LMFDB - Embedded newform 115.2.l.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	115.7
Dual form			115.2.l.a.33.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.643856 + 0.0460495i) q^{2} +(-0.683154 + 3.14041i) q^{3} +(-1.56721 + 0.225331i) q^{4} +(-0.267157 - 2.22005i) q^{5} +(0.295239 - 2.05343i) q^{6} +(-1.03991 + 1.90445i) q^{7} +(2.26018 - 0.491672i) q^{8} +(-6.66656 - 3.04452i) q^{9} +O(q^{10})$	\(q+(-0.643856 + 0.0460495i) q^{2} +(-0.683154 + 3.14041i) q^{3} +(-1.56721 + 0.225331i) q^{4} +(-0.267157 - 2.22005i) q^{5} +(0.295239 - 2.05343i) q^{6} +(-1.03991 + 1.90445i) q^{7} +(2.26018 - 0.491672i) q^{8} +(-6.66656 - 3.04452i) q^{9} +(0.274243 + 1.41709i) q^{10} +(-2.06089 + 1.78577i) q^{11} +(0.363016 - 5.07562i) q^{12} +(-2.00097 + 1.09261i) q^{13} +(0.581852 - 1.27408i) q^{14} +(7.15437 + 0.677656i) q^{15} +(1.60580 - 0.471504i) q^{16} +(2.72542 + 3.64074i) q^{17} +(4.43251 + 1.65324i) q^{18} +(0.508679 + 3.53794i) q^{19} +(0.918938 + 3.41909i) q^{20} +(-5.27033 - 4.56677i) q^{21} +(1.24468 - 1.24468i) q^{22} +(3.49802 + 3.28083i) q^{23} +7.43378i q^{24} +(-4.85725 + 1.18620i) q^{25} +(1.23803 - 0.795630i) q^{26} +(8.33734 - 11.1374i) q^{27} +(1.20063 - 3.21900i) q^{28} +(4.80488 + 0.690837i) q^{29} +(-4.63759 - 0.106857i) q^{30} +(-2.09072 - 1.34363i) q^{31} +(-5.34660 + 1.99418i) q^{32} +(-4.20014 - 7.69197i) q^{33} +(-1.92243 - 2.21861i) q^{34} +(4.50580 + 1.79986i) q^{35} +(11.1339 + 3.26922i) q^{36} +(-0.215837 - 0.578681i) q^{37} +(-0.490436 - 2.25450i) q^{38} +(-2.06428 - 7.03030i) q^{39} +(-1.69536 - 4.88636i) q^{40} +(-1.47573 - 3.23141i) q^{41} +(3.60363 + 2.69765i) q^{42} +(-9.03527 - 1.96550i) q^{43} +(2.82746 - 3.26306i) q^{44} +(-4.97797 + 15.6135i) q^{45} +(-2.40330 - 1.95130i) q^{46} +(6.88665 + 6.88665i) q^{47} +(0.383710 + 5.36496i) q^{48} +(1.23897 + 1.92787i) q^{49} +(3.07275 - 0.987418i) q^{50} +(-13.2953 + 6.07175i) q^{51} +(2.88975 - 2.16324i) q^{52} +(1.21721 + 0.664648i) q^{53} +(-4.85518 + 7.55480i) q^{54} +(4.51507 + 4.09819i) q^{55} +(-1.41402 + 4.81570i) q^{56} +(-11.4581 - 0.819498i) q^{57} +(-3.12546 - 0.223537i) q^{58} +(2.15250 - 7.33075i) q^{59} +(-11.3651 + 0.550073i) q^{60} +(3.03593 - 4.72400i) q^{61} +(1.40800 + 0.768825i) q^{62} +(12.7307 - 9.53012i) q^{63} +(0.305910 - 0.139704i) q^{64} +(2.96023 + 4.15037i) q^{65} +(3.05849 + 4.75911i) q^{66} +(0.140507 + 1.96455i) q^{67} +(-5.09168 - 5.09168i) q^{68} +(-12.6928 + 8.74390i) q^{69} +(-2.98397 - 0.951363i) q^{70} +(3.58134 - 4.13309i) q^{71} +(-16.5645 - 3.60340i) q^{72} +(6.40664 + 4.79595i) q^{73} +(0.165616 + 0.362648i) q^{74} +(-0.406909 - 16.0641i) q^{75} +(-1.59442 - 5.43008i) q^{76} +(-1.25777 - 5.78189i) q^{77} +(1.65284 + 4.43144i) q^{78} +(-2.46083 - 0.722566i) q^{79} +(-1.47576 - 3.43898i) q^{80} +(14.8821 + 17.1749i) q^{81} +(1.09896 + 2.01260i) q^{82} +(-6.56634 + 2.44912i) q^{83} +(9.28877 + 5.96953i) q^{84} +(7.35450 - 7.02322i) q^{85} +(5.90793 + 0.849431i) q^{86} +(-5.45198 + 14.6173i) q^{87} +(-3.77996 + 5.04944i) q^{88} +(9.99869 - 6.42577i) q^{89} +(2.48610 - 10.2821i) q^{90} -4.94697i q^{91} +(-6.22142 - 4.35355i) q^{92} +(5.64782 - 5.64782i) q^{93} +(-4.75114 - 4.11689i) q^{94} +(7.71851 - 2.07448i) q^{95} +(-2.60998 - 18.1528i) q^{96} +(-2.19321 - 0.818024i) q^{97} +(-0.886493 - 1.18422i) q^{98} +(19.1758 - 5.63053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

Coefficient data

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

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

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

$2$	−0.643856	+	0.0460495i	−0.455275	+	0.0325619i	−0.297094	−	0.954848i	$-0.596017\pi$
$2$	−0.643856	+	0.0460495i	−0.455275	+	0.0325619i	−0.158181	+	0.987410i	$0.550563\pi$
$3$	−0.683154	+	3.14041i	−0.394419	+	1.81312i	0.167440	+	0.985882i	$0.446450\pi$
$3$	−0.683154	+	3.14041i	−0.394419	+	1.81312i	−0.561859	+	0.827233i	$0.689914\pi$
$4$	−1.56721	+	0.225331i	−0.783606	+	0.112666i
$5$	−0.267157	−	2.22005i	−0.119476	−	0.992837i
$5$	−0.267157	−	2.22005i	−0.119476	−	0.992837i
$6$	0.295239	−	2.05343i	0.120531	−	0.838309i
$7$	−1.03991	+	1.90445i	−0.393048	+	0.719814i	−0.997016	−	0.0771944i	$-0.975404\pi$
$7$	−1.03991	+	1.90445i	−0.393048	+	0.719814i	0.603968	+	0.797009i	$0.293586\pi$
$8$	2.26018	−	0.491672i	0.799095	−	0.173832i
$9$	−6.66656	−	3.04452i	−2.22219	−	1.01484i
$10$	0.274243	+	1.41709i	0.0867232	+	0.448124i
$11$	−2.06089	+	1.78577i	−0.621380	+	0.538429i	−0.907654	−	0.419719i	$-0.862129\pi$
$11$	−2.06089	+	1.78577i	−0.621380	+	0.538429i	0.286274	+	0.958148i	$0.407583\pi$
$12$	0.363016	−	5.07562i	0.104794	−	1.46521i
$13$	−2.00097	+	1.09261i	−0.554970	+	0.303037i	−0.732152	−	0.681141i	$-0.761484\pi$
$13$	−2.00097	+	1.09261i	−0.554970	+	0.303037i	0.177181	+	0.984178i	$0.443302\pi$
$14$	0.581852	−	1.27408i	0.155507	−	0.340512i
$15$	7.15437	+	0.677656i	1.84725	+	0.174970i
$16$	1.60580	−	0.471504i	0.401449	−	0.117876i
$17$	2.72542	+	3.64074i	0.661011	+	0.883008i	0.998294	−	0.0583957i	$-0.0185985\pi$
$17$	2.72542	+	3.64074i	0.661011	+	0.883008i	−0.337282	+	0.941404i	$0.609508\pi$
$18$	4.43251	+	1.65324i	1.04475	+	0.389672i
$19$	0.508679	+	3.53794i	0.116699	+	0.811659i	0.961150	+	0.276026i	$0.0890177\pi$
$19$	0.508679	+	3.53794i	0.116699	+	0.811659i	−0.844451	+	0.535633i	$0.820073\pi$
$20$	0.918938	+	3.41909i	0.205481	+	0.764533i
$21$	−5.27033	−	4.56677i	−1.15008	−	0.996551i
$22$	1.24468	−	1.24468i	0.265367	−	0.265367i
$23$	3.49802	+	3.28083i	0.729388	+	0.684101i
$23$	3.49802	+	3.28083i	0.729388	+	0.684101i
$24$			7.43378i			1.51741i
$25$	−4.85725	+	1.18620i	−0.971451	+	0.237241i
$26$	1.23803	−	0.795630i	0.242797	−	0.156036i
$27$	8.33734	−	11.1374i	1.60452	−	2.14339i
$28$	1.20063	−	3.21900i	0.226897	−	0.608334i
$29$	4.80488	+	0.690837i	0.892243	+	0.128285i	0.573162	−	0.819442i	$-0.305717\pi$
$29$	4.80488	+	0.690837i	0.892243	+	0.128285i	0.319081	+	0.947727i	$0.396626\pi$
$30$	−4.63759	−	0.106857i	−0.846705	−	0.0195094i
$31$	−2.09072	−	1.34363i	−0.375505	−	0.241322i	0.339252	−	0.940696i	$-0.389826\pi$
$31$	−2.09072	−	1.34363i	−0.375505	−	0.241322i	−0.714757	+	0.699373i	$0.753463\pi$
$32$	−5.34660	+	1.99418i	−0.945154	+	0.352524i
$33$	−4.20014	−	7.69197i	−0.731150	−	1.33900i
$34$	−1.92243	−	2.21861i	−0.329694	−	0.380488i
$35$	4.50580	+	1.79986i	0.761618	+	0.304232i
$36$	11.1339	+	3.26922i	1.85566	+	0.544870i
$37$	−0.215837	−	0.578681i	−0.0354833	−	0.0951345i	0.918000	−	0.396581i	$-0.129803\pi$
$37$	−0.215837	−	0.578681i	−0.0354833	−	0.0951345i	−0.953483	+	0.301446i	$0.902531\pi$
$38$	−0.490436	−	2.25450i	−0.0795593	−	0.365728i
$39$	−2.06428	−	7.03030i	−0.330550	−	1.12575i
$40$	−1.69536	−	4.88636i	−0.268060	−	0.772602i
$41$	−1.47573	−	3.23141i	−0.230471	−	0.504661i	0.758698	−	0.651442i	$-0.225836\pi$
$41$	−1.47573	−	3.23141i	−0.230471	−	0.504661i	−0.989169	+	0.146782i	$0.953109\pi$
$42$	3.60363	+	2.69765i	0.556053	+	0.416256i
$43$	−9.03527	−	1.96550i	−1.37787	−	0.299736i	−0.538190	−	0.842824i	$-0.680892\pi$
$43$	−9.03527	−	1.96550i	−1.37787	−	0.299736i	−0.839676	+	0.543087i	$0.817255\pi$
$44$	2.82746	−	3.26306i	0.426255	−	0.491925i
$45$	−4.97797	+	15.6135i	−0.742072	+	2.32752i
$46$	−2.40330	−	1.95130i	−0.354348	−	0.287704i
$47$	6.88665	+	6.88665i	1.00452	+	1.00452i	0.999990	+	0.00453207i	$0.00144261\pi$
$47$	6.88665	+	6.88665i	1.00452	+	1.00452i	0.00453207	+	0.999990i	$0.498557\pi$
$48$	0.383710	+	5.36496i	0.0553837	+	0.774366i
$49$	1.23897	+	1.92787i	0.176995	+	0.275410i
$50$	3.07275	−	0.987418i	0.434552	−	0.139642i
$51$	−13.2953	+	6.07175i	−1.86171	+	0.850215i
$52$	2.88975	−	2.16324i	0.400737	−	0.299988i
$53$	1.21721	+	0.664648i	0.167197	+	0.0912964i	0.560668	−	0.828040i	$-0.310544\pi$
$53$	1.21721	+	0.664648i	0.167197	+	0.0912964i	−0.393472	+	0.919337i	$0.628726\pi$
$54$	−4.85518	+	7.55480i	−0.660706	+	1.02808i
$55$	4.51507	+	4.09819i	0.608812	+	0.552600i
$56$	−1.41402	+	4.81570i	−0.188956	+	0.643524i
$57$	−11.4581	−	0.819498i	−1.51766	−	0.108545i
$58$	−3.12546	−	0.223537i	−0.410393	−	0.0293519i
$59$	2.15250	−	7.33075i	0.280232	−	0.954383i	−0.692299	−	0.721611i	$-0.743402\pi$
$59$	2.15250	−	7.33075i	0.280232	−	0.954383i	0.972531	−	0.232772i	$-0.0747797\pi$
$60$	−11.3651	+	0.550073i	−1.46723	+	0.0710142i
$61$	3.03593	−	4.72400i	0.388711	−	0.604846i	−0.590659	−	0.806921i	$-0.701132\pi$
$61$	3.03593	−	4.72400i	0.388711	−	0.604846i	0.979370	+	0.202075i	$0.0647685\pi$
$62$	1.40800	+	0.768825i	0.178816	+	0.0976409i
$63$	12.7307	−	9.53012i	1.60392	−	1.20068i
$64$	0.305910	−	0.139704i	0.0382387	−	0.0174630i
$65$	2.96023	+	4.15037i	0.367172	+	0.514790i
$66$	3.05849	+	4.75911i	0.376475	+	0.585806i
$67$	0.140507	+	1.96455i	0.0171657	+	0.240008i	0.998790	+	0.0491828i	$0.0156617\pi$
$67$	0.140507	+	1.96455i	0.0171657	+	0.240008i	−0.981624	+	0.190825i	$0.938884\pi$
$68$	−5.09168	−	5.09168i	−0.617457	−	0.617457i
$69$	−12.6928	+	8.74390i	−1.52804	+	1.05264i
$70$	−2.98397	−	0.951363i	−0.356652	−	0.113710i
$71$	3.58134	−	4.13309i	0.425027	−	0.490507i	−0.502335	−	0.864673i	$-0.667526\pi$
$71$	3.58134	−	4.13309i	0.425027	−	0.490507i	0.927362	+	0.374166i	$0.122071\pi$
$72$	−16.5645	−	3.60340i	−1.95215	−	0.424664i
$73$	6.40664	+	4.79595i	0.749840	+	0.561323i	0.904413	−	0.426658i	$-0.140309\pi$
$73$	6.40664	+	4.79595i	0.749840	+	0.561323i	−0.154573	+	0.987981i	$0.549400\pi$
$74$	0.165616	+	0.362648i	0.0192524	+	0.0421570i
$75$	−0.406909	−	16.0641i	−0.0469858	−	1.85492i
$76$	−1.59442	−	5.43008i	−0.182892	−	0.622873i
$77$	−1.25777	−	5.78189i	−0.143336	−	0.658907i
$78$	1.65284	+	4.43144i	0.187148	+	0.501762i
$79$	−2.46083	−	0.722566i	−0.276865	−	0.0812950i	0.140352	−	0.990102i	$-0.455177\pi$
$79$	−2.46083	−	0.722566i	−0.276865	−	0.0812950i	−0.417218	+	0.908807i	$0.636995\pi$
$80$	−1.47576	−	3.43898i	−0.164995	−	0.384490i
$81$	14.8821	+	17.1749i	1.65357	+	1.90832i
$82$	1.09896	+	2.01260i	0.121360	+	0.222255i
$83$	−6.56634	+	2.44912i	−0.720750	+	0.268826i	−0.682956	−	0.730460i	$-0.739306\pi$
$83$	−6.56634	+	2.44912i	−0.720750	+	0.268826i	−0.0377941	+	0.999286i	$0.512033\pi$
$84$	9.28877	+	5.96953i	1.01349	+	0.651329i
$85$	7.35450	−	7.02322i	0.797708	−	0.761775i
$86$	5.90793	+	0.849431i	0.637068	+	0.0915965i
$87$	−5.45198	+	14.6173i	−0.584514	+	1.56714i
$88$	−3.77996	+	5.04944i	−0.402945	+	0.538272i
$89$	9.99869	−	6.42577i	1.05986	−	0.681130i	0.110039	−	0.993927i	$-0.464902\pi$
$89$	9.99869	−	6.42577i	1.05986	−	0.681130i	0.949820	+	0.312797i	$0.101266\pi$
$90$	2.48610	−	10.2821i	0.262058	−	1.08382i
$91$		−	4.94697i		−	0.518584i
$92$	−6.22142	−	4.35355i	−0.648627	−	0.453889i
$93$	5.64782	−	5.64782i	0.585651	−	0.585651i
$94$	−4.75114	−	4.11689i	−0.490043	−	0.424625i
$95$	7.71851	−	2.07448i	0.791902	−	0.212837i
$96$	−2.60998	−	18.1528i	−0.266380	−	1.85271i
$97$	−2.19321	−	0.818024i	−0.222686	−	0.0830577i	0.235645	−	0.971839i	$-0.424280\pi$
$97$	−2.19321	−	0.818024i	−0.222686	−	0.0830577i	−0.458331	+	0.888782i	$0.651553\pi$
$98$	−0.886493	−	1.18422i	−0.0895493	−	0.119624i
$99$	19.1758	−	5.63053i	1.92724	−	0.565890i
$100$	7.34506	−	2.95352i	0.734506	−	0.295352i
$101$	0.242798	−	0.531653i	0.0241593	−	0.0529014i	−0.897168	−	0.441690i	$-0.854379\pi$
$101$	0.242798	−	0.531653i	0.0241593	−	0.0529014i	0.921327	+	0.388789i	$0.127106\pi$
$102$	8.28064	−	4.52157i	0.819906	−	0.447702i
$103$	−0.731260	+	10.2243i	−0.0720532	+	1.00743i	0.824891	+	0.565291i	$0.191236\pi$
$103$	−0.731260	+	10.2243i	−0.0720532	+	1.00743i	−0.896944	+	0.442143i	$0.854218\pi$
$104$	−3.98536	+	3.45333i	−0.390796	+	0.338627i
$105$	−8.73046	+	12.9204i	−0.852005	+	1.26091i
$106$	−0.814316	−	0.371886i	−0.0790934	−	0.0361207i
$107$	−5.61282	+	1.22099i	−0.542612	+	0.118038i	−0.475513	−	0.879708i	$-0.657738\pi$
$107$	−5.61282	+	1.22099i	−0.542612	+	0.118038i	−0.0670982	+	0.997746i	$0.521374\pi$
$108$	−10.5568	+	19.3333i	−1.01583	+	1.86035i
$109$	−1.86724	+	12.9869i	−0.178849	+	1.24392i	0.680583	+	0.732671i	$0.261727\pi$
$109$	−1.86724	+	12.9869i	−0.178849	+	1.24392i	−0.859432	+	0.511250i	$0.829183\pi$
$110$	−3.09578	−	2.43073i	−0.295171	−	0.231761i
$111$	1.96474	−	0.282487i	0.186485	−	0.0268125i
$112$	−0.771924	+	3.54848i	−0.0729400	+	0.335300i
$113$	−6.73335	+	0.481579i	−0.633420	+	0.0453031i	−0.384358	−	0.923184i	$-0.625577\pi$
$113$	−6.73335	+	0.481579i	−0.633420	+	0.0453031i	−0.249063	+	0.968487i	$0.580123\pi$
$114$	7.41509			0.694487
$115$	6.34909	−	8.64228i	0.592056	−	0.805897i
$116$	−7.68593			−0.713621
$117$	16.6661	−	1.19198i	1.54078	−	0.110199i
$118$	−1.04832	+	4.81907i	−0.0965061	+	0.443632i
$119$	−9.76779	+	1.40440i	−0.895411	+	0.128741i
$120$	16.5034	−	1.98598i	1.50654	−	0.181295i
$121$	−0.507180	+	3.52751i	−0.0461073	+	0.320683i
$122$	−1.73716	+	3.18138i	−0.157275	+	0.288028i
$123$	11.1561	−	2.42686i	1.00591	−	0.218822i
$124$	3.57937	+	1.63464i	0.321437	+	0.146795i
$125$	3.93108	+	10.4665i	0.351606	+	0.936148i
$126$	−7.75791	+	6.72227i	−0.691130	+	0.598867i
$127$	−0.629089	+	8.79582i	−0.0558227	+	0.780503i	0.890029	+	0.455904i	$0.150684\pi$
$127$	−0.629089	+	8.79582i	−0.0558227	+	0.780503i	−0.945852	+	0.324599i	$0.894771\pi$
$128$	9.82622	−	5.36552i	0.868523	−	0.474250i
$129$	12.3450	−	27.0317i	1.08691	−	2.38001i
$130$	−2.09709	−	2.53592i	−0.183927	−	0.222415i
$131$	−3.15946	+	0.927702i	−0.276043	+	0.0810537i	−0.416824	−	0.908987i	$-0.636857\pi$
$131$	−3.15946	+	0.927702i	−0.276043	+	0.0810537i	0.140781	+	0.990041i	$0.455039\pi$
$132$	8.31575	+	11.1085i	0.723793	+	0.966874i
$133$	−7.26681	−	2.71038i	−0.630112	−	0.235020i
$134$	−0.180933	−	1.25842i	−0.0156302	−	0.108711i
$135$	−26.9529	−	15.5339i	−2.31974	−	1.33695i
$136$	7.94999	+	6.88871i	0.681706	+	0.590702i
$137$	7.35692	−	7.35692i	0.628544	−	0.628544i	−0.319157	−	0.947702i	$-0.603400\pi$
$137$	7.35692	−	7.35692i	0.628544	−	0.628544i	0.947702	+	0.319157i	$0.103400\pi$
$138$	7.76971	−	6.21431i	0.661401	−	0.528997i
$139$		−	18.7039i		−	1.58644i	−0.608935	−	0.793220i	$-0.708403\pi$
$139$		−	18.7039i		−	1.58644i	0.608935	−	0.793220i	$-0.291597\pi$
$140$	−7.46710	−	1.80547i	−0.631086	−	0.152590i
$141$	−26.3315	+	16.9223i	−2.21752	+	1.42511i
$142$	−2.11554	+	2.82603i	−0.177532	+	0.237155i
$143$	2.17262	−	5.82503i	0.181684	−	0.487113i
$144$	−12.1406	−	1.74556i	−1.01172	−	0.145463i
$145$	0.250038	−	10.8516i	0.0207646	−	0.901179i
$146$	−4.34580	−	2.79288i	−0.359661	−	0.231140i
$147$	−6.90069	+	2.57383i	−0.569160	+	0.212286i
$148$	0.468657	+	0.858281i	0.0385234	+	0.0705503i
$149$	5.98599	+	6.90820i	0.490391	+	0.565942i	0.945970	−	0.324254i	$-0.105113\pi$
$149$	5.98599	+	6.90820i	0.490391	+	0.565942i	−0.455579	+	0.890195i	$0.650568\pi$
$150$	1.00174	+	10.3242i	0.0817914	+	0.842971i
$151$	18.4978	+	5.43146i	1.50533	+	0.442006i	0.927398	−	0.374077i	$-0.122040\pi$
$151$	18.4978	+	5.43146i	1.50533	+	0.442006i	0.577935	+	0.816083i	$0.303859\pi$
$152$	2.88921	+	7.74628i	0.234346	+	0.628306i
$153$	−7.08491	−	32.5688i	−0.572781	−	2.63303i
$154$	1.07608	+	3.66478i	0.0867128	+	0.295317i
$155$	−2.42437	+	5.00047i	−0.194730	+	0.401647i
$156$	4.81931	+	10.5528i	0.385854	+	0.844902i
$157$	−15.4980	−	11.6017i	−1.23688	−	0.925913i	−0.237906	−	0.971288i	$-0.576461\pi$
$157$	−15.4980	−	11.6017i	−1.23688	−	0.925913i	−0.998970	+	0.0453748i	$0.985552\pi$
$158$	1.61770	+	0.351908i	0.128697	+	0.0279963i
$159$	−2.91881	+	3.36848i	−0.231477	+	0.267138i
$160$	5.85555	+	11.3370i	0.462922	+	0.896265i
$161$	−9.88580	+	3.25004i	−0.779110	+	0.256139i
$162$	−10.3728	−	10.3728i	−0.814966	−	0.814966i
$163$	0.0595949	+	0.833246i	0.00466784	+	0.0652649i	0.999252	−	0.0386686i	$-0.0123117\pi$
$163$	0.0595949	+	0.833246i	0.00466784	+	0.0652649i	−0.994584	+	0.103933i	$0.966857\pi$
$164$	3.04092	+	4.73177i	0.237456	+	0.369489i
$165$	−15.9545	+	11.3795i	−1.24205	+	0.885891i
$166$	4.11500	−	1.87926i	0.319386	−	0.145859i
$167$	−3.89338	+	2.91455i	−0.301279	+	0.225534i	−0.739212	−	0.673473i	$-0.764802\pi$
$167$	−3.89338	+	2.91455i	−0.301279	+	0.225534i	0.437933	+	0.899008i	$0.355711\pi$
$168$	−14.1573	−	7.73045i	−1.09226	−	0.596417i
$169$	−4.21824	+	6.56371i	−0.324480	+	0.504901i
$170$	−4.41183	+	4.86061i	−0.338372	+	0.372792i
$171$	7.38018	−	25.1346i	0.564376	−	1.92209i
$172$	14.6031	+	1.04443i	1.11347	+	0.0796373i
$173$	−1.18368	−	0.0846588i	−0.0899939	−	0.00643649i	0.0262696	−	0.999655i	$-0.491637\pi$
$173$	−1.18368	−	0.0846588i	−0.0899939	−	0.00643649i	−0.116264	+	0.993218i	$0.537092\pi$
$174$	2.83717	−	9.66252i	0.215085	−	0.732513i
$175$	2.79204	−	10.4839i	0.211058	−	0.792511i
$176$	−2.46736	+	3.83929i	−0.185985	+	0.289398i
$177$	21.5511	+	11.7678i	1.61988	+	0.884520i
$178$	−6.14182	+	4.59771i	−0.460349	+	0.344613i
$179$	−7.52232	+	3.43533i	−0.562245	+	0.256769i	−0.676201	−	0.736717i	$-0.736375\pi$
$179$	−7.52232	+	3.43533i	−0.562245	+	0.256769i	0.113956	+	0.993486i	$0.463648\pi$
$180$	4.28333	−	25.5913i	0.319261	−	1.90747i
$181$	8.59194	+	13.3693i	0.638634	+	0.993733i	0.998162	+	0.0605993i	$0.0193012\pi$
$181$	8.59194	+	13.3693i	0.638634	+	0.993733i	−0.359528	+	0.933134i	$0.617062\pi$
$182$	0.227806	+	3.18514i	0.0168861	+	0.236098i
$183$	12.7613	+	12.7613i	0.943341	+	0.943341i
$184$	9.51925	+	5.69539i	0.701769	+	0.419870i
$185$	−1.22704	+	0.633767i	−0.0902137	+	0.0465955i
$186$	−3.37630	+	3.89646i	−0.247563	+	0.285702i
$187$	−12.1183	−	2.63617i	−0.886177	−	0.192776i
$188$	−12.3446	−	9.24107i	−0.900325	−	0.673975i
$189$	12.5405	+	27.4599i	0.912189	+	1.99741i
$190$	−4.87408	+	1.69110i	−0.353603	+	0.122685i
$191$	0.434667	+	1.48034i	0.0314514	+	0.107114i	0.973723	−	0.227737i	$-0.0731325\pi$
$191$	0.434667	+	1.48034i	0.0314514	+	0.107114i	−0.942271	+	0.334850i	$0.891314\pi$
$192$	0.229745	+	1.05612i	0.0165804	+	0.0762190i
$193$	2.00922	+	5.38693i	0.144627	+	0.387759i	0.988984	−	0.148021i	$-0.0472903\pi$
$193$	2.00922	+	5.38693i	0.144627	+	0.387759i	−0.844357	+	0.535780i	$0.820018\pi$
$194$	1.44978	+	0.425694i	0.104088	+	0.0305630i
$195$	−15.0561	+	6.46100i	−1.07819	+	0.462682i
$196$	−2.37613	−	2.74220i	−0.169724	−	0.195872i
$197$	4.87807	+	8.93352i	0.347548	+	0.636487i	0.991724	−	0.128391i	$-0.0409811\pi$
$197$	4.87807	+	8.93352i	0.347548	+	0.636487i	−0.644175	+	0.764878i	$0.722799\pi$
$198$	−12.0872	+	4.50829i	−0.858999	+	0.320390i
$199$	10.4243	+	6.69931i	0.738961	+	0.474901i	0.855186	−	0.518322i	$-0.173443\pi$
$199$	10.4243	+	6.69931i	0.738961	+	0.474901i	−0.116225	+	0.993223i	$0.537079\pi$
$200$	−10.3951	+	5.06921i	−0.735041	+	0.358447i
$201$	−6.26547	−	0.900838i	−0.441932	−	0.0635402i
$202$	−0.131844	+	0.353489i	−0.00927654	+	0.0248714i
$203$	−6.31230	+	8.43224i	−0.443036	+	0.591827i
$204$	19.4684	−	12.5116i	1.36306	−	0.875984i
$205$	−6.77963	+	4.13950i	−0.473510	+	0.289115i
$206$		−	6.61668i		−	0.461006i
$207$	−13.3312	−	32.5217i	−0.926585	−	2.26041i
$208$	−2.69798	+	2.69798i	−0.187071	+	0.187071i
$209$	−7.36626	−	6.38290i	−0.509535	−	0.441515i
$210$	5.02618	−	8.72094i	0.346839	−	0.601802i
$211$	3.79014	+	26.3610i	0.260924	+	1.81477i	0.525940	+	0.850521i	$0.323714\pi$
$211$	3.79014	+	26.3610i	0.260924	+	1.81477i	−0.265016	+	0.964244i	$0.585377\pi$
$212$	−2.05740	−	0.767369i	−0.141303	−	0.0527031i
$213$	10.5330	+	14.0704i	0.721707	+	0.964088i
$214$	3.55762	−	1.04461i	0.243194	−	0.0714082i
$215$	−1.94968	+	20.5839i	−0.132967	+	1.40381i
$216$	13.3680	−	29.2718i	0.909575	−	1.99169i
$217$	4.73303	−	2.58443i	0.321299	−	0.175442i
$218$	0.604191	−	8.44769i	0.0409210	−	0.572150i
$219$	−19.4380	+	16.8431i	−1.31350	+	1.13815i
$220$	−7.99953	−	5.40535i	−0.539328	−	0.364429i
$221$	−9.43142	−	4.30718i	−0.634426	−	0.289733i
$222$	−1.25200	+	0.272357i	−0.0840290	+	0.0182794i
$223$	14.2290	−	26.0584i	0.952841	−	1.74500i	0.381209	−	0.924489i	$-0.375508\pi$
$223$	14.2290	−	26.0584i	0.952841	−	1.74500i	0.571633	−	0.820510i	$-0.306310\pi$
$224$	1.76216	−	12.2561i	0.117739	−	0.818894i
$225$	35.9926	+	6.88010i	2.39951	+	0.458673i
$226$	4.31313	−	0.620135i	0.286905	−	0.0412508i
$227$	1.15438	−	5.30660i	0.0766188	−	0.352211i	−0.922837	−	0.385190i	$-0.874136\pi$
$227$	1.15438	−	5.30660i	0.0766188	−	0.352211i	0.999456	+	0.0329791i	$0.0104995\pi$
$228$	18.1419	−	1.29753i	1.20148	−	0.0859313i
$229$	−28.5896			−1.88925			−0.944626	−	0.328149i	$-0.893575\pi$
$229$	−28.5896			−1.88925			−0.944626	+	0.328149i	$0.893575\pi$
$230$	−3.68993	+	5.85676i	−0.243307	+	0.386183i
$231$	19.0167			1.25121
$232$	11.1996	−	0.801008i	0.735287	−	0.0525888i
$233$	4.24345	−	19.5068i	0.277997	−	1.27793i	−0.600283	−	0.799788i	$-0.704945\pi$
$233$	4.24345	−	19.5068i	0.277997	−	1.27793i	0.878280	−	0.478146i	$-0.158691\pi$
$234$	−10.6757	+	1.53493i	−0.697891	+	0.100342i
$235$	13.4489	−	17.1285i	0.877310	−	1.11734i
$236$	−1.72158	+	11.9739i	−0.112066	+	0.779433i
$237$	3.95028	−	7.23439i	0.256598	−	0.469924i
$238$	6.22438	−	1.35403i	0.403466	−	0.0877687i
$239$	14.2255	+	6.49659i	0.920174	+	0.420229i	0.818446	−	0.574583i	$-0.194836\pi$
$239$	14.2255	+	6.49659i	0.920174	+	0.420229i	0.101727	+	0.994812i	$0.467563\pi$
$240$	11.8080	−	2.28514i	0.762202	−	0.147505i
$241$	4.00640	−	3.47156i	0.258075	−	0.223623i	−0.516207	−	0.856464i	$-0.672657\pi$
$241$	4.00640	−	3.47156i	0.258075	−	0.223623i	0.774282	+	0.632841i	$0.218111\pi$
$242$	0.164111	−	2.29457i	0.0105494	−	0.147500i
$243$	−27.4712	+	15.0004i	−1.76228	+	0.962275i
$244$	−3.69348	+	8.08760i	−0.236451	+	0.517756i
$245$	3.94897	−	3.26561i	0.252290	−	0.208632i
$246$	−7.07116	+	2.07628i	−0.450840	+	0.132379i
$247$	−4.88346	−	6.52353i	−0.310727	−	0.415083i
$248$	−5.38604	−	2.00889i	−0.342014	−	0.127564i
$249$	−3.20541	−	22.2941i	−0.203135	−	1.41283i
$250$	−3.01302	−	6.55786i	−0.190560	−	0.414756i
$251$	−20.4474	−	17.7178i	−1.29063	−	1.11834i	−0.986156	−	0.165818i	$-0.946974\pi$
$251$	−20.4474	−	17.7178i	−1.29063	−	1.11834i	−0.304475	−	0.952520i	$-0.598481\pi$
$252$	−17.8044	+	17.8044i	−1.12157	+	1.12157i
$253$	−13.0678	−	0.514765i	−0.821567	−	0.0323630i
$254$		−	5.69221i		−	0.357161i
$255$	17.0315	+	27.8941i	1.06655	+	1.74680i
$256$	−6.64542	+	4.27075i	−0.415339	+	0.266922i
$257$	15.7305	−	21.0135i	0.981244	−	1.31079i	0.0309221	−	0.999522i	$-0.490156\pi$
$257$	15.7305	−	21.0135i	0.981244	−	1.31079i	0.950322	−	0.311267i	$-0.100753\pi$
$258$	−6.70358	+	17.9730i	−0.417347	+	1.11895i
$259$	1.32652	+	0.190725i	0.0824259	+	0.0118511i
$260$	−5.57452	−	5.83747i	−0.345717	−	0.362025i
$261$	−29.9288	−	19.2340i	−1.85254	−	1.19056i
$262$	1.99152	−	0.742798i	0.123036	−	0.0458902i
$263$	11.8860	+	21.7676i	0.732922	+	1.34225i	0.932070	+	0.362277i	$0.118001\pi$
$263$	11.8860	+	21.7676i	0.732922	+	1.34225i	−0.199148	+	0.979969i	$0.563818\pi$
$264$	−13.2750	−	15.3202i	−0.817020	−	0.942891i
$265$	1.15037	−	2.87984i	0.0706664	−	0.176907i
$266$	4.80359	+	1.41046i	0.294527	+	0.0864809i
$267$	13.3489	+	35.7898i	0.816939	+	2.19030i
$268$	−0.662878	−	3.04720i	−0.0404917	−	0.186138i
$269$	−1.00066	−	3.40795i	−0.0610115	−	0.207786i	0.923346	−	0.383969i	$-0.125443\pi$
$269$	−1.00066	−	3.40795i	−0.0610115	−	0.207786i	−0.984357	+	0.176183i	$0.943625\pi$
$270$	18.0691	+	8.76043i	1.09965	+	0.533143i
$271$	−0.838744	−	1.83659i	−0.0509501	−	0.111565i	0.882445	−	0.470416i	$-0.155896\pi$
$271$	−0.838744	−	1.83659i	−0.0509501	−	0.111565i	−0.933395	+	0.358851i	$0.883169\pi$
$272$	6.09309	+	4.56123i	0.369448	+	0.276565i
$273$	15.5355	+	3.37954i	0.940252	+	0.204539i
$274$	−4.39802	+	5.07558i	−0.265694	+	0.306627i
$275$	7.89196	−	11.1186i	0.475903	−	0.670474i
$276$	17.9221	−	16.5636i	1.07878	−	0.997014i
$277$	−16.7455	−	16.7455i	−1.00614	−	1.00614i	−0.999981	−	0.00616098i	$-0.998039\pi$
$277$	−16.7455	−	16.7455i	−1.00614	−	1.00614i	−0.00616098	−	0.999981i	$-0.501961\pi$
$278$	0.861303	+	12.0426i	0.0516575	+	0.722267i
$279$	9.84724	+	15.3226i	0.589539	+	0.917341i
$280$	11.0689	+	1.85264i	0.661491	+	0.110717i
$281$	23.0722	−	10.5367i	1.37637	−	0.628569i	0.416535	−	0.909120i	$-0.363244\pi$
$281$	23.0722	−	10.5367i	1.37637	−	0.628569i	0.959839	+	0.280551i	$0.0905171\pi$
$282$	16.1745	−	12.1081i	0.963175	−	0.721024i
$283$	15.9232	+	8.69470i	0.946534	+	0.516847i	0.876872	−	0.480724i	$-0.159626\pi$
$283$	15.9232	+	8.69470i	0.946534	+	0.516847i	0.0696618	+	0.997571i	$0.477808\pi$
$284$	−4.68141	+	7.28442i	−0.277791	+	0.432251i
$285$	1.24177	+	25.6564i	0.0735564	+	1.51976i
$286$	−1.13062	+	3.85053i	−0.0668548	+	0.227686i
$287$	7.68868	+	0.549905i	0.453848	+	0.0324599i
$288$	41.7147	+	2.98350i	2.45806	+	0.175804i
$289$	−1.03758	+	3.53369i	−0.0610343	+	0.207864i
$290$	0.338724	+	6.99841i	0.0198905	+	0.410961i
$291$	4.06723	−	6.32873i	0.238425	−	0.370997i
$292$	−11.1212	−	6.07266i	−0.650821	−	0.355375i
$293$	−4.77946	+	3.57786i	−0.279219	+	0.209021i	−0.729704	−	0.683763i	$-0.760342\pi$
$293$	−4.77946	+	3.57786i	−0.279219	+	0.209021i	0.450485	+	0.892784i	$0.351251\pi$
$294$	4.32453	−	1.97495i	0.252212	−	0.115181i
$295$	−16.8497	−	2.82021i	−0.981028	−	0.164199i
$296$	−0.772351	−	1.20180i	−0.0448920	−	0.0698533i
$297$	2.70647	+	37.8414i	0.157045	+	2.19578i
$298$	−4.17223	−	4.17223i	−0.241691	−	0.241691i
$299$	−10.5841	−	2.74287i	−0.612096	−	0.158624i
$300$	4.25746	+	25.0842i	0.245805	+	1.44824i
$301$	13.1391	−	15.1633i	0.757323	−	0.873997i
$302$	−12.1601	−	2.64526i	−0.699733	−	0.152218i
$303$	1.50374	+	1.12568i	0.0863875	+	0.0646689i
$304$	2.48499	+	5.44136i	0.142524	+	0.312083i
$305$	−11.2986	−	5.47787i	−0.646955	−	0.313662i
$306$	6.06144	+	20.6434i	0.346509	+	1.18010i
$307$	3.29292	+	15.1373i	0.187937	+	0.863931i	0.970451	+	0.241299i	$0.0775733\pi$
$307$	3.29292	+	15.1373i	0.187937	+	0.863931i	−0.782514	+	0.622633i	$0.786063\pi$
$308$	3.27404	+	8.77803i	0.186556	+	0.500175i
$309$	−31.6091	−	9.28126i	−1.79818	−	0.527992i
$310$	1.33067	−	3.33122i	0.0755772	−	0.189201i
$311$	−10.9792	−	12.6706i	−0.622572	−	0.718486i	0.353621	−	0.935389i	$-0.384950\pi$
$311$	−10.9792	−	12.6706i	−0.622572	−	0.718486i	−0.976193	+	0.216902i	$0.930405\pi$
$312$	−8.12225	−	14.8748i	−0.459832	−	0.842120i
$313$	−6.68940	+	2.49502i	−0.378107	+	0.141027i	−0.531330	−	0.847165i	$-0.678308\pi$
$313$	−6.68940	+	2.49502i	−0.378107	+	0.141027i	0.153223	+	0.988192i	$0.451035\pi$
$314$	10.5127	+	6.75613i	0.593268	+	0.381270i
$315$	−24.5585	−	25.7169i	−1.38371	−	1.44898i
$316$	4.01946	+	0.577912i	0.226113	+	0.0325101i
$317$	4.66533	−	12.5082i	0.262031	−	0.702532i	−0.737597	−	0.675242i	$-0.764039\pi$
$317$	4.66533	−	12.5082i	0.262031	−	0.702532i	0.999628	−	0.0272904i	$-0.00868788\pi$
$318$	1.72418	−	2.30323i	0.0966870	−	0.129159i
$319$	−11.1360	+	7.15666i	−0.623495	+	0.400696i
$320$	−0.391877	−	0.641813i	−0.0219066	−	0.0358784i
$321$		−	18.4607i		−	1.03037i
$322$	6.21537	−	2.54780i	0.346369	−	0.141983i
$323$	−11.4943	+	11.4943i	−0.639562	+	0.639562i
$324$	−27.1934	−	23.5633i	−1.51075	−	1.30907i
$325$	8.42318	−	7.68067i	0.467234	−	0.426047i
$326$	−0.0767411	−	0.533746i	−0.00425030	−	0.0295615i
$327$	−39.5086	−	14.7360i	−2.18483	−	0.814900i
$328$	−4.92422	−	6.57798i	−0.271894	−	0.363208i
$329$	−20.2768	+	5.95380i	−1.11790	+	0.328244i
$330$	9.74837	−	8.06144i	0.536630	−	0.443768i
$331$	−0.760601	+	1.66548i	−0.0418064	+	0.0915433i	−0.929383	−	0.369117i	$-0.879660\pi$
$331$	−0.760601	+	1.66548i	−0.0418064	+	0.0915433i	0.887576	+	0.460660i	$0.152387\pi$
$332$	9.73900	−	5.31789i	0.534497	−	0.291857i
$333$	−0.322914	+	4.51493i	−0.0176956	+	0.247417i
$334$	2.37256	−	2.05584i	0.129821	−	0.112490i
$335$	4.32386	−	0.836775i	0.236238	−	0.0457179i
$336$	−10.6163	−	4.84831i	−0.579168	−	0.264497i
$337$	−24.5389	+	5.33810i	−1.33672	+	0.290785i	−0.823423	−	0.567428i	$-0.807939\pi$
$337$	−24.5389	+	5.33810i	−1.33672	+	0.290785i	−0.513294	+	0.858213i	$0.671575\pi$
$338$	2.41368	−	4.42033i	0.131287	−	0.240434i
$339$	3.08756	−	21.4745i	0.167693	−	1.16633i
$340$	−9.94352	+	12.6641i	−0.539263	+	0.686806i
$341$	6.70814	−	0.964485i	0.363266	−	0.0522298i
$342$	−3.59434	+	16.5229i	−0.194360	+	0.893456i
$343$	−20.1103	+	1.43832i	−1.08586	+	0.0776620i
$344$	−21.3877			−1.15315
$345$	22.8029	+	25.8427i	1.22767	+	1.39133i
$346$	0.766021			0.0411816
$347$	−0.982890	+	0.0702977i	−0.0527643	+	0.00377378i	−0.0976964	−	0.995216i	$-0.531147\pi$
$347$	−0.982890	+	0.0702977i	−0.0527643	+	0.00377378i	0.0449321	+	0.998990i	$0.485693\pi$
$348$	5.25067	−	24.1370i	0.281466	−	1.29388i
$349$	19.8058	−	2.84764i	1.06018	−	0.152431i	0.409904	−	0.912129i	$-0.365562\pi$
$349$	19.8058	−	2.84764i	1.06018	−	0.152431i	0.650276	+	0.759698i	$0.274653\pi$
$350$	−1.31489	+	6.87872i	−0.0702837	+	0.367683i
$351$	−4.51394	+	31.3951i	−0.240936	+	1.67575i
$352$	7.45758	−	13.6575i	0.397491	−	0.727950i
$353$	17.2372	−	3.74971i	0.917441	−	0.199577i	0.271034	−	0.962570i	$-0.412634\pi$
$353$	17.2372	−	3.74971i	0.917441	−	0.199577i	0.646407	+	0.762993i	$0.276271\pi$
$354$	−14.4177	−	6.58434i	−0.766291	−	0.349953i
$355$	−10.1324	−	6.84658i	−0.537774	−	0.363379i
$356$	−14.2222	+	12.3236i	−0.753773	+	0.653148i
$357$	2.26253	−	31.6342i	0.119746	−	1.67426i
$358$	4.68510	−	2.55826i	0.247615	−	0.135208i
$359$	5.42106	−	11.8705i	0.286113	−	0.626499i	−0.710937	−	0.703255i	$-0.751729\pi$
$359$	5.42106	−	11.8705i	0.286113	−	0.626499i	0.997050	+	0.0767562i	$0.0244563\pi$
$360$	−3.57440	+	37.7368i	−0.188387	+	1.98890i
$361$	5.97211	−	1.75357i	0.314322	−	0.0922932i
$362$	−6.14762	−	8.21226i	−0.323112	−	0.431627i
$363$	−10.7313	−	4.00259i	−0.563250	−	0.210081i
$364$	1.11471	+	7.75296i	0.0584266	+	0.406366i
$365$	8.93568	−	15.5043i	0.467715	−	0.811534i
$366$	−8.80407	−	7.62877i	−0.460196	−	0.398762i
$367$	3.44780	−	3.44780i	0.179974	−	0.179974i	−0.611371	−	0.791344i	$-0.709382\pi$
$367$	3.44780	−	3.44780i	0.179974	−	0.179974i	0.791344	+	0.611371i	$0.209382\pi$
$368$	7.16403	+	3.61901i	0.373451	+	0.188654i
$369$			26.0353i			1.35534i
$370$	0.760852	−	0.464559i	0.0395548	−	0.0241513i
$371$	−2.53158	+	1.62695i	−0.131433	+	0.0844668i
$372$	−7.57870	+	10.1240i	−0.392937	+	0.524903i
$373$	1.09629	−	2.93926i	0.0567637	−	0.152189i	−0.905473	−	0.424404i	$-0.860484\pi$
$373$	1.09629	−	2.93926i	0.0567637	−	0.152189i	0.962236	+	0.272215i	$0.0877562\pi$
$374$	7.92383	+	1.13927i	0.409731	+	0.0589105i
$375$	−35.5545	+	5.19500i	−1.83602	+	0.268268i
$376$	18.9511	+	12.1791i	0.977327	+	0.628090i
$377$	−10.3693	+	3.86753i	−0.534044	+	0.199188i
$378$	−9.33881	−	17.1027i	−0.480336	−	0.879670i
$379$	22.6926	+	26.1886i	1.16564	+	1.34522i	0.927426	+	0.374006i	$0.122016\pi$
$379$	22.6926	+	26.1886i	1.16564	+	1.34522i	0.238213	+	0.971213i	$0.423438\pi$
$380$	−11.6291	+	4.99037i	−0.596560	+	0.256000i
$381$	−27.1927	−	7.98449i	−1.39312	−	0.409058i
$382$	−0.348032	−	0.933109i	−0.0178068	−	0.0477420i
$383$	−0.693727	−	3.18901i	−0.0354478	−	0.162951i	0.956020	−	0.293301i	$-0.0947537\pi$
$383$	−0.693727	−	3.18901i	−0.0354478	−	0.162951i	−0.991468	+	0.130350i	$0.958390\pi$
$384$	10.1371	+	34.5238i	0.517307	+	1.76179i
$385$	−12.5001	+	4.33699i	−0.637062	+	0.221033i
$386$	−1.54171	−	3.37588i	−0.0784711	−	0.171828i
$387$	54.2502	+	40.6112i	2.75769	+	2.06438i
$388$	3.62155	+	0.787820i	0.183856	+	0.0399955i
$389$	8.21853	−	9.48469i	0.416696	−	0.480893i	−0.508132	−	0.861279i	$-0.669664\pi$
$389$	8.21853	−	9.48469i	0.416696	−	0.480893i	0.924828	+	0.380387i	$0.124209\pi$
$390$	9.39646	−	4.85328i	0.475808	−	0.245756i
$391$	−2.41106	+	21.6770i	−0.121933	+	1.09625i
$392$	3.74817	+	3.74817i	0.189311	+	0.189311i
$393$	−0.754963	−	10.5558i	−0.0380828	−	0.532468i
$394$	−3.55216	−	5.52727i	−0.178955	−	0.278460i
$395$	−0.946705	+	5.65621i	−0.0476339	+	0.284595i
$396$	−28.7839	+	13.1451i	−1.44644	+	0.660569i
$397$	16.1341	−	12.0778i	0.809746	−	0.606168i	−0.112112	−	0.993696i	$-0.535762\pi$
$397$	16.1341	−	12.0778i	0.809746	−	0.606168i	0.921858	+	0.387527i	$0.126671\pi$
$398$	−7.02027	−	3.83336i	−0.351894	−	0.192149i
$399$	13.4760	−	20.9691i	0.674646	−	1.04977i
$400$	−7.24046	+	4.19502i	−0.362023	+	0.209751i
$401$	−4.30777	+	14.6709i	−0.215120	+	0.732630i	0.779255	+	0.626707i	$0.215598\pi$
$401$	−4.30777	+	14.6709i	−0.215120	+	0.732630i	−0.994374	+	0.105923i	$0.966220\pi$
$402$	4.07554	+	0.291489i	0.203270	+	0.0145381i
$403$	5.65155	+	0.404207i	0.281524	+	0.0201350i
$404$	−0.260718	+	0.887923i	−0.0129712	+	0.0441758i
$405$	34.1532	−	37.6274i	1.69709	−	1.86972i
$406$	3.67591	−	5.71983i	0.182432	−	0.283870i
$407$	1.47820	+	0.807160i	0.0732718	+	0.0400094i
$408$	−27.0644	+	20.2602i	−1.33989	+	1.00303i
$409$	16.9595	−	7.74513i	0.838592	−	0.382972i	0.0506462	−	0.998717i	$-0.483872\pi$
$409$	16.9595	−	7.74513i	0.838592	−	0.382972i	0.787946	+	0.615744i	$0.211145\pi$
$410$	4.17449	−	2.97744i	0.206163	−	0.147045i
$411$	18.0778	+	28.1297i	0.891714	+	1.38753i
$412$	−1.15782	−	16.1885i	−0.0570419	−	0.797550i
$413$	11.7226	+	11.7226i	0.576834	+	0.576834i
$414$	10.0810	+	20.3254i	0.495454	+	0.998937i
$415$	7.19141	+	13.9233i	0.353013	+	0.683469i
$416$	8.51953	−	9.83207i	0.417704	−	0.482057i
$417$	58.7377	+	12.7776i	2.87640	+	0.625722i
$418$	5.03674	+	3.77046i	0.246355	+	0.184419i
$419$	−10.7493	−	23.5376i	−0.525137	−	1.14989i	−0.967458	−	0.253032i	$-0.918572\pi$
$419$	−10.7493	−	23.5376i	−0.525137	−	1.14989i	0.442321	−	0.896857i	$-0.354155\pi$
$420$	10.7711	−	22.2163i	0.525576	−	1.08405i
$421$	−2.06410	−	7.02969i	−0.100598	−	0.342606i	0.893778	−	0.448509i	$-0.148045\pi$
$421$	−2.06410	−	7.02969i	−0.100598	−	0.342606i	−0.994376	+	0.105903i	$0.966227\pi$
$422$	−3.65421	−	16.7981i	−0.177884	−	0.817721i
$423$	−24.9438	−	66.8769i	−1.21281	−	3.25166i
$424$	3.07791	+	0.903755i	0.149476	+	0.0438902i
$425$	−17.5567	−	14.4511i	−0.851626	−	0.700980i
$426$	−7.42965	−	8.57428i	−0.359968	−	0.415425i
$427$	5.83953	+	10.6943i	0.282595	+	0.517534i
$428$	8.52135	−	3.17830i	0.411895	−	0.153629i
$429$	16.8087	+	10.8023i	0.811533	+	0.521541i
$430$	0.307439	−	13.3428i	0.0148260	−	0.643448i
$431$	0.750054	+	0.107842i	0.0361288	+	0.00519454i	0.160356	−	0.987059i	$-0.448736\pi$
$431$	0.750054	+	0.107842i	0.0361288	+	0.00519454i	−0.124227	+	0.992254i	$0.539645\pi$
$432$	8.13674	−	21.8155i	0.391479	−	1.04960i
$433$	−13.5117	+	18.0495i	−0.649330	+	0.867403i	−0.997546	−	0.0700114i	$-0.977696\pi$
$433$	−13.5117	+	18.0495i	−0.649330	+	0.867403i	0.348217	+	0.937414i	$0.386787\pi$
$434$	−2.92838	+	1.88195i	−0.140567	+	0.0903367i
$435$	33.9077	+	8.19856i	1.62575	+	0.393091i
$436$		−	20.7740i		−	0.994895i
$437$	−9.82801	+	14.0447i	−0.470137	+	0.671848i
$438$	11.7396	−	11.7396i	0.560941	−	0.560941i
$439$	−12.8975	−	11.1757i	−0.615562	−	0.533387i	0.290314	−	0.956932i	$-0.406240\pi$
$439$	−12.8975	−	11.1757i	−0.615562	−	0.533387i	−0.905875	+	0.423544i	$0.860786\pi$
$440$	12.2199	+	7.04272i	0.582559	+	0.335748i
$441$	−2.39021	−	16.6243i	−0.113820	−	0.791634i
$442$	6.27082	+	2.33889i	0.298272	+	0.111250i
$443$	4.43272	+	5.92142i	0.210605	+	0.281335i	0.893388	−	0.449286i	$-0.148322\pi$
$443$	4.43272	+	5.92142i	0.210605	+	0.281335i	−0.682783	+	0.730621i	$0.739231\pi$
$444$	−3.01552	+	0.885436i	−0.143110	+	0.0420209i
$445$	−16.9368	−	20.4809i	−0.802879	−	0.970889i
$446$	−7.96142	+	17.4331i	−0.376984	+	0.825481i
$447$	−25.7839	+	14.0791i	−1.21954	+	0.665918i
$448$	−0.0520583	+	0.727870i	−0.00245952	+	0.0343886i
$449$	−15.1895	+	13.1617i	−0.716835	+	0.621141i	−0.934949	−	0.354782i	$-0.884555\pi$
$449$	−15.1895	+	13.1617i	−0.716835	+	0.621141i	0.218114	+	0.975923i	$0.430010\pi$
$450$	−23.4909	−	2.77235i	−1.10737	−	0.130690i
$451$	8.81186	+	4.02424i	0.414934	+	0.189494i
$452$	10.4441	−	2.27197i	0.491248	−	0.106865i
$453$	−29.6939	+	54.3802i	−1.39514	+	2.55501i
$454$	−0.498888	+	3.46984i	−0.0234140	+	0.162848i
$455$	−10.9825	+	1.32162i	−0.514869	+	0.0619584i
$456$	−26.3002	+	3.78140i	−1.23162	+	0.177081i
$457$	2.14302	−	9.85131i	0.100246	−	0.460825i	−0.899469	−	0.436984i	$-0.856047\pi$
$457$	2.14302	−	9.85131i	0.100246	−	0.460825i	0.999716	−	0.0238411i	$-0.00758959\pi$
$458$	18.4076	−	1.31654i	0.860129	−	0.0615176i
$459$	63.2710			2.95324
$460$	−8.00300	+	14.9749i	−0.373142	+	0.698210i
$461$	34.2242			1.59398			0.796989	−	0.603994i	$-0.206425\pi$
$461$	34.2242			1.59398			0.796989	+	0.603994i	$0.206425\pi$
$462$	−12.2440	+	0.875711i	−0.569644	+	0.0407418i
$463$	−1.04028	+	4.78211i	−0.0483461	+	0.222243i	−0.994981	−	0.100065i	$-0.968095\pi$
$463$	−1.04028	+	4.78211i	−0.0483461	+	0.222243i	0.946635	+	0.322308i	$0.104459\pi$
$464$	8.04138	−	1.15618i	0.373312	−	0.0536741i
$465$	−14.0473	−	11.0296i	−0.651428	−	0.511485i
$466$	−1.83389	+	12.7550i	−0.0849533	+	0.590863i
$467$	−13.4766	+	24.6806i	−0.623623	+	1.14208i	0.354697	+	0.934981i	$0.384584\pi$
$467$	−13.4766	+	24.6806i	−0.623623	+	1.14208i	−0.978320	+	0.207099i	$0.933598\pi$
$468$	−25.8507	+	5.62349i	−1.19495	+	0.259946i
$469$	−3.88750	−	1.77536i	−0.179508	−	0.0819785i
$470$	−7.87040	+	11.6476i	−0.363035	+	0.537265i
$471$	47.0215	−	40.7443i	2.16664	−	1.87740i
$472$	1.26072	−	17.6272i	0.0580293	−	0.811356i
$473$	22.1306	−	12.0842i	1.01757	−	0.555633i
$474$	−2.21027	+	4.83982i	−0.101521	+	0.222300i
$475$	−6.66750	−	16.5813i	−0.305926	−	0.760801i
$476$	14.9917	−	4.40197i	0.687145	−	0.201764i
$477$	−6.09109	−	8.13674i	−0.278892	−	0.372556i
$478$	−9.45837	−	3.52779i	−0.432616	−	0.161357i
$479$	1.56881	+	10.9113i	0.0716807	+	0.498550i	0.993759	+	0.111547i	$0.0355806\pi$
$479$	1.56881	+	10.9113i	0.0716807	+	0.498550i	−0.922079	+	0.387003i	$0.873510\pi$
$480$	−39.6029	+	10.6439i	−1.80762	+	0.485827i
$481$	1.06416	+	0.922099i	0.0485215	+	0.0420441i
$482$	−2.41968	+	2.41968i	−0.110213	+	0.110213i
$483$	−3.45293	−	33.2657i	−0.157114	−	1.51364i
$484$		−	5.64265i		−	0.256484i
$485$	−1.23012	+	5.08757i	−0.0558571	+	0.231015i
$486$	16.9967	−	10.9231i	0.770987	−	0.495483i
$487$	8.18704	−	10.9366i	0.370990	−	0.495585i	−0.575731	−	0.817639i	$-0.695282\pi$
$487$	8.18704	−	10.9366i	0.370990	−	0.495585i	0.946721	+	0.322054i	$0.104373\pi$
$488$	4.53909	−	12.1698i	0.205475	−	0.550900i
$489$	−2.65745	−	0.382083i	−0.120174	−	0.0172784i
$490$	−2.39219	+	2.28443i	−0.108068	+	0.103200i
$491$	24.1928	+	15.5478i	1.09181	+	0.701661i	0.957255	−	0.289245i	$-0.0934043\pi$
$491$	24.1928	+	15.5478i	1.09181	+	0.701661i	0.134551	+	0.990907i	$0.457041\pi$
$492$	−16.9371	+	6.31722i	−0.763584	+	0.284802i
$493$	10.5802	+	19.3761i	0.476506	+	0.872656i
$494$	3.44465	+	3.97534i	0.154982	+	0.178859i
$495$	−17.6230	−	41.0671i	−0.792096	−	1.84583i
$496$	−3.99080	−	1.17180i	−0.179192	−	0.0526156i
$497$	4.14699	+	11.1185i	0.186018	+	0.498734i
$498$	3.09046	+	14.2066i	0.138487	+	0.636613i
$499$	−6.05996	−	20.6383i	−0.271281	−	0.923898i	−0.976610	−	0.215018i	$-0.931019\pi$
$499$	−6.05996	−	20.6383i	−0.271281	−	0.923898i	0.705329	−	0.708880i	$-0.250799\pi$
$500$	−8.51926	−	15.5174i	−0.380993	−	0.693958i
$501$	−6.49309	−	14.2179i	−0.290090	−	0.635208i
$502$	13.9811	+	10.4661i	0.624007	+	0.467126i
$503$	4.60285	+	1.00129i	0.205231	+	0.0446453i	0.314005	−	0.949421i	$-0.398329\pi$
$503$	4.60285	+	1.00129i	0.205231	+	0.0446453i	−0.108774	+	0.994066i	$0.534693\pi$
$504$	24.0881	−	27.7992i	1.07297	−	1.23827i
$505$	−1.24516	−	0.396989i	−0.0554090	−	0.0176658i
$506$	8.43750	−	0.270332i	0.375093	−	0.0120177i
$507$	−17.7310	−	17.7310i	−0.787462	−	0.787462i
$508$	−0.996055	−	13.9267i	−0.0441928	−	0.617896i
$509$	3.99943	+	6.22324i	0.177272	+	0.275840i	0.918507	−	0.395405i	$-0.129396\pi$
$509$	3.99943	+	6.22324i	0.177272	+	0.275840i	−0.741235	+	0.671246i	$0.765760\pi$
$510$	−12.2504	−	17.1755i	−0.542455	−	0.760543i
$511$	−15.7960	+	7.21377i	−0.698772	+	0.319119i
$512$	−13.8432	+	10.3629i	−0.611788	+	0.457979i
$513$	43.6444	+	23.8317i	1.92695	+	1.05219i
$514$	−9.16054	+	14.2541i	−0.404054	+	0.628721i
$515$	22.8939	−	1.10807i	1.00883	−	0.0488274i
$516$	−13.2561	+	45.1461i	−0.583567	+	1.98745i
$517$	−26.4906	−	1.89464i	−1.16505	−	0.0833263i
$518$	−0.862870	−	0.0617137i	−0.0379123	−	0.00271154i
$519$	1.07450	−	3.65942i	0.0471654	−	0.160631i
$520$	8.73129	+	7.92511i	0.382892	+	0.347539i
$521$	−9.83811	+	15.3084i	−0.431015	+	0.670673i	−0.987037	−	0.160495i	$-0.948691\pi$
$521$	−9.83811	+	15.3084i	−0.431015	+	0.670673i	0.556021	+	0.831168i	$0.312327\pi$
$522$	20.1555	+	11.0058i	0.882184	+	0.481709i
$523$	−11.5017	+	8.61004i	−0.502933	+	0.376491i	−0.820410	−	0.571775i	$-0.806255\pi$
$523$	−11.5017	+	8.61004i	−0.502933	+	0.376491i	0.317478	+	0.948266i	$0.397164\pi$
$524$	4.74251	−	2.16583i	0.207177	−	0.0946148i
$525$	31.0165	+	15.9303i	1.35367	+	0.695254i
$526$	−8.65526	−	13.4678i	−0.377387	−	0.587226i
$527$	−0.806312	−	11.2737i	−0.0351235	−	0.491091i
$528$	−10.3714	−	10.3714i	−0.451355	−	0.451355i
$529$	1.47230	+	22.9528i	0.0640129	+	0.997949i
$530$	−0.608055	+	1.90717i	−0.0264122	+	0.0828424i
$531$	−36.6684	+	42.3176i	−1.59127	+	1.83643i
$532$	11.9994	+	2.61030i	0.520238	+	0.113171i
$533$	6.48359	+	4.85355i	0.280835	+	0.210231i
$534$	−10.2429	−	22.4287i	−0.443252	−	0.970587i
$535$	4.21017	+	12.1345i	0.182022	+	0.524622i
$536$	1.28349	+	4.37115i	0.0554381	+	0.188805i
$537$	−5.64943	−	25.9700i	−0.243791	−	1.12069i
$538$	0.801217	+	2.14815i	0.0345429	+	0.0926132i
$539$	−5.99609	−	1.76061i	−0.258270	−	0.0758349i
$540$	45.7413	+	18.2716i	1.96839	+	0.786284i
$541$	−3.51524	−	4.05680i	−0.151132	−	0.174415i	0.675135	−	0.737694i	$-0.264085\pi$
$541$	−3.51524	−	4.05680i	−0.151132	−	0.174415i	−0.826267	+	0.563279i	$0.809540\pi$
$542$	0.624605	+	1.14388i	0.0268291	+	0.0491338i
$543$	−47.8547	+	17.8489i	−2.05364	+	0.765969i
$544$	−21.8320	−	14.0306i	−0.936039	−	0.601556i
$545$	29.3305	+	0.675819i	1.25638	+	0.0289489i
$546$	−10.1583	−	1.46054i	−0.434734	−	0.0625052i
$547$	−7.56386	+	20.2795i	−0.323407	+	0.867088i	0.668907	+	0.743346i	$0.266762\pi$
$547$	−7.56386	+	20.2795i	−0.323407	+	0.867088i	−0.992314	+	0.123742i	$0.960510\pi$
$548$	−9.87212	+	13.1876i	−0.421716	+	0.563347i
$549$	−34.6215	+	22.2499i	−1.47761	+	0.949603i
$550$	−4.56928	+	7.52217i	−0.194835	+	0.320746i
$551$			17.3508i			0.739168i
$552$	−24.3890	+	26.0035i	−1.03806	+	1.10678i
$553$	3.93513	−	3.93513i	0.167339	−	0.167339i
$554$	11.5528	+	10.0106i	0.490833	+	0.425309i
$555$	−1.15203	−	4.28636i	−0.0489010	−	0.181946i
$556$	4.21456	+	29.3129i	0.178737	+	1.24314i
$557$	15.6110	+	5.82261i	0.661460	+	0.246712i	0.657699	−	0.753281i	$-0.271530\pi$
$557$	15.6110	+	5.82261i	0.661460	+	0.246712i	0.00376137	+	0.999993i	$0.498803\pi$
$558$	−7.04581	−	9.41210i	−0.298273	−	0.398446i
$559$	20.2269	−	5.93915i	0.855506	−	0.251199i
$560$	8.08403	+	0.765711i	0.341613	+	0.0323572i
$561$	16.5573	−	36.2554i	0.699050	−	1.53071i
$562$	−14.3700	+	7.84661i	−0.606161	+	0.330989i
$563$	2.17008	−	30.3416i	0.0914578	−	1.27875i	−0.719850	−	0.694129i	$-0.755790\pi$
$563$	2.17008	−	30.3416i	0.0914578	−	1.27875i	0.811308	−	0.584619i	$-0.198756\pi$
$564$	37.4540	−	32.4541i	1.57710	−	1.36656i
$565$	2.86799	+	14.8197i	0.120657	+	0.623471i
$566$	−10.6526	−	4.86488i	−0.447763	−	0.204486i
$567$	−48.1847	+	10.4819i	−2.02357	+	0.440200i
$568$	6.06235	−	11.1024i	0.254371	−	0.465845i
$569$	3.37215	−	23.4538i	0.141368	−	0.983235i	−0.788419	−	0.615138i	$-0.789100\pi$
$569$	3.37215	−	23.4538i	0.141368	−	0.983235i	0.929787	−	0.368097i	$-0.119991\pi$
$570$	−1.98099	−	16.4619i	−0.0829746	−	0.689512i
$571$	−10.9982	+	1.58130i	−0.460259	+	0.0661753i	−0.368545	−	0.929610i	$-0.620144\pi$
$571$	−10.9982	+	1.58130i	−0.460259	+	0.0661753i	−0.0917145	+	0.995785i	$0.529235\pi$
$572$	−2.09240	+	9.61862i	−0.0874877	+	0.402175i
$573$	−4.94581	+	0.353731i	−0.206614	+	0.0147773i
$574$	−4.97573			−0.207683
$575$	−20.8825	−	11.7865i	−0.870861	−	0.491530i
$576$	−2.46470			−0.102696
$577$	−8.30596	+	0.594054i	−0.345782	+	0.0247308i	−0.243150	−	0.969989i	$-0.578181\pi$
$577$	−8.30596	+	0.594054i	−0.345782	+	0.0247308i	−0.102632	+	0.994719i	$0.532726\pi$
$578$	0.505330	−	2.32297i	0.0210190	−	0.0966226i
$579$	−18.2897	+	2.62967i	−0.760096	+	0.109285i
$580$	2.05335	+	17.0632i	0.0852607	+	0.708509i
$581$	2.16417	−	15.0521i	0.0897849	−	0.624468i
$582$	−2.32727	+	4.26208i	−0.0964686	+	0.176669i
$583$	−3.69544	+	0.803894i	−0.153049	+	0.0332939i
$584$	16.8382	+	7.68975i	0.696770	+	0.318204i
$585$	−7.09873	−	36.6812i	−0.293496	−	1.51658i
$586$	2.91253	−	2.52372i	0.120315	−	0.104254i
$587$	0.222316	−	3.10838i	0.00917596	−	0.128297i	−0.990799	−	0.135340i	$-0.956787\pi$
$587$	0.222316	−	3.10838i	0.00917596	−	0.128297i	0.999975	+	0.00704317i	$0.00224193\pi$
$588$	10.2349	−	5.58867i	0.422080	−	0.230473i
$589$	3.69016	−	8.08032i	0.152050	−	0.332944i
$590$	10.9787	+	1.03989i	0.451984	+	0.0428115i
$591$	−31.3874	+	9.21617i	−1.29110	+	0.379102i
$592$	−0.619440	−	0.827475i	−0.0254588	−	0.0340090i
$593$	35.3650	+	13.1905i	1.45227	+	0.541667i	0.946982	−	0.321286i	$-0.104115\pi$
$593$	35.3650	+	13.1905i	1.45227	+	0.541667i	0.505284	+	0.862953i	$0.331388\pi$
$594$	−3.48516	−	24.2398i	−0.142998	−	0.994571i
$595$	5.72736	+	21.3098i	0.234799	+	0.873616i
$596$	−10.9380	−	9.47779i	−0.448036	−	0.388225i
$597$	−28.1600	+	28.1600i	−1.15251	+	1.15251i
$598$	6.94097	+	1.27862i	0.283837	+	0.0522866i
$599$			42.4365i			1.73391i	0.498388	+	0.866954i	$0.333925\pi$
$599$			42.4365i			1.73391i	−0.498388	+	0.866954i	$0.666075\pi$
$600$	−8.81797	−	36.1078i	−0.359992	−	1.47409i
$601$	1.94183	−	1.24794i	0.0792089	−	0.0509045i	−0.500437	−	0.865773i	$-0.666827\pi$
$601$	1.94183	−	1.24794i	0.0792089	−	0.0509045i	0.579646	+	0.814869i	$0.303191\pi$
$602$	−7.76140	+	10.3680i	−0.316331	+	0.422569i
$603$	5.04440	−	13.5246i	0.205424	−	0.550763i
$604$	−30.2139	−	4.34411i	−1.22939	−	0.176759i
$605$	7.96676	+	0.183566i	0.323895	+	0.00746303i
$606$	−1.02003	−	0.655532i	−0.0414358	−	0.0266292i
$607$	−4.77423	+	1.78070i	−0.193780	+	0.0722763i	−0.444481	−	0.895788i	$-0.646612\pi$
$607$	−4.77423	+	1.78070i	−0.193780	+	0.0722763i	0.250701	+	0.968065i	$0.419339\pi$
$608$	−9.77498	−	17.9015i	−0.396428	−	0.726003i
$609$	−22.1684	−	25.5837i	−0.898309	−	1.03670i
$610$	7.52692	+	3.00667i	0.304756	+	0.121736i
$611$	−21.3045	−	6.25556i	−0.861887	−	0.253073i
$612$	18.4423	+	49.4458i	0.745487	+	1.99873i
$613$	0.0700013	+	0.321791i	0.00282733	+	0.0129970i	0.978539	−	0.206062i	$-0.0660649\pi$
$613$	0.0700013	+	0.321791i	0.00282733	+	0.0129970i	−0.975712	+	0.219059i	$0.929701\pi$
$614$	−2.81723	−	9.59461i	−0.113694	−	0.387207i
$615$	−8.36817	−	24.1187i	−0.337437	−	0.972561i
$616$	−5.68559	−	12.4497i	−0.229079	−	0.501613i
$617$	−19.7616	−	14.7933i	−0.795570	−	0.595556i	0.122274	−	0.992496i	$-0.460981\pi$
$617$	−19.7616	−	14.7933i	−0.795570	−	0.595556i	−0.917845	+	0.396940i	$0.870072\pi$
$618$	20.7791	+	4.52021i	0.835857	+	0.181830i
$619$	10.2277	−	11.8034i	0.411087	−	0.474420i	−0.512014	−	0.858977i	$-0.671100\pi$
$619$	10.2277	−	11.8034i	0.411087	−	0.474420i	0.923101	+	0.384557i	$0.125646\pi$
$620$	2.67274	−	8.38309i	0.107340	−	0.336673i
$621$	65.7041	−	11.6054i	2.63661	−	0.465708i
$622$	7.65248	+	7.65248i	0.306837	+	0.306837i
$623$	1.83983	+	25.7242i	0.0737113	+	1.03062i
$624$	−6.62963	−	10.3159i	−0.265398	−	0.412967i
$625$	22.1858	−	11.5234i	0.887434	−	0.460935i
$626$	4.19212	−	1.91448i	0.167551	−	0.0765179i
$627$	25.0772	−	18.7726i	1.00149	−	0.749704i
$628$	26.9029	+	14.6901i	1.07354	+	0.586198i
$629$	1.51858	−	2.36295i	0.0605496	−	0.0942171i
$630$	16.9964	+	15.4271i	0.677151	+	0.614629i
$631$	6.90649	−	23.5213i	0.274943	−	0.936370i	−0.700043	−	0.714101i	$-0.746836\pi$
$631$	6.90649	−	23.5213i	0.274943	−	0.936370i	0.974985	−	0.222269i	$-0.0713462\pi$
$632$	−5.91719	−	0.423206i	−0.235373	−	0.0168342i
$633$	−85.3735	−	6.10603i	−3.39329	−	0.242693i
$634$	−2.42780	+	8.26833i	−0.0964203	+	0.328377i
$635$	19.6952	−	0.953252i	0.781581	−	0.0378286i
$636$	3.81537	−	5.93683i	0.151289	−	0.235411i
$637$	−4.58555	−	2.50390i	−0.181686	−	0.0992082i
$638$	6.84041	−	5.12066i	0.270814	−	0.202729i
$639$	−36.4585	+	16.6500i	−1.44228	+	0.658665i
$640$	−14.5369	−	20.3813i	−0.574620	−	0.805641i
$641$	12.9407	+	20.1361i	0.511126	+	0.795328i	0.996894	−	0.0787603i	$-0.0250962\pi$
$641$	12.9407	+	20.1361i	0.511126	+	0.795328i	−0.485767	+	0.874088i	$0.661460\pi$
$642$	0.850104	+	11.8860i	0.0335509	+	0.469103i
$643$	−32.2696	−	32.2696i	−1.27259	−	1.27259i	−0.944726	−	0.327861i	$-0.893672\pi$
$643$	−32.2696	−	32.2696i	−1.27259	−	1.27259i	−0.327861	−	0.944726i	$-0.606328\pi$
$644$	14.7608	−	7.32109i	0.581658	−	0.288491i
$645$	−63.3098	−	20.1847i	−2.49282	−	0.794774i
$646$	6.87139	−	7.93001i	0.270351	−	0.312002i
$647$	−3.15938	−	0.687281i	−0.124208	−	0.0270198i	0.150031	−	0.988681i	$-0.452062\pi$
$647$	−3.15938	−	0.687281i	−0.124208	−	0.0270198i	−0.274240	+	0.961661i	$0.588426\pi$
$648$	42.0806	+	31.5012i	1.65308	+	1.23748i
$649$	8.65496	+	18.9517i	0.339737	+	0.743920i
$650$	−5.06962	+	5.33313i	−0.198847	+	0.209183i
$651$	4.88277	+	16.6292i	0.191371	+	0.651750i
$652$	−0.281154	−	1.29245i	−0.0110109	−	0.0506161i
$653$	5.88652	+	15.7824i	0.230357	+	0.617612i	0.999777	−	0.0211321i	$-0.00672705\pi$
$653$	5.88652	+	15.7824i	0.230357	+	0.617612i	−0.769419	+	0.638744i	$0.779454\pi$
$654$	26.1164	+	7.66848i	1.02123	+	0.299861i
$655$	2.90362	+	6.76633i	0.113454	+	0.264382i
$656$	−3.89335	−	4.49316i	−0.152010	−	0.175429i
$657$	−28.1089	−	51.4776i	−1.09663	−	2.00833i
$658$	12.7812	−	4.76713i	0.498261	−	0.185842i
$659$	−20.9995	−	13.4956i	−0.818026	−	0.525714i	0.0634261	−	0.997987i	$-0.479797\pi$
$659$	−20.9995	−	13.4956i	−0.818026	−	0.525714i	−0.881452	+	0.472273i	$0.843434\pi$
$660$	22.4399	−	21.4291i	0.873472	−	0.834127i
$661$	8.29337	+	1.19241i	0.322575	+	0.0463792i	0.301700	−	0.953403i	$-0.402446\pi$
$661$	8.29337	+	1.19241i	0.322575	+	0.0463792i	0.0208745	+	0.999782i	$0.493355\pi$
$662$	0.413023	−	1.10736i	0.0160526	−	0.0430387i
$663$	19.9694	−	26.6760i	0.775548	−	1.03601i
$664$	−13.6370	+	8.76394i	−0.529217	+	0.340107i
$665$	−4.07580	+	16.8568i	−0.158053	+	0.653678i
$666$		−	2.92184i		−	0.113219i
$667$	14.5410	+	18.1806i	0.563031	+	0.703954i
$668$	5.44501	−	5.44501i	0.210674	−	0.210674i
$669$	72.1134	+	62.4866i	2.78806	+	2.41587i
$670$	−2.74541	+	0.737874i	−0.106064	+	0.0285066i
$671$	2.17926	+	15.1571i	0.0841294	+	0.585133i
$672$	37.2853	+	13.9067i	1.43831	+	0.536462i
$673$	9.93919	+	13.2772i	0.383128	+	0.511799i	0.950103	−	0.311936i	$-0.100977\pi$
$673$	9.93919	+	13.2772i	0.383128	+	0.511799i	−0.566975	+	0.823735i	$0.691887\pi$
$674$	15.5537	−	4.56697i	0.599105	−	0.175913i
$675$	−27.2854	+	63.9869i	−1.05022	+	2.46286i
$676$	5.13187	−	11.2372i	0.197380	−	0.432201i
$677$	25.3012	−	13.8155i	0.972403	−	0.530972i	0.0872068	−	0.996190i	$-0.472206\pi$
$677$	25.3012	−	13.8155i	0.972403	−	0.530972i	0.885196	+	0.465218i	$0.154024\pi$
$678$	−0.999057	+	13.9686i	−0.0383686	+	0.536463i
$679$	3.83862	−	3.32618i	0.147313	−	0.127647i
$680$	13.1694	−	19.4898i	0.505023	−	0.747398i
$681$	15.8763	+	7.25044i	0.608379	+	0.277838i
$682$	−4.27466	+	0.929896i	−0.163685	+	0.0356076i
$683$	−9.21357	+	16.8734i	−0.352548	+	0.645643i	−0.992427	−	0.122832i	$-0.960802\pi$
$683$	−9.21357	+	16.8734i	−0.352548	+	0.645643i	0.639880	+	0.768475i	$0.278984\pi$
$684$	−5.90270	+	41.0542i	−0.225696	+	1.56975i
$685$	−18.2982	−	14.3673i	−0.699138	−	0.548946i
$686$	12.8819	−	1.85214i	0.491834	−	0.0707151i
$687$	19.5311	−	89.7829i	0.745157	−	3.42543i
$688$	−15.4355	+	1.10397i	−0.588474	+	0.0420885i
$689$	−3.16181			−0.120455
$690$	−15.8718	−	15.5889i	−0.604230	−	0.593461i
$691$	−5.24413			−0.199496			−0.0997481	−	0.995013i	$-0.531804\pi$
$691$	−5.24413			−0.199496			−0.0997481	+	0.995013i	$0.531804\pi$
$692$	1.87416	−	0.134043i	0.0712450	−	0.00509554i
$693$	−9.21804	+	42.3746i	−0.350164	+	1.60968i
$694$	0.629602	−	0.0905232i	0.0238994	−	0.00343621i
$695$	−41.5235	+	4.99686i	−1.57508	+	0.189542i
$696$	−5.13553	+	35.7184i	−0.194662	+	1.35390i
$697$	7.74270	−	14.1797i	0.293276	−	0.537094i
$698$	−12.6210	+	2.74552i	−0.477710	+	0.103919i
$699$	58.3604	+	26.6523i	2.20739	+	1.00808i
$700$	−2.01335	+	17.0597i	−0.0760976	+	0.644796i
$701$	19.0485	−	16.5056i	0.719451	−	0.623408i	−0.216194	−	0.976350i	$-0.569364\pi$
$701$	19.0485	−	16.5056i	0.719451	−	0.623408i	0.935645	+	0.352943i	$0.114819\pi$
$702$	1.46060	−	20.4218i	0.0551267	−	0.770771i
$703$	1.93754	−	1.05798i	0.0730759	−	0.0399025i
$704$	−0.380966	+	0.834199i	−0.0143582	+	0.0314400i
$705$	44.6029	+	53.9365i	1.67984	+	2.03137i
$706$	−10.9256	+	3.20804i	−0.411190	+	0.120736i
$707$	0.760019	+	1.01527i	0.0285835	+	0.0381830i
$708$	−36.4267	−	13.5865i	−1.36900	−	0.510611i
$709$	0.921367	+	6.40825i	0.0346027	+	0.240667i	0.999781	−	0.0209259i	$-0.00666140\pi$
$709$	0.921367	+	6.40825i	0.0346027	+	0.240667i	−0.965178	+	0.261593i	$0.915752\pi$
$710$	6.83912	+	3.94162i	0.256668	+	0.147926i
$711$	14.2054	+	12.3091i	0.532745	+	0.461627i
$712$	19.4395	−	19.4395i	0.728525	−	0.728525i
$713$	−2.90518	−	11.5593i	−0.108800	−	0.432901i
$714$			20.4721i			0.766149i
$715$	−13.5123	−	3.26714i	−0.505331	−	0.122184i
$716$	11.0150	−	7.07891i	0.411650	−	0.264551i
$717$	−30.1202	+	40.2358i	−1.12486	+	1.50263i
$718$	−2.94375	+	7.89251i	−0.109860	+	0.294546i
$719$	19.0283	+	2.73585i	0.709634	+	0.102030i	0.487674	−	0.873026i	$-0.337845\pi$
$719$	19.0283	+	2.73585i	0.709634	+	0.102030i	0.221960	+	0.975056i	$0.428755\pi$
$720$	−0.631780	+	27.4192i	−0.0235451	+	1.02185i
$721$	−18.7113	−	12.0250i	−0.696846	−	0.447836i
$722$	−3.76443	+	1.40406i	−0.140098	+	0.0522537i
$723$	8.16514	+	14.9533i	0.303665	+	0.556120i
$724$	−16.4779	−	19.0165i	−0.612397	−	0.706744i
$725$	−24.1580	+	2.34399i	−0.897205	+	0.0870536i
$726$	7.09376	+	2.08292i	0.263274	+	0.0773043i
$727$	−3.25630	−	8.73048i	−0.120770	−	0.323796i	0.862472	−	0.506105i	$-0.168915\pi$
$727$	−3.25630	−	8.73048i	−0.120770	−	0.323796i	−0.983241	+	0.182310i	$0.941643\pi$
$728$	−2.43229	−	11.1811i	−0.0901467	−	0.414398i
$729$	−9.13269	−	31.1031i	−0.338248	−	1.15197i
$730$	−5.03932	+	10.3940i	−0.186514	+	0.384701i
$731$	−17.4690	−	38.2519i	−0.646116	−	1.41480i
$732$	−22.8751	−	17.1241i	−0.845490	−	0.632926i
$733$	−30.1417	−	6.55692i	−1.11331	−	0.242185i	−0.381953	−	0.924182i	$-0.624748\pi$
$733$	−30.1417	−	6.55692i	−1.11331	−	0.242185i	−0.731356	+	0.681996i	$0.761112\pi$
$734$	−2.06112	+	2.37866i	−0.0760773	+	0.0877978i
$735$	7.55759	+	14.6323i	0.278766	+	0.539720i
$736$	−25.2451	−	10.5656i	−0.930545	−	0.389453i
$737$	−3.79779	−	3.79779i	−0.139894	−	0.139894i
$738$	−1.19891	−	16.7630i	−0.0441325	−	0.617053i
$739$	−16.8841	−	26.2722i	−0.621093	−	0.966440i	−0.999173	−	0.0406668i	$-0.987052\pi$
$739$	−16.8841	−	26.2722i	−0.621093	−	0.966440i	0.378080	−	0.925773i	$-0.376585\pi$
$740$	1.78022	−	1.26974i	0.0654423	−	0.0466765i
$741$	23.8227	−	10.8795i	0.875149	−	0.399667i
$742$	1.55505	−	1.16410i	0.0570877	−	0.0427353i
$743$	−37.3511	−	20.3952i	−1.37028	−	0.748228i	−0.385609	−	0.922662i	$-0.626009\pi$
$743$	−37.3511	−	20.3952i	−1.37028	−	0.748228i	−0.984669	+	0.174434i	$0.944190\pi$
$744$	9.98822	−	15.5420i	0.366186	−	0.569796i
$745$	13.7374	−	15.1348i	0.503298	−	0.554495i
$746$	−0.570500	+	1.94295i	−0.0208875	+	0.0711363i
$747$	51.2313	+	3.66414i	1.87446	+	0.134064i
$748$	19.5859	+	1.40081i	0.716133	+	0.0512188i
$749$	3.51150	−	11.9591i	0.128307	−	0.436974i
$750$	22.6527	−	4.98210i	0.827161	−	0.181920i
$751$	−2.33859	+	3.63892i	−0.0853364	+	0.132786i	−0.881298	−	0.472561i	$-0.843329\pi$
$751$	−2.33859	+	3.63892i	−0.0853364	+	0.132786i	0.795961	+	0.605347i	$0.206966\pi$
$752$	14.3056	+	7.81147i	0.521673	+	0.284855i
$753$	69.6099	−	52.1093i	2.53673	−	1.89897i
$754$	6.49821	−	2.96763i	0.236651	−	0.108075i
$755$	7.11629	−	42.5172i	0.258988	−	1.54736i
$756$	−25.8412	−	40.2098i	−0.939837	−	1.46241i
$757$	3.69750	+	51.6978i	0.134388	+	1.87899i	0.402248	+	0.915531i	$0.368229\pi$
$757$	3.69750	+	51.6978i	0.134388	+	1.87899i	−0.267860	+	0.963458i	$0.586317\pi$
$758$	−15.8167	−	15.8167i	−0.574489	−	0.574489i
$759$	10.5439	−	40.6866i	0.382719	−	1.47683i
$760$	16.4253	−	8.48367i	0.595807	−	0.307735i
$761$	−28.1766	+	32.5175i	−1.02140	+	1.17876i	−0.0376366	+	0.999291i	$0.511983\pi$
$761$	−28.1766	+	32.5175i	−1.02140	+	1.17876i	−0.983764	+	0.179468i	$0.942563\pi$
$762$	17.8759	+	3.88866i	0.647574	+	0.140871i
$763$	−22.7912	−	17.0613i	−0.825096	−	0.617659i
$764$	−1.01478	−	2.22206i	−0.0367135	−	0.0803914i
$765$	−70.4116	+	24.4298i	−2.54574	+	0.883262i
$766$	0.593513	+	2.02132i	0.0214445	+	0.0730333i
$767$	3.70258	+	17.0205i	0.133693	+	0.614575i
$768$	−8.87206	−	23.7869i	−0.320143	−	0.858336i
$769$	25.5916	+	7.51437i	0.922857	+	0.270975i	0.708443	−	0.705768i	$-0.249398\pi$
$769$	25.5916	+	7.51437i	0.922857	+	0.270975i	0.214414	+	0.976743i	$0.431216\pi$
$770$	7.84853	−	3.36802i	0.282841	−	0.121375i
$771$	55.2447	+	63.7558i	1.98959	+	2.29611i
$772$	−4.36272	−	7.98972i	−0.157018	−	0.287556i
$773$	20.9493	−	7.81370i	0.753496	−	0.281039i	0.0567799	−	0.998387i	$-0.481917\pi$
$773$	20.9493	−	7.81370i	0.753496	−	0.281039i	0.696716	+	0.717347i	$0.254644\pi$
$774$	−36.7995	−	23.6496i	−1.32273	−	0.850066i
$775$	11.7490	+	4.04631i	0.422036	+	0.145348i
$776$	−5.35924	−	0.770543i	−0.192386	−	0.0276609i
$777$	−1.50517	+	4.03552i	−0.0539977	+	0.144773i
$778$	−4.85478	+	6.48523i	−0.174052	+	0.232507i
$779$	10.6818	−	6.86480i	0.382717	−	0.245957i
$780$	22.1403	−	13.5184i	0.792750	−	0.484036i
$781$			14.9133i			0.533638i
$782$	0.554160	−	14.0679i	0.0198167	−	0.503067i
$783$	47.7540	−	47.7540i	1.70659	−	1.70659i
$784$	2.89852	+	2.51158i	0.103519	+	0.0896994i
$785$	−21.6159	+	37.5058i	−0.771504	+	1.33864i
$786$	0.972175	+	6.76163i	0.0346763	+	0.241179i
$787$	47.0788	+	17.5595i	1.67818	+	0.625928i	0.994584	−	0.103934i	$-0.0331431\pi$
$787$	47.0788	+	17.5595i	1.67818	+	0.625928i	0.683594	+	0.729862i	$0.260416\pi$
$788$	−9.65798	−	12.9015i	−0.344051	−	0.459599i
$789$	−76.4790	+	22.4563i	−2.72273	+	0.799465i
$790$	0.349076	−	3.68538i	0.0124196	−	0.131120i
$791$	6.08493	−	13.3241i	0.216355	−	0.473752i
$792$	40.5725	−	22.1542i	1.44168	−	0.787217i
$793$	−0.913307	+	12.7697i	−0.0324325	+	0.453465i
$794$	−9.83184	+	8.51934i	−0.348919	+	0.302340i
$795$	8.25799	+	5.57999i	0.292881	+	0.197902i
$796$	−17.8467	−	8.15032i	−0.632560	−	0.288880i
$797$	−36.8171	+	8.00908i	−1.30413	+	0.283696i	−0.810378	−	0.585907i	$-0.800738\pi$
$797$	−36.8171	+	8.00908i	−1.30413	+	0.283696i	−0.493751	+	0.869603i	$0.664375\pi$
$798$	−7.71101	+	14.1217i	−0.272967	+	0.499902i
$799$	−6.30346	+	43.8415i	−0.223000	+	1.55100i
$800$	23.6043	−	16.0284i	0.834537	−	0.566689i
$801$	−86.2203	+	12.3966i	−3.04644	+	0.438013i
$802$	2.09799	−	9.64432i	0.0740827	−	0.340553i
$803$	−21.7678	+	1.55686i	−0.768169	+	0.0549405i
$804$	10.0223			0.353460
$805$	9.85632	+	21.0787i	0.347390	+	0.742927i
$806$	−3.65740			−0.128826
$807$	11.3859	−	0.814339i	0.400804	−	0.0286661i
$808$	0.287368	−	1.32101i	0.0101096	−	0.0464729i
$809$	−42.8772	+	6.16480i	−1.50748	+	0.216743i	−0.845985	−	0.533206i	$-0.820987\pi$
$809$	−42.8772	+	6.16480i	−1.50748	+	0.216743i	−0.661495	+	0.749949i	$0.730078\pi$
$810$	−20.2570	+	25.7994i	−0.711759	+	0.906497i
$811$	4.47170	−	31.1014i	0.157023	−	1.09212i	−0.747059	−	0.664757i	$-0.768535\pi$
$811$	4.47170	−	31.1014i	0.157023	−	1.09212i	0.904082	−	0.427359i	$-0.140556\pi$
$812$	7.99267	−	14.6375i	0.280488	−	0.513675i
$813$	6.34065	−	1.37932i	0.222376	−	0.0483750i
$814$	−0.988920	−	0.451625i	−0.0346616	−	0.0158294i
$815$	1.83393	−	0.354911i	0.0642397	−	0.0124320i
$816$	−18.4866	+	16.0188i	−0.647162	+	0.560769i
$817$	2.35778	−	32.9660i	0.0824882	−	1.15334i
$818$	−10.5628	+	5.76773i	−0.369320	+	0.201664i
$819$	−15.0612	+	32.9793i	−0.526279	+	1.15239i
$820$	9.69237	−	8.01513i	0.338472	−	0.279901i
$821$	−14.4879	+	4.25402i	−0.505630	+	0.148466i	−0.524592	−	0.851354i	$-0.675782\pi$
$821$	−14.4879	+	4.25402i	−0.505630	+	0.148466i	0.0189620	+	0.999820i	$0.493964\pi$
$822$	−12.9349	−	17.2790i	−0.451156	−	0.602673i
$823$	27.6649	+	10.3185i	0.964339	+	0.359680i	0.781807	−	0.623520i	$-0.214298\pi$
$823$	27.6649	+	10.3185i	0.964339	+	0.359680i	0.182532	+	0.983200i	$0.441571\pi$
$824$	3.37425	+	23.4684i	0.117548	+	0.817561i
$825$	29.5254	+	32.3797i	1.02794	+	1.12731i
$826$	−8.08752	−	7.00788i	−0.281401	−	0.243835i
$827$	13.7275	−	13.7275i	0.477353	−	0.477353i	−0.426931	−	0.904284i	$-0.640405\pi$
$827$	13.7275	−	13.7275i	0.477353	−	0.477353i	0.904284	+	0.426931i	$0.140405\pi$
$828$	28.2210	+	47.9644i	0.980748	+	1.66688i
$829$		−	55.5224i		−	1.92837i	−0.265224	−	0.964187i	$-0.585446\pi$
$829$		−	55.5224i		−	1.92837i	0.265224	−	0.964187i	$-0.414554\pi$
$830$	−5.27140	−	8.63345i	−0.182973	−	0.299672i
$831$	64.0276	−	41.1480i	2.22109	−	1.42741i
$832$	−0.459475	+	0.613786i	−0.0159294	+	0.0212792i
$833$	−3.64215	+	9.76499i	−0.126193	+	0.338337i
$834$	−38.4070	−	5.52210i	−1.32993	−	0.191215i
$835$	7.51058	+	7.86486i	0.259914	+	0.272175i
$836$	12.9828	+	8.34352i	0.449018	+	0.288567i
$837$	−32.3956	+	12.0829i	−1.11975	+	0.417647i
$838$	8.00488	+	14.6599i	0.276524	+	0.506416i
$839$	22.5820	+	26.0610i	0.779616	+	0.899725i	0.997082	−	0.0763433i	$-0.0243245\pi$
$839$	22.5820	+	26.0610i	0.779616	+	0.899725i	−0.217466	+	0.976068i	$0.569779\pi$
$840$	−13.3798	+	33.4951i	−0.461646	+	1.15569i
$841$	−5.21570	−	1.53147i	−0.179852	−	0.0528092i
$842$	1.65270	+	4.43106i	0.0569557	+	0.152704i
$843$	17.3278	+	79.6544i	0.596800	+	2.74344i
$844$	−11.8799	−	40.4592i	−0.408923	−	1.39266i
$845$	15.6987	+	7.61117i	0.540052	+	0.261832i
$846$	19.1399	+	41.9104i	0.658042	+	1.44091i
$847$	−6.19055	−	4.63419i	−0.212710	−	0.159233i
$848$	2.26798	+	0.493368i	0.0778827	+	0.0169423i
$849$	−38.1829	+	44.0654i	−1.31043	+	1.51232i
$850$	11.9695	+	8.49594i	0.410549	+	0.291408i
$851$	1.14355	−	2.73236i	0.0392005	−	0.0936641i
$852$	−19.6779	−	19.6779i	−0.674154	−	0.674154i
$853$	−2.64671	−	37.0058i	−0.0906215	−	1.26705i	−0.815735	−	0.578425i	$-0.803667\pi$
$853$	−2.64671	−	37.0058i	−0.0906215	−	1.26705i	0.725114	−	0.688629i	$-0.241787\pi$
$854$	−4.25228	−	6.61668i	−0.145510	−	0.226418i
$855$	−57.7717	−	9.66950i	−1.97575	−	0.330690i
$856$	−12.0857	+	5.51933i	−0.413079	+	0.188647i
$857$	−2.48722	+	1.86191i	−0.0849619	+	0.0636017i	−0.640914	−	0.767612i	$-0.721445\pi$
$857$	−2.48722	+	1.86191i	−0.0849619	+	0.0636017i	0.555952	+	0.831214i	$0.312354\pi$
$858$	−11.3198	−	6.18110i	−0.386453	−	0.211019i
$859$	26.7478	−	41.6204i	0.912623	−	1.42007i	0.00513682	−	0.999987i	$-0.498365\pi$
$859$	26.7478	−	41.6204i	0.912623	−	1.42007i	0.907486	−	0.420082i	$-0.137999\pi$
$860$	−1.58262	−	32.6986i	−0.0539668	−	1.11501i
$861$	−6.97948	+	23.7699i	−0.237860	+	0.810076i
$862$	−0.487893	−	0.0348948i	−0.0166177	−	0.00118852i
$863$	−7.49644	−	0.536156i	−0.255182	−	0.0182510i	−0.0568378	−	0.998383i	$-0.518102\pi$
$863$	−7.49644	−	0.536156i	−0.255182	−	0.0182510i	−0.198344	+	0.980132i	$0.563556\pi$
$864$	−22.3665	+	76.1732i	−0.760923	+	2.59147i
$865$	0.128282	+	2.65046i	0.00436174	+	0.0901183i
$866$	7.86840	−	12.2435i	0.267379	−	0.416050i
$867$	−10.3884	−	5.67249i	−0.352808	−	0.192648i
$868$	−6.83531	+	5.11685i	−0.232006	+	0.173677i
$869$	6.36183	−	2.90535i	0.215810	−	0.0985572i
$870$	−22.2092	−	3.71726i	−0.752964	−	0.126027i
$871$	−2.42764	−	3.77749i	−0.0822576	−	0.127995i
$872$	2.16501	+	30.2709i	0.0733167	+	1.02510i
$873$	12.1307	+	12.1307i	0.410561	+	0.410561i
$874$	5.68107	−	9.49532i	0.192165	−	0.321184i
$875$	−24.0208	−	3.39761i	−0.812051	−	0.114860i
$876$	26.6681	−	30.7767i	0.901033	−	1.03985i
$877$	12.6366	+	2.74893i	0.426708	+	0.0928247i	0.420791	−	0.907158i	$-0.361753\pi$
$877$	12.6366	+	2.74893i	0.426708	+	0.0928247i	0.00591767	+	0.999982i	$0.498116\pi$
$878$	8.81874	+	6.60162i	0.297618	+	0.222794i
$879$	−7.97083	−	17.4537i	−0.268849	−	0.588698i
$880$	9.18260	+	4.45198i	0.309545	+	0.150076i
$881$	−11.8438	−	40.3364i	−0.399029	−	1.35897i	−0.876957	−	0.480569i	$-0.840430\pi$
$881$	−11.8438	−	40.3364i	−0.399029	−	1.35897i	0.477928	−	0.878399i	$-0.341388\pi$
$882$	2.30449	+	10.5936i	0.0775964	+	0.356705i
$883$	−0.377287	−	1.01154i	−0.0126967	−	0.0340412i	0.930447	−	0.366427i	$-0.119419\pi$
$883$	−0.377287	−	1.01154i	−0.0126967	−	0.0340412i	−0.943143	+	0.332386i	$0.892146\pi$
$884$	15.7516	+	4.62508i	0.529783	+	0.155558i
$885$	20.3675	−	50.9883i	0.684647	−	1.71395i
$886$	−3.12671	−	3.60842i	−0.105044	−	0.121227i
$887$	4.05546	+	7.42702i	0.136169	+	0.249375i	0.936861	−	0.349701i	$-0.113717\pi$
$887$	4.05546	+	7.42702i	0.136169	+	0.249375i	−0.800692	+	0.599076i	$0.795535\pi$
$888$	4.30178	−	1.60448i	0.144358	−	0.0538429i
$889$	−16.0970	−	10.3449i	−0.539876	−	0.346957i
$890$	11.8480	+	12.4068i	0.397145	+	0.415878i
$891$	−61.3406	−	8.81945i	−2.05499	−	0.295463i
$892$	−16.4280	+	44.0453i	−0.550051	+	1.47474i
$893$	−20.8615	+	27.8677i	−0.698102	+	0.932556i
$894$	15.9528	−	10.2522i	0.533541	−	0.342886i
$895$	9.63625	+	15.7822i	0.322104	+	0.527540i
$896$			24.2932i			0.811579i
$897$	15.8443	−	31.3647i	0.529026	−	1.04724i
$898$	9.17373	−	9.17373i	0.306131	−	0.306131i
$899$	−9.11744	−	7.90031i	−0.304084	−	0.263490i
$900$	−57.9584	−	2.67232i	−1.93195	−	0.0890773i
$901$	0.897606	+	6.24299i	0.0299036	+	0.207984i
$902$	−5.85888	−	2.18525i	−0.195079	−	0.0727609i
$903$	38.6429	+	51.6208i	1.28595	+	1.71783i
$904$	−14.9818	+	4.39906i	−0.498288	+	0.146310i
$905$	27.3852	−	22.6462i	0.910314	−	0.752787i
$906$	16.6144	−	36.3804i	0.551976	−	1.20866i
$907$	−33.5371	+	18.3127i	−1.11358	+	0.608062i	−0.927257	−	0.374426i	$-0.877840\pi$
$907$	−33.5371	+	18.3127i	−1.11358	+	0.608062i	−0.186326	+	0.982488i	$0.559658\pi$
$908$	−0.613416	+	8.57668i	−0.0203569	+	0.284627i
$909$	−3.23725	+	2.80510i	−0.107373	+	0.0930392i
$910$	7.01031	−	1.35667i	0.232390	−	0.0449732i
$911$	−47.5979	−	21.7372i	−1.57699	−	0.720186i	−0.581364	−	0.813644i	$-0.697481\pi$
$911$	−47.5979	−	21.7372i	−1.57699	−	0.720186i	−0.995623	+	0.0934575i	$0.970208\pi$
$912$	−18.7857	+	4.08658i	−0.622057	+	0.135320i
$913$	9.15892	−	16.7733i	0.303116	−	0.555116i
$914$	−0.926149	+	6.44151i	−0.0306343	+	0.213066i
$915$	24.9214	−	31.7399i	0.823877	−	1.04929i
$916$	44.8059	−	6.44212i	1.48043	−	0.212854i
$917$	1.51879	−	6.98176i	0.0501548	−	0.230558i
$918$	−40.7374	+	2.91360i	−1.34454	+	0.0961631i
$919$	37.1881			1.22672			0.613361	−	0.789803i	$-0.289817\pi$
$919$	37.1881			1.22672			0.613361	+	0.789803i	$0.289817\pi$
$920$	10.1009	−	22.6548i	0.333018	−	0.746906i
$921$	−49.7869			−1.64053
$922$	−22.0354	+	1.57601i	−0.725698	+	0.0519030i
$923$	−2.65030	+	12.1832i	−0.0872356	+	0.401016i
$924$	−29.8033	+	4.28506i	−0.980456	+	0.140968i
$925$	1.73481	+	2.55477i	0.0570401	+	0.0840004i
$926$	0.449579	−	3.12689i	0.0147741	−	0.102756i
$927$	36.0032	−	65.9349i	1.18250	−	2.16559i
$928$	−27.0674	+	5.88815i	−0.888531	+	0.193288i
$929$	−54.3329	−	24.8130i	−1.78261	−	0.814089i	−0.974276	−	0.225358i	$-0.927645\pi$
$929$	−54.3329	−	24.8130i	−1.78261	−	0.814089i	−0.808329	−	0.588730i	$-0.799628\pi$
$930$	9.55235	+	6.45460i	0.313234	+	0.211655i
$931$	−6.19044	+	5.36405i	−0.202884	+	0.175800i
$932$	−2.25489	+	31.5275i	−0.0738614	+	1.03272i
$933$	47.2914	−	25.8231i	1.54825	−	0.845410i
$934$	7.54047	−	16.5113i	0.246732	−	0.540267i
$935$	−2.61495	+	27.6075i	−0.0855181	+	0.902861i
$936$	37.0824	−	10.8884i	1.21207	−	0.355897i
$937$	31.4130	+	41.9629i	1.02622	+	1.37087i	0.926688	+	0.375832i	$0.122643\pi$
$937$	31.4130	+	41.9629i	1.02622	+	1.37087i	0.0995305	+	0.995035i	$0.468266\pi$
$938$	2.58474	+	0.964059i	0.0843949	+	0.0314777i
$939$	−3.26548	−	22.7119i	−0.106565	−	0.741176i
$940$	−17.2177	+	29.8745i	−0.561580	+	0.974400i
$941$	32.3888	+	28.0651i	1.05585	+	0.914895i	0.996521	−	0.0833436i	$-0.0265599\pi$
$941$	32.3888	+	28.0651i	1.05585	+	0.914895i	0.0593244	+	0.998239i	$0.481105\pi$
$942$	−28.3988	+	28.3988i	−0.925283	+	0.925283i
$943$	5.43955	−	16.1452i	0.177136	−	0.525759i
$944$		−	12.7866i		−	0.416169i
$945$	57.6121	−	35.1767i	1.87412	−	1.14430i
$946$	−13.6924	+	8.79960i	−0.445180	+	0.286100i
$947$	−5.32112	+	7.10818i	−0.172913	+	0.230985i	−0.878623	−	0.477516i	$-0.841537\pi$
$947$	−5.32112	+	7.10818i	−0.172913	+	0.230985i	0.705710	+	0.708501i	$0.250628\pi$
$948$	−4.56079	+	12.2280i	−0.148128	+	0.397146i
$949$	−18.0596	−	2.59658i	−0.586241	−	0.0842887i
$950$	5.05647	+	10.3689i	0.164053	+	0.336412i
$951$	36.0938	+	23.1961i	1.17042	+	0.752184i
$952$	−21.3865	+	7.97674i	−0.693139	+	0.258528i
$953$	−19.0918	−	34.9641i	−0.618445	−	1.13260i	−0.979764	−	0.200156i	$-0.935855\pi$
$953$	−19.0918	−	34.9641i	−0.618445	−	1.13260i	0.361319	−	0.932442i	$-0.382327\pi$
$954$	4.29648	+	4.95840i	0.139104	+	0.160534i
$955$	3.17030	−	1.36046i	0.102589	−	0.0440236i
$956$	−23.7583	−	6.97608i	−0.768399	−	0.225622i
$957$	−14.8672	−	39.8606i	−0.480589	−	1.28851i
$958$	−1.51255	−	6.95306i	−0.0488681	−	0.224643i
$959$	6.36037	+	21.6614i	0.205387	+	0.699484i
$960$	2.28327	−	0.792196i	0.0736921	−	0.0255680i
$961$	−10.3121	−	22.5803i	−0.332648	−	0.728397i
$962$	−0.727627	−	0.544695i	−0.0234596	−	0.0175617i
$963$	41.1356	+	8.94849i	1.32557	+	0.288361i
$964$	−5.49663	+	6.34344i	−0.177034	+	0.204309i
$965$	11.4225	−	5.89972i	0.367702	−	0.189919i
$966$	3.75506	+	21.2593i	0.120817	+	0.684008i
$967$	2.76710	+	2.76710i	0.0889839	+	0.0889839i	0.750198	−	0.661214i	$-0.229958\pi$
$967$	2.76710	+	2.76710i	0.0889839	+	0.0889839i	−0.661214	+	0.750198i	$0.729958\pi$
$968$	0.588062	+	8.22219i	0.0189010	+	0.264271i
$969$	−28.2445	−	43.9493i	−0.907344	−	1.41185i
$970$	0.557743	−	3.33231i	0.0179081	−	0.106994i
$971$	13.7802	−	6.29319i	0.442227	−	0.201958i	−0.181842	−	0.983328i	$-0.558206\pi$
$971$	13.7802	−	6.29319i	0.442227	−	0.201958i	0.624068	+	0.781370i	$0.285479\pi$
$972$	39.6731	−	29.6989i	1.27252	−	0.952593i
$973$	35.6206	+	19.4503i	1.14194	+	0.623548i
$974$	−4.76765	+	7.41861i	−0.152765	+	0.237708i
$975$	18.3661	+	31.6993i	0.588186	+	1.01519i
$976$	2.64770	−	9.01723i	0.0847507	−	0.288634i
$977$	−21.0202	−	1.50340i	−0.672497	−	0.0480979i	−0.269085	−	0.963116i	$-0.586721\pi$
$977$	−21.0202	−	1.50340i	−0.672497	−	0.0480979i	−0.403412	+	0.915018i	$0.632176\pi$
$978$	1.72861	+	0.123632i	0.0552748	+	0.00395333i
$979$	−9.13123	+	31.0981i	−0.291835	+	0.993900i
$980$	−5.45303	+	6.00773i	−0.174191	+	0.191910i
$981$	51.9870	−	80.8933i	1.65982	−	2.58272i
$982$	−16.2927	−	8.89646i	−0.519920	−	0.283898i
$983$	−45.4300	+	34.0085i	−1.44899	+	1.08470i	−0.469566	+	0.882897i	$0.655590\pi$
$983$	−45.4300	+	34.0085i	−1.44899	+	1.08470i	−0.979426	+	0.201804i	$0.935319\pi$
$984$	24.0216	−	10.9703i	0.765779	−	0.349720i
$985$	18.5297	−	13.2162i	0.590404	−	0.421104i
$986$	−7.70436	−	11.9882i	−0.245357	−	0.381783i
$987$	−4.84520	−	67.7447i	−0.154224	−	2.15634i
$988$	9.12337	+	9.12337i	0.290253	+	0.290253i
$989$	−25.1571	−	36.5186i	−0.799949	−	1.16122i
$990$	13.2378	+	25.6298i	0.420725	+	0.814567i
$991$	−16.3180	+	18.8320i	−0.518358	+	0.598217i	−0.953219	−	0.302281i	$-0.902252\pi$
$991$	−16.3180	+	18.8320i	−0.518358	+	0.598217i	0.434861	+	0.900498i	$0.356798\pi$
$992$	13.8577	+	3.01455i	0.439982	+	0.0957122i
$993$	−4.71069	−	3.52638i	−0.149489	−	0.111906i
$994$	−3.18207	−	6.96776i	−0.100929	−	0.221004i
$995$	12.0879	−	24.9323i	0.383212	−	0.790407i
$996$	10.0471	+	34.2174i	0.318355	+	1.08422i
$997$	7.51485	+	34.5452i	0.237998	+	1.09406i	0.928675	+	0.370894i	$0.120949\pi$
$997$	7.51485	+	34.5452i	0.237998	+	1.09406i	−0.690677	+	0.723163i	$0.742688\pi$
$998$	4.85213	+	13.0091i	0.153591	+	0.411794i
$999$	−8.24449	−	2.42080i	−0.260844	−	0.0765908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.7.5	✓	200
5.2	odd	4		575.2.r.b.168.5		200
5.3	odd	4	inner	115.2.l.a.53.6	yes	200
5.4	even	2		575.2.r.b.7.6		200
23.10	odd	22	inner	115.2.l.a.102.6	yes	200
115.33	even	44	inner	115.2.l.a.33.5	yes	200
115.79	odd	22		575.2.r.b.332.5		200
115.102	even	44		575.2.r.b.493.6		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.5	✓	200	1.1	even	1	trivial
115.2.l.a.33.5	yes	200	115.33	even	44	inner
115.2.l.a.53.6	yes	200	5.3	odd	4	inner
115.2.l.a.102.6	yes	200	23.10	odd	22	inner
575.2.r.b.7.6		200	5.4	even	2
575.2.r.b.168.5		200	5.2	odd	4
575.2.r.b.332.5		200	115.79	odd	22
575.2.r.b.493.6		200	115.102	even	44

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.643856 + 0.0460495i) q^{2} +(-0.683154 + 3.14041i) q^{3} +(-1.56721 + 0.225331i) q^{4} +(-0.267157 - 2.22005i) q^{5} +(0.295239 - 2.05343i) q^{6} +(-1.03991 + 1.90445i) q^{7} +(2.26018 - 0.491672i) q^{8} +(-6.66656 - 3.04452i) q^{9} +O(q^{10})\)	\(q+(-0.643856 + 0.0460495i) q^{2} +(-0.683154 + 3.14041i) q^{3} +(-1.56721 + 0.225331i) q^{4} +(-0.267157 - 2.22005i) q^{5} +(0.295239 - 2.05343i) q^{6} +(-1.03991 + 1.90445i) q^{7} +(2.26018 - 0.491672i) q^{8} +(-6.66656 - 3.04452i) q^{9} +(0.274243 + 1.41709i) q^{10} +(-2.06089 + 1.78577i) q^{11} +(0.363016 - 5.07562i) q^{12} +(-2.00097 + 1.09261i) q^{13} +(0.581852 - 1.27408i) q^{14} +(7.15437 + 0.677656i) q^{15} +(1.60580 - 0.471504i) q^{16} +(2.72542 + 3.64074i) q^{17} +(4.43251 + 1.65324i) q^{18} +(0.508679 + 3.53794i) q^{19} +(0.918938 + 3.41909i) q^{20} +(-5.27033 - 4.56677i) q^{21} +(1.24468 - 1.24468i) q^{22} +(3.49802 + 3.28083i) q^{23} +7.43378i q^{24} +(-4.85725 + 1.18620i) q^{25} +(1.23803 - 0.795630i) q^{26} +(8.33734 - 11.1374i) q^{27} +(1.20063 - 3.21900i) q^{28} +(4.80488 + 0.690837i) q^{29} +(-4.63759 - 0.106857i) q^{30} +(-2.09072 - 1.34363i) q^{31} +(-5.34660 + 1.99418i) q^{32} +(-4.20014 - 7.69197i) q^{33} +(-1.92243 - 2.21861i) q^{34} +(4.50580 + 1.79986i) q^{35} +(11.1339 + 3.26922i) q^{36} +(-0.215837 - 0.578681i) q^{37} +(-0.490436 - 2.25450i) q^{38} +(-2.06428 - 7.03030i) q^{39} +(-1.69536 - 4.88636i) q^{40} +(-1.47573 - 3.23141i) q^{41} +(3.60363 + 2.69765i) q^{42} +(-9.03527 - 1.96550i) q^{43} +(2.82746 - 3.26306i) q^{44} +(-4.97797 + 15.6135i) q^{45} +(-2.40330 - 1.95130i) q^{46} +(6.88665 + 6.88665i) q^{47} +(0.383710 + 5.36496i) q^{48} +(1.23897 + 1.92787i) q^{49} +(3.07275 - 0.987418i) q^{50} +(-13.2953 + 6.07175i) q^{51} +(2.88975 - 2.16324i) q^{52} +(1.21721 + 0.664648i) q^{53} +(-4.85518 + 7.55480i) q^{54} +(4.51507 + 4.09819i) q^{55} +(-1.41402 + 4.81570i) q^{56} +(-11.4581 - 0.819498i) q^{57} +(-3.12546 - 0.223537i) q^{58} +(2.15250 - 7.33075i) q^{59} +(-11.3651 + 0.550073i) q^{60} +(3.03593 - 4.72400i) q^{61} +(1.40800 + 0.768825i) q^{62} +(12.7307 - 9.53012i) q^{63} +(0.305910 - 0.139704i) q^{64} +(2.96023 + 4.15037i) q^{65} +(3.05849 + 4.75911i) q^{66} +(0.140507 + 1.96455i) q^{67} +(-5.09168 - 5.09168i) q^{68} +(-12.6928 + 8.74390i) q^{69} +(-2.98397 - 0.951363i) q^{70} +(3.58134 - 4.13309i) q^{71} +(-16.5645 - 3.60340i) q^{72} +(6.40664 + 4.79595i) q^{73} +(0.165616 + 0.362648i) q^{74} +(-0.406909 - 16.0641i) q^{75} +(-1.59442 - 5.43008i) q^{76} +(-1.25777 - 5.78189i) q^{77} +(1.65284 + 4.43144i) q^{78} +(-2.46083 - 0.722566i) q^{79} +(-1.47576 - 3.43898i) q^{80} +(14.8821 + 17.1749i) q^{81} +(1.09896 + 2.01260i) q^{82} +(-6.56634 + 2.44912i) q^{83} +(9.28877 + 5.96953i) q^{84} +(7.35450 - 7.02322i) q^{85} +(5.90793 + 0.849431i) q^{86} +(-5.45198 + 14.6173i) q^{87} +(-3.77996 + 5.04944i) q^{88} +(9.99869 - 6.42577i) q^{89} +(2.48610 - 10.2821i) q^{90} -4.94697i q^{91} +(-6.22142 - 4.35355i) q^{92} +(5.64782 - 5.64782i) q^{93} +(-4.75114 - 4.11689i) q^{94} +(7.71851 - 2.07448i) q^{95} +(-2.60998 - 18.1528i) q^{96} +(-2.19321 - 0.818024i) q^{97} +(-0.886493 - 1.18422i) q^{98} +(19.1758 - 5.63053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more