LMFDB - Embedded newform 784.2.x.m.165.4

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.4
Character	$\chi$	$=$	784.165
Dual form			784.2.x.m.765.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.114575 + 1.40956i) q^{2} +(-0.509227 - 1.90046i) q^{3} +(-1.97375 + 0.323001i) q^{4} +(-0.792364 + 2.95714i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} +(-0.754366 + 0.435533i) q^{9} +O(q^{10})$	\(q+(0.114575 + 1.40956i) q^{2} +(-0.509227 - 1.90046i) q^{3} +(-1.97375 + 0.323001i) q^{4} +(-0.792364 + 2.95714i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} +(-0.754366 + 0.435533i) q^{9} +(-4.25907 - 0.778075i) q^{10} +(4.22870 - 1.13308i) q^{11} +(1.61893 + 3.58655i) q^{12} +(-1.75410 + 1.75410i) q^{13} +6.02343 q^{15} +(3.79134 - 1.27504i) q^{16} +(-2.60235 + 4.50740i) q^{17} +(-0.700343 - 1.01343i) q^{18} +(-1.16333 - 0.311715i) q^{19} +(0.608766 - 6.09258i) q^{20} +(2.08165 + 5.83081i) q^{22} +(-5.33038 + 3.07750i) q^{23} +(-4.86998 + 2.69292i) q^{24} +(-3.78672 - 2.18626i) q^{25} +(-2.67349 - 2.27154i) q^{26} +(-2.96185 - 2.96185i) q^{27} +(-6.24096 + 6.24096i) q^{29} +(0.690132 + 8.49041i) q^{30} +(-1.39123 + 2.40969i) q^{31} +(2.23165 + 5.19805i) q^{32} +(-4.30674 - 7.45950i) q^{33} +(-6.65164 - 3.15175i) q^{34} +(1.34825 - 1.10329i) q^{36} +(1.50511 - 5.61713i) q^{37} +(0.306093 - 1.67551i) q^{38} +(4.22683 + 2.44036i) q^{39} +(8.65763 + 0.160040i) q^{40} +6.32956i q^{41} +(3.05937 + 3.05937i) q^{43} +(-7.98040 + 3.60228i) q^{44} +(-0.690201 - 2.57587i) q^{45} +(-4.94866 - 7.16092i) q^{46} +(1.80192 + 3.12101i) q^{47} +(-4.35382 - 6.55601i) q^{48} +(2.64782 - 5.58812i) q^{50} +(9.89133 + 2.65037i) q^{51} +(2.89557 - 4.02872i) q^{52} +(-7.21798 + 1.93405i) q^{53} +(3.83556 - 4.51427i) q^{54} +13.4027i q^{55} +2.36961i q^{57} +(-9.51209 - 8.08198i) q^{58} +(-9.74734 + 2.61179i) q^{59} +(-11.8887 + 1.94557i) q^{60} +(1.42056 + 0.380638i) q^{61} +(-3.55601 - 1.68495i) q^{62} +(-7.07130 + 3.74121i) q^{64} +(-3.79723 - 6.57700i) q^{65} +(10.0212 - 6.92530i) q^{66} +(-0.353834 - 1.32053i) q^{67} +(3.68048 - 9.73703i) q^{68} +(8.56304 + 8.56304i) q^{69} +10.0597i q^{71} +(1.70964 + 1.77403i) q^{72} +(-13.1391 - 7.58585i) q^{73} +(8.09016 + 1.47796i) q^{74} +(-2.22661 + 8.30982i) q^{75} +(2.39681 + 0.239487i) q^{76} +(-2.95556 + 6.23759i) q^{78} +(3.30674 + 5.72745i) q^{79} +(0.766358 + 12.2218i) q^{80} +(-5.42722 + 9.40022i) q^{81} +(-8.92192 + 0.725206i) q^{82} +(7.41730 - 7.41730i) q^{83} +(-11.2670 - 11.2670i) q^{85} +(-3.96185 + 4.66290i) q^{86} +(15.0388 + 8.68264i) q^{87} +(-5.99200 - 10.8362i) q^{88} +(2.82449 - 1.63072i) q^{89} +(3.55177 - 1.26801i) q^{90} +(9.52678 - 7.79591i) q^{92} +(5.28798 + 1.41691i) q^{93} +(-4.19281 + 2.89750i) q^{94} +(1.84357 - 3.19315i) q^{95} +(8.74229 - 6.88815i) q^{96} +7.66352 q^{97} +(-2.69650 + 2.69650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.114575	+	1.40956i	0.0810165	+	0.996713i
$2$	0.114575	+	1.40956i	0.0810165	+	0.996713i
$3$	−0.509227	−	1.90046i	−0.294002	−	1.09723i	−0.942006	−	0.335595i	$-0.891063\pi$
$3$	−0.509227	−	1.90046i	−0.294002	−	1.09723i	0.648004	−	0.761637i	$-0.275604\pi$
$4$	−1.97375	+	0.323001i	−0.986873	+	0.161500i
$5$	−0.792364	+	2.95714i	−0.354356	+	1.32247i	0.526937	+	0.849904i	$0.323340\pi$
$5$	−0.792364	+	2.95714i	−0.354356	+	1.32247i	−0.881293	+	0.472570i	$0.843326\pi$
$6$	2.62048	−	0.935533i	1.06981	−	0.381930i
$7$		0			0
$7$		0			0
$8$	−0.681431	−	2.74511i	−0.240922	−	0.970544i
$9$	−0.754366	+	0.435533i	−0.251455	+	0.145178i
$10$	−4.25907	−	0.778075i	−1.34684	−	0.246049i
$11$	4.22870	−	1.13308i	1.27500	−	0.341636i	0.443057	−	0.896493i	$-0.353894\pi$
$11$	4.22870	−	1.13308i	1.27500	−	0.341636i	0.831945	+	0.554858i	$0.187227\pi$
$12$	1.61893	+	3.58655i	0.467346	+	1.03535i
$13$	−1.75410	+	1.75410i	−0.486499	+	0.486499i	−0.907200	−	0.420701i	$-0.861784\pi$
$13$	−1.75410	+	1.75410i	−0.486499	+	0.486499i	0.420701	+	0.907200i	$0.361784\pi$
$14$		0			0
$15$	6.02343			1.55524
$16$	3.79134	−	1.27504i	0.947835	−	0.318760i
$17$	−2.60235	+	4.50740i	−0.631163	+	1.09321i	0.356152	+	0.934428i	$0.384089\pi$
$17$	−2.60235	+	4.50740i	−0.631163	+	1.09321i	−0.987314	+	0.158778i	$0.949245\pi$
$18$	−0.700343	−	1.01343i	−0.165073	−	0.238867i
$19$	−1.16333	−	0.311715i	−0.266887	−	0.0715122i	0.122894	−	0.992420i	$-0.460783\pi$
$19$	−1.16333	−	0.311715i	−0.266887	−	0.0715122i	−0.389781	+	0.920908i	$0.627449\pi$
$20$	0.608766	−	6.09258i	0.136124	−	1.36234i
$21$		0			0
$22$	2.08165	+	5.83081i	0.443809	+	1.24313i
$23$	−5.33038	+	3.07750i	−1.11146	+	0.641703i	−0.939208	−	0.343350i	$-0.888438\pi$
$23$	−5.33038	+	3.07750i	−1.11146	+	0.641703i	−0.172254	+	0.985053i	$0.555105\pi$
$24$	−4.86998	+	2.69292i	−0.994081	+	0.549690i
$25$	−3.78672	−	2.18626i	−0.757344	−	0.437253i
$26$	−2.67349	−	2.27154i	−0.524314	−	0.445485i
$27$	−2.96185	−	2.96185i	−0.570007	−	0.570007i
$28$		0			0
$29$	−6.24096	+	6.24096i	−1.15892	+	1.15892i	−0.174208	+	0.984709i	$0.555736\pi$
$29$	−6.24096	+	6.24096i	−1.15892	+	1.15892i	−0.984709	+	0.174208i	$0.944264\pi$
$30$	0.690132	+	8.49041i	0.126000	+	1.55013i
$31$	−1.39123	+	2.40969i	−0.249873	+	0.432793i	−0.963490	−	0.267743i	$-0.913722\pi$
$31$	−1.39123	+	2.40969i	−0.249873	+	0.432793i	0.713617	+	0.700536i	$0.247056\pi$
$32$	2.23165	+	5.19805i	0.394503	+	0.918895i
$33$	−4.30674	−	7.45950i	−0.749708	−	1.29853i
$34$	−6.65164	−	3.15175i	−1.14075	−	0.540520i
$35$		0			0
$36$	1.34825	−	1.10329i	0.224708	−	0.183882i
$37$	1.50511	−	5.61713i	0.247438	−	0.923450i	−0.724705	−	0.689060i	$-0.758024\pi$
$37$	1.50511	−	5.61713i	0.247438	−	0.923450i	0.972142	−	0.234391i	$-0.0753095\pi$
$38$	0.306093	−	1.67551i	0.0496549	−	0.271804i
$39$	4.22683	+	2.44036i	0.676834	+	0.390770i
$40$	8.65763	+	0.160040i	1.36889	+	0.0253045i
$41$			6.32956i			0.988511i	0.869317	+	0.494255i	$0.164559\pi$
$41$			6.32956i			0.988511i	−0.869317	+	0.494255i	$0.835441\pi$
$42$		0			0
$43$	3.05937	+	3.05937i	0.466549	+	0.466549i	0.900795	−	0.434245i	$-0.142985\pi$
$43$	3.05937	+	3.05937i	0.466549	+	0.466549i	−0.434245	+	0.900795i	$0.642985\pi$
$44$	−7.98040	+	3.60228i	−1.20309	+	0.543064i
$45$	−0.690201	−	2.57587i	−0.102889	−	0.383988i
$46$	−4.94866	−	7.16092i	−0.729640	−	1.05582i
$47$	1.80192	+	3.12101i	0.262836	+	0.455246i	0.966994	−	0.254797i	$-0.0820087\pi$
$47$	1.80192	+	3.12101i	0.262836	+	0.455246i	−0.704158	+	0.710043i	$0.748675\pi$
$48$	−4.35382	−	6.55601i	−0.628420	−	0.946279i
$49$		0			0
$50$	2.64782	−	5.58812i	0.374458	−	0.790279i
$51$	9.89133	+	2.65037i	1.38506	+	0.371127i
$52$	2.89557	−	4.02872i	0.401543	−	0.558682i
$53$	−7.21798	+	1.93405i	−0.991466	+	0.265662i	−0.717866	−	0.696181i	$-0.754881\pi$
$53$	−7.21798	+	1.93405i	−0.991466	+	0.265662i	−0.273600	+	0.961844i	$0.588214\pi$
$54$	3.83556	−	4.51427i	0.521954	−	0.614314i
$55$			13.4027i			1.80722i
$56$		0			0
$57$			2.36961i			0.313862i
$58$	−9.51209	−	8.08198i	−1.24900	−	1.06122i
$59$	−9.74734	+	2.61179i	−1.26900	+	0.340026i	−0.829646	−	0.558290i	$-0.811458\pi$
$59$	−9.74734	+	2.61179i	−1.26900	+	0.340026i	−0.439350	+	0.898316i	$0.644791\pi$
$60$	−11.8887	+	1.94557i	−1.53483	+	0.251172i
$61$	1.42056	+	0.380638i	0.181884	+	0.0487357i	0.348611	−	0.937267i	$-0.386653\pi$
$61$	1.42056	+	0.380638i	0.181884	+	0.0487357i	−0.166727	+	0.986003i	$0.553320\pi$
$62$	−3.55601	−	1.68495i	−0.451614	−	0.213988i
$63$		0			0
$64$	−7.07130	+	3.74121i	−0.883913	+	0.467652i
$65$	−3.79723	−	6.57700i	−0.470988	−	0.815776i
$66$	10.0212	−	6.92530i	1.23352	−	0.852446i
$67$	−0.353834	−	1.32053i	−0.0432277	−	0.161328i	0.940938	−	0.338579i	$-0.109946\pi$
$67$	−0.353834	−	1.32053i	−0.0432277	−	0.161328i	−0.984166	+	0.177251i	$0.943280\pi$
$68$	3.68048	−	9.73703i	0.446324	−	1.18079i
$69$	8.56304	+	8.56304i	1.03087	+	1.03087i
$70$		0			0
$71$			10.0597i			1.19386i	0.802291	+	0.596932i	$0.203614\pi$
$71$			10.0597i			1.19386i	−0.802291	+	0.596932i	$0.796386\pi$
$72$	1.70964	+	1.77403i	0.201483	+	0.209072i
$73$	−13.1391	−	7.58585i	−1.53781	−	0.887857i	−0.998966	−	0.0454536i	$-0.985527\pi$
$73$	−13.1391	−	7.58585i	−1.53781	−	0.887857i	−0.538847	−	0.842404i	$-0.681140\pi$
$74$	8.09016	+	1.47796i	0.940461	+	0.171810i
$75$	−2.22661	+	8.30982i	−0.257107	+	0.959535i
$76$	2.39681	+	0.239487i	0.274933	+	0.0274711i
$77$		0			0
$78$	−2.95556	+	6.23759i	−0.334651	+	0.706268i
$79$	3.30674	+	5.72745i	0.372038	+	0.644388i	0.989879	−	0.141915i	$-0.0453259\pi$
$79$	3.30674	+	5.72745i	0.372038	+	0.644388i	−0.617841	+	0.786303i	$0.711993\pi$
$80$	0.766358	+	12.2218i	0.0856815	+	1.36644i
$81$	−5.42722	+	9.40022i	−0.603025	+	1.04447i
$82$	−8.92192	+	0.725206i	−0.985261	+	0.0800856i
$83$	7.41730	−	7.41730i	0.814154	−	0.814154i	−0.171100	−	0.985254i	$-0.554732\pi$
$83$	7.41730	−	7.41730i	0.814154	−	0.814154i	0.985254	+	0.171100i	$0.0547320\pi$
$84$		0			0
$85$	−11.2670	−	11.2670i	−1.22208	−	1.22208i
$86$	−3.96185	+	4.66290i	−0.427218	+	0.502814i
$87$	15.0388	+	8.68264i	1.61232	+	0.930876i
$88$	−5.99200	−	10.8362i	−0.638749	−	1.15514i
$89$	2.82449	−	1.63072i	0.299396	−	0.172856i	−0.342776	−	0.939417i	$-0.611367\pi$
$89$	2.82449	−	1.63072i	0.299396	−	0.172856i	0.642171	+	0.766561i	$0.278034\pi$
$90$	3.55177	−	1.26801i	0.374390	−	0.133660i
$91$		0			0
$92$	9.52678	−	7.79591i	0.993236	−	0.812780i
$93$	5.28798	+	1.41691i	0.548337	+	0.146927i
$94$	−4.19281	+	2.89750i	−0.432455	+	0.298855i
$95$	1.84357	−	3.19315i	0.189146	−	0.327611i
$96$	8.74229	−	6.88815i	0.892256	−	0.703018i
$97$	7.66352			0.778112			0.389056	−	0.921214i	$-0.372801\pi$
$97$	7.66352			0.778112			0.389056	+	0.921214i	$0.372801\pi$
$98$		0			0
$99$	−2.69650	+	2.69650i	−0.271008	+	0.271008i
$100$	8.18018	+	3.09201i	0.818018	+	0.309201i
$101$	13.5681	−	3.63555i	1.35007	−	0.361751i	0.489912	−	0.871772i	$-0.337029\pi$
$101$	13.5681	−	3.63555i	1.35007	−	0.361751i	0.860162	+	0.510021i	$0.170362\pi$
$102$	−2.60258	+	14.2461i	−0.257694	+	1.41058i
$103$	−1.39602	+	0.805993i	−0.137554	+	0.0794169i	−0.567198	−	0.823582i	$-0.691972\pi$
$103$	−1.39602	+	0.805993i	−0.137554	+	0.0794169i	0.429644	+	0.902998i	$0.358639\pi$
$104$	6.01049	+	3.61990i	0.589377	+	0.354960i
$105$		0			0
$106$	−3.55317	−	9.95262i	−0.345114	−	0.966684i
$107$	2.90028	−	10.8240i	0.280381	−	1.04640i	−0.671768	−	0.740762i	$-0.734465\pi$
$107$	2.90028	−	10.8240i	0.280381	−	1.04640i	0.952149	−	0.305634i	$-0.0988686\pi$
$108$	6.80261	+	4.88925i	0.654581	+	0.470468i
$109$	2.08261	+	7.77240i	0.199478	+	0.744461i	0.991062	+	0.133401i	$0.0425899\pi$
$109$	2.08261	+	7.77240i	0.199478	+	0.744461i	−0.791584	+	0.611060i	$0.790743\pi$
$110$	−18.8920	+	1.53561i	−1.80128	+	0.146414i
$111$	−11.4416			−1.08599
$112$		0			0
$113$	15.2609			1.43563			0.717813	−	0.696235i	$-0.245143\pi$
$113$	15.2609			1.43563			0.717813	+	0.696235i	$0.245143\pi$
$114$	−3.34011	+	0.271497i	−0.312830	+	0.0254280i
$115$	−4.87699	−	18.2012i	−0.454782	−	1.69727i
$116$	10.3022	−	14.3339i	0.956538	−	1.33087i
$117$	0.559263	−	2.08720i	0.0517039	−	0.192962i
$118$	−4.79829	−	13.4403i	−0.441718	−	1.23728i
$119$		0			0
$120$	−4.10455	−	16.5350i	−0.374693	−	1.50943i
$121$	7.07180	−	4.08290i	0.642891	−	0.371173i
$122$	−0.373774	+	2.04598i	−0.0338399	+	0.185235i
$123$	12.0291	−	3.22318i	1.08463	−	0.290624i
$124$	1.96761	−	5.20548i	0.176697	−	0.467466i
$125$	−1.35834	+	1.35834i	−0.121494	+	0.121494i
$126$		0			0
$127$	−1.80529			−0.160193			−0.0800966	−	0.996787i	$-0.525523\pi$
$127$	−1.80529			−0.160193			−0.0800966	+	0.996787i	$0.525523\pi$
$128$	−6.08367	−	9.53881i	−0.537726	−	0.843120i
$129$	4.25630	−	7.37213i	0.374746	−	0.649080i
$130$	8.83564	−	6.10600i	0.774937	−	0.535532i
$131$	12.6845	+	3.39881i	1.10825	+	0.296956i	0.766121	−	0.642696i	$-0.222184\pi$
$131$	12.6845	+	3.39881i	1.10825	+	0.296956i	0.342132	+	0.939652i	$0.388851\pi$
$132$	10.9098	+	13.3321i	0.949579	+	1.16041i
$133$		0			0
$134$	1.82083	−	0.650051i	0.157296	−	0.0561559i
$135$	11.1055	−	6.41174i	0.955805	−	0.551835i
$136$	14.1467	+	4.07226i	1.21307	+	0.349194i
$137$	6.87323	+	3.96826i	0.587220	+	0.339031i	0.763997	−	0.645219i	$-0.223234\pi$
$137$	6.87323	+	3.96826i	0.587220	+	0.339031i	−0.176778	+	0.984251i	$0.556567\pi$
$138$	−11.0891	+	13.0513i	−0.943963	+	1.11100i
$139$	2.06915	+	2.06915i	0.175503	+	0.175503i	0.789392	−	0.613889i	$-0.210396\pi$
$139$	2.06915	+	2.06915i	0.175503	+	0.175503i	−0.613889	+	0.789392i	$0.710396\pi$
$140$		0			0
$141$	5.01377	−	5.01377i	0.422236	−	0.422236i
$142$	−14.1798	+	1.15258i	−1.18994	+	0.0967227i
$143$	−5.43003	+	9.40509i	−0.454082	+	0.786493i
$144$	−2.30473	+	2.61310i	−0.192061	+	0.217759i
$145$	−13.5103	−	23.4005i	−1.12197	−	1.94331i
$146$	9.18735	−	19.3895i	0.760350	−	1.60469i
$147$		0			0
$148$	−1.15636	+	11.5729i	−0.0950521	+	0.951289i
$149$	3.35096	−	12.5060i	0.274521	−	1.02453i	−0.681640	−	0.731688i	$-0.738733\pi$
$149$	3.35096	−	12.5060i	0.274521	−	1.02453i	0.956161	−	0.292840i	$-0.0946004\pi$
$150$	−11.9683	−	2.18646i	−0.977211	−	0.178523i
$151$	2.42743	+	1.40148i	0.197541	+	0.114051i	0.595508	−	0.803349i	$-0.296951\pi$
$151$	2.42743	+	1.40148i	0.197541	+	0.114051i	−0.397967	+	0.917400i	$0.630284\pi$
$152$	−0.0629594	+	3.40590i	−0.00510668	+	0.276255i
$153$		−	4.53364i		−	0.366523i
$154$		0			0
$155$	−6.02343	−	6.02343i	−0.483813	−	0.483813i
$156$	−9.13092	−	3.45138i	−0.731059	−	0.276332i
$157$	−0.350944	−	1.30974i	−0.0280084	−	0.104529i	0.950507	−	0.310704i	$-0.100565\pi$
$157$	−0.350944	−	1.30974i	−0.0280084	−	0.104529i	−0.978515	+	0.206176i	$0.933898\pi$
$158$	−7.69434	+	5.31729i	−0.612129	+	0.423021i
$159$	7.35118	+	12.7326i	0.582987	+	1.00976i
$160$	−17.1397	+	2.48054i	−1.35501	+	0.196104i
$161$		0			0
$162$	−13.8720	−	6.57299i	−1.08989	−	0.516423i
$163$	−17.6498	−	4.72925i	−1.38244	−	0.370423i	−0.510432	−	0.859918i	$-0.670515\pi$
$163$	−17.6498	−	4.72925i	−1.38244	−	0.370423i	−0.872006	+	0.489495i	$0.837181\pi$
$164$	−2.04445	−	12.4929i	−0.159645	−	0.975534i
$165$	25.4713	−	6.82501i	1.98294	−	0.531326i
$166$	11.3050	+	9.60533i	0.877438	+	0.745518i
$167$		−	1.96111i		−	0.151755i	−0.997117	−	0.0758775i	$-0.975824\pi$
$167$		−	1.96111i		−	0.151755i	0.997117	−	0.0758775i	$-0.0241758\pi$
$168$		0			0
$169$			6.84629i			0.526637i
$170$	14.5907	−	17.1725i	1.11905	−	1.31707i
$171$	1.01334	−	0.271524i	0.0774922	−	0.0207640i
$172$	−7.02659	−	5.05024i	−0.535773	−	0.385077i
$173$	−5.65589	−	1.51549i	−0.430009	−	0.115221i	0.0373213	−	0.999303i	$-0.488117\pi$
$173$	−5.65589	−	1.51549i	−0.430009	−	0.115221i	−0.467330	+	0.884083i	$0.654784\pi$
$174$	−10.5157	+	22.1929i	−0.797191	+	1.68244i
$175$		0			0
$176$	14.5877	−	9.68766i	1.09959	−	0.730235i
$177$	9.92722	+	17.1945i	0.746176	+	1.29241i
$178$	2.62222	+	3.79447i	0.196544	+	0.284407i
$179$	−3.48281	−	12.9980i	−0.260318	−	0.971519i	−0.965054	−	0.262050i	$-0.915602\pi$
$179$	−3.48281	−	12.9980i	−0.260318	−	0.971519i	0.704737	−	0.709469i	$-0.251065\pi$
$180$	2.19429	+	4.86117i	0.163553	+	0.362330i
$181$	−7.60424	−	7.60424i	−0.565219	−	0.565219i	0.365566	−	0.930785i	$-0.380875\pi$
$181$	−7.60424	−	7.60424i	−0.565219	−	0.565219i	−0.930785	+	0.365566i	$0.880875\pi$
$182$		0			0
$183$		−	2.89355i		−	0.213897i
$184$	12.0804	+	12.5354i	0.890577	+	0.924122i
$185$	15.4181	+	8.90162i	1.13356	+	0.654460i
$186$	−1.39136	+	7.61608i	−0.102019	+	0.558438i
$187$	−5.89733	+	22.0091i	−0.431256	+	1.60947i
$188$	−4.56461	−	5.57806i	−0.332908	−	0.406822i
$189$		0			0
$190$	4.71218	+	2.23277i	0.341858	+	0.161982i
$191$	10.2439	+	17.7430i	0.741223	+	1.28384i	0.951939	+	0.306289i	$0.0990873\pi$
$191$	10.2439	+	17.7430i	0.741223	+	1.28384i	−0.210715	+	0.977547i	$0.567579\pi$
$192$	10.7109	+	11.5336i	0.772995	+	0.832367i
$193$	−6.35776	+	11.0120i	−0.457642	+	0.792659i	−0.998836	−	0.0482388i	$-0.984639\pi$
$193$	−6.35776	+	11.0120i	−0.457642	+	0.792659i	0.541194	+	0.840898i	$0.317972\pi$
$194$	0.878044	+	10.8022i	0.0630399	+	0.775554i
$195$	−10.5657	+	10.5657i	−0.756624	+	0.756624i
$196$		0			0
$197$	−12.8638	−	12.8638i	−0.916509	−	0.916509i	0.0802649	−	0.996774i	$-0.474423\pi$
$197$	−12.8638	−	12.8638i	−0.916509	−	0.916509i	−0.996774	+	0.0802649i	$0.974423\pi$
$198$	−4.10984	−	3.49194i	−0.292073	−	0.248161i
$199$	1.27174	+	0.734237i	0.0901510	+	0.0520487i	0.544398	−	0.838827i	$-0.316758\pi$
$199$	1.27174	+	0.734237i	0.0901510	+	0.0520487i	−0.454247	+	0.890876i	$0.650092\pi$
$200$	−3.42115	+	11.8848i	−0.241912	+	0.840380i
$201$	−2.32943	+	1.34490i	−0.164305	+	0.0948617i
$202$	6.67911	+	18.7085i	0.469940	+	1.31633i
$203$		0			0
$204$	−20.3790	−	2.03626i	−1.42682	−	0.142567i
$205$	−18.7174	−	5.01531i	−1.30728	−	0.350284i
$206$	−1.29605	−	1.87544i	−0.0903000	−	0.130668i
$207$	2.68070	−	4.64312i	0.186322	−	0.322719i
$208$	−4.41383	+	8.88693i	−0.306044	+	0.616198i
$209$	−5.27260			−0.364713
$210$		0			0
$211$	0.534767	−	0.534767i	0.0368149	−	0.0368149i	−0.688460	−	0.725275i	$-0.741713\pi$
$211$	0.534767	−	0.534767i	0.0368149	−	0.0368149i	0.725275	+	0.688460i	$0.241713\pi$
$212$	13.6218	−	6.14874i	0.935546	−	0.422297i
$213$	19.1180	−	5.12266i	1.30995	−	0.350999i
$214$	15.5894	+	2.84798i	1.06567	+	0.194684i
$215$	−11.4711	+	6.62285i	−0.782324	+	0.451675i
$216$	−6.11231	+	10.1489i	−0.415890	+	0.690545i
$217$		0			0
$218$	−10.7171	+	3.82609i	−0.725853	+	0.259136i
$219$	−7.72585	+	28.8333i	−0.522064	+	1.94837i
$220$	−4.32908	−	26.4535i	−0.291866	−	1.78349i
$221$	−3.34165	−	12.4712i	−0.224784	−	0.838903i
$222$	−1.31091	−	16.1276i	−0.0879828	−	1.08242i
$223$	7.83775			0.524855			0.262427	−	0.964952i	$-0.415477\pi$
$223$	7.83775			0.524855			0.262427	+	0.964952i	$0.415477\pi$
$224$		0			0
$225$	3.80876			0.253917
$226$	1.74851	+	21.5113i	0.116309	+	1.43091i
$227$	−0.0906182	−	0.338192i	−0.00601454	−	0.0224466i	0.962853	−	0.270025i	$-0.0870319\pi$
$227$	−0.0906182	−	0.338192i	−0.00601454	−	0.0224466i	−0.968868	+	0.247578i	$0.920365\pi$
$228$	−0.765384	−	4.67700i	−0.0506888	−	0.309742i
$229$	5.71108	−	21.3140i	0.377399	−	1.40847i	−0.472409	−	0.881379i	$-0.656616\pi$
$229$	5.71108	−	21.3140i	0.377399	−	1.40847i	0.849808	−	0.527092i	$-0.176718\pi$
$230$	25.0970	−	8.95983i	1.65485	−	0.590794i
$231$		0			0
$232$	21.3849	+	12.8794i	1.40399	+	0.845571i
$233$	−8.24017	+	4.75746i	−0.539831	+	0.311672i	−0.745011	−	0.667053i	$-0.767556\pi$
$233$	−8.24017	+	4.75746i	−0.539831	+	0.311672i	0.205179	+	0.978724i	$0.434222\pi$
$234$	3.00612	+	0.549178i	0.196516	+	0.0359009i
$235$	−10.6570	+	2.85554i	−0.695188	+	0.186275i
$236$	18.3952	−	8.30341i	1.19742	−	0.540506i
$237$	9.20091	−	9.20091i	0.597663	−	0.597663i
$238$		0			0
$239$	18.8469			1.21910			0.609552	−	0.792746i	$-0.291349\pi$
$239$	18.8469			1.21910			0.609552	+	0.792746i	$0.291349\pi$
$240$	22.8369	−	7.68012i	1.47411	−	0.495750i
$241$	−3.19914	+	5.54108i	−0.206075	+	0.356932i	−0.950475	−	0.310802i	$-0.899402\pi$
$241$	−3.19914	+	5.54108i	−0.206075	+	0.356932i	0.744400	+	0.667734i	$0.232736\pi$
$242$	6.56537	+	9.50036i	0.422038	+	0.610706i
$243$	8.49058	+	2.27504i	0.544671	+	0.145944i
$244$	−2.92677	−	0.292441i	−0.187367	−	0.0187216i
$245$		0			0
$246$	5.92151	+	16.5865i	0.377542	+	1.05751i
$247$	2.58738	−	1.49382i	0.164631	−	0.0950498i
$248$	7.56290	+	2.17706i	0.480245	+	0.138243i
$249$	−17.8734	−	10.3192i	−1.13268	−	0.653953i
$250$	−2.07030	−	1.75904i	−0.130937	−	0.111251i
$251$	2.93159	+	2.93159i	0.185040	+	0.185040i	0.793548	−	0.608508i	$-0.208232\pi$
$251$	2.93159	+	2.93159i	0.185040	+	0.185040i	−0.608508	+	0.793548i	$0.708232\pi$
$252$		0			0
$253$	−19.0536	+	19.0536i	−1.19789	+	1.19789i
$254$	−0.206840	−	2.54467i	−0.0129783	−	0.159667i
$255$	−15.6751	+	27.1500i	−0.981611	+	1.70020i
$256$	12.7485	−	9.66824i	0.796784	−	0.604265i
$257$	14.4838	+	25.0867i	0.903475	+	1.56487i	0.822951	+	0.568113i	$0.192326\pi$
$257$	14.4838	+	25.0867i	0.903475	+	1.56487i	0.0805246	+	0.996753i	$0.474340\pi$
$258$	10.8792	+	5.15487i	0.677306	+	0.320928i
$259$		0			0
$260$	9.61914	+	11.7548i	0.596554	+	0.729002i
$261$	1.98982	−	7.42611i	0.123167	−	0.459665i
$262$	−3.33752	+	18.2691i	−0.206193	+	1.12867i
$263$	0.298299	+	0.172223i	0.0183939	+	0.0106197i	0.509169	−	0.860667i	$-0.329953\pi$
$263$	0.298299	+	0.172223i	0.0183939	+	0.0106197i	−0.490775	+	0.871286i	$0.663286\pi$
$264$	−17.5424	+	16.9056i	−1.07966	+	1.04047i
$265$		−	22.8771i		−	1.40533i
$266$		0			0
$267$	−4.53743	−	4.53743i	−0.277686	−	0.277686i
$268$	1.12491	+	2.49210i	0.0687148	+	0.152229i
$269$	3.61587	+	13.4946i	0.220463	+	0.822781i	0.984171	+	0.177219i	$0.0567100\pi$
$269$	3.61587	+	13.4946i	0.220463	+	0.822781i	−0.763708	+	0.645562i	$0.776623\pi$
$270$	10.3102	+	14.9192i	0.627457	+	0.907956i
$271$	−6.24843	−	10.8226i	−0.379565	−	0.657426i	0.611434	−	0.791296i	$-0.290593\pi$
$271$	−6.24843	−	10.8226i	−0.379565	−	0.657426i	−0.990999	+	0.133869i	$0.957260\pi$
$272$	−4.11927	+	20.4072i	−0.249767	+	1.23737i
$273$		0			0
$274$	−4.80602	+	10.1429i	−0.290342	+	0.612756i
$275$	−18.4901	−	4.95441i	−1.11500	−	0.298762i
$276$	−19.6671	−	14.1354i	−1.18382	−	0.850851i
$277$	8.19541	−	2.19595i	0.492415	−	0.131942i	−0.00406280	−	0.999992i	$-0.501293\pi$
$277$	8.19541	−	2.19595i	0.492415	−	0.131942i	0.496477	+	0.868050i	$0.334627\pi$
$278$	−2.67953	+	3.15367i	−0.160708	+	0.189145i
$279$		−	2.42372i		−	0.145104i
$280$		0			0
$281$			9.56494i			0.570596i	0.958439	+	0.285298i	$0.0920926\pi$
$281$			9.56494i			0.570596i	−0.958439	+	0.285298i	$0.907907\pi$
$282$	7.64169	+	6.49279i	0.455056	+	0.386640i
$283$	15.9658	−	4.27803i	0.949070	−	0.254303i	0.249102	−	0.968477i	$-0.419864\pi$
$283$	15.9658	−	4.27803i	0.949070	−	0.254303i	0.699968	+	0.714175i	$0.253198\pi$
$284$	−3.24928	−	19.8553i	−0.192810	−	1.17819i
$285$	−7.00726	−	1.87759i	−0.415074	−	0.111219i
$286$	−13.8792	−	6.57639i	−0.820696	−	0.388870i
$287$		0			0
$288$	−3.94740	−	2.94928i	−0.232603	−	0.173788i
$289$	−5.04445	−	8.73725i	−0.296732	−	0.513956i
$290$	31.4366	−	21.7247i	1.84602	−	1.27572i
$291$	−3.90247	−	14.5642i	−0.228767	−	0.853769i
$292$	28.3834	+	10.7286i	1.66102	+	0.627845i
$293$	15.2913	+	15.2913i	0.893328	+	0.893328i	0.994835	−	0.101507i	$-0.0323664\pi$
$293$	15.2913	+	15.2913i	0.893328	+	0.893328i	−0.101507	+	0.994835i	$0.532366\pi$
$294$		0			0
$295$		−	30.8938i		−	1.79870i
$296$	−16.4453	−	0.303998i	−0.955863	−	0.0176695i
$297$	−15.8808	−	9.16877i	−0.921496	−	0.532026i
$298$	18.0119	+	3.29053i	1.04340	+	0.190615i
$299$	3.95178	−	14.7482i	0.228537	−	0.852913i
$300$	1.71068	−	17.1207i	0.0987663	−	0.988462i
$301$		0			0
$302$	−1.69735	+	3.58219i	−0.0976716	+	0.206132i
$303$	−13.8185	−	23.9343i	−0.793850	−	1.37499i
$304$	−4.80805	+	0.301484i	−0.275760	+	0.0172913i
$305$	−2.25120	+	3.89919i	−0.128903	+	0.223267i
$306$	6.39046	−	0.519440i	0.365318	−	0.0296944i
$307$	4.16259	−	4.16259i	0.237571	−	0.237571i	−0.578272	−	0.815844i	$-0.696273\pi$
$307$	4.16259	−	4.16259i	0.237571	−	0.237571i	0.815844	+	0.578272i	$0.196273\pi$
$308$		0			0
$309$	2.24265	+	2.24265i	0.127580	+	0.127580i
$310$	7.80028	−	9.18054i	0.443026	−	0.521420i
$311$	−0.695092	−	0.401312i	−0.0394151	−	0.0227563i	0.480163	−	0.877179i	$-0.340578\pi$
$311$	−0.695092	−	0.401312i	−0.0394151	−	0.0227563i	−0.519578	+	0.854423i	$0.673911\pi$
$312$	3.81877	−	13.2661i	0.216196	−	0.751043i
$313$	15.3533	−	8.86423i	0.867819	−	0.501036i	0.00119626	−	0.999999i	$-0.499619\pi$
$313$	15.3533	−	8.86423i	0.867819	−	0.501036i	0.866623	+	0.498964i	$0.166286\pi$
$314$	1.80596	−	0.644742i	0.101916	−	0.0363849i
$315$		0			0
$316$	−8.37664	−	10.2364i	−0.471223	−	0.575845i
$317$	−14.1644	−	3.79534i	−0.795552	−	0.213168i	−0.161922	−	0.986804i	$-0.551769\pi$
$317$	−14.1644	−	3.79534i	−0.795552	−	0.213168i	−0.633630	+	0.773636i	$0.718436\pi$
$318$	−17.1052	+	11.8208i	−0.959212	+	0.662878i
$319$	−19.3197	+	33.4627i	−1.08169	+	1.87355i
$320$	−5.46025	−	23.8752i	−0.305238	−	1.33467i
$321$	−22.0475			−1.23057
$322$		0			0
$323$	4.43243	−	4.43243i	0.246627	−	0.246627i
$324$	7.67567	−	20.3066i	0.426426	−	1.12815i
$325$	10.4772	−	2.80735i	0.581170	−	0.155724i
$326$	4.64396	−	25.4204i	0.257205	−	1.40790i
$327$	13.7106	−	7.91584i	0.758200	−	0.437747i
$328$	17.3754	−	4.31316i	0.959393	−	0.238154i
$329$		0			0
$330$	12.5387	+	35.1215i	0.690230	+	1.93337i
$331$	−0.0816464	+	0.304708i	−0.00448769	+	0.0167483i	−0.968133	−	0.250435i	$-0.919426\pi$
$331$	−0.0816464	+	0.304708i	−0.00448769	+	0.0167483i	0.963646	+	0.267183i	$0.0860930\pi$
$332$	−12.2441	+	17.0356i	−0.671980	+	0.934952i
$333$	1.31105	+	4.89289i	0.0718449	+	0.268129i
$334$	2.76431	−	0.224693i	0.151256	−	0.0122947i
$335$	4.18535			0.228670
$336$		0			0
$337$	−26.7633			−1.45789			−0.728944	−	0.684573i	$-0.759989\pi$
$337$	−26.7633			−1.45789			−0.728944	+	0.684573i	$0.759989\pi$
$338$	−9.65028	+	0.784411i	−0.524906	+	0.0426663i
$339$	−7.77128	−	29.0028i	−0.422078	−	1.57522i
$340$	25.8775	+	18.5990i	1.40340	+	1.00867i
$341$	−3.15275	+	11.7662i	−0.170731	+	0.637178i
$342$	0.498834	+	1.39726i	0.0269739	+	0.0755552i
$343$		0			0
$344$	6.31357	−	10.4831i	0.340405	−	0.565209i
$345$	−32.1072	+	18.5371i	−1.72859	+	0.998003i
$346$	1.48816	−	8.14597i	0.0800040	−	0.437930i
$347$	−33.6147	+	9.00704i	−1.80453	+	0.483523i	−0.994671	−	0.103098i	$-0.967124\pi$
$347$	−33.6147	+	9.00704i	−1.80453	+	0.483523i	−0.809861	+	0.586621i	$0.800458\pi$
$348$	−32.4872	−	12.2798i	−1.74150	−	0.658265i
$349$	−13.7818	+	13.7818i	−0.737725	+	0.737725i	−0.972137	−	0.234412i	$-0.924683\pi$
$349$	−13.7818	+	13.7818i	−0.737725	+	0.737725i	0.234412	+	0.972137i	$0.424683\pi$
$350$		0			0
$351$	10.3907			0.554616
$352$	15.3268	+	19.4524i	0.816920	+	1.03682i
$353$	−13.0221	+	22.5550i	−0.693099	+	1.20048i	0.277718	+	0.960663i	$0.410422\pi$
$353$	−13.0221	+	22.5550i	−0.693099	+	1.20048i	−0.970817	+	0.239820i	$0.922912\pi$
$354$	−23.0993	+	15.9631i	−1.22771	+	0.848430i
$355$	−29.7479	−	7.97093i	−1.57886	−	0.423053i
$356$	−5.04811	+	4.13094i	−0.267549	+	0.218940i
$357$		0			0
$358$	17.9225	−	6.39850i	0.947235	−	0.338171i
$359$	18.2196	−	10.5191i	0.961593	−	0.555176i	0.0649297	−	0.997890i	$-0.479318\pi$
$359$	18.2196	−	10.5191i	0.961593	−	0.555176i	0.896663	+	0.442714i	$0.145984\pi$
$360$	−6.60072	+	3.64996i	−0.347889	+	0.192370i
$361$	−15.1983	−	8.77474i	−0.799911	−	0.461829i
$362$	9.84742	−	11.5899i	0.517569	−	0.609153i
$363$	−11.3606	−	11.3606i	−0.596274	−	0.596274i
$364$		0			0
$365$	32.8434	−	32.8434i	1.71910	−	1.71910i
$366$	4.07865	−	0.331528i	0.213194	−	0.0173292i
$367$	3.70670	−	6.42020i	0.193488	−	0.335132i	−0.752916	−	0.658117i	$-0.771353\pi$
$367$	3.70670	−	6.42020i	0.193488	−	0.335132i	0.946404	+	0.322986i	$0.104687\pi$
$368$	−16.2854	+	18.4643i	−0.848933	+	0.962518i
$369$	−2.75673	−	4.77480i	−0.143510	−	0.248566i
$370$	−10.7809	+	22.7526i	−0.560472	+	1.18285i
$371$		0			0
$372$	−10.8948	−	1.08860i	−0.564868	−	0.0564412i
$373$	1.37367	−	5.12662i	0.0711261	−	0.265446i	−0.921201	−	0.389087i	$-0.872790\pi$
$373$	1.37367	−	5.12662i	0.0711261	−	0.265446i	0.992327	+	0.123641i	$0.0394571\pi$
$374$	−31.6990	−	5.79098i	−1.63912	−	0.299445i
$375$	3.27318	+	1.88977i	0.169026	+	0.0975873i
$376$	7.33964	−	7.07322i	0.378513	−	0.364773i
$377$		−	21.8945i		−	1.12762i
$378$		0			0
$379$	18.8387	+	18.8387i	0.967677	+	0.967677i	0.999494	−	0.0318167i	$-0.0101293\pi$
$379$	18.8387	+	18.8387i	0.967677	+	0.967677i	−0.0318167	+	0.999494i	$0.510129\pi$
$380$	−2.60734	+	6.89795i	−0.133754	+	0.353857i
$381$	0.919300	+	3.43087i	0.0470972	+	0.175769i
$382$	−23.8362	+	16.4723i	−1.21956	+	0.842799i
$383$	−2.47310	−	4.28353i	−0.126369	−	0.218878i	0.795898	−	0.605431i	$-0.206999\pi$
$383$	−2.47310	−	4.28353i	−0.126369	−	0.218878i	−0.922267	+	0.386553i	$0.873666\pi$
$384$	−15.0302	+	16.4192i	−0.767005	+	0.837889i
$385$		0			0
$386$	−16.2505	−	7.69999i	−0.827130	−	0.391919i
$387$	−3.64034	−	0.975426i	−0.185049	−	0.0495837i
$388$	−15.1258	+	2.47532i	−0.767898	+	0.125665i
$389$	−19.1608	+	5.13412i	−0.971491	+	0.260310i	−0.709457	−	0.704748i	$-0.751060\pi$
$389$	−19.1608	+	5.13412i	−0.971491	+	0.260310i	−0.262034	+	0.965059i	$0.584393\pi$
$390$	−16.1036	−	13.6824i	−0.815436	−	0.692838i
$391$		−	32.0349i		−	1.62007i
$392$		0			0
$393$		−	25.8372i		−	1.30332i
$394$	16.6585	−	19.6062i	0.839244	−	0.987748i
$395$	−19.5570	+	5.24028i	−0.984020	+	0.263667i
$396$	4.45123	−	6.19317i	0.223683	−	0.311218i
$397$	−0.0872772	−	0.0233859i	−0.00438032	−	0.00117370i	0.256628	−	0.966510i	$-0.417388\pi$
$397$	−0.0872772	−	0.0233859i	−0.00438032	−	0.00117370i	−0.261009	+	0.965336i	$0.584055\pi$
$398$	−0.889246	+	1.87672i	−0.0445739	+	0.0940714i
$399$		0			0
$400$	−17.1443	−	3.46064i	−0.857216	−	0.173032i
$401$	12.7052	+	22.0060i	0.634466	+	1.09893i	0.986628	+	0.162988i	$0.0521133\pi$
$401$	12.7052	+	22.0060i	0.634466	+	1.09893i	−0.352162	+	0.935939i	$0.614553\pi$
$402$	−2.16261	−	3.12939i	−0.107861	−	0.156080i
$403$	−1.78647	−	6.66719i	−0.0889903	−	0.332116i
$404$	−25.6056	+	11.5582i	−1.27393	+	0.575040i
$405$	−23.4975	−	23.4975i	−1.16760	−	1.16760i
$406$		0			0
$407$		−	25.4586i		−	1.26194i
$408$	0.535316	−	28.9589i	0.0265021	−	1.43368i
$409$	−19.4037	−	11.2027i	−0.959450	−	0.553939i	−0.0634462	−	0.997985i	$-0.520209\pi$
$409$	−19.4037	−	11.2027i	−0.959450	−	0.553939i	−0.896004	+	0.444047i	$0.853542\pi$
$410$	4.92487	−	26.9580i	0.243222	−	1.33136i
$411$	4.04149	−	15.0831i	0.199352	−	0.743992i
$412$	2.49505	−	2.04174i	0.122922	−	0.100589i
$413$		0			0
$414$	6.85191	+	3.24664i	0.336753	+	0.159564i
$415$	16.0568	+	27.8112i	0.788197	+	1.36520i
$416$	−13.0324	−	5.20337i	−0.638967	−	0.255116i
$417$	2.87867	−	4.98601i	0.140969	−	0.244166i
$418$	−0.604106	−	7.43207i	−0.0295478	−	0.363514i
$419$	24.2758	−	24.2758i	1.18595	−	1.18595i	0.207775	−	0.978177i	$-0.433378\pi$
$419$	24.2758	−	24.2758i	1.18595	−	1.18595i	0.978177	−	0.207775i	$-0.0666220\pi$
$420$		0			0
$421$	16.0270	+	16.0270i	0.781108	+	0.781108i	0.980018	−	0.198910i	$-0.0637400\pi$
$421$	16.0270	+	16.0270i	0.781108	+	0.781108i	−0.198910	+	0.980018i	$0.563740\pi$
$422$	0.815059	+	0.692518i	0.0396765	+	0.0337112i
$423$	−2.71861	−	1.56959i	−0.132183	−	0.0763160i
$424$	10.2278	+	18.4963i	0.496704	+	0.898258i
$425$	19.7087	−	11.3788i	0.956014	−	0.551955i
$426$	9.41117	+	26.3612i	0.455973	+	1.27720i
$427$		0			0
$428$	−2.22826	+	22.3006i	−0.107707	+	1.07794i
$429$	20.6391	+	5.53024i	0.996466	+	0.267002i
$430$	−10.6496	−	15.4105i	−0.513571	−	0.743159i
$431$	15.8307	−	27.4196i	0.762540	−	1.32076i	−0.178998	−	0.983849i	$-0.557285\pi$
$431$	15.8307	−	27.4196i	0.762540	−	1.32076i	0.941538	−	0.336908i	$-0.109381\pi$
$432$	−15.0058	−	7.45289i	−0.721969	−	0.358577i
$433$	11.6823			0.561413			0.280707	−	0.959794i	$-0.409431\pi$
$433$	11.6823			0.561413			0.280707	+	0.959794i	$0.409431\pi$
$434$		0			0
$435$	−37.5920	+	37.5920i	−1.80240	+	1.80240i
$436$	−6.62103	−	14.6681i	−0.317090	−	0.702473i
$437$	7.16032	−	1.91860i	0.342525	−	0.0917792i
$438$	−41.5275	−	7.58652i	−1.98426	−	0.362498i
$439$	−11.3637	+	6.56086i	−0.542362	+	0.313133i	−0.746036	−	0.665906i	$-0.768045\pi$
$439$	−11.3637	+	6.56086i	−0.542362	+	0.313133i	0.203674	+	0.979039i	$0.434712\pi$
$440$	36.7919	−	9.13301i	1.75399	−	0.435399i
$441$		0			0
$442$	17.1961	−	6.13915i	0.817935	−	0.292010i
$443$	−5.93692	+	22.1569i	−0.282071	+	1.05271i	0.668881	+	0.743369i	$0.266773\pi$
$443$	−5.93692	+	22.1569i	−0.282071	+	1.05271i	−0.950953	+	0.309336i	$0.899893\pi$
$444$	22.5828	−	3.69564i	1.07173	−	0.175387i
$445$	2.58425	+	9.64455i	0.122505	+	0.457196i
$446$	0.898007	+	11.0478i	0.0425219	+	0.523129i
$447$	−25.4735			−1.20485
$448$		0			0
$449$	−15.6396			−0.738077			−0.369038	−	0.929414i	$-0.620313\pi$
$449$	−15.6396			−0.738077			−0.369038	+	0.929414i	$0.620313\pi$
$450$	0.436387	+	5.36870i	0.0205715	+	0.253083i
$451$	7.17188	+	26.7658i	0.337711	+	1.26035i
$452$	−30.1212	+	4.92929i	−1.41678	+	0.231854i
$453$	1.42734	−	5.32691i	0.0670623	−	0.250280i
$454$	0.466321	−	0.166480i	0.0218855	−	0.00781331i
$455$		0			0
$456$	6.50484	−	1.61472i	0.304617	−	0.0756164i
$457$	10.5919	−	6.11523i	0.495468	−	0.286058i	−0.231372	−	0.972865i	$-0.574322\pi$
$457$	10.5919	−	6.11523i	0.495468	−	0.286058i	0.726840	+	0.686807i	$0.240988\pi$
$458$	30.6979	+	5.60809i	1.43442	+	0.262049i
$459$	21.0580	−	5.64247i	0.982903	−	0.263368i
$460$	15.5049	+	34.3492i	0.722922	+	1.60154i
$461$	13.4658	−	13.4658i	0.627163	−	0.627163i	−0.320191	−	0.947353i	$-0.603747\pi$
$461$	13.4658	−	13.4658i	0.627163	−	0.627163i	0.947353	+	0.320191i	$0.103747\pi$
$462$		0			0
$463$	−24.7807			−1.15166			−0.575829	−	0.817570i	$-0.695321\pi$
$463$	−24.7807			−1.15166			−0.575829	+	0.817570i	$0.695321\pi$
$464$	−15.7041	+	31.6191i	−0.729045	+	1.46788i
$465$	−8.38000	+	14.5146i	−0.388613	+	0.673098i
$466$	−7.65007	−	11.0700i	−0.354383	−	0.512806i
$467$	31.6485	+	8.48020i	1.46452	+	0.392417i	0.901048	−	0.433718i	$-0.142799\pi$
$467$	31.6485	+	8.48020i	1.46452	+	0.392417i	0.563472	+	0.826135i	$0.309465\pi$
$468$	−0.429677	+	4.30024i	−0.0198618	+	0.198779i
$469$		0			0
$470$	−5.24610	−	14.6946i	−0.241985	−	0.677812i
$471$	−2.31040	+	1.33391i	−0.106458	+	0.0614634i
$472$	13.8118	+	24.9778i	0.635740	+	1.14970i
$473$	16.4037	+	9.47066i	0.754242	+	0.435462i
$474$	14.0235	+	11.9151i	0.644119	+	0.547278i
$475$	3.72373	+	3.72373i	0.170857	+	0.170857i
$476$		0			0
$477$	4.60265	−	4.60265i	0.210741	−	0.210741i
$478$	2.15938	+	26.5659i	0.0987676	+	1.21510i
$479$	17.6824	−	30.6268i	0.807930	−	1.39938i	−0.106365	−	0.994327i	$-0.533921\pi$
$479$	17.6824	−	30.6268i	0.807930	−	1.39938i	0.914295	−	0.405049i	$-0.132746\pi$
$480$	13.4422	+	31.3101i	0.613548	+	1.42910i
$481$	7.21289	+	12.4931i	0.328879	+	0.569636i
$482$	−8.17705	−	3.87453i	−0.372454	−	0.176480i
$483$		0			0
$484$	−12.6391	+	10.3428i	−0.574507	+	0.470128i
$485$	−6.07229	+	22.6621i	−0.275729	+	1.02903i
$486$	−2.23402	+	12.2287i	−0.101337	+	0.554705i
$487$	14.4850	+	8.36292i	0.656378	+	0.378960i	0.790896	−	0.611951i	$-0.209615\pi$
$487$	14.4850	+	8.36292i	0.656378	+	0.378960i	−0.134517	+	0.990911i	$0.542948\pi$
$488$	0.0768804	−	4.15898i	0.00348021	−	0.188268i
$489$			35.9510i			1.62576i
$490$		0			0
$491$	5.93243	+	5.93243i	0.267727	+	0.267727i	0.828184	−	0.560457i	$-0.189374\pi$
$491$	5.93243	+	5.93243i	0.267727	+	0.267727i	−0.560457	+	0.828184i	$0.689374\pi$
$492$	−22.7012	+	10.2471i	−1.02345	+	0.461977i
$493$	−11.8894	−	44.3717i	−0.535470	−	1.99840i
$494$	2.40209	+	3.47593i	0.108075	+	0.156389i
$495$	−5.83732	−	10.1105i	−0.262368	−	0.454434i
$496$	−2.20219	+	10.9098i	−0.0988813	+	0.489866i
$497$		0			0
$498$	12.4977	−	26.3760i	0.560037	−	1.18194i
$499$	7.59066	+	2.03391i	0.339805	+	0.0910504i	0.424686	−	0.905341i	$-0.360384\pi$
$499$	7.59066	+	2.03391i	0.339805	+	0.0910504i	−0.0848814	+	0.996391i	$0.527051\pi$
$500$	2.24227	−	3.11976i	0.100278	−	0.139520i
$501$	−3.72701	+	0.998649i	−0.166510	+	0.0446164i
$502$	−3.79638	+	4.46815i	−0.169441	+	0.199423i
$503$		−	6.99765i		−	0.312010i	−0.987756	−	0.156005i	$-0.950138\pi$
$503$		−	6.99765i		−	0.312010i	0.987756	−	0.156005i	$-0.0498616\pi$
$504$		0			0
$505$			43.0034i			1.91363i
$506$	−29.0403	−	24.6742i	−1.29100	−	1.09690i
$507$	13.0111	−	3.48631i	0.577843	−	0.154833i
$508$	3.56317	−	0.583108i	0.158090	−	0.0258712i
$509$	4.88676	+	1.30940i	0.216602	+	0.0580383i	0.365488	−	0.930816i	$-0.380902\pi$
$509$	4.88676	+	1.30940i	0.216602	+	0.0580383i	−0.148886	+	0.988854i	$0.547569\pi$
$510$	−40.0657	−	18.9843i	−1.77414	−	0.840640i
$511$		0			0
$512$	15.0887	+	16.8622i	0.666831	+	0.745209i
$513$	2.52237	+	4.36887i	0.111365	+	0.192890i
$514$	−33.7018	+	23.2902i	−1.48652	+	1.02729i
$515$	−1.27728	−	4.76687i	−0.0562837	−	0.210053i
$516$	−6.01965	+	15.9255i	−0.265000	+	0.701080i
$517$	11.1561	+	11.1561i	0.490645	+	0.490645i
$518$		0			0
$519$			11.5205i			0.505695i
$520$	−15.4671	+	14.9056i	−0.678275	+	0.653654i
$521$	−15.0383	−	8.68234i	−0.658838	−	0.380380i	0.132996	−	0.991117i	$-0.457540\pi$
$521$	−15.0383	−	8.68234i	−0.658838	−	0.380380i	−0.791834	+	0.610736i	$0.790874\pi$
$522$	10.6956	+	1.95394i	0.468132	+	0.0855215i
$523$	9.49950	−	35.4526i	0.415384	−	1.55023i	−0.368681	−	0.929556i	$-0.620190\pi$
$523$	9.49950	−	35.4526i	0.415384	−	1.55023i	0.784065	−	0.620679i	$-0.213143\pi$
$524$	−26.1339	−	2.61128i	−1.14166	−	0.114074i
$525$		0			0
$526$	−0.208582	+	0.440204i	−0.00909461	+	0.0191938i
$527$	−7.24096	−	12.5417i	−0.315421	−	0.546325i
$528$	−25.8395	−	22.7902i	−1.12452	−	0.991817i
$529$	7.44198	−	12.8899i	0.323564	−	0.560430i
$530$	32.2467	−	2.62113i	1.40071	−	0.113855i
$531$	6.21554	−	6.21554i	0.269731	−	0.269731i
$532$		0			0
$533$	−11.1027	−	11.1027i	−0.480909	−	0.480909i
$534$	5.87593	−	6.91568i	0.254276	−	0.299271i
$535$	29.7100	+	17.1531i	1.28448	+	0.741593i
$536$	−3.38388	+	1.87116i	−0.146162	+	0.0808220i
$537$	−22.9287	+	13.2379i	−0.989448	+	0.571258i
$538$	−18.6072	+	6.64294i	−0.802215	+	0.286397i
$539$		0			0
$540$	−19.8483	+	16.2422i	−0.854137	+	0.698953i
$541$	15.4749	+	4.14648i	0.665317	+	0.178271i	0.575644	−	0.817700i	$-0.304751\pi$
$541$	15.4749	+	4.14648i	0.665317	+	0.178271i	0.0896726	+	0.995971i	$0.471418\pi$
$542$	14.5392	−	10.0476i	0.624514	−	0.431580i
$543$	−10.5793	+	18.3239i	−0.454001	+	0.786352i
$544$	−29.2372	−	3.46823i	−1.25354	−	0.148699i
$545$	−24.6343			−1.05522
$546$		0			0
$547$	−10.8422	+	10.8422i	−0.463578	+	0.463578i	−0.899826	−	0.436248i	$-0.856307\pi$
$547$	−10.8422	+	10.8422i	−0.463578	+	0.463578i	0.436248	+	0.899826i	$0.356307\pi$
$548$	−14.8478	−	5.61228i	−0.634265	−	0.239745i
$549$	−1.23740	+	0.331561i	−0.0528111	+	0.0141507i
$550$	4.86507	−	26.6307i	0.207447	−	1.13554i
$551$	9.20572	−	5.31493i	0.392177	−	0.226423i
$552$	17.6714	−	29.3416i	0.752145	−	1.24886i
$553$		0			0
$554$	4.03433	+	11.3004i	0.171402	+	0.480106i
$555$	9.06589	−	33.8344i	0.384826	−	1.43619i
$556$	−4.75231	−	3.41564i	−0.201543	−	0.144855i
$557$	−5.77540	−	21.5541i	−0.244711	−	0.913275i	−0.973528	−	0.228567i	$-0.926596\pi$
$557$	−5.77540	−	21.5541i	−0.244711	−	0.913275i	0.728817	−	0.684709i	$-0.240071\pi$
$558$	3.41638	−	0.277696i	0.144627	−	0.0117558i
$559$	−10.7329			−0.453952
$560$		0			0
$561$	44.8306			1.89275
$562$	−13.4824	+	1.09590i	−0.568721	+	0.0462277i
$563$	−5.40483	−	20.1711i	−0.227786	−	0.850110i	−0.981269	−	0.192643i	$-0.938294\pi$
$563$	−5.40483	−	20.1711i	−0.227786	−	0.850110i	0.753483	−	0.657468i	$-0.228372\pi$
$564$	−8.27646	+	11.5154i	−0.348502	+	0.484884i
$565$	−12.0922	+	45.1287i	−0.508723	+	1.89858i
$566$	7.85944	+	22.0147i	0.330357	+	0.925348i
$567$		0			0
$568$	27.6150	−	6.85498i	1.15870	−	0.287629i
$569$	15.2567	−	8.80848i	0.639596	−	0.369271i	−0.144863	−	0.989452i	$-0.546274\pi$
$569$	15.2567	−	8.80848i	0.639596	−	0.369271i	0.784459	+	0.620181i	$0.212941\pi$
$570$	1.84373	−	10.0923i	0.0772254	−	0.422720i
$571$	8.29448	−	2.22250i	0.347113	−	0.0930087i	−0.0810502	−	0.996710i	$-0.525827\pi$
$571$	8.29448	−	2.22250i	0.347113	−	0.0930087i	0.428164	+	0.903701i	$0.359161\pi$
$572$	7.67965	−	20.3171i	0.321102	−	0.849503i
$573$	28.5034	−	28.5034i	1.19074	−	1.19074i
$574$		0			0
$575$	26.9129			1.12234
$576$	3.70493	−	5.90203i	0.154372	−	0.245918i
$577$	−17.6514	+	30.5732i	−0.734838	+	1.27278i	0.219956	+	0.975510i	$0.429409\pi$
$577$	−17.6514	+	30.5732i	−0.734838	+	1.27278i	−0.954794	+	0.297268i	$0.903925\pi$
$578$	11.7377	−	8.11155i	0.488226	−	0.337396i
$579$	24.1654	+	6.47509i	1.00428	+	0.269096i
$580$	34.2242	+	41.8228i	1.42108	+	1.73660i
$581$		0			0
$582$	20.0821	−	7.16947i	0.832429	−	0.297184i
$583$	−28.3313	+	16.3571i	−1.17336	+	0.677441i
$584$	−11.8707	+	41.2375i	−0.491211	+	1.70642i
$585$	5.72900	+	3.30764i	0.236865	+	0.136754i
$586$	−19.8021	+	23.3061i	−0.818017	+	0.962766i
$587$	2.38838	+	2.38838i	0.0985791	+	0.0985791i	0.754676	−	0.656097i	$-0.227794\pi$
$587$	2.38838	+	2.38838i	0.0985791	+	0.0985791i	−0.656097	+	0.754676i	$0.727794\pi$
$588$		0			0
$589$	2.36961	−	2.36961i	0.0976379	−	0.0976379i
$590$	43.5467	−	3.53964i	1.79279	−	0.145725i
$591$	−17.8966	+	30.9978i	−0.736167	+	1.27508i
$592$	−1.45571	−	23.2155i	−0.0598292	−	0.954152i
$593$	5.78207	+	10.0148i	0.237441	+	0.411260i	0.959979	−	0.280071i	$-0.0903580\pi$
$593$	5.78207	+	10.0148i	0.237441	+	0.411260i	−0.722538	+	0.691331i	$0.757025\pi$
$594$	11.1044	−	23.4355i	0.455621	−	0.961570i
$595$		0			0
$596$	−2.57451	+	25.7659i	−0.105456	+	1.05541i
$597$	0.747787	−	2.79078i	0.0306049	−	0.114219i
$598$	21.2414	+	3.88051i	0.868624	+	0.158686i
$599$	10.6273	+	6.13567i	0.434219	+	0.250697i	0.701142	−	0.713021i	$-0.252674\pi$
$599$	10.6273	+	6.13567i	0.434219	+	0.250697i	−0.266923	+	0.963718i	$0.586007\pi$
$600$	24.3287	+	0.449725i	0.993214	+	0.0183600i
$601$			14.1538i			0.577347i	0.957428	+	0.288674i	$0.0932143\pi$
$601$			14.1538i			0.577347i	−0.957428	+	0.288674i	$0.906786\pi$
$602$		0			0
$603$	0.842054	+	0.842054i	0.0342911	+	0.0342911i
$604$	−5.24381	−	1.98210i	−0.213367	−	0.0806504i
$605$	6.47029	+	24.1474i	0.263055	+	0.981733i
$606$	32.1537	−	22.2203i	1.30615	−	0.902637i
$607$	−12.8174	−	22.2005i	−0.520244	−	0.901089i	−0.999723	−	0.0235358i	$-0.992508\pi$
$607$	−12.8174	−	22.2005i	−0.520244	−	0.901089i	0.479479	−	0.877553i	$-0.340826\pi$
$608$	−0.975842	−	6.74271i	−0.0395756	−	0.273453i
$609$		0			0
$610$	−5.75410	−	2.72646i	−0.232977	−	0.110391i
$611$	−8.63529	−	2.31382i	−0.349346	−	0.0936071i
$612$	1.46437	+	8.94825i	0.0591936	+	0.361712i
$613$	−9.30020	+	2.49198i	−0.375632	+	0.100650i	−0.441695	−	0.897165i	$-0.645623\pi$
$613$	−9.30020	+	2.49198i	−0.375632	+	0.100650i	0.0660634	+	0.997815i	$0.478956\pi$
$614$	6.34436	+	5.39051i	0.256038	+	0.217543i
$615$			38.1256i			1.53737i
$616$		0			0
$617$		−	23.1951i		−	0.933800i	−0.884310	−	0.466900i	$-0.845371\pi$
$617$		−	23.1951i		−	0.933800i	0.884310	−	0.466900i	$-0.154629\pi$
$618$	−2.90421	+	3.41811i	−0.116824	+	0.137497i
$619$	32.4267	−	8.68871i	1.30334	−	0.349229i	0.460627	−	0.887594i	$-0.347625\pi$
$619$	32.4267	−	8.68871i	1.30334	−	0.349229i	0.842712	+	0.538365i	$0.180958\pi$
$620$	13.8343	+	9.94314i	0.555598	+	0.399326i
$621$	24.9028	+	6.67270i	0.999317	+	0.267766i
$622$	0.486035	−	1.02576i	0.0194882	−	0.0411291i
$623$		0			0
$624$	19.1369	+	3.86286i	0.766089	+	0.154638i
$625$	−13.8718	−	24.0267i	−0.554873	−	0.961068i
$626$	14.2538	+	20.6258i	0.569696	+	0.824374i
$627$	2.68495	+	10.0204i	0.107227	+	0.400175i
$628$	1.11572	+	2.47174i	0.0445221	+	0.0986332i
$629$	21.4019	+	21.4019i	0.853348	+	0.853348i
$630$		0			0
$631$		−	30.2574i		−	1.20453i	−0.798296	−	0.602265i	$-0.794265\pi$
$631$		−	30.2574i		−	1.20453i	0.798296	−	0.602265i	$-0.205735\pi$
$632$	13.4692	−	12.9802i	0.535775	−	0.516326i
$633$	−1.28862	−	0.743986i	−0.0512181	−	0.0295708i
$634$	3.72690	−	20.4005i	0.148014	−	0.810207i
$635$	1.43044	−	5.33848i	0.0567654	−	0.211851i
$636$	−18.6220	−	22.7565i	−0.738411	−	0.902355i
$637$		0			0
$638$	−49.3813	−	23.3984i	−1.95503	−	0.926350i
$639$	−4.38133	−	7.58868i	−0.173323	−	0.300204i
$640$	33.0281	−	10.4321i	1.30555	−	0.412364i
$641$	3.34695	−	5.79709i	0.132197	−	0.228971i	−0.792326	−	0.610097i	$-0.791130\pi$
$641$	3.34695	−	5.79709i	0.132197	−	0.228971i	0.924523	+	0.381126i	$0.124464\pi$
$642$	−2.52608	−	31.0774i	−0.0996966	−	1.22653i
$643$	−24.7491	+	24.7491i	−0.976007	+	0.976007i	−0.999719	−	0.0237114i	$-0.992452\pi$
$643$	−24.7491	+	24.7491i	−0.976007	+	0.976007i	0.0237114	+	0.999719i	$0.492452\pi$
$644$		0			0
$645$	18.4279	+	18.4279i	0.725597	+	0.725597i
$646$	6.75564	+	5.73995i	0.265797	+	0.225835i
$647$	−37.7857	−	21.8156i	−1.48551	−	0.857659i	−0.485645	−	0.874156i	$-0.661415\pi$
$647$	−37.7857	−	21.8156i	−1.48551	−	0.857659i	−0.999864	+	0.0164976i	$0.994748\pi$
$648$	29.5030	+	8.49273i	1.15899	+	0.333626i
$649$	−38.2593	+	22.0890i	−1.50181	+	0.867069i
$650$	5.15757	+	14.4466i	0.202296	+	0.566643i
$651$		0			0
$652$	36.3637	+	3.63344i	1.42411	+	0.142296i
$653$	24.4355	+	6.54748i	0.956236	+	0.256223i	0.703006	−	0.711184i	$-0.251841\pi$
$653$	24.4355	+	6.54748i	0.956236	+	0.256223i	0.253230	+	0.967406i	$0.418507\pi$
$654$	12.7288	+	18.4191i	0.497734	+	0.720243i
$655$	−20.1015	+	34.8169i	−0.785432	+	1.36041i
$656$	8.07045	+	23.9975i	0.315098	+	0.936945i
$657$	13.2156			0.515588
$658$		0			0
$659$	−16.0357	+	16.0357i	−0.624662	+	0.624662i	−0.946720	−	0.322058i	$-0.895626\pi$
$659$	−16.0357	+	16.0357i	−0.624662	+	0.624662i	0.322058	+	0.946720i	$0.395626\pi$
$660$	−48.0694	+	21.6981i	−1.87110	+	0.844597i
$661$	10.5300	−	2.82150i	0.409568	−	0.109743i	−0.0481514	−	0.998840i	$-0.515333\pi$
$661$	10.5300	−	2.82150i	0.409568	−	0.109743i	0.457720	+	0.889097i	$0.348666\pi$
$662$	−0.438861	−	0.0801740i	−0.0170568	−	0.00311605i
$663$	−21.9994	+	12.7013i	−0.854385	+	0.493279i
$664$	−25.4157	−	15.3069i	−0.986321	−	0.594025i
$665$		0			0
$666$	−6.74664	+	2.40861i	−0.261427	+	0.0933316i
$667$	14.0602	−	52.4732i	0.544412	−	2.03177i
$668$	0.633439	+	3.87073i	0.0245085	+	0.149763i
$669$	−3.99120	−	14.8953i	−0.154309	−	0.575887i
$670$	0.479535	+	5.89952i	0.0185261	+	0.227918i
$671$	6.43842			0.248553
$672$		0			0
$673$	1.82580			0.0703795			0.0351897	−	0.999381i	$-0.488796\pi$
$673$	1.82580			0.0703795			0.0351897	+	0.999381i	$0.488796\pi$
$674$	−3.06639	−	37.7246i	−0.118113	−	1.45310i
$675$	4.74030	+	17.6911i	0.182454	+	0.680929i
$676$	−2.21135	−	13.5128i	−0.0850521	−	0.519724i
$677$	−7.00518	+	26.1437i	−0.269231	+	1.00478i	0.690379	+	0.723448i	$0.257444\pi$
$677$	−7.00518	+	26.1437i	−0.269231	+	1.00478i	−0.959610	+	0.281335i	$0.909223\pi$
$678$	39.9909	−	14.2771i	1.53584	−	0.548309i
$679$		0			0
$680$	−23.2516	+	38.6070i	−0.891656	+	1.48051i
$681$	−0.596575	+	0.344433i	−0.0228608	+	0.0131987i
$682$	−16.9465	−	3.09590i	−0.648915	−	0.118548i
$683$	19.3386	−	5.18175i	0.739970	−	0.198274i	0.130905	−	0.991395i	$-0.458212\pi$
$683$	19.3386	−	5.18175i	0.739970	−	0.198274i	0.609065	+	0.793121i	$0.291545\pi$
$684$	−1.91238	+	0.863230i	−0.0731215	+	0.0330064i
$685$	−17.1808	+	17.1808i	−0.656445	+	0.656445i
$686$		0			0
$687$	−43.4148			−1.65638
$688$	15.4999	+	7.69829i	0.590929	+	0.293494i
$689$	9.26852	−	16.0536i	0.353103	−	0.611592i
$690$	−29.8079	−	43.1333i	−1.13477	−	1.64205i
$691$	−14.7787	−	3.95994i	−0.562208	−	0.150643i	−0.0334874	−	0.999439i	$-0.510661\pi$
$691$	−14.7787	−	3.95994i	−0.562208	−	0.150643i	−0.528720	+	0.848796i	$0.677328\pi$
$692$	11.6528	+	1.16434i	0.442972	+	0.0442614i
$693$		0			0
$694$	−16.5474	−	46.3501i	−0.628130	−	1.75943i
$695$	−7.75829	+	4.47925i	−0.294289	+	0.169908i
$696$	13.5869	−	47.1997i	0.515012	−	1.78910i
$697$	−28.5299	−	16.4717i	−1.08065	−	0.623911i
$698$	−21.0054	−	17.8473i	−0.795068	−	0.675532i
$699$	13.2375	+	13.2375i	0.500688	+	0.500688i
$700$		0			0
$701$	2.64009	−	2.64009i	0.0997148	−	0.0997148i	−0.655490	−	0.755204i	$-0.727538\pi$
$701$	2.64009	−	2.64009i	0.0997148	−	0.0997148i	0.755204	+	0.655490i	$0.227538\pi$
$702$	1.19051	+	14.6464i	0.0449330	+	0.552793i
$703$	−3.50188	+	6.06544i	−0.132076	+	0.228762i
$704$	−25.6634	+	23.8328i	−0.967224	+	0.898233i
$705$	10.8537	+	18.7992i	0.408774	+	0.708018i
$706$	−33.2848	−	15.7713i	−1.25269	−	0.593562i
$707$		0			0
$708$	−25.1476	−	30.7310i	−0.945106	−	1.15494i
$709$	−7.42020	+	27.6926i	−0.278671	+	1.04002i	0.674669	+	0.738120i	$0.264286\pi$
$709$	−7.42020	+	27.6926i	−0.278671	+	1.04002i	−0.953341	+	0.301896i	$0.902380\pi$
$710$	7.82719	−	42.8449i	0.293749	−	1.60794i
$711$	−4.98899	−	2.88039i	−0.187102	−	0.108023i
$712$	−6.40122	−	6.64233i	−0.239896	−	0.248932i
$713$		−	17.1261i		−	0.641377i
$714$		0			0
$715$	−23.5096	−	23.5096i	−0.879210	−	0.879210i
$716$	11.0726	+	24.5299i	0.413801	+	0.916724i
$717$	−9.59735	−	35.8178i	−0.358420	−	1.33764i
$718$	16.9148	+	24.4765i	0.631256	+	0.913453i
$719$	10.0679	+	17.4381i	0.375468	+	0.650330i	0.990397	−	0.138253i	$-0.0441486\pi$
$719$	10.0679	+	17.4381i	0.375468	+	0.650330i	−0.614929	+	0.788583i	$0.710815\pi$
$720$	−5.90113	−	8.88595i	−0.219922	−	0.331160i
$721$		0			0
$722$	10.6272	−	22.4284i	0.395505	−	0.834697i
$723$	12.1597	+	3.25818i	0.452224	+	0.121173i
$724$	17.4650	+	12.5527i	0.649082	+	0.466516i
$725$	37.2771	−	9.98838i	1.38444	−	0.370959i
$726$	14.7118	−	17.3151i	0.546006	−	0.642622i
$727$			30.0313i			1.11380i	0.830580	+	0.556900i	$0.188009\pi$
$727$			30.0313i			1.11380i	−0.830580	+	0.556900i	$0.811991\pi$
$728$		0			0
$729$			15.2688i			0.565511i
$730$	50.0579	+	42.5319i	1.85273	+	1.57417i
$731$	−21.7514	+	5.82826i	−0.804503	+	0.215566i
$732$	0.934619	+	5.71113i	0.0345445	+	0.211090i
$733$	−12.3660	−	3.31347i	−0.456750	−	0.122386i	0.0231062	−	0.999733i	$-0.492644\pi$
$733$	−12.3660	−	3.31347i	−0.456750	−	0.122386i	−0.479856	+	0.877347i	$0.659311\pi$
$734$	9.47438	+	4.48925i	0.349706	+	0.165701i
$735$		0			0
$736$	−27.8925	−	20.8397i	−1.02813	−	0.768163i
$737$	−2.99252	−	5.18320i	−0.110231	−	0.190926i
$738$	6.41454	−	4.43286i	0.236122	−	0.163176i
$739$	7.39398	+	27.5947i	0.271992	+	1.01509i	0.957831	+	0.287334i	$0.0927689\pi$
$739$	7.39398	+	27.5947i	0.271992	+	1.01509i	−0.685839	+	0.727754i	$0.740564\pi$
$740$	−33.3065	−	12.5895i	−1.22437	−	0.462799i
$741$	−4.15652	−	4.15652i	−0.152694	−	0.152694i
$742$		0			0
$743$			32.8469i			1.20504i	0.798106	+	0.602518i	$0.205836\pi$
$743$			32.8469i			1.20504i	−0.798106	+	0.602518i	$0.794164\pi$
$744$	0.286184	−	15.4816i	0.0104920	−	0.567584i
$745$	34.3267	+	19.8185i	1.25763	+	0.726095i
$746$	7.38369	+	1.34890i	0.270336	+	0.0493868i
$747$	−2.36487	+	8.82583i	−0.0865262	+	0.322920i
$748$	4.53086	−	45.3453i	0.165665	−	1.65799i
$749$		0			0
$750$	−2.28873	+	4.83028i	−0.0835726	+	0.176377i
$751$	−8.80060	−	15.2431i	−0.321138	−	0.556228i	0.659585	−	0.751630i	$-0.270732\pi$
$751$	−8.80060	−	15.2431i	−0.321138	−	0.556228i	−0.980723	+	0.195402i	$0.937399\pi$
$752$	10.8111	+	9.53529i	0.394240	+	0.347716i
$753$	4.07852	−	7.06421i	0.148630	−	0.257434i
$754$	30.8617	−	2.50855i	1.12392	−	0.0913561i
$755$	−6.06777	+	6.06777i	−0.220829	+	0.220829i
$756$		0			0
$757$	−10.8261	−	10.8261i	−0.393480	−	0.393480i	0.482446	−	0.875926i	$-0.339749\pi$
$757$	−10.8261	−	10.8261i	−0.393480	−	0.393480i	−0.875926	+	0.482446i	$0.839749\pi$
$758$	−24.3959	+	28.7127i	−0.886098	+	1.04289i
$759$	45.9132	+	26.5080i	1.66654	+	0.962179i
$760$	−10.0218	−	2.88489i	−0.363530	−	0.104646i
$761$	−1.13395	+	0.654687i	−0.0411057	+	0.0237324i	−0.520412	−	0.853915i	$-0.674222\pi$
$761$	−1.13395	+	0.654687i	−0.0411057	+	0.0237324i	0.479306	+	0.877648i	$0.340888\pi$
$762$	−4.73071	+	1.68890i	−0.171376	+	0.0611825i
$763$		0			0
$764$	−25.9499	−	31.7113i	−0.938833	−	1.14728i
$765$	13.4066	+	3.59229i	0.484717	+	0.129880i
$766$	5.75456	−	3.97678i	0.207921	−	0.143687i
$767$	12.5164	−	21.6791i	0.451943	−	0.782788i
$768$	−24.8660	−	19.3048i	−0.897275	−	0.696601i
$769$	−22.6761			−0.817720			−0.408860	−	0.912597i	$-0.634074\pi$
$769$	−22.6761			−0.817720			−0.408860	+	0.912597i	$0.634074\pi$
$770$		0			0
$771$	40.3008	−	40.3008i	1.45140	−	1.45140i
$772$	8.99173	−	23.7884i	0.323620	−	0.856163i
$773$	−3.78685	+	1.01468i	−0.136203	+	0.0364956i	−0.326277	−	0.945274i	$-0.605794\pi$
$773$	−3.78685	+	1.01468i	−0.136203	+	0.0364956i	0.190073	+	0.981770i	$0.439127\pi$
$774$	0.957836	−	5.24305i	0.0344287	−	0.188458i
$775$	10.5364	−	6.08321i	0.378480	−	0.218515i
$776$	−5.22216	−	21.0372i	−0.187465	−	0.755192i
$777$		0			0
$778$	−9.43222	−	26.4201i	−0.338161	−	0.947208i
$779$	1.97301	−	7.36339i	0.0706906	−	0.263821i
$780$	17.4412	−	24.2667i	0.624496	−	0.868886i
$781$	11.3984	+	42.5394i	0.407867	+	1.52218i
$782$	45.1553	−	3.67039i	1.61475	−	0.131253i
$783$	36.9695			1.32118
$784$		0			0
$785$	4.15117			0.148161
$786$	36.4193	−	2.96029i	1.29903	−	0.105590i
$787$	−8.04395	−	30.0204i	−0.286736	−	1.07011i	−0.947562	−	0.319573i	$-0.896460\pi$
$787$	−8.04395	−	30.0204i	−0.286736	−	1.07011i	0.660826	−	0.750539i	$-0.270206\pi$
$788$	29.5449	+	21.2349i	1.05249	+	0.756461i
$789$	0.175401	−	0.654607i	0.00624445	−	0.0233046i
$790$	−9.62726	−	26.9665i	−0.342522	−	0.959424i
$791$		0			0
$792$	9.23967	+	5.56471i	0.328317	+	0.197733i
$793$	−3.15948	+	1.82412i	−0.112196	+	0.0647766i
$794$	0.0229641	−	0.125702i	0.000814967	−	0.00446101i
$795$	−43.4770	+	11.6496i	−1.54197	+	0.413170i
$796$	−2.74724	−	1.03843i	−0.0973734	−	0.0368060i
$797$	−27.7986	+	27.7986i	−0.984679	+	0.984679i	−0.999884	−	0.0152058i	$-0.995160\pi$
$797$	−27.7986	+	27.7986i	−0.984679	+	0.984679i	0.0152058	+	0.999884i	$0.495160\pi$
$798$		0			0
$799$	−18.7569			−0.663570
$800$	2.91370	−	24.5625i	0.103015	−	0.868417i
$801$	−1.42047	+	2.46032i	−0.0501897	+	0.0869312i
$802$	−29.5632	+	20.4301i	−1.04391	+	0.721412i
$803$	−64.1567	−	17.1907i	−2.26404	−	0.606648i
$804$	4.16330	−	3.40689i	0.146828	−	0.120152i
$805$		0			0
$806$	9.19315	−	3.28203i	0.323815	−	0.115605i
$807$	23.8047	−	13.7436i	0.837964	−	0.483799i
$808$	−19.2257	−	34.7685i	−0.676359	−	1.22315i
$809$	42.7813	+	24.6998i	1.50411	+	0.868398i	0.999989	+	0.00476483i	$0.00151670\pi$
$809$	42.7813	+	24.6998i	1.50411	+	0.868398i	0.504121	+	0.863633i	$0.331817\pi$
$810$	30.4290	−	35.8134i	1.06917	−	1.25835i
$811$	13.1428	+	13.1428i	0.461506	+	0.461506i	0.899149	−	0.437643i	$-0.144187\pi$
$811$	13.1428	+	13.1428i	0.461506	+	0.461506i	−0.437643	+	0.899149i	$0.644187\pi$
$812$		0			0
$813$	−17.3861	+	17.3861i	−0.609756	+	0.609756i
$814$	35.8855	−	2.91691i	1.25779	−	0.102238i
$815$	27.9701	−	48.4457i	0.979750	−	1.69698i
$816$	40.8808	−	2.56339i	1.43111	−	0.0897366i
$817$	−2.60542	−	4.51272i	−0.0911521	−	0.157880i
$818$	13.5678	−	28.6343i	0.474386	−	1.00117i
$819$		0			0
$820$	38.5633	+	3.85322i	1.34669	+	0.134560i
$821$	0.278293	−	1.03860i	0.00971248	−	0.0362475i	−0.960900	−	0.276897i	$-0.910694\pi$
$821$	0.278293	−	1.03860i	0.00971248	−	0.0362475i	0.970612	+	0.240650i	$0.0773605\pi$
$822$	21.7236	+	3.96861i	0.757697	+	0.138421i
$823$	−17.3926	−	10.0416i	−0.606268	−	0.350029i	0.165235	−	0.986254i	$-0.447162\pi$
$823$	−17.3926	−	10.0416i	−0.606268	−	0.350029i	−0.771504	+	0.636225i	$0.780495\pi$
$824$	3.16384	+	3.28301i	0.110217	+	0.114369i
$825$			37.6627i			1.31125i
$826$		0			0
$827$	6.99770	+	6.99770i	0.243334	+	0.243334i	0.818228	−	0.574894i	$-0.194957\pi$
$827$	6.99770	+	6.99770i	0.243334	+	0.243334i	−0.574894	+	0.818228i	$0.694957\pi$
$828$	−3.79130	+	10.0302i	−0.131757	+	0.348574i
$829$	11.9771	+	44.6990i	0.415980	+	1.55246i	0.782864	+	0.622193i	$0.213758\pi$
$829$	11.9771	+	44.6990i	0.415980	+	1.55246i	−0.366884	+	0.930267i	$0.619575\pi$
$830$	−37.3620	+	25.8196i	−1.29685	+	0.896210i
$831$	−8.34665	−	14.4568i	−0.289542	−	0.501502i
$832$	5.84130	−	18.9662i	0.202511	−	0.657535i
$833$		0			0
$834$	7.35793	+	3.48641i	0.254784	+	0.120724i
$835$	5.79927	+	1.55391i	0.200692	+	0.0537753i
$836$	10.4068	−	1.70305i	0.359925	−	0.0589013i
$837$	11.2577	−	3.01650i	0.389125	−	0.104266i
$838$	36.9997	+	31.4369i	1.27813	+	1.08597i
$839$		−	11.1872i		−	0.386225i	−0.981177	−	0.193113i	$-0.938142\pi$
$839$		−	11.1872i		−	0.386225i	0.981177	−	0.193113i	$-0.0618583\pi$
$840$		0			0
$841$		−	48.8991i		−	1.68618i
$842$	−20.7548	+	24.4274i	−0.715258	+	0.841823i
$843$	18.1778	−	4.87073i	0.626077	−	0.167757i
$844$	−0.882764	+	1.22822i	−0.0303860	+	0.0422772i
$845$	−20.2454	−	5.42475i	−0.696464	−	0.186617i
$846$	1.90095	−	4.01189i	0.0653561	−	0.137931i
$847$		0			0
$848$	−24.8998	+	16.5359i	−0.855064	+	0.567844i
$849$	−16.2605	−	28.1640i	−0.558058	−	0.966585i
$850$	18.2973	+	26.4770i	0.627594	+	0.908154i
$851$	9.26392	+	34.5734i	0.317563	+	1.18516i
$852$	−36.0795	+	16.2860i	−1.23606	+	0.557948i
$853$	25.4369	+	25.4369i	0.870944	+	0.870944i	0.992575	−	0.121632i	$-0.0388127\pi$
$853$	25.4369	+	25.4369i	0.870944	+	0.870944i	−0.121632	+	0.992575i	$0.538813\pi$
$854$		0			0
$855$			3.21174i			0.109839i
$856$	−31.6895	−	0.585792i	−1.08312	−	0.0200220i
$857$	28.5281	+	16.4707i	0.974500	+	0.562628i	0.900605	−	0.434638i	$-0.143124\pi$
$857$	28.5281	+	16.4707i	0.974500	+	0.562628i	0.0738951	+	0.997266i	$0.476457\pi$
$858$	−5.43051	+	29.7258i	−0.185394	+	1.01482i
$859$	10.9512	−	40.8704i	0.373649	−	1.39448i	−0.481659	−	0.876359i	$-0.659966\pi$
$859$	10.9512	−	40.8704i	0.373649	−	1.39448i	0.855308	−	0.518120i	$-0.173368\pi$
$860$	20.5019	−	16.7770i	0.699108	−	0.572091i
$861$		0			0
$862$	40.4636	+	19.1729i	1.37819	+	0.653030i
$863$	−10.9071	−	18.8916i	−0.371281	−	0.643078i	0.618482	−	0.785799i	$-0.287748\pi$
$863$	−10.9071	−	18.8916i	−0.371281	−	0.643078i	−0.989763	+	0.142721i	$0.954415\pi$
$864$	8.78604	−	22.0056i	0.298907	−	0.748646i
$865$	8.96304	−	15.5244i	0.304752	−	0.527847i
$866$	1.33849	+	16.4669i	0.0454837	+	0.559568i
$867$	−14.0360	+	14.0360i	−0.476689	+	0.476689i
$868$		0			0
$869$	20.4729	+	20.4729i	0.694495	+	0.694495i
$870$	−57.2954	−	48.6812i	−1.94250	−	1.65045i
$871$	2.93699	+	1.69567i	0.0995162	+	0.0574557i
$872$	19.9170	−	11.0134i	0.674474	−	0.372959i
$873$	−5.78109	+	3.33772i	−0.195660	+	0.112965i
$874$	3.52478	+	9.87311i	0.119228	+	0.333963i
$875$		0			0
$876$	5.93570	−	59.4049i	0.200549	−	2.00711i
$877$	−13.5170	−	3.62186i	−0.456435	−	0.122302i	0.0232736	−	0.999729i	$-0.492591\pi$
$877$	−13.5170	−	3.62186i	−0.456435	−	0.122302i	−0.479709	+	0.877428i	$0.659258\pi$
$878$	−10.5500	−	15.2662i	−0.356044	−	0.515210i
$879$	21.2738	−	36.8473i	0.717548	−	1.24283i
$880$	17.0890	+	50.8142i	0.576070	+	1.71295i
$881$	12.3319			0.415471			0.207735	−	0.978185i	$-0.433391\pi$
$881$	12.3319			0.415471			0.207735	+	0.978185i	$0.433391\pi$
$882$		0			0
$883$	24.3508	−	24.3508i	0.819469	−	0.819469i	−0.166562	−	0.986031i	$-0.553267\pi$
$883$	24.3508	−	24.3508i	0.819469	−	0.819469i	0.986031	+	0.166562i	$0.0532667\pi$
$884$	10.6238	+	23.5356i	0.357316	+	0.791588i
$885$	−58.7124	+	15.7319i	−1.97360	+	0.528823i
$886$	−31.9118	−	5.82985i	−1.07210	−	0.195858i
$887$	−3.69725	+	2.13461i	−0.124141	+	0.0716731i	−0.560785	−	0.827962i	$-0.689500\pi$
$887$	−3.69725	+	2.13461i	−0.124141	+	0.0716731i	0.436643	+	0.899635i	$0.356167\pi$
$888$	7.79665	+	31.4084i	0.261638	+	1.05400i
$889$		0			0
$890$	−13.2985	+	4.74769i	−0.445768	+	0.159143i
$891$	−12.2989	+	45.9002i	−0.412030	+	1.53772i
$892$	−15.4697	+	2.53160i	−0.517965	+	0.0847642i
$893$	−1.12337	−	4.19246i	−0.0375920	−	0.140295i
$894$	−2.91861	−	35.9065i	−0.0976131	−	1.20089i
$895$	41.1967			1.37705
$896$		0			0
$897$	−30.0408			−1.00303
$898$	−1.79190	−	22.0450i	−0.0597964	−	0.735651i
$899$	−6.35613	−	23.7214i	−0.211989	−	0.791153i
$900$	−7.51752	+	1.23023i	−0.250584	+	0.0410077i
$901$	10.0662	−	37.5674i	0.335352	−	1.25155i
$902$	−36.9064	+	13.1759i	−1.22885	+	0.438710i
$903$		0			0
$904$	−10.3993	−	41.8930i	−0.345875	−	1.39334i
$905$	28.5122	−	16.4615i	0.947776	−	0.547199i
$906$	7.67216	+	1.40160i	0.254890	+	0.0465651i
$907$	32.5246	−	8.71495i	1.07996	−	0.289375i	0.325382	−	0.945583i	$-0.394507\pi$
$907$	32.5246	−	8.71495i	1.07996	−	0.289375i	0.754580	+	0.656208i	$0.227840\pi$
$908$	0.288093	+	0.638235i	0.00956071	+	0.0211806i
$909$	−8.65188	+	8.65188i	−0.286965	+	0.286965i
$910$		0			0
$911$	4.22749			0.140063			0.0700315	−	0.997545i	$-0.477690\pi$
$911$	4.22749			0.140063			0.0700315	+	0.997545i	$0.477690\pi$
$912$	3.02135	+	8.98399i	0.100047	+	0.297490i
$913$	22.9612	−	39.7699i	0.759904	−	1.31619i
$914$	9.83337	+	14.2293i	0.325259	+	0.470663i
$915$	8.55664	+	2.29275i	0.282874	+	0.0757958i
$916$	−4.38777	+	43.9132i	−0.144976	+	1.45093i
$917$		0			0
$918$	10.3661	+	29.0361i	0.342134	+	0.958335i
$919$	18.8641	−	10.8912i	0.622270	−	0.359268i	−0.155482	−	0.987839i	$-0.549693\pi$
$919$	18.8641	−	10.8912i	0.622270	−	0.359268i	0.777752	+	0.628571i	$0.216360\pi$
$920$	−46.6410	+	25.7908i	−1.53771	+	0.850297i
$921$	−10.0305	−	5.79113i	−0.330517	−	0.190824i
$922$	20.5237	+	17.4380i	0.675911	+	0.574290i
$923$	−17.6457	−	17.6457i	−0.580814	−	0.580814i
$924$		0			0
$925$	−17.9799	+	17.9799i	−0.591177	+	0.591177i
$926$	−2.83924	−	34.9301i	−0.0933033	−	1.14787i
$927$	0.702074	−	1.21603i	0.0230591	−	0.0399396i
$928$	−46.3684	−	18.5132i	−1.52212	−	0.607726i
$929$	−15.6683	−	27.1384i	−0.514062	−	0.890381i	−0.999867	−	0.0163141i	$-0.994807\pi$
$929$	−15.6683	−	27.1384i	−0.514062	−	0.890381i	0.485805	−	0.874067i	$-0.338526\pi$
$930$	−21.4194	−	10.1491i	−0.702369	−	0.332804i
$931$		0			0
$932$	14.7273	−	12.0516i	0.482410	−	0.394763i
$933$	−0.408718	+	1.52535i	−0.0133808	+	0.0499379i
$934$	−8.32727	+	45.5823i	−0.272477	+	1.49150i
$935$	−60.4113	−	34.8785i	−1.97566	−	1.14065i
$936$	−6.11070	−	0.112959i	−0.199734	−	0.00369217i
$937$		−	53.9341i		−	1.76195i	−0.473162	−	0.880975i	$-0.656887\pi$
$937$		−	53.9341i		−	1.76195i	0.473162	−	0.880975i	$-0.343113\pi$
$938$		0			0
$939$	−24.6644	−	24.6644i	−0.804893	−	0.804893i
$940$	20.1119	−	9.07835i	0.655979	−	0.296103i
$941$	12.8332	+	47.8941i	0.418350	+	1.56130i	0.778030	+	0.628227i	$0.216219\pi$
$941$	12.8332	+	47.8941i	0.418350	+	1.56130i	−0.359680	+	0.933076i	$0.617114\pi$
$942$	−2.14495	−	3.10383i	−0.0698862	−	0.101128i
$943$	−19.4792	−	33.7390i	−0.634330	−	1.09869i
$944$	−33.6254	+	22.3305i	−1.09441	+	0.726795i
$945$		0			0
$946$	−11.4701	+	24.2071i	−0.372924	+	0.787042i
$947$	−0.0877997	−	0.0235259i	−0.00285311	−	0.000764488i	0.257392	−	0.966307i	$-0.417137\pi$
$947$	−0.0877997	−	0.0235259i	−0.00285311	−	0.000764488i	−0.260245	+	0.965543i	$0.583803\pi$
$948$	−15.1883	+	21.1321i	−0.493295	+	0.686340i
$949$	36.3536	−	9.74091i	1.18009	−	0.316203i
$950$	−4.82220	+	5.67549i	−0.156453	+	0.184137i
$951$			28.8516i			0.935577i
$952$		0			0
$953$			45.4195i			1.47128i	0.677371	+	0.735641i	$0.263119\pi$
$953$			45.4195i			1.47128i	−0.677371	+	0.735641i	$0.736881\pi$
$954$	7.01508	+	5.96039i	0.227122	+	0.192975i
$955$	−60.5854	+	16.2338i	−1.96050	+	0.525314i
$956$	−37.1990	+	6.08756i	−1.20310	+	0.196886i
$957$	73.4326	+	19.6762i	2.37374	+	0.636041i
$958$	45.1965	+	21.4155i	1.46023	+	0.691902i
$959$		0			0
$960$	−42.5935	+	22.5349i	−1.37470	+	0.727312i
$961$	11.6289	+	20.1419i	0.375127	+	0.649739i
$962$	−16.7834	+	11.5984i	−0.541119	+	0.373948i
$963$	2.52634	+	9.42843i	0.0814102	+	0.303827i
$964$	4.52452	−	11.9700i	0.145725	−	0.385528i
$965$	−27.5263	−	27.5263i	−0.886103	−	0.886103i
$966$		0			0
$967$			60.1289i			1.93362i	0.255506	+	0.966808i	$0.417758\pi$
$967$			60.1289i			1.93362i	−0.255506	+	0.966808i	$0.582242\pi$
$968$	−16.0270	−	16.6307i	−0.515127	−	0.534530i
$969$	−10.6808	−	6.16655i	−0.343116	−	0.198098i
$970$	−32.6394	−	5.96279i	−1.04799	−	0.191454i
$971$	−9.75682	+	36.4130i	−0.313111	+	1.16855i	0.612624	+	0.790375i	$0.290114\pi$
$971$	−9.75682	+	36.4130i	−0.313111	+	1.16855i	−0.925735	+	0.378173i	$0.876552\pi$
$972$	−17.4931	−	1.74790i	−0.561091	−	0.0560638i
$973$		0			0
$974$	−10.1285	+	21.3757i	−0.324537	+	0.684923i
$975$	−10.6705	−	18.4819i	−0.341731	−	0.591895i
$976$	5.87116	−	0.368145i	0.187931	−	0.0117840i
$977$	12.3444	−	21.3811i	0.394932	−	0.684042i	−0.598161	−	0.801376i	$-0.704102\pi$
$977$	12.3444	−	21.3811i	0.394932	−	0.684042i	0.993092	+	0.117334i	$0.0374349\pi$
$978$	−50.6753	+	4.11907i	−1.62042	+	0.131713i
$979$	10.0962	−	10.0962i	0.322676	−	0.322676i
$980$		0			0
$981$	−4.95619	−	4.95619i	−0.158239	−	0.158239i
$982$	−7.68244	+	9.04186i	−0.245157	+	0.288537i
$983$	−4.43148	−	2.55852i	−0.141342	−	0.0816041i	0.427661	−	0.903939i	$-0.359338\pi$
$983$	−4.43148	−	2.55852i	−0.141342	−	0.0816041i	−0.569004	+	0.822335i	$0.692671\pi$
$984$	−17.0450	−	30.8248i	−0.543374	−	0.982659i
$985$	48.2329	−	27.8473i	1.53683	−	0.887289i
$986$	61.1825	−	21.8427i	1.94845	−	0.695613i
$987$		0			0
$988$	−4.62432	+	3.78415i	−0.147119	+	0.120390i
$989$	−25.7228	−	6.89240i	−0.817938	−	0.219166i
$990$	13.5826	−	9.38648i	0.431684	−	0.298322i
$991$	2.71965	−	4.71056i	0.0863924	−	0.149636i	−0.819591	−	0.572949i	$-0.805799\pi$
$991$	2.71965	−	4.71056i	0.0863924	−	0.149636i	0.905984	+	0.423313i	$0.139133\pi$
$992$	−15.6304	−	1.85414i	−0.496267	−	0.0588690i
$993$	0.620663			0.0196961
$994$		0			0
$995$	−3.17892	+	3.17892i	−0.100779	+	0.100779i
$996$	38.6106	+	14.5944i	1.22342	+	0.462440i
$997$	−11.6799	+	3.12961i	−0.369905	+	0.0991157i	−0.438983	−	0.898496i	$-0.644661\pi$
$997$	−11.6799	+	3.12961i	−0.369905	+	0.0991157i	0.0690777	+	0.997611i	$0.477994\pi$
$998$	−1.99723	+	10.9326i	−0.0632213	+	0.346064i
$999$	−21.0950	+	12.1792i	−0.667415	+	0.385332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.m.165.4		24
7.2	even	3	inner	784.2.x.m.373.6		24
7.3	odd	6		112.2.m.d.85.1	yes	12
7.4	even	3		784.2.m.h.197.1		12
7.5	odd	6		784.2.x.l.373.6		24
7.6	odd	2		784.2.x.l.165.4		24
16.13	even	4	inner	784.2.x.m.557.6		24
28.3	even	6		448.2.m.d.113.2		12
56.3	even	6		896.2.m.h.225.5		12
56.45	odd	6		896.2.m.g.225.2		12
112.3	even	12		448.2.m.d.337.2		12
112.13	odd	4		784.2.x.l.557.6		24
112.45	odd	12		112.2.m.d.29.1	✓	12
112.59	even	12		896.2.m.h.673.5		12
112.61	odd	12		784.2.x.l.765.4		24
112.93	even	12	inner	784.2.x.m.765.4		24
112.101	odd	12		896.2.m.g.673.2		12
112.109	even	12		784.2.m.h.589.1		12
224.3	even	24		7168.2.a.bi.1.3		12
224.45	odd	24		7168.2.a.bj.1.3		12
224.115	even	24		7168.2.a.bi.1.10		12
224.157	odd	24		7168.2.a.bj.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.1	✓	12	112.45	odd	12
112.2.m.d.85.1	yes	12	7.3	odd	6
448.2.m.d.113.2		12	28.3	even	6
448.2.m.d.337.2		12	112.3	even	12
784.2.m.h.197.1		12	7.4	even	3
784.2.m.h.589.1		12	112.109	even	12
784.2.x.l.165.4		24	7.6	odd	2
784.2.x.l.373.6		24	7.5	odd	6
784.2.x.l.557.6		24	112.13	odd	4
784.2.x.l.765.4		24	112.61	odd	12
784.2.x.m.165.4		24	1.1	even	1	trivial
784.2.x.m.373.6		24	7.2	even	3	inner
784.2.x.m.557.6		24	16.13	even	4	inner
784.2.x.m.765.4		24	112.93	even	12	inner
896.2.m.g.225.2		12	56.45	odd	6
896.2.m.g.673.2		12	112.101	odd	12
896.2.m.h.225.5		12	56.3	even	6
896.2.m.h.673.5		12	112.59	even	12
7168.2.a.bi.1.3		12	224.3	even	24
7168.2.a.bi.1.10		12	224.115	even	24
7168.2.a.bj.1.3		12	224.45	odd	24
7168.2.a.bj.1.10		12	224.157	odd	24

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)

\(f(q)\)	\(=\)	\(q+(0.114575 + 1.40956i) q^{2} +(-0.509227 - 1.90046i) q^{3} +(-1.97375 + 0.323001i) q^{4} +(-0.792364 + 2.95714i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} +(-0.754366 + 0.435533i) q^{9} +O(q^{10})\)	\(q+(0.114575 + 1.40956i) q^{2} +(-0.509227 - 1.90046i) q^{3} +(-1.97375 + 0.323001i) q^{4} +(-0.792364 + 2.95714i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} +(-0.754366 + 0.435533i) q^{9} +(-4.25907 - 0.778075i) q^{10} +(4.22870 - 1.13308i) q^{11} +(1.61893 + 3.58655i) q^{12} +(-1.75410 + 1.75410i) q^{13} +6.02343 q^{15} +(3.79134 - 1.27504i) q^{16} +(-2.60235 + 4.50740i) q^{17} +(-0.700343 - 1.01343i) q^{18} +(-1.16333 - 0.311715i) q^{19} +(0.608766 - 6.09258i) q^{20} +(2.08165 + 5.83081i) q^{22} +(-5.33038 + 3.07750i) q^{23} +(-4.86998 + 2.69292i) q^{24} +(-3.78672 - 2.18626i) q^{25} +(-2.67349 - 2.27154i) q^{26} +(-2.96185 - 2.96185i) q^{27} +(-6.24096 + 6.24096i) q^{29} +(0.690132 + 8.49041i) q^{30} +(-1.39123 + 2.40969i) q^{31} +(2.23165 + 5.19805i) q^{32} +(-4.30674 - 7.45950i) q^{33} +(-6.65164 - 3.15175i) q^{34} +(1.34825 - 1.10329i) q^{36} +(1.50511 - 5.61713i) q^{37} +(0.306093 - 1.67551i) q^{38} +(4.22683 + 2.44036i) q^{39} +(8.65763 + 0.160040i) q^{40} +6.32956i q^{41} +(3.05937 + 3.05937i) q^{43} +(-7.98040 + 3.60228i) q^{44} +(-0.690201 - 2.57587i) q^{45} +(-4.94866 - 7.16092i) q^{46} +(1.80192 + 3.12101i) q^{47} +(-4.35382 - 6.55601i) q^{48} +(2.64782 - 5.58812i) q^{50} +(9.89133 + 2.65037i) q^{51} +(2.89557 - 4.02872i) q^{52} +(-7.21798 + 1.93405i) q^{53} +(3.83556 - 4.51427i) q^{54} +13.4027i q^{55} +2.36961i q^{57} +(-9.51209 - 8.08198i) q^{58} +(-9.74734 + 2.61179i) q^{59} +(-11.8887 + 1.94557i) q^{60} +(1.42056 + 0.380638i) q^{61} +(-3.55601 - 1.68495i) q^{62} +(-7.07130 + 3.74121i) q^{64} +(-3.79723 - 6.57700i) q^{65} +(10.0212 - 6.92530i) q^{66} +(-0.353834 - 1.32053i) q^{67} +(3.68048 - 9.73703i) q^{68} +(8.56304 + 8.56304i) q^{69} +10.0597i q^{71} +(1.70964 + 1.77403i) q^{72} +(-13.1391 - 7.58585i) q^{73} +(8.09016 + 1.47796i) q^{74} +(-2.22661 + 8.30982i) q^{75} +(2.39681 + 0.239487i) q^{76} +(-2.95556 + 6.23759i) q^{78} +(3.30674 + 5.72745i) q^{79} +(0.766358 + 12.2218i) q^{80} +(-5.42722 + 9.40022i) q^{81} +(-8.92192 + 0.725206i) q^{82} +(7.41730 - 7.41730i) q^{83} +(-11.2670 - 11.2670i) q^{85} +(-3.96185 + 4.66290i) q^{86} +(15.0388 + 8.68264i) q^{87} +(-5.99200 - 10.8362i) q^{88} +(2.82449 - 1.63072i) q^{89} +(3.55177 - 1.26801i) q^{90} +(9.52678 - 7.79591i) q^{92} +(5.28798 + 1.41691i) q^{93} +(-4.19281 + 2.89750i) q^{94} +(1.84357 - 3.19315i) q^{95} +(8.74229 - 6.88815i) q^{96} +7.66352 q^{97} +(-2.69650 + 2.69650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

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