LMFDB - Embedded newform 483.2.q.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	483.64
Dual form			483.2.q.a.400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52977 - 0.449181i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.455922 + 0.293003i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.34125 - 0.861971i) q^{6} +(0.415415 + 0.909632i) q^{7} +(1.52231 + 1.75684i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.52977 - 0.449181i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.455922 + 0.293003i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.34125 - 0.861971i) q^{6} +(0.415415 + 0.909632i) q^{7} +(1.52231 + 1.75684i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.662317 + 1.45027i) q^{10} +(-2.84695 + 0.835939i) q^{11} +(-0.520003 + 0.152687i) q^{12} +(1.10866 - 2.42763i) q^{13} +(-0.226900 - 1.57812i) q^{14} +(0.654861 + 0.755750i) q^{15} +(-1.98992 - 4.35731i) q^{16} +(-4.41153 + 2.83512i) q^{17} +(-0.226900 + 1.57812i) q^{18} +(1.87491 + 1.20493i) q^{19} +(0.354905 - 0.409583i) q^{20} +(-0.959493 - 0.281733i) q^{21} +4.73066 q^{22} +(3.73149 - 3.01264i) q^{23} -2.32463 q^{24} +(3.83797 + 1.12693i) q^{25} +(-2.78644 + 3.21572i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.0771283 + 0.536439i) q^{28} +(-6.05954 + 3.89423i) q^{29} +(-0.662317 - 1.45027i) q^{30} +(6.01024 + 6.93619i) q^{31} +(0.425234 + 2.95757i) q^{32} +(1.23259 - 2.69900i) q^{33} +(8.02210 - 2.35550i) q^{34} +(0.959493 - 0.281733i) q^{35} +(0.225136 - 0.492980i) q^{36} +(1.44712 + 10.0649i) q^{37} +(-2.32694 - 2.68544i) q^{38} +(1.10866 + 2.42763i) q^{39} +(1.95561 - 1.25679i) q^{40} +(-1.04427 + 7.26302i) q^{41} +(1.34125 + 0.861971i) q^{42} +(-4.45276 + 5.13876i) q^{43} +(-1.54292 - 0.453042i) q^{44} -1.00000 q^{45} +(-7.06153 + 2.93253i) q^{46} +6.10668 q^{47} +(4.59616 + 1.34955i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-5.36501 - 3.44789i) q^{50} +(0.746298 - 5.19062i) q^{51} +(1.21677 - 0.781968i) q^{52} +(-0.585189 - 1.28139i) q^{53} +(-1.04408 - 1.20493i) q^{54} +(0.422268 + 2.93694i) q^{55} +(-0.965688 + 2.11456i) q^{56} +(-2.13843 + 0.627899i) q^{57} +(11.0189 - 3.23544i) q^{58} +(-4.58634 + 10.0427i) q^{59} +(0.0771283 + 0.536439i) q^{60} +(-2.11157 - 2.43689i) q^{61} +(-6.07868 - 13.3105i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.685459 + 4.76747i) q^{64} +(-2.24514 - 1.44286i) q^{65} +(-3.09792 + 3.57519i) q^{66} +(13.2949 + 3.90373i) q^{67} -2.84201 q^{68} +(-0.166803 + 4.79293i) q^{69} -1.59435 q^{70} +(11.2720 + 3.30976i) q^{71} +(1.52231 - 1.75684i) q^{72} +(-4.02620 - 2.58748i) q^{73} +(2.30722 - 16.0470i) q^{74} +(-3.36501 + 2.16256i) q^{75} +(0.501763 + 1.09871i) q^{76} +(-1.94306 - 2.24241i) q^{77} +(-0.605551 - 4.21170i) q^{78} +(6.30442 - 13.8048i) q^{79} +(-4.59616 + 1.34955i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(4.85989 - 10.6417i) q^{82} +(-1.41248 - 9.82399i) q^{83} +(-0.354905 - 0.409583i) q^{84} +(2.17843 + 4.77011i) q^{85} +(9.11992 - 5.86102i) q^{86} +(1.02509 - 7.12967i) q^{87} +(-5.80255 - 3.72908i) q^{88} +(-3.36555 + 3.88406i) q^{89} +(1.52977 + 0.449181i) q^{90} +2.66880 q^{91} +(2.58398 - 0.280191i) q^{92} -9.17789 q^{93} +(-9.34181 - 2.74300i) q^{94} +(1.45949 - 1.68434i) q^{95} +(-2.51365 - 1.61543i) q^{96} +(1.48838 - 10.3519i) q^{97} +(1.34125 - 0.861971i) q^{98} +(1.23259 + 2.69900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9} - 4 q^{10} - q^{11} - 3 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 10 q^{16} - 24 q^{17} - 7 q^{18} + 5 q^{19} - 8 q^{20} - q^{21} + 26 q^{22} + 21 q^{23} - 18 q^{24} + 4 q^{25} + 6 q^{26} - q^{27} - 3 q^{28} - 22 q^{29} - 4 q^{30} - 8 q^{31} + 10 q^{32} - q^{33} + 8 q^{34} + q^{35} - 14 q^{36} - 2 q^{37} + 2 q^{38} + 15 q^{39} - 4 q^{40} + 7 q^{41} + 4 q^{42} + q^{43} + 19 q^{44} - 10 q^{45} + 15 q^{46} - 6 q^{47} + q^{48} - q^{49} - 16 q^{50} + 20 q^{51} - 21 q^{52} - q^{53} - 7 q^{54} + 12 q^{55} + 4 q^{56} - 6 q^{57} + 22 q^{58} + 10 q^{59} + 3 q^{60} + 5 q^{61} - 34 q^{62} - q^{63} + 13 q^{64} - 4 q^{65} - 7 q^{66} + 29 q^{67} - 28 q^{68} - q^{69} - 4 q^{70} + 22 q^{71} - 7 q^{72} - 33 q^{73} - 36 q^{74} + 4 q^{75} + 26 q^{76} - q^{77} + 28 q^{78} + 27 q^{79} - q^{80} - q^{81} + 38 q^{82} + 25 q^{83} + 8 q^{84} + 2 q^{85} + 18 q^{86} - 7 q^{88} - 38 q^{89} - 4 q^{90} - 18 q^{91} + 41 q^{92} - 30 q^{93} - 42 q^{94} + 6 q^{95} - 23 q^{96} - q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9 - 4 * q^10 - q^11 - 3 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 10 * q^16 - 24 * q^17 - 7 * q^18 + 5 * q^19 - 8 * q^20 - q^21 + 26 * q^22 + 21 * q^23 - 18 * q^24 + 4 * q^25 + 6 * q^26 - q^27 - 3 * q^28 - 22 * q^29 - 4 * q^30 - 8 * q^31 + 10 * q^32 - q^33 + 8 * q^34 + q^35 - 14 * q^36 - 2 * q^37 + 2 * q^38 + 15 * q^39 - 4 * q^40 + 7 * q^41 + 4 * q^42 + q^43 + 19 * q^44 - 10 * q^45 + 15 * q^46 - 6 * q^47 + q^48 - q^49 - 16 * q^50 + 20 * q^51 - 21 * q^52 - q^53 - 7 * q^54 + 12 * q^55 + 4 * q^56 - 6 * q^57 + 22 * q^58 + 10 * q^59 + 3 * q^60 + 5 * q^61 - 34 * q^62 - q^63 + 13 * q^64 - 4 * q^65 - 7 * q^66 + 29 * q^67 - 28 * q^68 - q^69 - 4 * q^70 + 22 * q^71 - 7 * q^72 - 33 * q^73 - 36 * q^74 + 4 * q^75 + 26 * q^76 - q^77 + 28 * q^78 + 27 * q^79 - q^80 - q^81 + 38 * q^82 + 25 * q^83 + 8 * q^84 + 2 * q^85 + 18 * q^86 - 7 * q^88 - 38 * q^89 - 4 * q^90 - 18 * q^91 + 41 * q^92 - 30 * q^93 - 42 * q^94 + 6 * q^95 - 23 * q^96 - q^97 + 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−1.52977	−	0.449181i	−1.08171	−	0.317619i	−0.308147	−	0.951339i	$-0.599709\pi$
$2$	−1.52977	−	0.449181i	−1.08171	−	0.317619i	−0.773563	+	0.633720i	$0.781527\pi$
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.455922	+	0.293003i	0.227961	+	0.146502i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i	−0.932936	−	0.360042i	$-0.882762\pi$
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i	0.996581	−	0.0826195i	$-0.0263286\pi$
$6$	1.34125	−	0.861971i	0.547564	−	0.351898i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$8$	1.52231	+	1.75684i	0.538219	+	0.621137i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−0.662317	+	1.45027i	−0.209443	+	0.458617i
$11$	−2.84695	+	0.835939i	−0.858387	+	0.252045i	−0.681169	−	0.732127i	$-0.738528\pi$
$11$	−2.84695	+	0.835939i	−0.858387	+	0.252045i	−0.177218	+	0.984172i	$0.556710\pi$
$12$	−0.520003	+	0.152687i	−0.150112	+	0.0440768i
$13$	1.10866	−	2.42763i	0.307487	−	0.673303i	−0.691299	−	0.722569i	$-0.742961\pi$
$13$	1.10866	−	2.42763i	0.307487	−	0.673303i	0.998786	+	0.0492664i	$0.0156883\pi$
$14$	−0.226900	−	1.57812i	−0.0606415	−	0.421771i
$15$	0.654861	+	0.755750i	0.169084	+	0.195134i
$16$	−1.98992	−	4.35731i	−0.497480	−	1.08933i
$17$	−4.41153	+	2.83512i	−1.06995	+	0.687617i	−0.952215	−	0.305428i	$-0.901201\pi$
$17$	−4.41153	+	2.83512i	−1.06995	+	0.687617i	−0.117738	+	0.993045i	$0.537564\pi$
$18$	−0.226900	+	1.57812i	−0.0534808	+	0.371967i
$19$	1.87491	+	1.20493i	0.430133	+	0.276430i	0.737742	−	0.675083i	$-0.235892\pi$
$19$	1.87491	+	1.20493i	0.430133	+	0.276430i	−0.307608	+	0.951513i	$0.599529\pi$
$20$	0.354905	−	0.409583i	0.0793593	−	0.0915855i
$21$	−0.959493	−	0.281733i	−0.209379	−	0.0614791i
$22$	4.73066			1.00858
$23$	3.73149	−	3.01264i	0.778069	−	0.628179i
$23$	3.73149	−	3.01264i	0.778069	−	0.628179i
$24$	−2.32463			−0.474514
$25$	3.83797	+	1.12693i	0.767594	+	0.225386i
$26$	−2.78644	+	3.21572i	−0.546465	+	0.630655i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	−0.0771283	+	0.536439i	−0.0145759	+	0.101377i
$29$	−6.05954	+	3.89423i	−1.12523	+	0.723140i	−0.964559	−	0.263868i	$-0.915002\pi$
$29$	−6.05954	+	3.89423i	−1.12523	+	0.723140i	−0.160669	+	0.987008i	$0.551365\pi$
$30$	−0.662317	−	1.45027i	−0.120922	−	0.264782i
$31$	6.01024	+	6.93619i	1.07947	+	1.24578i	0.967717	+	0.252041i	$0.0811017\pi$
$31$	6.01024	+	6.93619i	1.07947	+	1.24578i	0.111755	+	0.993736i	$0.464353\pi$
$32$	0.425234	+	2.95757i	0.0751715	+	0.522830i
$33$	1.23259	−	2.69900i	0.214567	−	0.469836i
$34$	8.02210	−	2.35550i	1.37578	−	0.403965i
$35$	0.959493	−	0.281733i	0.162184	−	0.0476215i
$36$	0.225136	−	0.492980i	0.0375227	−	0.0821634i
$37$	1.44712	+	10.0649i	0.237905	+	1.65466i	0.662338	+	0.749205i	$0.269564\pi$
$37$	1.44712	+	10.0649i	0.237905	+	1.65466i	−0.424433	+	0.905459i	$0.639526\pi$
$38$	−2.32694	−	2.68544i	−0.377480	−	0.435635i
$39$	1.10866	+	2.42763i	0.177528	+	0.388732i
$40$	1.95561	−	1.25679i	0.309209	−	0.198716i
$41$	−1.04427	+	7.26302i	−0.163087	+	1.13429i	0.729685	+	0.683784i	$0.239667\pi$
$41$	−1.04427	+	7.26302i	−0.163087	+	1.13429i	−0.892771	+	0.450510i	$0.851242\pi$
$42$	1.34125	+	0.861971i	0.206960	+	0.133005i
$43$	−4.45276	+	5.13876i	−0.679039	+	0.783653i	−0.985762	−	0.168146i	$-0.946222\pi$
$43$	−4.45276	+	5.13876i	−0.679039	+	0.783653i	0.306723	+	0.951799i	$0.400767\pi$
$44$	−1.54292	−	0.453042i	−0.232604	−	0.0682986i
$45$	−1.00000			−0.149071
$46$	−7.06153	+	2.93253i	−1.04117	+	0.432378i
$47$	6.10668			0.890751			0.445376	−	0.895344i	$-0.353070\pi$
$47$	6.10668			0.890751			0.445376	+	0.895344i	$0.353070\pi$
$48$	4.59616	+	1.34955i	0.663398	+	0.194791i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	−5.36501	−	3.44789i	−0.758728	−	0.487605i
$51$	0.746298	−	5.19062i	0.104503	−	0.726832i
$52$	1.21677	−	0.781968i	0.168735	−	0.108439i
$53$	−0.585189	−	1.28139i	−0.0803819	−	0.176012i	0.865174	−	0.501472i	$-0.167208\pi$
$53$	−0.585189	−	1.28139i	−0.0803819	−	0.176012i	−0.945556	+	0.325460i	$0.894481\pi$
$54$	−1.04408	−	1.20493i	−0.142081	−	0.163970i
$55$	0.422268	+	2.93694i	0.0569385	+	0.396016i
$56$	−0.965688	+	2.11456i	−0.129046	+	0.282570i
$57$	−2.13843	+	0.627899i	−0.283242	+	0.0831673i
$58$	11.0189	−	3.23544i	1.44685	−	0.424834i
$59$	−4.58634	+	10.0427i	−0.597091	+	1.30745i	0.333971	+	0.942583i	$0.391611\pi$
$59$	−4.58634	+	10.0427i	−0.597091	+	1.30745i	−0.931061	+	0.364862i	$0.881116\pi$
$60$	0.0771283	+	0.536439i	0.00995722	+	0.0692540i
$61$	−2.11157	−	2.43689i	−0.270359	−	0.312011i	0.604293	−	0.796762i	$-0.293456\pi$
$61$	−2.11157	−	2.43689i	−0.270359	−	0.312011i	−0.874652	+	0.484751i	$0.838910\pi$
$62$	−6.07868	−	13.3105i	−0.771993	−	1.69043i
$63$	0.841254	−	0.540641i	0.105988	−	0.0681143i
$64$	−0.685459	+	4.76747i	−0.0856823	+	0.595934i
$65$	−2.24514	−	1.44286i	−0.278475	−	0.178965i
$66$	−3.09792	+	3.57519i	−0.381328	+	0.440076i
$67$	13.2949	+	3.90373i	1.62423	+	0.476917i	0.962151	−	0.272518i	$-0.0878565\pi$
$67$	13.2949	+	3.90373i	1.62423	+	0.476917i	0.662078	+	0.749435i	$0.269675\pi$
$68$	−2.84201			−0.344645
$69$	−0.166803	+	4.79293i	−0.0200807	+	0.577001i
$70$	−1.59435			−0.190561
$71$	11.2720	+	3.30976i	1.33774	+	0.392796i	0.870863	−	0.491526i	$-0.163561\pi$
$71$	11.2720	+	3.30976i	1.33774	+	0.392796i	0.466877	+	0.884322i	$0.345379\pi$
$72$	1.52231	−	1.75684i	0.179406	−	0.207046i
$73$	−4.02620	−	2.58748i	−0.471231	−	0.302842i	0.283388	−	0.959005i	$-0.408542\pi$
$73$	−4.02620	−	2.58748i	−0.471231	−	0.302842i	−0.754619	+	0.656164i	$0.772178\pi$
$74$	2.30722	−	16.0470i	0.268208	−	1.86543i
$75$	−3.36501	+	2.16256i	−0.388558	+	0.249711i
$76$	0.501763	+	1.09871i	0.0575562	+	0.126031i
$77$	−1.94306	−	2.24241i	−0.221432	−	0.255547i
$78$	−0.605551	−	4.21170i	−0.0685651	−	0.476881i
$79$	6.30442	−	13.8048i	0.709303	−	1.55316i	−0.119011	−	0.992893i	$-0.537972\pi$
$79$	6.30442	−	13.8048i	0.709303	−	1.55316i	0.828314	−	0.560264i	$-0.189300\pi$
$80$	−4.59616	+	1.34955i	−0.513866	+	0.150885i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	4.85989	−	10.6417i	0.536685	−	1.17518i
$83$	−1.41248	−	9.82399i	−0.155039	−	1.07832i	−0.907611	−	0.419812i	$-0.862096\pi$
$83$	−1.41248	−	9.82399i	−0.155039	−	1.07832i	0.752572	−	0.658510i	$-0.228813\pi$
$84$	−0.354905	−	0.409583i	−0.0387234	−	0.0446891i
$85$	2.17843	+	4.77011i	0.236284	+	0.517391i
$86$	9.11992	−	5.86102i	0.983426	−	0.632010i
$87$	1.02509	−	7.12967i	0.109901	−	0.764381i
$88$	−5.80255	−	3.72908i	−0.618554	−	0.397521i
$89$	−3.36555	+	3.88406i	−0.356748	+	0.411709i	−0.905548	−	0.424245i	$-0.860540\pi$
$89$	−3.36555	+	3.88406i	−0.356748	+	0.411709i	0.548799	+	0.835954i	$0.315085\pi$
$90$	1.52977	+	0.449181i	0.161252	+	0.0473478i
$91$	2.66880			0.279766
$92$	2.58398	−	0.280191i	0.269399	−	0.0292120i
$93$	−9.17789			−0.951703
$94$	−9.34181	−	2.74300i	−0.963535	−	0.282919i
$95$	1.45949	−	1.68434i	0.149741	−	0.172810i
$96$	−2.51365	−	1.61543i	−0.256549	−	0.164874i
$97$	1.48838	−	10.3519i	0.151122	−	1.05108i	−0.763221	−	0.646138i	$-0.776383\pi$
$97$	1.48838	−	10.3519i	0.151122	−	1.05108i	0.914343	−	0.404940i	$-0.132708\pi$
$98$	1.34125	−	0.861971i	0.135487	−	0.0870723i
$99$	1.23259	+	2.69900i	0.123880	+	0.271260i
$100$	1.41962	+	1.63833i	0.141962	+	0.163833i
$101$	2.41767	+	16.8153i	0.240567	+	1.67318i	0.649304	+	0.760529i	$0.275060\pi$
$101$	2.41767	+	16.8153i	0.240567	+	1.67318i	−0.408737	+	0.912652i	$0.634031\pi$
$102$	−3.47319	+	7.60522i	−0.343897	+	0.753029i
$103$	−17.2793	+	5.07367i	−1.70258	+	0.499923i	−0.981262	−	0.192678i	$-0.938283\pi$
$103$	−17.2793	+	5.07367i	−1.70258	+	0.499923i	−0.721321	+	0.692601i	$0.756465\pi$
$104$	5.95268	−	1.74787i	0.583709	−	0.171392i
$105$	−0.415415	+	0.909632i	−0.0405404	+	0.0887710i
$106$	0.319630	+	2.22308i	0.0310453	+	0.215925i
$107$	3.05117	+	3.52124i	0.294968	+	0.340411i	0.883818	−	0.467831i	$-0.154965\pi$
$107$	3.05117	+	3.52124i	0.294968	+	0.340411i	−0.588850	+	0.808242i	$0.700419\pi$
$108$	0.225136	+	0.492980i	0.0216638	+	0.0474370i
$109$	−5.91194	+	3.79937i	−0.566261	+	0.363914i	−0.792232	−	0.610220i	$-0.791081\pi$
$109$	−5.91194	+	3.79937i	−0.566261	+	0.363914i	0.225971	+	0.974134i	$0.427445\pi$
$110$	0.673243	−	4.68251i	0.0641912	−	0.446459i
$111$	−8.55423	−	5.49747i	−0.811932	−	0.521797i
$112$	3.13691	−	3.62019i	0.296410	−	0.342076i
$113$	−11.8324	−	3.47432i	−1.11310	−	0.326836i	−0.327057	−	0.945005i	$-0.606057\pi$
$113$	−11.8324	−	3.47432i	−1.11310	−	0.326836i	−0.786046	+	0.618168i	$0.787875\pi$
$114$	3.55334			0.332801
$115$	−2.45093	−	4.12225i	−0.228550	−	0.384402i
$116$	−3.90370			−0.362449
$117$	−2.56070	−	0.751888i	−0.236736	−	0.0695121i
$118$	11.5270	−	13.3029i	1.06115	−	1.22463i
$119$	−4.41153	−	2.83512i	−0.404404	−	0.259895i
$120$	−0.330830	+	2.30097i	−0.0302005	+	0.210049i
$121$	−1.84748	+	1.18730i	−0.167952	+	0.107936i
$122$	2.13562	+	4.67635i	0.193350	+	0.423377i
$123$	−4.80518	−	5.54547i	−0.433268	−	0.500018i
$124$	0.707876	+	4.92338i	0.0635691	+	0.442133i
$125$	3.73874	−	8.18669i	0.334403	−	0.732240i
$126$	−1.52977	+	0.449181i	−0.136283	+	0.0400162i
$127$	6.94665	−	2.03972i	0.616415	−	0.180996i	0.0414055	−	0.999142i	$-0.486816\pi$
$127$	6.94665	−	2.03972i	0.616415	−	0.180996i	0.575010	+	0.818147i	$0.304998\pi$
$128$	5.67256	−	12.4212i	0.501388	−	1.09789i
$129$	−0.967677	−	6.73034i	−0.0851992	−	0.592573i
$130$	2.78644	+	3.21572i	0.244387	+	0.282037i
$131$	−2.82674	−	6.18970i	−0.246973	−	0.540796i	0.745026	−	0.667035i	$-0.232437\pi$
$131$	−2.82674	−	6.18970i	−0.246973	−	0.540796i	−0.992000	+	0.126238i	$0.959710\pi$
$132$	1.35278	−	0.869381i	0.117745	−	0.0756699i
$133$	−0.317178	+	2.20602i	−0.0275028	+	0.191286i
$134$	−18.5846	−	11.9436i	−1.60547	−	1.03177i
$135$	0.654861	−	0.755750i	0.0563614	−	0.0650446i
$136$	−11.6966	−	3.43443i	−1.00297	−	0.294500i
$137$	−2.58589			−0.220928			−0.110464	−	0.993880i	$-0.535234\pi$
$137$	−2.58589			−0.220928			−0.110464	+	0.993880i	$0.535234\pi$
$138$	2.40806	−	7.25715i	0.204988	−	0.617770i
$139$	−14.4325			−1.22414			−0.612072	−	0.790802i	$-0.709664\pi$
$139$	−14.4325			−1.22414			−0.612072	+	0.790802i	$0.709664\pi$
$140$	0.520003	+	0.152687i	0.0439482	+	0.0129044i
$141$	−3.99903	+	4.61512i	−0.336779	+	0.388664i
$142$	−15.7569	−	10.1263i	−1.32229	−	0.849783i
$143$	−1.12695	+	7.83810i	−0.0942402	+	0.655455i
$144$	−4.02977	+	2.58978i	−0.335814	+	0.215815i
$145$	2.99223	+	6.55207i	0.248491	+	0.544120i
$146$	4.99691	+	5.76674i	0.413547	+	0.477258i
$147$	−0.142315	−	0.989821i	−0.0117379	−	0.0816391i
$148$	−2.28929	+	5.01284i	−0.188178	+	0.412053i
$149$	17.8548	−	5.24264i	1.46272	−	0.429494i	0.548996	−	0.835825i	$-0.315010\pi$
$149$	17.8548	−	5.24264i	1.46272	−	0.429494i	0.913726	+	0.406331i	$0.133192\pi$
$150$	6.11907	−	1.79672i	0.499620	−	0.146702i
$151$	1.88084	−	4.11847i	0.153061	−	0.335156i	−0.817532	−	0.575883i	$-0.804658\pi$
$151$	1.88084	−	4.11847i	0.153061	−	0.335156i	0.970593	+	0.240727i	$0.0773857\pi$
$152$	0.737323	+	5.12820i	0.0598048	+	0.415952i
$153$	3.43409	+	3.96315i	0.277629	+	0.320401i
$154$	1.96519	+	4.30316i	0.158359	+	0.346758i
$155$	7.72094	−	4.96194i	0.620160	−	0.398553i
$156$	−0.205840	+	1.43165i	−0.0164804	+	0.114624i
$157$	−11.6865	−	7.51046i	−0.932684	−	0.599400i	−0.0163728	−	0.999866i	$-0.505212\pi$
$157$	−11.6865	−	7.51046i	−0.932684	−	0.599400i	−0.916312	+	0.400466i	$0.868848\pi$
$158$	−15.8451	+	18.2863i	−1.26057	+	1.45478i
$159$	1.35162	+	0.396873i	0.107191	+	0.0314740i
$160$	2.98798			0.236221
$161$	4.29051	+	2.14278i	0.338140	+	0.168875i
$162$	1.59435			0.125264
$163$	−1.37218	−	0.402909i	−0.107478	−	0.0315583i	0.227552	−	0.973766i	$-0.426928\pi$
$163$	−1.37218	−	0.402909i	−0.107478	−	0.0315583i	−0.335029	+	0.942208i	$0.608746\pi$
$164$	−2.60419	+	3.00540i	−0.203353	+	0.234682i
$165$	−2.49611	−	1.60416i	−0.194322	−	0.124883i
$166$	−2.25198	+	15.6629i	−0.174788	+	1.21568i
$167$	−6.69350	+	4.30165i	−0.517959	+	0.332872i	−0.773364	−	0.633962i	$-0.781428\pi$
$167$	−6.69350	+	4.30165i	−0.517959	+	0.332872i	0.255405	+	0.966834i	$0.417791\pi$
$168$	−0.965688	−	2.11456i	−0.0745045	−	0.163142i
$169$	3.84894	+	4.44192i	0.296072	+	0.341686i
$170$	−1.18986	−	8.27567i	−0.0912582	−	0.634715i
$171$	0.925839	−	2.02730i	0.0708006	−	0.155032i
$172$	−3.53578	+	1.03820i	−0.269601	+	0.0791620i
$173$	8.94894	−	2.62765i	0.680375	−	0.199776i	0.0767573	−	0.997050i	$-0.475543\pi$
$173$	8.94894	−	2.62765i	0.680375	−	0.199776i	0.603618	+	0.797274i	$0.293725\pi$
$174$	−4.77066	+	10.4463i	−0.361663	+	0.791932i
$175$	0.569259	+	3.95929i	0.0430320	+	0.299294i
$176$	9.30764	+	10.7416i	0.701590	+	0.809678i
$177$	−4.58634	−	10.0427i	−0.344730	−	0.754854i
$178$	6.89316	−	4.42997i	0.516664	−	0.332040i
$179$	−0.239843	+	1.66814i	−0.0179267	+	0.124683i	−0.996820	−	0.0796908i	$-0.974607\pi$
$179$	−0.239843	+	1.66814i	−0.0179267	+	0.124683i	0.978893	+	0.204374i	$0.0655158\pi$
$180$	−0.455922	−	0.293003i	−0.0339824	−	0.0218392i
$181$	−3.18599	+	3.67682i	−0.236813	+	0.273296i	−0.861699	−	0.507419i	$-0.830600\pi$
$181$	−3.18599	+	3.67682i	−0.236813	+	0.273296i	0.624887	+	0.780715i	$0.285145\pi$
$182$	−4.08265	−	1.19877i	−0.302626	−	0.0888590i
$183$	3.22446			0.238359
$184$	10.9732	+	1.96945i	0.808957	+	0.145190i
$185$	10.1684			0.747598
$186$	14.0401	+	4.12253i	1.02947	+	0.302279i
$187$	10.1894	−	11.7592i	0.745123	−	0.859918i
$188$	2.78417	+	1.78928i	0.203057	+	0.130497i
$189$	−0.142315	+	0.989821i	−0.0103519	+	0.0719989i
$190$	−2.98926	+	1.92108i	−0.216864	+	0.139370i
$191$	7.84738	+	17.1834i	0.567816	+	1.24334i	0.947952	+	0.318414i	$0.103150\pi$
$191$	7.84738	+	17.1834i	0.567816	+	1.24334i	−0.380135	+	0.924931i	$0.624123\pi$
$192$	−3.15413	−	3.64006i	−0.227630	−	0.262699i
$193$	1.05679	+	7.35010i	0.0760691	+	0.529072i	0.991852	+	0.127398i	$0.0406625\pi$
$193$	1.05679	+	7.35010i	0.0760691	+	0.529072i	−0.915783	+	0.401674i	$0.868428\pi$
$194$	−6.92676	+	15.1675i	−0.497312	+	1.08896i
$195$	2.56070	−	0.751888i	0.183375	−	0.0538438i
$196$	−0.520003	+	0.152687i	−0.0371430	+	0.0109062i
$197$	6.79310	−	14.8748i	0.483989	−	1.05979i	−0.497359	−	0.867545i	$-0.665697\pi$
$197$	6.79310	−	14.8748i	0.483989	−	1.05979i	0.981347	−	0.192242i	$-0.0615760\pi$
$198$	−0.673243	−	4.68251i	−0.0478453	−	0.332771i
$199$	13.4977	+	15.5772i	0.956827	+	1.10424i	0.994478	+	0.104946i	$0.0334670\pi$
$199$	13.4977	+	15.5772i	0.956827	+	1.10424i	−0.0376510	+	0.999291i	$0.511988\pi$
$200$	3.86275	+	8.45825i	0.273138	+	0.598089i
$201$	−11.6565	+	7.49120i	−0.822189	+	0.528389i
$202$	3.85461	−	26.8094i	0.271210	−	1.88631i
$203$	−6.05954	−	3.89423i	−0.425296	−	0.273321i
$204$	1.86112	−	2.14785i	0.130305	−	0.150380i
$205$	7.04048	+	2.06727i	0.491729	+	0.144385i
$206$	28.7124			2.00049
$207$	−3.51302	−	3.26476i	−0.244172	−	0.226917i
$208$	−12.7841			−0.886417
$209$	−6.34501	−	1.86306i	−0.438894	−	0.128871i
$210$	1.04408	−	1.20493i	0.0720482	−	0.0831481i
$211$	5.39703	+	3.46846i	0.371547	+	0.238779i	0.713067	−	0.701096i	$-0.247305\pi$
$211$	5.39703	+	3.46846i	0.371547	+	0.238779i	−0.341520	+	0.939874i	$0.610942\pi$
$212$	0.108650	−	0.755674i	0.00746208	−	0.0518999i
$213$	−9.88294	+	6.35138i	−0.677168	+	0.435189i
$214$	−3.08591	−	6.75721i	−0.210949	−	0.461913i
$215$	4.45276	+	5.13876i	0.303676	+	0.350460i
$216$	0.330830	+	2.30097i	0.0225101	+	0.156561i
$217$	−3.81264	+	8.34851i	−0.258819	+	0.566734i
$218$	10.7505	−	3.15663i	0.728116	−	0.213794i
$219$	4.59209	−	1.34836i	0.310304	−	0.0911136i
$220$	−0.668011	+	1.46274i	−0.0450373	+	0.0986179i
$221$	1.99172	+	13.8527i	0.133978	+	0.931836i
$222$	10.6166	+	12.2523i	0.712542	+	0.822317i
$223$	−6.57189	−	14.3904i	−0.440086	−	0.963654i	−0.991582	−	0.129477i	$-0.958670\pi$
$223$	−6.57189	−	14.3904i	−0.440086	−	0.963654i	0.551496	−	0.834177i	$-0.314057\pi$
$224$	−2.51365	+	1.61543i	−0.167950	+	0.107935i
$225$	0.569259	−	3.95929i	0.0379506	−	0.263952i
$226$	16.5403	+	10.6298i	1.10024	+	0.707084i
$227$	−2.03458	+	2.34804i	−0.135040	+	0.155845i	−0.819242	−	0.573448i	$-0.805605\pi$
$227$	−2.03458	+	2.34804i	−0.135040	+	0.155845i	0.684202	+	0.729293i	$0.260151\pi$
$228$	−1.15893	−	0.340294i	−0.0767523	−	0.0225365i
$229$	0.929743			0.0614391			0.0307196	−	0.999528i	$-0.490220\pi$
$229$	0.929743			0.0614391			0.0307196	+	0.999528i	$0.490220\pi$
$230$	1.89772	+	7.40700i	0.125132	+	0.488403i
$231$	2.96714			0.195223
$232$	−16.0660	−	4.71742i	−1.05479	−	0.309714i
$233$	9.02453	−	10.4149i	0.591217	−	0.682300i	−0.378761	−	0.925495i	$-0.623650\pi$
$233$	9.02453	−	10.4149i	0.591217	−	0.682300i	0.969978	+	0.243194i	$0.0781952\pi$
$234$	3.57954	+	2.30043i	0.234002	+	0.150384i
$235$	0.869072	−	6.04453i	0.0566920	−	0.394301i
$236$	−5.03355	+	3.23487i	−0.327656	+	0.210572i
$237$	6.30442	+	13.8048i	0.409516	+	0.896716i
$238$	5.47514	+	6.31865i	0.354901	+	0.409577i
$239$	−3.68005	−	25.5953i	−0.238043	−	1.65563i	−0.661675	−	0.749791i	$-0.730154\pi$
$239$	−3.68005	−	25.5953i	−0.238043	−	1.65563i	0.423632	−	0.905834i	$-0.360755\pi$
$240$	1.98992	−	4.35731i	0.128449	−	0.281263i
$241$	−9.90017	+	2.90695i	−0.637726	+	0.187253i	−0.584583	−	0.811334i	$-0.698742\pi$
$241$	−9.90017	+	2.90695i	−0.637726	+	0.187253i	−0.0531427	+	0.998587i	$0.516924\pi$
$242$	3.35952	−	0.986445i	0.215958	−	0.0634111i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	−0.248697	−	1.72973i	−0.0159212	−	0.110735i
$245$	0.654861	+	0.755750i	0.0418375	+	0.0482831i
$246$	4.85989	+	10.6417i	0.309855	+	0.678489i
$247$	5.00376	−	3.21572i	0.318381	−	0.204611i
$248$	−3.03632	+	21.1181i	−0.192807	+	1.34100i
$249$	8.34945	+	5.36586i	0.529125	+	0.340048i
$250$	−9.39670	+	10.8444i	−0.594300	+	0.685858i
$251$	4.33333	+	1.27238i	0.273517	+	0.0803119i	0.415615	−	0.909541i	$-0.363566\pi$
$251$	4.33333	+	1.27238i	0.273517	+	0.0803119i	−0.142098	+	0.989853i	$0.545385\pi$
$252$	0.541956			0.0341400
$253$	−8.10496	+	11.6961i	−0.509555	+	0.735329i
$254$	−11.5430			−0.724270
$255$	−5.03158	−	1.47740i	−0.315090	−	0.0925186i
$256$	−7.94878	+	9.17338i	−0.496799	+	0.573336i
$257$	−4.33260	−	2.78440i	−0.270260	−	0.173686i	0.398490	−	0.917173i	$-0.369534\pi$
$257$	−4.33260	−	2.78440i	−0.270260	−	0.173686i	−0.668751	+	0.743487i	$0.733171\pi$
$258$	−1.54282	+	10.7305i	−0.0960516	+	0.668053i
$259$	−8.55423	+	5.49747i	−0.531534	+	0.341596i
$260$	−0.600845	−	1.31567i	−0.0372628	−	0.0815942i
$261$	4.71695	+	5.44365i	0.291972	+	0.336954i
$262$	1.54397	+	10.7385i	0.0953866	+	0.663428i
$263$	11.9312	−	26.1257i	0.735710	−	1.61098i	−0.0547755	−	0.998499i	$-0.517444\pi$
$263$	11.9312	−	26.1257i	0.735710	−	1.61098i	0.790485	−	0.612481i	$-0.209828\pi$
$264$	6.61811	−	1.94325i	0.407317	−	0.119599i
$265$	−1.35162	+	0.396873i	−0.0830296	+	0.0243797i
$266$	1.47611	−	3.23223i	0.0905062	−	0.198181i
$267$	−0.731405	−	5.08703i	−0.0447612	−	0.311321i
$268$	4.91763	+	5.67524i	0.300392	+	0.346671i
$269$	8.22703	+	18.0147i	0.501611	+	1.09837i	0.975942	+	0.218028i	$0.0699625\pi$
$269$	8.22703	+	18.0147i	0.501611	+	1.09837i	−0.474332	+	0.880346i	$0.657310\pi$
$270$	−1.34125	+	0.861971i	−0.0816261	+	0.0524579i
$271$	−4.16732	+	28.9843i	−0.253146	+	1.76067i	0.325926	+	0.945395i	$0.394324\pi$
$271$	−4.16732	+	28.9843i	−0.253146	+	1.76067i	−0.579072	+	0.815276i	$0.696585\pi$
$272$	21.1321	+	13.5808i	1.28132	+	0.823455i
$273$	−1.74769	+	2.01695i	−0.105775	+	0.122071i
$274$	3.95582	+	1.16153i	0.238980	+	0.0701708i
$275$	−11.8685			−0.715700
$276$	−1.48039	+	2.13633i	−0.0891092	+	0.128592i
$277$	−5.97691			−0.359118			−0.179559	−	0.983747i	$-0.557467\pi$
$277$	−5.97691			−0.359118			−0.179559	+	0.983747i	$0.557467\pi$
$278$	22.0783	+	6.48278i	1.32417	+	0.388811i
$279$	6.01024	−	6.93619i	0.359824	−	0.415259i
$280$	1.95561	+	1.25679i	0.116870	+	0.0751077i
$281$	2.26943	−	15.7842i	0.135383	−	0.941607i	−0.802993	−	0.595989i	$-0.796760\pi$
$281$	2.26943	−	15.7842i	0.135383	−	0.941607i	0.938375	−	0.345618i	$-0.112331\pi$
$282$	8.19061	−	5.26379i	0.487744	−	0.313454i
$283$	−9.27440	−	20.3081i	−0.551306	−	1.20719i	−0.956169	−	0.292815i	$-0.905408\pi$
$283$	−9.27440	−	20.3081i	−0.551306	−	1.20719i	0.404863	−	0.914377i	$-0.367319\pi$
$284$	4.16938	+	4.81172i	0.247407	+	0.285523i
$285$	0.317178	+	2.20602i	0.0187880	+	0.130673i
$286$	5.24469	−	11.4843i	0.310125	−	0.679079i
$287$	−7.04048	+	2.06727i	−0.415586	+	0.122027i
$288$	2.86695	−	0.841812i	0.168937	−	0.0496043i
$289$	4.36164	−	9.55067i	0.256567	−	0.561804i
$290$	−1.63436	−	11.3672i	−0.0959727	−	0.667505i
$291$	6.84877	+	7.90391i	0.401482	+	0.463335i
$292$	−1.07749	−	2.35938i	−0.0630555	−	0.138072i
$293$	−15.7652	+	10.1317i	−0.921013	+	0.591899i	−0.912951	−	0.408068i	$-0.866203\pi$
$293$	−15.7652	+	10.1317i	−0.921013	+	0.591899i	−0.00806188	+	0.999968i	$0.502566\pi$
$294$	−0.226900	+	1.57812i	−0.0132331	+	0.0920380i
$295$	9.28776	+	5.96888i	0.540754	+	0.347522i
$296$	−15.4795	+	17.8643i	−0.899729	+	1.03834i
$297$	−2.84695	−	0.835939i	−0.165197	−	0.0485061i
$298$	−29.6686			−1.71866
$299$	−3.17662	−	12.3987i	−0.183709	−	0.717033i
$300$	−2.16782			−0.125159
$301$	−6.52412	−	1.91565i	−0.376044	−	0.110416i
$302$	−4.72719	+	5.45547i	−0.272019	+	0.313927i
$303$	−14.2914	−	9.18450i	−0.821017	−	0.527636i
$304$	1.51935	−	10.5673i	0.0871404	−	0.606075i
$305$	−2.71259	+	1.74328i	−0.155322	+	0.0998197i
$306$	−3.47319	−	7.60522i	−0.198549	−	0.434762i
$307$	3.08960	+	3.56558i	0.176333	+	0.203499i	0.837035	−	0.547149i	$-0.184287\pi$
$307$	3.08960	+	3.56558i	0.176333	+	0.203499i	−0.660703	+	0.750648i	$0.729742\pi$
$308$	−0.228850	−	1.59169i	−0.0130400	−	0.0906949i
$309$	7.48113	−	16.3814i	0.425587	−	0.931905i
$310$	−14.0401	+	4.12253i	−0.797422	+	0.234144i
$311$	15.9143	−	4.67286i	0.902417	−	0.264974i	0.202571	−	0.979268i	$-0.435070\pi$
$311$	15.9143	−	4.67286i	0.902417	−	0.264974i	0.699846	+	0.714294i	$0.253252\pi$
$312$	−2.57723	+	5.64335i	−0.145907	+	0.319492i
$313$	−0.636810	−	4.42911i	−0.0359946	−	0.250348i	0.963877	−	0.266346i	$-0.0858165\pi$
$313$	−0.636810	−	4.42911i	−0.0359946	−	0.250348i	−0.999872	+	0.0159982i	$0.994907\pi$
$314$	14.5041	+	16.7386i	0.818513	+	0.944615i
$315$	−0.415415	−	0.909632i	−0.0234060	−	0.0512520i
$316$	6.91917	−	4.44668i	0.389234	−	0.250145i
$317$	−1.64231	+	11.4225i	−0.0922412	+	0.641552i	0.890282	+	0.455410i	$0.150507\pi$
$317$	−1.64231	+	11.4225i	−0.0922412	+	0.641552i	−0.982523	+	0.186141i	$0.940402\pi$
$318$	−1.88940	−	1.21425i	−0.105953	−	0.0680916i
$319$	13.9958	−	16.1521i	0.783617	−	0.904342i
$320$	4.62139	+	1.35696i	0.258344	+	0.0758566i
$321$	−4.65927			−0.260055
$322$	−5.60099	−	5.20518i	−0.312131	−	0.290073i
$323$	−11.6873			−0.650300
$324$	−0.520003	−	0.152687i	−0.0288890	−	0.00848258i
$325$	6.99077	−	8.06778i	0.387778	−	0.447520i
$326$	1.91814	+	1.23271i	0.106236	+	0.0682738i
$327$	1.00012	−	6.95601i	0.0553069	−	0.384668i
$328$	−14.3497	+	9.22198i	−0.792329	+	0.509199i
$329$	2.53681	+	5.55484i	0.139859	+	0.306248i
$330$	3.09792	+	3.57519i	0.170535	+	0.196808i
$331$	2.60170	+	18.0952i	0.143002	+	0.994603i	0.927327	+	0.374252i	$0.122101\pi$
$331$	2.60170	+	18.0952i	0.143002	+	0.994603i	−0.784324	+	0.620351i	$0.786990\pi$
$332$	2.23448	−	4.89283i	0.122633	−	0.268529i
$333$	9.75654	−	2.86478i	0.534655	−	0.156989i
$334$	12.1717	−	3.57394i	0.666008	−	0.195557i
$335$	5.75606	−	12.6040i	0.314487	−	0.688630i
$336$	0.681716	+	4.74144i	0.0371906	+	0.258667i
$337$	8.64299	+	9.97455i	0.470814	+	0.543348i	0.940638	−	0.339412i	$-0.110228\pi$
$337$	8.64299	+	9.97455i	0.470814	+	0.543348i	−0.469824	+	0.882760i	$0.655683\pi$
$338$	−3.89277	−	8.52397i	−0.211739	−	0.463643i
$339$	10.3743	−	6.66717i	0.563455	−	0.362111i
$340$	−0.404461	+	2.81308i	−0.0219350	+	0.152561i
$341$	−22.9091	−	14.7228i	−1.24060	−	0.797283i
$342$	−2.32694	+	2.68544i	−0.125827	+	0.145212i
$343$	−0.959493	−	0.281733i	−0.0518078	−	0.0152121i
$344$	−15.8065			−0.852228
$345$	4.72041	+	0.847210i	0.254138	+	0.0456122i
$346$	−14.8701			−0.799421
$347$	11.1101	+	3.26221i	0.596420	+	0.175125i	0.565990	−	0.824412i	$-0.308494\pi$
$347$	11.1101	+	3.26221i	0.596420	+	0.175125i	0.0304300	+	0.999537i	$0.490312\pi$
$348$	2.55638	−	2.95022i	0.137036	−	0.158148i
$349$	−13.8403	−	8.89461i	−0.740853	−	0.476118i	0.114981	−	0.993368i	$-0.463319\pi$
$349$	−13.8403	−	8.89461i	−0.740853	−	0.476118i	−0.855834	+	0.517250i	$0.826956\pi$
$350$	0.907599	−	6.31249i	0.0485132	−	0.337417i
$351$	2.24514	−	1.44286i	0.119837	−	0.0770143i
$352$	−3.68297	−	8.06458i	−0.196303	−	0.429843i
$353$	−2.94968	−	3.40411i	−0.156996	−	0.181183i	0.671803	−	0.740730i	$-0.265520\pi$
$353$	−2.94968	−	3.40411i	−0.156996	−	0.181183i	−0.828798	+	0.559548i	$0.810975\pi$
$354$	2.50506	+	17.4231i	0.133142	+	0.926026i
$355$	4.88024	−	10.6862i	0.259016	−	0.567167i
$356$	−2.67247	+	0.784708i	−0.141641	+	0.0415895i
$357$	5.03158	−	1.47740i	0.266299	−	0.0781925i
$358$	1.11620	−	2.44414i	0.0589931	−	0.129177i
$359$	−0.371086	−	2.58096i	−0.0195852	−	0.136218i	0.977683	−	0.210087i	$-0.0673746\pi$
$359$	−0.371086	−	2.58096i	−0.0195852	−	0.136218i	−0.997268	+	0.0738685i	$0.976465\pi$
$360$	−1.52231	−	1.75684i	−0.0802329	−	0.0925937i
$361$	−5.82946	−	12.7647i	−0.306814	−	0.671828i
$362$	6.52538	−	4.19361i	0.342966	−	0.220411i
$363$	0.312538	−	2.17375i	0.0164040	−	0.114092i
$364$	1.21677	+	0.781968i	0.0637758	+	0.0409862i
$365$	−3.13413	+	3.61698i	−0.164048	+	0.189321i
$366$	−4.93268	−	1.44837i	−0.257835	−	0.0757073i
$367$	21.0690			1.09979			0.549897	−	0.835232i	$-0.314667\pi$
$367$	21.0690			1.09979			0.549897	+	0.835232i	$0.314667\pi$
$368$	−20.5524	−	10.2644i	−1.07137	−	0.535066i
$369$	7.33771			0.381986
$370$	−15.5554	−	4.56746i	−0.808684	−	0.237451i
$371$	0.922493	−	1.06461i	0.0478934	−	0.0552720i
$372$	−4.18440	−	2.68915i	−0.216951	−	0.139426i
$373$	1.79187	−	12.4627i	0.0927795	−	0.645296i	−0.889369	−	0.457190i	$-0.848856\pi$
$373$	1.79187	−	12.4627i	0.0927795	−	0.645296i	0.982149	−	0.188106i	$-0.0602349\pi$
$374$	−20.8694	+	13.4120i	−1.07913	+	0.693517i
$375$	3.73874	+	8.18669i	0.193067	+	0.422759i
$376$	9.29628	+	10.7285i	0.479419	+	0.553279i
$377$	2.73577	+	19.0277i	0.140899	+	0.979975i
$378$	0.662317	−	1.45027i	0.0340659	−	0.0745940i
$379$	−0.187190	+	0.0549641i	−0.00961533	+	0.00282331i	−0.286537	−	0.958069i	$-0.592504\pi$
$379$	−0.187190	+	0.0549641i	−0.00961533	+	0.00282331i	0.276921	+	0.960893i	$0.410686\pi$
$380$	1.15893	−	0.340294i	0.0594520	−	0.0174567i
$381$	−3.00757	+	6.58566i	−0.154082	+	0.337393i
$382$	−4.28624	−	29.8115i	−0.219303	−	1.52529i
$383$	4.73024	+	5.45898i	0.241704	+	0.278941i	0.863621	−	0.504142i	$-0.168191\pi$
$383$	4.73024	+	5.45898i	0.241704	+	0.278941i	−0.621917	+	0.783083i	$0.713646\pi$
$384$	5.67256	+	12.4212i	0.289476	+	0.633865i
$385$	−2.49611	+	1.60416i	−0.127214	+	0.0817553i
$386$	1.68489	−	11.7186i	0.0857585	−	0.596463i
$387$	5.72014	+	3.67611i	0.290771	+	0.186867i
$388$	3.71173	−	4.28357i	0.188435	−	0.217465i
$389$	−25.3690	−	7.44901i	−1.28626	−	0.377680i	−0.434054	−	0.900887i	$-0.642917\pi$
$389$	−25.3690	−	7.44901i	−1.28626	−	0.377680i	−0.852206	+	0.523207i	$0.824736\pi$
$390$	−4.25501			−0.215461
$391$	−7.92037	+	23.8696i	−0.400551	+	1.20714i
$392$	−2.32463			−0.117412
$393$	6.52898	+	1.91708i	0.329344	+	0.0967040i
$394$	−17.0734	+	19.7037i	−0.860143	+	0.992659i
$395$	−12.7670	−	8.20488i	−0.642379	−	0.412832i
$396$	−0.228850	+	1.59169i	−0.0115002	+	0.0799854i
$397$	−21.7232	+	13.9606i	−1.09025	+	0.700664i	−0.956904	−	0.290405i	$-0.906210\pi$
$397$	−21.7232	+	13.9606i	−1.09025	+	0.700664i	−0.133351	+	0.991069i	$0.542574\pi$
$398$	−13.6514	−	29.8924i	−0.684283	−	1.49837i
$399$	−1.45949	−	1.68434i	−0.0730660	−	0.0843227i
$400$	−2.72686	−	18.9658i	−0.136343	−	0.948288i
$401$	−11.4032	+	24.9696i	−0.569450	+	1.24692i	0.377640	+	0.925953i	$0.376736\pi$
$401$	−11.4032	+	24.9696i	−0.569450	+	1.24692i	−0.947090	+	0.320969i	$0.895992\pi$
$402$	21.1967	−	6.22392i	1.05720	−	0.310421i
$403$	23.5018	−	6.90075i	1.17071	−	0.343751i
$404$	−3.82466	+	8.37483i	−0.190284	+	0.416664i
$405$	0.142315	+	0.989821i	0.00707168	+	0.0491846i
$406$	7.52048	+	8.67910i	0.373235	+	0.430736i
$407$	−12.5335	−	27.4446i	−0.621265	−	1.36038i
$408$	10.2552	−	6.59061i	0.507708	−	0.326284i
$409$	1.98093	−	13.7777i	0.0979508	−	0.681263i	−0.880388	−	0.474254i	$-0.842718\pi$
$409$	1.98093	−	13.7777i	0.0979508	−	0.681263i	0.978339	−	0.207009i	$-0.0663730\pi$
$410$	−9.84173	−	6.32490i	−0.486048	−	0.312364i
$411$	1.69340	−	1.95429i	0.0835293	−	0.0963980i
$412$	−9.36463	−	2.74970i	−0.461362	−	0.135468i
$413$	−11.0404			−0.543262
$414$	3.90764	+	6.57231i	0.192050	+	0.323012i
$415$	−9.92501			−0.487199
$416$	7.65132	+	2.24663i	0.375137	+	0.110150i
$417$	9.45125	−	10.9073i	0.462829	−	0.534134i
$418$	8.86955	+	5.70011i	0.433824	+	0.278802i
$419$	−3.46036	+	24.0673i	−0.169050	+	1.17577i	0.711804	+	0.702378i	$0.247878\pi$
$419$	−3.46036	+	24.0673i	−0.169050	+	1.17577i	−0.880854	+	0.473388i	$0.843031\pi$
$420$	−0.455922	+	0.293003i	−0.0222467	+	0.0142971i
$421$	−6.16690	−	13.5036i	−0.300556	−	0.658127i	0.697748	−	0.716344i	$-0.254186\pi$
$421$	−6.16690	−	13.5036i	−0.300556	−	0.658127i	−0.998304	+	0.0582170i	$0.981458\pi$
$422$	−6.69825	−	7.73019i	−0.326066	−	0.376300i
$423$	−0.869072	−	6.04453i	−0.0422557	−	0.293895i
$424$	1.36035	−	2.97875i	0.0660645	−	0.144661i
$425$	−20.1263	+	5.90962i	−0.976269	+	0.286659i
$426$	17.9715	−	5.27692i	0.870723	−	0.255667i
$427$	1.33949	−	2.93307i	0.0648225	−	0.141941i
$428$	0.359362	+	2.49941i	0.0173704	+	0.120814i
$429$	−5.18565	−	5.98455i	−0.250365	−	0.288937i
$430$	−4.50346	−	9.86120i	−0.217176	−	0.475549i
$431$	16.2885	−	10.4680i	0.784588	−	0.504224i	−0.0859653	−	0.996298i	$-0.527397\pi$
$431$	16.2885	−	10.4680i	0.784588	−	0.504224i	0.870553	+	0.492074i	$0.163761\pi$
$432$	0.681716	−	4.74144i	0.0327991	−	0.228123i
$433$	11.8426	+	7.61076i	0.569118	+	0.365750i	0.793331	−	0.608790i	$-0.208345\pi$
$433$	11.8426	+	7.61076i	0.569118	+	0.365750i	−0.224213	+	0.974540i	$0.571981\pi$
$434$	9.58244	−	11.0587i	0.459972	−	0.530836i
$435$	−6.91121	−	2.02932i	−0.331367	−	0.0972982i
$436$	−3.80861			−0.182400
$437$	10.6262	−	1.15224i	0.508321	−	0.0551192i
$438$	−7.63049			−0.364599
$439$	−27.2564	−	8.00320i	−1.30088	−	0.381972i	−0.443321	−	0.896363i	$-0.646200\pi$
$439$	−27.2564	−	8.00320i	−1.30088	−	0.381972i	−0.857556	+	0.514391i	$0.828018\pi$
$440$	−4.51691	+	5.21279i	−0.215335	+	0.248510i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	3.17550	−	22.0861i	0.151043	−	1.05053i
$443$	20.1335	−	12.9390i	0.956570	−	0.614750i	0.0335234	−	0.999438i	$-0.489327\pi$
$443$	20.1335	−	12.9390i	0.956570	−	0.614750i	0.923047	+	0.384688i	$0.125691\pi$
$444$	−2.28929	−	5.01284i	−0.108645	−	0.237899i
$445$	3.36555	+	3.88406i	0.159543	+	0.184122i
$446$	3.58957	+	24.9660i	0.169971	+	1.18217i
$447$	−7.73029	+	16.9270i	−0.365630	+	0.800618i
$448$	−4.62139	+	1.35696i	−0.218340	+	0.0641105i
$449$	33.6247	−	9.87311i	1.58685	−	0.465941i	0.635000	−	0.772512i	$-0.281000\pi$
$449$	33.6247	−	9.87311i	1.58685	−	0.465941i	0.951848	+	0.306571i	$0.0991817\pi$
$450$	−2.64927	+	5.80109i	−0.124888	+	0.273466i
$451$	−3.09848	−	21.5504i	−0.145902	−	1.01477i
$452$	−4.37668	−	5.05096i	−0.205862	−	0.237577i
$453$	1.88084	+	4.11847i	0.0883697	+	0.193503i
$454$	4.16714	−	2.67806i	0.195573	−	0.125687i
$455$	0.379810	−	2.64164i	0.0178058	−	0.123842i
$456$	−4.35848	−	2.80102i	−0.204104	−	0.131170i
$457$	−4.89835	+	5.65299i	−0.229135	+	0.264436i	−0.858661	−	0.512543i	$-0.828703\pi$
$457$	−4.89835	+	5.65299i	−0.229135	+	0.264436i	0.629526	+	0.776979i	$0.283249\pi$
$458$	−1.42229	−	0.417623i	−0.0664593	−	0.0195142i
$459$	−5.24399			−0.244769
$460$	0.0903996	−	2.59756i	0.00421490	−	0.121112i
$461$	−11.7289			−0.546268			−0.273134	−	0.961976i	$-0.588060\pi$
$461$	−11.7289			−0.546268			−0.273134	+	0.961976i	$0.588060\pi$
$462$	−4.53903	−	1.33278i	−0.211175	−	0.0620066i
$463$	20.7053	−	23.8952i	0.962257	−	1.11050i	−0.0315635	−	0.999502i	$-0.510049\pi$
$463$	20.7053	−	23.8952i	0.962257	−	1.11050i	0.993820	−	0.111002i	$-0.0354059\pi$
$464$	29.0264	+	18.6541i	1.34752	+	0.865995i
$465$	−1.30615	+	9.08448i	−0.0605713	+	0.421283i
$466$	−18.4836	+	11.8787i	−0.856236	+	0.550270i
$467$	−7.03775	−	15.4105i	−0.325668	−	0.713114i	0.674004	−	0.738728i	$-0.264573\pi$
$467$	−7.03775	−	15.4105i	−0.325668	−	0.713114i	−0.999672	+	0.0256141i	$0.991846\pi$
$468$	−0.947172	−	1.09310i	−0.0437831	−	0.0505283i
$469$	1.97194	+	13.7151i	0.0910556	+	0.633305i
$470$	−4.04456	+	8.85636i	−0.186562	+	0.408513i
$471$	13.3291	−	3.91376i	0.614170	−	0.180337i
$472$	−24.6252	+	7.23062i	−1.13347	+	0.332816i
$473$	8.38108	−	18.3520i	0.385362	−	0.843826i
$474$	−3.44348	−	23.9499i	−0.158164	−	1.10006i
$475$	5.83797	+	6.73738i	0.267865	+	0.309132i
$476$	−1.18061	−	2.58519i	−0.0541134	−	0.118492i
$477$	−1.18506	+	0.761593i	−0.0542602	+	0.0348709i
$478$	−5.86730	+	40.8080i	−0.268364	+	1.86651i
$479$	−16.5745	−	10.6518i	−0.757307	−	0.486691i	0.104125	−	0.994564i	$-0.466796\pi$
$479$	−16.5745	−	10.6518i	−0.757307	−	0.486691i	−0.861432	+	0.507873i	$0.830432\pi$
$480$	−1.95671	+	2.25817i	−0.0893113	+	0.103071i
$481$	26.0383	+	7.64553i	1.18724	+	0.348606i
$482$	16.4507			0.749310
$483$	−4.42909	+	1.83933i	−0.201531	+	0.0836922i
$484$	−1.19019			−0.0540995
$485$	−10.0347	−	2.94646i	−0.455654	−	0.133792i
$486$	−1.04408	+	1.20493i	−0.0473603	+	0.0546567i
$487$	18.3628	+	11.8010i	0.832097	+	0.534756i	0.885944	−	0.463793i	$-0.153512\pi$
$487$	18.3628	+	11.8010i	0.832097	+	0.534756i	−0.0538466	+	0.998549i	$0.517148\pi$
$488$	1.06675	−	7.41940i	0.0482895	−	0.335861i
$489$	1.20309	−	0.773176i	0.0544054	−	0.0349642i
$490$	−0.662317	−	1.45027i	−0.0299205	−	0.0655166i
$491$	−5.49024	−	6.33607i	−0.247771	−	0.285943i	0.618217	−	0.786007i	$-0.287855\pi$
$491$	−5.49024	−	6.33607i	−0.247771	−	0.285943i	−0.865988	+	0.500064i	$0.833310\pi$
$492$	−0.565945	−	3.93624i	−0.0255148	−	0.177459i
$493$	15.6912	−	34.3590i	0.706698	−	1.54745i
$494$	−9.09903	+	2.67172i	−0.409385	+	0.120206i
$495$	2.84695	−	0.835939i	0.127961	−	0.0375727i
$496$	18.2633	−	39.9910i	0.820045	−	1.79565i
$497$	1.67190	+	11.6283i	0.0749948	+	0.521600i
$498$	−10.3625	−	11.9589i	−0.464354	−	0.535893i
$499$	−1.02889	−	2.25296i	−0.0460596	−	0.100857i	0.885203	−	0.465204i	$-0.154019\pi$
$499$	−1.02889	−	2.25296i	−0.0460596	−	0.100857i	−0.931263	+	0.364348i	$0.881292\pi$
$500$	4.10330	−	2.63703i	0.183505	−	0.117932i
$501$	1.13234	−	7.87560i	0.0505892	−	0.351856i
$502$	−6.05746	−	3.89289i	−0.270358	−	0.173748i
$503$	−0.273651	+	0.315811i	−0.0122015	+	0.0140813i	−0.761818	−	0.647792i	$-0.775693\pi$
$503$	−0.273651	+	0.315811i	−0.0122015	+	0.0140813i	0.749616	+	0.661873i	$0.230238\pi$
$504$	2.23047	+	0.654925i	0.0993531	+	0.0291727i
$505$	16.9882			0.755964
$506$	17.6524	−	14.2518i	0.784744	−	0.633569i
$507$	−5.87750			−0.261029
$508$	3.76477	+	1.10544i	0.167035	+	0.0490459i
$509$	−11.5536	+	13.3336i	−0.512105	+	0.591001i	−0.951636	−	0.307227i	$-0.900599\pi$
$509$	−11.5536	+	13.3336i	−0.512105	+	0.591001i	0.439531	+	0.898227i	$0.355144\pi$
$510$	7.03353	+	4.52017i	0.311450	+	0.200157i
$511$	0.681112	−	4.73724i	0.0301306	−	0.209563i
$512$	−6.69460	+	4.30236i	−0.295862	+	0.190139i
$513$	0.925839	+	2.02730i	0.0408768	+	0.0895076i
$514$	5.37719	+	6.20560i	0.237177	+	0.273717i
$515$	2.56292	+	17.8255i	0.112936	+	0.785486i
$516$	1.53083	−	3.35204i	0.0673909	−	0.147565i
$517$	−17.3854	+	5.10482i	−0.764609	+	0.224510i
$518$	15.5554	−	4.56746i	0.683463	−	0.200683i
$519$	−3.87447	+	8.48390i	−0.170070	+	0.372402i
$520$	−0.882920	−	6.14084i	−0.0387186	−	0.269294i
$521$	24.8665	+	28.6974i	1.08942	+	1.25726i	0.964213	+	0.265127i	$0.0854140\pi$
$521$	24.8665	+	28.6974i	1.08942	+	1.25726i	0.125207	+	0.992131i	$0.460041\pi$
$522$	−4.77066	−	10.4463i	−0.208806	−	0.457222i
$523$	17.7532	−	11.4093i	0.776292	−	0.498893i	−0.0915092	−	0.995804i	$-0.529169\pi$
$523$	17.7532	−	11.4093i	0.776292	−	0.498893i	0.867801	+	0.496912i	$0.165533\pi$
$524$	0.524829	−	3.65026i	0.0229273	−	0.159463i
$525$	−3.36501	−	2.16256i	−0.146861	−	0.0943820i
$526$	−29.9871	+	34.6070i	−1.30750	+	1.50894i
$527$	−46.1793	−	13.5595i	−2.01160	−	0.590659i
$528$	−14.2132			−0.618549
$529$	4.84799	−	22.4833i	0.210782	−	0.977533i
$530$	2.24594			0.0975574
$531$	10.5932	+	3.11043i	0.459704	+	0.134981i
$532$	−0.790980	+	0.912840i	−0.0342933	+	0.0395766i
$533$	16.4742	+	10.5873i	0.713576	+	0.458587i
$534$	−1.16612	+	8.11052i	−0.0504628	+	0.350976i
$535$	3.91963	−	2.51899i	0.169460	−	0.108905i
$536$	13.3807	+	29.2997i	0.577959	+	1.26555i
$537$	−1.10364	−	1.27366i	−0.0476254	−	0.0549626i
$538$	−4.49361	−	31.2537i	−0.193733	−	1.34744i
$539$	1.23259	−	2.69900i	0.0530915	−	0.116254i
$540$	0.520003	−	0.152687i	0.0223773	−	0.00657058i
$541$	−35.6079	+	10.4554i	−1.53090	+	0.449513i	−0.935326	−	0.353787i	$-0.884894\pi$
$541$	−35.6079	+	10.4554i	−1.53090	+	0.449513i	−0.595575	+	0.803300i	$0.703076\pi$
$542$	19.3942	−	42.4674i	0.833053	−	1.82413i
$543$	−0.692381	−	4.81562i	−0.0297129	−	0.206658i
$544$	−10.2610	−	11.8418i	−0.439937	−	0.507714i
$545$	2.91934	+	6.39247i	0.125051	+	0.273823i
$546$	3.57954	−	2.30043i	0.153190	−	0.0984493i
$547$	−5.40979	+	37.6259i	−0.231306	+	1.60877i	0.461160	+	0.887317i	$0.347433\pi$
$547$	−5.40979	+	37.6259i	−0.231306	+	1.60877i	−0.692466	+	0.721450i	$0.743476\pi$
$548$	−1.17897	−	0.757676i	−0.0503629	−	0.0323663i
$549$	−2.11157	+	2.43689i	−0.0901198	+	0.104004i
$550$	18.1561	+	5.33112i	0.774180	+	0.227320i
$551$	−16.0533			−0.683896
$552$	−8.67434	+	7.00329i	−0.369205	+	0.298080i
$553$	15.1762			0.645358
$554$	9.14329	+	2.68471i	0.388461	+	0.114062i
$555$	−6.65891	+	7.68479i	−0.282655	+	0.326201i
$556$	−6.58007	−	4.22876i	−0.279057	−	0.179339i
$557$	1.97051	−	13.7052i	0.0834933	−	0.580709i	−0.904531	−	0.426409i	$-0.859779\pi$
$557$	1.97051	−	13.7052i	0.0834933	−	0.580709i	0.988024	−	0.154300i	$-0.0493123\pi$
$558$	−12.3099	+	7.91108i	−0.521119	+	0.334903i
$559$	7.53839	+	16.5068i	0.318840	+	0.698162i
$560$	−3.13691	−	3.62019i	−0.132559	−	0.152981i
$561$	2.21437	+	15.4013i	0.0934907	+	0.650242i
$562$	−10.5617	+	23.1268i	−0.445517	+	0.975545i
$563$	−5.20068	+	1.52706i	−0.219183	+	0.0643578i	−0.389480	−	0.921035i	$-0.627345\pi$
$563$	−5.20068	+	1.52706i	−0.219183	+	0.0643578i	0.170298	+	0.985393i	$0.445527\pi$
$564$	−3.17549	+	0.932408i	−0.133712	+	0.0392615i
$565$	−5.12289	+	11.2176i	−0.215521	+	0.471926i
$566$	5.06568	+	35.2326i	0.212927	+	1.48094i
$567$	−0.654861	−	0.755750i	−0.0275016	−	0.0317385i
$568$	11.3448	+	24.8416i	0.476016	+	1.04233i
$569$	−8.91070	+	5.72656i	−0.373556	+	0.240070i	−0.713925	−	0.700222i	$-0.753084\pi$
$569$	−8.91070	+	5.72656i	−0.373556	+	0.240070i	0.340369	+	0.940292i	$0.389448\pi$
$570$	0.505693	−	3.51717i	0.0211812	−	0.147318i
$571$	−10.1173	−	6.50198i	−0.423395	−	0.272100i	0.311545	−	0.950231i	$-0.399153\pi$
$571$	−10.1173	−	6.50198i	−0.423395	−	0.272100i	−0.734940	+	0.678132i	$0.762790\pi$
$572$	−2.81039	+	3.24336i	−0.117508	+	0.135612i
$573$	−18.1253	−	5.32206i	−0.757194	−	0.222332i
$574$	11.6989			0.488302
$575$	17.7164	−	7.35730i	0.738824	−	0.306821i
$576$	4.81650			0.200687
$577$	10.5076	+	3.08531i	0.437437	+	0.128443i	0.493034	−	0.870010i	$-0.335888\pi$
$577$	10.5076	+	3.08531i	0.437437	+	0.128443i	−0.0555969	+	0.998453i	$0.517706\pi$
$578$	−10.9623	+	12.6511i	−0.455971	+	0.526218i
$579$	−6.24689	−	4.01463i	−0.259612	−	0.166842i
$580$	−0.555554	+	3.86396i	−0.0230681	+	0.160442i
$581$	8.34945	−	5.36586i	0.346393	−	0.222614i
$582$	−6.92676	−	15.1675i	−0.287123	−	0.628713i
$583$	2.73716	+	3.15885i	0.113362	+	0.130826i
$584$	−1.58334	−	11.0123i	−0.0655189	−	0.455694i
$585$	−1.10866	+	2.42763i	−0.0458375	+	0.100370i
$586$	28.6681	−	8.41771i	1.18427	−	0.347732i
$587$	−4.78522	+	1.40507i	−0.197507	+	0.0579934i	−0.378990	−	0.925401i	$-0.623729\pi$
$587$	−4.78522	+	1.40507i	−0.197507	+	0.0579934i	0.181483	+	0.983394i	$0.441910\pi$
$588$	0.225136	−	0.492980i	0.00928447	−	0.0203302i
$589$	2.91103	+	20.2466i	0.119947	+	0.834248i
$590$	−11.5270	−	13.3029i	−0.474560	−	0.547671i
$591$	6.79310	+	14.8748i	0.279431	+	0.611868i
$592$	40.9764	−	26.3340i	1.68412	−	1.08232i
$593$	2.48357	−	17.2736i	0.101988	−	0.709342i	−0.873103	−	0.487536i	$-0.837896\pi$
$593$	2.48357	−	17.2736i	0.101988	−	0.709342i	0.975091	−	0.221806i	$-0.0711952\pi$
$594$	3.97968	+	2.55759i	0.163288	+	0.104939i
$595$	−3.43409	+	3.96315i	−0.140784	+	0.162473i
$596$	9.67651	+	2.84128i	0.396365	+	0.116383i
$597$	−20.6116			−0.843575
$598$	−0.709746	+	20.3940i	−0.0290237	+	0.833971i
$599$	33.0231			1.34929			0.674644	−	0.738143i	$-0.264297\pi$
$599$	33.0231			1.34929			0.674644	+	0.738143i	$0.264297\pi$
$600$	−8.92188	−	2.61970i	−0.364234	−	0.106949i
$601$	15.9817	−	18.4439i	0.651907	−	0.752341i	−0.329526	−	0.944147i	$-0.606889\pi$
$601$	15.9817	−	18.4439i	0.651907	−	0.752341i	0.981433	+	0.191806i	$0.0614344\pi$
$602$	9.11992	+	5.86102i	0.371700	+	0.238877i
$603$	1.97194	−	13.7151i	0.0803035	−	0.558523i
$604$	2.06424	−	1.32661i	0.0839928	−	0.0539789i
$605$	0.912293	+	1.99764i	0.0370900	+	0.0812157i
$606$	17.7370	+	20.4696i	0.720516	+	0.831519i
$607$	5.33244	+	37.0879i	0.216437	+	1.50535i	0.751044	+	0.660252i	$0.229551\pi$
$607$	5.33244	+	37.0879i	0.216437	+	1.50535i	−0.534607	+	0.845101i	$0.679540\pi$
$608$	−2.76639	+	6.05755i	−0.112192	+	0.245666i
$609$	6.91121	−	2.02932i	0.280057	−	0.0822320i
$610$	4.93268	−	1.44837i	0.199718	−	0.0586426i
$611$	6.77024	−	14.8248i	0.273895	−	0.599745i
$612$	0.404461	+	2.81308i	0.0163493	+	0.113712i
$613$	15.9599	+	18.4188i	0.644616	+	0.743927i	0.980184	−	0.198089i	$-0.0634736\pi$
$613$	15.9599	+	18.4188i	0.644616	+	0.743927i	−0.335568	+	0.942016i	$0.608928\pi$
$614$	−3.12478	−	6.84231i	−0.126106	−	0.276133i
$615$	−6.17287	+	3.96707i	−0.248914	+	0.159968i
$616$	0.981618	−	6.82730i	0.0395505	−	0.275080i
$617$	14.9443	+	9.60414i	0.601636	+	0.386648i	0.805712	−	0.592307i	$-0.201783\pi$
$617$	14.9443	+	9.60414i	0.601636	+	0.386648i	−0.204076	+	0.978955i	$0.565419\pi$
$618$	−18.8026	+	21.6994i	−0.756352	+	0.872876i
$619$	1.70072	+	0.499378i	0.0683579	+	0.0200717i	0.315733	−	0.948848i	$-0.397750\pi$
$619$	1.70072	+	0.499378i	0.0683579	+	0.0200717i	−0.247375	+	0.968920i	$0.579568\pi$
$620$	4.97401			0.199761
$621$	4.76788	−	0.517000i	0.191329	−	0.0207465i
$622$	−26.4442			−1.06031
$623$	−4.93116	−	1.44792i	−0.197563	−	0.0580097i
$624$	8.37179	−	9.66156i	0.335140	−	0.386772i
$625$	9.25379	+	5.94705i	0.370152	+	0.237882i
$626$	−1.01530	+	7.06156i	−0.0405795	+	0.282237i
$627$	5.56311	−	3.57519i	0.222169	−	0.142779i
$628$	−3.12754	−	6.84837i	−0.124803	−	0.273280i
$629$	−34.9193	−	40.2990i	−1.39232	−	1.60683i
$630$	0.226900	+	1.57812i	0.00903991	+	0.0628739i
$631$	−10.3780	+	22.7247i	−0.413142	+	0.904656i	0.582625	+	0.812741i	$0.302026\pi$
$631$	−10.3780	+	22.7247i	−0.413142	+	0.904656i	−0.995767	+	0.0919141i	$0.970701\pi$
$632$	33.8501	−	9.93928i	1.34648	−	0.395363i
$633$	−6.15559	+	1.80745i	−0.244663	+	0.0718395i
$634$	7.64312	−	16.7361i	0.303547	−	0.664675i
$635$	−1.03035	−	7.16622i	−0.0408881	−	0.284383i
$636$	0.499950	+	0.576973i	0.0198243	+	0.0228785i
$637$	1.10866	+	2.42763i	0.0439267	+	0.0961861i
$638$	−28.6656	+	18.4223i	−1.13488	+	0.729344i
$639$	1.67190	−	11.6283i	0.0661392	−	0.460008i
$640$	−11.4874	−	7.38253i	−0.454081	−	0.291820i
$641$	−15.6699	+	18.0841i	−0.618925	+	0.714277i	−0.975503	−	0.219988i	$-0.929398\pi$
$641$	−15.6699	+	18.0841i	−0.618925	+	0.714277i	0.356578	+	0.934266i	$0.383944\pi$
$642$	7.12760	+	2.09285i	0.281304	+	0.0825983i
$643$	−29.5539			−1.16549			−0.582746	−	0.812654i	$-0.698022\pi$
$643$	−29.5539			−1.16549			−0.582746	+	0.812654i	$0.698022\pi$
$644$	1.32830	+	2.23408i	0.0523422	+	0.0880349i
$645$	−6.79955			−0.267732
$646$	17.8789	+	5.24972i	0.703436	+	0.206548i
$647$	−19.1023	+	22.0453i	−0.750990	+	0.866689i	−0.994664	−	0.103168i	$-0.967102\pi$
$647$	−19.1023	+	22.0453i	−0.750990	+	0.866689i	0.243674	+	0.969857i	$0.421647\pi$
$648$	−1.95561	−	1.25679i	−0.0768235	−	0.0493715i
$649$	4.66199	−	32.4249i	0.182999	−	1.27279i
$650$	−14.3182	+	9.20172i	−0.561604	+	0.360921i
$651$	−3.81264	−	8.34851i	−0.149429	−	0.327204i
$652$	−0.507554	−	0.585749i	−0.0198774	−	0.0229397i
$653$	4.75250	+	33.0544i	0.185980	+	1.29352i	0.842289	+	0.539026i	$0.181208\pi$
$653$	4.75250	+	33.0544i	0.185980	+	1.29352i	−0.656309	+	0.754492i	$0.727883\pi$
$654$	−4.65446	+	10.1918i	−0.182004	+	0.398533i
$655$	−6.52898	+	1.91708i	−0.255109	+	0.0749066i
$656$	33.7253	−	9.90264i	1.31675	−	0.386633i
$657$	−1.98816	+	4.35345i	−0.0775653	+	0.169844i
$658$	−1.38561	−	9.63710i	−0.0540165	−	0.375693i
$659$	−23.5696	−	27.2008i	−0.918142	−	1.05959i	−0.998027	−	0.0627878i	$-0.980001\pi$
$659$	−23.5696	−	27.2008i	−0.918142	−	1.05959i	0.0798853	−	0.996804i	$-0.474545\pi$
$660$	−0.668011	−	1.46274i	−0.0260023	−	0.0569371i
$661$	−11.9892	+	7.70498i	−0.466325	+	0.299689i	−0.752623	−	0.658452i	$-0.771212\pi$
$661$	−11.9892	+	7.70498i	−0.466325	+	0.299689i	0.286298	+	0.958141i	$0.407575\pi$
$662$	4.14802	−	28.8501i	0.161218	−	1.12129i
$663$	−11.7735	−	7.56637i	−0.457245	−	0.293853i
$664$	15.1090	−	17.4367i	0.586341	−	0.676674i
$665$	2.13843	+	0.627899i	0.0829247	+	0.0243489i
$666$	−16.2121			−0.628204
$667$	−10.8792	+	32.7865i	−0.421243	+	1.26950i
$668$	−4.31212			−0.166841
$669$	15.1792	+	4.45702i	0.586863	+	0.172319i
$670$	−14.4669	+	16.6957i	−0.558905	+	0.645011i
$671$	8.04863	+	5.17254i	0.310714	+	0.199684i
$672$	0.425234	−	2.95757i	0.0164038	−	0.114091i
$673$	1.85494	−	1.19210i	0.0715028	−	0.0459521i	−0.504401	−	0.863470i	$-0.668287\pi$
$673$	1.85494	−	1.19210i	0.0715028	−	0.0459521i	0.575904	+	0.817517i	$0.304650\pi$
$674$	−8.74141	−	19.1410i	−0.336706	−	0.737284i
$675$	2.61944	+	3.02300i	0.100822	+	0.116355i
$676$	0.453321	+	3.15292i	0.0174354	+	0.121266i
$677$	−2.05228	+	4.49388i	−0.0788757	+	0.172714i	−0.944961	−	0.327182i	$-0.893901\pi$
$677$	−2.05228	+	4.49388i	−0.0788757	+	0.172714i	0.866086	+	0.499896i	$0.166628\pi$
$678$	−18.8651	+	5.53928i	−0.724508	+	0.212735i
$679$	10.0347	−	2.94646i	0.385098	−	0.113075i
$680$	−5.06406	+	11.0888i	−0.194198	+	0.425234i
$681$	−0.442157	−	3.07527i	−0.0169435	−	0.117845i
$682$	28.4324	+	32.8127i	1.08873	+	1.25646i
$683$	2.83921	+	6.21701i	0.108640	+	0.237887i	0.956142	−	0.292905i	$-0.0946218\pi$
$683$	2.83921	+	6.21701i	0.108640	+	0.237887i	−0.847502	+	0.530792i	$0.821895\pi$
$684$	1.01612	−	0.653019i	0.0388522	−	0.0249688i
$685$	−0.368011	+	2.55957i	−0.0140610	+	0.0977963i
$686$	1.34125	+	0.861971i	0.0512093	+	0.0329102i
$687$	−0.608852	+	0.702653i	−0.0232292	+	0.0268079i
$688$	31.2518	+	9.17636i	1.19146	+	0.349845i
$689$	−3.75950			−0.143226
$690$	−6.84058	−	3.41635i	−0.260416	−	0.130058i
$691$	12.4129			0.472210			0.236105	−	0.971728i	$-0.424129\pi$
$691$	12.4129			0.472210			0.236105	+	0.971728i	$0.424129\pi$
$692$	4.84993	+	1.42407i	0.184367	+	0.0541349i
$693$	−1.94306	+	2.24241i	−0.0738108	+	0.0851822i
$694$	−15.5305	−	9.98085i	−0.589530	−	0.378868i
$695$	−2.05395	+	14.2855i	−0.0779108	+	0.541882i
$696$	14.0862	−	9.05266i	0.533936	−	0.343140i
$697$	−15.9847	−	35.0017i	−0.605464	−	1.32578i
$698$	17.1771	+	19.8235i	0.650165	+	0.750330i
$699$	1.96122	+	13.6406i	0.0741801	+	0.515934i
$700$	−0.900546	+	1.97192i	−0.0340374	+	0.0745316i
$701$	16.0526	−	4.71347i	0.606298	−	0.178025i	0.0358479	−	0.999357i	$-0.488587\pi$
$701$	16.0526	−	4.71347i	0.606298	−	0.178025i	0.570451	+	0.821332i	$0.306769\pi$
$702$	−4.08265	+	1.19877i	−0.154090	+	0.0452448i
$703$	−9.41433	+	20.6145i	−0.355068	+	0.777491i
$704$	−2.03385	−	14.1457i	−0.0766536	−	0.533137i
$705$	3.99903	+	4.61512i	0.150612	+	0.173816i
$706$	2.98327	+	6.53244i	0.112277	+	0.245852i
$707$	−14.2914	+	9.18450i	−0.537482	+	0.345419i
$708$	0.851526	−	5.92249i	0.0320023	−	0.222581i
$709$	−1.60321	−	1.03032i	−0.0602099	−	0.0386945i	0.510190	−	0.860062i	$-0.329575\pi$
$709$	−1.60321	−	1.03032i	−0.0602099	−	0.0386945i	−0.570399	+	0.821367i	$0.693212\pi$
$710$	−12.2657	+	14.1554i	−0.460323	+	0.531241i
$711$	−14.5615	−	4.27563i	−0.546098	−	0.160349i
$712$	−11.9471			−0.447736
$713$	43.3234	+	7.77560i	1.62247	+	0.291199i
$714$	−8.36077			−0.312894
$715$	7.59794	+	2.23096i	0.284147	+	0.0834330i
$716$	−0.598121	+	0.690269i	−0.0223528	+	0.0257966i
$717$	21.7536	+	13.9802i	0.812403	+	0.522100i
$718$	−0.591642	+	4.11496i	−0.0220799	+	0.153569i
$719$	31.0539	−	19.9572i	1.15812	−	0.744276i	0.186878	−	0.982383i	$-0.440163\pi$
$719$	31.0539	−	19.9572i	1.15812	−	0.744276i	0.971239	+	0.238107i	$0.0765269\pi$
$720$	1.98992	+	4.35731i	0.0741599	+	0.162388i
$721$	−11.7933	−	13.6102i	−0.439204	−	0.506869i
$722$	3.18405	+	22.1456i	0.118498	+	0.824173i
$723$	4.28630	−	9.38570i	0.159409	−	0.349058i
$724$	−2.52988	+	0.742841i	−0.0940224	+	0.0276075i
$725$	−27.6449	+	8.11726i	−1.02670	+	0.301468i
$726$	−1.45451	+	3.18494i	−0.0539821	+	0.118204i
$727$	−1.20291	−	8.36646i	−0.0446136	−	0.310295i	−0.999894	−	0.0145916i	$-0.995355\pi$
$727$	−1.20291	−	8.36646i	−0.0446136	−	0.310295i	0.955280	−	0.295703i	$-0.0955539\pi$
$728$	4.06275	+	4.68866i	0.150576	+	0.173773i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	6.41917	−	4.12535i	0.237584	−	0.152686i
$731$	5.07449	−	35.2939i	0.187687	−	1.30539i
$732$	1.47010	+	0.944778i	0.0543366	+	0.0349200i
$733$	21.2087	−	24.4761i	0.783361	−	0.904046i	−0.213987	−	0.976837i	$-0.568645\pi$
$733$	21.2087	−	24.4761i	0.783361	−	0.904046i	0.997347	+	0.0727902i	$0.0231903\pi$
$734$	−32.2307	−	9.46380i	−1.18966	−	0.349315i
$735$	−1.00000			−0.0368856
$736$	10.4969	+	9.75506i	0.386919	+	0.359576i
$737$	−41.1131			−1.51442
$738$	−11.2250	−	3.29596i	−0.413198	−	0.121326i
$739$	−22.2763	+	25.7082i	−0.819448	+	0.945693i	−0.999278	−	0.0380045i	$-0.987900\pi$
$739$	−22.2763	+	25.7082i	−0.819448	+	0.945693i	0.179830	+	0.983698i	$0.442445\pi$
$740$	4.63601	+	2.97938i	0.170423	+	0.109524i
$741$	−0.846486	+	5.88744i	−0.0310964	+	0.216280i
$742$	−1.88940	+	1.21425i	−0.0693622	+	0.0445764i
$743$	9.17056	+	20.0807i	0.336435	+	0.736690i	0.999934	−	0.0114872i	$-0.00365657\pi$
$743$	9.17056	+	20.0807i	0.336435	+	0.736690i	−0.663499	+	0.748177i	$0.730929\pi$
$744$	−13.9716	−	16.1241i	−0.512224	−	0.591138i
$745$	−2.64828	−	18.4192i	−0.0970254	−	0.674826i
$746$	−8.33917	+	18.2602i	−0.305319	+	0.668554i
$747$	−9.52298	+	2.79620i	−0.348427	+	0.102308i
$748$	8.09106	−	2.37575i	0.295838	−	0.0868660i
$749$	−1.93553	+	4.23822i	−0.0707227	+	0.154861i
$750$	−2.04210	−	14.2031i	−0.0745669	−	0.518624i
$751$	−25.9345	−	29.9300i	−0.946363	−	1.09216i	−0.995631	−	0.0933758i	$-0.970234\pi$
$751$	−25.9345	−	29.9300i	−0.946363	−	1.09216i	0.0492677	−	0.998786i	$-0.484311\pi$
$752$	−12.1518	−	26.6087i	−0.443131	−	0.970321i
$753$	−3.79933	+	2.44168i	−0.138455	+	0.0889797i
$754$	4.36177	−	30.3368i	0.158846	−	1.10480i
$755$	−3.80888	−	2.44782i	−0.138619	−	0.0890852i
$756$	−0.354905	+	0.409583i	−0.0129078	+	0.0148964i
$757$	−6.39844	−	1.87875i	−0.232555	−	0.0682844i	0.163378	−	0.986563i	$-0.447761\pi$
$757$	−6.39844	−	1.87875i	−0.232555	−	0.0682844i	−0.395934	+	0.918279i	$0.629579\pi$
$758$	0.311047			0.0112977
$759$	−3.53172	−	13.7847i	−0.128193	−	0.500351i
$760$	5.18093			0.187932
$761$	11.9306	+	3.50314i	0.432484	+	0.126989i	0.490726	−	0.871314i	$-0.336732\pi$
$761$	11.9306	+	3.50314i	0.432484	+	0.126989i	−0.0582427	+	0.998302i	$0.518550\pi$
$762$	7.55904	−	8.72359i	0.273835	−	0.316022i
$763$	−5.91194	−	3.79937i	−0.214027	−	0.137547i
$764$	−1.45699	+	10.1336i	−0.0527120	+	0.366620i
$765$	4.41153	−	2.83512i	0.159499	−	0.102504i
$766$	−4.78410	−	10.4757i	−0.172856	−	0.378503i
$767$	19.2952	+	22.2678i	0.696709	+	0.804045i
$768$	−1.72743	−	12.0146i	−0.0623334	−	0.433538i
$769$	4.15472	−	9.09757i	0.149823	−	0.328067i	−0.819808	−	0.572638i	$-0.805920\pi$
$769$	4.15472	−	9.09757i	0.149823	−	0.328067i	0.969631	+	0.244571i	$0.0786473\pi$
$770$	4.53903	−	1.33278i	0.163575	−	0.0480301i
$771$	4.94156	−	1.45097i	0.177966	−	0.0522555i
$772$	−1.67179	+	3.66072i	−0.0601691	+	0.131752i
$773$	−1.98079	−	13.7767i	−0.0712441	−	0.495514i	−0.993935	−	0.109972i	$-0.964924\pi$
$773$	−1.98079	−	13.7767i	−0.0712441	−	0.495514i	0.922691	−	0.385541i	$-0.125985\pi$
$774$	−7.09926	−	8.19298i	−0.255178	−	0.294491i
$775$	15.2505	+	33.3940i	0.547816	+	1.19955i
$776$	20.4525	−	13.1440i	0.734201	−	0.471842i
$777$	1.44712	−	10.0649i	0.0519151	−	0.361077i
$778$	35.4628	+	22.7905i	1.27140	+	0.817080i
$779$	−10.7093	+	12.3592i	−0.383702	+	0.442815i
$780$	1.38778	+	0.407490i	0.0496906	+	0.0145905i
$781$	−34.8575			−1.24730
$782$	22.8381	−	32.9572i	0.816688	−	1.17855i
$783$	−7.20299			−0.257414
$784$	4.59616	+	1.34955i	0.164149	+	0.0481984i
$785$	−9.09718	+	10.4987i	−0.324692	+	0.374715i
$786$	−9.12672	−	5.86539i	−0.325539	−	0.209211i
$787$	4.12069	−	28.6600i	0.146887	−	1.02162i	−0.774389	−	0.632709i	$-0.781943\pi$
$787$	4.12069	−	28.6600i	0.146887	−	1.02162i	0.921276	−	0.388910i	$-0.127148\pi$
$788$	7.45550	−	4.79136i	0.265591	−	0.170685i
$789$	11.9312	+	26.1257i	0.424762	+	0.930100i
$790$	15.8451	+	18.2863i	0.563745	+	0.650596i
$791$	−1.75502	−	12.2064i	−0.0624014	−	0.434011i
$792$	−2.86533	+	6.27420i	−0.101815	+	0.222944i
$793$	−8.25687	+	2.42444i	−0.293210	+	0.0860942i
$794$	39.5023	−	11.5989i	1.40188	−	0.411630i
$795$	0.585189	−	1.28139i	0.0207545	−	0.0454461i
$796$	1.58974	+	11.0569i	0.0563467	+	0.391900i
$797$	−7.58660	−	8.75540i	−0.268731	−	0.310132i	0.605305	−	0.795994i	$-0.293051\pi$
$797$	−7.58660	−	8.75540i	−0.268731	−	0.310132i	−0.874036	+	0.485862i	$0.838506\pi$
$798$	1.47611	+	3.23223i	0.0522538	+	0.114420i
$799$	−26.9398	+	17.3132i	−0.953062	+	0.612496i
$800$	−1.70094	+	11.8303i	−0.0601372	+	0.418264i
$801$	4.32349	+	2.77854i	0.152763	+	0.0981748i
$802$	28.6602	−	33.0756i	1.01203	−	1.16794i
$803$	13.6253	+	4.00076i	0.480828	+	0.141184i
$804$	−7.50942			−0.264837
$805$	2.73158	−	3.94189i	0.0962754	−	0.138933i
$806$	−39.0520			−1.37555
$807$	−19.0021	−	5.57953i	−0.668907	−	0.196409i
$808$	−25.8613	+	29.8455i	−0.909798	+	1.04996i
$809$	−8.29136	−	5.32853i	−0.291509	−	0.187341i	0.386710	−	0.922201i	$-0.373611\pi$
$809$	−8.29136	−	5.32853i	−0.291509	−	0.187341i	−0.678219	+	0.734860i	$0.737248\pi$
$810$	0.226900	−	1.57812i	0.00797245	−	0.0554496i
$811$	31.4032	−	20.1816i	1.10271	−	0.708672i	0.143021	−	0.989720i	$-0.454318\pi$
$811$	31.4032	−	20.1816i	1.10271	−	0.708672i	0.959694	+	0.281048i	$0.0906820\pi$
$812$	−1.62165	−	3.55093i	−0.0569089	−	0.124613i
$813$	−19.1759	−	22.1301i	−0.672527	−	0.776138i
$814$	6.84582	+	47.6138i	0.239946	+	1.66886i
$815$	−0.594090	+	1.30087i	−0.0208101	+	0.0455677i
$816$	−24.1022	+	7.07705i	−0.843747	+	0.247746i
$817$	−14.5404	+	4.26943i	−0.508703	+	0.149369i
$818$	−9.21904	+	20.1869i	−0.322336	+	0.705818i
$819$	−0.379810	−	2.64164i	−0.0132716	−	0.0923063i
$820$	2.60419	+	3.00540i	0.0909424	+	0.104953i
$821$	6.53457	+	14.3087i	0.228058	+	0.499377i	0.988721	−	0.149770i	$-0.0478532\pi$
$821$	6.53457	+	14.3087i	0.228058	+	0.499377i	−0.760663	+	0.649147i	$0.775126\pi$
$822$	−3.46834	+	2.22897i	−0.120972	+	0.0777441i
$823$	−7.40403	+	51.4962i	−0.258088	+	1.79504i	0.288329	+	0.957531i	$0.406900\pi$
$823$	−7.40403	+	51.4962i	−0.258088	+	1.79504i	−0.546418	+	0.837513i	$0.684009\pi$
$824$	−35.2182	−	22.6333i	−1.22688	−	0.788470i
$825$	7.77225	−	8.96965i	0.270595	−	0.312283i
$826$	16.8892	+	4.95912i	0.587651	+	0.172550i
$827$	23.3304			0.811276			0.405638	−	0.914034i	$-0.367049\pi$
$827$	23.3304			0.811276			0.405638	+	0.914034i	$0.367049\pi$
$828$	−0.645078	−	2.51780i	−0.0224180	−	0.0874997i
$829$	9.47233			0.328988			0.164494	−	0.986378i	$-0.447401\pi$
$829$	9.47233			0.328988			0.164494	+	0.986378i	$0.447401\pi$
$830$	15.1830	+	4.45812i	0.527008	+	0.154744i
$831$	3.91404	−	4.51705i	0.135777	−	0.156695i
$832$	10.8137	+	6.94954i	0.374898	+	0.240932i
$833$	0.746298	−	5.19062i	0.0258577	−	0.179844i
$834$	−19.3576	+	12.4404i	−0.670298	+	0.430774i
$835$	3.30528	+	7.23756i	0.114384	+	0.250466i
$836$	−2.34695	−	2.70852i	−0.0811709	−	0.0936762i
$837$	1.30615	+	9.08448i	0.0451472	+	0.314005i
$838$	16.1041	−	35.2631i	0.556308	−	1.21814i
$839$	−34.1512	+	10.0277i	−1.17903	+	0.346195i	−0.811800	−	0.583935i	$-0.801512\pi$
$839$	−34.1512	+	10.0277i	−1.17903	+	0.346195i	−0.367231	+	0.930130i	$0.619694\pi$
$840$	−2.23047	+	0.654925i	−0.0769586	+	0.0225971i
$841$	9.50594	−	20.8151i	0.327791	−	0.717763i
$842$	3.36836	+	23.4275i	0.116081	+	0.807365i
$843$	10.4427	+	12.0516i	0.359667	+	0.415078i
$844$	1.44436	+	3.16270i	0.0497168	+	0.108865i
$845$	4.94446	−	3.17761i	0.170095	−	0.109313i
$846$	−1.38561	+	9.63710i	−0.0476381	+	0.331330i
$847$	−1.84748	−	1.18730i	−0.0634800	−	0.0407961i
$848$	−4.41892	+	5.09971i	−0.151746	+	0.175125i
$849$	21.4213	+	6.28986i	0.735177	+	0.215867i
$850$	33.4431			1.14709
$851$	35.7219	+	33.1975i	1.22453	+	1.13800i
$852$	−6.36682			−0.218124
$853$	5.63414	+	1.65433i	0.192909	+	0.0566433i	0.376760	−	0.926311i	$-0.377038\pi$
$853$	5.63414	+	1.65433i	0.192909	+	0.0566433i	−0.183851	+	0.982954i	$0.558856\pi$
$854$	−3.36659	+	3.88525i	−0.115202	+	0.132951i
$855$	−1.87491	−	1.20493i	−0.0641205	−	0.0412077i
$856$	−1.54143	+	10.7209i	−0.0526849	+	0.366431i
$857$	44.9969	−	28.9177i	1.53706	−	0.987811i	0.548645	−	0.836055i	$-0.315144\pi$
$857$	44.9969	−	28.9177i	1.53706	−	0.987811i	0.988418	−	0.151755i	$-0.0484926\pi$
$858$	5.24469	+	11.4843i	0.179051	+	0.392067i
$859$	37.8618	+	43.6949i	1.29183	+	1.49085i	0.770408	+	0.637551i	$0.220052\pi$
$859$	37.8618	+	43.6949i	1.29183	+	1.49085i	0.521421	+	0.853300i	$0.325402\pi$
$860$	0.524438	+	3.64755i	0.0178832	+	0.124380i
$861$	3.04820	−	6.67462i	0.103882	−	0.227470i
$862$	−29.6196	+	8.69710i	−1.00885	+	0.296224i
$863$	15.6834	−	4.60507i	0.533870	−	0.156758i	−0.00367553	−	0.999993i	$-0.501170\pi$
$863$	15.6834	−	4.60507i	0.533870	−	0.156758i	0.537545	+	0.843235i	$0.319352\pi$
$864$	−1.24125	+	2.71797i	−0.0422283	+	0.0924671i
$865$	−1.32733	−	9.23181i	−0.0451307	−	0.313891i
$866$	−14.6978	−	16.9622i	−0.499451	−	0.576397i
$867$	4.36164	+	9.55067i	0.148129	+	0.324358i
$868$	−4.18440	+	2.68915i	−0.142028	+	0.0912758i
$869$	−6.40842	+	44.5715i	−0.217391	+	1.51199i
$870$	9.66103	+	6.20877i	0.327540	+	0.210497i
$871$	24.2163	−	27.9471i	0.820539	−	0.946952i
$872$	−15.6747	−	4.60251i	−0.530813	−	0.155861i
$873$	−10.4584			−0.353962
$874$	−16.7732	−	3.01043i	−0.567363	−	0.101829i
$875$	9.00000			0.304256
$876$	2.48871	+	0.730750i	0.0840856	+	0.0246898i
$877$	28.4969	−	32.8872i	0.962273	−	1.11052i	−0.0315448	−	0.999502i	$-0.510043\pi$
$877$	28.4969	−	32.8872i	0.962273	−	1.11052i	0.993818	−	0.111020i	$-0.0354119\pi$
$878$	38.1011	+	24.4861i	1.28585	+	0.826365i
$879$	2.66700	−	18.5494i	0.0899557	−	0.625655i
$880$	11.9569	−	7.68422i	0.403066	−	0.259035i
$881$	1.14065	+	2.49768i	0.0384295	+	0.0841488i	0.927873	−	0.372896i	$-0.121635\pi$
$881$	1.14065	+	2.49768i	0.0384295	+	0.0841488i	−0.889444	+	0.457045i	$0.848908\pi$
$882$	−1.04408	−	1.20493i	−0.0351559	−	0.0405721i
$883$	−1.29566	−	9.01148i	−0.0436023	−	0.303261i	−0.999940	−	0.0109952i	$-0.996500\pi$
$883$	−1.29566	−	9.01148i	−0.0436023	−	0.303261i	0.956337	−	0.292265i	$-0.0944090\pi$
$884$	−3.15083	+	6.89935i	−0.105974	+	0.232050i
$885$	−10.5932	+	3.11043i	−0.356085	+	0.104556i
$886$	−36.6115	+	10.7501i	−1.22999	+	0.361157i
$887$	11.3466	−	24.8455i	0.380981	−	0.834231i	−0.617869	−	0.786281i	$-0.712004\pi$
$887$	11.3466	−	24.8455i	0.380981	−	0.834231i	0.998850	−	0.0479503i	$-0.0152689\pi$
$888$	−3.36402	−	23.3973i	−0.112889	−	0.785162i
$889$	4.74114	+	5.47156i	0.159013	+	0.183510i
$890$	−3.40388	−	7.45345i	−0.114098	−	0.249840i
$891$	2.49611	−	1.60416i	0.0836230	−	0.0537412i
$892$	1.22017	−	8.48650i	0.0408545	−	0.284149i
$893$	11.4495	+	7.35813i	0.383142	+	0.246230i
$894$	19.4288	−	22.4220i	0.649797	−	0.749905i
$895$	1.61703	+	0.474803i	0.0540514	+	0.0158709i
$896$	13.6552			0.456187
$897$	11.4505	+	5.71867i	0.382322	+	0.190941i
$898$	−55.8728			−1.86450
$899$	−63.4304	−	18.6248i	−2.11552	−	0.621173i
$900$	1.41962	−	1.63833i	0.0473207	−	0.0546110i
$901$	6.21446	+	3.99379i	0.207034	+	0.133052i
$902$	−4.94006	+	34.3589i	−0.164486	+	1.14403i
$903$	5.72014	−	3.67611i	0.190354	−	0.122333i
$904$	−11.9088	−	26.0767i	−0.396082	−	0.867299i
$905$	3.18599	+	3.67682i	0.105906	+	0.122222i
$906$	−1.02732	−	7.14514i	−0.0341303	−	0.237381i
$907$	19.7394	−	43.2232i	0.655435	−	1.43520i	−0.231281	−	0.972887i	$-0.574292\pi$
$907$	19.7394	−	43.2232i	0.655435	−	1.43520i	0.886716	−	0.462315i	$-0.152981\pi$
$908$	−1.61559	+	0.474381i	−0.0536154	+	0.0157429i
$909$	16.3000	−	4.78612i	0.540638	−	0.158746i
$910$	−1.76759	+	3.87049i	−0.0585952	+	0.128306i
$911$	3.12129	+	21.7090i	0.103413	+	0.719252i	0.973886	+	0.227037i	$0.0729037\pi$
$911$	3.12129	+	21.7090i	0.103413	+	0.719252i	−0.870473	+	0.492216i	$0.836187\pi$
$912$	6.99126	+	8.06834i	0.231504	+	0.267169i
$913$	12.2335	+	26.7876i	0.404870	+	0.886541i
$914$	10.0326	−	6.44753i	0.331847	−	0.213265i
$915$	0.458889	−	3.19164i	0.0151704	−	0.105512i
$916$	0.423890	+	0.272418i	0.0140057	+	0.00900094i
$917$	4.45608	−	5.14259i	0.147153	−	0.169823i
$918$	8.02210	+	2.35550i	0.264769	+	0.0777431i
$919$	39.5619			1.30503			0.652513	−	0.757777i	$-0.273715\pi$
$919$	39.5619			1.30503			0.652513	+	0.757777i	$0.273715\pi$
$920$	3.51106	−	10.5812i	0.115756	−	0.348853i
$921$	−4.71794			−0.155462
$922$	17.9425	+	5.26838i	0.590903	+	0.173505i
$923$	20.5317	−	23.6948i	0.675808	−	0.779925i
$924$	1.35278	+	0.869381i	0.0445033	+	0.0286005i
$925$	−5.78848	+	40.2597i	−0.190324	+	1.32373i
$926$	−42.4076	+	27.2537i	−1.39360	+	0.895612i
$927$	7.48113	+	16.3814i	0.245713	+	0.538036i
$928$	−14.0942	−	16.2655i	−0.462664	−	0.533943i
$929$	−6.91911	−	48.1235i	−0.227009	−	1.57888i	−0.710607	−	0.703590i	$-0.751579\pi$
$929$	−6.91911	−	48.1235i	−0.227009	−	1.57888i	0.483598	−	0.875290i	$-0.339330\pi$
$930$	6.07868	−	13.3105i	0.199328	−	0.436467i
$931$	−2.13843	+	0.627899i	−0.0700842	+	0.0205786i
$932$	7.16607	−	2.10415i	0.234733	−	0.0689237i
$933$	−6.89014	+	15.0873i	−0.225573	+	0.493936i
$934$	3.84402	+	26.7358i	0.125780	+	0.874820i
$935$	−10.1894	−	11.7592i	−0.333229	−	0.384567i
$936$	−2.57723	−	5.64335i	−0.0842394	−	0.184459i
$937$	−24.4077	+	15.6859i	−0.797366	+	0.512436i	−0.874755	−	0.484565i	$-0.838978\pi$
$937$	−24.4077	+	15.6859i	−0.797366	+	0.512436i	0.0773895	+	0.997001i	$0.475341\pi$
$938$	3.14396	−	21.8667i	0.102654	−	0.713974i
$939$	3.76432	+	2.41918i	0.122844	+	0.0789470i
$940$	2.16730	−	2.50119i	0.0706894	−	0.0815799i
$941$	−51.7295	−	15.1891i	−1.68633	−	0.495152i	−0.708707	−	0.705503i	$-0.750721\pi$
$941$	−51.7295	−	15.1891i	−1.68633	−	0.495152i	−0.977626	+	0.210351i	$0.932539\pi$
$942$	−22.1484			−0.721633
$943$	17.9842	+	30.2479i	0.585647	+	0.985006i
$944$	52.8856			1.72128
$945$	0.959493	+	0.281733i	0.0312123	+	0.00916476i
$946$	−21.0645	+	24.3097i	−0.684865	+	0.790376i
$947$	−27.8731	−	17.9130i	−0.905755	−	0.582093i	0.00273703	−	0.999996i	$-0.499129\pi$
$947$	−27.8731	−	17.9130i	−0.905755	−	0.582093i	−0.908492	+	0.417903i	$0.862765\pi$
$948$	−1.17052	+	8.14111i	−0.0380166	+	0.264411i
$949$	−10.7451	+	6.90547i	−0.348801	+	0.224161i
$950$	−5.90445	−	12.9289i	−0.191566	−	0.419470i
$951$	−7.55707	−	8.72132i	−0.245055	−	0.282808i
$952$	−1.73487	−	12.0663i	−0.0562275	−	0.391071i
$953$	0.114439	−	0.250586i	0.00370703	−	0.00811726i	−0.907769	−	0.419470i	$-0.862216\pi$
$953$	0.114439	−	0.250586i	0.00370703	−	0.00811726i	0.911476	+	0.411352i	$0.134943\pi$
$954$	2.15496	−	0.632754i	0.0697695	−	0.0204862i
$955$	18.1253	−	5.32206i	0.586520	−	0.172218i
$956$	5.82170	−	12.7477i	0.188287	−	0.412292i
$957$	3.04159	+	21.1547i	0.0983206	+	0.683835i
$958$	20.5705	+	23.7397i	0.664604	+	0.766994i
$959$	−1.07422	−	2.35221i	−0.0346884	−	0.0759569i
$960$	−4.05189	+	2.60399i	−0.130774	+	0.0840435i
$961$	−7.57595	+	52.6919i	−0.244386	+	1.69974i
$962$	−36.3983	−	23.3918i	−1.17353	−	0.754181i
$963$	3.05117	−	3.52124i	0.0983227	−	0.113470i
$964$	−5.36545	−	1.57544i	−0.172810	−	0.0507415i
$965$	7.42569			0.239041
$966$	7.60168	−	0.824280i	0.244580	−	0.0265208i
$967$	−27.3572			−0.879748			−0.439874	−	0.898059i	$-0.644977\pi$
$967$	−27.3572			−0.879748			−0.439874	+	0.898059i	$0.644977\pi$
$968$	−4.89834	−	1.43828i	−0.157438	−	0.0462281i
$969$	7.65357	−	8.83270i	0.245868	−	0.283747i
$970$	14.0273	+	9.01481i	0.450390	+	0.289448i
$971$	4.99905	−	34.7692i	0.160427	−	1.11580i	−0.737403	−	0.675453i	$-0.763948\pi$
$971$	4.99905	−	34.7692i	0.160427	−	1.11580i	0.897830	−	0.440342i	$-0.145143\pi$
$972$	0.455922	−	0.293003i	0.0146237	−	0.00939809i
$973$	−5.99546	−	13.1282i	−0.192206	−	0.420871i
$974$	−22.7900	−	26.3011i	−0.730239	−	0.842741i
$975$	1.51924	+	10.5665i	0.0486546	+	0.338400i
$976$	−6.41642	+	14.0500i	−0.205385	+	0.449730i
$977$	1.37274	−	0.403072i	0.0439178	−	0.0128954i	−0.259700	−	0.965689i	$-0.583624\pi$
$977$	1.37274	−	0.403072i	0.0439178	−	0.0128954i	0.303618	+	0.952794i	$0.401805\pi$
$978$	−2.18774	+	0.642378i	−0.0699562	+	0.0205410i
$979$	6.33472	−	13.8711i	0.202459	−	0.443322i
$980$	0.0771283	+	0.536439i	0.00246377	+	0.0171359i
$981$	4.60206	+	5.31106i	0.146932	+	0.169569i
$982$	5.55276	+	12.1588i	0.177196	+	0.388004i
$983$	−14.0064	+	9.00140i	−0.446736	+	0.287100i	−0.744603	−	0.667507i	$-0.767361\pi$
$983$	−14.0064	+	9.00140i	−0.446736	+	0.287100i	0.297867	+	0.954607i	$0.403725\pi$
$984$	2.42753	−	16.8839i	0.0773870	−	0.538238i
$985$	−13.7567	−	8.84087i	−0.438324	−	0.281693i
$986$	−39.4374	+	45.5131i	−1.25594	+	1.44943i
$987$	−5.85932	−	1.72045i	−0.186504	−	0.0547626i
$988$	3.22354			0.102554
$989$	−1.13418	+	32.5898i	−0.0360649	+	1.03629i
$990$	−4.73066			−0.150350
$991$	−21.9840	−	6.45508i	−0.698344	−	0.205052i	−0.0867569	−	0.996230i	$-0.527650\pi$
$991$	−21.9840	−	6.45508i	−0.698344	−	0.205052i	−0.611587	+	0.791177i	$0.709469\pi$
$992$	−17.9585	+	20.7252i	−0.570183	+	0.658026i
$993$	−15.3792	−	9.88362i	−0.488044	−	0.313647i
$994$	2.66559	−	18.5396i	0.0845474	−	0.588040i
$995$	17.3396	−	11.1435i	0.549701	−	0.353271i
$996$	2.23448	+	4.89283i	0.0708023	+	0.155035i
$997$	19.9394	+	23.0113i	0.631486	+	0.728774i	0.977846	−	0.209328i	$-0.0671276\pi$
$997$	19.9394	+	23.0113i	0.631486	+	0.728774i	−0.346359	+	0.938102i	$0.612582\pi$
$998$	0.561982	+	3.90867i	0.0177892	+	0.123727i
$999$	−4.22412	+	9.24953i	−0.133645	+	0.292642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.a.64.1	✓	10
23.9	even	11	inner	483.2.q.a.400.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.a.64.1	✓	10	1.1	even	1	trivial
483.2.q.a.400.1	yes	10	23.9	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52977 - 0.449181i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.455922 + 0.293003i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.34125 - 0.861971i) q^{6} +(0.415415 + 0.909632i) q^{7} +(1.52231 + 1.75684i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.52977 - 0.449181i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.455922 + 0.293003i) q^{4} +(0.142315 - 0.989821i) q^{5} +(1.34125 - 0.861971i) q^{6} +(0.415415 + 0.909632i) q^{7} +(1.52231 + 1.75684i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-0.662317 + 1.45027i) q^{10} +(-2.84695 + 0.835939i) q^{11} +(-0.520003 + 0.152687i) q^{12} +(1.10866 - 2.42763i) q^{13} +(-0.226900 - 1.57812i) q^{14} +(0.654861 + 0.755750i) q^{15} +(-1.98992 - 4.35731i) q^{16} +(-4.41153 + 2.83512i) q^{17} +(-0.226900 + 1.57812i) q^{18} +(1.87491 + 1.20493i) q^{19} +(0.354905 - 0.409583i) q^{20} +(-0.959493 - 0.281733i) q^{21} +4.73066 q^{22} +(3.73149 - 3.01264i) q^{23} -2.32463 q^{24} +(3.83797 + 1.12693i) q^{25} +(-2.78644 + 3.21572i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.0771283 + 0.536439i) q^{28} +(-6.05954 + 3.89423i) q^{29} +(-0.662317 - 1.45027i) q^{30} +(6.01024 + 6.93619i) q^{31} +(0.425234 + 2.95757i) q^{32} +(1.23259 - 2.69900i) q^{33} +(8.02210 - 2.35550i) q^{34} +(0.959493 - 0.281733i) q^{35} +(0.225136 - 0.492980i) q^{36} +(1.44712 + 10.0649i) q^{37} +(-2.32694 - 2.68544i) q^{38} +(1.10866 + 2.42763i) q^{39} +(1.95561 - 1.25679i) q^{40} +(-1.04427 + 7.26302i) q^{41} +(1.34125 + 0.861971i) q^{42} +(-4.45276 + 5.13876i) q^{43} +(-1.54292 - 0.453042i) q^{44} -1.00000 q^{45} +(-7.06153 + 2.93253i) q^{46} +6.10668 q^{47} +(4.59616 + 1.34955i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-5.36501 - 3.44789i) q^{50} +(0.746298 - 5.19062i) q^{51} +(1.21677 - 0.781968i) q^{52} +(-0.585189 - 1.28139i) q^{53} +(-1.04408 - 1.20493i) q^{54} +(0.422268 + 2.93694i) q^{55} +(-0.965688 + 2.11456i) q^{56} +(-2.13843 + 0.627899i) q^{57} +(11.0189 - 3.23544i) q^{58} +(-4.58634 + 10.0427i) q^{59} +(0.0771283 + 0.536439i) q^{60} +(-2.11157 - 2.43689i) q^{61} +(-6.07868 - 13.3105i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.685459 + 4.76747i) q^{64} +(-2.24514 - 1.44286i) q^{65} +(-3.09792 + 3.57519i) q^{66} +(13.2949 + 3.90373i) q^{67} -2.84201 q^{68} +(-0.166803 + 4.79293i) q^{69} -1.59435 q^{70} +(11.2720 + 3.30976i) q^{71} +(1.52231 - 1.75684i) q^{72} +(-4.02620 - 2.58748i) q^{73} +(2.30722 - 16.0470i) q^{74} +(-3.36501 + 2.16256i) q^{75} +(0.501763 + 1.09871i) q^{76} +(-1.94306 - 2.24241i) q^{77} +(-0.605551 - 4.21170i) q^{78} +(6.30442 - 13.8048i) q^{79} +(-4.59616 + 1.34955i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(4.85989 - 10.6417i) q^{82} +(-1.41248 - 9.82399i) q^{83} +(-0.354905 - 0.409583i) q^{84} +(2.17843 + 4.77011i) q^{85} +(9.11992 - 5.86102i) q^{86} +(1.02509 - 7.12967i) q^{87} +(-5.80255 - 3.72908i) q^{88} +(-3.36555 + 3.88406i) q^{89} +(1.52977 + 0.449181i) q^{90} +2.66880 q^{91} +(2.58398 - 0.280191i) q^{92} -9.17789 q^{93} +(-9.34181 - 2.74300i) q^{94} +(1.45949 - 1.68434i) q^{95} +(-2.51365 - 1.61543i) q^{96} +(1.48838 - 10.3519i) q^{97} +(1.34125 - 0.861971i) q^{98} +(1.23259 + 2.69900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9	\( 10 q + 4 q^{2} - q^{3} + 8 q^{4} + q^{5} + 4 q^{6} - q^{7} - 7 q^{8} - q^{9} - 4 q^{10} - q^{11} - 3 q^{12} + 15 q^{13} - 7 q^{14} + q^{15} - 10 q^{16} - 24 q^{17} - 7 q^{18} + 5 q^{19} - 8 q^{20} - q^{21} + 26 q^{22} + 21 q^{23} - 18 q^{24} + 4 q^{25} + 6 q^{26} - q^{27} - 3 q^{28} - 22 q^{29} - 4 q^{30} - 8 q^{31} + 10 q^{32} - q^{33} + 8 q^{34} + q^{35} - 14 q^{36} - 2 q^{37} + 2 q^{38} + 15 q^{39} - 4 q^{40} + 7 q^{41} + 4 q^{42} + q^{43} + 19 q^{44} - 10 q^{45} + 15 q^{46} - 6 q^{47} + q^{48} - q^{49} - 16 q^{50} + 20 q^{51} - 21 q^{52} - q^{53} - 7 q^{54} + 12 q^{55} + 4 q^{56} - 6 q^{57} + 22 q^{58} + 10 q^{59} + 3 q^{60} + 5 q^{61} - 34 q^{62} - q^{63} + 13 q^{64} - 4 q^{65} - 7 q^{66} + 29 q^{67} - 28 q^{68} - q^{69} - 4 q^{70} + 22 q^{71} - 7 q^{72} - 33 q^{73} - 36 q^{74} + 4 q^{75} + 26 q^{76} - q^{77} + 28 q^{78} + 27 q^{79} - q^{80} - q^{81} + 38 q^{82} + 25 q^{83} + 8 q^{84} + 2 q^{85} + 18 q^{86} - 7 q^{88} - 38 q^{89} - 4 q^{90} - 18 q^{91} + 41 q^{92} - 30 q^{93} - 42 q^{94} + 6 q^{95} - 23 q^{96} - q^{97} + 4 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - q^3 + 8 * q^4 + q^5 + 4 * q^6 - q^7 - 7 * q^8 - q^9 - 4 * q^10 - q^11 - 3 * q^12 + 15 * q^13 - 7 * q^14 + q^15 - 10 * q^16 - 24 * q^17 - 7 * q^18 + 5 * q^19 - 8 * q^20 - q^21 + 26 * q^22 + 21 * q^23 - 18 * q^24 + 4 * q^25 + 6 * q^26 - q^27 - 3 * q^28 - 22 * q^29 - 4 * q^30 - 8 * q^31 + 10 * q^32 - q^33 + 8 * q^34 + q^35 - 14 * q^36 - 2 * q^37 + 2 * q^38 + 15 * q^39 - 4 * q^40 + 7 * q^41 + 4 * q^42 + q^43 + 19 * q^44 - 10 * q^45 + 15 * q^46 - 6 * q^47 + q^48 - q^49 - 16 * q^50 + 20 * q^51 - 21 * q^52 - q^53 - 7 * q^54 + 12 * q^55 + 4 * q^56 - 6 * q^57 + 22 * q^58 + 10 * q^59 + 3 * q^60 + 5 * q^61 - 34 * q^62 - q^63 + 13 * q^64 - 4 * q^65 - 7 * q^66 + 29 * q^67 - 28 * q^68 - q^69 - 4 * q^70 + 22 * q^71 - 7 * q^72 - 33 * q^73 - 36 * q^74 + 4 * q^75 + 26 * q^76 - q^77 + 28 * q^78 + 27 * q^79 - q^80 - q^81 + 38 * q^82 + 25 * q^83 + 8 * q^84 + 2 * q^85 + 18 * q^86 - 7 * q^88 - 38 * q^89 - 4 * q^90 - 18 * q^91 + 41 * q^92 - 30 * q^93 - 42 * q^94 + 6 * q^95 - 23 * q^96 - q^97 + 4 * q^98 - q^99

Introduction

L-functions

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