LMFDB - Embedded newform 15.11.c.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(11,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("15.11");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.c (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:	$9.53035879011$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11554 x^{12} + 52224391 x^{10} + 115670558124 x^{8} + 127683454012911 x^{6} + \cdots + 62\!\cdots\!00 $ x^14 + 11554x^12 + 52224391x^10 + 115670558124x^8 + 127683454012911x^6 + 62207430110604450x^4 + 9049402196955729225x^2 + 62911149236536050000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{20}\cdot 5^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.6
Root			$-15.0833i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.11.c.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.3194i q^{2} +(-236.663 + 55.1313i) q^{3} +724.039 q^{4} +1397.54i q^{5} +(954.839 + 4098.86i) q^{6} +2728.90 q^{7} -30275.0i q^{8} +(52970.1 - 26095.1i) q^{9} +O(q^{10})$	\(q-17.3194i q^{2} +(-236.663 + 55.1313i) q^{3} +724.039 q^{4} +1397.54i q^{5} +(954.839 + 4098.86i) q^{6} +2728.90 q^{7} -30275.0i q^{8} +(52970.1 - 26095.1i) q^{9} +24204.6 q^{10} -252561. i q^{11} +(-171353. + 39917.2i) q^{12} +502.829 q^{13} -47262.9i q^{14} +(-77048.3 - 330747. i) q^{15} +217072. q^{16} -2.15380e6i q^{17} +(-451951. - 917409. i) q^{18} +3.98898e6 q^{19} +1.01188e6i q^{20} +(-645831. + 150448. i) q^{21} -4.37420e6 q^{22} +6.75656e6i q^{23} +(1.66910e6 + 7.16497e6i) q^{24} -1.95312e6 q^{25} -8708.69i q^{26} +(-1.10974e7 + 9.09606e6i) q^{27} +1.97583e6 q^{28} -5.46532e6i q^{29} +(-5.72834e6 + 1.33443e6i) q^{30} +1.48229e7 q^{31} -3.47611e7i q^{32} +(1.39240e7 + 5.97719e7i) q^{33} -3.73025e7 q^{34} +3.81375e6i q^{35} +(3.83524e7 - 1.88939e7i) q^{36} +1.82670e7 q^{37} -6.90867e7i q^{38} +(-119001. + 27721.6i) q^{39} +4.23105e7 q^{40} -1.19846e8i q^{41} +(2.60566e6 + 1.11854e7i) q^{42} -1.16430e8 q^{43} -1.82864e8i q^{44} +(3.64690e7 + 7.40280e7i) q^{45} +1.17019e8 q^{46} -3.35443e7i q^{47} +(-5.13730e7 + 1.19675e7i) q^{48} -2.75028e8 q^{49} +3.38269e7i q^{50} +(1.18742e8 + 5.09726e8i) q^{51} +364068. q^{52} +1.31833e8i q^{53} +(1.57538e8 + 1.92201e8i) q^{54} +3.52964e8 q^{55} -8.26173e7i q^{56} +(-9.44045e8 + 2.19917e8i) q^{57} -9.46560e7 q^{58} +5.93333e8i q^{59} +(-5.57859e7 - 2.39474e8i) q^{60} +1.26724e9 q^{61} -2.56724e8i q^{62} +(1.44550e8 - 7.12109e7i) q^{63} -3.79759e8 q^{64} +702725. i q^{65} +(1.03521e9 - 2.41155e8i) q^{66} -2.41532e9 q^{67} -1.55944e9i q^{68} +(-3.72498e8 - 1.59903e9i) q^{69} +6.60519e7 q^{70} +2.75053e9i q^{71} +(-7.90028e8 - 1.60367e9i) q^{72} +1.71428e9 q^{73} -3.16372e8i q^{74} +(4.62233e8 - 1.07678e8i) q^{75} +2.88818e9 q^{76} -6.89213e8i q^{77} +(480121. + 2.06103e6i) q^{78} -1.62914e9 q^{79} +3.03368e8i q^{80} +(2.12488e9 - 2.76452e9i) q^{81} -2.07566e9 q^{82} +9.06922e8i q^{83} +(-4.67606e8 + 1.08930e8i) q^{84} +3.01003e9 q^{85} +2.01649e9i q^{86} +(3.01310e8 + 1.29344e9i) q^{87} -7.64627e9 q^{88} +5.65950e9i q^{89} +(1.28212e9 - 6.31621e8i) q^{90} +1.37217e6 q^{91} +4.89201e9i q^{92} +(-3.50805e9 + 8.17207e8i) q^{93} -5.80966e8 q^{94} +5.57477e9i q^{95} +(1.91642e9 + 8.22668e9i) q^{96} -2.30869e9 q^{97} +4.76332e9i q^{98} +(-6.59060e9 - 1.33782e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) $ 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	17.3194i		−	0.541231i	−0.962688	−	0.270615i	$-0.912773\pi$
$2$		−	17.3194i		−	0.541231i	0.962688	−	0.270615i	$-0.0872272\pi$
$3$	−236.663	+	55.1313i	−0.973923	+	0.226878i
$3$	−236.663	+	55.1313i	−0.973923	+	0.226878i
$4$	724.039			0.707069
$5$			1397.54i			0.447214i
$5$			1397.54i			0.447214i
$6$	954.839	+	4098.86i	0.122793	+	0.527117i
$7$	2728.90			0.162367			0.0811834	−	0.996699i	$-0.474130\pi$
$7$	2728.90			0.162367			0.0811834	+	0.996699i	$0.474130\pi$
$8$		−	30275.0i		−	0.923918i
$9$	52970.1	−	26095.1i	0.897053	−	0.441923i
$10$	24204.6			0.242046
$11$		−	252561.i		−	1.56820i	−0.620632	−	0.784102i	$-0.713124\pi$
$11$		−	252561.i		−	1.56820i	0.620632	−	0.784102i	$-0.286876\pi$
$12$	−171353.	+	39917.2i	−0.688631	+	0.160418i
$13$	502.829			0.00135427			0.000677133	−	1.00000i	$-0.499784\pi$
$13$	502.829			0.00135427			0.000677133		1.00000i	$0.499784\pi$
$14$		−	47262.9i		−	0.0878779i
$15$	−77048.3	−	330747.i	−0.101463	−	0.435552i
$16$	217072.			0.207016
$17$		−	2.15380e6i		−	1.51691i	−0.651723	−	0.758457i	$-0.725954\pi$
$17$		−	2.15380e6i		−	1.51691i	0.651723	−	0.758457i	$-0.274046\pi$
$18$	−451951.	−	917409.i	−0.239182	−	0.485513i
$19$	3.98898e6			1.61099			0.805497	−	0.592600i	$-0.201899\pi$
$19$	3.98898e6			1.61099			0.805497	+	0.592600i	$0.201899\pi$
$20$			1.01188e6i			0.316211i
$21$	−645831.	+	150448.i	−0.158133	+	0.0368374i
$22$	−4.37420e6			−0.848760
$23$			6.75656e6i			1.04975i	0.851179	+	0.524876i	$0.175888\pi$
$23$			6.75656e6i			1.04975i	−0.851179	+	0.524876i	$0.824112\pi$
$24$	1.66910e6	+	7.16497e6i	0.209616	+	0.899826i
$25$	−1.95312e6			−0.200000
$26$		−	8708.69i		−	0.000732970i
$27$	−1.10974e7	+	9.09606e6i	−0.773399	+	0.633920i
$28$	1.97583e6			0.114805
$29$		−	5.46532e6i		−	0.266456i	−0.991085	−	0.133228i	$-0.957466\pi$
$29$		−	5.46532e6i		−	0.266456i	0.991085	−	0.133228i	$-0.0425343\pi$
$30$	−5.72834e6	+	1.33443e6i	−0.235734	+	0.0549148i
$31$	1.48229e7			0.517757			0.258878	−	0.965910i	$-0.416647\pi$
$31$	1.48229e7			0.517757			0.258878	+	0.965910i	$0.416647\pi$
$32$		−	3.47611e7i		−	1.03596i
$33$	1.39240e7	+	5.97719e7i	0.355790	+	1.52731i
$34$	−3.73025e7			−0.821001
$35$			3.81375e6i			0.0726127i
$36$	3.83524e7	−	1.88939e7i	0.634279	−	0.312470i
$37$	1.82670e7			0.263425			0.131713	−	0.991288i	$-0.457952\pi$
$37$	1.82670e7			0.263425			0.131713	+	0.991288i	$0.457952\pi$
$38$		−	6.90867e7i		−	0.871919i
$39$	−119001.	+	27721.6i	−0.00131895	+	0.000307252i
$40$	4.23105e7			0.413189
$41$		−	1.19846e8i		−	1.03444i	−0.855853	−	0.517218i	$-0.826967\pi$
$41$		−	1.19846e8i		−	1.03444i	0.855853	−	0.517218i	$-0.173033\pi$
$42$	2.60566e6	+	1.11854e7i	0.0199375	+	0.0855864i
$43$	−1.16430e8			−0.791994			−0.395997	−	0.918252i	$-0.629601\pi$
$43$	−1.16430e8			−0.791994			−0.395997	+	0.918252i	$0.629601\pi$
$44$		−	1.82864e8i		−	1.10883i
$45$	3.64690e7	+	7.40280e7i	0.197634	+	0.401174i
$46$	1.17019e8			0.568158
$47$		−	3.35443e7i		−	0.146261i	−0.997322	−	0.0731306i	$-0.976701\pi$
$47$		−	3.35443e7i		−	0.146261i	0.997322	−	0.0731306i	$-0.0232990\pi$
$48$	−5.13730e7	+	1.19675e7i	−0.201618	+	0.0469673i
$49$	−2.75028e8			−0.973637
$50$			3.38269e7i			0.108246i
$51$	1.18742e8	+	5.09726e8i	0.344154	+	1.47736i
$52$	364068.			0.000957559
$53$			1.31833e8i			0.315243i	0.987500	+	0.157621i	$0.0503825\pi$
$53$			1.31833e8i			0.315243i	−0.987500	+	0.157621i	$0.949617\pi$
$54$	1.57538e8	+	1.92201e8i	0.343097	+	0.418587i
$55$	3.52964e8			0.701322
$56$		−	8.26173e7i		−	0.150014i
$57$	−9.44045e8	+	2.19917e8i	−1.56898	+	0.365498i
$58$	−9.46560e7			−0.144214
$59$			5.93333e8i			0.829924i	0.909839	+	0.414962i	$0.136205\pi$
$59$			5.93333e8i			0.829924i	−0.909839	+	0.414962i	$0.863795\pi$
$60$	−5.57859e7	−	2.39474e8i	−0.0717412	−	0.307965i
$61$	1.26724e9			1.50041			0.750206	−	0.661204i	$-0.229954\pi$
$61$	1.26724e9			1.50041			0.750206	+	0.661204i	$0.229954\pi$
$62$		−	2.56724e8i		−	0.280226i
$63$	1.44550e8	−	7.12109e7i	0.145652	−	0.0717536i
$64$	−3.79759e8			−0.353678
$65$			702725.i			0.000605646i
$66$	1.03521e9	−	2.41155e8i	0.826627	−	0.192565i
$67$	−2.41532e9			−1.78896			−0.894480	−	0.447107i	$-0.852454\pi$
$67$	−2.41532e9			−1.78896			−0.894480	+	0.447107i	$0.852454\pi$
$68$		−	1.55944e9i		−	1.07256i
$69$	−3.72498e8	−	1.59903e9i	−0.238165	−	1.02238i
$70$	6.60519e7			0.0393002
$71$			2.75053e9i			1.52449i	0.647289	+	0.762244i	$0.275903\pi$
$71$			2.75053e9i			1.52449i	−0.647289	+	0.762244i	$0.724097\pi$
$72$	−7.90028e8	−	1.60367e9i	−0.408301	−	0.828804i
$73$	1.71428e9			0.826930			0.413465	−	0.910520i	$-0.364318\pi$
$73$	1.71428e9			0.826930			0.413465	+	0.910520i	$0.364318\pi$
$74$		−	3.16372e8i		−	0.142574i
$75$	4.62233e8	−	1.07678e8i	0.194785	−	0.0453755i
$76$	2.88818e9			1.13908
$77$		−	6.89213e8i		−	0.254624i
$78$	480121.	+	2.06103e6i	0.000166294	+	0.000713857i
$79$	−1.62914e9			−0.529446			−0.264723	−	0.964324i	$-0.585281\pi$
$79$	−1.62914e9			−0.529446			−0.264723	+	0.964324i	$0.585281\pi$
$80$			3.03368e8i			0.0925805i
$81$	2.12488e9	−	2.76452e9i	0.609409	−	0.792856i
$82$	−2.07566e9			−0.559869
$83$			9.06922e8i			0.230239i	0.993352	+	0.115120i	$0.0367252\pi$
$83$			9.06922e8i			0.230239i	−0.993352	+	0.115120i	$0.963275\pi$
$84$	−4.67606e8	+	1.08930e8i	−0.111811	+	0.0260466i
$85$	3.01003e9			0.678385
$86$			2.01649e9i			0.428652i
$87$	3.01310e8	+	1.29344e9i	0.0604529	+	0.259508i
$88$	−7.64627e9			−1.44889
$89$			5.65950e9i			1.01351i	0.862090	+	0.506755i	$0.169155\pi$
$89$			5.65950e9i			1.01351i	−0.862090	+	0.506755i	$0.830845\pi$
$90$	1.28212e9	−	6.31621e8i	0.217128	−	0.106966i
$91$	1.37217e6			0.000219888
$92$			4.89201e9i			0.742247i
$93$	−3.50805e9	+	8.17207e8i	−0.504255	+	0.117467i
$94$	−5.80966e8			−0.0791611
$95$			5.57477e9i			0.720458i
$96$	1.91642e9	+	8.22668e9i	0.235037	+	1.00895i
$97$	−2.30869e9			−0.268849			−0.134424	−	0.990924i	$-0.542919\pi$
$97$	−2.30869e9			−0.268849			−0.134424	+	0.990924i	$0.542919\pi$
$98$			4.76332e9i			0.526962i
$99$	−6.59060e9	−	1.33782e10i	−0.693025	−	1.40676i
$100$	−1.41414e9			−0.141414
$101$		−	1.78514e10i		−	1.69850i	−0.527992	−	0.849249i	$-0.677055\pi$
$101$		−	1.78514e10i		−	1.69850i	0.527992	−	0.849249i	$-0.322945\pi$
$102$	8.82814e9	−	2.05653e9i	0.799592	−	0.186267i
$103$	1.60104e10			1.38107			0.690534	−	0.723300i	$-0.257376\pi$
$103$	1.60104e10			1.38107			0.690534	+	0.723300i	$0.257376\pi$
$104$		−	1.52231e7i		−	0.00125123i
$105$	−2.10257e8	−	9.02576e8i	−0.0164742	−	0.0707192i
$106$	2.28327e9			0.170619
$107$		−	8.97566e9i		−	0.639952i	−0.947426	−	0.319976i	$-0.896325\pi$
$107$		−	8.97566e9i		−	0.639952i	0.947426	−	0.319976i	$-0.103675\pi$
$108$	−8.03497e9	+	6.58590e9i	−0.546846	+	0.448225i
$109$	9.38320e9			0.609844			0.304922	−	0.952377i	$-0.401370\pi$
$109$	9.38320e9			0.609844			0.304922	+	0.952377i	$0.401370\pi$
$110$		−	6.11313e9i		−	0.379577i
$111$	−4.32312e9	+	1.00708e9i	−0.256556	+	0.0597653i
$112$	5.92368e8			0.0336126
$113$		−	1.57656e10i		−	0.855691i	−0.903852	−	0.427846i	$-0.859273\pi$
$113$		−	1.57656e10i		−	0.855691i	0.903852	−	0.427846i	$-0.140727\pi$
$114$	3.80883e9	+	1.63503e10i	0.197819	+	0.849182i
$115$	−9.44258e9			−0.469463
$116$		−	3.95710e9i		−	0.188403i
$117$	2.66349e7	−	1.31214e7i	0.00121485	−	0.000598481i
$118$	1.02762e10			0.449181
$119$		−	5.87751e9i		−	0.246297i
$120$	−1.00134e10	+	2.33263e9i	−0.402414	+	0.0937433i
$121$	−3.78495e10			−1.45926
$122$		−	2.19479e10i		−	0.812069i
$123$	6.60726e9	+	2.83631e10i	0.234691	+	1.00746i
$124$	1.07324e10			0.366090
$125$		−	2.72958e9i		−	0.0894427i
$126$	−1.23333e9	−	2.50352e9i	−0.0388353	−	0.0788312i
$127$	1.16400e10			0.352318			0.176159	−	0.984362i	$-0.443633\pi$
$127$	1.16400e10			0.352318			0.176159	+	0.984362i	$0.443633\pi$
$128$		−	2.90182e10i		−	0.844540i
$129$	2.75547e10	−	6.41892e9i	0.771341	−	0.179686i
$130$	1.21708e7			0.000327794
$131$			2.10936e10i			0.546756i	0.961907	+	0.273378i	$0.0881410\pi$
$131$			2.10936e10i			0.546756i	−0.961907	+	0.273378i	$0.911859\pi$
$132$	1.00815e10	+	4.32772e10i	0.251568	+	1.07991i
$133$	1.08855e10			0.261572
$134$			4.18319e10i			0.968241i
$135$	−1.27121e10	−	1.55091e10i	−0.283498	−	0.345874i
$136$	−6.52062e10			−1.40150
$137$			8.16990e10i			1.69283i	0.532522	+	0.846416i	$0.321244\pi$
$137$			8.16990e10i			1.69283i	−0.532522	+	0.846416i	$0.678756\pi$
$138$	−2.76942e10	+	6.45143e9i	−0.553342	+	0.128902i
$139$	−2.45762e9			−0.0473632			−0.0236816	−	0.999720i	$-0.507539\pi$
$139$	−2.45762e9			−0.0473632			−0.0236816	+	0.999720i	$0.507539\pi$
$140$			2.76131e9i			0.0513422i
$141$	1.84934e9	+	7.93870e9i	0.0331834	+	0.142447i
$142$	4.76374e10			0.825100
$143$		−	1.26995e8i		−	0.00212376i
$144$	1.14983e10	−	5.66452e9i	0.185705	−	0.0914852i
$145$	7.63802e9			0.119163
$146$		−	2.96904e10i		−	0.447560i
$147$	6.50891e10	−	1.51627e10i	0.948248	−	0.220896i
$148$	1.32260e10			0.186260
$149$		−	1.49660e10i		−	0.203786i	−0.994795	−	0.101893i	$-0.967510\pi$
$149$		−	1.49660e10i		−	0.203786i	0.994795	−	0.101893i	$-0.0324900\pi$
$150$	−1.86492e9	−	8.00559e9i	−0.0245586	−	0.105423i
$151$	−1.01136e11			−1.28831			−0.644156	−	0.764895i	$-0.722791\pi$
$151$	−1.01136e11			−1.28831			−0.644156	+	0.764895i	$0.722791\pi$
$152$		−	1.20766e11i		−	1.48843i
$153$	−5.62036e10	−	1.14087e11i	−0.670359	−	1.36075i
$154$	−1.19367e10			−0.137811
$155$			2.07157e10i			0.231548i
$156$	−8.61615e7	+	2.00715e7i	−0.000932589	+	0.000217249i
$157$	9.03124e10			0.946780			0.473390	−	0.880853i	$-0.343030\pi$
$157$	9.03124e10			0.946780			0.473390	+	0.880853i	$0.343030\pi$
$158$			2.82156e10i			0.286553i
$159$	−7.26812e9	−	3.12001e10i	−0.0715215	−	0.307022i
$160$	4.85801e10			0.463296
$161$			1.84380e10i			0.170445i
$162$	−4.78798e10	−	3.68015e10i	−0.429118	−	0.329831i
$163$	1.08732e11			0.944970			0.472485	−	0.881339i	$-0.343357\pi$
$163$	1.08732e11			0.944970			0.472485	+	0.881339i	$0.343357\pi$
$164$		−	8.67731e10i		−	0.731418i
$165$	−8.35338e10	+	1.94594e10i	−0.683034	+	0.159114i
$166$	1.57073e10			0.124613
$167$			2.17220e11i			1.67231i	0.548494	+	0.836155i	$0.315201\pi$
$167$			2.17220e11i			1.67231i	−0.548494	+	0.836155i	$0.684799\pi$
$168$	4.55480e9	+	1.95525e10i	0.0340348	+	0.146102i
$169$	−1.37858e11			−0.999998
$170$		−	5.21318e10i		−	0.367163i
$171$	2.11297e11	−	1.04093e11i	1.44515	−	0.711935i
$172$	−8.42997e10			−0.559995
$173$			1.78617e11i			1.15264i	0.817225	+	0.576318i	$0.195511\pi$
$173$			1.78617e11i			1.15264i	−0.817225	+	0.576318i	$0.804489\pi$
$174$	2.24016e10	−	5.21850e9i	0.140454	−	0.0327190i
$175$	−5.32988e9			−0.0324734
$176$		−	5.48239e10i		−	0.324644i
$177$	−3.27112e10	−	1.40420e11i	−0.188291	−	0.808283i
$178$	9.80190e10			0.548543
$179$			1.93932e11i			1.05532i	0.849455	+	0.527661i	$0.176931\pi$
$179$			1.93932e11i			1.05532i	−0.849455	+	0.527661i	$0.823069\pi$
$180$	2.64050e10	+	5.35991e10i	0.139741	+	0.283658i
$181$	1.21857e11			0.627277			0.313638	−	0.949543i	$-0.398452\pi$
$181$	1.21857e11			0.627277			0.313638	+	0.949543i	$0.398452\pi$
$182$		−	2.37651e7i		−	0.000119010i
$183$	−2.99910e11	+	6.98647e10i	−1.46129	+	0.340410i
$184$	2.04555e11			0.969885
$185$			2.55288e10i			0.117807i
$186$	1.41535e10	+	6.07572e10i	0.0635770	+	0.272919i
$187$	−5.43966e11			−2.37883
$188$		−	2.42874e10i		−	0.103417i
$189$	−3.02838e10	+	2.48222e10i	−0.125574	+	0.102928i
$190$	9.65516e10			0.389934
$191$			3.44967e11i			1.35710i	0.734556	+	0.678548i	$0.237390\pi$
$191$			3.44967e11i			1.35710i	−0.734556	+	0.678548i	$0.762610\pi$
$192$	8.98751e10	−	2.09366e10i	0.344455	−	0.0802417i
$193$	2.27955e11			0.851259			0.425630	−	0.904897i	$-0.360053\pi$
$193$	2.27955e11			0.851259			0.425630	+	0.904897i	$0.360053\pi$
$194$			3.99852e10i			0.145509i
$195$	−3.87421e7	−	1.66309e8i	−0.000137407	−	0.000589853i
$196$	−1.99131e11			−0.688429
$197$		−	4.87641e11i		−	1.64350i	−0.569849	−	0.821750i	$-0.692998\pi$
$197$		−	4.87641e11i		−	1.64350i	0.569849	−	0.821750i	$-0.307002\pi$
$198$	−2.31702e11	+	1.14145e11i	−0.761383	+	0.375086i
$199$	−1.17188e11			−0.375505			−0.187753	−	0.982216i	$-0.560120\pi$
$199$	−1.17188e11			−0.375505			−0.187753	+	0.982216i	$0.560120\pi$
$200$			5.91308e10i			0.184784i
$201$	5.71618e11	−	1.33160e11i	1.74231	−	0.405875i
$202$	−3.09175e11			−0.919280
$203$		−	1.49143e10i		−	0.0432636i
$204$	8.59737e10	+	3.69061e11i	0.243341	+	1.04459i
$205$	1.67490e11			0.462614
$206$		−	2.77289e11i		−	0.747476i
$207$	1.76313e11	+	3.57896e11i	0.463909	+	0.941683i
$208$	1.09150e8			0.000280355
$209$		−	1.00746e12i		−	2.52637i
$210$	−1.56321e10	+	3.64152e9i	−0.0382754	+	0.00891634i
$211$	2.99778e11			0.716782			0.358391	−	0.933572i	$-0.383325\pi$
$211$	2.99778e11			0.716782			0.358391	+	0.933572i	$0.383325\pi$
$212$			9.54523e10i			0.222898i
$213$	−1.51640e11	−	6.50949e11i	−0.345872	−	1.48473i
$214$	−1.55453e11			−0.346362
$215$		−	1.62716e11i		−	0.354190i
$216$	2.75383e11	+	3.35974e11i	0.585690	+	0.714557i
$217$	4.04503e10			0.0840665
$218$		−	1.62511e11i		−	0.330066i
$219$	−4.05708e11	+	9.45107e10i	−0.805366	+	0.187612i
$220$	2.55560e11			0.495883
$221$		−	1.08299e9i		−	0.00205430i
$222$	1.74420e10	+	7.48737e10i	0.0323468	+	0.138856i
$223$	8.51304e11			1.54369			0.771845	−	0.635810i	$-0.219334\pi$
$223$	8.51304e11			1.54369			0.771845	+	0.635810i	$0.219334\pi$
$224$		−	9.48596e10i		−	0.168206i
$225$	−1.03457e11	+	5.09670e10i	−0.179411	+	0.0883845i
$226$	−2.73050e11			−0.463126
$227$		−	4.56469e10i		−	0.0757325i	−0.999283	−	0.0378663i	$-0.987944\pi$
$227$		−	4.56469e10i		−	0.0757325i	0.999283	−	0.0378663i	$-0.0120561\pi$
$228$	−6.83526e11	+	1.59229e11i	−1.10938	+	0.258433i
$229$	−7.14042e11			−1.13383			−0.566913	−	0.823778i	$-0.691862\pi$
$229$	−7.14042e11			−1.13383			−0.566913	+	0.823778i	$0.691862\pi$
$230$			1.63540e11i			0.254088i
$231$	3.79972e10	+	1.63112e11i	0.0577686	+	0.247985i
$232$	−1.65462e11			−0.246184
$233$		−	3.98049e10i		−	0.0579638i	−0.999580	−	0.0289819i	$-0.990773\pi$
$233$		−	3.98049e10i		−	0.0579638i	0.999580	−	0.0289819i	$-0.00922652\pi$
$234$	−2.27254e8	−	4.61300e8i	−0.000323916	−	0.000657513i
$235$	4.68796e10			0.0654100
$236$			4.29596e11i			0.586814i
$237$	3.85557e11	−	8.98163e10i	0.515640	−	0.120120i
$238$	−1.01795e11			−0.133303
$239$			1.14739e12i			1.47136i	0.677327	+	0.735682i	$0.263138\pi$
$239$			1.14739e12i			1.47136i	−0.677327	+	0.735682i	$0.736862\pi$
$240$	−1.67250e10	−	7.17960e10i	−0.0210044	−	0.0901663i
$241$	−7.01041e11			−0.862299			−0.431150	−	0.902280i	$-0.641892\pi$
$241$	−7.01041e11			−0.862299			−0.431150	+	0.902280i	$0.641892\pi$
$242$			6.55531e11i			0.789798i
$243$	−3.50469e11	+	7.71407e11i	−0.413636	+	0.910442i
$244$	9.17533e11			1.06090
$245$		−	3.84364e11i		−	0.435424i
$246$	4.91232e11	−	1.14434e11i	0.545269	−	0.127022i
$247$	2.00578e9			0.00218171
$248$		−	4.48764e11i		−	0.478365i
$249$	−4.99998e10	−	2.14635e11i	−0.0522362	−	0.224236i
$250$	−4.72746e10			−0.0484092
$251$		−	9.87694e10i		−	0.0991411i	−0.998771	−	0.0495705i	$-0.984215\pi$
$251$		−	9.87694e10i		−	0.0991411i	0.998771	−	0.0495705i	$-0.0157853\pi$
$252$	1.04660e11	−	5.15595e10i	0.102986	−	0.0507348i
$253$	1.70644e12			1.64622
$254$		−	2.01598e11i		−	0.190685i
$255$	−7.12363e11	+	1.65947e11i	−0.660695	+	0.153910i
$256$	−8.91450e11			−0.810769
$257$			1.92931e11i			0.172082i	0.996292	+	0.0860410i	$0.0274216\pi$
$257$			1.92931e11i			0.172082i	−0.996292	+	0.0860410i	$0.972578\pi$
$258$	−1.11172e11	−	4.77230e11i	−0.0972514	−	0.417474i
$259$	4.98487e10			0.0427715
$260$			5.08800e8i			0.000428234i
$261$	−1.42618e11	−	2.89499e11i	−0.117753	−	0.239025i
$262$	3.65328e11			0.295921
$263$			1.02842e12i			0.817316i	0.912688	+	0.408658i	$0.134003\pi$
$263$			1.02842e12i			0.817316i	−0.912688	+	0.408658i	$0.865997\pi$
$264$	1.80959e12	−	4.21548e11i	1.41111	−	0.328721i
$265$	−1.84242e11			−0.140981
$266$		−	1.88531e11i		−	0.141571i
$267$	−3.12015e11	−	1.33940e12i	−0.229943	−	0.987081i
$268$	−1.74879e12			−1.26492
$269$		−	6.57159e10i		−	0.0466562i	−0.999728	−	0.0233281i	$-0.992574\pi$
$269$		−	6.57159e10i		−	0.0466562i	0.999728	−	0.0233281i	$-0.00742624\pi$
$270$	−2.68608e11	+	2.20166e11i	−0.187198	+	0.153438i
$271$	−2.45766e12			−1.68142			−0.840709	−	0.541487i	$-0.817862\pi$
$271$	−2.45766e12			−1.68142			−0.840709	+	0.541487i	$0.817862\pi$
$272$		−	4.67530e11i		−	0.314026i
$273$	−3.24742e8	+	7.56495e7i	−0.000214154	+	4.98876e-5i
$274$	1.41498e12			0.916213
$275$			4.93283e11i			0.313641i
$276$	−2.69703e11	−	1.15776e12i	−0.168399	−	0.722892i
$277$	1.41391e12			0.867007			0.433504	−	0.901152i	$-0.357277\pi$
$277$	1.41391e12			0.867007			0.433504	+	0.901152i	$0.357277\pi$
$278$			4.25645e10i			0.0256344i
$279$	7.85172e11	−	3.86806e11i	0.464455	−	0.228809i
$280$	1.15461e11			0.0670882
$281$		−	1.66491e12i		−	0.950298i	−0.879905	−	0.475149i	$-0.842394\pi$
$281$		−	1.66491e12i		−	0.950298i	0.879905	−	0.475149i	$-0.157606\pi$
$282$	1.37493e11	−	3.20294e10i	0.0770968	−	0.0179599i
$283$	1.74467e12			0.961126			0.480563	−	0.876960i	$-0.340432\pi$
$283$	1.74467e12			0.961126			0.480563	+	0.876960i	$0.340432\pi$
$284$			1.99149e12i			1.07792i
$285$	−3.07344e11	−	1.31934e12i	−0.163456	−	0.701671i
$286$	−2.19947e9			−0.00114945
$287$		−	3.27047e11i		−	0.167958i
$288$	−9.07095e11	−	1.84130e12i	−0.457815	−	0.929313i
$289$	−2.62287e12			−1.30103
$290$		−	1.32286e11i		−	0.0644946i
$291$	5.46383e11	−	1.27281e11i	0.261838	−	0.0609957i
$292$	1.24121e12			0.584697
$293$			1.62195e12i			0.751104i	0.926801	+	0.375552i	$0.122547\pi$
$293$			1.62195e12i			0.751104i	−0.926801	+	0.375552i	$0.877453\pi$
$294$	−2.62608e11	−	1.12730e12i	−0.119556	−	0.513221i
$295$	−8.29208e11			−0.371153
$296$		−	5.53031e11i		−	0.243383i
$297$	2.29731e12	+	2.80277e12i	0.994116	+	1.21285i
$298$	−2.59202e11			−0.110295
$299$			3.39740e9i			0.00142164i
$300$	3.34675e11	−	7.79632e10i	0.137726	−	0.0320836i
$301$	−3.17725e11			−0.128594
$302$			1.75161e12i			0.697274i
$303$	9.84170e11	+	4.22477e12i	0.385351	+	1.65421i
$304$	8.65897e11			0.333502
$305$			1.77103e12i			0.671005i
$306$	−1.97592e12	+	9.73413e11i	−0.736481	+	0.362819i
$307$	4.14443e11			0.151975			0.0759877	−	0.997109i	$-0.475789\pi$
$307$	4.14443e11			0.151975			0.0759877	+	0.997109i	$0.475789\pi$
$308$		−	4.99017e11i		−	0.180037i
$309$	−3.78906e12	+	8.82671e11i	−1.34505	+	0.313333i
$310$	3.58783e11			0.125321
$311$			3.84304e12i			1.32091i	0.750866	+	0.660455i	$0.229637\pi$
$311$			3.84304e12i			1.32091i	−0.750866	+	0.660455i	$0.770363\pi$
$312$	8.39270e8	+	3.60276e9i	0.000283876	+	0.00121860i
$313$	1.13398e12			0.377472			0.188736	−	0.982028i	$-0.439561\pi$
$313$	1.13398e12			0.377472			0.188736	+	0.982028i	$0.439561\pi$
$314$		−	1.56416e12i		−	0.512427i
$315$	9.95203e10	+	2.02015e11i	0.0320892	+	0.0651374i
$316$	−1.17956e12			−0.374355
$317$		−	1.47442e12i		−	0.460601i	−0.973120	−	0.230300i	$-0.926029\pi$
$317$		−	1.47442e12i		−	0.460601i	0.973120	−	0.230300i	$-0.0739709\pi$
$318$	−5.40366e11	+	1.25879e11i	−0.166170	+	0.0387096i
$319$	−1.38033e12			−0.417858
$320$		−	5.30730e11i		−	0.158170i
$321$	4.94839e11	+	2.12421e12i	0.145191	+	0.623264i
$322$	3.19334e11			0.0922500
$323$		−	8.59147e12i		−	2.44374i
$324$	1.53849e12	−	2.00162e12i	0.430894	−	0.560604i
$325$	−9.82088e8			−0.000270853
$326$		−	1.88317e12i		−	0.511447i
$327$	−2.22066e12	+	5.17308e11i	−0.593941	+	0.138360i
$328$	−3.62833e12			−0.955735
$329$		−	9.15390e10i		−	0.0237480i
$330$	3.37024e11	+	1.44675e12i	0.0861175	+	0.369679i
$331$	5.62796e12			1.41648			0.708241	−	0.705970i	$-0.249489\pi$
$331$	5.62796e12			1.41648			0.708241	+	0.705970i	$0.249489\pi$
$332$			6.56647e11i			0.162795i
$333$	9.67602e11	−	4.76678e11i	0.236306	−	0.116414i
$334$	3.76211e12			0.905105
$335$		−	3.37551e12i		−	0.800048i
$336$	−1.40192e11	+	3.26580e10i	−0.0327361	+	0.00762594i
$337$	−2.79776e12			−0.643667			−0.321834	−	0.946796i	$-0.604299\pi$
$337$	−2.79776e12			−0.643667			−0.321834	+	0.946796i	$0.604299\pi$
$338$			2.38762e12i			0.541230i
$339$	8.69175e11	+	3.73113e12i	0.194137	+	0.833378i
$340$	2.17938e12			0.479665
$341$		−	3.74369e12i		−	0.811948i
$342$	−1.80282e12	−	3.65953e12i	−0.385321	−	0.782158i
$343$	−1.52137e12			−0.320453
$344$			3.52491e12i			0.731738i
$345$	2.23471e12	−	5.20581e11i	0.457221	−	0.106511i
$346$	3.09354e12			0.623842
$347$		−	3.02026e12i		−	0.600339i	−0.953886	−	0.300170i	$-0.902957\pi$
$347$		−	3.02026e12i		−	0.600339i	0.953886	−	0.300170i	$-0.0970432\pi$
$348$	2.18160e11	+	9.36502e11i	0.0427444	+	0.183490i
$349$	9.69296e11			0.187210			0.0936050	−	0.995609i	$-0.470161\pi$
$349$	9.69296e11			0.187210			0.0936050	+	0.995609i	$0.470161\pi$
$350$			9.23103e10i			0.0175756i
$351$	−5.58011e9	+	4.57376e9i	−0.00104739	+	0.000858496i
$352$	−8.77930e12			−1.62460
$353$		−	1.78243e12i		−	0.325191i	−0.986693	−	0.162596i	$-0.948013\pi$
$353$		−	1.78243e12i		−	0.325191i	0.986693	−	0.162596i	$-0.0519866\pi$
$354$	−2.43199e12	+	5.66538e11i	−0.437467	+	0.101909i
$355$	−3.84398e12			−0.681772
$356$			4.09770e12i			0.716622i
$357$	3.24034e11	+	1.39099e12i	0.0558792	+	0.239874i
$358$	3.35879e12			0.571172
$359$		−	8.72597e12i		−	1.46333i	−0.681666	−	0.731664i	$-0.738744\pi$
$359$		−	8.72597e12i		−	1.46333i	0.681666	−	0.731664i	$-0.261256\pi$
$360$	2.24119e12	−	1.10410e12i	0.370652	−	0.182598i
$361$	9.78089e12			1.59530
$362$		−	2.11050e12i		−	0.339501i
$363$	8.95760e12	−	2.08669e12i	1.42121	−	0.331074i
$364$	9.93505e8			0.000155476
$365$			2.39579e12i			0.369814i
$366$	1.21001e12	+	5.19425e12i	0.184240	+	0.790893i
$367$	−6.36102e12			−0.955425			−0.477713	−	0.878516i	$-0.658534\pi$
$367$	−6.36102e12			−0.955425			−0.477713	+	0.878516i	$0.658534\pi$
$368$			1.46666e12i			0.217316i
$369$	−3.12739e12	−	6.34825e12i	−0.457141	−	0.927945i
$370$	4.42144e11			0.0637610
$371$			3.59759e11i			0.0511850i
$372$	−2.53996e12	+	5.91690e11i	−0.356543	+	0.0830576i
$373$	−1.33337e13			−1.84675			−0.923375	−	0.383899i	$-0.874581\pi$
$373$	−1.33337e13			−1.84675			−0.923375	+	0.383899i	$0.874581\pi$
$374$			9.42115e12i			1.28750i
$375$	1.50485e11	+	6.45990e11i	0.0202925	+	0.0871103i
$376$	−1.01555e12			−0.135133
$377$		−	2.74812e9i		−	0.000360852i
$378$	4.29906e11	+	5.24496e11i	0.0557076	+	0.0679647i
$379$	−4.17384e12			−0.533753			−0.266876	−	0.963731i	$-0.585992\pi$
$379$	−4.17384e12			−0.533753			−0.266876	+	0.963731i	$0.585992\pi$
$380$			4.03635e12i			0.509414i
$381$	−2.75476e12	+	6.41728e11i	−0.343131	+	0.0799330i
$382$	5.97461e12			0.734502
$383$			1.38161e13i			1.67645i	0.545323	+	0.838226i	$0.316407\pi$
$383$			1.38161e13i			1.67645i	−0.545323	+	0.838226i	$0.683593\pi$
$384$	1.59981e12	+	6.86754e12i	0.191607	+	0.822518i
$385$	9.63205e11			0.113871
$386$		−	3.94803e12i		−	0.460728i
$387$	−6.16730e12	+	3.03825e12i	−0.710461	+	0.350000i
$388$	−1.67158e12			−0.190095
$389$		−	1.52600e12i		−	0.171320i	−0.996324	−	0.0856599i	$-0.972700\pi$
$389$		−	1.52600e12i		−	0.171320i	0.996324	−	0.0856599i	$-0.0272998\pi$
$390$	−2.88037e9	+	6.70990e8i	−0.000319246	+	7.43691e-5i
$391$	1.45523e13			1.59238
$392$			8.32647e12i			0.899561i
$393$	−1.16291e12	−	4.99207e12i	−0.124047	−	0.532498i
$394$	−8.44565e12			−0.889512
$395$		−	2.27679e12i		−	0.236776i
$396$	−4.77185e12	−	9.68632e12i	−0.490017	−	0.994678i
$397$	1.42387e13			1.44384			0.721920	−	0.691977i	$-0.243260\pi$
$397$	1.42387e13			1.44384			0.721920	+	0.691977i	$0.243260\pi$
$398$			2.02962e12i			0.203235i
$399$	−2.57621e12	+	6.00133e11i	−0.254751	+	0.0593448i
$400$	−4.23969e11			−0.0414032
$401$			1.57377e13i			1.51781i	0.651198	+	0.758907i	$0.274267\pi$
$401$			1.57377e13i			1.51781i	−0.651198	+	0.758907i	$0.725733\pi$
$402$	−2.30624e12	−	9.90007e12i	−0.219672	−	0.942992i
$403$	7.45341e9			0.000701180
$404$		−	1.29251e13i		−	1.20096i
$405$	3.86353e12	+	2.96960e12i	0.354576	+	0.272536i
$406$	−2.58307e11			−0.0234156
$407$		−	4.61352e12i		−	0.413105i
$408$	1.54319e13	−	3.59490e12i	1.36496	−	0.317970i
$409$	−1.84735e12			−0.161411			−0.0807054	−	0.996738i	$-0.525717\pi$
$409$	−1.84735e12			−0.161411			−0.0807054	+	0.996738i	$0.525717\pi$
$410$		−	2.90082e12i		−	0.250381i
$411$	−4.50417e12	−	1.93352e13i	−0.384066	−	1.64869i
$412$	1.15921e13			0.976510
$413$			1.61915e12i			0.134752i
$414$	6.19853e12	−	3.05363e12i	0.509668	−	0.251082i
$415$	−1.26746e12			−0.102966
$416$		−	1.74789e10i		−	0.00140297i
$417$	5.81630e11	−	1.35492e11i	0.0461282	−	0.0107457i
$418$	−1.74486e13			−1.36735
$419$			1.04625e12i			0.0810153i	0.999179	+	0.0405076i	$0.0128975\pi$
$419$			1.04625e12i			0.0810153i	−0.999179	+	0.0405076i	$0.987102\pi$
$420$	−1.52234e11	−	6.53500e11i	−0.0116484	−	0.0500033i
$421$	−7.81960e12			−0.591254			−0.295627	−	0.955303i	$-0.595529\pi$
$421$	−7.81960e12			−0.591254			−0.295627	+	0.955303i	$0.595529\pi$
$422$		−	5.19197e12i		−	0.387945i
$423$	−8.75341e11	−	1.77684e12i	−0.0646362	−	0.131204i
$424$	3.99124e12			0.291259
$425$			4.20664e12i			0.303383i
$426$	−1.12740e13	+	2.62631e12i	−0.803584	+	0.187197i
$427$	3.45818e12			0.243617
$428$		−	6.49873e12i		−	0.452490i
$429$	7.00139e9	+	3.00551e10i	0.000481835	+	0.00206838i
$430$	−2.81813e12			−0.191699
$431$		−	8.23898e12i		−	0.553971i	−0.960874	−	0.276985i	$-0.910665\pi$
$431$		−	8.23898e12i		−	0.553971i	0.960874	−	0.276985i	$-0.0893354\pi$
$432$	−2.40894e12	+	1.97450e12i	−0.160106	+	0.131232i
$433$	−2.49973e12			−0.164231			−0.0821153	−	0.996623i	$-0.526168\pi$
$433$	−2.49973e12			−0.164231			−0.0821153	+	0.996623i	$0.526168\pi$
$434$		−	7.00574e11i		−	0.0454994i
$435$	−1.80764e12	+	4.21094e11i	−0.116055	+	0.0270354i
$436$	6.79380e12			0.431202
$437$			2.69518e13i			1.69114i
$438$	1.63687e12	+	7.02662e12i	0.101541	+	0.435889i
$439$	2.88715e13			1.77071			0.885354	−	0.464918i	$-0.153916\pi$
$439$	2.88715e13			1.77071			0.885354	+	0.464918i	$0.153916\pi$
$440$		−	1.06860e13i		−	0.647964i
$441$	−1.45683e13	+	7.17689e12i	−0.873404	+	0.430272i
$442$	−1.87568e10			−0.00111185
$443$		−	1.51173e13i		−	0.886045i	−0.896511	−	0.443022i	$-0.853906\pi$
$443$		−	1.51173e13i		−	0.886045i	0.896511	−	0.443022i	$-0.146094\pi$
$444$	−3.13011e12	+	7.29165e11i	−0.181403	+	0.0422582i
$445$	−7.90939e12			−0.453255
$446$		−	1.47441e13i		−	0.835493i
$447$	8.25095e11	+	3.54191e12i	0.0462345	+	0.198472i
$448$	−1.03632e12			−0.0574256
$449$			1.74559e13i			0.956559i	0.878208	+	0.478279i	$0.158739\pi$
$449$			1.74559e13i			0.956559i	−0.878208	+	0.478279i	$0.841261\pi$
$450$	8.82717e11	+	1.79182e12i	0.0478364	+	0.0971025i
$451$	−3.02684e13			−1.62221
$452$		−	1.14149e13i		−	0.605033i
$453$	2.39352e13	−	5.57575e12i	1.25472	−	0.292289i
$454$	−7.90577e11			−0.0409888
$455$			1.91767e9i			9.83368e-5i
$456$	6.65799e12	+	2.85809e13i	0.337691	+	1.44961i
$457$	4.61881e12			0.231713			0.115856	−	0.993266i	$-0.463039\pi$
$457$	4.61881e12			0.231713			0.115856	+	0.993266i	$0.463039\pi$
$458$			1.23668e13i			0.613661i
$459$	1.95911e13	+	2.39016e13i	0.961602	+	1.17318i
$460$	−6.83680e12			−0.331943
$461$			1.22996e13i			0.590726i	0.955385	+	0.295363i	$0.0954405\pi$
$461$			1.22996e13i			0.590726i	−0.955385	+	0.295363i	$0.904559\pi$
$462$	2.82499e12	−	6.58088e11i	0.134217	−	0.0312661i
$463$	−1.75194e12			−0.0823405			−0.0411703	−	0.999152i	$-0.513109\pi$
$463$	−1.75194e12			−0.0823405			−0.0411703	+	0.999152i	$0.513109\pi$
$464$		−	1.18637e12i		−	0.0551607i
$465$	−1.14208e12	−	4.90264e12i	−0.0525330	−	0.225510i
$466$	−6.89396e11			−0.0313718
$467$		−	1.94574e13i		−	0.875991i	−0.898977	−	0.437996i	$-0.855689\pi$
$467$		−	1.94574e13i		−	0.875991i	0.898977	−	0.437996i	$-0.144311\pi$
$468$	1.92847e10	−	9.50039e9i	0.000858982	−	0.000423167i
$469$	−6.59117e12			−0.290468
$470$		−	8.11925e11i		−	0.0354019i
$471$	−2.13736e13	+	4.97904e12i	−0.922091	+	0.214803i
$472$	1.79631e13			0.766782
$473$			2.94056e13i			1.24201i
$474$	−1.55556e12	−	6.67761e12i	−0.0650124	−	0.279080i
$475$	−7.79098e12			−0.322199
$476$		−	4.25554e12i		−	0.174149i
$477$	3.44020e12	+	6.98321e12i	0.139313	+	0.282789i
$478$	1.98720e13			0.796348
$479$		−	2.33156e13i		−	0.924632i	−0.886715	−	0.462316i	$-0.847019\pi$
$479$		−	2.33156e13i		−	0.924632i	0.886715	−	0.462316i	$-0.152981\pi$
$480$	−1.14971e13	+	2.67828e12i	−0.451215	+	0.105112i
$481$	9.18516e9			0.000356748
$482$			1.21416e13i			0.466703i
$483$	−1.01651e12	−	4.36359e12i	−0.0386701	−	0.166000i
$484$	−2.74045e13			−1.03180
$485$		−	3.22650e12i		−	0.120233i
$486$	1.33603e13	+	6.06991e12i	0.492759	+	0.223872i
$487$	−1.40293e13			−0.512144			−0.256072	−	0.966658i	$-0.582428\pi$
$487$	−1.40293e13			−0.512144			−0.256072	+	0.966658i	$0.582428\pi$
$488$		−	3.83657e13i		−	1.38626i
$489$	−2.57328e13	+	5.99451e12i	−0.920328	+	0.214392i
$490$	−6.65694e12			−0.235665
$491$		−	6.67391e12i		−	0.233869i	−0.993140	−	0.116935i	$-0.962693\pi$
$491$		−	6.67391e12i		−	0.233869i	0.993140	−	0.116935i	$-0.0373068\pi$
$492$	4.78391e12	+	2.05360e13i	0.165942	+	0.712345i
$493$	−1.17712e13			−0.404191
$494$		−	3.47388e10i		−	0.00118081i
$495$	1.86966e13	−	9.21064e12i	0.629123	−	0.309930i
$496$	3.21765e12			0.107184
$497$			7.50591e12i			0.247526i
$498$	−3.71735e12	+	8.65965e11i	−0.121363	+	0.0282718i
$499$	4.66860e13			1.50898			0.754490	−	0.656311i	$-0.227884\pi$
$499$	4.66860e13			1.50898			0.754490	+	0.656311i	$0.227884\pi$
$500$		−	1.97632e12i		−	0.0632422i
$501$	−1.19756e13	−	5.14079e13i	−0.379410	−	1.62870i
$502$	−1.71062e12			−0.0536582
$503$		−	2.75945e13i		−	0.857005i	−0.903541	−	0.428502i	$-0.859041\pi$
$503$		−	2.75945e13i		−	0.857005i	0.903541	−	0.428502i	$-0.140959\pi$
$504$	−2.15591e12	−	4.37625e12i	−0.0662945	−	0.134570i
$505$	2.49481e13			0.759592
$506$		−	2.95545e13i		−	0.890987i
$507$	3.26260e13	−	7.60030e12i	0.973921	−	0.226877i
$508$	8.42782e12			0.249113
$509$		−	1.17378e13i		−	0.343555i	−0.985136	−	0.171777i	$-0.945049\pi$
$509$		−	1.17378e13i		−	0.343555i	0.985136	−	0.171777i	$-0.0549510\pi$
$510$	2.87409e12	+	1.23377e13i	0.0833010	+	0.357588i
$511$	4.67811e12			0.134266
$512$		−	1.42753e13i		−	0.405727i
$513$	−4.42674e13	+	3.62840e13i	−1.24594	+	1.02124i
$514$	3.34144e12			0.0931361
$515$			2.23751e13i			0.617632i
$516$	1.99507e13	−	4.64755e12i	0.545392	−	0.127050i
$517$	−8.47197e12			−0.229367
$518$		−	8.63348e11i		−	0.0231493i
$519$	−9.84738e12	−	4.22721e13i	−0.261507	−	1.12258i
$520$	2.12750e10			0.000559567
$521$			1.40204e13i			0.365235i	0.983184	+	0.182617i	$0.0584570\pi$
$521$			1.40204e13i			0.365235i	−0.983184	+	0.182617i	$0.941543\pi$
$522$	−5.01394e12	+	2.47006e12i	−0.129368	+	0.0637315i
$523$	1.69107e12			0.0432170			0.0216085	−	0.999767i	$-0.493121\pi$
$523$	1.69107e12			0.0432170			0.0216085	+	0.999767i	$0.493121\pi$
$524$			1.52726e13i			0.386594i
$525$	1.26139e12	−	2.93843e11i	0.0316266	−	0.00736748i
$526$	1.78115e13			0.442356
$527$		−	3.19257e13i		−	0.785393i
$528$	3.02251e12	+	1.29748e13i	0.0736544	+	0.316178i
$529$	−4.22461e12			−0.101978
$530$			3.19096e12i			0.0763032i
$531$	1.54831e13	+	3.14289e13i	0.366762	+	0.744486i
$532$	7.88154e12			0.184949
$533$		−	6.02620e10i		−	0.00140090i
$534$	−2.31975e13	+	5.40391e12i	−0.534238	+	0.124452i
$535$	1.25439e13			0.286195
$536$			7.31237e13i			1.65285i
$537$	−1.06917e13	−	4.58966e13i	−0.239429	−	1.02780i
$538$	−1.13816e12			−0.0252518
$539$			6.94614e13i			1.52686i
$540$	−9.20408e12	−	1.12292e13i	−0.200453	−	0.244557i
$541$	1.64911e13			0.355847			0.177924	−	0.984044i	$-0.443062\pi$
$541$	1.64911e13			0.355847			0.177924	+	0.984044i	$0.443062\pi$
$542$			4.25652e13i			0.910035i
$543$	−2.88392e13	+	6.71815e12i	−0.610919	+	0.142315i
$544$	−7.48685e13			−1.57147
$545$			1.31134e13i			0.272730i
$546$	1.31020e9	+	5.62434e9i	2.70007e−5	+	0.000115907i
$547$	−6.50850e13			−1.32906			−0.664529	−	0.747262i	$-0.731368\pi$
$547$	−6.50850e13			−1.32906			−0.664529	+	0.747262i	$0.731368\pi$
$548$			5.91533e13i			1.19695i
$549$	6.71259e13	−	3.30688e13i	1.34595	−	0.663066i
$550$	8.54336e12			0.169752
$551$		−	2.18011e13i		−	0.429259i
$552$	−4.84106e13	+	1.12774e13i	−0.944593	+	0.220045i
$553$	−4.44575e12			−0.0859645
$554$		−	2.44880e13i		−	0.469251i
$555$	−1.40744e12	−	6.04174e12i	−0.0267279	−	0.114735i
$556$	−1.77942e12			−0.0334891
$557$			6.79683e12i			0.126774i	0.997989	+	0.0633871i	$0.0201903\pi$
$557$			6.79683e12i			0.126774i	−0.997989	+	0.0633871i	$0.979810\pi$
$558$	−6.69924e12	−	1.35987e13i	−0.123838	−	0.251378i
$559$	−5.85443e10			−0.00107257
$560$			8.27860e11i			0.0150320i
$561$	1.28737e14	−	2.99895e13i	2.31680	−	0.539703i
$562$	−2.88352e13			−0.514330
$563$			1.68596e13i			0.298061i	0.988833	+	0.149030i	$0.0476152\pi$
$563$			1.68596e13i			0.298061i	−0.988833	+	0.149030i	$0.952385\pi$
$564$	1.33899e12	+	5.74793e12i	0.0234630	+	0.100720i
$565$	2.20330e13			0.382677
$566$		−	3.02165e13i		−	0.520191i
$567$	5.79857e12	−	7.54410e12i	0.0989478	−	0.128734i
$568$	8.32721e13			1.40850
$569$			4.95321e13i			0.830473i	0.909713	+	0.415237i	$0.136301\pi$
$569$			4.95321e13i			0.830473i	−0.909713	+	0.415237i	$0.863699\pi$
$570$	−2.28502e13	+	5.32301e12i	−0.379766	+	0.0884673i
$571$	−2.67940e11			−0.00441425			−0.00220712	−	0.999998i	$-0.500703\pi$
$571$	−2.67940e11			−0.00441425			−0.00220712	+	0.999998i	$0.500703\pi$
$572$		−	9.19493e10i		−	0.00150165i
$573$	−1.90185e13	−	8.16410e13i	−0.307895	−	1.32171i
$574$	−5.66426e12			−0.0909042
$575$		−	1.31964e13i		−	0.209950i
$576$	−2.01159e13	+	9.90985e12i	−0.317268	+	0.156298i
$577$	−1.03800e14			−1.62300			−0.811498	−	0.584355i	$-0.801347\pi$
$577$	−1.03800e14			−1.62300			−0.811498	+	0.584355i	$0.801347\pi$
$578$			4.54264e13i			0.704157i
$579$	−5.39485e13	+	1.25674e13i	−0.829061	+	0.193132i
$580$	5.53022e12			0.0842563
$581$			2.47490e12i			0.0373832i
$582$	−2.20443e12	−	9.46302e12i	−0.0330128	−	0.141715i
$583$	3.32959e13			0.494365
$584$		−	5.18999e13i		−	0.764016i
$585$	1.83377e10	+	3.72234e10i	0.000267649	+	0.000543296i
$586$	2.80912e13			0.406520
$587$		−	2.51028e13i		−	0.360190i	−0.983649	−	0.180095i	$-0.942359\pi$
$587$		−	2.51028e13i		−	0.360190i	0.983649	−	0.180095i	$-0.0576405\pi$
$588$	4.71271e13	−	1.09784e13i	0.670477	−	0.156189i
$589$	5.91284e13			0.834103
$590$			1.43614e13i			0.200880i
$591$	2.68843e13	+	1.15407e14i	0.372873	+	1.60064i
$592$	3.96525e12			0.0545333
$593$		−	8.77412e13i		−	1.19655i	−0.801292	−	0.598274i	$-0.795854\pi$
$593$		−	8.77412e13i		−	1.19655i	0.801292	−	0.598274i	$-0.204146\pi$
$594$	4.85423e13	−	3.97880e13i	0.656430	−	0.538046i
$595$	8.21407e12			0.110147
$596$		−	1.08360e13i		−	0.144091i
$597$	2.77340e13	−	6.46070e12i	0.365713	−	0.0851937i
$598$	5.88408e10			0.000769436
$599$			1.25216e13i			0.162377i	0.996699	+	0.0811887i	$0.0258716\pi$
$599$			1.25216e13i			0.162377i	−0.996699	+	0.0811887i	$0.974128\pi$
$600$	−3.25995e12	−	1.39941e13i	−0.0419233	−	0.179965i
$601$	−6.12425e13			−0.781053			−0.390526	−	0.920592i	$-0.627707\pi$
$601$	−6.12425e13			−0.781053			−0.390526	+	0.920592i	$0.627707\pi$
$602$			5.50281e12i			0.0695988i
$603$	−1.27940e14	+	6.30280e13i	−1.60479	+	0.790583i
$604$	−7.32263e13			−0.910925
$605$		−	5.28963e13i		−	0.652603i
$606$	7.31704e13	−	1.70452e13i	0.895308	−	0.208564i
$607$	9.01472e13			1.09398			0.546989	−	0.837140i	$-0.315774\pi$
$607$	9.01472e13			1.09398			0.546989	+	0.837140i	$0.315774\pi$
$608$		−	1.38661e14i		−	1.66893i
$609$	8.22245e11	+	3.52967e12i	0.00981555	+	0.0421355i
$610$	3.06731e13			0.363168
$611$		−	1.68670e10i		−	0.000198077i
$612$	−4.06936e13	−	8.26035e13i	−0.473990	−	0.962146i
$613$	1.74248e13			0.201310			0.100655	−	0.994921i	$-0.467906\pi$
$613$	1.74248e13			0.201310			0.100655	+	0.994921i	$0.467906\pi$
$614$		−	7.17790e12i		−	0.0822538i
$615$	−3.96387e13	+	9.23392e12i	−0.450551	+	0.104957i
$616$	−2.08659e13			−0.235252
$617$		−	6.93311e13i		−	0.775358i	−0.921795	−	0.387679i	$-0.873277\pi$
$617$		−	6.93311e13i		−	0.775358i	0.921795	−	0.387679i	$-0.126723\pi$
$618$	1.52873e13	+	6.56243e13i	0.169586	+	0.727984i
$619$	−4.22866e13			−0.465318			−0.232659	−	0.972558i	$-0.574743\pi$
$619$	−4.22866e13			−0.465318			−0.232659	+	0.972558i	$0.574743\pi$
$620$			1.49990e13i			0.163720i
$621$	−6.14581e13	−	7.49804e13i	−0.665459	−	0.811876i
$622$	6.65591e13			0.714917
$623$			1.54442e13i			0.164560i
$624$	−2.58319e10	+	6.01759e9i	−0.000273044	+	6.36062e-5i
$625$	3.81470e12			0.0400000
$626$		−	1.96399e13i		−	0.204300i
$627$	5.55425e13	+	2.38429e14i	0.573176	+	2.46049i
$628$	6.53897e13			0.669439
$629$		−	3.93434e13i		−	0.399594i
$630$	3.49877e12	−	1.72363e12i	0.0352544	−	0.0173677i
$631$	−1.41897e14			−1.41849			−0.709246	−	0.704961i	$-0.750964\pi$
$631$	−1.41897e14			−1.41849			−0.709246	+	0.704961i	$0.750964\pi$
$632$			4.93220e13i			0.489165i
$633$	−7.09464e13	+	1.65271e13i	−0.698091	+	0.162622i
$634$	−2.55360e13			−0.249291
$635$			1.62674e13i			0.157561i
$636$	−5.26240e12	−	2.25901e13i	−0.0505707	−	0.217086i
$637$	−1.38292e11			−0.00131856
$638$			2.39064e13i			0.226157i
$639$	7.17753e13	+	1.45696e14i	0.673706	+	1.36755i
$640$	4.05541e13			0.377690
$641$			2.00581e14i			1.85353i	0.375642	+	0.926765i	$0.377422\pi$
$641$			2.00581e14i			1.85353i	−0.375642	+	0.926765i	$0.622578\pi$
$642$	3.67900e13	−	8.57031e12i	0.337330	−	0.0785817i
$643$	−2.67889e13			−0.243725			−0.121863	−	0.992547i	$-0.538887\pi$
$643$	−2.67889e13			−0.243725			−0.121863	+	0.992547i	$0.538887\pi$
$644$			1.33498e13i			0.120516i
$645$	8.97072e12	+	3.85088e13i	0.0803579	+	0.344954i
$646$	−1.48799e14			−1.32263
$647$			1.59646e14i			1.40811i	0.710145	+	0.704055i	$0.248629\pi$
$647$			1.59646e14i			1.40811i	−0.710145	+	0.704055i	$0.751371\pi$
$648$	−8.36957e13	−	6.43305e13i	−0.732535	−	0.563044i
$649$	1.49853e14			1.30149
$650$			1.70092e10i			0.000146594i
$651$	−9.57311e12	+	2.23008e12i	−0.0818744	+	0.0190728i
$652$	7.87259e13			0.668159
$653$		−	4.47885e12i		−	0.0377225i	−0.999822	−	0.0188613i	$-0.993996\pi$
$653$		−	4.47885e12i		−	0.0377225i	0.999822	−	0.0188613i	$-0.00600408\pi$
$654$	8.95945e12	+	3.84605e13i	0.0748846	+	0.321459i
$655$	−2.94792e13			−0.244517
$656$		−	2.60152e13i		−	0.214145i
$657$	9.08058e13	−	4.47344e13i	0.741800	−	0.365439i
$658$	−1.58540e12			−0.0128531
$659$		−	1.74089e14i		−	1.40070i	−0.713800	−	0.700349i	$-0.753028\pi$
$659$		−	1.74089e14i		−	1.40070i	0.713800	−	0.700349i	$-0.246972\pi$
$660$	−6.04817e13	+	1.40893e13i	−0.482952	+	0.112505i
$661$	5.57870e13			0.442106			0.221053	−	0.975262i	$-0.429051\pi$
$661$	5.57870e13			0.442106			0.221053	+	0.975262i	$0.429051\pi$
$662$		−	9.74729e13i		−	0.766644i
$663$	5.97068e10	+	2.56305e11i	0.000466076	+	0.00200073i
$664$	2.74570e13			0.212722
$665$			1.52130e13i			0.116979i
$666$	−8.25577e12	−	1.67583e13i	−0.0630066	−	0.127896i
$667$	3.69268e13			0.279713
$668$			1.57275e14i			1.18244i
$669$	−2.01472e14	+	4.69335e13i	−1.50344	+	0.350229i
$670$	−5.84618e13			−0.433010
$671$		−	3.20056e14i		−	2.35295i
$672$	5.22973e12	+	2.24498e13i	0.0381621	+	0.163820i
$673$	1.96033e14			1.41989			0.709944	−	0.704259i	$-0.248720\pi$
$673$	1.96033e14			1.41989			0.709944	+	0.704259i	$0.248720\pi$
$674$			4.84555e13i			0.348373i
$675$	2.16747e13	−	1.77657e13i	0.154680	−	0.126784i
$676$	−9.98147e13			−0.707068
$677$		−	1.68550e14i		−	1.18518i	−0.805503	−	0.592592i	$-0.798105\pi$
$677$		−	1.68550e14i		−	1.18518i	0.805503	−	0.592592i	$-0.201895\pi$
$678$	6.46209e13	−	1.50536e13i	0.451050	−	0.105073i
$679$	−6.30020e12			−0.0436521
$680$		−	9.11285e13i		−	0.626772i
$681$	2.51657e12	+	1.08030e13i	0.0171820	+	0.0737577i
$682$	−6.48385e13			−0.439451
$683$			1.13844e14i			0.765964i	0.923756	+	0.382982i	$0.125103\pi$
$683$			1.13844e14i			0.765964i	−0.923756	+	0.382982i	$0.874897\pi$
$684$	1.52987e14	−	7.53672e13i	1.02182	−	0.503387i
$685$	−1.14178e14			−0.757058
$686$			2.63492e13i			0.173439i
$687$	1.68988e14	−	3.93660e13i	1.10426	−	0.257240i
$688$	−2.52737e13			−0.163956
$689$			6.62895e10i			0.000426922i
$690$	−9.01615e12	−	3.87039e13i	−0.0576469	−	0.247462i
$691$	−5.32565e13			−0.338051			−0.169026	−	0.985612i	$-0.554062\pi$
$691$	−5.32565e13			−0.338051			−0.169026	+	0.985612i	$0.554062\pi$
$692$			1.29326e14i			0.814994i
$693$	−1.79851e13	−	3.65077e13i	−0.112524	−	0.228412i
$694$	−5.23090e13			−0.324922
$695$		−	3.43463e12i		−	0.0211815i
$696$	3.91589e13	−	9.12215e12i	0.239764	−	0.0558536i
$697$	−2.58124e14			−1.56915
$698$		−	1.67876e13i		−	0.101324i
$699$	2.19449e12	+	9.42036e12i	0.0131507	+	0.0564523i
$700$	−3.85904e12			−0.0229609
$701$		−	1.47169e14i		−	0.869416i	−0.900571	−	0.434708i	$-0.856852\pi$
$701$		−	1.47169e14i		−	0.869416i	0.900571	−	0.434708i	$-0.143148\pi$
$702$	7.92148e10	+	9.66440e10i	0.000464644	+	0.000566878i
$703$	7.28665e13			0.424376
$704$			9.59123e13i			0.554640i
$705$	−1.10947e13	+	2.58453e12i	−0.0637043	+	0.0148401i
$706$	−3.08706e13			−0.176004
$707$		−	4.87147e13i		−	0.275780i
$708$	−2.36842e13	−	1.01670e14i	−0.133135	−	0.571512i
$709$	1.84898e14			1.03205			0.516025	−	0.856573i	$-0.327411\pi$
$709$	1.84898e14			1.03205			0.516025	+	0.856573i	$0.327411\pi$
$710$			6.65753e13i			0.368996i
$711$	−8.62955e13	+	4.25125e13i	−0.474941	+	0.233974i
$712$	1.71341e14			0.936400
$713$			1.00152e14i			0.543516i
$714$	2.40911e13	−	5.61208e12i	0.129827	−	0.0302435i
$715$	1.77481e11			0.000949776
$716$			1.40414e14i			0.746185i
$717$	−6.32569e13	−	2.71544e14i	−0.333820	−	1.43300i
$718$	−1.51128e14			−0.791998
$719$		−	2.95132e13i		−	0.153593i	−0.997047	−	0.0767966i	$-0.975531\pi$
$719$		−	2.95132e13i		−	0.153593i	0.997047	−	0.0767966i	$-0.0244692\pi$
$720$	7.91641e12	+	1.60694e13i	0.0409134	+	0.0830496i
$721$	4.36906e13			0.224240
$722$		−	1.69399e14i		−	0.863426i
$723$	1.65911e14	−	3.86493e13i	0.839813	−	0.195636i
$724$	8.82295e13			0.443528
$725$			1.06745e13i			0.0532912i
$726$	−3.61402e13	−	1.55140e14i	−0.179188	−	0.769203i
$727$	1.54294e14			0.759763			0.379881	−	0.925035i	$-0.375965\pi$
$727$	1.54294e14			0.759763			0.379881	+	0.925035i	$0.375965\pi$
$728$		−	4.15424e10i		−	0.000203158i
$729$	4.04145e13	−	2.01886e14i	0.196291	−	0.980546i
$730$	4.14935e13			0.200155
$731$			2.50767e14i			1.20139i
$732$	−2.17146e14	+	5.05847e13i	−1.03323	+	0.240693i
$733$	5.92833e13			0.280164			0.140082	−	0.990140i	$-0.455263\pi$
$733$	5.92833e13			0.280164			0.140082	+	0.990140i	$0.455263\pi$
$734$			1.10169e14i			0.517105i
$735$	2.11905e13	+	9.09648e13i	0.0987879	+	0.424069i
$736$	2.34866e14			1.08750
$737$			6.10015e14i			2.80546i
$738$	−1.09948e14	+	5.41645e13i	−0.502232	+	0.247419i
$739$	−8.13108e13			−0.368915			−0.184457	−	0.982841i	$-0.559053\pi$
$739$	−8.13108e13			−0.368915			−0.184457	+	0.982841i	$0.559053\pi$
$740$			1.84839e13i			0.0832980i
$741$	−4.74694e11	+	1.10581e11i	−0.00212482	+	0.000494982i
$742$	6.23081e12			0.0277029
$743$		−	1.95664e14i		−	0.864107i	−0.901848	−	0.432054i	$-0.857789\pi$
$743$		−	1.95664e14i		−	0.864107i	0.901848	−	0.432054i	$-0.142211\pi$
$744$	2.47409e13	+	1.06206e14i	0.108530	+	0.465891i
$745$	2.09156e13			0.0911359
$746$			2.30932e14i			0.999518i
$747$	2.36662e13	+	4.80398e13i	0.101748	+	0.206537i
$748$	−3.93852e14			−1.68200
$749$		−	2.44937e13i		−	0.103907i
$750$	1.11882e13	−	2.60631e12i	0.0471468	−	0.0109830i
$751$	−1.51572e14			−0.634482			−0.317241	−	0.948345i	$-0.602756\pi$
$751$	−1.51572e14			−0.634482			−0.317241	+	0.948345i	$0.602756\pi$
$752$		−	7.28153e12i		−	0.0302785i
$753$	5.44528e12	+	2.33751e13i	0.0224929	+	0.0965558i
$754$	−4.75958e10			−0.000195304
$755$		−	1.41342e14i		−	0.576150i
$756$	−2.19266e13	+	1.79723e13i	−0.0887897	+	0.0727770i
$757$	−3.51514e14			−1.41405			−0.707023	−	0.707190i	$-0.749962\pi$
$757$	−3.51514e14			−1.41405			−0.707023	+	0.707190i	$0.749962\pi$
$758$			7.22884e13i			0.288883i
$759$	−4.03852e14	+	9.40783e13i	−1.60330	+	0.373491i
$760$	1.68776e14			0.665645
$761$		−	1.17198e14i		−	0.459195i	−0.973286	−	0.229598i	$-0.926259\pi$
$761$		−	1.17198e14i		−	0.459195i	0.973286	−	0.229598i	$-0.0737410\pi$
$762$	1.11143e13	+	4.77108e13i	0.0432622	+	0.185713i
$763$	2.56058e13			0.0990184
$764$			2.49769e14i			0.959561i
$765$	1.59441e14	−	7.85470e13i	0.608547	−	0.299794i
$766$	2.39286e14			0.907347
$767$			2.98345e11i			0.00112394i
$768$	2.10974e14	−	4.91468e13i	0.789627	−	0.183945i
$769$	−3.59838e14			−1.33806			−0.669030	−	0.743235i	$-0.733290\pi$
$769$	−3.59838e14			−1.33806			−0.669030	+	0.743235i	$0.733290\pi$
$770$		−	1.66821e13i		−	0.0616307i
$771$	−1.06365e13	−	4.56596e13i	−0.0390416	−	0.167595i
$772$	1.65048e14			0.601899
$773$			7.41248e13i			0.268575i	0.990942	+	0.134288i	$0.0428746\pi$
$773$			7.41248e13i			0.268575i	−0.990942	+	0.134288i	$0.957125\pi$
$774$	5.26206e13	+	1.06814e14i	0.189431	+	0.384523i
$775$	−2.89511e13			−0.103551
$776$			6.98956e13i			0.248394i
$777$	−1.17974e13	+	2.74822e12i	−0.0416562	+	0.00970390i
$778$	−2.64294e13			−0.0927235
$779$		−	4.78063e14i		−	1.66647i
$780$	−2.80508e10	−	1.20414e11i	−9.71566e−5	−	0.000417067i
$781$	6.94675e14			2.39071
$782$		−	2.52037e14i		−	0.861847i
$783$	4.97129e13	+	6.06510e13i	0.168912	+	0.206077i
$784$	−5.97010e13			−0.201559
$785$			1.26215e14i			0.423413i
$786$	−8.64597e13	+	2.01410e13i	−0.288204	+	0.0671379i
$787$	9.83962e13			0.325915			0.162958	−	0.986633i	$-0.447897\pi$
$787$	9.83962e13			0.325915			0.162958	+	0.986633i	$0.447897\pi$
$788$		−	3.53071e14i		−	1.16207i
$789$	−5.66978e13	−	2.43388e14i	−0.185431	−	0.796003i
$790$	−3.94325e13			−0.128150
$791$		−	4.30226e13i		−	0.138936i
$792$	−4.05024e14	+	1.99530e14i	−1.29973	+	0.640299i
$793$	6.37207e11			0.00203196
$794$		−	2.46606e14i		−	0.781450i
$795$	4.36034e13	−	1.01575e13i	0.137305	−	0.0319854i
$796$	−8.48483e13			−0.265508
$797$		−	5.07323e14i		−	1.57759i	−0.614659	−	0.788793i	$-0.710706\pi$
$797$		−	5.07323e14i		−	1.57759i	0.614659	−	0.788793i	$-0.289294\pi$
$798$	1.03939e13	+	4.46183e13i	0.0321192	+	0.137879i
$799$	−7.22477e13			−0.221866
$800$			6.78928e13i			0.207192i
$801$	1.47685e14	+	2.99784e14i	0.447893	+	0.909172i
$802$	2.72567e14			0.821488
$803$		−	4.32961e14i		−	1.29679i
$804$	4.13874e14	−	9.64128e13i	1.23193	−	0.286982i
$805$	−2.57679e13			−0.0762253
$806$		−	1.29088e11i		−	0.000379500i
$807$	3.62300e12	+	1.55525e13i	0.0105852	+	0.0454395i
$808$	−5.40450e14			−1.56927
$809$			5.73615e14i			1.65531i	0.561241	+	0.827653i	$0.310324\pi$
$809$			5.73615e14i			1.65531i	−0.561241	+	0.827653i	$0.689676\pi$
$810$	5.14317e13	−	6.69140e13i	0.147505	−	0.191908i
$811$	3.39398e14			0.967398			0.483699	−	0.875234i	$-0.339293\pi$
$811$	3.39398e14			0.967398			0.483699	+	0.875234i	$0.339293\pi$
$812$		−	1.07985e13i		−	0.0305904i
$813$	5.81639e14	−	1.35494e14i	1.63757	−	0.381476i
$814$	−7.99033e13			−0.223585
$815$			1.51957e14i			0.422603i
$816$	2.57755e13	+	1.10647e14i	0.0712454	+	0.305837i
$817$	−4.64436e14			−1.27590
$818$			3.19950e13i			0.0873605i
$819$	7.26840e10	−	3.58069e10i	0.000197251	−	9.71734e-5i
$820$	1.21269e14			0.327100
$821$		−	4.94013e13i		−	0.132441i	−0.997805	−	0.0662205i	$-0.978906\pi$
$821$		−	4.94013e13i		−	0.132441i	0.997805	−	0.0662205i	$-0.0210941\pi$
$822$	−3.34873e14	+	7.80094e13i	−0.892321	+	0.207868i
$823$	5.93640e13			0.157226			0.0786129	−	0.996905i	$-0.474951\pi$
$823$	5.93640e13			0.157226			0.0786129	+	0.996905i	$0.474951\pi$
$824$		−	4.84713e14i		−	1.27599i
$825$	−2.71953e13	−	1.16742e14i	−0.0711581	−	0.305462i
$826$	2.80426e13			0.0729320
$827$		−	1.48941e14i		−	0.385023i	−0.981295	−	0.192512i	$-0.938337\pi$
$827$		−	1.48941e14i		−	0.385023i	0.981295	−	0.192512i	$-0.0616633\pi$
$828$	1.27658e14	+	2.59130e14i	0.328016	+	0.665835i
$829$	−2.05601e14			−0.525113			−0.262557	−	0.964917i	$-0.584566\pi$
$829$	−2.05601e14			−0.525113			−0.262557	+	0.964917i	$0.584566\pi$
$830$			2.19517e13i			0.0557285i
$831$	−3.34620e14	+	7.79506e13i	−0.844398	+	0.196704i
$832$	−1.90954e11			−0.000478974
$833$			5.92356e14i			1.47692i
$834$	−2.34664e12	−	1.00735e13i	−0.00581588	−	0.0249660i
$835$	−3.03574e14			−0.747879
$836$		−	7.29440e14i		−	1.78632i
$837$	−1.64496e14	+	1.34830e14i	−0.400432	+	0.328216i
$838$	1.81205e13			0.0438480
$839$			4.81106e14i			1.15726i	0.815590	+	0.578630i	$0.196412\pi$
$839$			4.81106e14i			1.15726i	−0.815590	+	0.578630i	$0.803588\pi$
$840$	−2.73254e13	+	6.36552e12i	−0.0653387	+	0.0152208i
$841$	3.90838e14			0.929001
$842$			1.35431e14i			0.320005i
$843$	9.17887e13	+	3.94024e14i	0.215601	+	0.925517i
$844$	2.17051e14			0.506815
$845$		−	1.92663e14i		−	0.447213i
$846$	−3.07738e13	+	1.51604e13i	−0.0710117	+	0.0349831i
$847$	−1.03288e14			−0.236936
$848$			2.86173e13i			0.0652604i
$849$	−4.12899e14	+	9.61856e13i	−0.936063	+	0.218058i
$850$	7.28565e13			0.164200
$851$			1.23422e14i			0.276531i
$852$	−1.09793e14	−	4.71312e14i	−0.244556	−	1.04981i
$853$	−3.96662e14			−0.878366			−0.439183	−	0.898398i	$-0.644732\pi$
$853$	−3.96662e14			−0.878366			−0.439183	+	0.898398i	$0.644732\pi$
$854$		−	5.98935e13i		−	0.131853i
$855$	1.45474e14	+	2.95296e14i	0.318387	+	0.646289i
$856$	−2.71738e14			−0.591263
$857$			3.66642e14i			0.793119i	0.918009	+	0.396560i	$0.129796\pi$
$857$			3.66642e14i			0.793119i	−0.918009	+	0.396560i	$0.870204\pi$
$858$	5.20535e11	−	1.21260e11i	0.00111947	−	0.000260784i
$859$	5.43192e14			1.16142			0.580708	−	0.814112i	$-0.302776\pi$
$859$	5.43192e14			1.16142			0.580708	+	0.814112i	$0.302776\pi$
$860$		−	1.17812e14i		−	0.250437i
$861$	1.80305e13	+	7.74002e13i	0.0381060	+	0.163578i
$862$	−1.42694e14			−0.299826
$863$			1.88834e14i			0.394481i	0.980355	+	0.197240i	$0.0631979\pi$
$863$			1.88834e14i			0.394481i	−0.980355	+	0.197240i	$0.936802\pi$
$864$	3.16189e14	+	3.85759e14i	0.656717	+	0.801211i
$865$	−2.49625e14			−0.515475
$866$			4.32938e13i			0.0888866i
$867$	6.20736e14	−	1.44602e14i	1.26710	−	0.295174i
$868$	2.92876e13			0.0594409
$869$			4.11456e14i			0.830280i
$870$	7.29308e12	+	3.13072e13i	0.0146324	+	0.0628128i
$871$	−1.21449e12			−0.00242273
$872$		−	2.84076e14i		−	0.563446i
$873$	−1.22292e14	+	6.02456e13i	−0.241171	+	0.118810i
$874$	4.66788e14			0.915299
$875$		−	7.44874e12i		−	0.0145225i
$876$	−2.93749e14	+	6.84294e13i	−0.569450	+	0.132655i
$877$	2.18184e14			0.420557			0.210279	−	0.977642i	$-0.432563\pi$
$877$	2.18184e14			0.420557			0.210279	+	0.977642i	$0.432563\pi$
$878$		−	5.00037e14i		−	0.958361i
$879$	−8.94202e13	−	3.83857e14i	−0.170409	−	0.731517i
$880$	7.66188e13			0.145185
$881$			4.01280e14i			0.756080i	0.925789	+	0.378040i	$0.123402\pi$
$881$			4.01280e14i			0.756080i	−0.925789	+	0.378040i	$0.876598\pi$
$882$	1.24299e14	+	2.52314e14i	0.232877	+	0.472713i
$883$	−5.51870e14			−1.02809			−0.514047	−	0.857762i	$-0.671854\pi$
$883$	−5.51870e14			−1.02809			−0.514047	+	0.857762i	$0.671854\pi$
$884$		−	7.84130e11i		−	0.00145254i
$885$	1.96243e14	−	4.57153e13i	0.361475	−	0.0842064i
$886$	−2.61822e14			−0.479555
$887$			2.01914e14i			0.367747i	0.982950	+	0.183874i	$0.0588637\pi$
$887$			2.01914e14i			0.367747i	−0.982950	+	0.183874i	$0.941136\pi$
$888$	3.04893e13	+	1.30882e14i	0.0552183	+	0.237037i
$889$	3.17644e13			0.0572047
$890$			1.36986e14i			0.245316i
$891$	−6.98209e14	−	5.36661e14i	−1.24336	−	0.955677i
$892$	6.16377e14			1.09150
$893$		−	1.33807e14i		−	0.235626i
$894$	6.13436e13	−	1.42901e13i	0.107419	−	0.0250235i
$895$	−2.71028e14			−0.471954
$896$		−	7.91877e13i		−	0.137125i
$897$	−1.87303e11	−	8.04039e11i	−0.000322539	−	0.00138457i
$898$	3.02326e14			0.517719
$899$		−	8.10121e13i		−	0.137959i
$900$	−7.49070e13	+	3.69021e13i	−0.126856	+	0.0624940i
$901$	2.83942e14			0.478196
$902$			5.24230e14i			0.877989i
$903$	7.51939e13	−	1.75166e13i	0.125240	−	0.0291750i
$904$	−4.77302e14			−0.790589
$905$			1.70301e14i			0.280527i
$906$	−9.65686e13	−	4.14542e14i	−0.158196	−	0.679091i
$907$	7.41125e14			1.20741			0.603706	−	0.797207i	$-0.293690\pi$
$907$	7.41125e14			1.20741			0.603706	+	0.797207i	$0.293690\pi$
$908$		−	3.30502e13i		−	0.0535481i
$909$	−4.65834e14	−	9.45590e14i	−0.750605	−	1.52364i
$910$	3.32128e10			5.32229e−5
$911$		−	6.84759e14i		−	1.09130i	−0.838012	−	0.545652i	$-0.816282\pi$
$911$		−	6.84759e14i		−	1.09130i	0.838012	−	0.545652i	$-0.183718\pi$
$912$	−2.04926e14	+	4.77380e13i	−0.324805	+	0.0756641i
$913$	2.29053e14			0.361062
$914$		−	7.99950e13i		−	0.125410i
$915$	−9.76388e13	−	4.19137e14i	−0.152236	−	0.653507i
$916$	−5.16994e14			−0.801693
$917$			5.75622e13i			0.0887751i
$918$	4.13962e14	−	3.39306e14i	0.634961	−	0.520449i
$919$	4.42008e14			0.674299			0.337150	−	0.941451i	$-0.390537\pi$
$919$	4.42008e14			0.674299			0.337150	+	0.941451i	$0.390537\pi$
$920$			2.85874e14i			0.433746i
$921$	−9.80835e13	+	2.28488e13i	−0.148012	+	0.0344798i
$922$	2.13021e14			0.319719
$923$			1.38305e12i			0.00206456i
$924$	2.75114e13	+	1.18099e14i	0.0408464	+	0.175342i
$925$	−3.56776e13			−0.0526851
$926$			3.03425e13i			0.0445652i
$927$	8.48070e14	−	4.17792e14i	1.23889	−	0.610325i
$928$	−1.89981e14			−0.276038
$929$		−	2.53232e14i		−	0.365965i	−0.983116	−	0.182982i	$-0.941425\pi$
$929$		−	2.53232e14i		−	0.365965i	0.983116	−	0.182982i	$-0.0585752\pi$
$930$	−8.49108e13	+	1.97802e13i	−0.122053	+	0.0284325i
$931$	−1.09708e15			−1.56852
$932$		−	2.88203e13i		−	0.0409844i
$933$	−2.11872e14	−	9.09507e14i	−0.299685	−	1.28646i
$934$	−3.36990e14			−0.474113
$935$		−	7.60215e14i		−	1.06385i
$936$	−3.97249e11	−	8.06371e11i	−0.000552947	−	0.00112242i
$937$	3.76770e14			0.521649			0.260825	−	0.965386i	$-0.416006\pi$
$937$	3.76770e14			0.521649			0.260825	+	0.965386i	$0.416006\pi$
$938$			1.14155e14i			0.157210i
$939$	−2.68372e14	+	6.25180e13i	−0.367629	+	0.0856400i
$940$	3.39426e13			0.0462494
$941$			1.05447e15i			1.42917i	0.699548	+	0.714586i	$0.253385\pi$
$941$			1.05447e15i			1.42917i	−0.699548	+	0.714586i	$0.746615\pi$
$942$	8.62338e13	+	3.70178e14i	0.116258	+	0.499064i
$943$	8.09746e14			1.08590
$944$			1.28796e14i			0.171808i
$945$	−3.46901e13	−	4.23228e13i	−0.0460306	−	0.0561585i
$946$	5.09287e14			0.672213
$947$		−	1.88256e14i		−	0.247172i	−0.992334	−	0.123586i	$-0.960560\pi$
$947$		−	1.88256e14i		−	0.247172i	0.992334	−	0.123586i	$-0.0394395\pi$
$948$	2.79158e14	−	6.50305e13i	0.364593	−	0.0849328i
$949$	8.61992e11			0.00111988
$950$			1.34935e14i			0.174384i
$951$	8.12866e13	+	3.48941e14i	0.104500	+	0.448590i
$952$	−1.77941e14			−0.227558
$953$			6.56574e14i			0.835255i	0.908618	+	0.417627i	$0.137138\pi$
$953$			6.56574e14i			0.835255i	−0.908618	+	0.417627i	$0.862862\pi$
$954$	1.20945e14	−	5.95821e13i	0.153054	−	0.0754004i
$955$	−4.82106e14			−0.606912
$956$			8.30753e14i			1.04036i
$957$	3.26673e14	−	7.60991e13i	0.406961	−	0.0948025i
$958$	−4.03812e14			−0.500439
$959$			2.22948e14i			0.274860i
$960$	2.92598e13	+	1.25604e14i	0.0358852	+	0.154045i
$961$	−5.99909e14			−0.731928
$962$		−	1.59081e11i		−	0.000193083i
$963$	−2.34221e14	−	4.75441e14i	−0.282809	−	0.574071i
$964$	−5.07581e14			−0.609705
$965$			3.18576e14i			0.380695i
$966$	−7.55748e13	+	1.76053e13i	−0.0898444	+	0.0209295i
$967$	−6.91937e14			−0.818341			−0.409170	−	0.912458i	$-0.634182\pi$
$967$	−6.91937e14			−0.818341			−0.409170	+	0.912458i	$0.634182\pi$
$968$			1.14589e15i			1.34824i
$969$	4.73658e14	+	2.03329e15i	0.554430	+	2.38001i
$970$	−5.58810e13			−0.0650737
$971$		−	9.99579e14i		−	1.15803i	−0.815316	−	0.579016i	$-0.803437\pi$
$971$		−	9.99579e14i		−	1.15803i	0.815316	−	0.579016i	$-0.196563\pi$
$972$	−2.53753e14	+	5.58529e14i	−0.292469	+	0.643746i
$973$	−6.70661e12			−0.00769022
$974$			2.42979e14i			0.277188i
$975$	2.32424e11	−	5.41438e10i	0.000263790	−	6.14505e-5i
$976$	2.75083e14			0.310610
$977$			4.96414e14i			0.557662i	0.960340	+	0.278831i	$0.0899469\pi$
$977$			4.96414e14i			0.557662i	−0.960340	+	0.278831i	$0.910053\pi$
$978$	1.03821e14	+	4.45676e14i	0.116036	+	0.498110i
$979$	1.42937e15			1.58939
$980$		−	2.78294e14i		−	0.307875i
$981$	4.97029e14	−	2.44856e14i	0.547062	−	0.269504i
$982$	−1.15588e14			−0.126577
$983$		−	1.00717e15i		−	1.09732i	−0.836044	−	0.548662i	$-0.815137\pi$
$983$		−	1.00717e15i		−	1.09732i	0.836044	−	0.548662i	$-0.184863\pi$
$984$	8.58693e14	−	2.00034e14i	0.930813	−	0.216835i
$985$	6.81500e14			0.734995
$986$			2.03870e14i			0.218761i
$987$	5.04666e12	+	2.16639e13i	0.00538788	+	0.0231287i
$988$	1.45226e12			0.00154262
$989$		−	7.86665e14i		−	0.831397i
$990$	−1.59523e14	−	3.23813e14i	−0.167744	−	0.340501i
$991$	−5.64814e14			−0.590931			−0.295466	−	0.955353i	$-0.595475\pi$
$991$	−5.64814e14			−0.590931			−0.295466	+	0.955353i	$0.595475\pi$
$992$		−	5.15262e14i		−	0.536376i
$993$	−1.33193e15	+	3.10277e14i	−1.37955	+	0.321368i
$994$	1.29998e14			0.133969
$995$		−	1.63775e14i		−	0.167931i
$996$	−3.62018e13	−	1.55404e14i	−0.0369346	−	0.158550i
$997$	−1.95056e15			−1.98008			−0.990040	−	0.140788i	$-0.955036\pi$
$997$	−1.95056e15			−1.98008			−0.990040	+	0.140788i	$0.955036\pi$
$998$		−	8.08572e14i		−	0.816707i
$999$	−2.02716e14	+	1.66157e14i	−0.203733	+	0.166991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.c.a.11.6	✓	14
3.2	odd	2	inner	15.11.c.a.11.9	yes	14
4.3	odd	2		240.11.l.b.161.13		14
5.2	odd	4		75.11.d.d.74.18		28
5.3	odd	4		75.11.d.d.74.11		28
5.4	even	2		75.11.c.g.26.9		14
12.11	even	2		240.11.l.b.161.14		14
15.2	even	4		75.11.d.d.74.12		28
15.8	even	4		75.11.d.d.74.17		28
15.14	odd	2		75.11.c.g.26.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.c.a.11.6	✓	14	1.1	even	1	trivial
15.11.c.a.11.9	yes	14	3.2	odd	2	inner
75.11.c.g.26.6		14	15.14	odd	2
75.11.c.g.26.9		14	5.4	even	2
75.11.d.d.74.11		28	5.3	odd	4
75.11.d.d.74.12		28	15.2	even	4
75.11.d.d.74.17		28	15.8	even	4
75.11.d.d.74.18		28	5.2	odd	4
240.11.l.b.161.13		14	4.3	odd	2
240.11.l.b.161.14		14	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-17.3194i q^{2} +(-236.663 + 55.1313i) q^{3} +724.039 q^{4} +1397.54i q^{5} +(954.839 + 4098.86i) q^{6} +2728.90 q^{7} -30275.0i q^{8} +(52970.1 - 26095.1i) q^{9} +O(q^{10})\)	\(q-17.3194i q^{2} +(-236.663 + 55.1313i) q^{3} +724.039 q^{4} +1397.54i q^{5} +(954.839 + 4098.86i) q^{6} +2728.90 q^{7} -30275.0i q^{8} +(52970.1 - 26095.1i) q^{9} +24204.6 q^{10} -252561. i q^{11} +(-171353. + 39917.2i) q^{12} +502.829 q^{13} -47262.9i q^{14} +(-77048.3 - 330747. i) q^{15} +217072. q^{16} -2.15380e6i q^{17} +(-451951. - 917409. i) q^{18} +3.98898e6 q^{19} +1.01188e6i q^{20} +(-645831. + 150448. i) q^{21} -4.37420e6 q^{22} +6.75656e6i q^{23} +(1.66910e6 + 7.16497e6i) q^{24} -1.95312e6 q^{25} -8708.69i q^{26} +(-1.10974e7 + 9.09606e6i) q^{27} +1.97583e6 q^{28} -5.46532e6i q^{29} +(-5.72834e6 + 1.33443e6i) q^{30} +1.48229e7 q^{31} -3.47611e7i q^{32} +(1.39240e7 + 5.97719e7i) q^{33} -3.73025e7 q^{34} +3.81375e6i q^{35} +(3.83524e7 - 1.88939e7i) q^{36} +1.82670e7 q^{37} -6.90867e7i q^{38} +(-119001. + 27721.6i) q^{39} +4.23105e7 q^{40} -1.19846e8i q^{41} +(2.60566e6 + 1.11854e7i) q^{42} -1.16430e8 q^{43} -1.82864e8i q^{44} +(3.64690e7 + 7.40280e7i) q^{45} +1.17019e8 q^{46} -3.35443e7i q^{47} +(-5.13730e7 + 1.19675e7i) q^{48} -2.75028e8 q^{49} +3.38269e7i q^{50} +(1.18742e8 + 5.09726e8i) q^{51} +364068. q^{52} +1.31833e8i q^{53} +(1.57538e8 + 1.92201e8i) q^{54} +3.52964e8 q^{55} -8.26173e7i q^{56} +(-9.44045e8 + 2.19917e8i) q^{57} -9.46560e7 q^{58} +5.93333e8i q^{59} +(-5.57859e7 - 2.39474e8i) q^{60} +1.26724e9 q^{61} -2.56724e8i q^{62} +(1.44550e8 - 7.12109e7i) q^{63} -3.79759e8 q^{64} +702725. i q^{65} +(1.03521e9 - 2.41155e8i) q^{66} -2.41532e9 q^{67} -1.55944e9i q^{68} +(-3.72498e8 - 1.59903e9i) q^{69} +6.60519e7 q^{70} +2.75053e9i q^{71} +(-7.90028e8 - 1.60367e9i) q^{72} +1.71428e9 q^{73} -3.16372e8i q^{74} +(4.62233e8 - 1.07678e8i) q^{75} +2.88818e9 q^{76} -6.89213e8i q^{77} +(480121. + 2.06103e6i) q^{78} -1.62914e9 q^{79} +3.03368e8i q^{80} +(2.12488e9 - 2.76452e9i) q^{81} -2.07566e9 q^{82} +9.06922e8i q^{83} +(-4.67606e8 + 1.08930e8i) q^{84} +3.01003e9 q^{85} +2.01649e9i q^{86} +(3.01310e8 + 1.29344e9i) q^{87} -7.64627e9 q^{88} +5.65950e9i q^{89} +(1.28212e9 - 6.31621e8i) q^{90} +1.37217e6 q^{91} +4.89201e9i q^{92} +(-3.50805e9 + 8.17207e8i) q^{93} -5.80966e8 q^{94} +5.57477e9i q^{95} +(1.91642e9 + 8.22668e9i) q^{96} -2.30869e9 q^{97} +4.76332e9i q^{98} +(-6.59060e9 - 1.33782e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

Introduction

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