LMFDB - Embedded newform 10.11.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,11,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	10.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:	$6.35357252674$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.11.c.a.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} +(-1875.00 + 2500.00i) q^{5} -5856.00 q^{6} +(-8407.00 + 8407.00i) q^{7} +(-8192.00 - 8192.00i) q^{8} +7929.00i q^{9} +(10000.0 + 70000.0i) q^{10} -173398. q^{11} +(-93696.0 + 93696.0i) q^{12} +(-232623. - 232623. i) q^{13} +269024. i q^{14} +(800625. - 114375. i) q^{15} -262144. q^{16} +(1.88003e6 - 1.88003e6i) q^{17} +(126864. + 126864. i) q^{18} +1.10156e6i q^{19} +(1.28000e6 + 960000. i) q^{20} +3.07696e6 q^{21} +(-2.77437e6 + 2.77437e6i) q^{22} +(-5.22826e6 - 5.22826e6i) q^{23} +2.99827e6i q^{24} +(-2.73438e6 - 9.37500e6i) q^{25} -7.44394e6 q^{26} +(-9.35496e6 + 9.35496e6i) q^{27} +(4.30438e6 + 4.30438e6i) q^{28} +2.47908e7i q^{29} +(1.09800e7 - 1.46400e7i) q^{30} -1.00660e7 q^{31} +(-4.19430e6 + 4.19430e6i) q^{32} +(3.17318e7 + 3.17318e7i) q^{33} -6.01611e7i q^{34} +(-5.25438e6 - 3.67806e7i) q^{35} +4.05965e6 q^{36} +(5.63879e7 - 5.63879e7i) q^{37} +(1.76250e7 + 1.76250e7i) q^{38} +8.51400e7i q^{39} +(3.58400e7 - 5.12000e6i) q^{40} -1.53004e8 q^{41} +(4.92314e7 - 4.92314e7i) q^{42} +(5.93725e7 + 5.93725e7i) q^{43} +8.87798e7i q^{44} +(-1.98225e7 - 1.48669e7i) q^{45} -1.67304e8 q^{46} +(1.72339e8 - 1.72339e8i) q^{47} +(4.79724e7 + 4.79724e7i) q^{48} +1.41120e8i q^{49} +(-1.93750e8 - 1.06250e8i) q^{50} -6.88092e8 q^{51} +(-1.19103e8 + 1.19103e8i) q^{52} +(1.96386e8 + 1.96386e8i) q^{53} +2.99359e8i q^{54} +(3.25121e8 - 4.33495e8i) q^{55} +1.37740e8 q^{56} +(2.01585e8 - 2.01585e8i) q^{57} +(3.96653e8 + 3.96653e8i) q^{58} -6.94069e8i q^{59} +(-5.85600e7 - 4.09920e8i) q^{60} +9.06186e8 q^{61} +(-1.61056e8 + 1.61056e8i) q^{62} +(-6.66591e7 - 6.66591e7i) q^{63} +1.34218e8i q^{64} +(1.01773e9 - 1.45389e8i) q^{65} +1.01542e9 q^{66} +(-9.62074e8 + 9.62074e8i) q^{67} +(-9.62577e8 - 9.62577e8i) q^{68} +1.91354e9i q^{69} +(-6.72560e8 - 5.04420e8i) q^{70} -3.12088e9 q^{71} +(6.49544e7 - 6.49544e7i) q^{72} +(-6.36339e8 - 6.36339e8i) q^{73} -1.80441e9i q^{74} +(-1.21523e9 + 2.21602e9i) q^{75} +5.63999e8 q^{76} +(1.45776e9 - 1.45776e9i) q^{77} +(1.36224e9 + 1.36224e9i) q^{78} +1.96800e9i q^{79} +(4.91520e8 - 6.55360e8i) q^{80} +3.89211e9 q^{81} +(-2.44806e9 + 2.44806e9i) q^{82} +(-5.18382e9 - 5.18382e9i) q^{83} -1.57540e9i q^{84} +(1.17502e9 + 8.22514e9i) q^{85} +1.89992e9 q^{86} +(4.53672e9 - 4.53672e9i) q^{87} +(1.42048e9 + 1.42048e9i) q^{88} -7.77138e9i q^{89} +(-5.55030e8 + 7.92900e7i) q^{90} +3.91132e9 q^{91} +(-2.67687e9 + 2.67687e9i) q^{92} +(1.84208e9 + 1.84208e9i) q^{93} -5.51486e9i q^{94} +(-2.75390e9 - 2.06542e9i) q^{95} +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} - 3750 q^{5} - 11712 q^{6} - 16814 q^{7} - 16384 q^{8} + 20000 q^{10} - 346796 q^{11} - 187392 q^{12} - 465246 q^{13} + 1601250 q^{15} - 524288 q^{16} + 3760066 q^{17} + 253728 q^{18}+ \cdots + 4515838432 q^{98}+O(q^{100}) $ 2 * q + 32 * q^2 - 366 * q^3 - 3750 * q^5 - 11712 * q^6 - 16814 * q^7 - 16384 * q^8 + 20000 * q^10 - 346796 * q^11 - 187392 * q^12 - 465246 * q^13 + 1601250 * q^15 - 524288 * q^16 + 3760066 * q^17 + 253728 * q^18 + 2560000 * q^20 + 6153924 * q^21 - 5548736 * q^22 - 10456526 * q^23 - 5468750 * q^25 - 14887872 * q^26 - 18709920 * q^27 + 8608768 * q^28 + 21960000 * q^30 - 20131996 * q^31 - 8388608 * q^32 + 63463668 * q^33 - 10508750 * q^35 + 8119296 * q^36 + 112775826 * q^37 + 35249920 * q^38 + 71680000 * q^40 - 306007196 * q^41 + 98462784 * q^42 + 118744914 * q^43 - 39645000 * q^45 - 334608832 * q^46 + 344678706 * q^47 + 95944704 * q^48 - 387500000 * q^50 - 1376184156 * q^51 - 238205952 * q^52 + 392771234 * q^53 + 650242500 * q^55 + 275480576 * q^56 + 403170960 * q^57 + 793306880 * q^58 - 117120000 * q^60 + 1812371604 * q^61 - 322111936 * q^62 - 133318206 * q^63 + 2035451250 * q^65 + 2030837376 * q^66 - 1924147934 * q^67 - 1925153792 * q^68 - 1345120000 * q^70 - 6241755196 * q^71 + 129908736 * q^72 - 1272678526 * q^73 - 2430468750 * q^75 + 1127997440 * q^76 + 2915513972 * q^77 + 2724480576 * q^78 + 983040000 * q^80 + 7784229762 * q^81 - 4896115136 * q^82 - 10367644206 * q^83 + 2350041250 * q^85 + 3799837248 * q^86 + 9073447440 * q^87 + 2840952832 * q^88 - 1110060000 * q^90 + 7822646244 * q^91 - 5353741312 * q^92 + 3684155268 * q^93 - 5507800000 * q^95 + 3070230528 * q^96 - 1280722494 * q^97 + 4515838432 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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	0.221968	−	0.975054i	$-0.428752\pi$
$3$	−183.000	−	183.000i	−0.753086	−	0.753086i	−0.975054	+	0.221968i	$0.928752\pi$
$4$		−	512.000i		−	0.500000i
$5$	−1875.00	+	2500.00i	−0.600000	+	0.800000i
$5$	−1875.00	+	2500.00i	−0.600000	+	0.800000i
$6$	−5856.00			−0.753086
$7$	−8407.00	+	8407.00i	−0.500208	+	0.500208i	−0.911503	−	0.411294i	$-0.865077\pi$
$7$	−8407.00	+	8407.00i	−0.500208	+	0.500208i	0.411294	+	0.911503i	$0.365077\pi$
$8$	−8192.00	−	8192.00i	−0.250000	−	0.250000i
$9$			7929.00i			0.134278i
$10$	10000.0	+	70000.0i	0.100000	+	0.700000i
$11$	−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	0.320670	−	0.947191i	$-0.396092\pi$
$13$	−232623.	−	232623.i	−0.626521	−	0.626521i	−0.947191	+	0.320670i	$0.896092\pi$
$14$			269024.i			0.500208i
$15$	800625.	−	114375.i	1.05432	−	0.150617i
$16$	−262144.			−0.250000
$17$	1.88003e6	−	1.88003e6i	1.32410	−	1.32410i	0.413676	−	0.910424i	$-0.364245\pi$
$17$	1.88003e6	−	1.88003e6i	1.32410	−	1.32410i	0.910424	−	0.413676i	$-0.135755\pi$
$18$	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	$0.928598\pi$
$20$	1.28000e6	+	960000.i	0.400000	+	0.300000i
$21$	3.07696e6			0.753400
$22$	−2.77437e6	+	2.77437e6i	−0.538333	+	0.538333i
$23$	−5.22826e6	−	5.22826e6i	−0.812303	−	0.812303i	0.172675	−	0.984979i	$-0.444759\pi$
$23$	−5.22826e6	−	5.22826e6i	−0.812303	−	0.812303i	−0.984979	+	0.172675i	$0.944759\pi$
$24$			2.99827e6i			0.376543i
$25$	−2.73438e6	−	9.37500e6i	−0.280000	−	0.960000i
$26$	−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	$0.793442\pi$
$30$	1.09800e7	−	1.46400e7i	0.451852	−	0.602469i
$31$	−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
$35$	−5.25438e6	−	3.67806e7i	−0.100042	−	0.700292i
$36$	4.05965e6			0.0671392
$37$	5.63879e7	−	5.63879e7i	0.813163	−	0.813163i	−0.171944	−	0.985107i	$-0.555005\pi$
$37$	5.63879e7	−	5.63879e7i	0.813163	−	0.813163i	0.985107	+	0.171944i	$0.0550048\pi$
$38$	1.76250e7	+	1.76250e7i	0.222439	+	0.222439i
$39$			8.51400e7i			0.943649i
$40$	3.58400e7	−	5.12000e6i	0.350000	−	0.0500000i
$41$	−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	0.879595	−	0.475724i	$-0.157814\pi$
$43$	5.93725e7	+	5.93725e7i	0.403871	+	0.403871i	−0.475724	+	0.879595i	$0.657814\pi$
$44$			8.87798e7i			0.538333i
$45$	−1.98225e7	−	1.48669e7i	−0.107423	−	0.0805670i
$46$	−1.67304e8			−0.812303
$47$	1.72339e8	−	1.72339e8i	0.751441	−	0.751441i	−0.223307	−	0.974748i	$-0.571685\pi$
$47$	1.72339e8	−	1.72339e8i	0.751441	−	0.751441i	0.974748	+	0.223307i	$0.0716852\pi$
$48$	4.79724e7	+	4.79724e7i	0.188272	+	0.188272i
$49$			1.41120e8i			0.499583i
$50$	−1.93750e8	−	1.06250e8i	−0.620000	−	0.340000i
$51$	−6.88092e8			−1.99432
$52$	−1.19103e8	+	1.19103e8i	−0.313261	+	0.313261i
$53$	1.96386e8	+	1.96386e8i	0.469602	+	0.469602i	0.901786	−	0.432183i	$-0.142257\pi$
$53$	1.96386e8	+	1.96386e8i	0.469602	+	0.469602i	−0.432183	+	0.901786i	$0.642257\pi$
$54$			2.99359e8i			0.651963i
$55$	3.25121e8	−	4.33495e8i	0.645999	−	0.861332i
$56$	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	$-0.161331\pi$
$60$	−5.85600e7	−	4.09920e8i	−0.0753086	−	0.527160i
$61$	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
$65$	1.01773e9	−	1.45389e8i	0.877130	−	0.125304i
$66$	1.01542e9			0.810822
$67$	−9.62074e8	+	9.62074e8i	−0.712581	+	0.712581i	−0.967075	−	0.254493i	$-0.918091\pi$
$67$	−9.62074e8	+	9.62074e8i	−0.712581	+	0.712581i	0.254493	+	0.967075i	$0.418091\pi$
$68$	−9.62577e8	−	9.62577e8i	−0.662050	−	0.662050i
$69$			1.91354e9i			1.22347i
$70$	−6.72560e8	−	5.04420e8i	−0.400167	−	0.300125i
$71$	−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	0.536772	−	0.843727i	$-0.319643\pi$
$73$	−6.36339e8	−	6.36339e8i	−0.306955	−	0.306955i	−0.843727	+	0.536772i	$0.819643\pi$
$74$		−	1.80441e9i		−	0.813163i
$75$	−1.21523e9	+	2.21602e9i	−0.512099	+	0.933827i
$76$	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	$0.896389\pi$
$80$	4.91520e8	−	6.55360e8i	0.150000	−	0.200000i
$81$	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	$-0.869320\pi$
$83$	−5.18382e9	−	5.18382e9i	−1.31601	−	1.31601i	−0.399107	−	0.916904i	$-0.630680\pi$
$84$		−	1.57540e9i		−	0.376700i
$85$	1.17502e9	+	8.22514e9i	0.264820	+	1.85374i
$86$	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	$-0.244974\pi$
$90$	−5.55030e8	+	7.92900e7i	−0.0939948	+	0.0134278i
$91$	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
$95$	−2.75390e9	−	2.06542e9i	−0.355902	−	0.266926i
$96$	1.53512e9			0.188272
$97$	−6.40361e8	+	6.40361e8i	−0.0745704	+	0.0745704i	−0.743408	−	0.668838i	$-0.766792\pi$
$97$	−6.40361e8	+	6.40361e8i	−0.0745704	+	0.0745704i	0.668838	+	0.743408i	$0.266792\pi$
$98$	2.25792e9	+	2.25792e9i	0.249792	+	0.249792i
$99$		−	1.37487e9i		−	0.144573i
$100$	−4.80000e9	+	1.40000e9i	−0.480000	+	0.140000i
$101$	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	0.639326	−	0.768935i	$-0.279213\pi$
$103$	−1.50252e9	−	1.50252e9i	−0.129609	−	0.129609i	−0.768935	+	0.639326i	$0.779213\pi$
$104$			3.81130e9i			0.313261i
$105$	−5.76930e9	+	7.69240e9i	−0.452040	+	0.602720i
$106$	6.28434e9			0.469602
$107$	1.41812e9	−	1.41812e9i	0.101110	−	0.101110i	−0.654742	−	0.755852i	$-0.727223\pi$
$107$	1.41812e9	−	1.41812e9i	0.101110	−	0.101110i	0.755852	+	0.654742i	$0.227223\pi$
$108$	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	$0.935288\pi$
$110$	−1.73398e9	−	1.21379e10i	−0.107667	−	0.753666i
$111$	−2.06380e10			−1.22476
$112$	2.20384e9	−	2.20384e9i	0.125052	−	0.125052i
$113$	−1.79511e10	−	1.79511e10i	−0.974313	−	0.974313i	0.0253650	−	0.999678i	$-0.491925\pi$
$113$	−1.79511e10	−	1.79511e10i	−0.974313	−	0.974313i	−0.999678	+	0.0253650i	$0.991925\pi$
$114$		−	6.45074e9i		−	0.335031i
$115$	2.28737e10	−	3.26766e9i	1.13722	−	0.162461i
$116$	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
$120$	−7.49568e9	−	5.62176e9i	−0.301235	−	0.225926i
$121$	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
$125$	2.85645e10	+	1.07422e10i	0.936000	+	0.352000i
$126$	−2.13309e9			−0.0671671
$127$	1.30621e10	−	1.30621e10i	0.395362	−	0.395362i	−0.481232	−	0.876593i	$-0.659810\pi$
$127$	1.30621e10	−	1.30621e10i	0.395362	−	0.395362i	0.876593	+	0.481232i	$0.159810\pi$
$128$	2.14748e9	+	2.14748e9i	0.0625000	+	0.0625000i
$129$		−	2.17303e10i		−	0.608300i
$130$	1.39574e10	−	1.86098e10i	0.375913	−	0.501217i
$131$	−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
$135$	−5.84685e9	−	4.09280e10i	−0.130393	−	0.912749i
$136$	−3.08025e10			−0.662050
$137$	−1.63815e10	+	1.63815e10i	−0.339429	+	0.339429i	−0.856153	−	0.516723i	$-0.827152\pi$
$137$	−1.63815e10	+	1.63815e10i	−0.339429	+	0.339429i	0.516723	+	0.856153i	$0.327152\pi$
$138$	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	$0.918921\pi$
$140$	−1.88317e10	+	2.69024e9i	−0.350146	+	0.0500208i
$141$	−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
$145$	−6.19771e10	−	4.64828e10i	−0.966922	−	0.725191i
$146$	−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	$-0.00934962\pi$
$150$	1.60125e10	+	5.49000e10i	0.210864	+	0.722963i
$151$	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
$155$	1.88737e10	−	2.51650e10i	0.210960	−	0.281280i
$156$	4.35917e10			0.471825
$157$	1.04428e10	−	1.04428e10i	0.109476	−	0.109476i	−0.650247	−	0.759723i	$-0.725335\pi$
$157$	1.04428e10	−	1.04428e10i	0.109476	−	0.109476i	0.759723	+	0.650247i	$0.225335\pi$
$158$	3.14879e10	+	3.14879e10i	0.319786	+	0.319786i
$159$		−	7.18771e10i		−	0.707302i
$160$	−2.62144e9	−	1.83501e10i	−0.0250000	−	0.175000i
$161$	8.79080e10			0.812642
$162$	6.22738e10	−	6.22738e10i	0.558124	−	0.558124i
$163$	4.78305e10	+	4.78305e10i	0.415688	+	0.415688i	0.883714	−	0.468027i	$-0.155035\pi$
$163$	4.78305e10	+	4.78305e10i	0.415688	+	0.415688i	−0.468027	+	0.883714i	$0.655035\pi$
$164$			7.83378e10i			0.660317i
$165$	−1.38827e11	+	1.98324e10i	−1.13515	+	0.162164i
$166$	−1.65882e11			−1.31601
$167$	−1.18281e10	+	1.18281e10i	−0.0910613	+	0.0910613i	−0.751170	−	0.660109i	$-0.770510\pi$
$167$	−1.18281e10	+	1.18281e10i	−0.0910613	+	0.0910613i	0.660109	+	0.751170i	$0.270510\pi$
$168$	−2.52065e10	−	2.52065e10i	−0.188350	−	0.188350i
$169$		−	2.96316e10i		−	0.214942i
$170$	1.50403e11	+	1.12802e11i	1.05928	+	0.794460i
$171$	−8.73427e9			−0.0597374
$172$	3.03987e10	−	3.03987e10i	0.201936	−	0.201936i
$173$	−1.16377e11	−	1.16377e11i	−0.750997	−	0.750997i	0.223669	−	0.974665i	$-0.428197\pi$
$173$	−1.16377e11	−	1.16377e11i	−0.750997	−	0.750997i	−0.974665	+	0.223669i	$0.928197\pi$
$174$		−	1.45175e11i		−	0.910219i
$175$	1.01804e11	+	5.58277e10i	0.620258	+	0.340142i
$176$	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	$0.836082\pi$
$180$	−7.61184e9	+	1.01491e10i	−0.0402835	+	0.0537113i
$181$	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
$185$	3.52424e10	+	2.46697e11i	0.162633	+	1.13843i
$186$	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
$190$	−7.71092e10	+	1.10156e10i	−0.311414	+	0.0444877i
$191$	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	0.982244	−	0.187606i	$-0.0600727\pi$
$193$	2.12792e11	+	2.12792e11i	0.794639	+	0.794639i	−0.187606	+	0.982244i	$0.560073\pi$
$194$			2.04916e10i			0.0745704i
$195$	−2.12850e11	−	1.59638e11i	−0.754920	−	0.566190i
$196$	7.22534e10			0.249792
$197$	7.90246e10	−	7.90246e10i	0.266337	−	0.266337i	−0.561285	−	0.827622i	$-0.689693\pi$
$197$	7.90246e10	−	7.90246e10i	0.266337	−	0.266337i	0.827622	+	0.561285i	$0.189693\pi$
$198$	−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	$-0.258265\pi$
$200$	−5.44000e10	+	9.92000e10i	−0.170000	+	0.310000i
$201$	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
$205$	2.86882e11	−	3.82509e11i	0.792380	−	1.05651i
$206$	−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
$210$	3.07696e10	+	2.15387e11i	0.0753400	+	0.527380i
$211$	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
$215$	−2.59754e11	+	3.71078e10i	−0.565419	+	0.0807742i
$216$	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
$220$	−2.21949e11	−	1.66462e11i	−0.430666	−	0.323000i
$221$	−8.74678e11			−1.65915
$222$	−3.30208e11	+	3.30208e11i	−0.612382	+	0.612382i
$223$	−1.26054e11	−	1.26054e11i	−0.228576	−	0.228576i	0.583521	−	0.812098i	$-0.301674\pi$
$223$	−1.26054e11	−	1.26054e11i	−0.228576	−	0.228576i	−0.812098	+	0.583521i	$0.801674\pi$
$224$		−	7.05230e10i		−	0.125052i
$225$	7.43344e10	−	2.16809e10i	0.128907	−	0.0375979i
$226$	−5.74435e11			−0.974313
$227$	1.15268e11	−	1.15268e11i	0.191241	−	0.191241i	−0.604991	−	0.796232i	$-0.706823\pi$
$227$	1.15268e11	−	1.15268e11i	0.191241	−	0.191241i	0.796232	+	0.604991i	$0.206823\pi$
$228$	−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	$0.915846\pi$
$230$	3.13696e11	−	4.18261e11i	0.487382	−	0.649843i
$231$	−5.33539e11			−0.811160
$232$	2.03087e11	−	2.03087e11i	0.302163	−	0.302163i
$233$	−9.97948e10	−	9.97948e10i	−0.145321	−	0.145321i	0.630703	−	0.776024i	$-0.282767\pi$
$233$	−9.97948e10	−	9.97948e10i	−0.145321	−	0.145321i	−0.776024	+	0.630703i	$0.782767\pi$
$234$		−	5.90230e10i		−	0.0841282i
$235$	1.07712e11	+	7.53985e11i	0.150288	+	1.05202i
$236$	−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	$0.991925\pi$
$240$	−2.09879e11	+	2.99827e10i	−0.263580	+	0.0376543i
$241$	−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
$245$	−3.52800e11	−	2.64600e11i	−0.399667	−	0.299750i
$246$	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
$250$	6.28906e11	−	2.85156e11i	0.644000	−	0.292000i
$251$	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
$255$	1.29017e12	−	1.72023e12i	1.19659	−	1.59546i
$256$	6.87195e10			0.0625000
$257$	1.33579e12	−	1.33579e12i	1.19144	−	1.19144i	0.214777	−	0.976663i	$-0.431098\pi$
$257$	1.33579e12	−	1.33579e12i	1.19144	−	1.19144i	0.976663	−	0.214777i	$-0.0689025\pi$
$258$	−3.47685e11	−	3.47685e11i	−0.304150	−	0.304150i
$259$			9.48106e11i			0.813501i
$260$	−7.44394e10	−	5.21076e11i	−0.0626521	−	0.438565i
$261$	−1.96567e11			−0.162296
$262$	−8.32355e11	+	8.32355e11i	−0.674221	+	0.674221i
$263$	−9.12065e11	−	9.12065e11i	−0.724848	−	0.724848i	0.244740	−	0.969589i	$-0.421297\pi$
$263$	−9.12065e11	−	9.12065e11i	−0.724848	−	0.724848i	−0.969589	+	0.244740i	$0.921297\pi$
$264$		−	5.19894e11i		−	0.405411i
$265$	−8.59187e11	+	1.22741e11i	−0.657443	+	0.0939205i
$266$	−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	$-0.120785\pi$
$270$	−7.48397e11	−	5.61298e11i	−0.521571	−	0.391178i
$271$	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
$275$	4.74135e11	+	1.62561e12i	0.301466	+	1.03360i
$276$	9.79735e11			0.611735
$277$	−8.62576e11	+	8.62576e11i	−0.528931	+	0.528931i	−0.920253	−	0.391323i	$-0.872018\pi$
$277$	−8.62576e11	+	8.62576e11i	−0.528931	+	0.528931i	0.391323	+	0.920253i	$0.372018\pi$
$278$	4.18383e11	+	4.18383e11i	0.251971	+	0.251971i
$279$		−	7.98133e10i		−	0.0472122i
$280$	−2.58263e11	+	3.44351e11i	−0.150062	+	0.200083i
$281$	−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	0.501457	−	0.865182i	$-0.332797\pi$
$283$	−6.60245e11	−	6.60245e11i	−0.363725	−	0.363725i	−0.865182	+	0.501457i	$0.832797\pi$
$284$			1.59789e12i			0.864878i
$285$	1.25991e11	+	8.81936e11i	0.0670062	+	0.469043i
$286$	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
$290$	−1.73536e12	+	2.47908e11i	−0.846056	+	0.120865i
$291$	2.34372e11			0.112316
$292$	−3.25806e11	+	3.25806e11i	−0.153477	+	0.153477i
$293$	1.79236e11	+	1.79236e11i	0.0830019	+	0.0830019i	0.747389	−	0.664387i	$-0.231307\pi$
$293$	1.79236e11	+	1.79236e11i	0.0830019	+	0.0830019i	−0.664387	+	0.747389i	$0.731307\pi$
$294$		−	8.26398e11i		−	0.376229i
$295$	1.73517e12	+	1.30138e12i	0.776663	+	0.582497i
$296$	−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
$300$	1.13460e12	+	6.22200e11i	0.466914	+	0.256049i
$301$	−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
$305$	−1.69910e12	+	2.26546e12i	−0.643753	+	0.858337i
$306$	4.77017e11			0.177798
$307$	−1.10155e12	+	1.10155e12i	−0.403937	+	0.403937i	−0.879618	−	0.475681i	$-0.842202\pi$
$307$	−1.10155e12	+	1.10155e12i	−0.403937	+	0.403937i	0.475681	+	0.879618i	$0.342202\pi$
$308$	−7.46372e11	−	7.46372e11i	−0.269278	−	0.269278i
$309$			5.49924e11i			0.195214i
$310$	−1.00660e11	−	7.04620e11i	−0.0351600	−	0.246120i
$311$	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	0.553326	−	0.832965i	$-0.313358\pi$
$313$	−8.40078e11	−	8.40078e11i	−0.279639	−	0.279639i	−0.832965	+	0.553326i	$0.813358\pi$
$314$		−	3.34169e11i		−	0.109476i
$315$	2.91634e11	−	4.16619e10i	0.0940340	−	0.0134334i
$316$	1.00761e12			0.319786
$317$	−1.16635e12	+	1.16635e12i	−0.364361	+	0.364361i	−0.865416	−	0.501055i	$-0.832946\pi$
$317$	−1.16635e12	+	1.16635e12i	−0.364361	+	0.364361i	0.501055	+	0.865416i	$0.332946\pi$
$318$	−1.15003e12	−	1.15003e12i	−0.353651	−	0.353651i
$319$		−	4.29868e12i		−	1.30131i
$320$	−3.35544e11	−	2.51658e11i	−0.100000	−	0.0750000i
$321$	−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
$325$	−1.54476e12	+	2.81692e12i	−0.426035	+	0.776887i
$326$	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
$330$	−1.90391e12	+	2.53855e12i	−0.486493	+	0.648658i
$331$	−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
$335$	−6.01296e11	−	4.20907e12i	−0.142516	−	0.997614i
$336$	−8.06607e11			−0.188350
$337$	−3.68550e12	+	3.68550e12i	−0.847904	+	0.847904i	−0.989871	−	0.141967i	$-0.954657\pi$
$337$	−3.68550e12	+	3.68550e12i	−0.847904	+	0.847904i	0.141967	+	0.989871i	$0.454657\pi$
$338$	−4.74105e11	−	4.74105e11i	−0.107471	−	0.107471i
$339$			6.57010e12i			1.46748i
$340$	4.21127e12	−	6.01611e11i	0.926870	−	0.132410i
$341$	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
$345$	−4.78386e12	−	3.58790e12i	−0.978775	−	0.734082i
$346$	−3.72408e12			−0.750997
$347$	−5.38450e12	+	5.38450e12i	−1.07028	+	1.07028i	−0.0729452	+	0.997336i	$0.523240\pi$
$347$	−5.38450e12	+	5.38450e12i	−1.07028	+	1.07028i	−0.997336	+	0.0729452i	$0.976760\pi$
$348$	−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	$-0.287227\pi$
$350$	2.52210e12	−	7.35612e11i	0.480200	−	0.140058i
$351$	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	$0.000672280\pi$
$353$	5.49274e12	+	5.49274e12i	1.00211	+	1.00211i	0.00211203	+	0.999998i	$0.499328\pi$
$354$			4.06447e12i			0.731118i
$355$	5.85165e12	−	7.80219e12i	1.03785	−	1.38381i
$356$	−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	$0.834874\pi$
$360$	4.05965e10	+	2.84175e11i	0.00671392	+	0.0469974i
$361$	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
$365$	2.78398e12	−	3.97712e11i	0.429737	−	0.0613910i
$366$	−5.30662e12			−0.808003
$367$	1.75360e12	−	1.75360e12i	0.263390	−	0.263390i	−0.563040	−	0.826430i	$-0.690368\pi$
$367$	1.75360e12	−	1.75360e12i	0.263390	−	0.263390i	0.826430	+	0.563040i	$0.190368\pi$
$368$	1.37056e12	+	1.37056e12i	0.203076	+	0.203076i
$369$		−	1.21317e12i		−	0.177332i
$370$	4.51103e12	+	3.38327e12i	0.650530	+	0.487898i
$371$	−3.30203e12			−0.469798
$372$	9.43144e11	−	9.43144e11i	0.132392	−	0.132392i
$373$	4.25717e12	+	4.25717e12i	0.589627	+	0.589627i	0.937530	−	0.347904i	$-0.113106\pi$
$373$	4.25717e12	+	4.25717e12i	0.589627	+	0.589627i	−0.347904	+	0.937530i	$0.613106\pi$
$374$			1.04318e13i			1.42561i
$375$	−3.26147e12	−	7.19312e12i	−0.439802	−	0.969975i
$376$	−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	$0.847488\pi$
$380$	−1.05750e12	+	1.41000e12i	−0.133463	+	0.177951i
$381$	−4.78073e12			−0.595483
$382$	2.09670e12	−	2.09670e12i	0.257762	−	0.257762i
$383$	−6.93832e12	−	6.93832e12i	−0.841900	−	0.841900i	0.147206	−	0.989106i	$-0.452972\pi$
$383$	−6.93832e12	−	6.93832e12i	−0.841900	−	0.841900i	−0.989106	+	0.147206i	$0.952972\pi$
$384$		−	7.85979e11i		−	0.0941358i
$385$	9.11098e11	+	6.37769e12i	0.107711	+	0.753980i
$386$	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	$-0.217602\pi$
$390$	−5.95980e12	+	8.51400e11i	−0.660555	+	0.0943649i
$391$	−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
$395$	−4.91999e12	−	3.68999e12i	−0.511657	−	0.383743i
$396$	−7.03935e11			−0.0722864
$397$	−7.94628e12	+	7.94628e12i	−0.805770	+	0.805770i	−0.983991	−	0.178221i	$-0.942966\pi$
$397$	−7.94628e12	+	7.94628e12i	−0.805770	+	0.805770i	0.178221	+	0.983991i	$0.442966\pi$
$398$	−7.24252e12	−	7.24252e12i	−0.725227	−	0.725227i
$399$			3.38946e12i			0.335171i
$400$	7.16800e11	+	2.45760e12i	0.0700000	+	0.240000i
$401$	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
$405$	−7.29772e12	+	9.73029e12i	−0.669749	+	0.892998i
$406$	−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	$0.855839\pi$
$410$	−1.53004e12	−	1.07103e13i	−0.132063	−	0.924444i
$411$	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
$415$	2.26792e13	−	3.23989e12i	1.84242	−	0.263202i
$416$	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	$-0.194591\pi$
$420$	3.93851e12	+	2.95388e12i	0.301360	+	0.226020i
$421$	−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
$425$	−2.27660e13	−	1.24846e13i	−1.64188	−	0.900388i
$426$	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
$430$	−3.56235e12	+	4.74980e12i	−0.242323	+	0.323097i
$431$	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	0.682318	−	0.731055i	$-0.260972\pi$
$433$	−7.41823e11	−	7.41823e11i	−0.0487372	−	0.0487372i	−0.731055	+	0.682318i	$0.760972\pi$
$434$		−	2.70800e12i		−	0.175873i
$435$	2.83545e12	+	1.98482e13i	0.182044	+	1.27431i
$436$	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	$-0.222338\pi$
$440$	−6.21458e12	+	8.87798e11i	−0.376833	+	0.0538333i
$441$	−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	$-0.794722\pi$
$443$	−2.38909e13	−	2.38909e13i	−1.40028	−	1.40028i	−0.601118	−	0.799160i	$-0.705278\pi$
$444$			1.05666e13i			0.612382i
$445$	1.94285e13	+	1.45713e13i	1.11337	+	0.835025i
$446$	−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	$0.810643\pi$
$450$	8.42456e11	−	1.53624e12i	0.0456546	−	0.0832526i
$451$	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
$455$	−7.33373e12	+	9.77831e12i	−0.376069	+	0.501426i
$456$	−3.30278e12			−0.167515
$457$	6.88521e12	−	6.88521e12i	0.345411	−	0.345411i	−0.512986	−	0.858397i	$-0.671461\pi$
$457$	6.88521e12	−	6.88521e12i	0.345411	−	0.345411i	0.858397	+	0.512986i	$0.171461\pi$
$458$	5.26598e12	+	5.26598e12i	0.261308	+	0.261308i
$459$			3.51753e13i			1.72653i
$460$	−1.67304e12	−	1.17113e13i	−0.0812303	−	0.568612i
$461$	−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	0.696043	−	0.718000i	$-0.254942\pi$
$463$	−4.67192e11	−	4.67192e11i	−0.0219579	−	0.0219579i	−0.718000	+	0.696043i	$0.754942\pi$
$464$		−	6.49877e12i		−	0.302163i
$465$	−8.05909e12	+	1.15130e12i	−0.370699	+	0.0529570i
$466$	−3.19343e12			−0.145321
$467$	1.62768e13	−	1.62768e13i	0.732799	−	0.732799i	−0.238374	−	0.971173i	$-0.576615\pi$
$467$	1.62768e13	−	1.62768e13i	0.732799	−	0.732799i	0.971173	+	0.238374i	$0.0766146\pi$
$468$	−9.44367e11	−	9.44367e11i	−0.0420641	−	0.0420641i
$469$		−	1.61763e13i		−	0.712878i
$470$	1.37871e13	+	1.03404e13i	0.601153	+	0.450865i
$471$	−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
$475$	1.03271e13	−	3.01208e12i	0.427082	−	0.124566i
$476$	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	$0.775640\pi$
$480$	−2.87834e12	+	3.83779e12i	−0.112963	+	0.150617i
$481$	−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
$485$	−4.00226e11	−	2.80158e12i	−0.0149141	−	0.104399i
$486$	−5.11539e12			−0.188668
$487$	3.91617e12	−	3.91617e12i	0.142961	−	0.142961i	−0.632004	−	0.774965i	$-0.717768\pi$
$487$	3.91617e12	−	3.91617e12i	0.142961	−	0.142961i	0.774965	+	0.632004i	$0.217768\pi$
$488$	−7.42347e12	−	7.42347e12i	−0.268230	−	0.268230i
$489$		−	1.75060e13i		−	0.626098i
$490$	−9.87840e12	+	1.41120e12i	−0.349708	+	0.0499583i
$491$	−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
$495$	3.43718e12	+	2.57789e12i	0.115658	+	0.0867437i
$496$	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	$-0.143221\pi$
$500$	5.50000e12	−	1.46250e13i	0.176000	−	0.468000i
$501$	4.32910e12			0.137154
$502$	7.25074e12	−	7.25074e12i	0.227438	−	0.227438i
$503$	2.35501e13	+	2.35501e13i	0.731397	+	0.731397i	0.970897	−	0.239499i	$-0.0769833\pi$
$503$	2.35501e13	+	2.35501e13i	0.731397	+	0.731397i	−0.239499	+	0.970897i	$0.576983\pi$
$504$			1.09214e12i			0.0335836i
$505$	−3.79564e12	+	5.06086e12i	−0.115566	+	0.154087i
$506$	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	$0.959662\pi$
$510$	−6.88092e12	−	4.81664e13i	−0.199432	−	1.39603i
$511$	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
$515$	6.57355e12	−	9.39078e11i	0.181453	−	0.0259218i
$516$	−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
$520$	−9.52824e12	−	7.14618e12i	−0.250609	−	0.187956i
$521$	−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	0.725884	−	0.687818i	$-0.241431\pi$
$523$	1.48951e12	+	1.48951e12i	0.0380659	+	0.0380659i	−0.687818	+	0.725884i	$0.741431\pi$
$524$			2.66354e13i			0.674221i
$525$	−8.41357e12	−	2.88465e13i	−0.210952	−	0.723264i
$526$	−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
$530$	−1.17831e13	+	1.57108e13i	−0.281761	+	0.375682i
$531$	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
$535$	8.86323e11	+	6.20426e12i	0.0202219	+	0.141554i
$536$	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
$540$	−2.09551e13	+	2.99359e12i	−0.456374	+	0.0651963i
$541$	−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
$545$	−1.55324e13	−	1.16493e13i	−0.323040	−	0.242280i
$546$	−2.29047e13			−0.472021
$547$	3.39955e13	−	3.39955e13i	0.694200	−	0.694200i	−0.268953	−	0.963153i	$-0.586678\pi$
$547$	3.39955e13	−	3.39955e13i	0.694200	−	0.694200i	0.963153	+	0.268953i	$0.0866777\pi$
$548$	8.38730e12	+	8.38730e12i	0.169715	+	0.169715i
$549$			7.18515e12i			0.144070i
$550$	3.35959e13	+	1.84235e13i	0.667532	+	0.366066i
$551$	−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
$555$	3.86962e13	−	5.15949e13i	0.734858	−	0.979811i
$556$	1.33883e13			0.251971
$557$	9.51915e12	−	9.51915e12i	0.177551	−	0.177551i	−0.612737	−	0.790287i	$-0.709931\pi$
$557$	9.51915e12	−	9.51915e12i	0.177551	−	0.177551i	0.790287	+	0.612737i	$0.209931\pi$
$558$	−1.27701e12	−	1.27701e12i	−0.0236061	−	0.0236061i
$559$		−	2.76228e13i		−	0.506068i
$560$	1.37740e12	+	9.64182e12i	0.0250104	+	0.175073i
$561$	1.19314e14			2.14722
$562$	−1.26288e13	+	1.26288e13i	−0.225258	+	0.225258i
$563$	3.63651e13	+	3.63651e13i	0.642900	+	0.642900i	0.951267	−	0.308367i	$-0.0997826\pi$
$563$	3.63651e13	+	3.63651e13i	0.642900	+	0.642900i	−0.308367	+	0.951267i	$0.599783\pi$
$564$			3.22950e13i			0.565900i
$565$	7.85360e13	−	1.12194e13i	1.36404	−	0.194863i
$566$	−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	$0.923795\pi$
$570$	1.61268e13	+	1.20951e13i	0.268025	+	0.201019i
$571$	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
$575$	−3.47189e13	+	6.33110e13i	−0.552366	+	1.00726i
$576$	−1.06421e12			−0.0167848
$577$	−2.97579e13	+	2.97579e13i	−0.465289	+	0.465289i	−0.900384	−	0.435095i	$-0.856715\pi$
$577$	−2.97579e13	+	2.97579e13i	−0.465289	+	0.465289i	0.435095	+	0.900384i	$0.356715\pi$
$578$	−8.08489e13	−	8.08489e13i	−1.25324	−	1.25324i
$579$		−	7.78821e13i		−	1.19686i
$580$	−2.37992e13	+	3.17323e13i	−0.362596	+	0.483461i
$581$	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
$585$	1.15279e12	+	8.06955e12i	0.0168256	+	0.117780i
$586$	5.73556e12			0.0830019
$587$	4.60333e13	−	4.60333e13i	0.660513	−	0.660513i	−0.294988	−	0.955501i	$-0.595316\pi$
$587$	4.60333e13	−	4.60333e13i	0.660513	−	0.660513i	0.955501	+	0.294988i	$0.0953157\pi$
$588$	−1.32224e13	−	1.32224e13i	−0.188115	−	0.188115i
$589$		−	1.10883e13i		−	0.156419i
$590$	4.85848e13	−	6.94069e12i	0.679580	−	0.0970829i
$591$	−2.89230e13			−0.401149
$592$	−1.47818e13	+	1.47818e13i	−0.203291	+	0.203291i
$593$	−6.17714e12	−	6.17714e12i	−0.0842391	−	0.0842391i	0.663732	−	0.747971i	$-0.268972\pi$
$593$	−6.17714e12	−	6.17714e12i	−0.0842391	−	0.0842391i	−0.747971	+	0.663732i	$0.768972\pi$
$594$		−	5.19082e13i		−	0.701946i
$595$	−7.90272e13	−	5.92704e13i	−1.05972	−	0.794791i
$596$	−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	$0.877208\pi$
$600$	2.81088e13	−	8.19840e12i	0.361481	−	0.105432i
$601$	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
$605$	−7.74270e12	+	1.03236e13i	−0.0955247	+	0.127366i
$606$	−1.18546e13			−0.145051
$607$	−9.34184e13	+	9.34184e13i	−1.13368	+	1.13368i	−0.144115	+	0.989561i	$0.546033\pi$
$607$	−9.34184e13	+	9.34184e13i	−1.13368	+	1.13368i	−0.989561	+	0.144115i	$0.953967\pi$
$608$	−4.62028e12	−	4.62028e12i	−0.0556097	−	0.0556097i
$609$			7.62805e13i			0.910598i
$610$	9.06186e12	+	6.34330e13i	0.107292	+	0.751045i
$611$	−8.01802e13			−0.941588
$612$	7.63227e12	−	7.63227e12i	0.0888990	−	0.0888990i
$613$	1.42802e13	+	1.42802e13i	0.164980	+	0.164980i	0.784769	−	0.619789i	$-0.212782\pi$
$613$	1.42802e13	+	1.42802e13i	0.164980	+	0.164980i	−0.619789	+	0.784769i	$0.712782\pi$
$614$			3.52497e13i			0.403937i
$615$	−1.22499e14	+	1.74998e13i	−1.39237	+	0.198910i
$616$	−2.38839e13			−0.269278
$617$	−4.17740e12	+	4.17740e12i	−0.0467176	+	0.0467176i	−0.730080	−	0.683362i	$-0.760517\pi$
$617$	−4.17740e12	+	4.17740e12i	−0.0467176	+	0.0467176i	0.683362	+	0.730080i	$0.260517\pi$
$618$	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	$-0.0720642\pi$
$620$	−1.28845e13	−	9.66336e12i	−0.140640	−	0.105480i
$621$	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
$625$	−8.04138e13	+	5.12695e13i	−0.843200	+	0.537600i
$626$	−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
$630$	3.99955e12	−	5.33273e12i	0.0403003	−	0.0537337i
$631$	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
$635$	8.16382e12	+	5.71467e13i	0.0790723	+	0.553506i
$636$	−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
$640$	−9.39524e12	+	1.34218e12i	−0.0875000	+	0.0125000i
$641$	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	0.791783	−	0.610802i	$-0.209153\pi$
$643$	1.98925e13	+	1.98925e13i	0.180981	+	0.180981i	−0.610802	+	0.791783i	$0.709153\pi$
$644$		−	4.50089e13i		−	0.406321i
$645$	5.43258e13	+	4.07443e13i	0.486640	+	0.364980i
$646$	6.62710e13			0.589062
$647$	5.97289e13	−	5.97289e13i	0.526821	−	0.526821i	−0.392802	−	0.919623i	$-0.628494\pi$
$647$	5.97289e13	−	5.97289e13i	0.526821	−	0.526821i	0.919623	+	0.392802i	$0.128494\pi$
$648$	−3.18842e13	−	3.18842e13i	−0.279062	−	0.279062i
$649$			1.20350e14i			1.04526i
$650$	2.03545e13	+	6.97869e13i	0.175426	+	0.601461i
$651$	−3.09727e13			−0.264895
$652$	2.44892e13	−	2.44892e13i	0.207844	−	0.207844i
$653$	−9.87072e13	−	9.87072e13i	−0.831349	−	0.831349i	0.156353	−	0.987701i	$-0.450026\pi$
$653$	−9.87072e13	−	9.87072e13i	−0.831349	−	0.831349i	−0.987701	+	0.156353i	$0.950026\pi$
$654$		−	3.63831e13i		−	0.304096i
$655$	9.75416e13	−	1.30055e14i	0.809065	−	1.07875i
$656$	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	$-0.0750530\pi$
$660$	1.01542e13	+	7.10793e13i	0.0810822	+	0.567575i
$661$	−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
$665$	4.05161e13	−	5.78801e12i	0.311544	−	0.0445062i
$666$	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
$670$	−7.69659e13	−	5.77244e13i	−0.570065	−	0.427549i
$671$	−1.57131e14			−1.15518
$672$	−1.29057e13	+	1.29057e13i	−0.0941750	+	0.0941750i
$673$	−8.75360e13	−	8.75360e13i	−0.634032	−	0.634032i	0.315045	−	0.949077i	$-0.397980\pi$
$673$	−8.75360e13	−	8.75360e13i	−0.634032	−	0.634032i	−0.949077	+	0.315045i	$0.897980\pi$
$674$			1.17936e14i			0.847904i
$675$	1.13283e14	+	6.21228e13i	0.808434	+	0.443335i
$676$	−1.51714e13			−0.107471
$677$	1.59452e12	−	1.59452e12i	0.0112121	−	0.0112121i	−0.701478	−	0.712691i	$-0.747476\pi$
$677$	1.59452e12	−	1.59452e12i	0.0112121	−	0.0112121i	0.712691	+	0.701478i	$0.247476\pi$
$678$	1.05122e14	+	1.05122e14i	0.733742	+	0.733742i
$679$		−	1.07670e13i		−	0.0746014i
$680$	5.77546e13	−	7.70062e13i	0.397230	−	0.529640i
$681$	−4.21882e13			−0.288042
$682$	2.79268e13	−	2.79268e13i	0.189278	−	0.189278i
$683$	−5.65796e13	−	5.65796e13i	−0.380677	−	0.380677i	0.490669	−	0.871346i	$-0.336752\pi$
$683$	−5.65796e13	−	5.65796e13i	−0.380677	−	0.380677i	−0.871346	+	0.490669i	$0.836752\pi$
$684$			4.47195e12i			0.0298687i
$685$	−1.02384e13	−	7.16689e13i	−0.0678859	−	0.475201i
$686$	−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
$690$	−1.33948e14	+	1.91354e13i	−0.856428	+	0.122347i
$691$	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
$695$	−6.53724e13	−	4.90293e13i	−0.403153	−	0.302365i
$696$	−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
$700$	2.85838e13	−	5.21234e13i	0.170071	−	0.310129i
$701$	−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
$705$	1.18268e14	−	1.57691e14i	0.679080	−	0.905441i
$706$	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	$0.664458\pi$
$710$	−3.12088e13	−	2.18461e14i	−0.172976	−	1.21083i
$711$	−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
$715$	−1.76472e14	+	2.52102e13i	−0.944375	+	0.134911i
$716$	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	$0.858681\pi$
$720$	5.19635e12	+	3.89726e12i	0.0268557	+	0.0201417i
$721$	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
$725$	2.32414e14	−	6.77875e13i	1.16031	−	0.338423i
$726$	−2.41820e13			−0.119897
$727$	2.15314e14	−	2.15314e14i	1.06023	−	1.06023i	0.0621642	−	0.998066i	$-0.480200\pi$
$727$	2.15314e14	−	2.15314e14i	1.06023	−	1.06023i	0.998066	−	0.0621642i	$-0.0198002\pi$
$728$	−3.20416e13	−	3.20416e13i	−0.156696	−	0.156696i
$729$		−	1.71318e14i		−	0.832081i
$730$	3.81804e13	−	5.09071e13i	0.184173	−	0.245564i
$731$	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	$-0.868399\pi$
$733$	−2.78787e14	−	2.78787e14i	−1.31750	−	1.31750i	−0.401759	−	0.915746i	$-0.631601\pi$
$734$		−	5.61152e13i		−	0.263390i
$735$	1.61406e13	+	1.12984e14i	0.0752459	+	0.526721i
$736$	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	$0.845896\pi$
$740$	1.26309e14	−	1.80441e13i	0.569214	−	0.0813163i
$741$	−9.37868e13			−0.419808
$742$	−5.28324e13	+	5.28324e13i	−0.234899	+	0.234899i
$743$	1.59047e14	+	1.59047e14i	0.702396	+	0.702396i	0.964924	−	0.262528i	$-0.0845563\pi$
$743$	1.59047e14	+	1.59047e14i	0.702396	+	0.702396i	−0.262528	+	0.964924i	$0.584556\pi$
$744$		−	3.01806e13i		−	0.132392i
$745$	1.07841e13	+	8.08805e12i	0.0469895	+	0.0352422i
$746$	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
$750$	−1.67273e14	−	6.29063e13i	−0.704889	−	0.265086i
$751$	−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
$755$	−2.13503e14	+	2.84671e14i	−0.870302	+	1.16040i
$756$	−8.05347e13			−0.326117
$757$	7.07881e13	−	7.07881e13i	0.284761	−	0.284761i	−0.550243	−	0.835004i	$-0.685465\pi$
$757$	7.07881e13	−	7.07881e13i	0.284761	−	0.284761i	0.835004	+	0.550243i	$0.185465\pi$
$758$	1.15360e14	+

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	10.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} +(-1875.00 + 2500.00i) q^{5} -5856.00 q^{6} +(-8407.00 + 8407.00i) q^{7} +(-8192.00 - 8192.00i) q^{8} +7929.00i q^{9} +(10000.0 + 70000.0i) q^{10} -173398. q^{11} +(-93696.0 + 93696.0i) q^{12} +(-232623. - 232623. i) q^{13} +269024. i q^{14} +(800625. - 114375. i) q^{15} -262144. q^{16} +(1.88003e6 - 1.88003e6i) q^{17} +(126864. + 126864. i) q^{18} +1.10156e6i q^{19} +(1.28000e6 + 960000. i) q^{20} +3.07696e6 q^{21} +(-2.77437e6 + 2.77437e6i) q^{22} +(-5.22826e6 - 5.22826e6i) q^{23} +2.99827e6i q^{24} +(-2.73438e6 - 9.37500e6i) q^{25} -7.44394e6 q^{26} +(-9.35496e6 + 9.35496e6i) q^{27} +(4.30438e6 + 4.30438e6i) q^{28} +2.47908e7i q^{29} +(1.09800e7 - 1.46400e7i) q^{30} -1.00660e7 q^{31} +(-4.19430e6 + 4.19430e6i) q^{32} +(3.17318e7 + 3.17318e7i) q^{33} -6.01611e7i q^{34} +(-5.25438e6 - 3.67806e7i) q^{35} +4.05965e6 q^{36} +(5.63879e7 - 5.63879e7i) q^{37} +(1.76250e7 + 1.76250e7i) q^{38} +8.51400e7i q^{39} +(3.58400e7 - 5.12000e6i) q^{40} -1.53004e8 q^{41} +(4.92314e7 - 4.92314e7i) q^{42} +(5.93725e7 + 5.93725e7i) q^{43} +8.87798e7i q^{44} +(-1.98225e7 - 1.48669e7i) q^{45} -1.67304e8 q^{46} +(1.72339e8 - 1.72339e8i) q^{47} +(4.79724e7 + 4.79724e7i) q^{48} +1.41120e8i q^{49} +(-1.93750e8 - 1.06250e8i) q^{50} -6.88092e8 q^{51} +(-1.19103e8 + 1.19103e8i) q^{52} +(1.96386e8 + 1.96386e8i) q^{53} +2.99359e8i q^{54} +(3.25121e8 - 4.33495e8i) q^{55} +1.37740e8 q^{56} +(2.01585e8 - 2.01585e8i) q^{57} +(3.96653e8 + 3.96653e8i) q^{58} -6.94069e8i q^{59} +(-5.85600e7 - 4.09920e8i) q^{60} +9.06186e8 q^{61} +(-1.61056e8 + 1.61056e8i) q^{62} +(-6.66591e7 - 6.66591e7i) q^{63} +1.34218e8i q^{64} +(1.01773e9 - 1.45389e8i) q^{65} +1.01542e9 q^{66} +(-9.62074e8 + 9.62074e8i) q^{67} +(-9.62577e8 - 9.62577e8i) q^{68} +1.91354e9i q^{69} +(-6.72560e8 - 5.04420e8i) q^{70} -3.12088e9 q^{71} +(6.49544e7 - 6.49544e7i) q^{72} +(-6.36339e8 - 6.36339e8i) q^{73} -1.80441e9i q^{74} +(-1.21523e9 + 2.21602e9i) q^{75} +5.63999e8 q^{76} +(1.45776e9 - 1.45776e9i) q^{77} +(1.36224e9 + 1.36224e9i) q^{78} +1.96800e9i q^{79} +(4.91520e8 - 6.55360e8i) q^{80} +3.89211e9 q^{81} +(-2.44806e9 + 2.44806e9i) q^{82} +(-5.18382e9 - 5.18382e9i) q^{83} -1.57540e9i q^{84} +(1.17502e9 + 8.22514e9i) q^{85} +1.89992e9 q^{86} +(4.53672e9 - 4.53672e9i) q^{87} +(1.42048e9 + 1.42048e9i) q^{88} -7.77138e9i q^{89} +(-5.55030e8 + 7.92900e7i) q^{90} +3.91132e9 q^{91} +(-2.67687e9 + 2.67687e9i) q^{92} +(1.84208e9 + 1.84208e9i) q^{93} -5.51486e9i q^{94} +(-2.75390e9 - 2.06542e9i) q^{95} +1.53512e9 q^{96} +(-6.40361e8 + 6.40361e8i) q^{97} +(2.25792e9 + 2.25792e9i) q^{98} -1.37487e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{2} - 366 q^{3} - 3750 q^{5} - 11712 q^{6} - 16814 q^{7} - 16384 q^{8} + 20000 q^{10} - 346796 q^{11} - 187392 q^{12} - 465246 q^{13} + 1601250 q^{15} - 524288 q^{16} + 3760066 q^{17} + 253728 q^{18}+ \cdots + 4515838432 q^{98}+O(q^{100}) \) 2 * q + 32 * q^2 - 366 * q^3 - 3750 * q^5 - 11712 * q^6 - 16814 * q^7 - 16384 * q^8 + 20000 * q^10 - 346796 * q^11 - 187392 * q^12 - 465246 * q^13 + 1601250 * q^15 - 524288 * q^16 + 3760066 * q^17 + 253728 * q^18 + 2560000 * q^20 + 6153924 * q^21 - 5548736 * q^22 - 10456526 * q^23 - 5468750 * q^25 - 14887872 * q^26 - 18709920 * q^27 + 8608768 * q^28 + 21960000 * q^30 - 20131996 * q^31 - 8388608 * q^32 + 63463668 * q^33 - 10508750 * q^35 + 8119296 * q^36 + 112775826 * q^37 + 35249920 * q^38 + 71680000 * q^40 - 306007196 * q^41 + 98462784 * q^42 + 118744914 * q^43 - 39645000 * q^45 - 334608832 * q^46 + 344678706 * q^47 + 95944704 * q^48 - 387500000 * q^50 - 1376184156 * q^51 - 238205952 * q^52 + 392771234 * q^53 + 650242500 * q^55 + 275480576 * q^56 + 403170960 * q^57 + 793306880 * q^58 - 117120000 * q^60 + 1812371604 * q^61 - 322111936 * q^62 - 133318206 * q^63 + 2035451250 * q^65 + 2030837376 * q^66 - 1924147934 * q^67 - 1925153792 * q^68 - 1345120000 * q^70 - 6241755196 * q^71 + 129908736 * q^72 - 1272678526 * q^73 - 2430468750 * q^75 + 1127997440 * q^76 + 2915513972 * q^77 + 2724480576 * q^78 + 983040000 * q^80 + 7784229762 * q^81 - 4896115136 * q^82 - 10367644206 * q^83 + 2350041250 * q^85 + 3799837248 * q^86 + 9073447440 * q^87 + 2840952832 * q^88 - 1110060000 * q^90 + 7822646244 * q^91 - 5353741312 * q^92 + 3684155268 * q^93 - 5507800000 * q^95 + 3070230528 * q^96 - 1280722494 * q^97 + 4515838432 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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