LMFDB - Embedded newform 231.2.u.a.20.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(20,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

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

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

chi := DirichletCharacter("231.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.17
Character	$\chi$	$=$	231.20
Dual form			231.2.u.a.104.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.606621 + 0.197103i) q^{2} +(-1.57241 + 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(0.284064 + 0.874260i) q^{5} +(-1.09702 + 0.130675i) q^{6} +(-2.64176 + 0.145216i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} +O(q^{10})$	\(q+(0.606621 + 0.197103i) q^{2} +(-1.57241 + 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(0.284064 + 0.874260i) q^{5} +(-1.09702 + 0.130675i) q^{6} +(-2.64176 + 0.145216i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} +0.586335i q^{10} +(-2.52823 + 2.14664i) q^{11} +(2.70682 + 0.536309i) q^{12} +(-6.23392 - 2.02552i) q^{13} +(-1.63117 - 0.432609i) q^{14} +(-1.08166 - 1.16837i) q^{15} +(0.532894 + 1.64008i) q^{16} +(-1.08749 - 3.34694i) q^{17} +(1.63004 - 1.00226i) q^{18} +(0.0854645 + 0.117632i) q^{19} +(0.452560 - 1.39284i) q^{20} +(4.04845 - 2.14710i) q^{21} +(-1.95679 + 0.803875i) q^{22} +5.77943i q^{23} +(3.46493 + 1.93704i) q^{24} +(3.36145 - 2.44223i) q^{25} +(-3.38239 - 2.45745i) q^{26} +(-1.39919 + 5.00423i) q^{27} +(3.54094 + 2.28667i) q^{28} +(-0.170143 + 0.234182i) q^{29} +(-0.425867 - 0.921956i) q^{30} +(3.91775 + 1.27295i) q^{31} +5.68366i q^{32} +(2.41626 - 5.21169i) q^{33} -2.24467i q^{34} +(-0.877387 - 2.26834i) q^{35} +(-4.64575 + 1.12272i) q^{36} +(-1.56403 - 1.13634i) q^{37} +(0.0286590 + 0.0882033i) q^{38} +(11.2734 - 1.34287i) q^{39} +(1.23834 - 1.70443i) q^{40} +(-6.50747 + 4.72795i) q^{41} +(2.87908 - 0.504516i) q^{42} +3.78771 q^{43} +(5.26881 - 0.399264i) q^{44} +(2.54941 + 1.05152i) q^{45} +(-1.13914 + 3.50593i) q^{46} +(2.58114 - 1.87530i) q^{47} +(-2.02915 - 2.19182i) q^{48} +(6.95782 - 0.767254i) q^{49} +(2.52050 - 0.818960i) q^{50} +(4.14092 + 4.47289i) q^{51} +(6.13808 + 8.44835i) q^{52} +(-10.7279 - 3.48570i) q^{53} +(-1.83513 + 2.75989i) q^{54} +(-2.59490 - 1.60055i) q^{55} +(3.82803 + 4.70261i) q^{56} +(-0.219823 - 0.122890i) q^{57} +(-0.149371 + 0.108524i) q^{58} +(-4.30990 - 3.13133i) q^{59} +(0.300037 + 2.51881i) q^{60} +(-3.18676 + 1.03544i) q^{61} +(2.12569 + 1.54440i) q^{62} +(-4.80632 + 6.31659i) q^{63} +(-0.0544799 + 0.167672i) q^{64} -6.02544i q^{65} +(2.49299 - 2.68527i) q^{66} -5.90336 q^{67} +(-1.73254 + 5.33222i) q^{68} +(-4.19771 - 9.08761i) q^{69} +(-0.0851453 - 1.54896i) q^{70} +(-5.71118 + 1.85568i) q^{71} +(-6.85519 - 0.529168i) q^{72} +(4.90051 - 6.74497i) q^{73} +(-0.724801 - 0.997603i) q^{74} +(-3.51172 + 6.28167i) q^{75} -0.231647i q^{76} +(6.36726 - 6.03805i) q^{77} +(7.10338 + 1.40741i) q^{78} +(-1.96364 + 6.04346i) q^{79} +(-1.28248 + 0.931776i) q^{80} +(-1.43457 - 8.88493i) q^{81} +(-4.87947 + 1.58544i) q^{82} +(-4.62359 - 14.2299i) q^{83} +(-7.22865 - 1.02373i) q^{84} +(2.61718 - 1.90149i) q^{85} +(2.29771 + 0.746570i) q^{86} +(0.0974433 - 0.491808i) q^{87} +(7.38603 + 1.79594i) q^{88} +14.2572 q^{89} +(1.33927 + 1.14037i) q^{90} +(16.7627 + 4.44568i) q^{91} +(5.41207 - 7.44907i) q^{92} +(-7.08487 + 0.843939i) q^{93} +(1.93540 - 0.628850i) q^{94} +(-0.0785634 + 0.108133i) q^{95} +(-4.12816 - 8.93702i) q^{96} +(-13.3252 - 4.32964i) q^{97} +(4.37199 + 0.905977i) q^{98} +(-0.0139835 + 9.94986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.606621	+	0.197103i	0.428946	+	0.139373i	0.515530	−	0.856872i	$-0.327595\pi$
$2$	0.606621	+	0.197103i	0.428946	+	0.139373i	−0.0865839	+	0.996245i	$0.527595\pi$
$3$	−1.57241	+	0.726320i	−0.907829	+	0.419341i
$3$	−1.57241	+	0.726320i	−0.907829	+	0.419341i
$4$	−1.28889	−	0.936436i	−0.644447	−	0.468218i
$5$	0.284064	+	0.874260i	0.127037	+	0.390981i	0.994267	−	0.106928i	$-0.0341014\pi$
$5$	0.284064	+	0.874260i	0.127037	+	0.390981i	−0.867229	+	0.497909i	$0.834101\pi$
$6$	−1.09702	+	0.130675i	−0.447855	+	0.0533477i
$7$	−2.64176	+	0.145216i	−0.998493	+	0.0548866i
$7$	−2.64176	+	0.145216i	−0.998493	+	0.0548866i
$8$	−1.34712	−	1.85415i	−0.476279	−	0.655542i
$9$	1.94492	−	2.28414i	0.648307	−	0.761379i
$10$			0.586335i			0.185415i
$11$	−2.52823	+	2.14664i	−0.762290	+	0.647236i
$11$	−2.52823	+	2.14664i	−0.762290	+	0.647236i
$12$	2.70682	+	0.536309i	0.781391	+	0.154819i
$13$	−6.23392	−	2.02552i	−1.72898	−	0.561779i	−0.735676	−	0.677334i	$-0.763135\pi$
$13$	−6.23392	−	2.02552i	−1.72898	−	0.561779i	−0.993301	+	0.115555i	$0.963135\pi$
$14$	−1.63117	−	0.432609i	−0.435949	−	0.115620i
$15$	−1.08166	−	1.16837i	−0.279283	−	0.301672i
$16$	0.532894	+	1.64008i	0.133224	+	0.410020i
$17$	−1.08749	−	3.34694i	−0.263754	−	0.811753i	−0.991978	−	0.126413i	$-0.959654\pi$
$17$	−1.08749	−	3.34694i	−0.263754	−	0.811753i	0.728223	−	0.685340i	$-0.240346\pi$
$18$	1.63004	−	1.00226i	0.384204	−	0.236234i
$19$	0.0854645	+	0.117632i	0.0196069	+	0.0269866i	0.818708	−	0.574210i	$-0.194691\pi$
$19$	0.0854645	+	0.117632i	0.0196069	+	0.0269866i	−0.799101	+	0.601197i	$0.794691\pi$
$20$	0.452560	−	1.39284i	0.101196	−	0.311448i
$21$	4.04845	−	2.14710i	0.883444	−	0.468536i
$22$	−1.95679	+	0.803875i	−0.417189	+	0.171387i
$23$			5.77943i			1.20509i	0.798083	+	0.602547i	$0.205848\pi$
$23$			5.77943i			1.20509i	−0.798083	+	0.602547i	$0.794152\pi$
$24$	3.46493	+	1.93704i	0.707276	+	0.395397i
$25$	3.36145	−	2.44223i	0.672289	−	0.488447i
$26$	−3.38239	−	2.45745i	−0.663341	−	0.481946i
$27$	−1.39919	+	5.00423i	−0.269274	+	0.963064i
$28$	3.54094	+	2.28667i	0.669174	+	0.432141i
$29$	−0.170143	+	0.234182i	−0.0315948	+	0.0434866i	−0.824522	−	0.565830i	$-0.808556\pi$
$29$	−0.170143	+	0.234182i	−0.0315948	+	0.0434866i	0.792927	+	0.609316i	$0.208556\pi$
$30$	−0.425867	−	0.921956i	−0.0777522	−	0.168325i
$31$	3.91775	+	1.27295i	0.703649	+	0.228629i	0.638920	−	0.769273i	$-0.279382\pi$
$31$	3.91775	+	1.27295i	0.703649	+	0.228629i	0.0647293	+	0.997903i	$0.479382\pi$
$32$			5.68366i			1.00474i
$33$	2.41626	−	5.21169i	0.420616	−	0.907239i
$34$		−	2.24467i		−	0.384958i
$35$	−0.877387	−	2.26834i	−0.148306	−	0.383419i
$36$	−4.64575	+	1.12272i	−0.774291	+	0.187120i
$37$	−1.56403	−	1.13634i	−0.257126	−	0.186813i	0.451753	−	0.892143i	$-0.350799\pi$
$37$	−1.56403	−	1.13634i	−0.257126	−	0.186813i	−0.708879	+	0.705330i	$0.750799\pi$
$38$	0.0286590	+	0.0882033i	0.00464910	+	0.0143085i
$39$	11.2734	−	1.34287i	1.80519	−	0.215032i
$40$	1.23834	−	1.70443i	0.195799	−	0.269495i
$41$	−6.50747	+	4.72795i	−1.01630	+	0.738382i	−0.965520	−	0.260328i	$-0.916169\pi$
$41$	−6.50747	+	4.72795i	−1.01630	+	0.738382i	−0.0507759	+	0.998710i	$0.516169\pi$
$42$	2.87908	−	0.504516i	0.444251	−	0.0778485i
$43$	3.78771			0.577620			0.288810	−	0.957386i	$-0.406740\pi$
$43$	3.78771			0.577620			0.288810	+	0.957386i	$0.406740\pi$
$44$	5.26881	−	0.399264i	0.794303	−	0.0601913i
$45$	2.54941	+	1.05152i	0.380044	+	0.156752i
$46$	−1.13914	+	3.50593i	−0.167958	+	0.516921i
$47$	2.58114	−	1.87530i	0.376497	−	0.273541i	−0.383403	−	0.923581i	$-0.625248\pi$
$47$	2.58114	−	1.87530i	0.376497	−	0.273541i	0.759900	+	0.650040i	$0.225248\pi$
$48$	−2.02915	−	2.19182i	−0.292882	−	0.316362i
$49$	6.95782	−	0.767254i	0.993975	−	0.109608i
$50$	2.52050	−	0.818960i	0.356452	−	0.115818i
$51$	4.14092	+	4.47289i	0.579845	+	0.626329i
$52$	6.13808	+	8.44835i	0.851199	+	1.17158i
$53$	−10.7279	−	3.48570i	−1.47359	−	0.478797i	−0.541396	−	0.840768i	$-0.682104\pi$
$53$	−10.7279	−	3.48570i	−1.47359	−	0.478797i	−0.932190	+	0.361970i	$0.882104\pi$
$54$	−1.83513	+	2.75989i	−0.249729	+	0.375573i
$55$	−2.59490	−	1.60055i	−0.349896	−	0.215818i
$56$	3.82803	+	4.70261i	0.511542	+	0.628413i
$57$	−0.219823	−	0.122890i	−0.0291163	−	0.0162772i
$58$	−0.149371	+	0.108524i	−0.0196133	+	0.0142499i
$59$	−4.30990	−	3.13133i	−0.561101	−	0.407664i	0.270761	−	0.962647i	$-0.412725\pi$
$59$	−4.30990	−	3.13133i	−0.561101	−	0.407664i	−0.831862	+	0.554983i	$0.812725\pi$
$60$	0.300037	+	2.51881i	0.0387345	+	0.325177i
$61$	−3.18676	+	1.03544i	−0.408023	+	0.132575i	−0.505835	−	0.862630i	$-0.668816\pi$
$61$	−3.18676	+	1.03544i	−0.408023	+	0.132575i	0.0978119	+	0.995205i	$0.468816\pi$
$62$	2.12569	+	1.54440i	0.269963	+	0.196139i
$63$	−4.80632	+	6.31659i	−0.605540	+	0.795815i
$64$	−0.0544799	+	0.167672i	−0.00680999	+	0.0209590i
$65$		−	6.02544i		−	0.747364i
$66$	2.49299	−	2.68527i	0.306866	−	0.330534i
$67$	−5.90336			−0.721210			−0.360605	−	0.932719i	$-0.617430\pi$
$67$	−5.90336			−0.721210			−0.360605	+	0.932719i	$0.617430\pi$
$68$	−1.73254	+	5.33222i	−0.210102	+	0.646626i
$69$	−4.19771	−	9.08761i	−0.505345	−	1.09402i
$70$	−0.0851453	−	1.54896i	−0.0101768	−	0.185136i
$71$	−5.71118	+	1.85568i	−0.677793	+	0.220228i	−0.627629	−	0.778513i	$-0.715974\pi$
$71$	−5.71118	+	1.85568i	−0.677793	+	0.220228i	−0.0501640	+	0.998741i	$0.515974\pi$
$72$	−6.85519	−	0.529168i	−0.807891	−	0.0623631i
$73$	4.90051	−	6.74497i	0.573561	−	0.789440i	−0.419410	−	0.907797i	$-0.637763\pi$
$73$	4.90051	−	6.74497i	0.573561	−	0.789440i	0.992971	+	0.118358i	$0.0377629\pi$
$74$	−0.724801	−	0.997603i	−0.0842564	−	0.115969i
$75$	−3.51172	+	6.28167i	−0.405498	+	0.725345i
$76$		−	0.231647i		−	0.0265717i
$77$	6.36726	−	6.03805i	0.725616	−	0.688100i
$78$	7.10338	+	1.40741i	0.804300	+	0.159358i
$79$	−1.96364	+	6.04346i	−0.220927	+	0.679942i	0.777753	+	0.628570i	$0.216359\pi$
$79$	−1.96364	+	6.04346i	−0.220927	+	0.679942i	−0.998680	+	0.0513722i	$0.983641\pi$
$80$	−1.28248	+	0.931776i	−0.143386	+	0.104176i
$81$	−1.43457	−	8.88493i	−0.159397	−	0.987215i
$82$	−4.87947	+	1.58544i	−0.538847	+	0.175082i
$83$	−4.62359	−	14.2299i	−0.507505	−	1.56194i	−0.796519	−	0.604614i	$-0.793327\pi$
$83$	−4.62359	−	14.2299i	−0.507505	−	1.56194i	0.289014	−	0.957325i	$-0.406673\pi$
$84$	−7.22865	−	1.02373i	−0.788710	−	0.111698i
$85$	2.61718	−	1.90149i	0.283873	−	0.206246i
$86$	2.29771	+	0.746570i	0.247768	+	0.0805047i
$87$	0.0974433	−	0.491808i	0.0104470	−	0.0527274i
$88$	7.38603	+	1.79594i	0.787353	+	0.191448i
$89$	14.2572			1.51126			0.755631	−	0.654997i	$-0.227330\pi$
$89$	14.2572			1.51126			0.755631	+	0.654997i	$0.227330\pi$
$90$	1.33927	+	1.14037i	0.141171	+	0.120206i
$91$	16.7627	+	4.44568i	1.75720	+	0.466034i
$92$	5.41207	−	7.44907i	0.564247	−	0.776620i
$93$	−7.08487	+	0.843939i	−0.734667	+	0.0875123i
$94$	1.93540	−	0.628850i	0.199621	−	0.0648609i
$95$	−0.0785634	+	0.108133i	−0.00806043	+	0.0110942i
$96$	−4.12816	−	8.93702i	−0.421328	−	0.912131i
$97$	−13.3252	−	4.32964i	−1.35297	−	0.439608i	−0.459283	−	0.888290i	$-0.651894\pi$
$97$	−13.3252	−	4.32964i	−1.35297	−	0.439608i	−0.893691	+	0.448682i	$0.851894\pi$
$98$	4.37199	+	0.905977i	0.441638	+	0.0915175i
$99$	−0.0139835	+	9.94986i	−0.00140539	+	0.999999i
$100$	−6.61955			−0.661955
$101$	−3.97238	+	12.2257i	−0.395267	+	1.21651i	0.533487	+	0.845808i	$0.320881\pi$
$101$	−3.97238	+	12.2257i	−0.395267	+	1.21651i	−0.928754	+	0.370697i	$0.879119\pi$
$102$	1.63035	+	3.52954i	0.161429	+	0.349476i
$103$	−3.57933	+	4.92652i	−0.352682	+	0.485425i	−0.948092	−	0.317997i	$-0.896990\pi$
$103$	−3.57933	+	4.92652i	−0.352682	+	0.485425i	0.595410	+	0.803422i	$0.296990\pi$
$104$	4.64221	+	14.2873i	0.455206	+	1.40098i
$105$	3.02715	+	2.92948i	0.295419	+	0.285888i
$106$	−5.82071	−	4.22900i	−0.565358	−	0.410756i
$107$	−5.65793	−	7.78747i	−0.546972	−	0.752843i	0.442625	−	0.896707i	$-0.354047\pi$
$107$	−5.65793	−	7.78747i	−0.546972	−	0.752843i	−0.989597	+	0.143864i	$0.954047\pi$
$108$	6.48954	−	5.13967i	0.624457	−	0.494565i
$109$	1.22419			0.117256			0.0586281	−	0.998280i	$-0.481327\pi$
$109$	1.22419			0.117256			0.0586281	+	0.998280i	$0.481327\pi$
$110$	−1.25865	−	1.48239i	−0.120007	−	0.141340i
$111$	3.28464	+	0.650795i	0.311764	+	0.0617707i
$112$	−1.64595	−	4.25532i	−0.155527	−	0.402090i
$113$	6.69613	+	9.21643i	0.629919	+	0.867009i	0.998028	−	0.0627736i	$-0.0199946\pi$
$113$	6.69613	+	9.21643i	0.629919	+	0.867009i	−0.368109	+	0.929783i	$0.619995\pi$
$114$	−0.109127	−	0.117876i	−0.0102207	−	0.0110401i
$115$	−5.05273	+	1.64173i	−0.471169	+	0.153092i
$116$	0.438594	−	0.142508i	0.0407224	−	0.0132315i
$117$	−16.7510	+	10.2996i	−1.54863	+	0.952203i
$118$	−1.99728	−	2.74902i	−0.183865	−	0.253068i
$119$	3.35891	+	8.68391i	0.307911	+	0.796052i
$120$	−0.709215	+	3.57949i	−0.0647422	+	0.326762i
$121$	1.78389	−	10.8544i	0.162171	−	0.986763i
$122$	−2.13725			−0.193497
$123$	6.79838	−	12.1608i	0.612989	−	1.09650i
$124$	−3.85753	−	5.30943i	−0.346416	−	0.476801i
$125$	6.80846	+	4.94664i	0.608968	+	0.442441i
$126$	−4.16064	+	2.88443i	−0.370659	+	0.256966i
$127$	−4.77111	−	14.6840i	−0.423368	−	1.30299i	−0.904549	−	0.426370i	$-0.859792\pi$
$127$	−4.77111	−	14.6840i	−0.423368	−	1.30299i	0.481181	−	0.876621i	$-0.340208\pi$
$128$	6.61545	−	9.10539i	0.584729	−	0.804810i
$129$	−5.95582	+	2.75109i	−0.524380	+	0.242220i
$130$	1.18763	−	3.65516i	0.104162	−	0.320579i
$131$	−9.08829			−0.794047			−0.397024	−	0.917808i	$-0.629957\pi$
$131$	−9.08829			−0.794047			−0.397024	+	0.917808i	$0.629957\pi$
$132$	−7.99471	+	4.45465i	−0.695851	+	0.387727i
$133$	−0.242859	−	0.298345i	−0.0210586	−	0.0258698i
$134$	−3.58110	−	1.16357i	−0.309360	−	0.100517i
$135$	−4.77245	+	0.198267i	−0.410747	+	0.0170641i
$136$	−4.74077	+	6.52511i	−0.406517	+	0.559523i
$137$	−9.51199	+	3.09063i	−0.812664	+	0.264051i	−0.685726	−	0.727860i	$-0.740515\pi$
$137$	−9.51199	+	3.09063i	−0.812664	+	0.264051i	−0.126938	+	0.991911i	$0.540515\pi$
$138$	−0.755226	−	6.34012i	−0.0642891	−	0.539707i
$139$	1.43974	−	1.98163i	0.122117	−	0.168080i	−0.743582	−	0.668645i	$-0.766874\pi$
$139$	1.43974	−	1.98163i	0.122117	−	0.168080i	0.865699	+	0.500565i	$0.166874\pi$
$140$	−0.993294	+	3.74526i	−0.0839487	+	0.316533i
$141$	−2.69652	+	4.82347i	−0.227088	+	0.406209i
$142$	−3.83029			−0.321430
$143$	20.1088	−	8.26098i	1.68158	−	0.690818i
$144$	4.78261	+	1.97262i	0.398551	+	0.164385i
$145$	−0.253068	−	0.0822268i	−0.0210162	−	0.00682856i
$146$	4.30221	−	3.12574i	0.356054	−	0.258688i
$147$	−10.3833	+	6.26004i	−0.856396	+	0.516319i
$148$	0.951767	+	2.92924i	0.0782348	+	0.240782i
$149$	10.0597	−	3.26860i	0.824123	−	0.267774i	0.133555	−	0.991041i	$-0.457361\pi$
$149$	10.0597	−	3.26860i	0.824123	−	0.267774i	0.690568	+	0.723268i	$0.257361\pi$
$150$	−3.36842	+	3.11842i	−0.275030	+	0.254618i
$151$	−12.4694	+	9.05956i	−1.01475	+	0.737256i	−0.965199	−	0.261515i	$-0.915778\pi$
$151$	−12.4694	+	9.05956i	−1.01475	+	0.737256i	−0.0495470	+	0.998772i	$0.515778\pi$
$152$	0.102976	−	0.316929i	0.00835249	−	0.0257063i
$153$	−9.75995	−	4.02556i	−0.789045	−	0.325447i
$154$	5.05263	−	2.40780i	0.407153	−	0.194026i
$155$			3.78673i			0.304158i
$156$	−15.7878	−	8.82602i	−1.26403	−	0.706647i
$157$	−0.909416	−	1.25170i	−0.0725793	−	0.0998968i	0.771184	−	0.636612i	$-0.219665\pi$
$157$	−0.909416	−	1.25170i	−0.0725793	−	0.0998968i	−0.843763	+	0.536716i	$0.819665\pi$
$158$	−2.38237	+	3.27905i	−0.189531	+	0.260867i
$159$	19.4003	−	2.31093i	1.53854	−	0.183269i
$160$	−4.96900	+	1.61453i	−0.392834	+	0.127639i
$161$	−0.839267	−	15.2679i	−0.0661435	−	1.20328i
$162$	0.881005	−	5.67255i	0.0692183	−	0.445678i
$163$	−5.12784	+	15.7819i	−0.401644	+	1.23613i	0.522022	+	0.852932i	$0.325178\pi$
$163$	−5.12784	+	15.7819i	−0.401644	+	1.23613i	−0.923665	+	0.383200i	$0.874822\pi$
$164$	12.8149			1.00067
$165$	5.24274	+	0.631982i	0.408147	+	0.0491997i
$166$		−	9.54351i		−	0.740720i
$167$	−0.535930	+	1.64942i	−0.0414715	+	0.127636i	−0.969649	−	0.244502i	$-0.921375\pi$
$167$	−0.535930	+	1.64942i	−0.0414715	+	0.127636i	0.928177	+	0.372139i	$0.121375\pi$
$168$	−9.43481	−	4.61404i	−0.727912	−	0.355981i
$169$	24.2417	+	17.6127i	1.86475	+	1.35482i
$170$	1.96243	−	0.637632i	0.150511	−	0.0489041i
$171$	0.434909	+	0.0335717i	0.0332583	+	0.00256729i
$172$	−4.88196	−	3.54695i	−0.372246	−	0.270452i
$173$	−9.18868	+	6.67596i	−0.698602	+	0.507564i	−0.879477	−	0.475942i	$-0.842107\pi$
$173$	−9.18868	+	6.67596i	−0.698602	+	0.507564i	0.180875	+	0.983506i	$0.442107\pi$
$174$	0.156048	−	0.279135i	0.0118300	−	0.0211612i
$175$	−8.52549	+	6.93994i	−0.644467	+	0.524610i
$176$	−4.86794	−	3.00257i	−0.366935	−	0.226327i
$177$	9.05125	+	1.79335i	0.680334	+	0.134796i
$178$	8.64873	+	2.81014i	0.648250	+	0.210629i
$179$	−10.4264	−	14.3508i	−0.779309	−	1.07263i	−0.995358	−	0.0962447i	$-0.969317\pi$
$179$	−10.4264	−	14.3508i	−0.779309	−	1.07263i	0.216048	−	0.976383i	$-0.430683\pi$
$180$	−2.30124	−	3.74267i	−0.171524	−	0.278962i
$181$	8.98074	−	2.91802i	0.667533	−	0.216895i	0.0444041	−	0.999014i	$-0.485861\pi$
$181$	8.98074	−	2.91802i	0.667533	−	0.216895i	0.623129	+	0.782119i	$0.285861\pi$
$182$	9.29233	+	6.00082i	0.688794	+	0.444811i
$183$	4.25882	−	3.94275i	0.314821	−	0.291456i
$184$	10.7160	−	7.78560i	0.789991	−	0.573962i
$185$	0.549168	−	1.69017i	0.0403756	−	0.124263i
$186$	−4.46418	−	0.884499i	−0.327329	−	0.0648546i
$187$	9.93409	+	6.12739i	0.726453	+	0.448079i
$188$	−5.08291			−0.370710
$189$	2.96963	−	13.4232i	0.216009	−	0.976391i
$190$	−0.0689716	+	0.0501108i	−0.00500373	+	0.00363542i
$191$	0.957730	−	1.31820i	0.0692989	−	0.0953817i	−0.772961	−	0.634454i	$-0.781225\pi$
$191$	0.957730	−	1.31820i	0.0692989	−	0.0953817i	0.842260	+	0.539072i	$0.181225\pi$
$192$	−0.0361189	−	0.303218i	−0.00260665	−	0.0218829i
$193$	3.40317	+	10.4739i	0.244965	+	0.753926i	0.995642	+	0.0932562i	$0.0297276\pi$
$193$	3.40317	+	10.4739i	0.244965	+	0.753926i	−0.750677	+	0.660670i	$0.770272\pi$
$194$	−7.23000	−	5.25290i	−0.519084	−	0.377136i
$195$	4.37640	+	9.47444i	0.313400	+	0.678479i
$196$	−9.68638	−	5.52665i	−0.691885	−	0.394761i
$197$			0.607768i			0.0433017i	0.999766	+	0.0216508i	$0.00689221\pi$
$197$			0.607768i			0.0433017i	−0.999766	+	0.0216508i	$0.993108\pi$
$198$	−1.96963	+	6.03305i	−0.139976	+	0.428750i
$199$		−	6.00328i		−	0.425561i	−0.977100	−	0.212781i	$-0.931748\pi$
$199$		−	6.00328i		−	0.425561i	0.977100	−	0.212781i	$-0.0682519\pi$
$200$	−9.05655	−	2.94265i	−0.640395	−	0.208077i
$201$	9.28248	−	4.28773i	0.654735	−	0.302433i
$202$	−4.81946	+	6.63342i	−0.339096	+	0.466726i
$203$	0.415472	−	0.643362i	0.0291604	−	0.0451552i
$204$	−1.14863	−	9.64279i	−0.0804205	−	0.675130i
$205$	−5.98200	−	4.34618i	−0.417801	−	0.303550i
$206$	−3.14233	+	2.28304i	−0.218937	+	0.159067i
$207$	13.2010	+	11.2405i	0.917534	+	0.781271i
$208$		−	11.3035i		−	0.783757i
$209$	−0.468587	−	0.113939i	−0.0324128	−	0.00788131i
$210$	1.25892	+	2.37375i	0.0868738	+	0.163804i
$211$	−5.35273	+	16.4740i	−0.368497	+	1.13412i	0.579265	+	0.815139i	$0.303340\pi$
$211$	−5.35273	+	16.4740i	−0.368497	+	1.13412i	−0.947762	+	0.318978i	$0.896660\pi$
$212$	10.5630	+	14.5387i	0.725467	+	0.998519i
$213$	7.63248	−	7.06602i	0.522969	−	0.484156i
$214$	−1.89728	−	5.83924i	−0.129696	−	0.399162i
$215$	1.07595	+	3.31144i	0.0733794	+	0.225839i
$216$	11.1635	−	4.14699i	0.759579	−	0.282167i
$217$	−10.5346	−	2.79392i	−0.715137	−	0.189664i
$218$	0.742620	+	0.241292i	0.0502966	+	0.0163424i
$219$	−2.80658	+	14.1652i	−0.189651	+	0.957194i
$220$	1.84574	+	4.49289i	0.124440	+	0.302911i
$221$			23.0673i			1.55167i
$222$	1.86426	+	1.04220i	0.125121	+	0.0699479i
$223$	12.6355	+	17.3913i	0.846137	+	1.16461i	0.984701	+	0.174254i	$0.0557515\pi$
$223$	12.6355	+	17.3913i	0.846137	+	1.16461i	−0.138563	+	0.990354i	$0.544248\pi$
$224$	−0.825360	−	15.0149i	−0.0551467	−	1.00322i
$225$	0.959344	−	12.4280i	0.0639563	−	0.828531i
$226$	2.24543	+	6.91072i	0.149364	+	0.459694i
$227$	13.1328	+	9.54156i	0.871657	+	0.633296i	0.931031	−	0.364940i	$-0.118911\pi$
$227$	13.1328	+	9.54156i	0.871657	+	0.633296i	−0.0593744	+	0.998236i	$0.518911\pi$
$228$	0.168250	+	0.364243i	0.0111426	+	0.0241226i
$229$	24.3526	+	7.91264i	1.60926	+	0.522882i	0.969375	−	0.245585i	$-0.0789801\pi$
$229$	24.3526	+	7.91264i	1.60926	+	0.522882i	0.639890	+	0.768467i	$0.278980\pi$
$230$	−3.38868			−0.223443
$231$	−5.62636	+	14.1189i	−0.370187	+	0.928957i
$232$	0.663414			0.0435553
$233$	15.6399	+	5.08170i	1.02460	+	0.332913i	0.772654	−	0.634827i	$-0.218929\pi$
$233$	15.6399	+	5.08170i	1.02460	+	0.332913i	0.251948	+	0.967741i	$0.418929\pi$
$234$	−12.1916	+	2.94630i	−0.796992	+	0.192606i
$235$	2.37271	+	1.72388i	0.154779	+	0.112453i
$236$	2.62272	+	8.07189i	0.170724	+	0.525435i
$237$	−1.30185	−	10.9290i	−0.0845640	−	0.709915i
$238$	0.325963	+	5.92990i	0.0211290	+	0.384378i
$239$	−6.31195	−	8.68766i	−0.408286	−	0.561958i	0.554513	−	0.832175i	$-0.312905\pi$
$239$	−6.31195	−	8.68766i	−0.408286	−	0.561958i	−0.962799	+	0.270217i	$0.912905\pi$
$240$	1.33981	−	2.39662i	0.0864845	−	0.154701i
$241$		−	18.1478i		−	1.16900i	−0.811392	−	0.584502i	$-0.801290\pi$
$241$		−	18.1478i		−	1.16900i	0.811392	−	0.584502i	$-0.198710\pi$
$242$	3.22158	−	6.23290i	0.207091	−	0.400666i
$243$	8.70903	+	12.9288i	0.558685	+	0.829380i
$244$	5.07703	+	1.64963i	0.325023	+	0.105607i
$245$	2.64725	+	5.86500i	0.169127	+	0.374701i
$246$	6.52097	−	6.03700i	0.415762	−	0.384905i
$247$	−0.294513	−	0.906417i	−0.0187394	−	0.0576739i
$248$	−2.91743	−	8.97894i	−0.185257	−	0.570163i
$249$	17.6056	+	19.0170i	1.11571	+	1.20516i
$250$	3.15516	+	4.34271i	0.199550	+	0.274657i
$251$	2.67412	−	8.23010i	0.168789	−	0.519479i	−0.830506	−	0.557009i	$-0.811949\pi$
$251$	2.67412	−	8.23010i	0.168789	−	0.519479i	0.999296	+	0.0375296i	$0.0119489\pi$
$252$	12.1099	−	3.64059i	0.762853	−	0.229336i
$253$	−12.4064	−	14.6117i	−0.779981	−	0.918631i
$254$		−	9.84801i		−	0.617919i
$255$	−2.73418	+	4.89083i	−0.171221	+	0.306276i
$256$	6.09304	−	4.42685i	0.380815	−	0.276678i
$257$	5.40022	+	3.92349i	0.336856	+	0.244741i	0.743334	−	0.668920i	$-0.233243\pi$
$257$	5.40022	+	3.92349i	0.336856	+	0.244741i	−0.406478	+	0.913661i	$0.633243\pi$
$258$	−4.15517	+	0.494958i	−0.258690	+	0.0308147i
$259$	4.29682	+	2.77481i	0.266992	+	0.172418i
$260$	−5.64244	+	7.76616i	−0.349929	+	0.481637i
$261$	0.203990	+	0.844097i	0.0126266	+	0.0522483i
$262$	−5.51315	−	1.79133i	−0.340604	−	0.110669i
$263$		−	13.5884i		−	0.837898i	−0.908010	−	0.418949i	$-0.862399\pi$
$263$		−	13.5884i		−	0.837898i	0.908010	−	0.418949i	$-0.137601\pi$
$264$	−12.9183	+	2.54067i	−0.795064	+	0.156367i
$265$		−	10.3691i		−	0.636969i
$266$	−0.0885188	−	0.228851i	−0.00542744	−	0.0140317i
$267$	−22.4181	+	10.3553i	−1.37197	+	0.633734i
$268$	7.60881	+	5.52812i	0.464782	+	0.337684i
$269$	−6.04648	−	18.6092i	−0.368660	−	1.13462i	−0.947657	−	0.319290i	$-0.896556\pi$
$269$	−6.04648	−	18.6092i	−0.368660	−	1.13462i	0.578997	−	0.815330i	$-0.303444\pi$
$270$	−2.93415	−	0.820393i	−0.178567	−	0.0499275i
$271$	4.93000	−	6.78556i	0.299476	−	0.412194i	−0.632587	−	0.774489i	$-0.718007\pi$
$271$	4.93000	−	6.78556i	0.299476	−	0.412194i	0.932063	+	0.362296i	$0.118007\pi$
$272$	4.90974	−	3.56713i	0.297697	−	0.216289i
$273$	−29.5867	+	5.18463i	−1.79067	+	0.313788i
$274$	−6.37935			−0.385391
$275$	−3.25591	+	13.3903i	−0.196339	+	0.807468i
$276$	−3.09956	+	15.6439i	−0.186572	+	0.941650i
$277$	3.05926	−	9.41544i	0.183813	−	0.565719i	−0.816113	−	0.577893i	$-0.803875\pi$
$277$	3.05926	−	9.41544i	0.183813	−	0.565719i	0.999926	+	0.0121738i	$0.00387513\pi$
$278$	1.26396	−	0.918324i	0.0758075	−	0.0550774i
$279$	10.5273	−	6.47289i	0.630254	−	0.387522i
$280$	−3.02390	+	4.68254i	−0.180713	+	0.279835i
$281$	−19.4410	+	6.31675i	−1.15975	+	0.376826i	−0.824808	−	0.565413i	$-0.808717\pi$
$281$	−19.4410	+	6.31675i	−1.15975	+	0.376826i	−0.334942	+	0.942239i	$0.608717\pi$
$282$	−2.58649	+	2.39453i	−0.154023	+	0.142592i
$283$	−11.4365	−	15.7410i	−0.679830	−	0.935706i	0.320102	−	0.947383i	$-0.396283\pi$
$283$	−11.4365	−	15.7410i	−0.679830	−	0.935706i	−0.999932	+	0.0116772i	$0.996283\pi$
$284$	9.09883	+	2.95639i	0.539916	+	0.175429i
$285$	0.0449942	−	0.227091i	0.00266523	−	0.0134517i
$286$	13.8267	−	1.04777i	0.817591	−	0.0619560i
$287$	16.5046	−	13.4351i	0.974237	−	0.793050i
$288$	12.9823	+	11.0543i	0.764988	+	0.651379i
$289$	3.73390	−	2.71284i	0.219641	−	0.159579i
$290$	−0.137309	−	0.0997611i	−0.00806308	−	0.00585817i
$291$	24.0974	−	2.87045i	1.41261	−	0.168268i
$292$	−12.6325	+	4.10454i	−0.739260	+	0.240200i
$293$	10.8486	+	7.88194i	0.633780	+	0.460468i	0.857708	−	0.514138i	$-0.171888\pi$
$293$	10.8486	+	7.88194i	0.633780	+	0.460468i	−0.223928	+	0.974606i	$0.571888\pi$
$294$	−7.53258	+	1.75090i	−0.439309	+	0.102115i
$295$	1.51330	−	4.65747i	0.0881080	−	0.271168i
$296$			4.43075i			0.257532i
$297$	−7.20479	−	15.6554i	−0.418065	−	0.908417i
$298$	6.74668			0.390825
$299$	11.7064	−	36.0285i	0.676997	−	2.08358i
$300$	10.4086	−	4.80791i	0.600941	−	0.277585i
$301$	−10.0062	+	0.550037i	−0.576749	+	0.0317036i
$302$	−9.34988	+	3.03796i	−0.538025	+	0.174815i
$303$	−2.63359	−	22.1090i	−0.151296	−	1.27013i
$304$	−0.147382	+	0.202854i	−0.00845294	+	0.0116345i
$305$	−1.81049	−	2.49193i	−0.103668	−	0.142687i
$306$	−5.12715	−	4.36571i	−0.293099	−	0.249571i
$307$			23.0285i			1.31430i	0.753758	+	0.657152i	$0.228239\pi$
$307$			23.0285i			1.31430i	−0.753758	+	0.657152i	$0.771761\pi$
$308$	−13.8610	+	1.81988i	−0.789802	+	0.103697i
$309$	2.04993	−	10.3462i	0.116616	−	0.588576i
$310$	−0.746378	+	2.29711i	−0.0423914	+	0.130467i
$311$	−22.7672	+	16.5414i	−1.29101	+	0.937975i	−0.999825	−	0.0186916i	$-0.994050\pi$
$311$	−22.7672	+	16.5414i	−1.29101	+	0.937975i	−0.291186	+	0.956666i	$0.594050\pi$
$312$	−17.6766	−	19.0936i	−1.00074	−	1.08096i
$313$	−12.7112	+	4.13013i	−0.718482	+	0.233449i	−0.645365	−	0.763874i	$-0.723295\pi$
$313$	−12.7112	+	4.13013i	−0.718482	+	0.233449i	−0.0731170	+	0.997323i	$0.523295\pi$
$314$	−0.304956	−	0.938559i	−0.0172097	−	0.0529660i
$315$	−6.88764	−	2.40766i	−0.388075	−	0.135656i
$316$	8.19024	−	5.95056i	0.460737	−	0.334745i
$317$	−15.9452	−	5.18091i	−0.895572	−	0.290989i	−0.175164	−	0.984539i	$-0.556046\pi$
$317$	−15.9452	−	5.18091i	−0.895572	−	0.290989i	−0.720408	+	0.693550i	$0.756046\pi$
$318$	12.2241	+	2.42200i	0.685495	+	0.135819i
$319$	−0.0725433	−	0.957303i	−0.00406164	−	0.0535987i
$320$	−0.162065			−0.00905969
$321$	14.5527	+	8.13560i	0.812255	+	0.454085i
$322$	2.50023	−	9.42725i	0.139333	−	0.525360i
$323$	0.300765	−	0.413968i	0.0167350	−	0.0230338i
$324$	−6.47116	+	12.7951i	−0.359509	+	0.710840i
$325$	−25.9018	+	8.41600i	−1.43677	+	0.466835i
$326$	−6.22132	+	8.56291i	−0.344567	+	0.474256i
$327$	−1.92492	+	0.889154i	−0.106449	+	0.0491703i
$328$	17.5327	+	5.69672i	0.968082	+	0.314549i
$329$	−6.54642	+	5.32893i	−0.360916	+	0.293794i
$330$	3.05580	+	1.41674i	0.168216	+	0.0779887i
$331$	5.06225			0.278246			0.139123	−	0.990275i	$-0.455572\pi$
$331$	5.06225			0.278246			0.139123	+	0.990275i	$0.455572\pi$
$332$	−7.36612	+	22.6706i	−0.404268	+	1.24421i
$333$	−5.63747	+	1.36239i	−0.308932	+	0.0746583i
$334$	−0.650213	+	0.894941i	−0.0355781	+	0.0489690i
$335$	−1.67693	−	5.16107i	−0.0916207	−	0.281979i
$336$	5.67882	+	5.49560i	0.309805	+	0.299810i
$337$	−4.01931	−	2.92020i	−0.218946	−	0.159073i	0.472906	−	0.881113i	$-0.343205\pi$
$337$	−4.01931	−	2.92020i	−0.218946	−	0.159073i	−0.691852	+	0.722039i	$0.743205\pi$
$338$	11.2340	+	15.4623i	0.611052	+	0.841040i
$339$	−17.2231	−	9.62844i	−0.935431	−	0.522945i
$340$	−5.15390			−0.279509
$341$	−12.6375	+	5.19168i	−0.684362	+	0.281145i
$342$	0.257208	+	0.106087i	0.0139082	+	0.00573654i
$343$	−18.2695	+	3.03729i	−0.986461	+	0.163998i
$344$	−5.10250	−	7.02299i	−0.275109	−	0.378654i
$345$	6.75251	−	6.25136i	0.363543	−	0.336562i
$346$	−6.88990	+	2.23867i	−0.370403	+	0.120351i
$347$	−12.5410	+	4.07482i	−0.673236	+	0.218748i	−0.625631	−	0.780119i	$-0.715159\pi$
$347$	−12.5410	+	4.07482i	−0.673236	+	0.218748i	−0.0476042	+	0.998866i	$0.515159\pi$
$348$	−0.586141	+	0.542639i	−0.0314205	+	0.0290885i
$349$	3.45539	+	4.75594i	0.184963	+	0.254580i	0.891422	−	0.453174i	$-0.149709\pi$
$349$	3.45539	+	4.75594i	0.184963	+	0.254580i	−0.706459	+	0.707754i	$0.749709\pi$
$350$	−6.53963	+	2.52951i	−0.349558	+	0.135208i
$351$	18.8586	−	28.3618i	1.00660	−	1.51384i
$352$	−12.2008	−	14.3696i	−0.650303	−	0.765902i
$353$	−32.9898			−1.75587			−0.877934	−	0.478782i	$-0.841079\pi$
$353$	−32.9898			−1.75587			−0.877934	+	0.478782i	$0.841079\pi$
$354$	5.13721	+	2.87192i	0.273040	+	0.152641i
$355$	−3.24469	−	4.46593i	−0.172210	−	0.237027i
$356$	−18.3760	−	13.3510i	−0.973928	−	0.707600i
$357$	−11.5889	−	11.2150i	−0.613348	−	0.593560i
$358$	−3.49632	−	10.7606i	−0.184786	−	0.568714i
$359$	−6.14880	+	8.46309i	−0.324521	+	0.446665i	−0.939841	−	0.341613i	$-0.889027\pi$
$359$	−6.14880	+	8.46309i	−0.324521	+	0.446665i	0.615320	+	0.788278i	$0.289027\pi$
$360$	−1.48468	−	6.14353i	−0.0782497	−	0.323793i
$361$	5.86479	−	18.0500i	0.308673	−	0.949998i
$362$	6.02306			0.316565
$363$	5.07876	+	18.3632i	0.266566	+	0.963817i
$364$	−17.4422	−	21.4272i	−0.914220	−	1.12309i
$365$	7.28892	+	2.36831i	0.381520	+	0.123963i
$366$	3.36062	−	1.55233i	0.175663	−	0.0811414i
$367$	−3.55352	+	4.89101i	−0.185492	+	0.255308i	−0.891628	−	0.452768i	$-0.850437\pi$
$367$	−3.55352	+	4.89101i	−0.185492	+	0.255308i	0.706136	+	0.708076i	$0.250437\pi$
$368$	−9.47873	+	3.07983i	−0.494113	+	0.160547i
$369$	−1.85721	+	24.0595i	−0.0966824	+	1.25249i
$370$	0.666274	−	0.917048i	0.0346380	−	0.0476751i
$371$	28.8467	+	7.65052i	1.49764	+	0.397195i
$372$	9.92194	+	5.54678i	0.514429	+	0.287587i
$373$	6.05085			0.313301			0.156651	−	0.987654i	$-0.449930\pi$
$373$	6.05085			0.313301			0.156651	+	0.987654i	$0.449930\pi$
$374$	4.81850	+	5.67505i	0.249159	+	0.293450i
$375$	−14.2985	−	2.83300i	−0.738372	−	0.146296i
$376$	−6.95421	−	2.25956i	−0.358636	−	0.116528i
$377$	1.53500	−	1.11524i	0.0790566	−	0.0574380i
$378$	4.44719	−	7.55746i	0.228739	−	0.388714i
$379$	1.38172	+	4.25249i	0.0709741	+	0.218436i	0.980252	−	0.197755i	$-0.0633650\pi$
$379$	1.38172	+	4.25249i	0.0709741	+	0.218436i	−0.909277	+	0.416190i	$0.863365\pi$
$380$	0.202520	−	0.0658027i	0.0103890	−	0.00337561i
$381$	18.1674	+	19.6238i	0.930743	+	1.00536i
$382$	0.840801	−	0.610878i	0.0430191	−	0.0312552i
$383$	−5.53451	+	17.0335i	−0.282800	+	0.870370i	0.704249	+	0.709953i	$0.251284\pi$
$383$	−5.53451	+	17.0335i	−0.282800	+	0.870370i	−0.987049	+	0.160417i	$0.948716\pi$
$384$	−3.78875	+	19.1223i	−0.193344	+	0.975830i
$385$	7.08754	+	3.85144i	0.361214	+	0.196288i
$386$			7.02445i			0.357535i
$387$	7.36679	−	8.65165i	0.374475	−	0.439788i
$388$	13.1204	+	18.0587i	0.666088	+	0.916791i
$389$	−12.2732	+	16.8927i	−0.622278	+	0.856493i	−0.997516	−	0.0704358i	$-0.977561\pi$
$389$	−12.2732	+	16.8927i	−0.622278	+	0.856493i	0.375238	+	0.926929i	$0.377561\pi$
$390$	0.787373	+	6.61000i	0.0398702	+	0.334710i
$391$	19.3434	−	6.28506i	0.978239	−	0.317849i
$392$	−10.7956	−	11.8673i	−0.545262	−	0.599389i
$393$	14.2905	−	6.60100i	0.720859	−	0.332976i
$394$	−0.119793	+	0.368685i	−0.00603509	+	0.0185741i
$395$	−5.84136			−0.293910
$396$	9.33544	−	12.8112i	0.469123	−	0.643788i
$397$			28.1638i			1.41350i	0.707463	+	0.706750i	$0.249839\pi$
$397$			28.1638i			1.41350i	−0.707463	+	0.706750i	$0.750161\pi$
$398$	1.18327	−	3.64172i	0.0593117	−	0.182543i
$399$	0.598567	+	0.292725i	0.0299658	+	0.0146546i
$400$	5.79676	+	4.21159i	0.289838	+	0.210579i
$401$	22.6951	−	7.37408i	1.13334	−	0.368244i	0.318495	−	0.947925i	$-0.396823\pi$
$401$	22.6951	−	7.37408i	1.13334	−	0.368244i	0.814844	+	0.579680i	$0.196823\pi$
$402$	6.47607	−	0.771420i	0.322997	−	0.0384749i
$403$	−21.8445	−	15.8710i	−1.08815	−	0.790590i
$404$	16.5686	−	12.0378i	0.824318	−	0.598902i
$405$	7.36023	−	3.77808i	0.365733	−	0.187734i
$406$	0.378843	−	0.308386i	0.0188017	−	0.0153050i
$407$	6.39354	−	0.484495i	0.316916	−	0.0240155i
$408$	2.71510	−	13.7034i	0.134417	−	0.678421i
$409$	−28.3115	−	9.19898i	−1.39992	−	0.454860i	−0.490752	−	0.871299i	$-0.663278\pi$
$409$	−28.3115	−	9.19898i	−1.39992	−	0.454860i	−0.909164	+	0.416439i	$0.863278\pi$
$410$	−2.77217	−	3.81556i	−0.136907	−	0.188437i
$411$	12.7119	−	11.7685i	0.627033	−	0.580496i
$412$	9.22675	−	2.99795i	0.454569	−	0.147699i
$413$	11.8405	+	7.64635i	0.582631	+	0.376252i
$414$	5.79248	+	9.42071i	0.284685	+	0.463003i
$415$	11.1273	−	8.08443i	0.546216	−	0.396849i
$416$	11.5124	−	35.4315i	0.564441	−	1.73717i
$417$	−0.824558	+	4.16164i	−0.0403788	+	0.203797i
$418$	−0.261797	−	0.161478i	−0.0128049	−	0.00789813i
$419$	−18.1645			−0.887396			−0.443698	−	0.896176i	$-0.646334\pi$
$419$	−18.1645			−0.887396			−0.443698	+	0.896176i	$0.646334\pi$
$420$	−1.15840	−	6.61052i	−0.0565240	−	0.322561i
$421$	−6.12058	+	4.44686i	−0.298299	+	0.216727i	−0.726859	−	0.686786i	$-0.759021\pi$
$421$	−6.12058	+	4.44686i	−0.298299	+	0.216727i	0.428561	+	0.903513i	$0.359021\pi$
$422$	−6.49416	+	8.93844i	−0.316131	+	0.435117i
$423$	0.736646	−	9.54299i	0.0358170	−	0.463996i
$424$	7.98873	+	24.5868i	0.387967	+	1.19404i
$425$	−11.8295	−	8.59467i	−0.573817	−	0.416903i
$426$	6.02276	−	2.78201i	0.291804	−	0.134789i
$427$	8.26831	−	3.19816i	0.400132	−	0.154770i
$428$			15.3355i			0.741270i
$429$	−25.6191	+	27.5950i	−1.23690	+	1.33230i
$430$			2.22087i			0.107100i
$431$	4.85847	+	1.57861i	0.234024	+	0.0760390i	0.423681	−	0.905811i	$-0.360738\pi$
$431$	4.85847	+	1.57861i	0.234024	+	0.0760390i	−0.189657	+	0.981850i	$0.560738\pi$
$432$	−8.95295	+	0.371942i	−0.430749	+	0.0178951i
$433$	10.5750	−	14.5553i	0.508204	−	0.699483i	−0.475411	−	0.879764i	$-0.657701\pi$
$433$	10.5750	−	14.5553i	0.508204	−	0.699483i	0.983615	+	0.180281i	$0.0577007\pi$
$434$	−5.83984	−	3.77126i	−0.280321	−	0.181026i
$435$	0.457648	−	0.0545144i	0.0219426	−	0.00261376i
$436$	−1.57785	−	1.14638i	−0.0755654	−	0.0549015i
$437$	−0.679845	+	0.493936i	−0.0325214	+	0.0236282i
$438$	−4.49454	+	8.03971i	−0.214757	+	0.384152i
$439$		−	20.7576i		−	0.990705i	−0.868692	−	0.495352i	$-0.835039\pi$
$439$		−	20.7576i		−	0.990705i	0.868692	−	0.495352i	$-0.164961\pi$
$440$	0.527987	+	6.96747i	0.0251708	+	0.332161i
$441$	11.7799	−	17.3849i	0.560947	−	0.827851i
$442$	−4.54664	+	13.9931i	−0.216261	+	0.665584i
$443$	−14.7819	−	20.3456i	−0.702311	−	0.966649i	−0.999928	−	0.0119635i	$-0.996192\pi$
$443$	−14.7819	−	20.3456i	−0.702311	−	0.966649i	0.297617	−	0.954685i	$-0.403808\pi$
$444$	−3.62413	−	3.91466i	−0.171993	−	0.185782i
$445$	4.04997	+	12.4645i	0.191987	+	0.590875i
$446$	4.23710	+	13.0404i	0.200632	+	0.617483i
$447$	−13.4439	+	12.4461i	−0.635874	+	0.588681i
$448$	0.119574	−	0.450861i	0.00564935	−	0.0213012i
$449$	−0.846360	−	0.274999i	−0.0399422	−	0.0129780i	0.288978	−	0.957336i	$-0.406685\pi$
$449$	−0.846360	−	0.274999i	−0.0399422	−	0.0129780i	−0.328920	+	0.944358i	$0.606685\pi$
$450$	3.03155	−	7.34998i	0.142909	−	0.346481i
$451$	6.30317	−	25.9225i	0.296805	−	1.22064i
$452$		−	18.1495i		−	0.853681i
$453$	13.0268	−	23.3021i	0.612054	−	1.09483i
$454$	6.08598	+	8.37664i	0.285629	+	0.393135i
$455$	0.874992	+	15.9178i	0.0410203	+	0.746237i
$456$	0.0682709	+	0.573134i	0.00319708	+	0.0268395i
$457$	5.47067	+	16.8370i	0.255907	+	0.787601i	0.993650	+	0.112519i	$0.0358918\pi$
$457$	5.47067	+	16.8370i	0.255907	+	0.787601i	−0.737743	+	0.675082i	$0.764108\pi$
$458$	13.2132	+	9.59995i	0.617412	+	0.448576i
$459$	18.2705	−	0.759029i	0.852792	−	0.0354284i
$460$	8.04980	+	2.61554i	0.375324	+	0.121950i
$461$	−7.83221			−0.364782			−0.182391	−	0.983226i	$-0.558384\pi$
$461$	−7.83221			−0.364782			−0.182391	+	0.983226i	$0.558384\pi$
$462$	−6.19595	+	7.45587i	−0.288262	+	0.346879i
$463$	2.81171			0.130671			0.0653356	−	0.997863i	$-0.479188\pi$
$463$	2.81171			0.130671			0.0653356	+	0.997863i	$0.479188\pi$
$464$	−0.474746	−	0.154254i	−0.0220395	−	0.00716108i
$465$	−2.75038	−	5.95428i	−0.127546	−	0.276123i
$466$	8.48586	+	6.16534i	0.393100	+	0.285604i
$467$	2.79987	+	8.61713i	0.129563	+	0.398753i	0.994705	−	0.102774i	$-0.0327718\pi$
$467$	2.79987	+	8.61713i	0.129563	+	0.398753i	−0.865142	+	0.501527i	$0.832772\pi$
$468$	31.2353	+	2.41113i	1.44385	+	0.111454i
$469$	15.5953	−	0.857264i	0.720123	−	0.0395848i
$470$	1.09956	+	1.51341i	0.0507188	+	0.0698084i
$471$	2.33911	+	1.30766i	0.107780	+	0.0602538i
$472$			12.2095i			0.561987i
$473$	−9.57620	+	8.13084i	−0.440314	+	0.373857i
$474$	1.36441	−	6.88636i	0.0626696	−	0.316301i
$475$	0.574569	+	0.186689i	0.0263630	+	0.00856587i
$476$	3.80264	−	14.3380i	0.174294	−	0.657183i
$477$	−28.8266	+	17.7245i	−1.31988	+	0.811551i
$478$	−2.11660	−	6.51423i	−0.0968111	−	0.297954i
$479$	−0.625063	−	1.92375i	−0.0285599	−	0.0878982i	0.935761	−	0.352636i	$-0.114715\pi$
$479$	−0.625063	−	1.92375i	−0.0285599	−	0.0878982i	−0.964320	+	0.264738i	$0.914715\pi$
$480$	6.64062	−	6.14777i	0.303102	−	0.280606i
$481$	7.44838	+	10.2518i	0.339617	+	0.467443i
$482$	3.57699	−	11.0089i	0.162928	−	0.501440i
$483$	12.4090	+	23.3977i	0.564631	+	1.06463i
$484$	−12.4637	+	12.3197i	−0.566531	+	0.559985i
$485$		−	12.8796i		−	0.584834i
$486$	2.73479	+	9.55944i	0.124052	+	0.433625i
$487$	19.0912	−	13.8706i	0.865106	−	0.628536i	−0.0641633	−	0.997939i	$-0.520438\pi$
$487$	19.0912	−	13.8706i	0.865106	−	0.628536i	0.929269	+	0.369403i	$0.120438\pi$
$488$	6.21283	+	4.51388i	0.281242	+	0.204334i
$489$	−3.39964	−	28.5400i	−0.153737	−	1.29062i
$490$	0.449868	+	4.07962i	0.0203229	+	0.184298i
$491$	2.22240	−	3.05887i	0.100295	−	0.138045i	−0.755920	−	0.654664i	$-0.772810\pi$
$491$	2.22240	−	3.05887i	0.100295	−	0.138045i	0.856215	+	0.516620i	$0.172810\pi$
$492$	−20.1502	+	9.30769i	−0.908440	+	0.419623i
$493$	0.968824	+	0.314790i	0.0436336	+	0.0141774i
$494$		−	0.607901i		−	0.0273508i
$495$	−8.70274	+	2.81418i	−0.391159	+	0.126488i
$496$			7.10378i			0.318969i
$497$	14.8181	−	5.73161i	0.664683	−	0.257098i
$498$	6.93164	+	15.0063i	0.310614	+	0.672447i
$499$	−12.2622	−	8.90903i	−0.548933	−	0.398823i	0.278459	−	0.960448i	$-0.410176\pi$
$499$	−12.2622	−	8.90903i	−0.548933	−	0.398823i	−0.827392	+	0.561625i	$0.810176\pi$
$500$	−4.14318	−	12.7514i	−0.185289	−	0.570259i
$501$	−0.355309	−	2.98282i	−0.0158740	−	0.133262i
$502$	3.24436	−	4.46548i	0.144803	−	0.199304i
$503$	7.23058	−	5.25332i	0.322396	−	0.234234i	−0.414801	−	0.909912i	$-0.636149\pi$
$503$	7.23058	−	5.25332i	0.322396	−	0.234234i	0.737197	+	0.675678i	$0.236149\pi$
$504$	18.1866	+	0.402453i	0.810097	+	0.0179267i
$505$	−11.8169			−0.525844
$506$	−4.64594	−	11.3091i	−0.206537	−	0.502752i
$507$	−50.9103	−	10.0870i	−2.26100	−	0.447979i
$508$	−7.60115	+	23.3939i	−0.337246	+	1.03794i
$509$	8.31132	−	6.03853i	0.368393	−	0.267653i	−0.388151	−	0.921596i	$-0.626886\pi$
$509$	8.31132	−	6.03853i	0.368393	−	0.267653i	0.756544	+	0.653943i	$0.226886\pi$
$510$	−2.62261	+	2.42797i	−0.116131	+	0.107512i
$511$	−11.9665	+	18.5303i	−0.529367	+	0.819730i
$512$	−16.8393	+	5.47143i	−0.744200	+	0.241805i
$513$	−0.708237	+	0.263095i	−0.0312694	+	0.0116159i
$514$	2.50256	+	3.44447i	0.110383	+	0.151929i
$515$	−5.32382	−	1.72981i	−0.234596	−	0.0762247i
$516$	10.2526	+	2.03138i	0.451347	+	0.0894266i
$517$	−2.50010	+	10.2820i	−0.109954	+	0.452200i
$518$	2.05962	+	2.53018i	0.0904945	+	0.111170i
$519$	9.59944	−	17.1712i	0.421369	−	0.753734i
$520$	−11.1721	+	8.11700i	−0.489929	+	0.355954i
$521$	17.9055	+	13.0091i	0.784455	+	0.569940i	0.906313	−	0.422608i	$-0.138885\pi$
$521$	17.9055	+	13.0091i	0.784455	+	0.569940i	−0.121858	+	0.992548i	$0.538885\pi$
$522$	−0.0426299	+	0.552254i	−0.00186586	+	0.0241715i
$523$	3.93171	−	1.27749i	0.171922	−	0.0558608i	−0.221791	−	0.975094i	$-0.571190\pi$
$523$	3.93171	−	1.27749i	0.171922	−	0.0558608i	0.393713	+	0.919233i	$0.371190\pi$
$524$	11.7138	+	8.51060i	0.511722	+	0.371787i
$525$	8.36492	−	17.1046i	0.365075	−	0.746508i
$526$	2.67832	−	8.24303i	0.116780	−	0.359413i
$527$		−	14.4968i		−	0.631491i
$528$	9.83520	+	1.18557i	0.428022	+	0.0515955i
$529$	−10.4018			−0.452253
$530$	2.04378	−	6.29012i	0.0887763	−	0.273225i
$531$	−15.5348	+	3.75423i	−0.674152	+	0.162920i
$532$	0.0336389	+	0.611957i	0.00145843	+	0.0265317i
$533$	50.1436	−	16.2926i	2.17196	−	0.705713i
$534$	−15.6404	+	1.86306i	−0.676826	+	0.0806224i
$535$	5.20106	−	7.15864i	0.224861	−	0.309495i
$536$	7.95254	+	10.9457i	0.343498	+	0.472784i
$537$	26.8179	+	14.9923i	1.15728	+	0.646966i
$538$		−	12.4805i		−	0.538072i
$539$	−15.9440	+	16.8757i	−0.686755	+	0.726889i
$540$	6.33685	+	4.21355i	0.272695	+	0.181322i
$541$	−5.38295	+	16.5670i	−0.231431	+	0.712271i	0.766144	+	0.642669i	$0.222173\pi$
$541$	−5.38295	+	16.5670i	−0.231431	+	0.712271i	−0.997575	+	0.0696021i	$0.977827\pi$
$542$	4.32810	−	3.14455i	0.185908	−	0.135070i
$543$	−12.0020	+	11.1112i	−0.515053	+	0.476827i
$544$	19.0229	−	6.18091i	0.815600	−	0.265004i
$545$	0.347749	+	1.07026i	0.0148959	+	0.0458449i
$546$	−18.9698	−	2.68652i	−0.811834	−	0.114973i
$547$	2.04406	−	1.48510i	0.0873977	−	0.0634982i	−0.543228	−	0.839585i	$-0.682798\pi$
$547$	2.04406	−	1.48510i	0.0873977	−	0.0634982i	0.630626	+	0.776087i	$0.282798\pi$
$548$	15.1541	+	4.92387i	0.647352	+	0.210338i
$549$	−3.83291	+	9.29286i	−0.163585	+	0.396610i
$550$	−4.61439	+	7.48112i	−0.196758	+	0.318996i
$551$	−0.0420885			−0.00179303
$552$	−11.1950	+	20.0253i	−0.476491	+	0.852334i
$553$	4.30986	−	16.2505i	0.183274	−	0.691043i
$554$	3.71163	−	5.10862i	0.157692	−	0.217044i
$555$	0.364085	+	3.05650i	0.0154546	+	0.129741i
$556$	−3.71135	+	1.20589i	−0.157396	+	0.0511411i
$557$	10.6879	−	14.7106i	0.452860	−	0.623309i	−0.520149	−	0.854076i	$-0.674123\pi$
$557$	10.6879	−	14.7106i	0.452860	−	0.623309i	0.973009	+	0.230767i	$0.0741235\pi$
$558$	7.66192	−	1.85163i	0.324355	−	0.0783856i
$559$	−23.6123	−	7.67209i	−0.998692	−	0.324495i
$560$	3.25270	−	2.64777i	0.137452	−	0.111889i
$561$	−20.0709	−	2.41942i	−0.847393	−	0.102148i
$562$	−13.0383			−0.549990
$563$	−4.74436	+	14.6017i	−0.199951	+	0.615386i	0.799932	+	0.600091i	$0.204869\pi$
$563$	−4.74436	+	14.6017i	−0.199951	+	0.615386i	−0.999883	+	0.0152955i	$0.995131\pi$
$564$	7.99240	−	3.69182i	0.336541	−	0.155454i
$565$	−6.15543	+	8.47222i	−0.258961	+	0.356429i
$566$	−3.83503	−	11.8030i	−0.161198	−	0.496118i
$567$	5.08004	+	23.2636i	0.213342	+	0.976978i
$568$	11.1344	+	8.08959i	0.467188	+	0.339432i
$569$	−12.9845	−	17.8717i	−0.544340	−	0.749220i	0.444890	−	0.895585i	$-0.353243\pi$
$569$	−12.9845	−	17.8717i	−0.544340	−	0.749220i	−0.989231	+	0.146365i	$0.953243\pi$
$570$	0.0720549	−	0.128890i	0.00301805	−	0.00539861i
$571$	18.4614			0.772586			0.386293	−	0.922376i	$-0.373755\pi$
$571$	18.4614			0.772586			0.386293	+	0.922376i	$0.373755\pi$
$572$	−33.6540	−	8.18311i	−1.40715	−	0.342153i
$573$	−0.548504	+	2.76837i	−0.0229141	+	0.115650i
$574$	12.6602	−	4.89692i	0.528425	−	0.204394i
$575$	14.1147	+	19.4273i	0.588625	+	0.810172i
$576$	0.277027	+	0.450548i	0.0115428	+	0.0187728i
$577$	16.0183	−	5.20467i	0.666851	−	0.216673i	0.0440217	−	0.999031i	$-0.485983\pi$
$577$	16.0183	−	5.20467i	0.666851	−	0.216673i	0.622830	+	0.782357i	$0.285983\pi$
$578$	2.79977	−	0.909701i	0.116455	−	0.0378386i
$579$	−12.9585	−	13.9974i	−0.538538	−	0.581712i
$580$	0.249178	+	0.342964i	0.0103465	+	0.0142408i
$581$	14.2808	+	36.9207i	0.592469	+	1.53173i
$582$	15.1838	+	3.00840i	0.629388	+	0.124702i
$583$	34.6050	−	14.2162i	1.43319	−	0.588776i
$584$	−19.1078			−0.790687
$585$	−13.7629	−	11.7190i	−0.569028	−	0.484521i
$586$	5.02742	+	6.91964i	0.207681	+	0.285848i
$587$	37.3494	+	27.1359i	1.54158	+	1.12002i	0.949338	+	0.314257i	$0.101755\pi$
$587$	37.3494	+	27.1359i	1.54158	+	1.12002i	0.592238	+	0.805763i	$0.298245\pi$
$588$	19.2450	+	1.65473i	0.793652	+	0.0682398i
$589$	0.185089	+	0.569645i	0.00762645	+	0.0234718i
$590$	1.83601	−	2.52704i	0.0755871	−	0.104037i
$591$	−0.441434	−	0.955658i	−0.0181582	−	0.0393105i
$592$	1.03022	−	3.17069i	0.0423418	−	0.130315i
$593$	1.74812			0.0717866			0.0358933	−	0.999356i	$-0.488572\pi$
$593$	1.74812			0.0717866			0.0358933	+	0.999356i	$0.488572\pi$
$594$	−1.28486	−	10.9170i	−0.0527183	−	0.447929i
$595$	−6.63784	+	5.40335i	−0.272125	+	0.221516i
$596$	−16.0267	−	5.20740i	−0.656480	−	0.213303i
$597$	4.36030	+	9.43959i	0.178455	+	0.386337i
$598$	14.2027	−	19.5483i	0.580790	−	0.799389i
$599$	6.97933	−	2.26772i	0.285168	−	0.0926566i	−0.162941	−	0.986636i	$-0.552098\pi$
$599$	6.97933	−	2.26772i	0.285168	−	0.0926566i	0.448108	+	0.893979i	$0.352098\pi$
$600$	16.3779	−	1.95091i	0.668624	−	0.0796455i
$601$	15.7217	−	21.6390i	0.641300	−	0.882674i	−0.357384	−	0.933957i	$-0.616331\pi$
$601$	15.7217	−	21.6390i	0.641300	−	0.882674i	0.998684	+	0.0512838i	$0.0163313\pi$
$602$	−6.17841	−	1.63860i	−0.251813	−	0.0667842i
$603$	−11.4816	+	13.4841i	−0.467565	+	0.549115i
$604$	24.5554			0.999147
$605$	9.99630	−	1.52376i	0.406407	−	0.0619498i
$606$	2.76017	−	13.9309i	0.112124	−	0.565904i
$607$	−18.8295	−	6.11807i	−0.764265	−	0.248325i	−0.0991571	−	0.995072i	$-0.531615\pi$
$607$	−18.8295	−	6.11807i	−0.764265	−	0.248325i	−0.665108	+	0.746747i	$0.731615\pi$
$608$	−0.668580	+	0.485752i	−0.0271145	+	0.0196998i
$609$	−0.186004	+	1.31339i	−0.00753725	+	0.0532213i
$610$	−0.607116	−	1.86851i	−0.0245814	−	0.0756538i
$611$	−19.8891	+	6.46234i	−0.804625	+	0.261438i
$612$	8.80986	+	14.3281i	0.356118	+	0.579179i
$613$	−33.2953	+	24.1904i	−1.34478	+	0.977042i	−0.345530	+	0.938408i	$0.612301\pi$
$613$	−33.2953	+	24.1904i	−1.34478	+	0.977042i	−0.999253	+	0.0386344i	$0.987699\pi$
$614$	−4.53899	+	13.9696i	−0.183179	+	0.563766i
$615$	12.5629	+	2.48911i	0.506583	+	0.100371i
$616$	−19.7729	−	3.67188i	−0.796675	−	0.147944i
$617$		−	39.5281i		−	1.59134i	−0.605728	−	0.795672i	$-0.707118\pi$
$617$		−	39.5281i		−	1.59134i	0.605728	−	0.795672i	$-0.292882\pi$
$618$	3.28280	−	5.87220i	0.132054	−	0.236214i
$619$	1.24836	+	1.71822i	0.0501758	+	0.0690610i	0.833368	−	0.552719i	$-0.186410\pi$
$619$	1.24836	+	1.71822i	0.0501758	+	0.0690610i	−0.783192	+	0.621780i	$0.786410\pi$
$620$	3.54604	−	4.88070i	0.142412	−	0.196014i
$621$	−28.9216	−	8.08651i	−1.16058	−	0.324501i
$622$	−17.0715	+	5.54685i	−0.684503	+	0.222408i
$623$	−37.6642	+	2.07038i	−1.50898	+	0.0829480i
$624$	8.20996	+	17.7737i	0.328661	+	0.711518i
$625$	4.02918	−	12.4006i	0.161167	−	0.496022i
$626$	−8.52498			−0.340727
$627$	0.819565	−	0.161186i	0.0327303	−	0.00643714i
$628$			2.46492i			0.0983612i
$629$	−2.10239	+	6.47049i	−0.0838277	+	0.257995i
$630$	−3.70363	−	2.81812i	−0.147556	−	0.112276i
$631$	−2.52126	−	1.83180i	−0.100370	−	0.0729229i	0.536468	−	0.843920i	$-0.319758\pi$
$631$	−2.52126	−	1.83180i	−0.100370	−	0.0729229i	−0.636838	+	0.770997i	$0.719758\pi$
$632$	13.8508	−	4.50039i	0.550954	−	0.179016i
$633$	−3.54873	−	29.7916i	−0.141049	−	1.18411i
$634$	−8.65153	−	6.28571i	−0.343596	−	0.249637i
$635$	11.4823	−	8.34238i	0.455661	−	0.331057i
$636$	−27.1690	−	15.1886i	−1.07732	−	0.602267i
$637$	−44.9286	−	9.31023i	−1.78014	−	0.368885i
$638$	0.144681	−	0.595019i	0.00572799	−	0.0235570i
$639$	−6.86917	+	16.6543i	−0.271740	+	0.658833i
$640$	9.83969	+	3.19711i	0.388948	+	0.126377i
$641$	20.9623	+	28.8521i	0.827959	+	1.13959i	0.988299	+	0.152526i	$0.0487409\pi$
$641$	20.9623	+	28.8521i	0.827959	+	1.13959i	−0.160340	+	0.987062i	$0.551259\pi$
$642$	7.22446	+	7.80362i	0.285127	+	0.307984i
$643$	−41.5502	+	13.5005i	−1.63858	+	0.532407i	−0.976221	−	0.216778i	$-0.930445\pi$
$643$	−41.5502	+	13.5005i	−1.63858	+	0.532407i	−0.662360	+	0.749185i	$0.730445\pi$
$644$	−13.2157	+	20.4646i	−0.520771	+	0.806419i
$645$	−4.09700	−	4.42545i	−0.161319	−	0.174252i
$646$	0.264045	−	0.191840i	0.0103887	−	0.00754784i
$647$	10.6883	−	32.8951i	0.420199	−	1.29324i	−0.487318	−	0.873225i	$-0.662025\pi$
$647$	10.6883	−	32.8951i	0.420199	−	1.29324i	0.907517	−	0.420015i	$-0.137975\pi$
$648$	−14.5415	+	14.6290i	−0.571243	+	0.574682i
$649$	17.6182	−	1.33509i	0.691576	−	0.0524068i
$650$	−17.3714			−0.681362
$651$	18.5940	−	3.25832i	0.728756	−	0.127704i
$652$	21.3880	−	15.5393i	0.837618	−	0.608565i
$653$	−7.58534	+	10.4403i	−0.296837	+	0.408561i	−0.931220	−	0.364458i	$-0.881254\pi$
$653$	−7.58534	+	10.4403i	−0.296837	+	0.408561i	0.634383	+	0.773019i	$0.281254\pi$
$654$	−1.34296	+	0.159971i	−0.0525137	+	0.00625535i
$655$	−2.58166	−	7.94553i	−0.100874	−	0.310457i
$656$	−11.2220	−	8.15327i	−0.438146	−	0.318332i
$657$	−5.87535	−	24.3119i	−0.229219	−	0.948497i
$658$	−5.02155	+	1.94232i	−0.195760	+	0.0757197i
$659$			0.761612i			0.0296682i	0.999890	+	0.0148341i	$0.00472201\pi$
$659$			0.761612i			0.0296682i	−0.999890	+	0.0148341i	$0.995278\pi$
$660$	−6.16553	−	5.72405i	−0.239993	−	0.222808i
$661$			43.9258i			1.70851i	0.519851	+	0.854257i	$0.325988\pi$
$661$			43.9258i			1.70851i	−0.519851	+	0.854257i	$0.674012\pi$
$662$	3.07087	+	0.997786i	0.119353	+	0.0387800i
$663$	−16.7542	−	36.2711i	−0.650680	−	1.40865i
$664$	−20.1560	+	27.7423i	−0.782203	+	1.07661i
$665$	0.191843	−	0.297071i	0.00743936	−	0.0115199i
$666$	−3.68834	−	0.284712i	−0.142920	−	0.0110324i
$667$	−1.35344	−	0.983332i	−0.0524054	−	0.0380748i
$668$	2.23534	−	1.62407i	0.0864877	−	0.0628370i
$669$	−32.4998	−	18.1688i	−1.25652	−	0.702445i
$670$		−	3.46135i		−	0.133723i
$671$	5.83415	−	9.45867i	0.225225	−	0.365148i
$672$	12.2034	+	23.0100i	0.470757	+	0.887631i
$673$	4.83768	−	14.8888i	0.186479	−	0.573923i	−0.813492	−	0.581576i	$-0.802436\pi$
$673$	4.83768	−	14.8888i	0.186479	−	0.573923i	0.999971	+	0.00765336i	$0.00243616\pi$
$674$	−1.86262	−	2.56367i	−0.0717453	−	0.0987490i
$675$	7.51819	+	20.2386i	0.289375	+	0.778983i
$676$	−14.7519	−	45.4017i	−0.567381	−	1.74622i
$677$	13.0245	+	40.0854i	0.500574	+	1.54061i	0.808087	+	0.589064i	$0.200503\pi$
$677$	13.0245	+	40.0854i	0.500574	+	1.54061i	−0.307513	+	0.951544i	$0.599497\pi$
$678$	−8.55011	−	9.23555i	−0.328365	−	0.354689i
$679$	35.8309	+	9.50283i	1.37506	+	0.364685i
$680$	−7.05132	−	2.29111i	−0.270406	−	0.0878602i
$681$	−27.5804	−	5.46457i	−1.05688	−	0.209403i
$682$	−8.68950	+	0.658480i	−0.332738	+	0.0252145i
$683$		−	48.6985i		−	1.86339i	−0.363236	−	0.931697i	$-0.618328\pi$
$683$		−	48.6985i		−	1.86339i	0.363236	−	0.931697i	$-0.381672\pi$
$684$	−0.529114	−	0.450535i	−0.0202312	−	0.0172266i
$685$	−5.40403	−	7.43801i	−0.206478	−	0.284192i
$686$	−11.6813	−	1.75849i	−0.445995	−	0.0671396i
$687$	−44.0393	+	5.24589i	−1.68020	+	0.200143i
$688$	2.01845	+	6.21215i	0.0769526	+	0.236836i
$689$	59.8163	+	43.4591i	2.27882	+	1.65566i
$690$	5.32838	−	2.46127i	0.202848	−	0.0936988i
$691$	−6.04359	−	1.96368i	−0.229909	−	0.0747020i	0.191797	−	0.981435i	$-0.438569\pi$
$691$	−6.04359	−	1.96368i	−0.229909	−	0.0747020i	−0.421706	+	0.906733i	$0.638569\pi$
$692$	18.0948			0.687863
$693$	−1.40794	−	26.2872i	−0.0534832	−	0.998569i
$694$	−8.41079			−0.319269
$695$	2.14144	+	0.695797i	0.0812295	+	0.0263931i
$696$	−1.04316	+	0.481851i	−0.0395407	+	0.0182645i
$697$	22.9010	+	16.6385i	0.867437	+	0.630230i
$698$	1.15870	+	3.56612i	0.0438576	+	0.134980i
$699$	−28.2832	+	3.36905i	−1.06977	+	0.127429i
$700$	17.4873	−	0.961265i	0.660957	−	0.0363324i
$701$	8.80924	+	12.1249i	0.332720	+	0.457950i	0.942298	−	0.334776i	$-0.108661\pi$
$701$	8.80924	+	12.1249i	0.332720	+	0.457950i	−0.609577	+	0.792727i	$0.708661\pi$
$702$	17.0302	−	13.4878i	0.642765	−	0.509064i
$703$		−	0.281097i		−	0.0106018i
$704$	−0.222193	−	0.540862i	−0.00837422	−	0.0203845i
$705$	−4.98295	−	0.987286i	−0.187669	−	0.0371833i
$706$	−20.0123	−	6.50239i	−0.753173	−	0.244721i
$707$	8.71871	−	32.8743i	0.327901	−	1.23637i
$708$	−9.98675	−	10.7874i	−0.375325	−	0.405414i
$709$	−9.00152	−	27.7038i	−0.338059	−	1.04044i	−0.965195	−	0.261530i	$-0.915773\pi$
$709$	−9.00152	−	27.7038i	−0.338059	−	1.04044i	0.627136	−	0.778909i	$-0.284227\pi$
$710$	−1.08805	−	3.34867i	−0.0408337	−	0.125673i
$711$	9.98498	+	16.2393i	0.374466	+	0.609020i
$712$	−19.2062	−	26.4351i	−0.719783	−	0.990696i
$713$	−7.35695	+	22.6424i	−0.275520	+	0.847964i
$714$	−4.81955	−	9.08745i	−0.180367	−	0.340089i
$715$	12.9344	+	15.2337i	0.483721	+	0.569708i
$716$			28.2603i			1.05614i
$717$	16.2350	+	9.07603i	0.606306	+	0.338951i
$718$	−5.39810	+	3.92195i	−0.201455	+	0.146366i
$719$	−9.56768	−	6.95132i	−0.356814	−	0.259241i	0.394908	−	0.918721i	$-0.370776\pi$
$719$	−9.56768	−	6.95132i	−0.356814	−	0.259241i	−0.751722	+	0.659480i	$0.770776\pi$
$720$	−0.366015	+	4.74159i	−0.0136406	+	0.176709i
$721$	8.74032	−	13.5345i	0.325507	−	0.504050i
$722$	7.11541	−	9.79353i	0.264808	−	0.364477i
$723$	13.1811	+	28.5357i	0.490211	+	1.06126i
$724$	−14.3078	−	4.64887i	−0.531744	−	0.172774i
$725$			1.20272i			0.0446680i
$726$	−0.538555	+	12.1405i	−0.0199876	+	0.450578i
$727$		−	12.4488i		−	0.461701i	−0.972989	−	0.230850i	$-0.925849\pi$
$727$		−	12.4488i		−	0.461701i	0.972989	−	0.230850i	$-0.0741508\pi$
$728$	−14.3384	−	37.0694i	−0.531415	−	1.37388i
$729$	−23.0845	−	14.0037i	−0.854983	−	0.518656i
$730$	3.95481	+	2.87334i	0.146374	+	0.106347i
$731$	−4.11909	−	12.6772i	−0.152350	−	0.468885i
$732$	−9.18130	+	1.09366i	−0.339351	+	0.0404229i
$733$	−24.2405	+	33.3642i	−0.895344	+	1.23234i	0.0765850	+	0.997063i	$0.475598\pi$
$733$	−24.2405	+	33.3642i	−0.895344	+	1.23234i	−0.971929	+	0.235273i	$0.924402\pi$
$734$	−3.11968	+	2.26658i	−0.115149	+	0.0836609i
$735$	−8.42241	−	7.29941i	−0.310665	−	0.269243i
$736$	−32.8483			−1.21081
$737$	14.9250	−	12.6724i	0.549771	−	0.466793i
$738$	−5.86882	+	14.2289i	−0.216034	+	0.523774i
$739$	4.14775	−	12.7655i	0.152578	−	0.469586i	−0.845330	−	0.534245i	$-0.820596\pi$
$739$	4.14775	−	12.7655i	0.152578	−	0.469586i	0.997907	+	0.0646592i	$0.0205960\pi$
$740$	−2.29055	+	1.66418i	−0.0842024	+	0.0611766i
$741$	1.12144	+	1.21135i	0.0411972	+	0.0444999i
$742$	15.9911	+	10.3267i	0.587050	+	0.379107i
$743$	33.2762	−	10.8121i	1.22079	−	0.396657i	0.373417	−	0.927663i	$-0.378186\pi$
$743$	33.2762	−	10.8121i	1.22079	−	0.396657i	0.847368	+	0.531006i	$0.178186\pi$
$744$	11.1090	+	11.9995i	0.407275	+	0.439925i
$745$	5.71521	+	7.86631i	0.209389	+	0.288199i
$746$	3.67058	+	1.19264i	0.134389	+	0.0436657i
$747$	−41.4956	−	17.1152i	−1.51825	−	0.626211i
$748$	−7.06608	−	17.2002i	−0.258361	−	0.628902i
$749$	16.0778	+	19.7510i	0.587469	+	0.721687i
$750$	−8.11539	−	4.53684i	−0.296332	−	0.165662i
$751$	−15.1867	+	11.0338i	−0.554170	+	0.402628i	−0.829320	−	0.558773i	$-0.811272\pi$
$751$	−15.1867	+	11.0338i	−0.554170	+	0.402628i	0.275151	+	0.961401i	$0.411272\pi$
$752$	4.45112	+	3.23393i	0.162316	+	0.117929i
$753$	1.77288	+	14.8833i	0.0646073	+	0.542379i
$754$	1.15098	−	0.373977i	0.0419163	−	0.0136194i
$755$	−11.4625	−	8.32801i	−0.417164	−	0.303087i
$756$	−16.3975	+	14.5202i	−0.596370	+	0.528093i
$757$	−4.27923	+	13.1701i	−0.155531	+	0.478676i	−0.998214	−	0.0597337i	$-0.980975\pi$
$757$	−4.27923	+	13.1701i	−0.155531	+	0.478676i	0.842683	+	0.538410i	$0.180975\pi$
$758$			2.85199i			0.103589i
$759$	30.1206	+	13.9646i	1.09331	+	0.506882i
$760$	0.306330			0.0111118
$761$	9.15398	−	28.1730i	0.331831	−	1.02127i	−0.636431	−	0.771334i	$-0.719590\pi$
$761$	9.15398	−	28.1730i	0.331831	−	1.02127i	0.968262	−	0.249938i	$-0.0804102\pi$
$762$	7.15281	+	15.4851i	0.259119	+	0.560965i
$763$	−3.23402	+	0.177772i	−0.117079	+	0.00643579i
$764$	−2.46882	+	0.802169i	−0.0893189	+	0.0290215i
$765$	0.746933	−	9.67626i	0.0270054	−	0.349846i
$766$	−6.71471	+	9.24200i	−0.242612	+	0.333927i
$767$	20.5250	+	28.2502i	0.741114	+	1.02006i
$768$	−6.36542	+	11.3863i	−0.229692	+	0.410868i
$769$		−	16.3295i		−	0.588856i	−0.955674	−	0.294428i	$-0.904871\pi$
$769$		−	16.3295i		−	0.588856i	0.955674	−	0.294428i	$-0.0951291\pi$
$770$	3.54032	+	3.73334i	0.127584	+	0.134540i
$771$	−11.3410	−	2.24703i	−0.408438	−	0.0809249i
$772$	5.42179	−	16.6866i	0.195135	−	0.600562i
$773$	−0.756196	+	0.549409i	−0.0271985	+	0.0197609i	−0.601301	−	0.799022i	$-0.705351\pi$
$773$	−0.756196	+	0.549409i	−0.0271985	+	0.0197609i	0.574103	+	0.818783i	$0.305351\pi$
$774$	6.17412	−	3.79626i	0.221924	−	0.136454i
$775$	16.2782	−	5.28910i	0.584729	−	0.189990i
$776$	9.92292	+	30.5396i	0.356212	+	1.09631i
$777$	−8.77175	−	1.24226i	−0.314685	−	0.0445659i
$778$	−10.7748	+	7.82836i	−0.386296	+	0.280660i
$779$	−1.11232	−	0.361413i	−0.0398529	−	0.0129490i
$780$	3.23150	−	16.3098i	0.115706	−	0.583983i
$781$	10.4557	−	16.9514i	0.374135	−	0.606570i
$782$	12.9729			0.463911
$783$	−0.933839	−	1.17910i	−0.0333727	−	0.0421377i
$784$	4.96614	+	11.0025i	0.177362	+	0.392947i
$785$	0.835982	−	1.15063i	0.0298375	−	0.0410678i
$786$	9.96999	−	1.18761i	0.355618	−	0.0423606i
$787$	33.5176	−	10.8905i	1.19477	−	0.388205i	0.356937	−	0.934128i	$-0.383821\pi$
$787$	33.5176	−	10.8905i	1.19477	−	0.388205i	0.837835	+	0.545924i	$0.183821\pi$
$788$	0.569136	−	0.783348i	0.0202746	−	0.0279056i
$789$	9.86954	+	21.3665i	0.351365	+	0.760668i
$790$	−3.54349	−	1.15135i	−0.126072	−	0.0409632i
$791$	−19.0280	−	23.3752i	−0.676557	−	0.831128i
$792$	18.4674	−	13.3777i	0.656211	−	0.475358i
$793$	21.9633			0.779941
$794$	−5.55118	+	17.0848i	−0.197004	+	0.606315i
$795$	7.53129	+	16.3044i	0.267107	+	0.578259i
$796$	−5.62169	+	7.73759i	−0.199255	+	0.274252i
$797$	−5.14081	−	15.8218i	−0.182097	−	0.560437i	0.817789	−	0.575518i	$-0.195199\pi$
$797$	−5.14081	−	15.8218i	−0.182097	−	0.560437i	−0.999886	+	0.0150809i	$0.995199\pi$
$798$	0.305406	+	0.295553i	0.0108113	+	0.0104625i
$799$	−9.08349	−	6.59954i	−0.321351	−	0.233475i
$800$	13.8808	+	19.1053i	0.490762	+	0.675475i
$801$	27.7291	−	32.5655i	0.979761	−	1.15064i
$802$	15.2208			0.537465
$803$	2.08941	+	27.5725i	0.0737336	+	0.973011i
$804$	−15.9793	−	3.16602i	−0.563547	−	0.111657i
$805$	13.1097	−	5.07080i	0.462056	−	0.178722i
$806$	−10.1231	−	13.9333i	−0.356572	−	0.490780i
$807$	23.0237	+	24.8695i	0.810473	+	0.875446i
$808$	28.0197	−	9.10414i	0.985728	−	0.320282i
$809$	27.5339	−	8.94629i	0.968039	−	0.314535i	0.218015	−	0.975945i	$-0.430042\pi$
$809$	27.5339	−	8.94629i	0.968039	−	0.314535i	0.750024	+	0.661411i	$0.230042\pi$
$810$	5.20955	−	0.841141i	0.183045	−	0.0295547i
$811$	0.995512	+	1.37020i	0.0349571	+	0.0481144i	0.826138	−	0.563468i	$-0.190533\pi$
$811$	0.995512	+	1.37020i	0.0349571	+	0.0481144i	−0.791181	+	0.611583i	$0.790533\pi$
$812$	−1.13797	+	0.440163i	−0.0399348	+	0.0154467i
$813$	−2.82347	+	14.2504i	−0.0990235	+	0.499784i
$814$	3.97396	+	0.966283i	0.139287	+	0.0338682i
$815$	−15.2541			−0.534328
$816$	−5.12922	+	9.17502i	−0.179559	+	0.321190i
$817$	0.323715	+	0.445555i	0.0113253	+	0.0155880i
$818$	−15.3612	−	11.1606i	−0.537093	−	0.390221i
$819$	42.7566	−	29.6417i	1.49404	−	1.03577i
$820$	3.64025	+	11.2035i	0.127123	+	0.391244i
$821$	−21.7540	+	29.9418i	−0.759219	+	1.04498i	0.238059	+	0.971251i	$0.423489\pi$
$821$	−21.7540	+	29.9418i	−0.759219	+	1.04498i	−0.997279	+	0.0737249i	$0.976511\pi$
$822$	10.0309	−	4.63345i	0.349869	−	0.161610i
$823$	−3.67052	+	11.2967i	−0.127946	+	0.393778i	−0.994426	−	0.105434i	$-0.966377\pi$
$823$	−3.67052	+	11.2967i	−0.127946	+	0.393778i	0.866480	+	0.499212i	$0.166377\pi$
$824$	13.9563			0.486191
$825$	−4.60605	−	23.4199i	−0.160362	−	0.815376i
$826$	5.67555	+	6.97223i	0.197478	+	0.242595i
$827$	1.56101	+	0.507203i	0.0542816	+	0.0176372i	0.336032	−	0.941851i	$-0.390915\pi$
$827$	1.56101	+	0.507203i	0.0542816	+	0.0176372i	−0.281750	+	0.959488i	$0.590915\pi$
$828$	−6.48868	−	26.8498i	−0.225497	−	0.933094i
$829$	−15.3748	+	21.1615i	−0.533988	+	0.734971i	−0.987732	−	0.156161i	$-0.950088\pi$
$829$	−15.3748	+	21.1615i	−0.533988	+	0.734971i	0.453744	+	0.891132i	$0.350088\pi$
$830$	8.34351	−	2.71097i	0.289607	−	0.0940992i
$831$	2.02822	+	17.0269i	0.0703581	+	0.590657i
$832$	0.679246	−	0.934902i	0.0235486	−	0.0324119i
$833$	−10.1345	−	22.4531i	−0.351140	−	0.777952i
$834$	−1.32047	+	2.36202i	−0.0457241	+	0.0817901i
$835$	−1.59426			−0.0551717
$836$	0.497262	+	0.585657i	0.0171982	+	0.0202554i
$837$	−11.8518	+	17.8242i	−0.409659	+	0.616095i
$838$	−11.0190	−	3.58029i	−0.380645	−	0.123679i
$839$	−43.7807	+	31.8085i	−1.51148	+	1.09815i	−0.545960	+	0.837811i	$0.683835\pi$
$839$	−43.7807	+	31.8085i	−1.51148	+	1.09815i	−0.965517	+	0.260341i	$0.916165\pi$
$840$	1.35378	−	9.55916i	0.0467097	−	0.329823i
$841$	8.93560	+	27.5009i	0.308124	+	0.948309i
$842$	−4.58937	+	1.49118i	−0.158160	+	0.0513893i
$843$	25.9811	−	24.0528i	0.894836	−	0.828424i
$844$	22.3260	−	16.2208i	0.768491	−	0.558341i
$845$	−8.51183	+	26.1967i	−0.292816	+	0.901194i
$846$	2.32782	−	5.64379i	0.0800321	−	0.194037i
$847$	−3.13637	+	28.9338i	−0.107767	+	0.994176i
$848$		−	19.4521i		−	0.667987i
$849$	29.4158	+	16.4447i	1.00955	+	0.564380i
$850$	−5.48202	−	7.54535i	−0.188032	−	0.258803i
$851$	6.56739	−	9.03923i	0.225127	−	0.309861i
$852$	−16.4543	+	1.96002i	−0.563716	+	0.0671490i
$853$	9.81437	−	3.18888i	0.336038	−	0.109185i	−0.136138	−	0.990690i	$-0.543469\pi$
$853$	9.81437	−	3.18888i	0.336038	−	0.109185i	0.472175	+	0.881505i	$0.343469\pi$
$854$	5.64611	−	0.310363i	0.193206	−	0.0106204i
$855$	0.0941917	+	0.389760i	0.00322129	+	0.0133295i
$856$	−6.81725	+	20.9813i	−0.233009	+	0.717127i
$857$	−21.1871			−0.723738			−0.361869	−	0.932229i	$-0.617861\pi$
$857$	−21.1871			−0.723738			−0.361869	+	0.932229i	$0.617861\pi$
$858$	−20.9802	+	11.6901i	−0.716252	+	0.399095i
$859$		−	42.4009i		−	1.44670i	−0.690482	−	0.723350i	$-0.742601\pi$
$859$		−	42.4009i		−	1.44670i	0.690482	−	0.723350i	$-0.257399\pi$
$860$	1.71417	−	5.27566i	0.0584526	−	0.179899i
$861$	−16.1938	+	33.1131i	−0.551882	+	1.12849i
$862$	2.63610	+	1.91524i	0.0897859	+	0.0652333i
$863$	−47.6123	+	15.4702i	−1.62074	+	0.526611i	−0.972116	−	0.234499i	$-0.924655\pi$
$863$	−47.6123	+	15.4702i	−1.62074	+	0.526611i	−0.648624	+	0.761109i	$0.724655\pi$
$864$	−28.4423	−	7.95252i	−0.967628	−	0.270550i
$865$	−8.44670	−	6.13689i	−0.287197	−	0.208661i
$866$	9.28394	−	6.74518i	0.315481	−	0.229211i
$867$	−3.90082	+	6.97768i	−0.132479	+	0.236975i
$868$	10.9617	+	13.4661i	0.372064	+	0.457068i
$869$	−8.00859	−	19.4945i	−0.271673	−	0.661305i
$870$	0.288364	+	0.0571344i	0.00977647	+	0.00193704i
$871$	36.8010	+	11.9574i	1.24696	+	0.405160i
$872$	−1.64913	−	2.26984i	−0.0558467	−	0.0768664i
$873$	−35.8060	+	22.0159i	−1.21185	+	0.745126i
$874$	−0.509765	+	0.165633i	−0.0172431	+	0.00560261i
$875$	−18.7047	−	12.0791i	−0.632334	−	0.408350i
$876$	16.8822	−	15.6292i	0.570396	−	0.528062i
$877$	−9.12186	+	6.62742i	−0.308023	+	0.223792i	−0.731048	−	0.682326i	$-0.760968\pi$
$877$	−9.12186	+	6.62742i	−0.308023	+	0.223792i	0.423025	+	0.906118i	$0.360968\pi$
$878$	4.09138	−	12.5920i	0.138078	−	0.424959i
$879$	−22.7832	−	4.51409i	−0.768457	−	0.152256i
$880$	1.24222	−	5.10877i	0.0418751	−	0.172216i
$881$	7.27220			0.245007			0.122503	−	0.992468i	$-0.460908\pi$
$881$	7.27220			0.245007			0.122503	+	0.992468i	$0.460908\pi$
$882$	10.5726	−	8.22419i	0.355996	−	0.276923i
$883$	33.6795	−	24.4696i	1.13340	−	0.823467i	0.147218	−	0.989104i	$-0.452968\pi$
$883$	33.6795	−	24.4696i	1.13340	−	0.823467i	0.986187	+	0.165637i	$0.0529681\pi$
$884$	21.6010	−	29.7313i	0.726522	−	0.999971i
$885$	1.00328	+	8.42258i	0.0337250	+	0.283122i
$886$	−4.95686	−	15.2557i	−0.166529	−	0.512524i
$887$	−41.7380	−	30.3244i	−1.40142	−	1.01819i	−0.994500	−	0.104732i	$-0.966602\pi$
$887$	−41.7380	−	30.3244i	−1.40142	−	1.01819i	−0.406924	−	0.913462i	$-0.633398\pi$
$888$	−3.21814	−	6.96693i	−0.107994	−	0.233795i
$889$	14.7365	+	38.0987i	0.494246	+	1.27779i
$890$			8.35951i			0.280211i
$891$	22.6997	+	19.3836i	0.760468	+	0.649376i
$892$		−	34.2479i		−	1.14670i
$893$	0.441191	+	0.143352i	0.0147639	+	0.00479708i
$894$	−10.6085	+	4.90025i	−0.354802	+	0.163889i
$895$	9.58453	−	13.1920i	0.320375	−	0.440959i
$896$	−16.1542	+	25.0149i	−0.539674	+	0.835691i
$897$	7.76104	+	65.1540i	0.259134	+	2.17543i
$898$	−0.459217	−	0.333641i	−0.0153243	−	0.0111337i
$899$	−0.964683	+	0.700884i	−0.0321740	+	0.0233758i
$900$	−12.8745	+	15.1200i	−0.429149	+	0.503999i
$901$			39.6962i			1.32247i
$902$	8.93306	−	14.4828i	0.297438	−	0.482224i
$903$	15.3343	−	8.13260i	0.510295	−	0.270636i
$904$	8.06818	−	24.8313i	0.268344	−	0.825877i
$905$	5.10222	+	7.02260i	0.169603	+	0.233439i
$906$	12.4953	−	11.5679i	0.415128	−	0.384318i
$907$	10.7685	+	33.1421i	0.357563	+	1.10046i	0.954509	+	0.298183i	$0.0963806\pi$
$907$	10.7685	+	33.1421i	0.357563	+	1.10046i	−0.596946	+	0.802281i	$0.703619\pi$
$908$	−7.99176	−	24.5961i	−0.265216	−	0.816251i
$909$	20.1993	+	32.8515i	0.669968	+	1.08962i
$910$	−2.60666	+	9.82854i	−0.0864099	+	0.325813i
$911$	3.65800	+	1.18856i	0.121195	+	0.0393786i	0.368987	−	0.929435i	$-0.379705\pi$
$911$	3.65800	+	1.18856i	0.121195	+	0.0393786i	−0.247792	+	0.968813i	$0.579705\pi$
$912$	0.0844076	−	0.426015i	0.00279501	−	0.0141068i
$913$	42.2360	+	26.0514i	1.39781	+	0.862175i
$914$			11.2920i			0.373505i
$915$	4.65677	+	2.60333i	0.153948	+	0.0860633i
$916$	−23.9782	−	33.0032i	−0.792263	−	1.09046i
$917$	24.0091	−	1.31977i	0.792850	−	0.0435825i
$918$	11.2329	+	3.14072i	0.370739	+	0.103659i
$919$	5.63075	+	17.3297i	0.185741	+	0.571653i	0.999960	−	0.00890468i	$-0.00283449\pi$
$919$	5.63075	+	17.3297i	0.185741	+	0.571653i	−0.814219	+	0.580558i	$0.802834\pi$
$920$	9.85066	+	7.15692i	0.324767	+	0.235957i
$921$	−16.7260	−	36.2101i	−0.551141	−	1.19316i
$922$	−4.75119	−	1.54375i	−0.156472	−	0.0508408i
$923$	39.3617			1.29561
$924$	20.4733	−	12.9291i	0.673521	−	0.425335i
$925$	−8.03262			−0.264111
$926$	1.70564	+	0.554197i	0.0560509	+	0.0182120i
$927$	4.29135	+	17.7574i	0.140946	+	0.583228i
$928$	−1.33101	−	0.967038i	−0.0436927	−	0.0317446i
$929$	−8.36150	−	25.7341i	−0.274332	−	0.844307i	−0.989395	−	0.145248i	$-0.953602\pi$
$929$	−8.36150	−	25.7341i	−0.274332	−	0.844307i	0.715063	−	0.699060i	$-0.246398\pi$
$930$	−0.494831	−	4.15411i	−0.0162261	−	0.136218i
$931$	0.684901	+	0.752889i	0.0224467	+	0.0246749i
$932$	−15.3994	−	21.1955i	−0.504426	−	0.694282i
$933$	23.7850	−	42.5460i	0.778686	−	1.39289i
$934$			5.77920i			0.189101i
$935$	−2.53501	+	10.4256i	−0.0829038	+	0.340952i
$936$	41.6628	+	17.1841i	1.36179	+	0.561681i
$937$	5.07987	+	1.65055i	0.165952	+	0.0539212i	0.390815	−	0.920469i	$-0.372193\pi$
$937$	5.07987	+	1.65055i	0.165952	+	0.0539212i	−0.224863	+	0.974391i	$0.572193\pi$
$938$	9.62940	+	2.55385i	0.314411	+	0.0833860i
$939$	16.9874	−	15.7267i	0.554364	−	0.513220i
$940$	−1.44387	−	4.44379i	−0.0470940	−	0.144940i
$941$	−16.0310	−	49.3384i	−0.522597	−	1.60839i	−0.769020	−	0.639225i	$-0.779255\pi$
$941$	−16.0310	−	49.3384i	−0.522597	−	1.60839i	0.246423	−	0.969162i	$-0.420745\pi$
$942$	1.16121	+	1.25430i	0.0378342	+	0.0408673i
$943$	−27.3249	−	37.6095i	−0.889821	−	1.22473i
$944$	2.83890	−	8.73725i	0.0923984	−	0.284373i
$945$	12.5789	−	1.21681i	0.409192	−	0.0395829i
$946$	−7.41174	+	3.04484i	−0.240977	+	0.0989964i
$947$		−	3.70206i		−	0.120301i	−0.998189	−	0.0601504i	$-0.980842\pi$
$947$		−	3.70206i		−	0.120301i	0.998189	−	0.0601504i	$-0.0191580\pi$
$948$	−8.55637	+	15.3054i	−0.277898	+	0.497097i
$949$	−44.2115	+	32.1215i	−1.43516	+	1.04271i
$950$	0.311749	+	0.226499i	0.0101145	+	0.00734859i
$951$	28.8353	−	3.43482i	0.935050	−	0.111382i
$952$	11.5764	−	17.9262i	0.375194	−	0.580992i
$953$	−35.7696	+	49.2327i	−1.15869	+	1.59480i	−0.442744	+	0.896648i	$0.645995\pi$
$953$	−35.7696	+	49.2327i	−1.15869	+	1.59480i	−0.715947	+	0.698154i	$0.754005\pi$
$954$	−20.9804	+	5.07026i	−0.679266	+	0.164156i
$955$	1.42451	+	0.462851i	0.0460960	+	0.0149775i
$956$			17.1082i			0.553319i
$957$	0.809376	+	1.45258i	0.0261634	+	0.0469552i
$958$		−	1.29019i		−	0.0416841i
$959$	24.6796	−	9.54602i	0.796946	−	0.308257i
$960$	0.254831	−	0.117711i	0.00822465	−	0.00379910i
$961$	−11.3512	−	8.24710i	−0.366166	−	0.266036i
$962$	2.49768	+	7.68707i	0.0805285	+	0.247841i
$963$	−28.7919	−	2.22251i	−0.927805	−	0.0716195i
$964$	−16.9943	+	23.3906i	−0.547349	+	0.753361i
$965$	−8.19017	+	5.95051i	−0.263651	+	0.191554i
$966$	2.91582	+	16.6394i	0.0938149	+	0.535365i
$967$	0.0489497			0.00157412			0.000787058	−	1.00000i	$-0.499749\pi$
$967$	0.0489497			0.00157412			0.000787058		1.00000i	$0.499749\pi$
$968$	−22.5288	+	11.3146i	−0.724104	+	0.363664i
$969$	−0.172252	+	0.869377i	−0.00553353	+	0.0279284i
$970$	2.53862	−	7.81306i	0.0815101	−	0.250862i
$971$	13.3361	−	9.68927i	0.427977	−	0.310943i	−0.352863	−	0.935675i	$-0.614792\pi$
$971$	13.3361	−	9.68927i	0.427977	−	0.310943i	0.780839	+	0.624732i	$0.214792\pi$
$972$	0.881937	−	24.8193i	0.0282881	−	0.796078i
$973$	−3.51569	+	5.44408i	−0.112708	+	0.174529i
$974$	14.3151	−	4.65125i	0.458685	−	0.149036i
$975$	34.6154	−	32.0463i	1.10858	−	1.02630i
$976$	−3.39642	−	4.67477i	−0.108717	−	0.149636i
$977$	23.1164	+	7.51097i	0.739559	+	0.240297i	0.654482	−	0.756077i	$-0.272887\pi$
$977$	23.1164	+	7.51097i	0.739559	+	0.240297i	0.0850764	+	0.996374i	$0.472887\pi$
$978$	3.56303	−	17.9830i	0.113933	−	0.575034i
$979$	−36.0455	+	30.6051i	−1.15202	+	0.978143i
$980$	2.08017	−	10.0383i	0.0664487	−	0.320663i
$981$	2.38095	−	2.79622i	0.0760180	−	0.0892764i
$982$	1.95107	−	1.41753i	0.0622610	−	0.0452353i
$983$	−13.6836	−	9.94169i	−0.436438	−	0.317091i	0.347780	−	0.937576i	$-0.386936\pi$
$983$	−13.6836	−	9.94169i	−0.436438	−	0.317091i	−0.784218	+	0.620485i	$0.786936\pi$
$984$	−31.7062	+	3.77679i	−1.01076	+	0.120400i
$985$	−0.531347	+	0.172645i	−0.0169301	+	0.00550093i
$986$	0.525663	+	0.381917i	0.0167405	+	0.0121627i
$987$	6.42313	−	13.1340i	0.204450	−	0.418061i
$988$	−0.469206	+	1.44407i	−0.0149274	+	0.0459419i
$989$			21.8908i			0.696087i
$990$	−5.83395	−	0.00819899i	−0.185415	−	0.000260581i
$991$	13.3982			0.425608			0.212804	−	0.977095i	$-0.431740\pi$
$991$	13.3982			0.425608			0.212804	+	0.977095i	$0.431740\pi$
$992$	−7.23505	+	22.2672i	−0.229713	+	0.706984i
$993$	−7.95991	+	3.67681i	−0.252600	+	0.116680i
$994$	10.1187	−	0.556220i	0.320946	−	0.0176422i
$995$	5.24843	−	1.70532i	0.166386	−	0.0540622i
$996$	−4.88356	−	40.9975i	−0.154742	−	1.29906i
$997$	16.1879	−	22.2807i	0.512674	−	0.705636i	−0.471693	−	0.881763i	$-0.656357\pi$
$997$	16.1879	−	22.2807i	0.512674	−	0.705636i	0.984367	+	0.176127i	$0.0563569\pi$
$998$	−5.68253	−	7.82134i	−0.179877	−	0.247580i
$999$	7.87487	−	6.23683i	0.249150	−	0.197325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.u.a.20.17	yes	112
3.2	odd	2	inner	231.2.u.a.20.12	yes	112
7.6	odd	2	inner	231.2.u.a.20.18	yes	112
11.5	even	5	inner	231.2.u.a.104.11	yes	112
21.20	even	2	inner	231.2.u.a.20.11	✓	112
33.5	odd	10	inner	231.2.u.a.104.18	yes	112
77.27	odd	10	inner	231.2.u.a.104.12	yes	112
231.104	even	10	inner	231.2.u.a.104.17	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.u.a.20.11	✓	112	21.20	even	2	inner
231.2.u.a.20.12	yes	112	3.2	odd	2	inner
231.2.u.a.20.17	yes	112	1.1	even	1	trivial
231.2.u.a.20.18	yes	112	7.6	odd	2	inner
231.2.u.a.104.11	yes	112	11.5	even	5	inner
231.2.u.a.104.12	yes	112	77.27	odd	10	inner
231.2.u.a.104.17	yes	112	231.104	even	10	inner
231.2.u.a.104.18	yes	112	33.5	odd	10	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.606621 + 0.197103i) q^{2} +(-1.57241 + 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(0.284064 + 0.874260i) q^{5} +(-1.09702 + 0.130675i) q^{6} +(-2.64176 + 0.145216i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} +O(q^{10})\)	\(q+(0.606621 + 0.197103i) q^{2} +(-1.57241 + 0.726320i) q^{3} +(-1.28889 - 0.936436i) q^{4} +(0.284064 + 0.874260i) q^{5} +(-1.09702 + 0.130675i) q^{6} +(-2.64176 + 0.145216i) q^{7} +(-1.34712 - 1.85415i) q^{8} +(1.94492 - 2.28414i) q^{9} +0.586335i q^{10} +(-2.52823 + 2.14664i) q^{11} +(2.70682 + 0.536309i) q^{12} +(-6.23392 - 2.02552i) q^{13} +(-1.63117 - 0.432609i) q^{14} +(-1.08166 - 1.16837i) q^{15} +(0.532894 + 1.64008i) q^{16} +(-1.08749 - 3.34694i) q^{17} +(1.63004 - 1.00226i) q^{18} +(0.0854645 + 0.117632i) q^{19} +(0.452560 - 1.39284i) q^{20} +(4.04845 - 2.14710i) q^{21} +(-1.95679 + 0.803875i) q^{22} +5.77943i q^{23} +(3.46493 + 1.93704i) q^{24} +(3.36145 - 2.44223i) q^{25} +(-3.38239 - 2.45745i) q^{26} +(-1.39919 + 5.00423i) q^{27} +(3.54094 + 2.28667i) q^{28} +(-0.170143 + 0.234182i) q^{29} +(-0.425867 - 0.921956i) q^{30} +(3.91775 + 1.27295i) q^{31} +5.68366i q^{32} +(2.41626 - 5.21169i) q^{33} -2.24467i q^{34} +(-0.877387 - 2.26834i) q^{35} +(-4.64575 + 1.12272i) q^{36} +(-1.56403 - 1.13634i) q^{37} +(0.0286590 + 0.0882033i) q^{38} +(11.2734 - 1.34287i) q^{39} +(1.23834 - 1.70443i) q^{40} +(-6.50747 + 4.72795i) q^{41} +(2.87908 - 0.504516i) q^{42} +3.78771 q^{43} +(5.26881 - 0.399264i) q^{44} +(2.54941 + 1.05152i) q^{45} +(-1.13914 + 3.50593i) q^{46} +(2.58114 - 1.87530i) q^{47} +(-2.02915 - 2.19182i) q^{48} +(6.95782 - 0.767254i) q^{49} +(2.52050 - 0.818960i) q^{50} +(4.14092 + 4.47289i) q^{51} +(6.13808 + 8.44835i) q^{52} +(-10.7279 - 3.48570i) q^{53} +(-1.83513 + 2.75989i) q^{54} +(-2.59490 - 1.60055i) q^{55} +(3.82803 + 4.70261i) q^{56} +(-0.219823 - 0.122890i) q^{57} +(-0.149371 + 0.108524i) q^{58} +(-4.30990 - 3.13133i) q^{59} +(0.300037 + 2.51881i) q^{60} +(-3.18676 + 1.03544i) q^{61} +(2.12569 + 1.54440i) q^{62} +(-4.80632 + 6.31659i) q^{63} +(-0.0544799 + 0.167672i) q^{64} -6.02544i q^{65} +(2.49299 - 2.68527i) q^{66} -5.90336 q^{67} +(-1.73254 + 5.33222i) q^{68} +(-4.19771 - 9.08761i) q^{69} +(-0.0851453 - 1.54896i) q^{70} +(-5.71118 + 1.85568i) q^{71} +(-6.85519 - 0.529168i) q^{72} +(4.90051 - 6.74497i) q^{73} +(-0.724801 - 0.997603i) q^{74} +(-3.51172 + 6.28167i) q^{75} -0.231647i q^{76} +(6.36726 - 6.03805i) q^{77} +(7.10338 + 1.40741i) q^{78} +(-1.96364 + 6.04346i) q^{79} +(-1.28248 + 0.931776i) q^{80} +(-1.43457 - 8.88493i) q^{81} +(-4.87947 + 1.58544i) q^{82} +(-4.62359 - 14.2299i) q^{83} +(-7.22865 - 1.02373i) q^{84} +(2.61718 - 1.90149i) q^{85} +(2.29771 + 0.746570i) q^{86} +(0.0974433 - 0.491808i) q^{87} +(7.38603 + 1.79594i) q^{88} +14.2572 q^{89} +(1.33927 + 1.14037i) q^{90} +(16.7627 + 4.44568i) q^{91} +(5.41207 - 7.44907i) q^{92} +(-7.08487 + 0.843939i) q^{93} +(1.93540 - 0.628850i) q^{94} +(-0.0785634 + 0.108133i) q^{95} +(-4.12816 - 8.93702i) q^{96} +(-13.3252 - 4.32964i) q^{97} +(4.37199 + 0.905977i) q^{98} +(-0.0139835 + 9.94986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

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