LMFDB - Embedded newform 156.3.f.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(79,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("156.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.f (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:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			79.1
Character	$\chi$	$=$	156.79
Dual form			156.3.f.a.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99963 - 0.0384798i) q^{2} +1.73205i q^{3} +(3.99704 + 0.153891i) q^{4} -4.98564 q^{5} +(0.0666489 - 3.46346i) q^{6} -3.34189i q^{7} +(-7.98668 - 0.461529i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.99963 - 0.0384798i) q^{2} +1.73205i q^{3} +(3.99704 + 0.153891i) q^{4} -4.98564 q^{5} +(0.0666489 - 3.46346i) q^{6} -3.34189i q^{7} +(-7.98668 - 0.461529i) q^{8} -3.00000 q^{9} +(9.96944 + 0.191846i) q^{10} -8.65097i q^{11} +(-0.266546 + 6.92307i) q^{12} +3.60555 q^{13} +(-0.128595 + 6.68255i) q^{14} -8.63539i q^{15} +(15.9526 + 1.23021i) q^{16} -0.936203 q^{17} +(5.99889 + 0.115439i) q^{18} -29.3196i q^{19} +(-19.9278 - 0.767244i) q^{20} +5.78833 q^{21} +(-0.332887 + 17.2987i) q^{22} -33.3456i q^{23} +(0.799392 - 13.8333i) q^{24} -0.143370 q^{25} +(-7.20977 - 0.138741i) q^{26} -5.19615i q^{27} +(0.514286 - 13.3577i) q^{28} +0.223935 q^{29} +(-0.332288 + 17.2676i) q^{30} -35.7681i q^{31} +(-31.8520 - 3.07383i) q^{32} +14.9839 q^{33} +(1.87206 + 0.0360249i) q^{34} +16.6615i q^{35} +(-11.9911 - 0.461672i) q^{36} -22.5963 q^{37} +(-1.12821 + 58.6284i) q^{38} +6.24500i q^{39} +(39.8187 + 2.30102i) q^{40} -3.58506 q^{41} +(-11.5745 - 0.222734i) q^{42} +68.8231i q^{43} +(1.33130 - 34.5782i) q^{44} +14.9569 q^{45} +(-1.28313 + 66.6789i) q^{46} +5.87303i q^{47} +(-2.13079 + 27.6308i) q^{48} +37.8317 q^{49} +(0.286686 + 0.00551683i) q^{50} -1.62155i q^{51} +(14.4115 + 0.554861i) q^{52} -17.0444 q^{53} +(-0.199947 + 10.3904i) q^{54} +43.1306i q^{55} +(-1.54238 + 26.6906i) q^{56} +50.7831 q^{57} +(-0.447787 - 0.00861697i) q^{58} +66.0654i q^{59} +(1.32891 - 34.5160i) q^{60} -114.756 q^{61} +(-1.37635 + 71.5229i) q^{62} +10.0257i q^{63} +(63.5740 + 7.37217i) q^{64} -17.9760 q^{65} +(-29.9623 - 0.576578i) q^{66} +49.7915i q^{67} +(-3.74204 - 0.144073i) q^{68} +57.7563 q^{69} +(0.641130 - 33.3168i) q^{70} -78.4873i q^{71} +(23.9600 + 1.38459i) q^{72} -15.6030 q^{73} +(45.1842 + 0.869500i) q^{74} -0.248323i q^{75} +(4.51202 - 117.192i) q^{76} -28.9106 q^{77} +(0.240306 - 12.4877i) q^{78} -137.505i q^{79} +(-79.5341 - 6.13341i) q^{80} +9.00000 q^{81} +(7.16879 + 0.137952i) q^{82} -20.3475i q^{83} +(23.1362 + 0.890770i) q^{84} +4.66757 q^{85} +(2.64830 - 137.621i) q^{86} +0.387867i q^{87} +(-3.99268 + 69.0925i) q^{88} +24.0829 q^{89} +(-29.9083 - 0.575539i) q^{90} -12.0494i q^{91} +(5.13158 - 133.284i) q^{92} +61.9521 q^{93} +(0.225993 - 11.7439i) q^{94} +146.177i q^{95} +(5.32402 - 55.1693i) q^{96} -136.996 q^{97} +(-75.6495 - 1.45576i) q^{98} +25.9529i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	$ 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.99963	−	0.0384798i	−0.999815	−	0.0192399i
$2$	−1.99963	−	0.0384798i	−0.999815	−	0.0192399i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.99704	+	0.153891i	0.999260	+	0.0384727i
$5$	−4.98564			−0.997128			−0.498564	−	0.866853i	$-0.666139\pi$
$5$	−4.98564			−0.997128			−0.498564	+	0.866853i	$0.666139\pi$
$6$	0.0666489	−	3.46346i	0.0111082	−	0.577243i
$7$		−	3.34189i		−	0.477413i	−0.971092	−	0.238707i	$-0.923277\pi$
$7$		−	3.34189i		−	0.477413i	0.971092	−	0.238707i	$-0.0767235\pi$
$8$	−7.98668	−	0.461529i	−0.998334	−	0.0576912i
$9$	−3.00000			−0.333333
$10$	9.96944	+	0.191846i	0.996944	+	0.0191846i
$11$		−	8.65097i		−	0.786451i	−0.919442	−	0.393226i	$-0.871359\pi$
$11$		−	8.65097i		−	0.786451i	0.919442	−	0.393226i	$-0.128641\pi$
$12$	−0.266546	+	6.92307i	−0.0222122	+	0.576923i
$13$	3.60555			0.277350
$13$	3.60555			0.277350
$14$	−0.128595	+	6.68255i	−0.00918538	+	0.477325i
$15$		−	8.63539i		−	0.575692i
$16$	15.9526	+	1.23021i	0.997040	+	0.0768883i
$17$	−0.936203			−0.0550707			−0.0275354	−	0.999621i	$-0.508766\pi$
$17$	−0.936203			−0.0550707			−0.0275354	+	0.999621i	$0.508766\pi$
$18$	5.99889	+	0.115439i	0.333272	+	0.00641330i
$19$		−	29.3196i		−	1.54314i	−0.636145	−	0.771570i	$-0.719472\pi$
$19$		−	29.3196i		−	1.54314i	0.636145	−	0.771570i	$-0.280528\pi$
$20$	−19.9278	−	0.767244i	−0.996390	−	0.0383622i
$21$	5.78833			0.275635
$22$	−0.332887	+	17.2987i	−0.0151312	+	0.786306i
$23$		−	33.3456i		−	1.44981i	−0.688849	−	0.724904i	$-0.741884\pi$
$23$		−	33.3456i		−	1.44981i	0.688849	−	0.724904i	$-0.258116\pi$
$24$	0.799392	−	13.8333i	0.0333080	−	0.576389i
$25$	−0.143370			−0.00573478
$26$	−7.20977	−	0.138741i	−0.277299	−	0.00533619i
$27$		−	5.19615i		−	0.192450i
$28$	0.514286	−	13.3577i	0.0183674	−	0.477060i
$29$	0.223935			0.00772190			0.00386095	−	0.999993i	$-0.498771\pi$
$29$	0.223935			0.00772190			0.00386095	+	0.999993i	$0.498771\pi$
$30$	−0.332288	+	17.2676i	−0.0110763	+	0.575586i
$31$		−	35.7681i		−	1.15381i	−0.816812	−	0.576905i	$-0.804260\pi$
$31$		−	35.7681i		−	1.15381i	0.816812	−	0.576905i	$-0.195740\pi$
$32$	−31.8520	−	3.07383i	−0.995376	−	0.0960571i
$33$	14.9839			0.454058
$34$	1.87206	+	0.0360249i	0.0550605	+	0.00105955i
$35$			16.6615i			0.476043i
$36$	−11.9911	−	0.461672i	−0.333087	−	0.0128242i
$37$	−22.5963			−0.610710			−0.305355	−	0.952239i	$-0.598775\pi$
$37$	−22.5963			−0.610710			−0.305355	+	0.952239i	$0.598775\pi$
$38$	−1.12821	+	58.6284i	−0.0296898	+	1.54285i
$39$			6.24500i			0.160128i
$40$	39.8187	+	2.30102i	0.995468	+	0.0575255i
$41$	−3.58506			−0.0874404			−0.0437202	−	0.999044i	$-0.513921\pi$
$41$	−3.58506			−0.0874404			−0.0437202	+	0.999044i	$0.513921\pi$
$42$	−11.5745	−	0.222734i	−0.275584	−	0.00530318i
$43$			68.8231i			1.60054i	0.599642	+	0.800268i	$0.295310\pi$
$43$			68.8231i			1.60054i	−0.599642	+	0.800268i	$0.704690\pi$
$44$	1.33130	−	34.5782i	0.0302569	−	0.785869i
$45$	14.9569			0.332376
$46$	−1.28313	+	66.6789i	−0.0278942	+	1.44954i
$47$			5.87303i			0.124958i	0.998046	+	0.0624791i	$0.0199007\pi$
$47$			5.87303i			0.124958i	−0.998046	+	0.0624791i	$0.980099\pi$
$48$	−2.13079	+	27.6308i	−0.0443915	+	0.575641i
$49$	37.8317			0.772076
$50$	0.286686	+	0.00551683i	0.00573372	+	0.000110337i
$51$		−	1.62155i		−	0.0317951i
$52$	14.4115	+	0.554861i	0.277145	+	0.0106704i
$53$	−17.0444			−0.321592			−0.160796	−	0.986988i	$-0.551406\pi$
$53$	−17.0444			−0.321592			−0.160796	+	0.986988i	$0.551406\pi$
$54$	−0.199947	+	10.3904i	−0.00370272	+	0.192414i
$55$			43.1306i			0.784193i
$56$	−1.54238	+	26.6906i	−0.0275425	+	0.476618i
$57$	50.7831			0.890932
$58$	−0.447787	−	0.00861697i	−0.00772047	−	0.000148568i
$59$			66.0654i			1.11975i	0.828576	+	0.559876i	$0.189151\pi$
$59$			66.0654i			1.11975i	−0.828576	+	0.559876i	$0.810849\pi$
$60$	1.32891	−	34.5160i	0.0221484	−	0.575266i
$61$	−114.756			−1.88124			−0.940620	−	0.339462i	$-0.889755\pi$
$61$	−114.756			−1.88124			−0.940620	+	0.339462i	$0.889755\pi$
$62$	−1.37635	+	71.5229i	−0.0221992	+	1.15360i
$63$			10.0257i			0.159138i
$64$	63.5740	+	7.37217i	0.993343	+	0.115190i
$65$	−17.9760			−0.276554
$66$	−29.9623	−	0.576578i	−0.453974	−	0.00873603i
$67$			49.7915i			0.743157i	0.928402	+	0.371578i	$0.121183\pi$
$67$			49.7915i			0.743157i	−0.928402	+	0.371578i	$0.878817\pi$
$68$	−3.74204	−	0.144073i	−0.0550300	−	0.00211872i
$69$	57.7563			0.837047
$70$	0.641130	−	33.3168i	0.00915901	−	0.475954i
$71$		−	78.4873i		−	1.10545i	−0.833362	−	0.552727i	$-0.813587\pi$
$71$		−	78.4873i		−	1.10545i	0.833362	−	0.552727i	$-0.186413\pi$
$72$	23.9600	+	1.38459i	0.332778	+	0.0192304i
$73$	−15.6030			−0.213740			−0.106870	−	0.994273i	$-0.534083\pi$
$73$	−15.6030			−0.213740			−0.106870	+	0.994273i	$0.534083\pi$
$74$	45.1842	+	0.869500i	0.610597	+	0.0117500i
$75$		−	0.248323i		−	0.00331098i
$76$	4.51202	−	117.192i	0.0593687	−	1.54200i
$77$	−28.9106			−0.375463
$78$	0.240306	−	12.4877i	0.00308085	−	0.160099i
$79$		−	137.505i		−	1.74057i	−0.492551	−	0.870283i	$-0.663936\pi$
$79$		−	137.505i		−	1.74057i	0.492551	−	0.870283i	$-0.336064\pi$
$80$	−79.5341	−	6.13341i	−0.994177	−	0.0766676i
$81$	9.00000			0.111111
$82$	7.16879	+	0.137952i	0.0874242	+	0.00168234i
$83$		−	20.3475i		−	0.245150i	−0.992459	−	0.122575i	$-0.960885\pi$
$83$		−	20.3475i		−	0.245150i	0.992459	−	0.122575i	$-0.0391153\pi$
$84$	23.1362	+	0.890770i	0.275431	+	0.0106044i
$85$	4.66757			0.0549126
$86$	2.64830	−	137.621i	0.0307941	−	1.60024i
$87$			0.387867i			0.00445824i
$88$	−3.99268	+	69.0925i	−0.0453713	+	0.785142i
$89$	24.0829			0.270594			0.135297	−	0.990805i	$-0.456801\pi$
$89$	24.0829			0.270594			0.135297	+	0.990805i	$0.456801\pi$
$90$	−29.9083	−	0.575539i	−0.332315	−	0.00639488i
$91$		−	12.0494i		−	0.132411i
$92$	5.13158	−	133.284i	0.0557780	−	1.44874i
$93$	61.9521			0.666152
$94$	0.225993	−	11.7439i	0.00240418	−	0.124935i
$95$			146.177i			1.53871i
$96$	5.32402	−	55.1693i	0.0554586	−	0.574681i
$97$	−136.996			−1.41233			−0.706166	−	0.708046i	$-0.749577\pi$
$97$	−136.996			−1.41233			−0.706166	+	0.708046i	$0.749577\pi$
$98$	−75.6495	−	1.45576i	−0.771933	−	0.0148547i
$99$			25.9529i			0.262150i
$100$	−0.573054	−	0.0220632i	−0.00573054	−	0.000220632i
$101$	48.5723			0.480914			0.240457	−	0.970660i	$-0.422703\pi$
$101$	48.5723			0.480914			0.240457	+	0.970660i	$0.422703\pi$
$102$	−0.0623969	+	3.24250i	−0.000611734	+	0.0317892i
$103$			20.7100i			0.201068i	0.994934	+	0.100534i	$0.0320551\pi$
$103$			20.7100i			0.201068i	−0.994934	+	0.100534i	$0.967945\pi$
$104$	−28.7964	−	1.66407i	−0.276888	−	0.0160007i
$105$	−28.8585			−0.274843
$106$	34.0824	+	0.655863i	0.321532	+	0.00618739i
$107$			80.1149i			0.748738i	0.927280	+	0.374369i	$0.122141\pi$
$107$			80.1149i			0.748738i	−0.927280	+	0.374369i	$0.877859\pi$
$108$	0.799639	−	20.7692i	0.00740407	−	0.192308i
$109$	−126.510			−1.16064			−0.580320	−	0.814388i	$-0.697073\pi$
$109$	−126.510			−1.16064			−0.580320	+	0.814388i	$0.697073\pi$
$110$	1.65966	−	86.2453i	0.0150878	−	0.784048i
$111$		−	39.1379i		−	0.352594i
$112$	4.11124	−	53.3120i	0.0367075	−	0.476000i
$113$	202.600			1.79292			0.896461	−	0.443123i	$-0.146129\pi$
$113$	202.600			1.79292			0.896461	+	0.443123i	$0.146129\pi$
$114$	−101.547	−	1.95412i	−0.890767	−	0.0171414i
$115$			166.249i			1.44565i
$116$	0.895077	+	0.0344615i	0.00771618	+	0.000297082i
$117$	−10.8167			−0.0924500
$118$	2.54218	−	132.106i	0.0215439	−	1.11955i
$119$			3.12869i			0.0262915i
$120$	−3.98549	+	68.9680i	−0.0332124	+	0.574734i
$121$	46.1608			0.381494
$122$	229.469	+	4.41577i	1.88089	+	0.0361948i
$123$		−	6.20950i		−	0.0504838i
$124$	5.50437	−	142.966i	0.0443901	−	1.15295i
$125$	125.356			1.00285
$126$	0.385786	−	20.0477i	0.00306179	−	0.159108i
$127$		−	53.8312i		−	0.423868i	−0.977284	−	0.211934i	$-0.932024\pi$
$127$		−	53.8312i		−	0.423868i	0.977284	−	0.211934i	$-0.0679762\pi$
$128$	−126.841	−	17.1879i	−0.990943	−	0.134281i
$129$	−119.205			−0.924070
$130$	35.9453	+	0.691712i	0.276502	+	0.00532086i
$131$		−	255.421i		−	1.94978i	−0.222695	−	0.974888i	$-0.571485\pi$
$131$		−	255.421i		−	1.94978i	0.222695	−	0.974888i	$-0.428515\pi$
$132$	59.8913	+	2.30588i	0.453722	+	0.0174688i
$133$	−97.9832			−0.736715
$134$	1.91597	−	99.5646i	0.0142983	−	0.743019i
$135$			25.9062i			0.191897i
$136$	7.47715	+	0.432085i	0.0549790	+	0.00317710i
$137$	47.3297			0.345473			0.172736	−	0.984968i	$-0.444739\pi$
$137$	47.3297			0.345473			0.172736	+	0.984968i	$0.444739\pi$
$138$	−115.491	−	2.22245i	−0.836893	−	0.0161047i
$139$			151.671i			1.09116i	0.838059	+	0.545579i	$0.183690\pi$
$139$			151.671i			1.09116i	−0.838059	+	0.545579i	$0.816310\pi$
$140$	−2.56405	+	66.5966i	−0.0183146	+	0.475690i
$141$	−10.1724			−0.0721446
$142$	−3.02017	+	156.945i	−0.0212688	+	1.10525i
$143$		−	31.1915i		−	0.218122i
$144$	−47.8579	−	3.69064i	−0.332347	−	0.0256294i
$145$	−1.11646			−0.00769972
$146$	31.2003	+	0.600401i	0.213701	+	0.00411234i
$147$			65.5265i			0.445759i
$148$	−90.3182	−	3.47736i	−0.610258	−	0.0234957i
$149$	257.046			1.72514			0.862569	−	0.505939i	$-0.168854\pi$
$149$	257.046			1.72514			0.862569	+	0.505939i	$0.168854\pi$
$150$	−0.00955543	+	0.496555i	−6.37029e−5	+	0.00331037i
$151$		−	74.0102i		−	0.490134i	−0.969506	−	0.245067i	$-0.921190\pi$
$151$		−	74.0102i		−	0.490134i	0.969506	−	0.245067i	$-0.0788099\pi$
$152$	−13.5319	+	234.167i	−0.0890255	+	1.54057i
$153$	2.80861			0.0183569
$154$	57.8105	+	1.11247i	0.375393	+	0.00722386i
$155$			178.327i			1.15050i
$156$	−0.961047	+	24.9615i	−0.00616056	+	0.160010i
$157$	86.3013			0.549690			0.274845	−	0.961489i	$-0.411374\pi$
$157$	86.3013			0.549690			0.274845	+	0.961489i	$0.411374\pi$
$158$	−5.29115	+	274.959i	−0.0334883	+	1.74024i
$159$		−	29.5217i		−	0.185671i
$160$	158.803	+	15.3250i	0.992518	+	0.0957812i
$161$	−111.437			−0.692158
$162$	−17.9967	−	0.346318i	−0.111091	−	0.00213777i
$163$		−	124.211i		−	0.762029i	−0.924569	−	0.381015i	$-0.875575\pi$
$163$		−	124.211i		−	0.762029i	0.924569	−	0.381015i	$-0.124425\pi$
$164$	−14.3296	−	0.551707i	−0.0873757	−	0.00336407i
$165$	−74.7044			−0.452754
$166$	−0.782967	+	40.6874i	−0.00471667	+	0.245105i
$167$			168.354i			1.00811i	0.863672	+	0.504054i	$0.168159\pi$
$167$			168.354i			1.00811i	−0.863672	+	0.504054i	$0.831841\pi$
$168$	−46.2295	−	2.67148i	−0.275176	−	0.0159017i
$169$	13.0000			0.0769231
$170$	−9.33341	−	0.179607i	−0.0549024	−	0.00105651i
$171$			87.9589i			0.514380i
$172$	−10.5912	+	275.088i	−0.0615769	+	1.59935i
$173$	−323.241			−1.86844			−0.934222	−	0.356691i	$-0.883905\pi$
$173$	−323.241			−1.86844			−0.934222	+	0.356691i	$0.883905\pi$
$174$	0.0149250	−	0.775590i	8.57760e−5	−	0.00445741i
$175$			0.479126i			0.00273786i
$176$	10.6425	−	138.006i	0.0604690	−	0.784123i
$177$	−114.429			−0.646490
$178$	−48.1569	−	0.926705i	−0.270544	−	0.00520621i
$179$		−	106.891i		−	0.597157i	−0.954385	−	0.298579i	$-0.903487\pi$
$179$		−	106.891i		−	0.597157i	0.954385	−	0.298579i	$-0.0965125\pi$
$180$	59.7834	+	2.30173i	0.332130	+	0.0127874i
$181$	49.5800			0.273923			0.136961	−	0.990576i	$-0.456266\pi$
$181$	49.5800			0.273923			0.136961	+	0.990576i	$0.456266\pi$
$182$	−0.463657	+	24.0943i	−0.00254757	+	0.132386i
$183$		−	198.763i		−	1.08613i
$184$	−15.3900	+	266.321i	−0.0836412	+	1.44739i
$185$	112.657			0.608957
$186$	−123.881	−	2.38390i	−0.666029	−	0.0128167i
$187$			8.09906i			0.0433105i
$188$	−0.903805	+	23.4747i	−0.00480747	+	0.124866i
$189$	−17.3650			−0.0918783
$190$	5.62487	−	292.300i	0.0296046	−	1.53842i
$191$		−	126.760i		−	0.663663i	−0.943339	−	0.331832i	$-0.892333\pi$
$191$		−	126.760i		−	0.663663i	0.943339	−	0.331832i	$-0.107667\pi$
$192$	−12.7690	+	110.113i	−0.0665051	+	0.573507i
$193$	131.610			0.681915			0.340958	−	0.940079i	$-0.389249\pi$
$193$	131.610			0.681915			0.340958	+	0.940079i	$0.389249\pi$
$194$	273.942	+	5.27159i	1.41207	+	0.0271731i
$195$		−	31.1353i		−	0.159668i
$196$	151.215	+	5.82195i	0.771505	+	0.0297038i
$197$	−112.332			−0.570214			−0.285107	−	0.958496i	$-0.592029\pi$
$197$	−112.332			−0.570214			−0.285107	+	0.958496i	$0.592029\pi$
$198$	0.998662	−	51.8962i	0.00504375	−	0.262102i
$199$			243.277i			1.22250i	0.791439	+	0.611249i	$0.209332\pi$
$199$			243.277i			1.22250i	−0.791439	+	0.611249i	$0.790668\pi$
$200$	1.14505	+	0.0661693i	0.00572523	+	0.000330846i
$201$	−86.2414			−0.429062
$202$	−97.1266	−	1.86905i	−0.480825	−	0.00925273i
$203$		−	0.748367i		−	0.00368654i
$204$	0.249541	−	6.48140i	0.00122324	−	0.0317716i
$205$	17.8738			0.0871893
$206$	0.796915	−	41.4123i	0.00386852	−	0.201030i
$207$			100.037i			0.483270i
$208$	57.5180	+	4.43560i	0.276529	+	0.0213250i
$209$	−253.643			−1.21360
$210$	57.7064	+	1.11047i	0.274792	+	0.00528795i
$211$		−	322.242i		−	1.52721i	−0.645681	−	0.763607i	$-0.723426\pi$
$211$		−	322.242i		−	1.52721i	0.645681	−	0.763607i	$-0.276574\pi$
$212$	−68.1270	−	2.62297i	−0.321354	−	0.0123725i
$213$	135.944			0.638234
$214$	3.08280	−	160.200i	0.0144056	−	0.748599i
$215$		−	343.127i		−	1.59594i
$216$	−2.39818	+	41.5000i	−0.0111027	+	0.192130i
$217$	−119.533			−0.550844
$218$	252.973	+	4.86807i	1.16043	+	0.0223306i
$219$		−	27.0252i		−	0.123403i
$220$	−6.63740	+	172.395i	−0.0301700	+	0.783613i
$221$	−3.37553			−0.0152739
$222$	−1.50602	+	78.2613i	−0.00678387	+	0.352529i
$223$		−	197.953i		−	0.887681i	−0.896106	−	0.443840i	$-0.853616\pi$
$223$		−	197.953i		−	0.887681i	0.896106	−	0.443840i	$-0.146384\pi$
$224$	−10.2724	+	106.446i	−0.0458589	+	0.475206i
$225$	0.430109			0.00191159
$226$	−405.125	−	7.79601i	−1.79259	−	0.0344956i
$227$			324.837i			1.43100i	0.698613	+	0.715499i	$0.253801\pi$
$227$			324.837i			1.43100i	−0.698613	+	0.715499i	$0.746199\pi$
$228$	202.982	+	7.81505i	0.890272	+	0.0342765i
$229$	371.743			1.62333			0.811666	−	0.584122i	$-0.198561\pi$
$229$	371.743			1.62333			0.811666	+	0.584122i	$0.198561\pi$
$230$	6.39723	−	332.437i	0.0278141	−	1.44538i
$231$		−	50.0747i		−	0.216773i
$232$	−1.78850	−	0.103353i	−0.00770903	−	0.000445485i
$233$	210.436			0.903158			0.451579	−	0.892231i	$-0.350861\pi$
$233$	210.436			0.903158			0.451579	+	0.892231i	$0.350861\pi$
$234$	21.6293	+	0.416222i	0.0924329	+	0.00177873i
$235$		−	29.2808i		−	0.124599i
$236$	−10.1668	+	264.066i	−0.0430799	+	1.11892i
$237$	238.165			1.00492
$238$	0.120391	−	6.25622i	0.000505846	−	0.0262866i
$239$		−	317.305i		−	1.32763i	−0.747895	−	0.663817i	$-0.768935\pi$
$239$		−	317.305i		−	1.32763i	0.747895	−	0.663817i	$-0.231065\pi$
$240$	10.6234	−	137.757i	0.0442640	−	0.573988i
$241$	101.711			0.422038			0.211019	−	0.977482i	$-0.432322\pi$
$241$	101.711			0.422038			0.211019	+	0.977482i	$0.432322\pi$
$242$	−92.3045	−	1.77626i	−0.381423	−	0.00733990i
$243$			15.5885i			0.0641500i
$244$	−458.683	−	17.6598i	−1.87985	−	0.0723763i
$245$	−188.616			−0.769859
$246$	−0.238940	+	12.4167i	−0.000971302	+	0.0504744i
$247$		−	105.713i		−	0.427990i
$248$	−16.5080	+	285.668i	−0.0665646	+	1.15189i
$249$	35.2429			0.141538
$250$	−250.665	−	4.82367i	−1.00266	−	0.0192947i
$251$			401.077i			1.59792i	0.601387	+	0.798958i	$0.294615\pi$
$251$			401.077i			1.59792i	−0.601387	+	0.798958i	$0.705385\pi$
$252$	−1.54286	+	40.0730i	−0.00612245	+	0.159020i
$253$	−288.472			−1.14020
$254$	−2.07141	+	107.643i	−0.00815517	+	0.423790i
$255$			8.08447i			0.0317038i
$256$	252.973	+	39.2503i	0.988176	+	0.153321i
$257$	−1.84794			−0.00719042			−0.00359521	−	0.999994i	$-0.501144\pi$
$257$	−1.84794			−0.00719042			−0.00359521	+	0.999994i	$0.501144\pi$
$258$	238.366	+	4.58698i	0.923899	+	0.0177790i
$259$			75.5144i			0.291561i
$260$	−71.8507	−	2.76634i	−0.276349	−	0.0106398i
$261$	−0.671805			−0.00257397
$262$	−9.82853	+	510.747i	−0.0375135	+	1.94942i
$263$		−	366.786i		−	1.39463i	−0.716767	−	0.697313i	$-0.754379\pi$
$263$		−	366.786i		−	1.39463i	0.716767	−	0.697313i	$-0.245621\pi$
$264$	−119.672	−	6.91552i	−0.453302	−	0.0261951i
$265$	84.9771			0.320668
$266$	195.930	+	3.77037i	0.736579	+	0.0141743i
$267$			41.7128i			0.156228i
$268$	−7.66245	+	199.019i	−0.0285912	+	0.742607i
$269$	121.585			0.451990			0.225995	−	0.974128i	$-0.427437\pi$
$269$	121.585			0.451990			0.225995	+	0.974128i	$0.427437\pi$
$270$	0.996863	−	51.8027i	0.00369209	−	0.191862i
$271$			83.5517i			0.308309i	0.988047	+	0.154154i	$0.0492653\pi$
$271$			83.5517i			0.308309i	−0.988047	+	0.154154i	$0.950735\pi$
$272$	−14.9349	−	1.15173i	−0.0549077	−	0.00423430i
$273$	20.8701			0.0764473
$274$	−94.6420	−	1.82124i	−0.345409	−	0.00664685i
$275$			1.24029i			0.00451013i
$276$	230.854	+	8.88815i	0.836428	+	0.0322034i
$277$	295.425			1.06652			0.533258	−	0.845953i	$-0.320967\pi$
$277$	295.425			1.06652			0.533258	+	0.845953i	$0.320967\pi$
$278$	5.83627	−	303.286i	0.0209938	−	1.09096i
$279$			107.304i			0.384603i
$280$	7.68977	−	133.070i	0.0274635	−	0.475250i
$281$	−388.170			−1.38139			−0.690694	−	0.723147i	$-0.742695\pi$
$281$	−388.170			−1.38139			−0.690694	+	0.723147i	$0.742695\pi$
$282$	20.3410	+	0.391431i	0.0721313	+	0.00138805i
$283$		−	214.538i		−	0.758083i	−0.925380	−	0.379042i	$-0.876254\pi$
$283$		−	214.538i		−	0.758083i	0.925380	−	0.379042i	$-0.123746\pi$
$284$	12.0785	−	313.717i	0.0425298	−	1.10464i
$285$	−253.186			−0.888374
$286$	−1.20024	+	62.3715i	−0.00419665	+	0.218082i
$287$			11.9809i			0.0417452i
$288$	95.5561	+	9.22148i	0.331792	+	0.0320190i
$289$	−288.124			−0.996967
$290$	2.23251	+	0.0429611i	0.00769830	+	0.000148142i
$291$		−	237.285i		−	0.815411i
$292$	−62.3659	−	2.40116i	−0.213582	−	0.00822315i
$293$	−173.110			−0.590819			−0.295409	−	0.955371i	$-0.595456\pi$
$293$	−173.110			−0.590819			−0.295409	+	0.955371i	$0.595456\pi$
$294$	2.52145	−	131.029i	0.00857635	−	0.445676i
$295$		−	329.379i		−	1.11654i
$296$	180.469	+	10.4289i	0.609693	+	0.0352326i
$297$	−44.9517			−0.151353
$298$	−513.996	−	9.89106i	−1.72482	−	0.0331915i
$299$		−	120.229i		−	0.402105i
$300$	0.0382146	−	0.992558i	0.000127382	−	0.00330853i
$301$	229.999			0.764118
$302$	−2.84790	+	147.993i	−0.00943012	+	0.490043i
$303$			84.1297i			0.277656i
$304$	36.0694	−	467.726i	0.118649	−	1.53857i
$305$	572.130			1.87584
$306$	−5.61618	−	0.108075i	−0.0183535	−	0.000353185i
$307$			353.625i			1.15187i	0.817494	+	0.575937i	$0.195363\pi$
$307$			353.625i			1.15187i	−0.817494	+	0.575937i	$0.804637\pi$
$308$	−115.557	−	4.44907i	−0.375185	−	0.0144450i
$309$	−35.8707			−0.116086
$310$	6.86198	−	356.588i	0.0221354	−	1.15028i
$311$			0.0737574i			0.000237162i	1.00000		0.000118581i	$3.77455e-5\pi$
$311$			0.0737574i			0.000237162i	−1.00000		0.000118581i	$0.999962\pi$
$312$	2.88225	−	49.8768i	0.00923798	−	0.159861i
$313$	262.790			0.839585			0.419793	−	0.907620i	$-0.362103\pi$
$313$	262.790			0.839585			0.419793	+	0.907620i	$0.362103\pi$
$314$	−172.571	−	3.32085i	−0.549588	−	0.0105760i
$315$		−	49.9845i		−	0.158681i
$316$	21.1607	−	549.612i	0.0669642	−	1.73928i
$317$	−363.488			−1.14665			−0.573326	−	0.819328i	$-0.694347\pi$
$317$	−363.488			−1.14665			−0.573326	+	0.819328i	$0.694347\pi$
$318$	−1.13599	+	59.0325i	−0.00357229	+	0.185637i
$319$		−	1.93725i		−	0.00607290i
$320$	−316.957	−	36.7550i	−0.990491	−	0.114859i
$321$	−138.763			−0.432284
$322$	222.834	+	4.28809i	0.692030	+	0.0133170i
$323$			27.4491i			0.0849818i
$324$	35.9733	+	1.38502i	0.111029	+	0.00427474i
$325$	−0.516926			−0.00159054
$326$	−4.77960	+	248.376i	−0.0146614	+	0.761888i
$327$		−	219.121i		−	0.670096i
$328$	28.6327	+	1.65461i	0.0872948	+	0.00504454i
$329$	19.6271			0.0596567
$330$	149.381	+	2.87461i	0.452670	+	0.00871094i
$331$			534.064i			1.61349i	0.590902	+	0.806743i	$0.298772\pi$
$331$			534.064i			1.61349i	−0.590902	+	0.806743i	$0.701228\pi$
$332$	3.13129	−	81.3297i	0.00943159	−	0.244969i
$333$	67.7889			0.203570
$334$	6.47823	−	336.646i	0.0193959	−	1.00792i
$335$		−	248.243i		−	0.741023i
$336$	92.3391	+	7.12088i	0.274819	+	0.0211931i
$337$	537.056			1.59364			0.796819	−	0.604218i	$-0.206514\pi$
$337$	537.056			1.59364			0.796819	+	0.604218i	$0.206514\pi$
$338$	−25.9952	−	0.500237i	−0.0769088	−	0.00147999i
$339$			350.914i			1.03514i
$340$	18.6565	+	0.718295i	0.0548719	+	0.00211263i
$341$	−309.428			−0.907415
$342$	3.38464	−	175.885i	0.00989661	−	0.514285i
$343$		−	290.182i		−	0.846013i
$344$	31.7639	−	549.668i	0.0923368	−	1.59787i
$345$	−287.952			−0.834644
$346$	646.362	+	12.4382i	1.86810	+	0.0359487i
$347$			349.707i			1.00780i	0.863762	+	0.503900i	$0.168102\pi$
$347$			349.707i			1.00780i	−0.863762	+	0.503900i	$0.831898\pi$
$348$	−0.0596891	+	1.55032i	−0.000171520	+	0.00445494i
$349$	139.999			0.401144			0.200572	−	0.979679i	$-0.435720\pi$
$349$	139.999			0.401144			0.200572	+	0.979679i	$0.435720\pi$
$350$	0.0184367	−	0.958074i	5.26762e−5	−	0.00273736i
$351$		−	18.7350i		−	0.0533761i
$352$	−26.5916	+	275.551i	−0.0755442	+	0.782815i
$353$	−341.896			−0.968543			−0.484272	−	0.874918i	$-0.660915\pi$
$353$	−341.896			−0.968543			−0.484272	+	0.874918i	$0.660915\pi$
$354$	228.815	+	4.40319i	0.646370	+	0.0124384i
$355$			391.309i			1.10228i
$356$	96.2603	+	3.70613i	0.270394	+	0.0104105i
$357$	−5.41905			−0.0151794
$358$	−4.11315	+	213.743i	−0.0114892	+	0.597047i
$359$			534.175i			1.48795i	0.668206	+	0.743976i	$0.267062\pi$
$359$			534.175i			1.48795i	−0.668206	+	0.743976i	$0.732938\pi$
$360$	−119.456	−	6.90306i	−0.331823	−	0.0191752i
$361$	−498.642			−1.38128
$362$	−99.1417	−	1.90783i	−0.273872	−	0.00527024i
$363$			79.9528i			0.220256i
$364$	1.85429	−	48.1618i	0.00509419	−	0.132313i
$365$	77.7911			0.213126
$366$	−7.64834	+	397.451i	−0.0208971	+	1.08593i
$367$			453.584i			1.23592i	0.786208	+	0.617962i	$0.212042\pi$
$367$			453.584i			1.23592i	−0.786208	+	0.617962i	$0.787958\pi$
$368$	41.0222	−	531.950i	0.111473	−	1.44552i
$369$	10.7552			0.0291468
$370$	−225.272	−	4.33502i	−0.608844	−	0.0117163i
$371$			56.9605i			0.153532i
$372$	247.625	+	9.53385i	0.665659	+	0.0256286i
$373$	341.544			0.915668			0.457834	−	0.889038i	$-0.348625\pi$
$373$	341.544			0.915668			0.457834	+	0.889038i	$0.348625\pi$
$374$	0.311650	−	16.1951i	0.000833289	−	0.0433024i
$375$			217.123i			0.578994i
$376$	2.71058	−	46.9060i	0.00720898	−	0.124750i
$377$	0.807409			0.00214167
$378$	34.7236	+	0.668201i	0.0918613	+	0.00176773i
$379$		−	36.6412i		−	0.0966787i	−0.998831	−	0.0483393i	$-0.984607\pi$
$379$		−	36.6412i		−	0.0966787i	0.998831	−	0.0483393i	$-0.0153929\pi$
$380$	−22.4953	+	584.276i	−0.0591982	+	1.53757i
$381$	93.2384			0.244720
$382$	−4.87768	+	253.472i	−0.0127688	+	0.663540i
$383$			166.098i			0.433675i	0.976208	+	0.216838i	$0.0695742\pi$
$383$			166.098i			0.433675i	−0.976208	+	0.216838i	$0.930426\pi$
$384$	29.7704	−	219.695i	0.0775270	−	0.572121i
$385$	144.138			0.374384
$386$	−263.171	−	5.06431i	−0.681789	−	0.0131200i
$387$		−	206.469i		−	0.533512i
$388$	−547.579	−	21.0824i	−1.41129	−	0.0543362i
$389$	−408.616			−1.05043			−0.525213	−	0.850971i	$-0.676014\pi$
$389$	−408.616			−1.05043			−0.525213	+	0.850971i	$0.676014\pi$
$390$	−1.19808	+	62.2591i	−0.00307200	+	0.159639i
$391$			31.2182i			0.0798420i
$392$	−302.150	−	17.4605i	−0.770790	−	0.0445420i
$393$	442.402			1.12570
$394$	224.623	+	4.32252i	0.570109	+	0.0109709i
$395$			685.550i			1.73557i
$396$	−3.99391	+	103.735i	−0.0100856	+	0.261956i
$397$	476.592			1.20048			0.600242	−	0.799819i	$-0.295071\pi$
$397$	476.592			1.20048			0.600242	+	0.799819i	$0.295071\pi$
$398$	9.36124	−	486.464i	0.0235207	−	1.22227i
$399$		−	169.712i		−	0.425343i
$400$	−2.28712	−	0.176375i	−0.00571781	−	0.000440938i
$401$	134.833			0.336243			0.168121	−	0.985766i	$-0.446230\pi$
$401$	134.833			0.336243			0.168121	+	0.985766i	$0.446230\pi$
$402$	172.451	+	3.31855i	0.428982	+	0.00825510i
$403$		−	128.964i		−	0.320009i
$404$	194.145	+	7.47482i	0.480558	+	0.0185020i
$405$	−44.8708			−0.110792
$406$	−0.0287970	+	1.49646i	−7.09286e−5	+	0.00368585i
$407$			195.480i			0.480294i
$408$	−0.748393	+	12.9508i	−0.00183430	+	0.0317421i
$409$	−640.526			−1.56608			−0.783039	−	0.621972i	$-0.786332\pi$
$409$	−640.526			−1.56608			−0.783039	+	0.621972i	$0.786332\pi$
$410$	−35.7410	−	0.687780i	−0.0871732	−	0.00167751i
$411$			81.9775i			0.199459i
$412$	−3.18707	+	82.7785i	−0.00773561	+	0.200919i
$413$	220.784			0.534585
$414$	3.84939	−	200.037i	0.00929805	−	0.483180i
$415$			101.445i			0.244446i
$416$	−114.844	−	11.0828i	−0.276068	−	0.0266414i
$417$	−262.702			−0.629981
$418$	507.193	+	9.76014i	1.21338	+	0.0233496i
$419$		−	128.427i		−	0.306509i	−0.988187	−	0.153255i	$-0.951025\pi$
$419$		−	128.427i		−	0.306509i	0.988187	−	0.153255i	$-0.0489755\pi$
$420$	−115.349	−	4.44106i	−0.274640	−	0.0105740i
$421$	579.481			1.37644			0.688220	−	0.725502i	$-0.258392\pi$
$421$	579.481			1.37644			0.688220	+	0.725502i	$0.258392\pi$
$422$	−12.3998	+	644.365i	−0.0293834	+	1.52693i
$423$		−	17.6191i		−	0.0416527i
$424$	136.128	+	7.86648i	0.321056	+	0.0185530i
$425$	0.134223			0.000315819
$426$	−271.838	−	5.23109i	−0.638116	−	0.0122796i
$427$			383.501i			0.898129i
$428$	−12.3289	+	320.222i	−0.0288059	+	0.748183i
$429$	54.0253			0.125933
$430$	−13.2035	+	686.127i	−0.0307057	+	1.59565i
$431$		−	358.772i		−	0.832417i	−0.909269	−	0.416208i	$-0.863359\pi$
$431$		−	358.772i		−	0.832417i	0.909269	−	0.416208i	$-0.136641\pi$
$432$	6.39238	−	82.8923i	0.0147972	−	0.191880i
$433$	−406.338			−0.938424			−0.469212	−	0.883085i	$-0.655462\pi$
$433$	−406.338			−0.938424			−0.469212	+	0.883085i	$0.655462\pi$
$434$	239.022	+	4.59961i	0.550742	+	0.0105982i
$435$		−	1.93376i		−	0.00444544i
$436$	−505.665	−	19.4687i	−1.15978	−	0.0446529i
$437$	−977.681			−2.23726
$438$	−1.03993	+	54.0405i	−0.00237426	+	0.123380i
$439$		−	573.804i		−	1.30707i	−0.756896	−	0.653535i	$-0.773285\pi$
$439$		−	573.804i		−	1.30707i	0.756896	−	0.653535i	$-0.226715\pi$
$440$	19.9061	−	344.470i	0.0452410	−	0.782887i
$441$	−113.495			−0.257359
$442$	6.74980	+	0.129890i	0.0152710	+	0.000293868i
$443$		−	96.6497i		−	0.218171i	−0.994032	−	0.109085i	$-0.965208\pi$
$443$		−	96.6497i		−	0.218171i	0.994032	−	0.109085i	$-0.0347922\pi$
$444$	6.02296	−	156.436i	0.0135652	−	0.352333i
$445$	−120.069			−0.269817
$446$	−7.61718	+	395.832i	−0.0170789	+	0.887516i
$447$			445.216i			0.996009i
$448$	24.6370	−	212.458i	0.0549933	−	0.474236i
$449$	−11.9281			−0.0265660			−0.0132830	−	0.999912i	$-0.504228\pi$
$449$	−11.9281			−0.0265660			−0.0132830	+	0.999912i	$0.504228\pi$
$450$	−0.860058	−	0.0165505i	−0.00191124	−	3.67789e-5i
$451$			31.0142i			0.0687677i
$452$	809.801	+	31.1783i	1.79159	+	0.0689785i
$453$	128.189			0.282979
$454$	12.4996	−	649.553i	0.0275323	−	1.43073i
$455$			60.0739i			0.132030i
$456$	−405.588	−	23.4379i	−0.889448	−	0.0513989i
$457$	620.161			1.35703			0.678514	−	0.734588i	$-0.262624\pi$
$457$	620.161			1.35703			0.678514	+	0.734588i	$0.262624\pi$
$458$	−743.348	−	14.3046i	−1.62303	−	0.0312327i
$459$			4.86465i			0.0105984i
$460$	−25.5842	+	664.505i	−0.0556178	+	1.44458i
$461$	478.720			1.03844			0.519220	−	0.854641i	$-0.326223\pi$
$461$	478.720			1.03844			0.519220	+	0.854641i	$0.326223\pi$
$462$	−1.92686	+	100.131i	−0.00417070	+	0.216733i
$463$			59.7601i			0.129072i	0.997915	+	0.0645358i	$0.0205567\pi$
$463$			59.7601i			0.129072i	−0.997915	+	0.0645358i	$0.979443\pi$
$464$	3.57235	+	0.275488i	0.00769904	+	0.000593724i
$465$	−308.871			−0.664239
$466$	−420.794	−	8.09752i	−0.902991	−	0.0173767i
$467$		−	658.094i		−	1.40919i	−0.709608	−	0.704597i	$-0.751128\pi$
$467$		−	658.094i		−	1.40919i	0.709608	−	0.704597i	$-0.248872\pi$
$468$	−43.2346	−	1.66458i	−0.0923816	−	0.00355680i
$469$	166.398			0.354793
$470$	−1.12672	+	58.5508i	−0.00239728	+	0.124576i
$471$			149.478i			0.317364i
$472$	30.4911	−	527.643i	0.0645999	−	1.11789i
$473$	595.386			1.25874
$474$	−476.242	−	9.16455i	−1.00473	−	0.0193345i
$475$			4.20354i			0.00884957i
$476$	−0.481476	+	12.5055i	−0.00101150	+	0.0262720i
$477$	51.1331			0.107197
$478$	−12.2098	+	634.492i	−0.0255435	+	1.32739i
$479$			875.844i			1.82848i	0.405169	+	0.914242i	$0.367213\pi$
$479$			875.844i			1.82848i	−0.405169	+	0.914242i	$0.632787\pi$
$480$	−26.5437	+	275.055i	−0.0552993	+	0.573030i
$481$	−81.4721			−0.169381
$482$	−203.385	−	3.91383i	−0.421960	−	0.00811997i
$483$		−	193.015i		−	0.399618i
$484$	184.506	+	7.10371i	0.381212	+	0.0146771i
$485$	683.014			1.40828
$486$	0.599840	−	31.1711i	0.00123424	−	0.0641382i
$487$		−	138.229i		−	0.283838i	−0.989878	−	0.141919i	$-0.954673\pi$
$487$		−	138.229i		−	0.283838i	0.989878	−	0.141919i	$-0.0453273\pi$
$488$	916.516	+	52.9631i	1.87811	+	0.108531i
$489$	215.139			0.439958
$490$	377.161	+	7.25788i	0.769717	+	0.0148120i
$491$		−	515.656i		−	1.05022i	−0.851035	−	0.525108i	$-0.824025\pi$
$491$		−	515.656i		−	1.05022i	0.851035	−	0.525108i	$-0.175975\pi$
$492$	0.955584	−	24.8196i	0.00194224	−	0.0504464i
$493$	−0.209648			−0.000425250
$494$	−4.06783	+	211.388i	−0.00823448	+	0.427911i
$495$		−	129.392i		−	0.261398i
$496$	44.0024	−	570.595i	0.0887145	−	1.15039i
$497$	−262.296			−0.527759
$498$	−70.4727	−	1.35614i	−0.141511	−	0.00272317i
$499$			238.135i			0.477224i	0.971115	+	0.238612i	$0.0766924\pi$
$499$			238.135i			0.477224i	−0.971115	+	0.238612i	$0.923308\pi$
$500$	501.052	+	19.2911i	1.00210	+	0.0385822i
$501$	−291.598			−0.582032
$502$	15.4333	−	802.005i	0.0307437	−	1.59762i
$503$		−	702.621i		−	1.39686i	−0.715678	−	0.698430i	$-0.753882\pi$
$503$		−	702.621i		−	1.39686i	0.715678	−	0.698430i	$-0.246118\pi$
$504$	4.62715	−	80.0719i	0.00918085	−	0.158873i
$505$	−242.164			−0.479533
$506$	576.837	+	11.1003i	1.13999	+	0.0219374i
$507$			22.5167i			0.0444116i
$508$	8.28412	−	215.166i	0.0163073	−	0.423554i
$509$	−587.488			−1.15420			−0.577100	−	0.816673i	$-0.695816\pi$
$509$	−587.488			−1.15420			−0.577100	+	0.816673i	$0.695816\pi$
$510$	0.311089	−	16.1659i	0.000609978	−	0.0316979i
$511$			52.1437i			0.102042i
$512$	−504.342	−	88.2204i	−0.985044	−	0.172305i
$513$	−152.349			−0.296977
$514$	3.69519	+	0.0711083i	0.00718909	+	0.000138343i
$515$		−	103.253i		−	0.200490i
$516$	−476.467	−	18.3445i	−0.923386	−	0.0355514i
$517$	50.8074			0.0982735
$518$	2.90578	−	151.001i	0.00560961	−	0.291507i
$519$		−	559.870i		−	1.07875i
$520$	143.568	+	8.29645i	0.276093	+	0.0159547i
$521$	724.631			1.39085			0.695423	−	0.718600i	$-0.255217\pi$
$521$	724.631			1.39085			0.695423	+	0.718600i	$0.255217\pi$
$522$	1.34336	+	0.0258509i	0.00257349	+	4.95228e-5i
$523$		−	892.068i		−	1.70568i	−0.522176	−	0.852838i	$-0.674879\pi$
$523$		−	892.068i		−	1.70568i	0.522176	−	0.852838i	$-0.325121\pi$
$524$	39.3069	−	1020.93i	0.0750131	−	1.94833i
$525$	−0.829870			−0.00158071
$526$	−14.1139	+	733.437i	−0.0268324	+	1.39437i
$527$			33.4862i			0.0635411i
$528$	239.033	+	18.4334i	0.452714	+	0.0349118i
$529$	−582.929			−1.10195
$530$	−169.923	−	3.26990i	−0.320609	−	0.00616962i
$531$		−	198.196i		−	0.373251i
$532$	−391.642	−	15.0787i	−0.736170	−	0.0283434i
$533$	−12.9261			−0.0242516
$534$	1.60510	−	83.4102i	0.00300581	−	0.156199i
$535$		−	399.424i		−	0.746588i
$536$	22.9802	−	397.669i	0.0428736	−	0.741919i
$537$	185.141			0.344769
$538$	−243.126	−	4.67858i	−0.451907	−	0.00869625i
$539$		−	327.281i		−	0.607201i
$540$	−3.98672	+	103.548i	−0.00738281	+	0.191755i
$541$	−237.144			−0.438343			−0.219172	−	0.975686i	$-0.570335\pi$
$541$	−237.144			−0.438343			−0.219172	+	0.975686i	$0.570335\pi$
$542$	3.21505	−	167.073i	0.00593183	−	0.308252i
$543$			85.8751i			0.158149i
$544$	29.8199	+	2.87772i	0.0548161	+	0.00528993i
$545$	630.733			1.15731
$546$	−41.7325	−	0.803078i	−0.0764332	−	0.00147084i
$547$		−	855.557i		−	1.56409i	−0.623222	−	0.782045i	$-0.714177\pi$
$547$		−	855.557i		−	1.56409i	0.623222	−	0.782045i	$-0.285823\pi$
$548$	189.179	+	7.28360i	0.345217	+	0.0132912i
$549$	344.267			0.627080
$550$	0.0477259	−	2.48011i	8.67744e−5	−	0.00450929i
$551$		−	6.56569i		−	0.0119160i
$552$	−461.281	−	26.6562i	−0.835653	−	0.0482903i
$553$	−459.526			−0.830970
$554$	−590.741	−	11.3679i	−1.06632	−	0.0205197i
$555$			195.128i			0.351581i
$556$	−23.3408	+	606.235i	−0.0419798	+	1.09035i
$557$	−417.936			−0.750334			−0.375167	−	0.926957i	$-0.622415\pi$
$557$	−417.936			−0.750334			−0.375167	+	0.926957i	$0.622415\pi$
$558$	4.12904	−	214.569i	0.00739972	−	0.384532i
$559$			248.145i			0.443909i
$560$	−20.4972	+	265.795i	−0.0366021	+	0.474633i
$561$	−14.0280			−0.0250053
$562$	776.197	+	14.9367i	1.38113	+	0.0265778i
$563$		−	623.197i		−	1.10692i	−0.832875	−	0.553461i	$-0.813307\pi$
$563$		−	623.197i		−	1.10692i	0.832875	−	0.553461i	$-0.186693\pi$
$564$	−40.6594	−	1.56544i	−0.0720912	−	0.00277560i
$565$	−1010.09			−1.78777
$566$	−8.25536	+	428.996i	−0.0145854	+	0.757943i
$567$		−	30.0770i		−	0.0530459i
$568$	−36.2242	+	626.852i	−0.0637750	+	1.10361i
$569$	928.386			1.63161			0.815805	−	0.578328i	$-0.196294\pi$
$569$	928.386			1.63161			0.815805	+	0.578328i	$0.196294\pi$
$570$	506.279	+	9.74256i	0.888209	+	0.0170922i
$571$		−	668.041i		−	1.16995i	−0.811052	−	0.584974i	$-0.801105\pi$
$571$		−	668.041i		−	1.16995i	0.811052	−	0.584974i	$-0.198895\pi$
$572$	4.80008	−	124.674i	0.00839175	−	0.217961i
$573$	219.554			0.383166
$574$	0.461022	−	23.9573i	0.000803174	−	0.0417375i
$575$			4.78074i			0.00831434i
$576$	−190.722	−	22.1165i	−0.331114	−	0.0383967i
$577$	−396.211			−0.686675			−0.343337	−	0.939212i	$-0.611557\pi$
$577$	−396.211			−0.686675			−0.343337	+	0.939212i	$0.611557\pi$
$578$	576.140	+	11.0869i	0.996783	+	0.0191815i
$579$			227.955i			0.393704i
$580$	−4.46253	−	0.171813i	−0.00769402	−	0.000296229i
$581$	−67.9991			−0.117038
$582$	−9.13066	+	474.481i	−0.0156884	+	0.815260i
$583$			147.450i			0.252916i
$584$	124.616	+	7.20126i	0.213384	+	0.0123309i
$585$	53.9280			0.0921846
$586$	346.156	+	6.66123i	0.590709	+	0.0113673i
$587$		−	557.230i		−	0.949285i	−0.880179	−	0.474642i	$-0.842577\pi$
$587$		−	557.230i		−	0.949285i	0.880179	−	0.474642i	$-0.157423\pi$
$588$	−10.0839	+	261.912i	−0.0171495	+	0.445429i
$589$	−1048.71			−1.78049
$590$	−12.6744	+	658.635i	−0.0214821	+	1.11633i
$591$		−	194.565i		−	0.329213i
$592$	−360.470	−	27.7983i	−0.608902	−	0.0469565i
$593$	439.125			0.740515			0.370257	−	0.928929i	$-0.379269\pi$
$593$	439.125			0.740515			0.370257	+	0.928929i	$0.379269\pi$
$594$	89.8868	+	1.72973i	0.151325	+	0.00291201i
$595$		−	15.5985i		−	0.0262160i
$596$	1027.42	+	39.5569i	1.72386	+	0.0663707i
$597$	−421.368			−0.705809
$598$	−4.62640	+	240.414i	−0.00773645	+	0.402030i
$599$			26.3814i			0.0440424i	0.999758	+	0.0220212i	$0.00701013\pi$
$599$			26.3814i			0.0440424i	−0.999758	+	0.0220212i	$0.992990\pi$
$600$	−0.114609	+	1.98328i	−0.000191014	+	0.00330546i
$601$	−34.6958			−0.0577300			−0.0288650	−	0.999583i	$-0.509189\pi$
$601$	−34.6958			−0.0577300			−0.0288650	+	0.999583i	$0.509189\pi$
$602$	−459.914	−	8.85033i	−0.763976	−	0.0147015i
$603$		−	149.375i		−	0.247719i
$604$	11.3895	−	295.822i	0.0188567	−	0.489771i
$605$	−230.141			−0.380399
$606$	3.23729	−	168.228i	0.00534206	−	0.277604i
$607$		−	2.23322i		−	0.00367912i	−0.999998	−	0.00183956i	$-0.999414\pi$
$607$		−	2.23322i		−	0.00367912i	0.999998	−	0.00183956i	$-0.000585550\pi$
$608$	−90.1235	+	933.890i	−0.148229	+	1.53600i
$609$	1.29621			0.00212842
$610$	−1144.05	−	22.0155i	−1.87549	−	0.0360909i
$611$			21.1755i			0.0346572i
$612$	11.2261	+	0.432218i	0.0183433	+	0.000706239i
$613$	−784.667			−1.28004			−0.640022	−	0.768357i	$-0.721075\pi$
$613$	−784.667			−1.28004			−0.640022	+	0.768357i	$0.721075\pi$
$614$	13.6074	−	707.120i	0.0221619	−	1.15166i
$615$			30.9584i			0.0503388i
$616$	230.900	+	13.3431i	0.374837	+	0.0216609i
$617$	720.280			1.16739			0.583695	−	0.811973i	$-0.301606\pi$
$617$	720.280			1.16739			0.583695	+	0.811973i	$0.301606\pi$
$618$	71.7282	+	1.38030i	0.116065	+	0.00223349i
$619$			856.400i			1.38352i	0.722127	+	0.691761i	$0.243165\pi$
$619$			856.400i			1.38352i	−0.722127	+	0.691761i	$0.756835\pi$
$620$	−27.4428	+	712.779i	−0.0442626	+	1.14964i
$621$	−173.269			−0.279016
$622$	0.00283817	−	0.147487i	4.56297e−6	−	0.000237118i
$623$		−	80.4825i		−	0.129185i
$624$	−7.68268	+	99.6242i	−0.0123120	+	0.159654i
$625$	−621.395			−0.994232
$626$	−525.483	−	10.1121i	−0.839430	−	0.0161535i
$627$		−	439.323i		−	0.700675i
$628$	344.950	+	13.2810i	0.549283	+	0.0211480i
$629$	21.1547			0.0336323
$630$	−1.92339	+	99.9504i	−0.00305300	+	0.158651i
$631$			315.588i			0.500139i	0.968228	+	0.250070i	$0.0804535\pi$
$631$			315.588i			0.500139i	−0.968228	+	0.250070i	$0.919547\pi$
$632$	−63.4625	+	1098.21i	−0.100415	+	1.73767i
$633$	558.140			0.881738
$634$	726.842	+	13.9870i	1.14644	+	0.0220614i
$635$			268.383i			0.422651i
$636$	4.54311	−	117.999i	0.00714326	−	0.185534i
$637$	136.404			0.214135
$638$	−0.0745451	+	3.87379i	−0.000116842	+	0.00607177i
$639$			235.462i			0.368485i
$640$	632.383	+	85.6929i	0.988098	+	0.133895i
$641$	1033.39			1.61215			0.806073	−	0.591816i	$-0.201589\pi$
$641$	1033.39			1.61215			0.806073	+	0.591816i	$0.201589\pi$
$642$	277.475	+	5.33957i	0.432204	+	0.00831709i
$643$		−	316.889i		−	0.492828i	−0.969165	−	0.246414i	$-0.920748\pi$
$643$		−	316.889i		−	0.492828i	0.969165	−	0.246414i	$-0.0792523\pi$
$644$	−445.420	−	17.1492i	−0.691646	−	0.0266292i
$645$	594.314			0.921417
$646$	1.05624	−	54.8881i	0.00163504	−	0.0849661i
$647$			458.255i			0.708277i	0.935193	+	0.354138i	$0.115226\pi$
$647$			458.255i			0.708277i	−0.935193	+	0.354138i	$0.884774\pi$
$648$	−71.8801	−	4.15377i	−0.110926	−	0.00641013i
$649$	571.530			0.880631
$650$	1.03366	+	0.0198912i	0.00159025	+	3.06019e-5i
$651$		−	207.037i		−	0.318030i
$652$	19.1149	−	496.475i	0.0293173	−	0.761465i
$653$	12.9221			0.0197889			0.00989444	−	0.999951i	$-0.496850\pi$
$653$	12.9221			0.0197889			0.00989444	+	0.999951i	$0.496850\pi$
$654$	−8.43174	+	438.162i	−0.0128926	+	0.669972i
$655$			1273.44i			1.94418i
$656$	−57.1911	−	4.41039i	−0.0871816	−	0.00672315i
$657$	46.8091			0.0712467
$658$	−39.2468	−	0.755245i	−0.0596457	−	0.00114779i
$659$			345.890i			0.524871i	0.964949	+	0.262436i	$0.0845257\pi$
$659$			345.890i			0.524871i	−0.964949	+	0.262436i	$0.915474\pi$
$660$	−298.597	−	11.4963i	−0.452419	−	0.0174187i
$661$	1018.12			1.54026			0.770132	−	0.637884i	$-0.220190\pi$
$661$	1018.12			1.54026			0.770132	+	0.637884i	$0.220190\pi$
$662$	20.5507	−	1067.93i	0.0310433	−	1.61319i
$663$		−	5.84658i		−	0.00881838i
$664$	−9.39096	+	162.509i	−0.0141430	+	0.244742i
$665$	488.509			0.734600
$666$	−135.553	−	2.60850i	−0.203532	−	0.00391667i
$667$		−	7.46725i		−	0.0111953i
$668$	−25.9081	+	672.918i	−0.0387846	+	1.00736i
$669$	342.864			0.512503
$670$	−9.55232	+	496.393i	−0.0142572	+	0.740886i
$671$			992.747i			1.47950i
$672$	−184.370	−	17.7923i	−0.274360	−	0.0264767i
$673$	−970.343			−1.44182			−0.720909	−	0.693030i	$-0.756275\pi$
$673$	−970.343			−1.44182			−0.720909	+	0.693030i	$0.756275\pi$
$674$	−1073.91	−	20.6658i	−1.59334	−	0.0306614i
$675$			0.744970i			0.00110366i
$676$	51.9615	+	2.00058i	0.0768661	+	0.00295944i
$677$	−647.080			−0.955804			−0.477902	−	0.878413i	$-0.658603\pi$
$677$	−647.080			−0.955804			−0.477902	+	0.878413i	$0.658603\pi$
$678$	13.5031	−	701.698i	0.0199161	−	1.03495i
$679$			457.827i			0.674267i
$680$	−37.2784	−	2.15422i	−0.0548211	−	0.00316797i
$681$	−562.634			−0.826187
$682$	618.742	+	11.9067i	0.907247	+	0.0174586i
$683$			596.337i			0.873114i	0.899677	+	0.436557i	$0.143802\pi$
$683$			596.337i			0.873114i	−0.899677	+	0.436557i	$0.856198\pi$
$684$	−13.5361	+	351.575i	−0.0197896	+	0.513999i
$685$	−235.969			−0.344481
$686$	−11.1662	+	580.258i	−0.0162772	+	0.845856i
$687$			643.878i			0.937231i
$688$	−84.6671	+	1097.91i	−0.123063	+	1.59580i
$689$	−61.4543			−0.0891935
$690$	575.798	+	11.0803i	0.834489	+	0.0160585i
$691$		−	876.399i		−	1.26831i	−0.773208	−	0.634153i	$-0.781349\pi$
$691$		−	876.399i		−	1.26831i	0.773208	−	0.634153i	$-0.218651\pi$
$692$	−1292.01	−	49.7438i	−1.86706	−	0.0718840i
$693$	86.7318			0.125154
$694$	13.4566	−	699.284i	0.0193900	−	1.00761i
$695$		−	756.178i		−	1.08803i
$696$	0.179012	−	3.09777i	0.000257201	−	0.00445081i
$697$	3.35634			0.00481541
$698$	−279.947	−	5.38714i	−0.401070	−	0.00771797i
$699$			364.485i			0.521438i
$700$	−0.0737330	+	1.91508i	−0.000105333	+	0.00273584i
$701$	56.3928			0.0804462			0.0402231	−	0.999191i	$-0.487193\pi$
$701$	56.3928			0.0804462			0.0402231	+	0.999191i	$0.487193\pi$
$702$	−0.720918	+	37.4631i	−0.00102695	+	0.0533662i
$703$			662.515i			0.942411i
$704$	63.7764	−	549.976i	0.0905915	−	0.781216i
$705$	50.7159			0.0719375
$706$	683.665	+	13.1561i	0.968364	+	0.0186347i
$707$		−	162.323i		−	0.229595i
$708$	−457.376	−	17.6095i	−0.646011	−	0.0248722i
$709$	1151.81			1.62456			0.812280	−	0.583267i	$-0.198226\pi$
$709$	1151.81			1.62456			0.812280	+	0.583267i	$0.198226\pi$
$710$	15.0575	−	782.474i	0.0212077	−	1.10208i
$711$			412.514i			0.580189i
$712$	−192.342	−	11.1150i	−0.270144	−	0.0156109i
$713$	−1192.71			−1.67280
$714$	10.8361	+	0.208524i	0.0151766	+	0.000292050i
$715$			155.510i			0.217496i
$716$	16.4495	−	427.248i	0.0229742	−	0.596715i
$717$	549.588			0.766510
$718$	20.5549	−	1068.15i	0.0286280	−	1.48768i
$719$			876.648i			1.21926i	0.792686	+	0.609630i	$0.208682\pi$
$719$			876.648i			1.21926i	−0.792686	+	0.609630i	$0.791318\pi$
$720$	238.602	+	18.4002i	0.331392	+	0.0255559i
$721$	69.2105			0.0959924
$722$	997.099	+	19.1876i	1.38102	+	0.0265757i
$723$			176.169i			0.243664i
$724$	198.173	+	7.62990i	0.273720	+	0.0105385i
$725$	−0.0321055			−4.42834e−5
$726$	3.07657	−	159.876i	0.00423770	−	0.220215i
$727$		−	484.847i		−	0.666915i	−0.942765	−	0.333457i	$-0.891785\pi$
$727$		−	484.847i		−	0.666915i	0.942765	−	0.333457i	$-0.108215\pi$
$728$	−5.56114	+	96.2344i	−0.00763893	+	0.132190i
$729$	−27.0000			−0.0370370
$730$	−155.553	−	2.99339i	−0.213087	−	0.00410053i
$731$		−	64.4323i		−	0.0881427i
$732$	30.5877	−	794.461i	0.0417865	−	1.08533i
$733$	243.342			0.331980			0.165990	−	0.986127i	$-0.446918\pi$
$733$	243.342			0.331980			0.165990	+	0.986127i	$0.446918\pi$
$734$	17.4538	−	907.001i	0.0237791	−	1.23570i
$735$		−	326.692i		−	0.444479i
$736$	−102.499	+	1062.13i	−0.139264	+	1.44310i
$737$	430.745			0.584457
$738$	−21.5064	−	0.413857i	−0.0291414	−	0.000560781i
$739$		−	697.193i		−	0.943427i	−0.881752	−	0.471714i	$-0.843636\pi$
$739$		−	697.193i		−	0.943427i	0.881752	−	0.471714i	$-0.156364\pi$
$740$	450.294	+	17.3369i	0.608506	+	0.0234282i
$741$	183.101			0.247100
$742$	2.19183	−	113.900i	0.00295394	−	0.153504i
$743$		−	637.384i		−	0.857852i	−0.903340	−	0.428926i	$-0.858892\pi$
$743$		−	637.384i		−	0.857852i	0.903340	−	0.428926i	$-0.141108\pi$
$744$	−494.792	−	28.5927i	−0.665042	−	0.0384311i
$745$	−1281.54			−1.72019
$746$	−682.962	−	13.1425i	−0.915498	−	0.0176173i
$747$			61.0424i			0.0817168i
$748$	−1.24637	+	32.3722i	−0.00166627	+	0.0432784i
$749$	267.736			0.357457
$750$	8.35483	−	434.165i	0.0111398	−	0.578887i
$751$			576.281i			0.767352i	0.923468	+	0.383676i	$0.125342\pi$
$751$			576.281i			0.767352i	−0.923468	+	0.383676i	$0.874658\pi$
$752$	−7.22509	+	93.6904i	−0.00960783	+	0.124588i
$753$	−694.685			−0.922557
$754$	−1.61452	−	0.0310689i	−0.00214127	−	4.12055e-5i
$755$			368.988i			0.488726i
$756$	−69.4085	−	2.67231i	−0.0918102	−	0.00353480i
$757$	457.887			0.604870			0.302435	−	0.953170i	$-0.402200\pi$
$757$	457.887			0.604870			0.302435	+	0.953170i	$0.402200\pi$
$758$	−1.40995	+	73.2689i	−0.00186009	+	0.0966608i
$759$		−	499.648i		−	0.658297i
$760$	67.4651	−	1167.47i	0.0887699	−	1.53615i
$761$	−531.702			−0.698688			−0.349344	−	0.936995i	$-0.613596\pi$
$761$	−531.702			−0.698688			−0.349344	+	0.936995i	$0.613596\pi$
$762$	−186.442	−	3.58779i	−0.244675	−	0.00470839i
$763$			422.782i			0.554105i
$764$	19.5071	−	506.663i	0.0255329	−	0.663172i
$765$	−14.0027			−0.0183042
$766$	6.39140	−	332.134i	0.00834387	−	0.433595i
$767$			238.202i			0.310564i
$768$	−67.9835	+	438.162i	−0.0885202	+	0.570524i
$769$	458.481			0.596205			0.298102	−	0.954534i	$-0.403646\pi$
$769$	458.481			0.596205			0.298102	+	0.954534i	$0.403646\pi$
$770$	−288.223	−	5.54640i	−0.374315	−	0.00720311i
$771$		−	3.20072i		−	0.00415139i
$772$	526.049	+	20.2535i	0.681410	+	0.0262351i
$773$	481.016			0.622272			0.311136	−	0.950365i	$-0.399291\pi$
$773$	481.016			0.622272			0.311136	+	0.950365i	$0.399291\pi$
$774$	−7.94489	+	412.862i	−0.0102647	+	0.533413i
$775$			5.12805i			0.00661684i
$776$	1094.14	+	63.2278i	1.40998	+	0.0814791i
$777$	−130.795			−0.168333
$778$	817.080	+	15.7234i	1.05023	+	0.0202101i
$779$			105.113i			0.134933i
$780$	4.79144	−	124.449i	0.00614287	−	0.159550i
$781$	−678.991			−0.869386
$782$	1.20127	−	62.4249i	0.00153615	−	0.0798273i
$783$		−	1.16360i		−	0.00148608i
$784$	603.516	+	46.5411i	0.769791	+	0.0593637i
$785$	−430.267			−0.548111
$786$	−884.640	−	17.0235i	−1.12550	−	0.0216584i
$787$			375.007i			0.476502i	0.971204	+	0.238251i	$0.0765740\pi$
$787$			375.007i			0.476502i	−0.971204	+	0.238251i	$0.923426\pi$
$788$	−448.996	−	17.2869i	−0.569792	−	0.0219377i
$789$	635.293			0.805187
$790$	26.3798	−	1370.85i	0.0333922	−	1.73525i
$791$		−	677.068i		−	0.855965i
$792$	11.9780	−	207.277i	0.0151238	−	0.261714i
$793$	−413.757			−0.521762
$794$	−953.007	−	18.3391i	−1.20026	−	0.0230972i
$795$			147.185i			0.185138i
$796$	−37.4380	+	972.387i	−0.0470327	+	1.22159i
$797$	−609.620			−0.764893			−0.382447	−	0.923978i	$-0.624918\pi$
$797$	−609.620			−0.764893			−0.382447	+	0.923978i	$0.624918\pi$
$798$	−6.53047	+	339.361i	−0.00818355	+	0.425264i
$799$		−	5.49835i		−	0.00688154i
$800$	4.56661	+	0.440693i	0.00570826	+	0.000550866i
$801$	−72.2487			−0.0901982
$802$	−269.617	−	5.18836i	−0.336180	−	0.00646927i
$803$			134.981i			0.168096i
$804$	−344.710	−	13.2717i	−0.428744	−	0.0165071i
$805$	555.587			0.690171
$806$	−4.96249	+	257.880i	−0.00615694	+	0.319950i
$807$			210.592i			0.260957i
$808$	−387.931	−	22.4175i	−0.480113	−	0.0277445i
$809$	−422.519			−0.522273			−0.261136	−	0.965302i	$-0.584097\pi$
$809$	−422.519			−0.522273			−0.261136	+	0.965302i	$0.584097\pi$
$810$	89.7250	+	1.72662i	0.110772	+	0.00213163i
$811$			266.225i			0.328267i	0.986438	+	0.164134i	$0.0524829\pi$
$811$			266.225i			0.328267i	−0.986438	+	0.164134i	$0.947517\pi$
$812$	0.115167	−	2.99125i	0.000141831	−	0.00368381i
$813$	−144.716			−0.178002
$814$	7.52202	−	390.887i	0.00924081	−	0.480205i
$815$			619.270i			0.759841i
$816$	1.99485	−	25.8680i	0.00244467	−	0.0317010i
$817$	2017.87			2.46985
$818$	1280.81	+	24.6473i	1.56579	+	0.0301312i
$819$			36.1481i			0.0441369i
$820$	71.4423	+	2.75061i	0.0871248	+	0.00335441i
$821$	−1138.40			−1.38660			−0.693300	−	0.720649i	$-0.743844\pi$
$821$	−1138.40			−1.38660			−0.693300	+	0.720649i	$0.743844\pi$
$822$	3.15448	−	163.925i	0.00383756	−	0.199422i
$823$		−	708.475i		−	0.860845i	−0.902628	−	0.430422i	$-0.858365\pi$
$823$		−	708.475i		−	0.860845i	0.902628	−	0.430422i	$-0.141635\pi$
$824$	9.55826	−	165.404i	0.0115998	−	0.200733i
$825$	−2.14824			−0.00260392
$826$	−441.485	−	8.49570i	−0.534486	−	0.0102854i
$827$		−	1378.55i		−	1.66693i	−0.552573	−	0.833464i	$-0.686354\pi$
$827$		−	1378.55i		−	1.66693i	0.552573	−	0.833464i	$-0.313646\pi$
$828$	−15.3947	+	399.851i	−0.0185927	+	0.482912i
$829$	46.8483			0.0565119			0.0282559	−	0.999601i	$-0.491005\pi$
$829$	46.8483			0.0565119			0.0282559	+	0.999601i	$0.491005\pi$
$830$	3.90359	−	202.853i	0.00470312	−	0.244401i
$831$			511.691i			0.615754i
$832$	229.219	+	26.5807i	0.275504	+	0.0319480i
$833$	−35.4182			−0.0425188
$834$	525.307	+	10.1087i	0.629864	+	0.0121208i
$835$		−	839.354i		−	1.00521i
$836$	−1013.82	−	39.0333i	−1.21271	−	0.0466906i
$837$	−185.856			−0.222051
$838$	−4.94186	+	256.807i	−0.00589721	+	0.306453i
$839$			1278.61i			1.52396i	0.647598	+	0.761982i	$0.275774\pi$
$839$			1278.61i			1.52396i	−0.647598	+	0.761982i	$0.724226\pi$
$840$	230.484	+	13.3191i	0.274386	+	0.0158560i
$841$	−840.950			−0.999940
$842$	−1158.75	−	22.2983i	−1.37619	−	0.0264826i
$843$		−	672.331i		−	0.797545i
$844$	49.5901	−	1288.01i	0.0587560	−	1.52608i
$845$	−64.8134			−0.0767022
$846$	−0.677979	+	35.2317i	−0.000801394	+	0.0416450i
$847$		−	154.264i		−	0.182130i
$848$	−271.903	−	20.9682i	−0.320640	−	0.0247267i
$849$	371.590			0.437680
$850$	−0.268396	−	0.00516487i	−0.000315760	−	6.07632e-6i
$851$			753.487i			0.885413i
$852$	543.373	+	20.9205i	0.637762	+	0.0245546i
$853$	57.6539			0.0675895			0.0337948	−	0.999429i	$-0.489241\pi$
$853$	57.6539			0.0675895			0.0337948	+	0.999429i	$0.489241\pi$
$854$	14.7570	−	766.860i	0.0172799	−	0.897963i
$855$		−	438.532i		−	0.512903i
$856$	36.9754	−	639.852i	0.0431956	−	0.747491i
$857$	−831.023			−0.969689			−0.484844	−	0.874601i	$-0.661124\pi$
$857$	−831.023			−0.969689			−0.484844	+	0.874601i	$0.661124\pi$
$858$	−108.031	−	2.07888i	−0.125910	−	0.00242294i
$859$			909.734i			1.05906i	0.848291	+	0.529531i	$0.177632\pi$
$859$			909.734i			1.05906i	−0.848291	+	0.529531i	$0.822368\pi$
$860$	52.8041	−	1371.49i	0.0614001	−	1.59476i
$861$	−20.7515			−0.0241016
$862$	−13.8055	+	717.411i	−0.0160156	+	0.832263i
$863$		−	26.8875i		−	0.0311558i	−0.999879	−	0.0155779i	$-0.995041\pi$
$863$		−	26.8875i		−	0.0311558i	0.999879	−	0.0155779i	$-0.00495880\pi$
$864$	−15.9721	+	165.508i	−0.0184862	+	0.191560i
$865$	1611.56			1.86308
$866$	812.525	+	15.6358i	0.938251	+	0.0180552i
$867$		−	499.045i		−	0.575599i
$868$	−477.779	−	18.3950i	−0.550436	−	0.0211924i
$869$	−1189.55			−1.36887
$870$	−0.0744108	+	3.86681i	−8.55297e−5	+	0.00444461i
$871$			179.526i			0.206115i
$872$	1010.39	+	58.3880i	1.15871	+	0.0669587i
$873$	410.989			0.470778
$874$	1955.00	+	37.6210i	2.23684	+	0.0430446i
$875$		−	418.926i		−	0.478773i
$876$	4.15893	−	108.021i	0.00474764	−	0.123312i
$877$	33.1871			0.0378416			0.0189208	−	0.999821i	$-0.493977\pi$
$877$	33.1871			0.0378416			0.0189208	+	0.999821i	$0.493977\pi$
$878$	−22.0799	+	1147.40i	−0.0251479	+	1.30683i
$879$		−	299.835i		−	0.341109i
$880$	−53.0599	+	688.047i	−0.0602953	+	0.781872i
$881$	1372.98			1.55843			0.779217	−	0.626754i	$-0.215617\pi$
$881$	1372.98			1.55843			0.779217	+	0.626754i	$0.215617\pi$
$882$	226.948	+	4.36727i	0.257311	+	0.00495156i
$883$			341.308i			0.386532i	0.981146	+	0.193266i	$0.0619081\pi$
$883$			341.308i			0.386532i	−0.981146	+	0.193266i	$0.938092\pi$
$884$	−13.4921	−	0.519462i	−0.0152626	−	0.000587627i
$885$	570.500			0.644633
$886$	−3.71906	+	193.264i	−0.00419758	+	0.218130i
$887$			816.519i			0.920540i	0.887779	+	0.460270i	$0.152247\pi$
$887$			816.519i			0.920540i	−0.887779	+	0.460270i	$0.847753\pi$
$888$	−18.0633	+	312.582i	−0.0203416	+	0.352007i
$889$	−179.898			−0.202360
$890$	240.093	+	4.62022i	0.269768	+	0.00519126i
$891$		−	77.8587i		−	0.0873835i
$892$	30.4631	−	791.225i	0.0341514	−	0.887024i
$893$	172.195			0.192828
$894$	17.1318	−	890.268i	0.0191631	−	0.995825i
$895$			532.921i			0.595443i
$896$	−57.4402	+	423.888i	−0.0641074	+	0.473090i
$897$	208.243			0.232155
$898$	23.8518	+	0.458991i	0.0265610	+	0.000511126i
$899$		−	8.00972i		−	0.00890959i
$900$	1.71916	+	0.0661897i	0.00191018	+	7.35441e-5i
$901$	15.9570			0.0177103
$902$	1.19342	−	62.0169i	0.00132308	−	0.0687549i
$903$			398.371i			0.441164i
$904$	−1618.10	−	93.5060i	−1.78994	−	0.103436i
$905$	−247.188			−0.273136
$906$	−256.331	−	4.93270i	−0.282926	−	0.00544448i
$907$			410.472i			0.452560i	0.974062	+	0.226280i	$0.0726565\pi$
$907$			410.472i			0.452560i	−0.974062	+	0.226280i	$0.927343\pi$
$908$	−49.9893	+	1298.38i	−0.0550543	+	1.42994i
$909$	−145.717			−0.160305
$910$	2.31163	−	120.125i	0.00254025	−	0.132006i
$911$		−	50.0265i		−	0.0549138i	−0.999623	−	0.0274569i	$-0.991259\pi$
$911$		−	50.0265i		−	0.0549138i	0.999623	−	0.0274569i	$-0.00874090\pi$
$912$	810.125	+	62.4741i	0.888294	+	0.0685023i
$913$	−176.025			−0.192799
$914$	−1240.09	−	23.8637i	−1.35678	−	0.0261091i
$915$			990.959i			1.08302i
$916$	1485.87	+	57.2078i	1.62213	+	0.0624539i
$917$	−853.589			−0.930850
$918$	0.187191	−	9.72750i	0.000203911	−	0.0105964i
$919$		−	219.907i		−	0.239289i	−0.992817	−	0.119645i	$-0.961824\pi$
$919$		−	219.907i		−	0.239289i	0.992817	−	0.119645i	$-0.0381755\pi$
$920$	76.7289	−	1327.78i	0.0834010	−	1.44324i
$921$	−612.497			−0.665035
$922$	−957.264	−	18.4211i	−1.03825	−	0.0199795i
$923$		−	282.990i		−	0.306598i
$924$	7.70602	−	200.150i	0.00833985	−	0.216613i
$925$	3.23962			0.00350229
$926$	2.29956	−	119.498i	0.00248332	−	0.129048i
$927$		−	62.1299i		−	0.0670226i
$928$	−7.13278	−	0.688337i	−0.00768619	−	0.000741742i
$929$	−1432.81			−1.54231			−0.771157	−	0.636645i	$-0.780322\pi$
$929$	−1432.81			−1.54231			−0.771157	+	0.636645i	$0.780322\pi$
$930$	617.628	+	11.8853i	0.664116	+	0.0127799i
$931$		−	1109.21i		−	1.19142i
$932$	841.120	+	32.3841i	0.902489	+	0.0347469i
$933$	−0.127751			−0.000136925
$934$	−25.3233	+	1315.94i	−0.0271127	+	1.40893i
$935$		−	40.3790i		−	0.0431861i
$936$	86.3891	+	4.99220i	0.0922961	+	0.00533355i
$937$	208.757			0.222793			0.111397	−	0.993776i	$-0.464468\pi$
$937$	208.757			0.222793			0.111397	+	0.993776i	$0.464468\pi$
$938$	−332.734	−	6.40296i	−0.354727	−	0.00682618i
$939$			455.166i			0.484735i
$940$	4.50605	−	117.037i	0.00479367	−	0.124507i
$941$	431.307			0.458350			0.229175	−	0.973385i	$-0.426397\pi$
$941$	431.307			0.458350			0.229175	+	0.973385i	$0.426397\pi$
$942$	5.75189	−	298.901i	0.00610604	−	0.317305i
$943$			119.546i			0.126772i
$944$	−81.2746	+	1053.92i	−0.0860959	+	1.11644i
$945$	86.5756			0.0916144
$946$	−1190.55	−	22.9103i	−1.25851	−	0.0242181i
$947$		−	1737.46i		−	1.83470i	−0.398077	−	0.917352i	$-0.630322\pi$
$947$		−	1737.46i		−	1.83470i	0.398077	−	0.917352i	$-0.369678\pi$
$948$	951.956	+	36.6514i	1.00417	+	0.0386618i
$949$	−56.2575			−0.0592808
$950$	0.161751	−	8.40553i	0.000170265	−	0.00884793i
$951$		−	629.580i		−	0.662019i
$952$	1.44398	−	24.9878i	0.00151679	−	0.0262477i
$953$	883.649			0.927229			0.463615	−	0.886037i	$-0.346552\pi$
$953$	883.649			0.927229			0.463615	+	0.886037i	$0.346552\pi$
$954$	−102.247	−	1.96759i	−0.107177	−	0.00206246i
$955$			631.978i			0.661757i
$956$	48.8302	−	1268.28i	0.0510776	−	1.32665i
$957$	3.35542			0.00350619
$958$	33.7023	−	1751.36i	0.0351798	−	1.82815i
$959$		−	158.171i		−	0.164933i
$960$	63.6616	−	548.986i	0.0663141	−	0.571860i
$961$	−318.356			−0.331275
$962$	162.914	+	3.13503i	0.169349	+	0.00325886i
$963$		−	240.345i		−	0.249579i
$964$	406.544	+	15.6524i	0.421726	+	0.0162369i
$965$	−656.158			−0.679957
$966$	−7.42719	+	385.959i	−0.00768860	+	0.399544i
$967$		−	1605.15i		−	1.65992i	−0.557820	−	0.829962i	$-0.688362\pi$
$967$		−	1605.15i		−	1.65992i	0.557820	−	0.829962i	$-0.311638\pi$
$968$	−368.671	−	21.3046i	−0.380859	−	0.0220088i
$969$	−47.5433			−0.0490643
$970$	−1365.78	−	26.2822i	−1.40802	−	0.0270951i
$971$			229.236i			0.236083i	0.993009	+	0.118041i	$0.0376615\pi$
$971$			229.236i			0.236083i	−0.993009	+	0.118041i	$0.962338\pi$
$972$	−2.39892	+	62.3077i	−0.00246802	+	0.0641025i
$973$	506.869			0.520934
$974$	−5.31903	+	276.407i	−0.00546102	+	0.283786i
$975$		−	0.895343i		−	0.000918300i
$976$	−1830.65	−	141.174i	−1.87567	−	0.144645i
$977$	311.466			0.318798			0.159399	−	0.987214i	$-0.449044\pi$
$977$	311.466			0.318798			0.159399	+	0.987214i	$0.449044\pi$
$978$	−430.199	−	8.27851i	−0.439876	−	0.00846474i
$979$		−	208.340i		−	0.212809i
$980$	−753.904	−	29.0262i	−0.769289	−	0.0296185i
$981$	379.529			0.386880
$982$	−19.8423	+	1031.12i	−0.0202060	+	1.05002i
$983$		−	379.569i		−	0.386133i	−0.981186	−	0.193067i	$-0.938157\pi$
$983$		−	379.569i		−	0.386133i	0.981186	−	0.193067i	$-0.0618433\pi$
$984$	−2.86587	+	49.5933i	−0.00291247	+	0.0503997i
$985$	560.048			0.568577
$986$	0.419219	+	0.00806723i	0.000425172	+	8.18177e-6i
$987$			33.9951i			0.0344428i
$988$	16.2683	−	422.541i	0.0164659	−	0.427673i
$989$	2294.95			2.32047
$990$	−4.97897	+	258.736i	−0.00502926	+	0.261349i
$991$			900.695i			0.908875i	0.890779	+	0.454438i	$0.150160\pi$
$991$			900.695i			0.908875i	−0.890779	+	0.454438i	$0.849840\pi$
$992$	−109.945	+	1139.29i	−0.110831	+	1.14847i
$993$	−925.026			−0.931547
$994$	524.495	+	10.0931i	0.527661	+	0.0101540i
$995$		−	1212.89i		−	1.21899i
$996$	140.867	+	5.42355i	0.141433	+	0.00544533i
$997$	−875.161			−0.877795			−0.438897	−	0.898537i	$-0.644631\pi$
$997$	−875.161			−0.877795			−0.438897	+	0.898537i	$0.644631\pi$
$998$	9.16337	−	476.181i	0.00918173	−	0.477135i
$999$			117.414i			0.117531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.f.a.79.1	✓	24
3.2	odd	2		468.3.f.b.235.24		24
4.3	odd	2	inner	156.3.f.a.79.2	yes	24
8.3	odd	2		2496.3.k.e.703.12		24
8.5	even	2		2496.3.k.e.703.11		24
12.11	even	2		468.3.f.b.235.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.f.a.79.1	✓	24	1.1	even	1	trivial
156.3.f.a.79.2	yes	24	4.3	odd	2	inner
468.3.f.b.235.23		24	12.11	even	2
468.3.f.b.235.24		24	3.2	odd	2
2496.3.k.e.703.11		24	8.5	even	2
2496.3.k.e.703.12		24	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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99963 - 0.0384798i) q^{2} +1.73205i q^{3} +(3.99704 + 0.153891i) q^{4} -4.98564 q^{5} +(0.0666489 - 3.46346i) q^{6} -3.34189i q^{7} +(-7.98668 - 0.461529i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.99963 - 0.0384798i) q^{2} +1.73205i q^{3} +(3.99704 + 0.153891i) q^{4} -4.98564 q^{5} +(0.0666489 - 3.46346i) q^{6} -3.34189i q^{7} +(-7.98668 - 0.461529i) q^{8} -3.00000 q^{9} +(9.96944 + 0.191846i) q^{10} -8.65097i q^{11} +(-0.266546 + 6.92307i) q^{12} +3.60555 q^{13} +(-0.128595 + 6.68255i) q^{14} -8.63539i q^{15} +(15.9526 + 1.23021i) q^{16} -0.936203 q^{17} +(5.99889 + 0.115439i) q^{18} -29.3196i q^{19} +(-19.9278 - 0.767244i) q^{20} +5.78833 q^{21} +(-0.332887 + 17.2987i) q^{22} -33.3456i q^{23} +(0.799392 - 13.8333i) q^{24} -0.143370 q^{25} +(-7.20977 - 0.138741i) q^{26} -5.19615i q^{27} +(0.514286 - 13.3577i) q^{28} +0.223935 q^{29} +(-0.332288 + 17.2676i) q^{30} -35.7681i q^{31} +(-31.8520 - 3.07383i) q^{32} +14.9839 q^{33} +(1.87206 + 0.0360249i) q^{34} +16.6615i q^{35} +(-11.9911 - 0.461672i) q^{36} -22.5963 q^{37} +(-1.12821 + 58.6284i) q^{38} +6.24500i q^{39} +(39.8187 + 2.30102i) q^{40} -3.58506 q^{41} +(-11.5745 - 0.222734i) q^{42} +68.8231i q^{43} +(1.33130 - 34.5782i) q^{44} +14.9569 q^{45} +(-1.28313 + 66.6789i) q^{46} +5.87303i q^{47} +(-2.13079 + 27.6308i) q^{48} +37.8317 q^{49} +(0.286686 + 0.00551683i) q^{50} -1.62155i q^{51} +(14.4115 + 0.554861i) q^{52} -17.0444 q^{53} +(-0.199947 + 10.3904i) q^{54} +43.1306i q^{55} +(-1.54238 + 26.6906i) q^{56} +50.7831 q^{57} +(-0.447787 - 0.00861697i) q^{58} +66.0654i q^{59} +(1.32891 - 34.5160i) q^{60} -114.756 q^{61} +(-1.37635 + 71.5229i) q^{62} +10.0257i q^{63} +(63.5740 + 7.37217i) q^{64} -17.9760 q^{65} +(-29.9623 - 0.576578i) q^{66} +49.7915i q^{67} +(-3.74204 - 0.144073i) q^{68} +57.7563 q^{69} +(0.641130 - 33.3168i) q^{70} -78.4873i q^{71} +(23.9600 + 1.38459i) q^{72} -15.6030 q^{73} +(45.1842 + 0.869500i) q^{74} -0.248323i q^{75} +(4.51202 - 117.192i) q^{76} -28.9106 q^{77} +(0.240306 - 12.4877i) q^{78} -137.505i q^{79} +(-79.5341 - 6.13341i) q^{80} +9.00000 q^{81} +(7.16879 + 0.137952i) q^{82} -20.3475i q^{83} +(23.1362 + 0.890770i) q^{84} +4.66757 q^{85} +(2.64830 - 137.621i) q^{86} +0.387867i q^{87} +(-3.99268 + 69.0925i) q^{88} +24.0829 q^{89} +(-29.9083 - 0.575539i) q^{90} -12.0494i q^{91} +(5.13158 - 133.284i) q^{92} +61.9521 q^{93} +(0.225993 - 11.7439i) q^{94} +146.177i q^{95} +(5.32402 - 55.1693i) q^{96} -136.996 q^{97} +(-75.6495 - 1.45576i) q^{98} +25.9529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9	\( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^4 - 12 * q^6 - 32 * q^8 - 72 * q^9 - 12 * q^10 + 12 * q^12 + 32 * q^14 + 4 * q^16 - 12 * q^18 + 84 * q^20 + 28 * q^22 - 36 * q^24 + 104 * q^25 - 96 * q^28 + 64 * q^29 - 12 * q^30 + 44 * q^32 + 48 * q^33 + 40 * q^34 - 24 * q^36 - 192 * q^37 - 104 * q^38 + 220 * q^40 - 220 * q^44 - 104 * q^46 - 144 * q^48 - 248 * q^49 + 100 * q^50 - 52 * q^52 + 336 * q^53 + 36 * q^54 + 168 * q^56 - 16 * q^58 + 60 * q^60 + 16 * q^61 + 152 * q^62 - 16 * q^64 - 132 * q^66 + 400 * q^68 - 192 * q^69 + 208 * q^70 + 96 * q^72 + 112 * q^73 - 104 * q^74 - 264 * q^76 - 272 * q^77 - 300 * q^80 + 216 * q^81 - 4 * q^82 + 96 * q^84 + 64 * q^85 + 288 * q^86 - 492 * q^88 + 36 * q^90 + 328 * q^92 - 96 * q^93 - 884 * q^94 + 72 * q^96 - 80 * q^97 - 572 * q^98

Introduction

L-functions

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