LMFDB - Embedded newform 76.3.b.b.39.13

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

$q$-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	$-0.820947\pi$
$3$		−	3.19988i		−	1.06663i	0.845918	−	0.533313i	$-0.179053\pi$
$4$	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	$0.0605395\pi$
$7$			2.64664i			0.378092i	−0.981968	+	0.189046i	$0.939461\pi$
$8$	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	$0.205796\pi$
$11$			13.2532i			1.20484i	−0.798181	+	0.602418i	$0.794204\pi$
$12$	−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	$0.311967\pi$
$23$			38.2047i			1.66108i	−0.556962	+	0.830538i	$0.688033\pi$
$24$	−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	$-0.929332\pi$
$31$		−	13.6518i		−	0.440381i	0.975457	−	0.220191i	$-0.0706679\pi$
$32$	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	$-0.939636\pi$
$43$		−	16.2115i		−	0.377010i	0.982072	−	0.188505i	$-0.0603643\pi$
$44$	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	$-0.994601\pi$
$47$		−	1.59429i		−	0.0339210i	0.999856	−	0.0169605i	$-0.00539895\pi$
$48$	−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	$-0.641534\pi$
$59$		−	106.526i		−	1.80553i	0.430135	−	0.902765i	$-0.358466\pi$
$60$	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	$-0.884610\pi$
$67$		−	47.5191i		−	0.709240i	0.935011	−	0.354620i	$-0.115390\pi$
$68$	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	$0.347153\pi$
$71$			125.941i			1.77382i	−0.461941	+	0.886911i	$0.652847\pi$
$72$	−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	$-0.851260\pi$
$79$		−	71.1726i		−	0.900919i	0.892797	−	0.450460i	$-0.148740\pi$
$80$	−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	$0.356038\pi$
$83$			149.310i			1.79891i	−0.437010	+	0.899457i	$0.643962\pi$
$84$	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	$-0.946284\pi$
$103$		−	34.5985i		−	0.335908i	0.985795	−	0.167954i	$-0.0537160\pi$
$104$	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	$0.130382\pi$
$107$			85.2253i			0.796498i	−0.917277	+	0.398249i	$0.869618\pi$
$108$	−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	$0.133406\pi$
$127$			103.364i			0.813890i	−0.913453	+	0.406945i	$0.866594\pi$
$128$	−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	$-0.893991\pi$
$131$		−	85.6520i		−	0.653832i	0.945053	−	0.326916i	$-0.106009\pi$
$132$	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	$-0.782799\pi$
$139$		−	175.314i		−	1.26125i	0.776087	−	0.630625i	$-0.217201\pi$
$140$	−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	$-0.964834\pi$
$151$		−	33.2962i		−	0.220504i	0.993904	−	0.110252i	$-0.0351659\pi$
$152$	−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	$-0.866077\pi$
$163$		−	133.148i		−	0.816858i	0.912790	−	0.408429i	$-0.133923\pi$
$164$	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	$0.0810158\pi$
$167$			84.0944i			0.503559i	−0.967785	+	0.251780i	$0.918984\pi$
$168$	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	$-0.915087\pi$
$179$		−	94.3723i		−	0.527219i	0.964629	−	0.263610i	$-0.0849131\pi$
$180$	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	$-0.918287\pi$
$191$		−	96.9894i		−	0.507798i	0.967231	−	0.253899i	$-0.0817131\pi$
$192$	−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	$0.0164753\pi$
$199$			20.5908i			0.103471i	−0.998661	+	0.0517356i	$0.983525\pi$
$200$	−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	$0.125228\pi$
$211$			161.772i			0.766690i	−0.923605	+	0.383345i	$0.874772\pi$
$212$	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	$0.125379\pi$
$223$			171.167i			0.767567i	−0.923423	+	0.383784i	$0.874621\pi$
$224$	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	$-0.921976\pi$
$227$		−	110.173i		−	0.485343i	0.970109	−	0.242672i	$-0.0780237\pi$
$228$	−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	$-0.798910\pi$
$239$		−	282.285i		−	1.18111i	0.806999	−	0.590553i	$-0.201090\pi$
$240$	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	$0.183232\pi$
$251$			273.275i			1.08874i	−0.838844	+	0.544372i	$0.816768\pi$
$252$	−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	$-0.905604\pi$
$263$		−	153.711i		−	0.584454i	0.956349	−	0.292227i	$-0.0943962\pi$
$264$	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	$-0.717357\pi$
$271$		−	420.472i		−	1.55156i	0.631005	−	0.775778i	$-0.282643\pi$
$272$	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	$0.335457\pi$
$283$			492.048i			1.73868i	−0.494211	+	0.869342i	$0.664543\pi$
$284$	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	$0.283801\pi$
$307$			477.735i			1.55614i	−0.628178	+	0.778070i	$0.716199\pi$
$308$	−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	$-0.779309\pi$
$311$		−	397.518i		−	1.27819i	0.769127	−	0.639096i	$-0.220691\pi$
$312$	−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	$0.290950\pi$
$331$			524.291i			1.58396i	−0.610546	+	0.791981i	$0.709050\pi$
$332$	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	$0.0650470\pi$
$347$			140.835i			0.405864i	−0.979193	+	0.202932i	$0.934953\pi$
$348$	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	$0.0607836\pi$
$359$			136.276i			0.379598i	−0.981823	+	0.189799i	$0.939216\pi$
$360$	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	$0.122074\pi$
$367$			274.645i			0.748352i	−0.927358	+	0.374176i	$0.877926\pi$
$368$	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	$-0.762256\pi$
$379$		−	514.957i		−	1.35873i	0.733803	−	0.679363i	$-0.237744\pi$
$380$	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	$-0.661335\pi$
$383$		−	669.698i		−	1.74856i	0.485424	−	0.874279i	$-0.338665\pi$
$384$	−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	$-0.999944\pi$
$419$		−	0.146671i		−	0.000350050i	1.00000		0.000175025i	$-5.57122e-5\pi$
$420$	−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	$-0.882811\pi$
$431$		−	310.234i		−	0.719800i	0.932991	−	0.359900i	$-0.117189\pi$
$432$	−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	$0.126598\pi$
$439$			340.063i			0.774631i	−0.921947	+	0.387315i	$0.873402\pi$
$440$	−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	$0.258682\pi$
$443$			643.348i			1.45225i	−0.687561	+	0.726127i	$0.741318\pi$
$444$	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	$0.122908\pi$
$463$			348.734i			0.753206i	−0.926375	+	0.376603i	$0.877092\pi$
$464$	−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	$-0.985702\pi$
$467$		−	41.9400i		−	0.0898072i	0.998991	−	0.0449036i	$-0.0142981\pi$
$468$	−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	$0.0865770\pi$
$479$			257.365i			0.537297i	−0.963238	+	0.268648i	$0.913423\pi$
$480$	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	$0.103839\pi$
$487$			312.131i			0.640927i	−0.947261	+	0.320463i	$0.896161\pi$
$488$	−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	$0.336785\pi$
$491$			855.711i			1.74279i	−0.490581	+	0.871396i	$0.663215\pi$
$492$	−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	$0.144389\pi$
$499$			437.337i			0.876427i	−0.898871	+	0.438214i	$0.855611\pi$
$500$	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	$0.149260\pi$
$503$			454.628i			0.903834i	−0.892060	+	0.451917i	$0.850740\pi$
$504$	−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	$0.119533\pi$
$523$			383.630i			0.733518i	−0.930316	+	0.366759i	$0.880467\pi$
$524$	−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	$-0.972637\pi$
$547$		−	93.9282i		−	0.171715i	0.996307	−	0.0858576i	$-0.0273630\pi$
$548$	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	$-0.783022\pi$
$563$		−	709.470i		−	1.26016i	0.776531	−	0.630079i	$-0.216978\pi$
$564$	−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	$-0.875232\pi$
$571$		−	436.257i		−	0.764022i	0.924158	−	0.382011i	$-0.124768\pi$
$572$	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	$0.113961\pi$
$587$			411.394i			0.700842i	−0.936592	+	0.350421i	$0.886039\pi$
$588$	−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	$-0.808088\pi$
$599$		−	679.317i		−	1.13408i	0.823689	−	0.567042i	$-0.191912\pi$
$600$	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	$-0.996322\pi$
$607$		−	14.0258i		−	0.0231067i	0.999933	−	0.0115534i	$-0.00367763\pi$
$608$	−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	$0.0664475\pi$
$619$			256.561i			0.414476i	−0.978291	+	0.207238i	$0.933553\pi$
$620$	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	$0.138229\pi$
$631$			530.971i			0.841476i	−0.907182	+	0.420738i	$0.861771\pi$
$632$	−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	$-0.999004\pi$
$643$		−	4.02353i		−	0.00625743i	0.999995	−	0.00312871i	$-0.000995902\pi$
$644$	−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	$-0.838748\pi$
$647$		−	627.845i		−	0.970394i	0.874405	−	0.485197i	$-0.161252\pi$
$648$	−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	$0.123761\pi$
$659$			499.633i			0.758168i	−0.925362	+	0.379084i	$0.876239\pi$
$660$	−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	$-0.789284\pi$
$683$		−	839.655i		−	1.22936i	0.788775	−	0.614682i	$-0.210716\pi$
$684$	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	$0.289647\pi$
$691$			1091.05i			1.57895i	−0.613783	+	0.789475i	$0.710353\pi$
$692$	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	$-0.873762\pi$
$719$		−	555.460i		−	0.772545i	0.922385	−	0.386273i	$-0.126238\pi$
$720$	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	$0.00179296\pi$
$727$			8.18995i			0.0112654i	−0.999984	+	0.00563271i	$0.998207\pi$
$728$	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	$-0.752210\pi$
$739$		−	1037.82i		−	1.40436i	0.712000	−	0.702180i	$-0.247790\pi$
$740$	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	$-0.968154\pi$
$743$		−	148.421i		−	0.199759i	0.995000	−	0.0998795i	$-0.0318457\pi$
$744$	−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	$0.0953056\pi$
$751$			443.027i			0.589916i	−0.955510	+	0.294958i	$0.904694\pi$
$752$	−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	$-0.862265\pi$
$787$		−	660.023i		−	0.838657i	0.907834	−	0.419329i	$-0.137735\pi$
$788$	−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	$-0.758588\pi$
$811$		−	1115.57i		−	1.37555i	0.725925	−	0.687774i	$-0.241412\pi$
$812$	−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	$0.0327766\pi$
$823$			169.190i			0.205577i	−0.994703	+	0.102789i	$0.967223\pi$
$824$	−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	$0.368183\pi$
$827$			1514.19i			1.83095i	−0.402380	+	0.915473i	$0.631817\pi$
$828$	−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	$0.278939\pi$
$839$			1289.35i			1.53677i	−0.639989	+	0.768384i	$0.721061\pi$
$840$	−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	$0.0151954\pi$
$859$			81.9821i			0.0954390i	−0.998861	+	0.0477195i	$0.984805\pi$
$860$	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	$-0.766735\pi$
$863$		−	1154.64i		−	1.33794i	0.743289	−	0.668971i	$-0.233265\pi$
$864$	−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	$-0.940603\pi$
$883$		−	327.627i		−	0.371038i	0.982641	−	0.185519i	$-0.0593966\pi$
$884$	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	$-0.834957\pi$
$887$		−	879.152i		−	0.991152i	0.868565	−	0.495576i	$-0.165043\pi$
$888$	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	$-0.822904\pi$
$907$		−	957.974i		−	1.05620i	0.849182	−	0.528100i	$-0.177096\pi$
$908$	−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	$0.172722\pi$
$911$			940.851i			1.03277i	−0.856357	+	0.516383i	$0.827278\pi$
$912$	−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	$-0.677091\pi$
$919$		−	1560.81i		−	1.69838i	0.528087	−	0.849190i	$-0.322909\pi$
$920$	−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	$0.178970\pi$
$947$			1009.67i			1.06618i	−0.846058	+	0.533091i	$0.821030\pi$
$948$	−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	$0.210079\pi$
$967$			1185.74i			1.22620i	−0.790004	+	0.613102i	$0.789921\pi$
$968$	−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	$0.195398\pi$
$971$			1118.65i			1.15206i	−0.817430	+	0.576028i	$0.804602\pi$
$972$	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	$0.0116646\pi$
$983$			72.0290i			0.0732747i	−0.999329	+	0.0366373i	$0.988335\pi$
$984$	−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	$0.0465889\pi$
$991$			289.057i			0.291683i	−0.989308	+	0.145841i	$0.953411\pi$
$992$	−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.39.13	✓	14
3.2	odd	2		684.3.g.b.343.2		14
4.3	odd	2	inner	76.3.b.b.39.14	yes	14
8.3	odd	2		1216.3.d.d.191.4		14
8.5	even	2		1216.3.d.d.191.11		14
12.11	even	2		684.3.g.b.343.1		14

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