LMFDB - Embedded newform 950.2.r.b.11.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(11,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("950.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.r (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$25$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			11.21
Character	$\chi$	$=$	950.11
Dual form			950.2.r.b.691.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 - 0.994522i) q^{2} +(1.50267 + 1.66889i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.11017 + 0.739709i) q^{5} +(1.50267 - 1.66889i) q^{6} +0.927052 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.213575 + 2.03203i) q^{9} +O(q^{10})$	\(q+(-0.104528 - 0.994522i) q^{2} +(1.50267 + 1.66889i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.11017 + 0.739709i) q^{5} +(1.50267 - 1.66889i) q^{6} +0.927052 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.213575 + 2.03203i) q^{9} +(0.515083 - 2.17593i) q^{10} +(-2.60890 + 1.89548i) q^{11} +(-1.81682 - 1.32000i) q^{12} +(-0.121058 + 1.15179i) q^{13} +(-0.0969033 - 0.921973i) q^{14} +(1.93641 + 4.63319i) q^{15} +(0.913545 - 0.406737i) q^{16} +(5.51504 + 1.17226i) q^{17} +2.04322 q^{18} +(-1.43996 - 4.11418i) q^{19} +(-2.21785 - 0.284814i) q^{20} +(1.39306 + 1.54715i) q^{21} +(2.15780 + 2.39648i) q^{22} +(4.54481 + 2.02348i) q^{23} +(-1.12286 + 1.94484i) q^{24} +(3.90566 + 3.12183i) q^{25} +1.15814 q^{26} +(1.73829 - 1.26294i) q^{27} +(-0.906793 + 0.192745i) q^{28} +(-3.42158 + 0.727278i) q^{29} +(4.40540 - 2.41010i) q^{30} +(1.18060 + 3.63352i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-7.08366 - 1.50568i) q^{33} +(0.589358 - 5.60736i) q^{34} +(1.95624 + 0.685748i) q^{35} +(-0.213575 - 2.03203i) q^{36} +(-7.35584 - 5.34433i) q^{37} +(-3.94113 + 1.86212i) q^{38} +(-2.10413 + 1.52874i) q^{39} +(-0.0514252 + 2.23548i) q^{40} +(0.0589964 - 0.0262669i) q^{41} +(1.39306 - 1.54715i) q^{42} +(-6.06032 + 10.4968i) q^{43} +(2.15780 - 2.39648i) q^{44} +(-1.95379 + 4.12995i) q^{45} +(1.53733 - 4.73142i) q^{46} +(-4.54862 + 0.966840i) q^{47} +(2.05156 + 0.913413i) q^{48} -6.14058 q^{49} +(2.69647 - 4.21059i) q^{50} +(6.33094 + 10.9655i) q^{51} +(-0.121058 - 1.15179i) q^{52} +(9.68768 - 2.05918i) q^{53} +(-1.43772 - 1.59675i) q^{54} +(-6.90733 + 2.06996i) q^{55} +(0.286475 + 0.881678i) q^{56} +(4.70232 - 8.58542i) q^{57} +(1.08095 + 3.32681i) q^{58} +(1.51312 - 0.673684i) q^{59} +(-2.85739 - 4.12934i) q^{60} +(8.04349 + 3.58119i) q^{61} +(3.49021 - 1.55394i) q^{62} +(-0.197995 + 1.88380i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.10745 + 2.34094i) q^{65} +(-0.756987 + 7.20225i) q^{66} +(7.16726 - 7.96005i) q^{67} -5.63825 q^{68} +(3.45241 + 10.6254i) q^{69} +(0.477509 - 2.01720i) q^{70} +(-7.17110 - 7.96432i) q^{71} +(-1.99857 + 0.424810i) q^{72} +(-1.01843 - 9.68969i) q^{73} +(-4.54616 + 7.87418i) q^{74} +(0.658958 + 11.2092i) q^{75} +(2.26388 + 3.72489i) q^{76} +(-2.41858 + 1.75720i) q^{77} +(1.74030 + 1.93280i) q^{78} +(-1.72635 - 1.91731i) q^{79} +(2.22861 - 0.182527i) q^{80} +(10.7155 + 2.27765i) q^{81} +(-0.0322898 - 0.0559276i) q^{82} +(2.00104 + 6.15855i) q^{83} +(-1.68429 - 1.22370i) q^{84} +(10.7706 + 6.55319i) q^{85} +(11.0728 + 4.92991i) q^{86} +(-6.35526 - 4.61737i) q^{87} +(-2.60890 - 1.89548i) q^{88} +(-2.98820 - 1.33043i) q^{89} +(4.31155 + 1.51139i) q^{90} +(-0.112227 + 1.06777i) q^{91} +(-4.86620 - 1.03434i) q^{92} +(-4.28988 + 7.43029i) q^{93} +(1.43700 + 4.42264i) q^{94} +(0.00472319 - 9.74679i) q^{95} +(0.693963 - 2.13580i) q^{96} +(7.24732 + 8.04896i) q^{97} +(0.641865 + 6.10694i) q^{98} +(-3.29447 - 5.70619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9}+O(q^{10}) $ 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9} - 4 q^{10} + 14 q^{11} + 8 q^{13} + q^{14} - 4 q^{15} + 25 q^{16} - 5 q^{17} + 184 q^{18} + 24 q^{19} - 2 q^{20} + 32 q^{21} + 8 q^{22} + 11 q^{23} - 23 q^{25} + 64 q^{26} - 36 q^{27} + 6 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 100 q^{32} + 12 q^{33} + 2 q^{35} + 13 q^{36} + 8 q^{37} + 2 q^{38} - 52 q^{39} + q^{40} + 14 q^{41} + 32 q^{42} - 10 q^{43} + 8 q^{44} - 52 q^{45} + 8 q^{46} - 22 q^{47} + 204 q^{49} - 34 q^{50} - 10 q^{51} + 8 q^{52} - 18 q^{53} - 12 q^{54} + 10 q^{55} - 12 q^{56} + 34 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 16 q^{61} - 4 q^{62} - 21 q^{63} - 50 q^{64} + 96 q^{65} - 18 q^{66} - 54 q^{67} - 20 q^{68} - 20 q^{69} - 3 q^{70} - 5 q^{71} + 33 q^{72} - 16 q^{73} - 4 q^{74} + 56 q^{75} + 14 q^{76} - 116 q^{77} - 34 q^{78} + q^{80} + 57 q^{81} - 36 q^{82} - 72 q^{83} + 76 q^{84} - 5 q^{85} - 112 q^{87} + 14 q^{88} - 4 q^{89} - 49 q^{90} - 64 q^{91} - 4 q^{92} - 124 q^{93} + 44 q^{94} + 41 q^{95} + 13 q^{97} + 43 q^{98} - 28 q^{99}+O(q^{100}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9 - 4 * q^10 + 14 * q^11 + 8 * q^13 + q^14 - 4 * q^15 + 25 * q^16 - 5 * q^17 + 184 * q^18 + 24 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 11 * q^23 - 23 * q^25 + 64 * q^26 - 36 * q^27 + 6 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 100 * q^32 + 12 * q^33 + 2 * q^35 + 13 * q^36 + 8 * q^37 + 2 * q^38 - 52 * q^39 + q^40 + 14 * q^41 + 32 * q^42 - 10 * q^43 + 8 * q^44 - 52 * q^45 + 8 * q^46 - 22 * q^47 + 204 * q^49 - 34 * q^50 - 10 * q^51 + 8 * q^52 - 18 * q^53 - 12 * q^54 + 10 * q^55 - 12 * q^56 + 34 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 16 * q^61 - 4 * q^62 - 21 * q^63 - 50 * q^64 + 96 * q^65 - 18 * q^66 - 54 * q^67 - 20 * q^68 - 20 * q^69 - 3 * q^70 - 5 * q^71 + 33 * q^72 - 16 * q^73 - 4 * q^74 + 56 * q^75 + 14 * q^76 - 116 * q^77 - 34 * q^78 + q^80 + 57 * q^81 - 36 * q^82 - 72 * q^83 + 76 * q^84 - 5 * q^85 - 112 * q^87 + 14 * q^88 - 4 * q^89 - 49 * q^90 - 64 * q^91 - 4 * q^92 - 124 * q^93 + 44 * q^94 + 41 * q^95 + 13 * q^97 + 43 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	1.50267	+	1.66889i	0.867570	+	0.963534i	0.999616	−	0.0277098i	$-0.00882144\pi$
$3$	1.50267	+	1.66889i	0.867570	+	0.963534i	−0.132046	+	0.991244i	$0.542155\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	2.11017	+	0.739709i	0.943698	+	0.330808i
$5$	2.11017	+	0.739709i	0.943698	+	0.330808i
$6$	1.50267	−	1.66889i	0.613464	−	0.681321i
$7$	0.927052			0.350393			0.175196	−	0.984534i	$-0.443944\pi$
$7$	0.927052			0.350393			0.175196	+	0.984534i	$0.443944\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.213575	+	2.03203i	−0.0711917	+	0.677343i
$10$	0.515083	−	2.17593i	0.162884	−	0.688091i
$11$	−2.60890	+	1.89548i	−0.786612	+	0.571507i	−0.906956	−	0.421225i	$-0.861600\pi$
$11$	−2.60890	+	1.89548i	−0.786612	+	0.571507i	0.120344	+	0.992732i	$0.461600\pi$
$12$	−1.81682	−	1.32000i	−0.524471	−	0.381050i
$13$	−0.121058	+	1.15179i	−0.0335755	+	0.319450i	0.964824	+	0.262897i	$0.0846778\pi$
$13$	−0.121058	+	1.15179i	−0.0335755	+	0.319450i	−0.998400	+	0.0565534i	$0.981989\pi$
$14$	−0.0969033	−	0.921973i	−0.0258985	−	0.246408i
$15$	1.93641	+	4.63319i	0.499980	+	1.19628i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	5.51504	+	1.17226i	1.33759	+	0.284314i	0.820516	−	0.571624i	$-0.193686\pi$
$17$	5.51504	+	1.17226i	1.33759	+	0.284314i	0.517078	+	0.855938i	$0.327020\pi$
$18$	2.04322			0.481592
$19$	−1.43996	−	4.11418i	−0.330350	−	0.943858i
$19$	−1.43996	−	4.11418i	−0.330350	−	0.943858i
$20$	−2.21785	−	0.284814i	−0.495927	−	0.0636864i
$21$	1.39306	+	1.54715i	0.303990	+	0.337615i
$22$	2.15780	+	2.39648i	0.460044	+	0.510930i
$23$	4.54481	+	2.02348i	0.947658	+	0.421925i	0.821579	−	0.570095i	$-0.193094\pi$
$23$	4.54481	+	2.02348i	0.947658	+	0.421925i	0.126080	+	0.992020i	$0.459760\pi$
$24$	−1.12286	+	1.94484i	−0.229202	+	0.396990i
$25$	3.90566	+	3.12183i	0.781133	+	0.624365i
$26$	1.15814			0.227129
$27$	1.73829	−	1.26294i	0.334534	−	0.243053i
$28$	−0.906793	+	0.192745i	−0.171368	+	0.0364254i
$29$	−3.42158	+	0.727278i	−0.635371	+	0.135052i	−0.514326	−	0.857595i	$-0.671958\pi$
$29$	−3.42158	+	0.727278i	−0.635371	+	0.135052i	−0.121045	+	0.992647i	$0.538624\pi$
$30$	4.40540	−	2.41010i	0.804312	−	0.440023i
$31$	1.18060	+	3.63352i	0.212042	+	0.652599i	0.999350	+	0.0360395i	$0.0114742\pi$
$31$	1.18060	+	3.63352i	0.212042	+	0.652599i	−0.787308	+	0.616560i	$0.788526\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−7.08366	−	1.50568i	−1.23311	−	0.262105i
$34$	0.589358	−	5.60736i	0.101074	−	0.961655i
$35$	1.95624	+	0.685748i	0.330665	+	0.115913i
$36$	−0.213575	−	2.03203i	−0.0355958	−	0.338672i
$37$	−7.35584	−	5.34433i	−1.20929	−	0.878602i	−0.214126	−	0.976806i	$-0.568690\pi$
$37$	−7.35584	−	5.34433i	−1.20929	−	0.878602i	−0.995166	+	0.0982040i	$0.968690\pi$
$38$	−3.94113	+	1.86212i	−0.639335	+	0.302077i
$39$	−2.10413	+	1.52874i	−0.336930	+	0.244794i
$40$	−0.0514252	+	2.23548i	−0.00813104	+	0.353460i
$41$	0.0589964	−	0.0262669i	0.00921370	−	0.00410220i	−0.402125	−	0.915585i	$-0.631728\pi$
$41$	0.0589964	−	0.0262669i	0.00921370	−	0.00410220i	0.411338	+	0.911483i	$0.365061\pi$
$42$	1.39306	−	1.54715i	0.214953	−	0.238730i
$43$	−6.06032	+	10.4968i	−0.924190	+	1.60074i	−0.131332	+	0.991338i	$0.541925\pi$
$43$	−6.06032	+	10.4968i	−0.924190	+	1.60074i	−0.792858	+	0.609406i	$0.791408\pi$
$44$	2.15780	−	2.39648i	0.325300	−	0.361282i
$45$	−1.95379	+	4.12995i	−0.291254	+	0.615657i
$46$	1.53733	−	4.73142i	0.226667	−	0.697610i
$47$	−4.54862	+	0.966840i	−0.663485	+	0.141028i	−0.527331	−	0.849660i	$-0.676807\pi$
$47$	−4.54862	+	0.966840i	−0.663485	+	0.141028i	−0.136154	+	0.990688i	$0.543474\pi$
$48$	2.05156	+	0.913413i	0.296117	+	0.131840i
$49$	−6.14058			−0.877225
$50$	2.69647	−	4.21059i	0.381339	−	0.595467i
$51$	6.33094	+	10.9655i	0.886509	+	1.53548i
$52$	−0.121058	−	1.15179i	−0.0167878	−	0.159725i
$53$	9.68768	−	2.05918i	1.33070	−	0.282850i	0.512951	−	0.858418i	$-0.328552\pi$
$53$	9.68768	−	2.05918i	1.33070	−	0.282850i	0.817754	+	0.575568i	$0.195219\pi$
$54$	−1.43772	−	1.59675i	−0.195650	−	0.217291i
$55$	−6.90733	+	2.06996i	−0.931384	+	0.279113i
$56$	0.286475	+	0.881678i	0.0382818	+	0.117819i
$57$	4.70232	−	8.58542i	0.622837	−	1.13717i
$58$	1.08095	+	3.32681i	0.141935	+	0.436832i
$59$	1.51312	−	0.673684i	0.196991	−	0.0877062i	−0.305870	−	0.952073i	$-0.598947\pi$
$59$	1.51312	−	0.673684i	0.196991	−	0.0877062i	0.502861	+	0.864367i	$0.332281\pi$
$60$	−2.85739	−	4.12934i	−0.368888	−	0.533095i
$61$	8.04349	+	3.58119i	1.02986	+	0.458525i	0.850898	−	0.525331i	$-0.176058\pi$
$61$	8.04349	+	3.58119i	1.02986	+	0.458525i	0.178965	+	0.983855i	$0.442725\pi$
$62$	3.49021	−	1.55394i	0.443257	−	0.197351i
$63$	−0.197995	+	1.88380i	−0.0249450	+	0.237336i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.10745	+	2.34094i	−0.137362	+	0.290357i
$66$	−0.756987	+	7.20225i	−0.0931786	+	0.886535i
$67$	7.16726	−	7.96005i	0.875620	−	0.972475i	−0.124184	−	0.992259i	$-0.539631\pi$
$67$	7.16726	−	7.96005i	0.875620	−	0.972475i	0.999804	+	0.0197842i	$0.00629793\pi$
$68$	−5.63825			−0.683738
$69$	3.45241	+	10.6254i	0.415621	+	1.27915i
$70$	0.477509	−	2.01720i	0.0570732	−	0.241102i
$71$	−7.17110	−	7.96432i	−0.851053	−	0.945190i	0.147987	−	0.988989i	$-0.452721\pi$
$71$	−7.17110	−	7.96432i	−0.851053	−	0.945190i	−0.999040	+	0.0437989i	$0.986054\pi$
$72$	−1.99857	+	0.424810i	−0.235534	+	0.0500643i
$73$	−1.01843	−	9.68969i	−0.119198	−	1.13409i	−0.876625	−	0.481174i	$-0.840211\pi$
$73$	−1.01843	−	9.68969i	−0.119198	−	1.13409i	0.757427	−	0.652919i	$-0.226456\pi$
$74$	−4.54616	+	7.87418i	−0.528480	+	0.915354i
$75$	0.658958	+	11.2092i	0.0760899	+	1.29433i
$76$	2.26388	+	3.72489i	0.259685	+	0.427275i
$77$	−2.41858	+	1.75720i	−0.275623	+	0.200252i
$78$	1.74030	+	1.93280i	0.197051	+	0.218847i
$79$	−1.72635	−	1.91731i	−0.194230	−	0.215714i	0.638161	−	0.769903i	$-0.279695\pi$
$79$	−1.72635	−	1.91731i	−0.194230	−	0.215714i	−0.832391	+	0.554189i	$0.813029\pi$
$80$	2.22861	−	0.182527i	0.249166	−	0.0204072i
$81$	10.7155	+	2.27765i	1.19061	+	0.253073i
$82$	−0.0322898	−	0.0559276i	−0.00356581	−	0.00617617i
$83$	2.00104	+	6.15855i	0.219642	+	0.675989i	0.998791	+	0.0491505i	$0.0156514\pi$
$83$	2.00104	+	6.15855i	0.219642	+	0.675989i	−0.779149	+	0.626838i	$0.784349\pi$
$84$	−1.68429	−	1.22370i	−0.183771	−	0.133517i
$85$	10.7706	+	6.55319i	1.16823	+	0.710793i
$86$	11.0728	+	4.92991i	1.19401	+	0.531606i
$87$	−6.35526	−	4.61737i	−0.681356	−	0.495034i
$88$	−2.60890	−	1.89548i	−0.278110	−	0.202058i
$89$	−2.98820	−	1.33043i	−0.316748	−	0.141025i	0.242204	−	0.970225i	$-0.422130\pi$
$89$	−2.98820	−	1.33043i	−0.316748	−	0.141025i	−0.558952	+	0.829200i	$0.688796\pi$
$90$	4.31155	+	1.51139i	0.454478	+	0.159314i
$91$	−0.112227	+	1.06777i	−0.0117646	+	0.111933i
$92$	−4.86620	−	1.03434i	−0.507336	−	0.107838i
$93$	−4.28988	+	7.43029i	−0.444840	+	0.770486i
$94$	1.43700	+	4.42264i	0.148216	+	0.456161i
$95$	0.00472319	−	9.74679i	0.000484589	−	1.00000i
$96$	0.693963	−	2.13580i	0.0708273	−	0.217984i
$97$	7.24732	+	8.04896i	0.735854	+	0.817248i	0.988645	−	0.150273i	$-0.0480152\pi$
$97$	7.24732	+	8.04896i	0.735854	+	0.817248i	−0.252791	+	0.967521i	$0.581349\pi$
$98$	0.641865	+	6.10694i	0.0648381	+	0.616894i
$99$	−3.29447	−	5.70619i	−0.331107	−	0.573493i
$100$	−4.46938	−	2.24157i	−0.446938	−	0.224157i
$101$	−7.15627	−	12.3950i	−0.712076	−	1.23335i	−0.964077	−	0.265625i	$-0.914422\pi$
$101$	−7.15627	−	12.3950i	−0.712076	−	1.23335i	0.252001	−	0.967727i	$-0.418912\pi$
$102$	10.2437	−	7.44247i	1.01428	−	0.736914i
$103$	−0.102550	+	0.315616i	−0.0101045	+	0.0310985i	−0.955982	−	0.293426i	$-0.905204\pi$
$103$	−0.102550	+	0.315616i	−0.0101045	+	0.0310985i	0.945877	+	0.324525i	$0.105204\pi$
$104$	−1.13283	+	0.240790i	−0.111083	+	0.0236114i
$105$	1.79515	+	4.29520i	0.175189	+	0.419169i
$106$	−3.06054	−	9.41936i	−0.297266	−	0.914889i
$107$	0.593088			0.0573359			0.0286680	−	0.999589i	$-0.490873\pi$
$107$	0.593088			0.0573359			0.0286680	+	0.999589i	$0.490873\pi$
$108$	−1.43772	+	1.59675i	−0.138345	+	0.153648i
$109$	16.4800	−	7.33737i	1.57850	−	0.702792i	0.584418	−	0.811452i	$-0.301323\pi$
$109$	16.4800	−	7.33737i	1.57850	−	0.702792i	0.994079	+	0.108660i	$0.0346560\pi$
$110$	2.78063	+	6.65312i	0.265123	+	0.634350i
$111$	−2.13434	−	20.3069i	−0.202582	−	1.92744i
$112$	0.846904	−	0.377066i	0.0800249	−	0.0356294i
$113$	−6.52436	−	4.74023i	−0.613760	−	0.445923i	0.236976	−	0.971515i	$-0.423844\pi$
$113$	−6.52436	−	4.74023i	−0.613760	−	0.445923i	−0.850736	+	0.525592i	$0.823844\pi$
$114$	−9.02991	−	3.77914i	−0.845729	−	0.353949i
$115$	8.09355	+	7.63173i	0.754728	+	0.711662i
$116$	3.19560	−	1.42277i	0.296704	−	0.132101i
$117$	−2.31462	−	0.491988i	−0.213987	−	0.0454843i
$118$	−0.828158	−	1.43441i	−0.0762381	−	0.132048i
$119$	5.11273	+	1.08674i	0.468683	+	0.0996216i
$120$	−3.80804	+	3.27337i	−0.347625	+	0.298817i
$121$	−0.185664	+	0.571415i	−0.0168785	+	0.0519468i
$122$	2.72080	−	8.37376i	0.246330	−	0.758125i
$123$	0.132489	+	0.0589879i	0.0119461	+	0.00531876i
$124$	−1.91025	−	3.30866i	−0.171546	−	0.297126i
$125$	5.93238	+	9.47665i	0.530609	+	0.847617i
$126$	1.89417			0.168746
$127$	−13.8923	−	6.18523i	−1.23274	−	0.548851i	−0.316161	−	0.948706i	$-0.602394\pi$
$127$	−13.8923	−	6.18523i	−1.23274	−	0.548851i	−0.916578	+	0.399855i	$0.869061\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	−26.6247	+	5.65925i	−2.34417	+	0.498269i
$130$	2.44387	+	0.856684i	0.214342	+	0.0751362i
$131$	−12.3186	−	2.61840i	−1.07628	−	0.228770i	−0.364522	−	0.931195i	$-0.618768\pi$
$131$	−12.3186	−	2.61840i	−1.07628	−	0.228770i	−0.711758	+	0.702424i	$0.752101\pi$
$132$	7.24192			0.630328
$133$	−1.33492	−	3.81406i	−0.115752	−	0.330721i
$134$	−8.66563	−	6.29595i	−0.748596	−	0.543887i
$135$	4.60230	−	1.37920i	0.396103	−	0.118702i
$136$	0.589358	+	5.60736i	0.0505370	+	0.480827i
$137$	2.05820	−	19.5825i	0.175844	−	1.67305i	−0.449947	−	0.893055i	$-0.648557\pi$
$137$	2.05820	−	19.5825i	0.175844	−	1.67305i	0.625791	−	0.779991i	$-0.284776\pi$
$138$	10.2063	−	4.54415i	0.868821	−	0.386824i
$139$	−0.456826	−	0.203392i	−0.0387475	−	0.0172515i	0.387271	−	0.921966i	$-0.373418\pi$
$139$	−0.456826	−	0.203392i	−0.0387475	−	0.0172515i	−0.426019	+	0.904714i	$0.640084\pi$
$140$	−2.05607	−	0.264038i	−0.173769	−	0.0223153i
$141$	−8.44865	−	6.13830i	−0.711505	−	0.516938i
$142$	−7.17110	+	7.96432i	−0.601785	+	0.668351i
$143$	−1.86737	−	3.23437i	−0.156157	−	0.270472i
$144$	0.631391	+	1.94322i	0.0526159	+	0.161935i
$145$	−7.75809	−	0.996285i	−0.644274	−	0.0827370i
$146$	−9.53016	+	2.02570i	−0.788721	+	0.167648i
$147$	−9.22729	−	10.2479i	−0.761054	−	0.845236i
$148$	8.30624	+	3.69818i	0.682769	+	0.303988i
$149$	2.88100	−	4.99003i	0.236021	−	0.408800i	−0.723548	−	0.690274i	$-0.757490\pi$
$149$	2.88100	−	4.99003i	0.236021	−	0.408800i	0.959569	+	0.281474i	$0.0908234\pi$
$150$	11.0789	−	1.82703i	0.904590	−	0.149176i
$151$	3.85699			0.313878			0.156939	−	0.987608i	$-0.449837\pi$
$151$	3.85699			0.313878			0.156939	+	0.987608i	$0.449837\pi$
$152$	3.46785	−	2.64084i	0.281280	−	0.214200i
$153$	−3.55994	+	10.9564i	−0.287804	+	0.885770i
$154$	2.00039	+	2.22166i	0.161196	+	0.179026i
$155$	−0.196470	+	8.54066i	−0.0157809	+	0.686002i
$156$	1.74030	−	1.93280i	0.139336	−	0.154748i
$157$	−3.62352	+	6.27612i	−0.289188	+	0.500889i	−0.973616	−	0.228192i	$-0.926719\pi$
$157$	−3.62352	+	6.27612i	−0.289188	+	0.500889i	0.684428	+	0.729080i	$0.260052\pi$
$158$	−1.72635	+	1.91731i	−0.137341	+	0.152533i
$159$	17.9940	+	13.0734i	1.42701	+	1.03679i
$160$	−0.414480	−	2.19732i	−0.0327675	−	0.173713i
$161$	4.21327	+	1.87587i	0.332052	+	0.147839i
$162$	1.14510	−	10.8949i	0.0899675	−	0.855984i
$163$	−18.6596	−	13.5570i	−1.46153	−	1.06187i	−0.982960	−	0.183818i	$-0.941154\pi$
$163$	−18.6596	−	13.5570i	−1.46153	−	1.06187i	−0.478573	−	0.878048i	$-0.658846\pi$
$164$	−0.0522460	+	0.0379590i	−0.00407973	+	0.00296410i
$165$	−13.8340	−	8.41709i	−1.07698	−	0.655270i
$166$	5.91565	−	2.63382i	0.459144	−	0.204424i
$167$	6.50677	−	7.22650i	0.503509	−	0.559203i	−0.436786	−	0.899566i	$-0.643883\pi$
$167$	6.50677	−	7.22650i	0.503509	−	0.559203i	0.940294	+	0.340363i	$0.110550\pi$
$168$	−1.04095	+	1.80297i	−0.0803107	+	0.139102i
$169$	11.4039	+	2.42398i	0.877227	+	0.186460i
$170$	5.39146	−	11.3966i	0.413506	−	0.874076i
$171$	8.66768	−	2.04736i	0.662834	−	0.156566i
$172$	3.74548	−	11.5274i	0.285590	−	0.878957i
$173$	−0.538488	−	5.12337i	−0.0409405	−	0.389523i	−0.995735	−	0.0922569i	$-0.970592\pi$
$173$	−0.538488	−	5.12337i	−0.0409405	−	0.389523i	0.954795	−	0.297266i	$-0.0960748\pi$
$174$	−3.92777	+	6.80309i	−0.297763	+	0.515741i
$175$	3.62075	+	2.89409i	0.273703	+	0.218773i
$176$	−1.61239	+	2.79274i	−0.121538	+	0.210511i
$177$	3.39803	+	1.51290i	0.255412	+	0.113717i
$178$	−1.01079	+	3.11090i	−0.0757620	+	0.233172i
$179$	1.66932	−	5.13765i	0.124771	−	0.384006i	−0.869088	−	0.494657i	$-0.835294\pi$
$179$	1.66932	−	5.13765i	0.124771	−	0.384006i	0.993859	+	0.110651i	$0.0352937\pi$
$180$	1.05243	−	4.44592i	0.0784435	−	0.331379i
$181$	−4.53905	+	5.04113i	−0.337385	+	0.374704i	−0.887833	−	0.460165i	$-0.847790\pi$
$181$	−4.53905	+	5.04113i	−0.337385	+	0.374704i	0.550448	+	0.834869i	$0.314457\pi$
$182$	1.07365			0.0795845
$183$	6.11014	+	18.8051i	0.451674	+	1.39011i
$184$	−0.520020	+	4.94766i	−0.0383364	+	0.364746i
$185$	−11.5688	−	16.7186i	−0.850558	−	1.22918i
$186$	7.83800	+	3.48970i	0.574710	+	0.255878i
$187$	−16.6102	+	7.39532i	−1.21466	+	0.540800i
$188$	4.24821	−	1.89142i	0.309832	−	0.137946i
$189$	1.61149	−	1.17081i	0.117218	−	0.0851641i
$190$	−9.69389	+	1.01412i	−0.703269	+	0.0735720i
$191$	0.403986	+	0.293513i	0.0292314	+	0.0212379i	0.602305	−	0.798266i	$-0.294249\pi$
$191$	0.403986	+	0.293513i	0.0292314	+	0.0212379i	−0.573074	+	0.819504i	$0.694249\pi$
$192$	−2.19664	−	0.466910i	−0.158529	−	0.0336963i
$193$	8.21767	−	14.2334i	0.591521	−	1.02454i	−0.402507	−	0.915417i	$-0.631861\pi$
$193$	8.21767	−	14.2334i	0.591521	−	1.02454i	0.994028	−	0.109127i	$-0.0348056\pi$
$194$	7.24732	−	8.04896i	0.520327	−	0.577882i
$195$	−5.57089	+	1.66946i	−0.398940	+	0.119553i
$196$	6.00639	−	1.27670i	0.429028	−	0.0911927i
$197$	1.96721	−	6.05445i	0.140158	−	0.431362i	−0.856199	−	0.516647i	$-0.827180\pi$
$197$	1.96721	−	6.05445i	0.140158	−	0.431362i	0.996357	+	0.0852849i	$0.0271800\pi$
$198$	−5.33056	+	3.87288i	−0.378827	+	0.275234i
$199$	5.01987	+	8.69467i	0.355849	+	0.616349i	0.987263	−	0.159097i	$-0.0508584\pi$
$199$	5.01987	+	8.69467i	0.355849	+	0.616349i	−0.631414	+	0.775446i	$0.717525\pi$
$200$	−1.76212	+	4.67920i	−0.124600	+	0.330870i
$201$	24.0545			1.69667
$202$	−11.5791	+	8.41271i	−0.814702	+	0.591916i
$203$	−3.17198	+	0.674225i	−0.222629	+	0.0473213i
$204$	−8.47246	−	9.40962i	−0.593191	−	0.658805i
$205$	0.143923	−	0.0117876i	0.0100520	−	0.000823279i
$206$	0.324606	+	0.0689971i	0.0226164	+	0.00480726i
$207$	−5.08243	+	8.80303i	−0.353253	+	0.611853i
$208$	0.357884	+	1.10145i	0.0248148	+	0.0763721i
$209$	11.5551	+	8.00407i	0.799280	+	0.553653i
$210$	4.08403	−	2.23429i	0.281825	−	0.154181i
$211$	0.349783	+	3.32797i	0.0240801	+	0.229107i	0.999943	+	0.0107206i	$0.00341253\pi$
$211$	0.349783	+	3.32797i	0.0240801	+	0.229107i	−0.975862	+	0.218386i	$0.929921\pi$
$212$	−9.04785	+	4.02836i	−0.621409	+	0.276669i
$213$	2.51573	−	23.9356i	0.172375	−	1.64004i
$214$	−0.0619945	−	0.589839i	−0.00423786	−	0.0403205i
$215$	−20.5529	+	17.6672i	−1.40170	+	1.20489i
$216$	1.73829	+	1.26294i	0.118276	+	0.0859323i
$217$	1.09448	+	3.36846i	0.0742981	+	0.228666i
$218$	−9.01980	−	15.6228i	−0.610898	−	1.05811i
$219$	14.6407	−	16.2601i	0.989324	−	1.09876i
$220$	6.32602	−	3.46084i	0.426500	−	0.233330i
$221$	−2.01784	+	6.21028i	−0.135735	+	0.417748i
$222$	−19.9725	+	4.24529i	−1.34047	+	0.284925i
$223$	0.0722785	+	0.687684i	0.00484013	+	0.0460507i	0.996675	−	0.0814751i	$-0.0259631\pi$
$223$	0.0722785	+	0.687684i	0.00484013	+	0.0460507i	−0.991835	+	0.127526i	$0.959296\pi$
$224$	−0.463526	−	0.802850i	−0.0309706	−	0.0536427i
$225$	−7.17780	+	7.26968i	−0.478520	+	0.484645i
$226$	−4.03228	+	6.98411i	−0.268223	+	0.464576i
$227$	−18.6459	+	13.5470i	−1.23757	+	0.899146i	−0.997434	−	0.0715931i	$-0.977192\pi$
$227$	−18.6459	+	13.5470i	−1.23757	+	0.899146i	−0.240135	+	0.970740i	$0.577192\pi$
$228$	−2.81455	+	9.37547i	−0.186398	+	0.620906i
$229$	−5.20781	+	16.0280i	−0.344142	+	1.05916i	0.617900	+	0.786257i	$0.287984\pi$
$229$	−5.20781	+	16.0280i	−0.344142	+	1.05916i	−0.962042	+	0.272903i	$0.912016\pi$
$230$	6.74391	−	8.84695i	0.444681	−	0.583350i
$231$	−6.56692	−	1.39584i	−0.432072	−	0.0918397i
$232$	−1.74901	−	3.02937i	−0.114828	−	0.198888i
$233$	−21.4660	−	4.56273i	−1.40628	−	0.298914i	−0.558608	−	0.829432i	$-0.688664\pi$
$233$	−21.4660	−	4.56273i	−1.40628	−	0.298914i	−0.847674	+	0.530517i	$0.821998\pi$
$234$	−0.247349	+	2.35337i	−0.0161697	+	0.153845i
$235$	−10.3136	−	1.32446i	−0.672783	−	0.0863980i
$236$	−1.33999	+	0.973558i	−0.0872258	+	0.0633732i
$237$	0.605630	−	5.76219i	0.0393399	−	0.374294i
$238$	0.546365	−	5.19832i	0.0354156	−	0.336957i
$239$	5.55330	−	4.03471i	0.359213	−	0.260983i	−0.393511	−	0.919320i	$-0.628740\pi$
$239$	5.55330	−	4.03471i	0.359213	−	0.260983i	0.752724	+	0.658337i	$0.228740\pi$
$240$	3.65349	+	3.44502i	0.235832	+	0.222375i
$241$	−0.148182	+	1.40986i	−0.00954527	+	0.0908172i	−0.998257	−	0.0590108i	$-0.981205\pi$
$241$	−0.148182	+	1.40986i	−0.00954527	+	0.0908172i	0.988712	+	0.149828i	$0.0478720\pi$
$242$	0.587692	+	0.124918i	0.0377783	+	0.00803002i
$243$	9.07782	+	15.7232i	0.582342	+	1.00865i
$244$	−8.61229	−	1.83060i	−0.551346	−	0.117192i
$245$	−12.9577	−	4.54224i	−0.827836	−	0.290193i
$246$	0.0448159	−	0.137929i	0.00285736	−	0.00879404i
$247$	4.91301	−	1.16048i	0.312607	−	0.0738399i
$248$	−3.09086	+	2.24564i	−0.196270	+	0.142598i
$249$	−7.27104	+	12.5938i	−0.460783	+	0.798100i
$250$	8.80463	−	6.89046i	0.556854	−	0.435791i
$251$	−8.31573	−	14.4033i	−0.524884	−	0.909126i	−0.999580	−	0.0289762i	$-0.990775\pi$
$251$	−8.31573	−	14.4033i	−0.524884	−	0.909126i	0.474696	−	0.880150i	$-0.342558\pi$
$252$	−0.197995	−	1.88380i	−0.0124725	−	0.118668i
$253$	−15.6924	+	3.33552i	−0.986573	+	0.209703i
$254$	−4.69921	+	14.4627i	−0.294855	+	0.907470i
$255$	5.24810	+	27.8222i	0.328649	+	1.74229i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−3.16107	−	5.47514i	−0.197182	−	0.341530i	0.750431	−	0.660948i	$-0.229846\pi$
$257$	−3.16107	−	5.47514i	−0.197182	−	0.341530i	−0.947614	+	0.319419i	$0.896512\pi$
$258$	8.41128	+	25.8873i	0.523663	+	1.61167i
$259$	−6.81924	−	4.95447i	−0.423727	−	0.307856i
$260$	0.596537	−	2.52003i	0.0369957	−	0.156286i
$261$	−0.747089	−	7.10807i	−0.0462436	−	0.439979i
$262$	−1.31641	+	12.5248i	−0.0813281	+	0.773785i
$263$	−22.5609	+	10.0448i	−1.39117	+	0.619388i	−0.959259	−	0.282530i	$-0.908826\pi$
$263$	−22.5609	+	10.0448i	−1.39117	+	0.619388i	−0.431909	+	0.901917i	$0.642160\pi$
$264$	−0.756987	−	7.20225i	−0.0465893	−	0.443268i
$265$	21.9659	+	2.82083i	1.34935	+	0.173282i
$266$	−3.65363	+	1.72629i	−0.224018	+	0.105845i
$267$	−2.26995	−	6.98618i	−0.138919	−	0.427547i
$268$	−5.35565	+	9.27626i	−0.327149	+	0.566638i
$269$	21.2811	+	4.52343i	1.29753	+	0.275799i	0.804364	−	0.594137i	$-0.202506\pi$
$269$	21.2811	+	4.52343i	1.29753	+	0.275799i	0.493166	+	0.869935i	$0.335840\pi$
$270$	−1.85271	−	4.43293i	−0.112753	−	0.269779i
$271$	6.00464	+	6.66883i	0.364756	+	0.405103i	0.897387	−	0.441245i	$-0.145463\pi$
$271$	6.00464	+	6.66883i	0.364756	+	0.405103i	−0.532631	+	0.846348i	$0.678796\pi$
$272$	5.51504	−	1.17226i	0.334398	−	0.0710786i
$273$	−1.95063	+	1.41722i	−0.118058	+	0.0857740i
$274$	−19.6904			−1.18954
$275$	−16.1068	−	0.741439i	−0.971278	−	0.0447105i
$276$	−5.58611	−	9.67543i	−0.336244	−	0.582392i
$277$	12.3676	−	8.98562i	0.743100	−	0.539894i	−0.150581	−	0.988598i	$-0.548114\pi$
$277$	12.3676	−	8.98562i	0.743100	−	0.539894i	0.893680	+	0.448704i	$0.148114\pi$
$278$	−0.154527	+	0.475584i	−0.00926789	+	0.0285236i
$279$	−7.63557	+	1.62299i	−0.457130	+	0.0971659i
$280$	−0.0476738	+	2.07240i	−0.00284905	+	0.123850i
$281$	22.1097	−	24.5553i	1.31895	−	1.46485i	0.533701	−	0.845673i	$-0.320801\pi$
$281$	22.1097	−	24.5553i	1.31895	−	1.46485i	0.785253	−	0.619175i	$-0.212533\pi$
$282$	−5.22155	+	9.04400i	−0.310939	+	0.538562i
$283$	−16.4591	−	3.49848i	−0.978389	−	0.207963i	−0.309153	−	0.951012i	$-0.600045\pi$
$283$	−16.4591	−	3.49848i	−0.978389	−	0.207963i	−0.669237	+	0.743049i	$0.733379\pi$
$284$	8.67027	+	6.29932i	0.514486	+	0.373796i
$285$	16.2734	−	14.6384i	0.963954	−	0.867103i
$286$	−3.02146	+	2.19522i	−0.178663	+	0.129806i
$287$	0.0546927	−	0.0243508i	0.00322841	−	0.00143738i
$288$	1.86658	−	0.831054i	0.109989	−	0.0489703i
$289$	13.5112	+	6.01558i	0.794777	+	0.353858i
$290$	−0.179886	+	7.81973i	−0.0105633	+	0.459191i
$291$	−2.54247	+	24.1899i	−0.149042	+	1.41804i
$292$	3.01077	+	9.26621i	0.176192	+	0.542264i
$293$	−31.7783			−1.85651			−0.928254	−	0.371946i	$-0.878691\pi$
$293$	−31.7783			−1.85651			−0.928254	+	0.371946i	$0.878691\pi$
$294$	−9.22729	+	10.2479i	−0.538146	+	0.597672i
$295$	3.69128	−	0.302323i	0.214914	−	0.0176019i
$296$	2.80968	−	8.64730i	0.163309	−	0.502614i
$297$	−2.14115	+	6.58978i	−0.124242	+	0.382378i
$298$	−5.26384	−	2.34361i	−0.304926	−	0.135762i
$299$	−2.88082	+	4.98972i	−0.166602	+	0.288563i
$300$	−2.97508	−	10.8273i	−0.171767	−	0.625112i
$301$	−5.61823	+	9.73106i	−0.323829	+	0.560889i
$302$	−0.403166	−	3.83586i	−0.0231996	−	0.220729i
$303$	9.93238	−	30.5687i	0.570600	−	1.75613i
$304$	−2.98886	−	3.17281i	−0.171423	−	0.181973i
$305$	14.3241	+	13.5068i	0.820197	+	0.773396i
$306$	11.2685	+	2.39518i	0.644175	+	0.136924i
$307$	1.19225	−	2.06503i	0.0680452	−	0.117858i	−0.829996	−	0.557770i	$-0.811657\pi$
$307$	1.19225	−	2.06503i	0.0680452	−	0.117858i	0.898041	+	0.439912i	$0.144990\pi$
$308$	2.00039	−	2.22166i	0.113983	−	0.126591i
$309$	−0.680826	+	0.303123i	−0.0387309	+	0.0172441i
$310$	8.51441	−	0.697348i	0.483586	−	0.0396067i
$311$	16.7670	−	12.1819i	0.950770	−	0.690775i	−0.000219111	−	1.00000i	$-0.500070\pi$
$311$	16.7670	−	12.1819i	0.950770	−	0.690775i	0.950989	+	0.309225i	$0.100070\pi$
$312$	−2.10413	−	1.52874i	−0.119123	−	0.0865477i
$313$	1.05215	−	10.0105i	0.0594710	−	0.565828i	−0.923697	−	0.383124i	$-0.874848\pi$
$313$	1.05215	−	10.0105i	0.0594710	−	0.565828i	0.983168	−	0.182704i	$-0.0584852\pi$
$314$	6.62050	+	2.94764i	0.373616	+	0.166345i
$315$	−1.81126	+	3.82868i	−0.102053	+	0.215722i
$316$	2.08726	+	1.51648i	0.117418	+	0.0853088i
$317$	8.98156	−	9.97503i	0.504455	−	0.560254i	−0.436099	−	0.899899i	$-0.643640\pi$
$317$	8.98156	−	9.97503i	0.504455	−	0.560254i	0.940554	+	0.339645i	$0.110307\pi$
$318$	11.1209	−	19.2619i	0.623628	−	1.08016i
$319$	7.54801	−	8.38291i	0.422607	−	0.469353i
$320$	−2.14196	+	0.641892i	−0.119739	+	0.0358829i
$321$	0.891218	+	0.989798i	0.0497429	+	0.0552451i
$322$	1.42519	−	4.38627i	0.0794226	−	0.244438i
$323$	−3.11857	−	24.3779i	−0.173522	−	1.35642i
$324$	−10.9549			−0.608606
$325$	−4.06851	+	4.12059i	−0.225680	+	0.228569i
$326$	−11.5323	+	19.9745i	−0.638713	+	1.10628i
$327$	37.0093	+	16.4776i	2.04662	+	0.911214i
$328$	0.0432122	+	0.0479920i	0.00238600	+	0.00264992i
$329$	−4.21681	+	0.896310i	−0.232480	+	0.0494152i
$330$	−6.92494	+	14.6380i	−0.381205	+	0.805797i
$331$	−1.51906	−	4.67518i	−0.0834949	−	0.256971i	0.900590	−	0.434669i	$-0.143135\pi$
$331$	−1.51906	−	4.67518i	−0.0834949	−	0.256971i	−0.984085	+	0.177699i	$0.943135\pi$
$332$	−3.23774	−	5.60794i	−0.177694	−	0.307775i
$333$	12.4309	−	13.8059i	0.681207	−	0.756557i
$334$	−7.86705	−	5.71575i	−0.430466	−	0.312752i
$335$	21.0123	−	11.4954i	1.14802	−	0.628061i
$336$	1.90190	+	0.846781i	0.103757	+	0.0461957i
$337$	−26.4328	+	11.7686i	−1.43988	+	0.641078i	−0.970321	−	0.241821i	$-0.922255\pi$
$337$	−26.4328	+	11.7686i	−1.43988	+	0.641078i	−0.469564	+	0.882899i	$0.655589\pi$
$338$	1.21867	−	11.5948i	0.0662868	−	0.630677i
$339$	−1.89308	−	18.0115i	−0.102818	−	0.978248i
$340$	−11.8977	−	4.17066i	−0.645243	−	0.226186i
$341$	−9.96732	−	7.24168i	−0.539761	−	0.392159i
$342$	−2.94217	−	8.40619i	−0.159094	−	0.454555i
$343$	−12.1820			−0.657766
$344$	−11.8558	−	2.52002i	−0.639221	−	0.135871i
$345$	−0.574534	+	24.9752i	−0.0309319	+	1.34462i
$346$	−5.03902	+	1.07108i	−0.270899	+	0.0575814i
$347$	−2.53696	−	2.81758i	−0.136191	−	0.151256i	0.671191	−	0.741284i	$-0.265783\pi$
$347$	−2.53696	−	2.81758i	−0.136191	−	0.151256i	−0.807382	+	0.590029i	$0.799116\pi$
$348$	7.17639	+	3.19513i	0.384695	+	0.171277i
$349$	−11.7295			−0.627864			−0.313932	−	0.949446i	$-0.601646\pi$
$349$	−11.7295			−0.627864			−0.313932	+	0.949446i	$0.601646\pi$
$350$	2.49977	−	3.90343i	0.133618	−	0.208647i
$351$	1.24421	+	2.15504i	0.0664112	+	0.115028i
$352$	2.94598	+	1.31163i	0.157021	+	0.0699104i
$353$	1.20102	−	3.69636i	0.0639239	−	0.196738i	−0.913994	−	0.405728i	$-0.867018\pi$
$353$	1.20102	−	3.69636i	0.0639239	−	0.196738i	0.977918	+	0.208991i	$0.0670179\pi$
$354$	1.14942	−	3.53756i	0.0610911	−	0.188019i
$355$	−9.24100	−	22.1106i	−0.490461	−	1.17351i
$356$	3.19951	+	0.680077i	0.169574	+	0.0360440i
$357$	5.86911	+	10.1656i	0.310626	+	0.538021i
$358$	−5.28399	−	1.12315i	−0.279268	−	0.0593602i
$359$	−25.2491	+	11.2416i	−1.33260	+	0.593311i	−0.944562	−	0.328334i	$-0.893513\pi$
$359$	−25.2491	+	11.2416i	−1.33260	+	0.593311i	−0.388036	+	0.921644i	$0.626846\pi$
$360$	−4.53157	−	0.581939i	−0.238835	−	0.0306709i
$361$	−14.8530	+	11.8486i	−0.781737	+	0.623608i
$362$	5.48797	+	3.98725i	0.288441	+	0.209565i
$363$	−1.23262	+	0.548798i	−0.0646958	+	0.0288044i
$364$	−0.112227	−	1.06777i	−0.00588231	−	0.0559665i
$365$	5.01849	−	21.2003i	0.262680	−	1.10967i
$366$	18.0634	−	8.04233i	0.944187	−	0.420379i
$367$	−22.4302	+	24.9113i	−1.17085	+	1.30036i	−0.225518	+	0.974239i	$0.572407\pi$
$367$	−22.4302	+	24.9113i	−1.17085	+	1.30036i	−0.945329	+	0.326118i	$0.894259\pi$
$368$	4.97491			0.259335
$369$	0.0407750	+	0.125492i	0.00212266	+	0.00653288i
$370$	−15.4178	+	13.2530i	−0.801532	+	0.688993i
$371$	8.98098	−	1.90897i	0.466269	−	0.0991085i
$372$	2.65129	−	8.15984i	0.137463	−	0.423068i
$373$	1.93164	−	1.40342i	0.100017	−	0.0726664i	−0.536653	−	0.843803i	$-0.680312\pi$
$373$	1.93164	−	1.40342i	0.100017	−	0.0726664i	0.636670	+	0.771137i	$0.280312\pi$
$374$	9.09105	+	15.7462i	0.470087	+	0.814214i
$375$	−6.90103	+	24.1408i	−0.356368	+	1.24663i
$376$	−2.32512	−	4.02723i	−0.119909	−	0.207688i
$377$	−0.423464	−	4.02899i	−0.0218095	−	0.207504i
$378$	−1.33284	−	1.48027i	−0.0685541	−	0.0761371i
$379$	−9.74803	+	30.0013i	−0.500723	+	1.54107i	0.307122	+	0.951670i	$0.400634\pi$
$379$	−9.74803	+	30.0013i	−0.500723	+	1.54107i	−0.807845	+	0.589396i	$0.799366\pi$
$380$	2.02185	+	9.53478i	0.103719	+	0.489124i
$381$	−10.5531	−	32.4790i	−0.540651	−	1.66395i
$382$	0.249677	−	0.432453i	0.0127746	−	0.0221262i
$383$	27.4071	+	5.82555i	1.40044	+	0.297672i	0.845391	−	0.534148i	$-0.179368\pi$
$383$	27.4071	+	5.82555i	1.40044	+	0.297672i	0.555045	+	0.831820i	$0.312701\pi$
$384$	−0.234741	+	2.23341i	−0.0119791	+	0.113973i
$385$	−6.40345	+	1.91896i	−0.326350	+	0.0977991i
$386$	−15.0144	−	6.68486i	−0.764214	−	0.340250i
$387$	−20.0354	−	14.5566i	−1.01846	−	0.739954i
$388$	−8.76242	−	6.36627i	−0.444844	−	0.323198i
$389$	16.5083	+	7.34999i	0.837006	+	0.372659i	0.780050	−	0.625717i	$-0.215194\pi$
$389$	16.5083	+	7.34999i	0.837006	+	0.372659i	0.0569566	+	0.998377i	$0.481860\pi$
$390$	2.24263	+	5.36587i	0.113560	+	0.271711i
$391$	22.6928	+	16.4873i	1.14762	+	0.833797i
$392$	−1.89754	−	5.84003i	−0.0958404	−	0.294966i
$393$	−14.1410	−	24.4930i	−0.713320	−	1.23551i
$394$	−6.22692	−	1.32357i	−0.313707	−	0.0666806i
$395$	−2.22466	−	5.32286i	−0.111935	−	0.267822i
$396$	4.40886	+	4.89653i	0.221553	+	0.246060i
$397$	6.23580	+	6.92556i	0.312966	+	0.347584i	0.879020	−	0.476784i	$-0.158198\pi$
$397$	6.23580	+	6.92556i	0.312966	+	0.347584i	−0.566055	+	0.824368i	$0.691531\pi$
$398$	8.12232	−	5.90121i	0.407135	−	0.295801i
$399$	4.35929	−	7.95913i	0.218238	−	0.398455i
$400$	4.83776	+	1.26335i	0.241888	+	0.0631677i
$401$	17.3384	−	30.0310i	0.865838	−	1.49967i	−0.000375326	−	1.00000i	$-0.500119\pi$
$401$	17.3384	−	30.0310i	0.865838	−	1.49967i	0.866213	−	0.499675i	$-0.166547\pi$
$402$	−2.51438	−	23.9227i	−0.125406	−	1.19316i
$403$	−4.32799	+	0.919942i	−0.215592	+	0.0458256i
$404$	9.57696	+	10.6363i	0.476472	+	0.529176i
$405$	20.9268	+	12.7326i	1.03986	+	0.632688i
$406$	1.00209	+	3.08413i	0.0497330	+	0.153063i
$407$	29.3207			1.45337
$408$	−8.47246	+	9.40962i	−0.419449	+	0.465845i
$409$	−1.61658	+	15.3808i	−0.0799348	+	0.760529i	0.878984	+	0.476850i	$0.158222\pi$
$409$	−1.61658	+	15.3808i	−0.0799348	+	0.760529i	−0.958919	+	0.283679i	$0.908445\pi$
$410$	−0.0267670	−	0.141902i	−0.00132193	−	0.00700804i
$411$	35.7738	−	25.9912i	1.76459	−	1.28205i
$412$	0.0346886	−	0.330040i	0.00170898	−	0.0162599i
$413$	1.40274	−	0.624540i	0.0690243	−	0.0307316i
$414$	9.28606	+	4.13442i	0.456385	+	0.203196i
$415$	−0.333003	+	14.4758i	−0.0163465	+	0.710589i
$416$	1.05801	−	0.471057i	0.0518733	−	0.0230955i
$417$	−0.347022	−	1.06802i	−0.0169938	−	0.0523014i
$418$	6.75239	−	12.3284i	0.330270	−	0.603002i
$419$	4.07072	+	12.5284i	0.198868	+	0.612052i	0.999910	+	0.0134438i	$0.00427942\pi$
$419$	4.07072	+	12.5284i	0.198868	+	0.612052i	−0.801042	+	0.598608i	$0.795721\pi$
$420$	−2.64895	−	3.82811i	−0.129255	−	0.186793i
$421$	14.9414	+	16.5941i	0.728198	+	0.808746i	0.987595	−	0.157025i	$-0.0501904\pi$
$421$	14.9414	+	16.5941i	0.728198	+	0.808746i	−0.259397	+	0.965771i	$0.583524\pi$
$422$	3.27317	−	0.695734i	0.159336	−	0.0338678i
$423$	−0.993175	−	9.44943i	−0.0482898	−	0.459447i
$424$	4.95205	+	8.57721i	0.240493	+	0.416546i
$425$	17.8803	+	21.7954i	0.867322	+	1.05723i
$426$	−24.0674			−1.16607
$427$	7.45673	+	3.31995i	0.360856	+	0.160664i
$428$	−0.580127	+	0.123310i	−0.0280415	+	0.00596041i
$429$	2.59177	−	7.97664i	0.125132	−	0.385116i
$430$	19.7187	+	18.5936i	0.950922	+	0.896662i
$431$	10.4010	−	11.5515i	0.500998	−	0.556415i	−0.438605	−	0.898680i	$-0.644527\pi$
$431$	10.4010	−	11.5515i	0.500998	−	0.556415i	0.939603	+	0.342265i	$0.111194\pi$
$432$	1.07432	−	1.86078i	0.0516884	−	0.0895269i
$433$	3.49871	−	3.88571i	0.168137	−	0.186735i	−0.653188	−	0.757196i	$-0.726569\pi$
$433$	3.49871	−	3.88571i	0.168137	−	0.186735i	0.821325	+	0.570461i	$0.193235\pi$
$434$	3.23560	−	1.44058i	0.155314	−	0.0691502i
$435$	−9.99520	−	14.4445i	−0.479233	−	0.692560i
$436$	−14.5943	+	10.6034i	−0.698942	+	0.507811i
$437$	1.78060	−	21.6119i	0.0851779	−	1.03384i
$438$	−17.7014	−	12.8608i	−0.845805	−	0.614514i
$439$	0.707571	+	6.73209i	0.0337705	+	0.321305i	0.998346	+	0.0574970i	$0.0183119\pi$
$439$	0.707571	+	6.73209i	0.0337705	+	0.321305i	−0.964575	+	0.263808i	$0.915021\pi$
$440$	−4.10313	−	5.92961i	−0.195609	−	0.282683i
$441$	1.31147	−	12.4778i	0.0624511	−	0.594183i
$442$	6.38718	+	1.35764i	0.303807	+	0.0645762i
$443$	−2.10268	−	3.64196i	−0.0999016	−	0.173035i	0.811742	−	0.584016i	$-0.198519\pi$
$443$	−2.10268	−	3.64196i	−0.0999016	−	0.173035i	−0.911644	+	0.410981i	$0.865186\pi$
$444$	6.30973	+	19.4194i	0.299447	+	0.921602i
$445$	−5.32149	−	5.01784i	−0.252263	−	0.237868i
$446$	0.676362	−	0.143765i	0.0320267	−	0.00680748i
$447$	12.6570	−	2.69033i	0.598656	−	0.127248i
$448$	−0.750001	+	0.544907i	−0.0354342	+	0.0257444i
$449$	−18.7339			−0.884109			−0.442055	−	0.896988i	$-0.645750\pi$
$449$	−18.7339			−0.884109			−0.442055	+	0.896988i	$0.645750\pi$
$450$	7.98014	+	6.37859i	0.376187	+	0.300690i
$451$	−0.104127	+	0.180354i	−0.00490317	+	0.00849254i
$452$	7.36734	+	3.28015i	0.346530	+	0.154285i
$453$	5.79581	+	6.43689i	0.272311	+	0.302432i
$454$	15.4218	+	17.1277i	0.723782	+	0.803841i
$455$	−1.02666	+	2.17017i	−0.0481305	+	0.101739i
$456$	9.61832	+	1.81913i	0.450419	+	0.0851886i
$457$	28.3661			1.32691			0.663455	−	0.748216i	$-0.269089\pi$
$457$	28.3661			1.32691			0.663455	+	0.748216i	$0.269089\pi$
$458$	16.4846	+	3.50390i	0.770273	+	0.163727i
$459$	11.0672	−	4.92745i	0.516574	−	0.229994i
$460$	−9.50341	−	5.78221i	−0.443099	−	0.269597i
$461$	−2.65217	−	25.2337i	−0.123524	−	1.17525i	−0.864115	−	0.503295i	$-0.832121\pi$
$461$	−2.65217	−	25.2337i	−0.123524	−	1.17525i	0.740591	−	0.671956i	$-0.234546\pi$
$462$	−0.701766	+	6.67685i	−0.0326491	+	0.310635i
$463$	17.3754	+	12.6240i	0.807504	+	0.586686i	0.913106	−	0.407723i	$-0.133677\pi$
$463$	17.3754	+	12.6240i	0.807504	+	0.586686i	−0.105602	+	0.994408i	$0.533677\pi$
$464$	−2.82995	+	2.05608i	−0.131377	+	0.0954512i
$465$	−14.5486	+	12.5059i	−0.674677	+	0.579949i
$466$	−2.29393	+	21.8253i	−0.106264	+	1.01104i
$467$	6.88619	+	21.1935i	0.318655	+	0.980720i	0.974224	+	0.225584i	$0.0724290\pi$
$467$	6.88619	+	21.1935i	0.318655	+	0.980720i	−0.655569	+	0.755136i	$0.727571\pi$
$468$	2.36633			0.109384
$469$	6.64442	−	7.37938i	0.306811	−	0.340748i
$470$	−0.239140	+	10.3955i	−0.0110307	+	0.479509i
$471$	−15.9191	+	3.38371i	−0.733514	+	0.155913i
$472$	1.10829	+	1.23088i	0.0510133	+	0.0566560i
$473$	−4.08564	−	38.8722i	−0.187858	−	1.78735i
$474$	−5.79393			−0.266124
$475$	7.21975	−	20.5639i	0.331265	−	0.943538i
$476$	−5.22695			−0.239577
$477$	2.11527	+	20.1254i	0.0968515	+	0.921480i
$478$	−4.59308	−	5.10113i	−0.210083	−	0.233320i
$479$	16.4324	−	3.49282i	0.750816	−	0.159591i	0.183419	−	0.983035i	$-0.441284\pi$
$479$	16.4324	−	3.49282i	0.750816	−	0.159591i	0.567398	+	0.823444i	$0.307950\pi$
$480$	3.04425	−	3.99358i	0.138950	−	0.182281i
$481$	7.04605	−	7.82543i	0.321272	−	0.356809i
$482$	1.41763			0.0645712
$483$	3.20056	+	9.85031i	0.145631	+	0.448205i
$484$	0.0628029	−	0.597530i	0.00285468	−	0.0271605i
$485$	9.33921	+	22.3456i	0.424072	+	1.01466i
$486$	14.6882	−	10.6716i	0.666271	−	0.484074i
$487$	29.0364	+	21.0962i	1.31576	+	0.955958i	0.999975	+	0.00712910i	$0.00226928\pi$
$487$	29.0364	+	21.0962i	1.31576	+	0.955958i	0.315789	+	0.948829i	$0.397731\pi$
$488$	−0.920341	+	8.75646i	−0.0416619	+	0.396386i
$489$	−5.41419	−	51.5126i	−0.244838	−	2.32948i
$490$	−3.16291	+	13.3615i	−0.142886	+	0.603610i
$491$	−18.6974	+	8.32461i	−0.843801	+	0.375684i	−0.782664	−	0.622445i	$-0.786139\pi$
$491$	−18.6974	+	8.32461i	−0.843801	+	0.375684i	−0.0611374	+	0.998129i	$0.519473\pi$
$492$	−0.141858	−	0.0301529i	−0.00639546	−	0.00135940i
$493$	−19.7227			−0.888265
$494$	−1.66768	−	4.76479i	−0.0750323	−	0.214378i
$495$	−2.73098	−	14.4780i	−0.122749	−	0.650737i
$496$	2.55642	+	2.83919i	0.114787	+	0.127483i
$497$	−6.64798	−	7.38333i	−0.298203	−	0.331188i
$498$	13.2848	+	5.91480i	0.595308	+	0.265048i
$499$	−15.7204	+	27.2286i	−0.703743	+	1.21892i	0.263401	+	0.964686i	$0.415156\pi$
$499$	−15.7204	+	27.2286i	−0.703743	+	1.21892i	−0.967143	+	0.254231i	$0.918178\pi$
$500$	−7.77305	−	8.03615i	−0.347621	−	0.359387i
$501$	21.8378			0.975640
$502$	−13.4551	+	9.77573i	−0.600532	+	0.436312i
$503$	25.5317	−	5.42693i	1.13840	−	0.241975i	0.400117	−	0.916464i	$-0.368969\pi$
$503$	25.5317	−	5.42693i	1.13840	−	0.241975i	0.738285	+	0.674489i	$0.235636\pi$
$504$	−1.85278	+	0.393821i	−0.0825294	+	0.0175422i
$505$	−5.93227	−	31.4492i	−0.263983	−	1.39947i
$506$	4.95755	+	15.2578i	0.220390	+	0.678291i
$507$	13.0911	+	22.6744i	0.581394	+	1.00700i
$508$	14.8747	+	3.16171i	0.659957	+	0.140278i
$509$	−3.95876	+	37.6651i	−0.175469	+	1.66948i	0.452901	+	0.891561i	$0.350389\pi$
$509$	−3.95876	+	37.6651i	−0.175469	+	1.66948i	−0.628370	+	0.777915i	$0.716278\pi$
$510$	27.1212	−	8.12756i	1.20095	−	0.359895i
$511$	−0.944135	−	8.98285i	−0.0417661	−	0.397378i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−7.69905	−	5.33306i	−0.339921	−	0.235460i
$514$	−5.11472	+	3.71606i	−0.225601	+	0.163909i
$515$	−0.449861	+	0.590147i	−0.0198233	+	0.0260050i
$516$	24.8662	−	11.0712i	1.09467	−	0.487380i
$517$	10.0343	−	11.1442i	0.441307	−	0.490121i
$518$	−4.21452	+	7.29977i	−0.185175	+	0.320733i
$519$	7.74117	−	8.59744i	0.339800	−	0.377386i
$520$	−2.56858	−	0.329854i	−0.112640	−	0.0144651i
$521$	1.09260	−	3.36267i	0.0478675	−	0.147321i	−0.924266	−	0.381749i	$-0.875322\pi$
$521$	1.09260	−	3.36267i	0.0478675	−	0.147321i	0.972133	+	0.234428i	$0.0753218\pi$
$522$	−6.99104	+	1.48599i	−0.305990	+	0.0650401i
$523$	14.1768	+	6.31190i	0.619907	+	0.276000i	0.692564	−	0.721357i	$-0.256481\pi$
$523$	14.1768	+	6.31190i	0.619907	+	0.276000i	−0.0726570	+	0.997357i	$0.523148\pi$
$524$	12.5938			0.550163
$525$	0.610888	+	10.3915i	0.0266613	+	0.453523i
$526$	12.3480	+	21.3874i	0.538399	+	0.932534i
$527$	2.25165	+	21.4230i	0.0980833	+	0.933200i
$528$	−7.08366	+	1.50568i	−0.308277	+	0.0655263i
$529$	1.17082	+	1.30033i	0.0509054	+	0.0565362i
$530$	0.509320	−	22.1404i	0.0221235	−	0.961717i
$531$	1.04578	+	3.21859i	0.0453831	+	0.139675i
$532$	2.09874	+	3.45317i	0.0909918	+	0.149714i
$533$	0.0231120	+	0.0711315i	0.00100109	+	0.00308105i
$534$	−6.71063	+	2.98777i	−0.290398	+	0.129293i
$535$	1.25152	+	0.438712i	0.0541078	+	0.0189672i
$536$	9.78526	+	4.35668i	0.422659	+	0.188180i
$537$	11.0826	−	4.93430i	0.478250	−	0.212931i
$538$	2.27417	−	21.6373i	0.0980466	−	0.932851i
$539$	16.0201	−	11.6393i	0.690036	−	0.501341i
$540$	−4.21498	+	2.30593i	−0.181384	+	0.0992315i
$541$	−3.41837	+	32.5236i	−0.146967	+	1.39830i	0.633810	+	0.773489i	$0.281490\pi$
$541$	−3.41837	+	32.5236i	−0.146967	+	1.39830i	−0.780777	+	0.624809i	$0.785177\pi$
$542$	6.00464	−	6.66883i	0.257921	−	0.286451i
$543$	−15.2338			−0.653745
$544$	−1.74232	−	5.36229i	−0.0747011	−	0.229906i
$545$	40.2032	−	3.29272i	1.72211	−	0.141045i
$546$	1.61335	+	1.79181i	0.0690451	+	0.0766823i
$547$	−15.8903	+	3.37759i	−0.679420	+	0.144415i	−0.534680	−	0.845055i	$-0.679568\pi$
$547$	−15.8903	+	3.37759i	−0.679420	+	0.144415i	−0.144740	+	0.989470i	$0.546235\pi$
$548$	2.05820	+	19.5825i	0.0879221	+	0.836523i
$549$	−8.99498	+	15.5798i	−0.383896	+	0.664928i
$550$	0.946244	+	16.0961i	0.0403480	+	0.686340i
$551$	7.91910	+	13.0297i	0.337365	+	0.555085i
$552$	−9.03852	+	6.56687i	−0.384705	+	0.279505i
$553$	−1.60042	−	1.77745i	−0.0680567	−	0.0755847i
$554$	−10.2292	−	11.3606i	−0.434596	−	0.482667i
$555$	10.5173	−	44.4298i	0.446436	−	1.88594i
$556$	0.489131	+	0.103968i	0.0207438	+	0.00440923i
$557$	−19.9944	−	34.6313i	−0.847189	−	1.46737i	−0.883707	−	0.468041i	$-0.844960\pi$
$557$	−19.9944	−	34.6313i	−0.847189	−	1.46737i	0.0365181	−	0.999333i	$-0.488373\pi$
$558$	2.41223	+	7.42409i	0.102118	+	0.314287i
$559$	−11.3565	−	8.25096i	−0.480328	−	0.348978i
$560$	2.06603	−	0.169212i	0.0873058	−	0.00715053i
$561$	−37.3017	−	16.6078i	−1.57488	−	0.701181i
$562$	−26.7319	−	19.4219i	−1.12762	−	0.819262i
$563$	22.0668	+	16.0325i	0.930004	+	0.675687i	0.945994	−	0.324185i	$-0.105090\pi$
$563$	22.0668	+	16.0325i	0.930004	+	0.675687i	−0.0159900	+	0.999872i	$0.505090\pi$
$564$	9.54025	+	4.24759i	0.401717	+	0.178856i
$565$	−10.2611	−	14.8288i	−0.431690	−	0.623853i
$566$	−1.75888	+	16.7346i	−0.0739310	+	0.703407i
$567$	9.93384	+	2.11150i	0.417182	+	0.0886748i
$568$	5.35852	−	9.28123i	0.224839	−	0.389432i
$569$	3.54022	+	10.8957i	0.148414	+	0.456771i	0.997434	−	0.0715895i	$-0.0228071\pi$
$569$	3.54022	+	10.8957i	0.148414	+	0.456771i	−0.849020	+	0.528360i	$0.822807\pi$
$570$	−16.2592	−	14.6541i	−0.681024	−	0.613794i
$571$	−0.626866	+	1.92930i	−0.0262335	+	0.0807385i	−0.963316	−	0.268369i	$-0.913515\pi$
$571$	−0.626866	+	1.92930i	−0.0262335	+	0.0807385i	0.937083	+	0.349108i	$0.113515\pi$
$572$	2.49903	+	2.77545i	0.104489	+	0.116047i
$573$	0.117219	+	1.11526i	0.00489689	+	0.0465908i
$574$	−0.0299343	−	0.0518478i	−0.00124943	−	0.00216408i
$575$	11.4335	+	22.0911i	0.476812	+	0.921264i
$576$	−1.02161	−	1.76948i	−0.0425671	−	0.0737285i
$577$	27.6749	−	20.1070i	1.15212	−	0.837064i	0.163359	−	0.986567i	$-0.447767\pi$
$577$	27.6749	−	20.1070i	1.15212	−	0.837064i	0.988761	+	0.149502i	$0.0477672\pi$
$578$	4.57032	−	14.0660i	0.190100	−	0.585068i
$579$	36.1025	−	7.67382i	1.50037	−	0.318913i
$580$	7.79570	−	0.638484i	0.323699	−	0.0265116i
$581$	1.85506	+	5.70930i	0.0769610	+	0.236862i
$582$	24.3232			1.00823
$583$	−21.3710	+	23.7349i	−0.885098	+	0.983001i
$584$	8.90074	−	3.96286i	0.368315	−	0.163984i
$585$	−4.52033	−	2.75033i	−0.186893	−	0.113712i
$586$	3.32174	+	31.6042i	0.137220	+	1.30556i
$587$	22.6566	−	10.0874i	0.935139	−	0.416351i	0.118145	−	0.992996i	$-0.462305\pi$
$587$	22.6566	−	10.0874i	0.935139	−	0.416351i	0.816994	+	0.576646i	$0.195639\pi$
$588$	11.1563	+	8.10554i	0.460079	+	0.334267i
$589$	13.2489	−	10.0894i	0.545913	−	0.415724i
$590$	−0.686510	−	3.63945i	−0.0282632	−	0.149834i
$591$	13.0603	−	5.81482i	0.537229	−	0.239190i
$592$	−8.89363	−	1.89040i	−0.365526	−	0.0776949i
$593$	1.97576	+	3.42212i	0.0811348	+	0.140530i	0.903738	−	0.428087i	$-0.140812\pi$
$593$	1.97576	+	3.42212i	0.0811348	+	0.140530i	−0.822603	+	0.568616i	$0.807479\pi$
$594$	6.77749	+	1.44060i	0.278084	+	0.0591085i
$595$	9.98487	+	6.07515i	0.409340	+	0.249057i
$596$	−1.78055	+	5.47998i	−0.0729344	+	0.224469i
$597$	−6.96721	+	21.4429i	−0.285149	+	0.877598i
$598$	5.26352	+	2.34347i	0.215241	+	0.0958315i
$599$	−2.10478	−	3.64559i	−0.0859990	−	0.148955i	0.819817	−	0.572625i	$-0.194075\pi$
$599$	−2.10478	−	3.64559i	−0.0859990	−	0.148955i	−0.905816	+	0.423670i	$0.860742\pi$
$600$	−10.4570	+	4.09054i	−0.426904	+	0.166996i
$601$	−29.1223			−1.18792			−0.593962	−	0.804493i	$-0.702437\pi$
$601$	−29.1223			−1.18792			−0.593962	+	0.804493i	$0.702437\pi$
$602$	10.2650	+	4.57028i	0.418371	+	0.186271i
$603$	14.6443	+	16.2642i	0.596363	+	0.662328i
$604$	−3.77271	+	0.801914i	−0.153509	+	0.0326294i
$605$	−0.814464	+	1.06845i	−0.0331127	+	0.0434386i
$606$	−31.4395	−	6.68267i	−1.27714	−	0.271465i
$607$	−24.0802			−0.977386			−0.488693	−	0.872456i	$-0.662526\pi$
$607$	−24.0802			−0.977386			−0.488693	+	0.872456i	$0.662526\pi$
$608$	−2.84301	+	3.30414i	−0.115299	+	0.134000i
$609$	−5.89166	−	4.28054i	−0.238742	−	0.173456i
$610$	11.9355	−	15.6575i	0.483255	−	0.633953i
$611$	−0.562951	−	5.35612i	−0.0227745	−	0.216685i
$612$	1.20419	−	11.4571i	0.0486765	−	0.463126i
$613$	−0.646378	+	0.287786i	−0.0261070	+	0.0116236i	−0.419749	−	0.907640i	$-0.637882\pi$
$613$	−0.646378	+	0.287786i	−0.0261070	+	0.0116236i	0.393642	+	0.919264i	$0.371215\pi$
$614$	−2.17834	−	0.969862i	−0.0879108	−	0.0391404i
$615$	0.235941	+	0.222478i	0.00951406	+	0.00897118i
$616$	−2.41858	−	1.75720i	−0.0974475	−	0.0707998i
$617$	12.7034	−	14.1086i	0.511421	−	0.567991i	−0.431029	−	0.902338i	$-0.641849\pi$
$617$	12.7034	−	14.1086i	0.511421	−	0.567991i	0.942450	+	0.334347i	$0.108516\pi$
$618$	0.372629	+	0.645412i	0.0149893	+	0.0259623i
$619$	8.25879	+	25.4180i	0.331949	+	1.02163i	0.968205	+	0.250156i	$0.0804820\pi$
$619$	8.25879	+	25.4180i	0.331949	+	1.02163i	−0.636256	+	0.771478i	$0.719518\pi$
$620$	−1.58353	−	8.39487i	−0.0635959	−	0.337146i
$621$	10.4557	−	2.22244i	0.419574	−	0.0891833i
$622$	−13.8678	−	15.4018i	−0.556050	−	0.617556i
$623$	−2.77021	−	1.23338i	−0.110986	−	0.0494143i
$624$	−1.30042	+	2.25240i	−0.0520585	+	0.0901680i
$625$	5.50840	+	24.3856i	0.220336	+	0.975424i
$626$	−10.0657			−0.402305
$627$	4.00558	+	31.3116i	0.159967	+	1.25047i
$628$	2.23946	−	6.89234i	0.0893641	−	0.275034i
$629$	−34.3028	−	38.0971i	−1.36774	−	1.51903i
$630$	3.99703	+	1.40114i	0.159246	+	0.0558226i
$631$	5.38221	−	5.97755i	0.214262	−	0.237962i	−0.626427	−	0.779480i	$-0.715483\pi$
$631$	5.38221	−	5.97755i	0.214262	−	0.237962i	0.840689	+	0.541518i	$0.182150\pi$
$632$	1.29000	−	2.23434i	0.0513134	−	0.0888773i
$633$	−5.02840	+	5.58460i	−0.199861	+	0.221968i
$634$	−10.8592	−	7.88968i	−0.431275	−	0.313339i
$635$	−24.7398	−	23.3281i	−0.981770	−	0.925749i
$636$	−20.3189	−	9.04654i	−0.805695	−	0.358719i
$637$	0.743368	−	7.07267i	0.0294533	−	0.280230i
$638$	−9.12597	−	6.63040i	−0.361301	−	0.262500i
$639$	17.7153	−	12.8709i	0.700806	−	0.509166i
$640$	0.862271	+	2.06313i	0.0340843	+	0.0815522i
$641$	16.3523	−	7.28051i	0.645877	−	0.287563i	−0.0575369	−	0.998343i	$-0.518325\pi$
$641$	16.3523	−	7.28051i	0.645877	−	0.287563i	0.703414	+	0.710780i	$0.251658\pi$
$642$	0.891218	−	0.989798i	0.0351736	−	0.0390642i
$643$	−10.4090	+	18.0288i	−0.410489	+	0.710988i	−0.994943	−	0.100439i	$-0.967975\pi$
$643$	−10.4090	+	18.0288i	−0.410489	+	0.710988i	0.584454	+	0.811427i	$0.301309\pi$
$644$	−4.51122	−	0.958889i	−0.177767	−	0.0377855i
$645$	−60.3688	−	7.75250i	−2.37702	−	0.305254i
$646$	−23.9184	+	5.64968i	−0.941056	+	0.222283i
$647$	−13.8160	+	42.5212i	−0.543162	+	1.67168i	0.182158	+	0.983269i	$0.441692\pi$
$647$	−13.8160	+	42.5212i	−0.543162	+	1.67168i	−0.725320	+	0.688412i	$0.758308\pi$
$648$	1.14510	+	10.8949i	0.0449838	+	0.427992i
$649$	−2.67062	+	4.62566i	−0.104831	+	0.181573i
$650$	4.52330	+	3.61550i	0.177418	+	0.141812i
$651$	−3.97694	+	6.88827i	−0.155869	+	0.269972i
$652$	21.0705	+	9.38119i	0.825185	+	0.367396i
$653$	−11.9989	+	36.9289i	−0.469555	+	1.44514i	0.383608	+	0.923496i	$0.374681\pi$
$653$	−11.9989	+	36.9289i	−0.469555	+	1.44514i	−0.853163	+	0.521645i	$0.825319\pi$
$654$	12.5188	−	38.5290i	0.489525	−	1.50660i
$655$	−24.0575	−	14.6374i	−0.940005	−	0.571932i
$656$	0.0432122	−	0.0479920i	0.00168715	−	0.00187377i
$657$	19.9073			0.776656
$658$	1.33218	+	4.10002i	0.0519337	+	0.159835i
$659$	0.808798	−	7.69520i	0.0315063	−	0.299762i	−0.967410	−	0.253216i	$-0.918512\pi$
$659$	0.808798	−	7.69520i	0.0315063	−	0.299762i	0.998916	−	0.0465466i	$-0.0148216\pi$
$660$	15.2817	+	5.35691i	0.594839	+	0.208517i
$661$	10.3444	+	4.60562i	0.402350	+	0.179138i	0.597927	−	0.801551i	$-0.295991\pi$
$661$	10.3444	+	4.60562i	0.402350	+	0.179138i	−0.195577	+	0.980688i	$0.562658\pi$
$662$	−4.49078	+	1.99942i	−0.174539	+	0.0777098i
$663$	−13.3964	+	5.96447i	−0.520274	+	0.231641i
$664$	−5.23878	+	3.80619i	−0.203304	+	0.147709i
$665$	0.00437864	−	9.03578i	0.000169796	−	0.350393i
$666$	−15.0296	−	10.9197i	−0.582386	−	0.423128i
$667$	−17.0220	−	3.61815i	−0.659096	−	0.140095i
$668$	−4.86211	+	8.42141i	−0.188120	+	0.325834i
$669$	−1.03906	+	1.15399i	−0.0401723	+	0.0446159i
$670$	−13.6288	−	19.6956i	−0.526527	−	0.760907i
$671$	−27.7727	+	5.90327i	−1.07215	+	0.227893i
$672$	0.643340	−	1.98000i	0.0248174	−	0.0763800i
$673$	18.2562	−	13.2639i	0.703724	−	0.511286i	−0.177419	−	0.984135i	$-0.556775\pi$
$673$	18.2562	−	13.2639i	0.703724	−	0.511286i	0.881143	+	0.472850i	$0.156775\pi$
$674$	14.4671	+	25.0578i	0.557253	+	0.965191i
$675$	10.7319	+	0.494016i	0.413070	+	0.0190147i
$676$	−11.6587			−0.448412
$677$	5.47218	−	3.97577i	0.210313	−	0.152801i	−0.477642	−	0.878554i	$-0.658508\pi$
$677$	5.47218	−	3.97577i	0.210313	−	0.152801i	0.687955	+	0.725753i	$0.258508\pi$
$678$	−17.7149	+	3.76542i	−0.680337	+	0.144610i
$679$	6.71864	+	7.46180i	0.257838	+	0.286358i
$680$	−2.90417	+	12.2685i	−0.111370	+	0.470474i
$681$	−50.6271	−	10.7611i	−1.94004	−	0.412367i
$682$	−6.16014	+	10.6697i	−0.235884	+	0.408563i
$683$	−10.5871	−	32.5836i	−0.405102	−	1.24678i	−0.920810	−	0.390012i	$-0.872471\pi$
$683$	−10.5871	−	32.5836i	−0.405102	−	1.24678i	0.515707	−	0.856765i	$-0.327529\pi$
$684$	−8.05260	+	3.80474i	−0.307899	+	0.145478i
$685$	18.8285	−	39.8000i	0.719400	−	1.52068i
$686$	1.27336	+	12.1153i	0.0486173	+	0.462563i
$687$	−34.5746	+	15.3936i	−1.31910	+	0.587303i
$688$	−1.26695	+	12.0542i	−0.0483021	+	0.459564i
$689$	1.19897	+	11.4075i	0.0456773	+	0.434590i
$690$	24.8985	−	2.03924i	0.947869	−	0.0776325i
$691$	−18.3663	−	13.3439i	−0.698686	−	0.507625i	0.180818	−	0.983517i	$-0.442125\pi$
$691$	−18.3663	−	13.3439i	−0.698686	−	0.507625i	−0.879504	+	0.475892i	$0.842125\pi$
$692$	1.59193	+	4.89946i	0.0605161	+	0.186249i
$693$	−3.05414	−	5.28993i	−0.116017	−	0.200948i
$694$	−2.53696	+	2.81758i	−0.0963017	+	0.106954i
$695$	−0.813532	−	0.767111i	−0.0308590	−	0.0290982i
$696$	2.42749	−	7.47106i	0.0920139	−	0.283190i
$697$	0.356159	−	0.0757040i	0.0134905	−	0.00286749i
$698$	1.22606	+	11.6652i	0.0464072	+	0.441535i
$699$	−24.6417	−	42.6806i	−0.932033	−	1.61433i
$700$	−4.14334	−	2.07805i	−0.156604	−	0.0785431i
$701$	−15.5291	+	26.8972i	−0.586526	+	1.01589i	0.408157	+	0.912912i	$0.366171\pi$
$701$	−15.5291	+	26.8972i	−0.586526	+	1.01589i	−0.994683	+	0.102981i	$0.967162\pi$
$702$	2.01318	−	1.46266i	0.0759826	−	0.0552046i
$703$	−11.3954	+	37.9589i	−0.429786	+	1.43165i
$704$	0.996511	−	3.06694i	0.0375574	−	0.115590i
$705$	−13.2876	−	19.2024i	−0.500439	−	0.723205i
$706$	−3.80166	−	0.808067i	−0.143077	−	0.0304120i
$707$	−6.63424	−	11.4908i	−0.249506	−	0.432157i
$708$	−3.63833	−	0.773350i	−0.136737	−	0.0290643i
$709$	−2.76209	+	26.2795i	−0.103732	+	0.986948i	0.811590	+	0.584227i	$0.198602\pi$
$709$	−2.76209	+	26.2795i	−0.103732	+	0.986948i	−0.915323	+	0.402721i	$0.868065\pi$
$710$	−21.0235	+	11.5016i	−0.788999	+	0.431646i
$711$	4.26474	−	3.09851i	0.159940	−	0.116203i
$712$	0.341912	−	3.25307i	0.0128137	−	0.121914i
$713$	−1.98674	+	18.9026i	−0.0744041	+	0.707907i
$714$	9.49642	−	6.89955i	0.355395	−	0.258209i
$715$	−1.54797	−	8.20640i	−0.0578909	−	0.306902i
$716$	−0.564667	+	5.37245i	−0.0211026	+	0.200778i
$717$	15.0783	+	3.20499i	0.563108	+	0.119692i
$718$	13.8193	+	23.9357i	0.515732	+	0.893274i
$719$	24.9323	+	5.29953i	0.929819	+	0.197639i	0.647836	−	0.761780i	$-0.275674\pi$
$719$	24.9323	+	5.29953i	0.929819	+	0.197639i	0.281983	+	0.959419i	$0.409008\pi$
$720$	−0.105073	+	4.56758i	−0.00391584	+	0.170224i
$721$	−0.0950689	+	0.292592i	−0.00354055	+	0.0108967i
$722$	13.3362	+	13.5331i	0.496322	+	0.503651i
$723$	−2.57557	+	1.87126i	−0.0957866	+	0.0695931i
$724$	3.39175	−	5.87469i	0.126054	−	0.218331i
$725$	−15.6340	−	7.84106i	−0.580631	−	0.291210i
$726$	0.674636	+	1.16850i	0.0250381	+	0.0433672i
$727$	3.50468	+	33.3448i	0.129981	+	1.23669i	0.843915	+	0.536477i	$0.180245\pi$
$727$	3.50468	+	33.3448i	0.129981	+	1.23669i	−0.713933	+	0.700214i	$0.753088\pi$
$728$	−1.05019	+	0.223225i	−0.0389227	+	0.00827327i
$729$	−2.44358	+	7.52058i	−0.0905031	+	0.278540i
$730$	−21.6087	−	2.77497i	−0.799774	−	0.102706i
$731$	−45.7279	+	50.7859i	−1.69131	+	1.87839i
$732$	−9.88641	−	17.1238i	−0.365412	−	0.632912i
$733$	−0.00324076	−	0.00997405i	−0.000119700	−	0.000368400i	0.950997	−	0.309201i	$-0.100062\pi$
$733$	−0.00324076	−	0.00997405i	−0.000119700	−	0.000368400i	−0.951116	+	0.308833i	$0.900062\pi$
$734$	27.1194	+	19.7034i	1.00100	+	0.727265i
$735$	−11.8907	−	28.4504i	−0.438595	−	1.04941i
$736$	−0.520020	−	4.94766i	−0.0191682	−	0.182373i
$737$	−3.61058	+	34.3523i	−0.132997	+	1.26538i
$738$	0.120543	−	0.0536691i	0.00443724	−	0.00197559i
$739$	−0.206851	−	1.96805i	−0.00760912	−	0.0723960i	0.990058	−	0.140657i	$-0.0449215\pi$
$739$	−0.206851	−	1.96805i	−0.00760912	−	0.0723960i	−0.997667	+	0.0682612i	$0.978255\pi$
$740$	14.7920	+	13.9480i	0.543766	+	0.512738i
$741$	9.31937	+	6.45544i	0.342356	+	0.237146i
$742$	−2.83728	−	8.73224i	−0.104160	−	0.320570i
$743$	−15.0320	+	26.0362i	−0.551471	+	0.955176i	0.446697	+	0.894685i	$0.352600\pi$
$743$	−15.0320	+	26.0362i	−0.551471	+	0.955176i	−0.998169	+	0.0604913i	$0.980733\pi$
$744$	−8.39228	−	1.78383i	−0.307676	−	0.0653985i
$745$	9.77058	−	8.39874i	0.357966	−	0.307706i
$746$	−1.59764	−	1.77436i	−0.0584939	−	0.0649641i
$747$	−12.9417	+	2.75085i	−0.473513	+	0.100648i
$748$	14.7096	−	10.6872i	0.537837	−	0.390761i
$749$	0.549823			0.0200901
$750$	24.7299	+	4.33983i	0.903009	+	0.158468i
$751$	−25.6221	−	44.3787i	−0.934962	−	1.61940i	−0.774701	−	0.632327i	$-0.782100\pi$
$751$	−25.6221	−	44.3787i	−0.934962	−	1.61940i	−0.160261	−	0.987075i	$-0.551233\pi$
$752$	−3.76213	+	2.73334i	−0.137191	+	0.0996748i
$753$	11.5416	−	35.5215i	0.420600	−	1.29447i
$754$	−3.96266	+	0.842289i	−0.144311	+	0.0306743i
$755$	8.13892	+	2.85305i	0.296206	+	0.103833i
$756$	−1.33284	+	1.48027i	−0.0484751	+	0.0538370i
$757$	2.63864	−	4.57025i	0.0959028	−	0.166109i	−0.814082	−	0.580750i	$-0.802760\pi$
$757$	2.63864	−	4.57025i	0.0959028	−	0.166109i	0.909985	+	0.414641i	$0.136093\pi$
$758$	30.8559	+	6.55863i	1.12074	+	0.238220i
$759$	−29.1472	−	21.1767i	−1.05798	−	0.768665i
$760$	9.27121	−	3.00743i	0.336302	−	0.109091i
$761$	−1.77096	+	1.28668i	−0.0641974	+	0.0466421i	−0.619421	−	0.785059i	$-0.712633\pi$
$761$	−1.77096	+	1.28668i	−0.0641974	+	0.0466421i	0.555224	+	0.831701i	$0.312633\pi$
$762$	−31.1980	+	13.8903i	−1.13019	+	0.503191i
$763$	15.2778	−	6.80212i	0.553094	−	0.246253i
$764$	−0.456183	−	0.203106i	−0.0165041	−	0.00734810i
$765$	−15.6166	+	20.4865i	−0.564619	+	0.740691i
$766$	2.92882	−	27.8659i	0.105823	−	1.00684i
$767$	0.592769	+	1.82436i	0.0214037	+	0.0658737i
$768$	2.24571			0.0810352
$769$	−0.0847564	+	0.0941315i	−0.00305639	+	0.00339447i	−0.744671	−	0.667432i	$-0.767394\pi$
$769$	−0.0847564	+	0.0941315i	−0.00305639	+	0.00339447i	0.741615	+	0.670826i	$0.234060\pi$
$770$	2.57779	+	6.16778i	0.0928970	+	0.222272i
$771$	4.38734	−	13.5028i	0.158006	−	0.486293i
$772$	−5.07880	+	15.6309i	−0.182790	+	0.562570i
$773$	−21.2511	−	9.46159i	−0.764348	−	0.340310i	−0.0127393	−	0.999919i	$-0.504055\pi$
$773$	−21.2511	−	9.46159i	−0.764348	−	0.340310i	−0.751609	+	0.659609i	$0.770722\pi$
$774$	−12.3826	+	21.4473i	−0.445083	+	0.770906i
$775$	−6.73218	+	17.8769i	−0.241827	+	0.642159i
$776$	−5.41547	+	9.37987i	−0.194404	+	0.336718i
$777$	−1.97864	−	18.8255i	−0.0709834	−	0.675361i
$778$	5.58413	−	17.1862i	0.200201	−	0.616155i
$779$	−0.193020	−	0.204899i	−0.00691564	−	0.00734126i
$780$	5.10205	−	2.79123i	0.182683	−	0.0999422i
$781$	33.8048	+	7.18544i	1.20963	+	0.257115i
$782$	14.0249	−	24.2918i	0.501530	−	0.868675i
$783$	−5.02918	+	5.58547i	−0.179728	+	0.199609i
$784$	−5.60969	+	2.49760i	−0.200346	+	0.0891999i
$785$	−12.2887	+	10.5633i	−0.438604	+	0.377022i
$786$	−22.8807	+	16.6238i	−0.816126	+	0.592950i
$787$	−26.7494	−	19.4346i	−0.953512	−	0.692767i	−0.00187698	−	0.999998i	$-0.500597\pi$
$787$	−26.7494	−	19.4346i	−0.953512	−	0.692767i	−0.951635	+	0.307231i	$0.900597\pi$
$788$	−0.665431	+	6.33115i	−0.0237050	+	0.225538i
$789$	−50.6654	−	22.5577i	−1.80374	−	0.803075i
$790$	−5.06116	+	2.76886i	−0.180068	+	0.0985115i
$791$	−6.04842	−	4.39443i	−0.215057	−	0.156248i
$792$	4.40886	−	4.89653i	0.156662	−	0.173991i
$793$	−5.09853	+	8.83091i	−0.181054	+	0.313595i
$794$	6.23580	−	6.92556i	0.221300	−	0.245779i
$795$	28.2999	+	40.8974i	1.00369	+	1.45048i
$796$	−6.71789	−	7.46098i	−0.238109	−	0.264447i
$797$	−8.14374	+	25.0639i	−0.288466	+	0.887807i	0.696872	+	0.717195i	$0.254574\pi$
$797$	−8.14374	+	25.0639i	−0.288466	+	0.887807i	−0.985338	+	0.170612i	$0.945426\pi$
$798$	−8.37120	−	3.50346i	−0.296337	−	0.124021i
$799$	−26.2192			−0.927570
$800$	0.750750	−	4.94332i	0.0265430	−	0.174773i
$801$	3.34168	−	5.78796i	0.118073	−	0.204508i
$802$	−31.6788	−	14.1043i	−1.11862	−	0.498041i
$803$	21.0236	+	23.3490i	0.741905	+	0.823969i
$804$	−23.5289	+	5.00121i	−0.829799	+	0.176379i
$805$	7.50314	+	7.07501i	0.264451	+	0.249361i
$806$	1.36730	+	4.20812i	0.0481611	+	0.148225i
$807$	24.4294	+	42.3130i	0.859957	+	1.48949i
$808$	9.57696	−	10.6363i	0.336916	−	0.374184i
$809$	26.8855	+	19.5335i	0.945245	+	0.686761i	0.949678	−	0.313229i	$-0.101411\pi$
$809$	26.8855	+	19.5335i	0.945245	+	0.686761i	−0.00443216	+	0.999990i	$0.501411\pi$
$810$	10.4754	−	22.1431i	0.368068	−	0.778029i
$811$	8.24321	+	3.67011i	0.289458	+	0.128875i	0.546329	−	0.837571i	$-0.316025\pi$
$811$	8.24321	+	3.67011i	0.289458	+	0.128875i	−0.256871	+	0.966446i	$0.582692\pi$
$812$	2.96248	−	1.31898i	0.103963	−	0.0462872i
$813$	−2.10652	+	20.0422i	−0.0738788	+	0.702909i
$814$	−3.06485	−	29.1601i	−0.107423	−	1.02206i
$815$	−29.3468	−	42.4103i	−1.02797	−	1.48557i
$816$	10.2437	+	7.44247i	0.358601	+	0.260539i
$817$	51.9123	+	9.81828i	1.81618	+	0.343498i
$818$	15.4655			0.540738
$819$	−2.14578	−	0.456099i	−0.0749795	−	0.0159374i
$820$	−0.138327	+	0.0414532i	−0.00483058	+	0.00144761i
$821$	−52.8582	+	11.2354i	−1.84476	+	0.392117i	−0.991580	−	0.129494i	$-0.958665\pi$
$821$	−52.8582	+	11.2354i	−1.84476	+	0.392117i	−0.853183	+	0.521611i	$0.825331\pi$
$822$	−29.5882	−	32.8610i	−1.03201	−	1.14616i
$823$	44.8636	+	19.9746i	1.56385	+	0.696269i	0.992249	−	0.124265i	$-0.0396573\pi$
$823$	44.8636	+	19.9746i	1.56385	+	0.696269i	0.571597	+	0.820534i	$0.306324\pi$
$824$	−0.331858			−0.0115608
$825$	−22.9659	−	27.9946i	−0.799571	−	0.974649i
$826$	−0.767745	−	1.32977i	−0.0267133	−	0.0462687i
$827$	−38.8153	−	17.2817i	−1.34974	−	0.600942i	−0.400731	−	0.916196i	$-0.631244\pi$
$827$	−38.8153	−	17.2817i	−1.34974	−	0.600942i	−0.949008	+	0.315253i	$0.897910\pi$
$828$	3.14111	−	9.66736i	0.109161	−	0.335964i
$829$	0.251969	−	0.775482i	0.00875126	−	0.0269336i	−0.946586	−	0.322453i	$-0.895493\pi$
$829$	0.251969	−	0.775482i	0.00875126	−	0.0269336i	0.955337	+	0.295519i	$0.0954926\pi$
$830$	14.4313	−	1.18195i	0.500918	−	0.0410262i
$831$	33.5806	+	7.13777i	1.16490	+	0.247606i
$832$	−0.579069	−	1.00298i	−0.0200756	−	0.0347720i
$833$	−33.8655	−	7.19834i	−1.17337	−	0.249408i
$834$	−1.02590	+	0.456760i	−0.0355240	+	0.0158163i
$835$	19.0759	−	10.4360i	0.660149	−	0.361154i
$836$	−12.9667	−	5.42673i	−0.448462	−	0.187687i
$837$	6.64116	+	4.82508i	0.229552	+	0.166779i
$838$	12.0343	−	5.35800i	0.415717	−	0.185089i
$839$	−1.34863	−	12.8314i	−0.0465599	−	0.442988i	−0.992823	−	0.119591i	$-0.961842\pi$
$839$	−1.34863	−	12.8314i	−0.0465599	−	0.442988i	0.946263	−	0.323397i	$-0.104825\pi$
$840$	−3.53025	+	3.03458i	−0.121805	+	0.104703i
$841$	−15.3146	+	6.81849i	−0.528089	+	0.235120i
$842$	14.9414	−	16.5941i	0.514914	−	0.571869i
$843$	74.2038			2.55572
$844$	−1.03406	−	3.18252i	−0.0355939	−	0.109547i
$845$	22.2713	+	13.5506i	0.766155	+	0.466156i
$846$	−9.29385	+	1.97547i	−0.319529	+	0.0679180i
$847$	−0.172120	+	0.529731i	−0.00591412	+	0.0182018i
$848$	8.01259	−	5.82149i	0.275153	−	0.199911i
$849$	−18.8940	−	32.7254i	−0.648441	−	1.12313i
$850$	19.8070	−	20.0606i	0.679376	−	0.688073i
$851$	−22.6167	−	39.1733i	−0.775292	−	1.34284i
$852$	2.51573	+	23.9356i	0.0861874	+	0.820018i
$853$	−27.2094	−	30.2191i	−0.931633	−	1.03468i	−0.999316	−	0.0369764i	$-0.988227\pi$
$853$	−27.2094	−	30.2191i	−0.931633	−	1.03468i	0.0676831	−	0.997707i	$-0.478439\pi$
$854$	2.52232	−	7.76291i	0.0863121	−	0.265641i
$855$	19.8048	+	2.09127i	0.677309	+	0.0715199i
$856$	0.183274	+	0.564060i	0.00626418	+	0.0192792i
$857$	26.9539	−	46.6856i	0.920729	−	1.59475i	0.122438	−	0.992476i	$-0.460929\pi$
$857$	26.9539	−	46.6856i	0.920729	−	1.59475i	0.798291	−	0.602273i	$-0.205738\pi$
$858$	−8.20386	−	1.74378i	−0.280075	−	0.0595318i
$859$	2.37349	−	22.5822i	0.0809823	−	0.770496i	−0.876383	−	0.481615i	$-0.840050\pi$
$859$	2.37349	−	22.5822i	0.0809823	−	0.770496i	0.957365	−	0.288880i	$-0.0932830\pi$
$860$	16.4305	−	21.5543i	0.560277	−	0.734995i
$861$	0.122824	+	0.0546848i	0.00418584	+	0.00186365i
$862$	−12.5754	−	9.13656i	−0.428319	−	0.311192i
$863$	6.88007	+	4.99866i	0.234200	+	0.170156i	0.698696	−	0.715419i	$-0.253764\pi$
$863$	6.88007	+	4.99866i	0.234200	+	0.170156i	−0.464495	+	0.885576i	$0.653764\pi$
$864$	−1.96289	−	0.873933i	−0.0667787	−	0.0297318i
$865$	2.65350	−	11.2095i	0.0902217	−	0.381135i
$866$	−4.23014	−	3.07337i	−0.143746	−	0.104437i
$867$	10.2636	+	31.5882i	0.348571	+	1.07279i
$868$	−1.77090	−	3.06730i	−0.0601084	−	0.104111i
$869$	8.13810	+	1.72981i	0.276066	+	0.0586796i
$870$	−13.3206	+	11.4503i	−0.451610	+	0.388202i
$871$	8.30068	+	9.21884i	0.281258	+	0.312368i
$872$	12.0708	+	13.4060i	0.408771	+	0.453986i
$873$	−17.9036	+	13.0077i	−0.605944	+	0.440244i
$874$	−21.6797	+	0.488210i	−0.733325	+	0.0165140i
$875$	5.49963	+	8.78534i	0.185921	+	0.296999i
$876$	−10.9401	+	18.9487i	−0.369630	+	0.640219i
$877$	4.15911	+	39.5713i	0.140443	+	1.33623i	0.806902	+	0.590686i	$0.201143\pi$
$877$	4.15911	+	39.5713i	0.140443	+	1.33623i	−0.666459	+	0.745542i	$0.732191\pi$
$878$	6.62125	−	1.40739i	0.223456	−	0.0474971i
$879$	−47.7525	−	53.0345i	−1.61065	−	1.78881i
$880$	−5.46823	+	4.70046i	−0.184334	+	0.158453i
$881$	−1.26938	−	3.90675i	−0.0427665	−	0.131622i	0.927394	−	0.374087i	$-0.122044\pi$
$881$	−1.26938	−	3.90675i	−0.0427665	−	0.131622i	−0.970160	+	0.242465i	$0.922044\pi$
$882$	−12.5466			−0.422465
$883$	−16.8391	+	18.7017i	−0.566681	+	0.629363i	−0.956571	−	0.291499i	$-0.905846\pi$
$883$	−16.8391	+	18.7017i	−0.566681	+	0.629363i	0.389891	+	0.920861i	$0.372513\pi$
$884$	0.682557	−	6.49410i	0.0229569	−	0.218420i
$885$	6.05133	+	5.70604i	0.203413	+	0.191806i
$886$	−3.40222	+	2.47185i	−0.114300	+	0.0830436i
$887$	−0.231533	+	2.20289i	−0.00777413	+	0.0739659i	−0.997721	−	0.0674732i	$-0.978506\pi$
$887$	−0.231533	+	2.20289i	−0.00777413	+	0.0739659i	0.989947	+	0.141439i	$0.0451730\pi$
$888$	18.6534	−	8.30504i	0.625968	−	0.278699i
$889$	−12.8788	−	5.73403i	−0.431943	−	0.192313i
$890$	−4.43410	+	5.81684i	−0.148631	+	0.194981i
$891$	−32.2729	+	14.3688i	−1.08118	+	0.481374i
$892$	−0.213677	−	0.657629i	−0.00715442	−	0.0220191i
$893$	10.5276	+	17.3217i	0.352293	+	0.579647i
$894$	−3.99861	−	12.3065i	−0.133734	−	0.411590i
$895$	7.32292	−	9.60651i	0.244778	−	0.321110i
$896$	0.620319	+	0.688934i	0.0207234	+	0.0230157i
$897$	−12.6562	+	2.69016i	−0.422579	+	0.0898220i
$898$	1.95823	+	18.6313i	0.0653470	+	0.621735i
$899$	−6.68210	−	11.5737i	−0.222861	−	0.386006i
$900$	5.50949	−	8.60317i	0.183650	−	0.286772i
$901$	55.8418			1.86036
$902$	0.190250	+	0.0847049i	0.00633464	+	0.00282036i
$903$	−24.6824	+	5.24641i	−0.821380	+	0.174590i
$904$	2.49208	−	7.66985i	0.0828855	−	0.255095i
$905$	−13.3072	+	7.28008i	−0.442345	+	0.241998i
$906$	5.79581	−	6.43689i	0.192553	−	0.213851i
$907$	15.9619	−	27.6469i	0.530008	−	0.918000i	−0.469379	−	0.882997i	$-0.655522\pi$
$907$	15.9619	−	27.6469i	0.530008	−	0.918000i	0.999387	−	0.0350037i	$-0.0111443\pi$
$908$	15.4218	−	17.1277i	0.511791	−	0.568401i
$909$	26.7155	−	11.8945i	0.886096	−	0.394516i
$910$	2.26559	+	0.794191i	0.0751037	+	0.0263272i
$911$	−1.68380	+	1.22335i	−0.0557869	+	0.0405315i	−0.615329	−	0.788270i	$-0.710977\pi$
$911$	−1.68380	+	1.22335i	−0.0557869	+	0.0405315i	0.559542	+	0.828802i	$0.310977\pi$
$912$	0.803778	−	9.75578i	0.0266157	−	0.323046i
$913$	−16.8939	−	12.2741i	−0.559106	−	0.406214i
$914$	−2.96507	−	28.2107i	−0.0980757	−	0.933127i
$915$	−1.01682	+	44.2017i	−0.0336151	+	1.46126i
$916$	1.76160	−	16.7605i	0.0582049	−	0.553783i
$917$	−11.4200	−	2.42739i	−0.377121	−	0.0801595i
$918$	−6.05730	−	10.4916i	−0.199921	−	0.346273i
$919$	8.04443	+	24.7582i	0.265361	+	0.816698i	0.991610	+	0.129266i	$0.0412621\pi$
$919$	8.04443	+	24.7582i	0.265361	+	0.816698i	−0.726249	+	0.687432i	$0.758738\pi$
$920$	−4.75716	+	10.0558i	−0.156839	+	0.331529i
$921$	5.23787	−	1.11334i	0.172594	−	0.0366859i
$922$	−24.8182	+	5.27528i	−0.817345	+	0.173732i
$923$	10.0414	−	7.29548i	0.330516	−	0.240134i
$924$	6.71363			0.220862
$925$	−12.0454	−	43.8368i	−0.396049	−	1.44134i
$926$	10.7386	−	18.5998i	0.352892	−	0.611227i
$927$	−0.619438	−	0.275792i	−0.0203450	−	0.00905819i
$928$	2.34063	+	2.59953i	0.0768349	+	0.0853338i
$929$	10.1988	+	11.3270i	0.334613	+	0.371625i	0.886847	−	0.462064i	$-0.152891\pi$
$929$	10.1988	+	11.3270i	0.334613	+	0.371625i	−0.552234	+	0.833689i	$0.686224\pi$
$930$	13.9582	+	13.1617i	0.457707	+	0.431590i
$931$	8.84221	+	25.2635i	0.289792	+	0.827976i
$932$	21.9455			0.718849
$933$	45.5257	+	9.67678i	1.49044	+	0.316804i
$934$	20.3576	−	9.06380i	0.666122	−	0.296577i
$935$	−40.5207	+	3.31873i	−1.32517	+	0.108534i
$936$	−0.247349	−	2.35337i	−0.00808486	−	0.0769223i
$937$	−0.240544	+	2.28863i	−0.00785825	+	0.0747662i	−0.997748	−	0.0670715i	$-0.978634\pi$
$937$	−0.240544	+	2.28863i	−0.00785825	+	0.0747662i	0.989890	+	0.141838i	$0.0453011\pi$
$938$	−8.03348	−	5.83667i	−0.262303	−	0.190574i
$939$	18.2875	−	13.2866i	0.596790	−	0.433593i
$940$	10.3636	−	0.848797i	0.338022	−	0.0276847i
$941$	−3.31982	+	31.5860i	−0.108223	+	1.02967i	0.796781	+	0.604269i	$0.206535\pi$
$941$	−3.31982	+	31.5860i	−0.108223	+	1.02967i	−0.905004	+	0.425404i	$0.860132\pi$
$942$	5.02918	+	15.4782i	0.163859	+	0.504308i
$943$	0.321278			0.0104623
$944$	1.10829	−	1.23088i	0.0360718	−	0.0400618i
$945$	4.26657	−	1.27859i	0.138792	−	0.0415925i
$946$	−38.2322	+	8.12651i	−1.24304	+	0.264216i
$947$	0.0840147	+	0.0933078i	0.00273011	+	0.00303209i	0.744508	−	0.667613i	$-0.232684\pi$
$947$	0.0840147	+	0.0933078i	0.00273011	+	0.00303209i	−0.741778	+	0.670645i	$0.766017\pi$
$948$	0.605630	+	5.76219i	0.0196700	+	0.187147i
$949$	11.2838			0.366288
$950$	−21.2059	−	5.03069i	−0.688012	−	0.163217i
$951$	30.1436			0.977473
$952$	0.546365	+	5.19832i	0.0177078	+	0.168478i
$953$	−6.42466	−	7.13530i	−0.208115	−	0.231135i	0.630046	−	0.776558i	$-0.283036\pi$
$953$	−6.42466	−	7.13530i	−0.208115	−	0.231135i	−0.838161	+	0.545422i	$0.816369\pi$
$954$	19.7941	−	4.20736i	0.640857	−	0.136218i
$955$	0.635366	+	0.918195i	0.0205600	+	0.0297121i
$956$	−4.59308	+	5.10113i	−0.148551	+	0.164982i
$957$	25.3323			0.818878
$958$	−5.19134	−	15.9773i	−0.167725	−	0.516203i
$959$	1.90806	−	18.1540i	0.0616145	−	0.586223i
$960$	−4.28991	−	2.61013i	−0.138456	−	0.0842417i
$961$	13.2709	−	9.64186i	0.428093	−	0.311028i
$962$	−8.51907	−	6.18947i	−0.274666	−	0.199556i
$963$	−0.126669	+	1.20517i	−0.00408184	+	0.0388361i
$964$	−0.148182	−	1.40986i	−0.00477264	−	0.0454086i
$965$	27.8693	−	23.9563i	0.897144	−	0.771181i
$966$	9.46180	−	4.21266i	0.304428	−	0.135540i
$967$	44.9349	+	9.55120i	1.44501	+	0.307146i	0.862656	−	0.505791i	$-0.168799\pi$
$967$	44.9349	+	9.55120i	1.44501	+	0.307146i	0.582352	+	0.812937i	$0.302133\pi$
$968$	−0.600821			−0.0193111
$969$	35.9978	−	41.8366i	1.15642	−	1.34399i
$970$	21.2470	−	11.6238i	0.682199	−	0.373218i
$971$	2.39147	+	2.65600i	0.0767460	+	0.0852351i	0.780295	−	0.625412i	$-0.215069\pi$
$971$	2.39147	+	2.65600i	0.0767460	+	0.0852351i	−0.703549	+	0.710647i	$0.748402\pi$
$972$	−12.1485	−	13.4923i	−0.389663	−	0.432765i
$973$	−0.423502	−	0.188555i	−0.0135768	−	0.00604480i
$974$	17.9455	−	31.0825i	0.575010	−	0.995946i
$975$	−12.9905	−	0.597985i	−0.416028	−	0.0191508i
$976$	8.80470			0.281831
$977$	6.01121	−	4.36740i	0.192316	−	0.139726i	−0.487461	−	0.873145i	$-0.662077\pi$
$977$	6.01121	−	4.36740i	0.192316	−	0.139726i	0.679777	+	0.733419i	$0.262077\pi$
$978$	−50.6644	+	10.7691i	−1.62007	+	0.344357i
$979$	10.3177	−	2.19310i	0.329755	−	0.0700917i
$980$	13.6189	+	1.74892i	0.435040	+	0.0558673i
$981$	11.3900	+	35.0549i	0.363656	+	1.11922i
$982$	10.2334	+	17.7248i	0.326561	+	0.565621i
$983$	25.3277	+	5.38356i	0.807827	+	0.171709i	0.593271	−	0.805003i	$-0.297836\pi$
$983$	25.3277	+	5.38356i	0.807827	+	0.171709i	0.214556	+	0.976712i	$0.431170\pi$
$984$	−0.0151595	+	0.144233i	−0.000483267	+	0.00459797i
$985$	8.62969	−	11.3208i	0.274965	−	0.360710i
$986$	2.06158	+	19.6146i	0.0656542	+	0.624658i
$987$	−7.83234	−	5.69052i	−0.249306	−	0.181131i
$988$	−4.56437	+	2.15660i	−0.145212	+	0.0686105i
$989$	−48.7830	+	35.4429i	−1.55121	+	1.12702i
$990$	−14.1132	+	4.22939i	−0.448547	+	0.134419i
$991$	−2.34093	+	1.04225i	−0.0743622	+	0.0331082i	−0.443581	−	0.896234i	$-0.646292\pi$
$991$	−2.34093	+	1.04225i	−0.0743622	+	0.0331082i	0.369219	+	0.929343i	$0.379625\pi$
$992$	2.55642	−	2.83919i	0.0811664	−	0.0901444i
$993$	5.51970	−	9.56041i	0.175163	−	0.303390i
$994$	−6.64798	+	7.38333i	−0.210861	+	0.234185i
$995$	4.16127	+	22.0605i	0.131921	+	0.699365i
$996$	4.49375	−	13.8303i	0.142390	−	0.438231i
$997$	−15.9506	+	3.39041i	−0.505161	+	0.107375i	−0.453441	−	0.891286i	$-0.649804\pi$
$997$	−15.9506	+	3.39041i	−0.505161	+	0.107375i	−0.0517202	+	0.998662i	$0.516470\pi$
$998$	28.7226	+	12.7881i	0.909199	+	0.404802i
$999$	−19.5362			−0.618097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.r.b.11.21	✓	200
19.7	even	3	inner	950.2.r.b.311.5	yes	200
25.16	even	5	inner	950.2.r.b.391.5	yes	200
475.216	even	15	inner	950.2.r.b.691.21	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.r.b.11.21	✓	200	1.1	even	1	trivial
950.2.r.b.311.5	yes	200	19.7	even	3	inner
950.2.r.b.391.5	yes	200	25.16	even	5	inner
950.2.r.b.691.21	yes	200	475.216	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.r (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(1.50267 + 1.66889i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.11017 + 0.739709i) q^{5} +(1.50267 - 1.66889i) q^{6} +0.927052 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.213575 + 2.03203i) q^{9} +O(q^{10})\)	\(q+(-0.104528 - 0.994522i) q^{2} +(1.50267 + 1.66889i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.11017 + 0.739709i) q^{5} +(1.50267 - 1.66889i) q^{6} +0.927052 q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.213575 + 2.03203i) q^{9} +(0.515083 - 2.17593i) q^{10} +(-2.60890 + 1.89548i) q^{11} +(-1.81682 - 1.32000i) q^{12} +(-0.121058 + 1.15179i) q^{13} +(-0.0969033 - 0.921973i) q^{14} +(1.93641 + 4.63319i) q^{15} +(0.913545 - 0.406737i) q^{16} +(5.51504 + 1.17226i) q^{17} +2.04322 q^{18} +(-1.43996 - 4.11418i) q^{19} +(-2.21785 - 0.284814i) q^{20} +(1.39306 + 1.54715i) q^{21} +(2.15780 + 2.39648i) q^{22} +(4.54481 + 2.02348i) q^{23} +(-1.12286 + 1.94484i) q^{24} +(3.90566 + 3.12183i) q^{25} +1.15814 q^{26} +(1.73829 - 1.26294i) q^{27} +(-0.906793 + 0.192745i) q^{28} +(-3.42158 + 0.727278i) q^{29} +(4.40540 - 2.41010i) q^{30} +(1.18060 + 3.63352i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-7.08366 - 1.50568i) q^{33} +(0.589358 - 5.60736i) q^{34} +(1.95624 + 0.685748i) q^{35} +(-0.213575 - 2.03203i) q^{36} +(-7.35584 - 5.34433i) q^{37} +(-3.94113 + 1.86212i) q^{38} +(-2.10413 + 1.52874i) q^{39} +(-0.0514252 + 2.23548i) q^{40} +(0.0589964 - 0.0262669i) q^{41} +(1.39306 - 1.54715i) q^{42} +(-6.06032 + 10.4968i) q^{43} +(2.15780 - 2.39648i) q^{44} +(-1.95379 + 4.12995i) q^{45} +(1.53733 - 4.73142i) q^{46} +(-4.54862 + 0.966840i) q^{47} +(2.05156 + 0.913413i) q^{48} -6.14058 q^{49} +(2.69647 - 4.21059i) q^{50} +(6.33094 + 10.9655i) q^{51} +(-0.121058 - 1.15179i) q^{52} +(9.68768 - 2.05918i) q^{53} +(-1.43772 - 1.59675i) q^{54} +(-6.90733 + 2.06996i) q^{55} +(0.286475 + 0.881678i) q^{56} +(4.70232 - 8.58542i) q^{57} +(1.08095 + 3.32681i) q^{58} +(1.51312 - 0.673684i) q^{59} +(-2.85739 - 4.12934i) q^{60} +(8.04349 + 3.58119i) q^{61} +(3.49021 - 1.55394i) q^{62} +(-0.197995 + 1.88380i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.10745 + 2.34094i) q^{65} +(-0.756987 + 7.20225i) q^{66} +(7.16726 - 7.96005i) q^{67} -5.63825 q^{68} +(3.45241 + 10.6254i) q^{69} +(0.477509 - 2.01720i) q^{70} +(-7.17110 - 7.96432i) q^{71} +(-1.99857 + 0.424810i) q^{72} +(-1.01843 - 9.68969i) q^{73} +(-4.54616 + 7.87418i) q^{74} +(0.658958 + 11.2092i) q^{75} +(2.26388 + 3.72489i) q^{76} +(-2.41858 + 1.75720i) q^{77} +(1.74030 + 1.93280i) q^{78} +(-1.72635 - 1.91731i) q^{79} +(2.22861 - 0.182527i) q^{80} +(10.7155 + 2.27765i) q^{81} +(-0.0322898 - 0.0559276i) q^{82} +(2.00104 + 6.15855i) q^{83} +(-1.68429 - 1.22370i) q^{84} +(10.7706 + 6.55319i) q^{85} +(11.0728 + 4.92991i) q^{86} +(-6.35526 - 4.61737i) q^{87} +(-2.60890 - 1.89548i) q^{88} +(-2.98820 - 1.33043i) q^{89} +(4.31155 + 1.51139i) q^{90} +(-0.112227 + 1.06777i) q^{91} +(-4.86620 - 1.03434i) q^{92} +(-4.28988 + 7.43029i) q^{93} +(1.43700 + 4.42264i) q^{94} +(0.00472319 - 9.74679i) q^{95} +(0.693963 - 2.13580i) q^{96} +(7.24732 + 8.04896i) q^{97} +(0.641865 + 6.10694i) q^{98} +(-3.29447 - 5.70619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9}+O(q^{10}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9	\( 200 q + 25 q^{2} + 25 q^{4} + q^{5} + 28 q^{7} - 50 q^{8} + 13 q^{9} - 4 q^{10} + 14 q^{11} + 8 q^{13} + q^{14} - 4 q^{15} + 25 q^{16} - 5 q^{17} + 184 q^{18} + 24 q^{19} - 2 q^{20} + 32 q^{21} + 8 q^{22} + 11 q^{23} - 23 q^{25} + 64 q^{26} - 36 q^{27} + 6 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 100 q^{32} + 12 q^{33} + 2 q^{35} + 13 q^{36} + 8 q^{37} + 2 q^{38} - 52 q^{39} + q^{40} + 14 q^{41} + 32 q^{42} - 10 q^{43} + 8 q^{44} - 52 q^{45} + 8 q^{46} - 22 q^{47} + 204 q^{49} - 34 q^{50} - 10 q^{51} + 8 q^{52} - 18 q^{53} - 12 q^{54} + 10 q^{55} - 12 q^{56} + 34 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 16 q^{61} - 4 q^{62} - 21 q^{63} - 50 q^{64} + 96 q^{65} - 18 q^{66} - 54 q^{67} - 20 q^{68} - 20 q^{69} - 3 q^{70} - 5 q^{71} + 33 q^{72} - 16 q^{73} - 4 q^{74} + 56 q^{75} + 14 q^{76} - 116 q^{77} - 34 q^{78} + q^{80} + 57 q^{81} - 36 q^{82} - 72 q^{83} + 76 q^{84} - 5 q^{85} - 112 q^{87} + 14 q^{88} - 4 q^{89} - 49 q^{90} - 64 q^{91} - 4 q^{92} - 124 q^{93} + 44 q^{94} + 41 q^{95} + 13 q^{97} + 43 q^{98} - 28 q^{99}+O(q^{100}) \) 200 * q + 25 * q^2 + 25 * q^4 + q^5 + 28 * q^7 - 50 * q^8 + 13 * q^9 - 4 * q^10 + 14 * q^11 + 8 * q^13 + q^14 - 4 * q^15 + 25 * q^16 - 5 * q^17 + 184 * q^18 + 24 * q^19 - 2 * q^20 + 32 * q^21 + 8 * q^22 + 11 * q^23 - 23 * q^25 + 64 * q^26 - 36 * q^27 + 6 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 100 * q^32 + 12 * q^33 + 2 * q^35 + 13 * q^36 + 8 * q^37 + 2 * q^38 - 52 * q^39 + q^40 + 14 * q^41 + 32 * q^42 - 10 * q^43 + 8 * q^44 - 52 * q^45 + 8 * q^46 - 22 * q^47 + 204 * q^49 - 34 * q^50 - 10 * q^51 + 8 * q^52 - 18 * q^53 - 12 * q^54 + 10 * q^55 - 12 * q^56 + 34 * q^57 - 24 * q^58 - 2 * q^59 - 14 * q^60 + 16 * q^61 - 4 * q^62 - 21 * q^63 - 50 * q^64 + 96 * q^65 - 18 * q^66 - 54 * q^67 - 20 * q^68 - 20 * q^69 - 3 * q^70 - 5 * q^71 + 33 * q^72 - 16 * q^73 - 4 * q^74 + 56 * q^75 + 14 * q^76 - 116 * q^77 - 34 * q^78 + q^80 + 57 * q^81 - 36 * q^82 - 72 * q^83 + 76 * q^84 - 5 * q^85 - 112 * q^87 + 14 * q^88 - 4 * q^89 - 49 * q^90 - 64 * q^91 - 4 * q^92 - 124 * q^93 + 44 * q^94 + 41 * q^95 + 13 * q^97 + 43 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

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Database

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