LMFDB - Embedded newform 112.2.m.d.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(29,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("112.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.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:	$0.894324502638$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			85.1
Root			$-0.605558 - 1.27801i$ of defining polynomial
Character	$\chi$	$=$	112.85
Dual form			112.2.m.d.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27801 - 0.605558i) q^{2} +(1.39123 - 1.39123i) q^{3} +(1.26660 + 1.54781i) q^{4} +(2.16478 + 2.16478i) q^{5} +(-2.62048 + 0.935533i) q^{6} +1.00000i q^{7} +(-0.681431 - 2.74511i) q^{8} -0.871066i q^{9} +O(q^{10})$	\(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} +1.00000i q^{7} +(-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} +(0.605558 - 1.27801i) q^{14} +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} +(1.39123 + 1.39123i) q^{21} +(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} +(-1.54781 + 1.26660i) q^{28} +(-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} +(-2.16478 + 2.16478i) q^{35} +(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} +(-0.935533 - 2.62048i) q^{42} +(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} -1.00000 q^{49} +(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} +(2.74511 - 0.681431i) q^{56} +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} +0.871066 q^{63} +(-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} +(4.07750 - 1.45570i) q^{70} +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} +(3.09563 - 3.09563i) q^{77} +(-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} +(-0.391234 + 3.91551i) q^{84} +(-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} +(1.75410 + 1.75410i) q^{91} +(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} +(1.27801 + 0.605558i) q^{98} +(-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} + 4 q^{21} + 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} - 4 q^{35} - 16 q^{36} - 20 q^{37} + 16 q^{38} - 8 q^{40} - 12 q^{42} + 16 q^{43} + 14 q^{44} + 40 q^{45} - 28 q^{46} + 16 q^{47} + 16 q^{48} - 12 q^{49} + 44 q^{50} - 16 q^{51} - 16 q^{52} + 4 q^{53} + 64 q^{54} + 6 q^{56} + 14 q^{58} - 16 q^{59} + 60 q^{60} - 20 q^{61} + 8 q^{62} + 12 q^{63} - 18 q^{64} + 32 q^{65} + 12 q^{66} + 24 q^{67} - 28 q^{68} - 4 q^{69} + 20 q^{70} + 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^{84} - 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} - 2 q^{98} + 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 + 4 * q^21 + 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 - 4 * q^35 - 16 * q^36 - 20 * q^37 + 16 * q^38 - 8 * q^40 - 12 * q^42 + 16 * q^43 + 14 * q^44 + 40 * q^45 - 28 * q^46 + 16 * q^47 + 16 * q^48 - 12 * q^49 + 44 * q^50 - 16 * q^51 - 16 * q^52 + 4 * q^53 + 64 * q^54 + 6 * q^56 + 14 * q^58 - 16 * q^59 + 60 * q^60 - 20 * q^61 + 8 * q^62 + 12 * q^63 - 18 * q^64 + 32 * q^65 + 12 * q^66 + 24 * q^67 - 28 * q^68 - 4 * q^69 + 20 * q^70 + 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^84 - 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 - 2 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.27801	−	0.605558i	−0.903687	−	0.428194i
$2$	−1.27801	−	0.605558i	−0.903687	−	0.428194i
$3$	1.39123	−	1.39123i	0.803230	−	0.803230i	−0.180369	−	0.983599i	$-0.557729\pi$
$3$	1.39123	−	1.39123i	0.803230	−	0.803230i	0.983599	+	0.180369i	$0.0577293\pi$
$4$	1.26660	+	1.54781i	0.633300	+	0.773907i
$5$	2.16478	+	2.16478i	0.968118	+	0.968118i	0.999507	−	0.0313891i	$-0.00999312\pi$
$5$	2.16478	+	2.16478i	0.968118	+	0.968118i	−0.0313891	+	0.999507i	$0.509993\pi$
$6$	−2.62048	+	0.935533i	−1.06981	+	0.381930i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−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	−0.420701	−	0.907200i	$-0.638216\pi$
$13$	1.75410	−	1.75410i	0.486499	−	0.486499i	0.907200	+	0.420701i	$0.138216\pi$
$14$	0.605558	−	1.27801i	0.161842	−	0.341562i
$15$	6.02343			1.55524
$16$	−0.791452	+	3.92092i	−0.197863	+	0.980230i
$17$	−5.20470			−1.26233			−0.631163	−	0.775651i	$-0.717422\pi$
$17$	−5.20470			−1.26233			−0.631163	+	0.775651i	$0.717422\pi$
$18$	−0.527481	+	1.11323i	−0.124328	+	0.262390i
$19$	−0.851620	+	0.851620i	−0.195375	+	0.195375i	−0.798014	−	0.602639i	$-0.794116\pi$
$19$	−0.851620	+	0.851620i	−0.195375	+	0.195375i	0.602639	+	0.798014i	$0.294116\pi$
$20$	−0.608766	+	6.09258i	−0.136124	+	1.36234i
$21$	1.39123	+	1.39123i	0.303592	+	0.303592i
$22$	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
$28$	−1.54781	+	1.26660i	−0.292509	+	0.239365i
$29$	−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	$-0.580389\pi$
$31$	−2.78247			−0.499746			−0.249873	+	0.968279i	$0.580389\pi$
$32$	3.38582	−	4.53169i	0.598535	−	0.801097i
$33$	−8.61348			−1.49942
$34$	6.65164	+	3.15175i	1.14075	+	0.540520i
$35$	−2.16478	+	2.16478i	−0.365914	+	0.365914i
$36$	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	$-0.835441\pi$
$41$		−	6.32956i		−	0.988511i	0.869317	−	0.494255i	$-0.164559\pi$
$42$	−0.935533	−	2.62048i	−0.144356	−	0.404349i
$43$	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	$-0.415342\pi$
$47$	3.60383			0.525673			0.262836	+	0.964840i	$0.415342\pi$
$48$	4.35382	+	6.55601i	0.628420	+	0.946279i
$49$	−1.00000			−0.142857
$50$	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
$56$	2.74511	−	0.681431i	0.366831	−	0.0910601i
$57$			2.36961i			0.313862i
$58$	11.7552	−	4.19672i	1.54354	−	0.551057i
$59$	−7.13555	−	7.13555i	−0.928969	−	0.928969i	0.0686701	−	0.997639i	$-0.478124\pi$
$59$	−7.13555	−	7.13555i	−0.928969	−	0.928969i	−0.997639	+	0.0686701i	$0.978124\pi$
$60$	7.62927	+	9.32314i	0.984934	+	1.20361i
$61$	1.03992	−	1.03992i	0.133148	−	0.133148i	−0.637392	−	0.770540i	$-0.719987\pi$
$61$	1.03992	−	1.03992i	0.133148	−	0.133148i	0.770540	+	0.637392i	$0.219987\pi$
$62$	3.55601	+	1.68495i	0.451614	+	0.213988i
$63$	0.871066			0.109744
$64$	−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
$70$	4.07750	−	1.45570i	0.487354	−	0.173990i
$71$			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	$-0.652193\pi$
$73$		−	15.1717i		−	1.77571i	0.460119	−	0.887857i	$-0.347807\pi$
$74$	−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
$77$	3.09563	−	3.09563i	0.352779	−	0.352779i
$78$	−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	−0.985254	−	0.171100i	$-0.945268\pi$
$83$	−7.41730	+	7.41730i	−0.814154	+	0.814154i	0.171100	+	0.985254i	$0.445268\pi$
$84$	−0.391234	+	3.91551i	−0.0426872	+	0.427217i
$85$	−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	$-0.944700\pi$
$89$		−	3.26144i		−	0.345712i	0.984947	−	0.172856i	$-0.0552996\pi$
$90$	−3.55177	+	1.26801i	−0.374390	+	0.133660i
$91$	1.75410	+	1.75410i	0.183879	+	0.183879i
$92$	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	$-0.627199\pi$
$97$	−7.66352			−0.778112			−0.389056	+	0.921214i	$0.627199\pi$
$98$	1.27801	+	0.605558i	0.129098	+	0.0611706i
$99$	−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	0.999933	−	0.0116100i	$-0.00369566\pi$
$101$	9.93252	+	9.93252i	0.988323	+	0.988323i	−0.0116100	+	0.999933i	$0.503696\pi$
$102$	13.6388	−	4.86917i	1.35044	−	0.482120i
$103$			1.61199i			0.158834i	0.996841	+	0.0794169i	$0.0253058\pi$
$103$			1.61199i			0.158834i	−0.996841	+	0.0794169i	$0.974694\pi$
$104$	−6.01049	−	3.61990i	−0.589377	−	0.354960i
$105$			6.02343i			0.587826i
$106$	−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
$112$	−3.92092	−	0.791452i	−0.370492	−	0.0747852i
$113$	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
$119$		−	5.20470i		−	0.477114i
$120$	−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
$126$	−1.11323	−	0.527481i	−0.0991743	−	0.0469918i
$127$	−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	−0.173531	−	0.984828i	$-0.555518\pi$
$131$	9.28573	−	9.28573i	0.811298	−	0.811298i	0.984828	+	0.173531i	$0.0555176\pi$
$132$	−10.9098	−	13.3321i	−0.949579	−	1.16041i
$133$	−0.851620	−	0.851620i	−0.0738448	−	0.0738448i
$134$	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	0.613889	−	0.789392i	$-0.289604\pi$
$139$	−2.06915	−	2.06915i	−0.175503	−	0.175503i	−0.789392	+	0.613889i	$0.789604\pi$
$140$	−6.09258	−	0.608766i	−0.514917	−	0.0514501i
$141$	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
$147$	−1.39123	+	1.39123i	−0.114747	+	0.114747i
$148$	−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
$154$	−5.83081	+	2.08165i	−0.469860	+	0.167744i
$155$	−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	−0.667811	−	0.744331i	$-0.732768\pi$
$157$	0.958797	−	0.958797i	0.0765204	−	0.0765204i	0.744331	+	0.667811i	$0.232768\pi$
$158$	8.45207	+	4.00485i	0.672411	+	0.318609i
$159$	14.7024			1.16597
$160$	17.1397	−	2.48054i	1.35501	−	0.196104i
$161$	6.15500			0.485082
$162$	−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	$0.0241758\pi$
$167$			1.96111i			0.151755i	−0.997117	+	0.0758775i	$0.975824\pi$
$168$	2.87107	−	4.76713i	0.221508	−	0.367792i
$169$			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	−0.846761	−	0.531973i	$-0.821451\pi$
$173$	−4.14040	+	4.14040i	−0.314789	+	0.314789i	0.531973	+	0.846761i	$0.321451\pi$
$174$	10.5157	−	22.1929i	0.797191	−	1.68244i
$175$	−4.37253			−0.330532
$176$	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	0.930785	−	0.365566i	$-0.119125\pi$
$181$	7.60424	+	7.60424i	0.565219	+	0.565219i	−0.365566	+	0.930785i	$0.619125\pi$
$182$	−1.17954	−	3.30395i	−0.0874333	−	0.244905i
$183$		−	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
$189$	−2.96185	+	2.96185i	−0.215443	+	0.215443i
$190$	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
$196$	−1.26660	−	1.54781i	−0.0904714	−	0.110558i
$197$	−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	$0.0165751\pi$
$199$			1.46847i			0.104097i	−0.998645	+	0.0520487i	$0.983425\pi$
$200$	12.0031	−	2.97958i	0.848746	−	0.210688i
$201$			2.68979i			0.189723i
$202$	−6.67911	−	18.7085i	−0.469940	−	1.31633i
$203$	−6.24096	−	6.24096i	−0.438029	−	0.438029i
$204$	−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
$210$	3.64753	−	7.69798i	0.251704	−	0.531211i
$211$	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
$217$		−	2.78247i		−	0.188886i
$218$	−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	$-0.584523\pi$
$223$	−7.83775			−0.524855			−0.262427	+	0.964952i	$0.584523\pi$
$224$	4.53169	+	3.38582i	0.302786	+	0.226225i
$225$	3.80876			0.253917
$226$	−19.5036	−	9.24137i	−1.29736	−	0.614727i
$227$	0.247573	−	0.247573i	0.0164320	−	0.0164320i	−0.698843	−	0.715275i	$-0.746301\pi$
$227$	0.247573	−	0.247573i	0.0164320	−	0.0164320i	0.715275	+	0.698843i	$0.246301\pi$
$228$	−3.66771	+	3.00134i	−0.242900	+	0.198769i
$229$	−15.6030	−	15.6030i	−1.03107	−	1.03107i	−0.999502	−	0.0315714i	$-0.989949\pi$
$229$	−15.6030	−	15.6030i	−1.03107	−	1.03107i	−0.0315714	−	0.999502i	$-0.510051\pi$
$230$	−25.0970	+	8.95983i	−1.65485	+	0.590794i
$231$		−	8.61348i		−	0.566726i
$232$	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
$238$	−3.15175	+	6.65164i	−0.204297	+	0.431162i
$239$	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	$-0.566069\pi$
$241$	−6.39828			−0.412150			−0.206075	+	0.978536i	$0.566069\pi$
$242$	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
$245$	−2.16478	−	2.16478i	−0.138303	−	0.138303i
$246$	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	0.608508	−	0.793548i	$-0.291768\pi$
$251$	−2.93159	−	2.93159i	−0.185040	−	0.185040i	−0.793548	+	0.608508i	$0.791768\pi$
$252$	1.10329	+	1.34825i	0.0695009	+	0.0849317i
$253$	−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	$-0.141007\pi$
$257$	28.9676			1.80695			0.903475	+	0.428640i	$0.141007\pi$
$258$	−10.8792	−	5.15487i	−0.677306	−	0.320928i
$259$	−4.11202	+	4.11202i	−0.255509	+	0.255509i
$260$	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
$266$	0.572671	+	1.60408i	0.0351127	+	0.0983525i
$267$	−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	−0.940927	−	0.338610i	$-0.890043\pi$
$269$	−9.87874	+	9.87874i	−0.602317	+	0.602317i	0.338610	+	0.940927i	$0.390043\pi$
$270$	7.76536	−	16.3885i	0.472585	−	0.997371i
$271$	−12.4969			−0.759130			−0.379565	−	0.925165i	$-0.623926\pi$
$271$	−12.4969			−0.759130			−0.379565	+	0.925165i	$0.623926\pi$
$272$	4.11927	−	20.4072i	0.249767	−	1.23737i
$273$	4.88072			0.295395
$274$	−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
$280$	7.41771	+	4.46741i	0.443293	+	0.266979i
$281$			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	0.963277	−	0.268509i	$-0.0865311\pi$
$283$	11.6878	+	11.6878i	0.694768	+	0.694768i	−0.268509	+	0.963277i	$0.586531\pi$
$284$	−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
$287$	6.32956			0.373622
$288$	−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	0.101507	−	0.994835i	$-0.467634\pi$
$293$	−15.2913	−	15.2913i	−0.893328	−	0.893328i	−0.994835	+	0.101507i	$0.967634\pi$
$294$	2.62048	−	0.935533i	0.152829	−	0.0545614i
$295$		−	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
$301$	−3.05937	+	3.05937i	−0.176339	+	0.176339i
$302$	−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	−0.815844	−	0.578272i	$-0.803727\pi$
$307$	−4.16259	+	4.16259i	−0.237571	+	0.237571i	0.578272	+	0.815844i	$0.303727\pi$
$308$	8.71237	+	0.870533i	0.496433	+	0.0496032i
$309$	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	$-0.992756\pi$
$311$		−	0.802623i		−	0.0455126i	0.999741	−	0.0227563i	$-0.00724418\pi$
$312$	−13.3981	+	3.32588i	−0.758520	+	0.188291i
$313$		−	17.7285i		−	1.00207i	−0.865427	−	0.501036i	$-0.832953\pi$
$313$		−	17.7285i		−	1.00207i	0.865427	−	0.501036i	$-0.167047\pi$
$314$	−1.80596	+	0.644742i	−0.101916	+	0.0363849i
$315$	1.88567	+	1.88567i	0.106245	+	0.106245i
$316$	−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
$322$	−7.86612	−	3.72721i	−0.438362	−	0.207709i
$323$	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
$329$			3.60383i			0.198686i
$330$	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
$336$	−6.55601	+	4.35382i	−0.357660	+	0.237520i
$337$	−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
$343$		−	1.00000i		−	0.0539949i
$344$	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	−0.234412	−	0.972137i	$-0.575317\pi$
$349$	13.7818	−	13.7818i	0.737725	−	0.737725i	0.972137	+	0.234412i	$0.0753166\pi$
$350$	5.58812	+	2.64782i	0.298697	+	0.141532i
$351$	10.3907			0.554616
$352$	−24.5097	+	3.54717i	−1.30637	+	0.189065i
$353$	−26.0443			−1.38620			−0.693099	−	0.720842i	$-0.743755\pi$
$353$	−26.0443			−1.38620			−0.693099	+	0.720842i	$0.743755\pi$
$354$	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
$357$	−7.24096	−	7.24096i	−0.383232	−	0.383232i
$358$	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
$364$	−0.493276	+	4.93675i	−0.0258547	+	0.258756i
$365$	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	$-0.438020\pi$
$367$	7.41340			0.386977			0.193488	+	0.981103i	$0.438020\pi$
$368$	24.1332	+	4.87138i	1.25803	+	0.253938i
$369$	−5.51346			−0.287019
$370$	10.7809	−	22.7526i	0.560472	−	1.18285i
$371$	−5.28393	+	5.28393i	−0.274328	+	0.274328i
$372$	−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
$378$	5.57883	−	1.99169i	0.286944	−	0.102441i
$379$	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	$-0.540332\pi$
$383$	−4.94620			−0.252739			−0.126369	+	0.991983i	$0.540332\pi$
$384$	15.0302	−	16.4192i	0.767005	−	0.837889i
$385$	13.4027			0.683064
$386$	−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
$392$	0.681431	+	2.74511i	0.0344175	+	0.138649i
$393$		−	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	−0.708708	−	0.705502i	$-0.750722\pi$
$397$	−0.0638914	+	0.0638914i	−0.00320662	+	0.00320662i	0.705502	+	0.708708i	$0.250722\pi$
$398$	0.889246	−	1.87672i	0.0445739	−	0.0940714i
$399$	−2.36961			−0.118629
$400$	−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
$406$	4.19672	+	11.7552i	0.208280	+	0.583403i
$407$		−	25.4586i		−	1.26194i
$408$	24.8115	+	14.9430i	1.22835	+	0.739791i
$409$		−	22.4054i		−	1.10788i	−0.832557	−	0.553939i	$-0.813124\pi$
$409$		−	22.4054i		−	1.10788i	0.832557	−	0.553939i	$-0.186876\pi$
$410$	−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
$413$	7.13555	−	7.13555i	0.351117	−	0.351117i
$414$	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	$0.566622\pi$
$419$	−24.2758	+	24.2758i	−1.18595	+	1.18595i	−0.978177	+	0.207775i	$0.933378\pi$
$420$	−9.32314	+	7.62927i	−0.454923	+	0.372270i
$421$	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
$427$	1.03992	+	1.03992i	0.0503254	+	0.0503254i
$428$	−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	$-0.590569\pi$
$433$	−11.6823			−0.561413			−0.280707	+	0.959794i	$0.590569\pi$
$434$	−1.68495	+	3.55601i	−0.0808800	+	0.170694i
$435$	−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	$0.101378\pi$
$439$			13.1217i			0.626265i	−0.949709	+	0.313133i	$0.898622\pi$
$440$	−36.7919	+	9.13301i	−1.75399	+	0.435399i
$441$			0.871066i			0.0414794i
$442$	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
$448$	−3.74121	−	7.07130i	−0.176756	−	0.334088i
$449$	−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
$455$			7.59446i			0.356034i
$456$	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	−0.947353	−	0.320191i	$-0.896253\pi$
$461$	−13.4658	+	13.4658i	−0.627163	+	0.627163i	0.320191	+	0.947353i	$0.396253\pi$
$462$	−5.21596	+	11.0081i	−0.242669	+	0.512143i
$463$	−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	$-0.476132\pi$
$467$	23.1683	−	23.1683i	1.07210	−	1.07210i	0.997190	−	0.0749131i	$-0.0238679\pi$
$468$	0.429677	−	4.30024i	0.0198618	−	0.198779i
$469$	−0.966693	−	0.966693i	−0.0446377	−	0.0446377i
$470$	−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
$476$	8.05590	−	6.59227i	0.369242	−	0.302156i
$477$	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	$-0.200588\pi$
$479$	35.3648			1.61586			0.807930	+	0.589278i	$0.200588\pi$
$480$	20.3943	−	27.2963i	0.930866	−	1.24590i
$481$	14.4258			0.657759
$482$	8.17705	+	3.87453i	0.372454	+	0.176480i
$483$	8.56304	−	8.56304i	0.389632	−	0.389632i
$484$	−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
$490$	1.45570	+	4.07750i	0.0657619	+	0.184203i
$491$	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
$497$	−10.0597			−0.451239
$498$	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	$0.0498616\pi$
$503$			6.99765i			0.312010i	−0.987756	+	0.156005i	$0.950138\pi$
$504$	−0.593572	−	2.39118i	−0.0264398	−	0.106511i
$505$			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	−0.623366	−	0.781930i	$-0.714235\pi$
$509$	3.57736	−	3.57736i	0.158563	−	0.158563i	0.781930	+	0.623366i	$0.214235\pi$
$510$	40.0657	+	18.9843i	1.77414	+	0.840640i
$511$	15.1717			0.671157
$512$	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
$518$	7.74526	−	2.76512i	0.340307	−	0.121493i
$519$			11.5205i			0.505695i
$520$	−5.17510	−	20.8477i	−0.226943	−	0.914230i
$521$		−	17.3647i		−	0.760761i	−0.924830	−	0.380380i	$-0.875793\pi$
$521$		−	17.3647i		−	0.760761i	0.924830	−	0.380380i	$-0.124207\pi$
$522$	−3.65562	−	10.2396i	−0.160002	−	0.448175i
$523$	−25.9531	−	25.9531i	−1.13485	−	1.13485i	−0.989360	−	0.145491i	$-0.953524\pi$
$523$	−25.9531	−	25.9531i	−1.13485	−	1.13485i	−0.145491	−	0.989360i	$-0.546476\pi$
$524$	26.1339	+	2.61128i	1.14166	+	0.114074i
$525$	−6.08321	+	6.08321i	−0.265493	+	0.265493i
$526$	−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
$532$	0.239487	−	2.39681i	0.0103831	−	0.103915i
$533$	−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
$539$	3.09563	+	3.09563i	0.133338	+	0.133338i
$540$	−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
$546$	−6.23759	−	2.95556i	−0.266944	−	0.126486i
$547$	−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
$553$		−	6.61348i		−	0.281234i
$554$	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
$560$	−6.77460	−	10.2012i	−0.286279	−	0.431081i
$561$	44.8306			1.89275
$562$	5.79212	−	12.2240i	0.244326	−	0.515640i
$563$	14.7663	−	14.7663i	0.622324	−	0.622324i	−0.323801	−	0.946125i	$-0.604961\pi$
$563$	14.7663	−	14.7663i	0.622324	−	0.622324i	0.946125	+	0.323801i	$0.104961\pi$
$564$	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
$567$			10.8544i			0.455844i
$568$	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
$574$	−8.08921	−	3.83291i	−0.337637	−	0.159983i
$575$	26.9129			1.12234
$576$	3.25885	+	6.15957i	0.135785	+	0.256649i
$577$	−35.3028			−1.46968			−0.734838	−	0.678242i	$-0.762742\pi$
$577$	−35.3028			−1.46968			−0.734838	+	0.678242i	$0.762742\pi$
$578$	−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
$581$	−7.41730	−	7.41730i	−0.307721	−	0.307721i
$582$	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	0.656097	−	0.754676i	$-0.272206\pi$
$587$	−2.38838	−	2.38838i	−0.0985791	−	0.0985791i	−0.754676	+	0.656097i	$0.772206\pi$
$588$	−3.91551	−	0.391234i	−0.161473	−	0.0161342i
$589$	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	$-0.423691\pi$
$593$	11.5641			0.474882			0.237441	+	0.971402i	$0.423691\pi$
$594$	−11.1044	+	23.4355i	−0.455621	+	0.961570i
$595$	11.2670	−	11.2670i	0.461903	−	0.461903i
$596$	−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	$-0.906786\pi$
$601$		−	14.1538i		−	0.577347i	0.957428	−	0.288674i	$-0.0932143\pi$
$602$	5.76252	−	2.05727i	0.234863	−	0.0838480i
$603$	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	$-0.674159\pi$
$607$	−25.6349			−1.04049			−0.520244	+	0.854018i	$0.674159\pi$
$608$	0.975842	+	6.74271i	0.0395756	+	0.273453i
$609$	−17.3653			−0.703676
$610$	−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
$616$	−10.6073	−	6.38839i	−0.427380	−	0.257396i
$617$		−	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	0.998992	−	0.0448821i	$-0.0142912\pi$
$619$	23.7380	+	23.7380i	0.954110	+	0.954110i	−0.0448821	+	0.998992i	$0.514291\pi$
$620$	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
$623$	3.26144			0.130667
$624$	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
$630$	−1.26801	−	3.55177i	−0.0505188	−	0.141506i
$631$		−	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
$637$	−1.75410	+	1.75410i	−0.0694999	+	0.0694999i
$638$	−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	−0.0237114	−	0.999719i	$-0.507548\pi$
$643$	24.7491	−	24.7491i	0.976007	−	0.976007i	0.999719	+	0.0237114i	$0.00754828\pi$
$644$	7.79591	+	9.52678i	0.307202	+	0.375408i
$645$	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	$-0.671918\pi$
$647$		−	43.6311i		−	1.71532i	0.514219	−	0.857659i	$-0.328082\pi$
$648$	−7.39656	−	29.7967i	−0.290564	−	1.17052i
$649$			44.1780i			1.73414i
$650$	−5.15757	−	14.4466i	−0.202296	−	0.566643i
$651$	−3.87107	−	3.87107i	−0.151719	−	0.151719i
$652$	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
$658$	2.18233	−	4.60572i	0.0850760	−	0.179550i
$659$	−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	0.840945	−	0.541120i	$-0.182000\pi$
$661$	7.70847	+	7.70847i	0.299825	+	0.299825i	−0.541120	+	0.840945i	$0.682000\pi$
$662$	0.149998	+	0.420152i	0.00582982	+	0.0163297i
$663$			25.4027i			0.986559i
$664$	25.4157	+	15.3069i	0.986321	+	0.594025i
$665$		−	3.68714i		−	0.142981i
$666$	−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
$672$	11.0151	−	1.59417i	0.424917	−	0.0614963i
$673$	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	0.971714	−	0.236162i	$-0.0758894\pi$
$677$	19.1385	+	19.1385i	0.735552	+	0.735552i	−0.236162	+	0.971714i	$0.575889\pi$
$678$	−39.9909	+	14.2771i	−1.53584	+	0.548309i
$679$		−	7.66352i		−	0.294099i
$680$	−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
$686$	−0.605558	+	1.27801i	−0.0231203	+	0.0487945i
$687$	−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	−0.882283	−	0.470719i	$-0.843995\pi$
$691$	−10.8188	+	10.8188i	−0.411565	+	0.411565i	0.470719	+	0.882283i	$0.343995\pi$
$692$	−11.6528	−	1.16434i	−0.442972	−	0.0442614i
$693$	−2.69650	−	2.69650i	−0.102431	−	0.102431i
$694$	−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
$700$	−5.53824	−	6.76785i	−0.209326	−	0.255801i
$701$	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
$707$	−9.93252	+	9.93252i	−0.373551	+	0.373551i
$708$	−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
$714$	4.86917	+	13.6388i	0.182224	+	0.510420i
$715$	−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	$-0.377482\pi$
$719$	20.1357			0.750936			0.375468	+	0.926835i	$0.377482\pi$
$720$	5.90113	+	8.88595i	0.219922	+	0.331160i
$721$	−1.61199			−0.0600335
$722$	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	$-0.811991\pi$
$727$		−	30.0313i		−	1.11380i	0.830580	−	0.556900i	$-0.188009\pi$
$728$	3.61990	−	6.01049i	0.134162	−	0.222764i
$729$			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	−0.854241	−	0.519877i	$-0.825978\pi$
$733$	−9.05256	+	9.05256i	−0.334364	+	0.334364i	0.519877	+	0.854241i	$0.325978\pi$
$734$	−9.47438	−	4.48925i	−0.349706	−	0.165701i
$735$	−6.02343			−0.222177
$736$	−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
$742$	9.95262	−	3.55317i	0.365372	−	0.130441i
$743$			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
$749$	−7.92372	+	7.92372i	−0.289527	+	0.289527i
$750$	−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
$756$	−8.33586	−	0.832912i	−0.303172	−	0.0302927i
$757$	−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	$0.00755496\pi$
$761$			1.30937i			0.0474648i	−0.999718	+	0.0237324i	$0.992445\pi$
$762$	4.73071	−	1.68890i	0.171376	−	0.0611825i
$763$	5.68979	+	5.68979i	0.205984	+	0.205984i
$764$	−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	$-0.365926\pi$
$769$	22.6761			0.817720			0.408860	+	0.912597i	$0.365926\pi$
$770$	−17.1287	−	8.11610i	−0.617276	−	0.292484i
$771$	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	0.655493	−	0.755201i	$-0.272461\pi$
$773$	−2.77217	−	2.77217i	−0.0997079	−	0.0997079i	−0.755201	+	0.655493i	$0.772461\pi$
$774$	−5.01953	+	1.79202i	−0.180423	+	0.0644127i
$775$		−	12.1664i		−	0.437031i
$776$	5.22216	+	21.0372i	0.187465	+	0.755192i
$777$			11.4416i			0.410464i
$778$	−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
$784$	0.791452	−	3.92092i	0.0282661	−	0.140033i
$785$	4.15117			0.148161
$786$	−15.6459	+	33.0202i	−0.558072	+	1.17779i
$787$	21.9765	−	21.9765i	0.783377	−	0.783377i	−0.197022	−	0.980399i	$-0.563127\pi$
$787$	21.9765	−	21.9765i	0.783377	−	0.783377i	0.980399	+	0.197022i	$0.0631271\pi$
$788$	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
$791$			15.2609i			0.542616i
$792$	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	−0.0152058	−	0.999884i	$-0.504840\pi$
$797$	27.7986	−	27.7986i	0.984679	−	0.984679i	0.999884	+	0.0152058i	$0.00484033\pi$
$798$	3.02837	+	1.43493i	0.107203	+	0.0507961i
$799$	−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
$805$	13.3242	+	13.3242i	0.469616	+	0.469616i
$806$	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	0.437643	−	0.899149i	$-0.355813\pi$
$811$	−13.1428	−	13.1428i	−0.461506	−	0.461506i	−0.899149	+	0.437643i	$0.855813\pi$
$812$	1.75504	−	17.5646i	0.0615900	−	0.616398i
$813$	−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
$819$	1.52794	−	1.52794i	0.0533904	−	0.0533904i
$820$	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
$826$	−13.4403	+	4.79829i	−0.467647	+	0.166954i
$827$	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	$0.547091\pi$
$829$	−32.7219	+	32.7219i	−1.13648	+	1.13648i	−0.989077	+	0.147403i	$0.952909\pi$
$830$	41.0414	+	19.4466i	1.42457	+	0.675003i
$831$	−16.6933			−0.579084
$832$	−5.84130	+	18.9662i	−0.202511	+	0.657535i
$833$	5.20470			0.180332
$834$	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	$0.0618583\pi$
$839$			11.1872i			0.386225i	−0.981177	+	0.193113i	$0.938142\pi$
$840$	16.5350	−	4.10455i	0.570512	−	0.141620i
$841$		−	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
$847$	−8.16581			−0.280580
$848$	−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	0.121632	−	0.992575i	$-0.461187\pi$
$853$	−25.4369	−	25.4369i	−0.870944	−	0.870944i	−0.992575	+	0.121632i	$0.961187\pi$
$854$	−0.699294	−	1.95876i	−0.0239293	−	0.0670274i
$855$			3.21174i			0.109839i
$856$	16.3520	−	27.1510i	0.558902	−	0.928002i
$857$			32.9414i			1.12526i	0.826710	+	0.562628i	$0.190210\pi$
$857$			32.9414i			1.12526i	−0.826710	+	0.562628i	$0.809790\pi$
$858$	28.4586	−	10.1599i	0.971559	−	0.346855i
$859$	−29.9192	−	29.9192i	−1.02083	−	1.02083i	−0.999778	−	0.0210508i	$-0.993299\pi$
$859$	−29.9192	−	29.9192i	−1.02083	−	1.02083i	−0.0210508	−	0.999778i	$-0.506701\pi$
$860$	−20.5019	+	16.7770i	−0.699108	+	0.572091i
$861$	8.80590	−	8.80590i	0.300104	−	0.300104i
$862$	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
$868$	4.30674	−	3.52427i	0.146180	−	0.119622i
$869$	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
$875$	1.35834	+	1.35834i	0.0459203	+	0.0459203i
$876$	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	$-0.566609\pi$
$881$	−12.3319			−0.415471			−0.207735	+	0.978185i	$0.566609\pi$
$882$	0.527481	−	1.11323i	0.0177612	−	0.0374843i
$883$	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	$0.0228338\pi$
$887$			4.26921i			0.143346i	−0.997428	+	0.0716731i	$0.977166\pi$
$888$	−7.79665	−	31.4084i	−0.261638	−	1.05400i
$889$		−	1.80529i		−	0.0605473i
$890$	−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
$896$	0.499211	+	11.3027i	0.0166775	+	0.377596i
$897$	−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
$903$			8.51260i			0.283282i
$904$	−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
$910$	4.59889	−	9.70577i	0.152452	−	0.321743i
$911$	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
$917$	9.28573	+	9.28573i	0.306642	+	0.306642i
$918$	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
$924$	13.3321	−	10.9098i	0.438593	−	0.358907i
$925$	−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	$-0.671860\pi$
$929$	−31.3367			−1.02812			−0.514062	+	0.857753i	$0.671860\pi$
$930$	21.4194	+	10.1491i	0.702369	+	0.332804i
$931$	0.851620	−	0.851620i	0.0279107	−	0.0279107i
$932$	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	$0.343113\pi$
$937$			53.9341i			1.76195i	−0.473162	+	0.880975i	$0.656887\pi$
$938$	0.650051	+	1.82083i	0.0212249	+	0.0594521i
$939$	−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	$0.549552\pi$
$941$	−35.0609	+	35.0609i	−1.14295	+	1.14295i	−0.987907	+	0.155046i	$0.950448\pi$
$942$	−1.61552	+	3.40950i	−0.0526365	+	0.111087i
$943$	−38.9584			−1.26866
$944$	33.6254	−	22.3305i	1.09441	−	0.726795i
$945$	−12.8235			−0.417148
$946$	−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
$952$	−14.2875	+	3.54665i	−0.463060	+	0.114947i
$953$			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
$959$	7.93652			0.256284
$960$	−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
$966$	−16.1290	+	5.75820i	−0.518943	+	0.185267i
$967$			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	0.990796	−	0.135360i	$-0.0432192\pi$
$971$	26.6561	+	26.6561i	0.855436	+	0.855436i	−0.135360	+	0.990796i	$0.543219\pi$
$972$	17.4931	+	1.74790i	0.561091	+	0.0560638i
$973$	2.06915	−	2.06915i	0.0663339	−	0.0663339i
$974$	−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
$980$	0.608766	−	6.09258i	0.0194463	−	0.194620i
$981$	−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	$-0.973996\pi$
$983$		−	5.11704i		−	0.163208i	0.996665	−	0.0816041i	$-0.0260043\pi$
$984$	−18.1726	+	30.1738i	−0.579321	+	0.961906i
$985$		−	55.6946i		−	1.77458i
$986$	−61.1825	+	21.8427i	−1.94845	+	0.695613i
$987$	5.01377	+	5.01377i	0.159590	+	0.159590i
$988$	−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
$994$	12.8563	+	6.09172i	0.407778	+	0.193218i
$995$	−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	0.558629	−	0.829418i	$-0.311328\pi$
$997$	−8.55025	−	8.55025i	−0.270789	−	0.270789i	−0.829418	+	0.558629i	$0.811328\pi$
$998$	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	112.2.m.d.85.1	yes	12
4.3	odd	2		448.2.m.d.113.2		12
7.2	even	3		784.2.x.l.165.4		24
7.3	odd	6		784.2.x.m.373.6		24
7.4	even	3		784.2.x.l.373.6		24
7.5	odd	6		784.2.x.m.165.4		24
7.6	odd	2		784.2.m.h.197.1		12
8.3	odd	2		896.2.m.h.225.5		12
8.5	even	2		896.2.m.g.225.2		12
16.3	odd	4		448.2.m.d.337.2		12
16.5	even	4		896.2.m.g.673.2		12
16.11	odd	4		896.2.m.h.673.5		12
16.13	even	4	inner	112.2.m.d.29.1	✓	12
32.3	odd	8		7168.2.a.bi.1.3		12
32.13	even	8		7168.2.a.bj.1.3		12
32.19	odd	8		7168.2.a.bi.1.10		12
32.29	even	8		7168.2.a.bj.1.10		12
112.13	odd	4		784.2.m.h.589.1		12
112.45	odd	12		784.2.x.m.765.4		24
112.61	odd	12		784.2.x.m.557.6		24
112.93	even	12		784.2.x.l.557.6		24
112.109	even	12		784.2.x.l.765.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.1	✓	12	16.13	even	4	inner
112.2.m.d.85.1	yes	12	1.1	even	1	trivial
448.2.m.d.113.2		12	4.3	odd	2
448.2.m.d.337.2		12	16.3	odd	4
784.2.m.h.197.1		12	7.6	odd	2
784.2.m.h.589.1		12	112.13	odd	4
784.2.x.l.165.4		24	7.2	even	3
784.2.x.l.373.6		24	7.4	even	3
784.2.x.l.557.6		24	112.93	even	12
784.2.x.l.765.4		24	112.109	even	12
784.2.x.m.165.4		24	7.5	odd	6
784.2.x.m.373.6		24	7.3	odd	6
784.2.x.m.557.6		24	112.61	odd	12
784.2.x.m.765.4		24	112.45	odd	12
896.2.m.g.225.2		12	8.5	even	2
896.2.m.g.673.2		12	16.5	even	4
896.2.m.h.225.5		12	8.3	odd	2
896.2.m.h.673.5		12	16.11	odd	4
7168.2.a.bi.1.3		12	32.3	odd	8
7168.2.a.bi.1.10		12	32.19	odd	8
7168.2.a.bj.1.3		12	32.13	even	8
7168.2.a.bj.1.10		12	32.29	even	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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27801 - 0.605558i) q^{2} +(1.39123 - 1.39123i) q^{3} +(1.26660 + 1.54781i) q^{4} +(2.16478 + 2.16478i) q^{5} +(-2.62048 + 0.935533i) q^{6} +1.00000i q^{7} +(-0.681431 - 2.74511i) q^{8} -0.871066i q^{9} +O(q^{10})\)	\(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} +1.00000i q^{7} +(-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} +(0.605558 - 1.27801i) q^{14} +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} +(1.39123 + 1.39123i) q^{21} +(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} +(-1.54781 + 1.26660i) q^{28} +(-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} +(-2.16478 + 2.16478i) q^{35} +(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} +(-0.935533 - 2.62048i) q^{42} +(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} -1.00000 q^{49} +(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} +(2.74511 - 0.681431i) q^{56} +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} +0.871066 q^{63} +(-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} +(4.07750 - 1.45570i) q^{70} +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} +(3.09563 - 3.09563i) q^{77} +(-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} +(-0.391234 + 3.91551i) q^{84} +(-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} +(1.75410 + 1.75410i) q^{91} +(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} +(1.27801 + 0.605558i) q^{98} +(-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	\( 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8} - 4 q^{10} + 8 q^{12} - 24 q^{15} + 10 q^{16} - 8 q^{17} - 20 q^{20} + 4 q^{21} + 14 q^{22} - 8 q^{24} - 20 q^{26} + 4 q^{27} - 4 q^{29} - 28 q^{30} - 8 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 16 q^{36} - 20 q^{37} + 16 q^{38} - 8 q^{40} - 12 q^{42} + 16 q^{43} + 14 q^{44} + 40 q^{45} - 28 q^{46} + 16 q^{47} + 16 q^{48} - 12 q^{49} + 44 q^{50} - 16 q^{51} - 16 q^{52} + 4 q^{53} + 64 q^{54} + 6 q^{56} + 14 q^{58} - 16 q^{59} + 60 q^{60} - 20 q^{61} + 8 q^{62} + 12 q^{63} - 18 q^{64} + 32 q^{65} + 12 q^{66} + 24 q^{67} - 28 q^{68} - 4 q^{69} + 20 q^{70} + 6 q^{72} - 38 q^{74} - 40 q^{75} + 48 q^{76} - 76 q^{78} + 24 q^{79} + 24 q^{80} - 44 q^{81} - 16 q^{82} - 20 q^{83} + 8 q^{84} - 8 q^{85} + 38 q^{86} - 14 q^{88} - 40 q^{90} + 32 q^{92} - 48 q^{93} - 24 q^{94} - 16 q^{96} + 48 q^{97} - 2 q^{98} + 32 q^{99}+O(q^{100}) \) 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 + 4 * q^21 + 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 - 4 * q^35 - 16 * q^36 - 20 * q^37 + 16 * q^38 - 8 * q^40 - 12 * q^42 + 16 * q^43 + 14 * q^44 + 40 * q^45 - 28 * q^46 + 16 * q^47 + 16 * q^48 - 12 * q^49 + 44 * q^50 - 16 * q^51 - 16 * q^52 + 4 * q^53 + 64 * q^54 + 6 * q^56 + 14 * q^58 - 16 * q^59 + 60 * q^60 - 20 * q^61 + 8 * q^62 + 12 * q^63 - 18 * q^64 + 32 * q^65 + 12 * q^66 + 24 * q^67 - 28 * q^68 - 4 * q^69 + 20 * q^70 + 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^84 - 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 - 2 * q^98 + 32 * q^99

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