LMFDB - Embedded newform 198.4.f.d.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,4,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("198.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, degree $4$, 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:	$11.6823781811$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 $ x^8 - x^7 + 71x^6 - 141x^5 + 2911x^4 + 2710x^3 + 75340x^2 + 169400x + 5856400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$-4.79501 + 3.48378i$ of defining polynomial
Character	$\chi$	$=$	198.91
Dual form			198.4.f.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(10.3036 + 7.48598i) q^{5} +(7.24988 - 22.3128i) q^{7} +(2.47214 + 7.60845i) q^{8} +O(q^{10})$	\(q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(10.3036 + 7.48598i) q^{5} +(7.24988 - 22.3128i) q^{7} +(2.47214 + 7.60845i) q^{8} -25.4718 q^{10} +(3.69653 - 36.2951i) q^{11} +(-9.27574 + 6.73922i) q^{13} +(14.4998 + 44.6257i) q^{14} +(-12.9443 - 9.40456i) q^{16} +(-52.9924 - 38.5012i) q^{17} +(-2.24041 - 6.89528i) q^{19} +(41.2143 - 29.9439i) q^{20} +(36.6864 + 63.0723i) q^{22} +104.072 q^{23} +(11.4965 + 35.3825i) q^{25} +(7.08604 - 21.8086i) q^{26} +(-75.9218 - 55.1604i) q^{28} +(39.3536 - 121.118i) q^{29} +(233.653 - 169.759i) q^{31} +32.0000 q^{32} +131.004 q^{34} +(241.733 - 175.629i) q^{35} +(-26.3908 + 81.2224i) q^{37} +(11.7310 + 8.52303i) q^{38} +(-31.4849 + 96.9006i) q^{40} +(41.8544 + 128.815i) q^{41} +353.691 q^{43} +(-133.506 - 58.9257i) q^{44} +(-168.393 + 122.344i) q^{46} +(41.5948 + 128.016i) q^{47} +(-167.810 - 121.921i) q^{49} +(-60.1964 - 43.7352i) q^{50} +(14.1721 + 43.6171i) q^{52} +(405.666 - 294.734i) q^{53} +(309.792 - 346.297i) q^{55} +187.689 q^{56} +(78.7073 + 242.236i) q^{58} +(-201.373 + 619.763i) q^{59} +(-295.928 - 215.004i) q^{61} +(-178.495 + 549.352i) q^{62} +(-51.7771 + 37.6183i) q^{64} -146.023 q^{65} -294.576 q^{67} +(-211.969 + 154.005i) q^{68} +(-184.668 + 568.349i) q^{70} +(107.151 + 77.8500i) q^{71} +(145.080 - 446.511i) q^{73} +(-52.7815 - 162.445i) q^{74} -29.0005 q^{76} +(-783.048 - 345.616i) q^{77} +(-330.105 + 239.836i) q^{79} +(-62.9698 - 193.801i) q^{80} +(-219.152 - 159.224i) q^{82} +(-1099.89 - 799.119i) q^{83} +(-257.791 - 793.400i) q^{85} +(-572.283 + 415.788i) q^{86} +(285.288 - 61.6016i) q^{88} +260.255 q^{89} +(83.1232 + 255.827i) q^{91} +(128.641 - 395.915i) q^{92} +(-217.793 - 158.236i) q^{94} +(28.5337 - 87.8177i) q^{95} +(-1144.38 + 831.440i) q^{97} +414.848 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8	$ 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8} - 100 q^{10} + 155 q^{11} + 7 q^{13} - 2 q^{14} - 32 q^{16} - 161 q^{17} - 272 q^{19} - 20 q^{20} - 628 q^{23} - 17 q^{25} - 96 q^{26} + 16 q^{28} - 33 q^{29} + 323 q^{31} + 256 q^{32} + 208 q^{34} + 697 q^{35} + 49 q^{37} + 576 q^{38} + 240 q^{40} - 361 q^{41} + 1442 q^{43} - 620 q^{44} - 416 q^{46} + 1069 q^{47} - 709 q^{49} + 76 q^{50} - 192 q^{52} + 281 q^{53} - 7 q^{55} - 48 q^{56} - 66 q^{58} + 128 q^{59} - 617 q^{61} - 1044 q^{62} - 128 q^{64} + 138 q^{65} + 578 q^{67} - 644 q^{68} + 34 q^{70} - 115 q^{71} - 1487 q^{73} + 98 q^{74} - 128 q^{76} - 553 q^{77} + 71 q^{79} + 480 q^{80} + 658 q^{82} - 1942 q^{83} - 329 q^{85} - 2426 q^{86} + 560 q^{88} + 2202 q^{89} + 4523 q^{91} + 2088 q^{92} - 1332 q^{94} + 793 q^{95} - 5128 q^{97} + 3292 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8 - 100 * q^10 + 155 * q^11 + 7 * q^13 - 2 * q^14 - 32 * q^16 - 161 * q^17 - 272 * q^19 - 20 * q^20 - 628 * q^23 - 17 * q^25 - 96 * q^26 + 16 * q^28 - 33 * q^29 + 323 * q^31 + 256 * q^32 + 208 * q^34 + 697 * q^35 + 49 * q^37 + 576 * q^38 + 240 * q^40 - 361 * q^41 + 1442 * q^43 - 620 * q^44 - 416 * q^46 + 1069 * q^47 - 709 * q^49 + 76 * q^50 - 192 * q^52 + 281 * q^53 - 7 * q^55 - 48 * q^56 - 66 * q^58 + 128 * q^59 - 617 * q^61 - 1044 * q^62 - 128 * q^64 + 138 * q^65 + 578 * q^67 - 644 * q^68 + 34 * q^70 - 115 * q^71 - 1487 * q^73 + 98 * q^74 - 128 * q^76 - 553 * q^77 + 71 * q^79 + 480 * q^80 + 658 * q^82 - 1942 * q^83 - 329 * q^85 - 2426 * q^86 + 560 * q^88 + 2202 * q^89 + 4523 * q^91 + 2088 * q^92 - 1332 * q^94 + 793 * q^95 - 5128 * q^97 + 3292 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	10.3036	+	7.48598i	0.921579	+	0.669566i	0.943917	−	0.330184i	$-0.107111\pi$
$5$	10.3036	+	7.48598i	0.921579	+	0.669566i	−0.0223375	+	0.999750i	$0.507111\pi$
$6$		0			0
$7$	7.24988	−	22.3128i	0.391457	−	1.20478i	−0.540230	−	0.841518i	$-0.681663\pi$
$7$	7.24988	−	22.3128i	0.391457	−	1.20478i	0.931687	−	0.363263i	$-0.118337\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$		0			0
$10$	−25.4718			−0.805490
$11$	3.69653	−	36.2951i	0.101322	−	0.994854i
$11$	3.69653	−	36.2951i	0.101322	−	0.994854i
$12$		0			0
$13$	−9.27574	+	6.73922i	−0.197894	+	0.143779i	−0.682320	−	0.731054i	$-0.739029\pi$
$13$	−9.27574	+	6.73922i	−0.197894	+	0.143779i	0.484425	+	0.874833i	$0.339029\pi$
$14$	14.4998	+	44.6257i	0.276802	+	0.851908i
$15$		0			0
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	−52.9924	−	38.5012i	−0.756032	−	0.549289i	0.141659	−	0.989916i	$-0.454756\pi$
$17$	−52.9924	−	38.5012i	−0.756032	−	0.549289i	−0.897691	+	0.440626i	$0.854756\pi$
$18$		0			0
$19$	−2.24041	−	6.89528i	−0.0270519	−	0.0832571i	0.936619	−	0.350349i	$-0.113937\pi$
$19$	−2.24041	−	6.89528i	−0.0270519	−	0.0832571i	−0.963671	+	0.267092i	$0.913937\pi$
$20$	41.2143	−	29.9439i	0.460790	−	0.334783i
$21$		0			0
$22$	36.6864	+	63.0723i	0.355525	+	0.611230i
$23$	104.072			0.943504			0.471752	−	0.881731i	$-0.343622\pi$
$23$	104.072			0.943504			0.471752	+	0.881731i	$0.343622\pi$
$24$		0			0
$25$	11.4965	+	35.3825i	0.0919719	+	0.283060i
$26$	7.08604	−	21.8086i	0.0534495	−	0.164501i
$27$		0			0
$28$	−75.9218	−	55.1604i	−0.512424	−	0.372298i
$29$	39.3536	−	121.118i	0.251993	−	0.775554i	−0.742415	−	0.669941i	$-0.766319\pi$
$29$	39.3536	−	121.118i	0.251993	−	0.775554i	0.994407	−	0.105613i	$-0.0336805\pi$
$30$		0			0
$31$	233.653	−	169.759i	1.35372	−	0.983536i	0.354905	−	0.934903i	$-0.384513\pi$
$31$	233.653	−	169.759i	1.35372	−	0.983536i	0.998817	−	0.0486336i	$-0.0154867\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	131.004			0.660796
$35$	241.733	−	175.629i	1.16744	−	0.848194i
$36$		0			0
$37$	−26.3908	+	81.2224i	−0.117260	+	0.360889i	−0.992412	−	0.122960i	$-0.960761\pi$
$37$	−26.3908	+	81.2224i	−0.117260	+	0.360889i	0.875152	+	0.483849i	$0.160761\pi$
$38$	11.7310	+	8.52303i	0.0500792	+	0.0363847i
$39$		0			0
$40$	−31.4849	+	96.9006i	−0.124455	+	0.383033i
$41$	41.8544	+	128.815i	0.159428	+	0.490670i	0.998583	−	0.0532236i	$-0.0169496\pi$
$41$	41.8544	+	128.815i	0.159428	+	0.490670i	−0.839154	+	0.543893i	$0.816950\pi$
$42$		0			0
$43$	353.691			1.25436			0.627178	−	0.778876i	$-0.284210\pi$
$43$	353.691			1.25436			0.627178	+	0.778876i	$0.284210\pi$
$44$	−133.506	−	58.9257i	−0.457426	−	0.201895i
$45$		0			0
$46$	−168.393	+	122.344i	−0.539742	+	0.392146i
$47$	41.5948	+	128.016i	0.129090	+	0.397298i	0.994624	−	0.103552i	$-0.0330208\pi$
$47$	41.5948	+	128.016i	0.129090	+	0.397298i	−0.865534	+	0.500850i	$0.833021\pi$
$48$		0			0
$49$	−167.810	−	121.921i	−0.489241	−	0.355454i
$50$	−60.1964	−	43.7352i	−0.170261	−	0.123702i
$51$		0			0
$52$	14.1721	+	43.6171i	0.0377945	+	0.116319i
$53$	405.666	−	294.734i	1.05137	−	0.763864i	0.0788966	−	0.996883i	$-0.474860\pi$
$53$	405.666	−	294.734i	1.05137	−	0.763864i	0.972472	+	0.233019i	$0.0748603\pi$
$54$		0			0
$55$	309.792	−	346.297i	0.759497	−	0.848994i
$56$	187.689			0.447875
$57$		0			0
$58$	78.7073	+	242.236i	0.178186	+	0.548399i
$59$	−201.373	+	619.763i	−0.444349	+	1.36756i	0.438848	+	0.898561i	$0.355387\pi$
$59$	−201.373	+	619.763i	−0.444349	+	1.36756i	−0.883196	+	0.469003i	$0.844613\pi$
$60$		0			0
$61$	−295.928	−	215.004i	−0.621143	−	0.451287i	0.232178	−	0.972673i	$-0.425415\pi$
$61$	−295.928	−	215.004i	−0.621143	−	0.451287i	−0.853320	+	0.521387i	$0.825415\pi$
$62$	−178.495	+	549.352i	−0.365628	+	1.12529i
$63$		0			0
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	−146.023			−0.278645
$66$		0			0
$67$	−294.576			−0.537136			−0.268568	−	0.963261i	$-0.586550\pi$
$67$	−294.576			−0.537136			−0.268568	+	0.963261i	$0.586550\pi$
$68$	−211.969	+	154.005i	−0.378016	+	0.274645i
$69$		0			0
$70$	−184.668	+	568.349i	−0.315315	+	0.970438i
$71$	107.151	+	77.8500i	0.179106	+	0.130128i	0.673726	−	0.738981i	$-0.264693\pi$
$71$	107.151	+	77.8500i	0.179106	+	0.130128i	−0.494620	+	0.869109i	$0.664693\pi$
$72$		0			0
$73$	145.080	−	446.511i	0.232607	−	0.715892i	−0.764822	−	0.644241i	$-0.777173\pi$
$73$	145.080	−	446.511i	0.232607	−	0.715892i	0.997430	−	0.0716507i	$-0.0228267\pi$
$74$	−52.7815	−	162.445i	−0.0829153	−	0.255187i
$75$		0			0
$76$	−29.0005			−0.0437709
$77$	−783.048	−	345.616i	−1.15892	−	0.511514i
$78$		0			0
$79$	−330.105	+	239.836i	−0.470124	+	0.341565i	−0.797489	−	0.603333i	$-0.793839\pi$
$79$	−330.105	+	239.836i	−0.470124	+	0.341565i	0.327366	+	0.944898i	$0.393839\pi$
$80$	−62.9698	−	193.801i	−0.0880030	−	0.270845i
$81$		0			0
$82$	−219.152	−	159.224i	−0.295138	−	0.214431i
$83$	−1099.89	−	799.119i	−1.45457	−	1.05680i	−0.984738	−	0.174045i	$-0.944316\pi$
$83$	−1099.89	−	799.119i	−1.45457	−	1.05680i	−0.469827	−	0.882758i	$-0.655684\pi$
$84$		0			0
$85$	−257.791	−	793.400i	−0.328957	−	1.01243i
$86$	−572.283	+	415.788i	−0.717569	+	0.521344i
$87$		0			0
$88$	285.288	−	61.6016i	0.345589	−	0.0746222i
$89$	260.255			0.309966			0.154983	−	0.987917i	$-0.450468\pi$
$89$	260.255			0.309966			0.154983	+	0.987917i	$0.450468\pi$
$90$		0			0
$91$	83.1232	+	255.827i	0.0957547	+	0.294703i
$92$	128.641	−	395.915i	0.145779	−	0.448663i
$93$		0			0
$94$	−217.793	−	158.236i	−0.238975	−	0.173626i
$95$	28.5337	−	87.8177i	0.0308157	−	0.0948411i
$96$		0			0
$97$	−1144.38	+	831.440i	−1.19788	+	0.870309i	−0.994074	−	0.108703i	$-0.965330\pi$
$97$	−1144.38	+	831.440i	−1.19788	+	0.870309i	−0.203803	+	0.979012i	$0.565330\pi$
$98$	414.848			0.427612
$99$		0			0
$100$	148.814			0.148814
$101$	−150.976	+	109.691i	−0.148740	+	0.108066i	−0.659666	−	0.751559i	$-0.729302\pi$
$101$	−150.976	+	109.691i	−0.148740	+	0.108066i	0.510927	+	0.859624i	$0.329302\pi$
$102$		0			0
$103$	−362.450	+	1115.51i	−0.346731	+	1.06713i	0.613919	+	0.789369i	$0.289592\pi$
$103$	−362.450	+	1115.51i	−0.346731	+	1.06713i	−0.960651	+	0.277760i	$0.910408\pi$
$104$	−74.2059	−	53.9138i	−0.0699662	−	0.0508335i
$105$		0			0
$106$	−309.901	+	953.779i	−0.283965	+	0.873954i
$107$	220.241	+	677.831i	0.198986	+	0.612415i	0.999907	+	0.0136452i	$0.00434354\pi$
$107$	220.241	+	677.831i	0.198986	+	0.612415i	−0.800921	+	0.598770i	$0.795656\pi$
$108$		0			0
$109$	1247.22			1.09598			0.547989	−	0.836486i	$-0.315394\pi$
$109$	1247.22			1.09598			0.547989	+	0.836486i	$0.315394\pi$
$110$	−94.1574	+	924.503i	−0.0816141	+	0.801344i
$111$		0			0
$112$	−303.687	+	220.642i	−0.256212	+	0.186149i
$113$	303.455	+	933.939i	0.252625	+	0.777501i	0.994288	+	0.106728i	$0.0340374\pi$
$113$	303.455	+	933.939i	0.252625	+	0.777501i	−0.741663	+	0.670773i	$0.765963\pi$
$114$		0			0
$115$	1072.32	+	779.084i	0.869513	+	0.631739i
$116$	−412.117	−	299.420i	−0.329863	−	0.239659i
$117$		0			0
$118$	−402.747	−	1239.53i	−0.314202	−	0.967014i
$119$	−1243.26	+	903.281i	−0.957727	+	0.695829i
$120$		0			0
$121$	−1303.67	−	268.332i	−0.979468	−	0.201602i
$122$	731.574			0.542899
$123$		0			0
$124$	−356.990	−	1098.70i	−0.258538	−	0.795697i
$125$	345.533	−	1063.44i	0.247244	−	0.760937i
$126$		0			0
$127$	1254.52	+	911.460i	0.876538	+	0.636842i	0.932333	−	0.361600i	$-0.117769\pi$
$127$	1254.52	+	911.460i	0.876538	+	0.636842i	−0.0557950	+	0.998442i	$0.517769\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$		0			0
$130$	236.270	−	171.660i	0.159402	−	0.115812i
$131$	−742.114			−0.494953			−0.247476	−	0.968894i	$-0.579601\pi$
$131$	−742.114			−0.494953			−0.247476	+	0.968894i	$0.579601\pi$
$132$		0			0
$133$	−170.096			−0.110896
$134$	476.633	−	346.294i	0.307275	−	0.223248i
$135$		0			0
$136$	161.930	−	498.370i	0.102099	−	0.314227i
$137$	417.192	+	303.108i	0.260169	+	0.189024i	0.710222	−	0.703978i	$-0.248595\pi$
$137$	417.192	+	303.108i	0.260169	+	0.189024i	−0.450053	+	0.893002i	$0.648595\pi$
$138$		0			0
$139$	761.160	−	2342.61i	0.464466	−	1.42948i	−0.395187	−	0.918601i	$-0.629320\pi$
$139$	761.160	−	2342.61i	0.464466	−	1.42948i	0.859653	−	0.510878i	$-0.170680\pi$
$140$	−369.335	−	1136.70i	−0.222961	−	0.686203i
$141$		0			0
$142$	−264.893			−0.156544
$143$	210.313	+	361.576i	0.122988	+	0.211444i
$144$		0			0
$145$	1312.17	−	953.348i	0.751516	−	0.546008i
$146$	290.160	+	893.021i	0.164478	+	0.506212i
$147$		0			0
$148$	276.368	+	200.793i	0.153495	+	0.111521i
$149$	−351.726	−	255.544i	−0.193386	−	0.140503i	0.486879	−	0.873469i	$-0.338135\pi$
$149$	−351.726	−	255.544i	−0.193386	−	0.140503i	−0.680265	+	0.732966i	$0.738135\pi$
$150$		0			0
$151$	−241.340	−	742.768i	−0.130066	−	0.400302i	0.864724	−	0.502247i	$-0.167493\pi$
$151$	−241.340	−	742.768i	−0.130066	−	0.400302i	−0.994790	+	0.101945i	$0.967493\pi$
$152$	46.9238	−	34.0921i	0.0250396	−	0.0181924i
$153$		0			0
$154$	1673.29	−	361.311i	0.875570	−	0.189060i
$155$	3678.27			1.90610
$156$		0			0
$157$	161.425	+	496.815i	0.0820580	+	0.252549i	0.983665	−	0.180007i	$-0.0576120\pi$
$157$	161.425	+	496.815i	0.0820580	+	0.252549i	−0.901607	+	0.432555i	$0.857612\pi$
$158$	252.178	−	776.124i	0.126976	−	0.390792i
$159$		0			0
$160$	329.714	+	239.551i	0.162914	+	0.118364i
$161$	754.513	−	2322.15i	0.369341	−	1.13672i
$162$		0			0
$163$	−2057.56	+	1494.91i	−0.988716	+	0.718344i	−0.959639	−	0.281233i	$-0.909257\pi$
$163$	−2057.56	+	1494.91i	−0.988716	+	0.718344i	−0.0290761	+	0.999577i	$0.509257\pi$
$164$	541.775			0.257960
$165$		0			0
$166$	2719.08			1.27134
$167$	1120.85	−	814.342i	0.519363	−	0.377339i	−0.297001	−	0.954877i	$-0.595986\pi$
$167$	1120.85	−	814.342i	0.519363	−	0.377339i	0.816364	+	0.577538i	$0.195986\pi$
$168$		0			0
$169$	−638.288	+	1964.45i	−0.290527	+	0.894150i
$170$	1349.81	+	980.696i	0.608976	+	0.442447i
$171$		0			0
$172$	437.186	−	1345.52i	0.193809	−	0.596482i
$173$	137.052	+	421.804i	0.0602307	+	0.185371i	0.976645	−	0.214861i	$-0.0689297\pi$
$173$	137.052	+	421.804i	0.0602307	+	0.185371i	−0.916414	+	0.400232i	$0.868930\pi$
$174$		0			0
$175$	872.833			0.377029
$176$	−389.189	+	435.050i	−0.166683	+	0.186324i
$177$		0			0
$178$	−421.101	+	305.948i	−0.177319	+	0.128830i
$179$	−116.388	−	358.205i	−0.0485991	−	0.149573i	0.923812	−	0.382846i	$-0.125056\pi$
$179$	−116.388	−	358.205i	−0.0485991	−	0.149573i	−0.972411	+	0.233274i	$0.925056\pi$
$180$		0			0
$181$	−2664.71	−	1936.02i	−1.09429	−	0.795047i	−0.114170	−	0.993461i	$-0.536421\pi$
$181$	−2664.71	−	1936.02i	−1.09429	−	0.795047i	−0.980118	+	0.198414i	$0.936421\pi$
$182$	−435.238	−	316.219i	−0.177264	−	0.128790i
$183$		0			0
$184$	257.281	+	791.830i	0.103082	+	0.317252i
$185$	−879.949	+	639.320i	−0.349703	+	0.254074i
$186$		0			0
$187$	−1593.29	+	1781.04i	−0.623065	+	0.696486i
$188$	538.415			0.208872
$189$		0			0
$190$	57.0674	+	175.635i	0.0217900	+	0.0670628i
$191$	−707.730	+	2178.17i	−0.268113	+	0.825166i	0.722847	+	0.691008i	$0.242833\pi$
$191$	−707.730	+	2178.17i	−0.268113	+	0.825166i	−0.990960	+	0.134158i	$0.957167\pi$
$192$		0			0
$193$	1863.49	+	1353.90i	0.695010	+	0.504954i	0.878303	−	0.478104i	$-0.158676\pi$
$193$	1863.49	+	1353.90i	0.695010	+	0.504954i	−0.183293	+	0.983058i	$0.558676\pi$
$194$	874.228	−	2690.60i	0.323536	−	0.995740i
$195$		0			0
$196$	−671.238	+	487.683i	−0.244620	+	0.177727i
$197$	1041.86			0.376801			0.188400	−	0.982092i	$-0.439670\pi$
$197$	1041.86			0.376801			0.188400	+	0.982092i	$0.439670\pi$
$198$		0			0
$199$	3463.83			1.23389			0.616946	−	0.787005i	$-0.288370\pi$
$199$	3463.83			1.23389			0.616946	+	0.787005i	$0.288370\pi$
$200$	−240.785	+	174.941i	−0.0851305	+	0.0618509i
$201$		0			0
$202$	115.336	−	354.966i	0.0401732	−	0.123640i
$203$	−2417.18	−	1756.18i	−0.835728	−	0.607192i
$204$		0			0
$205$	−533.054	+	1640.57i	−0.181610	+	0.558939i
$206$	−724.901	−	2231.02i	−0.245176	−	0.754574i
$207$		0			0
$208$	183.447			0.0611527
$209$	−258.547	+	55.8274i	−0.0855696	+	0.0184769i
$210$		0			0
$211$	−1692.45	+	1229.63i	−0.552193	+	0.401192i	−0.828593	−	0.559851i	$-0.810858\pi$
$211$	−1692.45	+	1229.63i	−0.552193	+	0.401192i	0.276400	+	0.961043i	$0.410858\pi$
$212$	−619.803	−	1907.56i	−0.200794	−	0.617979i
$213$		0			0
$214$	−1153.20	−	837.845i	−0.368368	−	0.267635i
$215$	3644.28	+	2647.72i	1.15599	+	0.839875i
$216$		0			0
$217$	−2093.85	−	6444.20i	−0.655022	−	2.01595i
$218$	−2018.04	+	1466.19i	−0.626967	+	0.455518i
$219$		0			0
$220$	−934.468	−	1606.57i	−0.286372	−	0.492339i
$221$	751.012			0.228591
$222$		0			0
$223$	1144.45	+	3522.26i	0.343669	+	1.05770i	0.962292	+	0.272017i	$0.0876906\pi$
$223$	1144.45	+	3522.26i	0.343669	+	1.05770i	−0.618623	+	0.785688i	$0.712309\pi$
$224$	231.996	−	714.011i	0.0692005	−	0.212977i
$225$		0			0
$226$	−1588.91	−	1154.41i	−0.467667	−	0.339780i
$227$	1499.81	−	4615.95i	0.438529	−	1.34965i	−0.450897	−	0.892576i	$-0.648896\pi$
$227$	1499.81	−	4615.95i	0.438529	−	1.34965i	0.889426	−	0.457079i	$-0.151104\pi$
$228$		0			0
$229$	1081.53	−	785.778i	0.312094	−	0.226750i	−0.420700	−	0.907200i	$-0.638216\pi$
$229$	1081.53	−	785.778i	0.312094	−	0.226750i	0.732795	+	0.680450i	$0.238216\pi$
$230$	−2650.91			−0.759983
$231$		0			0
$232$	1018.81			0.288311
$233$	−4776.36	+	3470.23i	−1.34296	+	0.975718i	−0.343631	+	0.939105i	$0.611657\pi$
$233$	−4776.36	+	3470.23i	−1.34296	+	0.975718i	−0.999330	+	0.0366132i	$0.988343\pi$
$234$		0			0
$235$	−529.748	+	1630.40i	−0.147051	+	0.452576i
$236$	2108.81	+	1532.14i	0.581660	+	0.422601i
$237$		0			0
$238$	949.766	−	2923.08i	0.258673	−	0.796114i
$239$	1025.87	+	3157.30i	0.277649	+	0.854515i	0.988506	+	0.151179i	$0.0483070\pi$
$239$	1025.87	+	3157.30i	0.277649	+	0.854515i	−0.710858	+	0.703336i	$0.751693\pi$
$240$		0			0
$241$	−5275.95			−1.41018			−0.705091	−	0.709116i	$-0.749094\pi$
$241$	−5275.95			−1.41018			−0.705091	+	0.709116i	$0.749094\pi$
$242$	2424.83	−	1098.39i	0.644107	−	0.291764i
$243$		0			0
$244$	−1183.71	+	860.017i	−0.310571	+	0.225643i
$245$	−816.340	−	2512.44i	−0.212874	−	0.655158i
$246$		0			0
$247$	67.2503	+	48.8602i	0.0173240	+	0.0125866i
$248$	1869.23	+	1358.07i	0.478613	+	0.347733i
$249$		0			0
$250$	691.067	+	2126.88i	0.174828	+	0.538064i
$251$	−1587.17	+	1153.15i	−0.399129	+	0.289984i	−0.769186	−	0.639025i	$-0.779338\pi$
$251$	−1587.17	+	1153.15i	−0.399129	+	0.289984i	0.370057	+	0.929009i	$0.379338\pi$
$252$		0			0
$253$	384.707	−	3777.32i	0.0955980	−	0.938648i
$254$	−3101.34			−0.766123
$255$		0			0
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	−1836.17	+	5651.15i	−0.445669	+	1.37163i	0.436078	+	0.899909i	$0.356367\pi$
$257$	−1836.17	+	5651.15i	−0.445669	+	1.37163i	−0.881748	+	0.471721i	$0.843633\pi$
$258$		0			0
$259$	1620.97	+	1177.71i	0.388890	+	0.282545i
$260$	−180.494	+	555.504i	−0.0430530	+	0.132503i
$261$		0			0
$262$	1200.77	−	872.408i	0.283143	−	0.205716i
$263$	1704.11			0.399544			0.199772	−	0.979842i	$-0.435980\pi$
$263$	1704.11			0.399544			0.199772	+	0.979842i	$0.435980\pi$
$264$		0			0
$265$	6386.18			1.48038
$266$	275.221	−	199.960i	0.0634395	−	0.0460915i
$267$		0			0
$268$	−364.115	+	1120.63i	−0.0829921	+	0.255423i
$269$	−4728.97	−	3435.80i	−1.07186	−	0.778752i	−0.0956148	−	0.995418i	$-0.530482\pi$
$269$	−4728.97	−	3435.80i	−1.07186	−	0.778752i	−0.976246	+	0.216666i	$0.930482\pi$
$270$		0			0
$271$	1825.00	−	5616.79i	0.409082	−	1.25902i	−0.508357	−	0.861146i	$-0.669747\pi$
$271$	1825.00	−	5616.79i	0.409082	−	1.25902i	0.917439	−	0.397877i	$-0.130253\pi$
$272$	323.861	+	996.740i	0.0721946	+	0.222192i
$273$		0			0
$274$	−1031.36			−0.227396
$275$	1326.71	−	286.474i	0.290922	−	0.0628182i
$276$		0			0
$277$	−7186.00	+	5220.93i	−1.55872	+	1.13247i	−0.621667	+	0.783281i	$0.713544\pi$
$277$	−7186.00	+	5220.93i	−1.55872	+	1.13247i	−0.937051	+	0.349193i	$0.886456\pi$
$278$	1522.32	+	4685.22i	0.328427	+	1.01079i
$279$		0			0
$280$	1933.87	+	1405.04i	0.412752	+	0.299882i
$281$	−6594.92	−	4791.49i	−1.40007	−	1.01721i	−0.994674	−	0.103070i	$-0.967133\pi$
$281$	−6594.92	−	4791.49i	−1.40007	−	1.01721i	−0.405397	−	0.914141i	$-0.632867\pi$
$282$		0			0
$283$	1812.06	+	5576.96i	0.380622	+	1.17143i	0.939607	+	0.342256i	$0.111191\pi$
$283$	1812.06	+	5576.96i	0.380622	+	1.17143i	−0.558985	+	0.829178i	$0.688809\pi$
$284$	428.605	−	311.400i	0.0895529	−	0.0650640i
$285$		0			0
$286$	−765.351	−	337.805i	−0.158238	−	0.0698420i
$287$	3177.66			0.653559
$288$		0			0
$289$	−192.352	−	592.000i	−0.0391517	−	0.120497i
$290$	−1002.41	+	3085.10i	−0.202978	+	0.624701i
$291$		0			0
$292$	−1519.30	−	1103.83i	−0.304487	−	0.221223i
$293$	−2353.65	+	7243.79i	−0.469289	+	1.44432i	0.384218	+	0.923242i	$0.374471\pi$
$293$	−2353.65	+	7243.79i	−0.469289	+	1.44432i	−0.853507	+	0.521081i	$0.825529\pi$
$294$		0			0
$295$	−6714.40	+	4878.30i	−1.32518	+	0.962798i
$296$	−683.219			−0.134160
$297$		0			0
$298$	869.515			0.169026
$299$	−965.348	+	701.367i	−0.186714	+	0.135656i
$300$		0			0
$301$	2564.22	−	7891.85i	0.491026	−	1.51122i
$302$	1263.67	+	918.112i	0.240782	+	0.174938i
$303$		0			0
$304$	−35.8466	+	110.324i	−0.00676297	+	0.0208143i
$305$	−1439.60	−	4430.62i	−0.270266	−	0.831792i
$306$		0			0
$307$	4100.68			0.762339			0.381170	−	0.924505i	$-0.375521\pi$
$307$	4100.68			0.762339			0.381170	+	0.924505i	$0.375521\pi$
$308$	−2282.70	+	2551.69i	−0.422302	+	0.472065i
$309$		0			0
$310$	−5951.57	+	4324.07i	−1.09041	+	0.792228i
$311$	−449.969	−	1384.86i	−0.0820432	−	0.252503i	0.901618	−	0.432534i	$-0.142380\pi$
$311$	−449.969	−	1384.86i	−0.0820432	−	0.252503i	−0.983661	+	0.180031i	$0.942380\pi$
$312$		0			0
$313$	2800.56	+	2034.72i	0.505740	+	0.367442i	0.811205	−	0.584761i	$-0.198812\pi$
$313$	2800.56	+	2034.72i	0.505740	+	0.367442i	−0.305465	+	0.952203i	$0.598812\pi$
$314$	−845.232	−	614.097i	−0.151908	−	0.110368i
$315$		0			0
$316$	504.356	+	1552.25i	0.0897856	+	0.276332i
$317$	4038.86	−	2934.41i	0.715600	−	0.519914i	−0.169375	−	0.985552i	$-0.554175\pi$
$317$	4038.86	−	2934.41i	0.715600	−	0.519914i	0.884975	+	0.465638i	$0.154175\pi$
$318$		0			0
$319$	−4250.52	−	1876.06i	−0.746030	−	0.329277i
$320$	−815.098			−0.142392
$321$		0			0
$322$	1509.03	+	4644.30i	0.261164	+	0.803779i
$323$	−146.752	+	451.656i	−0.0252802	+	0.0778043i
$324$		0			0
$325$	−345.089	−	250.722i	−0.0588988	−	0.0427925i
$326$	1571.84	−	4837.62i	0.267043	−	0.821874i
$327$		0			0
$328$	−876.610	+	636.894i	−0.147569	+	0.107215i
$329$	3157.95			0.529190
$330$		0			0
$331$	10199.3			1.69366			0.846832	−	0.531861i	$-0.178507\pi$
$331$	10199.3			1.69366			0.846832	+	0.531861i	$0.178507\pi$
$332$	−4399.57	+	3196.48i	−0.727283	+	0.528402i
$333$		0			0
$334$	−856.250	+	2635.27i	−0.140275	+	0.431723i
$335$	−3035.18	−	2205.19i	−0.495014	−	0.359648i
$336$		0			0
$337$	−519.376	+	1598.48i	−0.0839532	+	0.258381i	−0.984218	−	0.176962i	$-0.943373\pi$
$337$	−519.376	+	1598.48i	−0.0839532	+	0.258381i	0.900264	+	0.435343i	$0.143373\pi$
$338$	−1276.58	−	3928.90i	−0.205434	−	0.632260i
$339$		0			0
$340$	−3336.92			−0.532264
$341$	−5297.72	−	9107.99i	−0.841312	−	1.44641i
$342$		0			0
$343$	2573.29	−	1869.61i	0.405087	−	0.294313i
$344$	874.371	+	2691.04i	0.137043	+	0.421776i
$345$		0			0
$346$	−717.616	−	521.378i	−0.111501	−	0.0810101i
$347$	8515.93	+	6187.19i	1.31746	+	0.957192i	0.999960	+	0.00893386i	$0.00284377\pi$
$347$	8515.93	+	6187.19i	1.31746	+	0.957192i	0.317501	+	0.948258i	$0.397156\pi$
$348$		0			0
$349$	−1637.90	−	5040.94i	−0.251217	−	0.773168i	−0.994551	−	0.104247i	$-0.966757\pi$
$349$	−1637.90	−	5040.94i	−0.251217	−	0.773168i	0.743334	−	0.668920i	$-0.233243\pi$
$350$	−1412.27	+	1026.08i	−0.215683	+	0.156703i
$351$		0			0
$352$	118.289	−	1161.44i	0.0179114	−	0.175867i
$353$	7438.40			1.12155			0.560773	−	0.827969i	$-0.310504\pi$
$353$	7438.40			1.12155			0.560773	+	0.827969i	$0.310504\pi$
$354$		0			0
$355$	521.257	+	1604.26i	0.0779309	+	0.239847i
$356$	321.693	−	990.068i	0.0478923	−	0.147397i
$357$		0			0
$358$	609.414	+	442.765i	0.0899680	+	0.0653656i
$359$	−3136.93	+	9654.47i	−0.461172	+	1.41934i	0.402562	+	0.915393i	$0.368120\pi$
$359$	−3136.93	+	9654.47i	−0.461172	+	1.41934i	−0.863734	+	0.503948i	$0.831880\pi$
$360$		0			0
$361$	5506.52	−	4000.72i	0.802817	−	0.583281i
$362$	6587.52			0.956443
$363$		0			0
$364$	1075.97			0.154934
$365$	4837.41	−	3514.59i	0.693703	−	0.504005i
$366$		0			0
$367$	147.340	−	453.466i	0.0209567	−	0.0644980i	−0.940031	−	0.341088i	$-0.889204\pi$
$367$	147.340	−	453.466i	0.0209567	−	0.0644980i	0.960988	+	0.276590i	$0.0892045\pi$
$368$	−1347.14	−	978.755i	−0.190828	−	0.138644i
$369$		0			0
$370$	672.221	−	2068.88i	0.0944516	−	0.290692i
$371$	−3635.32	−	11188.4i	−0.508723	−	1.56569i
$372$		0			0
$373$	−12738.5			−1.76829			−0.884146	−	0.467210i	$-0.845259\pi$
$373$	−12738.5			−1.76829			−0.884146	+	0.467210i	$0.845259\pi$
$374$	484.262	−	4754.82i	0.0669534	−	0.657395i
$375$		0			0
$376$	−871.173	+	632.944i	−0.119488	+	0.0868128i
$377$	451.207	+	1388.67i	0.0616402	+	0.189709i
$378$		0			0
$379$	1050.66	+	763.349i	0.142398	+	0.103458i	0.656704	−	0.754149i	$-0.271950\pi$
$379$	1050.66	+	763.349i	0.142398	+	0.103458i	−0.514306	+	0.857607i	$0.671950\pi$
$380$	−298.809	−	217.097i	−0.0403383	−	0.0293075i
$381$		0			0
$382$	−1415.46	−	4356.34i	−0.189584	−	0.583481i
$383$	−542.501	+	394.150i	−0.0723772	+	0.0525851i	−0.623386	−	0.781915i	$-0.714243\pi$
$383$	−542.501	+	394.150i	−0.0723772	+	0.0525851i	0.551008	+	0.834500i	$0.314243\pi$
$384$		0			0
$385$	−5480.92	−	9422.95i	−0.725541	−	1.24737i
$386$	−4606.80			−0.607461
$387$		0			0
$388$	1748.46	+	5381.20i	0.228774	+	0.704095i
$389$	−1617.98	+	4979.64i	−0.210887	+	0.649043i	0.788533	+	0.614992i	$0.210841\pi$
$389$	−1617.98	+	4979.64i	−0.210887	+	0.649043i	−0.999420	+	0.0340509i	$0.989159\pi$
$390$		0			0
$391$	−5515.04	−	4006.91i	−0.713319	−	0.518256i
$392$	512.780	−	1578.18i	0.0660697	−	0.203342i
$393$		0			0
$394$	−1685.77	+	1224.79i	−0.215553	+	0.156609i
$395$	−5196.67			−0.661956
$396$		0			0
$397$	1751.64			0.221442			0.110721	−	0.993852i	$-0.464684\pi$
$397$	1751.64			0.221442			0.110721	+	0.993852i	$0.464684\pi$
$398$	−5604.60	+	4071.98i	−0.705862	+	0.512839i
$399$		0			0
$400$	183.944	−	566.121i	0.0229930	−	0.0707651i
$401$	2922.80	+	2123.54i	0.363984	+	0.264450i	0.754712	−	0.656056i	$-0.227777\pi$
$401$	2922.80	+	2123.54i	0.363984	+	0.264450i	−0.390728	+	0.920506i	$0.627777\pi$
$402$		0			0
$403$	−1023.26	+	3149.28i	−0.126482	+	0.389273i
$404$	230.671	+	709.933i	0.0284067	+	0.0874269i
$405$		0			0
$406$	5975.60			0.730453
$407$	2850.42	+	1258.10i	0.347151	+	0.153223i
$408$		0			0
$409$	9137.83	−	6639.02i	1.10473	−	0.802637i	0.122908	−	0.992418i	$-0.460778\pi$
$409$	9137.83	−	6639.02i	1.10473	−	0.802637i	0.981826	+	0.189781i	$0.0607779\pi$
$410$	−1066.11	−	3281.14i	−0.128418	−	0.395229i
$411$		0			0
$412$	3795.63	+	2757.69i	0.453877	+	0.329761i
$413$	12368.8	+	8986.42i	1.47367	+	1.07069i
$414$		0			0
$415$	−5350.63	−	16467.5i	−0.632897	−	1.94786i
$416$	−296.824	+	215.655i	−0.0349831	+	0.0254167i
$417$		0			0
$418$	352.708	−	394.271i	0.0412716	−	0.0461349i
$419$	3680.45			0.429121			0.214560	−	0.976711i	$-0.431168\pi$
$419$	3680.45			0.429121			0.214560	+	0.976711i	$0.431168\pi$
$420$		0			0
$421$	2860.31	+	8803.14i	0.331124	+	1.01909i	0.968600	+	0.248625i	$0.0799786\pi$
$421$	2860.31	+	8803.14i	0.331124	+	1.01909i	−0.637476	+	0.770470i	$0.720021\pi$
$422$	1292.91	−	3979.18i	0.149142	−	0.459013i
$423$		0			0
$424$	3245.33	+	2357.87i	0.371715	+	0.270067i
$425$	753.045	−	2317.63i	0.0859483	−	0.264522i
$426$		0			0
$427$	−6942.80	+	5044.24i	−0.786852	+	0.571681i
$428$	2850.85			0.321966
$429$		0			0
$430$	−9009.14			−1.01037
$431$	2899.55	−	2106.64i	0.324052	−	0.235437i	−0.413851	−	0.910345i	$-0.635816\pi$
$431$	2899.55	−	2106.64i	0.324052	−	0.235437i	0.737902	+	0.674907i	$0.235816\pi$
$432$		0			0
$433$	−2566.94	+	7900.24i	−0.284895	+	0.876816i	0.701535	+	0.712635i	$0.252498\pi$
$433$	−2566.94	+	7900.24i	−0.284895	+	0.876816i	−0.986430	+	0.164181i	$0.947502\pi$
$434$	10963.5	+	7965.47i	1.21260	+	0.881002i
$435$		0			0
$436$	1541.64	−	4744.69i	0.169338	−	0.521168i
$437$	−233.165	−	717.608i	−0.0255236	−	0.0785534i
$438$		0			0
$439$	11932.4			1.29727			0.648634	−	0.761101i	$-0.275341\pi$
$439$	11932.4			1.29727			0.648634	+	0.761101i	$0.275341\pi$
$440$	3400.63	+	1500.94i	0.368452	+	0.162624i
$441$		0			0
$442$	−1215.16	+	882.867i	−0.130768	+	0.0950084i
$443$	−333.374	−	1026.02i	−0.0357541	−	0.110040i	0.931587	−	0.363519i	$-0.118425\pi$
$443$	−333.374	−	1026.02i	−0.0357541	−	0.110040i	−0.967341	+	0.253480i	$0.918425\pi$
$444$		0			0
$445$	2681.55	+	1948.26i	0.285658	+	0.207543i
$446$	−5992.43	−	4353.75i	−0.636210	−	0.462234i
$447$		0			0
$448$	463.993	+	1428.02i	0.0489321	+	0.150598i
$449$	10327.9	−	7503.63i	1.08553	−	0.788682i	0.106889	−	0.994271i	$-0.465911\pi$
$449$	10327.9	−	7503.63i	1.08553	−	0.788682i	0.978638	+	0.205589i	$0.0659111\pi$
$450$		0			0
$451$	4830.06	−	1042.94i	0.504298	−	0.108892i
$452$	3928.01			0.408756
$453$		0			0
$454$	2999.63	+	9231.91i	0.310087	+	0.954350i
$455$	−1058.65	+	3258.19i	−0.109077	+	0.335706i
$456$		0			0
$457$	9082.69	+	6598.96i	0.929695	+	0.675463i	0.945918	−	0.324406i	$-0.105164\pi$
$457$	9082.69	+	6598.96i	0.929695	+	0.675463i	−0.0162235	+	0.999868i	$0.505164\pi$
$458$	−826.216	+	2542.83i	−0.0842938	+	0.259430i
$459$		0			0
$460$	4289.27	−	3116.33i	0.434757	−	0.315869i
$461$	2160.58			0.218283			0.109141	−	0.994026i	$-0.465190\pi$
$461$	2160.58			0.218283			0.109141	+	0.994026i	$0.465190\pi$
$462$		0			0
$463$	11469.5			1.15125			0.575627	−	0.817712i	$-0.304758\pi$
$463$	11469.5			1.15125			0.575627	+	0.817712i	$0.304758\pi$
$464$	−1648.47	+	1197.68i	−0.164931	+	0.119830i
$465$		0			0
$466$	3648.81	−	11229.9i	0.362721	−	1.11634i
$467$	1632.91	+	1186.38i	0.161803	+	0.117557i	0.665741	−	0.746183i	$-0.268116\pi$
$467$	1632.91	+	1186.38i	0.161803	+	0.117557i	−0.503937	+	0.863740i	$0.668116\pi$
$468$		0			0
$469$	−2135.64	+	6572.82i	−0.210266	+	0.647131i
$470$	−1059.50	−	3260.79i	−0.103981	−	0.320019i
$471$		0			0
$472$	−5213.26			−0.508389
$473$	1307.43	−	12837.2i	0.127094	−	1.24790i
$474$		0			0
$475$	218.216	−	158.543i	0.0210788	−	0.0153146i
$476$	1899.53	+	5846.16i	0.182910	+	0.562938i
$477$		0			0
$478$	−5371.53	−	3902.64i	−0.513991	−	0.373437i
$479$	−5927.67	−	4306.71i	−0.565433	−	0.410811i	0.268011	−	0.963416i	$-0.413634\pi$
$479$	−5927.67	−	4306.71i	−0.565433	−	0.410811i	−0.833443	+	0.552605i	$0.813634\pi$
$480$		0			0
$481$	−302.582	−	931.252i	−0.0286831	−	0.0882774i
$482$	8536.67	−	6202.26i	0.806711	−	0.586110i
$483$		0			0
$484$	−2632.22	+	4627.78i	−0.247203	+	0.434615i
$485$	−18015.3			−1.68667
$486$		0			0
$487$	−1912.75	−	5886.85i	−0.177978	−	0.547759i	0.821779	−	0.569806i	$-0.192982\pi$
$487$	−1912.75	−	5886.85i	−0.177978	−	0.547759i	−0.999757	+	0.0220470i	$0.992982\pi$
$488$	904.276	−	2783.07i	0.0838824	−	0.258164i
$489$		0			0
$490$	4274.41	+	3105.54i	0.394078	+	0.286315i
$491$	3127.54	−	9625.57i	0.287462	−	0.884717i	−0.698188	−	0.715914i	$-0.746010\pi$
$491$	3127.54	−	9625.57i	0.287462	−	0.884717i	0.985650	−	0.168802i	$-0.0539900\pi$
$492$		0			0
$493$	−6748.64	+	4903.17i	−0.616518	+	0.447926i
$494$	−166.252			−0.0151418
$495$		0			0
$496$	−4620.98			−0.418323
$497$	2513.89	−	1826.45i	0.226888	−	0.164844i
$498$		0			0
$499$	791.952	−	2437.38i	0.0710474	−	0.218661i	−0.909228	−	0.416299i	$-0.863327\pi$
$499$	791.952	−	2437.38i	0.0710474	−	0.218661i	0.980275	+	0.197638i	$0.0633269\pi$
$500$	−3618.47	−	2628.97i	−0.323646	−	0.235143i
$501$		0			0
$502$	1212.49	−	3731.66i	0.107801	−	0.331777i
$503$	−2658.01	−	8180.53i	−0.235616	−	0.725152i	−0.997039	−	0.0768967i	$-0.975499\pi$
$503$	−2658.01	−	8180.53i	−0.235616	−	0.725152i	0.761423	−	0.648256i	$-0.224501\pi$
$504$		0			0
$505$	−2376.74			−0.209432
$506$	3818.04	+	6564.08i	0.335440	+	0.576698i
$507$		0			0
$508$	5018.07	−	3645.84i	0.438269	−	0.318421i
$509$	4309.27	+	13262.6i	0.375255	+	1.15492i	0.943306	+	0.331924i	$0.107698\pi$
$509$	4309.27	+	13262.6i	0.375255	+	1.15492i	−0.568051	+	0.822993i	$0.692302\pi$
$510$		0			0
$511$	−8911.11	−	6474.30i	−0.771437	−	0.560482i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	−3672.34	−	11302.3i	−0.315136	−	0.969889i
$515$	−12085.2	+	8780.41i	−1.03405	+	0.751284i
$516$		0			0
$517$	4800.10	−	1036.47i	0.408333	−	0.0881704i
$518$	−4007.27			−0.339902
$519$		0			0
$520$	−360.988	−	1111.01i	−0.0304431	−	0.0936941i
$521$	3736.89	−	11501.0i	0.314234	−	0.967113i	−0.661834	−	0.749650i	$-0.730222\pi$
$521$	3736.89	−	11501.0i	0.314234	−	0.967113i	0.976069	−	0.217463i	$-0.0697782\pi$
$522$		0			0
$523$	13504.0	+	9811.21i	1.12904	+	0.820295i	0.985555	−	0.169358i	$-0.0541693\pi$
$523$	13504.0	+	9811.21i	1.12904	+	0.820295i	0.143484	+	0.989653i	$0.454169\pi$
$524$	−917.304	+	2823.17i	−0.0764744	+	0.235364i
$525$		0			0
$526$	−2757.31	+	2003.30i	−0.228564	+	0.166061i
$527$	−18917.8			−1.56370
$528$		0			0
$529$	−1335.94			−0.109800
$530$	−10333.1	+	7507.41i	−0.846867	+	0.615285i
$531$		0			0
$532$	−210.250	+	647.084i	−0.0171344	+	0.0527343i
$533$	−1256.34	−	912.785i	−0.102098	−	0.0741784i
$534$		0			0
$535$	−2804.97	+	8632.79i	−0.226671	+	0.697623i
$536$	−728.231	−	2241.26i	−0.0586843	−	0.180612i
$537$		0			0
$538$	11690.7			0.936840
$539$	−5045.44	+	5639.98i	−0.403196	+	0.450707i
$540$		0			0
$541$	−16725.1	+	12151.5i	−1.32914	+	0.965679i	−0.329374	+	0.944200i	$0.606838\pi$
$541$	−16725.1	+	12151.5i	−1.32914	+	0.965679i	−0.999769	+	0.0214796i	$0.993162\pi$
$542$	3650.01	+	11233.6i	0.289264	+	0.890264i
$543$		0			0
$544$	−1695.76	−	1232.04i	−0.133649	−	0.0971015i
$545$	12850.8	+	9336.63i	1.01003	+	0.733830i
$546$		0			0
$547$	2833.62	+	8721.00i	0.221494	+	0.681687i	0.998629	+	0.0523532i	$0.0166722\pi$
$547$	2833.62	+	8721.00i	0.221494	+	0.681687i	−0.777135	+	0.629334i	$0.783328\pi$
$548$	1668.77	−	1212.43i	0.130084	−	0.0945119i
$549$		0			0
$550$	−1809.89	+	2023.17i	−0.140317	+	0.156851i
$551$	−923.311			−0.0713873
$552$		0			0
$553$	2958.19	+	9104.37i	0.227477	+	0.700104i
$554$	5489.62	−	16895.3i	0.420995	−	1.29569i
$555$		0			0
$556$	−7970.97	−	5791.25i	−0.607994	−	0.441733i
$557$	−6276.38	+	19316.7i	−0.477449	+	1.46944i	0.365178	+	0.930938i	$0.381008\pi$
$557$	−6276.38	+	19316.7i	−0.477449	+	1.46944i	−0.842627	+	0.538498i	$0.818992\pi$
$558$		0			0
$559$	−3280.74	+	2383.60i	−0.248230	+	0.180350i
$560$	−4780.78			−0.360759
$561$		0			0
$562$	16303.5			1.22371
$563$	4500.68	−	3269.94i	0.336911	−	0.244780i	−0.406446	−	0.913675i	$-0.633232\pi$
$563$	4500.68	−	3269.94i	0.336911	−	0.244780i	0.743357	+	0.668894i	$0.233232\pi$
$564$		0			0
$565$	−3864.78	+	11894.6i	−0.287774	+	0.885678i
$566$	−9488.08	−	6893.50i	−0.704618	−	0.511935i
$567$		0			0
$568$	−327.425	+	1007.71i	−0.0241874	+	0.0744412i
$569$	7041.09	+	21670.3i	0.518766	+	1.59660i	0.776323	+	0.630335i	$0.217083\pi$
$569$	7041.09	+	21670.3i	0.518766	+	1.59660i	−0.257557	+	0.966263i	$0.582917\pi$
$570$		0			0
$571$	−11157.6			−0.817743			−0.408871	−	0.912592i	$-0.634078\pi$
$571$	−11157.6			−0.817743			−0.408871	+	0.912592i	$0.634078\pi$
$572$	1635.48	−	353.145i	0.119550	−	0.0258142i
$573$		0			0
$574$	−5141.56	+	3735.56i	−0.373876	+	0.271637i
$575$	1196.47	+	3682.34i	0.0867758	+	0.267068i
$576$		0			0
$577$	−10055.4	−	7305.64i	−0.725494	−	0.527102i	0.162641	−	0.986685i	$-0.447999\pi$
$577$	−10055.4	−	7305.64i	−0.725494	−	0.527102i	−0.888135	+	0.459583i	$0.847999\pi$
$578$	1007.17	+	731.752i	0.0724788	+	0.0526589i
$579$		0			0
$580$	−2004.82	−	6170.20i	−0.143527	−	0.441730i
$581$	−25804.7	+	18748.2i	−1.84262	+	1.33874i
$582$		0			0
$583$	−9197.84	−	15813.2i	−0.653406	−	1.12335i
$584$	3755.91			0.266131
$585$		0			0
$586$	−4707.30	−	14487.6i	−0.331837	−	1.02129i
$587$	−1889.62	+	5815.66i	−0.132867	+	0.408923i	−0.995252	−	0.0973299i	$-0.968970\pi$
$587$	−1889.62	+	5815.66i	−0.132867	+	0.408923i	0.862385	+	0.506253i	$0.168970\pi$
$588$		0			0
$589$	−1694.02	−	1230.77i	−0.118507	−	0.0861005i
$590$	5129.35	−	15786.5i	0.357918	−	1.10156i
$591$		0			0
$592$	1105.47	−	803.172i	0.0767476	−	0.0557604i
$593$	−7188.32			−0.497789			−0.248894	−	0.968531i	$-0.580067\pi$
$593$	−7188.32			−0.497789			−0.248894	+	0.968531i	$0.580067\pi$
$594$		0			0
$595$	−19572.0			−1.34852
$596$	−1406.90	+	1022.18i	−0.0966930	+	0.0702516i
$597$		0			0
$598$	737.461	−	2269.67i	0.0504298	−	0.155207i
$599$	−818.874	−	594.947i	−0.0558569	−	0.0405824i	0.559506	−	0.828826i	$-0.310991\pi$
$599$	−818.874	−	594.947i	−0.0558569	−	0.0405824i	−0.615363	+	0.788244i	$0.710991\pi$
$600$		0			0
$601$	4134.93	−	12726.0i	0.280644	−	0.863734i	−0.707026	−	0.707187i	$-0.749964\pi$
$601$	4134.93	−	12726.0i	0.280644	−	0.863734i	0.987671	−	0.156547i	$-0.0500362\pi$
$602$	5128.43	+	15783.7i	0.347208	+	1.06860i
$603$		0			0
$604$	−3123.97			−0.210451
$605$	−11423.7	−	12524.0i	−0.767671	−	0.841611i
$606$		0			0
$607$	−442.493	+	321.490i	−0.0295885	+	0.0214973i	−0.602481	−	0.798133i	$-0.705821\pi$
$607$	−442.493	+	321.490i	−0.0295885	+	0.0214973i	0.572893	+	0.819630i	$0.305821\pi$
$608$	−71.6932	−	220.649i	−0.00478214	−	0.0147179i
$609$		0			0
$610$	7537.83	+	5476.55i	0.500324	+	0.363507i
$611$	−1248.55	−	907.124i	−0.0826692	−	0.0600627i
$612$		0			0
$613$	4247.62	+	13072.8i	0.279869	+	0.861349i	0.987890	+	0.155157i	$0.0495885\pi$
$613$	4247.62	+	13072.8i	0.279869	+	0.861349i	−0.708020	+	0.706192i	$0.750412\pi$
$614$	−6635.04	+	4820.64i	−0.436105	+	0.316849i
$615$		0			0
$616$	693.798	−	6812.19i	0.0453797	−	0.445570i
$617$	3323.39			0.216847			0.108423	−	0.994105i	$-0.465420\pi$
$617$	3323.39			0.216847			0.108423	+	0.994105i	$0.465420\pi$
$618$		0			0
$619$	−6699.20	−	20618.0i	−0.434998	−	1.33879i	−0.893089	−	0.449881i	$-0.851467\pi$
$619$	−6699.20	−	20618.0i	−0.434998	−	1.33879i	0.458091	−	0.888905i	$-0.348533\pi$
$620$	4546.60	−	13993.0i	0.294509	−	0.906406i
$621$		0			0
$622$	2356.07	+	1711.79i	0.151881	+	0.110348i
$623$	1886.82	−	5807.03i	0.121338	−	0.373441i
$624$		0			0
$625$	15283.4	−	11104.0i	0.978138	−	0.710659i
$626$	−6923.35			−0.442033
$627$		0			0
$628$	2089.53			0.132773
$629$	4525.67	−	3288.09i	0.286885	−	0.208434i
$630$		0			0
$631$	−9236.13	+	28425.9i	−0.582702	+	1.79337i	0.0256092	+	0.999672i	$0.491847\pi$
$631$	−9236.13	+	28425.9i	−0.582702	+	1.79337i	−0.608311	+	0.793699i	$0.708153\pi$
$632$	−2640.84	−	1918.68i	−0.166214	−	0.120761i
$633$		0			0
$634$	−3085.42	+	9495.94i	−0.193277	+	0.594845i
$635$	6102.83	+	18782.6i	0.381391	+	1.17380i
$636$		0			0
$637$	2378.21			0.147925
$638$	9082.93	−	1961.26i	0.563631	−	0.121704i
$639$		0			0
$640$	1318.86	−	958.205i	0.0814569	−	0.0591819i
$641$	−8398.45	−	25847.8i	−0.517502	−	1.59271i	−0.778683	−	0.627418i	$-0.784112\pi$
$641$	−8398.45	−	25847.8i	−0.517502	−	1.59271i	0.261181	−	0.965290i	$-0.415888\pi$
$642$		0			0
$643$	−13247.2	−	9624.69i	−0.812474	−	0.590297i	0.102073	−	0.994777i	$-0.467452\pi$
$643$	−13247.2	−	9624.69i	−0.812474	−	0.590297i	−0.914547	+	0.404480i	$0.867452\pi$
$644$	−7901.36	−	5740.67i	−0.483474	−	0.351264i
$645$		0			0
$646$	−293.504	−	903.312i	−0.0178758	−	0.0550160i
$647$	1850.76	−	1344.66i	0.112459	−	0.0817062i	−0.530134	−	0.847914i	$-0.677859\pi$
$647$	1850.76	−	1344.66i	0.112459	−	0.0817062i	0.642593	+	0.766207i	$0.277859\pi$
$648$		0			0
$649$	21750.0	+	9599.84i	1.31550	+	0.580627i
$650$	853.107			0.0514794
$651$		0			0
$652$	3143.67	+	9675.23i	0.188828	+	0.581152i
$653$	354.419	−	1090.79i	0.0212396	−	0.0653689i	−0.939875	−	0.341519i	$-0.889059\pi$
$653$	354.419	−	1090.79i	0.0212396	−	0.0653689i	0.961115	+	0.276150i	$0.0890587\pi$
$654$		0			0
$655$	−7646.43	−	5555.45i	−0.456138	−	0.331404i
$656$	669.670	−	2061.03i	0.0398571	−	0.122667i
$657$		0			0
$658$	−5109.67	+	3712.40i	−0.302729	+	0.219946i
$659$	377.923			0.0223396			0.0111698	−	0.999938i	$-0.496444\pi$
$659$	377.923			0.0223396			0.0111698	+	0.999938i	$0.496444\pi$
$660$		0			0
$661$	−17500.4			−1.02978			−0.514892	−	0.857255i	$-0.672168\pi$
$661$	−17500.4			−1.02978			−0.514892	+	0.857255i	$0.672168\pi$
$662$	−16502.8	+	11990.0i	−0.968880	+	0.703932i
$663$		0			0
$664$	3360.97	−	10344.0i	0.196432	−	0.604556i
$665$	−1752.60	−	1273.34i	−0.102200	−	0.0742524i
$666$		0			0
$667$	4095.63	−	12605.0i	0.237756	−	0.731738i
$668$	−1712.50	−	5270.53i	−0.0991895	−	0.305274i
$669$		0			0
$670$	7503.38			0.432658
$671$	−8897.51	+	9945.97i	−0.511900	+	0.572221i
$672$		0			0
$673$	11739.3	−	8529.08i	0.672386	−	0.488517i	−0.198437	−	0.980114i	$-0.563587\pi$
$673$	11739.3	−	8529.08i	0.672386	−	0.488517i	0.870823	+	0.491597i	$0.163587\pi$
$674$	−1038.75	−	3196.95i	−0.0593639	−	0.182703i
$675$		0			0
$676$	6684.24	+	4856.38i	0.380305	+	0.276308i
$677$	379.518	+	275.736i	0.0215451	+	0.0156534i	0.598506	−	0.801119i	$-0.295761\pi$
$677$	379.518	+	275.736i	0.0215451	+	0.0156534i	−0.576961	+	0.816772i	$0.695761\pi$
$678$		0			0
$679$	10255.2	+	31562.2i	0.579614	+	1.78387i
$680$	5399.25	−	3922.78i	0.304488	−	0.221223i
$681$		0			0
$682$	19279.0	+	8509.20i	1.08245	+	0.477763i
$683$	15892.3			0.890342			0.445171	−	0.895446i	$-0.353143\pi$
$683$	15892.3			0.890342			0.445171	+	0.895446i	$0.353143\pi$
$684$		0			0
$685$	2029.51	+	6246.19i	0.113202	+	0.348401i
$686$	−1965.82	+	6050.17i	−0.109410	+	0.336730i
$687$		0			0
$688$	−4578.27	−	3326.31i	−0.253699	−	0.184323i
$689$	−1776.58	+	5467.75i	−0.0982326	+	0.302329i
$690$		0			0
$691$	5020.47	−	3647.58i	0.276393	−	0.200811i	−0.440950	−	0.897532i	$-0.645358\pi$
$691$	5020.47	−	3647.58i	0.276393	−	0.200811i	0.717343	+	0.696721i	$0.245358\pi$
$692$	1774.04			0.0974553
$693$		0			0
$694$	−21052.5			−1.15150
$695$	25379.4	−	18439.2i	1.38517	−	1.00639i
$696$		0			0
$697$	2741.55	−	8437.64i	0.148987	−	0.458534i
$698$	8576.16	+	6230.95i	0.465061	+	0.337887i
$699$		0			0
$700$	1078.88	−	3320.46i	0.0582541	−	0.179288i
$701$	−578.646	−	1780.89i	−0.0311771	−	0.0959533i	0.934257	−	0.356600i	$-0.116064\pi$
$701$	−578.646	−	1780.89i	−0.0311771	−	0.0959533i	−0.965434	+	0.260647i	$0.916064\pi$
$702$		0			0
$703$	619.178			0.0332187
$704$	1173.96	+	2018.31i	0.0628486	+	0.108051i
$705$		0			0
$706$	−12035.6	+	8744.36i	−0.641594	+	0.466145i
$707$	1352.95	+	4163.95i	0.0719702	+	0.221502i
$708$		0			0
$709$	−4236.02	−	3077.65i	−0.224383	−	0.163023i	0.469915	−	0.882712i	$-0.344285\pi$
$709$	−4236.02	−	3077.65i	−0.224383	−	0.163023i	−0.694297	+	0.719688i	$0.744285\pi$
$710$	−2729.34	−	1982.98i	−0.144268	−	0.104817i
$711$		0			0
$712$	643.385	+	1980.14i	0.0338650	+	0.104226i
$713$	24316.8	−	17667.2i	1.27724	−	0.927970i
$714$		0			0
$715$	−539.778	+	5299.92i	−0.0282329	+	0.277211i
$716$	−1506.56			−0.0786349
$717$		0			0
$718$	−6273.85	−	19308.9i	−0.326098	−	1.00363i
$719$	5338.20	−	16429.3i	0.276886	−	0.852169i	−0.711828	−	0.702354i	$-0.752132\pi$
$719$	5338.20	−	16429.3i	0.276886	−	0.852169i	0.988714	−	0.149814i	$-0.0478676\pi$
$720$		0			0
$721$	22262.4	+	16174.6i	1.14993	+	0.835470i
$722$	−4206.61	+	12946.6i	−0.216833	+	0.667345i
$723$		0			0
$724$	−10658.8	+	7744.09i	−0.547144	+	0.397523i
$725$	4737.89			0.242705
$726$		0			0
$727$	17292.7			0.882190			0.441095	−	0.897461i	$-0.354590\pi$
$727$	17292.7			0.882190			0.441095	+	0.897461i	$0.354590\pi$
$728$	−1740.95	+	1264.88i	−0.0886319	+	0.0643949i
$729$		0			0
$730$	−3695.45	+	11373.4i	−0.187363	+	0.576644i
$731$	−18742.9	−	13617.5i	−0.948333	−	0.689004i
$732$		0			0
$733$	−4289.57	+	13201.9i	−0.216151	+	0.665245i	0.782919	+	0.622124i	$0.213730\pi$
$733$	−4289.57	+	13201.9i	−0.216151	+	0.665245i	−0.999070	+	0.0431210i	$0.986270\pi$
$734$	294.680	+	906.933i	0.0148186	+	0.0456069i
$735$		0			0
$736$	3330.32			0.166790
$737$	−1088.91	+	10691.7i	−0.0544239	+	0.534372i
$738$		0			0
$739$	−5160.93	+	3749.64i	−0.256898	+	0.186648i	−0.708779	−	0.705431i	$-0.750753\pi$
$739$	−5160.93	+	3749.64i	−0.256898	+	0.186648i	0.451880	+	0.892079i	$0.350753\pi$
$740$	1344.44	+	4137.77i	0.0667874	+	0.205550i
$741$		0			0
$742$	19034.8	+	13829.6i	0.941763	+	0.684231i
$743$	18641.9	+	13544.2i	0.920467	+	0.668758i	0.943640	−	0.330973i	$-0.107377\pi$
$743$	18641.9	+	13544.2i	0.920467	+	0.668758i	−0.0231734	+	0.999731i	$0.507377\pi$
$744$		0			0
$745$	−1711.04	−	5266.03i	−0.0841443	−	0.258970i
$746$	20611.3	−	14975.0i	1.01157	−	0.734950i
$747$		0			0
$748$	4806.07	+	8262.74i	0.234930	+	0.403898i
$749$	16721.1			0.815720
$750$		0			0
$751$	−6429.44	−	19787.8i	−0.312401	−	0.961473i	−0.976811	−	0.214104i	$-0.931317\pi$
$751$	−6429.44	−	19787.8i	−0.312401	−	0.961473i	0.664409	−	0.747369i	$-0.268683\pi$
$752$	665.517	−	2048.25i	0.0322725	−	0.0993245i
$753$		0			0
$754$	−2362.55	−	1716.49i	−0.114110	−	0.0829059i
$755$	3073.68	−	9459.83i	0.148163	−	0.455998i
$756$		0			0
$757$	17667.1	−	12835.9i	0.848246	−	0.616287i	−0.0764161	−	0.997076i	$-0.524348\pi$
$757$	17667.1	−	12835.9i	0.848246	−	0.616287i	0.924662	+	0.380789i	$0.124348\pi$
$758$	−2597.38			−0.124460
$759$		0			0
$760$	738.696			0.0352570
$761$	−5775.94	+	4196.47i	−0.275135	+	0.199897i	−0.716793	−	0.697286i	$-0.754391\pi$
$761$	−5775.94	+	4196.47i	−0.275135	+	0.199897i	0.441658	+	0.897184i	$0.354391\pi$
$762$		0			0
$763$	9042.17	−	27828.9i	0.429028	−	1.32041i
$764$	7411.45	+	5384.73i	0.350964	+	0.254990i
$765$		0			0
$766$	414.434	−	1275.50i	0.0195484	−	0.0601639i
$767$	−2308.84	−	7105.86i	−0.108693	−	0.334521i
$768$		0			0
$769$	15473.8			0.725618			0.362809	−	0.931864i	$-0.381818\pi$
$769$	15473.8			0.725618			0.362809	+	0.931864i	$0.381818\pi$
$770$	19945.7	+	8803.46i	0.933496	+	0.412019i
$771$		0			0
$772$	7453.96	−	5415.62i	0.347505	−	0.252477i
$773$	−4709.69	−	14494.9i	−0.219141	−	0.674446i	−0.998834	−	0.0482840i	$-0.984625\pi$
$773$	−4709.69	−	14494.9i	−0.219141	−	0.674446i	0.779693	−	0.626162i	$-0.215375\pi$
$774$		0			0
$775$	8692.69	+	6315.61i	0.402904	+	0.292727i
$776$	−9155.04	−	6651.52i	−0.423514	−	0.307701i
$777$		0			0
$778$	−3235.97	−	9959.28i	−0.149120	−	0.458943i
$779$	794.442	−	577.196i	0.0365389	−	0.0265471i
$780$		0			0
$781$	3221.66	−	3601.29i	0.147606	−	0.164999i
$782$	13633.9			0.623464
$783$		0			0
$784$	1025.56	+	3156.35i	0.0467183	+	0.143784i
$785$	−2055.89	+	6327.39i	−0.0934751	+	0.287687i
$786$		0			0
$787$	−29190.5	−	21208.1i	−1.32215	−	0.960595i	−0.999903	−	0.0139380i	$-0.995563\pi$
$787$	−29190.5	−	21208.1i	−1.32215	−	0.960595i	−0.322243	−	0.946657i	$-0.604437\pi$
$788$	1287.82	−	3963.49i	0.0582189	−	0.179179i
$789$		0			0
$790$	8408.39	−	6109.05i	0.378680	−	0.275127i
$791$	23038.9			1.03561
$792$		0			0
$793$	4193.91			0.187806
$794$	−2834.22	+	2059.18i	−0.126678	+	0.0920373i
$795$		0			0
$796$	4281.53	−	13177.2i	0.190647	−	0.586751i
$797$	2737.30	+	1988.76i	0.121656	+	0.0883885i	0.646950	−	0.762533i	$-0.276044\pi$
$797$	2737.30	+	1988.76i	0.121656	+	0.0883885i	−0.525293	+	0.850921i	$0.676044\pi$
$798$		0			0
$799$	2724.55	−	8385.31i	0.120635	−	0.371278i
$800$	367.887	+	1132.24i	0.0162585	+	0.0500385i
$801$		0			0
$802$	−7225.55			−0.318134
$803$	−15669.9	−	6916.24i	−0.688639	−	0.303946i
$804$		0			0
$805$	25157.7	−	18278.2i	1.10148	−	0.800274i
$806$	−2046.53	−	6298.56i	−0.0894365	−	0.275257i
$807$		0			0
$808$	−1207.81	−	877.525i	−0.0525874	−	0.0382070i
$809$	10905.8	+	7923.49i	0.473950	+	0.344345i	0.798979	−	0.601359i	$-0.205374\pi$
$809$	10905.8	+	7923.49i	0.473950	+	0.344345i	−0.325028	+	0.945704i	$0.605374\pi$
$810$		0			0
$811$	−6620.10	−	20374.6i	−0.286638	−	0.882180i	−0.985903	−	0.167318i	$-0.946489\pi$
$811$	−6620.10	−	20374.6i	−0.286638	−	0.882180i	0.699265	−	0.714862i	$-0.253511\pi$
$812$	−9668.72	+	7024.74i	−0.417864	+	0.303596i
$813$		0			0
$814$	−6091.07	+	1315.23i	−0.262275	+	0.0566324i
$815$	−32391.1			−1.39216
$816$		0			0
$817$	−792.413	−	2438.80i	−0.0339327	−	0.104434i
$818$	−6980.68	+	21484.3i	−0.298379	+	0.918315i
$819$		0			0
$820$	5582.21	+	4055.71i	0.237731	+	0.172722i
$821$	−3295.61	+	10142.8i	−0.140094	+	0.431166i	−0.996348	−	0.0853901i	$-0.972786\pi$
$821$	−3295.61	+	10142.8i	−0.140094	+	0.431166i	0.856253	+	0.516556i	$0.172786\pi$
$822$		0			0
$823$	9705.69	−	7051.60i	0.411080	−	0.298667i	−0.362959	−	0.931805i	$-0.618233\pi$
$823$	9705.69	−	7051.60i	0.411080	−	0.298667i	0.774039	+	0.633138i	$0.218233\pi$
$824$	−9383.31			−0.396703
$825$		0			0
$826$	−30577.2			−1.28804
$827$	33073.2	−	24029.1i	1.39065	−	1.01037i	0.394856	−	0.918743i	$-0.370794\pi$
$827$	33073.2	−	24029.1i	1.39065	−	1.01037i	0.995794	−	0.0916236i	$-0.0292057\pi$
$828$		0			0
$829$	−10270.8	+	31610.2i	−0.430301	+	1.32433i	0.467526	+	0.883979i	$0.345145\pi$
$829$	−10270.8	+	31610.2i	−0.430301	+	1.32433i	−0.897826	+	0.440350i	$0.854855\pi$
$830$	28016.3	+	20355.0i	1.17164	+	0.851244i
$831$		0			0
$832$	226.753	−	697.874i	0.00944862	−	0.0290799i
$833$	4198.53	+	12921.7i	0.174634	+	0.537469i
$834$		0			0
$835$	17644.9			0.731288
$836$	−107.201	+	1052.58i	−0.00443497	+	0.0435456i
$837$		0			0
$838$	−5955.09	+	4326.62i	−0.245483	+	0.178354i
$839$	1968.00	+	6056.87i	0.0809806	+	0.249233i	0.983347	−	0.181736i	$-0.0581718\pi$
$839$	1968.00	+	6056.87i	0.0809806	+	0.249233i	−0.902367	+	0.430969i	$0.858172\pi$
$840$		0			0
$841$	6610.24	+	4802.62i	0.271034	+	0.196917i
$842$	−14976.8	−	10881.3i	−0.612987	−	0.445361i
$843$		0			0
$844$	2585.83	+	7958.36i	0.105460	+	0.324571i
$845$	−21282.5	+	15462.6i	−0.866437	+	0.629503i
$846$		0			0
$847$	−15438.7	+	27143.2i	−0.626305	+	1.10113i
$848$	−8022.90			−0.324891
$849$		0			0
$850$	1506.09	+	4635.27i	0.0607746	+	0.187045i
$851$	−2746.55	+	8453.01i	−0.110635	+	0.340500i
$852$		0			0
$853$	−2456.51	−	1784.76i	−0.0986040	−	0.0716400i	0.537391	−	0.843333i	$-0.319410\pi$
$853$	−2456.51	−	1784.76i	−0.0986040	−	0.0716400i	−0.635995	+	0.771693i	$0.719410\pi$
$854$	5303.83	−	16323.5i	0.212521	−	0.654074i
$855$		0			0
$856$	−4612.78	+	3351.38i	−0.184184	+	0.133818i
$857$	10184.8			0.405959			0.202979	−	0.979183i	$-0.434938\pi$
$857$	10184.8			0.405959			0.202979	+	0.979183i	$0.434938\pi$
$858$		0			0
$859$	−34929.8			−1.38742			−0.693708	−	0.720256i	$-0.744024\pi$
$859$	−34929.8			−1.38742			−0.693708	+	0.720256i	$0.744024\pi$
$860$	14577.1	−	10590.9i	0.577994	−	0.419937i
$861$		0			0
$862$	−2215.06	+	6817.25i	−0.0875234	+	0.269369i
$863$	−9937.36	−	7219.91i	−0.391972	−	0.284784i	0.374291	−	0.927311i	$-0.377886\pi$
$863$	−9937.36	−	7219.91i	−0.391972	−	0.284784i	−0.766263	+	0.642527i	$0.777886\pi$
$864$		0			0
$865$	−1745.49	+	5372.06i	−0.0686108	+	0.211162i
$866$	−5133.89	−	15800.5i	−0.201451	−	0.620003i
$867$		0			0
$868$	−27103.3			−1.05985
$869$	7484.62	+	12867.8i	0.292173	+	0.502312i
$870$		0			0
$871$	2732.41	−	1985.21i	0.106296	−	0.0772288i
$872$	3083.29	+	9489.38i	0.119740	+	0.368522i
$873$		0			0
$874$	1220.87	+	887.012i	0.0472500	+	0.0343291i
$875$	−21223.4	−	15419.7i	−0.819977	−	0.595748i
$876$		0			0
$877$	5913.93	+	18201.2i	0.227707	+	0.700811i	0.998005	+	0.0631273i	$0.0201074\pi$
$877$	5913.93	+	18201.2i	0.227707	+	0.700811i	−0.770298	+	0.637684i	$0.779893\pi$
$878$	−19307.0	+	14027.3i	−0.742117	+	0.539179i
$879$		0			0
$880$	−7266.80	+	1569.10i	−0.278368	+	0.0601074i
$881$	16737.0			0.640049			0.320024	−	0.947409i	$-0.396309\pi$
$881$	16737.0			0.640049			0.320024	+	0.947409i	$0.396309\pi$
$882$		0			0
$883$	−5749.02	−	17693.7i	−0.219105	−	0.674336i	−0.998837	−	0.0482222i	$-0.984644\pi$
$883$	−5749.02	−	17693.7i	−0.219105	−	0.674336i	0.779731	−	0.626114i	$-0.215356\pi$
$884$	928.301	−	2857.02i	0.0353192	−	0.108701i
$885$		0			0
$886$	1745.57	+	1268.23i	0.0661891	+	0.0480892i
$887$	−4917.33	+	15134.0i	−0.186142	+	0.572886i	−0.999966	−	0.00822537i	$-0.997382\pi$
$887$	−4917.33	+	15134.0i	−0.186142	+	0.572886i	0.813824	+	0.581111i	$0.197382\pi$
$888$		0			0
$889$	29432.4	−	21383.9i	1.11038	−	0.806740i
$890$	−6629.16			−0.249674
$891$		0			0
$892$	14814.1			0.556068
$893$	789.514	−	573.616i	0.0295858	−	0.0214953i
$894$		0			0
$895$	1482.30	−	4562.06i	0.0553609	−	0.170383i
$896$	−2429.50	−	1765.13i	−0.0905846	−	0.0658135i
$897$		0			0
$898$	−7889.78	+	24282.3i	−0.293191	+	0.902349i
$899$	−11365.8	−	34980.3i	−0.421657	−	1.29773i
$900$		0			0
$901$	−32844.8			−1.21445
$902$	−6589.14	+	7365.59i	−0.243231	+	0.271893i
$903$		0			0
$904$	−6355.65	+	4617.65i	−0.233834	+	0.169890i
$905$	−12963.0	−	39895.9i	−0.476136	−	1.46540i
$906$		0			0
$907$	18247.6	+	13257.7i	0.668029	+	0.485351i	0.869365	−	0.494171i	$-0.164528\pi$
$907$	18247.6	+	13257.7i	0.668029	+	0.485351i	−0.201336	+	0.979522i	$0.564528\pi$
$908$	−15706.3	−	11411.3i	−0.574042	−	0.417066i
$909$		0			0
$910$	−2117.30	−	6516.37i	−0.0771294	−	0.237380i
$911$	39123.8	−	28425.1i	1.42286	−	1.03377i	0.431572	−	0.902078i	$-0.357959\pi$
$911$	39123.8	−	28425.1i	1.42286	−	1.03377i	0.991291	−	0.131692i	$-0.0420410\pi$
$912$		0			0
$913$	−33069.9	+	36966.8i	−1.19874	+	1.34000i
$914$	−22453.6			−0.812583
$915$		0			0
$916$	−1652.43	−	5085.66i	−0.0596047	−	0.183444i
$917$	−5380.24	+	16558.7i	−0.193753	+	0.596310i
$918$		0			0
$919$	−17000.9	−	12351.9i	−0.610238	−	0.443364i	0.239260	−	0.970955i	$-0.423095\pi$
$919$	−17000.9	−	12351.9i	−0.610238	−	0.443364i	−0.849498	+	0.527592i	$0.823095\pi$
$920$	−3276.71	+	10084.7i	−0.117424	+	0.361393i
$921$		0			0
$922$	−3495.90	+	2539.92i	−0.124871	+	0.0907243i
$923$	−1518.56			−0.0541537
$924$		0			0
$925$	−3177.26			−0.112938
$926$	−18558.0	+	13483.2i	−0.658588	+	0.478492i
$927$		0			0
$928$	1259.32	−	3875.78i	0.0445464	−	0.137100i
$929$	3980.09	+	2891.71i	0.140563	+	0.102125i	0.655844	−	0.754896i	$-0.272313\pi$
$929$	3980.09	+	2891.71i	0.140563	+	0.102125i	−0.515282	+	0.857021i	$0.672313\pi$
$930$		0			0
$931$	−464.715	+	1430.25i	−0.0163592	+	0.0503485i
$932$	7297.63	+	22459.8i	0.256483	+	0.789372i
$933$		0			0
$934$	−4036.78			−0.141421
$935$	−29749.5	+	6423.74i	−1.04055	+	0.224683i
$936$		0			0
$937$	13899.1	−	10098.3i	0.484594	−	0.352078i	−0.318507	−	0.947920i	$-0.603182\pi$
$937$	13899.1	−	10098.3i	0.484594	−	0.352078i	0.803102	+	0.595842i	$0.203182\pi$
$938$	−4271.28	−	13145.6i	−0.148680	−	0.457591i
$939$		0			0
$940$	5547.59	+	4030.56i	0.192492	+	0.139854i
$941$	−41653.8	−	30263.2i	−1.44301	−	1.04841i	−0.987402	−	0.158230i	$-0.949421\pi$
$941$	−41653.8	−	30263.2i	−1.44301	−	1.04841i	−0.455609	−	0.890180i	$-0.650579\pi$
$942$		0			0
$943$	4355.89	+	13406.0i	0.150421	+	0.462949i
$944$	8435.24	−	6128.56i	0.290830	−	0.211300i
$945$		0			0
$946$	12975.6	+	22308.1i	0.445955	+	0.766700i
$947$	−45107.8			−1.54784			−0.773920	−	0.633283i	$-0.781707\pi$
$947$	−45107.8			−1.54784			−0.773920	+	0.633283i	$0.781707\pi$
$948$		0			0
$949$	1663.41	+	5119.44i	0.0568983	+	0.175115i
$950$	−166.702	+	513.056i	−0.00569318	+	0.0175218i
$951$		0			0
$952$	−9946.08	−	7226.25i	−0.338608	−	0.246013i
$953$	−7844.63	+	24143.3i	−0.266645	+	0.820648i	0.724665	+	0.689101i	$0.241994\pi$
$953$	−7844.63	+	24143.3i	−0.266645	+	0.820648i	−0.991310	+	0.131547i	$0.958006\pi$
$954$		0			0
$955$	−23597.9	+	17144.9i	−0.799591	+	0.580937i
$956$	13279.1			0.449245
$957$		0			0
$958$	14654.0			0.494206
$959$	9787.80	−	7111.25i	0.329577	−	0.239452i
$960$		0			0
$961$	16569.8	−	50996.6i	0.556201	−	1.71181i
$962$	1584.34	+	1151.09i	0.0530989	+	0.0385786i
$963$		0			0
$964$	−6521.44	+	20070.9i	−0.217885	+	0.670582i
$965$	9065.29	+	27900.1i	0.302406	+	0.930710i
$966$		0			0
$967$	26837.3			0.892482			0.446241	−	0.894913i	$-0.352762\pi$
$967$	26837.3			0.892482			0.446241	+	0.894913i	$0.352762\pi$
$968$	−1181.26	−	10582.3i	−0.0392223	−	0.351371i
$969$		0			0
$970$	29149.4	−	21178.3i	0.964878	−	0.701025i
$971$	1684.71	+	5185.01i	0.0556797	+	0.171364i	0.975029	−	0.222078i	$-0.0712840\pi$
$971$	1684.71	+	5185.01i	0.0556797	+	0.171364i	−0.919349	+	0.393443i	$0.871284\pi$
$972$		0			0
$973$	−46752.0	−	33967.3i	−1.54039	−	1.11916i
$974$	10015.3	+	7276.55i	0.329478	+	0.239379i
$975$		0			0
$976$	1808.55	+	5566.15i	0.0593138	+	0.182549i
$977$	−2919.12	+	2120.87i	−0.0955896	+	0.0694499i	−0.634553	−	0.772879i	$-0.718816\pi$
$977$	−2919.12	+	2120.87i	−0.0955896	+	0.0694499i	0.538964	+	0.842329i	$0.318816\pi$
$978$		0			0
$979$	962.040	−	9445.98i	0.0314065	−	0.308371i
$980$	−10566.9			−0.344437
$981$		0			0
$982$	6255.08	+	19251.1i	0.203266	+	0.625589i
$983$	−17937.1	+	55204.6i	−0.581997	+	1.79120i	0.0290114	+	0.999579i	$0.490764\pi$
$983$	−17937.1	+	55204.6i	−0.581997	+	1.79120i	−0.611009	+	0.791624i	$0.709236\pi$
$984$		0			0
$985$	10734.9	+	7799.38i	0.347252	+	0.252293i
$986$	5155.50	−	15867.0i	0.166516	−	0.512483i
$987$		0			0
$988$	269.001	−	195.441i	0.00866201	−	0.00629332i
$989$	36809.4			1.18349
$990$		0			0
$991$	−18977.5			−0.608315			−0.304157	−	0.952622i	$-0.598375\pi$
$991$	−18977.5			−0.608315			−0.304157	+	0.952622i	$0.598375\pi$
$992$	7476.90	−	5432.29i	0.239306	−	0.173866i
$993$		0			0
$994$	−1920.44	+	5910.51i	−0.0612803	+	0.188602i
$995$	35689.8	+	25930.2i	1.13713	+	0.826173i
$996$		0			0
$997$	−7496.82	+	23072.8i	−0.238141	+	0.732923i	0.758548	+	0.651617i	$0.225909\pi$
$997$	−7496.82	+	23072.8i	−0.238141	+	0.732923i	−0.996689	+	0.0813060i	$0.974091\pi$
$998$	1583.90	+	4874.76i	0.0502381	+	0.154617i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.4.f.d.91.2		8
3.2	odd	2		22.4.c.b.3.2	✓	8
11.2	odd	10		2178.4.a.bt.1.2		4
11.4	even	5	inner	198.4.f.d.37.2		8
11.9	even	5		2178.4.a.by.1.2		4
12.11	even	2		176.4.m.b.113.1		8
33.2	even	10		242.4.a.o.1.4		4
33.5	odd	10		242.4.c.r.9.1		8
33.8	even	10		242.4.c.n.27.1		8
33.14	odd	10		242.4.c.r.27.1		8
33.17	even	10		242.4.c.n.9.1		8
33.20	odd	10		242.4.a.n.1.4		4
33.26	odd	10		22.4.c.b.15.2	yes	8
33.29	even	10		242.4.c.q.81.2		8
33.32	even	2		242.4.c.q.3.2		8
132.35	odd	10		1936.4.a.bm.1.1		4
132.59	even	10		176.4.m.b.81.1		8
132.119	even	10		1936.4.a.bn.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.3.2	✓	8	3.2	odd	2
22.4.c.b.15.2	yes	8	33.26	odd	10
176.4.m.b.81.1		8	132.59	even	10
176.4.m.b.113.1		8	12.11	even	2
198.4.f.d.37.2		8	11.4	even	5	inner
198.4.f.d.91.2		8	1.1	even	1	trivial
242.4.a.n.1.4		4	33.20	odd	10
242.4.a.o.1.4		4	33.2	even	10
242.4.c.n.9.1		8	33.17	even	10
242.4.c.n.27.1		8	33.8	even	10
242.4.c.q.3.2		8	33.32	even	2
242.4.c.q.81.2		8	33.29	even	10
242.4.c.r.9.1		8	33.5	odd	10
242.4.c.r.27.1		8	33.14	odd	10
1936.4.a.bm.1.1		4	132.35	odd	10
1936.4.a.bn.1.1		4	132.119	even	10
2178.4.a.bt.1.2		4	11.2	odd	10
2178.4.a.by.1.2		4	11.9	even	5

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(10.3036 + 7.48598i) q^{5} +(7.24988 - 22.3128i) q^{7} +(2.47214 + 7.60845i) q^{8} +O(q^{10})\)	\(q+(-1.61803 + 1.17557i) q^{2} +(1.23607 - 3.80423i) q^{4} +(10.3036 + 7.48598i) q^{5} +(7.24988 - 22.3128i) q^{7} +(2.47214 + 7.60845i) q^{8} -25.4718 q^{10} +(3.69653 - 36.2951i) q^{11} +(-9.27574 + 6.73922i) q^{13} +(14.4998 + 44.6257i) q^{14} +(-12.9443 - 9.40456i) q^{16} +(-52.9924 - 38.5012i) q^{17} +(-2.24041 - 6.89528i) q^{19} +(41.2143 - 29.9439i) q^{20} +(36.6864 + 63.0723i) q^{22} +104.072 q^{23} +(11.4965 + 35.3825i) q^{25} +(7.08604 - 21.8086i) q^{26} +(-75.9218 - 55.1604i) q^{28} +(39.3536 - 121.118i) q^{29} +(233.653 - 169.759i) q^{31} +32.0000 q^{32} +131.004 q^{34} +(241.733 - 175.629i) q^{35} +(-26.3908 + 81.2224i) q^{37} +(11.7310 + 8.52303i) q^{38} +(-31.4849 + 96.9006i) q^{40} +(41.8544 + 128.815i) q^{41} +353.691 q^{43} +(-133.506 - 58.9257i) q^{44} +(-168.393 + 122.344i) q^{46} +(41.5948 + 128.016i) q^{47} +(-167.810 - 121.921i) q^{49} +(-60.1964 - 43.7352i) q^{50} +(14.1721 + 43.6171i) q^{52} +(405.666 - 294.734i) q^{53} +(309.792 - 346.297i) q^{55} +187.689 q^{56} +(78.7073 + 242.236i) q^{58} +(-201.373 + 619.763i) q^{59} +(-295.928 - 215.004i) q^{61} +(-178.495 + 549.352i) q^{62} +(-51.7771 + 37.6183i) q^{64} -146.023 q^{65} -294.576 q^{67} +(-211.969 + 154.005i) q^{68} +(-184.668 + 568.349i) q^{70} +(107.151 + 77.8500i) q^{71} +(145.080 - 446.511i) q^{73} +(-52.7815 - 162.445i) q^{74} -29.0005 q^{76} +(-783.048 - 345.616i) q^{77} +(-330.105 + 239.836i) q^{79} +(-62.9698 - 193.801i) q^{80} +(-219.152 - 159.224i) q^{82} +(-1099.89 - 799.119i) q^{83} +(-257.791 - 793.400i) q^{85} +(-572.283 + 415.788i) q^{86} +(285.288 - 61.6016i) q^{88} +260.255 q^{89} +(83.1232 + 255.827i) q^{91} +(128.641 - 395.915i) q^{92} +(-217.793 - 158.236i) q^{94} +(28.5337 - 87.8177i) q^{95} +(-1144.38 + 831.440i) q^{97} +414.848 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8	\( 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8} - 100 q^{10} + 155 q^{11} + 7 q^{13} - 2 q^{14} - 32 q^{16} - 161 q^{17} - 272 q^{19} - 20 q^{20} - 628 q^{23} - 17 q^{25} - 96 q^{26} + 16 q^{28} - 33 q^{29} + 323 q^{31} + 256 q^{32} + 208 q^{34} + 697 q^{35} + 49 q^{37} + 576 q^{38} + 240 q^{40} - 361 q^{41} + 1442 q^{43} - 620 q^{44} - 416 q^{46} + 1069 q^{47} - 709 q^{49} + 76 q^{50} - 192 q^{52} + 281 q^{53} - 7 q^{55} - 48 q^{56} - 66 q^{58} + 128 q^{59} - 617 q^{61} - 1044 q^{62} - 128 q^{64} + 138 q^{65} + 578 q^{67} - 644 q^{68} + 34 q^{70} - 115 q^{71} - 1487 q^{73} + 98 q^{74} - 128 q^{76} - 553 q^{77} + 71 q^{79} + 480 q^{80} + 658 q^{82} - 1942 q^{83} - 329 q^{85} - 2426 q^{86} + 560 q^{88} + 2202 q^{89} + 4523 q^{91} + 2088 q^{92} - 1332 q^{94} + 793 q^{95} - 5128 q^{97} + 3292 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8 - 100 * q^10 + 155 * q^11 + 7 * q^13 - 2 * q^14 - 32 * q^16 - 161 * q^17 - 272 * q^19 - 20 * q^20 - 628 * q^23 - 17 * q^25 - 96 * q^26 + 16 * q^28 - 33 * q^29 + 323 * q^31 + 256 * q^32 + 208 * q^34 + 697 * q^35 + 49 * q^37 + 576 * q^38 + 240 * q^40 - 361 * q^41 + 1442 * q^43 - 620 * q^44 - 416 * q^46 + 1069 * q^47 - 709 * q^49 + 76 * q^50 - 192 * q^52 + 281 * q^53 - 7 * q^55 - 48 * q^56 - 66 * q^58 + 128 * q^59 - 617 * q^61 - 1044 * q^62 - 128 * q^64 + 138 * q^65 + 578 * q^67 - 644 * q^68 + 34 * q^70 - 115 * q^71 - 1487 * q^73 + 98 * q^74 - 128 * q^76 - 553 * q^77 + 71 * q^79 + 480 * q^80 + 658 * q^82 - 1942 * q^83 - 329 * q^85 - 2426 * q^86 + 560 * q^88 + 2202 * q^89 + 4523 * q^91 + 2088 * q^92 - 1332 * q^94 + 793 * q^95 - 5128 * q^97 + 3292 * q^98

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