LMFDB - Embedded newform 102.3.e.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [102,3,Mod(47,102)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(102, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("102.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 102 = 2 \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	102.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.77929869648$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	102.47
Dual form			102.3.e.a.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(-2.12132 + 2.12132i) q^{3} +2.00000 q^{4} +(-4.94975 + 4.94975i) q^{5} +(-3.00000 + 3.00000i) q^{6} +(-5.00000 + 5.00000i) q^{7} +2.82843 q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(-2.12132 + 2.12132i) q^{3} +2.00000 q^{4} +(-4.94975 + 4.94975i) q^{5} +(-3.00000 + 3.00000i) q^{6} +(-5.00000 + 5.00000i) q^{7} +2.82843 q^{8} -9.00000i q^{9} +(-7.00000 + 7.00000i) q^{10} +(3.53553 + 3.53553i) q^{11} +(-4.24264 + 4.24264i) q^{12} +15.0000 q^{13} +(-7.07107 + 7.07107i) q^{14} -21.0000i q^{15} +4.00000 q^{16} +(4.94975 + 16.2635i) q^{17} -12.7279i q^{18} +5.00000i q^{19} +(-9.89949 + 9.89949i) q^{20} -21.2132i q^{21} +(5.00000 + 5.00000i) q^{22} +(-14.8492 - 14.8492i) q^{23} +(-6.00000 + 6.00000i) q^{24} -24.0000i q^{25} +21.2132 q^{26} +(19.0919 + 19.0919i) q^{27} +(-10.0000 + 10.0000i) q^{28} +(28.2843 - 28.2843i) q^{29} -29.6985i q^{30} +(24.0000 + 24.0000i) q^{31} +5.65685 q^{32} -15.0000 q^{33} +(7.00000 + 23.0000i) q^{34} -49.4975i q^{35} -18.0000i q^{36} +(-15.0000 - 15.0000i) q^{37} +7.07107i q^{38} +(-31.8198 + 31.8198i) q^{39} +(-14.0000 + 14.0000i) q^{40} +(-38.8909 - 38.8909i) q^{41} -30.0000i q^{42} +75.0000i q^{43} +(7.07107 + 7.07107i) q^{44} +(44.5477 + 44.5477i) q^{45} +(-21.0000 - 21.0000i) q^{46} +11.3137i q^{47} +(-8.48528 + 8.48528i) q^{48} -1.00000i q^{49} -33.9411i q^{50} +(-45.0000 - 24.0000i) q^{51} +30.0000 q^{52} +67.8823 q^{53} +(27.0000 + 27.0000i) q^{54} -35.0000 q^{55} +(-14.1421 + 14.1421i) q^{56} +(-10.6066 - 10.6066i) q^{57} +(40.0000 - 40.0000i) q^{58} -63.6396 q^{59} -42.0000i q^{60} +(71.0000 - 71.0000i) q^{61} +(33.9411 + 33.9411i) q^{62} +(45.0000 + 45.0000i) q^{63} +8.00000 q^{64} +(-74.2462 + 74.2462i) q^{65} -21.2132 q^{66} -80.0000 q^{67} +(9.89949 + 32.5269i) q^{68} +63.0000 q^{69} -70.0000i q^{70} +(-28.2843 + 28.2843i) q^{71} -25.4558i q^{72} +(80.0000 + 80.0000i) q^{73} +(-21.2132 - 21.2132i) q^{74} +(50.9117 + 50.9117i) q^{75} +10.0000i q^{76} -35.3553 q^{77} +(-45.0000 + 45.0000i) q^{78} +(-11.0000 + 11.0000i) q^{79} +(-19.7990 + 19.7990i) q^{80} -81.0000 q^{81} +(-55.0000 - 55.0000i) q^{82} +124.451 q^{83} -42.4264i q^{84} +(-105.000 - 56.0000i) q^{85} +106.066i q^{86} +120.000i q^{87} +(10.0000 + 10.0000i) q^{88} +21.2132i q^{89} +(63.0000 + 63.0000i) q^{90} +(-75.0000 + 75.0000i) q^{91} +(-29.6985 - 29.6985i) q^{92} -101.823 q^{93} +16.0000i q^{94} +(-24.7487 - 24.7487i) q^{95} +(-12.0000 + 12.0000i) q^{96} +(-80.0000 - 80.0000i) q^{97} -1.41421i q^{98} +(31.8198 - 31.8198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 12 q^{6} - 20 q^{7}+O(q^{10}) $ 4 * q + 8 * q^4 - 12 * q^6 - 20 * q^7	$ 4 q + 8 q^{4} - 12 q^{6} - 20 q^{7} - 28 q^{10} + 60 q^{13} + 16 q^{16} + 20 q^{22} - 24 q^{24} - 40 q^{28} + 96 q^{31} - 60 q^{33} + 28 q^{34} - 60 q^{37} - 56 q^{40} - 84 q^{46} - 180 q^{51} + 120 q^{52} + 108 q^{54} - 140 q^{55} + 160 q^{58} + 284 q^{61} + 180 q^{63} + 32 q^{64} - 320 q^{67} + 252 q^{69} + 320 q^{73} - 180 q^{78} - 44 q^{79} - 324 q^{81} - 220 q^{82} - 420 q^{85} + 40 q^{88} + 252 q^{90} - 300 q^{91} - 48 q^{96} - 320 q^{97}+O(q^{100}) $ 4 * q + 8 * q^4 - 12 * q^6 - 20 * q^7 - 28 * q^10 + 60 * q^13 + 16 * q^16 + 20 * q^22 - 24 * q^24 - 40 * q^28 + 96 * q^31 - 60 * q^33 + 28 * q^34 - 60 * q^37 - 56 * q^40 - 84 * q^46 - 180 * q^51 + 120 * q^52 + 108 * q^54 - 140 * q^55 + 160 * q^58 + 284 * q^61 + 180 * q^63 + 32 * q^64 - 320 * q^67 + 252 * q^69 + 320 * q^73 - 180 * q^78 - 44 * q^79 - 324 * q^81 - 220 * q^82 - 420 * q^85 + 40 * q^88 + 252 * q^90 - 300 * q^91 - 48 * q^96 - 320 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/102\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	−2.12132	+	2.12132i	−0.707107	+	0.707107i
$3$	−2.12132	+	2.12132i	−0.707107	+	0.707107i
$4$	2.00000			0.500000
$5$	−4.94975	+	4.94975i	−0.989949	+	0.989949i	−0.999950	−	0.0100005i	$-0.996817\pi$
$5$	−4.94975	+	4.94975i	−0.989949	+	0.989949i	0.0100005	+	0.999950i	$0.496817\pi$
$6$	−3.00000	+	3.00000i	−0.500000	+	0.500000i
$7$	−5.00000	+	5.00000i	−0.714286	+	0.714286i	−0.967429	−	0.253143i	$-0.918536\pi$
$7$	−5.00000	+	5.00000i	−0.714286	+	0.714286i	0.253143	+	0.967429i	$0.418536\pi$
$8$	2.82843			0.353553
$9$		−	9.00000i		−	1.00000i
$10$	−7.00000	+	7.00000i	−0.700000	+	0.700000i
$11$	3.53553	+	3.53553i	0.321412	+	0.321412i	0.849309	−	0.527897i	$-0.177019\pi$
$11$	3.53553	+	3.53553i	0.321412	+	0.321412i	−0.527897	+	0.849309i	$0.677019\pi$
$12$	−4.24264	+	4.24264i	−0.353553	+	0.353553i
$13$	15.0000			1.15385			0.576923	−	0.816798i	$-0.304253\pi$
$13$	15.0000			1.15385			0.576923	+	0.816798i	$0.304253\pi$
$14$	−7.07107	+	7.07107i	−0.505076	+	0.505076i
$15$		−	21.0000i		−	1.40000i
$16$	4.00000			0.250000
$17$	4.94975	+	16.2635i	0.291162	+	0.956674i
$17$	4.94975	+	16.2635i	0.291162	+	0.956674i
$18$		−	12.7279i		−	0.707107i
$19$			5.00000i			0.263158i	0.991306	+	0.131579i	$0.0420047\pi$
$19$			5.00000i			0.263158i	−0.991306	+	0.131579i	$0.957995\pi$
$20$	−9.89949	+	9.89949i	−0.494975	+	0.494975i
$21$		−	21.2132i		−	1.01015i
$22$	5.00000	+	5.00000i	0.227273	+	0.227273i
$23$	−14.8492	−	14.8492i	−0.645619	−	0.645619i	0.306312	−	0.951931i	$-0.400905\pi$
$23$	−14.8492	−	14.8492i	−0.645619	−	0.645619i	−0.951931	+	0.306312i	$0.900905\pi$
$24$	−6.00000	+	6.00000i	−0.250000	+	0.250000i
$25$		−	24.0000i		−	0.960000i
$26$	21.2132			0.815892
$27$	19.0919	+	19.0919i	0.707107	+	0.707107i
$28$	−10.0000	+	10.0000i	−0.357143	+	0.357143i
$29$	28.2843	−	28.2843i	0.975320	−	0.975320i	−0.0243830	−	0.999703i	$-0.507762\pi$
$29$	28.2843	−	28.2843i	0.975320	−	0.975320i	0.999703	+	0.0243830i	$0.00776212\pi$
$30$		−	29.6985i		−	0.989949i
$31$	24.0000	+	24.0000i	0.774194	+	0.774194i	0.978837	−	0.204643i	$-0.0656034\pi$
$31$	24.0000	+	24.0000i	0.774194	+	0.774194i	−0.204643	+	0.978837i	$0.565603\pi$
$32$	5.65685			0.176777
$33$	−15.0000			−0.454545
$34$	7.00000	+	23.0000i	0.205882	+	0.676471i
$35$		−	49.4975i		−	1.41421i
$36$		−	18.0000i		−	0.500000i
$37$	−15.0000	−	15.0000i	−0.405405	−	0.405405i	0.474727	−	0.880133i	$-0.342547\pi$
$37$	−15.0000	−	15.0000i	−0.405405	−	0.405405i	−0.880133	+	0.474727i	$0.842547\pi$
$38$			7.07107i			0.186081i
$39$	−31.8198	+	31.8198i	−0.815892	+	0.815892i
$40$	−14.0000	+	14.0000i	−0.350000	+	0.350000i
$41$	−38.8909	−	38.8909i	−0.948558	−	0.948558i	0.0501822	−	0.998740i	$-0.484020\pi$
$41$	−38.8909	−	38.8909i	−0.948558	−	0.948558i	−0.998740	+	0.0501822i	$0.984020\pi$
$42$		−	30.0000i		−	0.714286i
$43$			75.0000i			1.74419i	0.489340	+	0.872093i	$0.337238\pi$
$43$			75.0000i			1.74419i	−0.489340	+	0.872093i	$0.662762\pi$
$44$	7.07107	+	7.07107i	0.160706	+	0.160706i
$45$	44.5477	+	44.5477i	0.989949	+	0.989949i
$46$	−21.0000	−	21.0000i	−0.456522	−	0.456522i
$47$			11.3137i			0.240717i	0.992730	+	0.120359i	$0.0384044\pi$
$47$			11.3137i			0.240717i	−0.992730	+	0.120359i	$0.961596\pi$
$48$	−8.48528	+	8.48528i	−0.176777	+	0.176777i
$49$		−	1.00000i		−	0.0204082i
$50$		−	33.9411i		−	0.678823i
$51$	−45.0000	−	24.0000i	−0.882353	−	0.470588i
$52$	30.0000			0.576923
$53$	67.8823			1.28080			0.640399	−	0.768043i	$-0.278769\pi$
$53$	67.8823			1.28080			0.640399	+	0.768043i	$0.278769\pi$
$54$	27.0000	+	27.0000i	0.500000	+	0.500000i
$55$	−35.0000			−0.636364
$56$	−14.1421	+	14.1421i	−0.252538	+	0.252538i
$57$	−10.6066	−	10.6066i	−0.186081	−	0.186081i
$58$	40.0000	−	40.0000i	0.689655	−	0.689655i
$59$	−63.6396			−1.07864			−0.539319	−	0.842102i	$-0.681318\pi$
$59$	−63.6396			−1.07864			−0.539319	+	0.842102i	$0.681318\pi$
$60$		−	42.0000i		−	0.700000i
$61$	71.0000	−	71.0000i	1.16393	−	1.16393i	0.180328	−	0.983607i	$-0.442284\pi$
$61$	71.0000	−	71.0000i	1.16393	−	1.16393i	0.983607	−	0.180328i	$-0.0577159\pi$
$62$	33.9411	+	33.9411i	0.547438	+	0.547438i
$63$	45.0000	+	45.0000i	0.714286	+	0.714286i
$64$	8.00000			0.125000
$65$	−74.2462	+	74.2462i	−1.14225	+	1.14225i
$66$	−21.2132			−0.321412
$67$	−80.0000			−1.19403			−0.597015	−	0.802230i	$-0.703647\pi$
$67$	−80.0000			−1.19403			−0.597015	+	0.802230i	$0.703647\pi$
$68$	9.89949	+	32.5269i	0.145581	+	0.478337i
$69$	63.0000			0.913043
$70$		−	70.0000i		−	1.00000i
$71$	−28.2843	+	28.2843i	−0.398370	+	0.398370i	−0.877658	−	0.479288i	$-0.840895\pi$
$71$	−28.2843	+	28.2843i	−0.398370	+	0.398370i	0.479288	+	0.877658i	$0.340895\pi$
$72$		−	25.4558i		−	0.353553i
$73$	80.0000	+	80.0000i	1.09589	+	1.09589i	0.994886	+	0.101004i	$0.0322056\pi$
$73$	80.0000	+	80.0000i	1.09589	+	1.09589i	0.101004	+	0.994886i	$0.467794\pi$
$74$	−21.2132	−	21.2132i	−0.286665	−	0.286665i
$75$	50.9117	+	50.9117i	0.678823	+	0.678823i
$76$			10.0000i			0.131579i
$77$	−35.3553			−0.459160
$78$	−45.0000	+	45.0000i	−0.576923	+	0.576923i
$79$	−11.0000	+	11.0000i	−0.139241	+	0.139241i	−0.773291	−	0.634051i	$-0.781391\pi$
$79$	−11.0000	+	11.0000i	−0.139241	+	0.139241i	0.634051	+	0.773291i	$0.281391\pi$
$80$	−19.7990	+	19.7990i	−0.247487	+	0.247487i
$81$	−81.0000			−1.00000
$82$	−55.0000	−	55.0000i	−0.670732	−	0.670732i
$83$	124.451			1.49941			0.749704	−	0.661774i	$-0.230196\pi$
$83$	124.451			1.49941			0.749704	+	0.661774i	$0.230196\pi$
$84$		−	42.4264i		−	0.505076i
$85$	−105.000	−	56.0000i	−1.23529	−	0.658824i
$86$			106.066i			1.23333i
$87$			120.000i			1.37931i
$88$	10.0000	+	10.0000i	0.113636	+	0.113636i
$89$			21.2132i			0.238351i	0.992873	+	0.119175i	$0.0380251\pi$
$89$			21.2132i			0.238351i	−0.992873	+	0.119175i	$0.961975\pi$
$90$	63.0000	+	63.0000i	0.700000	+	0.700000i
$91$	−75.0000	+	75.0000i	−0.824176	+	0.824176i
$92$	−29.6985	−	29.6985i	−0.322810	−	0.322810i
$93$	−101.823			−1.09488
$94$			16.0000i			0.170213i
$95$	−24.7487	−	24.7487i	−0.260513	−	0.260513i
$96$	−12.0000	+	12.0000i	−0.125000	+	0.125000i
$97$	−80.0000	−	80.0000i	−0.824742	−	0.824742i	0.162042	−	0.986784i	$-0.448192\pi$
$97$	−80.0000	−	80.0000i	−0.824742	−	0.824742i	−0.986784	+	0.162042i	$0.948192\pi$
$98$		−	1.41421i		−	0.0144308i
$99$	31.8198	−	31.8198i	0.321412	−	0.321412i
$100$		−	48.0000i		−	0.480000i
$101$		−	56.5685i		−	0.560085i	−0.959988	−	0.280042i	$-0.909652\pi$
$101$		−	56.5685i		−	0.560085i	0.959988	−	0.280042i	$-0.0903485\pi$
$102$	−63.6396	−	33.9411i	−0.623918	−	0.332756i
$103$	−5.00000			−0.0485437			−0.0242718	−	0.999705i	$-0.507727\pi$
$103$	−5.00000			−0.0485437			−0.0242718	+	0.999705i	$0.507727\pi$
$104$	42.4264			0.407946
$105$	105.000	+	105.000i	1.00000	+	1.00000i
$106$	96.0000			0.905660
$107$	144.957	−	144.957i	1.35474	−	1.35474i	0.474460	−	0.880277i	$-0.342643\pi$
$107$	144.957	−	144.957i	1.35474	−	1.35474i	0.880277	−	0.474460i	$-0.157357\pi$
$108$	38.1838	+	38.1838i	0.353553	+	0.353553i
$109$	104.000	−	104.000i	0.954128	−	0.954128i	−0.0448646	−	0.998993i	$-0.514286\pi$
$109$	104.000	−	104.000i	0.954128	−	0.954128i	0.998993	+	0.0448646i	$0.0142857\pi$
$110$	−49.4975			−0.449977
$111$	63.6396			0.573330
$112$	−20.0000	+	20.0000i	−0.178571	+	0.178571i
$113$	45.9619	+	45.9619i	0.406743	+	0.406743i	0.880601	−	0.473858i	$-0.157139\pi$
$113$	45.9619	+	45.9619i	0.406743	+	0.406743i	−0.473858	+	0.880601i	$0.657139\pi$
$114$	−15.0000	−	15.0000i	−0.131579	−	0.131579i
$115$	147.000			1.27826
$116$	56.5685	−	56.5685i	0.487660	−	0.487660i
$117$		−	135.000i		−	1.15385i
$118$	−90.0000			−0.762712
$119$	−106.066	−	56.5685i	−0.891311	−	0.475366i
$120$		−	59.3970i		−	0.494975i
$121$		−	96.0000i		−	0.793388i
$122$	100.409	−	100.409i	0.823026	−	0.823026i
$123$	165.000			1.34146
$124$	48.0000	+	48.0000i	0.387097	+	0.387097i
$125$	−4.94975	−	4.94975i	−0.0395980	−	0.0395980i
$126$	63.6396	+	63.6396i	0.505076	+	0.505076i
$127$		−	125.000i		−	0.984252i	−0.870524	−	0.492126i	$-0.836220\pi$
$127$		−	125.000i		−	0.984252i	0.870524	−	0.492126i	$-0.163780\pi$
$128$	11.3137			0.0883883
$129$	−159.099	−	159.099i	−1.23333	−	1.23333i
$130$	−105.000	+	105.000i	−0.807692	+	0.807692i
$131$	−3.53553	+	3.53553i	−0.0269888	+	0.0269888i	−0.720472	−	0.693484i	$-0.756075\pi$
$131$	−3.53553	+	3.53553i	−0.0269888	+	0.0269888i	0.693484	+	0.720472i	$0.256075\pi$
$132$	−30.0000			−0.227273
$133$	−25.0000	−	25.0000i	−0.187970	−	0.187970i
$134$	−113.137			−0.844307
$135$	−189.000			−1.40000
$136$	14.0000	+	46.0000i	0.102941	+	0.338235i
$137$			123.037i			0.898077i	0.893512	+	0.449039i	$0.148233\pi$
$137$			123.037i			0.898077i	−0.893512	+	0.449039i	$0.851767\pi$
$138$	89.0955			0.645619
$139$	−19.0000	−	19.0000i	−0.136691	−	0.136691i	0.635451	−	0.772141i	$-0.280814\pi$
$139$	−19.0000	−	19.0000i	−0.136691	−	0.136691i	−0.772141	+	0.635451i	$0.780814\pi$
$140$		−	98.9949i		−	0.707107i
$141$	−24.0000	−	24.0000i	−0.170213	−	0.170213i
$142$	−40.0000	+	40.0000i	−0.281690	+	0.281690i
$143$	53.0330	+	53.0330i	0.370860	+	0.370860i
$144$		−	36.0000i		−	0.250000i
$145$			280.000i			1.93103i
$146$	113.137	+	113.137i	0.774912	+	0.774912i
$147$	2.12132	+	2.12132i	0.0144308	+	0.0144308i
$148$	−30.0000	−	30.0000i	−0.202703	−	0.202703i
$149$			77.7817i			0.522025i	0.965335	+	0.261013i	$0.0840564\pi$
$149$			77.7817i			0.522025i	−0.965335	+	0.261013i	$0.915944\pi$
$150$	72.0000	+	72.0000i	0.480000	+	0.480000i
$151$		−	248.000i		−	1.64238i	−0.570652	−	0.821192i	$-0.693309\pi$
$151$		−	248.000i		−	1.64238i	0.570652	−	0.821192i	$-0.306691\pi$
$152$			14.1421i			0.0930404i
$153$	146.371	−	44.5477i	0.956674	−	0.291162i
$154$	−50.0000			−0.324675
$155$	−237.588			−1.53283
$156$	−63.6396	+	63.6396i	−0.407946	+	0.407946i
$157$	−55.0000			−0.350318			−0.175159	−	0.984540i	$-0.556044\pi$
$157$	−55.0000			−0.350318			−0.175159	+	0.984540i	$0.556044\pi$
$158$	−15.5563	+	15.5563i	−0.0984579	+	0.0984579i
$159$	−144.000	+	144.000i	−0.905660	+	0.905660i
$160$	−28.0000	+	28.0000i	−0.175000	+	0.175000i
$161$	148.492			0.922313
$162$	−114.551			−0.707107
$163$	120.000	−	120.000i	0.736196	−	0.736196i	−0.235643	−	0.971840i	$-0.575720\pi$
$163$	120.000	−	120.000i	0.736196	−	0.736196i	0.971840	+	0.235643i	$0.0757197\pi$
$164$	−77.7817	−	77.7817i	−0.474279	−	0.474279i
$165$	74.2462	−	74.2462i	0.449977	−	0.449977i
$166$	176.000			1.06024
$167$	−81.3173	+	81.3173i	−0.486930	+	0.486930i	−0.907336	−	0.420406i	$-0.861888\pi$
$167$	−81.3173	+	81.3173i	−0.486930	+	0.486930i	0.420406	+	0.907336i	$0.361888\pi$
$168$		−	60.0000i		−	0.357143i
$169$	56.0000			0.331361
$170$	−148.492	−	79.1960i	−0.873485	−	0.465859i
$171$	45.0000			0.263158
$172$			150.000i			0.872093i
$173$	−17.6777	+	17.6777i	−0.102183	+	0.102183i	−0.756350	−	0.654167i	$-0.773019\pi$
$173$	−17.6777	+	17.6777i	−0.102183	+	0.102183i	0.654167	+	0.756350i	$0.273019\pi$
$174$			169.706i			0.975320i
$175$	120.000	+	120.000i	0.685714	+	0.685714i
$176$	14.1421	+	14.1421i	0.0803530	+	0.0803530i
$177$	135.000	−	135.000i	0.762712	−	0.762712i
$178$			30.0000i			0.168539i
$179$	56.5685			0.316025			0.158013	−	0.987437i	$-0.449491\pi$
$179$	56.5685			0.316025			0.158013	+	0.987437i	$0.449491\pi$
$180$	89.0955	+	89.0955i	0.494975	+	0.494975i
$181$	−79.0000	+	79.0000i	−0.436464	+	0.436464i	−0.890820	−	0.454356i	$-0.849869\pi$
$181$	−79.0000	+	79.0000i	−0.436464	+	0.436464i	0.454356	+	0.890820i	$0.349869\pi$
$182$	−106.066	+	106.066i	−0.582780	+	0.582780i
$183$			301.227i			1.64605i
$184$	−42.0000	−	42.0000i	−0.228261	−	0.228261i
$185$	148.492			0.802662
$186$	−144.000			−0.774194
$187$	−40.0000	+	75.0000i	−0.213904	+	0.401070i
$188$			22.6274i			0.120359i
$189$	−190.919			−1.01015
$190$	−35.0000	−	35.0000i	−0.184211	−	0.184211i
$191$		−	63.6396i		−	0.333192i	−0.986025	−	0.166596i	$-0.946722\pi$
$191$		−	63.6396i		−	0.333192i	0.986025	−	0.166596i	$-0.0532775\pi$
$192$	−16.9706	+	16.9706i	−0.0883883	+	0.0883883i
$193$	−240.000	+	240.000i	−1.24352	+	1.24352i	−0.284994	+	0.958529i	$0.591992\pi$
$193$	−240.000	+	240.000i	−1.24352	+	1.24352i	−0.958529	+	0.284994i	$0.908008\pi$
$194$	−113.137	−	113.137i	−0.583181	−	0.583181i
$195$		−	315.000i		−	1.61538i
$196$		−	2.00000i		−	0.0102041i
$197$	57.2756	+	57.2756i	0.290739	+	0.290739i	0.837372	−	0.546633i	$-0.184091\pi$
$197$	57.2756	+	57.2756i	0.290739	+	0.290739i	−0.546633	+	0.837372i	$0.684091\pi$
$198$	45.0000	−	45.0000i	0.227273	−	0.227273i
$199$	104.000	+	104.000i	0.522613	+	0.522613i	0.918360	−	0.395747i	$-0.129514\pi$
$199$	104.000	+	104.000i	0.522613	+	0.522613i	−0.395747	+	0.918360i	$0.629514\pi$
$200$		−	67.8823i		−	0.339411i
$201$	169.706	−	169.706i	0.844307	−	0.844307i
$202$		−	80.0000i		−	0.396040i
$203$			282.843i			1.39331i
$204$	−90.0000	−	48.0000i	−0.441176	−	0.235294i
$205$	385.000			1.87805
$206$	−7.07107			−0.0343256
$207$	−133.643	+	133.643i	−0.645619	+	0.645619i
$208$	60.0000			0.288462
$209$	−17.6777	+	17.6777i	−0.0845822	+	0.0845822i
$210$	148.492	+	148.492i	0.707107	+	0.707107i
$211$	−216.000	+	216.000i	−1.02370	+	1.02370i	−0.0239843	+	0.999712i	$0.507635\pi$
$211$	−216.000	+	216.000i	−1.02370	+	1.02370i	−0.999712	+	0.0239843i	$0.992365\pi$
$212$	135.765			0.640399
$213$		−	120.000i		−	0.563380i
$214$	205.000	−	205.000i	0.957944	−	0.957944i
$215$	−371.231	−	371.231i	−1.72666	−	1.72666i
$216$	54.0000	+	54.0000i	0.250000	+	0.250000i
$217$	−240.000			−1.10599
$218$	147.078	−	147.078i	0.674671	−	0.674671i
$219$	−339.411			−1.54982
$220$	−70.0000			−0.318182
$221$	74.2462	+	243.952i	0.335956	+	1.10385i
$222$	90.0000			0.405405
$223$		−	155.000i		−	0.695067i	−0.937668	−	0.347534i	$-0.887019\pi$
$223$		−	155.000i		−	0.695067i	0.937668	−	0.347534i	$-0.112981\pi$
$224$	−28.2843	+	28.2843i	−0.126269	+	0.126269i
$225$	−216.000			−0.960000
$226$	65.0000	+	65.0000i	0.287611	+	0.287611i
$227$	109.602	+	109.602i	0.482826	+	0.482826i	0.906033	−	0.423207i	$-0.139096\pi$
$227$	109.602	+	109.602i	0.482826	+	0.482826i	−0.423207	+	0.906033i	$0.639096\pi$
$228$	−21.2132	−	21.2132i	−0.0930404	−	0.0930404i
$229$			40.0000i			0.174672i	0.996179	+	0.0873362i	$0.0278355\pi$
$229$			40.0000i			0.174672i	−0.996179	+	0.0873362i	$0.972165\pi$
$230$	207.889			0.903867
$231$	75.0000	−	75.0000i	0.324675	−	0.324675i
$232$	80.0000	−	80.0000i	0.344828	−	0.344828i
$233$	112.430	−	112.430i	0.482532	−	0.482532i	−0.423407	−	0.905939i	$-0.639166\pi$
$233$	112.430	−	112.430i	0.482532	−	0.482532i	0.905939	+	0.423407i	$0.139166\pi$
$234$		−	190.919i		−	0.815892i
$235$	−56.0000	−	56.0000i	−0.238298	−	0.238298i
$236$	−127.279			−0.539319
$237$		−	46.6690i		−	0.196916i
$238$	−150.000	−	80.0000i	−0.630252	−	0.336134i
$239$		−	282.843i		−	1.18344i	−0.806143	−	0.591721i	$-0.798449\pi$
$239$		−	282.843i		−	1.18344i	0.806143	−	0.591721i	$-0.201551\pi$
$240$		−	84.0000i		−	0.350000i
$241$	279.000	+	279.000i	1.15768	+	1.15768i	0.984974	+	0.172702i	$0.0552498\pi$
$241$	279.000	+	279.000i	1.15768	+	1.15768i	0.172702	+	0.984974i	$0.444750\pi$
$242$		−	135.765i		−	0.561010i
$243$	171.827	−	171.827i	0.707107	−	0.707107i
$244$	142.000	−	142.000i	0.581967	−	0.581967i
$245$	4.94975	+	4.94975i	0.0202031	+	0.0202031i
$246$	233.345			0.948558
$247$			75.0000i			0.303644i
$248$	67.8823	+	67.8823i	0.273719	+	0.273719i
$249$	−264.000	+	264.000i	−1.06024	+	1.06024i
$250$	−7.00000	−	7.00000i	−0.0280000	−	0.0280000i
$251$			63.6396i			0.253544i	0.991932	+	0.126772i	$0.0404617\pi$
$251$			63.6396i			0.253544i	−0.991932	+	0.126772i	$0.959538\pi$
$252$	90.0000	+	90.0000i	0.357143	+	0.357143i
$253$		−	105.000i		−	0.415020i
$254$		−	176.777i		−	0.695971i
$255$	341.533	−	103.945i	1.33934	−	0.407626i
$256$	16.0000			0.0625000
$257$	−159.806			−0.621814			−0.310907	−	0.950440i	$-0.600633\pi$
$257$	−159.806			−0.621814			−0.310907	+	0.950440i	$0.600633\pi$
$258$	−225.000	−	225.000i	−0.872093	−	0.872093i
$259$	150.000			0.579151
$260$	−148.492	+	148.492i	−0.571125	+	0.571125i
$261$	−254.558	−	254.558i	−0.975320	−	0.975320i
$262$	−5.00000	+	5.00000i	−0.0190840	+	0.0190840i
$263$	391.737			1.48949			0.744747	−	0.667346i	$-0.232570\pi$
$263$	391.737			1.48949			0.744747	+	0.667346i	$0.232570\pi$
$264$	−42.4264			−0.160706
$265$	−336.000	+	336.000i	−1.26792	+	1.26792i
$266$	−35.3553	−	35.3553i	−0.132915	−	0.132915i
$267$	−45.0000	−	45.0000i	−0.168539	−	0.168539i
$268$	−160.000			−0.597015
$269$	−130.815	+	130.815i	−0.486300	+	0.486300i	−0.907137	−	0.420836i	$-0.861737\pi$
$269$	−130.815	+	130.815i	−0.486300	+	0.486300i	0.420836	+	0.907137i	$0.361737\pi$
$270$	−267.286			−0.989949
$271$	−115.000			−0.424354			−0.212177	−	0.977231i	$-0.568055\pi$
$271$	−115.000			−0.424354			−0.212177	+	0.977231i	$0.568055\pi$
$272$	19.7990	+	65.0538i	0.0727904	+	0.239168i
$273$		−	318.198i		−	1.16556i
$274$			174.000i			0.635036i
$275$	84.8528	−	84.8528i	0.308556	−	0.308556i
$276$	126.000			0.456522
$277$	280.000	+	280.000i	1.01083	+	1.01083i	0.999941	+	0.0108896i	$0.00346634\pi$
$277$	280.000	+	280.000i	1.01083	+	1.01083i	0.0108896	+	0.999941i	$0.496534\pi$
$278$	−26.8701	−	26.8701i	−0.0966549	−	0.0966549i
$279$	216.000	−	216.000i	0.774194	−	0.774194i
$280$		−	140.000i		−	0.500000i
$281$	−35.3553			−0.125820			−0.0629099	−	0.998019i	$-0.520038\pi$
$281$	−35.3553			−0.125820			−0.0629099	+	0.998019i	$0.520038\pi$
$282$	−33.9411	−	33.9411i	−0.120359	−	0.120359i
$283$	155.000	−	155.000i	0.547703	−	0.547703i	−0.378073	−	0.925776i	$-0.623413\pi$
$283$	155.000	−	155.000i	0.547703	−	0.547703i	0.925776	+	0.378073i	$0.123413\pi$
$284$	−56.5685	+	56.5685i	−0.199185	+	0.199185i
$285$	105.000			0.368421
$286$	75.0000	+	75.0000i	0.262238	+	0.262238i
$287$	388.909			1.35508
$288$		−	50.9117i		−	0.176777i
$289$	−240.000	+	161.000i	−0.830450	+	0.557093i
$290$			395.980i			1.36545i
$291$	339.411			1.16636
$292$	160.000	+	160.000i	0.547945	+	0.547945i
$293$			46.6690i			0.159280i	0.996824	+	0.0796400i	$0.0253771\pi$
$293$			46.6690i			0.159280i	−0.996824	+	0.0796400i	$0.974623\pi$
$294$	3.00000	+	3.00000i	0.0102041	+	0.0102041i
$295$	315.000	−	315.000i	1.06780	−	1.06780i
$296$	−42.4264	−	42.4264i	−0.143332	−	0.143332i
$297$			135.000i			0.454545i
$298$			110.000i			0.369128i
$299$	−222.739	−	222.739i	−0.744945	−	0.744945i
$300$	101.823	+	101.823i	0.339411	+	0.339411i
$301$	−375.000	−	375.000i	−1.24585	−	1.24585i
$302$		−	350.725i		−	1.16134i
$303$	120.000	+	120.000i	0.396040	+	0.396040i
$304$			20.0000i			0.0657895i
$305$			702.864i			2.30447i
$306$	207.000	−	63.0000i	0.676471	−	0.205882i
$307$	−320.000			−1.04235			−0.521173	−	0.853451i	$-0.674505\pi$
$307$	−320.000			−1.04235			−0.521173	+	0.853451i	$0.674505\pi$
$308$	−70.7107			−0.229580
$309$	10.6066	−	10.6066i	0.0343256	−	0.0343256i
$310$	−336.000			−1.08387
$311$	−84.8528	+	84.8528i	−0.272839	+	0.272839i	−0.830242	−	0.557403i	$-0.811798\pi$
$311$	−84.8528	+	84.8528i	−0.272839	+	0.272839i	0.557403	+	0.830242i	$0.311798\pi$
$312$	−90.0000	+	90.0000i	−0.288462	+	0.288462i
$313$	160.000	−	160.000i	0.511182	−	0.511182i	−0.403706	−	0.914889i	$-0.632278\pi$
$313$	160.000	−	160.000i	0.511182	−	0.511182i	0.914889	+	0.403706i	$0.132278\pi$
$314$	−77.7817			−0.247713
$315$	−445.477			−1.41421
$316$	−22.0000	+	22.0000i	−0.0696203	+	0.0696203i
$317$	−141.421	−	141.421i	−0.446124	−	0.446124i	0.447940	−	0.894064i	$-0.352158\pi$
$317$	−141.421	−	141.421i	−0.446124	−	0.446124i	−0.894064	+	0.447940i	$0.852158\pi$
$318$	−203.647	+	203.647i	−0.640399	+	0.640399i
$319$	200.000			0.626959
$320$	−39.5980	+	39.5980i	−0.123744	+	0.123744i
$321$			615.000i			1.91589i
$322$	210.000			0.652174
$323$	−81.3173	+	24.7487i	−0.251756	+	0.0766215i
$324$	−162.000			−0.500000
$325$		−	360.000i		−	1.10769i
$326$	169.706	−	169.706i	0.520569	−	0.520569i
$327$			441.235i			1.34934i
$328$	−110.000	−	110.000i	−0.335366	−	0.335366i
$329$	−56.5685	−	56.5685i	−0.171941	−	0.171941i
$330$	105.000	−	105.000i	0.318182	−	0.318182i
$331$			45.0000i			0.135952i	0.997687	+	0.0679758i	$0.0216541\pi$
$331$			45.0000i			0.135952i	−0.997687	+	0.0679758i	$0.978346\pi$
$332$	248.902			0.749704
$333$	−135.000	+	135.000i	−0.405405	+	0.405405i
$334$	−115.000	+	115.000i	−0.344311	+	0.344311i
$335$	395.980	−	395.980i	1.18203	−	1.18203i
$336$		−	84.8528i		−	0.252538i
$337$	−95.0000	−	95.0000i	−0.281899	−	0.281899i	0.551967	−	0.833866i	$-0.313877\pi$
$337$	−95.0000	−	95.0000i	−0.281899	−	0.281899i	−0.833866	+	0.551967i	$0.813877\pi$
$338$	79.1960			0.234308
$339$	−195.000			−0.575221
$340$	−210.000	−	112.000i	−0.617647	−	0.329412i
$341$			169.706i			0.497670i
$342$	63.6396			0.186081
$343$	−240.000	−	240.000i	−0.699708	−	0.699708i
$344$			212.132i			0.616663i
$345$	−311.834	+	311.834i	−0.903867	+	0.903867i
$346$	−25.0000	+	25.0000i	−0.0722543	+	0.0722543i
$347$	−113.137	−	113.137i	−0.326043	−	0.326043i	0.525036	−	0.851080i	$-0.324052\pi$
$347$	−113.137	−	113.137i	−0.326043	−	0.326043i	−0.851080	+	0.525036i	$0.824052\pi$
$348$			240.000i			0.689655i
$349$		−	473.000i		−	1.35530i	−0.735384	−	0.677650i	$-0.762998\pi$
$349$		−	473.000i		−	1.35530i	0.735384	−	0.677650i	$-0.237002\pi$
$350$	169.706	+	169.706i	0.484873	+	0.484873i
$351$	286.378	+	286.378i	0.815892	+	0.815892i
$352$	20.0000	+	20.0000i	0.0568182	+	0.0568182i
$353$			9.89949i			0.0280439i	0.999902	+	0.0140219i	$0.00446347\pi$
$353$			9.89949i			0.0280439i	−0.999902	+	0.0140219i	$0.995537\pi$
$354$	190.919	−	190.919i	0.539319	−	0.539319i
$355$		−	280.000i		−	0.788732i
$356$			42.4264i			0.119175i
$357$	345.000	−	105.000i	0.966387	−	0.294118i
$358$	80.0000			0.223464
$359$	−120.208			−0.334842			−0.167421	−	0.985886i	$-0.553544\pi$
$359$	−120.208			−0.334842			−0.167421	+	0.985886i	$0.553544\pi$
$360$	126.000	+	126.000i	0.350000	+	0.350000i
$361$	336.000			0.930748
$362$	−111.723	+	111.723i	−0.308627	+	0.308627i
$363$	203.647	+	203.647i	0.561010	+	0.561010i
$364$	−150.000	+	150.000i	−0.412088	+	0.412088i
$365$	−791.960			−2.16975
$366$			426.000i			1.16393i
$367$	−75.0000	+	75.0000i	−0.204360	+	0.204360i	−0.801865	−	0.597505i	$-0.796159\pi$
$367$	−75.0000	+	75.0000i	−0.204360	+	0.204360i	0.597505	+	0.801865i	$0.296159\pi$
$368$	−59.3970	−	59.3970i	−0.161405	−	0.161405i
$369$	−350.018	+	350.018i	−0.948558	+	0.948558i
$370$	210.000			0.567568
$371$	−339.411	+	339.411i	−0.914855	+	0.914855i
$372$	−203.647			−0.547438
$373$	440.000			1.17962			0.589812	−	0.807540i	$-0.299202\pi$
$373$	440.000			1.17962			0.589812	+	0.807540i	$0.299202\pi$
$374$	−56.5685	+	106.066i	−0.151253	+	0.283599i
$375$	21.0000			0.0560000
$376$			32.0000i			0.0851064i
$377$	424.264	−	424.264i	1.12537	−	1.12537i
$378$	−270.000			−0.714286
$379$	−171.000	−	171.000i	−0.451187	−	0.451187i	0.444561	−	0.895748i	$-0.353360\pi$
$379$	−171.000	−	171.000i	−0.451187	−	0.451187i	−0.895748	+	0.444561i	$0.853360\pi$
$380$	−49.4975	−	49.4975i	−0.130257	−	0.130257i
$381$	265.165	+	265.165i	0.695971	+	0.695971i
$382$		−	90.0000i		−	0.235602i
$383$	−497.803			−1.29975			−0.649874	−	0.760042i	$-0.725178\pi$
$383$	−497.803			−1.29975			−0.649874	+	0.760042i	$0.725178\pi$
$384$	−24.0000	+	24.0000i	−0.0625000	+	0.0625000i
$385$	175.000	−	175.000i	0.454545	−	0.454545i
$386$	−339.411	+	339.411i	−0.879304	+	0.879304i
$387$	675.000			1.74419
$388$	−160.000	−	160.000i	−0.412371	−	0.412371i
$389$	700.036			1.79958			0.899789	−	0.436326i	$-0.143720\pi$
$389$	700.036			1.79958			0.899789	+	0.436326i	$0.143720\pi$
$390$		−	445.477i		−	1.14225i
$391$	168.000	−	315.000i	0.429668	−	0.805627i
$392$		−	2.82843i		−	0.00721538i
$393$		−	15.0000i		−	0.0381679i
$394$	81.0000	+	81.0000i	0.205584	+	0.205584i
$395$		−	108.894i		−	0.275682i
$396$	63.6396	−	63.6396i	0.160706	−	0.160706i
$397$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$397$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$398$	147.078	+	147.078i	0.369543	+	0.369543i
$399$	106.066			0.265830
$400$		−	96.0000i		−	0.240000i
$401$	−321.734	−	321.734i	−0.802328	−	0.802328i	0.181131	−	0.983459i	$-0.442024\pi$
$401$	−321.734	−	321.734i	−0.802328	−	0.802328i	−0.983459	+	0.181131i	$0.942024\pi$
$402$	240.000	−	240.000i	0.597015	−	0.597015i
$403$	360.000	+	360.000i	0.893300	+	0.893300i
$404$		−	113.137i		−	0.280042i
$405$	400.930	−	400.930i	0.989949	−	0.989949i
$406$			400.000i			0.985222i
$407$		−	106.066i		−	0.260604i
$408$	−127.279	−	67.8823i	−0.311959	−	0.166378i
$409$	−345.000			−0.843521			−0.421760	−	0.906707i	$-0.638588\pi$
$409$	−345.000			−0.843521			−0.421760	+	0.906707i	$0.638588\pi$
$410$	544.472			1.32798
$411$	−261.000	−	261.000i	−0.635036	−	0.635036i
$412$	−10.0000			−0.0242718
$413$	318.198	−	318.198i	0.770455	−	0.770455i
$414$	−189.000	+	189.000i	−0.456522	+	0.456522i
$415$	−616.000	+	616.000i	−1.48434	+	1.48434i
$416$	84.8528			0.203973
$417$	80.6102			0.193310
$418$	−25.0000	+	25.0000i	−0.0598086	+	0.0598086i
$419$	226.274	+	226.274i	0.540034	+	0.540034i	0.923539	−	0.383505i	$-0.125283\pi$
$419$	226.274	+	226.274i	0.540034	+	0.540034i	−0.383505	+	0.923539i	$0.625283\pi$
$420$	210.000	+	210.000i	0.500000	+	0.500000i
$421$	−695.000			−1.65083			−0.825416	−	0.564525i	$-0.809059\pi$
$421$	−695.000			−1.65083			−0.825416	+	0.564525i	$0.809059\pi$
$422$	−305.470	+	305.470i	−0.723863	+	0.723863i
$423$	101.823			0.240717
$424$	192.000			0.452830
$425$	390.323	−	118.794i	0.918407	−	0.279515i
$426$		−	169.706i		−	0.398370i
$427$			710.000i			1.66276i
$428$	289.914	−	289.914i	0.677369	−	0.677369i
$429$	−225.000			−0.524476
$430$	−525.000	−	525.000i	−1.22093	−	1.22093i
$431$	−197.990	−	197.990i	−0.459373	−	0.459373i	0.439076	−	0.898450i	$-0.355306\pi$
$431$	−197.990	−	197.990i	−0.459373	−	0.459373i	−0.898450	+	0.439076i	$0.855306\pi$
$432$	76.3675	+	76.3675i	0.176777	+	0.176777i
$433$			305.000i			0.704388i	0.935927	+	0.352194i	$0.114564\pi$
$433$			305.000i			0.704388i	−0.935927	+	0.352194i	$0.885436\pi$
$434$	−339.411			−0.782054
$435$	−593.970	−	593.970i	−1.36545	−	1.36545i
$436$	208.000	−	208.000i	0.477064	−	0.477064i
$437$	74.2462	−	74.2462i	0.169900	−	0.169900i
$438$	−480.000			−1.09589
$439$	−64.0000	−	64.0000i	−0.145786	−	0.145786i	0.630447	−	0.776233i	$-0.282872\pi$
$439$	−64.0000	−	64.0000i	−0.145786	−	0.145786i	−0.776233	+	0.630447i	$0.782872\pi$
$440$	−98.9949			−0.224989
$441$	−9.00000			−0.0204082
$442$	105.000	+	345.000i	0.237557	+	0.780543i
$443$			441.235i			0.996015i	0.867173	+	0.498007i	$0.165935\pi$
$443$			441.235i			0.996015i	−0.867173	+	0.498007i	$0.834065\pi$
$444$	127.279			0.286665
$445$	−105.000	−	105.000i	−0.235955	−	0.235955i
$446$		−	219.203i		−	0.491487i
$447$	−165.000	−	165.000i	−0.369128	−	0.369128i
$448$	−40.0000	+	40.0000i	−0.0892857	+	0.0892857i
$449$	−360.624	−	360.624i	−0.803173	−	0.803173i	0.180418	−	0.983590i	$-0.442255\pi$
$449$	−360.624	−	360.624i	−0.803173	−	0.803173i	−0.983590	+	0.180418i	$0.942255\pi$
$450$	−305.470			−0.678823
$451$		−	275.000i		−	0.609756i
$452$	91.9239	+	91.9239i	0.203371	+	0.203371i
$453$	526.087	+	526.087i	1.16134	+	1.16134i
$454$	155.000	+	155.000i	0.341410	+	0.341410i
$455$		−	742.462i		−	1.63178i
$456$	−30.0000	−	30.0000i	−0.0657895	−	0.0657895i
$457$			265.000i			0.579869i	0.957047	+	0.289934i	$0.0936335\pi$
$457$			265.000i			0.579869i	−0.957047	+	0.289934i	$0.906367\pi$
$458$			56.5685i			0.123512i
$459$	−216.000	+	405.000i	−0.470588	+	0.882353i
$460$	294.000			0.639130
$461$	148.492			0.322109			0.161055	−	0.986945i	$-0.448510\pi$
$461$	148.492			0.322109			0.161055	+	0.986945i	$0.448510\pi$
$462$	106.066	−	106.066i	0.229580	−	0.229580i
$463$	360.000			0.777538			0.388769	−	0.921335i	$-0.372900\pi$
$463$	360.000			0.777538			0.388769	+	0.921335i	$0.372900\pi$
$464$	113.137	−	113.137i	0.243830	−	0.243830i
$465$	504.000	−	504.000i	1.08387	−	1.08387i
$466$	159.000	−	159.000i	0.341202	−	0.341202i
$467$	−490.732			−1.05082			−0.525409	−	0.850850i	$-0.676088\pi$
$467$	−490.732			−1.05082			−0.525409	+	0.850850i	$0.676088\pi$
$468$		−	270.000i		−	0.576923i
$469$	400.000	−	400.000i	0.852878	−	0.852878i
$470$	−79.1960	−	79.1960i	−0.168502	−	0.168502i
$471$	116.673	−	116.673i	0.247713	−	0.247713i
$472$	−180.000			−0.381356
$473$	−265.165	+	265.165i	−0.560603	+	0.560603i
$474$		−	66.0000i		−	0.139241i
$475$	120.000			0.252632
$476$	−212.132	−	113.137i	−0.445656	−	0.237683i
$477$		−	610.940i		−	1.28080i
$478$		−	400.000i		−	0.836820i
$479$	−166.170	+	166.170i	−0.346910	+	0.346910i	−0.858957	−	0.512047i	$-0.828887\pi$
$479$	−166.170	+	166.170i	−0.346910	+	0.346910i	0.512047	+	0.858957i	$0.328887\pi$
$480$		−	118.794i		−	0.247487i
$481$	−225.000	−	225.000i	−0.467775	−	0.467775i
$482$	394.566	+	394.566i	0.818601	+	0.818601i
$483$	−315.000	+	315.000i	−0.652174	+	0.652174i
$484$		−	192.000i		−	0.396694i
$485$	791.960			1.63291
$486$	243.000	−	243.000i	0.500000	−	0.500000i
$487$	195.000	−	195.000i	0.400411	−	0.400411i	−0.477967	−	0.878378i	$-0.658626\pi$
$487$	195.000	−	195.000i	0.400411	−	0.400411i	0.878378	+	0.477967i	$0.158626\pi$
$488$	200.818	−	200.818i	0.411513	−	0.411513i
$489$			509.117i			1.04114i
$490$	7.00000	+	7.00000i	0.0142857	+	0.0142857i
$491$	565.685			1.15211			0.576054	−	0.817411i	$-0.304592\pi$
$491$	565.685			1.15211			0.576054	+	0.817411i	$0.304592\pi$
$492$	330.000			0.670732
$493$	600.000	+	320.000i	1.21704	+	0.649087i
$494$			106.066i			0.214709i
$495$			315.000i			0.636364i
$496$	96.0000	+	96.0000i	0.193548	+	0.193548i
$497$		−	282.843i		−	0.569100i
$498$	−373.352	+	373.352i	−0.749704	+	0.749704i
$499$	336.000	−	336.000i	0.673347	−	0.673347i	−0.285139	−	0.958486i	$-0.592040\pi$
$499$	336.000	−	336.000i	0.673347	−	0.673347i	0.958486	+	0.285139i	$0.0920399\pi$
$500$	−9.89949	−	9.89949i	−0.0197990	−	0.0197990i
$501$		−	345.000i		−	0.688623i
$502$			90.0000i			0.179283i
$503$	477.297	+	477.297i	0.948901	+	0.948901i	0.998756	−	0.0498557i	$-0.0158761\pi$
$503$	477.297	+	477.297i	0.948901	+	0.948901i	−0.0498557	+	0.998756i	$0.515876\pi$
$504$	127.279	+	127.279i	0.252538	+	0.252538i
$505$	280.000	+	280.000i	0.554455	+	0.554455i
$506$		−	148.492i		−	0.293463i
$507$	−118.794	+	118.794i	−0.234308	+	0.234308i
$508$		−	250.000i		−	0.492126i
$509$		−	226.274i		−	0.444547i	−0.974984	−	0.222273i	$-0.928652\pi$
$509$		−	226.274i		−	0.444547i	0.974984	−	0.222273i	$-0.0713477\pi$
$510$	483.000	−	147.000i	0.947059	−	0.288235i
$511$	−800.000			−1.56556
$512$	22.6274			0.0441942
$513$	−95.4594	+	95.4594i	−0.186081	+	0.186081i
$514$	−226.000			−0.439689
$515$	24.7487	−	24.7487i	0.0480558	−	0.0480558i
$516$	−318.198	−	318.198i	−0.616663	−	0.616663i
$517$	−40.0000	+	40.0000i	−0.0773694	+	0.0773694i
$518$	212.132			0.409521
$519$		−	75.0000i		−	0.144509i
$520$	−210.000	+	210.000i	−0.403846	+	0.403846i
$521$	−441.942	−	441.942i	−0.848257	−	0.848257i	0.141659	−	0.989916i	$-0.454756\pi$
$521$	−441.942	−	441.942i	−0.848257	−	0.848257i	−0.989916	+	0.141659i	$0.954756\pi$
$522$	−360.000	−	360.000i	−0.689655	−	0.689655i
$523$	−240.000			−0.458891			−0.229446	−	0.973322i	$-0.573691\pi$
$523$	−240.000			−0.458891			−0.229446	+	0.973322i	$0.573691\pi$
$524$	−7.07107	+	7.07107i	−0.0134944	+	0.0134944i
$525$	−509.117			−0.969746
$526$	554.000			1.05323
$527$	−271.529	+	509.117i	−0.515235	+	0.966066i
$528$	−60.0000			−0.113636
$529$		−	88.0000i		−	0.166352i
$530$	−475.176	+	475.176i	−0.896558	+	0.896558i
$531$			572.756i			1.07864i
$532$	−50.0000	−	50.0000i	−0.0939850	−	0.0939850i
$533$	−583.363	−	583.363i	−1.09449	−	1.09449i
$534$	−63.6396	−	63.6396i	−0.119175	−	0.119175i
$535$			1435.00i			2.68224i
$536$	−226.274			−0.422153
$537$	−120.000	+	120.000i	−0.223464	+	0.223464i
$538$	−185.000	+	185.000i	−0.343866	+	0.343866i
$539$	3.53553	−	3.53553i	0.00655943	−	0.00655943i
$540$	−378.000			−0.700000
$541$	321.000	+	321.000i	0.593346	+	0.593346i	0.938534	−	0.345188i	$-0.112185\pi$
$541$	321.000	+	321.000i	0.593346	+	0.593346i	−0.345188	+	0.938534i	$0.612185\pi$
$542$	−162.635			−0.300064
$543$		−	335.169i		−	0.617253i
$544$	28.0000	+	92.0000i	0.0514706	+	0.169118i
$545$			1029.55i			1.88908i
$546$		−	450.000i		−	0.824176i
$547$	−395.000	−	395.000i	−0.722121	−	0.722121i	0.246916	−	0.969037i	$-0.420583\pi$
$547$	−395.000	−	395.000i	−0.722121	−	0.722121i	−0.969037	+	0.246916i	$0.920583\pi$
$548$			246.073i			0.449039i
$549$	−639.000	−	639.000i	−1.16393	−	1.16393i
$550$	120.000	−	120.000i	0.218182	−	0.218182i
$551$	141.421	+	141.421i	0.256663	+	0.256663i
$552$	178.191			0.322810
$553$		−	110.000i		−	0.198915i
$554$	395.980	+	395.980i	0.714765	+	0.714765i
$555$	−315.000	+	315.000i	−0.567568	+	0.567568i
$556$	−38.0000	−	38.0000i	−0.0683453	−	0.0683453i
$557$			929.138i			1.66811i	0.551680	+	0.834056i	$0.313987\pi$
$557$			929.138i			1.66811i	−0.551680	+	0.834056i	$0.686013\pi$
$558$	305.470	−	305.470i	0.547438	−	0.547438i
$559$			1125.00i			2.01252i
$560$		−	197.990i		−	0.353553i
$561$	−74.2462	−	243.952i	−0.132346	−	0.434852i
$562$	−50.0000			−0.0889680
$563$	−101.823			−0.180859			−0.0904293	−	0.995903i	$-0.528824\pi$
$563$	−101.823			−0.180859			−0.0904293	+	0.995903i	$0.528824\pi$
$564$	−48.0000	−	48.0000i	−0.0851064	−	0.0851064i
$565$	−455.000			−0.805310
$566$	219.203	−	219.203i	0.387285	−	0.387285i
$567$	405.000	−	405.000i	0.714286	−	0.714286i
$568$	−80.0000	+	80.0000i	−0.140845	+	0.140845i
$569$	395.980			0.695922			0.347961	−	0.937509i	$-0.386874\pi$
$569$	395.980			0.695922			0.347961	+	0.937509i	$0.386874\pi$
$570$	148.492			0.260513
$571$	−104.000	+	104.000i	−0.182137	+	0.182137i	−0.792286	−	0.610150i	$-0.791109\pi$
$571$	−104.000	+	104.000i	−0.182137	+	0.182137i	0.610150	+	0.792286i	$0.291109\pi$
$572$	106.066	+	106.066i	0.185430	+	0.185430i
$573$	135.000	+	135.000i	0.235602	+	0.235602i
$574$	550.000			0.958188
$575$	−356.382	+	356.382i	−0.619794	+	0.619794i
$576$		−	72.0000i		−	0.125000i
$577$	−185.000			−0.320624			−0.160312	−	0.987066i	$-0.551250\pi$
$577$	−185.000			−0.320624			−0.160312	+	0.987066i	$0.551250\pi$
$578$	−339.411	+	227.688i	−0.587217	+	0.393925i
$579$		−	1018.23i		−	1.75861i
$580$			560.000i			0.965517i
$581$	−622.254	+	622.254i	−1.07101	+	1.07101i
$582$	480.000			0.824742
$583$	240.000	+	240.000i	0.411664	+	0.411664i
$584$	226.274	+	226.274i	0.387456	+	0.387456i
$585$	668.216	+	668.216i	1.14225	+	1.14225i
$586$			66.0000i			0.112628i
$587$	497.803			0.848046			0.424023	−	0.905651i	$-0.360618\pi$
$587$	497.803			0.848046			0.424023	+	0.905651i	$0.360618\pi$
$588$	4.24264	+	4.24264i	0.00721538	+	0.00721538i
$589$	−120.000	+	120.000i	−0.203735	+	0.203735i
$590$	445.477	−	445.477i	0.755046	−	0.755046i
$591$	−243.000			−0.411168
$592$	−60.0000	−	60.0000i	−0.101351	−	0.101351i
$593$	−916.410			−1.54538			−0.772690	−	0.634784i	$-0.781089\pi$
$593$	−916.410			−1.54538			−0.772690	+	0.634784i	$0.781089\pi$
$594$			190.919i			0.321412i
$595$	805.000	−	245.000i	1.35294	−	0.411765i
$596$			155.563i			0.261013i
$597$	−441.235			−0.739086
$598$	−315.000	−	315.000i	−0.526756	−	0.526756i
$599$		−	615.183i		−	1.02702i	−0.858085	−	0.513508i	$-0.828346\pi$
$599$		−	615.183i		−	1.02702i	0.858085	−	0.513508i	$-0.171654\pi$
$600$	144.000	+	144.000i	0.240000	+	0.240000i
$601$	−56.0000	+	56.0000i	−0.0931780	+	0.0931780i	−0.752159	−	0.658981i	$-0.770988\pi$
$601$	−56.0000	+	56.0000i	−0.0931780	+	0.0931780i	0.658981	+	0.752159i	$0.270988\pi$
$602$	−530.330	−	530.330i	−0.880947	−	0.880947i
$603$			720.000i			1.19403i
$604$		−	496.000i		−	0.821192i
$605$	475.176	+	475.176i	0.785414	+	0.785414i
$606$	169.706	+	169.706i	0.280042	+	0.280042i
$607$	−645.000	−	645.000i	−1.06260	−	1.06260i	−0.997905	−	0.0646981i	$-0.979392\pi$
$607$	−645.000	−	645.000i	−1.06260	−	1.06260i	−0.0646981	−	0.997905i	$-0.520608\pi$
$608$			28.2843i			0.0465202i
$609$	−600.000	−	600.000i	−0.985222	−	0.985222i
$610$			994.000i			1.62951i
$611$			169.706i			0.277751i
$612$	292.742	−	89.0955i	0.478337	−	0.145581i
$613$	495.000			0.807504			0.403752	−	0.914868i	$-0.367706\pi$
$613$	495.000			0.807504			0.403752	+	0.914868i	$0.367706\pi$
$614$	−452.548			−0.737049
$615$	−816.708	+	816.708i	−1.32798	+	1.32798i
$616$	−100.000			−0.162338
$617$	56.5685	−	56.5685i	0.0916832	−	0.0916832i	−0.659778	−	0.751461i	$-0.729350\pi$
$617$	56.5685	−	56.5685i	0.0916832	−	0.0916832i	0.751461	+	0.659778i	$0.229350\pi$
$618$	15.0000	−	15.0000i	0.0242718	−	0.0242718i
$619$	261.000	−	261.000i	0.421648	−	0.421648i	−0.464123	−	0.885771i	$-0.653630\pi$
$619$	261.000	−	261.000i	0.421648	−	0.421648i	0.885771	+	0.464123i	$0.153630\pi$
$620$	−475.176			−0.766413
$621$		−	567.000i		−	0.913043i
$622$	−120.000	+	120.000i	−0.192926	+	0.192926i
$623$	−106.066	−	106.066i	−0.170250	−	0.170250i
$624$	−127.279	+	127.279i	−0.203973	+	0.203973i
$625$	649.000			1.03840
$626$	226.274	−	226.274i	0.361460	−	0.361460i
$627$		−	75.0000i		−	0.119617i
$628$	−110.000			−0.175159
$629$	169.706	−	318.198i	0.269802	−	0.505879i
$630$	−630.000			−1.00000
$631$		−	213.000i		−	0.337559i	−0.985654	−	0.168780i	$-0.946017\pi$
$631$		−	213.000i		−	0.337559i	0.985654	−	0.168780i	$-0.0539826\pi$
$632$	−31.1127	+	31.1127i	−0.0492290	+	0.0492290i
$633$		−	916.410i		−	1.44773i
$634$	−200.000	−	200.000i	−0.315457	−	0.315457i
$635$	618.718	+	618.718i	0.974360	+	0.974360i
$636$	−288.000	+	288.000i	−0.452830	+	0.452830i
$637$		−	15.0000i		−	0.0235479i
$638$	282.843			0.443327
$639$	254.558	+	254.558i	0.398370	+	0.398370i
$640$	−56.0000	+	56.0000i	−0.0875000	+	0.0875000i
$641$	236.881	−	236.881i	0.369549	−	0.369549i	−0.497764	−	0.867313i	$-0.665845\pi$
$641$	236.881	−	236.881i	0.369549	−	0.369549i	0.867313	+	0.497764i	$0.165845\pi$
$642$			869.741i			1.35474i
$643$	520.000	+	520.000i	0.808709	+	0.808709i	0.984439	−	0.175729i	$-0.0562284\pi$
$643$	520.000	+	520.000i	0.808709	+	0.808709i	−0.175729	+	0.984439i	$0.556228\pi$
$644$	296.985			0.461157
$645$	1575.00			2.44186
$646$	−115.000	+	35.0000i	−0.178019	+	0.0541796i
$647$		−	1056.42i		−	1.63279i	−0.577491	−	0.816397i	$-0.695968\pi$
$647$		−	1056.42i		−	1.63279i	0.577491	−	0.816397i	$-0.304032\pi$
$648$	−229.103			−0.353553
$649$	−225.000	−	225.000i	−0.346687	−	0.346687i
$650$		−	509.117i		−	0.783257i
$651$	509.117	−	509.117i	0.782054	−	0.782054i
$652$	240.000	−	240.000i	0.368098	−	0.368098i
$653$	−894.490	−	894.490i	−1.36982	−	1.36982i	−0.860694	−	0.509122i	$-0.829970\pi$
$653$	−894.490	−	894.490i	−1.36982	−	1.36982i	−0.509122	−	0.860694i	$-0.670030\pi$
$654$			624.000i			0.954128i
$655$		−	35.0000i		−	0.0534351i
$656$	−155.563	−	155.563i	−0.237139	−	0.237139i
$657$	720.000	−	720.000i	1.09589	−	1.09589i
$658$	−80.0000	−	80.0000i	−0.121581	−	0.121581i
$659$		−	7.07107i		−	0.0107300i	−0.999986	−	0.00536500i	$-0.998292\pi$
$659$		−	7.07107i		−	0.0107300i	0.999986	−	0.00536500i	$-0.00170774\pi$
$660$	148.492	−	148.492i	0.224989	−	0.224989i
$661$		−	535.000i		−	0.809380i	−0.914454	−	0.404690i	$-0.867379\pi$
$661$		−	535.000i		−	0.809380i	0.914454	−	0.404690i	$-0.132621\pi$
$662$			63.6396i			0.0961323i
$663$	−675.000	−	360.000i	−1.01810	−	0.542986i
$664$	352.000			0.530120
$665$	247.487			0.372161
$666$	−190.919	+	190.919i	−0.286665	+	0.286665i
$667$	−840.000			−1.25937
$668$	−162.635	+	162.635i	−0.243465	+	0.243465i
$669$	328.805	+	328.805i	0.491487	+	0.491487i
$670$	560.000	−	560.000i	0.835821	−	0.835821i
$671$	502.046			0.748205
$672$		−	120.000i		−	0.178571i
$673$	−480.000	+	480.000i	−0.713224	+	0.713224i	−0.967208	−	0.253984i	$-0.918259\pi$
$673$	−480.000	+	480.000i	−0.713224	+	0.713224i	0.253984	+	0.967208i	$0.418259\pi$
$674$	−134.350	−	134.350i	−0.199333	−	0.199333i
$675$	458.205	−	458.205i	0.678823	−	0.678823i
$676$	112.000			0.165680
$677$	333.047	−	333.047i	0.491946	−	0.491946i	−0.416973	−	0.908919i	$-0.636909\pi$
$677$	333.047	−	333.047i	0.491946	−	0.491946i	0.908919	+	0.416973i	$0.136909\pi$
$678$	−275.772			−0.406743
$679$	800.000			1.17820
$680$	−296.985	−	158.392i	−0.436742	−	0.232929i
$681$	−465.000			−0.682819
$682$			240.000i			0.351906i
$683$	533.866	−	533.866i	0.781648	−	0.781648i	−0.198461	−	0.980109i	$-0.563594\pi$
$683$	533.866	−	533.866i	0.781648	−	0.781648i	0.980109	+	0.198461i	$0.0635942\pi$
$684$	90.0000			0.131579
$685$	−609.000	−	609.000i	−0.889051	−	0.889051i
$686$	−339.411	−	339.411i	−0.494769	−	0.494769i
$687$	−84.8528	−	84.8528i	−0.123512	−	0.123512i
$688$			300.000i			0.436047i
$689$	1018.23			1.47784
$690$	−441.000	+	441.000i	−0.639130	+	0.639130i
$691$	304.000	−	304.000i	0.439942	−	0.439942i	−0.452050	−	0.891992i	$-0.649307\pi$
$691$	304.000	−	304.000i	0.439942	−	0.439942i	0.891992	+	0.452050i	$0.149307\pi$
$692$	−35.3553	+	35.3553i	−0.0510915	+	0.0510915i
$693$			318.198i			0.459160i
$694$	−160.000	−	160.000i	−0.230548	−	0.230548i
$695$	188.090			0.270634
$696$			339.411i			0.487660i
$697$	440.000	−	825.000i	0.631277	−	1.18364i
$698$		−	668.923i		−	0.958342i
$699$			477.000i			0.682403i
$700$	240.000	+	240.000i	0.342857	+	0.342857i
$701$		−	169.706i		−	0.242091i	−0.992647	−	0.121045i	$-0.961375\pi$
$701$		−	169.706i		−	0.242091i	0.992647	−	0.121045i	$-0.0386247\pi$
$702$	405.000	+	405.000i	0.576923	+	0.576923i
$703$	75.0000	−	75.0000i	0.106686	−	0.106686i
$704$	28.2843	+	28.2843i	0.0401765	+	0.0401765i
$705$	237.588			0.337004
$706$			14.0000i			0.0198300i
$707$	282.843	+	282.843i	0.400060	+	0.400060i
$708$	270.000	−	270.000i	0.381356	−	0.381356i
$709$	344.000	+	344.000i	0.485190	+	0.485190i	0.906785	−	0.421594i	$-0.138529\pi$
$709$	344.000	+	344.000i	0.485190	+	0.485190i	−0.421594	+	0.906785i	$0.638529\pi$
$710$		−	395.980i		−	0.557718i
$711$	99.0000	+	99.0000i	0.139241	+	0.139241i
$712$			60.0000i			0.0842697i
$713$		−	712.764i		−	0.999668i
$714$	487.904	−	148.492i	0.683338	−	0.207973i
$715$	−525.000			−0.734266
$716$	113.137			0.158013
$717$	600.000	+	600.000i	0.836820	+	0.836820i
$718$	−170.000			−0.236769
$719$	−194.454	+	194.454i	−0.270451	+	0.270451i	−0.829282	−	0.558831i	$-0.811250\pi$
$719$	−194.454	+	194.454i	−0.270451	+	0.270451i	0.558831	+	0.829282i	$0.311250\pi$
$720$	178.191	+	178.191i	0.247487	+	0.247487i
$721$	25.0000	−	25.0000i	0.0346741	−	0.0346741i
$722$	475.176			0.658138
$723$	−1183.70			−1.63720
$724$	−158.000	+	158.000i	−0.218232	+	0.218232i
$725$	−678.823	−	678.823i	−0.936307	−	0.936307i
$726$	288.000	+	288.000i	0.396694	+	0.396694i
$727$	−1310.00			−1.80193			−0.900963	−	0.433896i	$-0.857138\pi$
$727$	−1310.00			−1.80193			−0.900963	+	0.433896i	$0.857138\pi$
$728$	−212.132	+	212.132i	−0.291390	+	0.291390i
$729$			729.000i			1.00000i
$730$	−1120.00			−1.53425
$731$	−1219.76	+	371.231i	−1.66862	+	0.507840i
$732$			602.455i			0.823026i
$733$		−	520.000i		−	0.709413i	−0.934978	−	0.354707i	$-0.884581\pi$
$733$		−	520.000i		−	0.709413i	0.934978	−	0.354707i	$-0.115419\pi$
$734$	−106.066	+	106.066i	−0.144504	+	0.144504i
$735$	−21.0000			−0.0285714
$736$	−84.0000	−	84.0000i	−0.114130	−	0.114130i
$737$	−282.843	−	282.843i	−0.383776	−	0.383776i
$738$	−495.000	+	495.000i	−0.670732	+	0.670732i
$739$		−	1197.00i		−	1.61976i	−0.586598	−	0.809878i	$-0.699533\pi$
$739$		−	1197.00i		−	1.61976i	0.586598	−	0.809878i	$-0.300467\pi$
$740$	296.985			0.401331
$741$	−159.099	−	159.099i	−0.214709	−	0.214709i
$742$	−480.000	+	480.000i	−0.646900	+	0.646900i
$743$	−318.198	+	318.198i	−0.428261	+	0.428261i	−0.888036	−	0.459775i	$-0.847930\pi$
$743$	−318.198	+	318.198i	−0.428261	+	0.428261i	0.459775	+	0.888036i	$0.347930\pi$
$744$	−288.000			−0.387097
$745$	−385.000	−	385.000i	−0.516779	−	0.516779i
$746$	622.254			0.834121
$747$		−	1120.06i		−	1.49941i
$748$	−80.0000	+	150.000i	−0.106952	+	0.200535i
$749$			1449.57i			1.93534i
$750$	29.6985			0.0395980
$751$	216.000	+	216.000i	0.287617	+	0.287617i	0.836137	−	0.548521i	$-0.184809\pi$
$751$	216.000	+	216.000i	0.287617	+	0.287617i	−0.548521	+	0.836137i	$0.684809\pi$
$752$			45.2548i			0.0601793i
$753$	−135.000	−	135.000i	−0.179283	−	0.179283i
$754$	600.000	−	600.000i	0.795756	−	0.795756i
$755$	1227.54	+	1227.54i	1.62588	+	1.62588i
$756$	−381.838			−0.505076
$757$			1105.00i			1.45971i	0.683602	+	0.729855i	$0.260412\pi$
$757$			1105.00i			1.45971i	−0.683602	+	0.729855i	$0.739588\pi$
$758$	−241.831	−	241.831i	−0.319038	−	0.319038i
$759$	222.739	+	222.739i	0.293463	+	0.293463i
$760$	−70.0000	−	70.0000i	−0.0921053	−	0.0921053i
$761$			1074.80i			1.41236i	0.708035	+	0.706178i	$0.249582\pi$
$761$			1074.80i			1.41236i	−0.708035	+	0.706178i	$0.750418\pi$
$762$	375.000	+	375.000i	0.492126	+	0.492126i
$763$			1040.00i			1.36304i
$764$		−	127.279i		−	0.166596i
$765$	−504.000	+	945.000i	−0.658824	+	1.23529i
$766$	−704.000			−0.919060
$767$	−954.594			−1.24458
$768$	−33.9411	+	33.9411i	−0.0441942	+	0.0441942i
$769$	287.000			0.373212			0.186606	−	0.982435i	$-0.440251\pi$
$769$	287.000			0.373212			0.186606	+	0.982435i	$0.440251\pi$
$770$	247.487	−	247.487i	0.321412	−	0.321412i
$771$	339.000	−	339.000i	0.439689	−	0.439689i
$772$	−480.000	+	480.000i	−0.621762	+	0.621762i
$773$	−520.431			−0.673261			−0.336630	−	0.941637i	$-0.609287\pi$
$773$	−520.431			−0.673261			−0.336630	+	0.941637i	$0.609287\pi$
$774$	954.594			1.23333
$775$	576.000	−	576.000i	0.743226	−	0.743226i
$776$	−226.274	−	226.274i	−0.291590	−	0.291590i
$777$	−318.198	+	318.198i	−0.409521	+	0.409521i
$778$	990.000			1.27249
$779$	194.454	−	194.454i	0.249620	−	0.249620i
$780$		−	630.000i		−	0.807692i
$781$	−200.000			−0.256082
$782$	237.588	−	445.477i	0.303821	−	0.569664i
$783$	1080.00			1.37931
$784$		−	4.00000i		−	0.00510204i
$785$	272.236	−	272.236i	0.346798	−	0.346798i
$786$		−	21.2132i		−	0.0269888i
$787$	−720.000	−	720.000i	−0.914867	−	0.914867i	0.0817835	−	0.996650i	$-0.473938\pi$
$787$	−720.000	−	720.000i	−0.914867	−	0.914867i	−0.996650	+	0.0817835i	$0.973938\pi$
$788$	114.551	+	114.551i	0.145370	+	0.145370i
$789$	−831.000	+	831.000i	−1.05323	+	1.05323i
$790$		−	154.000i		−	0.194937i
$791$	−459.619			−0.581061
$792$	90.0000	−	90.0000i	0.113636	−	0.113636i
$793$	1065.00	−	1065.00i	1.34300	−	1.34300i
$794$		0			0
$795$		−	1425.53i		−	1.79312i
$796$	208.000	+	208.000i	0.261307	+	0.261307i
$797$	−237.588			−0.298103			−0.149051	−	0.988829i	$-0.547622\pi$
$797$	−237.588			−0.298103			−0.149051	+	0.988829i	$0.547622\pi$
$798$	150.000			0.187970
$799$	−184.000	+	56.0000i	−0.230288	+	0.0700876i
$800$		−	135.765i		−	0.169706i
$801$	190.919			0.238351
$802$	−455.000	−	455.000i	−0.567332	−	0.567332i
$803$			565.685i			0.704465i
$804$	339.411	−	339.411i	0.422153	−	0.422153i
$805$	−735.000	+	735.000i	−0.913043	+	0.913043i
$806$	509.117	+	509.117i	0.631659	+	0.631659i
$807$		−	555.000i		−	0.687732i
$808$		−	160.000i		−	0.198020i
$809$	123.744	+	123.744i	0.152959	+	0.152959i	0.779438	−	0.626479i	$-0.215505\pi$
$809$	123.744	+	123.744i	0.152959	+	0.152959i	−0.626479	+	0.779438i	$0.715505\pi$
$810$	567.000	−	567.000i	0.700000	−	0.700000i
$811$	824.000	+	824.000i	1.01603	+	1.01603i	0.999869	+	0.0161602i	$0.00514417\pi$
$811$	824.000	+	824.000i	1.01603	+	1.01603i	0.0161602	+	0.999869i	$0.494856\pi$
$812$			565.685i			0.696657i
$813$	243.952	−	243.952i	0.300064	−	0.300064i
$814$		−	150.000i		−	0.184275i
$815$			1187.94i			1.45759i
$816$	−180.000	−	96.0000i	−0.220588	−	0.117647i
$817$	−375.000			−0.458996
$818$	−487.904			−0.596459
$819$	675.000	+	675.000i	0.824176	+	0.824176i
$820$	770.000			0.939024
$821$	300.520	−	300.520i	0.366042	−	0.366042i	−0.499990	−	0.866031i	$-0.666663\pi$
$821$	300.520	−	300.520i	0.366042	−	0.366042i	0.866031	+	0.499990i	$0.166663\pi$
$822$	−369.110	−	369.110i	−0.449039	−	0.449039i
$823$	1005.00	−	1005.00i	1.22114	−	1.22114i	0.253916	−	0.967226i	$-0.418281\pi$
$823$	1005.00	−	1005.00i	1.22114	−	1.22114i	0.967226	−	0.253916i	$-0.0817186\pi$
$824$	−14.1421			−0.0171628
$825$			360.000i			0.436364i
$826$	450.000	−	450.000i	0.544794	−	0.544794i
$827$	586.192	+	586.192i	0.708817	+	0.708817i	0.966286	−	0.257470i	$-0.0828887\pi$
$827$	586.192	+	586.192i	0.708817	+	0.708817i	−0.257470	+	0.966286i	$0.582889\pi$
$828$	−267.286	+	267.286i	−0.322810	+	0.322810i
$829$	8.00000			0.00965018			0.00482509	−	0.999988i	$-0.498464\pi$
$829$	8.00000			0.00965018			0.00482509	+	0.999988i	$0.498464\pi$
$830$	−871.156	+	871.156i	−1.04959	+	1.04959i
$831$	−1187.94			−1.42953
$832$	120.000			0.144231
$833$	16.2635	−	4.94975i	0.0195240	−	0.00594207i
$834$	114.000			0.136691
$835$		−	805.000i		−	0.964072i
$836$	−35.3553	+	35.3553i	−0.0422911	+	0.0422911i
$837$			916.410i			1.09488i
$838$	320.000	+	320.000i	0.381862	+	0.381862i
$839$	512.652	+	512.652i	0.611028	+	0.611028i	0.943214	−	0.332186i	$-0.107786\pi$
$839$	512.652	+	512.652i	0.611028	+	0.611028i	−0.332186	+	0.943214i	$0.607786\pi$
$840$	296.985	+	296.985i	0.353553	+	0.353553i
$841$		−	759.000i		−	0.902497i
$842$	−982.878			−1.16731
$843$	75.0000	−	75.0000i	0.0889680	−	0.0889680i
$844$	−432.000	+	432.000i	−0.511848	+	0.511848i
$845$	−277.186	+	277.186i	−0.328031	+	0.328031i
$846$	144.000			0.170213
$847$	480.000	+	480.000i	0.566706	+	0.566706i
$848$	271.529			0.320199
$849$			657.609i			0.774569i
$850$	552.000	−	168.000i	0.649412	−	0.197647i
$851$			445.477i			0.523475i
$852$		−	240.000i		−	0.281690i
$853$	−905.000	−	905.000i	−1.06096	−	1.06096i	−0.998017	−	0.0629443i	$-0.979951\pi$
$853$	−905.000	−	905.000i	−1.06096	−	1.06096i	−0.0629443	−	0.998017i	$-0.520049\pi$
$854$			1004.09i			1.17575i
$855$	−222.739	+	222.739i	−0.260513	+	0.260513i
$856$	410.000	−	410.000i	0.478972	−	0.478972i
$857$	−610.940	−	610.940i	−0.712882	−	0.712882i	0.254255	−	0.967137i	$-0.418170\pi$
$857$	−610.940	−	610.940i	−0.712882	−	0.712882i	−0.967137	+	0.254255i	$0.918170\pi$
$858$	−318.198			−0.370860
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	−742.462	−	742.462i	−0.863328	−	0.863328i
$861$	−825.000	+	825.000i	−0.958188	+	0.958188i
$862$	−280.000	−	280.000i	−0.324826	−	0.324826i
$863$		−	230.517i		−	0.267111i	−0.991041	−	0.133556i	$-0.957361\pi$
$863$		−	230.517i		−	0.267111i	0.991041	−	0.133556i	$-0.0426394\pi$
$864$	108.000	+	108.000i	0.125000	+	0.125000i
$865$		−	175.000i		−	0.202312i
$866$			431.335i			0.498078i
$867$	167.584	−	850.649i	0.193292	−	0.981141i
$868$	−480.000			−0.552995
$869$	−77.7817			−0.0895072
$870$	−840.000	−	840.000i	−0.965517	−	0.965517i
$871$	−1200.00			−1.37773
$872$	294.156	−	294.156i	0.337335	−	0.337335i
$873$	−720.000	+	720.000i	−0.824742	+	0.824742i
$874$	105.000	−	105.000i	0.120137	−	0.120137i
$875$	49.4975			0.0565685
$876$	−678.823			−0.774912
$877$	−815.000	+	815.000i	−0.929304	+	0.929304i	−0.997661	−	0.0683565i	$-0.978224\pi$
$877$	−815.000	+	815.000i	−0.929304	+	0.929304i	0.0683565	+	0.997661i	$0.478224\pi$
$878$	−90.5097	−	90.5097i	−0.103086	−	0.103086i
$879$	−99.0000	−	99.0000i	−0.112628	−	0.112628i
$880$	−140.000			−0.159091
$881$	883.883	−	883.883i	1.00327	−	1.00327i	0.00327833	−	0.999995i	$-0.498956\pi$
$881$	883.883	−	883.883i	1.00327	−	1.00327i	0.999995	−	0.00327833i	$-0.00104353\pi$
$882$	−12.7279			−0.0144308
$883$	−645.000			−0.730464			−0.365232	−	0.930916i	$-0.619010\pi$
$883$	−645.000			−0.730464			−0.365232	+	0.930916i	$0.619010\pi$
$884$	148.492	+	487.904i	0.167978	+	0.551927i
$885$			1336.43i			1.51009i
$886$			624.000i			0.704289i
$887$	529.623	−	529.623i	0.597095	−	0.597095i	−0.342444	−	0.939538i	$-0.611255\pi$
$887$	529.623	−	529.623i	0.597095	−	0.597095i	0.939538	+	0.342444i	$0.111255\pi$
$888$	180.000			0.202703
$889$	625.000	+	625.000i	0.703037	+	0.703037i
$890$	−148.492	−	148.492i	−0.166845	−	0.166845i
$891$	−286.378	−	286.378i	−0.321412	−	0.321412i
$892$		−	310.000i		−	0.347534i
$893$	−56.5685			−0.0633466
$894$	−233.345	−	233.345i	−0.261013	−	0.261013i
$895$	−280.000	+	280.000i	−0.312849	+	0.312849i
$896$	−56.5685	+	56.5685i	−0.0631345	+	0.0631345i
$897$	945.000			1.05351
$898$	−510.000	−	510.000i	−0.567929	−	0.567929i
$899$	1357.65			1.51017
$900$	−432.000			−0.480000
$901$	336.000	+	1104.00i	0.372919	+	1.22531i
$902$		−	388.909i		−	0.431163i
$903$	1590.99			1.76189
$904$	130.000	+	130.000i	0.143805	+	0.143805i
$905$		−	782.060i		−	0.864155i
$906$	744.000	+	744.000i	0.821192	+	0.821192i
$907$	−685.000	+	685.000i	−0.755237	+	0.755237i	−0.975451	−	0.220214i	$-0.929324\pi$
$907$	−685.000	+	685.000i	−0.755237	+	0.755237i	0.220214	+	0.975451i	$0.429324\pi$
$908$	219.203	+	219.203i	0.241413	+	0.241413i
$909$	−509.117			−0.560085
$910$		−	1050.00i		−	1.15385i
$911$	−936.916	−	936.916i	−1.02845	−	1.02845i	−0.999583	−	0.0288651i	$-0.990811\pi$
$911$	−936.916	−	936.916i	−1.02845	−	1.02845i	−0.0288651	−	0.999583i	$-0.509189\pi$
$912$	−42.4264	−	42.4264i	−0.0465202	−	0.0465202i
$913$	440.000	+	440.000i	0.481928	+	0.481928i
$914$			374.767i			0.410029i
$915$	−1491.00	−	1491.00i	−1.62951	−	1.62951i
$916$			80.0000i			0.0873362i
$917$		−	35.3553i		−	0.0385554i
$918$	−305.470	+	572.756i	−0.332756	+	0.623918i
$919$	1235.00			1.34385			0.671926	−	0.740618i	$-0.265467\pi$
$919$	1235.00			1.34385			0.671926	+	0.740618i	$0.265467\pi$
$920$	415.779			0.451933
$921$	678.823	−	678.823i	0.737049	−	0.737049i
$922$	210.000			0.227766
$923$	−424.264	+	424.264i	−0.459658	+	0.459658i
$924$	150.000	−	150.000i	0.162338	−	0.162338i
$925$	−360.000	+	360.000i	−0.389189	+	0.389189i
$926$	509.117			0.549802
$927$			45.0000i			0.0485437i
$928$	160.000	−	160.000i	0.172414	−	0.172414i
$929$	979.343	+	979.343i	1.05419	+	1.05419i	0.998445	+	0.0557454i	$0.0177535\pi$
$929$	979.343	+	979.343i	1.05419	+	1.05419i	0.0557454	+	0.998445i	$0.482246\pi$
$930$	712.764	−	712.764i	0.766413	−	0.766413i
$931$	5.00000			0.00537057
$932$	224.860	−	224.860i	0.241266	−	0.241266i
$933$		−	360.000i		−	0.385852i
$934$	−694.000			−0.743041
$935$	−173.241	−	569.221i	−0.185285	−	0.608792i
$936$		−	381.838i		−	0.407946i
$937$		−	530.000i		−	0.565635i	−0.959174	−	0.282818i	$-0.908731\pi$
$937$		−	530.000i		−	0.565635i	0.959174	−	0.282818i	$-0.0912691\pi$
$938$	565.685	−	565.685i	0.603076	−	0.603076i
$939$			678.823i			0.722921i
$940$	−112.000	−	112.000i	−0.119149	−	0.119149i
$941$	−593.970	−	593.970i	−0.631211	−	0.631211i	0.317161	−	0.948372i	$-0.397271\pi$
$941$	−593.970	−	593.970i	−0.631211	−	0.631211i	−0.948372	+	0.317161i	$0.897271\pi$
$942$	165.000	−	165.000i	0.175159	−	0.175159i
$943$			1155.00i			1.22481i
$944$	−254.558			−0.269659
$945$	945.000	−	945.000i	1.00000	−	1.00000i
$946$	−375.000	+	375.000i	−0.396406	+	0.396406i
$947$	−950.352	+	950.352i	−1.00354	+	1.00354i	−0.00354537	+	0.999994i	$0.501129\pi$
$947$	−950.352	+	950.352i	−1.00354	+	1.00354i	−0.999994	+	0.00354537i	$0.998871\pi$
$948$		−	93.3381i		−	0.0984579i
$949$	1200.00	+	1200.00i	1.26449	+	1.26449i
$950$	169.706			0.178638
$951$	600.000			0.630915
$952$	−300.000	−	160.000i	−0.315126	−	0.168067i
$953$			45.2548i			0.0474867i	0.999718	+	0.0237434i	$0.00755845\pi$
$953$			45.2548i			0.0474867i	−0.999718	+	0.0237434i	$0.992442\pi$
$954$		−	864.000i		−	0.905660i
$955$	315.000	+	315.000i	0.329843	+	0.329843i
$956$		−	565.685i		−	0.591721i
$957$	−424.264	+	424.264i	−0.443327	+	0.443327i
$958$	−235.000	+	235.000i	−0.245303	+	0.245303i
$959$	−615.183	−	615.183i	−0.641484	−	0.641484i
$960$		−	168.000i		−	0.175000i
$961$			191.000i			0.198751i
$962$	−318.198	−	318.198i	−0.330767	−	0.330767i
$963$	−1304.61	−	1304.61i	−1.35474	−	1.35474i
$964$	558.000	+	558.000i	0.578838	+	0.578838i
$965$		−	2375.88i		−	2.46205i
$966$	−445.477	+	445.477i	−0.461157	+	0.461157i
$967$		−	1115.00i		−	1.15305i	−0.817079	−	0.576525i	$-0.804408\pi$
$967$		−	1115.00i		−	1.15305i	0.817079	−	0.576525i	$-0.195592\pi$
$968$		−	271.529i		−	0.280505i
$969$	120.000	−	225.000i	0.123839	−	0.232198i
$970$	1120.00			1.15464
$971$	1866.76			1.92251			0.961257	−	0.275652i	$-0.0888938\pi$
$971$	1866.76			1.92251			0.961257	+	0.275652i	$0.0888938\pi$
$972$	343.654	−	343.654i	0.353553	−	0.353553i
$973$	190.000			0.195272
$974$	275.772	−	275.772i	0.283133	−	0.283133i
$975$	763.675	+	763.675i	0.783257	+	0.783257i
$976$	284.000	−	284.000i	0.290984	−	0.290984i
$977$	−612.354			−0.626770			−0.313385	−	0.949626i	$-0.601463\pi$
$977$	−612.354			−0.626770			−0.313385	+	0.949626i	$0.601463\pi$
$978$			720.000i			0.736196i
$979$	−75.0000	+	75.0000i	−0.0766088	+	0.0766088i
$980$	9.89949	+	9.89949i	0.0101015	+	0.0101015i
$981$	−936.000	−	936.000i	−0.954128	−	0.954128i
$982$	800.000			0.814664
$983$	−823.779	+	823.779i	−0.838026	+	0.838026i	−0.988599	−	0.150573i	$-0.951888\pi$
$983$	−823.779	+	823.779i	−0.838026	+	0.838026i	0.150573	+	0.988599i	$0.451888\pi$
$984$	466.690			0.474279
$985$	−567.000			−0.575635
$986$	848.528	+	452.548i	0.860576	+	0.458974i
$987$	240.000			0.243161
$988$			150.000i			0.151822i
$989$	1113.69	−	1113.69i	1.12608	−	1.12608i
$990$			445.477i			0.449977i
$991$	1024.00	+	1024.00i	1.03330	+	1.03330i	0.999426	+	0.0338736i	$0.0107844\pi$
$991$	1024.00	+	1024.00i	1.03330	+	1.03330i	0.0338736	+	0.999426i	$0.489216\pi$
$992$	135.765	+	135.765i	0.136859	+	0.136859i
$993$	−95.4594	−	95.4594i	−0.0961323	−	0.0961323i
$994$		−	400.000i		−	0.402414i
$995$	−1029.55			−1.03472
$996$	−528.000	+	528.000i	−0.530120	+	0.530120i
$997$	−1065.00	+	1065.00i	−1.06820	+	1.06820i	−0.0707075	+	0.997497i	$0.522526\pi$
$997$	−1065.00	+	1065.00i	−1.06820	+	1.06820i	−0.997497	+	0.0707075i	$0.977474\pi$
$998$	475.176	−	475.176i	0.476128	−	0.476128i
$999$		−	572.756i		−	0.573330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.3.e.a.47.2	yes	4
3.2	odd	2	inner	102.3.e.a.47.1	✓	4
17.4	even	4	inner	102.3.e.a.89.1	yes	4
51.38	odd	4	inner	102.3.e.a.89.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.3.e.a.47.1	✓	4	3.2	odd	2	inner
102.3.e.a.47.2	yes	4	1.1	even	1	trivial
102.3.e.a.89.1	yes	4	17.4	even	4	inner
102.3.e.a.89.2	yes	4	51.38	odd	4	inner

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:	\( N \)	\(=\)	\( 102 = 2 \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	102.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(-2.12132 + 2.12132i) q^{3} +2.00000 q^{4} +(-4.94975 + 4.94975i) q^{5} +(-3.00000 + 3.00000i) q^{6} +(-5.00000 + 5.00000i) q^{7} +2.82843 q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(-2.12132 + 2.12132i) q^{3} +2.00000 q^{4} +(-4.94975 + 4.94975i) q^{5} +(-3.00000 + 3.00000i) q^{6} +(-5.00000 + 5.00000i) q^{7} +2.82843 q^{8} -9.00000i q^{9} +(-7.00000 + 7.00000i) q^{10} +(3.53553 + 3.53553i) q^{11} +(-4.24264 + 4.24264i) q^{12} +15.0000 q^{13} +(-7.07107 + 7.07107i) q^{14} -21.0000i q^{15} +4.00000 q^{16} +(4.94975 + 16.2635i) q^{17} -12.7279i q^{18} +5.00000i q^{19} +(-9.89949 + 9.89949i) q^{20} -21.2132i q^{21} +(5.00000 + 5.00000i) q^{22} +(-14.8492 - 14.8492i) q^{23} +(-6.00000 + 6.00000i) q^{24} -24.0000i q^{25} +21.2132 q^{26} +(19.0919 + 19.0919i) q^{27} +(-10.0000 + 10.0000i) q^{28} +(28.2843 - 28.2843i) q^{29} -29.6985i q^{30} +(24.0000 + 24.0000i) q^{31} +5.65685 q^{32} -15.0000 q^{33} +(7.00000 + 23.0000i) q^{34} -49.4975i q^{35} -18.0000i q^{36} +(-15.0000 - 15.0000i) q^{37} +7.07107i q^{38} +(-31.8198 + 31.8198i) q^{39} +(-14.0000 + 14.0000i) q^{40} +(-38.8909 - 38.8909i) q^{41} -30.0000i q^{42} +75.0000i q^{43} +(7.07107 + 7.07107i) q^{44} +(44.5477 + 44.5477i) q^{45} +(-21.0000 - 21.0000i) q^{46} +11.3137i q^{47} +(-8.48528 + 8.48528i) q^{48} -1.00000i q^{49} -33.9411i q^{50} +(-45.0000 - 24.0000i) q^{51} +30.0000 q^{52} +67.8823 q^{53} +(27.0000 + 27.0000i) q^{54} -35.0000 q^{55} +(-14.1421 + 14.1421i) q^{56} +(-10.6066 - 10.6066i) q^{57} +(40.0000 - 40.0000i) q^{58} -63.6396 q^{59} -42.0000i q^{60} +(71.0000 - 71.0000i) q^{61} +(33.9411 + 33.9411i) q^{62} +(45.0000 + 45.0000i) q^{63} +8.00000 q^{64} +(-74.2462 + 74.2462i) q^{65} -21.2132 q^{66} -80.0000 q^{67} +(9.89949 + 32.5269i) q^{68} +63.0000 q^{69} -70.0000i q^{70} +(-28.2843 + 28.2843i) q^{71} -25.4558i q^{72} +(80.0000 + 80.0000i) q^{73} +(-21.2132 - 21.2132i) q^{74} +(50.9117 + 50.9117i) q^{75} +10.0000i q^{76} -35.3553 q^{77} +(-45.0000 + 45.0000i) q^{78} +(-11.0000 + 11.0000i) q^{79} +(-19.7990 + 19.7990i) q^{80} -81.0000 q^{81} +(-55.0000 - 55.0000i) q^{82} +124.451 q^{83} -42.4264i q^{84} +(-105.000 - 56.0000i) q^{85} +106.066i q^{86} +120.000i q^{87} +(10.0000 + 10.0000i) q^{88} +21.2132i q^{89} +(63.0000 + 63.0000i) q^{90} +(-75.0000 + 75.0000i) q^{91} +(-29.6985 - 29.6985i) q^{92} -101.823 q^{93} +16.0000i q^{94} +(-24.7487 - 24.7487i) q^{95} +(-12.0000 + 12.0000i) q^{96} +(-80.0000 - 80.0000i) q^{97} -1.41421i q^{98} +(31.8198 - 31.8198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 12 q^{6} - 20 q^{7}+O(q^{10}) \) 4 * q + 8 * q^4 - 12 * q^6 - 20 * q^7	\( 4 q + 8 q^{4} - 12 q^{6} - 20 q^{7} - 28 q^{10} + 60 q^{13} + 16 q^{16} + 20 q^{22} - 24 q^{24} - 40 q^{28} + 96 q^{31} - 60 q^{33} + 28 q^{34} - 60 q^{37} - 56 q^{40} - 84 q^{46} - 180 q^{51} + 120 q^{52} + 108 q^{54} - 140 q^{55} + 160 q^{58} + 284 q^{61} + 180 q^{63} + 32 q^{64} - 320 q^{67} + 252 q^{69} + 320 q^{73} - 180 q^{78} - 44 q^{79} - 324 q^{81} - 220 q^{82} - 420 q^{85} + 40 q^{88} + 252 q^{90} - 300 q^{91} - 48 q^{96} - 320 q^{97}+O(q^{100}) \) 4 * q + 8 * q^4 - 12 * q^6 - 20 * q^7 - 28 * q^10 + 60 * q^13 + 16 * q^16 + 20 * q^22 - 24 * q^24 - 40 * q^28 + 96 * q^31 - 60 * q^33 + 28 * q^34 - 60 * q^37 - 56 * q^40 - 84 * q^46 - 180 * q^51 + 120 * q^52 + 108 * q^54 - 140 * q^55 + 160 * q^58 + 284 * q^61 + 180 * q^63 + 32 * q^64 - 320 * q^67 + 252 * q^69 + 320 * q^73 - 180 * q^78 - 44 * q^79 - 324 * q^81 - 220 * q^82 - 420 * q^85 + 40 * q^88 + 252 * q^90 - 300 * q^91 - 48 * q^96 - 320 * q^97

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