LMFDB - Embedded newform 760.2.f.b.381.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [760,2,Mod(381,760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("760.381"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			381.20
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.188358 + 1.40161i) q^{2} +0.0766253i q^{3} +(-1.92904 - 0.528011i) q^{4} +1.00000i q^{5} +(-0.107399 - 0.0144330i) q^{6} +1.59941 q^{7} +(1.10342 - 2.60432i) q^{8} +2.99413 q^{9} +(-1.40161 - 0.188358i) q^{10} +0.418437i q^{11} +(0.0404590 - 0.147813i) q^{12} -6.12600i q^{13} +(-0.301262 + 2.24175i) q^{14} -0.0766253 q^{15} +(3.44241 + 2.03711i) q^{16} +2.23355 q^{17} +(-0.563969 + 4.19661i) q^{18} +1.00000i q^{19} +(0.528011 - 1.92904i) q^{20} +0.122555i q^{21} +(-0.586486 - 0.0788160i) q^{22} +4.81927 q^{23} +(0.199557 + 0.0845498i) q^{24} -1.00000 q^{25} +(8.58629 + 1.15388i) q^{26} +0.459302i q^{27} +(-3.08533 - 0.844506i) q^{28} -4.65242i q^{29} +(0.0144330 - 0.107399i) q^{30} +1.44903 q^{31} +(-3.50365 + 4.44122i) q^{32} -0.0320628 q^{33} +(-0.420708 + 3.13058i) q^{34} +1.59941i q^{35} +(-5.77580 - 1.58093i) q^{36} +10.2780i q^{37} +(-1.40161 - 0.188358i) q^{38} +0.469407 q^{39} +(2.60432 + 1.10342i) q^{40} -0.923621 q^{41} +(-0.171775 - 0.0230843i) q^{42} +4.94739i q^{43} +(0.220939 - 0.807182i) q^{44} +2.99413i q^{45} +(-0.907749 + 6.75475i) q^{46} +9.79140 q^{47} +(-0.156094 + 0.263776i) q^{48} -4.44189 q^{49} +(0.188358 - 1.40161i) q^{50} +0.171147i q^{51} +(-3.23460 + 11.8173i) q^{52} +3.92260i q^{53} +(-0.643764 - 0.0865133i) q^{54} -0.418437 q^{55} +(1.76482 - 4.16537i) q^{56} -0.0766253 q^{57} +(6.52090 + 0.876322i) q^{58} +8.15418i q^{59} +(0.147813 + 0.0404590i) q^{60} -10.8278i q^{61} +(-0.272936 + 2.03098i) q^{62} +4.78884 q^{63} +(-5.56493 - 5.74730i) q^{64} +6.12600 q^{65} +(0.00603930 - 0.0449397i) q^{66} +5.14793i q^{67} +(-4.30862 - 1.17934i) q^{68} +0.369278i q^{69} +(-2.24175 - 0.301262i) q^{70} +4.56590 q^{71} +(3.30378 - 7.79766i) q^{72} +3.75106 q^{73} +(-14.4058 - 1.93595i) q^{74} -0.0766253i q^{75} +(0.528011 - 1.92904i) q^{76} +0.669251i q^{77} +(-0.0884166 + 0.657927i) q^{78} -14.8533 q^{79} +(-2.03711 + 3.44241i) q^{80} +8.94719 q^{81} +(0.173972 - 1.29456i) q^{82} +0.561992i q^{83} +(0.0647105 - 0.236414i) q^{84} +2.23355i q^{85} +(-6.93433 - 0.931881i) q^{86} +0.356493 q^{87} +(1.08974 + 0.461711i) q^{88} -1.07995 q^{89} +(-4.19661 - 0.563969i) q^{90} -9.79799i q^{91} +(-9.29657 - 2.54463i) q^{92} +0.111032i q^{93} +(-1.84429 + 13.7238i) q^{94} -1.00000 q^{95} +(-0.340310 - 0.268468i) q^{96} -6.13874 q^{97} +(0.836667 - 6.22581i) q^{98} +1.25285i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.188358	+	1.40161i	−0.133189	+	0.991091i
$2$	−0.188358	+	1.40161i	−0.133189	+	0.991091i
$3$			0.0766253i			0.0442396i	0.999755	+	0.0221198i	$0.00704153\pi$
$3$			0.0766253i			0.0442396i	−0.999755	+	0.0221198i	$0.992958\pi$
$4$	−1.92904	−	0.528011i	−0.964521	−	0.264006i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.107399	−	0.0144330i	−0.0438455	−	0.00589225i
$7$	1.59941			0.604520			0.302260	−	0.953226i	$-0.402259\pi$
$7$	1.59941			0.604520			0.302260	+	0.953226i	$0.402259\pi$
$8$	1.10342	−	2.60432i	0.390117	−	0.920765i
$9$	2.99413			0.998043
$10$	−1.40161	−	0.188358i	−0.443229	−	0.0595641i
$11$			0.418437i			0.126163i	0.998008	+	0.0630817i	$0.0200929\pi$
$11$			0.418437i			0.126163i	−0.998008	+	0.0630817i	$0.979907\pi$
$12$	0.0404590	−	0.147813i	0.0116795	−	0.0426701i
$13$		−	6.12600i		−	1.69905i	−0.527550	−	0.849524i	$-0.676889\pi$
$13$		−	6.12600i		−	1.69905i	0.527550	−	0.849524i	$-0.323111\pi$
$14$	−0.301262	+	2.24175i	−0.0805156	+	0.599134i
$15$	−0.0766253			−0.0197846
$16$	3.44241	+	2.03711i	0.860602	+	0.509278i
$17$	2.23355			0.541716			0.270858	−	0.962619i	$-0.412693\pi$
$17$	2.23355			0.541716			0.270858	+	0.962619i	$0.412693\pi$
$18$	−0.563969	+	4.19661i	−0.132929	+	0.989151i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	0.528011	−	1.92904i	0.118067	−	0.431347i
$21$			0.122555i			0.0267437i
$22$	−0.586486	−	0.0788160i	−0.125039	−	0.0168036i
$23$	4.81927			1.00489			0.502443	−	0.864610i	$-0.332435\pi$
$23$	4.81927			1.00489			0.502443	+	0.864610i	$0.332435\pi$
$24$	0.199557	+	0.0845498i	0.0407343	+	0.0172586i
$25$	−1.00000			−0.200000
$26$	8.58629	+	1.15388i	1.68391	+	0.226295i
$27$			0.459302i			0.0883927i
$28$	−3.08533	−	0.844506i	−0.583072	−	0.159597i
$29$		−	4.65242i		−	0.863933i	−0.901890	−	0.431966i	$-0.857820\pi$
$29$		−	4.65242i		−	0.863933i	0.901890	−	0.431966i	$-0.142180\pi$
$30$	0.0144330	−	0.107399i	0.00263509	−	0.0196083i
$31$	1.44903			0.260253			0.130126	−	0.991497i	$-0.458462\pi$
$31$	1.44903			0.260253			0.130126	+	0.991497i	$0.458462\pi$
$32$	−3.50365	+	4.44122i	−0.619364	+	0.785104i
$33$	−0.0320628			−0.00558142
$34$	−0.420708	+	3.13058i	−0.0721508	+	0.536890i
$35$			1.59941i			0.270350i
$36$	−5.77580	−	1.58093i	−0.962633	−	0.263489i
$37$			10.2780i			1.68969i	0.535008	+	0.844847i	$0.320309\pi$
$37$			10.2780i			1.68969i	−0.535008	+	0.844847i	$0.679691\pi$
$38$	−1.40161	−	0.188358i	−0.227372	−	0.0305557i
$39$	0.469407			0.0751652
$40$	2.60432	+	1.10342i	0.411779	+	0.174466i
$41$	−0.923621			−0.144245			−0.0721226	−	0.997396i	$-0.522977\pi$
$41$	−0.923621			−0.144245			−0.0721226	+	0.997396i	$0.522977\pi$
$42$	−0.171775	−	0.0230843i	−0.0265055	−	0.00356198i
$43$			4.94739i			0.754470i	0.926118	+	0.377235i	$0.123125\pi$
$43$			4.94739i			0.754470i	−0.926118	+	0.377235i	$0.876875\pi$
$44$	0.220939	−	0.807182i	0.0333078	−	0.121687i
$45$			2.99413i			0.446338i
$46$	−0.907749	+	6.75475i	−0.133840	+	0.995934i
$47$	9.79140			1.42822			0.714111	−	0.700032i	$-0.246831\pi$
$47$	9.79140			1.42822			0.714111	+	0.700032i	$0.246831\pi$
$48$	−0.156094	+	0.263776i	−0.0225303	+	0.0380727i
$49$	−4.44189			−0.634556
$50$	0.188358	−	1.40161i	0.0266379	−	0.198218i
$51$			0.171147i			0.0239653i
$52$	−3.23460	+	11.8173i	−0.448558	+	1.63877i
$53$			3.92260i			0.538811i	0.963027	+	0.269405i	$0.0868271\pi$
$53$			3.92260i			0.538811i	−0.963027	+	0.269405i	$0.913173\pi$
$54$	−0.643764	−	0.0865133i	−0.0876051	−	0.0117730i
$55$	−0.418437			−0.0564220
$56$	1.76482	−	4.16537i	0.235834	−	0.556621i
$57$	−0.0766253			−0.0101493
$58$	6.52090	+	0.876322i	0.856236	+	0.115067i
$59$			8.15418i			1.06158i	0.847502	+	0.530792i	$0.178106\pi$
$59$			8.15418i			1.06158i	−0.847502	+	0.530792i	$0.821894\pi$
$60$	0.147813	+	0.0404590i	0.0190826	+	0.00522323i
$61$		−	10.8278i		−	1.38636i	−0.720767	−	0.693178i	$-0.756210\pi$
$61$		−	10.8278i		−	1.38636i	0.720767	−	0.693178i	$-0.243790\pi$
$62$	−0.272936	+	2.03098i	−0.0346629	+	0.257934i
$63$	4.78884			0.603337
$64$	−5.56493	−	5.74730i	−0.695617	−	0.718413i
$65$	6.12600			0.759837
$66$	0.00603930	−	0.0449397i	0.000743386	−	0.00553169i
$67$			5.14793i			0.628919i	0.949271	+	0.314460i	$0.101823\pi$
$67$			5.14793i			0.628919i	−0.949271	+	0.314460i	$0.898177\pi$
$68$	−4.30862	−	1.17934i	−0.522497	−	0.143016i
$69$			0.369278i			0.0444558i
$70$	−2.24175	−	0.301262i	−0.267941	−	0.0360077i
$71$	4.56590			0.541873			0.270936	−	0.962597i	$-0.412667\pi$
$71$	4.56590			0.541873			0.270936	+	0.962597i	$0.412667\pi$
$72$	3.30378	−	7.79766i	0.389354	−	0.918963i
$73$	3.75106			0.439028			0.219514	−	0.975609i	$-0.429553\pi$
$73$	3.75106			0.439028			0.219514	+	0.975609i	$0.429553\pi$
$74$	−14.4058	−	1.93595i	−1.67464	−	0.225049i
$75$		−	0.0766253i		−	0.00884793i
$76$	0.528011	−	1.92904i	0.0605670	−	0.221276i
$77$			0.669251i			0.0762683i
$78$	−0.0884166	+	0.657927i	−0.0100112	+	0.0744956i
$79$	−14.8533			−1.67113			−0.835565	−	0.549392i	$-0.814859\pi$
$79$	−14.8533			−1.67113			−0.835565	+	0.549392i	$0.814859\pi$
$80$	−2.03711	+	3.44241i	−0.227756	+	0.384873i
$81$	8.94719			0.994132
$82$	0.173972	−	1.29456i	0.0192119	−	0.142960i
$83$			0.561992i			0.0616866i	0.999524	+	0.0308433i	$0.00981928\pi$
$83$			0.561992i			0.0616866i	−0.999524	+	0.0308433i	$0.990181\pi$
$84$	0.0647105	−	0.236414i	0.00706049	−	0.0257949i
$85$			2.23355i			0.242263i
$86$	−6.93433	−	0.931881i	−0.747748	−	0.100487i
$87$	0.356493			0.0382201
$88$	1.08974	+	0.461711i	0.116167	+	0.0492185i
$89$	−1.07995			−0.114475			−0.0572374	−	0.998361i	$-0.518229\pi$
$89$	−1.07995			−0.114475			−0.0572374	+	0.998361i	$0.518229\pi$
$90$	−4.19661	−	0.563969i	−0.442362	−	0.0594475i
$91$		−	9.79799i		−	1.02711i
$92$	−9.29657	−	2.54463i	−0.969234	−	0.265296i
$93$			0.111032i			0.0115135i
$94$	−1.84429	+	13.7238i	−0.190224	+	1.41550i
$95$	−1.00000			−0.102598
$96$	−0.340310	−	0.268468i	−0.0347327	−	0.0274004i
$97$	−6.13874			−0.623295			−0.311647	−	0.950198i	$-0.600881\pi$
$97$	−6.13874			−0.623295			−0.311647	+	0.950198i	$0.600881\pi$
$98$	0.836667	−	6.22581i	0.0845161	−	0.628902i
$99$			1.25285i			0.125916i
$100$	1.92904	+	0.528011i	0.192904	+	0.0528011i
$101$		−	17.8006i		−	1.77122i	−0.464428	−	0.885611i	$-0.653740\pi$
$101$		−	17.8006i		−	1.77122i	0.464428	−	0.885611i	$-0.346260\pi$
$102$	−0.239881	−	0.0322369i	−0.0237518	−	0.00319193i
$103$	13.9742			1.37692			0.688460	−	0.725274i	$-0.258287\pi$
$103$	13.9742			1.37692			0.688460	+	0.725274i	$0.258287\pi$
$104$	−15.9541	−	6.75955i	−1.56442	−	0.662828i
$105$	−0.122555			−0.0119602
$106$	−5.49797	−	0.738854i	−0.534010	−	0.0717638i
$107$			0.472105i			0.0456401i	0.999740	+	0.0228200i	$0.00726448\pi$
$107$			0.472105i			0.0456401i	−0.999740	+	0.0228200i	$0.992736\pi$
$108$	0.242516	−	0.886013i	0.0233362	−	0.0852566i
$109$		−	18.4823i		−	1.77029i	−0.465319	−	0.885143i	$-0.654060\pi$
$109$		−	18.4823i		−	1.77029i	0.465319	−	0.885143i	$-0.345940\pi$
$110$	0.0788160	−	0.586486i	0.00751481	−	0.0559193i
$111$	−0.787555			−0.0747514
$112$	5.50582	+	3.25818i	0.520251	+	0.307869i
$113$	−6.50295			−0.611746			−0.305873	−	0.952072i	$-0.598948\pi$
$113$	−6.50295			−0.611746			−0.305873	+	0.952072i	$0.598948\pi$
$114$	0.0144330	−	0.107399i	0.00135177	−	0.0100588i
$115$			4.81927i			0.449399i
$116$	−2.45653	+	8.97472i	−0.228083	+	0.833281i
$117$		−	18.3420i		−	1.69572i
$118$	−11.4290	−	1.53591i	−1.05213	−	0.141392i
$119$	3.57236			0.327478
$120$	−0.0845498	+	0.199557i	−0.00771830	+	0.0182169i
$121$	10.8249			0.984083
$122$	15.1764	+	2.03950i	1.37400	+	0.184648i
$123$		−	0.0707727i		−	0.00638136i
$124$	−2.79523	−	0.765102i	−0.251019	−	0.0687082i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.902017	+	6.71210i	−0.0803581	+	0.597961i
$127$	−19.0423			−1.68973			−0.844866	−	0.534978i	$-0.820320\pi$
$127$	−19.0423			−1.68973			−0.844866	+	0.534978i	$0.820320\pi$
$128$	9.10370	−	6.71734i	0.804661	−	0.593734i
$129$	−0.379095			−0.0333775
$130$	−1.15388	+	8.58629i	−0.101202	+	0.753068i
$131$			7.21435i			0.630320i	0.949038	+	0.315160i	$0.102058\pi$
$131$			7.21435i			0.630320i	−0.949038	+	0.315160i	$0.897942\pi$
$132$	0.0618505	+	0.0169295i	0.00538340	+	0.00147353i
$133$			1.59941i			0.138686i
$134$	−7.21540	−	0.969654i	−0.623316	−	0.0837654i
$135$	−0.459302			−0.0395304
$136$	2.46454	−	5.81688i	0.211333	−	0.498793i
$137$	4.67144			0.399108			0.199554	−	0.979887i	$-0.436051\pi$
$137$	4.67144			0.399108			0.199554	+	0.979887i	$0.436051\pi$
$138$	−0.517585	−	0.0695565i	−0.0440597	−	0.00592104i
$139$			8.80887i			0.747158i	0.927598	+	0.373579i	$0.121870\pi$
$139$			8.80887i			0.747158i	−0.927598	+	0.373579i	$0.878130\pi$
$140$	0.844506	−	3.08533i	0.0713738	−	0.260758i
$141$			0.750269i			0.0631840i
$142$	−0.860025	+	6.39963i	−0.0721717	+	0.537045i
$143$	2.56334			0.214358
$144$	10.3070	+	6.09937i	0.858918	+	0.508281i
$145$	4.65242			0.386362
$146$	−0.706543	+	5.25754i	−0.0584739	+	0.435117i
$147$		−	0.340361i		−	0.0280725i
$148$	5.42690	−	19.8267i	0.446089	−	1.62975i
$149$			2.14796i			0.175967i	0.996122	+	0.0879837i	$0.0280424\pi$
$149$			2.14796i			0.175967i	−0.996122	+	0.0879837i	$0.971958\pi$
$150$	0.107399	+	0.0144330i	0.00876910	+	0.00117845i
$151$	−17.2514			−1.40390			−0.701950	−	0.712226i	$-0.747687\pi$
$151$	−17.2514			−1.40390			−0.701950	+	0.712226i	$0.747687\pi$
$152$	2.60432	+	1.10342i	0.211238	+	0.0894991i
$153$	6.68754			0.540656
$154$	−0.938032	−	0.126059i	−0.0755888	−	0.0101581i
$155$			1.44903i			0.116389i
$156$	−0.905506	−	0.247852i	−0.0724985	−	0.0198440i
$157$		−	2.28962i		−	0.182732i	−0.995817	−	0.0913660i	$-0.970877\pi$
$157$		−	2.28962i		−	0.182732i	0.995817	−	0.0913660i	$-0.0291233\pi$
$158$	2.79775	−	20.8186i	0.222577	−	1.65624i
$159$	−0.300570			−0.0238368
$160$	−4.44122	−	3.50365i	−0.351109	−	0.276988i
$161$	7.70798			0.607474
$162$	−1.68528	+	12.5405i	−0.132408	+	0.985275i
$163$			15.2225i			1.19232i	0.802867	+	0.596158i	$0.203307\pi$
$163$			15.2225i			1.19232i	−0.802867	+	0.596158i	$0.796693\pi$
$164$	1.78170	+	0.487682i	0.139128	+	0.0380816i
$165$		−	0.0320628i		−	0.00249609i
$166$	−0.787695	−	0.105856i	−0.0611370	−	0.00821600i
$167$	15.3311			1.18636			0.593179	−	0.805071i	$-0.297873\pi$
$167$	15.3311			1.18636			0.593179	+	0.805071i	$0.297873\pi$
$168$	0.319173	+	0.135230i	0.0246247	+	0.0104332i
$169$	−24.5279			−1.88676
$170$	−3.13058	−	0.420708i	−0.240104	−	0.0322668i
$171$			2.99413i			0.228967i
$172$	2.61228	−	9.54372i	0.199184	−	0.727702i
$173$		−	7.41336i		−	0.563627i	−0.959469	−	0.281814i	$-0.909064\pi$
$173$		−	7.41336i		−	0.563627i	0.959469	−	0.281814i	$-0.0909360\pi$
$174$	−0.0671484	+	0.499665i	−0.00509051	+	0.0378795i
$175$	−1.59941			−0.120904
$176$	−0.852402	+	1.44043i	−0.0642522	+	0.108576i
$177$	−0.624817			−0.0469641
$178$	0.203418	−	1.51368i	0.0152468	−	0.113455i
$179$		−	15.8925i		−	1.18786i	−0.804515	−	0.593932i	$-0.797575\pi$
$179$		−	15.8925i		−	1.18786i	0.804515	−	0.593932i	$-0.202425\pi$
$180$	1.58093	−	5.77580i	0.117836	−	0.430503i
$181$			10.0307i			0.745577i	0.927916	+	0.372789i	$0.121598\pi$
$181$			10.0307i			0.745577i	−0.927916	+	0.372789i	$0.878402\pi$
$182$	13.7330	+	1.84553i	1.01796	+	0.136800i
$183$	0.829682			0.0613318
$184$	5.31767	−	12.5509i	0.392024	−	0.925265i
$185$	−10.2780			−0.755654
$186$	−0.155624	−	0.0209138i	−0.0114109	−	0.00153347i
$187$			0.934600i			0.0683447i
$188$	−18.8880	−	5.16997i	−1.37755	−	0.377059i
$189$			0.734612i			0.0534351i
$190$	0.188358	−	1.40161i	0.0136649	−	0.101684i
$191$	−2.09111			−0.151307			−0.0756537	−	0.997134i	$-0.524104\pi$
$191$	−2.09111			−0.151307			−0.0756537	+	0.997134i	$0.524104\pi$
$192$	0.440389	−	0.426415i	0.0317823	−	0.0307738i
$193$	−0.866146			−0.0623466			−0.0311733	−	0.999514i	$-0.509924\pi$
$193$	−0.866146			−0.0623466			−0.0311733	+	0.999514i	$0.509924\pi$
$194$	1.15628	−	8.60414i	0.0830162	−	0.617741i
$195$			0.469407i			0.0336149i
$196$	8.56859	+	2.34537i	0.612042	+	0.167526i
$197$		−	21.3794i		−	1.52322i	−0.648037	−	0.761609i	$-0.724410\pi$
$197$		−	21.3794i		−	1.52322i	0.648037	−	0.761609i	$-0.275590\pi$
$198$	−1.75602	−	0.235985i	−0.124795	−	0.0167707i
$199$	−11.0393			−0.782557			−0.391279	−	0.920272i	$-0.627967\pi$
$199$	−11.0393			−0.782557			−0.391279	+	0.920272i	$0.627967\pi$
$200$	−1.10342	+	2.60432i	−0.0780235	+	0.184153i
$201$	−0.394461			−0.0278232
$202$	24.9495	+	3.35288i	1.75544	+	0.235908i
$203$		−	7.44112i		−	0.522265i
$204$	0.0903673	−	0.330149i	0.00632697	−	0.0231151i
$205$		−	0.923621i		−	0.0645085i
$206$	−2.63216	+	19.5864i	−0.183391	+	1.36465i
$207$	14.4295			1.00292
$208$	12.4794	−	21.0882i	0.865287	−	1.46220i
$209$	−0.418437			−0.0289439
$210$	0.0230843	−	0.171775i	0.00159297	−	0.0118536i
$211$		−	7.16443i		−	0.493220i	−0.969115	−	0.246610i	$-0.920683\pi$
$211$		−	7.16443i		−	0.493220i	0.969115	−	0.246610i	$-0.0793166\pi$
$212$	2.07118	−	7.56686i	0.142249	−	0.519694i
$213$			0.349863i			0.0239723i
$214$	−0.661709	−	0.0889248i	−0.0452335	−	0.00607878i
$215$	−4.94739			−0.337409
$216$	1.19617	+	0.506802i	0.0813889	+	0.0344835i
$217$	2.31759			0.157328
$218$	25.9051	+	3.48130i	1.75451	+	0.235783i
$219$			0.287426i			0.0194225i
$220$	0.807182	+	0.220939i	0.0544202	+	0.0148957i
$221$		−	13.6827i		−	0.920401i
$222$	0.148343	−	1.10385i	0.00995610	−	0.0740855i
$223$	18.2520			1.22224			0.611121	−	0.791537i	$-0.290719\pi$
$223$	18.2520			1.22224			0.611121	+	0.791537i	$0.290719\pi$
$224$	−5.60377	+	7.10333i	−0.374418	+	0.474611i
$225$	−2.99413			−0.199609
$226$	1.22488	−	9.11462i	0.0814781	−	0.606296i
$227$		−	17.2330i		−	1.14379i	−0.820326	−	0.571897i	$-0.806208\pi$
$227$		−	17.2330i		−	1.14379i	0.820326	−	0.571897i	$-0.193792\pi$
$228$	0.147813	+	0.0404590i	0.00978918	+	0.00267946i
$229$			18.3394i			1.21190i	0.795501	+	0.605952i	$0.207208\pi$
$229$			18.3394i			1.21190i	−0.795501	+	0.605952i	$0.792792\pi$
$230$	−6.75475	−	0.907749i	−0.445395	−	0.0598552i
$231$	−0.0512816			−0.00337408
$232$	−12.1164	−	5.13357i	−0.795479	−	0.337035i
$233$	−4.76361			−0.312075			−0.156037	−	0.987751i	$-0.549872\pi$
$233$	−4.76361			−0.312075			−0.156037	+	0.987751i	$0.549872\pi$
$234$	25.7085	+	3.45488i	1.68061	+	0.225852i
$235$			9.79140i			0.638721i
$236$	4.30550	−	15.7298i	0.280264	−	1.02392i
$237$		−	1.13814i		−	0.0739301i
$238$	−0.672884	+	5.00708i	−0.0436166	+	0.324560i
$239$	16.5810			1.07254			0.536269	−	0.844047i	$-0.319833\pi$
$239$	16.5810			1.07254			0.536269	+	0.844047i	$0.319833\pi$
$240$	−0.263776	−	0.156094i	−0.0170266	−	0.0100758i
$241$	3.92921			0.253103			0.126551	−	0.991960i	$-0.459609\pi$
$241$	3.92921			0.253103			0.126551	+	0.991960i	$0.459609\pi$
$242$	−2.03896	+	15.1723i	−0.131069	+	0.975315i
$243$			2.06349i			0.132373i
$244$	−5.71719	+	20.8872i	−0.366005	+	1.33717i
$245$		−	4.44189i		−	0.283782i
$246$	0.0991960	+	0.0133306i	0.00632450	+	0.000849929i
$247$	6.12600			0.389788
$248$	1.59888	−	3.77373i	0.101529	−	0.239632i
$249$	−0.0430628			−0.00272899
$250$	1.40161	+	0.188358i	0.0886458	+	0.0119128i
$251$		−	3.19066i		−	0.201392i	−0.994917	−	0.100696i	$-0.967893\pi$
$251$		−	3.19066i		−	0.201392i	0.994917	−	0.100696i	$-0.0321070\pi$
$252$	−9.23787	−	2.52856i	−0.581931	−	0.159284i
$253$			2.01656i			0.126780i
$254$	3.58678	−	26.6900i	0.225054	−	1.67468i
$255$	−0.171147			−0.0107176
$256$	7.70035	+	14.0251i	0.481272	+	0.876571i
$257$	−20.6005			−1.28502			−0.642510	−	0.766277i	$-0.722107\pi$
$257$	−20.6005			−1.28502			−0.642510	+	0.766277i	$0.722107\pi$
$258$	0.0714057	−	0.531345i	0.00444552	−	0.0330801i
$259$			16.4387i			1.02145i
$260$	−11.8173	−	3.23460i	−0.732879	−	0.200601i
$261$		−	13.9299i		−	0.862242i
$262$	−10.1117	−	1.35888i	−0.624705	−	0.0839520i
$263$	−9.40056			−0.579663			−0.289832	−	0.957078i	$-0.593599\pi$
$263$	−9.40056			−0.579663			−0.289832	+	0.957078i	$0.593599\pi$
$264$	−0.0353787	+	0.0835017i	−0.00217741	+	0.00513918i
$265$	−3.92260			−0.240963
$266$	−2.24175	−	0.301262i	−0.137451	−	0.0184716i
$267$		−	0.0827517i		−	0.00506432i
$268$	2.71816	−	9.93057i	0.166038	−	0.606606i
$269$		−	0.243729i		−	0.0148604i	−0.999972	−	0.00743020i	$-0.997635\pi$
$269$		−	0.243729i		−	0.0148604i	0.999972	−	0.00743020i	$-0.00236513\pi$
$270$	0.0865133	−	0.643764i	0.00526503	−	0.0391782i
$271$	−30.1127			−1.82922			−0.914608	−	0.404341i	$-0.867501\pi$
$271$	−30.1127			−1.82922			−0.914608	+	0.404341i	$0.867501\pi$
$272$	7.68880	+	4.54999i	0.466202	+	0.275884i
$273$	0.750774			0.0454389
$274$	−0.879904	+	6.54755i	−0.0531569	+	0.395552i
$275$		−	0.418437i		−	0.0252327i
$276$	0.194983	−	0.712352i	0.0117366	−	0.0428786i
$277$		−	5.90425i		−	0.354752i	−0.984143	−	0.177376i	$-0.943239\pi$
$277$		−	5.90425i		−	0.354752i	0.984143	−	0.177376i	$-0.0567608\pi$
$278$	−12.3466	−	1.65922i	−0.740501	−	0.0995136i
$279$	4.33857			0.259744
$280$	4.16537	+	1.76482i	0.248928	+	0.105468i
$281$	−21.1827			−1.26366			−0.631828	−	0.775109i	$-0.717695\pi$
$281$	−21.1827			−1.26366			−0.631828	+	0.775109i	$0.717695\pi$
$282$	−1.05159	−	0.141319i	−0.0626211	−	0.00841544i
$283$			31.1409i			1.85113i	0.378586	+	0.925566i	$0.376410\pi$
$283$			31.1409i			1.85113i	−0.378586	+	0.925566i	$0.623590\pi$
$284$	−8.80782	−	2.41085i	−0.522648	−	0.143057i
$285$		−	0.0766253i		−	0.00453889i
$286$	−0.482827	+	3.59282i	−0.0285502	+	0.212448i
$287$	−1.47725			−0.0871992
$288$	−10.4904	+	13.2976i	−0.618151	+	0.783568i
$289$	−12.0112			−0.706544
$290$	−0.876322	+	6.52090i	−0.0514594	+	0.382920i
$291$		−	0.470383i		−	0.0275743i
$292$	−7.23596	−	1.98060i	−0.423452	−	0.115906i
$293$			23.7608i			1.38812i	0.719917	+	0.694060i	$0.244180\pi$
$293$			23.7608i			1.38812i	−0.719917	+	0.694060i	$0.755820\pi$
$294$	0.477055	+	0.0641098i	0.0278224	+	0.00373896i
$295$	−8.15418			−0.474755
$296$	26.7672	+	11.3409i	1.55581	+	0.659179i
$297$	−0.192189			−0.0111519
$298$	−3.01061	−	0.404585i	−0.174400	−	0.0234370i
$299$		−	29.5228i		−	1.70735i
$300$	−0.0404590	+	0.147813i	−0.00233590	+	0.00853401i
$301$			7.91290i			0.456092i
$302$	3.24945	−	24.1798i	0.186985	−	1.39139i
$303$	1.36397			0.0783582
$304$	−2.03711	+	3.44241i	−0.116836	+	0.197436i
$305$	10.8278			0.619997
$306$	−1.25965	+	9.37335i	−0.0720096	+	0.535839i
$307$		−	2.28377i		−	0.130342i	−0.997874	−	0.0651708i	$-0.979241\pi$
$307$		−	2.28377i		−	0.130342i	0.997874	−	0.0651708i	$-0.0207592\pi$
$308$	0.353372	−	1.29101i	0.0201352	−	0.0735624i
$309$			1.07078i			0.0609144i
$310$	−2.03098	−	0.272936i	−0.115352	−	0.0155017i
$311$	−18.1331			−1.02823			−0.514117	−	0.857720i	$-0.671880\pi$
$311$	−18.1331			−1.02823			−0.514117	+	0.857720i	$0.671880\pi$
$312$	0.517952	−	1.22248i	0.0293233	−	0.0692095i
$313$	11.7824			0.665983			0.332992	−	0.942930i	$-0.391942\pi$
$313$	11.7824			0.665983			0.332992	+	0.942930i	$0.391942\pi$
$314$	3.20917	+	0.431270i	0.181104	+	0.0243380i
$315$			4.78884i			0.269820i
$316$	28.6527	+	7.84272i	1.61184	+	0.441187i
$317$			3.75891i			0.211121i	0.994413	+	0.105561i	$0.0336637\pi$
$317$			3.75891i			0.211121i	−0.994413	+	0.105561i	$0.966336\pi$
$318$	0.0566149	−	0.421283i	0.00317481	−	0.0236244i
$319$	1.94674			0.108997
$320$	5.74730	−	5.56493i	0.321284	−	0.311089i
$321$	−0.0361752			−0.00201910
$322$	−1.45186	+	10.8036i	−0.0809091	+	0.602062i
$323$			2.23355i			0.124278i
$324$	−17.2595	−	4.72422i	−0.958862	−	0.262456i
$325$			6.12600i			0.339810i
$326$	−21.3360	−	2.86728i	−1.18169	−	0.158804i
$327$	1.41621			0.0783168
$328$	−1.01914	+	2.40540i	−0.0562726	+	0.132816i
$329$	15.6605			0.863389
$330$	0.0449397	+	0.00603930i	0.00247385	+	0.000332452i
$331$		−	2.07032i		−	0.113795i	−0.998380	−	0.0568976i	$-0.981879\pi$
$331$		−	2.07032i		−	0.113795i	0.998380	−	0.0568976i	$-0.0181209\pi$
$332$	0.296738	−	1.08411i	0.0162856	−	0.0594980i
$333$			30.7737i			1.68639i
$334$	−2.88774	+	21.4883i	−0.158010	+	1.17579i
$335$	−5.14793			−0.281261
$336$	−0.249659	+	0.421885i	−0.0136200	+	0.0230157i
$337$	−22.0538			−1.20135			−0.600674	−	0.799494i	$-0.705101\pi$
$337$	−22.0538			−1.20135			−0.600674	+	0.799494i	$0.705101\pi$
$338$	4.62004	−	34.3787i	0.251297	−	1.86995i
$339$		−	0.498290i		−	0.0270634i
$340$	1.17934	−	4.30862i	0.0639587	−	0.233668i
$341$			0.606326i			0.0328344i
$342$	−4.19661	−	0.563969i	−0.226927	−	0.0304959i
$343$	−18.3003			−0.988121
$344$	12.8846	+	5.45904i	0.694689	+	0.294332i
$345$	−0.369278			−0.0198812
$346$	10.3907	+	1.39637i	0.558606	+	0.0750692i
$347$			25.1733i			1.35137i	0.737189	+	0.675687i	$0.236153\pi$
$347$			25.1733i			1.35137i	−0.737189	+	0.675687i	$0.763847\pi$
$348$	−0.687690	−	0.188232i	−0.0368641	−	0.0100903i
$349$			16.1246i			0.863129i	0.902082	+	0.431565i	$0.142038\pi$
$349$			16.1246i			0.863129i	−0.902082	+	0.431565i	$0.857962\pi$
$350$	0.301262	−	2.24175i	0.0161031	−	0.119827i
$351$	2.81368			0.150183
$352$	−1.85837	−	1.46605i	−0.0990514	−	0.0781410i
$353$	29.1352			1.55071			0.775355	−	0.631525i	$-0.217571\pi$
$353$	29.1352			1.55071			0.775355	+	0.631525i	$0.217571\pi$
$354$	0.117689	−	0.875752i	0.00625512	−	0.0465457i
$355$			4.56590i			0.242333i
$356$	2.08328	+	0.570227i	0.110413	+	0.0302220i
$357$			0.273733i			0.0144875i
$358$	22.2752	+	2.99349i	1.17728	+	0.158211i
$359$	−10.5305			−0.555778			−0.277889	−	0.960613i	$-0.589635\pi$
$359$	−10.5305			−0.555778			−0.277889	+	0.960613i	$0.589635\pi$
$360$	7.79766	+	3.30378i	0.410973	+	0.174124i
$361$	−1.00000			−0.0526316
$362$	−14.0592	−	1.88937i	−0.738935	−	0.0993030i
$363$			0.829462i			0.0435355i
$364$	−5.17345	+	18.9007i	−0.271162	+	0.990668i
$365$			3.75106i			0.196340i
$366$	−0.156277	+	1.16289i	−0.00816875	+	0.0607854i
$367$	12.4176			0.648193			0.324097	−	0.946024i	$-0.394940\pi$
$367$	12.4176			0.648193			0.324097	+	0.946024i	$0.394940\pi$
$368$	16.5899	+	9.81738i	0.864808	+	0.511766i
$369$	−2.76544			−0.143963
$370$	1.93595	−	14.4058i	0.100645	−	0.748922i
$371$			6.27384i			0.325722i
$372$	0.0586262	−	0.214186i	0.00303963	−	0.0111050i
$373$		−	2.77605i		−	0.143738i	−0.997414	−	0.0718691i	$-0.977104\pi$
$373$		−	2.77605i		−	0.143738i	0.997414	−	0.0718691i	$-0.0228964\pi$
$374$	−1.30995	−	0.176040i	−0.0677358	−	0.00910279i
$375$	0.0766253			0.00395691
$376$	10.8040	−	25.4999i	0.557174	−	1.31506i
$377$	−28.5007			−1.46786
$378$	−1.02964	−	0.138370i	−0.0529591	−	0.00711699i
$379$		−	3.63901i		−	0.186923i	−0.995623	−	0.0934616i	$-0.970207\pi$
$379$		−	3.63901i		−	0.186923i	0.995623	−	0.0934616i	$-0.0297932\pi$
$380$	1.92904	+	0.528011i	0.0989578	+	0.0270864i
$381$		−	1.45912i		−	0.0747531i
$382$	0.393878	−	2.93093i	0.0201525	−	0.149959i
$383$	−34.7408			−1.77517			−0.887587	−	0.460641i	$-0.847620\pi$
$383$	−34.7408			−1.77517			−0.887587	+	0.460641i	$0.847620\pi$
$384$	0.514718	+	0.697574i	0.0262666	+	0.0355979i
$385$	−0.669251			−0.0341082
$386$	0.163146	−	1.21400i	0.00830390	−	0.0617911i
$387$			14.8131i			0.752993i
$388$	11.8419	+	3.24132i	0.601181	+	0.164553i
$389$			13.5001i			0.684482i	0.939612	+	0.342241i	$0.111186\pi$
$389$			13.5001i			0.684482i	−0.939612	+	0.342241i	$0.888814\pi$
$390$	−0.657927	−	0.0884166i	−0.0333154	−	0.00447715i
$391$	10.7641			0.544363
$392$	−4.90126	+	11.5681i	−0.247551	+	0.584277i
$393$	−0.552801			−0.0278851
$394$	29.9656	+	4.02698i	1.50965	+	0.202877i
$395$		−	14.8533i		−	0.747352i
$396$	0.661520	−	2.41681i	0.0332426	−	0.121449i
$397$		−	0.702333i		−	0.0352491i	−0.999845	−	0.0176245i	$-0.994390\pi$
$397$		−	0.702333i		−	0.0352491i	0.999845	−	0.0176245i	$-0.00561036\pi$
$398$	2.07935	−	15.4729i	0.104228	−	0.775585i
$399$	−0.122555			−0.00613543
$400$	−3.44241	−	2.03711i	−0.172120	−	0.101856i
$401$	29.2258			1.45947			0.729734	−	0.683731i	$-0.239644\pi$
$401$	29.2258			1.45947			0.729734	+	0.683731i	$0.239644\pi$
$402$	0.0743000	−	0.552882i	0.00370575	−	0.0275753i
$403$		−	8.87674i		−	0.442182i
$404$	−9.39889	+	34.3380i	−0.467612	+	1.70838i
$405$			8.94719i			0.444590i
$406$	10.4296	+	1.40160i	0.517611	+	0.0695601i
$407$	−4.30069			−0.213178
$408$	0.445720	+	0.188846i	0.0220664	+	0.00934929i
$409$	−37.4701			−1.85278			−0.926389	−	0.376567i	$-0.877104\pi$
$409$	−37.4701			−1.85278			−0.926389	+	0.376567i	$0.877104\pi$
$410$	1.29456	+	0.173972i	0.0639337	+	0.00859184i
$411$			0.357950i			0.0176564i
$412$	−26.9568	−	7.37854i	−1.32807	−	0.363514i
$413$			13.0419i			0.641749i
$414$	−2.71792	+	20.2246i	−0.133578	+	0.993984i
$415$	−0.561992			−0.0275871
$416$	27.2069	+	21.4634i	1.33393	+	1.05233i
$417$	−0.674982			−0.0330540
$418$	0.0788160	−	0.586486i	0.00385502	−	0.0286860i
$419$			22.8832i			1.11792i	0.829196	+	0.558958i	$0.188799\pi$
$419$			22.8832i			1.11792i	−0.829196	+	0.558958i	$0.811201\pi$
$420$	0.236414	+	0.0647105i	0.0115358	+	0.00315755i
$421$		−	17.8464i		−	0.869778i	−0.900484	−	0.434889i	$-0.856788\pi$
$421$		−	17.8464i		−	0.869778i	0.900484	−	0.434889i	$-0.143212\pi$
$422$	10.0418	+	1.34948i	0.488825	+	0.0656916i
$423$	29.3167			1.42543
$424$	10.2157	+	4.32827i	0.496118	+	0.210199i
$425$	−2.23355			−0.108343
$426$	−0.490373	−	0.0658997i	−0.0237587	−	0.00319285i
$427$		−	17.3181i		−	0.838079i
$428$	0.249277	−	0.910710i	0.0120492	−	0.0440208i
$429$			0.196417i			0.00948310i
$430$	0.931881	−	6.93433i	0.0449393	−	0.334403i
$431$	−30.7218			−1.47981			−0.739907	−	0.672709i	$-0.765131\pi$
$431$	−30.7218			−1.47981			−0.739907	+	0.672709i	$0.765131\pi$
$432$	−0.935649	+	1.58110i	−0.0450164	+	0.0760709i
$433$	7.96332			0.382693			0.191346	−	0.981523i	$-0.438715\pi$
$433$	7.96332			0.382693			0.191346	+	0.981523i	$0.438715\pi$
$434$	−0.436537	+	3.24836i	−0.0209544	+	0.155926i
$435$			0.356493i			0.0170925i
$436$	−9.75887	+	35.6532i	−0.467365	+	1.70748i
$437$			4.81927i			0.230537i
$438$	−0.402860	−	0.0541391i	−0.0192494	−	0.00258687i
$439$	22.1711			1.05817			0.529086	−	0.848568i	$-0.322535\pi$
$439$	22.1711			1.05817			0.529086	+	0.848568i	$0.322535\pi$
$440$	−0.461711	+	1.08974i	−0.0220112	+	0.0519514i
$441$	−13.2996			−0.633314
$442$	19.1779	+	2.57726i	0.912201	+	0.122588i
$443$			13.8986i			0.660340i	0.943921	+	0.330170i	$0.107106\pi$
$443$			13.8986i			0.660340i	−0.943921	+	0.330170i	$0.892894\pi$
$444$	1.51923	+	0.415838i	0.0720994	+	0.0197348i
$445$		−	1.07995i		−	0.0511947i
$446$	−3.43791	+	25.5822i	−0.162790	+	1.21135i
$447$	−0.164588			−0.00778473
$448$	−8.90061	−	9.19229i	−0.420514	−	0.434295i
$449$	−9.93868			−0.469035			−0.234518	−	0.972112i	$-0.575351\pi$
$449$	−9.93868			−0.469035			−0.234518	+	0.972112i	$0.575351\pi$
$450$	0.563969	−	4.19661i	0.0265857	−	0.197830i
$451$		−	0.386477i		−	0.0181985i
$452$	12.5445	+	3.43363i	0.590042	+	0.161504i
$453$		−	1.32189i		−	0.0621080i
$454$	24.1540	+	3.24597i	1.13360	+	0.152341i
$455$	9.79799			0.459337
$456$	−0.0845498	+	0.199557i	−0.00395941	+	0.00934509i
$457$	−33.5915			−1.57134			−0.785671	−	0.618644i	$-0.787682\pi$
$457$	−33.5915			−1.57134			−0.785671	+	0.618644i	$0.787682\pi$
$458$	−25.7048	−	3.45439i	−1.20111	−	0.161413i
$459$			1.02587i			0.0478837i
$460$	2.54463	−	9.29657i	0.118644	−	0.433455i
$461$			4.40905i			0.205350i	0.994715	+	0.102675i	$0.0327402\pi$
$461$			4.40905i			0.205350i	−0.994715	+	0.102675i	$0.967260\pi$
$462$	0.00965931	−	0.0718770i	0.000449392	−	0.00334402i
$463$	13.1734			0.612220			0.306110	−	0.951996i	$-0.400972\pi$
$463$	13.1734			0.612220			0.306110	+	0.951996i	$0.400972\pi$
$464$	9.47750	−	16.0155i	0.439982	−	0.743502i
$465$	−0.111032			−0.00514899
$466$	0.897266	−	6.67675i	0.0415650	−	0.309294i
$467$		−	31.0554i		−	1.43707i	−0.695489	−	0.718537i	$-0.744812\pi$
$467$		−	31.0554i		−	1.43707i	0.695489	−	0.718537i	$-0.255188\pi$
$468$	−9.68480	+	35.3826i	−0.447680	+	1.63556i
$469$			8.23364i			0.380194i
$470$	−13.7238	−	1.84429i	−0.633030	−	0.0850708i
$471$	0.175443			0.00808399
$472$	21.2361	+	8.99748i	0.977470	+	0.414143i
$473$	−2.07017			−0.0951864
$474$	1.59523	+	0.214378i	0.0732715	+	0.00984671i
$475$		−	1.00000i		−	0.0458831i
$476$	−6.89124	−	1.88625i	−0.315860	−	0.0864560i
$477$			11.7448i			0.537756i
$478$	−3.12317	+	23.2402i	−0.142851	+	1.06298i
$479$	3.10822			0.142018			0.0710091	−	0.997476i	$-0.477378\pi$
$479$	3.10822			0.142018			0.0710091	+	0.997476i	$0.477378\pi$
$480$	0.268468	−	0.340310i	0.0122538	−	0.0155329i
$481$	62.9631			2.87087
$482$	−0.740100	+	5.50724i	−0.0337106	+	0.250848i
$483$			0.590626i			0.0268744i
$484$	−20.8817	−	5.71567i	−0.949169	−	0.259803i
$485$		−	6.13874i		−	0.278746i
$486$	−2.89221	−	0.388675i	−0.131193	−	0.0176306i
$487$	−6.94489			−0.314703			−0.157351	−	0.987543i	$-0.550296\pi$
$487$	−6.94489			−0.314703			−0.157351	+	0.987543i	$0.550296\pi$
$488$	−28.1990	−	11.9476i	−1.27651	−	0.540841i
$489$	−1.16643			−0.0527476
$490$	6.22581	+	0.836667i	0.281254	+	0.0377967i
$491$		−	38.9310i		−	1.75693i	−0.477807	−	0.878465i	$-0.658568\pi$
$491$		−	38.9310i		−	1.75693i	0.477807	−	0.878465i	$-0.341432\pi$
$492$	−0.0373688	+	0.136524i	−0.00168471	+	0.00615496i
$493$		−	10.3914i		−	0.468006i
$494$	−1.15388	+	8.58629i	−0.0519157	+	0.386316i
$495$	−1.25285			−0.0563115
$496$	4.98814	+	2.95183i	0.223974	+	0.132541i
$497$	7.30275			0.327573
$498$	0.00811123	−	0.0603574i	0.000363473	−	0.00270468i
$499$			12.3747i			0.553967i	0.960875	+	0.276984i	$0.0893348\pi$
$499$			12.3747i			0.553967i	−0.960875	+	0.276984i	$0.910665\pi$
$500$	−0.528011	+	1.92904i	−0.0236134	+	0.0862694i
$501$			1.17475i			0.0524840i
$502$	4.47207	+	0.600986i	0.199598	+	0.0268233i
$503$	−28.2996			−1.26182			−0.630908	−	0.775857i	$-0.717318\pi$
$503$	−28.2996			−1.26182			−0.630908	+	0.775857i	$0.717318\pi$
$504$	5.28409	−	12.4717i	0.235372	−	0.555532i
$505$	17.8006			0.792114
$506$	−2.82643	−	0.379835i	−0.125650	−	0.0168857i
$507$		−	1.87946i		−	0.0834697i
$508$	36.7334	+	10.0546i	1.62978	+	0.446099i
$509$		−	18.3754i		−	0.814476i	−0.913322	−	0.407238i	$-0.866492\pi$
$509$		−	18.3754i		−	0.814476i	0.913322	−	0.407238i	$-0.133508\pi$
$510$	0.0322369	−	0.239881i	0.00142747	−	0.0106221i
$511$	5.99948			0.265401
$512$	−21.1083	+	8.15117i	−0.932862	+	0.360234i
$513$	−0.459302			−0.0202787
$514$	3.88027	−	28.8739i	0.171151	−	1.27357i
$515$			13.9742i			0.615777i
$516$	0.731290	+	0.200166i	0.0321933	+	0.00881183i
$517$			4.09708i			0.180189i
$518$	−23.0408	−	3.09637i	−1.01235	−	0.136047i
$519$	0.568051			0.0249347
$520$	6.75955	−	15.9541i	0.296426	−	0.699632i
$521$	0.684995			0.0300102			0.0150051	−	0.999887i	$-0.495224\pi$
$521$	0.684995			0.0300102			0.0150051	+	0.999887i	$0.495224\pi$
$522$	19.5244	+	2.62382i	0.854560	+	0.114841i
$523$			30.8738i			1.35002i	0.737809	+	0.675009i	$0.235860\pi$
$523$			30.8738i			1.35002i	−0.737809	+	0.675009i	$0.764140\pi$
$524$	3.80925	−	13.9168i	0.166408	−	0.607957i
$525$		−	0.122555i		−	0.00534875i
$526$	1.77067	−	13.1760i	0.0772050	−	0.574499i
$527$	3.23648			0.140983
$528$	−0.110373	−	0.0653155i	−0.00480338	−	0.00284249i
$529$	0.225332			0.00979703
$530$	0.738854	−	5.49797i	0.0320938	−	0.238817i
$531$			24.4147i			1.05951i
$532$	0.844506	−	3.08533i	0.0366140	−	0.133766i
$533$			5.65810i			0.245080i
$534$	0.115986	+	0.0155870i	0.00501920	+	0.000674514i
$535$	−0.472105			−0.0204109
$536$	13.4068	+	5.68032i	0.579087	+	0.245352i
$537$	1.21777			0.0525507
$538$	0.341613	+	0.0459083i	0.0147280	+	0.00197925i
$539$		−	1.85865i		−	0.0800577i
$540$	0.886013	+	0.242516i	0.0381279	+	0.0104362i
$541$		−	10.4596i		−	0.449693i	−0.974394	−	0.224847i	$-0.927812\pi$
$541$		−	10.4596i		−	0.449693i	0.974394	−	0.224847i	$-0.0721881\pi$
$542$	5.67198	−	42.2064i	0.243632	−	1.81292i
$543$	−0.768607			−0.0329841
$544$	−7.82558	+	9.91970i	−0.335519	+	0.425304i
$545$	18.4823			0.791696
$546$	−0.141414	+	1.05229i	−0.00605198	+	0.0450341i
$547$		−	25.4555i		−	1.08840i	−0.838955	−	0.544200i	$-0.816833\pi$
$547$		−	25.4555i		−	1.08840i	0.838955	−	0.544200i	$-0.183167\pi$
$548$	−9.01140	−	2.46657i	−0.384948	−	0.105367i
$549$		−	32.4198i		−	1.38364i
$550$	0.586486	+	0.0788160i	0.0250079	+	0.00336072i
$551$	4.65242			0.198200
$552$	0.961716	+	0.407468i	0.0409334	+	0.0173430i
$553$	−23.7565			−1.01023
$554$	8.27547	+	1.11211i	0.351591	+	0.0472492i
$555$		−	0.787555i		−	0.0334299i
$556$	4.65118	−	16.9927i	0.197254	−	0.720650i
$557$			27.8317i			1.17927i	0.807671	+	0.589633i	$0.200728\pi$
$557$			27.8317i			1.17927i	−0.807671	+	0.589633i	$0.799272\pi$
$558$	−0.817206	+	6.08100i	−0.0345951	+	0.257429i
$559$	30.3077			1.28188
$560$	−3.25818	+	5.50582i	−0.137683	+	0.232663i
$561$	−0.0716140			−0.00302354
$562$	3.98994	−	29.6900i	0.168306	−	1.25240i
$563$		−	38.3026i		−	1.61426i	−0.590373	−	0.807131i	$-0.701019\pi$
$563$		−	38.3026i		−	1.61426i	0.590373	−	0.807131i	$-0.298981\pi$
$564$	0.396150	−	1.44730i	0.0166809	−	0.0609423i
$565$		−	6.50295i		−	0.273581i
$566$	−43.6475	−	5.86564i	−1.83464	−	0.246551i
$567$	14.3102			0.600973
$568$	5.03810	−	11.8911i	0.211394	−	0.498938i
$569$	15.0616			0.631417			0.315708	−	0.948856i	$-0.397758\pi$
$569$	15.0616			0.631417			0.315708	+	0.948856i	$0.397758\pi$
$570$	0.107399	+	0.0144330i	0.00449845	+	0.000604532i
$571$			4.52134i			0.189212i	0.995515	+	0.0946061i	$0.0301592\pi$
$571$			4.52134i			0.189212i	−0.995515	+	0.0946061i	$0.969841\pi$
$572$	−4.94480	−	1.35347i	−0.206752	−	0.0565916i
$573$		−	0.160232i		−	0.00669378i
$574$	0.278252	−	2.07053i	0.0116140	−	0.0864223i
$575$	−4.81927			−0.200977
$576$	−16.6621	−	17.2082i	−0.694255	−	0.717007i
$577$	10.6355			0.442760			0.221380	−	0.975188i	$-0.428944\pi$
$577$	10.6355			0.442760			0.221380	+	0.975188i	$0.428944\pi$
$578$	2.26242	−	16.8351i	0.0941041	−	0.700249i
$579$		−	0.0663687i		−	0.00275819i
$580$	−8.97472	−	2.45653i	−0.372655	−	0.102002i
$581$			0.898855i			0.0372908i
$582$	0.659295	+	0.0886004i	0.0273286	+	0.00367261i
$583$	−1.64136			−0.0679781
$584$	4.13899	−	9.76895i	0.171273	−	0.404242i
$585$	18.3420			0.758350
$586$	−33.3034	−	4.47554i	−1.37575	−	0.184883i
$587$		−	31.3093i		−	1.29227i	−0.763221	−	0.646137i	$-0.776383\pi$
$587$		−	31.3093i		−	1.29227i	0.763221	−	0.646137i	$-0.223617\pi$
$588$	−0.179714	+	0.656571i	−0.00741130	+	0.0270765i
$589$			1.44903i			0.0597061i
$590$	1.53591	−	11.4290i	0.0632323	−	0.470525i
$591$	1.63820			0.0673866
$592$	−20.9374	+	35.3811i	−0.860524	+	1.45415i
$593$	−20.2319			−0.830823			−0.415412	−	0.909634i	$-0.636362\pi$
$593$	−20.2319			−0.830823			−0.415412	+	0.909634i	$0.636362\pi$
$594$	0.0362003	−	0.269374i	0.00148532	−	0.0110526i
$595$			3.57236i			0.146453i
$596$	1.13414	−	4.14350i	0.0464564	−	0.169724i
$597$		−	0.845892i		−	0.0346200i
$598$	41.3796	+	5.56087i	1.69214	+	0.227401i
$599$	8.58923			0.350946			0.175473	−	0.984484i	$-0.443854\pi$
$599$	8.58923			0.350946			0.175473	+	0.984484i	$0.443854\pi$
$600$	−0.199557	−	0.0845498i	−0.00814686	−	0.00345173i
$601$	−41.6027			−1.69701			−0.848505	−	0.529187i	$-0.822497\pi$
$601$	−41.6027			−1.69701			−0.848505	+	0.529187i	$0.822497\pi$
$602$	−11.0908	−	1.49046i	−0.452028	−	0.0607466i
$603$			15.4136i			0.627688i
$604$	33.2787	+	9.10894i	1.35409	+	0.370637i
$605$			10.8249i			0.440095i
$606$	−0.256915	+	1.91176i	−0.0104365	+	0.0776600i
$607$	−21.1854			−0.859889			−0.429945	−	0.902855i	$-0.641467\pi$
$607$	−21.1854			−0.859889			−0.429945	+	0.902855i	$0.641467\pi$
$608$	−4.44122	−	3.50365i	−0.180115	−	0.142092i
$609$	0.570178			0.0231048
$610$	−2.03950	+	15.1764i	−0.0825770	+	0.614473i
$611$		−	59.9822i		−	2.42662i
$612$	−12.9006	−	3.53110i	−0.521474	−	0.142736i
$613$			28.8743i			1.16622i	0.812392	+	0.583111i	$0.198165\pi$
$613$			28.8743i			1.16622i	−0.812392	+	0.583111i	$0.801835\pi$
$614$	3.20096	+	0.430167i	0.129180	+	0.0173601i
$615$	0.0707727			0.00285383
$616$	1.74294	+	0.738464i	0.0702252	+	0.0297536i
$617$	−9.80103			−0.394575			−0.197287	−	0.980346i	$-0.563213\pi$
$617$	−9.80103			−0.394575			−0.197287	+	0.980346i	$0.563213\pi$
$618$	−1.50082	−	0.201690i	−0.0603717	−	0.00811315i
$619$		−	25.3438i		−	1.01865i	−0.860574	−	0.509326i	$-0.829895\pi$
$619$		−	25.3438i		−	1.01865i	0.860574	−	0.509326i	$-0.170105\pi$
$620$	0.765102	−	2.79523i	0.0307272	−	0.112259i
$621$			2.21350i			0.0888246i
$622$	3.41552	−	25.4156i	0.136950	−	1.01907i
$623$	−1.72729			−0.0692023
$624$	1.61589	+	0.956234i	0.0646874	+	0.0382800i
$625$	1.00000			0.0400000
$626$	−2.21932	+	16.5144i	−0.0887019	+	0.660050i
$627$		−	0.0320628i		−	0.00128047i
$628$	−1.20895	+	4.41678i	−0.0482422	+	0.176249i
$629$			22.9565i			0.915334i
$630$	−6.71210	−	0.902017i	−0.267416	−	0.0359372i
$631$	−22.5136			−0.896252			−0.448126	−	0.893970i	$-0.647908\pi$
$631$	−22.5136			−0.896252			−0.448126	+	0.893970i	$0.647908\pi$
$632$	−16.3894	+	38.6828i	−0.651937	+	1.53872i
$633$	0.548976			0.0218199
$634$	−5.26854	−	0.708021i	−0.209240	−	0.0281191i
$635$		−	19.0423i		−	0.755671i
$636$	0.579813	+	0.158704i	0.0229911	+	0.00629304i
$637$			27.2110i			1.07814i
$638$	−0.366685	+	2.72858i	−0.0145172	+	0.108026i
$639$	13.6709			0.540812
$640$	6.71734	+	9.10370i	0.265526	+	0.359855i
$641$	40.0549			1.58207			0.791037	−	0.611768i	$-0.209542\pi$
$641$	40.0549			1.58207			0.791037	+	0.611768i	$0.209542\pi$
$642$	0.00681389	−	0.0507036i	0.000268923	−	0.00200111i
$643$			22.0352i			0.868982i	0.900676	+	0.434491i	$0.143072\pi$
$643$			22.0352i			0.868982i	−0.900676	+	0.434491i	$0.856928\pi$
$644$	−14.8690	−	4.06990i	−0.585922	−	0.160376i
$645$		−	0.379095i		−	0.0149269i
$646$	−3.13058	−	0.420708i	−0.123171	−	0.0165525i
$647$	39.5234			1.55383			0.776914	−	0.629607i	$-0.216784\pi$
$647$	39.5234			1.55383			0.776914	+	0.629607i	$0.216784\pi$
$648$	9.87250	−	23.3013i	0.387828	−	0.915362i
$649$	−3.41201			−0.133933
$650$	−8.58629	−	1.15388i	−0.336782	−	0.0452590i
$651$			0.177586i			0.00696013i
$652$	8.03764	−	29.3648i	0.314778	−	1.15001i
$653$			6.20188i			0.242698i	0.992610	+	0.121349i	$0.0387221\pi$
$653$			6.20188i			0.242698i	−0.992610	+	0.121349i	$0.961278\pi$
$654$	−0.266756	+	1.98498i	−0.0104310	+	0.0776190i
$655$	−7.21435			−0.281888
$656$	−3.17948	−	1.88152i	−0.124138	−	0.0734609i
$657$	11.2312			0.438169
$658$	−2.94978	+	21.9499i	−0.114994	+	0.855697i
$659$			21.2302i			0.827010i	0.910502	+	0.413505i	$0.135696\pi$
$659$			21.2302i			0.827010i	−0.910502	+	0.413505i	$0.864304\pi$
$660$	−0.0169295	+	0.0618505i	−0.000658981	+	0.00240753i
$661$		−	18.6379i		−	0.724929i	−0.931998	−	0.362465i	$-0.881935\pi$
$661$		−	18.6379i		−	0.724929i	0.931998	−	0.362465i	$-0.118065\pi$
$662$	2.90179	+	0.389963i	0.112781	+	0.0151563i
$663$	1.04844			0.0407182
$664$	1.46360	+	0.620112i	0.0567989	+	0.0240650i
$665$	−1.59941			−0.0620224
$666$	−43.1328	−	5.79648i	−1.67136	−	0.224609i
$667$		−	22.4213i		−	0.868154i
$668$	−29.5744	−	8.09500i	−1.14427	−	0.313205i
$669$			1.39856i			0.0540716i
$670$	0.969654	−	7.21540i	0.0374610	−	0.278755i
$671$	4.53074			0.174907
$672$	−0.544295	−	0.429390i	−0.0209966	−	0.0165641i
$673$	44.9036			1.73091			0.865453	−	0.500990i	$-0.167031\pi$
$673$	44.9036			1.73091			0.865453	+	0.500990i	$0.167031\pi$
$674$	4.15402	−	30.9110i	0.160007	−	1.19065i
$675$		−	0.459302i		−	0.0176785i
$676$	47.3154	+	12.9510i	1.81982	+	0.498116i
$677$		−	1.59443i		−	0.0612791i	−0.999530	−	0.0306395i	$-0.990246\pi$
$677$		−	1.59443i		−	0.0612791i	0.999530	−	0.0306395i	$-0.00975439\pi$
$678$	0.698410	+	0.0938571i	0.0268223	+	0.00360456i
$679$	−9.81836			−0.376794
$680$	5.81688	+	2.46454i	0.223067	+	0.0945109i
$681$	1.32048			0.0506010
$682$	−0.849835	−	0.114206i	−0.0325418	−	0.00437319i
$683$		−	29.8487i		−	1.14213i	−0.820905	−	0.571065i	$-0.806531\pi$
$683$		−	29.8487i		−	1.14213i	0.820905	−	0.571065i	$-0.193469\pi$
$684$	1.58093	−	5.77580i	0.0604485	−	0.220843i
$685$			4.67144i			0.178486i
$686$	3.44701	−	25.6499i	0.131607	−	0.979318i
$687$	−1.40527			−0.0536142
$688$	−10.0784	+	17.0309i	−0.384235	+	0.649298i
$689$	24.0299			0.915465
$690$	0.0695565	−	0.517585i	0.00264797	−	0.0197041i
$691$		−	43.4358i		−	1.65237i	−0.563396	−	0.826187i	$-0.690505\pi$
$691$		−	43.4358i		−	1.65237i	0.563396	−	0.826187i	$-0.309495\pi$
$692$	−3.91433	+	14.3007i	−0.148801	+	0.543630i
$693$			2.00382i			0.0761190i
$694$	−35.2833	−	4.74160i	−1.33933	−	0.179989i
$695$	−8.80887			−0.334139
$696$	0.393361	−	0.928421i	0.0149103	−	0.0351917i
$697$	−2.06295			−0.0781400
$698$	−22.6004	−	3.03720i	−0.855439	−	0.114960i
$699$		−	0.365013i		−	0.0138061i
$700$	3.08533	+	0.844506i	0.116614	+	0.0319193i
$701$			38.0785i			1.43820i	0.694904	+	0.719102i	$0.255447\pi$
$701$			38.0785i			1.43820i	−0.694904	+	0.719102i	$0.744553\pi$
$702$	−0.529981	+	3.94370i	−0.0200028	+	0.148845i
$703$	−10.2780			−0.387642
$704$	2.40488	−	2.32857i	0.0906374	−	0.0877614i
$705$	−0.750269			−0.0282568
$706$	−5.48786	+	40.8363i	−0.206538	+	1.53689i
$707$		−	28.4704i		−	1.07074i
$708$	1.20530	+	0.329910i	0.0452979	+	0.0123988i
$709$			10.7427i			0.403449i	0.979442	+	0.201724i	$0.0646545\pi$
$709$			10.7427i			0.403449i	−0.979442	+	0.201724i	$0.935345\pi$
$710$	−6.39963	−	0.860025i	−0.240174	−	0.0322762i
$711$	−44.4728			−1.66786
$712$	−1.19164	+	2.81254i	−0.0446586	+	0.105404i
$713$	6.98325			0.261525
$714$	−0.383669	−	0.0515600i	−0.0143584	−	0.00192958i
$715$			2.56334i			0.0958636i
$716$	−8.39144	+	30.6574i	−0.313603	+	1.14572i
$717$			1.27053i			0.0474487i
$718$	1.98351	−	14.7597i	0.0740238	−	0.550827i
$719$	−1.90124			−0.0709043			−0.0354522	−	0.999371i	$-0.511287\pi$
$719$	−1.90124			−0.0709043			−0.0354522	+	0.999371i	$0.511287\pi$
$720$	−6.09937	+	10.3070i	−0.227310	+	0.384120i
$721$	22.3505			0.832375
$722$	0.188358	−	1.40161i	0.00700997	−	0.0521627i
$723$			0.301077i			0.0111972i
$724$	5.29633	−	19.3497i	0.196837	−	0.719125i
$725$			4.65242i			0.172787i
$726$	−1.16259	−	0.156236i	−0.0431476	−	0.00579846i
$727$	−32.4757			−1.20446			−0.602228	−	0.798324i	$-0.705720\pi$
$727$	−32.4757			−1.20446			−0.602228	+	0.798324i	$0.705720\pi$
$728$	−25.5171	−	10.8113i	−0.945725	−	0.400693i
$729$	26.6835			0.988276
$730$	−5.25754	−	0.706543i	−0.194590	−	0.0261503i
$731$			11.0503i			0.408708i
$732$	−1.60049	−	0.438081i	−0.0591559	−	0.0161919i
$733$		−	44.5108i		−	1.64404i	−0.569456	−	0.822022i	$-0.692846\pi$
$733$		−	44.5108i		−	1.64404i	0.569456	−	0.822022i	$-0.307154\pi$
$734$	−2.33896	+	17.4047i	−0.0863325	+	0.642418i
$735$	0.340361			0.0125544
$736$	−16.8850	+	21.4034i	−0.622390	+	0.788941i
$737$	−2.15408			−0.0793466
$738$	0.520893	−	3.87608i	0.0191743	−	0.142680i
$739$		−	37.4635i		−	1.37812i	−0.724706	−	0.689058i	$-0.758025\pi$
$739$		−	37.4635i		−	1.37812i	0.724706	−	0.689058i	$-0.241975\pi$
$740$	19.8267	+	5.42690i	0.728845	+	0.199497i
$741$			0.469407i			0.0172441i
$742$	−8.79350	−	1.18173i	−0.322820	−	0.0433827i
$743$	36.0557			1.32276			0.661378	−	0.750053i	$-0.269972\pi$
$743$	36.0557			1.32276			0.661378	+	0.750053i	$0.269972\pi$
$744$	0.289163	+	0.122515i	0.0106012	+	0.00449161i
$745$	−2.14796			−0.0786950
$746$	3.89095	+	0.522891i	0.142458	+	0.0191444i
$747$			1.68268i			0.0615659i
$748$	0.493479	−	1.80288i	0.0180434	−	0.0659199i
$749$			0.755089i			0.0275903i
$750$	−0.0144330	+	0.107399i	−0.000527019	+	0.00392166i
$751$	−4.40322			−0.160676			−0.0803379	−	0.996768i	$-0.525600\pi$
$751$	−4.40322			−0.160676			−0.0803379	+	0.996768i	$0.525600\pi$
$752$	33.7060	+	19.9462i	1.22913	+	0.727362i
$753$	0.244485			0.00890953
$754$	5.36835	−	39.9470i	0.195504	−	1.45479i
$755$		−	17.2514i		−	0.627843i
$756$	0.387883	−	1.41710i	0.0141072	−	0.0515393i
$757$		−	32.5290i		−	1.18229i	−0.806567	−	0.591143i	$-0.798677\pi$
$757$		−	32.5290i		−	1.18229i	0.806567	−	0.591143i	$-0.201323\pi$
$758$	5.10048	+	0.685437i	0.185258	+	0.0248962i
$759$	−0.154519			−0.00560869
$760$	−1.10342	+	2.60432i	−0.0400252	+	0.0944685i
$761$	−7.46645			−0.270658			−0.135329	−	0.990801i	$-0.543209\pi$
$761$	−7.46645			−0.270658			−0.135329	+	0.990801i	$0.543209\pi$
$762$	2.04513	+	0.274838i	0.0740871	+	0.00995632i
$763$		−	29.5608i		−	1.07017i
$764$	4.03384	+	1.10413i	0.145939	+	0.0399460i
$765$			6.68754i			0.241789i
$766$	6.54372	−	48.6932i	0.236434	−	1.75936i
$767$	49.9526			1.80368
$768$	−1.07468	+	0.590042i	−0.0387792	+	0.0212913i
$769$	16.9192			0.610123			0.305061	−	0.952333i	$-0.401323\pi$
$769$	16.9192			0.610123			0.305061	+	0.952333i	$0.401323\pi$
$770$	0.126059	−	0.938032i	0.00454285	−	0.0338043i
$771$		−	1.57852i		−	0.0568488i
$772$	1.67083	+	0.457335i	0.0601346	+	0.0164598i
$773$			7.99802i			0.287669i	0.989602	+	0.143834i	$0.0459432\pi$
$773$			7.99802i			0.287669i	−0.989602	+	0.143834i	$0.954057\pi$
$774$	−20.7623	−	2.79017i	−0.746284	−	0.100291i
$775$	−1.44903			−0.0520506
$776$	−6.77360	+	15.9872i	−0.243158	+	0.573908i
$777$	−1.25962			−0.0451887
$778$	−18.9219	−	2.54286i	−0.678384	−	0.0911658i
$779$		−	0.923621i		−	0.0330921i
$780$	0.247852	−	0.905506i	0.00887452	−	0.0324223i
$781$			1.91054i			0.0683645i
$782$	−2.02750	+	15.0871i	−0.0725034	+	0.539513i
$783$	2.13686			0.0763653
$784$	−15.2908	−	9.04862i	−0.546100	−	0.323165i
$785$	2.28962			0.0817202
$786$	0.104125	−	0.774814i	0.00371400	−	0.0276367i
$787$			46.8865i			1.67132i	0.549245	+	0.835661i	$0.314915\pi$
$787$			46.8865i			1.67132i	−0.549245	+	0.835661i	$0.685085\pi$
$788$	−11.2886	+	41.2417i	−0.402138	+	1.46918i
$789$		−	0.720320i		−	0.0256441i
$790$	20.8186	+	2.79775i	0.740693	+	0.0995393i
$791$	−10.4009			−0.369813
$792$	3.26283	+	1.38242i	0.115939	+	0.0491222i
$793$	−66.3310			−2.35548
$794$	0.984400	+	0.132290i	0.0349350	+	0.00469480i
$795$		−	0.300570i		−	0.0106601i
$796$	21.2953	+	5.82889i	0.754793	+	0.206599i
$797$			10.1191i			0.358437i	0.983809	+	0.179219i	$0.0573570\pi$
$797$			10.1191i			0.358437i	−0.983809	+	0.179219i	$0.942643\pi$
$798$	0.0230843	−	0.171775i	0.000817175	−	0.00608077i
$799$	21.8696			0.773691
$800$	3.50365	−	4.44122i	0.123873	−	0.157021i
$801$	−3.23352			−0.114251
$802$	−5.50493	+	40.9633i	−0.194386	+	1.44647i
$803$			1.56958i			0.0553893i
$804$	0.760933	+	0.208280i	0.0268360	+	0.00734547i
$805$			7.70798i			0.271671i
$806$	12.4418	+	1.67201i	0.438243	+	0.0588940i
$807$	0.0186758			0.000657418
$808$	−46.3583	−	19.6415i	−1.63088	−	0.690984i
$809$	21.1587			0.743902			0.371951	−	0.928252i	$-0.378689\pi$
$809$	21.1587			0.743902			0.371951	+	0.928252i	$0.378689\pi$
$810$	−12.5405	−	1.68528i	−0.440628	−	0.0592146i
$811$			26.1282i			0.917485i	0.888569	+	0.458742i	$0.151700\pi$
$811$			26.1282i			0.917485i	−0.888569	+	0.458742i	$0.848300\pi$
$812$	−3.92900	+	14.3542i	−0.137881	+	0.503735i
$813$		−	2.30739i		−	0.0809239i
$814$	0.810071	−	6.02791i	0.0283930	−	0.211278i
$815$	−15.2225			−0.533220
$816$	−0.348645	+	0.589156i	−0.0122050	+	0.0206246i
$817$	−4.94739			−0.173087
$818$	7.05781	−	52.5186i	0.246770	−	1.83627i
$819$		−	29.3364i		−	1.02510i
$820$	−0.487682	+	1.78170i	−0.0170306	+	0.0622198i
$821$			12.3934i			0.432532i	0.976335	+	0.216266i	$0.0693878\pi$
$821$			12.3934i			0.432532i	−0.976335	+	0.216266i	$0.930612\pi$
$822$	−0.501708	−	0.0674229i	−0.0174991	−	0.00235164i
$823$	−50.9542			−1.77615			−0.888076	−	0.459696i	$-0.847958\pi$
$823$	−50.9542			−1.77615			−0.888076	+	0.459696i	$0.847958\pi$
$824$	15.4194	−	36.3933i	0.537160	−	1.26782i
$825$	0.0320628			0.00111628
$826$	−18.2797	−	2.45655i	−0.636031	−	0.0854742i
$827$		−	4.93899i		−	0.171745i	−0.996306	−	0.0858727i	$-0.972632\pi$
$827$		−	4.93899i		−	0.171745i	0.996306	−	0.0858727i	$-0.0273678\pi$
$828$	−27.8351	−	7.61894i	−0.967337	−	0.264776i
$829$			19.1519i			0.665172i	0.943073	+	0.332586i	$0.107921\pi$
$829$			19.1519i			0.665172i	−0.943073	+	0.332586i	$0.892079\pi$
$830$	0.105856	−	0.787695i	0.00367431	−	0.0273413i
$831$	0.452414			0.0156941
$832$	−35.2080	+	34.0908i	−1.22062	+	1.18189i
$833$	−9.92119			−0.343749
$834$	0.127138	−	0.946064i	0.00440244	−	0.0327595i
$835$			15.3311i			0.530555i
$836$	0.807182	+	0.220939i	0.0279170	+	0.00764134i
$837$			0.665541i			0.0230044i
$838$	−32.0734	−	4.31024i	−1.10796	−	0.148895i
$839$	10.0369			0.346512			0.173256	−	0.984877i	$-0.444571\pi$
$839$	10.0369			0.346512			0.173256	+	0.984877i	$0.444571\pi$
$840$	−0.135230	+	0.319173i	−0.00466587	+	0.0110125i
$841$	7.35499			0.253620
$842$	25.0137	+	3.36151i	0.862029	+	0.115845i
$843$		−	1.62313i		−	0.0559037i
$844$	−3.78290	+	13.8205i	−0.130213	+	0.475721i
$845$		−	24.5279i		−	0.843786i
$846$	−5.52205	+	41.0907i	−0.189852	+	1.41273i
$847$	17.3135			0.594898
$848$	−7.99077	+	13.5032i	−0.274404	+	0.463701i
$849$	−2.38618			−0.0818934
$850$	0.420708	−	3.13058i	0.0144302	−	0.107378i
$851$			49.5325i			1.69795i
$852$	0.184732	−	0.674901i	0.00632881	−	0.0231217i
$853$			25.4072i			0.869927i	0.900448	+	0.434963i	$0.143239\pi$
$853$			25.4072i			0.869927i	−0.900448	+	0.434963i	$0.856761\pi$
$854$	24.2732	+	3.26200i	0.830613	+	0.111623i
$855$	−2.99413			−0.102397
$856$	1.22951	+	0.520929i	0.0420238	+	0.0178050i
$857$	−24.3216			−0.830812			−0.415406	−	0.909636i	$-0.636360\pi$
$857$	−24.3216			−0.830812			−0.415406	+	0.909636i	$0.636360\pi$
$858$	−0.275301	−	0.0369968i	−0.00939861	−	0.00126305i
$859$		−	10.9494i		−	0.373590i	−0.982399	−	0.186795i	$-0.940190\pi$
$859$		−	10.9494i		−	0.373590i	0.982399	−	0.186795i	$-0.0598101\pi$
$860$	9.54372	+	2.61228i	0.325438	+	0.0890779i
$861$		−	0.113195i		−	0.00385766i
$862$	5.78670	−	43.0600i	0.197096	−	1.46663i
$863$	53.6234			1.82536			0.912681	−	0.408672i	$-0.134008\pi$
$863$	53.6234			1.82536			0.912681	+	0.408672i	$0.134008\pi$
$864$	−2.03986	−	1.60923i	−0.0693975	−	0.0547472i
$865$	7.41336			0.252062
$866$	−1.49996	+	11.1615i	−0.0509706	+	0.379283i
$867$		−	0.920365i		−	0.0312572i
$868$	−4.47072	−	1.22371i	−0.151746	−	0.0415355i
$869$		−	6.21517i		−	0.210835i
$870$	−0.499665	−	0.0671484i	−0.0169402	−	0.00227654i
$871$	31.5362			1.06856
$872$	−48.1338	−	20.3937i	−1.63002	−	0.690619i
$873$	−18.3802			−0.622075
$874$	−6.75475	−	0.907749i	−0.228483	−	0.0307051i
$875$		−	1.59941i		−	0.0540699i
$876$	0.151764	−	0.554457i	0.00512764	−	0.0187334i
$877$		−	5.84805i		−	0.197475i	−0.995114	−	0.0987374i	$-0.968520\pi$
$877$		−	5.84805i		−	0.197475i	0.995114	−	0.0987374i	$-0.0314804\pi$
$878$	−4.17612	+	31.0754i	−0.140937	+	1.04874i
$879$	−1.82068			−0.0614099
$880$	−1.44043	−	0.852402i	−0.0485569	−	0.0287345i
$881$	21.6921			0.730824			0.365412	−	0.930846i	$-0.380928\pi$
$881$	21.6921			0.730824			0.365412	+	0.930846i	$0.380928\pi$
$882$	2.50509	−	18.6409i	0.0843507	−	0.627671i
$883$		−	14.0901i		−	0.474169i	−0.971489	−	0.237084i	$-0.923808\pi$
$883$		−	14.0901i		−	0.474169i	0.971489	−	0.237084i	$-0.0761918\pi$
$884$	−7.22464	+	26.3946i	−0.242991	+	0.887747i
$885$		−	0.624817i		−	0.0210030i
$886$	−19.4804	−	2.61791i	−0.654457	−	0.0879504i
$887$	23.2610			0.781028			0.390514	−	0.920597i	$-0.372297\pi$
$887$	23.2610			0.781028			0.390514	+	0.920597i	$0.372297\pi$
$888$	−0.869003	+	2.05104i	−0.0291618	+	0.0688285i
$889$	−30.4565			−1.02148
$890$	1.51368	+	0.203418i	0.0507386	+	0.00681859i
$891$			3.74383i			0.125423i
$892$	−35.2088	−	9.63725i	−1.17888	−	0.322679i
$893$			9.79140i			0.327657i
$894$	0.0310015	−	0.230688i	0.00103684	−	0.00771538i
$895$	15.8925			0.531229
$896$	14.5605	−	10.7438i	0.486434	−	0.358924i
$897$	2.26220			0.0755325
$898$	1.87203	−	13.9302i	0.0624705	−	0.464856i
$899$		−	6.74148i		−	0.224841i
$900$	5.77580	+	1.58093i	0.192527	+	0.0526978i
$901$			8.76133i			0.291882i
$902$	0.541691	+	0.0727961i	0.0180363	+	0.00242384i
$903$	−0.606328			−0.0201773
$904$	−7.17547	+	16.9357i	−0.238653	+	0.563274i
$905$	−10.0307			−0.333432
$906$	1.85279	+	0.248990i	0.0615547	+	0.00827213i
$907$			13.2234i			0.439077i	0.975604	+	0.219538i	$0.0704551\pi$
$907$			13.2234i			0.439077i	−0.975604	+	0.219538i	$0.929545\pi$
$908$	−9.09920	+	33.2431i	−0.301968	+	1.10321i
$909$		−	53.2971i		−	1.76775i
$910$	−1.84553	+	13.7330i	−0.0611788	+	0.455244i
$911$	−50.2776			−1.66577			−0.832885	−	0.553446i	$-0.813312\pi$
$911$	−50.2776			−1.66577			−0.832885	+	0.553446i	$0.813312\pi$
$912$	−0.263776	−	0.156094i	−0.00873448	−	0.00516880i
$913$	−0.235158			−0.00778259
$914$	6.32723	−	47.0823i	0.209286	−	1.55734i
$915$			0.829682i			0.0274284i
$916$	9.68343	−	35.3776i	0.319950	−	1.16891i
$917$			11.5387i			0.381041i
$918$	−1.43788	−	0.193232i	−0.0474571	−	0.00637760i
$919$	32.5485			1.07368			0.536839	−	0.843685i	$-0.319618\pi$
$919$	32.5485			1.07368			0.536839	+	0.843685i	$0.319618\pi$
$920$	12.5509	+	5.31767i	0.413791	+	0.175318i
$921$	0.174994			0.00576626
$922$	−6.17979	−	0.830482i	−0.203521	−	0.0273505i
$923$		−	27.9707i		−	0.920668i
$924$	0.0989243	+	0.0270772i	0.00325437	+	0.000890776i
$925$		−	10.2780i		−	0.337939i
$926$	−2.48132	+	18.4640i	−0.0815412	+	0.606765i
$927$	41.8406			1.37422
$928$	20.6624	+	16.3004i	0.678277	+	0.535088i
$929$	30.4672			0.999598			0.499799	−	0.866141i	$-0.333407\pi$
$929$	30.4672			0.999598			0.499799	+	0.866141i	$0.333407\pi$
$930$	0.0209138	−	0.155624i	0.000685791	−	0.00510312i
$931$		−	4.44189i		−	0.145577i
$932$	9.18921	+	2.51524i	0.301003	+	0.0823895i
$933$		−	1.38945i		−	0.0454887i
$934$	43.5277	+	5.84955i	1.42427	+	0.191403i
$935$	−0.934600			−0.0305647
$936$	−47.7685	−	20.2390i	−1.56136	−	0.661531i
$937$	29.5282			0.964645			0.482323	−	0.875994i	$-0.339793\pi$
$937$	29.5282			0.964645			0.482323	+	0.875994i	$0.339793\pi$
$938$	−11.5404	−	1.55087i	−0.376807	−	0.0506378i
$939$			0.902833i			0.0294628i
$940$	5.16997	−	18.8880i	0.168626	−	0.616060i
$941$			32.4760i			1.05869i	0.848407	+	0.529344i	$0.177562\pi$
$941$			32.4760i			1.05869i	−0.848407	+	0.529344i	$0.822438\pi$
$942$	−0.0330462	+	0.245904i	−0.00107670	+	0.00801197i
$943$	−4.45117			−0.144950
$944$	−16.6110	+	28.0700i	−0.540641	+	0.913602i
$945$	−0.734612			−0.0238969
$946$	0.389933	−	2.90158i	0.0126778	−	0.0943384i
$947$		−	37.7594i		−	1.22701i	−0.789689	−	0.613507i	$-0.789758\pi$
$947$		−	37.7594i		−	1.22701i	0.789689	−	0.613507i	$-0.210242\pi$
$948$	−0.600950	+	2.19552i	−0.0195180	+	0.0713072i
$949$		−	22.9790i		−	0.745930i
$950$	1.40161	+	0.188358i	0.0454744	+	0.00611115i
$951$	−0.288027			−0.00933993
$952$	3.94181	−	9.30357i	0.127755	−	0.301530i
$953$	−31.0548			−1.00597			−0.502983	−	0.864297i	$-0.667764\pi$
$953$	−31.0548			−1.00597			−0.502983	+	0.864297i	$0.667764\pi$
$954$	−16.4616	−	2.21222i	−0.532965	−	0.0716234i
$955$		−	2.09111i		−	0.0676667i
$956$	−31.9855	−	8.75496i	−1.03448	−	0.283156i
$957$			0.149170i			0.00482197i
$958$	−0.585459	+	4.35652i	−0.0189153	+	0.140753i
$959$	7.47154			0.241269
$960$	0.426415	+	0.440389i	0.0137625	+	0.0142135i
$961$	−28.9003			−0.932268
$962$	−11.8596	+	88.2500i	−0.382370	+	2.84529i
$963$			1.41354i			0.0455508i
$964$	−7.57962	−	2.07467i	−0.244123	−	0.0668206i
$965$		−	0.866146i		−	0.0278822i
$966$	−0.827830	−	0.111249i	−0.0266350	−	0.00357939i
$967$	3.27492			0.105314			0.0526572	−	0.998613i	$-0.483231\pi$
$967$	3.27492			0.105314			0.0526572	+	0.998613i	$0.483231\pi$
$968$	11.9444	−	28.1915i	0.383908	−	0.906109i
$969$	−0.171147			−0.00549802
$970$	8.60414	+	1.15628i	0.276262	+	0.0371260i
$971$			44.6586i			1.43316i	0.697504	+	0.716581i	$0.254294\pi$
$971$			44.6586i			1.43316i	−0.697504	+	0.716581i	$0.745706\pi$
$972$	1.08954	−	3.98055i	0.0349471	−	0.127676i
$973$			14.0890i			0.451672i
$974$	1.30813	−	9.73405i	0.0419151	−	0.311899i
$975$	−0.469407			−0.0150330
$976$	22.0574	−	37.2736i	0.706040	−	1.19310i
$977$	−18.8785			−0.603975			−0.301988	−	0.953312i	$-0.597650\pi$
$977$	−18.8785			−0.603975			−0.301988	+	0.953312i	$0.597650\pi$
$978$	0.219706	−	1.63488i	0.00702543	−	0.0522777i
$979$		−	0.451892i		−	0.0144425i
$980$	−2.34537	+	8.56859i	−0.0749200	+	0.273714i
$981$		−	55.3385i		−	1.76682i
$982$	54.5662	+	7.33297i	1.74128	+	0.234004i
$983$	19.2445			0.613803			0.306902	−	0.951741i	$-0.400708\pi$
$983$	19.2445			0.613803			0.306902	+	0.951741i	$0.400708\pi$
$984$	−0.184315	−	0.0780919i	−0.00587573	−	0.00248948i
$985$	21.3794			0.681204
$986$	14.5648	+	1.95731i	0.463836	+	0.0623335i
$987$			1.19999i			0.0381960i
$988$	−11.8173	−	3.23460i	−0.375959	−	0.102906i
$989$			23.8428i			0.758156i
$990$	0.235985	−	1.75602i	0.00750010	−	0.0558098i
$991$	−44.1785			−1.40338			−0.701688	−	0.712484i	$-0.747570\pi$
$991$	−44.1785			−1.40338			−0.701688	+	0.712484i	$0.747570\pi$
$992$	−5.07688	+	6.43545i	−0.161191	+	0.204326i
$993$	0.158639			0.00503426
$994$	−1.37553	+	10.2356i	−0.0436292	+	0.324654i
$995$		−	11.0393i		−	0.349970i
$996$	0.0830699	+	0.0227376i	0.00263217	+	0.000720469i
$997$		−	6.24439i		−	0.197762i	−0.995099	−	0.0988809i	$-0.968474\pi$
$997$		−	6.24439i		−	0.197762i	0.995099	−	0.0988809i	$-0.0315263\pi$
$998$	−17.3445	−	2.33088i	−0.549032	−	0.0737826i
$999$	−4.72071			−0.149357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.20	yes	44
4.3	odd	2		3040.2.f.b.1521.22		44
8.3	odd	2		3040.2.f.b.1521.23		44
8.5	even	2	inner	760.2.f.b.381.19	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.19	✓	44	8.5	even	2	inner
760.2.f.b.381.20	yes	44	1.1	even	1	trivial
3040.2.f.b.1521.22		44	4.3	odd	2
3040.2.f.b.1521.23		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.188358 + 1.40161i) q^{2} +0.0766253i q^{3} +(-1.92904 - 0.528011i) q^{4} +1.00000i q^{5} +(-0.107399 - 0.0144330i) q^{6} +1.59941 q^{7} +(1.10342 - 2.60432i) q^{8} +2.99413 q^{9} +(-1.40161 - 0.188358i) q^{10} +0.418437i q^{11} +(0.0404590 - 0.147813i) q^{12} -6.12600i q^{13} +(-0.301262 + 2.24175i) q^{14} -0.0766253 q^{15} +(3.44241 + 2.03711i) q^{16} +2.23355 q^{17} +(-0.563969 + 4.19661i) q^{18} +1.00000i q^{19} +(0.528011 - 1.92904i) q^{20} +0.122555i q^{21} +(-0.586486 - 0.0788160i) q^{22} +4.81927 q^{23} +(0.199557 + 0.0845498i) q^{24} -1.00000 q^{25} +(8.58629 + 1.15388i) q^{26} +0.459302i q^{27} +(-3.08533 - 0.844506i) q^{28} -4.65242i q^{29} +(0.0144330 - 0.107399i) q^{30} +1.44903 q^{31} +(-3.50365 + 4.44122i) q^{32} -0.0320628 q^{33} +(-0.420708 + 3.13058i) q^{34} +1.59941i q^{35} +(-5.77580 - 1.58093i) q^{36} +10.2780i q^{37} +(-1.40161 - 0.188358i) q^{38} +0.469407 q^{39} +(2.60432 + 1.10342i) q^{40} -0.923621 q^{41} +(-0.171775 - 0.0230843i) q^{42} +4.94739i q^{43} +(0.220939 - 0.807182i) q^{44} +2.99413i q^{45} +(-0.907749 + 6.75475i) q^{46} +9.79140 q^{47} +(-0.156094 + 0.263776i) q^{48} -4.44189 q^{49} +(0.188358 - 1.40161i) q^{50} +0.171147i q^{51} +(-3.23460 + 11.8173i) q^{52} +3.92260i q^{53} +(-0.643764 - 0.0865133i) q^{54} -0.418437 q^{55} +(1.76482 - 4.16537i) q^{56} -0.0766253 q^{57} +(6.52090 + 0.876322i) q^{58} +8.15418i q^{59} +(0.147813 + 0.0404590i) q^{60} -10.8278i q^{61} +(-0.272936 + 2.03098i) q^{62} +4.78884 q^{63} +(-5.56493 - 5.74730i) q^{64} +6.12600 q^{65} +(0.00603930 - 0.0449397i) q^{66} +5.14793i q^{67} +(-4.30862 - 1.17934i) q^{68} +0.369278i q^{69} +(-2.24175 - 0.301262i) q^{70} +4.56590 q^{71} +(3.30378 - 7.79766i) q^{72} +3.75106 q^{73} +(-14.4058 - 1.93595i) q^{74} -0.0766253i q^{75} +(0.528011 - 1.92904i) q^{76} +0.669251i q^{77} +(-0.0884166 + 0.657927i) q^{78} -14.8533 q^{79} +(-2.03711 + 3.44241i) q^{80} +8.94719 q^{81} +(0.173972 - 1.29456i) q^{82} +0.561992i q^{83} +(0.0647105 - 0.236414i) q^{84} +2.23355i q^{85} +(-6.93433 - 0.931881i) q^{86} +0.356493 q^{87} +(1.08974 + 0.461711i) q^{88} -1.07995 q^{89} +(-4.19661 - 0.563969i) q^{90} -9.79799i q^{91} +(-9.29657 - 2.54463i) q^{92} +0.111032i q^{93} +(-1.84429 + 13.7238i) q^{94} -1.00000 q^{95} +(-0.340310 - 0.268468i) q^{96} -6.13874 q^{97} +(0.836667 - 6.22581i) q^{98} +1.25285i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

Introduction

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