LMFDB - Embedded newform 224.2.bd.a.109.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.24
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.964603 + 1.03419i) q^{2} +(0.554270 + 0.722339i) q^{3} +(-0.139084 + 1.99516i) q^{4} +(0.772150 + 0.592492i) q^{5} +(-0.212383 + 1.26999i) q^{6} +(2.49088 - 0.891918i) q^{7} +(-2.19753 + 1.78070i) q^{8} +(0.561899 - 2.09704i) q^{9} +O(q^{10})$	\(q+(0.964603 + 1.03419i) q^{2} +(0.554270 + 0.722339i) q^{3} +(-0.139084 + 1.99516i) q^{4} +(0.772150 + 0.592492i) q^{5} +(-0.212383 + 1.26999i) q^{6} +(2.49088 - 0.891918i) q^{7} +(-2.19753 + 1.78070i) q^{8} +(0.561899 - 2.09704i) q^{9} +(0.132071 + 1.37007i) q^{10} +(-3.25828 - 0.428961i) q^{11} +(-1.51827 + 1.00539i) q^{12} +(-4.64317 - 1.92326i) q^{13} +(3.32512 + 1.71569i) q^{14} +0.886155i q^{15} +(-3.96131 - 0.554988i) q^{16} +(3.80021 + 2.19405i) q^{17} +(2.71073 - 1.44170i) q^{18} +(0.313906 + 2.38435i) q^{19} +(-1.28951 + 1.45816i) q^{20} +(2.02489 + 1.30490i) q^{21} +(-2.69932 - 3.78345i) q^{22} +(-1.12888 + 4.21303i) q^{23} +(-2.50429 - 0.600372i) q^{24} +(-1.04893 - 3.91464i) q^{25} +(-2.48980 - 6.65709i) q^{26} +(4.34976 - 1.80173i) q^{27} +(1.43308 + 5.09375i) q^{28} +(3.82570 - 9.23607i) q^{29} +(-0.916449 + 0.854787i) q^{30} +(0.642286 - 1.11247i) q^{31} +(-3.24713 - 4.63208i) q^{32} +(-1.49611 - 2.59135i) q^{33} +(1.39663 + 6.04652i) q^{34} +(2.45179 + 0.787131i) q^{35} +(4.10577 + 1.41274i) q^{36} +(-3.26384 - 2.50443i) q^{37} +(-2.16307 + 2.62459i) q^{38} +(-1.18432 - 4.41995i) q^{39} +(-2.75187 + 0.0729490i) q^{40} +(4.76536 + 4.76536i) q^{41} +(0.603706 + 3.35282i) q^{42} +(-0.0816679 - 0.197164i) q^{43} +(1.30902 - 6.44113i) q^{44} +(1.67635 - 1.28631i) q^{45} +(-5.44597 + 2.89643i) q^{46} +(-5.27770 + 3.04708i) q^{47} +(-1.79475 - 3.16902i) q^{48} +(5.40896 - 4.44332i) q^{49} +(3.03668 - 4.86086i) q^{50} +(0.521494 + 3.96114i) q^{51} +(4.48301 - 8.99637i) q^{52} +(-6.41100 - 0.844024i) q^{53} +(6.05911 + 2.76051i) q^{54} +(-2.26173 - 2.26173i) q^{55} +(-3.88554 + 6.39551i) q^{56} +(-1.54832 + 1.54832i) q^{57} +(13.2421 - 4.95264i) q^{58} +(-1.84624 + 14.0236i) q^{59} +(-1.76802 - 0.123250i) q^{60} +(-7.84817 + 1.03323i) q^{61} +(1.77005 - 0.408850i) q^{62} +(-0.470761 - 5.72463i) q^{63} +(1.65824 - 7.82625i) q^{64} +(-2.44571 - 4.23609i) q^{65} +(1.23678 - 4.04688i) q^{66} +(4.59209 + 5.98452i) q^{67} +(-4.90603 + 7.27687i) q^{68} +(-3.66894 + 1.51972i) q^{69} +(1.55096 + 3.29487i) q^{70} +(6.86973 - 6.86973i) q^{71} +(2.49940 + 5.60886i) q^{72} +(9.46798 - 2.53694i) q^{73} +(-0.558258 - 5.79120i) q^{74} +(2.24631 - 2.92745i) q^{75} +(-4.80081 + 0.294667i) q^{76} +(-8.49859 + 1.83763i) q^{77} +(3.42866 - 5.48831i) q^{78} +(-6.16956 + 3.56200i) q^{79} +(-2.72990 - 2.77558i) q^{80} +(-1.92805 - 1.11316i) q^{81} +(-0.331593 + 9.52495i) q^{82} +(4.32349 + 1.79085i) q^{83} +(-2.88510 + 3.85848i) q^{84} +(1.63438 + 3.94573i) q^{85} +(0.125127 - 0.274645i) q^{86} +(8.79205 - 2.35582i) q^{87} +(7.92401 - 4.85936i) q^{88} +(7.96664 + 2.13465i) q^{89} +(2.94729 + 0.492881i) q^{90} +(-13.2810 - 0.649292i) q^{91} +(-8.24864 - 2.83825i) q^{92} +(1.15958 - 0.152662i) q^{93} +(-8.24214 - 2.51891i) q^{94} +(-1.17033 + 2.02706i) q^{95} +(1.54614 - 4.91295i) q^{96} -16.7849 q^{97} +(9.81272 + 1.30784i) q^{98} +(-2.73037 + 6.59170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.964603	+	1.03419i	0.682077	+	0.731280i
$2$	0.964603	+	1.03419i	0.682077	+	0.731280i
$3$	0.554270	+	0.722339i	0.320008	+	0.417043i	0.925464	−	0.378836i	$-0.123676\pi$
$3$	0.554270	+	0.722339i	0.320008	+	0.417043i	−0.605456	+	0.795879i	$0.707009\pi$
$4$	−0.139084	+	1.99516i	−0.0695418	+	0.997579i
$5$	0.772150	+	0.592492i	0.345316	+	0.264970i	0.766828	−	0.641852i	$-0.221834\pi$
$5$	0.772150	+	0.592492i	0.345316	+	0.264970i	−0.421512	+	0.906823i	$0.638501\pi$
$6$	−0.212383	+	1.26999i	−0.0867049	+	0.518471i
$7$	2.49088	−	0.891918i	0.941464	−	0.337113i
$7$	2.49088	−	0.891918i	0.941464	−	0.337113i
$8$	−2.19753	+	1.78070i	−0.776943	+	0.629571i
$9$	0.561899	−	2.09704i	0.187300	−	0.699012i
$10$	0.132071	+	1.37007i	0.0417646	+	0.433253i
$11$	−3.25828	−	0.428961i	−0.982409	−	0.129337i	−0.377824	−	0.925877i	$-0.623328\pi$
$11$	−3.25828	−	0.428961i	−0.982409	−	0.129337i	−0.604585	+	0.796541i	$0.706661\pi$
$12$	−1.51827	+	1.00539i	−0.438287	+	0.290231i
$13$	−4.64317	−	1.92326i	−1.28778	−	0.533418i	−0.369460	−	0.929247i	$-0.620457\pi$
$13$	−4.64317	−	1.92326i	−1.28778	−	0.533418i	−0.918324	+	0.395829i	$0.870457\pi$
$14$	3.32512	+	1.71569i	0.888675	+	0.458537i
$15$			0.886155i			0.228804i
$16$	−3.96131	−	0.554988i	−0.990328	−	0.138747i
$17$	3.80021	+	2.19405i	0.921687	+	0.532136i	0.884173	−	0.467160i	$-0.154723\pi$
$17$	3.80021	+	2.19405i	0.921687	+	0.532136i	0.0375141	+	0.999296i	$0.488056\pi$
$18$	2.71073	−	1.44170i	0.638926	−	0.339811i
$19$	0.313906	+	2.38435i	0.0720149	+	0.547007i	0.988981	+	0.148042i	$0.0472972\pi$
$19$	0.313906	+	2.38435i	0.0720149	+	0.547007i	−0.916966	+	0.398965i	$0.869369\pi$
$20$	−1.28951	+	1.45816i	−0.288343	+	0.326053i
$21$	2.02489	+	1.30490i	0.441867	+	0.284752i
$22$	−2.69932	−	3.78345i	−0.575497	−	0.806634i
$23$	−1.12888	+	4.21303i	−0.235387	+	0.878476i	0.742587	+	0.669750i	$0.233599\pi$
$23$	−1.12888	+	4.21303i	−0.235387	+	0.878476i	−0.977974	+	0.208727i	$0.933068\pi$
$24$	−2.50429	−	0.600372i	−0.511186	−	0.122550i
$25$	−1.04893	−	3.91464i	−0.209785	−	0.782929i
$26$	−2.48980	−	6.65709i	−0.488290	−	1.30556i
$27$	4.34976	−	1.80173i	0.837112	−	0.346743i
$28$	1.43308	+	5.09375i	0.270826	+	0.962628i
$29$	3.82570	−	9.23607i	0.710415	−	1.71509i	0.0114544	−	0.999934i	$-0.496354\pi$
$29$	3.82570	−	9.23607i	0.710415	−	1.71509i	0.698961	−	0.715160i	$-0.253646\pi$
$30$	−0.916449	+	0.854787i	−0.167320	+	0.156062i
$31$	0.642286	−	1.11247i	0.115358	−	0.199806i	−0.802565	−	0.596565i	$-0.796532\pi$
$31$	0.642286	−	1.11247i	0.115358	−	0.199806i	0.917923	+	0.396759i	$0.129865\pi$
$32$	−3.24713	−	4.63208i	−0.574017	−	0.818843i
$33$	−1.49611	−	2.59135i	−0.260440	−	0.451095i
$34$	1.39663	+	6.04652i	0.239521	+	1.03697i
$35$	2.45179	+	0.787131i	0.414428	+	0.133049i
$36$	4.10577	+	1.41274i	0.684294	+	0.235457i
$37$	−3.26384	−	2.50443i	−0.536572	−	0.411726i	0.304611	−	0.952477i	$-0.401474\pi$
$37$	−3.26384	−	2.50443i	−0.536572	−	0.411726i	−0.841183	+	0.540751i	$0.818140\pi$
$38$	−2.16307	+	2.62459i	−0.350896	+	0.425764i
$39$	−1.18432	−	4.41995i	−0.189643	−	0.707759i
$40$	−2.75187	+	0.0729490i	−0.435108	+	0.0115343i
$41$	4.76536	+	4.76536i	0.744224	+	0.744224i	0.973388	−	0.229163i	$-0.0735990\pi$
$41$	4.76536	+	4.76536i	0.744224	+	0.744224i	−0.229163	+	0.973388i	$0.573599\pi$
$42$	0.603706	+	3.35282i	0.0931539	+	0.517351i
$43$	−0.0816679	−	0.197164i	−0.0124542	−	0.0300672i	0.917530	−	0.397666i	$-0.130180\pi$
$43$	−0.0816679	−	0.197164i	−0.0124542	−	0.0300672i	−0.929984	+	0.367599i	$0.880180\pi$
$44$	1.30902	−	6.44113i	0.197342	−	0.971036i
$45$	1.67635	−	1.28631i	0.249895	−	0.191751i
$46$	−5.44597	+	2.89643i	−0.802965	+	0.427055i
$47$	−5.27770	+	3.04708i	−0.769832	+	0.444463i	−0.832815	−	0.553552i	$-0.813272\pi$
$47$	−5.27770	+	3.04708i	−0.769832	+	0.444463i	0.0629825	+	0.998015i	$0.479939\pi$
$48$	−1.79475	−	3.16902i	−0.259050	−	0.457409i
$49$	5.40896	−	4.44332i	0.772709	−	0.634760i
$50$	3.03668	−	4.86086i	0.429451	−	0.687430i
$51$	0.521494	+	3.96114i	0.0730238	+	0.554671i
$52$	4.48301	−	8.99637i	0.621681	−	1.24757i
$53$	−6.41100	−	0.844024i	−0.880619	−	0.115936i	−0.323362	−	0.946275i	$-0.604813\pi$
$53$	−6.41100	−	0.844024i	−0.880619	−	0.115936i	−0.557257	+	0.830340i	$0.688146\pi$
$54$	6.05911	+	2.76051i	0.824541	+	0.375658i
$55$	−2.26173	−	2.26173i	−0.304971	−	0.304971i
$56$	−3.88554	+	6.39551i	−0.519227	+	0.854636i
$57$	−1.54832	+	1.54832i	−0.205080	+	0.205080i
$58$	13.2421	−	4.95264i	1.73877	−	0.650314i
$59$	−1.84624	+	14.0236i	−0.240360	+	1.82571i	0.266674	+	0.963787i	$0.414075\pi$
$59$	−1.84624	+	14.0236i	−0.240360	+	1.82571i	−0.507034	+	0.861926i	$0.669258\pi$
$60$	−1.76802	−	0.123250i	−0.228250	−	0.0159115i
$61$	−7.84817	+	1.03323i	−1.00486	+	0.132292i	−0.614952	−	0.788564i	$-0.710825\pi$
$61$	−7.84817	+	1.03323i	−1.00486	+	0.132292i	−0.389903	+	0.920856i	$0.627491\pi$
$62$	1.77005	−	0.408850i	0.224797	−	0.0519240i
$63$	−0.470761	−	5.72463i	−0.0593103	−	0.721236i
$64$	1.65824	−	7.82625i	0.207280	−	0.978282i
$65$	−2.44571	−	4.23609i	−0.303353	−	0.525422i
$66$	1.23678	−	4.04688i	0.152237	−	0.498136i
$67$	4.59209	+	5.98452i	0.561013	+	0.731126i	0.984618	−	0.174721i	$-0.0559023\pi$
$67$	4.59209	+	5.98452i	0.561013	+	0.731126i	−0.423605	+	0.905847i	$0.639236\pi$
$68$	−4.90603	+	7.27687i	−0.594944	+	0.882450i
$69$	−3.66894	+	1.51972i	−0.441688	+	0.182953i
$70$	1.55096	+	3.29487i	0.185375	+	0.393813i
$71$	6.86973	−	6.86973i	0.815287	−	0.815287i	−0.170134	−	0.985421i	$-0.554420\pi$
$71$	6.86973	−	6.86973i	0.815287	−	0.815287i	0.985421	+	0.170134i	$0.0544199\pi$
$72$	2.49940	+	5.60886i	0.294557	+	0.661011i
$73$	9.46798	−	2.53694i	1.10814	−	0.296926i	0.342067	−	0.939676i	$-0.388873\pi$
$73$	9.46798	−	2.53694i	1.10814	−	0.296926i	0.766076	+	0.642750i	$0.222206\pi$
$74$	−0.558258	−	5.79120i	−0.0648962	−	0.673213i
$75$	2.24631	−	2.92745i	0.259382	−	0.338033i
$76$	−4.80081	+	0.294667i	−0.550691	+	0.0338007i
$77$	−8.49859	+	1.83763i	−0.968504	+	0.209417i
$78$	3.42866	−	5.48831i	0.388219	−	0.621429i
$79$	−6.16956	+	3.56200i	−0.694129	+	0.400756i	−0.805157	−	0.593062i	$-0.797919\pi$
$79$	−6.16956	+	3.56200i	−0.694129	+	0.400756i	0.111028	+	0.993817i	$0.464586\pi$
$80$	−2.72990	−	2.77558i	−0.305212	−	0.310319i
$81$	−1.92805	−	1.11316i	−0.214228	−	0.123684i
$82$	−0.331593	+	9.52495i	−0.0366183	+	1.05186i
$83$	4.32349	+	1.79085i	0.474565	+	0.196571i	0.607129	−	0.794603i	$-0.292321\pi$
$83$	4.32349	+	1.79085i	0.474565	+	0.196571i	−0.132564	+	0.991174i	$0.542321\pi$
$84$	−2.88510	+	3.85848i	−0.314791	+	0.420995i
$85$	1.63438	+	3.94573i	0.177273	+	0.427975i
$86$	0.125127	−	0.274645i	0.0134928	−	0.0296157i
$87$	8.79205	−	2.35582i	0.942606	−	0.252571i
$88$	7.92401	−	4.85936i	0.844702	−	0.518009i
$89$	7.96664	+	2.13465i	0.844462	+	0.226273i	0.655013	−	0.755618i	$-0.272663\pi$
$89$	7.96664	+	2.13465i	0.844462	+	0.226273i	0.189449	+	0.981891i	$0.439330\pi$
$90$	2.94729	+	0.492881i	0.310671	+	0.0519542i
$91$	−13.2810	−	0.649292i	−1.39222	−	0.0680643i
$92$	−8.24864	−	2.83825i	−0.859980	−	0.295908i
$93$	1.15958	−	0.152662i	0.120243	−	0.0158303i
$94$	−8.24214	−	2.51891i	−0.850112	−	0.259805i
$95$	−1.17033	+	2.02706i	−0.120073	+	0.207972i
$96$	1.54614	−	4.91295i	0.157803	−	0.501426i
$97$	−16.7849			−1.70425			−0.852123	−	0.523341i	$-0.824685\pi$
$97$	−16.7849			−1.70425			−0.852123	+	0.523341i	$0.824685\pi$
$98$	9.81272	+	1.30784i	0.991235	+	0.132112i
$99$	−2.73037	+	6.59170i	−0.274413	+	0.662491i
$100$	7.95622	−	1.54831i	0.795622	−	0.154831i
$101$	−0.769688	+	5.84636i	−0.0765868	+	0.581734i	0.909525	+	0.415650i	$0.136446\pi$
$101$	−0.769688	+	5.84636i	−0.0765868	+	0.581734i	−0.986112	+	0.166085i	$0.946888\pi$
$102$	−3.59352	+	4.36025i	−0.355812	+	0.431729i
$103$	−2.08377	−	0.558345i	−0.205320	−	0.0550154i	0.154693	−	0.987963i	$-0.450561\pi$
$103$	−2.08377	−	0.558345i	−0.205320	−	0.0550154i	−0.360013	+	0.932947i	$0.617228\pi$
$104$	13.6282	−	4.04165i	1.33636	−	0.396317i
$105$	0.790377	+	2.20730i	0.0771329	+	0.215411i
$106$	−5.31119	−	7.44432i	−0.515868	−	0.723056i
$107$	−3.00987	+	3.92254i	−0.290976	+	0.379207i	−0.915851	−	0.401517i	$-0.868483\pi$
$107$	−3.00987	+	3.92254i	−0.290976	+	0.379207i	0.624876	+	0.780724i	$0.285150\pi$
$108$	2.98975	+	8.92905i	0.287689	+	0.859198i
$109$	4.28706	−	3.28957i	0.410625	−	0.315084i	−0.382710	−	0.923868i	$-0.625009\pi$
$109$	4.28706	−	3.28957i	0.410625	−	0.315084i	0.793336	+	0.608784i	$0.208343\pi$
$110$	0.157380	−	4.52072i	0.0150056	−	0.431033i
$111$		−	3.74573i		−	0.355529i
$112$	−10.3622	+	2.15076i	−0.979132	+	0.203228i
$113$			12.9952i			1.22248i	0.791445	+	0.611241i	$0.209329\pi$
$113$			12.9952i			1.22248i	−0.791445	+	0.611241i	$0.790671\pi$
$114$	−3.09477	−	0.107738i	−0.289852	−	0.0100906i
$115$	−3.36784	+	2.58424i	−0.314053	+	0.240981i
$116$	17.8953	+	8.91747i	1.66154	+	0.827966i
$117$	−6.64215	+	8.65621i	−0.614067	+	0.800267i
$118$	−16.2839	+	11.6178i	−1.49905	+	1.06951i
$119$	11.4228	+	2.07565i	1.04713	+	0.190274i
$120$	−1.57797	−	1.94735i	−0.144049	−	0.177768i
$121$	−0.192787	−	0.0516572i	−0.0175261	−	0.00469611i
$122$	−8.63892	−	7.11981i	−0.782131	−	0.644598i
$123$	−0.800909	+	6.08351i	−0.0722155	+	0.548531i
$124$	2.13022	+	1.43619i	0.191300	+	0.128973i
$125$	3.37174	−	8.14011i	0.301578	−	0.728074i
$126$	5.46624	−	6.00885i	0.486971	−	0.535311i
$127$	−15.0995			−1.33987			−0.669933	−	0.742422i	$-0.733677\pi$
$127$	−15.0995			−1.33987			−0.669933	+	0.742422i	$0.733677\pi$
$128$	9.69335	−	5.83429i	0.856779	−	0.515683i
$129$	0.0971530	−	0.168274i	0.00855385	−	0.0148157i
$130$	2.02177	−	6.61546i	0.177321	−	0.580214i
$131$	−11.0547	+	1.45538i	−0.965857	+	0.127157i	−0.596923	−	0.802298i	$-0.703610\pi$
$131$	−11.0547	+	1.45538i	−0.965857	+	0.127157i	−0.368934	+	0.929456i	$0.620277\pi$
$132$	5.37823	−	2.62457i	0.468115	−	0.228440i
$133$	2.90855	+	5.65915i	0.252203	+	0.490711i
$134$	−1.75958	+	10.5218i	−0.152004	+	0.908942i
$135$	4.42618	+	1.18599i	0.380945	+	0.102074i
$136$	−12.2580	+	1.94553i	−1.05112	+	0.166828i
$137$	1.36960	−	0.366982i	0.117013	−	0.0313534i	−0.199838	−	0.979829i	$-0.564041\pi$
$137$	1.36960	−	0.366982i	0.117013	−	0.0313534i	0.316850	+	0.948476i	$0.397375\pi$
$138$	−5.11074	−	2.32844i	−0.435055	−	0.198210i
$139$	−5.54591	−	13.3890i	−0.470398	−	1.13564i	−0.963988	−	0.265947i	$-0.914315\pi$
$139$	−5.54591	−	13.3890i	−0.470398	−	1.13564i	0.493589	−	0.869695i	$-0.335685\pi$
$140$	−1.91145	+	4.78223i	−0.161547	+	0.404172i
$141$	−5.12630	−	2.12338i	−0.431713	−	0.178821i
$142$	13.7311	+	0.478023i	1.15229	+	0.0401148i
$143$	14.3038	+	8.25828i	1.19614	+	0.690592i
$144$	−3.38969	+	7.99516i	−0.282474	+	0.666264i
$145$	8.42631	−	4.86493i	0.699767	−	0.404011i
$146$	11.7565	+	7.34452i	0.972975	+	0.607837i
$147$	6.20761	+	1.44431i	0.511995	+	0.119124i
$148$	5.45068	−	6.16355i	0.448044	−	0.506641i
$149$	−4.67224	+	6.08899i	−0.382765	+	0.498829i	−0.944511	−	0.328481i	$-0.893463\pi$
$149$	−4.67224	+	6.08899i	−0.382765	+	0.498829i	0.561745	+	0.827310i	$0.310130\pi$
$150$	5.19433	−	0.500721i	0.424115	−	0.0408837i
$151$	−14.5282	+	3.89282i	−1.18229	+	0.316793i	−0.795834	−	0.605515i	$-0.792967\pi$
$151$	−14.5282	+	3.89282i	−1.18229	+	0.316793i	−0.386455	+	0.922308i	$0.626300\pi$
$152$	−4.93562	−	4.68070i	−0.400332	−	0.379655i
$153$	6.73634	−	6.73634i	0.544601	−	0.544601i
$154$	−10.0982	−	7.01654i	−0.813737	−	0.565409i
$155$	1.15507	−	0.478446i	0.0927775	−	0.0384297i
$156$	8.98323	−	1.74817i	0.719234	−	0.139965i
$157$	6.25041	+	8.14570i	0.498837	+	0.650097i	0.973126	−	0.230272i	$-0.0739615\pi$
$157$	6.25041	+	8.14570i	0.498837	+	0.650097i	−0.474289	+	0.880369i	$0.657295\pi$
$158$	−9.63494	−	2.94456i	−0.766515	−	0.234257i
$159$	−2.94376	−	5.09874i	−0.233455	−	0.404356i
$160$	0.237195	−	5.50056i	0.0187519	−	0.434857i
$161$	0.945777	+	11.5010i	0.0745377	+	0.906406i
$162$	−0.708586	−	3.06772i	−0.0556718	−	0.241023i
$163$	6.32191	−	0.832296i	0.495171	−	0.0651904i	0.121194	−	0.992629i	$-0.461328\pi$
$163$	6.32191	−	0.832296i	0.495171	−	0.0651904i	0.373976	+	0.927438i	$0.377994\pi$
$164$	−10.1704	+	8.84487i	−0.794177	+	0.690668i
$165$	0.380126	−	2.88734i	0.0295928	−	0.224779i
$166$	2.31838	+	6.19875i	0.179941	+	0.481116i
$167$	12.7955	−	12.7955i	0.990142	−	0.990142i	−0.00980982	−	0.999952i	$-0.503123\pi$
$167$	12.7955	−	12.7955i	0.990142	−	0.990142i	0.999952	+	0.00980982i	$0.00312261\pi$
$168$	−6.77337	+	0.738167i	−0.522577	+	0.0569508i
$169$	8.66771	+	8.66771i	0.666747	+	0.666747i
$170$	−2.50410	+	5.49631i	−0.192056	+	0.421548i
$171$	5.17645	+	0.681493i	0.395853	+	0.0521150i
$172$	0.404732	−	0.135518i	0.0308605	−	0.0103332i
$173$	2.06811	+	15.7089i	0.157236	+	1.19433i	0.870047	+	0.492969i	$0.164088\pi$
$173$	2.06811	+	15.7089i	0.157236	+	1.19433i	−0.712811	+	0.701356i	$0.752578\pi$
$174$	10.9172	+	6.82018i	0.827630	+	0.517037i
$175$	−6.10429	−	8.81535i	−0.461441	−	0.666378i
$176$	12.6690	+	3.50755i	0.954962	+	0.264392i
$177$	−11.1531	+	6.43924i	−0.838317	+	0.484003i
$178$	5.47701	+	10.2981i	0.410519	+	0.771874i
$179$	11.8018	−	9.05582i	0.882106	−	0.676864i	−0.0649652	−	0.997888i	$-0.520694\pi$
$179$	11.8018	−	9.05582i	0.882106	−	0.676864i	0.947071	+	0.321024i	$0.104027\pi$
$180$	2.33323	+	3.52348i	0.173909	+	0.262625i
$181$	2.68280	+	6.47686i	0.199411	+	0.481421i	0.991676	−	0.128756i	$-0.0410984\pi$
$181$	2.68280	+	6.47686i	0.199411	+	0.481421i	−0.792265	+	0.610177i	$0.791098\pi$
$182$	−12.1394	−	14.3613i	−0.899831	−	1.06453i
$183$	−5.09635	−	5.09635i	−0.376733	−	0.376733i
$184$	−5.02138	−	11.2684i	−0.370181	−	0.830719i
$185$	−1.03632	−	3.86759i	−0.0761917	−	0.284351i
$186$	1.27642	+	1.05197i	0.0935914	+	0.0771339i
$187$	−11.4410	−	8.77899i	−0.836649	−	0.641983i
$188$	−5.34537	−	10.9537i	−0.389851	−	0.798877i
$189$	9.22773	−	8.36752i	0.671219	−	0.608648i
$190$	−3.22526	+	0.744975i	−0.233985	+	0.0540462i
$191$	−5.20734	−	9.01938i	−0.376790	−	0.652619i	0.613803	−	0.789459i	$-0.289639\pi$
$191$	−5.20734	−	9.01938i	−0.376790	−	0.652619i	−0.990593	+	0.136840i	$0.956305\pi$
$192$	6.57232	−	3.14005i	0.474317	−	0.226613i
$193$	2.34751	−	4.06601i	0.168978	−	0.292678i	−0.769083	−	0.639149i	$-0.779287\pi$
$193$	2.34751	−	4.06601i	0.168978	−	0.292678i	0.938061	+	0.346471i	$0.112620\pi$
$194$	−16.1907	−	17.3587i	−1.16243	−	1.24628i
$195$	1.70431	−	4.11457i	0.122048	−	0.294650i
$196$	8.11283	+	11.4097i	0.579488	+	0.814981i
$197$	3.93563	−	1.63019i	0.280402	−	0.116146i	−0.238051	−	0.971253i	$-0.576508\pi$
$197$	3.93563	−	1.63019i	0.280402	−	0.116146i	0.518452	+	0.855107i	$0.326508\pi$
$198$	−9.45077	+	3.53466i	−0.671637	+	0.251197i
$199$	−6.35268	−	23.7085i	−0.450329	−	1.68065i	−0.701468	−	0.712701i	$-0.747472\pi$
$199$	−6.35268	−	23.7085i	−0.450329	−	1.68065i	0.251139	−	0.967951i	$-0.419195\pi$
$200$	9.27583	+	6.73471i	0.655901	+	0.476216i
$201$	−1.77760	+	6.63409i	−0.125382	+	0.467932i
$202$	−6.78867	+	4.84341i	−0.477649	+	0.340781i
$203$	1.29155	−	26.4181i	0.0906493	−	1.85419i
$204$	−7.97563	+	0.489533i	−0.558406	+	0.0342742i
$205$	0.856138	+	6.50301i	0.0597952	+	0.454190i
$206$	−1.43258	−	2.69359i	−0.0998125	−	0.187671i
$207$	8.20055	+	4.73459i	0.569977	+	0.329077i
$208$	17.3257	+	10.1956i	1.20132	+	0.706934i
$209$		−	7.90354i		−	0.546699i
$210$	−1.52036	+	2.94657i	−0.104915	+	0.203333i
$211$	3.90524	+	1.61760i	0.268848	+	0.111360i	0.513035	−	0.858368i	$-0.328521\pi$
$211$	3.90524	+	1.61760i	0.268848	+	0.111360i	−0.244187	+	0.969728i	$0.578521\pi$
$212$	2.57563	−	12.6736i	0.176895	−	0.870425i
$213$	8.76997	+	1.15459i	0.600908	+	0.0791111i
$214$	−6.95998	+	0.670925i	−0.475774	+	0.0458635i
$215$	0.0537580	−	0.200628i	0.00366626	−	0.0136827i
$216$	−6.35038	+	11.7049i	−0.432088	+	0.796421i
$217$	0.607623	−	3.34390i	0.0412481	−	0.226999i
$218$	7.53734	+	1.26048i	0.510493	+	0.0853708i
$219$	7.08035	+	5.43294i	0.478446	+	0.367124i
$220$	4.82707	−	4.19793i	0.325441	−	0.283025i
$221$	−13.4253	−	17.4962i	−0.903083	−	1.17692i
$222$	3.87378	−	3.61314i	0.259991	−	0.242498i
$223$	12.8216			0.858601			0.429300	−	0.903162i	$-0.358760\pi$
$223$	12.8216			0.858601			0.429300	+	0.903162i	$0.358760\pi$
$224$	−12.2196	−	8.64177i	−0.816459	−	0.577403i
$225$	−8.79854			−0.586569
$226$	−13.4394	+	12.5352i	−0.893977	+	0.833827i
$227$	3.89033	+	5.06997i	0.258210	+	0.336506i	0.904412	−	0.426661i	$-0.140310\pi$
$227$	3.89033	+	5.06997i	0.258210	+	0.336506i	−0.646202	+	0.763167i	$0.723644\pi$
$228$	−2.87380	−	3.30449i	−0.190322	−	0.218845i
$229$	0.945872	+	0.725793i	0.0625050	+	0.0479618i	0.639541	−	0.768757i	$-0.279124\pi$
$229$	0.945872	+	0.725793i	0.0625050	+	0.0479618i	−0.577036	+	0.816718i	$0.695791\pi$
$230$	−5.92121	−	0.990217i	−0.390433	−	0.0652930i
$231$	−6.03791	−	5.12032i	−0.397265	−	0.336892i
$232$	8.03954	+	27.1089i	0.527822	+	1.77979i
$233$	−1.81173	+	6.76147i	−0.118690	+	0.442958i	−0.999536	−	0.0304443i	$-0.990308\pi$
$233$	−1.81173	+	6.76147i	−0.118690	+	0.442958i	0.880846	+	0.473403i	$0.156974\pi$
$234$	−15.3592	+	1.48059i	−1.00406	+	0.0967891i
$235$	−5.88055	−	0.774189i	−0.383605	−	0.0505025i
$236$	−27.7225	−	5.63398i	−1.80458	−	0.366741i
$237$	−5.99257	−	2.48220i	−0.389259	−	0.161236i
$238$	8.87185	+	13.8155i	0.575076	+	0.895524i
$239$			14.0986i			0.911963i	0.889989	+	0.455981i	$0.150712\pi$
$239$			14.0986i			0.911963i	−0.889989	+	0.455981i	$0.849288\pi$
$240$	0.491805	−	3.51033i	0.0317459	−	0.226591i
$241$	−9.83693	−	5.67935i	−0.633652	−	0.365839i	0.148513	−	0.988910i	$-0.452551\pi$
$241$	−9.83693	−	5.67935i	−0.633652	−	0.365839i	−0.782165	+	0.623071i	$0.785885\pi$
$242$	−0.132540	−	0.249207i	−0.00851999	−	0.0160196i
$243$	−2.10819	−	16.0133i	−0.135240	−	1.02725i
$244$	−0.969907	−	15.8020i	−0.0620920	−	1.01162i
$245$	6.80916	−	0.226145i	0.435021	−	0.0144479i
$246$	−7.06404	+	5.03988i	−0.450387	+	0.321331i
$247$	3.12822	−	11.6747i	0.199044	−	0.742842i
$248$	0.569534	+	3.58840i	0.0361655	+	0.227864i
$249$	1.10278	+	4.11564i	0.0698860	+	0.260818i
$250$	11.6708	−	4.36496i	0.738125	−	0.276064i
$251$	3.14274	−	1.30177i	0.198368	−	0.0821667i	−0.281288	−	0.959623i	$-0.590762\pi$
$251$	3.14274	−	1.30177i	0.198368	−	0.0821667i	0.479656	+	0.877457i	$0.340762\pi$
$252$	11.4870	−	0.143041i	0.723614	−	0.00901071i
$253$	5.48542	−	13.2430i	0.344866	−	0.832579i
$254$	−14.5650	−	15.6157i	−0.913892	−	0.979818i
$255$	−1.94427	+	3.36758i	−0.121755	+	0.210886i
$256$	15.3840	+	4.39696i	0.961499	+	0.274810i
$257$	2.47657	+	4.28954i	0.154484	+	0.267574i	0.932871	−	0.360211i	$-0.117295\pi$
$257$	2.47657	+	4.28954i	0.154484	+	0.267574i	−0.778387	+	0.627785i	$0.783962\pi$
$258$	0.267741	−	0.0618432i	0.0166688	−	0.00385019i
$259$	−10.3636	−	3.32716i	−0.643962	−	0.206740i
$260$	8.79183	−	4.29040i	0.545246	−	0.266079i
$261$	−17.2187	−	13.2124i	−1.06581	−	0.817825i
$262$	−12.1686	−	10.0288i	−0.751777	−	0.619581i
$263$	7.69251	+	28.7089i	0.474341	+	1.77026i	0.623893	+	0.781510i	$0.285550\pi$
$263$	7.69251	+	28.7089i	0.474341	+	1.77026i	−0.149552	+	0.988754i	$0.547783\pi$
$264$	7.90215	+	3.03042i	0.486344	+	0.186510i
$265$	−4.45018	−	4.45018i	−0.273372	−	0.273372i
$266$	−3.04703	+	8.46681i	−0.186825	+	0.519134i
$267$	2.87373	+	6.93779i	0.175869	+	0.424586i
$268$	−12.5788	+	8.32959i	−0.768370	+	0.508811i
$269$	10.9242	−	8.38240i	0.666058	−	0.511084i	−0.219500	−	0.975612i	$-0.570443\pi$
$269$	10.9242	−	8.38240i	0.666058	−	0.511084i	0.885558	+	0.464528i	$0.153776\pi$
$270$	3.04297	+	5.72150i	0.185189	+	0.348200i
$271$	3.99121	−	2.30433i	0.242449	−	0.139978i	−0.373853	−	0.927488i	$-0.621964\pi$
$271$	3.99121	−	2.30433i	0.242449	−	0.139978i	0.616302	+	0.787510i	$0.288630\pi$
$272$	−13.8362	−	10.8004i	−0.838940	−	0.654871i
$273$	−6.89224	−	9.95325i	−0.417138	−	0.602398i
$274$	1.70064	+	1.06243i	0.102740	+	0.0641835i
$275$	1.73847	+	13.2050i	0.104833	+	0.796289i
$276$	−2.52180	−	7.53148i	−0.151794	−	0.453342i
$277$	19.2642	+	2.53618i	1.15747	+	0.152384i	0.684716	−	0.728810i	$-0.259926\pi$
$277$	19.2642	+	2.53618i	1.15747	+	0.152384i	0.472755	+	0.881194i	$0.343259\pi$
$278$	8.49714	−	18.6506i	0.509625	−	1.11859i
$279$	−1.97199	−	1.97199i	−0.118060	−	0.118060i
$280$	−6.78951	+	2.63615i	−0.405751	+	0.157540i
$281$	12.2720	−	12.2720i	0.732086	−	0.732086i	−0.238947	−	0.971033i	$-0.576802\pi$
$281$	12.2720	−	12.2720i	0.732086	−	0.732086i	0.971033	+	0.238947i	$0.0768021\pi$
$282$	−2.74887	−	7.34978i	−0.163693	−	0.437673i
$283$	2.03782	−	15.4788i	0.121136	−	0.920118i	−0.817674	−	0.575682i	$-0.804737\pi$
$283$	2.03782	−	15.4788i	0.121136	−	0.920118i	0.938810	−	0.344436i	$-0.111930\pi$
$284$	12.7507	+	14.6617i	0.756617	+	0.870010i
$285$	−2.11290	+	0.278169i	−0.125158	+	0.0164773i
$286$	5.25684	+	22.7587i	0.310844	+	1.34575i
$287$	16.1203	+	7.61963i	0.951549	+	0.449773i
$288$	−11.5382	+	4.20659i	−0.679894	+	0.247876i
$289$	1.12774	+	1.95331i	0.0663379	+	0.114901i
$290$	13.1593	+	4.02165i	0.772740	+	0.236159i
$291$	−9.30336	−	12.1244i	−0.545373	−	0.710743i
$292$	3.74475	+	19.2430i	0.219145	+	1.12611i
$293$	−3.70761	+	1.53574i	−0.216601	+	0.0897191i	−0.488346	−	0.872650i	$-0.662399\pi$
$293$	−3.70761	+	1.53574i	−0.216601	+	0.0897191i	0.271744	+	0.962369i	$0.412399\pi$
$294$	4.49420	+	7.81301i	0.262107	+	0.455664i
$295$	−9.73442	+	9.73442i	−0.566760	+	0.566760i
$296$	11.6320	−	0.308352i	0.676097	−	0.0179226i
$297$	−14.9456	+	4.00467i	−0.867233	+	0.232374i
$298$	−10.8040	+	1.04148i	−0.625859	+	0.0603314i
$299$	13.3443	−	17.3907i	0.771723	−	1.00573i
$300$	5.52830	+	4.88891i	0.319177	+	0.282261i
$301$	−0.379279	−	0.418270i	−0.0218613	−	0.0241087i
$302$	−18.0398	−	11.2699i	−1.03808	−	0.648507i
$303$	−4.64967	+	2.68449i	−0.267116	+	0.154220i
$304$	0.0798068	−	9.61937i	0.00457723	−	0.551709i
$305$	−6.67214	−	3.85216i	−0.382046	−	0.220574i
$306$	13.4645	+	0.468741i	0.769716	+	0.0267962i
$307$	23.1155	+	9.57475i	1.31927	+	0.546460i	0.927576	−	0.373635i	$-0.121889\pi$
$307$	23.1155	+	9.57475i	1.31927	+	0.546460i	0.391695	+	0.920095i	$0.371889\pi$
$308$	−2.48435	−	17.2116i	−0.141559	−	0.980723i
$309$	−0.751658	−	1.81466i	−0.0427603	−	0.103233i
$310$	1.60899	+	0.733048i	0.0913843	+	0.0416344i
$311$	−11.3503	+	3.04130i	−0.643616	+	0.172456i	−0.565841	−	0.824515i	$-0.691448\pi$
$311$	−11.3503	+	3.04130i	−0.643616	+	0.172456i	−0.0777752	+	0.996971i	$0.524782\pi$
$312$	10.4732	+	7.60404i	0.592927	+	0.430494i
$313$	28.7598	+	7.70616i	1.62560	+	0.435578i	0.952640	−	0.304101i	$-0.0983559\pi$
$313$	28.7598	+	7.70616i	1.62560	+	0.435578i	0.672960	+	0.739679i	$0.265023\pi$
$314$	−2.39500	+	14.3215i	−0.135158	+	0.808206i
$315$	3.02830	−	4.69920i	0.170625	−	0.264770i
$316$	−6.24866	−	12.8047i	−0.351515	−	0.720318i
$317$	19.1884	−	2.52620i	1.07773	−	0.141886i	0.429301	−	0.903161i	$-0.358760\pi$
$317$	19.1884	−	2.52620i	1.07773	−	0.141886i	0.648428	+	0.761276i	$0.275427\pi$
$318$	2.43349	−	7.96265i	0.136463	−	0.446523i
$319$	−16.4271	+	28.4526i	−0.919743	+	1.59304i
$320$	5.91740	−	5.06055i	0.330793	−	0.282893i
$321$	−4.50169			−0.251260
$322$	−10.9819	+	12.0720i	−0.611997	+	0.672747i
$323$	−4.03848	+	9.74976i	−0.224707	+	0.542491i
$324$	2.48909	−	3.69194i	0.138283	−	0.205108i
$325$	−2.65855	+	20.1937i	−0.147470	+	1.12015i
$326$	6.95888	+	5.73520i	0.385417	+	0.317644i
$327$	4.75238	+	1.27340i	0.262807	+	0.0704189i
$328$	−18.9577	−	1.98634i	−1.04676	−	0.109678i
$329$	−10.4284	+	12.2972i	−0.574935	+	0.677967i
$330$	3.35272	−	2.39202i	0.184561	−	0.131676i
$331$	−9.60864	+	12.5222i	−0.528139	+	0.688284i	−0.978895	−	0.204363i	$-0.934488\pi$
$331$	−9.60864	+	12.5222i	−0.528139	+	0.688284i	0.450756	+	0.892647i	$0.351154\pi$
$332$	−4.17435	+	8.37697i	−0.229097	+	0.459746i
$333$	−7.08583	+	5.43715i	−0.388301	+	0.297954i
$334$	25.5754	+	0.890358i	1.39942	+	0.0487182i
$335$			7.34172i			0.401121i
$336$	−7.29701	−	6.29289i	−0.398085	−	0.343305i
$337$			29.8112i			1.62392i	0.583714	+	0.811959i	$0.301599\pi$
$337$			29.8112i			1.62392i	−0.583714	+	0.811959i	$0.698401\pi$
$338$	−0.603134	+	17.3249i	−0.0328061	+	0.942352i
$339$	−9.38691	+	7.20283i	−0.509827	+	0.391204i
$340$	−8.09968	+	2.71205i	−0.439267	+	0.147082i
$341$	−2.56995	+	3.34923i	−0.139171	+	0.181371i
$342$	4.28843	+	6.01078i	0.231892	+	0.325026i
$343$	9.51000	−	15.8921i	0.513492	−	0.858095i
$344$	0.530556	+	0.287847i	0.0286057	+	0.0155197i
$345$	−3.73339	−	1.00036i	−0.200999	−	0.0538575i
$346$	−14.2510	+	17.2917i	−0.766139	+	0.929605i
$347$	0.628295	−	4.77238i	0.0337286	−	0.256195i	−0.966270	−	0.257529i	$-0.917092\pi$
$347$	0.628295	−	4.77238i	0.0337286	−	0.256195i	0.999999	+	0.00133489i	$0.000424910\pi$
$348$	3.47741	+	17.8692i	0.186409	+	0.957888i
$349$	−11.6607	+	28.1515i	−0.624184	+	1.50691i	0.222563	+	0.974918i	$0.428558\pi$
$349$	−11.6607	+	28.1515i	−0.624184	+	1.50691i	−0.846747	+	0.531995i	$0.821442\pi$
$350$	3.22850	−	14.8163i	0.172571	−	0.791964i
$351$	−23.6619			−1.26298
$352$	8.59309	+	16.4855i	0.458013	+	0.878681i
$353$	3.14470	−	5.44679i	0.167376	−	0.289903i	−0.770121	−	0.637898i	$-0.779804\pi$
$353$	3.14470	−	5.44679i	0.167376	−	0.289903i	0.937496	+	0.347995i	$0.113137\pi$
$354$	−17.4177	−	5.32307i	−0.925739	−	0.282918i
$355$	9.37472	−	1.23421i	0.497559	−	0.0655048i
$356$	−5.36700	+	15.5978i	−0.284450	+	0.826682i
$357$	4.83199	+	9.40160i	0.255736	+	0.497585i
$358$	20.7494	+	3.46997i	1.09664	+	0.183394i
$359$	14.4771	+	3.87913i	0.764073	+	0.204733i	0.619751	−	0.784798i	$-0.287233\pi$
$359$	14.4771	+	3.87913i	0.764073	+	0.204733i	0.144321	+	0.989531i	$0.453900\pi$
$360$	−1.39329	+	5.81175i	−0.0734331	+	0.306306i
$361$	12.7660	−	3.42064i	0.671895	−	0.180034i
$362$	−4.11044	+	9.02211i	−0.216040	+	0.474192i
$363$	−0.0695423	−	0.167890i	−0.00365002	−	0.00881193i
$364$	3.14261	−	26.4073i	0.164717	−	1.38412i
$365$	8.81381	+	3.65080i	0.461336	+	0.191092i
$366$	0.354624	−	10.1865i	0.0185365	−	0.532458i
$367$	13.5153	+	7.80306i	0.705492	+	0.407316i	0.809390	−	0.587272i	$-0.199798\pi$
$367$	13.5153	+	7.80306i	0.705492	+	0.407316i	−0.103897	+	0.994588i	$0.533131\pi$
$368$	6.81001	−	16.0626i	0.354996	−	0.837320i
$369$	12.6708	−	7.31548i	0.659615	−	0.380829i
$370$	3.00018	−	4.80244i	0.155972	−	0.249667i
$371$	−16.7218	+	3.61573i	−0.868155	+	0.187719i
$372$	0.143306	+	2.33478i	0.00743005	+	0.121053i
$373$	9.69218	−	12.6311i	0.501842	−	0.654013i	−0.471904	−	0.881650i	$-0.656433\pi$
$373$	9.69218	−	12.6311i	0.501842	−	0.654013i	0.973746	+	0.227637i	$0.0730998\pi$
$374$	−1.95691	−	20.3004i	−0.101189	−	1.04971i
$375$	7.74878	−	2.07628i	0.400145	−	0.107219i
$376$	6.17196	−	16.0940i	0.318295	−	0.829987i
$377$	−35.5268	+	35.5268i	−1.82972	+	1.82972i
$378$	17.5547	+	1.47186i	0.902915	+	0.0757046i
$379$	17.3836	−	7.20051i	0.892933	−	0.369865i	0.111435	−	0.993772i	$-0.464455\pi$
$379$	17.3836	−	7.20051i	0.892933	−	0.369865i	0.781499	+	0.623907i	$0.214455\pi$
$380$	−3.88154	−	2.61691i	−0.199119	−	0.134245i
$381$	−8.36922	−	10.9070i	−0.428768	−	0.558781i
$382$	4.30470	−	14.0855i	0.220248	−	0.720676i
$383$	0.998277	+	1.72907i	0.0510096	+	0.0883512i	0.890403	−	0.455173i	$-0.150423\pi$
$383$	0.998277	+	1.72907i	0.0510096	+	0.0883512i	−0.839393	+	0.543525i	$0.817089\pi$
$384$	9.58707	+	3.76811i	0.489238	+	0.192291i
$385$	−7.65097	−	3.61641i	−0.389929	−	0.184310i
$386$	6.46944	−	1.49432i	0.329286	−	0.0760589i
$387$	−0.459349	+	0.0604744i	−0.0233500	+	0.00307409i
$388$	2.33450	−	33.4885i	0.118516	−	1.70012i
$389$	3.07128	−	23.3287i	0.155720	−	1.18281i	−0.717880	−	0.696167i	$-0.754887\pi$
$389$	3.07128	−	23.3287i	0.155720	−	1.18281i	0.873600	−	0.486645i	$-0.161780\pi$
$390$	5.89921	−	2.20635i	0.298718	−	0.111723i
$391$	−13.5336	+	13.5336i	−0.684422	+	0.684422i
$392$	−3.97413	+	19.3960i	−0.200724	+	0.979648i
$393$	−7.17859	−	7.17859i	−0.362112	−	0.362112i
$394$	5.48224	+	2.49769i	0.276191	+	0.125832i
$395$	−6.87428	−	0.905016i	−0.345882	−	0.0455363i
$396$	−12.7717	−	6.36432i	−0.641804	−	0.319819i
$397$	−3.70805	−	28.1654i	−0.186102	−	1.41358i	−0.788328	−	0.615256i	$-0.789053\pi$
$397$	−3.70805	−	28.1654i	−0.186102	−	1.41358i	0.602226	−	0.798326i	$-0.294281\pi$
$398$	18.3912	−	29.4391i	0.921868	−	1.47565i
$399$	−2.47571	+	5.23766i	−0.123940	+	0.262211i
$400$	1.98254	+	16.0893i	0.0991271	+	0.804463i
$401$	−11.5784	+	6.68480i	−0.578199	+	0.333823i	−0.760417	−	0.649435i	$-0.775006\pi$
$401$	−11.5784	+	6.68480i	−0.578199	+	0.333823i	0.182218	+	0.983258i	$0.441672\pi$
$402$	−8.57556	+	4.56089i	−0.427710	+	0.227477i
$403$	−5.12182	+	3.93011i	−0.255136	+	0.195773i
$404$	−11.5574	−	2.34878i	−0.575000	−	0.116856i
$405$	−0.829205	−	2.00188i	−0.0412035	−	0.0994741i
$406$	28.5671	−	24.1473i	1.41776	−	1.19841i
$407$	9.56021	+	9.56021i	0.473882	+	0.473882i
$408$	−8.19959	−	7.77609i	−0.405940	−	0.384974i
$409$	−9.07394	−	33.8644i	−0.448678	−	1.67449i	−0.706040	−	0.708172i	$-0.749520\pi$
$409$	−9.07394	−	33.8644i	−0.448678	−	1.67449i	0.257362	−	0.966315i	$-0.417147\pi$
$410$	−5.89949	+	7.15823i	−0.291355	+	0.353520i
$411$	1.02421	+	0.785906i	0.0505207	+	0.0387659i
$412$	1.40380	−	4.07980i	0.0691605	−	0.200997i
$413$	7.90912	+	36.5777i	0.389182	+	1.79987i
$414$	3.01382	+	13.0479i	0.148121	+	0.641269i
$415$	2.27732	+	3.94443i	0.111789	+	0.193625i
$416$	6.16827	+	27.7526i	0.302425	+	1.36068i
$417$	6.59748	−	11.4272i	0.323080	−	0.559591i
$418$	8.17373	−	7.62378i	0.399790	−	0.372891i
$419$	−1.55708	+	3.75913i	−0.0760686	+	0.183646i	−0.957339	−	0.288966i	$-0.906689\pi$
$419$	−1.55708	+	3.75913i	−0.0760686	+	0.183646i	0.881271	+	0.472612i	$0.156689\pi$
$420$	−4.51385	+	1.26993i	−0.220253	+	0.0619661i
$421$	9.17801	−	3.80165i	0.447309	−	0.185281i	−0.147647	−	0.989040i	$-0.547170\pi$
$421$	9.17801	−	3.80165i	0.447309	−	0.185281i	0.594955	+	0.803759i	$0.297170\pi$
$422$	2.09410	+	5.59909i	0.101939	+	0.272559i
$423$	3.42431	+	12.7797i	0.166495	+	0.621370i
$424$	15.5913	−	9.56128i	0.757180	−	0.464337i
$425$	4.60280	−	17.1779i	0.223269	−	0.833250i
$426$	7.26547	+	10.1835i	0.352013	+	0.493392i
$427$	−18.6273	+	9.57358i	−0.901438	+	0.463298i
$428$	−7.40747	−	6.55074i	−0.358054	−	0.316642i
$429$	1.96287	+	14.9095i	0.0947683	+	0.719837i
$430$	0.259341	−	0.137930i	0.0125066	−	0.00665158i
$431$	−19.6623	−	11.3520i	−0.947099	−	0.546808i	−0.0549204	−	0.998491i	$-0.517490\pi$
$431$	−19.6623	−	11.3520i	−0.947099	−	0.546808i	−0.892179	+	0.451683i	$0.850824\pi$
$432$	−18.2307	+	4.72315i	−0.877125	+	0.227243i
$433$		−	8.11220i		−	0.389847i	−0.980818	−	0.194924i	$-0.937554\pi$
$433$		−	8.11220i		−	0.389847i	0.980818	−	0.194924i	$-0.0624459\pi$
$434$	4.04433	−	2.59714i	0.194134	−	0.124667i
$435$	8.18458	+	3.39017i	0.392421	+	0.162546i
$436$	5.96696	+	9.01088i	0.285766	+	0.431543i
$437$	−10.3997	−	1.36914i	−0.497485	−	0.0654951i
$438$	1.21105	+	12.5630i	0.0578660	+	0.600285i
$439$	−10.7256	+	40.0286i	−0.511906	+	1.91046i	−0.112603	+	0.993640i	$0.535919\pi$
$439$	−10.7256	+	40.0286i	−0.511906	+	1.91046i	−0.399303	+	0.916819i	$0.630748\pi$
$440$	8.99765	+	0.942755i	0.428946	+	0.0449441i
$441$	−6.27851	−	13.8395i	−0.298977	−	0.659023i
$442$	5.14424	−	30.7611i	0.244687	−	1.46316i
$443$	−18.4109	−	14.1272i	−0.874731	−	0.671204i	0.0705339	−	0.997509i	$-0.477530\pi$
$443$	−18.4109	−	14.1272i	−0.874731	−	0.671204i	−0.945265	+	0.326305i	$0.894196\pi$
$444$	7.47333	+	0.520970i	0.354668	+	0.0247241i
$445$	4.88667	+	6.36844i	0.231651	+	0.301893i
$446$	12.3678	+	13.2600i	0.585632	+	0.627878i
$447$	−6.98800			−0.330521
$448$	−2.84990	−	20.9733i	−0.134645	−	0.990894i
$449$	−29.3565			−1.38542			−0.692708	−	0.721218i	$-0.743583\pi$
$449$	−29.3565			−1.38542			−0.692708	+	0.721218i	$0.743583\pi$
$450$	−8.48709	−	9.09933i	−0.400085	−	0.428946i
$451$	−13.4827	−	17.5710i	−0.634877	−	0.827388i
$452$	−25.9274	−	1.80741i	−1.21952	−	0.0850136i
$453$	−10.8645	−	8.33662i	−0.510458	−	0.391688i
$454$	−1.49068	+	8.91383i	−0.0699610	+	0.418347i
$455$	−9.87021	−	8.37022i	−0.462722	−	0.392402i
$456$	0.645386	−	6.15957i	0.0302230	−	0.288448i
$457$	7.79648	−	29.0969i	0.364704	−	1.36109i	−0.503118	−	0.864218i	$-0.667814\pi$
$457$	7.79648	−	29.0969i	0.364704	−	1.36109i	0.867822	−	0.496876i	$-0.165519\pi$
$458$	0.161785	+	1.67831i	0.00755972	+	0.0784223i
$459$	20.4831	+	2.69665i	0.956069	+	0.125869i
$460$	−4.68755	−	7.07881i	−0.218558	−	0.330051i
$461$	−17.6705	−	7.31937i	−0.822999	−	0.340897i	−0.0688715	−	0.997626i	$-0.521940\pi$
$461$	−17.6705	−	7.31937i	−0.822999	−	0.340897i	−0.754127	+	0.656728i	$0.771940\pi$
$462$	−0.528817	−	11.1834i	−0.0246028	−	0.520299i
$463$		−	29.7043i		−	1.38048i	−0.723582	−	0.690238i	$-0.757506\pi$
$463$		−	29.7043i		−	1.38048i	0.723582	−	0.690238i	$-0.242494\pi$
$464$	−20.2807	+	34.4637i	−0.941508	+	1.59994i
$465$	0.985822	+	0.569164i	0.0457164	+	0.0263944i
$466$	−8.74022	+	4.64846i	−0.404883	+	0.215336i
$467$	−3.44726	−	26.1846i	−0.159520	−	1.21168i	−0.864568	−	0.502517i	$-0.832408\pi$
$467$	−3.44726	−	26.1846i	−0.159520	−	1.21168i	0.705047	−	0.709160i	$-0.250926\pi$
$468$	−16.3467	−	14.4561i	−0.755627	−	0.668232i
$469$	16.7760	+	10.8110i	0.774646	+	0.499204i
$470$	−4.87174	−	6.82837i	−0.224717	−	0.314969i
$471$	−2.41954	+	9.02983i	−0.111486	+	0.416073i
$472$	−20.9146	−	34.1047i	−0.962671	−	1.56980i
$473$	0.181522	+	0.677448i	0.00834637	+	0.0311491i
$474$	−3.21339	−	8.59178i	−0.147596	−	0.394633i
$475$	9.00462	−	3.72984i	0.413160	−	0.171137i
$476$	−5.72996	+	22.5016i	−0.262632	+	1.03136i
$477$	−5.37228	+	12.9698i	−0.245980	+	0.593848i
$478$	−14.5806	+	13.5995i	−0.666900	+	0.622029i
$479$	−2.90084	+	5.02440i	−0.132543	+	0.229571i	−0.924656	−	0.380803i	$-0.875647\pi$
$479$	−2.90084	+	5.02440i	−0.132543	+	0.229571i	0.792113	+	0.610374i	$0.208981\pi$
$480$	4.10474	−	2.87746i	0.187355	−	0.131337i
$481$	10.3379	+	17.9057i	0.471367	+	0.816431i
$482$	−3.61522	−	15.6515i	−0.164669	−	0.712908i
$483$	−7.78341	+	7.05784i	−0.354157	+	0.321143i
$484$	0.129878	−	0.377456i	0.00590354	−	0.0171571i
$485$	−12.9604	−	9.94490i	−0.588503	−	0.451575i
$486$	14.5272	−	17.6267i	0.658966	−	0.799565i
$487$	1.66405	+	6.21031i	0.0754052	+	0.281416i	0.993325	−	0.115350i	$-0.0367990\pi$
$487$	1.66405	+	6.21031i	0.0754052	+	0.281416i	−0.917920	+	0.396766i	$0.870132\pi$
$488$	15.4067	−	16.2458i	0.697428	−	0.735411i
$489$	4.10525	+	4.10525i	0.185646	+	0.185646i
$490$	6.80201	+	6.82380i	0.307284	+	0.308268i
$491$	4.89496	+	11.8175i	0.220906	+	0.533315i	0.995014	−	0.0997395i	$-0.0318009\pi$
$491$	4.89496	+	11.8175i	0.220906	+	0.533315i	−0.774107	+	0.633054i	$0.781801\pi$
$492$	−12.0262	−	2.44406i	−0.542181	−	0.110187i
$493$	34.8029	−	26.7052i	1.56744	−	1.20274i
$494$	15.0913	−	8.02626i	0.678989	−	0.361118i
$495$	−6.01378	+	3.47206i	−0.270299	+	0.156057i
$496$	−3.16170	+	4.05039i	−0.141965	+	0.181868i
$497$	10.9844	−	23.2389i	0.492719	−	1.04241i
$498$	−3.19259	+	5.11044i	−0.143063	+	0.229004i
$499$	−2.81442	−	21.3776i	−0.125991	−	0.956994i	−0.931329	−	0.364179i	$-0.881350\pi$
$499$	−2.81442	−	21.3776i	−0.125991	−	0.956994i	0.805338	−	0.592815i	$-0.201984\pi$
$500$	15.7719	+	7.85932i	0.705339	+	0.351479i
$501$	16.3348	+	2.15052i	0.729785	+	0.0960780i
$502$	4.37776	+	1.99449i	0.195389	+	0.0890186i
$503$	7.63379	+	7.63379i	0.340374	+	0.340374i	0.856508	−	0.516134i	$-0.172629\pi$
$503$	7.63379	+	7.63379i	0.340374	+	0.340374i	−0.516134	+	0.856508i	$0.672629\pi$
$504$	11.2283	+	11.7417i	0.500150	+	0.523019i
$505$	−4.05823	+	4.05823i	−0.180589	+	0.180589i
$506$	18.9870	−	7.10126i	0.844074	−	0.315690i
$507$	−1.45677	+	11.0653i	−0.0646975	+	0.491426i
$508$	2.10010	−	30.1259i	0.0931767	−	1.33662i
$509$	14.6663	−	1.93086i	0.650072	−	0.0855837i	0.201724	−	0.979442i	$-0.435346\pi$
$509$	14.6663	−	1.93086i	0.650072	−	0.0855837i	0.448349	+	0.893859i	$0.352012\pi$
$510$	−5.35815	+	1.23763i	−0.237263	+	0.0548033i
$511$	21.3209	−	14.7639i	0.943179	−	0.653115i
$512$	10.2922	+	20.1512i	0.454853	+	0.890566i
$513$	5.66137	+	9.80578i	0.249956	+	0.432936i
$514$	−2.04728	+	6.69894i	−0.0903017	+	0.295477i
$515$	−1.27817	−	1.66574i	−0.0563229	−	0.0734014i
$516$	0.322221	+	0.217240i	0.0141850	+	0.00956345i
$517$	18.5033	−	7.66433i	0.813776	−	0.337077i
$518$	−6.55583	−	13.9273i	−0.288047	−	0.611929i
$519$	−10.2009	+	10.2009i	−0.447768	+	0.447768i
$520$	12.9177	+	4.95385i	0.566478	+	0.217241i
$521$	−37.3500	+	10.0079i	−1.63633	+	0.438454i	−0.955741	−	0.294208i	$-0.904944\pi$
$521$	−37.3500	+	10.0079i	−1.63633	+	0.438454i	−0.680592	+	0.732663i	$0.738277\pi$
$522$	−2.94514	−	30.5520i	−0.128905	−	1.33723i
$523$	−25.3854	+	33.0829i	−1.11003	+	1.44661i	−0.229073	+	0.973409i	$0.573570\pi$
$523$	−25.3854	+	33.0829i	−1.11003	+	1.44661i	−0.880953	+	0.473205i	$0.843097\pi$
$524$	−1.36619	−	22.2584i	−0.0596822	−	0.972361i
$525$	2.98425	−	9.29546i	0.130243	−	0.405687i
$526$	−22.2701	+	35.6481i	−0.971022	+	1.55433i
$527$	4.88164	−	2.81842i	0.212648	−	0.122772i
$528$	4.48841	+	11.0955i	0.195333	+	0.482868i
$529$	3.44337	+	1.98803i	0.149712	+	0.0864360i
$530$	0.309661	−	8.89497i	0.0134508	−	0.386373i
$531$	28.3705	+	11.7515i	1.23118	+	0.509970i
$532$	−11.6954	+	5.01591i	−0.507061	+	0.217467i
$533$	−12.9613	−	31.2914i	−0.561418	−	1.35538i
$534$	−4.40296	+	9.66418i	−0.190535	+	0.418210i
$535$	−4.64815	+	1.24547i	−0.200957	+	0.0538463i
$536$	−20.7479	−	4.97404i	−0.896171	−	0.214846i
$537$	13.0827	+	3.50551i	0.564562	+	0.151274i
$538$	19.2064	+	3.21193i	0.828049	+	0.138476i
$539$	−19.5299	+	12.1574i	−0.841214	+	0.523655i
$540$	−2.98185	+	8.66597i	−0.128318	+	0.372924i
$541$	−6.83484	+	0.899824i	−0.293853	+	0.0386865i	−0.276011	−	0.961154i	$-0.589013\pi$
$541$	−6.83484	+	0.899824i	−0.293853	+	0.0386865i	−0.0178415	+	0.999841i	$0.505679\pi$
$542$	6.23304	+	1.90490i	0.267732	+	0.0818223i
$543$	−3.19149	+	5.52782i	−0.136960	+	0.237222i
$544$	−2.17676	−	24.7273i	−0.0933278	−	1.06017i
$545$	5.25929			0.225283
$546$	3.64525	−	16.7288i	0.156002	−	0.715927i
$547$	11.0146	−	26.5915i	0.470949	−	1.13697i	−0.492796	−	0.870145i	$-0.664025\pi$
$547$	11.0146	−	26.5915i	0.470949	−	1.13697i	0.963745	−	0.266826i	$-0.0859750\pi$
$548$	0.541699	+	2.78360i	0.0231402	+	0.118910i
$549$	−2.24316	+	17.0385i	−0.0957355	+	0.727184i
$550$	−11.9795	+	14.5354i	−0.510806	+	0.619793i
$551$	23.2229	+	6.22256i	0.989330	+	0.265090i
$552$	5.35642	−	9.87289i	0.227984	−	0.420218i
$553$	−12.1906	+	14.3752i	−0.518398	+	0.611297i
$554$	15.9594	+	22.3691i	0.678050	+	0.950374i
$555$	2.21931	−	2.89227i	0.0942046	−	0.122770i
$556$	27.4846	−	9.20278i	1.16561	−	0.390285i
$557$	12.6429	−	9.70127i	0.535698	−	0.411056i	−0.305168	−	0.952299i	$-0.598713\pi$
$557$	12.6429	−	9.70127i	0.535698	−	0.411056i	0.840866	+	0.541243i	$0.182046\pi$
$558$	0.137219	−	3.94160i	0.00580894	−	0.166861i
$559$			1.07253i			0.0453634i
$560$	−9.27544	−	4.47878i	−0.391959	−	0.189263i
$561$		−	13.1302i		−	0.554358i
$562$	24.5291	+	0.853934i	1.03470	+	0.0360210i
$563$	−25.1024	+	19.2617i	−1.05794	+	0.811785i	−0.982667	−	0.185378i	$-0.940649\pi$
$563$	−25.1024	+	19.2617i	−1.05794	+	0.811785i	−0.0752714	+	0.997163i	$0.523982\pi$
$564$	4.94947	−	9.93246i	0.208410	−	0.418232i
$565$	−7.69952	+	10.0342i	−0.323921	+	0.422143i
$566$	17.9736	−	12.8234i	0.755488	−	0.539007i
$567$	−5.79538	−	1.05308i	−0.243383	−	0.0442254i
$568$	−2.86351	+	27.3293i	−0.120150	+	1.14671i
$569$	−25.4581	−	6.82148i	−1.06726	−	0.285971i	−0.317893	−	0.948127i	$-0.602975\pi$
$569$	−25.4581	−	6.82148i	−1.06726	−	0.285971i	−0.749367	+	0.662155i	$0.769642\pi$
$570$	−2.32579	−	1.91681i	−0.0974166	−	0.0802865i
$571$	−1.33193	+	10.1170i	−0.0557393	+	0.423382i	0.940712	+	0.339207i	$0.110159\pi$
$571$	−1.33193	+	10.1170i	−0.0557393	+	0.423382i	−0.996451	+	0.0841750i	$0.973175\pi$
$572$	−18.4660	+	27.3897i	−0.772102	+	1.14522i
$573$	3.62878	−	8.76064i	0.151594	−	0.365981i
$574$	7.66952	+	24.0213i	0.320120	+	1.00263i
$575$	17.6766			0.737165
$576$	−15.4802	−	7.87495i	−0.645007	−	0.328123i
$577$	−5.80520	+	10.0549i	−0.241674	+	0.418591i	−0.961191	−	0.275883i	$-0.911030\pi$
$577$	−5.80520	+	10.0549i	−0.241674	+	0.418591i	0.719517	+	0.694474i	$0.244363\pi$
$578$	−0.932262	+	3.05047i	−0.0387770	+	0.126883i
$579$	4.23820	−	0.557969i	0.176134	−	0.0231884i
$580$	8.53435	+	17.4884i	0.354369	+	0.726168i
$581$	12.3666	+	0.604588i	0.513052	+	0.0250825i
$582$	3.56482	−	21.3166i	0.147767	−	0.883602i
$583$	20.5268	+	5.50014i	0.850133	+	0.227793i
$584$	−16.2886	+	22.4346i	−0.674028	+	0.928349i
$585$	−10.2575	+	2.74848i	−0.424094	+	0.113636i
$586$	−5.16462	−	2.35298i	−0.213349	−	0.0972008i
$587$	6.69352	+	16.1596i	0.276271	+	0.666978i	0.999726	−	0.0233936i	$-0.00744708\pi$
$587$	6.69352	+	16.1596i	0.276271	+	0.666978i	−0.723455	+	0.690372i	$0.757447\pi$
$588$	−3.74499	+	12.1843i	−0.154441	+	0.502472i
$589$	2.85414	+	1.18222i	0.117603	+	0.0487126i
$590$	−19.4570	−	0.677359i	−0.801034	−	0.0278864i
$591$	3.35895	+	1.93929i	0.138169	+	0.0797718i
$592$	11.5392	+	11.7322i	0.474256	+	0.482192i
$593$	−9.30507	+	5.37229i	−0.382113	+	0.220613i	−0.678737	−	0.734381i	$-0.737473\pi$
$593$	−9.30507	+	5.37229i	−0.382113	+	0.220613i	0.296624	+	0.954994i	$0.404139\pi$
$594$	−18.5582	−	11.5936i	−0.761450	−	0.475693i
$595$	7.59030	+	8.37062i	0.311172	+	0.343162i
$596$	−11.4987	−	10.1687i	−0.471003	−	0.416528i
$597$	13.6045	−	17.7297i	0.556794	−	0.725629i
$598$	30.8572	−	2.97456i	1.26184	−	0.121639i
$599$	−5.29975	+	1.42006i	−0.216542	+	0.0580223i	−0.365459	−	0.930827i	$-0.619088\pi$
$599$	−5.29975	+	1.42006i	−0.216542	+	0.0580223i	0.148917	+	0.988850i	$0.452421\pi$
$600$	0.276572	+	10.4332i	0.0112910	+	0.425932i
$601$	−10.9312	+	10.9312i	−0.445894	+	0.445894i	−0.893987	−	0.448093i	$-0.852103\pi$
$601$	−10.9312	+	10.9312i	−0.445894	+	0.445894i	0.448093	+	0.893987i	$0.352103\pi$
$602$	0.0667160	−	0.795710i	0.00271914	−	0.0324307i
$603$	15.1300	−	6.26707i	0.616143	−	0.255215i
$604$	−5.74616	−	29.5275i	−0.233808	−	1.20146i
$605$	−0.118254	−	0.154112i	−0.00480772	−	0.00626554i
$606$	−7.26134	−	2.21916i	−0.294972	−	0.0901473i
$607$	15.5748	+	26.9763i	0.632161	+	1.09494i	0.987109	+	0.160049i	$0.0511652\pi$
$607$	15.5748	+	26.9763i	0.632161	+	1.09494i	−0.354948	+	0.934886i	$0.615501\pi$
$608$	10.0252	−	9.19633i	0.406576	−	0.372961i
$609$	19.7987	−	13.7099i	0.802285	−	0.555551i
$610$	−2.45211	−	10.6160i	−0.0992831	−	0.429831i
$611$	30.3656	−	3.99771i	1.22846	−	0.161730i
$612$	12.5032	+	14.3770i	0.505410	+	0.581155i
$613$	0.400595	−	3.04282i	0.0161799	−	0.122899i	−0.981449	−	0.191725i	$-0.938592\pi$
$613$	0.400595	−	3.04282i	0.0161799	−	0.122899i	0.997629	+	0.0688260i	$0.0219253\pi$
$614$	12.3952	+	33.1416i	0.500229	+	1.33748i
$615$	−4.22285	+	4.22285i	−0.170282	+	0.170282i
$616$	15.4036	−	19.1716i	0.620629	−	0.772448i
$617$	14.2796	+	14.2796i	0.574876	+	0.574876i	0.933487	−	0.358611i	$-0.116749\pi$
$617$	14.2796	+	14.2796i	0.574876	+	0.574876i	−0.358611	+	0.933487i	$0.616749\pi$
$618$	1.15165	−	2.52778i	0.0463261	−	0.101682i
$619$	25.0619	+	3.29946i	1.00732	+	0.132616i	0.616090	−	0.787676i	$-0.288716\pi$
$619$	25.0619	+	3.29946i	1.00732	+	0.132616i	0.391231	+	0.920292i	$0.372049\pi$
$620$	0.793924	+	2.37109i	0.0318848	+	0.0952254i
$621$	2.68039	+	20.3596i	0.107560	+	0.817002i
$622$	−14.0938	−	8.80467i	−0.565110	−	0.353035i
$623$	21.7479	−	1.78842i	0.871310	−	0.0716516i
$624$	2.23845	+	18.1661i	0.0896098	+	0.727226i
$625$	−10.1224	+	5.84419i	−0.404897	+	0.233768i
$626$	19.7722	+	37.1764i	0.790255	+	1.48587i
$627$	5.70904	−	4.38070i	0.227997	−	0.174948i
$628$	−17.1213	+	11.3376i	−0.683213	+	0.452421i
$629$	−6.90843	−	16.6784i	−0.275457	−	0.665012i
$630$	7.78095	−	1.40103i	0.310000	−	0.0558185i
$631$	−20.5874	−	20.5874i	−0.819572	−	0.819572i	0.166474	−	0.986046i	$-0.446762\pi$
$631$	−20.5874	−	20.5874i	−0.819572	−	0.819572i	−0.986046	+	0.166474i	$0.946762\pi$
$632$	7.21493	−	18.8137i	0.286995	−	0.748368i
$633$	0.996100	+	3.71749i	0.0395914	+	0.147757i
$634$	21.1218	+	17.4076i	0.838853	+	0.691345i
$635$	−11.6591	−	8.94634i	−0.462677	−	0.355025i
$636$	10.5822	−	5.16411i	0.419612	−	0.204770i
$637$	−33.6604	+	10.2282i	−1.33368	+	0.405258i
$638$	−45.2710	+	10.4568i	−1.79230	+	0.413987i
$639$	−10.5460	−	18.2662i	−0.417192	−	0.722598i
$640$	10.9415	+	1.23828i	0.432500	+	0.0489473i
$641$	−5.47454	+	9.48218i	−0.216231	+	0.374524i	−0.953653	−	0.300909i	$-0.902710\pi$
$641$	−5.47454	+	9.48218i	−0.216231	+	0.374524i	0.737421	+	0.675433i	$0.236043\pi$
$642$	−4.34234	−	4.65559i	−0.171379	−	0.183741i
$643$	2.33757	−	5.64338i	0.0921846	−	0.222553i	−0.871061	−	0.491174i	$-0.836568\pi$
$643$	2.33757	−	5.64338i	0.0921846	−	0.222553i	0.963246	+	0.268621i	$0.0865679\pi$
$644$	−23.0779	+	0.287374i	−0.909395	+	0.0113241i
$645$	0.174718	−	0.0723704i	0.00687950	−	0.00284958i
$646$	−13.9786	+	5.22810i	−0.549981	+	0.205697i
$647$	−11.9783	−	44.7036i	−0.470916	−	1.75748i	−0.636492	−	0.771284i	$-0.719615\pi$
$647$	−11.9783	−	44.7036i	−0.470916	−	1.75748i	0.165576	−	0.986197i	$-0.447052\pi$
$648$	6.21914	−	0.987072i	0.244311	−	0.0387759i
$649$	12.0311	−	44.9008i	0.472263	−	1.76251i
$650$	−23.4485	+	16.7295i	−0.919727	+	0.656184i
$651$	2.75222	−	1.41451i	0.107868	−	0.0554392i
$652$	0.781287	+	12.7290i	0.0305976	+	0.498505i
$653$	0.649359	+	4.93237i	0.0254114	+	0.193018i	0.999442	−	0.0333971i	$-0.0106326\pi$
$653$	0.649359	+	4.93237i	0.0254114	+	0.193018i	−0.974031	+	0.226416i	$0.927299\pi$
$654$	3.26723	+	6.14316i	0.127759	+	0.240217i
$655$	−9.39822	−	5.42606i	−0.367219	−	0.212014i
$656$	−16.2324	−	21.5218i	−0.633767	−	0.840285i
$657$		−	21.2802i		−	0.830219i
$658$	−22.7768	+	1.07702i	−0.887934	+	0.0419868i
$659$	−38.3411	−	15.8814i	−1.49356	−	0.618652i	−0.521469	−	0.853270i	$-0.674616\pi$
$659$	−38.3411	−	15.8814i	−1.49356	−	0.618652i	−0.972088	+	0.234618i	$0.924616\pi$
$660$	5.70783	+	1.15999i	0.222177	+	0.0451527i
$661$	−22.5111	−	2.96364i	−0.875579	−	0.115272i	−0.320678	−	0.947188i	$-0.603911\pi$
$661$	−22.5111	−	2.96364i	−0.875579	−	0.115272i	−0.554901	+	0.831916i	$0.687244\pi$
$662$	−22.2188	+	2.14184i	−0.863560	+	0.0832451i
$663$	5.19694	−	19.3952i	0.201832	−	0.753248i
$664$	−12.6899	+	3.76339i	−0.492465	+	0.146048i
$665$	−1.10717	+	6.09300i	−0.0429340	+	0.236277i
$666$	−12.4580	−	2.08338i	−0.482739	−	0.0807294i
$667$	34.5930	+	26.5442i	1.33945	+	1.02779i
$668$	23.7493	+	27.3086i	0.918889	+	1.05660i
$669$	7.10666	+	9.26157i	0.274759	+	0.358073i
$670$	−7.59271	+	7.08185i	−0.293332	+	0.273596i
$671$	26.0148			1.00429
$672$	−0.530696	−	13.6166i	−0.0204720	−	0.525272i
$673$	50.0708			1.93009			0.965043	−	0.262091i	$-0.0844122\pi$
$673$	50.0708			1.93009			0.965043	+	0.262091i	$0.0844122\pi$
$674$	−30.8303	+	28.7559i	−1.18754	+	1.10764i
$675$	−11.6157	−	15.1379i	−0.447089	−	0.582657i
$676$	−18.4990	+	16.0879i	−0.711500	+	0.618766i
$677$	−1.75858	−	1.34941i	−0.0675878	−	0.0518620i	0.574415	−	0.818564i	$-0.305230\pi$
$677$	−1.75858	−	1.34941i	−0.0675878	−	0.0518620i	−0.642003	+	0.766702i	$0.721896\pi$
$678$	−16.5037	−	2.75995i	−0.633821	−	0.105995i
$679$	−41.8091	+	14.9707i	−1.60449	+	0.574524i
$680$	−10.6177	−	5.76052i	−0.407172	−	0.220906i
$681$	−1.50595	+	5.62027i	−0.0577080	+	0.215369i
$682$	−5.94271	+	0.572864i	−0.227558	+	0.0219361i
$683$	−12.2513	−	1.61292i	−0.468784	−	0.0617166i	−0.107566	−	0.994198i	$-0.534306\pi$
$683$	−12.2513	−	1.61292i	−0.468784	−	0.0617166i	−0.361218	+	0.932481i	$0.617639\pi$
$684$	−2.07964	+	10.2331i	−0.0795172	+	0.391270i
$685$	1.27497	+	0.528109i	0.0487140	+	0.0201780i
$686$	25.6088	−	5.49448i	0.977749	−	0.209780i
$687$			1.08553i			0.0414154i
$688$	0.214089	+	0.826352i	0.00816205	+	0.0315044i
$689$	28.1441	+	16.2490i	1.07221	+	0.619038i
$690$	−2.56668	−	4.82597i	−0.0977119	−	0.183722i
$691$	−6.20663	−	47.1440i	−0.236111	−	1.79344i	−0.540965	−	0.841045i	$-0.681941\pi$
$691$	−6.20663	−	47.1440i	−0.236111	−	1.79344i	0.304854	−	0.952399i	$-0.401392\pi$
$692$	−31.6294	+	1.94137i	−1.20237	+	0.0737997i
$693$	−0.921770	+	18.8544i	−0.0350152	+	0.716219i
$694$	5.54158	−	3.95367i	0.210356	−	0.150079i
$695$	3.65060	−	13.6242i	0.138475	−	0.516797i
$696$	−15.1257	+	20.8329i	−0.573340	+	0.789671i
$697$	7.65393	+	28.5648i	0.289913	+	1.08197i
$698$	−40.3618	+	15.0956i	−1.52772	+	0.571378i
$699$	−5.88826	+	2.43900i	−0.222714	+	0.0922513i
$700$	18.4370	−	10.9530i	0.696854	−	0.413983i
$701$	12.7621	−	30.8104i	0.482017	−	1.16369i	−0.476633	−	0.879102i	$-0.658143\pi$
$701$	12.7621	−	30.8104i	0.482017	−	1.16369i	0.958650	−	0.284589i	$-0.0918571\pi$
$702$	−22.8243	−	24.4708i	−0.861448	−	0.923591i
$703$	4.94691	−	8.56829i	0.186576	−	0.323159i
$704$	−8.76018	+	24.7888i	−0.330162	+	0.934264i
$705$	−2.70019	−	4.67686i	−0.101695	−	0.176141i
$706$	8.66638	−	2.00177i	0.326164	−	0.0753378i
$707$	3.29727	+	15.2491i	0.124007	+	0.573500i
$708$	−11.2961	−	23.1478i	−0.424533	−	0.869946i
$709$	34.1862	+	26.2320i	1.28389	+	0.985162i	0.999651	+	0.0264078i	$0.00840684\pi$
$709$	34.1862	+	26.2320i	1.28389	+	0.985162i	0.284237	+	0.958754i	$0.408260\pi$
$710$	10.3193	+	8.50469i	0.387276	+	0.319176i
$711$	4.00296	+	14.9393i	0.150123	+	0.560266i
$712$	−21.3081	+	9.49520i	−0.798553	+	0.355848i
$713$	3.96181	+	3.96181i	0.148371	+	0.148371i
$714$	−5.06205	+	14.0660i	−0.189443	+	0.526406i
$715$	6.15169	+	14.8515i	0.230060	+	0.555414i
$716$	16.4264	+	24.8059i	0.613882	+	0.927041i
$717$	−10.1840	+	7.81444i	−0.380327	+	0.291835i
$718$	9.95292	+	18.7139i	0.371440	+	0.698395i
$719$	1.01514	−	0.586090i	0.0378583	−	0.0218575i	−0.480951	−	0.876747i	$-0.659709\pi$
$719$	1.01514	−	0.586090i	0.0378583	−	0.0218575i	0.518810	+	0.854890i	$0.326375\pi$
$720$	−7.35441	+	4.16511i	−0.274083	+	0.155224i
$721$	−5.68842	+	0.467784i	−0.211848	+	0.0174212i
$722$	15.8517	+	9.90287i	0.589939	+	0.368547i
$723$	−1.34990	−	10.2535i	−0.0502033	−	0.381332i
$724$	−13.2955	+	4.45179i	−0.494123	+	0.165449i
$725$	−40.1688	−	5.28832i	−1.49183	−	0.196403i
$726$	0.106549	−	0.233867i	0.00395440	−	0.00867961i
$727$	−15.4155	−	15.4155i	−0.571727	−	0.571727i	0.360883	−	0.932611i	$-0.382475\pi$
$727$	−15.4155	−	15.4155i	−0.571727	−	0.571727i	−0.932611	+	0.360883i	$0.882475\pi$
$728$	30.3415	−	22.2226i	1.12453	−	0.823623i
$729$	5.67579	−	5.67579i	0.210214	−	0.210214i
$730$	4.72622	+	12.6367i	0.174925	+	0.467705i
$731$	0.122233	−	0.928448i	0.00452093	−	0.0343399i
$732$	10.8768	−	9.45921i	0.402020	−	0.349622i
$733$	−36.6402	+	4.82377i	−1.35334	+	0.178170i	−0.772067	−	0.635541i	$-0.780777\pi$
$733$	−36.6402	+	4.82377i	−1.35334	+	0.178170i	−0.581269	+	0.813712i	$0.697444\pi$
$734$	4.96707	+	21.5042i	0.183338	+	0.793734i
$735$	3.93747	+	4.79318i	0.145236	+	0.176799i
$736$	23.1807	−	8.45120i	0.854451	−	0.311515i
$737$	−12.3952	−	21.4691i	−0.456583	−	0.790824i
$738$	19.7878	+	6.04742i	0.728400	+	0.222609i
$739$	19.9418	+	25.9887i	0.733571	+	0.956009i	0.999969	−	0.00785441i	$-0.00250016\pi$
$739$	19.9418	+	25.9887i	0.733571	+	0.956009i	−0.266398	+	0.963863i	$0.585833\pi$
$740$	7.86060	−	1.52970i	0.288961	−	0.0562329i
$741$	10.1670	−	4.21129i	0.373492	−	0.154706i
$742$	−19.8693	−	13.8058i	−0.729424	−	0.506825i
$743$	1.07158	−	1.07158i	0.0393126	−	0.0393126i	−0.687177	−	0.726490i	$-0.741150\pi$
$743$	1.07158	−	1.07158i	0.0393126	−	0.0393126i	0.726490	+	0.687177i	$0.241150\pi$
$744$	−2.27637	+	2.40034i	−0.0834556	+	0.0880008i
$745$	−7.21535	+	1.93335i	−0.264350	+	0.0708323i
$746$	22.4120	−	2.16046i	0.820562	−	0.0791002i
$747$	6.18484	−	8.06023i	0.226291	−	0.294909i
$748$	19.1067	−	21.6056i	0.698611	−	0.789979i
$749$	−3.99865	+	12.4551i	−0.146107	+	0.455101i
$750$	9.62175	+	6.01090i	0.351337	+	0.219487i
$751$	−1.92961	+	1.11406i	−0.0704124	+	0.0406526i	−0.534793	−	0.844983i	$-0.679610\pi$
$751$	−1.92961	+	1.11406i	−0.0704124	+	0.0406526i	0.464380	+	0.885636i	$0.346277\pi$
$752$	22.5977	−	9.14139i	0.824054	−	0.333352i
$753$	2.68224	+	1.54859i	0.0977464	+	0.0564339i
$754$	−71.0106	−	2.47209i	−2.58605	−	0.0900284i
$755$	−13.5244	−	5.60200i	−0.492204	−	0.203878i
$756$	15.4111	+	19.5746i	0.560496	+	0.711920i
$757$	−0.781145	−	1.88585i	−0.0283912	−	0.0685424i	0.909048	−	0.416691i	$-0.136810\pi$
$757$	−0.781145	−	1.88585i	−0.0283912	−	0.0685424i	−0.937439	+	0.348149i	$0.886810\pi$
$758$	24.2149	+	11.0322i	0.879525	+	0.400708i
$759$	12.6063	−	3.37786i	0.457581	−	0.122608i
$760$	−1.03776	−	6.53852i	−0.0376436	−	0.237177i
$761$	−16.9724	−	4.54773i	−0.615248	−	0.164855i	−0.0622814	−	0.998059i	$-0.519838\pi$
$761$	−16.9724	−	4.54773i	−0.615248	−	0.164855i	−0.552967	+	0.833203i	$0.686504\pi$
$762$	3.20688	−	19.1762i	0.116173	−	0.694682i
$763$	7.74451	−	12.0176i	0.280370	−	0.435068i
$764$	18.7193	−	9.13502i	0.677242	−	0.330493i
$765$	9.19269	−	1.21024i	0.332363	−	0.0437564i
$766$	−0.825237	+	2.70027i	−0.0298170	+	0.0975646i
$767$	35.5434	−	61.5630i	1.28340	−	2.22291i
$768$	5.35079	+	13.5496i	0.193080	+	0.488927i
$769$	49.4314			1.78254			0.891271	−	0.453471i	$-0.149814\pi$
$769$	49.4314			1.78254			0.891271	+	0.453471i	$0.149814\pi$
$770$	−3.64009	−	11.4009i	−0.131180	−	0.410861i
$771$	−1.72582	+	4.16649i	−0.0621537	+	0.150052i
$772$	7.78584	+	5.24918i	0.280219	+	0.188922i
$773$	−0.963800	+	7.32079i	−0.0346655	+	0.263310i	0.965332	+	0.261025i	$0.0840606\pi$
$773$	−0.963800	+	7.32079i	−0.0346655	+	0.263310i	−0.999997	+	0.00228493i	$0.999273\pi$
$774$	−0.505631	−	0.416718i	−0.0181745	−	0.0149786i
$775$	−5.02864	−	1.34742i	−0.180634	−	0.0484008i
$776$	36.8852	−	29.8888i	1.32410	−	1.07294i
$777$	−3.34089	−	9.33017i	−0.119854	−	0.334718i
$778$	27.0888	−	19.3267i	0.971181	−	0.692894i
$779$	−9.86642	+	12.8582i	−0.353501	+	0.460692i
$780$	7.97217	+	3.97264i	0.285450	+	0.142243i
$781$	−25.3304	+	19.4367i	−0.906392	+	0.695499i
$782$	−27.0508	−	0.941720i	−0.967333	−	0.0336758i
$783$		−	47.0675i		−	1.68206i
$784$	−23.8926	+	14.5995i	−0.853306	+	0.521410i
$785$			9.99302i			0.356666i
$786$	0.499515	−	14.3485i	0.0178171	−	0.511794i
$787$	−34.1030	+	26.1682i	−1.21564	+	0.932794i	−0.999055	−	0.0434693i	$-0.986159\pi$
$787$	−34.1030	+	26.1682i	−1.21564	+	0.932794i	−0.216586	+	0.976263i	$0.569492\pi$
$788$	2.70511	+	8.07893i	0.0963654	+	0.287800i
$789$	−16.4738	+	21.4691i	−0.586483	+	0.764319i
$790$	−5.69499	−	7.98226i	−0.202619	−	0.283996i
$791$	11.5906	+	32.3694i	0.412115	+	1.15092i
$792$	−5.73775	−	19.3474i	−0.203882	−	0.687480i
$793$	38.4276	+	10.2966i	1.36460	+	0.365644i
$794$	25.5515	−	31.0032i	0.906789	−	1.10026i
$795$	0.747936	−	5.68114i	0.0265266	−	0.201489i
$796$	48.1858	−	9.37713i	1.70790	−	0.332363i
$797$	−9.53022	+	23.0080i	−0.337578	+	0.814985i	0.660369	+	0.750941i	$0.270400\pi$
$797$	−9.53022	+	23.0080i	−0.337578	+	0.814985i	−0.997947	+	0.0640439i	$0.979600\pi$
$798$	−7.80479	+	2.49192i	−0.276286	+	0.0882129i
$799$	−26.7419			−0.946059
$800$	−14.7269	+	17.5701i	−0.520676	+	0.621196i
$801$	8.95289	−	15.5069i	0.316335	−	0.547908i
$802$	−18.0819	−	5.52607i	−0.638494	−	0.195132i
$803$	−31.9376	+	4.20466i	−1.12705	+	0.148379i
$804$	−12.9888	−	4.46928i	−0.458080	−	0.157619i
$805$	−6.08397	+	9.44087i	−0.214432	+	0.332747i
$806$	−9.00499	−	1.50592i	−0.317187	−	0.0530439i
$807$	12.1099	+	3.24483i	0.426288	+	0.114223i
$808$	−8.71918	−	14.2181i	−0.306740	−	0.500191i
$809$	31.7577	−	8.50944i	1.11654	−	0.299176i	0.347057	−	0.937844i	$-0.387181\pi$
$809$	31.7577	−	8.50944i	1.11654	−	0.299176i	0.769482	+	0.638668i	$0.220514\pi$
$810$	1.27046	−	2.78857i	0.0446395	−	0.0979804i
$811$	−5.24775	−	12.6692i	−0.184274	−	0.444876i	0.804565	−	0.593864i	$-0.202398\pi$
$811$	−5.24775	−	12.6692i	−0.184274	−	0.444876i	−0.988839	+	0.148988i	$0.952398\pi$
$812$	52.5287	+	6.25118i	1.84340	+	0.219374i
$813$	3.87672	+	1.60579i	0.135962	+	0.0563174i
$814$	−0.665237	+	19.1088i	−0.0233165	+	0.669764i
$815$	5.37459	+	3.10302i	0.188264	+	0.108694i
$816$	0.132584	−	15.9807i	0.00464136	−	0.559438i
$817$	0.444472	−	0.256616i	0.0155501	−	0.00897785i
$818$	26.2694	−	42.0498i	0.918487	−	1.47024i
$819$	−8.82416	+	27.4858i	−0.308341	+	0.960433i
$820$	−13.0936	+	0.803668i	−0.457249	+	0.0280653i
$821$	27.4974	−	35.8353i	0.959666	−	1.25066i	−0.00839939	−	0.999965i	$-0.502674\pi$
$821$	27.4974	−	35.8353i	0.959666	−	1.25066i	0.968066	−	0.250697i	$-0.0806597\pi$
$822$	0.175185	+	1.81731i	0.00611027	+	0.0633861i
$823$	7.36430	−	1.97326i	0.256703	−	0.0687835i	−0.128172	−	0.991752i	$-0.540911\pi$
$823$	7.36430	−	1.97326i	0.256703	−	0.0687835i	0.384876	+	0.922968i	$0.374244\pi$
$824$	5.57339	−	2.48359i	0.194158	−	0.0865198i
$825$	−8.57488	+	8.57488i	−0.298539	+	0.298539i
$826$	−30.1990	+	43.4625i	−1.05076	+	1.51225i
$827$	36.9855	−	15.3199i	1.28611	−	0.532725i	0.368287	−	0.929712i	$-0.379944\pi$
$827$	36.9855	−	15.3199i	1.28611	−	0.532725i	0.917824	+	0.396987i	$0.129944\pi$
$828$	−10.5868	+	15.7029i	−0.367917	+	0.545713i
$829$	5.12585	+	6.68013i	0.178028	+	0.232011i	0.873840	−	0.486213i	$-0.161622\pi$
$829$	5.12585	+	6.68013i	0.178028	+	0.232011i	−0.695812	+	0.718224i	$0.744955\pi$
$830$	−1.88257	+	6.15999i	−0.0653450	+	0.213816i
$831$	8.84558	+	15.3210i	0.306850	+	0.531479i
$832$	−22.7515	+	33.1494i	−0.788765	+	1.14925i
$833$	30.3041	−	5.01801i	1.04997	−	0.173864i
$834$	18.1818	−	4.19965i	0.629583	−	0.145422i
$835$	17.4612	−	2.29881i	0.604270	−	0.0795537i
$836$	15.7688	+	1.09925i	0.545376	+	0.0380185i
$837$	0.789416	−	5.99621i	0.0272862	−	0.207259i
$838$	−5.38961	+	2.01576i	−0.186181	+	0.0696331i
$839$	−40.5214	+	40.5214i	−1.39896	+	1.39896i	−0.595887	+	0.803068i	$0.703199\pi$
$839$	−40.5214	+	40.5214i	−1.39896	+	1.39896i	−0.803068	+	0.595887i	$0.796801\pi$
$840$	−5.66741	−	3.44319i	−0.195544	−	0.118801i
$841$	−50.1628	−	50.1628i	−1.72975	−	1.72975i
$842$	12.7847	+	5.82468i	0.440592	+	0.200732i
$843$	15.6665	+	2.06254i	0.539585	+	0.0710377i
$844$	−3.77053	+	7.56658i	−0.129787	+	0.260453i
$845$	1.55723	+	11.8283i	0.0535703	+	0.406907i
$846$	−9.91348	+	15.8687i	−0.340833	+	0.545577i
$847$	−0.526284	+	0.0432786i	−0.0180833	+	0.00148707i
$848$	24.9276	+	6.90147i	0.856016	+	0.236997i
$849$	12.3104	−	7.10743i	0.422493	−	0.243926i
$850$	22.2050	−	11.8097i	0.761625	−	0.405069i
$851$	14.2357	−	10.9234i	0.487994	−	0.374451i
$852$	−3.52334	+	17.3369i	−0.120708	+	0.593952i
$853$	−4.42841	−	10.6911i	−0.151626	−	0.366058i	0.829755	−	0.558127i	$-0.188480\pi$
$853$	−4.42841	−	10.6911i	−0.151626	−	0.366058i	−0.981381	+	0.192070i	$0.938480\pi$
$854$	−27.8688	−	10.0294i	−0.953651	−	0.343199i
$855$	3.59322	+	3.59322i	0.122885	+	0.122885i
$856$	−0.370583	−	13.9796i	−0.0126663	−	0.477812i
$857$	−4.19142	−	15.6426i	−0.143176	−	0.534340i	−0.999830	−	0.0184485i	$-0.994127\pi$
$857$	−4.19142	−	15.6426i	−0.143176	−	0.534340i	0.856654	−	0.515892i	$-0.172539\pi$
$858$	−13.5258	+	16.4117i	−0.461763	+	0.560286i
$859$	1.51268	+	1.16072i	0.0516119	+	0.0396032i	0.634245	−	0.773132i	$-0.281311\pi$
$859$	1.51268	+	1.16072i	0.0516119	+	0.0396032i	−0.582633	+	0.812735i	$0.697978\pi$
$860$	0.392807	+	0.135160i	0.0133946	+	0.00460891i
$861$	3.43102	+	15.8676i	0.116929	+	0.540767i
$862$	−7.22618	−	31.2847i	−0.246125	−	1.06556i
$863$	−23.6121	−	40.8974i	−0.803765	−	1.39216i	−0.917122	−	0.398608i	$-0.869494\pi$
$863$	−23.6121	−	40.8974i	−0.803765	−	1.39216i	0.113356	−	0.993554i	$-0.463840\pi$
$864$	−22.4700	−	14.2980i	−0.764445	−	0.486427i
$865$	−7.71049	+	13.3550i	−0.262165	+	0.454082i
$866$	8.38952	−	7.82504i	0.285088	−	0.265906i
$867$	−0.785877	+	1.89728i	−0.0266898	+	0.0644349i
$868$	6.58710	+	1.67739i	0.223581	+	0.0569342i
$869$	21.6301	−	8.95949i	0.733751	−	0.303930i
$870$	4.38881	+	11.7345i	0.148794	+	0.397838i
$871$	−9.81202	−	36.6190i	−0.332468	−	1.24079i
$872$	−3.56319	+	14.8629i	−0.120665	+	0.503320i
$873$	−9.43140	+	35.1985i	−0.319205	+	1.19129i
$874$	−8.61562	−	12.0759i	−0.291428	−	0.408473i
$875$	1.13830	−	23.2834i	0.0384815	−	0.787121i
$876$	−11.8243	+	13.3708i	−0.399507	+	0.451757i
$877$	2.95235	+	22.4253i	0.0996939	+	0.757250i	0.966147	+	0.257992i	$0.0830608\pi$
$877$	2.95235	+	22.4253i	0.0996939	+	0.757250i	−0.866453	+	0.499258i	$0.833606\pi$
$878$	−51.7430	+	27.5194i	−1.74624	+	0.928734i
$879$	−3.16435	−	1.82694i	−0.106731	−	0.0616211i
$880$	7.70417	+	10.2146i	0.259708	+	0.344335i
$881$			41.1844i			1.38754i	0.720198	+	0.693768i	$0.244051\pi$
$881$			41.1844i			1.38754i	−0.720198	+	0.693768i	$0.755949\pi$
$882$	8.25634	−	19.8428i	0.278005	−	0.668140i
$883$	−7.40154	−	3.06582i	−0.249082	−	0.103173i	0.254650	−	0.967033i	$-0.418040\pi$
$883$	−7.40154	−	3.06582i	−0.249082	−	0.103173i	−0.503731	+	0.863860i	$0.668040\pi$
$884$	36.7749	−	24.3522i	1.23687	−	0.819052i
$885$	−12.4271	−	1.63605i	−0.417731	−	0.0549953i
$886$	−3.14907	−	32.6675i	−0.105795	−	1.09749i
$887$	−5.96242	+	22.2521i	−0.200199	+	0.747151i	0.790661	+	0.612254i	$0.209737\pi$
$887$	−5.96242	+	22.2521i	−0.200199	+	0.747151i	−0.990860	+	0.134897i	$0.956930\pi$
$888$	6.67001	+	8.23134i	0.223831	+	0.276226i
$889$	−37.6111	+	13.4675i	−1.26144	+	0.451687i
$890$	−1.87245	+	11.1967i	−0.0627648	+	0.375316i
$891$	5.80462	+	4.45404i	0.194462	+	0.149216i
$892$	−1.78328	+	25.5812i	−0.0597086	+	0.856522i
$893$	−8.92202	−	11.6274i	−0.298564	−	0.389096i
$894$	−6.74064	−	7.22690i	−0.225441	−	0.241704i
$895$	14.4782			0.483954
$896$	18.9413	−	23.1782i	0.632783	−	0.774329i
$897$	19.9583			0.666389
$898$	−28.3173	−	30.3600i	−0.944961	−	1.01313i
$899$	−7.81766	−	10.1882i	−0.260734	−	0.339795i
$900$	1.22373	−	17.5545i	0.0407911	−	0.585149i
$901$	−22.5113	−	17.2736i	−0.749961	−	0.575466i
$902$	5.16626	−	30.8927i	0.172018	−	1.02862i
$903$	0.0919099	−	0.505803i	0.00305857	−	0.0168321i
$904$	−23.1404	−	28.5572i	−0.769639	−	0.949799i
$905$	−1.76596	+	6.59064i	−0.0587024	+	0.219080i
$906$	−1.85830	−	19.2774i	−0.0617379	−	0.640450i
$907$	12.6626	+	1.66707i	0.420456	+	0.0553541i	0.337786	−	0.941223i	$-0.390322\pi$
$907$	12.6626	+	1.66707i	0.420456	+	0.0553541i	0.0826701	+	0.996577i	$0.473655\pi$
$908$	−10.6565	+	7.05667i	−0.353648	+	0.234184i
$909$	11.8275	+	4.89912i	0.392294	+	0.162494i
$910$	−0.864461	−	18.2816i	−0.0286566	−	0.606028i
$911$		−	17.3910i		−	0.576188i	−0.957602	−	0.288094i	$-0.906978\pi$
$911$		−	17.3910i		−	0.576188i	0.957602	−	0.288094i	$-0.0930216\pi$
$912$	6.99268	−	5.27408i	0.231551	−	0.174642i
$913$	−13.3189	−	7.68970i	−0.440793	−	0.254492i
$914$	37.6121	−	20.0039i	1.24410	−	0.661670i
$915$	−0.915602	−	6.95469i	−0.0302689	−	0.229915i
$916$	−1.57963	+	1.78622i	−0.0521924	+	0.0590183i
$917$	−26.2379	+	13.4851i	−0.866453	+	0.445317i
$918$	16.9692	+	23.7845i	0.560068	+	0.785007i
$919$	12.5385	−	46.7944i	0.413608	−	1.54361i	−0.374000	−	0.927429i	$-0.622014\pi$
$919$	12.5385	−	46.7944i	0.413608	−	1.54361i	0.787608	−	0.616177i	$-0.211319\pi$
$920$	2.79918	−	11.6760i	0.0922863	−	0.384948i
$921$	5.89602	+	22.0042i	0.194280	+	0.725064i
$922$	−9.47544	−	25.3349i	−0.312057	−	0.834361i
$923$	−45.1097	+	18.6850i	−1.48480	+	0.615025i
$924$	11.0556	−	11.3344i	0.363703	−	0.372875i
$925$	−6.38044	+	15.4037i	−0.209787	+	0.506472i
$926$	30.7198	−	28.6529i	1.00952	−	0.941591i
$927$	−2.34174	+	4.05601i	−0.0769128	+	0.133217i
$928$	−55.2047	+	12.2698i	−1.81218	+	0.402774i
$929$	6.11431	+	10.5903i	0.200604	+	0.347456i	0.948723	−	0.316108i	$-0.102376\pi$
$929$	6.11431	+	10.5903i	0.200604	+	0.347456i	−0.748119	+	0.663564i	$0.769043\pi$
$930$	0.362304	+	1.56854i	0.0118804	+	0.0514345i
$931$	12.2923	+	11.5021i	0.402865	+	0.376965i
$932$	−13.2382	−	4.55510i	−0.433632	−	0.149207i
$933$	−8.48798	−	6.51306i	−0.277884	−	0.213228i
$934$	23.7545	−	28.8228i	0.777270	−	0.943111i
$935$	−3.63269	−	13.5574i	−0.118802	−	0.443374i
$936$	−0.817798	−	30.8499i	−0.0267306	−	1.00836i
$937$	24.2539	+	24.2539i	0.792340	+	0.792340i	0.981874	−	0.189534i	$-0.0606977\pi$
$937$	24.2539	+	24.2539i	0.792340	+	0.792340i	−0.189534	+	0.981874i	$0.560698\pi$
$938$	5.00166	+	27.7778i	0.163310	+	0.906979i
$939$	10.3742	+	25.0456i	0.338550	+	0.817333i
$940$	2.36252	−	11.6250i	0.0770569	−	0.379164i
$941$	18.9461	−	14.5378i	0.617625	−	0.473920i	−0.251938	−	0.967743i	$-0.581068\pi$
$941$	18.9461	−	14.5378i	0.617625	−	0.473920i	0.869562	+	0.493823i	$0.164401\pi$
$942$	−11.6724	+	6.20795i	−0.380308	+	0.202266i
$943$	−25.4561	+	14.6971i	−0.828964	+	0.478603i
$944$	15.0964	−	54.5271i	0.491347	−	1.77471i
$945$	12.0829	−	0.993628i	0.393056	−	0.0323227i
$946$	−0.525511	+	0.841195i	−0.0170858	+	0.0273496i
$947$	−3.37621	−	25.6449i	−0.109712	−	0.833347i	−0.954493	−	0.298234i	$-0.903602\pi$
$947$	−3.37621	−	25.6449i	−0.109712	−	0.833347i	0.844781	−	0.535113i	$-0.179731\pi$
$948$	5.78586	−	11.6109i	0.187916	−	0.377104i
$949$	−48.8407	−	6.42999i	−1.58543	−	0.208726i
$950$	12.5432	+	5.71465i	0.406956	+	0.185408i
$951$	12.4604	+	12.4604i	0.404055	+	0.404055i
$952$	−28.7980	+	15.7792i	−0.933348	+	0.511408i
$953$	−38.2377	+	38.2377i	−1.23864	+	1.23864i	−0.278082	+	0.960557i	$0.589699\pi$
$953$	−38.2377	+	38.2377i	−1.23864	+	1.23864i	−0.960557	+	0.278082i	$0.910301\pi$
$954$	−18.5954	+	6.95480i	−0.602047	+	0.225170i
$955$	1.32306	−	10.0496i	0.0428131	−	0.325198i
$956$	−28.1289	−	1.96088i	−0.909755	−	0.0634195i
$957$	−29.6575	+	3.90449i	−0.958692	+	0.126214i
$958$	−7.99432	+	1.84654i	−0.258285	+	0.0596590i
$959$	3.08418	−	2.13568i	0.0995934	−	0.0689646i
$960$	6.93527	+	1.46946i	0.223835	+	0.0474266i
$961$	14.6749	+	25.4177i	0.473385	+	0.819927i
$962$	−8.54592	+	27.9632i	−0.275532	+	0.901570i
$963$	6.53447	+	8.51589i	0.210570	+	0.274421i
$964$	12.6994	−	18.8363i	0.409019	−	0.606677i
$965$	4.22171	−	1.74869i	0.135902	−	0.0562923i
$966$	−14.8070	−	1.24149i	−0.476408	−	0.0399442i
$967$	5.00565	−	5.00565i	0.160971	−	0.160971i	−0.622026	−	0.782997i	$-0.713690\pi$
$967$	5.00565	−	5.00565i	0.160971	−	0.160971i	0.782997	+	0.622026i	$0.213690\pi$
$968$	0.515641	−	0.229778i	0.0165733	−	0.00738533i
$969$	−9.28105	+	2.48685i	−0.298150	+	0.0798891i
$970$	−2.21680	−	22.9964i	−0.0711771	−	0.738370i
$971$	23.1958	−	30.2294i	0.744389	−	0.970107i	−0.255605	−	0.966781i	$-0.582275\pi$
$971$	23.1958	−	30.2294i	0.744389	−	0.970107i	0.999994	−	0.00332566i	$-0.00105859\pi$
$972$	32.2423	−	1.97899i	1.03417	−	0.0634760i
$973$	−25.7561	−	28.4039i	−0.825703	−	0.910589i
$974$	−4.81747	+	7.71142i	−0.154362	+	0.247090i
$975$	−16.0603	+	9.27241i	−0.514341	+	0.296955i
$976$	31.6625	+	0.262687i	1.01349	+	0.00840840i
$977$	16.8022	+	9.70077i	0.537551	+	0.310355i	0.744086	−	0.668084i	$-0.232885\pi$
$977$	16.8022	+	9.70077i	0.537551	+	0.310355i	−0.206535	+	0.978439i	$0.566219\pi$
$978$	−0.285659	+	8.20553i	−0.00913438	+	0.262384i
$979$	−25.0419	−	10.3727i	−0.800342	−	0.331512i
$980$	−0.495847	+	13.6168i	−0.0158393	+	0.434973i
$981$	−4.48946	−	10.8385i	−0.143337	−	0.346047i
$982$	−7.49978	+	16.4615i	−0.239328	+	0.525306i
$983$	7.34689	−	1.96859i	0.234329	−	0.0627884i	−0.139743	−	0.990188i	$-0.544628\pi$
$983$	7.34689	−	1.96859i	0.234329	−	0.0627884i	0.374073	+	0.927399i	$0.377961\pi$
$984$	−9.07286	−	14.7948i	−0.289232	−	0.471642i
$985$	4.00477	+	1.07307i	0.127603	+	0.0341910i
$986$	61.1892	+	10.2328i	1.94866	+	0.325878i
$987$	−14.6629	−	0.716852i	−0.466725	−	0.0228177i
$988$	22.8577	+	7.86505i	0.727201	+	0.250220i
$989$	0.922849	−	0.121495i	0.0293449	−	0.00386333i
$990$	−9.39167	−	2.87022i	−0.298487	−	0.0912215i
$991$	4.63856	−	8.03422i	0.147349	−	0.255215i	−0.782898	−	0.622150i	$-0.786259\pi$
$991$	4.63856	−	8.03422i	0.147349	−	0.255215i	0.930247	+	0.366935i	$0.119593\pi$
$992$	−7.23864	+	0.637223i	−0.229827	+	0.0202318i
$993$	−14.3711			−0.456052
$994$	34.6290	−	11.0564i	1.09837	−	0.350687i
$995$	9.14187	−	22.0704i	0.289817	−	0.699680i
$996$	−8.36473	+	1.62781i	−0.265047	+	0.0515790i
$997$	−5.52736	+	41.9845i	−0.175053	+	1.32966i	0.647975	+	0.761661i	$0.275616\pi$
$997$	−5.52736	+	41.9845i	−0.175053	+	1.32966i	−0.823028	+	0.568000i	$0.807717\pi$
$998$	19.3937	−	23.5316i	0.613896	−	0.744878i
$999$	−18.7092	−	5.01312i	−0.591934	−	0.158608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.24	yes	240
4.3	odd	2		896.2.bh.a.529.12		240
7.2	even	3	inner	224.2.bd.a.205.18	yes	240
28.23	odd	6		896.2.bh.a.401.19		240
32.5	even	8	inner	224.2.bd.a.165.18	yes	240
32.27	odd	8		896.2.bh.a.753.19		240
224.37	even	24	inner	224.2.bd.a.37.24	✓	240
224.219	odd	24		896.2.bh.a.625.12		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.24	✓	240	224.37	even	24	inner
224.2.bd.a.109.24	yes	240	1.1	even	1	trivial
224.2.bd.a.165.18	yes	240	32.5	even	8	inner
224.2.bd.a.205.18	yes	240	7.2	even	3	inner
896.2.bh.a.401.19		240	28.23	odd	6
896.2.bh.a.529.12		240	4.3	odd	2
896.2.bh.a.625.12		240	224.219	odd	24
896.2.bh.a.753.19		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.964603 + 1.03419i) q^{2} +(0.554270 + 0.722339i) q^{3} +(-0.139084 + 1.99516i) q^{4} +(0.772150 + 0.592492i) q^{5} +(-0.212383 + 1.26999i) q^{6} +(2.49088 - 0.891918i) q^{7} +(-2.19753 + 1.78070i) q^{8} +(0.561899 - 2.09704i) q^{9} +O(q^{10})\)	\(q+(0.964603 + 1.03419i) q^{2} +(0.554270 + 0.722339i) q^{3} +(-0.139084 + 1.99516i) q^{4} +(0.772150 + 0.592492i) q^{5} +(-0.212383 + 1.26999i) q^{6} +(2.49088 - 0.891918i) q^{7} +(-2.19753 + 1.78070i) q^{8} +(0.561899 - 2.09704i) q^{9} +(0.132071 + 1.37007i) q^{10} +(-3.25828 - 0.428961i) q^{11} +(-1.51827 + 1.00539i) q^{12} +(-4.64317 - 1.92326i) q^{13} +(3.32512 + 1.71569i) q^{14} +0.886155i q^{15} +(-3.96131 - 0.554988i) q^{16} +(3.80021 + 2.19405i) q^{17} +(2.71073 - 1.44170i) q^{18} +(0.313906 + 2.38435i) q^{19} +(-1.28951 + 1.45816i) q^{20} +(2.02489 + 1.30490i) q^{21} +(-2.69932 - 3.78345i) q^{22} +(-1.12888 + 4.21303i) q^{23} +(-2.50429 - 0.600372i) q^{24} +(-1.04893 - 3.91464i) q^{25} +(-2.48980 - 6.65709i) q^{26} +(4.34976 - 1.80173i) q^{27} +(1.43308 + 5.09375i) q^{28} +(3.82570 - 9.23607i) q^{29} +(-0.916449 + 0.854787i) q^{30} +(0.642286 - 1.11247i) q^{31} +(-3.24713 - 4.63208i) q^{32} +(-1.49611 - 2.59135i) q^{33} +(1.39663 + 6.04652i) q^{34} +(2.45179 + 0.787131i) q^{35} +(4.10577 + 1.41274i) q^{36} +(-3.26384 - 2.50443i) q^{37} +(-2.16307 + 2.62459i) q^{38} +(-1.18432 - 4.41995i) q^{39} +(-2.75187 + 0.0729490i) q^{40} +(4.76536 + 4.76536i) q^{41} +(0.603706 + 3.35282i) q^{42} +(-0.0816679 - 0.197164i) q^{43} +(1.30902 - 6.44113i) q^{44} +(1.67635 - 1.28631i) q^{45} +(-5.44597 + 2.89643i) q^{46} +(-5.27770 + 3.04708i) q^{47} +(-1.79475 - 3.16902i) q^{48} +(5.40896 - 4.44332i) q^{49} +(3.03668 - 4.86086i) q^{50} +(0.521494 + 3.96114i) q^{51} +(4.48301 - 8.99637i) q^{52} +(-6.41100 - 0.844024i) q^{53} +(6.05911 + 2.76051i) q^{54} +(-2.26173 - 2.26173i) q^{55} +(-3.88554 + 6.39551i) q^{56} +(-1.54832 + 1.54832i) q^{57} +(13.2421 - 4.95264i) q^{58} +(-1.84624 + 14.0236i) q^{59} +(-1.76802 - 0.123250i) q^{60} +(-7.84817 + 1.03323i) q^{61} +(1.77005 - 0.408850i) q^{62} +(-0.470761 - 5.72463i) q^{63} +(1.65824 - 7.82625i) q^{64} +(-2.44571 - 4.23609i) q^{65} +(1.23678 - 4.04688i) q^{66} +(4.59209 + 5.98452i) q^{67} +(-4.90603 + 7.27687i) q^{68} +(-3.66894 + 1.51972i) q^{69} +(1.55096 + 3.29487i) q^{70} +(6.86973 - 6.86973i) q^{71} +(2.49940 + 5.60886i) q^{72} +(9.46798 - 2.53694i) q^{73} +(-0.558258 - 5.79120i) q^{74} +(2.24631 - 2.92745i) q^{75} +(-4.80081 + 0.294667i) q^{76} +(-8.49859 + 1.83763i) q^{77} +(3.42866 - 5.48831i) q^{78} +(-6.16956 + 3.56200i) q^{79} +(-2.72990 - 2.77558i) q^{80} +(-1.92805 - 1.11316i) q^{81} +(-0.331593 + 9.52495i) q^{82} +(4.32349 + 1.79085i) q^{83} +(-2.88510 + 3.85848i) q^{84} +(1.63438 + 3.94573i) q^{85} +(0.125127 - 0.274645i) q^{86} +(8.79205 - 2.35582i) q^{87} +(7.92401 - 4.85936i) q^{88} +(7.96664 + 2.13465i) q^{89} +(2.94729 + 0.492881i) q^{90} +(-13.2810 - 0.649292i) q^{91} +(-8.24864 - 2.83825i) q^{92} +(1.15958 - 0.152662i) q^{93} +(-8.24214 - 2.51891i) q^{94} +(-1.17033 + 2.02706i) q^{95} +(1.54614 - 4.91295i) q^{96} -16.7849 q^{97} +(9.81272 + 1.30784i) q^{98} +(-2.73037 + 6.59170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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