LMFDB - Embedded newform 325.2.n.b.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(101,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	325.101
Dual form			325.2.n.b.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89564 + 1.09445i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.39564 - 2.41733i) q^{4} +(-1.89564 - 1.09445i) q^{6} +(1.50000 + 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(2.29129 - 1.32288i) q^{11} +2.79129 q^{12} +(1.00000 + 3.46410i) q^{13} -3.79129 q^{14} +(0.895644 + 1.55130i) q^{16} +(2.29129 - 3.96863i) q^{17} +4.37780i q^{18} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-2.89564 + 5.01540i) q^{22} +(-2.29129 - 3.96863i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(-5.68693 - 5.47225i) q^{26} +5.00000 q^{27} +(4.18693 - 2.41733i) q^{28} +(2.29129 + 3.96863i) q^{29} +9.66930i q^{31} +(-6.39564 - 3.69253i) q^{32} +(2.29129 + 1.32288i) q^{33} +10.0308i q^{34} +(-2.79129 - 4.83465i) q^{36} +(-6.87386 + 3.96863i) q^{37} -3.79129 q^{38} +(-2.50000 + 2.59808i) q^{39} +(-2.29129 + 1.32288i) q^{41} +(-1.89564 - 3.28335i) q^{42} +(0.708712 - 1.22753i) q^{43} -7.38505i q^{44} +(8.68693 + 5.01540i) q^{46} +8.75560i q^{47} +(-0.895644 + 1.55130i) q^{48} +(-2.00000 - 3.46410i) q^{49} +4.58258 q^{51} +(9.76951 + 2.41733i) q^{52} +1.58258 q^{53} +(-9.47822 + 5.47225i) q^{54} +(-1.50000 + 2.59808i) q^{56} +1.73205i q^{57} +(-8.68693 - 5.01540i) q^{58} +(2.91742 + 1.68438i) q^{59} +(5.29129 - 9.16478i) q^{61} +(-10.5826 - 18.3296i) q^{62} +(3.00000 - 1.73205i) q^{63} +12.5826 q^{64} -5.79129 q^{66} +(12.8739 - 7.43273i) q^{67} +(-6.39564 - 11.0776i) q^{68} +(2.29129 - 3.96863i) q^{69} +(-3.08258 - 1.77973i) q^{71} +(3.00000 + 1.73205i) q^{72} +(8.68693 - 15.0462i) q^{74} +(4.18693 - 2.41733i) q^{76} +4.58258 q^{77} +(1.89564 - 7.66115i) q^{78} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.89564 - 5.01540i) q^{82} -11.3060i q^{83} +(4.18693 + 2.41733i) q^{84} +3.10260i q^{86} +(-2.29129 + 3.96863i) q^{87} +(2.29129 + 3.96863i) q^{88} +(-3.70871 + 2.14123i) q^{89} +(-1.50000 + 6.06218i) q^{91} -12.7913 q^{92} +(-8.37386 + 4.83465i) q^{93} +(-9.58258 - 16.5975i) q^{94} -7.38505i q^{96} +(-3.87386 - 2.23658i) q^{97} +(7.58258 + 4.37780i) q^{98} -5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 2 q^{3} + q^{4} - 3 q^{6} + 6 q^{7} + 4 q^{9} + 2 q^{12} + 4 q^{13} - 6 q^{14} - q^{16} + 6 q^{19} - 7 q^{22} - 6 q^{24} - 9 q^{26} + 20 q^{27} + 3 q^{28} - 21 q^{32} - 2 q^{36} - 6 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 + 2 * q^3 + q^4 - 3 * q^6 + 6 * q^7 + 4 * q^9 + 2 * q^12 + 4 * q^13 - 6 * q^14 - q^16 + 6 * q^19 - 7 * q^22 - 6 * q^24 - 9 * q^26 + 20 * q^27 + 3 * q^28 - 21 * q^32 - 2 * q^36 - 6 * q^38 - 10 * q^39 - 3 * q^42 + 12 * q^43 + 21 * q^46 + q^48 - 8 * q^49 + 7 * q^52 - 12 * q^53 - 15 * q^54 - 6 * q^56 - 21 * q^58 + 30 * q^59 + 12 * q^61 - 24 * q^62 + 12 * q^63 + 32 * q^64 - 14 * q^66 + 24 * q^67 - 21 * q^68 + 6 * q^71 + 12 * q^72 + 21 * q^74 + 3 * q^76 + 3 * q^78 - 24 * q^79 - 2 * q^81 + 7 * q^82 + 3 * q^84 - 24 * q^89 - 6 * q^91 - 42 * q^92 - 6 * q^93 - 20 * q^94 + 12 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.89564	+	1.09445i	−1.34042	+	0.773893i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−1.89564	+	1.09445i	−1.34042	+	0.773893i	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	1.39564	−	2.41733i	0.697822	−	1.20866i
$5$		0			0
$5$		0			0
$6$	−1.89564	−	1.09445i	−0.773893	−	0.446808i
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	−0.188982	+	0.981981i	$0.560519\pi$
$8$			1.73205i			0.612372i
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	−0.113081	−	0.993586i	$-0.536072\pi$
$11$	2.29129	−	1.32288i	0.690849	−	0.398862i	0.803930	+	0.594724i	$0.202739\pi$
$12$	2.79129			0.805775
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	−3.79129			−1.01326
$15$		0			0
$16$	0.895644	+	1.55130i	0.223911	+	0.387825i
$17$	2.29129	−	3.96863i	0.555719	−	0.962533i	−0.442128	−	0.896952i	$-0.645776\pi$
$17$	2.29129	−	3.96863i	0.555719	−	0.962533i	0.997847	−	0.0655816i	$-0.0208903\pi$
$18$			4.37780i			1.03186i
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$			1.73205i			0.377964i
$22$	−2.89564	+	5.01540i	−0.617353	+	1.06929i
$23$	−2.29129	−	3.96863i	−0.477767	−	0.827516i	0.521909	−	0.853001i	$-0.325220\pi$
$23$	−2.29129	−	3.96863i	−0.477767	−	0.827516i	−0.999675	+	0.0254855i	$0.991887\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$		0			0
$26$	−5.68693	−	5.47225i	−1.11530	−	1.07320i
$27$	5.00000			0.962250
$28$	4.18693	−	2.41733i	0.791256	−	0.456832i
$29$	2.29129	+	3.96863i	0.425481	+	0.736956i	0.996465	−	0.0840058i	$-0.0267714\pi$
$29$	2.29129	+	3.96863i	0.425481	+	0.736956i	−0.570984	+	0.820961i	$0.693438\pi$
$30$		0			0
$31$			9.66930i			1.73666i	0.495988	+	0.868329i	$0.334806\pi$
$31$			9.66930i			1.73666i	−0.495988	+	0.868329i	$0.665194\pi$
$32$	−6.39564	−	3.69253i	−1.13060	−	0.652753i
$33$	2.29129	+	1.32288i	0.398862	+	0.230283i
$34$			10.0308i			1.72027i
$35$		0			0
$36$	−2.79129	−	4.83465i	−0.465215	−	0.805775i
$37$	−6.87386	+	3.96863i	−1.13006	+	0.652438i	−0.943949	−	0.330091i	$-0.892920\pi$
$37$	−6.87386	+	3.96863i	−1.13006	+	0.652438i	−0.186107	+	0.982529i	$0.559587\pi$
$38$	−3.79129			−0.615028
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	−2.29129	+	1.32288i	−0.357839	+	0.206598i	−0.668132	−	0.744042i	$-0.732906\pi$
$41$	−2.29129	+	1.32288i	−0.357839	+	0.206598i	0.310293	+	0.950641i	$0.399573\pi$
$42$	−1.89564	−	3.28335i	−0.292504	−	0.506632i
$43$	0.708712	−	1.22753i	0.108078	−	0.187196i	−0.806914	−	0.590669i	$-0.798864\pi$
$43$	0.708712	−	1.22753i	0.108078	−	0.187196i	0.914991	+	0.403473i	$0.132197\pi$
$44$		−	7.38505i		−	1.11334i
$45$		0			0
$46$	8.68693	+	5.01540i	1.28082	+	0.739481i
$47$			8.75560i			1.27714i	0.769565	+	0.638568i	$0.220473\pi$
$47$			8.75560i			1.27714i	−0.769565	+	0.638568i	$0.779527\pi$
$48$	−0.895644	+	1.55130i	−0.129275	+	0.223911i
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$		0			0
$51$	4.58258			0.641689
$52$	9.76951	+	2.41733i	1.35479	+	0.335223i
$53$	1.58258			0.217383			0.108692	−	0.994076i	$-0.465334\pi$
$53$	1.58258			0.217383			0.108692	+	0.994076i	$0.465334\pi$
$54$	−9.47822	+	5.47225i	−1.28982	+	0.744679i
$55$		0			0
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$			1.73205i			0.229416i
$58$	−8.68693	−	5.01540i	−1.14065	−	0.658555i
$59$	2.91742	+	1.68438i	0.379816	+	0.219287i	0.677738	−	0.735303i	$-0.262960\pi$
$59$	2.91742	+	1.68438i	0.379816	+	0.219287i	−0.297922	+	0.954590i	$0.596294\pi$
$60$		0			0
$61$	5.29129	−	9.16478i	0.677480	−	1.17343i	−0.298257	−	0.954485i	$-0.596405\pi$
$61$	5.29129	−	9.16478i	0.677480	−	1.17343i	0.975737	−	0.218944i	$-0.0702613\pi$
$62$	−10.5826	−	18.3296i	−1.34399	−	2.32786i
$63$	3.00000	−	1.73205i	0.377964	−	0.218218i
$64$	12.5826			1.57282
$65$		0			0
$66$	−5.79129			−0.712858
$67$	12.8739	−	7.43273i	1.57279	−	0.908052i	0.576968	−	0.816767i	$-0.304236\pi$
$67$	12.8739	−	7.43273i	1.57279	−	0.908052i	0.995825	−	0.0912856i	$-0.0290976\pi$
$68$	−6.39564	−	11.0776i	−0.775586	−	1.34335i
$69$	2.29129	−	3.96863i	0.275839	−	0.477767i
$70$		0			0
$71$	−3.08258	−	1.77973i	−0.365834	−	0.211215i	0.305803	−	0.952095i	$-0.401075\pi$
$71$	−3.08258	−	1.77973i	−0.365834	−	0.211215i	−0.671637	+	0.740880i	$0.734409\pi$
$72$	3.00000	+	1.73205i	0.353553	+	0.204124i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	8.68693	−	15.0462i	1.00984	−	1.74909i
$75$		0			0
$76$	4.18693	−	2.41733i	0.480274	−	0.277286i
$77$	4.58258			0.522233
$78$	1.89564	−	7.66115i	0.214639	−	0.867455i
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.89564	−	5.01540i	0.319770	−	0.553859i
$83$		−	11.3060i		−	1.24100i	−0.784208	−	0.620498i	$-0.786931\pi$
$83$		−	11.3060i		−	1.24100i	0.784208	−	0.620498i	$-0.213069\pi$
$84$	4.18693	+	2.41733i	0.456832	+	0.263752i
$85$		0			0
$86$			3.10260i			0.334562i
$87$	−2.29129	+	3.96863i	−0.245652	+	0.425481i
$88$	2.29129	+	3.96863i	0.244252	+	0.423057i
$89$	−3.70871	+	2.14123i	−0.393123	+	0.226969i	−0.683512	−	0.729939i	$-0.739548\pi$
$89$	−3.70871	+	2.14123i	−0.393123	+	0.226969i	0.290390	+	0.956909i	$0.406215\pi$
$90$		0			0
$91$	−1.50000	+	6.06218i	−0.157243	+	0.635489i
$92$	−12.7913			−1.33358
$93$	−8.37386	+	4.83465i	−0.868329	+	0.501330i
$94$	−9.58258	−	16.5975i	−0.988367	−	1.71190i
$95$		0			0
$96$		−	7.38505i		−	0.753734i
$97$	−3.87386	−	2.23658i	−0.393331	−	0.227090i	0.290271	−	0.956944i	$-0.406254\pi$
$97$	−3.87386	−	2.23658i	−0.393331	−	0.227090i	−0.683603	+	0.729854i	$0.739588\pi$
$98$	7.58258	+	4.37780i	0.765956	+	0.442225i
$99$		−	5.29150i		−	0.531816i
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−8.68693	+	5.01540i	−0.860134	+	0.496599i
$103$	15.1652			1.49427			0.747133	−	0.664674i	$-0.231430\pi$
$103$	15.1652			1.49427			0.747133	+	0.664674i	$0.231430\pi$
$104$	−6.00000	+	1.73205i	−0.588348	+	0.169842i
$105$		0			0
$106$	−3.00000	+	1.73205i	−0.291386	+	0.168232i
$107$	−0.708712	−	1.22753i	−0.0685138	−	0.118669i	0.829733	−	0.558160i	$-0.188492\pi$
$107$	−0.708712	−	1.22753i	−0.0685138	−	0.118669i	−0.898247	+	0.439490i	$0.855159\pi$
$108$	6.97822	−	12.0866i	0.671479	−	1.16304i
$109$			2.74110i			0.262550i	0.991346	+	0.131275i	$0.0419071\pi$
$109$			2.74110i			0.262550i	−0.991346	+	0.131275i	$0.958093\pi$
$110$		0			0
$111$	−6.87386	−	3.96863i	−0.652438	−	0.376685i
$112$			3.10260i			0.293168i
$113$	−8.29129	+	14.3609i	−0.779979	+	1.35096i	0.151975	+	0.988384i	$0.451437\pi$
$113$	−8.29129	+	14.3609i	−0.779979	+	1.35096i	−0.931953	+	0.362578i	$0.881897\pi$
$114$	−1.89564	−	3.28335i	−0.177543	−	0.307514i
$115$		0			0
$116$	12.7913			1.18764
$117$	7.00000	+	1.73205i	0.647150	+	0.160128i
$118$	−7.37386			−0.678819
$119$	6.87386	−	3.96863i	0.630126	−	0.363803i
$120$		0			0
$121$	−2.00000	+	3.46410i	−0.181818	+	0.314918i
$122$			23.1642i			2.09719i
$123$	−2.29129	−	1.32288i	−0.206598	−	0.119280i
$124$	23.3739	+	13.4949i	2.09903	+	1.21188i
$125$		0			0
$126$	−3.79129	+	6.56670i	−0.337755	+	0.585008i
$127$	−4.87386	−	8.44178i	−0.432485	−	0.749087i	0.564601	−	0.825364i	$-0.309030\pi$
$127$	−4.87386	−	8.44178i	−0.432485	−	0.749087i	−0.997087	+	0.0762771i	$0.975697\pi$
$128$	−11.0608	+	6.38595i	−0.977645	+	0.564444i
$129$	1.41742			0.124797
$130$		0			0
$131$	1.58258			0.138270			0.0691351	−	0.997607i	$-0.477976\pi$
$131$	1.58258			0.138270			0.0691351	+	0.997607i	$0.477976\pi$
$132$	6.39564	−	3.69253i	0.556669	−	0.321393i
$133$	1.50000	+	2.59808i	0.130066	+	0.225282i
$134$	−16.2695	+	28.1796i	−1.40547	+	2.43435i
$135$		0			0
$136$	6.87386	+	3.96863i	0.589429	+	0.340307i
$137$	0.0825757	+	0.0476751i	0.00705492	+	0.00407316i	0.503523	−	0.863982i	$-0.332037\pi$
$137$	0.0825757	+	0.0476751i	0.00705492	+	0.00407316i	−0.496468	+	0.868055i	$0.665370\pi$
$138$			10.0308i			0.853879i
$139$	−2.87386	+	4.97768i	−0.243758	+	0.422201i	−0.961782	−	0.273817i	$-0.911714\pi$
$139$	−2.87386	+	4.97768i	−0.243758	+	0.422201i	0.718024	+	0.696019i	$0.245047\pi$
$140$		0			0
$141$	−7.58258	+	4.37780i	−0.638568	+	0.368677i
$142$	7.79129			0.653830
$143$	6.87386	+	6.61438i	0.574821	+	0.553122i
$144$	3.58258			0.298548
$145$		0			0
$146$		0			0
$147$	2.00000	−	3.46410i	0.164957	−	0.285714i
$148$			22.1552i			1.82114i
$149$	−8.45644	−	4.88233i	−0.692778	−	0.399976i	0.111874	−	0.993722i	$-0.464315\pi$
$149$	−8.45644	−	4.88233i	−0.692778	−	0.399976i	−0.804652	+	0.593747i	$0.797648\pi$
$150$		0			0
$151$		−	6.20520i		−	0.504972i	−0.967601	−	0.252486i	$-0.918752\pi$
$151$		−	6.20520i		−	0.504972i	0.967601	−	0.252486i	$-0.0812482\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$	−4.58258	−	7.93725i	−0.370479	−	0.641689i
$154$	−8.68693	+	5.01540i	−0.700013	+	0.404153i
$155$		0			0
$156$	2.79129	+	9.66930i	0.223482	+	0.774164i
$157$	9.16515			0.731459			0.365729	−	0.930721i	$-0.380820\pi$
$157$	9.16515			0.731459			0.365729	+	0.930721i	$0.380820\pi$
$158$	11.3739	−	6.56670i	0.904856	−	0.522419i
$159$	0.791288	+	1.37055i	0.0627532	+	0.108692i
$160$		0			0
$161$		−	7.93725i		−	0.625543i
$162$	1.89564	+	1.09445i	0.148936	+	0.0859882i
$163$	−9.24773	−	5.33918i	−0.724338	−	0.418197i	0.0920093	−	0.995758i	$-0.470671\pi$
$163$	−9.24773	−	5.33918i	−0.724338	−	0.418197i	−0.816347	+	0.577561i	$0.804004\pi$
$164$			7.38505i			0.576676i
$165$		0			0
$166$	12.3739	+	21.4322i	0.960398	+	1.66346i
$167$	−3.70871	+	2.14123i	−0.286989	+	0.165693i	−0.636583	−	0.771208i	$-0.719653\pi$
$167$	−3.70871	+	2.14123i	−0.286989	+	0.165693i	0.349594	+	0.936901i	$0.386319\pi$
$168$	−3.00000			−0.231455
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$	−1.97822	−	3.42638i	−0.150838	−	0.261259i
$173$	−3.70871	+	6.42368i	−0.281968	+	0.488383i	−0.971869	−	0.235520i	$-0.924321\pi$
$173$	−3.70871	+	6.42368i	−0.281968	+	0.488383i	0.689901	+	0.723903i	$0.257654\pi$
$174$		−	10.0308i		−	0.760433i
$175$		0			0
$176$	4.10436	+	2.36965i	0.309377	+	0.178619i
$177$			3.36875i			0.253211i
$178$	4.68693	−	8.11800i	0.351300	−	0.608470i
$179$	0.0825757	+	0.143025i	0.00617200	+	0.0106902i	0.869095	−	0.494645i	$-0.164702\pi$
$179$	0.0825757	+	0.143025i	0.00617200	+	0.0106902i	−0.862923	+	0.505336i	$0.831369\pi$
$180$		0			0
$181$	−18.7477			−1.39351			−0.696754	−	0.717310i	$-0.745373\pi$
$181$	−18.7477			−1.39351			−0.696754	+	0.717310i	$0.745373\pi$
$182$	−3.79129	−	13.1334i	−0.281029	−	0.973513i
$183$	10.5826			0.782287
$184$	6.87386	−	3.96863i	0.506748	−	0.292571i
$185$		0			0
$186$	10.5826	−	18.3296i	0.775952	−	1.34399i
$187$		−	12.1244i		−	0.886621i
$188$	21.1652	+	12.2197i	1.54363	+	0.891214i
$189$	7.50000	+	4.33013i	0.545545	+	0.314970i
$190$		0			0
$191$	3.70871	−	6.42368i	0.268353	−	0.464801i	−0.700084	−	0.714061i	$-0.746854\pi$
$191$	3.70871	−	6.42368i	0.268353	−	0.464801i	0.968437	+	0.249260i	$0.0801873\pi$
$192$	6.29129	+	10.8968i	0.454035	+	0.786411i
$193$	0.873864	−	0.504525i	0.0629021	−	0.0363165i	−0.468219	−	0.883612i	$-0.655104\pi$
$193$	0.873864	−	0.504525i	0.0629021	−	0.0363165i	0.531121	+	0.847296i	$0.321771\pi$
$194$	9.79129			0.702973
$195$		0			0
$196$	−11.1652			−0.797511
$197$	−17.2913	+	9.98313i	−1.23195	+	0.711269i	−0.967437	−	0.253113i	$-0.918546\pi$
$197$	−17.2913	+	9.98313i	−1.23195	+	0.711269i	−0.264516	+	0.964381i	$0.585212\pi$
$198$	5.79129	+	10.0308i	0.411569	+	0.712858i
$199$	−0.708712	+	1.22753i	−0.0502393	+	0.0870170i	−0.890051	−	0.455860i	$-0.849332\pi$
$199$	−0.708712	+	1.22753i	−0.0502393	+	0.0870170i	0.839812	+	0.542877i	$0.182665\pi$
$200$		0			0
$201$	12.8739	+	7.43273i	0.908052	+	0.524264i
$202$	17.0608	+	9.85005i	1.20039	+	0.693047i
$203$			7.93725i			0.557086i
$204$	6.39564	−	11.0776i	0.447785	−	0.775586i
$205$		0			0
$206$	−28.7477	+	16.5975i	−2.00295	+	1.15640i
$207$	−9.16515			−0.637022
$208$	−4.47822	+	4.65390i	−0.310509	+	0.322690i
$209$	4.58258			0.316983
$210$		0			0
$211$	−9.08258	−	15.7315i	−0.625270	−	1.08300i	−0.988489	−	0.151296i	$-0.951655\pi$
$211$	−9.08258	−	15.7315i	−0.625270	−	1.08300i	0.363218	−	0.931704i	$-0.381678\pi$
$212$	2.20871	−	3.82560i	0.151695	−	0.262743i
$213$		−	3.55945i		−	0.243890i
$214$	2.68693	+	1.55130i	0.183675	+	0.106045i
$215$		0			0
$216$			8.66025i			0.589256i
$217$	−8.37386	+	14.5040i	−0.568455	+	0.984593i
$218$	−3.00000	−	5.19615i	−0.203186	−	0.351928i
$219$		0			0
$220$		0			0
$221$	16.0390	+	3.96863i	1.07890	+	0.266959i
$222$	17.3739			1.16606
$223$	7.50000	−	4.33013i	0.502237	−	0.289967i	−0.227400	−	0.973801i	$-0.573022\pi$
$223$	7.50000	−	4.33013i	0.502237	−	0.289967i	0.729637	+	0.683835i	$0.239689\pi$
$224$	−6.39564	−	11.0776i	−0.427327	−	0.740152i
$225$		0			0
$226$		−	36.2976i		−	2.41448i
$227$	−5.29129	−	3.05493i	−0.351195	−	0.202763i	0.314016	−	0.949418i	$-0.398325\pi$
$227$	−5.29129	−	3.05493i	−0.351195	−	0.202763i	−0.665212	+	0.746655i	$0.731659\pi$
$228$	4.18693	+	2.41733i	0.277286	+	0.160091i
$229$		−	5.48220i		−	0.362274i	−0.983458	−	0.181137i	$-0.942022\pi$
$229$		−	5.48220i		−	0.362274i	0.983458	−	0.181137i	$-0.0579778\pi$
$230$		0			0
$231$	2.29129	+	3.96863i	0.150756	+	0.261116i
$232$	−6.87386	+	3.96863i	−0.451291	+	0.260553i
$233$	−21.1652			−1.38658			−0.693288	−	0.720661i	$-0.743838\pi$
$233$	−21.1652			−1.38658			−0.693288	+	0.720661i	$0.743838\pi$
$234$	−15.1652	+	4.37780i	−0.991377	+	0.286186i
$235$		0			0
$236$	8.14337	−	4.70158i	0.530088	−	0.306047i
$237$	−3.00000	−	5.19615i	−0.194871	−	0.337526i
$238$	−8.68693	+	15.0462i	−0.563090	+	0.975301i
$239$		−	20.9753i		−	1.35678i	−0.734702	−	0.678390i	$-0.762678\pi$
$239$		−	20.9753i		−	1.35678i	0.734702	−	0.678390i	$-0.237322\pi$
$240$		0			0
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$		−	8.75560i		−	0.562832i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	−14.7695	−	25.5815i	−0.945521	−	1.63769i
$245$		0			0
$246$	5.79129			0.369239
$247$	−1.50000	+	6.06218i	−0.0954427	+	0.385727i
$248$	−16.7477			−1.06348
$249$	9.79129	−	5.65300i	0.620498	−	0.358244i
$250$		0			0
$251$	−9.08258	+	15.7315i	−0.573287	+	0.992962i	0.422938	+	0.906158i	$0.360999\pi$
$251$	−9.08258	+	15.7315i	−0.573287	+	0.992962i	−0.996225	+	0.0868039i	$0.972335\pi$
$252$		−	9.66930i		−	0.609109i
$253$	−10.5000	−	6.06218i	−0.660129	−	0.381126i
$254$	18.4782	+	10.6684i	1.15943	+	0.669395i
$255$		0			0
$256$	1.39564	−	2.41733i	0.0872277	−	0.151083i
$257$	0.0825757	+	0.143025i	0.00515093	+	0.00892167i	0.868589	−	0.495533i	$-0.165027\pi$
$257$	0.0825757	+	0.143025i	0.00515093	+	0.00892167i	−0.863438	+	0.504454i	$0.831694\pi$
$258$	−2.68693	+	1.55130i	−0.167281	+	0.0965798i
$259$	−13.7477			−0.854242
$260$		0			0
$261$	9.16515			0.567309
$262$	−3.00000	+	1.73205i	−0.185341	+	0.107006i
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$	−2.29129	+	3.96863i	−0.141019	+	0.244252i
$265$		0			0
$266$	−5.68693	−	3.28335i	−0.348688	−	0.201315i
$267$	−3.70871	−	2.14123i	−0.226969	−	0.131041i
$268$		−	41.4938i		−	2.53464i
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	−0.254597	−	0.967047i	$-0.581943\pi$
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	0.710189	+	0.704011i	$0.248609\pi$
$272$	8.20871			0.497726
$273$	−6.00000	+	1.73205i	−0.363137	+	0.104828i
$274$	−0.208712			−0.0126088
$275$		0			0
$276$	−6.39564	−	11.0776i	−0.384973	−	0.666792i
$277$	−8.29129	+	14.3609i	−0.498175	+	0.862865i	−0.999998	−	0.00210581i	$-0.999330\pi$
$277$	−8.29129	+	14.3609i	−0.498175	+	0.862865i	0.501823	+	0.864971i	$0.332663\pi$
$278$		−	12.5812i		−	0.754571i
$279$	16.7477	+	9.66930i	1.00266	+	0.578886i
$280$		0			0
$281$			17.5112i			1.04463i	0.852752	+	0.522316i	$0.174932\pi$
$281$			17.5112i			1.04463i	−0.852752	+	0.522316i	$0.825068\pi$
$282$	9.58258	−	16.5975i	0.570634	−	0.988367i
$283$	−0.126136	−	0.218475i	−0.00749803	−	0.0129870i	0.862252	−	0.506479i	$-0.169053\pi$
$283$	−0.126136	−	0.218475i	−0.00749803	−	0.0129870i	−0.869750	+	0.493492i	$0.835720\pi$
$284$	−8.60436	+	4.96773i	−0.510575	+	0.294780i
$285$		0			0
$286$	−20.2695	−	5.01540i	−1.19856	−	0.296567i
$287$	−4.58258			−0.270501
$288$	−12.7913	+	7.38505i	−0.753734	+	0.435168i
$289$	−2.00000	−	3.46410i	−0.117647	−	0.203771i
$290$		0			0
$291$		−	4.47315i		−	0.262221i
$292$		0			0
$293$	−20.2913	−	11.7152i	−1.18543	−	0.684408i	−0.228165	−	0.973622i	$-0.573273\pi$
$293$	−20.2913	−	11.7152i	−1.18543	−	0.684408i	−0.957264	+	0.289214i	$0.906606\pi$
$294$			8.75560i			0.510637i
$295$		0			0
$296$	−6.87386	−	11.9059i	−0.399535	−	0.692015i
$297$	11.4564	−	6.61438i	0.664770	−	0.383805i
$298$	21.3739			1.23815
$299$	11.4564	−	11.9059i	0.662543	−	0.688535i
$300$		0			0
$301$	2.12614	−	1.22753i	0.122548	−	0.0707534i
$302$	6.79129	+	11.7629i	0.390795	+	0.676876i
$303$	4.50000	−	7.79423i	0.258518	−	0.447767i
$304$			3.10260i			0.177946i
$305$		0			0
$306$	17.3739	+	10.0308i	0.993198	+	0.573423i
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$	6.39564	−	11.0776i	0.364426	−	0.631204i
$309$	7.58258	+	13.1334i	0.431358	+	0.747133i
$310$		0			0
$311$	−1.58258			−0.0897396			−0.0448698	−	0.998993i	$-0.514287\pi$
$311$	−1.58258			−0.0897396			−0.0448698	+	0.998993i	$0.514287\pi$
$312$	−4.50000	−	4.33013i	−0.254762	−	0.245145i
$313$	30.7477			1.73796			0.868982	−	0.494843i	$-0.164775\pi$
$313$	30.7477			1.73796			0.868982	+	0.494843i	$0.164775\pi$
$314$	−17.3739	+	10.0308i	−0.980464	+	0.566071i
$315$		0			0
$316$	−8.37386	+	14.5040i	−0.471067	+	0.815911i
$317$		−	20.9753i		−	1.17809i	−0.808100	−	0.589045i	$-0.799504\pi$
$317$		−	20.9753i		−	1.17809i	0.808100	−	0.589045i	$-0.200496\pi$
$318$	−3.00000	−	1.73205i	−0.168232	−	0.0971286i
$319$	10.5000	+	6.06218i	0.587887	+	0.339417i
$320$		0			0
$321$	0.708712	−	1.22753i	0.0395565	−	0.0685138i
$322$	8.68693	+	15.0462i	0.484104	+	0.838492i
$323$	6.87386	−	3.96863i	0.382472	−	0.220820i
$324$	−2.79129			−0.155072
$325$		0			0
$326$	23.3739			1.29456
$327$	−2.37386	+	1.37055i	−0.131275	+	0.0757916i
$328$	−2.29129	−	3.96863i	−0.126515	−	0.219131i
$329$	−7.58258	+	13.1334i	−0.418041	+	0.724068i
$330$		0			0
$331$	9.87386	+	5.70068i	0.542717	+	0.313338i	0.746179	−	0.665745i	$-0.231886\pi$
$331$	9.87386	+	5.70068i	0.542717	+	0.313338i	−0.203463	+	0.979083i	$0.565220\pi$
$332$	−27.3303	−	15.7792i	−1.49995	−	0.865994i
$333$			15.8745i			0.869918i
$334$	4.68693	−	8.11800i	0.256457	−	0.444197i
$335$		0			0
$336$	−2.68693	+	1.55130i	−0.146584	+	0.0846304i
$337$	−3.25227			−0.177163			−0.0885813	−	0.996069i	$-0.528233\pi$
$337$	−3.25227			−0.177163			−0.0885813	+	0.996069i	$0.528233\pi$
$338$	13.2695	−	25.1724i	0.721766	−	1.36920i
$339$	−16.5826			−0.900642
$340$		0			0
$341$	12.7913	+	22.1552i	0.692687	+	1.19977i
$342$	−3.79129	+	6.56670i	−0.205009	+	0.355087i
$343$		−	19.0526i		−	1.02874i
$344$	2.12614	+	1.22753i	0.114634	+	0.0661837i
$345$		0			0
$346$		−	16.2360i		−	0.872853i
$347$	7.66515	−	13.2764i	0.411487	−	0.712716i	−0.583566	−	0.812066i	$-0.698343\pi$
$347$	7.66515	−	13.2764i	0.411487	−	0.712716i	0.995053	+	0.0993497i	$0.0316763\pi$
$348$	6.39564	+	11.0776i	0.342843	+	0.593821i
$349$	−15.8739	+	9.16478i	−0.849708	+	0.490579i	−0.860552	−	0.509362i	$-0.829882\pi$
$349$	−15.8739	+	9.16478i	−0.849708	+	0.490579i	0.0108440	+	0.999941i	$0.496548\pi$
$350$		0			0
$351$	5.00000	+	17.3205i	0.266880	+	0.924500i
$352$	−19.5390			−1.04143
$353$	−15.0826	+	8.70793i	−0.802765	+	0.463476i	−0.844437	−	0.535655i	$-0.820065\pi$
$353$	−15.0826	+	8.70793i	−0.802765	+	0.463476i	0.0416724	+	0.999131i	$0.486731\pi$
$354$	−3.68693	−	6.38595i	−0.195958	−	0.339410i
$355$		0			0
$356$			11.9536i			0.633537i
$357$	6.87386	+	3.96863i	0.363803	+	0.210042i
$358$	−0.313068	−	0.180750i	−0.0165462	−	0.00955294i
$359$			33.3857i			1.76203i	0.473088	+	0.881015i	$0.343139\pi$
$359$			33.3857i			1.76203i	−0.473088	+	0.881015i	$0.656861\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	35.5390	−	20.5185i	1.86789	−	1.07843i
$363$	−4.00000			−0.209946
$364$	12.5608	+	12.0866i	0.658365	+	0.633512i
$365$		0			0
$366$	−20.0608	+	11.5821i	−1.04859	+	0.605406i
$367$	12.8739	+	22.2982i	0.672010	+	1.16396i	0.977333	+	0.211707i	$0.0679022\pi$
$367$	12.8739	+	22.2982i	0.672010	+	1.16396i	−0.305323	+	0.952249i	$0.598764\pi$
$368$	4.10436	−	7.10895i	0.213954	−	0.370580i
$369$			5.29150i			0.275465i
$370$		0			0
$371$	2.37386	+	1.37055i	0.123245	+	0.0711554i
$372$			26.9898i			1.39936i
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	0.647225	+	0.762299i	$0.275929\pi$
$374$	13.2695	+	22.9835i	0.686150	+	1.18845i
$375$		0			0
$376$	−15.1652			−0.782083
$377$	−11.4564	+	11.9059i	−0.590037	+	0.613184i
$378$	−18.9564			−0.975014
$379$	−18.2477	+	10.5353i	−0.937323	+	0.541164i	−0.889120	−	0.457674i	$-0.848683\pi$
$379$	−18.2477	+	10.5353i	−0.937323	+	0.541164i	−0.0482027	+	0.998838i	$0.515349\pi$
$380$		0			0
$381$	4.87386	−	8.44178i	0.249696	−	0.432485i
$382$			16.2360i			0.830706i
$383$	−2.45644	−	1.41823i	−0.125518	−	0.0724680i	0.435926	−	0.899982i	$-0.356421\pi$
$383$	−2.45644	−	1.41823i	−0.125518	−	0.0724680i	−0.561444	+	0.827514i	$0.689754\pi$
$384$	−11.0608	−	6.38595i	−0.564444	−	0.325882i
$385$		0			0
$386$	−1.10436	+	1.91280i	−0.0562102	+	0.0973590i
$387$	−1.41742	−	2.45505i	−0.0720517	−	0.124797i
$388$	−10.8131	+	6.24293i	−0.548950	+	0.316937i
$389$	15.1652			0.768904			0.384452	−	0.923145i	$-0.374390\pi$
$389$	15.1652			0.768904			0.384452	+	0.923145i	$0.374390\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	6.00000	−	3.46410i	0.303046	−	0.174964i
$393$	0.791288	+	1.37055i	0.0399152	+	0.0691351i
$394$	21.8521	−	37.8489i	1.10089	−	1.90680i
$395$		0			0
$396$	−12.7913	−	7.38505i	−0.642786	−	0.371113i
$397$	−23.6216	−	13.6379i	−1.18553	−	0.684468i	−0.228245	−	0.973604i	$-0.573299\pi$
$397$	−23.6216	−	13.6379i	−1.18553	−	0.684468i	−0.957288	+	0.289135i	$0.906632\pi$
$398$		−	3.10260i		−	0.155519i
$399$	−1.50000	+	2.59808i	−0.0750939	+	0.130066i
$400$		0			0
$401$	10.8303	−	6.25288i	0.540840	−	0.312254i	−0.204580	−	0.978850i	$-0.565583\pi$
$401$	10.8303	−	6.25288i	0.540840	−	0.312254i	0.745419	+	0.666596i	$0.232249\pi$
$402$	−32.5390			−1.62290
$403$	−33.4955	+	9.66930i	−1.66853	+	0.481662i
$404$	−25.1216			−1.24985
$405$		0			0
$406$	−8.68693	−	15.0462i	−0.431125	−	0.746731i
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$			7.93725i			0.392953i
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$		0			0
$411$			0.0953502i			0.00470328i
$412$	21.1652	−	36.6591i	1.04273	−	1.80607i
$413$	2.91742	+	5.05313i	0.143557	+	0.248648i
$414$	17.3739	−	10.0308i	0.853879	−	0.492987i
$415$		0			0
$416$	6.39564	−	25.8477i	0.313572	−	1.26729i
$417$	−5.74773			−0.281467
$418$	−8.68693	+	5.01540i	−0.424892	+	0.245311i
$419$	12.0826	+	20.9276i	0.590272	+	1.02238i	0.994195	+	0.107589i	$0.0343130\pi$
$419$	12.0826	+	20.9276i	0.590272	+	1.02238i	−0.403923	+	0.914793i	$0.632354\pi$
$420$		0			0
$421$			26.2668i			1.28017i	0.768306	+	0.640083i	$0.221100\pi$
$421$			26.2668i			1.28017i	−0.768306	+	0.640083i	$0.778900\pi$
$422$	34.4347	+	19.8809i	1.67625	+	0.967785i
$423$	15.1652	+	8.75560i	0.737355	+	0.425712i
$424$			2.74110i			0.133120i
$425$		0			0
$426$	3.89564	+	6.74745i	0.188745	+	0.326915i
$427$	15.8739	−	9.16478i	0.768190	−	0.443515i
$428$	−3.95644			−0.191242
$429$	−2.29129	+	9.26013i	−0.110624	+	0.447083i
$430$		0			0
$431$	25.6652	−	14.8178i	1.23625	−	0.713747i	0.267922	−	0.963441i	$-0.413663\pi$
$431$	25.6652	−	14.8178i	1.23625	−	0.713747i	0.968325	+	0.249693i	$0.0803298\pi$
$432$	4.47822	+	7.75650i	0.215458	+	0.373185i
$433$	−8.87386	+	15.3700i	−0.426451	+	0.738634i	−0.996555	−	0.0829383i	$-0.973570\pi$
$433$	−8.87386	+	15.3700i	−0.426451	+	0.738634i	0.570104	+	0.821573i	$0.306903\pi$
$434$		−	36.6591i		−	1.75969i
$435$		0			0
$436$	6.62614	+	3.82560i	0.317334	+	0.183213i
$437$		−	7.93725i		−	0.379690i
$438$		0			0
$439$	−20.2477	−	35.0701i	−0.966371	−	1.67380i	−0.705885	−	0.708327i	$-0.749450\pi$
$439$	−20.2477	−	35.0701i	−0.966371	−	1.67380i	−0.260487	−	0.965477i	$-0.583883\pi$
$440$		0			0
$441$	−8.00000			−0.380952
$442$	−34.7477	+	10.0308i	−1.65278	+	0.477117i
$443$	25.9129			1.23116			0.615579	−	0.788075i	$-0.288922\pi$
$443$	25.9129			1.23116			0.615579	+	0.788075i	$0.288922\pi$
$444$	−19.1869	+	11.0776i	−0.910571	+	0.525719i
$445$		0			0
$446$	−9.47822	+	16.4168i	−0.448807	+	0.777356i
$447$		−	9.76465i		−	0.461852i
$448$	18.8739	+	10.8968i	0.891706	+	0.514827i
$449$	−32.4564	−	18.7387i	−1.53171	−	0.884336i	−0.999283	−	0.0378622i	$-0.987945\pi$
$449$	−32.4564	−	18.7387i	−1.53171	−	0.884336i	−0.532431	−	0.846473i	$-0.678721\pi$
$450$		0			0
$451$	−3.50000	+	6.06218i	−0.164809	+	0.285457i
$452$	23.1434	+	40.0855i	1.08857	+	1.88546i
$453$	5.37386	−	3.10260i	0.252486	−	0.145773i
$454$	13.3739			0.627667
$455$		0			0
$456$	−3.00000			−0.140488
$457$	1.50000	−	0.866025i	0.0701670	−	0.0405110i	−0.464506	−	0.885570i	$-0.653768\pi$
$457$	1.50000	−	0.866025i	0.0701670	−	0.0405110i	0.534673	+	0.845059i	$0.320435\pi$
$458$	6.00000	+	10.3923i	0.280362	+	0.485601i
$459$	11.4564	−	19.8431i	0.534741	−	0.926198i
$460$		0			0
$461$	−1.03901	−	0.599876i	−0.0483917	−	0.0279390i	0.475609	−	0.879657i	$-0.342228\pi$
$461$	−1.03901	−	0.599876i	−0.0483917	−	0.0279390i	−0.524001	+	0.851718i	$0.675561\pi$
$462$	−8.68693	−	5.01540i	−0.404153	−	0.233338i
$463$		−	8.22330i		−	0.382169i	−0.981574	−	0.191085i	$-0.938799\pi$
$463$		−	8.22330i		−	0.382169i	0.981574	−	0.191085i	$-0.0612005\pi$
$464$	−4.10436	+	7.10895i	−0.190540	+	0.330025i
$465$		0			0
$466$	40.1216	−	23.1642i	1.85860	−	1.07306i
$467$	−12.3303			−0.570578			−0.285289	−	0.958441i	$-0.592090\pi$
$467$	−12.3303			−0.570578			−0.285289	+	0.958441i	$0.592090\pi$
$468$	13.9564	−	14.5040i	0.645137	−	0.670446i
$469$	25.7477			1.18892
$470$		0			0
$471$	4.58258	+	7.93725i	0.211154	+	0.365729i
$472$	−2.91742	+	5.05313i	−0.134285	+	0.232589i
$473$		−	3.75015i		−	0.172432i
$474$	11.3739	+	6.56670i	0.522419	+	0.301619i
$475$		0			0
$476$		−	22.1552i		−	1.01548i
$477$	1.58258	−	2.74110i	0.0724612	−	0.125506i
$478$	22.9564	+	39.7617i	1.05000	+	1.81866i
$479$	28.0390	−	16.1883i	1.28114	−	0.739664i	0.304079	−	0.952647i	$-0.401651\pi$
$479$	28.0390	−	16.1883i	1.28114	−	0.739664i	0.977056	+	0.212983i	$0.0683179\pi$
$480$		0			0
$481$	−20.6216	−	19.8431i	−0.940264	−	0.904769i
$482$	3.79129			0.172688
$483$	6.87386	−	3.96863i	0.312772	−	0.180579i
$484$	5.58258	+	9.66930i	0.253753	+	0.439514i
$485$		0			0
$486$			35.0224i			1.58865i
$487$	18.2477	+	10.5353i	0.826883	+	0.477401i	0.852784	−	0.522263i	$-0.174912\pi$
$487$	18.2477	+	10.5353i	0.826883	+	0.477401i	−0.0259009	+	0.999665i	$0.508245\pi$
$488$	15.8739	+	9.16478i	0.718576	+	0.414870i
$489$		−	10.6784i		−	0.482892i
$490$		0			0
$491$	−14.2913	−	24.7532i	−0.644957	−	1.11710i	−0.984311	−	0.176439i	$-0.943542\pi$
$491$	−14.2913	−	24.7532i	−0.644957	−	1.11710i	0.339355	−	0.940658i	$-0.389791\pi$
$492$	−6.39564	+	3.69253i	−0.288338	+	0.166472i
$493$	21.0000			0.945792
$494$	−3.79129	−	13.1334i	−0.170578	−	0.590900i
$495$		0			0
$496$	−15.0000	+	8.66025i	−0.673520	+	0.388857i
$497$	−3.08258	−	5.33918i	−0.138272	−	0.239495i
$498$	−12.3739	+	21.4322i	−0.554486	+	0.960398i
$499$			16.5975i			0.743006i	0.928432	+	0.371503i	$0.121158\pi$
$499$			16.5975i			0.743006i	−0.928432	+	0.371503i	$0.878842\pi$
$500$		0			0
$501$	−3.70871	−	2.14123i	−0.165693	−	0.0956629i
$502$		−	39.7617i		−	1.77465i
$503$	−9.08258	+	15.7315i	−0.404972	+	0.701432i	−0.994318	−	0.106448i	$-0.966052\pi$
$503$	−9.08258	+	15.7315i	−0.404972	+	0.701432i	0.589346	+	0.807881i	$0.299385\pi$
$504$	3.00000	+	5.19615i	0.133631	+	0.231455i
$505$		0			0
$506$	26.5390			1.17980
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	−27.2087			−1.20719
$509$	25.6652	−	14.8178i	1.13759	−	0.656787i	0.191756	−	0.981443i	$-0.438582\pi$
$509$	25.6652	−	14.8178i	1.13759	−	0.656787i	0.945832	+	0.324656i	$0.105249\pi$
$510$		0			0
$511$		0			0
$512$		−	19.4340i		−	0.858868i
$513$	7.50000	+	4.33013i	0.331133	+	0.191180i
$514$	−0.313068	−	0.180750i	−0.0138088	−	0.00797254i
$515$		0			0
$516$	1.97822	−	3.42638i	0.0870863	−	0.150838i
$517$	11.5826	+	20.0616i	0.509401	+	0.882309i
$518$	26.0608	−	15.0462i	1.14505	−	0.661092i
$519$	−7.41742			−0.325589
$520$		0			0
$521$	−27.4955			−1.20460			−0.602299	−	0.798271i	$-0.705748\pi$
$521$	−27.4955			−1.20460			−0.602299	+	0.798271i	$0.705748\pi$
$522$	−17.3739	+	10.0308i	−0.760433	+	0.439036i
$523$	−9.08258	−	15.7315i	−0.397153	−	0.687890i	0.596220	−	0.802821i	$-0.296669\pi$
$523$	−9.08258	−	15.7315i	−0.397153	−	0.687890i	−0.993373	+	0.114931i	$0.963335\pi$
$524$	2.20871	−	3.82560i	0.0964880	−	0.167122i
$525$		0			0
$526$	−17.0608	−	9.85005i	−0.743886	−	0.429483i
$527$	38.3739	+	22.1552i	1.67159	+	0.965094i
$528$			4.73930i			0.206252i
$529$	1.00000	−	1.73205i	0.0434783	−	0.0753066i
$530$		0			0
$531$	5.83485	−	3.36875i	0.253211	−	0.146191i
$532$	8.37386			0.363053
$533$	−6.87386	−	6.61438i	−0.297740	−	0.286501i
$534$	9.37386			0.405647
$535$		0			0
$536$	12.8739	+	22.2982i	0.556066	+	0.963135i
$537$	−0.0825757	+	0.143025i	−0.00356340	+	0.00617200i
$538$			32.8335i			1.41555i
$539$	−9.16515	−	5.29150i	−0.394771	−	0.227921i
$540$		0			0
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$	−9.47822	+	16.4168i	−0.407124	+	0.705160i
$543$	−9.37386	−	16.2360i	−0.402271	−	0.696754i
$544$	−29.3085	+	16.9213i	−1.25659	+	0.725494i
$545$		0			0
$546$	9.47822	−	9.85005i	0.405630	−	0.421543i
$547$	−1.25227			−0.0535433			−0.0267717	−	0.999642i	$-0.508523\pi$
$547$	−1.25227			−0.0535433			−0.0267717	+	0.999642i	$0.508523\pi$
$548$	0.230493	−	0.133075i	0.00984615	−	0.00568468i
$549$	−10.5826	−	18.3296i	−0.451653	−	0.782287i
$550$		0			0
$551$			7.93725i			0.338138i
$552$	6.87386	+	3.96863i	0.292571	+	0.168916i
$553$	−9.00000	−	5.19615i	−0.382719	−	0.220963i
$554$		−	36.2976i		−	1.54214i
$555$		0			0
$556$	8.02178	+	13.8941i	0.340199	+	0.589242i
$557$	11.2913	−	6.51903i	0.478427	−	0.276220i	−0.241334	−	0.970442i	$-0.577585\pi$
$557$	11.2913	−	6.51903i	0.478427	−	0.276220i	0.719761	+	0.694222i	$0.244251\pi$
$558$	−42.3303			−1.79198
$559$	4.96099	+	1.22753i	0.209827	+	0.0519188i
$560$		0			0
$561$	10.5000	−	6.06218i	0.443310	−	0.255945i
$562$	−19.1652	−	33.1950i	−0.808433	−	1.40025i
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	−0.945134	−	0.326682i	$-0.894069\pi$
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	0.755482	+	0.655169i	$0.227403\pi$
$564$			24.4394i			1.02908i
$565$		0			0
$566$	0.478220	+	0.276100i	0.0201011	+	0.0116054i
$567$		−	1.73205i		−	0.0727393i
$568$	3.08258	−	5.33918i	0.129342	−	0.224027i
$569$	9.87386	+	17.1020i	0.413934	+	0.716955i	0.995316	−	0.0966762i	$-0.0308211\pi$
$569$	9.87386	+	17.1020i	0.413934	+	0.716955i	−0.581382	+	0.813631i	$0.697488\pi$
$570$		0			0
$571$	29.0780			1.21688			0.608439	−	0.793601i	$-0.291796\pi$
$571$	29.0780			1.21688			0.608439	+	0.793601i	$0.291796\pi$
$572$	25.5826	−	7.38505i	1.06966	−	0.308785i
$573$	7.41742			0.309867
$574$	8.68693	−	5.01540i	0.362586	−	0.209339i
$575$		0			0
$576$	12.5826	−	21.7937i	0.524274	−	0.908069i
$577$			6.92820i			0.288425i	0.989547	+	0.144212i	$0.0460649\pi$
$577$			6.92820i			0.288425i	−0.989547	+	0.144212i	$0.953935\pi$
$578$	7.58258	+	4.37780i	0.315394	+	0.182093i
$579$	0.873864	+	0.504525i	0.0363165	+	0.0209674i
$580$		0			0
$581$	9.79129	−	16.9590i	0.406211	−	0.703578i
$582$	4.89564	+	8.47950i	0.202931	+	0.351487i
$583$	3.62614	−	2.09355i	0.150179	−	0.0867060i
$584$		0			0
$585$		0			0
$586$	51.2867			2.11864
$587$	−16.2042	+	9.35548i	−0.668818	+	0.386142i	−0.795628	−	0.605785i	$-0.792859\pi$
$587$	−16.2042	+	9.35548i	−0.668818	+	0.386142i	0.126811	+	0.991927i	$0.459526\pi$
$588$	−5.58258	−	9.66930i	−0.230222	−	0.398755i
$589$	−8.37386	+	14.5040i	−0.345039	+	0.597625i
$590$		0			0
$591$	−17.2913	−	9.98313i	−0.711269	−	0.410651i
$592$	−12.3131	−	7.10895i	−0.506064	−	0.292176i
$593$			21.1660i			0.869184i	0.900627	+	0.434592i	$0.143107\pi$
$593$			21.1660i			0.869184i	−0.900627	+	0.434592i	$0.856893\pi$
$594$	−14.4782	+	25.0770i	−0.594049	+	1.02892i
$595$		0			0
$596$	−23.6044	+	13.6280i	−0.966872	+	0.558224i
$597$	−1.41742			−0.0580113
$598$	−8.68693	+	35.1078i	−0.355235	+	1.43567i
$599$	−39.4955			−1.61374			−0.806870	−	0.590729i	$-0.798840\pi$
$599$	−39.4955			−1.61374			−0.806870	+	0.590729i	$0.798840\pi$
$600$		0			0
$601$	14.4564	+	25.0393i	0.589690	+	1.02137i	0.994273	+	0.106872i	$0.0340836\pi$
$601$	14.4564	+	25.0393i	0.589690	+	1.02137i	−0.404582	+	0.914502i	$0.632583\pi$
$602$	−2.68693	+	4.65390i	−0.109511	+	0.189679i
$603$		−	29.7309i		−	1.21074i
$604$	−15.0000	−	8.66025i	−0.610341	−	0.352381i
$605$		0			0
$606$			19.7001i			0.800262i
$607$	−9.87386	+	17.1020i	−0.400768	+	0.694150i	−0.993819	−	0.111015i	$-0.964590\pi$
$607$	−9.87386	+	17.1020i	−0.400768	+	0.694150i	0.593051	+	0.805165i	$0.297923\pi$
$608$	−6.39564	−	11.0776i	−0.259378	−	0.449255i
$609$	−6.87386	+	3.96863i	−0.278543	+	0.160817i
$610$		0			0
$611$	−30.3303	+	8.75560i	−1.22703	+	0.354214i
$612$	−25.5826			−1.03411
$613$	18.8739	−	10.8968i	0.762308	−	0.440119i	−0.0678157	−	0.997698i	$-0.521603\pi$
$613$	18.8739	−	10.8968i	0.762308	−	0.440119i	0.830124	+	0.557579i	$0.188270\pi$
$614$	26.5390	+	45.9669i	1.07103	+	1.85507i
$615$		0			0
$616$			7.93725i			0.319801i
$617$	2.91742	+	1.68438i	0.117451	+	0.0678104i	0.557575	−	0.830127i	$-0.311732\pi$
$617$	2.91742	+	1.68438i	0.117451	+	0.0678104i	−0.440124	+	0.897937i	$0.645065\pi$
$618$	−28.7477	−	16.5975i	−1.15640	−	0.667650i
$619$			2.01810i			0.0811143i	0.999177	+	0.0405572i	$0.0129133\pi$
$619$			2.01810i			0.0811143i	−0.999177	+	0.0405572i	$0.987087\pi$
$620$		0			0
$621$	−11.4564	−	19.8431i	−0.459731	−	0.796278i
$622$	3.00000	−	1.73205i	0.120289	−	0.0694489i
$623$	−7.41742			−0.297173
$624$	−6.26951	−	1.55130i	−0.250981	−	0.0621017i
$625$		0			0
$626$	−58.2867	+	33.6519i	−2.32961	+	1.34500i
$627$	2.29129	+	3.96863i	0.0915052	+	0.158492i
$628$	12.7913	−	22.1552i	0.510428	−	0.884087i
$629$			36.3731i			1.45029i
$630$		0			0
$631$	−18.8739	−	10.8968i	−0.751357	−	0.433796i	0.0748272	−	0.997197i	$-0.476159\pi$
$631$	−18.8739	−	10.8968i	−0.751357	−	0.433796i	−0.826184	+	0.563401i	$0.809493\pi$
$632$		−	10.3923i		−	0.413384i
$633$	9.08258	−	15.7315i	0.361000	−	0.625270i
$634$	22.9564	+	39.7617i	0.911717	+	1.57914i
$635$		0			0
$636$	4.41742			0.175162
$637$	10.0000	−	10.3923i	0.396214	−	0.411758i
$638$	−26.5390			−1.05069
$639$	−6.16515	+	3.55945i	−0.243890	+	0.140810i
$640$		0			0
$641$	0.0825757	−	0.143025i	0.00326154	−	0.00564916i	−0.864390	−	0.502822i	$-0.832295\pi$
$641$	0.0825757	−	0.143025i	0.00326154	−	0.00564916i	0.867652	+	0.497173i	$0.165628\pi$
$642$			3.10260i			0.122450i
$643$	−5.12614	−	2.95958i	−0.202155	−	0.116714i	0.395505	−	0.918464i	$-0.370570\pi$
$643$	−5.12614	−	2.95958i	−0.202155	−	0.116714i	−0.597660	+	0.801749i	$0.703903\pi$
$644$	−19.1869	−	11.0776i	−0.756071	−	0.436518i
$645$		0			0
$646$	−8.68693	+	15.0462i	−0.341783	+	0.591985i
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	0.999357	+	0.0358667i	$0.0114192\pi$
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	−0.468617	+	0.883402i	$0.655247\pi$
$648$	1.50000	−	0.866025i	0.0589256	−	0.0340207i
$649$	8.91288			0.349861
$650$		0			0
$651$	−16.7477			−0.656395
$652$	−25.8131	+	14.9032i	−1.01092	+	0.583654i
$653$	24.4129	+	42.2843i	0.955350	+	1.65471i	0.733566	+	0.679619i	$0.237855\pi$
$653$	24.4129	+	42.2843i	0.955350	+	1.65471i	0.221784	+	0.975096i	$0.428812\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$		0			0
$656$	−4.10436	−	2.36965i	−0.160248	−	0.0925193i
$657$		0			0
$658$		−	33.1950i		−	1.29408i
$659$	12.2477	−	21.2137i	0.477104	−	0.826368i	−0.522552	−	0.852607i	$-0.675020\pi$
$659$	12.2477	−	21.2137i	0.477104	−	0.826368i	0.999656	+	0.0262396i	$0.00835327\pi$
$660$		0			0
$661$	2.12614	−	1.22753i	0.0826971	−	0.0477452i	−0.458081	−	0.888910i	$-0.651463\pi$
$661$	2.12614	−	1.22753i	0.0826971	−	0.0477452i	0.540778	+	0.841165i	$0.318130\pi$
$662$	−24.9564			−0.969960
$663$	4.58258	+	15.8745i	0.177972	+	0.616515i
$664$	19.5826			0.759951
$665$		0			0
$666$	−17.3739	−	30.0924i	−0.673224	−	1.16606i
$667$	10.5000	−	18.1865i	0.406562	−	0.704185i
$668$			11.9536i			0.462497i
$669$	7.50000	+	4.33013i	0.289967	+	0.167412i
$670$		0			0
$671$		−	27.9989i		−	1.08088i
$672$	6.39564	−	11.0776i	0.246717	−	0.427327i
$673$	−2.91742	−	5.05313i	−0.112458	−	0.194784i	0.804302	−	0.594220i	$-0.202539\pi$
$673$	−2.91742	−	5.05313i	−0.112458	−	0.194784i	−0.916761	+	0.399436i	$0.869206\pi$
$674$	6.16515	−	3.55945i	0.237473	−	0.137105i
$675$		0			0
$676$	1.39564	+	36.2599i	0.0536786	+	1.39461i
$677$	21.1652			0.813443			0.406721	−	0.913552i	$-0.366672\pi$
$677$	21.1652			0.813443			0.406721	+	0.913552i	$0.366672\pi$
$678$	31.4347	−	18.1488i	1.20724	−	0.697001i
$679$	−3.87386	−	6.70973i	−0.148665	−	0.257496i
$680$		0			0
$681$		−	6.10985i		−	0.234130i
$682$	−48.4955	−	27.9989i	−1.85699	−	1.07213i
$683$	10.3348	+	5.96683i	0.395452	+	0.228314i	0.684520	−	0.728994i	$-0.260012\pi$
$683$	10.3348	+	5.96683i	0.395452	+	0.228314i	−0.289068	+	0.957309i	$0.593345\pi$
$684$		−	9.66930i		−	0.369715i
$685$		0			0
$686$	20.8521	+	36.1169i	0.796136	+	1.37895i
$687$	4.74773	−	2.74110i	0.181137	−	0.104580i
$688$	2.53901			0.0967990
$689$	1.58258	+	5.48220i	0.0602913	+	0.208855i
$690$		0			0
$691$	30.8739	−	17.8250i	1.17450	−	0.678096i	0.219762	−	0.975554i	$-0.429472\pi$
$691$	30.8739	−	17.8250i	1.17450	−	0.678096i	0.954735	+	0.297457i	$0.0961386\pi$
$692$	10.3521	+	17.9303i	0.393527	+	0.681609i
$693$	4.58258	−	7.93725i	0.174078	−	0.301511i
$694$			33.5565i			1.27379i
$695$		0			0
$696$	−6.87386	−	3.96863i	−0.260553	−	0.150430i
$697$			12.1244i			0.459243i
$698$	20.0608	−	34.7463i	0.759312	−	1.31517i
$699$	−10.5826	−	18.3296i	−0.400270	−	0.693288i
$700$		0			0
$701$	−2.83485			−0.107071			−0.0535354	−	0.998566i	$-0.517049\pi$
$701$	−2.83485			−0.107071			−0.0535354	+	0.998566i	$0.517049\pi$
$702$	−28.4347	−	27.3613i	−1.07320	−	1.03268i
$703$	−13.7477			−0.518505
$704$	28.8303	−	16.6452i	1.08658	−	0.627339i
$705$		0			0
$706$	19.0608	−	33.0143i	0.717362	−	1.24251i
$707$		−	15.5885i		−	0.586264i
$708$	8.14337	+	4.70158i	0.306047	+	0.176696i
$709$	−31.5000	−	18.1865i	−1.18301	−	0.683010i	−0.226299	−	0.974058i	$-0.572663\pi$
$709$	−31.5000	−	18.1865i	−1.18301	−	0.683010i	−0.956708	+	0.291048i	$0.905996\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	−3.70871	−	6.42368i	−0.138990	−	0.240738i
$713$	38.3739	−	22.1552i	1.43711	−	0.829717i
$714$	−17.3739			−0.650201
$715$		0			0
$716$	0.460985			0.0172278
$717$	18.1652	−	10.4877i	0.678390	−	0.391669i
$718$	−36.5390	−	63.2874i	−1.36362	−	2.36187i
$719$	−15.2477	+	26.4098i	−0.568644	+	0.984921i	0.428056	+	0.903752i	$0.359199\pi$
$719$	−15.2477	+	26.4098i	−0.568644	+	0.984921i	−0.996700	+	0.0811686i	$0.974135\pi$
$720$		0			0
$721$	22.7477	+	13.1334i	0.847170	+	0.489114i
$722$	30.3303	+	17.5112i	1.12878	+	0.651700i
$723$		−	1.73205i		−	0.0644157i
$724$	−26.1652	+	45.3194i	−0.972420	+	1.68428i
$725$		0			0
$726$	7.58258	−	4.37780i	0.281416	−	0.162475i
$727$	42.7477			1.58543			0.792713	−	0.609595i	$-0.208668\pi$
$727$	42.7477			1.58543			0.792713	+	0.609595i	$0.208668\pi$
$728$	−10.5000	−	2.59808i	−0.389156	−	0.0962911i
$729$	13.0000			0.481481
$730$		0			0
$731$	−3.24773	−	5.62523i	−0.120122	−	0.208057i
$732$	14.7695	−	25.5815i	0.545897	−	0.945521i
$733$		−	8.94630i		−	0.330439i	−0.986257	−	0.165220i	$-0.947167\pi$
$733$		−	8.94630i		−	0.330439i	0.986257	−	0.165220i	$-0.0528333\pi$
$734$	−48.8085	−	28.1796i	−1.80156	−	1.04013i
$735$		0			0
$736$			33.8426i			1.24745i
$737$	19.6652	−	34.0610i	0.724375	−	1.25465i
$738$	−5.79129	−	10.0308i	−0.213180	−	0.369239i
$739$	42.2477	−	24.3917i	1.55411	−	0.897265i	0.556307	−	0.830977i	$-0.312218\pi$
$739$	42.2477	−	24.3917i	1.55411	−	0.897265i	0.997801	−	0.0662878i	$-0.0211156\pi$
$740$		0			0
$741$	−6.00000	+	1.73205i	−0.220416	+	0.0636285i
$742$	−6.00000			−0.220267
$743$	−37.0390	+	21.3845i	−1.35883	+	0.784521i	−0.989466	−	0.144764i	$-0.953758\pi$
$743$	−37.0390	+	21.3845i	−1.35883	+	0.784521i	−0.369364	+	0.929285i	$0.620424\pi$
$744$	−8.37386	−	14.5040i	−0.307001	−	0.531741i
$745$		0			0
$746$		−	28.4557i		−	1.04184i
$747$	−19.5826	−	11.3060i	−0.716489	−	0.413665i
$748$	−29.3085	−	16.9213i	−1.07163	−	0.618703i
$749$		−	2.45505i		−	0.0897056i
$750$		0			0
$751$	7.87386	+	13.6379i	0.287321	+	0.497655i	0.973169	−	0.230090i	$-0.0739019\pi$
$751$	7.87386	+	13.6379i	0.287321	+	0.497655i	−0.685848	+	0.727745i	$0.740569\pi$
$752$	−13.5826	+	7.84190i	−0.495306	+	0.285965i
$753$	−18.1652			−0.661975
$754$	8.68693	−	35.1078i	0.316359	−	1.27855i
$755$		0			0
$756$	20.9347	−	12.0866i	0.761386	−	0.439587i
$757$	−8.87386	−	15.3700i	−0.322526	−	0.558632i	0.658482	−	0.752596i	$-0.271199\pi$
$757$	−8.87386	−	15.3700i	−0.322526	−	0.558632i	−0.981009	+	0.193965i	$0.937865\pi$
$758$	23.0608	−	39.9425i	0.837606	−	1.45078i
$759$		−	12.1244i		−	0.440086i
$760$		0			0
$761$	−35.2913	−	20.3754i	−1.27931	−	0.738609i	−0.302587	−	0.953122i	$-0.597850\pi$
$761$	−35.2913	−	20.3754i	−1.27931	−	0.738609i	−0.976721	+	0.214513i	$0.931184\pi$
$762$			21.3368i			0.772951i
$763$	−2.37386	+	4.11165i	−0.0859396	+	0.148852i
$764$	−10.3521	−	17.9303i	−0.374525	−	0.648697i
$765$		0			0
$766$	6.20871			0.224330
$767$	−2.91742	+	11.7906i	−0.105342	+	0.425735i
$768$	2.79129			0.100722
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	−0.236433	−	0.971648i	$-0.575978\pi$
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	0.723255	+	0.690581i	$0.242645\pi$
$770$		0			0
$771$	−0.0825757	+	0.143025i	−0.00297389	+	0.00515093i
$772$		−	2.81655i		−	0.101370i
$773$	−30.0826	−	17.3682i	−1.08200	−	0.624690i	−0.150561	−	0.988601i	$-0.548108\pi$
$773$	−30.0826	−	17.3682i	−1.08200	−	0.624690i	−0.931434	+	0.363911i	$0.881441\pi$
$774$	5.37386	+	3.10260i	0.193160	+	0.111521i
$775$		0			0
$776$	3.87386	−	6.70973i	0.139064	−	0.240865i
$777$	−6.87386	−	11.9059i	−0.246598	−	0.427121i
$778$	−28.7477	+	16.5975i	−1.03066	+	0.595049i
$779$	−4.58258			−0.164188
$780$		0			0
$781$	−9.41742			−0.336982
$782$	39.8085	−	22.9835i	1.42355	−	0.821887i
$783$	11.4564	+	19.8431i	0.409420	+	0.709136i
$784$	3.58258	−	6.20520i	0.127949	−	0.221614i
$785$		0			0
$786$	−3.00000	−	1.73205i	−0.107006	−	0.0617802i
$787$	−27.8739	−	16.0930i	−0.993596	−	0.573653i	−0.0872487	−	0.996187i	$-0.527807\pi$
$787$	−27.8739	−	16.0930i	−0.993596	−	0.573653i	−0.906347	+	0.422534i	$0.861141\pi$
$788$			55.7316i			1.98536i
$789$	−4.50000	+	7.79423i	−0.160204	+	0.277482i
$790$		0			0
$791$	−24.8739	+	14.3609i	−0.884413	+	0.510616i
$792$	9.16515			0.325669
$793$	37.0390	+	9.16478i	1.31529	+	0.325451i
$794$	59.7042			2.11882
$795$		0			0
$796$	1.97822	+	3.42638i	0.0701161	+	0.121445i
$797$	−10.0390	+	17.3881i	−0.355600	+	0.615918i	−0.987220	−	0.159360i	$-0.949057\pi$
$797$	−10.0390	+	17.3881i	−0.355600	+	0.615918i	0.631620	+	0.775278i	$0.282390\pi$
$798$		−	6.56670i		−	0.232459i
$799$	34.7477	+	20.0616i	1.22929	+	0.709729i
$800$		0			0
$801$			8.56490i			0.302626i
$802$	−13.6869	+	23.7065i	−0.483302	+	0.837104i
$803$		0			0
$804$	35.9347	−	20.7469i	1.26732	−	0.731686i
$805$		0			0
$806$	52.9129	−	54.9887i	1.86378	−	1.93689i
$807$	15.0000			0.528025
$808$	13.5000	−	7.79423i	0.474928	−	0.274200i
$809$	−18.4129	−	31.8920i	−0.647362	−	1.12126i	−0.983750	−	0.179541i	$-0.942539\pi$
$809$	−18.4129	−	31.8920i	−0.647362	−	1.12126i	0.336388	−	0.941723i	$-0.390795\pi$
$810$		0			0
$811$			18.7665i			0.658981i	0.944159	+	0.329491i	$0.106877\pi$
$811$			18.7665i			0.658981i	−0.944159	+	0.329491i	$0.893123\pi$
$812$	19.1869	+	11.0776i	0.673329	+	0.388747i
$813$	7.50000	+	4.33013i	0.263036	+	0.151864i
$814$		−	45.9669i		−	1.61114i
$815$		0			0
$816$	4.10436	+	7.10895i	0.143681	+	0.248863i
$817$	2.12614	−	1.22753i	0.0743841	−	0.0429457i
$818$	18.9564			0.662796
$819$	9.00000	+	8.66025i	0.314485	+	0.302614i
$820$		0			0
$821$	20.2913	−	11.7152i	0.708171	−	0.408863i	−0.102213	−	0.994763i	$-0.532592\pi$
$821$	20.2913	−	11.7152i	0.708171	−	0.408863i	0.810383	+	0.585900i	$0.199259\pi$
$822$	−0.104356	−	0.180750i	−0.00363984	−	0.00630438i
$823$	−20.2913	+	35.1455i	−0.707310	+	1.22510i	0.258542	+	0.966000i	$0.416758\pi$
$823$	−20.2913	+	35.1455i	−0.707310	+	1.22510i	−0.965851	+	0.259096i	$0.916575\pi$
$824$			26.2668i			0.915048i
$825$		0			0
$826$	−11.0608	−	6.38595i	−0.384854	−	0.222196i
$827$			31.5583i			1.09739i	0.836023	+	0.548695i	$0.184875\pi$
$827$			31.5583i			1.09739i	−0.836023	+	0.548695i	$0.815125\pi$
$828$	−12.7913	+	22.1552i	−0.444528	+	0.769945i
$829$	−1.66515	−	2.88413i	−0.0578331	−	0.100170i	0.835659	−	0.549248i	$-0.185086\pi$
$829$	−1.66515	−	2.88413i	−0.0578331	−	0.100170i	−0.893492	+	0.449078i	$0.851752\pi$
$830$		0			0
$831$	−16.5826			−0.575243
$832$	12.5826	+	43.5873i	0.436222	+	1.51112i
$833$	−18.3303			−0.635107
$834$	10.8956	−	6.29060i	0.377285	−	0.217826i
$835$		0			0
$836$	6.39564	−	11.0776i	0.221198	−	0.383126i
$837$			48.3465i			1.67110i
$838$	−45.8085	−	26.4476i	−1.58243	−	0.913616i
$839$	−1.16970	−	0.675325i	−0.0403824	−	0.0233148i	0.479673	−	0.877447i	$-0.340755\pi$
$839$	−1.16970	−	0.675325i	−0.0403824	−	0.0233148i	−0.520055	+	0.854133i	$0.674089\pi$
$840$		0			0
$841$	4.00000	−	6.92820i	0.137931	−	0.238904i
$842$	−28.7477	−	49.7925i	−0.990712	−	1.71596i
$843$	−15.1652	+	8.75560i	−0.522316	+	0.301559i
$844$	−50.7042			−1.74531
$845$		0			0
$846$	−38.3303			−1.31782
$847$	−6.00000	+	3.46410i	−0.206162	+	0.119028i
$848$	1.41742	+	2.45505i	0.0486746	+	0.0843068i
$849$	0.126136	−	0.218475i	0.00432899	−	0.00749803i
$850$		0			0
$851$	31.5000	+	18.1865i	1.07981	+	0.623426i
$852$	−8.60436	−	4.96773i	−0.294780	−	0.170192i
$853$		−	53.2566i		−	1.82347i	−0.410777	−	0.911736i	$-0.634742\pi$
$853$		−	53.2566i		−	1.82347i	0.410777	−	0.911736i	$-0.365258\pi$
$854$	−20.0608	+	34.7463i	−0.686466	+	1.18899i
$855$		0			0
$856$	2.12614	−	1.22753i	0.0726698	−	0.0419560i
$857$	−22.7477			−0.777048			−0.388524	−	0.921439i	$-0.627015\pi$
$857$	−22.7477			−0.777048			−0.388524	+	0.921439i	$0.627015\pi$
$858$	−5.79129	−	20.0616i	−0.197711	−	0.684892i
$859$	38.2432			1.30484			0.652420	−	0.757857i	$-0.273754\pi$
$859$	38.2432			1.30484			0.652420	+	0.757857i	$0.273754\pi$
$860$		0			0
$861$	−2.29129	−	3.96863i	−0.0780869	−	0.135250i
$862$	−32.4347	+	56.1785i	−1.10473	+	1.91345i
$863$			34.8317i			1.18569i	0.805318	+	0.592843i	$0.201994\pi$
$863$			34.8317i			1.18569i	−0.805318	+	0.592843i	$0.798006\pi$
$864$	−31.9782	−	18.4626i	−1.08792	−	0.628112i
$865$		0			0
$866$		−	38.8480i		−	1.32011i
$867$	2.00000	−	3.46410i	0.0679236	−	0.117647i
$868$	23.3739	+	40.4847i	0.793361	+	1.37414i
$869$	−13.7477	+	7.93725i	−0.466360	+	0.269253i
$870$		0			0
$871$	38.6216	+	37.1636i	1.30864	+	1.25924i
$872$	−4.74773			−0.160778
$873$	−7.74773	+	4.47315i	−0.262221	+	0.151393i
$874$	8.68693	+	15.0462i	0.293840	+	0.508946i
$875$		0			0
$876$		0			0
$877$	−6.87386	−	3.96863i	−0.232114	−	0.134011i	0.379433	−	0.925219i	$-0.376119\pi$
$877$	−6.87386	−	3.96863i	−0.232114	−	0.134011i	−0.611547	+	0.791208i	$0.709452\pi$
$878$	76.7650	+	44.3203i	2.59069	+	1.49574i
$879$		−	23.4304i		−	0.790286i
$880$		0			0
$881$	9.24773	+	16.0175i	0.311564	+	0.539644i	0.978701	−	0.205290i	$-0.0658139\pi$
$881$	9.24773	+	16.0175i	0.311564	+	0.539644i	−0.667137	+	0.744935i	$0.732481\pi$
$882$	15.1652	−	8.75560i	0.510637	−	0.294817i
$883$	46.2432			1.55621			0.778103	−	0.628136i	$-0.216182\pi$
$883$	46.2432			1.55621			0.778103	+	0.628136i	$0.216182\pi$
$884$	31.9782	−	33.2327i	1.07554	−	1.11774i
$885$		0			0
$886$	−49.1216	+	28.3604i	−1.65027	+	0.952785i
$887$	−0.247727	−	0.429076i	−0.00831786	−	0.0144070i	0.861837	−	0.507186i	$-0.169314\pi$
$887$	−0.247727	−	0.429076i	−0.00831786	−	0.0144070i	−0.870154	+	0.492779i	$0.835981\pi$
$888$	6.87386	−	11.9059i	0.230672	−	0.399535i
$889$		−	16.8836i		−	0.566256i
$890$		0			0
$891$	−2.29129	−	1.32288i	−0.0767610	−	0.0443180i
$892$		−	24.1733i		−	0.809381i
$893$	−7.58258	+	13.1334i	−0.253741	+	0.439493i
$894$	10.6869	+	18.5103i	0.357424	+	0.619077i
$895$		0			0
$896$	−22.1216			−0.739030
$897$	16.0390	+	3.96863i	0.535527	+	0.132509i
$898$	82.0345			2.73753
$899$	−38.3739	+	22.1552i	−1.27984	+	0.738916i
$900$		0			0
$901$	3.62614	−	6.28065i	0.120804	−	0.209239i
$902$		−	15.3223i		−	0.510177i
$903$	2.12614	+	1.22753i	0.0707534	+	0.0408495i
$904$	−24.8739	−	14.3609i	−0.827292	−	0.477637i
$905$		0			0
$906$	−6.79129	+	11.7629i	−0.225625	+	0.390795i
$907$	−16.8739	−	29.2264i	−0.560287	−	0.970446i	−0.997471	−	0.0710740i	$-0.977357\pi$
$907$	−16.8739	−	29.2264i	−0.560287	−	0.970446i	0.437184	−	0.899372i	$-0.355976\pi$
$908$	−14.7695	+	8.52718i	−0.490143	+	0.282984i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	37.9129			1.25611			0.628055	−	0.778169i	$-0.283851\pi$
$911$	37.9129			1.25611			0.628055	+	0.778169i	$0.283851\pi$
$912$	−2.68693	+	1.55130i	−0.0889732	+	0.0513687i
$913$	−14.9564	−	25.9053i	−0.494986	−	0.857341i
$914$	−1.89564	+	3.28335i	−0.0627023	+	0.108604i
$915$		0			0
$916$	−13.2523	−	7.65120i	−0.437867	−	0.252803i
$917$	2.37386	+	1.37055i	0.0783919	+	0.0452596i
$918$			50.1540i			1.65533i
$919$	−17.9174	+	31.0339i	−0.591041	+	1.02371i	0.403051	+	0.915177i	$0.367950\pi$
$919$	−17.9174	+	31.0339i	−0.591041	+	1.02371i	−0.994093	+	0.108536i	$0.965384\pi$
$920$		0			0
$921$	21.0000	−	12.1244i	0.691974	−	0.399511i
$922$	2.62614			0.0864872
$923$	3.08258	−	12.4581i	0.101464	−	0.410063i
$924$	12.7913			0.420802
$925$		0			0
$926$	9.00000	+	15.5885i	0.295758	+	0.512268i
$927$	15.1652	−	26.2668i	0.498089	−	0.862715i
$928$		−	33.8426i		−	1.11094i
$929$	13.8303	+	7.98493i	0.453758	+	0.261977i	0.709416	−	0.704790i	$-0.248959\pi$
$929$	13.8303	+	7.98493i	0.453758	+	0.261977i	−0.255658	+	0.966767i	$0.582292\pi$
$930$		0			0
$931$		−	6.92820i		−	0.227063i
$932$	−29.5390	+	51.1631i	−0.967583	+	1.67590i
$933$	−0.791288	−	1.37055i	−0.0259056	−	0.0448698i
$934$	23.3739	−	13.4949i	0.764816	−	0.441567i
$935$		0			0
$936$	−3.00000	+	12.1244i	−0.0980581	+	0.396297i
$937$	23.4955			0.767563			0.383782	−	0.923424i	$-0.374622\pi$
$937$	23.4955			0.767563			0.383782	+	0.923424i	$0.374622\pi$
$938$	−48.8085	+	28.1796i	−1.59365	+	0.920097i
$939$	15.3739	+	26.6283i	0.501707	+	0.868982i
$940$		0			0
$941$		−	26.4575i		−	0.862490i	−0.902235	−	0.431245i	$-0.858074\pi$
$941$		−	26.4575i		−	0.862490i	0.902235	−	0.431245i	$-0.141926\pi$
$942$	−17.3739	−	10.0308i	−0.566071	−	0.326821i
$943$	10.5000	+	6.06218i	0.341927	+	0.197412i
$944$			6.03440i			0.196403i
$945$		0			0
$946$	4.10436	+	7.10895i	0.133444	+	0.231132i
$947$	−33.4129	+	19.2909i	−1.08577	+	0.626871i	−0.932448	−	0.361305i	$-0.882331\pi$
$947$	−33.4129	+	19.2909i	−1.08577	+	0.626871i	−0.153325	+	0.988176i	$0.548998\pi$
$948$	−16.7477			−0.543941
$949$		0			0
$950$		0			0
$951$	18.1652	−	10.4877i	0.589045	−	0.340086i
$952$	6.87386	+	11.9059i	0.222783	+	0.385872i
$953$	28.0390	−	48.5650i	0.908273	−	1.57317i	0.0918100	−	0.995777i	$-0.470735\pi$
$953$	28.0390	−	48.5650i	0.908273	−	1.57317i	0.816463	−	0.577398i	$-0.195932\pi$
$954$			6.92820i			0.224309i
$955$		0			0
$956$	−50.7042	−	29.2741i	−1.63989	−	0.946791i
$957$			12.1244i			0.391925i
$958$	−35.4347	+	61.3746i	−1.14484	+	1.98292i
$959$	0.0825757	+	0.143025i	0.00266651	+	0.00461853i
$960$		0			0
$961$	−62.4955			−2.01598
$962$	60.8085	+	15.0462i	1.96055	+	0.485109i
$963$	−2.83485			−0.0913517
$964$	−4.18693	+	2.41733i	−0.134852	+	0.0778568i
$965$		0			0
$966$	−8.68693	+	15.0462i	−0.279497	+	0.484104i
$967$			21.5076i			0.691638i	0.938301	+	0.345819i	$0.112399\pi$
$967$			21.5076i			0.691638i	−0.938301	+	0.345819i	$0.887601\pi$
$968$	−6.00000	−	3.46410i	−0.192847	−	0.111340i
$969$	6.87386	+	3.96863i	0.220820	+	0.127491i
$970$		0			0
$971$	−18.2477	+	31.6060i	−0.585597	+	1.01428i	0.409203	+	0.912443i	$0.365807\pi$
$971$	−18.2477	+	31.6060i	−0.585597	+	1.01428i	−0.994801	+	0.101841i	$0.967527\pi$
$972$	−22.3303	−	38.6772i	−0.716245	−	1.24057i
$973$	−8.62159	+	4.97768i	−0.276396	+	0.159577i
$974$	−46.1216			−1.47783
$975$		0			0
$976$	18.9564			0.606781
$977$	33.5780	−	19.3863i	1.07426	−	0.620222i	0.144915	−	0.989444i	$-0.453709\pi$
$977$	33.5780	−	19.3863i	1.07426	−	0.620222i	0.929341	+	0.369222i	$0.120376\pi$
$978$	11.6869	+	20.2424i	0.373707	+	0.647279i
$979$	−5.66515	+	9.81233i	−0.181059	+	0.313603i
$980$		0			0
$981$	4.74773	+	2.74110i	0.151583	+	0.0875166i
$982$	54.1824	+	31.2822i	1.72903	+	0.998256i
$983$		−	3.12250i		−	0.0995924i	−0.998759	−	0.0497962i	$-0.984143\pi$
$983$		−	3.12250i		−	0.0995924i	0.998759	−	0.0497962i	$-0.0158572\pi$
$984$	2.29129	−	3.96863i	0.0730436	−	0.126515i
$985$		0			0
$986$	−39.8085	+	22.9835i	−1.26776	+	0.731943i
$987$	−15.1652			−0.482712
$988$	12.5608	+	12.0866i	0.399612	+	0.384527i
$989$	−6.49545			−0.206543
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$	35.7042	−	61.8414i	1.13361	−	1.96347i
$993$			11.4014i			0.361811i
$994$	11.6869	+	6.74745i	0.370687	+	0.214016i
$995$		0			0
$996$		−	31.5583i		−	0.999963i
$997$	−9.08258	+	15.7315i	−0.287648	+	0.498221i	−0.973248	−	0.229758i	$-0.926207\pi$
$997$	−9.08258	+	15.7315i	−0.287648	+	0.498221i	0.685600	+	0.727979i	$0.259540\pi$
$998$	−18.1652	−	31.4630i	−0.575008	−	0.995943i
$999$	−34.3693	+	19.8431i	−1.08740	+	0.627809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.b.101.1		4
5.2	odd	4		65.2.l.a.49.1	yes	8
5.3	odd	4		65.2.l.a.49.4	yes	8
5.4	even	2		325.2.n.c.101.2		4
13.2	odd	12		4225.2.a.bj.1.1		4
13.4	even	6	inner	325.2.n.b.251.1		4
13.11	odd	12		4225.2.a.bj.1.4		4
15.2	even	4		585.2.bf.a.244.4		8
15.8	even	4		585.2.bf.a.244.1		8
20.3	even	4		1040.2.df.b.49.3		8
20.7	even	4		1040.2.df.b.49.2		8
65.2	even	12		845.2.b.f.339.2		8
65.3	odd	12		845.2.d.c.844.1		8
65.4	even	6		325.2.n.c.251.2		4
65.7	even	12		845.2.n.c.529.1		8
65.8	even	4		845.2.n.c.484.1		8
65.12	odd	4		845.2.l.c.699.4		8
65.17	odd	12		65.2.l.a.4.4	yes	8
65.18	even	4		845.2.n.d.484.3		8
65.22	odd	12		845.2.l.c.654.1		8
65.23	odd	12		845.2.d.c.844.7		8
65.24	odd	12		4225.2.a.bk.1.1		4
65.28	even	12		845.2.b.f.339.7		8
65.32	even	12		845.2.n.d.529.3		8
65.33	even	12		845.2.n.d.529.4		8
65.37	even	12		845.2.b.f.339.8		8
65.38	odd	4		845.2.l.c.699.1		8
65.42	odd	12		845.2.d.c.844.8		8
65.43	odd	12		65.2.l.a.4.1	✓	8
65.47	even	4		845.2.n.d.484.4		8
65.48	odd	12		845.2.l.c.654.4		8
65.54	odd	12		4225.2.a.bk.1.4		4
65.57	even	4		845.2.n.c.484.2		8
65.58	even	12		845.2.n.c.529.2		8
65.62	odd	12		845.2.d.c.844.2		8
65.63	even	12		845.2.b.f.339.1		8
195.17	even	12		585.2.bf.a.199.1		8
195.173	even	12		585.2.bf.a.199.4		8
260.43	even	12		1040.2.df.b.849.2		8
260.147	even	12		1040.2.df.b.849.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.1	✓	8	65.43	odd	12
65.2.l.a.4.4	yes	8	65.17	odd	12
65.2.l.a.49.1	yes	8	5.2	odd	4
65.2.l.a.49.4	yes	8	5.3	odd	4
325.2.n.b.101.1		4	1.1	even	1	trivial
325.2.n.b.251.1		4	13.4	even	6	inner
325.2.n.c.101.2		4	5.4	even	2
325.2.n.c.251.2		4	65.4	even	6
585.2.bf.a.199.1		8	195.17	even	12
585.2.bf.a.199.4		8	195.173	even	12
585.2.bf.a.244.1		8	15.8	even	4
585.2.bf.a.244.4		8	15.2	even	4
845.2.b.f.339.1		8	65.63	even	12
845.2.b.f.339.2		8	65.2	even	12
845.2.b.f.339.7		8	65.28	even	12
845.2.b.f.339.8		8	65.37	even	12
845.2.d.c.844.1		8	65.3	odd	12
845.2.d.c.844.2		8	65.62	odd	12
845.2.d.c.844.7		8	65.23	odd	12
845.2.d.c.844.8		8	65.42	odd	12
845.2.l.c.654.1		8	65.22	odd	12
845.2.l.c.654.4		8	65.48	odd	12
845.2.l.c.699.1		8	65.38	odd	4
845.2.l.c.699.4		8	65.12	odd	4
845.2.n.c.484.1		8	65.8	even	4
845.2.n.c.484.2		8	65.57	even	4
845.2.n.c.529.1		8	65.7	even	12
845.2.n.c.529.2		8	65.58	even	12
845.2.n.d.484.3		8	65.18	even	4
845.2.n.d.484.4		8	65.47	even	4
845.2.n.d.529.3		8	65.32	even	12
845.2.n.d.529.4		8	65.33	even	12
1040.2.df.b.49.2		8	20.7	even	4
1040.2.df.b.49.3		8	20.3	even	4
1040.2.df.b.849.2		8	260.43	even	12
1040.2.df.b.849.3		8	260.147	even	12
4225.2.a.bj.1.1		4	13.2	odd	12
4225.2.a.bj.1.4		4	13.11	odd	12
4225.2.a.bk.1.1		4	65.24	odd	12
4225.2.a.bk.1.4		4	65.54	odd	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89564 + 1.09445i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.39564 - 2.41733i) q^{4} +(-1.89564 - 1.09445i) q^{6} +(1.50000 + 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(2.29129 - 1.32288i) q^{11} +2.79129 q^{12} +(1.00000 + 3.46410i) q^{13} -3.79129 q^{14} +(0.895644 + 1.55130i) q^{16} +(2.29129 - 3.96863i) q^{17} +4.37780i q^{18} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-2.89564 + 5.01540i) q^{22} +(-2.29129 - 3.96863i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(-5.68693 - 5.47225i) q^{26} +5.00000 q^{27} +(4.18693 - 2.41733i) q^{28} +(2.29129 + 3.96863i) q^{29} +9.66930i q^{31} +(-6.39564 - 3.69253i) q^{32} +(2.29129 + 1.32288i) q^{33} +10.0308i q^{34} +(-2.79129 - 4.83465i) q^{36} +(-6.87386 + 3.96863i) q^{37} -3.79129 q^{38} +(-2.50000 + 2.59808i) q^{39} +(-2.29129 + 1.32288i) q^{41} +(-1.89564 - 3.28335i) q^{42} +(0.708712 - 1.22753i) q^{43} -7.38505i q^{44} +(8.68693 + 5.01540i) q^{46} +8.75560i q^{47} +(-0.895644 + 1.55130i) q^{48} +(-2.00000 - 3.46410i) q^{49} +4.58258 q^{51} +(9.76951 + 2.41733i) q^{52} +1.58258 q^{53} +(-9.47822 + 5.47225i) q^{54} +(-1.50000 + 2.59808i) q^{56} +1.73205i q^{57} +(-8.68693 - 5.01540i) q^{58} +(2.91742 + 1.68438i) q^{59} +(5.29129 - 9.16478i) q^{61} +(-10.5826 - 18.3296i) q^{62} +(3.00000 - 1.73205i) q^{63} +12.5826 q^{64} -5.79129 q^{66} +(12.8739 - 7.43273i) q^{67} +(-6.39564 - 11.0776i) q^{68} +(2.29129 - 3.96863i) q^{69} +(-3.08258 - 1.77973i) q^{71} +(3.00000 + 1.73205i) q^{72} +(8.68693 - 15.0462i) q^{74} +(4.18693 - 2.41733i) q^{76} +4.58258 q^{77} +(1.89564 - 7.66115i) q^{78} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.89564 - 5.01540i) q^{82} -11.3060i q^{83} +(4.18693 + 2.41733i) q^{84} +3.10260i q^{86} +(-2.29129 + 3.96863i) q^{87} +(2.29129 + 3.96863i) q^{88} +(-3.70871 + 2.14123i) q^{89} +(-1.50000 + 6.06218i) q^{91} -12.7913 q^{92} +(-8.37386 + 4.83465i) q^{93} +(-9.58258 - 16.5975i) q^{94} -7.38505i q^{96} +(-3.87386 - 2.23658i) q^{97} +(7.58258 + 4.37780i) q^{98} -5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 2 q^{3} + q^{4} - 3 q^{6} + 6 q^{7} + 4 q^{9} + 2 q^{12} + 4 q^{13} - 6 q^{14} - q^{16} + 6 q^{19} - 7 q^{22} - 6 q^{24} - 9 q^{26} + 20 q^{27} + 3 q^{28} - 21 q^{32} - 2 q^{36} - 6 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 + 2 * q^3 + q^4 - 3 * q^6 + 6 * q^7 + 4 * q^9 + 2 * q^12 + 4 * q^13 - 6 * q^14 - q^16 + 6 * q^19 - 7 * q^22 - 6 * q^24 - 9 * q^26 + 20 * q^27 + 3 * q^28 - 21 * q^32 - 2 * q^36 - 6 * q^38 - 10 * q^39 - 3 * q^42 + 12 * q^43 + 21 * q^46 + q^48 - 8 * q^49 + 7 * q^52 - 12 * q^53 - 15 * q^54 - 6 * q^56 - 21 * q^58 + 30 * q^59 + 12 * q^61 - 24 * q^62 + 12 * q^63 + 32 * q^64 - 14 * q^66 + 24 * q^67 - 21 * q^68 + 6 * q^71 + 12 * q^72 + 21 * q^74 + 3 * q^76 + 3 * q^78 - 24 * q^79 - 2 * q^81 + 7 * q^82 + 3 * q^84 - 24 * q^89 - 6 * q^91 - 42 * q^92 - 6 * q^93 - 20 * q^94 + 12 * q^97 + 12 * q^98

Introduction

L-functions

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