LMFDB - Embedded newform 950.2.l.f.351.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	950.351
Dual form			950.2.l.f.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(1.17365 - 0.984808i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-0.939693 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.113341 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(1.17365 - 0.984808i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-0.939693 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.113341 + 0.642788i) q^{9} +(0.0812519 + 0.140732i) q^{11} +(-0.766044 + 1.32683i) q^{12} +(3.61334 + 3.03195i) q^{13} +(1.76604 + 0.642788i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.754900 + 4.28125i) q^{17} +0.652704 q^{18} +(2.77719 - 3.35965i) q^{19} +(0.500000 + 2.83564i) q^{21} +(0.124485 - 0.104455i) q^{22} +(5.73783 - 2.08840i) q^{23} +(1.43969 + 0.524005i) q^{24} +(2.35844 - 4.08494i) q^{26} +(2.79813 + 4.84651i) q^{27} +(0.326352 - 1.85083i) q^{28} +(0.414878 - 2.35289i) q^{29} +(1.81908 - 3.15074i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.233956 + 0.0851529i) q^{33} +(4.08512 - 1.48686i) q^{34} +(-0.113341 - 0.642788i) q^{36} -7.36959 q^{37} +(-3.79086 - 2.15160i) q^{38} +7.22668 q^{39} +(1.81521 - 1.52314i) q^{41} +(2.70574 - 0.984808i) q^{42} +(0.613341 + 0.223238i) q^{43} +(-0.124485 - 0.104455i) q^{44} +(-3.05303 - 5.28801i) q^{46} +(-1.19459 + 6.77487i) q^{47} +(0.266044 - 1.50881i) q^{48} +(1.73396 + 3.00330i) q^{49} +(5.10220 + 4.28125i) q^{51} +(-4.43242 - 1.61327i) q^{52} +(5.58512 - 2.03282i) q^{53} +(4.28699 - 3.59721i) q^{54} -1.87939 q^{56} +(-0.0491630 - 6.67804i) q^{57} -2.38919 q^{58} +(-0.708263 - 4.01676i) q^{59} +(-2.21301 + 0.805470i) q^{61} +(-3.41875 - 1.24432i) q^{62} +(-0.939693 - 0.788496i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0432332 - 0.245188i) q^{66} +(-0.284463 + 1.61327i) q^{67} +(-2.17365 - 3.76487i) q^{68} +(4.67752 - 8.10170i) q^{69} +(2.39780 + 0.872729i) q^{71} +(-0.613341 + 0.223238i) q^{72} +(-12.0287 + 10.0933i) q^{73} +(1.27972 + 7.25762i) q^{74} +(-1.46064 + 4.10689i) q^{76} -0.305407 q^{77} +(-1.25490 - 7.11689i) q^{78} +(-0.766044 + 0.642788i) q^{79} +(6.21688 + 2.26276i) q^{81} +(-1.81521 - 1.52314i) q^{82} +(-0.511144 + 0.885328i) q^{83} +(-1.43969 - 2.49362i) q^{84} +(0.113341 - 0.642788i) q^{86} +(-1.83022 - 3.17004i) q^{87} +(-0.0812519 + 0.140732i) q^{88} +(-2.57011 - 2.15658i) q^{89} +(-8.33022 + 3.03195i) q^{91} +(-4.67752 + 3.92490i) q^{92} +(-0.967911 - 5.48930i) q^{93} +6.87939 q^{94} -1.53209 q^{96} +(-3.10354 - 17.6011i) q^{97} +(2.65657 - 2.22913i) q^{98} +(-0.0996702 + 0.0362770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} - 6 q^{6} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 - 6 * q^6 + 3 * q^8 + 6 * q^9	$ 6 q + 6 q^{3} - 6 q^{6} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{17} + 6 q^{18} + 6 q^{19} + 3 q^{21} - 12 q^{22} + 15 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} + 3 q^{28} + 24 q^{29} - 6 q^{31} + 6 q^{33} + 3 q^{34} + 6 q^{36} - 30 q^{37} + 9 q^{38} + 30 q^{39} + 18 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 6 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} + 30 q^{51} - 3 q^{52} + 12 q^{53} + 18 q^{54} - 12 q^{57} - 6 q^{58} + 21 q^{59} - 21 q^{61} - 18 q^{62} - 3 q^{64} - 15 q^{66} - 9 q^{67} - 12 q^{68} + 3 q^{69} + 15 q^{71} + 3 q^{72} - 21 q^{73} - 18 q^{74} - 6 q^{77} - 9 q^{78} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 3 q^{84} - 6 q^{86} + 12 q^{87} - 3 q^{88} - 24 q^{89} - 27 q^{91} - 3 q^{92} - 15 q^{93} + 30 q^{94} - 9 q^{97} - 6 q^{98} - 15 q^{99}+O(q^{100}) $ 6 * q + 6 * q^3 - 6 * q^6 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^17 + 6 * q^18 + 6 * q^19 + 3 * q^21 - 12 * q^22 + 15 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 + 3 * q^28 + 24 * q^29 - 6 * q^31 + 6 * q^33 + 3 * q^34 + 6 * q^36 - 30 * q^37 + 9 * q^38 + 30 * q^39 + 18 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 6 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 + 30 * q^51 - 3 * q^52 + 12 * q^53 + 18 * q^54 - 12 * q^57 - 6 * q^58 + 21 * q^59 - 21 * q^61 - 18 * q^62 - 3 * q^64 - 15 * q^66 - 9 * q^67 - 12 * q^68 + 3 * q^69 + 15 * q^71 + 3 * q^72 - 21 * q^73 - 18 * q^74 - 6 * q^77 - 9 * q^78 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 3 * q^84 - 6 * q^86 + 12 * q^87 - 3 * q^88 - 24 * q^89 - 27 * q^91 - 3 * q^92 - 15 * q^93 + 30 * q^94 - 9 * q^97 - 6 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	1.17365	−	0.984808i	0.677606	−	0.568579i	−0.237700	−	0.971339i	$-0.576393\pi$
$3$	1.17365	−	0.984808i	0.677606	−	0.568579i	0.915306	+	0.402760i	$0.131949\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	−1.17365	−	0.984808i	−0.479140	−	0.402046i
$7$	−0.939693	+	1.62760i	−0.355170	+	0.615173i	−0.987147	−	0.159814i	$-0.948910\pi$
$7$	−0.939693	+	1.62760i	−0.355170	+	0.615173i	0.631977	+	0.774987i	$0.282244\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.113341	+	0.642788i	−0.0377803	+	0.214263i
$10$		0			0
$11$	0.0812519	+	0.140732i	0.0244984	+	0.0424324i	0.878015	−	0.478634i	$-0.158868\pi$
$11$	0.0812519	+	0.140732i	0.0244984	+	0.0424324i	−0.853516	+	0.521066i	$0.825534\pi$
$12$	−0.766044	+	1.32683i	−0.221138	+	0.383022i
$13$	3.61334	+	3.03195i	1.00216	+	0.840912i	0.987282	−	0.158977i	$-0.0508195\pi$
$13$	3.61334	+	3.03195i	1.00216	+	0.840912i	0.0148781	+	0.999889i	$0.495264\pi$
$14$	1.76604	+	0.642788i	0.471995	+	0.171792i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.754900	+	4.28125i	0.183090	+	1.03836i	0.928385	+	0.371621i	$0.121198\pi$
$17$	0.754900	+	4.28125i	0.183090	+	1.03836i	−0.745295	+	0.666735i	$0.767691\pi$
$18$	0.652704			0.153844
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$20$		0			0
$21$	0.500000	+	2.83564i	0.109109	+	0.618788i
$22$	0.124485	−	0.104455i	0.0265403	−	0.0222700i
$23$	5.73783	−	2.08840i	1.19642	−	0.435461i	0.334446	−	0.942415i	$-0.391451\pi$
$23$	5.73783	−	2.08840i	1.19642	−	0.435461i	0.861973	+	0.506954i	$0.169229\pi$
$24$	1.43969	+	0.524005i	0.293876	+	0.106962i
$25$		0			0
$26$	2.35844	−	4.08494i	0.462528	−	0.801122i
$27$	2.79813	+	4.84651i	0.538501	+	0.932711i
$28$	0.326352	−	1.85083i	0.0616747	−	0.349775i
$29$	0.414878	−	2.35289i	0.0770409	−	0.436920i	−0.921751	−	0.387782i	$-0.873241\pi$
$29$	0.414878	−	2.35289i	0.0770409	−	0.436920i	0.998792	−	0.0491384i	$-0.0156475\pi$
$30$		0			0
$31$	1.81908	−	3.15074i	0.326716	−	0.565889i	−0.655142	−	0.755506i	$-0.727391\pi$
$31$	1.81908	−	3.15074i	0.326716	−	0.565889i	0.981858	+	0.189617i	$0.0607246\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	0.233956	+	0.0851529i	0.0407264	+	0.0148232i
$34$	4.08512	−	1.48686i	0.700593	−	0.254995i
$35$		0			0
$36$	−0.113341	−	0.642788i	−0.0188901	−	0.107131i
$37$	−7.36959			−1.21155			−0.605776	−	0.795635i	$-0.707137\pi$
$37$	−7.36959			−1.21155			−0.605776	+	0.795635i	$0.707137\pi$
$38$	−3.79086	−	2.15160i	−0.614959	−	0.349036i
$39$	7.22668			1.15720
$40$		0			0
$41$	1.81521	−	1.52314i	0.283488	−	0.237874i	−0.489944	−	0.871754i	$-0.662983\pi$
$41$	1.81521	−	1.52314i	0.283488	−	0.237874i	0.773432	+	0.633879i	$0.218538\pi$
$42$	2.70574	−	0.984808i	0.417504	−	0.151959i
$43$	0.613341	+	0.223238i	0.0935336	+	0.0340434i	0.388363	−	0.921506i	$-0.373041\pi$
$43$	0.613341	+	0.223238i	0.0935336	+	0.0340434i	−0.294830	+	0.955550i	$0.595263\pi$
$44$	−0.124485	−	0.104455i	−0.0187668	−	0.0157473i
$45$		0			0
$46$	−3.05303	−	5.28801i	−0.450145	−	0.779674i
$47$	−1.19459	+	6.77487i	−0.174249	+	0.988217i	0.764758	+	0.644318i	$0.222859\pi$
$47$	−1.19459	+	6.77487i	−0.174249	+	0.988217i	−0.939007	+	0.343899i	$0.888252\pi$
$48$	0.266044	−	1.50881i	0.0384002	−	0.217778i
$49$	1.73396	+	3.00330i	0.247708	+	0.429043i
$50$		0			0
$51$	5.10220	+	4.28125i	0.714450	+	0.599495i
$52$	−4.43242	−	1.61327i	−0.614666	−	0.223720i
$53$	5.58512	−	2.03282i	0.767176	−	0.279229i	0.0713610	−	0.997451i	$-0.477266\pi$
$53$	5.58512	−	2.03282i	0.767176	−	0.279229i	0.695815	+	0.718221i	$0.255044\pi$
$54$	4.28699	−	3.59721i	0.583385	−	0.489518i
$55$		0			0
$56$	−1.87939			−0.251143
$57$	−0.0491630	−	6.67804i	−0.00651180	−	0.884528i
$58$	−2.38919			−0.313715
$59$	−0.708263	−	4.01676i	−0.0922080	−	0.522938i	−0.995567	−	0.0940529i	$-0.970018\pi$
$59$	−0.708263	−	4.01676i	−0.0922080	−	0.522938i	0.903359	−	0.428885i	$-0.141093\pi$
$60$		0			0
$61$	−2.21301	+	0.805470i	−0.283347	+	0.103130i	−0.479784	−	0.877387i	$-0.659285\pi$
$61$	−2.21301	+	0.805470i	−0.283347	+	0.103130i	0.196437	+	0.980516i	$0.437063\pi$
$62$	−3.41875	−	1.24432i	−0.434181	−	0.158029i
$63$	−0.939693	−	0.788496i	−0.118390	−	0.0993411i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	0.0432332	−	0.245188i	0.00532164	−	0.0301805i
$67$	−0.284463	+	1.61327i	−0.0347527	+	0.197092i	−0.997241	−	0.0742305i	$-0.976350\pi$
$67$	−0.284463	+	1.61327i	−0.0347527	+	0.197092i	0.962488	+	0.271323i	$0.0874610\pi$
$68$	−2.17365	−	3.76487i	−0.263594	−	0.456557i
$69$	4.67752	−	8.10170i	0.563107	−	0.975330i
$70$		0			0
$71$	2.39780	+	0.872729i	0.284567	+	0.103574i	0.480360	−	0.877071i	$-0.340506\pi$
$71$	2.39780	+	0.872729i	0.284567	+	0.103574i	−0.195793	+	0.980645i	$0.562728\pi$
$72$	−0.613341	+	0.223238i	−0.0722829	+	0.0263088i
$73$	−12.0287	+	10.0933i	−1.40785	+	1.18133i	−0.450366	+	0.892844i	$0.648707\pi$
$73$	−12.0287	+	10.0933i	−1.40785	+	1.18133i	−0.957485	+	0.288483i	$0.906849\pi$
$74$	1.27972	+	7.25762i	0.148764	+	0.843682i
$75$		0			0
$76$	−1.46064	+	4.10689i	−0.167547	+	0.471093i
$77$	−0.305407			−0.0348044
$78$	−1.25490	−	7.11689i	−0.142089	−	0.805829i
$79$	−0.766044	+	0.642788i	−0.0861867	+	0.0723193i	−0.684863	−	0.728672i	$-0.740138\pi$
$79$	−0.766044	+	0.642788i	−0.0861867	+	0.0723193i	0.598676	+	0.800991i	$0.295694\pi$
$80$		0			0
$81$	6.21688	+	2.26276i	0.690765	+	0.251418i
$82$	−1.81521	−	1.52314i	−0.200456	−	0.168203i
$83$	−0.511144	+	0.885328i	−0.0561054	+	0.0971774i	−0.892714	−	0.450624i	$-0.851202\pi$
$83$	−0.511144	+	0.885328i	−0.0561054	+	0.0971774i	0.836609	+	0.547801i	$0.184535\pi$
$84$	−1.43969	−	2.49362i	−0.157083	−	0.272076i
$85$		0			0
$86$	0.113341	−	0.642788i	0.0122219	−	0.0693136i
$87$	−1.83022	−	3.17004i	−0.196220	−	0.339864i
$88$	−0.0812519	+	0.140732i	−0.00866148	+	0.0150021i
$89$	−2.57011	−	2.15658i	−0.272431	−	0.228597i	0.496328	−	0.868135i	$-0.334681\pi$
$89$	−2.57011	−	2.15658i	−0.272431	−	0.228597i	−0.768759	+	0.639538i	$0.779126\pi$
$90$		0			0
$91$	−8.33022	+	3.03195i	−0.873245	+	0.317835i
$92$	−4.67752	+	3.92490i	−0.487665	+	0.409200i
$93$	−0.967911	−	5.48930i	−0.100368	−	0.569214i
$94$	6.87939			0.709554
$95$		0			0
$96$	−1.53209			−0.156368
$97$	−3.10354	−	17.6011i	−0.315117	−	1.78712i	−0.571563	−	0.820558i	$-0.693663\pi$
$97$	−3.10354	−	17.6011i	−0.315117	−	1.78712i	0.256447	−	0.966558i	$-0.417448\pi$
$98$	2.65657	−	2.22913i	0.268355	−	0.225176i
$99$	−0.0996702	+	0.0362770i	−0.0100172	+	0.00364598i
$100$		0			0
$101$	6.82295	+	5.72513i	0.678909	+	0.569672i	0.915687	−	0.401892i	$-0.131647\pi$
$101$	6.82295	+	5.72513i	0.678909	+	0.569672i	−0.236779	+	0.971564i	$0.576092\pi$
$102$	3.33022	−	5.76811i	0.329741	−	0.571128i
$103$	4.12449	+	7.14382i	0.406398	+	0.703901i	0.994483	−	0.104898i	$-0.0334515\pi$
$103$	4.12449	+	7.14382i	0.406398	+	0.703901i	−0.588085	+	0.808799i	$0.700118\pi$
$104$	−0.819078	+	4.64522i	−0.0803172	+	0.455501i
$105$		0			0
$106$	−2.97178	−	5.14728i	−0.288645	−	0.499948i
$107$	1.83022	−	3.17004i	0.176934	−	0.306459i	−0.763895	−	0.645341i	$-0.776715\pi$
$107$	1.83022	−	3.17004i	0.176934	−	0.306459i	0.940829	+	0.338882i	$0.110049\pi$
$108$	−4.28699	−	3.59721i	−0.412516	−	0.346142i
$109$	−3.03936	−	1.10624i	−0.291118	−	0.105958i	0.192333	−	0.981330i	$-0.438395\pi$
$109$	−3.03936	−	1.10624i	−0.291118	−	0.105958i	−0.483451	+	0.875371i	$0.660617\pi$
$110$		0			0
$111$	−8.64930	+	7.25762i	−0.820955	+	0.688863i
$112$	0.326352	+	1.85083i	0.0308373	+	0.174887i
$113$	15.1753			1.42757			0.713786	−	0.700364i	$-0.246979\pi$
$113$	15.1753			1.42757			0.713786	+	0.700364i	$0.246979\pi$
$114$	−6.56805	+	1.20805i	−0.615154	+	0.113144i
$115$		0			0
$116$	0.414878	+	2.35289i	0.0385204	+	0.218460i
$117$	−2.35844	+	1.97897i	−0.218038	+	0.182956i
$118$	−3.83275	+	1.39501i	−0.352833	+	0.128421i
$119$	−7.67752	−	2.79439i	−0.703797	−	0.256161i
$120$		0			0
$121$	5.48680	−	9.50341i	0.498800	−	0.863946i
$122$	1.17752	+	2.03952i	0.106608	+	0.184650i
$123$	0.630415	−	3.57526i	0.0568426	−	0.322370i
$124$	−0.631759	+	3.58288i	−0.0567336	+	0.321752i
$125$		0			0
$126$	−0.613341	+	1.06234i	−0.0546407	+	0.0946405i
$127$	15.2815	+	12.8227i	1.35602	+	1.13783i	0.977191	+	0.212365i	$0.0681164\pi$
$127$	15.2815	+	12.8227i	1.35602	+	1.13783i	0.378826	+	0.925468i	$0.376328\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	0.939693	−	0.342020i	0.0827353	−	0.0301132i
$130$		0			0
$131$	−2.93376	−	16.6382i	−0.256324	−	1.45369i	−0.792651	−	0.609676i	$-0.791300\pi$
$131$	−2.93376	−	16.6382i	−0.256324	−	1.45369i	0.536327	−	0.844010i	$-0.319811\pi$
$132$	−0.248970			−0.0216701
$133$	2.85844	+	7.67717i	0.247858	+	0.665695i
$134$	1.63816			0.141515
$135$		0			0
$136$	−3.33022	+	2.79439i	−0.285564	+	0.239617i
$137$	−4.67752	+	1.70248i	−0.399627	+	0.145452i	−0.534012	−	0.845477i	$-0.679316\pi$
$137$	−4.67752	+	1.70248i	−0.399627	+	0.145452i	0.134385	+	0.990929i	$0.457094\pi$
$138$	−8.79086	−	3.19961i	−0.748328	−	0.272369i
$139$	−14.3439	−	12.0360i	−1.21663	−	1.02088i	−0.998994	−	0.0448471i	$-0.985720\pi$
$139$	−14.3439	−	12.0360i	−1.21663	−	1.02088i	−0.217639	−	0.976029i	$-0.569836\pi$
$140$		0			0
$141$	5.26991	+	9.12776i	0.443807	+	0.768696i
$142$	0.443096	−	2.51292i	0.0371838	−	0.210880i
$143$	−0.133103	+	0.754866i	−0.0111307	+	0.0631251i
$144$	0.326352	+	0.565258i	0.0271960	+	0.0471048i
$145$		0			0
$146$	12.0287	+	10.0933i	0.995501	+	0.835325i
$147$	4.99273	+	1.81720i	0.411793	+	0.149880i
$148$	6.92514	−	2.52055i	0.569243	−	0.207188i
$149$	−10.2476	+	8.59878i	−0.839518	+	0.704439i	−0.957455	−	0.288582i	$-0.906816\pi$
$149$	−10.2476	+	8.59878i	−0.839518	+	0.704439i	0.117937	+	0.993021i	$0.462372\pi$
$150$		0			0
$151$	−14.8648			−1.20968			−0.604842	−	0.796346i	$-0.706764\pi$
$151$	−14.8648			−1.20968			−0.604842	+	0.796346i	$0.706764\pi$
$152$	4.29813	+	0.725293i	0.348625	+	0.0588290i
$153$	−2.83750			−0.229398
$154$	0.0530334	+	0.300767i	0.00427355	+	0.0242365i
$155$		0			0
$156$	−6.79086	+	2.47167i	−0.543704	+	0.197892i
$157$	−6.99912	−	2.54747i	−0.558591	−	0.203310i	0.0472685	−	0.998882i	$-0.484948\pi$
$157$	−6.99912	−	2.54747i	−0.558591	−	0.203310i	−0.605859	+	0.795572i	$0.707171\pi$
$158$	0.766044	+	0.642788i	0.0609432	+	0.0511374i
$159$	4.55303	−	7.88609i	0.361079	−	0.625407i
$160$		0			0
$161$	−1.99273	+	11.3013i	−0.157049	+	0.890668i
$162$	1.14883	−	6.51536i	0.0902609	−	0.511895i
$163$	3.37598	+	5.84737i	0.264427	+	0.458002i	0.967413	−	0.253202i	$-0.0814837\pi$
$163$	3.37598	+	5.84737i	0.264427	+	0.458002i	−0.702986	+	0.711204i	$0.748150\pi$
$164$	−1.18479	+	2.05212i	−0.0925168	+	0.160244i
$165$		0			0
$166$	0.960637	+	0.349643i	0.0745599	+	0.0271376i
$167$	15.2738	−	5.55920i	1.18192	−	0.430184i	0.325041	−	0.945700i	$-0.394622\pi$
$167$	15.2738	−	5.55920i	1.18192	−	0.430184i	0.856880	+	0.515516i	$0.172400\pi$
$168$	−2.20574	+	1.85083i	−0.170176	+	0.142795i
$169$	1.60607	+	9.10846i	0.123544	+	0.700651i
$170$		0			0
$171$	1.84477	+	2.16593i	0.141073	+	0.165633i
$172$	−0.652704			−0.0497682
$173$	0.979055	+	5.55250i	0.0744362	+	0.422149i	0.999140	+	0.0414616i	$0.0132014\pi$
$173$	0.979055	+	5.55250i	0.0744362	+	0.422149i	−0.924704	+	0.380687i	$0.875687\pi$
$174$	−2.80406	+	2.35289i	−0.212575	+	0.178372i
$175$		0			0
$176$	0.152704	+	0.0555796i	0.0115105	+	0.00418947i
$177$	−4.78699	−	4.01676i	−0.359812	−	0.301918i
$178$	−1.67752	+	2.90555i	−0.125735	+	0.217780i
$179$	−5.74763	−	9.95518i	−0.429598	−	0.744085i	0.567240	−	0.823553i	$-0.308011\pi$
$179$	−5.74763	−	9.95518i	−0.429598	−	0.744085i	−0.996837	+	0.0794676i	$0.974678\pi$
$180$		0			0
$181$	2.61200	−	14.8134i	0.194148	−	1.10107i	−0.719478	−	0.694515i	$-0.755619\pi$
$181$	2.61200	−	14.8134i	0.194148	−	1.10107i	0.913627	−	0.406554i	$-0.133270\pi$
$182$	4.43242	+	7.67717i	0.328553	+	0.569070i
$183$	−1.80406	+	3.12473i	−0.133360	+	0.230987i
$184$	4.67752	+	3.92490i	0.344831	+	0.289348i
$185$		0			0
$186$	−5.23783	+	1.90641i	−0.384056	+	0.139785i
$187$	−0.541174	+	0.454099i	−0.0395746	+	0.0332070i
$188$	−1.19459	−	6.77487i	−0.0871246	−	0.494108i
$189$	−10.5175			−0.765039
$190$		0			0
$191$	20.2131			1.46257			0.731283	−	0.682074i	$-0.238922\pi$
$191$	20.2131			1.46257			0.731283	+	0.682074i	$0.238922\pi$
$192$	0.266044	+	1.50881i	0.0192001	+	0.108889i
$193$	−7.71941	+	6.47735i	−0.555655	+	0.466250i	−0.876851	−	0.480763i	$-0.840360\pi$
$193$	−7.71941	+	6.47735i	−0.555655	+	0.466250i	0.321196	+	0.947013i	$0.395915\pi$
$194$	−16.7947	+	6.11278i	−1.20579	+	0.438872i
$195$		0			0
$196$	−2.65657	−	2.22913i	−0.189755	−	0.159224i
$197$	6.54916	−	11.3435i	0.466609	−	0.808190i	−0.532664	−	0.846327i	$-0.678809\pi$
$197$	6.54916	−	11.3435i	0.466609	−	0.808190i	0.999273	+	0.0381371i	$0.0121424\pi$
$198$	0.0530334	+	0.0918566i	0.00376892	+	0.00652796i
$199$	−3.05257	+	17.3120i	−0.216391	+	1.22721i	0.662086	+	0.749428i	$0.269671\pi$
$199$	−3.05257	+	17.3120i	−0.216391	+	1.22721i	−0.878477	+	0.477785i	$0.841440\pi$
$200$		0			0
$201$	1.25490	+	2.17355i	0.0885138	+	0.153310i
$202$	4.45336	−	7.71345i	0.313338	−	0.542717i
$203$	3.43969	+	2.88624i	0.241419	+	0.202575i
$204$	−6.25877	−	2.27801i	−0.438202	−	0.159492i
$205$		0			0
$206$	6.31908	−	5.30234i	0.440271	−	0.369431i
$207$	0.692066	+	3.92490i	0.0481019	+	0.272800i
$208$	4.71688			0.327057
$209$	0.698463	+	0.117863i	0.0483137	+	0.00815275i
$210$		0			0
$211$	−4.29561	−	24.3616i	−0.295722	−	1.67712i	−0.664254	−	0.747507i	$-0.731251\pi$
$211$	−4.29561	−	24.3616i	−0.295722	−	1.67712i	0.368532	−	0.929615i	$-0.379860\pi$
$212$	−4.55303	+	3.82045i	−0.312704	+	0.262389i
$213$	3.67365	−	1.33710i	0.251714	−	0.0916165i
$214$	−3.43969	−	1.25195i	−0.235133	−	0.0855812i
$215$		0			0
$216$	−2.79813	+	4.84651i	−0.190389	+	0.329763i
$217$	3.41875	+	5.92145i	0.232080	+	0.401974i
$218$	−0.561652	+	3.18528i	−0.0380398	+	0.215735i
$219$	−4.17752	+	23.6919i	−0.282291	+	1.60095i
$220$		0			0
$221$	−10.2528	+	17.7584i	−0.689681	+	1.19456i
$222$	8.64930	+	7.25762i	0.580503	+	0.487100i
$223$	−14.2836	−	5.19880i	−0.956500	−	0.348137i	−0.183839	−	0.982956i	$-0.558852\pi$
$223$	−14.2836	−	5.19880i	−0.956500	−	0.348137i	−0.772661	+	0.634819i	$0.781075\pi$
$224$	1.76604	−	0.642788i	0.117999	−	0.0429481i
$225$		0			0
$226$	−2.63516	−	14.9448i	−0.175288	−	0.994110i
$227$	18.6973			1.24098			0.620491	−	0.784214i	$-0.286933\pi$
$227$	18.6973			1.24098			0.620491	+	0.784214i	$0.286933\pi$
$228$	2.33022	+	6.25849i	0.154323	+	0.414479i
$229$	−19.9094			−1.31565			−0.657826	−	0.753170i	$-0.728524\pi$
$229$	−19.9094			−1.31565			−0.657826	+	0.753170i	$0.728524\pi$
$230$		0			0
$231$	−0.358441	+	0.300767i	−0.0235837	+	0.0197890i
$232$	2.24510	−	0.817150i	0.147398	−	0.0536485i
$233$	−26.2913	−	9.56926i	−1.72240	−	0.626903i	−0.724358	−	0.689424i	$-0.757864\pi$
$233$	−26.2913	−	9.56926i	−1.72240	−	0.626903i	−0.998044	+	0.0625206i	$0.980086\pi$
$234$	2.35844	+	1.97897i	0.154176	+	0.129369i
$235$		0			0
$236$	2.03936	+	3.53228i	0.132751	+	0.229932i
$237$	−0.266044	+	1.50881i	−0.0172814	+	0.0980079i
$238$	−1.41875	+	8.04612i	−0.0919638	+	0.521553i
$239$	13.1814	+	22.8308i	0.852633	+	1.47680i	0.878823	+	0.477147i	$0.158329\pi$
$239$	13.1814	+	22.8308i	0.852633	+	1.47680i	−0.0261903	+	0.999657i	$0.508338\pi$
$240$		0			0
$241$	13.1570	+	11.0401i	0.847520	+	0.711153i	0.959242	−	0.282586i	$-0.0911923\pi$
$241$	13.1570	+	11.0401i	0.847520	+	0.711153i	−0.111722	+	0.993739i	$0.535637\pi$
$242$	−10.3118	−	3.75319i	−0.662868	−	0.241264i
$243$	−6.25150	+	2.27536i	−0.401034	+	0.145964i
$244$	1.80406	−	1.51379i	0.115493	−	0.0969104i
$245$		0			0
$246$	−3.63041			−0.231467
$247$	20.2212	−	3.71924i	1.28665	−	0.236650i
$248$	3.63816			0.231023
$249$	0.271974	+	1.54244i	0.0172357	+	0.0977483i
$250$		0			0
$251$	−15.1211	+	5.50362i	−0.954434	+	0.347386i	−0.771850	−	0.635805i	$-0.780668\pi$
$251$	−15.1211	+	5.50362i	−0.954434	+	0.347386i	−0.182584	+	0.983190i	$0.558446\pi$
$252$	1.15270	+	0.419550i	0.0726135	+	0.0264292i
$253$	0.760115	+	0.637812i	0.0477880	+	0.0400989i
$254$	9.97431	−	17.2760i	0.625844	−	1.08399i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−2.45605	+	13.9290i	−0.153204	+	0.868865i	0.807205	+	0.590271i	$0.200979\pi$
$257$	−2.45605	+	13.9290i	−0.153204	+	0.868865i	−0.960409	+	0.278593i	$0.910132\pi$
$258$	−0.500000	−	0.866025i	−0.0311286	−	0.0539164i
$259$	6.92514	−	11.9947i	0.430308	−	0.745315i
$260$		0			0
$261$	1.46538	+	0.533356i	0.0907050	+	0.0330139i
$262$	−15.8760	+	5.77838i	−0.980821	+	0.356990i
$263$	−10.0517	+	8.43437i	−0.619814	+	0.520085i	−0.897745	−	0.440515i	$-0.854796\pi$
$263$	−10.0517	+	8.43437i	−0.619814	+	0.520085i	0.277931	+	0.960601i	$0.410351\pi$
$264$	0.0432332	+	0.245188i	0.00266082	+	0.0150903i
$265$		0			0
$266$	7.06418	−	4.14814i	0.433133	−	0.254339i
$267$	−5.14022			−0.314576
$268$	−0.284463	−	1.61327i	−0.0173763	−	0.0985461i
$269$	−17.2003	+	14.4327i	−1.04872	+	0.879980i	−0.992958	−	0.118464i	$-0.962203\pi$
$269$	−17.2003	+	14.4327i	−1.04872	+	0.879980i	−0.0557609	+	0.998444i	$0.517758\pi$
$270$		0			0
$271$	5.41787	+	1.97194i	0.329112	+	0.119787i	0.501291	−	0.865279i	$-0.332859\pi$
$271$	5.41787	+	1.97194i	0.329112	+	0.119787i	−0.172179	+	0.985066i	$0.555081\pi$
$272$	3.33022	+	2.79439i	0.201924	+	0.169435i
$273$	−6.79086	+	11.7621i	−0.411002	+	0.711875i
$274$	2.48886	+	4.31082i	0.150357	+	0.260426i
$275$		0			0
$276$	−1.62449	+	9.21291i	−0.0977825	+	0.554552i
$277$	−9.88666	−	17.1242i	−0.594032	−	1.02889i	−0.993683	−	0.112226i	$-0.964202\pi$
$277$	−9.88666	−	17.1242i	−0.594032	−	1.02889i	0.399651	−	0.916667i	$-0.369131\pi$
$278$	−9.36231	+	16.2160i	−0.561514	+	0.972571i
$279$	1.81908	+	1.52639i	0.108905	+	0.0913824i
$280$		0			0
$281$	−29.7904	+	10.8428i	−1.77715	+	0.646829i	−0.777306	+	0.629123i	$0.783414\pi$
$281$	−29.7904	+	10.8428i	−1.77715	+	0.646829i	−0.999843	+	0.0177066i	$0.994364\pi$
$282$	8.07398	−	6.77487i	0.480798	−	0.403438i
$283$	0.510678	+	2.89620i	0.0303566	+	0.172161i	0.996217	−	0.0869031i	$-0.0276970\pi$
$283$	0.510678	+	2.89620i	0.0303566	+	0.172161i	−0.965860	+	0.259064i	$0.916586\pi$
$284$	−2.55169			−0.151415
$285$		0			0
$286$	0.766511			0.0453248
$287$	0.773318	+	4.38571i	0.0456475	+	0.258880i
$288$	0.500000	−	0.419550i	0.0294628	−	0.0247222i
$289$	−1.78446	+	0.649491i	−0.104968	+	0.0382054i
$290$		0			0
$291$	−20.9761	−	17.6011i	−1.22964	−	1.03179i
$292$	7.85117	−	13.5986i	0.459455	−	0.795799i
$293$	−8.14883	−	14.1142i	−0.476060	−	0.824560i	0.523564	−	0.851986i	$-0.324602\pi$
$293$	−8.14883	−	14.1142i	−0.476060	−	0.824560i	−0.999624	+	0.0274264i	$0.991269\pi$
$294$	0.922618	−	5.23243i	0.0538082	−	0.305161i
$295$		0			0
$296$	−3.68479	−	6.38225i	−0.214174	−	0.370961i
$297$	−0.454707	+	0.787576i	−0.0263848	+	0.0456998i
$298$	10.2476	+	8.59878i	0.593629	+	0.498114i
$299$	27.0646	+	9.85073i	1.56519	+	0.569682i
$300$		0			0
$301$	−0.939693	+	0.788496i	−0.0541630	+	0.0454481i
$302$	2.58125	+	14.6390i	0.148534	+	0.842380i
$303$	13.6459			0.783936
$304$	−0.0320889	−	4.35878i	−0.00184042	−	0.249993i
$305$		0			0
$306$	0.492726	+	2.79439i	0.0281673	+	0.159745i
$307$	−16.9932	+	14.2590i	−0.969853	+	0.813803i	−0.982528	−	0.186117i	$-0.940410\pi$
$307$	−16.9932	+	14.2590i	−0.969853	+	0.813803i	0.0126749	+	0.999920i	$0.495965\pi$
$308$	0.286989	−	0.104455i	0.0163527	−	0.00595190i
$309$	11.8760	+	4.32250i	0.675601	+	0.245899i
$310$		0			0
$311$	4.46198	−	7.72838i	0.253016	−	0.438236i	−0.711339	−	0.702849i	$-0.751911\pi$
$311$	4.46198	−	7.72838i	0.253016	−	0.438236i	0.964355	+	0.264613i	$0.0852442\pi$
$312$	3.61334	+	6.25849i	0.204565	+	0.354317i
$313$	3.18227	−	18.0475i	0.179872	−	1.02011i	−0.752496	−	0.658597i	$-0.771150\pi$
$313$	3.18227	−	18.0475i	0.179872	−	1.02011i	0.932368	−	0.361510i	$-0.117739\pi$
$314$	−1.29339	+	7.33515i	−0.0729900	+	0.413947i
$315$		0			0
$316$	0.500000	−	0.866025i	0.0281272	−	0.0487177i
$317$	18.5856	+	15.5952i	1.04387	+	0.875912i	0.992436	−	0.122765i	$-0.0391761\pi$
$317$	18.5856	+	15.5952i	1.04387	+	0.875912i	0.0514349	+	0.998676i	$0.483621\pi$
$318$	−8.55690	−	3.11446i	−0.479847	−	0.174650i
$319$	0.364837	−	0.132790i	0.0204270	−	0.00743481i
$320$		0			0
$321$	−0.973841	−	5.52293i	−0.0543545	−	0.308260i
$322$	11.4757			0.639513
$323$	16.4800	+	9.35365i	0.916971	+	0.520451i
$324$	−6.61587			−0.367548
$325$		0			0
$326$	5.17230	−	4.34008i	0.286467	−	0.240375i
$327$	−4.65657	+	1.69485i	−0.257509	+	0.0937257i
$328$	2.22668	+	0.810446i	0.122948	+	0.0447494i
$329$	−9.90420	−	8.31061i	−0.546036	−	0.458179i
$330$		0			0
$331$	−16.8974	−	29.2671i	−0.928765	−	1.60867i	−0.785392	−	0.618999i	$-0.787539\pi$
$331$	−16.8974	−	29.2671i	−0.928765	−	1.60867i	−0.143373	−	0.989669i	$-0.545795\pi$
$332$	0.177519	−	1.00676i	0.00974260	−	0.0552530i
$333$	0.835275	−	4.73708i	0.0457728	−	0.259590i
$334$	−8.12701	−	14.0764i	−0.444690	−	0.770226i
$335$		0			0
$336$	2.20574	+	1.85083i	0.120333	+	0.100971i
$337$	−27.9761	−	10.1825i	−1.52396	−	0.554675i	−0.561824	−	0.827257i	$-0.689900\pi$
$337$	−27.9761	−	10.1825i	−1.52396	−	0.554675i	−0.962132	+	0.272582i	$0.912122\pi$
$338$	8.69119	−	3.16333i	0.472738	−	0.172063i
$339$	17.8105	−	14.9448i	0.967331	−	0.811687i
$340$		0			0
$341$	0.591214			0.0320160
$342$	1.81268	−	2.19285i	0.0980186	−	0.118576i
$343$	−19.6732			−1.06225
$344$	0.113341	+	0.642788i	0.00611093	+	0.0346568i
$345$		0			0
$346$	5.29813	−	1.92836i	0.284829	−	0.103669i
$347$	2.93717	+	1.06904i	0.157675	+	0.0573891i	0.419652	−	0.907685i	$-0.362152\pi$
$347$	2.93717	+	1.06904i	0.157675	+	0.0573891i	−0.261977	+	0.965074i	$0.584374\pi$
$348$	2.80406	+	2.35289i	0.150314	+	0.126128i
$349$	3.88666	−	6.73189i	0.208048	−	0.360350i	−0.743052	−	0.669234i	$-0.766622\pi$
$349$	3.88666	−	6.73189i	0.208048	−	0.360350i	0.951100	+	0.308884i	$0.0999556\pi$
$350$		0			0
$351$	−4.58378	+	25.9959i	−0.244664	+	1.38756i
$352$	0.0282185	−	0.160035i	0.00150405	−	0.00852990i
$353$	−14.6163	−	25.3162i	−0.777949	−	1.34745i	−0.933122	−	0.359560i	$-0.882927\pi$
$353$	−14.6163	−	25.3162i	−0.777949	−	1.34745i	0.155173	−	0.987887i	$-0.450406\pi$
$354$	−3.12449	+	5.41177i	−0.166065	+	0.287632i
$355$		0			0
$356$	3.15270	+	1.14749i	0.167093	+	0.0608169i
$357$	−11.7626	+	4.28125i	−0.622545	+	0.226588i
$358$	−8.80587	+	7.38901i	−0.465405	+	0.390521i
$359$	3.13310	+	17.7687i	0.165359	+	0.937797i	0.948694	+	0.316197i	$0.102406\pi$
$359$	3.13310	+	17.7687i	0.165359	+	0.937797i	−0.783335	+	0.621600i	$0.786483\pi$
$360$		0			0
$361$	−3.57444	−	18.6607i	−0.188129	−	0.982144i
$362$	−15.0419			−0.790584
$363$	−2.91946	−	16.5571i	−0.153232	−	0.869022i
$364$	6.79086	−	5.69821i	0.355938	−	0.298667i
$365$		0			0
$366$	3.39053	+	1.23405i	0.177226	+	0.0645049i
$367$	−12.7818	−	10.7252i	−0.667203	−	0.559850i	0.245033	−	0.969515i	$-0.421201\pi$
$367$	−12.7818	−	10.7252i	−0.667203	−	0.559850i	−0.912236	+	0.409665i	$0.865646\pi$
$368$	3.05303	−	5.28801i	0.159150	−	0.275657i
$369$	0.773318	+	1.33943i	0.0402573	+	0.0697278i
$370$		0			0
$371$	−1.93969	+	11.0005i	−0.100704	+	0.571120i
$372$	2.78699	+	4.82721i	0.144499	+	0.250279i
$373$	3.89915	−	6.75352i	0.201890	−	0.349684i	−0.747247	−	0.664546i	$-0.768625\pi$
$373$	3.89915	−	6.75352i	0.201890	−	0.349684i	0.949137	+	0.314862i	$0.101958\pi$
$374$	0.541174	+	0.454099i	0.0279834	+	0.0234809i
$375$		0			0
$376$	−6.46451	+	2.35289i	−0.333382	+	0.121341i
$377$	8.63294	−	7.24390i	0.444619	−	0.373080i
$378$	1.82635	+	10.3578i	0.0939374	+	0.532745i
$379$	1.31996			0.0678015			0.0339008	−	0.999425i	$-0.489207\pi$
$379$	1.31996			0.0678015			0.0339008	+	0.999425i	$0.489207\pi$
$380$		0			0
$381$	30.5631			1.56579
$382$	−3.50996	−	19.9060i	−0.179585	−	1.01848i
$383$	25.4349	−	21.3425i	1.29966	−	1.09055i	0.309462	−	0.950912i	$-0.399851\pi$
$383$	25.4349	−	21.3425i	1.29966	−	1.09055i	0.990203	−	0.139637i	$-0.0445934\pi$
$384$	1.43969	−	0.524005i	0.0734690	−	0.0267405i
$385$		0			0
$386$	7.71941	+	6.47735i	0.392908	+	0.329689i
$387$	−0.213011	+	0.368946i	−0.0108280	+	0.0187546i
$388$	8.93629	+	15.4781i	0.453671	+	0.785782i
$389$	2.57991	−	14.6314i	0.130807	−	0.741841i	−0.846882	−	0.531781i	$-0.821523\pi$
$389$	2.57991	−	14.6314i	0.130807	−	0.741841i	0.977689	−	0.210060i	$-0.0673659\pi$
$390$		0			0
$391$	13.2724	+	22.9885i	0.671216	+	1.16258i
$392$	−1.73396	+	3.00330i	−0.0875780	+	0.151690i
$393$	−19.8286	−	16.6382i	−1.00022	−	0.839286i
$394$	−12.3084	−	4.47989i	−0.620088	−	0.225694i
$395$		0			0
$396$	0.0812519	−	0.0681784i	0.00408306	−	0.00342610i
$397$	−1.49566	−	8.48233i	−0.0750652	−	0.425716i	−0.999061	−	0.0433144i	$-0.986208\pi$
$397$	−1.49566	−	8.48233i	−0.0750652	−	0.425716i	0.923996	−	0.382401i	$-0.124903\pi$
$398$	17.5790			0.881157
$399$	10.9153	+	6.19529i	0.546451	+	0.310152i
$400$		0			0
$401$	−0.886821	−	5.02941i	−0.0442857	−	0.251157i	0.954625	−	0.297809i	$-0.0962559\pi$
$401$	−0.886821	−	5.02941i	−0.0442857	−	0.251157i	−0.998911	+	0.0466521i	$0.985145\pi$
$402$	1.92262	−	1.61327i	0.0958915	−	0.0804625i
$403$	16.1258	−	5.86932i	0.803285	−	0.292372i
$404$	−8.36959	−	3.04628i	−0.416402	−	0.151558i
$405$		0			0
$406$	2.24510	−	3.88863i	0.111422	−	0.192989i
$407$	−0.598793	−	1.03714i	−0.0296811	−	0.0514091i
$408$	−1.15657	+	6.55926i	−0.0572589	+	0.324732i
$409$	5.00640	−	28.3927i	0.247550	−	1.40393i	−0.566944	−	0.823756i	$-0.691874\pi$
$409$	5.00640	−	28.3927i	0.247550	−	1.40393i	0.814494	−	0.580172i	$-0.197015\pi$
$410$		0			0
$411$	−3.81315	+	6.60457i	−0.188089	+	0.325779i
$412$	−6.31908	−	5.30234i	−0.311319	−	0.261227i
$413$	7.20321	+	2.62175i	0.354447	+	0.129008i
$414$	3.74510	−	1.36310i	0.184062	−	0.0669930i
$415$		0			0
$416$	−0.819078	−	4.64522i	−0.0401586	−	0.227751i
$417$	−28.6878			−1.40485
$418$	−0.00521457	−	0.708319i	−0.000255053	−	0.0346450i
$419$	−7.66313			−0.374369			−0.187184	−	0.982325i	$-0.559936\pi$
$419$	−7.66313			−0.374369			−0.187184	+	0.982325i	$0.559936\pi$
$420$		0			0
$421$	5.14930	−	4.32078i	0.250962	−	0.210582i	−0.508625	−	0.860988i	$-0.669846\pi$
$421$	5.14930	−	4.32078i	0.250962	−	0.210582i	0.759586	+	0.650407i	$0.225401\pi$
$422$	−23.2456	+	8.46069i	−1.13158	+	0.411860i
$423$	−4.21941	−	1.53574i	−0.205155	−	0.0746702i
$424$	4.55303	+	3.82045i	0.221115	+	0.185537i
$425$		0			0
$426$	−1.95471	−	3.38565i	−0.0947059	−	0.164035i
$427$	0.768571	−	4.35878i	0.0371937	−	0.210936i
$428$	−0.635630	+	3.60483i	−0.0307243	+	0.174246i
$429$	0.587182	+	1.01703i	0.0283494	+	0.0491026i
$430$		0			0
$431$	12.5307	+	10.5145i	0.603585	+	0.506468i	0.892596	−	0.450858i	$-0.148882\pi$
$431$	12.5307	+	10.5145i	0.603585	+	0.506468i	−0.289011	+	0.957326i	$0.593326\pi$
$432$	5.25877	+	1.91404i	0.253013	+	0.0920891i
$433$	9.59152	−	3.49103i	0.460939	−	0.167768i	−0.101104	−	0.994876i	$-0.532238\pi$
$433$	9.59152	−	3.49103i	0.460939	−	0.167768i	0.562043	+	0.827108i	$0.310015\pi$
$434$	5.23783	−	4.39506i	0.251424	−	0.210970i
$435$		0			0
$436$	3.23442			0.154901
$437$	8.91875	−	25.0769i	0.426642	−	1.19959i
$438$	24.0574			1.14951
$439$	−1.65523	−	9.38728i	−0.0789998	−	0.448030i	−0.998491	−	0.0549191i	$-0.982510\pi$
$439$	−1.65523	−	9.38728i	−0.0789998	−	0.448030i	0.919491	−	0.393111i	$-0.128601\pi$
$440$		0			0
$441$	−2.12701	+	0.774169i	−0.101286	+	0.0368652i
$442$	19.2690	+	7.01336i	0.916535	+	0.333591i
$443$	4.58306	+	3.84565i	0.217748	+	0.182712i	0.745136	−	0.666912i	$-0.232384\pi$
$443$	4.58306	+	3.84565i	0.217748	+	0.182712i	−0.527389	+	0.849624i	$0.676829\pi$
$444$	5.64543	−	9.77817i	0.267920	−	0.464051i
$445$		0			0
$446$	−2.63950	+	14.9693i	−0.124984	+	0.708819i
$447$	−3.55896	+	20.1839i	−0.168333	+	0.954665i
$448$	−0.939693	−	1.62760i	−0.0443963	−	0.0768967i
$449$	7.67752	−	13.2979i	0.362325	−	0.627564i	−0.626018	−	0.779808i	$-0.715317\pi$
$449$	7.67752	−	13.2979i	0.362325	−	0.627564i	0.988343	+	0.152244i	$0.0486499\pi$
$450$		0			0
$451$	0.361844	+	0.131701i	0.0170386	+	0.00620154i
$452$	−14.2601	+	5.19026i	−0.670739	+	0.244129i
$453$	−17.4461	+	14.6390i	−0.819689	+	0.687801i
$454$	−3.24675	−	18.4132i	−0.152377	−	0.864176i
$455$		0			0
$456$	5.75877	−	3.38160i	0.269679	−	0.158358i
$457$	−11.3987			−0.533208			−0.266604	−	0.963806i	$-0.585902\pi$
$457$	−11.3987			−0.533208			−0.266604	+	0.963806i	$0.585902\pi$
$458$	3.45723	+	19.6069i	0.161546	+	0.916172i
$459$	−18.6368	+	15.6381i	−0.869892	+	0.729926i
$460$		0			0
$461$	37.9847	+	13.8253i	1.76913	+	0.643909i	0.999988	+	0.00482537i	$0.00153597\pi$
$461$	37.9847	+	13.8253i	1.76913	+	0.643909i	0.769137	+	0.639084i	$0.220686\pi$
$462$	0.358441	+	0.300767i	0.0166762	+	0.0139930i
$463$	−4.97818	+	8.62246i	−0.231356	+	0.400720i	−0.958207	−	0.286075i	$-0.907649\pi$
$463$	−4.97818	+	8.62246i	−0.231356	+	0.400720i	0.726852	+	0.686794i	$0.240983\pi$
$464$	−1.19459	−	2.06910i	−0.0554576	−	0.0960553i
$465$		0			0
$466$	−4.85844	+	27.5536i	−0.225063	+	1.27640i
$467$	2.80406	+	4.85678i	0.129757	+	0.224745i	0.923582	−	0.383400i	$-0.125247\pi$
$467$	2.80406	+	4.85678i	0.129757	+	0.224745i	−0.793826	+	0.608145i	$0.791914\pi$
$468$	1.53936	−	2.66625i	0.0711571	−	0.123248i
$469$	−2.35844	−	1.97897i	−0.108903	−	0.0913802i
$470$		0			0
$471$	−10.7233	+	3.90295i	−0.494103	+	0.179839i
$472$	3.12449	−	2.62175i	0.143816	−	0.120676i
$473$	0.0184183	+	0.104455i	0.000846875	+	0.00480287i
$474$	1.53209			0.0703712
$475$		0			0
$476$	8.17024			0.374483
$477$	0.673648	+	3.82045i	0.0308442	+	0.174926i
$478$	20.1951	−	16.9457i	0.923701	−	0.775077i
$479$	23.2383	−	8.45805i	1.06178	−	0.386458i	0.248686	−	0.968584i	$-0.420001\pi$
$479$	23.2383	−	8.45805i	1.06178	−	0.386458i	0.813099	+	0.582126i	$0.197779\pi$
$480$		0			0
$481$	−26.6288	−	22.3442i	−1.21417	−	1.01881i
$482$	8.58765	−	14.8742i	0.391157	−	0.677503i
$483$	8.79086	+	15.2262i	0.399998	+	0.692817i
$484$	−1.90554	+	10.8069i	−0.0866157	+	0.491222i
$485$		0			0
$486$	3.32635	+	5.76141i	0.150886	+	0.261343i
$487$	6.49525	−	11.2501i	0.294328	−	0.509791i	−0.680500	−	0.732748i	$-0.738238\pi$
$487$	6.49525	−	11.2501i	0.294328	−	0.509791i	0.974828	+	0.222957i	$0.0715709\pi$
$488$	−1.80406	−	1.51379i	−0.0816661	−	0.0685260i
$489$	9.72075	+	3.53806i	0.439588	+	0.159997i
$490$		0			0
$491$	14.2947	−	11.9947i	0.645112	−	0.541313i	−0.260471	−	0.965482i	$-0.583878\pi$
$491$	14.2947	−	11.9947i	0.645112	−	0.541313i	0.905583	+	0.424168i	$0.139433\pi$
$492$	0.630415	+	3.57526i	0.0284213	+	0.161185i
$493$	10.3865			0.467784
$494$	−7.17412	−	19.2682i	−0.322779	−	0.866916i
$495$		0			0
$496$	−0.631759	−	3.58288i	−0.0283668	−	0.160876i
$497$	−3.67365	+	3.08256i	−0.164786	+	0.138272i
$498$	1.47178	−	0.535685i	0.0659521	−	0.0240046i
$499$	16.2353	+	5.90917i	0.726792	+	0.264531i	0.678806	−	0.734317i	$-0.262498\pi$
$499$	16.2353	+	5.90917i	0.726792	+	0.264531i	0.0479856	+	0.998848i	$0.484720\pi$
$500$		0			0
$501$	12.4513	−	21.5663i	0.556283	−	0.963511i
$502$	8.04576	+	13.9357i	0.359100	+	0.621979i
$503$	6.48111	−	36.7562i	0.288979	−	1.63888i	−0.401739	−	0.915754i	$-0.631594\pi$
$503$	6.48111	−	36.7562i	0.288979	−	1.63888i	0.690717	−	0.723125i	$-0.257295\pi$
$504$	0.213011	−	1.20805i	0.00948827	−	0.0538106i
$505$		0			0
$506$	0.496130	−	0.859322i	0.0220557	−	0.0382015i
$507$	10.8550	+	9.10846i	0.482089	+	0.404521i
$508$	−18.7456	−	6.82283i	−0.831700	−	0.302714i
$509$	17.9522	−	6.53406i	0.795716	−	0.289617i	0.0880062	−	0.996120i	$-0.471950\pi$
$509$	17.9522	−	6.53406i	0.795716	−	0.289617i	0.707710	+	0.706503i	$0.249728\pi$
$510$		0			0
$511$	−5.12449	−	29.0624i	−0.226694	−	1.28564i
$512$	−1.00000			−0.0441942
$513$	24.0535	+	4.05893i	1.06199	+	0.179206i
$514$	14.1438			0.623858
$515$		0			0
$516$	−0.766044	+	0.642788i	−0.0337232	+	0.0282971i
$517$	−1.05051	+	0.382353i	−0.0462013	+	0.0168159i
$518$	−13.0150	−	4.73708i	−0.571847	−	0.208135i
$519$	6.61721	+	5.55250i	0.290463	+	0.243728i
$520$		0			0
$521$	17.5287	+	30.3606i	0.767946	+	1.33012i	0.938675	+	0.344803i	$0.112054\pi$
$521$	17.5287	+	30.3606i	0.767946	+	1.33012i	−0.170729	+	0.985318i	$0.554612\pi$
$522$	0.270792	−	1.53574i	0.0118523	−	0.0672175i
$523$	−4.20305	+	23.8367i	−0.183786	+	1.04230i	0.743718	+	0.668493i	$0.233060\pi$
$523$	−4.20305	+	23.8367i	−0.183786	+	1.04230i	−0.927505	+	0.373812i	$0.878051\pi$
$524$	8.44743	+	14.6314i	0.369028	+	0.639175i
$525$		0			0
$526$	10.0517	+	8.43437i	0.438274	+	0.367756i
$527$	14.8623	+	5.40944i	0.647412	+	0.235639i
$528$	0.233956	−	0.0851529i	0.0101816	−	0.00370580i
$529$	10.9422	−	9.18161i	0.475749	−	0.399201i
$530$		0			0
$531$	2.66220			0.115530
$532$	−5.31180	−	6.23654i	−0.230296	−	0.270388i
$533$	11.1771			0.484132
$534$	0.892589	+	5.06212i	0.0386261	+	0.219060i
$535$		0			0
$536$	−1.53936	+	0.560282i	−0.0664903	+	0.0242005i
$537$	−16.5496	−	6.02357i	−0.714169	−	0.259936i
$538$	17.2003	+	14.4327i	0.741556	+	0.622240i
$539$	−0.281774	+	0.488048i	−0.0121369	+	0.0210217i
$540$		0			0
$541$	6.37955	−	36.1802i	0.274278	−	1.55551i	−0.466967	−	0.884275i	$-0.654653\pi$
$541$	6.37955	−	36.1802i	0.274278	−	1.55551i	0.741245	−	0.671234i	$-0.234235\pi$
$542$	1.00118	−	5.67799i	0.0430045	−	0.243890i
$543$	−11.5228	−	19.9580i	−0.494489	−	0.856480i
$544$	2.17365	−	3.76487i	0.0931944	−	0.161417i
$545$		0			0
$546$	12.7626	+	4.64522i	0.546191	+	0.198797i
$547$	18.1138	−	6.59289i	0.774490	−	0.281891i	0.0756171	−	0.997137i	$-0.475907\pi$
$547$	18.1138	−	6.59289i	0.774490	−	0.281891i	0.698873	+	0.715245i	$0.253685\pi$
$548$	3.81315	−	3.19961i	0.162890	−	0.136681i
$549$	−0.266922	−	1.51379i	−0.0113919	−	0.0646069i
$550$		0			0
$551$	−6.75268	−	7.92826i	−0.287674	−	0.337755i
$552$	9.35504			0.398177
$553$	−0.326352	−	1.85083i	−0.0138779	−	0.0787054i
$554$	−15.1472	+	12.7100i	−0.643545	+	0.539998i
$555$		0			0
$556$	17.5954	+	6.40420i	0.746211	+	0.271598i
$557$	−32.6798	−	27.4216i	−1.38469	−	1.16189i	−0.967441	−	0.253097i	$-0.918551\pi$
$557$	−32.6798	−	27.4216i	−1.38469	−	1.16189i	−0.417247	−	0.908793i	$-0.637005\pi$
$558$	1.18732	−	2.05650i	0.0502632	−	0.0870584i
$559$	1.53936	+	2.66625i	0.0651081	+	0.112771i
$560$		0			0
$561$	−0.187948	+	1.06590i	−0.00793516	+	0.0450025i
$562$	15.8512	+	27.4550i	0.668641	+	1.15812i
$563$	5.89915	−	10.2176i	0.248619	−	0.430621i	−0.714524	−	0.699611i	$-0.753356\pi$
$563$	5.89915	−	10.2176i	0.248619	−	0.430621i	0.963143	+	0.268990i	$0.0866898\pi$
$564$	−8.07398	−	6.77487i	−0.339976	−	0.285274i
$565$		0			0
$566$	2.76352	−	1.00584i	0.116159	−	0.0422785i
$567$	−9.52481	+	7.99227i	−0.400005	+	0.335644i
$568$	0.443096	+	2.51292i	0.0185919	+	0.105440i
$569$	−1.87164			−0.0784634			−0.0392317	−	0.999230i	$-0.512491\pi$
$569$	−1.87164			−0.0784634			−0.0392317	+	0.999230i	$0.512491\pi$
$570$		0			0
$571$	−8.14197			−0.340731			−0.170365	−	0.985381i	$-0.554495\pi$
$571$	−8.14197			−0.340731			−0.170365	+	0.985381i	$0.554495\pi$
$572$	−0.133103	−	0.754866i	−0.00556533	−	0.0315625i
$573$	23.7230	−	19.9060i	0.991044	−	0.831584i
$574$	4.18479	−	1.52314i	0.174670	−	0.0635746i
$575$		0			0
$576$	−0.500000	−	0.419550i	−0.0208333	−	0.0174812i
$577$	−4.51707	+	7.82380i	−0.188048	+	0.325709i	−0.944599	−	0.328225i	$-0.893549\pi$
$577$	−4.51707	+	7.82380i	−0.188048	+	0.325709i	0.756551	+	0.653934i	$0.226883\pi$
$578$	0.949493	+	1.64457i	0.0394937	+	0.0684051i
$579$	−2.68092	+	15.2043i	−0.111415	+	0.631868i
$580$		0			0
$581$	−0.960637	−	1.66387i	−0.0398539	−	0.0690291i
$582$	−13.6912	+	23.7138i	−0.567518	+	0.982970i
$583$	0.739885	+	0.620838i	0.0306429	+	0.0257125i
$584$	−14.7554	−	5.37051i	−0.610581	−	0.222233i
$585$		0			0
$586$	−12.4847	+	10.4759i	−0.515740	+	0.432757i
$587$	−6.85797	−	38.8935i	−0.283059	−	1.60531i	−0.712138	−	0.702040i	$-0.752273\pi$
$587$	−6.85797	−	38.8935i	−0.283059	−	1.60531i	0.429079	−	0.903267i	$-0.358838\pi$
$588$	−5.31315			−0.219111
$589$	−5.53343	−	14.8616i	−0.228001	−	0.612363i
$590$		0			0
$591$	−3.48474	−	19.7629i	−0.143343	−	0.812938i
$592$	−5.64543	+	4.73708i	−0.232026	+	0.194693i
$593$	−27.1685	+	9.88852i	−1.11568	+	0.406073i	−0.833072	−	0.553164i	$-0.813420\pi$
$593$	−27.1685	+	9.88852i	−1.11568	+	0.406073i	−0.282604	+	0.959237i	$0.591198\pi$
$594$	0.854570	+	0.311038i	0.0350634	+	0.0127621i
$595$		0			0
$596$	6.68866	−	11.5851i	0.273978	−	0.474544i
$597$	13.4663	+	23.3243i	0.551140	+	0.954602i
$598$	5.00134	−	28.3640i	0.204520	−	1.15989i
$599$	3.16931	−	17.9741i	0.129495	−	0.734400i	−0.849042	−	0.528326i	$-0.822820\pi$
$599$	3.16931	−	17.9741i	0.129495	−	0.734400i	0.978536	−	0.206074i	$-0.0660689\pi$
$600$		0			0
$601$	−4.18433	+	7.24746i	−0.170682	+	0.295630i	−0.938659	−	0.344848i	$-0.887930\pi$
$601$	−4.18433	+	7.24746i	−0.170682	+	0.295630i	0.767976	+	0.640478i	$0.221264\pi$
$602$	0.939693	+	0.788496i	0.0382990	+	0.0321367i
$603$	−1.00475	−	0.365698i	−0.0409165	−	0.0148924i
$604$	13.9684	−	5.08407i	0.568365	−	0.206868i
$605$		0			0
$606$	−2.36959	−	13.4386i	−0.0962578	−	0.545905i
$607$	−28.1138			−1.14110			−0.570552	−	0.821261i	$-0.693271\pi$
$607$	−28.1138			−1.14110			−0.570552	+	0.821261i	$0.693271\pi$
$608$	−4.28699	+	0.788496i	−0.173860	+	0.0319777i
$609$	6.87939			0.278767
$610$		0			0
$611$	−24.8576	+	20.8580i	−1.00563	+	0.843823i
$612$	2.66637	−	0.970481i	0.107782	−	0.0392294i
$613$	20.0253	+	7.28861i	0.808814	+	0.294384i	0.713134	−	0.701028i	$-0.247275\pi$
$613$	20.0253	+	7.28861i	0.808814	+	0.294384i	0.0956799	+	0.995412i	$0.469497\pi$
$614$	16.9932	+	14.2590i	0.685789	+	0.575446i
$615$		0			0
$616$	−0.152704	−	0.264490i	−0.00615261	−	0.0106566i
$617$	−2.75520	+	15.6255i	−0.110920	+	0.629061i	0.877769	+	0.479084i	$0.159031\pi$
$617$	−2.75520	+	15.6255i	−0.110920	+	0.629061i	−0.988690	+	0.149977i	$0.952080\pi$
$618$	2.19459	−	12.4462i	0.0882795	−	0.500658i
$619$	1.20527	+	2.08759i	0.0484439	+	0.0839073i	0.889231	−	0.457459i	$-0.151240\pi$
$619$	1.20527	+	2.08759i	0.0484439	+	0.0839073i	−0.840787	+	0.541367i	$0.817907\pi$
$620$		0			0
$621$	26.1766	+	21.9648i	1.05043	+	0.881417i
$622$	−8.38578	−	3.05217i	−0.336239	−	0.122381i
$623$	5.92514	−	2.15658i	0.237386	−	0.0864014i
$624$	5.53596	−	4.64522i	0.221616	−	0.185958i
$625$		0			0
$626$	−18.3259			−0.732452
$627$	0.935822	−	0.549522i	0.0373731	−	0.0219458i
$628$	7.44831			0.297220
$629$	−5.56330	−	31.5510i	−0.221823	−	1.25802i
$630$		0			0
$631$	1.26769	−	0.461403i	0.0504661	−	0.0183681i	−0.316664	−	0.948538i	$-0.602563\pi$
$631$	1.26769	−	0.461403i	0.0504661	−	0.0183681i	0.367130	+	0.930170i	$0.380340\pi$
$632$	−0.939693	−	0.342020i	−0.0373790	−	0.0136048i
$633$	−29.0330	−	24.3616i	−1.15396	−	0.968287i
$634$	12.1309	−	21.0113i	0.481779	−	0.834465i
$635$		0			0
$636$	−1.58125	+	8.96773i	−0.0627007	+	0.355593i
$637$	−2.84049	+	16.1092i	−0.112544	+	0.638270i
$638$	−0.194126	−	0.336236i	−0.00768552	−	0.0133117i
$639$	−0.832748	+	1.44236i	−0.0329430	+	0.0570590i
$640$		0			0
$641$	−32.3910	−	11.7894i	−1.27937	−	0.465652i	−0.389144	−	0.921177i	$-0.627229\pi$
$641$	−32.3910	−	11.7894i	−1.27937	−	0.465652i	−0.890223	+	0.455525i	$0.849452\pi$
$642$	−5.26991	+	1.91809i	−0.207987	+	0.0757011i
$643$	−15.5797	+	13.0729i	−0.614402	+	0.515544i	−0.896038	−	0.443977i	$-0.853567\pi$
$643$	−15.5797	+	13.0729i	−0.614402	+	0.515544i	0.281636	+	0.959521i	$0.409123\pi$
$644$	−1.99273	−	11.3013i	−0.0785244	−	0.445334i
$645$		0			0
$646$	6.34982	−	17.8539i	0.249830	−	0.702451i
$647$	41.9427			1.64894			0.824470	−	0.565906i	$-0.191474\pi$
$647$	41.9427			1.64894			0.824470	+	0.565906i	$0.191474\pi$
$648$	1.14883	+	6.51536i	0.0451304	+	0.255947i
$649$	0.507741	−	0.426045i	0.0199306	−	0.0167237i
$650$		0			0
$651$	9.84389	+	3.58288i	0.385813	+	0.140424i
$652$	−5.17230	−	4.34008i	−0.202563	−	0.169971i
$653$	−15.0398	+	26.0497i	−0.588554	+	1.01941i	0.405868	+	0.913932i	$0.366969\pi$
$653$	−15.0398	+	26.0497i	−0.588554	+	1.01941i	−0.994422	+	0.105474i	$0.966364\pi$
$654$	2.47771	+	4.29152i	0.0968862	+	0.167812i
$655$		0			0
$656$	0.411474	−	2.33359i	0.0160654	−	0.0911112i
$657$	−5.12449	−	8.87587i	−0.199925	−	0.346281i
$658$	−6.46451	+	11.1969i	−0.252013	+	0.436499i
$659$	37.7001	+	31.6342i	1.46859	+	1.23229i	0.917434	+	0.397888i	$0.130257\pi$
$659$	37.7001	+	31.6342i	1.46859	+	1.23229i	0.551154	+	0.834404i	$0.314188\pi$
$660$		0			0
$661$	−44.5330	+	16.2087i	−1.73213	+	0.630445i	−0.998779	−	0.0494010i	$-0.984269\pi$
$661$	−44.5330	+	16.2087i	−1.73213	+	0.630445i	−0.733355	+	0.679846i	$0.762047\pi$
$662$	−25.8883	+	21.7229i	−1.00618	+	0.844283i
$663$	5.45542	+	30.9392i	0.211871	+	1.20158i
$664$	−1.02229			−0.0396725
$665$		0			0
$666$	−4.81016			−0.186390
$667$	−2.53327	−	14.3669i	−0.0980886	−	0.556288i
$668$	−12.4513	+	10.4479i	−0.481755	+	0.404241i
$669$	−21.8837	+	7.96502i	−0.846074	+	0.307946i
$670$		0			0
$671$	−0.293167	−	0.245996i	−0.0113176	−	0.00949659i
$672$	1.43969	−	2.49362i	0.0555373	−	0.0961935i
$673$	0.771259	+	1.33586i	0.0297299	+	0.0514936i	0.880508	−	0.474032i	$-0.157202\pi$
$673$	0.771259	+	1.33586i	0.0297299	+	0.0514936i	−0.850778	+	0.525526i	$0.823869\pi$
$674$	−5.16978	+	29.3193i	−0.199132	+	1.12934i
$675$		0			0
$676$	−4.62449	−	8.00984i	−0.177865	−	0.308071i
$677$	−9.04101	+	15.6595i	−0.347474	+	0.601843i	−0.985800	−	0.167923i	$-0.946294\pi$
$677$	−9.04101	+	15.6595i	−0.347474	+	0.601843i	0.638326	+	0.769766i	$0.279627\pi$
$678$	−17.8105	−	14.9448i	−0.684007	−	0.573950i
$679$	31.5638	+	11.4883i	1.21131	+	0.440879i
$680$		0			0
$681$	21.9440	−	18.4132i	0.840897	−	0.705596i
$682$	−0.102663	−	0.582232i	−0.00393118	−	0.0222948i
$683$	−22.1976			−0.849367			−0.424684	−	0.905342i	$-0.639615\pi$
$683$	−22.1976			−0.849367			−0.424684	+	0.905342i	$0.639615\pi$
$684$	−2.47431	−	1.40436i	−0.0946075	−	0.0536970i
$685$		0			0
$686$	3.41622	+	19.3744i	0.130432	+	0.739716i
$687$	−23.3666	+	19.6069i	−0.891493	+	0.748052i
$688$	0.613341	−	0.223238i	0.0233834	−	0.00851086i
$689$	26.3444	+	9.58856i	1.00364	+	0.365295i
$690$		0			0
$691$	21.9449	−	38.0097i	0.834824	−	1.44596i	−0.0593503	−	0.998237i	$-0.518903\pi$
$691$	21.9449	−	38.0097i	0.834824	−	1.44596i	0.894174	−	0.447720i	$-0.147764\pi$
$692$	−2.81908	−	4.88279i	−0.107165	−	0.185616i
$693$	0.0346151	−	0.196312i	0.00131492	−	0.00745728i
$694$	0.542766	−	3.07818i	0.0206031	−	0.116846i
$695$		0			0
$696$	1.83022	−	3.17004i	0.0693744	−	0.120160i
$697$	7.89124	+	6.62154i	0.298902	+	0.250809i
$698$	−7.30453	−	2.65863i	−0.276481	−	0.100631i
$699$	−40.2806	+	14.6610i	−1.52355	+	0.554528i
$700$		0			0
$701$	−0.955423	−	5.41847i	−0.0360858	−	0.204653i	0.961434	−	0.275035i	$-0.0886893\pi$
$701$	−0.955423	−	5.41847i	−0.0360858	−	0.204653i	−0.997520	+	0.0703819i	$0.977578\pi$
$702$	26.3969			0.996288
$703$	−20.4667	+	24.7592i	−0.771917	+	0.933811i
$704$	−0.162504			−0.00612459
$705$		0			0
$706$	−22.3935	+	18.7904i	−0.842791	+	0.707186i
$707$	−15.7297	+	5.72513i	−0.591575	+	0.215316i
$708$	5.87211	+	2.13727i	0.220687	+	0.0803237i
$709$	−35.7105	−	29.9647i	−1.34114	−	1.12535i	−0.981332	−	0.192321i	$-0.938399\pi$
$709$	−35.7105	−	29.9647i	−1.34114	−	1.12535i	−0.359805	−	0.933027i	$-0.617157\pi$
$710$		0			0
$711$	−0.326352	−	0.565258i	−0.0122391	−	0.0211988i
$712$	0.582596	−	3.30407i	0.0218337	−	0.123825i
$713$	3.85756	−	21.8773i	0.144467	−	0.819312i
$714$	6.25877	+	10.8405i	0.234229	+	0.405696i
$715$		0			0
$716$	8.80587	+	7.38901i	0.329091	+	0.276140i
$717$	37.9543	+	13.8142i	1.41743	+	0.515902i
$718$	16.9547	−	6.17101i	0.632744	−	0.230300i
$719$	−9.20052	+	7.72016i	−0.343122	+	0.287913i	−0.798021	−	0.602630i	$-0.794120\pi$
$719$	−9.20052	+	7.72016i	−0.343122	+	0.287913i	0.454899	+	0.890543i	$0.349675\pi$
$720$		0			0
$721$	−15.5030			−0.577362
$722$	−17.7565	+	6.76055i	−0.660830	+	0.251601i
$723$	26.3141			0.978631
$724$	2.61200	+	14.8134i	0.0970741	+	0.550535i
$725$		0			0
$726$	−15.7986	+	5.75022i	−0.586341	+	0.213411i
$727$	29.1215	+	10.5994i	1.08006	+	0.393109i	0.819929	−	0.572465i	$-0.194013\pi$
$727$	29.1215	+	10.5994i	1.08006	+	0.393109i	0.260129	+	0.965574i	$0.416235\pi$
$728$	−6.79086	−	5.69821i	−0.251686	−	0.211190i
$729$	−15.0201	+	26.0155i	−0.556299	+	0.963538i
$730$		0			0
$731$	−0.492726	+	2.79439i	−0.0182241	+	0.103354i
$732$	0.626545	−	3.55331i	0.0231578	−	0.131334i
$733$	0.600137	+	1.03947i	0.0221666	+	0.0383936i	0.876896	−	0.480680i	$-0.159610\pi$
$733$	0.600137	+	1.03947i	0.0221666	+	0.0383936i	−0.854729	+	0.519074i	$0.826277\pi$
$734$	−8.34271	+	14.4500i	−0.307935	+	0.533359i
$735$		0			0
$736$	−5.73783	−	2.08840i	−0.211499	−	0.0769794i
$737$	−0.250152	+	0.0910480i	−0.00921448	+	0.00335380i
$738$	1.18479	−	0.994159i	0.0436128	−	0.0365955i
$739$	−2.15880	−	12.2431i	−0.0794126	−	0.450371i	−0.998423	−	0.0561379i	$-0.982121\pi$
$739$	−2.15880	−	12.2431i	−0.0794126	−	0.450371i	0.919010	−	0.394233i	$-0.128990\pi$
$740$		0			0
$741$	20.0699	−	24.2791i	0.737285	−	0.891915i
$742$	11.1702			0.410073
$743$	0.488140	+	2.76838i	0.0179081	+	0.101562i	0.992452	−	0.122636i	$-0.0391348\pi$
$743$	0.488140	+	2.76838i	0.0179081	+	0.101562i	−0.974544	+	0.224198i	$0.928024\pi$
$744$	4.26991	−	3.58288i	0.156543	−	0.131355i
$745$		0			0
$746$	−7.32800	−	2.66717i	−0.268297	−	0.0976522i
$747$	−0.511144	−	0.428901i	−0.0187018	−	0.0156927i
$748$	0.353226	−	0.611806i	0.0129152	−	0.0223698i
$749$	3.43969	+	5.95772i	0.125684	+	0.217690i
$750$		0			0
$751$	−1.38326	+	7.84483i	−0.0504757	+	0.286262i	−0.999589	−	0.0286734i	$-0.990872\pi$
$751$	−1.38326	+	7.84483i	−0.0504757	+	0.286262i	0.949113	+	0.314935i	$0.101983\pi$
$752$	3.43969	+	5.95772i	0.125433	+	0.217256i
$753$	−12.3268	+	21.3507i	−0.449214	+	0.778062i
$754$	−8.63294	−	7.24390i	−0.314393	−	0.263807i
$755$		0			0
$756$	9.88326	−	3.59721i	0.359451	−	0.130829i
$757$	10.6834	−	8.96448i	0.388297	−	0.325819i	−0.427653	−	0.903943i	$-0.640659\pi$
$757$	10.6834	−	8.96448i	0.388297	−	0.325819i	0.815949	+	0.578124i	$0.196215\pi$
$758$	−0.229208	−	1.29990i	−0.00832520	−	0.0472146i
$759$	1.52023			0.0551808
$760$		0			0
$761$	−47.8043			−1.73290			−0.866452	−	0.499261i	$-0.833605\pi$
$761$	−47.8043			−1.73290			−0.866452	+	0.499261i	$0.833605\pi$
$762$	−5.30722	−	30.0987i	−0.192260	−	1.09036i
$763$	4.65657	−	3.90733i	0.168579	−	0.141455i
$764$	−18.9941	+	6.91328i	−0.687181	+	0.250114i
$765$		0			0
$766$	−25.4349	−	21.3425i	−0.919002	−	0.771134i
$767$	9.61943	−	16.6613i	0.347338	−	0.601606i
$768$	−0.766044	−	1.32683i	−0.0276422	−	0.0478778i
$769$	−2.86080	+	16.2244i	−0.103163	+	0.585068i	0.888775	+	0.458344i	$0.151557\pi$
$769$	−2.86080	+	16.2244i	−0.103163	+	0.585068i	−0.991938	+	0.126724i	$0.959554\pi$
$770$		0			0
$771$	10.8348	+	18.7664i	0.390206	+	0.675857i
$772$	5.03849	−	8.72691i	0.181339	−	0.314088i
$773$	−7.72534	−	6.48233i	−0.277861	−	0.233153i	0.493197	−	0.869917i	$-0.335828\pi$
$773$	−7.72534	−	6.48233i	−0.277861	−	0.233153i	−0.771059	+	0.636764i	$0.780272\pi$
$774$	0.400330	+	0.145708i	0.0143896	+	0.00523737i
$775$		0			0
$776$	13.6912	−	11.4883i	0.491485	−	0.412405i
$777$	−3.68479	−	20.8975i	−0.132191	−	0.749694i
$778$	−14.8571			−0.532653
$779$	−0.0760373	−	10.3285i	−0.00272432	−	0.370057i
$780$		0			0
$781$	0.0720048	+	0.408360i	0.00257654	+	0.0146123i
$782$	20.3346	−	17.0627i	0.727162	−	0.610162i
$783$	12.5642	−	4.57299i	0.449007	−	0.163425i
$784$	3.25877	+	1.18610i	0.116385	+	0.0423606i
$785$		0			0
$786$	−12.9422	+	22.4166i	−0.461634	+	0.799573i
$787$	−18.0219	−	31.2148i	−0.642411	−	1.11269i	−0.984893	−	0.173164i	$-0.944601\pi$
$787$	−18.0219	−	31.2148i	−0.642411	−	1.11269i	0.342483	−	0.939524i	$-0.388732\pi$
$788$	−2.27450	+	12.8993i	−0.0810257	+	0.459520i
$789$	−3.49092	+	19.7980i	−0.124280	+	0.704826i
$790$		0			0
$791$	−14.2601	+	24.6992i	−0.507031	+	0.878204i
$792$	−0.0812519	−	0.0681784i	−0.00288716	−	0.00242262i
$793$	−10.4385	−	3.79931i	−0.370682	−	0.134917i
$794$	−8.09374	+	2.94588i	−0.287236	+	0.104545i
$795$		0			0
$796$	−3.05257	−	17.3120i	−0.108195	−	0.613606i
$797$	3.42190			0.121210			0.0606050	−	0.998162i	$-0.480697\pi$
$797$	3.42190			0.121210			0.0606050	+	0.998162i	$0.480697\pi$
$798$	4.20574	−	11.8253i	0.148881	−	0.418612i
$799$	−29.9067			−1.05802
$800$		0			0
$801$	1.67752	−	1.40761i	0.0592722	−	0.0497353i
$802$	−4.79901	+	1.74670i	−0.169459	+	0.0616780i
$803$	−2.39780	−	0.872729i	−0.0846166	−	0.0307979i
$804$	−1.92262	−	1.61327i	−0.0678055	−	0.0568956i
$805$		0			0
$806$	−8.58037	−	14.8616i	−0.302231	−	0.523479i
$807$	−5.97359	+	33.8779i	−0.210280	+	1.19256i
$808$	−1.54664	+	8.77141i	−0.0544105	+	0.308577i
$809$	−3.73870	−	6.47562i	−0.131446	−	0.227671i	0.792788	−	0.609497i	$-0.208629\pi$
$809$	−3.73870	−	6.47562i	−0.131446	−	0.227671i	−0.924234	+	0.381826i	$0.875295\pi$
$810$		0			0
$811$	37.6810	+	31.6181i	1.32316	+	1.11026i	0.985625	+	0.168948i	$0.0540369\pi$
$811$	37.6810	+	31.6181i	1.32316	+	1.11026i	0.337533	+	0.941314i	$0.390408\pi$
$812$	−4.21941	−	1.53574i	−0.148072	−	0.0538939i
$813$	8.30066	−	3.02119i	0.291117	−	0.105958i
$814$	−0.917404	+	0.769793i	−0.0321550	+	0.0269812i
$815$		0			0
$816$	6.66044			0.233162
$817$	2.45336	−	1.44063i	0.0858323	−	0.0504014i
$818$	−28.8307			−1.00804
$819$	−1.00475	−	5.69821i	−0.0351087	−	0.199111i
$820$		0			0
$821$	−8.84611	+	3.21972i	−0.308732	+	0.112369i	−0.491740	−	0.870742i	$-0.663639\pi$
$821$	−8.84611	+	3.21972i	−0.308732	+	0.112369i	0.183008	+	0.983111i	$0.441417\pi$
$822$	7.16637	+	2.60835i	0.249956	+	0.0909765i
$823$	32.4165	+	27.2007i	1.12997	+	0.948157i	0.999065	−	0.0432384i	$-0.0137675\pi$
$823$	32.4165	+	27.2007i	1.12997	+	0.948157i	0.130904	+	0.991395i	$0.458212\pi$
$824$	−4.12449	+	7.14382i	−0.143683	+	0.248867i
$825$		0			0
$826$	1.33110	−	7.54904i	0.0463149	−	0.262665i
$827$	−4.63950	+	26.3119i	−0.161331	+	0.914955i	0.791436	+	0.611252i	$0.209334\pi$
$827$	−4.63950	+	26.3119i	−0.161331	+	0.914955i	−0.952767	+	0.303702i	$0.901777\pi$
$828$	−1.99273	−	3.45150i	−0.0692520	−	0.119948i
$829$	−7.24257	+	12.5445i	−0.251545	+	0.435689i	−0.963951	−	0.266078i	$-0.914272\pi$
$829$	−7.24257	+	12.5445i	−0.251545	+	0.435689i	0.712406	+	0.701767i	$0.247605\pi$
$830$		0			0
$831$	−28.4675	−	10.3613i	−0.987527	−	0.359430i
$832$	−4.43242	+	1.61327i	−0.153666	+	0.0559300i
$833$	−11.5489	+	9.69069i	−0.400146	+	0.335763i
$834$	4.98158	+	28.2520i	0.172498	+	0.978285i
$835$		0			0
$836$	−0.696652	+	0.128134i	−0.0240942	+	0.00443159i
$837$	20.3601			0.703748
$838$	1.33069	+	7.54671i	0.0459679	+	0.260697i
$839$	0.409663	−	0.343748i	0.0141431	−	0.0118675i	−0.635689	−	0.771946i	$-0.719284\pi$
$839$	0.409663	−	0.343748i	0.0141431	−	0.0118675i	0.649832	+	0.760078i	$0.274839\pi$
$840$		0			0
$841$	21.8871	+	7.96626i	0.754728	+	0.274699i
$842$	−5.14930	−	4.32078i	−0.177457	−	0.148904i
$843$	−24.2854	+	42.0635i	−0.836433	+	1.44875i
$844$	12.3687	+	21.4232i	0.425748	+	0.737418i
$845$		0			0
$846$	−0.779715	+	4.42198i	−0.0268072	+	0.152031i
$847$	10.3118	+	17.8606i	0.354318	+	0.613696i
$848$	2.97178	−	5.14728i	0.102051	−	0.176758i
$849$	3.45155	+	2.89620i	0.118457	+	0.0993972i
$850$		0			0
$851$	−42.2854	+	15.3906i	−1.44952	+	0.527584i
$852$	−2.99479	+	2.51292i	−0.102600	+	0.0860913i
$853$	1.08424	+	6.14906i	0.0371238	+	0.210540i	0.997727	−	0.0673834i	$-0.0214651\pi$
$853$	1.08424	+	6.14906i	0.0371238	+	0.210540i	−0.960603	+	0.277923i	$0.910354\pi$
$854$	−4.42602			−0.151455
$855$		0			0
$856$	3.66044			0.125111
$857$	2.31996	+	13.1571i	0.0792482	+	0.449439i	0.998450	+	0.0556524i	$0.0177239\pi$
$857$	2.31996	+	13.1571i	0.0792482	+	0.449439i	−0.919202	+	0.393786i	$0.871165\pi$
$858$	0.899615	−	0.754866i	0.0307123	−	0.0257707i
$859$	6.98070	−	2.54077i	0.238179	−	0.0866899i	−0.220173	−	0.975461i	$-0.570662\pi$
$859$	6.98070	−	2.54077i	0.238179	−	0.0866899i	0.458352	+	0.888771i	$0.348440\pi$
$860$		0			0
$861$	5.22668	+	4.38571i	0.178125	+	0.149464i
$862$	8.17886	−	14.1662i	0.278573	−	0.482503i
$863$	−9.23277	−	15.9916i	−0.314287	−	0.544362i	0.664998	−	0.746845i	$-0.268432\pi$
$863$	−9.23277	−	15.9916i	−0.314287	−	0.544362i	−0.979286	+	0.202483i	$0.935099\pi$
$864$	0.971782	−	5.51125i	0.0330607	−	0.187496i
$865$		0			0
$866$	−5.10354	−	8.83959i	−0.173425	−	0.300382i
$867$	−1.45471	+	2.51963i	−0.0494045	+	0.0855710i
$868$	−5.23783	−	4.39506i	−0.177783	−	0.149178i
$869$	−0.152704	−	0.0555796i	−0.00518012	−	0.00188541i
$870$		0			0
$871$	−5.91921	+	4.96681i	−0.200565	+	0.168294i
$872$	−0.561652	−	3.18528i	−0.0190199	−	0.107867i
$873$	11.6655			0.394817
$874$	−26.2447	−	4.42869i	−0.887740	−	0.149803i
$875$		0			0
$876$	−4.17752	−	23.6919i	−0.141145	−	0.800475i
$877$	11.4349	−	9.59506i	0.386131	−	0.324002i	−0.428973	−	0.903317i	$-0.641124\pi$
$877$	11.4349	−	9.59506i	0.386131	−	0.324002i	0.815104	+	0.579315i	$0.196680\pi$
$878$	−8.95723	+	3.26017i	−0.302292	+	0.110025i
$879$	−23.4636	−	8.54006i	−0.791409	−	0.288049i
$880$		0			0
$881$	11.8491	−	20.5233i	0.399207	−	0.691446i	−0.594422	−	0.804154i	$-0.702619\pi$
$881$	11.8491	−	20.5233i	0.399207	−	0.691446i	0.993628	+	0.112707i	$0.0359523\pi$
$882$	1.13176	+	1.96026i	0.0381083	+	0.0660055i
$883$	2.33868	−	13.2633i	0.0787028	−	0.446346i	−0.919836	−	0.392303i	$-0.871678\pi$
$883$	2.33868	−	13.2633i	0.0787028	−	0.446346i	0.998539	−	0.0540423i	$-0.0172106\pi$
$884$	3.56077	−	20.1942i	0.119762	−	0.679203i
$885$		0			0
$886$	2.99138	−	5.18123i	0.100497	−	0.174067i
$887$	21.2017	+	17.7903i	0.711884	+	0.597341i	0.925127	−	0.379658i	$-0.123958\pi$
$887$	21.2017	+	17.7903i	0.711884	+	0.597341i	−0.213243	+	0.976999i	$0.568403\pi$
$888$	−10.6099	−	3.86170i	−0.356046	−	0.129590i
$889$	−35.2301	+	12.8227i	−1.18158	+	0.430060i
$890$		0			0
$891$	0.186690	+	1.05877i	0.00625434	+	0.0354701i
$892$	15.2003			0.508943
$893$	19.4436	+	22.8285i	0.650654	+	0.763927i
$894$	20.4953			0.685464
$895$		0			0
$896$	−1.43969	+	1.20805i	−0.0480968	+	0.0403580i
$897$	41.4654	−	15.0922i	1.38449	−	0.503913i
$898$	−14.4290	−	5.25173i	−0.481502	−	0.175253i
$899$	−6.65863	−	5.58726i	−0.222078	−	0.186345i
$900$		0			0
$901$	12.9192	+	22.3767i	0.430401	+	0.745477i
$902$	0.0668661	−	0.379217i	0.00222640	−	0.0126265i
$903$	−0.326352	+	1.85083i	−0.0108603	+	0.0615919i
$904$	7.58765	+	13.1422i	0.252361	+	0.437103i
$905$		0			0
$906$	17.4461	+	14.6390i	0.579607	+	0.486348i
$907$	0.426022	+	0.155059i	0.0141458	+	0.00514866i	0.349083	−	0.937092i	$-0.386493\pi$
$907$	0.426022	+	0.155059i	0.0141458	+	0.00514866i	−0.334938	+	0.942240i	$0.608715\pi$
$908$	−17.5697	+	6.39485i	−0.583071	+	0.212220i
$909$	−4.45336	+	3.73682i	−0.147709	+	0.123942i
$910$		0			0
$911$	48.6492			1.61182			0.805910	−	0.592038i	$-0.201677\pi$
$911$	48.6492			1.61182			0.805910	+	0.592038i	$0.201677\pi$
$912$	−4.33022	−	5.08407i	−0.143388	−	0.168351i
$913$	−0.166126			−0.00549796
$914$	1.97936	+	11.2255i	0.0654714	+	0.371307i
$915$		0			0
$916$	18.7087	−	6.80942i	0.618154	−	0.224990i
$917$	29.8371	+	10.8598i	0.985307	+	0.358623i
$918$	18.6368	+	15.6381i	0.615106	+	0.516136i
$919$	−16.7733	+	29.0522i	−0.553301	+	0.958345i	0.444733	+	0.895663i	$0.353299\pi$
$919$	−16.7733	+	29.0522i	−0.553301	+	0.958345i	−0.998034	+	0.0626817i	$0.980035\pi$
$920$		0			0
$921$	−5.90167	+	33.4701i	−0.194467	+	1.10288i
$922$	7.01930	−	39.8084i	0.231168	−	1.31102i
$923$	6.01801	+	10.4235i	0.198085	+	0.343094i
$924$	0.233956	−	0.405223i	0.00769657	−	0.0133309i
$925$		0			0
$926$	9.35591	+	3.40527i	0.307454	+	0.111904i
$927$	−5.05943	+	1.84148i	−0.166173	+	0.0604822i
$928$	−1.83022	+	1.53574i	−0.0600800	+	0.0504131i
$929$	−6.50016	−	36.8643i	−0.213263	−	1.20948i	−0.883895	−	0.467686i	$-0.845088\pi$
$929$	−6.50016	−	36.8643i	−0.213263	−	1.20948i	0.670631	−	0.741791i	$-0.266023\pi$
$930$		0			0
$931$	14.9055	+	2.51525i	0.488509	+	0.0824340i
$932$	27.9786			0.916471
$933$	−2.37417	−	13.4646i	−0.0777269	−	0.440811i
$934$	4.29607	−	3.60483i	0.140572	−	0.117954i
$935$		0			0
$936$	−2.89306	−	1.05299i	−0.0945625	−	0.0344179i
$937$	−2.76533	−	2.32039i	−0.0903394	−	0.0758037i	0.596500	−	0.802613i	$-0.296558\pi$
$937$	−2.76533	−	2.32039i	−0.0903394	−	0.0758037i	−0.686839	+	0.726810i	$0.741002\pi$
$938$	−1.53936	+	2.66625i	−0.0502620	+	0.0870563i
$939$	−14.0385	−	24.3154i	−0.458129	−	0.793502i
$940$		0			0
$941$	−6.28540	+	35.6463i	−0.204898	+	1.16203i	0.692702	+	0.721224i	$0.256420\pi$
$941$	−6.28540	+	35.6463i	−0.204898	+	1.16203i	−0.897600	+	0.440811i	$0.854691\pi$
$942$	5.70574	+	9.88263i	0.185903	+	0.321993i
$943$	7.23442	−	12.5304i	0.235585	−	0.408046i
$944$	−3.12449	−	2.62175i	−0.101693	−	0.0853308i
$945$		0			0
$946$	0.0996702	−	0.0362770i	0.00324056	−	0.00117947i
$947$	22.7388	−	19.0801i	0.738910	−	0.620019i	−0.193634	−	0.981074i	$-0.562028\pi$
$947$	22.7388	−	19.0801i	0.738910	−	0.620019i	0.932545	+	0.361054i	$0.117583\pi$
$948$	−0.266044	−	1.50881i	−0.00864072	−	0.0490040i
$949$	−74.0660			−2.40429
$950$		0			0
$951$	37.1712			1.20536
$952$	−1.41875	−	8.04612i	−0.0459819	−	0.260776i
$953$	−11.3300	+	9.50698i	−0.367014	+	0.307961i	−0.807579	−	0.589759i	$-0.799223\pi$
$953$	−11.3300	+	9.50698i	−0.367014	+	0.307961i	0.440565	+	0.897721i	$0.354778\pi$
$954$	3.64543	−	1.32683i	0.118025	−	0.0429576i
$955$		0			0
$956$	−20.1951	−	16.9457i	−0.653155	−	0.548062i
$957$	0.297418	−	0.515143i	0.00961416	−	0.0166522i
$958$	−12.3648	−	21.4165i	−0.399490	−	0.691937i
$959$	1.62449	−	9.21291i	0.0524574	−	0.297500i
$960$		0			0
$961$	8.88191	+	15.3839i	0.286513	+	0.496256i
$962$	−17.3807	+	30.1043i	−0.560377	+	0.970602i
$963$	1.83022	+	1.53574i	0.0589781	+	0.0494885i
$964$	−16.1395	−	5.87430i	−0.519818	−	0.189198i
$965$		0			0
$966$	13.4684	−	11.3013i	0.433338	−	0.363614i
$967$	−7.80288	−	44.2523i	−0.250924	−	1.42306i	−0.806323	−	0.591475i	$-0.798546\pi$
$967$	−7.80288	−	44.2523i	−0.250924	−	1.42306i	0.555399	−	0.831584i	$-0.312565\pi$
$968$	10.9736			0.352705
$969$	28.5533	−	5.25173i	0.917263	−	0.168710i
$970$		0			0
$971$	−6.95946	−	39.4690i	−0.223340	−	1.26662i	−0.865834	−	0.500331i	$-0.833212\pi$
$971$	−6.95946	−	39.4690i	−0.223340	−	1.26662i	0.642495	−	0.766290i	$-0.277900\pi$
$972$	5.09627	−	4.27628i	0.163463	−	0.137162i
$973$	33.0685	−	12.0360i	1.06013	−	0.385855i
$974$	−12.2071	−	4.44301i	−0.391140	−	0.142363i
$975$		0			0
$976$	−1.17752	+	2.03952i	−0.0376915	+	0.0652835i
$977$	−25.6109	−	44.3593i	−0.819364	−	1.41918i	−0.906151	−	0.422954i	$-0.860993\pi$
$977$	−25.6109	−	44.3593i	−0.819364	−	1.41918i	0.0867869	−	0.996227i	$-0.472340\pi$
$978$	1.79632	−	10.1875i	0.0574401	−	0.325759i
$979$	0.0946741	−	0.536923i	0.00302580	−	0.0171601i
$980$		0			0
$981$	1.05556	−	1.82828i	0.0337014	−	0.0583726i
$982$	−14.2947	−	11.9947i	−0.456163	−	0.382766i
$983$	8.59792	+	3.12939i	0.274231	+	0.0998119i	0.475475	−	0.879729i	$-0.342276\pi$
$983$	8.59792	+	3.12939i	0.274231	+	0.0998119i	−0.201244	+	0.979541i	$0.564498\pi$
$984$	3.41147	−	1.24168i	0.108754	−	0.0395832i
$985$		0			0
$986$	−1.80360	−	10.2287i	−0.0574382	−	0.325748i
$987$	−19.8084			−0.630508
$988$	−17.7297	+	10.4110i	−0.564056	+	0.331218i
$989$	3.98545			0.126730
$990$		0			0
$991$	−21.2153	+	17.8017i	−0.673926	+	0.565491i	−0.914224	−	0.405208i	$-0.867199\pi$
$991$	−21.2153	+	17.8017i	−0.673926	+	0.565491i	0.240299	+	0.970699i	$0.422755\pi$
$992$	−3.41875	+	1.24432i	−0.108545	+	0.0395073i
$993$	−48.6541	−	17.7086i	−1.54399	−	0.561967i
$994$	3.67365	+	3.08256i	0.116521	+	0.0977728i
$995$		0			0
$996$	−0.783119	−	1.35640i	−0.0248141	−	0.0429792i
$997$	−6.28328	+	35.6343i	−0.198993	+	1.12855i	0.707622	+	0.706591i	$0.249768\pi$
$997$	−6.28328	+	35.6343i	−0.198993	+	1.12855i	−0.906616	+	0.421957i	$0.861343\pi$
$998$	3.00016	−	17.0148i	0.0949685	−	0.538593i
$999$	−20.6211	−	35.7168i	−0.652422	−	1.13003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.f.351.1	yes	6
5.2	odd	4		950.2.u.a.199.2		12
5.3	odd	4		950.2.u.a.199.1		12
5.4	even	2		950.2.l.a.351.1	✓	6
19.17	even	9	inner	950.2.l.f.701.1	yes	6
95.17	odd	36		950.2.u.a.549.1		12
95.74	even	18		950.2.l.a.701.1	yes	6
95.93	odd	36		950.2.u.a.549.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.a.351.1	✓	6	5.4	even	2
950.2.l.a.701.1	yes	6	95.74	even	18
950.2.l.f.351.1	yes	6	1.1	even	1	trivial
950.2.l.f.701.1	yes	6	19.17	even	9	inner
950.2.u.a.199.1		12	5.3	odd	4
950.2.u.a.199.2		12	5.2	odd	4
950.2.u.a.549.1		12	95.17	odd	36
950.2.u.a.549.2		12	95.93	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(1.17365 - 0.984808i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-0.939693 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.113341 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(1.17365 - 0.984808i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.17365 - 0.984808i) q^{6} +(-0.939693 + 1.62760i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.113341 + 0.642788i) q^{9} +(0.0812519 + 0.140732i) q^{11} +(-0.766044 + 1.32683i) q^{12} +(3.61334 + 3.03195i) q^{13} +(1.76604 + 0.642788i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.754900 + 4.28125i) q^{17} +0.652704 q^{18} +(2.77719 - 3.35965i) q^{19} +(0.500000 + 2.83564i) q^{21} +(0.124485 - 0.104455i) q^{22} +(5.73783 - 2.08840i) q^{23} +(1.43969 + 0.524005i) q^{24} +(2.35844 - 4.08494i) q^{26} +(2.79813 + 4.84651i) q^{27} +(0.326352 - 1.85083i) q^{28} +(0.414878 - 2.35289i) q^{29} +(1.81908 - 3.15074i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.233956 + 0.0851529i) q^{33} +(4.08512 - 1.48686i) q^{34} +(-0.113341 - 0.642788i) q^{36} -7.36959 q^{37} +(-3.79086 - 2.15160i) q^{38} +7.22668 q^{39} +(1.81521 - 1.52314i) q^{41} +(2.70574 - 0.984808i) q^{42} +(0.613341 + 0.223238i) q^{43} +(-0.124485 - 0.104455i) q^{44} +(-3.05303 - 5.28801i) q^{46} +(-1.19459 + 6.77487i) q^{47} +(0.266044 - 1.50881i) q^{48} +(1.73396 + 3.00330i) q^{49} +(5.10220 + 4.28125i) q^{51} +(-4.43242 - 1.61327i) q^{52} +(5.58512 - 2.03282i) q^{53} +(4.28699 - 3.59721i) q^{54} -1.87939 q^{56} +(-0.0491630 - 6.67804i) q^{57} -2.38919 q^{58} +(-0.708263 - 4.01676i) q^{59} +(-2.21301 + 0.805470i) q^{61} +(-3.41875 - 1.24432i) q^{62} +(-0.939693 - 0.788496i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0432332 - 0.245188i) q^{66} +(-0.284463 + 1.61327i) q^{67} +(-2.17365 - 3.76487i) q^{68} +(4.67752 - 8.10170i) q^{69} +(2.39780 + 0.872729i) q^{71} +(-0.613341 + 0.223238i) q^{72} +(-12.0287 + 10.0933i) q^{73} +(1.27972 + 7.25762i) q^{74} +(-1.46064 + 4.10689i) q^{76} -0.305407 q^{77} +(-1.25490 - 7.11689i) q^{78} +(-0.766044 + 0.642788i) q^{79} +(6.21688 + 2.26276i) q^{81} +(-1.81521 - 1.52314i) q^{82} +(-0.511144 + 0.885328i) q^{83} +(-1.43969 - 2.49362i) q^{84} +(0.113341 - 0.642788i) q^{86} +(-1.83022 - 3.17004i) q^{87} +(-0.0812519 + 0.140732i) q^{88} +(-2.57011 - 2.15658i) q^{89} +(-8.33022 + 3.03195i) q^{91} +(-4.67752 + 3.92490i) q^{92} +(-0.967911 - 5.48930i) q^{93} +6.87939 q^{94} -1.53209 q^{96} +(-3.10354 - 17.6011i) q^{97} +(2.65657 - 2.22913i) q^{98} +(-0.0996702 + 0.0362770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} - 6 q^{6} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 - 6 * q^6 + 3 * q^8 + 6 * q^9	\( 6 q + 6 q^{3} - 6 q^{6} + 3 q^{8} + 6 q^{9} + 3 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{17} + 6 q^{18} + 6 q^{19} + 3 q^{21} - 12 q^{22} + 15 q^{23} + 3 q^{24} + 6 q^{26} + 3 q^{27} + 3 q^{28} + 24 q^{29} - 6 q^{31} + 6 q^{33} + 3 q^{34} + 6 q^{36} - 30 q^{37} + 9 q^{38} + 30 q^{39} + 18 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 6 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} + 30 q^{51} - 3 q^{52} + 12 q^{53} + 18 q^{54} - 12 q^{57} - 6 q^{58} + 21 q^{59} - 21 q^{61} - 18 q^{62} - 3 q^{64} - 15 q^{66} - 9 q^{67} - 12 q^{68} + 3 q^{69} + 15 q^{71} + 3 q^{72} - 21 q^{73} - 18 q^{74} - 6 q^{77} - 9 q^{78} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 3 q^{84} - 6 q^{86} + 12 q^{87} - 3 q^{88} - 24 q^{89} - 27 q^{91} - 3 q^{92} - 15 q^{93} + 30 q^{94} - 9 q^{97} - 6 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q + 6 * q^3 - 6 * q^6 + 3 * q^8 + 6 * q^9 + 3 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^17 + 6 * q^18 + 6 * q^19 + 3 * q^21 - 12 * q^22 + 15 * q^23 + 3 * q^24 + 6 * q^26 + 3 * q^27 + 3 * q^28 + 24 * q^29 - 6 * q^31 + 6 * q^33 + 3 * q^34 + 6 * q^36 - 30 * q^37 + 9 * q^38 + 30 * q^39 + 18 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 6 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 + 30 * q^51 - 3 * q^52 + 12 * q^53 + 18 * q^54 - 12 * q^57 - 6 * q^58 + 21 * q^59 - 21 * q^61 - 18 * q^62 - 3 * q^64 - 15 * q^66 - 9 * q^67 - 12 * q^68 + 3 * q^69 + 15 * q^71 + 3 * q^72 - 21 * q^73 - 18 * q^74 - 6 * q^77 - 9 * q^78 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 3 * q^84 - 6 * q^86 + 12 * q^87 - 3 * q^88 - 24 * q^89 - 27 * q^91 - 3 * q^92 - 15 * q^93 + 30 * q^94 - 9 * q^97 - 6 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more