LMFDB - Embedded newform 538.3.c.b.187.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	538.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.3
Character	$\chi$	$=$	538.187
Dual form			538.3.c.b.351.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(-3.24321 - 3.24321i) q^{3} +2.00000i q^{4} +4.65083 q^{5} +6.48641i q^{6} +(4.88017 - 4.88017i) q^{7} +(2.00000 - 2.00000i) q^{8} +12.0368i q^{9} +(-4.65083 - 4.65083i) q^{10} +17.7265i q^{11} +(6.48641 - 6.48641i) q^{12} +4.34344i q^{13} -9.76035 q^{14} +(-15.0836 - 15.0836i) q^{15} -4.00000 q^{16} +(-11.3436 - 11.3436i) q^{17} +(12.0368 - 12.0368i) q^{18} +(-7.80386 + 7.80386i) q^{19} +9.30167i q^{20} -31.6548 q^{21} +(17.7265 - 17.7265i) q^{22} -40.0305 q^{23} -12.9728 q^{24} -3.36973 q^{25} +(4.34344 - 4.34344i) q^{26} +(9.84884 - 9.84884i) q^{27} +(9.76035 + 9.76035i) q^{28} +(-3.41094 + 3.41094i) q^{29} +30.1672i q^{30} +(-41.6217 + 41.6217i) q^{31} +(4.00000 + 4.00000i) q^{32} +(57.4906 - 57.4906i) q^{33} +22.6871i q^{34} +(22.6969 - 22.6969i) q^{35} -24.0735 q^{36} -3.25116 q^{37} +15.6077 q^{38} +(14.0867 - 14.0867i) q^{39} +(9.30167 - 9.30167i) q^{40} +11.4842 q^{41} +(31.6548 + 31.6548i) q^{42} -8.80977i q^{43} -35.4530 q^{44} +55.9810i q^{45} +(40.0305 + 40.0305i) q^{46} -41.4763 q^{47} +(12.9728 + 12.9728i) q^{48} +1.36783i q^{49} +(3.36973 + 3.36973i) q^{50} +73.5790i q^{51} -8.68688 q^{52} -17.5716 q^{53} -19.6977 q^{54} +82.4429i q^{55} -19.5207i q^{56} +50.6191 q^{57} +6.82188 q^{58} +(-5.47396 + 5.47396i) q^{59} +(30.1672 - 30.1672i) q^{60} +27.1650 q^{61} +83.2434 q^{62} +(58.7415 + 58.7415i) q^{63} -8.00000i q^{64} +20.2006i q^{65} -114.981 q^{66} +2.74007 q^{67} +(22.6871 - 22.6871i) q^{68} +(129.827 + 129.827i) q^{69} -45.3938 q^{70} +(-61.4762 + 61.4762i) q^{71} +(24.0735 + 24.0735i) q^{72} -79.1820i q^{73} +(3.25116 + 3.25116i) q^{74} +(10.9287 + 10.9287i) q^{75} +(-15.6077 - 15.6077i) q^{76} +(86.5083 + 86.5083i) q^{77} -28.1734 q^{78} +6.12702i q^{79} -18.6033 q^{80} +44.4472 q^{81} +(-11.4842 - 11.4842i) q^{82} +(58.7815 - 58.7815i) q^{83} -63.3096i q^{84} +(-52.7570 - 52.7570i) q^{85} +(-8.80977 + 8.80977i) q^{86} +22.1247 q^{87} +(35.4530 + 35.4530i) q^{88} +113.961i q^{89} +(55.9810 - 55.9810i) q^{90} +(21.1967 + 21.1967i) q^{91} -80.0610i q^{92} +269.975 q^{93} +(41.4763 + 41.4763i) q^{94} +(-36.2945 + 36.2945i) q^{95} -25.9456i q^{96} -9.11196i q^{97} +(1.36783 - 1.36783i) q^{98} -213.369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) $ 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−3.24321	−	3.24321i	−1.08107	−	1.08107i	−0.996410	−	0.0846584i	$-0.973020\pi$
$3$	−3.24321	−	3.24321i	−1.08107	−	1.08107i	−0.0846584	−	0.996410i	$-0.526980\pi$
$4$			2.00000i			0.500000i
$5$	4.65083			0.930167			0.465083	−	0.885267i	$-0.346024\pi$
$5$	4.65083			0.930167			0.465083	+	0.885267i	$0.346024\pi$
$6$			6.48641i			1.08107i
$7$	4.88017	−	4.88017i	0.697168	−	0.697168i	−0.266631	−	0.963799i	$-0.585911\pi$
$7$	4.88017	−	4.88017i	0.697168	−	0.697168i	0.963799	+	0.266631i	$0.0859105\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			12.0368i			1.33742i
$10$	−4.65083	−	4.65083i	−0.465083	−	0.465083i
$11$			17.7265i			1.61150i	0.592257	+	0.805749i	$0.298237\pi$
$11$			17.7265i			1.61150i	−0.592257	+	0.805749i	$0.701763\pi$
$12$	6.48641	−	6.48641i	0.540534	−	0.540534i
$13$			4.34344i			0.334111i	0.985947	+	0.167055i	$0.0534259\pi$
$13$			4.34344i			0.334111i	−0.985947	+	0.167055i	$0.946574\pi$
$14$	−9.76035			−0.697168
$15$	−15.0836	−	15.0836i	−1.00557	−	1.00557i
$16$	−4.00000			−0.250000
$17$	−11.3436	−	11.3436i	−0.667268	−	0.667268i	0.289815	−	0.957083i	$-0.406406\pi$
$17$	−11.3436	−	11.3436i	−0.667268	−	0.667268i	−0.957083	+	0.289815i	$0.906406\pi$
$18$	12.0368	−	12.0368i	0.668709	−	0.668709i
$19$	−7.80386	+	7.80386i	−0.410730	+	0.410730i	−0.881993	−	0.471263i	$-0.843798\pi$
$19$	−7.80386	+	7.80386i	−0.410730	+	0.410730i	0.471263	+	0.881993i	$0.343798\pi$
$20$			9.30167i			0.465083i
$21$	−31.6548			−1.50737
$22$	17.7265	−	17.7265i	0.805749	−	0.805749i
$23$	−40.0305			−1.74046			−0.870229	−	0.492648i	$-0.836029\pi$
$23$	−40.0305			−1.74046			−0.870229	+	0.492648i	$0.836029\pi$
$24$	−12.9728			−0.540534
$25$	−3.36973			−0.134789
$26$	4.34344	−	4.34344i	0.167055	−	0.167055i
$27$	9.84884	−	9.84884i	0.364772	−	0.364772i
$28$	9.76035	+	9.76035i	0.348584	+	0.348584i
$29$	−3.41094	+	3.41094i	−0.117619	+	0.117619i	−0.763466	−	0.645848i	$-0.776504\pi$
$29$	−3.41094	+	3.41094i	−0.117619	+	0.117619i	0.645848	+	0.763466i	$0.276504\pi$
$30$			30.1672i			1.00557i
$31$	−41.6217	+	41.6217i	−1.34263	+	1.34263i	−0.449208	+	0.893427i	$0.648294\pi$
$31$	−41.6217	+	41.6217i	−1.34263	+	1.34263i	−0.893427	+	0.449208i	$0.851706\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	57.4906	−	57.4906i	1.74214	−	1.74214i
$34$			22.6871i			0.667268i
$35$	22.6969	−	22.6969i	0.648482	−	0.648482i
$36$	−24.0735			−0.668709
$37$	−3.25116			−0.0878691			−0.0439346	−	0.999034i	$-0.513989\pi$
$37$	−3.25116			−0.0878691			−0.0439346	+	0.999034i	$0.513989\pi$
$38$	15.6077			0.410730
$39$	14.0867	−	14.0867i	0.361197	−	0.361197i
$40$	9.30167	−	9.30167i	0.232542	−	0.232542i
$41$	11.4842			0.280103			0.140052	−	0.990144i	$-0.455273\pi$
$41$	11.4842			0.280103			0.140052	+	0.990144i	$0.455273\pi$
$42$	31.6548	+	31.6548i	0.753686	+	0.753686i
$43$		−	8.80977i		−	0.204878i	−0.994739	−	0.102439i	$-0.967335\pi$
$43$		−	8.80977i		−	0.204878i	0.994739	−	0.102439i	$-0.0326647\pi$
$44$	−35.4530			−0.805749
$45$			55.9810i			1.24402i
$46$	40.0305	+	40.0305i	0.870229	+	0.870229i
$47$	−41.4763			−0.882475			−0.441237	−	0.897390i	$-0.645460\pi$
$47$	−41.4763			−0.882475			−0.441237	+	0.897390i	$0.645460\pi$
$48$	12.9728	+	12.9728i	0.270267	+	0.270267i
$49$			1.36783i			0.0279148i
$50$	3.36973	+	3.36973i	0.0673947	+	0.0673947i
$51$			73.5790i			1.44272i
$52$	−8.68688			−0.167055
$53$	−17.5716			−0.331540			−0.165770	−	0.986164i	$-0.553011\pi$
$53$	−17.5716			−0.331540			−0.165770	+	0.986164i	$0.553011\pi$
$54$	−19.6977			−0.364772
$55$			82.4429i			1.49896i
$56$		−	19.5207i		−	0.348584i
$57$	50.6191			0.888054
$58$	6.82188			0.117619
$59$	−5.47396	+	5.47396i	−0.0927790	+	0.0927790i	−0.751973	−	0.659194i	$-0.770898\pi$
$59$	−5.47396	+	5.47396i	−0.0927790	+	0.0927790i	0.659194	+	0.751973i	$0.270898\pi$
$60$	30.1672	−	30.1672i	0.502787	−	0.502787i
$61$	27.1650			0.445329			0.222664	−	0.974895i	$-0.428525\pi$
$61$	27.1650			0.445329			0.222664	+	0.974895i	$0.428525\pi$
$62$	83.2434			1.34263
$63$	58.7415	+	58.7415i	0.932404	+	0.932404i
$64$		−	8.00000i		−	0.125000i
$65$			20.2006i			0.310779i
$66$	−114.981			−1.74214
$67$	2.74007			0.0408965			0.0204483	−	0.999791i	$-0.493491\pi$
$67$	2.74007			0.0408965			0.0204483	+	0.999791i	$0.493491\pi$
$68$	22.6871	−	22.6871i	0.333634	−	0.333634i
$69$	129.827	+	129.827i	1.88155	+	1.88155i
$70$	−45.3938			−0.648482
$71$	−61.4762	+	61.4762i	−0.865863	+	0.865863i	−0.992011	−	0.126149i	$-0.959738\pi$
$71$	−61.4762	+	61.4762i	−0.865863	+	0.865863i	0.126149	+	0.992011i	$0.459738\pi$
$72$	24.0735	+	24.0735i	0.334355	+	0.334355i
$73$		−	79.1820i		−	1.08468i	−0.840158	−	0.542342i	$-0.817538\pi$
$73$		−	79.1820i		−	1.08468i	0.840158	−	0.542342i	$-0.182462\pi$
$74$	3.25116	+	3.25116i	0.0439346	+	0.0439346i
$75$	10.9287	+	10.9287i	0.145717	+	0.145717i
$76$	−15.6077	−	15.6077i	−0.205365	−	0.205365i
$77$	86.5083	+	86.5083i	1.12348	+	1.12348i
$78$	−28.1734			−0.361197
$79$			6.12702i			0.0775572i	0.999248	+	0.0387786i	$0.0123467\pi$
$79$			6.12702i			0.0775572i	−0.999248	+	0.0387786i	$0.987653\pi$
$80$	−18.6033			−0.232542
$81$	44.4472			0.548731
$82$	−11.4842	−	11.4842i	−0.140052	−	0.140052i
$83$	58.7815	−	58.7815i	0.708210	−	0.708210i	−0.257948	−	0.966159i	$-0.583046\pi$
$83$	58.7815	−	58.7815i	0.708210	−	0.708210i	0.966159	+	0.257948i	$0.0830464\pi$
$84$		−	63.3096i		−	0.753686i
$85$	−52.7570	−	52.7570i	−0.620671	−	0.620671i
$86$	−8.80977	+	8.80977i	−0.102439	+	0.102439i
$87$	22.1247			0.254307
$88$	35.4530	+	35.4530i	0.402875	+	0.402875i
$89$			113.961i			1.28046i	0.768181	+	0.640232i	$0.221162\pi$
$89$			113.961i			1.28046i	−0.768181	+	0.640232i	$0.778838\pi$
$90$	55.9810	−	55.9810i	0.622011	−	0.622011i
$91$	21.1967	+	21.1967i	0.232931	+	0.232931i
$92$		−	80.0610i		−	0.870229i
$93$	269.975			2.90296
$94$	41.4763	+	41.4763i	0.441237	+	0.441237i
$95$	−36.2945	+	36.2945i	−0.382047	+	0.382047i
$96$		−	25.9456i		−	0.270267i
$97$		−	9.11196i		−	0.0939378i	−0.998896	−	0.0469689i	$-0.985044\pi$
$97$		−	9.11196i		−	0.0939378i	0.998896	−	0.0469689i	$-0.0149562\pi$
$98$	1.36783	−	1.36783i	0.0139574	−	0.0139574i
$99$	−213.369			−2.15525
$100$		−	6.73947i		−	0.0673947i
$101$	2.08356	+	2.08356i	0.0206293	+	0.0206293i	0.717346	−	0.696717i	$-0.245357\pi$
$101$	2.08356	+	2.08356i	0.0206293	+	0.0206293i	−0.696717	+	0.717346i	$0.745357\pi$
$102$	73.5790	−	73.5790i	0.721362	−	0.721362i
$103$		−	45.5958i		−	0.442677i	−0.975197	−	0.221339i	$-0.928957\pi$
$103$		−	45.5958i		−	0.442677i	0.975197	−	0.221339i	$-0.0710426\pi$
$104$	8.68688	+	8.68688i	0.0835277	+	0.0835277i
$105$	−147.221			−1.40211
$106$	17.5716	+	17.5716i	0.165770	+	0.165770i
$107$	−83.6935	+	83.6935i	−0.782182	+	0.782182i	−0.980199	−	0.198016i	$-0.936550\pi$
$107$	−83.6935	+	83.6935i	−0.782182	+	0.782182i	0.198016	+	0.980199i	$0.436550\pi$
$108$	19.6977	+	19.6977i	0.182386	+	0.182386i
$109$	17.4640	−	17.4640i	0.160220	−	0.160220i	−0.622444	−	0.782664i	$-0.713860\pi$
$109$	17.4640	−	17.4640i	0.160220	−	0.160220i	0.782664	+	0.622444i	$0.213860\pi$
$110$	82.4429	−	82.4429i	0.749481	−	0.749481i
$111$	10.5442	+	10.5442i	0.0949925	+	0.0949925i
$112$	−19.5207	+	19.5207i	−0.174292	+	0.174292i
$113$	90.7656	−	90.7656i	0.803236	−	0.803236i	−0.180364	−	0.983600i	$-0.557728\pi$
$113$	90.7656	−	90.7656i	0.803236	−	0.803236i	0.983600	+	0.180364i	$0.0577276\pi$
$114$	−50.6191	−	50.6191i	−0.444027	−	0.444027i
$115$	−186.175			−1.61892
$116$	−6.82188	−	6.82188i	−0.0588093	−	0.0588093i
$117$	−52.2810			−0.446846
$118$	10.9479			0.0927790
$119$	−110.717			−0.930395
$120$	−60.3345			−0.502787
$121$	−193.228			−1.59693
$122$	−27.1650	−	27.1650i	−0.222664	−	0.222664i
$123$	−37.2457	−	37.2457i	−0.302811	−	0.302811i
$124$	−83.2434	−	83.2434i	−0.671317	−	0.671317i
$125$	−131.943			−1.05554
$126$		−	117.483i		−	0.932404i
$127$		−	195.393i		−	1.53853i	−0.638930	−	0.769265i	$-0.720623\pi$
$127$		−	195.393i		−	1.53853i	0.638930	−	0.769265i	$-0.279377\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	−28.5719	+	28.5719i	−0.221488	+	0.221488i
$130$	20.2006	−	20.2006i	0.155389	−	0.155389i
$131$	−51.8047			−0.395455			−0.197728	−	0.980257i	$-0.563356\pi$
$131$	−51.8047			−0.395455			−0.197728	+	0.980257i	$0.563356\pi$
$132$	114.981	+	114.981i	0.871070	+	0.871070i
$133$			76.1684i			0.572695i
$134$	−2.74007	−	2.74007i	−0.0204483	−	0.0204483i
$135$	45.8053	−	45.8053i	0.339299	−	0.339299i
$136$	−45.3742			−0.333634
$137$	−110.932	+	110.932i	−0.809726	+	0.809726i	−0.984592	−	0.174866i	$-0.944051\pi$
$137$	−110.932	+	110.932i	−0.809726	+	0.809726i	0.174866	+	0.984592i	$0.444051\pi$
$138$		−	259.654i		−	1.88155i
$139$	−64.5863	−	64.5863i	−0.464650	−	0.464650i	0.435526	−	0.900176i	$-0.356562\pi$
$139$	−64.5863	−	64.5863i	−0.464650	−	0.464650i	−0.900176	+	0.435526i	$0.856562\pi$
$140$	45.3938	+	45.3938i	0.324241	+	0.324241i
$141$	134.516	+	134.516i	0.954015	+	0.954015i
$142$	122.952			0.865863
$143$	−76.9939			−0.538419
$144$		−	48.1470i		−	0.334355i
$145$	−15.8637	+	15.8637i	−0.109405	+	0.109405i
$146$	−79.1820	+	79.1820i	−0.542342	+	0.542342i
$147$	4.43614	−	4.43614i	0.0301778	−	0.0301778i
$148$		−	6.50231i		−	0.0439346i
$149$		−	230.957i		−	1.55005i	−0.631932	−	0.775024i	$-0.717738\pi$
$149$		−	230.957i		−	1.55005i	0.631932	−	0.775024i	$-0.282262\pi$
$150$		−	21.8575i		−	0.145717i
$151$		−	251.195i		−	1.66354i	−0.555120	−	0.831770i	$-0.687328\pi$
$151$		−	251.195i		−	1.66354i	0.555120	−	0.831770i	$-0.312672\pi$
$152$			31.2155i			0.205365i
$153$	136.540	−	136.540i	0.892416	−	0.892416i
$154$		−	173.017i		−	1.12348i
$155$	−193.576	+	193.576i	−1.24887	+	1.24887i
$156$	28.1734	+	28.1734i	0.180598	+	0.180598i
$157$	192.662	+	192.662i	1.22714	+	1.22714i	0.965040	+	0.262104i	$0.0844165\pi$
$157$	192.662	+	192.662i	1.22714	+	1.22714i	0.262104	+	0.965040i	$0.415583\pi$
$158$	6.12702	−	6.12702i	0.0387786	−	0.0387786i
$159$	56.9884	+	56.9884i	0.358417	+	0.358417i
$160$	18.6033	+	18.6033i	0.116271	+	0.116271i
$161$	−195.356	+	195.356i	−1.21339	+	1.21339i
$162$	−44.4472	−	44.4472i	−0.274366	−	0.274366i
$163$	−128.235	+	128.235i	−0.786715	+	0.786715i	−0.980954	−	0.194239i	$-0.937776\pi$
$163$	−128.235	+	128.235i	−0.786715	+	0.786715i	0.194239	+	0.980954i	$0.437776\pi$
$164$			22.9685i			0.140052i
$165$	267.379	−	267.379i	1.62048	−	1.62048i
$166$	−117.563			−0.708210
$167$	203.727	+	203.727i	1.21992	+	1.21992i	0.967659	+	0.252262i	$0.0811745\pi$
$167$	203.727	+	203.727i	1.21992	+	1.21992i	0.252262	+	0.967659i	$0.418826\pi$
$168$	−63.3096	+	63.3096i	−0.376843	+	0.376843i
$169$	150.135			0.888370
$170$			105.514i			0.620671i
$171$	−93.9332	−	93.9332i	−0.549317	−	0.549317i
$172$	17.6195			0.102439
$173$	−300.872			−1.73914			−0.869571	−	0.493808i	$-0.835605\pi$
$173$	−300.872			−1.73914			−0.869571	+	0.493808i	$0.835605\pi$
$174$	−22.1247	−	22.1247i	−0.127154	−	0.127154i
$175$	−16.4449	+	16.4449i	−0.0939708	+	0.0939708i
$176$		−	70.9059i		−	0.402875i
$177$	35.5064			0.200601
$178$	113.961	−	113.961i	0.640232	−	0.640232i
$179$	7.39567	+	7.39567i	0.0413166	+	0.0413166i	0.727463	−	0.686147i	$-0.240699\pi$
$179$	7.39567	+	7.39567i	0.0413166	+	0.0413166i	−0.686147	+	0.727463i	$0.740699\pi$
$180$	−111.962			−0.622011
$181$	200.292	−	200.292i	1.10659	−	1.10659i	0.112991	−	0.993596i	$-0.463957\pi$
$181$	200.292	−	200.292i	1.10659	−	1.10659i	0.993596	−	0.112991i	$-0.0360432\pi$
$182$		−	42.3935i		−	0.232931i
$183$	−88.1018	−	88.1018i	−0.481431	−	0.481431i
$184$	−80.0610	+	80.0610i	−0.435114	+	0.435114i
$185$	−15.1206			−0.0817329
$186$	−269.975	−	269.975i	−1.45148	−	1.45148i
$187$	201.081	−	201.081i	1.07530	−	1.07530i
$188$		−	82.9526i		−	0.441237i
$189$		−	96.1281i		−	0.508614i
$190$	72.5890			0.382047
$191$			89.3960i			0.468042i	0.972232	+	0.234021i	$0.0751884\pi$
$191$			89.3960i			0.468042i	−0.972232	+	0.234021i	$0.924812\pi$
$192$	−25.9456	+	25.9456i	−0.135134	+	0.135134i
$193$	151.033	−	151.033i	0.782554	−	0.782554i	−0.197707	−	0.980261i	$-0.563350\pi$
$193$	151.033	−	151.033i	0.782554	−	0.782554i	0.980261	+	0.197707i	$0.0633496\pi$
$194$	−9.11196	+	9.11196i	−0.0469689	+	0.0469689i
$195$	65.5148	−	65.5148i	0.335973	−	0.335973i
$196$	−2.73565			−0.0139574
$197$	−53.3615	+	53.3615i	−0.270871	+	0.270871i	−0.829451	−	0.558580i	$-0.811346\pi$
$197$	−53.3615	+	53.3615i	−0.270871	+	0.270871i	0.558580	+	0.829451i	$0.311346\pi$
$198$	213.369	+	213.369i	1.07762	+	1.07762i
$199$			97.4643i			0.489770i	0.969552	+	0.244885i	$0.0787503\pi$
$199$			97.4643i			0.489770i	−0.969552	+	0.244885i	$0.921250\pi$
$200$	−6.73947	+	6.73947i	−0.0336973	+	0.0336973i
$201$	−8.88660	−	8.88660i	−0.0442120	−	0.0442120i
$202$		−	4.16713i		−	0.0206293i
$203$			33.2919i			0.164000i
$204$	−147.158			−0.721362
$205$	53.4113			0.260543
$206$	−45.5958	+	45.5958i	−0.221339	+	0.221339i
$207$		−	481.838i		−	2.32772i
$208$		−	17.3738i		−	0.0835277i
$209$	−138.335	−	138.335i	−0.661890	−	0.661890i
$210$	147.221	+	147.221i	0.701054	+	0.701054i
$211$		−	186.048i		−	0.881745i	−0.897570	−	0.440872i	$-0.854669\pi$
$211$		−	186.048i		−	0.881745i	0.897570	−	0.440872i	$-0.145331\pi$
$212$		−	35.1432i		−	0.165770i
$213$	398.760			1.87211
$214$	167.387			0.782182
$215$		−	40.9728i		−	0.190571i
$216$		−	39.3954i		−	0.182386i
$217$			406.242i			1.87208i
$218$	−34.9279			−0.160220
$219$	−256.803	+	256.803i	−1.17262	+	1.17262i
$220$	−164.886			−0.749481
$221$	49.2701	−	49.2701i	0.222942	−	0.222942i
$222$		−	21.0883i		−	0.0949925i
$223$	−164.625	+	164.625i	−0.738230	+	0.738230i	−0.972235	−	0.234005i	$-0.924817\pi$
$223$	−164.625	+	164.625i	−0.738230	+	0.738230i	0.234005	+	0.972235i	$0.424817\pi$
$224$	39.0414			0.174292
$225$		−	40.5607i		−	0.180270i
$226$	−181.531			−0.803236
$227$	49.7130	−	49.7130i	0.219000	−	0.219000i	−0.589077	−	0.808077i	$-0.700509\pi$
$227$	49.7130	−	49.7130i	0.219000	−	0.219000i	0.808077	+	0.589077i	$0.200509\pi$
$228$			101.238i			0.444027i
$229$	255.416	+	255.416i	1.11535	+	1.11535i	0.992414	+	0.122938i	$0.0392318\pi$
$229$	255.416	+	255.416i	1.11535	+	1.11535i	0.122938	+	0.992414i	$0.460768\pi$
$230$	186.175	+	186.175i	0.809458	+	0.809458i
$231$		−	561.128i		−	2.42913i
$232$			13.6438i			0.0588093i
$233$			417.135i			1.79028i	0.445786	+	0.895140i	$0.352924\pi$
$233$			417.135i			1.79028i	−0.445786	+	0.895140i	$0.647076\pi$
$234$	52.2810	+	52.2810i	0.223423	+	0.223423i
$235$	−192.899			−0.820849
$236$	−10.9479	−	10.9479i	−0.0463895	−	0.0463895i
$237$	19.8712	−	19.8712i	0.0838447	−	0.0838447i
$238$	110.717	+	110.717i	0.465198	+	0.465198i
$239$	361.322			1.51181			0.755904	−	0.654683i	$-0.227198\pi$
$239$	361.322			1.51181			0.755904	+	0.654683i	$0.227198\pi$
$240$	60.3345	+	60.3345i	0.251394	+	0.251394i
$241$	−146.401	+	146.401i	−0.607472	+	0.607472i	−0.942285	−	0.334813i	$-0.891327\pi$
$241$	−146.401	+	146.401i	−0.607472	+	0.607472i	0.334813	+	0.942285i	$0.391327\pi$
$242$	193.228	+	193.228i	0.798463	+	0.798463i
$243$	−232.791	−	232.791i	−0.957988	−	0.957988i
$244$			54.3301i			0.222664i
$245$			6.36153i			0.0259654i
$246$			74.4915i			0.302811i
$247$	−33.8956	−	33.8956i	−0.137229	−	0.137229i
$248$			166.487i			0.671317i
$249$	−381.281			−1.53125
$250$	131.943	+	131.943i	0.527772	+	0.527772i
$251$	−156.154	−	156.154i	−0.622127	−	0.622127i	0.323948	−	0.946075i	$-0.394990\pi$
$251$	−156.154	−	156.154i	−0.622127	−	0.622127i	−0.946075	+	0.323948i	$0.894990\pi$
$252$	−117.483	+	117.483i	−0.466202	+	0.466202i
$253$		−	709.600i		−	2.80474i
$254$	−195.393	+	195.393i	−0.769265	+	0.769265i
$255$			342.204i			1.34198i
$256$	16.0000			0.0625000
$257$	128.944	+	128.944i	0.501726	+	0.501726i	0.911974	−	0.410248i	$-0.134558\pi$
$257$	128.944	+	128.944i	0.501726	+	0.501726i	−0.410248	+	0.911974i	$0.634558\pi$
$258$	57.1438			0.221488
$259$	−15.8662	+	15.8662i	−0.0612595	+	0.0612595i
$260$	−40.4013			−0.155389
$261$	−41.0566	−	41.0566i	−0.157305	−	0.157305i
$262$	51.8047	+	51.8047i	0.197728	+	0.197728i
$263$	9.95329			0.0378452			0.0189226	−	0.999821i	$-0.493976\pi$
$263$	9.95329			0.0378452			0.0189226	+	0.999821i	$0.493976\pi$
$264$		−	229.962i		−	0.871070i
$265$	−81.7227			−0.308388
$266$	76.1684	−	76.1684i	0.286347	−	0.286347i
$267$	369.600	−	369.600i	1.38427	−	1.38427i
$268$			5.48014i			0.0204483i
$269$	−263.956	+	51.8506i	−0.981247	+	0.192753i
$269$	−263.956	+	51.8506i	−0.981247	+	0.192753i
$270$	−91.6107			−0.339299
$271$	190.256	+	190.256i	0.702051	+	0.702051i	0.964851	−	0.262799i	$-0.0846457\pi$
$271$	190.256	+	190.256i	0.702051	+	0.702051i	−0.262799	+	0.964851i	$0.584646\pi$
$272$	45.3742	+	45.3742i	0.166817	+	0.166817i
$273$		−	137.491i		−	0.503629i
$274$	221.865			0.809726
$275$		−	59.7335i		−	0.217213i
$276$	−259.654	+	259.654i	−0.940777	+	0.940777i
$277$	172.223	−	172.223i	0.621745	−	0.621745i	−0.324232	−	0.945977i	$-0.605106\pi$
$277$	172.223	−	172.223i	0.621745	−	0.621745i	0.945977	+	0.324232i	$0.105106\pi$
$278$			129.173i			0.464650i
$279$	−500.990	−	500.990i	−1.79566	−	1.79566i
$280$		−	90.7875i		−	0.324241i
$281$	69.4108	−	69.4108i	0.247014	−	0.247014i	−0.572730	−	0.819744i	$-0.694116\pi$
$281$	69.4108	−	69.4108i	0.247014	−	0.247014i	0.819744	+	0.572730i	$0.194116\pi$
$282$		−	269.032i		−	0.954015i
$283$	75.3669			0.266314			0.133157	−	0.991095i	$-0.457489\pi$
$283$	75.3669			0.266314			0.133157	+	0.991095i	$0.457489\pi$
$284$	−122.952	−	122.952i	−0.432931	−	0.432931i
$285$	235.421			0.826038
$286$	76.9939	+	76.9939i	0.269210	+	0.269210i
$287$	56.0450	−	56.0450i	0.195279	−	0.195279i
$288$	−48.1470	+	48.1470i	−0.167177	+	0.167177i
$289$		−	31.6474i		−	0.109507i
$290$	31.7274			0.109405
$291$	−29.5520	+	29.5520i	−0.101553	+	0.101553i
$292$	158.364			0.542342
$293$	−52.8258			−0.180293			−0.0901463	−	0.995929i	$-0.528733\pi$
$293$	−52.8258			−0.180293			−0.0901463	+	0.995929i	$0.528733\pi$
$294$	−8.87228			−0.0301778
$295$	−25.4585	+	25.4585i	−0.0862999	+	0.0862999i
$296$	−6.50231	+	6.50231i	−0.0219673	+	0.0219673i
$297$	174.585	+	174.585i	0.587829	+	0.587829i
$298$	−230.957	+	230.957i	−0.775024	+	0.775024i
$299$		−	173.870i		−	0.581506i
$300$	−21.8575	+	21.8575i	−0.0728583	+	0.0728583i
$301$	−42.9932	−	42.9932i	−0.142835	−	0.142835i
$302$	−251.195	+	251.195i	−0.831770	+	0.831770i
$303$		−	13.5149i		−	0.0446035i
$304$	31.2155	−	31.2155i	0.102682	−	0.102682i
$305$	126.340			0.414230
$306$	−273.079			−0.892416
$307$	−71.2554			−0.232102			−0.116051	−	0.993243i	$-0.537024\pi$
$307$	−71.2554			−0.232102			−0.116051	+	0.993243i	$0.537024\pi$
$308$	−173.017	+	173.017i	−0.561742	+	0.561742i
$309$	−147.876	+	147.876i	−0.478564	+	0.478564i
$310$	387.151			1.24887
$311$	357.948	+	357.948i	1.15096	+	1.15096i	0.986361	+	0.164595i	$0.0526319\pi$
$311$	357.948	+	357.948i	1.15096	+	1.15096i	0.164595	+	0.986361i	$0.447368\pi$
$312$		−	56.3467i		−	0.180598i
$313$	−325.811			−1.04093			−0.520465	−	0.853883i	$-0.674241\pi$
$313$	−325.811			−1.04093			−0.520465	+	0.853883i	$0.674241\pi$
$314$		−	385.323i		−	1.22714i
$315$	273.197	+	273.197i	0.867292	+	0.867292i
$316$	−12.2540			−0.0387786
$317$	−65.7703	−	65.7703i	−0.207477	−	0.207477i	0.595717	−	0.803194i	$-0.296868\pi$
$317$	−65.7703	−	65.7703i	−0.207477	−	0.207477i	−0.803194	+	0.595717i	$0.796868\pi$
$318$		−	113.977i		−	0.358417i
$319$	−60.4639	−	60.4639i	−0.189542	−	0.189542i
$320$		−	37.2067i		−	0.116271i
$321$	542.870			1.69119
$322$	390.712			1.21339
$323$	177.047			0.548134
$324$			88.8944i			0.274366i
$325$		−	14.6362i		−	0.0450346i
$326$	256.469			0.786715
$327$	−113.278			−0.346417
$328$	22.9685	−	22.9685i	0.0700258	−	0.0700258i
$329$	−202.412	+	202.412i	−0.615233	+	0.615233i
$330$	−534.759			−1.62048
$331$	226.887			0.685459			0.342729	−	0.939434i	$-0.388649\pi$
$331$	226.887			0.685459			0.342729	+	0.939434i	$0.388649\pi$
$332$	117.563	+	117.563i	0.354105	+	0.354105i
$333$		−	39.1334i		−	0.117518i
$334$		−	407.454i		−	1.21992i
$335$	12.7436			0.0380406
$336$	126.619			0.376843
$337$	195.474	−	195.474i	0.580042	−	0.580042i	−0.354873	−	0.934915i	$-0.615476\pi$
$337$	195.474	−	195.474i	0.580042	−	0.580042i	0.934915	+	0.354873i	$0.115476\pi$
$338$	−150.135	−	150.135i	−0.444185	−	0.444185i
$339$	−588.743			−1.73671
$340$	105.514	−	105.514i	0.310335	−	0.310335i
$341$	−737.806	−	737.806i	−2.16365	−	2.16365i
$342$			187.866i			0.549317i
$343$	245.804	+	245.804i	0.716629	+	0.716629i
$344$	−17.6195	−	17.6195i	−0.0512196	−	0.0512196i
$345$	603.805	+	603.805i	1.75016	+	1.75016i
$346$	300.872	+	300.872i	0.869571	+	0.869571i
$347$	−366.063			−1.05494			−0.527468	−	0.849575i	$-0.676859\pi$
$347$	−366.063			−1.05494			−0.527468	+	0.849575i	$0.676859\pi$
$348$			44.2495i			0.127154i
$349$	404.957			1.16034			0.580168	−	0.814497i	$-0.302987\pi$
$349$	404.957			1.16034			0.580168	+	0.814497i	$0.302987\pi$
$350$	32.8898			0.0939708
$351$	42.7779	+	42.7779i	0.121874	+	0.121874i
$352$	−70.9059	+	70.9059i	−0.201437	+	0.201437i
$353$		−	186.759i		−	0.529062i	−0.964377	−	0.264531i	$-0.914783\pi$
$353$		−	186.759i		−	0.529062i	0.964377	−	0.264531i	$-0.0852171\pi$
$354$	−35.5064	−	35.5064i	−0.100300	−	0.100300i
$355$	−285.916	+	285.916i	−0.805397	+	0.805397i
$356$	−227.923			−0.640232
$357$	359.078	+	359.078i	1.00582	+	1.00582i
$358$		−	14.7913i		−	0.0413166i
$359$	−137.869	+	137.869i	−0.384037	+	0.384037i	−0.872554	−	0.488518i	$-0.837538\pi$
$359$	−137.869	+	137.869i	−0.384037	+	0.384037i	0.488518	+	0.872554i	$0.337538\pi$
$360$	111.962	+	111.962i	0.311006	+	0.311006i
$361$			239.199i			0.662602i
$362$	−400.585			−1.10659
$363$	626.678	+	626.678i	1.72639	+	1.72639i
$364$	−42.3935	+	42.3935i	−0.116466	+	0.116466i
$365$		−	368.262i		−	1.00894i
$366$			176.204i			0.481431i
$367$	−405.724	+	405.724i	−1.10552	+	1.10552i	−0.111783	+	0.993733i	$0.535656\pi$
$367$	−405.724	+	405.724i	−1.10552	+	1.10552i	−0.993733	+	0.111783i	$0.964344\pi$
$368$	160.122			0.435114
$369$			138.233i			0.374615i
$370$	15.1206	+	15.1206i	0.0408665	+	0.0408665i
$371$	−85.7525	+	85.7525i	−0.231139	+	0.231139i
$372$			539.951i			1.45148i
$373$	−460.015	−	460.015i	−1.23328	−	1.23328i	−0.962695	−	0.270588i	$-0.912782\pi$
$373$	−460.015	−	460.015i	−1.23328	−	1.23328i	−0.270588	−	0.962695i	$-0.587218\pi$
$374$	−402.163			−1.07530
$375$	427.918	+	427.918i	1.14111	+	1.14111i
$376$	−82.9526	+	82.9526i	−0.220619	+	0.220619i
$377$	−14.8152	−	14.8152i	−0.0392976	−	0.0392976i
$378$	−96.1281	+	96.1281i	−0.254307	+	0.254307i
$379$	241.236	−	241.236i	0.636508	−	0.636508i	−0.313184	−	0.949692i	$-0.601396\pi$
$379$	241.236	−	241.236i	0.636508	−	0.636508i	0.949692	+	0.313184i	$0.101396\pi$
$380$	−72.5890	−	72.5890i	−0.191024	−	0.191024i
$381$	−633.701	+	633.701i	−1.66326	+	1.66326i
$382$	89.3960	−	89.3960i	0.234021	−	0.234021i
$383$	−197.526	−	197.526i	−0.515733	−	0.515733i	0.400544	−	0.916277i	$-0.368821\pi$
$383$	−197.526	−	197.526i	−0.515733	−	0.515733i	−0.916277	+	0.400544i	$0.868821\pi$
$384$	51.8913			0.135134
$385$	402.336	+	402.336i	1.04503	+	1.04503i
$386$	−302.066			−0.782554
$387$	106.041			0.274008
$388$	18.2239			0.0469689
$389$	−585.938			−1.50627			−0.753134	−	0.657867i	$-0.771459\pi$
$389$	−585.938			−1.50627			−0.753134	+	0.657867i	$0.771459\pi$
$390$	−131.030			−0.335973
$391$	454.088	+	454.088i	1.16135	+	1.16135i
$392$	2.73565	+	2.73565i	0.00697870	+	0.00697870i
$393$	168.013	+	168.013i	0.427514	+	0.427514i
$394$	106.723			0.270871
$395$			28.4958i			0.0721412i
$396$		−	426.739i		−	1.07762i
$397$	34.3580	−	34.3580i	0.0865440	−	0.0865440i	−0.662509	−	0.749054i	$-0.730509\pi$
$397$	34.3580	−	34.3580i	0.0865440	−	0.0865440i	0.749054	+	0.662509i	$0.230509\pi$
$398$	97.4643	−	97.4643i	0.244885	−	0.244885i
$399$	247.030	−	247.030i	0.619122	−	0.619122i
$400$	13.4789			0.0336973
$401$	−117.728	−	117.728i	−0.293587	−	0.293587i	0.544909	−	0.838495i	$-0.316564\pi$
$401$	−117.728	−	117.728i	−0.293587	−	0.293587i	−0.838495	+	0.544909i	$0.816564\pi$
$402$			17.7732i			0.0442120i
$403$	−180.781	−	180.781i	−0.448589	−	0.448589i
$404$	−4.16713	+	4.16713i	−0.0103147	+	0.0103147i
$405$	206.717			0.510411
$406$	33.2919	−	33.2919i	0.0819998	−	0.0819998i
$407$		−	57.6316i		−	0.141601i
$408$	147.158	+	147.158i	0.360681	+	0.360681i
$409$	108.614	+	108.614i	0.265560	+	0.265560i	0.827308	−	0.561748i	$-0.189871\pi$
$409$	108.614	+	108.614i	0.265560	+	0.265560i	−0.561748	+	0.827308i	$0.689871\pi$
$410$	−53.4113	−	53.4113i	−0.130271	−	0.130271i
$411$	719.553			1.75074
$412$	91.1915			0.221339
$413$			53.4277i			0.129365i
$414$	−481.838	+	481.838i	−1.16386	+	1.16386i
$415$	273.383	−	273.383i	0.658754	−	0.658754i
$416$	−17.3738	+	17.3738i	−0.0417639	+	0.0417639i
$417$			418.933i			1.00464i
$418$			276.670i			0.661890i
$419$			201.551i			0.481030i	0.970645	+	0.240515i	$0.0773162\pi$
$419$			201.551i			0.481030i	−0.970645	+	0.240515i	$0.922684\pi$
$420$		−	294.443i		−	0.701054i
$421$		−	689.634i		−	1.63809i	−0.573733	−	0.819043i	$-0.694505\pi$
$421$		−	689.634i		−	1.63809i	0.573733	−	0.819043i	$-0.305495\pi$
$422$	−186.048	+	186.048i	−0.440872	+	0.440872i
$423$		−	499.240i		−	1.18024i
$424$	−35.1432	+	35.1432i	−0.0828850	+	0.0828850i
$425$	38.2248	+	38.2248i	0.0899406	+	0.0899406i
$426$	−398.760	−	398.760i	−0.936057	−	0.936057i
$427$	132.570	−	132.570i	0.310469	−	0.310469i
$428$	−167.387	−	167.387i	−0.391091	−	0.391091i
$429$	249.707	+	249.707i	0.582068	+	0.582068i
$430$	−40.9728	+	40.9728i	−0.0952856	+	0.0952856i
$431$	−124.538	−	124.538i	−0.288951	−	0.288951i	0.547714	−	0.836665i	$-0.315498\pi$
$431$	−124.538	−	124.538i	−0.288951	−	0.288951i	−0.836665	+	0.547714i	$0.815498\pi$
$432$	−39.3954	+	39.3954i	−0.0911930	+	0.0911930i
$433$			10.7776i			0.0248905i	0.999923	+	0.0124452i	$0.00396155\pi$
$433$			10.7776i			0.0248905i	−0.999923	+	0.0124452i	$0.996038\pi$
$434$	406.242	−	406.242i	0.936042	−	0.936042i
$435$	102.899			0.236548
$436$	34.9279	+	34.9279i	0.0801099	+	0.0801099i
$437$	312.393	−	312.393i	0.714857	−	0.714857i
$438$	513.607			1.17262
$439$		−	659.978i		−	1.50337i	−0.659524	−	0.751684i	$-0.729242\pi$
$439$		−	659.978i		−	1.50337i	0.659524	−	0.751684i	$-0.270758\pi$
$440$	164.886	+	164.886i	0.374741	+	0.374741i
$441$	−16.4642			−0.0373338
$442$	−98.5402			−0.222942
$443$	69.5007	+	69.5007i	0.156886	+	0.156886i	0.781185	−	0.624299i	$-0.214615\pi$
$443$	69.5007	+	69.5007i	0.156886	+	0.156886i	−0.624299	+	0.781185i	$0.714615\pi$
$444$	−21.0883	+	21.0883i	−0.0474963	+	0.0474963i
$445$			530.016i			1.19105i
$446$	329.251			0.738230
$447$	−749.042	+	749.042i	−1.67571	+	1.67571i
$448$	−39.0414	−	39.0414i	−0.0871459	−	0.0871459i
$449$	−476.210			−1.06060			−0.530301	−	0.847810i	$-0.677921\pi$
$449$	−476.210			−1.06060			−0.530301	+	0.847810i	$0.677921\pi$
$450$	−40.5607	+	40.5607i	−0.0901349	+	0.0901349i
$451$			203.575i			0.451386i
$452$	181.531	+	181.531i	0.401618	+	0.401618i
$453$	−814.675	+	814.675i	−1.79840	+	1.79840i
$454$	−99.4260			−0.219000
$455$	98.5826	+	98.5826i	0.216665	+	0.216665i
$456$	101.238	−	101.238i	0.222013	−	0.222013i
$457$			411.084i			0.899527i	0.893148	+	0.449763i	$0.148492\pi$
$457$			411.084i			0.899527i	−0.893148	+	0.449763i	$0.851508\pi$
$458$		−	510.832i		−	1.11535i
$459$	−223.442			−0.486801
$460$		−	372.351i		−	0.809458i
$461$	−496.304	+	496.304i	−1.07658	+	1.07658i	−0.0797675	+	0.996813i	$0.525418\pi$
$461$	−496.304	+	496.304i	−1.07658	+	1.07658i	−0.996813	+	0.0797675i	$0.974582\pi$
$462$	−561.128	+	561.128i	−1.21456	+	1.21456i
$463$	−527.308	+	527.308i	−1.13889	+	1.13889i	−0.150245	+	0.988649i	$0.548006\pi$
$463$	−527.308	+	527.308i	−1.13889	+	1.13889i	−0.988649	+	0.150245i	$0.951994\pi$
$464$	13.6438	−	13.6438i	0.0294046	−	0.0294046i
$465$	1255.61			2.70024
$466$	417.135	−	417.135i	0.895140	−	0.895140i
$467$	410.785	+	410.785i	0.879625	+	0.879625i	0.993496	−	0.113871i	$-0.0363250\pi$
$467$	410.785	+	410.785i	0.879625	+	0.879625i	−0.113871	+	0.993496i	$0.536325\pi$
$468$		−	104.562i		−	0.223423i
$469$	13.3720	−	13.3720i	0.0285117	−	0.0285117i
$470$	192.899	+	192.899i	0.410424	+	0.410424i
$471$		−	1249.68i		−	2.65325i
$472$			21.8958i			0.0463895i
$473$	156.166			0.330161
$474$	−39.7424			−0.0838447
$475$	26.2969	−	26.2969i	0.0553620	−	0.0553620i
$476$		−	221.434i		−	0.465198i
$477$		−	211.505i		−	0.443408i
$478$	−361.322	−	361.322i	−0.755904	−	0.755904i
$479$	476.992	+	476.992i	0.995808	+	0.995808i	0.999991	−	0.00418306i	$-0.00133151\pi$
$479$	476.992	+	476.992i	0.995808	+	0.995808i	−0.00418306	+	0.999991i	$0.501332\pi$
$480$		−	120.669i		−	0.251394i
$481$		−	14.1212i		−	0.0293580i
$482$	292.801			0.607472
$483$	1267.16			2.62352
$484$		−	386.456i		−	0.798463i
$485$		−	42.3782i		−	0.0873778i
$486$			465.582i			0.957988i
$487$	−29.8493			−0.0612923			−0.0306461	−	0.999530i	$-0.509756\pi$
$487$	−29.8493			−0.0612923			−0.0306461	+	0.999530i	$0.509756\pi$
$488$	54.3301	−	54.3301i	0.111332	−	0.111332i
$489$	831.782			1.70098
$490$	6.36153	−	6.36153i	0.0129827	−	0.0129827i
$491$		−	648.671i		−	1.32112i	−0.750772	−	0.660561i	$-0.770318\pi$
$491$		−	648.671i		−	1.32112i	0.750772	−	0.660561i	$-0.229682\pi$
$492$	74.4915	−	74.4915i	0.151405	−	0.151405i
$493$	77.3843			0.156966
$494$			67.7913i			0.137229i
$495$	−992.346			−2.00474
$496$	166.487	−	166.487i	0.335659	−	0.335659i
$497$			600.029i			1.20730i
$498$	381.281	+	381.281i	0.765624	+	0.765624i
$499$	−589.524	−	589.524i	−1.18141	−	1.18141i	−0.979379	−	0.202031i	$-0.935246\pi$
$499$	−589.524	−	589.524i	−1.18141	−	1.18141i	−0.202031	−	0.979379i	$-0.564754\pi$
$500$		−	263.886i		−	0.527772i
$501$		−	1321.46i		−	2.63764i
$502$			312.308i			0.622127i
$503$	−388.751	−	388.751i	−0.772865	−	0.772865i	0.205742	−	0.978606i	$-0.434039\pi$
$503$	−388.751	−	388.751i	−0.772865	−	0.772865i	−0.978606	+	0.205742i	$0.934039\pi$
$504$	234.966			0.466202
$505$	9.69031	+	9.69031i	0.0191887	+	0.0191887i
$506$	−709.600	+	709.600i	−1.40237	+	1.40237i
$507$	−486.917	−	486.917i	−0.960389	−	0.960389i
$508$	390.787			0.769265
$509$	11.4967	+	11.4967i	0.0225869	+	0.0225869i	0.718310	−	0.695723i	$-0.244916\pi$
$509$	11.4967	+	11.4967i	0.0225869	+	0.0225869i	−0.695723	+	0.718310i	$0.744916\pi$
$510$	342.204	−	342.204i	0.670988	−	0.670988i
$511$	−386.422	−	386.422i	−0.756207	−	0.756207i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$			153.718i			0.299645i
$514$		−	257.887i		−	0.501726i
$515$		−	212.058i		−	0.411764i
$516$	−57.1438	−	57.1438i	−0.110744	−	0.110744i
$517$		−	735.229i		−	1.42211i
$518$	31.7324			0.0612595
$519$	975.788	+	975.788i	1.88013	+	1.88013i
$520$	40.4013	+	40.4013i	0.0776947	+	0.0776947i
$521$	513.038	−	513.038i	0.984717	−	0.984717i	−0.0151678	−	0.999885i	$-0.504828\pi$
$521$	513.038	−	513.038i	0.984717	−	0.984717i	0.999885	+	0.0151678i	$0.00482826\pi$
$522$			82.1133i			0.157305i
$523$	152.358	−	152.358i	0.291316	−	0.291316i	−0.546284	−	0.837600i	$-0.683958\pi$
$523$	152.358	−	152.358i	0.291316	−	0.291316i	0.837600	+	0.546284i	$0.183958\pi$
$524$		−	103.609i		−	0.197728i
$525$	106.668			0.203178
$526$	−9.95329	−	9.95329i	−0.0189226	−	0.0189226i
$527$	944.276			1.79179
$528$	−229.962	+	229.962i	−0.435535	+	0.435535i
$529$	1073.44			2.02919
$530$	81.7227	+	81.7227i	0.154194	+	0.154194i
$531$	−65.8888	−	65.8888i	−0.124084	−	0.124084i
$532$	−152.337			−0.286347
$533$			49.8811i			0.0935856i
$534$	−739.200			−1.38427
$535$	−389.245	+	389.245i	−0.727560	+	0.727560i
$536$	5.48014	−	5.48014i	0.0102241	−	0.0102241i
$537$		−	47.9713i		−	0.0893321i
$538$	315.806	+	212.105i	0.587000	+	0.394247i
$539$	−24.2467			−0.0449847
$540$	91.6107	+	91.6107i	0.169649	+	0.169649i
$541$	−591.764	−	591.764i	−1.09383	−	1.09383i	−0.995115	−	0.0987185i	$-0.968526\pi$
$541$	−591.764	−	591.764i	−1.09383	−	1.09383i	−0.0987185	−	0.995115i	$-0.531474\pi$
$542$		−	380.512i		−	0.702051i
$543$	−1299.18			−2.39259
$544$		−	90.7485i		−	0.166817i
$545$	81.2220	−	81.2220i	0.149031	−	0.149031i
$546$	−137.491	+	137.491i	−0.251815	+	0.251815i
$547$		−	131.614i		−	0.240611i	−0.992737	−	0.120305i	$-0.961613\pi$
$547$		−	131.614i		−	0.240611i	0.992737	−	0.120305i	$-0.0383873\pi$
$548$	−221.865	−	221.865i	−0.404863	−	0.404863i
$549$			326.979i			0.595590i
$550$	−59.7335	+	59.7335i	−0.108606	+	0.108606i
$551$		−	53.2370i		−	0.0966188i
$552$	519.309			0.940777
$553$	29.9009	+	29.9009i	0.0540704	+	0.0540704i
$554$	−344.447			−0.621745
$555$	49.0392	+	49.0392i	0.0883589	+	0.0883589i
$556$	129.173	−	129.173i	0.232325	−	0.232325i
$557$	−319.474	+	319.474i	−0.573563	+	0.573563i	−0.933122	−	0.359559i	$-0.882927\pi$
$557$	−319.474	+	319.474i	−0.573563	+	0.573563i	0.359559	+	0.933122i	$0.382927\pi$
$558$			1001.98i			1.79566i
$559$	38.2647			0.0684521
$560$	−90.7875	+	90.7875i	−0.162121	+	0.162121i
$561$	−1304.30			−2.32495
$562$	−138.822			−0.247014
$563$	−1020.14			−1.81198			−0.905989	−	0.423300i	$-0.860872\pi$
$563$	−1020.14			−1.81198			−0.905989	+	0.423300i	$0.860872\pi$
$564$	−269.032	+	269.032i	−0.477008	+	0.477008i
$565$	422.136	−	422.136i	0.747143	−	0.747143i
$566$	−75.3669	−	75.3669i	−0.133157	−	0.133157i
$567$	216.910	−	216.910i	0.382557	−	0.382557i
$568$			245.905i			0.432931i
$569$	−748.079	+	748.079i	−1.31473	+	1.31473i	−0.396836	+	0.917889i	$0.629892\pi$
$569$	−748.079	+	748.079i	−1.31473	+	1.31473i	−0.917889	+	0.396836i	$0.870108\pi$
$570$	−235.421	−	235.421i	−0.413019	−	0.413019i
$571$	366.353	−	366.353i	0.641599	−	0.641599i	−0.309350	−	0.950948i	$-0.600111\pi$
$571$	366.353	−	366.353i	0.641599	−	0.641599i	0.950948	+	0.309350i	$0.100111\pi$
$572$		−	153.988i		−	0.269210i
$573$	289.930	−	289.930i	0.505985	−	0.505985i
$574$	−112.090			−0.195279
$575$	134.892			0.234595
$576$	96.2941			0.167177
$577$	−783.122	+	783.122i	−1.35723	+	1.35723i	−0.479917	+	0.877314i	$0.659333\pi$
$577$	−783.122	+	783.122i	−1.35723	+	1.35723i	−0.877314	+	0.479917i	$0.840667\pi$
$578$	−31.6474	+	31.6474i	−0.0547534	+	0.0547534i
$579$	−979.661			−1.69199
$580$	−31.7274	−	31.7274i	−0.0547024	−	0.0547024i
$581$		−	573.727i		−	0.987483i
$582$	59.1039			0.101553
$583$		−	311.483i		−	0.534276i
$584$	−158.364	−	158.364i	−0.271171	−	0.271171i
$585$	−243.150			−0.415641
$586$	52.8258	+	52.8258i	0.0901463	+	0.0901463i
$587$			312.119i			0.531718i	0.964012	+	0.265859i	$0.0856556\pi$
$587$			312.119i			0.531718i	−0.964012	+	0.265859i	$0.914344\pi$
$588$	8.87228	+	8.87228i	0.0150889	+	0.0150889i
$589$		−	649.620i		−	1.10292i
$590$	50.9170			0.0862999
$591$	346.125			0.585659
$592$	13.0046			0.0219673
$593$		−	698.996i		−	1.17875i	−0.807861	−	0.589373i	$-0.799375\pi$
$593$		−	698.996i		−	1.17875i	0.807861	−	0.589373i	$-0.200625\pi$
$594$		−	349.171i		−	0.587829i
$595$	−514.927			−0.865423
$596$	461.914			0.775024
$597$	316.097	−	316.097i	0.529475	−	0.529475i
$598$	−173.870	+	173.870i	−0.290753	+	0.290753i
$599$	−527.549			−0.880716			−0.440358	−	0.897822i	$-0.645148\pi$
$599$	−527.549			−0.880716			−0.440358	+	0.897822i	$0.645148\pi$
$600$	43.7150			0.0728583
$601$	−291.321	−	291.321i	−0.484728	−	0.484728i	0.421910	−	0.906638i	$-0.361360\pi$
$601$	−291.321	−	291.321i	−0.484728	−	0.484728i	−0.906638	+	0.421910i	$0.861360\pi$
$602$			85.9864i			0.142835i
$603$			32.9815i			0.0546958i
$604$	502.389			0.831770
$605$	−898.672			−1.48541
$606$	−13.5149	+	13.5149i	−0.0223017	+	0.0223017i
$607$	−218.193	−	218.193i	−0.359461	−	0.359461i	0.504153	−	0.863614i	$-0.331805\pi$
$607$	−218.193	−	218.193i	−0.359461	−	0.359461i	−0.863614	+	0.504153i	$0.831805\pi$
$608$	−62.4309			−0.102682
$609$	107.973	−	107.973i	0.177295	−	0.177295i
$610$	−126.340	−	126.340i	−0.207115	−	0.207115i
$611$		−	180.150i		−	0.294844i
$612$	273.079	+	273.079i	0.446208	+	0.446208i
$613$	452.233	+	452.233i	0.737738	+	0.737738i	0.972140	−	0.234402i	$-0.0753132\pi$
$613$	452.233	+	452.233i	0.737738	+	0.737738i	−0.234402	+	0.972140i	$0.575313\pi$
$614$	71.2554	+	71.2554i	0.116051	+	0.116051i
$615$	−173.224	−	173.224i	−0.281665	−	0.281665i
$616$	346.033			0.561742
$617$			267.924i			0.434236i	0.976145	+	0.217118i	$0.0696656\pi$
$617$			267.924i			0.434236i	−0.976145	+	0.217118i	$0.930334\pi$
$618$	295.753			0.478564
$619$	−296.911			−0.479663			−0.239831	−	0.970815i	$-0.577092\pi$
$619$	−296.911			−0.479663			−0.239831	+	0.970815i	$0.577092\pi$
$620$	−387.151	−	387.151i	−0.624437	−	0.624437i
$621$	−394.254	+	394.254i	−0.634870	+	0.634870i
$622$		−	715.895i		−	1.15096i
$623$	556.151	+	556.151i	0.892699	+	0.892699i
$624$	−56.3467	+	56.3467i	−0.0902992	+	0.0902992i
$625$	−529.402			−0.847042
$626$	325.811	+	325.811i	0.520465	+	0.520465i
$627$			897.298i			1.43110i
$628$	−385.323	+	385.323i	−0.613572	+	0.613572i
$629$	36.8797	+	36.8797i	0.0586322	+	0.0586322i
$630$		−	546.394i		−	0.867292i
$631$	284.390			0.450698			0.225349	−	0.974278i	$-0.427648\pi$
$631$	284.390			0.450698			0.225349	+	0.974278i	$0.427648\pi$
$632$	12.2540	+	12.2540i	0.0193893	+	0.0193893i
$633$	−603.392	+	603.392i	−0.953227	+	0.953227i
$634$			131.541i			0.207477i
$635$		−	908.742i		−	1.43109i
$636$	−113.977	+	113.977i	−0.179209	+	0.179209i
$637$	−5.94107			−0.00932665
$638$			120.928i			0.189542i
$639$	−739.975	−	739.975i	−1.15802	−	1.15802i
$640$	−37.2067	+	37.2067i	−0.0581354	+	0.0581354i
$641$			124.117i			0.193630i	0.995302	+	0.0968152i	$0.0308656\pi$
$641$			124.117i			0.193630i	−0.995302	+	0.0968152i	$0.969134\pi$
$642$	−542.870	−	542.870i	−0.845593	−	0.845593i
$643$	−418.214			−0.650410			−0.325205	−	0.945644i	$-0.605433\pi$
$643$	−418.214			−0.650410			−0.325205	+	0.945644i	$0.605433\pi$
$644$	−390.712	−	390.712i	−0.606695	−	0.606695i
$645$	−132.883	+	132.883i	−0.206020	+	0.206020i
$646$	−177.047	−	177.047i	−0.274067	−	0.274067i
$647$	277.424	−	277.424i	0.428786	−	0.428786i	−0.459429	−	0.888215i	$-0.651946\pi$
$647$	277.424	−	277.424i	0.428786	−	0.428786i	0.888215	+	0.459429i	$0.151946\pi$
$648$	88.8944	−	88.8944i	0.137183	−	0.137183i
$649$	−97.0340	−	97.0340i	−0.149513	−	0.149513i
$650$	−14.6362	+	14.6362i	−0.0225173	+	0.0225173i
$651$	1317.53	−	1317.53i	2.02385	−	2.02385i
$652$	−256.469	−	256.469i	−0.393357	−	0.393357i
$653$	−157.807			−0.241665			−0.120832	−	0.992673i	$-0.538556\pi$
$653$	−157.807			−0.241665			−0.120832	+	0.992673i	$0.538556\pi$
$654$	113.278	+	113.278i	0.173209	+	0.173209i
$655$	−240.935			−0.367840
$656$	−45.9369			−0.0700258
$657$	953.094			1.45068
$658$	404.823			0.615233
$659$	−300.321			−0.455723			−0.227861	−	0.973694i	$-0.573173\pi$
$659$	−300.321			−0.455723			−0.227861	+	0.973694i	$0.573173\pi$
$660$	534.759	+	534.759i	0.810241	+	0.810241i
$661$	644.216	+	644.216i	0.974608	+	0.974608i	0.999686	−	0.0250771i	$-0.00798313\pi$
$661$	644.216	+	644.216i	0.974608	+	0.974608i	−0.0250771	+	0.999686i	$0.507983\pi$
$662$	−226.887	−	226.887i	−0.342729	−	0.342729i
$663$	−319.586			−0.482030
$664$		−	235.126i		−	0.354105i
$665$			354.247i			0.532702i
$666$	−39.1334	+	39.1334i	−0.0587589	+	0.0587589i
$667$	136.542	−	136.542i	0.204710	−	0.204710i
$668$	−407.454	+	407.454i	−0.609960	+	0.609960i
$669$	1067.83			1.59616
$670$	−12.7436	−	12.7436i	−0.0190203	−	0.0190203i
$671$			481.541i			0.717646i
$672$	−126.619	−	126.619i	−0.188421	−	0.188421i
$673$	435.829	−	435.829i	0.647591	−	0.647591i	−0.304819	−	0.952410i	$-0.598596\pi$
$673$	435.829	−	435.829i	0.647591	−	0.647591i	0.952410	+	0.304819i	$0.0985961\pi$
$674$	−390.948			−0.580042
$675$	−33.1880	+	33.1880i	−0.0491674	+	0.0491674i
$676$			300.269i			0.444185i
$677$	878.629	+	878.629i	1.29783	+	1.29783i	0.929825	+	0.368002i	$0.119958\pi$
$677$	878.629	+	878.629i	1.29783	+	1.29783i	0.368002	+	0.929825i	$0.380042\pi$
$678$	588.743	+	588.743i	0.868353	+	0.868353i
$679$	−44.4680	−	44.4680i	−0.0654904	−	0.0654904i
$680$	−211.028			−0.310335
$681$	−322.459			−0.473508
$682$			1475.61i			2.16365i
$683$	41.5498	−	41.5498i	0.0608343	−	0.0608343i	−0.676035	−	0.736869i	$-0.736303\pi$
$683$	41.5498	−	41.5498i	0.0608343	−	0.0608343i	0.736869	+	0.676035i	$0.236303\pi$
$684$	187.866	−	187.866i	0.274659	−	0.274659i
$685$	−515.928	+	515.928i	−0.753180	+	0.753180i
$686$		−	491.607i		−	0.716629i
$687$		−	1656.73i		−	2.41155i
$688$			35.2391i			0.0512196i
$689$		−	76.3213i		−	0.110771i
$690$		−	1207.61i		−	1.75016i
$691$	−47.9903	+	47.9903i	−0.0694505	+	0.0694505i	−0.740979	−	0.671528i	$-0.765638\pi$
$691$	−47.9903	+	47.9903i	−0.0694505	+	0.0694505i	0.671528	+	0.740979i	$0.265638\pi$
$692$		−	601.743i		−	0.869571i
$693$	−1041.28	+	1041.28i	−1.50257	+	1.50257i
$694$	366.063	+	366.063i	0.527468	+	0.527468i
$695$	−300.380	−	300.380i	−0.432202	−	0.432202i
$696$	44.2495	−	44.2495i	0.0635768	−	0.0635768i
$697$	−130.272	−	130.272i	−0.186904	−	0.186904i
$698$	−404.957	−	404.957i	−0.580168	−	0.580168i
$699$	1352.85	−	1352.85i	1.93541	−	1.93541i
$700$	−32.8898	−	32.8898i	−0.0469854	−	0.0469854i
$701$	165.521	−	165.521i	0.236121	−	0.236121i	−0.579121	−	0.815242i	$-0.696604\pi$
$701$	165.521	−	165.521i	0.236121	−	0.236121i	0.815242	+	0.579121i	$0.196604\pi$
$702$		−	85.5558i		−	0.121874i
$703$	25.3716	−	25.3716i	0.0360904	−	0.0360904i
$704$	141.812			0.201437
$705$	625.613	+	625.613i	0.887394	+	0.887394i
$706$	−186.759	+	186.759i	−0.264531	+	0.264531i
$707$	20.3363			0.0287642
$708$			71.0127i			0.100300i
$709$	705.800	+	705.800i	0.995486	+	0.995486i	0.999990	−	0.00450375i	$-0.00143359\pi$
$709$	705.800	+	705.800i	0.995486	+	0.995486i	−0.00450375	+	0.999990i	$0.501434\pi$
$710$	571.832			0.805397
$711$	−73.7495			−0.103726
$712$	227.923	+	227.923i	0.320116	+	0.320116i
$713$	1666.14	−	1666.14i	2.33680	−	2.33680i
$714$		−	718.156i		−	1.00582i
$715$	−358.086			−0.500820
$716$	−14.7913	+	14.7913i	−0.0206583	+	0.0206583i
$717$	−1171.84	−	1171.84i	−1.63437	−	1.63437i
$718$	275.738			0.384037
$719$	−482.421	+	482.421i	−0.670962	+	0.670962i	−0.957938	−	0.286976i	$-0.907350\pi$
$719$	−482.421	+	482.421i	−0.670962	+	0.670962i	0.286976	+	0.957938i	$0.407350\pi$
$720$		−	223.924i		−	0.311006i
$721$	−222.515	−	222.515i	−0.308620	−	0.308620i
$722$	239.199	−	239.199i	0.331301	−	0.331301i
$723$	949.615			1.31344
$724$	400.585	+	400.585i	0.553294	+	0.553294i
$725$	11.4940	−	11.4940i	0.0158537	−	0.0158537i
$726$		−	1253.36i		−	1.72639i
$727$		−	903.795i		−	1.24318i	−0.783341	−	0.621592i	$-0.786486\pi$
$727$		−	903.795i		−	1.24318i	0.783341	−	0.621592i	$-0.213514\pi$
$728$	84.7870			0.116466
$729$			1109.95i			1.52257i
$730$	−368.262	+	368.262i	−0.504469	+	0.504469i
$731$	−99.9341	+	99.9341i	−0.136709	+	0.136709i
$732$	176.204	−	176.204i	0.240715	−	0.240715i
$733$	52.7615	−	52.7615i	0.0719802	−	0.0719802i	−0.670200	−	0.742180i	$-0.733792\pi$
$733$	52.7615	−	52.7615i	0.0719802	−	0.0719802i	0.742180	+	0.670200i	$0.233792\pi$
$734$	811.449			1.10552
$735$	20.6318	−	20.6318i	0.0280704	−	0.0280704i
$736$	−160.122	−	160.122i	−0.217557	−	0.217557i
$737$			48.5718i			0.0659047i
$738$	138.233	−	138.233i	0.187308	−	0.187308i
$739$	963.523	+	963.523i	1.30382	+	1.30382i	0.925795	+	0.378025i	$0.123397\pi$
$739$	963.523	+	963.523i	1.30382	+	1.30382i	0.378025	+	0.925795i	$0.376603\pi$
$740$		−	30.2412i		−	0.0408665i
$741$			219.861i			0.296708i
$742$	171.505			0.231139
$743$	440.376			0.592700			0.296350	−	0.955079i	$-0.404230\pi$
$743$	440.376			0.592700			0.296350	+	0.955079i	$0.404230\pi$
$744$	539.951	−	539.951i	0.725740	−	0.725740i
$745$		−	1074.14i		−	1.44180i
$746$			920.030i			1.23328i
$747$	707.538	+	707.538i	0.947173	+	0.947173i
$748$	402.163	+	402.163i	0.537651	+	0.537651i
$749$			816.878i			1.09062i
$750$		−	855.836i		−	1.14111i
$751$	1037.35			1.38129			0.690643	−	0.723196i	$-0.257328\pi$
$751$	1037.35			1.38129			0.690643	+	0.723196i	$0.257328\pi$
$752$	165.905			0.220619
$753$			1012.88i			1.34512i
$754$			29.6304i			0.0392976i
$755$		−	1168.26i		−	1.54737i
$756$	192.256			0.254307
$757$	−66.0668	+	66.0668i	−0.0872745	+	0.0872745i	−0.749396	−	0.662122i	$-0.769656\pi$
$757$	−66.0668	+	66.0668i	−0.0872745	+	0.0872745i	0.662122	+	0.749396i	$0.269656\pi$
$758$	−482.473			−0.636508
$759$	−2301.38	+	2301.38i	−3.03212	+	3.03212i
$760$			145.178i			0.191024i
$761$	−613.704	+	613.704i	−0.806444	+	0.806444i	−0.984094	−	0.177649i	$-0.943151\pi$
$761$	−613.704	+	613.704i	−0.806444	+	0.806444i	0.177649	+	0.984094i	$0.443151\pi$
$762$	1267.40			1.66326
$763$		−	170.454i		−	0.223400i
$764$	−178.792			−0.234021
$765$	635.024	−	635.024i	0.830096	−	0.830096i
$766$			395.051i			0.515733i
$767$	−23.7758	−	23.7758i	−0.0309985	−	0.0309985i
$768$	−51.8913	−	51.8913i	−0.0675668	−	0.0675668i
$769$		−	657.413i		−	0.854894i	−0.904040	−	0.427447i	$-0.859413\pi$
$769$		−	657.413i		−	0.854894i	0.904040	−	0.427447i	$-0.140587\pi$
$770$		−	804.672i		−	1.04503i
$771$		−	836.381i		−	1.08480i
$772$	302.066	+	302.066i	0.391277	+	0.391277i
$773$	−239.707			−0.310099			−0.155050	−	0.987907i	$-0.549554\pi$
$773$	−239.707			−0.310099			−0.155050	+	0.987907i	$0.549554\pi$
$774$	−106.041	−	106.041i	−0.137004	−	0.137004i
$775$	140.254	−	140.254i	0.180973	−	0.180973i
$776$	−18.2239	−	18.2239i	−0.0234844	−	0.0234844i
$777$	102.915			0.132451
$778$	585.938	+	585.938i	0.753134	+	0.753134i
$779$	−89.6214	+	89.6214i	−0.115047	+	0.115047i
$780$	131.030	+	131.030i	0.167987	+	0.167987i
$781$	−1089.76	−	1089.76i	−1.39534	−	1.39534i
$782$		−	908.177i		−	1.16135i
$783$			67.1876i			0.0858079i
$784$		−	5.47130i		−	0.00697870i
$785$	896.037	+	896.037i	1.14145	+	1.14145i
$786$		−	336.026i		−	0.427514i
$787$	−1402.92			−1.78262			−0.891308	−	0.453398i	$-0.850211\pi$
$787$	−1402.92			−1.78262			−0.891308	+	0.453398i	$0.850211\pi$
$788$	−106.723	−	106.723i	−0.135435	−	0.135435i
$789$	−32.2806	−	32.2806i	−0.0409133	−	0.0409133i
$790$	28.4958	−	28.4958i	0.0360706	−	0.0360706i
$791$		−	885.904i		−	1.11998i
$792$	−426.739	+	426.739i	−0.538812	+	0.538812i
$793$			117.990i			0.148789i
$794$	−68.7160			−0.0865440
$795$	265.043	+	265.043i	0.333388	+	0.333388i
$796$	−194.929			−0.244885
$797$	−18.3790	+	18.3790i	−0.0230603	+	0.0230603i	−0.718543	−	0.695483i	$-0.755191\pi$
$797$	−18.3790	+	18.3790i	−0.0230603	+	0.0230603i	0.695483	+	0.718543i	$0.255191\pi$
$798$	−494.060			−0.619122
$799$	470.489	+	470.489i	0.588847	+	0.588847i
$800$	−13.4789	−	13.4789i	−0.0168487	−	0.0168487i
$801$	−1371.73			−1.71252
$802$			235.456i			0.293587i
$803$	1403.62			1.74797
$804$	17.7732	−	17.7732i	0.0221060	−	0.0221060i
$805$	−908.568	+	908.568i	−1.12866	+	1.12866i
$806$			361.563i			0.448589i
$807$	1024.22	+	687.900i	1.26917	+	0.852416i
$808$	8.33426			0.0103147
$809$	910.227	+	910.227i	1.12513	+	1.12513i	0.990959	+	0.134167i	$0.0428359\pi$
$809$	910.227	+	910.227i	1.12513	+	1.12513i	0.134167	+	0.990959i	$0.457164\pi$
$810$	−206.717	−	206.717i	−0.255206	−	0.255206i
$811$			196.995i			0.242904i	0.992597	+	0.121452i	$0.0387551\pi$
$811$			196.995i			0.242904i	−0.992597	+	0.121452i	$0.961245\pi$
$812$	−66.5839			−0.0819998
$813$		−	1234.08i		−	1.51793i
$814$	−57.6316	+	57.6316i	−0.0708005	+	0.0708005i
$815$	−596.397	+	596.397i	−0.731776	+	0.731776i
$816$		−	294.316i		−	0.360681i
$817$	68.7503	+	68.7503i	0.0841496	+	0.0841496i
$818$		−	217.228i		−	0.265560i
$819$	−255.140	+	255.140i	−0.311527	+	0.311527i
$820$			106.823i			0.130271i
$821$	1604.12			1.95386			0.976929	−	0.213563i	$-0.0685068\pi$
$821$	1604.12			1.95386			0.976929	+	0.213563i	$0.0685068\pi$
$822$	−719.553	−	719.553i	−0.875369	−	0.875369i
$823$	−1149.18			−1.39632			−0.698162	−	0.715939i	$-0.745999\pi$
$823$	−1149.18			−1.39632			−0.698162	+	0.715939i	$0.745999\pi$
$824$	−91.1915	−	91.1915i	−0.110669	−	0.110669i
$825$	−193.728	+	193.728i	−0.234822	+	0.234822i
$826$	53.4277	−	53.4277i	0.0646825	−	0.0646825i
$827$			1447.99i			1.75089i	0.483316	+	0.875446i	$0.339432\pi$
$827$			1447.99i			1.75089i	−0.483316	+	0.875446i	$0.660568\pi$
$828$	963.676			1.16386
$829$	−202.788	+	202.788i	−0.244617	+	0.244617i	−0.818757	−	0.574140i	$-0.805337\pi$
$829$	−202.788	+	202.788i	−0.244617	+	0.244617i	0.574140	+	0.818757i	$0.305337\pi$
$830$	−546.766			−0.658754
$831$	−1117.11			−1.34430
$832$	34.7475			0.0417639
$833$	15.5160	−	15.5160i	0.0186267	−	0.0186267i
$834$	418.933	−	418.933i	0.502318	−	0.502318i
$835$	947.500	+	947.500i	1.13473	+	1.13473i
$836$	276.670	−	276.670i	0.330945	−	0.330945i
$837$			819.851i			0.979511i
$838$	201.551	−	201.551i	0.240515	−	0.240515i
$839$	−173.794	−	173.794i	−0.207144	−	0.207144i	0.595908	−	0.803052i	$-0.296792\pi$
$839$	−173.794	−	173.794i	−0.207144	−	0.207144i	−0.803052	+	0.595908i	$0.796792\pi$
$840$	−294.443	+	294.443i	−0.350527	+	0.350527i
$841$			817.731i			0.972332i
$842$	−689.634	+	689.634i	−0.819043	+	0.819043i
$843$	−450.227			−0.534077
$844$	372.096			0.440872
$845$	698.251			0.826332
$846$	−499.240	+	499.240i	−0.590119	+	0.590119i
$847$	−942.987	+	942.987i	−1.11333	+	1.11333i
$848$	70.2865			0.0828850
$849$	−244.430	−	244.430i	−0.287904	−	0.287904i
$850$		−	76.4495i		−	0.0899406i
$851$	130.145			0.152932
$852$			797.520i			0.936057i
$853$	385.375	+	385.375i	0.451788	+	0.451788i	0.895948	−	0.444160i	$-0.146498\pi$
$853$	385.375	+	385.375i	0.451788	+	0.451788i	−0.444160	+	0.895948i	$0.646498\pi$
$854$	−265.140			−0.310469
$855$	−436.868	−	436.868i	−0.510957	−	0.510957i
$856$			334.774i			0.391091i
$857$	749.750	+	749.750i	0.874854	+	0.874854i	0.992997	−	0.118143i	$-0.0376941\pi$
$857$	749.750	+	749.750i	0.874854	+	0.874854i	−0.118143	+	0.992997i	$0.537694\pi$
$858$		−	499.414i		−	0.582068i
$859$	−89.1312			−0.103762			−0.0518808	−	0.998653i	$-0.516522\pi$
$859$	−89.1312			−0.103762			−0.0518808	+	0.998653i	$0.516522\pi$
$860$	81.9456			0.0952856
$861$	−363.531			−0.422220
$862$			249.076i			0.288951i
$863$			1389.87i			1.61051i	0.592928	+	0.805256i	$0.297972\pi$
$863$			1389.87i			1.61051i	−0.592928	+	0.805256i	$0.702028\pi$
$864$	78.7908			0.0911930
$865$	−1399.30			−1.61769
$866$	10.7776	−	10.7776i	0.0124452	−	0.0124452i
$867$	−102.639	+	102.639i	−0.118384	+	0.118384i
$868$	−812.484			−0.936042
$869$	−108.611			−0.124983
$870$	−102.899	−	102.899i	−0.118274	−	0.118274i
$871$			11.9013i			0.0136640i
$872$		−	69.8558i		−	0.0801099i
$873$	109.679			0.125634
$874$	−624.785			−0.714857
$875$	−643.904	+	643.904i	−0.735891	+	0.735891i
$876$	−513.607	−	513.607i	−0.586309	−	0.586309i
$877$	95.5592			0.108961			0.0544807	−	0.998515i	$-0.482650\pi$
$877$	95.5592			0.108961			0.0544807	+	0.998515i	$0.482650\pi$
$878$	−659.978	+	659.978i	−0.751684	+	0.751684i
$879$	171.325	+	171.325i	0.194909	+	0.194909i
$880$		−	329.772i		−	0.374741i
$881$	−1045.37	−	1045.37i	−1.18657	−	1.18657i	−0.978010	−	0.208556i	$-0.933124\pi$
$881$	−1045.37	−	1045.37i	−1.18657	−	1.18657i	−0.208556	−	0.978010i	$-0.566876\pi$
$882$	16.4642	+	16.4642i	0.0186669	+	0.0186669i
$883$	574.613	+	574.613i	0.650751	+	0.650751i	0.953174	−	0.302423i	$-0.0977954\pi$
$883$	574.613	+	574.613i	0.650751	+	0.650751i	−0.302423	+	0.953174i	$0.597795\pi$
$884$	98.5402	+	98.5402i	0.111471	+	0.111471i
$885$	165.134			0.186592
$886$		−	139.001i		−	0.156886i
$887$	−548.626			−0.618519			−0.309259	−	0.950978i	$-0.600081\pi$
$887$	−548.626			−0.618519			−0.309259	+	0.950978i	$0.600081\pi$
$888$	42.1767			0.0474963
$889$	−953.553	−	953.553i	−1.07261	−	1.07261i
$890$	530.016	−	530.016i	0.595523	−	0.595523i
$891$			787.893i			0.884279i
$892$	−329.251	−	329.251i	−0.369115	−	0.369115i
$893$	323.675	−	323.675i	0.362458	−	0.362458i
$894$	1498.08			1.67571
$895$	34.3960	+	34.3960i	0.0384313	+	0.0384313i
$896$			78.0828i			0.0871459i
$897$	−563.897	+	563.897i	−0.628648	+	0.628648i
$898$	476.210	+	476.210i	0.530301	+	0.530301i
$899$		−	283.938i		−	0.315838i
$900$	81.1214			0.0901349
$901$	199.325	+	199.325i	0.221226	+	0.221226i
$902$	203.575	−	203.575i	0.225693	−	0.225693i
$903$			278.872i			0.308828i
$904$		−	363.063i		−	0.401618i
$905$	931.526	−	931.526i	1.02931	−	1.02931i
$906$	1629.35			1.79840
$907$		−	76.3254i		−	0.0841515i	−0.999114	−	0.0420758i	$-0.986603\pi$
$907$		−	76.3254i		−	0.0841515i	0.999114	−	0.0420758i	$-0.0133971\pi$
$908$	99.4260	+	99.4260i	0.109500	+	0.109500i
$909$	−25.0794	+	25.0794i	−0.0275901	+	0.0275901i
$910$		−	197.165i		−	0.216665i
$911$	−836.780	−	836.780i	−0.918529	−	0.918529i	0.0783937	−	0.996922i	$-0.475021\pi$
$911$	−836.780	−	836.780i	−0.918529	−	0.918529i	−0.996922	+	0.0783937i	$0.975021\pi$
$912$	−202.476			−0.222013
$913$	1041.99	+	1041.99i	1.14128	+	1.14128i
$914$	411.084	−	411.084i	0.449763	−	0.449763i
$915$	−409.747	−	409.747i	−0.447811	−	0.447811i
$916$	−510.832	+	510.832i	−0.557676	+	0.557676i
$917$	−252.816	+	252.816i	−0.275699	+	0.275699i
$918$	223.442	+	223.442i	0.243401	+	0.243401i
$919$	−560.470	+	560.470i	−0.609869	+	0.609869i	−0.942912	−	0.333042i	$-0.891925\pi$
$919$	−560.470	+	560.470i	−0.609869	+	0.609869i	0.333042	+	0.942912i	$0.391925\pi$
$920$	−372.351	+	372.351i	−0.404729	+	0.404729i
$921$	231.096	+	231.096i	0.250918	+	0.250918i
$922$	992.608			1.07658
$923$	−267.019	−	267.019i	−0.289294	−	0.289294i
$924$	1122.26			1.21456
$925$	10.9555			0.0118438
$926$	1054.62			1.13889
$927$	548.825			0.592045
$928$	−27.2875			−0.0294046
$929$	1227.95	+	1227.95i	1.32180	+	1.32180i	0.912319	+	0.409481i	$0.134290\pi$
$929$	1227.95	+	1227.95i	1.32180	+	1.32180i	0.409481	+	0.912319i	$0.365710\pi$
$930$	−1255.61	−	1255.61i	−1.35012	−	1.35012i
$931$	−10.6743	−	10.6743i	−0.0114654	−	0.0114654i
$932$	−834.270			−0.895140
$933$		−	2321.79i		−	2.48853i
$934$		−	821.570i		−	0.879625i
$935$	935.196	−	935.196i	1.00021	−	1.00021i
$936$	−104.562	+	104.562i	−0.111712	+	0.111712i
$937$	105.483	−	105.483i	0.112575	−	0.112575i	−0.648576	−	0.761150i	$-0.724635\pi$
$937$	105.483	−	105.483i	0.112575	−	0.112575i	0.761150	+	0.648576i	$0.224635\pi$
$938$	−26.7440			−0.0285117
$939$	1056.67	+	1056.67i	1.12532	+	1.12532i
$940$		−	385.799i		−	0.410424i
$941$	−826.783	−	826.783i	−0.878621	−	0.878621i	0.114771	−	0.993392i	$-0.463387\pi$
$941$	−826.783	−	826.783i	−0.878621	−	0.878621i	−0.993392	+	0.114771i	$0.963387\pi$
$942$	−1249.68	+	1249.68i	−1.32663	+	1.32663i
$943$	−459.720			−0.487508
$944$	21.8958	−	21.8958i	0.0231947	−	0.0231947i
$945$		−	447.076i		−	0.473096i
$946$	−156.166	−	156.166i	−0.165081	−	0.165081i
$947$	1189.52	+	1189.52i	1.25609	+	1.25609i	0.952945	+	0.303145i	$0.0980365\pi$
$947$	1189.52	+	1189.52i	1.25609	+	1.25609i	0.303145	+	0.952945i	$0.401964\pi$
$948$	39.7424	+	39.7424i	0.0419223	+	0.0419223i
$949$	343.922			0.362405
$950$	−52.5939			−0.0553620
$951$			426.613i			0.448594i
$952$	−221.434	+	221.434i	−0.232599	+	0.232599i
$953$	482.280	−	482.280i	0.506065	−	0.506065i	−0.407251	−	0.913316i	$-0.633513\pi$
$953$	482.280	−	482.280i	0.506065	−	0.506065i	0.913316	+	0.407251i	$0.133513\pi$
$954$	−211.505	+	211.505i	−0.221704	+	0.221704i
$955$			415.766i			0.435357i
$956$			722.644i			0.755904i
$957$			392.194i			0.409816i
$958$		−	953.984i		−	0.995808i
$959$			1082.74i			1.12903i
$960$	−120.669	+	120.669i	−0.125697	+	0.125697i
$961$		−	2503.73i		−	2.60534i
$962$	−14.1212	+	14.1212i	−0.0146790	+	0.0146790i
$963$	−1007.40	−	1007.40i	−1.04610	−	1.04610i
$964$	−292.801	−	292.801i	−0.303736	−	0.303736i
$965$	702.429	−	702.429i	0.727906	−	0.727906i
$966$	−1267.16	−	1267.16i	−1.31176	−	1.31176i
$967$	1278.70	+	1278.70i	1.32233	+	1.32233i	0.911884	+	0.410448i	$0.134628\pi$
$967$	1278.70	+	1278.70i	1.32233	+	1.32233i	0.410448	+	0.911884i	$0.365372\pi$
$968$	−386.456	+	386.456i	−0.399232	+	0.399232i
$969$	−574.200	−	574.200i	−0.592570	−	0.592570i
$970$	−42.3782	+	42.3782i	−0.0436889	+	0.0436889i
$971$		−	103.072i		−	0.106151i	−0.998591	−	0.0530754i	$-0.983098\pi$
$971$		−	103.072i		−	0.106151i	0.998591	−	0.0530754i	$-0.0169024\pi$
$972$	465.582	−	465.582i	0.478994	−	0.478994i
$973$	−630.385			−0.647878
$974$	29.8493	+	29.8493i	0.0306461	+	0.0306461i
$975$	−47.4684	+	47.4684i	−0.0486855	+	0.0486855i
$976$	−108.660			−0.111332
$977$		−	1372.54i		−	1.40485i	−0.711759	−	0.702424i	$-0.752101\pi$
$977$		−	1372.54i		−	1.40485i	0.711759	−	0.702424i	$-0.247899\pi$
$978$	−831.782	−	831.782i	−0.850492	−	0.850492i
$979$	−2020.13			−2.06347
$980$	−12.7231			−0.0129827
$981$	210.210	+	210.210i	0.214281	+	0.214281i
$982$	−648.671	+	648.671i	−0.660561	+	0.660561i
$983$			1395.65i			1.41979i	0.704309	+	0.709894i	$0.251257\pi$
$983$			1395.65i			1.41979i	−0.704309	+	0.709894i	$0.748743\pi$
$984$	−148.983			−0.151405
$985$	−248.176	+	248.176i	−0.251955	+	0.251955i
$986$	−77.3843	−	77.3843i	−0.0784831	−	0.0784831i
$987$	1312.92			1.33022
$988$	67.7913	−	67.7913i	0.0686146	−	0.0686146i
$989$			352.660i			0.356582i
$990$	992.346	+	992.346i	1.00237	+	1.00237i
$991$	−842.735	+	842.735i	−0.850388	+	0.850388i	−0.990181	−	0.139793i	$-0.955356\pi$
$991$	−842.735	+	842.735i	−0.850388	+	0.850388i	0.139793	+	0.990181i	$0.455356\pi$
$992$	−332.973			−0.335659
$993$	−735.840	−	735.840i	−0.741028	−	0.741028i
$994$	600.029	−	600.029i	0.603651	−	0.603651i
$995$			453.290i			0.455568i
$996$		−	762.561i		−	0.765624i
$997$	724.949			0.727131			0.363565	−	0.931569i	$-0.381559\pi$
$997$	724.949			0.727131			0.363565	+	0.931569i	$0.381559\pi$
$998$			1179.05i			1.18141i
$999$	−32.0201	+	32.0201i	−0.0320522	+	0.0320522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.b.187.3	✓	46
269.82	odd	4	inner	538.3.c.b.351.3	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.3	✓	46	1.1	even	1	trivial
538.3.c.b.351.3	yes	46	269.82	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	538.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-3.24321 - 3.24321i) q^{3} +2.00000i q^{4} +4.65083 q^{5} +6.48641i q^{6} +(4.88017 - 4.88017i) q^{7} +(2.00000 - 2.00000i) q^{8} +12.0368i q^{9} +(-4.65083 - 4.65083i) q^{10} +17.7265i q^{11} +(6.48641 - 6.48641i) q^{12} +4.34344i q^{13} -9.76035 q^{14} +(-15.0836 - 15.0836i) q^{15} -4.00000 q^{16} +(-11.3436 - 11.3436i) q^{17} +(12.0368 - 12.0368i) q^{18} +(-7.80386 + 7.80386i) q^{19} +9.30167i q^{20} -31.6548 q^{21} +(17.7265 - 17.7265i) q^{22} -40.0305 q^{23} -12.9728 q^{24} -3.36973 q^{25} +(4.34344 - 4.34344i) q^{26} +(9.84884 - 9.84884i) q^{27} +(9.76035 + 9.76035i) q^{28} +(-3.41094 + 3.41094i) q^{29} +30.1672i q^{30} +(-41.6217 + 41.6217i) q^{31} +(4.00000 + 4.00000i) q^{32} +(57.4906 - 57.4906i) q^{33} +22.6871i q^{34} +(22.6969 - 22.6969i) q^{35} -24.0735 q^{36} -3.25116 q^{37} +15.6077 q^{38} +(14.0867 - 14.0867i) q^{39} +(9.30167 - 9.30167i) q^{40} +11.4842 q^{41} +(31.6548 + 31.6548i) q^{42} -8.80977i q^{43} -35.4530 q^{44} +55.9810i q^{45} +(40.0305 + 40.0305i) q^{46} -41.4763 q^{47} +(12.9728 + 12.9728i) q^{48} +1.36783i q^{49} +(3.36973 + 3.36973i) q^{50} +73.5790i q^{51} -8.68688 q^{52} -17.5716 q^{53} -19.6977 q^{54} +82.4429i q^{55} -19.5207i q^{56} +50.6191 q^{57} +6.82188 q^{58} +(-5.47396 + 5.47396i) q^{59} +(30.1672 - 30.1672i) q^{60} +27.1650 q^{61} +83.2434 q^{62} +(58.7415 + 58.7415i) q^{63} -8.00000i q^{64} +20.2006i q^{65} -114.981 q^{66} +2.74007 q^{67} +(22.6871 - 22.6871i) q^{68} +(129.827 + 129.827i) q^{69} -45.3938 q^{70} +(-61.4762 + 61.4762i) q^{71} +(24.0735 + 24.0735i) q^{72} -79.1820i q^{73} +(3.25116 + 3.25116i) q^{74} +(10.9287 + 10.9287i) q^{75} +(-15.6077 - 15.6077i) q^{76} +(86.5083 + 86.5083i) q^{77} -28.1734 q^{78} +6.12702i q^{79} -18.6033 q^{80} +44.4472 q^{81} +(-11.4842 - 11.4842i) q^{82} +(58.7815 - 58.7815i) q^{83} -63.3096i q^{84} +(-52.7570 - 52.7570i) q^{85} +(-8.80977 + 8.80977i) q^{86} +22.1247 q^{87} +(35.4530 + 35.4530i) q^{88} +113.961i q^{89} +(55.9810 - 55.9810i) q^{90} +(21.1967 + 21.1967i) q^{91} -80.0610i q^{92} +269.975 q^{93} +(41.4763 + 41.4763i) q^{94} +(-36.2945 + 36.2945i) q^{95} -25.9456i q^{96} -9.11196i q^{97} +(1.36783 - 1.36783i) q^{98} -213.369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Introduction

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