LMFDB - Embedded newform 784.2.m.h.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$-0.605558 - 1.27801i$ of defining polynomial
Character	$\chi$	$=$	784.197
Dual form			784.2.m.h.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27801 - 0.605558i) q^{2} +(-1.39123 + 1.39123i) q^{3} +(1.26660 + 1.54781i) q^{4} +(-2.16478 - 2.16478i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} -0.871066i q^{9} +O(q^{10})$	\(q+(-1.27801 - 0.605558i) q^{2} +(-1.39123 + 1.39123i) q^{3} +(1.26660 + 1.54781i) q^{4} +(-2.16478 - 2.16478i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} -0.871066i q^{9} +(1.45570 + 4.07750i) q^{10} +(-3.09563 - 3.09563i) q^{11} +(-3.91551 - 0.391234i) q^{12} +(-1.75410 + 1.75410i) q^{13} +6.02343 q^{15} +(-0.791452 + 3.92092i) q^{16} +5.20470 q^{17} +(-0.527481 + 1.11323i) q^{18} +(0.851620 - 0.851620i) q^{19} +(0.608766 - 6.09258i) q^{20} +(2.08165 + 5.83081i) q^{22} -6.15500i q^{23} +(4.76713 + 2.87107i) q^{24} +4.37253i q^{25} +(3.30395 - 1.17954i) q^{26} +(-2.96185 - 2.96185i) q^{27} +(-6.24096 + 6.24096i) q^{29} +(-7.69798 - 3.64753i) q^{30} +2.78247 q^{31} +(3.38582 - 4.53169i) q^{32} +8.61348 q^{33} +(-6.65164 - 3.15175i) q^{34} +(1.34825 - 1.10329i) q^{36} +(4.11202 + 4.11202i) q^{37} +(-1.60408 + 0.572671i) q^{38} -4.88072i q^{39} +(-4.46741 + 7.41771i) q^{40} +6.32956i q^{41} +(3.05937 + 3.05937i) q^{43} +(0.870533 - 8.71237i) q^{44} +(-1.88567 + 1.88567i) q^{45} +(-3.72721 + 7.86612i) q^{46} -3.60383 q^{47} +(-4.35382 - 6.55601i) q^{48} +(2.64782 - 5.58812i) q^{50} +(-7.24096 + 7.24096i) q^{51} +(-4.93675 - 0.493276i) q^{52} +(5.28393 + 5.28393i) q^{53} +(1.99169 + 5.57883i) q^{54} +13.4027i q^{55} +2.36961i q^{57} +(11.7552 - 4.19672i) q^{58} +(7.13555 + 7.13555i) q^{59} +(7.62927 + 9.32314i) q^{60} +(-1.03992 + 1.03992i) q^{61} +(-3.55601 - 1.68495i) q^{62} +(-7.07130 + 3.74121i) q^{64} +7.59446 q^{65} +(-11.0081 - 5.21596i) q^{66} +(-0.966693 + 0.966693i) q^{67} +(6.59227 + 8.05590i) q^{68} +(8.56304 + 8.56304i) q^{69} +10.0597i q^{71} +(-2.39118 + 0.593572i) q^{72} +15.1717i q^{73} +(-2.76512 - 7.74526i) q^{74} +(-6.08321 - 6.08321i) q^{75} +(2.39681 + 0.239487i) q^{76} +(-2.95556 + 6.23759i) q^{78} -6.61348 q^{79} +(10.2012 - 6.77460i) q^{80} +10.8544 q^{81} +(3.83291 - 8.08921i) q^{82} +(7.41730 - 7.41730i) q^{83} +(-11.2670 - 11.2670i) q^{85} +(-2.05727 - 5.76252i) q^{86} -17.3653i q^{87} +(-6.38839 + 10.6073i) q^{88} +3.26144i q^{89} +(3.55177 - 1.26801i) q^{90} +(9.52678 - 7.79591i) q^{92} +(-3.87107 + 3.87107i) q^{93} +(4.60572 + 2.18233i) q^{94} -3.68714 q^{95} +(1.59417 + 11.0151i) q^{96} +7.66352 q^{97} +(-2.69650 + 2.69650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8	$ 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{10} - 8 q^{12} - 24 q^{15} + 10 q^{16} + 8 q^{17} + 20 q^{20} + 14 q^{22} + 8 q^{24} + 20 q^{26} - 4 q^{27} - 4 q^{29} - 28 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{34} - 16 q^{36} - 20 q^{37} - 16 q^{38} + 8 q^{40} + 16 q^{43} + 14 q^{44} - 40 q^{45} - 28 q^{46} - 16 q^{47} - 16 q^{48} + 44 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} - 8 q^{62} - 18 q^{64} + 32 q^{65} - 12 q^{66} + 24 q^{67} + 28 q^{68} + 4 q^{69} + 6 q^{72} - 38 q^{74} + 40 q^{75} - 48 q^{76} - 76 q^{78} + 24 q^{79} - 24 q^{80} - 44 q^{81} + 16 q^{82} + 20 q^{83} - 8 q^{85} + 38 q^{86} - 14 q^{88} + 40 q^{90} + 32 q^{92} - 48 q^{93} + 24 q^{94} + 16 q^{96} - 48 q^{97} + 32 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^10 - 8 * q^12 - 24 * q^15 + 10 * q^16 + 8 * q^17 + 20 * q^20 + 14 * q^22 + 8 * q^24 + 20 * q^26 - 4 * q^27 - 4 * q^29 - 28 * q^30 + 8 * q^31 + 12 * q^32 - 8 * q^34 - 16 * q^36 - 20 * q^37 - 16 * q^38 + 8 * q^40 + 16 * q^43 + 14 * q^44 - 40 * q^45 - 28 * q^46 - 16 * q^47 - 16 * q^48 + 44 * 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 - 8 * q^62 - 18 * q^64 + 32 * q^65 - 12 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 6 * q^72 - 38 * q^74 + 40 * q^75 - 48 * q^76 - 76 * q^78 + 24 * q^79 - 24 * q^80 - 44 * q^81 + 16 * q^82 + 20 * q^83 - 8 * q^85 + 38 * q^86 - 14 * q^88 + 40 * q^90 + 32 * q^92 - 48 * q^93 + 24 * q^94 + 16 * q^96 - 48 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.27801	−	0.605558i	−0.903687	−	0.428194i
$2$	−1.27801	−	0.605558i	−0.903687	−	0.428194i
$3$	−1.39123	+	1.39123i	−0.803230	+	0.803230i	−0.983599	−	0.180369i	$-0.942271\pi$
$3$	−1.39123	+	1.39123i	−0.803230	+	0.803230i	0.180369	+	0.983599i	$0.442271\pi$
$4$	1.26660	+	1.54781i	0.633300	+	0.773907i
$5$	−2.16478	−	2.16478i	−0.968118	−	0.968118i	0.0313891	−	0.999507i	$-0.490007\pi$
$5$	−2.16478	−	2.16478i	−0.968118	−	0.968118i	−0.999507	+	0.0313891i	$0.990007\pi$
$6$	2.62048	−	0.935533i	1.06981	−	0.381930i
$7$		0			0
$7$		0			0
$8$	−0.681431	−	2.74511i	−0.240922	−	0.970544i
$9$		−	0.871066i		−	0.290355i
$10$	1.45570	+	4.07750i	0.460333	+	1.28942i
$11$	−3.09563	−	3.09563i	−0.933367	−	0.933367i	0.0645481	−	0.997915i	$-0.479439\pi$
$11$	−3.09563	−	3.09563i	−0.933367	−	0.933367i	−0.997915	+	0.0645481i	$0.979439\pi$
$12$	−3.91551	−	0.391234i	−1.13031	−	0.112940i
$13$	−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
$16$	−0.791452	+	3.92092i	−0.197863	+	0.980230i
$17$	5.20470			1.26233			0.631163	−	0.775651i	$-0.282578\pi$
$17$	5.20470			1.26233			0.631163	+	0.775651i	$0.282578\pi$
$18$	−0.527481	+	1.11323i	−0.124328	+	0.262390i
$19$	0.851620	−	0.851620i	0.195375	−	0.195375i	−0.602639	−	0.798014i	$-0.705884\pi$
$19$	0.851620	−	0.851620i	0.195375	−	0.195375i	0.798014	+	0.602639i	$0.205884\pi$
$20$	0.608766	−	6.09258i	0.136124	−	1.36234i
$21$		0			0
$22$	2.08165	+	5.83081i	0.443809	+	1.24313i
$23$		−	6.15500i		−	1.28341i	−0.766954	−	0.641703i	$-0.778228\pi$
$23$		−	6.15500i		−	1.28341i	0.766954	−	0.641703i	$-0.221772\pi$
$24$	4.76713	+	2.87107i	0.973086	+	0.586054i
$25$			4.37253i			0.874505i
$26$	3.30395	−	1.17954i	0.647959	−	0.231327i
$27$	−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	$0.944264\pi$
$30$	−7.69798	−	3.64753i	−1.40545	−	0.665945i
$31$	2.78247			0.499746			0.249873	−	0.968279i	$-0.419611\pi$
$31$	2.78247			0.499746			0.249873	+	0.968279i	$0.419611\pi$
$32$	3.38582	−	4.53169i	0.598535	−	0.801097i
$33$	8.61348			1.49942
$34$	−6.65164	−	3.15175i	−1.14075	−	0.540520i
$35$		0			0
$36$	1.34825	−	1.10329i	0.224708	−	0.183882i
$37$	4.11202	+	4.11202i	0.676013	+	0.676013i	0.959095	−	0.283083i	$-0.0913571\pi$
$37$	4.11202	+	4.11202i	0.676013	+	0.676013i	−0.283083	+	0.959095i	$0.591357\pi$
$38$	−1.60408	+	0.572671i	−0.260216	+	0.0928994i
$39$		−	4.88072i		−	0.781541i
$40$	−4.46741	+	7.41771i	−0.706360	+	1.17284i
$41$			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	$0.642985\pi$
$44$	0.870533	−	8.71237i	0.131238	−	1.31344i
$45$	−1.88567	+	1.88567i	−0.281098	+	0.281098i
$46$	−3.72721	+	7.86612i	−0.549546	+	1.15980i
$47$	−3.60383			−0.525673			−0.262836	−	0.964840i	$-0.584658\pi$
$47$	−3.60383			−0.525673			−0.262836	+	0.964840i	$0.584658\pi$
$48$	−4.35382	−	6.55601i	−0.628420	−	0.946279i
$49$		0			0
$50$	2.64782	−	5.58812i	0.374458	−	0.790279i
$51$	−7.24096	+	7.24096i	−1.01394	+	1.01394i
$52$	−4.93675	−	0.493276i	−0.684604	−	0.0684051i
$53$	5.28393	+	5.28393i	0.725803	+	0.725803i	0.969781	−	0.243977i	$-0.0784523\pi$
$53$	5.28393	+	5.28393i	0.725803	+	0.725803i	−0.243977	+	0.969781i	$0.578452\pi$
$54$	1.99169	+	5.57883i	0.271034	+	0.759182i
$55$			13.4027i			1.80722i
$56$		0			0
$57$			2.36961i			0.313862i
$58$	11.7552	−	4.19672i	1.54354	−	0.551057i
$59$	7.13555	+	7.13555i	0.928969	+	0.928969i	0.997639	−	0.0686701i	$-0.0218756\pi$
$59$	7.13555	+	7.13555i	0.928969	+	0.928969i	−0.0686701	+	0.997639i	$0.521876\pi$
$60$	7.62927	+	9.32314i	0.984934	+	1.20361i
$61$	−1.03992	+	1.03992i	−0.133148	+	0.133148i	−0.770540	−	0.637392i	$-0.780013\pi$
$61$	−1.03992	+	1.03992i	−0.133148	+	0.133148i	0.637392	+	0.770540i	$0.280013\pi$
$62$	−3.55601	−	1.68495i	−0.451614	−	0.213988i
$63$		0			0
$64$	−7.07130	+	3.74121i	−0.883913	+	0.467652i
$65$	7.59446			0.941977
$66$	−11.0081	−	5.21596i	−1.35500	−	0.642041i
$67$	−0.966693	+	0.966693i	−0.118100	+	0.118100i	−0.763687	−	0.645587i	$-0.776613\pi$
$67$	−0.966693	+	0.966693i	−0.118100	+	0.118100i	0.645587	+	0.763687i	$0.276613\pi$
$68$	6.59227	+	8.05590i	0.799430	+	0.976922i
$69$	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	$0.796386\pi$
$72$	−2.39118	+	0.593572i	−0.281803	+	0.0699531i
$73$			15.1717i			1.77571i	0.460119	+	0.887857i	$0.347807\pi$
$73$			15.1717i			1.77571i	−0.460119	+	0.887857i	$0.652193\pi$
$74$	−2.76512	−	7.74526i	−0.321439	−	0.900368i
$75$	−6.08321	−	6.08321i	−0.702428	−	0.702428i
$76$	2.39681	+	0.239487i	0.274933	+	0.0274711i
$77$		0			0
$78$	−2.95556	+	6.23759i	−0.334651	+	0.706268i
$79$	−6.61348			−0.744075			−0.372038	−	0.928218i	$-0.621341\pi$
$79$	−6.61348			−0.744075			−0.372038	+	0.928218i	$0.621341\pi$
$80$	10.2012	−	6.77460i	1.14053	−	0.757423i
$81$	10.8544			1.20605
$82$	3.83291	−	8.08921i	0.423274	−	0.893304i
$83$	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
$86$	−2.05727	−	5.76252i	−0.221841	−	0.621388i
$87$		−	17.3653i		−	1.86175i
$88$	−6.38839	+	10.6073i	−0.681005	+	1.13074i
$89$			3.26144i			0.345712i	0.984947	+	0.172856i	$0.0552996\pi$
$89$			3.26144i			0.345712i	−0.984947	+	0.172856i	$0.944700\pi$
$90$	3.55177	−	1.26801i	0.374390	−	0.133660i
$91$		0			0
$92$	9.52678	−	7.79591i	0.993236	−	0.812780i
$93$	−3.87107	+	3.87107i	−0.401411	+	0.401411i
$94$	4.60572	+	2.18233i	0.475043	+	0.225090i
$95$	−3.68714			−0.378292
$96$	1.59417	+	11.0151i	0.162704	+	1.12423i
$97$	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
$100$	−6.76785	+	5.53824i	−0.676785	+	0.553824i
$101$	−9.93252	−	9.93252i	−0.988323	−	0.988323i	0.0116100	−	0.999933i	$-0.496304\pi$
$101$	−9.93252	−	9.93252i	−0.988323	−	0.988323i	−0.999933	+	0.0116100i	$0.996304\pi$
$102$	13.6388	−	4.86917i	1.35044	−	0.482120i
$103$		−	1.61199i		−	0.158834i	−0.996841	−	0.0794169i	$-0.974694\pi$
$103$		−	1.61199i		−	0.158834i	0.996841	−	0.0794169i	$-0.0253058\pi$
$104$	6.01049	+	3.61990i	0.589377	+	0.354960i
$105$		0			0
$106$	−3.55317	−	9.95262i	−0.345114	−	0.966684i
$107$	7.92372	+	7.92372i	0.766015	+	0.766015i	0.977402	−	0.211387i	$-0.0677981\pi$
$107$	7.92372	+	7.92372i	0.766015	+	0.766015i	−0.211387	+	0.977402i	$0.567798\pi$
$108$	0.832912	−	8.33586i	0.0801470	−	0.802118i
$109$	5.68979	−	5.68979i	0.544983	−	0.544983i	−0.380002	−	0.924986i	$-0.624077\pi$
$109$	5.68979	−	5.68979i	0.544983	−	0.544983i	0.924986	+	0.380002i	$0.124077\pi$
$110$	8.11610	−	17.1287i	0.773840	−	1.63316i
$111$	−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	$0.245143\pi$
$114$	1.43493	−	3.02837i	0.134394	−	0.283633i
$115$	−13.3242	+	13.3242i	−1.24249	+	1.24249i
$116$	−17.5646	−	1.75504i	−1.63084	−	0.162952i
$117$	1.52794	+	1.52794i	0.141258	+	0.141258i
$118$	−4.79829	−	13.4403i	−0.441718	−	1.23728i
$119$		0			0
$120$	−4.10455	−	16.5350i	−0.374693	−	1.50943i
$121$			8.16581i			0.742346i
$122$	1.95876	−	0.699294i	0.177338	−	0.0633111i
$123$	−8.80590	−	8.80590i	−0.794001	−	0.794001i
$124$	3.52427	+	4.30674i	0.316489	+	0.386757i
$125$	−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	$0.525523\pi$
$128$	11.3027	−	0.499211i	0.999026	−	0.0441245i
$129$	−8.51260			−0.749492
$130$	−9.70577	−	4.59889i	−0.851252	−	0.403349i
$131$	−9.28573	+	9.28573i	−0.811298	+	0.811298i	−0.984828	−	0.173531i	$-0.944482\pi$
$131$	−9.28573	+	9.28573i	−0.811298	+	0.811298i	0.173531	+	0.984828i	$0.444482\pi$
$132$	10.9098	+	13.3321i	0.949579	+	1.16041i
$133$		0			0
$134$	1.82083	−	0.650051i	0.157296	−	0.0561559i
$135$			12.8235i			1.10367i
$136$	−3.54665	−	14.2875i	−0.304122	−	1.22514i
$137$		−	7.93652i		−	0.678063i	−0.940775	−	0.339031i	$-0.889901\pi$
$137$		−	7.93652i		−	0.678063i	0.940775	−	0.339031i	$-0.110099\pi$
$138$	−5.75820	−	16.1290i	−0.490171	−	1.37299i
$139$	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
$142$	6.09172	−	12.8563i	0.511206	−	1.07888i
$143$	10.8601			0.908164
$144$	3.41538	+	0.689407i	0.284615	+	0.0574506i
$145$	27.0206			2.24394
$146$	9.18735	−	19.3895i	0.760350	−	1.60469i
$147$		0			0
$148$	−1.15636	+	11.5729i	−0.0950521	+	0.951289i
$149$	9.15500	+	9.15500i	0.750006	+	0.750006i	0.974480	−	0.224474i	$-0.0720663\pi$
$149$	9.15500	+	9.15500i	0.750006	+	0.750006i	−0.224474	+	0.974480i	$0.572066\pi$
$150$	4.09064	+	11.4581i	0.334000	+	0.935551i
$151$		−	2.80295i		−	0.228101i	−0.993475	−	0.114051i	$-0.963617\pi$
$151$		−	2.80295i		−	0.228101i	0.993475	−	0.114051i	$-0.0363826\pi$
$152$	−2.91812	−	1.75747i	−0.236690	−	0.142550i
$153$		−	4.53364i		−	0.366523i
$154$		0			0
$155$	−6.02343	−	6.02343i	−0.483813	−	0.483813i
$156$	7.55444	−	6.18192i	0.604840	−	0.494950i
$157$	−0.958797	+	0.958797i	−0.0765204	+	0.0765204i	−0.744331	−	0.667811i	$-0.767232\pi$
$157$	−0.958797	+	0.958797i	−0.0765204	+	0.0765204i	0.667811	+	0.744331i	$0.267232\pi$
$158$	8.45207	+	4.00485i	0.672411	+	0.318609i
$159$	−14.7024			−1.16597
$160$	−17.1397	+	2.48054i	−1.35501	+	0.196104i
$161$		0			0
$162$	−13.8720	−	6.57299i	−1.08989	−	0.516423i
$163$	12.9205	−	12.9205i	1.01202	−	1.01202i	0.0120883	−	0.999927i	$-0.496152\pi$
$163$	12.9205	−	12.9205i	1.01202	−	1.01202i	0.999927	−	0.0120883i	$-0.00384792\pi$
$164$	−9.79697	+	8.01701i	−0.765015	+	0.626023i
$165$	−18.6463	−	18.6463i	−1.45161	−	1.45161i
$166$	−13.9710	+	4.98775i	−1.08436	+	0.387124i
$167$		−	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
$170$	7.57649	+	21.2222i	0.581090	+	1.62766i
$171$	−0.741818	−	0.741818i	−0.0567282	−	0.0567282i
$172$	−0.860337	+	8.61033i	−0.0656001	+	0.656531i
$173$	4.14040	−	4.14040i	0.314789	−	0.314789i	−0.531973	−	0.846761i	$-0.678549\pi$
$173$	4.14040	−	4.14040i	0.314789	−	0.314789i	0.846761	+	0.531973i	$0.178549\pi$
$174$	−10.5157	+	22.1929i	−0.797191	+	1.68244i
$175$		0			0
$176$	14.5877	−	9.68766i	1.09959	−	0.730235i
$177$	−19.8544			−1.49235
$178$	1.97499	−	4.16815i	0.148032	−	0.312416i
$179$	−9.51522	+	9.51522i	−0.711201	+	0.711201i	−0.966787	−	0.255585i	$-0.917732\pi$
$179$	−9.51522	+	9.51522i	−0.711201	+	0.711201i	0.255585	+	0.966787i	$0.417732\pi$
$180$	−5.30704	−	0.530275i	−0.395563	−	0.0395244i
$181$	−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
$184$	−16.8962	+	4.19421i	−1.24560	+	0.309201i
$185$		−	17.8032i		−	1.30892i
$186$	7.29140	−	2.60309i	0.534631	−	0.190868i
$187$	−16.1118	−	16.1118i	−1.17821	−	1.17821i
$188$	−4.56461	−	5.57806i	−0.332908	−	0.406822i
$189$		0			0
$190$	4.71218	+	2.23277i	0.341858	+	0.161982i
$191$	−20.4878			−1.48245			−0.741223	−	0.671259i	$-0.765754\pi$
$191$	−20.4878			−1.48245			−0.741223	+	0.671259i	$0.765754\pi$
$192$	4.63293	−	15.0427i	0.334353	−	1.08562i
$193$	12.7155			0.915284			0.457642	−	0.889137i	$-0.348694\pi$
$193$	12.7155			0.915284			0.457642	+	0.889137i	$0.348694\pi$
$194$	−9.79402	−	4.64070i	−0.703170	−	0.333183i
$195$	−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	$0.974423\pi$
$198$	5.07902	−	1.81325i	0.360950	−	0.128862i
$199$		−	1.46847i		−	0.104097i	−0.998645	−	0.0520487i	$-0.983425\pi$
$199$		−	1.46847i		−	0.104097i	0.998645	−	0.0520487i	$-0.0165751\pi$
$200$	12.0031	−	2.97958i	0.848746	−	0.210688i
$201$		−	2.68979i		−	0.189723i
$202$	6.67911	+	18.7085i	0.469940	+	1.31633i
$203$		0			0
$204$	−20.3790	−	2.03626i	−1.42682	−	0.142567i
$205$	13.7021	−	13.7021i	0.956995	−	0.956995i
$206$	−0.976151	+	2.06013i	−0.0680117	+	0.143536i
$207$	−5.36141			−0.372644
$208$	−5.48939	−	8.26596i	−0.380621	−	0.573141i
$209$	−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	$0.241713\pi$
$212$	−1.48591	+	14.8712i	−0.102053	+	1.02136i
$213$	−13.9954	−	13.9954i	−0.958948	−	0.958948i
$214$	−5.32829	−	14.9248i	−0.364235	−	1.02024i
$215$		−	13.2457i		−	0.903350i
$216$	−6.11231	+	10.1489i	−0.415890	+	0.690545i
$217$		0			0
$218$	−10.7171	+	3.82609i	−0.725853	+	0.259136i
$219$	−21.1074	−	21.1074i	−1.42631	−	1.42631i
$220$	−20.7449	+	16.9758i	−1.39862	+	1.14451i
$221$	−9.12955	+	9.12955i	−0.614120	+	0.614120i
$222$	14.6224	+	6.92854i	0.981392	+	0.465013i
$223$	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
$226$	−19.5036	−	9.24137i	−1.29736	−	0.614727i
$227$	−0.247573	+	0.247573i	−0.0164320	+	0.0164320i	−0.715275	−	0.698843i	$-0.753699\pi$
$227$	−0.247573	+	0.247573i	−0.0164320	+	0.0164320i	0.698843	+	0.715275i	$0.253699\pi$
$228$	−3.66771	+	3.00134i	−0.242900	+	0.198769i
$229$	15.6030	+	15.6030i	1.03107	+	1.03107i	0.999502	+	0.0315714i	$0.0100511\pi$
$229$	15.6030	+	15.6030i	1.03107	+	1.03107i	0.0315714	+	0.999502i	$0.489949\pi$
$230$	25.0970	−	8.95983i	1.65485	−	0.590794i
$231$		0			0
$232$	21.3849	+	12.8794i	1.40399	+	0.845571i
$233$		−	9.51493i		−	0.623344i	−0.950190	−	0.311672i	$-0.899111\pi$
$233$		−	9.51493i		−	0.623344i	0.950190	−	0.311672i	$-0.100889\pi$
$234$	−1.02746	−	2.87796i	−0.0671670	−	0.188138i
$235$	7.80149	+	7.80149i	0.508913	+	0.508913i
$236$	−2.00662	+	20.0824i	−0.130620	+	1.30725i
$237$	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	$0.291349\pi$
$240$	−4.76725	+	23.6174i	−0.307725	+	1.52449i
$241$	6.39828			0.412150			0.206075	−	0.978536i	$-0.433931\pi$
$241$	6.39828			0.412150			0.206075	+	0.978536i	$0.433931\pi$
$242$	4.94487	−	10.4360i	0.317868	−	0.670848i
$243$	−6.21554	+	6.21554i	−0.398727	+	0.398727i
$244$	−2.92677	−	0.292441i	−0.187367	−	0.0187216i
$245$		0			0
$246$	5.92151	+	16.5865i	0.377542	+	1.05751i
$247$			2.98765i			0.190100i
$248$	−1.89606	−	7.63819i	−0.120400	−	0.485026i
$249$			20.6384i			1.30791i
$250$	2.55852	−	0.913414i	0.161815	−	0.0577694i
$251$	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
$254$	2.30717	+	1.09320i	0.144764	+	0.0685938i
$255$	31.3501			1.96322
$256$	−14.7472	−	6.20644i	−0.921700	−	0.387902i
$257$	−28.9676			−1.80695			−0.903475	−	0.428640i	$-0.858993\pi$
$257$	−28.9676			−1.80695			−0.903475	+	0.428640i	$0.858993\pi$
$258$	10.8792	+	5.15487i	0.677306	+	0.320928i
$259$		0			0
$260$	9.61914	+	11.7548i	0.596554	+	0.729002i
$261$	5.43629	+	5.43629i	0.336498	+	0.336498i
$262$	17.4903	−	6.24417i	1.08055	−	0.385766i
$263$		−	0.344446i		−	0.0212395i	−0.999944	−	0.0106197i	$-0.996620\pi$
$263$		−	0.344446i		−	0.0212395i	0.999944	−	0.0106197i	$-0.00338043\pi$
$264$	−5.86950	−	23.6450i	−0.361243	−	1.45525i
$265$		−	22.8771i		−	1.40533i
$266$		0			0
$267$	−4.53743	−	4.53743i	−0.277686	−	0.277686i
$268$	−2.72067	−	0.271847i	−0.166192	−	0.0166057i
$269$	9.87874	−	9.87874i	0.602317	−	0.602317i	−0.338610	−	0.940927i	$-0.609957\pi$
$269$	9.87874	−	9.87874i	0.602317	−	0.602317i	0.940927	+	0.338610i	$0.109957\pi$
$270$	7.76536	−	16.3885i	0.472585	−	0.997371i
$271$	12.4969			0.759130			0.379565	−	0.925165i	$-0.376074\pi$
$271$	12.4969			0.759130			0.379565	+	0.925165i	$0.376074\pi$
$272$	−4.11927	+	20.4072i	−0.249767	+	1.23737i
$273$		0			0
$274$	−4.80602	+	10.1429i	−0.290342	+	0.612756i
$275$	13.5357	−	13.5357i	0.816234	−	0.816234i
$276$	−2.40805	+	24.0999i	−0.144947	+	1.45065i
$277$	−5.99946	−	5.99946i	−0.360472	−	0.360472i	0.503514	−	0.863987i	$-0.332040\pi$
$277$	−5.99946	−	5.99946i	−0.360472	−	0.360472i	−0.863987	+	0.503514i	$0.832040\pi$
$278$	−1.39140	−	3.89738i	−0.0834505	−	0.233749i
$279$		−	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	$0.907907\pi$
$282$	−9.44376	+	3.37150i	−0.562368	+	0.200770i
$283$	−11.6878	−	11.6878i	−0.694768	−	0.694768i	0.268509	−	0.963277i	$-0.413469\pi$
$283$	−11.6878	−	11.6878i	−0.694768	−	0.694768i	−0.963277	+	0.268509i	$0.913469\pi$
$284$	−15.5705	+	12.7416i	−0.923940	+	0.756074i
$285$	5.12967	−	5.12967i	0.303856	−	0.303856i
$286$	−13.8792	−	6.57639i	−0.820696	−	0.388870i
$287$		0			0
$288$	−3.94740	−	2.94928i	−0.232603	−	0.173788i
$289$	10.0889			0.593465
$290$	−34.5325	−	16.3625i	−2.02782	−	0.960840i
$291$	−10.6617	+	10.6617i	−0.625003	+	0.625003i
$292$	−23.4830	+	19.2165i	−1.37424	+	1.12456i
$293$	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
$296$	8.48591	−	14.0900i	0.493234	−	0.818967i
$297$			18.3375i			1.06405i
$298$	−6.15626	−	17.2440i	−0.356623	−	0.998919i
$299$	10.7965	+	10.7965i	0.624375	+	0.624375i
$300$	1.71068	−	17.1207i	0.0987663	−	0.988462i
$301$		0			0
$302$	−1.69735	+	3.58219i	−0.0976716	+	0.206132i
$303$	27.6369			1.58770
$304$	2.66512	+	4.01315i	0.152855	+	0.230170i
$305$	4.50240			0.257807
$306$	−2.74538	+	5.79402i	−0.156943	+	0.331222i
$307$	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
$310$	4.05044	+	11.3455i	0.230050	+	0.644382i
$311$			0.802623i			0.0455126i	0.999741	+	0.0227563i	$0.00724418\pi$
$311$			0.802623i			0.0455126i	−0.999741	+	0.0227563i	$0.992756\pi$
$312$	−13.3981	+	3.32588i	−0.758520	+	0.188291i
$313$			17.7285i			1.00207i	0.865427	+	0.501036i	$0.167047\pi$
$313$			17.7285i			1.00207i	−0.865427	+	0.501036i	$0.832953\pi$
$314$	1.80596	−	0.644742i	0.101916	−	0.0363849i
$315$		0			0
$316$	−8.37664	−	10.2364i	−0.471223	−	0.575845i
$317$	10.3691	−	10.3691i	0.582385	−	0.582385i	−0.353173	−	0.935558i	$-0.614897\pi$
$317$	10.3691	−	10.3691i	0.582385	−	0.582385i	0.935558	+	0.353173i	$0.114897\pi$
$318$	18.7897	+	8.90313i	1.05367	+	0.499263i
$319$	38.6394			2.16339
$320$	23.4067	+	7.20890i	1.30847	+	0.402990i
$321$	−22.0475			−1.23057
$322$		0			0
$323$	4.43243	−	4.43243i	0.246627	−	0.246627i
$324$	13.7482	+	16.8007i	0.763791	+	0.933369i
$325$	−7.66984	−	7.66984i	−0.425446	−	0.425446i
$326$	−24.3367	+	8.68840i	−1.34788	+	0.481206i
$327$			15.8317i			0.875493i
$328$	17.3754	−	4.31316i	0.959393	−	0.238154i
$329$		0			0
$330$	12.5387	+	35.1215i	0.690230	+	1.93337i
$331$	−0.223062	−	0.223062i	−0.0122606	−	0.0122606i	0.700950	−	0.713211i	$-0.252760\pi$
$331$	−0.223062	−	0.223062i	−0.0122606	−	0.0122606i	−0.713211	+	0.700950i	$0.752760\pi$
$332$	20.8753	+	2.08585i	1.14568	+	0.114476i
$333$	3.58185	−	3.58185i	0.196284	−	0.196284i
$334$	−1.18756	+	2.50631i	−0.0649806	+	0.137139i
$335$	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	$0.759989\pi$
$338$	4.14582	−	8.74960i	0.225503	−	0.475915i
$339$	−21.2315	+	21.2315i	−1.15314	+	1.15314i
$340$	3.16844	−	31.7100i	0.171833	−	1.71972i
$341$	−8.61348	−	8.61348i	−0.466446	−	0.466446i
$342$	0.498834	+	1.39726i	0.0269739	+	0.0755552i
$343$		0			0
$344$	6.31357	−	10.4831i	0.340405	−	0.565209i
$345$		−	37.0742i		−	1.99601i
$346$	−7.79870	+	2.78420i	−0.419261	+	0.149680i
$347$	24.6077	+	24.6077i	1.32101	+	1.32101i	0.912960	+	0.408050i	$0.133791\pi$
$347$	24.6077	+	24.6077i	1.32101	+	1.32101i	0.408050	+	0.912960i	$0.366209\pi$
$348$	26.8782	−	21.9948i	1.44082	−	1.17905i
$349$	−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
$352$	−24.5097	+	3.54717i	−1.30637	+	0.189065i
$353$	26.0443			1.38620			0.693099	−	0.720842i	$-0.256245\pi$
$353$	26.0443			1.38620			0.693099	+	0.720842i	$0.256245\pi$
$354$	25.3741	+	12.0230i	1.34862	+	0.639016i
$355$	21.7770	−	21.7770i	1.15580	−	1.15580i
$356$	−5.04811	+	4.13094i	−0.267549	+	0.218940i
$357$		0			0
$358$	17.9225	−	6.39850i	0.947235	−	0.338171i
$359$			21.0382i			1.11035i	0.831733	+	0.555176i	$0.187349\pi$
$359$			21.0382i			1.11035i	−0.831733	+	0.555176i	$0.812651\pi$
$360$	6.46132	+	3.89142i	0.340541	+	0.205096i
$361$			17.5495i			0.923657i
$362$	5.11346	+	14.3231i	0.268758	+	0.752804i
$363$	−11.3606	−	11.3606i	−0.596274	−	0.596274i
$364$		0			0
$365$	32.8434	−	32.8434i	1.71910	−	1.71910i
$366$	−1.75221	+	3.69798i	−0.0915896	+	0.193296i
$367$	−7.41340			−0.386977			−0.193488	−	0.981103i	$-0.561980\pi$
$367$	−7.41340			−0.386977			−0.193488	+	0.981103i	$0.561980\pi$
$368$	24.1332	+	4.87138i	1.25803	+	0.253938i
$369$	5.51346			0.287019
$370$	−10.7809	+	22.7526i	−0.560472	+	1.18285i
$371$		0			0
$372$	−10.8948	−	1.08860i	−0.564868	−	0.0564412i
$373$	3.75295	+	3.75295i	0.194320	+	0.194320i	0.797560	−	0.603240i	$-0.206124\pi$
$373$	3.75295	+	3.75295i	0.194320	+	0.194320i	−0.603240	+	0.797560i	$0.706124\pi$
$374$	10.8344	+	30.3476i	0.560231	+	1.56924i
$375$		−	3.77954i		−	0.195175i
$376$	2.45576	+	9.89293i	0.126646	+	0.510189i
$377$		−	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	$0.510129\pi$
$380$	−4.67013	−	5.70700i	−0.239572	−	0.292763i
$381$	2.51157	−	2.51157i	0.128672	−	0.128672i
$382$	26.1836	+	12.4066i	1.33967	+	0.634775i
$383$	4.94620			0.252739			0.126369	−	0.991983i	$-0.459668\pi$
$383$	4.94620			0.252739			0.126369	+	0.991983i	$0.459668\pi$
$384$	−15.0302	+	16.4192i	−0.767005	+	0.837889i
$385$		0			0
$386$	−16.2505	−	7.69999i	−0.827130	−	0.391919i
$387$	2.66491	−	2.66491i	0.135465	−	0.135465i
$388$	9.70660	+	11.8617i	0.492778	+	0.602186i
$389$	14.0267	+	14.0267i	0.711181	+	0.711181i	0.966782	−	0.255601i	$-0.0822735\pi$
$389$	14.0267	+	14.0267i	0.711181	+	0.711181i	−0.255601	+	0.966782i	$0.582273\pi$
$390$	19.9011	−	7.10487i	1.00773	−	0.359769i
$391$		−	32.0349i		−	1.62007i
$392$		0			0
$393$		−	25.8372i		−	1.30332i
$394$	8.65025	+	24.2298i	0.435793	+	1.22068i
$395$	14.3167	+	14.3167i	0.720353	+	0.720353i
$396$	−7.58905	−	0.758292i	−0.381364	−	0.0381056i
$397$	0.0638914	−	0.0638914i	0.00320662	−	0.00320662i	−0.705502	−	0.708708i	$-0.749278\pi$
$397$	0.0638914	−	0.0638914i	0.00320662	−	0.00320662i	0.708708	+	0.705502i	$0.249278\pi$
$398$	−0.889246	+	1.87672i	−0.0445739	+	0.0940714i
$399$		0			0
$400$	−17.1443	−	3.46064i	−0.857216	−	0.173032i
$401$	−25.4103			−1.26893			−0.634466	−	0.772951i	$-0.718780\pi$
$401$	−25.4103			−1.26893			−0.634466	+	0.772951i	$0.718780\pi$
$402$	−1.62883	+	3.43757i	−0.0812384	+	0.171451i
$403$	−4.88072	+	4.88072i	−0.243126	+	0.243126i
$404$	2.79316	−	27.9542i	0.138965	−	1.39077i
$405$	−23.4975	−	23.4975i	−1.16760	−	1.16760i
$406$		0			0
$407$		−	25.4586i		−	1.26194i
$408$	24.8115	+	14.9430i	1.22835	+	0.739791i
$409$			22.4054i			1.10788i	0.832557	+	0.553939i	$0.186876\pi$
$409$			22.4054i			1.10788i	−0.832557	+	0.553939i	$0.813124\pi$
$410$	−25.8087	+	9.21394i	−1.27460	+	0.455044i
$411$	11.0416	+	11.0416i	0.544640	+	0.544640i
$412$	2.49505	−	2.04174i	0.122922	−	0.100589i
$413$		0			0
$414$	6.85191	+	3.24664i	0.336753	+	0.159564i
$415$	−32.1136			−1.57639
$416$	2.00996	+	13.8881i	0.0985463	+	0.680919i
$417$	−5.75735			−0.281939
$418$	6.73841	+	3.19286i	0.329586	+	0.156168i
$419$	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	$0.563740\pi$
$422$	−1.00727	+	0.359603i	−0.0490330	+	0.0175052i
$423$			3.13918i			0.152632i
$424$	10.9044	−	18.1056i	0.529562	−	0.879287i
$425$			22.7577i			1.10391i
$426$	9.41117	+	26.3612i	0.455973	+	1.27720i
$427$		0			0
$428$	−2.22826	+	22.3006i	−0.107707	+	1.07794i
$429$	−15.1089	+	15.1089i	−0.729464	+	0.729464i
$430$	−8.02104	+	16.9281i	−0.386809	+	0.816345i
$431$	−31.6615			−1.52508			−0.762540	−	0.646941i	$-0.776048\pi$
$431$	−31.6615			−1.52508			−0.762540	+	0.646941i	$0.776048\pi$
$432$	13.9573	−	9.26900i	0.671522	−	0.445955i
$433$	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
$436$	16.0134	+	1.60005i	0.766904	+	0.0766284i
$437$	−5.24172	−	5.24172i	−0.250745	−	0.250745i
$438$	14.1936	+	39.7571i	0.678198	+	1.89967i
$439$		−	13.1217i		−	0.626265i	−0.949709	−	0.313133i	$-0.898622\pi$
$439$		−	13.1217i		−	0.626265i	0.949709	−	0.313133i	$-0.101378\pi$
$440$	36.7919	−	9.13301i	1.75399	−	0.435399i
$441$		0			0
$442$	17.1961	−	6.13915i	0.817935	−	0.292010i
$443$	−16.2200	−	16.2200i	−0.770634	−	0.770634i	0.207584	−	0.978217i	$-0.433440\pi$
$443$	−16.2200	−	16.2200i	−0.770634	−	0.770634i	−0.978217	+	0.207584i	$0.933440\pi$
$444$	−14.4919	−	17.7094i	−0.687755	−	0.840452i
$445$	7.06030	−	7.06030i	0.334690	−	0.334690i
$446$	−10.0167	−	4.74621i	−0.474304	−	0.224740i
$447$	−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	$0.620313\pi$
$450$	−4.86762	−	2.30643i	−0.229462	−	0.108726i
$451$	19.5939	−	19.5939i	0.922643	−	0.922643i
$452$	19.3295	+	23.6211i	0.909182	+	1.11104i
$453$	3.89957	+	3.89957i	0.183218	+	0.183218i
$454$	0.466321	−	0.166480i	0.0218855	−	0.00781331i
$455$		0			0
$456$	6.50484	−	1.61472i	0.304617	−	0.0756164i
$457$			12.2305i			0.572117i	0.958212	+	0.286058i	$0.0923451\pi$
$457$			12.2305i			0.572117i	−0.958212	+	0.286058i	$0.907655\pi$
$458$	−10.4922	−	29.3892i	−0.490268	−	1.37327i
$459$	−15.4155	−	15.4155i	−0.719535	−	0.719535i
$460$	−37.4998	−	3.74695i	−1.74844	−	0.174702i
$461$	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	$0.695321\pi$
$464$	−19.5309	−	29.4097i	−0.906698	−	1.36531i
$465$	16.7600			0.777226
$466$	−5.76184	+	12.1601i	−0.266912	+	0.563307i
$467$	−23.1683	+	23.1683i	−1.07210	+	1.07210i	−0.0749131	+	0.997190i	$0.523868\pi$
$467$	−23.1683	+	23.1683i	−1.07210	+	1.07210i	−0.997190	+	0.0749131i	$0.976132\pi$
$468$	−0.429677	+	4.30024i	−0.0198618	+	0.198779i
$469$		0			0
$470$	−5.24610	−	14.6946i	−0.241985	−	0.677812i
$471$		−	2.66782i		−	0.122927i
$472$	14.7255	−	24.4503i	0.677796	−	1.12542i
$473$		−	18.9413i		−	0.870923i
$474$	−17.3305	+	6.18713i	−0.796016	+	0.284184i
$475$	3.72373	+	3.72373i	0.170857	+	0.170857i
$476$		0			0
$477$	4.60265	−	4.60265i	0.210741	−	0.210741i
$478$	−24.0865	−	11.4129i	−1.10169	−	0.522013i
$479$	−35.3648			−1.61586			−0.807930	−	0.589278i	$-0.799412\pi$
$479$	−35.3648			−1.61586			−0.807930	+	0.589278i	$0.799412\pi$
$480$	20.3943	−	27.2963i	0.930866	−	1.24590i
$481$	−14.4258			−0.657759
$482$	−8.17705	−	3.87453i	−0.372454	−	0.176480i
$483$		0			0
$484$	−12.6391	+	10.3428i	−0.574507	+	0.470128i
$485$	−16.5898	−	16.5898i	−0.753304	−	0.753304i
$486$	11.7074	−	4.17963i	0.531057	−	0.189592i
$487$		−	16.7258i		−	0.757921i	−0.925413	−	0.378960i	$-0.876282\pi$
$487$		−	16.7258i		−	0.757921i	0.925413	−	0.378960i	$-0.123718\pi$
$488$	3.56334	+	2.14607i	0.161305	+	0.0971480i
$489$			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	$0.689374\pi$
$492$	2.47634	−	24.7834i	0.111642	−	1.11732i
$493$	−32.4823	+	32.4823i	−1.46293	+	1.46293i
$494$	1.80919	−	3.81823i	0.0813995	−	0.171790i
$495$	11.6746			0.524736
$496$	−2.20219	+	10.9098i	−0.0988813	+	0.489866i
$497$		0			0
$498$	12.4977	−	26.3760i	0.560037	−	1.18194i
$499$	−5.55675	+	5.55675i	−0.248754	+	0.248754i	−0.820459	−	0.571705i	$-0.806282\pi$
$499$	−5.55675	+	5.55675i	−0.248754	+	0.248754i	0.571705	+	0.820459i	$0.306282\pi$
$500$	−3.82293	−	0.381984i	−0.170967	−	0.0170829i
$501$	2.72836	+	2.72836i	0.121894	+	0.121894i
$502$	−1.97134	−	5.52183i	−0.0879852	−	0.246451i
$503$		−	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
$506$	35.8886	−	12.8125i	1.59544	−	0.569587i
$507$	−9.52479	−	9.52479i	−0.423011	−	0.423011i
$508$	−2.28657	−	2.79424i	−0.101450	−	0.123975i
$509$	−3.57736	+	3.57736i	−0.158563	+	0.158563i	−0.781930	−	0.623366i	$-0.785765\pi$
$509$	−3.57736	+	3.57736i	−0.158563	+	0.158563i	0.623366	+	0.781930i	$0.285765\pi$
$510$	−40.0657	−	18.9843i	−1.77414	−	0.840640i
$511$		0			0
$512$	15.0887	+	16.8622i	0.666831	+	0.745209i
$513$	−5.04473			−0.222730
$514$	37.0208	+	17.5416i	1.63292	+	0.773726i
$515$	−3.48959	+	3.48959i	−0.153770	+	0.153770i
$516$	−10.7821	−	13.1759i	−0.474653	−	0.580037i
$517$	11.1561	+	11.1561i	0.490645	+	0.490645i
$518$		0			0
$519$			11.5205i			0.505695i
$520$	−5.17510	−	20.8477i	−0.226943	−	0.914230i
$521$			17.3647i			0.760761i	0.924830	+	0.380380i	$0.124207\pi$
$521$			17.3647i			0.760761i	−0.924830	+	0.380380i	$0.875793\pi$
$522$	−3.65562	−	10.2396i	−0.160002	−	0.448175i
$523$	25.9531	+	25.9531i	1.13485	+	1.13485i	0.989360	+	0.145491i	$0.0464762\pi$
$523$	25.9531	+	25.9531i	1.13485	+	1.13485i	0.145491	+	0.989360i	$0.453524\pi$
$524$	−26.1339	−	2.61128i	−1.14166	−	0.114074i
$525$		0			0
$526$	−0.208582	+	0.440204i	−0.00909461	+	0.0191938i
$527$	14.4819			0.630842
$528$	−6.81716	+	33.7728i	−0.296679	+	1.46977i
$529$	−14.8840			−0.647129
$530$	−13.8534	+	29.2370i	−0.601753	+	1.26998i
$531$	6.21554	−	6.21554i	0.269731	−	0.269731i
$532$		0			0
$533$	−11.1027	−	11.1027i	−0.480909	−	0.480909i
$534$	3.05119	+	8.54654i	0.132038	+	0.369845i
$535$		−	34.3062i		−	1.48319i
$536$	3.31242	+	1.99495i	0.143075	+	0.0861686i
$537$		−	26.4758i		−	1.14252i
$538$	−18.6072	+	6.64294i	−0.802215	+	0.286397i
$539$		0			0
$540$	−19.8483	+	16.2422i	−0.854137	+	0.698953i
$541$	−11.3284	+	11.3284i	−0.487046	+	0.487046i	−0.907373	−	0.420327i	$-0.861915\pi$
$541$	−11.3284	+	11.3284i	−0.487046	+	0.487046i	0.420327	+	0.907373i	$0.361915\pi$
$542$	−15.9711	−	7.56757i	−0.686016	−	0.325055i
$543$	21.1586			0.908001
$544$	17.6222	−	23.5861i	0.755545	−	1.01124i
$545$	−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	$0.356307\pi$
$548$	12.2843	−	10.0524i	0.524757	−	0.429417i
$549$	0.905841	+	0.905841i	0.0386604	+	0.0386604i
$550$	−25.4954	+	9.10206i	−1.08713	+	0.388113i
$551$			10.6299i			0.452847i
$552$	17.6714	−	29.3416i	0.752145	−	1.24886i
$553$		0			0
$554$	4.03433	+	11.3004i	0.171402	+	0.480106i
$555$	24.7685	+	24.7685i	1.05136	+	1.05136i
$556$	−0.581874	+	5.82345i	−0.0246770	+	0.246969i
$557$	−15.7787	+	15.7787i	−0.668564	+	0.668564i	−0.957384	−	0.288820i	$-0.906737\pi$
$557$	−15.7787	+	15.7787i	−0.668564	+	0.668564i	0.288820	+	0.957384i	$0.406737\pi$
$558$	−1.46770	+	3.09752i	−0.0621327	+	0.131129i
$559$	−10.7329			−0.453952
$560$		0			0
$561$	44.8306			1.89275
$562$	5.79212	−	12.2240i	0.244326	−	0.515640i
$563$	−14.7663	+	14.7663i	−0.622324	+	0.622324i	−0.946125	−	0.323801i	$-0.895039\pi$
$563$	−14.7663	+	14.7663i	−0.622324	+	0.622324i	0.323801	+	0.946125i	$0.395039\pi$
$564$	14.1108	+	1.40994i	0.594173	+	0.0593693i
$565$	−33.0365	−	33.0365i	−1.38986	−	1.38986i
$566$	7.85944	+	22.0147i	0.330357	+	0.925348i
$567$		0			0
$568$	27.6150	−	6.85498i	1.15870	−	0.287629i
$569$			17.6170i			0.738542i	0.929322	+	0.369271i	$0.120393\pi$
$569$			17.6170i			0.738542i	−0.929322	+	0.369271i	$0.879607\pi$
$570$	−9.66207	+	3.44944i	−0.404699	+	0.144481i
$571$	−6.07198	−	6.07198i	−0.254105	−	0.254105i	0.568547	−	0.822651i	$-0.307506\pi$
$571$	−6.07198	−	6.07198i	−0.254105	−	0.254105i	−0.822651	+	0.568547i	$0.807506\pi$
$572$	13.7553	+	16.8093i	0.575140	+	0.702834i
$573$	28.5034	−	28.5034i	1.19074	−	1.19074i
$574$		0			0
$575$	26.9129			1.12234
$576$	3.25885	+	6.15957i	0.135785	+	0.256649i
$577$	35.3028			1.46968			0.734838	−	0.678242i	$-0.237258\pi$
$577$	35.3028			1.46968			0.734838	+	0.678242i	$0.237258\pi$
$578$	−12.8937	−	6.10942i	−0.536306	−	0.254118i
$579$	−17.6903	+	17.6903i	−0.735183	+	0.735183i
$580$	34.2242	+	41.8228i	1.42108	+	1.73660i
$581$		0			0
$582$	20.0821	−	7.16947i	0.832429	−	0.297184i
$583$		−	32.7141i		−	1.35488i
$584$	41.6481	−	10.3385i	1.72341	−	0.427809i
$585$		−	6.61528i		−	0.273508i
$586$	−10.2826	−	28.8022i	−0.424771	−	1.18981i
$587$	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
$590$	−18.7080	+	39.4824i	−0.770194	+	1.62547i
$591$	35.7932			1.47233
$592$	−19.3774	+	12.8684i	−0.796406	+	0.528890i
$593$	−11.5641			−0.474882			−0.237441	−	0.971402i	$-0.576309\pi$
$593$	−11.5641			−0.474882			−0.237441	+	0.971402i	$0.576309\pi$
$594$	11.1044	−	23.4355i	0.455621	−	0.961570i
$595$		0			0
$596$	−2.57451	+	25.7659i	−0.105456	+	1.05541i
$597$	2.04299	+	2.04299i	0.0836141	+	0.0836141i
$598$	−7.26006	−	20.3358i	−0.296886	−	0.831594i
$599$		−	12.2713i		−	0.501393i	−0.968066	−	0.250697i	$-0.919340\pi$
$599$		−	12.2713i		−	0.501393i	0.968066	−	0.250697i	$-0.0806596\pi$
$600$	−12.5538	+	20.8444i	−0.512507	+	0.850969i
$601$			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
$604$	4.33845	−	3.55022i	0.176529	−	0.144456i
$605$	17.6772	−	17.6772i	0.718679	−	0.718679i
$606$	−35.3202	−	16.7358i	−1.43478	−	0.679844i
$607$	25.6349			1.04049			0.520244	−	0.854018i	$-0.325841\pi$
$607$	25.6349			1.04049			0.520244	+	0.854018i	$0.325841\pi$
$608$	−0.975842	−	6.74271i	−0.0395756	−	0.273453i
$609$		0			0
$610$	−5.75410	−	2.72646i	−0.232977	−	0.110391i
$611$	6.32147	−	6.32147i	0.255739	−	0.255739i
$612$	7.01723	−	5.74231i	0.283655	−	0.232119i
$613$	6.80822	+	6.80822i	0.274981	+	0.274981i	0.831102	−	0.556120i	$-0.187711\pi$
$613$	6.80822	+	6.80822i	0.274981	+	0.274981i	−0.556120	+	0.831102i	$0.687711\pi$
$614$	−7.84050	+	2.79912i	−0.316417	+	0.112963i
$615$			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	$-0.154629\pi$
$618$	−1.50807	−	4.22418i	−0.0606633	−	0.169921i
$619$	−23.7380	−	23.7380i	−0.954110	−	0.954110i	0.0448821	−	0.998992i	$-0.485709\pi$
$619$	−23.7380	−	23.7380i	−0.954110	−	0.954110i	−0.998992	+	0.0448821i	$0.985709\pi$
$620$	1.69387	−	16.9524i	0.0680275	−	0.680825i
$621$	−18.2301	+	18.2301i	−0.731551	+	0.731551i
$622$	0.486035	−	1.02576i	0.0194882	−	0.0411291i
$623$		0			0
$624$	19.1369	+	3.86286i	0.766089	+	0.154638i
$625$	27.7436			1.10975
$626$	10.7356	−	22.6571i	0.429081	−	0.905559i
$627$	7.33542	−	7.33542i	0.292948	−	0.292948i
$628$	−2.69845	−	0.269627i	−0.107680	−	0.0107593i
$629$	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	$-0.205735\pi$
$632$	4.50664	+	18.1548i	0.179264	+	0.722158i
$633$			1.48797i			0.0591416i
$634$	−19.5308	+	6.97266i	−0.775667	+	0.276920i
$635$	3.90804	+	3.90804i	0.155086	+	0.155086i
$636$	−18.6220	−	22.7565i	−0.738411	−	0.902355i
$637$		0			0
$638$	−49.3813	−	23.3984i	−1.95503	−	0.926350i
$639$	8.76265			0.346645
$640$	−25.5485	−	23.3871i	−1.00989	−	0.924458i
$641$	−6.69390			−0.264393			−0.132197	−	0.991224i	$-0.542203\pi$
$641$	−6.69390			−0.264393			−0.132197	+	0.991224i	$0.542203\pi$
$642$	28.1769	+	13.3510i	1.11205	+	0.526924i
$643$	−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
$646$	−8.34876	+	2.98058i	−0.328478	+	0.117269i
$647$			43.6311i			1.71532i	0.514219	+	0.857659i	$0.328082\pi$
$647$			43.6311i			1.71532i	−0.514219	+	0.857659i	$0.671918\pi$
$648$	−7.39656	−	29.7967i	−0.290564	−	1.17052i
$649$		−	44.1780i		−	1.73414i
$650$	5.15757	+	14.4466i	0.202296	+	0.566643i
$651$		0			0
$652$	36.3637	+	3.63344i	1.42411	+	0.142296i
$653$	−17.8880	+	17.8880i	−0.700013	+	0.700013i	−0.964413	−	0.264400i	$-0.914826\pi$
$653$	−17.8880	+	17.8880i	−0.700013	+	0.700013i	0.264400	+	0.964413i	$0.414826\pi$
$654$	9.58699	−	20.2330i	0.374881	−	0.791172i
$655$	40.2031			1.57086
$656$	−24.8177	−	5.00954i	−0.968967	−	0.195590i
$657$	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	$0.395626\pi$
$660$	5.24359	−	52.4783i	0.204107	−	2.04272i
$661$	−7.70847	−	7.70847i	−0.299825	−	0.299825i	0.541120	−	0.840945i	$-0.318000\pi$
$661$	−7.70847	−	7.70847i	−0.299825	−	0.299825i	−0.840945	+	0.541120i	$0.818000\pi$
$662$	0.149998	+	0.420152i	0.00582982	+	0.0163297i
$663$		−	25.4027i		−	0.986559i
$664$	−25.4157	−	15.3069i	−0.986321	−	0.594025i
$665$		0			0
$666$	−6.74664	+	2.40861i	−0.261427	+	0.0933316i
$667$	38.4131	+	38.4131i	1.48736	+	1.48736i
$668$	3.03543	−	2.48394i	0.117444	−	0.0961064i
$669$	−10.9041	+	10.9041i	−0.421579	+	0.421579i
$670$	−5.34890	−	2.53447i	−0.206646	−	0.0979152i
$671$	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	$0.488796\pi$
$674$	34.2036	+	16.2067i	1.31747	+	0.624259i
$675$	12.9507	−	12.9507i	0.498475	−	0.498475i
$676$	−10.5968	+	8.67150i	−0.407568	+	0.333519i
$677$	−19.1385	−	19.1385i	−0.735552	−	0.735552i	0.236162	−	0.971714i	$-0.424111\pi$
$677$	−19.1385	−	19.1385i	−0.735552	−	0.735552i	−0.971714	+	0.236162i	$0.924111\pi$
$678$	39.9909	−	14.2771i	1.53584	−	0.548309i
$679$		0			0
$680$	−23.2516	+	38.6070i	−0.891656	+	1.48051i
$681$		−	0.688866i		−	0.0263974i
$682$	5.79212	+	16.2240i	0.221792	+	0.621251i
$683$	−14.1568	−	14.1568i	−0.541695	−	0.541695i	0.382330	−	0.924026i	$-0.375122\pi$
$683$	−14.1568	−	14.1568i	−0.541695	−	0.541695i	−0.924026	+	0.382330i	$0.875122\pi$
$684$	0.208609	−	2.08778i	0.00797638	−	0.0798283i
$685$	−17.1808	+	17.1808i	−0.656445	+	0.656445i
$686$		0			0
$687$	−43.4148			−1.65638
$688$	−14.4169	+	9.57419i	−0.549638	+	0.365013i
$689$	−18.5370			−0.706205
$690$	−22.4506	+	47.3810i	−0.854678	+	1.80376i
$691$	10.8188	−	10.8188i	0.411565	−	0.411565i	−0.470719	−	0.882283i	$-0.656005\pi$
$691$	10.8188	−	10.8188i	0.411565	−	0.411565i	0.882283	+	0.470719i	$0.156005\pi$
$692$	11.6528	+	1.16434i	0.442972	+	0.0442614i
$693$		0			0
$694$	−16.5474	−	46.3501i	−0.628130	−	1.75943i
$695$		−	8.95851i		−	0.339815i
$696$	−47.6697	+	11.8332i	−1.80691	+	0.448538i
$697$			32.9434i			1.24782i
$698$	25.9590	−	9.26757i	0.982562	−	0.350783i
$699$	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	$0.227538\pi$
$702$	−13.2794	−	6.29219i	−0.501199	−	0.237483i
$703$	7.00377			0.264152
$704$	33.4715	+	10.3087i	1.26151	+	0.388524i
$705$	−21.7074			−0.817548
$706$	−33.2848	−	15.7713i	−1.25269	−	0.593562i
$707$		0			0
$708$	−25.1476	−	30.7310i	−0.945106	−	1.15494i
$709$	−20.2724	−	20.2724i	−0.761345	−	0.761345i	0.215221	−	0.976565i	$-0.430953\pi$
$709$	−20.2724	−	20.2724i	−0.761345	−	0.761345i	−0.976565	+	0.215221i	$0.930953\pi$
$710$	−41.0183	+	14.6439i	−1.53939	+	0.549576i
$711$			5.76078i			0.216046i
$712$	8.95303	−	2.22245i	0.335529	−	0.0832898i
$713$		−	17.1261i		−	0.641377i
$714$		0			0
$715$	−23.5096	−	23.5096i	−0.879210	−	0.879210i
$716$	−26.7798	−	2.67581i	−1.00081	−	0.0999998i
$717$	−26.2205	+	26.2205i	−0.979221	+	0.979221i
$718$	12.7398	−	26.8869i	0.475446	−	1.00341i
$719$	−20.1357			−0.750936			−0.375468	−	0.926835i	$-0.622518\pi$
$719$	−20.1357			−0.750936			−0.375468	+	0.926835i	$0.622518\pi$
$720$	−5.90113	−	8.88595i	−0.219922	−	0.331160i
$721$		0			0
$722$	10.6272	−	22.4284i	0.395505	−	0.834697i
$723$	−8.90151	+	8.90151i	−0.331051	+	0.331051i
$724$	2.13842	−	21.4015i	0.0794737	−	0.795380i
$725$	−27.2888	−	27.2888i	−1.01348	−	1.01348i
$726$	7.63938	+	21.3983i	0.283524	+	0.794166i
$727$			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
$730$	−61.8626	+	22.0855i	−2.28964	+	0.817420i
$731$	15.9231	+	15.9231i	0.588937	+	0.588937i
$732$	4.47868	−	3.66497i	0.165537	−	0.135461i
$733$	9.05256	−	9.05256i	0.334364	−	0.334364i	−0.519877	−	0.854241i	$-0.674022\pi$
$733$	9.05256	−	9.05256i	0.334364	−	0.334364i	0.854241	+	0.519877i	$0.174022\pi$
$734$	9.47438	+	4.48925i	0.349706	+	0.165701i
$735$		0			0
$736$	−27.8925	−	20.8397i	−1.02813	−	0.768163i
$737$	5.98504			0.220462
$738$	−7.04624	−	3.33872i	−0.259376	−	0.122900i
$739$	20.2007	−	20.2007i	0.743096	−	0.743096i	−0.230077	−	0.973172i	$-0.573898\pi$
$739$	20.2007	−	20.2007i	0.743096	−	0.743096i	0.973172	+	0.230077i	$0.0738978\pi$
$740$	27.5561	−	22.5496i	1.01298	−	0.828939i
$741$	−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	$0.794164\pi$
$744$	13.2644	+	7.98865i	0.486296	+	0.292878i
$745$		−	39.6371i		−	1.45219i
$746$	−2.52366	−	7.06891i	−0.0923978	−	0.258811i
$747$	−6.46096	−	6.46096i	−0.236394	−	0.236394i
$748$	4.53086	−	45.3453i	0.165665	−	1.65799i
$749$		0			0
$750$	−2.28873	+	4.83028i	−0.0835726	+	0.176377i
$751$	17.6012			0.642277			0.321138	−	0.947032i	$-0.395935\pi$
$751$	17.6012			0.642277			0.321138	+	0.947032i	$0.395935\pi$
$752$	2.85226	−	14.1303i	0.104011	−	0.515280i
$753$	−8.15705			−0.297259
$754$	−13.2584	+	27.9813i	−0.482842	+	1.01902i
$755$	−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	$0.839749\pi$
$758$	−12.6680	−	35.4838i	−0.460123	−	1.28883i
$759$		−	53.0160i		−	1.92436i
$760$	2.51253	+	10.1216i	0.0911391	+	0.367149i
$761$		−	1.30937i		−	0.0474648i	−0.999718	−	0.0237324i	$-0.992445\pi$
$761$		−	1.30937i		−	0.0474648i	0.999718	−	0.0237324i	$-0.00755496\pi$
$762$	−4.73071	+	1.68890i	−0.171376	+	0.0611825i
$763$		0			0
$764$	−25.9499	−	31.7113i	−0.938833	−	1.14728i
$765$	−9.81432	+	9.81432i	−0.354838	+	0.354838i
$766$	−6.32127	−	2.99521i	−0.228397	−	0.108221i
$767$	−25.0329			−0.903885
$768$	29.1514	−	11.8822i	1.05191	−	0.428762i
$769$	−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
$772$	16.1055	+	19.6813i	0.579649	+	0.708344i
$773$	2.77217	+	2.77217i	0.0997079	+	0.0997079i	0.755201	−	0.655493i	$-0.227539\pi$
$773$	2.77217	+	2.77217i	0.0997079	+	0.0997079i	−0.655493	+	0.755201i	$0.727539\pi$
$774$	−5.01953	+	1.79202i	−0.180423	+	0.0644127i
$775$			12.1664i			0.437031i
$776$	−5.22216	−	21.0372i	−0.187465	−	0.755192i
$777$		0			0
$778$	−9.43222	−	26.4201i	−0.338161	−	0.947208i
$779$	5.39038	+	5.39038i	0.193130	+	0.193130i
$780$	−29.7362	−	2.97121i	−1.06473	−	0.106387i
$781$	31.1410	−	31.1410i	1.11431	−	1.11431i
$782$	−19.3990	+	40.9408i	−0.693706	+	1.46404i
$783$	36.9695			1.32118
$784$		0			0
$785$	4.15117			0.148161
$786$	−15.6459	+	33.0202i	−0.558072	+	1.17779i
$787$	−21.9765	+	21.9765i	−0.783377	+	0.783377i	−0.980399	−	0.197022i	$-0.936873\pi$
$787$	−21.9765	+	21.9765i	−0.783377	+	0.783377i	0.197022	+	0.980399i	$0.436873\pi$
$788$	3.61748	−	36.2041i	0.128867	−	1.28972i
$789$	0.479205	+	0.479205i	0.0170602	+	0.0170602i
$790$	−9.62726	−	26.9665i	−0.342522	−	0.959424i
$791$		0			0
$792$	9.23967	+	5.56471i	0.328317	+	0.197733i
$793$		−	3.64825i		−	0.129553i
$794$	−0.120343	+	0.0429636i	−0.00427083	+	0.00152472i
$795$	31.8274	+	31.8274i	1.12880	+	1.12880i
$796$	2.27292	−	1.85997i	0.0805617	−	0.0659248i
$797$	−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
$800$	19.8149	+	14.8046i	0.700563	+	0.523422i
$801$	2.84093			0.100379
$802$	32.4746	+	15.3874i	1.14672	+	0.543349i
$803$	46.9659	−	46.9659i	1.65739	−	1.65739i
$804$	4.16330	−	3.40689i	0.146828	−	0.120152i
$805$		0			0
$806$	9.19315	−	3.28203i	0.323815	−	0.115605i
$807$			27.4873i			0.967598i
$808$	−20.4976	+	34.0342i	−0.721102	+	1.19732i
$809$		−	49.3996i		−	1.73680i	−0.495868	−	0.868398i	$-0.665150\pi$
$809$		−	49.3996i		−	1.73680i	0.495868	−	0.868398i	$-0.334850\pi$
$810$	15.8008	+	44.2590i	0.555184	+	1.55510i
$811$	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
$814$	−15.4166	+	32.5362i	−0.540353	+	1.14039i
$815$	−55.9402			−1.95950
$816$	−22.6603	−	34.1221i	−0.793271	−	1.19451i
$817$	5.21084			0.182304
$818$	13.5678	−	28.6343i	0.474386	−	1.00117i
$819$		0			0
$820$	38.5633	+	3.85322i	1.34669	+	0.134560i
$821$	0.760309	+	0.760309i	0.0265350	+	0.0265350i	0.720250	−	0.693715i	$-0.244027\pi$
$821$	0.760309	+	0.760309i	0.0265350	+	0.0265350i	−0.693715	+	0.720250i	$0.744027\pi$
$822$	−7.42488	−	20.7975i	−0.258972	−	0.725396i
$823$			20.0833i			0.700058i	0.936739	+	0.350029i	$0.113828\pi$
$823$			20.0833i			0.700058i	−0.936739	+	0.350029i	$0.886172\pi$
$824$	−4.42509	+	1.09846i	−0.154155	+	0.0382666i
$825$			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	$0.694957\pi$
$828$	−6.79076	−	8.29846i	−0.235995	−	0.288391i
$829$	32.7219	−	32.7219i	1.13648	−	1.13648i	0.147403	−	0.989077i	$-0.452909\pi$
$829$	32.7219	−	32.7219i	1.13648	−	1.13648i	0.989077	−	0.147403i	$-0.0470913\pi$
$830$	41.0414	+	19.4466i	1.42457	+	0.675003i
$831$	16.6933			0.579084
$832$	5.84130	−	18.9662i	0.202511	−	0.657535i
$833$		0			0
$834$	7.35793	+	3.48641i	0.254784	+	0.120724i
$835$	−4.24536	+	4.24536i	−0.146917	+	0.146917i
$836$	−6.67827	−	8.16099i	−0.230973	−	0.282254i
$837$	−8.24124	−	8.24124i	−0.284859	−	0.284859i
$838$	−45.7251	+	16.3242i	−1.57955	+	0.563911i
$839$		−	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
$842$	−10.7773	−	30.1879i	−0.371411	−	1.04034i
$843$	−13.3071	−	13.3071i	−0.458320	−	0.458320i
$844$	1.50505	+	0.150384i	0.0518061	+	0.00517643i
$845$	14.8207	−	14.8207i	0.509847	−	0.509847i
$846$	1.90095	−	4.01189i	0.0653561	−	0.137931i
$847$		0			0
$848$	−24.8998	+	16.5359i	−0.855064	+	0.567844i
$849$	32.5209			1.11612
$850$	13.7811	−	29.0845i	0.472688	−	0.997589i
$851$	25.3095	−	25.3095i	0.867598	−	0.867598i
$852$	3.93570	−	39.3888i	0.134835	−	1.34944i
$853$	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
$856$	16.3520	−	27.1510i	0.558902	−	0.928002i
$857$		−	32.9414i		−	1.12526i	−0.826710	−	0.562628i	$-0.809790\pi$
$857$		−	32.9414i		−	1.12526i	0.826710	−	0.562628i	$-0.190210\pi$
$858$	28.4586	−	10.1599i	0.971559	−	0.346855i
$859$	29.9192	+	29.9192i	1.02083	+	1.02083i	0.999778	+	0.0210508i	$0.00670116\pi$
$859$	29.9192	+	29.9192i	1.02083	+	1.02083i	0.0210508	+	0.999778i	$0.493299\pi$
$860$	20.5019	−	16.7770i	0.699108	−	0.572091i
$861$		0			0
$862$	40.4636	+	19.1729i	1.37819	+	0.653030i
$863$	21.8142			0.742562			0.371281	−	0.928520i	$-0.378919\pi$
$863$	21.8142			0.742562			0.371281	+	0.928520i	$0.378919\pi$
$864$	−23.4504	+	3.39387i	−0.797800	+	0.115462i
$865$	−17.9261			−0.609505
$866$	−14.9300	−	7.07428i	−0.507342	−	0.240394i
$867$	−14.0360	+	14.0360i	−0.476689	+	0.476689i
$868$		0			0
$869$	20.4729	+	20.4729i	0.694495	+	0.694495i
$870$	70.8069	−	25.2786i	2.40058	−	0.857026i
$871$		−	3.39135i		−	0.114911i
$872$	−19.4963	−	11.7419i	−0.660229	−	0.397632i
$873$		−	6.67543i		−	0.225929i
$874$	3.52478	+	9.87311i	0.119228	+	0.333963i
$875$		0			0
$876$	5.93570	−	59.4049i	0.200549	−	2.00711i
$877$	9.89510	−	9.89510i	0.334134	−	0.334134i	−0.520020	−	0.854154i	$-0.674076\pi$
$877$	9.89510	−	9.89510i	0.334134	−	0.334134i	0.854154	+	0.520020i	$0.174076\pi$
$878$	−7.94596	+	16.7696i	−0.268163	+	0.565948i
$879$	−42.5476			−1.43510
$880$	−52.5508	−	10.6076i	−1.77149	−	0.357582i
$881$	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	$0.0532667\pi$
$884$	−25.6943	−	2.56736i	−0.864194	−	0.0863495i
$885$	42.9805	+	42.9805i	1.44477	+	1.44477i
$886$	10.9071	+	30.5513i	0.366431	+	1.02639i
$887$		−	4.26921i		−	0.143346i	−0.997428	−	0.0716731i	$-0.977166\pi$
$887$		−	4.26921i		−	0.143346i	0.997428	−	0.0716731i	$-0.0228338\pi$
$888$	7.79665	+	31.4084i	0.261638	+	1.05400i
$889$		0			0
$890$	−13.2985	+	4.74769i	−0.445768	+	0.159143i
$891$	−33.6013	−	33.6013i	−1.12569	−	1.12569i
$892$	9.92729	+	12.1314i	0.332390	+	0.406188i
$893$	−3.06909	+	3.06909i	−0.102703	+	0.102703i
$894$	32.5553	+	15.4257i	1.08881	+	0.515912i
$895$	41.1967			1.37705
$896$		0			0
$897$	−30.0408			−1.00303
$898$	19.9875	+	9.47066i	0.666990	+	0.316040i
$899$	−17.3653	+	17.3653i	−0.579164	+	0.579164i
$900$	4.82417	+	5.89525i	0.160806	+	0.196508i
$901$	27.5013	+	27.5013i	0.916200	+	0.916200i
$902$	−36.9064	+	13.1759i	−1.22885	+	0.438710i
$903$		0			0
$904$	−10.3993	−	41.8930i	−0.345875	−	1.39334i
$905$			32.9230i			1.09440i
$906$	−2.62226	−	7.34508i	−0.0871187	−	0.244024i
$907$	−23.8097	−	23.8097i	−0.790587	−	0.790587i	0.191002	−	0.981590i	$-0.438826\pi$
$907$	−23.8097	−	23.8097i	−0.790587	−	0.790587i	−0.981590	+	0.191002i	$0.938826\pi$
$908$	−0.696774	−	0.0696211i	−0.0231233	−	0.00231046i
$909$	−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	$0.477690\pi$
$912$	−9.29103	−	1.87543i	−0.307657	−	0.0621017i
$913$	−45.9224			−1.51981
$914$	7.40625	−	15.6306i	0.244977	−	0.517014i
$915$	−6.26390	+	6.26390i	−0.207078	+	0.207078i
$916$	−4.38777	+	43.9132i	−0.144976	+	1.45093i
$917$		0			0
$918$	10.3661	+	29.0361i	0.342134	+	0.958335i
$919$			21.7824i			0.718536i	0.933234	+	0.359268i	$0.116974\pi$
$919$			21.7824i			0.718536i	−0.933234	+	0.359268i	$0.883026\pi$
$920$	45.6560	+	27.4969i	1.50523	+	0.906546i
$921$			11.5823i			0.381649i
$922$	−25.3636	+	9.05502i	−0.835306	+	0.298211i
$923$	−17.6457	−	17.6457i	−0.580814	−	0.580814i
$924$		0			0
$925$	−17.9799	+	17.9799i	−0.591177	+	0.591177i
$926$	31.6699	+	15.0062i	1.04074	+	0.493133i
$927$	−1.40415			−0.0461182
$928$	7.15129	+	49.4129i	0.234753	+	1.62206i
$929$	31.3367			1.02812			0.514062	−	0.857753i	$-0.328140\pi$
$929$	31.3367			1.02812			0.514062	+	0.857753i	$0.328140\pi$
$930$	−21.4194	−	10.1491i	−0.702369	−	0.332804i
$931$		0			0
$932$	14.7273	−	12.0516i	0.482410	−	0.394763i
$933$	−1.11664	−	1.11664i	−0.0365571	−	0.0365571i
$934$	43.6391	−	15.5795i	1.42791	−	0.509777i
$935$			69.7570i			2.28130i
$936$	3.15317	−	5.23554i	0.103065	−	0.171129i
$937$		−	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
$940$	−2.19389	+	21.9566i	−0.0715567	+	0.716146i
$941$	35.0609	−	35.0609i	1.14295	−	1.14295i	0.155046	−	0.987907i	$-0.450448\pi$
$941$	35.0609	−	35.0609i	1.14295	−	1.14295i	0.987907	−	0.155046i	$-0.0495525\pi$
$942$	−1.61552	+	3.40950i	−0.0526365	+	0.111087i
$943$	38.9584			1.26866
$944$	−33.6254	+	22.3305i	−1.09441	+	0.726795i
$945$		0			0
$946$	−11.4701	+	24.2071i	−0.372924	+	0.787042i
$947$	0.0642739	−	0.0642739i	0.00208862	−	0.00208862i	−0.706062	−	0.708150i	$-0.749530\pi$
$947$	0.0642739	−	0.0642739i	0.00208862	−	0.00208862i	0.708150	+	0.706062i	$0.249530\pi$
$948$	25.8952	+	2.58742i	0.841035	+	0.0840356i
$949$	−26.6127	−	26.6127i	−0.863883	−	0.863883i
$950$	−2.50402	−	7.01389i	−0.0812410	−	0.227561i
$951$			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	$0.736881\pi$
$954$	−8.66939	+	3.09505i	−0.280682	+	0.100206i
$955$	44.3516	+	44.3516i	1.43518	+	1.43518i
$956$	23.8715	+	29.1715i	0.772059	+	0.943473i
$957$	−53.7564	+	53.7564i	−1.73770	+	1.73770i
$958$	45.1965	+	21.4155i	1.46023	+	0.691902i
$959$		0			0
$960$	−42.5935	+	22.5349i	−1.37470	+	0.727312i
$961$	−23.2579			−0.750254
$962$	18.4362	+	8.73564i	0.594408	+	0.281648i
$963$	6.90209	−	6.90209i	0.222417	−	0.222417i
$964$	8.10406	+	9.90335i	0.261014	+	0.318965i
$965$	−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	$0.582242\pi$
$968$	22.4161	−	5.56444i	0.720480	−	0.178848i
$969$			12.3331i			0.396196i
$970$	11.1558	+	31.2480i	0.358191	+	1.00331i
$971$	−26.6561	−	26.6561i	−0.855436	−	0.855436i	0.135360	−	0.990796i	$-0.456781\pi$
$971$	−26.6561	−	26.6561i	−0.855436	−	0.855436i	−0.990796	+	0.135360i	$0.956781\pi$
$972$	−17.4931	−	1.74790i	−0.561091	−	0.0560638i
$973$		0			0
$974$	−10.1285	+	21.3757i	−0.324537	+	0.684923i
$975$	21.3411			0.683462
$976$	−3.25440	−	4.90050i	−0.104171	−	0.156861i
$977$	−24.6888			−0.789864			−0.394932	−	0.918710i	$-0.629232\pi$
$977$	−24.6888			−0.789864			−0.394932	+	0.918710i	$0.629232\pi$
$978$	21.7704	−	45.9456i	0.696141	−	1.46918i
$979$	10.0962	−	10.0962i	0.322676	−	0.322676i
$980$		0			0
$981$	−4.95619	−	4.95619i	−0.158239	−	0.158239i
$982$	−3.98926	−	11.1741i	−0.127302	−	0.356581i
$983$			5.11704i			0.163208i	0.996665	+	0.0816041i	$0.0260043\pi$
$983$			5.11704i			0.163208i	−0.996665	+	0.0816041i	$0.973996\pi$
$984$	−18.1726	+	30.1738i	−0.579321	+	0.961906i
$985$			55.6946i			1.77458i
$986$	61.1825	−	21.8427i	1.94845	−	0.695613i
$987$		0			0
$988$	−4.62432	+	3.78415i	−0.147119	+	0.120390i
$989$	18.8304	−	18.8304i	0.598772	−	0.598772i
$990$	−14.9203	−	7.06966i	−0.474197	−	0.224689i
$991$	−5.43929			−0.172785			−0.0863924	−	0.996261i	$-0.527534\pi$
$991$	−5.43929			−0.172785			−0.0863924	+	0.996261i	$0.527534\pi$
$992$	9.42095	−	12.6093i	0.299115	−	0.400345i
$993$	0.620663			0.0196961
$994$		0			0
$995$	−3.17892	+	3.17892i	−0.100779	+	0.100779i
$996$	−31.9444	+	26.1406i	−1.01220	+	0.828296i
$997$	8.55025	+	8.55025i	0.270789	+	0.270789i	0.829418	−	0.558629i	$-0.188672\pi$
$997$	8.55025	+	8.55025i	0.270789	+	0.270789i	−0.558629	+	0.829418i	$0.688672\pi$
$998$	10.4665	−	3.73663i	0.331311	−	0.118281i
$999$		−	24.3584i		−	0.770665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.h.197.1		12
7.2	even	3		784.2.x.m.165.4		24
7.3	odd	6		784.2.x.l.373.6		24
7.4	even	3		784.2.x.m.373.6		24
7.5	odd	6		784.2.x.l.165.4		24
7.6	odd	2		112.2.m.d.85.1	yes	12
16.13	even	4	inner	784.2.m.h.589.1		12
28.27	even	2		448.2.m.d.113.2		12
56.13	odd	2		896.2.m.g.225.2		12
56.27	even	2		896.2.m.h.225.5		12
112.13	odd	4		112.2.m.d.29.1	✓	12
112.27	even	4		896.2.m.h.673.5		12
112.45	odd	12		784.2.x.l.765.4		24
112.61	odd	12		784.2.x.l.557.6		24
112.69	odd	4		896.2.m.g.673.2		12
112.83	even	4		448.2.m.d.337.2		12
112.93	even	12		784.2.x.m.557.6		24
112.109	even	12		784.2.x.m.765.4		24
224.13	odd	8		7168.2.a.bj.1.3		12
224.83	even	8		7168.2.a.bi.1.10		12
224.125	odd	8		7168.2.a.bj.1.10		12
224.195	even	8		7168.2.a.bi.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.1	✓	12	112.13	odd	4
112.2.m.d.85.1	yes	12	7.6	odd	2
448.2.m.d.113.2		12	28.27	even	2
448.2.m.d.337.2		12	112.83	even	4
784.2.m.h.197.1		12	1.1	even	1	trivial
784.2.m.h.589.1		12	16.13	even	4	inner
784.2.x.l.165.4		24	7.5	odd	6
784.2.x.l.373.6		24	7.3	odd	6
784.2.x.l.557.6		24	112.61	odd	12
784.2.x.l.765.4		24	112.45	odd	12
784.2.x.m.165.4		24	7.2	even	3
784.2.x.m.373.6		24	7.4	even	3
784.2.x.m.557.6		24	112.93	even	12
784.2.x.m.765.4		24	112.109	even	12
896.2.m.g.225.2		12	56.13	odd	2
896.2.m.g.673.2		12	112.69	odd	4
896.2.m.h.225.5		12	56.27	even	2
896.2.m.h.673.5		12	112.27	even	4
7168.2.a.bi.1.3		12	224.195	even	8
7168.2.a.bi.1.10		12	224.83	even	8
7168.2.a.bj.1.3		12	224.13	odd	8
7168.2.a.bj.1.10		12	224.125	odd	8

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.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27801 - 0.605558i) q^{2} +(-1.39123 + 1.39123i) q^{3} +(1.26660 + 1.54781i) q^{4} +(-2.16478 - 2.16478i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} -0.871066i q^{9} +O(q^{10})\)	\(q+(-1.27801 - 0.605558i) q^{2} +(-1.39123 + 1.39123i) q^{3} +(1.26660 + 1.54781i) q^{4} +(-2.16478 - 2.16478i) q^{5} +(2.62048 - 0.935533i) q^{6} +(-0.681431 - 2.74511i) q^{8} -0.871066i q^{9} +(1.45570 + 4.07750i) q^{10} +(-3.09563 - 3.09563i) q^{11} +(-3.91551 - 0.391234i) q^{12} +(-1.75410 + 1.75410i) q^{13} +6.02343 q^{15} +(-0.791452 + 3.92092i) q^{16} +5.20470 q^{17} +(-0.527481 + 1.11323i) q^{18} +(0.851620 - 0.851620i) q^{19} +(0.608766 - 6.09258i) q^{20} +(2.08165 + 5.83081i) q^{22} -6.15500i q^{23} +(4.76713 + 2.87107i) q^{24} +4.37253i q^{25} +(3.30395 - 1.17954i) q^{26} +(-2.96185 - 2.96185i) q^{27} +(-6.24096 + 6.24096i) q^{29} +(-7.69798 - 3.64753i) q^{30} +2.78247 q^{31} +(3.38582 - 4.53169i) q^{32} +8.61348 q^{33} +(-6.65164 - 3.15175i) q^{34} +(1.34825 - 1.10329i) q^{36} +(4.11202 + 4.11202i) q^{37} +(-1.60408 + 0.572671i) q^{38} -4.88072i q^{39} +(-4.46741 + 7.41771i) q^{40} +6.32956i q^{41} +(3.05937 + 3.05937i) q^{43} +(0.870533 - 8.71237i) q^{44} +(-1.88567 + 1.88567i) q^{45} +(-3.72721 + 7.86612i) q^{46} -3.60383 q^{47} +(-4.35382 - 6.55601i) q^{48} +(2.64782 - 5.58812i) q^{50} +(-7.24096 + 7.24096i) q^{51} +(-4.93675 - 0.493276i) q^{52} +(5.28393 + 5.28393i) q^{53} +(1.99169 + 5.57883i) q^{54} +13.4027i q^{55} +2.36961i q^{57} +(11.7552 - 4.19672i) q^{58} +(7.13555 + 7.13555i) q^{59} +(7.62927 + 9.32314i) q^{60} +(-1.03992 + 1.03992i) q^{61} +(-3.55601 - 1.68495i) q^{62} +(-7.07130 + 3.74121i) q^{64} +7.59446 q^{65} +(-11.0081 - 5.21596i) q^{66} +(-0.966693 + 0.966693i) q^{67} +(6.59227 + 8.05590i) q^{68} +(8.56304 + 8.56304i) q^{69} +10.0597i q^{71} +(-2.39118 + 0.593572i) q^{72} +15.1717i q^{73} +(-2.76512 - 7.74526i) q^{74} +(-6.08321 - 6.08321i) q^{75} +(2.39681 + 0.239487i) q^{76} +(-2.95556 + 6.23759i) q^{78} -6.61348 q^{79} +(10.2012 - 6.77460i) q^{80} +10.8544 q^{81} +(3.83291 - 8.08921i) q^{82} +(7.41730 - 7.41730i) q^{83} +(-11.2670 - 11.2670i) q^{85} +(-2.05727 - 5.76252i) q^{86} -17.3653i q^{87} +(-6.38839 + 10.6073i) q^{88} +3.26144i q^{89} +(3.55177 - 1.26801i) q^{90} +(9.52678 - 7.79591i) q^{92} +(-3.87107 + 3.87107i) q^{93} +(4.60572 + 2.18233i) q^{94} -3.68714 q^{95} +(1.59417 + 11.0151i) q^{96} +7.66352 q^{97} +(-2.69650 + 2.69650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8	\( 12 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{10} - 8 q^{12} - 24 q^{15} + 10 q^{16} + 8 q^{17} + 20 q^{20} + 14 q^{22} + 8 q^{24} + 20 q^{26} - 4 q^{27} - 4 q^{29} - 28 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{34} - 16 q^{36} - 20 q^{37} - 16 q^{38} + 8 q^{40} + 16 q^{43} + 14 q^{44} - 40 q^{45} - 28 q^{46} - 16 q^{47} - 16 q^{48} + 44 q^{50} - 16 q^{51} + 16 q^{52} + 4 q^{53} - 64 q^{54} + 14 q^{58} + 16 q^{59} + 60 q^{60} + 20 q^{61} - 8 q^{62} - 18 q^{64} + 32 q^{65} - 12 q^{66} + 24 q^{67} + 28 q^{68} + 4 q^{69} + 6 q^{72} - 38 q^{74} + 40 q^{75} - 48 q^{76} - 76 q^{78} + 24 q^{79} - 24 q^{80} - 44 q^{81} + 16 q^{82} + 20 q^{83} - 8 q^{85} + 38 q^{86} - 14 q^{88} + 40 q^{90} + 32 q^{92} - 48 q^{93} + 24 q^{94} + 16 q^{96} - 48 q^{97} + 32 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^10 - 8 * q^12 - 24 * q^15 + 10 * q^16 + 8 * q^17 + 20 * q^20 + 14 * q^22 + 8 * q^24 + 20 * q^26 - 4 * q^27 - 4 * q^29 - 28 * q^30 + 8 * q^31 + 12 * q^32 - 8 * q^34 - 16 * q^36 - 20 * q^37 - 16 * q^38 + 8 * q^40 + 16 * q^43 + 14 * q^44 - 40 * q^45 - 28 * q^46 - 16 * q^47 - 16 * q^48 + 44 * 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 - 8 * q^62 - 18 * q^64 + 32 * q^65 - 12 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 6 * q^72 - 38 * q^74 + 40 * q^75 - 48 * q^76 - 76 * q^78 + 24 * q^79 - 24 * q^80 - 44 * q^81 + 16 * q^82 + 20 * q^83 - 8 * q^85 + 38 * q^86 - 14 * q^88 + 40 * q^90 + 32 * q^92 - 48 * q^93 + 24 * q^94 + 16 * q^96 - 48 * q^97 + 32 * q^99

Introduction

L-functions

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