LMFDB - Embedded newform 84.2.e.a.71.10

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			71.10
Root			$-1.19877 + 0.750295i$ of defining polynomial
Character	$\chi$	$=$	84.71
Dual form			84.2.e.a.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} -3.56257i q^{5} +(-1.66903 + 1.79285i) q^{6} -1.00000i q^{7} +(-2.81228 + 0.301817i) q^{8} +(-2.59774 + 1.50059i) q^{9} +O(q^{10})$	\(q+(0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} -3.56257i q^{5} +(-1.66903 + 1.79285i) 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} +(-3.40149 - 0.655624i) 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} +(-3.74794 - 1.98821i) 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} +(-1.76618 - 4.56953i) 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} +(6.38717 + 5.94606i) 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} +(-0.428647 - 5.98467i) 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} +(1.79285 + 1.66903i) 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} +(4.15267 - 5.54575i) 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} +(1.64537 - 7.16190i) 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} +(-2.33571 + 12.1181i) 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} +(0.560068 - 0.601617i) 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} +(6.85265 - 5.00412i) 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} +(-5.58453 + 5.99882i) 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} +(-0.655624 + 3.40149i) 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} +(-7.08314 + 13.3523i) 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} +(9.76382 + 0.817168i) 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	$-0.706622\pi$
$5$		−	3.56257i		−	1.59323i	0.604486	−	0.796616i	$-0.293378\pi$
$6$	−1.66903	+	1.79285i	−0.681381	+	0.731929i
$7$		−	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	$-0.516110\pi$
$11$	−0.335564			−0.101176			−0.0505881	+	0.998720i	$0.516110\pi$
$12$	−3.40149	−	0.655624i	−0.981927	−	0.189262i
$13$	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	$-0.987043\pi$
$17$		−	0.335564i		−	0.0813862i	0.999172	−	0.0406931i	$-0.0129566\pi$
$18$	−3.74794	−	1.98821i	−0.883397	−	0.468625i
$19$			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	$-0.653923\pi$
$23$	−4.45953			−0.929876			−0.464938	+	0.885343i	$0.653923\pi$
$24$	−1.76618	−	4.56953i	−0.360520	−	0.932752i
$25$	−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	$0.185167\pi$
$29$			5.91788i			1.09892i	−0.835519	+	0.549461i	$0.814833\pi$
$30$	6.38717	+	5.94606i	1.16613	+	1.08560i
$31$		−	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
$36$	−0.428647	−	5.98467i	−0.0714411	−	0.997445i
$37$	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	$-0.963673\pi$
$41$		−	1.45835i		−	0.227756i	0.993495	−	0.113878i	$-0.0363272\pi$
$42$	1.79285	+	1.66903i	0.276643	+	0.257538i
$43$			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	$-0.725436\pi$
$47$	−8.91906			−1.30098			−0.650489	+	0.759516i	$0.725436\pi$
$48$	4.15267	−	5.54575i	0.599387	−	0.800459i
$49$	−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	$0.106822\pi$
$53$			4.79509i			0.658657i	−0.944215	+	0.329328i	$0.893178\pi$
$54$	1.64537	−	7.16190i	0.223907	−	0.974611i
$55$			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	$-0.133826\pi$
$59$	14.0245			1.82583			0.912915	+	0.408150i	$0.133826\pi$
$60$	−2.33571	+	12.1181i	−0.301539	+	1.56444i
$61$	−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
$66$	0.560068	−	0.601617i	0.0689395	−	0.0740539i
$67$		−	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	$-0.288839\pi$
$71$	10.3774			1.23157			0.615786	+	0.787914i	$0.288839\pi$
$72$	6.85265	−	5.00412i	0.807592	−	0.589741i
$73$	−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
$78$	−5.58453	+	5.99882i	−0.632323	+	0.679233i
$79$		−	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	$-0.623611\pi$
$83$	−6.89932			−0.757299			−0.378649	+	0.925540i	$0.623611\pi$
$84$	−0.655624	+	3.40149i	−0.0715345	+	0.371133i
$85$	−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	$0.0658048\pi$
$89$			3.87289i			0.410525i	−0.978707	+	0.205263i	$0.934195\pi$
$90$	−7.08314	+	13.3523i	−0.746629	+	1.40746i
$91$		−	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
$96$	9.76382	+	0.817168i	0.996516	+	0.0834019i
$97$	−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	$-0.772932\pi$
$101$		−	13.1528i		−	1.30875i	0.756171	−	0.654374i	$-0.227068\pi$
$102$	0.601617	+	0.560068i	0.0595689	+	0.0554549i
$103$			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	$-0.371414\pi$
$107$	8.13184			0.786134			0.393067	+	0.919510i	$0.371414\pi$
$108$	9.82000	−	3.40111i	0.944930	−	0.327272i
$109$	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	$0.201759\pi$
$113$			12.5914i			1.18450i	−0.805756	+	0.592248i	$0.798241\pi$
$114$	−3.31590	−	3.08689i	−0.310562	−	0.289114i
$115$			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
$120$	−16.2793	+	6.29214i	−1.48609	+	0.574391i
$121$	−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
$126$	−1.98821	+	3.74794i	−0.177124	+	0.333893i
$127$		−	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	$-0.348518\pi$
$131$	10.4871			0.916266			0.458133	+	0.888884i	$0.348518\pi$
$132$	1.14142	+	0.220004i	0.0993477	+	0.0191489i
$133$	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	$0.124421\pi$
$137$			8.91906i			0.762007i	−0.924574	+	0.381003i	$0.875579\pi$
$138$	7.44311	−	7.99528i	0.633599	−	0.680604i
$139$		−	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
$144$	11.1403	+	4.46020i	0.928359	+	0.371684i
$145$	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	$0.218245\pi$
$149$			15.4576i			1.26633i	−0.774016	+	0.633166i	$0.781755\pi$
$150$	12.8381	−	13.7905i	1.04823	−	1.12599i
$151$		−	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
$156$	−11.3813	−	2.19370i	−0.911231	−	0.175636i
$157$	−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
$162$	12.7196	−	0.459276i	0.999349	−	0.0360841i
$163$		−	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	$-0.513832\pi$
$167$	−1.12278			−0.0868836			−0.0434418	+	0.999056i	$0.513832\pi$
$168$	−4.56953	+	1.76618i	−0.352547	+	0.136264i
$169$	−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	$-0.798425\pi$
$173$		−	15.5673i		−	1.18356i	0.806100	−	0.591780i	$-0.201575\pi$
$174$	−10.6099	−	9.87714i	−0.804333	−	0.748784i
$175$			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	$-0.801282\pi$
$179$	−21.7110			−1.62276			−0.811378	+	0.584521i	$0.801282\pi$
$180$	−21.3208	+	1.52709i	−1.58916	+	0.113822i
$181$	−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
$186$	9.31472	+	8.67142i	0.682988	+	0.635819i
$187$			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	$-0.355504\pi$
$191$	12.1208			0.877032			0.438516	+	0.898723i	$0.355504\pi$
$192$	6.34615	+	12.3177i	0.457994	+	0.888955i
$193$	−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	$-0.919302\pi$
$197$		−	7.04066i		−	0.501626i	0.968036	−	0.250813i	$-0.0806980\pi$
$198$	1.25767	+	0.667171i	0.0893788	+	0.0474138i
$199$		−	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
$204$	−0.220004	+	1.14142i	−0.0154033	+	0.0799152i
$205$	−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
$210$	5.94606	−	6.38717i	0.410317	−	0.440757i
$211$			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
$216$	11.4451	+	9.22012i	0.778738	+	0.627350i
$217$	−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
$222$	−5.33335	+	5.72901i	−0.357951	+	0.384506i
$223$			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	$-0.646733\pi$
$227$	−13.4038			−0.889644			−0.444822	+	0.895619i	$0.646733\pi$
$228$	1.21258	−	6.29109i	0.0803052	−	0.416637i
$229$	−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	$-0.759636\pi$
$233$		−	20.9238i		−	1.37076i	0.728184	−	0.685381i	$-0.240364\pi$
$234$	−12.5405	−	6.65248i	−0.819795	−	0.434886i
$235$			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	$-0.739417\pi$
$239$	−21.1244			−1.36642			−0.683211	+	0.730221i	$0.739417\pi$
$240$	−19.7571	−	14.7942i	−1.27532	−	0.954962i
$241$	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
$246$	2.61460	+	2.43403i	0.166701	+	0.155188i
$247$			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	$-0.443369\pi$
$251$	5.60756			0.353946			0.176973	+	0.984216i	$0.443369\pi$
$252$	−5.98467	+	0.428647i	−0.376999	+	0.0270022i
$253$	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	$0.191827\pi$
$257$			18.1737i			1.13364i	−0.823841	+	0.566821i	$0.808173\pi$
$258$	−13.4400	−	12.5118i	−0.836741	−	0.778953i
$259$		−	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	$-0.684000\pi$
$263$	−17.7220			−1.09279			−0.546393	+	0.837529i	$0.684000\pi$
$264$	0.592666	+	1.53337i	0.0364761	+	0.0943723i
$265$	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	$-0.875749\pi$
$269$		−	12.4816i		−	0.761018i	0.924777	−	0.380509i	$-0.124251\pi$
$270$	−25.5148	−	5.86175i	−1.55278	−	0.356735i
$271$			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
$276$	15.1691	+	2.92378i	0.913070	+	0.175991i
$277$	−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	$-0.757134\pi$
$281$		−	23.1693i		−	1.38217i	0.722775	−	0.691084i	$-0.242866\pi$
$282$	14.8862	−	15.9906i	0.886461	−	0.952224i
$283$		−	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
$288$	3.01175	+	16.7012i	0.177469	+	0.984126i
$289$	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	$0.0144092\pi$
$293$			1.54919i			0.0905047i	−0.998976	+	0.0452523i	$0.985591\pi$
$294$	1.66903	−	1.79285i	0.0973401	−	0.104561i
$295$		−	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
$300$	26.1640	+	5.04302i	1.51058	+	0.291159i
$301$	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
$306$	−0.667171	+	1.25767i	−0.0381396	+	0.0718963i
$307$		−	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	$-0.388965\pi$
$311$	12.0552			0.683589			0.341795	+	0.939775i	$0.388965\pi$
$312$	−5.90957	−	15.2895i	−0.334564	−	0.865596i
$313$	−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	$0.0309136\pi$
$317$			3.45284i			0.193931i	−0.995288	+	0.0969653i	$0.969086\pi$
$318$	−8.59690	−	8.00318i	−0.482090	−	0.448796i
$319$		−	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
$324$	10.0940	+	14.9034i	0.560780	+	0.827965i
$325$	−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
$330$	−2.14330	−	1.99528i	−0.117985	−	0.109837i
$331$			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
$336$	−5.54575	−	4.15267i	−0.302545	−	0.226547i
$337$	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
$342$	3.67721	−	6.93183i	0.198841	−	0.374831i
$343$			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	$-0.262977\pi$
$347$	25.2483			1.35540			0.677701	+	0.735338i	$0.262977\pi$
$348$	3.87990	−	20.1296i	0.207985	−	1.07906i
$349$	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	$0.0733581\pi$
$353$			8.58349i			0.456853i	−0.973561	+	0.228427i	$0.926642\pi$
$354$	−23.4073	+	25.1438i	−1.24408	+	1.33638i
$355$		−	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	$-0.556620\pi$
$359$	−6.70510			−0.353881			−0.176941	+	0.984222i	$0.556620\pi$
$360$	−17.8275	−	24.4131i	−0.939594	−	1.28668i
$361$	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
$366$	0.589254	−	0.632968i	0.0308008	−	0.0330858i
$367$			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
$372$	−3.40628	+	17.6724i	−0.176607	+	0.916269i
$373$	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
$378$	−7.16190	−	1.64537i	−0.368368	−	0.0846288i
$379$			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	$-0.708467\pi$
$383$	−23.8405			−1.21819			−0.609096	+	0.793097i	$0.708467\pi$
$384$	−10.0047	+	16.8495i	−0.510549	+	0.859849i
$385$	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	$-0.829170\pi$
$389$		−	20.1682i		−	1.02257i	0.859412	−	0.511283i	$-0.170830\pi$
$390$	21.3712	+	19.8953i	1.08217	+	1.00744i
$391$			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
$396$	0.143838	+	2.00824i	0.00722815	+	0.100918i
$397$	−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	$0.0689071\pi$
$401$			8.60239i			0.429583i	−0.976660	+	0.214791i	$0.931093\pi$
$402$	5.72901	+	5.33335i	0.285737	+	0.266003i
$403$		−	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
$408$	−1.53337	+	0.592666i	−0.0759131	+	0.0293413i
$409$	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
$414$	16.7140	+	8.86648i	0.821450	+	0.435764i
$415$			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	$-0.133072\pi$
$419$	37.4133			1.82776			0.913879	+	0.405986i	$0.133072\pi$
$420$	12.1181	+	2.33571i	0.591301	+	0.113971i
$421$	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
$426$	−17.3202	+	18.6052i	−0.839169	+	0.901423i
$427$			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	$-0.474004\pi$
$431$	3.38724			0.163158			0.0815789	+	0.996667i	$0.474004\pi$
$432$	−2.46566	+	20.6378i	−0.118629	+	0.992939i
$433$	−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
$438$	7.83099	−	8.41194i	0.374179	−	0.401938i
$439$			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	$-0.551566\pi$
$443$	−6.78958			−0.322583			−0.161291	+	0.986907i	$0.551566\pi$
$444$	−10.8694	−	2.09503i	−0.515838	−	0.0994257i
$445$	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	$0.0985174\pi$
$449$			12.9080i			0.609168i	−0.952485	+	0.304584i	$0.901483\pi$
$450$	28.8288	+	15.2932i	1.35900	+	0.720926i
$451$			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
$456$	8.45138	−	3.26656i	0.395772	−	0.152971i
$457$	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	$0.0545216\pi$
$461$			7.31937i			0.340897i	−0.985367	+	0.170448i	$0.945478\pi$
$462$	−0.601617	−	0.560068i	−0.0279897	−	0.0260567i
$463$		−	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	$-0.261395\pi$
$467$	29.4480			1.36269			0.681346	+	0.731961i	$0.261395\pi$
$468$	−1.43424	−	20.0245i	−0.0662976	−	0.925632i
$469$	−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
$474$	7.17141	+	6.67614i	0.329394	+	0.306645i
$475$		−	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	$-0.220731\pi$
$479$	33.6628			1.53809			0.769047	+	0.639192i	$0.220731\pi$
$480$	2.91122	−	34.7843i	0.132878	−	1.58768i
$481$	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
$486$	6.47283	+	21.0737i	0.293614	+	0.955924i
$487$			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	$-0.411818\pi$
$491$	12.1208			0.547005			0.273502	+	0.961871i	$0.411818\pi$
$492$	−0.956128	+	4.96056i	−0.0431056	+	0.223639i
$493$	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
$498$	11.5152	−	12.3695i	0.516008	−	0.554289i
$499$		−	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	$-0.506320\pi$
$503$	−0.890599			−0.0397098			−0.0198549	+	0.999803i	$0.506320\pi$
$504$	−5.00412	−	6.85265i	−0.222901	−	0.305241i
$505$	−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	$-0.989069\pi$
$509$		−	1.54919i		−	0.0686667i	0.999410	−	0.0343333i	$-0.0109308\pi$
$510$	1.99528	−	2.14330i	0.0883525	−	0.0949071i
$511$			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
$516$	4.91486	−	25.4991i	0.216365	−	1.12254i
$517$	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	$0.284252\pi$
$521$			35.5601i			1.55792i	−0.627075	+	0.778959i	$0.715748\pi$
$522$	11.7660	−	22.1798i	0.514983	−	0.970784i
$523$		−	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
$528$	−1.39349	+	1.86095i	−0.0606437	+	0.0809875i
$529$	−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
$534$	−6.94352	−	6.46398i	−0.300475	−	0.279724i
$535$		−	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
$540$	−12.1167	−	34.9845i	−0.521420	−	1.50549i
$541$	−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
$546$	5.99882	+	5.58453i	0.256726	+	0.238996i
$547$			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
$552$	7.87633	+	20.3780i	0.335239	+	0.867343i
$553$	−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	$0.215228\pi$
$557$			29.5389i			1.25160i	−0.779983	+	0.625801i	$0.784772\pi$
$558$	−10.3297	+	19.4723i	−0.437290	+	0.824328i
$559$			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	$-0.644037\pi$
$563$	−20.7485			−0.874443			−0.437222	+	0.899354i	$0.644037\pi$
$564$	30.3381	+	5.84755i	1.27747	+	0.246226i
$565$	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	$0.0317089\pi$
$569$			4.74459i			0.198904i	−0.995042	+	0.0994518i	$0.968291\pi$
$570$	−10.9973	+	11.8131i	−0.460625	+	0.494797i
$571$			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
$576$	−17.7612	+	16.1412i	−0.740051	+	0.672551i
$577$	−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
$582$	3.33807	−	3.58571i	0.138367	−	0.148632i
$583$		−	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	$-0.613335\pi$
$587$	−16.8907			−0.697152			−0.348576	+	0.937280i	$0.613335\pi$
$588$	3.40149	+	0.655624i	0.140275	+	0.0270375i
$589$	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	$-0.685411\pi$
$593$		−	40.6719i		−	1.67019i	0.550102	−	0.835097i	$-0.314589\pi$
$594$	−0.552127	+	2.40327i	−0.0226540	+	0.0986075i
$595$			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	$-0.547595\pi$
$599$	−7.29174			−0.297932			−0.148966	+	0.988842i	$0.547595\pi$
$600$	13.5853	+	35.1485i	0.554618	+	1.43493i
$601$	−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
$606$	23.5810	+	21.9524i	0.957911	+	0.891756i
$607$			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
$612$	−2.00824	+	0.143838i	−0.0811782	+	0.00581432i
$613$	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	$-0.930592\pi$
$617$		−	10.7470i		−	0.432656i	0.976321	−	0.216328i	$-0.0694081\pi$
$618$	−14.1409	−	13.1643i	−0.568832	−	0.529547i
$619$			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
$624$	13.8947	−	18.5559i	0.556233	−	0.742829i
$625$	−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
$630$	13.3523	+	7.08314i	0.531968	+	0.282199i
$631$			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
$636$	3.14378	−	16.3105i	0.124659	−	0.646752i
$637$	−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	$0.147145\pi$
$641$			22.5827i			0.891963i	−0.895042	+	0.445982i	$0.852855\pi$
$642$	−13.5723	+	14.5792i	−0.535657	+	0.575395i
$643$			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	$-0.598827\pi$
$647$	−15.5420			−0.611021			−0.305510	+	0.952189i	$0.598827\pi$
$648$	−10.2922	+	23.2824i	−0.404317	+	0.914619i
$649$	−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	$-0.941090\pi$
$653$		−	9.40470i		−	0.368034i	0.982923	−	0.184017i	$-0.0589102\pi$
$654$	−31.8500	+	34.2128i	−1.24543	+	1.33783i
$655$		−	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	$-0.291701\pi$
$659$	31.2507			1.21735			0.608677	+	0.793418i	$0.291701\pi$
$660$	0.783780	−	4.06638i	0.0305086	−	0.158284i
$661$	−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
$666$	−11.9764	−	6.35326i	−0.464077	−	0.246184i
$667$		−	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
$672$	0.817168	−	9.76382i	0.0315230	−	0.376648i
$673$	−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	$0.173291\pi$
$677$			26.9514i			1.03583i	−0.855433	+	0.517913i	$0.826709\pi$
$678$	−22.5745	−	21.0154i	−0.866967	−	0.807093i
$679$			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	$-0.648812\pi$
$683$	−23.5554			−0.901323			−0.450661	+	0.892695i	$0.648812\pi$
$684$	11.0687	−	0.792785i	0.423222	−	0.0303129i
$685$	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
$690$	−28.4838	−	26.5166i	−1.08436	−	1.00947i
$691$		−	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
$696$	27.0419	−	10.4520i	1.02502	−	0.396183i
$697$	−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	$-0.948059\pi$
$701$		−	8.60239i		−	0.324908i	0.986716	−	0.162454i	$-0.0519409\pi$
$702$	5.50535	−	23.9634i	0.207786	−	0.904442i
$703$			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
$708$	−47.7041	−	9.19478i	−1.79283	−	0.345561i
$709$	−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
$714$	0.560068	−	0.601617i	0.0209600	−	0.0225149i
$715$			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	$-0.565347\pi$
$719$	−10.9324			−0.407711			−0.203856	+	0.979001i	$0.565347\pi$
$720$	15.8898	−	39.6882i	0.592178	−	1.47909i
$721$	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
$726$	18.1714	−	19.5195i	0.674405	−	0.724437i
$727$		−	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
$732$	1.20090	+	0.231469i	0.0443865	+	0.00855533i
$733$	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
$738$	−2.89950	+	5.46579i	−0.106732	+	0.201199i
$739$		−	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	$-0.351352\pi$
$743$	24.5432			0.900403			0.450202	+	0.892927i	$0.351352\pi$
$744$	−23.7409	+	9.17613i	−0.870382	+	0.336413i
$745$	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
$750$	−17.1938	−	16.0064i	−0.627829	−	0.584469i
$751$			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
$756$	−3.40111	−	9.82000i	−0.123697	−	0.357150i
$757$	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	$0.0523629\pi$
$761$			9.03515i			0.327524i	−0.986500	+	0.163762i	$0.947637\pi$
$762$	18.2663	+	17.0048i	0.661717	+	0.616018i
$763$		−	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
$768$	−27.7052	+	0.648787i	−0.999726	+	0.0234111i
$769$	−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	$0.0235788\pi$
$773$			4.11523i			0.148015i	−0.997258	+	0.0740073i	$0.976421\pi$
$774$	14.9045	−	28.0962i	0.535732	−	1.00990i
$775$			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
$780$	−7.81520	+	40.5466i	−0.279829	+	1.45180i
$781$	−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
$786$	−17.5034	+	18.8019i	−0.624326	+	0.670642i
$787$		−	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
$792$	−2.29950	+	1.67920i	−0.0817092	+	0.0596678i
$793$	−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	$-0.664961\pi$
$797$		−	49.0485i		−	1.73739i	0.495351	−	0.868693i	$-0.335039\pi$
$798$	−3.08689	+	3.31590i	−0.109275	+	0.117381i
$799$			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
$804$	−2.09503	+	10.8694i	−0.0738860	+	0.383333i
$805$	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	$-0.623499\pi$
$809$		−	52.6577i		−	1.85135i	0.378323	−	0.925674i	$-0.376501\pi$
$810$	−1.63620	−	45.3146i	−0.0574904	−	1.59219i
$811$		−	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
$816$	−1.86095	−	1.39349i	−0.0651463	−	0.0487818i
$817$	−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	$-0.988274\pi$
$821$		−	2.11058i		−	0.0736598i	0.999322	−	0.0368299i	$-0.0117260\pi$
$822$	−15.9906	−	14.8862i	−0.557735	−	0.519216i
$823$			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	$-0.557749\pi$
$827$	−10.3774			−0.360858			−0.180429	+	0.983588i	$0.557749\pi$
$828$	1.91156	+	26.6888i	0.0664314	+	0.927500i
$829$	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
$834$	3.65364	+	3.40131i	0.126515	+	0.117778i
$835$			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	$-0.492347\pi$
$839$	1.39275			0.0480832			0.0240416	+	0.999711i	$0.492347\pi$
$840$	6.29214	+	16.2793i	0.217100	+	0.561689i
$841$	−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
$846$	33.4281	+	17.7330i	1.14928	+	0.609671i
$847$			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
$852$	−35.2987	−	6.80368i	−1.20931	−	0.233090i
$853$	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	$-0.823273\pi$
$857$		−	30.8622i		−	1.05423i	0.849793	−	0.527117i	$-0.176727\pi$
$858$	1.87397	−	2.01299i	0.0639761	−	0.0687222i
$859$			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	$-0.527372\pi$
$863$	−5.04617			−0.171774			−0.0858868	+	0.996305i	$0.527372\pi$
$864$	−26.5901	+	12.5287i	−0.904612	+	0.426235i
$865$	−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
$870$	−35.1880	+	37.7985i	−1.19299	+	1.28149i
$871$		−	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
$876$	15.9596	+	3.07614i	0.539223	+	0.103933i
$877$	−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	$0.222918\pi$
$881$			38.2574i			1.28892i	−0.764637	+	0.644462i	$0.777082\pi$
$882$	3.74794	+	1.98821i	0.126200	+	0.0669465i
$883$		−	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	$-0.592988\pi$
$887$	−17.1543			−0.575984			−0.287992	+	0.957633i	$0.592988\pi$
$888$	−5.64377	−	14.6018i	−0.189393	−	0.490004i
$889$	−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
$894$	−27.7131	−	25.7992i	−0.926866	−	0.862855i
$895$			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
$900$	3.29712	+	46.0336i	0.109904	+	1.53445i
$901$	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
$906$	27.2433	+	25.3618i	0.905096	+	0.842588i
$907$			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	$-0.420667\pi$
$911$	14.8898			0.493321			0.246661	+	0.969102i	$0.420667\pi$
$912$	10.2569	+	7.68040i	0.339640	+	0.254323i
$913$	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
$918$	−2.40327	−	0.552127i	−0.0793198	−	0.0182229i
$919$			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
$924$	0.220004	−	1.14142i	0.00723759	−	0.0375499i
$925$	−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	$-0.939587\pi$
$929$		−	11.5002i		−	0.377309i	0.982044	−	0.188654i	$-0.0604126\pi$
$930$	30.8926	−	33.1844i	1.01301	−	1.08816i
$931$		−	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
$936$	22.9287	−	16.7436i	0.749448	−	0.547282i
$937$	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	$0.181922\pi$
$941$			33.1859i			1.08183i	−0.841077	+	0.540915i	$0.818078\pi$
$942$	1.59397	−	1.71222i	0.0519342	−	0.0557870i
$943$			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	$-0.197900\pi$
$947$	50.0299			1.62575			0.812877	+	0.582436i	$0.197900\pi$
$948$	−2.62250	+	13.6060i	−0.0851748	+	0.441901i
$949$	−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	$-0.738044\pi$
$953$		−	45.2664i		−	1.46632i	0.680055	−	0.733162i	$-0.261956\pi$
$954$	9.53365	−	17.9717i	0.308663	−	0.581855i
$955$		−	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
$960$	43.8828	−	22.6086i	1.41631	−	0.729690i
$961$	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
$966$	−7.99528	−	7.44311i	−0.257244	−	0.239478i
$967$			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	$-0.324163\pi$
$971$	32.7027			1.04948			0.524739	+	0.851263i	$0.324163\pi$
$972$	−20.4061	+	23.5710i	−0.654526	+	0.756040i
$973$	−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	$-0.909124\pi$
$977$		−	17.6059i		−	0.563264i	0.959523	−	0.281632i	$-0.0908757\pi$
$978$	17.7267	+	16.5024i	0.566836	+	0.527689i
$979$		−	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	$-0.759308\pi$
$983$	−45.6171			−1.45496			−0.727479	+	0.686130i	$0.759308\pi$
$984$	−6.66396	+	2.57570i	−0.212439	+	0.0821104i
$985$	−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
$990$	2.37685	−	4.48055i	0.0755411	−	0.142401i
$991$		−	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
$996$	23.4680	+	4.52336i	0.743612	+	0.143328i
$997$	−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.71.10	yes	12
3.2	odd	2	inner	84.2.e.a.71.3	✓	12
4.3	odd	2	inner	84.2.e.a.71.4	yes	12
7.2	even	3		588.2.n.f.263.8		24
7.3	odd	6		588.2.n.g.275.1		24
7.4	even	3		588.2.n.f.275.1		24
7.5	odd	6		588.2.n.g.263.8		24
7.6	odd	2		588.2.e.c.491.10		12
8.3	odd	2		1344.2.h.h.575.8		12
8.5	even	2		1344.2.h.h.575.5		12
12.11	even	2	inner	84.2.e.a.71.9	yes	12
21.2	odd	6		588.2.n.f.263.5		24
21.5	even	6		588.2.n.g.263.5		24
21.11	odd	6		588.2.n.f.275.12		24
21.17	even	6		588.2.n.g.275.12		24
21.20	even	2		588.2.e.c.491.3		12
24.5	odd	2		1344.2.h.h.575.7		12
24.11	even	2		1344.2.h.h.575.6		12
28.3	even	6		588.2.n.g.275.5		24
28.11	odd	6		588.2.n.f.275.5		24
28.19	even	6		588.2.n.g.263.12		24
28.23	odd	6		588.2.n.f.263.12		24
28.27	even	2		588.2.e.c.491.4		12
84.11	even	6		588.2.n.f.275.8		24
84.23	even	6		588.2.n.f.263.1		24
84.47	odd	6		588.2.n.g.263.1		24
84.59	odd	6		588.2.n.g.275.8		24
84.83	odd	2		588.2.e.c.491.9		12

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

\(f(q)\)	\(=\)	\(q+(0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} -3.56257i q^{5} +(-1.66903 + 1.79285i) q^{6} -1.00000i q^{7} +(-2.81228 + 0.301817i) q^{8} +(-2.59774 + 1.50059i) q^{9} +O(q^{10})\)	\(q+(0.750295 + 1.19877i) q^{2} +(0.448478 + 1.67298i) q^{3} +(-0.874114 + 1.79887i) q^{4} -3.56257i q^{5} +(-1.66903 + 1.79285i) 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} +(-3.40149 - 0.655624i) 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} +(-3.74794 - 1.98821i) 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} +(-1.76618 - 4.56953i) 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} +(6.38717 + 5.94606i) 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} +(-0.428647 - 5.98467i) 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} +(1.79285 + 1.66903i) 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} +(4.15267 - 5.54575i) 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} +(1.64537 - 7.16190i) 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} +(-2.33571 + 12.1181i) 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} +(0.560068 - 0.601617i) 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} +(6.85265 - 5.00412i) 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} +(-5.58453 + 5.99882i) 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} +(-0.655624 + 3.40149i) 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} +(-7.08314 + 13.3523i) 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} +(9.76382 + 0.817168i) 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

Related objects

Downloads

Learn more