LMFDB - Embedded newform 24.4.d.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,4,Mod(13,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("24.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	24.d (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:	$1.41604584014$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.8248384.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + x^{4} - 12x^{3} + 4x^{2} + 64 $ x^6 + x^4 - 12x^3 + 4x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.1
Root			$-1.24181 + 1.56777i$ of defining polynomial
Character	$\chi$	$=$	24.13
Dual form			24.4.d.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.80958 - 0.325969i) q^{2} +3.00000i q^{3} +(7.78749 + 1.83167i) q^{4} +18.5422i q^{5} +(0.977907 - 8.42874i) q^{6} +9.32669 q^{7} +(-21.2825 - 7.68472i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(-2.80958 - 0.325969i) q^{2} +3.00000i q^{3} +(7.78749 + 1.83167i) q^{4} +18.5422i q^{5} +(0.977907 - 8.42874i) q^{6} +9.32669 q^{7} +(-21.2825 - 7.68472i) q^{8} -9.00000 q^{9} +(6.04419 - 52.0958i) q^{10} -39.7378i q^{11} +(-5.49502 + 23.3625i) q^{12} +32.9533i q^{13} +(-26.2041 - 3.04021i) q^{14} -55.6266 q^{15} +(57.2899 + 28.5283i) q^{16} +90.5998 q^{17} +(25.2862 + 2.93372i) q^{18} -72.5998i q^{19} +(-33.9633 + 144.397i) q^{20} +27.9801i q^{21} +(-12.9533 + 111.647i) q^{22} +45.3466 q^{23} +(23.0541 - 63.8475i) q^{24} -218.813 q^{25} +(10.7418 - 92.5849i) q^{26} -27.0000i q^{27} +(72.6315 + 17.0835i) q^{28} -143.364i q^{29} +(156.287 + 18.1326i) q^{30} +90.4865 q^{31} +(-151.661 - 98.8272i) q^{32} +119.213 q^{33} +(-254.547 - 29.5327i) q^{34} +172.937i q^{35} +(-70.0874 - 16.4851i) q^{36} +1.77977i q^{37} +(-23.6653 + 203.975i) q^{38} -98.8599 q^{39} +(142.492 - 394.625i) q^{40} +195.827 q^{41} +(9.12064 - 78.6123i) q^{42} +407.027i q^{43} +(72.7866 - 309.458i) q^{44} -166.880i q^{45} +(-127.405 - 14.7816i) q^{46} -278.467 q^{47} +(-85.5848 + 171.870i) q^{48} -256.013 q^{49} +(614.773 + 71.3263i) q^{50} +271.799i q^{51} +(-60.3597 + 256.623i) q^{52} +241.303i q^{53} +(-8.80117 + 75.8587i) q^{54} +736.826 q^{55} +(-198.495 - 71.6730i) q^{56} +217.799 q^{57} +(-46.7324 + 402.794i) q^{58} -149.724i q^{59} +(-433.191 - 101.890i) q^{60} -508.314i q^{61} +(-254.229 - 29.4958i) q^{62} -83.9402 q^{63} +(393.890 + 327.100i) q^{64} -611.027 q^{65} +(-334.940 - 38.8599i) q^{66} -950.026i q^{67} +(705.545 + 165.949i) q^{68} +136.040i q^{69} +(56.3723 - 485.882i) q^{70} -803.559 q^{71} +(191.543 + 69.1624i) q^{72} +449.786 q^{73} +(0.580152 - 5.00042i) q^{74} -656.440i q^{75} +(132.979 - 565.370i) q^{76} -370.622i q^{77} +(277.755 + 32.2253i) q^{78} -157.220 q^{79} +(-528.977 + 1062.28i) q^{80} +81.0000 q^{81} +(-550.192 - 63.8335i) q^{82} +175.063i q^{83} +(-51.2504 + 217.895i) q^{84} +1679.92i q^{85} +(132.678 - 1143.57i) q^{86} +430.093 q^{87} +(-305.374 + 845.720i) q^{88} +127.200 q^{89} +(-54.3977 + 468.862i) q^{90} +307.345i q^{91} +(353.136 + 83.0602i) q^{92} +271.459i q^{93} +(782.374 + 90.7715i) q^{94} +1346.16 q^{95} +(296.482 - 454.984i) q^{96} +158.826 q^{97} +(719.289 + 83.4523i) q^{98} +357.640i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9	$ 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9} + 60 q^{10} - 12 q^{12} - 100 q^{14} - 60 q^{15} + 56 q^{16} + 52 q^{17} - 18 q^{18} + 56 q^{20} + 224 q^{22} + 328 q^{23} + 204 q^{24} - 106 q^{25} + 56 q^{26} - 352 q^{28} + 372 q^{30} - 636 q^{31} - 248 q^{32} - 548 q^{34} - 144 q^{36} - 776 q^{38} + 312 q^{39} + 232 q^{40} + 236 q^{41} - 564 q^{42} + 1152 q^{44} + 328 q^{46} - 408 q^{47} + 576 q^{48} + 654 q^{49} + 1970 q^{50} - 368 q^{52} + 54 q^{54} + 1024 q^{55} - 1864 q^{56} - 168 q^{57} + 140 q^{58} - 1152 q^{60} - 2108 q^{62} - 252 q^{63} + 832 q^{64} - 1744 q^{65} - 1440 q^{66} + 2976 q^{68} + 1352 q^{70} - 1704 q^{71} + 684 q^{72} + 956 q^{73} + 1568 q^{74} - 1744 q^{76} + 1608 q^{78} - 44 q^{79} - 2112 q^{80} + 486 q^{81} - 2236 q^{82} - 1992 q^{84} - 760 q^{86} + 1044 q^{87} + 1856 q^{88} - 220 q^{89} - 540 q^{90} + 1728 q^{92} + 2088 q^{94} + 5104 q^{95} + 2184 q^{96} - 2444 q^{97} + 3354 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9 + 60 * q^10 - 12 * q^12 - 100 * q^14 - 60 * q^15 + 56 * q^16 + 52 * q^17 - 18 * q^18 + 56 * q^20 + 224 * q^22 + 328 * q^23 + 204 * q^24 - 106 * q^25 + 56 * q^26 - 352 * q^28 + 372 * q^30 - 636 * q^31 - 248 * q^32 - 548 * q^34 - 144 * q^36 - 776 * q^38 + 312 * q^39 + 232 * q^40 + 236 * q^41 - 564 * q^42 + 1152 * q^44 + 328 * q^46 - 408 * q^47 + 576 * q^48 + 654 * q^49 + 1970 * q^50 - 368 * q^52 + 54 * q^54 + 1024 * q^55 - 1864 * q^56 - 168 * q^57 + 140 * q^58 - 1152 * q^60 - 2108 * q^62 - 252 * q^63 + 832 * q^64 - 1744 * q^65 - 1440 * q^66 + 2976 * q^68 + 1352 * q^70 - 1704 * q^71 + 684 * q^72 + 956 * q^73 + 1568 * q^74 - 1744 * q^76 + 1608 * q^78 - 44 * q^79 - 2112 * q^80 + 486 * q^81 - 2236 * q^82 - 1992 * q^84 - 760 * q^86 + 1044 * q^87 + 1856 * q^88 - 220 * q^89 - 540 * q^90 + 1728 * q^92 + 2088 * q^94 + 5104 * q^95 + 2184 * q^96 - 2444 * q^97 + 3354 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−2.80958	−	0.325969i	−0.993337	−	0.115247i
$2$	−2.80958	−	0.325969i	−0.993337	−	0.115247i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	7.78749	+	1.83167i	0.973436	+	0.228959i
$5$			18.5422i			1.65846i	0.558904	+	0.829232i	$0.311222\pi$
$5$			18.5422i			1.65846i	−0.558904	+	0.829232i	$0.688778\pi$
$6$	0.977907	−	8.42874i	0.0665382	−	0.573503i
$7$	9.32669			0.503594			0.251797	−	0.967780i	$-0.418978\pi$
$7$	9.32669			0.503594			0.251797	+	0.967780i	$0.418978\pi$
$8$	−21.2825	−	7.68472i	−0.940563	−	0.339620i
$9$	−9.00000			−0.333333
$10$	6.04419	−	52.0958i	0.191134	−	1.64741i
$11$		−	39.7378i		−	1.08922i	−0.838690	−	0.544609i	$-0.816678\pi$
$11$		−	39.7378i		−	1.08922i	0.838690	−	0.544609i	$-0.183322\pi$
$12$	−5.49502	+	23.3625i	−0.132190	+	0.562014i
$13$			32.9533i			0.703046i	0.936179	+	0.351523i	$0.114336\pi$
$13$			32.9533i			0.703046i	−0.936179	+	0.351523i	$0.885664\pi$
$14$	−26.2041	−	3.04021i	−0.500239	−	0.0580380i
$15$	−55.6266			−0.957515
$16$	57.2899	+	28.5283i	0.895155	+	0.445754i
$17$	90.5998			1.29257			0.646285	−	0.763096i	$-0.276322\pi$
$17$	90.5998			1.29257			0.646285	+	0.763096i	$0.276322\pi$
$18$	25.2862	+	2.93372i	0.331112	+	0.0384158i
$19$		−	72.5998i		−	0.876607i	−0.898827	−	0.438304i	$-0.855579\pi$
$19$		−	72.5998i		−	0.876607i	0.898827	−	0.438304i	$-0.144421\pi$
$20$	−33.9633	+	144.397i	−0.379721	+	1.61441i
$21$			27.9801i			0.290750i
$22$	−12.9533	+	111.647i	−0.125530	+	1.08196i
$23$	45.3466			0.411105			0.205553	−	0.978646i	$-0.434101\pi$
$23$	45.3466			0.411105			0.205553	+	0.978646i	$0.434101\pi$
$24$	23.0541	−	63.8475i	0.196079	−	0.543034i
$25$	−218.813			−1.75051
$26$	10.7418	−	92.5849i	0.0810243	−	0.698362i
$27$		−	27.0000i		−	0.192450i
$28$	72.6315	+	17.0835i	0.490217	+	0.115302i
$29$		−	143.364i		−	0.918003i	−0.888435	−	0.459002i	$-0.848207\pi$
$29$		−	143.364i		−	0.918003i	0.888435	−	0.459002i	$-0.151793\pi$
$30$	156.287	+	18.1326i	0.951135	+	0.110351i
$31$	90.4865			0.524253			0.262127	−	0.965033i	$-0.415576\pi$
$31$	90.4865			0.524253			0.262127	+	0.965033i	$0.415576\pi$
$32$	−151.661	−	98.8272i	−0.837819	−	0.545948i
$33$	119.213			0.628860
$34$	−254.547	−	29.5327i	−1.28396	−	0.148965i
$35$			172.937i			0.835193i
$36$	−70.0874	−	16.4851i	−0.324479	−	0.0763197i
$37$			1.77977i			0.00790792i	0.999992	+	0.00395396i	$0.00125859\pi$
$37$			1.77977i			0.00790792i	−0.999992	+	0.00395396i	$0.998741\pi$
$38$	−23.6653	+	203.975i	−0.101027	+	0.870766i
$39$	−98.8599			−0.405904
$40$	142.492	−	394.625i	0.563247	−	1.55989i
$41$	195.827			0.745927			0.372964	−	0.927846i	$-0.378342\pi$
$41$	195.827			0.745927			0.372964	+	0.927846i	$0.378342\pi$
$42$	9.12064	−	78.6123i	0.0335082	−	0.288813i
$43$			407.027i			1.44351i	0.692148	+	0.721755i	$0.256664\pi$
$43$			407.027i			1.44351i	−0.692148	+	0.721755i	$0.743336\pi$
$44$	72.7866	−	309.458i	0.249386	−	1.06028i
$45$		−	166.880i		−	0.552822i
$46$	−127.405	−	14.7816i	−0.408366	−	0.0473789i
$47$	−278.467			−0.864224			−0.432112	−	0.901820i	$-0.642231\pi$
$47$	−278.467			−0.864224			−0.432112	+	0.901820i	$0.642231\pi$
$48$	−85.5848	+	171.870i	−0.257356	+	0.516818i
$49$	−256.013			−0.746393
$50$	614.773	+	71.3263i	1.73884	+	0.201741i
$51$			271.799i			0.746265i
$52$	−60.3597	+	256.623i	−0.160969	+	0.684370i
$53$			241.303i			0.625386i	0.949854	+	0.312693i	$0.101231\pi$
$53$			241.303i			0.625386i	−0.949854	+	0.312693i	$0.898769\pi$
$54$	−8.80117	+	75.8587i	−0.0221794	+	0.191168i
$55$	736.826			1.80643
$56$	−198.495	−	71.6730i	−0.473662	−	0.171030i
$57$	217.799			0.506109
$58$	−46.7324	+	402.794i	−0.105798	+	0.911887i
$59$		−	149.724i		−	0.330380i	−0.986262	−	0.165190i	$-0.947176\pi$
$59$		−	149.724i		−	0.330380i	0.986262	−	0.165190i	$-0.0528237\pi$
$60$	−433.191	−	101.890i	−0.932080	−	0.219232i
$61$		−	508.314i		−	1.06693i	−0.845821	−	0.533466i	$-0.820889\pi$
$61$		−	508.314i		−	1.06693i	0.845821	−	0.533466i	$-0.179111\pi$
$62$	−254.229	−	29.4958i	−0.520760	−	0.0604189i
$63$	−83.9402			−0.167865
$64$	393.890	+	327.100i	0.769317	+	0.638867i
$65$	−611.027			−1.16598
$66$	−334.940	−	38.8599i	−0.624670	−	0.0724745i
$67$		−	950.026i		−	1.73230i	−0.499784	−	0.866150i	$-0.666587\pi$
$67$		−	950.026i		−	1.73230i	0.499784	−	0.866150i	$-0.333413\pi$
$68$	705.545	+	165.949i	1.25823	+	0.295946i
$69$			136.040i			0.237352i
$70$	56.3723	−	485.882i	0.0962539	−	0.829628i
$71$	−803.559			−1.34317			−0.671584	−	0.740929i	$-0.734386\pi$
$71$	−803.559			−1.34317			−0.671584	+	0.740929i	$0.734386\pi$
$72$	191.543	+	69.1624i	0.313521	+	0.113207i
$73$	449.786			0.721143			0.360571	−	0.932732i	$-0.382582\pi$
$73$	449.786			0.721143			0.360571	+	0.932732i	$0.382582\pi$
$74$	0.580152	−	5.00042i	0.000911368	−	0.00785523i
$75$		−	656.440i		−	1.01065i
$76$	132.979	−	565.370i	0.200707	−	0.853321i
$77$		−	370.622i		−	0.548524i
$78$	277.755	+	32.2253i	0.403199	+	0.0467794i
$79$	−157.220			−0.223906			−0.111953	−	0.993713i	$-0.535711\pi$
$79$	−157.220			−0.223906			−0.111953	+	0.993713i	$0.535711\pi$
$80$	−528.977	+	1062.28i	−0.739268	+	1.48458i
$81$	81.0000			0.111111
$82$	−550.192	−	63.8335i	−0.740957	−	0.0859663i
$83$			175.063i			0.231513i	0.993278	+	0.115757i	$0.0369293\pi$
$83$			175.063i			0.231513i	−0.993278	+	0.115757i	$0.963071\pi$
$84$	−51.2504	+	217.895i	−0.0665699	+	0.283027i
$85$			1679.92i			2.14368i
$86$	132.678	−	1143.57i	0.166361	−	1.43389i
$87$	430.093			0.530009
$88$	−305.374	+	845.720i	−0.369920	+	1.02448i
$89$	127.200			0.151496			0.0757479	−	0.997127i	$-0.475866\pi$
$89$	127.200			0.151496			0.0757479	+	0.997127i	$0.475866\pi$
$90$	−54.3977	+	468.862i	−0.0637113	+	0.549138i
$91$			307.345i			0.354050i
$92$	353.136	+	83.0602i	0.400185	+	0.0941263i
$93$			271.459i			0.302678i
$94$	782.374	+	90.7715i	0.858465	+	0.0995996i
$95$	1346.16			1.45382
$96$	296.482	−	454.984i	0.315203	−	0.483715i
$97$	158.826			0.166251			0.0831254	−	0.996539i	$-0.473510\pi$
$97$	158.826			0.166251			0.0831254	+	0.996539i	$0.473510\pi$
$98$	719.289	+	83.4523i	0.741420	+	0.0860199i
$99$			357.640i			0.363073i
$100$	−1704.00	−	400.794i	−1.70400	−	0.400794i
$101$			1366.26i			1.34602i	0.739633	+	0.673010i	$0.234999\pi$
$101$			1366.26i			1.34602i	−0.739633	+	0.673010i	$0.765001\pi$
$102$	88.5982	−	763.642i	0.0860052	−	0.741293i
$103$	−1741.30			−1.66578			−0.832889	−	0.553440i	$-0.813315\pi$
$103$	−1741.30			−1.66578			−0.832889	+	0.553440i	$0.813315\pi$
$104$	253.237	−	701.329i	0.238768	−	0.661259i
$105$	−518.812			−0.482199
$106$	78.6572	−	677.960i	0.0720742	−	0.621219i
$107$		−	649.378i		−	0.586708i	−0.956004	−	0.293354i	$-0.905229\pi$
$107$		−	649.378i		−	0.586708i	0.956004	−	0.293354i	$-0.0947714\pi$
$108$	49.4552	−	210.262i	0.0440632	−	0.187338i
$109$		−	1413.18i		−	1.24182i	−0.783883	−	0.620908i	$-0.786764\pi$
$109$		−	1413.18i		−	1.24182i	0.783883	−	0.620908i	$-0.213236\pi$
$110$	−2070.17	−	240.183i	−1.79439	−	0.208186i
$111$	−5.33932			−0.00456564
$112$	534.326	+	266.074i	0.450795	+	0.224479i
$113$	1096.43			0.912771			0.456386	−	0.889782i	$-0.349144\pi$
$113$	1096.43			0.912771			0.456386	+	0.889782i	$0.349144\pi$
$114$	−611.925	−	70.9959i	−0.502737	−	0.0583279i
$115$			840.826i			0.681804i
$116$	262.597	−	1116.45i	0.210185	−	0.893618i
$117$		−	296.580i		−	0.234349i
$118$	−48.8054	+	420.662i	−0.0380755	+	0.328178i
$119$	844.997			0.650930
$120$	1183.87	+	427.475i	0.900603	+	0.325191i
$121$	−248.092			−0.186395
$122$	−165.695	+	1428.15i	−0.122961	+	1.05982i
$123$			587.481i			0.430661i
$124$	704.662	+	165.742i	0.510327	+	0.120033i
$125$		−	1739.50i		−	1.24469i
$126$	235.837	+	27.3619i	0.166746	+	0.0193460i
$127$	−737.794			−0.515501			−0.257751	−	0.966211i	$-0.582981\pi$
$127$	−737.794			−0.515501			−0.257751	+	0.966211i	$0.582981\pi$
$128$	−1000.04	−	1047.41i	−0.690563	−	0.723272i
$129$	−1221.08			−0.833411
$130$	1716.73	+	199.176i	1.15821	+	0.134376i
$131$		−	147.698i		−	0.0985074i	−0.998786	−	0.0492537i	$-0.984316\pi$
$131$		−	147.698i		−	0.0985074i	0.998786	−	0.0492537i	$-0.0156843\pi$
$132$	928.373	+	218.360i	0.612155	+	0.143983i
$133$		−	677.116i		−	0.441454i
$134$	−309.679	+	2669.17i	−0.199643	+	1.72076i
$135$	500.639			0.319172
$136$	−1928.19	−	696.234i	−1.21574	−	0.438982i
$137$	−1880.79			−1.17289			−0.586447	−	0.809988i	$-0.699474\pi$
$137$	−1880.79			−1.17289			−0.586447	+	0.809988i	$0.699474\pi$
$138$	44.3448	−	382.215i	0.0273542	−	0.235770i
$139$			629.333i			0.384024i	0.981393	+	0.192012i	$0.0615013\pi$
$139$			629.333i			0.384024i	−0.981393	+	0.192012i	$0.938499\pi$
$140$	−316.765	+	1346.75i	−0.191225	+	0.813007i
$141$		−	835.400i		−	0.498960i
$142$	2257.66	+	261.935i	1.33422	+	0.154797i
$143$	1309.49			0.765770
$144$	−515.610	−	256.754i	−0.298385	−	0.148585i
$145$	2658.29			1.52248
$146$	−1263.71	−	146.616i	−0.716338	−	0.0831099i
$147$		−	768.038i		−	0.430930i
$148$	−3.25997	+	13.8600i	−0.00181059	+	0.00769786i
$149$		−	429.457i		−	0.236124i	−0.993006	−	0.118062i	$-0.962332\pi$
$149$		−	429.457i		−	0.236124i	0.993006	−	0.118062i	$-0.0376681\pi$
$150$	−213.979	+	1844.32i	−0.116475	+	1.00392i
$151$	−27.3124			−0.0147196			−0.00735978	−	0.999973i	$-0.502343\pi$
$151$	−27.3124			−0.0147196			−0.00735978	+	0.999973i	$0.502343\pi$
$152$	−557.909	+	1545.11i	−0.297713	+	0.824504i
$153$	−815.398			−0.430857
$154$	−120.811	+	1041.29i	−0.0632160	+	0.544869i
$155$			1677.82i			0.869456i
$156$	−769.870	−	181.079i	−0.395121	−	0.0929354i
$157$		−	1251.08i		−	0.635970i	−0.948096	−	0.317985i	$-0.896994\pi$
$157$		−	1251.08i		−	0.635970i	0.948096	−	0.317985i	$-0.103006\pi$
$158$	441.721	+	51.2487i	0.222414	+	0.0258046i
$159$	−723.908			−0.361067
$160$	1832.47	−	2812.14i	0.905436	−	1.38949i
$161$	422.934			0.207030
$162$	−227.576	−	26.4035i	−0.110371	−	0.0128053i
$163$		−	127.884i		−	0.0614517i	−0.999528	−	0.0307258i	$-0.990218\pi$
$163$		−	127.884i		−	0.0614517i	0.999528	−	0.0307258i	$-0.00978188\pi$
$164$	1525.00	+	358.691i	0.726113	+	0.170787i
$165$			2210.48i			1.04294i
$166$	57.0650	−	491.852i	0.0266813	−	0.229971i
$167$	−2079.65			−0.963642			−0.481821	−	0.876270i	$-0.660024\pi$
$167$	−2079.65			−0.963642			−0.481821	+	0.876270i	$0.660024\pi$
$168$	215.019	−	595.486i	0.0987445	−	0.273469i
$169$	1111.08			0.505726
$170$	547.602	−	4719.87i	0.247054	−	2.12940i
$171$			653.398i			0.292202i
$172$	−745.540	+	3169.71i	−0.330505	+	1.40517i
$173$		−	685.140i		−	0.301099i	−0.988602	−	0.150550i	$-0.951896\pi$
$173$		−	685.140i		−	0.301099i	0.988602	−	0.150550i	$-0.0481044\pi$
$174$	−1208.38	−	140.197i	−0.526478	−	0.0610823i
$175$	−2040.80			−0.881544
$176$	1133.65	−	2276.58i	0.485523	−	0.975019i
$177$	449.172			0.190745
$178$	−357.378	−	41.4632i	−0.150486	−	0.0174595i
$179$			429.423i			0.179310i	0.995973	+	0.0896552i	$0.0285765\pi$
$179$			429.423i			0.179310i	−0.995973	+	0.0896552i	$0.971424\pi$
$180$	305.669	−	1299.57i	0.126574	−	0.538136i
$181$			2842.85i			1.16745i	0.811953	+	0.583723i	$0.198404\pi$
$181$			2842.85i			1.16745i	−0.811953	+	0.583723i	$0.801596\pi$
$182$	100.185	−	863.511i	0.0408034	−	0.351691i
$183$	1524.94			0.615994
$184$	−965.090	−	348.476i	−0.386670	−	0.139619i
$185$	−33.0009			−0.0131150
$186$	88.4874	−	762.687i	0.0348829	−	0.300661i
$187$		−	3600.24i		−	1.40789i
$188$	−2168.56	−	510.060i	−0.841267	−	0.197872i
$189$		−	251.821i		−	0.0969167i
$190$	−3782.15	−	438.807i	−1.44414	−	0.167549i
$191$	2546.78			0.964808			0.482404	−	0.875949i	$-0.339764\pi$
$191$	2546.78			0.964808			0.482404	+	0.875949i	$0.339764\pi$
$192$	−981.300	+	1181.67i	−0.368850	+	0.444165i
$193$	−3579.97			−1.33519			−0.667596	−	0.744524i	$-0.732677\pi$
$193$	−3579.97			−1.33519			−0.667596	+	0.744524i	$0.732677\pi$
$194$	−446.234	−	51.7724i	−0.165143	−	0.0191600i
$195$		−	1833.08i		−	0.673177i
$196$	−1993.70	−	468.932i	−0.726566	−	0.170894i
$197$			3872.58i			1.40056i	0.713869	+	0.700280i	$0.246941\pi$
$197$			3872.58i			1.40056i	−0.713869	+	0.700280i	$0.753059\pi$
$198$	116.580	−	1004.82i	0.0418432	−	0.360653i
$199$	5558.64			1.98011			0.990054	−	0.140686i	$-0.0449307\pi$
$199$	5558.64			1.98011			0.990054	+	0.140686i	$0.0449307\pi$
$200$	4656.89	+	1681.52i	1.64646	+	0.594506i
$201$	2850.08			1.00014
$202$	445.359	−	3838.62i	0.155125	−	1.33705i
$203$		−	1337.12i		−	0.462301i
$204$	−497.848	+	2116.63i	−0.170864	+	0.726442i
$205$			3631.06i			1.23709i
$206$	4892.32	+	567.609i	1.65468	+	0.191977i
$207$	−408.120			−0.137035
$208$	−940.100	+	1887.89i	−0.313386	+	0.629335i
$209$	−2884.96			−0.954816
$210$	1457.64	+	169.117i	0.478986	+	0.0555722i
$211$			4658.93i			1.52007i	0.649884	+	0.760034i	$0.274818\pi$
$211$			4658.93i			1.52007i	−0.649884	+	0.760034i	$0.725182\pi$
$212$	−441.988	+	1879.14i	−0.143188	+	0.608774i
$213$		−	2410.68i		−	0.775478i
$214$	−211.677	+	1824.48i	−0.0676166	+	0.582798i
$215$	−7547.17			−2.39401
$216$	−207.487	+	574.628i	−0.0653598	+	0.181011i
$217$	843.940			0.264011
$218$	−460.653	+	3970.44i	−0.143116	+	1.23354i
$219$			1349.36i			0.416352i
$220$	5738.02	+	1349.62i	1.75844	+	0.413598i
$221$			2985.56i			0.908736i
$222$	15.0013	+	1.74046i	0.00453522	+	0.000526179i
$223$	−1545.42			−0.464077			−0.232038	−	0.972707i	$-0.574540\pi$
$223$	−1545.42			−0.464077			−0.232038	+	0.972707i	$0.574540\pi$
$224$	−1414.50	−	921.731i	−0.421921	−	0.274936i
$225$	1969.32			0.583502
$226$	−3080.50	−	357.401i	−0.906689	−	0.105195i
$227$		−	6545.76i		−	1.91391i	−0.290240	−	0.956954i	$-0.593735\pi$
$227$		−	6545.76i		−	1.91391i	0.290240	−	0.956954i	$-0.406265\pi$
$228$	1696.11	+	398.937i	0.492665	+	0.115878i
$229$		−	5463.48i		−	1.57658i	−0.615303	−	0.788291i	$-0.710966\pi$
$229$		−	5463.48i		−	1.57658i	0.615303	−	0.788291i	$-0.289034\pi$
$230$	274.083	−	2362.37i	0.0785762	−	0.677261i
$231$	1111.87			0.316690
$232$	−1101.71	+	3051.15i	−0.311772	+	0.863440i
$233$	4722.40			1.32779			0.663894	−	0.747827i	$-0.268903\pi$
$233$	4722.40			1.32779			0.663894	+	0.747827i	$0.268903\pi$
$234$	−96.6758	+	833.264i	−0.0270081	+	0.232787i
$235$		−	5163.38i		−	1.43328i
$236$	274.246	−	1165.97i	0.0756435	−	0.321604i
$237$		−	471.659i		−	0.129272i
$238$	−2374.09	−	275.443i	−0.646593	−	0.0750181i
$239$	−1054.38			−0.285363			−0.142682	−	0.989769i	$-0.545573\pi$
$239$	−1054.38			−0.285363			−0.142682	+	0.989769i	$0.545573\pi$
$240$	−3186.84	−	1586.93i	−0.857125	−	0.426816i
$241$	−3134.40			−0.837777			−0.418888	−	0.908038i	$-0.637580\pi$
$241$	−3134.40			−0.837777			−0.418888	+	0.908038i	$0.637580\pi$
$242$	697.033	+	80.8702i	0.185153	+	0.0214815i
$243$			243.000i			0.0641500i
$244$	931.065	−	3958.49i	0.244284	−	1.03859i
$245$		−	4747.04i		−	1.23787i
$246$	191.501	−	1650.57i	0.0496326	−	0.427792i
$247$	2392.40			0.616295
$248$	−1925.78	−	695.363i	−0.493093	−	0.178047i
$249$	−525.188			−0.133664
$250$	−567.024	+	4887.27i	−0.143447	+	1.23639i
$251$			4881.91i			1.22766i	0.789437	+	0.613831i	$0.210372\pi$
$251$			4881.91i			1.22766i	−0.789437	+	0.613831i	$0.789628\pi$
$252$	−653.684	−	153.751i	−0.163406	−	0.0384342i
$253$		−	1801.97i		−	0.447783i
$254$	2072.89	+	240.498i	0.512066	+	0.0594102i
$255$	−5039.76			−1.23765
$256$	2468.28	+	3268.77i	0.602606	+	0.798039i
$257$	−540.458			−0.131178			−0.0655892	−	0.997847i	$-0.520893\pi$
$257$	−540.458			−0.131178			−0.0655892	+	0.997847i	$0.520893\pi$
$258$	3430.72	+	398.034i	0.827858	+	0.0960486i
$259$			16.5994i			0.00398238i
$260$	−4758.36	−	1119.20i	−1.13500	−	0.266961i
$261$			1290.28i			0.306001i
$262$	−48.1451	+	414.971i	−0.0113527	+	0.0978511i
$263$	4800.12			1.12543			0.562715	−	0.826651i	$-0.309757\pi$
$263$	4800.12			1.12543			0.562715	+	0.826651i	$0.309757\pi$
$264$	−2537.16	−	916.121i	−0.591482	−	0.213573i
$265$	−4474.28			−1.03718
$266$	−220.719	+	1902.41i	−0.0508765	+	0.438513i
$267$			381.599i			0.0874662i
$268$	1740.14	−	7398.31i	0.396626	−	1.68628i
$269$		−	3321.28i		−	0.752795i	−0.926458	−	0.376397i	$-0.877163\pi$
$269$		−	3321.28i		−	0.752795i	0.926458	−	0.376397i	$-0.122837\pi$
$270$	−1406.59	−	163.193i	−0.317045	−	0.0367837i
$271$	5274.04			1.18220			0.591098	−	0.806600i	$-0.298695\pi$
$271$	5274.04			1.18220			0.591098	+	0.806600i	$0.298695\pi$
$272$	5190.46	+	2584.66i	1.15705	+	0.576168i
$273$	−922.036			−0.204411
$274$	5284.22	+	613.078i	1.16508	+	0.135173i
$275$			8695.15i			1.90668i
$276$	−249.181	+	1059.41i	−0.0543439	+	0.231047i
$277$			3190.24i			0.691996i	0.938235	+	0.345998i	$0.112460\pi$
$277$			3190.24i			0.691996i	−0.938235	+	0.345998i	$0.887540\pi$
$278$	205.143	−	1768.16i	0.0442578	−	0.381465i
$279$	−814.378			−0.174751
$280$	1328.97	−	3680.54i	0.283648	−	0.785552i
$281$	−545.619			−0.115832			−0.0579162	−	0.998321i	$-0.518446\pi$
$281$	−545.619			−0.115832			−0.0579162	+	0.998321i	$0.518446\pi$
$282$	−272.315	+	2347.12i	−0.0575039	+	0.495635i
$283$			5927.74i			1.24511i	0.782574	+	0.622557i	$0.213906\pi$
$283$			5927.74i			1.24511i	−0.782574	+	0.622557i	$0.786094\pi$
$284$	−6257.71	−	1471.86i	−1.30749	−	0.307531i
$285$			4038.48i			0.839365i
$286$	−3679.12	−	426.854i	−0.760668	−	0.0882531i
$287$	1826.42			0.375645
$288$	1364.95	+	889.445i	0.279273	+	0.181983i
$289$	3295.33			0.670736
$290$	−7468.68	−	866.521i	−1.51233	−	0.175462i
$291$			476.478i			0.0959850i
$292$	3502.70	+	823.860i	0.701987	+	0.165112i
$293$		−	5406.01i		−	1.07789i	−0.842340	−	0.538946i	$-0.818823\pi$
$293$		−	5406.01i		−	1.07789i	0.842340	−	0.538946i	$-0.181177\pi$
$294$	−250.357	+	2157.87i	−0.0496636	+	0.428059i
$295$	2776.21			0.547923
$296$	13.6771	−	37.8781i	0.00268569	−	0.00743790i
$297$	−1072.92			−0.209620
$298$	−139.990	+	1206.59i	−0.0272127	+	0.234551i
$299$			1494.32i			0.289026i
$300$	1202.38	−	5112.01i	0.231399	−	0.983808i
$301$			3796.21i			0.726944i
$302$	76.7365	+	8.90301i	0.0146215	+	0.00169639i
$303$	−4098.78			−0.777125
$304$	2071.15	−	4159.24i	0.390751	−	0.784700i
$305$	9425.25			1.76947
$306$	2290.93	+	265.795i	0.427986	+	0.0496551i
$307$			1558.56i			0.289745i	0.989450	+	0.144873i	$0.0462772\pi$
$307$			1558.56i			0.289745i	−0.989450	+	0.144873i	$0.953723\pi$
$308$	678.859	−	2886.22i	0.125589	−	0.533953i
$309$		−	5223.89i		−	0.961738i
$310$	546.917	−	4713.97i	0.100203	−	0.863662i
$311$	−8348.21			−1.52213			−0.761067	−	0.648673i	$-0.775324\pi$
$311$	−8348.21			−1.52213			−0.761067	+	0.648673i	$0.775324\pi$
$312$	2103.99	+	759.710i	0.381778	+	0.137853i
$313$	−5213.09			−0.941410			−0.470705	−	0.882291i	$-0.656000\pi$
$313$	−5213.09			−0.941410			−0.470705	+	0.882291i	$0.656000\pi$
$314$	−407.815	+	3515.02i	−0.0732940	+	0.631733i
$315$		−	1556.44i		−	0.278398i
$316$	−1224.35	−	287.975i	−0.217958	−	0.0512653i
$317$			9070.57i			1.60711i	0.595230	+	0.803555i	$0.297061\pi$
$317$			9070.57i			1.60711i	−0.595230	+	0.803555i	$0.702939\pi$
$318$	2033.88	+	235.972i	0.358661	+	0.0416121i
$319$	−5696.98			−0.999905
$320$	−6065.15	+	7303.59i	−1.05954	+	1.27589i
$321$	1948.13			0.338736
$322$	−1188.27	−	137.863i	−0.205651	−	0.0238597i
$323$		−	6577.53i		−	1.13308i
$324$	630.787	+	148.366i	0.108160	+	0.0254399i
$325$		−	7210.61i		−	1.23069i
$326$	−41.6861	+	359.300i	−0.00708215	+	0.0610422i
$327$	4239.54			0.716963
$328$	−4167.69	−	1504.87i	−0.701592	−	0.253332i
$329$	−2597.17			−0.435218
$330$	720.548	−	6210.52i	0.120196	−	1.03599i
$331$		−	186.537i		−	0.0309758i	−0.999880	−	0.0154879i	$-0.995070\pi$
$331$		−	186.537i		−	0.0309758i	0.999880	−	0.0154879i	$-0.00493014\pi$
$332$	−320.657	+	1363.30i	−0.0530071	+	0.225364i
$333$		−	16.0180i		−	0.00263597i
$334$	5842.95	+	677.902i	0.957221	+	0.111057i
$335$	17615.6			2.87296
$336$	−798.223	+	1602.98i	−0.129603	+	0.260267i
$337$	829.350			0.134058			0.0670290	−	0.997751i	$-0.478648\pi$
$337$	829.350			0.134058			0.0670290	+	0.997751i	$0.478648\pi$
$338$	−3121.67	−	362.178i	−0.502356	−	0.0582837i
$339$			3289.28i			0.526989i
$340$	−3077.06	+	13082.4i	−0.490815	+	2.08674i
$341$		−	3595.73i		−	0.571026i
$342$	212.988	−	1835.78i	0.0336756	−	0.290255i
$343$	−5586.81			−0.879473
$344$	3127.88	−	8662.55i	0.490245	−	1.35771i
$345$	−2522.48			−0.393640
$346$	−223.334	+	1924.96i	−0.0347010	+	0.299093i
$347$		−	12005.6i		−	1.85734i	−0.370908	−	0.928669i	$-0.620954\pi$
$347$		−	12005.6i		−	1.85734i	0.370908	−	0.928669i	$-0.379046\pi$
$348$	3349.35	+	787.790i	0.515930	+	0.121351i
$349$			77.8551i			0.0119412i	0.999982	+	0.00597062i	$0.00190052\pi$
$349$			77.8551i			0.0119412i	−0.999982	+	0.00597062i	$0.998099\pi$
$350$	5733.80	+	665.239i	0.875670	+	0.101596i
$351$	889.739			0.135301
$352$	−3927.18	+	6026.69i	−0.594657	+	0.912567i
$353$	−4925.06			−0.742591			−0.371296	−	0.928515i	$-0.621086\pi$
$353$	−4925.06			−0.742591			−0.371296	+	0.928515i	$0.621086\pi$
$354$	−1261.99	−	146.416i	−0.189474	−	0.0219829i
$355$		−	14899.8i		−	2.22760i
$356$	990.566	+	232.988i	0.147472	+	0.0346864i
$357$			2534.99i			0.375815i
$358$	139.978	−	1206.50i	0.0206651	−	0.178116i
$359$	−12260.2			−1.80242			−0.901209	−	0.433384i	$-0.857319\pi$
$359$	−12260.2			−1.80242			−0.901209	+	0.433384i	$0.857319\pi$
$360$	−1282.42	+	3551.62i	−0.187749	+	0.519963i
$361$	1588.27			0.231560
$362$	926.683	−	7987.23i	0.134545	−	1.15967i
$363$		−	744.275i		−	0.107615i
$364$	−562.956	+	2393.45i	−0.0810630	+	0.344645i
$365$			8340.02i			1.19599i
$366$	−4284.44	−	497.084i	−0.611889	−	0.0709918i
$367$	−8600.86			−1.22333			−0.611664	−	0.791118i	$-0.709500\pi$
$367$	−8600.86			−1.22333			−0.611664	+	0.791118i	$0.709500\pi$
$368$	2597.91	+	1293.66i	0.368003	+	0.183252i
$369$	−1762.44			−0.248642
$370$	92.7188	+	10.7573i	0.0130276	+	0.00151147i
$371$			2250.56i			0.314941i
$372$	−497.225	+	2113.99i	−0.0693008	+	0.294637i
$373$			3996.47i			0.554770i	0.960759	+	0.277385i	$0.0894678\pi$
$373$			3996.47i			0.554770i	−0.960759	+	0.277385i	$0.910532\pi$
$374$	−1173.57	+	10115.2i	−0.162256	+	1.39851i
$375$	5218.51			0.718620
$376$	5926.47	+	2139.94i	0.812857	+	0.293507i
$377$	4724.33			0.645399
$378$	−82.0858	+	707.511i	−0.0111694	+	0.0962710i
$379$			10404.7i			1.41017i	0.709121	+	0.705087i	$0.249092\pi$
$379$			10404.7i			1.41017i	−0.709121	+	0.705087i	$0.750908\pi$
$380$	10483.2	+	2465.73i	1.41520	+	0.332866i
$381$		−	2213.38i		−	0.297625i
$382$	−7155.38	−	830.171i	−0.958379	−	0.111192i
$383$	6814.19			0.909109			0.454554	−	0.890719i	$-0.349798\pi$
$383$	6814.19			0.909109			0.454554	+	0.890719i	$0.349798\pi$
$384$	3142.23	−	3000.13i	0.417581	−	0.398697i
$385$	6872.15			0.909707
$386$	10058.2	+	1166.96i	1.32630	+	0.153878i
$387$		−	3663.24i		−	0.481170i
$388$	1236.86	+	290.917i	0.161835	+	0.0380647i
$389$			779.329i			0.101577i	0.998709	+	0.0507886i	$0.0161735\pi$
$389$			779.329i			0.101577i	−0.998709	+	0.0507886i	$0.983827\pi$
$390$	−597.527	+	5150.19i	−0.0775820	+	0.668692i
$391$	4108.39			0.531382
$392$	5448.59	+	1967.39i	0.702030	+	0.253490i
$393$	443.095			0.0568733
$394$	1262.34	−	10880.3i	0.161411	−	1.39123i
$395$		−	2915.20i		−	0.371340i
$396$	−655.080	+	2785.12i	−0.0831288	+	0.353428i
$397$			12514.1i			1.58202i	0.611802	+	0.791011i	$0.290445\pi$
$397$			12514.1i			1.58202i	−0.611802	+	0.791011i	$0.709555\pi$
$398$	−15617.5	−	1811.95i	−1.96691	−	0.228203i
$399$	2031.35			0.254874
$400$	−12535.8	−	6242.36i	−1.56697	−	0.780295i
$401$	−7949.68			−0.989995			−0.494998	−	0.868894i	$-0.664831\pi$
$401$	−7949.68			−0.989995			−0.494998	+	0.868894i	$0.664831\pi$
$402$	−8007.52	−	929.037i	−0.993480	−	0.115264i
$403$			2981.83i			0.368574i
$404$	−2502.54	+	10639.7i	−0.308184	+	1.31026i
$405$			1501.92i			0.184274i
$406$	−435.858	+	3756.73i	−0.0532790	+	0.459221i
$407$	70.7243			0.00861345
$408$	2088.70	−	5784.57i	0.253446	−	0.701909i
$409$	15183.9			1.83569			0.917846	−	0.396937i	$-0.129927\pi$
$409$	15183.9			1.83569			0.917846	+	0.396937i	$0.129927\pi$
$410$	1183.61	−	10201.8i	0.142572	−	1.22885i
$411$		−	5642.36i		−	0.677170i
$412$	−13560.3	−	3189.49i	−1.62153	−	0.381395i
$413$		−	1396.43i		−	0.166377i
$414$	1146.64	+	133.034i	0.136122	+	0.0157930i
$415$	−3246.05			−0.383957
$416$	3256.68	−	4997.74i	0.383827	−	0.589025i
$417$	−1888.00			−0.221716
$418$	8105.52	+	940.407i	0.948454	+	0.110040i
$419$			11767.2i			1.37199i	0.727606	+	0.685996i	$0.240633\pi$
$419$			11767.2i			1.37199i	−0.727606	+	0.685996i	$0.759367\pi$
$420$	−4040.24	−	950.295i	−0.469390	−	0.110404i
$421$		−	14459.8i		−	1.67394i	−0.547248	−	0.836970i	$-0.684325\pi$
$421$		−	14459.8i		−	1.67394i	0.547248	−	0.836970i	$-0.315675\pi$
$422$	1518.67	−	13089.7i	0.175184	−	1.50994i
$423$	2506.20			0.288075
$424$	1854.34	−	5135.53i	0.212394	−	0.588215i
$425$	−19824.4			−2.26265
$426$	−785.806	+	6772.99i	−0.0893719	+	0.770311i
$427$		−	4740.89i		−	0.537301i
$428$	1189.45	−	5057.02i	0.134332	−	0.571122i
$429$			3928.47i			0.442118i
$430$	21204.4	+	2460.14i	2.37806	+	0.275904i
$431$	−9248.50			−1.03361			−0.516804	−	0.856104i	$-0.672878\pi$
$431$	−9248.50			−1.03361			−0.516804	+	0.856104i	$0.672878\pi$
$432$	770.263	−	1546.83i	0.0857854	−	0.172273i
$433$	−3456.12			−0.383581			−0.191790	−	0.981436i	$-0.561429\pi$
$433$	−3456.12			−0.383581			−0.191790	+	0.981436i	$0.561429\pi$
$434$	−2371.12	−	275.098i	−0.262252	−	0.0304266i
$435$			7974.87i			0.879002i
$436$	2588.48	−	11005.1i	0.284325	−	1.20883i
$437$		−	3292.16i		−	0.360378i
$438$	439.849	−	3791.13i	0.0479835	−	0.413578i
$439$	8075.68			0.877975			0.438988	−	0.898493i	$-0.355337\pi$
$439$	8075.68			0.877975			0.438988	+	0.898493i	$0.355337\pi$
$440$	−15681.5	−	5662.30i	−1.69906	−	0.613499i
$441$	2304.12			0.248798
$442$	973.201	−	8388.18i	0.104730	−	0.902681i
$443$			11447.7i			1.22776i	0.789401	+	0.613878i	$0.210391\pi$
$443$			11447.7i			1.22776i	−0.789401	+	0.613878i	$0.789609\pi$
$444$	−41.5799	−	9.77990i	−0.00444436	−	0.00104535i
$445$			2358.56i			0.251251i
$446$	4341.99	+	503.760i	0.460985	+	0.0534837i
$447$	1288.37			0.136326
$448$	3673.69	+	3050.76i	0.387424	+	0.321730i
$449$	−1010.18			−0.106177			−0.0530886	−	0.998590i	$-0.516907\pi$
$449$	−1010.18			−0.106177			−0.0530886	+	0.998590i	$0.516907\pi$
$450$	−5532.96	−	641.937i	−0.579614	−	0.0672471i
$451$		−	7781.73i		−	0.812477i
$452$	8538.41	+	2008.30i	0.888524	+	0.208987i
$453$		−	81.9373i		−	0.00849835i
$454$	−2133.71	+	18390.8i	−0.220573	+	1.90116i
$455$	−5698.86			−0.587179
$456$	−4635.32	−	1673.73i	−0.476028	−	0.171885i
$457$	15949.2			1.63254			0.816272	−	0.577667i	$-0.196037\pi$
$457$	15949.2			1.63254			0.816272	+	0.577667i	$0.196037\pi$
$458$	−1780.93	+	15350.1i	−0.181697	+	1.56608i
$459$		−	2446.19i		−	0.248755i
$460$	−1540.12	+	6547.92i	−0.156105	+	0.663692i
$461$		−	6737.61i		−	0.680698i	−0.940299	−	0.340349i	$-0.889455\pi$
$461$		−	6737.61i		−	0.680698i	0.940299	−	0.340349i	$-0.110545\pi$
$462$	−3123.88	−	362.434i	−0.314580	−	0.0364978i
$463$	−2602.69			−0.261246			−0.130623	−	0.991432i	$-0.541698\pi$
$463$	−2602.69			−0.261246			−0.130623	+	0.991432i	$0.541698\pi$
$464$	4089.94	−	8213.34i	0.409204	−	0.821756i
$465$	−5033.45			−0.501980
$466$	−13268.0	−	1539.36i	−1.31894	−	0.153024i
$467$			9326.18i			0.924120i	0.886849	+	0.462060i	$0.152890\pi$
$467$			9326.18i			0.924120i	−0.886849	+	0.462060i	$0.847110\pi$
$468$	543.237	−	2309.61i	0.0536563	−	0.228123i
$469$		−	8860.60i		−	0.872376i
$470$	−1683.10	+	14506.9i	−0.165182	+	1.42373i
$471$	3753.25			0.367178
$472$	−1150.59	+	3186.50i	−0.112203	+	0.310743i
$473$	16174.3			1.57230
$474$	−153.746	+	1325.16i	−0.0148983	+	0.128411i
$475$			15885.8i			1.53451i
$476$	6580.40	+	1547.76i	0.633639	+	0.149036i
$477$		−	2171.72i		−	0.208462i
$478$	2962.35	+	343.694i	0.283462	+	0.0328874i
$479$	11472.0			1.09430			0.547149	−	0.837035i	$-0.315713\pi$
$479$	11472.0			1.09430			0.547149	+	0.837035i	$0.315713\pi$
$480$	8436.41	+	5497.42i	0.802224	+	0.522754i
$481$	−58.6494			−0.00555963
$482$	8806.34	+	1021.72i	0.832194	+	0.0965517i
$483$			1268.80i			0.119529i
$484$	−1932.01	−	454.423i	−0.181444	−	0.0426768i
$485$			2944.98i			0.275721i
$486$	79.2105	−	682.728i	0.00739313	−	0.0637226i
$487$	−15048.0			−1.40018			−0.700090	−	0.714054i	$-0.746857\pi$
$487$	−15048.0			−1.40018			−0.700090	+	0.714054i	$0.746857\pi$
$488$	−3906.25	+	10818.2i	−0.362351	+	1.00352i
$489$	383.651			0.0354792
$490$	−1547.39	+	13337.2i	−0.142661	+	1.22962i
$491$		−	14373.5i		−	1.32112i	−0.750775	−	0.660558i	$-0.770320\pi$
$491$		−	14373.5i		−	1.32112i	0.750775	−	0.660558i	$-0.229680\pi$
$492$	−1076.07	+	4575.00i	−0.0986039	+	0.419221i
$493$		−	12988.8i		−	1.18658i
$494$	−6721.65	−	779.850i	−0.612189	−	0.0710265i
$495$	−6631.43			−0.602143
$496$	5183.97	+	2581.42i	0.469288	+	0.233688i
$497$	−7494.55			−0.676411
$498$	1475.56	+	171.195i	0.132774	+	0.0154045i
$499$			9167.08i			0.822395i	0.911546	+	0.411197i	$0.134889\pi$
$499$			9167.08i			0.822395i	−0.911546	+	0.411197i	$0.865111\pi$
$500$	3186.20	−	13546.4i	0.284982	−	1.21162i
$501$		−	6238.95i		−	0.556359i
$502$	1591.35	−	13716.1i	0.141485	−	1.21948i
$503$	7690.02			0.681672			0.340836	−	0.940123i	$-0.389290\pi$
$503$	7690.02			0.681672			0.340836	+	0.940123i	$0.389290\pi$
$504$	1786.46	+	645.057i	0.157887	+	0.0570101i
$505$	−25333.5			−2.23233
$506$	−587.388	+	5062.79i	−0.0516059	+	0.444799i
$507$			3333.24i			0.291981i
$508$	−5745.56	−	1351.40i	−0.501807	−	0.118029i
$509$		−	6854.21i		−	0.596872i	−0.954430	−	0.298436i	$-0.903535\pi$
$509$		−	6854.21i		−	0.596872i	0.954430	−	0.298436i	$-0.0964649\pi$
$510$	14159.6	+	1642.81i	1.22941	+	0.142637i
$511$	4195.01			0.363163
$512$	−5869.30	−	9988.44i	−0.506619	−	0.862170i
$513$	−1960.19			−0.168703
$514$	1518.46	+	176.173i	0.130304	+	0.0151180i
$515$		−	32287.5i		−	2.76264i
$516$	−9509.14	−	2236.62i	−0.811273	−	0.190817i
$517$			11065.6i			0.941328i
$518$	5.41090	−	46.6374i	0.000458960	−	0.00395585i
$519$	2055.42			0.173840
$520$	13004.2	+	4695.56i	1.09667	+	0.395989i
$521$	1641.63			0.138044			0.0690221	−	0.997615i	$-0.478012\pi$
$521$	1641.63			0.138044			0.0690221	+	0.997615i	$0.478012\pi$
$522$	420.591	−	3625.14i	0.0352659	−	0.303962i
$523$		−	1976.34i		−	0.165238i	−0.996581	−	0.0826188i	$-0.973672\pi$
$523$		−	1976.34i		−	0.165238i	0.996581	−	0.0826188i	$-0.0263284\pi$
$524$	270.535	−	1150.20i	0.0225542	−	0.0958907i
$525$		−	6122.41i		−	0.508960i
$526$	−13486.3	−	1564.69i	−1.11793	−	0.129703i
$527$	8198.06			0.677634
$528$	6829.73	+	3400.95i	0.562927	+	0.280317i
$529$	−10110.7			−0.830992
$530$	12570.9	+	1458.48i	1.03027	+	0.119533i
$531$			1347.52i			0.110127i
$532$	1240.26	−	5273.03i	0.101075	−	0.429727i
$533$			6453.14i			0.524421i
$534$	124.389	−	1072.13i	0.0100803	−	0.0868834i
$535$	12040.9			0.973034
$536$	−7300.68	+	20218.9i	−0.588323	+	1.62934i
$537$	−1288.27			−0.103525
$538$	−1082.63	+	9331.39i	−0.0867577	+	0.747779i
$539$			10173.4i			0.812984i
$540$	3898.72	+	917.008i	0.310693	+	0.0730773i
$541$			2892.17i			0.229841i	0.993375	+	0.114921i	$0.0366613\pi$
$541$			2892.17i			0.229841i	−0.993375	+	0.114921i	$0.963339\pi$
$542$	−14817.8	−	1719.17i	−1.17432	−	0.136245i
$543$	−8528.56			−0.674025
$544$	−13740.5	−	8953.73i	−1.08294	−	0.705676i
$545$	26203.5			2.05951
$546$	2590.53	+	300.555i	0.203049	+	0.0235578i
$547$		−	7033.62i		−	0.549791i	−0.961474	−	0.274896i	$-0.911357\pi$
$547$		−	7033.62i		−	0.549791i	0.961474	−	0.274896i	$-0.0886433\pi$
$548$	−14646.6	−	3444.99i	−1.14174	−	0.268545i
$549$			4574.82i			0.355644i
$550$	2834.35	−	24429.7i	0.219740	−	1.89398i
$551$	−10408.2			−0.804728
$552$	1045.43	−	2895.27i	0.0806093	−	0.223244i
$553$	−1466.34			−0.112758
$554$	1039.92	−	8963.24i	0.0797509	−	0.687386i
$555$		−	99.0028i		−	0.00757196i
$556$	−1152.73	+	4900.92i	−0.0879258	+	0.373823i
$557$			8702.92i			0.662037i	0.943624	+	0.331019i	$0.107392\pi$
$557$			8702.92i			0.662037i	−0.943624	+	0.331019i	$0.892608\pi$
$558$	2288.06	+	265.462i	0.173587	+	0.0201396i
$559$	−13412.9			−1.01485
$560$	−4933.60	+	9907.57i	−0.372291	+	0.747628i
$561$	10800.7			0.812845
$562$	1532.96	+	177.855i	0.115061	+	0.0133494i
$563$			14119.7i			1.05697i	0.848943	+	0.528484i	$0.177239\pi$
$563$			14119.7i			1.05697i	−0.848943	+	0.528484i	$0.822761\pi$
$564$	1530.18	−	6505.67i	0.114241	−	0.485706i
$565$			20330.2i			1.51380i
$566$	1932.26	−	16654.5i	0.143496	−	1.23682i
$567$	755.462			0.0559549
$568$	17101.8	+	6175.12i	1.26333	+	0.456166i
$569$	383.132			0.0282280			0.0141140	−	0.999900i	$-0.495507\pi$
$569$	383.132			0.0282280			0.0141140	+	0.999900i	$0.495507\pi$
$570$	1316.42	−	11346.4i	0.0967347	−	0.833772i
$571$		−	21917.8i		−	1.60636i	−0.595739	−	0.803178i	$-0.703141\pi$
$571$		−	21917.8i		−	1.60636i	0.595739	−	0.803178i	$-0.296859\pi$
$572$	10197.6	+	2398.56i	0.745428	+	0.175330i
$573$			7640.33i			0.557032i
$574$	−5131.47	−	595.356i	−0.373142	−	0.0432921i
$575$	−9922.44			−0.719642
$576$	−3545.01	−	2943.90i	−0.256439	−	0.212956i
$577$	1570.50			0.113311			0.0566556	−	0.998394i	$-0.481956\pi$
$577$	1570.50			0.113311			0.0566556	+	0.998394i	$0.481956\pi$
$578$	−9258.48	−	1074.17i	−0.666267	−	0.0773006i
$579$		−	10739.9i		−	0.770873i
$580$	20701.4	+	4869.12i	1.48203	+	0.348585i
$581$			1632.76i			0.116589i
$582$	155.317	−	1338.70i	0.0110620	−	0.0953454i
$583$	9588.84			0.681182
$584$	−9572.57	−	3456.47i	−0.678280	−	0.244914i
$585$	5499.24			0.388659
$586$	−1762.19	+	15188.6i	−0.124224	+	1.07071i
$587$			14387.7i			1.01166i	0.862633	+	0.505830i	$0.168814\pi$
$587$			14387.7i			1.01166i	−0.862633	+	0.505830i	$0.831186\pi$
$588$	1406.80	−	5981.09i	0.0986654	−	0.419483i
$589$		−	6569.30i		−	0.459564i
$590$	−7800.00	−	904.960i	−0.544272	−	0.0631468i
$591$	−11617.8			−0.808613
$592$	−50.7739	+	101.963i	−0.00352499	+	0.00707882i
$593$	17903.0			1.23978			0.619889	−	0.784690i	$-0.287178\pi$
$593$	17903.0			1.23978			0.619889	+	0.784690i	$0.287178\pi$
$594$	3014.46	+	349.739i	0.208223	+	0.0241582i
$595$			15668.1i			1.07955i
$596$	786.624	−	3344.39i	0.0540627	−	0.229852i
$597$			16675.9i			1.14322i
$598$	487.102	−	4198.41i	0.0333095	−	0.287100i
$599$	9474.88			0.646299			0.323150	−	0.946348i	$-0.395258\pi$
$599$	9474.88			0.646299			0.323150	+	0.946348i	$0.395258\pi$
$600$	−5044.55	+	13970.7i	−0.343238	+	0.950584i
$601$	−16945.6			−1.15012			−0.575061	−	0.818110i	$-0.695022\pi$
$601$	−16945.6			−1.15012			−0.575061	+	0.818110i	$0.695022\pi$
$602$	1237.45	−	10665.8i	0.0837784	−	0.722100i
$603$			8550.23i			0.577433i
$604$	−212.695	−	50.0275i	−0.0143286	−	0.00337018i
$605$		−	4600.16i		−	0.309129i
$606$	11515.9	+	1336.08i	0.771947	+	0.0895617i
$607$	18736.2			1.25285			0.626423	−	0.779483i	$-0.284518\pi$
$607$	18736.2			1.25285			0.626423	+	0.779483i	$0.284518\pi$
$608$	−7174.84	+	11010.6i	−0.478582	+	0.734438i
$609$	4011.35			0.266910
$610$	−26481.0	−	3072.34i	−1.75768	−	0.203927i
$611$		−	9176.39i		−	0.607589i
$612$	−6349.90	−	1493.54i	−0.419411	−	0.0986485i
$613$			27850.0i			1.83499i	0.397742	+	0.917497i	$0.369794\pi$
$613$			27850.0i			1.83499i	−0.397742	+	0.917497i	$0.630206\pi$
$614$	508.043	−	4378.90i	0.0333924	−	0.287815i
$615$	−10893.2			−0.714237
$616$	−2848.13	+	7887.77i	−0.186289	+	0.515921i
$617$	−12836.3			−0.837551			−0.418776	−	0.908090i	$-0.637541\pi$
$617$	−12836.3			−0.837551			−0.418776	+	0.908090i	$0.637541\pi$
$618$	−1702.83	+	14677.0i	−0.110838	+	0.955330i
$619$		−	18030.3i		−	1.17076i	−0.810760	−	0.585378i	$-0.800946\pi$
$619$		−	18030.3i		−	1.17076i	0.810760	−	0.585378i	$-0.199054\pi$
$620$	−3073.22	+	13066.0i	−0.199070	+	0.846359i
$621$		−	1224.36i		−	0.0791173i
$622$	23455.0	+	2721.26i	1.51199	+	0.175422i
$623$	1186.35			0.0762924
$624$	−5663.68	−	2820.30i	−0.363347	−	0.180933i
$625$	4902.56			0.313764
$626$	14646.6	+	1699.31i	0.935137	+	0.108495i
$627$		−	8654.87i		−	0.551263i
$628$	2291.58	−	9742.80i	0.145611	−	0.619077i
$629$			161.247i			0.0102215i
$630$	−507.350	+	4372.93i	−0.0320846	+	0.276543i
$631$	16460.1			1.03846			0.519229	−	0.854635i	$-0.326219\pi$
$631$	16460.1			1.03846			0.519229	+	0.854635i	$0.326219\pi$
$632$	3346.03	+	1208.19i	0.210598	+	0.0760429i
$633$	−13976.8			−0.877611
$634$	2956.73	−	25484.5i	0.185215	−	1.59640i
$635$		−	13680.3i		−	0.854940i
$636$	−5637.43	−	1325.96i	−0.351476	−	0.0826696i
$637$		−	8436.46i		−	0.524749i
$638$	16006.1	+	1857.04i	0.993243	+	0.115237i
$639$	7232.03			0.447723
$640$	19421.3	−	18543.0i	1.19952	−	1.14527i
$641$	−19443.3			−1.19807			−0.599035	−	0.800723i	$-0.704449\pi$
$641$	−19443.3			−1.19807			−0.599035	+	0.800723i	$0.704449\pi$
$642$	−5473.44	−	635.031i	−0.336479	−	0.0390385i
$643$			7368.87i			0.451944i	0.974134	+	0.225972i	$0.0725558\pi$
$643$			7368.87i			0.451944i	−0.974134	+	0.225972i	$0.927444\pi$
$644$	3293.59	+	774.677i	0.201531	+	0.0474015i
$645$		−	22641.5i		−	1.38218i
$646$	−2144.07	+	18480.1i	−0.130584	+	1.12553i
$647$	−11042.3			−0.670969			−0.335484	−	0.942046i	$-0.608900\pi$
$647$	−11042.3			−0.670969			−0.335484	+	0.942046i	$0.608900\pi$
$648$	−1723.88	−	622.462i	−0.104507	−	0.0377355i
$649$	−5949.70			−0.359856
$650$	−2350.44	+	20258.8i	−0.141833	+	1.22249i
$651$			2531.82i			0.152427i
$652$	234.241	−	995.893i	0.0140699	−	0.0598193i
$653$		−	14174.3i		−	0.849440i	−0.905325	−	0.424720i	$-0.860373\pi$
$653$		−	14174.3i		−	0.849440i	0.905325	−	0.424720i	$-0.139627\pi$
$654$	−11911.3	−	1381.96i	−0.712186	−	0.0826282i
$655$	2738.65			0.163371
$656$	11218.9	+	5586.60i	0.667721	+	0.332500i
$657$	−4048.07			−0.240381
$658$	7296.96	+	846.598i	0.432318	+	0.0501578i
$659$		−	1917.19i		−	0.113328i	−0.998393	−	0.0566640i	$-0.981954\pi$
$659$		−	1917.19i		−	0.113328i	0.998393	−	0.0566640i	$-0.0180464\pi$
$660$	−4048.87	+	17214.1i	−0.238791	+	1.01524i
$661$		−	28084.2i		−	1.65257i	−0.563254	−	0.826284i	$-0.690451\pi$
$661$		−	28084.2i		−	1.65257i	0.563254	−	0.826284i	$-0.309549\pi$
$662$	−60.8052	+	524.090i	−0.00356988	+	0.0307694i
$663$	−8956.69			−0.524659
$664$	1345.31	−	3725.77i	0.0786265	−	0.217753i
$665$	12555.2			0.732136
$666$	−5.22137	+	45.0038i	−0.000303789	+	0.00261841i
$667$		−	6501.09i		−	0.377396i
$668$	−16195.3	−	3809.24i	−0.938044	−	0.220635i
$669$		−	4636.27i		−	0.267935i
$670$	−49492.4	−	5742.13i	−2.85382	−	0.331101i
$671$	−20199.3			−1.16212
$672$	2765.19	−	4243.50i	0.158735	−	0.243596i
$673$	1756.20			0.100589			0.0502947	−	0.998734i	$-0.483984\pi$
$673$	1756.20			0.100589			0.0502947	+	0.998734i	$0.483984\pi$
$674$	−2330.12	−	270.342i	−0.133165	−	0.0154499i
$675$			5907.96i			0.336885i
$676$	8652.53	+	2035.14i	0.492292	+	0.115791i
$677$			10424.0i			0.591766i	0.955224	+	0.295883i	$0.0956139\pi$
$677$			10424.0i			0.591766i	−0.955224	+	0.295883i	$0.904386\pi$
$678$	1072.20	−	9241.50i	0.0607341	−	0.523477i
$679$	1481.32			0.0837230
$680$	12909.7	−	35752.9i	0.728036	−	2.01627i
$681$	19637.3			1.10500
$682$	−1172.10	+	10102.5i	−0.0658093	+	0.567221i
$683$		−	5828.41i		−	0.326527i	−0.986582	−	0.163264i	$-0.947798\pi$
$683$		−	5828.41i		−	0.326527i	0.986582	−	0.163264i	$-0.0522021\pi$
$684$	−1196.81	+	5088.33i	−0.0669024	+	0.284440i
$685$		−	34873.9i		−	1.94520i
$686$	15696.6	+	1821.13i	0.873613	+	0.101357i
$687$	16390.4			0.910240
$688$	−11611.8	+	23318.5i	−0.643451	+	1.29217i
$689$	−7951.72			−0.439675
$690$	7087.11	+	822.250i	0.391017	+	0.0453660i
$691$			10673.5i			0.587611i	0.955865	+	0.293806i	$0.0949218\pi$
$691$			10673.5i			0.587611i	−0.955865	+	0.293806i	$0.905078\pi$
$692$	1254.95	−	5335.52i	0.0689395	−	0.293101i
$693$			3335.60i			0.182841i
$694$	−3913.47	+	33730.8i	−0.214054	+	1.84496i
$695$	−11669.2			−0.636890
$696$	−9153.46	−	3305.14i	−0.498507	−	0.180002i
$697$	17741.9			0.964163
$698$	25.3784	−	218.740i	0.00137620	−	0.0118617i
$699$			14167.2i			0.766599i
$700$	−15892.7	−	3738.08i	−0.858127	−	0.201838i
$701$		−	14367.0i		−	0.774084i	−0.922062	−	0.387042i	$-0.873497\pi$
$701$		−	14367.0i		−	0.774084i	0.922062	−	0.387042i	$-0.126503\pi$
$702$	−2499.79	−	290.027i	−0.134400	−	0.0155931i
$703$	129.211			0.00693214
$704$	12998.2	−	15652.3i	0.695865	−	0.837954i
$705$	15490.1			0.827507
$706$	13837.4	+	1605.42i	0.737643	+	0.0855818i
$707$			12742.7i			0.677848i
$708$	3497.92	+	822.737i	0.185678	+	0.0436728i
$709$			25026.4i			1.32565i	0.748774	+	0.662825i	$0.230643\pi$
$709$			25026.4i			1.32565i	−0.748774	+	0.662825i	$0.769357\pi$
$710$	−4856.86	+	41862.1i	−0.256725	+	2.21275i
$711$	1414.98			0.0746354
$712$	−2707.13	−	977.493i	−0.142491	−	0.0514510i
$713$	4103.26			0.215523
$714$	826.329	−	7122.26i	0.0433117	−	0.373311i
$715$			24280.8i			1.27000i
$716$	−786.562	+	3344.12i	−0.0410547	+	0.174547i
$717$		−	3163.13i		−	0.164755i
$718$	34446.0	+	3996.44i	1.79041	+	0.207724i
$719$	692.065			0.0358966			0.0179483	−	0.999839i	$-0.494287\pi$
$719$	692.065			0.0358966			0.0179483	+	0.999839i	$0.494287\pi$
$720$	4760.79	−	9560.53i	0.246423	−	0.494861i
$721$	−16240.6			−0.838876
$722$	−4462.37	−	517.726i	−0.230017	−	0.0266867i
$723$		−	9403.19i		−	0.483691i
$724$	−5207.18	+	22138.7i	−0.267297	+	1.13643i
$725$			31370.0i			1.60697i
$726$	−242.611	+	2091.10i	−0.0124024	+	0.106898i
$727$	−23929.5			−1.22076			−0.610382	−	0.792107i	$-0.708984\pi$
$727$	−23929.5			−1.22076			−0.610382	+	0.792107i	$0.708984\pi$
$728$	2361.86	−	6541.08i	0.120242	−	0.333006i
$729$	−729.000			−0.0370370
$730$	2718.59	−	23431.9i	0.137835	−	1.18802i
$731$			36876.5i			1.86584i
$732$	11875.5	+	2793.19i	0.599631	+	0.141037i
$733$		−	5613.22i		−	0.282850i	−0.989949	−	0.141425i	$-0.954832\pi$
$733$		−	5613.22i		−	0.282850i	0.989949	−	0.141425i	$-0.0451684\pi$
$734$	24164.8	+	2803.62i	1.21518	+	0.140985i
$735$	14241.1			0.714683
$736$	−6877.33	−	4481.48i	−0.344432	−	0.224442i
$737$	−37751.9			−1.88685
$738$	4951.72	+	574.502i	0.246986	+	0.0286554i
$739$			4790.30i			0.238449i	0.992867	+	0.119225i	$0.0380408\pi$
$739$			4790.30i			0.238449i	−0.992867	+	0.119225i	$0.961959\pi$
$740$	−256.994	−	60.4469i	−0.0127666	−	0.00300280i
$741$			7177.21i			0.355818i
$742$	733.612	−	6323.12i	0.0362962	−	0.312842i
$743$	16695.0			0.824333			0.412166	−	0.911109i	$-0.364772\pi$
$743$	16695.0			0.824333			0.412166	+	0.911109i	$0.364772\pi$
$744$	2086.09	−	5777.34i	0.102795	−	0.284687i
$745$	7963.07			0.391603
$746$	1302.73	−	11228.4i	0.0639359	−	0.551074i
$747$		−	1575.56i		−	0.0771711i
$748$	6594.46	−	28036.8i	0.322349	−	1.37049i
$749$		−	6056.55i		−	0.295463i
$750$	−14661.8	−	1701.07i	−0.713832	−	0.0828192i
$751$	27366.8			1.32973			0.664866	−	0.746963i	$-0.268489\pi$
$751$	27366.8			1.32973			0.664866	+	0.746963i	$0.268489\pi$
$752$	−15953.3	−	7944.17i	−0.773615	−	0.385231i
$753$	−14645.7			−0.708791
$754$	−13273.4	−	1539.99i	−0.641098	−	0.0743806i
$755$		−	506.433i		−	0.0244119i
$756$	461.253	−	1961.05i	0.0221900	−	0.0943422i
$757$		−	5712.23i		−	0.274260i	−0.990553	−	0.137130i	$-0.956212\pi$
$757$		−	5712.23i		−	0.274260i	0.990553	−	0.137130i	$-0.0437878\pi$
$758$	3391.63	−	29233.0i	0.162519	−	1.40078i
$759$	5405.92			0.258528
$760$	−28649.7	−	10344.9i	−1.36741	−	0.493747i
$761$	14015.9			0.667643			0.333822	−	0.942636i	$-0.391662\pi$
$761$	14015.9			0.667643			0.333822	+	0.942636i	$0.391662\pi$
$762$	−721.494	+	6218.68i	−0.0343005	+	0.295642i
$763$		−	13180.3i		−	0.625372i
$764$	19833.0	+	4664.86i	0.939179	+	0.220902i
$765$		−	15119.3i		−	0.714560i
$766$	−19145.0	−	2221.21i	−0.903051	−	0.104773i
$767$	4933.90			0.232272
$768$	−9806.30	+	7404.83i	−0.460748	+	0.347915i
$769$	−3430.70			−0.160877			−0.0804384	−	0.996760i	$-0.525632\pi$
$769$	−3430.70			−0.160877			−0.0804384	+	0.996760i	$0.525632\pi$
$770$	−19307.9	−	2240.11i	−0.903645	−	0.104841i
$771$		−	1621.37i		−	0.0757359i
$772$	−27879.0	−	6557.34i	−1.29972	−	0.305704i
$773$		−	14821.8i		−	0.689654i	−0.938666	−	0.344827i	$-0.887938\pi$
$773$		−	14821.8i		−	0.689654i	0.938666	−	0.344827i	$-0.112062\pi$
$774$	−1194.10	+	10292.2i	−0.0554537	+	0.477964i
$775$	−19799.6			−0.917708
$776$	−3380.21	−	1220.53i	−0.156369	−	0.0564621i
$777$	−49.7982			−0.00229923
$778$	254.037	−	2189.59i	0.0117065	−	0.100900i
$779$		−	14217.0i		−	0.653885i
$780$	3357.60	−	14275.1i	0.154130	−	0.655295i
$781$			31931.7i			1.46300i
$782$	−11542.9	−	1339.21i	−0.527842	−	0.0612405i
$783$	−3870.84			−0.176670
$784$	−14667.0	−	7303.60i	−0.668138	−	0.332708i
$785$	23197.8			1.05473
$786$	−1244.91	−	144.435i	−0.0564943	−	0.00655451i
$787$			16917.4i			0.766253i	0.923696	+	0.383126i	$0.125153\pi$
$787$			16917.4i			0.766253i	−0.923696	+	0.383126i	$0.874847\pi$
$788$	−7093.31	+	30157.7i	−0.320671	+	1.36335i
$789$			14400.4i			0.649768i
$790$	−950.264	+	8190.48i	−0.0427960	+	0.368866i
$791$	10226.0			0.459666
$792$	2748.36	−	7611.48i	0.123307	−	0.341493i
$793$	16750.6			0.750103
$794$	4079.20	−	35159.3i	0.182324	−	1.57148i
$795$		−	13422.9i		−	0.598817i
$796$	43287.9	+	10181.6i	1.92751	+	0.453364i
$797$		−	23546.7i		−	1.04651i	−0.852177	−	0.523254i	$-0.824718\pi$
$797$		−	23546.7i		−	1.04651i	0.852177	−	0.523254i	$-0.175282\pi$
$798$	−5707.24	−	662.157i	−0.253175	−	0.0293736i
$799$	−25229.0			−1.11707
$800$	33185.5	+	21624.7i	1.46661	+	0.955686i
$801$	−1144.80			−0.0504986
$802$	22335.3	+	2591.35i	0.983399	+	0.114094i
$803$		−	17873.5i		−	0.785482i
$804$	22194.9	+	5220.41i	0.973576	+	0.228992i
$805$			7842.13i			0.343352i
$806$	971.984	−	8377.68i	0.0424773	−	0.366118i
$807$	9963.83			0.434626
$808$	10499.3	−	29077.5i	0.457135	−	1.26602i
$809$	−17647.6			−0.766942			−0.383471	−	0.923553i	$-0.625271\pi$
$809$	−17647.6			−0.766942			−0.383471	+	0.923553i	$0.625271\pi$
$810$	489.579	−	4219.76i	0.0212371	−	0.183046i
$811$		−	11690.3i		−	0.506169i	−0.967444	−	0.253085i	$-0.918555\pi$
$811$		−	11690.3i		−	0.506169i	0.967444	−	0.253085i	$-0.0814451\pi$
$812$	2449.16	−	10412.8i	0.105848	−	0.450021i
$813$			15822.1i			0.682541i
$814$	−198.706	−	23.0539i	−0.00855606	−	0.000992679i
$815$	2371.25			0.101915
$816$	−7753.97	+	15571.4i	−0.332651	+	0.668023i
$817$	29550.0			1.26539
$818$	−42660.5	−	4949.50i	−1.82346	−	0.211559i
$819$		−	2766.11i		−	0.118017i
$820$	−6650.92	+	28276.8i	−0.283244	+	1.20423i
$821$			10576.3i			0.449594i	0.974406	+	0.224797i	$0.0721718\pi$
$821$			10576.3i			0.449594i	−0.974406	+	0.224797i	$0.927828\pi$
$822$	−1839.24	+	15852.7i	−0.0780422	+	0.672658i
$823$	−44624.4			−1.89005			−0.945023	−	0.327005i	$-0.893961\pi$
$823$	−44624.4			−1.89005			−0.945023	+	0.327005i	$0.893961\pi$
$824$	37059.2	+	13381.4i	1.56677	+	0.565731i
$825$	−26085.5			−1.10082
$826$	−455.193	+	3923.38i	−0.0191746	+	0.165269i
$827$		−	2532.98i		−	0.106506i	−0.998581	−	0.0532528i	$-0.983041\pi$
$827$		−	2532.98i		−	0.106506i	0.998581	−	0.0532528i	$-0.0169589\pi$
$828$	−3178.23	−	747.542i	−0.133395	−	0.0313754i
$829$			24029.6i			1.00673i	0.864073	+	0.503366i	$0.167905\pi$
$829$			24029.6i			1.00673i	−0.864073	+	0.503366i	$0.832095\pi$
$830$	9120.03	+	1058.11i	0.381399	+	0.0442501i
$831$	−9570.72			−0.399524
$832$	−10779.0	+	12980.0i	−0.449153	+	0.540865i
$833$	−23194.7			−0.964765
$834$	5304.49	+	615.430i	0.220239	+	0.0255523i
$835$		−	38561.3i		−	1.59817i
$836$	−22466.6	−	5284.30i	−0.929452	−	0.218614i
$837$		−	2443.13i		−	0.100893i
$838$	3835.74	−	33060.8i	0.158119	−	1.36285i
$839$	39117.5			1.60964			0.804819	−	0.593520i	$-0.202262\pi$
$839$	39117.5			1.60964			0.804819	+	0.593520i	$0.202262\pi$
$840$	11041.6	+	3986.92i	0.453538	+	0.163764i
$841$	3835.65			0.157270
$842$	−4713.46	+	40626.1i	−0.192917	+	1.66279i
$843$		−	1636.86i		−	0.0668758i
$844$	−8533.65	+	36281.4i	−0.348033	+	1.47969i
$845$			20601.9i			0.838729i
$846$	−7041.37	−	816.944i	−0.286155	−	0.0331999i
$847$	−2313.87			−0.0938674
$848$	−6883.95	+	13824.2i	−0.278769	+	0.559818i
$849$	−17783.2			−0.718867
$850$	55698.3	+	6462.15i	2.24757	+	0.260765i
$851$			80.7068i			0.00325099i
$852$	4415.57	−	18773.1i	0.177553	−	0.754878i
$853$		−	35436.1i		−	1.42240i	−0.702988	−	0.711201i	$-0.748151\pi$
$853$		−	35436.1i		−	1.42240i	0.702988	−	0.711201i	$-0.251849\pi$
$854$	−1545.38	+	13319.9i	−0.0619226	+	0.533721i
$855$	−12115.4			−0.484607
$856$	−4990.28	+	13820.4i	−0.199257	+	0.551836i
$857$	20451.8			0.815191			0.407596	−	0.913163i	$-0.366367\pi$
$857$	20451.8			0.815191			0.407596	+	0.913163i	$0.366367\pi$
$858$	1280.56	−	11037.4i	0.0509529	−	0.439172i
$859$		−	6477.74i		−	0.257297i	−0.991690	−	0.128648i	$-0.958936\pi$
$859$		−	6477.74i		−	0.257297i	0.991690	−	0.128648i	$-0.0410638\pi$
$860$	−58773.5	−	13823.9i	−2.33042	−	0.548131i
$861$			5479.25i			0.216879i
$862$	25984.4	+	3014.73i	1.02672	+	0.119121i
$863$	−2068.34			−0.0815843			−0.0407922	−	0.999168i	$-0.512988\pi$
$863$	−2068.34			−0.0815843			−0.0407922	+	0.999168i	$0.512988\pi$
$864$	−2668.34	+	4094.86i	−0.105068	+	0.161238i
$865$	12704.0			0.499363
$866$	9710.24	+	1126.59i	0.381025	+	0.0442067i
$867$			9885.98i			0.387250i
$868$	6572.17	+	1545.82i	0.256998	+	0.0604477i
$869$			6247.56i			0.243882i
$870$	2599.56	−	22406.1i	0.101303	−	0.873145i
$871$	31306.5			1.21789
$872$	−10859.9	+	30076.0i	−0.421745	+	1.16801i
$873$	−1429.43			−0.0554170
$874$	−1073.14	+	9249.58i	−0.0415327	+	0.357977i
$875$		−	16223.8i		−	0.626817i
$876$	−2471.58	+	10508.1i	−0.0953276	+	0.405292i
$877$		−	33095.0i		−	1.27427i	−0.770750	−	0.637137i	$-0.780118\pi$
$877$		−	33095.0i		−	1.27427i	0.770750	−	0.637137i	$-0.219882\pi$
$878$	−22689.3	−	2632.42i	−0.872125	−	0.101184i
$879$	16218.0			0.622321
$880$	42212.7	+	21020.4i	1.61703	+	0.805223i
$881$	33169.3			1.26845			0.634225	−	0.773149i	$-0.281319\pi$
$881$	33169.3			1.26845			0.634225	+	0.773149i	$0.281319\pi$
$882$	−6473.60	−	751.070i	−0.247140	−	0.0286733i
$883$		−	28990.4i		−	1.10488i	−0.833554	−	0.552438i	$-0.813698\pi$
$883$		−	28990.4i		−	1.10488i	0.833554	−	0.552438i	$-0.186302\pi$
$884$	−5468.57	+	23250.0i	−0.208063	+	0.884596i
$885$			8328.64i			0.316344i
$886$	3731.59	−	32163.2i	0.141496	−	1.21957i
$887$	458.565			0.0173586			0.00867931	−	0.999962i	$-0.497237\pi$
$887$	458.565			0.0173586			0.00867931	+	0.999962i	$0.497237\pi$
$888$	113.634	+	41.0312i	0.00429427	+	0.00155058i
$889$	−6881.18			−0.259603
$890$	768.818	−	6626.57i	0.0289560	−	0.249576i
$891$		−	3218.76i		−	0.121024i
$892$	−12035.0	−	2830.71i	−0.451749	−	0.106255i
$893$			20216.6i			0.757585i
$894$	−3619.78	−	419.969i	−0.135418	−	0.0157113i
$895$	−7962.44			−0.297380
$896$	−9327.09	−	9768.87i	−0.347763	−	0.364236i
$897$	−4482.96			−0.166869
$898$	2838.19	+	329.289i	0.105470	+	0.0122367i
$899$		−	12972.5i		−	0.481266i
$900$	15336.0	+	3607.15i	0.568002	+	0.133598i
$901$			21862.0i			0.808355i
$902$	−2536.60	+	21863.4i	−0.0936360	+	0.807064i
$903$	−11388.6			−0.419701
$904$	−23334.7	−	8425.73i	−0.858519	−	0.309995i
$905$	−52712.8			−1.93617
$906$	−26.7090	+	230.210i	−0.000979413	+	0.00844172i
$907$			45653.8i			1.67134i	0.549229	+	0.835672i	$0.314922\pi$
$907$			45653.8i			1.67134i	−0.549229	+	0.835672i	$0.685078\pi$
$908$	11989.7	−	50975.0i	0.438207	−	1.86307i
$909$		−	12296.3i		−	0.448673i
$910$	16011.4	+	1857.65i	0.583267	+	0.0676709i
$911$	−50760.6			−1.84608			−0.923038	−	0.384710i	$-0.874302\pi$
$911$	−50760.6			−1.84608			−0.923038	+	0.384710i	$0.874302\pi$
$912$	12477.7	+	6213.44i	0.453047	+	0.225600i
$913$	6956.60			0.252169
$914$	−44810.6	−	5198.95i	−1.62167	−	0.188147i
$915$			28275.8i			1.02160i
$916$	10007.3	−	42546.8i	0.360973	−	1.53470i
$917$		−	1377.54i		−	0.0496078i
$918$	−797.384	+	6872.78i	−0.0286684	+	0.247098i
$919$	−25939.0			−0.931065			−0.465532	−	0.885031i	$-0.654137\pi$
$919$	−25939.0			−0.931065			−0.465532	+	0.885031i	$0.654137\pi$
$920$	6461.51	−	17894.9i	0.231554	−	0.641279i
$921$	−4675.68			−0.167284
$922$	−2196.25	+	18929.9i	−0.0784488	+	0.676163i
$923$		−	26479.9i		−	0.944309i
$924$	8658.65	+	2036.58i	0.308278	+	0.0725091i
$925$		−	389.438i		−	0.0138429i
$926$	7312.46	+	848.396i	0.259506	+	0.0301080i
$927$	15671.7			0.555260
$928$	−14168.3	+	21742.8i	−0.501183	+	0.769120i
$929$	41850.4			1.47801			0.739003	−	0.673702i	$-0.235297\pi$
$929$	41850.4			1.47801			0.739003	+	0.673702i	$0.235297\pi$
$930$	14141.9	+	1640.75i	0.498636	+	0.0578520i
$931$			18586.5i			0.654294i
$932$	36775.6	+	8649.89i	1.29252	+	0.304009i
$933$		−	25044.6i		−	0.878805i
$934$	3040.05	−	26202.7i	0.106503	−	0.917963i
$935$	66756.3			2.33494
$936$	−2279.13	+	6311.96i	−0.0795894	+	0.220420i
$937$	18888.1			0.658534			0.329267	−	0.944237i	$-0.393198\pi$
$937$	18888.1			0.658534			0.329267	+	0.944237i	$0.393198\pi$
$938$	−2888.28	+	24894.6i	−0.100539	+	0.866563i
$939$		−	15639.3i		−	0.543523i
$940$	9457.63	−	40209.8i	0.328164	−	1.39521i
$941$			21571.8i			0.747313i	0.927567	+	0.373656i	$0.121896\pi$
$941$			21571.8i			0.747313i	−0.927567	+	0.373656i	$0.878104\pi$
$942$	−10545.1	−	1223.44i	−0.364731	−	0.0423163i
$943$	8880.09			0.306655
$944$	4271.37	−	8577.68i	0.147268	−	0.295741i
$945$	4669.31			0.160733
$946$	−45443.1	−	5272.33i	−1.56182	−	0.181203i
$947$		−	2981.14i		−	0.102296i	−0.998691	−	0.0511479i	$-0.983712\pi$
$947$		−	2981.14i		−	0.102296i	0.998691	−	0.0511479i	$-0.0162880\pi$
$948$	863.925	−	3673.04i	0.0295981	−	0.125838i
$949$			14821.9i			0.506997i
$950$	5178.28	−	44632.4i	0.176848	−	1.52428i
$951$	−27211.7			−0.927865
$952$	−17983.6	−	6493.56i	−0.612241	−	0.221069i
$953$	−8353.84			−0.283953			−0.141977	−	0.989870i	$-0.545346\pi$
$953$	−8353.84			−0.283953			−0.141977	+	0.989870i	$0.545346\pi$
$954$	−707.915	+	6101.64i	−0.0240247	+	0.207073i
$955$			47222.9i			1.60010i
$956$	−8210.93	−	1931.27i	−0.277783	−	0.0653366i
$957$		−	17090.9i		−	0.577296i
$958$	−32231.5	−	3739.51i	−1.08701	−	0.126115i
$959$	−17541.5			−0.590662
$960$	−21910.8	−	18195.5i	−0.736633	−	0.611725i
$961$	−21603.2			−0.725159
$962$	164.780	+	19.1179i	0.00552259	+	0.000640734i
$963$			5844.40i			0.195569i
$964$	−24409.1	−	5741.19i	−0.815522	−	0.191817i
$965$		−	66380.6i		−	2.21437i
$966$	413.590	−	3564.80i	0.0137754	−	0.118733i
$967$	−20156.9			−0.670323			−0.335162	−	0.942161i	$-0.608791\pi$
$967$	−20156.9			−0.670323			−0.335162	+	0.942161i	$0.608791\pi$
$968$	5280.01	+	1906.51i	0.175316	+	0.0633034i
$969$	19732.6			0.654182
$970$	959.974	−	8274.17i	0.0317762	−	0.273884i
$971$			32976.8i			1.08988i	0.838474	+	0.544941i	$0.183448\pi$
$971$			32976.8i			1.08988i	−0.838474	+	0.544941i	$0.816552\pi$
$972$	−445.097	+	1892.36i	−0.0146877	+	0.0624460i
$973$			5869.60i			0.193392i
$974$	42278.5	+	4905.17i	1.39085	+	0.161367i
$975$	21631.8			0.710537
$976$	14501.3	−	29121.3i	0.475590	−	0.955071i
$977$	2934.18			0.0960827			0.0480413	−	0.998845i	$-0.484702\pi$
$977$	2934.18			0.0960827			0.0480413	+	0.998845i	$0.484702\pi$
$978$	−1077.90	−	125.058i	−0.0352427	−	0.00408888i
$979$		−	5054.63i		−	0.165012i
$980$	8695.03	−	36967.5i	0.283421	−	1.20498i
$981$			12718.6i			0.413939i
$982$	−4685.33	+	40383.6i	−0.152255	+	1.31231i
$983$	11965.0			0.388223			0.194111	−	0.980979i	$-0.437818\pi$
$983$	11965.0			0.388223			0.194111	+	0.980979i	$0.437818\pi$
$984$	4514.62	−	12503.1i	0.146261	−	0.405064i
$985$	−71806.2			−2.32278
$986$	−4233.94	+	36493.0i	−0.136751	+	1.17868i
$987$		−	7791.52i		−	0.251273i
$988$	18630.8	+	4382.10i	0.599924	+	0.141106i
$989$			18457.3i			0.593435i
$990$	18631.5	+	2161.64i	0.598131	+	0.0693955i
$991$	43262.0			1.38674			0.693371	−	0.720581i	$-0.256125\pi$
$991$	43262.0			1.38674			0.693371	+	0.720581i	$0.256125\pi$
$992$	−13723.3	−	8942.53i	−0.439229	−	0.286215i
$993$	559.610			0.0178839
$994$	21056.5	+	2442.99i	0.671904	+	0.0779547i
$995$			103069.i			3.28394i
$996$	−4089.89	−	961.972i	−0.130114	−	0.0306037i
$997$		−	35664.7i		−	1.13291i	−0.824092	−	0.566456i	$-0.808314\pi$
$997$		−	35664.7i		−	1.13291i	0.824092	−	0.566456i	$-0.191686\pi$
$998$	2988.19	−	25755.7i	0.0947790	−	0.816915i
$999$	48.0539			0.00152188

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.4.d.a.13.1	✓	6
3.2	odd	2		72.4.d.d.37.6		6
4.3	odd	2		96.4.d.a.49.3		6
8.3	odd	2		96.4.d.a.49.4		6
8.5	even	2	inner	24.4.d.a.13.2	yes	6
12.11	even	2		288.4.d.d.145.1		6
16.3	odd	4		768.4.a.t.1.3		3
16.5	even	4		768.4.a.s.1.1		3
16.11	odd	4		768.4.a.q.1.1		3
16.13	even	4		768.4.a.r.1.3		3
24.5	odd	2		72.4.d.d.37.5		6
24.11	even	2		288.4.d.d.145.6		6
48.5	odd	4		2304.4.a.bv.1.3		3
48.11	even	4		2304.4.a.bw.1.3		3
48.29	odd	4		2304.4.a.bt.1.1		3
48.35	even	4		2304.4.a.bu.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.d.a.13.1	✓	6	1.1	even	1	trivial
24.4.d.a.13.2	yes	6	8.5	even	2	inner
72.4.d.d.37.5		6	24.5	odd	2
72.4.d.d.37.6		6	3.2	odd	2
96.4.d.a.49.3		6	4.3	odd	2
96.4.d.a.49.4		6	8.3	odd	2
288.4.d.d.145.1		6	12.11	even	2
288.4.d.d.145.6		6	24.11	even	2
768.4.a.q.1.1		3	16.11	odd	4
768.4.a.r.1.3		3	16.13	even	4
768.4.a.s.1.1		3	16.5	even	4
768.4.a.t.1.3		3	16.3	odd	4
2304.4.a.bt.1.1		3	48.29	odd	4
2304.4.a.bu.1.1		3	48.35	even	4
2304.4.a.bv.1.3		3	48.5	odd	4
2304.4.a.bw.1.3		3	48.11	even	4

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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	24.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.80958 - 0.325969i) q^{2} +3.00000i q^{3} +(7.78749 + 1.83167i) q^{4} +18.5422i q^{5} +(0.977907 - 8.42874i) q^{6} +9.32669 q^{7} +(-21.2825 - 7.68472i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(-2.80958 - 0.325969i) q^{2} +3.00000i q^{3} +(7.78749 + 1.83167i) q^{4} +18.5422i q^{5} +(0.977907 - 8.42874i) q^{6} +9.32669 q^{7} +(-21.2825 - 7.68472i) q^{8} -9.00000 q^{9} +(6.04419 - 52.0958i) q^{10} -39.7378i q^{11} +(-5.49502 + 23.3625i) q^{12} +32.9533i q^{13} +(-26.2041 - 3.04021i) q^{14} -55.6266 q^{15} +(57.2899 + 28.5283i) q^{16} +90.5998 q^{17} +(25.2862 + 2.93372i) q^{18} -72.5998i q^{19} +(-33.9633 + 144.397i) q^{20} +27.9801i q^{21} +(-12.9533 + 111.647i) q^{22} +45.3466 q^{23} +(23.0541 - 63.8475i) q^{24} -218.813 q^{25} +(10.7418 - 92.5849i) q^{26} -27.0000i q^{27} +(72.6315 + 17.0835i) q^{28} -143.364i q^{29} +(156.287 + 18.1326i) q^{30} +90.4865 q^{31} +(-151.661 - 98.8272i) q^{32} +119.213 q^{33} +(-254.547 - 29.5327i) q^{34} +172.937i q^{35} +(-70.0874 - 16.4851i) q^{36} +1.77977i q^{37} +(-23.6653 + 203.975i) q^{38} -98.8599 q^{39} +(142.492 - 394.625i) q^{40} +195.827 q^{41} +(9.12064 - 78.6123i) q^{42} +407.027i q^{43} +(72.7866 - 309.458i) q^{44} -166.880i q^{45} +(-127.405 - 14.7816i) q^{46} -278.467 q^{47} +(-85.5848 + 171.870i) q^{48} -256.013 q^{49} +(614.773 + 71.3263i) q^{50} +271.799i q^{51} +(-60.3597 + 256.623i) q^{52} +241.303i q^{53} +(-8.80117 + 75.8587i) q^{54} +736.826 q^{55} +(-198.495 - 71.6730i) q^{56} +217.799 q^{57} +(-46.7324 + 402.794i) q^{58} -149.724i q^{59} +(-433.191 - 101.890i) q^{60} -508.314i q^{61} +(-254.229 - 29.4958i) q^{62} -83.9402 q^{63} +(393.890 + 327.100i) q^{64} -611.027 q^{65} +(-334.940 - 38.8599i) q^{66} -950.026i q^{67} +(705.545 + 165.949i) q^{68} +136.040i q^{69} +(56.3723 - 485.882i) q^{70} -803.559 q^{71} +(191.543 + 69.1624i) q^{72} +449.786 q^{73} +(0.580152 - 5.00042i) q^{74} -656.440i q^{75} +(132.979 - 565.370i) q^{76} -370.622i q^{77} +(277.755 + 32.2253i) q^{78} -157.220 q^{79} +(-528.977 + 1062.28i) q^{80} +81.0000 q^{81} +(-550.192 - 63.8335i) q^{82} +175.063i q^{83} +(-51.2504 + 217.895i) q^{84} +1679.92i q^{85} +(132.678 - 1143.57i) q^{86} +430.093 q^{87} +(-305.374 + 845.720i) q^{88} +127.200 q^{89} +(-54.3977 + 468.862i) q^{90} +307.345i q^{91} +(353.136 + 83.0602i) q^{92} +271.459i q^{93} +(782.374 + 90.7715i) q^{94} +1346.16 q^{95} +(296.482 - 454.984i) q^{96} +158.826 q^{97} +(719.289 + 83.4523i) q^{98} +357.640i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9	\( 6 q + 2 q^{2} + 16 q^{4} - 6 q^{6} + 28 q^{7} - 76 q^{8} - 54 q^{9} + 60 q^{10} - 12 q^{12} - 100 q^{14} - 60 q^{15} + 56 q^{16} + 52 q^{17} - 18 q^{18} + 56 q^{20} + 224 q^{22} + 328 q^{23} + 204 q^{24} - 106 q^{25} + 56 q^{26} - 352 q^{28} + 372 q^{30} - 636 q^{31} - 248 q^{32} - 548 q^{34} - 144 q^{36} - 776 q^{38} + 312 q^{39} + 232 q^{40} + 236 q^{41} - 564 q^{42} + 1152 q^{44} + 328 q^{46} - 408 q^{47} + 576 q^{48} + 654 q^{49} + 1970 q^{50} - 368 q^{52} + 54 q^{54} + 1024 q^{55} - 1864 q^{56} - 168 q^{57} + 140 q^{58} - 1152 q^{60} - 2108 q^{62} - 252 q^{63} + 832 q^{64} - 1744 q^{65} - 1440 q^{66} + 2976 q^{68} + 1352 q^{70} - 1704 q^{71} + 684 q^{72} + 956 q^{73} + 1568 q^{74} - 1744 q^{76} + 1608 q^{78} - 44 q^{79} - 2112 q^{80} + 486 q^{81} - 2236 q^{82} - 1992 q^{84} - 760 q^{86} + 1044 q^{87} + 1856 q^{88} - 220 q^{89} - 540 q^{90} + 1728 q^{92} + 2088 q^{94} + 5104 q^{95} + 2184 q^{96} - 2444 q^{97} + 3354 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 16 * q^4 - 6 * q^6 + 28 * q^7 - 76 * q^8 - 54 * q^9 + 60 * q^10 - 12 * q^12 - 100 * q^14 - 60 * q^15 + 56 * q^16 + 52 * q^17 - 18 * q^18 + 56 * q^20 + 224 * q^22 + 328 * q^23 + 204 * q^24 - 106 * q^25 + 56 * q^26 - 352 * q^28 + 372 * q^30 - 636 * q^31 - 248 * q^32 - 548 * q^34 - 144 * q^36 - 776 * q^38 + 312 * q^39 + 232 * q^40 + 236 * q^41 - 564 * q^42 + 1152 * q^44 + 328 * q^46 - 408 * q^47 + 576 * q^48 + 654 * q^49 + 1970 * q^50 - 368 * q^52 + 54 * q^54 + 1024 * q^55 - 1864 * q^56 - 168 * q^57 + 140 * q^58 - 1152 * q^60 - 2108 * q^62 - 252 * q^63 + 832 * q^64 - 1744 * q^65 - 1440 * q^66 + 2976 * q^68 + 1352 * q^70 - 1704 * q^71 + 684 * q^72 + 956 * q^73 + 1568 * q^74 - 1744 * q^76 + 1608 * q^78 - 44 * q^79 - 2112 * q^80 + 486 * q^81 - 2236 * q^82 - 1992 * q^84 - 760 * q^86 + 1044 * q^87 + 1856 * q^88 - 220 * q^89 - 540 * q^90 + 1728 * q^92 + 2088 * q^94 + 5104 * q^95 + 2184 * q^96 - 2444 * q^97 + 3354 * q^98

Introduction

L-functions

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