LMFDB - Embedded newform 56.3.g.b.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(43,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("56.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.4
Root			$-1.05468 - 1.69931i$ of defining polynomial
Character	$\chi$	$=$	56.43
Dual form			56.3.g.b.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05468 + 1.69931i) q^{2} -3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} -4.88287i q^{5} +(3.62943 - 5.84780i) q^{6} -2.64575i q^{7} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +O(q^{10})$	\(q+(-1.05468 + 1.69931i) q^{2} -3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} -4.88287i q^{5} +(3.62943 - 5.84780i) q^{6} -2.64575i q^{7} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +(8.29751 + 5.14984i) q^{10} -21.4776 q^{11} +(6.10935 + 12.3351i) q^{12} -13.0760i q^{13} +(4.49595 + 2.79041i) q^{14} +16.8033i q^{15} +(-9.69651 + 12.7270i) q^{16} -0.234889 q^{17} +(-2.99780 + 4.83011i) q^{18} +4.55872 q^{19} +(-17.5024 + 8.66863i) q^{20} +9.10476i q^{21} +(22.6519 - 36.4971i) q^{22} +10.9523i q^{23} +(-27.4045 - 2.62782i) q^{24} +1.15761 q^{25} +(22.2202 + 13.7910i) q^{26} +21.1900 q^{27} +(-9.48355 + 4.69704i) q^{28} +34.6435i q^{29} +(-28.5540 - 17.7220i) q^{30} -34.1079i q^{31} +(-11.4005 - 29.9003i) q^{32} +73.9103 q^{33} +(0.247732 - 0.399150i) q^{34} -12.9189 q^{35} +(-5.04614 - 10.1884i) q^{36} -54.2370i q^{37} +(-4.80798 + 7.74669i) q^{38} +44.9982i q^{39} +(3.72865 - 38.8846i) q^{40} -37.8300 q^{41} +(-15.4718 - 9.60258i) q^{42} -4.84714 q^{43} +(38.1295 + 76.9852i) q^{44} -13.8790i q^{45} +(-18.6114 - 11.5511i) q^{46} -72.3368i q^{47} +(33.3684 - 43.7973i) q^{48} -7.00000 q^{49} +(-1.22090 + 1.96714i) q^{50} +0.808319 q^{51} +(-46.8703 + 23.2141i) q^{52} +21.6707i q^{53} +(-22.3486 + 36.0085i) q^{54} +104.872i q^{55} +(2.02034 - 21.0694i) q^{56} -15.6878 q^{57} +(-58.8701 - 36.5377i) q^{58} +34.9007 q^{59} +(60.2305 - 29.8312i) q^{60} +63.6012i q^{61} +(57.9599 + 35.9728i) q^{62} -7.52026i q^{63} +(62.8338 + 12.1621i) q^{64} -63.8485 q^{65} +(-77.9514 + 125.597i) q^{66} +18.4344 q^{67} +(0.417002 + 0.841948i) q^{68} -37.6899i q^{69} +(13.6252 - 21.9531i) q^{70} -47.5244i q^{71} +(22.6353 + 2.17050i) q^{72} +55.9103 q^{73} +(92.1655 + 57.2024i) q^{74} -3.98365 q^{75} +(-8.09317 - 16.3405i) q^{76} +56.8243i q^{77} +(-76.4660 - 47.4586i) q^{78} -95.0135i q^{79} +(62.1445 + 47.3468i) q^{80} -98.5023 q^{81} +(39.8984 - 64.2849i) q^{82} +71.5156 q^{83} +(32.6355 - 16.1638i) q^{84} +1.14693i q^{85} +(5.11217 - 8.23680i) q^{86} -119.218i q^{87} +(-171.036 - 16.4007i) q^{88} -159.756 q^{89} +(23.5848 + 14.6379i) q^{90} -34.5959 q^{91} +(39.2579 - 19.4438i) q^{92} +117.375i q^{93} +(122.923 + 76.2920i) q^{94} -22.2596i q^{95} +(39.2324 + 102.895i) q^{96} -90.4794 q^{97} +(7.38273 - 11.8952i) q^{98} -61.0477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) $ 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9	$ 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9} + 16 q^{10} - 32 q^{11} + 30 q^{12} + 7 q^{14} - 71 q^{16} - 80 q^{17} - 29 q^{18} + 56 q^{19} - 108 q^{20} + 66 q^{22} + 22 q^{24} - 16 q^{25} + 24 q^{26} - 32 q^{27} + 7 q^{28} + 96 q^{30} - 19 q^{32} + 32 q^{33} + 74 q^{34} + 56 q^{35} - 33 q^{36} - 14 q^{38} + 84 q^{40} + 128 q^{41} - 98 q^{42} + 50 q^{44} - 152 q^{46} + 134 q^{48} - 56 q^{49} + 33 q^{50} - 368 q^{51} + 132 q^{52} - 228 q^{54} - 49 q^{56} + 56 q^{57} + 24 q^{58} + 104 q^{59} + 192 q^{60} + 120 q^{62} - 55 q^{64} - 72 q^{65} - 276 q^{66} + 304 q^{67} - 190 q^{68} + 56 q^{70} - 209 q^{72} - 112 q^{73} + 8 q^{74} + 72 q^{75} + 70 q^{76} - 304 q^{78} + 124 q^{80} + 48 q^{81} + 450 q^{82} + 72 q^{83} + 42 q^{84} + 210 q^{86} - 486 q^{88} - 512 q^{89} - 184 q^{90} - 56 q^{91} - 472 q^{92} + 472 q^{94} + 558 q^{96} + 64 q^{97} - 7 q^{98} + 256 q^{99}+O(q^{100}) $ 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9 + 16 * q^10 - 32 * q^11 + 30 * q^12 + 7 * q^14 - 71 * q^16 - 80 * q^17 - 29 * q^18 + 56 * q^19 - 108 * q^20 + 66 * q^22 + 22 * q^24 - 16 * q^25 + 24 * q^26 - 32 * q^27 + 7 * q^28 + 96 * q^30 - 19 * q^32 + 32 * q^33 + 74 * q^34 + 56 * q^35 - 33 * q^36 - 14 * q^38 + 84 * q^40 + 128 * q^41 - 98 * q^42 + 50 * q^44 - 152 * q^46 + 134 * q^48 - 56 * q^49 + 33 * q^50 - 368 * q^51 + 132 * q^52 - 228 * q^54 - 49 * q^56 + 56 * q^57 + 24 * q^58 + 104 * q^59 + 192 * q^60 + 120 * q^62 - 55 * q^64 - 72 * q^65 - 276 * q^66 + 304 * q^67 - 190 * q^68 + 56 * q^70 - 209 * q^72 - 112 * q^73 + 8 * q^74 + 72 * q^75 + 70 * q^76 - 304 * q^78 + 124 * q^80 + 48 * q^81 + 450 * q^82 + 72 * q^83 + 42 * q^84 + 210 * q^86 - 486 * q^88 - 512 * q^89 - 184 * q^90 - 56 * q^91 - 472 * q^92 + 472 * q^94 + 558 * q^96 + 64 * q^97 - 7 * q^98 + 256 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.05468	+	1.69931i	−0.527338	+	0.849655i
$2$	−1.05468	+	1.69931i	−0.527338	+	0.849655i
$3$	−3.44128			−1.14709			−0.573546	−	0.819173i	$-0.694433\pi$
$3$	−3.44128			−1.14709			−0.573546	+	0.819173i	$0.694433\pi$
$4$	−1.77532	−	3.58445i	−0.443829	−	0.896112i
$5$		−	4.88287i		−	0.976573i	−0.872683	−	0.488287i	$-0.837622\pi$
$5$		−	4.88287i		−	0.976573i	0.872683	−	0.488287i	$-0.162378\pi$
$6$	3.62943	−	5.84780i	0.604906	−	0.974633i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	7.96347	+	0.763618i	0.995434	+	0.0954523i
$9$	2.84239			0.315821
$10$	8.29751	+	5.14984i	0.829751	+	0.514984i
$11$	−21.4776			−1.95251			−0.976253	−	0.216632i	$-0.930493\pi$
$11$	−21.4776			−1.95251			−0.976253	+	0.216632i	$0.930493\pi$
$12$	6.10935	+	12.3351i	0.509113	+	1.02792i
$13$		−	13.0760i		−	1.00585i	−0.864331	−	0.502924i	$-0.832258\pi$
$13$		−	13.0760i		−	1.00585i	0.864331	−	0.502924i	$-0.167742\pi$
$14$	4.49595	+	2.79041i	0.321140	+	0.199315i
$15$			16.8033i			1.12022i
$16$	−9.69651	+	12.7270i	−0.606032	+	0.795440i
$17$	−0.234889			−0.0138170			−0.00690851	−	0.999976i	$-0.502199\pi$
$17$	−0.234889			−0.0138170			−0.00690851	+	0.999976i	$0.502199\pi$
$18$	−2.99780	+	4.83011i	−0.166545	+	0.268339i
$19$	4.55872			0.239933			0.119966	−	0.992778i	$-0.461721\pi$
$19$	4.55872			0.239933			0.119966	+	0.992778i	$0.461721\pi$
$20$	−17.5024	+	8.66863i	−0.875119	+	0.433431i
$21$			9.10476i			0.433560i
$22$	22.6519	−	36.4971i	1.02963	−	1.65896i
$23$			10.9523i			0.476187i	0.971242	+	0.238094i	$0.0765225\pi$
$23$			10.9523i			0.476187i	−0.971242	+	0.238094i	$0.923478\pi$
$24$	−27.4045	−	2.62782i	−1.14185	−	0.109493i
$25$	1.15761			0.0463043
$26$	22.2202	+	13.7910i	0.854624	+	0.530422i
$27$	21.1900			0.784816
$28$	−9.48355	+	4.69704i	−0.338698	+	0.167752i
$29$			34.6435i			1.19460i	0.802016	+	0.597302i	$0.203761\pi$
$29$			34.6435i			1.19460i	−0.802016	+	0.597302i	$0.796239\pi$
$30$	−28.5540	−	17.7220i	−0.951801	−	0.590735i
$31$		−	34.1079i		−	1.10025i	−0.835081	−	0.550127i	$-0.814579\pi$
$31$		−	34.1079i		−	1.10025i	0.835081	−	0.550127i	$-0.185421\pi$
$32$	−11.4005	−	29.9003i	−0.356266	−	0.934384i
$33$	73.9103			2.23971
$34$	0.247732	−	0.399150i	0.00728624	−	0.0117397i
$35$	−12.9189			−0.369110
$36$	−5.04614	−	10.1884i	−0.140171	−	0.283011i
$37$		−	54.2370i		−	1.46586i	−0.680302	−	0.732932i	$-0.738151\pi$
$37$		−	54.2370i		−	1.46586i	0.680302	−	0.732932i	$-0.261849\pi$
$38$	−4.80798	+	7.74669i	−0.126526	+	0.203860i
$39$			44.9982i			1.15380i
$40$	3.72865	−	38.8846i	0.0932162	−	0.972114i
$41$	−37.8300			−0.922682			−0.461341	−	0.887223i	$-0.652632\pi$
$41$	−37.8300			−0.922682			−0.461341	+	0.887223i	$0.652632\pi$
$42$	−15.4718	−	9.60258i	−0.368377	−	0.228633i
$43$	−4.84714			−0.112724			−0.0563621	−	0.998410i	$-0.517950\pi$
$43$	−4.84714			−0.112724			−0.0563621	+	0.998410i	$0.517950\pi$
$44$	38.1295	+	76.9852i	0.866579	+	1.74966i
$45$		−	13.8790i		−	0.308423i
$46$	−18.6114	−	11.5511i	−0.404595	−	0.251112i
$47$		−	72.3368i		−	1.53908i	−0.638598	−	0.769541i	$-0.720485\pi$
$47$		−	72.3368i		−	1.53908i	0.638598	−	0.769541i	$-0.279515\pi$
$48$	33.3684	−	43.7973i	0.695175	−	0.912444i
$49$	−7.00000			−0.142857
$50$	−1.22090	+	1.96714i	−0.0244180	+	0.0393427i
$51$	0.808319			0.0158494
$52$	−46.8703	+	23.2141i	−0.901352	+	0.446424i
$53$			21.6707i			0.408881i	0.978879	+	0.204440i	$0.0655374\pi$
$53$			21.6707i			0.408881i	−0.978879	+	0.204440i	$0.934463\pi$
$54$	−22.3486	+	36.0085i	−0.413864	+	0.666823i
$55$			104.872i			1.90677i
$56$	2.02034	−	21.0694i	0.0360776	−	0.376239i
$57$	−15.6878			−0.275225
$58$	−58.8701	−	36.5377i	−1.01500	−	0.629961i
$59$	34.9007			0.591537			0.295768	−	0.955260i	$-0.404424\pi$
$59$	34.9007			0.591537			0.295768	+	0.955260i	$0.404424\pi$
$60$	60.2305	−	29.8312i	1.00384	−	0.497186i
$61$			63.6012i			1.04264i	0.853360	+	0.521321i	$0.174561\pi$
$61$			63.6012i			1.04264i	−0.853360	+	0.521321i	$0.825439\pi$
$62$	57.9599	+	35.9728i	0.934837	+	0.580206i
$63$		−	7.52026i		−	0.119369i
$64$	62.8338	+	12.1621i	0.981778	+	0.190033i
$65$	−63.8485			−0.982284
$66$	−77.9514	+	125.597i	−1.18108	+	1.90298i
$67$	18.4344			0.275140			0.137570	−	0.990492i	$-0.456071\pi$
$67$	18.4344			0.275140			0.137570	+	0.990492i	$0.456071\pi$
$68$	0.417002	+	0.841948i	0.00613239	+	0.0123816i
$69$		−	37.6899i		−	0.546231i
$70$	13.6252	−	21.9531i	0.194646	−	0.313616i
$71$		−	47.5244i		−	0.669358i	−0.942332	−	0.334679i	$-0.891372\pi$
$71$		−	47.5244i		−	0.669358i	0.942332	−	0.334679i	$-0.108628\pi$
$72$	22.6353	+	2.17050i	0.314379	+	0.0301459i
$73$	55.9103			0.765894			0.382947	−	0.923770i	$-0.374909\pi$
$73$	55.9103			0.765894			0.382947	+	0.923770i	$0.374909\pi$
$74$	92.1655	+	57.2024i	1.24548	+	0.773006i
$75$	−3.98365			−0.0531153
$76$	−8.09317	−	16.3405i	−0.106489	−	0.215007i
$77$			56.8243i			0.737978i
$78$	−76.4660	−	47.4586i	−0.980333	−	0.608443i
$79$		−	95.0135i		−	1.20270i	−0.798985	−	0.601351i	$-0.794629\pi$
$79$		−	95.0135i		−	1.20270i	0.798985	−	0.601351i	$-0.205371\pi$
$80$	62.1445	+	47.3468i	0.776806	+	0.591835i
$81$	−98.5023			−1.21608
$82$	39.8984	−	64.2849i	0.486566	−	0.783962i
$83$	71.5156			0.861634			0.430817	−	0.902439i	$-0.358225\pi$
$83$	71.5156			0.861634			0.430817	+	0.902439i	$0.358225\pi$
$84$	32.6355	−	16.1638i	0.388518	−	0.192427i
$85$			1.14693i			0.0134933i
$86$	5.11217	−	8.23680i	0.0594438	−	0.0957768i
$87$		−	119.218i		−	1.37032i
$88$	−171.036	−	16.4007i	−1.94359	−	0.186371i
$89$	−159.756			−1.79501			−0.897504	−	0.441006i	$-0.854622\pi$
$89$	−159.756			−1.79501			−0.897504	+	0.441006i	$0.854622\pi$
$90$	23.5848	+	14.6379i	0.262053	+	0.162643i
$91$	−34.5959			−0.380175
$92$	39.2579	−	19.4438i	0.426717	−	0.211346i
$93$			117.375i			1.26209i
$94$	122.923	+	76.2920i	1.30769	+	0.811617i
$95$		−	22.2596i		−	0.234312i
$96$	39.2324	+	102.895i	0.408671	+	1.07183i
$97$	−90.4794			−0.932777			−0.466389	−	0.884580i	$-0.654445\pi$
$97$	−90.4794			−0.932777			−0.466389	+	0.884580i	$0.654445\pi$
$98$	7.38273	−	11.8952i	0.0753340	−	0.121379i
$99$	−61.0477			−0.616643
$100$	−2.05512	−	4.14938i	−0.0205512	−	0.0414938i
$101$		−	181.147i		−	1.79353i	−0.442503	−	0.896767i	$-0.645909\pi$
$101$		−	181.147i		−	1.79353i	0.442503	−	0.896767i	$-0.354091\pi$
$102$	−0.852515	+	1.37359i	−0.00835799	+	0.0134665i
$103$			39.3003i			0.381556i	0.981633	+	0.190778i	$0.0611010\pi$
$103$			39.3003i			0.381556i	−0.981633	+	0.190778i	$0.938899\pi$
$104$	9.98509	−	104.131i	0.0960105	−	1.00126i
$105$	44.4574			0.423403
$106$	−36.8252	−	22.8556i	−0.347408	−	0.215618i
$107$	38.4498			0.359344			0.179672	−	0.983727i	$-0.442496\pi$
$107$	38.4498			0.359344			0.179672	+	0.983727i	$0.442496\pi$
$108$	−37.6190	−	75.9546i	−0.348324	−	0.703283i
$109$			27.8786i			0.255767i	0.991789	+	0.127883i	$0.0408183\pi$
$109$			27.8786i			0.255767i	−0.991789	+	0.127883i	$0.959182\pi$
$110$	−178.210	−	110.606i	−1.62009	−	1.00551i
$111$			186.644i			1.68148i
$112$	33.6726	+	25.6546i	0.300648	+	0.229059i
$113$	82.4419			0.729574			0.364787	−	0.931091i	$-0.381142\pi$
$113$	82.4419			0.729574			0.364787	+	0.931091i	$0.381142\pi$
$114$	16.5456	−	26.6585i	0.145137	−	0.233846i
$115$	53.4786			0.465032
$116$	124.178	−	61.5032i	1.07050	−	0.530200i
$117$		−	37.1672i		−	0.317668i
$118$	−36.8089	+	59.3071i	−0.311940	+	0.502603i
$119$			0.621458i			0.00522234i
$120$	−12.8313	+	133.813i	−0.106928	+	1.11511i
$121$	340.286			2.81228
$122$	−108.078	−	67.0787i	−0.885887	−	0.549825i
$123$	130.183			1.05840
$124$	−122.258	+	60.5522i	−0.985951	+	0.488325i
$125$		−	127.724i		−	1.02179i
$126$	12.7793	+	7.93144i	0.101423	+	0.0629480i
$127$			25.1408i			0.197959i	0.995089	+	0.0989796i	$0.0315579\pi$
$127$			25.1408i			0.197959i	−0.995089	+	0.0989796i	$0.968442\pi$
$128$	−86.9365	+	93.9470i	−0.679191	+	0.733961i
$129$	16.6804			0.129305
$130$	67.3395	−	108.498i	0.517996	−	0.834603i
$131$	−126.398			−0.964872			−0.482436	−	0.875931i	$-0.660248\pi$
$131$	−126.398			−0.964872			−0.482436	+	0.875931i	$0.660248\pi$
$132$	−131.214	−	264.928i	−0.994046	−	2.00703i
$133$		−	12.0612i		−	0.0906861i
$134$	−19.4423	+	31.3257i	−0.145092	+	0.233774i
$135$		−	103.468i		−	0.766431i
$136$	−1.87053	−	0.179366i	−0.0137539	−	0.00131887i
$137$	34.9456			0.255078			0.127539	−	0.991834i	$-0.459292\pi$
$137$	34.9456			0.255078			0.127539	+	0.991834i	$0.459292\pi$
$138$	64.0469	+	39.7507i	0.464108	+	0.288048i
$139$	−119.148			−0.857177			−0.428589	−	0.903500i	$-0.640989\pi$
$139$	−119.148			−0.857177			−0.428589	+	0.903500i	$0.640989\pi$
$140$	22.9350	+	46.3069i	0.163822	+	0.330764i
$141$			248.931i			1.76547i
$142$	80.7587	+	50.1229i	0.568723	+	0.352978i
$143$			280.841i			1.96392i
$144$	−27.5613	+	36.1753i	−0.191398	+	0.251217i
$145$	169.160			1.16662
$146$	−58.9673	+	95.0090i	−0.403885	+	0.650746i
$147$	24.0889			0.163870
$148$	−194.409	+	96.2877i	−1.31358	+	0.650593i
$149$			121.932i			0.818334i	0.912460	+	0.409167i	$0.134181\pi$
$149$			121.932i			0.818334i	−0.912460	+	0.409167i	$0.865819\pi$
$150$	4.20146	−	6.76946i	0.0280097	−	0.0451297i
$151$			220.404i			1.45963i	0.683645	+	0.729815i	$0.260394\pi$
$151$			220.404i			1.45963i	−0.683645	+	0.729815i	$0.739606\pi$
$152$	36.3033	+	3.48112i	0.238837	+	0.0229021i
$153$	−0.667647			−0.00436371
$154$	−96.5622	−	59.9313i	−0.627027	−	0.389164i
$155$	−166.544			−1.07448
$156$	161.294	−	79.8860i	1.03393	−	0.512090i
$157$			6.77014i			0.0431219i	0.999768	+	0.0215610i	$0.00686360\pi$
$157$			6.77014i			0.0431219i	−0.999768	+	0.0215610i	$0.993136\pi$
$158$	161.457	+	100.208i	1.02188	+	0.634231i
$159$		−	74.5748i		−	0.469024i
$160$	−145.999	+	55.6672i	−0.912495	+	0.347920i
$161$	28.9771			0.179982
$162$	103.888	−	167.386i	0.641285	−	1.03325i
$163$	−207.243			−1.27143			−0.635715	−	0.771924i	$-0.719294\pi$
$163$	−207.243			−1.27143			−0.635715	+	0.771924i	$0.719294\pi$
$164$	67.1601	+	135.600i	0.409513	+	0.826826i
$165$		−	360.894i		−	2.18724i
$166$	−75.4259	+	121.527i	−0.454373	+	0.732092i
$167$		−	165.529i		−	0.991193i	−0.868553	−	0.495596i	$-0.834950\pi$
$167$		−	165.529i		−	0.991193i	0.868553	−	0.495596i	$-0.165050\pi$
$168$	−6.95257	+	72.5055i	−0.0413843	+	0.431581i
$169$	−1.98237			−0.0117300
$170$	−1.94900	−	1.20964i	−0.0114647	−	0.00711555i
$171$	12.9577			0.0757759
$172$	8.60521	+	17.3743i	0.0500303	+	0.101014i
$173$			88.8530i			0.513601i	0.966464	+	0.256800i	$0.0826683\pi$
$173$			88.8530i			0.513601i	−0.966464	+	0.256800i	$0.917332\pi$
$174$	202.588	+	125.736i	1.16430	+	0.722623i
$175$		−	3.06274i		−	0.0175014i
$176$	208.258	−	273.346i	1.18328	−	1.55310i
$177$	−120.103			−0.678548
$178$	168.491	−	271.475i	0.946576	−	1.52514i
$179$	80.3791			0.449045			0.224523	−	0.974469i	$-0.427918\pi$
$179$	80.3791			0.449045			0.224523	+	0.974469i	$0.427918\pi$
$180$	−49.7486	+	24.6396i	−0.276381	+	0.136887i
$181$		−	276.353i		−	1.52681i	−0.645919	−	0.763406i	$-0.723526\pi$
$181$		−	276.353i		−	1.52681i	0.645919	−	0.763406i	$-0.276474\pi$
$182$	36.4875	−	58.7892i	0.200481	−	0.323018i
$183$		−	218.869i		−	1.19601i
$184$	−8.36338	+	87.2184i	−0.0454532	+	0.474013i
$185$	−264.832			−1.43152
$186$	−199.456	−	123.792i	−1.07234	−	0.665550i
$187$	5.04485			0.0269778
$188$	−259.288	+	128.421i	−1.37919	+	0.683089i
$189$		−	56.0636i		−	0.296633i
$190$	37.8260	+	23.4767i	0.199084	+	0.123562i
$191$		−	203.015i		−	1.06290i	−0.847088	−	0.531452i	$-0.821647\pi$
$191$		−	203.015i		−	1.06290i	0.847088	−	0.531452i	$-0.178353\pi$
$192$	−216.228	−	41.8532i	−1.12619	−	0.217985i
$193$	87.3328			0.452502			0.226251	−	0.974069i	$-0.427353\pi$
$193$	87.3328			0.452502			0.226251	+	0.974069i	$0.427353\pi$
$194$	95.4265	−	153.753i	0.491889	−	0.792539i
$195$	219.720			1.12677
$196$	12.4272	+	25.0911i	0.0634041	+	0.128016i
$197$		−	21.6639i		−	0.109969i	−0.998487	−	0.0549845i	$-0.982489\pi$
$197$		−	21.6639i		−	0.109969i	0.998487	−	0.0549845i	$-0.0175109\pi$
$198$	64.3856	−	103.739i	0.325180	−	0.523934i
$199$			181.933i			0.914235i	0.889406	+	0.457118i	$0.151118\pi$
$199$			181.933i			0.914235i	−0.889406	+	0.457118i	$0.848882\pi$
$200$	9.21858	+	0.883971i	0.0460929	+	0.00441985i
$201$	−63.4378			−0.315611
$202$	307.825	+	191.051i	1.52389	+	0.945799i
$203$	91.6582			0.451518
$204$	−1.43502	−	2.89738i	−0.00703442	−	0.0142028i
$205$			184.719i			0.901067i
$206$	−66.7834	−	41.4491i	−0.324191	−	0.201209i
$207$			31.1307i			0.150390i
$208$	166.419	+	126.792i	0.800092	+	0.609576i
$209$	−97.9103			−0.468470
$210$	−46.8881	+	75.5469i	−0.223277	+	0.359747i
$211$	−21.4204			−0.101519			−0.0507594	−	0.998711i	$-0.516164\pi$
$211$	−21.4204			−0.101519			−0.0507594	+	0.998711i	$0.516164\pi$
$212$	77.6774	−	38.4723i	0.366403	−	0.181473i
$213$			163.545i			0.767815i
$214$	−40.5521	+	65.3382i	−0.189496	+	0.305319i
$215$			23.6680i			0.110084i
$216$	168.746	+	16.1811i	0.781233	+	0.0749125i
$217$	−90.2410			−0.415857
$218$	−47.3744	−	29.4029i	−0.217314	−	0.134876i
$219$	−192.403			−0.878552
$220$	375.909	−	186.181i	1.70868	−	0.846278i
$221$			3.07142i			0.0138978i
$222$	−317.167	−	196.850i	−1.42868	−	0.886710i
$223$			195.958i			0.878735i	0.898307	+	0.439367i	$0.144797\pi$
$223$			195.958i			0.878735i	−0.898307	+	0.439367i	$0.855203\pi$
$224$	−79.1088	+	30.1630i	−0.353164	+	0.134656i
$225$	3.29038			0.0146239
$226$	−86.9495	+	140.094i	−0.384732	+	0.619887i
$227$	−27.2652			−0.120111			−0.0600554	−	0.998195i	$-0.519128\pi$
$227$	−27.2652			−0.120111			−0.0600554	+	0.998195i	$0.519128\pi$
$228$	27.8508	+	56.2322i	0.122153	+	0.246632i
$229$		−	176.347i		−	0.770076i	−0.922901	−	0.385038i	$-0.874188\pi$
$229$		−	176.347i		−	0.770076i	0.922901	−	0.385038i	$-0.125812\pi$
$230$	−56.4027	+	90.8768i	−0.245229	+	0.395117i
$231$		−	195.548i		−	0.846529i
$232$	−26.4544	+	275.883i	−0.114028	+	1.18915i
$233$	71.8366			0.308312			0.154156	−	0.988047i	$-0.450734\pi$
$233$	71.8366			0.308312			0.154156	+	0.988047i	$0.450734\pi$
$234$	63.1586	+	39.1994i	0.269909	+	0.167519i
$235$	−353.211			−1.50303
$236$	−61.9597	−	125.100i	−0.262541	−	0.530083i
$237$			326.968i			1.37961i
$238$	−1.05605	−	0.655438i	−0.00443719	−	0.00275394i
$239$		−	71.0926i		−	0.297459i	−0.988878	−	0.148729i	$-0.952482\pi$
$239$		−	71.0926i		−	0.297459i	0.988878	−	0.148729i	$-0.0475183\pi$
$240$	−213.856	−	162.933i	−0.891068	−	0.678889i
$241$	56.1113			0.232827			0.116413	−	0.993201i	$-0.462860\pi$
$241$	56.1113			0.232827			0.116413	+	0.993201i	$0.462860\pi$
$242$	−358.892	+	578.252i	−1.48302	+	2.38947i
$243$	148.264			0.610138
$244$	227.975	−	112.912i	0.934324	−	0.462755i
$245$			34.1801i			0.139510i
$246$	−137.301	+	221.222i	−0.558136	+	0.899277i
$247$		−	59.6100i		−	0.241336i
$248$	26.0454	−	271.617i	0.105022	−	1.09523i
$249$	−246.105			−0.988374
$250$	217.043	+	134.708i	0.868172	+	0.538830i
$251$	368.953			1.46993			0.734966	−	0.678104i	$-0.237198\pi$
$251$	368.953			1.46993			0.734966	+	0.678104i	$0.237198\pi$
$252$	−26.9560	+	13.3508i	−0.106968	+	0.0529795i
$253$		−	235.229i		−	0.929759i
$254$	−42.7221	−	26.5154i	−0.168197	−	0.104391i
$255$		−	3.94691i		−	0.0154781i
$256$	−67.9553	−	246.816i	−0.265451	−	0.964124i
$257$	23.7428			0.0923845			0.0461923	−	0.998933i	$-0.485291\pi$
$257$	23.7428			0.0923845			0.0461923	+	0.998933i	$0.485291\pi$
$258$	−17.5924	+	28.3451i	−0.0681876	+	0.109865i
$259$	−143.498			−0.554044
$260$	113.351	+	228.861i	0.435966	+	0.880236i
$261$			98.4705i			0.377282i
$262$	133.309	−	214.790i	0.508814	−	0.819809i
$263$		−	73.9707i		−	0.281257i	−0.990062	−	0.140629i	$-0.955088\pi$
$263$		−	73.9707i		−	0.281257i	0.990062	−	0.140629i	$-0.0449124\pi$
$264$	588.583	+	56.4393i	2.22948	+	0.213785i
$265$	105.815			0.399302
$266$	20.4958	+	12.7207i	0.0770519	+	0.0478222i
$267$	549.764			2.05904
$268$	−32.7268	−	66.0770i	−0.122115	−	0.246556i
$269$			335.593i			1.24756i	0.781601	+	0.623779i	$0.214403\pi$
$269$			335.593i			1.24756i	−0.781601	+	0.623779i	$0.785597\pi$
$270$	175.825	+	109.125i	0.651202	+	0.404168i
$271$			187.276i			0.691054i	0.938409	+	0.345527i	$0.112300\pi$
$271$			187.276i			0.691054i	−0.938409	+	0.345527i	$0.887700\pi$
$272$	2.27761	−	2.98945i	0.00837355	−	0.0109906i
$273$	119.054			0.436096
$274$	−36.8564	+	59.3835i	−0.134512	+	0.216728i
$275$	−24.8626			−0.0904095
$276$	−135.097	+	66.9115i	−0.489484	+	0.242433i
$277$			132.592i			0.478670i	0.970937	+	0.239335i	$0.0769294\pi$
$277$			132.592i			0.478670i	−0.970937	+	0.239335i	$0.923071\pi$
$278$	125.662	−	202.469i	0.452022	−	0.728305i
$279$		−	96.9480i		−	0.347484i
$280$	−102.879	−	9.86507i	−0.367425	−	0.0352324i
$281$	331.520			1.17979			0.589894	−	0.807481i	$-0.299170\pi$
$281$	331.520			1.17979			0.589894	+	0.807481i	$0.299170\pi$
$282$	−423.011	−	262.542i	−1.50004	−	0.930999i
$283$	−66.7158			−0.235745			−0.117873	−	0.993029i	$-0.537607\pi$
$283$	−66.7158			−0.235745			−0.117873	+	0.993029i	$0.537607\pi$
$284$	−170.349	+	84.3708i	−0.599819	+	0.297080i
$285$			76.6016i			0.268778i
$286$	−477.237	−	296.197i	−1.66866	−	1.03565i
$287$			100.089i			0.348741i
$288$	−32.4048	−	84.9884i	−0.112517	−	0.295099i
$289$	−288.945			−0.999809
$290$	−178.409	+	287.455i	−0.615203	+	0.991224i
$291$	311.365			1.06998
$292$	−99.2584	−	200.407i	−0.339926	−	0.686327i
$293$		−	289.215i		−	0.987082i	−0.869723	−	0.493541i	$-0.835702\pi$
$293$		−	289.215i		−	0.987082i	0.869723	−	0.493541i	$-0.164298\pi$
$294$	−25.4060	+	40.9346i	−0.0864151	+	0.139233i
$295$		−	170.415i		−	0.577679i
$296$	41.4163	−	431.915i	0.139920	−	1.45917i
$297$	−455.111			−1.53236
$298$	−207.200	−	128.598i	−0.695302	−	0.431539i
$299$	143.213			0.478972
$300$	7.07223	+	14.2792i	0.0235741	+	0.0475973i
$301$			12.8243i			0.0426058i
$302$	−374.535	−	232.455i	−1.24018	−	0.769719i
$303$			623.377i			2.05735i
$304$	−44.2037	+	58.0191i	−0.145407	+	0.190852i
$305$	310.556			1.01822
$306$	0.704152	−	1.13454i	0.00230115	−	0.00370765i
$307$	0.693177			0.00225790			0.00112895	−	0.999999i	$-0.499641\pi$
$307$	0.693177			0.00225790			0.00112895	+	0.999999i	$0.499641\pi$
$308$	203.684	−	100.881i	0.661311	−	0.327536i
$309$		−	135.243i		−	0.437680i
$310$	175.650	−	283.010i	0.566614	−	0.912937i
$311$		−	62.1583i		−	0.199866i	−0.994994	−	0.0999330i	$-0.968137\pi$
$311$		−	62.1583i		−	0.199866i	0.994994	−	0.0999330i	$-0.0318628\pi$
$312$	−34.3615	+	358.342i	−0.110133	+	1.14853i
$313$	213.594			0.682408			0.341204	−	0.939989i	$-0.389165\pi$
$313$	213.594			0.682408			0.341204	+	0.939989i	$0.389165\pi$
$314$	−11.5046	−	7.14031i	−0.0366388	−	0.0227398i
$315$	−36.7204			−0.116573
$316$	−340.571	+	168.679i	−1.07776	+	0.533794i
$317$		−	23.4577i		−	0.0739990i	−0.999315	−	0.0369995i	$-0.988220\pi$
$317$		−	23.4577i		−	0.0739990i	0.999315	−	0.0369995i	$-0.0117800\pi$
$318$	126.726	+	78.6523i	0.398509	+	0.247334i
$319$		−	744.059i		−	2.33247i
$320$	59.3860	−	306.809i	0.185581	−	0.958778i
$321$	−132.317			−0.412201
$322$	−30.5614	+	49.2411i	−0.0949113	+	0.152923i
$323$	−1.07079			−0.00331515
$324$	174.873	+	353.076i	0.539731	+	1.08974i
$325$		−	15.1369i		−	0.0465751i
$326$	218.574	−	352.170i	0.670473	−	1.08028i
$327$		−	95.9380i		−	0.293388i
$328$	−301.258	−	28.8877i	−0.918469	−	0.0880721i
$329$	−191.385			−0.581718
$330$	613.271	+	380.627i	1.85840	+	1.15341i
$331$	507.406			1.53295			0.766474	−	0.642275i	$-0.222009\pi$
$331$	507.406			1.53295			0.766474	+	0.642275i	$0.222009\pi$
$332$	−126.963	−	256.344i	−0.382418	−	0.772120i
$333$		−	154.163i		−	0.462951i
$334$	281.286	+	174.580i	0.842172	+	0.522694i
$335$		−	90.0126i		−	0.268694i
$336$	−115.877	−	88.2845i	−0.344871	−	0.262751i
$337$	−342.726			−1.01699			−0.508495	−	0.861065i	$-0.669798\pi$
$337$	−342.726			−1.01699			−0.508495	+	0.861065i	$0.669798\pi$
$338$	2.09076	−	3.36866i	0.00618567	−	0.00996645i
$339$	−283.705			−0.836889
$340$	4.11112	−	2.03617i	0.0120915	−	0.00598873i
$341$			732.555i			2.14825i
$342$	−13.6662	+	22.0191i	−0.0399595	+	0.0643834i
$343$			18.5203i			0.0539949i
$344$	−38.6001	−	3.70137i	−0.112210	−	0.0107598i
$345$	−184.035			−0.533434
$346$	−150.989	−	93.7111i	−0.436384	−	0.270841i
$347$	136.745			0.394079			0.197039	−	0.980396i	$-0.436867\pi$
$347$	136.745			0.394079			0.197039	+	0.980396i	$0.436867\pi$
$348$	−427.331	+	211.650i	−1.22796	+	0.608188i
$349$		−	82.0565i		−	0.235119i	−0.993066	−	0.117559i	$-0.962493\pi$
$349$		−	82.0565i		−	0.235119i	0.993066	−	0.117559i	$-0.0375071\pi$
$350$	5.20455	+	3.23020i	0.0148701	+	0.00922915i
$351$		−	277.081i		−	0.789406i
$352$	244.856	+	642.186i	0.695613	+	1.82439i
$353$	507.367			1.43730			0.718651	−	0.695371i	$-0.244760\pi$
$353$	507.367			1.43730			0.718651	+	0.695371i	$0.244760\pi$
$354$	126.670	−	204.092i	0.357824	−	0.576532i
$355$	−232.055			−0.653677
$356$	283.617	+	572.636i	0.796676	+	1.60853i
$357$		−	2.13861i		−	0.00599051i
$358$	−84.7740	+	136.589i	−0.236799	+	0.381534i
$359$			560.809i			1.56214i	0.624442	+	0.781071i	$0.285326\pi$
$359$			560.809i			1.56214i	−0.624442	+	0.781071i	$0.714674\pi$
$360$	10.5983	−	110.525i	0.0294397	−	0.307014i
$361$	−340.218			−0.942432
$362$	469.610	+	291.463i	1.29726	+	0.805147i
$363$	−1171.02			−3.22595
$364$	61.4186	+	124.007i	0.168733	+	0.340679i
$365$		−	273.003i		−	0.747952i
$366$	371.927	+	230.836i	1.01619	+	0.630701i
$367$			26.9431i			0.0734145i	0.999326	+	0.0367072i	$0.0116869\pi$
$367$			26.9431i			0.0734145i	−0.999326	+	0.0367072i	$0.988313\pi$
$368$	−139.390	−	106.199i	−0.378778	−	0.288585i
$369$	−107.528			−0.291403
$370$	279.312	−	450.032i	0.754897	−	1.21630i
$371$	57.3352			0.154542
$372$	420.723	−	208.377i	1.13098	−	0.560153i
$373$		−	538.034i		−	1.44245i	−0.692701	−	0.721225i	$-0.743579\pi$
$373$		−	538.034i		−	1.44245i	0.692701	−	0.721225i	$-0.256421\pi$
$374$	−5.32069	+	8.57277i	−0.0142264	+	0.0229218i
$375$			439.534i			1.17209i
$376$	55.2377	−	576.052i	0.146909	−	1.53205i
$377$	453.000			1.20159
$378$	95.2694	+	59.1289i	0.252036	+	0.156426i
$379$	−182.132			−0.480560			−0.240280	−	0.970704i	$-0.577239\pi$
$379$	−182.132			−0.480560			−0.240280	+	0.970704i	$0.577239\pi$
$380$	−79.7885	+	39.5179i	−0.209970	+	0.103994i
$381$		−	86.5166i		−	0.227078i
$382$	344.985	+	214.115i	0.903102	+	0.560510i
$383$		−	333.271i		−	0.870160i	−0.900392	−	0.435080i	$-0.856720\pi$
$383$		−	333.271i		−	0.870160i	0.900392	−	0.435080i	$-0.143280\pi$
$384$	299.173	−	323.298i	0.779095	−	0.841921i
$385$	277.466			0.720690
$386$	−92.1079	+	148.406i	−0.238621	+	0.384471i
$387$	−13.7775			−0.0356007
$388$	160.629	+	324.319i	0.413993	+	0.835873i
$389$			109.639i			0.281847i	0.990020	+	0.140924i	$0.0450072\pi$
$389$			109.639i			0.281847i	−0.990020	+	0.140924i	$0.954993\pi$
$390$	−231.734	+	373.373i	−0.594189	+	0.957367i
$391$		−	2.57258i		−	0.00657948i
$392$	−55.7443	−	5.34533i	−0.142205	−	0.0136360i
$393$	434.971			1.10680
$394$	36.8137	+	22.8484i	0.0934358	+	0.0579909i
$395$	−463.938			−1.17453
$396$	108.379	+	218.822i	0.273684	+	0.552581i
$397$		−	310.938i		−	0.783219i	−0.920131	−	0.391610i	$-0.871918\pi$
$397$		−	310.938i		−	0.783219i	0.920131	−	0.391610i	$-0.128082\pi$
$398$	−309.160	−	191.880i	−0.776785	−	0.482111i
$399$			41.5061i			0.104025i
$400$	−11.2248	+	14.7329i	−0.0280619	+	0.0368323i
$401$	−423.903			−1.05711			−0.528557	−	0.848898i	$-0.677267\pi$
$401$	−423.903			−1.05711			−0.528557	+	0.848898i	$0.677267\pi$
$402$	66.9063	−	107.801i	0.166434	−	0.268160i
$403$	−445.995			−1.10669
$404$	−649.311	+	321.593i	−1.60721	+	0.796022i
$405$			480.974i			1.18759i
$406$	−96.6697	+	155.756i	−0.238103	+	0.383635i
$407$			1164.88i			2.86211i
$408$	6.43703	+	0.617247i	0.0157770	+	0.00151286i
$409$	444.543			1.08690			0.543451	−	0.839441i	$-0.317117\pi$
$409$	444.543			1.08690			0.543451	+	0.839441i	$0.317117\pi$
$410$	−313.895	−	194.818i	−0.765596	−	0.475167i
$411$	−120.258			−0.292598
$412$	140.870	−	69.7703i	0.341917	−	0.169345i
$413$		−	92.3385i		−	0.223580i
$414$	−52.9008	−	32.8329i	−0.127780	−	0.0793064i
$415$		−	349.201i		−	0.841449i
$416$	−390.977	+	149.074i	−0.939849	+	0.358350i
$417$	410.020			0.983261
$418$	103.264	−	166.380i	0.247042	−	0.398038i
$419$	457.129			1.09100			0.545500	−	0.838111i	$-0.316340\pi$
$419$	457.129			1.09100			0.545500	+	0.838111i	$0.316340\pi$
$420$	−78.9258	−	159.355i	−0.187919	−	0.379417i
$421$			25.4812i			0.0605255i	0.999542	+	0.0302628i	$0.00963441\pi$
$421$			25.4812i			0.0605255i	−0.999542	+	0.0302628i	$0.990366\pi$
$422$	22.5916	−	36.4000i	0.0535347	−	0.0862559i
$423$		−	205.610i		−	0.486075i
$424$	−16.5481	+	172.574i	−0.0390286	+	0.407014i
$425$	−0.271910			−0.000639787
$426$	−277.913	−	172.487i	−0.652378	−	0.404898i
$427$	168.273			0.394082
$428$	−68.2606	−	137.821i	−0.159487	−	0.322013i
$429$		−	966.453i		−	2.25280i
$430$	−40.2192	−	24.9620i	−0.0935331	−	0.0580512i
$431$		−	124.595i		−	0.289084i	−0.989499	−	0.144542i	$-0.953829\pi$
$431$		−	124.595i		−	0.289084i	0.989499	−	0.144542i	$-0.0461709\pi$
$432$	−205.469	+	269.687i	−0.475624	+	0.624274i
$433$	−272.271			−0.628802			−0.314401	−	0.949290i	$-0.601804\pi$
$433$	−272.271			−0.628802			−0.314401	+	0.949290i	$0.601804\pi$
$434$	95.1750	−	153.347i	0.219297	−	0.353335i
$435$	−582.126			−1.33822
$436$	99.9293	−	49.4933i	0.229196	−	0.113517i
$437$			49.9285i			0.114253i
$438$	202.923	−	326.952i	0.463294	−	0.746466i
$439$			255.069i			0.581023i	0.956871	+	0.290512i	$0.0938255\pi$
$439$			255.069i			0.581023i	−0.956871	+	0.290512i	$0.906174\pi$
$440$	−80.0823	+	835.146i	−0.182005	+	1.89806i
$441$	−19.8967			−0.0451173
$442$	−5.21929	−	3.23935i	−0.0118084	−	0.00732885i
$443$	131.274			0.296330			0.148165	−	0.988963i	$-0.452663\pi$
$443$	131.274			0.296330			0.148165	+	0.988963i	$0.452663\pi$
$444$	669.017	−	331.353i	1.50680	−	0.746290i
$445$			780.066i			1.75296i
$446$	−332.993	−	206.672i	−0.746622	−	0.463391i
$447$		−	419.601i		−	0.938704i
$448$	32.1779	−	166.243i	0.0718257	−	0.371077i
$449$	−642.824			−1.43168			−0.715839	−	0.698265i	$-0.753956\pi$
$449$	−642.824			−1.43168			−0.715839	+	0.698265i	$0.753956\pi$
$450$	−3.47028	+	5.59137i	−0.00771174	+	0.0124253i
$451$	812.496			1.80154
$452$	−146.360	−	295.509i	−0.323806	−	0.653780i
$453$		−	758.472i		−	1.67433i
$454$	28.7559	−	46.3320i	0.0633390	−	0.102053i
$455$			168.927i			0.371269i
$456$	−124.930	−	11.9795i	−0.273968	−	0.0262709i
$457$	693.088			1.51660			0.758302	−	0.651903i	$-0.226029\pi$
$457$	693.088			1.51660			0.758302	+	0.651903i	$0.226029\pi$
$458$	299.669	+	185.990i	0.654300	+	0.406091i
$459$	−4.97731			−0.0108438
$460$	−94.9415	−	191.691i	−0.206394	−	0.416720i
$461$		−	258.699i		−	0.561170i	−0.959829	−	0.280585i	$-0.909472\pi$
$461$		−	258.699i		−	0.561170i	0.959829	−	0.280585i	$-0.0905285\pi$
$462$	332.297	+	206.240i	0.719258	+	0.446407i
$463$			637.226i			1.37630i	0.725569	+	0.688150i	$0.241577\pi$
$463$			637.226i			1.37630i	−0.725569	+	0.688150i	$0.758423\pi$
$464$	−440.910	−	335.921i	−0.950237	−	0.723969i
$465$	573.125			1.23253
$466$	−75.7644	+	122.073i	−0.162584	+	0.261959i
$467$	−199.483			−0.427159			−0.213580	−	0.976926i	$-0.568512\pi$
$467$	−199.483			−0.427159			−0.213580	+	0.976926i	$0.568512\pi$
$468$	−133.224	+	65.9835i	−0.284666	+	0.140990i
$469$		−	48.7727i		−	0.103993i
$470$	372.524	−	600.216i	0.792603	−	1.27705i
$471$		−	23.2979i		−	0.0494648i
$472$	277.931	+	26.6508i	0.588836	+	0.0564636i
$473$	104.105			0.220095
$474$	−555.620	−	344.845i	−1.17219	−	0.727521i
$475$	5.27721			0.0111099
$476$	2.22758	−	1.10328i	0.00467980	−	0.00231782i
$477$			61.5966i			0.129133i
$478$	120.809	+	74.9797i	0.252737	+	0.156861i
$479$		−	674.160i		−	1.40743i	−0.710481	−	0.703716i	$-0.751523\pi$
$479$		−	674.160i		−	1.40743i	0.710481	−	0.703716i	$-0.248477\pi$
$480$	502.424	−	191.566i	1.04672	−	0.399097i
$481$	−709.204			−1.47444
$482$	−59.1792	+	95.3505i	−0.122778	+	0.197823i
$483$	−99.7182			−0.206456
$484$	−604.115	−	1219.74i	−1.24817	−	2.52012i
$485$			441.799i			0.910926i
$486$	−156.370	+	251.946i	−0.321749	+	0.518407i
$487$		−	401.718i		−	0.824883i	−0.910984	−	0.412442i	$-0.864676\pi$
$487$		−	401.718i		−	0.824883i	0.910984	−	0.412442i	$-0.135324\pi$
$488$	−48.5670	+	506.486i	−0.0995226	+	1.03788i
$489$	713.181			1.45845
$490$	−58.0826	−	36.0489i	−0.118536	−	0.0735692i
$491$	428.880			0.873482			0.436741	−	0.899587i	$-0.356133\pi$
$491$	428.880			0.873482			0.436741	+	0.899587i	$0.356133\pi$
$492$	−231.117	−	466.636i	−0.469749	−	0.948446i
$493$		−	8.13739i		−	0.0165059i
$494$	101.296	+	62.8692i	0.205052	+	0.127266i
$495$			298.088i			0.602198i
$496$	434.093	+	330.727i	0.875187	+	0.666789i
$497$	−125.738			−0.252993
$498$	259.561	−	418.209i	0.521207	−	0.839778i
$499$	182.619			0.365970			0.182985	−	0.983116i	$-0.441424\pi$
$499$	182.619			0.365970			0.182985	+	0.983116i	$0.441424\pi$
$500$	−457.820	+	226.751i	−0.915641	+	0.453501i
$501$			569.632i			1.13699i
$502$	−389.126	+	626.966i	−0.775152	+	1.24894i
$503$		−	380.158i		−	0.755781i	−0.925850	−	0.377891i	$-0.876650\pi$
$503$		−	380.158i		−	0.755781i	0.925850	−	0.377891i	$-0.123350\pi$
$504$	5.74261	−	59.8874i	0.0113941	−	0.118824i
$505$	−884.516			−1.75152
$506$	399.727	+	248.090i	0.789974	+	0.490297i
$507$	6.82188			0.0134554
$508$	90.1160	−	44.6329i	0.177394	−	0.0878600i
$509$		−	289.538i		−	0.568836i	−0.958700	−	0.284418i	$-0.908200\pi$
$509$		−	289.538i		−	0.568836i	0.958700	−	0.284418i	$-0.0918004\pi$
$510$	6.70703	+	4.16272i	0.0131510	+	0.00816219i
$511$		−	147.925i		−	0.289481i
$512$	491.088	+	144.834i	0.959156	+	0.282878i
$513$	96.5995			0.188303
$514$	−25.0410	+	40.3464i	−0.0487179	+	0.0784950i
$515$	191.898			0.372617
$516$	−29.6129	−	59.7899i	−0.0573894	−	0.115872i
$517$			1553.62i			3.00507i
$518$	151.343	−	243.847i	0.292169	−	0.470747i
$519$		−	305.768i		−	0.589148i
$520$	−508.456	−	48.7559i	−0.977799	−	0.0937613i
$521$	−738.899			−1.41823			−0.709116	−	0.705092i	$-0.750906\pi$
$521$	−738.899			−1.41823			−0.709116	+	0.705092i	$0.750906\pi$
$522$	−167.332	−	103.855i	−0.320559	−	0.198955i
$523$	647.126			1.23734			0.618668	−	0.785653i	$-0.287673\pi$
$523$	647.126			1.23734			0.618668	+	0.785653i	$0.287673\pi$
$524$	224.397	+	453.068i	0.428238	+	0.864633i
$525$			10.5397i			0.0200757i
$526$	125.699	+	78.0151i	0.238972	+	0.148318i
$527$			8.01157i			0.0152022i
$528$	−716.672	+	940.660i	−1.35733	+	1.78155i
$529$	409.047			0.773246
$530$	−111.601	+	179.813i	−0.210567	+	0.339269i
$531$	99.2014			0.186820
$532$	−43.2329	+	21.4125i	−0.0812648	+	0.0402491i
$533$			494.666i			0.928078i
$534$	−579.823	+	934.220i	−1.08581	+	1.74948i
$535$		−	187.745i		−	0.350926i
$536$	146.802	+	14.0768i	0.273884	+	0.0262627i
$537$	−276.607			−0.515097
$538$	−570.277	−	353.942i	−1.05999	−	0.657885i
$539$	150.343			0.278930
$540$	−370.876	+	183.689i	−0.686807	+	0.340164i
$541$			178.722i			0.330355i	0.986264	+	0.165178i	$0.0528198\pi$
$541$			178.722i			0.330355i	−0.986264	+	0.165178i	$0.947180\pi$
$542$	−318.240	−	197.515i	−0.587158	−	0.364419i
$543$			951.008i			1.75140i
$544$	2.67786	+	7.02326i	0.00492254	+	0.0129104i
$545$	136.127			0.249775
$546$	−125.564	+	202.310i	−0.229970	+	0.370531i
$547$	452.236			0.826758			0.413379	−	0.910559i	$-0.364349\pi$
$547$	452.236			0.826758			0.413379	+	0.910559i	$0.364349\pi$
$548$	−62.0395	−	125.261i	−0.113211	−	0.228578i
$549$			180.780i			0.329289i
$550$	26.2220	−	42.2493i	0.0476764	−	0.0768169i
$551$			157.930i			0.286625i
$552$	28.7807	−	300.143i	0.0521390	−	0.543737i
$553$	−251.382			−0.454579
$554$	−225.314	−	139.841i	−0.406705	−	0.252421i
$555$	911.360			1.64209
$556$	211.525	+	427.078i	0.380440	+	0.768126i
$557$		−	854.108i		−	1.53341i	−0.642001	−	0.766704i	$-0.721895\pi$
$557$		−	854.108i		−	1.53341i	0.642001	−	0.766704i	$-0.278105\pi$
$558$	164.745	+	102.249i	0.295242	+	0.183241i
$559$			63.3814i			0.113383i
$560$	125.268	−	164.419i	0.223692	−	0.293605i
$561$	−17.3607			−0.0309460
$562$	−349.647	+	563.356i	−0.622147	+	1.00241i
$563$	249.654			0.443436			0.221718	−	0.975111i	$-0.428834\pi$
$563$	249.654			0.443436			0.221718	+	0.975111i	$0.428834\pi$
$564$	892.280	−	441.931i	1.58206	−	0.783566i
$565$		−	402.553i		−	0.712483i
$566$	70.3636	−	113.371i	0.124317	−	0.200302i
$567$			260.613i			0.459634i
$568$	36.2905	−	378.459i	0.0638917	−	0.666301i
$569$	104.353			0.183396			0.0916982	−	0.995787i	$-0.470771\pi$
$569$	104.353			0.183396			0.0916982	+	0.995787i	$0.470771\pi$
$570$	−130.170	−	80.7899i	−0.228368	−	0.141737i
$571$	−649.705			−1.13784			−0.568919	−	0.822394i	$-0.692638\pi$
$571$	−649.705			−1.13784			−0.568919	+	0.822394i	$0.692638\pi$
$572$	1006.66	−	498.582i	1.75990	−	0.871646i
$573$			698.630i			1.21925i
$574$	−170.082	−	105.561i	−0.296310	−	0.183905i
$575$			12.6785i			0.0220495i
$576$	178.598	+	34.5695i	0.310066	+	0.0600165i
$577$	−346.022			−0.599692			−0.299846	−	0.953988i	$-0.596935\pi$
$577$	−346.022			−0.599692			−0.299846	+	0.953988i	$0.596935\pi$
$578$	304.743	−	491.007i	0.527238	−	0.849493i
$579$	−300.537			−0.519061
$580$	−300.312	−	606.344i	−0.517779	−	1.04542i
$581$		−	189.213i		−	0.325667i
$582$	−328.389	+	529.106i	−0.564242	+	0.909116i
$583$		−	465.434i		−	0.798342i
$584$	445.240	+	42.6941i	0.762397	+	0.0731064i
$585$	−181.482			−0.310226
$586$	491.466	+	305.028i	0.838679	+	0.520526i
$587$	−1153.54			−1.96514			−0.982572	−	0.185885i	$-0.940485\pi$
$587$	−1153.54			−1.96514			−0.982572	+	0.185885i	$0.940485\pi$
$588$	−42.7655	−	86.3455i	−0.0727304	−	0.146846i
$589$		−	155.488i		−	0.263987i
$590$	289.589	+	179.733i	0.490828	+	0.304632i
$591$			74.5515i			0.126145i
$592$	690.276	+	525.909i	1.16601	+	0.888360i
$593$	880.135			1.48421			0.742104	−	0.670285i	$-0.233828\pi$
$593$	880.135			1.48421			0.742104	+	0.670285i	$0.233828\pi$
$594$	479.994	−	773.374i	0.808071	−	1.30198i
$595$	3.03450			0.00510000
$596$	437.058	−	216.467i	0.733318	−	0.363200i
$597$		−	626.081i		−	1.04871i
$598$	−151.043	+	243.363i	−0.252580	+	0.406961i
$599$		−	554.939i		−	0.926442i	−0.886243	−	0.463221i	$-0.846694\pi$
$599$		−	554.939i		−	0.926442i	0.886243	−	0.463221i	$-0.153306\pi$
$600$	−31.7237	−	3.04199i	−0.0528728	−	0.00506998i
$601$	−666.057			−1.10825			−0.554124	−	0.832434i	$-0.686946\pi$
$601$	−666.057			−1.10825			−0.554124	+	0.832434i	$0.686946\pi$
$602$	−21.7925	−	13.5255i	−0.0362002	−	0.0224676i
$603$	52.3977			0.0868950
$604$	790.027	−	391.287i	1.30799	−	0.647826i
$605$		−	1661.57i		−	2.74640i
$606$	−1059.31	−	657.461i	−1.74804	−	1.08492i
$607$		−	192.927i		−	0.317836i	−0.987292	−	0.158918i	$-0.949199\pi$
$607$		−	192.927i		−	0.317836i	0.987292	−	0.158918i	$-0.0508006\pi$
$608$	−51.9718	−	136.307i	−0.0854800	−	0.224189i
$609$	−315.421			−0.517933
$610$	−327.536	+	527.732i	−0.536945	+	0.865134i
$611$	−945.878			−1.54808
$612$	1.18528	+	2.39315i	0.00193674	+	0.00391037i
$613$			608.234i			0.992226i	0.868258	+	0.496113i	$0.165240\pi$
$613$			608.234i			0.992226i	−0.868258	+	0.496113i	$0.834760\pi$
$614$	−0.731077	+	1.17792i	−0.00119068	+	0.00191844i
$615$		−	635.668i		−	1.03361i
$616$	−43.3921	+	452.519i	−0.0704417	+	0.734609i
$617$	0.884056			0.00143283			0.000716415	−	1.00000i	$-0.499772\pi$
$617$	0.884056			0.00143283			0.000716415		1.00000i	$0.499772\pi$
$618$	229.820	+	142.638i	0.371877	+	0.230805i
$619$	358.525			0.579200			0.289600	−	0.957148i	$-0.406478\pi$
$619$	358.525			0.579200			0.289600	+	0.957148i	$0.406478\pi$
$620$	295.669	+	596.969i	0.476885	+	0.962853i
$621$			232.080i			0.373719i
$622$	105.626	+	65.5569i	0.169817	+	0.105397i
$623$			422.674i			0.678449i
$624$	−572.694	−	436.326i	−0.917780	−	0.699240i
$625$	−594.720			−0.951552
$626$	−225.272	+	362.962i	−0.359860	+	0.579812i
$627$	336.937			0.537379
$628$	24.2672	−	12.0191i	0.0386421	−	0.0191388i
$629$			12.7397i			0.0202539i
$630$	38.7282	−	62.3995i	0.0614733	−	0.0990468i
$631$		−	390.515i		−	0.618883i	−0.950918	−	0.309442i	$-0.899858\pi$
$631$		−	390.515i		−	0.618883i	0.950918	−	0.309442i	$-0.100142\pi$
$632$	72.5540	−	756.637i	0.114801	−	1.19721i
$633$	73.7137			0.116451
$634$	39.8619	+	24.7403i	0.0628737	+	0.0390225i
$635$	122.759			0.193322
$636$	−267.309	+	132.394i	−0.420298	+	0.208166i
$637$			91.5322i			0.143693i
$638$	1264.39	+	784.742i	1.98180	+	1.23000i
$639$		−	135.083i		−	0.211397i
$640$	458.731	+	424.499i	0.716767	+	0.663280i
$641$	−431.936			−0.673848			−0.336924	−	0.941532i	$-0.609386\pi$
$641$	−431.936			−0.673848			−0.336924	+	0.941532i	$0.609386\pi$
$642$	139.551	−	224.847i	0.217369	−	0.350229i
$643$	49.9370			0.0776625			0.0388313	−	0.999246i	$-0.487637\pi$
$643$	49.9370			0.0776625			0.0388313	+	0.999246i	$0.487637\pi$
$644$	−51.4434	−	103.867i	−0.0798811	−	0.161284i
$645$		−	81.4480i		−	0.126276i
$646$	1.12934	−	1.81961i	0.00174821	−	0.00281674i
$647$		−	224.141i		−	0.346431i	−0.984884	−	0.173216i	$-0.944584\pi$
$647$		−	224.141i		−	0.346431i	0.984884	−	0.173216i	$-0.0554157\pi$
$648$	−784.421	−	75.2182i	−1.21053	−	0.116077i
$649$	−749.582			−1.15498
$650$	25.7223	+	15.9645i	0.0395728	+	0.0245608i
$651$	310.544			0.477027
$652$	367.922	+	742.851i	0.564297	+	1.13934i
$653$			80.7637i			0.123681i	0.998086	+	0.0618405i	$0.0196970\pi$
$653$			80.7637i			0.123681i	−0.998086	+	0.0618405i	$0.980303\pi$
$654$	163.028	+	101.183i	0.249279	+	0.154715i
$655$			617.186i			0.942268i
$656$	366.819	−	481.464i	0.559175	−	0.733939i
$657$	158.919			0.241886
$658$	201.850	−	325.223i	0.306762	−	0.494260i
$659$	−940.466			−1.42711			−0.713555	−	0.700599i	$-0.752916\pi$
$659$	−940.466			−1.42711			−0.713555	+	0.700599i	$0.752916\pi$
$660$	−1293.61	+	640.701i	−1.96001	+	0.970759i
$661$			119.930i			0.181437i	0.995877	+	0.0907184i	$0.0289163\pi$
$661$			119.930i			0.181437i	−0.995877	+	0.0907184i	$0.971084\pi$
$662$	−535.149	+	862.240i	−0.808382	+	1.30248i
$663$		−	10.5696i		−	0.0159421i
$664$	569.513	+	54.6107i	0.857700	+	0.0822450i
$665$	−58.8935			−0.0885616
$666$	261.970	+	162.592i	0.393349	+	0.244132i
$667$	−379.426			−0.568855
$668$	−593.330	+	293.866i	−0.888219	+	0.439920i
$669$		−	674.346i		−	1.00799i
$670$	152.959	+	94.9341i	0.228298	+	0.141693i
$671$		−	1366.00i		−	2.03577i
$672$	272.235	−	103.799i	0.405112	−	0.154463i
$673$	1085.06			1.61227			0.806136	−	0.591731i	$-0.201555\pi$
$673$	1085.06			1.61227			0.806136	+	0.591731i	$0.201555\pi$
$674$	361.465	−	582.398i	0.536298	−	0.864091i
$675$	24.5298			0.0363404
$676$	3.51933	+	7.10569i	0.00520611	+	0.0105114i
$677$			949.901i			1.40310i	0.712618	+	0.701552i	$0.247509\pi$
$677$			949.901i			1.40310i	−0.712618	+	0.701552i	$0.752491\pi$
$678$	299.217	−	482.104i	0.441324	−	0.711068i
$679$			239.386i			0.352557i
$680$	−0.875819	+	9.13357i	−0.00128797	+	0.0134317i
$681$	93.8270			0.137778
$682$	−1244.84	−	772.608i	−1.82528	−	1.13286i
$683$	−893.785			−1.30862			−0.654308	−	0.756228i	$-0.727040\pi$
$683$	−893.785			−1.30862			−0.654308	+	0.756228i	$0.727040\pi$
$684$	−23.0040	−	46.4461i	−0.0336315	−	0.0679037i
$685$		−	170.635i		−	0.249102i
$686$	−31.4717	−	19.5329i	−0.0458771	−	0.0284736i
$687$			606.861i			0.883349i
$688$	47.0004	−	61.6898i	0.0683145	−	0.0896654i
$689$	283.366			0.411272
$690$	194.097	−	312.732i	0.281300	−	0.453235i
$691$	1208.56			1.74901			0.874504	−	0.485019i	$-0.161187\pi$
$691$	1208.56			1.74901			0.874504	+	0.485019i	$0.161187\pi$
$692$	318.489	−	157.742i	0.460244	−	0.227951i
$693$			161.517i			0.233069i
$694$	−144.222	+	232.373i	−0.207813	+	0.334831i
$695$			581.782i			0.837096i
$696$	91.0371	−	949.389i	0.130800	−	1.36407i
$697$	8.88585			0.0127487
$698$	139.439	+	86.5430i	0.199770	+	0.123987i
$699$	−247.210			−0.353662
$700$	−10.9782	+	5.43733i	−0.0156832	+	0.00776762i
$701$			219.477i			0.313091i	0.987671	+	0.156546i	$0.0500358\pi$
$701$			219.477i			0.313091i	−0.987671	+	0.156546i	$0.949964\pi$
$702$	470.847	+	292.231i	0.670723	+	0.416284i
$703$		−	247.251i		−	0.351709i
$704$	−1349.52	−	261.213i	−1.91693	−	0.371041i
$705$	1215.50			1.72411
$706$	−535.108	+	862.175i	−0.757944	+	1.22121i
$707$	−479.270			−0.677892
$708$	213.221	+	430.502i	0.301159	+	0.608054i
$709$			1265.13i			1.78439i	0.451651	+	0.892195i	$0.350835\pi$
$709$			1265.13i			1.78439i	−0.451651	+	0.892195i	$0.649165\pi$
$710$	244.743	−	394.334i	0.344709	−	0.555400i
$711$		−	270.066i		−	0.379839i
$712$	−1272.21	−	121.992i	−1.78681	−	0.171338i
$713$	373.560			0.523927
$714$	3.63417	+	2.25554i	0.00508987	+	0.00315902i
$715$	1371.31			1.91792
$716$	−142.698	−	288.115i	−0.199299	−	0.402395i
$717$			244.650i			0.341213i
$718$	−952.989	−	591.472i	−1.32728	−	0.823777i
$719$			1163.47i			1.61818i	0.587687	+	0.809089i	$0.300039\pi$
$719$			1163.47i			1.61818i	−0.587687	+	0.809089i	$0.699961\pi$
$720$	176.639	+	134.578i	0.245332	+	0.186914i
$721$	103.979			0.144215
$722$	358.820	−	578.136i	0.496981	−	0.800743i
$723$	−193.094			−0.267074
$724$	−990.573	+	490.614i	−1.36819	+	0.677643i
$725$			40.1036i			0.0553153i
$726$	1235.05	−	1989.93i	1.70117	−	2.74094i
$727$			1303.68i			1.79324i	0.442803	+	0.896619i	$0.353984\pi$
$727$			1303.68i			1.79324i	−0.442803	+	0.896619i	$0.646016\pi$
$728$	−275.504	−	26.4181i	−0.378439	−	0.0362886i
$729$	376.305			0.516193
$730$	463.916	+	287.929i	0.635502	+	0.394424i
$731$	1.13854			0.00155751
$732$	−784.526	+	388.562i	−1.07176	+	0.530823i
$733$		−	1256.12i		−	1.71367i	−0.515589	−	0.856836i	$-0.672427\pi$
$733$		−	1256.12i		−	1.71367i	0.515589	−	0.856836i	$-0.327573\pi$
$734$	−45.7847	−	28.4163i	−0.0623770	−	0.0387143i
$735$		−	117.623i		−	0.160031i
$736$	327.477	−	124.862i	0.444942	−	0.169649i
$737$	−395.925			−0.537212
$738$	113.407	−	182.723i	0.153668	−	0.247592i
$739$	687.168			0.929862			0.464931	−	0.885347i	$-0.346079\pi$
$739$	687.168			0.929862			0.464931	+	0.885347i	$0.346079\pi$
$740$	470.160	+	949.276i	0.635352	+	1.28281i
$741$			205.134i			0.276835i
$742$	−60.4701	+	97.4304i	−0.0814961	+	0.131308i
$743$		−	362.628i		−	0.488059i	−0.969768	−	0.244030i	$-0.921531\pi$
$743$		−	362.628i		−	0.488059i	0.969768	−	0.244030i	$-0.0784694\pi$
$744$	−89.6295	+	934.710i	−0.120470	+	1.25633i
$745$	595.376			0.799163
$746$	914.287	+	567.452i	1.22559	+	0.760659i
$747$	203.275			0.272122
$748$	−8.95620	−	18.0830i	−0.0119735	−	0.0241751i
$749$		−	101.729i		−	0.135819i
$750$	−746.905	−	463.566i	−0.995874	−	0.618088i
$751$			261.366i			0.348024i	0.984744	+	0.174012i	$0.0556732\pi$
$751$			261.366i			0.348024i	−0.984744	+	0.174012i	$0.944327\pi$
$752$	920.634	+	701.415i	1.22425	+	0.932733i
$753$	−1269.67			−1.68615
$754$	−477.768	+	769.787i	−0.633645	+	1.02094i
$755$	1076.20			1.42544
$756$	−200.957	+	99.5305i	−0.265816	+	0.131654i
$757$		−	1395.34i		−	1.84325i	−0.388081	−	0.921625i	$-0.626862\pi$
$757$		−	1395.34i		−	1.84325i	0.388081	−	0.921625i	$-0.373138\pi$
$758$	192.091	−	309.500i	0.253418	−	0.408311i
$759$			809.488i			1.06652i
$760$	16.9979	−	177.264i	0.0223656	−	0.233242i
$761$	−319.500			−0.419843			−0.209921	−	0.977718i	$-0.567321\pi$
$761$	−319.500			−0.419843			−0.209921	+	0.977718i	$0.567321\pi$
$762$	147.019	+	91.2470i	0.192938	+	0.119747i
$763$	73.7598			0.0966708
$764$	−727.695	+	360.415i	−0.952481	+	0.471747i
$765$			3.26003i			0.00426148i
$766$	566.331	+	351.493i	0.739336	+	0.458868i
$767$		−	456.362i		−	0.594996i
$768$	233.853	+	849.362i	0.304496	+	1.10594i
$769$	634.936			0.825664			0.412832	−	0.910807i	$-0.364540\pi$
$769$	634.936			0.825664			0.412832	+	0.910807i	$0.364540\pi$
$770$	−292.636	+	471.500i	−0.380047	+	0.612338i
$771$	−81.7056			−0.105974
$772$	−155.043	−	313.040i	−0.200833	−	0.405492i
$773$			96.1663i			0.124407i	0.998063	+	0.0622033i	$0.0198127\pi$
$773$			96.1663i			0.124407i	−0.998063	+	0.0622033i	$0.980187\pi$
$774$	14.5308	−	23.4122i	0.0187736	−	0.0302484i
$775$		−	39.4836i		−	0.0509465i
$776$	−720.530	−	69.0917i	−0.928518	−	0.0890358i
$777$	493.815			0.635540
$778$	−186.310	−	115.633i	−0.239473	−	0.148629i
$779$	−172.456			−0.221382
$780$	−390.073	−	787.576i	−0.500093	−	1.00971i
$781$			1020.71i			1.30693i
$782$	4.37161	+	2.71324i	0.00559029	+	0.00346961i
$783$			734.098i			0.937545i
$784$	67.8756	−	89.0893i	0.0865760	−	0.113634i
$785$	33.0577			0.0421117
$786$	−458.754	+	739.151i	−0.583656	+	0.940396i
$787$	−1319.25			−1.67630			−0.838148	−	0.545442i	$-0.816362\pi$
$787$	−1319.25			−1.67630			−0.838148	+	0.545442i	$0.816362\pi$
$788$	−77.6531	+	38.4603i	−0.0985445	+	0.0488074i
$789$			254.554i			0.322628i
$790$	489.305	−	788.375i	0.619373	−	0.997943i
$791$		−	218.121i		−	0.275753i
$792$	−486.152	−	46.6171i	−0.613828	−	0.0588600i
$793$	831.651			1.04874
$794$	528.380	+	327.939i	0.665466	+	0.413021i
$795$	−364.139			−0.458036
$796$	652.128	−	322.988i	0.819257	−	0.405764i
$797$		−	818.575i		−	1.02707i	−0.858068	−	0.513535i	$-0.828336\pi$
$797$		−	818.575i		−	1.02707i	0.858068	−	0.513535i	$-0.171664\pi$
$798$	−70.5318	−	43.7755i	−0.0883857	−	0.0548565i
$799$			16.9911i			0.0212655i
$800$	−13.1973	−	34.6128i	−0.0164967	−	0.0432660i
$801$	−454.088			−0.566902
$802$	447.081	−	720.343i	0.557457	−	0.898183i
$803$	−1200.82			−1.49541
$804$	112.622	+	227.389i	0.140077	+	0.282823i
$805$		−	141.491i		−	0.175765i
$806$	470.381	−	757.885i	0.583599	−	0.940304i
$807$		−	1154.87i		−	1.43106i
$808$	138.327	−	1442.56i	0.171197	−	1.78534i
$809$	1232.72			1.52376			0.761881	−	0.647717i	$-0.224276\pi$
$809$	1232.72			1.52376			0.761881	+	0.647717i	$0.224276\pi$
$810$	−817.324	−	507.272i	−1.00904	−	0.626261i
$811$	−1009.05			−1.24421			−0.622103	−	0.782935i	$-0.713722\pi$
$811$	−1009.05			−1.24421			−0.622103	+	0.782935i	$0.713722\pi$
$812$	−162.722	−	328.544i	−0.200397	−	0.404611i
$813$		−	644.468i		−	0.792703i
$814$	−1979.49	−	1228.57i	−2.43181	−	1.50930i
$815$			1011.94i			1.24164i
$816$	−7.83787	+	10.2875i	−0.00960524	+	0.0126072i
$817$	−22.0968			−0.0270462
$818$	−468.849	+	755.417i	−0.573165	+	0.923493i
$819$	−98.3351			−0.120067
$820$	662.114	−	327.934i	0.807457	−	0.399919i
$821$		−	939.093i		−	1.14384i	−0.820309	−	0.571920i	$-0.806199\pi$
$821$		−	939.093i		−	1.14384i	0.820309	−	0.571920i	$-0.193801\pi$
$822$	126.833	−	204.355i	0.154298	−	0.248607i
$823$		−	911.100i		−	1.10705i	−0.832833	−	0.553524i	$-0.813283\pi$
$823$		−	911.100i		−	1.10705i	0.832833	−	0.553524i	$-0.186717\pi$
$824$	−30.0104	+	312.966i	−0.0364204	+	0.379814i
$825$	85.5591			0.103708
$826$	156.912	+	97.3872i	0.189966	+	0.117902i
$827$	−65.6564			−0.0793910			−0.0396955	−	0.999212i	$-0.512639\pi$
$827$	−65.6564			−0.0793910			−0.0396955	+	0.999212i	$0.512639\pi$
$828$	111.586	−	55.2669i	0.134766	−	0.0667474i
$829$			1515.94i			1.82864i	0.404997	+	0.914318i	$0.367272\pi$
$829$			1515.94i			1.82864i	−0.404997	+	0.914318i	$0.632728\pi$
$830$	593.402	+	368.294i	0.714942	+	0.443728i
$831$		−	456.285i		−	0.549079i
$832$	159.032	−	821.616i	0.191144	−	0.987519i
$833$	1.64422			0.00197386
$834$	−432.438	+	696.752i	−0.518511	+	0.835433i
$835$	−808.257			−0.967972
$836$	173.822	+	350.954i	0.207921	+	0.419802i
$837$		−	722.747i		−	0.863497i
$838$	−482.123	+	776.804i	−0.575326	+	0.926974i
$839$			869.972i			1.03692i	0.855103	+	0.518458i	$0.173494\pi$
$839$			869.972i			1.03692i	−0.855103	+	0.518458i	$0.826506\pi$
$840$	354.035	+	33.9485i	0.421470	+	0.0404148i
$841$	−359.174			−0.427080
$842$	−43.3006	−	26.8745i	−0.0514258	−	0.0319174i
$843$	−1140.85			−1.35333
$844$	38.0280	+	76.7804i	0.0450569	+	0.0909721i
$845$			9.67964i			0.0114552i
$846$	349.395	+	216.852i	0.412996	+	0.256326i
$847$		−	900.313i		−	1.06294i
$848$	−275.804	−	210.130i	−0.325240	−	0.247795i
$849$	229.588			0.270421
$850$	0.286777	−	0.462059i	0.000337384	−	0.000543599i
$851$	594.020			0.698026
$852$	586.217	−	290.343i	0.688048	−	0.340778i
$853$		−	1643.91i		−	1.92721i	−0.267322	−	0.963607i	$-0.586139\pi$
$853$		−	1643.91i		−	1.92721i	0.267322	−	0.963607i	$-0.413861\pi$
$854$	−177.474	+	285.948i	−0.207814	+	0.334834i
$855$		−	63.2706i		−	0.0740007i
$856$	306.194	+	29.3610i	0.357703	+	0.0343002i
$857$	286.059			0.333791			0.166895	−	0.985975i	$-0.446626\pi$
$857$	286.059			0.333791			0.166895	+	0.985975i	$0.446626\pi$
$858$	1642.30	+	1019.29i	1.91411	+	1.18799i
$859$	719.782			0.837930			0.418965	−	0.908002i	$-0.362393\pi$
$859$	719.782			0.837930			0.418965	+	0.908002i	$0.362393\pi$
$860$	84.8365	−	42.0181i	0.0986471	−	0.0488582i
$861$		−	344.433i		−	0.400038i
$862$	211.726	+	131.408i	0.245622	+	0.152445i
$863$			1120.47i			1.29835i	0.760641	+	0.649173i	$0.224885\pi$
$863$			1120.47i			1.29835i	−0.760641	+	0.649173i	$0.775115\pi$
$864$	−241.578	−	633.589i	−0.279604	−	0.733320i
$865$	433.857			0.501569
$866$	287.158	−	462.674i	0.331592	−	0.534265i
$867$	994.339			1.14687
$868$	160.206	+	323.464i	0.184569	+	0.372654i
$869$			2040.66i			2.34828i
$870$	613.954	−	989.213i	0.705695	−	1.13703i
$871$		−	241.048i		−	0.276749i
$872$	−21.2886	+	222.010i	−0.0244135	+	0.254599i
$873$	−257.178			−0.294591
$874$	−84.8441	−	52.6584i	−0.0970756	−	0.0602499i
$875$	−337.926			−0.386201
$876$	341.576	+	689.658i	0.389927	+	0.787281i
$877$			145.400i			0.165792i	0.996558	+	0.0828960i	$0.0264169\pi$
$877$			145.400i			0.165792i	−0.996558	+	0.0828960i	$0.973583\pi$
$878$	−433.442	−	269.016i	−0.493670	−	0.306396i
$879$			995.269i			1.13227i
$880$	−1334.71	−	1016.89i	−1.51672	−	1.15556i
$881$	476.080			0.540386			0.270193	−	0.962806i	$-0.412913\pi$
$881$	476.080			0.540386			0.270193	+	0.962806i	$0.412913\pi$
$882$	20.9846	−	33.8108i	0.0237921	−	0.0383342i
$883$	−1101.22			−1.24714			−0.623568	−	0.781769i	$-0.714318\pi$
$883$	−1101.22			−1.24714			−0.623568	+	0.781769i	$0.714318\pi$
$884$	11.0093	−	5.45273i	0.0124540	−	0.00616825i
$885$			586.447i			0.662652i
$886$	−138.452	+	223.075i	−0.156266	+	0.251778i
$887$		−	1491.49i		−	1.68150i	−0.541427	−	0.840748i	$-0.682116\pi$
$887$		−	1491.49i		−	1.68150i	0.541427	−	0.840748i	$-0.317884\pi$
$888$	−142.525	+	1486.34i	−0.160501	+	1.67380i
$889$	66.5164			0.0748216
$890$	−1325.57	−	822.717i	−1.48941	−	0.924401i
$891$	2115.59			2.37440
$892$	702.401	−	347.887i	0.787445	−	0.390008i
$893$		−	329.764i		−	0.369276i
$894$	713.032	+	442.543i	0.797575	+	0.495015i
$895$		−	392.481i		−	0.438526i
$896$	248.560	+	230.012i	0.277411	+	0.256710i
$897$	−492.834			−0.549425
$898$	677.971	−	1092.36i	0.754979	−	1.21643i
$899$	1181.62			1.31437
$900$	−5.84145	−	11.7942i	−0.00649050	−	0.0131046i
$901$		−	5.09021i		−	0.00564951i
$902$	−856.920	+	1380.68i	−0.950023	+	1.53069i
$903$		−	44.1321i		−	0.0488728i
$904$	656.524	+	62.9541i	0.726243	+	0.0696395i
$905$	−1349.40			−1.49104
$906$	1288.88	+	799.942i	1.42260	+	0.882938i
$907$	1155.46			1.27394			0.636969	−	0.770889i	$-0.280188\pi$
$907$	1155.46			1.27394			0.636969	+	0.770889i	$0.280188\pi$
$908$	48.4043	+	97.7305i	0.0533087	+	0.107633i
$909$		−	514.891i		−	0.566436i
$910$	−287.060	−	178.164i	−0.315450	−	0.195784i
$911$		−	944.690i		−	1.03698i	−0.855083	−	0.518491i	$-0.826494\pi$
$911$		−	944.690i		−	1.03698i	0.855083	−	0.518491i	$-0.173506\pi$
$912$	152.117	−	199.660i	0.166795	−	0.218925i
$913$	−1535.98			−1.68235
$914$	−730.984	+	1177.77i	−0.799764	+	1.28859i
$915$	−1068.71			−1.16799
$916$	−632.108	+	313.072i	−0.690074	+	0.341782i
$917$			334.418i			0.364687i
$918$	5.24945	−	8.45800i	0.00571836	−	0.00921351i
$919$			149.150i			0.162296i	0.996702	+	0.0811478i	$0.0258586\pi$
$919$			149.150i			0.162296i	−0.996702	+	0.0811478i	$0.974141\pi$
$920$	425.876	+	40.8373i	0.462908	+	0.0443883i
$921$	−2.38541			−0.00259003
$922$	439.611	+	272.844i	0.476801	+	0.295926i
$923$	−621.430			−0.673272
$924$	−700.932	+	347.160i	−0.758585	+	0.375714i
$925$		−	62.7851i		−	0.0678758i
$926$	−1082.85	−	672.068i	−1.16938	−	0.725775i
$927$			111.707i			0.120503i
$928$	1035.85	−	394.954i	1.11622	−	0.425597i
$929$	−58.8399			−0.0633368			−0.0316684	−	0.999498i	$-0.510082\pi$
$929$	−58.8399			−0.0633368			−0.0316684	+	0.999498i	$0.510082\pi$
$930$	−604.462	+	973.918i	−0.649959	+	1.04722i
$931$	−31.9111			−0.0342761
$932$	−127.533	−	257.494i	−0.136838	−	0.276282i
$933$			213.904i			0.229265i
$934$	210.390	−	338.984i	0.225257	−	0.362938i
$935$		−	24.6333i		−	0.0263458i
$936$	28.3815	−	295.980i	0.0303222	−	0.316218i
$937$	−1700.18			−1.81449			−0.907246	−	0.420601i	$-0.861819\pi$
$937$	−1700.18			−1.81449			−0.907246	+	0.420601i	$0.861819\pi$
$938$	82.8801	+	51.4395i	0.0883583	+	0.0548395i
$939$	−735.036			−0.782786
$940$	627.061	+	1266.07i	0.667086	+	1.34688i
$941$		−	56.6116i		−	0.0601611i	−0.999547	−	0.0300805i	$-0.990424\pi$
$941$		−	56.6116i		−	0.0601611i	0.999547	−	0.0300805i	$-0.00957637\pi$
$942$	39.5904	+	24.5718i	0.0420281	+	0.0260847i
$943$		−	414.325i		−	0.439369i
$944$	−338.415	+	444.182i	−0.358490	+	0.470532i
$945$	−273.751			−0.289684
$946$	−109.797	+	176.907i	−0.116064	+	0.187005i
$947$	242.533			0.256107			0.128053	−	0.991767i	$-0.459127\pi$
$947$	242.533			0.256107			0.128053	+	0.991767i	$0.459127\pi$
$948$	1172.00	−	580.471i	1.23629	−	0.612311i
$949$		−	731.084i		−	0.770373i
$950$	−5.56575	+	8.96763i	−0.00585869	+	0.00943961i
$951$			80.7244i			0.0848837i
$952$	−0.474557	+	4.94897i	−0.000498484	+	0.00519849i
$953$	−364.070			−0.382025			−0.191013	−	0.981588i	$-0.561177\pi$
$953$	−364.070			−0.382025			−0.191013	+	0.981588i	$0.561177\pi$
$954$	−104.672	−	64.9644i	−0.109719	−	0.0680969i
$955$	−991.294			−1.03800
$956$	−254.828	+	126.212i	−0.266556	+	0.132021i
$957$			2560.51i			2.67556i
$958$	1145.61	+	711.021i	1.19583	+	0.742193i
$959$		−	92.4575i		−	0.0964103i
$960$	−204.364	+	1055.81i	−0.212879	+	1.09981i
$961$	−202.348			−0.210560
$962$	747.981	−	1205.16i	0.777527	−	1.25276i
$963$	109.290			0.113489
$964$	−99.6152	−	201.128i	−0.103335	−	0.208639i
$965$		−	426.435i		−	0.441901i
$966$	105.170	−	169.452i	0.108872	−	0.175416i
$967$			1221.99i			1.26369i	0.775093	+	0.631847i	$0.217703\pi$
$967$			1221.99i			1.26369i	−0.775093	+	0.631847i	$0.782297\pi$
$968$	2709.86	+	259.849i	2.79944	+	0.268439i
$969$	3.68490			0.00380279
$970$	−750.754	−	465.955i	−0.773973	−	0.480366i
$971$	−1088.53			−1.12104			−0.560521	−	0.828140i	$-0.689399\pi$
$971$	−1088.53			−1.12104			−0.560521	+	0.828140i	$0.689399\pi$
$972$	−263.215	−	531.443i	−0.270797	−	0.546752i
$973$			315.235i			0.323982i
$974$	682.644	+	423.683i	0.700866	+	0.434992i
$975$			52.0903i			0.0534259i
$976$	−809.455	−	616.710i	−0.829360	−	0.631875i
$977$	−1061.51			−1.08650			−0.543252	−	0.839570i	$-0.682807\pi$
$977$	−1061.51			−1.08650			−0.543252	+	0.839570i	$0.682807\pi$
$978$	−752.175	+	1211.92i	−0.769095	+	1.23918i
$979$	3431.17			3.50477
$980$	122.517	−	60.6804i	0.125017	−	0.0619188i
$981$			79.2419i			0.0807766i
$982$	−452.329	+	728.800i	−0.460621	+	0.742159i
$983$			1322.61i			1.34549i	0.739877	+	0.672743i	$0.234884\pi$
$983$			1322.61i			1.34549i	−0.739877	+	0.672743i	$0.765116\pi$
$984$	1036.71	+	99.4105i	1.05357	+	0.101027i
$985$	−105.782			−0.107393
$986$	13.8280	+	8.58232i	0.0140243	+	0.00870417i
$987$	658.610			0.667285
$988$	−213.669	+	105.826i	−0.216264	+	0.107112i
$989$		−	53.0874i		−	0.0536778i
$990$	−506.544	−	314.386i	−0.511660	−	0.317562i
$991$		−	675.806i		−	0.681944i	−0.940073	−	0.340972i	$-0.889244\pi$
$991$		−	675.806i		−	0.681944i	0.940073	−	0.340972i	$-0.110756\pi$
$992$	−1019.84	+	388.848i	−1.02806	+	0.391984i
$993$	−1746.12			−1.75843
$994$	132.613	−	213.667i	0.133413	−	0.214957i
$995$	888.354			0.892818
$996$	436.914	+	882.151i	0.438669	+	0.885694i
$997$		−	409.220i		−	0.410452i	−0.978715	−	0.205226i	$-0.934207\pi$
$997$		−	409.220i		−	0.410452i	0.978715	−	0.205226i	$-0.0657929\pi$
$998$	−192.604	+	310.327i	−0.192990	+	0.310949i
$999$		−	1149.28i		−	1.15043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.g.b.43.4	yes	8
3.2	odd	2		504.3.g.b.379.5		8
4.3	odd	2		224.3.g.b.15.5		8
7.2	even	3		392.3.k.o.67.8		16
7.3	odd	6		392.3.k.n.275.3		16
7.4	even	3		392.3.k.o.275.3		16
7.5	odd	6		392.3.k.n.67.8		16
7.6	odd	2		392.3.g.m.99.4		8
8.3	odd	2	inner	56.3.g.b.43.3	✓	8
8.5	even	2		224.3.g.b.15.6		8
12.11	even	2		2016.3.g.b.1135.6		8
16.3	odd	4		1792.3.d.j.1023.11		16
16.5	even	4		1792.3.d.j.1023.12		16
16.11	odd	4		1792.3.d.j.1023.6		16
16.13	even	4		1792.3.d.j.1023.5		16
24.5	odd	2		2016.3.g.b.1135.3		8
24.11	even	2		504.3.g.b.379.6		8
28.27	even	2		1568.3.g.m.687.4		8
56.3	even	6		392.3.k.n.275.8		16
56.11	odd	6		392.3.k.o.275.8		16
56.13	odd	2		1568.3.g.m.687.3		8
56.19	even	6		392.3.k.n.67.3		16
56.27	even	2		392.3.g.m.99.3		8
56.51	odd	6		392.3.k.o.67.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.3	✓	8	8.3	odd	2	inner
56.3.g.b.43.4	yes	8	1.1	even	1	trivial
224.3.g.b.15.5		8	4.3	odd	2
224.3.g.b.15.6		8	8.5	even	2
392.3.g.m.99.3		8	56.27	even	2
392.3.g.m.99.4		8	7.6	odd	2
392.3.k.n.67.3		16	56.19	even	6
392.3.k.n.67.8		16	7.5	odd	6
392.3.k.n.275.3		16	7.3	odd	6
392.3.k.n.275.8		16	56.3	even	6
392.3.k.o.67.3		16	56.51	odd	6
392.3.k.o.67.8		16	7.2	even	3
392.3.k.o.275.3		16	7.4	even	3
392.3.k.o.275.8		16	56.11	odd	6
504.3.g.b.379.5		8	3.2	odd	2
504.3.g.b.379.6		8	24.11	even	2
1568.3.g.m.687.3		8	56.13	odd	2
1568.3.g.m.687.4		8	28.27	even	2
1792.3.d.j.1023.5		16	16.13	even	4
1792.3.d.j.1023.6		16	16.11	odd	4
1792.3.d.j.1023.11		16	16.3	odd	4
1792.3.d.j.1023.12		16	16.5	even	4
2016.3.g.b.1135.3		8	24.5	odd	2
2016.3.g.b.1135.6		8	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05468 + 1.69931i) q^{2} -3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} -4.88287i q^{5} +(3.62943 - 5.84780i) q^{6} -2.64575i q^{7} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +O(q^{10})\)	\(q+(-1.05468 + 1.69931i) q^{2} -3.44128 q^{3} +(-1.77532 - 3.58445i) q^{4} -4.88287i q^{5} +(3.62943 - 5.84780i) q^{6} -2.64575i q^{7} +(7.96347 + 0.763618i) q^{8} +2.84239 q^{9} +(8.29751 + 5.14984i) q^{10} -21.4776 q^{11} +(6.10935 + 12.3351i) q^{12} -13.0760i q^{13} +(4.49595 + 2.79041i) q^{14} +16.8033i q^{15} +(-9.69651 + 12.7270i) q^{16} -0.234889 q^{17} +(-2.99780 + 4.83011i) q^{18} +4.55872 q^{19} +(-17.5024 + 8.66863i) q^{20} +9.10476i q^{21} +(22.6519 - 36.4971i) q^{22} +10.9523i q^{23} +(-27.4045 - 2.62782i) q^{24} +1.15761 q^{25} +(22.2202 + 13.7910i) q^{26} +21.1900 q^{27} +(-9.48355 + 4.69704i) q^{28} +34.6435i q^{29} +(-28.5540 - 17.7220i) q^{30} -34.1079i q^{31} +(-11.4005 - 29.9003i) q^{32} +73.9103 q^{33} +(0.247732 - 0.399150i) q^{34} -12.9189 q^{35} +(-5.04614 - 10.1884i) q^{36} -54.2370i q^{37} +(-4.80798 + 7.74669i) q^{38} +44.9982i q^{39} +(3.72865 - 38.8846i) q^{40} -37.8300 q^{41} +(-15.4718 - 9.60258i) q^{42} -4.84714 q^{43} +(38.1295 + 76.9852i) q^{44} -13.8790i q^{45} +(-18.6114 - 11.5511i) q^{46} -72.3368i q^{47} +(33.3684 - 43.7973i) q^{48} -7.00000 q^{49} +(-1.22090 + 1.96714i) q^{50} +0.808319 q^{51} +(-46.8703 + 23.2141i) q^{52} +21.6707i q^{53} +(-22.3486 + 36.0085i) q^{54} +104.872i q^{55} +(2.02034 - 21.0694i) q^{56} -15.6878 q^{57} +(-58.8701 - 36.5377i) q^{58} +34.9007 q^{59} +(60.2305 - 29.8312i) q^{60} +63.6012i q^{61} +(57.9599 + 35.9728i) q^{62} -7.52026i q^{63} +(62.8338 + 12.1621i) q^{64} -63.8485 q^{65} +(-77.9514 + 125.597i) q^{66} +18.4344 q^{67} +(0.417002 + 0.841948i) q^{68} -37.6899i q^{69} +(13.6252 - 21.9531i) q^{70} -47.5244i q^{71} +(22.6353 + 2.17050i) q^{72} +55.9103 q^{73} +(92.1655 + 57.2024i) q^{74} -3.98365 q^{75} +(-8.09317 - 16.3405i) q^{76} +56.8243i q^{77} +(-76.4660 - 47.4586i) q^{78} -95.0135i q^{79} +(62.1445 + 47.3468i) q^{80} -98.5023 q^{81} +(39.8984 - 64.2849i) q^{82} +71.5156 q^{83} +(32.6355 - 16.1638i) q^{84} +1.14693i q^{85} +(5.11217 - 8.23680i) q^{86} -119.218i q^{87} +(-171.036 - 16.4007i) q^{88} -159.756 q^{89} +(23.5848 + 14.6379i) q^{90} -34.5959 q^{91} +(39.2579 - 19.4438i) q^{92} +117.375i q^{93} +(122.923 + 76.2920i) q^{94} -22.2596i q^{95} +(39.2324 + 102.895i) q^{96} -90.4794 q^{97} +(7.38273 - 11.8952i) q^{98} -61.0477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) \) 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9	\( 8 q + q^{2} - 8 q^{3} + 5 q^{4} - 22 q^{6} + 13 q^{8} + 48 q^{9} + 16 q^{10} - 32 q^{11} + 30 q^{12} + 7 q^{14} - 71 q^{16} - 80 q^{17} - 29 q^{18} + 56 q^{19} - 108 q^{20} + 66 q^{22} + 22 q^{24} - 16 q^{25} + 24 q^{26} - 32 q^{27} + 7 q^{28} + 96 q^{30} - 19 q^{32} + 32 q^{33} + 74 q^{34} + 56 q^{35} - 33 q^{36} - 14 q^{38} + 84 q^{40} + 128 q^{41} - 98 q^{42} + 50 q^{44} - 152 q^{46} + 134 q^{48} - 56 q^{49} + 33 q^{50} - 368 q^{51} + 132 q^{52} - 228 q^{54} - 49 q^{56} + 56 q^{57} + 24 q^{58} + 104 q^{59} + 192 q^{60} + 120 q^{62} - 55 q^{64} - 72 q^{65} - 276 q^{66} + 304 q^{67} - 190 q^{68} + 56 q^{70} - 209 q^{72} - 112 q^{73} + 8 q^{74} + 72 q^{75} + 70 q^{76} - 304 q^{78} + 124 q^{80} + 48 q^{81} + 450 q^{82} + 72 q^{83} + 42 q^{84} + 210 q^{86} - 486 q^{88} - 512 q^{89} - 184 q^{90} - 56 q^{91} - 472 q^{92} + 472 q^{94} + 558 q^{96} + 64 q^{97} - 7 q^{98} + 256 q^{99}+O(q^{100}) \) 8 * q + q^2 - 8 * q^3 + 5 * q^4 - 22 * q^6 + 13 * q^8 + 48 * q^9 + 16 * q^10 - 32 * q^11 + 30 * q^12 + 7 * q^14 - 71 * q^16 - 80 * q^17 - 29 * q^18 + 56 * q^19 - 108 * q^20 + 66 * q^22 + 22 * q^24 - 16 * q^25 + 24 * q^26 - 32 * q^27 + 7 * q^28 + 96 * q^30 - 19 * q^32 + 32 * q^33 + 74 * q^34 + 56 * q^35 - 33 * q^36 - 14 * q^38 + 84 * q^40 + 128 * q^41 - 98 * q^42 + 50 * q^44 - 152 * q^46 + 134 * q^48 - 56 * q^49 + 33 * q^50 - 368 * q^51 + 132 * q^52 - 228 * q^54 - 49 * q^56 + 56 * q^57 + 24 * q^58 + 104 * q^59 + 192 * q^60 + 120 * q^62 - 55 * q^64 - 72 * q^65 - 276 * q^66 + 304 * q^67 - 190 * q^68 + 56 * q^70 - 209 * q^72 - 112 * q^73 + 8 * q^74 + 72 * q^75 + 70 * q^76 - 304 * q^78 + 124 * q^80 + 48 * q^81 + 450 * q^82 + 72 * q^83 + 42 * q^84 + 210 * q^86 - 486 * q^88 - 512 * q^89 - 184 * q^90 - 56 * q^91 - 472 * q^92 + 472 * q^94 + 558 * q^96 + 64 * q^97 - 7 * q^98 + 256 * q^99

Introduction

L-functions

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