.998369	−	0.0570969i	$-0.0181844\pi$
$13$	3.39380	+	3.39380i	0.941272	+	0.941272i	−0.0570969	+	0.998369i	$0.518184\pi$
$14$		0			0
$15$	−3.04839			−0.787092
$16$	−2.62484	+	3.01831i	−0.656210	+	0.754578i
$17$	−1.40768	+	2.43817i	−0.341411	+	0.591342i	−0.984695	−	0.174286i	$-0.944238\pi$
$17$	−1.40768	+	2.43817i	−0.341411	+	0.591342i	0.643284	+	0.765628i	$0.277572\pi$
$18$	11.2199	+	0.539495i	2.64456	+	0.127160i
$19$	0.392879	−	1.46625i	0.0901327	−	0.336380i	−0.906104	−	0.423055i	$-0.860958\pi$
$19$	0.392879	−	1.46625i	0.0901327	−	0.336380i	0.996237	+	0.0866754i	$0.0276243\pi$
$20$	0.304008	+	1.81780i	0.0679783	+	0.406472i
$21$		0			0
$22$	−1.45603	+	4.54785i	−0.310426	+	0.969604i
$23$	−3.94180	+	2.27580i	−0.821923	+	0.474537i	−0.851079	−	0.525038i	$-0.824051\pi$
$23$	−3.94180	+	2.27580i	−0.821923	+	0.474537i	0.0291564	+	0.999575i	$0.490718\pi$
$24$	−1.09834	−	9.29175i	−0.224197	−	1.89667i
$25$	−3.59470	−	2.07540i	−0.718939	−	0.415080i
$26$	1.43985	+	6.63313i	0.282377	+	1.30086i
$27$	−11.5619	+	11.5619i	−2.22509	+	2.22509i
$28$		0			0
$29$	−5.76129	−	5.76129i	−1.06984	−	1.06984i	−0.997370	−	0.0724745i	$-0.976910\pi$
$29$	−5.76129	−	5.76129i	−1.06984	−	1.06984i	−0.0724745	−	0.997370i	$-0.523090\pi$
$30$	−3.62567	−	2.33237i	−0.661954	−	0.425830i
$31$	0.611172	−	1.05858i	0.109770	−	0.190127i	−0.805907	−	0.592042i	$-0.798322\pi$
$31$	0.611172	−	1.05858i	0.109770	−	0.190127i	0.915677	+	0.401915i	$0.131655\pi$
$32$	−5.43126	+	1.58159i	−0.960120	+	0.279589i
$33$	−5.58490	−	9.67334i	−0.972207	−	1.68391i
$34$	−3.53972	+	1.82285i	−0.607057	+	0.312616i
$35$		0			0
$36$	12.9319	+	9.22618i	2.15531	+	1.53770i
$37$	9.40318	+	2.51957i	1.54587	+	0.414215i	0.928158	−	0.372187i	$-0.121392\pi$
$37$	9.40318	+	2.51957i	1.54587	+	0.414215i	0.617715	+	0.786402i	$0.288059\pi$
$38$	1.58912	−	1.44331i	0.257790	−	0.234136i
$39$	−13.7498	−	7.93848i	−2.20174	−	1.27117i
$40$	−1.02924	+	2.39464i	−0.162738	+	0.378625i
$41$		−	5.10326i		−	0.796995i	−0.917169	−	0.398498i	$-0.869532\pi$
$41$		−	5.10326i		−	0.796995i	0.917169	−	0.398498i	$-0.130468\pi$
$42$		0			0
$43$	−2.53146	+	2.53146i	−0.386045	+	0.386045i	−0.873274	−	0.487229i	$-0.838008\pi$
$43$	−2.53146	+	2.53146i	−0.386045	+	0.386045i	0.487229	+	0.873274i	$0.338008\pi$
$44$	−5.21137	+	4.29505i	−0.785644	+	0.647503i
$45$	7.07011	−	1.89443i	1.05395	−	0.282405i
$46$	−6.42951	−	0.309154i	−0.947979	−	0.0455823i
$47$	−1.77664	−	3.07723i	−0.259149	−	0.448860i	0.706865	−	0.707348i	$-0.250109\pi$
$47$	−1.77664	−	3.07723i	−0.259149	−	0.448860i	−0.966014	+	0.258489i	$0.916775\pi$
$48$	5.80291	−	11.8917i	0.837577	−	1.71642i
$49$		0			0
$50$	−2.68751	−	5.21877i	−0.380071	−	0.738045i
$51$	2.41043	−	8.99584i	0.337527	−	1.25967i
$52$	−3.36258	+	8.99090i	−0.466307	+	1.24681i
$53$	1.48464	+	5.54077i	0.203932	+	0.761083i	0.989773	+	0.142654i	$0.0455637\pi$
$53$	1.48464	+	5.54077i	0.203932	+	0.761083i	−0.785841	+	0.618429i	$0.787770\pi$
$54$	−22.5975	+	4.90522i	−3.07513	+	0.667515i
$55$			3.11162i			0.419570i
$56$		0			0
$57$			5.02144i			0.665106i
$58$	−2.44427	−	11.2603i	−0.320948	−	1.47856i
$59$	0.724612	+	2.70429i	0.0943365	+	0.352068i	0.996918	−	0.0784505i	$-0.0249972\pi$
$59$	0.724612	+	2.70429i	0.0943365	+	0.352068i	−0.902582	+	0.430519i	$0.858331\pi$
$60$	−2.52774	−	5.54809i	−0.326330	−	0.716256i
$61$	−3.53690	+	13.1999i	−0.452853	+	1.69007i	0.241469	+	0.970408i	$0.422371\pi$
$61$	−3.53690	+	13.1999i	−0.452853	+	1.69007i	−0.694323	+	0.719664i	$0.744296\pi$
$62$	1.53684	−	0.791429i	0.195179	−	0.100512i
$63$		0			0
$64$	−7.66988	−	2.27443i	−0.958734	−	0.284303i
$65$	2.21145	+	3.83035i	0.274297	+	0.475096i
$66$	0.758676	−	15.7783i	0.0933865	−	1.94217i
$67$	−1.30397	+	0.349397i	−0.159305	+	0.0426857i	−0.337590	−	0.941293i	$-0.609612\pi$
$67$	−1.30397	+	0.349397i	−0.159305	+	0.0426857i	0.178285	+	0.983979i	$0.442945\pi$
$68$	−5.60473	−	0.540240i	−0.679673	−	0.0655137i
$69$	10.6467	−	10.6467i	1.28171	−	1.28171i
$70$		0			0
$71$		−	0.695700i		−	0.0825644i	−0.999148	−	0.0412822i	$-0.986856\pi$
$71$		−	0.695700i		−	0.0825644i	0.999148	−	0.0412822i	$-0.0131443\pi$
$72$	8.32173	+	20.8677i	0.980726	+	2.45928i
$73$	0.275624	+	0.159132i	0.0322593	+	0.0186249i	0.516043	−	0.856563i	$-0.327404\pi$
$73$	0.275624	+	0.159132i	0.0322593	+	0.0186249i	−0.483784	+	0.875188i	$0.660738\pi$
$74$	9.25610	+	10.1912i	1.07600	+	1.18470i
$75$	13.2630	+	3.55380i	1.53148	+	0.410358i
$76$	2.99435	−	0.500775i	0.343476	−	0.0574428i
$77$		0			0
$78$	−10.2798	−	19.9620i	−1.16396	−	2.26025i
$79$	−1.32165	−	2.28916i	−0.148697	−	0.257550i	0.782049	−	0.623217i	$-0.214174\pi$
$79$	−1.32165	−	2.28916i	−0.148697	−	0.257550i	−0.930746	+	0.365666i	$0.880841\pi$
$80$	−3.05632	+	2.06062i	−0.341707	+	0.230385i
$81$	15.1302	−	26.2063i	1.68113	−	2.91181i
$82$	3.90457	−	6.06967i	0.431188	−	0.670283i
$83$	6.22648	+	6.22648i	0.683445	+	0.683445i	0.960775	−	0.277330i	$-0.0894494\pi$
$83$	6.22648	+	6.22648i	0.683445	+	0.683445i	−0.277330	+	0.960775i	$0.589449\pi$
$84$		0			0
$85$	−1.83452	+	1.83452i	−0.198982	+	0.198982i
$86$	−4.94770	+	1.07399i	−0.533525	+	0.115812i
$87$	23.3416	+	13.4763i	2.50248	+	1.44481i
$88$	−9.48445	+	1.12111i	−1.01105	+	0.119511i
$89$	−5.18733	+	2.99491i	−0.549856	+	0.317460i	−0.749064	−	0.662498i	$-0.769496\pi$
$89$	−5.18733	+	2.99491i	−0.549856	+	0.317460i	0.199208	+	0.979957i	$0.436163\pi$
$90$	9.85844	+	3.15625i	1.03917	+	0.332698i
$91$		0			0
$92$	−7.41053	−	5.28700i	−0.772601	−	0.551208i
$93$	−1.04654	+	3.90573i	−0.108521	+	0.405005i
$94$	0.241346	−	5.01929i	0.0248929	−	0.517700i
$95$	0.699421	−	1.21143i	0.0717591	−	0.124290i
$96$	16.0003	−	9.70373i	1.63302	−	0.990383i
$97$	11.0724			1.12423			0.562117	−	0.827058i	$-0.309987\pi$
$97$	11.0724			1.12423			0.562117	+	0.827058i	$0.309987\pi$
$98$		0			0
$99$	18.9645	+	18.9645i	1.90601	+	1.90601i
$100$	0.796500	−	8.26330i	0.0796500	−	0.826330i
$101$	0.349172	+	1.30313i	0.0347439	+	0.129666i	0.981120	−	0.193402i	$-0.0619523\pi$
$101$	0.349172	+	1.30313i	0.0347439	+	0.129666i	−0.946376	+	0.323068i	$0.895286\pi$
$102$	9.74973	−	8.85514i	0.965367	−	0.876789i
$103$	−2.00191	+	1.15580i	−0.197254	+	0.113884i	−0.595374	−	0.803449i	$-0.702996\pi$
$103$	−2.00191	+	1.15580i	−0.197254	+	0.113884i	0.398120	+	0.917333i	$0.369663\pi$
$104$	−10.8784	+	8.12075i	−1.06672	+	0.796305i
$105$		0			0
$106$	−2.47352	+	7.72595i	−0.240250	+	0.750410i
$107$	10.0925	+	2.70428i	0.975679	+	0.261432i	0.711224	−	0.702966i	$-0.248141\pi$
$107$	10.0925	+	2.70428i	0.975679	+	0.261432i	0.264455	+	0.964398i	$0.414808\pi$
$108$	−30.6299	−	11.4555i	−2.94736	−	1.10231i
$109$	−12.2134	+	3.27256i	−1.16983	+	0.313455i	−0.790885	−	0.611965i	$-0.790379\pi$
$109$	−12.2134	+	3.27256i	−1.16983	+	0.313455i	−0.378944	+	0.925420i	$0.623713\pi$
$110$	−2.38074	+	3.70086i	−0.226994	+	0.352864i
$111$	−32.2030			−3.05657
$112$		0			0
$113$	−4.10440			−0.386110			−0.193055	−	0.981188i	$-0.561840\pi$
$113$	−4.10440			−0.386110			−0.193055	+	0.981188i	$0.561840\pi$
$114$	−3.84197	+	5.97235i	−0.359833	+	0.559362i
$115$	−4.05148	+	1.08559i	−0.377802	+	0.101232i
$116$	5.70829	−	15.2629i	0.530002	−	1.41712i
$117$	36.8233	+	9.86676i	3.40431	+	0.912183i
$118$	−1.20725	+	3.77081i	−0.111137	+	0.347131i
$119$		0			0
$120$	1.23850	−	8.53275i	0.113059	−	0.778930i
$121$	−0.347676	+	0.200731i	−0.0316069	+	0.0182483i
$122$	−14.3061	+	12.9934i	−1.29521	+	1.17637i
$123$	4.36928	+	16.3064i	0.393964	+	1.47029i
$124$	2.43341	+	0.234556i	0.218526	+	0.0210638i
$125$	−5.96279	−	5.96279i	−0.533328	−	0.533328i
$126$		0			0
$127$	3.02458			0.268388			0.134194	−	0.990955i	$-0.457155\pi$
$127$	3.02458			0.268388			0.134194	+	0.990955i	$0.457155\pi$
$128$	−7.38213	−	8.57346i	−0.652494	−	0.757794i
$129$	5.92137	−	10.2561i	0.521347	−	0.903000i
$130$	−0.300412	+	6.24771i	−0.0263479	+	0.547960i
$131$	2.21938	−	8.28282i	0.193908	−	0.723673i	−0.798639	−	0.601810i	$-0.794446\pi$
$131$	2.21938	−	8.28282i	0.193908	−	0.723673i	0.992547	−	0.121863i	$-0.0388870\pi$
$132$	12.9745	−	18.1857i	1.12929	−	1.58286i
$133$		0			0
$134$	−1.81823	−	0.582121i	−0.157071	−	0.0502876i
$135$	−13.0491	+	7.53389i	−1.12309	+	0.648414i
$136$	−6.25275	−	4.93079i	−0.536169	−	0.422812i
$137$	9.88514	+	5.70719i	0.844545	+	0.487598i	0.858806	−	0.512300i	$-0.171206\pi$
$137$	9.88514	+	5.70719i	0.844545	+	0.487598i	−0.0142618	+	0.999898i	$0.504540\pi$
$138$	20.8088	−	4.51694i	1.77136	−	0.384507i
$139$	13.0393	−	13.0393i	1.10598	−	1.10598i	0.112303	−	0.993674i	$-0.464177\pi$
$139$	13.0393	−	13.0393i	1.10598	−	1.10598i	0.993674	−	0.112303i	$-0.0358229\pi$
$140$		0			0
$141$	8.31150	+	8.31150i	0.699954	+	0.699954i
$142$	0.532289	−	0.827445i	0.0446687	−	0.0694376i
$143$	−8.10311	+	14.0350i	−0.677616	+	1.17367i
$144$	−6.06852	+	31.1865i	−0.505710	+	2.59887i
$145$	−3.75414	−	6.50236i	−0.311764	−	0.539992i
$146$	0.206065	+	0.400150i	0.0170541	+	0.0331166i
$147$		0			0
$148$	3.21152	+	19.2031i	0.263985	+	1.57848i
$149$	−1.45833	−	0.390759i	−0.119471	−	0.0320122i	0.198588	−	0.980083i	$-0.436364\pi$
$149$	−1.45833	−	0.390759i	−0.119471	−	0.0320122i	−0.318059	+	0.948071i	$0.603031\pi$
$150$	13.0555	+	14.3745i	1.06598	+	1.17367i
$151$	15.0327	+	8.67916i	1.22335	+	0.706300i	0.965630	−	0.259920i	$-0.0836963\pi$
$151$	15.0327	+	8.67916i	1.22335	+	0.706300i	0.257718	+	0.966220i	$0.417030\pi$
$152$	3.94454	+	1.69541i	0.319945	+	0.137516i
$153$			22.3619i			1.80786i
$154$		0			0
$155$	0.796496	−	0.796496i	0.0639761	−	0.0639761i
$156$	3.04664	−	31.6074i	0.243926	−	2.53062i
$157$	12.4331	−	3.33144i	0.992268	−	0.265877i	0.274065	−	0.961711i	$-0.411632\pi$
$157$	12.4331	−	3.33144i	0.992268	−	0.265877i	0.718203	+	0.695834i	$0.244965\pi$
$158$	0.179538	−	3.73386i	0.0142833	−	0.297050i
$159$	−9.48771	−	16.4332i	−0.752425	−	1.30324i
$160$	−5.21170	+	0.112415i	−0.412021	+	0.00888718i
$161$		0			0
$162$	38.0462	−	19.5927i	2.98919	−	1.53935i
$163$	2.75338	−	10.2757i	0.215661	−	0.804858i	−0.770272	−	0.637716i	$-0.779879\pi$
$163$	2.75338	−	10.2757i	0.215661	−	0.804858i	0.985933	−	0.167142i	$-0.0534539\pi$
$164$	9.28796	−	4.23165i	0.725268	−	0.330436i
$165$	−2.66408	−	9.94249i	−0.207399	−	0.774022i
$166$	2.64163	+	12.1696i	0.205030	+	0.944541i
$167$		−	13.3166i		−	1.03047i	−0.857050	−	0.515233i	$-0.827705\pi$
$167$		−	13.3166i		−	1.03047i	0.857050	−	0.515233i	$-0.172295\pi$
$168$		0			0
$169$			10.0358i			0.771985i
$170$	−3.58555	+	0.778310i	−0.274999	+	0.0596937i
$171$	−3.12058	−	11.6462i	−0.238637	−	0.890606i
$172$	−6.70638	−	2.50818i	−0.511357	−	0.191247i
$173$	1.89666	−	7.07844i	0.144200	−	0.538163i	−0.855589	−	0.517655i	$-0.826805\pi$
$173$	1.89666	−	7.07844i	0.144200	−	0.538163i	0.999790	−	0.0205081i	$-0.00652839\pi$
$174$	17.4509	+	33.8873i	1.32295	+	2.56899i
$175$		0			0
$176$	−12.1383	−	5.92326i	−0.914959	−	0.446482i
$177$	−4.63068	−	8.02057i	−0.348063	−	0.602863i
$178$	−8.46111	−	0.406841i	−0.634187	−	0.0304940i
$179$	12.4398	−	3.33324i	0.929797	−	0.249138i	0.238029	−	0.971258i	$-0.423499\pi$
$179$	12.4398	−	3.33324i	0.929797	−	0.249138i	0.691768	+	0.722120i	$0.256832\pi$
$180$	9.31044	+	11.2968i	0.693959	+	0.842012i
$181$	2.20069	−	2.20069i	0.163576	−	0.163576i	−0.620573	−	0.784149i	$-0.713100\pi$
$181$	2.20069	−	2.20069i	0.163576	−	0.163576i	0.784149	+	0.620573i	$0.213100\pi$
$182$		0			0
$183$		−	45.2056i		−	3.34169i
$184$	−4.76871	−	11.9581i	−0.351554	−	0.881562i
$185$	7.76904	+	4.48546i	0.571191	+	0.329777i
$186$	−4.23305	+	3.84464i	−0.310382	+	0.281903i
$187$	−9.18241	−	2.46042i	−0.671484	−	0.179924i
$188$	4.12737	−	5.78514i	0.301020	−	0.421925i
$189$		0			0
$190$	1.75875	−	0.905706i	0.127593	−	0.0657068i
$191$	8.51959	+	14.7564i	0.616456	+	1.06773i	0.990127	+	0.140172i	$0.0447655\pi$
$191$	8.51959	+	14.7564i	0.616456	+	1.06773i	−0.373671	+	0.927561i	$0.621901\pi$
$192$	26.4547	+	0.700691i	1.90920	+	0.0505680i
$193$	2.57652	−	4.46266i	0.185462	−	0.321229i	−0.758270	−	0.651940i	$-0.773955\pi$
$193$	2.57652	−	4.46266i	0.185462	−	0.321229i	0.943732	+	0.330711i	$0.107289\pi$
$194$	13.1692	+	8.47166i	0.945494	+	0.608229i
$195$	−10.3456	−	10.3456i	−0.740867	−	0.740867i
$196$		0			0
$197$	9.89572	−	9.89572i	0.705041	−	0.705041i	−0.260447	−	0.965488i	$-0.583870\pi$
$197$	9.89572	−	9.89572i	0.705041	−	0.705041i	0.965488	+	0.260447i	$0.0838701\pi$
$198$	8.04584	+	37.0659i	0.571793	+	2.63416i
$199$	−4.72104	−	2.72570i	−0.334666	−	0.193219i	0.323245	−	0.946315i	$-0.395226\pi$
$199$	−4.72104	−	2.72570i	−0.334666	−	0.193219i	−0.657911	+	0.753096i	$0.728560\pi$
$200$	7.26969	−	9.21871i	0.514045	−	0.651861i
$201$	3.86740	−	2.23285i	0.272786	−	0.157493i
$202$	−0.581745	+	1.81706i	−0.0409314	+	0.127848i
$203$		0			0
$204$	18.3712	−	3.07240i	1.28624	−	0.215111i
$205$	1.21717	−	4.54252i	0.0850105	−	0.317264i
$206$	−3.26532	−	0.157009i	−0.227506	−	0.0109393i
$207$	−18.0764	+	31.3092i	−1.25639	+	2.17614i
$208$	−19.1518	+	1.33537i	−1.32794	+	0.0925911i
$209$	5.12558			0.354544
$210$		0			0
$211$	−1.81247	−	1.81247i	−0.124775	−	0.124775i	0.641962	−	0.766737i	$-0.278121\pi$
$211$	−1.81247	−	1.81247i	−0.124775	−	0.124775i	−0.766737	+	0.641962i	$0.778121\pi$
$212$	−8.85315	+	7.29649i	−0.608037	+	0.501125i
$213$	0.595640	+	2.22296i	0.0408126	+	0.152315i
$214$	9.93464	+	10.9383i	0.679118	+	0.747726i
$215$	−2.85708	+	1.64954i	−0.194852	+	0.112498i
$216$	−27.6655	−	37.0602i	−1.88240	−	2.52162i
$217$		0			0
$218$	−17.0301	−	5.45232i	−1.15342	−	0.369278i
$219$	−1.01694	−	0.272488i	−0.0687185	−	0.0184131i
$220$	−5.66316	+	2.58017i	−0.381810	+	0.173955i
$221$	−13.0520	+	3.49728i	−0.877974	+	0.235253i
$222$	−38.3013	−	24.6389i	−2.57061	−	1.65366i
$223$	19.7001			1.31922			0.659609	−	0.751609i	$-0.270722\pi$
$223$	19.7001			1.31922			0.659609	+	0.751609i	$0.270722\pi$
$224$		0			0
$225$	−32.9692			−2.19795
$226$	−4.88165	−	3.14033i	−0.324723	−	0.208892i
$227$	−25.8294	+	6.92097i	−1.71436	+	0.459361i	−0.976486	−	0.215580i	$-0.930836\pi$
$227$	−25.8294	+	6.92097i	−1.71436	+	0.459361i	−0.737872	+	0.674941i	$0.764169\pi$
$228$	−9.13905	+	4.16380i	−0.605248	+	0.275754i
$229$	8.80030	+	2.35803i	0.581540	+	0.155823i	0.537584	−	0.843210i	$-0.319337\pi$
$229$	8.80030	+	2.35803i	0.581540	+	0.155823i	0.0439562	+	0.999033i	$0.486004\pi$
$230$	−5.64931	−	1.80867i	−0.372505	−	0.119260i
$231$		0			0
$232$	18.4671	−	13.7857i	1.21242	−	0.905076i
$233$	−8.80234	+	5.08203i	−0.576661	+	0.332935i	−0.759805	−	0.650151i	$-0.774706\pi$
$233$	−8.80234	+	5.08203i	−0.576661	+	0.332935i	0.183145	+	0.983086i	$0.441372\pi$
$234$	36.2473	+	39.9092i	2.36956	+	2.60895i
$235$	−0.847483	−	3.16285i	−0.0552837	−	0.206321i
$236$	−4.32097	+	3.56121i	−0.281271	+	0.231815i
$237$	6.18294	+	6.18294i	0.401625	+	0.401625i
$238$		0			0
$239$	23.4901			1.51945			0.759723	−	0.650247i	$-0.225335\pi$
$239$	23.4901			1.51945			0.759723	+	0.650247i	$0.225335\pi$
$240$	8.00155	−	9.20101i	0.516498	−	0.593922i
$241$	−2.15942	+	3.74022i	−0.139100	+	0.240929i	−0.927156	−	0.374675i	$-0.877754\pi$
$241$	−2.15942	+	3.74022i	−0.139100	+	0.240929i	0.788056	+	0.615604i	$0.211088\pi$
$242$	−0.567098	−	0.0272681i	−0.0364544	−	0.00175286i
$243$	−13.2123	+	49.3091i	−0.847572	+	3.16318i
$244$	−26.9567	+	4.50823i	−1.72572	+	0.288610i
$245$		0			0
$246$	−7.27952	+	22.7373i	−0.464125	+	1.44968i
$247$	6.30950	−	3.64279i	0.401464	−	0.231785i
$248$	2.71476	+	2.14081i	0.172388	+	0.135941i
$249$	−25.2263	−	14.5644i	−1.59865	−	0.922982i
$250$	−2.52976	−	11.6542i	−0.159996	−	0.737075i
$251$	−8.57308	+	8.57308i	−0.541128	+	0.541128i	−0.923860	−	0.382732i	$-0.874983\pi$
$251$	−8.57308	+	8.57308i	−0.541128	+	0.541128i	0.382732	+	0.923860i	$0.374983\pi$
$252$		0			0
$253$	−10.8675	−	10.8675i	−0.683234	−	0.683234i
$254$	3.59735	+	2.31415i	0.225718	+	0.145203i
$255$	4.29115	−	7.43249i	0.268722	−	0.465441i
$256$	−2.22043	−	15.8452i	−0.138777	−	0.990324i
$257$	5.82353	+	10.0866i	0.363262	+	0.629187i	0.988496	−	0.151250i	$-0.0483298\pi$
$257$	5.82353	+	10.0866i	0.363262	+	0.629187i	−0.625234	+	0.780437i	$0.714996\pi$
$258$	14.8898	−	7.66780i	0.926998	−	0.477376i
$259$		0			0
$260$	−5.13751	+	7.20099i	−0.318615	+	0.446587i
$261$	−62.5108	−	16.7497i	−3.86932	−	1.03678i
$262$	8.97695	−	8.15327i	0.554598	−	0.503711i
$263$	−5.69017	−	3.28522i	−0.350871	−	0.202576i	0.314198	−	0.949358i	$-0.398265\pi$
$263$	−5.69017	−	3.28522i	−0.350871	−	0.202576i	−0.665069	+	0.746782i	$0.731598\pi$
$264$	29.3456	−	11.7026i	1.80610	−	0.720246i
$265$			5.28606i			0.324720i
$266$		0			0
$267$	14.0108	−	14.0108i	0.857449	−	0.857449i
$268$	−1.71716	−	2.08351i	−0.104892	−	0.127271i
$269$	−28.1670	+	7.54733i	−1.71737	+	0.460169i	−0.977213	−	0.212260i	$-0.931918\pi$
$269$	−28.1670	+	7.54733i	−1.71737	+	0.460169i	−0.740161	+	0.672429i	$0.765251\pi$
$270$	−21.2845	−	1.02343i	−1.29533	−	0.0622842i
$271$	−7.14131	−	12.3691i	−0.433804	−	0.751370i	0.563393	−	0.826189i	$-0.309496\pi$
$271$	−7.14131	−	12.3691i	−0.433804	−	0.751370i	−0.997197	+	0.0748185i	$0.976162\pi$
$272$	−3.66422	−	10.6486i	−0.222176	−	0.645666i
$273$		0			0
$274$	7.39045	+	14.3512i	0.446473	+	0.866988i
$275$	3.62751	−	13.5380i	0.218747	−	0.816374i
$276$	28.2053	+	10.5488i	1.69776	+	0.634960i
$277$	0.177371	+	0.661956i	0.0106572	+	0.0397731i	0.971050	−	0.238878i	$-0.0767795\pi$
$277$	0.177371	+	0.661956i	0.0106572	+	0.0397731i	−0.960393	+	0.278651i	$0.910113\pi$
$278$	25.4851	−	5.53201i	1.52849	−	0.331788i
$279$		−	9.70890i		−	0.581257i
$280$		0			0
$281$		−	0.446622i		−	0.0266432i	−0.999911	−	0.0133216i	$-0.995759\pi$
$281$		−	0.446622i		−	0.0266432i	0.999911	−	0.0133216i	$-0.00424053\pi$
$282$	3.52622	+	16.2447i	0.209983	+	0.967357i
$283$	7.04484	+	26.2917i	0.418772	+	1.56288i	0.777158	+	0.629306i	$0.216661\pi$
$283$	7.04484	+	26.2917i	0.418772	+	1.56288i	−0.358386	+	0.933574i	$0.616673\pi$
$284$	1.26618	−	0.576877i	0.0751338	−	0.0342314i
$285$	−1.19765	+	4.46969i	−0.0709427	+	0.264762i
$286$	−20.3760	+	10.4930i	−1.20486	+	0.620465i
$287$		0			0
$288$	−31.0789	+	32.4492i	−1.83134	+	1.91209i
$289$	4.53690	+	7.85814i	0.266876	+	0.462244i
$290$	0.509978	−	10.6061i	0.0299469	−	0.622809i
$291$	−35.3795	+	9.47991i	−2.07398	+	0.555722i
$292$	−0.0610718	+	0.633590i	−0.00357395	+	0.0370780i
$293$	−2.23558	+	2.23558i	−0.130604	+	0.130604i	−0.769387	−	0.638783i	$-0.779438\pi$
$293$	−2.23558	+	2.23558i	−0.130604	+	0.130604i	0.638783	+	0.769387i	$0.279438\pi$
$294$		0			0
$295$			2.57997i			0.150212i
$296$	−10.8728	+	25.2967i	−0.631971	+	1.47034i
$297$	−47.8139	−	27.6054i	−2.77445	−	1.60183i
$298$	−1.43552	−	1.58055i	−0.0831576	−	0.0915586i
$299$	−21.1013	−	5.65408i	−1.22032	−	0.326984i
$300$	4.52977	+	27.0855i	0.261526	+	1.56378i
$301$		0			0
$302$	11.2390	+	21.8245i	0.646730	+	1.25586i
$303$	−2.23141	−	3.86491i	−0.128191	−	0.222033i
$304$	3.39434	+	5.03449i	0.194679	+	0.288748i
$305$	−6.29654	+	10.9059i	−0.360539	+	0.624472i
$306$	−17.1094	+	26.5966i	−0.978080	+	1.52043i
$307$	18.3542	+	18.3542i	1.04753	+	1.04753i	0.998813	+	0.0487150i	$0.0155126\pi$
$307$	18.3542	+	18.3542i	1.04753	+	1.04753i	0.0487150	+	0.998813i	$0.484487\pi$
$308$		0			0
$309$	5.40709	−	5.40709i	0.307598	−	0.307598i
$310$	1.55674	−	0.337920i	0.0884168	−	0.0191925i
$311$	−19.6457	−	11.3425i	−1.11401	−	0.643172i	−0.174142	−	0.984721i	$-0.555715\pi$
$311$	−19.6457	−	11.3425i	−1.11401	−	0.643172i	−0.939864	+	0.341549i	$0.889049\pi$
$312$	27.8068	−	35.2619i	1.57425	−	1.99631i
$313$	−26.4395	+	15.2648i	−1.49445	+	0.862820i	−0.999980	−	0.00637592i	$-0.997970\pi$
$313$	−26.4395	+	15.2648i	−1.49445	+	0.862820i	−0.494468	+	0.869196i	$0.664637\pi$
$314$	17.3365	+	5.55040i	0.978354	+	0.313227i
$315$		0			0
$316$	3.07036	−	4.30358i	0.172722	−	0.242095i
$317$	−8.75652	+	32.6798i	−0.491815	+	1.83548i	0.0553676	+	0.998466i	$0.482367\pi$
$317$	−8.75652	+	32.6798i	−0.491815	+	1.83548i	−0.547183	+	0.837013i	$0.684300\pi$
$318$	1.28885	−	26.8043i	0.0722751	−	1.50311i
$319$	13.7558	−	23.8257i	0.770175	−	1.33398i
$320$	−6.28466	−	3.85384i	−0.351323	−	0.215436i
$321$	−34.5637			−1.92916
$322$		0			0
$323$	3.02190	+	3.02190i	0.168143	+	0.168143i
$324$	60.2416	+	5.80670i	3.34676	+	0.322594i
$325$	−5.15620	−	19.2432i	−0.286014	−	1.06742i
$326$	11.1369	−	10.1150i	0.616815	−	0.560219i
$327$	36.2233	−	20.9135i	2.00315	−	1.15652i
$328$	14.2845	+	2.07335i	0.788731	+	0.114481i
$329$		0			0
$330$	4.43855	−	13.8636i	0.244334	−	0.763168i
$331$	0.514908	+	0.137969i	0.0283019	+	0.00758348i	0.272942	−	0.962030i	$-0.412003\pi$
$331$	0.514908	+	0.137969i	0.0283019	+	0.00758348i	−0.244640	+	0.969614i	$0.578670\pi$
$332$	−6.16921	+	16.4953i	−0.338579	+	0.905295i
$333$	74.6881	−	20.0126i	4.09288	−	1.09668i
$334$	10.1887	−	15.8383i	0.557499	−	0.866635i
$335$	−1.24403			−0.0679684
$336$		0			0
$337$	−6.66419			−0.363021			−0.181511	−	0.983389i	$-0.558099\pi$
$337$	−6.66419			−0.363021			−0.181511	+	0.983389i	$0.558099\pi$
$338$	−7.67852	+	11.9363i	−0.417657	+	0.649249i
$339$	13.1147	−	3.51408i	0.712294	−	0.190859i
$340$	−4.86004	−	1.81765i	−0.263573	−	0.0985758i
$341$	3.98673	+	1.06824i	0.215894	+	0.0578485i
$342$	5.19911	−	16.2392i	0.281136	−	0.878117i
$343$		0			0
$344$	−6.05733	−	8.11429i	−0.326589	−	0.437493i
$345$	12.0162	−	6.93754i	0.646929	−	0.373504i
$346$	7.67164	−	6.96772i	0.412430	−	0.374587i
$347$	4.79283	+	17.8871i	0.257293	+	0.960230i	0.966801	+	0.255532i	$0.0822507\pi$
$347$	4.79283	+	17.8871i	0.257293	+	0.960230i	−0.709508	+	0.704698i	$0.751083\pi$
$348$	−5.17195	+	53.6564i	−0.277246	+	2.87629i
$349$	21.2584	+	21.2584i	1.13794	+	1.13794i	0.988820	+	0.149116i	$0.0476427\pi$
$349$	21.2584	+	21.2584i	1.13794	+	1.13794i	0.149116	+	0.988820i	$0.452357\pi$
$350$		0			0
$351$	−78.4775			−4.18882
$352$	−9.90498	−	16.3321i	−0.527937	−	0.870505i
$353$	12.7092	−	22.0129i	0.676440	−	1.17163i	−0.299605	−	0.954063i	$-0.596855\pi$
$353$	12.7092	−	22.0129i	0.676440	−	1.17163i	0.976046	−	0.217566i	$-0.0698117\pi$
$354$	0.629050	−	13.0824i	0.0334336	−	0.695323i
$355$	0.165930	−	0.619258i	0.00880663	−	0.0328668i
$356$	−9.75211	−	6.95759i	−0.516861	−	0.368751i
$357$		0			0
$358$	17.3459	+	5.55342i	0.916759	+	0.293507i
$359$	21.7293	−	12.5454i	1.14683	−	0.662121i	0.198715	−	0.980057i	$-0.436323\pi$
$359$	21.7293	−	12.5454i	1.14683	−	0.662121i	0.948112	+	0.317937i	$0.102990\pi$
$360$	2.43026	+	20.5596i	0.128086	+	1.08359i
$361$	14.4590	+	8.34788i	0.760998	+	0.439362i
$362$	4.30122	−	0.933661i	0.226067	−	0.0490721i
$363$	0.939063	−	0.939063i	0.0492880	−	0.0492880i
$364$		0			0
$365$	0.207385	+	0.207385i	0.0108550	+	0.0108550i
$366$	34.5874	−	53.7661i	1.80791	−	2.81040i
$367$	18.1378	−	31.4156i	0.946786	−	1.63988i	0.194649	−	0.980873i	$-0.437643\pi$
$367$	18.1378	−	31.4156i	0.946786	−	1.63988i	0.752136	−	0.659008i	$-0.229024\pi$
$368$	3.47752	−	17.8712i	0.181278	−	0.931601i
$369$	−20.2672	−	35.1039i	−1.05507	−	1.82744i
$370$	5.80838	+	11.2791i	0.301963	+	0.586370i
$371$		0			0
$372$	−7.97624	+	1.33394i	−0.413549	+	0.0691618i
$373$	18.5810	+	4.97877i	0.962090	+	0.257791i	0.705485	−	0.708725i	$-0.250729\pi$
$373$	18.5810	+	4.97877i	0.962090	+	0.257791i	0.256605	+	0.966516i	$0.417396\pi$
$374$	−9.03879	−	9.95193i	−0.467385	−	0.514602i
$375$	24.1580	+	13.9476i	1.24751	+	0.720252i
$376$	9.33526	−	3.72277i	0.481429	−	0.191987i
$377$		−	39.1054i		−	2.01403i
$378$		0			0
$379$	−3.27551	+	3.27551i	−0.168251	+	0.168251i	−0.786210	−	0.617959i	$-0.787960\pi$
$379$	−3.27551	+	3.27551i	−0.168251	+	0.168251i	0.617959	+	0.786210i	$0.287960\pi$
$380$	2.78478	+	0.268425i	0.142856	+	0.0137699i
$381$	−9.66440	+	2.58957i	−0.495122	+	0.132668i
$382$	−1.15734	+	24.0692i	−0.0592144	+	1.23149i
$383$	−1.55766	−	2.69794i	−0.0795926	−	0.137858i	0.823482	−	0.567343i	$-0.192029\pi$
$383$	−1.55766	−	2.69794i	−0.0795926	−	0.137858i	−0.903074	+	0.429485i	$0.858695\pi$
$384$	30.9283	+	21.0742i	1.57831	+	1.07544i
$385$		0			0
$386$	6.47887	−	3.33643i	0.329766	−	0.169820i
$387$	−7.35969	+	27.4668i	−0.374114	+	1.39621i
$388$	9.18130	+	20.1519i	0.466110	+	1.02306i
$389$	−4.45946	−	16.6429i	−0.226104	−	0.843830i	−0.981959	−	0.189092i	$-0.939446\pi$
$389$	−4.45946	−	16.6429i	−0.226104	−	0.843830i	0.755856	−	0.654738i	$-0.227221\pi$
$390$	−4.38922	−	20.2204i	−0.222257	−	1.02390i
$391$		−	12.8144i		−	0.648050i
$392$		0			0
$393$			28.3661i			1.43088i
$394$	19.3410	−	4.19833i	0.974386	−	0.211509i
$395$	−0.630445	−	2.35285i	−0.0317211	−	0.118385i
$396$	−18.7901	+	50.2410i	−0.944237	+	2.52471i
$397$	1.72489	−	6.43740i	0.0865700	−	0.323084i	−0.909037	−	0.416716i	$-0.863181\pi$
$397$	1.72489	−	6.43740i	0.0865700	−	0.323084i	0.995607	+	0.0936321i	$0.0298477\pi$
$398$	−3.52960	−	6.85399i	−0.176923	−	0.343560i
$399$		0			0
$400$	15.6997	−	5.40233i	0.784985	−	0.270116i
$401$	12.2403	+	21.2008i	0.611250	+	1.05872i	0.991030	+	0.133639i	$0.0426663\pi$
$401$	12.2403	+	21.2008i	0.611250	+	1.05872i	−0.379780	+	0.925077i	$0.624000\pi$
$402$	6.30816	+	0.303319i	0.314622	+	0.0151282i
$403$	5.66681	−	1.51842i	0.282284	−	0.0756377i
$404$	−2.08217	+	1.71605i	−0.103592	+	0.0853769i
$405$	19.7181	−	19.7181i	0.979802	−	0.979802i
$406$		0			0
$407$			32.8709i			1.62935i
$408$	24.2009	+	10.4018i	1.19812	+	0.514968i
$409$	6.08442	+	3.51284i	0.300855	+	0.173699i	0.642827	−	0.766011i	$-0.277761\pi$
$409$	6.08442	+	3.51284i	0.300855	+	0.173699i	−0.341972	+	0.939710i	$0.611095\pi$
$410$	4.92321	−	4.47148i	0.243140	−	0.220830i
$411$	−36.4722	−	9.77268i	−1.79904	−	0.482051i
$412$	−3.76355	−	2.68508i	−0.185417	−	0.132285i
$413$		0			0
$414$	−45.4546	+	23.4078i	−2.23397	+	1.15043i
$415$	4.05727	+	7.02739i	0.199163	+	0.344961i
$416$	−23.8002	−	13.0650i	−1.16690	−	0.640565i
$417$	−30.5003	+	52.8281i	−1.49361	+	2.58700i
$418$	6.09622	+	3.92165i	0.298176	+	0.191814i
$419$	−11.6163	−	11.6163i	−0.567496	−	0.567496i	0.363931	−	0.931426i	$-0.381435\pi$
$419$	−11.6163	−	11.6163i	−0.567496	−	0.567496i	−0.931426	+	0.363931i	$0.881435\pi$
$420$		0			0
$421$	19.5555	−	19.5555i	0.953078	−	0.953078i	−0.0458696	−	0.998947i	$-0.514606\pi$
$421$	19.5555	−	19.5555i	0.953078	−	0.953078i	0.998947	+	0.0458696i	$0.0146059\pi$
$422$	−0.768952	−	3.54243i	−0.0374320	−	0.172443i
$423$	−24.4420	−	14.1116i	−1.18841	−	0.686129i
$424$	−16.1123	+	1.90457i	−0.782483	+	0.0924939i
$425$	10.1203	−	5.84298i	0.490908	−	0.283426i
$426$	−0.992377	+	3.09965i	−0.0480808	+	0.150179i
$427$		0			0
$428$	3.44694	+	20.6108i	0.166614	+	0.996261i
$429$	13.8753	−	51.7835i	0.669908	−	2.50013i
$430$	−4.66021	−	0.224080i	−0.224736	−	0.0108061i
$431$	15.7271	−	27.2401i	0.757548	−	1.31211i	−0.186550	−	0.982445i	$-0.559731\pi$
$431$	15.7271	−	27.2401i	0.757548	−	1.31211i	0.944098	−	0.329666i	$-0.106936\pi$
$432$	−4.54928	−	65.2455i	−0.218877	−	3.13912i
$433$	−8.42081			−0.404679			−0.202339	−	0.979315i	$-0.564854\pi$
$433$	−8.42081			−0.404679			−0.202339	+	0.979315i	$0.564854\pi$
$434$		0			0
$435$	17.5627	+	17.5627i	0.842066	+	0.842066i
$436$	−16.0835	−	19.5148i	−0.770258	−	0.934588i
$437$	1.78823	+	6.67377i	0.0855427	+	0.319250i
$438$	−1.00103	−	1.10216i	−0.0478313	−	0.0526634i
$439$	23.1802	−	13.3831i	1.10633	−	0.638739i	0.168453	−	0.985710i	$-0.446123\pi$
$439$	23.1802	−	13.3831i	1.10633	−	0.638739i	0.937876	+	0.346970i	$0.112790\pi$
$440$	−8.70971	−	1.26418i	−0.415219	−	0.0602676i
$441$		0			0
$442$	−18.1995	−	5.82671i	−0.865663	−	0.277149i
$443$	−37.6048	−	10.0762i	−1.78666	−	0.478734i	−0.794887	−	0.606757i	$-0.792470\pi$
$443$	−37.6048	−	10.0762i	−1.78666	−	0.478734i	−0.991771	+	0.128023i	$0.959137\pi$
$444$	−26.7029	−	58.6096i	−1.26726	−	2.78149i
$445$	−5.33167	+	1.42862i	−0.252745	+	0.0677229i
$446$	23.4308	+	15.0728i	1.10948	+	0.713719i
$447$	4.99434			0.236224
$448$		0			0
$449$	−11.4353			−0.539666			−0.269833	−	0.962907i	$-0.586969\pi$
$449$	−11.4353			−0.539666			−0.269833	+	0.962907i	$0.586969\pi$
$450$	−39.2126	−	25.2252i	−1.84850	−	1.18913i
$451$	16.6445	−	4.45989i	0.783761	−	0.210008i
$452$	−3.40339	−	7.47003i	−0.160082	−	0.351361i
$453$	−55.4647	−	14.8617i	−2.60596	−	0.698265i
$454$	−36.0161	−	11.5308i	−1.69032	−	0.541168i
$455$		0			0
$456$	−14.0555	−	2.04010i	−0.658209	−	0.0955367i
$457$	−3.73653	+	2.15729i	−0.174788	+	0.100914i	−0.584841	−	0.811148i	$-0.698843\pi$
$457$	−3.73653	+	2.15729i	−0.174788	+	0.100914i	0.410054	+	0.912061i	$0.365510\pi$
$458$	8.66265	+	9.53780i	0.404779	+	0.445672i
$459$	−11.9144	−	44.4652i	−0.556117	−	2.07546i
$460$	−5.33529	−	6.47354i	−0.248759	−	0.301830i
$461$	−11.9675	−	11.9675i	−0.557383	−	0.557383i	0.371178	−	0.928562i	$-0.378954\pi$
$461$	−11.9675	−	11.9675i	−0.557383	−	0.557383i	−0.928562	+	0.371178i	$0.878954\pi$
$462$		0			0
$463$	17.1701			0.797961			0.398981	−	0.916959i	$-0.369364\pi$
$463$	17.1701			0.797961			0.398981	+	0.916959i	$0.369364\pi$
$464$	32.5118	−	2.26691i	1.50932	−	0.105239i
$465$	−1.86309	+	3.22697i	−0.0863988	+	0.149647i
$466$	−14.3576	−	0.690364i	−0.665102	−	0.0319805i
$467$	−9.25715	+	34.5481i	−0.428370	+	1.59870i	0.328083	+	0.944649i	$0.393597\pi$
$467$	−9.25715	+	34.5481i	−0.428370	+	1.59870i	−0.756453	+	0.654048i	$0.773069\pi$
$468$	12.5764	+	75.2001i	0.581346	+	3.47613i
$469$		0			0
$470$	1.41197	−	4.41022i	0.0651291	−	0.203428i
$471$	−36.8749	+	21.2897i	−1.69911	+	0.980980i
$472$	−7.86396	+	0.929564i	−0.361968	+	0.0427866i
$473$	−10.4688	−	6.04417i	−0.481357	−	0.277911i
$474$	2.62316	+	12.0845i	0.120486	+	0.555058i
$475$	−4.45533	+	4.45533i	−0.204424	+	0.204424i
$476$		0			0
$477$	32.2172	+	32.2172i	1.47512	+	1.47512i
$478$	27.9384	+	17.9725i	1.27787	+	0.822045i
$479$	7.23016	−	12.5230i	0.330354	−	0.572191i	−0.652227	−	0.758024i	$-0.726165\pi$
$479$	7.23016	−	12.5230i	0.330354	−	0.572191i	0.982581	+	0.185833i	$0.0594984\pi$
$480$	16.5566	−	4.82132i	0.755703	−	0.220062i
$481$	23.3616	+	40.4635i	1.06520	+	1.84498i
$482$	−5.43004	+	2.79631i	−0.247332	+	0.127368i
$483$		0			0
$484$	−0.653626	−	0.466326i	−0.0297103	−	0.0211966i
$485$	9.85581	+	2.64086i	0.447529	+	0.119915i
$486$	−53.4414	+	48.5379i	−2.42415	+	2.20172i
$487$	22.4507	+	12.9619i	1.01734	+	0.587360i	0.913332	−	0.407216i	$-0.133500\pi$
$487$	22.4507	+	12.9619i	1.01734	+	0.587360i	0.104006	+	0.994577i	$0.466834\pi$
$488$	−35.5108	−	15.2630i	−1.60750	−	0.690921i
$489$			35.1912i			1.59140i
$490$		0			0
$491$	−7.59186	+	7.59186i	−0.342616	+	0.342616i	−0.857350	−	0.514734i	$-0.827891\pi$
$491$	−7.59186	+	7.59186i	−0.342616	+	0.342616i	0.514734	+	0.857350i	$0.327891\pi$
$492$	−26.0546	+	21.4734i	−1.17463	+	0.968096i
$493$	22.1570	−	5.93695i	0.997901	−	0.267387i
$494$	10.2915	+	0.494852i	0.463036	+	0.0222644i
$495$	12.3576	+	21.4039i	0.555431	+	0.962035i
$496$	1.59090	+	4.62331i	0.0714334	+	0.207593i
$497$		0			0
$498$	−18.8600	−	36.6235i	−0.845137	−	1.64114i
$499$	−4.19091	+	15.6407i	−0.187611	+	0.700174i	0.806446	+	0.591308i	$0.201388\pi$
$499$	−4.19091	+	15.6407i	−0.187611	+	0.700174i	−0.994057	+	0.108865i	$0.965278\pi$
$500$	5.90794	−	15.7967i	0.264211	−	0.706449i
$501$	11.4013	+	42.5502i	0.509372	+	1.90100i
$502$	−16.7559	+	3.63719i	−0.747854	+	0.162336i
$503$			15.2856i			0.681550i	0.940145	+	0.340775i	$0.110690\pi$
$503$			15.2856i			0.681550i	−0.940145	+	0.340775i	$0.889310\pi$
$504$		0			0
$505$			1.24322i			0.0553227i
$506$	−4.61062	−	21.2403i	−0.204967	−	0.944248i
$507$	−8.59239	−	32.0672i	−0.381601	−	1.42416i
$508$	2.50800	+	5.50476i	0.111274	+	0.244234i
$509$	−0.864527	+	3.22646i	−0.0383195	+	0.143010i	−0.982435	−	0.186604i	$-0.940252\pi$
$509$	−0.864527	+	3.22646i	−0.0383195	+	0.143010i	0.944116	+	0.329614i	$0.106919\pi$
$510$	10.7905	−	5.55677i	0.477810	−	0.246058i
$511$		0			0
$512$	9.48244	−	20.5447i	0.419069	−	0.907954i
$513$	12.4101	+	21.4950i	0.547921	+	0.949027i
$514$	−0.791091	+	16.4524i	−0.0348935	+	0.725685i
$515$	−2.05761	+	0.551334i	−0.0906690	+	0.0242947i
$516$	23.5762	+	2.27251i	1.03788	+	0.100042i
$517$	8.48387	−	8.48387i	0.373120	−	0.373120i
$518$		0			0
$519$			24.2415i			1.06408i
$520$	−11.6200	+	4.63388i	−0.509569	+	0.203209i
$521$	28.6924	+	16.5655i	1.25704	+	0.725750i	0.972497	−	0.232915i	$-0.0748265\pi$
$521$	28.6924	+	16.5655i	1.25704	+	0.725750i	0.284538	+	0.958665i	$0.408160\pi$
$522$	−61.5331	−	67.7495i	−2.69323	−	2.96531i
$523$	23.5450	+	6.30888i	1.02955	+	0.275868i	0.733778	−	0.679390i	$-0.237755\pi$
$523$	23.5450	+	6.30888i	1.02955	+	0.275868i	0.295775	+	0.955258i	$0.404422\pi$
$524$	16.9151	−	2.82888i	0.738939	−	0.123580i
$525$		0			0
$526$	−4.25416	−	8.26098i	−0.185490	−	0.360196i
$527$	1.72066	+	2.98027i	0.0749532	+	0.129823i
$528$	43.8566	+	8.53398i	1.90862	+	0.371394i
$529$	−1.14146	+	1.97707i	−0.0496288	+	0.0859596i
$530$	−4.04443	+	6.28708i	−0.175679	+	0.273093i
$531$	15.7243	+	15.7243i	0.682376	+	0.682376i
$532$		0			0
$533$	17.3195	−	17.3195i	0.750189	−	0.750189i
$534$	27.3839	−	5.94420i	1.18502	−	0.257231i
$535$	8.33856	+	4.81427i	0.360508	+	0.208139i
$536$	−0.448222	−	3.79189i	−0.0193602	−	0.163785i
$537$	−36.8950	+	21.3013i	−1.59213	+	0.919219i
$538$	−39.2756	−	12.5744i	−1.69329	−	0.542120i
$539$		0			0
$540$	−24.5321	−	17.5023i	−1.05569	−	0.753178i
$541$	5.36693	−	20.0296i	0.230742	−	0.861142i	−0.749280	−	0.662253i	$-0.769600\pi$
$541$	5.36693	−	20.0296i	0.230742	−	0.861142i	0.980022	−	0.198888i	$-0.0637331\pi$
$542$	0.970105	−	20.1754i	0.0416696	−	0.866607i
$543$	−5.14766	+	8.91602i	−0.220907	+	0.382623i
$544$	3.78926	−	15.4687i	0.162463	−	0.663214i
$545$	−11.6519			−0.499113
$546$		0			0
$547$	−16.8729	−	16.8729i	−0.721432	−	0.721432i	0.247465	−	0.968897i	$-0.420403\pi$
$547$	−16.8729	−	16.8729i	−0.721432	−	0.721432i	−0.968897	+	0.247465i	$0.920403\pi$
$548$	−2.19031	+	22.7234i	−0.0935656	+	0.970697i
$549$	28.0931	+	104.845i	1.19898	+	4.47467i
$550$	14.6726	−	13.3263i	0.625641	−	0.568235i
$551$	−10.7110	+	6.18397i	−0.456302	+	0.263446i
$552$	25.4756	+	34.1266i	1.08431	+	1.45253i
$553$		0			0
$554$	−0.295512	+	0.923019i	−0.0125551	+	0.0392153i
$555$	−28.6646	−	7.68065i	−1.21674	−	0.326026i
$556$	34.5438	+	12.9193i	1.46498	+	0.547902i
$557$	−9.58919	+	2.56941i	−0.406307	+	0.108870i	−0.456183	−	0.889886i	$-0.650784\pi$
$557$	−9.58919	+	2.56941i	−0.406307	+	0.108870i	0.0498765	+	0.998755i	$0.484117\pi$
$558$	7.42840	−	11.5475i	0.314469	−	0.488844i
$559$	−17.1826			−0.726746
$560$		0			0
$561$	31.4469			1.32769
$562$	0.341716	−	0.531199i	0.0144144	−	0.0224073i
$563$	−27.4777	+	7.36264i	−1.15805	+	0.310298i	−0.786186	−	0.617990i	$-0.787947\pi$
$563$	−27.4777	+	7.36264i	−1.15805	+	0.310298i	−0.371862	+	0.928288i	$0.621281\pi$
$564$	−8.23504	+	22.0189i	−0.346758	+	0.927163i
$565$	−3.65342	−	0.978930i	−0.153700	−	0.0411839i
$566$	−11.7372	+	36.6607i	−0.493351	+	1.54096i
$567$		0			0
$568$	1.94733	+	0.282648i	0.0817082	+	0.0118596i
$569$	−12.6659	+	7.31263i	−0.530980	+	0.306562i	−0.741415	−	0.671046i	$-0.765845\pi$
$569$	−12.6659	+	7.31263i	−0.530980	+	0.306562i	0.210435	+	0.977608i	$0.432512\pi$
$570$	−4.84427	+	4.39978i	−0.202904	+	0.184287i
$571$	−12.0466	−	44.9586i	−0.504135	−	1.88146i	−0.471254	−	0.881998i	$-0.656198\pi$
$571$	−12.0466	−	44.9586i	−0.504135	−	1.88146i	−0.0328809	−	0.999459i	$-0.510468\pi$
$572$	−32.2629	−	3.10983i	−1.34898	−	0.130028i
$573$	−39.8565	−	39.8565i	−1.66503	−	1.66503i
$574$		0			0
$575$	18.8928			0.787883
$576$	−61.7916	+	14.8152i	−2.57465	+	0.617301i
$577$	18.4484	−	31.9535i	0.768016	−	1.33024i	−0.170622	−	0.985337i	$-0.554578\pi$
$577$	18.4484	−	31.9535i	0.768016	−	1.33024i	0.938637	−	0.344905i	$-0.112089\pi$
$578$	−0.616311	+	12.8175i	−0.0256351	+	0.533137i
$579$	−4.41189	+	16.4654i	−0.183352	+	0.684278i
$580$	8.72138	−	12.2243i	0.362136	−	0.507588i
$581$		0			0
$582$	−49.3326	−	15.7942i	−2.04490	−	0.654691i
$583$	−16.7740	+	9.68448i	−0.694709	+	0.401090i
$584$	−0.557405	+	0.706846i	−0.0230656	+	0.0292495i
$585$	30.4239	+	17.5652i	1.25787	+	0.726234i
$586$	−4.36940	+	0.948461i	−0.180498	+	0.0391806i
$587$	12.3269	−	12.3269i	0.508786	−	0.508786i	−0.405368	−	0.914154i	$-0.632857\pi$
$587$	12.3269	−	12.3269i	0.508786	−	0.508786i	0.914154	+	0.405368i	$0.132857\pi$
$588$		0			0
$589$	−1.31202	−	1.31202i	−0.0540609	−	0.0540609i
$590$	−1.97397	+	3.06854i	−0.0812671	+	0.126330i
$591$	−23.1472	+	40.0920i	−0.952147	+	1.64917i
$592$	−32.2867	+	21.7683i	−1.32698	+	0.894670i
$593$	−7.68414	−	13.3093i	−0.315550	−	0.546548i	0.664004	−	0.747729i	$-0.268856\pi$
$593$	−7.68414	−	13.3093i	−0.315550	−	0.546548i	−0.979554	+	0.201180i	$0.935522\pi$
$594$	−35.7472	−	69.4161i	−1.46673	−	2.84818i
$595$		0			0
$596$	−0.498072	−	2.97819i	−0.0204018	−	0.121992i
$597$	17.4187	+	4.66733i	0.712901	+	0.191021i
$598$	−20.7713	−	22.8697i	−0.849401	−	0.935211i
$599$	11.8979	+	6.86923i	0.486133	+	0.280669i	0.722969	−	0.690881i	$-0.242777\pi$
$599$	11.8979	+	6.86923i	0.486133	+	0.280669i	−0.236836	+	0.971550i	$0.576110\pi$
$600$	−15.3359	+	35.6805i	−0.626085	+	1.45665i
$601$		−	19.3065i		−	0.787529i	−0.919211	−	0.393764i	$-0.871173\pi$
$601$		−	19.3065i		−	0.787529i	0.919211	−	0.393764i	$-0.128827\pi$
$602$		0			0
$603$	−7.58203	+	7.58203i	−0.308764	+	0.308764i
$604$	−3.33090	+	34.5565i	−0.135532	+	1.40608i
$605$	−0.357350	+	0.0957516i	−0.0145283	+	0.00389286i
$606$	0.303123	−	6.30409i	0.0123135	−	0.256086i
$607$	0.370114	+	0.641056i	0.0150225	+	0.0260197i	0.873439	−	0.486934i	$-0.161885\pi$
$607$	0.370114	+	0.641056i	0.0150225	+	0.0260197i	−0.858416	+	0.512953i	$0.828551\pi$
$608$	0.185174	+	8.58493i	0.00750982	+	0.348165i
$609$		0			0
$610$	−15.8332	+	8.15363i	−0.641067	+	0.330131i
$611$	4.41394	−	16.4731i	0.178569	−	0.666429i
$612$	−40.6988	+	18.5426i	−1.64515	+	0.749541i
$613$	−10.2043	−	38.0829i	−0.412147	−	1.53815i	−0.790482	−	0.612485i	$-0.790170\pi$
$613$	−10.2043	−	38.0829i	−0.412147	−	1.53815i	0.378335	−	0.925669i	$-0.376497\pi$
$614$	7.78689	+	35.8729i	0.314253	+	1.44771i
$615$			15.5568i			0.627309i
$616$		0			0
$617$		−	22.2077i		−	0.894049i	−0.894522	−	0.447025i	$-0.852484\pi$
$617$		−	22.2077i		−	0.894049i	0.894522	−	0.447025i	$-0.147516\pi$
$618$	10.5681	−	2.29400i	0.425110	−	0.0922781i
$619$	3.51954	+	13.1351i	0.141462	+	0.527944i	0.999887	+	0.0150051i	$0.00477647\pi$
$619$	3.51954	+	13.1351i	0.141462	+	0.527944i	−0.858425	+	0.512939i	$0.828557\pi$
$620$	2.11009	+	0.789170i	0.0847431	+	0.0316938i
$621$	19.2621	−	71.8872i	0.772962	−	2.88473i
$622$	−14.6878	−	28.5216i	−0.588926	−	1.14361i
$623$		0			0
$624$	60.0519	−	20.6641i	2.40400	−	0.827226i
$625$	6.49155	+	11.2437i	0.259662	+	0.449748i
$626$	−43.1257	−	2.07364i	−1.72365	−	0.0828792i
$627$	−16.3777	+	4.38839i	−0.654062	+	0.175255i
$628$	16.3728	+	19.8658i	0.653346	+	0.792734i
$629$	−19.3798	+	19.3798i	−0.772722	+	0.772722i
$630$		0			0
$631$		−	18.6771i		−	0.743522i	−0.928328	−	0.371761i	$-0.878754\pi$
$631$		−	18.6771i		−	0.743522i	0.928328	−	0.371761i	$-0.121246\pi$
$632$	6.94453	−	2.76938i	0.276238	−	0.110160i
$633$	7.34312	+	4.23955i	0.291863	+	0.168507i
$634$	−35.4185	+	32.1686i	−1.40665	+	1.27758i
$635$	2.69225	+	0.721386i	0.106839	+	0.0286273i
$636$	22.0413	−	30.8942i	0.873993	−	1.22503i
$637$		0			0
$638$	34.5901	−	17.8129i	1.36943	−	0.705218i
$639$	−2.76292	−	4.78552i	−0.109300	−	0.189312i
$640$	−4.52616	−	9.39211i	−0.178912	−	0.371256i
$641$	−16.0557	+	27.8093i	−0.634161	+	1.09840i	0.352531	+	0.935800i	$0.385321\pi$
$641$	−16.0557	+	27.8093i	−0.634161	+	1.09840i	−0.986692	+	0.162599i	$0.948012\pi$
$642$	−41.1091	−	26.4451i	−1.62244	−	1.04371i
$643$	14.5428	+	14.5428i	0.573511	+	0.573511i	0.933108	−	0.359597i	$-0.117086\pi$
$643$	14.5428	+	14.5428i	0.573511	+	0.573511i	−0.359597	+	0.933108i	$0.617086\pi$
$644$		0			0
$645$	7.71690	−	7.71690i	0.303853	−	0.303853i
$646$	1.28207	+	5.90626i	0.0504422	+	0.232379i
$647$	7.40420	+	4.27482i	0.291089	+	0.168060i	0.638433	−	0.769677i	$-0.279583\pi$
$647$	7.40420	+	4.27482i	0.291089	+	0.168060i	−0.347344	+	0.937738i	$0.612916\pi$
$648$	67.2069	+	52.9980i	2.64013	+	2.08196i
$649$	−8.18691	+	4.72672i	−0.321365	+	0.185540i
$650$	8.59058	−	26.8324i	0.336950	−	1.05245i
$651$		0			0
$652$	20.9850	−	3.50953i	0.821836	−	0.137444i
$653$	−5.00948	+	18.6956i	−0.196036	+	0.731616i	0.795960	+	0.605349i	$0.206966\pi$
$653$	−5.00948	+	18.6956i	−0.196036	+	0.731616i	−0.991996	+	0.126267i	$0.959700\pi$
$654$	59.0841	+	2.84098i	2.31037	+	0.111091i
$655$	3.95103	−	6.84338i	0.154379	−	0.267393i
$656$	15.4032	+	13.3952i	0.601395	+	0.522996i
$657$	2.52792			0.0986235
$658$		0			0
$659$	6.00059	+	6.00059i	0.233750	+	0.233750i	0.814256	−	0.580506i	$-0.197145\pi$
$659$	6.00059	+	6.00059i	0.233750	+	0.233750i	−0.580506	+	0.814256i	$0.697145\pi$
$660$	15.8863	−	13.0930i	0.618374	−	0.509644i
$661$	−11.2691	−	42.0568i	−0.438316	−	1.63582i	−0.733003	−	0.680225i	$-0.761882\pi$
$661$	−11.2691	−	42.0568i	−0.438316	−	1.63582i	0.294687	−	0.955594i	$-0.404785\pi$
$662$	0.506855	+	0.558060i	0.0196995	+	0.0216896i
$663$	38.7106	−	22.3496i	1.50340	−	0.867986i
$664$	−19.9582	+	14.8988i	−0.774529	+	0.578187i
$665$		0			0
$666$	104.144	+	33.3424i	4.03549	+	1.29199i
$667$	35.8214	+	9.59832i	1.38701	+	0.371648i
$668$	24.2362	−	11.0421i	0.937727	−	0.427234i
$669$	−62.9475	+	16.8667i	−2.43369	+	0.652105i
$670$	−1.47961	−	0.951820i	−0.0571622	−	0.0367720i
$671$	−46.1431			−1.78133
$672$		0			0
$673$	−11.6027			−0.447253			−0.223626	−	0.974675i	$-0.571790\pi$
$673$	−11.6027			−0.447253			−0.223626	+	0.974675i	$0.571790\pi$
$674$	−7.92619	−	5.09886i	−0.305305	−	0.196401i
$675$	65.5570	−	17.5659i	2.52329	−	0.676113i
$676$	−18.2652	+	8.32173i	−0.702508	+	0.320067i
$677$	21.1070	+	5.65560i	0.811207	+	0.217362i	0.640499	−	0.767959i	$-0.278728\pi$
$677$	21.1070	+	5.65560i	0.811207	+	0.217362i	0.170708	+	0.985322i	$0.445394\pi$
$678$	18.2869	+	5.85470i	0.702305	+	0.224848i
$679$		0			0
$680$	−4.38968	−	5.88033i	−0.168337	−	0.225501i
$681$	76.6067	−	44.2289i	2.93558	−	1.69486i
$682$	3.92438	+	4.32084i	0.150272	+	0.165453i
$683$	−7.79300	−	29.0839i	−0.298191	−	1.11286i	−0.938650	−	0.344872i	$-0.887922\pi$
$683$	−7.79300	−	29.0839i	−0.298191	−	1.11286i	0.640459	−	0.767992i	$-0.278744\pi$
$684$	18.6085	−	15.3365i	0.711514	−	0.586407i
$685$	7.43777	+	7.43777i	0.284183	+	0.284183i
$686$		0			0
$687$	−30.1383			−1.14985
$688$	−0.996061	−	14.2854i	−0.0379745	−	0.544627i
$689$	−13.7657	+	23.8429i	−0.524431	+	0.908341i
$690$	19.5997	+	0.942423i	0.746147	+	0.0358774i
$691$	11.6040	−	43.3069i	0.441439	−	1.64747i	−0.283733	−	0.958903i	$-0.591573\pi$
$691$	11.6040	−	43.3069i	0.441439	−	1.64747i	0.725171	−	0.688568i	$-0.241760\pi$
$692$	14.4555	−	2.41754i	0.549516	−	0.0919009i
$693$		0			0
$694$	−7.98520	+	24.9414i	−0.303114	+	0.946764i
$695$	14.7165	−	8.49658i	0.558229	−	0.322294i
$696$	−47.2046	+	59.8603i	−1.78929	+	2.26900i
$697$	12.4426	+	7.18374i	0.471297	+	0.272103i
$698$	9.01903	+	41.5492i	0.341375	+	1.57266i
$699$	23.7749	−	23.7749i	0.899248	−	0.899248i
$700$		0			0
$701$	−23.8599	−	23.8599i	−0.901177	−	0.901177i	0.0943615	−	0.995538i	$-0.469919\pi$
$701$	−23.8599	−	23.8599i	−0.901177	−	0.901177i	−0.995538	+	0.0943615i	$0.969919\pi$
$702$	−93.3388	−	60.0442i	−3.52285	−	2.26622i
$703$	7.38863	−	12.7975i	0.278667	−	0.482666i
$704$	0.715223	−	27.0034i	0.0269560	−	1.01773i
$705$	5.41589	+	9.38060i	0.203974	+	0.353294i
$706$	31.9583	−	16.4576i	1.20277	−	0.619389i
$707$		0			0
$708$	10.7577	−	15.0786i	0.404299	−	0.566687i
$709$	−24.4726	−	6.55740i	−0.919086	−	0.246268i	−0.231892	−	0.972742i	$-0.574491\pi$
$709$	−24.4726	−	6.55740i	−0.919086	−	0.246268i	−0.687195	+	0.726473i	$0.741158\pi$
$710$	0.671154	−	0.609572i	0.0251880	−	0.0228768i
$711$	−18.1825	−	10.4976i	−0.681895	−	0.393692i
$712$	−6.27553	−	15.7366i	−0.235186	−	0.589755i
$713$			5.56362i			0.208359i
$714$		0			0
$715$	−10.5602	+	10.5602i	−0.394930	+	0.394930i
$716$	16.3817	+	19.8766i	0.612213	+	0.742825i
$717$	−75.0573	+	20.1116i	−2.80307	+	0.751080i
$718$	35.4428	+	1.70422i	1.32271	+	0.0636008i
$719$	3.53018	+	6.11446i	0.131654	+	0.228031i	0.924314	−	0.381632i	$-0.124638\pi$
$719$	3.53018	+	6.11446i	0.131654	+	0.228031i	−0.792660	+	0.609663i	$0.791305\pi$
$720$	−12.8399	+	26.3124i	−0.478516	+	0.980605i
$721$		0			0
$722$	10.8100	+	20.9915i	0.402306	+	0.781221i
$723$	3.69767	−	13.7999i	0.137518	−	0.513224i
$724$	5.83010	+	2.18045i	0.216674	+	0.0810358i
$725$	8.75311	+	32.6671i	0.325082	+	1.21322i
$726$	1.83538	−	0.398405i	0.0681175	−	0.0147862i
$727$			11.9751i			0.444132i	0.975032	+	0.222066i	$0.0712801\pi$
$727$			11.9751i			0.444132i	−0.975032	+	0.222066i	$0.928720\pi$
$728$		0			0
$729$		−	78.0873i		−	2.89212i
$730$	0.0879846	+	0.405330i	0.00325646	+	0.0150019i
$731$	−2.60865	−	9.73561i	−0.0964843	−	0.360084i
$732$	82.2744	−	37.4846i	3.04095	−	1.38547i
$733$	−5.12993	+	19.1451i	−0.189478	+	0.707142i	0.804149	+	0.594427i	$0.202621\pi$
$733$	−5.12993	+	19.1451i	−0.189478	+	0.707142i	−0.993627	+	0.112715i	$0.964045\pi$
$734$	45.6090	−	23.4873i	1.68346	−	0.866933i
$735$		0			0
$736$	17.8096	−	18.5948i	0.656469	−	0.685413i
$737$	−2.27915	−	3.94761i	−0.0839537	−	0.145412i
$738$	2.75318	−	57.2583i	0.101346	−	2.10771i
$739$	40.5335	−	10.8609i	1.49105	−	0.399525i	0.580957	−	0.813934i	$-0.302678\pi$
$739$	40.5335	−	10.8609i	1.49105	−	0.399525i	0.910091	+	0.414409i	$0.136012\pi$
$740$	−1.72144	+	17.8591i	−0.0632812	+	0.656512i
$741$	−17.0418	+	17.0418i	−0.626046	+	0.626046i
$742$		0			0
$743$		−	3.76555i		−	0.138145i	−0.997612	−	0.0690723i	$-0.977996\pi$
$743$		−	3.76555i		−	0.138145i	0.997612	−	0.0690723i	$-0.0220039\pi$
$744$	−10.5073	−	4.51617i	−0.385217	−	0.165571i
$745$	−1.20489	−	0.695646i	−0.0441439	−	0.0254865i
$746$	18.2904	+	20.1382i	0.669660	+	0.737312i
$747$	67.5582	+	18.1022i	2.47183	+	0.662324i
$748$	−3.13612	−	18.7522i	−0.114668	−	0.685649i
$749$		0			0
$750$	18.0613	+	35.0725i	0.659505	+	1.28067i
$751$	−15.8009	−	27.3680i	−0.576583	−	0.998671i	−0.995868	−	0.0908164i	$-0.971052\pi$
$751$	−15.8009	−	27.3680i	−0.576583	−	0.998671i	0.419285	−	0.907855i	$-0.362281\pi$
$752$	13.9514	+	2.71478i	0.508756	+	0.0989979i
$753$	20.0534	−	34.7334i	0.730785	−	1.26576i
$754$	29.9200	−	46.5108i	1.08962	−	1.69382i
$755$	11.3109	+	11.3109i	0.411647	+	0.411647i
$756$		0			0
$757$	−17.1747	+	17.1747i	−0.624224	+	0.624224i	−0.946609	−	0.322384i	$-0.895516\pi$
$757$	−17.1747	+	17.1747i	−0.624224	+	0.624224i	0.322384	+	0.946609i	$0.395516\pi$
$758$	−6.40192	+	1.38966i	−0.232528	+	0.0504747i
$759$	44.0292	+	25.4203i	1.59816	+	0.922697i
$760$	3.10676	+	2.44993i	0.112694	+	0.0888681i
$761$	15.9240	−	9.19373i	0.577245	−	0.333273i	−0.182793	−	0.983151i	$-0.558514\pi$
$761$	15.9240	−	9.19373i	0.577245	−	0.333273i	0.760038	+	0.649879i	$0.225180\pi$
$762$	−13.4759	−	4.31440i	−0.488179	−	0.156294i
$763$		0			0
$764$	−19.7922	+	27.7417i	−0.716056	+	1.00366i
$765$	−5.33349	+	19.9048i	−0.192833	+	0.719661i
$766$	0.211598	−	4.40064i	0.00764536	−	0.159001i
$767$	−6.71864	+	11.6370i	−0.242596	+	0.420188i
$768$	20.6611	+	48.7287i	0.745543	+	1.75835i
$769$	19.7886			0.713594			0.356797	−	0.934182i	$-0.383869\pi$
$769$	19.7886			0.713594			0.356797	+	0.934182i	$0.383869\pi$
$770$		0			0
$771$	−27.2437	−	27.2437i	−0.981158	−	0.981158i
$772$	10.2585	+	0.988819i	0.369212	+	0.0355884i
$773$	−6.43198	−	24.0045i	−0.231342	−	0.863381i	−0.979764	−	0.200158i	$-0.935855\pi$
$773$	−6.43198	−	24.0045i	−0.231342	−	0.863381i	0.748421	−	0.663224i	$-0.230812\pi$
$774$	−29.7686	+	27.0371i	−1.07001	+	0.971830i
$775$	−4.39395	+	2.53685i	−0.157835	+	0.0911263i
$776$	−4.49849	+	30.9928i	−0.161486	+	1.11258i
$777$		0			0
$778$	7.42977	−	23.2066i	0.266370	−	0.831997i
$779$	−7.48263	−	2.00497i	−0.268093	−	0.0718354i
$780$	10.2505	−	27.4078i	0.367026	−	0.981357i
$781$	2.26906	−	0.607993i	0.0811934	−	0.0217557i
$782$	9.80443	−	15.2410i	0.350606	−	0.545018i
$783$	133.223			4.76099
$784$		0			0
$785$	11.8615			0.423356
$786$	−21.7033	+	33.7378i	−0.774131	+	1.20339i
$787$	−35.1235	+	9.41132i	−1.25202	+	0.335477i	−0.823116	−	0.567874i	$-0.807766\pi$
$787$	−35.1235	+	9.41132i	−1.25202	+	0.335477i	−0.428902	+	0.903351i	$0.641100\pi$
$788$	26.2158	+	9.80469i	0.933900	+	0.349278i
$789$	20.9944	+	5.62544i	0.747422	+	0.200271i
$790$	1.05036	−	3.28077i	0.0373703	−	0.116725i
$791$		0			0
$792$	−60.7884	+	45.3787i	−2.16002	+	1.61246i
$793$	−56.8014	+	32.7943i	−2.01708	+	1.16456i
$794$	6.97687	−	6.33671i	0.247600	−	0.224881i
$795$	−4.52578	−	16.8904i	−0.160513	−	0.599042i
$796$	1.04607	−	10.8525i	0.0370770	−	0.384656i
$797$	2.26883	+	2.26883i	0.0803660	+	0.0803660i	0.746147	−	0.665781i	$-0.231902\pi$
$797$	2.26883	+	2.26883i	0.0803660	+	0.0803660i	−0.665781	+	0.746147i	$0.731902\pi$
$798$		0			0
$799$	10.0037			0.353906
$800$	22.8062	+	5.58668i	0.806319	+	0.197519i
$801$	−23.7881	+	41.2023i	−0.840513	+	1.45581i
$802$	−1.66277	+	34.5808i	−0.0587144	+	1.22109i
$803$	−0.278140	+	1.03803i	−0.00981533	+	0.0366313i
$804$	7.27066	+	5.18721i	0.256416	+	0.182939i
$805$		0			0
$806$	7.90170	+	2.52979i	0.278325	+	0.0891080i
$807$	83.5398	−	48.2317i	2.94074	−	1.69784i
$808$	−3.78944	+	0.447933i	−0.133312	+	0.0157582i
$809$	4.56022	+	2.63285i	0.160329	+	0.0925660i	0.578018	−	0.816024i	$-0.303826\pi$
$809$	4.56022	+	2.63285i	0.160329	+	0.0925660i	−0.417689	+	0.908590i	$0.637160\pi$
$810$	38.5388	−	8.36557i	1.35411	−	0.293936i
$811$	5.65233	−	5.65233i	0.198480	−	0.198480i	−0.600868	−	0.799348i	$-0.705178\pi$
$811$	5.65233	−	5.65233i	0.198480	−	0.198480i	0.799348	+	0.600868i	$0.205178\pi$
$812$		0			0
$813$	33.4086	+	33.4086i	1.17169	+	1.17169i
$814$	−25.1499	+	39.0956i	−0.881504	+	1.37030i
$815$	4.90168	−	8.48996i	0.171698	−	0.297390i
$816$	20.8253	+	30.8881i	0.729030	+	1.08130i
$817$	2.71719	+	4.70631i	0.0950624	+	0.164653i
$818$	4.54891	+	8.83333i	0.159049	+	0.308850i
$819$		0			0
$820$	9.27670	−	1.55143i	0.323956	−	0.0541784i
$821$	−23.5781	−	6.31772i	−0.822880	−	0.220490i	−0.177275	−	0.984161i	$-0.556728\pi$
$821$	−23.5781	−	6.31772i	−0.822880	−	0.220490i	−0.645605	+	0.763671i	$0.723395\pi$
$822$	−35.9017	−	39.5287i	−1.25222	−	1.37872i
$823$	−36.3975	−	21.0141i	−1.26874	−	0.732507i	−0.293990	−	0.955809i	$-0.594983\pi$
$823$	−36.3975	−	21.0141i	−1.26874	−	0.732507i	−0.974749	+	0.223302i	$0.928316\pi$
$824$	−2.42186	−	6.07310i	−0.0843697	−	0.211567i
$825$			46.3636i			1.61417i
$826$		0			0
$827$	−27.2304	+	27.2304i	−0.946892	+	0.946892i	−0.998659	−	0.0517667i	$-0.983515\pi$
$827$	−27.2304	+	27.2304i	−0.946892	+	0.946892i	0.0517667	+	0.998659i	$0.483515\pi$
$828$	−71.9719	−	6.93738i	−2.50120	−	0.241090i
$829$	2.10076	−	0.562897i	0.0729624	−	0.0195502i	−0.222153	−	0.975012i	$-0.571309\pi$
$829$	2.10076	−	0.562897i	0.0729624	−	0.0195502i	0.295116	+	0.955462i	$0.404642\pi$
$830$	−0.551155	+	11.4624i	−0.0191309	+	0.397867i
$831$	−1.13350	−	1.96328i	−0.0393206	−	0.0681053i
$832$	−18.3111	−	33.7490i	−0.634823	−	1.17004i
$833$		0			0
$834$	−76.6956	+	39.4960i	−2.65575	+	1.36763i
$835$	3.17610	−	11.8534i	0.109913	−	0.410202i
$836$	4.25016	+	9.32859i	0.146995	+	0.322636i
$837$	5.17289	+	19.3055i	0.178801	+	0.667295i
$838$	−4.92832	−	22.7040i	−0.170246	−	0.784295i
$839$			46.6490i			1.61050i	0.592934	+	0.805251i	$0.297969\pi$
$839$			46.6490i			1.61050i	−0.592934	+	0.805251i	$0.702031\pi$
$840$		0			0
$841$			37.3849i			1.28914i
$842$	38.2209	−	8.29658i	1.31718	−	0.285919i
$843$	0.382386	+	1.42708i	0.0131701	+	0.0491514i
$844$	1.79579	−	4.80160i	0.0618138	−	0.165278i
$845$	−2.39361	+	8.93309i	−0.0823428	+	0.307308i
$846$	−18.2736	−	35.4848i	−0.628260	−	1.21999i
$847$		0			0
$848$	−20.6207	−	10.0625i	−0.708119	−	0.345548i
$849$	−45.0205	−	77.9778i	−1.54510	−	2.67619i
$850$	16.5074	+	0.793733i	0.566198	+	0.0272248i
$851$	−42.7995	+	11.4681i	−1.46715	+	0.393121i
$852$	−3.55189	+	2.92735i	−0.121686	+	0.100289i
$853$	−19.5231	+	19.5231i	−0.668459	+	0.668459i	−0.957359	−	0.288900i	$-0.906710\pi$
$853$	−19.5231	+	19.5231i	−0.668459	+	0.668459i	0.288900	+	0.957359i	$0.406710\pi$
$854$		0			0
$855$		−	11.1108i		−	0.379981i
$856$	−11.6699	+	27.1512i	−0.398869	+	0.928008i
$857$	26.1805	+	15.1153i	0.894310	+	0.516330i	0.875350	−	0.483490i	$-0.160631\pi$
$857$	26.1805	+	15.1153i	0.894310	+	0.516330i	0.0189603	+	0.999820i	$0.493964\pi$
$858$	56.1231	−	50.9735i	1.91601	−	1.74021i
$859$	34.9840	+	9.37395i	1.19364	+	0.319835i	0.800324	−	0.599568i	$-0.204661\pi$
$859$	34.9840	+	9.37395i	1.19364	+	0.319835i	0.393316	+	0.919403i	$0.371328\pi$
$860$	−5.37128	−	3.83210i	−0.183159	−	0.130674i
$861$		0			0
$862$	39.5471	−	20.3656i	1.34698	−	0.693655i
$863$	9.69978	+	16.8005i	0.330185	+	0.571896i	0.982548	−	0.186010i	$-0.0595557\pi$
$863$	9.69978	+	16.8005i	0.330185	+	0.571896i	−0.652363	+	0.757906i	$0.726222\pi$
$864$	44.5094	−	81.0818i	1.51424	−	2.75846i
$865$	3.37652	−	5.84830i	0.114805	−	0.198848i
$866$	−10.0155	−	6.44287i	−0.340339	−	0.218938i
$867$	−21.2246	−	21.2246i	−0.720825	−	0.720825i
$868$		0			0
$869$	6.31118	−	6.31118i	0.214092	−	0.214092i
$870$	7.45110	+	34.3260i	0.252616	+	1.16376i
$871$	−5.61120	−	3.23963i	−0.190128	−	0.109771i
$872$	−4.19818	−	35.5160i	−0.142168	−	1.20272i
$873$	76.1641	−	43.9733i	2.57776	−	1.48827i
$874$	−2.97932	+	9.30578i	−0.100777	+	0.314773i
$875$		0			0
$876$	−0.347321	−	2.07679i	−0.0117349	−	0.0701681i
$877$	8.09195	−	30.1996i	0.273246	−	1.01977i	−0.683762	−	0.729705i	$-0.739657\pi$
$877$	8.09195	−	30.1996i	0.273246	−	1.01977i	0.957008	−	0.290062i	$-0.0936759\pi$
$878$	37.8094	+	1.81801i	1.27600	+	0.0613549i
$879$	5.22926	−	9.05735i	0.176379	−	0.305497i
$880$	−9.39183	−	8.16750i	−0.316599	−	0.275326i
$881$	−36.4587			−1.22832			−0.614162	−	0.789180i	$-0.710506\pi$
$881$	−36.4587			−1.22832			−0.614162	+	0.789180i	$0.710506\pi$
$882$		0			0
$883$	−27.3119	−	27.3119i	−0.919120	−	0.919120i	0.0778457	−	0.996965i	$-0.475196\pi$
$883$	−27.3119	−	27.3119i	−0.919120	−	0.919120i	−0.996965	+	0.0778457i	$0.975196\pi$
$884$	−17.1879	−	20.8548i	−0.578091	−	0.701423i
$885$	−2.20890	−	8.24374i	−0.0742515	−	0.277110i
$886$	−37.0166	−	40.7562i	−1.24360	−	1.36923i
$887$	−12.2544	+	7.07509i	−0.411463	+	0.237558i	−0.691418	−	0.722455i	$-0.743014\pi$
$887$	−12.2544	+	7.07509i	−0.411463	+	0.237558i	0.279955	+	0.960013i	$0.409680\pi$
$888$	13.0834	−	90.1393i	0.439050	−	3.02488i
$889$		0			0
$890$	−7.43438	−	2.38017i	−0.249201	−	0.0797836i
$891$	98.6959	+	26.4455i	3.30644	+	0.885957i
$892$	16.3354	+	35.8544i	0.546951	+	1.20049i
$893$	−5.20997	+	1.39601i	−0.174345	+	0.0467156i
$894$	5.94012	+	3.82123i	0.198667	+	0.127801i
$895$	11.8680			0.396703
$896$		0			0
$897$	72.2656			2.41288
$898$	−13.6008	−	8.74932i	−0.453866	−	0.291969i
$899$	−9.61992	+	2.57765i	−0.320842	+	0.0859695i
$900$	−27.3382	−	60.0041i	−0.911273	−	2.00014i
$901$	−15.5992	−	4.17979i	−0.519685	−	0.139249i
$902$	23.2088	+	7.43049i	0.772770	+	0.247408i
$903$		0			0
$904$	1.66753	−	11.4886i	0.0554613	−	0.382106i
$905$	2.48377	−	1.43400i	0.0825633	−	0.0476679i
$906$	−54.5972	−	60.1129i	−1.81387	−	1.99712i
$907$	15.1656	+	56.5990i	0.503567	+	1.87934i	0.475469	+	0.879732i	$0.342278\pi$
$907$	15.1656	+	56.5990i	0.503567	+	1.87934i	0.0280980	+	0.999605i	$0.491055\pi$
$908$	−34.0141	−	41.2708i	−1.12880	−	1.36962i
$909$	7.57714	+	7.57714i	0.251318	+	0.251318i
$910$		0			0
$911$	32.2947			1.06997			0.534985	−	0.844861i	$-0.320317\pi$
$911$	32.2947			1.06997			0.534985	+	0.844861i	$0.320317\pi$
$912$	−15.1563	−	13.1805i	−0.501875	−	0.436449i
$913$	−14.8665	+	25.7495i	−0.492009	+	0.852184i
$914$	−6.09469	−	0.293055i	−0.201594	−	0.00969339i
$915$	10.7819	−	40.2384i	0.356437	−	1.33024i
$916$	3.00561	+	17.9719i	0.0993082	+	0.593808i
$917$		0			0
$918$	19.8502	−	62.0014i	0.655155	−	2.04635i
$919$	−41.8369	+	24.1546i	−1.38007	+	0.796786i	−0.992168	−	0.124913i	$-0.960135\pi$
$919$	−41.8369	+	24.1546i	−1.38007	+	0.796786i	−0.387906	+	0.921699i	$0.626801\pi$
$920$	−1.39264	−	11.7815i	−0.0459141	−	0.388426i
$921$	−74.3611	−	42.9324i	−2.45028	−	1.41467i
$922$	−5.07731	−	23.3903i	−0.167212	−	0.770320i
$923$	2.36107	−	2.36107i	0.0777155	−	0.0777155i
$924$		0			0
$925$	−28.5724	−	28.5724i	−0.939456	−	0.939456i
$926$	20.4216	+	13.1371i	0.671095	+	0.431710i
$927$	−9.18036	+	15.9008i	−0.301523	+	0.522252i
$928$	40.4031	+	22.1790i	1.32630	+	0.728063i
$929$	−6.81960	−	11.8119i	−0.223744	−	0.387536i	0.732198	−	0.681092i	$-0.238495\pi$
$929$	−6.81960	−	11.8119i	−0.223744	−	0.387536i	−0.955942	+	0.293556i	$0.905161\pi$
$930$	−4.68490	+	2.41259i	−0.153624	+	0.0791118i
$931$		0			0
$932$	−16.5483	−	11.8063i	−0.542057	−	0.386727i
$933$	72.4847	+	19.4222i	2.37304	+	0.635855i
$934$	−37.4434	+	34.0078i	−1.22519	+	1.11277i
$935$	−7.58663	−	4.38015i	−0.248109	−	0.143246i
$936$	−42.5785	+	99.0632i	−1.39172	+	3.23798i
$937$		−	8.02413i		−	0.262137i	−0.991373	−	0.131068i	$-0.958159\pi$
$937$		−	8.02413i		−	0.262137i	0.991373	−	0.131068i	$-0.0418408\pi$
$938$		0			0
$939$	71.4122	−	71.4122i	2.33045	−	2.33045i
$940$	5.05366	−	4.16507i	0.164832	−	0.135850i
$941$	36.8859	−	9.88355i	1.20245	−	0.322195i	0.398652	−	0.917102i	$-0.369478\pi$
$941$	36.8859	−	9.88355i	1.20245	−	0.322195i	0.803794	+	0.594908i	$0.202811\pi$
$942$	−60.1470	−	2.89209i	−1.95970	−	0.0942292i
$943$	11.6140	+	20.1160i	0.378204	+	0.655069i
$944$	−10.0644	−	4.91122i	−0.327568	−	0.159847i
$945$		0			0
$946$	−7.82683	−	15.1986i	−0.254472	−	0.494149i
$947$	4.56705	−	17.0445i	0.148409	−	0.553871i	−0.851171	−	0.524889i	$-0.824107\pi$
$947$	4.56705	−	17.0445i	0.148409	−	0.553871i	0.999580	−	0.0289819i	$-0.00922651\pi$
$948$	−6.12607	+	16.3799i	−0.198965	+	0.531995i
$949$	0.395352	+	1.47547i	0.0128337	+	0.0478959i
$950$	−8.70786	+	1.89021i	−0.282520	+	0.0613264i
$951$		−	111.918i		−	3.62920i
$952$		0			0
$953$			46.5382i			1.50752i	0.657150	+	0.753760i	$0.271762\pi$
$953$			46.5382i			1.50752i	−0.657150	+	0.753760i	$0.728238\pi$
$954$	13.6684	+	62.9680i	0.442531	+	2.03866i
$955$	4.06397	+	15.1669i	0.131507	+	0.490791i
$956$	19.4781	+	42.7520i	0.629965	+	1.38270i
$957$	−23.5546	+	87.9071i	−0.761414	+	2.84163i
$958$	18.1809	−	9.36260i	0.587397	−	0.302492i
$959$		0			0
$960$	23.3808	+	6.93335i	0.754612	+	0.223773i
$961$	14.7529	+	25.5528i	0.475901	+	0.824285i
$962$	−3.17353	+	66.0003i	−0.102319	+	2.12794i
$963$	80.1633	−	21.4797i	2.58323	−	0.692173i
$964$	−8.59782	−	0.828745i	−0.276917	−	0.0266921i
$965$	3.35779	−	3.35779i	0.108091	−	0.108091i
$966$		0			0
$967$		−	16.7738i		−	0.539408i	−0.962943	−	0.269704i	$-0.913074\pi$
$967$		−	16.7738i		−	0.539408i	0.962943	−	0.269704i	$-0.0869259\pi$
$968$	−0.420612	−	1.05473i	−0.0135190	−	0.0339004i
$969$	−12.2431	−	7.06856i	−0.393305	−	0.227075i
$970$	9.70165	+	10.6818i	0.311501	+	0.342971i
$971$	−38.1759	−	10.2292i	−1.22512	−	0.328271i	−0.412444	−	0.910983i	$-0.635325\pi$
$971$	−38.1759	−	10.2292i	−1.22512	−	0.328271i	−0.812679	+	0.582712i	$0.801992\pi$
$972$	−100.699	+	16.8408i	−3.22991	+	0.540169i
$973$		0			0
$974$	16.7849	+	32.5938i	0.537822	+	1.04437i
$975$	32.9510	+	57.0728i	1.05528	+	1.82779i
$976$	−30.5576	−	45.3231i	−0.978125	−	1.45076i
$977$	14.6702	−	25.4096i	0.469342	−	0.812924i	−0.530044	−	0.847970i	$-0.677824\pi$
$977$	14.6702	−	25.4096i	0.469342	−	0.812924i	0.999386	+	0.0350462i	$0.0111578\pi$
$978$	−26.9253	+	41.8554i	−0.860975	+	1.33839i
$979$	−14.3014	−	14.3014i	−0.457075	−	0.457075i
$980$		0			0
$981$	−71.0156	+	71.0156i	−2.26735	+	2.26735i
$982$	−14.8382	+	3.22090i	−0.473505	+	0.102783i
$983$	−12.5874	−	7.26732i	−0.401475	−	0.231792i	0.285645	−	0.958335i	$-0.407792\pi$
$983$	−12.5874	−	7.26732i	−0.401475	−	0.231792i	−0.687120	+	0.726544i	$0.741125\pi$
$984$	−47.4182	+	5.60509i	−1.51164	+	0.178684i
$985$	11.1686	−	6.44819i	0.355861	−	0.205456i
$986$	30.8953	+	9.89138i	0.983908	+	0.315006i
$987$		0			0
$988$	11.8618	+	8.46271i	0.377373	+	0.269235i
$989$	4.21742	−	15.7396i	0.134106	−	0.500491i
$990$	−1.67870	+	34.9121i	−0.0533526	+	1.10958i
$991$	16.0466	−	27.7935i	0.509736	−	0.882889i	−0.490200	−	0.871610i	$-0.663076\pi$
$991$	16.0466	−	27.7935i	0.509736	−	0.882889i	0.999936	−	0.0112794i	$-0.00359043\pi$
$992$	−1.64519	+	6.71605i	−0.0522348	+	0.213235i
$993$	−1.76340			−0.0559599
$994$		0			0
$995$	−3.55220	−	3.55220i	−0.112612	−	0.112612i
$996$	5.58956	−	57.9889i	0.177112	−	1.83745i
$997$	12.7779	+	47.6880i	0.404682	+	1.51029i	0.804642	+	0.593760i	$0.202357\pi$
$997$	12.7779	+	47.6880i	0.404682	+	1.51029i	−0.399960	+	0.916532i	$0.630976\pi$
$998$	−16.9514	+	15.3961i	−0.536589	+	0.487354i
$999$	−137.849	+	79.5874i	−4.36136	+	2.51803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.557.21		96
7.2	even	3	inner	784.2.x.p.765.12		96
7.3	odd	6		784.2.m.l.589.3	yes	48
7.4	even	3		784.2.m.l.589.4	yes	48
7.5	odd	6	inner	784.2.x.p.765.11		96
7.6	odd	2	inner	784.2.x.p.557.22		96
16.5	even	4	inner	784.2.x.p.165.12		96
112.5	odd	12	inner	784.2.x.p.373.22		96
112.37	even	12	inner	784.2.x.p.373.21		96
112.53	even	12		784.2.m.l.197.4	yes	48
112.69	odd	4	inner	784.2.x.p.165.11		96
112.101	odd	12		784.2.m.l.197.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.3	✓	48	112.101	odd	12
784.2.m.l.197.4	yes	48	112.53	even	12
784.2.m.l.589.3	yes	48	7.3	odd	6
784.2.m.l.589.4	yes	48	7.4	even	3
784.2.x.p.165.11		96	112.69	odd	4	inner
784.2.x.p.165.12		96	16.5	even	4	inner
784.2.x.p.373.21		96	112.37	even	12	inner
784.2.x.p.373.22		96	112.5	odd	12	inner
784.2.x.p.557.21		96	1.1	even	1	trivial
784.2.x.p.557.22		96	7.6	odd	2	inner
784.2.x.p.765.11		96	7.5	odd	6	inner
784.2.x.p.765.12		96	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18937 + 0.765113i) q^{2} +(-3.19528 + 0.856173i) q^{3} +(0.829204 + 1.82001i) q^{4} +(0.890122 + 0.238507i) q^{5} +(-4.45544 - 1.42644i) q^{6} +(-0.406279 + 2.79910i) q^{8} +(6.87872 - 3.97143i) q^{9} +O(q^{10})\)	\(q+(1.18937 + 0.765113i) q^{2} +(-3.19528 + 0.856173i) q^{3} +(0.829204 + 1.82001i) q^{4} +(0.890122 + 0.238507i) q^{5} +(-4.45544 - 1.42644i) q^{6} +(-0.406279 + 2.79910i) q^{8} +(6.87872 - 3.97143i) q^{9} +(0.876200 + 0.964717i) q^{10} +(0.873930 + 3.26155i) q^{11} +(-4.20778 - 5.10549i) q^{12} +(3.39380 + 3.39380i) q^{13} -3.04839 q^{15} +(-2.62484 + 3.01831i) q^{16} +(-1.40768 + 2.43817i) q^{17} +(11.2199 + 0.539495i) q^{18} +(0.392879 - 1.46625i) q^{19} +(0.304008 + 1.81780i) q^{20} +(-1.45603 + 4.54785i) q^{22} +(-3.94180 + 2.27580i) q^{23} +(-1.09834 - 9.29175i) q^{24} +(-3.59470 - 2.07540i) q^{25} +(1.43985 + 6.63313i) q^{26} +(-11.5619 + 11.5619i) q^{27} +(-5.76129 - 5.76129i) q^{29} +(-3.62567 - 2.33237i) q^{30} +(0.611172 - 1.05858i) q^{31} +(-5.43126 + 1.58159i) q^{32} +(-5.58490 - 9.67334i) q^{33} +(-3.53972 + 1.82285i) q^{34} +(12.9319 + 9.22618i) q^{36} +(9.40318 + 2.51957i) q^{37} +(1.58912 - 1.44331i) q^{38} +(-13.7498 - 7.93848i) q^{39} +(-1.02924 + 2.39464i) q^{40} -5.10326i q^{41} +(-2.53146 + 2.53146i) q^{43} +(-5.21137 + 4.29505i) q^{44} +(7.07011 - 1.89443i) q^{45} +(-6.42951 - 0.309154i) q^{46} +(-1.77664 - 3.07723i) q^{47} +(5.80291 - 11.8917i) q^{48} +(-2.68751 - 5.21877i) q^{50} +(2.41043 - 8.99584i) q^{51} +(-3.36258 + 8.99090i) q^{52} +(1.48464 + 5.54077i) q^{53} +(-22.5975 + 4.90522i) q^{54} +3.11162i q^{55} +5.02144i q^{57} +(-2.44427 - 11.2603i) q^{58} +(0.724612 + 2.70429i) q^{59} +(-2.52774 - 5.54809i) q^{60} +(-3.53690 + 13.1999i) q^{61} +(1.53684 - 0.791429i) q^{62} +(-7.66988 - 2.27443i) q^{64} +(2.21145 + 3.83035i) q^{65} +(0.758676 - 15.7783i) q^{66} +(-1.30397 + 0.349397i) q^{67} +(-5.60473 - 0.540240i) q^{68} +(10.6467 - 10.6467i) q^{69} -0.695700i q^{71} +(8.32173 + 20.8677i) q^{72} +(0.275624 + 0.159132i) q^{73} +(9.25610 + 10.1912i) q^{74} +(13.2630 + 3.55380i) q^{75} +(2.99435 - 0.500775i) q^{76} +(-10.2798 - 19.9620i) q^{78} +(-1.32165 - 2.28916i) q^{79} +(-3.05632 + 2.06062i) q^{80} +(15.1302 - 26.2063i) q^{81} +(3.90457 - 6.06967i) q^{82} +(6.22648 + 6.22648i) q^{83} +(-1.83452 + 1.83452i) q^{85} +(-4.94770 + 1.07399i) q^{86} +(23.3416 + 13.4763i) q^{87} +(-9.48445 + 1.12111i) q^{88} +(-5.18733 + 2.99491i) q^{89} +(9.85844 + 3.15625i) q^{90} +(-7.41053 - 5.28700i) q^{92} +(-1.04654 + 3.90573i) q^{93} +(0.241346 - 5.01929i) q^{94} +(0.699421 - 1.21143i) q^{95} +(16.0003 - 9.70373i) q^{96} +11.0724 q^{97} +(18.9645 + 18.9645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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