LMFDB - Embedded newform 1183.2.e.j.170.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.1
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.j.508.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29430 + 2.24179i) q^{2} +(-0.259233 - 0.449005i) q^{3} +(-2.35043 - 4.07106i) q^{4} +(-0.806027 + 1.39608i) q^{5} +1.34210 q^{6} +(2.13104 + 1.56802i) q^{7} +6.99143 q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})$	\(q+(-1.29430 + 2.24179i) q^{2} +(-0.259233 - 0.449005i) q^{3} +(-2.35043 - 4.07106i) q^{4} +(-0.806027 + 1.39608i) q^{5} +1.34210 q^{6} +(2.13104 + 1.56802i) q^{7} +6.99143 q^{8} +(1.36560 - 2.36528i) q^{9} +(-2.08648 - 3.61389i) q^{10} +(-1.35248 - 2.34256i) q^{11} +(-1.21862 + 2.11070i) q^{12} +(-6.27337 + 2.74787i) q^{14} +0.835795 q^{15} +(-4.34816 + 7.53123i) q^{16} +(-1.56330 - 2.70772i) q^{17} +(3.53498 + 6.12277i) q^{18} +(-1.84075 + 3.18828i) q^{19} +7.57803 q^{20} +(0.151611 - 1.36333i) q^{21} +7.00205 q^{22} +(-0.993019 + 1.71996i) q^{23} +(-1.81241 - 3.13918i) q^{24} +(1.20064 + 2.07957i) q^{25} -2.97143 q^{27} +(1.37463 - 12.3611i) q^{28} -5.37271 q^{29} +(-1.08177 + 1.87368i) q^{30} +(-5.23902 - 9.07425i) q^{31} +(-4.26421 - 7.38583i) q^{32} +(-0.701214 + 1.21454i) q^{33} +8.09354 q^{34} +(-3.90675 + 1.71124i) q^{35} -12.8389 q^{36} +(-2.97673 + 5.15585i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(-5.63528 + 9.76059i) q^{40} -7.70150 q^{41} +(2.86007 + 2.10444i) q^{42} -3.35600 q^{43} +(-6.35780 + 11.0120i) q^{44} +(2.20141 + 3.81296i) q^{45} +(-2.57053 - 4.45229i) q^{46} +(-0.527542 + 0.913730i) q^{47} +4.50874 q^{48} +(2.08265 + 6.68300i) q^{49} -6.21596 q^{50} +(-0.810520 + 1.40386i) q^{51} +(-3.63284 - 6.29226i) q^{53} +(3.84592 - 6.66133i) q^{54} +4.36054 q^{55} +(14.8990 + 10.9627i) q^{56} +1.90873 q^{57} +(6.95390 - 12.0445i) q^{58} +(-5.71203 - 9.89352i) q^{59} +(-1.96447 - 3.40257i) q^{60} +(1.46254 - 2.53319i) q^{61} +27.1235 q^{62} +(6.61894 - 2.89923i) q^{63} +4.68406 q^{64} +(-1.81516 - 3.14395i) q^{66} +(6.79091 + 11.7622i) q^{67} +(-7.34886 + 12.7286i) q^{68} +1.02969 q^{69} +(1.22027 - 10.9730i) q^{70} -1.35111 q^{71} +(9.54747 - 16.5367i) q^{72} +(-4.55168 - 7.88374i) q^{73} +(-7.70557 - 13.3464i) q^{74} +(0.622492 - 1.07819i) q^{75} +17.3062 q^{76} +(0.790989 - 7.11280i) q^{77} +(3.10289 - 5.37436i) q^{79} +(-7.00946 - 12.1407i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(9.96806 - 17.2652i) q^{82} -2.69672 q^{83} +(-5.90654 + 2.58718i) q^{84} +5.04026 q^{85} +(4.34367 - 7.52346i) q^{86} +(1.39278 + 2.41237i) q^{87} +(-9.45576 - 16.3779i) q^{88} +(-0.879938 + 1.52410i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(-2.71625 + 4.70469i) q^{93} +(-1.36560 - 2.36528i) q^{94} +(-2.96739 - 5.13967i) q^{95} +(-2.21085 + 3.82930i) q^{96} +15.4820 q^{97} +(-17.6775 - 3.98094i) q^{98} -7.38776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.29430	+	2.24179i	−0.915209	+	1.58519i	−0.108613	+	0.994084i	$0.534641\pi$
$2$	−1.29430	+	2.24179i	−0.915209	+	1.58519i	−0.806596	+	0.591104i	$0.798692\pi$
$3$	−0.259233	−	0.449005i	−0.149668	−	0.259233i	0.781437	−	0.623985i	$-0.214487\pi$
$3$	−0.259233	−	0.449005i	−0.149668	−	0.259233i	−0.931105	+	0.364752i	$0.881154\pi$
$4$	−2.35043	−	4.07106i	−1.17521	−	2.03553i
$5$	−0.806027	+	1.39608i	−0.360466	+	0.624346i	−0.988038	−	0.154213i	$-0.950716\pi$
$5$	−0.806027	+	1.39608i	−0.360466	+	0.624346i	0.627571	+	0.778559i	$0.284049\pi$
$6$	1.34210			0.547910
$7$	2.13104	+	1.56802i	0.805457	+	0.592654i
$7$	2.13104	+	1.56802i	0.805457	+	0.592654i
$8$	6.99143			2.47184
$9$	1.36560	−	2.36528i	0.455199	−	0.788428i
$10$	−2.08648	−	3.61389i	−0.659803	−	1.14281i
$11$	−1.35248	−	2.34256i	−0.407788	−	0.706309i	0.586854	−	0.809693i	$-0.300366\pi$
$11$	−1.35248	−	2.34256i	−0.407788	−	0.706309i	−0.994642	+	0.103384i	$0.967033\pi$
$12$	−1.21862	+	2.11070i	−0.351784	+	0.609308i
$13$		0			0
$13$		0			0
$14$	−6.27337	+	2.74787i	−1.67663	+	0.734398i
$15$	0.835795			0.215801
$16$	−4.34816	+	7.53123i	−1.08704	+	1.88281i
$17$	−1.56330	−	2.70772i	−0.379157	−	0.656719i	0.611783	−	0.791026i	$-0.290453\pi$
$17$	−1.56330	−	2.70772i	−0.379157	−	0.656719i	−0.990940	+	0.134307i	$0.957119\pi$
$18$	3.53498	+	6.12277i	0.833204	+	1.44315i
$19$	−1.84075	+	3.18828i	−0.422297	+	0.731441i	−0.996164	−	0.0875083i	$-0.972110\pi$
$19$	−1.84075	+	3.18828i	−0.422297	+	0.731441i	0.573866	+	0.818949i	$0.305443\pi$
$20$	7.57803			1.69450
$21$	0.151611	−	1.36333i	0.0330842	−	0.297502i
$22$	7.00205			1.49284
$23$	−0.993019	+	1.71996i	−0.207059	+	0.358636i	−0.950787	−	0.309846i	$-0.899722\pi$
$23$	−0.993019	+	1.71996i	−0.207059	+	0.358636i	0.743728	+	0.668482i	$0.233056\pi$
$24$	−1.81241	−	3.13918i	−0.369956	−	0.640783i
$25$	1.20064	+	2.07957i	0.240128	+	0.415914i
$26$		0			0
$27$	−2.97143			−0.571852
$28$	1.37463	−	12.3611i	0.259781	−	2.33603i
$29$	−5.37271			−0.997687			−0.498844	−	0.866692i	$-0.666242\pi$
$29$	−5.37271			−0.997687			−0.498844	+	0.866692i	$0.666242\pi$
$30$	−1.08177	+	1.87368i	−0.197503	+	0.342086i
$31$	−5.23902	−	9.07425i	−0.940956	−	1.62978i	−0.763653	−	0.645627i	$-0.776596\pi$
$31$	−5.23902	−	9.07425i	−0.940956	−	1.62978i	−0.177303	−	0.984156i	$-0.556737\pi$
$32$	−4.26421	−	7.38583i	−0.753813	−	1.30564i
$33$	−0.701214	+	1.21454i	−0.122066	+	0.211424i
$34$	8.09354			1.38803
$35$	−3.90675	+	1.71124i	−0.660361	+	0.289252i
$36$	−12.8389			−2.13982
$37$	−2.97673	+	5.15585i	−0.489371	+	0.847616i	−0.999925	−	0.0122297i	$-0.996107\pi$
$37$	−2.97673	+	5.15585i	−0.489371	+	0.847616i	0.510554	+	0.859846i	$0.329440\pi$
$38$	−4.76497	−	8.25317i	−0.772981	−	1.33884i
$39$		0			0
$40$	−5.63528	+	9.76059i	−0.891016	+	1.54329i
$41$	−7.70150			−1.20277			−0.601386	−	0.798958i	$-0.705385\pi$
$41$	−7.70150			−1.20277			−0.601386	+	0.798958i	$0.705385\pi$
$42$	2.86007	+	2.10444i	0.441318	+	0.324721i
$43$	−3.35600			−0.511785			−0.255892	−	0.966705i	$-0.582369\pi$
$43$	−3.35600			−0.511785			−0.255892	+	0.966705i	$0.582369\pi$
$44$	−6.35780	+	11.0120i	−0.958475	+	1.66013i
$45$	2.20141	+	3.81296i	0.328168	+	0.568403i
$46$	−2.57053	−	4.45229i	−0.379004	−	0.656454i
$47$	−0.527542	+	0.913730i	−0.0769500	+	0.133281i	−0.901933	−	0.431877i	$-0.857852\pi$
$47$	−0.527542	+	0.913730i	−0.0769500	+	0.133281i	0.824983	+	0.565158i	$0.191185\pi$
$48$	4.50874			0.650781
$49$	2.08265	+	6.68300i	0.297522	+	0.954715i
$50$	−6.21596			−0.879070
$51$	−0.810520	+	1.40386i	−0.113495	+	0.196580i
$52$		0			0
$53$	−3.63284	−	6.29226i	−0.499009	−	0.864308i	0.500991	−	0.865453i	$-0.332969\pi$
$53$	−3.63284	−	6.29226i	−0.499009	−	0.864308i	−0.999999	+	0.00114437i	$0.999636\pi$
$54$	3.84592	−	6.66133i	0.523363	−	0.906492i
$55$	4.36054			0.587975
$56$	14.8990	+	10.9627i	1.99096	+	1.46495i
$57$	1.90873			0.252818
$58$	6.95390	−	12.0445i	0.913092	−	1.58152i
$59$	−5.71203	−	9.89352i	−0.743643	−	1.28803i	−0.950826	−	0.309725i	$-0.899763\pi$
$59$	−5.71203	−	9.89352i	−0.743643	−	1.28803i	0.207183	−	0.978302i	$-0.433570\pi$
$60$	−1.96447	−	3.40257i	−0.253613	−	0.439270i
$61$	1.46254	−	2.53319i	0.187259	−	0.324341i	−0.757077	−	0.653326i	$-0.773373\pi$
$61$	1.46254	−	2.53319i	0.187259	−	0.324341i	0.944335	+	0.328985i	$0.106706\pi$
$62$	27.1235			3.44468
$63$	6.61894	−	2.89923i	0.833908	−	0.365269i
$64$	4.68406			0.585507
$65$		0			0
$66$	−1.81516	−	3.14395i	−0.223431	−	0.386994i
$67$	6.79091	+	11.7622i	0.829642	+	1.43698i	0.898320	+	0.439343i	$0.144789\pi$
$67$	6.79091	+	11.7622i	0.829642	+	1.43698i	−0.0686778	+	0.997639i	$0.521878\pi$
$68$	−7.34886	+	12.7286i	−0.891180	+	1.54357i
$69$	1.02969			0.123960
$70$	1.22027	−	10.9730i	0.145850	−	1.31152i
$71$	−1.35111			−0.160347			−0.0801736	−	0.996781i	$-0.525547\pi$
$71$	−1.35111			−0.160347			−0.0801736	+	0.996781i	$0.525547\pi$
$72$	9.54747	−	16.5367i	1.12518	−	1.94887i
$73$	−4.55168	−	7.88374i	−0.532733	−	0.922721i	−0.999269	−	0.0382192i	$-0.987831\pi$
$73$	−4.55168	−	7.88374i	−0.532733	−	0.922721i	0.466536	−	0.884502i	$-0.345502\pi$
$74$	−7.70557	−	13.3464i	−0.895754	−	1.55149i
$75$	0.622492	−	1.07819i	0.0718791	−	0.124498i
$76$	17.3062			1.98516
$77$	0.790989	−	7.11280i	0.0901416	−	0.810578i
$78$		0			0
$79$	3.10289	−	5.37436i	0.349102	−	0.604663i	−0.636988	−	0.770874i	$-0.719820\pi$
$79$	3.10289	−	5.37436i	0.349102	−	0.604663i	0.986090	+	0.166211i	$0.0531532\pi$
$80$	−7.00946	−	12.1407i	−0.783682	−	1.35738i
$81$	−3.32650	−	5.76166i	−0.369611	−	0.640185i
$82$	9.96806	−	17.2652i	1.10079	−	1.90662i
$83$	−2.69672			−0.296003			−0.148002	−	0.988987i	$-0.547284\pi$
$83$	−2.69672			−0.296003			−0.148002	+	0.988987i	$0.547284\pi$
$84$	−5.90654	+	2.58718i	−0.644456	+	0.282285i
$85$	5.04026			0.546693
$86$	4.34367	−	7.52346i	0.468390	−	0.811275i
$87$	1.39278	+	2.41237i	0.149322	+	0.258633i
$88$	−9.45576	−	16.3779i	−1.00799	−	1.74589i
$89$	−0.879938	+	1.52410i	−0.0932732	+	0.161554i	−0.908887	−	0.417043i	$-0.863066\pi$
$89$	−0.879938	+	1.52410i	−0.0932732	+	0.161554i	0.815613	+	0.578597i	$0.196400\pi$
$90$	−11.3972			−1.20137
$91$		0			0
$92$	9.33607			0.973353
$93$	−2.71625	+	4.70469i	−0.281662	+	0.487853i
$94$	−1.36560	−	2.36528i	−0.140851	−	0.243960i
$95$	−2.96739	−	5.13967i	−0.304448	−	0.527319i
$96$	−2.21085	+	3.82930i	−0.225644	+	0.390827i
$97$	15.4820			1.57196			0.785981	−	0.618250i	$-0.212158\pi$
$97$	15.4820			1.57196			0.785981	+	0.618250i	$0.212158\pi$
$98$	−17.6775	−	3.98094i	−1.78570	−	0.402135i
$99$	−7.38776			−0.742498
$100$	5.64404	−	9.77576i	0.564404	−	0.977576i
$101$	0.639651	+	1.10791i	0.0636477	+	0.110241i	0.896093	−	0.443866i	$-0.146393\pi$
$101$	0.639651	+	1.10791i	0.0636477	+	0.110241i	−0.832446	+	0.554107i	$0.813060\pi$
$102$	−2.09811	−	3.63404i	−0.207744	−	0.359823i
$103$	5.73367	−	9.93101i	0.564956	−	0.978532i	−0.432098	−	0.901827i	$-0.642227\pi$
$103$	5.73367	−	9.93101i	0.564956	−	0.978532i	0.997054	−	0.0767054i	$-0.0244401\pi$
$104$		0			0
$105$	1.78111	+	1.31054i	0.173819	+	0.127896i
$106$	18.8079			1.82679
$107$	2.56763	−	4.44726i	0.248222	−	0.429933i	−0.714811	−	0.699318i	$-0.753487\pi$
$107$	2.56763	−	4.44726i	0.248222	−	0.429933i	0.963033	+	0.269385i	$0.0868205\pi$
$108$	6.98412	+	12.0969i	0.672048	+	1.16402i
$109$	−0.863916	−	1.49635i	−0.0827481	−	0.143324i	0.821681	−	0.569947i	$-0.193036\pi$
$109$	−0.863916	−	1.49635i	−0.0827481	−	0.143324i	−0.904429	+	0.426623i	$0.859703\pi$
$110$	−5.64384	+	9.77542i	−0.538119	+	0.932050i
$111$	3.08667			0.292973
$112$	−21.0752	+	9.23136i	−1.99142	+	0.872282i
$113$	−8.59113			−0.808185			−0.404093	−	0.914718i	$-0.632413\pi$
$113$	−8.59113			−0.808185			−0.404093	+	0.914718i	$0.632413\pi$
$114$	−2.47048	+	4.27899i	−0.231381	+	0.400764i
$115$	−1.60080	−	2.77267i	−0.149275	−	0.258552i
$116$	12.6282	+	21.8726i	1.17250	+	2.03082i
$117$		0			0
$118$	29.5723			2.72235
$119$	0.914289	−	8.22154i	0.0838127	−	0.753668i
$120$	5.84340			0.533427
$121$	1.84160	−	3.18975i	0.167419	−	0.289977i
$122$	3.78592	+	6.55741i	0.342761	+	0.593680i
$123$	1.99648	+	3.45801i	0.180017	+	0.311798i
$124$	−24.6279	+	42.6567i	−2.21165	+	3.83069i
$125$	−11.9313			−1.06716
$126$	−2.06741	+	18.5908i	−0.184180	+	1.65620i
$127$	−3.12412			−0.277221			−0.138610	−	0.990347i	$-0.544264\pi$
$127$	−3.12412			−0.277221			−0.138610	+	0.990347i	$0.544264\pi$
$128$	2.46585	−	4.27097i	0.217952	−	0.377504i
$129$	0.869985	+	1.50686i	0.0765979	+	0.132671i
$130$		0			0
$131$	−5.10460	+	8.84142i	−0.445991	+	0.772479i	−0.998121	−	0.0612793i	$-0.980482\pi$
$131$	−5.10460	+	8.84142i	−0.445991	+	0.772479i	0.552130	+	0.833758i	$0.313815\pi$
$132$	6.59261			0.573813
$133$	−8.92198	+	3.90801i	−0.773634	+	0.338868i
$134$	−35.1579			−3.03718
$135$	2.39505	−	4.14835i	0.206133	−	0.357033i
$136$	−10.9297	−	18.9308i	−0.937216	−	1.62331i
$137$	4.99630	+	8.65385i	0.426863	+	0.739348i	0.996592	−	0.0824839i	$-0.0262853\pi$
$137$	4.99630	+	8.65385i	0.426863	+	0.739348i	−0.569729	+	0.821832i	$0.692952\pi$
$138$	−1.33273	+	2.30836i	−0.113450	+	0.196501i
$139$	−1.66420			−0.141156			−0.0705778	−	0.997506i	$-0.522484\pi$
$139$	−1.66420			−0.141156			−0.0705778	+	0.997506i	$0.522484\pi$
$140$	16.1491	+	11.8825i	1.36485	+	1.00425i
$141$	0.547025			0.0460679
$142$	1.74874	−	3.02891i	0.146751	−	0.254180i
$143$		0			0
$144$	11.8757	+	20.5692i	0.989638	+	1.71410i
$145$	4.33055	−	7.50073i	0.359633	−	0.622902i
$146$	23.5649			1.95025
$147$	2.46081	−	2.66758i	0.202964	−	0.220018i
$148$	27.9863			2.30046
$149$	−9.89902	+	17.1456i	−0.810959	+	1.40462i	0.101234	+	0.994863i	$0.467721\pi$
$149$	−9.89902	+	17.1456i	−0.810959	+	1.40462i	−0.912193	+	0.409760i	$0.865613\pi$
$150$	1.61138	+	2.79100i	0.131569	+	0.227884i
$151$	−3.76746	−	6.52544i	−0.306592	−	0.531033i	0.671023	−	0.741437i	$-0.265855\pi$
$151$	−3.76746	−	6.52544i	−0.306592	−	0.531033i	−0.977614	+	0.210404i	$0.932522\pi$
$152$	−12.8695	+	22.2906i	−1.04385	+	1.80801i
$153$	−8.53937			−0.690367
$154$	14.9216	+	10.9793i	1.20242	+	0.884740i
$155$	16.8912			1.35673
$156$		0			0
$157$	−7.00223	−	12.1282i	−0.558839	−	0.967938i	−0.997594	−	0.0693309i	$-0.977914\pi$
$157$	−7.00223	−	12.1282i	−0.558839	−	0.967938i	0.438755	−	0.898607i	$-0.355420\pi$
$158$	8.03214	+	13.9121i	0.639003	+	1.10679i
$159$	−1.88350	+	3.26232i	−0.149371	+	0.258719i
$160$	13.7483			1.08690
$161$	−4.81308	+	2.10823i	−0.379324	+	0.166152i
$162$	17.2219			1.35308
$163$	3.58498	−	6.20936i	0.280797	−	0.486355i	−0.690784	−	0.723061i	$-0.742735\pi$
$163$	3.58498	−	6.20936i	0.280797	−	0.486355i	0.971581	+	0.236706i	$0.0760679\pi$
$164$	18.1018	+	31.3533i	1.41351	+	2.44828i
$165$	−1.13039	−	1.95790i	−0.0880011	−	0.152422i
$166$	3.49036	−	6.04548i	0.270904	−	0.469220i
$167$	−17.9805			−1.39138			−0.695688	−	0.718344i	$-0.744901\pi$
$167$	−17.9805			−1.39138			−0.695688	+	0.718344i	$0.744901\pi$
$168$	1.05998	−	9.53161i	0.0817790	−	0.735380i
$169$		0			0
$170$	−6.52361	+	11.2992i	−0.500338	+	0.866611i
$171$	5.02745	+	8.70780i	0.384459	+	0.665902i
$172$	7.88803	+	13.6625i	0.601456	+	1.04175i
$173$	6.40579	−	11.0952i	0.487023	−	0.843549i	−0.512865	−	0.858469i	$-0.671416\pi$
$173$	6.40579	−	11.0952i	0.487023	−	0.843549i	0.999889	+	0.0149198i	$0.00474930\pi$
$174$	−7.21072			−0.546643
$175$	−0.702188	+	6.31427i	−0.0530804	+	0.477314i
$176$	23.5232			1.77312
$177$	−2.96149	+	5.12945i	−0.222599	+	0.385553i
$178$	−2.27781	−	3.94528i	−0.170729	−	0.295711i
$179$	−0.920110	−	1.59368i	−0.0687723	−	0.119117i	0.829589	−	0.558375i	$-0.188575\pi$
$179$	−0.920110	−	1.59368i	−0.0687723	−	0.119117i	−0.898361	+	0.439258i	$0.855242\pi$
$180$	10.3485	−	17.9242i	0.771334	−	1.33599i
$181$	3.29928			0.245234			0.122617	−	0.992454i	$-0.460871\pi$
$181$	3.29928			0.245234			0.122617	+	0.992454i	$0.460871\pi$
$182$		0			0
$183$	−1.51655			−0.112107
$184$	−6.94262	+	12.0250i	−0.511817	+	0.886493i
$185$	−4.79865	−	8.31150i	−0.352804	−	0.611074i
$186$	−7.03129	−	12.1786i	−0.515560	−	0.892975i
$187$	−4.22867	+	7.32427i	−0.309231	+	0.535604i
$188$	4.95980			0.361731
$189$	−6.33223	−	4.65925i	−0.460602	−	0.338910i
$190$	15.3628			1.11453
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	−0.940898	−	0.338689i	$-0.890017\pi$
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	0.763762	+	0.645498i	$0.223350\pi$
$192$	−1.21426	−	2.10316i	−0.0876318	−	0.151783i
$193$	−1.50955	−	2.61462i	−0.108660	−	0.188204i	0.806568	−	0.591142i	$-0.201323\pi$
$193$	−1.50955	−	2.61462i	−0.108660	−	0.188204i	−0.915228	+	0.402937i	$0.867989\pi$
$194$	−20.0384	+	34.7075i	−1.43867	+	2.49186i
$195$		0			0
$196$	22.3118	−	24.1865i	1.59370	−	1.72761i
$197$	4.64991			0.331292			0.165646	−	0.986185i	$-0.447029\pi$
$197$	4.64991			0.331292			0.165646	+	0.986185i	$0.447029\pi$
$198$	9.56198	−	16.5618i	0.679540	−	1.17700i
$199$	−0.205360	−	0.355694i	−0.0145576	−	0.0252145i	0.858655	−	0.512554i	$-0.171301\pi$
$199$	−0.205360	−	0.355694i	−0.0145576	−	0.0252145i	−0.873212	+	0.487340i	$0.837967\pi$
$200$	8.39420	+	14.5392i	0.593560	+	1.02808i
$201$	3.52085	−	6.09830i	0.248342	−	0.430141i
$202$	−3.31160			−0.233004
$203$	−11.4495	−	8.42450i	−0.803594	−	0.591284i
$204$	7.62027			0.533525
$205$	6.20762	−	10.7519i	0.433559	−	0.750946i
$206$	14.8422	+	25.7074i	1.03410	+	1.79112i
$207$	2.71213	+	4.69754i	0.188506	+	0.326502i
$208$		0			0
$209$	9.95831			0.688831
$210$	−5.24325	+	2.29665i	−0.361819	+	0.158484i
$211$	−7.51600			−0.517423			−0.258711	−	0.965955i	$-0.583298\pi$
$211$	−7.51600			−0.517423			−0.258711	+	0.965955i	$0.583298\pi$
$212$	−17.0774	+	29.5790i	−1.17288	+	2.03149i
$213$	0.350252	+	0.606654i	0.0239989	+	0.0415672i
$214$	6.64656	+	11.5122i	0.454349	+	0.786956i
$215$	2.70502	−	4.68524i	0.184481	−	0.319531i
$216$	−20.7745			−1.41353
$217$	3.06401	−	27.5524i	0.207999	−	1.87038i
$218$	4.47267			0.302927
$219$	−2.35989	+	4.08745i	−0.159467	+	0.276204i
$220$	−10.2491	−	17.7520i	−0.690996	−	1.19684i
$221$		0			0
$222$	−3.99507	+	6.91967i	−0.268132	+	0.464418i
$223$	−22.5794			−1.51203			−0.756016	−	0.654553i	$-0.772857\pi$
$223$	−22.5794			−1.51203			−0.756016	+	0.654553i	$0.772857\pi$
$224$	2.49390	−	22.4259i	0.166631	−	1.49839i
$225$	6.55837			0.437225
$226$	11.1195	−	19.2595i	0.739658	−	1.28113i
$227$	−6.83586	−	11.8401i	−0.453712	−	0.785853i	0.544901	−	0.838500i	$-0.316567\pi$
$227$	−6.83586	−	11.8401i	−0.453712	−	0.785853i	−0.998613	+	0.0526478i	$0.983234\pi$
$228$	−4.48634	−	7.77057i	−0.297115	−	0.514618i
$229$	−3.96543	+	6.86832i	−0.262043	+	0.453872i	−0.966785	−	0.255592i	$-0.917730\pi$
$229$	−3.96543	+	6.86832i	−0.262043	+	0.453872i	0.704742	+	0.709464i	$0.251063\pi$
$230$	8.28766			0.546472
$231$	−3.39873	+	1.48871i	−0.223620	+	0.0979502i
$232$	−37.5629			−2.46613
$233$	3.28585	−	5.69127i	0.215263	−	0.372847i	−0.738091	−	0.674702i	$-0.764272\pi$
$233$	3.28585	−	5.69127i	0.215263	−	0.372847i	0.953354	+	0.301854i	$0.0976056\pi$
$234$		0			0
$235$	−0.850427	−	1.47298i	−0.0554757	−	0.0960868i
$236$	−26.8514	+	46.5080i	−1.74788	+	3.02741i
$237$	−3.21749			−0.208998
$238$	17.2476	+	12.6908i	1.11800	+	0.822622i
$239$	−9.39284			−0.607572			−0.303786	−	0.952740i	$-0.598251\pi$
$239$	−9.39284			−0.607572			−0.303786	+	0.952740i	$0.598251\pi$
$240$	−3.63417	+	6.29456i	−0.234584	+	0.406312i
$241$	5.04292	+	8.73460i	0.324843	+	0.562645i	0.981481	−	0.191562i	$-0.0613552\pi$
$241$	5.04292	+	8.73460i	0.324843	+	0.562645i	−0.656637	+	0.754206i	$0.728022\pi$
$242$	4.76718	+	8.25699i	0.306446	+	0.530780i
$243$	−6.18182	+	10.7072i	−0.396564	+	0.686869i
$244$	−13.7503			−0.880275
$245$	−11.0087	−	2.47913i	−0.703319	−	0.158386i
$246$	−10.3362			−0.659012
$247$		0			0
$248$	−36.6282	−	63.4420i	−2.32590	−	4.02857i
$249$	0.699078	+	1.21084i	0.0443022	+	0.0767337i
$250$	15.4426	−	26.7474i	0.976678	−	1.69166i
$251$	−10.3485			−0.653194			−0.326597	−	0.945164i	$-0.605902\pi$
$251$	−10.3485			−0.653194			−0.326597	+	0.945164i	$0.605902\pi$
$252$	−27.3603	−	20.1317i	−1.72354	−	1.26818i
$253$	5.37215			0.337744
$254$	4.04355	−	7.00363i	0.253715	−	0.439447i
$255$	−1.30660	−	2.26310i	−0.0818225	−	0.141721i
$256$	11.0672	+	19.1689i	0.691697	+	1.19805i
$257$	−3.99329	+	6.91658i	−0.249095	+	0.431445i	−0.963275	−	0.268517i	$-0.913466\pi$
$257$	−3.99329	+	6.91658i	−0.249095	+	0.431445i	0.714180	+	0.699962i	$0.246800\pi$
$258$	−4.50409			−0.280412
$259$	−14.4280	+	6.31975i	−0.896511	+	0.392690i
$260$		0			0
$261$	−7.33696	+	12.7080i	−0.454146	+	0.786604i
$262$	−13.2138	−	22.8869i	−0.816349	−	1.41396i
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	0.777431	−	0.628968i	$-0.216522\pi$
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	−0.933418	+	0.358792i	$0.883189\pi$
$264$	−4.90249	+	8.49136i	−0.301727	+	0.522607i
$265$	11.7127			0.719503
$266$	2.78677	−	25.0594i	0.170868	−	1.53649i
$267$	0.912435			0.0558401
$268$	31.9231	−	55.2924i	1.95001	−	3.37752i
$269$	−6.94512	−	12.0293i	−0.423451	−	0.733439i	0.572823	−	0.819679i	$-0.305848\pi$
$269$	−6.94512	−	12.0293i	−0.423451	−	0.733439i	−0.996274	+	0.0862400i	$0.972515\pi$
$270$	6.19983	+	10.7384i	0.377310	+	0.653519i
$271$	4.16361	−	7.21158i	0.252921	−	0.438072i	−0.711408	−	0.702780i	$-0.751942\pi$
$271$	4.16361	−	7.21158i	0.252921	−	0.438072i	0.964329	+	0.264707i	$0.0852754\pi$
$272$	27.1900			1.64863
$273$		0			0
$274$	−25.8669			−1.56267
$275$	3.24768	−	5.62515i	0.195843	−	0.339210i
$276$	−2.42022	−	4.19194i	−0.145680	−	0.252325i
$277$	11.6058	+	20.1018i	0.697325	+	1.20780i	0.969391	+	0.245523i	$0.0789598\pi$
$277$	11.6058	+	20.1018i	0.697325	+	1.20780i	−0.272066	+	0.962279i	$0.587707\pi$
$278$	2.15398	−	3.73080i	0.129187	−	0.223758i
$279$	−28.6176			−1.71329
$280$	−27.3138	+	11.9640i	−1.63231	+	0.714985i
$281$	27.1595			1.62020			0.810100	−	0.586292i	$-0.199413\pi$
$281$	27.1595			1.62020			0.810100	+	0.586292i	$0.199413\pi$
$282$	−0.708015	+	1.22632i	−0.0421617	+	0.0730262i
$283$	8.07563	+	13.9874i	0.480046	+	0.831464i	0.999738	−	0.0228894i	$-0.00728654\pi$
$283$	8.07563	+	13.9874i	0.480046	+	0.831464i	−0.519692	+	0.854354i	$0.673953\pi$
$284$	3.17568	+	5.50044i	0.188442	+	0.326391i
$285$	−1.53849	+	2.66474i	−0.0911323	+	0.157846i
$286$		0			0
$287$	−16.4122	−	12.0761i	−0.968782	−	0.712828i
$288$	−23.2928			−1.37254
$289$	3.61216	−	6.25645i	0.212480	−	0.368027i
$290$	11.2101	+	19.4164i	0.658278	+	1.14017i
$291$	−4.01345	−	6.95151i	−0.235273	−	0.407504i
$292$	−21.3968	+	37.0603i	−1.25215	+	2.16879i
$293$	−14.6452			−0.855582			−0.427791	−	0.903878i	$-0.640708\pi$
$293$	−14.6452			−0.855582			−0.427791	+	0.903878i	$0.640708\pi$
$294$	2.79513	+	8.96927i	0.163015	+	0.523098i
$295$	18.4162			1.07223
$296$	−20.8116	+	36.0468i	−1.20965	+	2.09517i
$297$	4.01879	+	6.96075i	0.233194	+	0.403904i
$298$	−25.6246	−	44.3831i	−1.48439	−	2.57104i
$299$		0			0
$300$	−5.85248			−0.337893
$301$	−7.15176	−	5.26226i	−0.412221	−	0.303311i
$302$	19.5049			1.12238
$303$	0.331637	−	0.574412i	0.0190521	−	0.0329991i
$304$	−16.0078	−	27.7263i	−0.918108	−	1.59021i
$305$	2.35769	+	4.08363i	0.135001	+	0.233828i
$306$	11.0525	−	19.1435i	0.631830	−	1.09436i
$307$	−8.97844			−0.512427			−0.256213	−	0.966620i	$-0.582475\pi$
$307$	−8.97844			−0.512427			−0.256213	+	0.966620i	$0.582475\pi$
$308$	−30.8158	+	13.4979i	−1.75589	+	0.769117i
$309$	−5.94543			−0.338224
$310$	−21.8622	+	37.8665i	−1.24169	+	2.15067i
$311$	−6.09080	−	10.5496i	−0.345378	−	0.598212i	0.640045	−	0.768338i	$-0.278916\pi$
$311$	−6.09080	−	10.5496i	−0.345378	−	0.598212i	−0.985422	+	0.170126i	$0.945583\pi$
$312$		0			0
$313$	−6.56198	+	11.3657i	−0.370905	+	0.642427i	−0.989705	−	0.143122i	$-0.954286\pi$
$313$	−6.56198	+	11.3657i	−0.370905	+	0.642427i	0.618800	+	0.785549i	$0.287619\pi$
$314$	36.2520			2.04582
$315$	−1.28748	+	11.5774i	−0.0725415	+	0.652314i
$316$	−29.1725			−1.64108
$317$	8.35775	−	14.4761i	0.469418	−	0.813056i	−0.529971	−	0.848016i	$-0.677797\pi$
$317$	8.35775	−	14.4761i	0.469418	−	0.813056i	0.999389	+	0.0349599i	$0.0111304\pi$
$318$	−4.87563	−	8.44485i	−0.273412	−	0.473564i
$319$	7.26648	+	12.5859i	0.406845	+	0.704675i
$320$	−3.77548	+	6.53932i	−0.211056	+	0.365559i
$321$	−2.66245			−0.148604
$322$	1.50336	−	13.5186i	0.0837789	−	0.753364i
$323$	11.5106			0.640468
$324$	−15.6374	+	27.0847i	−0.868743	+	1.50471i
$325$		0			0
$326$	9.28007	+	16.0736i	0.513976	+	0.890232i
$327$	−0.447911	+	0.775804i	−0.0247695	+	0.0429021i
$328$	−53.8445			−2.97307
$329$	−2.55696	+	1.12000i	−0.140970	+	0.0617476i
$330$	5.85228			0.322157
$331$	1.98332	−	3.43522i	0.109013	−	0.188817i	−0.806357	−	0.591428i	$-0.798564\pi$
$331$	1.98332	−	3.43522i	0.109013	−	0.188817i	0.915371	+	0.402612i	$0.131898\pi$
$332$	6.33843	+	10.9785i	0.347867	+	0.602523i
$333$	8.13002	+	14.0816i	0.445523	+	0.771668i
$334$	23.2722	−	40.3087i	1.27340	−	2.20559i
$335$	−21.8946			−1.19623
$336$	9.60831	+	7.06978i	0.524176	+	0.385688i
$337$	13.7032			0.746461			0.373230	−	0.927739i	$-0.378250\pi$
$337$	13.7032			0.746461			0.373230	+	0.927739i	$0.378250\pi$
$338$		0			0
$339$	2.22710	+	3.85746i	0.120960	+	0.209508i
$340$	−11.8468	−	20.5192i	−0.642481	−	1.11281i
$341$	−14.1713	+	24.5455i	−0.767420	+	1.32921i
$342$	−26.0281			−1.40744
$343$	−6.04084	+	17.5074i	−0.326175	+	0.945309i
$344$	−23.4632			−1.26505
$345$	−0.829960	+	1.43753i	−0.0446835	+	0.0773942i
$346$	16.5820	+	28.7209i	0.891456	+	1.54405i
$347$	13.1989	+	22.8612i	0.708556	+	1.22725i	0.965393	+	0.260800i	$0.0839863\pi$
$347$	13.1989	+	22.8612i	0.708556	+	1.22725i	−0.256837	+	0.966455i	$0.582680\pi$
$348$	6.54727	−	11.3402i	0.350971	−	0.607899i
$349$	4.89024			0.261769			0.130884	−	0.991398i	$-0.458218\pi$
$349$	4.89024			0.261769			0.130884	+	0.991398i	$0.458218\pi$
$350$	−13.2465	−	9.74673i	−0.708053	−	0.520984i
$351$		0			0
$352$	−11.5345	+	19.9784i	−0.614792	+	1.06485i
$353$	−6.77886	−	11.7413i	−0.360802	−	0.624928i	0.627291	−	0.778785i	$-0.284164\pi$
$353$	−6.77886	−	11.7413i	−0.360802	−	0.624928i	−0.988093	+	0.153857i	$0.950830\pi$
$354$	−7.66612	−	13.2781i	−0.407450	−	0.705724i
$355$	1.08903	−	1.88626i	0.0577997	−	0.100112i
$356$	8.27291			0.438464
$357$	−3.92852	+	1.72077i	−0.207920	+	0.0910731i
$358$	4.76360			0.251764
$359$	−4.29284	+	7.43541i	−0.226567	+	0.392426i	−0.956789	−	0.290785i	$-0.906084\pi$
$359$	−4.29284	+	7.43541i	−0.226567	+	0.392426i	0.730221	+	0.683211i	$0.239417\pi$
$360$	15.3910	+	26.6581i	0.811179	+	1.40500i
$361$	2.72326	+	4.71683i	0.143330	+	0.248254i
$362$	−4.27026	+	7.39632i	−0.224440	+	0.388742i
$363$	−1.90962			−0.100229
$364$		0			0
$365$	14.6751			0.768130
$366$	1.96287	−	3.39979i	0.102601	−	0.177710i
$367$	0.831612	+	1.44039i	0.0434098	+	0.0751880i	0.886914	−	0.461935i	$-0.152845\pi$
$367$	0.831612	+	1.44039i	0.0434098	+	0.0751880i	−0.843504	+	0.537123i	$0.819511\pi$
$368$	−8.63560	−	14.9573i	−0.450162	−	0.779703i
$369$	−10.5171	+	18.2162i	−0.547501	+	0.948299i
$370$	24.8436			1.29156
$371$	2.12464	−	19.1054i	0.110306	−	0.991903i
$372$	25.5374			1.32405
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	−0.988208	−	0.153117i	$-0.951069\pi$
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	0.626707	+	0.779255i	$0.284402\pi$
$374$	−10.9463	−	18.9596i	−0.566022	−	0.980378i
$375$	3.09298	+	5.35719i	0.159721	+	0.276644i
$376$	−3.68828	+	6.38828i	−0.190208	+	0.329450i
$377$		0			0
$378$	18.6409	−	8.16509i	0.958783	−	0.419967i
$379$	−31.5758			−1.62194			−0.810969	−	0.585089i	$-0.801059\pi$
$379$	−31.5758			−1.62194			−0.810969	+	0.585089i	$0.801059\pi$
$380$	−13.9493	+	24.1608i	−0.715582	+	1.23943i
$381$	0.809874	+	1.40274i	0.0414911	+	0.0718647i
$382$	−6.33707	−	10.9761i	−0.324233	−	0.561588i
$383$	15.9541	−	27.6333i	0.815217	−	1.41200i	−0.0939554	−	0.995576i	$-0.529951\pi$
$383$	15.9541	−	27.6333i	0.815217	−	1.41200i	0.909172	−	0.416420i	$-0.136716\pi$
$384$	−2.55692			−0.130482
$385$	9.29247	+	6.83739i	0.473588	+	0.348466i
$386$	7.81525			0.397786
$387$	−4.58294	+	7.93788i	−0.232964	+	0.403505i
$388$	−36.3894	−	63.0283i	−1.84739	−	3.19978i
$389$	12.7075	+	22.0100i	0.644296	+	1.11595i	0.984464	+	0.175589i	$0.0561829\pi$
$389$	12.7075	+	22.0100i	0.644296	+	1.11595i	−0.340168	+	0.940365i	$0.610484\pi$
$390$		0			0
$391$	6.20956			0.314031
$392$	14.5607	+	46.7238i	0.735428	+	2.35991i
$393$	5.29312			0.267003
$394$	−6.01838	+	10.4241i	−0.303202	+	0.525161i
$395$	5.00203	+	8.66376i	0.251679	+	0.435921i
$396$	17.3644	+	30.0760i	0.872593	+	1.51138i
$397$	−2.07949	+	3.60178i	−0.104366	+	0.180768i	−0.913479	−	0.406885i	$-0.866615\pi$
$397$	−2.07949	+	3.60178i	−0.104366	+	0.180768i	0.809113	+	0.587653i	$0.199948\pi$
$398$	1.06319			0.0532930
$399$	4.06759	+	2.99293i	0.203634	+	0.149834i
$400$	−20.8823			−1.04412
$401$	9.80067	−	16.9753i	0.489422	−	0.847704i	−0.510504	−	0.859875i	$-0.670541\pi$
$401$	9.80067	−	16.9753i	0.489422	−	0.847704i	0.999926	+	0.0121716i	$0.00387443\pi$
$402$	9.11409	+	15.7861i	0.454569	+	0.787337i
$403$		0			0
$404$	3.00691	−	5.20811i	0.149599	−	0.259113i
$405$	10.7250			0.532929
$406$	33.7050	−	14.7635i	1.67275	−	0.732700i
$407$	16.1039			0.798238
$408$	−5.66669	+	9.81500i	−0.280543	+	0.485915i
$409$	8.81685	+	15.2712i	0.435965	+	0.755114i	0.997374	−	0.0724249i	$-0.0230738\pi$
$409$	8.81685	+	15.2712i	0.435965	+	0.755114i	−0.561409	+	0.827539i	$0.689740\pi$
$410$	16.0690	+	27.8324i	0.793594	+	1.37454i
$411$	2.59041	−	4.48673i	0.127776	−	0.221314i
$412$	−53.9063			−2.65577
$413$	3.34065	−	30.0400i	0.164382	−	1.47817i
$414$	−14.0412			−0.690088
$415$	2.17363	−	3.76483i	0.106699	−	0.184808i
$416$		0			0
$417$	0.431416	+	0.747234i	0.0211265	+	0.0365922i
$418$	−12.8890	+	22.3245i	−0.630424	+	1.09193i
$419$	29.8911			1.46027			0.730137	−	0.683301i	$-0.239456\pi$
$419$	29.8911			1.46027			0.730137	+	0.683301i	$0.239456\pi$
$420$	1.14891	−	10.3313i	0.0560611	−	0.504117i
$421$	−12.8528			−0.626407			−0.313203	−	0.949686i	$-0.601402\pi$
$421$	−12.8528			−0.626407			−0.313203	+	0.949686i	$0.601402\pi$
$422$	9.72796	−	16.8493i	0.473550	−	0.820212i
$423$	1.44082	+	2.49557i	0.0700551	+	0.121339i
$424$	−25.3987	−	43.9919i	−1.23347	−	2.13644i
$425$	3.75393	−	6.50200i	0.182093	−	0.315394i
$426$	−1.81332			−0.0878559
$427$	7.08880	−	3.10504i	0.343051	−	0.150263i
$428$	−24.1401			−1.16685
$429$		0			0
$430$	7.00223	+	12.1282i	0.337677	+	0.584874i
$431$	4.48530	+	7.76876i	0.216049	+	0.374208i	0.953597	−	0.301087i	$-0.0973495\pi$
$431$	4.48530	+	7.76876i	0.216049	+	0.374208i	−0.737547	+	0.675295i	$0.764016\pi$
$432$	12.9202	−	22.3785i	0.621625	−	1.07669i
$433$	−3.45062			−0.165826			−0.0829132	−	0.996557i	$-0.526422\pi$
$433$	−3.45062			−0.165826			−0.0829132	+	0.996557i	$0.526422\pi$
$434$	57.8012	+	42.5300i	2.77454	+	2.04151i
$435$	−4.49048			−0.215302
$436$	−4.06114	+	7.03410i	−0.194493	+	0.336872i
$437$	−3.65580	−	6.33204i	−0.174881	−	0.302902i
$438$	−6.10881	−	10.5808i	−0.291890	−	0.505569i
$439$	19.2572	−	33.3544i	0.919096	−	1.59192i	0.118304	−	0.992977i	$-0.462254\pi$
$439$	19.2572	−	33.3544i	0.919096	−	1.59192i	0.800792	−	0.598943i	$-0.204412\pi$
$440$	30.4864			1.45338
$441$	18.6513	+	4.20023i	0.888155	+	0.200011i
$442$		0			0
$443$	7.51997	−	13.0250i	0.357284	−	0.618835i	−0.630222	−	0.776415i	$-0.717036\pi$
$443$	7.51997	−	13.0250i	0.357284	−	0.618835i	0.987506	+	0.157580i	$0.0503693\pi$
$444$	−7.25498	−	12.5660i	−0.344306	−	0.596356i
$445$	−1.41851	−	2.45693i	−0.0672437	−	0.116469i
$446$	29.2246	−	50.6185i	1.38382	−	2.39685i
$447$	10.2646			0.485499
$448$	9.98191	+	7.34468i	0.471601	+	0.347003i
$449$	38.9235			1.83691			0.918456	−	0.395522i	$-0.129436\pi$
$449$	38.9235			1.83691			0.918456	+	0.395522i	$0.129436\pi$
$450$	−8.48850	+	14.7025i	−0.400152	+	0.693083i
$451$	10.4161	+	18.0412i	0.490476	+	0.849529i
$452$	20.1928	+	34.9750i	0.949790	+	1.64509i
$453$	−1.95330	+	3.38322i	−0.0917741	+	0.158957i
$454$	35.3906			1.66097
$455$		0			0
$456$	13.3448			0.624927
$457$	−6.96982	+	12.0721i	−0.326034	+	0.564708i	−0.981721	−	0.190325i	$-0.939046\pi$
$457$	−6.96982	+	12.0721i	−0.326034	+	0.564708i	0.655687	+	0.755033i	$0.272379\pi$
$458$	−10.2649	−	17.7793i	−0.479648	−	0.830774i
$459$	4.64524	+	8.04580i	0.216821	+	0.375546i
$460$	−7.52512	+	13.0339i	−0.350861	+	0.607709i
$461$	−37.4635			−1.74485			−0.872424	−	0.488749i	$-0.837453\pi$
$461$	−37.4635			−1.74485			−0.872424	+	0.488749i	$0.837453\pi$
$462$	1.06159	−	9.54609i	0.0493895	−	0.444124i
$463$	−6.75275			−0.313827			−0.156913	−	0.987612i	$-0.550154\pi$
$463$	−6.75275			−0.313827			−0.156913	+	0.987612i	$0.550154\pi$
$464$	23.3614	−	40.4631i	1.08453	−	1.87845i
$465$	−4.37875	−	7.58421i	−0.203059	−	0.351709i
$466$	8.50576	+	14.7324i	0.394022	+	0.682466i
$467$	−2.52516	+	4.37371i	−0.116851	+	0.202391i	−0.918518	−	0.395379i	$-0.870613\pi$
$467$	−2.52516	+	4.37371i	−0.116851	+	0.202391i	0.801667	+	0.597770i	$0.203947\pi$
$468$		0			0
$469$	−3.97162	+	35.7140i	−0.183393	+	1.64912i
$470$	4.40283			0.203087
$471$	−3.63042	+	6.28807i	−0.167281	+	0.289739i
$472$	−39.9353	−	69.1699i	−1.83817	−	3.18380i
$473$	4.53892	+	7.86163i	0.208700	+	0.361478i
$474$	4.16439	−	7.21294i	0.191277	−	0.331301i
$475$	−8.84033			−0.405622
$476$	−35.6194	+	15.6020i	−1.63261	+	0.715117i
$477$	−19.8440			−0.908593
$478$	12.1572	−	21.0568i	0.556055	−	0.963116i
$479$	−4.72659	−	8.18670i	−0.215964	−	0.374060i	0.737607	−	0.675231i	$-0.235956\pi$
$479$	−4.72659	−	8.18670i	−0.215964	−	0.374060i	−0.953570	+	0.301171i	$0.902623\pi$
$480$	−3.56401	−	6.17304i	−0.162674	−	0.281759i
$481$		0			0
$482$	−26.1082			−1.18920
$483$	2.19432	+	1.61457i	0.0998448	+	0.0734657i
$484$	−17.3142			−0.787010
$485$	−12.4789	+	21.6142i	−0.566639	+	0.981448i
$486$	−16.0023	−	27.7167i	−0.725877	−	1.25726i
$487$	−19.9998	−	34.6407i	−0.906277	−	1.56972i	−0.819194	−	0.573517i	$-0.805579\pi$
$487$	−19.9998	−	34.6407i	−0.906277	−	1.56972i	−0.0870831	−	0.996201i	$-0.527755\pi$
$488$	10.2252	−	17.7106i	0.462874	−	0.801721i
$489$	−3.71737			−0.168105
$490$	19.8062	−	21.4705i	0.894755	−	0.969936i
$491$	−6.76097			−0.305118			−0.152559	−	0.988294i	$-0.548751\pi$
$491$	−6.76097			−0.305118			−0.152559	+	0.988294i	$0.548751\pi$
$492$	9.38518	−	16.2556i	0.423116	−	0.732859i
$493$	8.39918	+	14.5478i	0.378280	+	0.655200i
$494$		0			0
$495$	5.95473	−	10.3139i	0.267645	−	0.463575i
$496$	91.1203			4.09142
$497$	−2.87927	−	2.11856i	−0.129153	−	0.0950304i
$498$	−3.61927			−0.162183
$499$	−5.67877	+	9.83591i	−0.254217	+	0.440316i	−0.964682	−	0.263416i	$-0.915151\pi$
$499$	−5.67877	+	9.83591i	−0.254217	+	0.440316i	0.710466	+	0.703732i	$0.248484\pi$
$500$	28.0436	+	48.5729i	1.25415	+	2.17225i
$501$	4.66115	+	8.07335i	0.208245	+	0.360691i
$502$	13.3941	−	23.1993i	0.597808	−	1.03543i
$503$	−13.9285			−0.621040			−0.310520	−	0.950567i	$-0.600503\pi$
$503$	−13.9285			−0.621040			−0.310520	+	0.950567i	$0.600503\pi$
$504$	46.2759	−	20.2698i	2.06129	−	0.902888i
$505$	−2.06230			−0.0917713
$506$	−6.95317	+	12.0432i	−0.309106	+	0.535388i
$507$		0			0
$508$	7.34301	+	12.7185i	0.325793	+	0.564290i
$509$	9.90746	−	17.1602i	0.439141	−	0.760614i	−0.558483	−	0.829516i	$-0.688616\pi$
$509$	9.90746	−	17.1602i	0.439141	−	0.760614i	0.997623	+	0.0689022i	$0.0219497\pi$
$510$	6.76454			0.299539
$511$	2.66202	−	23.9376i	0.117761	−	1.05894i
$512$	−47.4335			−2.09628
$513$	5.46966	−	9.47373i	0.241491	−	0.418276i
$514$	−10.3370	−	17.9043i	−0.455947	−	0.789724i
$515$	9.24299	+	16.0093i	0.407295	+	0.705455i
$516$	4.08967	−	7.08352i	0.180038	−	0.311835i
$517$	2.85396			0.125517
$518$	4.50655	−	40.5242i	0.198007	−	1.78053i
$519$	−6.64237			−0.291568
$520$		0			0
$521$	15.5476	+	26.9292i	0.681151	+	1.17979i	0.974630	+	0.223823i	$0.0718537\pi$
$521$	15.5476	+	26.9292i	0.681151	+	1.17979i	−0.293479	+	0.955966i	$0.594813\pi$
$522$	−18.9924	−	32.8959i	−0.831277	−	1.43981i
$523$	−11.3601	+	19.6763i	−0.496742	+	0.860383i	−0.999993	−	0.00375758i	$-0.998804\pi$
$523$	−11.3601	+	19.6763i	−0.496742	+	0.860383i	0.503251	+	0.864140i	$0.332137\pi$
$524$	47.9919			2.09654
$525$	3.01717	−	1.32158i	0.131680	−	0.0576786i
$526$	13.0966			0.571040
$527$	−16.3804	+	28.3716i	−0.713540	+	1.23589i
$528$	−6.09798	−	10.5620i	−0.265380	−	0.459652i
$529$	9.52783	+	16.5027i	0.414253	+	0.717508i
$530$	−15.1597	+	26.2574i	−0.658495	+	1.14055i
$531$	−31.2013			−1.35402
$532$	36.8802	+	27.1364i	1.59896	+	1.17651i
$533$		0			0
$534$	−1.18097	+	2.04549i	−0.0511054	+	0.0885171i
$535$	4.13915	+	7.16922i	0.178951	+	0.309952i
$536$	47.4782	+	82.2346i	2.05074	+	3.55199i
$537$	−0.477046	+	0.826267i	−0.0205860	+	0.0356561i
$538$	35.9563			1.55018
$539$	12.8386	−	13.9174i	0.552998	−	0.599463i
$540$	−22.5176			−0.969002
$541$	−1.04936	+	1.81754i	−0.0451155	+	0.0781423i	−0.887701	−	0.460420i	$-0.847699\pi$
$541$	−1.04936	+	1.81754i	−0.0451155	+	0.0781423i	0.842586	+	0.538562i	$0.181032\pi$
$542$	10.7779	+	18.6679i	0.462951	+	0.801855i
$543$	−0.855283	−	1.48139i	−0.0367037	−	0.0635727i
$544$	−13.3325	+	23.0926i	−0.571627	+	0.990087i
$545$	2.78536			0.119312
$546$		0			0
$547$	25.3770			1.08504			0.542521	−	0.840042i	$-0.317470\pi$
$547$	25.3770			1.08504			0.542521	+	0.840042i	$0.317470\pi$
$548$	23.4869	−	40.6805i	1.00331	−	1.73778i
$549$	−3.99447	−	6.91862i	−0.170480	−	0.295280i
$550$	8.40696	+	14.5613i	0.358474	+	0.620895i
$551$	9.88983	−	17.1297i	0.421321	−	0.729749i
$552$	7.19902			0.306411
$553$	15.0395	−	6.58760i	0.639543	−	0.280133i
$554$	−60.0855			−2.55279
$555$	−2.48794	+	4.30923i	−0.105607	+	0.182917i
$556$	3.91158	+	6.77506i	0.165888	+	0.287327i
$557$	22.1252	+	38.3219i	0.937473	+	1.62375i	0.770164	+	0.637846i	$0.220174\pi$
$557$	22.1252	+	38.3219i	0.937473	+	1.62375i	0.167309	+	0.985904i	$0.446492\pi$
$558$	37.0397	−	64.1547i	1.56802	−	2.71588i
$559$		0			0
$560$	4.09944	−	36.8634i	0.173233	−	1.55776i
$561$	4.38484			0.185128
$562$	−35.1526	+	60.8860i	−1.48282	+	2.56832i
$563$	19.4453	+	33.6803i	0.819523	+	1.41946i	0.906034	+	0.423205i	$0.139095\pi$
$563$	19.4453	+	33.6803i	0.819523	+	1.41946i	−0.0865108	+	0.996251i	$0.527572\pi$
$564$	−1.28574	−	2.22697i	−0.0541396	−	0.0937725i
$565$	6.92468	−	11.9939i	0.291324	−	0.504587i
$566$	−41.8092			−1.75737
$567$	1.94548	−	17.4943i	0.0817026	−	0.734693i
$568$	−9.44618			−0.396353
$569$	−23.0789	+	39.9739i	−0.967520	+	1.67579i	−0.264832	+	0.964294i	$0.585317\pi$
$569$	−23.0789	+	39.9739i	−0.967520	+	1.67579i	−0.702687	+	0.711499i	$0.748017\pi$
$570$	−3.98254	−	6.89796i	−0.166810	−	0.288924i
$571$	−10.5684	−	18.3050i	−0.442274	−	0.766041i	0.555584	−	0.831461i	$-0.312495\pi$
$571$	−10.5684	−	18.3050i	−0.442274	−	0.766041i	−0.997858	+	0.0654194i	$0.979161\pi$
$572$		0			0
$573$	2.53848			0.106047
$574$	48.3144	−	21.1627i	2.01660	−	0.883314i
$575$	−4.76904			−0.198883
$576$	6.39653	−	11.0791i	0.266522	−	0.461630i
$577$	−12.6652	−	21.9368i	−0.527259	−	0.913239i	−0.999495	−	0.0317671i	$-0.989887\pi$
$577$	−12.6652	−	21.9368i	−0.527259	−	0.913239i	0.472237	−	0.881472i	$-0.343447\pi$
$578$	9.35045	+	16.1955i	0.388927	+	0.673642i
$579$	−0.782650	+	1.35559i	−0.0325258	+	0.0563364i
$580$	−40.7146			−1.69058
$581$	−5.74681	−	4.22849i	−0.238418	−	0.175427i
$582$	20.7785			0.861295
$583$	−9.82667	+	17.0203i	−0.406979	+	0.704908i
$584$	−31.8227	−	55.1186i	−1.31683	−	2.28082i
$585$		0			0
$586$	18.9553	−	32.8315i	0.783036	−	1.35626i
$587$	3.56287			0.147056			0.0735278	−	0.997293i	$-0.476574\pi$
$587$	3.56287			0.147056			0.0735278	+	0.997293i	$0.476574\pi$
$588$	−16.6438	−	3.74815i	−0.686379	−	0.154571i
$589$	38.5749			1.58945
$590$	−23.8361	+	41.2853i	−0.981316	+	1.69969i
$591$	−1.20541	−	2.08783i	−0.0495839	−	0.0858819i
$592$	−25.8866	−	44.8369i	−1.06393	−	1.84278i
$593$	−12.6768	+	21.9568i	−0.520573	+	0.901659i	0.479141	+	0.877738i	$0.340948\pi$
$593$	−12.6768	+	21.9568i	−0.520573	+	0.901659i	−0.999714	+	0.0239212i	$0.992385\pi$
$594$	−20.8061			−0.853685
$595$	10.7410	+	7.90320i	0.440338	+	0.324000i
$596$	93.0677			3.81220
$597$	−0.106472	+	0.184415i	−0.00435762	+	0.00754762i
$598$		0			0
$599$	−5.46078	−	9.45835i	−0.223122	−	0.386458i	0.732633	−	0.680624i	$-0.238291\pi$
$599$	−5.46078	−	9.45835i	−0.223122	−	0.386458i	−0.955754	+	0.294166i	$0.904958\pi$
$600$	4.35211	−	7.53807i	0.177674	−	0.307740i
$601$	24.2564			0.989439			0.494720	−	0.869053i	$-0.335271\pi$
$601$	24.2564			0.989439			0.494720	+	0.869053i	$0.335271\pi$
$602$	21.0534	−	9.22183i	0.858074	−	0.375854i
$603$	37.0946			1.51061
$604$	−17.7103	+	30.6751i	−0.720621	+	1.24815i
$605$	2.96876	+	5.14205i	0.120697	+	0.209054i
$606$	0.858476	+	1.48692i	0.0348732	+	0.0604022i
$607$	4.92724	−	8.53422i	0.199990	−	0.346393i	−0.748535	−	0.663096i	$-0.769242\pi$
$607$	4.92724	−	8.53422i	0.199990	−	0.346393i	0.948525	+	0.316702i	$0.102576\pi$
$608$	31.3974			1.27333
$609$	−0.814561	+	7.32476i	−0.0330077	+	0.296814i
$610$	−12.2062			−0.494215
$611$		0			0
$612$	20.0712	+	34.7643i	0.811328	+	1.40526i
$613$	−1.83844	−	3.18428i	−0.0742540	−	0.128612i	0.826508	−	0.562926i	$-0.190324\pi$
$613$	−1.83844	−	3.18428i	−0.0742540	−	0.128612i	−0.900762	+	0.434314i	$0.856991\pi$
$614$	11.6208	−	20.1278i	0.468977	−	0.812293i
$615$	−6.43688			−0.259560
$616$	5.53015	−	49.7286i	0.222816	−	2.00362i
$617$	−18.7468			−0.754718			−0.377359	−	0.926067i	$-0.623168\pi$
$617$	−18.7468			−0.754718			−0.377359	+	0.926067i	$0.623168\pi$
$618$	7.69517	−	13.3284i	0.309545	−	0.536148i
$619$	7.94725	+	13.7650i	0.319427	+	0.553264i	0.980369	−	0.197174i	$-0.0631763\pi$
$619$	7.94725	+	13.7650i	0.319427	+	0.553264i	−0.660942	+	0.750437i	$0.729843\pi$
$620$	−39.7014	−	68.7649i	−1.59445	−	2.76167i
$621$	2.95068	−	5.11073i	0.118407	−	0.205087i
$622$	31.5333			1.26437
$623$	−4.26499	+	1.86815i	−0.170873	+	0.0748460i
$624$		0			0
$625$	3.61371	−	6.25913i	0.144549	−	0.250365i
$626$	−16.9864	−	29.4212i	−0.678911	−	1.17591i
$627$	−2.58152	−	4.47133i	−0.103096	−	0.178568i
$628$	−32.9165	+	57.0130i	−1.31351	+	2.27507i
$629$	18.6141			0.742194
$630$	−24.2878	−	17.8709i	−0.967649	−	0.711995i
$631$	−19.7451			−0.786040			−0.393020	−	0.919530i	$-0.628570\pi$
$631$	−19.7451			−0.786040			−0.393020	+	0.919530i	$0.628570\pi$
$632$	21.6936	−	37.5745i	0.862927	−	1.49463i
$633$	1.94839	+	3.37472i	0.0774417	+	0.134133i
$634$	21.6349	+	37.4727i	0.859231	+	1.48823i
$635$	2.51812	−	4.36151i	0.0999286	−	0.173081i
$636$	17.7081			0.702173
$637$		0			0
$638$	−37.6200			−1.48939
$639$	−1.84507	+	3.19575i	−0.0729898	+	0.126422i
$640$	3.97508	+	6.88504i	0.157129	+	0.272155i
$641$	14.8893	+	25.7890i	0.588092	+	1.01860i	0.994482	+	0.104905i	$0.0334539\pi$
$641$	14.8893	+	25.7890i	0.588092	+	1.01860i	−0.406390	+	0.913699i	$0.633213\pi$
$642$	3.44601	−	5.96867i	0.136003	−	0.235565i
$643$	−11.5725			−0.456373			−0.228187	−	0.973617i	$-0.573280\pi$
$643$	−11.5725			−0.456373			−0.228187	+	0.973617i	$0.573280\pi$
$644$	19.8955	+	14.6391i	0.783994	+	0.576862i
$645$	−2.80493			−0.110444
$646$	−14.8982	+	25.8044i	−0.586162	+	1.01526i
$647$	−12.7533	−	22.0893i	−0.501382	−	0.868420i	−0.999999	−	0.00159698i	$-0.999492\pi$
$647$	−12.7533	−	22.0893i	−0.501382	−	0.868420i	0.498616	−	0.866823i	$-0.333842\pi$
$648$	−23.2570	−	40.2823i	−0.913620	−	1.58244i
$649$	−15.4508	+	26.7616i	−0.606497	+	1.05048i
$650$		0			0
$651$	−13.1655	+	5.76675i	−0.515995	+	0.226017i
$652$	−33.7049			−1.31999
$653$	22.4146	−	38.8233i	0.877152	−	1.51927i	0.0227004	−	0.999742i	$-0.492774\pi$
$653$	22.4146	−	38.8233i	0.877152	−	1.51927i	0.854452	−	0.519530i	$-0.173893\pi$
$654$	−1.15946	−	2.00825i	−0.0453386	−	0.0785287i
$655$	−8.22889	−	14.2529i	−0.321529	−	0.556905i
$656$	33.4874	−	58.0018i	1.30746	−	2.26459i
$657$	−24.8630			−0.969999
$658$	0.798661	−	7.18179i	0.0311350	−	0.279975i
$659$	41.1734			1.60389			0.801944	−	0.597399i	$-0.203799\pi$
$659$	41.1734			1.60389			0.801944	+	0.597399i	$0.203799\pi$
$660$	−5.31382	+	9.20380i	−0.206840	+	0.358258i
$661$	10.9469	+	18.9606i	0.425785	+	0.737481i	0.996493	−	0.0836719i	$-0.0266648\pi$
$661$	10.9469	+	18.9606i	0.425785	+	0.737481i	−0.570709	+	0.821153i	$0.693331\pi$
$662$	5.13404	+	8.89241i	0.199540	+	0.345613i
$663$		0			0
$664$	−18.8539			−0.731673
$665$	1.73546	−	15.6058i	0.0672983	−	0.605165i
$666$	−42.0908			−1.63098
$667$	5.33520	−	9.24084i	0.206580	−	0.357807i
$668$	42.2620	+	73.1999i	1.63516	+	2.83219i
$669$	5.85334	+	10.1383i	0.226303	+	0.391968i
$670$	28.3382	−	49.0832i	1.09480	−	1.89625i
$671$	−7.91219			−0.305447
$672$	−10.7158	+	4.69375i	−0.413371	+	0.181065i
$673$	35.6688			1.37493			0.687466	−	0.726217i	$-0.258723\pi$
$673$	35.6688			1.37493			0.687466	+	0.726217i	$0.258723\pi$
$674$	−17.7361	+	30.7197i	−0.683167	+	1.18328i
$675$	−3.56762	−	6.17930i	−0.137318	−	0.237841i
$676$		0			0
$677$	−1.27766	+	2.21297i	−0.0491044	+	0.0850514i	−0.889533	−	0.456871i	$-0.848970\pi$
$677$	−1.27766	+	2.21297i	−0.0491044	+	0.0850514i	0.840428	+	0.541923i	$0.182303\pi$
$678$	−11.5302			−0.442813
$679$	32.9928	+	24.2761i	1.26615	+	0.931630i
$680$	35.2386			1.35134
$681$	−3.54416	+	6.13867i	−0.135813	+	0.235234i
$682$	−36.6839	−	63.5384i	−1.40470	−	2.43301i
$683$	−17.8700	−	30.9517i	−0.683775	−	1.18433i	−0.973820	−	0.227320i	$-0.927004\pi$
$683$	−17.8700	−	30.9517i	−0.683775	−	1.18433i	0.290045	−	0.957013i	$-0.406330\pi$
$684$	23.6333	−	40.9341i	0.903642	−	1.56515i
$685$	−16.1086			−0.615479
$686$	−31.4293	−	36.2021i	−1.19997	−	1.38220i
$687$	4.11188			0.156878
$688$	14.5924	−	25.2748i	0.556330	−	0.963592i
$689$		0			0
$690$	−2.14843	−	3.72120i	−0.0817895	−	0.141664i
$691$	13.0146	−	22.5419i	0.495099	−	0.857536i	−0.504885	−	0.863186i	$-0.668465\pi$
$691$	13.0146	−	22.5419i	0.495099	−	0.857536i	0.999984	+	0.00565028i	$0.00179855\pi$
$692$	−60.2254			−2.28943
$693$	−15.7436	−	11.5841i	−0.598050	−	0.440045i
$694$	−68.3335			−2.59391
$695$	1.34139	−	2.32336i	0.0508818	−	0.0881299i
$696$	9.73755	+	16.8659i	0.369101	+	0.639301i
$697$	12.0398	+	20.8535i	0.456040	+	0.789884i
$698$	−6.32944	+	10.9629i	−0.239573	+	0.414952i
$699$	−3.40721			−0.128872
$700$	27.3562	−	11.9826i	1.03397	−	0.452899i
$701$	1.12731			0.0425779			0.0212890	−	0.999773i	$-0.493223\pi$
$701$	1.12731			0.0425779			0.0212890	+	0.999773i	$0.493223\pi$
$702$		0			0
$703$	−10.9588	−	18.9813i	−0.413321	−	0.715892i
$704$	−6.33509	−	10.9727i	−0.238763	−	0.413549i
$705$	−0.440917	+	0.763691i	−0.0166059	+	0.0287623i
$706$	35.0955			1.32084
$707$	−0.374096	+	3.36398i	−0.0140693	+	0.126515i
$708$	27.8431			1.04641
$709$	−3.02515	+	5.23972i	−0.113612	+	0.196782i	−0.917224	−	0.398372i	$-0.869575\pi$
$709$	−3.02515	+	5.23972i	−0.113612	+	0.196782i	0.803612	+	0.595153i	$0.202909\pi$
$710$	2.81906	+	4.88276i	0.105798	+	0.183247i
$711$	−8.47459	−	14.6784i	−0.317822	−	0.550484i
$712$	−6.15202	+	10.6556i	−0.230557	+	0.399336i
$713$	20.8098			0.779332
$714$	1.22707	−	11.0341i	0.0459219	−	0.412942i
$715$		0			0
$716$	−4.32530	+	7.49164i	−0.161644	+	0.279976i
$717$	2.43493	+	4.21743i	0.0909342	+	0.157503i
$718$	−11.1124	−	19.2473i	−0.414713	−	0.718304i
$719$	−23.5589	+	40.8052i	−0.878597	+	1.52178i	−0.0257170	+	0.999669i	$0.508187\pi$
$719$	−23.5589	+	40.8052i	−0.878597	+	1.52178i	−0.852880	+	0.522106i	$0.825146\pi$
$720$	−38.2884			−1.42692
$721$	27.7907	−	12.1729i	1.03498	−	0.453342i
$722$	−14.0989			−0.524706
$723$	2.61458	−	4.52859i	0.0972374	−	0.168420i
$724$	−7.75473	−	13.4316i	−0.288202	−	0.499181i
$725$	−6.45070	−	11.1729i	−0.239573	−	0.414953i
$726$	2.47162	−	4.28097i	0.0917303	−	0.158882i
$727$	−17.9215			−0.664671			−0.332335	−	0.943161i	$-0.607837\pi$
$727$	−17.9215			−0.664671			−0.332335	+	0.943161i	$0.607837\pi$
$728$		0			0
$729$	−13.5489			−0.501810
$730$	−18.9940	+	32.8985i	−0.702999	+	1.21763i
$731$	5.24644	+	9.08711i	0.194047	+	0.336099i
$732$	3.56454	+	6.17396i	0.131749	+	0.228196i
$733$	−22.6343	+	39.2037i	−0.836016	+	1.44802i	0.0571848	+	0.998364i	$0.481788\pi$
$733$	−22.6343	+	39.2037i	−0.836016	+	1.44802i	−0.893201	+	0.449658i	$0.851546\pi$
$734$	−4.30542			−0.158916
$735$	1.74067	+	5.58562i	0.0642056	+	0.206029i
$736$	16.9378			0.624335
$737$	18.3691	−	31.8163i	0.676635	−	1.17197i
$738$	−27.2247	−	47.1546i	−1.00215	−	1.73578i
$739$	−9.63066	−	16.6808i	−0.354270	−	0.613613i	0.632723	−	0.774378i	$-0.281937\pi$
$739$	−9.63066	−	16.6808i	−0.354270	−	0.613613i	−0.986993	+	0.160765i	$0.948604\pi$
$740$	−22.5577	+	39.0712i	−0.829239	+	1.43628i
$741$		0			0
$742$	40.0804	+	29.4911i	1.47140	+	1.08265i
$743$	34.8853			1.27982			0.639908	−	0.768452i	$-0.278972\pi$
$743$	34.8853			1.27982			0.639908	+	0.768452i	$0.278972\pi$
$744$	−18.9905	+	32.8925i	−0.696225	+	1.20590i
$745$	−15.9577	−	27.6396i	−0.584647	−	1.01264i
$746$	−18.0729	−	31.3032i	−0.661697	−	1.14609i
$747$	−3.68263	+	6.37850i	−0.134740	+	0.233377i
$748$	39.7567			1.45365
$749$	12.4451	−	5.45120i	0.454733	−	0.199183i
$750$	−16.0130			−0.584711
$751$	12.4834	−	21.6219i	0.455526	−	0.788993i	−0.543193	−	0.839608i	$-0.682785\pi$
$751$	12.4834	−	21.6219i	0.455526	−	0.788993i	0.998718	+	0.0506146i	$0.0161180\pi$
$752$	−4.58767	−	7.94609i	−0.167295	−	0.289764i
$753$	2.68268	+	4.64654i	0.0977623	+	0.169329i
$754$		0			0
$755$	12.1467			0.442064
$756$	−4.08462	+	36.7301i	−0.148556	+	1.33586i
$757$	−10.6049			−0.385440			−0.192720	−	0.981254i	$-0.561731\pi$
$757$	−10.6049			−0.385440			−0.192720	+	0.981254i	$0.561731\pi$
$758$	40.8685	−	70.7863i	1.48441	−	2.57108i
$759$	−1.39264	−	2.41212i	−0.0505495	−	0.0875543i
$760$	−20.7463	−	35.9337i	−0.752548	−	1.30345i
$761$	16.3194	−	28.2660i	0.591578	−	1.02464i	−0.402442	−	0.915446i	$-0.631838\pi$
$761$	16.3194	−	28.2660i	0.591578	−	1.02464i	0.994020	−	0.109198i	$-0.0348282\pi$
$762$	−4.19288			−0.151892
$763$	0.505256	−	4.54340i	0.0182915	−	0.164482i
$764$	23.0160			0.832691
$765$	6.88296	−	11.9216i	0.248854	−	0.431028i
$766$	41.2988	+	71.5316i	1.49219	+	2.58454i
$767$		0			0
$768$	5.73794	−	9.93841i	0.207050	−	0.358621i
$769$	−52.1752			−1.88149			−0.940744	−	0.339119i	$-0.889871\pi$
$769$	−52.1752			−1.88149			−0.940744	+	0.339119i	$0.889871\pi$
$770$	−27.3553	+	11.9822i	−0.985815	+	0.431807i
$771$	4.14077			0.149126
$772$	−7.09618	+	12.2909i	−0.255397	+	0.442360i
$773$	17.8529	+	30.9221i	0.642123	+	1.11219i	0.984958	+	0.172794i	$0.0552794\pi$
$773$	17.8529	+	30.9221i	0.642123	+	1.11219i	−0.342835	+	0.939396i	$0.611387\pi$
$774$	−11.8634	−	20.5480i	−0.426421	−	0.738583i
$775$	12.5804	−	21.7898i	0.451900	−	0.782714i
$776$	108.242			3.88565
$777$	6.57780	+	4.83994i	0.235977	+	0.173632i
$778$	−65.7893			−2.35866
$779$	14.1766	−	24.5545i	0.507928	−	0.879757i
$780$		0			0
$781$	1.82735	+	3.16506i	0.0653876	+	0.113255i
$782$	−8.03703	+	13.9206i	−0.287404	+	0.497798i
$783$	15.9646			0.570529
$784$	−59.3870	−	13.3738i	−2.12096	−	0.477636i
$785$	22.5760			0.805770
$786$	−6.85089	+	11.8661i	−0.244363	+	0.423249i
$787$	3.05310	+	5.28813i	0.108831	+	0.188501i	0.915297	−	0.402779i	$-0.131956\pi$
$787$	3.05310	+	5.28813i	0.108831	+	0.188501i	−0.806466	+	0.591281i	$0.798622\pi$
$788$	−10.9293	−	18.9301i	−0.389339	−	0.674356i
$789$	−1.31155	+	2.27167i	−0.0466923	+	0.0808735i
$790$	−25.8965			−0.921356
$791$	−18.3080	−	13.4710i	−0.650959	−	0.478975i
$792$	−51.6510			−1.83534
$793$		0			0
$794$	−5.38296	−	9.32356i	−0.191034	−	0.330881i
$795$	−3.03631	−	5.25904i	−0.107687	−	0.186519i
$796$	−0.965369	+	1.67207i	−0.0342166	+	0.0592649i
$797$	−46.2299			−1.63755			−0.818773	−	0.574117i	$-0.805346\pi$
$797$	−46.2299			−1.63755			−0.818773	+	0.574117i	$0.805346\pi$
$798$	−11.9742	+	5.24495i	−0.423882	+	0.185669i
$799$	3.29884			0.116704
$800$	10.2396	−	17.7355i	0.362024	−	0.627044i
$801$	2.40328	+	4.16260i	0.0849157	+	0.147078i
$802$	25.3700	+	43.9422i	0.895847	+	1.55165i
$803$	−12.3121	+	21.3252i	−0.434484	+	0.752549i
$804$	−33.1020			−1.16742
$805$	0.936218	−	8.41874i	0.0329974	−	0.296722i
$806$		0			0
$807$	−3.60080	+	6.23678i	−0.126754	+	0.219545i
$808$	4.47208	+	7.74586i	0.157327	+	0.272498i
$809$	−19.6439	−	34.0243i	−0.690644	−	1.19623i	−0.971627	−	0.236518i	$-0.923994\pi$
$809$	−19.6439	−	34.0243i	−0.690644	−	1.19623i	0.280983	−	0.959713i	$-0.409339\pi$
$810$	−13.8814	+	24.0432i	−0.487741	+	0.844792i
$811$	−6.90664			−0.242525			−0.121262	−	0.992620i	$-0.538694\pi$
$811$	−6.90664			−0.242525			−0.121262	+	0.992620i	$0.538694\pi$
$812$	−7.38551	+	66.4126i	−0.259180	+	2.33062i
$813$	−4.31738			−0.151417
$814$	−20.8432	+	36.1015i	−0.730555	+	1.26536i
$815$	5.77917	+	10.0098i	0.202436	+	0.350629i
$816$	−7.04853	−	12.2084i	−0.246748	−	0.427380i
$817$	6.17756	−	10.6998i	0.216125	−	0.374340i
$818$	−45.6466			−1.59600
$819$		0			0
$820$	−58.3622			−2.03810
$821$	−0.955244	+	1.65453i	−0.0333382	+	0.0577435i	−0.882213	−	0.470850i	$-0.843947\pi$
$821$	−0.955244	+	1.65453i	−0.0333382	+	0.0577435i	0.848875	+	0.528594i	$0.177281\pi$
$822$	6.70554	+	11.6143i	0.233883	+	0.405097i
$823$	−0.789844	−	1.36805i	−0.0275322	−	0.0476872i	0.851931	−	0.523654i	$-0.175432\pi$
$823$	−0.789844	−	1.36805i	−0.0275322	−	0.0476872i	−0.879463	+	0.475967i	$0.842098\pi$
$824$	40.0866	−	69.4320i	1.39648	−	2.41878i
$825$	−3.36763			−0.117246
$826$	63.0198	+	46.3699i	2.19274	+	1.61341i
$827$	32.5050			1.13031			0.565155	−	0.824985i	$-0.308816\pi$
$827$	32.5050			1.13031			0.565155	+	0.824985i	$0.308816\pi$
$828$	12.7493	−	22.0824i	0.443069	−	0.767418i
$829$	17.5269	+	30.3575i	0.608735	+	1.05436i	0.991449	+	0.130493i	$0.0416561\pi$
$829$	17.5269	+	30.3575i	0.608735	+	1.05436i	−0.382714	+	0.923867i	$0.625011\pi$
$830$	5.62665	+	9.74564i	0.195304	+	0.338276i
$831$	6.01721	−	10.4221i	0.208735	−	0.361539i
$832$		0			0
$833$	14.8399	−	16.0868i	0.514172	−	0.557375i
$834$	−2.23353			−0.0773407
$835$	14.4928	−	25.1023i	0.501544	−	0.868700i
$836$	−23.4063	−	40.5409i	−0.809523	−	1.40214i
$837$	15.5674	+	26.9635i	0.538087	+	0.931994i
$838$	−38.6880	+	67.0096i	−1.33645	+	2.31481i
$839$	5.35487			0.184871			0.0924354	−	0.995719i	$-0.470535\pi$
$839$	5.35487			0.184871			0.0924354	+	0.995719i	$0.470535\pi$
$840$	12.4525	+	9.16254i	0.429653	+	0.316138i
$841$	−0.133978			−0.00461993
$842$	16.6354	−	28.8133i	0.573293	−	0.992973i
$843$	−7.04064	−	12.1947i	−0.242492	−	0.420009i
$844$	17.6658	+	30.5981i	0.608082	+	1.05323i
$845$		0			0
$846$	−7.45942			−0.256460
$847$	8.92611	−	3.90982i	0.306705	−	0.134343i
$848$	63.1846			2.16977
$849$	4.18694	−	7.25199i	0.143695	−	0.248888i
$850$	9.71744	+	16.8311i	0.333305	+	0.577302i
$851$	−5.91190	−	10.2397i	−0.202657	−	0.351013i
$852$	1.64648	−	2.85179i	0.0564076	−	0.0977008i
$853$	49.6270			1.69920			0.849598	−	0.527431i	$-0.176845\pi$
$853$	49.6270			1.69920			0.849598	+	0.527431i	$0.176845\pi$
$854$	−2.21417	+	19.9105i	−0.0757675	+	0.681322i
$855$	−16.2090			−0.554337
$856$	17.9514	−	31.0927i	0.613566	−	1.06273i
$857$	−2.94196	−	5.09563i	−0.100496	−	0.174063i	0.811393	−	0.584500i	$-0.198709\pi$
$857$	−2.94196	−	5.09563i	−0.100496	−	0.174063i	−0.911889	+	0.410437i	$0.865376\pi$
$858$		0			0
$859$	−21.6931	+	37.5735i	−0.740159	+	1.28199i	0.212264	+	0.977212i	$0.431916\pi$
$859$	−21.6931	+	37.5735i	−0.740159	+	1.28199i	−0.952423	+	0.304780i	$0.901417\pi$
$860$	−25.4318			−0.867219
$861$	−1.16763	+	10.4997i	−0.0397928	+	0.357828i
$862$	−23.2213			−0.790920
$863$	15.5636	−	26.9570i	0.529792	−	0.917626i	−0.469604	−	0.882877i	$-0.655603\pi$
$863$	15.5636	−	26.9570i	0.529792	−	0.917626i	0.999396	−	0.0347490i	$-0.0110632\pi$
$864$	12.6708	+	21.9465i	0.431069	+	0.746634i
$865$	10.3265	+	17.8860i	0.351111	+	0.608142i
$866$	4.46614	−	7.73558i	0.151766	−	0.262866i
$867$	−3.74557			−0.127206
$868$	−119.369	+	52.2862i	−4.05166	+	1.77471i
$869$	−16.7864			−0.569439
$870$	5.81203	−	10.0667i	0.197046	−	0.341294i
$871$		0			0
$872$	−6.04001	−	10.4616i	−0.204540	−	0.354274i
$873$	21.1422	−	36.6194i	0.715556	−	1.23938i
$874$	18.9268			0.640209
$875$	−25.4260	−	18.7084i	−0.859555	−	0.632460i
$876$	22.1870			0.749629
$877$	−14.9553	+	25.9033i	−0.505004	+	0.874693i	0.494979	+	0.868905i	$0.335176\pi$
$877$	−14.9553	+	25.9033i	−0.505004	+	0.874693i	−0.999983	+	0.00578807i	$0.998158\pi$
$878$	49.8492	+	86.3413i	1.68233	+	2.91388i
$879$	3.79652	+	6.57576i	0.128053	+	0.221795i
$880$	−18.9603	+	32.8402i	−0.639152	+	1.10704i
$881$	14.5695			0.490860			0.245430	−	0.969414i	$-0.421071\pi$
$881$	14.5695			0.490860			0.245430	+	0.969414i	$0.421071\pi$
$882$	−33.5564	+	36.3759i	−1.12990	+	1.22484i
$883$	−48.9296			−1.64661			−0.823307	−	0.567597i	$-0.807873\pi$
$883$	−48.9296			−1.64661			−0.823307	+	0.567597i	$0.807873\pi$
$884$		0			0
$885$	−4.77408	−	8.26896i	−0.160479	−	0.277958i
$886$	19.4662	+	33.7164i	0.653980	+	1.13273i
$887$	−27.2951	+	47.2765i	−0.916480	+	1.58739i	−0.111761	+	0.993735i	$0.535649\pi$
$887$	−27.2951	+	47.2765i	−0.916480	+	1.58739i	−0.804719	+	0.593655i	$0.797684\pi$
$888$	21.5802			0.724184
$889$	−6.65761	−	4.89866i	−0.223289	−	0.164296i
$890$	7.34389			0.246168
$891$	−8.99803	+	15.5851i	−0.301445	+	0.522119i
$892$	53.0713	+	91.9222i	1.77696	+	3.07778i
$893$	−1.94215	−	3.36390i	−0.0649916	−	0.112569i
$894$	−13.2855	+	23.0111i	−0.444333	+	0.769607i
$895$	2.96653			0.0991603
$896$	11.9518	−	5.23512i	0.399281	−	0.174893i
$897$		0			0
$898$	−50.3787	+	87.2584i	−1.68116	+	2.91185i
$899$	28.1477	+	48.7533i	0.938780	+	1.62601i
$900$	−15.4150	−	26.6995i	−0.513832	−	0.889983i
$901$	−11.3585	+	19.6734i	−0.378405	+	0.655417i
$902$	−53.9263			−1.79555
$903$	−0.508806	+	4.57532i	−0.0169320	+	0.152257i
$904$	−60.0643			−1.99771
$905$	−2.65931	+	4.60606i	−0.0883985	+	0.153111i
$906$	−5.05632	−	8.75780i	−0.167985	−	0.290958i
$907$	−11.3628	−	19.6809i	−0.377295	−	0.653494i	0.613373	−	0.789793i	$-0.289812\pi$
$907$	−11.3628	−	19.6809i	−0.377295	−	0.653494i	−0.990668	+	0.136300i	$0.956479\pi$
$908$	−32.1344	+	55.6584i	−1.06642	+	1.84709i
$909$	3.49402			0.115889
$910$		0			0
$911$	−42.2359			−1.39934			−0.699669	−	0.714467i	$-0.746669\pi$
$911$	−42.2359			−1.39934			−0.699669	+	0.714467i	$0.746669\pi$
$912$	−8.29948	+	14.3751i	−0.274823	+	0.476008i
$913$	3.64725	+	6.31722i	0.120706	+	0.209070i
$914$	−18.0421	−	31.2498i	−0.596779	−	1.03365i
$915$	1.22238	−	2.11722i	0.0404106	−	0.0699933i
$916$	37.2818			1.23182
$917$	−24.7416	+	10.8373i	−0.817039	+	0.357880i
$918$	−24.0494			−0.793747
$919$	−15.3470	+	26.5818i	−0.506251	+	0.876853i	0.493722	+	0.869620i	$0.335636\pi$
$919$	−15.3470	+	26.5818i	−0.506251	+	0.876853i	−0.999974	+	0.00723365i	$0.997697\pi$
$920$	−11.1919	−	19.3849i	−0.368985	−	0.639101i
$921$	2.32751	+	4.03136i	0.0766940	+	0.132838i
$922$	48.4890	−	83.9854i	1.59690	−	2.76591i
$923$		0			0
$924$	14.0491	+	10.3373i	0.462182	+	0.340073i
$925$	−14.2959			−0.470048
$926$	8.74009	−	15.1383i	0.287217	−	0.497474i
$927$	−15.6598	−	27.1235i	−0.514334	−	0.890853i
$928$	22.9104	+	39.6819i	0.752070	+	1.30262i
$929$	18.7125	−	32.4110i	0.613936	−	1.06337i	−0.376634	−	0.926362i	$-0.622918\pi$
$929$	18.7125	−	32.4110i	0.613936	−	1.06337i	0.990570	−	0.137007i	$-0.0437482\pi$
$930$	22.6696			0.743367
$931$	−25.1409	−	5.66168i	−0.823960	−	0.185554i
$932$	−30.8926			−1.01192
$933$	−3.15787	+	5.46960i	−0.103384	+	0.179067i
$934$	−6.53663	−	11.3218i	−0.213885	−	0.370460i
$935$	−6.81684	−	11.8071i	−0.222935	−	0.386134i
$936$		0			0
$937$	44.3386			1.44848			0.724239	−	0.689549i	$-0.242191\pi$
$937$	44.3386			1.44848			0.724239	+	0.689549i	$0.242191\pi$
$938$	−74.9229	−	55.1282i	−2.44632	−	1.80000i
$939$	6.80433			0.222051
$940$	−3.99773	+	6.92427i	−0.130392	+	0.225845i
$941$	13.7526	+	23.8202i	0.448323	+	0.776518i	0.998277	−	0.0586770i	$-0.0186882\pi$
$941$	13.7526	+	23.8202i	0.448323	+	0.776518i	−0.549954	+	0.835195i	$0.685355\pi$
$942$	−9.39771	−	16.2773i	−0.306194	−	0.530343i
$943$	7.64774	−	13.2463i	0.249045	−	0.431358i
$944$	99.3472			3.23348
$945$	11.6086	−	5.08482i	0.377629	−	0.165409i
$946$	−23.4989			−0.764014
$947$	−2.54165	+	4.40226i	−0.0825925	+	0.143054i	−0.904363	−	0.426765i	$-0.859653\pi$
$947$	−2.54165	+	4.40226i	−0.0825925	+	0.143054i	0.821770	+	0.569819i	$0.192987\pi$
$948$	7.56246	+	13.0986i	0.245617	+	0.425422i
$949$		0			0
$950$	11.4420	−	19.8182i	0.371229	−	0.642987i
$951$	−8.66642			−0.281028
$952$	6.39219	−	57.4804i	0.207172	−	1.86295i
$953$	9.81437			0.317919			0.158959	−	0.987285i	$-0.449186\pi$
$953$	9.81437			0.317919			0.158959	+	0.987285i	$0.449186\pi$
$954$	25.6840	−	44.4861i	0.831552	−	1.44029i
$955$	−3.94642	−	6.83540i	−0.127703	−	0.221188i
$956$	22.0772	+	38.2388i	0.714027	+	1.23673i
$957$	3.76742	−	6.52536i	0.121783	−	0.210935i
$958$	24.4705			0.790607
$959$	−2.92206	+	26.2760i	−0.0943582	+	0.848496i
$960$	3.91491			0.126353
$961$	−39.3947	+	68.2336i	−1.27080	+	2.20108i
$962$		0			0
$963$	−7.01268	−	12.1463i	−0.225981	−	0.391410i
$964$	23.7060	−	41.0601i	0.763520	−	1.32246i
$965$	4.86695			0.156673
$966$	−6.45965	+	2.82946i	−0.207836	+	0.0910363i
$967$	−2.69619			−0.0867036			−0.0433518	−	0.999060i	$-0.513804\pi$
$967$	−2.69619			−0.0867036			−0.0433518	+	0.999060i	$0.513804\pi$
$968$	12.8754	−	22.3009i	0.413832	−	0.716779i
$969$	−2.98393	−	5.16832i	−0.0958577	−	0.166030i
$970$	−32.3030	−	55.9504i	−1.03719	−	1.79646i
$971$	−12.4620	+	21.5848i	−0.399925	+	0.692691i	−0.993716	−	0.111929i	$-0.964297\pi$
$971$	−12.4620	+	21.5848i	−0.399925	+	0.692691i	0.593791	+	0.804619i	$0.297631\pi$
$972$	58.1196			1.86419
$973$	−3.54648	−	2.60949i	−0.113695	−	0.0836565i
$974$	103.543			3.31773
$975$		0			0
$976$	12.7187	+	22.0294i	0.407115	+	0.705144i
$977$	14.1565	+	24.5197i	0.452906	+	0.784456i	0.998565	−	0.0535514i	$-0.0170541\pi$
$977$	14.1565	+	24.5197i	0.452906	+	0.784456i	−0.545659	+	0.838007i	$0.683721\pi$
$978$	4.81140	−	8.33359i	0.153852	−	0.266479i
$979$	4.76039			0.152143
$980$	15.7824	+	50.6440i	0.504150	+	1.61776i
$981$	−4.71904			−0.150667
$982$	8.75073	−	15.1567i	0.279247	−	0.483670i
$983$	−18.9258	−	32.7805i	−0.603641	−	1.04554i	−0.992265	−	0.124140i	$-0.960383\pi$
$983$	−18.9258	−	32.7805i	−0.603641	−	1.04554i	0.388624	−	0.921396i	$-0.372951\pi$
$984$	13.9583	+	24.1764i	0.444974	+	0.770717i
$985$	−3.74795	+	6.49165i	−0.119420	+	0.206841i
$986$	−43.4842			−1.38482
$987$	1.16573	+	0.857744i	0.0371057	+	0.0273023i
$988$		0			0
$989$	3.33257	−	5.77218i	0.105970	−	0.183545i
$990$	15.4144	+	26.6986i	0.489903	+	0.848536i
$991$	−29.2079	−	50.5896i	−0.927820	−	1.60703i	−0.786962	−	0.617001i	$-0.788347\pi$
$991$	−29.2079	−	50.5896i	−0.927820	−	1.60703i	−0.140858	−	0.990030i	$-0.544986\pi$
$992$	−44.6806	+	77.3891i	−1.41861	+	2.45711i
$993$	−2.05657			−0.0652633
$994$	8.47601	−	3.71267i	0.268843	−	0.117759i
$995$	0.662104			0.0209901
$996$	3.28626	−	5.69197i	0.104129	−	0.180357i
$997$	−14.0294	−	24.2997i	−0.444316	−	0.769578i	0.553688	−	0.832724i	$-0.313220\pi$
$997$	−14.0294	−	24.2997i	−0.444316	−	0.769578i	−0.998004	+	0.0631462i	$0.979887\pi$
$998$	−14.7001	−	25.4613i	−0.465322	−	0.805962i
$999$	8.84514	−	15.3202i	0.279848	−	0.484711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.j.170.1		24
7.2	even	3		8281.2.a.cp.1.12		12
7.4	even	3	inner	1183.2.e.j.508.1		24
7.5	odd	6		8281.2.a.co.1.12		12
13.2	odd	12		91.2.u.b.30.1	yes	12
13.7	odd	12		91.2.k.b.23.6	yes	12
13.12	even	2	inner	1183.2.e.j.170.12		24
39.2	even	12		819.2.do.e.667.6		12
39.20	even	12		819.2.bm.f.478.1		12
91.2	odd	12		637.2.q.g.589.6		12
91.12	odd	6		8281.2.a.co.1.1		12
91.20	even	12		637.2.k.i.569.6		12
91.25	even	6	inner	1183.2.e.j.508.12		24
91.33	even	12		637.2.q.i.491.6		12
91.41	even	12		637.2.u.g.30.1		12
91.46	odd	12		91.2.u.b.88.1	yes	12
91.51	even	6		8281.2.a.cp.1.1		12
91.54	even	12		637.2.q.i.589.6		12
91.59	even	12		637.2.u.g.361.1		12
91.67	odd	12		91.2.k.b.4.1	✓	12
91.72	odd	12		637.2.q.g.491.6		12
91.80	even	12		637.2.k.i.459.1		12
273.137	even	12		819.2.do.e.361.6		12
273.158	even	12		819.2.bm.f.550.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.1	✓	12	91.67	odd	12
91.2.k.b.23.6	yes	12	13.7	odd	12
91.2.u.b.30.1	yes	12	13.2	odd	12
91.2.u.b.88.1	yes	12	91.46	odd	12
637.2.k.i.459.1		12	91.80	even	12
637.2.k.i.569.6		12	91.20	even	12
637.2.q.g.491.6		12	91.72	odd	12
637.2.q.g.589.6		12	91.2	odd	12
637.2.q.i.491.6		12	91.33	even	12
637.2.q.i.589.6		12	91.54	even	12
637.2.u.g.30.1		12	91.41	even	12
637.2.u.g.361.1		12	91.59	even	12
819.2.bm.f.478.1		12	39.20	even	12
819.2.bm.f.550.6		12	273.158	even	12
819.2.do.e.361.6		12	273.137	even	12
819.2.do.e.667.6		12	39.2	even	12
1183.2.e.j.170.1		24	1.1	even	1	trivial
1183.2.e.j.170.12		24	13.12	even	2	inner
1183.2.e.j.508.1		24	7.4	even	3	inner
1183.2.e.j.508.12		24	91.25	even	6	inner
8281.2.a.co.1.1		12	91.12	odd	6
8281.2.a.co.1.12		12	7.5	odd	6
8281.2.a.cp.1.1		12	91.51	even	6
8281.2.a.cp.1.12		12	7.2	even	3

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29430 + 2.24179i) q^{2} +(-0.259233 - 0.449005i) q^{3} +(-2.35043 - 4.07106i) q^{4} +(-0.806027 + 1.39608i) q^{5} +1.34210 q^{6} +(2.13104 + 1.56802i) q^{7} +6.99143 q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})\)	\(q+(-1.29430 + 2.24179i) q^{2} +(-0.259233 - 0.449005i) q^{3} +(-2.35043 - 4.07106i) q^{4} +(-0.806027 + 1.39608i) q^{5} +1.34210 q^{6} +(2.13104 + 1.56802i) q^{7} +6.99143 q^{8} +(1.36560 - 2.36528i) q^{9} +(-2.08648 - 3.61389i) q^{10} +(-1.35248 - 2.34256i) q^{11} +(-1.21862 + 2.11070i) q^{12} +(-6.27337 + 2.74787i) q^{14} +0.835795 q^{15} +(-4.34816 + 7.53123i) q^{16} +(-1.56330 - 2.70772i) q^{17} +(3.53498 + 6.12277i) q^{18} +(-1.84075 + 3.18828i) q^{19} +7.57803 q^{20} +(0.151611 - 1.36333i) q^{21} +7.00205 q^{22} +(-0.993019 + 1.71996i) q^{23} +(-1.81241 - 3.13918i) q^{24} +(1.20064 + 2.07957i) q^{25} -2.97143 q^{27} +(1.37463 - 12.3611i) q^{28} -5.37271 q^{29} +(-1.08177 + 1.87368i) q^{30} +(-5.23902 - 9.07425i) q^{31} +(-4.26421 - 7.38583i) q^{32} +(-0.701214 + 1.21454i) q^{33} +8.09354 q^{34} +(-3.90675 + 1.71124i) q^{35} -12.8389 q^{36} +(-2.97673 + 5.15585i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(-5.63528 + 9.76059i) q^{40} -7.70150 q^{41} +(2.86007 + 2.10444i) q^{42} -3.35600 q^{43} +(-6.35780 + 11.0120i) q^{44} +(2.20141 + 3.81296i) q^{45} +(-2.57053 - 4.45229i) q^{46} +(-0.527542 + 0.913730i) q^{47} +4.50874 q^{48} +(2.08265 + 6.68300i) q^{49} -6.21596 q^{50} +(-0.810520 + 1.40386i) q^{51} +(-3.63284 - 6.29226i) q^{53} +(3.84592 - 6.66133i) q^{54} +4.36054 q^{55} +(14.8990 + 10.9627i) q^{56} +1.90873 q^{57} +(6.95390 - 12.0445i) q^{58} +(-5.71203 - 9.89352i) q^{59} +(-1.96447 - 3.40257i) q^{60} +(1.46254 - 2.53319i) q^{61} +27.1235 q^{62} +(6.61894 - 2.89923i) q^{63} +4.68406 q^{64} +(-1.81516 - 3.14395i) q^{66} +(6.79091 + 11.7622i) q^{67} +(-7.34886 + 12.7286i) q^{68} +1.02969 q^{69} +(1.22027 - 10.9730i) q^{70} -1.35111 q^{71} +(9.54747 - 16.5367i) q^{72} +(-4.55168 - 7.88374i) q^{73} +(-7.70557 - 13.3464i) q^{74} +(0.622492 - 1.07819i) q^{75} +17.3062 q^{76} +(0.790989 - 7.11280i) q^{77} +(3.10289 - 5.37436i) q^{79} +(-7.00946 - 12.1407i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(9.96806 - 17.2652i) q^{82} -2.69672 q^{83} +(-5.90654 + 2.58718i) q^{84} +5.04026 q^{85} +(4.34367 - 7.52346i) q^{86} +(1.39278 + 2.41237i) q^{87} +(-9.45576 - 16.3779i) q^{88} +(-0.879938 + 1.52410i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(-2.71625 + 4.70469i) q^{93} +(-1.36560 - 2.36528i) q^{94} +(-2.96739 - 5.13967i) q^{95} +(-2.21085 + 3.82930i) q^{96} +15.4820 q^{97} +(-17.6775 - 3.98094i) q^{98} -7.38776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

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