LMFDB - Embedded newform 950.2.u.a.549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			549.1
Root			$-0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	950.549
Dual form			950.2.u.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(0.984808 - 1.17365i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.17365 + 0.984808i) q^{6} +(1.62760 - 0.939693i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.113341 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(0.984808 - 1.17365i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.17365 + 0.984808i) q^{6} +(1.62760 - 0.939693i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.113341 + 0.642788i) q^{9} +(0.0812519 - 0.140732i) q^{11} +(1.32683 - 0.766044i) q^{12} +(-3.03195 - 3.61334i) q^{13} +(-1.76604 + 0.642788i) q^{14} +(0.766044 + 0.642788i) q^{16} +(4.28125 + 0.754900i) q^{17} -0.652704i q^{18} +(-2.77719 - 3.35965i) q^{19} +(0.500000 - 2.83564i) q^{21} +(-0.104455 + 0.124485i) q^{22} +(2.08840 - 5.73783i) q^{23} +(-1.43969 + 0.524005i) q^{24} +(2.35844 + 4.08494i) q^{26} +(4.84651 + 2.79813i) q^{27} +(1.85083 - 0.326352i) q^{28} +(-0.414878 - 2.35289i) q^{29} +(1.81908 + 3.15074i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-0.0851529 - 0.233956i) q^{33} +(-4.08512 - 1.48686i) q^{34} +(-0.113341 + 0.642788i) q^{36} -7.36959i q^{37} +(2.15160 + 3.79086i) q^{38} -7.22668 q^{39} +(1.81521 + 1.52314i) q^{41} +(-0.984808 + 2.70574i) q^{42} +(-0.223238 - 0.613341i) q^{43} +(0.124485 - 0.104455i) q^{44} +(-3.05303 + 5.28801i) q^{46} +(6.77487 - 1.19459i) q^{47} +(1.50881 - 0.266044i) q^{48} +(-1.73396 + 3.00330i) q^{49} +(5.10220 - 4.28125i) q^{51} +(-1.61327 - 4.43242i) q^{52} +(2.03282 - 5.58512i) q^{53} +(-4.28699 - 3.59721i) q^{54} -1.87939 q^{56} +(-6.67804 - 0.0491630i) q^{57} +2.38919i q^{58} +(0.708263 - 4.01676i) q^{59} +(-2.21301 - 0.805470i) q^{61} +(-1.24432 - 3.41875i) q^{62} +(0.788496 + 0.939693i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.0432332 + 0.245188i) q^{66} +(1.61327 - 0.284463i) q^{67} +(3.76487 + 2.17365i) q^{68} +(-4.67752 - 8.10170i) q^{69} +(2.39780 - 0.872729i) q^{71} +(0.223238 - 0.613341i) q^{72} +(-10.0933 + 12.0287i) q^{73} +(-1.27972 + 7.25762i) q^{74} +(-1.46064 - 4.10689i) q^{76} -0.305407i q^{77} +(7.11689 + 1.25490i) q^{78} +(0.766044 + 0.642788i) q^{79} +(6.21688 - 2.26276i) q^{81} +(-1.52314 - 1.81521i) q^{82} +(-0.885328 + 0.511144i) q^{83} +(1.43969 - 2.49362i) q^{84} +(0.113341 + 0.642788i) q^{86} +(-3.17004 - 1.83022i) q^{87} +(-0.140732 + 0.0812519i) q^{88} +(2.57011 - 2.15658i) q^{89} +(-8.33022 - 3.03195i) q^{91} +(3.92490 - 4.67752i) q^{92} +(5.48930 + 0.967911i) q^{93} -6.87939 q^{94} -1.53209 q^{96} +(-17.6011 - 3.10354i) q^{97} +(2.22913 - 2.65657i) q^{98} +(0.0996702 + 0.0362770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^6 - 12 * q^9	$ 12 q - 12 q^{6} - 12 q^{9} + 6 q^{11} - 12 q^{14} - 12 q^{19} + 6 q^{21} - 6 q^{24} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 6 q^{34} + 12 q^{36} - 60 q^{39} + 36 q^{41} - 24 q^{44} - 12 q^{46} - 30 q^{49} + 60 q^{51} - 36 q^{54} - 42 q^{59} - 42 q^{61} + 6 q^{64} - 30 q^{66} - 6 q^{69} + 30 q^{71} + 36 q^{74} + 42 q^{81} + 6 q^{84} - 12 q^{86} + 48 q^{89} - 54 q^{91} - 60 q^{94} + 30 q^{99}+O(q^{100}) $ 12 * q - 12 * q^6 - 12 * q^9 + 6 * q^11 - 12 * q^14 - 12 * q^19 + 6 * q^21 - 6 * q^24 + 12 * q^26 - 48 * q^29 - 12 * q^31 - 6 * q^34 + 12 * q^36 - 60 * q^39 + 36 * q^41 - 24 * q^44 - 12 * q^46 - 30 * q^49 + 60 * q^51 - 36 * q^54 - 42 * q^59 - 42 * q^61 + 6 * q^64 - 30 * q^66 - 6 * q^69 + 30 * q^71 + 36 * q^74 + 42 * q^81 + 6 * q^84 - 12 * q^86 + 48 * q^89 - 54 * q^91 - 60 * q^94 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	0.984808	−	1.17365i	0.568579	−	0.677606i	−0.402760	−	0.915306i	$-0.631949\pi$
$3$	0.984808	−	1.17365i	0.568579	−	0.677606i	0.971339	+	0.237700i	$0.0763934\pi$
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	−1.17365	+	0.984808i	−0.479140	+	0.402046i
$7$	1.62760	−	0.939693i	0.615173	−	0.355170i	−0.159814	−	0.987147i	$-0.551090\pi$
$7$	1.62760	−	0.939693i	0.615173	−	0.355170i	0.774987	+	0.631977i	$0.217756\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.113341	+	0.642788i	0.0377803	+	0.214263i
$10$		0			0
$11$	0.0812519	−	0.140732i	0.0244984	−	0.0424324i	−0.853516	−	0.521066i	$-0.825534\pi$
$11$	0.0812519	−	0.140732i	0.0244984	−	0.0424324i	0.878015	+	0.478634i	$0.158868\pi$
$12$	1.32683	−	0.766044i	0.383022	−	0.221138i
$13$	−3.03195	−	3.61334i	−0.840912	−	1.00216i	−0.999889	−	0.0148781i	$-0.995264\pi$
$13$	−3.03195	−	3.61334i	−0.840912	−	1.00216i	0.158977	−	0.987282i	$-0.449180\pi$
$14$	−1.76604	+	0.642788i	−0.471995	+	0.171792i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	4.28125	+	0.754900i	1.03836	+	0.183090i	0.666735	−	0.745295i	$-0.267691\pi$
$17$	4.28125	+	0.754900i	1.03836	+	0.183090i	0.371621	+	0.928385i	$0.378802\pi$
$18$		−	0.652704i		−	0.153844i
$19$	−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
$22$	−0.104455	+	0.124485i	−0.0222700	+	0.0265403i
$23$	2.08840	−	5.73783i	0.435461	−	1.19642i	−0.506954	−	0.861973i	$-0.669229\pi$
$23$	2.08840	−	5.73783i	0.435461	−	1.19642i	0.942415	−	0.334446i	$-0.108549\pi$
$24$	−1.43969	+	0.524005i	−0.293876	+	0.106962i
$25$		0			0
$26$	2.35844	+	4.08494i	0.462528	+	0.801122i
$27$	4.84651	+	2.79813i	0.932711	+	0.538501i
$28$	1.85083	−	0.326352i	0.349775	−	0.0616747i
$29$	−0.414878	−	2.35289i	−0.0770409	−	0.436920i	−0.998792	−	0.0491384i	$-0.984352\pi$
$29$	−0.414878	−	2.35289i	−0.0770409	−	0.436920i	0.921751	−	0.387782i	$-0.126759\pi$
$30$		0			0
$31$	1.81908	+	3.15074i	0.326716	+	0.565889i	0.981858	−	0.189617i	$-0.0607246\pi$
$31$	1.81908	+	3.15074i	0.326716	+	0.565889i	−0.655142	+	0.755506i	$0.727391\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−0.0851529	−	0.233956i	−0.0148232	−	0.0407264i
$34$	−4.08512	−	1.48686i	−0.700593	−	0.254995i
$35$		0			0
$36$	−0.113341	+	0.642788i	−0.0188901	+	0.107131i
$37$		−	7.36959i		−	1.21155i	−0.795635	−	0.605776i	$-0.792863\pi$
$37$		−	7.36959i		−	1.21155i	0.795635	−	0.605776i	$-0.207137\pi$
$38$	2.15160	+	3.79086i	0.349036	+	0.614959i
$39$	−7.22668			−1.15720
$40$		0			0
$41$	1.81521	+	1.52314i	0.283488	+	0.237874i	0.773432	−	0.633879i	$-0.218538\pi$
$41$	1.81521	+	1.52314i	0.283488	+	0.237874i	−0.489944	+	0.871754i	$0.662983\pi$
$42$	−0.984808	+	2.70574i	−0.151959	+	0.417504i
$43$	−0.223238	−	0.613341i	−0.0340434	−	0.0935336i	0.921506	−	0.388363i	$-0.126959\pi$
$43$	−0.223238	−	0.613341i	−0.0340434	−	0.0935336i	−0.955550	+	0.294830i	$0.904737\pi$
$44$	0.124485	−	0.104455i	0.0187668	−	0.0157473i
$45$		0			0
$46$	−3.05303	+	5.28801i	−0.450145	+	0.779674i
$47$	6.77487	−	1.19459i	0.988217	−	0.174249i	0.343899	−	0.939007i	$-0.388252\pi$
$47$	6.77487	−	1.19459i	0.988217	−	0.174249i	0.644318	+	0.764758i	$0.277141\pi$
$48$	1.50881	−	0.266044i	0.217778	−	0.0384002i
$49$	−1.73396	+	3.00330i	−0.247708	+	0.429043i
$50$		0			0
$51$	5.10220	−	4.28125i	0.714450	−	0.599495i
$52$	−1.61327	−	4.43242i	−0.223720	−	0.614666i
$53$	2.03282	−	5.58512i	0.279229	−	0.767176i	−0.718221	−	0.695815i	$-0.755044\pi$
$53$	2.03282	−	5.58512i	0.279229	−	0.767176i	0.997451	−	0.0713610i	$-0.0227342\pi$
$54$	−4.28699	−	3.59721i	−0.583385	−	0.489518i
$55$		0			0
$56$	−1.87939			−0.251143
$57$	−6.67804	−	0.0491630i	−0.884528	−	0.00651180i
$58$			2.38919i			0.313715i
$59$	0.708263	−	4.01676i	0.0922080	−	0.522938i	−0.903359	−	0.428885i	$-0.858907\pi$
$59$	0.708263	−	4.01676i	0.0922080	−	0.522938i	0.995567	−	0.0940529i	$-0.0299823\pi$
$60$		0			0
$61$	−2.21301	−	0.805470i	−0.283347	−	0.103130i	0.196437	−	0.980516i	$-0.437063\pi$
$61$	−2.21301	−	0.805470i	−0.283347	−	0.103130i	−0.479784	+	0.877387i	$0.659285\pi$
$62$	−1.24432	−	3.41875i	−0.158029	−	0.434181i
$63$	0.788496	+	0.939693i	0.0993411	+	0.118390i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	0.0432332	+	0.245188i	0.00532164	+	0.0301805i
$67$	1.61327	−	0.284463i	0.197092	−	0.0347527i	−0.0742305	−	0.997241i	$-0.523650\pi$
$67$	1.61327	−	0.284463i	0.197092	−	0.0347527i	0.271323	+	0.962488i	$0.412539\pi$
$68$	3.76487	+	2.17365i	0.456557	+	0.263594i
$69$	−4.67752	−	8.10170i	−0.563107	−	0.975330i
$70$		0			0
$71$	2.39780	−	0.872729i	0.284567	−	0.103574i	−0.195793	−	0.980645i	$-0.562728\pi$
$71$	2.39780	−	0.872729i	0.284567	−	0.103574i	0.480360	+	0.877071i	$0.340506\pi$
$72$	0.223238	−	0.613341i	0.0263088	−	0.0722829i
$73$	−10.0933	+	12.0287i	−1.18133	+	1.40785i	−0.288483	+	0.957485i	$0.593151\pi$
$73$	−10.0933	+	12.0287i	−1.18133	+	1.40785i	−0.892844	+	0.450366i	$0.851293\pi$
$74$	−1.27972	+	7.25762i	−0.148764	+	0.843682i
$75$		0			0
$76$	−1.46064	−	4.10689i	−0.167547	−	0.471093i
$77$		−	0.305407i		−	0.0348044i
$78$	7.11689	+	1.25490i	0.805829	+	0.142089i
$79$	0.766044	+	0.642788i	0.0861867	+	0.0723193i	0.684863	−	0.728672i	$-0.259862\pi$
$79$	0.766044	+	0.642788i	0.0861867	+	0.0723193i	−0.598676	+	0.800991i	$0.704306\pi$
$80$		0			0
$81$	6.21688	−	2.26276i	0.690765	−	0.251418i
$82$	−1.52314	−	1.81521i	−0.168203	−	0.200456i
$83$	−0.885328	+	0.511144i	−0.0971774	+	0.0561054i	−0.547801	−	0.836609i	$-0.684535\pi$
$83$	−0.885328	+	0.511144i	−0.0971774	+	0.0561054i	0.450624	+	0.892714i	$0.351202\pi$
$84$	1.43969	−	2.49362i	0.157083	−	0.272076i
$85$		0			0
$86$	0.113341	+	0.642788i	0.0122219	+	0.0693136i
$87$	−3.17004	−	1.83022i	−0.339864	−	0.196220i
$88$	−0.140732	+	0.0812519i	−0.0150021	+	0.00866148i
$89$	2.57011	−	2.15658i	0.272431	−	0.228597i	−0.496328	−	0.868135i	$-0.665319\pi$
$89$	2.57011	−	2.15658i	0.272431	−	0.228597i	0.768759	+	0.639538i	$0.220874\pi$
$90$		0			0
$91$	−8.33022	−	3.03195i	−0.873245	−	0.317835i
$92$	3.92490	−	4.67752i	0.409200	−	0.487665i
$93$	5.48930	+	0.967911i	0.569214	+	0.100368i
$94$	−6.87939			−0.709554
$95$		0			0
$96$	−1.53209			−0.156368
$97$	−17.6011	−	3.10354i	−1.78712	−	0.315117i	−0.820558	−	0.571563i	$-0.806337\pi$
$97$	−17.6011	−	3.10354i	−1.78712	−	0.315117i	−0.966558	+	0.256447i	$0.917448\pi$
$98$	2.22913	−	2.65657i	0.225176	−	0.268355i
$99$	0.0996702	+	0.0362770i	0.0100172	+	0.00364598i
$100$		0			0
$101$	6.82295	−	5.72513i	0.678909	−	0.569672i	−0.236779	−	0.971564i	$-0.576092\pi$
$101$	6.82295	−	5.72513i	0.678909	−	0.569672i	0.915687	+	0.401892i	$0.131647\pi$
$102$	−5.76811	+	3.33022i	−0.571128	+	0.329741i
$103$	−7.14382	−	4.12449i	−0.703901	−	0.406398i	0.104898	−	0.994483i	$-0.466549\pi$
$103$	−7.14382	−	4.12449i	−0.703901	−	0.406398i	−0.808799	+	0.588085i	$0.799882\pi$
$104$	0.819078	+	4.64522i	0.0803172	+	0.455501i
$105$		0			0
$106$	−2.97178	+	5.14728i	−0.288645	+	0.499948i
$107$	−3.17004	+	1.83022i	−0.306459	+	0.176934i	−0.645341	−	0.763895i	$-0.723285\pi$
$107$	−3.17004	+	1.83022i	−0.306459	+	0.176934i	0.338882	+	0.940829i	$0.389951\pi$
$108$	3.59721	+	4.28699i	0.346142	+	0.412516i
$109$	3.03936	−	1.10624i	0.291118	−	0.105958i	−0.192333	−	0.981330i	$-0.561605\pi$
$109$	3.03936	−	1.10624i	0.291118	−	0.105958i	0.483451	+	0.875371i	$0.339383\pi$
$110$		0			0
$111$	−8.64930	−	7.25762i	−0.820955	−	0.688863i
$112$	1.85083	+	0.326352i	0.174887	+	0.0308373i
$113$		−	15.1753i		−	1.42757i	−0.700364	−	0.713786i	$-0.746979\pi$
$113$		−	15.1753i		−	1.42757i	0.700364	−	0.713786i	$-0.253021\pi$
$114$	6.56805	+	1.20805i	0.615154	+	0.113144i
$115$		0			0
$116$	0.414878	−	2.35289i	0.0385204	−	0.218460i
$117$	1.97897	−	2.35844i	0.182956	−	0.218038i
$118$	−1.39501	+	3.83275i	−0.128421	+	0.352833i
$119$	7.67752	−	2.79439i	0.703797	−	0.256161i
$120$		0			0
$121$	5.48680	+	9.50341i	0.498800	+	0.863946i
$122$	2.03952	+	1.17752i	0.184650	+	0.106608i
$123$	3.57526	−	0.630415i	0.322370	−	0.0568426i
$124$	0.631759	+	3.58288i	0.0567336	+	0.321752i
$125$		0			0
$126$	−0.613341	−	1.06234i	−0.0546407	−	0.0946405i
$127$	12.8227	+	15.2815i	1.13783	+	1.35602i	0.925468	+	0.378826i	$0.123672\pi$
$127$	12.8227	+	15.2815i	1.13783	+	1.35602i	0.212365	+	0.977191i	$0.431884\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	−0.939693	−	0.342020i	−0.0827353	−	0.0301132i
$130$		0			0
$131$	−2.93376	+	16.6382i	−0.256324	+	1.45369i	0.536327	+	0.844010i	$0.319811\pi$
$131$	−2.93376	+	16.6382i	−0.256324	+	1.45369i	−0.792651	+	0.609676i	$0.791300\pi$
$132$		−	0.248970i		−	0.0216701i
$133$	−7.67717	−	2.85844i	−0.665695	−	0.247858i
$134$	−1.63816			−0.141515
$135$		0			0
$136$	−3.33022	−	2.79439i	−0.285564	−	0.239617i
$137$	1.70248	−	4.67752i	0.145452	−	0.399627i	−0.845477	−	0.534012i	$-0.820684\pi$
$137$	1.70248	−	4.67752i	0.145452	−	0.399627i	0.990929	+	0.134385i	$0.0429058\pi$
$138$	3.19961	+	8.79086i	0.272369	+	0.748328i
$139$	14.3439	−	12.0360i	1.21663	−	1.02088i	0.217639	−	0.976029i	$-0.430164\pi$
$139$	14.3439	−	12.0360i	1.21663	−	1.02088i	0.998994	−	0.0448471i	$-0.0142801\pi$
$140$		0			0
$141$	5.26991	−	9.12776i	0.443807	−	0.768696i
$142$	−2.51292	+	0.443096i	−0.210880	+	0.0371838i
$143$	−0.754866	+	0.133103i	−0.0631251	+	0.0111307i
$144$	−0.326352	+	0.565258i	−0.0271960	+	0.0471048i
$145$		0			0
$146$	12.0287	−	10.0933i	0.995501	−	0.835325i
$147$	1.81720	+	4.99273i	0.149880	+	0.411793i
$148$	2.52055	−	6.92514i	0.207188	−	0.569243i
$149$	10.2476	+	8.59878i	0.839518	+	0.704439i	0.957455	−	0.288582i	$-0.0931837\pi$
$149$	10.2476	+	8.59878i	0.839518	+	0.704439i	−0.117937	+	0.993021i	$0.537628\pi$
$150$		0			0
$151$	−14.8648			−1.20968			−0.604842	−	0.796346i	$-0.706764\pi$
$151$	−14.8648			−1.20968			−0.604842	+	0.796346i	$0.706764\pi$
$152$	0.725293	+	4.29813i	0.0588290	+	0.348625i
$153$			2.83750i			0.229398i
$154$	−0.0530334	+	0.300767i	−0.00427355	+	0.0242365i
$155$		0			0
$156$	−6.79086	−	2.47167i	−0.543704	−	0.197892i
$157$	−2.54747	−	6.99912i	−0.203310	−	0.558591i	0.795572	−	0.605859i	$-0.207171\pi$
$157$	−2.54747	−	6.99912i	−0.203310	−	0.558591i	−0.998882	+	0.0472685i	$0.984948\pi$
$158$	−0.642788	−	0.766044i	−0.0511374	−	0.0609432i
$159$	−4.55303	−	7.88609i	−0.361079	−	0.625407i
$160$		0			0
$161$	−1.99273	−	11.3013i	−0.157049	−	0.890668i
$162$	−6.51536	+	1.14883i	−0.511895	+	0.0902609i
$163$	−5.84737	−	3.37598i	−0.458002	−	0.264427i	0.253202	−	0.967413i	$-0.418516\pi$
$163$	−5.84737	−	3.37598i	−0.458002	−	0.264427i	−0.711204	+	0.702986i	$0.751850\pi$
$164$	1.18479	+	2.05212i	0.0925168	+	0.160244i
$165$		0			0
$166$	0.960637	−	0.349643i	0.0745599	−	0.0271376i
$167$	−5.55920	+	15.2738i	−0.430184	+	1.18192i	0.515516	+	0.856880i	$0.327600\pi$
$167$	−5.55920	+	15.2738i	−0.430184	+	1.18192i	−0.945700	+	0.325041i	$0.894622\pi$
$168$	−1.85083	+	2.20574i	−0.142795	+	0.170176i
$169$	−1.60607	+	9.10846i	−0.123544	+	0.700651i
$170$		0			0
$171$	1.84477	−	2.16593i	0.141073	−	0.165633i
$172$		−	0.652704i		−	0.0497682i
$173$	−5.55250	−	0.979055i	−0.422149	−	0.0744362i	−0.0414616	−	0.999140i	$-0.513201\pi$
$173$	−5.55250	−	0.979055i	−0.422149	−	0.0744362i	−0.380687	+	0.924704i	$0.624313\pi$
$174$	2.80406	+	2.35289i	0.212575	+	0.178372i
$175$		0			0
$176$	0.152704	−	0.0555796i	0.0115105	−	0.00418947i
$177$	−4.01676	−	4.78699i	−0.301918	−	0.359812i
$178$	−2.90555	+	1.67752i	−0.217780	+	0.125735i
$179$	5.74763	−	9.95518i	0.429598	−	0.744085i	−0.567240	−	0.823553i	$-0.691989\pi$
$179$	5.74763	−	9.95518i	0.429598	−	0.744085i	0.996837	+	0.0794676i	$0.0253220\pi$
$180$		0			0
$181$	2.61200	+	14.8134i	0.194148	+	1.10107i	0.913627	+	0.406554i	$0.133270\pi$
$181$	2.61200	+	14.8134i	0.194148	+	1.10107i	−0.719478	+	0.694515i	$0.755619\pi$
$182$	7.67717	+	4.43242i	0.569070	+	0.328553i
$183$	−3.12473	+	1.80406i	−0.230987	+	0.133360i
$184$	−4.67752	+	3.92490i	−0.344831	+	0.289348i
$185$		0			0
$186$	−5.23783	−	1.90641i	−0.384056	−	0.139785i
$187$	0.454099	−	0.541174i	0.0332070	−	0.0395746i
$188$	6.77487	+	1.19459i	0.494108	+	0.0871246i
$189$	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	$0.238922\pi$
$192$	1.50881	+	0.266044i	0.108889	+	0.0192001i
$193$	−6.47735	+	7.71941i	−0.466250	+	0.555655i	−0.947013	−	0.321196i	$-0.895915\pi$
$193$	−6.47735	+	7.71941i	−0.466250	+	0.555655i	0.480763	+	0.876851i	$0.340360\pi$
$194$	16.7947	+	6.11278i	1.20579	+	0.438872i
$195$		0			0
$196$	−2.65657	+	2.22913i	−0.189755	+	0.159224i
$197$	−11.3435	+	6.54916i	−0.808190	+	0.466609i	−0.846327	−	0.532664i	$-0.821191\pi$
$197$	−11.3435	+	6.54916i	−0.808190	+	0.466609i	0.0381371	+	0.999273i	$0.487858\pi$
$198$	−0.0918566	−	0.0530334i	−0.00652796	−	0.00376892i
$199$	3.05257	+	17.3120i	0.216391	+	1.22721i	0.878477	+	0.477785i	$0.158560\pi$
$199$	3.05257	+	17.3120i	0.216391	+	1.22721i	−0.662086	+	0.749428i	$0.730329\pi$
$200$		0			0
$201$	1.25490	−	2.17355i	0.0885138	−	0.153310i
$202$	−7.71345	+	4.45336i	−0.542717	+	0.313338i
$203$	−2.88624	−	3.43969i	−0.202575	−	0.241419i
$204$	6.25877	−	2.27801i	0.438202	−	0.159492i
$205$		0			0
$206$	6.31908	+	5.30234i	0.440271	+	0.369431i
$207$	3.92490	+	0.692066i	0.272800	+	0.0481019i
$208$		−	4.71688i		−	0.327057i
$209$	−0.698463	+	0.117863i	−0.0483137	+	0.00815275i
$210$		0			0
$211$	−4.29561	+	24.3616i	−0.295722	+	1.67712i	0.368532	+	0.929615i	$0.379860\pi$
$211$	−4.29561	+	24.3616i	−0.295722	+	1.67712i	−0.664254	+	0.747507i	$0.731251\pi$
$212$	3.82045	−	4.55303i	0.262389	−	0.312704i
$213$	1.33710	−	3.67365i	0.0916165	−	0.251714i
$214$	3.43969	−	1.25195i	0.235133	−	0.0855812i
$215$		0			0
$216$	−2.79813	−	4.84651i	−0.190389	−	0.329763i
$217$	5.92145	+	3.41875i	0.401974	+	0.232080i
$218$	−3.18528	+	0.561652i	−0.215735	+	0.0380398i
$219$	4.17752	+	23.6919i	0.282291	+	1.60095i
$220$		0			0
$221$	−10.2528	−	17.7584i	−0.689681	−	1.19456i
$222$	7.25762	+	8.64930i	0.487100	+	0.580503i
$223$	5.19880	+	14.2836i	0.348137	+	0.956500i	0.982956	+	0.183839i	$0.0588524\pi$
$223$	5.19880	+	14.2836i	0.348137	+	0.956500i	−0.634819	+	0.772661i	$0.718925\pi$
$224$	−1.76604	−	0.642788i	−0.117999	−	0.0429481i
$225$		0			0
$226$	−2.63516	+	14.9448i	−0.175288	+	0.994110i
$227$			18.6973i			1.24098i	0.784214	+	0.620491i	$0.213067\pi$
$227$			18.6973i			1.24098i	−0.784214	+	0.620491i	$0.786933\pi$
$228$	−6.25849	−	2.33022i	−0.414479	−	0.154323i
$229$	19.9094			1.31565			0.657826	−	0.753170i	$-0.271476\pi$
$229$	19.9094			1.31565			0.657826	+	0.753170i	$0.271476\pi$
$230$		0			0
$231$	−0.358441	−	0.300767i	−0.0235837	−	0.0197890i
$232$	−0.817150	+	2.24510i	−0.0536485	+	0.147398i
$233$	9.56926	+	26.2913i	0.626903	+	1.72240i	0.689424	+	0.724358i	$0.257864\pi$
$233$	9.56926	+	26.2913i	0.626903	+	1.72240i	−0.0625206	+	0.998044i	$0.519914\pi$
$234$	−2.35844	+	1.97897i	−0.154176	+	0.129369i
$235$		0			0
$236$	2.03936	−	3.53228i	0.132751	−	0.229932i
$237$	1.50881	−	0.266044i	0.0980079	−	0.0172814i
$238$	−8.04612	+	1.41875i	−0.521553	+	0.0919638i
$239$	−13.1814	+	22.8308i	−0.852633	+	1.47680i	0.0261903	+	0.999657i	$0.491662\pi$
$239$	−13.1814	+	22.8308i	−0.852633	+	1.47680i	−0.878823	+	0.477147i	$0.841671\pi$
$240$		0			0
$241$	13.1570	−	11.0401i	0.847520	−	0.711153i	−0.111722	−	0.993739i	$-0.535637\pi$
$241$	13.1570	−	11.0401i	0.847520	−	0.711153i	0.959242	+	0.282586i	$0.0911923\pi$
$242$	−3.75319	−	10.3118i	−0.241264	−	0.662868i
$243$	−2.27536	+	6.25150i	−0.145964	+	0.401034i
$244$	−1.80406	−	1.51379i	−0.115493	−	0.0969104i
$245$		0			0
$246$	−3.63041			−0.231467
$247$	−3.71924	+	20.2212i	−0.236650	+	1.28665i
$248$		−	3.63816i		−	0.231023i
$249$	−0.271974	+	1.54244i	−0.0172357	+	0.0977483i
$250$		0			0
$251$	−15.1211	−	5.50362i	−0.954434	−	0.347386i	−0.182584	−	0.983190i	$-0.558446\pi$
$251$	−15.1211	−	5.50362i	−0.954434	−	0.347386i	−0.771850	+	0.635805i	$0.780668\pi$
$252$	0.419550	+	1.15270i	0.0264292	+	0.0726135i
$253$	−0.637812	−	0.760115i	−0.0400989	−	0.0477880i
$254$	−9.97431	−	17.2760i	−0.625844	−	1.08399i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	13.9290	−	2.45605i	0.868865	−	0.153204i	0.278593	−	0.960409i	$-0.410132\pi$
$257$	13.9290	−	2.45605i	0.868865	−	0.153204i	0.590271	+	0.807205i	$0.299021\pi$
$258$	0.866025	+	0.500000i	0.0539164	+	0.0311286i
$259$	−6.92514	−	11.9947i	−0.430308	−	0.745315i
$260$		0			0
$261$	1.46538	−	0.533356i	0.0907050	−	0.0330139i
$262$	5.77838	−	15.8760i	0.356990	−	0.980821i
$263$	−8.43437	+	10.0517i	−0.520085	+	0.619814i	−0.960601	−	0.277931i	$-0.910351\pi$
$263$	−8.43437	+	10.0517i	−0.520085	+	0.619814i	0.440515	+	0.897745i	$0.354796\pi$
$264$	−0.0432332	+	0.245188i	−0.00266082	+	0.0150903i
$265$		0			0
$266$	7.06418	+	4.14814i	0.433133	+	0.254339i
$267$		−	5.14022i		−	0.314576i
$268$	1.61327	+	0.284463i	0.0985461	+	0.0173763i
$269$	17.2003	+	14.4327i	1.04872	+	0.879980i	0.992958	−	0.118464i	$-0.0377971\pi$
$269$	17.2003	+	14.4327i	1.04872	+	0.879980i	0.0557609	+	0.998444i	$0.482242\pi$
$270$		0			0
$271$	5.41787	−	1.97194i	0.329112	−	0.119787i	−0.172179	−	0.985066i	$-0.555081\pi$
$271$	5.41787	−	1.97194i	0.329112	−	0.119787i	0.501291	+	0.865279i	$0.332859\pi$
$272$	2.79439	+	3.33022i	0.169435	+	0.201924i
$273$	−11.7621	+	6.79086i	−0.711875	+	0.411002i
$274$	−2.48886	+	4.31082i	−0.150357	+	0.260426i
$275$		0			0
$276$	−1.62449	−	9.21291i	−0.0977825	−	0.554552i
$277$	−17.1242	−	9.88666i	−1.02889	−	0.594032i	−0.112226	−	0.993683i	$-0.535798\pi$
$277$	−17.1242	−	9.88666i	−1.02889	−	0.594032i	−0.916667	+	0.399651i	$0.869131\pi$
$278$	−16.2160	+	9.36231i	−0.972571	+	0.561514i
$279$	−1.81908	+	1.52639i	−0.108905	+	0.0913824i
$280$		0			0
$281$	−29.7904	−	10.8428i	−1.77715	−	0.646829i	−0.999843	−	0.0177066i	$-0.994364\pi$
$281$	−29.7904	−	10.8428i	−1.77715	−	0.646829i	−0.777306	−	0.629123i	$-0.783414\pi$
$282$	−6.77487	+	8.07398i	−0.403438	+	0.480798i
$283$	−2.89620	−	0.510678i	−0.172161	−	0.0303566i	0.0869031	−	0.996217i	$-0.472303\pi$
$283$	−2.89620	−	0.510678i	−0.172161	−	0.0303566i	−0.259064	+	0.965860i	$0.583414\pi$
$284$	2.55169			0.151415
$285$		0			0
$286$	0.766511			0.0453248
$287$	4.38571	+	0.773318i	0.258880	+	0.0456475i
$288$	0.419550	−	0.500000i	0.0247222	−	0.0294628i
$289$	1.78446	+	0.649491i	0.104968	+	0.0382054i
$290$		0			0
$291$	−20.9761	+	17.6011i	−1.22964	+	1.03179i
$292$	−13.5986	+	7.85117i	−0.795799	+	0.459455i
$293$	14.1142	+	8.14883i	0.824560	+	0.476060i	0.851986	−	0.523564i	$-0.175398\pi$
$293$	14.1142	+	8.14883i	0.824560	+	0.476060i	−0.0274264	+	0.999624i	$0.508731\pi$
$294$	−0.922618	−	5.23243i	−0.0538082	−	0.305161i
$295$		0			0
$296$	−3.68479	+	6.38225i	−0.214174	+	0.370961i
$297$	0.787576	−	0.454707i	0.0456998	−	0.0263848i
$298$	−8.59878	−	10.2476i	−0.498114	−	0.593629i
$299$	−27.0646	+	9.85073i	−1.56519	+	0.569682i
$300$		0			0
$301$	−0.939693	−	0.788496i	−0.0541630	−	0.0454481i
$302$	14.6390	+	2.58125i	0.842380	+	0.148534i
$303$		−	13.6459i		−	0.783936i
$304$	0.0320889	−	4.35878i	0.00184042	−	0.249993i
$305$		0			0
$306$	0.492726	−	2.79439i	0.0281673	−	0.159745i
$307$	14.2590	−	16.9932i	0.813803	−	0.969853i	−0.186117	−	0.982528i	$-0.559590\pi$
$307$	14.2590	−	16.9932i	0.813803	−	0.969853i	0.999920	+	0.0126749i	$0.00403466\pi$
$308$	0.104455	−	0.286989i	0.00595190	−	0.0163527i
$309$	−11.8760	+	4.32250i	−0.675601	+	0.245899i
$310$		0			0
$311$	4.46198	+	7.72838i	0.253016	+	0.438236i	0.964355	−	0.264613i	$-0.0852442\pi$
$311$	4.46198	+	7.72838i	0.253016	+	0.438236i	−0.711339	+	0.702849i	$0.751911\pi$
$312$	6.25849	+	3.61334i	0.354317	+	0.204565i
$313$	18.0475	−	3.18227i	1.02011	−	0.179872i	0.361510	−	0.932368i	$-0.382261\pi$
$313$	18.0475	−	3.18227i	1.02011	−	0.179872i	0.658597	+	0.752496i	$0.271150\pi$
$314$	1.29339	+	7.33515i	0.0729900	+	0.413947i
$315$		0			0
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	15.5952	+	18.5856i	0.875912	+	1.04387i	0.998676	+	0.0514349i	$0.0163795\pi$
$317$	15.5952	+	18.5856i	0.875912	+	1.04387i	−0.122765	+	0.992436i	$0.539176\pi$
$318$	3.11446	+	8.55690i	0.174650	+	0.479847i
$319$	−0.364837	−	0.132790i	−0.0204270	−	0.00743481i
$320$		0			0
$321$	−0.973841	+	5.52293i	−0.0543545	+	0.308260i
$322$			11.4757i			0.639513i
$323$	−9.35365	−	16.4800i	−0.520451	−	0.916971i
$324$	6.61587			0.367548
$325$		0			0
$326$	5.17230	+	4.34008i	0.286467	+	0.240375i
$327$	1.69485	−	4.65657i	0.0937257	−	0.257509i
$328$	−0.810446	−	2.22668i	−0.0447494	−	0.122948i
$329$	9.90420	−	8.31061i	0.546036	−	0.458179i
$330$		0			0
$331$	−16.8974	+	29.2671i	−0.928765	+	1.60867i	−0.143373	+	0.989669i	$0.545795\pi$
$331$	−16.8974	+	29.2671i	−0.928765	+	1.60867i	−0.785392	+	0.618999i	$0.787539\pi$
$332$	−1.00676	+	0.177519i	−0.0552530	+	0.00974260i
$333$	4.73708	−	0.835275i	0.259590	−	0.0457728i
$334$	8.12701	−	14.0764i	0.444690	−	0.770226i
$335$		0			0
$336$	2.20574	−	1.85083i	0.120333	−	0.100971i
$337$	−10.1825	−	27.9761i	−0.554675	−	1.52396i	−0.827257	−	0.561824i	$-0.810100\pi$
$337$	−10.1825	−	27.9761i	−0.554675	−	1.52396i	0.272582	−	0.962132i	$-0.412122\pi$
$338$	3.16333	−	8.69119i	0.172063	−	0.472738i
$339$	−17.8105	−	14.9448i	−0.967331	−	0.811687i
$340$		0			0
$341$	0.591214			0.0320160
$342$	−2.19285	+	1.81268i	−0.118576	+	0.0980186i
$343$			19.6732i			1.06225i
$344$	−0.113341	+	0.642788i	−0.00611093	+	0.0346568i
$345$		0			0
$346$	5.29813	+	1.92836i	0.284829	+	0.103669i
$347$	1.06904	+	2.93717i	0.0573891	+	0.157675i	0.965074	−	0.261977i	$-0.0843743\pi$
$347$	1.06904	+	2.93717i	0.0573891	+	0.157675i	−0.907685	+	0.419652i	$0.862152\pi$
$348$	−2.35289	−	2.80406i	−0.126128	−	0.150314i
$349$	−3.88666	−	6.73189i	−0.208048	−	0.360350i	0.743052	−	0.669234i	$-0.233378\pi$
$349$	−3.88666	−	6.73189i	−0.208048	−	0.360350i	−0.951100	+	0.308884i	$0.900044\pi$
$350$		0			0
$351$	−4.58378	−	25.9959i	−0.244664	−	1.38756i
$352$	−0.160035	+	0.0282185i	−0.00852990	+	0.00150405i
$353$	25.3162	+	14.6163i	1.34745	+	0.777949i	0.987887	−	0.155173i	$-0.0495935\pi$
$353$	25.3162	+	14.6163i	1.34745	+	0.777949i	0.359560	+	0.933122i	$0.382927\pi$
$354$	3.12449	+	5.41177i	0.166065	+	0.287632i
$355$		0			0
$356$	3.15270	−	1.14749i	0.167093	−	0.0608169i
$357$	4.28125	−	11.7626i	0.226588	−	0.622545i
$358$	−7.38901	+	8.80587i	−0.390521	+	0.465405i
$359$	−3.13310	+	17.7687i	−0.165359	+	0.937797i	0.783335	+	0.621600i	$0.213517\pi$
$359$	−3.13310	+	17.7687i	−0.165359	+	0.937797i	−0.948694	+	0.316197i	$0.897594\pi$
$360$		0			0
$361$	−3.57444	+	18.6607i	−0.188129	+	0.982144i
$362$		−	15.0419i		−	0.790584i
$363$	16.5571	+	2.91946i	0.869022	+	0.153232i
$364$	−6.79086	−	5.69821i	−0.355938	−	0.298667i
$365$		0			0
$366$	3.39053	−	1.23405i	0.177226	−	0.0645049i
$367$	−10.7252	−	12.7818i	−0.559850	−	0.667203i	0.409665	−	0.912236i	$-0.365646\pi$
$367$	−10.7252	−	12.7818i	−0.559850	−	0.667203i	−0.969515	+	0.245033i	$0.921201\pi$
$368$	5.28801	−	3.05303i	0.275657	−	0.159150i
$369$	−0.773318	+	1.33943i	−0.0402573	+	0.0697278i
$370$		0			0
$371$	−1.93969	−	11.0005i	−0.100704	−	0.571120i
$372$	4.82721	+	2.78699i	0.250279	+	0.144499i
$373$	6.75352	−	3.89915i	0.349684	−	0.201890i	−0.314862	−	0.949137i	$-0.601958\pi$
$373$	6.75352	−	3.89915i	0.349684	−	0.201890i	0.664546	+	0.747247i	$0.268625\pi$
$374$	−0.541174	+	0.454099i	−0.0279834	+	0.0234809i
$375$		0			0
$376$	−6.46451	−	2.35289i	−0.333382	−	0.121341i
$377$	−7.24390	+	8.63294i	−0.373080	+	0.444619i
$378$	−10.3578	−	1.82635i	−0.532745	−	0.0939374i
$379$	−1.31996			−0.0678015			−0.0339008	−	0.999425i	$-0.510793\pi$
$379$	−1.31996			−0.0678015			−0.0339008	+	0.999425i	$0.510793\pi$
$380$		0			0
$381$	30.5631			1.56579
$382$	−19.9060	−	3.50996i	−1.01848	−	0.179585i
$383$	21.3425	−	25.4349i	1.09055	−	1.29966i	0.139637	−	0.990203i	$-0.455407\pi$
$383$	21.3425	−	25.4349i	1.09055	−	1.29966i	0.950912	−	0.309462i	$-0.100149\pi$
$384$	−1.43969	−	0.524005i	−0.0734690	−	0.0267405i
$385$		0			0
$386$	7.71941	−	6.47735i	0.392908	−	0.329689i
$387$	0.368946	−	0.213011i	0.0187546	−	0.0108280i
$388$	−15.4781	−	8.93629i	−0.785782	−	0.453671i
$389$	−2.57991	−	14.6314i	−0.130807	−	0.741841i	−0.977689	−	0.210060i	$-0.932634\pi$
$389$	−2.57991	−	14.6314i	−0.130807	−	0.741841i	0.846882	−	0.531781i	$-0.178477\pi$
$390$		0			0
$391$	13.2724	−	22.9885i	0.671216	−	1.16258i
$392$	3.00330	−	1.73396i	0.151690	−	0.0875780i
$393$	16.6382	+	19.8286i	0.839286	+	1.00022i
$394$	12.3084	−	4.47989i	0.620088	−	0.225694i
$395$		0			0
$396$	0.0812519	+	0.0681784i	0.00408306	+	0.00342610i
$397$	−8.48233	−	1.49566i	−0.425716	−	0.0750652i	−0.0433144	−	0.999061i	$-0.513792\pi$
$397$	−8.48233	−	1.49566i	−0.425716	−	0.0750652i	−0.382401	+	0.923996i	$0.624903\pi$
$398$		−	17.5790i		−	0.881157i
$399$	−10.9153	+	6.19529i	−0.546451	+	0.310152i
$400$		0			0
$401$	−0.886821	+	5.02941i	−0.0442857	+	0.251157i	−0.998911	−	0.0466521i	$-0.985145\pi$
$401$	−0.886821	+	5.02941i	−0.0442857	+	0.251157i	0.954625	+	0.297809i	$0.0962559\pi$
$402$	−1.61327	+	1.92262i	−0.0804625	+	0.0958915i
$403$	5.86932	−	16.1258i	0.292372	−	0.803285i
$404$	8.36959	−	3.04628i	0.416402	−	0.151558i
$405$		0			0
$406$	2.24510	+	3.88863i	0.111422	+	0.192989i
$407$	−1.03714	−	0.598793i	−0.0514091	−	0.0296811i
$408$	−6.55926	+	1.15657i	−0.324732	+	0.0572589i
$409$	−5.00640	−	28.3927i	−0.247550	−	1.40393i	−0.814494	−	0.580172i	$-0.802985\pi$
$409$	−5.00640	−	28.3927i	−0.247550	−	1.40393i	0.566944	−	0.823756i	$-0.308126\pi$
$410$		0			0
$411$	−3.81315	−	6.60457i	−0.188089	−	0.325779i
$412$	−5.30234	−	6.31908i	−0.261227	−	0.311319i
$413$	−2.62175	−	7.20321i	−0.129008	−	0.354447i
$414$	−3.74510	−	1.36310i	−0.184062	−	0.0669930i
$415$		0			0
$416$	−0.819078	+	4.64522i	−0.0401586	+	0.227751i
$417$		−	28.6878i		−	1.40485i
$418$	0.708319	+	0.00521457i	0.0346450	+	0.000255053i
$419$	7.66313			0.374369			0.187184	−	0.982325i	$-0.440064\pi$
$419$	7.66313			0.374369			0.187184	+	0.982325i	$0.440064\pi$
$420$		0			0
$421$	5.14930	+	4.32078i	0.250962	+	0.210582i	0.759586	−	0.650407i	$-0.225401\pi$
$421$	5.14930	+	4.32078i	0.250962	+	0.210582i	−0.508625	+	0.860988i	$0.669846\pi$
$422$	8.46069	−	23.2456i	0.411860	−	1.13158i
$423$	1.53574	+	4.21941i	0.0746702	+	0.205155i
$424$	−4.55303	+	3.82045i	−0.221115	+	0.185537i
$425$		0			0
$426$	−1.95471	+	3.38565i	−0.0947059	+	0.164035i
$427$	−4.35878	+	0.768571i	−0.210936	+	0.0371937i
$428$	−3.60483	+	0.635630i	−0.174246	+	0.0307243i
$429$	−0.587182	+	1.01703i	−0.0283494	+	0.0491026i
$430$		0			0
$431$	12.5307	−	10.5145i	0.603585	−	0.506468i	−0.289011	−	0.957326i	$-0.593326\pi$
$431$	12.5307	−	10.5145i	0.603585	−	0.506468i	0.892596	+	0.450858i	$0.148882\pi$
$432$	1.91404	+	5.25877i	0.0920891	+	0.253013i
$433$	3.49103	−	9.59152i	0.167768	−	0.460939i	−0.827108	−	0.562043i	$-0.810015\pi$
$433$	3.49103	−	9.59152i	0.167768	−	0.460939i	0.994876	+	0.101104i	$0.0322376\pi$
$434$	−5.23783	−	4.39506i	−0.251424	−	0.210970i
$435$		0			0
$436$	3.23442			0.154901
$437$	−25.0769	+	8.91875i	−1.19959	+	0.426642i
$438$		−	24.0574i		−	1.14951i
$439$	1.65523	−	9.38728i	0.0789998	−	0.448030i	−0.919491	−	0.393111i	$-0.871399\pi$
$439$	1.65523	−	9.38728i	0.0789998	−	0.448030i	0.998491	−	0.0549191i	$-0.0174901\pi$
$440$		0			0
$441$	−2.12701	−	0.774169i	−0.101286	−	0.0368652i
$442$	7.01336	+	19.2690i	0.333591	+	0.916535i
$443$	−3.84565	−	4.58306i	−0.182712	−	0.217748i	0.666912	−	0.745136i	$-0.267616\pi$
$443$	−3.84565	−	4.58306i	−0.182712	−	0.217748i	−0.849624	+	0.527389i	$0.823171\pi$
$444$	−5.64543	−	9.77817i	−0.267920	−	0.464051i
$445$		0			0
$446$	−2.63950	−	14.9693i	−0.124984	−	0.708819i
$447$	20.1839	−	3.55896i	0.954665	−	0.168333i
$448$	1.62760	+	0.939693i	0.0768967	+	0.0443963i
$449$	−7.67752	−	13.2979i	−0.362325	−	0.627564i	0.626018	−	0.779808i	$-0.284683\pi$
$449$	−7.67752	−	13.2979i	−0.362325	−	0.627564i	−0.988343	+	0.152244i	$0.951350\pi$
$450$		0			0
$451$	0.361844	−	0.131701i	0.0170386	−	0.00620154i
$452$	5.19026	−	14.2601i	0.244129	−	0.670739i
$453$	−14.6390	+	17.4461i	−0.687801	+	0.819689i
$454$	3.24675	−	18.4132i	0.152377	−	0.864176i
$455$		0			0
$456$	5.75877	+	3.38160i	0.269679	+	0.158358i
$457$		−	11.3987i		−	0.533208i	−0.963806	−	0.266604i	$-0.914098\pi$
$457$		−	11.3987i		−	0.533208i	0.963806	−	0.266604i	$-0.0859015\pi$
$458$	−19.6069	−	3.45723i	−0.916172	−	0.161546i
$459$	18.6368	+	15.6381i	0.869892	+	0.729926i
$460$		0			0
$461$	37.9847	−	13.8253i	1.76913	−	0.643909i	0.769137	−	0.639084i	$-0.220686\pi$
$461$	37.9847	−	13.8253i	1.76913	−	0.643909i	0.999988	−	0.00482537i	$-0.00153597\pi$
$462$	0.300767	+	0.358441i	0.0139930	+	0.0166762i
$463$	−8.62246	+	4.97818i	−0.400720	+	0.231356i	−0.686794	−	0.726852i	$-0.740983\pi$
$463$	−8.62246	+	4.97818i	−0.400720	+	0.231356i	0.286075	+	0.958207i	$0.407649\pi$
$464$	1.19459	−	2.06910i	0.0554576	−	0.0960553i
$465$		0			0
$466$	−4.85844	−	27.5536i	−0.225063	−	1.27640i
$467$	4.85678	+	2.80406i	0.224745	+	0.129757i	0.608145	−	0.793826i	$-0.291914\pi$
$467$	4.85678	+	2.80406i	0.224745	+	0.129757i	−0.383400	+	0.923582i	$0.625247\pi$
$468$	2.66625	−	1.53936i	0.123248	−	0.0711571i
$469$	2.35844	−	1.97897i	0.108903	−	0.0913802i
$470$		0			0
$471$	−10.7233	−	3.90295i	−0.494103	−	0.179839i
$472$	−2.62175	+	3.12449i	−0.120676	+	0.143816i
$473$	−0.104455	−	0.0184183i	−0.00480287	−	0.000846875i
$474$	−1.53209			−0.0703712
$475$		0			0
$476$	8.17024			0.374483
$477$	3.82045	+	0.673648i	0.174926	+	0.0308442i
$478$	16.9457	−	20.1951i	0.775077	−	0.923701i
$479$	−23.2383	−	8.45805i	−1.06178	−	0.386458i	−0.248686	−	0.968584i	$-0.579999\pi$
$479$	−23.2383	−	8.45805i	−1.06178	−	0.386458i	−0.813099	+	0.582126i	$0.802221\pi$
$480$		0			0
$481$	−26.6288	+	22.3442i	−1.21417	+	1.01881i
$482$	−14.8742	+	8.58765i	−0.677503	+	0.391157i
$483$	−15.2262	−	8.79086i	−0.692817	−	0.399998i
$484$	1.90554	+	10.8069i	0.0866157	+	0.491222i
$485$		0			0
$486$	3.32635	−	5.76141i	0.150886	−	0.261343i
$487$	−11.2501	+	6.49525i	−0.509791	+	0.294328i	−0.732748	−	0.680500i	$-0.761762\pi$
$487$	−11.2501	+	6.49525i	−0.509791	+	0.294328i	0.222957	+	0.974828i	$0.428429\pi$
$488$	1.51379	+	1.80406i	0.0685260	+	0.0816661i
$489$	−9.72075	+	3.53806i	−0.439588	+	0.159997i
$490$		0			0
$491$	14.2947	+	11.9947i	0.645112	+	0.541313i	0.905583	−	0.424168i	$-0.139433\pi$
$491$	14.2947	+	11.9947i	0.645112	+	0.541313i	−0.260471	+	0.965482i	$0.583878\pi$
$492$	3.57526	+	0.630415i	0.161185	+	0.0284213i
$493$		−	10.3865i		−	0.467784i
$494$	7.17412	−	19.2682i	0.322779	−	0.866916i
$495$		0			0
$496$	−0.631759	+	3.58288i	−0.0283668	+	0.160876i
$497$	3.08256	−	3.67365i	0.138272	−	0.164786i
$498$	0.535685	−	1.47178i	0.0240046	−	0.0659521i
$499$	−16.2353	+	5.90917i	−0.726792	+	0.264531i	−0.678806	−	0.734317i	$-0.737502\pi$
$499$	−16.2353	+	5.90917i	−0.726792	+	0.264531i	−0.0479856	+	0.998848i	$0.515280\pi$
$500$		0			0
$501$	12.4513	+	21.5663i	0.556283	+	0.963511i
$502$	13.9357	+	8.04576i	0.621979	+	0.359100i
$503$	36.7562	−	6.48111i	1.63888	−	0.288979i	0.723125	−	0.690717i	$-0.242705\pi$
$503$	36.7562	−	6.48111i	1.63888	−	0.288979i	0.915754	+	0.401739i	$0.131594\pi$
$504$	−0.213011	−	1.20805i	−0.00948827	−	0.0538106i
$505$		0			0
$506$	0.496130	+	0.859322i	0.0220557	+	0.0382015i
$507$	9.10846	+	10.8550i	0.404521	+	0.482089i
$508$	6.82283	+	18.7456i	0.302714	+	0.831700i
$509$	−17.9522	−	6.53406i	−0.795716	−	0.289617i	−0.0880062	−	0.996120i	$-0.528050\pi$
$509$	−17.9522	−	6.53406i	−0.795716	−	0.289617i	−0.707710	+	0.706503i	$0.750272\pi$
$510$		0			0
$511$	−5.12449	+	29.0624i	−0.226694	+	1.28564i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.05893	−	24.0535i	−0.179206	−	1.06199i
$514$	−14.1438			−0.623858
$515$		0			0
$516$	−0.766044	−	0.642788i	−0.0337232	−	0.0282971i
$517$	0.382353	−	1.05051i	0.0168159	−	0.0462013i
$518$	4.73708	+	13.0150i	0.208135	+	0.571847i
$519$	−6.61721	+	5.55250i	−0.290463	+	0.243728i
$520$		0			0
$521$	17.5287	−	30.3606i	0.767946	−	1.33012i	−0.170729	−	0.985318i	$-0.554612\pi$
$521$	17.5287	−	30.3606i	0.767946	−	1.33012i	0.938675	−	0.344803i	$-0.112054\pi$
$522$	−1.53574	+	0.270792i	−0.0672175	+	0.0118523i
$523$	−23.8367	+	4.20305i	−1.04230	+	0.183786i	−0.668493	−	0.743718i	$-0.733060\pi$
$523$	−23.8367	+	4.20305i	−1.04230	+	0.183786i	−0.373812	+	0.927505i	$0.621949\pi$
$524$	−8.44743	+	14.6314i	−0.369028	+	0.639175i
$525$		0			0
$526$	10.0517	−	8.43437i	0.438274	−	0.367756i
$527$	5.40944	+	14.8623i	0.235639	+	0.647412i
$528$	0.0851529	−	0.233956i	0.00370580	−	0.0101816i
$529$	−10.9422	−	9.18161i	−0.475749	−	0.399201i
$530$		0			0
$531$	2.66220			0.115530
$532$	−6.23654	−	5.31180i	−0.270388	−	0.230296i
$533$		−	11.1771i		−	0.484132i
$534$	−0.892589	+	5.06212i	−0.0386261	+	0.219060i
$535$		0			0
$536$	−1.53936	−	0.560282i	−0.0664903	−	0.0242005i
$537$	−6.02357	−	16.5496i	−0.259936	−	0.714169i
$538$	−14.4327	−	17.2003i	−0.622240	−	0.741556i
$539$	0.281774	+	0.488048i	0.0121369	+	0.0210217i
$540$		0			0
$541$	6.37955	+	36.1802i	0.274278	+	1.55551i	0.741245	+	0.671234i	$0.234235\pi$
$541$	6.37955	+	36.1802i	0.274278	+	1.55551i	−0.466967	+	0.884275i	$0.654653\pi$
$542$	−5.67799	+	1.00118i	−0.243890	+	0.0430045i
$543$	19.9580	+	11.5228i	0.856480	+	0.494489i
$544$	−2.17365	−	3.76487i	−0.0931944	−	0.161417i
$545$		0			0
$546$	12.7626	−	4.64522i	0.546191	−	0.198797i
$547$	−6.59289	+	18.1138i	−0.281891	+	0.774490i	0.715245	+	0.698873i	$0.246315\pi$
$547$	−6.59289	+	18.1138i	−0.281891	+	0.774490i	−0.997137	+	0.0756171i	$0.975907\pi$
$548$	3.19961	−	3.81315i	0.136681	−	0.162890i
$549$	0.266922	−	1.51379i	0.0113919	−	0.0646069i
$550$		0			0
$551$	−6.75268	+	7.92826i	−0.287674	+	0.337755i
$552$			9.35504i			0.398177i
$553$	1.85083	+	0.326352i	0.0787054	+	0.0138779i
$554$	15.1472	+	12.7100i	0.643545	+	0.539998i
$555$		0			0
$556$	17.5954	−	6.40420i	0.746211	−	0.271598i
$557$	−27.4216	−	32.6798i	−1.16189	−	1.38469i	−0.908793	−	0.417247i	$-0.862995\pi$
$557$	−27.4216	−	32.6798i	−1.16189	−	1.38469i	−0.253097	−	0.967441i	$-0.581449\pi$
$558$	2.05650	−	1.18732i	0.0870584	−	0.0502632i
$559$	−1.53936	+	2.66625i	−0.0651081	+	0.112771i
$560$		0			0
$561$	−0.187948	−	1.06590i	−0.00793516	−	0.0450025i
$562$	27.4550	+	15.8512i	1.15812	+	0.668641i
$563$	10.2176	−	5.89915i	0.430621	−	0.248619i	−0.268990	−	0.963143i	$-0.586690\pi$
$563$	10.2176	−	5.89915i	0.430621	−	0.248619i	0.699611	+	0.714524i	$0.253356\pi$
$564$	8.07398	−	6.77487i	0.339976	−	0.285274i
$565$		0			0
$566$	2.76352	+	1.00584i	0.116159	+	0.0422785i
$567$	7.99227	−	9.52481i	0.335644	−	0.400005i
$568$	−2.51292	−	0.443096i	−0.105440	−	0.0185919i
$569$	1.87164			0.0784634			0.0392317	−	0.999230i	$-0.487509\pi$
$569$	1.87164			0.0784634			0.0392317	+	0.999230i	$0.487509\pi$
$570$		0			0
$571$	−8.14197			−0.340731			−0.170365	−	0.985381i	$-0.554495\pi$
$571$	−8.14197			−0.340731			−0.170365	+	0.985381i	$0.554495\pi$
$572$	−0.754866	−	0.133103i	−0.0315625	−	0.00556533i
$573$	19.9060	−	23.7230i	0.831584	−	0.991044i
$574$	−4.18479	−	1.52314i	−0.174670	−	0.0635746i
$575$		0			0
$576$	−0.500000	+	0.419550i	−0.0208333	+	0.0174812i
$577$	7.82380	−	4.51707i	0.325709	−	0.188048i	−0.328225	−	0.944599i	$-0.606451\pi$
$577$	7.82380	−	4.51707i	0.325709	−	0.188048i	0.653934	+	0.756551i	$0.273117\pi$
$578$	−1.64457	−	0.949493i	−0.0684051	−	0.0394937i
$579$	2.68092	+	15.2043i	0.111415	+	0.631868i
$580$		0			0
$581$	−0.960637	+	1.66387i	−0.0398539	+	0.0690291i
$582$	23.7138	−	13.6912i	0.982970	−	0.567518i
$583$	−0.620838	−	0.739885i	−0.0257125	−	0.0306429i
$584$	14.7554	−	5.37051i	0.610581	−	0.222233i
$585$		0			0
$586$	−12.4847	−	10.4759i	−0.515740	−	0.432757i
$587$	−38.8935	−	6.85797i	−1.60531	−	0.283059i	−0.702040	−	0.712138i	$-0.747727\pi$
$587$	−38.8935	−	6.85797i	−1.60531	−	0.283059i	−0.903267	+	0.429079i	$0.858838\pi$
$588$			5.31315i			0.219111i
$589$	5.53343	−	14.8616i	0.228001	−	0.612363i
$590$		0			0
$591$	−3.48474	+	19.7629i	−0.143343	+	0.812938i
$592$	4.73708	−	5.64543i	0.194693	−	0.232026i
$593$	−9.88852	+	27.1685i	−0.406073	+	1.11568i	0.553164	+	0.833072i	$0.313420\pi$
$593$	−9.88852	+	27.1685i	−0.406073	+	1.11568i	−0.959237	+	0.282604i	$0.908802\pi$
$594$	−0.854570	+	0.311038i	−0.0350634	+	0.0127621i
$595$		0			0
$596$	6.68866	+	11.5851i	0.273978	+	0.474544i
$597$	23.3243	+	13.4663i	0.954602	+	0.551140i
$598$	28.3640	−	5.00134i	1.15989	−	0.204520i
$599$	−3.16931	−	17.9741i	−0.129495	−	0.734400i	−0.978536	−	0.206074i	$-0.933931\pi$
$599$	−3.16931	−	17.9741i	−0.129495	−	0.734400i	0.849042	−	0.528326i	$-0.177180\pi$
$600$		0			0
$601$	−4.18433	−	7.24746i	−0.170682	−	0.295630i	0.767976	−	0.640478i	$-0.221264\pi$
$601$	−4.18433	−	7.24746i	−0.170682	−	0.295630i	−0.938659	+	0.344848i	$0.887930\pi$
$602$	0.788496	+	0.939693i	0.0321367	+	0.0382990i
$603$	0.365698	+	1.00475i	0.0148924	+	0.0409165i
$604$	−13.9684	−	5.08407i	−0.568365	−	0.206868i
$605$		0			0
$606$	−2.36959	+	13.4386i	−0.0962578	+	0.545905i
$607$		−	28.1138i		−	1.14110i	−0.821261	−	0.570552i	$-0.806729\pi$
$607$		−	28.1138i		−	1.14110i	0.821261	−	0.570552i	$-0.193271\pi$
$608$	−0.788496	+	4.28699i	−0.0319777	+	0.173860i
$609$	−6.87939			−0.278767
$610$		0			0
$611$	−24.8576	−	20.8580i	−1.00563	−	0.843823i
$612$	−0.970481	+	2.66637i	−0.0392294	+	0.107782i
$613$	−7.28861	−	20.0253i	−0.294384	−	0.808814i	−0.995412	−	0.0956799i	$-0.969497\pi$
$613$	−7.28861	−	20.0253i	−0.294384	−	0.808814i	0.701028	−	0.713134i	$-0.252725\pi$
$614$	−16.9932	+	14.2590i	−0.685789	+	0.575446i
$615$		0			0
$616$	−0.152704	+	0.264490i	−0.00615261	+	0.0106566i
$617$	15.6255	−	2.75520i	0.629061	−	0.110920i	0.149977	−	0.988690i	$-0.452080\pi$
$617$	15.6255	−	2.75520i	0.629061	−	0.110920i	0.479084	+	0.877769i	$0.340969\pi$
$618$	12.4462	−	2.19459i	0.500658	−	0.0882795i
$619$	−1.20527	+	2.08759i	−0.0484439	+	0.0839073i	−0.889231	−	0.457459i	$-0.848760\pi$
$619$	−1.20527	+	2.08759i	−0.0484439	+	0.0839073i	0.840787	+	0.541367i	$0.182093\pi$
$620$		0			0
$621$	26.1766	−	21.9648i	1.05043	−	0.881417i
$622$	−3.05217	−	8.38578i	−0.122381	−	0.336239i
$623$	2.15658	−	5.92514i	0.0864014	−	0.237386i
$624$	−5.53596	−	4.64522i	−0.221616	−	0.185958i
$625$		0			0
$626$	−18.3259			−0.732452
$627$	−0.549522	+	0.935822i	−0.0219458	+	0.0373731i
$628$		−	7.44831i		−	0.297220i
$629$	5.56330	−	31.5510i	0.221823	−	1.25802i
$630$		0			0
$631$	1.26769	+	0.461403i	0.0504661	+	0.0183681i	0.367130	−	0.930170i	$-0.380340\pi$
$631$	1.26769	+	0.461403i	0.0504661	+	0.0183681i	−0.316664	+	0.948538i	$0.602563\pi$
$632$	−0.342020	−	0.939693i	−0.0136048	−	0.0373790i
$633$	24.3616	+	29.0330i	0.968287	+	1.15396i
$634$	−12.1309	−	21.0113i	−0.481779	−	0.834465i
$635$		0			0
$636$	−1.58125	−	8.96773i	−0.0627007	−	0.355593i
$637$	16.1092	−	2.84049i	0.638270	−	0.112544i
$638$	0.336236	+	0.194126i	0.0133117	+	0.00768552i
$639$	0.832748	+	1.44236i	0.0329430	+	0.0570590i
$640$		0			0
$641$	−32.3910	+	11.7894i	−1.27937	+	0.465652i	−0.890223	−	0.455525i	$-0.849452\pi$
$641$	−32.3910	+	11.7894i	−1.27937	+	0.465652i	−0.389144	+	0.921177i	$0.627229\pi$
$642$	1.91809	−	5.26991i	0.0757011	−	0.207987i
$643$	−13.0729	+	15.5797i	−0.515544	+	0.614402i	−0.959521	−	0.281636i	$-0.909123\pi$
$643$	−13.0729	+	15.5797i	−0.515544	+	0.614402i	0.443977	+	0.896038i	$0.353567\pi$
$644$	1.99273	−	11.3013i	0.0785244	−	0.445334i
$645$		0			0
$646$	6.34982	+	17.8539i	0.249830	+	0.702451i
$647$			41.9427i			1.64894i	0.565906	+	0.824470i	$0.308526\pi$
$647$			41.9427i			1.64894i	−0.565906	+	0.824470i	$0.691474\pi$
$648$	−6.51536	−	1.14883i	−0.255947	−	0.0451304i
$649$	−0.507741	−	0.426045i	−0.0199306	−	0.0167237i
$650$		0			0
$651$	9.84389	−	3.58288i	0.385813	−	0.140424i
$652$	−4.34008	−	5.17230i	−0.169971	−	0.202563i
$653$	−26.0497	+	15.0398i	−1.01941	+	0.588554i	−0.913932	−	0.405868i	$-0.866969\pi$
$653$	−26.0497	+	15.0398i	−1.01941	+	0.588554i	−0.105474	+	0.994422i	$0.533636\pi$
$654$	−2.47771	+	4.29152i	−0.0968862	+	0.167812i
$655$		0			0
$656$	0.411474	+	2.33359i	0.0160654	+	0.0911112i
$657$	−8.87587	−	5.12449i	−0.346281	−	0.199925i
$658$	−11.1969	+	6.46451i	−0.436499	+	0.252013i
$659$	−37.7001	+	31.6342i	−1.46859	+	1.23229i	−0.551154	+	0.834404i	$0.685812\pi$
$659$	−37.7001	+	31.6342i	−1.46859	+	1.23229i	−0.917434	+	0.397888i	$0.869743\pi$
$660$		0			0
$661$	−44.5330	−	16.2087i	−1.73213	−	0.630445i	−0.733355	−	0.679846i	$-0.762047\pi$
$661$	−44.5330	−	16.2087i	−1.73213	−	0.630445i	−0.998779	+	0.0494010i	$0.984269\pi$
$662$	21.7229	−	25.8883i	0.844283	−	1.00618i
$663$	−30.9392	−	5.45542i	−1.20158	−	0.211871i
$664$	1.02229			0.0396725
$665$		0			0
$666$	−4.81016			−0.186390
$667$	−14.3669	−	2.53327i	−0.556288	−	0.0980886i
$668$	−10.4479	+	12.4513i	−0.404241	+	0.481755i
$669$	21.8837	+	7.96502i	0.846074	+	0.307946i
$670$		0			0
$671$	−0.293167	+	0.245996i	−0.0113176	+	0.00949659i
$672$	−2.49362	+	1.43969i	−0.0961935	+	0.0555373i
$673$	−1.33586	−	0.771259i	−0.0514936	−	0.0297299i	0.474032	−	0.880508i	$-0.342798\pi$
$673$	−1.33586	−	0.771259i	−0.0514936	−	0.0297299i	−0.525526	+	0.850778i	$0.676131\pi$
$674$	5.16978	+	29.3193i	0.199132	+	1.12934i
$675$		0			0
$676$	−4.62449	+	8.00984i	−0.177865	+	0.308071i
$677$	15.6595	−	9.04101i	0.601843	−	0.347474i	−0.167923	−	0.985800i	$-0.553706\pi$
$677$	15.6595	−	9.04101i	0.601843	−	0.347474i	0.769766	+	0.638326i	$0.220373\pi$
$678$	14.9448	+	17.8105i	0.573950	+	0.684007i
$679$	−31.5638	+	11.4883i	−1.21131	+	0.440879i
$680$		0			0
$681$	21.9440	+	18.4132i	0.840897	+	0.705596i
$682$	−0.582232	−	0.102663i	−0.0222948	−	0.00393118i
$683$			22.1976i			0.849367i	0.905342	+	0.424684i	$0.139615\pi$
$683$			22.1976i			0.849367i	−0.905342	+	0.424684i	$0.860385\pi$
$684$	2.47431	−	1.40436i	0.0946075	−	0.0536970i
$685$		0			0
$686$	3.41622	−	19.3744i	0.130432	−	0.739716i
$687$	19.6069	−	23.3666i	0.748052	−	0.891493i
$688$	0.223238	−	0.613341i	0.00851086	−	0.0233834i
$689$	−26.3444	+	9.58856i	−1.00364	+	0.365295i
$690$		0			0
$691$	21.9449	+	38.0097i	0.834824	+	1.44596i	0.894174	+	0.447720i	$0.147764\pi$
$691$	21.9449	+	38.0097i	0.834824	+	1.44596i	−0.0593503	+	0.998237i	$0.518903\pi$
$692$	−4.88279	−	2.81908i	−0.185616	−	0.107165i
$693$	0.196312	−	0.0346151i	0.00745728	−	0.00131492i
$694$	−0.542766	−	3.07818i	−0.0206031	−	0.116846i
$695$		0			0
$696$	1.83022	+	3.17004i	0.0693744	+	0.120160i
$697$	6.62154	+	7.89124i	0.250809	+	0.298902i
$698$	2.65863	+	7.30453i	0.100631	+	0.276481i
$699$	40.2806	+	14.6610i	1.52355	+	0.554528i
$700$		0			0
$701$	−0.955423	+	5.41847i	−0.0360858	+	0.204653i	−0.997520	−	0.0703819i	$-0.977578\pi$
$701$	−0.955423	+	5.41847i	−0.0360858	+	0.204653i	0.961434	+	0.275035i	$0.0886893\pi$
$702$			26.3969i			0.996288i
$703$	−24.7592	+	20.4667i	−0.933811	+	0.771917i
$704$	0.162504			0.00612459
$705$		0			0
$706$	−22.3935	−	18.7904i	−0.842791	−	0.707186i
$707$	5.72513	−	15.7297i	0.215316	−	0.591575i
$708$	−2.13727	−	5.87211i	−0.0803237	−	0.220687i
$709$	35.7105	−	29.9647i	1.34114	−	1.12535i	0.359805	−	0.933027i	$-0.382843\pi$
$709$	35.7105	−	29.9647i	1.34114	−	1.12535i	0.981332	−	0.192321i	$-0.0616014\pi$
$710$		0			0
$711$	−0.326352	+	0.565258i	−0.0122391	+	0.0211988i
$712$	−3.30407	+	0.582596i	−0.123825	+	0.0218337i
$713$	21.8773	−	3.85756i	0.819312	−	0.144467i
$714$	−6.25877	+	10.8405i	−0.234229	+	0.405696i
$715$		0			0
$716$	8.80587	−	7.38901i	0.329091	−	0.276140i
$717$	13.8142	+	37.9543i	0.515902	+	1.41743i
$718$	6.17101	−	16.9547i	0.230300	−	0.632744i
$719$	9.20052	+	7.72016i	0.343122	+	0.287913i	0.798021	−	0.602630i	$-0.205880\pi$
$719$	9.20052	+	7.72016i	0.343122	+	0.287913i	−0.454899	+	0.890543i	$0.650325\pi$
$720$		0			0
$721$	−15.5030			−0.577362
$722$	6.76055	−	17.7565i	0.251601	−	0.660830i
$723$		−	26.3141i		−	0.978631i
$724$	−2.61200	+	14.8134i	−0.0970741	+	0.550535i
$725$		0			0
$726$	−15.7986	−	5.75022i	−0.586341	−	0.213411i
$727$	10.5994	+	29.1215i	0.393109	+	1.08006i	0.965574	+	0.260129i	$0.0837651\pi$
$727$	10.5994	+	29.1215i	0.393109	+	1.08006i	−0.572465	+	0.819929i	$0.694013\pi$
$728$	5.69821	+	6.79086i	0.211190	+	0.251686i
$729$	15.0201	+	26.0155i	0.556299	+	0.963538i
$730$		0			0
$731$	−0.492726	−	2.79439i	−0.0182241	−	0.103354i
$732$	−3.55331	+	0.626545i	−0.131334	+	0.0231578i
$733$	−1.03947	−	0.600137i	−0.0383936	−	0.0221666i	0.480680	−	0.876896i	$-0.340390\pi$
$733$	−1.03947	−	0.600137i	−0.0383936	−	0.0221666i	−0.519074	+	0.854729i	$0.673723\pi$
$734$	8.34271	+	14.4500i	0.307935	+	0.533359i
$735$		0			0
$736$	−5.73783	+	2.08840i	−0.211499	+	0.0769794i
$737$	0.0910480	−	0.250152i	0.00335380	−	0.00921448i
$738$	0.994159	−	1.18479i	0.0365955	−	0.0436128i
$739$	2.15880	−	12.2431i	0.0794126	−	0.450371i	−0.919010	−	0.394233i	$-0.871010\pi$
$739$	2.15880	−	12.2431i	0.0794126	−	0.450371i	0.998423	−	0.0561379i	$-0.0178787\pi$
$740$		0			0
$741$	20.0699	+	24.2791i	0.737285	+	0.891915i
$742$			11.1702i			0.410073i
$743$	−2.76838	−	0.488140i	−0.101562	−	0.0179081i	0.122636	−	0.992452i	$-0.460865\pi$
$743$	−2.76838	−	0.488140i	−0.101562	−	0.0179081i	−0.224198	+	0.974544i	$0.571976\pi$
$744$	−4.26991	−	3.58288i	−0.156543	−	0.131355i
$745$		0			0
$746$	−7.32800	+	2.66717i	−0.268297	+	0.0976522i
$747$	−0.428901	−	0.511144i	−0.0156927	−	0.0187018i
$748$	0.611806	−	0.353226i	0.0223698	−	0.0129152i
$749$	−3.43969	+	5.95772i	−0.125684	+	0.217690i
$750$		0			0
$751$	−1.38326	−	7.84483i	−0.0504757	−	0.286262i	0.949113	−	0.314935i	$-0.101983\pi$
$751$	−1.38326	−	7.84483i	−0.0504757	−	0.286262i	−0.999589	+	0.0286734i	$0.990872\pi$
$752$	5.95772	+	3.43969i	0.217256	+	0.125433i
$753$	−21.3507	+	12.3268i	−0.778062	+	0.449214i
$754$	8.63294	−	7.24390i	0.314393	−	0.263807i
$755$		0			0
$756$	9.88326	+	3.59721i	0.359451	+	0.130829i
$757$	−8.96448	+	10.6834i	−0.325819	+	0.388297i	−0.903943	−	0.427653i	$-0.859341\pi$
$757$	−8.96448	+	10.6834i	−0.325819	+	0.388297i	0.578124	+	0.815949i	$0.303785\pi$
$758$	1.29990	+	0.229208i	0.0472146	+	0.00832520i
$759$	−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	$0.833605\pi$
$762$	−30.0987	−	5.30722i	−1.09036	−	0.192260i
$763$	3.90733	−	4.65657i	0.141455	−	0.168579i
$764$	18.9941	+	6.91328i	0.687181	+	0.250114i
$765$		0			0
$766$	−25.4349	+	21.3425i	−0.919002	+	0.771134i
$767$	−16.6613	+	9.61943i	−0.601606	+	0.347338i
$768$	1.32683	+	0.766044i	0.0478778	+	0.0276422i
$769$	2.86080	+	16.2244i	0.103163	+	0.585068i	0.991938	+	0.126724i	$0.0404462\pi$
$769$	2.86080	+	16.2244i	0.103163	+	0.585068i	−0.888775	+	0.458344i	$0.848443\pi$
$770$		0			0
$771$	10.8348	−	18.7664i	0.390206	−	0.675857i
$772$	−8.72691	+	5.03849i	−0.314088	+	0.181339i
$773$	6.48233	+	7.72534i	0.233153	+	0.277861i	0.869917	−	0.493197i	$-0.164172\pi$
$773$	6.48233	+	7.72534i	0.233153	+	0.277861i	−0.636764	+	0.771059i	$0.719728\pi$
$774$	−0.400330	+	0.145708i	−0.0143896	+	0.00523737i
$775$		0			0
$776$	13.6912	+	11.4883i	0.491485	+	0.412405i
$777$	−20.8975	−	3.68479i	−0.749694	−	0.132191i
$778$			14.8571i			0.532653i
$779$	0.0760373	−	10.3285i	0.00272432	−	0.370057i
$780$		0			0
$781$	0.0720048	−	0.408360i	0.00257654	−	0.0146123i
$782$	−17.0627	+	20.3346i	−0.610162	+	0.727162i
$783$	4.57299	−	12.5642i	0.163425	−	0.449007i
$784$	−3.25877	+	1.18610i	−0.116385	+	0.0423606i
$785$		0			0
$786$	−12.9422	−	22.4166i	−0.461634	−	0.799573i
$787$	−31.2148	−	18.0219i	−1.11269	−	0.642411i	−0.173164	−	0.984893i	$-0.555399\pi$
$787$	−31.2148	−	18.0219i	−1.11269	−	0.642411i	−0.939524	+	0.342483i	$0.888732\pi$
$788$	−12.8993	+	2.27450i	−0.459520	+	0.0810257i
$789$	3.49092	+	19.7980i	0.124280	+	0.704826i
$790$		0			0
$791$	−14.2601	−	24.6992i	−0.507031	−	0.878204i
$792$	−0.0681784	−	0.0812519i	−0.00242262	−	0.00288716i
$793$	3.79931	+	10.4385i	0.134917	+	0.370682i
$794$	8.09374	+	2.94588i	0.287236	+	0.104545i
$795$		0			0
$796$	−3.05257	+	17.3120i	−0.108195	+	0.613606i
$797$			3.42190i			0.121210i	0.998162	+	0.0606050i	$0.0193030\pi$
$797$			3.42190i			0.121210i	−0.998162	+	0.0606050i	$0.980697\pi$
$798$	11.8253	−	4.20574i	0.418612	−	0.148881i
$799$	29.9067			1.05802
$800$		0			0
$801$	1.67752	+	1.40761i	0.0592722	+	0.0497353i
$802$	1.74670	−	4.79901i	0.0616780	−	0.169459i
$803$	0.872729	+	2.39780i	0.0307979	+	0.0846166i
$804$	1.92262	−	1.61327i	0.0678055	−	0.0568956i
$805$		0			0
$806$	−8.58037	+	14.8616i	−0.302231	+	0.523479i
$807$	33.8779	−	5.97359i	1.19256	−	0.210280i
$808$	−8.77141	+	1.54664i	−0.308577	+	0.0544105i
$809$	3.73870	−	6.47562i	0.131446	−	0.227671i	−0.792788	−	0.609497i	$-0.791371\pi$
$809$	3.73870	−	6.47562i	0.131446	−	0.227671i	0.924234	+	0.381826i	$0.124705\pi$
$810$		0			0
$811$	37.6810	−	31.6181i	1.32316	−	1.11026i	0.337533	−	0.941314i	$-0.390408\pi$
$811$	37.6810	−	31.6181i	1.32316	−	1.11026i	0.985625	−	0.168948i	$-0.0540369\pi$
$812$	−1.53574	−	4.21941i	−0.0538939	−	0.148072i
$813$	3.02119	−	8.30066i	0.105958	−	0.291117i
$814$	0.917404	+	0.769793i	0.0321550	+	0.0269812i
$815$		0			0
$816$	6.66044			0.233162
$817$	−1.44063	+	2.45336i	−0.0504014	+	0.0858323i
$818$			28.8307i			1.00804i
$819$	1.00475	−	5.69821i	0.0351087	−	0.199111i
$820$		0			0
$821$	−8.84611	−	3.21972i	−0.308732	−	0.112369i	0.183008	−	0.983111i	$-0.441417\pi$
$821$	−8.84611	−	3.21972i	−0.308732	−	0.112369i	−0.491740	+	0.870742i	$0.663639\pi$
$822$	2.60835	+	7.16637i	0.0909765	+	0.249956i
$823$	−27.2007	−	32.4165i	−0.948157	−	1.12997i	−0.991395	−	0.130904i	$-0.958212\pi$
$823$	−27.2007	−	32.4165i	−0.948157	−	1.12997i	0.0432384	−	0.999065i	$-0.486233\pi$
$824$	4.12449	+	7.14382i	0.143683	+	0.248867i
$825$		0			0
$826$	1.33110	+	7.54904i	0.0463149	+	0.262665i
$827$	26.3119	−	4.63950i	0.914955	−	0.161331i	0.303702	−	0.952767i	$-0.401777\pi$
$827$	26.3119	−	4.63950i	0.914955	−	0.161331i	0.611252	+	0.791436i	$0.290666\pi$
$828$	3.45150	+	1.99273i	0.119948	+	0.0692520i
$829$	7.24257	+	12.5445i	0.251545	+	0.435689i	0.963951	−	0.266078i	$-0.0857280\pi$
$829$	7.24257	+	12.5445i	0.251545	+	0.435689i	−0.712406	+	0.701767i	$0.752395\pi$
$830$		0			0
$831$	−28.4675	+	10.3613i	−0.987527	+	0.359430i
$832$	1.61327	−	4.43242i	0.0559300	−	0.153666i
$833$	−9.69069	+	11.5489i	−0.335763	+	0.400146i
$834$	−4.98158	+	28.2520i	−0.172498	+	0.978285i
$835$		0			0
$836$	−0.696652	−	0.128134i	−0.0240942	−	0.00443159i
$837$			20.3601i			0.703748i
$838$	−7.54671	−	1.33069i	−0.260697	−	0.0459679i
$839$	−0.409663	−	0.343748i	−0.0141431	−	0.0118675i	0.635689	−	0.771946i	$-0.280716\pi$
$839$	−0.409663	−	0.343748i	−0.0141431	−	0.0118675i	−0.649832	+	0.760078i	$0.725161\pi$
$840$		0			0
$841$	21.8871	−	7.96626i	0.754728	−	0.274699i
$842$	−4.32078	−	5.14930i	−0.148904	−	0.177457i
$843$	−42.0635	+	24.2854i	−1.44875	+	0.836433i
$844$	−12.3687	+	21.4232i	−0.425748	+	0.737418i
$845$		0			0
$846$	−0.779715	−	4.42198i	−0.0268072	−	0.152031i
$847$	17.8606	+	10.3118i	0.613696	+	0.354318i
$848$	5.14728	−	2.97178i	0.176758	−	0.102051i
$849$	−3.45155	+	2.89620i	−0.118457	+	0.0993972i
$850$		0			0
$851$	−42.2854	−	15.3906i	−1.44952	−	0.527584i
$852$	2.51292	−	2.99479i	0.0860913	−	0.102600i
$853$	−6.14906	−	1.08424i	−0.210540	−	0.0371238i	0.0673834	−	0.997727i	$-0.478535\pi$
$853$	−6.14906	−	1.08424i	−0.210540	−	0.0371238i	−0.277923	+	0.960603i	$0.589646\pi$
$854$	4.42602			0.151455
$855$		0			0
$856$	3.66044			0.125111
$857$	13.1571	+	2.31996i	0.449439	+	0.0792482i	0.393786	−	0.919202i	$-0.371165\pi$
$857$	13.1571	+	2.31996i	0.449439	+	0.0792482i	0.0556524	+	0.998450i	$0.482276\pi$
$858$	0.754866	−	0.899615i	0.0257707	−	0.0307123i
$859$	−6.98070	−	2.54077i	−0.238179	−	0.0866899i	0.220173	−	0.975461i	$-0.429338\pi$
$859$	−6.98070	−	2.54077i	−0.238179	−	0.0866899i	−0.458352	+	0.888771i	$0.651560\pi$
$860$		0			0
$861$	5.22668	−	4.38571i	0.178125	−	0.149464i
$862$	−14.1662	+	8.17886i	−0.482503	+	0.278573i
$863$	15.9916	+	9.23277i	0.544362	+	0.314287i	0.746845	−	0.664998i	$-0.231568\pi$
$863$	15.9916	+	9.23277i	0.544362	+	0.314287i	−0.202483	+	0.979286i	$0.564901\pi$
$864$	−0.971782	−	5.51125i	−0.0330607	−	0.187496i
$865$		0			0
$866$	−5.10354	+	8.83959i	−0.173425	+	0.300382i
$867$	2.51963	−	1.45471i	0.0855710	−	0.0494045i
$868$	4.39506	+	5.23783i	0.149178	+	0.177783i
$869$	0.152704	−	0.0555796i	0.00518012	−	0.00188541i
$870$		0			0
$871$	−5.91921	−	4.96681i	−0.200565	−	0.168294i
$872$	−3.18528	−	0.561652i	−0.107867	−	0.0190199i
$873$		−	11.6655i		−	0.394817i
$874$	26.2447	−	4.42869i	0.887740	−	0.149803i
$875$		0			0
$876$	−4.17752	+	23.6919i	−0.141145	+	0.800475i
$877$	−9.59506	+	11.4349i	−0.324002	+	0.386131i	−0.903317	−	0.428973i	$-0.858876\pi$
$877$	−9.59506	+	11.4349i	−0.324002	+	0.386131i	0.579315	+	0.815104i	$0.303320\pi$
$878$	−3.26017	+	8.95723i	−0.110025	+	0.302292i
$879$	23.4636	−	8.54006i	0.791409	−	0.288049i
$880$		0			0
$881$	11.8491	+	20.5233i	0.399207	+	0.691446i	0.993628	−	0.112707i	$-0.0359523\pi$
$881$	11.8491	+	20.5233i	0.399207	+	0.691446i	−0.594422	+	0.804154i	$0.702619\pi$
$882$	1.96026	+	1.13176i	0.0660055	+	0.0381083i
$883$	13.2633	−	2.33868i	0.446346	−	0.0787028i	0.0540423	−	0.998539i	$-0.482789\pi$
$883$	13.2633	−	2.33868i	0.446346	−	0.0787028i	0.392303	+	0.919836i	$0.371678\pi$
$884$	−3.56077	−	20.1942i	−0.119762	−	0.679203i
$885$		0			0
$886$	2.99138	+	5.18123i	0.100497	+	0.174067i
$887$	17.7903	+	21.2017i	0.597341	+	0.711884i	0.976999	−	0.213243i	$-0.0684027\pi$
$887$	17.7903	+	21.2017i	0.597341	+	0.711884i	−0.379658	+	0.925127i	$0.623958\pi$
$888$	3.86170	+	10.6099i	0.129590	+	0.356046i
$889$	35.2301	+	12.8227i	1.18158	+	0.430060i
$890$		0			0
$891$	0.186690	−	1.05877i	0.00625434	−	0.0354701i
$892$			15.2003i			0.508943i
$893$	−22.8285	−	19.4436i	−0.763927	−	0.650654i
$894$	−20.4953			−0.685464
$895$		0			0
$896$	−1.43969	−	1.20805i	−0.0480968	−	0.0403580i
$897$	−15.0922	+	41.4654i	−0.503913	+	1.38449i
$898$	5.25173	+	14.4290i	0.175253	+	0.481502i
$899$	6.65863	−	5.58726i	0.222078	−	0.186345i
$900$		0			0
$901$	12.9192	−	22.3767i	0.430401	−	0.745477i
$902$	−0.379217	+	0.0668661i	−0.0126265	+	0.00222640i
$903$	−1.85083	+	0.326352i	−0.0615919	+	0.0108603i
$904$	−7.58765	+	13.1422i	−0.252361	+	0.437103i
$905$		0			0
$906$	17.4461	−	14.6390i	0.579607	−	0.486348i
$907$	0.155059	+	0.426022i	0.00514866	+	0.0141458i	0.942240	−	0.334938i	$-0.108715\pi$
$907$	0.155059	+	0.426022i	0.00514866	+	0.0141458i	−0.937092	+	0.349083i	$0.886493\pi$
$908$	−6.39485	+	17.5697i	−0.212220	+	0.583071i
$909$	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	$0.201677\pi$
$912$	−5.08407	−	4.33022i	−0.168351	−	0.143388i
$913$			0.166126i			0.00549796i
$914$	−1.97936	+	11.2255i	−0.0654714	+	0.371307i
$915$		0			0
$916$	18.7087	+	6.80942i	0.618154	+	0.224990i
$917$	10.8598	+	29.8371i	0.358623	+	0.985307i
$918$	−15.6381	−	18.6368i	−0.516136	−	0.615106i
$919$	16.7733	+	29.0522i	0.553301	+	0.958345i	0.998034	+	0.0626817i	$0.0199653\pi$
$919$	16.7733	+	29.0522i	0.553301	+	0.958345i	−0.444733	+	0.895663i	$0.646701\pi$
$920$		0			0
$921$	−5.90167	−	33.4701i	−0.194467	−	1.10288i
$922$	−39.8084	+	7.01930i	−1.31102	+	0.231168i
$923$	−10.4235	−	6.01801i	−0.343094	−	0.198085i
$924$	−0.233956	−	0.405223i	−0.00769657	−	0.0133309i
$925$		0			0
$926$	9.35591	−	3.40527i	0.307454	−	0.111904i
$927$	1.84148	−	5.05943i	0.0604822	−	0.166173i
$928$	−1.53574	+	1.83022i	−0.0504131	+	0.0600800i
$929$	6.50016	−	36.8643i	0.213263	−	1.20948i	−0.670631	−	0.741791i	$-0.733977\pi$
$929$	6.50016	−	36.8643i	0.213263	−	1.20948i	0.883895	−	0.467686i	$-0.154912\pi$
$930$		0			0
$931$	14.9055	−	2.51525i	0.488509	−	0.0824340i
$932$			27.9786i			0.916471i
$933$	13.4646	+	2.37417i	0.440811	+	0.0777269i
$934$	−4.29607	−	3.60483i	−0.140572	−	0.117954i
$935$		0			0
$936$	−2.89306	+	1.05299i	−0.0945625	+	0.0344179i
$937$	−2.32039	−	2.76533i	−0.0758037	−	0.0903394i	0.726810	−	0.686839i	$-0.241002\pi$
$937$	−2.32039	−	2.76533i	−0.0758037	−	0.0903394i	−0.802613	+	0.596500i	$0.796558\pi$
$938$	−2.66625	+	1.53936i	−0.0870563	+	0.0502620i
$939$	14.0385	−	24.3154i	0.458129	−	0.793502i
$940$		0			0
$941$	−6.28540	−	35.6463i	−0.204898	−	1.16203i	−0.897600	−	0.440811i	$-0.854691\pi$
$941$	−6.28540	−	35.6463i	−0.204898	−	1.16203i	0.692702	−	0.721224i	$-0.256420\pi$
$942$	9.88263	+	5.70574i	0.321993	+	0.185903i
$943$	12.5304	−	7.23442i	0.408046	−	0.235585i
$944$	3.12449	−	2.62175i	0.101693	−	0.0853308i
$945$		0			0
$946$	0.0996702	+	0.0362770i	0.00324056	+	0.00117947i
$947$	−19.0801	+	22.7388i	−0.620019	+	0.738910i	−0.981074	−	0.193634i	$-0.937972\pi$
$947$	−19.0801	+	22.7388i	−0.620019	+	0.738910i	0.361054	+	0.932545i	$0.382417\pi$
$948$	1.50881	+	0.266044i	0.0490040	+	0.00864072i
$949$	74.0660			2.40429
$950$		0			0
$951$	37.1712			1.20536
$952$	−8.04612	−	1.41875i	−0.260776	−	0.0459819i
$953$	−9.50698	+	11.3300i	−0.307961	+	0.367014i	−0.897721	−	0.440565i	$-0.854778\pi$
$953$	−9.50698	+	11.3300i	−0.307961	+	0.367014i	0.589759	+	0.807579i	$0.299223\pi$
$954$	−3.64543	−	1.32683i	−0.118025	−	0.0429576i
$955$		0			0
$956$	−20.1951	+	16.9457i	−0.653155	+	0.548062i
$957$	−0.515143	+	0.297418i	−0.0166522	+	0.00961416i
$958$	21.4165	+	12.3648i	0.691937	+	0.399490i
$959$	−1.62449	−	9.21291i	−0.0524574	−	0.297500i
$960$		0			0
$961$	8.88191	−	15.3839i	0.286513	−	0.496256i
$962$	30.1043	−	17.3807i	0.970602	−	0.560377i
$963$	−1.53574	−	1.83022i	−0.0494885	−	0.0589781i
$964$	16.1395	−	5.87430i	0.519818	−	0.189198i
$965$		0			0
$966$	13.4684	+	11.3013i	0.433338	+	0.363614i
$967$	−44.2523	−	7.80288i	−1.42306	−	0.250924i	−0.591475	−	0.806323i	$-0.701454\pi$
$967$	−44.2523	−	7.80288i	−1.42306	−	0.250924i	−0.831584	+	0.555399i	$0.812565\pi$
$968$		−	10.9736i		−	0.352705i
$969$	−28.5533	−	5.25173i	−0.917263	−	0.168710i
$970$		0			0
$971$	−6.95946	+	39.4690i	−0.223340	+	1.26662i	0.642495	+	0.766290i	$0.277900\pi$
$971$	−6.95946	+	39.4690i	−0.223340	+	1.26662i	−0.865834	+	0.500331i	$0.833212\pi$
$972$	−4.27628	+	5.09627i	−0.137162	+	0.163463i
$973$	12.0360	−	33.0685i	0.385855	−	1.06013i
$974$	12.2071	−	4.44301i	0.391140	−	0.142363i
$975$		0			0
$976$	−1.17752	−	2.03952i	−0.0376915	−	0.0652835i
$977$	−44.3593	−	25.6109i	−1.41918	−	0.819364i	−0.422954	−	0.906151i	$-0.639007\pi$
$977$	−44.3593	−	25.6109i	−1.41918	−	0.819364i	−0.996227	+	0.0867869i	$0.972340\pi$
$978$	10.1875	−	1.79632i	0.325759	−	0.0574401i
$979$	−0.0946741	−	0.536923i	−0.00302580	−	0.0171601i
$980$		0			0
$981$	1.05556	+	1.82828i	0.0337014	+	0.0583726i
$982$	−11.9947	−	14.2947i	−0.382766	−	0.456163i
$983$	−3.12939	−	8.59792i	−0.0998119	−	0.274231i	0.879729	−	0.475475i	$-0.157724\pi$
$983$	−3.12939	−	8.59792i	−0.0998119	−	0.274231i	−0.979541	+	0.201244i	$0.935502\pi$
$984$	−3.41147	−	1.24168i	−0.108754	−	0.0395832i
$985$		0			0
$986$	−1.80360	+	10.2287i	−0.0574382	+	0.325748i
$987$		−	19.8084i		−	0.630508i
$988$	−10.4110	+	17.7297i	−0.331218	+	0.564056i
$989$	−3.98545			−0.126730
$990$		0			0
$991$	−21.2153	−	17.8017i	−0.673926	−	0.565491i	0.240299	−	0.970699i	$-0.422755\pi$
$991$	−21.2153	−	17.8017i	−0.673926	−	0.565491i	−0.914224	+	0.405208i	$0.867199\pi$
$992$	1.24432	−	3.41875i	0.0395073	−	0.108545i
$993$	17.7086	+	48.6541i	0.561967	+	1.54399i
$994$	−3.67365	+	3.08256i	−0.116521	+	0.0977728i
$995$		0			0
$996$	−0.783119	+	1.35640i	−0.0248141	+	0.0429792i
$997$	35.6343	−	6.28328i	1.12855	−	0.198993i	0.421957	−	0.906616i	$-0.361343\pi$
$997$	35.6343	−	6.28328i	1.12855	−	0.198993i	0.706591	+	0.707622i	$0.250232\pi$
$998$	17.0148	−	3.00016i	0.538593	−	0.0949685i
$999$	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.u.a.549.1		12
5.2	odd	4		950.2.l.a.701.1	yes	6
5.3	odd	4		950.2.l.f.701.1	yes	6
5.4	even	2	inner	950.2.u.a.549.2		12
19.9	even	9	inner	950.2.u.a.199.2		12
95.9	even	18	inner	950.2.u.a.199.1		12
95.28	odd	36		950.2.l.f.351.1	yes	6
95.47	odd	36		950.2.l.a.351.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.a.351.1	✓	6	95.47	odd	36
950.2.l.a.701.1	yes	6	5.2	odd	4
950.2.l.f.351.1	yes	6	95.28	odd	36
950.2.l.f.701.1	yes	6	5.3	odd	4
950.2.u.a.199.1		12	95.9	even	18	inner
950.2.u.a.199.2		12	19.9	even	9	inner
950.2.u.a.549.1		12	1.1	even	1	trivial
950.2.u.a.549.2		12	5.4	even	2	inner

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.984808 - 1.17365i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.17365 + 0.984808i) q^{6} +(1.62760 - 0.939693i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.113341 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.984808 - 1.17365i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.17365 + 0.984808i) q^{6} +(1.62760 - 0.939693i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.113341 + 0.642788i) q^{9} +(0.0812519 - 0.140732i) q^{11} +(1.32683 - 0.766044i) q^{12} +(-3.03195 - 3.61334i) q^{13} +(-1.76604 + 0.642788i) q^{14} +(0.766044 + 0.642788i) q^{16} +(4.28125 + 0.754900i) q^{17} -0.652704i q^{18} +(-2.77719 - 3.35965i) q^{19} +(0.500000 - 2.83564i) q^{21} +(-0.104455 + 0.124485i) q^{22} +(2.08840 - 5.73783i) q^{23} +(-1.43969 + 0.524005i) q^{24} +(2.35844 + 4.08494i) q^{26} +(4.84651 + 2.79813i) q^{27} +(1.85083 - 0.326352i) q^{28} +(-0.414878 - 2.35289i) q^{29} +(1.81908 + 3.15074i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-0.0851529 - 0.233956i) q^{33} +(-4.08512 - 1.48686i) q^{34} +(-0.113341 + 0.642788i) q^{36} -7.36959i q^{37} +(2.15160 + 3.79086i) q^{38} -7.22668 q^{39} +(1.81521 + 1.52314i) q^{41} +(-0.984808 + 2.70574i) q^{42} +(-0.223238 - 0.613341i) q^{43} +(0.124485 - 0.104455i) q^{44} +(-3.05303 + 5.28801i) q^{46} +(6.77487 - 1.19459i) q^{47} +(1.50881 - 0.266044i) q^{48} +(-1.73396 + 3.00330i) q^{49} +(5.10220 - 4.28125i) q^{51} +(-1.61327 - 4.43242i) q^{52} +(2.03282 - 5.58512i) q^{53} +(-4.28699 - 3.59721i) q^{54} -1.87939 q^{56} +(-6.67804 - 0.0491630i) q^{57} +2.38919i q^{58} +(0.708263 - 4.01676i) q^{59} +(-2.21301 - 0.805470i) q^{61} +(-1.24432 - 3.41875i) q^{62} +(0.788496 + 0.939693i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.0432332 + 0.245188i) q^{66} +(1.61327 - 0.284463i) q^{67} +(3.76487 + 2.17365i) q^{68} +(-4.67752 - 8.10170i) q^{69} +(2.39780 - 0.872729i) q^{71} +(0.223238 - 0.613341i) q^{72} +(-10.0933 + 12.0287i) q^{73} +(-1.27972 + 7.25762i) q^{74} +(-1.46064 - 4.10689i) q^{76} -0.305407i q^{77} +(7.11689 + 1.25490i) q^{78} +(0.766044 + 0.642788i) q^{79} +(6.21688 - 2.26276i) q^{81} +(-1.52314 - 1.81521i) q^{82} +(-0.885328 + 0.511144i) q^{83} +(1.43969 - 2.49362i) q^{84} +(0.113341 + 0.642788i) q^{86} +(-3.17004 - 1.83022i) q^{87} +(-0.140732 + 0.0812519i) q^{88} +(2.57011 - 2.15658i) q^{89} +(-8.33022 - 3.03195i) q^{91} +(3.92490 - 4.67752i) q^{92} +(5.48930 + 0.967911i) q^{93} -6.87939 q^{94} -1.53209 q^{96} +(-17.6011 - 3.10354i) q^{97} +(2.22913 - 2.65657i) q^{98} +(0.0996702 + 0.0362770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^6 - 12 * q^9	\( 12 q - 12 q^{6} - 12 q^{9} + 6 q^{11} - 12 q^{14} - 12 q^{19} + 6 q^{21} - 6 q^{24} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 6 q^{34} + 12 q^{36} - 60 q^{39} + 36 q^{41} - 24 q^{44} - 12 q^{46} - 30 q^{49} + 60 q^{51} - 36 q^{54} - 42 q^{59} - 42 q^{61} + 6 q^{64} - 30 q^{66} - 6 q^{69} + 30 q^{71} + 36 q^{74} + 42 q^{81} + 6 q^{84} - 12 q^{86} + 48 q^{89} - 54 q^{91} - 60 q^{94} + 30 q^{99}+O(q^{100}) \) 12 * q - 12 * q^6 - 12 * q^9 + 6 * q^11 - 12 * q^14 - 12 * q^19 + 6 * q^21 - 6 * q^24 + 12 * q^26 - 48 * q^29 - 12 * q^31 - 6 * q^34 + 12 * q^36 - 60 * q^39 + 36 * q^41 - 24 * q^44 - 12 * q^46 - 30 * q^49 + 60 * q^51 - 36 * q^54 - 42 * q^59 - 42 * q^61 + 6 * q^64 - 30 * q^66 - 6 * q^69 + 30 * q^71 + 36 * q^74 + 42 * q^81 + 6 * q^84 - 12 * q^86 + 48 * q^89 - 54 * q^91 - 60 * q^94 + 30 * q^99

Introduction

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