LMFDB - Embedded newform 798.2.bo.d.631.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(43,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bo (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,9,0,6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{10} + 153x^{8} - 773x^{6} + 2448x^{4} - 4608x^{2} + 4096 $ x^12 - 18x^10 + 153x^8 - 773x^6 + 2448x^4 - 4608*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			631.1
Root			$-1.74073 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	798.631
Dual form			798.2.bo.d.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0268090 + 0.0224954i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.0328860 + 0.0119695i) q^{10} +(1.79285 + 3.10531i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.575695 + 3.26493i) q^{13} +(0.766044 - 0.642788i) q^{14} +(-0.0268090 - 0.0224954i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.77099 - 0.644587i) q^{17} -1.00000 q^{18} +(4.35731 + 0.117758i) q^{19} -0.0349966 q^{20} +(0.939693 + 0.342020i) q^{21} +(0.622651 + 3.53123i) q^{22} +(-0.485735 - 0.407580i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-0.868028 + 4.92283i) q^{25} +(-1.65765 + 2.87113i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.939693 - 0.342020i) q^{28} +(2.72720 - 0.992620i) q^{29} +(-0.0174983 - 0.0303079i) q^{30} +(-1.02067 + 1.76785i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-2.74681 + 2.30485i) q^{33} +(-1.44372 - 1.21143i) q^{34} +(0.00607710 + 0.0344649i) q^{35} +(-0.939693 - 0.342020i) q^{36} +4.18821 q^{37} +(4.05425 + 1.60094i) q^{38} -3.31530 q^{39} +(-0.0328860 - 0.0119695i) q^{40} +(-0.400191 - 2.26960i) q^{41} +(0.766044 + 0.642788i) q^{42} +(4.76977 - 4.00232i) q^{43} +(-0.622651 + 3.53123i) q^{44} +(0.0174983 - 0.0303079i) q^{45} +(-0.317041 - 0.549131i) q^{46} +(-2.53554 + 0.922859i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.49939 + 4.32907i) q^{50} +(0.327266 - 1.85601i) q^{51} +(-2.53966 + 2.13103i) q^{52} +(2.27984 + 1.91301i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-0.117920 - 0.0429193i) q^{55} +1.00000 q^{56} +(0.640670 + 4.31156i) q^{57} +2.90223 q^{58} +(-11.9834 - 4.36161i) q^{59} +(-0.00607710 - 0.0344649i) q^{60} +(-3.60202 - 3.02245i) q^{61} +(-1.56375 + 1.31215i) q^{62} +(-0.173648 + 0.984808i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0580120 - 0.100480i) q^{65} +(-3.36946 + 1.22638i) q^{66} +(4.57755 - 1.66609i) q^{67} +(-0.942323 - 1.63215i) q^{68} +(0.317041 - 0.549131i) q^{69} +(-0.00607710 + 0.0344649i) q^{70} +(-10.8142 + 9.07419i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-2.01999 - 11.4559i) q^{73} +(3.93563 + 1.43245i) q^{74} -4.99878 q^{75} +(3.26220 + 2.89103i) q^{76} +3.58571 q^{77} +(-3.11536 - 1.13390i) q^{78} +(-0.666895 - 3.78215i) q^{79} +(-0.0268090 - 0.0224954i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.400191 - 2.26960i) q^{82} +(2.58714 - 4.48106i) q^{83} +(0.500000 + 0.866025i) q^{84} +(0.0619786 - 0.0225584i) q^{85} +(5.85099 - 2.12959i) q^{86} +(1.45111 + 2.51340i) q^{87} +(-1.79285 + 3.10531i) q^{88} +(2.33987 - 13.2701i) q^{89} +(0.0268090 - 0.0224954i) q^{90} +(2.53966 + 2.13103i) q^{91} +(-0.110107 - 0.624449i) q^{92} +(-1.91823 - 0.698178i) q^{93} -2.69826 q^{94} +(-0.119464 + 0.0948623i) q^{95} -1.00000 q^{96} +(13.9434 + 5.07499i) q^{97} +(-0.173648 - 0.984808i) q^{98} +(-2.74681 - 2.30485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{5} + 6 q^{7} + 6 q^{8} + 9 q^{10} + 3 q^{11} - 6 q^{12} - 9 q^{13} + 9 q^{15} + 15 q^{17} - 12 q^{18} + 9 q^{19} - 15 q^{22} + 3 q^{23} + 3 q^{25} + 3 q^{26} - 6 q^{27} + 3 q^{29} + 6 q^{31}+ \cdots - 12 q^{99}+O(q^{100}) $ 12 * q + 9 * q^5 + 6 * q^7 + 6 * q^8 + 9 * q^10 + 3 * q^11 - 6 * q^12 - 9 * q^13 + 9 * q^15 + 15 * q^17 - 12 * q^18 + 9 * q^19 - 15 * q^22 + 3 * q^23 + 3 * q^25 + 3 * q^26 - 6 * q^27 + 3 * q^29 + 6 * q^31 - 12 * q^33 - 6 * q^34 - 9 * q^38 + 6 * q^39 + 9 * q^40 - 27 * q^41 + 6 * q^43 + 15 * q^44 - 15 * q^46 - 6 * q^47 - 6 * q^49 - 21 * q^51 + 9 * q^52 - 9 * q^53 - 9 * q^55 + 12 * q^56 - 18 * q^57 + 12 * q^58 - 24 * q^59 - 15 * q^61 - 24 * q^62 - 6 * q^64 - 24 * q^65 + 3 * q^66 + 33 * q^67 - 6 * q^68 + 15 * q^69 - 33 * q^71 + 33 * q^73 + 12 * q^74 + 9 * q^76 + 6 * q^77 + 33 * q^79 + 9 * q^80 + 27 * q^82 - 36 * q^83 + 6 * q^84 + 15 * q^85 - 6 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 9 * q^90 - 9 * q^91 + 3 * q^92 - 21 * q^93 - 18 * q^94 - 18 * q^95 - 12 * q^96 + 21 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.0268090	+	0.0224954i	−0.0119893	+	0.0100602i	−0.648763	−	0.760991i	$-0.724713\pi$
$5$	−0.0268090	+	0.0224954i	−0.0119893	+	0.0100602i	0.636773	+	0.771051i	$0.280269\pi$
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−0.0328860	+	0.0119695i	−0.0103995	+	0.00378510i
$11$	1.79285	+	3.10531i	0.540566	+	0.936287i	0.998872	+	0.0474927i	$0.0151231\pi$
$11$	1.79285	+	3.10531i	0.540566	+	0.936287i	−0.458306	+	0.888794i	$0.651544\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.575695	+	3.26493i	−0.159669	+	0.905528i	0.794723	+	0.606972i	$0.207616\pi$
$13$	−0.575695	+	3.26493i	−0.159669	+	0.905528i	−0.954392	+	0.298556i	$0.903495\pi$
$14$	0.766044	−	0.642788i	0.204734	−	0.171792i
$15$	−0.0268090	−	0.0224954i	−0.00692204	−	0.00580828i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.77099	−	0.644587i	−0.429528	−	0.156335i	0.118204	−	0.992989i	$-0.462286\pi$
$17$	−1.77099	−	0.644587i	−0.429528	−	0.156335i	−0.547732	+	0.836654i	$0.684509\pi$
$18$	−1.00000			−0.235702
$19$	4.35731	+	0.117758i	0.999635	+	0.0270154i
$19$	4.35731	+	0.117758i	0.999635	+	0.0270154i
$20$	−0.0349966			−0.00782548
$21$	0.939693	+	0.342020i	0.205058	+	0.0746349i
$22$	0.622651	+	3.53123i	0.132750	+	0.752861i
$23$	−0.485735	−	0.407580i	−0.101283	−	0.0849864i	0.590740	−	0.806862i	$-0.298836\pi$
$23$	−0.485735	−	0.407580i	−0.101283	−	0.0849864i	−0.692023	+	0.721876i	$0.743280\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	−0.868028	+	4.92283i	−0.173606	+	0.984567i
$26$	−1.65765	+	2.87113i	−0.325092	+	0.563075i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	0.939693	−	0.342020i	0.177585	−	0.0646357i
$29$	2.72720	−	0.992620i	0.506429	−	0.184325i	−0.0761545	−	0.997096i	$-0.524264\pi$
$29$	2.72720	−	0.992620i	0.506429	−	0.184325i	0.582583	+	0.812771i	$0.302042\pi$
$30$	−0.0174983	−	0.0303079i	−0.00319474	−	0.00553345i
$31$	−1.02067	+	1.76785i	−0.183317	+	0.317515i	−0.943008	−	0.332769i	$-0.892017\pi$
$31$	−1.02067	+	1.76785i	−0.183317	+	0.317515i	0.759691	+	0.650284i	$0.225350\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−2.74681	+	2.30485i	−0.478158	+	0.401223i
$34$	−1.44372	−	1.21143i	−0.247597	−	0.207758i
$35$	0.00607710	+	0.0344649i	0.00102722	+	0.00582564i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	4.18821			0.688538			0.344269	−	0.938871i	$-0.388127\pi$
$37$	4.18821			0.688538			0.344269	+	0.938871i	$0.388127\pi$
$38$	4.05425	+	1.60094i	0.657687	+	0.259707i
$39$	−3.31530			−0.530872
$40$	−0.0328860	−	0.0119695i	−0.00519974	−	0.00189255i
$41$	−0.400191	−	2.26960i	−0.0624993	−	0.354451i	−0.999979	−	0.00641245i	$-0.997959\pi$
$41$	−0.400191	−	2.26960i	−0.0624993	−	0.354451i	0.937480	−	0.348039i	$-0.113152\pi$
$42$	0.766044	+	0.642788i	0.118203	+	0.0991843i
$43$	4.76977	−	4.00232i	0.727384	−	0.610347i	−0.202033	−	0.979379i	$-0.564755\pi$
$43$	4.76977	−	4.00232i	0.727384	−	0.610347i	0.929417	+	0.369031i	$0.120310\pi$
$44$	−0.622651	+	3.53123i	−0.0938682	+	0.532353i
$45$	0.0174983	−	0.0303079i	0.00260849	−	0.00451804i
$46$	−0.317041	−	0.549131i	−0.0467452	−	0.0809650i
$47$	−2.53554	+	0.922859i	−0.369846	+	0.134613i	−0.520255	−	0.854011i	$-0.674163\pi$
$47$	−2.53554	+	0.922859i	−0.369846	+	0.134613i	0.150409	+	0.988624i	$0.451941\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.49939	+	4.32907i	−0.353467	+	0.612222i
$51$	0.327266	−	1.85601i	0.0458263	−	0.259894i
$52$	−2.53966	+	2.13103i	−0.352188	+	0.295521i
$53$	2.27984	+	1.91301i	0.313160	+	0.262772i	0.785797	−	0.618485i	$-0.212253\pi$
$53$	2.27984	+	1.91301i	0.313160	+	0.262772i	−0.472637	+	0.881257i	$0.656698\pi$
$54$	−0.173648	−	0.984808i	−0.0236305	−	0.134015i
$55$	−0.117920	−	0.0429193i	−0.0159003	−	0.00578723i
$56$	1.00000			0.133631
$57$	0.640670	+	4.31156i	0.0848588	+	0.571080i
$58$	2.90223			0.381081
$59$	−11.9834	−	4.36161i	−1.56011	−	0.567833i	−0.589346	−	0.807881i	$-0.700615\pi$
$59$	−11.9834	−	4.36161i	−1.56011	−	0.567833i	−0.970761	+	0.240048i	$0.922837\pi$
$60$	−0.00607710	−	0.0344649i	−0.000784550	−	0.00444940i
$61$	−3.60202	−	3.02245i	−0.461191	−	0.386985i	0.382378	−	0.924006i	$-0.375105\pi$
$61$	−3.60202	−	3.02245i	−0.461191	−	0.386985i	−0.843569	+	0.537021i	$0.819550\pi$
$62$	−1.56375	+	1.31215i	−0.198597	+	0.166643i
$63$	−0.173648	+	0.984808i	−0.0218776	+	0.124074i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.0580120	−	0.100480i	−0.00719551	−	0.0124630i
$66$	−3.36946	+	1.22638i	−0.414752	+	0.150957i
$67$	4.57755	−	1.66609i	0.559236	−	0.203545i	−0.0469091	−	0.998899i	$-0.514937\pi$
$67$	4.57755	−	1.66609i	0.559236	−	0.203545i	0.606146	+	0.795354i	$0.292715\pi$
$68$	−0.942323	−	1.63215i	−0.114274	−	0.197928i
$69$	0.317041	−	0.549131i	0.0381673	−	0.0661077i
$70$	−0.00607710	+	0.0344649i	−0.000726352	+	0.00411935i
$71$	−10.8142	+	9.07419i	−1.28341	+	1.07691i	−0.290645	+	0.956831i	$0.593870\pi$
$71$	−10.8142	+	9.07419i	−1.28341	+	1.07691i	−0.992765	+	0.120077i	$0.961686\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	−2.01999	−	11.4559i	−0.236422	−	1.34082i	−0.839598	−	0.543208i	$-0.817209\pi$
$73$	−2.01999	−	11.4559i	−0.236422	−	1.34082i	0.603176	−	0.797608i	$-0.293902\pi$
$74$	3.93563	+	1.43245i	0.457508	+	0.166519i
$75$	−4.99878			−0.577209
$76$	3.26220	+	2.89103i	0.374200	+	0.331624i
$77$	3.58571			0.408629
$78$	−3.11536	−	1.13390i	−0.352745	−	0.128389i
$79$	−0.666895	−	3.78215i	−0.0750315	−	0.425525i	−0.999066	−	0.0432152i	$-0.986240\pi$
$79$	−0.666895	−	3.78215i	−0.0750315	−	0.425525i	0.924034	−	0.382310i	$-0.124871\pi$
$80$	−0.0268090	−	0.0224954i	−0.00299733	−	0.00251506i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	0.400191	−	2.26960i	0.0441937	−	0.250635i
$83$	2.58714	−	4.48106i	0.283976	−	0.491860i	−0.688385	−	0.725346i	$-0.741680\pi$
$83$	2.58714	−	4.48106i	0.283976	−	0.491860i	0.972360	+	0.233486i	$0.0750132\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	0.0619786	−	0.0225584i	0.00672252	−	0.00244680i
$86$	5.85099	−	2.12959i	0.630929	−	0.229639i
$87$	1.45111	+	2.51340i	0.155576	+	0.269465i
$88$	−1.79285	+	3.10531i	−0.191119	+	0.331027i
$89$	2.33987	−	13.2701i	0.248026	−	1.40663i	−0.565332	−	0.824863i	$-0.691252\pi$
$89$	2.33987	−	13.2701i	0.248026	−	1.40663i	0.813358	−	0.581763i	$-0.197637\pi$
$90$	0.0268090	−	0.0224954i	0.00282591	−	0.00237122i
$91$	2.53966	+	2.13103i	0.266229	+	0.223393i
$92$	−0.110107	−	0.624449i	−0.0114795	−	0.0651033i
$93$	−1.91823	−	0.698178i	−0.198911	−	0.0723977i
$94$	−2.69826			−0.278304
$95$	−0.119464	+	0.0948623i	−0.0122567	+	0.00973267i
$96$	−1.00000			−0.102062
$97$	13.9434	+	5.07499i	1.41574	+	0.515287i	0.932809	−	0.360371i	$-0.117350\pi$
$97$	13.9434	+	5.07499i	1.41574	+	0.515287i	0.482931	+	0.875659i	$0.339572\pi$
$98$	−0.173648	−	0.984808i	−0.0175411	−	0.0994806i
$99$	−2.74681	−	2.30485i	−0.276065	−	0.231646i
$100$	−3.82928	+	3.21315i	−0.382928	+	0.321315i
$101$	−0.666946	+	3.78244i	−0.0663636	+	0.376367i	0.933479	+	0.358632i	$0.116757\pi$
$101$	−0.666946	+	3.78244i	−0.0663636	+	0.376367i	−0.999843	+	0.0177350i	$0.994354\pi$
$102$	0.942323	−	1.63215i	0.0933039	−	0.161607i
$103$	0.475422	+	0.823455i	0.0468447	+	0.0811375i	0.888497	−	0.458882i	$-0.151750\pi$
$103$	0.475422	+	0.823455i	0.0468447	+	0.0811375i	−0.841652	+	0.540020i	$0.818417\pi$
$104$	−3.11536	+	1.13390i	−0.305486	+	0.111188i
$105$	−0.0328860	+	0.0119695i	−0.00320935	+	0.00116811i
$106$	1.48806	+	2.57739i	0.144533	+	0.250339i
$107$	6.51163	−	11.2785i	0.629503	−	1.09033i	−0.358148	−	0.933665i	$-0.616592\pi$
$107$	6.51163	−	11.2785i	0.629503	−	1.09033i	0.987652	−	0.156667i	$-0.0500748\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	10.3823	−	8.71182i	0.994448	−	0.834441i	0.00824270	−	0.999966i	$-0.497376\pi$
$109$	10.3823	−	8.71182i	0.994448	−	0.834441i	0.986206	+	0.165525i	$0.0529318\pi$
$110$	−0.0961290	−	0.0806618i	−0.00916554	−	0.00769080i
$111$	0.727276	+	4.12459i	0.0690300	+	0.391488i
$112$	0.939693	+	0.342020i	0.0887926	+	0.0323179i
$113$	9.54828			0.898227			0.449113	−	0.893475i	$-0.351740\pi$
$113$	9.54828			0.898227			0.449113	+	0.893475i	$0.351740\pi$
$114$	−0.872607	+	4.27066i	−0.0817271	+	0.399984i
$115$	0.0221907			0.00206930
$116$	2.72720	+	0.992620i	0.253214	+	0.0921625i
$117$	−0.575695	−	3.26493i	−0.0532230	−	0.301843i
$118$	−9.76897	−	8.19714i	−0.899306	−	0.754608i
$119$	−1.44372	+	1.21143i	−0.132346	+	0.111051i
$120$	0.00607710	−	0.0344649i	0.000554760	−	0.00314620i
$121$	−0.928647	+	1.60846i	−0.0844224	+	0.146224i
$122$	−2.35105	−	4.07214i	−0.212854	−	0.368674i
$123$	2.16562	−	0.788222i	0.195268	−	0.0710716i
$124$	−1.91823	+	0.698178i	−0.172262	+	0.0626982i
$125$	−0.174962	−	0.303042i	−0.0156490	−	0.0271049i
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	0.232841	−	1.32051i	0.0206613	−	0.117176i	−0.972733	−	0.231929i	$-0.925496\pi$
$127$	0.232841	−	1.32051i	0.0206613	−	0.117176i	0.993394	+	0.114753i	$0.0366075\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	4.76977	+	4.00232i	0.419955	+	0.352384i
$130$	−0.0201474	−	0.114261i	−0.00176704	−	0.0100214i
$131$	−14.1040	−	5.13344i	−1.23227	−	0.448510i	−0.357897	−	0.933761i	$-0.616506\pi$
$131$	−14.1040	−	5.13344i	−1.23227	−	0.448510i	−0.874375	+	0.485251i	$0.838728\pi$
$132$	−3.58571			−0.312096
$133$	2.28064	−	3.71466i	0.197756	−	0.322102i
$134$	4.87132			0.420818
$135$	0.0328860	+	0.0119695i	0.00283038	+	0.00103017i
$136$	−0.327266	−	1.85601i	−0.0280628	−	0.159152i
$137$	5.54433	+	4.65225i	0.473684	+	0.397468i	0.848136	−	0.529778i	$-0.177725\pi$
$137$	5.54433	+	4.65225i	0.473684	+	0.397468i	−0.374452	+	0.927246i	$0.622169\pi$
$138$	0.485735	−	0.407580i	0.0413485	−	0.0346955i
$139$	0.329246	−	1.86725i	0.0279263	−	0.158378i	−0.967656	−	0.252275i	$-0.918821\pi$
$139$	0.329246	−	1.86725i	0.0279263	−	0.158378i	0.995582	+	0.0938970i	$0.0299324\pi$
$140$	−0.0174983	+	0.0303079i	−0.00147888	+	0.00256149i
$141$	−1.34913	−	2.33676i	−0.113617	−	0.196791i
$142$	−13.2656	+	4.82828i	−1.11322	+	0.405180i
$143$	−11.1708	+	4.06583i	−0.934146	+	0.340001i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.0507841	+	0.0879606i	−0.00421739	+	0.00730473i
$146$	2.01999	−	11.4559i	0.167176	−	0.948100i
$147$	0.766044	−	0.642788i	0.0631823	−	0.0530162i
$148$	3.20836	+	2.69213i	0.263725	+	0.221292i
$149$	−2.91099	−	16.5090i	−0.238477	−	1.35247i	−0.835165	−	0.549999i	$-0.814628\pi$
$149$	−2.91099	−	16.5090i	−0.238477	−	1.35247i	0.596688	−	0.802473i	$-0.296483\pi$
$150$	−4.69731	−	1.70968i	−0.383534	−	0.139595i
$151$	9.11755			0.741976			0.370988	−	0.928638i	$-0.379019\pi$
$151$	9.11755			0.741976			0.370988	+	0.928638i	$0.379019\pi$
$152$	2.07667	+	3.83242i	0.168440	+	0.310850i
$153$	1.88465			0.152365
$154$	3.36946	+	1.22638i	0.271519	+	0.0988248i
$155$	−0.0124054	−	0.0703545i	−0.000996425	−	0.00565101i
$156$	−2.53966	−	2.13103i	−0.203336	−	0.170619i
$157$	6.08932	−	5.10954i	0.485980	−	0.407786i	−0.366603	−	0.930378i	$-0.619479\pi$
$157$	6.08932	−	5.10954i	0.485980	−	0.407786i	0.852583	+	0.522592i	$0.175035\pi$
$158$	0.666895	−	3.78215i	0.0530553	−	0.300891i
$159$	−1.48806	+	2.57739i	−0.118011	+	0.204401i
$160$	−0.0174983	−	0.0303079i	−0.00138336	−	0.00239605i
$161$	−0.595842	+	0.216869i	−0.0469590	+	0.0170917i
$162$	0.939693	−	0.342020i	0.0738292	−	0.0268716i
$163$	2.31095	+	4.00269i	0.181008	+	0.313515i	0.942224	−	0.334983i	$-0.108731\pi$
$163$	2.31095	+	4.00269i	0.181008	+	0.313515i	−0.761216	+	0.648498i	$0.775397\pi$
$164$	1.15230	−	1.99585i	0.0899798	−	0.155850i
$165$	0.0217907	−	0.123581i	0.00169640	−	0.00962078i
$166$	3.96373	−	3.32596i	0.307645	−	0.258145i
$167$	0.0329288	+	0.0276305i	0.00254811	+	0.00213811i	0.644061	−	0.764974i	$-0.277248\pi$
$167$	0.0329288	+	0.0276305i	0.00254811	+	0.00213811i	−0.641513	+	0.767112i	$0.721693\pi$
$168$	0.173648	+	0.984808i	0.0133972	+	0.0759796i
$169$	1.88767	+	0.687054i	0.145205	+	0.0528503i
$170$	0.0659562			0.00505861
$171$	−4.13481	+	1.37963i	−0.316196	+	0.105503i
$172$	6.22650			0.474766
$173$	−21.6056	−	7.86378i	−1.64264	−	0.597872i	−0.655143	−	0.755505i	$-0.727392\pi$
$173$	−21.6056	−	7.86378i	−1.64264	−	0.597872i	−0.987498	+	0.157633i	$0.949614\pi$
$174$	0.503967	+	2.85814i	0.0382056	+	0.216675i
$175$	3.82928	+	3.21315i	0.289467	+	0.242891i
$176$	−2.74681	+	2.30485i	−0.207049	+	0.173734i
$177$	2.21445	−	12.5587i	0.166448	−	0.943973i
$178$	6.73740	−	11.6695i	0.504989	−	0.874667i
$179$	2.09481	+	3.62831i	0.156573	+	0.271193i	0.933631	−	0.358237i	$-0.116622\pi$
$179$	2.09481	+	3.62831i	0.156573	+	0.271193i	−0.777057	+	0.629430i	$0.783289\pi$
$180$	0.0328860	−	0.0119695i	0.00245118	−	0.000892157i
$181$	14.8709	−	5.41258i	1.10535	−	0.402314i	0.276063	−	0.961139i	$-0.410970\pi$
$181$	14.8709	−	5.41258i	1.10535	−	0.402314i	0.829285	+	0.558825i	$0.188748\pi$
$182$	1.65765	+	2.87113i	0.122873	+	0.212822i
$183$	2.35105	−	4.07214i	0.173795	−	0.301021i
$184$	0.110107	−	0.624449i	0.00811721	−	0.0460350i
$185$	−0.112282	+	0.0942155i	−0.00825511	+	0.00692686i
$186$	−1.56375	−	1.31215i	−0.114660	−	0.0962111i
$187$	−1.17348	−	6.65513i	−0.0858132	−	0.486671i
$188$	−2.53554	−	0.922859i	−0.184923	−	0.0673064i
$189$	−1.00000			−0.0727393
$190$	−0.144704	+	0.0482824i	−0.0104979	+	0.00350277i
$191$	−10.8677			−0.786358			−0.393179	−	0.919462i	$-0.628625\pi$
$191$	−10.8677			−0.786358			−0.393179	+	0.919462i	$0.628625\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	2.03930	+	11.5655i	0.146792	+	0.832500i	0.965911	+	0.258876i	$0.0833520\pi$
$193$	2.03930	+	11.5655i	0.146792	+	0.832500i	−0.819118	+	0.573624i	$0.805537\pi$
$194$	11.3668	+	9.53786i	0.816087	+	0.684778i
$195$	0.0888796	−	0.0745788i	0.00636480	−	0.00534070i
$196$	0.173648	−	0.984808i	0.0124034	−	0.0703434i
$197$	−9.08304	+	15.7323i	−0.647140	+	1.12088i	0.336663	+	0.941625i	$0.390702\pi$
$197$	−9.08304	+	15.7323i	−0.647140	+	1.12088i	−0.983803	+	0.179254i	$0.942632\pi$
$198$	−1.79285	−	3.10531i	−0.127413	−	0.220685i
$199$	1.71109	−	0.622787i	0.121296	−	0.0441482i	−0.280659	−	0.959808i	$-0.590553\pi$
$199$	1.71109	−	0.622787i	0.121296	−	0.0441482i	0.401955	+	0.915659i	$0.368331\pi$
$200$	−4.69731	+	1.70968i	−0.332150	+	0.120893i
$201$	2.43566	+	4.21869i	0.171798	+	0.297563i
$202$	−1.92039	+	3.32622i	−0.135119	+	0.234032i
$203$	0.503967	−	2.85814i	0.0353715	−	0.200602i
$204$	1.44372	−	1.21143i	0.101081	−	0.0848169i
$205$	0.0617841	+	0.0518430i	0.00431519	+	0.00362087i
$206$	0.165112	+	0.936399i	0.0115039	+	0.0652420i
$207$	0.595842	+	0.216869i	0.0414139	+	0.0150734i
$208$	−3.31530			−0.229874
$209$	7.44634	+	13.7419i	0.515074	+	0.950549i
$210$	−0.0349966			−0.00241499
$211$	−13.5957	−	4.94844i	−0.935969	−	0.340665i	−0.171396	−	0.985202i	$-0.554828\pi$
$211$	−13.5957	−	4.94844i	−0.935969	−	0.340665i	−0.764573	+	0.644537i	$0.777050\pi$
$212$	0.516797	+	2.93090i	0.0354938	+	0.201295i
$213$	−10.8142	−	9.07419i	−0.740977	−	0.621753i
$214$	9.97640	−	8.37119i	0.681972	−	0.572243i
$215$	−0.0378390	+	0.214596i	−0.00258060	+	0.0146353i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	1.02067	+	1.76785i	0.0692874	+	0.120009i
$218$	12.7358	−	4.63546i	0.862579	−	0.313953i
$219$	10.9311	−	3.97861i	0.738657	−	0.268849i
$220$	−0.0627438	−	0.108675i	−0.00423018	−	0.00732689i
$221$	3.12408	−	5.41107i	0.210148	−	0.363988i
$222$	−0.727276	+	4.12459i	−0.0488116	+	0.276824i
$223$	−5.18215	+	4.34834i	−0.347023	+	0.291187i	−0.799593	−	0.600542i	$-0.794952\pi$
$223$	−5.18215	+	4.34834i	−0.347023	+	0.291187i	0.452571	+	0.891729i	$0.350507\pi$
$224$	0.766044	+	0.642788i	0.0511835	+	0.0429481i
$225$	−0.868028	−	4.92283i	−0.0578685	−	0.328189i
$226$	8.97245	+	3.26570i	0.596838	+	0.217231i
$227$	−16.9521			−1.12515			−0.562576	−	0.826746i	$-0.690189\pi$
$227$	−16.9521			−1.12515			−0.562576	+	0.826746i	$0.690189\pi$
$228$	−2.28064	+	3.71466i	−0.151039	+	0.246009i
$229$	−7.84659			−0.518517			−0.259259	−	0.965808i	$-0.583478\pi$
$229$	−7.84659			−0.518517			−0.259259	+	0.965808i	$0.583478\pi$
$230$	0.0208525	+	0.00758968i	0.00137497	+	0.000500448i
$231$	0.622651	+	3.53123i	0.0409675	+	0.232338i
$232$	2.22324	+	1.86552i	0.145963	+	0.122477i
$233$	1.17533	−	0.986220i	0.0769985	−	0.0646094i	−0.603476	−	0.797381i	$-0.706218\pi$
$233$	1.17533	−	0.986220i	0.0769985	−	0.0646094i	0.680475	+	0.732772i	$0.261774\pi$
$234$	0.575695	−	3.26493i	0.0376344	−	0.213435i
$235$	0.0472150	−	0.0817787i	0.00307996	−	0.00533466i
$236$	−6.37624	−	11.0440i	−0.415058	−	0.718901i
$237$	3.60888	−	1.31353i	0.234422	−	0.0853227i
$238$	−1.77099	+	0.644587i	−0.114796	+	0.0417824i
$239$	−1.06079	−	1.83734i	−0.0686166	−	0.118847i	0.829676	−	0.558245i	$-0.188525\pi$
$239$	−1.06079	−	1.83734i	−0.0686166	−	0.118847i	−0.898293	+	0.439398i	$0.855192\pi$
$240$	0.0174983	−	0.0303079i	0.00112951	−	0.00195637i
$241$	5.12534	−	29.0672i	0.330152	−	1.87239i	−0.140520	−	0.990078i	$-0.544877\pi$
$241$	5.12534	−	29.0672i	0.330152	−	1.87239i	0.470672	−	0.882308i	$-0.344011\pi$
$242$	−1.42277	+	1.19385i	−0.0914591	+	0.0767433i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	−0.816511	−	4.63066i	−0.0522718	−	0.296448i
$245$	0.0328860	+	0.0119695i	0.00210101	+	0.000764706i
$246$	2.30461			0.146936
$247$	−2.89295	+	14.1585i	−0.184074	+	0.900884i
$248$	−2.04134			−0.129625
$249$	4.86223	+	1.76971i	0.308132	+	0.112151i
$250$	−0.0607635	−	0.344607i	−0.00384302	−	0.0217949i
$251$	−6.96775	−	5.84663i	−0.439800	−	0.369036i	0.395834	−	0.918322i	$-0.370455\pi$
$251$	−6.96775	−	5.84663i	−0.439800	−	0.369036i	−0.835635	+	0.549286i	$0.814900\pi$
$252$	−0.766044	+	0.642788i	−0.0482563	+	0.0404918i
$253$	0.394812	−	2.23909i	0.0248216	−	0.140770i
$254$	0.670439	−	1.16123i	0.0420671	−	0.0728623i
$255$	0.0329781	+	0.0571198i	0.00206517	+	0.00357698i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−6.65694	+	2.42293i	−0.415248	+	0.151138i	−0.541191	−	0.840899i	$-0.682027\pi$
$257$	−6.65694	+	2.42293i	−0.415248	+	0.151138i	0.125943	+	0.992037i	$0.459804\pi$
$258$	3.11325	+	5.39230i	0.193822	+	0.335710i
$259$	2.09411	−	3.62710i	0.130121	−	0.225377i
$260$	0.0201474	−	0.114261i	0.00124949	−	0.00708619i
$261$	−2.22324	+	1.86552i	−0.137615	+	0.115473i
$262$	−11.4977	−	9.64770i	−0.710329	−	0.596037i
$263$	−0.509093	−	2.88721i	−0.0313920	−	0.178033i	0.965080	−	0.261954i	$-0.0843668\pi$
$263$	−0.509093	−	2.88721i	−0.0313920	−	0.178033i	−0.996472	+	0.0839209i	$0.973256\pi$
$264$	−3.36946	−	1.22638i	−0.207376	−	0.0754787i
$265$	−0.104154			−0.00639813
$266$	3.41358	−	2.71062i	0.209300	−	0.166199i
$267$	13.4748			0.824644
$268$	4.57755	+	1.66609i	0.279618	+	0.101773i
$269$	4.42796	+	25.1122i	0.269978	+	1.53112i	0.754476	+	0.656327i	$0.227891\pi$
$269$	4.42796	+	25.1122i	0.269978	+	1.53112i	−0.484499	+	0.874792i	$0.660998\pi$
$270$	0.0268090	+	0.0224954i	0.00163154	+	0.00136903i
$271$	−1.71099	+	1.43569i	−0.103935	+	0.0872120i	−0.693274	−	0.720674i	$-0.743833\pi$
$271$	−1.71099	+	1.43569i	−0.103935	+	0.0872120i	0.589339	+	0.807886i	$0.299388\pi$
$272$	0.327266	−	1.85601i	0.0198434	−	0.112537i
$273$	−1.65765	+	2.87113i	−0.100325	+	0.173769i
$274$	3.61881	+	6.26796i	0.218620	+	0.378661i
$275$	−16.8432	+	6.13042i	−1.01568	+	0.369678i
$276$	0.595842	−	0.216869i	0.0358655	−	0.0130540i
$277$	8.63438	+	14.9552i	0.518790	+	0.898570i	0.999762	+	0.0218340i	$0.00695054\pi$
$277$	8.63438	+	14.9552i	0.518790	+	0.898570i	−0.480972	+	0.876736i	$0.659716\pi$
$278$	0.948025	−	1.64203i	0.0568588	−	0.0984823i
$279$	0.354474	−	2.01032i	0.0212218	−	0.120355i
$280$	−0.0268090	+	0.0224954i	−0.00160214	+	0.00134436i
$281$	17.4692	+	14.6584i	1.04213	+	0.874448i	0.992244	−	0.124307i	$-0.0396709\pi$
$281$	17.4692	+	14.6584i	1.04213	+	0.874448i	0.0498823	+	0.998755i	$0.484115\pi$
$282$	−0.468548	−	2.65727i	−0.0279016	−	0.158238i
$283$	−22.8671	−	8.32295i	−1.35931	−	0.494748i	−0.443469	−	0.896290i	$-0.646252\pi$
$283$	−22.8671	−	8.32295i	−1.35931	−	0.494748i	−0.915841	+	0.401542i	$0.868475\pi$
$284$	−14.1169			−0.837686
$285$	−0.114166	−	0.101176i	−0.00676260	−	0.00599316i
$286$	−11.8877			−0.702933
$287$	−2.16562	−	0.788222i	−0.127833	−	0.0465273i
$288$	−0.173648	−	0.984808i	−0.0102323	−	0.0580304i
$289$	−10.3018	−	8.64428i	−0.605991	−	0.508487i
$290$	−0.0778057	+	0.0652867i	−0.00456891	+	0.00383377i
$291$	−2.57664	+	14.6128i	−0.151045	+	0.856620i
$292$	5.81633	−	10.0742i	0.340375	−	0.589547i
$293$	7.66890	+	13.2829i	0.448022	+	0.775997i	0.998257	−	0.0590129i	$-0.0187953\pi$
$293$	7.66890	+	13.2829i	0.448022	+	0.775997i	−0.550235	+	0.835010i	$0.685462\pi$
$294$	0.939693	−	0.342020i	0.0548040	−	0.0199470i
$295$	0.419379	−	0.152641i	0.0244172	−	0.00888712i
$296$	2.09411	+	3.62710i	0.121718	+	0.210821i
$297$	1.79285	−	3.10531i	0.104032	−	0.180189i
$298$	2.91099	−	16.5090i	0.168629	−	0.956343i
$299$	1.61036	−	1.35125i	0.0931293	−	0.0781448i
$300$	−3.82928	−	3.21315i	−0.221084	−	0.185511i
$301$	−1.08122	−	6.13190i	−0.0623205	−	0.353437i
$302$	8.56769	+	3.11839i	0.493015	+	0.179443i
$303$	−3.84079			−0.220648
$304$	0.640670	+	4.31156i	0.0367449	+	0.247285i
$305$	0.164558			0.00942254
$306$	1.77099	+	0.644587i	0.101241	+	0.0368486i
$307$	5.58913	+	31.6975i	0.318989	+	1.80907i	0.548928	+	0.835870i	$0.315036\pi$
$307$	5.58913	+	31.6975i	0.318989	+	1.80907i	−0.229939	+	0.973205i	$0.573853\pi$
$308$	2.74681	+	2.30485i	0.156514	+	0.131331i
$309$	−0.728389	+	0.611191i	−0.0414366	+	0.0347694i
$310$	0.0124054	−	0.0703545i	0.000704579	−	0.00399587i
$311$	−7.69009	+	13.3196i	−0.436065	+	0.755287i	−0.997382	−	0.0723139i	$-0.976962\pi$
$311$	−7.69009	+	13.3196i	−0.436065	+	0.755287i	0.561317	+	0.827601i	$0.310295\pi$
$312$	−1.65765	−	2.87113i	−0.0938458	−	0.162546i
$313$	−9.66698	+	3.51849i	−0.546410	+	0.198877i	−0.600451	−	0.799662i	$-0.705012\pi$
$313$	−9.66698	+	3.51849i	−0.546410	+	0.198877i	0.0540406	+	0.998539i	$0.482790\pi$
$314$	7.46965	−	2.71873i	0.421537	−	0.153427i
$315$	−0.0174983	−	0.0303079i	−0.000985918	−	0.00170766i
$316$	1.92025	−	3.32596i	0.108022	−	0.187100i
$317$	4.24744	−	24.0884i	0.238560	−	1.35294i	−0.596425	−	0.802669i	$-0.703413\pi$
$317$	4.24744	−	24.0884i	0.238560	−	1.35294i	0.834985	−	0.550272i	$-0.185476\pi$
$318$	−2.27984	+	1.91301i	−0.127847	+	0.107276i
$319$	7.97187	+	6.68919i	0.446339	+	0.374523i
$320$	−0.00607710	−	0.0344649i	−0.000339720	−	0.00192665i
$321$	12.2379	+	4.45422i	0.683051	+	0.248610i
$322$	−0.634082			−0.0353360
$323$	−7.64084	−	3.01721i	−0.425148	−	0.167882i
$324$	1.00000			0.0555556
$325$	−15.5730	−	5.66810i	−0.863834	−	0.314410i
$326$	0.802586	+	4.55169i	0.0444511	+	0.252095i
$327$	10.3823	+	8.71182i	0.574145	+	0.481765i
$328$	1.76543	−	1.48137i	0.0974797	−	0.0817952i
$329$	−0.468548	+	2.65727i	−0.0258319	+	0.146500i
$330$	0.0627438	−	0.108675i	0.00345393	−	0.00598238i
$331$	10.5737	+	18.3142i	0.581184	+	1.00664i	0.995339	+	0.0964344i	$0.0307438\pi$
$331$	10.5737	+	18.3142i	0.581184	+	1.00664i	−0.414155	+	0.910206i	$0.635923\pi$
$332$	4.86223	−	1.76971i	0.266850	−	0.0971254i
$333$	−3.93563	+	1.43245i	−0.215671	+	0.0784980i
$334$	0.0214927	+	0.0372265i	0.00117603	+	0.00203694i
$335$	−0.0852399	+	0.147640i	−0.00465715	+	0.00806642i
$336$	−0.173648	+	0.984808i	−0.00947328	+	0.0537257i
$337$	19.0185	−	15.9584i	1.03600	−	0.869309i	0.0444495	−	0.999012i	$-0.485847\pi$
$337$	19.0185	−	15.9584i	1.03600	−	0.869309i	0.991553	+	0.129702i	$0.0414022\pi$
$338$	1.53884	+	1.29124i	0.0837018	+	0.0702342i
$339$	1.65804	+	9.40322i	0.0900524	+	0.510713i
$340$	0.0619786	+	0.0225584i	0.00336126	+	0.00122340i
$341$	−7.31963			−0.396380
$342$	−4.35731	−	0.117758i	−0.235616	−	0.00636760i
$343$	−1.00000			−0.0539949
$344$	5.85099	+	2.12959i	0.315464	+	0.114820i
$345$	0.00385338	+	0.0218536i	0.000207459	+	0.00117656i
$346$	−17.6130	−	14.7791i	−0.946882	−	0.794528i
$347$	3.57165	−	2.99697i	0.191736	−	0.160886i	−0.541866	−	0.840465i	$-0.682282\pi$
$347$	3.57165	−	2.99697i	0.191736	−	0.160886i	0.733602	+	0.679579i	$0.237837\pi$
$348$	−0.503967	+	2.85814i	−0.0270154	+	0.153212i
$349$	−3.32726	+	5.76298i	−0.178104	+	0.308485i	−0.941231	−	0.337763i	$-0.890330\pi$
$349$	−3.32726	+	5.76298i	−0.178104	+	0.308485i	0.763127	+	0.646249i	$0.223663\pi$
$350$	2.49939	+	4.32907i	0.133598	+	0.231398i
$351$	3.11536	−	1.13390i	0.166286	−	0.0605230i
$352$	−3.36946	+	1.22638i	−0.179593	+	0.0653665i
$353$	−4.66102	−	8.07312i	−0.248081	−	0.429689i	0.714912	−	0.699214i	$-0.246467\pi$
$353$	−4.66102	−	8.07312i	−0.248081	−	0.429689i	−0.962993	+	0.269525i	$0.913133\pi$
$354$	6.37624	−	11.0440i	0.338893	−	0.586980i
$355$	0.0857900	−	0.486539i	0.00455326	−	0.0258228i
$356$	10.3223	−	8.66143i	0.547080	−	0.459055i
$357$	−1.44372	−	1.21143i	−0.0764099	−	0.0641156i
$358$	0.727519	+	4.12597i	0.0384506	+	0.218064i
$359$	−22.8602	−	8.32043i	−1.20651	−	0.439135i	−0.341021	−	0.940056i	$-0.610773\pi$
$359$	−22.8602	−	8.32043i	−1.20651	−	0.439135i	−0.865493	+	0.500920i	$0.832995\pi$
$360$	0.0349966			0.00184448
$361$	18.9723	+	1.02621i	0.998540	+	0.0540111i
$362$	15.8253			0.831761
$363$	−1.74528	−	0.635232i	−0.0916037	−	0.0333410i
$364$	0.575695	+	3.26493i	0.0301746	+	0.171129i
$365$	0.311860	+	0.261681i	0.0163235	+	0.0136970i
$366$	3.60202	−	3.02245i	0.188280	−	0.157986i
$367$	−1.44017	+	8.16759i	−0.0751761	+	0.426345i	0.923871	+	0.382704i	$0.125007\pi$
$367$	−1.44017	+	8.16759i	−0.0751761	+	0.426345i	−0.999047	+	0.0436412i	$0.986104\pi$
$368$	0.317041	−	0.549131i	0.0165269	−	0.0286255i
$369$	1.15230	+	1.99585i	0.0599865	+	0.103900i
$370$	−0.137734	+	0.0501310i	−0.00716044	+	0.00260619i
$371$	2.79664	−	1.01789i	0.145194	−	0.0528463i
$372$	−1.02067	−	1.76785i	−0.0529192	−	0.0916587i
$373$	−13.6332	+	23.6133i	−0.705899	+	1.22265i	0.260467	+	0.965483i	$0.416123\pi$
$373$	−13.6332	+	23.6133i	−0.705899	+	1.22265i	−0.966366	+	0.257170i	$0.917210\pi$
$374$	1.17348	−	6.65513i	0.0606791	−	0.344128i
$375$	0.268057	−	0.224926i	0.0138424	−	0.0116151i
$376$	−2.06699	−	1.73441i	−0.106597	−	0.0894453i
$377$	1.67080	+	9.47557i	0.0860505	+	0.488017i
$378$	−0.939693	−	0.342020i	−0.0483326	−	0.0175916i
$379$	−5.16558			−0.265338			−0.132669	−	0.991160i	$-0.542355\pi$
$379$	−5.16558			−0.265338			−0.132669	+	0.991160i	$0.542355\pi$
$380$	−0.152491	−	0.00412111i	−0.00782262	−	0.000211409i
$381$	1.34088			0.0686953
$382$	−10.2123	−	3.71697i	−0.522506	−	0.190177i
$383$	2.95463	+	16.7565i	0.150974	+	0.856218i	0.962374	+	0.271727i	$0.0875948\pi$
$383$	2.95463	+	16.7565i	0.150974	+	0.856218i	−0.811400	+	0.584491i	$0.801294\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$	−0.0961290	+	0.0806618i	−0.00489919	+	0.00411091i
$386$	−2.03930	+	11.5655i	−0.103798	+	0.588666i
$387$	−3.11325	+	5.39230i	−0.158255	+	0.274106i
$388$	7.41914	+	12.8503i	0.376650	+	0.652376i
$389$	−0.245776	+	0.0894553i	−0.0124614	+	0.00453556i	−0.348243	−	0.937404i	$-0.613222\pi$
$389$	−0.245776	+	0.0894553i	−0.0124614	+	0.00453556i	0.335782	+	0.941940i	$0.390999\pi$
$390$	0.109027	−	0.0396826i	0.00552080	−	0.00200941i
$391$	0.597511	+	1.03492i	0.0302174	+	0.0523381i
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$	2.60631	−	14.7811i	0.131471	−	0.745610i
$394$	−13.9160	+	11.6769i	−0.701079	+	0.588275i
$395$	0.102960	+	0.0863933i	0.00518046	+	0.00434692i
$396$	−0.622651	−	3.53123i	−0.0312894	−	0.177451i
$397$	18.3499	+	6.67882i	0.920955	+	0.335200i	0.758618	−	0.651535i	$-0.225875\pi$
$397$	18.3499	+	6.67882i	0.920955	+	0.335200i	0.162337	+	0.986735i	$0.448097\pi$
$398$	1.82091			0.0912738
$399$	4.05425	+	1.60094i	0.202967	+	0.0801474i
$400$	−4.99878			−0.249939
$401$	−17.5953	−	6.40417i	−0.878668	−	0.319809i	−0.136996	−	0.990572i	$-0.543745\pi$
$401$	−17.5953	−	6.40417i	−0.878668	−	0.319809i	−0.741672	+	0.670763i	$0.765967\pi$
$402$	0.845897	+	4.79732i	0.0421895	+	0.239268i
$403$	−5.18431	−	4.35015i	−0.258249	−	0.216696i
$404$	−2.94222	+	2.46881i	−0.146381	+	0.122828i
$405$	−0.00607710	+	0.0344649i	−0.000301973	+	0.00171258i
$406$	1.45111	−	2.51340i	0.0720176	−	0.124738i
$407$	7.50885	+	13.0057i	0.372200	+	0.644669i
$408$	1.77099	−	0.644587i	0.0876770	−	0.0319118i
$409$	0.875499	−	0.318656i	0.0432906	−	0.0157565i	−0.320284	−	0.947322i	$-0.603778\pi$
$409$	0.875499	−	0.318656i	0.0432906	−	0.0157565i	0.363575	+	0.931565i	$0.381556\pi$
$410$	0.0403267	+	0.0698479i	0.00199159	+	0.00344954i
$411$	−3.61881	+	6.26796i	−0.178503	+	0.309175i
$412$	−0.165112	+	0.936399i	−0.00813450	+	0.0461331i
$413$	−9.76897	+	8.19714i	−0.480699	+	0.403355i
$414$	0.485735	+	0.407580i	0.0238726	+	0.0200315i
$415$	0.0314446	+	0.178331i	0.00154355	+	0.00875394i
$416$	−3.11536	−	1.13390i	−0.152743	−	0.0555939i
$417$	1.89605			0.0928500
$418$	2.29725	+	15.4600i	0.112362	+	0.756173i
$419$	20.9513			1.02354			0.511770	−	0.859122i	$-0.328990\pi$
$419$	20.9513			1.02354			0.511770	+	0.859122i	$0.328990\pi$
$420$	−0.0328860	−	0.0119695i	−0.00160467	−	0.000584054i
$421$	−1.78984	−	10.1507i	−0.0872315	−	0.494714i	−0.996853	−	0.0792757i	$-0.974739\pi$
$421$	−1.78984	−	10.1507i	−0.0872315	−	0.494714i	0.909621	−	0.415439i	$-0.136372\pi$
$422$	−11.0833	−	9.30003i	−0.539529	−	0.452718i
$423$	2.06699	−	1.73441i	0.100500	−	0.0843298i
$424$	−0.516797	+	2.93090i	−0.0250979	+	0.142337i
$425$	4.71046	−	8.15876i	0.228491	−	0.395758i
$426$	−7.05847	−	12.2256i	−0.341984	−	0.592333i
$427$	−4.41853	+	1.60821i	−0.213828	+	0.0778269i
$428$	12.2379	−	4.45422i	0.591539	−	0.215303i
$429$	−5.94384	−	10.2950i	−0.286971	−	0.497049i
$430$	−0.108953	+	0.188712i	−0.00525419	+	0.00910052i
$431$	0.754991	−	4.28177i	0.0363666	−	0.206245i	−0.961210	−	0.275816i	$-0.911052\pi$
$431$	0.754991	−	4.28177i	0.0363666	−	0.206245i	0.997577	+	0.0695708i	$0.0221630\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	10.8521	+	9.10597i	0.521517	+	0.437605i	0.865160	−	0.501496i	$-0.167217\pi$
$433$	10.8521	+	9.10597i	0.521517	+	0.437605i	−0.343643	+	0.939100i	$0.611661\pi$
$434$	0.354474	+	2.01032i	0.0170153	+	0.0964986i
$435$	−0.0954428	−	0.0347383i	−0.00457613	−	0.00166558i
$436$	13.5532			0.649080
$437$	−2.06850	−	1.83315i	−0.0989499	−	0.0876915i
$438$	11.6327			0.555830
$439$	−32.1206	−	11.6909i	−1.53303	−	0.557978i	−0.568671	−	0.822565i	$-0.692542\pi$
$439$	−32.1206	−	11.6909i	−1.53303	−	0.557978i	−0.964362	+	0.264587i	$0.914764\pi$
$440$	−0.0217907	−	0.123581i	−0.00103883	−	0.00589150i
$441$	0.766044	+	0.642788i	0.0364783	+	0.0306089i
$442$	4.78637	−	4.01624i	0.227664	−	0.191033i
$443$	2.82197	−	16.0042i	0.134076	−	0.760383i	−0.841423	−	0.540378i	$-0.818281\pi$
$443$	2.82197	−	16.0042i	0.134076	−	0.760383i	0.975499	−	0.220005i	$-0.0706075\pi$
$444$	−2.09411	+	3.62710i	−0.0993819	+	0.172135i
$445$	0.235786	+	0.408393i	0.0111773	+	0.0193597i
$446$	−6.35685	+	2.31370i	−0.301006	+	0.109557i
$447$	15.7527	−	5.73353i	0.745079	−	0.271187i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−1.55351	+	2.69075i	−0.0733146	+	0.126985i	−0.900352	−	0.435162i	$-0.856691\pi$
$449$	−1.55351	+	2.69075i	−0.0733146	+	0.126985i	0.827038	+	0.562147i	$0.190024\pi$
$450$	0.868028	−	4.92283i	0.0409192	−	0.232065i
$451$	6.33032	−	5.31177i	0.298083	−	0.250122i
$452$	7.31441	+	6.13752i	0.344041	+	0.288684i
$453$	1.58325	+	8.97903i	0.0743874	+	0.421872i
$454$	−15.9298	−	5.79796i	−0.747621	−	0.272112i
$455$	−0.116024			−0.00543929
$456$	−3.41358	+	2.71062i	−0.159856	+	0.126936i
$457$	−12.1543			−0.568555			−0.284277	−	0.958742i	$-0.591754\pi$
$457$	−12.1543			−0.568555			−0.284277	+	0.958742i	$0.591754\pi$
$458$	−7.37338	−	2.68369i	−0.344536	−	0.125401i
$459$	0.327266	+	1.85601i	0.0152754	+	0.0866314i
$460$	0.0169991	+	0.0142639i	0.000792586	+	0.000665059i
$461$	10.2402	−	8.59252i	0.476932	−	0.400194i	−0.372383	−	0.928079i	$-0.621459\pi$
$461$	10.2402	−	8.59252i	0.476932	−	0.400194i	0.849316	+	0.527885i	$0.177015\pi$
$462$	−0.622651	+	3.53123i	−0.0289684	+	0.164288i
$463$	−8.04258	+	13.9302i	−0.373771	+	0.647390i	−0.990142	−	0.140066i	$-0.955269\pi$
$463$	−8.04258	+	13.9302i	−0.373771	+	0.647390i	0.616372	+	0.787455i	$0.288602\pi$
$464$	1.45111	+	2.51340i	0.0673663	+	0.116682i
$465$	0.0671315	−	0.0244338i	0.00311315	−	0.00113309i
$466$	1.44176	−	0.524757i	0.0667881	−	0.0243089i
$467$	0.624510	+	1.08168i	0.0288989	+	0.0500543i	0.880113	−	0.474764i	$-0.157467\pi$
$467$	0.624510	+	1.08168i	0.0288989	+	0.0500543i	−0.851214	+	0.524818i	$0.824133\pi$
$468$	1.65765	−	2.87113i	0.0766248	−	0.132718i
$469$	0.845897	−	4.79732i	0.0390599	−	0.221520i
$470$	0.0723375	−	0.0606984i	0.00333668	−	0.00279981i
$471$	6.08932	+	5.10954i	0.280581	+	0.235435i
$472$	−2.21445	−	12.5587i	−0.101928	−	0.578063i
$473$	20.9799	+	7.63608i	0.964659	+	0.351107i
$474$	3.84049			0.176400
$475$	−4.36197	+	21.3481i	−0.200141	+	0.979517i
$476$	−1.88465			−0.0863827
$477$	−2.79664	−	1.01789i	−0.128049	−	0.0466061i
$478$	−0.368408	−	2.08934i	−0.0168506	−	0.0955643i
$479$	25.2433	+	21.1816i	1.15340	+	0.967814i	0.999794	−	0.0203188i	$-0.00646812\pi$
$479$	25.2433	+	21.1816i	1.15340	+	0.967814i	0.153602	+	0.988133i	$0.450913\pi$
$480$	0.0268090	−	0.0224954i	0.00122366	−	0.00102677i
$481$	−2.41113	+	13.6742i	−0.109938	+	0.623491i
$482$	14.7578	−	25.5613i	0.672201	−	1.16429i
$483$	−0.317041	−	0.549131i	−0.0144259	−	0.0249863i
$484$	−1.74528	+	0.635232i	−0.0793311	+	0.0288742i
$485$	−0.487972	+	0.177607i	−0.0221577	+	0.00806474i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−2.93281	+	5.07978i	−0.132898	+	0.230187i	−0.924793	−	0.380472i	$-0.875762\pi$
$487$	−2.93281	+	5.07978i	−0.132898	+	0.230187i	0.791894	+	0.610658i	$0.209095\pi$
$488$	0.816511	−	4.63066i	0.0369617	−	0.209620i
$489$	−3.54059	+	2.97091i	−0.160111	+	0.134349i
$490$	0.0268090	+	0.0224954i	0.00121110	+	0.00101624i
$491$	0.645589	+	3.66131i	0.0291350	+	0.165233i	0.995904	−	0.0904196i	$-0.0288208\pi$
$491$	0.645589	+	3.66131i	0.0291350	+	0.165233i	−0.966769	+	0.255652i	$0.917710\pi$
$492$	2.16562	+	0.788222i	0.0976338	+	0.0355358i
$493$	−5.46967			−0.246342
$494$	−7.56098	+	12.3152i	−0.340185	+	0.554087i
$495$	0.125488			0.00564025
$496$	−1.91823	−	0.698178i	−0.0861310	−	0.0313491i
$497$	2.45138	+	13.9025i	0.109959	+	0.623611i
$498$	3.96373	+	3.32596i	0.177619	+	0.149040i
$499$	−33.1657	+	27.8293i	−1.48470	+	1.24581i	−0.583717	+	0.811957i	$0.698402\pi$
$499$	−33.1657	+	27.8293i	−1.48470	+	1.24581i	−0.900983	+	0.433854i	$0.857153\pi$
$500$	0.0607635	−	0.344607i	0.00271743	−	0.0154113i
$501$	−0.0214927	+	0.0372265i	−0.000960225	+	0.00166316i
$502$	−4.54787	−	7.87715i	−0.202982	−	0.351574i
$503$	−16.3507	+	5.95118i	−0.729043	+	0.265350i	−0.679760	−	0.733435i	$-0.737916\pi$
$503$	−16.3507	+	5.95118i	−0.729043	+	0.265350i	−0.0492832	+	0.998785i	$0.515694\pi$
$504$	−0.939693	+	0.342020i	−0.0418572	+	0.0152348i
$505$	−0.0672073	−	0.116406i	−0.00299069	−	0.00518002i
$506$	1.13682	−	1.96902i	0.0505377	−	0.0875338i
$507$	−0.348827	+	1.97829i	−0.0154919	+	0.0878591i
$508$	1.02717	−	0.861900i	0.0455734	−	0.0382406i
$509$	15.8667	+	13.3138i	0.703280	+	0.590122i	0.922705	−	0.385507i	$-0.125974\pi$
$509$	15.8667	+	13.3138i	0.703280	+	0.590122i	−0.219425	+	0.975629i	$0.570418\pi$
$510$	0.0114532	+	0.0649542i	0.000507155	+	0.00287622i
$511$	−10.9311	−	3.97861i	−0.483565	−	0.176003i
$512$	−1.00000			−0.0441942
$513$	−2.07667	−	3.83242i	−0.0916874	−	0.169205i
$514$	−7.08416			−0.312469
$515$	−0.0312695	−	0.0113812i	−0.00137790	−	0.000501514i
$516$	1.08122	+	6.13190i	0.0475981	+	0.269942i
$517$	−7.41161	−	6.21908i	−0.325962	−	0.273515i
$518$	3.20836	−	2.69213i	0.140967	−	0.118285i
$519$	3.99255	−	22.6429i	0.175253	−	0.993911i
$520$	0.0580120	−	0.100480i	0.00254400	−	0.00440633i
$521$	−1.20007	−	2.07858i	−0.0525760	−	0.0910643i	0.838540	−	0.544841i	$-0.183410\pi$
$521$	−1.20007	−	2.07858i	−0.0525760	−	0.0910643i	−0.891116	+	0.453776i	$0.850077\pi$
$522$	−2.72720	+	0.992620i	−0.119366	+	0.0434458i
$523$	13.1468	−	4.78505i	0.574870	−	0.209235i	−0.0381921	−	0.999270i	$-0.512160\pi$
$523$	13.1468	−	4.78505i	0.574870	−	0.209235i	0.613062	+	0.790035i	$0.289938\pi$
$524$	−7.50458	−	12.9983i	−0.327839	−	0.567834i
$525$	−2.49939	+	4.32907i	−0.109082	+	0.188936i
$526$	0.509093	−	2.88721i	0.0221975	−	0.125888i
$527$	2.94712	−	2.47293i	0.128379	−	0.107723i
$528$	−2.74681	−	2.30485i	−0.119540	−	0.100306i
$529$	−3.92409	−	22.2546i	−0.170613	−	0.967592i
$530$	−0.0978727	−	0.0356228i	−0.00425132	−	0.00154735i
$531$	12.7525			0.553411
$532$	4.13481	−	1.37963i	0.179267	−	0.0598146i
$533$	7.64046			0.330945
$534$	12.6622	+	4.60865i	0.547946	+	0.199436i
$535$	0.0791436	+	0.448846i	0.00342168	+	0.0194053i
$536$	3.73165	+	3.13123i	0.161183	+	0.135248i
$537$	−3.20943	+	2.69303i	−0.138497	+	0.116213i
$538$	−4.42796	+	25.1122i	−0.190903	+	1.08266i
$539$	1.79285	−	3.10531i	0.0772237	−	0.133755i
$540$	0.0174983	+	0.0303079i	0.000753007	+	0.00130425i
$541$	−38.2378	+	13.9174i	−1.64397	+	0.598357i	−0.987727	−	0.156191i	$-0.950078\pi$
$541$	−38.2378	+	13.9174i	−1.64397	+	0.598357i	−0.656245	+	0.754548i	$0.727856\pi$
$542$	−2.09884	+	0.763915i	−0.0901528	+	0.0328130i
$543$	7.91266	+	13.7051i	0.339565	+	0.588144i
$544$	0.942323	−	1.63215i	0.0404018	−	0.0699779i
$545$	−0.0823640	+	0.467110i	−0.00352809	+	0.0200088i
$546$	−2.53966	+	2.13103i	−0.108688	+	0.0911997i
$547$	27.5901	+	23.1508i	1.17967	+	0.989859i	0.999981	+	0.00613486i	$0.00195280\pi$
$547$	27.5901	+	23.1508i	1.17967	+	0.989859i	0.179687	+	0.983724i	$0.442492\pi$
$548$	1.25680	+	7.12766i	0.0536877	+	0.304478i
$549$	4.41853	+	1.60821i	0.188578	+	0.0686369i
$550$	−17.9241			−0.764288
$551$	12.0001	−	4.00400i	0.511223	−	0.170576i
$552$	0.634082			0.0269883
$553$	−3.60888	−	1.31353i	−0.153465	−	0.0558568i
$554$	2.99869	+	17.0064i	0.127402	+	0.722533i
$555$	−0.112282	−	0.0942155i	−0.00476609	−	0.00399922i
$556$	1.45246	−	1.21876i	0.0615980	−	0.0516869i
$557$	−4.83482	+	27.4196i	−0.204858	+	1.16181i	0.692805	+	0.721125i	$0.256375\pi$
$557$	−4.83482	+	27.4196i	−0.204858	+	1.16181i	−0.897663	+	0.440682i	$0.854737\pi$
$558$	1.02067	−	1.76785i	0.0432083	−	0.0748390i
$559$	10.3213	+	17.8771i	0.436546	+	0.756120i
$560$	−0.0328860	+	0.0119695i	−0.00138969	+	0.000505805i
$561$	6.35025	−	2.31130i	0.268108	−	0.0975832i
$562$	11.4022	+	19.7492i	0.480974	+	0.833071i
$563$	0.780059	−	1.35110i	0.0328756	−	0.0569422i	−0.849119	−	0.528201i	$-0.822867\pi$
$563$	0.780059	−	1.35110i	0.0328756	−	0.0569422i	0.881995	+	0.471259i	$0.156200\pi$
$564$	0.468548	−	2.65727i	0.0197294	−	0.111891i
$565$	−0.255979	+	0.214792i	−0.0107691	+	0.00903638i
$566$	−18.6415	−	15.6420i	−0.783559	−	0.657484i
$567$	−0.173648	−	0.984808i	−0.00729254	−	0.0413580i
$568$	−13.2656	−	4.82828i	−0.556611	−	0.202590i
$569$	45.0846			1.89005			0.945023	−	0.327003i	$-0.106039\pi$
$569$	45.0846			1.89005			0.945023	+	0.327003i	$0.106039\pi$
$570$	−0.0726765	−	0.134122i	−0.00304408	−	0.00561774i
$571$	−39.6156			−1.65786			−0.828930	−	0.559353i	$-0.811050\pi$
$571$	−39.6156			−1.65786			−0.828930	+	0.559353i	$0.811050\pi$
$572$	−11.1708	−	4.06583i	−0.467073	−	0.170001i
$573$	−1.88715	−	10.7026i	−0.0788370	−	0.447107i
$574$	−1.76543	−	1.48137i	−0.0736877	−	0.0618313i
$575$	2.42808	−	2.03740i	0.101258	−	0.0849655i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	9.68632	−	16.7772i	0.403247	−	0.698444i	−0.590869	−	0.806767i	$-0.701215\pi$
$577$	9.68632	−	16.7772i	0.403247	−	0.698444i	0.994116	+	0.108324i	$0.0345484\pi$
$578$	−6.72405	−	11.6464i	−0.279684	−	0.484426i
$579$	−11.0356	+	4.01664i	−0.458625	+	0.166926i
$580$	−0.0954428	+	0.0347383i	−0.00396305	+	0.00144243i
$581$	−2.58714	−	4.48106i	−0.107333	−	0.185906i
$582$	−7.41914	+	12.8503i	−0.307533	+	0.532663i
$583$	−1.85308	+	10.5094i	−0.0767469	+	0.435253i
$584$	8.91114	−	7.47733i	0.368746	−	0.309414i
$585$	0.0888796	+	0.0745788i	0.00367472	+	0.00308346i
$586$	2.66338	+	15.1048i	0.110023	+	0.623973i
$587$	19.4747	+	7.08821i	0.803807	+	0.292562i	0.711063	−	0.703128i	$-0.248214\pi$
$587$	19.4747	+	7.08821i	0.803807	+	0.292562i	0.0927436	+	0.995690i	$0.470436\pi$
$588$	1.00000			0.0412393
$589$	−4.65554	+	7.58287i	−0.191828	+	0.312447i
$590$	0.446293			0.0183736
$591$	−17.0705	−	6.21317i	−0.702188	−	0.255576i
$592$	0.727276	+	4.12459i	0.0298908	+	0.169519i
$593$	−1.19061	−	0.999039i	−0.0488924	−	0.0410256i	0.618014	−	0.786167i	$-0.287937\pi$
$593$	−1.19061	−	0.999039i	−0.0488924	−	0.0410256i	−0.666906	+	0.745141i	$0.732382\pi$
$594$	2.74681	−	2.30485i	0.112703	−	0.0945691i
$595$	0.0114532	−	0.0649542i	0.000469535	−	0.00266286i
$596$	8.38186	−	14.5178i	0.343334	−	0.594672i
$597$	0.910454	+	1.57695i	0.0372624	+	0.0645403i
$598$	1.97539	−	0.718985i	0.0807799	−	0.0294015i
$599$	−14.3386	+	5.21883i	−0.585860	+	0.213236i	−0.617908	−	0.786251i	$-0.712019\pi$
$599$	−14.3386	+	5.21883i	−0.585860	+	0.213236i	0.0320476	+	0.999486i	$0.489797\pi$
$600$	−2.49939	−	4.32907i	−0.102037	−	0.176733i
$601$	−1.81900	+	3.15060i	−0.0741984	+	0.128515i	−0.900737	−	0.434364i	$-0.856973\pi$
$601$	−1.81900	+	3.15060i	−0.0741984	+	0.128515i	0.826539	+	0.562879i	$0.190306\pi$
$602$	1.08122	−	6.13190i	0.0440672	−	0.249918i
$603$	−3.73165	+	3.13123i	−0.151965	+	0.127513i
$604$	6.98445	+	5.86065i	0.284193	+	0.238466i
$605$	−0.0112869	−	0.0640115i	−0.000458880	−	0.00260244i
$606$	−3.60916	−	1.31363i	−0.146612	−	0.0533625i
$607$	31.3480			1.27237			0.636187	−	0.771535i	$-0.280511\pi$
$607$	31.3480			1.27237			0.636187	+	0.771535i	$0.280511\pi$
$608$	−0.872607	+	4.27066i	−0.0353889	+	0.173198i
$609$	2.90223			0.117604
$610$	0.154633	+	0.0562820i	0.00626093	+	0.00227879i
$611$	−1.55338	−	8.80963i	−0.0628428	−	0.356399i
$612$	1.44372	+	1.21143i	0.0583591	+	0.0489691i
$613$	−22.4177	+	18.8107i	−0.905443	+	0.759757i	−0.971247	−	0.238076i	$-0.923483\pi$
$613$	−22.4177	+	18.8107i	−0.905443	+	0.759757i	0.0658037	+	0.997833i	$0.479039\pi$
$614$	−5.58913	+	31.6975i	−0.225559	+	1.27921i
$615$	−0.0403267	+	0.0698479i	−0.00162613	+	0.00281654i
$616$	1.79285	+	3.10531i	0.0722361	+	0.125117i
$617$	7.99111	−	2.90853i	0.321710	−	0.117093i	−0.176117	−	0.984369i	$-0.556354\pi$
$617$	7.99111	−	2.90853i	0.321710	−	0.117093i	0.497827	+	0.867276i	$0.334131\pi$
$618$	−0.893501	+	0.325208i	−0.0359419	+	0.0130818i
$619$	−5.35433	−	9.27396i	−0.215209	−	0.372752i	0.738129	−	0.674660i	$-0.235710\pi$
$619$	−5.35433	−	9.27396i	−0.215209	−	0.372752i	−0.953337	+	0.301908i	$0.902376\pi$
$620$	0.0357199	−	0.0618687i	0.00143455	−	0.00248471i
$621$	−0.110107	+	0.624449i	−0.00441845	+	0.0250583i
$622$	−11.7819	+	9.88620i	−0.472411	+	0.396400i
$623$	−10.3223	−	8.66143i	−0.413554	−	0.347013i
$624$	−0.575695	−	3.26493i	−0.0230462	−	0.130702i
$625$	−23.4751	−	8.54422i	−0.939002	−	0.341769i
$626$	−10.2874			−0.411167
$627$	−12.2401	+	9.71947i	−0.488823	+	0.388158i
$628$	7.94904			0.317201
$629$	−7.41728	−	2.69967i	−0.295746	−	0.107643i
$630$	−0.00607710	−	0.0344649i	−0.000242117	−	0.00137312i
$631$	−23.0015	−	19.3005i	−0.915674	−	0.768342i	0.0575161	−	0.998345i	$-0.481682\pi$
$631$	−23.0015	−	19.3005i	−0.915674	−	0.768342i	−0.973190	+	0.230003i	$0.926126\pi$
$632$	2.94199	−	2.46862i	0.117026	−	0.0981965i
$633$	2.51239	−	14.2485i	0.0998586	−	0.566326i
$634$	12.2300	−	21.1830i	0.485716	−	0.841285i
$635$	0.0234631	+	0.0406393i	0.000931104	+	0.00161272i
$636$	−2.79664	+	1.01789i	−0.110894	+	0.0403620i
$637$	3.11536	−	1.13390i	0.123435	−	0.0449267i
$638$	5.20327	+	9.01233i	0.205999	+	0.356801i
$639$	7.05847	−	12.2256i	0.279229	−	0.483638i
$640$	0.00607710	−	0.0344649i	0.000240218	−	0.00136235i
$641$	26.7472	−	22.4436i	1.05645	−	0.886469i	0.0626955	−	0.998033i	$-0.480030\pi$
$641$	26.7472	−	22.4436i	1.05645	−	0.886469i	0.993757	+	0.111564i	$0.0355859\pi$
$642$	9.97640	+	8.37119i	0.393737	+	0.330385i
$643$	3.33110	+	18.8916i	0.131366	+	0.745012i	0.977322	+	0.211760i	$0.0679194\pi$
$643$	3.33110	+	18.8916i	0.131366	+	0.745012i	−0.845956	+	0.533253i	$0.820969\pi$
$644$	−0.595842	−	0.216869i	−0.0234795	−	0.00854583i
$645$	−0.217906			−0.00858005
$646$	−6.14809	−	5.44857i	−0.241893	−	0.214371i
$647$	5.30007			0.208367			0.104184	−	0.994558i	$-0.466777\pi$
$647$	5.30007			0.208367			0.104184	+	0.994558i	$0.466777\pi$
$648$	0.939693	+	0.342020i	0.0369146	+	0.0134358i
$649$	−7.94035	−	45.0320i	−0.311686	−	1.76766i
$650$	−12.6952	−	10.6525i	−0.497947	−	0.417827i
$651$	−1.56375	+	1.31215i	−0.0612883	+	0.0514270i
$652$	−0.802586	+	4.55169i	−0.0314317	+	0.178258i
$653$	17.7863	−	30.8068i	0.696031	−	1.20556i	−0.273801	−	0.961786i	$-0.588281\pi$
$653$	17.7863	−	30.8068i	0.696031	−	1.20556i	0.969832	−	0.243775i	$-0.0783858\pi$
$654$	6.77659	+	11.7374i	0.264986	+	0.458969i
$655$	0.493592	−	0.179653i	0.0192862	−	0.00701962i
$656$	2.16562	−	0.788222i	0.0845534	−	0.0307749i
$657$	5.81633	+	10.0742i	0.226917	+	0.393031i
$658$	−1.34913	+	2.33676i	−0.0525946	+	0.0910965i
$659$	8.66179	−	49.1235i	0.337416	−	1.91358i	−0.0645314	−	0.997916i	$-0.520555\pi$
$659$	8.66179	−	49.1235i	0.337416	−	1.91358i	0.401947	−	0.915663i	$-0.368334\pi$
$660$	0.0961290	−	0.0806618i	0.00374182	−	0.00313976i
$661$	−20.5233	−	17.2211i	−0.798263	−	0.669822i	0.149513	−	0.988760i	$-0.452229\pi$
$661$	−20.5233	−	17.2211i	−0.798263	−	0.669822i	−0.947776	+	0.318938i	$0.896674\pi$
$662$	3.67221	+	20.8262i	0.142725	+	0.809432i
$663$	5.87135	+	2.13700i	0.228024	+	0.0829941i
$664$	5.17428			0.200801
$665$	0.0224213	+	0.150890i	0.000869460	+	0.00585126i
$666$	−4.18821			−0.162290
$667$	−1.72927	−	0.629403i	−0.0669576	−	0.0243706i
$668$	0.00746435	+	0.0423324i	0.000288804	+	0.00163789i
$669$	−5.18215	−	4.34834i	−0.200354	−	0.168117i
$670$	−0.130595	+	0.109582i	−0.00504533	+	0.00423353i
$671$	2.92777	−	16.6042i	0.113025	−	0.640998i
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	24.6177	+	42.6391i	0.948943	+	1.64362i	0.747657	+	0.664085i	$0.231179\pi$
$673$	24.6177	+	42.6391i	0.948943	+	1.64362i	0.201287	+	0.979532i	$0.435488\pi$
$674$	23.3296	−	8.49129i	0.898623	−	0.327072i
$675$	4.69731	−	1.70968i	0.180800	−	0.0658057i
$676$	1.00441	+	1.73968i	0.0386310	+	0.0669108i
$677$	24.4519	−	42.3520i	0.939764	−	1.62772i	0.173855	−	0.984771i	$-0.444378\pi$
$677$	24.4519	−	42.3520i	0.939764	−	1.62772i	0.765910	−	0.642948i	$-0.222289\pi$
$678$	−1.65804	+	9.40322i	−0.0636767	+	0.361128i
$679$	11.3668	−	9.53786i	0.436217	−	0.366029i
$680$	0.0505254	+	0.0423959i	0.00193756	+	0.00162581i
$681$	−2.94370	−	16.6946i	−0.112803	−	0.639737i
$682$	−6.87820	−	2.50346i	−0.263380	−	0.0958625i
$683$	−7.75146			−0.296601			−0.148301	−	0.988942i	$-0.547380\pi$
$683$	−7.75146			−0.296601			−0.148301	+	0.988942i	$0.547380\pi$
$684$	−4.05425	−	1.60094i	−0.155018	−	0.0612136i
$685$	−0.253292			−0.00967778
$686$	−0.939693	−	0.342020i	−0.0358776	−	0.0130584i
$687$	−1.36255	−	7.72738i	−0.0519844	−	0.294818i
$688$	4.76977	+	4.00232i	0.181846	+	0.152587i
$689$	−7.55834	+	6.34220i	−0.287950	+	0.241619i
$690$	−0.00385338	+	0.0218536i	−0.000146696	+	0.000831952i
$691$	10.9083	−	18.8938i	0.414973	−	0.718754i	−0.580453	−	0.814294i	$-0.697124\pi$
$691$	10.9083	−	18.8938i	0.414973	−	0.718754i	0.995426	+	0.0955401i	$0.0304578\pi$
$692$	−11.4961	−	19.9118i	−0.437015	−	0.756933i
$693$	−3.36946	+	1.22638i	−0.127995	+	0.0465865i
$694$	4.38128	−	1.59466i	0.166311	−	0.0605323i
$695$	0.0331777	+	0.0574654i	0.00125850	+	0.00217979i
$696$	−1.45111	+	2.51340i	−0.0550043	+	0.0952703i
$697$	−0.754219	+	4.27739i	−0.0285681	+	0.162018i
$698$	−5.09766	+	4.27744i	−0.192949	+	0.161904i
$699$	1.17533	+	0.986220i	0.0444551	+	0.0373023i
$700$	0.868028	+	4.92283i	0.0328084	+	0.186066i
$701$	−4.57262	−	1.66430i	−0.172705	−	0.0628596i	0.254220	−	0.967146i	$-0.418181\pi$
$701$	−4.57262	−	1.66430i	−0.172705	−	0.0628596i	−0.426926	+	0.904287i	$0.640403\pi$
$702$	3.31530			0.125128
$703$	18.2493	+	0.493194i	0.688287	+	0.0186012i
$704$	−3.58571			−0.135141
$705$	0.0887351	+	0.0322969i	0.00334196	+	0.00121637i
$706$	−1.61876	−	9.18042i	−0.0609227	−	0.345510i
$707$	2.94222	+	2.46881i	0.110653	+	0.0928492i
$708$	9.76897	−	8.19714i	0.367140	−	0.308067i
$709$	−3.12699	+	17.7341i	−0.117437	+	0.666016i	0.868078	+	0.496427i	$0.165355\pi$
$709$	−3.12699	+	17.7341i	−0.117437	+	0.666016i	−0.985515	+	0.169589i	$0.945756\pi$
$710$	0.247022	−	0.427855i	0.00927058	−	0.0160571i
$711$	1.92025	+	3.32596i	0.0720149	+	0.124733i
$712$	12.6622	−	4.60865i	0.474535	−	0.172717i
$713$	1.21631	−	0.442702i	0.0455513	−	0.0165793i
$714$	−0.942323	−	1.63215i	−0.0352656	−	0.0610818i
$715$	0.208014	−	0.360291i	0.00777929	−	0.0134741i
$716$	−0.727519	+	4.12597i	−0.0271887	+	0.154195i
$717$	1.62522	−	1.36372i	0.0606950	−	0.0509291i
$718$	−18.6358	−	15.6373i	−0.695482	−	0.583578i
$719$	2.51778	+	14.2791i	0.0938974	+	0.532519i	0.995080	+	0.0990784i	$0.0315895\pi$
$719$	2.51778	+	14.2791i	0.0938974	+	0.532519i	−0.901182	+	0.433441i	$0.857299\pi$
$720$	0.0328860	+	0.0119695i	0.00122559	+	0.000446079i
$721$	0.950844			0.0354113
$722$	17.4771	+	7.45322i	0.650431	+	0.277380i
$723$	29.5157			1.09770
$724$	14.8709	+	5.41258i	0.552674	+	0.201157i
$725$	2.51922	+	14.2872i	0.0935613	+	0.530613i
$726$	−1.42277	−	1.19385i	−0.0528039	−	0.0443077i
$727$	−0.161055	+	0.135141i	−0.00597319	+	0.00501210i	−0.645769	−	0.763533i	$-0.723463\pi$
$727$	−0.161055	+	0.135141i	−0.00597319	+	0.00501210i	0.639796	+	0.768545i	$0.279019\pi$
$728$	−0.575695	+	3.26493i	−0.0213367	+	0.121006i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.203552	+	0.352562i	0.00753379	+	0.0130489i
$731$	−11.0271	+	4.01352i	−0.407850	+	0.148445i
$732$	4.41853	−	1.60821i	0.163314	−	0.0594413i
$733$	−7.21852	−	12.5028i	−0.266622	−	0.461803i	0.701365	−	0.712802i	$-0.252574\pi$
$733$	−7.21852	−	12.5028i	−0.266622	−	0.461803i	−0.967987	+	0.250999i	$0.919241\pi$
$734$	−4.14680	+	7.18246i	−0.153061	+	0.265109i
$735$	−0.00607710	+	0.0344649i	−0.000224157	+	0.00127126i
$736$	0.485735	−	0.407580i	0.0179044	−	0.0150236i
$737$	13.3806	+	11.2277i	0.492881	+	0.413576i
$738$	0.400191	+	2.26960i	0.0147312	+	0.0835450i
$739$	−10.7706	−	3.92019i	−0.396204	−	0.144206i	0.136231	−	0.990677i	$-0.456501\pi$
$739$	−10.7706	−	3.92019i	−0.396204	−	0.144206i	−0.532436	+	0.846471i	$0.678723\pi$
$740$	−0.146573			−0.00538814
$741$	−14.4458	−	0.390401i	−0.530678	−	0.0143417i
$742$	2.97612			0.109257
$743$	−40.6758	−	14.8048i	−1.49225	−	0.543135i	−0.538211	−	0.842810i	$-0.680899\pi$
$743$	−40.6758	−	14.8048i	−1.49225	−	0.543135i	−0.954041	+	0.299675i	$0.903122\pi$
$744$	−0.354474	−	2.01032i	−0.0129957	−	0.0737020i
$745$	0.449418	+	0.377106i	0.0164654	+	0.0138161i
$746$	−20.8872	+	17.5265i	−0.764736	+	0.641690i
$747$	−0.898505	+	5.09567i	−0.0328746	+	0.186441i
$748$	3.37890	−	5.85242i	0.123545	−	0.213986i
$749$	−6.51163	−	11.2785i	−0.237930	−	0.412106i
$750$	0.328820	−	0.119681i	0.0120068	−	0.00437012i
$751$	−4.98638	+	1.81490i	−0.181956	+	0.0662265i	−0.431391	−	0.902165i	$-0.641977\pi$
$751$	−4.98638	+	1.81490i	−0.181956	+	0.0662265i	0.249436	+	0.968391i	$0.419755\pi$
$752$	−1.34913	−	2.33676i	−0.0491977	−	0.0852129i
$753$	4.54787	−	7.87715i	0.165734	−	0.287059i
$754$	−1.67080	+	9.47557i	−0.0608469	+	0.345080i
$755$	−0.244432	+	0.205103i	−0.00889579	+	0.00746445i
$756$	−0.766044	−	0.642788i	−0.0278608	−	0.0233780i
$757$	−7.25627	−	41.1523i	−0.263733	−	1.49571i	−0.772618	−	0.634872i	$-0.781053\pi$
$757$	−7.25627	−	41.1523i	−0.263733	−	1.49571i	0.508884	−	0.860835i	$-0.330058\pi$
$758$	−4.85406	−	1.76673i	−0.176307	−	0.0641706i
$759$	2.27363			0.0825277
$760$	−0.141885	−	0.0560276i	−0.00514671	−	0.00203233i
$761$	36.1760			1.31138			0.655689	−	0.755031i	$-0.272378\pi$
$761$	36.1760			1.31138			0.655689	+	0.755031i	$0.272378\pi$
$762$	1.26001	+	0.458607i	0.0456455	+	0.0166136i
$763$	−2.35349	−	13.3473i	−0.0852019	−	0.483204i
$764$	−8.32513	−	6.98561i	−0.301193	−	0.252731i
$765$	−0.0505254	+	0.0423959i	−0.00182675	+	0.00153283i
$766$	−2.95463	+	16.7565i	−0.106755	+	0.605438i
$767$	21.1391	−	36.6140i	0.763290	−	1.32206i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−15.2808	+	5.56174i	−0.551039	+	0.200562i	−0.602508	−	0.798113i	$-0.705832\pi$
$769$	−15.2808	+	5.56174i	−0.551039	+	0.200562i	0.0514693	+	0.998675i	$0.483610\pi$
$770$	−0.117920	+	0.0429193i	−0.00424953	+	0.00154670i
$771$	−3.54208	−	6.13507i	−0.127565	−	0.220949i
$772$	−5.87194	+	10.1705i	−0.211336	+	0.366044i
$773$	0.178791	−	1.01398i	0.00643067	−	0.0364702i	−0.981424	−	0.191853i	$-0.938550\pi$
$773$	0.178791	−	1.01398i	0.00643067	−	0.0364702i	0.987854	+	0.155383i	$0.0496613\pi$
$774$	−4.76977	+	4.00232i	−0.171446	+	0.143860i
$775$	−7.81685	−	6.55912i	−0.280790	−	0.235610i
$776$	2.57664	+	14.6128i	0.0924960	+	0.524571i
$777$	3.93563	+	1.43245i	0.141190	+	0.0513890i
$778$	−0.261550			−0.00937702
$779$	−1.47649	−	9.93645i	−0.0529009	−	0.356010i
$780$	0.116024			0.00415433
$781$	−47.5665	−	17.3128i	−1.70206	−	0.619500i
$782$	0.207513	+	1.17687i	0.00742066	+	0.0420847i
$783$	−2.22324	−	1.86552i	−0.0794520	−	0.0666681i
$784$	0.766044	−	0.642788i	0.0273587	−	0.0229567i
$785$	−0.0483071	+	0.273963i	−0.00172415	+	0.00977816i
$786$	7.50458	−	12.9983i	0.267680	−	0.463635i
$787$	14.4053	+	24.9507i	0.513493	+	0.889396i	0.999878	+	0.0156512i	$0.00498215\pi$
$787$	14.4053	+	24.9507i	0.513493	+	0.889396i	−0.486384	+	0.873745i	$0.661685\pi$
$788$	−17.0705	+	6.21317i	−0.608113	+	0.221335i
$789$	2.75494	−	1.00272i	0.0980786	−	0.0356977i
$790$	0.0672021	+	0.116397i	0.00239094	+	0.00414123i
$791$	4.77414	−	8.26905i	0.169749	−	0.294014i
$792$	0.622651	−	3.53123i	0.0221250	−	0.125477i
$793$	11.9418	−	10.0203i	0.424064	−	0.355832i
$794$	14.9590	+	12.5521i	0.530874	+	0.445456i
$795$	−0.0180861	−	0.102572i	−0.000641450	−	0.00363784i
$796$	1.71109	+	0.622787i	0.0606481	+	0.0220741i
$797$	−26.5055			−0.938871			−0.469436	−	0.882967i	$-0.655543\pi$
$797$	−26.5055			−0.938871			−0.469436	+	0.882967i	$0.655543\pi$
$798$	3.26220	+	2.89103i	0.115481	+	0.102341i
$799$	5.08527			0.179904
$800$	−4.69731	−	1.70968i	−0.166075	−	0.0604464i
$801$	2.33987	+	13.2701i	0.0826754	+	0.468875i
$802$	−14.3438	−	12.0359i	−0.506498	−	0.425003i
$803$	31.9527	−	26.8115i	1.12759	−	0.946158i
$804$	−0.845897	+	4.79732i	−0.0298325	+	0.169188i
$805$	0.0110954	−	0.0192177i	0.000391060	−	0.000677336i
$806$	−3.38382	−	5.86094i	−0.119190	−	0.206443i
$807$	−23.9618	+	8.72138i	−0.843495	+	0.307007i
$808$	−3.60916	+	1.31363i	−0.126970	+	0.0462133i
$809$	−0.978661	−	1.69509i	−0.0344079	−	0.0595962i	0.848309	−	0.529502i	$-0.177621\pi$
$809$	−0.978661	−	1.69509i	−0.0344079	−	0.0595962i	−0.882717	+	0.469906i	$0.844288\pi$
$810$	−0.0174983	+	0.0303079i	−0.000614828	+	0.00106491i
$811$	8.29515	−	47.0441i	0.291282	−	1.65194i	−0.390659	−	0.920535i	$-0.627753\pi$
$811$	8.29515	−	47.0441i	0.291282	−	1.65194i	0.681941	−	0.731407i	$-0.261136\pi$
$812$	2.22324	−	1.86552i	0.0780203	−	0.0654668i
$813$	−1.71099	−	1.43569i	−0.0600070	−	0.0503519i
$814$	2.60780	+	14.7896i	0.0914033	+	0.518374i
$815$	−0.151996	−	0.0553221i	−0.00532420	−	0.00193785i
$816$	1.88465			0.0659758
$817$	21.2547	−	16.8776i	0.743607	−	0.590474i
$818$	0.931686			0.0325757
$819$	−3.11536	−	1.13390i	−0.108859	−	0.0396216i
$820$	0.0140053	+	0.0794281i	0.000489087	+	0.00277375i
$821$	9.30800	+	7.81034i	0.324852	+	0.272583i	0.790598	−	0.612335i	$-0.209770\pi$
$821$	9.30800	+	7.81034i	0.324852	+	0.272583i	−0.465747	+	0.884918i	$0.654214\pi$
$822$	−5.54433	+	4.65225i	−0.193381	+	0.162266i
$823$	6.44139	−	36.5309i	0.224533	−	1.27339i	−0.639044	−	0.769170i	$-0.720670\pi$
$823$	6.44139	−	36.5309i	0.224533	−	1.27339i	0.863577	−	0.504218i	$-0.168219\pi$
$824$	−0.475422	+	0.823455i	−0.0165621	+	0.0286864i
$825$	−8.96207	−	15.5228i	−0.312019	−	0.540433i
$826$	−11.9834	+	4.36161i	−0.416956	+	0.151760i
$827$	−6.65654	+	2.42278i	−0.231470	+	0.0842484i	−0.455151	−	0.890414i	$-0.650415\pi$
$827$	−6.65654	+	2.42278i	−0.231470	+	0.0842484i	0.223681	+	0.974662i	$0.428193\pi$
$828$	0.317041	+	0.549131i	0.0110179	+	0.0190836i
$829$	21.1780	−	36.6813i	0.735541	−	1.27399i	−0.218944	−	0.975737i	$-0.570261\pi$
$829$	21.1780	−	36.6813i	0.735541	−	1.27399i	0.954486	−	0.298257i	$-0.0964053\pi$
$830$	−0.0314446	+	0.178331i	−0.00109146	+	0.00618997i
$831$	−13.2286	+	11.1001i	−0.458896	+	0.385060i
$832$	−2.53966	−	2.13103i	−0.0880470	−	0.0738802i
$833$	0.327266	+	1.85601i	0.0113391	+	0.0643071i
$834$	1.78170	+	0.648488i	0.0616954	+	0.0224553i
$835$	−0.00150435			−5.20600e−5
$836$	−3.12891	+	15.3133i	−0.108216	+	0.529623i
$837$	2.04134			0.0705589
$838$	19.6878	+	7.16578i	0.680105	+	0.247538i
$839$	1.31203	+	7.44089i	0.0452963	+	0.256888i	0.999044	−	0.0437208i	$-0.0139212\pi$
$839$	1.31203	+	7.44089i	0.0452963	+	0.256888i	−0.953747	+	0.300609i	$0.902810\pi$
$840$	−0.0268090	−	0.0224954i	−0.000924997	−	0.000776164i
$841$	−15.7630	+	13.2267i	−0.543550	+	0.456093i
$842$	1.78984	−	10.1507i	0.0616820	−	0.349816i
$843$	−11.4022	+	19.7492i	−0.392713	+	0.680199i
$844$	−7.23414	−	12.5299i	−0.249009	−	0.431297i
$845$	−0.0660619	+	0.0240446i	−0.00227260	+	0.000827158i
$846$	2.53554	−	0.922859i	0.0871735	−	0.0317286i
$847$	0.928647	+	1.60846i	0.0319087	+	0.0552674i
$848$	−1.48806	+	2.57739i	−0.0511001	+	0.0885080i
$849$	4.22567	−	23.9650i	0.145025	−	0.822476i
$850$	7.21685	−	6.05565i	0.247536	−	0.207707i
$851$	−2.03436	−	1.70703i	−0.0697371	−	0.0585164i
$852$	−2.45138	−	13.9025i	−0.0839829	−	0.476291i
$853$	−30.9028	−	11.2477i	−1.05809	−	0.385114i	−0.246382	−	0.969173i	$-0.579242\pi$
$853$	−30.9028	−	11.2477i	−1.05809	−	0.385114i	−0.811712	+	0.584058i	$0.801464\pi$
$854$	−4.70210			−0.160903
$855$	0.0798145	−	0.130000i	0.00272960	−	0.00444592i
$856$	13.0233			0.445126
$857$	17.3504	+	6.31502i	0.592678	+	0.215717i	0.620907	−	0.783884i	$-0.286765\pi$
$857$	17.3504	+	6.31502i	0.592678	+	0.215717i	−0.0282290	+	0.999601i	$0.508987\pi$
$858$	−2.06427	−	11.7071i	−0.0704731	−	0.399673i
$859$	1.18301	+	0.992660i	0.0403636	+	0.0338691i	0.662746	−	0.748844i	$-0.269391\pi$
$859$	1.18301	+	0.992660i	0.0403636	+	0.0338691i	−0.622383	+	0.782713i	$0.713835\pi$
$860$	−0.166926	+	0.140067i	−0.00569212	+	0.00477626i
$861$	0.400191	−	2.26960i	0.0136385	−	0.0773476i
$862$	2.17391	−	3.76532i	0.0740437	−	0.128247i
$863$	−14.3435	−	24.8436i	−0.488257	−	0.845686i	0.511652	−	0.859193i	$-0.329034\pi$
$863$	−14.3435	−	24.8436i	−0.488257	−	0.845686i	−0.999909	+	0.0135068i	$0.995701\pi$
$864$	0.939693	−	0.342020i	0.0319690	−	0.0116358i
$865$	0.756121	−	0.275206i	0.0257089	−	0.00935727i
$866$	7.08318	+	12.2684i	0.240696	+	0.416898i
$867$	6.72405	−	11.6464i	0.228361	−	0.395533i
$868$	−0.354474	+	2.01032i	−0.0120316	+	0.0682348i
$869$	10.5491	−	8.85175i	0.357854	−	0.300275i
$870$	−0.0778057	−	0.0652867i	−0.00263786	−	0.00221343i
$871$	2.80440	+	15.9045i	0.0950234	+	0.538904i
$872$	12.7358	+	4.63546i	0.431290	+	0.156977i
$873$	−14.8383			−0.502200
$874$	−1.31678	−	2.43007i	−0.0445408	−	0.0821983i
$875$	−0.349923			−0.0118296
$876$	10.9311	+	3.97861i	0.369329	+	0.134425i
$877$	−4.86701	−	27.6022i	−0.164347	−	0.932059i	−0.949735	−	0.313055i	$-0.898648\pi$
$877$	−4.86701	−	27.6022i	−0.164347	−	0.932059i	0.785388	−	0.619004i	$-0.212463\pi$
$878$	−26.1850	−	21.9718i	−0.883699	−	0.741512i
$879$	−11.7494	+	9.85895i	−0.396299	+	0.332534i
$880$	0.0217907	−	0.123581i	0.000734564	−	0.00416592i
$881$	−5.95785	+	10.3193i	−0.200725	+	0.347666i	−0.948762	−	0.315991i	$-0.897663\pi$
$881$	−5.95785	+	10.3193i	−0.200725	+	0.347666i	0.748037	+	0.663657i	$0.230996\pi$
$882$	0.500000	+	0.866025i	0.0168359	+	0.0291606i
$883$	−17.4392	+	6.34736i	−0.586877	+	0.213606i	−0.618355	−	0.785899i	$-0.712201\pi$
$883$	−17.4392	+	6.34736i	−0.586877	+	0.213606i	0.0314784	+	0.999504i	$0.489978\pi$
$884$	5.87135	−	2.13700i	0.197475	−	0.0718750i
$885$	0.223147	+	0.386501i	0.00750100	+	0.0129921i
$886$	8.12555	−	14.0739i	0.272983	−	0.472821i
$887$	−0.278021	+	1.57674i	−0.00933504	+	0.0529416i	−0.989119	−	0.147115i	$-0.953001\pi$
$887$	−0.278021	+	1.57674i	−0.00933504	+	0.0529416i	0.979784	+	0.200056i	$0.0641125\pi$
$888$	−3.20836	+	2.69213i	−0.107665	+	0.0903420i
$889$	−1.02717	−	0.861900i	−0.0344503	−	0.0289072i
$890$	0.0818876	+	0.464408i	0.00274488	+	0.0155670i
$891$	3.36946	+	1.22638i	0.112881	+	0.0410854i
$892$	−6.76482			−0.226503
$893$	−11.1568	+	3.72260i	−0.373347	+	0.124572i
$894$	16.7637			0.560662
$895$	−0.137780	−	0.0501478i	−0.00460547	−	0.00167626i
$896$	0.173648	+	0.984808i	0.00580118	+	0.0329001i
$897$	1.61036	+	1.35125i	0.0537682	+	0.0451169i
$898$	−2.38011	+	1.99715i	−0.0794254	+	0.0666458i
$899$	−1.02876	+	5.83441i	−0.0343112	+	0.194589i
$900$	2.49939	−	4.32907i	0.0833129	−	0.144302i
$901$	−2.80446	−	4.85748i	−0.0934303	−	0.161826i
$902$	7.76529	−	2.82633i	0.258556	−	0.0941066i
$903$	5.85099	−	2.12959i	0.194709	−	0.0708682i
$904$	4.77414	+	8.26905i	0.158786	+	0.275025i
$905$	−0.276916	+	0.479633i	−0.00920501	+	0.0159435i
$906$	−1.58325	+	8.97903i	−0.0525998	+	0.298308i
$907$	38.3574	−	32.1857i	1.27364	−	1.06871i	0.279548	−	0.960132i	$-0.409815\pi$
$907$	38.3574	−	32.1857i	1.27364	−	1.06871i	0.994088	−	0.108576i	$-0.0346290\pi$
$908$	−12.9861	−	10.8966i	−0.430958	−	0.361617i
$909$	−0.666946	−	3.78244i	−0.0221212	−	0.125456i
$910$	−0.109027	−	0.0396826i	−0.00361421	−	0.00131546i
$911$	−47.5980			−1.57699			−0.788496	−	0.615040i	$-0.789140\pi$
$911$	−47.5980			−1.57699			−0.788496	+	0.615040i	$0.789140\pi$
$912$	−4.13481	+	1.37963i	−0.136917	+	0.0456842i
$913$	18.5535			0.614030
$914$	−11.4213	−	4.15702i	−0.377783	−	0.137502i
$915$	0.0285751	+	0.162058i	0.000944664	+	0.00535746i
$916$	−6.01084	−	5.04369i	−0.198604	−	0.166648i
$917$	−11.4977	+	9.64770i	−0.379687	+	0.318595i
$918$	−0.327266	+	1.85601i	−0.0108014	+	0.0612576i
$919$	11.3990	−	19.7436i	0.376018	−	0.651282i	−0.614461	−	0.788947i	$-0.710627\pi$
$919$	11.3990	−	19.7436i	0.376018	−	0.651282i	0.990479	+	0.137665i	$0.0439599\pi$
$920$	0.0110954	+	0.0192177i	0.000365803	+	0.000633590i
$921$	−30.2454	+	11.0084i	−0.996621	+	0.362741i
$922$	12.5614	−	4.57199i	0.413689	−	0.150570i
$923$	−23.4009	−	40.5316i	−0.770250	−	1.33411i
$924$	−1.79285	+	3.10531i	−0.0589805	+	0.102157i
$925$	−3.63549	+	20.6179i	−0.119534	+	0.677912i
$926$	−12.3220	+	10.3393i	−0.404924	+	0.339772i
$927$	−0.728389	−	0.611191i	−0.0239234	−	0.0200741i
$928$	0.503967	+	2.85814i	0.0165435	+	0.0938229i
$929$	1.10118	+	0.400796i	0.0361285	+	0.0131497i	0.360021	−	0.932944i	$-0.382769\pi$
$929$	1.10118	+	0.400796i	0.0361285	+	0.0131497i	−0.323893	+	0.946094i	$0.604992\pi$
$930$	0.0714398			0.00234260
$931$	−2.07667	−	3.83242i	−0.0680602	−	0.125602i
$932$	1.53429			0.0502572
$933$	−14.4527	−	5.26033i	−0.473159	−	0.172216i
$934$	0.216890	+	1.23004i	0.00709685	+	0.0402483i
$935$	0.181169	+	0.152019i	0.00592487	+	0.00497156i
$936$	2.53966	−	2.13103i	0.0830115	−	0.0696549i
$937$	−6.36232	+	36.0825i	−0.207848	+	1.17876i	0.685047	+	0.728499i	$0.259782\pi$
$937$	−6.36232	+	36.0825i	−0.207848	+	1.17876i	−0.892895	+	0.450266i	$0.851329\pi$
$938$	2.43566	−	4.21869i	0.0795272	−	0.137745i
$939$	−5.14369	−	8.90914i	−0.167858	−	0.290739i
$940$	0.0887351	−	0.0322969i	0.00289422	−	0.00105341i
$941$	−3.42870	+	1.24795i	−0.111773	+	0.0406819i	−0.397301	−	0.917688i	$-0.630053\pi$
$941$	−3.42870	+	1.24795i	−0.111773	+	0.0406819i	0.285528	+	0.958370i	$0.407831\pi$
$942$	3.97452	+	6.88407i	0.129497	+	0.224295i
$943$	−0.730656	+	1.26553i	−0.0237934	+	0.0412114i
$944$	2.21445	−	12.5587i	0.0720740	−	0.408752i
$945$	0.0268090	−	0.0224954i	0.000872095	−	0.000731775i
$946$	17.1030	+	14.3511i	0.556067	+	0.466595i
$947$	−0.897385	−	5.08932i	−0.0291611	−	0.165381i	0.966749	−	0.255725i	$-0.0823143\pi$
$947$	−0.897385	−	5.08932i	−0.0291611	−	0.165381i	−0.995911	+	0.0903446i	$0.971203\pi$
$948$	3.60888	+	1.31353i	0.117211	+	0.0426613i
$949$	38.5657			1.25190
$950$	−11.4004	+	18.5688i	−0.369877	+	0.602450i
$951$	24.4600			0.793171
$952$	−1.77099	−	0.644587i	−0.0573981	−	0.0208912i
$953$	8.51189	+	48.2733i	0.275727	+	1.56373i	0.736643	+	0.676282i	$0.236410\pi$
$953$	8.51189	+	48.2733i	0.275727	+	1.56373i	−0.460916	+	0.887444i	$0.652479\pi$
$954$	−2.27984	−	1.91301i	−0.0738125	−	0.0619360i
$955$	0.291351	−	0.244473i	0.00942791	−	0.00791095i
$956$	0.368408	−	2.08934i	0.0119152	−	0.0675742i
$957$	−5.20327	+	9.01233i	−0.168198	+	0.291327i
$958$	16.4764	+	28.5380i	0.532328	+	0.922019i
$959$	6.80113	−	2.47541i	0.219620	−	0.0799351i
$960$	0.0328860	−	0.0119695i	0.00106139	−	0.000386315i
$961$	13.4165	+	23.2380i	0.432790	+	0.749613i
$962$	−6.94259	+	12.0249i	−0.223838	+	0.387699i
$963$	−2.26147	+	12.8254i	−0.0728747	+	0.413293i
$964$	22.6103	−	18.9723i	0.728229	−	0.611057i
$965$	−0.314841	−	0.264183i	−0.0101351	−	0.00850435i
$966$	−0.110107	−	0.624449i	−0.00354264	−	0.0200913i
$967$	−21.3504	−	7.77093i	−0.686584	−	0.249896i	−0.0249122	−	0.999690i	$-0.507931\pi$
$967$	−21.3504	−	7.77093i	−0.686584	−	0.249896i	−0.661672	+	0.749793i	$0.730153\pi$
$968$	−1.85729			−0.0596957
$969$	1.64456	−	8.04869i	0.0528308	−	0.258561i
$970$	−0.519289			−0.0166734
$971$	−15.0902	−	5.49237i	−0.484266	−	0.176259i	0.0883378	−	0.996091i	$-0.471845\pi$
$971$	−15.0902	−	5.49237i	−0.484266	−	0.176259i	−0.572604	+	0.819832i	$0.694067\pi$
$972$	0.173648	+	0.984808i	0.00556977	+	0.0315877i
$973$	−1.45246	−	1.21876i	−0.0465637	−	0.0390716i
$974$	−4.49333	+	3.77035i	−0.143975	+	0.120810i
$975$	2.87777	−	16.3206i	0.0921624	−	0.522679i
$976$	2.35105	−	4.07214i	0.0752553	−	0.130346i
$977$	22.5616	+	39.0779i	0.721811	+	1.25021i	0.960273	+	0.279061i	$0.0900233\pi$
$977$	22.5616	+	39.0779i	0.721811	+	1.25021i	−0.238462	+	0.971152i	$0.576643\pi$
$978$	−4.34317	+	1.58079i	−0.138879	+	0.0505480i
$979$	45.4028	−	16.5253i	1.45108	−	0.528150i
$980$	0.0174983	+	0.0303079i	0.000558963	+	0.000968152i
$981$	−6.77659	+	11.7374i	−0.216360	+	0.374747i
$982$	−0.645589	+	3.66131i	−0.0206016	+	0.116837i
$983$	23.0613	−	19.3507i	0.735540	−	0.617191i	−0.196096	−	0.980585i	$-0.562826\pi$
$983$	23.0613	−	19.3507i	0.735540	−	0.617191i	0.931636	+	0.363393i	$0.118382\pi$
$984$	1.76543	+	1.48137i	0.0562799	+	0.0472245i
$985$	−0.110397	−	0.626093i	−0.00351754	−	0.0199490i
$986$	−5.13981	−	1.87074i	−0.163685	−	0.0595765i
$987$	−2.69826			−0.0858866
$988$	−11.3170	+	8.98649i	−0.360043	+	0.285898i
$989$	−3.94811			−0.125543
$990$	0.117920	+	0.0429193i	0.00374773	+	0.00136406i
$991$	−9.82377	−	55.7134i	−0.312062	−	1.76979i	−0.588239	−	0.808687i	$-0.700178\pi$
$991$	−9.82377	−	55.7134i	−0.312062	−	1.76979i	0.276176	−	0.961107i	$-0.410933\pi$
$992$	−1.56375	−	1.31215i	−0.0496492	−	0.0416606i
$993$	−16.1999	+	13.5933i	−0.514088	+	0.431371i
$994$	−2.45138	+	13.9025i	−0.0777530	+	0.440959i
$995$	−0.0318628	+	0.0551880i	−0.00101012	+	0.00174958i
$996$	2.58714	+	4.48106i	0.0819767	+	0.141988i
$997$	42.0112	−	15.2908i	1.33051	−	0.484265i	0.423697	−	0.905804i	$-0.360732\pi$
$997$	42.0112	−	15.2908i	1.33051	−	0.484265i	0.906810	+	0.421539i	$0.138510\pi$
$998$	−40.6837	+	14.8077i	−1.28782	+	0.468729i
$999$	−2.09411	−	3.62710i	−0.0662546	−	0.114756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bo.d.631.1	yes	12
19.5	even	9	inner	798.2.bo.d.43.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bo.d.43.1	✓	12	19.5	even	9	inner
798.2.bo.d.631.1	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0268090 + 0.0224954i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.0328860 + 0.0119695i) q^{10} +(1.79285 + 3.10531i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.575695 + 3.26493i) q^{13} +(0.766044 - 0.642788i) q^{14} +(-0.0268090 - 0.0224954i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.77099 - 0.644587i) q^{17} -1.00000 q^{18} +(4.35731 + 0.117758i) q^{19} -0.0349966 q^{20} +(0.939693 + 0.342020i) q^{21} +(0.622651 + 3.53123i) q^{22} +(-0.485735 - 0.407580i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-0.868028 + 4.92283i) q^{25} +(-1.65765 + 2.87113i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.939693 - 0.342020i) q^{28} +(2.72720 - 0.992620i) q^{29} +(-0.0174983 - 0.0303079i) q^{30} +(-1.02067 + 1.76785i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-2.74681 + 2.30485i) q^{33} +(-1.44372 - 1.21143i) q^{34} +(0.00607710 + 0.0344649i) q^{35} +(-0.939693 - 0.342020i) q^{36} +4.18821 q^{37} +(4.05425 + 1.60094i) q^{38} -3.31530 q^{39} +(-0.0328860 - 0.0119695i) q^{40} +(-0.400191 - 2.26960i) q^{41} +(0.766044 + 0.642788i) q^{42} +(4.76977 - 4.00232i) q^{43} +(-0.622651 + 3.53123i) q^{44} +(0.0174983 - 0.0303079i) q^{45} +(-0.317041 - 0.549131i) q^{46} +(-2.53554 + 0.922859i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.49939 + 4.32907i) q^{50} +(0.327266 - 1.85601i) q^{51} +(-2.53966 + 2.13103i) q^{52} +(2.27984 + 1.91301i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-0.117920 - 0.0429193i) q^{55} +1.00000 q^{56} +(0.640670 + 4.31156i) q^{57} +2.90223 q^{58} +(-11.9834 - 4.36161i) q^{59} +(-0.00607710 - 0.0344649i) q^{60} +(-3.60202 - 3.02245i) q^{61} +(-1.56375 + 1.31215i) q^{62} +(-0.173648 + 0.984808i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0580120 - 0.100480i) q^{65} +(-3.36946 + 1.22638i) q^{66} +(4.57755 - 1.66609i) q^{67} +(-0.942323 - 1.63215i) q^{68} +(0.317041 - 0.549131i) q^{69} +(-0.00607710 + 0.0344649i) q^{70} +(-10.8142 + 9.07419i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-2.01999 - 11.4559i) q^{73} +(3.93563 + 1.43245i) q^{74} -4.99878 q^{75} +(3.26220 + 2.89103i) q^{76} +3.58571 q^{77} +(-3.11536 - 1.13390i) q^{78} +(-0.666895 - 3.78215i) q^{79} +(-0.0268090 - 0.0224954i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.400191 - 2.26960i) q^{82} +(2.58714 - 4.48106i) q^{83} +(0.500000 + 0.866025i) q^{84} +(0.0619786 - 0.0225584i) q^{85} +(5.85099 - 2.12959i) q^{86} +(1.45111 + 2.51340i) q^{87} +(-1.79285 + 3.10531i) q^{88} +(2.33987 - 13.2701i) q^{89} +(0.0268090 - 0.0224954i) q^{90} +(2.53966 + 2.13103i) q^{91} +(-0.110107 - 0.624449i) q^{92} +(-1.91823 - 0.698178i) q^{93} -2.69826 q^{94} +(-0.119464 + 0.0948623i) q^{95} -1.00000 q^{96} +(13.9434 + 5.07499i) q^{97} +(-0.173648 - 0.984808i) q^{98} +(-2.74681 - 2.30485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{5} + 6 q^{7} + 6 q^{8} + 9 q^{10} + 3 q^{11} - 6 q^{12} - 9 q^{13} + 9 q^{15} + 15 q^{17} - 12 q^{18} + 9 q^{19} - 15 q^{22} + 3 q^{23} + 3 q^{25} + 3 q^{26} - 6 q^{27} + 3 q^{29} + 6 q^{31}+ \cdots - 12 q^{99}+O(q^{100}) \) 12 * q + 9 * q^5 + 6 * q^7 + 6 * q^8 + 9 * q^10 + 3 * q^11 - 6 * q^12 - 9 * q^13 + 9 * q^15 + 15 * q^17 - 12 * q^18 + 9 * q^19 - 15 * q^22 + 3 * q^23 + 3 * q^25 + 3 * q^26 - 6 * q^27 + 3 * q^29 + 6 * q^31 - 12 * q^33 - 6 * q^34 - 9 * q^38 + 6 * q^39 + 9 * q^40 - 27 * q^41 + 6 * q^43 + 15 * q^44 - 15 * q^46 - 6 * q^47 - 6 * q^49 - 21 * q^51 + 9 * q^52 - 9 * q^53 - 9 * q^55 + 12 * q^56 - 18 * q^57 + 12 * q^58 - 24 * q^59 - 15 * q^61 - 24 * q^62 - 6 * q^64 - 24 * q^65 + 3 * q^66 + 33 * q^67 - 6 * q^68 + 15 * q^69 - 33 * q^71 + 33 * q^73 + 12 * q^74 + 9 * q^76 + 6 * q^77 + 33 * q^79 + 9 * q^80 + 27 * q^82 - 36 * q^83 + 6 * q^84 + 15 * q^85 - 6 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 9 * q^90 - 9 * q^91 + 3 * q^92 - 21 * q^93 - 18 * q^94 - 18 * q^95 - 12 * q^96 + 21 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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