LMFDB - Embedded newform 21.3.f.c.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,3,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, 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:	$0.572208555157$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.3.f.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} -3.46410i q^{6} +(-3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.00000 - 3.46410i) q^{10} +(-5.00000 + 8.66025i) q^{11} +12.1244i q^{13} +(7.00000 - 12.1244i) q^{14} +6.00000 q^{15} +(8.00000 + 13.8564i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(28.5000 - 16.4545i) q^{19} +12.1244i q^{21} -20.0000 q^{22} +(-20.0000 - 34.6410i) q^{23} +(-12.0000 - 6.92820i) q^{24} +(-6.50000 + 11.2583i) q^{25} +(-21.0000 + 12.1244i) q^{26} -5.19615i q^{27} +16.0000 q^{29} +(6.00000 + 10.3923i) q^{30} +(4.50000 + 2.59808i) q^{31} +(15.0000 - 8.66025i) q^{33} -13.8564i q^{34} +(21.0000 + 12.1244i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(57.0000 + 32.9090i) q^{38} +(10.5000 - 18.1865i) q^{39} +(-24.0000 + 13.8564i) q^{40} +24.2487i q^{41} +(-21.0000 + 12.1244i) q^{42} -19.0000 q^{43} +(-9.00000 - 5.19615i) q^{45} +(40.0000 - 69.2820i) q^{46} +(-45.0000 + 25.9808i) q^{47} -27.7128i q^{48} +(-24.5000 + 42.4352i) q^{49} -26.0000 q^{50} +(6.00000 + 10.3923i) q^{51} +(16.0000 - 27.7128i) q^{53} +(9.00000 - 5.19615i) q^{54} -34.6410i q^{55} +(-28.0000 - 48.4974i) q^{56} -57.0000 q^{57} +(16.0000 + 27.7128i) q^{58} +(36.0000 + 20.7846i) q^{59} +(18.0000 - 10.3923i) q^{61} +10.3923i q^{62} +(10.5000 - 18.1865i) q^{63} +64.0000 q^{64} +(-21.0000 - 36.3731i) q^{65} +(30.0000 + 17.3205i) q^{66} +(-29.5000 + 51.0955i) q^{67} +69.2820i q^{69} +48.4974i q^{70} -26.0000 q^{71} +(12.0000 + 20.7846i) q^{72} +(-16.5000 - 9.52628i) q^{73} +(5.00000 - 8.66025i) q^{74} +(19.5000 - 11.2583i) q^{75} +70.0000 q^{77} +42.0000 q^{78} +(-23.5000 - 40.7032i) q^{79} +(-48.0000 - 27.7128i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-42.0000 + 24.2487i) q^{82} -24.2487i q^{83} +24.0000 q^{85} +(-19.0000 - 32.9090i) q^{86} +(-24.0000 - 13.8564i) q^{87} +(-40.0000 + 69.2820i) q^{88} +(102.000 - 58.8897i) q^{89} -20.7846i q^{90} +(73.5000 - 42.4352i) q^{91} +(-4.50000 - 7.79423i) q^{93} +(-90.0000 - 51.9615i) q^{94} +(-57.0000 + 98.7269i) q^{95} -48.4974i q^{97} -98.0000 q^{98} -30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 6 q^{5} - 7 q^{7} + 16 q^{8} + 3 q^{9} - 12 q^{10} - 10 q^{11} + 14 q^{14} + 12 q^{15} + 16 q^{16} - 12 q^{17} - 6 q^{18} + 57 q^{19} - 40 q^{22} - 40 q^{23} - 24 q^{24} - 13 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 - 6 * q^5 - 7 * q^7 + 16 * q^8 + 3 * q^9 - 12 * q^10 - 10 * q^11 + 14 * q^14 + 12 * q^15 + 16 * q^16 - 12 * q^17 - 6 * q^18 + 57 * q^19 - 40 * q^22 - 40 * q^23 - 24 * q^24 - 13 * q^25 - 42 * q^26 + 32 * q^29 + 12 * q^30 + 9 * q^31 + 30 * q^33 + 42 * q^35 - 5 * q^37 + 114 * q^38 + 21 * q^39 - 48 * q^40 - 42 * q^42 - 38 * q^43 - 18 * q^45 + 80 * q^46 - 90 * q^47 - 49 * q^49 - 52 * q^50 + 12 * q^51 + 32 * q^53 + 18 * q^54 - 56 * q^56 - 114 * q^57 + 32 * q^58 + 72 * q^59 + 36 * q^61 + 21 * q^63 + 128 * q^64 - 42 * q^65 + 60 * q^66 - 59 * q^67 - 52 * q^71 + 24 * q^72 - 33 * q^73 + 10 * q^74 + 39 * q^75 + 140 * q^77 + 84 * q^78 - 47 * q^79 - 96 * q^80 - 9 * q^81 - 84 * q^82 + 48 * q^85 - 38 * q^86 - 48 * q^87 - 80 * q^88 + 204 * q^89 + 147 * q^91 - 9 * q^93 - 180 * q^94 - 114 * q^95 - 196 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.00000	+	1.73205i	0.500000	+	0.866025i	1.00000			$0$
$2$	1.00000	+	1.73205i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	−3.00000	+	1.73205i	−0.600000	+	0.346410i	−0.769042	−	0.639199i	$-0.779266\pi$
$5$	−3.00000	+	1.73205i	−0.600000	+	0.346410i	0.169042	+	0.985609i	$0.445933\pi$
$6$		−	3.46410i		−	0.577350i
$7$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$7$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$8$	8.00000			1.00000
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−6.00000	−	3.46410i	−0.600000	−	0.346410i
$11$	−5.00000	+	8.66025i	−0.454545	+	0.787296i	−0.998662	−	0.0517139i	$-0.983532\pi$
$11$	−5.00000	+	8.66025i	−0.454545	+	0.787296i	0.544116	+	0.839010i	$0.316865\pi$
$12$		0			0
$13$			12.1244i			0.932643i	0.884615	+	0.466321i	$0.154421\pi$
$13$			12.1244i			0.932643i	−0.884615	+	0.466321i	$0.845579\pi$
$14$	7.00000	−	12.1244i	0.500000	−	0.866025i
$15$	6.00000			0.400000
$16$	8.00000	+	13.8564i	0.500000	+	0.866025i
$17$	−6.00000	−	3.46410i	−0.352941	−	0.203771i	0.313039	−	0.949740i	$-0.398653\pi$
$17$	−6.00000	−	3.46410i	−0.352941	−	0.203771i	−0.665980	+	0.745970i	$0.731986\pi$
$18$	−3.00000	+	5.19615i	−0.166667	+	0.288675i
$19$	28.5000	−	16.4545i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$19$	28.5000	−	16.4545i	1.50000	−	0.866025i	1.00000			$0$
$20$		0			0
$21$			12.1244i			0.577350i
$22$	−20.0000			−0.909091
$23$	−20.0000	−	34.6410i	−0.869565	−	1.50613i	−0.862442	−	0.506157i	$-0.831066\pi$
$23$	−20.0000	−	34.6410i	−0.869565	−	1.50613i	−0.00712357	−	0.999975i	$-0.502268\pi$
$24$	−12.0000	−	6.92820i	−0.500000	−	0.288675i
$25$	−6.50000	+	11.2583i	−0.260000	+	0.450333i
$26$	−21.0000	+	12.1244i	−0.807692	+	0.466321i
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	16.0000			0.551724			0.275862	−	0.961197i	$-0.411037\pi$
$29$	16.0000			0.551724			0.275862	+	0.961197i	$0.411037\pi$
$30$	6.00000	+	10.3923i	0.200000	+	0.346410i
$31$	4.50000	+	2.59808i	0.145161	+	0.0838089i	0.570822	−	0.821074i	$-0.306625\pi$
$31$	4.50000	+	2.59808i	0.145161	+	0.0838089i	−0.425660	+	0.904883i	$0.639958\pi$
$32$		0			0
$33$	15.0000	−	8.66025i	0.454545	−	0.262432i
$34$		−	13.8564i		−	0.407541i
$35$	21.0000	+	12.1244i	0.600000	+	0.346410i
$36$		0			0
$37$	−2.50000	−	4.33013i	−0.0675676	−	0.117030i	0.830262	−	0.557373i	$-0.188190\pi$
$37$	−2.50000	−	4.33013i	−0.0675676	−	0.117030i	−0.897830	+	0.440342i	$0.854857\pi$
$38$	57.0000	+	32.9090i	1.50000	+	0.866025i
$39$	10.5000	−	18.1865i	0.269231	−	0.466321i
$40$	−24.0000	+	13.8564i	−0.600000	+	0.346410i
$41$			24.2487i			0.591432i	0.955276	+	0.295716i	$0.0955582\pi$
$41$			24.2487i			0.591432i	−0.955276	+	0.295716i	$0.904442\pi$
$42$	−21.0000	+	12.1244i	−0.500000	+	0.288675i
$43$	−19.0000			−0.441860			−0.220930	−	0.975290i	$-0.570909\pi$
$43$	−19.0000			−0.441860			−0.220930	+	0.975290i	$0.570909\pi$
$44$		0			0
$45$	−9.00000	−	5.19615i	−0.200000	−	0.115470i
$46$	40.0000	−	69.2820i	0.869565	−	1.50613i
$47$	−45.0000	+	25.9808i	−0.957447	+	0.552782i	−0.895386	−	0.445290i	$-0.853101\pi$
$47$	−45.0000	+	25.9808i	−0.957447	+	0.552782i	−0.0620605	+	0.998072i	$0.519767\pi$
$48$		−	27.7128i		−	0.577350i
$49$	−24.5000	+	42.4352i	−0.500000	+	0.866025i
$50$	−26.0000			−0.520000
$51$	6.00000	+	10.3923i	0.117647	+	0.203771i
$52$		0			0
$53$	16.0000	−	27.7128i	0.301887	−	0.522883i	−0.674677	−	0.738114i	$-0.735717\pi$
$53$	16.0000	−	27.7128i	0.301887	−	0.522883i	0.976563	+	0.215230i	$0.0690502\pi$
$54$	9.00000	−	5.19615i	0.166667	−	0.0962250i
$55$		−	34.6410i		−	0.629837i
$56$	−28.0000	−	48.4974i	−0.500000	−	0.866025i
$57$	−57.0000			−1.00000
$58$	16.0000	+	27.7128i	0.275862	+	0.477807i
$59$	36.0000	+	20.7846i	0.610169	+	0.352282i	0.773032	−	0.634367i	$-0.218739\pi$
$59$	36.0000	+	20.7846i	0.610169	+	0.352282i	−0.162862	+	0.986649i	$0.552073\pi$
$60$		0			0
$61$	18.0000	−	10.3923i	0.295082	−	0.170366i	−0.345149	−	0.938548i	$-0.612172\pi$
$61$	18.0000	−	10.3923i	0.295082	−	0.170366i	0.640231	+	0.768182i	$0.278838\pi$
$62$			10.3923i			0.167618i
$63$	10.5000	−	18.1865i	0.166667	−	0.288675i
$64$	64.0000			1.00000
$65$	−21.0000	−	36.3731i	−0.323077	−	0.559586i
$66$	30.0000	+	17.3205i	0.454545	+	0.262432i
$67$	−29.5000	+	51.0955i	−0.440299	+	0.762619i	−0.997711	−	0.0676160i	$-0.978461\pi$
$67$	−29.5000	+	51.0955i	−0.440299	+	0.762619i	0.557413	+	0.830235i	$0.311794\pi$
$68$		0			0
$69$			69.2820i			1.00409i
$70$			48.4974i			0.692820i
$71$	−26.0000			−0.366197			−0.183099	−	0.983095i	$-0.558613\pi$
$71$	−26.0000			−0.366197			−0.183099	+	0.983095i	$0.558613\pi$
$72$	12.0000	+	20.7846i	0.166667	+	0.288675i
$73$	−16.5000	−	9.52628i	−0.226027	−	0.130497i	0.382711	−	0.923868i	$-0.374991\pi$
$73$	−16.5000	−	9.52628i	−0.226027	−	0.130497i	−0.608738	+	0.793371i	$0.708324\pi$
$74$	5.00000	−	8.66025i	0.0675676	−	0.117030i
$75$	19.5000	−	11.2583i	0.260000	−	0.150111i
$76$		0			0
$77$	70.0000			0.909091
$78$	42.0000			0.538462
$79$	−23.5000	−	40.7032i	−0.297468	−	0.515230i	0.678088	−	0.734981i	$-0.262809\pi$
$79$	−23.5000	−	40.7032i	−0.297468	−	0.515230i	−0.975556	+	0.219751i	$0.929476\pi$
$80$	−48.0000	−	27.7128i	−0.600000	−	0.346410i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−42.0000	+	24.2487i	−0.512195	+	0.295716i
$83$		−	24.2487i		−	0.292153i	−0.989273	−	0.146077i	$-0.953335\pi$
$83$		−	24.2487i		−	0.292153i	0.989273	−	0.146077i	$-0.0466646\pi$
$84$		0			0
$85$	24.0000			0.282353
$86$	−19.0000	−	32.9090i	−0.220930	−	0.382662i
$87$	−24.0000	−	13.8564i	−0.275862	−	0.159269i
$88$	−40.0000	+	69.2820i	−0.454545	+	0.787296i
$89$	102.000	−	58.8897i	1.14607	−	0.661682i	0.198142	−	0.980173i	$-0.436509\pi$
$89$	102.000	−	58.8897i	1.14607	−	0.661682i	0.947926	+	0.318491i	$0.103176\pi$
$90$		−	20.7846i		−	0.230940i
$91$	73.5000	−	42.4352i	0.807692	−	0.466321i
$92$		0			0
$93$	−4.50000	−	7.79423i	−0.0483871	−	0.0838089i
$94$	−90.0000	−	51.9615i	−0.957447	−	0.552782i
$95$	−57.0000	+	98.7269i	−0.600000	+	1.03923i
$96$		0			0
$97$		−	48.4974i		−	0.499973i	−0.968249	−	0.249987i	$-0.919574\pi$
$97$		−	48.4974i		−	0.499973i	0.968249	−	0.249987i	$-0.0804263\pi$
$98$	−98.0000			−1.00000
$99$	−30.0000			−0.303030
$100$		0			0
$101$	−111.000	−	64.0859i	−1.09901	−	0.634514i	−0.163049	−	0.986618i	$-0.552133\pi$
$101$	−111.000	−	64.0859i	−1.09901	−	0.634514i	−0.935961	+	0.352104i	$0.885466\pi$
$102$	−12.0000	+	20.7846i	−0.117647	+	0.203771i
$103$	7.50000	−	4.33013i	0.0728155	−	0.0420401i	−0.463150	−	0.886280i	$-0.653281\pi$
$103$	7.50000	−	4.33013i	0.0728155	−	0.0420401i	0.535966	+	0.844240i	$0.319948\pi$
$104$			96.9948i			0.932643i
$105$	−21.0000	−	36.3731i	−0.200000	−	0.346410i
$106$	64.0000			0.603774
$107$	106.000	+	183.597i	0.990654	+	1.71586i	0.613451	+	0.789733i	$0.289781\pi$
$107$	106.000	+	183.597i	0.990654	+	1.71586i	0.377204	+	0.926130i	$0.376886\pi$
$108$		0			0
$109$	−8.50000	+	14.7224i	−0.0779817	+	0.135068i	−0.902379	−	0.430943i	$-0.858181\pi$
$109$	−8.50000	+	14.7224i	−0.0779817	+	0.135068i	0.824397	+	0.566011i	$0.191514\pi$
$110$	60.0000	−	34.6410i	0.545455	−	0.314918i
$111$			8.66025i			0.0780203i
$112$	56.0000	−	96.9948i	0.500000	−	0.866025i
$113$	142.000			1.25664			0.628319	−	0.777956i	$-0.283743\pi$
$113$	142.000			1.25664			0.628319	+	0.777956i	$0.283743\pi$
$114$	−57.0000	−	98.7269i	−0.500000	−	0.866025i
$115$	120.000	+	69.2820i	1.04348	+	0.602452i
$116$		0			0
$117$	−31.5000	+	18.1865i	−0.269231	+	0.155440i
$118$			83.1384i			0.704563i
$119$			48.4974i			0.407541i
$120$	48.0000			0.400000
$121$	10.5000	+	18.1865i	0.0867769	+	0.150302i
$122$	36.0000	+	20.7846i	0.295082	+	0.170366i
$123$	21.0000	−	36.3731i	0.170732	−	0.295716i
$124$		0			0
$125$		−	131.636i		−	1.05309i
$126$	42.0000			0.333333
$127$	−145.000			−1.14173			−0.570866	−	0.821043i	$-0.693392\pi$
$127$	−145.000			−1.14173			−0.570866	+	0.821043i	$0.693392\pi$
$128$	64.0000	+	110.851i	0.500000	+	0.866025i
$129$	28.5000	+	16.4545i	0.220930	+	0.127554i
$130$	42.0000	−	72.7461i	0.323077	−	0.559586i
$131$	−129.000	+	74.4782i	−0.984733	+	0.568536i	−0.903696	−	0.428175i	$-0.859157\pi$
$131$	−129.000	+	74.4782i	−0.984733	+	0.568536i	−0.0810371	+	0.996711i	$0.525823\pi$
$132$		0			0
$133$	−199.500	−	115.181i	−1.50000	−	0.866025i
$134$	−118.000			−0.880597
$135$	9.00000	+	15.5885i	0.0666667	+	0.115470i
$136$	−48.0000	−	27.7128i	−0.352941	−	0.203771i
$137$	58.0000	−	100.459i	0.423358	−	0.733277i	−0.572908	−	0.819620i	$-0.694185\pi$
$137$	58.0000	−	100.459i	0.423358	−	0.733277i	0.996265	+	0.0863428i	$0.0275180\pi$
$138$	−120.000	+	69.2820i	−0.869565	+	0.502044i
$139$			84.8705i			0.610579i	0.952260	+	0.305290i	$0.0987532\pi$
$139$			84.8705i			0.610579i	−0.952260	+	0.305290i	$0.901247\pi$
$140$		0			0
$141$	90.0000			0.638298
$142$	−26.0000	−	45.0333i	−0.183099	−	0.317136i
$143$	−105.000	−	60.6218i	−0.734266	−	0.423929i
$144$	−24.0000	+	41.5692i	−0.166667	+	0.288675i
$145$	−48.0000	+	27.7128i	−0.331034	+	0.191123i
$146$		−	38.1051i		−	0.260994i
$147$	73.5000	−	42.4352i	0.500000	−	0.288675i
$148$		0			0
$149$	−62.0000	−	107.387i	−0.416107	−	0.720719i	0.579437	−	0.815017i	$-0.303273\pi$
$149$	−62.0000	−	107.387i	−0.416107	−	0.720719i	−0.995544	+	0.0942982i	$0.969939\pi$
$150$	39.0000	+	22.5167i	0.260000	+	0.150111i
$151$	23.0000	−	39.8372i	0.152318	−	0.263822i	−0.779761	−	0.626077i	$-0.784660\pi$
$151$	23.0000	−	39.8372i	0.152318	−	0.263822i	0.932079	+	0.362255i	$0.117993\pi$
$152$	228.000	−	131.636i	1.50000	−	0.866025i
$153$		−	20.7846i		−	0.135847i
$154$	70.0000	+	121.244i	0.454545	+	0.787296i
$155$	−18.0000			−0.116129
$156$		0			0
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.917513	−	0.397705i	$-0.130193\pi$
$157$	162.000	+	93.5307i	1.03185	+	0.595737i	0.114334	+	0.993442i	$0.463527\pi$
$158$	47.0000	−	81.4064i	0.297468	−	0.515230i
$159$	−48.0000	+	27.7128i	−0.301887	+	0.174294i
$160$		0			0
$161$	−140.000	+	242.487i	−0.869565	+	1.50613i
$162$	−18.0000			−0.111111
$163$	29.0000	+	50.2295i	0.177914	+	0.308156i	0.941166	−	0.337945i	$-0.109732\pi$
$163$	29.0000	+	50.2295i	0.177914	+	0.308156i	−0.763252	+	0.646101i	$0.776398\pi$
$164$		0			0
$165$	−30.0000	+	51.9615i	−0.181818	+	0.314918i
$166$	42.0000	−	24.2487i	0.253012	−	0.146077i
$167$		−	266.736i		−	1.59722i	−0.601849	−	0.798610i	$-0.705569\pi$
$167$		−	266.736i		−	1.59722i	0.601849	−	0.798610i	$-0.294431\pi$
$168$			96.9948i			0.577350i
$169$	22.0000			0.130178
$170$	24.0000	+	41.5692i	0.141176	+	0.244525i
$171$	85.5000	+	49.3634i	0.500000	+	0.288675i
$172$		0			0
$173$	−108.000	+	62.3538i	−0.624277	+	0.360427i	−0.778532	−	0.627604i	$-0.784036\pi$
$173$	−108.000	+	62.3538i	−0.624277	+	0.360427i	0.154255	+	0.988031i	$0.450702\pi$
$174$		−	55.4256i		−	0.318538i
$175$	91.0000			0.520000
$176$	−160.000			−0.909091
$177$	−36.0000	−	62.3538i	−0.203390	−	0.352282i
$178$	204.000	+	117.779i	1.14607	+	0.661682i
$179$	−5.00000	+	8.66025i	−0.0279330	+	0.0483813i	−0.879654	−	0.475614i	$-0.842226\pi$
$179$	−5.00000	+	8.66025i	−0.0279330	+	0.0483813i	0.851721	+	0.523996i	$0.175559\pi$
$180$		0			0
$181$			327.358i			1.80861i	0.426892	+	0.904303i	$0.359609\pi$
$181$			327.358i			1.80861i	−0.426892	+	0.904303i	$0.640391\pi$
$182$	147.000	+	84.8705i	0.807692	+	0.466321i
$183$	−36.0000			−0.196721
$184$	−160.000	−	277.128i	−0.869565	−	1.50613i
$185$	15.0000	+	8.66025i	0.0810811	+	0.0468122i
$186$	9.00000	−	15.5885i	0.0483871	−	0.0838089i
$187$	60.0000	−	34.6410i	0.320856	−	0.185246i
$188$		0			0
$189$	−31.5000	+	18.1865i	−0.166667	+	0.0962250i
$190$	−228.000			−1.20000
$191$	1.00000	+	1.73205i	0.00523560	+	0.00906833i	0.868631	−	0.495459i	$-0.165000\pi$
$191$	1.00000	+	1.73205i	0.00523560	+	0.00906833i	−0.863396	+	0.504527i	$0.831667\pi$
$192$	−96.0000	−	55.4256i	−0.500000	−	0.288675i
$193$	117.500	−	203.516i	0.608808	−	1.05449i	−0.382629	−	0.923902i	$-0.624981\pi$
$193$	117.500	−	203.516i	0.608808	−	1.05449i	0.991437	−	0.130585i	$-0.0416855\pi$
$194$	84.0000	−	48.4974i	0.432990	−	0.249987i
$195$			72.7461i			0.373057i
$196$		0			0
$197$	100.000			0.507614			0.253807	−	0.967255i	$-0.418317\pi$
$197$	100.000			0.507614			0.253807	+	0.967255i	$0.418317\pi$
$198$	−30.0000	−	51.9615i	−0.151515	−	0.262432i
$199$	−174.000	−	100.459i	−0.874372	−	0.504819i	−0.00557327	−	0.999984i	$-0.501774\pi$
$199$	−174.000	−	100.459i	−0.874372	−	0.504819i	−0.868799	+	0.495166i	$0.835107\pi$
$200$	−52.0000	+	90.0666i	−0.260000	+	0.450333i
$201$	88.5000	−	51.0955i	0.440299	−	0.254206i
$202$		−	256.344i		−	1.26903i
$203$	−56.0000	−	96.9948i	−0.275862	−	0.477807i
$204$		0			0
$205$	−42.0000	−	72.7461i	−0.204878	−	0.354859i
$206$	15.0000	+	8.66025i	0.0728155	+	0.0420401i
$207$	60.0000	−	103.923i	0.289855	−	0.502044i
$208$	−168.000	+	96.9948i	−0.807692	+	0.466321i
$209$			329.090i			1.57459i
$210$	42.0000	−	72.7461i	0.200000	−	0.346410i
$211$	2.00000			0.00947867			0.00473934	−	0.999989i	$-0.498491\pi$
$211$	2.00000			0.00947867			0.00473934	+	0.999989i	$0.498491\pi$
$212$		0			0
$213$	39.0000	+	22.5167i	0.183099	+	0.105712i
$214$	−212.000	+	367.195i	−0.990654	+	1.71586i
$215$	57.0000	−	32.9090i	0.265116	−	0.153065i
$216$		−	41.5692i		−	0.192450i
$217$		−	36.3731i		−	0.167618i
$218$	−34.0000			−0.155963
$219$	16.5000	+	28.5788i	0.0753425	+	0.130497i
$220$		0			0
$221$	42.0000	−	72.7461i	0.190045	−	0.329168i
$222$	−15.0000	+	8.66025i	−0.0675676	+	0.0390102i
$223$		−	339.482i		−	1.52234i	−0.648552	−	0.761170i	$-0.724625\pi$
$223$		−	339.482i		−	1.52234i	0.648552	−	0.761170i	$-0.275375\pi$
$224$		0			0
$225$	−39.0000			−0.173333
$226$	142.000	+	245.951i	0.628319	+	1.08828i
$227$	141.000	+	81.4064i	0.621145	+	0.358618i	0.777315	−	0.629112i	$-0.216581\pi$
$227$	141.000	+	81.4064i	0.621145	+	0.358618i	−0.156169	+	0.987730i	$0.549915\pi$
$228$		0			0
$229$	7.50000	−	4.33013i	0.0327511	−	0.0189089i	−0.483535	−	0.875325i	$-0.660647\pi$
$229$	7.50000	−	4.33013i	0.0327511	−	0.0189089i	0.516286	+	0.856416i	$0.327314\pi$
$230$			277.128i			1.20490i
$231$	−105.000	−	60.6218i	−0.454545	−	0.262432i
$232$	128.000			0.551724
$233$	85.0000	+	147.224i	0.364807	+	0.631864i	0.988745	−	0.149610i	$-0.0478017\pi$
$233$	85.0000	+	147.224i	0.364807	+	0.631864i	−0.623938	+	0.781474i	$0.714468\pi$
$234$	−63.0000	−	36.3731i	−0.269231	−	0.155440i
$235$	90.0000	−	155.885i	0.382979	−	0.663339i
$236$		0			0
$237$			81.4064i			0.343487i
$238$	−84.0000	+	48.4974i	−0.352941	+	0.203771i
$239$	142.000			0.594142			0.297071	−	0.954855i	$-0.403990\pi$
$239$	142.000			0.594142			0.297071	+	0.954855i	$0.403990\pi$
$240$	48.0000	+	83.1384i	0.200000	+	0.346410i
$241$	−132.000	−	76.2102i	−0.547718	−	0.316225i	0.200483	−	0.979697i	$-0.435749\pi$
$241$	−132.000	−	76.2102i	−0.547718	−	0.316225i	−0.748201	+	0.663472i	$0.769082\pi$
$242$	−21.0000	+	36.3731i	−0.0867769	+	0.150302i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$		−	169.741i		−	0.692820i
$246$	84.0000			0.341463
$247$	199.500	+	345.544i	0.807692	+	1.39896i
$248$	36.0000	+	20.7846i	0.145161	+	0.0838089i
$249$	−21.0000	+	36.3731i	−0.0843373	+	0.146077i
$250$	228.000	−	131.636i	0.912000	−	0.526543i
$251$		−	290.985i		−	1.15930i	−0.814865	−	0.579650i	$-0.803189\pi$
$251$		−	290.985i		−	1.15930i	0.814865	−	0.579650i	$-0.196811\pi$
$252$		0			0
$253$	400.000			1.58103
$254$	−145.000	−	251.147i	−0.570866	−	0.988769i
$255$	−36.0000	−	20.7846i	−0.141176	−	0.0815083i
$256$		0			0
$257$	−381.000	+	219.970i	−1.48249	+	0.855916i	−0.999802	−	0.0198763i	$-0.993673\pi$
$257$	−381.000	+	219.970i	−1.48249	+	0.855916i	−0.482688	+	0.875792i	$0.660339\pi$
$258$			65.8179i			0.255108i
$259$	−17.5000	+	30.3109i	−0.0675676	+	0.117030i
$260$		0			0
$261$	24.0000	+	41.5692i	0.0919540	+	0.159269i
$262$	−258.000	−	148.956i	−0.984733	−	0.568536i
$263$	−68.0000	+	117.779i	−0.258555	+	0.447831i	−0.965855	−	0.259083i	$-0.916580\pi$
$263$	−68.0000	+	117.779i	−0.258555	+	0.447831i	0.707300	+	0.706914i	$0.249913\pi$
$264$	120.000	−	69.2820i	0.454545	−	0.262432i
$265$			110.851i			0.418307i
$266$		−	460.726i		−	1.73205i
$267$	−204.000			−0.764045
$268$		0			0
$269$	−195.000	−	112.583i	−0.724907	−	0.418525i	0.0916490	−	0.995791i	$-0.470786\pi$
$269$	−195.000	−	112.583i	−0.724907	−	0.418525i	−0.816556	+	0.577266i	$0.804120\pi$
$270$	−18.0000	+	31.1769i	−0.0666667	+	0.115470i
$271$	−318.000	+	183.597i	−1.17343	+	0.677481i	−0.954486	−	0.298256i	$-0.903595\pi$
$271$	−318.000	+	183.597i	−1.17343	+	0.677481i	−0.218946	+	0.975737i	$0.570262\pi$
$272$		−	110.851i		−	0.407541i
$273$	−147.000			−0.538462
$274$	232.000			0.846715
$275$	−65.0000	−	112.583i	−0.236364	−	0.409394i
$276$		0			0
$277$	−197.500	+	342.080i	−0.712996	+	1.23495i	0.250731	+	0.968057i	$0.419329\pi$
$277$	−197.500	+	342.080i	−0.712996	+	1.23495i	−0.963727	+	0.266889i	$0.914004\pi$
$278$	−147.000	+	84.8705i	−0.528777	+	0.305290i
$279$			15.5885i			0.0558726i
$280$	168.000	+	96.9948i	0.600000	+	0.346410i
$281$	100.000			0.355872			0.177936	−	0.984042i	$-0.443058\pi$
$281$	100.000			0.355872			0.177936	+	0.984042i	$0.443058\pi$
$282$	90.0000	+	155.885i	0.319149	+	0.552782i
$283$	−310.500	−	179.267i	−1.09717	−	0.633453i	−0.161696	−	0.986841i	$-0.551696\pi$
$283$	−310.500	−	179.267i	−1.09717	−	0.633453i	−0.935477	+	0.353387i	$0.885030\pi$
$284$		0			0
$285$	171.000	−	98.7269i	0.600000	−	0.346410i
$286$		−	242.487i		−	0.847857i
$287$	147.000	−	84.8705i	0.512195	−	0.295716i
$288$		0			0
$289$	−120.500	−	208.712i	−0.416955	−	0.722187i
$290$	−96.0000	−	55.4256i	−0.331034	−	0.191123i
$291$	−42.0000	+	72.7461i	−0.144330	+	0.249987i
$292$		0			0
$293$			242.487i			0.827601i	0.910368	+	0.413801i	$0.135799\pi$
$293$			242.487i			0.827601i	−0.910368	+	0.413801i	$0.864201\pi$
$294$	147.000	+	84.8705i	0.500000	+	0.288675i
$295$	−144.000			−0.488136
$296$	−20.0000	−	34.6410i	−0.0675676	−	0.117030i
$297$	45.0000	+	25.9808i	0.151515	+	0.0874773i
$298$	124.000	−	214.774i	0.416107	−	0.720719i
$299$	420.000	−	242.487i	1.40468	−	0.810994i
$300$		0			0
$301$	66.5000	+	115.181i	0.220930	+	0.382662i
$302$	92.0000			0.304636
$303$	111.000	+	192.258i	0.366337	+	0.634514i
$304$	456.000	+	263.272i	1.50000	+	0.866025i
$305$	−36.0000	+	62.3538i	−0.118033	+	0.204439i
$306$	36.0000	−	20.7846i	0.117647	−	0.0679236i
$307$			181.865i			0.592395i	0.955127	+	0.296198i	$0.0957187\pi$
$307$			181.865i			0.592395i	−0.955127	+	0.296198i	$0.904281\pi$
$308$		0			0
$309$	−15.0000			−0.0485437
$310$	−18.0000	−	31.1769i	−0.0580645	−	0.100571i
$311$	477.000	+	275.396i	1.53376	+	0.885518i	0.999184	+	0.0403991i	$0.0128629\pi$
$311$	477.000	+	275.396i	1.53376	+	0.885518i	0.534578	+	0.845119i	$0.320470\pi$
$312$	84.0000	−	145.492i	0.269231	−	0.466321i
$313$	175.500	−	101.325i	0.560703	−	0.323722i	−0.192725	−	0.981253i	$-0.561732\pi$
$313$	175.500	−	101.325i	0.560703	−	0.323722i	0.753428	+	0.657531i	$0.228399\pi$
$314$			374.123i			1.19147i
$315$			72.7461i			0.230940i
$316$		0			0
$317$	−146.000	−	252.879i	−0.460568	−	0.797727i	0.538421	−	0.842676i	$-0.319021\pi$
$317$	−146.000	−	252.879i	−0.460568	−	0.797727i	−0.998989	+	0.0449488i	$0.985688\pi$
$318$	−96.0000	−	55.4256i	−0.301887	−	0.174294i
$319$	−80.0000	+	138.564i	−0.250784	+	0.434370i
$320$	−192.000	+	110.851i	−0.600000	+	0.346410i
$321$		−	367.195i		−	1.14391i
$322$	−560.000			−1.73913
$323$	−228.000			−0.705882
$324$		0			0
$325$	−136.500	−	78.8083i	−0.420000	−	0.242487i
$326$	−58.0000	+	100.459i	−0.177914	+	0.308156i
$327$	25.5000	−	14.7224i	0.0779817	−	0.0450227i
$328$			193.990i			0.591432i
$329$	315.000	+	181.865i	0.957447	+	0.552782i
$330$	−120.000			−0.363636
$331$	−2.50000	−	4.33013i	−0.00755287	−	0.0130820i	0.862224	−	0.506527i	$-0.169071\pi$
$331$	−2.50000	−	4.33013i	−0.00755287	−	0.0130820i	−0.869777	+	0.493445i	$0.835738\pi$
$332$		0			0
$333$	7.50000	−	12.9904i	0.0225225	−	0.0390102i
$334$	462.000	−	266.736i	1.38323	−	0.798610i
$335$		−	204.382i		−	0.610096i
$336$	−168.000	+	96.9948i	−0.500000	+	0.288675i
$337$	−439.000			−1.30267			−0.651335	−	0.758790i	$-0.725791\pi$
$337$	−439.000			−1.30267			−0.651335	+	0.758790i	$0.725791\pi$
$338$	22.0000	+	38.1051i	0.0650888	+	0.112737i
$339$	−213.000	−	122.976i	−0.628319	−	0.362760i
$340$		0			0
$341$	−45.0000	+	25.9808i	−0.131965	+	0.0761899i
$342$			197.454i			0.577350i
$343$	343.000			1.00000
$344$	−152.000			−0.441860
$345$	−120.000	−	207.846i	−0.347826	−	0.602452i
$346$	−216.000	−	124.708i	−0.624277	−	0.360427i
$347$	−110.000	+	190.526i	−0.317003	+	0.549065i	−0.979861	−	0.199680i	$-0.936010\pi$
$347$	−110.000	+	190.526i	−0.317003	+	0.549065i	0.662858	+	0.748745i	$0.269343\pi$
$348$		0			0
$349$		−	339.482i		−	0.972728i	−0.873756	−	0.486364i	$-0.838323\pi$
$349$		−	339.482i		−	0.972728i	0.873756	−	0.486364i	$-0.161677\pi$
$350$	91.0000	+	157.617i	0.260000	+	0.450333i
$351$	63.0000			0.179487
$352$		0			0
$353$	267.000	+	154.153i	0.756374	+	0.436693i	0.827992	−	0.560739i	$-0.189483\pi$
$353$	267.000	+	154.153i	0.756374	+	0.436693i	−0.0716184	+	0.997432i	$0.522816\pi$
$354$	72.0000	−	124.708i	0.203390	−	0.352282i
$355$	78.0000	−	45.0333i	0.219718	−	0.126854i
$356$		0			0
$357$	42.0000	−	72.7461i	0.117647	−	0.203771i
$358$	−20.0000			−0.0558659
$359$	−146.000	−	252.879i	−0.406685	−	0.704399i	0.587831	−	0.808984i	$-0.299982\pi$
$359$	−146.000	−	252.879i	−0.406685	−	0.704399i	−0.994516	+	0.104584i	$0.966649\pi$
$360$	−72.0000	−	41.5692i	−0.200000	−	0.115470i
$361$	361.000	−	625.270i	1.00000	−	1.73205i
$362$	−567.000	+	327.358i	−1.56630	+	0.904303i
$363$		−	36.3731i		−	0.100201i
$364$		0			0
$365$	66.0000			0.180822
$366$	−36.0000	−	62.3538i	−0.0983607	−	0.170366i
$367$	466.500	+	269.334i	1.27112	+	0.733880i	0.975198	−	0.221333i	$-0.0710408\pi$
$367$	466.500	+	269.334i	1.27112	+	0.733880i	0.295919	+	0.955213i	$0.404374\pi$
$368$	320.000	−	554.256i	0.869565	−	1.50613i
$369$	−63.0000	+	36.3731i	−0.170732	+	0.0985720i
$370$			34.6410i			0.0936244i
$371$	−224.000			−0.603774
$372$		0			0
$373$	102.500	+	177.535i	0.274799	+	0.475966i	0.970084	−	0.242768i	$-0.0780554\pi$
$373$	102.500	+	177.535i	0.274799	+	0.475966i	−0.695285	+	0.718734i	$0.744722\pi$
$374$	120.000	+	69.2820i	0.320856	+	0.185246i
$375$	−114.000	+	197.454i	−0.304000	+	0.526543i
$376$	−360.000	+	207.846i	−0.957447	+	0.552782i
$377$			193.990i			0.514562i
$378$	−63.0000	−	36.3731i	−0.166667	−	0.0962250i
$379$	−523.000			−1.37995			−0.689974	−	0.723835i	$-0.742378\pi$
$379$	−523.000			−1.37995			−0.689974	+	0.723835i	$0.742378\pi$
$380$		0			0
$381$	217.500	+	125.574i	0.570866	+	0.329590i
$382$	−2.00000	+	3.46410i	−0.00523560	+	0.00906833i
$383$	−66.0000	+	38.1051i	−0.172324	+	0.0994912i	−0.583681	−	0.811983i	$-0.698388\pi$
$383$	−66.0000	+	38.1051i	−0.172324	+	0.0994912i	0.411357	+	0.911474i	$0.365055\pi$
$384$		−	221.703i		−	0.577350i
$385$	−210.000	+	121.244i	−0.545455	+	0.314918i
$386$	470.000			1.21762
$387$	−28.5000	−	49.3634i	−0.0736434	−	0.127554i
$388$		0			0
$389$	37.0000	−	64.0859i	0.0951157	−	0.164745i	−0.814541	−	0.580106i	$-0.803011\pi$
$389$	37.0000	−	64.0859i	0.0951157	−	0.164745i	0.909657	+	0.415361i	$0.136345\pi$
$390$	−126.000	+	72.7461i	−0.323077	+	0.186529i
$391$			277.128i			0.708768i
$392$	−196.000	+	339.482i	−0.500000	+	0.866025i
$393$	258.000			0.656489
$394$	100.000	+	173.205i	0.253807	+	0.439607i
$395$	141.000	+	81.4064i	0.356962	+	0.206092i
$396$		0			0
$397$	280.500	−	161.947i	0.706549	−	0.407926i	−0.103233	−	0.994657i	$-0.532919\pi$
$397$	280.500	−	161.947i	0.706549	−	0.407926i	0.809782	+	0.586731i	$0.199585\pi$
$398$		−	401.836i		−	1.00964i
$399$	199.500	+	345.544i	0.500000	+	0.866025i
$400$	−208.000			−0.520000
$401$	64.0000	+	110.851i	0.159601	+	0.276437i	0.934725	−	0.355372i	$-0.115646\pi$
$401$	64.0000	+	110.851i	0.159601	+	0.276437i	−0.775124	+	0.631809i	$0.782313\pi$
$402$	177.000	+	102.191i	0.440299	+	0.254206i
$403$	−31.5000	+	54.5596i	−0.0781638	+	0.135384i
$404$		0			0
$405$		−	31.1769i		−	0.0769800i
$406$	112.000	−	193.990i	0.275862	−	0.477807i
$407$	50.0000			0.122850
$408$	48.0000	+	83.1384i	0.117647	+	0.203771i
$409$	256.500	+	148.090i	0.627139	+	0.362079i	0.779643	−	0.626224i	$-0.215400\pi$
$409$	256.500	+	148.090i	0.627139	+	0.362079i	−0.152504	+	0.988303i	$0.548734\pi$
$410$	84.0000	−	145.492i	0.204878	−	0.354859i
$411$	−174.000	+	100.459i	−0.423358	+	0.244426i
$412$		0			0
$413$		−	290.985i		−	0.704563i
$414$	240.000			0.579710
$415$	42.0000	+	72.7461i	0.101205	+	0.175292i
$416$		0			0
$417$	73.5000	−	127.306i	0.176259	−	0.305290i
$418$	−570.000	+	329.090i	−1.36364	+	0.787296i
$419$		−	412.228i		−	0.983838i	−0.870641	−	0.491919i	$-0.836296\pi$
$419$		−	412.228i		−	0.983838i	0.870641	−	0.491919i	$-0.163704\pi$
$420$		0			0
$421$	107.000			0.254157			0.127078	−	0.991893i	$-0.459440\pi$
$421$	107.000			0.254157			0.127078	+	0.991893i	$0.459440\pi$
$422$	2.00000	+	3.46410i	0.00473934	+	0.00820877i
$423$	−135.000	−	77.9423i	−0.319149	−	0.184261i
$424$	128.000	−	221.703i	0.301887	−	0.522883i
$425$	78.0000	−	45.0333i	0.183529	−	0.105961i
$426$			90.0666i			0.211424i
$427$	−126.000	−	72.7461i	−0.295082	−	0.170366i
$428$		0			0
$429$	105.000	+	181.865i	0.244755	+	0.423929i
$430$	114.000	+	65.8179i	0.265116	+	0.153065i
$431$	−131.000	+	226.899i	−0.303944	+	0.526447i	−0.977026	−	0.213121i	$-0.931637\pi$
$431$	−131.000	+	226.899i	−0.303944	+	0.526447i	0.673081	+	0.739568i	$0.264970\pi$
$432$	72.0000	−	41.5692i	0.166667	−	0.0962250i
$433$		−	36.3731i		−	0.0840025i	−0.999118	−	0.0420012i	$-0.986627\pi$
$433$		−	36.3731i		−	0.0840025i	0.999118	−	0.0420012i	$-0.0133733\pi$
$434$	63.0000	−	36.3731i	0.145161	−	0.0838089i
$435$	96.0000			0.220690
$436$		0			0
$437$	−1140.00	−	658.179i	−2.60870	−	1.50613i
$438$	−33.0000	+	57.1577i	−0.0753425	+	0.130497i
$439$	270.000	−	155.885i	0.615034	−	0.355090i	−0.159899	−	0.987133i	$-0.551117\pi$
$439$	270.000	−	155.885i	0.615034	−	0.355090i	0.774933	+	0.632043i	$0.217784\pi$
$440$		−	277.128i		−	0.629837i
$441$	−147.000			−0.333333
$442$	168.000			0.380090
$443$	106.000	+	183.597i	0.239278	+	0.414441i	0.960507	−	0.278255i	$-0.0897561\pi$
$443$	106.000	+	183.597i	0.239278	+	0.414441i	−0.721230	+	0.692696i	$0.756423\pi$
$444$		0			0
$445$	−204.000	+	353.338i	−0.458427	+	0.794019i
$446$	588.000	−	339.482i	1.31839	−	0.761170i
$447$			214.774i			0.480479i
$448$	−224.000	−	387.979i	−0.500000	−	0.866025i
$449$	−782.000			−1.74165			−0.870824	−	0.491595i	$-0.836414\pi$
$449$	−782.000			−1.74165			−0.870824	+	0.491595i	$0.836414\pi$
$450$	−39.0000	−	67.5500i	−0.0866667	−	0.150111i
$451$	−210.000	−	121.244i	−0.465632	−	0.268833i
$452$		0			0
$453$	−69.0000	+	39.8372i	−0.152318	+	0.0879408i
$454$			325.626i			0.717237i
$455$	−147.000	+	254.611i	−0.323077	+	0.559586i
$456$	−456.000			−1.00000
$457$	−338.500	−	586.299i	−0.740700	−	1.28293i	−0.952177	−	0.305547i	$-0.901161\pi$
$457$	−338.500	−	586.299i	−0.740700	−	1.28293i	0.211477	−	0.977383i	$-0.432173\pi$
$458$	15.0000	+	8.66025i	0.0327511	+	0.0189089i
$459$	−18.0000	+	31.1769i	−0.0392157	+	0.0679236i
$460$		0			0
$461$			484.974i			1.05200i	0.850483	+	0.526002i	$0.176310\pi$
$461$			484.974i			1.05200i	−0.850483	+	0.526002i	$0.823690\pi$
$462$		−	242.487i		−	0.524864i
$463$	443.000			0.956803			0.478402	−	0.878141i	$-0.341216\pi$
$463$	443.000			0.956803			0.478402	+	0.878141i	$0.341216\pi$
$464$	128.000	+	221.703i	0.275862	+	0.477807i
$465$	27.0000	+	15.5885i	0.0580645	+	0.0335236i
$466$	−170.000	+	294.449i	−0.364807	+	0.631864i
$467$	39.0000	−	22.5167i	0.0835118	−	0.0482155i	−0.457663	−	0.889126i	$-0.651313\pi$
$467$	39.0000	−	22.5167i	0.0835118	−	0.0482155i	0.541174	+	0.840910i	$0.317980\pi$
$468$		0			0
$469$	413.000			0.880597
$470$	360.000			0.765957
$471$	−162.000	−	280.592i	−0.343949	−	0.595737i
$472$	288.000	+	166.277i	0.610169	+	0.352282i
$473$	95.0000	−	164.545i	0.200846	−	0.347875i
$474$	−141.000	+	81.4064i	−0.297468	+	0.171743i
$475$			427.817i			0.900666i
$476$		0			0
$477$	96.0000			0.201258
$478$	142.000	+	245.951i	0.297071	+	0.514542i
$479$	−48.0000	−	27.7128i	−0.100209	−	0.0578556i	0.449058	−	0.893503i	$-0.351760\pi$
$479$	−48.0000	−	27.7128i	−0.100209	−	0.0578556i	−0.549267	+	0.835647i	$0.685093\pi$
$480$		0			0
$481$	52.5000	−	30.3109i	0.109148	−	0.0630164i
$482$		−	304.841i		−	0.632450i
$483$	420.000	−	242.487i	0.869565	−	0.502044i
$484$		0			0
$485$	84.0000	+	145.492i	0.173196	+	0.299984i
$486$	27.0000	+	15.5885i	0.0555556	+	0.0320750i
$487$	33.5000	−	58.0237i	0.0687885	−	0.119145i	−0.829580	−	0.558388i	$-0.811420\pi$
$487$	33.5000	−	58.0237i	0.0687885	−	0.119145i	0.898368	+	0.439243i	$0.144753\pi$
$488$	144.000	−	83.1384i	0.295082	−	0.170366i
$489$		−	100.459i		−	0.205438i
$490$	294.000	−	169.741i	0.600000	−	0.346410i
$491$	−68.0000			−0.138493			−0.0692464	−	0.997600i	$-0.522059\pi$
$491$	−68.0000			−0.138493			−0.0692464	+	0.997600i	$0.522059\pi$
$492$		0			0
$493$	−96.0000	−	55.4256i	−0.194726	−	0.112425i
$494$	−399.000	+	691.088i	−0.807692	+	1.39896i
$495$	90.0000	−	51.9615i	0.181818	−	0.104973i
$496$			83.1384i			0.167618i
$497$	91.0000	+	157.617i	0.183099	+	0.317136i
$498$	−84.0000			−0.168675
$499$	−254.500	−	440.807i	−0.510020	−	0.883381i	−0.999933	−	0.0116091i	$-0.996305\pi$
$499$	−254.500	−	440.807i	−0.510020	−	0.883381i	0.489913	−	0.871772i	$-0.337029\pi$
$500$		0			0
$501$	−231.000	+	400.104i	−0.461078	+	0.798610i
$502$	504.000	−	290.985i	1.00398	−	0.579650i
$503$			654.715i			1.30162i	0.759240	+	0.650810i	$0.225571\pi$
$503$			654.715i			1.30162i	−0.759240	+	0.650810i	$0.774429\pi$
$504$	84.0000	−	145.492i	0.166667	−	0.288675i
$505$	444.000			0.879208
$506$	400.000	+	692.820i	0.790514	+	1.36921i
$507$	−33.0000	−	19.0526i	−0.0650888	−	0.0375790i
$508$		0			0
$509$	753.000	−	434.745i	1.47937	−	0.854115i	0.479644	−	0.877463i	$-0.340766\pi$
$509$	753.000	−	434.745i	1.47937	−	0.854115i	0.999727	+	0.0233478i	$0.00743251\pi$
$510$		−	83.1384i		−	0.163017i
$511$			133.368i			0.260994i
$512$	512.000			1.00000
$513$	−85.5000	−	148.090i	−0.166667	−	0.288675i
$514$	−762.000	−	439.941i	−1.48249	−	0.855916i
$515$	−15.0000	+	25.9808i	−0.0291262	+	0.0504481i
$516$		0			0
$517$		−	519.615i		−	1.00506i
$518$	−70.0000			−0.135135
$519$	216.000			0.416185
$520$	−168.000	−	290.985i	−0.323077	−	0.559586i
$521$	372.000	+	214.774i	0.714012	+	0.412235i	0.812545	−	0.582899i	$-0.198082\pi$
$521$	372.000	+	214.774i	0.714012	+	0.412235i	−0.0985331	+	0.995134i	$0.531415\pi$
$522$	−48.0000	+	83.1384i	−0.0919540	+	0.159269i
$523$	−853.500	+	492.768i	−1.63193	+	0.942196i	−0.648434	+	0.761271i	$0.724576\pi$
$523$	−853.500	+	492.768i	−1.63193	+	0.942196i	−0.983497	+	0.180925i	$0.942091\pi$
$524$		0			0
$525$	−136.500	−	78.8083i	−0.260000	−	0.150111i
$526$	−272.000			−0.517110
$527$	−18.0000	−	31.1769i	−0.0341556	−	0.0591592i
$528$	240.000	+	138.564i	0.454545	+	0.262432i
$529$	−535.500	+	927.513i	−1.01229	+	1.75333i
$530$	−192.000	+	110.851i	−0.362264	+	0.209153i
$531$			124.708i			0.234854i
$532$		0			0
$533$	−294.000			−0.551595
$534$	−204.000	−	353.338i	−0.382022	−	0.661682i
$535$	−636.000	−	367.195i	−1.18879	−	0.686345i
$536$	−236.000	+	408.764i	−0.440299	+	0.762619i
$537$	15.0000	−	8.66025i	0.0279330	−	0.0161271i
$538$		−	450.333i		−	0.837051i
$539$	−245.000	−	424.352i	−0.454545	−	0.787296i
$540$		0			0
$541$	60.5000	+	104.789i	0.111830	+	0.193695i	0.916508	−	0.400016i	$-0.130995\pi$
$541$	60.5000	+	104.789i	0.111830	+	0.193695i	−0.804678	+	0.593711i	$0.797662\pi$
$542$	−636.000	−	367.195i	−1.17343	−	0.677481i
$543$	283.500	−	491.036i	0.522099	−	0.904303i
$544$		0			0
$545$		−	58.8897i		−	0.108055i
$546$	−147.000	−	254.611i	−0.269231	−	0.466321i
$547$	926.000			1.69287			0.846435	−	0.532492i	$-0.178744\pi$
$547$	926.000			1.69287			0.846435	+	0.532492i	$0.178744\pi$
$548$		0			0
$549$	54.0000	+	31.1769i	0.0983607	+	0.0567886i
$550$	130.000	−	225.167i	0.236364	−	0.409394i
$551$	456.000	−	263.272i	0.827586	−	0.477807i
$552$			554.256i			1.00409i
$553$	−164.500	+	284.922i	−0.297468	+	0.515230i
$554$	−790.000			−1.42599
$555$	−15.0000	−	25.9808i	−0.0270270	−	0.0468122i
$556$		0			0
$557$	331.000	−	573.309i	0.594255	−	1.02928i	−0.399397	−	0.916778i	$-0.630780\pi$
$557$	331.000	−	573.309i	0.594255	−	1.02928i	0.993652	−	0.112502i	$-0.0358863\pi$
$558$	−27.0000	+	15.5885i	−0.0483871	+	0.0279363i
$559$		−	230.363i		−	0.412098i
$560$			387.979i			0.692820i
$561$	−120.000			−0.213904
$562$	100.000	+	173.205i	0.177936	+	0.308194i
$563$	−279.000	−	161.081i	−0.495560	−	0.286111i	0.231318	−	0.972878i	$-0.425696\pi$
$563$	−279.000	−	161.081i	−0.495560	−	0.286111i	−0.726878	+	0.686767i	$0.759029\pi$
$564$		0			0
$565$	−426.000	+	245.951i	−0.753982	+	0.435312i
$566$		−	717.069i		−	1.26691i
$567$	63.0000			0.111111
$568$	−208.000			−0.366197
$569$	379.000	+	656.447i	0.666081	+	1.15369i	0.978991	+	0.203903i	$0.0653628\pi$
$569$	379.000	+	656.447i	0.666081	+	1.15369i	−0.312910	+	0.949783i	$0.601304\pi$
$570$	342.000	+	197.454i	0.600000	+	0.346410i
$571$	432.500	−	749.112i	0.757443	−	1.31193i	−0.186707	−	0.982416i	$-0.559782\pi$
$571$	432.500	−	749.112i	0.757443	−	1.31193i	0.944151	−	0.329514i	$-0.106885\pi$
$572$		0			0
$573$		−	3.46410i		−	0.00604555i
$574$	294.000	+	169.741i	0.512195	+	0.295716i
$575$	520.000			0.904348
$576$	96.0000	+	166.277i	0.166667	+	0.288675i
$577$	928.500	+	536.070i	1.60919	+	0.929064i	0.989553	+	0.144172i	$0.0460518\pi$
$577$	928.500	+	536.070i	1.60919	+	0.929064i	0.619633	+	0.784892i	$0.287282\pi$
$578$	241.000	−	417.424i	0.416955	−	0.722187i
$579$	−352.500	+	203.516i	−0.608808	+	0.351496i
$580$		0			0
$581$	−147.000	+	84.8705i	−0.253012	+	0.146077i
$582$	−168.000			−0.288660
$583$	160.000	+	277.128i	0.274443	+	0.475348i
$584$	−132.000	−	76.2102i	−0.226027	−	0.130497i
$585$	63.0000	−	109.119i	0.107692	−	0.186529i
$586$	−420.000	+	242.487i	−0.716724	+	0.413801i
$587$			339.482i			0.578334i	0.957279	+	0.289167i	$0.0933783\pi$
$587$			339.482i			0.578334i	−0.957279	+	0.289167i	$0.906622\pi$
$588$		0			0
$589$	171.000			0.290323
$590$	−144.000	−	249.415i	−0.244068	−	0.422738i
$591$	−150.000	−	86.6025i	−0.253807	−	0.146536i
$592$	40.0000	−	69.2820i	0.0675676	−	0.117030i
$593$	−213.000	+	122.976i	−0.359191	+	0.207379i	−0.668726	−	0.743509i	$-0.733160\pi$
$593$	−213.000	+	122.976i	−0.359191	+	0.207379i	0.309535	+	0.950888i	$0.399827\pi$
$594$			103.923i			0.174955i
$595$	−84.0000	−	145.492i	−0.141176	−	0.244525i
$596$		0			0
$597$	174.000	+	301.377i	0.291457	+	0.504819i
$598$	840.000	+	484.974i	1.40468	+	0.810994i
$599$	142.000	−	245.951i	0.237062	−	0.410603i	−0.722808	−	0.691049i	$-0.757149\pi$
$599$	142.000	−	245.951i	0.237062	−	0.410603i	0.959870	+	0.280446i	$0.0904823\pi$
$600$	156.000	−	90.0666i	0.260000	−	0.150111i
$601$		−	594.093i		−	0.988508i	−0.869317	−	0.494254i	$-0.835441\pi$
$601$		−	594.093i		−	0.988508i	0.869317	−	0.494254i	$-0.164559\pi$
$602$	−133.000	+	230.363i	−0.220930	+	0.382662i
$603$	−177.000			−0.293532
$604$		0			0
$605$	−63.0000	−	36.3731i	−0.104132	−	0.0601208i
$606$	−222.000	+	384.515i	−0.366337	+	0.634514i
$607$	7.50000	−	4.33013i	0.0123558	−	0.00713365i	−0.493809	−	0.869570i	$-0.664396\pi$
$607$	7.50000	−	4.33013i	0.0123558	−	0.00713365i	0.506165	+	0.862437i	$0.331063\pi$
$608$		0			0
$609$			193.990i			0.318538i
$610$	−144.000			−0.236066
$611$	−315.000	−	545.596i	−0.515548	−	0.892956i
$612$		0			0
$613$	−439.000	+	760.370i	−0.716150	+	1.24041i	0.246364	+	0.969177i	$0.420764\pi$
$613$	−439.000	+	760.370i	−0.716150	+	1.24041i	−0.962514	+	0.271231i	$0.912569\pi$
$614$	−315.000	+	181.865i	−0.513029	+	0.296198i
$615$			145.492i			0.236573i
$616$	560.000			0.909091
$617$	−194.000			−0.314425			−0.157212	−	0.987565i	$-0.550251\pi$
$617$	−194.000			−0.314425			−0.157212	+	0.987565i	$0.550251\pi$
$618$	−15.0000	−	25.9808i	−0.0242718	−	0.0420401i
$619$	529.500	+	305.707i	0.855412	+	0.493872i	0.862473	−	0.506103i	$-0.168914\pi$
$619$	529.500	+	305.707i	0.855412	+	0.493872i	−0.00706124	+	0.999975i	$0.502248\pi$
$620$		0			0
$621$	−180.000	+	103.923i	−0.289855	+	0.167348i
$622$			1101.58i			1.77104i
$623$	−714.000	−	412.228i	−1.14607	−	0.661682i
$624$	336.000			0.538462
$625$	65.5000	+	113.449i	0.104800	+	0.181519i
$626$	351.000	+	202.650i	0.560703	+	0.323722i
$627$	285.000	−	493.634i	0.454545	−	0.787296i
$628$		0			0
$629$			34.6410i			0.0550732i
$630$	−126.000	+	72.7461i	−0.200000	+	0.115470i
$631$	−250.000			−0.396197			−0.198098	−	0.980182i	$-0.563477\pi$
$631$	−250.000			−0.396197			−0.198098	+	0.980182i	$0.563477\pi$
$632$	−188.000	−	325.626i	−0.297468	−	0.515230i
$633$	−3.00000	−	1.73205i	−0.00473934	−	0.00273626i
$634$	292.000	−	505.759i	0.460568	−	0.797727i
$635$	435.000	−	251.147i	0.685039	−	0.395508i
$636$		0			0
$637$	−514.500	−	297.047i	−0.807692	−	0.466321i
$638$	−320.000			−0.501567
$639$	−39.0000	−	67.5500i	−0.0610329	−	0.105712i
$640$	−384.000	−	221.703i	−0.600000	−	0.346410i
$641$	562.000	−	973.413i	0.876755	−	1.51858i	0.0218737	−	0.999761i	$-0.493037\pi$
$641$	562.000	−	973.413i	0.876755	−	1.51858i	0.854881	−	0.518824i	$-0.173630\pi$
$642$	636.000	−	367.195i	0.990654	−	0.571954i
$643$		−	569.845i		−	0.886228i	−0.896465	−	0.443114i	$-0.853874\pi$
$643$		−	569.845i		−	0.886228i	0.896465	−	0.443114i	$-0.146126\pi$
$644$		0			0
$645$	−114.000			−0.176744
$646$	−228.000	−	394.908i	−0.352941	−	0.611312i
$647$	939.000	+	542.132i	1.45131	+	0.837916i	0.998556	−	0.0537173i	$-0.0171070\pi$
$647$	939.000	+	542.132i	1.45131	+	0.837916i	0.452758	+	0.891634i	$0.350440\pi$
$648$	−36.0000	+	62.3538i	−0.0555556	+	0.0962250i
$649$	−360.000	+	207.846i	−0.554700	+	0.320256i
$650$		−	315.233i		−	0.484974i
$651$	−31.5000	+	54.5596i	−0.0483871	+	0.0838089i
$652$		0			0
$653$	505.000	+	874.686i	0.773354	+	1.33949i	0.935715	+	0.352757i	$0.114756\pi$
$653$	505.000	+	874.686i	0.773354	+	1.33949i	−0.162361	+	0.986731i	$0.551911\pi$
$654$	51.0000	+	29.4449i	0.0779817	+	0.0450227i
$655$	258.000	−	446.869i	0.393893	−	0.682243i
$656$	−336.000	+	193.990i	−0.512195	+	0.295716i
$657$		−	57.1577i		−	0.0869980i
$658$			727.461i			1.10556i
$659$	−908.000			−1.37785			−0.688923	−	0.724835i	$-0.741916\pi$
$659$	−908.000			−1.37785			−0.688923	+	0.724835i	$0.741916\pi$
$660$		0			0
$661$	−625.500	−	361.133i	−0.946293	−	0.546343i	−0.0543659	−	0.998521i	$-0.517314\pi$
$661$	−625.500	−	361.133i	−0.946293	−	0.546343i	−0.891928	+	0.452178i	$0.850647\pi$
$662$	5.00000	−	8.66025i	0.00755287	−	0.0130820i
$663$	−126.000	+	72.7461i	−0.190045	+	0.109723i
$664$		−	193.990i		−	0.292153i
$665$	798.000			1.20000
$666$	30.0000			0.0450450
$667$	−320.000	−	554.256i	−0.479760	−	0.830969i
$668$		0			0
$669$	−294.000	+	509.223i	−0.439462	+	0.761170i
$670$	354.000	−	204.382i	0.528358	−	0.305048i
$671$			207.846i			0.309756i
$672$		0			0
$673$	−1027.00			−1.52600			−0.763001	−	0.646397i	$-0.776275\pi$
$673$	−1027.00			−1.52600			−0.763001	+	0.646397i	$0.776275\pi$
$674$	−439.000	−	760.370i	−0.651335	−	1.12815i
$675$	58.5000	+	33.7750i	0.0866667	+	0.0500370i
$676$		0			0
$677$	−486.000	+	280.592i	−0.717873	+	0.414464i	−0.813969	−	0.580908i	$-0.802698\pi$
$677$	−486.000	+	280.592i	−0.717873	+	0.414464i	0.0960963	+	0.995372i	$0.469364\pi$
$678$		−	491.902i		−	0.725520i
$679$	−294.000	+	169.741i	−0.432990	+	0.249987i
$680$	192.000			0.282353
$681$	−141.000	−	244.219i	−0.207048	−	0.358618i
$682$	−90.0000	−	51.9615i	−0.131965	−	0.0761899i
$683$	−488.000	+	845.241i	−0.714495	+	1.23754i	0.248659	+	0.968591i	$0.420010\pi$
$683$	−488.000	+	845.241i	−0.714495	+	1.23754i	−0.963154	+	0.268950i	$0.913323\pi$
$684$		0			0
$685$			401.836i			0.586622i
$686$	343.000	+	594.093i	0.500000	+	0.866025i
$687$	−15.0000			−0.0218341
$688$	−152.000	−	263.272i	−0.220930	−	0.382662i
$689$	336.000	+	193.990i	0.487663	+	0.281553i
$690$	240.000	−	415.692i	0.347826	−	0.602452i
$691$	490.500	−	283.190i	0.709841	−	0.409827i	−0.101161	−	0.994870i	$-0.532256\pi$
$691$	490.500	−	283.190i	0.709841	−	0.409827i	0.811002	+	0.585043i	$0.198922\pi$
$692$		0			0
$693$	105.000	+	181.865i	0.151515	+	0.262432i
$694$	−440.000			−0.634006
$695$	−147.000	−	254.611i	−0.211511	−	0.366347i
$696$	−192.000	−	110.851i	−0.275862	−	0.159269i
$697$	84.0000	−	145.492i	0.120516	−	0.208741i
$698$	588.000	−	339.482i	0.842407	−	0.486364i
$699$		−	294.449i		−	0.421243i
$700$		0			0
$701$	352.000			0.502140			0.251070	−	0.967969i	$-0.419218\pi$
$701$	352.000			0.502140			0.251070	+	0.967969i	$0.419218\pi$
$702$	63.0000	+	109.119i	0.0897436	+	0.155440i
$703$	−142.500	−	82.2724i	−0.202703	−	0.117030i
$704$	−320.000	+	554.256i	−0.454545	+	0.787296i
$705$	−270.000	+	155.885i	−0.382979	+	0.221113i
$706$			616.610i			0.873385i
$707$			897.202i			1.26903i
$708$		0			0
$709$	575.000	+	995.929i	0.811001	+	1.40470i	0.912164	+	0.409826i	$0.134410\pi$
$709$	575.000	+	995.929i	0.811001	+	1.40470i	−0.101162	+	0.994870i	$0.532256\pi$
$710$	156.000	+	90.0666i	0.219718	+	0.126854i
$711$	70.5000	−	122.110i	0.0991561	−	0.171743i
$712$	816.000	−	471.118i	1.14607	−	0.661682i
$713$		−	207.846i		−	0.291509i
$714$	168.000			0.235294
$715$	420.000			0.587413
$716$		0			0
$717$	−213.000	−	122.976i	−0.297071	−	0.171514i
$718$	292.000	−	505.759i	0.406685	−	0.704399i
$719$	−843.000	+	486.706i	−1.17246	+	0.676921i	−0.954259	−	0.298982i	$-0.903353\pi$
$719$	−843.000	+	486.706i	−1.17246	+	0.676921i	−0.218203	+	0.975903i	$0.570020\pi$
$720$		−	166.277i		−	0.230940i
$721$	−52.5000	−	30.3109i	−0.0728155	−	0.0420401i
$722$	1444.00			2.00000
$723$	132.000	+	228.631i	0.182573	+	0.316225i
$724$		0			0
$725$	−104.000	+	180.133i	−0.143448	+	0.248460i
$726$	63.0000	−	36.3731i	0.0867769	−	0.0501006i
$727$			206.114i			0.283513i	0.989902	+	0.141757i	$0.0452750\pi$
$727$			206.114i			0.283513i	−0.989902	+	0.141757i	$0.954725\pi$
$728$	588.000	−	339.482i	0.807692	−	0.466321i
$729$	−27.0000			−0.0370370
$730$	66.0000	+	114.315i	0.0904110	+	0.156596i
$731$	114.000	+	65.8179i	0.155951	+	0.0900382i
$732$		0			0
$733$	1078.50	−	622.672i	1.47135	−	0.849485i	0.471869	−	0.881669i	$-0.343580\pi$
$733$	1078.50	−	622.672i	1.47135	−	0.849485i	0.999482	+	0.0321842i	$0.0102463\pi$
$734$			1077.34i			1.46776i
$735$	−147.000	+	254.611i	−0.200000	+	0.346410i
$736$		0			0
$737$	−295.000	−	510.955i	−0.400271	−	0.693290i
$738$	−126.000	−	72.7461i	−0.170732	−	0.0985720i
$739$	−155.500	+	269.334i	−0.210419	+	0.364457i	−0.951846	−	0.306577i	$-0.900816\pi$
$739$	−155.500	+	269.334i	−0.210419	+	0.364457i	0.741426	+	0.671034i	$0.234150\pi$
$740$		0			0
$741$		−	691.088i		−	0.932643i
$742$	−224.000	−	387.979i	−0.301887	−	0.522883i
$743$	394.000			0.530283			0.265141	−	0.964210i	$-0.414581\pi$
$743$	394.000			0.530283			0.265141	+	0.964210i	$0.414581\pi$
$744$	−36.0000	−	62.3538i	−0.0483871	−	0.0838089i
$745$	372.000	+	214.774i	0.499329	+	0.288288i
$746$	−205.000	+	355.070i	−0.274799	+	0.475966i
$747$	63.0000	−	36.3731i	0.0843373	−	0.0486922i
$748$		0			0
$749$	742.000	−	1285.18i	0.990654	−	1.71586i
$750$	−456.000			−0.608000
$751$	39.5000	+	68.4160i	0.0525965	+	0.0910999i	0.891125	−	0.453758i	$-0.149917\pi$
$751$	39.5000	+	68.4160i	0.0525965	+	0.0910999i	−0.838528	+	0.544858i	$0.816584\pi$
$752$	−720.000	−	415.692i	−0.957447	−	0.552782i
$753$	−252.000	+	436.477i	−0.334661	+	0.579650i
$754$	−336.000	+	193.990i	−0.445623	+	0.257281i
$755$			159.349i			0.211058i
$756$		0			0
$757$	−250.000			−0.330251			−0.165125	−	0.986273i	$-0.552803\pi$
$757$	−250.000			−0.330251			−0.165125	+	0.986273i	$0.552803\pi$
$758$	−523.000	−	905.863i	−0.689974	−	1.19507i
$759$	−600.000	−	346.410i	−0.790514	−	0.456403i
$760$	−456.000	+	789.815i	−0.600000	+	1.03923i
$761$	−822.000	+	474.582i	−1.08016	+	0.623629i	−0.930939	−	0.365175i	$-0.881009\pi$
$761$	−822.000	+	474.582i	−1.08016	+	0.623629i	−0.149219	+	0.988804i	$0.547676\pi$
$762$			502.295i			0.659179i
$763$	119.000			0.155963
$764$		0			0
$765$	36.0000	+	62.3538i	0.0470588	+	0.0815083i
$766$	−132.000	−	76.2102i	−0.172324	−	0.0994912i
$767$	−252.000	+	436.477i	−0.328553	+	0.569070i
$768$		0			0
$769$		−	860.829i		−	1.11941i	−0.828691	−	0.559707i	$-0.810914\pi$
$769$		−	860.829i		−	1.11941i	0.828691	−	0.559707i	$-0.189086\pi$
$770$	−420.000	−	242.487i	−0.545455	−	0.314918i
$771$	762.000			0.988327
$772$		0			0
$773$	−195.000	−	112.583i	−0.252264	−	0.145645i	0.368537	−	0.929613i	$-0.379859\pi$
$773$	−195.000	−	112.583i	−0.252264	−	0.145645i	−0.620800	+	0.783969i	$0.713192\pi$
$774$	57.0000	−	98.7269i	0.0736434	−	0.127554i
$775$	−58.5000	+	33.7750i	−0.0754839	+	0.0435806i
$776$		−	387.979i		−	0.499973i
$777$	52.5000	−	30.3109i	0.0675676	−	0.0390102i
$778$	148.000			0.190231
$779$	399.000	+	691.088i	0.512195	+	0.887148i
$780$		0			0
$781$	130.000	−	225.167i	0.166453	−	0.288306i
$782$	−480.000	+	277.128i	−0.613811	+	0.354384i
$783$		−	83.1384i		−	0.106179i
$784$	−784.000			−1.00000
$785$	−648.000			−0.825478
$786$	258.000	+	446.869i	0.328244	+	0.568536i
$787$	−216.000	−	124.708i	−0.274460	−	0.158460i	0.356453	−	0.934313i	$-0.383986\pi$
$787$	−216.000	−	124.708i	−0.274460	−	0.158460i	−0.630913	+	0.775854i	$0.717319\pi$
$788$		0			0
$789$	204.000	−	117.779i	0.258555	−	0.149277i
$790$			325.626i			0.412184i
$791$	−497.000	−	860.829i	−0.628319	−	1.08828i
$792$	−240.000			−0.303030
$793$	126.000	+	218.238i	0.158890	+	0.275206i
$794$	561.000	+	323.894i	0.706549	+	0.407926i
$795$	96.0000	−	166.277i	0.120755	−	0.209153i
$796$		0			0
$797$		−	1357.93i		−	1.70380i	−0.523705	−	0.851900i	$-0.675451\pi$
$797$		−	1357.93i		−	1.70380i	0.523705	−	0.851900i	$-0.324549\pi$
$798$	−399.000	+	691.088i	−0.500000	+	0.866025i
$799$	360.000			0.450563
$800$		0			0
$801$	306.000	+	176.669i	0.382022	+	0.220561i
$802$	−128.000	+	221.703i	−0.159601	+	0.276437i
$803$	165.000	−	95.2628i	0.205479	−	0.118634i
$804$		0			0
$805$		−	969.948i		−	1.20490i
$806$	−126.000			−0.156328
$807$	195.000	+	337.750i	0.241636	+	0.418525i
$808$	−888.000	−	512.687i	−1.09901	−	0.634514i
$809$	709.000	−	1228.02i	0.876391	−	1.51795i	0.0211166	−	0.999777i	$-0.493278\pi$
$809$	709.000	−	1228.02i	0.876391	−	1.51795i	0.855274	−	0.518176i	$-0.173389\pi$
$810$	54.0000	−	31.1769i	0.0666667	−	0.0384900i
$811$			872.954i			1.07639i	0.842820	+	0.538196i	$0.180894\pi$
$811$			872.954i			1.07639i	−0.842820	+	0.538196i	$0.819106\pi$
$812$		0			0
$813$	636.000			0.782288
$814$	50.0000	+	86.6025i	0.0614251	+	0.106391i
$815$	−174.000	−	100.459i	−0.213497	−	0.123263i
$816$	−96.0000	+	166.277i	−0.117647	+	0.203771i
$817$	−541.500	+	312.635i	−0.662791	+	0.382662i
$818$			592.361i			0.724158i
$819$	220.500	+	127.306i	0.269231	+	0.155440i
$820$		0			0
$821$	−125.000	−	216.506i	−0.152253	−	0.263711i	0.779802	−	0.626026i	$-0.215320\pi$
$821$	−125.000	−	216.506i	−0.152253	−	0.263711i	−0.932056	+	0.362315i	$0.881986\pi$
$822$	−348.000	−	200.918i	−0.423358	−	0.244426i
$823$	−103.000	+	178.401i	−0.125152	+	0.216769i	−0.921792	−	0.387684i	$-0.873275\pi$
$823$	−103.000	+	178.401i	−0.125152	+	0.216769i	0.796640	+	0.604454i	$0.206608\pi$
$824$	60.0000	−	34.6410i	0.0728155	−	0.0420401i
$825$			225.167i			0.272929i
$826$	504.000	−	290.985i	0.610169	−	0.352282i
$827$	1234.00			1.49214			0.746070	−	0.665867i	$-0.231938\pi$
$827$	1234.00			1.49214			0.746070	+	0.665867i	$0.231938\pi$
$828$		0			0
$829$	298.500	+	172.339i	0.360072	+	0.207888i	0.669113	−	0.743161i	$-0.266674\pi$
$829$	298.500	+	172.339i	0.360072	+	0.207888i	−0.309040	+	0.951049i	$0.600008\pi$
$830$	−84.0000	+	145.492i	−0.101205	+	0.175292i
$831$	592.500	−	342.080i	0.712996	−	0.411649i
$832$			775.959i			0.932643i
$833$	294.000	−	169.741i	0.352941	−	0.203771i
$834$	294.000			0.352518
$835$	462.000	+	800.207i	0.553293	+	0.958332i
$836$		0			0
$837$	13.5000	−	23.3827i	0.0161290	−	0.0279363i
$838$	714.000	−	412.228i	0.852029	−	0.491919i
$839$			484.974i			0.578038i	0.957323	+	0.289019i	$0.0933291\pi$
$839$			484.974i			0.578038i	−0.957323	+	0.289019i	$0.906671\pi$
$840$	−168.000	−	290.985i	−0.200000	−	0.346410i
$841$	−585.000			−0.695600
$842$	107.000	+	185.329i	0.127078	+	0.220106i
$843$	−150.000	−	86.6025i	−0.177936	−	0.102731i
$844$		0			0
$845$	−66.0000	+	38.1051i	−0.0781065	+	0.0450948i
$846$		−	311.769i		−	0.368521i
$847$	73.5000	−	127.306i	0.0867769	−	0.150302i
$848$	512.000			0.603774
$849$	310.500	+	537.802i	0.365724	+	0.633453i
$850$	156.000	+	90.0666i	0.183529	+	0.105961i
$851$	−100.000	+	173.205i	−0.117509	+	0.203531i
$852$		0			0
$853$			278.860i			0.326917i	0.986550	+	0.163458i	$0.0522650\pi$
$853$			278.860i			0.326917i	−0.986550	+	0.163458i	$0.947735\pi$
$854$		−	290.985i		−	0.340731i
$855$	−342.000			−0.400000
$856$	848.000	+	1468.78i	0.990654	+	1.71586i
$857$	−552.000	−	318.697i	−0.644107	−	0.371876i	0.142088	−	0.989854i	$-0.454619\pi$
$857$	−552.000	−	318.697i	−0.644107	−	0.371876i	−0.786195	+	0.617979i	$0.787952\pi$
$858$	−210.000	+	363.731i	−0.244755	+	0.423929i
$859$	−528.000	+	304.841i	−0.614668	+	0.354879i	−0.774790	−	0.632218i	$-0.782145\pi$
$859$	−528.000	+	304.841i	−0.614668	+	0.354879i	0.160122	+	0.987097i	$0.448811\pi$
$860$		0			0
$861$	−294.000			−0.341463
$862$	−524.000			−0.607889
$863$	−335.000	−	580.237i	−0.388181	−	0.672349i	0.604024	−	0.796966i	$-0.293563\pi$
$863$	−335.000	−	580.237i	−0.388181	−	0.672349i	−0.992205	+	0.124617i	$0.960230\pi$
$864$		0			0
$865$	216.000	−	374.123i	0.249711	−	0.432512i
$866$	63.0000	−	36.3731i	0.0727483	−	0.0420012i
$867$			417.424i			0.481458i
$868$		0			0
$869$	470.000			0.540852
$870$	96.0000	+	166.277i	0.110345	+	0.191123i
$871$	−619.500	−	357.668i	−0.711251	−	0.410641i
$872$	−68.0000	+	117.779i	−0.0779817	+	0.135068i
$873$	126.000	−	72.7461i	0.144330	−	0.0833289i
$874$		−	2632.72i		−	3.01226i
$875$	−798.000	+	460.726i	−0.912000	+	0.526543i
$876$		0			0
$877$	197.000	+	341.214i	0.224629	+	0.389070i	0.956208	−	0.292687i	$-0.0945495\pi$
$877$	197.000	+	341.214i	0.224629	+	0.389070i	−0.731579	+	0.681757i	$0.761216\pi$
$878$	540.000	+	311.769i	0.615034	+	0.355090i
$879$	210.000	−	363.731i	0.238908	−	0.413801i
$880$	480.000	−	277.128i	0.545455	−	0.314918i
$881$			1163.94i			1.32116i	0.750758	+	0.660578i	$0.229689\pi$
$881$			1163.94i			1.32116i	−0.750758	+	0.660578i	$0.770311\pi$
$882$	−147.000	−	254.611i	−0.166667	−	0.288675i
$883$	737.000			0.834655			0.417327	−	0.908756i	$-0.362967\pi$
$883$	737.000			0.834655			0.417327	+	0.908756i	$0.362967\pi$
$884$		0			0
$885$	216.000	+	124.708i	0.244068	+	0.140913i
$886$	−212.000	+	367.195i	−0.239278	+	0.414441i
$887$	−633.000	+	365.463i	−0.713641	+	0.412021i	−0.812408	−	0.583090i	$-0.801844\pi$
$887$	−633.000	+	365.463i	−0.713641	+	0.412021i	0.0987664	+	0.995111i	$0.468510\pi$
$888$			69.2820i			0.0780203i
$889$	507.500	+	879.016i	0.570866	+	0.988769i
$890$	−816.000			−0.916854
$891$	−45.0000	−	77.9423i	−0.0505051	−	0.0874773i
$892$		0			0
$893$	−855.000	+	1480.90i	−0.957447	+	1.65835i
$894$	−372.000	+	214.774i	−0.416107	+	0.240240i
$895$		−	34.6410i		−	0.0387050i
$896$	448.000	−	775.959i	0.500000	−	0.866025i
$897$	−840.000			−0.936455
$898$	−782.000	−	1354.46i	−0.870824	−	1.50831i
$899$	72.0000	+	41.5692i	0.0800890	+	0.0462394i
$900$		0			0
$901$	−192.000	+	110.851i	−0.213097	+	0.123031i
$902$		−	484.974i		−	0.537665i
$903$		−	230.363i		−	0.255108i
$904$	1136.00			1.25664
$905$	−567.000	−	982.073i	−0.626519	−	1.08516i
$906$	−138.000	−	79.6743i	−0.152318	−	0.0879408i
$907$	117.500	−	203.516i	0.129548	−	0.224384i	−0.793954	−	0.607978i	$-0.791981\pi$
$907$	117.500	−	203.516i	0.129548	−	0.224384i	0.923502	+	0.383595i	$0.125314\pi$
$908$		0			0
$909$		−	384.515i		−	0.423009i
$910$	−588.000			−0.646154
$911$	−740.000			−0.812294			−0.406147	−	0.913808i	$-0.633128\pi$
$911$	−740.000			−0.812294			−0.406147	+	0.913808i	$0.633128\pi$
$912$	−456.000	−	789.815i	−0.500000	−	0.866025i
$913$	210.000	+	121.244i	0.230011	+	0.132797i
$914$	677.000	−	1172.60i	0.740700	−	1.28293i
$915$	108.000	−	62.3538i	0.118033	−	0.0681463i
$916$		0			0
$917$	903.000	+	521.347i	0.984733	+	0.568536i
$918$	−72.0000			−0.0784314
$919$	−758.500	−	1313.76i	−0.825354	−	1.42955i	−0.901649	−	0.432469i	$-0.857642\pi$
$919$	−758.500	−	1313.76i	−0.825354	−	1.42955i	0.0762951	−	0.997085i	$-0.475691\pi$
$920$	960.000	+	554.256i	1.04348	+	0.602452i
$921$	157.500	−	272.798i	0.171010	−	0.296198i
$922$	−840.000	+	484.974i	−0.911063	+	0.526002i
$923$		−	315.233i		−	0.341531i
$924$		0			0
$925$	65.0000			0.0702703
$926$	443.000	+	767.299i	0.478402	+	0.828616i
$927$	22.5000	+	12.9904i	0.0242718	+	0.0140134i
$928$		0			0
$929$	963.000	−	555.988i	1.03660	−	0.598480i	0.117731	−	0.993046i	$-0.462438\pi$
$929$	963.000	−	555.988i	1.03660	−	0.598480i	0.918868	+	0.394565i	$0.129105\pi$
$930$			62.3538i			0.0670471i
$931$			1612.54i			1.73205i
$932$		0			0
$933$	−477.000	−	826.188i	−0.511254	−	0.885518i
$934$	78.0000	+	45.0333i	0.0835118	+	0.0482155i
$935$	−120.000	+	207.846i	−0.128342	+	0.222295i
$936$	−252.000	+	145.492i	−0.269231	+	0.155440i
$937$		−	836.581i		−	0.892829i	−0.894826	−	0.446414i	$-0.852701\pi$
$937$		−	836.581i		−	0.892829i	0.894826	−	0.446414i	$-0.147299\pi$
$938$	413.000	+	715.337i	0.440299	+	0.762619i
$939$	−351.000			−0.373802
$940$		0			0
$941$	−342.000	−	197.454i	−0.363443	−	0.209834i	0.307147	−	0.951662i	$-0.400626\pi$
$941$	−342.000	−	197.454i	−0.363443	−	0.209834i	−0.670590	+	0.741828i	$0.733959\pi$
$942$	324.000	−	561.184i	0.343949	−	0.595737i
$943$	840.000	−	484.974i	0.890774	−	0.514289i
$944$			665.108i			0.704563i
$945$	63.0000	−	109.119i	0.0666667	−	0.115470i
$946$	380.000			0.401691
$947$	169.000	+	292.717i	0.178458	+	0.309099i	0.941353	−	0.337424i	$-0.109556\pi$
$947$	169.000	+	292.717i	0.178458	+	0.309099i	−0.762894	+	0.646523i	$0.776222\pi$
$948$		0			0
$949$	115.500	−	200.052i	0.121707	−	0.210803i
$950$	−741.000	+	427.817i	−0.780000	+	0.450333i
$951$			505.759i			0.531818i
$952$			387.979i			0.407541i
$953$	−1244.00			−1.30535			−0.652676	−	0.757637i	$-0.726354\pi$
$953$	−1244.00			−1.30535			−0.652676	+	0.757637i	$0.726354\pi$
$954$	96.0000	+	166.277i	0.100629	+	0.174294i
$955$	−6.00000	−	3.46410i	−0.00628272	−	0.00362733i
$956$		0			0
$957$	240.000	−	138.564i	0.250784	−	0.144790i
$958$		−	110.851i		−	0.115711i
$959$	−812.000			−0.846715
$960$	384.000			0.400000
$961$	−467.000	−	808.868i	−0.485952	−	0.841694i
$962$	105.000	+	60.6218i	0.109148	+	0.0630164i
$963$	−318.000	+	550.792i	−0.330218	+	0.571954i
$964$		0			0
$965$			814.064i			0.843590i
$966$	840.000	+	484.974i	0.869565	+	0.502044i
$967$	−1741.00			−1.80041			−0.900207	−	0.435463i	$-0.856585\pi$
$967$	−1741.00			−1.80041			−0.900207	+	0.435463i	$0.856585\pi$
$968$	84.0000	+	145.492i	0.0867769	+	0.150302i
$969$	342.000	+	197.454i	0.352941	+	0.203771i
$970$	−168.000	+	290.985i	−0.173196	+	0.299984i
$971$	1110.00	−	640.859i	1.14315	−	0.659999i	0.195942	−	0.980615i	$-0.437223\pi$
$971$	1110.00	−	640.859i	1.14315	−	0.659999i	0.947209	+	0.320617i	$0.103890\pi$
$972$		0			0
$973$	514.500	−	297.047i	0.528777	−	0.305290i
$974$	134.000			0.137577
$975$	136.500	+	236.425i	0.140000	+	0.242487i
$976$	288.000	+	166.277i	0.295082	+	0.170366i
$977$	−131.000	+	226.899i	−0.134084	+	0.232240i	−0.925247	−	0.379365i	$-0.876143\pi$
$977$	−131.000	+	226.899i	−0.134084	+	0.232240i	0.791163	+	0.611605i	$0.209476\pi$
$978$	174.000	−	100.459i	0.177914	−	0.102719i
$979$			1177.79i			1.20306i
$980$		0			0
$981$	−51.0000			−0.0519878
$982$	−68.0000	−	117.779i	−0.0692464	−	0.119938i
$983$	960.000	+	554.256i	0.976602	+	0.563842i	0.901243	−	0.433315i	$-0.142656\pi$
$983$	960.000	+	554.256i	0.976602	+	0.563842i	0.0753596	+	0.997156i	$0.475990\pi$
$984$	168.000	−	290.985i	0.170732	−	0.295716i
$985$	−300.000	+	173.205i	−0.304569	+	0.175843i
$986$		−	221.703i		−	0.224850i
$987$	−315.000	−	545.596i	−0.319149	−	0.552782i
$988$		0			0
$989$	380.000	+	658.179i	0.384226	+	0.665500i
$990$	180.000	+	103.923i	0.181818	+	0.104973i
$991$	33.5000	−	58.0237i	0.0338042	−	0.0585507i	−0.848628	−	0.528990i	$-0.822571\pi$
$991$	33.5000	−	58.0237i	0.0338042	−	0.0585507i	0.882433	+	0.470439i	$0.155904\pi$
$992$		0			0
$993$			8.66025i			0.00872130i
$994$	−182.000	+	315.233i	−0.183099	+	0.317136i
$995$	696.000			0.699497
$996$		0			0
$997$	−856.500	−	494.501i	−0.859077	−	0.495988i	0.00462594	−	0.999989i	$-0.498528\pi$
$997$	−856.500	−	494.501i	−0.859077	−	0.495988i	−0.863703	+	0.504001i	$0.831861\pi$
$998$	509.000	−	881.614i	0.510020	−	0.883381i
$999$	−22.5000	+	12.9904i	−0.0225225	+	0.0130034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.3.f.c.10.1	✓	2
3.2	odd	2		63.3.m.a.10.1		2
4.3	odd	2		336.3.bh.c.241.1		2
5.2	odd	4		525.3.s.d.199.1		4
5.3	odd	4		525.3.s.d.199.2		4
5.4	even	2		525.3.o.b.451.1		2
7.2	even	3		147.3.f.e.19.1		2
7.3	odd	6		147.3.d.a.97.1		2
7.4	even	3		147.3.d.a.97.2		2
7.5	odd	6	inner	21.3.f.c.19.1	yes	2
7.6	odd	2		147.3.f.e.31.1		2
12.11	even	2		1008.3.cg.f.577.1		2
21.2	odd	6		441.3.m.b.19.1		2
21.5	even	6		63.3.m.a.19.1		2
21.11	odd	6		441.3.d.d.244.2		2
21.17	even	6		441.3.d.d.244.1		2
21.20	even	2		441.3.m.b.325.1		2
28.3	even	6		2352.3.f.b.97.2		2
28.11	odd	6		2352.3.f.b.97.1		2
28.19	even	6		336.3.bh.c.145.1		2
35.12	even	12		525.3.s.d.124.2		4
35.19	odd	6		525.3.o.b.376.1		2
35.33	even	12		525.3.s.d.124.1		4
84.47	odd	6		1008.3.cg.f.145.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.c.10.1	✓	2	1.1	even	1	trivial
21.3.f.c.19.1	yes	2	7.5	odd	6	inner
63.3.m.a.10.1		2	3.2	odd	2
63.3.m.a.19.1		2	21.5	even	6
147.3.d.a.97.1		2	7.3	odd	6
147.3.d.a.97.2		2	7.4	even	3
147.3.f.e.19.1		2	7.2	even	3
147.3.f.e.31.1		2	7.6	odd	2
336.3.bh.c.145.1		2	28.19	even	6
336.3.bh.c.241.1		2	4.3	odd	2
441.3.d.d.244.1		2	21.17	even	6
441.3.d.d.244.2		2	21.11	odd	6
441.3.m.b.19.1		2	21.2	odd	6
441.3.m.b.325.1		2	21.20	even	2
525.3.o.b.376.1		2	35.19	odd	6
525.3.o.b.451.1		2	5.4	even	2
525.3.s.d.124.1		4	35.33	even	12
525.3.s.d.124.2		4	35.12	even	12
525.3.s.d.199.1		4	5.2	odd	4
525.3.s.d.199.2		4	5.3	odd	4
1008.3.cg.f.145.1		2	84.47	odd	6
1008.3.cg.f.577.1		2	12.11	even	2
2352.3.f.b.97.1		2	28.11	odd	6
2352.3.f.b.97.2		2	28.3	even	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-3.00000 + 1.73205i) q^{5} -3.46410i q^{6} +(-3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-6.00000 - 3.46410i) q^{10} +(-5.00000 + 8.66025i) q^{11} +12.1244i q^{13} +(7.00000 - 12.1244i) q^{14} +6.00000 q^{15} +(8.00000 + 13.8564i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(28.5000 - 16.4545i) q^{19} +12.1244i q^{21} -20.0000 q^{22} +(-20.0000 - 34.6410i) q^{23} +(-12.0000 - 6.92820i) q^{24} +(-6.50000 + 11.2583i) q^{25} +(-21.0000 + 12.1244i) q^{26} -5.19615i q^{27} +16.0000 q^{29} +(6.00000 + 10.3923i) q^{30} +(4.50000 + 2.59808i) q^{31} +(15.0000 - 8.66025i) q^{33} -13.8564i q^{34} +(21.0000 + 12.1244i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(57.0000 + 32.9090i) q^{38} +(10.5000 - 18.1865i) q^{39} +(-24.0000 + 13.8564i) q^{40} +24.2487i q^{41} +(-21.0000 + 12.1244i) q^{42} -19.0000 q^{43} +(-9.00000 - 5.19615i) q^{45} +(40.0000 - 69.2820i) q^{46} +(-45.0000 + 25.9808i) q^{47} -27.7128i q^{48} +(-24.5000 + 42.4352i) q^{49} -26.0000 q^{50} +(6.00000 + 10.3923i) q^{51} +(16.0000 - 27.7128i) q^{53} +(9.00000 - 5.19615i) q^{54} -34.6410i q^{55} +(-28.0000 - 48.4974i) q^{56} -57.0000 q^{57} +(16.0000 + 27.7128i) q^{58} +(36.0000 + 20.7846i) q^{59} +(18.0000 - 10.3923i) q^{61} +10.3923i q^{62} +(10.5000 - 18.1865i) q^{63} +64.0000 q^{64} +(-21.0000 - 36.3731i) q^{65} +(30.0000 + 17.3205i) q^{66} +(-29.5000 + 51.0955i) q^{67} +69.2820i q^{69} +48.4974i q^{70} -26.0000 q^{71} +(12.0000 + 20.7846i) q^{72} +(-16.5000 - 9.52628i) q^{73} +(5.00000 - 8.66025i) q^{74} +(19.5000 - 11.2583i) q^{75} +70.0000 q^{77} +42.0000 q^{78} +(-23.5000 - 40.7032i) q^{79} +(-48.0000 - 27.7128i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-42.0000 + 24.2487i) q^{82} -24.2487i q^{83} +24.0000 q^{85} +(-19.0000 - 32.9090i) q^{86} +(-24.0000 - 13.8564i) q^{87} +(-40.0000 + 69.2820i) q^{88} +(102.000 - 58.8897i) q^{89} -20.7846i q^{90} +(73.5000 - 42.4352i) q^{91} +(-4.50000 - 7.79423i) q^{93} +(-90.0000 - 51.9615i) q^{94} +(-57.0000 + 98.7269i) q^{95} -48.4974i q^{97} -98.0000 q^{98} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 6 q^{5} - 7 q^{7} + 16 q^{8} + 3 q^{9} - 12 q^{10} - 10 q^{11} + 14 q^{14} + 12 q^{15} + 16 q^{16} - 12 q^{17} - 6 q^{18} + 57 q^{19} - 40 q^{22} - 40 q^{23} - 24 q^{24} - 13 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 6 * q^5 - 7 * q^7 + 16 * q^8 + 3 * q^9 - 12 * q^10 - 10 * q^11 + 14 * q^14 + 12 * q^15 + 16 * q^16 - 12 * q^17 - 6 * q^18 + 57 * q^19 - 40 * q^22 - 40 * q^23 - 24 * q^24 - 13 * q^25 - 42 * q^26 + 32 * q^29 + 12 * q^30 + 9 * q^31 + 30 * q^33 + 42 * q^35 - 5 * q^37 + 114 * q^38 + 21 * q^39 - 48 * q^40 - 42 * q^42 - 38 * q^43 - 18 * q^45 + 80 * q^46 - 90 * q^47 - 49 * q^49 - 52 * q^50 + 12 * q^51 + 32 * q^53 + 18 * q^54 - 56 * q^56 - 114 * q^57 + 32 * q^58 + 72 * q^59 + 36 * q^61 + 21 * q^63 + 128 * q^64 - 42 * q^65 + 60 * q^66 - 59 * q^67 - 52 * q^71 + 24 * q^72 - 33 * q^73 + 10 * q^74 + 39 * q^75 + 140 * q^77 + 84 * q^78 - 47 * q^79 - 96 * q^80 - 9 * q^81 - 84 * q^82 + 48 * q^85 - 38 * q^86 - 48 * q^87 - 80 * q^88 + 204 * q^89 + 147 * q^91 - 9 * q^93 - 180 * q^94 - 114 * q^95 - 196 * q^98 - 60 * q^99

Introduction

L-functions

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