LMFDB - Embedded newform 84.2.e.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("84.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, 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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.2593100598870016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + x^8 + 4x^6 + 4x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.3
Root			$1.19877 - 0.750295i$ of defining polynomial
Character	$\chi$	$=$	84.71
Dual form			84.2.e.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.750295 - 1.19877i) q^{2} +(-0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} +3.56257i q^{5} +(2.34202 - 0.717607i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(-2.59774 - 1.50059i) q^{9} +O(q^{10})$	\(q+(-0.750295 - 1.19877i) q^{2} +(-0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} +3.56257i q^{5} +(2.34202 - 0.717607i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(-2.59774 - 1.50059i) q^{9} +(4.27072 - 2.67298i) q^{10} +0.335564 q^{11} +(-2.61745 - 2.26913i) q^{12} +3.34596 q^{13} +(-1.19877 + 0.750295i) q^{14} +(-5.96012 - 1.59774i) q^{15} +(-2.47185 - 3.14483i) q^{16} +0.335564i q^{17} +(0.150201 + 4.23998i) q^{18} +1.84951i q^{19} +(-6.40860 - 3.11410i) q^{20} +(1.67298 + 0.448478i) q^{21} +(-0.251772 - 0.402265i) q^{22} +4.45953 q^{23} +(-0.756309 + 4.84025i) q^{24} -7.69193 q^{25} +(-2.51046 - 4.01105i) q^{26} +(3.67549 - 3.67298i) q^{27} +(1.79887 + 0.874114i) q^{28} -5.91788i q^{29} +(2.55653 + 8.34360i) q^{30} -5.19547i q^{31} +(-1.91532 + 5.32274i) q^{32} +(-0.150493 + 0.561392i) q^{33} +(0.402265 - 0.251772i) q^{34} +3.56257 q^{35} +(4.97008 - 3.36129i) q^{36} +3.19547 q^{37} +(2.21714 - 1.38768i) q^{38} +(-1.50059 + 5.59774i) q^{39} +(1.07525 + 10.0189i) q^{40} +1.45835i q^{41} +(-0.717607 - 2.34202i) q^{42} +7.49646i q^{43} +(-0.293321 + 0.603635i) q^{44} +(5.34596 - 9.25462i) q^{45} +(-3.34596 - 5.34596i) q^{46} +8.91906 q^{47} +(6.36981 - 2.72497i) q^{48} -1.00000 q^{49} +(5.77122 + 9.22087i) q^{50} +(-0.561392 - 0.150493i) q^{51} +(-2.92475 + 6.01894i) q^{52} -4.79509i q^{53} +(-7.16077 - 1.65025i) q^{54} +1.19547i q^{55} +(-0.301817 - 2.81228i) q^{56} +(-3.09419 - 0.829463i) q^{57} +(-7.09419 + 4.44015i) q^{58} -14.0245 q^{59} +(8.08394 - 9.32486i) q^{60} -0.353051 q^{61} +(-6.22819 + 3.89814i) q^{62} +(-1.50059 + 2.59774i) q^{63} +(7.81781 - 1.69759i) q^{64} +11.9202i q^{65} +(0.785896 - 0.240803i) q^{66} -3.19547i q^{67} +(-0.603635 - 0.293321i) q^{68} +(-2.00000 + 7.46071i) q^{69} +(-2.67298 - 4.27072i) q^{70} -10.3774 q^{71} +(-7.75846 - 3.43604i) q^{72} -4.69193 q^{73} +(-2.39755 - 3.83064i) q^{74} +(3.44966 - 12.8685i) q^{75} +(-3.32702 - 1.61668i) q^{76} -0.335564i q^{77} +(7.83630 - 2.40109i) q^{78} -4.00000i q^{79} +(11.2037 - 8.80614i) q^{80} +(4.49646 + 7.79627i) q^{81} +(1.74823 - 1.09419i) q^{82} +6.89932 q^{83} +(-2.26913 + 2.61745i) q^{84} -1.19547 q^{85} +(8.98655 - 5.62456i) q^{86} +(9.90050 + 2.65404i) q^{87} +(0.943698 - 0.101279i) q^{88} -3.87289i q^{89} +(-15.1052 + 0.535101i) q^{90} -3.34596i q^{91} +(-3.89814 + 8.02210i) q^{92} +(8.69193 + 2.33005i) q^{93} +(-6.69193 - 10.6919i) q^{94} -6.58900 q^{95} +(-8.04586 - 5.59143i) q^{96} -2.00000 q^{97} +(0.750295 + 1.19877i) q^{98} +(-0.871706 - 0.503544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9	$ 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} + 2 q^{24} - 12 q^{25} + 8 q^{28} + 20 q^{30} - 16 q^{33} + 32 q^{34} - 20 q^{36} - 16 q^{37} + 20 q^{40} + 10 q^{42} + 24 q^{45} + 46 q^{48} - 12 q^{49} - 28 q^{52} + 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} - 16 q^{61} + 20 q^{64} - 12 q^{66} - 24 q^{69} - 12 q^{70} - 32 q^{72} + 24 q^{73} - 60 q^{76} + 20 q^{78} + 28 q^{81} + 8 q^{82} - 14 q^{84} + 40 q^{85} - 56 q^{88} - 80 q^{90} + 24 q^{93} - 34 q^{96} - 24 q^{97}+O(q^{100}) $ 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 + 2 * q^24 - 12 * q^25 + 8 * q^28 + 20 * q^30 - 16 * q^33 + 32 * q^34 - 20 * q^36 - 16 * q^37 + 20 * q^40 + 10 * q^42 + 24 * q^45 + 46 * q^48 - 12 * q^49 - 28 * q^52 + 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 - 16 * q^61 + 20 * q^64 - 12 * q^66 - 24 * q^69 - 12 * q^70 - 32 * q^72 + 24 * q^73 - 60 * q^76 + 20 * q^78 + 28 * q^81 + 8 * q^82 - 14 * q^84 + 40 * q^85 - 56 * q^88 - 80 * q^90 + 24 * q^93 - 34 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.750295	−	1.19877i	−0.530539	−	0.847661i
$2$	−0.750295	−	1.19877i	−0.530539	−	0.847661i
$3$	−0.448478	+	1.67298i	−0.258929	+	0.965896i
$3$	−0.448478	+	1.67298i	−0.258929	+	0.965896i
$4$	−0.874114	+	1.79887i	−0.437057	+	0.899434i
$5$			3.56257i			1.59323i	0.604486	+	0.796616i	$0.293378\pi$
$5$			3.56257i			1.59323i	−0.604486	+	0.796616i	$0.706622\pi$
$6$	2.34202	−	0.717607i	0.956124	−	0.292962i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.81228	−	0.301817i	0.994290	−	0.106709i
$9$	−2.59774	−	1.50059i	−0.865912	−	0.500197i
$10$	4.27072	−	2.67298i	1.35052	−	0.845271i
$11$	0.335564			0.101176			0.0505881	−	0.998720i	$-0.483890\pi$
$11$	0.335564			0.101176			0.0505881	+	0.998720i	$0.483890\pi$
$12$	−2.61745	−	2.26913i	−0.755593	−	0.655041i
$13$	3.34596			0.928003			0.464002	−	0.885834i	$-0.346413\pi$
$13$	3.34596			0.928003			0.464002	+	0.885834i	$0.346413\pi$
$14$	−1.19877	+	0.750295i	−0.320386	+	0.200525i
$15$	−5.96012	−	1.59774i	−1.53890	−	0.412533i
$16$	−2.47185	−	3.14483i	−0.617962	−	0.786208i
$17$			0.335564i			0.0813862i	0.999172	+	0.0406931i	$0.0129566\pi$
$17$			0.335564i			0.0813862i	−0.999172	+	0.0406931i	$0.987043\pi$
$18$	0.150201	+	4.23998i	0.0354027	+	0.999373i
$19$			1.84951i			0.424306i	0.977236	+	0.212153i	$0.0680475\pi$
$19$			1.84951i			0.424306i	−0.977236	+	0.212153i	$0.931952\pi$
$20$	−6.40860	−	3.11410i	−1.43301	−	0.696333i
$21$	1.67298	+	0.448478i	0.365075	+	0.0978659i
$22$	−0.251772	−	0.402265i	−0.0536779	−	0.0857631i
$23$	4.45953			0.929876			0.464938	−	0.885343i	$-0.346077\pi$
$23$	4.45953			0.929876			0.464938	+	0.885343i	$0.346077\pi$
$24$	−0.756309	+	4.84025i	−0.154381	+	0.988011i
$25$	−7.69193			−1.53839
$26$	−2.51046	−	4.01105i	−0.492342	−	0.786632i
$27$	3.67549	−	3.67298i	0.707348	−	0.706866i
$28$	1.79887	+	0.874114i	0.339954	+	0.165192i
$29$		−	5.91788i		−	1.09892i	−0.835519	−	0.549461i	$-0.814833\pi$
$29$		−	5.91788i		−	1.09892i	0.835519	−	0.549461i	$-0.185167\pi$
$30$	2.55653	+	8.34360i	0.466756	+	1.52333i
$31$		−	5.19547i		−	0.933134i	−0.884486	−	0.466567i	$-0.845491\pi$
$31$		−	5.19547i		−	0.933134i	0.884486	−	0.466567i	$-0.154509\pi$
$32$	−1.91532	+	5.32274i	−0.338584	+	0.940936i
$33$	−0.150493	+	0.561392i	−0.0261975	+	0.0977258i
$34$	0.402265	−	0.251772i	0.0689878	−	0.0431785i
$35$	3.56257			0.602185
$36$	4.97008	−	3.36129i	0.828347	−	0.560216i
$37$	3.19547			0.525332			0.262666	−	0.964887i	$-0.415398\pi$
$37$	3.19547			0.525332			0.262666	+	0.964887i	$0.415398\pi$
$38$	2.21714	−	1.38768i	0.359668	−	0.225111i
$39$	−1.50059	+	5.59774i	−0.240287	+	0.896355i
$40$	1.07525	+	10.0189i	0.170011	+	1.58413i
$41$			1.45835i			0.227756i	0.993495	+	0.113878i	$0.0363272\pi$
$41$			1.45835i			0.227756i	−0.993495	+	0.113878i	$0.963673\pi$
$42$	−0.717607	−	2.34202i	−0.110729	−	0.361381i
$43$			7.49646i			1.14320i	0.820533	+	0.571599i	$0.193677\pi$
$43$			7.49646i			1.14320i	−0.820533	+	0.571599i	$0.806323\pi$
$44$	−0.293321	+	0.603635i	−0.0442198	+	0.0910014i
$45$	5.34596	−	9.25462i	0.796929	−	1.37960i
$46$	−3.34596	−	5.34596i	−0.493335	−	0.788219i
$47$	8.91906			1.30098			0.650489	−	0.759516i	$-0.274564\pi$
$47$	8.91906			1.30098			0.650489	+	0.759516i	$0.274564\pi$
$48$	6.36981	−	2.72497i	0.919403	−	0.393316i
$49$	−1.00000			−0.142857
$50$	5.77122	+	9.22087i	0.816173	+	1.30403i
$51$	−0.561392	−	0.150493i	−0.0786106	−	0.0210732i
$52$	−2.92475	+	6.01894i	−0.405590	+	0.834677i
$53$		−	4.79509i		−	0.658657i	−0.944215	−	0.329328i	$-0.893178\pi$
$53$		−	4.79509i		−	0.658657i	0.944215	−	0.329328i	$-0.106822\pi$
$54$	−7.16077	−	1.65025i	−0.974458	−	0.224571i
$55$			1.19547i			0.161197i
$56$	−0.301817	−	2.81228i	−0.0403320	−	0.375806i
$57$	−3.09419	−	0.829463i	−0.409836	−	0.109865i
$58$	−7.09419	+	4.44015i	−0.931513	+	0.583021i
$59$	−14.0245			−1.82583			−0.912915	−	0.408150i	$-0.866174\pi$
$59$	−14.0245			−1.82583			−0.912915	+	0.408150i	$0.866174\pi$
$60$	8.08394	−	9.32486i	1.04363	−	1.20383i
$61$	−0.353051			−0.0452035			−0.0226018	−	0.999745i	$-0.507195\pi$
$61$	−0.353051			−0.0452035			−0.0226018	+	0.999745i	$0.507195\pi$
$62$	−6.22819	+	3.89814i	−0.790981	+	0.495064i
$63$	−1.50059	+	2.59774i	−0.189057	+	0.327284i
$64$	7.81781	−	1.69759i	0.977227	−	0.212199i
$65$			11.9202i			1.47852i
$66$	0.785896	−	0.240803i	0.0967371	−	0.0296408i
$67$		−	3.19547i		−	0.390389i	−0.980765	−	0.195194i	$-0.937466\pi$
$67$		−	3.19547i		−	0.390389i	0.980765	−	0.195194i	$-0.0625338\pi$
$68$	−0.603635	−	0.293321i	−0.0732015	−	0.0355704i
$69$	−2.00000	+	7.46071i	−0.240772	+	0.898164i
$70$	−2.67298	−	4.27072i	−0.319482	−	0.510448i
$71$	−10.3774			−1.23157			−0.615786	−	0.787914i	$-0.711161\pi$
$71$	−10.3774			−1.23157			−0.615786	+	0.787914i	$0.711161\pi$
$72$	−7.75846	−	3.43604i	−0.914343	−	0.404941i
$73$	−4.69193			−0.549148			−0.274574	−	0.961566i	$-0.588537\pi$
$73$	−4.69193			−0.549148			−0.274574	+	0.961566i	$0.588537\pi$
$74$	−2.39755	−	3.83064i	−0.278709	−	0.445303i
$75$	3.44966	−	12.8685i	0.398332	−	1.48592i
$76$	−3.32702	−	1.61668i	−0.381635	−	0.185446i
$77$		−	0.335564i		−	0.0382410i
$78$	7.83630	−	2.40109i	0.887286	−	0.271870i
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$	11.2037	−	8.80614i	1.25261	−	0.984557i
$81$	4.49646	+	7.79627i	0.499606	+	0.866253i
$82$	1.74823	−	1.09419i	0.193059	−	0.120833i
$83$	6.89932			0.757299			0.378649	−	0.925540i	$-0.376389\pi$
$83$	6.89932			0.757299			0.378649	+	0.925540i	$0.376389\pi$
$84$	−2.26913	+	2.61745i	−0.247582	+	0.285587i
$85$	−1.19547			−0.129667
$86$	8.98655	−	5.62456i	0.969045	−	0.606511i
$87$	9.90050	+	2.65404i	1.06144	+	0.284543i
$88$	0.943698	−	0.101279i	0.100599	−	0.0107964i
$89$		−	3.87289i		−	0.410525i	−0.978707	−	0.205263i	$-0.934195\pi$
$89$		−	3.87289i		−	0.410525i	0.978707	−	0.205263i	$-0.0658048\pi$
$90$	−15.1052	+	0.535101i	−1.59223	+	0.0564046i
$91$		−	3.34596i		−	0.350752i
$92$	−3.89814	+	8.02210i	−0.406409	+	0.836362i
$93$	8.69193	+	2.33005i	0.901311	+	0.241615i
$94$	−6.69193	−	10.6919i	−0.690220	−	1.10279i
$95$	−6.58900			−0.676018
$96$	−8.04586	−	5.59143i	−0.821178	−	0.570673i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	0.750295	+	1.19877i	0.0757913	+	0.121094i
$99$	−0.871706	−	0.503544i	−0.0876097	−	0.0506081i
$100$	6.72362	−	13.8368i	0.672362	−	1.38368i
$101$			13.1528i			1.30875i	0.756171	+	0.654374i	$0.227068\pi$
$101$			13.1528i			1.30875i	−0.756171	+	0.654374i	$0.772932\pi$
$102$	0.240803	+	0.785896i	0.0238430	+	0.0778153i
$103$			7.88740i			0.777168i	0.921413	+	0.388584i	$0.127036\pi$
$103$			7.88740i			0.777168i	−0.921413	+	0.388584i	$0.872964\pi$
$104$	9.40978	−	1.00987i	0.922705	−	0.0990259i
$105$	−1.59774	+	5.96012i	−0.155923	+	0.581648i
$106$	−5.74823	+	3.59774i	−0.558317	+	0.349443i
$107$	−8.13184			−0.786134			−0.393067	−	0.919510i	$-0.628586\pi$
$107$	−8.13184			−0.786134			−0.393067	+	0.919510i	$0.628586\pi$
$108$	3.39441	+	9.82232i	0.326628	+	0.945153i
$109$	19.0829			1.82781			0.913904	−	0.405931i	$-0.133053\pi$
$109$	19.0829			1.82781			0.913904	+	0.405931i	$0.133053\pi$
$110$	1.43310	−	0.896956i	0.136641	−	0.0855214i
$111$	−1.43310	+	5.34596i	−0.136024	+	0.507416i
$112$	−3.14483	+	2.47185i	−0.297159	+	0.233568i
$113$		−	12.5914i		−	1.18450i	−0.805756	−	0.592248i	$-0.798241\pi$
$113$		−	12.5914i		−	1.18450i	0.805756	−	0.592248i	$-0.201759\pi$
$114$	1.32722	+	4.33158i	0.124305	+	0.405689i
$115$			15.8874i			1.48151i
$116$	10.6455	+	5.17290i	0.988408	+	0.480292i
$117$	−8.69193	−	5.02092i	−0.803569	−	0.464184i
$118$	10.5225	+	16.8122i	0.968674	+	1.54768i
$119$	0.335564			0.0307611
$120$	−17.2437	−	2.69441i	−1.57413	−	0.245965i
$121$	−10.8874			−0.989763
$122$	0.264892	+	0.423228i	0.0239822	+	0.0383173i
$123$	−2.43979	−	0.654037i	−0.219988	−	0.0589725i
$124$	9.34596	+	4.54143i	0.839292	+	0.407833i
$125$		−	9.59019i		−	0.857772i
$126$	4.23998	−	0.150201i	0.377728	−	0.0133810i
$127$		−	10.1884i		−	0.904073i	−0.891999	−	0.452036i	$-0.850698\pi$
$127$		−	10.1884i		−	0.904073i	0.891999	−	0.452036i	$-0.149302\pi$
$128$	−7.90069	−	8.09809i	−0.698329	−	0.715777i
$129$	−12.5414	−	3.36199i	−1.10421	−	0.296007i
$130$	14.2897	−	8.94370i	1.25329	−	0.784414i
$131$	−10.4871			−0.916266			−0.458133	−	0.888884i	$-0.651482\pi$
$131$	−10.4871			−0.916266			−0.458133	+	0.888884i	$0.651482\pi$
$132$	−0.878322	−	0.761437i	−0.0764481	−	0.0662746i
$133$	1.84951			0.160373
$134$	−3.83064	+	2.39755i	−0.330917	+	0.207116i
$135$	13.0853	+	13.0942i	1.12620	+	1.12697i
$136$	0.101279	+	0.943698i	0.00868460	+	0.0809215i
$137$		−	8.91906i		−	0.762007i	−0.924574	−	0.381003i	$-0.875579\pi$
$137$		−	8.91906i		−	0.762007i	0.924574	−	0.381003i	$-0.124421\pi$
$138$	10.4443	−	3.20019i	0.889077	−	0.272418i
$139$		−	2.03789i		−	0.172852i	−0.996258	−	0.0864258i	$-0.972455\pi$
$139$		−	2.03789i		−	0.172852i	0.996258	−	0.0864258i	$-0.0275445\pi$
$140$	−3.11410	+	6.40860i	−0.263189	+	0.541625i
$141$	−4.00000	+	14.9214i	−0.336861	+	1.25661i
$142$	7.78612	+	12.4402i	0.653397	+	1.04395i
$143$	1.12278			0.0938919
$144$	1.70211	+	11.8787i	0.141842	+	0.989889i
$145$	21.0829			1.75084
$146$	3.52033	+	5.62456i	0.291345	+	0.465492i
$147$	0.448478	−	1.67298i	0.0369898	−	0.137985i
$148$	−2.79321	+	5.74823i	−0.229600	+	0.472501i
$149$		−	15.4576i		−	1.26633i	−0.774016	−	0.633166i	$-0.781755\pi$
$149$		−	15.4576i		−	1.26633i	0.774016	−	0.633166i	$-0.218245\pi$
$150$	−18.0146	+	5.51978i	−1.47089	+	0.450688i
$151$		−	15.1955i		−	1.23659i	−0.785946	−	0.618295i	$-0.787824\pi$
$151$		−	15.1955i		−	1.23659i	0.785946	−	0.618295i	$-0.212176\pi$
$152$	0.558213	+	5.20133i	0.0452771	+	0.421883i
$153$	0.503544	−	0.871706i	0.0407091	−	0.0704732i
$154$	−0.402265	+	0.251772i	−0.0324154	+	0.0202884i
$155$	18.5092			1.48670
$156$	−8.75790	−	7.59242i	−0.701193	−	0.607880i
$157$	−0.955023			−0.0762191			−0.0381095	−	0.999274i	$-0.512134\pi$
$157$	−0.955023			−0.0762191			−0.0381095	+	0.999274i	$0.512134\pi$
$158$	−4.79509	+	3.00118i	−0.381477	+	0.238761i
$159$	8.02210	+	2.15049i	0.636194	+	0.170545i
$160$	−18.9626	−	6.82347i	−1.49913	−	0.539443i
$161$		−	4.45953i		−	0.351460i
$162$	5.97229	−	11.2397i	0.469228	−	0.883077i
$163$		−	9.88740i		−	0.774441i	−0.921987	−	0.387220i	$-0.873435\pi$
$163$		−	9.88740i		−	0.774441i	0.921987	−	0.387220i	$-0.126565\pi$
$164$	−2.62337	−	1.27476i	−0.204851	−	0.0995422i
$165$	−2.00000	−	0.536142i	−0.155700	−	0.0417386i
$166$	−5.17653	−	8.27072i	−0.401776	−	0.641932i
$167$	1.12278			0.0868836			0.0434418	−	0.999056i	$-0.486168\pi$
$167$	1.12278			0.0868836			0.0434418	+	0.999056i	$0.486168\pi$
$168$	4.84025	+	0.756309i	0.373433	+	0.0583505i
$169$	−1.80453			−0.138810
$170$	0.896956	+	1.43310i	0.0687934	+	0.109914i
$171$	2.77535	−	4.80453i	0.212237	−	0.367412i
$172$	−13.4851	−	6.55276i	−1.02823	−	0.499643i
$173$			15.5673i			1.18356i	0.806100	+	0.591780i	$0.201575\pi$
$173$			15.5673i			1.18356i	−0.806100	+	0.591780i	$0.798425\pi$
$174$	−4.24671	−	13.8598i	−0.321942	−	1.05071i
$175$			7.69193i			0.581455i
$176$	−0.829463	−	1.05529i	−0.0625231	−	0.0795456i
$177$	6.28966	−	23.4627i	0.472760	−	1.76356i
$178$	−4.64271	+	2.90581i	−0.347986	+	0.217800i
$179$	21.7110			1.62276			0.811378	−	0.584521i	$-0.198718\pi$
$179$	21.7110			1.62276			0.811378	+	0.584521i	$0.198718\pi$
$180$	11.9749	+	17.7063i	0.892553	+	1.31975i
$181$	−16.4288			−1.22115			−0.610573	−	0.791960i	$-0.709061\pi$
$181$	−16.4288			−1.22115			−0.610573	+	0.791960i	$0.709061\pi$
$182$	−4.01105	+	2.51046i	−0.297319	+	0.186088i
$183$	0.158336	−	0.590648i	0.0117045	−	0.0436619i
$184$	12.5414	−	1.34596i	0.924567	−	0.0992257i
$185$			11.3841i			0.836975i
$186$	−3.72831	−	12.1679i	−0.273373	−	0.892192i
$187$			0.112603i			0.00823435i
$188$	−7.79627	+	16.0442i	−0.568602	+	1.17014i
$189$	−3.67298	−	3.67549i	−0.267170	−	0.267352i
$190$	4.94370	+	7.89872i	0.358654	+	0.573033i
$191$	−12.1208			−0.877032			−0.438516	−	0.898723i	$-0.644496\pi$
$191$	−12.1208			−0.877032			−0.438516	+	0.898723i	$0.644496\pi$
$192$	−0.666081	+	13.8404i	−0.0480703	+	0.998844i
$193$	−7.69901			−0.554187			−0.277094	−	0.960843i	$-0.589371\pi$
$193$	−7.69901			−0.554187			−0.277094	+	0.960843i	$0.589371\pi$
$194$	1.50059	+	2.39755i	0.107736	+	0.172134i
$195$	−19.9423	−	5.34596i	−1.42810	−	0.382832i
$196$	0.874114	−	1.79887i	0.0624367	−	0.128491i
$197$			7.04066i			0.501626i	0.968036	+	0.250813i	$0.0806980\pi$
$197$			7.04066i			0.501626i	−0.968036	+	0.250813i	$0.919302\pi$
$198$	0.0504019	+	1.42278i	0.00358191	+	0.101113i
$199$		−	21.3839i		−	1.51586i	−0.652335	−	0.757931i	$-0.726211\pi$
$199$		−	21.3839i		−	1.51586i	0.652335	−	0.757931i	$-0.273789\pi$
$200$	−21.6318	+	2.32156i	−1.52960	+	0.164159i
$201$	5.34596	+	1.43310i	0.377075	+	0.101083i
$202$	15.7672	−	9.86845i	1.10937	−	0.694342i
$203$	−5.91788			−0.415354
$204$	0.761437	−	0.878322i	0.0533113	−	0.0614948i
$205$	−5.19547			−0.362867
$206$	9.45520	−	5.91788i	0.658775	−	0.412318i
$207$	−11.5847	−	6.69193i	−0.805191	−	0.465121i
$208$	−8.27072	−	10.5225i	−0.573471	−	0.729603i
$209$			0.620628i			0.0429297i
$210$	8.34360	−	2.55653i	0.575763	−	0.176417i
$211$			22.9703i			1.58134i	0.612244	+	0.790669i	$0.290267\pi$
$211$			22.9703i			1.58134i	−0.612244	+	0.790669i	$0.709733\pi$
$212$	8.62574	+	4.19146i	0.592418	+	0.287871i
$213$	4.65404	−	17.3612i	0.318889	−	1.18957i
$214$	6.10128	+	9.74823i	0.417075	+	0.666375i
$215$	−26.7067			−1.82138
$216$	9.22792	−	11.4388i	0.627881	−	0.778310i
$217$	−5.19547			−0.352692
$218$	−14.3178	−	22.8760i	−0.969723	−	1.54936i
$219$	2.10423	−	7.84951i	0.142190	−	0.530421i
$220$	−2.15049	−	1.04498i	−0.144986	−	0.0704524i
$221$			1.12278i			0.0755266i
$222$	7.48384	−	2.29309i	0.502283	−	0.153902i
$223$			9.68484i			0.648545i	0.945964	+	0.324272i	$0.105119\pi$
$223$			9.68484i			0.648545i	−0.945964	+	0.324272i	$0.894881\pi$
$224$	5.32274	+	1.91532i	0.355640	+	0.127973i
$225$	19.9816	+	11.5424i	1.33211	+	0.769495i
$226$	−15.0942	+	9.44724i	−1.00405	+	0.628421i
$227$	13.4038			0.889644			0.444822	−	0.895619i	$-0.353267\pi$
$227$	13.4038			0.889644			0.444822	+	0.895619i	$0.353267\pi$
$228$	4.19677	−	4.84100i	0.277938	−	0.320603i
$229$	−16.7298			−1.10554			−0.552769	−	0.833335i	$-0.686429\pi$
$229$	−16.7298			−1.10554			−0.552769	+	0.833335i	$0.686429\pi$
$230$	19.0454	−	11.9202i	1.25582	−	0.785997i
$231$	0.561392	+	0.150493i	0.0369369	+	0.00990171i
$232$	−1.78612	−	16.6427i	−0.117264	−	1.09265i
$233$			20.9238i			1.37076i	0.728184	+	0.685381i	$0.240364\pi$
$233$			20.9238i			1.37076i	−0.728184	+	0.685381i	$0.759636\pi$
$234$	0.502566	+	14.1868i	0.0328538	+	0.927422i
$235$			31.7748i			2.07276i
$236$	12.2590	−	25.2282i	0.797992	−	1.64221i
$237$	6.69193	+	1.79391i	0.434687	+	0.116527i
$238$	−0.251772	−	0.402265i	−0.0163199	−	0.0260750i
$239$	21.1244			1.36642			0.683211	−	0.730221i	$-0.260583\pi$
$239$	21.1244			1.36642			0.683211	+	0.730221i	$0.260583\pi$
$240$	9.70791	+	22.6929i	0.626643	+	1.46482i
$241$	26.3768			1.69908			0.849538	−	0.527527i	$-0.176881\pi$
$241$	26.3768			1.69908			0.849538	+	0.527527i	$0.176881\pi$
$242$	8.16876	+	13.0515i	0.525108	+	0.838983i
$243$	−15.0596	+	4.02603i	−0.966073	+	0.258270i
$244$	0.308607	−	0.635092i	0.0197565	−	0.0406576i
$245$		−	3.56257i		−	0.227604i
$246$	1.04652	+	3.41547i	0.0667237	+	0.217763i
$247$			6.18838i			0.393757i
$248$	−1.56808	−	14.6111i	−0.0995734	−	0.927806i
$249$	−3.09419	+	11.5424i	−0.196086	+	0.731472i
$250$	−11.4965	+	7.19547i	−0.727100	+	0.455082i
$251$	−5.60756			−0.353946			−0.176973	−	0.984216i	$-0.556631\pi$
$251$	−5.60756			−0.353946			−0.176973	+	0.984216i	$0.556631\pi$
$252$	−3.36129	−	4.97008i	−0.211742	−	0.313086i
$253$	1.49646			0.0940814
$254$	−12.2136	+	7.64430i	−0.766347	+	0.479646i
$255$	0.536142	−	2.00000i	0.0335745	−	0.125245i
$256$	−3.77992	+	15.5471i	−0.236245	+	0.971693i
$257$		−	18.1737i		−	1.13364i	−0.823841	−	0.566821i	$-0.808173\pi$
$257$		−	18.1737i		−	1.13364i	0.823841	−	0.566821i	$-0.191827\pi$
$258$	5.37951	+	17.5568i	0.334914	+	1.09304i
$259$		−	3.19547i		−	0.198557i
$260$	−21.4429	−	10.4196i	−1.32983	−	0.646199i
$261$	−8.88031	+	15.3731i	−0.549677	+	0.951570i
$262$	7.86845	+	12.5717i	0.486115	+	0.776682i
$263$	17.7220			1.09279			0.546393	−	0.837529i	$-0.316000\pi$
$263$	17.7220			1.09279			0.546393	+	0.837529i	$0.316000\pi$
$264$	−0.253790	+	1.62421i	−0.0156197	+	0.0999633i
$265$	17.0829			1.04939
$266$	−1.38768	−	2.21714i	−0.0850839	−	0.135942i
$267$	6.47927	+	1.73690i	0.396525	+	0.106297i
$268$	5.74823	+	2.79321i	0.351129	+	0.170622i
$269$			12.4816i			0.761018i	0.924777	+	0.380509i	$0.124251\pi$
$269$			12.4816i			0.761018i	−0.924777	+	0.380509i	$0.875749\pi$
$270$	5.87915	−	25.5108i	0.357794	−	1.55254i
$271$			1.79744i			0.109187i	0.998509	+	0.0545934i	$0.0173863\pi$
$271$			1.79744i			0.109187i	−0.998509	+	0.0545934i	$0.982614\pi$
$272$	1.05529	−	0.829463i	0.0639864	−	0.0502936i
$273$	5.59774	+	1.50059i	0.338790	+	0.0908199i
$274$	−10.6919	+	6.69193i	−0.645923	+	0.404274i
$275$	−2.58113			−0.155648
$276$	−11.6726	−	10.1192i	−0.702608	−	0.609107i
$277$	−23.2713			−1.39823			−0.699117	−	0.715007i	$-0.746423\pi$
$277$	−23.2713			−1.39823			−0.699117	+	0.715007i	$0.746423\pi$
$278$	−2.44297	+	1.52902i	−0.146519	+	0.0917045i
$279$	−7.79627	+	13.4965i	−0.466751	+	0.808012i
$280$	10.0189	−	1.07525i	0.598746	−	0.0642583i
$281$			23.1693i			1.38217i	0.722775	+	0.691084i	$0.242866\pi$
$281$			23.1693i			1.38217i	−0.722775	+	0.691084i	$0.757134\pi$
$282$	20.8886	−	6.40038i	1.24390	−	0.381137i
$283$		−	1.84951i		−	0.109942i	−0.998488	−	0.0549709i	$-0.982493\pi$
$283$		−	1.84951i		−	0.109942i	0.998488	−	0.0549709i	$-0.0175066\pi$
$284$	9.07104	−	18.6676i	0.538267	−	1.10772i
$285$	2.95502	−	11.0233i	0.175040	−	0.652963i
$286$	−0.842420	−	1.34596i	−0.0498133	−	0.0795885i
$287$	1.45835			0.0860835
$288$	12.9627	−	10.9530i	0.763837	−	0.645409i
$289$	16.8874			0.993376
$290$	−15.8184	−	25.2736i	−0.928887	−	1.48412i
$291$	0.896956	−	3.34596i	0.0525805	−	0.196144i
$292$	4.10128	−	8.44015i	0.240009	−	0.493923i
$293$		−	1.54919i		−	0.0905047i	−0.998976	−	0.0452523i	$-0.985591\pi$
$293$		−	1.54919i		−	0.0905047i	0.998976	−	0.0452523i	$-0.0144092\pi$
$294$	−2.34202	+	0.717607i	−0.136589	+	0.0418517i
$295$		−	49.9632i		−	2.90897i
$296$	8.98655	−	0.964448i	0.522333	−	0.0560574i
$297$	1.23336	−	1.23252i	0.0715668	−	0.0715180i
$298$	−18.5301	+	11.5977i	−1.07342	+	0.671839i
$299$	14.9214			0.862928
$300$	20.1332	+	17.4540i	1.16239	+	1.00771i
$301$	7.49646			0.432089
$302$	−18.2159	+	11.4011i	−1.04821	+	0.656059i
$303$	−22.0043	−	5.89872i	−1.26412	−	0.338873i
$304$	5.81639	−	4.57170i	0.333593	−	0.262205i
$305$		−	1.25777i		−	0.0720197i
$306$	−1.42278	+	0.0504019i	−0.0813351	+	0.00288129i
$307$		−	12.5414i		−	0.715777i	−0.933764	−	0.357889i	$-0.883497\pi$
$307$		−	12.5414i		−	0.715777i	0.933764	−	0.357889i	$-0.116503\pi$
$308$	0.603635	+	0.293321i	0.0343953	+	0.0167135i
$309$	−13.1955	−	3.53732i	−0.750664	−	0.201231i
$310$	−13.8874	−	22.1884i	−0.788751	−	1.26022i
$311$	−12.0552			−0.683589			−0.341795	−	0.939775i	$-0.611035\pi$
$311$	−12.0552			−0.683589			−0.341795	+	0.939775i	$0.611035\pi$
$312$	−2.53058	+	16.1953i	−0.143266	+	0.916878i
$313$	−22.0758			−1.24780			−0.623898	−	0.781505i	$-0.714452\pi$
$313$	−22.0758			−1.24780			−0.623898	+	0.781505i	$0.714452\pi$
$314$	0.716549	+	1.14486i	0.0404372	+	0.0646079i
$315$	−9.25462	−	5.34596i	−0.521439	−	0.301211i
$316$	7.19547	+	3.49646i	0.404777	+	0.196691i
$317$		−	3.45284i		−	0.193931i	−0.995288	−	0.0969653i	$-0.969086\pi$
$317$		−	3.45284i		−	0.193931i	0.995288	−	0.0969653i	$-0.0309136\pi$
$318$	−3.44099	−	11.2302i	−0.192961	−	0.629757i
$319$		−	1.98582i		−	0.111185i
$320$	6.04778	+	27.8515i	0.338081	+	1.55695i
$321$	3.64695	−	13.6044i	0.203553	−	0.759324i
$322$	−5.34596	+	3.34596i	−0.297919	+	0.186463i
$323$	−0.620628			−0.0345326
$324$	−17.9549	+	1.27370i	−0.997493	+	0.0707609i
$325$	−25.7369			−1.42763
$326$	−11.8527	+	7.41847i	−0.656463	+	0.410871i
$327$	−8.55824	+	31.9253i	−0.473272	+	1.76547i
$328$	0.440155	+	4.10128i	0.0243035	+	0.226455i
$329$		−	8.91906i		−	0.491724i
$330$	0.857878	+	2.79981i	0.0472246	+	0.154125i
$331$			26.8945i			1.47825i	0.673566	+	0.739127i	$0.264762\pi$
$331$			26.8945i			1.47825i	−0.673566	+	0.739127i	$0.735238\pi$
$332$	−6.03079	+	12.4110i	−0.330983	+	0.681140i
$333$	−8.30099	−	4.79509i	−0.454891	−	0.262769i
$334$	−0.842420	−	1.34596i	−0.0460951	−	0.0736478i
$335$	11.3841			0.621980
$336$	−2.72497	−	6.36981i	−0.148659	−	0.347502i
$337$	10.5793			0.576292			0.288146	−	0.957586i	$-0.406961\pi$
$337$	10.5793			0.576292			0.288146	+	0.957586i	$0.406961\pi$
$338$	1.35393	+	2.16322i	0.0736441	+	0.117664i
$339$	21.0651	+	5.64695i	1.14410	+	0.306700i
$340$	1.04498	−	2.15049i	0.0566719	−	0.116627i
$341$		−	1.74341i		−	0.0944110i
$342$	−7.84188	+	0.277797i	−0.424040	+	0.0150216i
$343$			1.00000i			0.0539949i
$344$	2.26256	+	21.0821i	0.121989	+	1.13667i
$345$	−26.5793	−	7.12515i	−1.43098	−	0.383605i
$346$	18.6617	−	11.6801i	1.00326	−	0.627924i
$347$	−25.2483			−1.35540			−0.677701	−	0.735338i	$-0.737023\pi$
$347$	−25.2483			−1.35540			−0.677701	+	0.735338i	$0.737023\pi$
$348$	−13.4284	+	15.4898i	−0.719839	+	0.830338i
$349$	21.4359			1.14744			0.573719	−	0.819052i	$-0.305500\pi$
$349$	21.4359			1.14744			0.573719	+	0.819052i	$0.305500\pi$
$350$	9.22087	−	5.77122i	0.492876	−	0.308484i
$351$	12.2980	−	12.2897i	0.656421	−	0.655974i
$352$	−0.642713	+	1.78612i	−0.0342567	+	0.0952004i
$353$		−	8.58349i		−	0.456853i	−0.973561	−	0.228427i	$-0.926642\pi$
$353$		−	8.58349i		−	0.456853i	0.973561	−	0.228427i	$-0.0733581\pi$
$354$	−32.8455	+	10.0641i	−1.74572	+	0.534898i
$355$		−	36.9703i		−	1.96218i
$356$	6.96681	+	3.38534i	0.369240	+	0.179423i
$357$	−0.150493	+	0.561392i	−0.00796493	+	0.0297120i
$358$	−16.2897	−	26.0266i	−0.860935	−	1.37555i
$359$	6.70510			0.353881			0.176941	−	0.984222i	$-0.443380\pi$
$359$	6.70510			0.353881			0.176941	+	0.984222i	$0.443380\pi$
$360$	12.2411	−	27.6401i	0.645164	−	1.45676i
$361$	15.5793			0.819964
$362$	12.3265	+	19.6944i	0.647865	+	1.03512i
$363$	4.88276	−	18.2144i	0.256278	−	0.956009i
$364$	6.01894	+	2.92475i	0.315478	+	0.153299i
$365$		−	16.7153i		−	0.874920i
$366$	−0.826851	+	0.253352i	−0.0432202	+	0.0132429i
$367$			24.4809i			1.27789i	0.769251	+	0.638946i	$0.220629\pi$
$367$			24.4809i			1.27789i	−0.769251	+	0.638946i	$0.779371\pi$
$368$	−11.0233	−	14.0245i	−0.574628	−	0.731076i
$369$	2.18838	−	3.78840i	0.113923	−	0.197216i
$370$	13.6469	−	8.54143i	0.709471	−	0.444048i
$371$	−4.79509			−0.248949
$372$	−11.7892	+	13.5989i	−0.611241	+	0.705070i
$373$	4.39094			0.227354			0.113677	−	0.993518i	$-0.463737\pi$
$373$	4.39094			0.227354			0.113677	+	0.993518i	$0.463737\pi$
$374$	0.134985	−	0.0844855i	0.00697993	−	0.00436864i
$375$	16.0442	+	4.30099i	0.828519	+	0.222102i
$376$	25.0829	−	2.69193i	1.29355	−	0.138826i
$377$		−	19.8010i		−	1.01980i
$378$	−1.65025	+	7.16077i	−0.0848799	+	0.368310i
$379$			16.8803i			0.867083i	0.901134	+	0.433542i	$0.142736\pi$
$379$			16.8803i			0.867083i	−0.901134	+	0.433542i	$0.857264\pi$
$380$	5.75954	−	11.8527i	0.295458	−	0.608033i
$381$	17.0450	+	4.56926i	0.873241	+	0.234091i
$382$	9.09419	+	14.5301i	0.465299	+	0.743425i
$383$	23.8405			1.21819			0.609096	−	0.793097i	$-0.291533\pi$
$383$	23.8405			1.21819			0.609096	+	0.793097i	$0.291533\pi$
$384$	17.0912	−	9.58590i	0.872184	−	0.489178i
$385$	1.19547			0.0609268
$386$	5.77653	+	9.22937i	0.294018	+	0.469763i
$387$	11.2491	−	19.4738i	0.571824	−	0.989909i
$388$	1.74823	−	3.59774i	0.0887528	−	0.182647i
$389$			20.1682i			1.02257i	0.859412	+	0.511283i	$0.170830\pi$
$389$			20.1682i			1.02257i	−0.859412	+	0.511283i	$0.829170\pi$
$390$	8.55405	+	27.9174i	0.433151	+	1.41365i
$391$			1.49646i			0.0756790i
$392$	−2.81228	+	0.301817i	−0.142041	+	0.0152441i
$393$	4.70325	−	17.5448i	0.237248	−	0.885018i
$394$	8.44015	−	5.28257i	0.425209	−	0.266132i
$395$	14.2503			0.717010
$396$	1.66778	−	1.12793i	0.0838090	−	0.0566805i
$397$	−18.3389			−0.920402			−0.460201	−	0.887815i	$-0.652223\pi$
$397$	−18.3389			−0.920402			−0.460201	+	0.887815i	$0.652223\pi$
$398$	−25.6344	+	16.0442i	−1.28494	+	0.804223i
$399$	−0.829463	+	3.09419i	−0.0415251	+	0.154903i
$400$	19.0133	+	24.1898i	0.950664	+	1.20949i
$401$		−	8.60239i		−	0.429583i	−0.976660	−	0.214791i	$-0.931093\pi$
$401$		−	8.60239i		−	0.429583i	0.976660	−	0.214791i	$-0.0689071\pi$
$402$	−2.29309	−	7.48384i	−0.114369	−	0.373260i
$403$		−	17.3839i		−	0.865951i
$404$	−23.6601	−	11.4970i	−1.17713	−	0.571998i
$405$	−27.7748	+	16.0190i	−1.38014	+	0.795988i
$406$	4.44015	+	7.09419i	0.220361	+	0.352079i
$407$	1.07228			0.0531511
$408$	−1.62421	−	0.253790i	−0.0804105	−	0.0125645i
$409$	4.31516			0.213371			0.106685	−	0.994293i	$-0.465976\pi$
$409$	4.31516			0.213371			0.106685	+	0.994293i	$0.465976\pi$
$410$	3.89814	+	6.22819i	0.192515	+	0.307588i
$411$	14.9214	+	4.00000i	0.736019	+	0.197305i
$412$	−14.1884	−	6.89448i	−0.699011	−	0.339667i
$413$			14.0245i			0.690099i
$414$	0.669825	+	18.9083i	0.0329201	+	0.929293i
$415$			24.5793i			1.20655i
$416$	−6.40860	+	17.8097i	−0.314207	+	0.873192i
$417$	3.40935	+	0.913949i	0.166957	+	0.0447563i
$418$	0.743992	−	0.465654i	0.0363898	−	0.0227759i
$419$	−37.4133			−1.82776			−0.913879	−	0.405986i	$-0.866928\pi$
$419$	−37.4133			−1.82776			−0.913879	+	0.405986i	$0.866928\pi$
$420$	−9.32486	−	8.08394i	−0.455007	−	0.394456i
$421$	11.9016			0.580047			0.290024	−	0.957020i	$-0.406337\pi$
$421$	11.9016			0.580047			0.290024	+	0.957020i	$0.406337\pi$
$422$	27.5361	−	17.2345i	1.34044	−	0.838961i
$423$	−23.1693	−	13.3839i	−1.12653	−	0.650745i
$424$	−1.44724	−	13.4851i	−0.0702843	−	0.654896i
$425$		−	2.58113i		−	0.125203i
$426$	−24.3041	+	7.44690i	−1.17754	+	0.360803i
$427$			0.353051i			0.0170853i
$428$	7.10815	−	14.6281i	0.343586	−	0.707076i
$429$	−0.503544	+	1.87840i	−0.0243113	+	0.0906899i
$430$	20.0379	+	32.0152i	0.966313	+	1.54391i
$431$	−3.38724			−0.163158			−0.0815789	−	0.996667i	$-0.525996\pi$
$431$	−3.38724			−0.163158			−0.0815789	+	0.996667i	$0.525996\pi$
$432$	−20.6362	−	2.47973i	−0.992858	−	0.119306i
$433$	−26.7819			−1.28706			−0.643528	−	0.765423i	$-0.722530\pi$
$433$	−26.7819			−1.28706			−0.643528	+	0.765423i	$0.722530\pi$
$434$	3.89814	+	6.22819i	0.187117	+	0.298963i
$435$	−9.45520	+	35.2713i	−0.453342	+	1.69113i
$436$	−16.6806	+	34.3276i	−0.798856	+	1.64399i
$437$			8.24793i			0.394552i
$438$	−10.9886	+	3.36696i	−0.525054	+	0.160880i
$439$			3.77479i			0.180161i	0.995934	+	0.0900805i	$0.0287124\pi$
$439$			3.77479i			0.180161i	−0.995934	+	0.0900805i	$0.971288\pi$
$440$	0.360814	+	3.36199i	0.0172011	+	0.160277i
$441$	2.59774	+	1.50059i	0.123702	+	0.0714567i
$442$	1.34596	−	0.842420i	0.0640209	−	0.0400698i
$443$	6.78958			0.322583			0.161291	−	0.986907i	$-0.448434\pi$
$443$	6.78958			0.322583			0.161291	+	0.986907i	$0.448434\pi$
$444$	−8.36399	−	7.25093i	−0.396937	−	0.344114i
$445$	13.7974			0.654061
$446$	11.6099	−	7.26649i	0.549746	−	0.344078i
$447$	25.8602	+	6.93237i	1.22315	+	0.327890i
$448$	−1.69759	−	7.81781i	−0.0802035	−	0.369357i
$449$		−	12.9080i		−	0.609168i	−0.952485	−	0.304584i	$-0.901483\pi$
$449$		−	12.9080i		−	0.609168i	0.952485	−	0.304584i	$-0.0985174\pi$
$450$	−1.15533	−	32.6136i	−0.0544629	−	1.53742i
$451$			0.489369i			0.0230435i
$452$	22.6502	+	11.0063i	1.06538	+	0.517692i
$453$	25.4217	+	6.81483i	1.19442	+	0.320189i
$454$	−10.0568	−	16.0682i	−0.471991	−	0.754116i
$455$	11.9202			0.558829
$456$	−8.95207	−	1.39880i	−0.419219	−	0.0655048i
$457$	27.1813			1.27149			0.635744	−	0.771900i	$-0.280694\pi$
$457$	27.1813			1.27149			0.635744	+	0.771900i	$0.280694\pi$
$458$	12.5523	+	20.0553i	0.586531	+	0.937121i
$459$	1.23252	+	1.23336i	0.0575291	+	0.0575683i
$460$	−28.5793	−	13.8874i	−1.33252	−	0.647503i
$461$		−	7.31937i		−	0.340897i	−0.985367	−	0.170448i	$-0.945478\pi$
$461$		−	7.31937i		−	0.340897i	0.985367	−	0.170448i	$-0.0545216\pi$
$462$	−0.240803	−	0.785896i	−0.0112032	−	0.0365632i
$463$		−	3.77479i		−	0.175430i	−0.996146	−	0.0877148i	$-0.972044\pi$
$463$		−	3.77479i		−	0.175430i	0.996146	−	0.0877148i	$-0.0279564\pi$
$464$	−18.6107	+	14.6281i	−0.863981	+	0.679092i
$465$	−8.30099	+	30.9656i	−0.384949	+	1.43600i
$466$	25.0829	−	15.6990i	1.16194	−	0.727243i
$467$	−29.4480			−1.36269			−0.681346	−	0.731961i	$-0.738605\pi$
$467$	−29.4480			−1.36269			−0.681346	+	0.731961i	$0.738605\pi$
$468$	16.6297	−	11.2468i	0.768708	−	0.519882i
$469$	−3.19547			−0.147553
$470$	38.0908	−	23.8405i	1.75700	−	1.09968i
$471$	0.428306	−	1.59774i	0.0197353	−	0.0736198i
$472$	−39.4407	+	4.23283i	−1.81540	+	0.194832i
$473$			2.51554i			0.115665i
$474$	−2.87043	−	9.36807i	−0.131843	−	0.430289i
$475$		−	14.2263i		−	0.652746i
$476$	−0.293321	+	0.603635i	−0.0134443	+	0.0276676i
$477$	−7.19547	+	12.4564i	−0.329458	+	0.570338i
$478$	−15.8495	−	25.3233i	−0.724940	−	1.15826i
$479$	−33.6628			−1.53809			−0.769047	−	0.639192i	$-0.779269\pi$
$479$	−33.6628			−1.53809			−0.769047	+	0.639192i	$0.779269\pi$
$480$	19.9199	−	28.6640i	0.909214	−	1.30833i
$481$	10.6919			0.487510
$482$	−19.7904	−	31.6198i	−0.901426	−	1.44024i
$483$	7.46071	+	2.00000i	0.339474	+	0.0910032i
$484$	9.51683	−	19.5850i	0.432583	−	0.890227i
$485$		−	7.12515i		−	0.323536i
$486$	16.1254	+	15.0323i	0.731465	+	0.681879i
$487$			21.1813i			0.959816i	0.877319	+	0.479908i	$0.159330\pi$
$487$			21.1813i			0.959816i	−0.877319	+	0.479908i	$0.840670\pi$
$488$	−0.992877	+	0.106557i	−0.0449454	+	0.00482360i
$489$	16.5414	+	4.43428i	0.748029	+	0.200525i
$490$	−4.27072	+	2.67298i	−0.192931	+	0.120753i
$491$	−12.1208			−0.547005			−0.273502	−	0.961871i	$-0.588182\pi$
$491$	−12.1208			−0.547005			−0.273502	+	0.961871i	$0.588182\pi$
$492$	3.30918	−	3.81715i	0.149189	−	0.172091i
$493$	1.98582			0.0894371
$494$	7.41847	−	4.64311i	0.333773	−	0.208904i
$495$	1.79391	−	3.10552i	0.0806303	−	0.139583i
$496$	−16.3389	+	12.8424i	−0.733637	+	0.576642i
$497$			10.3774i			0.465490i
$498$	16.1583	−	4.95100i	0.724071	−	0.221860i
$499$		−	36.5793i		−	1.63752i	−0.574139	−	0.818758i	$-0.694663\pi$
$499$		−	36.5793i		−	1.63752i	0.574139	−	0.818758i	$-0.305337\pi$
$500$	17.2515	+	8.38292i	0.771509	+	0.374895i
$501$	−0.503544	+	1.87840i	−0.0224967	+	0.0839206i
$502$	4.20733	+	6.72220i	0.187782	+	0.300026i
$503$	0.890599			0.0397098			0.0198549	−	0.999803i	$-0.493680\pi$
$503$	0.890599			0.0397098			0.0198549	+	0.999803i	$0.493680\pi$
$504$	−3.43604	+	7.75846i	−0.153053	+	0.345589i
$505$	−46.8577			−2.08514
$506$	−1.12278	−	1.79391i	−0.0499138	−	0.0797491i
$507$	0.809292	−	3.01894i	0.0359419	−	0.134076i
$508$	18.3276	+	8.90581i	0.813154	+	0.395131i
$509$			1.54919i			0.0686667i	0.999410	+	0.0343333i	$0.0109308\pi$
$509$			1.54919i			0.0686667i	−0.999410	+	0.0343333i	$0.989069\pi$
$510$	−2.79981	+	0.857878i	−0.123978	+	0.0379875i
$511$			4.69193i			0.207559i
$512$	21.4735	−	7.13364i	0.949004	−	0.315265i
$513$	6.79321	+	6.79784i	0.299927	+	0.300132i
$514$	−21.7861	+	13.6356i	−0.960944	+	0.601442i
$515$	−28.0994			−1.23821
$516$	17.0104	−	19.6216i	0.748842	−	0.863793i
$517$	2.99291			0.131628
$518$	−3.83064	+	2.39755i	−0.168309	+	0.105342i
$519$	−26.0438	−	6.98159i	−1.14320	−	0.306458i
$520$	3.59774	+	33.5230i	0.157771	+	1.47008i
$521$		−	35.5601i		−	1.55792i	−0.627075	−	0.778959i	$-0.715748\pi$
$521$		−	35.5601i		−	1.55792i	0.627075	−	0.778959i	$-0.284252\pi$
$522$	25.0917	−	0.888870i	1.09823	−	0.0389048i
$523$		−	14.0379i		−	0.613834i	−0.951736	−	0.306917i	$-0.900703\pi$
$523$		−	14.0379i		−	0.613834i	0.951736	−	0.306917i	$-0.0992974\pi$
$524$	9.16696	−	18.8650i	0.400460	−	0.824120i
$525$	−12.8685	−	3.44966i	−0.561625	−	0.150555i
$526$	−13.2967	−	21.2447i	−0.579766	−	0.926312i
$527$	1.74341			0.0759442
$528$	2.13748	−	0.914402i	0.0930218	−	0.0397942i
$529$	−3.11260			−0.135331
$530$	−12.8172	−	20.4785i	−0.556743	−	0.889528i
$531$	36.4318	+	21.0450i	1.58101	+	0.913274i
$532$	−1.61668	+	3.32702i	−0.0700920	+	0.144245i
$533$			4.87958i			0.211358i
$534$	−2.77921	−	9.07036i	−0.120268	−	0.392513i
$535$		−	28.9703i		−	1.25249i
$536$	−0.964448	−	8.98655i	−0.0416578	−	0.388160i
$537$	−9.73690	+	36.3221i	−0.420178	+	1.56741i
$538$	14.9626	−	9.36491i	0.645085	−	0.403750i
$539$	−0.335564			−0.0144538
$540$	−34.9927	+	12.0928i	−1.50585	+	0.520393i
$541$	−32.2783			−1.38775			−0.693877	−	0.720093i	$-0.744099\pi$
$541$	−32.2783			−1.38775			−0.693877	+	0.720093i	$0.744099\pi$
$542$	2.15473	−	1.34861i	0.0925534	−	0.0579279i
$543$	7.36797	−	27.4851i	0.316190	−	1.17950i
$544$	−1.78612	−	0.642713i	−0.0765792	−	0.0275561i
$545$			67.9841i			2.91212i
$546$	−2.40109	−	7.83630i	−0.102757	−	0.335363i
$547$			19.8732i			0.849718i	0.905260	+	0.424859i	$0.139676\pi$
$547$			19.8732i			0.849718i	−0.905260	+	0.424859i	$0.860324\pi$
$548$	16.0442	+	7.79627i	0.685374	+	0.333040i
$549$	0.917133	+	0.529785i	0.0391423	+	0.0226107i
$550$	1.93661	+	3.09419i	0.0825774	+	0.131937i
$551$	10.9452			0.466279
$552$	−3.37278	+	21.5852i	−0.143555	+	0.918728i
$553$	−4.00000			−0.170097
$554$	17.4603	+	27.8969i	0.741817	+	1.18523i
$555$	−19.0454	−	5.10552i	−0.808432	−	0.216717i
$556$	3.66589	+	1.78135i	0.155469	+	0.0755460i
$557$		−	29.5389i		−	1.25160i	−0.779983	−	0.625801i	$-0.784772\pi$
$557$		−	29.5389i		−	1.25160i	0.779983	−	0.625801i	$-0.215228\pi$
$558$	22.0287	−	0.780364i	0.932549	−	0.0330354i
$559$			25.0829i			1.06089i
$560$	−8.80614	−	11.2037i	−0.372127	−	0.473442i
$561$	−0.188383	−	0.0505000i	−0.00795353	−	0.00213211i
$562$	27.7748	−	17.3839i	1.17161	−	0.733294i
$563$	20.7485			0.874443			0.437222	−	0.899354i	$-0.355963\pi$
$563$	20.7485			0.874443			0.437222	+	0.899354i	$0.355963\pi$
$564$	−23.3452	−	20.2385i	−0.983010	−	0.852194i
$565$	44.8577			1.88718
$566$	−2.21714	+	1.38768i	−0.0931933	+	0.0583284i
$567$	7.79627	−	4.49646i	0.327413	−	0.188833i
$568$	−29.1841	+	3.13208i	−1.22454	+	0.131419i
$569$		−	4.74459i		−	0.198904i	−0.995042	−	0.0994518i	$-0.968291\pi$
$569$		−	4.74459i		−	0.198904i	0.995042	−	0.0994518i	$-0.0317089\pi$
$570$	−15.4316	+	4.72832i	−0.646357	+	0.198047i
$571$			18.2642i			0.764331i	0.924094	+	0.382166i	$0.124822\pi$
$571$			18.2642i			0.764331i	−0.924094	+	0.382166i	$0.875178\pi$
$572$	−0.981441	+	2.01974i	−0.0410361	+	0.0844496i
$573$	5.43592	−	20.2779i	0.227089	−	0.847122i
$574$	−1.09419	−	1.74823i	−0.0456707	−	0.0729696i
$575$	−34.3024			−1.43051
$576$	−22.8560	−	7.32145i	−0.952333	−	0.305060i
$577$	−6.37677			−0.265468			−0.132734	−	0.991152i	$-0.542376\pi$
$577$	−6.37677			−0.265468			−0.132734	+	0.991152i	$0.542376\pi$
$578$	−12.6705	−	20.2442i	−0.527025	−	0.842046i
$579$	3.45284	−	12.8803i	0.143495	−	0.535287i
$580$	−18.4288	+	37.9253i	−0.765216	+	1.57476i
$581$		−	6.89932i		−	0.286232i
$582$	−4.68403	+	1.43521i	−0.194159	+	0.0594915i
$583$		−	1.60906i		−	0.0666404i
$584$	−13.1950	+	1.41610i	−0.546013	+	0.0585988i
$585$	17.8874	−	30.9656i	0.739553	−	1.28027i
$586$	−1.85713	+	1.16235i	−0.0767172	+	0.0480162i
$587$	16.8907			0.697152			0.348576	−	0.937280i	$-0.386665\pi$
$587$	16.8907			0.697152			0.348576	+	0.937280i	$0.386665\pi$
$588$	2.61745	+	2.26913i	0.107942	+	0.0935773i
$589$	9.60906			0.395934
$590$	−59.8945	+	37.4871i	−2.46582	+	1.54332i
$591$	−11.7789	−	3.15758i	−0.484519	−	0.129886i
$592$	−7.89872	−	10.0492i	−0.324635	−	0.413020i
$593$			40.6719i			1.67019i	0.550102	+	0.835097i	$0.314589\pi$
$593$			40.6719i			1.67019i	−0.550102	+	0.835097i	$0.685411\pi$
$594$	−2.40290	−	0.553766i	−0.0985920	−	0.0227213i
$595$			1.19547i			0.0490095i
$596$	27.8061	+	13.5117i	1.13898	+	0.553460i
$597$	35.7748	+	9.59019i	1.46416	+	0.392500i
$598$	−11.1955	−	17.8874i	−0.457817	−	0.731470i
$599$	7.29174			0.297932			0.148966	−	0.988842i	$-0.452405\pi$
$599$	7.29174			0.297932			0.148966	+	0.988842i	$0.452405\pi$
$600$	5.81748	−	37.2308i	0.237497	−	1.51994i
$601$	−30.6778			−1.25137			−0.625686	−	0.780075i	$-0.715181\pi$
$601$	−30.6778			−1.25137			−0.625686	+	0.780075i	$0.715181\pi$
$602$	−5.62456	−	8.98655i	−0.229240	−	0.366264i
$603$	−4.79509	+	8.30099i	−0.195271	+	0.338042i
$604$	27.3346	+	13.2826i	1.11223	+	0.540460i
$605$		−	38.7871i		−	1.57692i
$606$	9.43851	+	30.8040i	0.383413	+	1.25133i
$607$			13.3081i			0.540158i	0.962838	+	0.270079i	$0.0870498\pi$
$607$			13.3081i			0.540158i	−0.962838	+	0.270079i	$0.912950\pi$
$608$	−9.84444	−	3.54240i	−0.399245	−	0.143663i
$609$	2.65404	−	9.90050i	0.107547	−	0.401188i
$610$	−1.50778	+	0.943698i	−0.0610482	+	0.0382092i
$611$	29.8428			1.20731
$612$	1.12793	+	1.66778i	0.0455938	+	0.0674160i
$613$	19.6848			0.795063			0.397532	−	0.917588i	$-0.369867\pi$
$613$	19.6848			0.795063			0.397532	+	0.917588i	$0.369867\pi$
$614$	−15.0343	+	9.40978i	−0.606736	+	0.379748i
$615$	2.33005	−	8.69193i	0.0939568	−	0.350492i
$616$	−0.101279	−	0.943698i	−0.00408065	−	0.0380227i
$617$			10.7470i			0.432656i	0.976321	+	0.216328i	$0.0694081\pi$
$617$			10.7470i			0.432656i	−0.976321	+	0.216328i	$0.930592\pi$
$618$	5.66005	+	18.4724i	0.227681	+	0.743069i
$619$			45.7369i			1.83832i	0.393883	+	0.919161i	$0.371132\pi$
$619$			45.7369i			1.83832i	−0.393883	+	0.919161i	$0.628868\pi$
$620$	−16.1792	+	33.2957i	−0.649772	+	1.33719i
$621$	16.3909	−	16.3798i	0.657746	−	0.657297i
$622$	9.04498	+	14.4515i	0.362671	+	0.579452i
$623$	−3.87289			−0.155164
$624$	21.3132	−	9.11765i	0.853209	−	0.364998i
$625$	−4.29390			−0.171756
$626$	16.5634	+	26.4639i	0.662005	+	1.05771i
$627$	−1.03830	−	0.278338i	−0.0414656	−	0.0111157i
$628$	0.834799	−	1.71796i	0.0333121	−	0.0685540i
$629$			1.07228i			0.0427548i
$630$	0.535101	+	15.1052i	0.0213189	+	0.601807i
$631$			2.61615i			0.104147i	0.998643	+	0.0520736i	$0.0165830\pi$
$631$			2.61615i			0.104147i	−0.998643	+	0.0520736i	$0.983417\pi$
$632$	−1.20727	−	11.2491i	−0.0480226	−	0.447466i
$633$	−38.4288	−	10.3017i	−1.52741	−	0.409454i
$634$	−4.13917	+	2.59065i	−0.164387	+	0.102888i
$635$	36.2969			1.44040
$636$	−10.8807	+	12.5509i	−0.431447	+	0.497676i
$637$	−3.34596			−0.132572
$638$	−2.38055	+	1.48995i	−0.0942470	+	0.0589879i
$639$	26.9578	+	15.5722i	1.06643	+	0.616028i
$640$	28.8500	−	28.1468i	1.14040	−	1.11260i
$641$		−	22.5827i		−	0.891963i	−0.895042	−	0.445982i	$-0.852855\pi$
$641$		−	22.5827i		−	0.891963i	0.895042	−	0.445982i	$-0.147145\pi$
$642$	−19.0449	+	5.83546i	−0.751642	+	0.230307i
$643$			9.32332i			0.367676i	0.982957	+	0.183838i	$0.0588521\pi$
$643$			9.32332i			0.367676i	−0.982957	+	0.183838i	$0.941148\pi$
$644$	8.02210	+	3.89814i	0.316115	+	0.153608i
$645$	11.9774	−	44.6798i	0.471608	−	1.75926i
$646$	0.465654	+	0.743992i	0.0183209	+	0.0292720i
$647$	15.5420			0.611021			0.305510	−	0.952189i	$-0.401173\pi$
$647$	15.5420			0.611021			0.305510	+	0.952189i	$0.401173\pi$
$648$	14.9983	+	20.5682i	0.589190	+	0.807994i
$649$	−4.70610			−0.184731
$650$	19.3103	+	30.8527i	0.757411	+	1.21014i
$651$	2.33005	−	8.69193i	0.0913220	−	0.340663i
$652$	17.7861	+	8.64271i	0.696558	+	0.338475i
$653$			9.40470i			0.368034i	0.982923	+	0.184017i	$0.0589102\pi$
$653$			9.40470i			0.368034i	−0.982923	+	0.184017i	$0.941090\pi$
$654$	44.6924	−	13.6940i	1.74761	−	0.535478i
$655$		−	37.3612i		−	1.45982i
$656$	4.58626	−	3.60482i	0.179063	−	0.140744i
$657$	12.1884	+	7.04066i	0.475514	+	0.274682i
$658$	−10.6919	+	6.69193i	−0.416815	+	0.260878i
$659$	−31.2507			−1.21735			−0.608677	−	0.793418i	$-0.708299\pi$
$659$	−31.2507			−1.21735			−0.608677	+	0.793418i	$0.708299\pi$
$660$	2.71268	−	3.12909i	0.105591	−	0.121800i
$661$	−23.9479			−0.931467			−0.465733	−	0.884925i	$-0.654209\pi$
$661$	−23.9479			−0.931467			−0.465733	+	0.884925i	$0.654209\pi$
$662$	32.2404	−	20.1788i	1.25306	−	0.784271i
$663$	−1.87840	−	0.503544i	−0.0729509	−	0.0195560i
$664$	19.4028	−	2.08233i	0.752975	−	0.0808102i
$665$			6.58900i			0.255511i
$666$	0.479962	+	13.5487i	0.0185982	+	0.525003i
$667$		−	26.3909i		−	1.02186i
$668$	−0.981441	+	2.01974i	−0.0379731	+	0.0781461i
$669$	−16.2026	−	4.34344i	−0.626427	−	0.167927i
$670$	−8.54143	−	13.6469i	−0.329984	−	0.527228i
$671$	−0.118471			−0.00457353
$672$	−5.59143	+	8.04586i	−0.215694	+	0.310376i
$673$	−23.8732			−0.920245			−0.460123	−	0.887855i	$-0.652195\pi$
$673$	−23.8732			−0.920245			−0.460123	+	0.887855i	$0.652195\pi$
$674$	−7.93762	−	12.6822i	−0.305746	−	0.488500i
$675$	−28.2716	+	28.2523i	−1.08817	+	1.08743i
$676$	1.57736	−	3.24611i	0.0606679	−	0.124850i
$677$		−	26.9514i		−	1.03583i	−0.855433	−	0.517913i	$-0.826709\pi$
$677$		−	26.9514i		−	1.03583i	0.855433	−	0.517913i	$-0.173291\pi$
$678$	−9.03565	−	29.4892i	−0.347012	−	1.13253i
$679$			2.00000i			0.0767530i
$680$	−3.36199	+	0.360814i	−0.128927	+	0.0138366i
$681$	−6.01132	+	22.4244i	−0.230354	+	0.859304i
$682$	−2.08995	+	1.30807i	−0.0800285	+	0.0500887i
$683$	23.5554			0.901323			0.450661	−	0.892695i	$-0.351188\pi$
$683$	23.5554			0.901323			0.450661	+	0.892695i	$0.351188\pi$
$684$	6.21674	+	9.19220i	0.237703	+	0.351473i
$685$	31.7748			1.21405
$686$	1.19877	−	0.750295i	0.0457694	−	0.0286464i
$687$	7.50295	−	27.9887i	0.286255	−	1.06783i
$688$	23.5751	−	18.5301i	0.898792	−	0.706454i
$689$		−	16.0442i		−	0.611235i
$690$	11.4009	+	37.2085i	0.434025	+	1.41650i
$691$		−	4.24892i		−	0.161637i	−0.996729	−	0.0808183i	$-0.974247\pi$
$691$		−	4.24892i		−	0.161637i	0.996729	−	0.0808183i	$-0.0257533\pi$
$692$	−28.0035	−	13.6076i	−1.06453	−	0.517283i
$693$	−0.503544	+	0.871706i	−0.0191280	+	0.0331134i
$694$	18.9437	+	30.2670i	0.719093	+	1.14892i
$695$	7.26013			0.275392
$696$	28.6440	+	4.47575i	1.08575	+	0.169653i
$697$	−0.489369			−0.0185362
$698$	−16.0833	−	25.6968i	−0.608761	−	0.972638i
$699$	−35.0051	−	9.38385i	−1.32401	−	0.354930i
$700$	−13.8368	−	6.72362i	−0.522980	−	0.254129i
$701$			8.60239i			0.324908i	0.986716	+	0.162454i	$0.0519409\pi$
$701$			8.60239i			0.324908i	−0.986716	+	0.162454i	$0.948059\pi$
$702$	−23.9597	−	5.52169i	−0.904300	−	0.208403i
$703$			5.91005i			0.222902i
$704$	2.62337	−	0.569649i	0.0988721	−	0.0214695i
$705$	−53.1586	−	14.2503i	−2.00207	−	0.536697i
$706$	−10.2897	+	6.44015i	−0.387257	+	0.242378i
$707$	13.1528			0.494660
$708$	36.7084	+	31.8233i	1.37958	+	1.19599i
$709$	−14.7061			−0.552299			−0.276150	−	0.961115i	$-0.589059\pi$
$709$	−14.7061			−0.552299			−0.276150	+	0.961115i	$0.589059\pi$
$710$	−44.3190	+	27.7386i	−1.66326	+	1.04101i
$711$	−6.00236	+	10.3909i	−0.225106	+	0.389691i
$712$	−1.16890	−	10.8916i	−0.0438066	−	0.408181i
$713$		−	23.1693i		−	0.867699i
$714$	0.785896	−	0.240803i	0.0294114	−	0.00901182i
$715$			4.00000i			0.149592i
$716$	−18.9779	+	39.0552i	−0.709237	+	1.45956i
$717$	−9.47381	+	35.3407i	−0.353806	+	1.31982i
$718$	−5.03080	−	8.03789i	−0.187748	−	0.299971i
$719$	10.9324			0.407711			0.203856	−	0.979001i	$-0.434653\pi$
$719$	10.9324			0.407711			0.203856	+	0.979001i	$0.434653\pi$
$720$	−42.3186	+	6.06388i	−1.57712	+	0.225987i
$721$	7.88740			0.293742
$722$	−11.6891	−	18.6761i	−0.435023	−	0.695052i
$723$	−11.8294	+	44.1278i	−0.439940	+	1.64113i
$724$	14.3607	−	29.5533i	0.533710	−	1.09834i
$725$			45.5199i			1.69057i
$726$	−25.4985	+	7.81287i	−0.946337	+	0.289963i
$727$		−	38.8803i		−	1.44199i	−0.692940	−	0.720995i	$-0.743685\pi$
$727$		−	38.8803i		−	1.44199i	0.692940	−	0.720995i	$-0.256315\pi$
$728$	−1.00987	−	9.40978i	−0.0374283	−	0.348750i
$729$	0.0184116	−	27.0000i	0.000681912	−	1.00000i
$730$	−20.0379	+	12.5414i	−0.741636	+	0.464179i
$731$	−2.51554			−0.0930406
$732$	0.924094	+	0.801118i	0.0341555	+	0.0296102i
$733$	11.1208			0.410755			0.205377	−	0.978683i	$-0.434158\pi$
$733$	11.1208			0.410755			0.205377	+	0.978683i	$0.434158\pi$
$734$	29.3470	−	18.3679i	1.08322	−	0.677972i
$735$	5.96012	+	1.59774i	0.219842	+	0.0589334i
$736$	−8.54143	+	23.7369i	−0.314841	+	0.874954i
$737$		−	1.07228i		−	0.0394981i
$738$	−6.18337	+	0.219045i	−0.227613	+	0.00806316i
$739$		−	31.8732i		−	1.17248i	−0.810139	−	0.586238i	$-0.800608\pi$
$739$		−	31.8732i		−	1.17248i	0.810139	−	0.586238i	$-0.199392\pi$
$740$	−20.4785	−	9.95100i	−0.752804	−	0.365806i
$741$	−10.3531	−	2.77535i	−0.380329	−	0.101955i
$742$	3.59774	+	5.74823i	0.132077	+	0.211024i
$743$	−24.5432			−0.900403			−0.450202	−	0.892927i	$-0.648648\pi$
$743$	−24.5432			−0.900403			−0.450202	+	0.892927i	$0.648648\pi$
$744$	25.1474	+	3.92938i	0.921947	+	0.144058i
$745$	55.0687			2.01756
$746$	−3.29450	−	5.26374i	−0.120620	−	0.192719i
$747$	−17.9226	−	10.3531i	−0.655754	−	0.378798i
$748$	−0.202558	−	0.0984279i	−0.00740625	−	0.00359888i
$749$			8.13184i			0.297131i
$750$	−6.88198	−	22.4604i	−0.251295	−	0.820137i
$751$			0.427764i			0.0156093i	0.999970	+	0.00780467i	$0.00248433\pi$
$751$			0.427764i			0.0156093i	−0.999970	+	0.00780467i	$0.997516\pi$
$752$	−22.0466	−	28.0489i	−0.803956	−	1.02284i
$753$	2.51487	−	9.38135i	0.0916469	−	0.341875i
$754$	−23.7369	+	14.8566i	−0.864447	+	0.541045i
$755$	54.1350			1.97017
$756$	9.82232	−	3.39441i	0.357234	−	0.123454i
$757$	51.4596			1.87033			0.935166	−	0.354210i	$-0.115250\pi$
$757$	51.4596			1.87033			0.935166	+	0.354210i	$0.115250\pi$
$758$	20.2357	−	12.6652i	0.734992	−	0.460021i
$759$	−0.671128	+	2.50354i	−0.0243604	+	0.0908729i
$760$	−18.5301	+	1.98868i	−0.672158	+	0.0721369i
$761$		−	9.03515i		−	0.327524i	−0.986500	−	0.163762i	$-0.947637\pi$
$761$		−	9.03515i		−	0.327524i	0.986500	−	0.163762i	$-0.0523629\pi$
$762$	−7.31125	−	23.8614i	−0.264859	−	0.864406i
$763$		−	19.0829i		−	0.690846i
$764$	10.5950	−	21.8037i	0.383313	−	0.788832i
$765$	3.10552	+	1.79391i	0.112280	+	0.0648590i
$766$	−17.8874	−	28.5793i	−0.646298	−	1.03261i
$767$	−46.9253			−1.69438
$768$	−24.3148	−	13.2963i	−0.877385	−	0.479788i
$769$	−21.1728			−0.763511			−0.381756	−	0.924263i	$-0.624680\pi$
$769$	−21.1728			−0.763511			−0.381756	+	0.924263i	$0.624680\pi$
$770$	−0.896956	−	1.43310i	−0.0323240	−	0.0516453i
$771$	30.4042	+	8.15049i	1.09498	+	0.293533i
$772$	6.72982	−	13.8495i	0.242211	−	0.498455i
$773$		−	4.11523i		−	0.148015i	−0.997258	−	0.0740073i	$-0.976421\pi$
$773$		−	4.11523i		−	0.148015i	0.997258	−	0.0740073i	$-0.0235788\pi$
$774$	−31.7848	+	1.12597i	−1.14248	+	0.0404723i
$775$			39.9632i			1.43552i
$776$	−5.62456	+	0.603635i	−0.201910	+	0.0216692i
$777$	5.34596	+	1.43310i	0.191785	+	0.0514121i
$778$	24.1771	−	15.1321i	0.866790	−	0.542511i
$779$	−2.69722			−0.0966381
$780$	27.0486	−	31.2006i	0.968494	−	1.11716i
$781$	−3.48228			−0.124606
$782$	1.79391	−	1.12278i	0.0641501	−	0.0401507i
$783$	−21.7363	−	21.7511i	−0.776790	−	0.777320i
$784$	2.47185	+	3.14483i	0.0882803	+	0.112315i
$785$		−	3.40234i		−	0.121435i
$786$	−24.5611	+	7.52565i	−0.876064	+	0.268431i
$787$		−	29.9621i		−	1.06803i	−0.845474	−	0.534017i	$-0.820682\pi$
$787$		−	29.9621i		−	1.06803i	0.845474	−	0.534017i	$-0.179318\pi$
$788$	−12.6652	−	6.15434i	−0.451180	−	0.219239i
$789$	−7.94793	+	29.6486i	−0.282954	+	1.05552i
$790$	−10.6919	−	17.0829i	−0.380402	−	0.607781i
$791$	−12.5914			−0.447697
$792$	−2.60346	−	1.15301i	−0.0925098	−	0.0409704i
$793$	−1.18130			−0.0419490
$794$	13.7596	+	21.9842i	0.488309	+	0.780188i
$795$	−7.66129	+	28.5793i	−0.271718	+	1.01360i
$796$	38.4667	+	18.6919i	1.36342	+	0.662518i
$797$			49.0485i			1.73739i	0.495351	+	0.868693i	$0.335039\pi$
$797$			49.0485i			1.73739i	−0.495351	+	0.868693i	$0.664961\pi$
$798$	4.33158	−	1.32722i	0.153336	−	0.0469830i
$799$			2.99291i			0.105882i
$800$	14.7325	−	40.9421i	0.520873	−	1.44752i
$801$	−5.81162	+	10.0607i	−0.205343	+	0.355479i
$802$	−10.3123	+	6.45433i	−0.364140	+	0.227910i
$803$	−1.57444			−0.0555608
$804$	−7.25093	+	8.36399i	−0.255721	+	0.294975i
$805$	15.8874			0.559957
$806$	−20.8393	+	13.0430i	−0.734033	+	0.459421i
$807$	−20.8815	−	5.59774i	−0.735065	−	0.197050i
$808$	3.96973	+	36.9892i	0.139655	+	1.30128i
$809$			52.6577i			1.85135i	0.378323	+	0.925674i	$0.376501\pi$
$809$			52.6577i			1.85135i	−0.378323	+	0.925674i	$0.623499\pi$
$810$	40.0424	+	21.2767i	1.40695	+	0.747588i
$811$		−	37.5117i		−	1.31721i	−0.752487	−	0.658607i	$-0.771146\pi$
$811$		−	37.5117i		−	1.31721i	0.752487	−	0.658607i	$-0.228854\pi$
$812$	5.17290	−	10.6455i	0.181533	−	0.373583i
$813$	−3.00709	−	0.806113i	−0.105463	−	0.0282716i
$814$	−0.804530	−	1.28543i	−0.0281987	−	0.0450541i
$815$	35.2246			1.23386
$816$	0.914402	+	2.13748i	0.0320105	+	0.0748267i
$817$	−13.8647			−0.485066
$818$	−3.23764	−	5.17290i	−0.113202	−	0.180866i
$819$	−5.02092	+	8.69193i	−0.175445	+	0.303720i
$820$	4.54143	−	9.34596i	0.158594	−	0.326375i
$821$			2.11058i			0.0736598i	0.999322	+	0.0368299i	$0.0117260\pi$
$821$			2.11058i			0.0736598i	−0.999322	+	0.0368299i	$0.988274\pi$
$822$	−6.40038	−	20.8886i	−0.223239	−	0.728573i
$823$			52.5567i			1.83201i	0.401166	+	0.916005i	$0.368605\pi$
$823$			52.5567i			1.83201i	−0.401166	+	0.916005i	$0.631395\pi$
$824$	2.38055	+	22.1816i	0.0829305	+	0.772731i
$825$	1.15758	−	4.31819i	0.0403018	−	0.150340i
$826$	16.8122	−	10.5225i	0.584970	−	0.366124i
$827$	10.3774			0.360858			0.180429	−	0.983588i	$-0.442251\pi$
$827$	10.3774			0.360858			0.180429	+	0.983588i	$0.442251\pi$
$828$	22.1642	−	14.9898i	0.770260	−	0.520931i
$829$	1.43592			0.0498715			0.0249358	−	0.999689i	$-0.492062\pi$
$829$	1.43592			0.0498715			0.0249358	+	0.999689i	$0.492062\pi$
$830$	29.4650	−	18.4417i	1.02275	−	0.640122i
$831$	10.4366	−	38.9324i	0.362043	−	1.35055i
$832$	26.1581	−	5.68007i	0.906869	−	0.196921i
$833$		−	0.335564i		−	0.0116266i
$834$	−1.46240	−	4.77277i	−0.0506389	−	0.165268i
$835$			4.00000i			0.138426i
$836$	−1.11643	−	0.542499i	−0.0386124	−	0.0187627i
$837$	−19.0829	−	19.0959i	−0.659600	−	0.660050i
$838$	28.0710	+	44.8500i	0.969697	+	1.54932i
$839$	−1.39275			−0.0480832			−0.0240416	−	0.999711i	$-0.507653\pi$
$839$	−1.39275			−0.0480832			−0.0240416	+	0.999711i	$0.507653\pi$
$840$	−2.69441	+	17.2437i	−0.0929659	+	0.594965i
$841$	−6.02126			−0.207630
$842$	−8.92969	−	14.2673i	−0.307738	−	0.491683i
$843$	−38.7619	−	10.3909i	−1.33503	−	0.357883i
$844$	−41.3205	−	20.0786i	−1.42231	−	0.691135i
$845$		−	6.42877i		−	0.221156i
$846$	1.33965	+	37.8166i	0.0460581	+	1.30016i
$847$			10.8874i			0.374095i
$848$	−15.0798	+	11.8527i	−0.517841	+	0.407025i
$849$	3.09419	+	0.829463i	0.106192	+	0.0284671i
$850$	−3.09419	+	1.93661i	−0.106130	+	0.0664252i
$851$	14.2503			0.488494
$852$	27.1624	+	23.5477i	0.930567	+	0.806730i
$853$	18.6399			0.638217			0.319108	−	0.947718i	$-0.396617\pi$
$853$	18.6399			0.638217			0.319108	+	0.947718i	$0.396617\pi$
$854$	0.423228	−	0.264892i	0.0144826	−	0.00906443i
$855$	17.1165	+	9.88740i	0.585372	+	0.338142i
$856$	−22.8690	+	2.45433i	−0.781646	+	0.0838873i
$857$			30.8622i			1.05423i	0.849793	+	0.527117i	$0.176727\pi$
$857$			30.8622i			1.05423i	−0.849793	+	0.527117i	$0.823273\pi$
$858$	2.62958	−	0.805718i	0.0897723	−	0.0275067i
$859$			17.9253i			0.611603i	0.952095	+	0.305801i	$0.0989244\pi$
$859$			17.9253i			0.611603i	−0.952095	+	0.305801i	$0.901076\pi$
$860$	23.3447	−	48.0418i	0.796047	−	1.63821i
$861$	−0.654037	+	2.43979i	−0.0222895	+	0.0831478i
$862$	2.54143	+	4.06054i	0.0865616	+	0.138302i
$863$	5.04617			0.171774			0.0858868	−	0.996305i	$-0.472628\pi$
$863$	5.04617			0.171774			0.0858868	+	0.996305i	$0.472628\pi$
$864$	12.5106	+	26.5986i	0.425619	+	0.904903i
$865$	−55.4596			−1.88568
$866$	20.0943	+	32.1054i	0.682833	+	1.09099i
$867$	−7.57362	+	28.2523i	−0.257214	+	0.959499i
$868$	4.54143	−	9.34596i	0.154146	−	0.317223i
$869$		−	1.34226i		−	0.0455329i
$870$	49.3764	−	15.1292i	1.67402	−	0.512928i
$871$		−	10.6919i		−	0.362282i
$872$	53.6663	−	5.75954i	1.81737	−	0.195043i
$873$	5.19547	+	3.00118i	0.175840	+	0.101575i
$874$	9.88740	−	6.18838i	0.334446	−	0.209325i
$875$	−9.59019			−0.324207
$876$	12.2809	+	10.6466i	0.414933	+	0.359715i
$877$	−0.691927			−0.0233647			−0.0116824	−	0.999932i	$-0.503719\pi$
$877$	−0.691927			−0.0233647			−0.0116824	+	0.999932i	$0.503719\pi$
$878$	4.52512	−	2.83221i	0.152715	−	0.0955825i
$879$	2.59177	+	0.694778i	0.0874181	+	0.0234343i
$880$	3.75955	−	2.95502i	0.126734	−	0.0996138i
$881$		−	38.2574i		−	1.28892i	−0.764637	−	0.644462i	$-0.777082\pi$
$881$		−	38.2574i		−	1.28892i	0.764637	−	0.644462i	$-0.222918\pi$
$882$	−0.150201	−	4.23998i	−0.00505752	−	0.142768i
$883$		−	3.42068i		−	0.115115i	−0.998342	−	0.0575575i	$-0.981669\pi$
$883$		−	3.42068i		−	0.115115i	0.998342	−	0.0575575i	$-0.0183312\pi$
$884$	−2.01974	−	0.981441i	−0.0679312	−	0.0330094i
$885$	83.5875	+	22.4074i	2.80976	+	0.753216i
$886$	−5.09419	−	8.13917i	−0.171143	−	0.273441i
$887$	17.1543			0.575984			0.287992	−	0.957633i	$-0.407012\pi$
$887$	17.1543			0.575984			0.287992	+	0.957633i	$0.407012\pi$
$888$	−2.41676	+	15.4669i	−0.0811013	+	0.519034i
$889$	−10.1884			−0.341707
$890$	−10.3522	−	16.5400i	−0.347005	−	0.554422i
$891$	1.50885	+	2.61615i	0.0505483	+	0.0876442i
$892$	−17.4217	−	8.46565i	−0.583323	−	0.283451i
$893$			16.4959i			0.552013i
$894$	−11.0925	−	36.2019i	−0.370987	−	1.21077i
$895$			77.3470i			2.58543i
$896$	−8.09809	+	7.90069i	−0.270538	+	0.263944i
$897$	−6.69193	+	24.9633i	−0.223437	+	0.833499i
$898$	−15.4738	+	9.68484i	−0.516368	+	0.323187i
$899$	−30.7462			−1.02544
$900$	−38.2295	+	25.8548i	−1.27432	+	0.861828i
$901$	1.60906			0.0536055
$902$	0.586642	−	0.367171i	0.0195330	−	0.0122255i
$903$	−3.36199	+	12.5414i	−0.111880	+	0.417353i
$904$	−3.80029	−	35.4104i	−0.126396	−	1.17773i
$905$		−	58.5289i		−	1.94557i
$906$	−10.9044	−	35.5880i	−0.362274	−	1.18233i
$907$			30.7904i			1.02238i	0.859469	+	0.511188i	$0.170795\pi$
$907$			30.7904i			1.02238i	−0.859469	+	0.511188i	$0.829205\pi$
$908$	−11.7165	+	24.1117i	−0.388825	+	0.800176i
$909$	19.7369	−	34.1674i	0.654632	−	1.13326i
$910$	−8.94370	−	14.2897i	−0.296481	−	0.473698i
$911$	−14.8898			−0.493321			−0.246661	−	0.969102i	$-0.579333\pi$
$911$	−14.8898			−0.493321			−0.246661	+	0.969102i	$0.579333\pi$
$912$	5.03985	+	11.7810i	0.166886	+	0.390108i
$913$	2.31516			0.0766206
$914$	−20.3940	−	32.5842i	−0.674573	−	1.07779i
$915$	2.10423	+	0.564082i	0.0695635	+	0.0186480i
$916$	14.6238	−	30.0947i	0.483183	−	0.994358i
$917$			10.4871i			0.346316i
$918$	0.553766	−	2.40290i	0.0182770	−	0.0793074i
$919$			2.99291i			0.0987271i	0.998781	+	0.0493635i	$0.0157193\pi$
$919$			2.99291i			0.0987271i	−0.998781	+	0.0493635i	$0.984281\pi$
$920$	4.79509	+	44.6798i	0.158090	+	1.47305i
$921$	20.9816	+	5.62456i	0.691367	+	0.185335i
$922$	−8.77426	+	5.49169i	−0.288965	+	0.180859i
$923$	−34.7224			−1.14290
$924$	−0.761437	+	0.878322i	−0.0250495	+	0.0288947i
$925$	−24.5793			−0.808163
$926$	−4.52512	+	2.83221i	−0.148705	+	0.0930722i
$927$	11.8358	−	20.4894i	0.388737	−	0.672959i
$928$	31.4993	+	11.3346i	1.03402	+	0.372078i
$929$			11.5002i			0.377309i	0.982044	+	0.188654i	$0.0604126\pi$
$929$			11.5002i			0.377309i	−0.982044	+	0.188654i	$0.939587\pi$
$930$	43.3489	−	13.2824i	1.42147	−	0.435546i
$931$		−	1.84951i		−	0.0606151i
$932$	−37.6391	−	18.2898i	−1.23291	−	0.599101i
$933$	5.40650	−	20.1682i	0.177001	−	0.660276i
$934$	22.0947	+	35.3015i	0.722961	+	1.15510i
$935$	−0.401157			−0.0131192
$936$	−25.9595	−	11.4968i	−0.848513	−	0.375786i
$937$	49.6254			1.62119			0.810595	−	0.585607i	$-0.199144\pi$
$937$	49.6254			1.62119			0.810595	+	0.585607i	$0.199144\pi$
$938$	2.39755	+	3.83064i	0.0782827	+	0.125075i
$939$	9.90050	−	36.9324i	0.323091	−	1.20524i
$940$	−57.1586	−	27.7748i	−1.86431	−	0.905914i
$941$		−	33.1859i		−	1.08183i	−0.841077	−	0.540915i	$-0.818078\pi$
$941$		−	33.1859i		−	1.08183i	0.841077	−	0.540915i	$-0.181922\pi$
$942$	−2.23668	+	0.685331i	−0.0728749	+	0.0223293i
$943$			6.50354i			0.211785i
$944$	34.6664	+	44.1046i	1.12829	+	1.43548i
$945$	13.0942	−	13.0853i	0.425954	−	0.425664i
$946$	3.01556	−	1.88740i	0.0980443	−	0.0613646i
$947$	−50.0299			−1.62575			−0.812877	−	0.582436i	$-0.802100\pi$
$947$	−50.0299			−1.62575			−0.812877	+	0.582436i	$0.802100\pi$
$948$	−9.07652	+	10.4698i	−0.294792	+	0.340044i
$949$	−15.6990			−0.509612
$950$	−17.0541	+	10.6739i	−0.553307	+	0.346307i
$951$	5.77653	+	1.54852i	0.187317	+	0.0502142i
$952$	0.943698	−	0.101279i	0.0305854	−	0.00328247i
$953$			45.2664i			1.46632i	0.680055	+	0.733162i	$0.261956\pi$
$953$			45.2664i			1.46632i	−0.680055	+	0.733162i	$0.738044\pi$
$954$	20.3311	−	0.720227i	0.658244	−	0.0233182i
$955$		−	43.1813i		−	1.39731i
$956$	−18.4651	+	37.9999i	−0.597204	+	1.22901i
$957$	3.32225	+	0.890599i	0.107393	+	0.0287890i
$958$	25.2571	+	40.3541i	0.816019	+	1.30378i
$959$	−8.91906			−0.288011
$960$	−49.3074	−	2.37296i	−1.59139	−	0.0765871i
$961$	4.00709			0.129261
$962$	−8.02210	−	12.8172i	−0.258643	−	0.413243i
$963$	21.1244	+	12.2026i	0.680723	+	0.393222i
$964$	−23.0563	+	47.4483i	−0.742593	+	1.52821i
$965$		−	27.4283i		−	0.882948i
$966$	−3.20019	−	10.4443i	−0.102964	−	0.336039i
$967$			3.60059i			0.115787i	0.998323	+	0.0578935i	$0.0184384\pi$
$967$			3.60059i			0.115787i	−0.998323	+	0.0578935i	$0.981562\pi$
$968$	−30.6184	+	3.28601i	−0.984112	+	0.105616i
$969$	0.278338	−	1.03830i	0.00894150	−	0.0333550i
$970$	−8.54143	+	5.34596i	−0.274249	+	0.171649i
$971$	−32.7027			−1.04948			−0.524739	−	0.851263i	$-0.675837\pi$
$971$	−32.7027			−1.04948			−0.524739	+	0.851263i	$0.675837\pi$
$972$	5.92149	−	30.6094i	0.189932	−	0.981797i
$973$	−2.03789			−0.0653318
$974$	25.3916	−	15.8922i	0.813598	−	0.509220i
$975$	11.5424	−	43.0574i	0.369654	−	1.37894i
$976$	0.872689	+	1.11029i	0.0279341	+	0.0355394i
$977$			17.6059i			0.563264i	0.959523	+	0.281632i	$0.0908757\pi$
$977$			17.6059i			0.563264i	−0.959523	+	0.281632i	$0.909124\pi$
$978$	−7.09526	−	23.1564i	−0.226882	−	0.740461i
$979$		−	1.29960i		−	0.0415354i
$980$	6.40860	+	3.11410i	0.204715	+	0.0994761i
$981$	−49.5722	−	28.6356i	−1.58272	−	0.914263i
$982$	9.09419	+	14.5301i	0.290207	+	0.463674i
$983$	45.6171			1.45496			0.727479	−	0.686130i	$-0.240692\pi$
$983$	45.6171			1.45496			0.727479	+	0.686130i	$0.240692\pi$
$984$	−7.05876	−	1.10296i	−0.225025	−	0.0351611i
$985$	−25.0829			−0.799207
$986$	−1.48995	−	2.38055i	−0.0474498	−	0.0758123i
$987$	14.9214	+	4.00000i	0.474954	+	0.127321i
$988$	−11.1321	−	5.40935i	−0.354159	−	0.172094i
$989$			33.4307i			1.06303i
$990$	−5.06877	+	0.179561i	−0.161096	+	0.00570681i
$991$		−	49.5354i		−	1.57354i	−0.617244	−	0.786772i	$-0.711751\pi$
$991$		−	49.5354i		−	1.57354i	0.617244	−	0.786772i	$-0.288249\pi$
$992$	27.6541	+	9.95100i	0.878019	+	0.315945i
$993$	−44.9940	−	12.0616i	−1.42784	−	0.382763i
$994$	12.4402	−	7.78612i	0.394578	−	0.246961i
$995$	76.1815			2.41512
$996$	−18.0586	−	15.6554i	−0.572210	−	0.496062i
$997$	−55.5259			−1.75852			−0.879261	−	0.476340i	$-0.841963\pi$
$997$	−55.5259			−1.75852			−0.879261	+	0.476340i	$0.841963\pi$
$998$	−43.8503	+	27.4453i	−1.38806	+	0.868766i
$999$	11.7449	−	11.7369i	0.371593	−	0.371339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.e.a.71.3	✓	12
3.2	odd	2	inner	84.2.e.a.71.10	yes	12
4.3	odd	2	inner	84.2.e.a.71.9	yes	12
7.2	even	3		588.2.n.f.263.5		24
7.3	odd	6		588.2.n.g.275.12		24
7.4	even	3		588.2.n.f.275.12		24
7.5	odd	6		588.2.n.g.263.5		24
7.6	odd	2		588.2.e.c.491.3		12
8.3	odd	2		1344.2.h.h.575.6		12
8.5	even	2		1344.2.h.h.575.7		12
12.11	even	2	inner	84.2.e.a.71.4	yes	12
21.2	odd	6		588.2.n.f.263.8		24
21.5	even	6		588.2.n.g.263.8		24
21.11	odd	6		588.2.n.f.275.1		24
21.17	even	6		588.2.n.g.275.1		24
21.20	even	2		588.2.e.c.491.10		12
24.5	odd	2		1344.2.h.h.575.5		12
24.11	even	2		1344.2.h.h.575.8		12
28.3	even	6		588.2.n.g.275.8		24
28.11	odd	6		588.2.n.f.275.8		24
28.19	even	6		588.2.n.g.263.1		24
28.23	odd	6		588.2.n.f.263.1		24
28.27	even	2		588.2.e.c.491.9		12
84.11	even	6		588.2.n.f.275.5		24
84.23	even	6		588.2.n.f.263.12		24
84.47	odd	6		588.2.n.g.263.12		24
84.59	odd	6		588.2.n.g.275.5		24
84.83	odd	2		588.2.e.c.491.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.3	✓	12	1.1	even	1	trivial
84.2.e.a.71.4	yes	12	12.11	even	2	inner
84.2.e.a.71.9	yes	12	4.3	odd	2	inner
84.2.e.a.71.10	yes	12	3.2	odd	2	inner
588.2.e.c.491.3		12	7.6	odd	2
588.2.e.c.491.4		12	84.83	odd	2
588.2.e.c.491.9		12	28.27	even	2
588.2.e.c.491.10		12	21.20	even	2
588.2.n.f.263.1		24	28.23	odd	6
588.2.n.f.263.5		24	7.2	even	3
588.2.n.f.263.8		24	21.2	odd	6
588.2.n.f.263.12		24	84.23	even	6
588.2.n.f.275.1		24	21.11	odd	6
588.2.n.f.275.5		24	84.11	even	6
588.2.n.f.275.8		24	28.11	odd	6
588.2.n.f.275.12		24	7.4	even	3
588.2.n.g.263.1		24	28.19	even	6
588.2.n.g.263.5		24	7.5	odd	6
588.2.n.g.263.8		24	21.5	even	6
588.2.n.g.263.12		24	84.47	odd	6
588.2.n.g.275.1		24	21.17	even	6
588.2.n.g.275.5		24	84.59	odd	6
588.2.n.g.275.8		24	28.3	even	6
588.2.n.g.275.12		24	7.3	odd	6
1344.2.h.h.575.5		12	24.5	odd	2
1344.2.h.h.575.6		12	8.3	odd	2
1344.2.h.h.575.7		12	8.5	even	2
1344.2.h.h.575.8		12	24.11	even	2

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.750295 - 1.19877i) q^{2} +(-0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} +3.56257i q^{5} +(2.34202 - 0.717607i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(-2.59774 - 1.50059i) q^{9} +O(q^{10})\)	\(q+(-0.750295 - 1.19877i) q^{2} +(-0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} +3.56257i q^{5} +(2.34202 - 0.717607i) q^{6} -1.00000i q^{7} +(2.81228 - 0.301817i) q^{8} +(-2.59774 - 1.50059i) q^{9} +(4.27072 - 2.67298i) q^{10} +0.335564 q^{11} +(-2.61745 - 2.26913i) q^{12} +3.34596 q^{13} +(-1.19877 + 0.750295i) q^{14} +(-5.96012 - 1.59774i) q^{15} +(-2.47185 - 3.14483i) q^{16} +0.335564i q^{17} +(0.150201 + 4.23998i) q^{18} +1.84951i q^{19} +(-6.40860 - 3.11410i) q^{20} +(1.67298 + 0.448478i) q^{21} +(-0.251772 - 0.402265i) q^{22} +4.45953 q^{23} +(-0.756309 + 4.84025i) q^{24} -7.69193 q^{25} +(-2.51046 - 4.01105i) q^{26} +(3.67549 - 3.67298i) q^{27} +(1.79887 + 0.874114i) q^{28} -5.91788i q^{29} +(2.55653 + 8.34360i) q^{30} -5.19547i q^{31} +(-1.91532 + 5.32274i) q^{32} +(-0.150493 + 0.561392i) q^{33} +(0.402265 - 0.251772i) q^{34} +3.56257 q^{35} +(4.97008 - 3.36129i) q^{36} +3.19547 q^{37} +(2.21714 - 1.38768i) q^{38} +(-1.50059 + 5.59774i) q^{39} +(1.07525 + 10.0189i) q^{40} +1.45835i q^{41} +(-0.717607 - 2.34202i) q^{42} +7.49646i q^{43} +(-0.293321 + 0.603635i) q^{44} +(5.34596 - 9.25462i) q^{45} +(-3.34596 - 5.34596i) q^{46} +8.91906 q^{47} +(6.36981 - 2.72497i) q^{48} -1.00000 q^{49} +(5.77122 + 9.22087i) q^{50} +(-0.561392 - 0.150493i) q^{51} +(-2.92475 + 6.01894i) q^{52} -4.79509i q^{53} +(-7.16077 - 1.65025i) q^{54} +1.19547i q^{55} +(-0.301817 - 2.81228i) q^{56} +(-3.09419 - 0.829463i) q^{57} +(-7.09419 + 4.44015i) q^{58} -14.0245 q^{59} +(8.08394 - 9.32486i) q^{60} -0.353051 q^{61} +(-6.22819 + 3.89814i) q^{62} +(-1.50059 + 2.59774i) q^{63} +(7.81781 - 1.69759i) q^{64} +11.9202i q^{65} +(0.785896 - 0.240803i) q^{66} -3.19547i q^{67} +(-0.603635 - 0.293321i) q^{68} +(-2.00000 + 7.46071i) q^{69} +(-2.67298 - 4.27072i) q^{70} -10.3774 q^{71} +(-7.75846 - 3.43604i) q^{72} -4.69193 q^{73} +(-2.39755 - 3.83064i) q^{74} +(3.44966 - 12.8685i) q^{75} +(-3.32702 - 1.61668i) q^{76} -0.335564i q^{77} +(7.83630 - 2.40109i) q^{78} -4.00000i q^{79} +(11.2037 - 8.80614i) q^{80} +(4.49646 + 7.79627i) q^{81} +(1.74823 - 1.09419i) q^{82} +6.89932 q^{83} +(-2.26913 + 2.61745i) q^{84} -1.19547 q^{85} +(8.98655 - 5.62456i) q^{86} +(9.90050 + 2.65404i) q^{87} +(0.943698 - 0.101279i) q^{88} -3.87289i q^{89} +(-15.1052 + 0.535101i) q^{90} -3.34596i q^{91} +(-3.89814 + 8.02210i) q^{92} +(8.69193 + 2.33005i) q^{93} +(-6.69193 - 10.6919i) q^{94} -6.58900 q^{95} +(-8.04586 - 5.59143i) q^{96} -2.00000 q^{97} +(0.750295 + 1.19877i) q^{98} +(-0.871706 - 0.503544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9	\( 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} + 2 q^{24} - 12 q^{25} + 8 q^{28} + 20 q^{30} - 16 q^{33} + 32 q^{34} - 20 q^{36} - 16 q^{37} + 20 q^{40} + 10 q^{42} + 24 q^{45} + 46 q^{48} - 12 q^{49} - 28 q^{52} + 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} - 16 q^{61} + 20 q^{64} - 12 q^{66} - 24 q^{69} - 12 q^{70} - 32 q^{72} + 24 q^{73} - 60 q^{76} + 20 q^{78} + 28 q^{81} + 8 q^{82} - 14 q^{84} + 40 q^{85} - 56 q^{88} - 80 q^{90} + 24 q^{93} - 34 q^{96} - 24 q^{97}+O(q^{100}) \) 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 + 2 * q^24 - 12 * q^25 + 8 * q^28 + 20 * q^30 - 16 * q^33 + 32 * q^34 - 20 * q^36 - 16 * q^37 + 20 * q^40 + 10 * q^42 + 24 * q^45 + 46 * q^48 - 12 * q^49 - 28 * q^52 + 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 - 16 * q^61 + 20 * q^64 - 12 * q^66 - 24 * q^69 - 12 * q^70 - 32 * q^72 + 24 * q^73 - 60 * q^76 + 20 * q^78 + 28 * q^81 + 8 * q^82 - 14 * q^84 + 40 * q^85 - 56 * q^88 - 80 * q^90 + 24 * q^93 - 34 * q^96 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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