LMFDB - Embedded newform 925.2.e.c.26.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(26,925)] 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("925.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11 x^{12} - 2 x^{11} + 86 x^{10} - 18 x^{9} + 332 x^{8} - 110 x^{7} + 935 x^{6} - 290 x^{5} + \cdots + 81 $ x^14 + 11x^12 - 2x^11 + 86x^10 - 18x^9 + 332x^8 - 110x^7 + 935x^6 - 290x^5 + 985x^4 - 441x^3 + 792x^2 - 243x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.2
Root			$0.985880 - 1.70759i$ of defining polynomial
Character	$\chi$	$=$	925.26
Dual form			925.2.e.c.676.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.985880 - 1.70759i) q^{2} +(-1.32465 + 2.29437i) q^{3} +(-0.943918 + 1.63491i) q^{4} +5.22380 q^{6} +(0.391800 - 0.678617i) q^{7} -0.221160 q^{8} +(-2.00941 - 3.48041i) q^{9} -0.568551 q^{11} +(-2.50073 - 4.33139i) q^{12} +(-0.00305561 + 0.00529246i) q^{13} -1.54507 q^{14} +(2.10587 + 3.64748i) q^{16} +(1.48282 + 2.56833i) q^{17} +(-3.96208 + 6.86253i) q^{18} +(-0.517765 + 0.896796i) q^{19} +(1.03800 + 1.79787i) q^{21} +(0.560523 + 0.970854i) q^{22} +8.65194 q^{23} +(0.292960 - 0.507422i) q^{24} +0.0120498 q^{26} +2.69919 q^{27} +(0.739654 + 1.28112i) q^{28} -4.06655 q^{29} -9.38666 q^{31} +(3.93112 - 6.80889i) q^{32} +(0.753133 - 1.30446i) q^{33} +(2.92377 - 5.06412i) q^{34} +7.58689 q^{36} +(-5.80482 - 1.81772i) q^{37} +2.04182 q^{38} +(-0.00809524 - 0.0140214i) q^{39} +(2.06584 - 3.57814i) q^{41} +(2.04668 - 3.54496i) q^{42} -7.06722 q^{43} +(0.536666 - 0.929532i) q^{44} +(-8.52978 - 14.7740i) q^{46} -5.52310 q^{47} -11.1582 q^{48} +(3.19299 + 5.53041i) q^{49} -7.85691 q^{51} +(-0.00576848 - 0.00999130i) q^{52} +(-4.57125 - 7.91765i) q^{53} +(-2.66107 - 4.60911i) q^{54} +(-0.0866504 + 0.150083i) q^{56} +(-1.37172 - 2.37589i) q^{57} +(4.00913 + 6.94402i) q^{58} +(-4.62211 - 8.00573i) q^{59} +(4.99164 - 8.64577i) q^{61} +(9.25412 + 16.0286i) q^{62} -3.14915 q^{63} -7.07894 q^{64} -2.96999 q^{66} +(-5.67853 + 9.83551i) q^{67} -5.59866 q^{68} +(-11.4608 + 19.8507i) q^{69} +(-1.96400 + 3.40174i) q^{71} +(0.444402 + 0.769726i) q^{72} -16.5499 q^{73} +(2.61893 + 11.7043i) q^{74} +(-0.977456 - 1.69300i) q^{76} +(-0.222758 + 0.385829i) q^{77} +(-0.0159619 + 0.0276468i) q^{78} +(-5.45167 + 9.44257i) q^{79} +(2.45275 - 4.24830i) q^{81} -8.14668 q^{82} +(0.430541 + 0.745719i) q^{83} -3.91914 q^{84} +(6.96743 + 12.0679i) q^{86} +(5.38677 - 9.33017i) q^{87} +0.125741 q^{88} +(0.143625 + 0.248765i) q^{89} +(0.00239437 + 0.00414717i) q^{91} +(-8.16673 + 14.1452i) q^{92} +(12.4341 - 21.5364i) q^{93} +(5.44512 + 9.43122i) q^{94} +(10.4147 + 18.0388i) q^{96} +4.33052 q^{97} +(6.29580 - 10.9046i) q^{98} +(1.14245 + 1.97879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{3} - 8 q^{4} - 4 q^{6} - 6 q^{8} - 13 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 20 q^{14} + 2 q^{16} + 3 q^{17} + 6 q^{18} - 14 q^{19} + q^{21} - 7 q^{22} + 15 q^{24} - 22 q^{26} + 14 q^{27}+ \cdots + 56 q^{99}+O(q^{100}) $ 14 * q + 2 * q^3 - 8 * q^4 - 4 * q^6 - 6 * q^8 - 13 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 20 * q^14 + 2 * q^16 + 3 * q^17 + 6 * q^18 - 14 * q^19 + q^21 - 7 * q^22 + 15 * q^24 - 22 * q^26 + 14 * q^27 - 9 * q^28 - 12 * q^29 - 4 * q^32 + 11 * q^33 + 33 * q^34 + 40 * q^36 - 18 * q^37 + 4 * q^38 - 25 * q^39 - 7 * q^41 + 29 * q^42 - 38 * q^43 - 19 * q^44 - 14 * q^46 - 8 * q^47 - 36 * q^48 + 5 * q^49 + 58 * q^51 + 8 * q^52 + 6 * q^53 - 9 * q^54 - 25 * q^56 + 44 * q^57 + 12 * q^58 + 2 * q^59 - 4 * q^61 + 25 * q^62 - 10 * q^63 - 62 * q^64 - 2 * q^66 + 8 * q^67 - 26 * q^68 - 11 * q^69 + 33 * q^71 - 43 * q^72 + 18 * q^74 - 12 * q^76 + 5 * q^77 + 22 * q^78 - 9 * q^79 - 35 * q^81 - 152 * q^82 + 11 * q^83 - 80 * q^84 + 17 * q^86 + 29 * q^87 - 40 * q^88 - 12 * q^89 - 24 * q^91 + 7 * q^92 + 47 * q^93 + 10 * q^94 - 15 * q^96 - 30 * q^97 - 54 * q^98 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.985880	−	1.70759i	−0.697122	−	1.20745i	−0.969460	−	0.245250i	$-0.921130\pi$
$2$	−0.985880	−	1.70759i	−0.697122	−	1.20745i	0.272338	−	0.962202i	$-0.412203\pi$
$3$	−1.32465	+	2.29437i	−0.764789	+	1.32465i	0.175569	+	0.984467i	$0.443823\pi$
$3$	−1.32465	+	2.29437i	−0.764789	+	1.32465i	−0.940358	+	0.340186i	$0.889510\pi$
$4$	−0.943918	+	1.63491i	−0.471959	+	0.817457i
$5$		0			0
$5$		0			0
$6$	5.22380			2.13261
$7$	0.391800	−	0.678617i	0.148086	−	0.256493i	−0.782434	−	0.622734i	$-0.786022\pi$
$7$	0.391800	−	0.678617i	0.148086	−	0.256493i	0.930520	+	0.366241i	$0.119355\pi$
$8$	−0.221160			−0.0781918
$9$	−2.00941	−	3.48041i	−0.669805	−	1.16014i
$10$		0			0
$11$	−0.568551			−0.171425			−0.0857123	−	0.996320i	$-0.527317\pi$
$11$	−0.568551			−0.171425			−0.0857123	+	0.996320i	$0.527317\pi$
$12$	−2.50073	−	4.33139i	−0.721898	−	1.25036i
$13$	−0.00305561	+	0.00529246i	−0.000847472	+	0.00146787i	−0.866449	−	0.499266i	$-0.833603\pi$
$13$	−0.00305561	+	0.00529246i	−0.000847472	+	0.00146787i	0.865601	+	0.500734i	$0.166936\pi$
$14$	−1.54507			−0.412937
$15$		0			0
$16$	2.10587	+	3.64748i	0.526468	+	0.911870i
$17$	1.48282	+	2.56833i	0.359638	+	0.622911i	0.987900	−	0.155091i	$-0.0495670\pi$
$17$	1.48282	+	2.56833i	0.359638	+	0.622911i	−0.628263	+	0.778001i	$0.716234\pi$
$18$	−3.96208	+	6.86253i	−0.933871	+	1.61751i
$19$	−0.517765	+	0.896796i	−0.118783	+	0.205739i	−0.919286	−	0.393591i	$-0.871233\pi$
$19$	−0.517765	+	0.896796i	−0.118783	+	0.205739i	0.800502	+	0.599330i	$0.204566\pi$
$20$		0			0
$21$	1.03800	+	1.79787i	0.226510	+	0.392326i
$22$	0.560523	+	0.970854i	0.119504	+	0.206987i
$23$	8.65194			1.80405			0.902027	−	0.431679i	$-0.142079\pi$
$23$	8.65194			1.80405			0.902027	+	0.431679i	$0.142079\pi$
$24$	0.292960	−	0.507422i	0.0598003	−	0.103577i
$25$		0			0
$26$	0.0120498			0.00236317
$27$	2.69919			0.519459
$28$	0.739654	+	1.28112i	0.139781	+	0.242109i
$29$	−4.06655			−0.755140			−0.377570	−	0.925981i	$-0.623240\pi$
$29$	−4.06655			−0.755140			−0.377570	+	0.925981i	$0.623240\pi$
$30$		0			0
$31$	−9.38666			−1.68589			−0.842947	−	0.537997i	$-0.819181\pi$
$31$	−9.38666			−1.68589			−0.842947	+	0.537997i	$0.819181\pi$
$32$	3.93112	−	6.80889i	0.694930	−	1.20365i
$33$	0.753133	−	1.30446i	0.131104	−	0.227078i
$34$	2.92377	−	5.06412i	0.501423	−	0.868490i
$35$		0			0
$36$	7.58689			1.26448
$37$	−5.80482	−	1.81772i	−0.954306	−	0.298831i
$37$	−5.80482	−	1.81772i	−0.954306	−	0.298831i
$38$	2.04182			0.331227
$39$	−0.00809524	−	0.0140214i	−0.00129628	−	0.00224521i
$40$		0			0
$41$	2.06584	−	3.57814i	0.322630	−	0.558811i	−0.658400	−	0.752668i	$-0.728766\pi$
$41$	2.06584	−	3.57814i	0.322630	−	0.558811i	0.981030	+	0.193857i	$0.0620997\pi$
$42$	2.04668	−	3.54496i	0.315810	−	0.546999i
$43$	−7.06722			−1.07774			−0.538870	−	0.842389i	$-0.681149\pi$
$43$	−7.06722			−1.07774			−0.538870	+	0.842389i	$0.681149\pi$
$44$	0.536666	−	0.929532i	0.0809054	−	0.140132i
$45$		0			0
$46$	−8.52978	−	14.7740i	−1.25765	−	2.17831i
$47$	−5.52310			−0.805628			−0.402814	−	0.915282i	$-0.631968\pi$
$47$	−5.52310			−0.805628			−0.402814	+	0.915282i	$0.631968\pi$
$48$	−11.1582			−1.61055
$49$	3.19299	+	5.53041i	0.456141	+	0.790059i
$50$		0			0
$51$	−7.85691			−1.10019
$52$	−0.00576848	−	0.00999130i	−0.000799945	−	0.00138554i
$53$	−4.57125	−	7.91765i	−0.627910	−	1.08757i	−0.987970	−	0.154643i	$-0.950577\pi$
$53$	−4.57125	−	7.91765i	−0.627910	−	1.08757i	0.360060	−	0.932929i	$-0.382756\pi$
$54$	−2.66107	−	4.60911i	−0.362126	−	0.627221i
$55$		0			0
$56$	−0.0866504	+	0.150083i	−0.0115792	+	0.0200557i
$57$	−1.37172	−	2.37589i	−0.181689	−	0.314694i
$58$	4.00913	+	6.94402i	0.526425	+	0.911795i
$59$	−4.62211	−	8.00573i	−0.601747	−	1.04226i	−0.992556	−	0.121785i	$-0.961138\pi$
$59$	−4.62211	−	8.00573i	−0.601747	−	1.04226i	0.390809	−	0.920472i	$-0.372195\pi$
$60$		0			0
$61$	4.99164	−	8.64577i	0.639114	−	1.10698i	−0.346514	−	0.938045i	$-0.612635\pi$
$61$	4.99164	−	8.64577i	0.639114	−	1.10698i	0.985628	−	0.168933i	$-0.0540321\pi$
$62$	9.25412	+	16.0286i	1.17527	+	2.03563i
$63$	−3.14915			−0.396756
$64$	−7.07894			−0.884867
$65$		0			0
$66$	−2.96999			−0.365581
$67$	−5.67853	+	9.83551i	−0.693743	+	1.20160i	0.276859	+	0.960911i	$0.410706\pi$
$67$	−5.67853	+	9.83551i	−0.693743	+	1.20160i	−0.970602	+	0.240688i	$0.922627\pi$
$68$	−5.59866			−0.678937
$69$	−11.4608	+	19.8507i	−1.37972	+	2.38975i
$70$		0			0
$71$	−1.96400	+	3.40174i	−0.233084	+	0.403713i	−0.958714	−	0.284372i	$-0.908215\pi$
$71$	−1.96400	+	3.40174i	−0.233084	+	0.403713i	0.725630	+	0.688085i	$0.241548\pi$
$72$	0.444402	+	0.769726i	0.0523732	+	0.0907131i
$73$	−16.5499			−1.93701			−0.968507	−	0.248987i	$-0.919902\pi$
$73$	−16.5499			−1.93701			−0.968507	+	0.248987i	$0.919902\pi$
$74$	2.61893	+	11.7043i	0.304445	+	1.36060i
$75$		0			0
$76$	−0.977456	−	1.69300i	−0.112122	−	0.194201i
$77$	−0.222758	+	0.385829i	−0.0253857	+	0.0439692i
$78$	−0.0159619	+	0.0276468i	−0.00180732	+	0.00313038i
$79$	−5.45167	+	9.44257i	−0.613361	+	1.06237i	0.377309	+	0.926087i	$0.376849\pi$
$79$	−5.45167	+	9.44257i	−0.613361	+	1.06237i	−0.990670	+	0.136284i	$0.956484\pi$
$80$		0			0
$81$	2.45275	−	4.24830i	0.272528	−	0.472033i
$82$	−8.14668			−0.899650
$83$	0.430541	+	0.745719i	0.0472580	+	0.0818533i	0.888687	−	0.458515i	$-0.151618\pi$
$83$	0.430541	+	0.745719i	0.0472580	+	0.0818533i	−0.841429	+	0.540368i	$0.818285\pi$
$84$	−3.91914			−0.427613
$85$		0			0
$86$	6.96743	+	12.0679i	0.751317	+	1.30132i
$87$	5.38677	−	9.33017i	0.577523	−	1.00030i
$88$	0.125741			0.0134040
$89$	0.143625	+	0.248765i	0.0152242	+	0.0263691i	0.873537	−	0.486758i	$-0.161820\pi$
$89$	0.143625	+	0.248765i	0.0152242	+	0.0263691i	−0.858313	+	0.513127i	$0.828487\pi$
$90$		0			0
$91$	0.00239437	+	0.00414717i	0.000250998	+	0.000434742i
$92$	−8.16673	+	14.1452i	−0.851440	+	1.47474i
$93$	12.4341	−	21.5364i	1.28935	−	2.23323i
$94$	5.44512	+	9.43122i	0.561621	+	0.972756i
$95$		0			0
$96$	10.4147	+	18.0388i	1.06295	+	1.84108i
$97$	4.33052			0.439697			0.219849	−	0.975534i	$-0.429444\pi$
$97$	4.33052			0.439697			0.219849	+	0.975534i	$0.429444\pi$
$98$	6.29580	−	10.9046i	0.635972	−	1.10154i
$99$	1.14245	+	1.97879i	0.114821	+	0.198876i
$100$		0			0
$101$	−5.40523			−0.537840			−0.268920	−	0.963163i	$-0.586667\pi$
$101$	−5.40523			−0.537840			−0.268920	+	0.963163i	$0.586667\pi$
$102$	7.74597	+	13.4164i	0.766966	+	1.32842i
$103$	−12.2753			−1.20952			−0.604759	−	0.796409i	$-0.706731\pi$
$103$	−12.2753			−1.20952			−0.604759	+	0.796409i	$0.706731\pi$
$104$	0.000675777	−	0.00117048i	6.62654e−5	−	0.000114775i
$105$		0			0
$106$	−9.01342	+	15.6117i	−0.875460	+	1.51634i
$107$	6.84634	−	11.8582i	0.661860	−	1.14638i	−0.318266	−	0.948002i	$-0.603100\pi$
$107$	6.84634	−	11.8582i	0.661860	−	1.14638i	0.980126	−	0.198374i	$-0.0635662\pi$
$108$	−2.54781	+	4.41294i	−0.245163	+	0.424635i
$109$	−3.66237	−	6.34340i	−0.350791	−	0.607588i	0.635597	−	0.772021i	$-0.280754\pi$
$109$	−3.66237	−	6.34340i	−0.350791	−	0.607588i	−0.986388	+	0.164433i	$0.947421\pi$
$110$		0			0
$111$	11.8599	−	10.9105i	1.12569	−	1.03558i
$112$	3.30032			0.311851
$113$	−2.18762	−	3.78908i	−0.205794	−	0.356446i	0.744591	−	0.667521i	$-0.232644\pi$
$113$	−2.18762	−	3.78908i	−0.205794	−	0.356446i	−0.950386	+	0.311075i	$0.899311\pi$
$114$	−2.70470	+	4.68468i	−0.253318	+	0.438760i
$115$		0			0
$116$	3.83849	−	6.64847i	0.356395	−	0.617295i
$117$	0.0245599			0.00227056
$118$	−9.11369	+	15.7854i	−0.838983	+	1.45316i
$119$	2.32388			0.213030
$120$		0			0
$121$	−10.6767			−0.970614
$122$	−19.6846			−1.78216
$123$	5.47304	+	9.47959i	0.493488	+	0.854746i
$124$	8.86024	−	15.3464i	0.795673	−	1.37815i
$125$		0			0
$126$	3.10469	+	5.37747i	0.276587	+	0.479063i
$127$	9.77590	+	16.9324i	0.867471	+	1.50250i	0.864573	+	0.502508i	$0.167589\pi$
$127$	9.77590	+	16.9324i	0.867471	+	1.50250i	0.00289830	+	0.999996i	$0.499077\pi$
$128$	−0.883248	−	1.52983i	−0.0780689	−	0.135219i
$129$	9.36162	−	16.2148i	0.824244	−	1.42763i
$130$		0			0
$131$	−4.77698	−	8.27397i	−0.417366	−	0.722900i	0.578307	−	0.815819i	$-0.303713\pi$
$131$	−4.77698	−	8.27397i	−0.417366	−	0.722900i	−0.995674	+	0.0929193i	$0.970380\pi$
$132$	1.42179	+	2.46262i	0.123751	+	0.214343i
$133$	0.405721	+	0.702729i	0.0351804	+	0.0609343i
$134$	22.3934			1.93450
$135$		0			0
$136$	−0.327941	−	0.568011i	−0.0281207	−	0.0487065i
$137$	5.12953			0.438245			0.219123	−	0.975697i	$-0.429681\pi$
$137$	5.12953			0.438245			0.219123	+	0.975697i	$0.429681\pi$
$138$	45.1960			3.84734
$139$	5.17051	+	8.95559i	0.438557	+	0.759603i	0.997578	−	0.0695499i	$-0.0221563\pi$
$139$	5.17051	+	8.95559i	0.438557	+	0.759603i	−0.559021	+	0.829153i	$0.688823\pi$
$140$		0			0
$141$	7.31620	−	12.6720i	0.616135	−	1.06718i
$142$	7.74506			0.649951
$143$	0.00173727	−	0.00300904i	0.000145278	−	0.000251628i
$144$	8.46314	−	14.6586i	0.705262	−	1.22155i
$145$		0			0
$146$	16.3162	+	28.2604i	1.35034	+	2.33885i
$147$	−16.9184			−1.39541
$148$	8.45108	−	7.77460i	0.694675	−	0.639069i
$149$	−10.8779			−0.891149			−0.445575	−	0.895245i	$-0.647001\pi$
$149$	−10.8779			−0.891149			−0.445575	+	0.895245i	$0.647001\pi$
$150$		0			0
$151$	−0.00770952	+	0.0133533i	−0.000627392	+	0.00108667i	−0.866339	−	0.499457i	$-0.833533\pi$
$151$	−0.00770952	+	0.0133533i	−0.000627392	+	0.00108667i	0.865712	+	0.500543i	$0.166866\pi$
$152$	0.114509	−	0.198335i	0.00928790	−	0.0160871i
$153$	5.95921	−	10.3217i	0.481774	−	0.834457i
$154$	0.878451			0.0707876
$155$		0			0
$156$	0.0305650			0.00244716
$157$	−7.06603	−	12.2387i	−0.563930	−	0.976756i	−0.997148	−	0.0754667i	$-0.975955\pi$
$157$	−7.06603	−	12.2387i	−0.563930	−	0.976756i	0.433218	−	0.901289i	$-0.357378\pi$
$158$	21.4988			1.71035
$159$	24.2213			1.92088
$160$		0			0
$161$	3.38983	−	5.87136i	0.267156	−	0.462728i
$162$	−9.67249			−0.759942
$163$	10.6469	+	18.4409i	0.833926	+	1.44440i	0.894902	+	0.446264i	$0.147246\pi$
$163$	10.6469	+	18.4409i	0.833926	+	1.44440i	−0.0609751	+	0.998139i	$0.519421\pi$
$164$	3.89997	+	6.75494i	0.304536	+	0.527472i
$165$		0			0
$166$	0.848923	−	1.47038i	0.0658892	−	0.114123i
$167$	−3.98568	+	6.90340i	−0.308421	+	0.534201i	−0.978017	−	0.208524i	$-0.933134\pi$
$167$	−3.98568	+	6.90340i	−0.308421	+	0.534201i	0.669596	+	0.742726i	$0.266467\pi$
$168$	−0.229564	−	0.397616i	−0.0177112	−	0.0306767i
$169$	6.49998	+	11.2583i	0.499999	+	0.866023i
$170$		0			0
$171$	4.16162			0.318247
$172$	6.67088	−	11.5543i	0.508650	−	0.881007i
$173$	−7.45671	−	12.9154i	−0.566923	−	0.981940i	−0.996868	−	0.0790846i	$-0.974800\pi$
$173$	−7.45671	−	12.9154i	−0.566923	−	0.981940i	0.429945	−	0.902855i	$-0.358533\pi$
$174$	−21.2429			−1.61042
$175$		0			0
$176$	−1.19730	−	2.07378i	−0.0902496	−	0.156317i
$177$	24.4908			1.84084
$178$	0.283193	−	0.490505i	0.0212262	−	0.0367649i
$179$	−7.73854			−0.578406			−0.289203	−	0.957268i	$-0.593390\pi$
$179$	−7.73854			−0.578406			−0.289203	+	0.957268i	$0.593390\pi$
$180$		0			0
$181$	−6.57794	+	11.3933i	−0.488935	+	0.846859i	−0.999919	−	0.0127305i	$-0.995948\pi$
$181$	−6.57794	+	11.3933i	−0.488935	+	0.846859i	0.510984	+	0.859590i	$0.329281\pi$
$182$	0.00472113	−	0.00817723i	0.000349953	−	0.000606137i
$183$	13.2244	+	22.9053i	0.977575	+	1.69321i
$184$	−1.91346			−0.141062
$185$		0			0
$186$	−49.0340			−3.59535
$187$	−0.843061	−	1.46022i	−0.0616507	−	0.106782i
$188$	5.21336	−	9.02980i	0.380223	−	0.658566i
$189$	1.05754	−	1.83171i	0.0769248	−	0.133238i
$190$		0			0
$191$	23.2461			1.68203			0.841014	−	0.541013i	$-0.181959\pi$
$191$	23.2461			1.68203			0.841014	+	0.541013i	$0.181959\pi$
$192$	9.37714	−	16.2417i	0.676737	−	1.17214i
$193$	−5.38208			−0.387411			−0.193705	−	0.981060i	$-0.562051\pi$
$193$	−5.38208			−0.387411			−0.193705	+	0.981060i	$0.562051\pi$
$194$	−4.26937	−	7.39476i	−0.306523	−	0.530913i
$195$		0			0
$196$	−12.0557			−0.861119
$197$	−0.368609	−	0.638450i	−0.0262623	−	0.0454877i	0.852596	−	0.522571i	$-0.175027\pi$
$197$	−0.368609	−	0.638450i	−0.0262623	−	0.0454877i	−0.878858	+	0.477084i	$0.841694\pi$
$198$	2.25265	−	3.90170i	0.160089	−	0.277281i
$199$	3.52332			0.249762			0.124881	−	0.992172i	$-0.460145\pi$
$199$	3.52332			0.249762			0.124881	+	0.992172i	$0.460145\pi$
$200$		0			0
$201$	−15.0442	−	26.0573i	−1.06113	−	1.83794i
$202$	5.32890	+	9.22993i	0.374940	+	0.649416i
$203$	−1.59328	+	2.75963i	−0.111826	+	0.193688i
$204$	7.41628	−	12.8454i	0.519244	−	0.899356i
$205$		0			0
$206$	12.1019	+	20.9612i	0.843182	+	1.46043i
$207$	−17.3853	−	30.1123i	−1.20836	−	2.09295i
$208$	−0.0257389			−0.00178467
$209$	0.294376	−	0.509874i	0.0203624	−	0.0352687i
$210$		0			0
$211$	−14.6000			−1.00511			−0.502554	−	0.864546i	$-0.667606\pi$
$211$	−14.6000			−1.00511			−0.502554	+	0.864546i	$0.667606\pi$
$212$	17.2596			1.18539
$213$	−5.20323	−	9.01226i	−0.356520	−	0.617510i
$214$	−26.9987			−1.84559
$215$		0			0
$216$	−0.596952			−0.0406174
$217$	−3.67769	+	6.36995i	−0.249658	+	0.432420i
$218$	−7.22130	+	12.5077i	−0.489088	+	0.847126i
$219$	21.9228	−	37.9714i	1.48141	−	2.56587i
$220$		0			0
$221$	−0.0181237			−0.00121913
$222$	−30.3232	−	9.49538i	−2.03516	−	0.637288i
$223$	−15.9258			−1.06647			−0.533236	−	0.845967i	$-0.679024\pi$
$223$	−15.9258			−1.06647			−0.533236	+	0.845967i	$0.679024\pi$
$224$	−3.08042	−	5.33545i	−0.205819	−	0.356490i
$225$		0			0
$226$	−4.31347	+	7.47115i	−0.286928	+	0.496973i
$227$	7.45104	−	12.9056i	0.494543	−	0.856573i	−0.505438	−	0.862863i	$-0.668669\pi$
$227$	7.45104	−	12.9056i	0.494543	−	0.856573i	0.999980	+	0.00629015i	$0.00200223\pi$
$228$	5.17916			0.342998
$229$	3.19623	−	5.53604i	0.211213	−	0.365832i	−0.740881	−	0.671636i	$-0.765592\pi$
$229$	3.19623	−	5.53604i	0.211213	−	0.365832i	0.952094	+	0.305804i	$0.0989253\pi$
$230$		0			0
$231$	−0.590155	−	1.02218i	−0.0388293	−	0.0672544i
$232$	0.899359			0.0590458
$233$	11.8008			0.773094			0.386547	−	0.922270i	$-0.373668\pi$
$233$	11.8008			0.773094			0.386547	+	0.922270i	$0.373668\pi$
$234$	−0.0242131	−	0.0419383i	−0.00158286	−	0.00274159i
$235$		0			0
$236$	17.4516			1.13600
$237$	−14.4431	−	25.0163i	−0.938183	−	1.62498i
$238$	−2.29107	−	3.96825i	−0.148508	−	0.257223i
$239$	1.91458	+	3.31616i	0.123844	+	0.214504i	0.921281	−	0.388899i	$-0.127144\pi$
$239$	1.91458	+	3.31616i	0.123844	+	0.214504i	−0.797436	+	0.603403i	$0.793811\pi$
$240$		0			0
$241$	9.66017	−	16.7319i	0.622266	−	1.07780i	−0.366797	−	0.930301i	$-0.619545\pi$
$241$	9.66017	−	16.7319i	0.622266	−	1.07780i	0.989063	−	0.147495i	$-0.0471212\pi$
$242$	10.5260	+	18.2316i	0.676636	+	1.17197i
$243$	10.5469	+	18.2677i	0.676583	+	1.17188i
$244$	9.42340	+	16.3218i	0.603271	+	1.04490i
$245$		0			0
$246$	10.7915	−	18.6915i	0.688043	−	1.19172i
$247$	−0.00316417	−	0.00548051i	−0.000201331	−	0.000348716i
$248$	2.07595			0.131823
$249$	−2.28127			−0.144570
$250$		0			0
$251$	−0.889477			−0.0561433			−0.0280716	−	0.999606i	$-0.508937\pi$
$251$	−0.889477			−0.0561433			−0.0280716	+	0.999606i	$0.508937\pi$
$252$	2.97254	−	5.14859i	0.187253	−	0.324331i
$253$	−4.91907			−0.309259
$254$	19.2757	−	33.3865i	1.20947	−	2.09486i
$255$		0			0
$256$	−8.82049	+	15.2775i	−0.551281	+	0.954846i
$257$	7.12546	+	12.3417i	0.444474	+	0.769851i	0.998015	−	0.0629705i	$-0.0200574\pi$
$257$	7.12546	+	12.3417i	0.444474	+	0.769851i	−0.553542	+	0.832821i	$0.686724\pi$
$258$	−36.9177			−2.29840
$259$	−3.50786	+	3.22707i	−0.217968	+	0.200520i
$260$		0			0
$261$	8.17139	+	14.1533i	0.505796	+	0.876065i
$262$	−9.41905	+	16.3143i	−0.581911	+	1.00790i
$263$	−12.3919	+	21.4635i	−0.764120	+	1.32349i	0.176591	+	0.984284i	$0.443493\pi$
$263$	−12.3919	+	21.4635i	−0.764120	+	1.32349i	−0.940711	+	0.339210i	$0.889840\pi$
$264$	−0.166563	+	0.288495i	−0.0102512	+	0.0177557i
$265$		0			0
$266$	0.799984	−	1.38561i	0.0490502	−	0.0849574i
$267$	−0.761012			−0.0465732
$268$	−10.7201	−	18.5678i	−0.654837	−	1.13421i
$269$	−9.55497			−0.582577			−0.291289	−	0.956635i	$-0.594084\pi$
$269$	−9.55497			−0.582577			−0.291289	+	0.956635i	$0.594084\pi$
$270$		0			0
$271$	−4.23718	−	7.33902i	−0.257391	−	0.445814i	0.708151	−	0.706061i	$-0.249529\pi$
$271$	−4.23718	−	7.33902i	−0.257391	−	0.445814i	−0.965542	+	0.260247i	$0.916196\pi$
$272$	−6.24528	+	10.8171i	−0.378676	+	0.655886i
$273$	−0.0126868			−0.000767843
$274$	−5.05710	−	8.75915i	−0.305510	−	0.529160i
$275$		0			0
$276$	−21.6362	−	37.4749i	−1.30234	−	2.25573i
$277$	14.6366	−	25.3513i	0.879426	−	1.52321i	0.0274542	−	0.999623i	$-0.491260\pi$
$277$	14.6366	−	25.3513i	0.879426	−	1.52321i	0.851972	−	0.523588i	$-0.175407\pi$
$278$	10.1950	−	17.6583i	0.611456	−	1.05907i
$279$	18.8617	+	32.6694i	1.12922	+	1.95587i
$280$		0			0
$281$	7.29433	+	12.6342i	0.435143	+	0.753690i	0.997307	−	0.0733354i	$-0.0233644\pi$
$281$	7.29433	+	12.6342i	0.435143	+	0.753690i	−0.562164	+	0.827026i	$0.690031\pi$
$282$	−28.8516			−1.71809
$283$	9.29663	−	16.1022i	0.552627	−	0.957178i	−0.445457	−	0.895303i	$-0.646959\pi$
$283$	9.29663	−	16.1022i	0.552627	−	0.957178i	0.998084	−	0.0618747i	$-0.0197079\pi$
$284$	−3.70771	−	6.42193i	−0.220012	−	0.381072i
$285$		0			0
$286$	−0.00685095			−0.000405105
$287$	−1.61879	−	2.80383i	−0.0955542	−	0.165505i
$288$	−31.5970			−1.86187
$289$	4.10246	−	7.10568i	0.241321	−	0.417981i
$290$		0			0
$291$	−5.73643	+	9.93579i	−0.336276	+	0.582446i
$292$	15.6217	−	27.0576i	0.914191	−	1.58343i
$293$	2.90144	−	5.02544i	0.169504	−	0.293589i	−0.768742	−	0.639559i	$-0.779117\pi$
$293$	2.90144	−	5.02544i	0.169504	−	0.293589i	0.938246	+	0.345970i	$0.112450\pi$
$294$	16.6795	+	28.8898i	0.972769	+	1.68488i
$295$		0			0
$296$	1.28379	+	0.402006i	0.0746190	+	0.0233661i
$297$	−1.53462			−0.0890480
$298$	10.7243	+	18.5750i	0.621240	+	1.07602i
$299$	−0.0264369	+	0.0457901i	−0.00152889	+	0.00264811i
$300$		0			0
$301$	−2.76894	+	4.79594i	−0.159599	+	0.276433i
$302$	0.0304027			0.00174948
$303$	7.16005	−	12.4016i	0.411334	−	0.712452i
$304$	−4.36139			−0.250143
$305$		0			0
$306$	−23.5003			−1.34342
$307$	21.6882			1.23781			0.618907	−	0.785464i	$-0.287576\pi$
$307$	21.6882			1.23781			0.618907	+	0.785464i	$0.287576\pi$
$308$	−0.420531	−	0.728381i	−0.0239620	−	0.0415034i
$309$	16.2605	−	28.1640i	0.925026	−	1.60219i
$310$		0			0
$311$	−3.51294	−	6.08460i	−0.199201	−	0.345026i	0.749069	−	0.662492i	$-0.230501\pi$
$311$	−3.51294	−	6.08460i	−0.199201	−	0.345026i	−0.948270	+	0.317466i	$0.897168\pi$
$312$	0.00179034	+	0.00310096i	0.000101358	+	0.000175557i
$313$	−11.8855	−	20.5863i	−0.671808	−	1.16361i	−0.977391	−	0.211440i	$-0.932185\pi$
$313$	−11.8855	−	20.5863i	−0.671808	−	1.16361i	0.305583	−	0.952165i	$-0.401149\pi$
$314$	−13.9325	+	24.1318i	−0.786257	+	1.36184i
$315$		0			0
$316$	−10.2919	−	17.8260i	−0.578962	−	1.00279i
$317$	11.5553	+	20.0144i	0.649012	+	1.12412i	0.983359	+	0.181672i	$0.0581509\pi$
$317$	11.5553	+	20.0144i	0.649012	+	1.12412i	−0.334347	+	0.942450i	$0.608516\pi$
$318$	−23.8793	−	41.3602i	−1.33908	−	2.31936i
$319$	2.31204			0.129450
$320$		0			0
$321$	18.1381	+	31.4160i	1.01237	+	1.75347i
$322$	−13.3679			−0.744962
$323$	−3.07102			−0.170876
$324$	4.63040	+	8.02009i	0.257244	+	0.445560i
$325$		0			0
$326$	20.9930	−	36.3610i	1.16270	−	2.01385i
$327$	19.4055			1.07312
$328$	−0.456881	+	0.791341i	−0.0252270	+	0.0436945i
$329$	−2.16395	+	3.74807i	−0.119303	+	0.206638i
$330$		0			0
$331$	5.23346	+	9.06462i	0.287657	+	0.498237i	0.973250	−	0.229748i	$-0.0737904\pi$
$331$	5.23346	+	9.06462i	0.287657	+	0.498237i	−0.685593	+	0.727985i	$0.740457\pi$
$332$	−1.62558			−0.0892154
$333$	5.33789	+	23.8557i	0.292515	+	1.30728i
$334$	15.7176			0.860029
$335$		0			0
$336$	−4.37179	+	7.57215i	−0.238500	+	0.413095i
$337$	−5.26707	+	9.12282i	−0.286915	+	0.496952i	−0.973072	−	0.230502i	$-0.925963\pi$
$337$	−5.26707	+	9.12282i	−0.286915	+	0.496952i	0.686157	+	0.727454i	$0.259297\pi$
$338$	12.8164	−	22.1987i	0.697120	−	1.20745i
$339$	11.5914			0.629557
$340$		0			0
$341$	5.33680			0.289004
$342$	−4.10286	−	7.10635i	−0.221857	−	0.384268i
$343$	10.4892			0.566366
$344$	1.56299			0.0842705
$345$		0			0
$346$	−14.7028	+	25.4661i	−0.790430	+	1.36906i
$347$	21.5633			1.15758			0.578789	−	0.815478i	$-0.303526\pi$
$347$	21.5633			1.15758			0.578789	+	0.815478i	$0.303526\pi$
$348$	10.1693	+	17.6138i	0.545134	+	0.944200i
$349$	−5.28986	−	9.16231i	−0.283160	−	0.490447i	0.689001	−	0.724760i	$-0.258049\pi$
$349$	−5.28986	−	9.16231i	−0.283160	−	0.490447i	−0.972161	+	0.234313i	$0.924716\pi$
$350$		0			0
$351$	−0.00824765	+	0.0142853i	−0.000440227	+	0.000762495i
$352$	−2.23504	+	3.87120i	−0.119128	+	0.206336i
$353$	5.49760	+	9.52213i	0.292608	+	0.506812i	0.974426	−	0.224710i	$-0.0721436\pi$
$353$	5.49760	+	9.52213i	0.292608	+	0.506812i	−0.681818	+	0.731522i	$0.738810\pi$
$354$	−24.1450	−	41.8203i	−1.28329	−	2.22272i
$355$		0			0
$356$	−0.542280			−0.0287408
$357$	−3.07834	+	5.33184i	−0.162923	+	0.282191i
$358$	7.62927	+	13.2143i	0.403220	+	0.698397i
$359$	−34.6984			−1.83131			−0.915657	−	0.401961i	$-0.868329\pi$
$359$	−34.6984			−1.83131			−0.915657	+	0.401961i	$0.868329\pi$
$360$		0			0
$361$	8.96384	+	15.5258i	0.471781	+	0.817149i
$362$	25.9402			1.36339
$363$	14.1430	−	24.4964i	0.742315	−	1.28573i
$364$	−0.00904036			−0.000473844
$365$		0			0
$366$	26.0753	−	45.1638i	1.36298	−	2.36075i
$367$	−5.77858	+	10.0088i	−0.301639	+	0.522455i	−0.976507	−	0.215484i	$-0.930867\pi$
$367$	−5.77858	+	10.0088i	−0.301639	+	0.522455i	0.674868	+	0.737938i	$0.264201\pi$
$368$	18.2199	+	31.5578i	0.949778	+	1.64506i
$369$	−16.6045			−0.864396
$370$		0			0
$371$	−7.16407			−0.371940
$372$	23.4735	+	40.6573i	1.21704	+	2.10798i
$373$	5.12736	−	8.88085i	0.265485	−	0.459833i	−0.702206	−	0.711974i	$-0.747801\pi$
$373$	5.12736	−	8.88085i	0.265485	−	0.459833i	0.967691	+	0.252141i	$0.0811347\pi$
$374$	−1.66231	+	2.87921i	−0.0859562	+	0.148881i
$375$		0			0
$376$	1.22149			0.0629935
$377$	0.0124258	−	0.0215221i	0.000639960	−	0.00110844i
$378$	−4.17043			−0.214504
$379$	−2.67929	−	4.64067i	−0.137626	−	0.238375i	0.788972	−	0.614430i	$-0.210614\pi$
$379$	−2.67929	−	4.64067i	−0.137626	−	0.238375i	−0.926598	+	0.376055i	$0.877281\pi$
$380$		0			0
$381$	−51.7987			−2.65373
$382$	−22.9179	−	39.6949i	−1.17258	−	2.03097i
$383$	−11.6302	+	20.1441i	−0.594276	+	1.02932i	0.399372	+	0.916789i	$0.369228\pi$
$383$	−11.6302	+	20.1441i	−0.594276	+	1.02932i	−0.993649	+	0.112528i	$0.964105\pi$
$384$	4.67999			0.238825
$385$		0			0
$386$	5.30609	+	9.19041i	0.270073	+	0.467780i
$387$	14.2010	+	24.5968i	0.721876	+	1.25033i
$388$	−4.08765	+	7.08002i	−0.207519	+	0.359434i
$389$	−8.61377	+	14.9195i	−0.436735	+	0.756448i	−0.997435	−	0.0715711i	$-0.977199\pi$
$389$	−8.61377	+	14.9195i	−0.436735	+	0.756448i	0.560700	+	0.828019i	$0.310532\pi$
$390$		0			0
$391$	12.8293	+	22.2210i	0.648806	+	1.12377i
$392$	−0.706160	−	1.22311i	−0.0356665	−	0.0617762i
$393$	25.3114			1.27679
$394$	−0.726809	+	1.25887i	−0.0366161	+	0.0634210i
$395$		0			0
$396$	−4.31353			−0.216763
$397$	−30.2268			−1.51704			−0.758520	−	0.651650i	$-0.774077\pi$
$397$	−30.2268			−1.51704			−0.758520	+	0.651650i	$0.774077\pi$
$398$	−3.47357	−	6.01640i	−0.174114	−	0.301575i
$399$	−2.14976			−0.107622
$400$		0			0
$401$	12.0733			0.602909			0.301455	−	0.953480i	$-0.402528\pi$
$401$	12.0733			0.602909			0.301455	+	0.953480i	$0.402528\pi$
$402$	−29.6635	+	51.3787i	−1.47948	+	2.56254i
$403$	0.0286819	−	0.0496786i	0.00142875	−	0.00247467i
$404$	5.10209	−	8.83708i	0.253839	−	0.439661i
$405$		0			0
$406$	6.28311			0.311826
$407$	3.30034	+	1.03346i	0.163592	+	0.0512269i
$408$	1.73763			0.0860257
$409$	−0.454742	−	0.787637i	−0.0224856	−	0.0389461i	0.854564	−	0.519347i	$-0.173825\pi$
$409$	−0.454742	−	0.787637i	−0.0224856	−	0.0389461i	−0.877049	+	0.480401i	$0.840491\pi$
$410$		0			0
$411$	−6.79485	+	11.7690i	−0.335165	+	0.580523i
$412$	11.5868	−	20.0690i	0.570843	−	0.988729i
$413$	−7.24377			−0.356442
$414$	−34.2797	+	59.3742i	−1.68476	+	2.91808i
$415$		0			0
$416$	0.0240239	+	0.0416106i	0.00117787	+	0.00204013i
$417$	−27.3966			−1.34162
$418$	−1.16088			−0.0567804
$419$	−2.72019	−	4.71151i	−0.132890	−	0.230172i	0.791899	−	0.610652i	$-0.209092\pi$
$419$	−2.72019	−	4.71151i	−0.132890	−	0.230172i	−0.924789	+	0.380479i	$0.875759\pi$
$420$		0			0
$421$	32.1650			1.56762			0.783812	−	0.620998i	$-0.213273\pi$
$421$	32.1650			1.56762			0.783812	+	0.620998i	$0.213273\pi$
$422$	14.3939	+	24.9310i	0.700684	+	1.21362i
$423$	11.0982	+	19.2226i	0.539613	+	0.934637i
$424$	1.01098	+	1.75107i	0.0490974	+	0.0850393i
$425$		0			0
$426$	−10.2595	+	17.7700i	−0.497076	+	0.860960i
$427$	−3.91145	−	6.77483i	−0.189288	−	0.327857i
$428$	12.9248	+	22.3864i	0.624742	+	1.08209i
$429$	0.00460255	+	0.00797186i	0.000222213	+	0.000384885i
$430$		0			0
$431$	−1.28753	+	2.23008i	−0.0620184	+	0.107419i	−0.895367	−	0.445328i	$-0.853087\pi$
$431$	−1.28753	+	2.23008i	−0.0620184	+	0.107419i	0.833349	+	0.552747i	$0.186420\pi$
$432$	5.68414	+	9.84523i	0.273478	+	0.473679i
$433$	−32.5699			−1.56521			−0.782605	−	0.622519i	$-0.786109\pi$
$433$	−32.5699			−1.56521			−0.782605	+	0.622519i	$0.786109\pi$
$434$	14.5031			0.696169
$435$		0			0
$436$	13.8279			0.662236
$437$	−4.47968	+	7.75903i	−0.214292	+	0.371165i
$438$	−86.4531			−4.13089
$439$	−19.0316	+	32.9636i	−0.908326	+	1.57327i	−0.0919376	+	0.995765i	$0.529306\pi$
$439$	−19.0316	+	32.9636i	−0.908326	+	1.57327i	−0.816389	+	0.577503i	$0.804027\pi$
$440$		0			0
$441$	12.8321	−	22.2258i	0.611050	−	1.05837i
$442$	0.0178678	+	0.0309479i	0.000849884	+	0.00147204i
$443$	9.79268			0.465264			0.232632	−	0.972565i	$-0.425266\pi$
$443$	9.79268			0.465264			0.232632	+	0.972565i	$0.425266\pi$
$444$	6.64304	+	29.6885i	0.315265	+	1.40896i
$445$		0			0
$446$	15.7009	+	27.1948i	0.743461	+	1.28771i
$447$	14.4094	−	24.9578i	0.681541	−	1.18046i
$448$	−2.77353	+	4.80389i	−0.131037	+	0.226963i
$449$	−6.14383	+	10.6414i	−0.289945	+	0.502200i	−0.973796	−	0.227422i	$-0.926970\pi$
$449$	−6.14383	+	10.6414i	−0.289945	+	0.502200i	0.683851	+	0.729622i	$0.260304\pi$
$450$		0			0
$451$	−1.17454	+	2.03435i	−0.0553067	+	0.0957940i
$452$	8.25975			0.388506
$453$	−0.0204249	−	0.0353770i	−0.000959645	−	0.00166215i
$454$	−29.3833			−1.37903
$455$		0			0
$456$	0.303369	+	0.525451i	0.0142066	+	0.0246065i
$457$	−5.60472	+	9.70766i	−0.262178	+	0.454105i	−0.966820	−	0.255457i	$-0.917774\pi$
$457$	−5.60472	+	9.70766i	−0.262178	+	0.454105i	0.704643	+	0.709562i	$0.251107\pi$
$458$	−12.6044			−0.588965
$459$	4.00242	+	6.93239i	0.186817	+	0.323576i
$460$		0			0
$461$	−11.0096	−	19.0691i	−0.512767	−	0.888138i	−0.999890	−	0.0148053i	$-0.995287\pi$
$461$	−11.0096	−	19.0691i	−0.512767	−	0.888138i	0.487123	−	0.873333i	$-0.338046\pi$
$462$	−1.16364	+	2.01549i	−0.0541376	+	0.0937691i
$463$	10.4737	−	18.1409i	0.486752	−	0.843079i	−0.513132	−	0.858310i	$-0.671515\pi$
$463$	10.4737	−	18.1409i	0.486752	−	0.843079i	0.999884	+	0.0152306i	$0.00484823\pi$
$464$	−8.56365	−	14.8327i	−0.397557	−	0.688590i
$465$		0			0
$466$	−11.6341	−	20.1509i	−0.538941	−	0.933473i
$467$	1.71804			0.0795016			0.0397508	−	0.999210i	$-0.487344\pi$
$467$	1.71804			0.0795016			0.0397508	+	0.999210i	$0.487344\pi$
$468$	−0.0231825	+	0.0401533i	−0.00107161	+	0.00185609i
$469$	4.44970	+	7.70710i	0.205468	+	0.355881i
$470$		0			0
$471$	37.4401			1.72515
$472$	1.02222	+	1.77055i	0.0470517	+	0.0814960i
$473$	4.01808			0.184751
$474$	−28.4784	+	49.3260i	−1.30806	+	2.26562i
$475$		0			0
$476$	−2.19355	+	3.79935i	−0.100541	+	0.174143i
$477$	−18.3711	+	31.8196i	−0.841154	+	1.45692i
$478$	3.77510	−	6.53867i	0.172669	−	0.299072i
$479$	16.5168	+	28.6080i	0.754674	+	1.30713i	0.945536	+	0.325517i	$0.105538\pi$
$479$	16.5168	+	28.6080i	0.754674	+	1.30713i	−0.190863	+	0.981617i	$0.561128\pi$
$480$		0			0
$481$	0.0273574	−	0.0251676i	0.00124739	−	0.00114754i
$482$	−38.0951			−1.73518
$483$	8.98070	+	15.5550i	0.408636	+	0.707778i
$484$	10.0780	−	17.4556i	0.458090	−	0.793435i
$485$		0			0
$486$	20.7959	−	36.0196i	0.943322	−	1.63388i
$487$	−13.4557			−0.609734			−0.304867	−	0.952395i	$-0.598612\pi$
$487$	−13.4557			−0.609734			−0.304867	+	0.952395i	$0.598612\pi$
$488$	−1.10395	+	1.91210i	−0.0499735	+	0.0865566i
$489$	−56.4136			−2.55111
$490$		0			0
$491$	13.8635			0.625650			0.312825	−	0.949811i	$-0.398725\pi$
$491$	13.8635			0.625650			0.312825	+	0.949811i	$0.398725\pi$
$492$	−20.6644			−0.931624
$493$	−6.02998	−	10.4442i	−0.271577	−	0.470385i
$494$	−0.00623899	+	0.0108062i	−0.000280705	+	0.000486196i
$495$		0			0
$496$	−19.7671	−	34.2377i	−0.887570	−	1.53732i
$497$	1.53899	+	2.66561i	0.0690330	+	0.119569i
$498$	2.24906	+	3.89548i	0.100783	+	0.174561i
$499$	−16.1046	+	27.8939i	−0.720940	+	1.24870i	0.239684	+	0.970851i	$0.422956\pi$
$499$	−16.1046	+	27.8939i	−0.720940	+	1.24870i	−0.960624	+	0.277853i	$0.910377\pi$
$500$		0			0
$501$	−10.5593	−	18.2892i	−0.471754	−	0.817102i
$502$	0.876917	+	1.51887i	0.0391387	+	0.0677903i
$503$	19.0525	+	32.9999i	0.849510	+	1.47139i	0.881646	+	0.471911i	$0.156436\pi$
$503$	19.0525	+	32.9999i	0.849510	+	1.47139i	−0.0321365	+	0.999483i	$0.510231\pi$
$504$	0.696466			0.0310231
$505$		0			0
$506$	4.84961	+	8.39978i	0.215592	+	0.373416i
$507$	−34.4409			−1.52957
$508$	−36.9106			−1.63764
$509$	−20.2427	−	35.0613i	−0.897240	−	1.55406i	−0.831008	−	0.556261i	$-0.812236\pi$
$509$	−20.2427	−	35.0613i	−0.897240	−	1.55406i	−0.0662319	−	0.997804i	$-0.521098\pi$
$510$		0			0
$511$	−6.48423	+	11.2310i	−0.286845	+	0.496831i
$512$	31.2508			1.38110
$513$	−1.39754	+	2.42062i	−0.0617031	+	0.106873i
$514$	14.0497	−	24.3348i	0.619705	−	1.07336i
$515$		0			0
$516$	17.6732	+	30.6109i	0.778019	+	1.34757i
$517$	3.14017			0.138104
$518$	8.96885	+	2.80850i	0.394069	+	0.123398i
$519$	39.5102			1.73431
$520$		0			0
$521$	−0.919502	+	1.59262i	−0.0402841	+	0.0697742i	−0.885464	−	0.464707i	$-0.846160\pi$
$521$	−0.919502	+	1.59262i	−0.0402841	+	0.0697742i	0.845180	+	0.534481i	$0.179493\pi$
$522$	16.1120	−	27.9068i	0.705204	−	1.22145i
$523$	6.11530	−	10.5920i	0.267403	−	0.463156i	−0.700787	−	0.713370i	$-0.747168\pi$
$523$	6.11530	−	10.5920i	0.267403	−	0.463156i	0.968190	+	0.250214i	$0.0805011\pi$
$524$	18.0363			0.787919
$525$		0			0
$526$	48.8679			2.13074
$527$	−13.9188	−	24.1080i	−0.606311	−	1.05016i
$528$	6.34401			0.276088
$529$	51.8561			2.25461
$530$		0			0
$531$	−18.5755	+	32.1736i	−0.806106	+	1.39622i
$532$	−1.53187			−0.0664149
$533$	0.0126248	+	0.0218668i	0.000546840	+	0.000947155i
$534$	0.750266	+	1.29950i	0.0324672	+	0.0562348i
$535$		0			0
$536$	1.25586	−	2.17522i	0.0542451	−	0.0939552i
$537$	10.2509	−	17.7551i	0.442359	−	0.766187i
$538$	9.42006	+	16.3160i	0.406127	+	0.703433i
$539$	−1.81538	−	3.14432i	−0.0781938	−	0.135436i
$540$		0			0
$541$	−9.85561			−0.423726			−0.211863	−	0.977299i	$-0.567953\pi$
$541$	−9.85561			−0.423726			−0.211863	+	0.977299i	$0.567953\pi$
$542$	−8.35471	+	14.4708i	−0.358865	+	0.621573i
$543$	−17.4270	−	30.1844i	−0.747864	−	1.29534i
$544$	23.3166			0.999692
$545$		0			0
$546$	0.0125077	+	0.0216640i	0.000535281	+	0.000927133i
$547$	22.7670			0.973447			0.486723	−	0.873556i	$-0.338192\pi$
$547$	22.7670			0.973447			0.486723	+	0.873556i	$0.338192\pi$
$548$	−4.84185	+	8.38634i	−0.206834	+	0.358247i
$549$	−40.1211			−1.71233
$550$		0			0
$551$	2.10552	−	3.64687i	0.0896982	−	0.155362i
$552$	2.53468	−	4.39019i	0.107883	−	0.186859i
$553$	4.27193	+	7.39919i	0.181661	+	0.314646i
$554$	−57.7196			−2.45227
$555$		0			0
$556$	−19.5222			−0.827924
$557$	−21.8322	−	37.8144i	−0.925058	−	1.60225i	−0.791467	−	0.611211i	$-0.790683\pi$
$557$	−21.8322	−	37.8144i	−0.925058	−	1.60225i	−0.133591	−	0.991037i	$-0.542651\pi$
$558$	37.1907	−	64.4162i	1.57441	−	2.72695i
$559$	0.0215946	−	0.0374030i	0.000913356	−	0.00158198i
$560$		0			0
$561$	4.46706			0.188599
$562$	14.3827	−	24.9115i	0.606696	−	1.05083i
$563$	−24.4057			−1.02858			−0.514288	−	0.857617i	$-0.671944\pi$
$563$	−24.4057			−1.02858			−0.514288	+	0.857617i	$0.671944\pi$
$564$	13.8118	+	23.9227i	0.581581	+	1.00733i
$565$		0			0
$566$	−36.6614			−1.54099
$567$	−1.92198	−	3.32896i	−0.0807155	−	0.139803i
$568$	0.434358	−	0.752329i	0.0182252	−	0.0315670i
$569$	41.3282			1.73257			0.866285	−	0.499550i	$-0.166501\pi$
$569$	41.3282			1.73257			0.866285	+	0.499550i	$0.166501\pi$
$570$		0			0
$571$	−9.18338	−	15.9061i	−0.384313	−	0.665649i	0.607361	−	0.794426i	$-0.292228\pi$
$571$	−9.18338	−	15.9061i	−0.384313	−	0.665649i	−0.991674	+	0.128777i	$0.958895\pi$
$572$	0.00327968	+	0.00568057i	0.000137130	+	0.000237516i
$573$	−30.7930	+	53.3351i	−1.28640	+	2.22810i
$574$	−3.19187	+	5.52848i	−0.133226	+	0.230754i
$575$		0			0
$576$	14.2245	+	24.6376i	0.592688	+	1.02657i
$577$	9.87431	+	17.1028i	0.411073	+	0.711999i	0.995007	−	0.0998015i	$-0.0318208\pi$
$577$	9.87431	+	17.1028i	0.411073	+	0.711999i	−0.583934	+	0.811801i	$0.698487\pi$
$578$	−16.1781			−0.672922
$579$	7.12939	−	12.3485i	0.296288	−	0.513185i
$580$		0			0
$581$	0.674744			0.0279931
$582$	22.6217			0.937701
$583$	2.59899	+	4.50159i	0.107639	+	0.186437i
$584$	3.66016			0.151459
$585$		0			0
$586$	−11.4419			−0.472660
$587$	−16.4636	+	28.5157i	−0.679524	+	1.17697i	0.295601	+	0.955311i	$0.404480\pi$
$587$	−16.4636	+	28.5157i	−0.679524	+	1.17697i	−0.975125	+	0.221658i	$0.928853\pi$
$588$	15.9696	−	27.6601i	0.658575	−	1.14068i
$589$	4.86009	−	8.41792i	0.200256	−	0.346854i
$590$		0			0
$591$	1.95312			0.0803405
$592$	−5.59413	−	25.0008i	−0.229917	−	1.02753i
$593$	−16.7712			−0.688712			−0.344356	−	0.938839i	$-0.611903\pi$
$593$	−16.7712			−0.688712			−0.344356	+	0.938839i	$0.611903\pi$
$594$	1.51296	+	2.62052i	0.0620773	+	0.107521i
$595$		0			0
$596$	10.2678	−	17.7844i	0.420586	−	0.728476i
$597$	−4.66718	+	8.08379i	−0.191015	+	0.330848i
$598$	0.104255			0.00426328
$599$	−5.75661	+	9.97074i	−0.235209	+	0.407393i	−0.959333	−	0.282276i	$-0.908911\pi$
$599$	−5.75661	+	9.97074i	−0.235209	+	0.407393i	0.724125	+	0.689669i	$0.242244\pi$
$600$		0			0
$601$	−4.67853	−	8.10346i	−0.190841	−	0.330547i	0.754688	−	0.656084i	$-0.227788\pi$
$601$	−4.67853	−	8.10346i	−0.190841	−	0.330547i	−0.945529	+	0.325537i	$0.894455\pi$
$602$	10.9194			0.445040
$603$	45.6421			1.85869
$604$	−0.0145543	−	0.0252088i	−0.000592207	−	0.00102573i
$605$		0			0
$606$	−28.2358			−1.14700
$607$	4.02620	+	6.97358i	0.163418	+	0.283049i	0.936092	−	0.351754i	$-0.114415\pi$
$607$	4.02620	+	6.97358i	0.163418	+	0.283049i	−0.772674	+	0.634803i	$0.781081\pi$
$608$	4.07079	+	7.05082i	0.165092	+	0.285948i
$609$	−4.22108	−	7.31112i	−0.171047	−	0.296261i
$610$		0			0
$611$	0.0168764	−	0.0292308i	0.000682747	−	0.00118255i
$612$	11.2500	+	19.4856i	0.454755	+	0.787659i
$613$	1.71014	+	2.96205i	0.0690720	+	0.119636i	0.898493	−	0.438988i	$-0.144663\pi$
$613$	1.71014	+	2.96205i	0.0690720	+	0.119636i	−0.829421	+	0.558624i	$0.811330\pi$
$614$	−21.3820	−	37.0347i	−0.862907	−	1.49460i
$615$		0			0
$616$	0.0492652	−	0.0853298i	0.00198495	−	0.00343804i
$617$	−8.94688	−	15.4965i	−0.360188	−	0.623864i	0.627804	−	0.778372i	$-0.283954\pi$
$617$	−8.94688	−	15.4965i	−0.360188	−	0.623864i	−0.987992	+	0.154508i	$0.950621\pi$
$618$	−64.1235			−2.57943
$619$	1.02595			0.0412363			0.0206182	−	0.999787i	$-0.493437\pi$
$619$	1.02595			0.0412363			0.0206182	+	0.999787i	$0.493437\pi$
$620$		0			0
$621$	23.3532			0.937132
$622$	−6.92668	+	11.9974i	−0.277735	+	0.481050i
$623$	0.225089			0.00901798
$624$	0.0340951	−	0.0590544i	0.00136490	−	0.00236407i
$625$		0			0
$626$	−23.4353	+	40.5912i	−0.936665	+	1.62235i
$627$	0.779892	+	1.35081i	0.0311459	+	0.0539463i
$628$	26.6790			1.06461
$629$	−3.93904	−	17.6040i	−0.157060	−	0.701918i
$630$		0			0
$631$	−22.8117	−	39.5110i	−0.908119	−	1.57291i	−0.816674	−	0.577099i	$-0.804185\pi$
$631$	−22.8117	−	39.5110i	−0.908119	−	1.57291i	−0.0914449	−	0.995810i	$-0.529149\pi$
$632$	1.20569	−	2.08832i	0.0479598	−	0.0830688i
$633$	19.3400	−	33.4979i	0.768696	−	1.33142i
$634$	22.7843	−	39.4636i	0.904882	−	1.56730i
$635$		0			0
$636$	−22.8629	+	39.5998i	−0.906574	+	1.57023i
$637$	−0.0390260			−0.00154627
$638$	−2.27940	−	3.94803i	−0.0902422	−	0.156304i
$639$	15.7859			0.624482
$640$		0			0
$641$	−3.99054	−	6.91182i	−0.157617	−	0.273000i	0.776392	−	0.630250i	$-0.217048\pi$
$641$	−3.99054	−	6.91182i	−0.157617	−	0.273000i	−0.934009	+	0.357250i	$0.883714\pi$
$642$	35.7639	−	61.9449i	1.41149	−	2.44477i
$643$	11.7007			0.461432			0.230716	−	0.973021i	$-0.425893\pi$
$643$	11.7007			0.461432			0.230716	+	0.973021i	$0.425893\pi$
$644$	6.39944	+	11.0842i	0.252173	+	0.436777i
$645$		0			0
$646$	3.02766	+	5.24405i	0.119122	+	0.206325i
$647$	1.00933	−	1.74821i	0.0396807	−	0.0687291i	−0.845503	−	0.533971i	$-0.820699\pi$
$647$	1.00933	−	1.74821i	0.0396807	−	0.0687291i	0.885184	+	0.465242i	$0.154033\pi$
$648$	−0.542451	+	0.939553i	−0.0213095	+	0.0369091i
$649$	2.62790	+	4.55166i	0.103154	+	0.178668i
$650$		0			0
$651$	−9.74334	−	16.8760i	−0.381871	−	0.661421i
$652$	−40.1991			−1.57432
$653$	−15.5042	+	26.8541i	−0.606728	+	1.05088i	0.385048	+	0.922896i	$0.374185\pi$
$653$	−15.5042	+	26.8541i	−0.606728	+	1.05088i	−0.991776	+	0.127987i	$0.959149\pi$
$654$	−19.1315	−	33.1366i	−0.748099	−	1.29575i
$655$		0			0
$656$	17.4016			0.679418
$657$	33.2555	+	57.6002i	1.29742	+	2.24720i
$658$	8.53359			0.332674
$659$	6.49329	−	11.2467i	0.252943	−	0.438110i	−0.711392	−	0.702795i	$-0.751935\pi$
$659$	6.49329	−	11.2467i	0.252943	−	0.438110i	0.964335	+	0.264686i	$0.0852683\pi$
$660$		0			0
$661$	1.63687	−	2.83514i	0.0636668	−	0.110274i	−0.832435	−	0.554123i	$-0.813054\pi$
$661$	1.63687	−	2.83514i	0.0636668	−	0.110274i	0.896102	+	0.443849i	$0.146387\pi$
$662$	10.3191	−	17.8732i	0.401064	−	0.694664i
$663$	0.0240076	−	0.0415824i	0.000932379	−	0.00161493i
$664$	−0.0952184	−	0.164923i	−0.00369519	−	0.00640026i
$665$		0			0
$666$	35.4733	−	32.6338i	1.37456	−	1.26453i
$667$	−35.1836			−1.36231
$668$	−7.52431	−	13.0325i	−0.291124	−	0.504242i
$669$	21.0962	−	36.5397i	0.815626	−	1.41271i
$670$		0			0
$671$	−2.83800	+	4.91556i	−0.109560	+	0.189763i
$672$	16.3220			0.629633
$673$	11.6797	−	20.2299i	0.450220	−	0.779804i	−0.548179	−	0.836361i	$-0.684679\pi$
$673$	11.6797	−	20.2299i	0.450220	−	0.779804i	0.998399	+	0.0565566i	$0.0180121\pi$
$674$	20.7708			0.800060
$675$		0			0
$676$	−24.5418			−0.943915
$677$	15.6182			0.600255			0.300127	−	0.953899i	$-0.402971\pi$
$677$	15.6182			0.600255			0.300127	+	0.953899i	$0.402971\pi$
$678$	−11.4277	−	19.7934i	−0.438878	−	0.760159i
$679$	1.69670	−	2.93876i	0.0651132	−	0.112779i
$680$		0			0
$681$	19.7401	+	34.1908i	0.756442	+	1.31020i
$682$	−5.26144	−	9.11308i	−0.201471	−	0.348958i
$683$	−10.1178	−	17.5245i	−0.387145	−	0.670555i	0.604919	−	0.796287i	$-0.293205\pi$
$683$	−10.1178	−	17.5245i	−0.387145	−	0.670555i	−0.992064	+	0.125732i	$0.959872\pi$
$684$	−3.92823	+	6.80389i	−0.150200	+	0.260153i
$685$		0			0
$686$	−10.3411	−	17.9114i	−0.394826	−	0.683859i
$687$	8.46780	+	14.6667i	0.323067	+	0.559568i
$688$	−14.8827	−	25.7775i	−0.567396	−	0.982760i
$689$	0.0558718			0.00212855
$690$		0			0
$691$	3.30811	+	5.72981i	0.125846	+	0.217972i	0.922063	−	0.387039i	$-0.126502\pi$
$691$	3.30811	+	5.72981i	0.125846	+	0.217972i	−0.796217	+	0.605011i	$0.793169\pi$
$692$	28.1541			1.07026
$693$	1.79045			0.0680137
$694$	−21.2588	−	36.8213i	−0.806973	−	1.39772i
$695$		0			0
$696$	−1.19134	+	2.06346i	−0.0451576	+	0.0782152i
$697$	12.2531			0.464120
$698$	−10.4303	+	18.0659i	−0.394794	+	0.683803i
$699$	−15.6319	+	27.0753i	−0.591253	+	1.02408i
$700$		0			0
$701$	18.0334	+	31.2347i	0.681111	+	1.17972i	0.974642	+	0.223769i	$0.0718362\pi$
$701$	18.0334	+	31.2347i	0.681111	+	1.17972i	−0.293531	+	0.955950i	$0.594830\pi$
$702$	0.0325248			0.00122757
$703$	4.63565	−	4.26459i	0.174837	−	0.160842i
$704$	4.02474			0.151688
$705$		0			0
$706$	10.8400	−	18.7753i	0.407967	−	0.706619i
$707$	−2.11777	+	3.66808i	−0.0796468	+	0.137952i
$708$	−23.1173	+	40.0403i	−0.868800	+	1.50481i
$709$	−12.5403			−0.470960			−0.235480	−	0.971879i	$-0.575666\pi$
$709$	−12.5403			−0.470960			−0.235480	+	0.971879i	$0.575666\pi$
$710$		0			0
$711$	43.8186			1.64333
$712$	−0.0317640	−	0.0550169i	−0.00119041	−	0.00206185i
$713$	−81.2129			−3.04145
$714$	12.1395			0.454309
$715$		0			0
$716$	7.30455	−	12.6519i	0.272984	−	0.472822i
$717$	−10.1446			−0.378859
$718$	34.2085	+	59.2508i	1.27665	+	2.21122i
$719$	8.49541	+	14.7145i	0.316825	+	0.548758i	0.979824	−	0.199863i	$-0.0640497\pi$
$719$	8.49541	+	14.7145i	0.316825	+	0.548758i	−0.662998	+	0.748621i	$0.730716\pi$
$720$		0			0
$721$	−4.80945	+	8.33021i	−0.179113	+	0.310233i
$722$	17.6745	−	30.6132i	0.657778	−	1.13931i
$723$	25.5928	+	44.3279i	0.951805	+	1.64857i
$724$	−12.4181	−	21.5087i	−0.461514	−	0.799366i
$725$		0			0
$726$	−55.7732			−2.06994
$727$	11.4863	−	19.8949i	0.426004	−	0.737860i	−0.570510	−	0.821291i	$-0.693254\pi$
$727$	11.4863	−	19.8949i	0.426004	−	0.737860i	0.996514	+	0.0834305i	$0.0265876\pi$
$728$	−0.000529539	0	0.000917188i	−1.96260e−5	0	3.39933e-5i
$729$	−41.1673			−1.52472
$730$		0			0
$731$	−10.4794	−	18.1509i	−0.387596	−	0.671336i
$732$	−49.9309			−1.84550
$733$	3.10435	−	5.37689i	0.114662	−	0.198600i	−0.802983	−	0.596002i	$-0.796755\pi$
$733$	3.10435	−	5.37689i	0.114662	−	0.198600i	0.917644	+	0.397402i	$0.130088\pi$
$734$	22.7879			0.841118
$735$		0			0
$736$	34.0118	−	58.9102i	1.25369	−	2.17146i
$737$	3.22854	−	5.59199i	0.118925	−	0.205984i
$738$	16.3700	+	28.3538i	0.602590	+	1.04372i
$739$	−9.96051			−0.366403			−0.183202	−	0.983075i	$-0.558646\pi$
$739$	−9.96051			−0.366403			−0.183202	+	0.983075i	$0.558646\pi$
$740$		0			0
$741$	0.0167657			0.000615904
$742$	7.06291	+	12.2333i	0.259288	+	0.449099i
$743$	17.5892	−	30.4655i	0.645287	−	1.11767i	−0.338949	−	0.940805i	$-0.610071\pi$
$743$	17.5892	−	30.4655i	0.645287	−	1.11767i	0.984235	−	0.176864i	$-0.0565953\pi$
$744$	−2.74992	+	4.76300i	−0.100817	+	0.174620i
$745$		0			0
$746$	−20.2199			−0.740302
$747$	1.73027	−	2.99692i	0.0633073	−	0.109651i
$748$	3.18312			0.116387
$749$	−5.36479	−	9.29209i	−0.196025	−	0.339525i
$750$		0			0
$751$	−37.7381			−1.37708			−0.688542	−	0.725197i	$-0.741749\pi$
$751$	−37.7381			−1.37708			−0.688542	+	0.725197i	$0.741749\pi$
$752$	−11.6310	−	20.1454i	−0.424137	−	0.734628i
$753$	1.17825	−	2.04079i	0.0429378	−	0.0743704i
$754$	−0.0490013			−0.00178452
$755$		0			0
$756$	1.99646	+	3.45798i	0.0726107	+	0.125765i
$757$	1.19262	+	2.06568i	0.0433465	+	0.0750783i	0.886885	−	0.461991i	$-0.152865\pi$
$757$	1.19262	+	2.06568i	0.0433465	+	0.0750783i	−0.843538	+	0.537069i	$0.819531\pi$
$758$	−5.28292	+	9.15028i	−0.191884	+	0.332353i
$759$	6.51607	−	11.2862i	0.236518	−	0.409662i
$760$		0			0
$761$	−0.239975	−	0.415648i	−0.00869907	−	0.0150672i	0.861643	−	0.507515i	$-0.169436\pi$
$761$	−0.239975	−	0.415648i	−0.00869907	−	0.0150672i	−0.870342	+	0.492447i	$0.836102\pi$
$762$	51.0673	+	88.4512i	1.84997	+	3.20425i
$763$	−5.73966			−0.207790
$764$	−21.9424	+	38.0054i	−0.793849	+	1.37499i
$765$		0			0
$766$	45.8640			1.65713
$767$	0.0564933			0.00203986
$768$	−23.3682	−	40.4749i	−0.843227	−	1.46051i
$769$	−45.6865			−1.64750			−0.823748	−	0.566956i	$-0.808121\pi$
$769$	−45.6865			−1.64750			−0.823748	+	0.566956i	$0.808121\pi$
$770$		0			0
$771$	−37.7550			−1.35971
$772$	5.08025	−	8.79924i	0.182842	−	0.316692i
$773$	7.54812	−	13.0737i	0.271487	−	0.470229i	−0.697756	−	0.716336i	$-0.745818\pi$
$773$	7.54812	−	13.0737i	0.271487	−	0.470229i	0.969243	+	0.246107i	$0.0791513\pi$
$774$	28.0009	−	48.4990i	1.00647	−	1.74326i
$775$		0			0
$776$	−0.957736			−0.0343807
$777$	−2.75738	−	12.3231i	−0.0989205	−	0.442088i
$778$	33.9686			1.21783
$779$	2.13924	+	3.70527i	0.0766462	+	0.132755i
$780$		0			0
$781$	1.11663	−	1.93406i	0.0399563	−	0.0692063i
$782$	25.2963	−	43.8145i	0.904595	−	1.56680i
$783$	−10.9764			−0.392264
$784$	−13.4480	+	23.2927i	−0.480287	+	0.831882i
$785$		0			0
$786$	−24.9540	−	43.2215i	−0.890078	−	1.54166i
$787$	−20.9934			−0.748334			−0.374167	−	0.927361i	$-0.622071\pi$
$787$	−20.9934			−0.748334			−0.374167	+	0.927361i	$0.622071\pi$
$788$	1.39175			0.0495790
$789$	−32.8301	−	56.8633i	−1.16878	−	2.02439i
$790$		0			0
$791$	−3.42844			−0.121901
$792$	−0.252665	−	0.437629i	−0.00897806	−	0.0155505i
$793$	0.0305050	+	0.0528361i	0.00108326	+	0.00187627i
$794$	29.8000	+	51.6151i	1.05756	+	1.83175i
$795$		0			0
$796$	−3.32573	+	5.76033i	−0.117877	+	0.204169i
$797$	−10.4826	−	18.1564i	−0.371314	−	0.643134i	0.618454	−	0.785821i	$-0.287759\pi$
$797$	−10.4826	−	18.1564i	−0.371314	−	0.643134i	−0.989768	+	0.142687i	$0.954426\pi$
$798$	2.11940	+	3.67091i	0.0750260	+	0.129949i
$799$	−8.18979	−	14.1851i	−0.289734	−	0.501834i
$800$		0			0
$801$	0.577203	−	0.999745i	0.0203945	−	0.0353242i
$802$	−11.9028	−	20.6162i	−0.420302	−	0.727984i
$803$	9.40944			0.332052
$804$	56.8019			2.00325
$805$		0			0
$806$	−0.113108			−0.00398405
$807$	12.6570	−	21.9226i	0.445549	−	0.771713i
$808$	1.19542			0.0420547
$809$	4.09933	−	7.10024i	0.144125	−	0.249631i	−0.784921	−	0.619595i	$-0.787297\pi$
$809$	4.09933	−	7.10024i	0.144125	−	0.249631i	0.929046	+	0.369964i	$0.120630\pi$
$810$		0			0
$811$	−13.7999	+	23.9021i	−0.484579	+	0.839316i	−0.999843	−	0.0177158i	$-0.994361\pi$
$811$	−13.7999	+	23.9021i	−0.484579	+	0.839316i	0.515264	+	0.857032i	$0.327694\pi$
$812$	−3.00784	−	5.20974i	−0.105555	−	0.182826i
$813$	22.4512			0.787398
$814$	−1.48900	−	6.65450i	−0.0521893	−	0.233240i
$815$		0			0
$816$	−16.5457	−	28.6579i	−0.579214	−	1.00323i
$817$	3.65916	−	6.33785i	0.128018	−	0.221733i
$818$	−0.896643	+	1.55303i	−0.0313504	+	0.0543005i
$819$	0.00962256	−	0.0166668i	0.000336240	−	0.000582384i
$820$		0			0
$821$	5.10922	−	8.84943i	0.178313	−	0.308847i	−0.762990	−	0.646411i	$-0.776269\pi$
$821$	5.10922	−	8.84943i	0.178313	−	0.308847i	0.941303	+	0.337563i	$0.109603\pi$
$822$	26.7956			0.934604
$823$	11.1505	+	19.3132i	0.388681	+	0.673216i	0.992272	−	0.124078i	$-0.0395974\pi$
$823$	11.1505	+	19.3132i	0.388681	+	0.673216i	−0.603591	+	0.797294i	$0.706264\pi$
$824$	2.71480			0.0945744
$825$		0			0
$826$	7.14148	+	12.3694i	0.248484	+	0.430387i
$827$	−21.3714	+	37.0164i	−0.743157	+	1.28719i	0.207894	+	0.978151i	$0.433339\pi$
$827$	−21.3714	+	37.0164i	−0.743157	+	1.28719i	−0.951051	+	0.309034i	$0.899994\pi$
$828$	65.6413			2.28119
$829$	4.77897	+	8.27742i	0.165981	+	0.287487i	0.937003	−	0.349321i	$-0.113588\pi$
$829$	4.77897	+	8.27742i	0.165981	+	0.287487i	−0.771022	+	0.636808i	$0.780254\pi$
$830$		0			0
$831$	38.7768	+	67.1633i	1.34515	+	2.32987i
$832$	0.0216304	−	0.0374650i	0.000749901	−	0.00129887i
$833$	−9.46927	+	16.4013i	−0.328091	+	0.568270i
$834$	27.0097	+	46.7822i	0.935270	+	1.61993i
$835$		0			0
$836$	0.555734	+	0.962559i	0.0192204	+	0.0332908i
$837$	−25.3363			−0.875752
$838$	−5.36356	+	9.28996i	−0.185281	+	0.320916i
$839$	−16.4527	−	28.4968i	−0.568009	−	0.983820i	−0.996763	−	0.0803989i	$-0.974381\pi$
$839$	−16.4527	−	28.4968i	−0.568009	−	0.983820i	0.428754	−	0.903421i	$-0.358953\pi$
$840$		0			0
$841$	−12.4631			−0.429763
$842$	−31.7108	−	54.9247i	−1.09283	−	1.89283i
$843$	−38.6498			−1.33117
$844$	13.7812	−	23.8698i	0.474370	−	0.821633i
$845$		0			0
$846$	21.8830	−	37.9024i	0.752353	−	1.30311i
$847$	−4.18315	+	7.24543i	−0.143735	+	0.248956i
$848$	19.2530	−	33.3471i	0.661150	−	1.14514i
$849$	24.6296	+	42.6597i	0.845286	+	1.46408i
$850$		0			0
$851$	−50.2230	−	15.7268i	−1.72162	−	0.539107i
$852$	19.6457			0.673051
$853$	12.0712	+	20.9079i	0.413310	+	0.715874i	0.995249	−	0.0973579i	$-0.0310391\pi$
$853$	12.0712	+	20.9079i	0.413310	+	0.715874i	−0.581939	+	0.813232i	$0.697706\pi$
$854$	−7.71243	+	13.3583i	−0.263914	+	0.457113i
$855$		0			0
$856$	−1.51414	+	2.62256i	−0.0517521	+	0.0896372i
$857$	42.5290			1.45276			0.726382	−	0.687292i	$-0.241200\pi$
$857$	42.5290			1.45276			0.726382	+	0.687292i	$0.241200\pi$
$858$	0.00907513	−	0.0157186i	0.000309820	−	0.000536624i
$859$	51.3470			1.75194			0.875968	−	0.482370i	$-0.160224\pi$
$859$	51.3470			1.75194			0.875968	+	0.482370i	$0.160224\pi$
$860$		0			0
$861$	8.57735			0.292315
$862$	5.07742			0.172938
$863$	−24.7874	−	42.9330i	−0.843772	−	1.46146i	−0.886684	−	0.462377i	$-0.846997\pi$
$863$	−24.7874	−	42.9330i	−0.843772	−	1.46146i	0.0429117	−	0.999079i	$-0.486337\pi$
$864$	10.6108	−	18.3785i	0.360987	−	0.625248i
$865$		0			0
$866$	32.1100	+	55.6162i	1.09114	+	1.88991i
$867$	10.8687	+	18.8251i	0.369120	+	0.639335i
$868$	−6.94288	−	12.0254i	−0.235657	−	0.408169i
$869$	3.09955	−	5.36858i	0.105145	−	0.182117i
$870$		0			0
$871$	−0.0347027	−	0.0601069i	−0.00117586	−	0.00203664i
$872$	0.809968	+	1.40291i	0.0274290	+	0.0475084i
$873$	−8.70180	−	15.0720i	−0.294511	−	0.510108i
$874$	17.6657			0.597551
$875$		0			0
$876$	41.3867	+	71.6839i	1.39833	+	2.42197i
$877$	−27.7964			−0.938618			−0.469309	−	0.883034i	$-0.655497\pi$
$877$	−27.7964			−0.938618			−0.469309	+	0.883034i	$0.655497\pi$
$878$	75.0513			2.53286
$879$	7.68680	+	13.3139i	0.259269	+	0.449068i
$880$		0			0
$881$	−24.9175	+	43.1584i	−0.839492	+	1.45404i	0.0508281	+	0.998707i	$0.483814\pi$
$881$	−24.9175	+	43.1584i	−0.839492	+	1.45404i	−0.890320	+	0.455335i	$0.849519\pi$
$882$	−50.6035			−1.70391
$883$	18.5385	−	32.1096i	0.623870	−	1.08057i	−0.364889	−	0.931051i	$-0.618893\pi$
$883$	18.5385	−	32.1096i	0.623870	−	1.08057i	0.988758	−	0.149523i	$-0.0477738\pi$
$884$	0.0171073	−	0.0296307i	0.000575380	−	0.000996588i
$885$		0			0
$886$	−9.65441	−	16.7219i	−0.324346	−	0.561784i
$887$	−37.5487			−1.26076			−0.630380	−	0.776286i	$-0.717101\pi$
$887$	−37.5487			−1.26076			−0.630380	+	0.776286i	$0.717101\pi$
$888$	−2.62293	+	2.41297i	−0.0880198	+	0.0809741i
$889$	15.3208			0.513843
$890$		0			0
$891$	−1.39452	+	2.41537i	−0.0467181	+	0.0809180i
$892$	15.0327	−	26.0374i	0.503331	−	0.871795i
$893$	2.85967	−	4.95310i	0.0956953	−	0.165749i
$894$	−56.8237			−1.90047
$895$		0			0
$896$	−1.38423			−0.0462438
$897$	−0.0700395	−	0.121312i	−0.00233855	−	0.00405049i
$898$	24.2283			0.808510
$899$	38.1714			1.27309
$900$		0			0
$901$	13.5567	−	23.4810i	0.451640	−	0.782264i
$902$	4.63180			0.154222
$903$	−7.33576	−	12.7059i	−0.244119	−	0.422826i
$904$	0.483815	+	0.837992i	0.0160914	+	0.0278712i
$905$		0			0
$906$	−0.0402730	+	0.0697548i	−0.00133798	+	0.00231745i
$907$	−16.0352	+	27.7739i	−0.532441	+	0.922216i	0.466841	+	0.884341i	$0.345392\pi$
$907$	−16.0352	+	27.7739i	−0.532441	+	0.922216i	−0.999283	+	0.0378744i	$0.987941\pi$
$908$	14.0663	+	24.3636i	0.466808	+	0.808535i
$909$	10.8613	+	18.8124i	0.360248	+	0.623967i
$910$		0			0
$911$	26.0546			0.863229			0.431614	−	0.902058i	$-0.357944\pi$
$911$	26.0546			0.863229			0.431614	+	0.902058i	$0.357944\pi$
$912$	5.77733	−	10.0066i	0.191307	−	0.331353i
$913$	−0.244785	−	0.423979i	−0.00810119	−	0.0140317i
$914$	22.1023			0.731080
$915$		0			0
$916$	6.03396	+	10.4511i	0.199368	+	0.345315i
$917$	−7.48647			−0.247225
$918$	7.89181	−	13.6690i	0.260468	−	0.451145i
$919$	−5.23024			−0.172530			−0.0862648	−	0.996272i	$-0.527493\pi$
$919$	−5.23024			−0.172530			−0.0862648	+	0.996272i	$0.527493\pi$
$920$		0			0
$921$	−28.7294	+	49.7608i	−0.946666	+	1.63967i
$922$	−21.7082	+	37.5998i	−0.714923	+	1.23828i
$923$	−0.0120024	−	0.0207888i	−0.000395064	−	0.000684271i
$924$	2.22823			0.0733034
$925$		0			0
$926$	−41.3031			−1.35730
$927$	24.6661	+	42.7229i	0.810141	+	1.40320i
$928$	−15.9861	+	27.6887i	−0.524769	+	0.908927i
$929$	1.59438	−	2.76154i	0.0523099	−	0.0906033i	−0.838685	−	0.544617i	$-0.816675\pi$
$929$	1.59438	−	2.76154i	0.0523099	−	0.0906033i	0.890995	+	0.454014i	$0.150008\pi$
$930$		0			0
$931$	−6.61287			−0.216728
$932$	−11.1390	+	19.2932i	−0.364868	+	0.631971i
$933$	18.6137			0.609386
$934$	−1.69378	−	2.93372i	−0.0554223	−	0.0959943i
$935$		0			0
$936$	−0.00543166			−0.000177540
$937$	27.2384	+	47.1783i	0.889840	+	1.54125i	0.840064	+	0.542488i	$0.182518\pi$
$937$	27.2384	+	47.1783i	0.889840	+	1.54125i	0.0497763	+	0.998760i	$0.484149\pi$
$938$	8.77373	−	15.1966i	0.286473	−	0.496185i
$939$	62.9767			2.05517
$940$		0			0
$941$	22.1090	+	38.2939i	0.720733	+	1.24835i	0.960707	+	0.277566i	$0.0895277\pi$
$941$	22.1090	+	38.2939i	0.720733	+	1.24835i	−0.239974	+	0.970779i	$0.577139\pi$
$942$	−36.9115	−	63.9326i	−1.20264	−	2.08304i
$943$	17.8735	−	30.9579i	0.582042	−	1.00813i
$944$	19.4671	−	33.7181i	0.633602	−	1.09743i
$945$		0			0
$946$	−3.96134	−	6.86124i	−0.128794	−	0.223078i
$947$	5.53233	+	9.58228i	0.179777	+	0.311382i	0.941804	−	0.336163i	$-0.109129\pi$
$947$	5.53233	+	9.58228i	0.179777	+	0.311382i	−0.762027	+	0.647545i	$0.775796\pi$
$948$	54.5326			1.77114
$949$	0.0505698	−	0.0875895i	0.00164157	−	0.00284328i
$950$		0			0
$951$	−61.2272			−1.98543
$952$	−0.513949			−0.0166572
$953$	21.8629	+	37.8677i	0.708210	+	1.22666i	0.965521	+	0.260327i	$0.0838303\pi$
$953$	21.8629	+	37.8677i	0.708210	+	1.22666i	−0.257311	+	0.966329i	$0.582836\pi$
$954$	72.4467			2.34555
$955$		0			0
$956$	−7.22884			−0.233798
$957$	−3.06266	+	5.30468i	−0.0990016	+	0.171476i
$958$	32.5672	−	56.4081i	1.05220	−	1.82246i
$959$	2.00975	−	3.48099i	0.0648982	−	0.112407i
$960$		0			0
$961$	57.1094			1.84224
$962$	−0.0699471	−	0.0219032i	−0.00225519	−	0.000706187i
$963$	−55.0285			−1.77327
$964$	18.2368	+	31.5871i	0.587368	+	1.01735i
$965$		0			0
$966$	17.7078	−	30.6708i	0.569739	−	0.986816i
$967$	−14.5173	+	25.1448i	−0.466846	+	0.808601i	−0.999283	−	0.0378687i	$-0.987943\pi$
$967$	−14.5173	+	25.1448i	−0.466846	+	0.808601i	0.532437	+	0.846470i	$0.321276\pi$
$968$	2.36127			0.0758941
$969$	4.06804	−	7.04605i	0.130684	−	0.226352i
$970$		0			0
$971$	−8.15440	−	14.1238i	−0.261687	−	0.453255i	0.705003	−	0.709204i	$-0.250946\pi$
$971$	−8.15440	−	14.1238i	−0.261687	−	0.453255i	−0.966690	+	0.255949i	$0.917612\pi$
$972$	−39.8216			−1.27728
$973$	8.10323			0.259778
$974$	13.2657	+	22.9768i	0.425059	+	0.736224i
$975$		0			0
$976$	42.0470			1.34589
$977$	−9.80571	−	16.9840i	−0.313712	−	0.543366i	0.665450	−	0.746442i	$-0.268239\pi$
$977$	−9.80571	−	16.9840i	−0.313712	−	0.543366i	−0.979163	+	0.203076i	$0.934906\pi$
$978$	55.6170	+	96.3315i	1.77844	+	3.08034i
$979$	−0.0816580	−	0.141436i	−0.00260980	−	0.00452031i
$980$		0			0
$981$	−14.7184	+	25.4930i	−0.469923	+	0.813930i
$982$	−13.6677	−	23.6732i	−0.436154	−	0.755442i
$983$	−26.7020	−	46.2491i	−0.851660	−	1.47512i	−0.879709	−	0.475512i	$-0.842263\pi$
$983$	−26.7020	−	46.2491i	−0.851660	−	1.47512i	0.0280494	−	0.999607i	$-0.491070\pi$
$984$	−1.21042	−	2.09651i	−0.0385867	−	0.0668341i
$985$		0			0
$986$	−11.8897	+	20.5935i	−0.378645	+	0.655832i
$987$	−5.73297	−	9.92980i	−0.182483	−	0.316069i
$988$	0.0119469			0.000380081
$989$	−61.1452			−1.94430
$990$		0			0
$991$	47.7930			1.51820			0.759098	−	0.650976i	$-0.225640\pi$
$991$	47.7930			1.51820			0.759098	+	0.650976i	$0.225640\pi$
$992$	−36.9001	+	63.9128i	−1.17158	+	2.02923i
$993$	−27.7301			−0.879988
$994$	3.03451	−	5.25593i	0.0962490	−	0.166708i
$995$		0			0
$996$	2.15333	−	3.72968i	0.0682309	−	0.118179i
$997$	28.3125	+	49.0387i	0.896667	+	1.55307i	0.831728	+	0.555183i	$0.187352\pi$
$997$	28.3125	+	49.0387i	0.896667	+	1.55307i	0.0649381	+	0.997889i	$0.479315\pi$
$998$	63.5087			2.01033
$999$	−15.6683	−	4.90635i	−0.495723	−	0.155230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.e.c.26.2		14
5.2	odd	4		925.2.o.b.174.11		28
5.3	odd	4		925.2.o.b.174.4		28
5.4	even	2		185.2.e.a.26.6	✓	14
37.10	even	3	inner	925.2.e.c.676.2		14
185.47	odd	12		925.2.o.b.824.4		28
185.84	even	6		185.2.e.a.121.6	yes	14
185.158	odd	12		925.2.o.b.824.11		28
185.159	even	6		6845.2.a.k.1.6		7
185.174	even	6		6845.2.a.l.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.a.26.6	✓	14	5.4	even	2
185.2.e.a.121.6	yes	14	185.84	even	6
925.2.e.c.26.2		14	1.1	even	1	trivial
925.2.e.c.676.2		14	37.10	even	3	inner
925.2.o.b.174.4		28	5.3	odd	4
925.2.o.b.174.11		28	5.2	odd	4
925.2.o.b.824.4		28	185.47	odd	12
925.2.o.b.824.11		28	185.158	odd	12
6845.2.a.k.1.6		7	185.159	even	6
6845.2.a.l.1.2		7	185.174	even	6

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.985880 - 1.70759i) q^{2} +(-1.32465 + 2.29437i) q^{3} +(-0.943918 + 1.63491i) q^{4} +5.22380 q^{6} +(0.391800 - 0.678617i) q^{7} -0.221160 q^{8} +(-2.00941 - 3.48041i) q^{9} -0.568551 q^{11} +(-2.50073 - 4.33139i) q^{12} +(-0.00305561 + 0.00529246i) q^{13} -1.54507 q^{14} +(2.10587 + 3.64748i) q^{16} +(1.48282 + 2.56833i) q^{17} +(-3.96208 + 6.86253i) q^{18} +(-0.517765 + 0.896796i) q^{19} +(1.03800 + 1.79787i) q^{21} +(0.560523 + 0.970854i) q^{22} +8.65194 q^{23} +(0.292960 - 0.507422i) q^{24} +0.0120498 q^{26} +2.69919 q^{27} +(0.739654 + 1.28112i) q^{28} -4.06655 q^{29} -9.38666 q^{31} +(3.93112 - 6.80889i) q^{32} +(0.753133 - 1.30446i) q^{33} +(2.92377 - 5.06412i) q^{34} +7.58689 q^{36} +(-5.80482 - 1.81772i) q^{37} +2.04182 q^{38} +(-0.00809524 - 0.0140214i) q^{39} +(2.06584 - 3.57814i) q^{41} +(2.04668 - 3.54496i) q^{42} -7.06722 q^{43} +(0.536666 - 0.929532i) q^{44} +(-8.52978 - 14.7740i) q^{46} -5.52310 q^{47} -11.1582 q^{48} +(3.19299 + 5.53041i) q^{49} -7.85691 q^{51} +(-0.00576848 - 0.00999130i) q^{52} +(-4.57125 - 7.91765i) q^{53} +(-2.66107 - 4.60911i) q^{54} +(-0.0866504 + 0.150083i) q^{56} +(-1.37172 - 2.37589i) q^{57} +(4.00913 + 6.94402i) q^{58} +(-4.62211 - 8.00573i) q^{59} +(4.99164 - 8.64577i) q^{61} +(9.25412 + 16.0286i) q^{62} -3.14915 q^{63} -7.07894 q^{64} -2.96999 q^{66} +(-5.67853 + 9.83551i) q^{67} -5.59866 q^{68} +(-11.4608 + 19.8507i) q^{69} +(-1.96400 + 3.40174i) q^{71} +(0.444402 + 0.769726i) q^{72} -16.5499 q^{73} +(2.61893 + 11.7043i) q^{74} +(-0.977456 - 1.69300i) q^{76} +(-0.222758 + 0.385829i) q^{77} +(-0.0159619 + 0.0276468i) q^{78} +(-5.45167 + 9.44257i) q^{79} +(2.45275 - 4.24830i) q^{81} -8.14668 q^{82} +(0.430541 + 0.745719i) q^{83} -3.91914 q^{84} +(6.96743 + 12.0679i) q^{86} +(5.38677 - 9.33017i) q^{87} +0.125741 q^{88} +(0.143625 + 0.248765i) q^{89} +(0.00239437 + 0.00414717i) q^{91} +(-8.16673 + 14.1452i) q^{92} +(12.4341 - 21.5364i) q^{93} +(5.44512 + 9.43122i) q^{94} +(10.4147 + 18.0388i) q^{96} +4.33052 q^{97} +(6.29580 - 10.9046i) q^{98} +(1.14245 + 1.97879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{3} - 8 q^{4} - 4 q^{6} - 6 q^{8} - 13 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 20 q^{14} + 2 q^{16} + 3 q^{17} + 6 q^{18} - 14 q^{19} + q^{21} - 7 q^{22} + 15 q^{24} - 22 q^{26} + 14 q^{27}+ \cdots + 56 q^{99}+O(q^{100}) \) 14 * q + 2 * q^3 - 8 * q^4 - 4 * q^6 - 6 * q^8 - 13 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 20 * q^14 + 2 * q^16 + 3 * q^17 + 6 * q^18 - 14 * q^19 + q^21 - 7 * q^22 + 15 * q^24 - 22 * q^26 + 14 * q^27 - 9 * q^28 - 12 * q^29 - 4 * q^32 + 11 * q^33 + 33 * q^34 + 40 * q^36 - 18 * q^37 + 4 * q^38 - 25 * q^39 - 7 * q^41 + 29 * q^42 - 38 * q^43 - 19 * q^44 - 14 * q^46 - 8 * q^47 - 36 * q^48 + 5 * q^49 + 58 * q^51 + 8 * q^52 + 6 * q^53 - 9 * q^54 - 25 * q^56 + 44 * q^57 + 12 * q^58 + 2 * q^59 - 4 * q^61 + 25 * q^62 - 10 * q^63 - 62 * q^64 - 2 * q^66 + 8 * q^67 - 26 * q^68 - 11 * q^69 + 33 * q^71 - 43 * q^72 + 18 * q^74 - 12 * q^76 + 5 * q^77 + 22 * q^78 - 9 * q^79 - 35 * q^81 - 152 * q^82 + 11 * q^83 - 80 * q^84 + 17 * q^86 + 29 * q^87 - 40 * q^88 - 12 * q^89 - 24 * q^91 + 7 * q^92 + 47 * q^93 + 10 * q^94 - 15 * q^96 - 30 * q^97 - 54 * q^98 + 56 * q^99

Introduction

L-functions

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