LMFDB - Embedded newform 693.2.j.f.232.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(232,693)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("693.232"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(693, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 11 x^{16} - 12 x^{15} + 83 x^{14} - 88 x^{13} + 337 x^{12} - 336 x^{11} + 966 x^{10} + \cdots + 4 $ x^18 - x^17 + 11x^16 - 12x^15 + 83x^14 - 88x^13 + 337x^12 - 336x^11 + 966x^10 - 828x^9 + 1343x^8 - 646x^7 + 895x^6 - 371x^5 + 373x^4 - 60x^3 + 42*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			232.1
Root			$1.10861 - 1.92017i$ of defining polynomial
Character	$\chi$	$=$	693.232
Dual form			693.2.j.f.463.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10861 + 1.92017i) q^{2} +(0.386186 - 1.68845i) q^{3} +(-1.45802 - 2.52537i) q^{4} +(0.197834 + 0.342659i) q^{5} +(2.81397 + 2.61337i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.03107 q^{8} +(-2.70172 - 1.30411i) q^{9} -0.877282 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-4.82702 + 1.48653i) q^{12} +(1.29696 + 2.24640i) q^{13} +(-1.10861 - 1.92017i) q^{14} +(0.654963 - 0.201703i) q^{15} +(0.664386 - 1.15075i) q^{16} -3.07406 q^{17} +(5.49926 - 3.74200i) q^{18} -3.72212 q^{19} +(0.576893 - 0.999209i) q^{20} +(1.26915 + 1.17867i) q^{21} +(-1.10861 - 1.92017i) q^{22} +(4.64146 + 8.03925i) q^{23} +(0.784370 - 3.42936i) q^{24} +(2.42172 - 4.19455i) q^{25} -5.75128 q^{26} +(-3.24529 + 4.05809i) q^{27} +2.91604 q^{28} +(-3.90081 + 6.75641i) q^{29} +(-0.338794 + 1.48125i) q^{30} +(-1.26962 - 2.19905i) q^{31} +(3.50416 + 6.06938i) q^{32} +(1.26915 + 1.17867i) q^{33} +(3.40792 - 5.90270i) q^{34} -0.395668 q^{35} +(0.645809 + 8.72426i) q^{36} -8.16157 q^{37} +(4.12637 - 7.14708i) q^{38} +(4.29380 - 1.32232i) q^{39} +(0.401815 + 0.695964i) q^{40} +(4.60133 + 7.96974i) q^{41} +(-3.67023 + 1.13029i) q^{42} +(-2.30102 + 3.98548i) q^{43} +2.91604 q^{44} +(-0.0876277 - 1.18377i) q^{45} -20.5822 q^{46} +(-3.60794 + 6.24913i) q^{47} +(-1.68641 - 1.56619i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(5.36948 + 9.30022i) q^{50} +(-1.18716 + 5.19039i) q^{51} +(3.78199 - 6.55060i) q^{52} -9.08450 q^{53} +(-4.19445 - 10.7303i) q^{54} -0.395668 q^{55} +(-1.01553 + 1.75896i) q^{56} +(-1.43743 + 6.28461i) q^{57} +(-8.64895 - 14.9804i) q^{58} +(-4.94818 - 8.57050i) q^{59} +(-1.46433 - 1.35994i) q^{60} +(-3.28199 + 5.68457i) q^{61} +5.63005 q^{62} +(2.48025 - 1.68770i) q^{63} -12.8814 q^{64} +(-0.513166 + 0.888829i) q^{65} +(-3.67023 + 1.13029i) q^{66} +(5.07368 + 8.78787i) q^{67} +(4.48204 + 7.76313i) q^{68} +(15.3663 - 4.73223i) q^{69} +(0.438641 - 0.759749i) q^{70} -10.0289 q^{71} +(-5.48738 - 2.64874i) q^{72} +6.77635 q^{73} +(9.04798 - 15.6716i) q^{74} +(-6.14704 - 5.70883i) q^{75} +(5.42693 + 9.39972i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(-2.22106 + 9.71074i) q^{78} +(2.66476 - 4.61550i) q^{79} +0.525753 q^{80} +(5.59859 + 7.04669i) q^{81} -20.4043 q^{82} +(7.92859 - 13.7327i) q^{83} +(1.12614 - 4.92359i) q^{84} +(-0.608154 - 1.05335i) q^{85} +(-5.10185 - 8.83667i) q^{86} +(9.90141 + 9.19556i) q^{87} +(-1.01553 + 1.75896i) q^{88} +10.0445 q^{89} +(2.37017 + 1.14407i) q^{90} -2.59392 q^{91} +(13.5347 - 23.4428i) q^{92} +(-4.20330 + 1.29445i) q^{93} +(-7.99957 - 13.8557i) q^{94} +(-0.736362 - 1.27542i) q^{95} +(11.6011 - 3.57268i) q^{96} +(5.65281 - 9.79096i) q^{97} +2.21722 q^{98} +(2.48025 - 1.68770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{2} + q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} - 9 q^{7} - 12 q^{8} - 5 q^{9} - 26 q^{10} - 9 q^{11} - 5 q^{12} + 8 q^{13} - q^{14} + 16 q^{15} + 5 q^{16} - 28 q^{17} - 16 q^{18} - 24 q^{19} - 19 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) $ 18 * q - q^2 + q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 - 9 * q^7 - 12 * q^8 - 5 * q^9 - 26 * q^10 - 9 * q^11 - 5 * q^12 + 8 * q^13 - q^14 + 16 * q^15 + 5 * q^16 - 28 * q^17 - 16 * q^18 - 24 * q^19 - 19 * q^20 + q^21 - q^22 + 19 * q^23 - 6 * q^24 + q^25 - 20 * q^26 - 14 * q^27 + 6 * q^28 + 12 * q^29 + 2 * q^30 + 3 * q^31 - 4 * q^32 + q^33 + 12 * q^35 - 8 * q^36 - 38 * q^37 + 20 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 - 4 * q^42 + 32 * q^43 + 6 * q^44 + 22 * q^45 - 4 * q^46 - 8 * q^47 - 21 * q^48 - 9 * q^49 + 18 * q^50 - 3 * q^51 + 4 * q^52 + 30 * q^53 + 35 * q^54 + 12 * q^55 + 6 * q^56 + 18 * q^57 + 3 * q^58 - 8 * q^59 - 5 * q^60 + 2 * q^61 + 24 * q^62 + 10 * q^63 - 68 * q^64 + 20 * q^65 - 4 * q^66 + 49 * q^67 + 46 * q^68 - q^69 + 13 * q^70 - 18 * q^71 + 27 * q^72 - 70 * q^73 - 19 * q^74 - 34 * q^75 + 25 * q^76 - 9 * q^77 + 2 * q^78 + 21 * q^79 - 52 * q^80 + 19 * q^81 - 20 * q^82 + 16 * q^83 - 11 * q^84 + 52 * q^85 - 31 * q^86 - 28 * q^87 + 6 * q^88 + 38 * q^89 + 20 * q^90 - 16 * q^91 + 32 * q^92 + 18 * q^93 - 50 * q^94 - 4 * q^95 + 18 * q^96 + 24 * q^97 + 2 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.10861	+	1.92017i	−0.783904	+	1.35776i	0.145747	+	0.989322i	$0.453441\pi$
$2$	−1.10861	+	1.92017i	−0.783904	+	1.35776i	−0.929652	+	0.368440i	$0.879892\pi$
$3$	0.386186	−	1.68845i	0.222965	−	0.974827i
$3$	0.386186	−	1.68845i	0.222965	−	0.974827i
$4$	−1.45802	−	2.52537i	−0.729011	−	1.26268i
$5$	0.197834	+	0.342659i	0.0884741	+	0.153242i	0.906866	−	0.421418i	$-0.138468\pi$
$5$	0.197834	+	0.342659i	0.0884741	+	0.153242i	−0.818392	+	0.574660i	$0.805134\pi$
$6$	2.81397	+	2.61337i	1.14880	+	1.06690i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	2.03107			0.718091
$9$	−2.70172	−	1.30411i	−0.900574	−	0.434704i
$10$	−0.877282			−0.277421
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−4.82702	+	1.48653i	−1.39344	+	0.429126i
$13$	1.29696	+	2.24640i	0.359712	+	0.623039i	0.987913	−	0.155012i	$-0.0495417\pi$
$13$	1.29696	+	2.24640i	0.359712	+	0.623039i	−0.628201	+	0.778051i	$0.716208\pi$
$14$	−1.10861	−	1.92017i	−0.296288	−	0.513186i
$15$	0.654963	−	0.201703i	0.169111	−	0.0520795i
$16$	0.664386	−	1.15075i	0.166096	−	0.287688i
$17$	−3.07406			−0.745568			−0.372784	−	0.927918i	$-0.621597\pi$
$17$	−3.07406			−0.745568			−0.372784	+	0.927918i	$0.621597\pi$
$18$	5.49926	−	3.74200i	1.29619	−	0.881999i
$19$	−3.72212			−0.853912			−0.426956	−	0.904272i	$-0.640414\pi$
$19$	−3.72212			−0.853912			−0.426956	+	0.904272i	$0.640414\pi$
$20$	0.576893	−	0.999209i	0.128997	−	0.223430i
$21$	1.26915	+	1.17867i	0.276951	+	0.257207i
$22$	−1.10861	−	1.92017i	−0.236356	−	0.409381i
$23$	4.64146	+	8.03925i	0.967812	+	1.67630i	0.701863	+	0.712312i	$0.252352\pi$
$23$	4.64146	+	8.03925i	0.967812	+	1.67630i	0.265949	+	0.963987i	$0.414315\pi$
$24$	0.784370	−	3.42936i	0.160109	−	0.700015i
$25$	2.42172	−	4.19455i	0.484345	−	0.838910i
$26$	−5.75128			−1.12792
$27$	−3.24529	+	4.05809i	−0.624557	+	0.780980i
$28$	2.91604			0.551081
$29$	−3.90081	+	6.75641i	−0.724363	+	1.25463i	0.234872	+	0.972026i	$0.424533\pi$
$29$	−3.90081	+	6.75641i	−0.724363	+	1.25463i	−0.959236	+	0.282608i	$0.908801\pi$
$30$	−0.338794	+	1.48125i	−0.0618550	+	0.270437i
$31$	−1.26962	−	2.19905i	−0.228031	−	0.394961i	0.729194	−	0.684308i	$-0.239895\pi$
$31$	−1.26962	−	2.19905i	−0.228031	−	0.394961i	−0.957224	+	0.289346i	$0.906562\pi$
$32$	3.50416	+	6.06938i	0.619453	+	1.07292i
$33$	1.26915	+	1.17867i	0.220930	+	0.205180i
$34$	3.40792	−	5.90270i	0.584454	−	1.01230i
$35$	−0.395668			−0.0668802
$36$	0.645809	+	8.72426i	0.107635	+	1.45404i
$37$	−8.16157			−1.34175			−0.670877	−	0.741568i	$-0.734082\pi$
$37$	−8.16157			−1.34175			−0.670877	+	0.741568i	$0.734082\pi$
$38$	4.12637	−	7.14708i	0.669385	−	1.15941i
$39$	4.29380	−	1.32232i	0.687558	−	0.211741i
$40$	0.401815	+	0.695964i	0.0635325	+	0.110042i
$41$	4.60133	+	7.96974i	0.718607	+	1.24466i	0.961552	+	0.274624i	$0.0885533\pi$
$41$	4.60133	+	7.96974i	0.718607	+	1.24466i	−0.242945	+	0.970040i	$0.578113\pi$
$42$	−3.67023	+	1.13029i	−0.566329	+	0.174407i
$43$	−2.30102	+	3.98548i	−0.350902	+	0.607780i	−0.986408	−	0.164316i	$-0.947458\pi$
$43$	−2.30102	+	3.98548i	−0.350902	+	0.607780i	0.635506	+	0.772096i	$0.280792\pi$
$44$	2.91604			0.439610
$45$	−0.0876277	−	1.18377i	−0.0130628	−	0.176465i
$46$	−20.5822			−3.03469
$47$	−3.60794	+	6.24913i	−0.526272	+	0.911529i	0.473260	+	0.880923i	$0.343077\pi$
$47$	−3.60794	+	6.24913i	−0.526272	+	0.911529i	−0.999532	+	0.0306064i	$0.990256\pi$
$48$	−1.68641	−	1.56619i	−0.243412	−	0.226059i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	5.36948	+	9.30022i	0.759360	+	1.31525i
$51$	−1.18716	+	5.19039i	−0.166235	+	0.726800i
$52$	3.78199	−	6.55060i	0.524468	−	0.908405i
$53$	−9.08450			−1.24785			−0.623926	−	0.781484i	$-0.714463\pi$
$53$	−9.08450			−1.24785			−0.623926	+	0.781484i	$0.714463\pi$
$54$	−4.19445	−	10.7303i	−0.570792	−	1.46021i
$55$	−0.395668			−0.0533519
$56$	−1.01553	+	1.75896i	−0.135707	+	0.235051i
$57$	−1.43743	+	6.28461i	−0.190392	+	0.832416i
$58$	−8.64895	−	14.9804i	−1.13566	−	1.96703i
$59$	−4.94818	−	8.57050i	−0.644198	−	1.11578i	−0.984486	−	0.175462i	$-0.943858\pi$
$59$	−4.94818	−	8.57050i	−0.644198	−	1.11578i	0.340288	−	0.940321i	$-0.389475\pi$
$60$	−1.46433	−	1.35994i	−0.189044	−	0.175567i
$61$	−3.28199	+	5.68457i	−0.420215	+	0.727835i	−0.995960	−	0.0897949i	$-0.971379\pi$
$61$	−3.28199	+	5.68457i	−0.420215	+	0.727835i	0.575745	+	0.817629i	$0.304712\pi$
$62$	5.63005			0.715018
$63$	2.48025	−	1.68770i	0.312483	−	0.212631i
$64$	−12.8814			−1.61017
$65$	−0.513166	+	0.888829i	−0.0636504	+	0.110246i
$66$	−3.67023	+	1.13029i	−0.451774	+	0.139129i
$67$	5.07368	+	8.78787i	0.619849	+	1.07361i	0.989513	+	0.144444i	$0.0461394\pi$
$67$	5.07368	+	8.78787i	0.619849	+	1.07361i	−0.369664	+	0.929165i	$0.620527\pi$
$68$	4.48204	+	7.76313i	0.543528	+	0.941417i
$69$	15.3663	−	4.73223i	1.84989	−	0.569693i
$70$	0.438641	−	0.759749i	0.0524276	−	0.0908073i
$71$	−10.0289			−1.19021			−0.595106	−	0.803647i	$-0.702890\pi$
$71$	−10.0289			−1.19021			−0.595106	+	0.803647i	$0.702890\pi$
$72$	−5.48738	−	2.64874i	−0.646694	−	0.312157i
$73$	6.77635			0.793112			0.396556	−	0.918011i	$-0.370205\pi$
$73$	6.77635			0.793112			0.396556	+	0.918011i	$0.370205\pi$
$74$	9.04798	−	15.6716i	1.05181	−	1.82178i
$75$	−6.14704	−	5.70883i	−0.709800	−	0.659199i
$76$	5.42693	+	9.39972i	0.622512	+	1.07822i
$77$	−0.500000	−	0.866025i	−0.0569803	−	0.0986928i
$78$	−2.22106	+	9.71074i	−0.251486	+	1.09952i
$79$	2.66476	−	4.61550i	0.299809	−	0.519285i	−0.676283	−	0.736642i	$-0.736410\pi$
$79$	2.66476	−	4.61550i	0.299809	−	0.519285i	0.976092	+	0.217357i	$0.0697437\pi$
$80$	0.525753			0.0587810
$81$	5.59859	+	7.04669i	0.622066	+	0.782965i
$82$	−20.4043			−2.25328
$83$	7.92859	−	13.7327i	0.870276	−	1.50736i	0.00856400	−	0.999963i	$-0.497274\pi$
$83$	7.92859	−	13.7327i	0.870276	−	1.50736i	0.861712	−	0.507398i	$-0.169393\pi$
$84$	1.12614	−	4.92359i	0.122871	−	0.537208i
$85$	−0.608154	−	1.05335i	−0.0659635	−	0.114252i
$86$	−5.10185	−	8.83667i	−0.550147	−	0.952882i
$87$	9.90141	+	9.19556i	1.06154	+	0.985867i
$88$	−1.01553	+	1.75896i	−0.108256	+	0.187505i
$89$	10.0445			1.06472			0.532359	−	0.846519i	$-0.321306\pi$
$89$	10.0445			1.06472			0.532359	+	0.846519i	$0.321306\pi$
$90$	2.37017	+	1.14407i	0.249838	+	0.120596i
$91$	−2.59392			−0.271917
$92$	13.5347	−	23.4428i	1.41109	−	2.44408i
$93$	−4.20330	+	1.29445i	−0.435862	+	0.134228i
$94$	−7.99957	−	13.8557i	−0.825093	−	1.42910i
$95$	−0.736362	−	1.27542i	−0.0755492	−	0.130855i
$96$	11.6011	−	3.57268i	1.18403	−	0.364635i
$97$	5.65281	−	9.79096i	0.573956	−	0.994121i	−0.422198	−	0.906504i	$-0.638741\pi$
$97$	5.65281	−	9.79096i	0.573956	−	0.994121i	0.996154	−	0.0876176i	$-0.0279254\pi$
$98$	2.21722			0.223973
$99$	2.48025	−	1.68770i	0.249275	−	0.169621i
$100$	−14.1237			−1.41237
$101$	−9.18884	+	15.9155i	−0.914324	+	1.58366i	−0.106436	+	0.994320i	$0.533944\pi$
$101$	−9.18884	+	15.9155i	−0.914324	+	1.58366i	−0.807888	+	0.589336i	$0.799389\pi$
$102$	−8.65031	−	8.03364i	−0.856508	−	0.795449i
$103$	−3.61136	−	6.25506i	−0.355838	−	0.616329i	0.631423	−	0.775438i	$-0.282471\pi$
$103$	−3.61136	−	6.25506i	−0.355838	−	0.616329i	−0.987261	+	0.159109i	$0.949138\pi$
$104$	2.63421	+	4.56259i	0.258306	+	0.447399i
$105$	−0.152802	+	0.668066i	−0.0149119	+	0.0651966i
$106$	10.0711	−	17.4437i	0.978196	−	1.69429i
$107$	7.77578			0.751713			0.375856	−	0.926678i	$-0.377349\pi$
$107$	7.77578			0.751713			0.375856	+	0.926678i	$0.377349\pi$
$108$	14.9799	+	2.27877i	1.44144	+	0.219275i
$109$	−1.16616			−0.111698			−0.0558489	−	0.998439i	$-0.517787\pi$
$109$	−1.16616			−0.111698			−0.0558489	+	0.998439i	$0.517787\pi$
$110$	0.438641	−	0.759749i	0.0418228	−	0.0724392i
$111$	−3.15188	+	13.7804i	−0.299164	+	1.30798i
$112$	0.664386	+	1.15075i	0.0627786	+	0.108736i
$113$	−0.836105	−	1.44818i	−0.0786542	−	0.136233i	0.824015	−	0.566568i	$-0.191729\pi$
$113$	−0.836105	−	1.44818i	−0.0786542	−	0.136233i	−0.902670	+	0.430334i	$0.858396\pi$
$114$	−10.4739	−	9.72726i	−0.980974	−	0.911042i
$115$	−1.83648	+	3.18088i	−0.171253	+	0.296618i
$116$	22.7499			2.11228
$117$	−0.574469	−	7.76052i	−0.0531097	−	0.717461i
$118$	21.9424			2.01996
$119$	1.53703	−	2.66221i	0.140899	−	0.244044i
$120$	1.33027	−	0.409673i	0.121437	−	0.0373978i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−7.27687	−	12.6039i	−0.658817	−	1.14110i
$123$	15.2335	−	4.69131i	1.37356	−	0.423001i
$124$	−3.70228	+	6.41253i	−0.332474	+	0.575862i
$125$	3.89474			0.348356
$126$	0.491041	+	6.63350i	0.0437454	+	0.590959i
$127$	−14.3277			−1.27138			−0.635690	−	0.771944i	$-0.719284\pi$
$127$	−14.3277			−1.27138			−0.635690	+	0.771944i	$0.719284\pi$
$128$	7.27210	−	12.5957i	0.642769	−	1.11331i
$129$	5.84066	+	5.42429i	0.514241	+	0.477582i
$130$	−1.13780	−	1.97073i	−0.0997916	−	0.172844i
$131$	−9.15453	−	15.8561i	−0.799835	−	1.38536i	−0.919723	−	0.392568i	$-0.871587\pi$
$131$	−9.15453	−	15.8561i	−0.799835	−	1.38536i	0.119888	−	0.992787i	$-0.461746\pi$
$132$	1.12614	−	4.92359i	0.0980175	−	0.428544i
$133$	1.86106	−	3.22345i	0.161374	−	0.279508i
$134$	−22.4989			−1.94361
$135$	−2.03257	−	0.309199i	−0.174936	−	0.0266116i
$136$	−6.24362			−0.535386
$137$	0.499835	−	0.865740i	0.0427038	−	0.0739652i	−0.843883	−	0.536526i	$-0.819736\pi$
$137$	0.499835	−	0.865740i	0.0427038	−	0.0739652i	0.886587	+	0.462561i	$0.153069\pi$
$138$	−7.94857	+	34.7521i	−0.676628	+	2.95829i
$139$	0.581523	+	1.00723i	0.0493241	+	0.0854319i	0.889633	−	0.456675i	$-0.150960\pi$
$139$	0.581523	+	1.00723i	0.0493241	+	0.0854319i	−0.840309	+	0.542107i	$0.817627\pi$
$140$	0.576893	+	0.999209i	0.0487564	+	0.0844486i
$141$	9.15800	+	8.50514i	0.771243	+	0.716262i
$142$	11.1181	−	19.2572i	0.933012	−	1.61602i
$143$	−2.59392			−0.216914
$144$	−3.29569	+	2.24257i	−0.274641	+	0.186881i
$145$	−3.08686			−0.256350
$146$	−7.51232	+	13.0117i	−0.621724	+	1.07686i
$147$	−1.65533	+	0.509778i	−0.136530	+	0.0420458i
$148$	11.8998	+	20.6110i	0.978154	+	1.69421i
$149$	6.33940	+	10.9802i	0.519343	+	0.899529i	0.999747	+	0.0224819i	$0.00715680\pi$
$149$	6.33940	+	10.9802i	0.519343	+	0.899529i	−0.480404	+	0.877047i	$0.659510\pi$
$150$	17.7766	−	5.47449i	1.45145	−	0.446990i
$151$	−6.19310	+	10.7268i	−0.503987	+	0.872932i	0.496002	+	0.868321i	$0.334801\pi$
$151$	−6.19310	+	10.7268i	−0.503987	+	0.872932i	−0.999989	+	0.00461040i	$0.998532\pi$
$152$	−7.55988			−0.613187
$153$	8.30524	+	4.00891i	0.671439	+	0.324101i
$154$	2.21722			0.178668
$155$	0.502350	−	0.870095i	0.0403497	−	0.0698877i
$156$	−9.59981	−	8.91545i	−0.768600	−	0.713807i
$157$	9.41654	+	16.3099i	0.751521	+	1.30167i	0.947085	+	0.320982i	$0.104013\pi$
$157$	9.41654	+	16.3099i	0.751521	+	1.30167i	−0.195564	+	0.980691i	$0.562654\pi$
$158$	5.90835	+	10.2336i	0.470043	+	0.814139i
$159$	−3.50830	+	15.3387i	−0.278227	+	1.21644i
$160$	−1.38648	+	2.40146i	−0.109611	+	0.189852i
$161$	−9.28293			−0.731597
$162$	−19.7374	+	2.93821i	−1.55072	+	0.230848i
$163$	8.32185			0.651818			0.325909	−	0.945401i	$-0.394330\pi$
$163$	8.32185			0.651818			0.325909	+	0.945401i	$0.394330\pi$
$164$	13.4177	−	23.2401i	1.04775	−	1.81475i
$165$	−0.152802	+	0.668066i	−0.0118956	+	0.0520089i
$166$	17.5794	+	30.4484i	1.36443	+	2.36325i
$167$	2.57387	+	4.45808i	0.199172	+	0.344976i	0.948260	−	0.317494i	$-0.102841\pi$
$167$	2.57387	+	4.45808i	0.199172	+	0.344976i	−0.749088	+	0.662470i	$0.769508\pi$
$168$	2.57773	+	2.39396i	0.198876	+	0.184698i
$169$	3.13579	−	5.43135i	0.241215	−	0.417796i
$170$	2.69682			0.206836
$171$	10.0561	+	4.85405i	0.769011	+	0.371199i
$172$	13.4197			1.02325
$173$	−0.637649	+	1.10444i	−0.0484796	+	0.0839691i	−0.889247	−	0.457428i	$-0.848771\pi$
$173$	−0.637649	+	1.10444i	−0.0484796	+	0.0839691i	0.840767	+	0.541397i	$0.182104\pi$
$174$	−28.6338	+	8.81808i	−2.17072	+	0.668497i
$175$	2.42172	+	4.19455i	0.183065	+	0.317078i
$176$	0.664386	+	1.15075i	0.0500800	+	0.0867411i
$177$	−16.3818	+	5.04494i	−1.23133	+	0.379201i
$178$	−11.1354	+	19.2871i	−0.834636	+	1.44563i
$179$	6.77748			0.506573			0.253286	−	0.967391i	$-0.418488\pi$
$179$	6.77748			0.506573			0.253286	+	0.967391i	$0.418488\pi$
$180$	−2.86168	+	1.94725i	−0.213297	+	0.145139i
$181$	10.6037			0.788170			0.394085	−	0.919074i	$-0.371062\pi$
$181$	10.6037			0.788170			0.394085	+	0.919074i	$0.371062\pi$
$182$	2.87564	−	4.98075i	0.213157	−	0.369198i
$183$	8.33065	+	7.73677i	0.615819	+	0.571918i
$184$	9.42713	+	16.3283i	0.694977	+	1.20374i
$185$	−1.61464	−	2.79664i	−0.118711	−	0.205613i
$186$	2.17425	−	9.50606i	0.159424	−	0.697018i
$187$	1.53703	−	2.66221i	0.112399	−	0.194680i
$188$	21.0418			1.53463
$189$	−1.89176	−	4.83955i	−0.137605	−	0.352025i
$190$	3.26535			0.236893
$191$	−6.27589	+	10.8702i	−0.454107	+	0.786537i	−0.998636	−	0.0522049i	$-0.983375\pi$
$191$	−6.27589	+	10.8702i	−0.454107	+	0.786537i	0.544529	+	0.838742i	$0.316708\pi$
$192$	−4.97461	+	21.7496i	−0.359012	+	1.56964i
$193$	−2.12627	−	3.68281i	−0.153052	−	0.265094i	0.779296	−	0.626656i	$-0.215577\pi$
$193$	−2.12627	−	3.68281i	−0.153052	−	0.265094i	−0.932348	+	0.361562i	$0.882244\pi$
$194$	12.5335	+	21.7087i	0.899853	+	1.55859i
$195$	1.30257	+	1.20971i	0.0932787	+	0.0866290i
$196$	−1.45802	+	2.52537i	−0.104144	+	0.180383i
$197$	4.43489			0.315973			0.157986	−	0.987441i	$-0.449500\pi$
$197$	4.43489			0.315973			0.157986	+	0.987441i	$0.449500\pi$
$198$	0.491041	+	6.63350i	0.0348968	+	0.471422i
$199$	3.60190			0.255332			0.127666	−	0.991817i	$-0.459251\pi$
$199$	3.60190			0.255332			0.127666	+	0.991817i	$0.459251\pi$
$200$	4.91869	−	8.51942i	0.347804	−	0.602414i
$201$	16.7973	−	5.17290i	1.18479	−	0.364868i
$202$	−20.3736	−	35.2882i	−1.43348	−	2.48287i
$203$	−3.90081	−	6.75641i	−0.273784	−	0.474207i
$204$	14.8385	−	4.56969i	1.03891	−	0.319942i
$205$	−1.82060	+	3.15337i	−0.127156	+	0.220241i
$206$	16.0143			1.11577
$207$	−2.05587	−	27.7728i	−0.142893	−	1.93034i
$208$	3.44673			0.238987
$209$	1.86106	−	3.22345i	0.128732	−	0.222971i
$210$	−1.11340	−	1.03403i	−0.0768319	−	0.0713547i
$211$	−7.03107	−	12.1782i	−0.484039	−	0.838380i	0.515793	−	0.856713i	$-0.327497\pi$
$211$	−7.03107	−	12.1782i	−0.484039	−	0.838380i	−0.999832	+	0.0183331i	$0.994164\pi$
$212$	13.2454	+	22.9417i	0.909698	+	1.57564i
$213$	−3.87302	+	16.9333i	−0.265375	+	1.16025i
$214$	−8.62029	+	14.9308i	−0.589271	+	1.02065i
$215$	−1.82088			−0.124183
$216$	−6.59141	+	8.24226i	−0.448489	+	0.560815i
$217$	2.53925			0.172375
$218$	1.29281	−	2.23922i	0.0875604	−	0.151659i
$219$	2.61693	−	11.4415i	0.176836	−	0.773147i
$220$	0.576893	+	0.999209i	0.0388941	+	0.0673666i
$221$	−3.98693	−	6.90556i	−0.268190	−	0.464518i
$222$	−22.9664	−	21.3292i	−1.54141	−	1.43152i
$223$	9.11992	−	15.7962i	0.610715	−	1.05779i	−0.380405	−	0.924820i	$-0.624216\pi$
$223$	9.11992	−	15.7962i	0.610715	−	1.05779i	0.991120	−	0.132969i	$-0.0424511\pi$
$224$	−7.00831			−0.468263
$225$	−12.0130	+	8.17430i	−0.800865	+	0.544953i
$226$	3.70765			0.246629
$227$	6.04128	−	10.4638i	0.400974	−	0.694507i	−0.592870	−	0.805298i	$-0.702005\pi$
$227$	6.04128	−	10.4638i	0.400974	−	0.694507i	0.993844	+	0.110791i	$0.0353385\pi$
$228$	17.9668	−	5.53306i	1.18988	−	0.366436i
$229$	13.5376	+	23.4478i	0.894590	+	1.54948i	0.834311	+	0.551294i	$0.185866\pi$
$229$	13.5376	+	23.4478i	0.894590	+	1.54948i	0.0602793	+	0.998182i	$0.480801\pi$
$230$	−4.07187	−	7.05269i	−0.268491	−	0.465041i
$231$	−1.65533	+	0.509778i	−0.108913	+	0.0335409i
$232$	−7.92282	+	13.7227i	−0.520159	+	0.900942i
$233$	−0.215784			−0.0141365			−0.00706823	−	0.999975i	$-0.502250\pi$
$233$	−0.215784			−0.0141365			−0.00706823	+	0.999975i	$0.502250\pi$
$234$	15.5383	+	7.50030i	1.01577	+	0.490310i
$235$	−2.85509			−0.186246
$236$	−14.4291	+	24.9919i	−0.939255	+	1.62684i
$237$	−6.76395	−	6.28176i	−0.439366	−	0.408044i
$238$	3.40792	+	5.90270i	0.220903	+	0.382615i
$239$	−15.1070	−	26.1660i	−0.977188	−	1.69254i	−0.672517	−	0.740081i	$-0.734787\pi$
$239$	−15.1070	−	26.1660i	−0.977188	−	1.69254i	−0.304670	−	0.952458i	$-0.598546\pi$
$240$	0.203038	−	0.887707i	0.0131061	−	0.0573013i
$241$	4.45115	−	7.70962i	0.286724	−	0.496621i	−0.686302	−	0.727317i	$-0.740767\pi$
$241$	4.45115	−	7.70962i	0.286724	−	0.496621i	0.973026	+	0.230696i	$0.0741004\pi$
$242$	2.21722			0.142528
$243$	14.0601	−	6.73161i	0.901954	−	0.431833i
$244$	19.1408			1.22537
$245$	0.197834	−	0.342659i	0.0126392	−	0.0218917i
$246$	−7.87985	+	34.4516i	−0.502401	+	2.19655i
$247$	−4.82744	−	8.36136i	−0.307162	−	0.532021i
$248$	−2.57869	−	4.46642i	−0.163747	−	0.283618i
$249$	−20.1251	−	18.6904i	−1.27538	−	1.18446i
$250$	−4.31774	+	7.47855i	−0.273078	+	0.472985i
$251$	−19.3184			−1.21937			−0.609683	−	0.792645i	$-0.708703\pi$
$251$	−19.3184			−1.21937			−0.609683	+	0.792645i	$0.708703\pi$
$252$	−7.87834	−	3.80284i	−0.496289	−	0.239557i
$253$	−9.28293			−0.583613
$254$	15.8838	−	27.5116i	0.996640	−	1.72623i
$255$	−2.01339	+	0.620046i	−0.126084	+	0.0388288i
$256$	3.24242	+	5.61604i	0.202652	+	0.351003i
$257$	6.48221	+	11.2275i	0.404349	+	0.700353i	0.994245	−	0.107126i	$-0.0341648\pi$
$257$	6.48221	+	11.2275i	0.404349	+	0.700353i	−0.589896	+	0.807479i	$0.700831\pi$
$258$	−16.8905	+	5.20162i	−1.05156	+	0.323839i
$259$	4.08079	−	7.06813i	0.253568	−	0.439192i
$260$	2.99283			0.185607
$261$	19.3500	−	13.1668i	1.19774	−	0.815007i
$262$	40.5951			2.50798
$263$	10.7693	−	18.6530i	0.664066	−	1.15020i	−0.315472	−	0.948935i	$-0.602163\pi$
$263$	10.7693	−	18.6530i	0.664066	−	1.15020i	0.979538	−	0.201261i	$-0.0645039\pi$
$264$	2.57773	+	2.39396i	0.158648	+	0.147338i
$265$	−1.79722	−	3.11288i	−0.110403	−	0.191223i
$266$	4.12637	+	7.14708i	0.253004	+	0.438216i
$267$	3.87905	−	16.9597i	0.237394	−	1.03791i
$268$	14.7951	−	25.6258i	0.903753	−	1.56535i
$269$	−8.30750			−0.506517			−0.253259	−	0.967399i	$-0.581502\pi$
$269$	−8.30750			−0.506517			−0.253259	+	0.967399i	$0.581502\pi$
$270$	2.84704	−	3.56009i	0.173265	−	0.216660i
$271$	10.5409			0.640314			0.320157	−	0.947364i	$-0.396264\pi$
$271$	10.5409			0.640314			0.320157	+	0.947364i	$0.396264\pi$
$272$	−2.04236	+	3.53747i	−0.123836	+	0.214491i
$273$	−1.00173	+	4.37970i	−0.0606278	+	0.265072i
$274$	1.10824	+	1.91953i	0.0669514	+	0.115963i
$275$	2.42172	+	4.19455i	0.146035	+	0.252941i
$276$	−34.3551	−	31.9060i	−2.06793	−	1.92051i
$277$	2.39095	−	4.14125i	0.143658	−	0.248823i	−0.785213	−	0.619225i	$-0.787447\pi$
$277$	2.39095	−	4.14125i	0.143658	−	0.248823i	0.928872	+	0.370402i	$0.120780\pi$
$278$	−2.57872			−0.154662
$279$	0.562361	+	7.59695i	0.0336676	+	0.454818i
$280$	−0.803630			−0.0480261
$281$	0.943315	−	1.63387i	0.0562734	−	0.0974684i	−0.836516	−	0.547942i	$-0.815411\pi$
$281$	0.943315	−	1.63387i	0.0562734	−	0.0974684i	0.892790	+	0.450473i	$0.148745\pi$
$282$	−26.4839	+	8.15601i	−1.57709	+	0.485683i
$283$	6.43236	+	11.1412i	0.382364	+	0.662274i	0.991400	−	0.130869i	$-0.0417768\pi$
$283$	6.43236	+	11.1412i	0.382364	+	0.662274i	−0.609036	+	0.793143i	$0.708443\pi$
$284$	14.6224	+	25.3267i	0.867678	+	1.50286i
$285$	−2.43785	+	0.750762i	−0.144406	+	0.0444713i
$286$	2.87564	−	4.98075i	0.170040	−	0.294518i
$287$	−9.20266			−0.543216
$288$	−1.55211	−	20.9676i	−0.0914592	−	1.23553i
$289$	−7.55018			−0.444128
$290$	3.42212	−	5.92728i	0.200954	−	0.348062i
$291$	−14.3485	−	13.3256i	−0.841124	−	0.781162i
$292$	−9.88007	−	17.1128i	−0.578188	−	1.00145i
$293$	−6.35633	−	11.0095i	−0.371341	−	0.643181i	0.618431	−	0.785839i	$-0.287768\pi$
$293$	−6.35633	−	11.0095i	−0.371341	−	0.643181i	−0.989772	+	0.142658i	$0.954435\pi$
$294$	0.856257	−	3.74366i	0.0499379	−	0.218334i
$295$	1.95784	−	3.39107i	0.113990	−	0.197436i
$296$	−16.5767			−0.963502
$297$	−1.89176	−	4.83955i	−0.109771	−	0.280819i
$298$	−28.1116			−1.62846
$299$	−12.0396	+	20.8532i	−0.696267	+	1.20597i
$300$	−5.45438	+	23.8472i	−0.314909	+	1.37682i
$301$	−2.30102	−	3.98548i	−0.132628	−	0.229719i
$302$	−13.7314	−	23.7836i	−0.790156	−	1.36859i
$303$	23.3240	+	21.6613i	1.33993	+	1.24441i
$304$	−2.47292	+	4.28323i	−0.141832	+	0.245660i
$305$	−2.59716			−0.148713
$306$	−16.9050	+	11.5031i	−0.966396	+	0.657590i
$307$	21.2200			1.21109			0.605545	−	0.795811i	$-0.292955\pi$
$307$	21.2200			1.21109			0.605545	+	0.795811i	$0.292955\pi$
$308$	−1.45802	+	2.52537i	−0.0830785	+	0.143896i
$309$	−11.9560	+	3.68198i	−0.680153	+	0.209461i
$310$	1.11382	+	1.92919i	0.0632606	+	0.109571i
$311$	2.54086	+	4.40090i	0.144079	+	0.249552i	0.929029	−	0.370007i	$-0.120645\pi$
$311$	2.54086	+	4.40090i	0.144079	+	0.249552i	−0.784950	+	0.619559i	$0.787311\pi$
$312$	8.72100	−	2.68573i	0.493730	−	0.152049i
$313$	−3.95226	+	6.84552i	−0.223395	+	0.386932i	−0.955837	−	0.293898i	$-0.905047\pi$
$313$	−3.95226	+	6.84552i	−0.223395	+	0.386932i	0.732442	+	0.680830i	$0.238381\pi$
$314$	−41.7570			−2.35648
$315$	1.06899	+	0.515995i	0.0602305	+	0.0290730i
$316$	−15.5411			−0.874257
$317$	0.107048	−	0.185413i	0.00601243	−	0.0104138i	−0.863004	−	0.505198i	$-0.831420\pi$
$317$	0.107048	−	0.185413i	0.00601243	−	0.0104138i	0.869016	+	0.494784i	$0.164753\pi$
$318$	−25.5635	−	23.7411i	−1.43353	−	1.33134i
$319$	−3.90081	−	6.75641i	−0.218404	−	0.378286i
$320$	−2.54838	−	4.41392i	−0.142459	−	0.246746i
$321$	3.00290	−	13.1290i	0.167605	−	0.732790i
$322$	10.2911	−	17.8247i	0.573502	−	0.993334i
$323$	11.4420			0.636650
$324$	9.63261	−	24.4127i	0.535145	−	1.35626i
$325$	12.5635			0.696898
$326$	−9.22567	+	15.9793i	−0.510963	+	0.885013i
$327$	−0.450354	+	1.96900i	−0.0249047	+	0.108886i
$328$	9.34562	+	16.1871i	0.516025	+	0.893782i
$329$	−3.60794	−	6.24913i	−0.198912	−	0.344526i
$330$	−1.11340	−	1.03403i	−0.0612907	−	0.0569213i
$331$	4.88566	−	8.46222i	0.268540	−	0.465126i	−0.699945	−	0.714197i	$-0.746792\pi$
$331$	4.88566	−	8.46222i	0.268540	−	0.465126i	0.968485	+	0.249071i	$0.0801254\pi$
$332$	−46.2402			−2.53776
$333$	22.0503	+	10.6436i	1.20835	+	0.583265i
$334$	−11.4137			−0.624528
$335$	−2.00750	+	3.47708i	−0.109681	+	0.189973i
$336$	2.19956	−	0.677378i	0.119996	−	0.0369540i
$337$	13.5825	+	23.5256i	0.739886	+	1.28152i	0.952546	+	0.304394i	$0.0984538\pi$
$337$	13.5825	+	23.5256i	0.739886	+	1.28152i	−0.212661	+	0.977126i	$0.568213\pi$
$338$	6.95273	+	12.0425i	0.378179	+	0.655024i
$339$	−2.76807	+	0.852456i	−0.150341	+	0.0462991i
$340$	−1.77340	+	3.07162i	−0.0961763	+	0.166582i
$341$	2.53925			0.137508
$342$	−20.4689	+	13.9282i	−1.10683	+	0.753149i
$343$	1.00000			0.0539949
$344$	−4.67353	+	8.09478i	−0.251980	+	0.436441i
$345$	4.66153	+	4.32921i	0.250968	+	0.233077i
$346$	−1.41381	−	2.44878i	−0.0760067	−	0.131647i
$347$	10.1618	+	17.6007i	0.545512	+	0.944854i	0.998575	+	0.0533757i	$0.0169981\pi$
$347$	10.1618	+	17.6007i	0.545512	+	0.944854i	−0.453063	+	0.891479i	$0.649669\pi$
$348$	8.78569	−	38.4121i	0.470963	−	2.05910i
$349$	−3.59032	+	6.21862i	−0.192186	+	0.332875i	−0.945974	−	0.324242i	$-0.894891\pi$
$349$	−3.59032	+	6.21862i	−0.192186	+	0.332875i	0.753789	+	0.657117i	$0.228224\pi$
$350$	−10.7390			−0.574022
$351$	−13.3251	−	2.02704i	−0.711241	−	0.108196i
$352$	−7.00831			−0.373544
$353$	3.68423	−	6.38128i	0.196092	−	0.339641i	−0.751166	−	0.660113i	$-0.770508\pi$
$353$	3.68423	−	6.38128i	0.196092	−	0.339641i	0.947258	+	0.320472i	$0.103842\pi$
$354$	8.47383	−	37.0485i	0.450379	−	1.96911i
$355$	−1.98406	−	3.43649i	−0.105303	−	0.182390i
$356$	−14.6451	−	25.3661i	−0.776191	−	1.34440i
$357$	−3.90143	−	3.62330i	−0.206486	−	0.191766i
$358$	−7.51357	+	13.0139i	−0.397104	+	0.687805i
$359$	−14.1862			−0.748721			−0.374361	−	0.927283i	$-0.622138\pi$
$359$	−14.1862			−0.748721			−0.374361	+	0.927283i	$0.622138\pi$
$360$	−0.177978	−	2.40431i	−0.00938026	−	0.126718i
$361$	−5.14584			−0.270834
$362$	−11.7554	+	20.3609i	−0.617850	+	1.07015i
$363$	−1.65533	+	0.509778i	−0.0868824	+	0.0267564i
$364$	3.78199	+	6.55060i	0.198230	+	0.343345i
$365$	1.34059	+	2.32198i	0.0701699	+	0.121538i
$366$	−24.0913	+	7.41918i	−1.25927	+	0.387807i
$367$	0.456878	−	0.791335i	0.0238488	−	0.0413074i	−0.853855	−	0.520511i	$-0.825741\pi$
$367$	0.456878	−	0.791335i	0.0238488	−	0.0413074i	0.877703	+	0.479204i	$0.159075\pi$
$368$	12.3349			0.643001
$369$	−2.03809	−	27.5326i	−0.106099	−	1.43329i
$370$	7.16000			0.372231
$371$	4.54225	−	7.86740i	0.235822	−	0.408455i
$372$	9.39747	+	8.72754i	0.487236	+	0.452502i
$373$	10.3964	+	18.0071i	0.538305	+	0.932372i	0.998995	+	0.0448112i	$0.0142686\pi$
$373$	10.3964	+	18.0071i	0.538305	+	0.932372i	−0.460690	+	0.887561i	$0.652398\pi$
$374$	3.40792	+	5.90270i	0.176220	+	0.305221i
$375$	1.50409	−	6.57607i	0.0776711	−	0.339587i
$376$	−7.32797	+	12.6924i	−0.377911	+	0.654561i
$377$	−20.2368			−1.04225
$378$	11.3900	+	1.73266i	0.585836	+	0.0891187i
$379$	−30.3655			−1.55977			−0.779886	−	0.625921i	$-0.784723\pi$
$379$	−30.3655			−1.55977			−0.779886	+	0.625921i	$0.784723\pi$
$380$	−2.14726	+	3.71917i	−0.110152	+	0.190789i
$381$	−5.53317	+	24.1916i	−0.283473	+	1.23938i
$382$	−13.9150	−	24.1015i	−0.711953	−	1.23314i
$383$	−15.9892	−	27.6942i	−0.817012	−	1.41511i	−0.907874	−	0.419243i	$-0.862296\pi$
$383$	−15.9892	−	27.6942i	−0.817012	−	1.41511i	0.0908623	−	0.995863i	$-0.471038\pi$
$384$	−18.4587	−	17.1428i	−0.941968	−	0.874817i
$385$	0.197834	−	0.342659i	0.0100826	−	0.0174635i
$386$	9.42880			0.479913
$387$	11.4142	−	7.76687i	0.580217	−	0.394812i
$388$	−32.9677			−1.67368
$389$	4.91428	−	8.51178i	0.249164	−	0.431564i	−0.714130	−	0.700013i	$-0.753178\pi$
$389$	4.91428	−	8.51178i	0.249164	−	0.431564i	0.963294	+	0.268448i	$0.0865109\pi$
$390$	−3.76687	+	1.16005i	−0.190743	+	0.0587414i
$391$	−14.2681	−	24.7131i	−0.721570	−	1.24980i
$392$	−1.01553	−	1.75896i	−0.0512922	−	0.0888408i
$393$	−30.3076	+	9.33355i	−1.52882	+	0.470815i
$394$	−4.91656	+	8.51572i	−0.247693	+	0.429016i
$395$	2.10872			0.106101
$396$	−7.87834	−	3.80284i	−0.395901	−	0.191100i
$397$	10.1465			0.509238			0.254619	−	0.967041i	$-0.418050\pi$
$397$	10.1465			0.509238			0.254619	+	0.967041i	$0.418050\pi$
$398$	−3.99310	+	6.91625i	−0.200156	+	0.346680i
$399$	−4.72391	−	4.38715i	−0.236491	−	0.219632i
$400$	−3.21792	−	5.57360i	−0.160896	−	0.278680i
$401$	3.62521	+	6.27905i	0.181034	+	0.313561i	0.942233	−	0.334958i	$-0.108722\pi$
$401$	3.62521	+	6.27905i	0.181034	+	0.313561i	−0.761199	+	0.648519i	$0.775389\pi$
$402$	−8.68875	+	37.9882i	−0.433356	+	1.89468i
$403$	3.29330	−	5.70416i	0.164051	−	0.284144i
$404$	53.5902			2.66621
$405$	−1.30702	+	3.31248i	−0.0649462	+	0.164599i
$406$	17.2979			0.858480
$407$	4.08079	−	7.06813i	0.202277	−	0.350354i
$408$	−2.41120	+	10.5420i	−0.119372	+	0.521909i
$409$	3.51889	+	6.09489i	0.173998	+	0.301373i	0.939814	−	0.341686i	$-0.110998\pi$
$409$	3.51889	+	6.09489i	0.173998	+	0.301373i	−0.765816	+	0.643060i	$0.777665\pi$
$410$	−4.03666	−	6.99171i	−0.199357	−	0.345296i
$411$	−1.26873	−	1.17828i	−0.0625818	−	0.0581204i
$412$	−10.5309	+	18.2400i	−0.518820	+	0.898622i
$413$	9.89636			0.486968
$414$	55.6075	+	26.8415i	2.73296	+	1.31919i
$415$	6.27418			0.307988
$416$	−9.08950	+	15.7435i	−0.445649	+	0.771887i
$417$	1.92523	−	0.592895i	0.0942788	−	0.0290342i
$418$	4.12637	+	7.14708i	0.201827	+	0.349575i
$419$	−1.81650	−	3.14626i	−0.0887417	−	0.153705i	0.818238	−	0.574880i	$-0.194951\pi$
$419$	−1.81650	−	3.14626i	−0.0887417	−	0.153705i	−0.906979	+	0.421175i	$0.861618\pi$
$420$	1.90990	−	0.588175i	0.0931936	−	0.0287000i
$421$	0.260595	−	0.451364i	0.0127006	−	0.0219981i	−0.859605	−	0.510959i	$-0.829290\pi$
$421$	0.260595	−	0.451364i	0.0127006	−	0.0219981i	0.872306	+	0.488961i	$0.162624\pi$
$422$	31.1788			1.51776
$423$	17.8972	−	12.1783i	0.870191	−	0.592127i
$424$	−18.4512			−0.896071
$425$	−7.44451	+	12.8943i	−0.361112	+	0.625464i
$426$	−28.2211	−	26.2092i	−1.36732	−	1.26984i
$427$	−3.28199	−	5.68457i	−0.158827	−	0.275096i
$428$	−11.3373	−	19.6367i	−0.548007	−	0.949176i
$429$	−1.00173	+	4.37970i	−0.0483642	+	0.211454i
$430$	2.01864	−	3.49639i	0.0973475	−	0.168611i
$431$	−27.8197			−1.34003			−0.670014	−	0.742349i	$-0.733712\pi$
$431$	−27.8197			−1.34003			−0.670014	+	0.742349i	$0.733712\pi$
$432$	2.51372	+	6.43066i	0.120941	+	0.309395i
$433$	1.72432			0.0828654			0.0414327	−	0.999141i	$-0.486808\pi$
$433$	1.72432			0.0828654			0.0414327	+	0.999141i	$0.486808\pi$
$434$	−2.81503	+	4.87577i	−0.135126	+	0.234044i
$435$	−1.19210	+	5.21200i	−0.0571569	+	0.249896i
$436$	1.70029	+	2.94498i	0.0814290	+	0.141039i
$437$	−17.2761	−	29.9230i	−0.826426	−	1.43141i
$438$	19.0685	+	17.7091i	0.911127	+	0.846174i
$439$	−6.06036	+	10.4969i	−0.289245	+	0.500988i	−0.973630	−	0.228134i	$-0.926738\pi$
$439$	−6.06036	+	10.4969i	−0.289245	+	0.500988i	0.684384	+	0.729121i	$0.260071\pi$
$440$	−0.803630			−0.0383116
$441$	0.221468	+	2.99181i	0.0105461	+	0.142467i
$442$	17.6798			0.840940
$443$	−18.9874	+	32.8871i	−0.902118	+	1.56251i	−0.0773792	+	0.997002i	$0.524655\pi$
$443$	−18.9874	+	32.8871i	−0.902118	+	1.56251i	−0.824739	+	0.565513i	$0.808678\pi$
$444$	39.3961	−	12.1325i	1.86966	−	0.575781i
$445$	1.98715	+	3.44184i	0.0941999	+	0.163159i
$446$	20.2208	+	35.0235i	0.957484	+	1.65841i
$447$	20.9876	−	6.46337i	0.992680	−	0.305707i
$448$	6.44070	−	11.1556i	0.304294	−	0.527053i
$449$	−3.51234			−0.165758			−0.0828788	−	0.996560i	$-0.526411\pi$
$449$	−3.51234			−0.165758			−0.0828788	+	0.996560i	$0.526411\pi$
$450$	−2.37833	−	32.1290i	−0.112116	−	1.51458i
$451$	−9.20266			−0.433336
$452$	−2.43812	+	4.22295i	−0.114680	+	0.198631i
$453$	15.7199	+	14.5993i	0.738586	+	0.685933i
$454$	13.3948	+	23.2005i	0.628650	+	1.08885i
$455$	−0.513166	−	0.888829i	−0.0240576	−	0.0416690i
$456$	−2.91952	+	12.7645i	−0.136719	+	0.597751i
$457$	−7.02452	+	12.1668i	−0.328593	+	0.569140i	−0.982233	−	0.187666i	$-0.939908\pi$
$457$	−7.02452	+	12.1668i	−0.328593	+	0.569140i	0.653640	+	0.756806i	$0.273241\pi$
$458$	−60.0316			−2.80509
$459$	9.97621	−	12.4748i	0.465650	−	0.582274i
$460$	10.7105			0.499380
$461$	−18.6808	+	32.3561i	−0.870052	+	1.50697i	−0.00810963	+	0.999967i	$0.502581\pi$
$461$	−18.6808	+	32.3561i	−0.870052	+	1.50697i	−0.861942	+	0.507007i	$0.830752\pi$
$462$	0.856257	−	3.74366i	0.0398367	−	0.174171i
$463$	5.86205	+	10.1534i	0.272432	+	0.471867i	0.969484	−	0.245154i	$-0.0788385\pi$
$463$	5.86205	+	10.1534i	0.272432	+	0.471867i	−0.697052	+	0.717021i	$0.745505\pi$
$464$	5.18329	+	8.97773i	0.240628	+	0.416780i
$465$	−1.27511	−	1.18421i	−0.0591319	−	0.0549164i
$466$	0.239220	−	0.414340i	0.0110816	−	0.0191939i
$467$	20.0977			0.930012			0.465006	−	0.885308i	$-0.346052\pi$
$467$	20.0977			0.930012			0.465006	+	0.885308i	$0.346052\pi$
$468$	−18.7606	+	12.7658i	−0.867209	+	0.590098i
$469$	−10.1474			−0.468562
$470$	3.16518	−	5.48225i	0.145999	−	0.252877i
$471$	31.1750	−	9.60068i	1.43647	−	0.442376i
$472$	−10.0501	−	17.4073i	−0.462593	−	0.801234i
$473$	−2.30102	−	3.98548i	−0.105801	−	0.183253i
$474$	19.5606	−	6.02389i	0.898447	−	0.276686i
$475$	−9.01394	+	15.6126i	−0.413588	+	0.716355i
$476$	−8.96409			−0.410868
$477$	24.5438	+	11.8472i	1.12378	+	0.542445i
$478$	66.9908			3.06409
$479$	14.6122	−	25.3090i	0.667648	−	1.15640i	−0.310913	−	0.950438i	$-0.600635\pi$
$479$	14.6122	−	25.3090i	0.667648	−	1.15640i	0.978560	−	0.205961i	$-0.0660320\pi$
$480$	3.51930	+	3.26842i	0.160633	+	0.149182i
$481$	−10.5852	−	18.3342i	−0.482645	−	0.835966i
$482$	9.86917	+	17.0939i	0.449528	+	0.778606i
$483$	−3.58494	+	15.6737i	−0.163120	+	0.713180i
$484$	−1.45802	+	2.52537i	−0.0662737	+	0.114789i
$485$	4.47328			0.203121
$486$	−2.66130	+	34.4604i	−0.120719	+	1.56315i
$487$	−27.3975			−1.24150			−0.620749	−	0.784009i	$-0.713172\pi$
$487$	−27.3975			−1.24150			−0.620749	+	0.784009i	$0.713172\pi$
$488$	−6.66594	+	11.5458i	−0.301753	+	0.522652i
$489$	3.21378	−	14.0510i	0.145332	−	0.635409i
$490$	0.438641	+	0.759749i	0.0198158	+	0.0343219i
$491$	−17.1989	−	29.7894i	−0.776177	−	1.34438i	−0.934130	−	0.356932i	$-0.883823\pi$
$491$	−17.1989	−	29.7894i	−0.776177	−	1.34438i	0.157953	−	0.987447i	$-0.449510\pi$
$492$	−34.0580	−	31.6301i	−1.53545	−	1.42599i
$493$	11.9913	−	20.7696i	0.540062	−	0.935415i
$494$	21.4069			0.963143
$495$	1.06899	+	0.515995i	0.0480473	+	0.0231923i
$496$	−3.37408			−0.151501
$497$	5.01445	−	8.68529i	0.224929	−	0.389588i
$498$	58.1995	−	17.9232i	2.60798	−	0.803156i
$499$	−0.319365	−	0.553157i	−0.0142968	−	0.0247627i	0.858789	−	0.512330i	$-0.171218\pi$
$499$	−0.319365	−	0.553157i	−0.0142968	−	0.0247627i	−0.873085	+	0.487568i	$0.837884\pi$
$500$	−5.67862	−	9.83566i	−0.253956	−	0.439864i
$501$	8.52123	−	2.62421i	0.380701	−	0.117241i
$502$	21.4165	−	37.0945i	0.955867	−	1.65561i
$503$	0.734098			0.0327318			0.0163659	−	0.999866i	$-0.494790\pi$
$503$	0.734098			0.0327318			0.0163659	+	0.999866i	$0.494790\pi$
$504$	5.03757	−	3.42784i	0.224391	−	0.152688i
$505$	−7.27147			−0.323576
$506$	10.2911	−	17.8247i	0.457496	−	0.792407i
$507$	−7.95956	−	7.39214i	−0.353497	−	0.328296i
$508$	20.8901	+	36.1828i	0.926850	+	1.60535i
$509$	−11.8269	−	20.4848i	−0.524219	−	0.907974i	−0.999602	−	0.0281952i	$-0.991024\pi$
$509$	−11.8269	−	20.4848i	−0.524219	−	0.907974i	0.475383	−	0.879779i	$-0.342309\pi$
$510$	1.04147	−	4.55344i	0.0461172	−	0.201629i
$511$	−3.38818	+	5.86849i	−0.149884	+	0.259607i
$512$	14.7101			0.650101
$513$	12.0794	−	15.1047i	0.533316	−	0.666888i
$514$	−28.7449			−1.26788
$515$	1.42890	−	2.47493i	0.0629649	−	0.109058i
$516$	5.18251	−	22.6585i	0.228147	−	0.997487i
$517$	−3.60794	−	6.24913i	−0.158677	−	0.274836i
$518$	9.04798	+	15.6716i	0.397546	+	0.688569i
$519$	1.61854	+	1.50316i	0.0710461	+	0.0659813i
$520$	−1.04228	+	1.80527i	−0.0457068	+	0.0791665i
$521$	30.3317			1.32886			0.664428	−	0.747352i	$-0.268675\pi$
$521$	30.3317			1.32886			0.664428	+	0.747352i	$0.268675\pi$
$522$	3.83092	+	51.7521i	0.167675	+	2.26513i
$523$	−29.6224			−1.29530			−0.647648	−	0.761940i	$-0.724247\pi$
$523$	−29.6224			−1.29530			−0.647648	+	0.761940i	$0.724247\pi$
$524$	−26.6950	+	46.2371i	−1.16618	+	2.01988i
$525$	8.01752	−	2.46908i	0.349913	−	0.107760i
$526$	23.8779	+	41.3578i	1.04113	+	1.80329i
$527$	3.90289	+	6.76001i	0.170013	+	0.294471i
$528$	2.19956	−	0.677378i	0.0957235	−	0.0294791i
$529$	−31.5864	+	54.7092i	−1.37332	+	2.37866i
$530$	7.96967			0.346180
$531$	2.19172	+	29.6081i	0.0951126	+	1.28488i
$532$	−10.8539			−0.470575
$533$	−11.9355	+	20.6729i	−0.516983	+	0.895441i
$534$	28.2650	+	26.2500i	1.22315	+	1.13595i
$535$	1.53832	+	2.66444i	0.0665072	+	0.115194i
$536$	10.3050	+	17.8488i	0.445108	+	0.770950i
$537$	2.61737	−	11.4434i	0.112948	−	0.493821i
$538$	9.20976	−	15.9518i	0.397061	−	0.687730i
$539$	1.00000			0.0430730
$540$	2.18269	+	5.58381i	0.0939281	+	0.240289i
$541$	−12.6878			−0.545492			−0.272746	−	0.962086i	$-0.587932\pi$
$541$	−12.6878			−0.545492			−0.272746	+	0.962086i	$0.587932\pi$
$542$	−11.6857	+	20.2403i	−0.501945	+	0.869394i
$543$	4.09502	−	17.9039i	0.175734	−	0.768329i
$544$	−10.7720	−	18.6576i	−0.461845	−	0.799938i
$545$	−0.230706	−	0.399595i	−0.00988237	−	0.0171168i
$546$	−7.29922	−	6.77887i	−0.312378	−	0.290109i
$547$	3.68623	−	6.38474i	0.157612	−	0.272992i	−0.776395	−	0.630246i	$-0.782954\pi$
$547$	3.68623	−	6.38474i	0.157612	−	0.272992i	0.934007	+	0.357255i	$0.116287\pi$
$548$	−2.91508			−0.124526
$549$	16.2803	−	11.0780i	0.694827	−	0.472799i
$550$	−10.7390			−0.457911
$551$	14.5193	−	25.1481i	0.618543	−	1.07135i
$552$	31.2101	−	9.61148i	1.32839	−	0.409092i
$553$	2.66476	+	4.61550i	0.113317	+	0.196271i
$554$	5.30125	+	9.18203i	0.225229	+	0.390107i
$555$	−5.34553	+	1.64621i	−0.226905	+	0.0698779i
$556$	1.69575	−	2.93712i	0.0719157	−	0.124562i
$557$	−8.58633			−0.363814			−0.181907	−	0.983316i	$-0.558227\pi$
$557$	−8.58633			−0.363814			−0.181907	+	0.983316i	$0.558227\pi$
$558$	−15.2108	−	7.34221i	−0.643926	−	0.310821i
$559$	−11.9373			−0.504894
$560$	−0.262877	+	0.455315i	−0.0111086	+	0.0192406i
$561$	−3.90143	−	3.62330i	−0.164718	−	0.152976i
$562$	2.09153	+	3.62264i	0.0882259	+	0.152812i
$563$	13.7478	+	23.8119i	0.579400	+	1.00355i	0.995548	+	0.0942533i	$0.0300464\pi$
$563$	13.7478	+	23.8119i	0.579400	+	1.00355i	−0.416148	+	0.909297i	$0.636620\pi$
$564$	8.12605	−	35.5280i	0.342168	−	1.49600i
$565$	0.330821	−	0.572998i	0.0139177	−	0.0241062i
$566$	−28.5238			−1.19895
$567$	−8.90190	+	1.32518i	−0.373845	+	0.0556523i
$568$	−20.3694			−0.854681
$569$	−15.2884	+	26.4803i	−0.640922	+	1.11011i	0.344305	+	0.938858i	$0.388115\pi$
$569$	−15.2884	+	26.4803i	−0.640922	+	1.11011i	−0.985227	+	0.171252i	$0.945219\pi$
$570$	1.26103	−	5.51337i	0.0528188	−	0.230930i
$571$	−0.312507	−	0.541278i	−0.0130780	−	0.0226518i	0.859412	−	0.511283i	$-0.170830\pi$
$571$	−0.312507	−	0.541278i	−0.0130780	−	0.0226518i	−0.872490	+	0.488631i	$0.837496\pi$
$572$	3.78199	+	6.55060i	0.158133	+	0.273894i
$573$	15.9300	+	14.7944i	0.665487	+	0.618046i
$574$	10.2021	−	17.6706i	0.425829	−	0.737558i
$575$	44.9614			1.87502
$576$	34.8019	+	16.7988i	1.45008	+	0.699948i
$577$	9.35615			0.389502			0.194751	−	0.980853i	$-0.437610\pi$
$577$	9.35615			0.389502			0.194751	+	0.980853i	$0.437610\pi$
$578$	8.37018	−	14.4976i	0.348154	−	0.603020i
$579$	−7.03937	+	2.16785i	−0.292546	+	0.0900928i
$580$	4.50071	+	7.79546i	0.186882	+	0.323689i
$581$	7.92859	+	13.7327i	0.328933	+	0.569729i
$582$	41.4942	−	12.7786i	1.71999	−	0.529690i
$583$	4.54225	−	7.86740i	0.188121	−	0.325835i
$584$	13.7632			0.569527
$585$	2.54556	−	1.73214i	0.105246	−	0.0716153i
$586$	28.1867			1.16438
$587$	−6.98207	+	12.0933i	−0.288181	+	0.499144i	−0.973376	−	0.229216i	$-0.926384\pi$
$587$	−6.98207	+	12.0933i	−0.288181	+	0.499144i	0.685195	+	0.728360i	$0.259717\pi$
$588$	3.70089	+	3.43706i	0.152622	+	0.141742i
$589$	4.72568	+	8.18513i	0.194718	+	0.337262i
$590$	4.34095	+	7.51874i	0.178714	+	0.309542i
$591$	1.71269	−	7.48809i	0.0704508	−	0.308019i
$592$	−5.42243	+	9.39193i	−0.222861	+	0.386006i
$593$	−12.3633			−0.507702			−0.253851	−	0.967243i	$-0.581697\pi$
$593$	−12.3633			−0.507702			−0.253851	+	0.967243i	$0.581697\pi$
$594$	11.3900	+	1.73266i	0.467336	+	0.0710921i
$595$	1.21631			0.0498637
$596$	18.4860	−	32.0186i	0.757214	−	1.31153i
$597$	1.39100	−	6.08163i	0.0569300	−	0.248905i
$598$	−26.6943	−	46.2360i	−1.09161	−	1.89073i
$599$	14.8911	+	25.7922i	0.608434	+	1.05384i	0.991499	+	0.130117i	$0.0415354\pi$
$599$	14.8911	+	25.7922i	0.608434	+	1.05384i	−0.383064	+	0.923722i	$0.625131\pi$
$600$	−12.4851	−	11.5950i	−0.509701	−	0.473365i
$601$	−17.1808	+	29.7581i	−0.700821	+	1.21386i	0.267357	+	0.963597i	$0.413850\pi$
$601$	−17.1808	+	29.7581i	−0.700821	+	1.21386i	−0.968179	+	0.250260i	$0.919484\pi$
$602$	10.2037			0.415872
$603$	−2.24731	−	30.3590i	−0.0915176	−	1.23631i
$604$	36.1187			1.46965
$605$	0.197834	−	0.342659i	0.00804310	−	0.0139311i
$606$	−67.4503	+	20.7721i	−2.73998	+	0.843807i
$607$	24.0074	+	41.5820i	0.974429	+	1.68776i	0.681807	+	0.731532i	$0.261194\pi$
$607$	24.0074	+	41.5820i	0.974429	+	1.68776i	0.292621	+	0.956228i	$0.405472\pi$
$608$	−13.0429	−	22.5909i	−0.528959	−	0.916183i
$609$	−12.9143	+	3.97710i	−0.523314	+	0.161160i
$610$	2.87923	−	4.98697i	0.116577	−	0.201917i
$611$	−18.7174			−0.757225
$612$	−1.98525	−	26.8189i	−0.0802492	−	1.08409i
$613$	13.3746			0.540195			0.270098	−	0.962833i	$-0.412944\pi$
$613$	13.3746			0.540195			0.270098	+	0.962833i	$0.412944\pi$
$614$	−23.5247	+	40.7459i	−0.949378	+	1.64437i
$615$	4.62122	+	4.29178i	0.186346	+	0.173061i
$616$	−1.01553	−	1.75896i	−0.0409171	−	0.0708704i
$617$	−2.50528	−	4.33927i	−0.100859	−	0.174693i	0.811180	−	0.584797i	$-0.198826\pi$
$617$	−2.50528	−	4.33927i	−0.100859	−	0.174693i	−0.912039	+	0.410104i	$0.865492\pi$
$618$	6.18451	−	27.0394i	0.248777	−	1.08768i
$619$	−19.5136	+	33.7986i	−0.784320	+	1.35848i	0.145085	+	0.989419i	$0.453654\pi$
$619$	−19.5136	+	33.7986i	−0.784320	+	1.35848i	−0.929405	+	0.369062i	$0.879679\pi$
$620$	−2.92975			−0.117662
$621$	−47.6869	−	7.25423i	−1.91361	−	0.291102i
$622$	−11.2673			−0.451776
$623$	−5.02226	+	8.69881i	−0.201213	+	0.348511i
$624$	1.33108	−	5.81962i	0.0532857	−	0.232971i
$625$	−11.3381	−	19.6382i	−0.453524	−	0.785527i
$626$	−8.76302	−	15.1780i	−0.350241	−	0.606635i
$627$	−4.72391	−	4.38715i	−0.188655	−	0.175206i
$628$	27.4590	−	47.5605i	1.09574	−	1.89787i
$629$	25.0891			1.00037
$630$	−2.17588	+	1.48059i	−0.0866892	+	0.0589882i
$631$	32.2057			1.28209			0.641045	−	0.767503i	$-0.278501\pi$
$631$	32.2057			1.28209			0.641045	+	0.767503i	$0.278501\pi$
$632$	5.41231	−	9.37440i	0.215290	−	0.372894i
$633$	−23.2775	+	7.16857i	−0.925199	+	0.284925i
$634$	0.237349	+	0.411101i	0.00942634	+	0.0163269i
$635$	−2.83451	−	4.90952i	−0.112484	−	0.194828i
$636$	43.8511	−	13.5044i	1.73881	−	0.535485i
$637$	1.29696	−	2.24640i	0.0513874	−	0.0890056i
$638$	17.2979			0.684830
$639$	27.0953	+	13.0788i	1.07187	+	0.517390i
$640$	5.75468			0.227474
$641$	−14.0929	+	24.4096i	−0.556637	+	0.964123i	0.441138	+	0.897439i	$0.354575\pi$
$641$	−14.0929	+	24.4096i	−0.556637	+	0.964123i	−0.997774	+	0.0666833i	$0.978758\pi$
$642$	21.8808	+	20.3210i	0.863567	+	0.802005i
$643$	−10.7671	−	18.6492i	−0.424614	−	0.735452i	0.571771	−	0.820414i	$-0.306257\pi$
$643$	−10.7671	−	18.6492i	−0.424614	−	0.735452i	−0.996384	+	0.0849611i	$0.972923\pi$
$644$	13.5347	+	23.4428i	0.533342	+	0.923776i
$645$	−0.703198	+	3.07446i	−0.0276884	+	0.121057i
$646$	−12.6847	+	21.9705i	−0.499072	+	0.864419i
$647$	21.8957			0.860808			0.430404	−	0.902636i	$-0.358371\pi$
$647$	21.8957			0.860808			0.430404	+	0.902636i	$0.358371\pi$
$648$	11.3711	+	14.3123i	0.446700	+	0.562240i
$649$	9.89636			0.388466
$650$	−13.9280	+	24.1240i	−0.546301	+	0.946221i
$651$	0.980621	−	4.28739i	0.0384336	−	0.168036i
$652$	−12.1334	−	21.0157i	−0.475183	−	0.823040i
$653$	−10.5849	−	18.3335i	−0.414217	−	0.717445i	0.581129	−	0.813812i	$-0.302611\pi$
$653$	−10.5849	−	18.3335i	−0.414217	−	0.717445i	−0.995346	+	0.0963664i	$0.969278\pi$
$654$	−3.28154	−	3.04760i	−0.128318	−	0.119171i
$655$	3.62216	−	6.27376i	0.141529	−	0.245136i
$656$	12.2282			0.477432
$657$	−18.3078	−	8.83711i	−0.714256	−	0.344769i
$658$	15.9991			0.623712
$659$	−11.8655	+	20.5516i	−0.462213	+	0.800576i	−0.999071	−	0.0430966i	$-0.986278\pi$
$659$	−11.8655	+	20.5516i	−0.462213	+	0.800576i	0.536858	+	0.843672i	$0.319611\pi$
$660$	1.90990	−	0.588175i	0.0743428	−	0.0228947i
$661$	−6.59106	−	11.4160i	−0.256362	−	0.444033i	0.708902	−	0.705307i	$-0.249191\pi$
$661$	−6.59106	−	11.4160i	−0.256362	−	0.444033i	−0.965265	+	0.261274i	$0.915857\pi$
$662$	10.8326	+	18.7626i	0.421020	+	0.729228i
$663$	−13.1994	+	4.06489i	−0.512622	+	0.157867i
$664$	16.1035	−	27.8921i	0.624937	−	1.08242i
$665$	1.47272			0.0571098
$666$	−44.8826	+	30.5406i	−1.73916	+	1.18343i
$667$	−72.4219			−2.80419
$668$	7.50553	−	13.0000i	0.290398	−	0.502983i
$669$	−23.1490	−	21.4988i	−0.894993	−	0.831190i
$670$	−4.45105	−	7.70944i	−0.171959	−	0.297842i
$671$	−3.28199	−	5.68457i	−0.126700	−	0.219450i
$672$	−2.70651	+	11.8332i	−0.104406	+	0.456475i
$673$	23.8552	−	41.3184i	0.919550	−	1.59271i	0.119450	−	0.992840i	$-0.461887\pi$
$673$	23.8552	−	41.3184i	0.919550	−	1.59271i	0.800100	−	0.599867i	$-0.204780\pi$
$674$	−60.2306			−2.32000
$675$	9.16265	+	23.4401i	0.352671	+	0.902210i
$676$	−18.2882			−0.703393
$677$	−22.2023	+	38.4556i	−0.853305	+	1.47797i	0.0249035	+	0.999690i	$0.492072\pi$
$677$	−22.2023	+	38.4556i	−0.853305	+	1.47797i	−0.878209	+	0.478278i	$0.841261\pi$
$678$	1.43184	−	6.26018i	0.0549896	−	0.240421i
$679$	5.65281	+	9.79096i	0.216935	+	0.375743i
$680$	−1.23520	−	2.13943i	−0.0473678	−	0.0820435i
$681$	−15.3345	−	14.2414i	−0.587621	−	0.545730i
$682$	−2.81503	+	4.87577i	−0.107793	+	0.186703i
$683$	17.3405			0.663516			0.331758	−	0.943364i	$-0.392358\pi$
$683$	17.3405			0.663516			0.331758	+	0.943364i	$0.392358\pi$
$684$	−2.40378	−	32.4727i	−0.0919108	−	1.24163i
$685$	0.395538			0.0151127
$686$	−1.10861	+	1.92017i	−0.0423268	+	0.0733122i
$687$	44.8185	−	13.8023i	1.70993	−	0.526592i
$688$	3.05753	+	5.29579i	0.116567	+	0.201900i
$689$	−11.7822	−	20.4074i	−0.448867	−	0.777460i
$690$	−13.4806	+	4.15150i	−0.513198	+	0.158045i
$691$	19.2854	−	33.4033i	0.733650	−	1.27072i	−0.221663	−	0.975123i	$-0.571148\pi$
$691$	19.2854	−	33.4033i	0.733650	−	1.27072i	0.955313	−	0.295596i	$-0.0955183\pi$
$692$	3.71883			0.141369
$693$	0.221468	+	2.99181i	0.00841286	+	0.113650i
$694$	−45.0616			−1.71052
$695$	−0.230090	+	0.398528i	−0.00872782	+	0.0151170i
$696$	20.1105	+	18.6768i	0.762285	+	0.707943i
$697$	−14.1447	−	24.4994i	−0.535771	−	0.927982i
$698$	−7.96052	−	13.7880i	−0.301310	−	0.521885i
$699$	−0.0833326	+	0.364340i	−0.00315193	+	0.0137806i
$700$	7.06185	−	12.2315i	0.266913	−	0.462307i
$701$	−48.1238			−1.81761			−0.908805	−	0.417220i	$-0.863004\pi$
$701$	−48.1238			−1.81761			−0.908805	+	0.417220i	$0.863004\pi$
$702$	18.6646	−	23.3392i	0.704449	−	0.880881i
$703$	30.3783			1.14574
$704$	6.44070	−	11.1556i	0.242743	−	0.420443i
$705$	−1.10260	+	4.82068i	−0.0415262	+	0.181557i
$706$	8.16874	+	14.1487i	0.307435	+	0.532492i
$707$	−9.18884	−	15.9155i	−0.345582	−	0.598566i
$708$	36.6253	+	34.0144i	1.37646	+	1.27834i
$709$	1.46770	−	2.54214i	0.0551208	−	0.0954720i	−0.837148	−	0.546976i	$-0.815779\pi$
$709$	1.46770	−	2.54214i	0.0551208	−	0.0954720i	0.892269	+	0.451504i	$0.149112\pi$
$710$	8.79818			0.330190
$711$	−13.2186	+	8.99465i	−0.495735	+	0.337326i
$712$	20.4011			0.764564
$713$	11.7858	−	20.4136i	0.441382	−	0.764496i
$714$	11.2825	−	3.47457i	0.422237	−	0.130032i
$715$	−0.513166	−	0.888829i	−0.0191913	−	0.0332403i
$716$	−9.88172	−	17.1156i	−0.369297	−	0.639642i
$717$	−50.0141	+	15.4024i	−1.86781	+	0.575213i
$718$	15.7270	−	27.2399i	0.586926	−	1.01659i
$719$	49.1746			1.83390			0.916951	−	0.399000i	$-0.130643\pi$
$719$	49.1746			1.83390			0.916951	+	0.399000i	$0.130643\pi$
$720$	−1.42044	−	0.685640i	−0.0529366	−	0.0255523i
$721$	7.22272			0.268988
$722$	5.70472	−	9.88087i	0.212308	−	0.367728i
$723$	−11.2983	−	10.4929i	−0.420190	−	0.390235i
$724$	−15.4605	−	26.7784i	−0.574585	−	0.995210i
$725$	18.8934	+	32.7243i	0.701683	+	1.21535i
$726$	0.856257	−	3.74366i	0.0317787	−	0.138940i
$727$	15.4259	−	26.7184i	0.572115	−	0.990932i	−0.424234	−	0.905553i	$-0.639457\pi$
$727$	15.4259	−	26.7184i	0.572115	−	0.990932i	0.996349	−	0.0853790i	$-0.0272101\pi$
$728$	−5.26843			−0.195261
$729$	−5.93617	−	26.3394i	−0.219858	−	0.975532i
$730$	−5.94477			−0.220026
$731$	7.07346	−	12.2516i	0.261621	−	0.453141i
$732$	7.39193	−	32.3183i	0.273213	−	1.19452i
$733$	2.24887	+	3.89515i	0.0830638	+	0.143871i	0.904565	−	0.426337i	$-0.140196\pi$
$733$	2.24887	+	3.89515i	0.0830638	+	0.143871i	−0.821501	+	0.570207i	$0.806863\pi$
$734$	1.01300	+	1.75456i	0.0373904	+	0.0647620i
$735$	−0.502161	−	0.466363i	−0.0185225	−	0.0172021i
$736$	−32.5288	+	56.3416i	−1.19903	+	2.07678i
$737$	−10.1474			−0.373783
$738$	55.1267	+	26.6094i	2.02924	+	0.979507i
$739$	45.6282			1.67846			0.839230	−	0.543776i	$-0.183006\pi$
$739$	45.6282			1.67846			0.839230	+	0.543776i	$0.183006\pi$
$740$	−4.70836	+	8.15512i	−0.173083	+	0.299788i
$741$	−15.9820	+	4.92184i	−0.587114	+	0.180808i
$742$	10.0711	+	17.4437i	0.369723	+	0.640380i
$743$	−23.3144	−	40.3817i	−0.855321	−	1.48146i	−0.876347	−	0.481681i	$-0.840027\pi$
$743$	−23.3144	−	40.3817i	−0.855321	−	1.48146i	0.0210258	−	0.999779i	$-0.493307\pi$
$744$	−8.53719	+	2.62912i	−0.312988	+	0.0963882i
$745$	−2.50830	+	4.34450i	−0.0918969	+	0.159170i
$746$	−46.1021			−1.68792
$747$	−39.3298	+	26.7622i	−1.43900	+	0.979178i
$748$	−8.96409			−0.327759
$749$	−3.88789	+	6.73402i	−0.142060	+	0.246056i
$750$	10.9597	+	10.1784i	0.400191	+	0.371662i
$751$	14.4235	+	24.9823i	0.526322	+	0.911617i	0.999530	+	0.0306660i	$0.00976283\pi$
$751$	14.4235	+	24.9823i	0.526322	+	0.911617i	−0.473207	+	0.880951i	$0.656904\pi$
$752$	4.79412	+	8.30367i	0.174824	+	0.302804i
$753$	−7.46050	+	32.6181i	−0.271876	+	1.18867i
$754$	22.4347	−	38.8580i	0.817022	−	1.41512i
$755$	−4.90083			−0.178359
$756$	−9.46341	+	11.8336i	−0.344181	+	0.430383i
$757$	−16.6393			−0.604765			−0.302382	−	0.953187i	$-0.597782\pi$
$757$	−16.6393			−0.604765			−0.302382	+	0.953187i	$0.597782\pi$
$758$	33.6635	−	58.3068i	1.22271	−	2.11780i
$759$	−3.58494	+	15.6737i	−0.130125	+	0.568921i
$760$	−1.49560	−	2.59046i	−0.0542512	−	0.0939658i
$761$	−4.32287	−	7.48743i	−0.156704	−	0.271419i	0.776974	−	0.629532i	$-0.216753\pi$
$761$	−4.32287	−	7.48743i	−0.156704	−	0.271419i	−0.933678	+	0.358113i	$0.883420\pi$
$762$	−40.3178	−	37.4436i	−1.46056	−	1.35644i
$763$	0.583080	−	1.00992i	0.0211089	−	0.0365617i
$764$	36.6015			1.32420
$765$	0.269373	+	3.63896i	0.00973919	+	0.131567i
$766$	70.9032			2.56184
$767$	12.8352	−	22.2312i	0.463451	−	0.802721i
$768$	10.7346	−	3.30583i	0.387351	−	0.119289i
$769$	10.6684	+	18.4783i	0.384714	+	0.666344i	0.991729	−	0.128346i	$-0.0409668\pi$
$769$	10.6684	+	18.4783i	0.384714	+	0.666344i	−0.607016	+	0.794690i	$0.707633\pi$
$770$	0.438641	+	0.759749i	0.0158075	+	0.0273794i
$771$	21.4604	−	6.60897i	0.772878	−	0.238016i
$772$	−6.20030	+	10.7392i	−0.223154	+	0.386513i
$773$	−0.692723			−0.0249155			−0.0124578	−	0.999922i	$-0.503966\pi$
$773$	−0.692723			−0.0249155			−0.0124578	+	0.999922i	$0.503966\pi$
$774$	2.25979	+	30.5276i	0.0812265	+	1.09729i
$775$	−12.2987			−0.441782
$776$	11.4813	−	19.8861i	0.412153	−	0.713870i
$777$	−10.3582	−	9.61981i	−0.371600	−	0.345109i
$778$	10.8960	+	18.8725i	0.390641	+	0.676610i
$779$	−17.1267	−	29.6643i	−0.613627	−	1.06283i
$780$	1.15579	−	5.05324i	0.0413839	−	0.180935i
$781$	5.01445	−	8.68529i	0.179431	−	0.310784i
$782$	63.2710			2.26257
$783$	−14.7588	−	37.7564i	−0.527438	−	1.34930i
$784$	−1.32877			−0.0474561
$785$	−3.72583	+	6.45332i	−0.132980	+	0.230329i
$786$	15.6773	−	68.5428i	0.559190	−	2.44484i
$787$	10.4395	+	18.0817i	0.372127	+	0.644542i	0.989892	−	0.141820i	$-0.0452954\pi$
$787$	10.4395	+	18.0817i	0.372127	+	0.644542i	−0.617766	+	0.786362i	$0.711962\pi$
$788$	−6.46617	−	11.1997i	−0.230348	−	0.398974i
$789$	−27.3357	−	25.3870i	−0.973178	−	0.903802i
$790$	−2.33775	+	4.04910i	−0.0831733	+	0.144060i
$791$	1.67221			0.0594570
$792$	5.03757	−	3.42784i	0.179002	−	0.121803i
$793$	−17.0264			−0.604626
$794$	−11.2485	+	19.4830i	−0.399194	+	0.691424i
$795$	−5.95001	+	1.83237i	−0.211025	+	0.0649875i
$796$	−5.25166	−	9.09613i	−0.186140	−	0.322404i
$797$	−1.85195	−	3.20767i	−0.0655993	−	0.113621i	0.831360	−	0.555734i	$-0.187563\pi$
$797$	−1.85195	−	3.20767i	−0.0655993	−	0.113621i	−0.896960	+	0.442112i	$0.854229\pi$
$798$	13.6610	−	4.20706i	0.483595	−	0.148928i
$799$	11.0910	−	19.2102i	0.392371	−	0.679607i
$800$	33.9444			1.20012
$801$	−27.1375	−	13.0992i	−0.958856	−	0.462836i
$802$	−16.0757			−0.567654
$803$	−3.38818	+	5.86849i	−0.119566	+	0.207095i
$804$	−37.5543	−	34.8771i	−1.32444	−	1.23002i
$805$	−1.83648	−	3.18088i	−0.0647274	−	0.112111i
$806$	7.30195	+	12.6474i	0.257200	+	0.445484i
$807$	−3.20824	+	14.0268i	−0.112935	+	0.493767i
$808$	−18.6632	+	32.3256i	−0.656568	+	1.13721i
$809$	−12.7810			−0.449358			−0.224679	−	0.974433i	$-0.572133\pi$
$809$	−12.7810			−0.449358			−0.224679	+	0.974433i	$0.572133\pi$
$810$	−4.91154	−	6.18193i	−0.172574	−	0.217211i
$811$	−2.12382			−0.0745775			−0.0372888	−	0.999305i	$-0.511872\pi$
$811$	−2.12382			−0.0745775			−0.0372888	+	0.999305i	$0.511872\pi$
$812$	−11.3750	+	19.7020i	−0.399183	+	0.691404i
$813$	4.07075	−	17.7978i	0.142767	−	0.624195i
$814$	9.04798	+	15.6716i	0.317132	+	0.549288i
$815$	1.64635	+	2.85156i	0.0576690	+	0.0998857i
$816$	5.18411	+	4.81454i	0.181480	+	0.168543i
$817$	8.56466	−	14.8344i	0.299639	−	0.518991i
$818$	−15.6043			−0.545590
$819$	7.00805	+	3.38276i	0.244881	+	0.118203i
$820$	10.6179			0.370793
$821$	−11.1291	+	19.2761i	−0.388407	+	0.672740i	−0.992235	−	0.124374i	$-0.960308\pi$
$821$	−11.1291	+	19.2761i	−0.388407	+	0.672740i	0.603829	+	0.797114i	$0.293641\pi$
$822$	3.66902	−	1.12991i	0.127972	−	0.0394103i
$823$	20.7561	+	35.9506i	0.723512	+	1.25316i	0.959584	+	0.281424i	$0.0908067\pi$
$823$	20.7561	+	35.9506i	0.723512	+	1.25316i	−0.236072	+	0.971736i	$0.575860\pi$
$824$	−7.33492	−	12.7045i	−0.255524	−	0.442581i
$825$	8.01752	−	2.46908i	0.279134	−	0.0859624i
$826$	−10.9712	+	19.0026i	−0.381736	+	0.661186i
$827$	33.5721			1.16741			0.583707	−	0.811964i	$-0.301602\pi$
$827$	33.5721			1.16741			0.583707	+	0.811964i	$0.301602\pi$
$828$	−67.1390	+	45.6852i	−2.33324	+	1.58767i
$829$	−1.07185			−0.0372268			−0.0186134	−	0.999827i	$-0.505925\pi$
$829$	−1.07185			−0.0372268			−0.0186134	+	0.999827i	$0.505925\pi$
$830$	−6.95561	+	12.0475i	−0.241433	+	0.418174i
$831$	−6.06893	−	5.63629i	−0.210529	−	0.195521i
$832$	−16.7066	−	28.9368i	−0.579199	−	1.00320i
$833$	1.53703	+	2.66221i	0.0532549	+	0.0922401i
$834$	−0.995867	+	4.35404i	−0.0344840	+	0.150768i
$835$	−1.01840	+	1.76392i	−0.0352432	+	0.0610430i
$836$	−10.8539			−0.375389
$837$	13.0442	+	1.98432i	0.450875	+	0.0685881i
$838$	8.05513			0.278260
$839$	11.8341	−	20.4973i	0.408559	−	0.707644i	−0.586170	−	0.810188i	$-0.699365\pi$
$839$	11.8341	−	20.4973i	0.408559	−	0.707644i	0.994728	+	0.102544i	$0.0326982\pi$
$840$	−0.310351	+	1.35689i	−0.0107081	+	0.0468171i
$841$	−15.9327	−	27.5963i	−0.549404	−	0.951596i
$842$	0.577795	+	1.00077i	0.0199121	+	0.0344888i
$843$	−2.39441	−	2.22372i	−0.0824678	−	0.0765888i
$844$	−20.5029	+	35.5121i	−0.705740	+	1.22238i
$845$	2.48147			0.0853651
$846$	3.54329	+	47.8665i	0.121821	+	1.64568i
$847$	1.00000			0.0343604
$848$	−6.03561	+	10.4540i	−0.207264	+	0.358991i
$849$	21.2954	−	6.55814i	0.730855	−	0.225075i
$850$	−16.5061	−	28.5894i	−0.566154	−	0.980608i
$851$	−37.8816	−	65.6129i	−1.29857	−	2.24918i
$852$	48.4098	−	14.9083i	1.65849	−	0.510751i
$853$	−17.7080	+	30.6711i	−0.606310	+	1.05016i	0.385533	+	0.922694i	$0.374017\pi$
$853$	−17.7080	+	30.6711i	−0.606310	+	1.05016i	−0.991843	+	0.127465i	$0.959316\pi$
$854$	14.5537			0.498019
$855$	0.326161	+	4.40612i	0.0111545	+	0.150686i
$856$	15.7931			0.539799
$857$	−2.74511	+	4.75467i	−0.0937712	+	0.162416i	−0.909095	−	0.416589i	$-0.863226\pi$
$857$	−2.74511	+	4.75467i	−0.0937712	+	0.162416i	0.815324	+	0.579005i	$0.196559\pi$
$858$	−7.29922	−	6.77887i	−0.249191	−	0.231427i
$859$	23.6691	+	40.9961i	0.807580	+	1.39877i	0.914536	+	0.404505i	$0.132556\pi$
$859$	23.6691	+	40.9961i	0.807580	+	1.39877i	−0.106956	+	0.994264i	$0.534110\pi$
$860$	2.65488	+	4.59839i	0.0905308	+	0.156804i
$861$	−3.55394	+	15.5382i	−0.121118	+	0.529541i
$862$	30.8411	−	53.4184i	1.05045	−	1.81944i
$863$	50.5488			1.72070			0.860351	−	0.509702i	$-0.170244\pi$
$863$	50.5488			1.72070			0.860351	+	0.509702i	$0.170244\pi$
$864$	−36.0021	−	5.47671i	−1.22482	−	0.186322i
$865$	−0.504596			−0.0171568
$866$	−1.91159	+	3.31097i	−0.0649586	+	0.112512i
$867$	−2.91577	+	12.7481i	−0.0990248	+	0.432948i
$868$	−3.70228	−	6.41253i	−0.125663	−	0.217656i
$869$	2.66476	+	4.61550i	0.0903958	+	0.156570i
$870$	−8.68633	−	8.06710i	−0.294494	−	0.273500i
$871$	−13.1607	+	22.7950i	−0.445934	+	0.772380i
$872$	−2.36855			−0.0802092
$873$	−28.0408	+	19.0805i	−0.949038	+	0.645779i
$874$	76.6095			2.59136
$875$	−1.94737	+	3.37294i	−0.0658331	+	0.114026i
$876$	−32.7096	+	10.0733i	−1.10516	+	0.340345i
$877$	9.94015	+	17.2169i	0.335655	+	0.581372i	0.983610	−	0.180307i	$-0.0577090\pi$
$877$	9.94015	+	17.2169i	0.335655	+	0.581372i	−0.647955	+	0.761678i	$0.724376\pi$
$878$	−13.4371	−	23.2738i	−0.453481	−	0.785453i
$879$	−21.0437	+	6.48063i	−0.709786	+	0.218586i
$880$	−0.262877	+	0.455315i	−0.00886157	+	0.0153487i
$881$	35.5597			1.19804			0.599018	−	0.800735i	$-0.295558\pi$
$881$	35.5597			1.19804			0.599018	+	0.800735i	$0.295558\pi$
$882$	−5.99030	−	2.89149i	−0.201704	−	0.0973617i
$883$	−54.8106			−1.84452			−0.922261	−	0.386568i	$-0.873661\pi$
$883$	−54.8106			−1.84452			−0.922261	+	0.386568i	$0.873661\pi$
$884$	−11.6261	+	20.1369i	−0.391027	+	0.677278i
$885$	−4.96957	−	4.61529i	−0.167050	−	0.155141i
$886$	−42.0992	−	72.9179i	−1.41435	−	2.44972i
$887$	0.269856	+	0.467405i	0.00906089	+	0.0156939i	0.870520	−	0.492133i	$-0.163782\pi$
$887$	0.269856	+	0.467405i	0.00906089	+	0.0156939i	−0.861459	+	0.507826i	$0.830449\pi$
$888$	−6.40170	+	27.9889i	−0.214827	+	0.939248i
$889$	7.16386	−	12.4082i	0.240268	−	0.416157i
$890$	−8.81188			−0.295375
$891$	−8.90190	+	1.32518i	−0.298225	+	0.0443952i
$892$	−53.1882			−1.78087
$893$	13.4292	−	23.2600i	0.449390	−	0.778366i
$894$	−10.8563	+	47.4650i	−0.363089	+	1.58747i
$895$	1.34082	+	2.32236i	0.0448186	+	0.0776281i
$896$	7.27210	+	12.5957i	0.242944	+	0.420791i
$897$	30.5600	+	28.3814i	1.02037	+	0.947628i
$898$	3.89381	−	6.74427i	0.129938	−	0.225059i
$899$	19.8103			0.660709
$900$	38.1583	+	18.4189i	1.27194	+	0.613963i
$901$	27.9263			0.930358
$902$	10.2021	−	17.6706i	0.339694	−	0.588367i
$903$	−7.61790	+	2.34601i	−0.253508	+	0.0780705i
$904$	−1.69819	−	2.94135i	−0.0564809	−	0.0978278i
$905$	2.09778	+	3.63347i	0.0697327	+	0.120781i
$906$	−45.4602	+	14.0000i	−1.51031	+	0.465118i
$907$	15.0236	−	26.0216i	0.498850	−	0.864034i	−0.501149	−	0.865361i	$-0.667089\pi$
$907$	15.0236	−	26.0216i	0.498850	−	0.864034i	0.999999	+	0.00132730i	$0.000422492\pi$
$908$	−35.2333			−1.16926
$909$	45.5813	−	31.0161i	1.51184	−	1.02874i
$910$	2.27560			0.0754354
$911$	−1.09989	+	1.90506i	−0.0364408	+	0.0631174i	−0.883671	−	0.468109i	$-0.844935\pi$
$911$	−1.09989	+	1.90506i	−0.0364408	+	0.0631174i	0.847230	+	0.531227i	$0.178269\pi$
$912$	6.27700	+	5.82952i	0.207852	+	0.193035i
$913$	7.92859	+	13.7327i	0.262398	+	0.454487i
$914$	−15.5749	−	26.9765i	−0.515171	−	0.892303i
$915$	−1.00299	+	4.38517i	−0.0331577	+	0.144969i
$916$	39.4763	−	68.3749i	1.30433	−	2.25917i
$917$	18.3091			0.604619
$918$	12.8940	+	32.9856i	0.425564	+	1.08869i
$919$	−42.0318			−1.38650			−0.693251	−	0.720696i	$-0.743822\pi$
$919$	−42.0318			−1.38650			−0.693251	+	0.720696i	$0.743822\pi$
$920$	−3.73002	+	6.46058i	−0.122975	+	0.212999i
$921$	8.19486	−	35.8289i	0.270030	−	1.18060i
$922$	−41.4194	−	71.7404i	−1.36407	−	2.36265i
$923$	−13.0071	−	22.5289i	−0.428134	−	0.741549i
$924$	3.70089	+	3.43706i	0.121750	+	0.113071i
$925$	−19.7651	+	34.2341i	−0.649872	+	1.12561i
$926$	−25.9948			−0.854244
$927$	1.59960	+	21.6090i	0.0525377	+	0.709734i
$928$	−54.6763			−1.79484
$929$	−2.38459	+	4.13023i	−0.0782358	+	0.135508i	−0.902489	−	0.430713i	$-0.858262\pi$
$929$	−2.38459	+	4.13023i	−0.0782358	+	0.135508i	0.824253	+	0.566222i	$0.191595\pi$
$930$	3.68748	−	1.13560i	0.120917	−	0.0372377i
$931$	1.86106	+	3.22345i	0.0609937	+	0.105644i
$932$	0.314618	+	0.544934i	0.0103056	+	0.0178499i
$933$	8.41193	−	2.59055i	0.275394	−	0.0848107i
$934$	−22.2805	+	38.5910i	−0.729040	+	1.26273i
$935$	1.21631			0.0397775
$936$	−1.16679	−	15.7622i	−0.0381376	−	0.515202i
$937$	44.4897			1.45342			0.726708	−	0.686947i	$-0.241050\pi$
$937$	44.4897			1.45342			0.726708	+	0.686947i	$0.241050\pi$
$938$	11.2494	−	19.4846i	0.367307	−	0.636195i
$939$	10.0320	+	9.31684i	0.327382	+	0.304044i
$940$	4.16279	+	7.21016i	0.135775	+	0.235170i
$941$	19.2517	+	33.3450i	0.627588	+	1.08701i	0.988034	+	0.154234i	$0.0492911\pi$
$941$	19.2517	+	33.3450i	0.627588	+	1.08701i	−0.360446	+	0.932780i	$0.617376\pi$
$942$	−16.1260	+	70.5045i	−0.525412	+	2.29716i
$943$	−42.7138	+	73.9825i	−1.39095	+	2.40920i
$944$	−13.1500			−0.427996
$945$	1.28406	−	1.60566i	0.0417704	−	0.0522321i
$946$	10.2037			0.331751
$947$	−8.17871	+	14.1659i	−0.265772	+	0.460331i	−0.967766	−	0.251852i	$-0.918960\pi$
$947$	−8.17871	+	14.1659i	−0.265772	+	0.460331i	0.701993	+	0.712184i	$0.252294\pi$
$948$	−6.00176	+	26.2404i	−0.194928	+	0.852249i
$949$	8.78866	+	15.2224i	0.285292	+	0.494140i
$950$	−19.9858	−	34.6165i	−0.648426	−	1.12311i
$951$	−0.271720	−	0.252349i	−0.00881112	−	0.00818299i
$952$	3.12181	−	5.40713i	0.101178	−	0.175246i
$953$	−38.9775			−1.26260			−0.631302	−	0.775537i	$-0.717479\pi$
$953$	−38.9775			−1.26260			−0.631302	+	0.775537i	$0.717479\pi$
$954$	−49.9580	+	33.9942i	−1.61745	+	1.10060i
$955$	−4.96634			−0.160707
$956$	−44.0526	+	76.3013i	−1.42476	+	2.46776i
$957$	−12.9143	+	3.97710i	−0.417460	+	0.128561i
$958$	32.3984	+	56.1156i	1.04674	+	1.81301i
$959$	0.499835	+	0.865740i	0.0161405	+	0.0279562i
$960$	−8.43684	+	2.59822i	−0.272298	+	0.0838570i
$961$	12.2761	−	21.2629i	0.396004	−	0.685899i
$962$	46.9395			1.51339
$963$	−21.0080	−	10.1405i	−0.676973	−	0.326772i
$964$	−25.9595			−0.836100
$965$	0.841298	−	1.45717i	0.0270823	−	0.0469080i
$966$	−26.1219	−	24.2597i	−0.840458	−	0.780543i
$967$	−4.75754	−	8.24030i	−0.152992	−	0.264990i	0.779334	−	0.626609i	$-0.215558\pi$
$967$	−4.75754	−	8.24030i	−0.152992	−	0.264990i	−0.932326	+	0.361619i	$0.882224\pi$
$968$	−1.01553	−	1.75896i	−0.0326405	−	0.0565350i
$969$	4.41874	−	19.3192i	0.141950	−	0.620623i
$970$	−4.95911	+	8.58943i	−0.159227	+	0.275790i
$971$	1.14791			0.0368383			0.0184192	−	0.999830i	$-0.494137\pi$
$971$	1.14791			0.0368383			0.0184192	+	0.999830i	$0.494137\pi$
$972$	−37.4997	−	25.6920i	−1.20280	−	0.824072i
$973$	−1.16305			−0.0372855
$974$	30.3731	−	52.6077i	0.973216	−	1.68566i
$975$	4.85185	−	21.2128i	0.155384	−	0.679355i
$976$	4.36101	+	7.55350i	0.139593	+	0.241782i
$977$	20.1748	+	34.9438i	0.645450	+	1.11795i	0.984197	+	0.177075i	$0.0566635\pi$
$977$	20.1748	+	34.9438i	0.645450	+	1.11795i	−0.338747	+	0.940877i	$0.610003\pi$
$978$	23.4175	+	21.7481i	0.748808	+	0.695427i
$979$	−5.02226	+	8.69881i	−0.160512	+	0.278015i
$980$	−1.15379			−0.0368564
$981$	3.15064	+	1.52080i	0.100592	+	0.0485554i
$982$	76.2675			2.43379
$983$	6.00762	−	10.4055i	0.191613	−	0.331884i	−0.754172	−	0.656677i	$-0.771961\pi$
$983$	6.00762	−	10.4055i	0.191613	−	0.331884i	0.945785	+	0.324793i	$0.105295\pi$
$984$	30.9402	−	9.52838i	0.986338	−	0.303754i
$985$	0.877373	+	1.51966i	0.0279554	+	0.0484202i
$986$	26.5874	+	46.0506i	0.846714	+	1.46655i
$987$	−11.9447	+	3.67849i	−0.380203	+	0.117088i
$988$	−14.0770	+	24.3821i	−0.447850	+	0.775698i
$989$	−42.7203			−1.35843
$990$	−2.17588	+	1.48059i	−0.0691541	+	0.0470563i
$991$	17.4757			0.555135			0.277567	−	0.960706i	$-0.410472\pi$
$991$	17.4757			0.555135			0.277567	+	0.960706i	$0.410472\pi$
$992$	8.89791	−	15.4116i	0.282509	−	0.489320i
$993$	−12.4012	−	11.5172i	−0.393542	−	0.365487i
$994$	11.1181	+	19.2572i	0.352646	+	0.610800i
$995$	0.712580	+	1.23422i	0.0225903	+	0.0391275i
$996$	−17.8573	+	78.0743i	−0.565831	+	2.47388i
$997$	16.7129	−	28.9475i	0.529302	−	0.916778i	−0.470114	−	0.882606i	$-0.655787\pi$
$997$	16.7129	−	28.9475i	0.529302	−	0.916778i	0.999416	−	0.0341723i	$-0.0108795\pi$
$998$	1.41620			0.0448291
$999$	26.4867	−	33.1204i	0.838002	−	1.04788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.j.f.232.1	✓	18
9.2	odd	6		6237.2.a.ba.1.1		9
9.4	even	3	inner	693.2.j.f.463.1	yes	18
9.7	even	3		6237.2.a.bb.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.j.f.232.1	✓	18	1.1	even	1	trivial
693.2.j.f.463.1	yes	18	9.4	even	3	inner
6237.2.a.ba.1.1		9	9.2	odd	6
6237.2.a.bb.1.9		9	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10861 + 1.92017i) q^{2} +(0.386186 - 1.68845i) q^{3} +(-1.45802 - 2.52537i) q^{4} +(0.197834 + 0.342659i) q^{5} +(2.81397 + 2.61337i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.03107 q^{8} +(-2.70172 - 1.30411i) q^{9} -0.877282 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-4.82702 + 1.48653i) q^{12} +(1.29696 + 2.24640i) q^{13} +(-1.10861 - 1.92017i) q^{14} +(0.654963 - 0.201703i) q^{15} +(0.664386 - 1.15075i) q^{16} -3.07406 q^{17} +(5.49926 - 3.74200i) q^{18} -3.72212 q^{19} +(0.576893 - 0.999209i) q^{20} +(1.26915 + 1.17867i) q^{21} +(-1.10861 - 1.92017i) q^{22} +(4.64146 + 8.03925i) q^{23} +(0.784370 - 3.42936i) q^{24} +(2.42172 - 4.19455i) q^{25} -5.75128 q^{26} +(-3.24529 + 4.05809i) q^{27} +2.91604 q^{28} +(-3.90081 + 6.75641i) q^{29} +(-0.338794 + 1.48125i) q^{30} +(-1.26962 - 2.19905i) q^{31} +(3.50416 + 6.06938i) q^{32} +(1.26915 + 1.17867i) q^{33} +(3.40792 - 5.90270i) q^{34} -0.395668 q^{35} +(0.645809 + 8.72426i) q^{36} -8.16157 q^{37} +(4.12637 - 7.14708i) q^{38} +(4.29380 - 1.32232i) q^{39} +(0.401815 + 0.695964i) q^{40} +(4.60133 + 7.96974i) q^{41} +(-3.67023 + 1.13029i) q^{42} +(-2.30102 + 3.98548i) q^{43} +2.91604 q^{44} +(-0.0876277 - 1.18377i) q^{45} -20.5822 q^{46} +(-3.60794 + 6.24913i) q^{47} +(-1.68641 - 1.56619i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(5.36948 + 9.30022i) q^{50} +(-1.18716 + 5.19039i) q^{51} +(3.78199 - 6.55060i) q^{52} -9.08450 q^{53} +(-4.19445 - 10.7303i) q^{54} -0.395668 q^{55} +(-1.01553 + 1.75896i) q^{56} +(-1.43743 + 6.28461i) q^{57} +(-8.64895 - 14.9804i) q^{58} +(-4.94818 - 8.57050i) q^{59} +(-1.46433 - 1.35994i) q^{60} +(-3.28199 + 5.68457i) q^{61} +5.63005 q^{62} +(2.48025 - 1.68770i) q^{63} -12.8814 q^{64} +(-0.513166 + 0.888829i) q^{65} +(-3.67023 + 1.13029i) q^{66} +(5.07368 + 8.78787i) q^{67} +(4.48204 + 7.76313i) q^{68} +(15.3663 - 4.73223i) q^{69} +(0.438641 - 0.759749i) q^{70} -10.0289 q^{71} +(-5.48738 - 2.64874i) q^{72} +6.77635 q^{73} +(9.04798 - 15.6716i) q^{74} +(-6.14704 - 5.70883i) q^{75} +(5.42693 + 9.39972i) q^{76} +(-0.500000 - 0.866025i) q^{77} +(-2.22106 + 9.71074i) q^{78} +(2.66476 - 4.61550i) q^{79} +0.525753 q^{80} +(5.59859 + 7.04669i) q^{81} -20.4043 q^{82} +(7.92859 - 13.7327i) q^{83} +(1.12614 - 4.92359i) q^{84} +(-0.608154 - 1.05335i) q^{85} +(-5.10185 - 8.83667i) q^{86} +(9.90141 + 9.19556i) q^{87} +(-1.01553 + 1.75896i) q^{88} +10.0445 q^{89} +(2.37017 + 1.14407i) q^{90} -2.59392 q^{91} +(13.5347 - 23.4428i) q^{92} +(-4.20330 + 1.29445i) q^{93} +(-7.99957 - 13.8557i) q^{94} +(-0.736362 - 1.27542i) q^{95} +(11.6011 - 3.57268i) q^{96} +(5.65281 - 9.79096i) q^{97} +2.21722 q^{98} +(2.48025 - 1.68770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{2} + q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} - 9 q^{7} - 12 q^{8} - 5 q^{9} - 26 q^{10} - 9 q^{11} - 5 q^{12} + 8 q^{13} - q^{14} + 16 q^{15} + 5 q^{16} - 28 q^{17} - 16 q^{18} - 24 q^{19} - 19 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) \) 18 * q - q^2 + q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 - 9 * q^7 - 12 * q^8 - 5 * q^9 - 26 * q^10 - 9 * q^11 - 5 * q^12 + 8 * q^13 - q^14 + 16 * q^15 + 5 * q^16 - 28 * q^17 - 16 * q^18 - 24 * q^19 - 19 * q^20 + q^21 - q^22 + 19 * q^23 - 6 * q^24 + q^25 - 20 * q^26 - 14 * q^27 + 6 * q^28 + 12 * q^29 + 2 * q^30 + 3 * q^31 - 4 * q^32 + q^33 + 12 * q^35 - 8 * q^36 - 38 * q^37 + 20 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 - 4 * q^42 + 32 * q^43 + 6 * q^44 + 22 * q^45 - 4 * q^46 - 8 * q^47 - 21 * q^48 - 9 * q^49 + 18 * q^50 - 3 * q^51 + 4 * q^52 + 30 * q^53 + 35 * q^54 + 12 * q^55 + 6 * q^56 + 18 * q^57 + 3 * q^58 - 8 * q^59 - 5 * q^60 + 2 * q^61 + 24 * q^62 + 10 * q^63 - 68 * q^64 + 20 * q^65 - 4 * q^66 + 49 * q^67 + 46 * q^68 - q^69 + 13 * q^70 - 18 * q^71 + 27 * q^72 - 70 * q^73 - 19 * q^74 - 34 * q^75 + 25 * q^76 - 9 * q^77 + 2 * q^78 + 21 * q^79 - 52 * q^80 + 19 * q^81 - 20 * q^82 + 16 * q^83 - 11 * q^84 + 52 * q^85 - 31 * q^86 - 28 * q^87 + 6 * q^88 + 38 * q^89 + 20 * q^90 - 16 * q^91 + 32 * q^92 + 18 * q^93 - 50 * q^94 - 4 * q^95 + 18 * q^96 + 24 * q^97 + 2 * q^98 + 10 * q^99

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