LMFDB - Embedded newform 1620.4.i.c.1081.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,4,Mod(541,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1620.541");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1620.i (of order $3$, degree $2$, not 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:	$95.5830942093$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1081.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1620.1081
Dual form			1620.4.i.c.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50000 + 4.33013i) q^{5} +(-1.00000 - 1.73205i) q^{7} +O(q^{10})$	$q+(-2.50000 + 4.33013i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-15.0000 - 25.9808i) q^{11} +(2.00000 - 3.46410i) q^{13} +90.0000 q^{17} -28.0000 q^{19} +(-60.0000 + 103.923i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(-105.000 - 181.865i) q^{29} +(2.00000 - 3.46410i) q^{31} +10.0000 q^{35} +200.000 q^{37} +(-120.000 + 207.846i) q^{41} +(68.0000 + 117.779i) q^{43} +(60.0000 + 103.923i) q^{47} +(169.500 - 293.583i) q^{49} -30.0000 q^{53} +150.000 q^{55} +(225.000 - 389.711i) q^{59} +(83.0000 + 143.760i) q^{61} +(10.0000 + 17.3205i) q^{65} +(-454.000 + 786.351i) q^{67} -1020.00 q^{71} -250.000 q^{73} +(-30.0000 + 51.9615i) q^{77} +(458.000 + 793.279i) q^{79} +(570.000 + 987.269i) q^{83} +(-225.000 + 389.711i) q^{85} -420.000 q^{89} -8.00000 q^{91} +(70.0000 - 121.244i) q^{95} +(-769.000 - 1331.95i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 5 q^{5} - 2 q^{7}+O(q^{10}) $ 2 * q - 5 * q^5 - 2 * q^7	$ 2 q - 5 q^{5} - 2 q^{7} - 30 q^{11} + 4 q^{13} + 180 q^{17} - 56 q^{19} - 120 q^{23} - 25 q^{25} - 210 q^{29} + 4 q^{31} + 20 q^{35} + 400 q^{37} - 240 q^{41} + 136 q^{43} + 120 q^{47} + 339 q^{49} - 60 q^{53} + 300 q^{55} + 450 q^{59} + 166 q^{61} + 20 q^{65} - 908 q^{67} - 2040 q^{71} - 500 q^{73} - 60 q^{77} + 916 q^{79} + 1140 q^{83} - 450 q^{85} - 840 q^{89} - 16 q^{91} + 140 q^{95} - 1538 q^{97}+O(q^{100}) $ 2 * q - 5 * q^5 - 2 * q^7 - 30 * q^11 + 4 * q^13 + 180 * q^17 - 56 * q^19 - 120 * q^23 - 25 * q^25 - 210 * q^29 + 4 * q^31 + 20 * q^35 + 400 * q^37 - 240 * q^41 + 136 * q^43 + 120 * q^47 + 339 * q^49 - 60 * q^53 + 300 * q^55 + 450 * q^59 + 166 * q^61 + 20 * q^65 - 908 * q^67 - 2040 * q^71 - 500 * q^73 - 60 * q^77 + 916 * q^79 + 1140 * q^83 - 450 * q^85 - 840 * q^89 - 16 * q^91 + 140 * q^95 - 1538 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.0539949	−	0.0935220i	0.837765	−	0.546032i	$-0.183862\pi$
$7$	−1.00000	−	1.73205i	−0.0539949	−	0.0935220i	−0.891760	+	0.452510i	$0.850529\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	0.583864	−	0.811851i	$-0.301540\pi$
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	−0.995016	+	0.0997155i	$0.968207\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.0426692	−	0.0739053i	−0.843902	−	0.536497i	$-0.819747\pi$
$13$	2.00000	−	3.46410i	0.0426692	−	0.0739053i	0.886571	+	0.462592i	$0.153080\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	90.0000			1.28401			0.642006	−	0.766700i	$-0.278102\pi$
$17$	90.0000			1.28401			0.642006	+	0.766700i	$0.278102\pi$
$18$		0			0
$19$	−28.0000			−0.338086			−0.169043	−	0.985609i	$-0.554068\pi$
$19$	−28.0000			−0.338086			−0.169043	+	0.985609i	$0.554068\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−60.0000	+	103.923i	−0.543951	+	0.942150i	0.454721	+	0.890634i	$0.349739\pi$
$23$	−60.0000	+	103.923i	−0.543951	+	0.942150i	−0.998672	+	0.0515165i	$0.983595\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−105.000	−	181.865i	−0.672345	−	1.16454i	−0.977237	−	0.212149i	$-0.931954\pi$
$29$	−105.000	−	181.865i	−0.672345	−	1.16454i	0.304892	−	0.952387i	$-0.401380\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.0115874	−	0.0200700i	−0.860174	−	0.510001i	$-0.829645\pi$
$31$	2.00000	−	3.46410i	0.0115874	−	0.0200700i	0.871761	+	0.489931i	$0.162978\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	10.0000			0.0482945
$36$		0			0
$37$	200.000			0.888643			0.444322	−	0.895867i	$-0.353445\pi$
$37$	200.000			0.888643			0.444322	+	0.895867i	$0.353445\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−120.000	+	207.846i	−0.457094	+	0.791710i	−0.998806	−	0.0488543i	$-0.984443\pi$
$41$	−120.000	+	207.846i	−0.457094	+	0.791710i	0.541712	+	0.840564i	$0.317776\pi$
$42$		0			0
$43$	68.0000	+	117.779i	0.241161	+	0.417702i	0.961045	−	0.276391i	$-0.0891386\pi$
$43$	68.0000	+	117.779i	0.241161	+	0.417702i	−0.719885	+	0.694094i	$0.755805\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	60.0000	+	103.923i	0.186211	+	0.322526i	0.943984	−	0.329992i	$-0.107046\pi$
$47$	60.0000	+	103.923i	0.186211	+	0.322526i	−0.757773	+	0.652518i	$0.773713\pi$
$48$		0			0
$49$	169.500	−	293.583i	0.494169	−	0.855926i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−30.0000			−0.0777513			−0.0388756	−	0.999244i	$-0.512378\pi$
$53$	−30.0000			−0.0777513			−0.0388756	+	0.999244i	$0.512378\pi$
$54$		0			0
$55$	150.000			0.367745
$56$		0			0
$57$		0			0
$58$		0			0
$59$	225.000	−	389.711i	0.496483	−	0.859934i	−0.503509	−	0.863990i	$-0.667958\pi$
$59$	225.000	−	389.711i	0.496483	−	0.859934i	0.999992	+	0.00405618i	$0.00129112\pi$
$60$		0			0
$61$	83.0000	+	143.760i	0.174214	+	0.301748i	0.939889	−	0.341480i	$-0.110928\pi$
$61$	83.0000	+	143.760i	0.174214	+	0.301748i	−0.765675	+	0.643228i	$0.777595\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.0000	+	17.3205i	0.0190823	+	0.0330515i
$66$		0			0
$67$	−454.000	+	786.351i	−0.827835	+	1.43385i	0.0718987	+	0.997412i	$0.477094\pi$
$67$	−454.000	+	786.351i	−0.827835	+	1.43385i	−0.899733	+	0.436440i	$0.856239\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1020.00			−1.70495			−0.852477	−	0.522765i	$-0.824901\pi$
$71$	−1020.00			−1.70495			−0.852477	+	0.522765i	$0.824901\pi$
$72$		0			0
$73$	−250.000			−0.400826			−0.200413	−	0.979712i	$-0.564228\pi$
$73$	−250.000			−0.400826			−0.200413	+	0.979712i	$0.564228\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−30.0000	+	51.9615i	−0.0444002	+	0.0769034i
$78$		0			0
$79$	458.000	+	793.279i	0.652266	+	1.12976i	0.982572	+	0.185884i	$0.0595149\pi$
$79$	458.000	+	793.279i	0.652266	+	1.12976i	−0.330306	+	0.943874i	$0.607152\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	570.000	+	987.269i	0.753803	+	1.30562i	0.945967	+	0.324262i	$0.105116\pi$
$83$	570.000	+	987.269i	0.753803	+	1.30562i	−0.192165	+	0.981363i	$0.561551\pi$
$84$		0			0
$85$	−225.000	+	389.711i	−0.287114	+	0.497296i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−420.000			−0.500224			−0.250112	−	0.968217i	$-0.580467\pi$
$89$	−420.000			−0.500224			−0.250112	+	0.968217i	$0.580467\pi$
$90$		0			0
$91$	−8.00000			−0.00921569
$92$		0			0
$93$		0			0
$94$		0			0
$95$	70.0000	−	121.244i	0.0755984	−	0.130940i
$96$		0			0
$97$	−769.000	−	1331.95i	−0.804950	−	1.39421i	−0.916325	−	0.400435i	$-0.868859\pi$
$97$	−769.000	−	1331.95i	−0.804950	−	1.39421i	0.111375	−	0.993778i	$-0.464474\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−225.000	−	389.711i	−0.221667	−	0.383938i	0.733647	−	0.679530i	$-0.237816\pi$
$101$	−225.000	−	389.711i	−0.221667	−	0.383938i	−0.955314	+	0.295592i	$0.904483\pi$
$102$		0			0
$103$	575.000	−	995.929i	0.550062	−	0.952736i	−0.448207	−	0.893930i	$-0.647937\pi$
$103$	575.000	−	995.929i	0.550062	−	0.952736i	0.998269	−	0.0588063i	$-0.0187294\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1620.00			−1.46366			−0.731829	−	0.681489i	$-0.761333\pi$
$107$	−1620.00			−1.46366			−0.731829	+	0.681489i	$0.761333\pi$
$108$		0			0
$109$	−1702.00			−1.49561			−0.747807	−	0.663916i	$-0.768893\pi$
$109$	−1702.00			−1.49561			−0.747807	+	0.663916i	$0.768893\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−675.000	+	1169.13i	−0.561935	+	0.973300i	0.435393	+	0.900241i	$0.356610\pi$
$113$	−675.000	+	1169.13i	−0.561935	+	0.973300i	−0.997328	+	0.0730593i	$0.976724\pi$
$114$		0			0
$115$	−300.000	−	519.615i	−0.243262	−	0.421342i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−90.0000	−	155.885i	−0.0693301	−	0.120083i
$120$		0			0
$121$	215.500	−	373.257i	0.161908	−	0.280433i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	2450.00			1.71183			0.855915	−	0.517117i	$-0.172995\pi$
$127$	2450.00			1.71183			0.855915	+	0.517117i	$0.172995\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−345.000	+	597.558i	−0.230098	+	0.398541i	−0.957837	−	0.287313i	$-0.907238\pi$
$131$	−345.000	+	597.558i	−0.230098	+	0.398541i	0.727739	+	0.685854i	$0.240571\pi$
$132$		0			0
$133$	28.0000	+	48.4974i	0.0182549	+	0.0316185i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1035.00	−	1792.67i	−0.645445	−	1.11794i	−0.984198	−	0.177069i	$-0.943338\pi$
$137$	−1035.00	−	1792.67i	−0.645445	−	1.11794i	0.338753	−	0.940875i	$-0.389995\pi$
$138$		0			0
$139$	962.000	−	1666.23i	0.587020	−	1.01675i	−0.407600	−	0.913160i	$-0.633634\pi$
$139$	962.000	−	1666.23i	0.587020	−	1.01675i	0.994620	−	0.103588i	$-0.0330323\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−120.000			−0.0701742
$144$		0			0
$145$	1050.00			0.601364
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1455.00	+	2520.13i	−0.799988	+	1.38562i	0.119635	+	0.992818i	$0.461828\pi$
$149$	−1455.00	+	2520.13i	−0.799988	+	1.38562i	−0.919623	+	0.392802i	$0.871506\pi$
$150$		0			0
$151$	−88.0000	−	152.420i	−0.0474261	−	0.0821444i	0.841338	−	0.540510i	$-0.181769\pi$
$151$	−88.0000	−	152.420i	−0.0474261	−	0.0821444i	−0.888764	+	0.458365i	$0.848435\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.0000	+	17.3205i	0.00518206	+	0.00897559i
$156$		0			0
$157$	−1174.00	+	2033.43i	−0.596786	+	1.03366i	0.396506	+	0.918032i	$0.370223\pi$
$157$	−1174.00	+	2033.43i	−0.596786	+	1.03366i	−0.993292	+	0.115632i	$0.963111\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	240.000			0.117482
$162$		0			0
$163$	−1996.00			−0.959134			−0.479567	−	0.877505i	$-0.659206\pi$
$163$	−1996.00			−0.959134			−0.479567	+	0.877505i	$0.659206\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1560.00	+	2702.00i	−0.722853	+	1.25202i	0.236999	+	0.971510i	$0.423836\pi$
$167$	−1560.00	+	2702.00i	−0.722853	+	1.25202i	−0.959852	+	0.280508i	$0.909497\pi$
$168$		0			0
$169$	1090.50	+	1888.80i	0.496359	+	0.859718i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−885.000	−	1532.86i	−0.388932	−	0.673651i	0.603374	−	0.797458i	$-0.293823\pi$
$173$	−885.000	−	1532.86i	−0.388932	−	0.673651i	−0.992306	+	0.123808i	$0.960489\pi$
$174$		0			0
$175$	−25.0000	+	43.3013i	−0.0107990	+	0.0187044i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2130.00			−0.889406			−0.444703	−	0.895678i	$-0.646691\pi$
$179$	−2130.00			−0.889406			−0.444703	+	0.895678i	$0.646691\pi$
$180$		0			0
$181$	−1654.00			−0.679231			−0.339616	−	0.940564i	$-0.610297\pi$
$181$	−1654.00			−0.679231			−0.339616	+	0.940564i	$0.610297\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−500.000	+	866.025i	−0.198707	+	0.344170i
$186$		0			0
$187$	−1350.00	−	2338.27i	−0.527924	−	0.914391i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−870.000	−	1506.88i	−0.329586	−	0.570860i	0.652843	−	0.757493i	$-0.273576\pi$
$191$	−870.000	−	1506.88i	−0.329586	−	0.570860i	−0.982430	+	0.186633i	$0.940243\pi$
$192$		0			0
$193$	−43.0000	+	74.4782i	−0.0160373	+	0.0277775i	−0.873933	−	0.486047i	$-0.838438\pi$
$193$	−43.0000	+	74.4782i	−0.0160373	+	0.0277775i	0.857895	+	0.513824i	$0.171772\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2490.00			−0.900534			−0.450267	−	0.892894i	$-0.648671\pi$
$197$	−2490.00			−0.900534			−0.450267	+	0.892894i	$0.648671\pi$
$198$		0			0
$199$	−832.000			−0.296376			−0.148188	−	0.988959i	$-0.547344\pi$
$199$	−832.000			−0.296376			−0.148188	+	0.988959i	$0.547344\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−210.000	+	363.731i	−0.0726065	+	0.125758i
$204$		0			0
$205$	−600.000	−	1039.23i	−0.204419	−	0.354063i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	420.000	+	727.461i	0.139005	+	0.240763i
$210$		0			0
$211$	−1042.00	+	1804.80i	−0.339973	+	0.588850i	−0.984427	−	0.175793i	$-0.943751\pi$
$211$	−1042.00	+	1804.80i	−0.339973	+	0.588850i	0.644455	+	0.764643i	$0.277085\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−680.000			−0.215701
$216$		0			0
$217$	−8.00000			−0.00250265
$218$		0			0
$219$		0			0
$220$		0			0
$221$	180.000	−	311.769i	0.0547878	−	0.0948953i
$222$		0			0
$223$	587.000	+	1016.71i	0.176271	+	0.305310i	0.940600	−	0.339516i	$-0.110263\pi$
$223$	587.000	+	1016.71i	0.176271	+	0.305310i	−0.764329	+	0.644826i	$0.776930\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1560.00	+	2702.00i	0.456127	+	0.790035i	0.998752	−	0.0499397i	$-0.0159029\pi$
$227$	1560.00	+	2702.00i	0.456127	+	0.790035i	−0.542625	+	0.839975i	$0.682570\pi$
$228$		0			0
$229$	29.0000	−	50.2295i	0.00836845	−	0.0144946i	−0.861811	−	0.507230i	$-0.830670\pi$
$229$	29.0000	−	50.2295i	0.00836845	−	0.0144946i	0.870179	+	0.492735i	$0.164003\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5910.00			−1.66170			−0.830852	−	0.556494i	$-0.812146\pi$
$233$	−5910.00			−1.66170			−0.830852	+	0.556494i	$0.812146\pi$
$234$		0			0
$235$	−600.000			−0.166552
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1650.00	+	2857.88i	−0.446567	+	0.773478i	−0.998160	−	0.0606362i	$-0.980687\pi$
$239$	−1650.00	+	2857.88i	−0.446567	+	0.773478i	0.551592	+	0.834114i	$0.314020\pi$
$240$		0			0
$241$	1493.00	+	2585.95i	0.399056	+	0.691186i	0.993610	−	0.112870i	$-0.0360044\pi$
$241$	1493.00	+	2585.95i	0.399056	+	0.691186i	−0.594553	+	0.804056i	$0.702671\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	847.500	+	1467.91i	0.220999	+	0.382782i
$246$		0			0
$247$	−56.0000	+	96.9948i	−0.0144259	+	0.0249864i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6630.00			−1.66726			−0.833629	−	0.552324i	$-0.813741\pi$
$251$	−6630.00			−1.66726			−0.833629	+	0.552324i	$0.813741\pi$
$252$		0			0
$253$	3600.00			0.894585
$254$		0			0
$255$		0			0
$256$		0			0
$257$	765.000	−	1325.02i	0.185679	−	0.321605i	−0.758126	−	0.652108i	$-0.773885\pi$
$257$	765.000	−	1325.02i	0.185679	−	0.321605i	0.943805	+	0.330503i	$0.107218\pi$
$258$		0			0
$259$	−200.000	−	346.410i	−0.0479822	−	0.0831076i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1320.00	−	2286.31i	−0.309486	−	0.536045i	0.668764	−	0.743474i	$-0.266823\pi$
$263$	−1320.00	−	2286.31i	−0.309486	−	0.536045i	−0.978250	+	0.207430i	$0.933490\pi$
$264$		0			0
$265$	75.0000	−	129.904i	0.0173857	−	0.0301129i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7350.00			−1.66594			−0.832969	−	0.553319i	$-0.813361\pi$
$269$	−7350.00			−1.66594			−0.832969	+	0.553319i	$0.813361\pi$
$270$		0			0
$271$	3512.00			0.787228			0.393614	−	0.919276i	$-0.371225\pi$
$271$	3512.00			0.787228			0.393614	+	0.919276i	$0.371225\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−375.000	+	649.519i	−0.0822304	+	0.142427i
$276$		0			0
$277$	2684.00	+	4648.82i	0.582187	+	1.00838i	0.995220	+	0.0976619i	$0.0311364\pi$
$277$	2684.00	+	4648.82i	0.582187	+	1.00838i	−0.413032	+	0.910716i	$0.635530\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1530.00	+	2650.04i	0.324812	+	0.562591i	0.981474	−	0.191594i	$-0.0613657\pi$
$281$	1530.00	+	2650.04i	0.324812	+	0.562591i	−0.656662	+	0.754185i	$0.728032\pi$
$282$		0			0
$283$	2522.00	−	4368.23i	0.529743	−	0.917542i	−0.469655	−	0.882850i	$-0.655622\pi$
$283$	2522.00	−	4368.23i	0.529743	−	0.917542i	0.999398	−	0.0346921i	$-0.0110450\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	480.000			0.0987230
$288$		0			0
$289$	3187.00			0.648687
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1005.00	−	1740.71i	0.200385	−	0.347077i	−0.748268	−	0.663397i	$-0.769114\pi$
$293$	1005.00	−	1740.71i	0.200385	−	0.347077i	0.948652	+	0.316320i	$0.102447\pi$
$294$		0			0
$295$	1125.00	+	1948.56i	0.222034	+	0.384574i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	240.000	+	415.692i	0.0464199	+	0.0804017i
$300$		0			0
$301$	136.000	−	235.559i	0.0260429	−	0.0451076i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−830.000			−0.155822
$306$		0			0
$307$	−2752.00			−0.511612			−0.255806	−	0.966728i	$-0.582341\pi$
$307$	−2752.00			−0.511612			−0.255806	+	0.966728i	$0.582341\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4770.00	+	8261.88i	−0.869717	+	1.50639i	−0.00743035	+	0.999972i	$0.502365\pi$
$311$	−4770.00	+	8261.88i	−0.869717	+	1.50639i	−0.862286	+	0.506421i	$0.830968\pi$
$312$		0			0
$313$	−4627.00	−	8014.20i	−0.835570	−	1.44725i	−0.893565	−	0.448933i	$-0.851804\pi$
$313$	−4627.00	−	8014.20i	−0.835570	−	1.44725i	0.0579950	−	0.998317i	$-0.481529\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−75.0000	−	129.904i	−0.0132884	−	0.0230162i	0.859305	−	0.511464i	$-0.170897\pi$
$317$	−75.0000	−	129.904i	−0.0132884	−	0.0230162i	−0.872593	+	0.488448i	$0.837563\pi$
$318$		0			0
$319$	−3150.00	+	5455.96i	−0.552872	+	0.957602i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2520.00			−0.434107
$324$		0			0
$325$	−100.000			−0.0170677
$326$		0			0
$327$		0			0
$328$		0			0
$329$	120.000	−	207.846i	0.0201089	−	0.0348296i
$330$		0			0
$331$	−946.000	−	1638.52i	−0.157090	−	0.272088i	0.776728	−	0.629836i	$-0.216878\pi$
$331$	−946.000	−	1638.52i	−0.157090	−	0.272088i	−0.933818	+	0.357748i	$0.883545\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2270.00	−	3931.76i	−0.370219	−	0.641238i
$336$		0			0
$337$	3689.00	−	6389.54i	0.596299	−	1.03282i	−0.397064	−	0.917791i	$-0.629971\pi$
$337$	3689.00	−	6389.54i	0.596299	−	1.03282i	0.993362	−	0.115028i	$-0.0366959\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−120.000			−0.0190568
$342$		0			0
$343$	−1364.00			−0.214720
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3360.00	+	5819.69i	−0.519811	+	0.900338i	0.479924	+	0.877310i	$0.340664\pi$
$347$	−3360.00	+	5819.69i	−0.519811	+	0.900338i	−0.999735	+	0.0230283i	$0.992669\pi$
$348$		0			0
$349$	−2593.00	−	4491.21i	−0.397708	−	0.688851i	0.595735	−	0.803181i	$-0.296861\pi$
$349$	−2593.00	−	4491.21i	−0.397708	−	0.688851i	−0.993443	+	0.114331i	$0.963528\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1665.00	−	2883.86i	−0.251045	−	0.434823i	0.712769	−	0.701399i	$-0.247441\pi$
$353$	−1665.00	−	2883.86i	−0.251045	−	0.434823i	−0.963814	+	0.266576i	$0.914108\pi$
$354$		0			0
$355$	2550.00	−	4416.73i	0.381239	−	0.660326i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9000.00			1.32312			0.661562	−	0.749890i	$-0.269894\pi$
$359$	9000.00			1.32312			0.661562	+	0.749890i	$0.269894\pi$
$360$		0			0
$361$	−6075.00			−0.885698
$362$		0			0
$363$		0			0
$364$		0			0
$365$	625.000	−	1082.53i	0.0896274	−	0.155239i
$366$		0			0
$367$	4379.00	+	7584.65i	0.622839	+	1.07879i	0.988954	+	0.148219i	$0.0473542\pi$
$367$	4379.00	+	7584.65i	0.622839	+	1.07879i	−0.366115	+	0.930569i	$0.619312\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	30.0000	+	51.9615i	0.00419817	+	0.00727145i
$372$		0			0
$373$	−2362.00	+	4091.10i	−0.327881	+	0.567907i	−0.982091	−	0.188406i	$-0.939668\pi$
$373$	−2362.00	+	4091.10i	−0.327881	+	0.567907i	0.654210	+	0.756313i	$0.273001\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−840.000			−0.114754
$378$		0			0
$379$	7292.00			0.988298			0.494149	−	0.869377i	$-0.335480\pi$
$379$	7292.00			0.988298			0.494149	+	0.869377i	$0.335480\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7260.00	+	12574.7i	−0.968587	+	1.67764i	−0.268933	+	0.963159i	$0.586671\pi$
$383$	−7260.00	+	12574.7i	−0.968587	+	1.67764i	−0.699653	+	0.714482i	$0.746662\pi$
$384$		0			0
$385$	−150.000	−	259.808i	−0.0198564	−	0.0343923i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3555.00	−	6157.44i	−0.463356	−	0.802557i	0.535769	−	0.844364i	$-0.320022\pi$
$389$	−3555.00	−	6157.44i	−0.463356	−	0.802557i	−0.999126	+	0.0418076i	$0.986688\pi$
$390$		0			0
$391$	−5400.00	+	9353.07i	−0.698439	+	1.20973i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4580.00			−0.583405
$396$		0			0
$397$	−11488.0			−1.45231			−0.726154	−	0.687532i	$-0.758694\pi$
$397$	−11488.0			−1.45231			−0.726154	+	0.687532i	$0.758694\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−390.000	+	675.500i	−0.0485678	+	0.0841218i	−0.889287	−	0.457349i	$-0.848799\pi$
$401$	−390.000	+	675.500i	−0.0485678	+	0.0841218i	0.840720	+	0.541471i	$0.182132\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.000988855	−	0.00171275i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3000.00	−	5196.15i	−0.365367	−	0.632835i
$408$		0			0
$409$	−2701.00	+	4678.27i	−0.326542	+	0.565588i	−0.981823	−	0.189797i	$-0.939217\pi$
$409$	−2701.00	+	4678.27i	−0.326542	+	0.565588i	0.655281	+	0.755385i	$0.272550\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−900.000			−0.107230
$414$		0			0
$415$	−5700.00			−0.674222
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1095.00	−	1896.60i	0.127671	−	0.221133i	−0.795103	−	0.606475i	$-0.792583\pi$
$419$	1095.00	−	1896.60i	0.127671	−	0.221133i	0.922774	+	0.385342i	$0.125916\pi$
$420$		0			0
$421$	3581.00	+	6202.47i	0.414554	+	0.718029i	0.995382	−	0.0959980i	$-0.0306042\pi$
$421$	3581.00	+	6202.47i	0.414554	+	0.718029i	−0.580827	+	0.814027i	$0.697271\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1125.00	−	1948.56i	−0.128401	−	0.222397i
$426$		0			0
$427$	166.000	−	287.520i	0.0188134	−	0.0325857i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9360.00			1.04607			0.523034	−	0.852312i	$-0.324800\pi$
$431$	9360.00			1.04607			0.523034	+	0.852312i	$0.324800\pi$
$432$		0			0
$433$	12806.0			1.42129			0.710643	−	0.703552i	$-0.248404\pi$
$433$	12806.0			1.42129			0.710643	+	0.703552i	$0.248404\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1680.00	−	2909.85i	0.183902	−	0.318528i
$438$		0			0
$439$	−5644.00	−	9775.69i	−0.613607	−	1.06280i	−0.990627	−	0.136593i	$-0.956385\pi$
$439$	−5644.00	−	9775.69i	−0.613607	−	1.06280i	0.377020	−	0.926205i	$-0.376949\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4260.00	+	7378.54i	0.456882	+	0.791343i	0.998794	−	0.0490923i	$-0.0156328\pi$
$443$	4260.00	+	7378.54i	0.456882	+	0.791343i	−0.541912	+	0.840435i	$0.682300\pi$
$444$		0			0
$445$	1050.00	−	1818.65i	0.111853	−	0.193736i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1260.00			−0.132434			−0.0662172	−	0.997805i	$-0.521093\pi$
$449$	−1260.00			−0.132434			−0.0662172	+	0.997805i	$0.521093\pi$
$450$		0			0
$451$	7200.00			0.751740
$452$		0			0
$453$		0			0
$454$		0			0
$455$	20.0000	−	34.6410i	0.00206069	−	0.00356922i
$456$		0			0
$457$	6875.00	+	11907.8i	0.703718	+	1.21887i	0.967152	+	0.254197i	$0.0818113\pi$
$457$	6875.00	+	11907.8i	0.703718	+	1.21887i	−0.263435	+	0.964677i	$0.584855\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1605.00	+	2779.94i	0.162152	+	0.280856i	0.935640	−	0.352955i	$-0.114823\pi$
$461$	1605.00	+	2779.94i	0.162152	+	0.280856i	−0.773488	+	0.633811i	$0.781490\pi$
$462$		0			0
$463$	6425.00	−	11128.4i	0.644914	−	1.11702i	−0.339408	−	0.940639i	$-0.610227\pi$
$463$	6425.00	−	11128.4i	0.644914	−	1.11702i	0.984321	−	0.176384i	$-0.0564401\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8220.00			−0.814510			−0.407255	−	0.913314i	$-0.633514\pi$
$467$	−8220.00			−0.814510			−0.407255	+	0.913314i	$0.633514\pi$
$468$		0			0
$469$	1816.00			0.178795
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2040.00	−	3533.38i	0.198307	−	0.343478i
$474$		0			0
$475$	350.000	+	606.218i	0.0338086	+	0.0585583i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3510.00	+	6079.50i	0.334814	+	0.579915i	0.983449	−	0.181184i	$-0.0579931\pi$
$479$	3510.00	+	6079.50i	0.334814	+	0.579915i	−0.648635	+	0.761100i	$0.724660\pi$
$480$		0			0
$481$	400.000	−	692.820i	0.0379177	−	0.0656754i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7690.00			0.719969
$486$		0			0
$487$	−8122.00			−0.755735			−0.377868	−	0.925860i	$-0.623343\pi$
$487$	−8122.00			−0.755735			−0.377868	+	0.925860i	$0.623343\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6735.00	−	11665.4i	0.619035	−	1.07220i	−0.370627	−	0.928782i	$-0.620857\pi$
$491$	6735.00	−	11665.4i	0.619035	−	1.07220i	0.989662	−	0.143419i	$-0.0458095\pi$
$492$		0			0
$493$	−9450.00	−	16367.9i	−0.863299	−	1.49528i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1020.00	+	1766.69i	0.0920589	+	0.159451i
$498$		0			0
$499$	−1234.00	+	2137.35i	−0.110704	+	0.191745i	−0.916054	−	0.401054i	$-0.868644\pi$
$499$	−1234.00	+	2137.35i	−0.110704	+	0.191745i	0.805350	+	0.592799i	$0.201977\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4440.00			−0.393578			−0.196789	−	0.980446i	$-0.563051\pi$
$503$	−4440.00			−0.393578			−0.196789	+	0.980446i	$0.563051\pi$
$504$		0			0
$505$	2250.00			0.198265
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5595.00	−	9690.82i	0.487218	−	0.843887i	−0.512674	−	0.858583i	$-0.671345\pi$
$509$	5595.00	−	9690.82i	0.487218	−	0.843887i	0.999892	+	0.0146969i	$0.00467834\pi$
$510$		0			0
$511$	250.000	+	433.013i	0.0216426	+	0.0374860i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2875.00	+	4979.65i	0.245995	+	0.426077i
$516$		0			0
$517$	1800.00	−	3117.69i	0.153122	−	0.265215i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4020.00			−0.338041			−0.169021	−	0.985613i	$-0.554060\pi$
$521$	−4020.00			−0.338041			−0.169021	+	0.985613i	$0.554060\pi$
$522$		0			0
$523$	−9076.00			−0.758826			−0.379413	−	0.925228i	$-0.623874\pi$
$523$	−9076.00			−0.758826			−0.379413	+	0.925228i	$0.623874\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	180.000	−	311.769i	0.0148784	−	0.0257702i
$528$		0			0
$529$	−1116.50	−	1933.83i	−0.0917646	−	0.158941i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	480.000	+	831.384i	0.0390077	+	0.0675633i
$534$		0			0
$535$	4050.00	−	7014.81i	0.327284	−	0.566872i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10170.0			−0.812714
$540$		0			0
$541$	−7486.00			−0.594914			−0.297457	−	0.954735i	$-0.596138\pi$
$541$	−7486.00			−0.594914			−0.297457	+	0.954735i	$0.596138\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4255.00	−	7369.88i	0.334430	−	0.579249i
$546$		0			0
$547$	−3700.00	−	6408.59i	−0.289215	−	0.500935i	0.684408	−	0.729100i	$-0.260061\pi$
$547$	−3700.00	−	6408.59i	−0.289215	−	0.500935i	−0.973623	+	0.228165i	$0.926728\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2940.00	+	5092.23i	0.227311	+	0.393714i
$552$		0			0
$553$	916.000	−	1586.56i	0.0704381	−	0.122002i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11490.0			0.874052			0.437026	−	0.899449i	$-0.356032\pi$
$557$	11490.0			0.874052			0.437026	+	0.899449i	$0.356032\pi$
$558$		0			0
$559$	544.000			0.0411606
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9660.00	−	16731.6i	0.723127	−	1.25249i	−0.236613	−	0.971604i	$-0.576037\pi$
$563$	9660.00	−	16731.6i	0.723127	−	1.25249i	0.959740	−	0.280889i	$-0.0906292\pi$
$564$		0			0
$565$	−3375.00	−	5845.67i	−0.251305	−	0.435273i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4170.00	−	7222.65i	−0.307233	−	0.532143i	0.670523	−	0.741889i	$-0.266070\pi$
$569$	−4170.00	−	7222.65i	−0.307233	−	0.532143i	−0.977756	+	0.209746i	$0.932736\pi$
$570$		0			0
$571$	−10522.0	+	18224.6i	−0.771159	+	1.33569i	0.165769	+	0.986165i	$0.446990\pi$
$571$	−10522.0	+	18224.6i	−0.771159	+	1.33569i	−0.936928	+	0.349523i	$0.886344\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3000.00			0.217580
$576$		0			0
$577$	1418.00			0.102309			0.0511543	−	0.998691i	$-0.483710\pi$
$577$	1418.00			0.102309			0.0511543	+	0.998691i	$0.483710\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1140.00	−	1974.54i	0.0814030	−	0.140994i
$582$		0			0
$583$	450.000	+	779.423i	0.0319676	+	0.0553695i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11010.0	+	19069.9i	0.774159	+	1.34088i	0.935266	+	0.353946i	$0.115160\pi$
$587$	11010.0	+	19069.9i	0.774159	+	1.34088i	−0.161107	+	0.986937i	$0.551506\pi$
$588$		0			0
$589$	−56.0000	+	96.9948i	−0.00391755	+	0.00678540i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	25230.0			1.74717			0.873585	−	0.486671i	$-0.161789\pi$
$593$	25230.0			1.74717			0.873585	+	0.486671i	$0.161789\pi$
$594$		0			0
$595$	900.000			0.0620108
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4140.00	+	7170.69i	−0.282397	+	0.489126i	−0.971975	−	0.235086i	$-0.924463\pi$
$599$	−4140.00	+	7170.69i	−0.282397	+	0.489126i	0.689578	+	0.724212i	$0.257796\pi$
$600$		0			0
$601$	9437.00	+	16345.4i	0.640505	+	1.10939i	0.985320	+	0.170716i	$0.0546081\pi$
$601$	9437.00	+	16345.4i	0.640505	+	1.10939i	−0.344816	+	0.938670i	$0.612059\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1077.50	+	1866.28i	0.0724076	+	0.125414i
$606$		0			0
$607$	−5275.00	+	9136.57i	−0.352728	+	0.610942i	−0.986726	−	0.162392i	$-0.948079\pi$
$607$	−5275.00	+	9136.57i	−0.352728	+	0.610942i	0.633999	+	0.773334i	$0.281412\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	480.000			0.0317819
$612$		0			0
$613$	11000.0			0.724773			0.362386	−	0.932028i	$-0.381962\pi$
$613$	11000.0			0.724773			0.362386	+	0.932028i	$0.381962\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5655.00	−	9794.75i	0.368982	−	0.639095i	−0.620425	−	0.784266i	$-0.713040\pi$
$617$	5655.00	−	9794.75i	0.368982	−	0.639095i	0.989407	+	0.145171i	$0.0463732\pi$
$618$		0			0
$619$	8786.00	+	15217.8i	0.570499	+	0.988134i	0.996515	+	0.0834180i	$0.0265837\pi$
$619$	8786.00	+	15217.8i	0.570499	+	0.988134i	−0.426015	+	0.904716i	$0.640083\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	420.000	+	727.461i	0.0270095	+	0.0467819i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18000.0			1.14103
$630$		0			0
$631$	1604.00			0.101195			0.0505976	−	0.998719i	$-0.483887\pi$
$631$	1604.00			0.101195			0.0505976	+	0.998719i	$0.483887\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6125.00	+	10608.8i	−0.382777	+	0.662989i
$636$		0			0
$637$	−678.000	−	1174.33i	−0.0421716	−	0.0730434i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15660.0	−	27123.9i	−0.964950	−	1.67134i	−0.709750	−	0.704454i	$-0.751192\pi$
$641$	−15660.0	−	27123.9i	−0.964950	−	1.67134i	−0.255200	−	0.966888i	$-0.582141\pi$
$642$		0			0
$643$	15650.0	−	27106.6i	0.959838	−	1.66249i	0.236951	−	0.971522i	$-0.423852\pi$
$643$	15650.0	−	27106.6i	0.959838	−	1.66249i	0.722887	−	0.690966i	$-0.242815\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10920.0			0.663539			0.331769	−	0.943361i	$-0.392354\pi$
$647$	10920.0			0.663539			0.331769	+	0.943361i	$0.392354\pi$
$648$		0			0
$649$	−13500.0			−0.816520
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1605.00	−	2779.94i	0.0961845	−	0.166597i	−0.813918	−	0.580980i	$-0.802669\pi$
$653$	1605.00	−	2779.94i	0.0961845	−	0.166597i	0.910102	+	0.414384i	$0.136003\pi$
$654$		0			0
$655$	−1725.00	−	2987.79i	−0.102903	−	0.178233i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5955.00	+	10314.4i	0.352009	+	0.609697i	0.986601	−	0.163150i	$-0.0521653\pi$
$659$	5955.00	+	10314.4i	0.352009	+	0.609697i	−0.634592	+	0.772847i	$0.718832\pi$
$660$		0			0
$661$	1691.00	−	2928.90i	0.0995042	−	0.172346i	−0.811975	−	0.583692i	$-0.801608\pi$
$661$	1691.00	−	2928.90i	0.0995042	−	0.172346i	0.911480	+	0.411345i	$0.134941\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−280.000			−0.0163277
$666$		0			0
$667$	25200.0			1.46289
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2490.00	−	4312.81i	0.143257	−	0.248128i
$672$		0			0
$673$	−7975.00	−	13813.1i	−0.456781	−	0.791168i	0.542008	−	0.840374i	$-0.317664\pi$
$673$	−7975.00	−	13813.1i	−0.456781	−	0.791168i	−0.998789	+	0.0492056i	$0.984331\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16095.0	−	27877.4i	−0.913709	−	1.58259i	−0.808780	−	0.588111i	$-0.799872\pi$
$677$	−16095.0	−	27877.4i	−0.913709	−	1.58259i	−0.104929	−	0.994480i	$-0.533462\pi$
$678$		0			0
$679$	−1538.00	+	2663.89i	−0.0869264	+	0.150561i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	22140.0			1.24036			0.620178	−	0.784461i	$-0.287060\pi$
$683$	22140.0			1.24036			0.620178	+	0.784461i	$0.287060\pi$
$684$		0			0
$685$	10350.0			0.577304
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−60.0000	+	103.923i	−0.00331759	+	0.00574623i
$690$		0			0
$691$	3086.00	+	5345.11i	0.169894	+	0.294266i	0.938383	−	0.345598i	$-0.112324\pi$
$691$	3086.00	+	5345.11i	0.169894	+	0.294266i	−0.768488	+	0.639864i	$0.778991\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4810.00	+	8331.16i	0.262523	+	0.454704i
$696$		0			0
$697$	−10800.0	+	18706.1i	−0.586914	+	1.01657i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	19170.0			1.03287			0.516434	−	0.856327i	$-0.327259\pi$
$701$	19170.0			1.03287			0.516434	+	0.856327i	$0.327259\pi$
$702$		0			0
$703$	−5600.00			−0.300438
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−450.000	+	779.423i	−0.0239378	+	0.0414614i
$708$		0			0
$709$	10949.0	+	18964.2i	0.579969	+	1.00454i	0.995482	+	0.0949491i	$0.0302688\pi$
$709$	10949.0	+	18964.2i	0.579969	+	1.00454i	−0.415513	+	0.909587i	$0.636398\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	240.000	+	415.692i	0.0126060	+	0.0218342i
$714$		0			0
$715$	300.000	−	519.615i	0.0156914	−	0.0271783i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16680.0			0.865173			0.432586	−	0.901593i	$-0.357601\pi$
$719$	16680.0			0.865173			0.432586	+	0.901593i	$0.357601\pi$
$720$		0			0
$721$	−2300.00			−0.118802
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2625.00	+	4546.63i	−0.134469	+	0.232907i
$726$		0			0
$727$	−3259.00	−	5644.75i	−0.166258	−	0.287967i	0.770843	−	0.637025i	$-0.219835\pi$
$727$	−3259.00	−	5644.75i	−0.166258	−	0.287967i	−0.937101	+	0.349057i	$0.886502\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6120.00	+	10600.2i	0.309653	+	0.536335i
$732$		0			0
$733$	11600.0	−	20091.8i	0.584524	−	1.01242i	−0.410411	−	0.911901i	$-0.634615\pi$
$733$	11600.0	−	20091.8i	0.584524	−	1.01242i	0.994935	−	0.100524i	$-0.0320519\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	27240.0			1.36146
$738$		0			0
$739$	−16324.0			−0.812568			−0.406284	−	0.913747i	$-0.633176\pi$
$739$	−16324.0			−0.812568			−0.406284	+	0.913747i	$0.633176\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	60.0000	−	103.923i	0.00296257	−	0.00513131i	−0.864540	−	0.502563i	$-0.832390\pi$
$743$	60.0000	−	103.923i	0.00296257	−	0.00513131i	0.867503	+	0.497432i	$0.165724\pi$
$744$		0			0
$745$	−7275.00	−	12600.7i	−0.357766	−	0.619668i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1620.00	+	2805.92i	0.0790301	+	0.136884i
$750$		0			0
$751$	−15274.0	+	26455.3i	−0.742152	+	1.28545i	0.209362	+	0.977838i	$0.432861\pi$
$751$	−15274.0	+	26455.3i	−0.742152	+	1.28545i	−0.951514	+	0.307607i	$0.900472\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	880.000			0.0424192
$756$		0			0
$757$	16952.0			0.813911			0.406956	−	0.913448i	$-0.366590\pi$
$757$	16952.0			0.813911			0.406956	+	0.913448i	$0.366590\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10110.0	−	17511.0i	0.481586	−	0.834132i	−0.518190	−	0.855265i	$-0.673394\pi$
$761$	10110.0	−	17511.0i	0.481586	−	0.834132i	0.999777	+	0.0211333i	$0.00672744\pi$
$762$		0			0
$763$	1702.00	+	2947.95i	0.0807556	+	0.139873i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−900.000	−	1558.85i	−0.0423691	−	0.0733855i
$768$		0			0
$769$	10361.0	−	17945.8i	0.485861	−	0.841536i	−0.514007	−	0.857786i	$-0.671839\pi$
$769$	10361.0	−	17945.8i	0.485861	−	0.841536i	0.999868	+	0.0162499i	$0.00517274\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4350.00			0.202404			0.101202	−	0.994866i	$-0.467731\pi$
$773$	4350.00			0.202404			0.101202	+	0.994866i	$0.467731\pi$
$774$		0			0
$775$	−100.000			−0.00463498
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3360.00	−	5819.69i	0.154537	−	0.267666i
$780$		0			0
$781$	15300.0	+	26500.4i	0.700995	+	1.21416i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5870.00	−	10167.1i	−0.266891	−	0.462268i
$786$		0			0
$787$	−20986.0	+	36348.8i	−0.950534	+	1.64637i	−0.206261	+	0.978497i	$0.566130\pi$
$787$	−20986.0	+	36348.8i	−0.950534	+	1.64637i	−0.744273	+	0.667876i	$0.767204\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2700.00			0.121367
$792$		0			0
$793$	664.000			0.0297343
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19755.0	−	34216.7i	0.877990	−	1.52072i	0.0244468	−	0.999701i	$-0.492218\pi$
$797$	19755.0	−	34216.7i	0.877990	−	1.52072i	0.853543	−	0.521022i	$-0.174449\pi$
$798$		0			0
$799$	5400.00	+	9353.07i	0.239097	+	0.414128i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3750.00	+	6495.19i	0.164800	+	0.285442i
$804$		0			0
$805$	−600.000	+	1039.23i	−0.0262698	+	0.0455007i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	16680.0			0.724892			0.362446	−	0.932005i	$-0.381942\pi$
$809$	16680.0			0.724892			0.362446	+	0.932005i	$0.381942\pi$
$810$		0			0
$811$	−15484.0			−0.670428			−0.335214	−	0.942142i	$-0.608809\pi$
$811$	−15484.0			−0.670428			−0.335214	+	0.942142i	$0.608809\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4990.00	−	8642.93i	0.214469	−	0.371471i
$816$		0			0
$817$	−1904.00	−	3297.82i	−0.0815331	−	0.141219i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2085.00	−	3611.33i	−0.0886322	−	0.153515i	0.818301	−	0.574790i	$-0.194916\pi$
$821$	−2085.00	−	3611.33i	−0.0886322	−	0.153515i	−0.906933	+	0.421275i	$0.861583\pi$
$822$		0			0
$823$	15113.0	−	26176.5i	0.640105	−	1.10869i	−0.345304	−	0.938491i	$-0.612224\pi$
$823$	15113.0	−	26176.5i	0.640105	−	1.10869i	0.985409	−	0.170203i	$-0.0544423\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14760.0			−0.620623			−0.310312	−	0.950635i	$-0.600433\pi$
$827$	−14760.0			−0.620623			−0.310312	+	0.950635i	$0.600433\pi$
$828$		0			0
$829$	−9934.00			−0.416191			−0.208095	−	0.978109i	$-0.566726\pi$
$829$	−9934.00			−0.416191			−0.208095	+	0.978109i	$0.566726\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	15255.0	−	26422.4i	0.634519	−	1.09902i
$834$		0			0
$835$	−7800.00	−	13510.0i	−0.323270	−	0.559919i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11760.0	+	20368.9i	0.483910	+	0.838156i	0.999829	−	0.0184808i	$-0.00588296\pi$
$839$	11760.0	+	20368.9i	0.483910	+	0.838156i	−0.515919	+	0.856637i	$0.672550\pi$
$840$		0			0
$841$	−9855.50	+	17070.2i	−0.404096	+	0.699915i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10905.0			−0.443957
$846$		0			0
$847$	−862.000			−0.0349689
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−12000.0	+	20784.6i	−0.483378	+	0.837235i
$852$		0			0
$853$	−14908.0	−	25821.4i	−0.598406	−	1.03647i	−0.993057	−	0.117638i	$-0.962468\pi$
$853$	−14908.0	−	25821.4i	−0.598406	−	1.03647i	0.394651	−	0.918831i	$-0.370866\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17715.0	+	30683.3i	0.706106	+	1.22301i	0.966291	+	0.257453i	$0.0828832\pi$
$857$	17715.0	+	30683.3i	0.706106	+	1.22301i	−0.260185	+	0.965559i	$0.583784\pi$
$858$		0			0
$859$	18098.0	−	31346.7i	0.718854	−	1.24509i	−0.242600	−	0.970126i	$-0.578000\pi$
$859$	18098.0	−	31346.7i	0.718854	−	1.24509i	0.961454	−	0.274966i	$-0.0886665\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	480.000			0.0189332			0.00946662	−	0.999955i	$-0.496987\pi$
$863$	480.000			0.0189332			0.00946662	+	0.999955i	$0.496987\pi$
$864$		0			0
$865$	8850.00			0.347872
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13740.0	−	23798.4i	0.536361	−	0.929004i
$870$		0			0
$871$	1816.00	+	3145.40i	0.0706462	+	0.122363i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−125.000	−	216.506i	−0.00482945	−	0.00836486i
$876$		0			0
$877$	−14266.0	+	24709.4i	−0.549291	+	0.951401i	0.449032	+	0.893516i	$0.351769\pi$
$877$	−14266.0	+	24709.4i	−0.549291	+	0.951401i	−0.998323	+	0.0578849i	$0.981564\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−20340.0			−0.777834			−0.388917	−	0.921273i	$-0.627151\pi$
$881$	−20340.0			−0.777834			−0.388917	+	0.921273i	$0.627151\pi$
$882$		0			0
$883$	−10756.0			−0.409930			−0.204965	−	0.978769i	$-0.565708\pi$
$883$	−10756.0			−0.409930			−0.204965	+	0.978769i	$0.565708\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−300.000	+	519.615i	−0.0113563	+	0.0196696i	−0.871648	−	0.490133i	$-0.836948\pi$
$887$	−300.000	+	519.615i	−0.0113563	+	0.0196696i	0.860291	+	0.509803i	$0.170282\pi$
$888$		0			0
$889$	−2450.00	−	4243.52i	−0.0924301	−	0.160094i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1680.00	−	2909.85i	−0.0629553	−	0.109042i
$894$		0			0
$895$	5325.00	−	9223.17i	0.198877	−	0.344465i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−840.000			−0.0311630
$900$		0			0
$901$	−2700.00			−0.0998336
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4135.00	−	7162.03i	0.151881	−	0.263065i
$906$		0			0
$907$	−12700.0	−	21997.0i	−0.464936	−	0.805292i	0.534263	−	0.845318i	$-0.320589\pi$
$907$	−12700.0	−	21997.0i	−0.464936	−	0.805292i	−0.999199	+	0.0400262i	$0.987256\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	18120.0	+	31384.8i	0.658993	+	1.14141i	0.980877	+	0.194630i	$0.0623505\pi$
$911$	18120.0	+	31384.8i	0.658993	+	1.14141i	−0.321884	+	0.946779i	$0.604316\pi$
$912$		0			0
$913$	17100.0	−	29618.1i	0.619855	−	1.07362i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1380.00			0.0496964
$918$		0			0
$919$	6572.00			0.235898			0.117949	−	0.993020i	$-0.462368\pi$
$919$	6572.00			0.235898			0.117949	+	0.993020i	$0.462368\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2040.00	+	3533.38i	−0.0727491	+	0.126005i
$924$		0			0
$925$	−2500.00	−	4330.13i	−0.0888643	−	0.153918i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1170.00	−	2026.50i	−0.0413202	−	0.0715687i	0.844626	−	0.535357i	$-0.179823\pi$
$929$	−1170.00	−	2026.50i	−0.0413202	−	0.0715687i	−0.885946	+	0.463789i	$0.846490\pi$
$930$		0			0
$931$	−4746.00	+	8220.31i	−0.167072	+	0.289377i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13500.0			0.472190
$936$		0			0
$937$	2522.00			0.0879297			0.0439649	−	0.999033i	$-0.486001\pi$
$937$	2522.00			0.0879297			0.0439649	+	0.999033i	$0.486001\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26385.0	−	45700.2i	0.914056	−	1.58319i	0.105778	−	0.994390i	$-0.466267\pi$
$941$	26385.0	−	45700.2i	0.914056	−	1.58319i	0.808278	−	0.588801i	$-0.200400\pi$
$942$		0			0
$943$	−14400.0	−	24941.5i	−0.497273	−	0.861302i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14100.0	−	24421.9i	−0.483832	−	0.838021i	0.515996	−	0.856591i	$-0.327422\pi$
$947$	−14100.0	−	24421.9i	−0.483832	−	0.838021i	−0.999828	+	0.0185702i	$0.994089\pi$
$948$		0			0
$949$	−500.000	+	866.025i	−0.0171029	+	0.0296232i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−15570.0			−0.529236			−0.264618	−	0.964353i	$-0.585246\pi$
$953$	−15570.0			−0.529236			−0.264618	+	0.964353i	$0.585246\pi$
$954$		0			0
$955$	8700.00			0.294791
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2070.00	+	3585.35i	−0.0697015	+	0.120727i
$960$		0			0
$961$	14887.5	+	25785.9i	0.499731	+	0.865560i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−215.000	−	372.391i	−0.00717212	−	0.0124225i
$966$		0			0
$967$	4175.00	−	7231.31i	0.138841	−	0.240479i	−0.788217	−	0.615397i	$-0.788996\pi$
$967$	4175.00	−	7231.31i	0.138841	−	0.240479i	0.927058	+	0.374918i	$0.122329\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	43650.0			1.44263			0.721316	−	0.692606i	$-0.243538\pi$
$971$	43650.0			1.44263			0.721316	+	0.692606i	$0.243538\pi$
$972$		0			0
$973$	−3848.00			−0.126784
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9405.00	+	16289.9i	−0.307976	+	0.533430i	−0.977919	−	0.208982i	$-0.932985\pi$
$977$	−9405.00	+	16289.9i	−0.307976	+	0.533430i	0.669943	+	0.742412i	$0.266318\pi$
$978$		0			0
$979$	6300.00	+	10911.9i	0.205668	+	0.356227i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12660.0	+	21927.8i	0.410774	+	0.711482i	0.994975	−	0.100127i	$-0.0319250\pi$
$983$	12660.0	+	21927.8i	0.410774	+	0.711482i	−0.584200	+	0.811610i	$0.698592\pi$
$984$		0			0
$985$	6225.00	−	10782.0i	0.201365	−	0.348775i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16320.0			−0.524718
$990$		0			0
$991$	−6736.00			−0.215919			−0.107960	−	0.994155i	$-0.534432\pi$
$991$	−6736.00			−0.215919			−0.107960	+	0.994155i	$0.534432\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2080.00	−	3602.67i	0.0662718	−	0.114786i
$996$		0			0
$997$	10250.0	+	17753.5i	0.325598	+	0.563951i	0.981633	−	0.190778i	$-0.0611012\pi$
$997$	10250.0	+	17753.5i	0.325598	+	0.563951i	−0.656036	+	0.754730i	$0.727768\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.4.i.c.1081.1		2
3.2	odd	2		1620.4.i.i.1081.1		2
9.2	odd	6		1620.4.i.i.541.1		2
9.4	even	3		180.4.a.e.1.1	yes	1
9.5	odd	6		180.4.a.b.1.1	✓	1
9.7	even	3	inner	1620.4.i.c.541.1		2
36.23	even	6		720.4.a.h.1.1		1
36.31	odd	6		720.4.a.w.1.1		1
45.4	even	6		900.4.a.j.1.1		1
45.13	odd	12		900.4.d.i.649.1		2
45.14	odd	6		900.4.a.i.1.1		1
45.22	odd	12		900.4.d.i.649.2		2
45.23	even	12		900.4.d.d.649.1		2
45.32	even	12		900.4.d.d.649.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.4.a.b.1.1	✓	1	9.5	odd	6
180.4.a.e.1.1	yes	1	9.4	even	3
720.4.a.h.1.1		1	36.23	even	6
720.4.a.w.1.1		1	36.31	odd	6
900.4.a.i.1.1		1	45.14	odd	6
900.4.a.j.1.1		1	45.4	even	6
900.4.d.d.649.1		2	45.23	even	12
900.4.d.d.649.2		2	45.32	even	12
900.4.d.i.649.1		2	45.13	odd	12
900.4.d.i.649.2		2	45.22	odd	12
1620.4.i.c.541.1		2	9.7	even	3	inner
1620.4.i.c.1081.1		2	1.1	even	1	trivial
1620.4.i.i.541.1		2	9.2	odd	6
1620.4.i.i.1081.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1620.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.50000 + 4.33013i) q^{5} +(-1.00000 - 1.73205i) q^{7} +O(q^{10})\)	\(q+(-2.50000 + 4.33013i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-15.0000 - 25.9808i) q^{11} +(2.00000 - 3.46410i) q^{13} +90.0000 q^{17} -28.0000 q^{19} +(-60.0000 + 103.923i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(-105.000 - 181.865i) q^{29} +(2.00000 - 3.46410i) q^{31} +10.0000 q^{35} +200.000 q^{37} +(-120.000 + 207.846i) q^{41} +(68.0000 + 117.779i) q^{43} +(60.0000 + 103.923i) q^{47} +(169.500 - 293.583i) q^{49} -30.0000 q^{53} +150.000 q^{55} +(225.000 - 389.711i) q^{59} +(83.0000 + 143.760i) q^{61} +(10.0000 + 17.3205i) q^{65} +(-454.000 + 786.351i) q^{67} -1020.00 q^{71} -250.000 q^{73} +(-30.0000 + 51.9615i) q^{77} +(458.000 + 793.279i) q^{79} +(570.000 + 987.269i) q^{83} +(-225.000 + 389.711i) q^{85} -420.000 q^{89} -8.00000 q^{91} +(70.0000 - 121.244i) q^{95} +(-769.000 - 1331.95i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 5 q^{5} - 2 q^{7}+O(q^{10}) \) 2 * q - 5 * q^5 - 2 * q^7	\( 2 q - 5 q^{5} - 2 q^{7} - 30 q^{11} + 4 q^{13} + 180 q^{17} - 56 q^{19} - 120 q^{23} - 25 q^{25} - 210 q^{29} + 4 q^{31} + 20 q^{35} + 400 q^{37} - 240 q^{41} + 136 q^{43} + 120 q^{47} + 339 q^{49} - 60 q^{53} + 300 q^{55} + 450 q^{59} + 166 q^{61} + 20 q^{65} - 908 q^{67} - 2040 q^{71} - 500 q^{73} - 60 q^{77} + 916 q^{79} + 1140 q^{83} - 450 q^{85} - 840 q^{89} - 16 q^{91} + 140 q^{95} - 1538 q^{97}+O(q^{100}) \) 2 * q - 5 * q^5 - 2 * q^7 - 30 * q^11 + 4 * q^13 + 180 * q^17 - 56 * q^19 - 120 * q^23 - 25 * q^25 - 210 * q^29 + 4 * q^31 + 20 * q^35 + 400 * q^37 - 240 * q^41 + 136 * q^43 + 120 * q^47 + 339 * q^49 - 60 * q^53 + 300 * q^55 + 450 * q^59 + 166 * q^61 + 20 * q^65 - 908 * q^67 - 2040 * q^71 - 500 * q^73 - 60 * q^77 + 916 * q^79 + 1140 * q^83 - 450 * q^85 - 840 * q^89 - 16 * q^91 + 140 * q^95 - 1538 * q^97

Introduction

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