LMFDB - Embedded newform 150.4.e.c.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,4,Mod(107,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("150.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	150.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.85028650086$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 1577x^{8} + 284056x^{4} + 810000 $ x^12 + 1577x^8 + 284056x^4 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.5
Root			$-4.30203 + 4.30203i$ of defining polynomial
Character	$\chi$	$=$	150.107
Dual form			150.4.e.c.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 - 1.41421i) q^{2} +(-2.56513 + 4.51886i) q^{3} -4.00000i q^{4} +(2.76299 + 10.0183i) q^{6} +(-10.4050 - 10.4050i) q^{7} +(-5.65685 - 5.65685i) q^{8} +(-13.8402 - 23.1830i) q^{9} +O(q^{10})$	\(q+(1.41421 - 1.41421i) q^{2} +(-2.56513 + 4.51886i) q^{3} -4.00000i q^{4} +(2.76299 + 10.0183i) q^{6} +(-10.4050 - 10.4050i) q^{7} +(-5.65685 - 5.65685i) q^{8} +(-13.8402 - 23.1830i) q^{9} -20.5881i q^{11} +(18.0754 + 10.2605i) q^{12} +(49.2349 - 49.2349i) q^{13} -29.4298 q^{14} -16.0000 q^{16} +(37.9030 - 37.9030i) q^{17} +(-52.3586 - 13.2127i) q^{18} +16.7360i q^{19} +(73.7089 - 20.3285i) q^{21} +(-29.1160 - 29.1160i) q^{22} +(-151.484 - 151.484i) q^{23} +(40.0731 - 11.0519i) q^{24} -139.257i q^{26} +(140.262 - 3.07453i) q^{27} +(-41.6200 + 41.6200i) q^{28} -198.731 q^{29} +36.4698 q^{31} +(-22.6274 + 22.6274i) q^{32} +(93.0349 + 52.8113i) q^{33} -107.206i q^{34} +(-92.7318 + 55.3608i) q^{36} +(97.5568 + 97.5568i) q^{37} +(23.6683 + 23.6683i) q^{38} +(96.1916 + 348.780i) q^{39} +47.4492i q^{41} +(75.4913 - 132.989i) q^{42} +(49.4682 - 49.4682i) q^{43} -82.3526 q^{44} -428.462 q^{46} +(-328.073 + 328.073i) q^{47} +(41.0421 - 72.3018i) q^{48} -126.472i q^{49} +(74.0521 + 268.504i) q^{51} +(-196.940 - 196.940i) q^{52} +(275.517 + 275.517i) q^{53} +(194.013 - 202.709i) q^{54} +117.719i q^{56} +(-75.6278 - 42.9301i) q^{57} +(-281.048 + 281.048i) q^{58} -137.910 q^{59} +661.984 q^{61} +(51.5761 - 51.5761i) q^{62} +(-97.2114 + 385.226i) q^{63} +64.0000i q^{64} +(206.258 - 56.8848i) q^{66} +(-81.5055 - 81.5055i) q^{67} +(-151.612 - 151.612i) q^{68} +(1073.11 - 295.959i) q^{69} -398.982i q^{71} +(-52.8506 + 209.435i) q^{72} +(546.298 - 546.298i) q^{73} +275.932 q^{74} +66.9441 q^{76} +(-214.220 + 214.220i) q^{77} +(629.284 + 357.214i) q^{78} +490.653i q^{79} +(-345.898 + 641.713i) q^{81} +(67.1034 + 67.1034i) q^{82} +(211.431 + 211.431i) q^{83} +(-81.3141 - 294.836i) q^{84} -139.917i q^{86} +(509.771 - 898.036i) q^{87} +(-116.464 + 116.464i) q^{88} -354.864 q^{89} -1024.58 q^{91} +(-605.936 + 605.936i) q^{92} +(-93.5499 + 164.802i) q^{93} +927.929i q^{94} +(-44.2078 - 160.292i) q^{96} +(178.103 + 178.103i) q^{97} +(-178.858 - 178.858i) q^{98} +(-477.294 + 284.944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{3} + 8 q^{6} - 12 q^{7}+O(q^{10}) $ 12 * q - 8 * q^3 + 8 * q^6 - 12 * q^7	$ 12 q - 8 q^{3} + 8 q^{6} - 12 q^{7} + 32 q^{12} + 120 q^{13} - 192 q^{16} + 16 q^{18} + 464 q^{21} - 312 q^{22} + 688 q^{27} - 48 q^{28} - 504 q^{31} - 788 q^{33} + 368 q^{36} - 768 q^{37} + 872 q^{42} + 1968 q^{43} - 1152 q^{46} + 128 q^{48} + 256 q^{51} - 480 q^{52} - 968 q^{57} - 2280 q^{58} + 1848 q^{61} - 1268 q^{63} + 944 q^{66} + 1752 q^{67} - 64 q^{72} - 180 q^{73} - 1152 q^{76} + 4080 q^{78} - 4316 q^{81} - 2208 q^{82} - 3620 q^{87} - 1248 q^{88} + 4080 q^{91} - 584 q^{93} - 128 q^{96} + 7596 q^{97}+O(q^{100}) $ 12 * q - 8 * q^3 + 8 * q^6 - 12 * q^7 + 32 * q^12 + 120 * q^13 - 192 * q^16 + 16 * q^18 + 464 * q^21 - 312 * q^22 + 688 * q^27 - 48 * q^28 - 504 * q^31 - 788 * q^33 + 368 * q^36 - 768 * q^37 + 872 * q^42 + 1968 * q^43 - 1152 * q^46 + 128 * q^48 + 256 * q^51 - 480 * q^52 - 968 * q^57 - 2280 * q^58 + 1848 * q^61 - 1268 * q^63 + 944 * q^66 + 1752 * q^67 - 64 * q^72 - 180 * q^73 - 1152 * q^76 + 4080 * q^78 - 4316 * q^81 - 2208 * q^82 - 3620 * q^87 - 1248 * q^88 + 4080 * q^91 - 584 * q^93 - 128 * q^96 + 7596 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.41421	−	1.41421i	0.500000	−	0.500000i
$2$	1.41421	−	1.41421i	0.500000	−	0.500000i
$3$	−2.56513	+	4.51886i	−0.493660	+	0.869655i
$3$	−2.56513	+	4.51886i	−0.493660	+	0.869655i
$4$		−	4.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	2.76299	+	10.0183i	0.187997	+	0.681657i
$7$	−10.4050	−	10.4050i	−0.561817	−	0.561817i	0.368006	−	0.929823i	$-0.380040\pi$
$7$	−10.4050	−	10.4050i	−0.561817	−	0.561817i	−0.929823	+	0.368006i	$0.880040\pi$
$8$	−5.65685	−	5.65685i	−0.250000	−	0.250000i
$9$	−13.8402	−	23.1830i	−0.512600	−	0.858628i
$10$		0			0
$11$		−	20.5881i		−	0.564324i	−0.959367	−	0.282162i	$-0.908948\pi$
$11$		−	20.5881i		−	0.564324i	0.959367	−	0.282162i	$-0.0910515\pi$
$12$	18.0754	+	10.2605i	0.434827	+	0.246830i
$13$	49.2349	−	49.2349i	1.05041	−	1.05041i	0.0517478	−	0.998660i	$-0.483521\pi$
$13$	49.2349	−	49.2349i	1.05041	−	1.05041i	0.998660	−	0.0517478i	$-0.0164792\pi$
$14$	−29.4298			−0.561817
$15$		0			0
$16$	−16.0000			−0.250000
$17$	37.9030	−	37.9030i	0.540754	−	0.540754i	−0.382996	−	0.923750i	$-0.625108\pi$
$17$	37.9030	−	37.9030i	0.540754	−	0.540754i	0.923750	+	0.382996i	$0.125108\pi$
$18$	−52.3586	−	13.2127i	−0.685614	−	0.173014i
$19$			16.7360i			0.202079i	0.994882	+	0.101040i	$0.0322169\pi$
$19$			16.7360i			0.202079i	−0.994882	+	0.101040i	$0.967783\pi$
$20$		0			0
$21$	73.7089	−	20.3285i	0.765934	−	0.211240i
$22$	−29.1160	−	29.1160i	−0.282162	−	0.282162i
$23$	−151.484	−	151.484i	−1.37333	−	1.37333i	−0.855457	−	0.517874i	$-0.826724\pi$
$23$	−151.484	−	151.484i	−1.37333	−	1.37333i	−0.517874	−	0.855457i	$-0.673276\pi$
$24$	40.0731	−	11.0519i	0.340829	−	0.0939987i
$25$		0			0
$26$		−	139.257i		−	1.05041i
$27$	140.262	−	3.07453i	0.999760	−	0.0219146i
$28$	−41.6200	+	41.6200i	−0.280909	+	0.280909i
$29$	−198.731			−1.27253			−0.636265	−	0.771471i	$-0.719522\pi$
$29$	−198.731			−1.27253			−0.636265	+	0.771471i	$0.719522\pi$
$30$		0			0
$31$	36.4698			0.211296			0.105648	−	0.994404i	$-0.466308\pi$
$31$	36.4698			0.211296			0.105648	+	0.994404i	$0.466308\pi$
$32$	−22.6274	+	22.6274i	−0.125000	+	0.125000i
$33$	93.0349	+	52.8113i	0.490767	+	0.278584i
$34$		−	107.206i		−	0.540754i
$35$		0			0
$36$	−92.7318	+	55.3608i	−0.429314	+	0.256300i
$37$	97.5568	+	97.5568i	0.433466	+	0.433466i	0.889806	−	0.456340i	$-0.150840\pi$
$37$	97.5568	+	97.5568i	0.433466	+	0.433466i	−0.456340	+	0.889806i	$0.650840\pi$
$38$	23.6683	+	23.6683i	0.101040	+	0.101040i
$39$	96.1916	+	348.780i	0.394948	+	1.43204i
$40$		0			0
$41$			47.4492i			0.180740i	0.995908	+	0.0903698i	$0.0288049\pi$
$41$			47.4492i			0.180740i	−0.995908	+	0.0903698i	$0.971195\pi$
$42$	75.4913	−	132.989i	0.277347	−	0.488587i
$43$	49.4682	−	49.4682i	0.175438	−	0.175438i	−0.613926	−	0.789364i	$-0.710411\pi$
$43$	49.4682	−	49.4682i	0.175438	−	0.175438i	0.789364	+	0.613926i	$0.210411\pi$
$44$	−82.3526			−0.282162
$45$		0			0
$46$	−428.462			−1.37333
$47$	−328.073	+	328.073i	−1.01818	+	1.01818i	−0.0183447	+	0.999832i	$0.505840\pi$
$47$	−328.073	+	328.073i	−1.01818	+	1.01818i	−0.999832	+	0.0183447i	$0.994160\pi$
$48$	41.0421	−	72.3018i	0.123415	−	0.217414i
$49$		−	126.472i		−	0.368723i
$50$		0			0
$51$	74.0521	+	268.504i	0.203321	+	0.737218i
$52$	−196.940	−	196.940i	−0.525204	−	0.525204i
$53$	275.517	+	275.517i	0.714060	+	0.714060i	0.967382	−	0.253322i	$-0.0815231\pi$
$53$	275.517	+	275.517i	0.714060	+	0.714060i	−0.253322	+	0.967382i	$0.581523\pi$
$54$	194.013	−	202.709i	0.488923	−	0.510837i
$55$		0			0
$56$			117.719i			0.280909i
$57$	−75.6278	−	42.9301i	−0.175739	−	0.0997585i
$58$	−281.048	+	281.048i	−0.636265	+	0.636265i
$59$	−137.910			−0.304311			−0.152156	−	0.988357i	$-0.548622\pi$
$59$	−137.910			−0.304311			−0.152156	+	0.988357i	$0.548622\pi$
$60$		0			0
$61$	661.984			1.38948			0.694740	−	0.719261i	$-0.255519\pi$
$61$	661.984			1.38948			0.694740	+	0.719261i	$0.255519\pi$
$62$	51.5761	−	51.5761i	0.105648	−	0.105648i
$63$	−97.2114	+	385.226i	−0.194405	+	0.770379i
$64$			64.0000i			0.125000i
$65$		0			0
$66$	206.258	−	56.8848i	0.384675	−	0.106091i
$67$	−81.5055	−	81.5055i	−0.148619	−	0.148619i	0.628882	−	0.777501i	$-0.283513\pi$
$67$	−81.5055	−	81.5055i	−0.148619	−	0.148619i	−0.777501	+	0.628882i	$0.783513\pi$
$68$	−151.612	−	151.612i	−0.270377	−	0.270377i
$69$	1073.11	−	295.959i	1.87228	−	0.516366i
$70$		0			0
$71$		−	398.982i		−	0.666907i	−0.942766	−	0.333454i	$-0.891786\pi$
$71$		−	398.982i		−	0.666907i	0.942766	−	0.333454i	$-0.108214\pi$
$72$	−52.8506	+	209.435i	−0.0865070	+	0.342807i
$73$	546.298	−	546.298i	0.875881	−	0.875881i	−0.117225	−	0.993105i	$-0.537400\pi$
$73$	546.298	−	546.298i	0.875881	−	0.875881i	0.993105	+	0.117225i	$0.0373997\pi$
$74$	275.932			0.433466
$75$		0			0
$76$	66.9441			0.101040
$77$	−214.220	+	214.220i	−0.317047	+	0.317047i
$78$	629.284	+	357.214i	0.913493	+	0.518544i
$79$			490.653i			0.698769i	0.936980	+	0.349384i	$0.113609\pi$
$79$			490.653i			0.698769i	−0.936980	+	0.349384i	$0.886391\pi$
$80$		0			0
$81$	−345.898	+	641.713i	−0.474483	+	0.880264i
$82$	67.1034	+	67.1034i	0.0903698	+	0.0903698i
$83$	211.431	+	211.431i	0.279609	+	0.279609i	0.832953	−	0.553344i	$-0.186648\pi$
$83$	211.431	+	211.431i	0.279609	+	0.279609i	−0.553344	+	0.832953i	$0.686648\pi$
$84$	−81.3141	−	294.836i	−0.105620	−	0.382967i
$85$		0			0
$86$		−	139.917i		−	0.175438i
$87$	509.771	−	898.036i	0.628197	−	1.10666i
$88$	−116.464	+	116.464i	−0.141081	+	0.141081i
$89$	−354.864			−0.422647			−0.211323	−	0.977416i	$-0.567777\pi$
$89$	−354.864			−0.422647			−0.211323	+	0.977416i	$0.567777\pi$
$90$		0			0
$91$	−1024.58			−1.18027
$92$	−605.936	+	605.936i	−0.686665	+	0.686665i
$93$	−93.5499	+	164.802i	−0.104308	+	0.183754i
$94$			927.929i			1.01818i
$95$		0			0
$96$	−44.2078	−	160.292i	−0.0469994	−	0.170414i
$97$	178.103	+	178.103i	0.186429	+	0.186429i	0.794150	−	0.607721i	$-0.207916\pi$
$97$	178.103	+	178.103i	0.186429	+	0.186429i	−0.607721	+	0.794150i	$0.707916\pi$
$98$	−178.858	−	178.858i	−0.184362	−	0.184362i
$99$	−477.294	+	284.944i	−0.484544	+	0.289272i
$100$		0			0
$101$		−	206.875i		−	0.203810i	−0.994794	−	0.101905i	$-0.967506\pi$
$101$		−	206.875i		−	0.203810i	0.994794	−	0.101905i	$-0.0324938\pi$
$102$	484.448	+	274.997i	0.470270	+	0.266949i
$103$	−709.067	+	709.067i	−0.678315	+	0.678315i	−0.959619	−	0.281304i	$-0.909233\pi$
$103$	−709.067	+	709.067i	−0.678315	+	0.678315i	0.281304	+	0.959619i	$0.409233\pi$
$104$	−557.029			−0.525204
$105$		0			0
$106$	779.280			0.714060
$107$	−209.414	+	209.414i	−0.189203	+	0.189203i	−0.795352	−	0.606148i	$-0.792714\pi$
$107$	−209.414	+	209.414i	−0.189203	+	0.189203i	0.606148	+	0.795352i	$0.292714\pi$
$108$	−12.2981	−	561.050i	−0.0109573	−	0.499880i
$109$		−	1261.89i		−	1.10887i	−0.832226	−	0.554437i	$-0.812934\pi$
$109$		−	1261.89i		−	1.10887i	0.832226	−	0.554437i	$-0.187066\pi$
$110$		0			0
$111$	−691.091	+	190.599i	−0.590950	+	0.162981i
$112$	166.480	+	166.480i	0.140454	+	0.140454i
$113$	−922.628	−	922.628i	−0.768084	−	0.768084i	0.209685	−	0.977769i	$-0.432756\pi$
$113$	−922.628	−	922.628i	−0.768084	−	0.768084i	−0.977769	+	0.209685i	$0.932756\pi$
$114$	−167.666	+	46.2414i	−0.137749	+	0.0379904i
$115$		0			0
$116$			794.923i			0.636265i
$117$	−1822.83	−	459.990i	−1.44035	−	0.363471i
$118$	−195.034	+	195.034i	−0.152156	+	0.152156i
$119$	−788.761			−0.607610
$120$		0			0
$121$	907.128			0.681539
$122$	936.186	−	936.186i	0.694740	−	0.694740i
$123$	−214.416	−	121.714i	−0.157181	−	0.0892239i
$124$		−	145.879i		−	0.105648i
$125$		0			0
$126$	407.314	+	682.269i	0.287987	+	0.482392i
$127$	1690.78	+	1690.78i	1.18136	+	1.18136i	0.979393	+	0.201964i	$0.0647323\pi$
$127$	1690.78	+	1690.78i	1.18136	+	1.18136i	0.201964	+	0.979393i	$0.435268\pi$
$128$	90.5097	+	90.5097i	0.0625000	+	0.0625000i
$129$	96.6474	+	350.433i	0.0659638	+	0.239177i
$130$		0			0
$131$		−	1641.31i		−	1.09467i	−0.836914	−	0.547335i	$-0.815642\pi$
$131$		−	1641.31i		−	1.09467i	0.836914	−	0.547335i	$-0.184358\pi$
$132$	211.245	−	372.140i	0.139292	−	0.245383i
$133$	174.138	−	174.138i	0.113532	−	0.113532i
$134$	−230.532			−0.148619
$135$		0			0
$136$	−428.823			−0.270377
$137$	1746.79	−	1746.79i	1.08933	−	1.08933i	0.0937335	−	0.995597i	$-0.470120\pi$
$137$	1746.79	−	1746.79i	1.08933	−	1.08933i	0.995597	−	0.0937335i	$-0.0298802\pi$
$138$	1099.06	−	1936.16i	0.677959	−	1.19432i
$139$		−	527.771i		−	0.322050i	−0.986950	−	0.161025i	$-0.948520\pi$
$139$		−	527.771i		−	0.322050i	0.986950	−	0.161025i	$-0.0514800\pi$
$140$		0			0
$141$	−640.964	−	2324.06i	−0.382829	−	1.38810i
$142$	−564.245	−	564.245i	−0.333454	−	0.333454i
$143$	−1013.66	−	1013.66i	−0.592770	−	0.592770i
$144$	221.443	+	370.927i	0.128150	+	0.214657i
$145$		0			0
$146$		−	1545.16i		−	0.875881i
$147$	571.509	+	324.418i	0.320662	+	0.182024i
$148$	390.227	−	390.227i	0.216733	−	0.216733i
$149$	808.506			0.444533			0.222267	−	0.974986i	$-0.428654\pi$
$149$	808.506			0.444533			0.222267	+	0.974986i	$0.428654\pi$
$150$		0			0
$151$	98.6026			0.0531401			0.0265701	−	0.999647i	$-0.491541\pi$
$151$	98.6026			0.0531401			0.0265701	+	0.999647i	$0.491541\pi$
$152$	94.6733	−	94.6733i	0.0505198	−	0.0505198i
$153$	−1403.29	−	354.119i	−0.741497	−	0.187116i
$154$			605.905i			0.317047i
$155$		0			0
$156$	1395.12	−	384.766i	0.716019	−	0.197474i
$157$	−1652.40	−	1652.40i	−0.839971	−	0.839971i	0.148883	−	0.988855i	$-0.452432\pi$
$157$	−1652.40	−	1652.40i	−0.839971	−	0.839971i	−0.988855	+	0.148883i	$0.952432\pi$
$158$	693.887	+	693.887i	0.349384	+	0.349384i
$159$	−1951.76	+	538.286i	−0.973489	+	0.268483i
$160$		0			0
$161$			3152.38i			1.54312i
$162$	418.345	+	1396.69i	0.202891	+	0.677374i
$163$	1162.74	−	1162.74i	0.558731	−	0.558731i	−0.370215	−	0.928946i	$-0.620716\pi$
$163$	1162.74	−	1162.74i	0.558731	−	0.558731i	0.928946	+	0.370215i	$0.120716\pi$
$164$	189.797			0.0903698
$165$		0			0
$166$	598.017			0.279609
$167$	−570.377	+	570.377i	−0.264294	+	0.264294i	−0.826796	−	0.562502i	$-0.809839\pi$
$167$	−570.377	+	570.377i	−0.264294	+	0.264294i	0.562502	+	0.826796i	$0.309839\pi$
$168$	−531.956	−	301.965i	−0.244294	−	0.138673i
$169$		−	2651.15i		−	1.20671i
$170$		0			0
$171$	387.990	−	231.630i	0.173511	−	0.103586i
$172$	−197.873	−	197.873i	−0.0877190	−	0.0877190i
$173$	773.658	+	773.658i	0.340001	+	0.340001i	0.856367	−	0.516367i	$-0.172716\pi$
$173$	773.658	+	773.658i	0.340001	+	0.340001i	−0.516367	+	0.856367i	$0.672716\pi$
$174$	−549.091	−	1990.94i	−0.239232	−	0.867430i
$175$		0			0
$176$			329.410i			0.141081i
$177$	353.758	−	623.197i	0.150226	−	0.264646i
$178$	−501.854	+	501.854i	−0.211323	+	0.211323i
$179$	3294.57			1.37568			0.687842	−	0.725860i	$-0.258558\pi$
$179$	3294.57			1.37568			0.687842	+	0.725860i	$0.258558\pi$
$180$		0			0
$181$	−927.712			−0.380974			−0.190487	−	0.981690i	$-0.561007\pi$
$181$	−927.712			−0.380974			−0.190487	+	0.981690i	$0.561007\pi$
$182$	−1448.97	+	1448.97i	−0.590137	+	0.590137i
$183$	−1698.08	+	2991.41i	−0.685931	+	1.20837i
$184$			1713.85i			0.686665i
$185$		0			0
$186$	100.766	+	365.365i	0.0397231	+	0.144031i
$187$	−780.352	−	780.352i	−0.305160	−	0.305160i
$188$	1312.29	+	1312.29i	0.509088	+	0.509088i
$189$	−1491.42	−	1427.44i	−0.573994	−	0.549370i
$190$		0			0
$191$			3599.78i			1.36372i	0.731482	+	0.681861i	$0.238829\pi$
$191$			3599.78i			1.36372i	−0.731482	+	0.681861i	$0.761171\pi$
$192$	−289.207	−	164.168i	−0.108707	−	0.0617075i
$193$	35.7324	−	35.7324i	0.0133268	−	0.0133268i	−0.700412	−	0.713739i	$-0.747000\pi$
$193$	35.7324	−	35.7324i	0.0133268	−	0.0133268i	0.713739	+	0.700412i	$0.247000\pi$
$194$	503.751			0.186429
$195$		0			0
$196$	−505.888			−0.184362
$197$	147.526	−	147.526i	0.0533543	−	0.0533543i	−0.679926	−	0.733281i	$-0.737988\pi$
$197$	147.526	−	147.526i	0.0533543	−	0.0533543i	0.733281	+	0.679926i	$0.237988\pi$
$198$	−272.024	+	1077.97i	−0.0976359	+	0.386908i
$199$			2990.21i			1.06518i	0.846374	+	0.532589i	$0.178781\pi$
$199$			2990.21i			1.06518i	−0.846374	+	0.532589i	$0.821219\pi$
$200$		0			0
$201$	577.385	−	159.240i	0.202615	−	0.0558801i
$202$	−292.566	−	292.566i	−0.101905	−	0.101905i
$203$	2067.79	+	2067.79i	0.714929	+	0.714929i
$204$	1074.02	−	296.208i	0.368609	−	0.101660i
$205$		0			0
$206$			2005.54i			0.678315i
$207$	−1415.28	+	5608.42i	−0.475211	+	1.88315i
$208$	−787.758	+	787.758i	−0.262602	+	0.262602i
$209$	344.564			0.114038
$210$		0			0
$211$	−3426.67			−1.11802			−0.559008	−	0.829162i	$-0.688818\pi$
$211$	−3426.67			−1.11802			−0.559008	+	0.829162i	$0.688818\pi$
$212$	1102.07	−	1102.07i	0.357030	−	0.357030i
$213$	1802.94	+	1023.44i	0.579979	+	0.329225i
$214$			592.311i			0.189203i
$215$		0			0
$216$	−810.836	−	776.052i	−0.255419	−	0.244461i
$217$	−379.468	−	379.468i	−0.118710	−	0.118710i
$218$	−1784.58	−	1784.58i	−0.554437	−	0.554437i
$219$	1067.32	+	3869.97i	0.329327	+	1.19410i
$220$		0			0
$221$		−	3732.30i		−	1.13603i
$222$	−707.803	+	1246.90i	−0.213985	+	0.376966i
$223$	2748.23	−	2748.23i	0.825269	−	0.825269i	−0.161589	−	0.986858i	$-0.551662\pi$
$223$	2748.23	−	2748.23i	0.825269	−	0.825269i	0.986858	+	0.161589i	$0.0516619\pi$
$224$	470.876			0.140454
$225$		0			0
$226$	−2609.58			−0.768084
$227$	807.249	−	807.249i	0.236031	−	0.236031i	−0.579173	−	0.815204i	$-0.696625\pi$
$227$	807.249	−	807.249i	0.236031	−	0.236031i	0.815204	+	0.579173i	$0.196625\pi$
$228$	−171.721	+	302.511i	−0.0498792	+	0.0878697i
$229$			974.680i			0.281261i	0.990062	+	0.140630i	$0.0449129\pi$
$229$			974.680i			0.281261i	−0.990062	+	0.140630i	$0.955087\pi$
$230$		0			0
$231$	−418.527	−	1517.53i	−0.119208	−	0.432234i
$232$	1124.19	+	1124.19i	0.318133	+	0.318133i
$233$	3684.63	+	3684.63i	1.03600	+	1.03600i	0.999327	+	0.0366725i	$0.0116758\pi$
$233$	3684.63	+	3684.63i	1.03600	+	1.03600i	0.0366725	+	0.999327i	$0.488324\pi$
$234$	−3228.40	+	1927.35i	−0.901910	+	0.538439i
$235$		0			0
$236$			551.641i			0.152156i
$237$	−2217.19	−	1258.59i	−0.607688	−	0.344954i
$238$	−1115.48	+	1115.48i	−0.303805	+	0.303805i
$239$	4210.95			1.13968			0.569840	−	0.821755i	$-0.307005\pi$
$239$	4210.95			1.13968			0.569840	+	0.821755i	$0.307005\pi$
$240$		0			0
$241$	5209.53			1.39243			0.696214	−	0.717834i	$-0.254866\pi$
$241$	5209.53			1.39243			0.696214	+	0.717834i	$0.254866\pi$
$242$	1282.87	−	1282.87i	0.340769	−	0.340769i
$243$	−2012.54	−	3209.14i	−0.531293	−	0.847188i
$244$		−	2647.93i		−	0.694740i
$245$		0			0
$246$	−475.360	+	131.102i	−0.123203	+	0.0339786i
$247$	823.997	+	823.997i	0.212266	+	0.212266i
$248$	−206.304	−	206.304i	−0.0528239	−	0.0528239i
$249$	−1497.78	+	413.079i	−0.381196	+	0.105132i
$250$		0			0
$251$		−	549.751i		−	0.138247i	−0.997608	−	0.0691235i	$-0.977980\pi$
$251$		−	549.751i		−	0.138247i	0.997608	−	0.0691235i	$-0.0220202\pi$
$252$	1540.90	+	388.846i	0.385189	+	0.0972023i
$253$	−3118.78	+	3118.78i	−0.775003	+	0.775003i
$254$	4782.24			1.18136
$255$		0			0
$256$	256.000			0.0625000
$257$	−618.174	+	618.174i	−0.150041	+	0.150041i	−0.778137	−	0.628095i	$-0.783835\pi$
$257$	−618.174	+	618.174i	−0.150041	+	0.150041i	0.628095	+	0.778137i	$0.283835\pi$
$258$	632.267	+	358.906i	0.152571	+	0.0866067i
$259$		−	2030.16i		−	0.487057i
$260$		0			0
$261$	2750.47	+	4607.17i	0.652298	+	1.09263i
$262$	−2321.16	−	2321.16i	−0.547335	−	0.547335i
$263$	−874.452	−	874.452i	−0.205023	−	0.205023i	0.597125	−	0.802148i	$-0.296310\pi$
$263$	−874.452	−	874.452i	−0.205023	−	0.205023i	−0.802148	+	0.597125i	$0.796310\pi$
$264$	−227.539	−	825.031i	−0.0530457	−	0.192338i
$265$		0			0
$266$		−	492.538i		−	0.113532i
$267$	910.274	−	1603.58i	0.208644	−	0.367557i
$268$	−326.022	+	326.022i	−0.0743096	+	0.0743096i
$269$	374.939			0.0849830			0.0424915	−	0.999097i	$-0.486470\pi$
$269$	374.939			0.0849830			0.0424915	+	0.999097i	$0.486470\pi$
$270$		0			0
$271$	4980.70			1.11644			0.558221	−	0.829692i	$-0.311484\pi$
$271$	4980.70			1.11644			0.558221	+	0.829692i	$0.311484\pi$
$272$	−606.448	+	606.448i	−0.135189	+	0.135189i
$273$	2628.18	−	4629.92i	0.582654	−	1.02643i
$274$		−	4940.67i		−	1.08933i
$275$		0			0
$276$	−1183.83	−	4292.45i	−0.258183	−	0.936141i
$277$	4700.50	+	4700.50i	1.01959	+	1.01959i	0.999804	+	0.0197823i	$0.00629732\pi$
$277$	4700.50	+	4700.50i	1.01959	+	1.01959i	0.0197823	+	0.999804i	$0.493703\pi$
$278$	−746.381	−	746.381i	−0.161025	−	0.161025i
$279$	−504.749	−	845.478i	−0.108310	−	0.181424i
$280$		0			0
$281$			2603.01i			0.552607i	0.961070	+	0.276303i	$0.0891095\pi$
$281$			2603.01i			0.552607i	−0.961070	+	0.276303i	$0.910891\pi$
$282$	−4193.18	−	2380.26i	−0.885462	−	0.502633i
$283$	−1489.80	+	1489.80i	−0.312930	+	0.312930i	−0.846044	−	0.533114i	$-0.821022\pi$
$283$	−1489.80	+	1489.80i	−0.312930	+	0.312930i	0.533114	+	0.846044i	$0.321022\pi$
$284$	−1595.93			−0.333454
$285$		0			0
$286$	−2867.05			−0.592770
$287$	493.709	−	493.709i	0.101543	−	0.101543i
$288$	837.738	+	211.403i	0.171403	+	0.0432535i
$289$			2039.73i			0.415169i
$290$		0			0
$291$	−1261.68	+	347.964i	−0.254161	+	0.0700963i
$292$	−2185.19	−	2185.19i	−0.437940	−	0.437940i
$293$	−5114.67	−	5114.67i	−1.01980	−	1.01980i	−0.999800	−	0.0200028i	$-0.993632\pi$
$293$	−5114.67	−	5114.67i	−1.01980	−	1.01980i	−0.0200028	−	0.999800i	$-0.506368\pi$
$294$	1267.03	−	349.441i	0.251343	−	0.0693190i
$295$		0			0
$296$		−	1103.73i		−	0.216733i
$297$	−63.2989	−	2887.74i	−0.0123669	−	0.564188i
$298$	1143.40	−	1143.40i	0.222267	−	0.222267i
$299$	−14916.6			−2.88512
$300$		0			0
$301$	−1029.43			−0.197128
$302$	139.445	−	139.445i	0.0265701	−	0.0265701i
$303$	934.840	+	530.662i	0.177245	+	0.100613i
$304$		−	267.776i		−	0.0505198i
$305$		0			0
$306$	−2485.35	+	1483.75i	−0.464307	+	0.277190i
$307$	−2216.09	−	2216.09i	−0.411983	−	0.411983i	0.470446	−	0.882429i	$-0.344093\pi$
$307$	−2216.09	−	2216.09i	−0.411983	−	0.411983i	−0.882429	+	0.470446i	$0.844093\pi$
$308$	856.878	+	856.878i	0.158523	+	0.158523i
$309$	−1385.32	−	5023.02i	−0.255043	−	0.924756i
$310$		0			0
$311$			126.689i			0.0230993i	0.999933	+	0.0115497i	$0.00367646\pi$
$311$			126.689i			0.0230993i	−0.999933	+	0.0115497i	$0.996324\pi$
$312$	1428.85	−	2517.14i	0.259272	−	0.456746i
$313$	5445.69	−	5445.69i	0.983415	−	0.983415i	−0.0164497	−	0.999865i	$-0.505236\pi$
$313$	5445.69	−	5445.69i	0.983415	−	0.983415i	0.999865	+	0.0164497i	$0.00523635\pi$
$314$	−4673.68			−0.839971
$315$		0			0
$316$	1962.61			0.349384
$317$	−250.356	+	250.356i	−0.0443577	+	0.0443577i	−0.728938	−	0.684580i	$-0.759986\pi$
$317$	−250.356	+	250.356i	−0.0443577	+	0.0443577i	0.684580	+	0.728938i	$0.259986\pi$
$318$	−1998.96	+	3521.46i	−0.352503	+	0.620986i
$319$			4091.50i			0.718119i
$320$		0			0
$321$	−409.137	−	1483.48i	−0.0711396	−	0.257944i
$322$	4458.14	+	4458.14i	0.771561	+	0.771561i
$323$	634.345	+	634.345i	0.109275	+	0.109275i
$324$	2566.85	+	1383.59i	0.440132	+	0.237242i
$325$		0			0
$326$		−	3288.74i		−	0.558731i
$327$	5702.31	+	3236.92i	0.964338	+	0.547407i
$328$	268.413	−	268.413i	0.0451849	−	0.0451849i
$329$	6827.19			1.14406
$330$		0			0
$331$	−4145.40			−0.688375			−0.344187	−	0.938901i	$-0.611846\pi$
$331$	−4145.40			−0.688375			−0.344187	+	0.938901i	$0.611846\pi$
$332$	845.724	−	845.724i	0.139805	−	0.139805i
$333$	911.450	−	3611.86i	0.149991	−	0.594380i
$334$			1613.27i			0.264294i
$335$		0			0
$336$	−1179.34	+	325.256i	−0.191483	+	0.0528101i
$337$	896.758	+	896.758i	0.144954	+	0.144954i	0.775860	−	0.630906i	$-0.217316\pi$
$337$	896.758	+	896.758i	0.144954	+	0.144954i	−0.630906	+	0.775860i	$0.717316\pi$
$338$	−3749.29	−	3749.29i	−0.603357	−	0.603357i
$339$	6535.89	−	1802.56i	1.04714	−	0.288796i
$340$		0			0
$341$		−	750.846i		−	0.119239i
$342$	221.127	−	876.275i	0.0349626	−	0.138548i
$343$	−4884.86	+	4884.86i	−0.768972	+	0.768972i
$344$	−559.669			−0.0877190
$345$		0			0
$346$	2188.23			0.340001
$347$	3274.45	−	3274.45i	0.506575	−	0.506575i	−0.406898	−	0.913473i	$-0.633390\pi$
$347$	3274.45	−	3274.45i	0.506575	−	0.506575i	0.913473	+	0.406898i	$0.133390\pi$
$348$	−3592.15	−	2039.08i	−0.553331	−	0.314099i
$349$		−	343.458i		−	0.0526788i	−0.999653	−	0.0263394i	$-0.991615\pi$
$349$		−	343.458i		−	0.0526788i	0.999653	−	0.0263394i	$-0.00838506\pi$
$350$		0			0
$351$	6754.43	−	7057.18i	1.02714	−	1.07318i
$352$	465.857	+	465.857i	0.0705404	+	0.0705404i
$353$	−1163.64	−	1163.64i	−0.175452	−	0.175452i	0.613918	−	0.789370i	$-0.289593\pi$
$353$	−1163.64	−	1163.64i	−0.175452	−	0.175452i	−0.789370	+	0.613918i	$0.789593\pi$
$354$	−381.044	−	1381.62i	−0.0572098	−	0.207436i
$355$		0			0
$356$			1419.46i			0.211323i
$357$	2023.28	−	3564.30i	0.299953	−	0.528411i
$358$	4659.22	−	4659.22i	0.687842	−	0.687842i
$359$	−8649.83			−1.27165			−0.635823	−	0.771835i	$-0.719339\pi$
$359$	−8649.83			−1.27165			−0.635823	+	0.771835i	$0.719339\pi$
$360$		0			0
$361$	6578.91			0.959164
$362$	−1311.98	+	1311.98i	−0.190487	+	0.190487i
$363$	−2326.90	+	4099.19i	−0.336448	+	0.592704i
$364$			4098.31i			0.590137i
$365$		0			0
$366$	1829.05	+	6631.94i	0.261219	+	0.947150i
$367$	−3280.64	−	3280.64i	−0.466615	−	0.466615i	0.434201	−	0.900816i	$-0.357031\pi$
$367$	−3280.64	−	3280.64i	−0.466615	−	0.466615i	−0.900816	+	0.434201i	$0.857031\pi$
$368$	2423.74	+	2423.74i	0.343333	+	0.343333i
$369$	1100.01	−	656.706i	0.155188	−	0.0926471i
$370$		0			0
$371$		−	5733.51i		−	0.802343i
$372$	659.208	+	374.200i	0.0918772	+	0.0521541i
$373$	−3638.98	+	3638.98i	−0.505145	+	0.505145i	−0.913032	−	0.407887i	$-0.866266\pi$
$373$	−3638.98	+	3638.98i	−0.505145	+	0.505145i	0.407887	+	0.913032i	$0.366266\pi$
$374$	−2207.17			−0.305160
$375$		0			0
$376$	3711.72			0.509088
$377$	−9784.49	+	9784.49i	−1.33668	+	1.33668i
$378$	−4127.89	+	90.4827i	−0.561682	+	0.0123120i
$379$			3127.02i			0.423811i	0.977290	+	0.211906i	$0.0679669\pi$
$379$			3127.02i			0.423811i	−0.977290	+	0.211906i	$0.932033\pi$
$380$		0			0
$381$	−11977.5	+	3303.32i	−1.61056	+	0.444184i
$382$	5090.85	+	5090.85i	0.681861	+	0.681861i
$383$	−6462.80	−	6462.80i	−0.862229	−	0.862229i	0.129368	−	0.991597i	$-0.458705\pi$
$383$	−6462.80	−	6462.80i	−0.862229	−	0.862229i	−0.991597	+	0.129368i	$0.958705\pi$
$384$	−641.170	+	176.831i	−0.0852072	+	0.0234997i
$385$		0			0
$386$		−	101.066i		−	0.0133268i
$387$	−1831.47	−	462.170i	−0.240565	−	0.0607065i
$388$	712.411	−	712.411i	0.0932144	−	0.0932144i
$389$	3982.98			0.519139			0.259570	−	0.965724i	$-0.416419\pi$
$389$	3982.98			0.519139			0.259570	+	0.965724i	$0.416419\pi$
$390$		0			0
$391$	−11483.4			−1.48527
$392$	−715.434	+	715.434i	−0.0921808	+	0.0921808i
$393$	7416.84	+	4210.17i	0.951985	+	0.540395i
$394$		−	417.267i		−	0.0533543i
$395$		0			0
$396$	1139.78	+	1909.18i	0.144636	+	0.242272i
$397$	−2512.25	−	2512.25i	−0.317598	−	0.317598i	0.530246	−	0.847844i	$-0.322100\pi$
$397$	−2512.25	−	2512.25i	−0.317598	−	0.317598i	−0.847844	+	0.530246i	$0.822100\pi$
$398$	4228.79	+	4228.79i	0.532589	+	0.532589i
$399$	340.219	+	1233.59i	0.0426873	+	0.154779i
$400$		0			0
$401$		−	13243.2i		−	1.64921i	−0.565711	−	0.824604i	$-0.691398\pi$
$401$		−	13243.2i		−	1.64921i	0.565711	−	0.824604i	$-0.308602\pi$
$402$	591.346	−	1041.74i	0.0733673	−	0.129247i
$403$	1795.59	−	1795.59i	0.221947	−	0.221947i
$404$	−827.501			−0.101905
$405$		0			0
$406$	5848.60			0.714929
$407$	2008.51	−	2008.51i	0.244615	−	0.244615i
$408$	1099.99	−	1937.79i	0.133474	−	0.235135i
$409$			3535.21i			0.427396i	0.976900	+	0.213698i	$0.0685508\pi$
$409$			3535.21i			0.427396i	−0.976900	+	0.213698i	$0.931449\pi$
$410$		0			0
$411$	3412.75	+	12374.2i	0.409583	+	1.48510i
$412$	2836.27	+	2836.27i	0.339157	+	0.339157i
$413$	1434.95	+	1434.95i	0.170967	+	0.170967i
$414$	5929.99	+	9933.00i	0.703969	+	1.17918i
$415$		0			0
$416$			2228.12i			0.262602i
$417$	2384.92	+	1353.80i	0.280072	+	0.158983i
$418$	487.287	−	487.287i	0.0570191	−	0.0570191i
$419$	8827.84			1.02928			0.514640	−	0.857407i	$-0.327926\pi$
$419$	8827.84			1.02928			0.514640	+	0.857407i	$0.327926\pi$
$420$		0			0
$421$	−10634.8			−1.23114			−0.615571	−	0.788081i	$-0.711075\pi$
$421$	−10634.8			−1.23114			−0.615571	+	0.788081i	$0.711075\pi$
$422$	−4846.04	+	4846.04i	−0.559008	+	0.559008i
$423$	12146.3	+	3065.10i	1.39615	+	0.352318i
$424$		−	3117.12i		−	0.357030i
$425$		0			0
$426$	3997.11	−	1102.38i	0.454602	−	0.125377i
$427$	−6887.94	−	6887.94i	−0.780634	−	0.780634i
$428$	837.654	+	837.654i	0.0946017	+	0.0946017i
$429$	7180.73	−	1980.41i	0.808132	−	0.222879i
$430$		0			0
$431$			14838.4i			1.65833i	0.559005	+	0.829164i	$0.311183\pi$
$431$			14838.4i			1.65833i	−0.559005	+	0.829164i	$0.688817\pi$
$432$	−2244.20	+	49.1925i	−0.249940	+	0.00547865i
$433$	−9333.69	+	9333.69i	−1.03591	+	1.03591i	−0.0365781	+	0.999331i	$0.511646\pi$
$433$	−9333.69	+	9333.69i	−1.03591	+	1.03591i	−0.999331	+	0.0365781i	$0.988354\pi$
$434$	−1073.30			−0.118710
$435$		0			0
$436$	−5047.56			−0.554437
$437$	2535.24	−	2535.24i	0.277522	−	0.277522i
$438$	6982.37	+	3963.55i	0.761714	+	0.432387i
$439$		−	18022.8i		−	1.95941i	−0.200455	−	0.979703i	$-0.564242\pi$
$439$		−	18022.8i		−	1.95941i	0.200455	−	0.979703i	$-0.435758\pi$
$440$		0			0
$441$	−2932.00	+	1750.40i	−0.316596	+	0.189007i
$442$	−5278.27	−	5278.27i	−0.568013	−	0.568013i
$443$	9630.21	+	9630.21i	1.03283	+	1.03283i	0.999442	+	0.0333905i	$0.0106305\pi$
$443$	9630.21	+	9630.21i	1.03283	+	1.03283i	0.0333905	+	0.999442i	$0.489369\pi$
$444$	762.397	+	2764.37i	0.0814905	+	0.295475i
$445$		0			0
$446$		−	7773.16i		−	0.825269i
$447$	−2073.93	+	3653.53i	−0.219448	+	0.386590i
$448$	665.920	−	665.920i	0.0702271	−	0.0702271i
$449$	−16623.3			−1.74722			−0.873609	−	0.486628i	$-0.838227\pi$
$449$	−16623.3			−1.74722			−0.873609	+	0.486628i	$0.838227\pi$
$450$		0			0
$451$	976.892			0.101996
$452$	−3690.51	+	3690.51i	−0.384042	+	0.384042i
$453$	−252.929	+	445.571i	−0.0262332	+	0.0462136i
$454$		−	2283.25i		−	0.236031i
$455$		0			0
$456$	184.966	+	670.665i	0.0189952	+	0.0688745i
$457$	6244.62	+	6244.62i	0.639193	+	0.639193i	0.950356	−	0.311163i	$-0.100719\pi$
$457$	6244.62	+	6244.62i	0.639193	+	0.639193i	−0.311163	+	0.950356i	$0.600719\pi$
$458$	1378.41	+	1378.41i	0.140630	+	0.140630i
$459$	5199.83	−	5432.90i	0.528774	−	0.552475i
$460$		0			0
$461$			14891.9i			1.50453i	0.658862	+	0.752263i	$0.271038\pi$
$461$			14891.9i			1.50453i	−0.658862	+	0.752263i	$0.728962\pi$
$462$	−2738.00	−	1554.23i	−0.275721	−	0.156513i
$463$	−1014.37	+	1014.37i	−0.101819	+	0.101819i	−0.756181	−	0.654362i	$-0.772937\pi$
$463$	−1014.37	+	1014.37i	−0.101819	+	0.101819i	0.654362	+	0.756181i	$0.272937\pi$
$464$	3179.69			0.318133
$465$		0			0
$466$	10421.7			1.03600
$467$	−7331.30	+	7331.30i	−0.726450	+	0.726450i	−0.969911	−	0.243461i	$-0.921717\pi$
$467$	−7331.30	+	7331.30i	−0.726450	+	0.726450i	0.243461	+	0.969911i	$0.421717\pi$
$468$	−1839.96	+	7291.32i	−0.181735	+	0.720174i
$469$			1696.13i			0.166994i
$470$		0			0
$471$	11705.6	−	3228.33i	1.14515	−	0.315825i
$472$	780.138	+	780.138i	0.0760779	+	0.0760779i
$473$	−1018.46	−	1018.46i	−0.0990038	−	0.0990038i
$474$	−4915.49	+	1355.67i	−0.476321	+	0.131367i
$475$		0			0
$476$			3155.04i			0.303805i
$477$	2574.09	−	10200.5i	0.247085	−	0.979139i
$478$	5955.18	−	5955.18i	0.569840	−	0.569840i
$479$	16969.0			1.61865			0.809326	−	0.587360i	$-0.199833\pi$
$479$	16969.0			1.61865			0.809326	+	0.587360i	$0.199833\pi$
$480$		0			0
$481$	9606.39			0.910632
$482$	7367.39	−	7367.39i	0.696214	−	0.696214i
$483$	−14245.2	−	8086.28i	−1.34198	−	0.761777i
$484$		−	3628.51i		−	0.340769i
$485$		0			0
$486$	−7384.57	−	1692.26i	−0.689241	−	0.157948i
$487$	−10468.7	−	10468.7i	−0.974089	−	0.974089i	0.0255832	−	0.999673i	$-0.491856\pi$
$487$	−10468.7	−	10468.7i	−0.974089	−	0.974089i	−0.999673	+	0.0255832i	$0.991856\pi$
$488$	−3744.75	−	3744.75i	−0.347370	−	0.347370i
$489$	2271.69	+	8236.88i	0.210080	+	0.761727i
$490$		0			0
$491$		−	18966.9i		−	1.74331i	−0.490124	−	0.871653i	$-0.663048\pi$
$491$		−	18966.9i		−	1.74331i	0.490124	−	0.871653i	$-0.336952\pi$
$492$	−486.854	+	857.666i	−0.0446120	+	0.0785906i
$493$	−7532.49	+	7532.49i	−0.688126	+	0.688126i
$494$	2330.61			0.212266
$495$		0			0
$496$	−583.517			−0.0528239
$497$	−4151.40	+	4151.40i	−0.374680	+	0.374680i
$498$	−1533.99	+	2702.36i	−0.138032	+	0.243164i
$499$		−	5155.10i		−	0.462473i	−0.972898	−	0.231236i	$-0.925723\pi$
$499$		−	5155.10i		−	0.462473i	0.972898	−	0.231236i	$-0.0742770\pi$
$500$		0			0
$501$	−1114.36	−	4040.54i	−0.0993732	−	0.360316i
$502$	−777.465	−	777.465i	−0.0691235	−	0.0691235i
$503$	−3447.31	−	3447.31i	−0.305583	−	0.305583i	0.537611	−	0.843193i	$-0.319327\pi$
$503$	−3447.31	−	3447.31i	−0.305583	−	0.305583i	−0.843193	+	0.537611i	$0.819327\pi$
$504$	2729.08	−	1629.25i	0.241196	−	0.143994i
$505$		0			0
$506$			8821.23i			0.775003i
$507$	11980.2	+	6800.55i	1.04942	+	0.595706i
$508$	6763.11	−	6763.11i	0.590678	−	0.590678i
$509$	−10490.7			−0.913544			−0.456772	−	0.889584i	$-0.650995\pi$
$509$	−10490.7			−0.913544			−0.456772	+	0.889584i	$0.650995\pi$
$510$		0			0
$511$	−11368.5			−0.984170
$512$	362.039	−	362.039i	0.0312500	−	0.0312500i
$513$	51.4554	+	2347.44i	0.00442848	+	0.202031i
$514$			1748.46i			0.150041i
$515$		0			0
$516$	1401.73	−	386.590i	0.119589	−	0.0329819i
$517$	6754.40	+	6754.40i	0.574581	+	0.574581i
$518$	−2871.07	−	2871.07i	−0.243528	−	0.243528i
$519$	−5480.59	+	1511.52i	−0.463528	+	0.127839i
$520$		0			0
$521$		−	8555.99i		−	0.719472i	−0.933054	−	0.359736i	$-0.882867\pi$
$521$		−	8555.99i		−	0.719472i	0.933054	−	0.359736i	$-0.117133\pi$
$522$	10405.3	+	2625.76i	0.872464	+	0.220166i
$523$	12002.2	−	12002.2i	1.00348	−	1.00348i	0.00348595	−	0.999994i	$-0.498890\pi$
$523$	12002.2	−	12002.2i	1.00348	−	1.00348i	0.999994	−	0.00348595i	$-0.00110962\pi$
$524$	−6565.23			−0.547335
$525$		0			0
$526$	−2473.32			−0.205023
$527$	1382.31	−	1382.31i	0.114259	−	0.114259i
$528$	−1488.56	−	844.981i	−0.122692	−	0.0696460i
$529$			33727.8i			2.77208i
$530$		0			0
$531$	1908.70	+	3197.16i	0.155990	+	0.261290i
$532$	−696.553	−	696.553i	−0.0567658	−	0.0567658i
$533$	2336.16	+	2336.16i	0.189850	+	0.189850i
$534$	−980.486	−	3555.13i	−0.0794565	−	0.288100i
$535$		0			0
$536$			922.130i			0.0743096i
$537$	−8451.00	+	14887.7i	−0.679120	+	1.19637i
$538$	530.243	−	530.243i	0.0424915	−	0.0424915i
$539$	−2603.83			−0.208079
$540$		0			0
$541$	−14192.5			−1.12788			−0.563942	−	0.825815i	$-0.690716\pi$
$541$	−14192.5			−1.12788			−0.563942	+	0.825815i	$0.690716\pi$
$542$	7043.77	−	7043.77i	0.558221	−	0.558221i
$543$	2379.70	−	4192.20i	0.188072	−	0.331316i
$544$			1715.29i			0.135189i
$545$		0			0
$546$	−2830.90	−	10264.5i	−0.221889	−	0.804543i
$547$	−7518.49	−	7518.49i	−0.587692	−	0.587692i	0.349314	−	0.937006i	$-0.386415\pi$
$547$	−7518.49	−	7518.49i	−0.587692	−	0.587692i	−0.937006	+	0.349314i	$0.886415\pi$
$548$	−6987.16	−	6987.16i	−0.544665	−	0.544665i
$549$	−9161.98	−	15346.7i	−0.712247	−	1.19305i
$550$		0			0
$551$		−	3325.96i		−	0.257152i
$552$	−7744.63	−	4396.24i	−0.597162	−	0.338979i
$553$	5105.24	−	5105.24i	0.392580	−	0.392580i
$554$	13295.0			1.01959
$555$		0			0
$556$	−2111.08			−0.161025
$557$	12618.1	−	12618.1i	0.959865	−	0.959865i	−0.0393599	−	0.999225i	$-0.512532\pi$
$557$	12618.1	−	12618.1i	0.959865	−	0.959865i	0.999225	+	0.0393599i	$0.0125319\pi$
$558$	−1909.51	−	481.863i	−0.144867	−	0.0365572i
$559$		−	4871.13i		−	0.368563i
$560$		0			0
$561$	5528.01	−	1524.60i	0.416030	−	0.114739i
$562$	3681.21	+	3681.21i	0.276303	+	0.276303i
$563$	−5866.97	−	5866.97i	−0.439189	−	0.439189i	0.452550	−	0.891739i	$-0.350514\pi$
$563$	−5866.97	−	5866.97i	−0.439189	−	0.439189i	−0.891739	+	0.452550i	$0.850514\pi$
$564$	−9296.25	+	2563.86i	−0.694048	+	0.191415i
$565$		0			0
$566$			4213.78i			0.312930i
$567$	10276.1	−	3077.95i	0.761120	−	0.227975i
$568$	−2256.98	+	2256.98i	−0.166727	+	0.166727i
$569$	−4529.45			−0.333716			−0.166858	−	0.985981i	$-0.553362\pi$
$569$	−4529.45			−0.333716			−0.166858	+	0.985981i	$0.553362\pi$
$570$		0			0
$571$	20295.0			1.48742			0.743710	−	0.668502i	$-0.233064\pi$
$571$	20295.0			1.48742			0.743710	+	0.668502i	$0.233064\pi$
$572$	−4054.62	+	4054.62i	−0.296385	+	0.296385i
$573$	−16266.9	−	9233.91i	−1.18597	−	0.673215i
$574$		−	1396.42i		−	0.101543i
$575$		0			0
$576$	1483.71	−	885.772i	0.107328	−	0.0640749i
$577$	17860.3	+	17860.3i	1.28862	+	1.28862i	0.935624	+	0.352997i	$0.114837\pi$
$577$	17860.3	+	17860.3i	1.28862	+	1.28862i	0.352997	+	0.935624i	$0.385163\pi$
$578$	2884.61	+	2884.61i	0.207585	+	0.207585i
$579$	69.8113	+	253.128i	0.00501081	+	0.0181686i
$580$		0			0
$581$		−	4399.88i		−	0.314179i
$582$	−1292.19	+	2276.38i	−0.0920324	+	0.162129i
$583$	5672.39	−	5672.39i	0.402961	−	0.402961i
$584$	−6180.65			−0.437940
$585$		0			0
$586$	−14466.5			−1.01980
$587$	−2003.24	+	2003.24i	−0.140856	+	0.140856i	−0.774019	−	0.633163i	$-0.781756\pi$
$587$	−2003.24	+	2003.24i	−0.140856	+	0.140856i	0.633163	+	0.774019i	$0.281756\pi$
$588$	1297.67	−	2286.04i	0.0910119	−	0.160331i
$589$			610.360i			0.0426985i
$590$		0			0
$591$	288.226	+	1045.07i	0.0200609	+	0.0727387i
$592$	−1560.91	−	1560.91i	−0.108366	−	0.108366i
$593$	6410.93	+	6410.93i	0.443955	+	0.443955i	0.893339	−	0.449384i	$-0.148356\pi$
$593$	6410.93	+	6410.93i	0.443955	+	0.443955i	−0.449384	+	0.893339i	$0.648356\pi$
$594$	−4173.40	−	3994.37i	−0.288277	−	0.275911i
$595$		0			0
$596$		−	3234.03i		−	0.222267i
$597$	−13512.3	−	7670.28i	−0.926337	−	0.525835i
$598$	−21095.3	+	21095.3i	−1.44256	+	1.44256i
$599$	3209.61			0.218934			0.109467	−	0.993990i	$-0.465086\pi$
$599$	3209.61			0.218934			0.109467	+	0.993990i	$0.465086\pi$
$600$		0			0
$601$	12372.3			0.839726			0.419863	−	0.907587i	$-0.362078\pi$
$601$	12372.3			0.839726			0.419863	+	0.907587i	$0.362078\pi$
$602$	−1455.84	+	1455.84i	−0.0985641	+	0.0985641i
$603$	−761.487	+	3017.59i	−0.0514264	+	0.203791i
$604$		−	394.410i		−	0.0265701i
$605$		0			0
$606$	2072.53	−	571.594i	0.138929	−	0.0383159i
$607$	−8440.46	−	8440.46i	−0.564395	−	0.564395i	0.366158	−	0.930553i	$-0.380673\pi$
$607$	−8440.46	−	8440.46i	−0.564395	−	0.564395i	−0.930553	+	0.366158i	$0.880673\pi$
$608$	−378.693	−	378.693i	−0.0252599	−	0.0252599i
$609$	−14648.2	+	4039.90i	−0.974674	+	0.268810i
$610$		0			0
$611$			32305.2i			2.13900i
$612$	−1416.47	+	5613.15i	−0.0935581	+	0.370749i
$613$	−10419.9	+	10419.9i	−0.686554	+	0.686554i	−0.961469	−	0.274915i	$-0.911350\pi$
$613$	−10419.9	+	10419.9i	−0.686554	+	0.686554i	0.274915	+	0.961469i	$0.411350\pi$
$614$	−6268.03			−0.411983
$615$		0			0
$616$	2423.62			0.158523
$617$	21019.7	−	21019.7i	1.37151	−	1.37151i	0.513300	−	0.858210i	$-0.328423\pi$
$617$	21019.7	−	21019.7i	1.37151	−	1.37151i	0.858210	−	0.513300i	$-0.171577\pi$
$618$	−9062.77	−	5144.48i	−0.589900	−	0.334857i
$619$		−	22111.2i		−	1.43574i	−0.696175	−	0.717872i	$-0.745116\pi$
$619$		−	22111.2i		−	1.43574i	0.696175	−	0.717872i	$-0.254884\pi$
$620$		0			0
$621$	−21713.3	−	20781.8i	−1.40310	−	1.34291i
$622$	179.166	+	179.166i	0.0115497	+	0.0115497i
$623$	3692.36	+	3692.36i	0.237450	+	0.237450i
$624$	−1539.06	−	5580.47i	−0.0987370	−	0.358009i
$625$		0			0
$626$		−	15402.8i		−	0.983415i
$627$	−883.852	+	1557.04i	−0.0562961	+	0.0991738i
$628$	−6609.58	+	6609.58i	−0.419986	+	0.419986i
$629$	7395.38			0.468797
$630$		0			0
$631$	11224.6			0.708155			0.354077	−	0.935216i	$-0.384795\pi$
$631$	11224.6			0.708155			0.354077	+	0.935216i	$0.384795\pi$
$632$	2775.55	−	2775.55i	0.174692	−	0.174692i
$633$	8789.86	−	15484.6i	0.551920	−	0.972289i
$634$			708.114i			0.0443577i
$635$		0			0
$636$	2153.14	+	7807.05i	0.134242	+	0.486745i
$637$	−6226.84	−	6226.84i	−0.387310	−	0.387310i
$638$	5786.25	+	5786.25i	0.359059	+	0.359059i
$639$	−9249.57	+	5521.98i	−0.572625	+	0.341856i
$640$		0			0
$641$			20337.2i			1.25315i	0.779360	+	0.626577i	$0.215545\pi$
$641$			20337.2i			1.25315i	−0.779360	+	0.626577i	$0.784455\pi$
$642$	−2676.57	−	1519.36i	−0.164542	−	0.0934022i
$643$	16706.9	−	16706.9i	1.02466	−	1.02466i	0.0249740	−	0.999688i	$-0.492050\pi$
$643$	16706.9	−	16706.9i	1.02466	−	1.02466i	0.999688	−	0.0249740i	$-0.00795031\pi$
$644$	12609.5			0.771561
$645$		0			0
$646$	1794.20			0.109275
$647$	2963.71	−	2963.71i	0.180085	−	0.180085i	−0.611308	−	0.791393i	$-0.709356\pi$
$647$	2963.71	−	2963.71i	0.180085	−	0.180085i	0.791393	+	0.611308i	$0.209356\pi$
$648$	5586.77	−	1673.38i	0.338687	−	0.101445i
$649$			2839.31i			0.171730i
$650$		0			0
$651$	2688.15	−	741.377i	0.161839	−	0.0446342i
$652$	−4650.98	−	4650.98i	−0.279366	−	0.279366i
$653$	−14651.6	−	14651.6i	−0.878040	−	0.878040i	0.115291	−	0.993332i	$-0.463220\pi$
$653$	−14651.6	−	14651.6i	−0.878040	−	0.878040i	−0.993332	+	0.115291i	$0.963220\pi$
$654$	12642.0	−	3486.59i	0.755872	−	0.208465i
$655$		0			0
$656$		−	759.188i		−	0.0451849i
$657$	−20225.7	−	5103.93i	−1.20103	−	0.303079i
$658$	9655.10	−	9655.10i	0.572029	−	0.572029i
$659$	5082.76			0.300449			0.150225	−	0.988652i	$-0.452000\pi$
$659$	5082.76			0.300449			0.150225	+	0.988652i	$0.452000\pi$
$660$		0			0
$661$	−4510.62			−0.265420			−0.132710	−	0.991155i	$-0.542368\pi$
$661$	−4510.62			−0.265420			−0.132710	+	0.991155i	$0.542368\pi$
$662$	−5862.49	+	5862.49i	−0.344187	+	0.344187i
$663$	16865.7	+	9573.84i	0.987950	+	0.560810i
$664$		−	2392.07i		−	0.139805i
$665$		0			0
$666$	−3818.95	−	6396.92i	−0.222194	−	0.372186i
$667$	30104.5	+	30104.5i	1.74760	+	1.74760i
$668$	2281.51	+	2281.51i	0.132147	+	0.132147i
$669$	5369.29	+	19468.4i	0.310297	+	1.12510i
$670$		0			0
$671$		−	13629.0i		−	0.784117i
$672$	−1207.86	+	2127.82i	−0.0693367	+	0.122147i
$673$	−714.862	+	714.862i	−0.0409449	+	0.0409449i	−0.727283	−	0.686338i	$-0.759217\pi$
$673$	−714.862	+	714.862i	−0.0409449	+	0.0409449i	0.686338	+	0.727283i	$0.259217\pi$
$674$	2536.41			0.144954
$675$		0			0
$676$	−10604.6			−0.603357
$677$	−16044.7	+	16044.7i	−0.910855	+	0.910855i	−0.996340	−	0.0854844i	$-0.972756\pi$
$677$	−16044.7	+	16044.7i	−0.910855	+	0.910855i	0.0854844	+	0.996340i	$0.472756\pi$
$678$	6693.93	−	11792.3i	0.379172	−	0.667968i
$679$		−	3706.32i		−	0.209478i
$680$		0			0
$681$	1577.14	+	5718.55i	0.0887464	+	0.321784i
$682$	−1061.86	−	1061.86i	−0.0596196	−	0.0596196i
$683$	12528.4	+	12528.4i	0.701882	+	0.701882i	0.964814	−	0.262932i	$-0.0846895\pi$
$683$	12528.4	+	12528.4i	0.701882	+	0.701882i	−0.262932	+	0.964814i	$0.584690\pi$
$684$	−926.519	−	1551.96i	−0.0517929	−	0.0867555i
$685$		0			0
$686$			13816.5i			0.768972i
$687$	−4404.44	−	2500.18i	−0.244600	−	0.138847i
$688$	−791.492	+	791.492i	−0.0438595	+	0.0438595i
$689$	27130.1			1.50011
$690$		0			0
$691$	20266.0			1.11571			0.557856	−	0.829938i	$-0.311624\pi$
$691$	20266.0			1.11571			0.557856	+	0.829938i	$0.311624\pi$
$692$	3094.63	−	3094.63i	0.170000	−	0.170000i
$693$	7931.08	+	2001.40i	0.434743	+	0.109707i
$694$		−	9261.54i		−	0.506575i
$695$		0			0
$696$	−7963.76	+	2196.36i	−0.433715	+	0.119616i
$697$	1798.47	+	1798.47i	0.0977358	+	0.0977358i
$698$	−485.723	−	485.723i	−0.0263394	−	0.0263394i
$699$	−26101.9	+	7198.76i	−1.41239	+	0.389531i
$700$		0			0
$701$		−	7518.86i		−	0.405112i	−0.979271	−	0.202556i	$-0.935075\pi$
$701$		−	7518.86i		−	0.405112i	0.979271	−	0.202556i	$-0.0649248\pi$
$702$	−428.151	−	19532.6i	−0.0230193	−	1.05016i
$703$	−1632.71	+	1632.71i	−0.0875945	+	0.0875945i
$704$	1317.64			0.0705404
$705$		0			0
$706$	−3291.28			−0.175452
$707$	−2152.54	+	2152.54i	−0.114504	+	0.114504i
$708$	−2492.79	−	1415.03i	−0.132323	−	0.0751132i
$709$			1532.31i			0.0811665i	0.999176	+	0.0405833i	$0.0129216\pi$
$709$			1532.31i			0.0811665i	−0.999176	+	0.0405833i	$0.987078\pi$
$710$		0			0
$711$	11374.8	−	6790.72i	0.599982	−	0.358189i
$712$	2007.42	+	2007.42i	0.105662	+	0.105662i
$713$	−5524.59	−	5524.59i	−0.290179	−	0.290179i
$714$	−2179.34	−	7902.03i	−0.114229	−	0.414182i
$715$		0			0
$716$		−	13178.3i		−	0.687842i
$717$	−10801.6	+	19028.7i	−0.562615	+	0.991129i
$718$	−12232.7	+	12232.7i	−0.635823	+	0.635823i
$719$	19659.8			1.01973			0.509865	−	0.860255i	$-0.329695\pi$
$719$	19659.8			1.01973			0.509865	+	0.860255i	$0.329695\pi$
$720$		0			0
$721$	14755.7			0.762177
$722$	9303.98	−	9303.98i	0.479582	−	0.479582i
$723$	−13363.1	+	23541.1i	−0.687386	+	1.21093i
$724$			3710.85i			0.190487i
$725$		0			0
$726$	2506.38	+	9087.86i	0.128128	+	0.464576i
$727$	−18566.8	−	18566.8i	−0.947187	−	0.947187i	0.0514870	−	0.998674i	$-0.483604\pi$
$727$	−18566.8	−	18566.8i	−0.947187	−	0.947187i	−0.998674	+	0.0514870i	$0.983604\pi$
$728$	5795.89	+	5795.89i	0.295069	+	0.295069i
$729$	19664.1	−	862.482i	0.999040	−	0.0438186i
$730$		0			0
$731$		−	3749.99i		−	0.189738i
$732$	11965.6	+	6792.30i	0.604184	+	0.342966i
$733$	−12011.3	+	12011.3i	−0.605249	+	0.605249i	−0.941701	−	0.336452i	$-0.890773\pi$
$733$	−12011.3	+	12011.3i	−0.605249	+	0.605249i	0.336452	+	0.941701i	$0.390773\pi$
$734$	−9279.04			−0.466615
$735$		0			0
$736$	6855.39			0.343333
$737$	−1678.05	+	1678.05i	−0.0838693	+	0.0838693i
$738$	626.931	−	2484.38i	0.0312705	−	0.123918i
$739$			11805.8i			0.587665i	0.955857	+	0.293833i	$0.0949308\pi$
$739$			11805.8i			0.587665i	−0.955857	+	0.293833i	$0.905069\pi$
$740$		0			0
$741$	−5837.19	+	1609.86i	−0.289385	+	0.0798109i
$742$	−8108.41	−	8108.41i	−0.401171	−	0.401171i
$743$	12053.1	+	12053.1i	0.595134	+	0.595134i	0.939014	−	0.343880i	$-0.111741\pi$
$743$	12053.1	+	12053.1i	0.595134	+	0.595134i	−0.343880	+	0.939014i	$0.611741\pi$
$744$	1461.46	−	403.062i	0.0720157	−	0.0198615i
$745$		0			0
$746$			10292.6i			0.505145i
$747$	1975.35	−	7827.84i	0.0967527	−	0.383408i
$748$	−3121.41	+	3121.41i	−0.152580	+	0.152580i
$749$	4357.90			0.212595
$750$		0			0
$751$	−24162.2			−1.17402			−0.587011	−	0.809579i	$-0.699695\pi$
$751$	−24162.2			−1.17402			−0.587011	+	0.809579i	$0.699695\pi$
$752$	5249.16	−	5249.16i	0.254544	−	0.254544i
$753$	2484.25	+	1410.18i	0.120227	+	0.0682470i
$754$			27674.7i			1.33668i
$755$		0			0
$756$	−5709.76	+	5965.68i	−0.274685	+	0.286997i
$757$	13034.1	+	13034.1i	0.625804	+	0.625804i	0.947010	−	0.321205i	$-0.104088\pi$
$757$	13034.1	+	13034.1i	0.625804	+	0.625804i	−0.321205	+	0.947010i	$0.604088\pi$
$758$	4422.28	+	4422.28i	0.211906	+	0.211906i
$759$	−6093.24	−	22093.4i	−0.291397	−	1.05657i
$760$		0			0
$761$			31372.9i			1.49444i	0.664578	+	0.747219i	$0.268611\pi$
$761$			31372.9i			1.49444i	−0.664578	+	0.747219i	$0.731389\pi$
$762$	−12267.1	+	21610.3i	−0.583189	+	1.02737i
$763$	−13130.0	+	13130.0i	−0.622984	+	0.622984i
$764$	14399.1			0.681861
$765$		0			0
$766$	−18279.6			−0.862229
$767$	−6789.99	+	6789.99i	−0.319651	+	0.319651i
$768$	−656.674	+	1156.83i	−0.0308538	+	0.0543534i
$769$		−	154.976i		−	0.00726732i	−0.999993	−	0.00363366i	$-0.998843\pi$
$769$		−	154.976i		−	0.00726732i	0.999993	−	0.00363366i	$-0.00115663\pi$
$770$		0			0
$771$	−1207.74	−	4379.14i	−0.0564148	−	0.204554i
$772$	−142.929	−	142.929i	−0.00666340	−	0.00666340i
$773$	26752.1	+	26752.1i	1.24477	+	1.24477i	0.958000	+	0.286770i	$0.0925814\pi$
$773$	26752.1	+	26752.1i	1.24477	+	1.24477i	0.286770	+	0.958000i	$0.407419\pi$
$774$	−3243.70	+	1936.48i	−0.150636	+	0.0899294i
$775$		0			0
$776$		−	2015.00i		−	0.0932144i
$777$	9173.99	+	5207.62i	0.423571	+	0.240441i
$778$	5632.79	−	5632.79i	0.259570	−	0.259570i
$779$	−794.112			−0.0365238
$780$		0			0
$781$	−8214.29			−0.376352
$782$	−16240.0	+	16240.0i	−0.742635	+	0.742635i
$783$	−27874.5	+	611.004i	−1.27222	+	0.0278870i
$784$			2023.55i			0.0921808i
$785$		0			0
$786$	16443.1	−	4534.91i	0.746190	−	0.205795i
$787$	−87.5660	−	87.5660i	−0.00396619	−	0.00396619i	0.705121	−	0.709087i	$-0.250893\pi$
$787$	−87.5660	−	87.5660i	−0.00396619	−	0.00396619i	−0.709087	+	0.705121i	$0.750893\pi$
$788$	−590.104	−	590.104i	−0.0266771	−	0.0266771i
$789$	6194.61	−	1708.44i	0.279511	−	0.0770876i
$790$		0			0
$791$			19199.9i			0.863045i
$792$	4311.87	+	1088.10i	0.193454	+	0.0488180i
$793$	32592.7	−	32592.7i	1.45952	−	1.45952i
$794$	−7105.72			−0.317598
$795$		0			0
$796$	11960.8			0.532589
$797$	−2302.20	+	2302.20i	−0.102319	+	0.102319i	−0.756413	−	0.654094i	$-0.773050\pi$
$797$	−2302.20	+	2302.20i	−0.102319	+	0.102319i	0.654094	+	0.756413i	$0.273050\pi$
$798$	2225.71	+	1263.42i	0.0987333	+	0.0560460i
$799$			24869.9i			1.10117i
$800$		0			0
$801$	4911.39	+	8226.80i	0.216648	+	0.362896i
$802$	−18728.7	−	18728.7i	−0.824604	−	0.824604i
$803$	−11247.3	−	11247.3i	−0.494280	−	0.494280i
$804$	−636.958	−	2309.54i	−0.0279400	−	0.101307i
$805$		0			0
$806$		−	5078.69i		−	0.221947i
$807$	−961.768	+	1694.30i	−0.0419527	+	0.0739059i
$808$	−1170.26	+	1170.26i	−0.0509526	+	0.0509526i
$809$	−39967.5			−1.73694			−0.868470	−	0.495742i	$-0.834896\pi$
$809$	−39967.5			−1.73694			−0.868470	+	0.495742i	$0.834896\pi$
$810$		0			0
$811$	−38920.2			−1.68517			−0.842586	−	0.538562i	$-0.818968\pi$
$811$	−38920.2			−1.68517			−0.842586	+	0.538562i	$0.818968\pi$
$812$	8271.17	−	8271.17i	0.357465	−	0.357465i
$813$	−12776.1	+	22507.1i	−0.551143	+	0.970919i
$814$		−	5680.93i		−	0.244615i
$815$		0			0
$816$	−1184.83	−	4296.07i	−0.0508302	−	0.184305i
$817$	827.902	+	827.902i	0.0354524	+	0.0354524i
$818$	4999.54	+	4999.54i	0.213698	+	0.213698i
$819$	14180.4	+	23752.7i	0.605008	+	1.01342i
$820$		0			0
$821$		−	26714.4i		−	1.13561i	−0.823162	−	0.567807i	$-0.807792\pi$
$821$		−	26714.4i		−	1.13561i	0.823162	−	0.567807i	$-0.192208\pi$
$822$	22326.2	+	12673.5i	0.947342	+	0.537759i
$823$	12934.5	−	12934.5i	0.547837	−	0.547837i	−0.377978	−	0.925815i	$-0.623380\pi$
$823$	12934.5	−	12934.5i	0.547837	−	0.547837i	0.925815	+	0.377978i	$0.123380\pi$
$824$	8022.17			0.339157
$825$		0			0
$826$	4058.67			0.170967
$827$	5618.41	−	5618.41i	0.236241	−	0.236241i	−0.579051	−	0.815292i	$-0.696577\pi$
$827$	5618.41	−	5618.41i	0.236241	−	0.236241i	0.815292	+	0.579051i	$0.196577\pi$
$828$	22433.7	+	5661.12i	0.941574	+	0.237606i
$829$		−	29970.7i		−	1.25564i	−0.778359	−	0.627820i	$-0.783947\pi$
$829$		−	29970.7i		−	1.25564i	0.778359	−	0.627820i	$-0.216053\pi$
$830$		0			0
$831$	−33298.3	+	9183.49i	−1.39002	+	0.383359i
$832$	3151.03	+	3151.03i	0.131301	+	0.131301i
$833$	−4793.67	−	4793.67i	−0.199389	−	0.199389i
$834$	5287.36	−	1458.22i	0.219528	−	0.0605446i
$835$		0			0
$836$		−	1378.25i		−	0.0570191i
$837$	5115.34	−	112.128i	0.211245	−	0.00463046i
$838$	12484.4	−	12484.4i	0.514640	−	0.514640i
$839$	−27039.3			−1.11264			−0.556318	−	0.830970i	$-0.687786\pi$
$839$	−27039.3			−1.11264			−0.556318	+	0.830970i	$0.687786\pi$
$840$		0			0
$841$	15104.9			0.619333
$842$	−15039.9	+	15039.9i	−0.615571	+	0.615571i
$843$	−11762.6	−	6677.07i	−0.480577	−	0.272800i
$844$			13706.7i			0.559008i
$845$		0			0
$846$	21512.1	−	12842.7i	0.874235	−	0.521917i
$847$	−9438.67	−	9438.67i	−0.382900	−	0.382900i
$848$	−4408.28	−	4408.28i	−0.178515	−	0.178515i
$849$	−2910.65	−	10553.7i	−0.117660	−	0.426622i
$850$		0			0
$851$		−	29556.6i		−	1.19058i
$852$	4093.76	−	7211.77i	0.164613	−	0.289990i
$853$	2627.55	−	2627.55i	0.105470	−	0.105470i	−0.652403	−	0.757872i	$-0.726239\pi$
$853$	2627.55	−	2627.55i	0.105470	−	0.105470i	0.757872	+	0.652403i	$0.226239\pi$
$854$	−19482.0			−0.780634
$855$		0			0
$856$	2369.24			0.0946017
$857$	5084.59	−	5084.59i	0.202668	−	0.202668i	−0.598474	−	0.801142i	$-0.704226\pi$
$857$	5084.59	−	5084.59i	0.202668	−	0.202668i	0.801142	+	0.598474i	$0.204226\pi$
$858$	7354.36	−	12955.8i	0.292627	−	0.515505i
$859$		−	14839.7i		−	0.589434i	−0.955585	−	0.294717i	$-0.904775\pi$
$859$		−	14839.7i		−	0.589434i	0.955585	−	0.294717i	$-0.0952254\pi$
$860$		0			0
$861$	964.573	+	3497.43i	0.0381795	+	0.138435i
$862$	20984.6	+	20984.6i	0.829164	+	0.829164i
$863$	−30314.7	−	30314.7i	−1.19574	−	1.19574i	−0.975430	−	0.220309i	$-0.929293\pi$
$863$	−30314.7	−	30314.7i	−1.19574	−	1.19574i	−0.220309	−	0.975430i	$-0.570707\pi$
$864$	−3104.21	+	3243.35i	−0.122231	+	0.127709i
$865$		0			0
$866$			26399.7i			1.03591i
$867$	−9217.24	−	5232.17i	−0.361054	−	0.204953i
$868$	−1517.87	+	1517.87i	−0.0593548	+	0.0593548i
$869$	10101.6			0.394332
$870$		0			0
$871$	−8025.83			−0.312222
$872$	−7138.33	+	7138.33i	−0.277218	+	0.277218i
$873$	1663.97	−	6593.92i	0.0645096	−	0.255636i
$874$		−	7170.74i		−	0.277522i
$875$		0			0
$876$	15479.9	−	4269.27i	0.597051	−	0.164663i
$877$	−16039.3	−	16039.3i	−0.617568	−	0.617568i	0.327339	−	0.944907i	$-0.393848\pi$
$877$	−16039.3	−	16039.3i	−0.617568	−	0.617568i	−0.944907	+	0.327339i	$0.893848\pi$
$878$	−25488.0	−	25488.0i	−0.979703	−	0.979703i
$879$	36232.3	−	9992.67i	1.39031	−	0.383441i
$880$		0			0
$881$		−	1324.73i		−	0.0506600i	−0.999679	−	0.0253300i	$-0.991936\pi$
$881$		−	1324.73i		−	0.0506600i	0.999679	−	0.0253300i	$-0.00806364\pi$
$882$	−1671.03	+	6621.90i	−0.0637943	+	0.252802i
$883$	−15408.2	+	15408.2i	−0.587234	+	0.587234i	−0.936882	−	0.349647i	$-0.886302\pi$
$883$	−15408.2	+	15408.2i	−0.587234	+	0.587234i	0.349647	+	0.936882i	$0.386302\pi$
$884$	−14929.2			−0.568013
$885$		0			0
$886$	27238.3			1.03283
$887$	19011.1	−	19011.1i	0.719649	−	0.719649i	−0.248884	−	0.968533i	$-0.580064\pi$
$887$	19011.1	−	19011.1i	0.719649	−	0.719649i	0.968533	+	0.248884i	$0.0800639\pi$
$888$	4987.60	+	2831.21i	0.188483	+	0.106992i
$889$		−	35185.1i		−	1.32741i
$890$		0			0
$891$	13211.7	+	7121.41i	0.496754	+	0.267762i
$892$	−10992.9	−	10992.9i	−0.412634	−	0.412634i
$893$	−5490.63	−	5490.63i	−0.205752	−	0.205752i
$894$	2233.89	+	8099.84i	0.0835711	+	0.303019i
$895$		0			0
$896$		−	1883.51i		−	0.0702271i
$897$	38263.1	−	67406.0i	1.42427	−	2.50906i
$898$	−23508.9	+	23508.9i	−0.873609	+	0.873609i
$899$	−7247.67			−0.268880
$900$		0			0
$901$	20885.9			0.772263
$902$	1381.53	−	1381.53i	0.0509978	−	0.0509978i
$903$	2640.63	−	4651.87i	0.0973143	−	0.171433i
$904$			10438.3i			0.384042i
$905$		0			0
$906$	272.438	+	987.828i	0.00999021	+	0.0362234i
$907$	−16881.6	−	16881.6i	−0.618021	−	0.618021i	0.327003	−	0.945023i	$-0.393961\pi$
$907$	−16881.6	−	16881.6i	−0.618021	−	0.618021i	−0.945023	+	0.327003i	$0.893961\pi$
$908$	−3229.00	−	3229.00i	−0.118015	−	0.118015i
$909$	−4795.98	+	2863.19i	−0.174997	+	0.104473i
$910$		0			0
$911$		−	44232.0i		−	1.60864i	−0.594195	−	0.804321i	$-0.702529\pi$
$911$		−	44232.0i		−	1.60864i	0.594195	−	0.804321i	$-0.297471\pi$
$912$	1210.04	+	686.882i	0.0439348	+	0.0249396i
$913$	4352.97	−	4352.97i	0.157790	−	0.157790i
$914$	17662.5			0.639193
$915$		0			0
$916$	3898.72			0.140630
$917$	−17077.8	+	17077.8i	−0.615004	+	0.615004i
$918$	−329.608	−	15036.9i	−0.0118504	−	0.540624i
$919$		−	11727.2i		−	0.420940i	−0.977600	−	0.210470i	$-0.932501\pi$
$919$		−	11727.2i		−	0.420940i	0.977600	−	0.210470i	$-0.0674994\pi$
$920$		0			0
$921$	15698.7	−	4329.63i	0.561662	−	0.154903i
$922$	21060.4	+	21060.4i	0.752263	+	0.752263i
$923$	−19643.8	−	19643.8i	−0.700525	−	0.700525i
$924$	−6070.12	+	1674.11i	−0.216117	+	0.0596040i
$925$		0			0
$926$			2869.08i			0.101819i
$927$	26251.9	+	6624.64i	0.930124	+	0.234716i
$928$	4496.76	−	4496.76i	0.159066	−	0.159066i
$929$	−4463.99			−0.157652			−0.0788261	−	0.996888i	$-0.525117\pi$
$929$	−4463.99			−0.157652			−0.0788261	+	0.996888i	$0.525117\pi$
$930$		0			0
$931$	2116.64			0.0745113
$932$	14738.5	−	14738.5i	0.518000	−	0.518000i
$933$	−572.491	−	324.975i	−0.0200885	−	0.0114032i
$934$			20736.0i			0.726450i
$935$		0			0
$936$	7709.39	+	12913.6i	0.269219	+	0.450955i
$937$	17877.8	+	17877.8i	0.623310	+	0.623310i	0.946376	−	0.323066i	$-0.104714\pi$
$937$	17877.8	+	17877.8i	0.623310	+	0.623310i	−0.323066	+	0.946376i	$0.604714\pi$
$938$	2398.69	+	2398.69i	0.0834968	+	0.0834968i
$939$	10639.4	+	38577.3i	0.369759	+	1.34070i
$940$		0			0
$941$		−	44256.3i		−	1.53317i	−0.642142	−	0.766586i	$-0.721954\pi$
$941$		−	44256.3i		−	1.53317i	0.642142	−	0.766586i	$-0.278046\pi$
$942$	11988.6	−	21119.7i	0.414660	−	0.730485i
$943$	7187.80	−	7187.80i	0.248215	−	0.248215i
$944$	2206.56			0.0760779
$945$		0			0
$946$	−2880.64			−0.0990038
$947$	−19536.7	+	19536.7i	−0.670387	+	0.670387i	−0.957805	−	0.287418i	$-0.907203\pi$
$947$	−19536.7	+	19536.7i	−0.670387	+	0.670387i	0.287418	+	0.957805i	$0.407203\pi$
$948$	−5034.36	+	8868.76i	−0.172477	+	0.303844i
$949$		−	53793.8i		−	1.84006i
$950$		0			0
$951$	−489.128	−	1773.52i	−0.0166783	−	0.0604736i
$952$	4461.91	+	4461.91i	0.151903	+	0.151903i
$953$	15633.5	+	15633.5i	0.531395	+	0.531395i	0.920987	−	0.389593i	$-0.127384\pi$
$953$	15633.5	+	15633.5i	0.531395	+	0.531395i	−0.389593	+	0.920987i	$0.627384\pi$
$954$	−10785.4	−	18066.0i	−0.366027	−	0.613112i
$955$		0			0
$956$		−	16843.8i		−	0.569840i
$957$	−18488.9	−	10495.2i	−0.624516	−	0.354507i
$958$	23997.8	−	23997.8i	0.809326	−	0.809326i
$959$	−36350.7			−1.22401
$960$		0			0
$961$	−28461.0			−0.955354
$962$	13585.5	−	13585.5i	0.455316	−	0.455316i
$963$	7753.15	+	1956.50i	0.259441	+	0.0654697i
$964$		−	20838.1i		−	0.696214i
$965$		0			0
$966$	−31581.4	+	8709.99i	−1.05188	+	0.290103i
$967$	28145.8	+	28145.8i	0.935995	+	0.935995i	0.998071	−	0.0620762i	$-0.0197722\pi$
$967$	28145.8	+	28145.8i	0.935995	+	0.935995i	−0.0620762	+	0.998071i	$0.519772\pi$
$968$	−5131.49	−	5131.49i	−0.170385	−	0.170385i
$969$	−4493.70	+	1239.34i	−0.148977	+	0.0410870i
$970$		0			0
$971$			29658.9i			0.980224i	0.871659	+	0.490112i	$0.163044\pi$
$971$			29658.9i			0.980224i	−0.871659	+	0.490112i	$0.836956\pi$
$972$	−12836.6	+	8050.14i	−0.423594	+	0.265646i
$973$	−5491.46	+	5491.46i	−0.180933	+	0.180933i
$974$	−29609.9			−0.974089
$975$		0			0
$976$	−10591.7			−0.347370
$977$	−8620.37	+	8620.37i	−0.282283	+	0.282283i	−0.834019	−	0.551736i	$-0.813966\pi$
$977$	−8620.37	+	8620.37i	−0.282283	+	0.282283i	0.551736	+	0.834019i	$0.313966\pi$
$978$	14861.4	+	8436.05i	0.485904	+	0.275823i
$979$			7306.00i			0.238509i
$980$		0			0
$981$	−29254.4	+	17464.8i	−0.952110	+	0.568408i
$982$	−26823.2	−	26823.2i	−0.871653	−	0.871653i
$983$	26404.4	+	26404.4i	0.856733	+	0.856733i	0.990952	−	0.134219i	$-0.0428525\pi$
$983$	26404.4	+	26404.4i	0.856733	+	0.856733i	−0.134219	+	0.990952i	$0.542852\pi$
$984$	524.407	+	1901.44i	0.0169893	+	0.0616013i
$985$		0			0
$986$			21305.1i			0.688126i
$987$	−17512.6	+	30851.1i	−0.564776	+	0.994936i
$988$	3295.99	−	3295.99i	0.106133	−	0.106133i
$989$	−14987.3			−0.481869
$990$		0			0
$991$	19257.2			0.617280			0.308640	−	0.951179i	$-0.400126\pi$
$991$	19257.2			0.617280			0.308640	+	0.951179i	$0.400126\pi$
$992$	−825.217	+	825.217i	−0.0264120	+	0.0264120i
$993$	10633.5	−	18732.5i	0.339823	−	0.598648i
$994$			11741.9i			0.374680i
$995$		0			0
$996$	1652.31	+	5991.10i	0.0525658	+	0.190598i
$997$	−30812.8	−	30812.8i	−0.978789	−	0.978789i	0.0209909	−	0.999780i	$-0.493318\pi$
$997$	−30812.8	−	30812.8i	−0.978789	−	0.978789i	−0.999780	+	0.0209909i	$0.993318\pi$
$998$	−7290.41	−	7290.41i	−0.231236	−	0.231236i
$999$	13983.5	+	13383.6i	0.442861	+	0.423862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.4.e.c.107.5		12
3.2	odd	2	inner	150.4.e.c.107.1		12
5.2	odd	4		30.4.e.a.23.6	yes	12
5.3	odd	4	inner	150.4.e.c.143.1		12
5.4	even	2		30.4.e.a.17.2	✓	12
15.2	even	4		30.4.e.a.23.2	yes	12
15.8	even	4	inner	150.4.e.c.143.5		12
15.14	odd	2		30.4.e.a.17.6	yes	12
20.7	even	4		240.4.v.d.113.1		12
20.19	odd	2		240.4.v.d.17.3		12
60.47	odd	4		240.4.v.d.113.3		12
60.59	even	2		240.4.v.d.17.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.4.e.a.17.2	✓	12	5.4	even	2
30.4.e.a.17.6	yes	12	15.14	odd	2
30.4.e.a.23.2	yes	12	15.2	even	4
30.4.e.a.23.6	yes	12	5.2	odd	4
150.4.e.c.107.1		12	3.2	odd	2	inner
150.4.e.c.107.5		12	1.1	even	1	trivial
150.4.e.c.143.1		12	5.3	odd	4	inner
150.4.e.c.143.5		12	15.8	even	4	inner
240.4.v.d.17.1		12	60.59	even	2
240.4.v.d.17.3		12	20.19	odd	2
240.4.v.d.113.1		12	20.7	even	4
240.4.v.d.113.3		12	60.47	odd	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 - 1.41421i) q^{2} +(-2.56513 + 4.51886i) q^{3} -4.00000i q^{4} +(2.76299 + 10.0183i) q^{6} +(-10.4050 - 10.4050i) q^{7} +(-5.65685 - 5.65685i) q^{8} +(-13.8402 - 23.1830i) q^{9} +O(q^{10})\)	\(q+(1.41421 - 1.41421i) q^{2} +(-2.56513 + 4.51886i) q^{3} -4.00000i q^{4} +(2.76299 + 10.0183i) q^{6} +(-10.4050 - 10.4050i) q^{7} +(-5.65685 - 5.65685i) q^{8} +(-13.8402 - 23.1830i) q^{9} -20.5881i q^{11} +(18.0754 + 10.2605i) q^{12} +(49.2349 - 49.2349i) q^{13} -29.4298 q^{14} -16.0000 q^{16} +(37.9030 - 37.9030i) q^{17} +(-52.3586 - 13.2127i) q^{18} +16.7360i q^{19} +(73.7089 - 20.3285i) q^{21} +(-29.1160 - 29.1160i) q^{22} +(-151.484 - 151.484i) q^{23} +(40.0731 - 11.0519i) q^{24} -139.257i q^{26} +(140.262 - 3.07453i) q^{27} +(-41.6200 + 41.6200i) q^{28} -198.731 q^{29} +36.4698 q^{31} +(-22.6274 + 22.6274i) q^{32} +(93.0349 + 52.8113i) q^{33} -107.206i q^{34} +(-92.7318 + 55.3608i) q^{36} +(97.5568 + 97.5568i) q^{37} +(23.6683 + 23.6683i) q^{38} +(96.1916 + 348.780i) q^{39} +47.4492i q^{41} +(75.4913 - 132.989i) q^{42} +(49.4682 - 49.4682i) q^{43} -82.3526 q^{44} -428.462 q^{46} +(-328.073 + 328.073i) q^{47} +(41.0421 - 72.3018i) q^{48} -126.472i q^{49} +(74.0521 + 268.504i) q^{51} +(-196.940 - 196.940i) q^{52} +(275.517 + 275.517i) q^{53} +(194.013 - 202.709i) q^{54} +117.719i q^{56} +(-75.6278 - 42.9301i) q^{57} +(-281.048 + 281.048i) q^{58} -137.910 q^{59} +661.984 q^{61} +(51.5761 - 51.5761i) q^{62} +(-97.2114 + 385.226i) q^{63} +64.0000i q^{64} +(206.258 - 56.8848i) q^{66} +(-81.5055 - 81.5055i) q^{67} +(-151.612 - 151.612i) q^{68} +(1073.11 - 295.959i) q^{69} -398.982i q^{71} +(-52.8506 + 209.435i) q^{72} +(546.298 - 546.298i) q^{73} +275.932 q^{74} +66.9441 q^{76} +(-214.220 + 214.220i) q^{77} +(629.284 + 357.214i) q^{78} +490.653i q^{79} +(-345.898 + 641.713i) q^{81} +(67.1034 + 67.1034i) q^{82} +(211.431 + 211.431i) q^{83} +(-81.3141 - 294.836i) q^{84} -139.917i q^{86} +(509.771 - 898.036i) q^{87} +(-116.464 + 116.464i) q^{88} -354.864 q^{89} -1024.58 q^{91} +(-605.936 + 605.936i) q^{92} +(-93.5499 + 164.802i) q^{93} +927.929i q^{94} +(-44.2078 - 160.292i) q^{96} +(178.103 + 178.103i) q^{97} +(-178.858 - 178.858i) q^{98} +(-477.294 + 284.944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{3} + 8 q^{6} - 12 q^{7}+O(q^{10}) \) 12 * q - 8 * q^3 + 8 * q^6 - 12 * q^7	\( 12 q - 8 q^{3} + 8 q^{6} - 12 q^{7} + 32 q^{12} + 120 q^{13} - 192 q^{16} + 16 q^{18} + 464 q^{21} - 312 q^{22} + 688 q^{27} - 48 q^{28} - 504 q^{31} - 788 q^{33} + 368 q^{36} - 768 q^{37} + 872 q^{42} + 1968 q^{43} - 1152 q^{46} + 128 q^{48} + 256 q^{51} - 480 q^{52} - 968 q^{57} - 2280 q^{58} + 1848 q^{61} - 1268 q^{63} + 944 q^{66} + 1752 q^{67} - 64 q^{72} - 180 q^{73} - 1152 q^{76} + 4080 q^{78} - 4316 q^{81} - 2208 q^{82} - 3620 q^{87} - 1248 q^{88} + 4080 q^{91} - 584 q^{93} - 128 q^{96} + 7596 q^{97}+O(q^{100}) \) 12 * q - 8 * q^3 + 8 * q^6 - 12 * q^7 + 32 * q^12 + 120 * q^13 - 192 * q^16 + 16 * q^18 + 464 * q^21 - 312 * q^22 + 688 * q^27 - 48 * q^28 - 504 * q^31 - 788 * q^33 + 368 * q^36 - 768 * q^37 + 872 * q^42 + 1968 * q^43 - 1152 * q^46 + 128 * q^48 + 256 * q^51 - 480 * q^52 - 968 * q^57 - 2280 * q^58 + 1848 * q^61 - 1268 * q^63 + 944 * q^66 + 1752 * q^67 - 64 * q^72 - 180 * q^73 - 1152 * q^76 + 4080 * q^78 - 4316 * q^81 - 2208 * q^82 - 3620 * q^87 - 1248 * q^88 + 4080 * q^91 - 584 * q^93 - 128 * q^96 + 7596 * q^97

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