LMFDB - Embedded newform 50.11.c.c.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,11,Mod(7,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("50.7");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	50.c (of order $4$, degree $2$, 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:	$31.7678626337$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.43
Dual form			50.11.c.c.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.0000 + 16.0000i) q^{2} +(183.000 + 183.000i) q^{3} -512.000i q^{4} -5856.00 q^{6} +(8407.00 - 8407.00i) q^{7} +(8192.00 + 8192.00i) q^{8} +7929.00i q^{9} +O(q^{10})$	\(q+(-16.0000 + 16.0000i) q^{2} +(183.000 + 183.000i) q^{3} -512.000i q^{4} -5856.00 q^{6} +(8407.00 - 8407.00i) q^{7} +(8192.00 + 8192.00i) q^{8} +7929.00i q^{9} -173398. q^{11} +(93696.0 - 93696.0i) q^{12} +(232623. + 232623. i) q^{13} +269024. i q^{14} -262144. q^{16} +(-1.88003e6 + 1.88003e6i) q^{17} +(-126864. - 126864. i) q^{18} +1.10156e6i q^{19} +3.07696e6 q^{21} +(2.77437e6 - 2.77437e6i) q^{22} +(5.22826e6 + 5.22826e6i) q^{23} +2.99827e6i q^{24} -7.44394e6 q^{26} +(9.35496e6 - 9.35496e6i) q^{27} +(-4.30438e6 - 4.30438e6i) q^{28} +2.47908e7i q^{29} -1.00660e7 q^{31} +(4.19430e6 - 4.19430e6i) q^{32} +(-3.17318e7 - 3.17318e7i) q^{33} -6.01611e7i q^{34} +4.05965e6 q^{36} +(-5.63879e7 + 5.63879e7i) q^{37} +(-1.76250e7 - 1.76250e7i) q^{38} +8.51400e7i q^{39} -1.53004e8 q^{41} +(-4.92314e7 + 4.92314e7i) q^{42} +(-5.93725e7 - 5.93725e7i) q^{43} +8.87798e7i q^{44} -1.67304e8 q^{46} +(-1.72339e8 + 1.72339e8i) q^{47} +(-4.79724e7 - 4.79724e7i) q^{48} +1.41120e8i q^{49} -6.88092e8 q^{51} +(1.19103e8 - 1.19103e8i) q^{52} +(-1.96386e8 - 1.96386e8i) q^{53} +2.99359e8i q^{54} +1.37740e8 q^{56} +(-2.01585e8 + 2.01585e8i) q^{57} +(-3.96653e8 - 3.96653e8i) q^{58} -6.94069e8i q^{59} +9.06186e8 q^{61} +(1.61056e8 - 1.61056e8i) q^{62} +(6.66591e7 + 6.66591e7i) q^{63} +1.34218e8i q^{64} +1.01542e9 q^{66} +(9.62074e8 - 9.62074e8i) q^{67} +(9.62577e8 + 9.62577e8i) q^{68} +1.91354e9i q^{69} -3.12088e9 q^{71} +(-6.49544e7 + 6.49544e7i) q^{72} +(6.36339e8 + 6.36339e8i) q^{73} -1.80441e9i q^{74} +5.63999e8 q^{76} +(-1.45776e9 + 1.45776e9i) q^{77} +(-1.36224e9 - 1.36224e9i) q^{78} +1.96800e9i q^{79} +3.89211e9 q^{81} +(2.44806e9 - 2.44806e9i) q^{82} +(5.18382e9 + 5.18382e9i) q^{83} -1.57540e9i q^{84} +1.89992e9 q^{86} +(-4.53672e9 + 4.53672e9i) q^{87} +(-1.42048e9 - 1.42048e9i) q^{88} -7.77138e9i q^{89} +3.91132e9 q^{91} +(2.67687e9 - 2.67687e9i) q^{92} +(-1.84208e9 - 1.84208e9i) q^{93} -5.51486e9i q^{94} +1.53512e9 q^{96} +(6.40361e8 - 6.40361e8i) q^{97} +(-2.25792e9 - 2.25792e9i) q^{98} -1.37487e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} + 366 q^{3} - 11712 q^{6} + 16814 q^{7} + 16384 q^{8}+O(q^{10}) $ 2 * q - 32 * q^2 + 366 * q^3 - 11712 * q^6 + 16814 * q^7 + 16384 * q^8	\( 2 q - 32 q^{2} + 366 q^{3} - 11712 q^{6} + 16814 q^{7} + 16384 q^{8} - 346796 q^{11} + 187392 q^{12} + 465246 q^{13} - 524288 q^{16} - 3760066 q^{17} - 253728 q^{18} + 6153924 q^{21} + 5548736 q^{22} + 10456526 q^{23} - 14887872 q^{26} + 18709920 q^{27} - 8608768 q^{28} - 20131996 q^{31} + 8388608 q^{32} - 63463668 q^{33} + 8119296 q^{36} - 112775826 q^{37} - 35249920 q^{38} - 306007196 q^{41} - 98462784 q^{42} - 118744914 q^{43} - 334608832 q^{46} - 344678706 q^{47} - 95944704 q^{48} - 1376184156 q^{51} + 238205952 q^{52} - 392771234 q^{53} + 275480576 q^{56} - 403170960 q^{57} - 793306880 q^{58} + 1812371604 q^{61} + 322111936 q^{62} + 133318206 q^{63} + 2030837376 q^{66} + 1924147934 q^{67} + 1925153792 q^{68} - 6241755196 q^{71} - 129908736 q^{72} + 1272678526 q^{73} + 1127997440 q^{76} - 2915513972 q^{77} - 2724480576 q^{78} + 7784229762 q^{81} + 4896115136 q^{82} + 10367644206 q^{83} + 3799837248 q^{86} - 9073447440 q^{87} - 2840952832 q^{88} + 7822646244 q^{91} + 5353741312 q^{92} - 3684155268 q^{93} + 3070230528 q^{96} + 1280722494 q^{97} - 4515838432 q^{98}+O(q^{100}) \) 2 * q - 32 * q^2 + 366 * q^3 - 11712 * q^6 + 16814 * q^7 + 16384 * q^8 - 346796 * q^11 + 187392 * q^12 + 465246 * q^13 - 524288 * q^16 - 3760066 * q^17 - 253728 * q^18 + 6153924 * q^21 + 5548736 * q^22 + 10456526 * q^23 - 14887872 * q^26 + 18709920 * q^27 - 8608768 * q^28 - 20131996 * q^31 + 8388608 * q^32 - 63463668 * q^33 + 8119296 * q^36 - 112775826 * q^37 - 35249920 * q^38 - 306007196 * q^41 - 98462784 * q^42 - 118744914 * q^43 - 334608832 * q^46 - 344678706 * q^47 - 95944704 * q^48 - 1376184156 * q^51 + 238205952 * q^52 - 392771234 * q^53 + 275480576 * q^56 - 403170960 * q^57 - 793306880 * q^58 + 1812371604 * q^61 + 322111936 * q^62 + 133318206 * q^63 + 2030837376 * q^66 + 1924147934 * q^67 + 1925153792 * q^68 - 6241755196 * q^71 - 129908736 * q^72 + 1272678526 * q^73 + 1127997440 * q^76 - 2915513972 * q^77 - 2724480576 * q^78 + 7784229762 * q^81 + 4896115136 * q^82 + 10367644206 * q^83 + 3799837248 * q^86 - 9073447440 * q^87 - 2840952832 * q^88 + 7822646244 * q^91 + 5353741312 * q^92 - 3684155268 * q^93 + 3070230528 * q^96 + 1280722494 * q^97 - 4515838432 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−16.0000	+	16.0000i	−0.500000	+	0.500000i
$2$	−16.0000	+	16.0000i	−0.500000	+	0.500000i
$3$	183.000	+	183.000i	0.753086	+	0.753086i	0.975054	−	0.221968i	$-0.0712479\pi$
$3$	183.000	+	183.000i	0.753086	+	0.753086i	−0.221968	+	0.975054i	$0.571248\pi$
$4$		−	512.000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−5856.00			−0.753086
$7$	8407.00	−	8407.00i	0.500208	−	0.500208i	−0.411294	−	0.911503i	$-0.634923\pi$
$7$	8407.00	−	8407.00i	0.500208	−	0.500208i	0.911503	+	0.411294i	$0.134923\pi$
$8$	8192.00	+	8192.00i	0.250000	+	0.250000i
$9$			7929.00i			0.134278i
$10$		0			0
$11$	−173398.			−1.07667			−0.538333	−	0.842732i	$-0.680946\pi$
$11$	−173398.			−1.07667			−0.538333	+	0.842732i	$0.680946\pi$
$12$	93696.0	−	93696.0i	0.376543	−	0.376543i
$13$	232623.	+	232623.i	0.626521	+	0.626521i	0.947191	−	0.320670i	$-0.103908\pi$
$13$	232623.	+	232623.i	0.626521	+	0.626521i	−0.320670	+	0.947191i	$0.603908\pi$
$14$			269024.i			0.500208i
$15$		0			0
$16$	−262144.			−0.250000
$17$	−1.88003e6	+	1.88003e6i	−1.32410	+	1.32410i	−0.413676	+	0.910424i	$0.635755\pi$
$17$	−1.88003e6	+	1.88003e6i	−1.32410	+	1.32410i	−0.910424	+	0.413676i	$0.864245\pi$
$18$	−126864.	−	126864.i	−0.0671392	−	0.0671392i
$19$			1.10156e6i			0.444877i	0.974947	+	0.222439i	$0.0714017\pi$
$19$			1.10156e6i			0.444877i	−0.974947	+	0.222439i	$0.928598\pi$
$20$		0			0
$21$	3.07696e6			0.753400
$22$	2.77437e6	−	2.77437e6i	0.538333	−	0.538333i
$23$	5.22826e6	+	5.22826e6i	0.812303	+	0.812303i	0.984979	−	0.172675i	$-0.0552412\pi$
$23$	5.22826e6	+	5.22826e6i	0.812303	+	0.812303i	−0.172675	+	0.984979i	$0.555241\pi$
$24$			2.99827e6i			0.376543i
$25$		0			0
$26$	−7.44394e6			−0.626521
$27$	9.35496e6	−	9.35496e6i	0.651963	−	0.651963i
$28$	−4.30438e6	−	4.30438e6i	−0.250104	−	0.250104i
$29$			2.47908e7i			1.20865i	0.796737	+	0.604326i	$0.206558\pi$
$29$			2.47908e7i			1.20865i	−0.796737	+	0.604326i	$0.793442\pi$
$30$		0			0
$31$	−1.00660e7			−0.351600			−0.175800	−	0.984426i	$-0.556251\pi$
$31$	−1.00660e7			−0.351600			−0.175800	+	0.984426i	$0.556251\pi$
$32$	4.19430e6	−	4.19430e6i	0.125000	−	0.125000i
$33$	−3.17318e7	−	3.17318e7i	−0.810822	−	0.810822i
$34$		−	6.01611e7i		−	1.32410i
$35$		0			0
$36$	4.05965e6			0.0671392
$37$	−5.63879e7	+	5.63879e7i	−0.813163	+	0.813163i	−0.985107	−	0.171944i	$-0.944995\pi$
$37$	−5.63879e7	+	5.63879e7i	−0.813163	+	0.813163i	0.171944	+	0.985107i	$0.444995\pi$
$38$	−1.76250e7	−	1.76250e7i	−0.222439	−	0.222439i
$39$			8.51400e7i			0.943649i
$40$		0			0
$41$	−1.53004e8			−1.32063			−0.660317	−	0.750987i	$-0.729578\pi$
$41$	−1.53004e8			−1.32063			−0.660317	+	0.750987i	$0.729578\pi$
$42$	−4.92314e7	+	4.92314e7i	−0.376700	+	0.376700i
$43$	−5.93725e7	−	5.93725e7i	−0.403871	−	0.403871i	0.475724	−	0.879595i	$-0.342186\pi$
$43$	−5.93725e7	−	5.93725e7i	−0.403871	−	0.403871i	−0.879595	+	0.475724i	$0.842186\pi$
$44$			8.87798e7i			0.538333i
$45$		0			0
$46$	−1.67304e8			−0.812303
$47$	−1.72339e8	+	1.72339e8i	−0.751441	+	0.751441i	−0.974748	−	0.223307i	$-0.928315\pi$
$47$	−1.72339e8	+	1.72339e8i	−0.751441	+	0.751441i	0.223307	+	0.974748i	$0.428315\pi$
$48$	−4.79724e7	−	4.79724e7i	−0.188272	−	0.188272i
$49$			1.41120e8i			0.499583i
$50$		0			0
$51$	−6.88092e8			−1.99432
$52$	1.19103e8	−	1.19103e8i	0.313261	−	0.313261i
$53$	−1.96386e8	−	1.96386e8i	−0.469602	−	0.469602i	0.432183	−	0.901786i	$-0.357743\pi$
$53$	−1.96386e8	−	1.96386e8i	−0.469602	−	0.469602i	−0.901786	+	0.432183i	$0.857743\pi$
$54$			2.99359e8i			0.651963i
$55$		0			0
$56$	1.37740e8			0.250104
$57$	−2.01585e8	+	2.01585e8i	−0.335031	+	0.335031i
$58$	−3.96653e8	−	3.96653e8i	−0.604326	−	0.604326i
$59$		−	6.94069e8i		−	0.970829i	−0.874284	−	0.485414i	$-0.838669\pi$
$59$		−	6.94069e8i		−	0.970829i	0.874284	−	0.485414i	$-0.161331\pi$
$60$		0			0
$61$	9.06186e8			1.07292			0.536461	−	0.843925i	$-0.319761\pi$
$61$	9.06186e8			1.07292			0.536461	+	0.843925i	$0.319761\pi$
$62$	1.61056e8	−	1.61056e8i	0.175800	−	0.175800i
$63$	6.66591e7	+	6.66591e7i	0.0671671	+	0.0671671i
$64$			1.34218e8i			0.125000i
$65$		0			0
$66$	1.01542e9			0.810822
$67$	9.62074e8	−	9.62074e8i	0.712581	−	0.712581i	−0.254493	−	0.967075i	$-0.581909\pi$
$67$	9.62074e8	−	9.62074e8i	0.712581	−	0.712581i	0.967075	+	0.254493i	$0.0819087\pi$
$68$	9.62577e8	+	9.62577e8i	0.662050	+	0.662050i
$69$			1.91354e9i			1.22347i
$70$		0			0
$71$	−3.12088e9			−1.72976			−0.864878	−	0.501982i	$-0.832605\pi$
$71$	−3.12088e9			−1.72976			−0.864878	+	0.501982i	$0.832605\pi$
$72$	−6.49544e7	+	6.49544e7i	−0.0335696	+	0.0335696i
$73$	6.36339e8	+	6.36339e8i	0.306955	+	0.306955i	0.843727	−	0.536772i	$-0.180357\pi$
$73$	6.36339e8	+	6.36339e8i	0.306955	+	0.306955i	−0.536772	+	0.843727i	$0.680357\pi$
$74$		−	1.80441e9i		−	0.813163i
$75$		0			0
$76$	5.63999e8			0.222439
$77$	−1.45776e9	+	1.45776e9i	−0.538557	+	0.538557i
$78$	−1.36224e9	−	1.36224e9i	−0.471825	−	0.471825i
$79$			1.96800e9i			0.639571i	0.947490	+	0.319786i	$0.103611\pi$
$79$			1.96800e9i			0.639571i	−0.947490	+	0.319786i	$0.896389\pi$
$80$		0			0
$81$	3.89211e9			1.11625
$82$	2.44806e9	−	2.44806e9i	0.660317	−	0.660317i
$83$	5.18382e9	+	5.18382e9i	1.31601	+	1.31601i	0.916904	+	0.399107i	$0.130680\pi$
$83$	5.18382e9	+	5.18382e9i	1.31601	+	1.31601i	0.399107	+	0.916904i	$0.369320\pi$
$84$		−	1.57540e9i		−	0.376700i
$85$		0			0
$86$	1.89992e9			0.403871
$87$	−4.53672e9	+	4.53672e9i	−0.910219	+	0.910219i
$88$	−1.42048e9	−	1.42048e9i	−0.269166	−	0.269166i
$89$		−	7.77138e9i		−	1.39171i	−0.718183	−	0.695854i	$-0.755026\pi$
$89$		−	7.77138e9i		−	1.39171i	0.718183	−	0.695854i	$-0.244974\pi$
$90$		0			0
$91$	3.91132e9			0.626782
$92$	2.67687e9	−	2.67687e9i	0.406152	−	0.406152i
$93$	−1.84208e9	−	1.84208e9i	−0.264785	−	0.264785i
$94$		−	5.51486e9i		−	0.751441i
$95$		0			0
$96$	1.53512e9			0.188272
$97$	6.40361e8	−	6.40361e8i	0.0745704	−	0.0745704i	−0.668838	−	0.743408i	$-0.733208\pi$
$97$	6.40361e8	−	6.40361e8i	0.0745704	−	0.0745704i	0.743408	+	0.668838i	$0.233208\pi$
$98$	−2.25792e9	−	2.25792e9i	−0.249792	−	0.249792i
$99$		−	1.37487e9i		−	0.144573i
$100$		0			0
$101$	2.02434e9			0.192609			0.0963047	−	0.995352i	$-0.469298\pi$
$101$	2.02434e9			0.192609			0.0963047	+	0.995352i	$0.469298\pi$
$102$	1.10095e10	−	1.10095e10i	0.997162	−	0.997162i
$103$	1.50252e9	+	1.50252e9i	0.129609	+	0.129609i	0.768935	−	0.639326i	$-0.220787\pi$
$103$	1.50252e9	+	1.50252e9i	0.129609	+	0.129609i	−0.639326	+	0.768935i	$0.720787\pi$
$104$			3.81130e9i			0.313261i
$105$		0			0
$106$	6.28434e9			0.469602
$107$	−1.41812e9	+	1.41812e9i	−0.101110	+	0.101110i	−0.755852	−	0.654742i	$-0.772777\pi$
$107$	−1.41812e9	+	1.41812e9i	−0.101110	+	0.101110i	0.654742	+	0.755852i	$0.272777\pi$
$108$	−4.78974e9	−	4.78974e9i	−0.325982	−	0.325982i
$109$			6.21296e9i			0.403800i	0.979406	+	0.201900i	$0.0647116\pi$
$109$			6.21296e9i			0.403800i	−0.979406	+	0.201900i	$0.935288\pi$
$110$		0			0
$111$	−2.06380e10			−1.22476
$112$	−2.20384e9	+	2.20384e9i	−0.125052	+	0.125052i
$113$	1.79511e10	+	1.79511e10i	0.974313	+	0.974313i	0.999678	−	0.0253650i	$-0.00807480\pi$
$113$	1.79511e10	+	1.79511e10i	0.974313	+	0.974313i	−0.0253650	+	0.999678i	$0.508075\pi$
$114$		−	6.45074e9i		−	0.335031i
$115$		0			0
$116$	1.26929e10			0.604326
$117$	−1.84447e9	+	1.84447e9i	−0.0841282	+	0.0841282i
$118$	1.11051e10	+	1.11051e10i	0.485414	+	0.485414i
$119$			3.16109e10i			1.32465i
$120$		0			0
$121$	4.12944e9			0.159208
$122$	−1.44990e10	+	1.44990e10i	−0.536461	+	0.536461i
$123$	−2.79997e10	−	2.79997e10i	−0.994551	−	0.994551i
$124$			5.15379e9i			0.175800i
$125$		0			0
$126$	−2.13309e9			−0.0671671
$127$	−1.30621e10	+	1.30621e10i	−0.395362	+	0.395362i	−0.876593	−	0.481232i	$-0.840190\pi$
$127$	−1.30621e10	+	1.30621e10i	−0.395362	+	0.395362i	0.481232	+	0.876593i	$0.340190\pi$
$128$	−2.14748e9	−	2.14748e9i	−0.0625000	−	0.0625000i
$129$		−	2.17303e10i		−	0.608300i
$130$		0			0
$131$	−5.20222e10			−1.34844			−0.674221	−	0.738530i	$-0.735520\pi$
$131$	−5.20222e10			−1.34844			−0.674221	+	0.738530i	$0.735520\pi$
$132$	−1.62467e10	+	1.62467e10i	−0.405411	+	0.405411i
$133$	9.26081e9	+	9.26081e9i	0.222531	+	0.222531i
$134$			3.07864e10i			0.712581i
$135$		0			0
$136$	−3.08025e10			−0.662050
$137$	1.63815e10	−	1.63815e10i	0.339429	−	0.339429i	−0.516723	−	0.856153i	$-0.672848\pi$
$137$	1.63815e10	−	1.63815e10i	0.339429	−	0.339429i	0.856153	+	0.516723i	$0.172848\pi$
$138$	−3.06167e10	−	3.06167e10i	−0.611735	−	0.611735i
$139$			2.61490e10i			0.503942i	0.967735	+	0.251971i	$0.0810787\pi$
$139$			2.61490e10i			0.503942i	−0.967735	+	0.251971i	$0.918921\pi$
$140$		0			0
$141$	−6.30762e10			−1.13180
$142$	4.99340e10	−	4.99340e10i	0.864878	−	0.864878i
$143$	−4.03364e10	−	4.03364e10i	−0.674554	−	0.674554i
$144$		−	2.07854e9i		−	0.0335696i
$145$		0			0
$146$	−2.03629e10			−0.306955
$147$	−2.58250e10	+	2.58250e10i	−0.376229	+	0.376229i
$148$	2.88706e10	+	2.88706e10i	0.406581	+	0.406581i
$149$		−	4.31363e9i		−	0.0587369i	−0.999569	−	0.0293685i	$-0.990650\pi$
$149$		−	4.31363e9i		−	0.0587369i	0.999569	−	0.0293685i	$-0.00934962\pi$
$150$		0			0
$151$	1.13868e11			1.45050			0.725251	−	0.688484i	$-0.241724\pi$
$151$	1.13868e11			1.45050			0.725251	+	0.688484i	$0.241724\pi$
$152$	−9.02398e9	+	9.02398e9i	−0.111219	+	0.111219i
$153$	−1.49068e10	−	1.49068e10i	−0.177798	−	0.177798i
$154$		−	4.66482e10i		−	0.538557i
$155$		0			0
$156$	4.35917e10			0.471825
$157$	−1.04428e10	+	1.04428e10i	−0.109476	+	0.109476i	−0.759723	−	0.650247i	$-0.774665\pi$
$157$	−1.04428e10	+	1.04428e10i	−0.109476	+	0.109476i	0.650247	+	0.759723i	$0.274665\pi$
$158$	−3.14879e10	−	3.14879e10i	−0.319786	−	0.319786i
$159$		−	7.18771e10i		−	0.707302i
$160$		0			0
$161$	8.79080e10			0.812642
$162$	−6.22738e10	+	6.22738e10i	−0.558124	+	0.558124i
$163$	−4.78305e10	−	4.78305e10i	−0.415688	−	0.415688i	0.468027	−	0.883714i	$-0.344965\pi$
$163$	−4.78305e10	−	4.78305e10i	−0.415688	−	0.415688i	−0.883714	+	0.468027i	$0.844965\pi$
$164$			7.83378e10i			0.660317i
$165$		0			0
$166$	−1.65882e11			−1.31601
$167$	1.18281e10	−	1.18281e10i	0.0910613	−	0.0910613i	−0.660109	−	0.751170i	$-0.729490\pi$
$167$	1.18281e10	−	1.18281e10i	0.0910613	−	0.0910613i	0.751170	+	0.660109i	$0.229490\pi$
$168$	2.52065e10	+	2.52065e10i	0.188350	+	0.188350i
$169$		−	2.96316e10i		−	0.214942i
$170$		0			0
$171$	−8.73427e9			−0.0597374
$172$	−3.03987e10	+	3.03987e10i	−0.201936	+	0.201936i
$173$	1.16377e11	+	1.16377e11i	0.750997	+	0.750997i	0.974665	−	0.223669i	$-0.0718033\pi$
$173$	1.16377e11	+	1.16377e11i	0.750997	+	0.750997i	−0.223669	+	0.974665i	$0.571803\pi$
$174$		−	1.45175e11i		−	0.910219i
$175$		0			0
$176$	4.54552e10			0.269166
$177$	1.27015e11	−	1.27015e11i	0.731118	−	0.731118i
$178$	1.24342e11	+	1.24342e11i	0.695854	+	0.695854i
$179$			1.81011e11i			0.985008i	0.870310	+	0.492504i	$0.163918\pi$
$179$			1.81011e11i			0.985008i	−0.870310	+	0.492504i	$0.836082\pi$
$180$		0			0
$181$	1.33000e11			0.684636			0.342318	−	0.939584i	$-0.388788\pi$
$181$	1.33000e11			0.684636			0.342318	+	0.939584i	$0.388788\pi$
$182$	−6.25812e10	+	6.25812e10i	−0.313391	+	0.313391i
$183$	1.65832e11	+	1.65832e11i	0.808003	+	0.808003i
$184$			8.56599e10i			0.406152i
$185$		0			0
$186$	5.89465e10			0.264785
$187$	3.25994e11	−	3.25994e11i	1.42561	−	1.42561i
$188$	8.82377e10	+	8.82377e10i	0.375721	+	0.375721i
$189$		−	1.57294e11i		−	0.652235i
$190$		0			0
$191$	1.31044e11			0.515525			0.257762	−	0.966208i	$-0.417015\pi$
$191$	1.31044e11			0.515525			0.257762	+	0.966208i	$0.417015\pi$
$192$	−2.45618e10	+	2.45618e10i	−0.0941358	+	0.0941358i
$193$	−2.12792e11	−	2.12792e11i	−0.794639	−	0.794639i	0.187606	−	0.982244i	$-0.439927\pi$
$193$	−2.12792e11	−	2.12792e11i	−0.794639	−	0.794639i	−0.982244	+	0.187606i	$0.939927\pi$
$194$			2.04916e10i			0.0745704i
$195$		0			0
$196$	7.22534e10			0.249792
$197$	−7.90246e10	+	7.90246e10i	−0.266337	+	0.266337i	−0.827622	−	0.561285i	$-0.810307\pi$
$197$	−7.90246e10	+	7.90246e10i	−0.266337	+	0.266337i	0.561285	+	0.827622i	$0.310307\pi$
$198$	2.19980e10	+	2.19980e10i	0.0722864	+	0.0722864i
$199$		−	4.52657e11i		−	1.45045i	−0.688510	−	0.725227i	$-0.741735\pi$
$199$		−	4.52657e11i		−	1.45045i	0.688510	−	0.725227i	$-0.258265\pi$
$200$		0			0
$201$	3.52119e11			1.07327
$202$	−3.23895e10	+	3.23895e10i	−0.0963047	+	0.0963047i
$203$	2.08417e11	+	2.08417e11i	0.604578	+	0.604578i
$204$			3.52303e11i			0.997162i
$205$		0			0
$206$	−4.80808e10			−0.129609
$207$	−4.14549e10	+	4.14549e10i	−0.109075	+	0.109075i
$208$	−6.09807e10	−	6.09807e10i	−0.156630	−	0.156630i
$209$		−	1.91008e11i		−	0.478984i
$210$		0			0
$211$	1.37995e11			0.329951			0.164976	−	0.986298i	$-0.447245\pi$
$211$	1.37995e11			0.329951			0.164976	+	0.986298i	$0.447245\pi$
$212$	−1.00549e11	+	1.00549e11i	−0.234801	+	0.234801i
$213$	−5.71121e11	−	5.71121e11i	−1.30266	−	1.30266i
$214$		−	4.53797e10i		−	0.101110i
$215$		0			0
$216$	1.53272e11			0.325982
$217$	−8.46248e10	+	8.46248e10i	−0.175873	+	0.175873i
$218$	−9.94074e10	−	9.94074e10i	−0.201900	−	0.201900i
$219$			2.32900e11i			0.462327i
$220$		0			0
$221$	−8.74678e11			−1.65915
$222$	3.30208e11	−	3.30208e11i	0.612382	−	0.612382i
$223$	1.26054e11	+	1.26054e11i	0.228576	+	0.228576i	0.812098	−	0.583521i	$-0.198326\pi$
$223$	1.26054e11	+	1.26054e11i	0.228576	+	0.228576i	−0.583521	+	0.812098i	$0.698326\pi$
$224$		−	7.05230e10i		−	0.125052i
$225$		0			0
$226$	−5.74435e11			−0.974313
$227$	−1.15268e11	+	1.15268e11i	−0.191241	+	0.191241i	−0.796232	−	0.604991i	$-0.793177\pi$
$227$	−1.15268e11	+	1.15268e11i	−0.191241	+	0.191241i	0.604991	+	0.796232i	$0.293177\pi$
$228$	1.03212e11	+	1.03212e11i	0.167515	+	0.167515i
$229$			3.29124e11i			0.522615i	0.965256	+	0.261308i	$0.0841537\pi$
$229$			3.29124e11i			0.522615i	−0.965256	+	0.261308i	$0.915846\pi$
$230$		0			0
$231$	−5.33539e11			−0.811160
$232$	−2.03087e11	+	2.03087e11i	−0.302163	+	0.302163i
$233$	9.97948e10	+	9.97948e10i	0.145321	+	0.145321i	0.776024	−	0.630703i	$-0.217233\pi$
$233$	9.97948e10	+	9.97948e10i	0.145321	+	0.145321i	−0.630703	+	0.776024i	$0.717233\pi$
$234$		−	5.90230e10i		−	0.0841282i
$235$		0			0
$236$	−3.55363e11			−0.485414
$237$	−3.60143e11	+	3.60143e11i	−0.481652	+	0.481652i
$238$	−5.05774e11	−	5.05774e11i	−0.662326	−	0.662326i
$239$			3.95622e10i			0.0507331i	0.999678	+	0.0253665i	$0.00807529\pi$
$239$			3.95622e10i			0.0507331i	−0.999678	+	0.0253665i	$0.991925\pi$
$240$		0			0
$241$	−8.14271e11			−1.00158			−0.500788	−	0.865570i	$-0.666956\pi$
$241$	−8.14271e11			−1.00158			−0.500788	+	0.865570i	$0.666956\pi$
$242$	−6.60711e10	+	6.60711e10i	−0.0796039	+	0.0796039i
$243$	1.59856e11	+	1.59856e11i	0.188668	+	0.188668i
$244$		−	4.63967e11i		−	0.536461i
$245$		0			0
$246$	8.95989e11			0.994551
$247$	−2.56248e11	+	2.56248e11i	−0.278725	+	0.278725i
$248$	−8.24607e10	−	8.24607e10i	−0.0878999	−	0.0878999i
$249$			1.89728e12i			1.98214i
$250$		0			0
$251$	4.53171e11			0.454877			0.227438	−	0.973793i	$-0.426965\pi$
$251$	4.53171e11			0.454877			0.227438	+	0.973793i	$0.426965\pi$
$252$	3.41295e10	−	3.41295e10i	0.0335836	−	0.0335836i
$253$	−9.06570e11	−	9.06570e11i	−0.874579	−	0.874579i
$254$		−	4.17987e11i		−	0.395362i
$255$		0			0
$256$	6.87195e10			0.0625000
$257$	−1.33579e12	+	1.33579e12i	−1.19144	+	1.19144i	−0.214777	+	0.976663i	$0.568902\pi$
$257$	−1.33579e12	+	1.33579e12i	−1.19144	+	1.19144i	−0.976663	+	0.214777i	$0.931098\pi$
$258$	3.47685e11	+	3.47685e11i	0.304150	+	0.304150i
$259$			9.48106e11i			0.813501i
$260$		0			0
$261$	−1.96567e11			−0.162296
$262$	8.32355e11	−	8.32355e11i	0.674221	−	0.674221i
$263$	9.12065e11	+	9.12065e11i	0.724848	+	0.724848i	0.969589	−	0.244740i	$-0.0787027\pi$
$263$	9.12065e11	+	9.12065e11i	0.724848	+	0.724848i	−0.244740	+	0.969589i	$0.578703\pi$
$264$		−	5.19894e11i		−	0.405411i
$265$		0			0
$266$	−2.96346e11			−0.222531
$267$	1.42216e12	−	1.42216e12i	1.04808	−	1.04808i
$268$	−4.92582e11	−	4.92582e11i	−0.356291	−	0.356291i
$269$		−	1.04348e12i		−	0.740835i	−0.928865	−	0.370417i	$-0.879215\pi$
$269$		−	1.04348e12i		−	0.740835i	0.928865	−	0.370417i	$-0.120785\pi$
$270$		0			0
$271$	7.19445e11			0.492211			0.246105	−	0.969243i	$-0.420849\pi$
$271$	7.19445e11			0.492211			0.246105	+	0.969243i	$0.420849\pi$
$272$	4.92839e11	−	4.92839e11i	0.331025	−	0.331025i
$273$	7.15772e11	+	7.15772e11i	0.472021	+	0.472021i
$274$			5.24206e11i			0.339429i
$275$		0			0
$276$	9.79735e11			0.611735
$277$	8.62576e11	−	8.62576e11i	0.528931	−	0.528931i	−0.391323	−	0.920253i	$-0.627982\pi$
$277$	8.62576e11	−	8.62576e11i	0.528931	−	0.528931i	0.920253	+	0.391323i	$0.127982\pi$
$278$	−4.18383e11	−	4.18383e11i	−0.251971	−	0.251971i
$279$		−	7.98133e10i		−	0.0472122i
$280$		0			0
$281$	−7.89300e11			−0.450516			−0.225258	−	0.974299i	$-0.572323\pi$
$281$	−7.89300e11			−0.450516			−0.225258	+	0.974299i	$0.572323\pi$
$282$	1.00922e12	−	1.00922e12i	0.565900	−	0.565900i
$283$	6.60245e11	+	6.60245e11i	0.363725	+	0.363725i	0.865182	−	0.501457i	$-0.167203\pi$
$283$	6.60245e11	+	6.60245e11i	0.363725	+	0.363725i	−0.501457	+	0.865182i	$0.667203\pi$
$284$			1.59789e12i			0.864878i
$285$		0			0
$286$	1.29076e12			0.674554
$287$	−1.28630e12	+	1.28630e12i	−0.660592	+	0.660592i
$288$	3.32566e10	+	3.32566e10i	0.0167848	+	0.0167848i
$289$		−	5.05305e12i		−	2.50648i
$290$		0			0
$291$	2.34372e11			0.112316
$292$	3.25806e11	−	3.25806e11i	0.153477	−	0.153477i
$293$	−1.79236e11	−	1.79236e11i	−0.0830019	−	0.0830019i	0.664387	−	0.747389i	$-0.268693\pi$
$293$	−1.79236e11	−	1.79236e11i	−0.0830019	−	0.0830019i	−0.747389	+	0.664387i	$0.768693\pi$
$294$		−	8.26398e11i		−	0.376229i
$295$		0			0
$296$	−9.23860e11			−0.406581
$297$	−1.62213e12	+	1.62213e12i	−0.701946	+	0.701946i
$298$	6.90180e10	+	6.90180e10i	0.0293685	+	0.0293685i
$299$			2.43243e12i			1.01785i
$300$		0			0
$301$	−9.98288e11			−0.404039
$302$	−1.82189e12	+	1.82189e12i	−0.725251	+	0.725251i
$303$	3.70455e11	+	3.70455e11i	0.145051	+	0.145051i
$304$		−	2.88767e11i		−	0.111219i
$305$		0			0
$306$	4.77017e11			0.177798
$307$	1.10155e12	−	1.10155e12i	0.403937	−	0.403937i	−0.475681	−	0.879618i	$-0.657798\pi$
$307$	1.10155e12	−	1.10155e12i	0.403937	−	0.403937i	0.879618	+	0.475681i	$0.157798\pi$
$308$	7.46372e11	+	7.46372e11i	0.269278	+	0.269278i
$309$			5.49924e11i			0.195214i
$310$		0			0
$311$	5.31138e12			1.82560			0.912800	−	0.408406i	$-0.133915\pi$
$311$	5.31138e12			1.82560			0.912800	+	0.408406i	$0.133915\pi$
$312$	−6.97467e11	+	6.97467e11i	−0.235912	+	0.235912i
$313$	8.40078e11	+	8.40078e11i	0.279639	+	0.279639i	0.832965	−	0.553326i	$-0.186642\pi$
$313$	8.40078e11	+	8.40078e11i	0.279639	+	0.279639i	−0.553326	+	0.832965i	$0.686642\pi$
$314$		−	3.34169e11i		−	0.109476i
$315$		0			0
$316$	1.00761e12			0.319786
$317$	1.16635e12	−	1.16635e12i	0.364361	−	0.364361i	−0.501055	−	0.865416i	$-0.667054\pi$
$317$	1.16635e12	−	1.16635e12i	0.364361	−	0.364361i	0.865416	+	0.501055i	$0.167054\pi$
$318$	1.15003e12	+	1.15003e12i	0.353651	+	0.353651i
$319$		−	4.29868e12i		−	1.30131i
$320$		0			0
$321$	−5.19031e11			−0.152289
$322$	−1.40653e12	+	1.40653e12i	−0.406321	+	0.406321i
$323$	−2.07097e12	−	2.07097e12i	−0.589062	−	0.589062i
$324$		−	1.99276e12i		−	0.558124i
$325$		0			0
$326$	1.53058e12			0.415688
$327$	−1.13697e12	+	1.13697e12i	−0.304096	+	0.304096i
$328$	−1.25341e12	−	1.25341e12i	−0.330158	−	0.330158i
$329$			2.89771e12i			0.751754i
$330$		0			0
$331$	−4.82042e12			−1.21324			−0.606618	−	0.794994i	$-0.707474\pi$
$331$	−4.82042e12			−1.21324			−0.606618	+	0.794994i	$0.707474\pi$
$332$	2.65412e12	−	2.65412e12i	0.658006	−	0.658006i
$333$	−4.47100e11	−	4.47100e11i	−0.109190	−	0.109190i
$334$			3.78500e11i			0.0910613i
$335$		0			0
$336$	−8.06607e11			−0.188350
$337$	3.68550e12	−	3.68550e12i	0.847904	−	0.847904i	−0.141967	−	0.989871i	$-0.545343\pi$
$337$	3.68550e12	−	3.68550e12i	0.847904	−	0.847904i	0.989871	+	0.141967i	$0.0453428\pi$
$338$	4.74105e11	+	4.74105e11i	0.107471	+	0.107471i
$339$			6.57010e12i			1.46748i
$340$		0			0
$341$	1.74542e12			0.378555
$342$	1.39748e11	−	1.39748e11i	0.0298687	−	0.0298687i
$343$	3.56116e12	+	3.56116e12i	0.750104	+	0.750104i
$344$		−	9.72758e11i		−	0.201936i
$345$		0			0
$346$	−3.72408e12			−0.750997
$347$	5.38450e12	−	5.38450e12i	1.07028	−	1.07028i	0.0729452	−	0.997336i	$-0.476760\pi$
$347$	5.38450e12	−	5.38450e12i	1.07028	−	1.07028i	0.997336	−	0.0729452i	$-0.0232398\pi$
$348$	2.32280e12	+	2.32280e12i	0.455110	+	0.455110i
$349$		−	8.12658e12i		−	1.56957i	−0.619768	−	0.784785i	$-0.712773\pi$
$349$		−	8.12658e12i		−	1.56957i	0.619768	−	0.784785i	$-0.287227\pi$
$350$		0			0
$351$	4.35236e12			0.816938
$352$	−7.27284e11	+	7.27284e11i	−0.134583	+	0.134583i
$353$	−5.49274e12	−	5.49274e12i	−1.00211	−	1.00211i	−0.999998	−	0.00211203i	$-0.999328\pi$
$353$	−5.49274e12	−	5.49274e12i	−1.00211	−	1.00211i	−0.00211203	−	0.999998i	$-0.500672\pi$
$354$			4.06447e12i			0.731118i
$355$		0			0
$356$	−3.97895e12			−0.695854
$357$	−5.78479e12	+	5.78479e12i	−0.997577	+	0.997577i
$358$	−2.89617e12	−	2.89617e12i	−0.492504	−	0.492504i
$359$			5.91305e12i			0.991606i	0.868435	+	0.495803i	$0.165126\pi$
$359$			5.91305e12i			0.991606i	−0.868435	+	0.495803i	$0.834874\pi$
$360$		0			0
$361$	4.91763e12			0.802084
$362$	−2.12801e12	+	2.12801e12i	−0.342318	+	0.342318i
$363$	7.55688e11	+	7.55688e11i	0.119897	+	0.119897i
$364$		−	2.00260e12i		−	0.313391i
$365$		0			0
$366$	−5.30662e12			−0.808003
$367$	−1.75360e12	+	1.75360e12i	−0.263390	+	0.263390i	−0.826430	−	0.563040i	$-0.809632\pi$
$367$	−1.75360e12	+	1.75360e12i	−0.263390	+	0.263390i	0.563040	+	0.826430i	$0.309632\pi$
$368$	−1.37056e12	−	1.37056e12i	−0.203076	−	0.203076i
$369$		−	1.21317e12i		−	0.177332i
$370$		0			0
$371$	−3.30203e12			−0.469798
$372$	−9.43144e11	+	9.43144e11i	−0.132392	+	0.132392i
$373$	−4.25717e12	−	4.25717e12i	−0.589627	−	0.589627i	0.347904	−	0.937530i	$-0.386894\pi$
$373$	−4.25717e12	−	4.25717e12i	−0.589627	−	0.589627i	−0.937530	+	0.347904i	$0.886894\pi$
$374$			1.04318e13i			1.42561i
$375$		0			0
$376$	−2.82361e12			−0.375721
$377$	−5.76692e12	+	5.76692e12i	−0.757246	+	0.757246i
$378$	2.51671e12	+	2.51671e12i	0.326117	+	0.326117i
$379$			7.20999e12i			0.922016i	0.887396	+	0.461008i	$0.152512\pi$
$379$			7.20999e12i			0.922016i	−0.887396	+	0.461008i	$0.847488\pi$
$380$		0			0
$381$	−4.78073e12			−0.595483
$382$	−2.09670e12	+	2.09670e12i	−0.257762	+	0.257762i
$383$	6.93832e12	+	6.93832e12i	0.841900	+	0.841900i	0.989106	−	0.147206i	$-0.0470281\pi$
$383$	6.93832e12	+	6.93832e12i	0.841900	+	0.841900i	−0.147206	+	0.989106i	$0.547028\pi$
$384$		−	7.85979e11i		−	0.0941358i
$385$		0			0
$386$	6.80936e12			0.794639
$387$	4.70764e11	−	4.70764e11i	0.0542311	−	0.0542311i
$388$	−3.27865e11	−	3.27865e11i	−0.0372852	−	0.0372852i
$389$		−	1.12518e13i		−	1.26320i	−0.775293	−	0.631601i	$-0.782398\pi$
$389$		−	1.12518e13i		−	1.26320i	0.775293	−	0.631601i	$-0.217602\pi$
$390$		0			0
$391$	−1.96586e13			−2.15114
$392$	−1.15605e12	+	1.15605e12i	−0.124896	+	0.124896i
$393$	−9.52006e12	−	9.52006e12i	−1.01549	−	1.01549i
$394$		−	2.52879e12i		−	0.266337i
$395$		0			0
$396$	−7.03935e11			−0.0722864
$397$	7.94628e12	−	7.94628e12i	0.805770	−	0.805770i	−0.178221	−	0.983991i	$-0.557034\pi$
$397$	7.94628e12	−	7.94628e12i	0.805770	−	0.805770i	0.983991	+	0.178221i	$0.0570340\pi$
$398$	7.24252e12	+	7.24252e12i	0.725227	+	0.725227i
$399$			3.38946e12i			0.335171i
$400$		0			0
$401$	8.81072e12			0.849747			0.424874	−	0.905253i	$-0.360319\pi$
$401$	8.81072e12			0.849747			0.424874	+	0.905253i	$0.360319\pi$
$402$	−5.63391e12	+	5.63391e12i	−0.536635	+	0.536635i
$403$	−2.34158e12	−	2.34158e12i	−0.220285	−	0.220285i
$404$		−	1.03646e12i		−	0.0963047i
$405$		0			0
$406$	−6.66933e12			−0.604578
$407$	9.77755e12	−	9.77755e12i	0.875504	−	0.875504i
$408$	−5.63685e12	−	5.63685e12i	−0.498581	−	0.498581i
$409$			1.00160e13i			0.875141i	0.899184	+	0.437571i	$0.144161\pi$
$409$			1.00160e13i			0.875141i	−0.899184	+	0.437571i	$0.855839\pi$
$410$		0			0
$411$	5.99561e12			0.511239
$412$	7.69293e11	−	7.69293e11i	0.0648045	−	0.0648045i
$413$	−5.83504e12	−	5.83504e12i	−0.485616	−	0.485616i
$414$		−	1.32656e12i		−	0.109075i
$415$		0			0
$416$	1.95138e12			0.156630
$417$	−4.78526e12	+	4.78526e12i	−0.379512	+	0.379512i
$418$	3.05613e12	+	3.05613e12i	0.239492	+	0.239492i
$419$		−	1.48244e13i		−	1.14791i	−0.818888	−	0.573954i	$-0.805409\pi$
$419$		−	1.48244e13i		−	1.14791i	0.818888	−	0.573954i	$-0.194591\pi$
$420$		0			0
$421$	−4.68500e12			−0.354241			−0.177121	−	0.984189i	$-0.556678\pi$
$421$	−4.68500e12			−0.354241			−0.177121	+	0.984189i	$0.556678\pi$
$422$	−2.20791e12	+	2.20791e12i	−0.164976	+	0.164976i
$423$	−1.36648e12	−	1.36648e12i	−0.100902	−	0.100902i
$424$		−	3.21758e12i		−	0.234801i
$425$		0			0
$426$	1.82759e13			1.30266
$427$	7.61830e12	−	7.61830e12i	0.536684	−	0.536684i
$428$	7.26075e11	+	7.26075e11i	0.0505549	+	0.0505549i
$429$		−	1.47631e13i		−	1.01599i
$430$		0			0
$431$	2.39126e13			1.60783			0.803917	−	0.594741i	$-0.202746\pi$
$431$	2.39126e13			1.60783			0.803917	+	0.594741i	$0.202746\pi$
$432$	−2.45235e12	+	2.45235e12i	−0.162991	+	0.162991i
$433$	7.41823e11	+	7.41823e11i	0.0487372	+	0.0487372i	0.731055	−	0.682318i	$-0.239028\pi$
$433$	7.41823e11	+	7.41823e11i	0.0487372	+	0.0487372i	−0.682318	+	0.731055i	$0.739028\pi$
$434$		−	2.70800e12i		−	0.175873i
$435$		0			0
$436$	3.18104e12			0.201900
$437$	−5.75925e12	+	5.75925e12i	−0.361375	+	0.361375i
$438$	−3.72640e12	−	3.72640e12i	−0.231163	−	0.231163i
$439$		−	2.09704e13i		−	1.28613i	−0.765811	−	0.643065i	$-0.777662\pi$
$439$		−	2.09704e13i		−	1.28613i	0.765811	−	0.643065i	$-0.222338\pi$
$440$		0			0
$441$	−1.11894e12			−0.0670832
$442$	1.39948e13	−	1.39948e13i	0.829577	−	0.829577i
$443$	2.38909e13	+	2.38909e13i	1.40028	+	1.40028i	0.799160	+	0.601118i	$0.205278\pi$
$443$	2.38909e13	+	2.38909e13i	1.40028	+	1.40028i	0.601118	+	0.799160i	$0.294722\pi$
$444$			1.05666e13i			0.612382i
$445$		0			0
$446$	−4.03372e12			−0.228576
$447$	7.89394e11	−	7.89394e11i	0.0442340	−	0.0442340i
$448$	1.12837e12	+	1.12837e12i	0.0625260	+	0.0625260i
$449$			2.04535e13i			1.12082i	0.828215	+	0.560411i	$0.189357\pi$
$449$			2.04535e13i			1.12082i	−0.828215	+	0.560411i	$0.810643\pi$
$450$		0			0
$451$	2.65305e13			1.42188
$452$	9.19096e12	−	9.19096e12i	0.487157	−	0.487157i
$453$	2.08379e13	+	2.08379e13i	1.09235	+	1.09235i
$454$		−	3.68858e12i		−	0.191241i
$455$		0			0
$456$	−3.30278e12			−0.167515
$457$	−6.88521e12	+	6.88521e12i	−0.345411	+	0.345411i	−0.858397	−	0.512986i	$-0.828539\pi$
$457$	−6.88521e12	+	6.88521e12i	−0.345411	+	0.345411i	0.512986	+	0.858397i	$0.328539\pi$
$458$	−5.26598e12	−	5.26598e12i	−0.261308	−	0.261308i
$459$			3.51753e13i			1.72653i
$460$		0			0
$461$	−1.72039e13			−0.826268			−0.413134	−	0.910670i	$-0.635566\pi$
$461$	−1.72039e13			−0.826268			−0.413134	+	0.910670i	$0.635566\pi$
$462$	8.53662e12	−	8.53662e12i	0.405580	−	0.405580i
$463$	4.67192e11	+	4.67192e11i	0.0219579	+	0.0219579i	0.718000	−	0.696043i	$-0.245058\pi$
$463$	4.67192e11	+	4.67192e11i	0.0219579	+	0.0219579i	−0.696043	+	0.718000i	$0.745058\pi$
$464$		−	6.49877e12i		−	0.302163i
$465$		0			0
$466$	−3.19343e12			−0.145321
$467$	−1.62768e13	+	1.62768e13i	−0.732799	+	0.732799i	−0.971173	−	0.238374i	$-0.923385\pi$
$467$	−1.62768e13	+	1.62768e13i	−0.732799	+	0.732799i	0.238374	+	0.971173i	$0.423385\pi$
$468$	9.44367e11	+	9.44367e11i	0.0420641	+	0.0420641i
$469$		−	1.61763e13i		−	0.712878i
$470$		0			0
$471$	−3.82206e12			−0.164889
$472$	5.68581e12	−	5.68581e12i	0.242707	−	0.242707i
$473$	1.02951e13	+	1.02951e13i	0.434834	+	0.434834i
$474$		−	1.15246e13i		−	0.481652i
$475$		0			0
$476$	1.61848e13			0.662326
$477$	1.55714e12	−	1.55714e12i	0.0630574	−	0.0630574i
$478$	−6.32996e11	−	6.32996e11i	−0.0253665	−	0.0253665i
$479$			3.26759e13i			1.29584i	0.761710	+	0.647918i	$0.224360\pi$
$479$			3.26759e13i			1.29584i	−0.761710	+	0.647918i	$0.775640\pi$
$480$		0			0
$481$	−2.62343e13			−1.01893
$482$	1.30283e13	−	1.30283e13i	0.500788	−	0.500788i
$483$	1.60872e13	+	1.60872e13i	0.611989	+	0.611989i
$484$		−	2.11427e12i		−	0.0796039i
$485$		0			0
$486$	−5.11539e12			−0.188668
$487$	−3.91617e12	+	3.91617e12i	−0.142961	+	0.142961i	−0.774965	−	0.632004i	$-0.782232\pi$
$487$	−3.91617e12	+	3.91617e12i	−0.142961	+	0.142961i	0.632004	+	0.774965i	$0.282232\pi$
$488$	7.42347e12	+	7.42347e12i	0.268230	+	0.268230i
$489$		−	1.75060e13i		−	0.626098i
$490$		0			0
$491$	−1.66945e12			−0.0585015			−0.0292508	−	0.999572i	$-0.509312\pi$
$491$	−1.66945e12			−0.0585015			−0.0292508	+	0.999572i	$0.509312\pi$
$492$	−1.43358e13	+	1.43358e13i	−0.497276	+	0.497276i
$493$	−4.66076e13	−	4.66076e13i	−1.60038	−	1.60038i
$494$		−	8.19994e12i		−	0.278725i
$495$		0			0
$496$	2.63874e12			0.0878999
$497$	−2.62372e13	+	2.62372e13i	−0.865239	+	0.865239i
$498$	−3.03565e13	−	3.03565e13i	−0.991070	−	0.991070i
$499$		−	2.69113e13i		−	0.869824i	−0.900473	−	0.434912i	$-0.856779\pi$
$499$		−	2.69113e13i		−	0.869824i	0.900473	−	0.434912i	$-0.143221\pi$
$500$		0			0
$501$	4.32910e12			0.137154
$502$	−7.25074e12	+	7.25074e12i	−0.227438	+	0.227438i
$503$	−2.35501e13	−	2.35501e13i	−0.731397	−	0.731397i	0.239499	−	0.970897i	$-0.423017\pi$
$503$	−2.35501e13	−	2.35501e13i	−0.731397	−	0.731397i	−0.970897	+	0.239499i	$0.923017\pi$
$504$			1.09214e12i			0.0335836i
$505$		0			0
$506$	2.90103e13			0.874579
$507$	5.42258e12	−	5.42258e12i	0.161870	−	0.161870i
$508$	6.68780e12	+	6.68780e12i	0.197681	+	0.197681i
$509$			8.63621e12i			0.252775i	0.991981	+	0.126388i	$0.0403383\pi$
$509$			8.63621e12i			0.252775i	−0.991981	+	0.126388i	$0.959662\pi$
$510$		0			0
$511$	1.06994e13			0.307083
$512$	−1.09951e12	+	1.09951e12i	−0.0312500	+	0.0312500i
$513$	1.03050e13	+	1.03050e13i	0.290044	+	0.290044i
$514$		−	4.27452e13i		−	1.19144i
$515$		0			0
$516$	−1.11259e13			−0.304150
$517$	2.98833e13	−	2.98833e13i	0.809051	−	0.809051i
$518$	−1.51697e13	−	1.51697e13i	−0.406751	−	0.406751i
$519$			4.25941e13i			1.13113i
$520$		0			0
$521$	−6.27326e13			−1.63420			−0.817099	−	0.576497i	$-0.804419\pi$
$521$	−6.27326e13			−1.63420			−0.817099	+	0.576497i	$0.804419\pi$
$522$	3.14507e12	−	3.14507e12i	0.0811479	−	0.0811479i
$523$	−1.48951e12	−	1.48951e12i	−0.0380659	−	0.0380659i	0.687818	−	0.725884i	$-0.258569\pi$
$523$	−1.48951e12	−	1.48951e12i	−0.0380659	−	0.0380659i	−0.725884	+	0.687818i	$0.758569\pi$
$524$			2.66354e13i			0.674221i
$525$		0			0
$526$	−2.91861e13			−0.724848
$527$	1.89244e13	−	1.89244e13i	0.465553	−	0.465553i
$528$	8.31831e12	+	8.31831e12i	0.202705	+	0.202705i
$529$			1.32430e13i			0.319673i
$530$		0			0
$531$	5.50327e12			0.130361
$532$	4.74154e12	−	4.74154e12i	0.111266	−	0.111266i
$533$	−3.55922e13	−	3.55922e13i	−0.827405	−	0.827405i
$534$			4.55092e13i			1.04808i
$535$		0			0
$536$	1.57626e13			0.356291
$537$	−3.31250e13	+	3.31250e13i	−0.741796	+	0.741796i
$538$	1.66956e13	+	1.66956e13i	0.370417	+	0.370417i
$539$		−	2.44699e13i		−	0.537884i
$540$		0			0
$541$	−8.97115e13			−1.93581			−0.967903	−	0.251324i	$-0.919134\pi$
$541$	−8.97115e13			−1.93581			−0.967903	+	0.251324i	$0.919134\pi$
$542$	−1.15111e13	+	1.15111e13i	−0.246105	+	0.246105i
$543$	2.43391e13	+	2.43391e13i	0.515590	+	0.515590i
$544$			1.57709e13i			0.331025i
$545$		0			0
$546$	−2.29047e13			−0.472021
$547$	−3.39955e13	+	3.39955e13i	−0.694200	+	0.694200i	−0.963153	−	0.268953i	$-0.913322\pi$
$547$	−3.39955e13	+	3.39955e13i	−0.694200	+	0.694200i	0.268953	+	0.963153i	$0.413322\pi$
$548$	−8.38730e12	−	8.38730e12i	−0.169715	−	0.169715i
$549$			7.18515e12i			0.144070i
$550$		0			0
$551$	−2.73086e13			−0.537702
$552$	−1.56758e13	+	1.56758e13i	−0.305867	+	0.305867i
$553$	1.65449e13	+	1.65449e13i	0.319919	+	0.319919i
$554$			2.76024e13i			0.528931i
$555$		0			0
$556$	1.33883e13			0.251971
$557$	−9.51915e12	+	9.51915e12i	−0.177551	+	0.177551i	−0.790287	−	0.612737i	$-0.790069\pi$
$557$	−9.51915e12	+	9.51915e12i	−0.177551	+	0.177551i	0.612737	+	0.790287i	$0.290069\pi$
$558$	1.27701e12	+	1.27701e12i	0.0236061	+	0.0236061i
$559$		−	2.76228e13i		−	0.506068i
$560$		0			0
$561$	1.19314e14			2.14722
$562$	1.26288e13	−	1.26288e13i	0.225258	−	0.225258i
$563$	−3.63651e13	−	3.63651e13i	−0.642900	−	0.642900i	0.308367	−	0.951267i	$-0.400217\pi$
$563$	−3.63651e13	−	3.63651e13i	−0.642900	−	0.642900i	−0.951267	+	0.308367i	$0.900217\pi$
$564$			3.22950e13i			0.565900i
$565$		0			0
$566$	−2.11278e13			−0.363725
$567$	3.27210e13	−	3.27210e13i	0.558356	−	0.558356i
$568$	−2.55662e13	−	2.55662e13i	−0.432439	−	0.432439i
$569$			2.82859e13i			0.474252i	0.971479	+	0.237126i	$0.0762054\pi$
$569$			2.82859e13i			0.474252i	−0.971479	+	0.237126i	$0.923795\pi$
$570$		0			0
$571$	2.19201e12			0.0361129			0.0180564	−	0.999837i	$-0.494252\pi$
$571$	2.19201e12			0.0361129			0.0180564	+	0.999837i	$0.494252\pi$
$572$	−2.06522e13	+	2.06522e13i	−0.337277	+	0.337277i
$573$	2.39810e13	+	2.39810e13i	0.388235	+	0.388235i
$574$		−	4.11616e13i		−	0.660592i
$575$		0			0
$576$	−1.06421e12			−0.0167848
$577$	2.97579e13	−	2.97579e13i	0.465289	−	0.465289i	−0.435095	−	0.900384i	$-0.643285\pi$
$577$	2.97579e13	−	2.97579e13i	0.465289	−	0.465289i	0.900384	+	0.435095i	$0.143285\pi$
$578$	8.08489e13	+	8.08489e13i	1.25324	+	1.25324i
$579$		−	7.78821e13i		−	1.19686i
$580$		0			0
$581$	8.71608e13			1.31656
$582$	−3.74996e12	+	3.74996e12i	−0.0561579	+	0.0561579i
$583$	3.40529e13	+	3.40529e13i	0.505605	+	0.505605i
$584$			1.04258e13i			0.153477i
$585$		0			0
$586$	5.73556e12			0.0830019
$587$	−4.60333e13	+	4.60333e13i	−0.660513	+	0.660513i	−0.955501	−	0.294988i	$-0.904684\pi$
$587$	−4.60333e13	+	4.60333e13i	−0.660513	+	0.660513i	0.294988	+	0.955501i	$0.404684\pi$
$588$	1.32224e13	+	1.32224e13i	0.188115	+	0.188115i
$589$		−	1.10883e13i		−	0.156419i
$590$		0			0
$591$	−2.89230e13			−0.401149
$592$	1.47818e13	−	1.47818e13i	0.203291	−	0.203291i
$593$	6.17714e12	+	6.17714e12i	0.0842391	+	0.0842391i	0.747971	−	0.663732i	$-0.231028\pi$
$593$	6.17714e12	+	6.17714e12i	0.0842391	+	0.0842391i	−0.663732	+	0.747971i	$0.731028\pi$
$594$		−	5.19082e13i		−	0.701946i
$595$		0			0
$596$	−2.20858e12			−0.0293685
$597$	8.28363e13	−	8.28363e13i	1.09232	−	1.09232i
$598$	−3.89189e13	−	3.89189e13i	−0.508925	−	0.508925i
$599$			5.80310e13i			0.752534i	0.926511	+	0.376267i	$0.122792\pi$
$599$			5.80310e13i			0.752534i	−0.926511	+	0.376267i	$0.877208\pi$
$600$		0			0
$601$	1.24750e14			1.59100			0.795499	−	0.605955i	$-0.207209\pi$
$601$	1.24750e14			1.59100			0.795499	+	0.605955i	$0.207209\pi$
$602$	1.59726e13	−	1.59726e13i	0.202020	−	0.202020i
$603$	7.62828e12	+	7.62828e12i	0.0956842	+	0.0956842i
$604$		−	5.83006e13i		−	0.725251i
$605$		0			0
$606$	−1.18546e13			−0.145051
$607$	9.34184e13	−	9.34184e13i	1.13368	−	1.13368i	0.144115	−	0.989561i	$-0.453967\pi$
$607$	9.34184e13	−	9.34184e13i	1.13368	−	1.13368i	0.989561	−	0.144115i	$-0.0460335\pi$
$608$	4.62028e12	+	4.62028e12i	0.0556097	+	0.0556097i
$609$			7.62805e13i			0.910598i
$610$		0			0
$611$	−8.01802e13			−0.941588
$612$	−7.63227e12	+	7.63227e12i	−0.0888990	+	0.0888990i
$613$	−1.42802e13	−	1.42802e13i	−0.164980	−	0.164980i	0.619789	−	0.784769i	$-0.287218\pi$
$613$	−1.42802e13	−	1.42802e13i	−0.164980	−	0.164980i	−0.784769	+	0.619789i	$0.787218\pi$
$614$			3.52497e13i			0.403937i
$615$		0			0
$616$	−2.38839e13			−0.269278
$617$	4.17740e12	−	4.17740e12i	0.0467176	−	0.0467176i	−0.683362	−	0.730080i	$-0.739483\pi$
$617$	4.17740e12	−	4.17740e12i	0.0467176	−	0.0467176i	0.730080	+	0.683362i	$0.239483\pi$
$618$	−8.79878e12	−	8.79878e12i	−0.0976068	−	0.0976068i
$619$		−	4.07977e13i		−	0.448934i	−0.974482	−	0.224467i	$-0.927936\pi$
$619$		−	4.07977e13i		−	0.448934i	0.974482	−	0.224467i	$-0.0720642\pi$
$620$		0			0
$621$	9.78204e13			1.05918
$622$	−8.49822e13	+	8.49822e13i	−0.912800	+	0.912800i
$623$	−6.53340e13	−	6.53340e13i	−0.696144	−	0.696144i
$624$		−	2.23189e13i		−	0.235912i
$625$		0			0
$626$	−2.68825e13			−0.279639
$627$	3.49545e13	−	3.49545e13i	0.360716	−	0.360716i
$628$	5.34670e12	+	5.34670e12i	0.0547379	+	0.0547379i
$629$		−	2.12022e14i		−	2.15342i
$630$		0			0
$631$	8.03556e13			0.803284			0.401642	−	0.915797i	$-0.368440\pi$
$631$	8.03556e13			0.803284			0.401642	+	0.915797i	$0.368440\pi$
$632$	−1.61218e13	+	1.61218e13i	−0.159893	+	0.159893i
$633$	2.52530e13	+	2.52530e13i	0.248482	+	0.248482i
$634$			3.73231e13i			0.364361i
$635$		0			0
$636$	−3.68011e13			−0.353651
$637$	−3.28277e13	+	3.28277e13i	−0.313000	+	0.313000i
$638$	6.87789e13	+	6.87789e13i	0.650657	+	0.650657i
$639$		−	2.47454e13i		−	0.232269i
$640$		0			0
$641$	9.43477e13			0.871849			0.435924	−	0.899983i	$-0.356421\pi$
$641$	9.43477e13			0.871849			0.435924	+	0.899983i	$0.356421\pi$
$642$	8.30449e12	−	8.30449e12i	0.0761444	−	0.0761444i
$643$	−1.98925e13	−	1.98925e13i	−0.180981	−	0.180981i	0.610802	−	0.791783i	$-0.290847\pi$
$643$	−1.98925e13	−	1.98925e13i	−0.180981	−	0.180981i	−0.791783	+	0.610802i	$0.790847\pi$
$644$		−	4.50089e13i		−	0.406321i
$645$		0			0
$646$	6.62710e13			0.589062
$647$	−5.97289e13	+	5.97289e13i	−0.526821	+	0.526821i	−0.919623	−	0.392802i	$-0.871506\pi$
$647$	−5.97289e13	+	5.97289e13i	−0.526821	+	0.526821i	0.392802	+	0.919623i	$0.371506\pi$
$648$	3.18842e13	+	3.18842e13i	0.279062	+	0.279062i
$649$			1.20350e14i			1.04526i
$650$		0			0
$651$	−3.09727e13			−0.264895
$652$	−2.44892e13	+	2.44892e13i	−0.207844	+	0.207844i
$653$	9.87072e13	+	9.87072e13i	0.831349	+	0.831349i	0.987701	−	0.156353i	$-0.0499737\pi$
$653$	9.87072e13	+	9.87072e13i	0.831349	+	0.831349i	−0.156353	+	0.987701i	$0.549974\pi$
$654$		−	3.63831e13i		−	0.304096i
$655$		0			0
$656$	4.01090e13			0.330158
$657$	−5.04553e12	+	5.04553e12i	−0.0412174	+	0.0412174i
$658$	−4.63634e13	−	4.63634e13i	−0.375877	−	0.375877i
$659$		−	5.80689e13i		−	0.467215i	−0.972331	−	0.233607i	$-0.924947\pi$
$659$		−	5.80689e13i		−	0.467215i	0.972331	−	0.233607i	$-0.0750530\pi$
$660$		0			0
$661$	−1.53137e14			−1.21360			−0.606798	−	0.794856i	$-0.707546\pi$
$661$	−1.53137e14			−1.21360			−0.606798	+	0.794856i	$0.707546\pi$
$662$	7.71268e13	−	7.71268e13i	0.606618	−	0.606618i
$663$	−1.60066e14	−	1.60066e14i	−1.24949	−	1.24949i
$664$			8.49317e13i			0.658006i
$665$		0			0
$666$	1.43072e13			0.109190
$667$	−1.29613e14	+	1.29613e14i	−0.981792	+	0.981792i
$668$	−6.05600e12	−	6.05600e12i	−0.0455306	−	0.0455306i
$669$			4.61357e13i			0.344275i
$670$		0			0
$671$	−1.57131e14			−1.15518
$672$	1.29057e13	−	1.29057e13i	0.0941750	−	0.0941750i
$673$	8.75360e13	+	8.75360e13i	0.634032	+	0.634032i	0.949077	−	0.315045i	$-0.102020\pi$
$673$	8.75360e13	+	8.75360e13i	0.634032	+	0.634032i	−0.315045	+	0.949077i	$0.602020\pi$
$674$			1.17936e14i			0.847904i
$675$		0			0
$676$	−1.51714e13			−0.107471
$677$	−1.59452e12	+	1.59452e12i	−0.0112121	+	0.0112121i	−0.712691	−	0.701478i	$-0.752524\pi$
$677$	−1.59452e12	+	1.59452e12i	−0.0112121	+	0.0112121i	0.701478	+	0.712691i	$0.252524\pi$
$678$	−1.05122e14	−	1.05122e14i	−0.733742	−	0.733742i
$679$		−	1.07670e13i		−	0.0746014i
$680$		0			0
$681$	−4.21882e13			−0.288042
$682$	−2.79268e13	+	2.79268e13i	−0.189278	+	0.189278i
$683$	5.65796e13	+	5.65796e13i	0.380677	+	0.380677i	0.871346	−	0.490669i	$-0.163248\pi$
$683$	5.65796e13	+	5.65796e13i	0.380677	+	0.380677i	−0.490669	+	0.871346i	$0.663248\pi$
$684$			4.47195e12i			0.0298687i
$685$		0			0
$686$	−1.13957e14			−0.750104
$687$	−6.02297e13	+	6.02297e13i	−0.393575	+	0.393575i
$688$	1.55641e13	+	1.55641e13i	0.100968	+	0.100968i
$689$		−	9.13676e13i		−	0.588432i
$690$		0			0
$691$	4.98558e12			0.0316465			0.0158232	−	0.999875i	$-0.494963\pi$
$691$	4.98558e12			0.0316465			0.0158232	+	0.999875i	$0.494963\pi$
$692$	5.95852e13	−	5.95852e13i	0.375498	−	0.375498i
$693$	−1.15586e13	−	1.15586e13i	−0.0723165	−	0.0723165i
$694$			1.72304e14i			1.07028i
$695$		0			0
$696$	−7.43297e13			−0.455110
$697$	2.87652e14	−	2.87652e14i	1.74865	−	1.74865i
$698$	1.30025e14	+	1.30025e14i	0.784785	+	0.784785i
$699$			3.65249e13i			0.218879i
$700$		0			0
$701$	−1.80303e14			−1.06516			−0.532578	−	0.846381i	$-0.678777\pi$
$701$	−1.80303e14			−1.06516			−0.532578	+	0.846381i	$0.678777\pi$
$702$	−6.96377e13	+	6.96377e13i	−0.408469	+	0.408469i
$703$	−6.21147e13	−	6.21147e13i	−0.361758	−	0.361758i
$704$		−	2.32731e13i		−	0.134583i
$705$		0			0
$706$	1.75768e14			1.00211
$707$	1.70187e13	−	1.70187e13i	0.0963448	−	0.0963448i
$708$	−6.50315e13	−	6.50315e13i	−0.365559	−	0.365559i
$709$			3.11543e14i			1.73895i	0.493979	+	0.869474i	$0.335542\pi$
$709$			3.11543e14i			1.73895i	−0.493979	+	0.869474i	$0.664458\pi$
$710$		0			0
$711$	−1.56042e13			−0.0858805
$712$	6.36632e13	−	6.36632e13i	0.347927	−	0.347927i
$713$	−5.26277e13	−	5.26277e13i	−0.285606	−	0.285606i
$714$		−	1.85113e14i		−	0.997577i
$715$		0			0
$716$	9.26776e13			0.492504
$717$	−7.23989e12	+	7.23989e12i	−0.0382064	+	0.0382064i
$718$	−9.46087e13	−	9.46087e13i	−0.495803	−	0.495803i
$719$			1.65068e14i			0.859051i	0.903055	+	0.429525i	$0.141319\pi$
$719$			1.65068e14i			0.859051i	−0.903055	+	0.429525i	$0.858681\pi$
$720$		0			0
$721$	2.52634e13			0.129663
$722$	−7.86821e13	+	7.86821e13i	−0.401042	+	0.401042i
$723$	−1.49012e14	−	1.49012e14i	−0.754273	−	0.754273i
$724$		−	6.80962e13i		−	0.342318i
$725$		0			0
$726$	−2.41820e13			−0.119897
$727$	−2.15314e14	+	2.15314e14i	−1.06023	+	1.06023i	−0.0621642	+	0.998066i	$0.519800\pi$
$727$	−2.15314e14	+	2.15314e14i	−1.06023	+	1.06023i	−0.998066	+	0.0621642i	$0.980200\pi$
$728$	3.20416e13	+	3.20416e13i	0.156696	+	0.156696i
$729$		−	1.71318e14i		−	0.832081i
$730$		0			0
$731$	2.23244e14			1.06953
$732$	8.49060e13	−	8.49060e13i	0.404001	−	0.404001i
$733$	2.78787e14	+	2.78787e14i	1.31750	+	1.31750i	0.915746	+	0.401759i	$0.131601\pi$
$733$	2.78787e14	+	2.78787e14i	1.31750	+	1.31750i	0.401759	+	0.915746i	$0.368399\pi$
$734$		−	5.61152e13i		−	0.263390i
$735$		0			0
$736$	4.38578e13			0.203076
$737$	−1.66822e14	+	1.66822e14i	−0.767212	+	0.767212i
$738$	1.94106e13	+	1.94106e13i	0.0886662	+	0.0886662i
$739$			2.05171e14i			0.930879i	0.885080	+	0.465440i	$0.154104\pi$
$739$			2.05171e14i			0.930879i	−0.885080	+	0.465440i	$0.845896\pi$
$740$		0			0
$741$	−9.37868e13			−0.419808
$742$	5.28324e13	−	5.28324e13i	0.234899	−	0.234899i
$743$	−1.59047e14	−	1.59047e14i	−0.702396	−	0.702396i	0.262528	−	0.964924i	$-0.415444\pi$
$743$	−1.59047e14	−	1.59047e14i	−0.702396	−	0.702396i	−0.964924	+	0.262528i	$0.915444\pi$
$744$		−	3.01806e13i		−	0.132392i
$745$		0			0
$746$	1.36230e14			0.589627
$747$	−4.11025e13	+	4.11025e13i	−0.176712	+	0.176712i
$748$	−1.66909e14	−	1.66909e14i	−0.712806	−	0.712806i
$749$			2.38442e13i			0.101152i
$750$		0			0
$751$	−1.40008e14			−0.586074			−0.293037	−	0.956101i	$-0.594666\pi$
$751$	−1.40008e14			−0.586074			−0.293037	+	0.956101i	$0.594666\pi$
$752$	4.51777e13	−	4.51777e13i	0.187860	−	0.187860i
$753$	8.29303e13	+	8.29303e13i	0.342561	+	0.342561i
$754$		−	1.84541e14i		−	0.757246i
$755$		0			0
$756$	−8.05347e13			−0.326117
$757$	−7.07881e13	+	7.07881e13i	−0.284761	+	0.284761i	−0.835004	−	0.550243i	$-0.814535\pi$
$757$	−7.07881e13	+	7.07881e13i	−0.284761	+	0.284761i	0.550243	+	0.835004i	$0.314535\pi$
$758$	−1.15360e14	−	1.15360e14i	−0.461008	−	0.461008i
$759$		−	3.31805e14i		−	1.31727i
$760$		0			0
$761$	−2.84953e14			−1.11648			−0.558238	−	0.829681i	$-0.688523\pi$
$761$	−2.84953e14			−1.11648			−0.558238	+	0.829681i	$0.688523\pi$
$762$	7.64917e13	−	7.64917e13i	0.297742	−	0.297742i
$763$	5.22324e13	+	5.22324e13i	0.201984	+	0.201984i
$764$		−	6.70944e13i		−	0.257762i
$765$		0			0
$766$	−2.22026e14			−0.841900
$767$	1.61456e14	−	1.61456e14i	0.608245	−	0.608245i
$768$	1.25757e13	+	1.25757e13i	0.0470679	+	0.0470679i
$769$			3.59991e14i			1.33863i	0.742980	+	0.669314i	$0.233412\pi$
$769$			3.59991e14i			1.33863i	−0.742980	+	0.669314i	$0.766588\pi$
$770$		0			0
$771$	−4.88899e14			−1.79451
$772$	−1.08950e14	+	1.08950e14i	−0.397319	+	0.397319i
$773$	−1.40032e14	−	1.40032e14i	−0.507375	−	0.507375i	0.406345	−	0.913720i	$-0.366803\pi$
$773$	−1.40032e14	−	1.40032e14i	−0.507375	−	0.507375i	−0.913720	+	0.406345i	$0.866803\pi$
$774$			1.50645e13i			0.0542311i
$775$		0			0
$776$	1.04917e13			0.0372852
$777$	−1.73503e14	+	1.73503e14i	−0.612637	+	0.612637i
$778$	1.80028e14	+	1.80028e14i	0.631601	+	0.631601i
$779$		−	1.68543e14i		−	0.587520i
$780$		0			0
$781$	5.41154e14			1.86237
$782$	3.14538e14	−	3.14538e14i	1.07557	−	1.07557i
$783$	2.31917e14	+	2.31917e14i	0.787997	+	0.787997i
$784$		−	3.69937e13i		−	0.124896i
$785$		0			0
$786$	3.04642e14			1.01549
$787$	−2.99888e14	+	2.99888e14i	−0.993312	+	0.993312i	−0.999978	−	0.00666595i	$-0.997878\pi$
$787$	−2.99888e14	+	2.99888e14i	−0.993312	+	0.993312i	0.00666595	+	0.999978i	$0.497878\pi$
$788$	4.04606e13	+	4.04606e13i	0.133168	+	0.133168i
$789$			3.33816e14i			1.09175i
$790$		0			0
$791$	3.01830e14			0.974719
$792$	1.12630e13	−	1.12630e13i	0.0361432	−	0.0361432i
$793$	2.10800e14	+	2.10800e14i	0.672208	+	0.672208i
$794$			2.54281e14i			0.805770i
$795$		0			0
$796$	−2.31761e14			−0.725227
$797$	2.14433e14	−	2.14433e14i	0.666807	−	0.666807i	−0.290169	−	0.956976i	$-0.593711\pi$
$797$	2.14433e14	−	2.14433e14i	0.666807	−	0.666807i	0.956976	+	0.290169i	$0.0937114\pi$
$798$	−5.42313e13	−	5.42313e13i	−0.167585	−	0.167585i
$799$		−	6.48007e14i		−	1.98997i
$800$		0			0
$801$	6.16193e13			0.186876
$802$	−1.40972e14	+	1.40972e14i	−0.424874	+	0.424874i
$803$	−1.10340e14	−	1.10340e14i	−0.330488	−	0.330488i
$804$		−	1.80285e14i		−	0.536635i
$805$		0			0
$806$	7.49306e13			0.220285
$807$	1.90956e14	−	1.90956e14i	0.557913	−	0.557913i
$808$	1.65834e13	+	1.65834e13i	0.0481523	+	0.0481523i
$809$		−	3.71569e14i		−	1.07225i	−0.844138	−	0.536126i	$-0.819887\pi$
$809$		−	3.71569e14i		−	1.07225i	0.844138	−	0.536126i	$-0.180113\pi$
$810$		0			0
$811$	4.25889e14			1.21393			0.606963	−	0.794730i	$-0.292388\pi$
$811$	4.25889e14			1.21393			0.606963	+	0.794730i	$0.292388\pi$
$812$	1.06709e14	−	1.06709e14i	0.302289	−	0.302289i
$813$	1.31658e14	+	1.31658e14i	0.370677	+	0.370677i
$814$			3.12882e14i			0.875504i
$815$		0			0
$816$	1.80379e14			0.498581
$817$	6.54023e13	−	6.54023e13i	0.179673	−	0.179673i
$818$	−1.60256e14	−	1.60256e14i	−0.437571	−	0.437571i
$819$			3.10129e13i			0.0841633i
$820$		0			0
$821$	4.73944e14			1.27061			0.635304	−	0.772262i	$-0.280875\pi$
$821$	4.73944e14			1.27061			0.635304	+	0.772262i	$0.280875\pi$
$822$	−9.59298e13	+	9.59298e13i	−0.255620	+	0.255620i
$823$	3.93378e14	+	3.93378e14i	1.04186	+	1.04186i	0.999085	+	0.0427794i	$0.0136212\pi$
$823$	3.93378e14	+	3.93378e14i	1.04186	+	1.04186i	0.0427794	+	0.999085i	$0.486379\pi$
$824$			2.46174e13i			0.0648045i
$825$		0			0
$826$	1.86721e14			0.485616
$827$	2.32822e14	−	2.32822e14i	0.601861	−	0.601861i	−0.338945	−	0.940806i	$-0.610070\pi$
$827$	2.32822e14	−	2.32822e14i	0.601861	−	0.601861i	0.940806	+	0.338945i	$0.110070\pi$
$828$	2.12249e13	+	2.12249e13i	0.0545374	+	0.0545374i
$829$			9.73337e13i			0.248594i	0.992245	+	0.124297i	$0.0396675\pi$
$829$			9.73337e13i			0.248594i	−0.992245	+	0.124297i	$0.960332\pi$
$830$		0			0
$831$	3.15703e14			0.796661
$832$	−3.12221e13	+	3.12221e13i	−0.0783152	+	0.0783152i
$833$	−2.65310e14	−	2.65310e14i	−0.661499	−	0.661499i
$834$		−	1.53128e14i		−	0.379512i
$835$		0			0
$836$	−9.77963e13			−0.239492
$837$	−9.41670e13	+	9.41670e13i	−0.229230	+	0.229230i
$838$	2.37190e14	+	2.37190e14i	0.573954	+	0.573954i
$839$		−	3.82848e14i		−	0.920910i	−0.887683	−	0.460455i	$-0.847686\pi$
$839$		−	3.82848e14i		−	0.920910i	0.887683	−	0.460455i	$-0.152314\pi$
$840$		0			0
$841$	−1.93879e14			−0.460840
$842$	7.49601e13	−	7.49601e13i	0.177121	−	0.177121i
$843$	−1.44442e14	−	1.44442e14i	−0.339278	−	0.339278i
$844$		−	7.06533e13i		−	0.164976i
$845$		0			0
$846$	4.37273e13			0.100902
$847$	3.47162e13	−	3.47162e13i	0.0796371	−	0.0796371i
$848$	5.14813e13	+	5.14813e13i	0.117401	+	0.117401i
$849$			2.41650e14i			0.547833i
$850$		0			0
$851$	−5.89622e14			−1.32107
$852$	−2.92414e14	+	2.92414e14i	−0.651328	+	0.651328i
$853$	−4.25918e14	−	4.25918e14i	−0.943149	−	0.943149i	0.0553196	−	0.998469i	$-0.482382\pi$
$853$	−4.25918e14	−	4.25918e14i	−0.943149	−	0.943149i	−0.998469	+	0.0553196i	$0.982382\pi$
$854$			2.43786e14i			0.536684i
$855$		0			0
$856$	−2.32344e13			−0.0505549
$857$	3.58497e14	−	3.58497e14i	0.775498	−	0.775498i	−0.203563	−	0.979062i	$-0.565252\pi$
$857$	3.58497e14	−	3.58497e14i	0.775498	−	0.775498i	0.979062	+	0.203563i	$0.0652523\pi$
$858$	2.36210e14	+	2.36210e14i	0.507997	+	0.507997i
$859$			7.30888e14i			1.56273i	0.624071	+	0.781367i	$0.285477\pi$
$859$			7.30888e14i			1.56273i	−0.624071	+	0.781367i	$0.714523\pi$
$860$		0			0
$861$	−4.70786e14			−0.994965
$862$	−3.82602e14	+	3.82602e14i	−0.803917	+	0.803917i
$863$	−1.48513e14	−	1.48513e14i	−0.310249	−	0.310249i	0.534757	−	0.845006i	$-0.320403\pi$
$863$	−1.48513e14	−	1.48513e14i	−0.310249	−	0.310249i	−0.845006	+	0.534757i	$0.820403\pi$
$864$		−	7.84751e13i		−	0.162991i
$865$		0			0
$866$	−2.37383e13			−0.0487372
$867$	9.24709e14	−	9.24709e14i	1.88760	−	1.88760i
$868$	4.33279e13	+	4.33279e13i	0.0879365	+	0.0879365i
$869$		−	3.41247e14i		−	0.688604i
$870$		0			0
$871$	4.47601e14			0.892895
$872$	−5.08966e13	+	5.08966e13i	−0.100950	+	0.100950i
$873$	5.07742e12	+	5.07742e12i	0.0100132	+	0.0100132i
$874$		−	1.84296e14i		−	0.361375i
$875$		0			0
$876$	1.19245e14			0.231163
$877$	3.85609e13	−	3.85609e13i	0.0743274	−	0.0743274i	−0.668966	−	0.743293i	$-0.733263\pi$
$877$	3.85609e13	−	3.85609e13i	0.0743274	−	0.0743274i	0.743293	+	0.668966i	$0.233263\pi$
$878$	3.35527e14	+	3.35527e14i	0.643065	+	0.643065i
$879$		−	6.56005e13i		−	0.125015i
$880$		0			0
$881$	−4.11264e14			−0.774892			−0.387446	−	0.921892i	$-0.626643\pi$
$881$	−4.11264e14			−0.774892			−0.387446	+	0.921892i	$0.626643\pi$
$882$	1.79030e13	−	1.79030e13i	0.0335416	−	0.0335416i
$883$	6.34116e14	+	6.34116e14i	1.18131	+	1.18131i	0.979404	+	0.201908i	$0.0647143\pi$
$883$	6.34116e14	+	6.34116e14i	1.18131	+	1.18131i	0.201908	+	0.979404i	$0.435286\pi$
$884$			4.47835e14i			0.829577i
$885$		0			0
$886$	−7.64510e14			−1.40028
$887$	−7.15241e14	+	7.15241e14i	−1.30267	+	1.30267i	−0.376083	+	0.926586i	$0.622729\pi$
$887$	−7.15241e14	+	7.15241e14i	−1.30267	+	1.30267i	−0.926586	+	0.376083i	$0.877271\pi$
$888$	−1.69066e14	−	1.69066e14i	−0.306191	−	0.306191i
$889$			2.19626e14i			0.395526i
$890$		0			0
$891$	−6.74885e14			−1.20182
$892$	6.45395e13	−	6.45395e13i	0.114288	−	0.114288i
$893$	−1.89842e14	−	1.89842e14i	−0.334299	−	0.334299i
$894$			2.52606e13i			0.0442340i
$895$		0			0
$896$	−3.61078e13			−0.0625260
$897$	−4.45134e14	+	4.45134e14i	−0.766530	+	0.766530i
$898$	−3.27257e14	−	3.27257e14i	−0.560411	−	0.560411i
$899$		−	2.49545e14i		−	0.424962i
$900$		0			0
$901$	7.38423e14			1.24360
$902$	−4.24488e14	+	4.24488e14i	−0.710940	+	0.710940i
$903$	−1.82687e14	−	1.82687e14i	−0.304276	−	0.304276i
$904$			2.94111e14i			0.487157i
$905$		0			0
$906$	−6.66813e14			−1.09235
$907$	−4.62743e14	+	4.62743e14i	−0.753882	+	0.753882i	−0.975201	−	0.221320i	$-0.928964\pi$
$907$	−4.62743e14	+	4.62743e14i	−0.753882	+	0.753882i	0.221320	+	0.975201i	$0.428964\pi$
$908$	5.90173e13	+	5.90173e13i	0.0956203	+	0.0956203i
$909$			1.60510e13i			0.0258633i
$910$		0			0
$911$	−2.41312e14			−0.384580			−0.192290	−	0.981338i	$-0.561591\pi$
$911$	−2.41312e14			−0.384580			−0.192290	+	0.981338i	$0.561591\pi$
$912$	5.28444e13	−	5.28444e13i	0.0837577	−	0.0837577i
$913$	−8.98864e14	−	8.98864e14i	−1.41690	−	1.41690i
$914$		−	2.20327e14i		−	0.345411i
$915$		0			0
$916$	1.68512e14			0.261308
$917$	−4.37351e14	+	4.37351e14i	−0.674502	+	0.674502i
$918$	−5.62804e14	−	5.62804e14i	−0.863265	−	0.863265i
$919$			3.74682e14i			0.571591i	0.958291	+	0.285795i	$0.0922577\pi$
$919$			3.74682e14i			0.571591i	−0.958291	+	0.285795i	$0.907742\pi$
$920$		0			0
$921$	4.03169e14			0.608399
$922$	2.75262e14	−	2.75262e14i	0.413134	−	0.413134i
$923$	−7.25988e14	−	7.25988e14i	−1.08373	−	1.08373i
$924$			2.73172e14i			0.405580i
$925$		0			0
$926$	−1.49501e13			−0.0219579
$927$	−1.19135e13	+	1.19135e13i	−0.0174037	+	0.0174037i
$928$	1.03980e14	+	1.03980e14i	0.151081	+	0.151081i
$929$		−	4.47351e14i		−	0.646501i	−0.946313	−	0.323251i	$-0.895224\pi$
$929$		−	4.47351e14i		−	0.646501i	0.946313	−	0.323251i	$-0.104776\pi$
$930$		0			0
$931$	−1.55452e14			−0.222253
$932$	5.10949e13	−	5.10949e13i	0.0726605	−	0.0726605i
$933$	9.71983e14	+	9.71983e14i	1.37484	+	1.37484i
$934$		−	5.20858e14i		−	0.732799i
$935$		0			0
$936$	−3.02198e13			−0.0420641
$937$	2.34215e14	−	2.34215e14i	0.324278	−	0.324278i	−0.526128	−	0.850405i	$-0.676357\pi$
$937$	2.34215e14	−	2.34215e14i	0.324278	−	0.324278i	0.850405	+	0.526128i	$0.176357\pi$
$938$	2.58821e14	+	2.58821e14i	0.356439	+	0.356439i
$939$			3.07469e14i			0.421185i
$940$		0			0
$941$	−3.80526e13			−0.0515746			−0.0257873	−	0.999667i	$-0.508209\pi$
$941$	−3.80526e13			−0.0515746			−0.0257873	+	0.999667i	$0.508209\pi$
$942$	6.11529e13	−	6.11529e13i	0.0824447	−	0.0824447i
$943$	−7.99943e14	−	7.99943e14i	−1.07276	−	1.07276i
$944$			1.81946e14i			0.242707i
$945$		0			0
$946$	−3.29442e14			−0.434834
$947$	−1.26567e13	+	1.26567e13i	−0.0166176	+	0.0166176i	−0.715367	−	0.698749i	$-0.753740\pi$
$947$	−1.26567e13	+	1.26567e13i	−0.0166176	+	0.0166176i	0.698749	+	0.715367i	$0.253740\pi$
$948$	1.84393e14	+	1.84393e14i	0.240826	+	0.240826i
$949$			2.96054e14i			0.384627i
$950$		0			0
$951$	4.26883e14			0.548790
$952$	−2.58956e14	+	2.58956e14i	−0.331163	+	0.331163i
$953$	7.73544e14	+	7.73544e14i	0.984057	+	0.984057i	0.999875	−	0.0158178i	$-0.00503519\pi$
$953$	7.73544e14	+	7.73544e14i	0.984057	+	0.984057i	−0.0158178	+	0.999875i	$0.505035\pi$
$954$			4.98285e13i			0.0630574i
$955$		0			0
$956$	2.02559e13			0.0253665
$957$	7.86659e14	−	7.86659e14i	0.980001	−	0.980001i
$958$	−5.22815e14	−	5.22815e14i	−0.647918	−	0.647918i
$959$		−	2.75438e14i		−	0.339571i
$960$		0			0
$961$	−7.18304e14			−0.876378
$962$	4.19748e14	−	4.19748e14i	0.509464	−	0.509464i
$963$	−1.12442e13	−	1.12442e13i	−0.0135768	−	0.0135768i
$964$			4.16907e14i			0.500788i
$965$		0			0
$966$	−5.14789e14			−0.611989
$967$	5.57904e14	−	5.57904e14i	0.659822	−	0.659822i	−0.295516	−	0.955338i	$-0.595492\pi$
$967$	5.57904e14	−	5.57904e14i	0.659822	−	0.659822i	0.955338	+	0.295516i	$0.0954915\pi$
$968$	3.38284e13	+	3.38284e13i	0.0398020	+	0.0398020i
$969$		−	7.57975e14i		−	0.887229i
$970$		0			0
$971$	1.01087e14			0.117112			0.0585559	−	0.998284i	$-0.481350\pi$
$971$	1.01087e14			0.117112			0.0585559	+	0.998284i	$0.481350\pi$
$972$	8.18463e13	−	8.18463e13i	0.0943338	−	0.0943338i
$973$	2.19834e14	+	2.19834e14i	0.252076	+	0.252076i
$974$		−	1.25317e14i		−	0.142961i
$975$		0			0
$976$	−2.37551e14			−0.268230
$977$	7.13366e14	−	7.13366e14i	0.801382	−	0.801382i	−0.181929	−	0.983312i	$-0.558234\pi$
$977$	7.13366e14	−	7.13366e14i	0.801382	−	0.801382i	0.983312	+	0.181929i	$0.0582342\pi$
$978$	2.80096e14	+	2.80096e14i	0.313049	+	0.313049i
$979$			1.34754e15i			1.49840i
$980$		0			0
$981$	−4.92626e13			−0.0542215
$982$	2.67113e13	−	2.67113e13i	0.0292508	−	0.0292508i
$983$	5.14731e14	+	5.14731e14i	0.560806	+	0.560806i	0.929536	−	0.368731i	$-0.120208\pi$
$983$	5.14731e14	+	5.14731e14i	0.560806	+	0.560806i	−0.368731	+	0.929536i	$0.620208\pi$
$984$		−	4.58746e14i		−	0.497276i
$985$		0			0
$986$	1.49144e15			1.60038
$987$	−5.30282e14	+	5.30282e14i	−0.566136	+	0.566136i
$988$	1.31199e14	+	1.31199e14i	0.139363	+	0.139363i
$989$		−	6.20830e14i		−	0.656132i
$990$		0			0
$991$	1.13356e15			1.18598			0.592990	−	0.805210i	$-0.297947\pi$
$991$	1.13356e15			1.18598			0.592990	+	0.805210i	$0.297947\pi$
$992$	−4.22199e13	+	4.22199e13i	−0.0439499	+	0.0439499i
$993$	−8.82137e14	−	8.82137e14i	−0.913671	−	0.913671i
$994$		−	8.39591e14i		−	0.865239i
$995$		0			0
$996$	9.71407e14			0.991070
$997$	−6.55685e14	+	6.55685e14i	−0.665609	+	0.665609i	−0.956696	−	0.291087i	$-0.905983\pi$
$997$	−6.55685e14	+	6.55685e14i	−0.665609	+	0.665609i	0.291087	+	0.956696i	$0.405983\pi$
$998$	4.30580e14	+	4.30580e14i	0.434912	+	0.434912i
$999$			1.05501e15i			1.06030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.11.c.c.43.1		2
5.2	odd	4	inner	50.11.c.c.7.1		2
5.3	odd	4		10.11.c.a.7.1	yes	2
5.4	even	2		10.11.c.a.3.1	✓	2
15.8	even	4		90.11.g.b.37.1		2
15.14	odd	2		90.11.g.b.73.1		2
20.3	even	4		80.11.p.b.17.1		2
20.19	odd	2		80.11.p.b.33.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.11.c.a.3.1	✓	2	5.4	even	2
10.11.c.a.7.1	yes	2	5.3	odd	4
50.11.c.c.7.1		2	5.2	odd	4	inner
50.11.c.c.43.1		2	1.1	even	1	trivial
80.11.p.b.17.1		2	20.3	even	4
80.11.p.b.33.1		2	20.19	odd	2
90.11.g.b.37.1		2	15.8	even	4
90.11.g.b.73.1		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	50.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.0000 + 16.0000i) q^{2} +(183.000 + 183.000i) q^{3} -512.000i q^{4} -5856.00 q^{6} +(8407.00 - 8407.00i) q^{7} +(8192.00 + 8192.00i) q^{8} +7929.00i q^{9} +O(q^{10})\)	\(q+(-16.0000 + 16.0000i) q^{2} +(183.000 + 183.000i) q^{3} -512.000i q^{4} -5856.00 q^{6} +(8407.00 - 8407.00i) q^{7} +(8192.00 + 8192.00i) q^{8} +7929.00i q^{9} -173398. q^{11} +(93696.0 - 93696.0i) q^{12} +(232623. + 232623. i) q^{13} +269024. i q^{14} -262144. q^{16} +(-1.88003e6 + 1.88003e6i) q^{17} +(-126864. - 126864. i) q^{18} +1.10156e6i q^{19} +3.07696e6 q^{21} +(2.77437e6 - 2.77437e6i) q^{22} +(5.22826e6 + 5.22826e6i) q^{23} +2.99827e6i q^{24} -7.44394e6 q^{26} +(9.35496e6 - 9.35496e6i) q^{27} +(-4.30438e6 - 4.30438e6i) q^{28} +2.47908e7i q^{29} -1.00660e7 q^{31} +(4.19430e6 - 4.19430e6i) q^{32} +(-3.17318e7 - 3.17318e7i) q^{33} -6.01611e7i q^{34} +4.05965e6 q^{36} +(-5.63879e7 + 5.63879e7i) q^{37} +(-1.76250e7 - 1.76250e7i) q^{38} +8.51400e7i q^{39} -1.53004e8 q^{41} +(-4.92314e7 + 4.92314e7i) q^{42} +(-5.93725e7 - 5.93725e7i) q^{43} +8.87798e7i q^{44} -1.67304e8 q^{46} +(-1.72339e8 + 1.72339e8i) q^{47} +(-4.79724e7 - 4.79724e7i) q^{48} +1.41120e8i q^{49} -6.88092e8 q^{51} +(1.19103e8 - 1.19103e8i) q^{52} +(-1.96386e8 - 1.96386e8i) q^{53} +2.99359e8i q^{54} +1.37740e8 q^{56} +(-2.01585e8 + 2.01585e8i) q^{57} +(-3.96653e8 - 3.96653e8i) q^{58} -6.94069e8i q^{59} +9.06186e8 q^{61} +(1.61056e8 - 1.61056e8i) q^{62} +(6.66591e7 + 6.66591e7i) q^{63} +1.34218e8i q^{64} +1.01542e9 q^{66} +(9.62074e8 - 9.62074e8i) q^{67} +(9.62577e8 + 9.62577e8i) q^{68} +1.91354e9i q^{69} -3.12088e9 q^{71} +(-6.49544e7 + 6.49544e7i) q^{72} +(6.36339e8 + 6.36339e8i) q^{73} -1.80441e9i q^{74} +5.63999e8 q^{76} +(-1.45776e9 + 1.45776e9i) q^{77} +(-1.36224e9 - 1.36224e9i) q^{78} +1.96800e9i q^{79} +3.89211e9 q^{81} +(2.44806e9 - 2.44806e9i) q^{82} +(5.18382e9 + 5.18382e9i) q^{83} -1.57540e9i q^{84} +1.89992e9 q^{86} +(-4.53672e9 + 4.53672e9i) q^{87} +(-1.42048e9 - 1.42048e9i) q^{88} -7.77138e9i q^{89} +3.91132e9 q^{91} +(2.67687e9 - 2.67687e9i) q^{92} +(-1.84208e9 - 1.84208e9i) q^{93} -5.51486e9i q^{94} +1.53512e9 q^{96} +(6.40361e8 - 6.40361e8i) q^{97} +(-2.25792e9 - 2.25792e9i) q^{98} -1.37487e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} + 366 q^{3} - 11712 q^{6} + 16814 q^{7} + 16384 q^{8}+O(q^{10}) \) 2 * q - 32 * q^2 + 366 * q^3 - 11712 * q^6 + 16814 * q^7 + 16384 * q^8	\( 2 q - 32 q^{2} + 366 q^{3} - 11712 q^{6} + 16814 q^{7} + 16384 q^{8} - 346796 q^{11} + 187392 q^{12} + 465246 q^{13} - 524288 q^{16} - 3760066 q^{17} - 253728 q^{18} + 6153924 q^{21} + 5548736 q^{22} + 10456526 q^{23} - 14887872 q^{26} + 18709920 q^{27} - 8608768 q^{28} - 20131996 q^{31} + 8388608 q^{32} - 63463668 q^{33} + 8119296 q^{36} - 112775826 q^{37} - 35249920 q^{38} - 306007196 q^{41} - 98462784 q^{42} - 118744914 q^{43} - 334608832 q^{46} - 344678706 q^{47} - 95944704 q^{48} - 1376184156 q^{51} + 238205952 q^{52} - 392771234 q^{53} + 275480576 q^{56} - 403170960 q^{57} - 793306880 q^{58} + 1812371604 q^{61} + 322111936 q^{62} + 133318206 q^{63} + 2030837376 q^{66} + 1924147934 q^{67} + 1925153792 q^{68} - 6241755196 q^{71} - 129908736 q^{72} + 1272678526 q^{73} + 1127997440 q^{76} - 2915513972 q^{77} - 2724480576 q^{78} + 7784229762 q^{81} + 4896115136 q^{82} + 10367644206 q^{83} + 3799837248 q^{86} - 9073447440 q^{87} - 2840952832 q^{88} + 7822646244 q^{91} + 5353741312 q^{92} - 3684155268 q^{93} + 3070230528 q^{96} + 1280722494 q^{97} - 4515838432 q^{98}+O(q^{100}) \) 2 * q - 32 * q^2 + 366 * q^3 - 11712 * q^6 + 16814 * q^7 + 16384 * q^8 - 346796 * q^11 + 187392 * q^12 + 465246 * q^13 - 524288 * q^16 - 3760066 * q^17 - 253728 * q^18 + 6153924 * q^21 + 5548736 * q^22 + 10456526 * q^23 - 14887872 * q^26 + 18709920 * q^27 - 8608768 * q^28 - 20131996 * q^31 + 8388608 * q^32 - 63463668 * q^33 + 8119296 * q^36 - 112775826 * q^37 - 35249920 * q^38 - 306007196 * q^41 - 98462784 * q^42 - 118744914 * q^43 - 334608832 * q^46 - 344678706 * q^47 - 95944704 * q^48 - 1376184156 * q^51 + 238205952 * q^52 - 392771234 * q^53 + 275480576 * q^56 - 403170960 * q^57 - 793306880 * q^58 + 1812371604 * q^61 + 322111936 * q^62 + 133318206 * q^63 + 2030837376 * q^66 + 1924147934 * q^67 + 1925153792 * q^68 - 6241755196 * q^71 - 129908736 * q^72 + 1272678526 * q^73 + 1127997440 * q^76 - 2915513972 * q^77 - 2724480576 * q^78 + 7784229762 * q^81 + 4896115136 * q^82 + 10367644206 * q^83 + 3799837248 * q^86 - 9073447440 * q^87 - 2840952832 * q^88 + 7822646244 * q^91 + 5353741312 * q^92 - 3684155268 * q^93 + 3070230528 * q^96 + 1280722494 * q^97 - 4515838432 * q^98

Introduction

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