LMFDB - Embedded newform 76.3.b.b.39.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$14$
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} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.14
Root			$1.94929 - 0.447510i$ of defining polynomial
Character	$\chi$	$=$	76.39
Dual form			76.3.b.b.39.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94929 + 0.447510i) q^{2} +3.19988i q^{3} +(3.59947 + 1.74465i) q^{4} -3.90374 q^{5} +(-1.43198 + 6.23749i) q^{6} -2.64664i q^{7} +(6.23566 + 5.01164i) q^{8} -1.23921 q^{9} +O(q^{10})$	\(q+(1.94929 + 0.447510i) q^{2} +3.19988i q^{3} +(3.59947 + 1.74465i) q^{4} -3.90374 q^{5} +(-1.43198 + 6.23749i) q^{6} -2.64664i q^{7} +(6.23566 + 5.01164i) q^{8} -1.23921 q^{9} +(-7.60953 - 1.74696i) q^{10} -13.2532i q^{11} +(-5.58268 + 11.5179i) q^{12} +1.60050 q^{13} +(1.18440 - 5.15907i) q^{14} -12.4915i q^{15} +(9.91236 + 12.5597i) q^{16} +8.10013 q^{17} +(-2.41559 - 0.554561i) q^{18} +4.35890i q^{19} +(-14.0514 - 6.81068i) q^{20} +8.46893 q^{21} +(5.93094 - 25.8343i) q^{22} -38.2047i q^{23} +(-16.0366 + 19.9534i) q^{24} -9.76079 q^{25} +(3.11984 + 0.716239i) q^{26} +24.8336i q^{27} +(4.61747 - 9.52650i) q^{28} -51.1656 q^{29} +(5.59007 - 24.3496i) q^{30} +13.6518i q^{31} +(13.7015 + 28.9183i) q^{32} +42.4086 q^{33} +(15.7895 + 3.62489i) q^{34} +10.3318i q^{35} +(-4.46052 - 2.16200i) q^{36} -35.3910 q^{37} +(-1.95065 + 8.49676i) q^{38} +5.12140i q^{39} +(-24.3424 - 19.5641i) q^{40} +8.06155 q^{41} +(16.5084 + 3.78993i) q^{42} +16.2115i q^{43} +(23.1223 - 47.7045i) q^{44} +4.83758 q^{45} +(17.0970 - 74.4721i) q^{46} +1.59429i q^{47} +(-40.1894 + 31.7183i) q^{48} +41.9953 q^{49} +(-19.0266 - 4.36805i) q^{50} +25.9194i q^{51} +(5.76095 + 2.79232i) q^{52} +56.8772 q^{53} +(-11.1133 + 48.4078i) q^{54} +51.7371i q^{55} +(13.2640 - 16.5036i) q^{56} -13.9479 q^{57} +(-99.7366 - 22.8971i) q^{58} +106.526i q^{59} +(21.7934 - 44.9628i) q^{60} -35.9021 q^{61} +(-6.10933 + 26.6114i) q^{62} +3.27976i q^{63} +(13.7670 + 62.5018i) q^{64} -6.24794 q^{65} +(82.6667 + 18.9783i) q^{66} +47.5191i q^{67} +(29.1562 + 14.1319i) q^{68} +122.250 q^{69} +(-4.62359 + 20.1397i) q^{70} -125.941i q^{71} +(-7.72733 - 6.21050i) q^{72} +34.2172 q^{73} +(-68.9874 - 15.8378i) q^{74} -31.2333i q^{75} +(-7.60477 + 15.6897i) q^{76} -35.0765 q^{77} +(-2.29188 + 9.98310i) q^{78} +71.1726i q^{79} +(-38.6953 - 49.0297i) q^{80} -90.6173 q^{81} +(15.7143 + 3.60763i) q^{82} -149.310i q^{83} +(30.4836 + 14.7754i) q^{84} -31.6208 q^{85} +(-7.25479 + 31.6008i) q^{86} -163.724i q^{87} +(66.4202 - 82.6425i) q^{88} -169.809 q^{89} +(9.42984 + 2.16486i) q^{90} -4.23595i q^{91} +(66.6541 - 137.517i) q^{92} -43.6841 q^{93} +(-0.713460 + 3.10773i) q^{94} -17.0160i q^{95} +(-92.5351 + 43.8431i) q^{96} +109.526 q^{97} +(81.8610 + 18.7933i) q^{98} +16.4236i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9	$ 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9} - 12 q^{10} + 4 q^{12} + 54 q^{13} + 30 q^{14} + 58 q^{16} + 34 q^{17} + 36 q^{18} + 32 q^{20} - 38 q^{21} + 36 q^{22} - 98 q^{24} - 86 q^{25} - 16 q^{26} + 18 q^{28} + 54 q^{29} - 204 q^{30} + 72 q^{32} + 20 q^{33} - 82 q^{34} + 96 q^{36} + 100 q^{37} - 148 q^{40} + 224 q^{41} + 224 q^{42} - 96 q^{44} - 168 q^{45} + 46 q^{46} + 296 q^{48} - 220 q^{49} - 58 q^{50} - 288 q^{52} + 14 q^{53} - 128 q^{54} + 12 q^{56} + 38 q^{57} - 72 q^{58} + 188 q^{60} + 28 q^{61} + 396 q^{62} - 118 q^{64} - 472 q^{65} - 32 q^{66} + 30 q^{68} + 122 q^{69} + 156 q^{70} + 80 q^{72} + 70 q^{73} - 224 q^{74} + 228 q^{77} + 274 q^{78} - 348 q^{80} + 334 q^{81} - 400 q^{82} - 216 q^{84} + 48 q^{85} - 124 q^{86} + 472 q^{88} + 416 q^{90} + 126 q^{92} - 176 q^{93} - 88 q^{94} - 106 q^{96} + 308 q^{97} + 68 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9 - 12 * q^10 + 4 * q^12 + 54 * q^13 + 30 * q^14 + 58 * q^16 + 34 * q^17 + 36 * q^18 + 32 * q^20 - 38 * q^21 + 36 * q^22 - 98 * q^24 - 86 * q^25 - 16 * q^26 + 18 * q^28 + 54 * q^29 - 204 * q^30 + 72 * q^32 + 20 * q^33 - 82 * q^34 + 96 * q^36 + 100 * q^37 - 148 * q^40 + 224 * q^41 + 224 * q^42 - 96 * q^44 - 168 * q^45 + 46 * q^46 + 296 * q^48 - 220 * q^49 - 58 * q^50 - 288 * q^52 + 14 * q^53 - 128 * q^54 + 12 * q^56 + 38 * q^57 - 72 * q^58 + 188 * q^60 + 28 * q^61 + 396 * q^62 - 118 * q^64 - 472 * q^65 - 32 * q^66 + 30 * q^68 + 122 * q^69 + 156 * q^70 + 80 * q^72 + 70 * q^73 - 224 * q^74 + 228 * q^77 + 274 * q^78 - 348 * q^80 + 334 * q^81 - 400 * q^82 - 216 * q^84 + 48 * q^85 - 124 * q^86 + 472 * q^88 + 416 * q^90 + 126 * q^92 - 176 * q^93 - 88 * q^94 - 106 * q^96 + 308 * q^97 + 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.94929	+	0.447510i	0.974645	+	0.223755i
$2$	1.94929	+	0.447510i	0.974645	+	0.223755i
$3$			3.19988i			1.06663i	0.845918	+	0.533313i	$0.179053\pi$
$3$			3.19988i			1.06663i	−0.845918	+	0.533313i	$0.820947\pi$
$4$	3.59947	+	1.74465i	0.899867	+	0.436164i
$5$	−3.90374			−0.780749			−0.390374	−	0.920656i	$-0.627654\pi$
$5$	−3.90374			−0.780749			−0.390374	+	0.920656i	$0.627654\pi$
$6$	−1.43198	+	6.23749i	−0.238663	+	1.03958i
$7$		−	2.64664i		−	0.378092i	−0.981968	−	0.189046i	$-0.939461\pi$
$7$		−	2.64664i		−	0.378092i	0.981968	−	0.189046i	$-0.0605395\pi$
$8$	6.23566	+	5.01164i	0.779458	+	0.626455i
$9$	−1.23921			−0.137691
$10$	−7.60953	−	1.74696i	−0.760953	−	0.174696i
$11$		−	13.2532i		−	1.20484i	−0.798181	−	0.602418i	$-0.794204\pi$
$11$		−	13.2532i		−	1.20484i	0.798181	−	0.602418i	$-0.205796\pi$
$12$	−5.58268	+	11.5179i	−0.465223	+	0.959822i
$13$	1.60050			0.123115			0.0615576	−	0.998104i	$-0.480393\pi$
$13$	1.60050			0.123115			0.0615576	+	0.998104i	$0.480393\pi$
$14$	1.18440	−	5.15907i	0.0845999	−	0.368505i
$15$		−	12.4915i		−	0.832767i
$16$	9.91236	+	12.5597i	0.619523	+	0.784979i
$17$	8.10013			0.476478			0.238239	−	0.971207i	$-0.423430\pi$
$17$	8.10013			0.476478			0.238239	+	0.971207i	$0.423430\pi$
$18$	−2.41559	−	0.554561i	−0.134199	−	0.0308089i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−14.0514	−	6.81068i	−0.702570	−	0.340534i
$21$	8.46893			0.403282
$22$	5.93094	−	25.8343i	0.269588	−	1.17429i
$23$		−	38.2047i		−	1.66108i	−0.556962	−	0.830538i	$-0.688033\pi$
$23$		−	38.2047i		−	1.66108i	0.556962	−	0.830538i	$-0.311967\pi$
$24$	−16.0366	+	19.9534i	−0.668193	+	0.831390i
$25$	−9.76079			−0.390431
$26$	3.11984	+	0.716239i	0.119994	+	0.0275477i
$27$			24.8336i			0.919762i
$28$	4.61747	−	9.52650i	0.164910	−	0.340232i
$29$	−51.1656			−1.76433			−0.882165	−	0.470940i	$-0.843915\pi$
$29$	−51.1656			−1.76433			−0.882165	+	0.470940i	$0.843915\pi$
$30$	5.59007	−	24.3496i	0.186336	−	0.811652i
$31$			13.6518i			0.440381i	0.975457	+	0.220191i	$0.0706679\pi$
$31$			13.6518i			0.440381i	−0.975457	+	0.220191i	$0.929332\pi$
$32$	13.7015	+	28.9183i	0.428172	+	0.903697i
$33$	42.4086			1.28511
$34$	15.7895	+	3.62489i	0.464397	+	0.106614i
$35$			10.3318i			0.295195i
$36$	−4.46052	−	2.16200i	−0.123903	−	0.0600556i
$37$	−35.3910			−0.956514			−0.478257	−	0.878220i	$-0.658731\pi$
$37$	−35.3910			−0.956514			−0.478257	+	0.878220i	$0.658731\pi$
$38$	−1.95065	+	8.49676i	−0.0513329	+	0.223599i
$39$			5.12140i			0.131318i
$40$	−24.3424	−	19.5641i	−0.608561	−	0.489104i
$41$	8.06155			0.196623			0.0983116	−	0.995156i	$-0.468656\pi$
$41$	8.06155			0.196623			0.0983116	+	0.995156i	$0.468656\pi$
$42$	16.5084	+	3.78993i	0.393057	+	0.0902364i
$43$			16.2115i			0.377010i	0.982072	+	0.188505i	$0.0603643\pi$
$43$			16.2115i			0.377010i	−0.982072	+	0.188505i	$0.939636\pi$
$44$	23.1223	−	47.7045i	0.525506	−	1.08419i
$45$	4.83758			0.107502
$46$	17.0970	−	74.4721i	0.371674	−	1.61896i
$47$			1.59429i			0.0339210i	0.999856	+	0.0169605i	$0.00539895\pi$
$47$			1.59429i			0.0339210i	−0.999856	+	0.0169605i	$0.994601\pi$
$48$	−40.1894	+	31.7183i	−0.837279	+	0.660799i
$49$	41.9953			0.857047
$50$	−19.0266	−	4.36805i	−0.380532	−	0.0873610i
$51$			25.9194i			0.508224i
$52$	5.76095	+	2.79232i	0.110787	+	0.0536984i
$53$	56.8772			1.07315			0.536577	−	0.843851i	$-0.319717\pi$
$53$	56.8772			1.07315			0.536577	+	0.843851i	$0.319717\pi$
$54$	−11.1133	+	48.4078i	−0.205801	+	0.896441i
$55$			51.7371i			0.940675i
$56$	13.2640	−	16.5036i	0.236857	−	0.294706i
$57$	−13.9479			−0.244701
$58$	−99.7366	−	22.8971i	−1.71960	−	0.394778i
$59$			106.526i			1.80553i	0.430135	+	0.902765i	$0.358466\pi$
$59$			106.526i			1.80553i	−0.430135	+	0.902765i	$0.641534\pi$
$60$	21.7934	−	44.9628i	0.363223	−	0.749380i
$61$	−35.9021			−0.588558			−0.294279	−	0.955720i	$-0.595080\pi$
$61$	−35.9021			−0.588558			−0.294279	+	0.955720i	$0.595080\pi$
$62$	−6.10933	+	26.6114i	−0.0985375	+	0.429216i
$63$			3.27976i			0.0520596i
$64$	13.7670	+	62.5018i	0.215109	+	0.976590i
$65$	−6.24794			−0.0961221
$66$	82.6667	+	18.9783i	1.25253	+	0.287550i
$67$			47.5191i			0.709240i	0.935011	+	0.354620i	$0.115390\pi$
$67$			47.5191i			0.709240i	−0.935011	+	0.354620i	$0.884610\pi$
$68$	29.1562	+	14.1319i	0.428767	+	0.207822i
$69$	122.250			1.77175
$70$	−4.62359	+	20.1397i	−0.0660513	+	0.287710i
$71$		−	125.941i		−	1.77382i	−0.461941	−	0.886911i	$-0.652847\pi$
$71$		−	125.941i		−	1.77382i	0.461941	−	0.886911i	$-0.347153\pi$
$72$	−7.72733	−	6.21050i	−0.107324	−	0.0862569i
$73$	34.2172			0.468729			0.234364	−	0.972149i	$-0.424699\pi$
$73$	34.2172			0.468729			0.234364	+	0.972149i	$0.424699\pi$
$74$	−68.9874	−	15.8378i	−0.932262	−	0.214025i
$75$		−	31.2333i		−	0.416444i
$76$	−7.60477	+	15.6897i	−0.100063	+	0.206444i
$77$	−35.0765			−0.455539
$78$	−2.29188	+	9.98310i	−0.0293830	+	0.127988i
$79$			71.1726i			0.900919i	0.892797	+	0.450460i	$0.148740\pi$
$79$			71.1726i			0.900919i	−0.892797	+	0.450460i	$0.851260\pi$
$80$	−38.6953	−	49.0297i	−0.483692	−	0.612871i
$81$	−90.6173			−1.11873
$82$	15.7143	+	3.60763i	0.191638	+	0.0439954i
$83$		−	149.310i		−	1.79891i	−0.437010	−	0.899457i	$-0.643962\pi$
$83$		−	149.310i		−	1.79891i	0.437010	−	0.899457i	$-0.356038\pi$
$84$	30.4836	+	14.7754i	0.362901	+	0.175897i
$85$	−31.6208			−0.372010
$86$	−7.25479	+	31.6008i	−0.0843580	+	0.367452i
$87$		−	163.724i		−	1.88188i
$88$	66.4202	−	82.6425i	0.754776	−	0.939119i
$89$	−169.809			−1.90797			−0.953983	−	0.299861i	$-0.903060\pi$
$89$	−169.809			−1.90797			−0.953983	+	0.299861i	$0.903060\pi$
$90$	9.42984	+	2.16486i	0.104776	+	0.0240540i
$91$		−	4.23595i		−	0.0465488i
$92$	66.6541	−	137.517i	0.724501	−	1.49475i
$93$	−43.6841			−0.469722
$94$	−0.713460	+	3.10773i	−0.00758999	+	0.0330610i
$95$		−	17.0160i		−	0.179116i
$96$	−92.5351	+	43.8431i	−0.963907	+	0.456699i
$97$	109.526			1.12914			0.564569	−	0.825386i	$-0.309042\pi$
$97$	109.526			1.12914			0.564569	+	0.825386i	$0.309042\pi$
$98$	81.8610	+	18.7933i	0.835317	+	0.191769i
$99$			16.4236i			0.165895i
$100$	−35.1336	−	17.0292i	−0.351336	−	0.170292i
$101$	−118.435			−1.17263			−0.586313	−	0.810084i	$-0.699421\pi$
$101$	−118.435			−1.17263			−0.586313	+	0.810084i	$0.699421\pi$
$102$	−11.5992	+	50.5245i	−0.113718	+	0.495338i
$103$			34.5985i			0.335908i	0.985795	+	0.167954i	$0.0537160\pi$
$103$			34.5985i			0.335908i	−0.985795	+	0.167954i	$0.946284\pi$
$104$	9.98017	+	8.02112i	0.0959632	+	0.0771261i
$105$	−33.0605			−0.314862
$106$	110.870	+	25.4531i	1.04595	+	0.240124i
$107$		−	85.2253i		−	0.796498i	−0.917277	−	0.398249i	$-0.869618\pi$
$107$		−	85.2253i		−	0.796498i	0.917277	−	0.398249i	$-0.130382\pi$
$108$	−43.3260	+	89.3876i	−0.401166	+	0.827663i
$109$	146.541			1.34442			0.672208	−	0.740362i	$-0.265346\pi$
$109$	146.541			1.34442			0.672208	+	0.740362i	$0.265346\pi$
$110$	−23.1529	+	100.851i	−0.210481	+	0.916824i
$111$		−	113.247i		−	1.02024i
$112$	33.2409	−	26.2345i	0.296794	−	0.234236i
$113$	36.0565			0.319084			0.159542	−	0.987191i	$-0.448998\pi$
$113$	36.0565			0.319084			0.159542	+	0.987191i	$0.448998\pi$
$114$	−27.1886	−	6.24184i	−0.238496	−	0.0547530i
$115$			149.141i			1.29688i
$116$	−184.169	−	89.2662i	−1.58766	−	0.769537i
$117$	−1.98336			−0.0169518
$118$	−47.6716	+	207.651i	−0.403996	+	1.75975i
$119$		−	21.4381i		−	0.180152i
$120$	62.6029	−	77.8928i	0.521691	−	0.649107i
$121$	−54.6474			−0.451631
$122$	−69.9836	−	16.0665i	−0.573636	−	0.131693i
$123$			25.7960i			0.209723i
$124$	−23.8177	+	49.1393i	−0.192078	+	0.396285i
$125$	135.697			1.08558
$126$	−1.46772	+	6.39320i	−0.0116486	+	0.0507397i
$127$		−	103.364i		−	0.813890i	−0.913453	−	0.406945i	$-0.866594\pi$
$127$		−	103.364i		−	0.813890i	0.913453	−	0.406945i	$-0.133406\pi$
$128$	−1.13432	+	127.995i	−0.00886188	+	0.999961i
$129$	−51.8747			−0.402129
$130$	−12.1790	−	2.79601i	−0.0936850	−	0.0215078i
$131$			85.6520i			0.653832i	0.945053	+	0.326916i	$0.106009\pi$
$131$			85.6520i			0.653832i	−0.945053	+	0.326916i	$0.893991\pi$
$132$	152.649	+	73.9884i	1.15643	+	0.560518i
$133$	11.5364			0.0867402
$134$	−21.2653	+	92.6285i	−0.158696	+	0.691257i
$135$		−	96.9439i		−	0.718103i
$136$	50.5097	+	40.5949i	0.371395	+	0.298492i
$137$	89.4114			0.652638			0.326319	−	0.945260i	$-0.394192\pi$
$137$	89.4114			0.652638			0.326319	+	0.945260i	$0.394192\pi$
$138$	238.302	+	54.7083i	1.72682	+	0.396437i
$139$			175.314i			1.26125i	0.776087	+	0.630625i	$0.217201\pi$
$139$			175.314i			1.26125i	−0.776087	+	0.630625i	$0.782799\pi$
$140$	−18.0254	+	37.1890i	−0.128753	+	0.265636i
$141$	−5.10152			−0.0361810
$142$	56.3600	−	245.496i	0.396901	−	1.72885i
$143$		−	21.2117i		−	0.148334i
$144$	−12.2835	−	15.5641i	−0.0853024	−	0.108084i
$145$	199.737			1.37750
$146$	66.6993	+	15.3125i	0.456844	+	0.104880i
$147$			134.380i			0.914148i
$148$	−127.389	−	61.7451i	−0.860736	−	0.417197i
$149$	207.665			1.39372			0.696862	−	0.717205i	$-0.254579\pi$
$149$	207.665			1.39372			0.696862	+	0.717205i	$0.254579\pi$
$150$	13.9772	−	60.8828i	0.0931815	−	0.405885i
$151$			33.2962i			0.220504i	0.993904	+	0.110252i	$0.0351659\pi$
$151$			33.2962i			0.220504i	−0.993904	+	0.110252i	$0.964834\pi$
$152$	−21.8452	+	27.1806i	−0.143719	+	0.178820i
$153$	−10.0378			−0.0656065
$154$	−68.3742	−	15.6971i	−0.443989	−	0.101929i
$155$		−	53.2932i		−	0.343827i
$156$	−8.93507	+	18.4343i	−0.0572761	+	0.118169i
$157$	−232.843			−1.48308			−0.741539	−	0.670910i	$-0.765904\pi$
$157$	−232.843			−1.48308			−0.741539	+	0.670910i	$0.765904\pi$
$158$	−31.8505	+	138.736i	−0.201585	+	0.878077i
$159$			182.000i			1.14465i
$160$	−53.4872	−	112.890i	−0.334295	−	0.705561i
$161$	−101.114			−0.628039
$162$	−176.639	−	40.5521i	−1.09037	−	0.250322i
$163$			133.148i			0.816858i	0.912790	+	0.408429i	$0.133923\pi$
$163$			133.148i			0.816858i	−0.912790	+	0.408429i	$0.866077\pi$
$164$	29.0173	+	14.0646i	0.176935	+	0.0857599i
$165$	−165.552			−1.00335
$166$	66.8177	−	291.048i	0.402516	−	1.75330i
$167$		−	84.0944i		−	0.503559i	−0.967785	−	0.251780i	$-0.918984\pi$
$167$		−	84.0944i		−	0.503559i	0.967785	−	0.251780i	$-0.0810158\pi$
$168$	52.8094	+	42.4432i	0.314341	+	0.252638i
$169$	−166.438			−0.984843
$170$	−61.6382	−	14.1506i	−0.362578	−	0.0832390i
$171$		−	5.40161i		−	0.0315884i
$172$	−28.2834	+	58.3526i	−0.164438	+	0.339259i
$173$	40.8353			0.236042			0.118021	−	0.993011i	$-0.462345\pi$
$173$	40.8353			0.236042			0.118021	+	0.993011i	$0.462345\pi$
$174$	73.2679	−	319.145i	0.421080	−	1.83417i
$175$			25.8333i			0.147619i
$176$	166.456	−	131.371i	0.945771	−	0.746424i
$177$	−340.871			−1.92582
$178$	−331.007	−	75.9912i	−1.85959	−	0.426917i
$179$			94.3723i			0.527219i	0.964629	+	0.263610i	$0.0849131\pi$
$179$			94.3723i			0.527219i	−0.964629	+	0.263610i	$0.915087\pi$
$180$	17.4127	+	8.43990i	0.0967373	+	0.0468883i
$181$	101.869			0.562811			0.281405	−	0.959589i	$-0.409199\pi$
$181$	101.869			0.562811			0.281405	+	0.959589i	$0.409199\pi$
$182$	1.89563	−	8.25709i	0.0104155	−	0.0453686i
$183$		−	114.882i		−	0.627772i
$184$	191.468	−	238.232i	1.04059	−	1.29474i
$185$	138.157			0.746797
$186$	−85.1531	−	19.5491i	−0.457812	−	0.105103i
$187$		−	107.353i		−	0.574078i
$188$	−2.78148	+	5.73859i	−0.0147951	+	0.0305244i
$189$	65.7255			0.347754
$190$	7.61484	−	33.1692i	0.0400781	−	0.174575i
$191$			96.9894i			0.507798i	0.967231	+	0.253899i	$0.0817131\pi$
$191$			96.9894i			0.507798i	−0.967231	+	0.253899i	$0.918287\pi$
$192$	−199.998	+	44.0526i	−1.04166	+	0.229441i
$193$	218.158			1.13035			0.565177	−	0.824970i	$-0.308808\pi$
$193$	218.158			1.13035			0.565177	+	0.824970i	$0.308808\pi$
$194$	213.499	+	49.0142i	1.10051	+	0.252650i
$195$		−	19.9926i		−	0.102526i
$196$	151.161	+	73.2673i	0.771228	+	0.373813i
$197$	−0.646370			−0.00328107			−0.00164053	−	0.999999i	$-0.500522\pi$
$197$	−0.646370			−0.00328107			−0.00164053	+	0.999999i	$0.500522\pi$
$198$	−7.34971	+	32.0143i	−0.0371197	+	0.161688i
$199$		−	20.5908i		−	0.103471i	−0.998661	−	0.0517356i	$-0.983525\pi$
$199$		−	20.5908i		−	0.103471i	0.998661	−	0.0517356i	$-0.0164753\pi$
$200$	−60.8650	−	48.9175i	−0.304325	−	0.244588i
$201$	−152.055			−0.756494
$202$	−230.865	−	53.0010i	−1.14290	−	0.262381i
$203$			135.417i			0.667078i
$204$	−45.2204	+	93.2961i	−0.221669	+	0.457334i
$205$	−31.4702			−0.153513
$206$	−15.4832	+	67.4426i	−0.0751611	+	0.327391i
$207$			47.3439i			0.228714i
$208$	15.8647	+	20.1017i	0.0762727	+	0.0966429i
$209$	57.7694			0.276408
$210$	−64.4446	−	14.7949i	−0.306879	−	0.0704520i
$211$		−	161.772i		−	0.766690i	−0.923605	−	0.383345i	$-0.874772\pi$
$211$		−	161.772i		−	0.766690i	0.923605	−	0.383345i	$-0.125228\pi$
$212$	204.728	+	99.2311i	0.965697	+	0.468071i
$213$	402.997			1.89200
$214$	38.1392	−	166.129i	0.178221	−	0.776303i
$215$		−	63.2854i		−	0.294350i
$216$	−124.457	+	154.854i	−0.576189	+	0.716915i
$217$	36.1315			0.166504
$218$	285.652	+	65.5787i	1.31033	+	0.300820i
$219$			109.491i			0.499958i
$220$	−90.2634	+	186.226i	−0.410288	+	0.846482i
$221$	12.9642			0.0586617
$222$	50.6791	−	220.751i	0.228284	−	0.994375i
$223$		−	171.167i		−	0.767567i	−0.923423	−	0.383784i	$-0.874621\pi$
$223$		−	171.167i		−	0.767567i	0.923423	−	0.383784i	$-0.125379\pi$
$224$	76.5364	−	36.2630i	0.341680	−	0.161888i
$225$	12.0957			0.0537587
$226$	70.2845	+	16.1356i	0.310994	+	0.0713966i
$227$			110.173i			0.485343i	0.970109	+	0.242672i	$0.0780237\pi$
$227$			110.173i			0.485343i	−0.970109	+	0.242672i	$0.921976\pi$
$228$	−50.2052	−	24.3343i	−0.220198	−	0.106730i
$229$	184.830			0.807120			0.403560	−	0.914953i	$-0.367773\pi$
$229$	184.830			0.807120			0.403560	+	0.914953i	$0.367773\pi$
$230$	−66.7423	+	290.720i	−0.290184	+	1.26400i
$231$		−	112.240i		−	0.485889i
$232$	−319.051	−	256.423i	−1.37522	−	1.10527i
$233$	−226.138			−0.970550			−0.485275	−	0.874362i	$-0.661281\pi$
$233$	−226.138			−0.970550			−0.485275	+	0.874362i	$0.661281\pi$
$234$	−3.86615	−	0.887574i	−0.0165220	−	0.00379305i
$235$		−	6.22369i		−	0.0264838i
$236$	−185.851	+	383.438i	−0.787506	+	1.62474i
$237$	−227.744			−0.960944
$238$	9.59378	−	41.7891i	0.0403100	−	0.175585i
$239$			282.285i			1.18111i	0.806999	+	0.590553i	$0.201090\pi$
$239$			282.285i			1.18111i	−0.806999	+	0.590553i	$0.798910\pi$
$240$	156.889	−	123.820i	0.653704	−	0.515918i
$241$	−8.68875			−0.0360529			−0.0180265	−	0.999838i	$-0.505738\pi$
$241$	−8.68875			−0.0360529			−0.0180265	+	0.999838i	$0.505738\pi$
$242$	−106.524	−	24.4552i	−0.440180	−	0.101055i
$243$		−	66.4621i		−	0.273507i
$244$	−129.228	−	62.6367i	−0.529624	−	0.256708i
$245$	−163.939			−0.669138
$246$	−11.5440	+	50.2839i	−0.0469267	+	0.204406i
$247$			6.97641i			0.0282446i
$248$	−68.4180	+	85.1281i	−0.275879	+	0.343259i
$249$	477.773			1.91877
$250$	264.513	+	60.7259i	1.05805	+	0.242903i
$251$		−	273.275i		−	1.08874i	−0.838844	−	0.544372i	$-0.816768\pi$
$251$		−	273.275i		−	1.08874i	0.838844	−	0.544372i	$-0.183232\pi$
$252$	−5.72204	+	11.8054i	−0.0227065	+	0.0468468i
$253$	−506.335			−2.00132
$254$	46.2565	−	201.487i	0.182112	−	0.793255i
$255$		−	101.183i		−	0.396795i
$256$	−59.4902	+	248.992i	−0.232383	+	0.972624i
$257$	225.614			0.877877			0.438938	−	0.898517i	$-0.355355\pi$
$257$	225.614			0.877877			0.438938	+	0.898517i	$0.355355\pi$
$258$	−101.119	−	23.2144i	−0.391933	−	0.0899784i
$259$			93.6673i			0.361650i
$260$	−22.4893	−	10.9005i	−0.0864971	−	0.0419250i
$261$	63.4051			0.242932
$262$	−38.3301	+	166.961i	−0.146298	+	0.637255i
$263$			153.711i			0.584454i	0.956349	+	0.292227i	$0.0943962\pi$
$263$			153.711i			0.584454i	−0.956349	+	0.292227i	$0.905604\pi$
$264$	264.446	+	212.537i	1.00169	+	0.805063i
$265$	−222.034			−0.837864
$266$	22.4879	+	5.16267i	0.0845409	+	0.0194085i
$267$		−	543.368i		−	2.03509i
$268$	−82.9044	+	171.043i	−0.309345	+	0.638222i
$269$	−266.196			−0.989575			−0.494788	−	0.869014i	$-0.664754\pi$
$269$	−266.196			−0.989575			−0.494788	+	0.869014i	$0.664754\pi$
$270$	43.3833	−	188.972i	0.160679	−	0.699895i
$271$			420.472i			1.55156i	0.631005	+	0.775778i	$0.282643\pi$
$271$			420.472i			1.55156i	−0.631005	+	0.775778i	$0.717357\pi$
$272$	80.2914	+	101.735i	0.295189	+	0.374025i
$273$	13.5545			0.0496502
$274$	174.289	+	40.0125i	0.636091	+	0.146031i
$275$			129.362i			0.470406i
$276$	440.037	+	213.285i	1.59434	+	0.772771i
$277$	−51.6625			−0.186507			−0.0932536	−	0.995642i	$-0.529727\pi$
$277$	−51.6625			−0.186507			−0.0932536	+	0.995642i	$0.529727\pi$
$278$	−78.4547	+	341.738i	−0.282211	+	1.22927i
$279$		−	16.9175i		−	0.0606363i
$280$	−51.7793	+	64.4257i	−0.184926	+	0.230092i
$281$	412.087			1.46650			0.733251	−	0.679958i	$-0.238002\pi$
$281$	412.087			1.46650			0.733251	+	0.679958i	$0.238002\pi$
$282$	−9.94435	−	2.28298i	−0.0352637	−	0.00809568i
$283$		−	492.048i		−	1.73868i	−0.494211	−	0.869342i	$-0.664543\pi$
$283$		−	492.048i		−	1.73868i	0.494211	−	0.869342i	$-0.335457\pi$
$284$	219.724	−	453.322i	0.773676	−	1.59620i
$285$	54.4492			0.191050
$286$	9.49246	−	41.3478i	0.0331904	−	0.144573i
$287$		−	21.3360i		−	0.0743416i
$288$	−16.9791	−	35.8360i	−0.0589552	−	0.124431i
$289$	−223.388			−0.772969
$290$	389.346	+	89.3844i	1.34257	+	0.308222i
$291$			350.471i			1.20437i
$292$	123.164	+	59.6972i	0.421794	+	0.204442i
$293$	−462.881			−1.57980			−0.789899	−	0.613237i	$-0.789867\pi$
$293$	−462.881			−1.57980			−0.789899	+	0.613237i	$0.789867\pi$
$294$	−60.1363	+	261.945i	−0.204545	+	0.890970i
$295$		−	415.851i		−	1.40966i
$296$	−220.686	−	177.367i	−0.745562	−	0.599213i
$297$	329.124			1.10816
$298$	404.799	+	92.9321i	1.35839	+	0.311853i
$299$		−	61.1466i		−	0.204504i
$300$	54.4913	−	112.423i	0.181638	−	0.374745i
$301$	42.9059			0.142544
$302$	−14.9004	+	64.9039i	−0.0493390	+	0.214914i
$303$		−	378.978i		−	1.25075i
$304$	−54.7463	+	43.2070i	−0.180086	+	0.142128i
$305$	140.152			0.459516
$306$	−19.5666	−	4.49201i	−0.0639431	−	0.0146798i
$307$		−	477.735i		−	1.55614i	−0.628178	−	0.778070i	$-0.716199\pi$
$307$		−	477.735i		−	1.55614i	0.628178	−	0.778070i	$-0.283801\pi$
$308$	−126.257	−	61.1963i	−0.409924	−	0.198689i
$309$	−110.711			−0.358288
$310$	23.8492	−	103.884i	0.0769330	−	0.335109i
$311$			397.518i			1.27819i	0.769127	+	0.639096i	$0.220691\pi$
$311$			397.518i			1.27819i	−0.769127	+	0.639096i	$0.779309\pi$
$312$	−25.6666	+	31.9353i	−0.0822647	+	0.102357i
$313$	−249.717			−0.797818			−0.398909	−	0.916991i	$-0.630611\pi$
$313$	−249.717			−0.797818			−0.398909	+	0.916991i	$0.630611\pi$
$314$	−453.879	−	104.200i	−1.44548	−	0.331846i
$315$		−	12.8033i		−	0.0406455i
$316$	−124.172	+	256.184i	−0.392948	+	0.810708i
$317$	17.5401			0.0553317			0.0276658	−	0.999617i	$-0.491193\pi$
$317$	17.5401			0.0553317			0.0276658	+	0.999617i	$0.491193\pi$
$318$	−81.4469	+	354.771i	−0.256122	+	1.11563i
$319$			678.108i			2.12573i
$320$	−53.7428	−	243.991i	−0.167946	−	0.762471i
$321$	272.711			0.849566
$322$	−197.101	−	45.2496i	−0.612115	−	0.140527i
$323$			35.3076i			0.109312i
$324$	−326.174	−	158.096i	−1.00671	−	0.487950i
$325$	−15.6221			−0.0480681
$326$	−59.5850	+	259.544i	−0.182776	+	0.796147i
$327$			468.914i			1.43399i
$328$	50.2691	+	40.4016i	0.153260	+	0.123176i
$329$	4.21951			0.0128252
$330$	−322.710	−	74.0864i	−0.977908	−	0.224504i
$331$		−	524.291i		−	1.58396i	−0.610546	−	0.791981i	$-0.709050\pi$
$331$		−	524.291i		−	1.58396i	0.610546	−	0.791981i	$-0.290950\pi$
$332$	260.494	−	537.436i	0.784621	−	1.61878i
$333$	43.8571			0.131703
$334$	37.6331	−	163.924i	0.112674	−	0.490792i
$335$		−	185.502i		−	0.553738i
$336$	83.9471	+	106.367i	0.249842	+	0.316568i
$337$	−10.3787			−0.0307974			−0.0153987	−	0.999881i	$-0.504902\pi$
$337$	−10.3787			−0.0307974			−0.0153987	+	0.999881i	$0.504902\pi$
$338$	−324.437	−	74.4829i	−0.959872	−	0.220363i
$339$			115.376i			0.340343i
$340$	−113.818	−	55.1674i	−0.334759	−	0.162257i
$341$	180.930			0.530587
$342$	2.41728	−	10.5293i	0.00706806	−	0.0307875i
$343$		−	240.832i		−	0.702134i
$344$	−81.2459	+	101.089i	−0.236180	+	0.293864i
$345$	−477.234			−1.38329
$346$	79.5998	+	18.2742i	0.230057	+	0.0528156i
$347$		−	140.835i		−	0.405864i	−0.979193	−	0.202932i	$-0.934953\pi$
$347$		−	140.835i		−	0.405864i	0.979193	−	0.202932i	$-0.0650470\pi$
$348$	285.641	−	589.318i	0.820808	−	1.69344i
$349$	588.176			1.68532			0.842659	−	0.538447i	$-0.180989\pi$
$349$	588.176			1.68532			0.842659	+	0.538447i	$0.180989\pi$
$350$	−11.5607	+	50.3566i	−0.0330305	+	0.143876i
$351$			39.7461i			0.113237i
$352$	383.260	−	181.589i	1.08881	−	0.515877i
$353$	−67.7579			−0.191949			−0.0959744	−	0.995384i	$-0.530597\pi$
$353$	−67.7579			−0.191949			−0.0959744	+	0.995384i	$0.530597\pi$
$354$	−664.456	−	152.543i	−1.87700	−	0.430913i
$355$			491.643i			1.38491i
$356$	−611.222	−	296.258i	−1.71692	−	0.832185i
$357$	68.5994			0.192155
$358$	−42.2325	+	183.959i	−0.117968	+	0.513852i
$359$		−	136.276i		−	0.379598i	−0.981823	−	0.189799i	$-0.939216\pi$
$359$		−	136.276i		−	0.379598i	0.981823	−	0.189799i	$-0.0607836\pi$
$360$	30.1655	+	24.2442i	0.0837930	+	0.0673449i
$361$	−19.0000			−0.0526316
$362$	198.572	+	45.5873i	0.548541	+	0.125932i
$363$		−	174.865i		−	0.481721i
$364$	7.39026	−	15.2472i	0.0203029	−	0.0418878i
$365$	−133.575			−0.365959
$366$	51.4109	−	223.939i	0.140467	−	0.611855i
$367$		−	274.645i		−	0.748352i	−0.927358	−	0.374176i	$-0.877926\pi$
$367$		−	274.645i		−	0.748352i	0.927358	−	0.374176i	$-0.122074\pi$
$368$	479.838	−	378.699i	1.30391	−	1.02907i
$369$	−9.99000			−0.0270732
$370$	269.309	+	61.8268i	0.727862	+	0.167100i
$371$		−	150.534i		−	0.405751i
$372$	−157.240	−	76.2137i	−0.422687	−	0.204876i
$373$	7.96701			0.0213593			0.0106796	−	0.999943i	$-0.496601\pi$
$373$	7.96701			0.0213593			0.0106796	+	0.999943i	$0.496601\pi$
$374$	48.0414	−	209.261i	0.128453	−	0.559523i
$375$			434.214i			1.15791i
$376$	−7.98999	+	9.94144i	−0.0212500	+	0.0264400i
$377$	−81.8904			−0.217216
$378$	128.118	+	29.4128i	0.338937	+	0.0778117i
$379$			514.957i			1.35873i	0.733803	+	0.679363i	$0.237744\pi$
$379$			514.957i			1.35873i	−0.733803	+	0.679363i	$0.762256\pi$
$380$	29.6871	−	61.2487i	0.0781239	−	0.161181i
$381$	330.752			0.868116
$382$	−43.4037	+	189.061i	−0.113622	+	0.494923i
$383$			669.698i			1.74856i	0.485424	+	0.874279i	$0.338665\pi$
$383$			669.698i			1.74856i	−0.485424	+	0.874279i	$0.661335\pi$
$384$	−409.568	−	3.62969i	−1.06658	−	0.00945231i
$385$	136.930			0.355661
$386$	425.254	+	97.6280i	1.10169	+	0.252922i
$387$		−	20.0895i		−	0.0519108i
$388$	394.237	+	191.086i	1.01607	+	0.492489i
$389$	−374.922			−0.963809			−0.481905	−	0.876224i	$-0.660055\pi$
$389$	−374.922			−0.963809			−0.481905	+	0.876224i	$0.660055\pi$
$390$	8.94690	−	38.9714i	0.0229408	−	0.0999268i
$391$		−	309.463i		−	0.791466i
$392$	261.868	+	210.465i	0.668032	+	0.536901i
$393$	−274.076			−0.697394
$394$	−1.25996	−	0.289257i	−0.00319788	−	0.000734155i
$395$		−	277.840i		−	0.703391i
$396$	−28.6534	+	59.1161i	−0.0723572	+	0.149283i
$397$	−32.0134			−0.0806384			−0.0403192	−	0.999187i	$-0.512837\pi$
$397$	−32.0134			−0.0806384			−0.0403192	+	0.999187i	$0.512837\pi$
$398$	9.21458	−	40.1374i	0.0231522	−	0.100848i
$399$			36.9152i			0.0925193i
$400$	−96.7524	−	122.592i	−0.241881	−	0.306480i
$401$	380.066			0.947796			0.473898	−	0.880580i	$-0.342847\pi$
$401$	380.066			0.947796			0.473898	+	0.880580i	$0.342847\pi$
$402$	−296.400	−	68.0462i	−0.737313	−	0.169269i
$403$			21.8497i			0.0542177i
$404$	−426.304	−	206.629i	−1.05521	−	0.511457i
$405$	353.747			0.873448
$406$	−60.6004	+	263.967i	−0.149262	+	0.650165i
$407$			469.044i			1.15244i
$408$	−129.899	+	161.625i	−0.318379	+	0.396139i
$409$	116.916			0.285858			0.142929	−	0.989733i	$-0.454348\pi$
$409$	116.916			0.285858			0.142929	+	0.989733i	$0.454348\pi$
$410$	−61.3446	−	14.0832i	−0.149621	−	0.0343494i
$411$			286.106i			0.696121i
$412$	−60.3625	+	124.536i	−0.146511	+	0.302273i
$413$	281.937			0.682655
$414$	−21.1869	+	92.2870i	−0.0511760	+	0.222915i
$415$			582.867i			1.40450i
$416$	21.9292	+	46.2837i	0.0527145	+	0.111259i
$417$	−560.983			−1.34528
$418$	112.609	+	25.8524i	0.269400	+	0.0618478i
$419$			0.146671i			0.000350050i	1.00000		0.000175025i	$5.57122e-5\pi$
$419$			0.146671i			0.000350050i	−1.00000		0.000175025i	$0.999944\pi$
$420$	−119.000	−	57.6792i	−0.283334	−	0.137331i
$421$	−613.336			−1.45686			−0.728428	−	0.685123i	$-0.759749\pi$
$421$	−613.336			−1.45686			−0.728428	+	0.685123i	$0.759749\pi$
$422$	72.3944	−	315.340i	0.171551	−	0.747251i
$423$		−	1.97566i		−	0.00467060i
$424$	354.667	+	285.048i	0.836479	+	0.672283i
$425$	−79.0636			−0.186032
$426$	785.558	+	180.345i	1.84403	+	0.423345i
$427$			95.0199i			0.222529i
$428$	148.689	−	306.766i	0.347404	−	0.716743i
$429$	67.8749			0.158217
$430$	28.3208	−	123.362i	0.0658624	−	0.286887i
$431$			310.234i			0.719800i	0.932991	+	0.359900i	$0.117189\pi$
$431$			310.234i			0.719800i	−0.932991	+	0.359900i	$0.882811\pi$
$432$	−311.901	+	246.159i	−0.721993	+	0.569813i
$433$	−194.780			−0.449838			−0.224919	−	0.974378i	$-0.572212\pi$
$433$	−194.780			−0.449838			−0.224919	+	0.974378i	$0.572212\pi$
$434$	70.4307	+	16.1692i	0.162283	+	0.0372562i
$435$			639.135i			1.46928i
$436$	527.471	+	255.664i	1.20980	+	0.586385i
$437$	166.531			0.381077
$438$	−48.9982	+	213.429i	−0.111868	+	0.487282i
$439$		−	340.063i		−	0.774631i	−0.921947	−	0.387315i	$-0.873402\pi$
$439$		−	340.063i		−	0.774631i	0.921947	−	0.387315i	$-0.126598\pi$
$440$	−259.288	+	322.615i	−0.589290	+	0.733216i
$441$	−52.0412			−0.118007
$442$	25.2711	+	5.80163i	0.0571744	+	0.0131259i
$443$		−	643.348i		−	1.45225i	−0.687561	−	0.726127i	$-0.741318\pi$
$443$		−	643.348i		−	1.45225i	0.687561	−	0.726127i	$-0.258682\pi$
$444$	197.577	−	407.629i	0.444993	−	0.918083i
$445$	662.891			1.48964
$446$	76.5992	−	333.655i	0.171747	−	0.748106i
$447$			664.502i			1.48658i
$448$	165.420	−	36.4363i	0.369240	−	0.0813309i
$449$	−416.379			−0.927348			−0.463674	−	0.886006i	$-0.653469\pi$
$449$	−416.379			−0.927348			−0.463674	+	0.886006i	$0.653469\pi$
$450$	23.5781	+	5.41295i	0.0523957	+	0.0120288i
$451$		−	106.841i		−	0.236899i
$452$	129.784	+	62.9061i	0.287133	+	0.139173i
$453$	−106.544			−0.235196
$454$	−49.3035	+	214.759i	−0.108598	+	0.473037i
$455$			16.5360i			0.0363430i
$456$	−86.9747	−	69.9020i	−0.190734	−	0.153294i
$457$	814.576			1.78244			0.891221	−	0.453568i	$-0.149849\pi$
$457$	814.576			1.78244			0.891221	+	0.453568i	$0.149849\pi$
$458$	360.288	+	82.7134i	0.786655	+	0.180597i
$459$			201.155i			0.438246i
$460$	−260.200	+	536.830i	−0.565653	+	1.16702i
$461$	122.745			0.266259			0.133129	−	0.991099i	$-0.457497\pi$
$461$	122.745			0.266259			0.133129	+	0.991099i	$0.457497\pi$
$462$	50.2287	−	218.789i	0.108720	−	0.473570i
$463$		−	348.734i		−	0.753206i	−0.926375	−	0.376603i	$-0.877092\pi$
$463$		−	348.734i		−	0.753206i	0.926375	−	0.376603i	$-0.122908\pi$
$464$	−507.172	−	642.622i	−1.09304	−	1.38496i
$465$	170.532			0.366735
$466$	−440.809	−	101.199i	−0.945942	−	0.217165i
$467$			41.9400i			0.0898072i	0.998991	+	0.0449036i	$0.0142981\pi$
$467$			41.9400i			0.0898072i	−0.998991	+	0.0449036i	$0.985702\pi$
$468$	−7.13905	−	3.46028i	−0.0152544	−	0.00739376i
$469$	125.766			0.268158
$470$	2.78516	−	12.1318i	0.00592588	−	0.0258123i
$471$		−	745.070i		−	1.58189i
$472$	−533.871	+	664.262i	−1.13108	+	1.40733i
$473$	214.854			0.454236
$474$	−443.939	−	101.918i	−0.936579	−	0.215016i
$475$		−	42.5463i		−	0.0895711i
$476$	37.4021	−	77.1659i	0.0785759	−	0.162113i
$477$	−70.4831			−0.147763
$478$	−126.325	+	550.255i	−0.264279	+	1.15116i
$479$		−	257.365i		−	0.537297i	−0.963238	−	0.268648i	$-0.913423\pi$
$479$		−	257.365i		−	0.537297i	0.963238	−	0.268648i	$-0.0865770\pi$
$480$	361.233	−	171.152i	0.752569	−	0.356567i
$481$	−56.6433			−0.117761
$482$	−16.9369	−	3.88830i	−0.0351388	−	0.00806702i
$483$		−	323.553i		−	0.669882i
$484$	−196.702	−	95.3408i	−0.406408	−	0.196985i
$485$	−427.563			−0.881573
$486$	29.7425	−	129.554i	0.0611985	−	0.266572i
$487$		−	312.131i		−	0.640927i	−0.947261	−	0.320463i	$-0.896161\pi$
$487$		−	312.131i		−	0.640927i	0.947261	−	0.320463i	$-0.103839\pi$
$488$	−223.873	−	179.928i	−0.458756	−	0.368705i
$489$	−426.057			−0.871282
$490$	−319.565	−	73.3643i	−0.652172	−	0.149723i
$491$		−	855.711i		−	1.74279i	−0.490581	−	0.871396i	$-0.663215\pi$
$491$		−	855.711i		−	1.74279i	0.490581	−	0.871396i	$-0.336785\pi$
$492$	−45.0051	+	92.8519i	−0.0914737	+	0.188723i
$493$	−414.448			−0.840665
$494$	−3.12201	+	13.5991i	−0.00631987	+	0.0275285i
$495$		−	64.1134i		−	0.129522i
$496$	−171.462	+	135.322i	−0.345690	+	0.272826i
$497$	−333.321			−0.670667
$498$	931.319	+	213.808i	1.87012	+	0.429334i
$499$		−	437.337i		−	0.876427i	−0.898871	−	0.438214i	$-0.855611\pi$
$499$		−	437.337i		−	0.876427i	0.898871	−	0.438214i	$-0.144389\pi$
$500$	488.438	+	236.745i	0.976876	+	0.473489i
$501$	269.092			0.537109
$502$	122.293	−	532.692i	0.243612	−	1.06114i
$503$		−	454.628i		−	0.903834i	−0.892060	−	0.451917i	$-0.850740\pi$
$503$		−	454.628i		−	0.903834i	0.892060	−	0.451917i	$-0.149260\pi$
$504$	−16.4370	+	20.4515i	−0.0326130	+	0.0405783i
$505$	462.341			0.915527
$506$	−986.994	−	226.590i	−1.95058	−	0.447806i
$507$		−	532.582i		−	1.05046i
$508$	180.335	−	372.056i	0.354989	−	0.732393i
$509$	330.296			0.648912			0.324456	−	0.945901i	$-0.394819\pi$
$509$	330.296			0.648912			0.324456	+	0.945901i	$0.394819\pi$
$510$	45.2803	−	197.235i	0.0887849	−	0.386735i
$511$		−	90.5606i		−	0.177222i
$512$	−227.390	+	458.735i	−0.444121	+	0.895967i
$513$	−108.247			−0.211008
$514$	439.788	+	100.965i	0.855619	+	0.196429i
$515$		−	135.064i		−	0.262260i
$516$	−186.721	−	90.5033i	−0.361863	−	0.175394i
$517$	21.1294			0.0408693
$518$	−41.9171	+	182.585i	−0.0809210	+	0.352480i
$519$			130.668i			0.251768i
$520$	−38.9600	−	31.3124i	−0.0749231	−	0.0602161i
$521$	−156.351			−0.300098			−0.150049	−	0.988679i	$-0.547943\pi$
$521$	−156.351			−0.300098			−0.150049	+	0.988679i	$0.547943\pi$
$522$	123.595	+	28.3744i	0.236772	+	0.0543572i
$523$		−	383.630i		−	0.733518i	−0.930316	−	0.366759i	$-0.880467\pi$
$523$		−	383.630i		−	0.733518i	0.930316	−	0.366759i	$-0.119533\pi$
$524$	−149.433	+	308.302i	−0.285178	+	0.588362i
$525$	−82.6634			−0.157454
$526$	−68.7874	+	299.628i	−0.130774	+	0.569635i
$527$			110.581i			0.209832i
$528$	420.370	+	532.638i	0.796155	+	1.00878i
$529$	−930.602			−1.75917
$530$	−432.809	−	99.3624i	−0.816620	−	0.187476i
$531$		−	132.009i		−	0.248604i
$532$	41.5251	+	20.1271i	0.0780546	+	0.0378329i
$533$	12.9025			0.0242073
$534$	243.163	−	1059.18i	0.455361	−	1.98349i
$535$			332.698i			0.621865i
$536$	−238.148	+	296.313i	−0.444307	+	0.552823i
$537$	−301.980			−0.562346
$538$	−518.893	−	119.125i	−0.964485	−	0.221422i
$539$		−	556.572i		−	1.03260i
$540$	169.134	−	348.946i	0.313210	−	0.646197i
$541$	−167.893			−0.310337			−0.155169	−	0.987888i	$-0.549592\pi$
$541$	−167.893			−0.310337			−0.155169	+	0.987888i	$0.549592\pi$
$542$	−188.165	+	819.622i	−0.347169	+	1.51222i
$543$			325.968i			0.600309i
$544$	110.984	+	234.242i	0.204015	+	0.430592i
$545$	−572.060			−1.04965
$546$	26.4217	+	6.06578i	0.0483913	+	0.0111095i
$547$			93.9282i			0.171715i	0.996307	+	0.0858576i	$0.0273630\pi$
$547$			93.9282i			0.171715i	−0.996307	+	0.0858576i	$0.972637\pi$
$548$	321.834	+	155.992i	0.587288	+	0.284657i
$549$	44.4904			0.0810389
$550$	−57.8906	+	252.164i	−0.105256	+	0.458479i
$551$		−	223.026i		−	0.404765i
$552$	762.313	+	612.675i	1.38100	+	1.10992i
$553$	188.368			0.340630
$554$	−100.705	−	23.1195i	−0.181778	−	0.0417319i
$555$			442.087i			0.796553i
$556$	−305.862	+	631.037i	−0.550112	+	1.13496i
$557$	658.999			1.18312			0.591561	−	0.806260i	$-0.298512\pi$
$557$	658.999			1.18312			0.591561	+	0.806260i	$0.298512\pi$
$558$	7.57077	−	32.9772i	0.0135677	−	0.0590989i
$559$			25.9464i			0.0464158i
$560$	−129.764	+	102.413i	−0.231721	+	0.182880i
$561$	343.515			0.612327
$562$	803.277	+	184.413i	1.42932	+	0.328137i
$563$			709.470i			1.26016i	0.776531	+	0.630079i	$0.216978\pi$
$563$			709.470i			1.26016i	−0.776531	+	0.630079i	$0.783022\pi$
$564$	−18.3628	−	8.90040i	−0.0325581	−	0.0157808i
$565$	−140.755			−0.249124
$566$	220.196	−	959.144i	0.389039	−	1.69460i
$567$			239.831i			0.422983i
$568$	631.172	−	785.328i	1.11122	−	1.38262i
$569$	613.773			1.07869			0.539344	−	0.842086i	$-0.318672\pi$
$569$	613.773			1.07869			0.539344	+	0.842086i	$0.318672\pi$
$570$	106.137	+	24.3666i	0.186206	+	0.0427483i
$571$			436.257i			0.764022i	0.924158	+	0.382011i	$0.124768\pi$
$571$			436.257i			0.764022i	−0.924158	+	0.382011i	$0.875232\pi$
$572$	37.0071	−	76.3510i	0.0646978	−	0.133481i
$573$	−310.354			−0.541631
$574$	9.54809	−	41.5901i	0.0166343	−	0.0724567i
$575$			372.908i			0.648536i
$576$	−17.0602	−	77.4531i	−0.0296185	−	0.134467i
$577$	356.629			0.618074			0.309037	−	0.951050i	$-0.399993\pi$
$577$	356.629			0.618074			0.309037	+	0.951050i	$0.399993\pi$
$578$	−435.448	−	99.9683i	−0.753370	−	0.172956i
$579$			698.080i			1.20566i
$580$	718.948	+	348.473i	1.23957	+	0.600815i
$581$	−395.170			−0.680154
$582$	−156.839	+	683.170i	−0.269483	+	1.17383i
$583$		−	753.805i		−	1.29298i
$584$	213.367	+	171.484i	0.365354	+	0.293637i
$585$	7.74253			0.0132351
$586$	−902.290	−	207.144i	−1.53974	−	0.353488i
$587$		−	411.394i		−	0.700842i	−0.936592	−	0.350421i	$-0.886039\pi$
$587$		−	411.394i		−	0.700842i	0.936592	−	0.350421i	$-0.113961\pi$
$588$	−234.446	+	483.696i	−0.398718	+	0.822612i
$589$	−59.5069			−0.101030
$590$	186.098	−	810.615i	0.315420	−	1.37392i
$591$		−	2.06831i		−	0.00349967i
$592$	−350.809	−	444.499i	−0.592582	−	0.750843i
$593$	110.332			0.186057			0.0930285	−	0.995663i	$-0.470345\pi$
$593$	110.332			0.186057			0.0930285	+	0.995663i	$0.470345\pi$
$594$	641.559	+	147.286i	1.08007	+	0.247957i
$595$			83.6890i			0.140654i
$596$	747.483	+	362.303i	1.25417	+	0.607892i
$597$	65.8880			0.110365
$598$	27.3637	−	119.193i	0.0457587	−	0.199319i
$599$			679.317i			1.13408i	0.823689	+	0.567042i	$0.191912\pi$
$599$			679.317i			1.13408i	−0.823689	+	0.567042i	$0.808088\pi$
$600$	156.530	−	194.760i	0.260883	−	0.324601i
$601$	−873.422			−1.45328			−0.726641	−	0.687018i	$-0.758920\pi$
$601$	−873.422			−1.45328			−0.726641	+	0.687018i	$0.758920\pi$
$602$	83.6361	+	19.2008i	0.138930	+	0.0318950i
$603$		−	58.8863i		−	0.0976556i
$604$	−58.0903	+	119.849i	−0.0961760	+	0.198425i
$605$	213.329			0.352610
$606$	169.597	−	738.739i	0.279862	−	1.21904i
$607$			14.0258i			0.0231067i	0.999933	+	0.0115534i	$0.00367763\pi$
$607$			14.0258i			0.0231067i	−0.999933	+	0.0115534i	$0.996322\pi$
$608$	−126.052	+	59.7235i	−0.207322	+	0.0982294i
$609$	−433.318			−0.711523
$610$	273.198	+	62.7196i	0.447865	+	0.102819i
$611$			2.55165i			0.00417619i
$612$	−36.1307	−	17.5125i	−0.0590372	−	0.0286152i
$613$	22.8620			0.0372953			0.0186477	−	0.999826i	$-0.494064\pi$
$613$	22.8620			0.0372953			0.0186477	+	0.999826i	$0.494064\pi$
$614$	213.791	−	931.244i	0.348194	−	1.51668i
$615$		−	100.701i		−	0.163741i
$616$	−218.725	−	175.791i	−0.355073	−	0.285374i
$617$	935.677			1.51649			0.758247	−	0.651968i	$-0.226056\pi$
$617$	935.677			1.51649			0.758247	+	0.651968i	$0.226056\pi$
$618$	−215.808	−	49.5443i	−0.349204	−	0.0801688i
$619$		−	256.561i		−	0.414476i	−0.978291	−	0.207238i	$-0.933553\pi$
$619$		−	256.561i		−	0.414476i	0.978291	−	0.207238i	$-0.0664475\pi$
$620$	92.9782	−	191.827i	0.149965	−	0.309399i
$621$	948.760			1.52779
$622$	−177.893	+	774.877i	−0.286002	+	1.24578i
$623$			449.423i			0.721386i
$624$	−64.3230	+	50.7652i	−0.103082	+	0.0813544i
$625$	−285.707			−0.457132
$626$	−486.771	−	111.751i	−0.777589	−	0.178516i
$627$			184.855i			0.294824i
$628$	−838.112	−	406.231i	−1.33457	−	0.646865i
$629$	−286.672			−0.455758
$630$	5.72962	−	24.9574i	0.00909463	−	0.0396149i
$631$		−	530.971i		−	0.841476i	−0.907182	−	0.420738i	$-0.861771\pi$
$631$		−	530.971i		−	0.841476i	0.907182	−	0.420738i	$-0.138229\pi$
$632$	−356.691	+	443.808i	−0.564385	+	0.702228i
$633$	517.649			0.817771
$634$	34.1908	+	7.84939i	0.0539288	+	0.0123807i
$635$			403.507i			0.635444i
$636$	−317.527	+	655.104i	−0.499257	+	1.03004i
$637$	67.2134			0.105516
$638$	−303.460	+	1321.83i	−0.475643	+	2.07183i
$639$			156.068i			0.244238i
$640$	4.42810	−	499.660i	0.00691890	−	0.780718i
$641$	−394.362			−0.615230			−0.307615	−	0.951511i	$-0.599531\pi$
$641$	−394.362			−0.615230			−0.307615	+	0.951511i	$0.599531\pi$
$642$	531.592	+	122.041i	0.828025	+	0.190095i
$643$			4.02353i			0.00625743i	0.999995	+	0.00312871i	$0.000995902\pi$
$643$			4.02353i			0.00625743i	−0.999995	+	0.00312871i	$0.999004\pi$
$644$	−363.958	−	176.409i	−0.565151	−	0.273928i
$645$	202.505			0.313962
$646$	−15.8005	+	68.8249i	−0.0244590	+	0.106540i
$647$			627.845i			0.970394i	0.874405	+	0.485197i	$0.161252\pi$
$647$			627.845i			0.970394i	−0.874405	+	0.485197i	$0.838748\pi$
$648$	−565.059	−	454.141i	−0.872004	−	0.700835i
$649$	1411.81			2.17537
$650$	−30.4521	−	6.99106i	−0.0468493	−	0.0107555i
$651$			115.616i			0.177598i
$652$	−232.297	+	479.262i	−0.356284	+	0.735064i
$653$	−548.722			−0.840309			−0.420155	−	0.907453i	$-0.638024\pi$
$653$	−548.722			−0.840309			−0.420155	+	0.907453i	$0.638024\pi$
$654$	−209.844	+	914.051i	−0.320862	+	1.39763i
$655$		−	334.364i		−	0.510479i
$656$	79.9090	+	101.250i	0.121813	+	0.154345i
$657$	−42.4025			−0.0645395
$658$	8.22504	+	1.88827i	0.0125001	+	0.00286971i
$659$		−	499.633i		−	0.758168i	−0.925362	−	0.379084i	$-0.876239\pi$
$659$		−	499.633i		−	0.758168i	0.925362	−	0.379084i	$-0.123761\pi$
$660$	−595.901	−	288.832i	−0.902880	−	0.437624i
$661$	−655.267			−0.991326			−0.495663	−	0.868515i	$-0.665075\pi$
$661$	−655.267			−0.991326			−0.495663	+	0.868515i	$0.665075\pi$
$662$	234.626	−	1022.00i	0.354419	−	1.54380i
$663$			41.4840i			0.0625701i
$664$	748.287	−	931.046i	1.12694	−	1.40218i
$665$	−45.0353			−0.0677223
$666$	85.4902	+	19.6265i	0.128364	+	0.0294692i
$667$			1954.77i			2.93069i
$668$	146.716	−	302.695i	0.219634	−	0.453136i
$669$	547.715			0.818707
$670$	83.0141	−	361.598i	0.123902	−	0.539698i
$671$			475.817i			0.709117i
$672$	116.037	+	244.907i	0.172674	+	0.364445i
$673$	686.513			1.02008			0.510039	−	0.860151i	$-0.329631\pi$
$673$	686.513			1.02008			0.510039	+	0.860151i	$0.329631\pi$
$674$	−20.2311	−	4.64458i	−0.0300165	−	0.00689107i
$675$		−	242.395i		−	0.359104i
$676$	−599.090	−	290.377i	−0.886228	−	0.429553i
$677$	−639.146			−0.944085			−0.472043	−	0.881576i	$-0.656483\pi$
$677$	−639.146			−0.944085			−0.472043	+	0.881576i	$0.656483\pi$
$678$	−51.6320	+	224.902i	−0.0761535	+	0.331714i
$679$		−	289.877i		−	0.426918i
$680$	−197.177	−	158.472i	−0.289966	−	0.233047i
$681$	−352.540			−0.517679
$682$	352.686	+	80.9681i	0.517135	+	0.118722i
$683$			839.655i			1.22936i	0.788775	+	0.614682i	$0.210716\pi$
$683$			839.655i			1.22936i	−0.788775	+	0.614682i	$0.789284\pi$
$684$	9.42395	−	19.4429i	0.0137777	−	0.0284253i
$685$	−349.039			−0.509546
$686$	107.775	−	469.451i	0.157106	−	0.684331i
$687$			591.435i			0.860894i
$688$	−203.610	+	160.694i	−0.295945	+	0.233567i
$689$	91.0319			0.132122
$690$	−930.269	−	213.567i	−1.34822	−	0.309518i
$691$		−	1091.05i		−	1.57895i	−0.613783	−	0.789475i	$-0.710353\pi$
$691$		−	1091.05i		−	1.57895i	0.613783	−	0.789475i	$-0.289647\pi$
$692$	146.985	+	71.2434i	0.212406	+	0.102953i
$693$	43.4673			0.0627233
$694$	63.0249	−	274.528i	0.0908140	−	0.395573i
$695$		−	684.380i		−	0.984720i
$696$	820.523	−	1020.92i	1.17891	−	1.46685i
$697$	65.2996			0.0936867
$698$	1146.53	+	263.215i	1.64259	+	0.377098i
$699$		−	723.614i		−	1.03521i
$700$	−45.0702	+	92.9862i	−0.0643860	+	0.132837i
$701$	431.165			0.615071			0.307536	−	0.951537i	$-0.400496\pi$
$701$	431.165			0.615071			0.307536	+	0.951537i	$0.400496\pi$
$702$	−17.7868	+	77.4767i	−0.0253373	+	0.110366i
$703$		−	154.266i		−	0.219439i
$704$	828.349	−	182.457i	1.17663	−	0.259171i
$705$	19.9150			0.0282483
$706$	−132.080	−	30.3223i	−0.187082	−	0.0429495i
$707$			313.456i			0.443360i
$708$	−1226.95	−	594.702i	−1.73299	−	0.839974i
$709$	−197.989			−0.279251			−0.139626	−	0.990204i	$-0.544590\pi$
$709$	−197.989			−0.279251			−0.139626	+	0.990204i	$0.544590\pi$
$710$	−220.015	+	958.355i	−0.309880	+	1.34980i
$711$		−	88.1982i		−	0.124048i
$712$	−1058.87	−	851.021i	−1.48718	−	1.19525i
$713$	521.564			0.731506
$714$	133.720	+	30.6989i	0.187283	+	0.0429957i
$715$			82.8052i			0.115811i
$716$	−164.647	+	339.690i	−0.229954	+	0.474427i
$717$	−903.276			−1.25980
$718$	60.9847	−	265.641i	0.0849369	−	0.369973i
$719$			555.460i			0.772545i	0.922385	+	0.386273i	$0.126238\pi$
$719$			555.460i			0.772545i	−0.922385	+	0.386273i	$0.873762\pi$
$720$	47.9518	+	60.7583i	0.0665997	+	0.0843866i
$721$	91.5699			0.127004
$722$	−37.0365	−	8.50269i	−0.0512971	−	0.0117766i
$723$		−	27.8029i		−	0.0384550i
$724$	366.674	+	177.726i	0.506455	+	0.245478i
$725$	499.416			0.688850
$726$	78.2538	−	340.863i	0.107788	−	0.469508i
$727$		−	8.18995i		−	0.0112654i	−0.999984	−	0.00563271i	$-0.998207\pi$
$727$		−	8.18995i		−	0.0112654i	0.999984	−	0.00563271i	$-0.00179296\pi$
$728$	21.2290	−	26.4139i	0.0291607	−	0.0362829i
$729$	−602.885			−0.827003
$730$	−260.377	−	59.7762i	−0.356681	−	0.0818852i
$731$			131.315i			0.179637i
$732$	200.430	−	413.515i	0.273811	−	0.564911i
$733$	−491.152			−0.670058			−0.335029	−	0.942208i	$-0.608746\pi$
$733$	−491.152			−0.670058			−0.335029	+	0.942208i	$0.608746\pi$
$734$	122.907	−	535.364i	0.167448	−	0.729378i
$735$		−	524.584i		−	0.713720i
$736$	1104.82	−	523.462i	1.50111	−	0.711226i
$737$	629.780			0.854518
$738$	−19.4734	−	4.47062i	−0.0263867	−	0.00605776i
$739$			1037.82i			1.40436i	0.712000	+	0.702180i	$0.247790\pi$
$739$			1037.82i			1.40436i	−0.712000	+	0.702180i	$0.752210\pi$
$740$	497.294	+	241.037i	0.672018	+	0.325726i
$741$	−22.3237			−0.0301264
$742$	67.3653	−	293.434i	0.0907888	−	0.395463i
$743$			148.421i			0.199759i	0.995000	+	0.0998795i	$0.0318457\pi$
$743$			148.421i			0.199759i	−0.995000	+	0.0998795i	$0.968154\pi$
$744$	−272.400	−	218.929i	−0.366128	−	0.294260i
$745$	−810.670			−1.08815
$746$	15.5300	+	3.56532i	0.0208177	+	0.00477925i
$747$			185.027i			0.247693i
$748$	187.293	−	386.413i	0.250392	−	0.516594i
$749$	−225.561			−0.301149
$750$	−194.315	+	846.410i	−0.259087	+	1.12855i
$751$		−	443.027i		−	0.589916i	−0.955510	−	0.294958i	$-0.904694\pi$
$751$		−	443.027i		−	0.589916i	0.955510	−	0.294958i	$-0.0953056\pi$
$752$	−20.0237	+	15.8032i	−0.0266273	+	0.0210148i
$753$	874.445			1.16128
$754$	−159.628	−	36.6468i	−0.211709	−	0.0486032i
$755$		−	129.980i		−	0.172159i
$756$	236.577	+	114.668i	0.312933	+	0.151678i
$757$	878.626			1.16067			0.580334	−	0.814379i	$-0.302922\pi$
$757$	878.626			1.16067			0.580334	+	0.814379i	$0.302922\pi$
$758$	−230.448	+	1003.80i	−0.304022	+	1.32428i
$759$		−	1620.21i		−	2.13466i
$760$	85.2781	−	106.106i	0.112208	−	0.139613i
$761$	−750.924			−0.986760			−0.493380	−	0.869814i	$-0.664239\pi$
$761$	−750.924			−0.986760			−0.493380	+	0.869814i	$0.664239\pi$
$762$	644.733	+	148.015i	0.846106	+	0.194245i
$763$		−	387.842i		−	0.508312i
$764$	−169.213	+	349.111i	−0.221483	+	0.456951i
$765$	39.1850			0.0512222
$766$	−299.696	+	1305.44i	−0.391249	+	1.70422i
$767$			170.495i			0.222288i
$768$	−796.743	−	190.361i	−1.03743	−	0.247866i
$769$	−315.536			−0.410319			−0.205160	−	0.978729i	$-0.565771\pi$
$769$	−315.536			−0.410319			−0.205160	+	0.978729i	$0.565771\pi$
$770$	266.916	+	61.2773i	0.346644	+	0.0795810i
$771$			721.938i			0.936366i
$772$	785.254	+	380.611i	1.01717	+	0.493019i
$773$	−110.053			−0.142371			−0.0711853	−	0.997463i	$-0.522678\pi$
$773$	−110.053			−0.142371			−0.0711853	+	0.997463i	$0.522678\pi$
$774$	8.99024	−	39.1602i	0.0116153	−	0.0505946i
$775$		−	133.252i		−	0.171939i
$776$	682.970	+	548.907i	0.880116	+	0.707354i
$777$	−299.724			−0.385745
$778$	−730.832	−	167.781i	−0.939372	−	0.215657i
$779$			35.1395i			0.0451085i
$780$	34.8802	−	71.9629i	0.0447182	−	0.0922601i
$781$	−1669.13			−2.13716
$782$	138.488	−	603.234i	0.177094	−	0.771399i
$783$		−	1270.62i		−	1.62276i
$784$	416.273	+	527.447i	0.530960	+	0.672764i
$785$	908.961			1.15791
$786$	−534.254	−	122.652i	−0.679712	−	0.156046i
$787$			660.023i			0.838657i	0.907834	+	0.419329i	$0.137735\pi$
$787$			660.023i			0.838657i	−0.907834	+	0.419329i	$0.862265\pi$
$788$	−2.32659	−	1.12769i	−0.00295253	−	0.00143108i
$789$	−491.857			−0.623393
$790$	124.336	−	541.590i	0.157387	−	0.685557i
$791$		−	95.4285i		−	0.120643i
$792$	−82.3090	+	102.412i	−0.103925	+	0.129308i
$793$	−57.4612			−0.0724605
$794$	−62.4035	−	14.3263i	−0.0785939	−	0.0180432i
$795$		−	710.482i		−	0.893688i
$796$	35.9238	−	74.1159i	0.0451304	−	0.0931104i
$797$	764.458			0.959170			0.479585	−	0.877495i	$-0.340787\pi$
$797$	764.458			0.959170			0.479585	+	0.877495i	$0.340787\pi$
$798$	−16.5199	+	71.9585i	−0.0207017	+	0.0901735i
$799$			12.9139i			0.0161626i
$800$	−133.737	−	282.265i	−0.167172	−	0.352832i
$801$	210.430			0.262709
$802$	740.859	+	170.083i	0.923765	+	0.212074i
$803$		−	453.487i		−	0.564742i
$804$	−547.318	−	265.284i	−0.680744	−	0.329955i
$805$	394.724			0.490340
$806$	−9.77797	+	42.5915i	−0.0121315	+	0.0528430i
$807$		−	851.794i		−	1.05551i
$808$	−738.523	−	593.555i	−0.914013	−	0.734597i
$809$	−1281.35			−1.58387			−0.791933	−	0.610608i	$-0.790925\pi$
$809$	−1281.35			−1.58387			−0.791933	+	0.610608i	$0.790925\pi$
$810$	689.555	+	158.305i	0.851303	+	0.195438i
$811$			1115.57i			1.37555i	0.725925	+	0.687774i	$0.241412\pi$
$811$			1115.57i			1.37555i	−0.725925	+	0.687774i	$0.758588\pi$
$812$	−236.256	+	487.429i	−0.290955	+	0.600282i
$813$	−1345.46			−1.65493
$814$	−209.902	+	914.304i	−0.257865	+	1.12322i
$815$		−	519.775i		−	0.637761i
$816$	−325.539	+	256.923i	−0.398945	+	0.314856i
$817$	−70.6641			−0.0864921
$818$	227.903	+	52.3211i	0.278610	+	0.0639622i
$819$			5.24925i			0.00640934i
$820$	−113.276	−	54.9047i	−0.138142	−	0.0669569i
$821$	−766.597			−0.933736			−0.466868	−	0.884327i	$-0.654618\pi$
$821$	−766.597			−0.933736			−0.466868	+	0.884327i	$0.654618\pi$
$822$	−128.035	+	557.703i	−0.155760	+	0.678471i
$823$		−	169.190i		−	0.205577i	−0.994703	−	0.102789i	$-0.967223\pi$
$823$		−	169.190i		−	0.205577i	0.994703	−	0.102789i	$-0.0327766\pi$
$824$	−173.395	+	215.745i	−0.210431	+	0.261826i
$825$	−413.941			−0.501747
$826$	549.577	+	126.170i	0.665347	+	0.152748i
$827$		−	1514.19i		−	1.83095i	−0.402380	−	0.915473i	$-0.631817\pi$
$827$		−	1514.19i		−	1.83095i	0.402380	−	0.915473i	$-0.368183\pi$
$828$	−82.5987	+	170.413i	−0.0997569	+	0.205813i
$829$	485.979			0.586224			0.293112	−	0.956078i	$-0.405309\pi$
$829$	485.979			0.586224			0.293112	+	0.956078i	$0.405309\pi$
$830$	−260.839	+	1136.18i	−0.314264	+	1.36889i
$831$		−	165.314i		−	0.198933i
$832$	22.0340	+	100.034i	0.0264832	+	0.120233i
$833$	340.167			0.408364
$834$	−1093.52	−	251.045i	−1.31117	−	0.301014i
$835$			328.283i			0.393153i
$836$	207.939	+	100.788i	0.248731	+	0.120559i
$837$	−339.023			−0.405046
$838$	−0.0656367	+	0.285904i	−7.83254e−5	+	0.000341175i
$839$		−	1289.35i		−	1.53677i	−0.639989	−	0.768384i	$-0.721061\pi$
$839$		−	1289.35i		−	1.53677i	0.639989	−	0.768384i	$-0.278939\pi$
$840$	−206.154	−	165.687i	−0.245422	−	0.197247i
$841$	1776.92			2.11286
$842$	−1195.57	−	274.474i	−1.41992	−	0.325979i
$843$			1318.63i			1.56421i
$844$	282.235	−	582.292i	0.334402	−	0.689919i
$845$	649.733			0.768915
$846$	0.884130	−	3.85114i	0.00104507	−	0.00455218i
$847$			144.632i			0.170758i
$848$	563.787	+	714.358i	0.664844	+	0.842404i
$849$	1574.49			1.85453
$850$	−154.118	−	35.3818i	−0.181315	−	0.0416256i
$851$			1352.10i			1.58884i
$852$	1450.57	+	703.090i	1.70255	+	0.825223i
$853$	785.466			0.920828			0.460414	−	0.887704i	$-0.347701\pi$
$853$	785.466			0.920828			0.460414	+	0.887704i	$0.347701\pi$
$854$	−42.5223	+	185.221i	−0.0497920	+	0.216887i
$855$			21.0865i			0.0246626i
$856$	427.118	−	531.436i	0.498970	−	0.620837i
$857$	−80.7663			−0.0942431			−0.0471215	−	0.998889i	$-0.515005\pi$
$857$	−80.7663			−0.0942431			−0.0471215	+	0.998889i	$0.515005\pi$
$858$	132.308	+	30.3747i	0.154205	+	0.0354018i
$859$		−	81.9821i		−	0.0954390i	−0.998861	−	0.0477195i	$-0.984805\pi$
$859$		−	81.9821i		−	0.0954390i	0.998861	−	0.0477195i	$-0.0151954\pi$
$860$	110.411	−	227.794i	0.128385	−	0.264876i
$861$	68.2727			0.0792947
$862$	−138.833	+	604.736i	−0.161059	+	0.701549i
$863$			1154.64i			1.33794i	0.743289	+	0.668971i	$0.233265\pi$
$863$			1154.64i			1.33794i	−0.743289	+	0.668971i	$0.766735\pi$
$864$	−718.145	+	340.257i	−0.831186	+	0.393816i
$865$	−159.410			−0.184289
$866$	−379.682	−	87.1658i	−0.438432	−	0.100653i
$867$		−	714.814i		−	0.824468i
$868$	130.054	+	63.0369i	0.149832	+	0.0726232i
$869$	943.265			1.08546
$870$	−286.019	+	1245.86i	−0.328758	+	1.43202i
$871$			76.0542i			0.0873183i
$872$	913.783	+	734.412i	1.04792	+	0.842216i
$873$	−135.727			−0.155472
$874$	324.617	+	74.5241i	0.371415	+	0.0852679i
$875$		−	359.142i		−	0.410448i
$876$	−191.024	+	394.109i	−0.218064	+	0.449896i
$877$	1055.61			1.20367			0.601833	−	0.798622i	$-0.294437\pi$
$877$	1055.61			1.20367			0.601833	+	0.798622i	$0.294437\pi$
$878$	152.182	−	662.881i	0.173327	−	0.754990i
$879$		−	1481.16i		−	1.68505i
$880$	−649.800	+	512.837i	−0.738410	+	0.582769i
$881$	−1253.11			−1.42237			−0.711185	−	0.703005i	$-0.751841\pi$
$881$	−1253.11			−1.42237			−0.711185	+	0.703005i	$0.751841\pi$
$882$	−101.443	−	23.2890i	−0.115015	−	0.0264047i
$883$			327.627i			0.371038i	0.982641	+	0.185519i	$0.0593966\pi$
$883$			327.627i			0.371038i	−0.982641	+	0.185519i	$0.940603\pi$
$884$	46.6644	+	22.6181i	0.0527878	+	0.0255861i
$885$	1330.67			1.50358
$886$	287.905	−	1254.07i	0.324949	−	1.41543i
$887$			879.152i			0.991152i	0.868565	+	0.495576i	$0.165043\pi$
$887$			879.152i			0.991152i	−0.868565	+	0.495576i	$0.834957\pi$
$888$	567.552	−	706.170i	0.639136	−	0.795236i
$889$	−273.568			−0.307725
$890$	1292.17	+	296.650i	1.45187	+	0.333315i
$891$			1200.97i			1.34789i
$892$	298.628	−	616.112i	0.334785	−	0.690709i
$893$	−6.94934			−0.00778201
$894$	−297.371	+	1295.31i	−0.332630	+	1.44889i
$895$		−	368.405i		−	0.411626i
$896$	338.757	+	3.00214i	0.378077	+	0.00335060i
$897$	195.662			0.218129
$898$	−811.645	−	186.334i	−0.903836	−	0.207499i
$899$		−	698.503i		−	0.776978i
$900$	43.5381	+	21.1028i	0.0483757	+	0.0234476i
$901$	460.713			0.511335
$902$	47.8126	−	208.265i	0.0530073	−	0.230892i
$903$			137.294i			0.152042i
$904$	224.836	+	180.702i	0.248712	+	0.199892i
$905$	−397.670			−0.439414
$906$	−207.685	−	47.6793i	−0.229232	−	0.0526262i
$907$			957.974i			1.05620i	0.849182	+	0.528100i	$0.177096\pi$
$907$			957.974i			1.05620i	−0.849182	+	0.528100i	$0.822904\pi$
$908$	−192.214	+	396.564i	−0.211689	+	0.436744i
$909$	146.767			0.161460
$910$	−7.40005	+	32.2336i	−0.00813192	+	0.0354215i
$911$		−	940.851i		−	1.03277i	−0.856357	−	0.516383i	$-0.827278\pi$
$911$		−	940.851i		−	1.03277i	0.856357	−	0.516383i	$-0.172722\pi$
$912$	−138.257	−	175.181i	−0.151598	−	0.192085i
$913$	−1978.83			−2.16740
$914$	1587.85	+	364.531i	1.73725	+	0.398831i
$915$			448.471i			0.490132i
$916$	665.291	+	322.465i	0.726301	+	0.352036i
$917$	226.690			0.247209
$918$	−90.0189	+	392.110i	−0.0980598	+	0.427135i
$919$			1560.81i			1.69838i	0.528087	+	0.849190i	$0.322909\pi$
$919$			1560.81i			1.69838i	−0.528087	+	0.849190i	$0.677091\pi$
$920$	−747.443	+	929.996i	−0.812438	+	1.01087i
$921$	1528.69			1.65982
$922$	239.266	+	54.9298i	0.259508	+	0.0595767i
$923$		−	201.569i		−	0.218385i
$924$	195.821	−	404.006i	0.211927	−	0.437236i
$925$	345.444			0.373453
$926$	156.062	−	679.784i	0.168534	−	0.734108i
$927$		−	42.8750i		−	0.0462514i
$928$	−701.045	−	1479.62i	−0.755437	−	1.59442i
$929$	−851.219			−0.916274			−0.458137	−	0.888881i	$-0.651483\pi$
$929$	−851.219			−0.916274			−0.458137	+	0.888881i	$0.651483\pi$
$930$	332.416	+	76.3146i	0.357436	+	0.0820588i
$931$			183.053i			0.196620i
$932$	−813.978	−	394.533i	−0.873366	−	0.423319i
$933$	−1272.01			−1.36335
$934$	−18.7686	+	81.7532i	−0.0200948	+	0.0875302i
$935$			419.077i			0.448211i
$936$	−12.3676	−	9.93989i	−0.0132132	−	0.0106195i
$937$	−1552.45			−1.65683			−0.828415	−	0.560115i	$-0.810757\pi$
$937$	−1552.45			−1.65683			−0.828415	+	0.560115i	$0.810757\pi$
$938$	245.154	+	56.2815i	0.261359	+	0.0600016i
$939$		−	799.064i		−	0.850973i
$940$	10.8582	−	22.4020i	0.0115513	−	0.0238319i
$941$	−1257.79			−1.33665			−0.668325	−	0.743869i	$-0.732988\pi$
$941$	−1257.79			−1.33665			−0.668325	+	0.743869i	$0.732988\pi$
$942$	333.426	−	1452.36i	0.353956	−	1.54178i
$943$		−	307.990i		−	0.326606i
$944$	−1337.93	+	1055.93i	−1.41730	+	1.11857i
$945$	−256.576			−0.271509
$946$	418.812	+	96.1492i	0.442719	+	0.101638i
$947$		−	1009.67i		−	1.06618i	−0.846058	−	0.533091i	$-0.821030\pi$
$947$		−	1009.67i		−	1.06618i	0.846058	−	0.533091i	$-0.178970\pi$
$948$	−819.756	−	397.334i	−0.864722	−	0.419129i
$949$	54.7646			0.0577077
$950$	19.0399	−	82.9351i	0.0200420	−	0.0873001i
$951$			56.1263i			0.0590182i
$952$	107.440	−	133.681i	0.112857	−	0.140421i
$953$	703.529			0.738225			0.369113	−	0.929385i	$-0.379662\pi$
$953$	703.529			0.738225			0.369113	+	0.929385i	$0.379662\pi$
$954$	−137.392	−	31.5419i	−0.144017	−	0.0330628i
$955$		−	378.622i		−	0.396463i
$956$	−492.489	+	1016.07i	−0.515156	+	1.06284i
$957$	−2169.86			−2.26736
$958$	115.174	−	501.680i	0.120223	−	0.523674i
$959$		−	236.640i		−	0.246757i
$960$	780.741	−	171.970i	0.813272	−	0.179136i
$961$	774.628			0.806064
$962$	−110.414	−	25.3484i	−0.114776	−	0.0263497i
$963$			105.612i			0.109670i
$964$	−31.2749	−	15.1589i	−0.0324428	−	0.0157250i
$965$	−851.634			−0.882522
$966$	144.793	−	630.699i	0.149889	−	0.652898i
$967$		−	1185.74i		−	1.22620i	−0.790004	−	0.613102i	$-0.789921\pi$
$967$		−	1185.74i		−	1.22620i	0.790004	−	0.613102i	$-0.210079\pi$
$968$	−340.763	−	273.873i	−0.352027	−	0.282926i
$969$	−112.980			−0.116595
$970$	−833.445	−	191.339i	−0.859221	−	0.197256i
$971$		−	1118.65i		−	1.15206i	−0.817430	−	0.576028i	$-0.804602\pi$
$971$		−	1118.65i		−	1.15206i	0.817430	−	0.576028i	$-0.195398\pi$
$972$	115.953	−	239.228i	0.119294	−	0.246120i
$973$	463.993			0.476868
$974$	139.682	−	608.435i	0.143411	−	0.624677i
$975$		−	49.9889i		−	0.0512706i
$976$	−355.874	−	450.918i	−0.364625	−	0.462006i
$977$	−1310.18			−1.34102			−0.670511	−	0.741900i	$-0.733925\pi$
$977$	−1310.18			−1.34102			−0.670511	+	0.741900i	$0.733925\pi$
$978$	−830.509	−	190.665i	−0.849191	−	0.194954i
$979$			2250.51i			2.29879i
$980$	−590.093	−	286.017i	−0.602136	−	0.291854i
$981$	−181.596			−0.185113
$982$	382.939	−	1668.03i	0.389958	−	1.69860i
$983$		−	72.0290i		−	0.0732747i	−0.999329	−	0.0366373i	$-0.988335\pi$
$983$		−	72.0290i		−	0.0732747i	0.999329	−	0.0366373i	$-0.0116646\pi$
$984$	−129.280	+	160.855i	−0.131382	+	0.163471i
$985$	2.52326			0.00256169
$986$	−807.879	−	185.469i	−0.819350	−	0.188103i
$987$			13.5019i			0.0136797i
$988$	−12.1714	+	25.1114i	−0.0123193	+	0.0254164i
$989$	619.354			0.626243
$990$	28.6914	−	124.976i	0.0289812	−	0.126238i
$991$		−	289.057i		−	0.291683i	−0.989308	−	0.145841i	$-0.953411\pi$
$991$		−	289.057i		−	0.291683i	0.989308	−	0.145841i	$-0.0465889\pi$
$992$	−394.788	+	187.050i	−0.397971	+	0.188559i
$993$	1677.67			1.68949
$994$	−649.741	−	149.165i	−0.653662	−	0.150065i
$995$			80.3812i			0.0807851i
$996$	1719.73	+	833.549i	1.72664	+	0.836897i
$997$	419.170			0.420432			0.210216	−	0.977655i	$-0.432583\pi$
$997$	419.170			0.420432			0.210216	+	0.977655i	$0.432583\pi$
$998$	195.713	−	852.498i	0.196105	−	0.854206i
$999$		−	878.885i		−	0.879765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.b.b.39.14	yes	14
3.2	odd	2		684.3.g.b.343.1		14
4.3	odd	2	inner	76.3.b.b.39.13	✓	14
8.3	odd	2		1216.3.d.d.191.11		14
8.5	even	2		1216.3.d.d.191.4		14
12.11	even	2		684.3.g.b.343.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.13	✓	14	4.3	odd	2	inner
76.3.b.b.39.14	yes	14	1.1	even	1	trivial
684.3.g.b.343.1		14	3.2	odd	2
684.3.g.b.343.2		14	12.11	even	2
1216.3.d.d.191.4		14	8.5	even	2
1216.3.d.d.191.11		14	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94929 + 0.447510i) q^{2} +3.19988i q^{3} +(3.59947 + 1.74465i) q^{4} -3.90374 q^{5} +(-1.43198 + 6.23749i) q^{6} -2.64664i q^{7} +(6.23566 + 5.01164i) q^{8} -1.23921 q^{9} +O(q^{10})\)	\(q+(1.94929 + 0.447510i) q^{2} +3.19988i q^{3} +(3.59947 + 1.74465i) q^{4} -3.90374 q^{5} +(-1.43198 + 6.23749i) q^{6} -2.64664i q^{7} +(6.23566 + 5.01164i) q^{8} -1.23921 q^{9} +(-7.60953 - 1.74696i) q^{10} -13.2532i q^{11} +(-5.58268 + 11.5179i) q^{12} +1.60050 q^{13} +(1.18440 - 5.15907i) q^{14} -12.4915i q^{15} +(9.91236 + 12.5597i) q^{16} +8.10013 q^{17} +(-2.41559 - 0.554561i) q^{18} +4.35890i q^{19} +(-14.0514 - 6.81068i) q^{20} +8.46893 q^{21} +(5.93094 - 25.8343i) q^{22} -38.2047i q^{23} +(-16.0366 + 19.9534i) q^{24} -9.76079 q^{25} +(3.11984 + 0.716239i) q^{26} +24.8336i q^{27} +(4.61747 - 9.52650i) q^{28} -51.1656 q^{29} +(5.59007 - 24.3496i) q^{30} +13.6518i q^{31} +(13.7015 + 28.9183i) q^{32} +42.4086 q^{33} +(15.7895 + 3.62489i) q^{34} +10.3318i q^{35} +(-4.46052 - 2.16200i) q^{36} -35.3910 q^{37} +(-1.95065 + 8.49676i) q^{38} +5.12140i q^{39} +(-24.3424 - 19.5641i) q^{40} +8.06155 q^{41} +(16.5084 + 3.78993i) q^{42} +16.2115i q^{43} +(23.1223 - 47.7045i) q^{44} +4.83758 q^{45} +(17.0970 - 74.4721i) q^{46} +1.59429i q^{47} +(-40.1894 + 31.7183i) q^{48} +41.9953 q^{49} +(-19.0266 - 4.36805i) q^{50} +25.9194i q^{51} +(5.76095 + 2.79232i) q^{52} +56.8772 q^{53} +(-11.1133 + 48.4078i) q^{54} +51.7371i q^{55} +(13.2640 - 16.5036i) q^{56} -13.9479 q^{57} +(-99.7366 - 22.8971i) q^{58} +106.526i q^{59} +(21.7934 - 44.9628i) q^{60} -35.9021 q^{61} +(-6.10933 + 26.6114i) q^{62} +3.27976i q^{63} +(13.7670 + 62.5018i) q^{64} -6.24794 q^{65} +(82.6667 + 18.9783i) q^{66} +47.5191i q^{67} +(29.1562 + 14.1319i) q^{68} +122.250 q^{69} +(-4.62359 + 20.1397i) q^{70} -125.941i q^{71} +(-7.72733 - 6.21050i) q^{72} +34.2172 q^{73} +(-68.9874 - 15.8378i) q^{74} -31.2333i q^{75} +(-7.60477 + 15.6897i) q^{76} -35.0765 q^{77} +(-2.29188 + 9.98310i) q^{78} +71.1726i q^{79} +(-38.6953 - 49.0297i) q^{80} -90.6173 q^{81} +(15.7143 + 3.60763i) q^{82} -149.310i q^{83} +(30.4836 + 14.7754i) q^{84} -31.6208 q^{85} +(-7.25479 + 31.6008i) q^{86} -163.724i q^{87} +(66.4202 - 82.6425i) q^{88} -169.809 q^{89} +(9.42984 + 2.16486i) q^{90} -4.23595i q^{91} +(66.6541 - 137.517i) q^{92} -43.6841 q^{93} +(-0.713460 + 3.10773i) q^{94} -17.0160i q^{95} +(-92.5351 + 43.8431i) q^{96} +109.526 q^{97} +(81.8610 + 18.7933i) q^{98} +16.4236i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9	\( 14 q + 2 q^{2} + 2 q^{4} - 40 q^{8} - 68 q^{9} - 12 q^{10} + 4 q^{12} + 54 q^{13} + 30 q^{14} + 58 q^{16} + 34 q^{17} + 36 q^{18} + 32 q^{20} - 38 q^{21} + 36 q^{22} - 98 q^{24} - 86 q^{25} - 16 q^{26} + 18 q^{28} + 54 q^{29} - 204 q^{30} + 72 q^{32} + 20 q^{33} - 82 q^{34} + 96 q^{36} + 100 q^{37} - 148 q^{40} + 224 q^{41} + 224 q^{42} - 96 q^{44} - 168 q^{45} + 46 q^{46} + 296 q^{48} - 220 q^{49} - 58 q^{50} - 288 q^{52} + 14 q^{53} - 128 q^{54} + 12 q^{56} + 38 q^{57} - 72 q^{58} + 188 q^{60} + 28 q^{61} + 396 q^{62} - 118 q^{64} - 472 q^{65} - 32 q^{66} + 30 q^{68} + 122 q^{69} + 156 q^{70} + 80 q^{72} + 70 q^{73} - 224 q^{74} + 228 q^{77} + 274 q^{78} - 348 q^{80} + 334 q^{81} - 400 q^{82} - 216 q^{84} + 48 q^{85} - 124 q^{86} + 472 q^{88} + 416 q^{90} + 126 q^{92} - 176 q^{93} - 88 q^{94} - 106 q^{96} + 308 q^{97} + 68 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 + 2 * q^4 - 40 * q^8 - 68 * q^9 - 12 * q^10 + 4 * q^12 + 54 * q^13 + 30 * q^14 + 58 * q^16 + 34 * q^17 + 36 * q^18 + 32 * q^20 - 38 * q^21 + 36 * q^22 - 98 * q^24 - 86 * q^25 - 16 * q^26 + 18 * q^28 + 54 * q^29 - 204 * q^30 + 72 * q^32 + 20 * q^33 - 82 * q^34 + 96 * q^36 + 100 * q^37 - 148 * q^40 + 224 * q^41 + 224 * q^42 - 96 * q^44 - 168 * q^45 + 46 * q^46 + 296 * q^48 - 220 * q^49 - 58 * q^50 - 288 * q^52 + 14 * q^53 - 128 * q^54 + 12 * q^56 + 38 * q^57 - 72 * q^58 + 188 * q^60 + 28 * q^61 + 396 * q^62 - 118 * q^64 - 472 * q^65 - 32 * q^66 + 30 * q^68 + 122 * q^69 + 156 * q^70 + 80 * q^72 + 70 * q^73 - 224 * q^74 + 228 * q^77 + 274 * q^78 - 348 * q^80 + 334 * q^81 - 400 * q^82 - 216 * q^84 + 48 * q^85 - 124 * q^86 + 472 * q^88 + 416 * q^90 + 126 * q^92 - 176 * q^93 - 88 * q^94 - 106 * q^96 + 308 * q^97 + 68 * q^98

Introduction

L-functions

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