LMFDB - Embedded newform 102.3.e.a.89.1

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			89.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	102.89
Dual form			102.3.e.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421 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} - 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}+ \cdots - 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

Character values

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

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−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	$-0.00318331\pi$
$5$	4.94975	+	4.94975i	0.989949	+	0.989949i	−0.0100005	+	0.999950i	$0.503183\pi$
$6$	−3.00000	−	3.00000i	−0.500000	−	0.500000i
$7$	−5.00000	−	5.00000i	−0.714286	−	0.714286i	0.253143	−	0.967429i	$-0.418536\pi$
$7$	−5.00000	−	5.00000i	−0.714286	−	0.714286i	−0.967429	+	0.253143i	$0.918536\pi$
$8$	−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	$-0.822981\pi$
$11$	−3.53553	+	3.53553i	−0.321412	+	0.321412i	0.527897	+	0.849309i	$0.322981\pi$
$12$	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	$-0.957995\pi$
$19$		−	5.00000i		−	0.263158i	0.991306	−	0.131579i	$-0.0420047\pi$
$20$	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	$-0.599095\pi$
$23$	14.8492	−	14.8492i	0.645619	−	0.645619i	0.951931	+	0.306312i	$0.0990951\pi$
$24$	−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	$-0.492238\pi$
$29$	−28.2843	−	28.2843i	−0.975320	−	0.975320i	−0.999703	+	0.0243830i	$0.992238\pi$
$30$		−	29.6985i		−	0.989949i
$31$	24.0000	−	24.0000i	0.774194	−	0.774194i	−0.204643	−	0.978837i	$-0.565603\pi$
$31$	24.0000	−	24.0000i	0.774194	−	0.774194i	0.978837	+	0.204643i	$0.0656034\pi$
$32$	−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	−0.880133	−	0.474727i	$-0.842547\pi$
$37$	−15.0000	+	15.0000i	−0.405405	+	0.405405i	0.474727	+	0.880133i	$0.342547\pi$
$38$			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	$-0.515980\pi$
$41$	38.8909	−	38.8909i	0.948558	−	0.948558i	0.998740	+	0.0501822i	$0.0159802\pi$
$42$			30.0000i			0.714286i
$43$		−	75.0000i		−	1.74419i	−0.489340	−	0.872093i	$-0.662762\pi$
$43$		−	75.0000i		−	1.74419i	0.489340	−	0.872093i	$-0.337238\pi$
$44$	−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	$-0.721231\pi$
$53$	−67.8823			−1.28080			−0.640399	+	0.768043i	$0.721231\pi$
$54$	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	$-0.318682\pi$
$59$	63.6396			1.07864			0.539319	+	0.842102i	$0.318682\pi$
$60$			42.0000i			0.700000i
$61$	71.0000	+	71.0000i	1.16393	+	1.16393i	0.983607	+	0.180328i	$0.0577159\pi$
$61$	71.0000	+	71.0000i	1.16393	+	1.16393i	0.180328	+	0.983607i	$0.442284\pi$
$62$	−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	$-0.159105\pi$
$71$	28.2843	+	28.2843i	0.398370	+	0.398370i	−0.479288	+	0.877658i	$0.659105\pi$
$72$		−	25.4558i		−	0.353553i
$73$	80.0000	−	80.0000i	1.09589	−	1.09589i	0.101004	−	0.994886i	$-0.467794\pi$
$73$	80.0000	−	80.0000i	1.09589	−	1.09589i	0.994886	−	0.101004i	$-0.0322056\pi$
$74$	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	0.634051	−	0.773291i	$-0.281391\pi$
$79$	−11.0000	−	11.0000i	−0.139241	−	0.139241i	−0.773291	+	0.634051i	$0.781391\pi$
$80$	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	$-0.769804\pi$
$83$	−124.451			−1.49941			−0.749704	+	0.661774i	$0.769804\pi$
$84$		−	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	−0.986784	−	0.162042i	$-0.948192\pi$
$97$	−80.0000	+	80.0000i	−0.824742	+	0.824742i	0.162042	+	0.986784i	$0.448192\pi$
$98$		−	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	−0.880277	−	0.474460i	$-0.842643\pi$
$107$	−144.957	−	144.957i	−1.35474	−	1.35474i	−0.474460	−	0.880277i	$-0.657357\pi$
$108$	−38.1838	+	38.1838i	−0.353553	+	0.353553i
$109$	104.000	+	104.000i	0.954128	+	0.954128i	0.998993	−	0.0448646i	$-0.0142857\pi$
$109$	104.000	+	104.000i	0.954128	+	0.954128i	−0.0448646	+	0.998993i	$0.514286\pi$
$110$	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	$-0.842861\pi$
$113$	−45.9619	+	45.9619i	−0.406743	+	0.406743i	0.473858	+	0.880601i	$0.342861\pi$
$114$	−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	$0.163780\pi$
$127$			125.000i			0.984252i	−0.870524	+	0.492126i	$0.836220\pi$
$128$	−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	$-0.243925\pi$
$131$	3.53553	+	3.53553i	0.0269888	+	0.0269888i	−0.693484	+	0.720472i	$0.743925\pi$
$132$	−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	−0.772141	−	0.635451i	$-0.780814\pi$
$139$	−19.0000	+	19.0000i	−0.136691	+	0.136691i	0.635451	+	0.772141i	$0.280814\pi$
$140$		−	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	$0.306691\pi$
$151$			248.000i			1.64238i	−0.570652	+	0.821192i	$0.693309\pi$
$152$			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	0.971840	−	0.235643i	$-0.0757197\pi$
$163$	120.000	+	120.000i	0.736196	+	0.736196i	−0.235643	+	0.971840i	$0.575720\pi$
$164$	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	$-0.138112\pi$
$167$	81.3173	+	81.3173i	0.486930	+	0.486930i	−0.420406	+	0.907336i	$0.638112\pi$
$168$			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	$-0.226981\pi$
$173$	17.6777	+	17.6777i	0.102183	+	0.102183i	−0.654167	+	0.756350i	$0.726981\pi$
$174$			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	$-0.550509\pi$
$179$	−56.5685			−0.316025			−0.158013	+	0.987437i	$0.550509\pi$
$180$	−89.0955	+	89.0955i	−0.494975	+	0.494975i
$181$	−79.0000	−	79.0000i	−0.436464	−	0.436464i	0.454356	−	0.890820i	$-0.349869\pi$
$181$	−79.0000	−	79.0000i	−0.436464	−	0.436464i	−0.890820	+	0.454356i	$0.849869\pi$
$182$	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	−0.958529	−	0.284994i	$-0.908008\pi$
$193$	−240.000	−	240.000i	−1.24352	−	1.24352i	−0.284994	−	0.958529i	$-0.591992\pi$
$194$	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	$-0.815909\pi$
$197$	−57.2756	+	57.2756i	−0.290739	+	0.290739i	0.546633	+	0.837372i	$0.315909\pi$
$198$	45.0000	+	45.0000i	0.227273	+	0.227273i
$199$	104.000	−	104.000i	0.522613	−	0.522613i	−0.395747	−	0.918360i	$-0.629514\pi$
$199$	104.000	−	104.000i	0.522613	−	0.522613i	0.918360	+	0.395747i	$0.129514\pi$
$200$		−	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	−0.999712	−	0.0239843i	$-0.992365\pi$
$211$	−216.000	−	216.000i	−1.02370	−	1.02370i	−0.0239843	−	0.999712i	$-0.507635\pi$
$212$	−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	$0.112981\pi$
$223$			155.000i			0.695067i	−0.937668	+	0.347534i	$0.887019\pi$
$224$	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	$-0.860904\pi$
$227$	−109.602	+	109.602i	−0.482826	+	0.482826i	0.423207	+	0.906033i	$0.360904\pi$
$228$	21.2132	−	21.2132i	0.0930404	−	0.0930404i
$229$		−	40.0000i		−	0.174672i	−0.996179	−	0.0873362i	$-0.972165\pi$
$229$		−	40.0000i		−	0.174672i	0.996179	−	0.0873362i	$-0.0278355\pi$
$230$	−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	$-0.360834\pi$
$233$	−112.430	−	112.430i	−0.482532	−	0.482532i	−0.905939	+	0.423407i	$0.860834\pi$
$234$		−	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	0.172702	−	0.984974i	$-0.444750\pi$
$241$	279.000	−	279.000i	1.15768	−	1.15768i	0.984974	−	0.172702i	$-0.0552498\pi$
$242$		−	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	$-0.399367\pi$
$257$	159.806			0.621814			0.310907	+	0.950440i	$0.399367\pi$
$258$	−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	$-0.767430\pi$
$263$	−391.737			−1.48949			−0.744747	+	0.667346i	$0.767430\pi$
$264$	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	$-0.138263\pi$
$269$	130.815	+	130.815i	0.486300	+	0.486300i	−0.420836	+	0.907137i	$0.638263\pi$
$270$	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	0.0108896	−	0.999941i	$-0.496534\pi$
$277$	280.000	−	280.000i	1.01083	−	1.01083i	0.999941	−	0.0108896i	$-0.00346634\pi$
$278$	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	$-0.479962\pi$
$281$	35.3553			0.125820			0.0629099	+	0.998019i	$0.479962\pi$
$282$	33.9411	−	33.9411i	0.120359	−	0.120359i
$283$	155.000	+	155.000i	0.547703	+	0.547703i	0.925776	−	0.378073i	$-0.123413\pi$
$283$	155.000	+	155.000i	0.547703	+	0.547703i	−0.378073	+	0.925776i	$0.623413\pi$
$284$	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	$-0.188202\pi$
$311$	84.8528	+	84.8528i	0.272839	+	0.272839i	−0.557403	+	0.830242i	$0.688202\pi$
$312$	−90.0000	−	90.0000i	−0.288462	−	0.288462i
$313$	160.000	+	160.000i	0.511182	+	0.511182i	0.914889	−	0.403706i	$-0.132278\pi$
$313$	160.000	+	160.000i	0.511182	+	0.511182i	−0.403706	+	0.914889i	$0.632278\pi$
$314$	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	$-0.647842\pi$
$317$	141.421	−	141.421i	0.446124	−	0.446124i	0.894064	+	0.447940i	$0.147842\pi$
$318$	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	$-0.978346\pi$
$331$		−	45.0000i		−	0.135952i	0.997687	−	0.0679758i	$-0.0216541\pi$
$332$	−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	−0.833866	−	0.551967i	$-0.813877\pi$
$337$	−95.0000	+	95.0000i	−0.281899	+	0.281899i	0.551967	+	0.833866i	$0.313877\pi$
$338$	−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	$-0.675948\pi$
$347$	113.137	−	113.137i	0.326043	−	0.326043i	0.851080	+	0.525036i	$0.175948\pi$
$348$		−	240.000i		−	0.689655i
$349$			473.000i			1.35530i	0.735384	+	0.677650i	$0.237002\pi$
$349$			473.000i			1.35530i	−0.735384	+	0.677650i	$0.762998\pi$
$350$	−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	$-0.446456\pi$
$359$	120.208			0.334842			0.167421	+	0.985886i	$0.446456\pi$
$360$	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	0.597505	−	0.801865i	$-0.296159\pi$
$367$	−75.0000	−	75.0000i	−0.204360	−	0.204360i	−0.801865	+	0.597505i	$0.796159\pi$
$368$	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	−0.895748	−	0.444561i	$-0.853360\pi$
$379$	−171.000	+	171.000i	−0.451187	+	0.451187i	0.444561	+	0.895748i	$0.353360\pi$
$380$	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	$-0.274822\pi$
$383$	497.803			1.29975			0.649874	+	0.760042i	$0.274822\pi$
$384$	−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	$-0.856280\pi$
$389$	−700.036			−1.79958			−0.899789	+	0.436326i	$0.856280\pi$
$390$		−	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	$-0.250000\pi$
$397$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$398$	−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	$-0.557976\pi$
$401$	321.734	−	321.734i	0.802328	−	0.802328i	0.983459	+	0.181131i	$0.0579758\pi$
$402$	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	$-0.874717\pi$
$419$	−226.274	+	226.274i	−0.540034	+	0.540034i	0.383505	+	0.923539i	$0.374717\pi$
$420$	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	$-0.644694\pi$
$431$	197.990	−	197.990i	0.459373	−	0.459373i	0.898450	+	0.439076i	$0.144694\pi$
$432$	−76.3675	+	76.3675i	−0.176777	+	0.176777i
$433$		−	305.000i		−	0.704388i	−0.935927	−	0.352194i	$-0.885436\pi$
$433$		−	305.000i		−	0.704388i	0.935927	−	0.352194i	$-0.114564\pi$
$434$	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	−0.776233	−	0.630447i	$-0.782872\pi$
$439$	−64.0000	+	64.0000i	−0.145786	+	0.145786i	0.630447	+	0.776233i	$0.282872\pi$
$440$	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	$-0.557745\pi$
$449$	360.624	−	360.624i	0.803173	−	0.803173i	0.983590	+	0.180418i	$0.0577449\pi$
$450$	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	$-0.906367\pi$
$457$		−	265.000i		−	0.579869i	0.957047	−	0.289934i	$-0.0936335\pi$
$458$			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	$-0.551490\pi$
$461$	−148.492			−0.322109			−0.161055	+	0.986945i	$0.551490\pi$
$462$	−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	$-0.323912\pi$
$467$	490.732			1.05082			0.525409	+	0.850850i	$0.323912\pi$
$468$			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	$-0.171113\pi$
$479$	166.170	+	166.170i	0.346910	+	0.346910i	−0.512047	+	0.858957i	$0.671113\pi$
$480$		−	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	0.878378	−	0.477967i	$-0.158626\pi$
$487$	195.000	+	195.000i	0.400411	+	0.400411i	−0.477967	+	0.878378i	$0.658626\pi$
$488$	−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	$-0.695408\pi$
$491$	−565.685			−1.15211			−0.576054	+	0.817411i	$0.695408\pi$
$492$	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	0.958486	−	0.285139i	$-0.0920399\pi$
$499$	336.000	+	336.000i	0.673347	+	0.673347i	−0.285139	+	0.958486i	$0.592040\pi$
$500$	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	$-0.984124\pi$
$503$	−477.297	+	477.297i	−0.948901	+	0.948901i	0.0498557	+	0.998756i	$0.484124\pi$
$504$	−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	$-0.545244\pi$
$521$	441.942	−	441.942i	0.848257	−	0.848257i	0.989916	+	0.141659i	$0.0452436\pi$
$522$	−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	−0.345188	−	0.938534i	$-0.612185\pi$
$541$	321.000	−	321.000i	0.593346	−	0.593346i	0.938534	+	0.345188i	$0.112185\pi$
$542$	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	−0.969037	−	0.246916i	$-0.920583\pi$
$547$	−395.000	+	395.000i	−0.722121	+	0.722121i	0.246916	+	0.969037i	$0.420583\pi$
$548$			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	$-0.471176\pi$
$563$	101.823			0.180859			0.0904293	+	0.995903i	$0.471176\pi$
$564$	−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	$-0.613126\pi$
$569$	−395.980			−0.695922			−0.347961	+	0.937509i	$0.613126\pi$
$570$	−148.492			−0.260513
$571$	−104.000	−	104.000i	−0.182137	−	0.182137i	0.610150	−	0.792286i	$-0.291109\pi$
$571$	−104.000	−	104.000i	−0.182137	−	0.182137i	−0.792286	+	0.610150i	$0.791109\pi$
$572$	−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	$-0.639382\pi$
$587$	−497.803			−0.848046			−0.424023	+	0.905651i	$0.639382\pi$
$588$	−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	$-0.218911\pi$
$593$	916.410			1.54538			0.772690	+	0.634784i	$0.218911\pi$
$594$			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	0.658981	−	0.752159i	$-0.270988\pi$
$601$	−56.0000	−	56.0000i	−0.0931780	−	0.0931780i	−0.752159	+	0.658981i	$0.770988\pi$
$602$	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	−0.0646981	+	0.997905i	$0.520608\pi$
$607$	−645.000	+	645.000i	−1.06260	+	1.06260i	−0.997905	+	0.0646981i	$0.979392\pi$
$608$			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	$-0.270650\pi$
$617$	−56.5685	−	56.5685i	−0.0916832	−	0.0916832i	−0.751461	+	0.659778i	$0.770650\pi$
$618$	15.0000	+	15.0000i	0.0242718	+	0.0242718i
$619$	261.000	+	261.000i	0.421648	+	0.421648i	0.885771	−	0.464123i	$-0.153630\pi$
$619$	261.000	+	261.000i	0.421648	+	0.421648i	−0.464123	+	0.885771i	$0.653630\pi$
$620$	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	$0.0539826\pi$
$631$			213.000i			0.337559i	−0.985654	+	0.168780i	$0.946017\pi$
$632$	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	$-0.334155\pi$
$641$	−236.881	−	236.881i	−0.369549	−	0.369549i	−0.867313	+	0.497764i	$0.834155\pi$
$642$			869.741i			1.35474i
$643$	520.000	−	520.000i	0.808709	−	0.808709i	−0.175729	−	0.984439i	$-0.556228\pi$
$643$	520.000	−	520.000i	0.808709	−	0.808709i	0.984439	+	0.175729i	$0.0562284\pi$
$644$	−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	0.509122	−	0.860694i	$-0.329970\pi$
$653$	894.490	−	894.490i	1.36982	−	1.36982i	0.860694	−	0.509122i	$-0.170030\pi$
$654$		−	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	$0.132621\pi$
$661$			535.000i			0.809380i	−0.914454	+	0.404690i	$0.867379\pi$
$662$			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	0.253984	−	0.967208i	$-0.418259\pi$
$673$	−480.000	−	480.000i	−0.713224	−	0.713224i	−0.967208	+	0.253984i	$0.918259\pi$
$674$	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	$-0.363091\pi$
$677$	−333.047	−	333.047i	−0.491946	−	0.491946i	−0.908919	+	0.416973i	$0.863091\pi$
$678$	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	$-0.436406\pi$
$683$	−533.866	−	533.866i	−0.781648	−	0.781648i	−0.980109	+	0.198461i	$0.936406\pi$
$684$	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	0.891992	−	0.452050i	$-0.149307\pi$
$691$	304.000	+	304.000i	0.439942	+	0.439942i	−0.452050	+	0.891992i	$0.649307\pi$
$692$	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	−0.421594	−	0.906785i	$-0.638529\pi$
$709$	344.000	−	344.000i	0.485190	−	0.485190i	0.906785	+	0.421594i	$0.138529\pi$
$710$		−	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	$-0.188750\pi$
$719$	194.454	+	194.454i	0.270451	+	0.270451i	−0.558831	+	0.829282i	$0.688750\pi$
$720$	−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	$0.115419\pi$
$733$			520.000i			0.709413i	−0.934978	+	0.354707i	$0.884581\pi$
$734$	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	$0.300467\pi$
$739$			1197.00i			1.61976i	−0.586598	+	0.809878i	$0.699533\pi$
$740$	−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	$-0.152070\pi$
$743$	318.198	+	318.198i	0.428261	+	0.428261i	−0.459775	+	0.888036i	$0.652070\pi$
$744$	−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	−0.548521	−	0.836137i	$-0.684809\pi$
$751$	216.000	−	216.000i	0.287617	−	0.287617i	0.836137	+	0.548521i	$0.184809\pi$
$752$			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	$-0.739588\pi$
$757$		−	1105.00i		−	1.45971i	0.683602	−	0.729855i	$-0.260412\pi$
$758$	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	$-0.390713\pi$
$773$	520.431			0.673261			0.336630	+	0.941637i	$0.390713\pi$
$774$	−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	−0.996650	−	0.0817835i	$-0.973938\pi$
$787$	−720.000	+	720.000i	−0.914867	+	0.914867i	0.0817835	+	0.996650i	$0.473938\pi$
$788$	−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	$-0.452378\pi$
$797$	237.588			0.298103			0.149051	+	0.988829i	$0.452378\pi$
$798$	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	$-0.784495\pi$
$809$	−123.744	+	123.744i	−0.152959	+	0.152959i	0.626479	+	0.779438i	$0.284495\pi$
$810$	567.000	+	567.000i	0.700000	+	0.700000i
$811$	824.000	−	824.000i	1.01603	−	1.01603i	0.0161602	−	0.999869i	$-0.494856\pi$
$811$	824.000	−	824.000i	1.01603	−	1.01603i	0.999869	−	0.0161602i	$-0.00514417\pi$
$812$			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	$-0.333337\pi$
$821$	−300.520	−	300.520i	−0.366042	−	0.366042i	−0.866031	+	0.499990i	$0.833337\pi$
$822$	369.110	−	369.110i	0.449039	−	0.449039i
$823$	1005.00	+	1005.00i	1.22114	+	1.22114i	0.967226	+	0.253916i	$0.0817186\pi$
$823$	1005.00	+	1005.00i	1.22114	+	1.22114i	0.253916	+	0.967226i	$0.418281\pi$
$824$	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	$-0.917111\pi$
$827$	−586.192	+	586.192i	−0.708817	+	0.708817i	0.257470	+	0.966286i	$0.417111\pi$
$828$	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	$-0.892214\pi$
$839$	−512.652	+	512.652i	−0.611028	+	0.611028i	0.332186	+	0.943214i	$0.392214\pi$
$840$	−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	−0.0629443	+	0.998017i	$0.520049\pi$
$853$	−905.000	+	905.000i	−1.06096	+	1.06096i	−0.998017	+	0.0629443i	$0.979951\pi$
$854$			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	$-0.581830\pi$
$857$	610.940	−	610.940i	0.712882	−	0.712882i	0.967137	+	0.254255i	$0.0818302\pi$
$858$	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	0.0683565	−	0.997661i	$-0.478224\pi$
$877$	−815.000	−	815.000i	−0.929304	−	0.929304i	−0.997661	+	0.0683565i	$0.978224\pi$
$878$	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	−0.999995	−	0.00327833i	$-0.998956\pi$
$881$	−883.883	−	883.883i	−1.00327	−	1.00327i	−0.00327833	−	0.999995i	$-0.501044\pi$
$882$	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	$-0.388745\pi$
$887$	−529.623	−	529.623i	−0.597095	−	0.597095i	−0.939538	+	0.342444i	$0.888745\pi$
$888$	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	0.220214	−	0.975451i	$-0.429324\pi$
$907$	−685.000	−	685.000i	−0.755237	−	0.755237i	−0.975451	+	0.220214i	$0.929324\pi$
$908$	−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	0.0288651	−	0.999583i	$-0.490811\pi$
$911$	936.916	−	936.916i	1.02845	−	1.02845i	0.999583	−	0.0288651i	$-0.00918932\pi$
$912$	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	−0.0557454	+	0.998445i	$0.517754\pi$
$929$	−979.343	+	979.343i	−1.05419	+	1.05419i	−0.998445	+	0.0557454i	$0.982246\pi$
$930$	−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	$0.0912691\pi$
$937$			530.000i			0.565635i	−0.959174	+	0.282818i	$0.908731\pi$
$938$	−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	$-0.602729\pi$
$941$	593.970	−	593.970i	0.631211	−	0.631211i	0.948372	+	0.317161i	$0.102729\pi$
$942$	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	0.999994	+	0.00354537i	$0.00112853\pi$
$947$	950.352	+	950.352i	1.00354	+	1.00354i	0.00354537	+	0.999994i	$0.498871\pi$
$948$		−	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	$0.195592\pi$
$967$			1115.00i			1.15305i	−0.817079	+	0.576525i	$0.804408\pi$
$968$		−	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	$-0.911106\pi$
$971$	−1866.76			−1.92251			−0.961257	+	0.275652i	$0.911106\pi$
$972$	−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	$-0.398537\pi$
$977$	612.354			0.626770			0.313385	+	0.949626i	$0.398537\pi$
$978$		−	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	$-0.0481119\pi$
$983$	823.779	+	823.779i	0.838026	+	0.838026i	−0.150573	+	0.988599i	$0.548112\pi$
$984$	−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	0.0338736	−	0.999426i	$-0.489216\pi$
$991$	1024.00	−	1024.00i	1.03330	−	1.03330i	0.999426	−	0.0338736i	$-0.0107844\pi$
$992$	−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	−0.997497	−	0.0707075i	$-0.977474\pi$
$997$	−1065.00	−	1065.00i	−1.06820	−	1.06820i	−0.0707075	−	0.997497i	$-0.522526\pi$
$998$	−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.89.1	yes	4
3.2	odd	2	inner	102.3.e.a.89.2	yes	4
17.13	even	4	inner	102.3.e.a.47.2	yes	4
51.47	odd	4	inner	102.3.e.a.47.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.3.e.a.47.1	✓	4	51.47	odd	4	inner
102.3.e.a.47.2	yes	4	17.13	even	4	inner
102.3.e.a.89.1	yes	4	1.1	even	1	trivial
102.3.e.a.89.2	yes	4	3.2	odd	2	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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 12 q^{6} - 20 q^{7} - 28 q^{10} + 60 q^{13} + 16 q^{16} + 20 q^{22} - 24 q^{24} - 40 q^{28} + 96 q^{31} - 60 q^{33} + 28 q^{34} - 60 q^{37} - 56 q^{40} - 84 q^{46} - 180 q^{51} + 120 q^{52}+ \cdots - 320 q^{97}+O(q^{100}) \) 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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