LMFDB - Embedded newform 3750.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.a (trivial)

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:	yes
Analytic conductor:	$29.9439007580$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.90211$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.273457 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.273457 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.79360 q^{11} +1.00000 q^{12} -1.73311 q^{13} -0.273457 q^{14} +1.00000 q^{16} -1.89149 q^{17} -1.00000 q^{18} -3.01062 q^{19} +0.273457 q^{21} +4.79360 q^{22} +4.64584 q^{23} -1.00000 q^{24} +1.73311 q^{26} +1.00000 q^{27} +0.273457 q^{28} +9.08715 q^{29} +3.83390 q^{31} -1.00000 q^{32} -4.79360 q^{33} +1.89149 q^{34} +1.00000 q^{36} +9.00947 q^{37} +3.01062 q^{38} -1.73311 q^{39} -7.58064 q^{41} -0.273457 q^{42} +2.88963 q^{43} -4.79360 q^{44} -4.64584 q^{46} +1.18806 q^{47} +1.00000 q^{48} -6.92522 q^{49} -1.89149 q^{51} -1.73311 q^{52} -11.6150 q^{53} -1.00000 q^{54} -0.273457 q^{56} -3.01062 q^{57} -9.08715 q^{58} -14.2895 q^{59} -5.15131 q^{61} -3.83390 q^{62} +0.273457 q^{63} +1.00000 q^{64} +4.79360 q^{66} +6.29000 q^{67} -1.89149 q^{68} +4.64584 q^{69} -1.40217 q^{71} -1.00000 q^{72} +1.78112 q^{73} -9.00947 q^{74} -3.01062 q^{76} -1.31085 q^{77} +1.73311 q^{78} -16.0593 q^{79} +1.00000 q^{81} +7.58064 q^{82} -15.1392 q^{83} +0.273457 q^{84} -2.88963 q^{86} +9.08715 q^{87} +4.79360 q^{88} -14.8273 q^{89} -0.473931 q^{91} +4.64584 q^{92} +3.83390 q^{93} -1.18806 q^{94} -1.00000 q^{96} -5.88597 q^{97} +6.92522 q^{98} -4.79360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} - 10 q^{11} + 4 q^{12} - 2 q^{13} - 4 q^{14} + 4 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 4 q^{21} + 10 q^{22} - 4 q^{24} + 2 q^{26} + 4 q^{27} + 4 q^{28} - 14 q^{29} - 18 q^{31} - 4 q^{32} - 10 q^{33} + 6 q^{34} + 4 q^{36} - 2 q^{37} + 6 q^{38} - 2 q^{39} - 14 q^{41} - 4 q^{42} + 14 q^{43} - 10 q^{44} - 10 q^{47} + 4 q^{48} - 4 q^{49} - 6 q^{51} - 2 q^{52} - 14 q^{53} - 4 q^{54} - 4 q^{56} - 6 q^{57} + 14 q^{58} - 20 q^{59} + 18 q^{62} + 4 q^{63} + 4 q^{64} + 10 q^{66} + 14 q^{67} - 6 q^{68} - 30 q^{71} - 4 q^{72} + 8 q^{73} + 2 q^{74} - 6 q^{76} - 20 q^{77} + 2 q^{78} - 28 q^{79} + 4 q^{81} + 14 q^{82} - 12 q^{83} + 4 q^{84} - 14 q^{86} - 14 q^{87} + 10 q^{88} - 28 q^{89} - 22 q^{91} - 18 q^{93} + 10 q^{94} - 4 q^{96} + 8 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 - 10 * q^11 + 4 * q^12 - 2 * q^13 - 4 * q^14 + 4 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 + 4 * q^21 + 10 * q^22 - 4 * q^24 + 2 * q^26 + 4 * q^27 + 4 * q^28 - 14 * q^29 - 18 * q^31 - 4 * q^32 - 10 * q^33 + 6 * q^34 + 4 * q^36 - 2 * q^37 + 6 * q^38 - 2 * q^39 - 14 * q^41 - 4 * q^42 + 14 * q^43 - 10 * q^44 - 10 * q^47 + 4 * q^48 - 4 * q^49 - 6 * q^51 - 2 * q^52 - 14 * q^53 - 4 * q^54 - 4 * q^56 - 6 * q^57 + 14 * q^58 - 20 * q^59 + 18 * q^62 + 4 * q^63 + 4 * q^64 + 10 * q^66 + 14 * q^67 - 6 * q^68 - 30 * q^71 - 4 * q^72 + 8 * q^73 + 2 * q^74 - 6 * q^76 - 20 * q^77 + 2 * q^78 - 28 * q^79 + 4 * q^81 + 14 * q^82 - 12 * q^83 + 4 * q^84 - 14 * q^86 - 14 * q^87 + 10 * q^88 - 28 * q^89 - 22 * q^91 - 18 * q^93 + 10 * q^94 - 4 * q^96 + 8 * q^97 + 4 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	0.273457	0.103357	0.0516786	−	0.998664i	$-0.483543\pi$
$7$	0.273457	0.103357	0.0516786	+	0.998664i	$0.483543\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.79360	−1.44533	−0.722663	−	0.691200i	$-0.757082\pi$
$11$	−4.79360	−1.44533	−0.722663	+	0.691200i	$0.757082\pi$
$12$	1.00000	0.288675
$13$	−1.73311	−0.480677	−0.240339	−	0.970689i	$-0.577259\pi$
$13$	−1.73311	−0.480677	−0.240339	+	0.970689i	$0.577259\pi$
$14$	−0.273457	−0.0730846
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.89149	−0.458754	−0.229377	−	0.973338i	$-0.573669\pi$
$17$	−1.89149	−0.458754	−0.229377	+	0.973338i	$0.573669\pi$
$18$	−1.00000	−0.235702
$19$	−3.01062	−0.690684	−0.345342	−	0.938477i	$-0.612237\pi$
$19$	−3.01062	−0.690684	−0.345342	+	0.938477i	$0.612237\pi$
$20$	0	0
$21$	0.273457	0.0596733
$22$	4.79360	1.02200
$23$	4.64584	0.968725	0.484362	−	0.874867i	$-0.339052\pi$
$23$	4.64584	0.968725	0.484362	+	0.874867i	$0.339052\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	1.73311	0.339890
$27$	1.00000	0.192450
$28$	0.273457	0.0516786
$29$	9.08715	1.68744	0.843721	−	0.536782i	$-0.180360\pi$
$29$	9.08715	1.68744	0.843721	+	0.536782i	$0.180360\pi$
$30$	0	0
$31$	3.83390	0.688589	0.344294	−	0.938862i	$-0.388118\pi$
$31$	3.83390	0.688589	0.344294	+	0.938862i	$0.388118\pi$
$32$	−1.00000	−0.176777
$33$	−4.79360	−0.834459
$34$	1.89149	0.324388
$35$	0	0
$36$	1.00000	0.166667
$37$	9.00947	1.48115	0.740574	−	0.671975i	$-0.234554\pi$
$37$	9.00947	1.48115	0.740574	+	0.671975i	$0.234554\pi$
$38$	3.01062	0.488387
$39$	−1.73311	−0.277519
$40$	0	0
$41$	−7.58064	−1.18390	−0.591949	−	0.805976i	$-0.701641\pi$
$41$	−7.58064	−1.18390	−0.591949	+	0.805976i	$0.701641\pi$
$42$	−0.273457	−0.0421954
$43$	2.88963	0.440664	0.220332	−	0.975425i	$-0.429286\pi$
$43$	2.88963	0.440664	0.220332	+	0.975425i	$0.429286\pi$
$44$	−4.79360	−0.722663
$45$	0	0
$46$	−4.64584	−0.684992
$47$	1.18806	0.173296	0.0866480	−	0.996239i	$-0.472384\pi$
$47$	1.18806	0.173296	0.0866480	+	0.996239i	$0.472384\pi$
$48$	1.00000	0.144338
$49$	−6.92522	−0.989317
$50$	0	0
$51$	−1.89149	−0.264862
$52$	−1.73311	−0.240339
$53$	−11.6150	−1.59545	−0.797723	−	0.603025i	$-0.793962\pi$
$53$	−11.6150	−1.59545	−0.797723	+	0.603025i	$0.793962\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−0.273457	−0.0365423
$57$	−3.01062	−0.398767
$58$	−9.08715	−1.19320
$59$	−14.2895	−1.86033	−0.930167	−	0.367138i	$-0.880338\pi$
$59$	−14.2895	−1.86033	−0.930167	+	0.367138i	$0.880338\pi$
$60$	0	0
$61$	−5.15131	−0.659558	−0.329779	−	0.944058i	$-0.606974\pi$
$61$	−5.15131	−0.659558	−0.329779	+	0.944058i	$0.606974\pi$
$62$	−3.83390	−0.486906
$63$	0.273457	0.0344524
$64$	1.00000	0.125000
$65$	0	0
$66$	4.79360	0.590052
$67$	6.29000	0.768446	0.384223	−	0.923240i	$-0.374469\pi$
$67$	6.29000	0.768446	0.384223	+	0.923240i	$0.374469\pi$
$68$	−1.89149	−0.229377
$69$	4.64584	0.559294
$70$	0	0
$71$	−1.40217	−0.166407	−0.0832034	−	0.996533i	$-0.526515\pi$
$71$	−1.40217	−0.166407	−0.0832034	+	0.996533i	$0.526515\pi$
$72$	−1.00000	−0.117851
$73$	1.78112	0.208464	0.104232	−	0.994553i	$-0.466762\pi$
$73$	1.78112	0.208464	0.104232	+	0.994553i	$0.466762\pi$
$74$	−9.00947	−1.04733
$75$	0	0
$76$	−3.01062	−0.345342
$77$	−1.31085	−0.149385
$78$	1.73311	0.196236
$79$	−16.0593	−1.80682	−0.903409	−	0.428780i	$-0.858943\pi$
$79$	−16.0593	−1.80682	−0.903409	+	0.428780i	$0.858943\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	7.58064	0.837142
$83$	−15.1392	−1.66175	−0.830873	−	0.556463i	$-0.812158\pi$
$83$	−15.1392	−1.66175	−0.830873	+	0.556463i	$0.812158\pi$
$84$	0.273457	0.0298367
$85$	0	0
$86$	−2.88963	−0.311596
$87$	9.08715	0.974245
$88$	4.79360	0.511000
$89$	−14.8273	−1.57169	−0.785847	−	0.618421i	$-0.787773\pi$
$89$	−14.8273	−1.57169	−0.785847	+	0.618421i	$0.787773\pi$
$90$	0	0
$91$	−0.473931	−0.0496815
$92$	4.64584	0.484362
$93$	3.83390	0.397557
$94$	−1.18806	−0.122539
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−5.88597	−0.597629	−0.298815	−	0.954311i	$-0.596591\pi$
$97$	−5.88597	−0.597629	−0.298815	+	0.954311i	$0.596591\pi$
$98$	6.92522	0.699553
$99$	−4.79360	−0.481775
$100$	0	0
$101$	4.83576	0.481176	0.240588	−	0.970627i	$-0.422660\pi$
$101$	4.83576	0.481176	0.240588	+	0.970627i	$0.422660\pi$
$102$	1.89149	0.187286
$103$	−0.0729839	−0.00719132	−0.00359566	−	0.999994i	$-0.501145\pi$
$103$	−0.0729839	−0.00719132	−0.00359566	+	0.999994i	$0.501145\pi$
$104$	1.73311	0.169945
$105$	0	0
$106$	11.6150	1.12815
$107$	5.84754	0.565303	0.282651	−	0.959223i	$-0.408786\pi$
$107$	5.84754	0.565303	0.282651	+	0.959223i	$0.408786\pi$
$108$	1.00000	0.0962250
$109$	−9.80609	−0.939253	−0.469627	−	0.882865i	$-0.655611\pi$
$109$	−9.80609	−0.939253	−0.469627	+	0.882865i	$0.655611\pi$
$110$	0	0
$111$	9.00947	0.855141
$112$	0.273457	0.0258393
$113$	−17.3291	−1.63019	−0.815094	−	0.579328i	$-0.803315\pi$
$113$	−17.3291	−1.63019	−0.815094	+	0.579328i	$0.803315\pi$
$114$	3.01062	0.281971
$115$	0	0
$116$	9.08715	0.843721
$117$	−1.73311	−0.160226
$118$	14.2895	1.31545
$119$	−0.517242	−0.0474155
$120$	0	0
$121$	11.9786	1.08897
$122$	5.15131	0.466378
$123$	−7.58064	−0.683524
$124$	3.83390	0.344294
$125$	0	0
$126$	−0.273457	−0.0243615
$127$	18.3677	1.62987	0.814934	−	0.579553i	$-0.196773\pi$
$127$	18.3677	1.62987	0.814934	+	0.579553i	$0.196773\pi$
$128$	−1.00000	−0.0883883
$129$	2.88963	0.254417
$130$	0	0
$131$	−7.57357	−0.661706	−0.330853	−	0.943682i	$-0.607336\pi$
$131$	−7.57357	−0.661706	−0.330853	+	0.943682i	$0.607336\pi$
$132$	−4.79360	−0.417230
$133$	−0.823277	−0.0713872
$134$	−6.29000	−0.543373
$135$	0	0
$136$	1.89149	0.162194
$137$	−19.6095	−1.67535	−0.837676	−	0.546168i	$-0.816086\pi$
$137$	−19.6095	−1.67535	−0.837676	+	0.546168i	$0.816086\pi$
$138$	−4.64584	−0.395480
$139$	9.56514	0.811305	0.405652	−	0.914027i	$-0.367044\pi$
$139$	9.56514	0.811305	0.405652	+	0.914027i	$0.367044\pi$
$140$	0	0
$141$	1.18806	0.100052
$142$	1.40217	0.117667
$143$	8.30783	0.694736
$144$	1.00000	0.0833333
$145$	0	0
$146$	−1.78112	−0.147406
$147$	−6.92522	−0.571183
$148$	9.00947	0.740574
$149$	−4.64398	−0.380449	−0.190225	−	0.981741i	$-0.560922\pi$
$149$	−4.64398	−0.380449	−0.190225	+	0.981741i	$0.560922\pi$
$150$	0	0
$151$	−16.7881	−1.36619	−0.683097	−	0.730327i	$-0.739368\pi$
$151$	−16.7881	−1.36619	−0.683097	+	0.730327i	$0.739368\pi$
$152$	3.01062	0.244194
$153$	−1.89149	−0.152918
$154$	1.31085	0.105631
$155$	0	0
$156$	−1.73311	−0.138760
$157$	5.57763	0.445143	0.222572	−	0.974916i	$-0.428555\pi$
$157$	5.57763	0.445143	0.222572	+	0.974916i	$0.428555\pi$
$158$	16.0593	1.27761
$159$	−11.6150	−0.921131
$160$	0	0
$161$	1.27044	0.100125
$162$	−1.00000	−0.0785674
$163$	−18.3753	−1.43926	−0.719632	−	0.694356i	$-0.755689\pi$
$163$	−18.3753	−1.43926	−0.719632	+	0.694356i	$0.755689\pi$
$164$	−7.58064	−0.591949
$165$	0	0
$166$	15.1392	1.17503
$167$	8.94427	0.692129	0.346064	−	0.938211i	$-0.387518\pi$
$167$	8.94427	0.692129	0.346064	+	0.938211i	$0.387518\pi$
$168$	−0.273457	−0.0210977
$169$	−9.99634	−0.768949
$170$	0	0
$171$	−3.01062	−0.230228
$172$	2.88963	0.220332
$173$	11.9151	0.905890	0.452945	−	0.891538i	$-0.350373\pi$
$173$	11.9151	0.905890	0.452945	+	0.891538i	$0.350373\pi$
$174$	−9.08715	−0.688895
$175$	0	0
$176$	−4.79360	−0.361332
$177$	−14.2895	−1.07406
$178$	14.8273	1.11136
$179$	−3.75621	−0.280753	−0.140376	−	0.990098i	$-0.544831\pi$
$179$	−3.75621	−0.280753	−0.140376	+	0.990098i	$0.544831\pi$
$180$	0	0
$181$	−18.0626	−1.34258	−0.671290	−	0.741194i	$-0.734260\pi$
$181$	−18.0626	−1.34258	−0.671290	+	0.741194i	$0.734260\pi$
$182$	0.473931	0.0351301
$183$	−5.15131	−0.380796
$184$	−4.64584	−0.342496
$185$	0	0
$186$	−3.83390	−0.281115
$187$	9.06706	0.663049
$188$	1.18806	0.0866480
$189$	0.273457	0.0198911
$190$	0	0
$191$	−16.6007	−1.20119	−0.600594	−	0.799555i	$-0.705069\pi$
$191$	−16.6007	−1.20119	−0.600594	+	0.799555i	$0.705069\pi$
$192$	1.00000	0.0721688
$193$	3.84858	0.277027	0.138513	−	0.990361i	$-0.455768\pi$
$193$	3.84858	0.277027	0.138513	+	0.990361i	$0.455768\pi$
$194$	5.88597	0.422588
$195$	0	0
$196$	−6.92522	−0.494659
$197$	10.7432	0.765423	0.382711	−	0.923868i	$-0.374990\pi$
$197$	10.7432	0.765423	0.382711	+	0.923868i	$0.374990\pi$
$198$	4.79360	0.340667
$199$	2.49808	0.177084	0.0885421	−	0.996072i	$-0.471779\pi$
$199$	2.49808	0.177084	0.0885421	+	0.996072i	$0.471779\pi$
$200$	0	0
$201$	6.29000	0.443662
$202$	−4.83576	−0.340243
$203$	2.48495	0.174409
$204$	−1.89149	−0.132431
$205$	0	0
$206$	0.0729839	0.00508503
$207$	4.64584	0.322908
$208$	−1.73311	−0.120169
$209$	14.4317	0.998264
$210$	0	0
$211$	24.2741	1.67109	0.835547	−	0.549418i	$-0.185151\pi$
$211$	24.2741	1.67109	0.835547	+	0.549418i	$0.185151\pi$
$212$	−11.6150	−0.797723
$213$	−1.40217	−0.0960751
$214$	−5.84754	−0.399729
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	1.04841	0.0711706
$218$	9.80609	0.664152
$219$	1.78112	0.120357
$220$	0	0
$221$	3.27816	0.220513
$222$	−9.00947	−0.604676
$223$	13.0539	0.874156	0.437078	−	0.899424i	$-0.356013\pi$
$223$	13.0539	0.874156	0.437078	+	0.899424i	$0.356013\pi$
$224$	−0.273457	−0.0182711
$225$	0	0
$226$	17.3291	1.15272
$227$	7.06154	0.468691	0.234345	−	0.972153i	$-0.424705\pi$
$227$	7.06154	0.468691	0.234345	+	0.972153i	$0.424705\pi$
$228$	−3.01062	−0.199383
$229$	−12.5771	−0.831119	−0.415560	−	0.909566i	$-0.636414\pi$
$229$	−12.5771	−0.831119	−0.415560	+	0.909566i	$0.636414\pi$
$230$	0	0
$231$	−1.31085	−0.0862474
$232$	−9.08715	−0.596601
$233$	−9.80527	−0.642364	−0.321182	−	0.947017i	$-0.604080\pi$
$233$	−9.80527	−0.642364	−0.321182	+	0.947017i	$0.604080\pi$
$234$	1.73311	0.113297
$235$	0	0
$236$	−14.2895	−0.930167
$237$	−16.0593	−1.04317
$238$	0.517242	0.0335278
$239$	5.04029	0.326030	0.163015	−	0.986624i	$-0.447878\pi$
$239$	5.04029	0.326030	0.163015	+	0.986624i	$0.447878\pi$
$240$	0	0
$241$	6.84097	0.440666	0.220333	−	0.975425i	$-0.429286\pi$
$241$	6.84097	0.440666	0.220333	+	0.975425i	$0.429286\pi$
$242$	−11.9786	−0.770016
$243$	1.00000	0.0641500
$244$	−5.15131	−0.329779
$245$	0	0
$246$	7.58064	0.483324
$247$	5.21773	0.331996
$248$	−3.83390	−0.243453
$249$	−15.1392	−0.959409
$250$	0	0
$251$	−7.07549	−0.446601	−0.223301	−	0.974750i	$-0.571683\pi$
$251$	−7.07549	−0.446601	−0.223301	+	0.974750i	$0.571683\pi$
$252$	0.273457	0.0172262
$253$	−22.2703	−1.40012
$254$	−18.3677	−1.15249
$255$	0	0
$256$	1.00000	0.0625000
$257$	4.47318	0.279029	0.139515	−	0.990220i	$-0.455446\pi$
$257$	4.47318	0.279029	0.139515	+	0.990220i	$0.455446\pi$
$258$	−2.88963	−0.179900
$259$	2.46371	0.153087
$260$	0	0
$261$	9.08715	0.562481
$262$	7.57357	0.467897
$263$	2.50232	0.154300	0.0771498	−	0.997020i	$-0.475418\pi$
$263$	2.50232	0.154300	0.0771498	+	0.997020i	$0.475418\pi$
$264$	4.79360	0.295026
$265$	0	0
$266$	0.823277	0.0504783
$267$	−14.8273	−0.907418
$268$	6.29000	0.384223
$269$	6.18870	0.377332	0.188666	−	0.982041i	$-0.439584\pi$
$269$	6.18870	0.377332	0.188666	+	0.982041i	$0.439584\pi$
$270$	0	0
$271$	13.1689	0.799953	0.399977	−	0.916525i	$-0.369018\pi$
$271$	13.1689	0.799953	0.399977	+	0.916525i	$0.369018\pi$
$272$	−1.89149	−0.114689
$273$	−0.473931	−0.0286836
$274$	19.6095	1.18465
$275$	0	0
$276$	4.64584	0.279647
$277$	−5.16714	−0.310463	−0.155232	−	0.987878i	$-0.549612\pi$
$277$	−5.16714	−0.310463	−0.155232	+	0.987878i	$0.549612\pi$
$278$	−9.56514	−0.573679
$279$	3.83390	0.229530
$280$	0	0
$281$	−0.0469714	−0.00280208	−0.00140104	−	0.999999i	$-0.500446\pi$
$281$	−0.0469714	−0.00280208	−0.00140104	+	0.999999i	$0.500446\pi$
$282$	−1.18806	−0.0707478
$283$	−21.8712	−1.30011	−0.650053	−	0.759889i	$-0.725253\pi$
$283$	−21.8712	−1.30011	−0.650053	+	0.759889i	$0.725253\pi$
$284$	−1.40217	−0.0832034
$285$	0	0
$286$	−8.30783	−0.491252
$287$	−2.07298	−0.122364
$288$	−1.00000	−0.0589256
$289$	−13.4223	−0.789545
$290$	0	0
$291$	−5.88597	−0.345041
$292$	1.78112	0.104232
$293$	8.35289	0.487981	0.243991	−	0.969778i	$-0.421543\pi$
$293$	8.35289	0.487981	0.243991	+	0.969778i	$0.421543\pi$
$294$	6.92522	0.403887
$295$	0	0
$296$	−9.00947	−0.523665
$297$	−4.79360	−0.278153
$298$	4.64398	0.269018
$299$	−8.05174	−0.465644
$300$	0	0
$301$	0.790190	0.0455458
$302$	16.7881	0.966045
$303$	4.83576	0.277807
$304$	−3.01062	−0.172671
$305$	0	0
$306$	1.89149	0.108129
$307$	−2.28918	−0.130650	−0.0653251	−	0.997864i	$-0.520808\pi$
$307$	−2.28918	−0.130650	−0.0653251	+	0.997864i	$0.520808\pi$
$308$	−1.31085	−0.0746924
$309$	−0.0729839	−0.00415191
$310$	0	0
$311$	25.6673	1.45546	0.727729	−	0.685865i	$-0.240576\pi$
$311$	25.6673	1.45546	0.727729	+	0.685865i	$0.240576\pi$
$312$	1.73311	0.0981179
$313$	30.2110	1.70763	0.853813	−	0.520580i	$-0.174284\pi$
$313$	30.2110	1.70763	0.853813	+	0.520580i	$0.174284\pi$
$314$	−5.57763	−0.314764
$315$	0	0
$316$	−16.0593	−0.903409
$317$	−25.8613	−1.45251	−0.726257	−	0.687424i	$-0.758742\pi$
$317$	−25.8613	−1.45251	−0.726257	+	0.687424i	$0.758742\pi$
$318$	11.6150	0.651338
$319$	−43.5602	−2.43890
$320$	0	0
$321$	5.84754	0.326378
$322$	−1.27044	−0.0707989
$323$	5.69456	0.316854
$324$	1.00000	0.0555556
$325$	0	0
$326$	18.3753	1.01771
$327$	−9.80609	−0.542278
$328$	7.58064	0.418571
$329$	0.324883	0.0179114
$330$	0	0
$331$	14.5094	0.797509	0.398755	−	0.917058i	$-0.369442\pi$
$331$	14.5094	0.797509	0.398755	+	0.917058i	$0.369442\pi$
$332$	−15.1392	−0.830873
$333$	9.00947	0.493716
$334$	−8.94427	−0.489409
$335$	0	0
$336$	0.273457	0.0149183
$337$	11.0676	0.602889	0.301445	−	0.953484i	$-0.402531\pi$
$337$	11.0676	0.602889	0.301445	+	0.953484i	$0.402531\pi$
$338$	9.99634	0.543729
$339$	−17.3291	−0.941190
$340$	0	0
$341$	−18.3782	−0.995235
$342$	3.01062	0.162796
$343$	−3.80796	−0.205610
$344$	−2.88963	−0.155798
$345$	0	0
$346$	−11.9151	−0.640561
$347$	1.01062	0.0542530	0.0271265	−	0.999632i	$-0.491364\pi$
$347$	1.01062	0.0542530	0.0271265	+	0.999632i	$0.491364\pi$
$348$	9.08715	0.487123
$349$	30.4268	1.62871	0.814356	−	0.580366i	$-0.197090\pi$
$349$	30.4268	1.62871	0.814356	+	0.580366i	$0.197090\pi$
$350$	0	0
$351$	−1.73311	−0.0925064
$352$	4.79360	0.255500
$353$	15.6597	0.833481	0.416740	−	0.909026i	$-0.363172\pi$
$353$	15.6597	0.833481	0.416740	+	0.909026i	$0.363172\pi$
$354$	14.2895	0.759478
$355$	0	0
$356$	−14.8273	−0.785847
$357$	−0.517242	−0.0273754
$358$	3.75621	0.198522
$359$	4.37321	0.230809	0.115405	−	0.993319i	$-0.463184\pi$
$359$	4.37321	0.230809	0.115405	+	0.993319i	$0.463184\pi$
$360$	0	0
$361$	−9.93616	−0.522956
$362$	18.0626	0.949348
$363$	11.9786	0.628716
$364$	−0.473931	−0.0248407
$365$	0	0
$366$	5.15131	0.269263
$367$	21.8334	1.13969	0.569847	−	0.821751i	$-0.307003\pi$
$367$	21.8334	1.13969	0.569847	+	0.821751i	$0.307003\pi$
$368$	4.64584	0.242181
$369$	−7.58064	−0.394633
$370$	0	0
$371$	−3.17621	−0.164901
$372$	3.83390	0.198778
$373$	−1.41871	−0.0734582	−0.0367291	−	0.999325i	$-0.511694\pi$
$373$	−1.41871	−0.0734582	−0.0367291	+	0.999325i	$0.511694\pi$
$374$	−9.06706	−0.468847
$375$	0	0
$376$	−1.18806	−0.0612694
$377$	−15.7490	−0.811115
$378$	−0.273457	−0.0140651
$379$	−26.0806	−1.33967	−0.669835	−	0.742510i	$-0.733635\pi$
$379$	−26.0806	−1.33967	−0.669835	+	0.742510i	$0.733635\pi$
$380$	0	0
$381$	18.3677	0.941005
$382$	16.6007	0.849367
$383$	−32.7645	−1.67419	−0.837095	−	0.547058i	$-0.815748\pi$
$383$	−32.7645	−1.67419	−0.837095	+	0.547058i	$0.815748\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−3.84858	−0.195887
$387$	2.88963	0.146888
$388$	−5.88597	−0.298815
$389$	−4.46133	−0.226199	−0.113099	−	0.993584i	$-0.536078\pi$
$389$	−4.46133	−0.226199	−0.113099	+	0.993584i	$0.536078\pi$
$390$	0	0
$391$	−8.78757	−0.444407
$392$	6.92522	0.349776
$393$	−7.57357	−0.382036
$394$	−10.7432	−0.541236
$395$	0	0
$396$	−4.79360	−0.240888
$397$	−2.11727	−0.106262	−0.0531312	−	0.998588i	$-0.516920\pi$
$397$	−2.11727	−0.106262	−0.0531312	+	0.998588i	$0.516920\pi$
$398$	−2.49808	−0.125217
$399$	−0.823277	−0.0412154
$400$	0	0
$401$	−28.6530	−1.43086	−0.715431	−	0.698683i	$-0.753770\pi$
$401$	−28.6530	−1.43086	−0.715431	+	0.698683i	$0.753770\pi$
$402$	−6.29000	−0.313717
$403$	−6.64456	−0.330989
$404$	4.83576	0.240588
$405$	0	0
$406$	−2.48495	−0.123326
$407$	−43.1878	−2.14074
$408$	1.89149	0.0936428
$409$	39.3546	1.94596	0.972979	−	0.230893i	$-0.0741646\pi$
$409$	39.3546	1.94596	0.972979	+	0.230893i	$0.0741646\pi$
$410$	0	0
$411$	−19.6095	−0.967265
$412$	−0.0729839	−0.00359566
$413$	−3.90757	−0.192279
$414$	−4.64584	−0.228331
$415$	0	0
$416$	1.73311	0.0849726
$417$	9.56514	0.468407
$418$	−14.4317	−0.705879
$419$	14.1068	0.689165	0.344582	−	0.938756i	$-0.388021\pi$
$419$	14.1068	0.689165	0.344582	+	0.938756i	$0.388021\pi$
$420$	0	0
$421$	16.3046	0.794636	0.397318	−	0.917681i	$-0.369941\pi$
$421$	16.3046	0.794636	0.397318	+	0.917681i	$0.369941\pi$
$422$	−24.2741	−1.18164
$423$	1.18806	0.0577653
$424$	11.6150	0.564075
$425$	0	0
$426$	1.40217	0.0679353
$427$	−1.40866	−0.0681700
$428$	5.84754	0.282651
$429$	8.30783	0.401106
$430$	0	0
$431$	−1.98217	−0.0954778	−0.0477389	−	0.998860i	$-0.515202\pi$
$431$	−1.98217	−0.0954778	−0.0477389	+	0.998860i	$0.515202\pi$
$432$	1.00000	0.0481125
$433$	−4.48943	−0.215748	−0.107874	−	0.994165i	$-0.534404\pi$
$433$	−4.48943	−0.215748	−0.107874	+	0.994165i	$0.534404\pi$
$434$	−1.04841	−0.0503252
$435$	0	0
$436$	−9.80609	−0.469627
$437$	−13.9869	−0.669083
$438$	−1.78112	−0.0851051
$439$	25.7158	1.22735	0.613674	−	0.789559i	$-0.289691\pi$
$439$	25.7158	1.22735	0.613674	+	0.789559i	$0.289691\pi$
$440$	0	0
$441$	−6.92522	−0.329772
$442$	−3.27816	−0.155926
$443$	−29.1477	−1.38485	−0.692423	−	0.721491i	$-0.743457\pi$
$443$	−29.1477	−1.38485	−0.692423	+	0.721491i	$0.743457\pi$
$444$	9.00947	0.427570
$445$	0	0
$446$	−13.0539	−0.618122
$447$	−4.64398	−0.219653
$448$	0.273457	0.0129197
$449$	−5.14037	−0.242589	−0.121295	−	0.992617i	$-0.538705\pi$
$449$	−5.14037	−0.242589	−0.121295	+	0.992617i	$0.538705\pi$
$450$	0	0
$451$	36.3386	1.71112
$452$	−17.3291	−0.815094
$453$	−16.7881	−0.788773
$454$	−7.06154	−0.331414
$455$	0	0
$456$	3.01062	0.140985
$457$	20.8445	0.975066	0.487533	−	0.873105i	$-0.337897\pi$
$457$	20.8445	0.975066	0.487533	+	0.873105i	$0.337897\pi$
$458$	12.5771	0.587690
$459$	−1.89149	−0.0882873
$460$	0	0
$461$	−4.96989	−0.231471	−0.115735	−	0.993280i	$-0.536922\pi$
$461$	−4.96989	−0.231471	−0.115735	+	0.993280i	$0.536922\pi$
$462$	1.31085	0.0609861
$463$	7.10664	0.330274	0.165137	−	0.986271i	$-0.447193\pi$
$463$	7.10664	0.330274	0.165137	+	0.986271i	$0.447193\pi$
$464$	9.08715	0.421860
$465$	0	0
$466$	9.80527	0.454220
$467$	−30.1821	−1.39666	−0.698331	−	0.715775i	$-0.746074\pi$
$467$	−30.1821	−1.39666	−0.698331	+	0.715775i	$0.746074\pi$
$468$	−1.73311	−0.0801129
$469$	1.72005	0.0794244
$470$	0	0
$471$	5.57763	0.257003
$472$	14.2895	0.657727
$473$	−13.8517	−0.636903
$474$	16.0593	0.737630
$475$	0	0
$476$	−0.517242	−0.0237078
$477$	−11.6150	−0.531815
$478$	−5.04029	−0.230538
$479$	27.8415	1.27211	0.636055	−	0.771643i	$-0.280565\pi$
$479$	27.8415	1.27211	0.636055	+	0.771643i	$0.280565\pi$
$480$	0	0
$481$	−15.6144	−0.711954
$482$	−6.84097	−0.311598
$483$	1.27044	0.0578070
$484$	11.9786	0.544484
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−1.29951	−0.0588866	−0.0294433	−	0.999566i	$-0.509373\pi$
$487$	−1.29951	−0.0588866	−0.0294433	+	0.999566i	$0.509373\pi$
$488$	5.15131	0.233189
$489$	−18.3753	−0.830959
$490$	0	0
$491$	19.1650	0.864905	0.432453	−	0.901657i	$-0.357648\pi$
$491$	19.1650	0.864905	0.432453	+	0.901657i	$0.357648\pi$
$492$	−7.58064	−0.341762
$493$	−17.1883	−0.774121
$494$	−5.21773	−0.234757
$495$	0	0
$496$	3.83390	0.172147
$497$	−0.383434	−0.0171994
$498$	15.1392	0.678405
$499$	6.41339	0.287103	0.143551	−	0.989643i	$-0.454148\pi$
$499$	6.41339	0.287103	0.143551	+	0.989643i	$0.454148\pi$
$500$	0	0
$501$	8.94427	0.399601
$502$	7.07549	0.315795
$503$	35.7696	1.59489	0.797444	−	0.603392i	$-0.206185\pi$
$503$	35.7696	1.59489	0.797444	+	0.603392i	$0.206185\pi$
$504$	−0.273457	−0.0121808
$505$	0	0
$506$	22.2703	0.990037
$507$	−9.99634	−0.443953
$508$	18.3677	0.814934
$509$	12.0587	0.534493	0.267246	−	0.963628i	$-0.413886\pi$
$509$	12.0587	0.534493	0.267246	+	0.963628i	$0.413886\pi$
$510$	0	0
$511$	0.487060	0.0215463
$512$	−1.00000	−0.0441942
$513$	−3.01062	−0.132922
$514$	−4.47318	−0.197303
$515$	0	0
$516$	2.88963	0.127209
$517$	−5.69507	−0.250469
$518$	−2.46371	−0.108249
$519$	11.9151	0.523016
$520$	0	0
$521$	3.51319	0.153915	0.0769577	−	0.997034i	$-0.475479\pi$
$521$	3.51319	0.153915	0.0769577	+	0.997034i	$0.475479\pi$
$522$	−9.08715	−0.397734
$523$	−24.4468	−1.06898	−0.534492	−	0.845174i	$-0.679497\pi$
$523$	−24.4468	−1.06898	−0.534492	+	0.845174i	$0.679497\pi$
$524$	−7.57357	−0.330853
$525$	0	0
$526$	−2.50232	−0.109106
$527$	−7.25179	−0.315893
$528$	−4.79360	−0.208615
$529$	−1.41616	−0.0615720
$530$	0	0
$531$	−14.2895	−0.620111
$532$	−0.823277	−0.0356936
$533$	13.1381	0.569073
$534$	14.8273	0.641641
$535$	0	0
$536$	−6.29000	−0.271687
$537$	−3.75621	−0.162093
$538$	−6.18870	−0.266814
$539$	33.1968	1.42989
$540$	0	0
$541$	−38.7392	−1.66553	−0.832765	−	0.553627i	$-0.813243\pi$
$541$	−38.7392	−1.66553	−0.832765	+	0.553627i	$0.813243\pi$
$542$	−13.1689	−0.565652
$543$	−18.0626	−0.775139
$544$	1.89149	0.0810970
$545$	0	0
$546$	0.473931	0.0202824
$547$	30.3218	1.29646	0.648232	−	0.761443i	$-0.275509\pi$
$547$	30.3218	1.29646	0.648232	+	0.761443i	$0.275509\pi$
$548$	−19.6095	−0.837676
$549$	−5.15131	−0.219853
$550$	0	0
$551$	−27.3580	−1.16549
$552$	−4.64584	−0.197740
$553$	−4.39155	−0.186748
$554$	5.16714	0.219531
$555$	0	0
$556$	9.56514	0.405652
$557$	−25.7254	−1.09002	−0.545010	−	0.838430i	$-0.683474\pi$
$557$	−25.7254	−1.09002	−0.545010	+	0.838430i	$0.683474\pi$
$558$	−3.83390	−0.162302
$559$	−5.00803	−0.211817
$560$	0	0
$561$	9.06706	0.382812
$562$	0.0469714	0.00198137
$563$	−30.6333	−1.29104	−0.645520	−	0.763743i	$-0.723359\pi$
$563$	−30.6333	−1.29104	−0.645520	+	0.763743i	$0.723359\pi$
$564$	1.18806	0.0500262
$565$	0	0
$566$	21.8712	0.919314
$567$	0.273457	0.0114841
$568$	1.40217	0.0588337
$569$	12.4856	0.523423	0.261712	−	0.965146i	$-0.415713\pi$
$569$	12.4856	0.523423	0.261712	+	0.965146i	$0.415713\pi$
$570$	0	0
$571$	−24.3564	−1.01929	−0.509643	−	0.860386i	$-0.670222\pi$
$571$	−24.3564	−1.01929	−0.509643	+	0.860386i	$0.670222\pi$
$572$	8.30783	0.347368
$573$	−16.6007	−0.693506
$574$	2.07298	0.0865247
$575$	0	0
$576$	1.00000	0.0416667
$577$	−3.21252	−0.133739	−0.0668695	−	0.997762i	$-0.521301\pi$
$577$	−3.21252	−0.133739	−0.0668695	+	0.997762i	$0.521301\pi$
$578$	13.4223	0.558292
$579$	3.84858	0.159941
$580$	0	0
$581$	−4.13993	−0.171753
$582$	5.88597	0.243981
$583$	55.6778	2.30594
$584$	−1.78112	−0.0737032
$585$	0	0
$586$	−8.35289	−0.345055
$587$	15.1892	0.626924	0.313462	−	0.949601i	$-0.398511\pi$
$587$	15.1892	0.626924	0.313462	+	0.949601i	$0.398511\pi$
$588$	−6.92522	−0.285591
$589$	−11.5424	−0.475597
$590$	0	0
$591$	10.7432	0.441917
$592$	9.00947	0.370287
$593$	4.96989	0.204089	0.102044	−	0.994780i	$-0.467462\pi$
$593$	4.96989	0.204089	0.102044	+	0.994780i	$0.467462\pi$
$594$	4.79360	0.196684
$595$	0	0
$596$	−4.64398	−0.190225
$597$	2.49808	0.102240
$598$	8.05174	0.329260
$599$	−3.23524	−0.132188	−0.0660942	−	0.997813i	$-0.521054\pi$
$599$	−3.23524	−0.132188	−0.0660942	+	0.997813i	$0.521054\pi$
$600$	0	0
$601$	−8.78152	−0.358205	−0.179103	−	0.983830i	$-0.557319\pi$
$601$	−8.78152	−0.358205	−0.179103	+	0.983830i	$0.557319\pi$
$602$	−0.790190	−0.0322057
$603$	6.29000	0.256149
$604$	−16.7881	−0.683097
$605$	0	0
$606$	−4.83576	−0.196439
$607$	39.5692	1.60606	0.803031	−	0.595937i	$-0.203219\pi$
$607$	39.5692	1.60606	0.803031	+	0.595937i	$0.203219\pi$
$608$	3.01062	0.122097
$609$	2.48495	0.100695
$610$	0	0
$611$	−2.05903	−0.0832994
$612$	−1.89149	−0.0764590
$613$	−46.8849	−1.89366	−0.946831	−	0.321730i	$-0.895736\pi$
$613$	−46.8849	−1.89366	−0.946831	+	0.321730i	$0.895736\pi$
$614$	2.28918	0.0923836
$615$	0	0
$616$	1.31085	0.0528155
$617$	14.1520	0.569739	0.284869	−	0.958566i	$-0.408050\pi$
$617$	14.1520	0.569739	0.284869	+	0.958566i	$0.408050\pi$
$618$	0.0729839	0.00293584
$619$	−6.54669	−0.263134	−0.131567	−	0.991307i	$-0.542001\pi$
$619$	−6.54669	−0.263134	−0.131567	+	0.991307i	$0.542001\pi$
$620$	0	0
$621$	4.64584	0.186431
$622$	−25.6673	−1.02916
$623$	−4.05465	−0.162446
$624$	−1.73311	−0.0693798
$625$	0	0
$626$	−30.2110	−1.20747
$627$	14.4317	0.576348
$628$	5.57763	0.222572
$629$	−17.0413	−0.679482
$630$	0	0
$631$	6.04884	0.240800	0.120400	−	0.992725i	$-0.461582\pi$
$631$	6.04884	0.240800	0.120400	+	0.992725i	$0.461582\pi$
$632$	16.0593	0.638806
$633$	24.2741	0.964807
$634$	25.8613	1.02708
$635$	0	0
$636$	−11.6150	−0.460565
$637$	12.0021	0.475542
$638$	43.5602	1.72457
$639$	−1.40217	−0.0554690
$640$	0	0
$641$	32.2843	1.27515	0.637576	−	0.770388i	$-0.279937\pi$
$641$	32.2843	1.27515	0.637576	+	0.770388i	$0.279937\pi$
$642$	−5.84754	−0.230784
$643$	−12.1187	−0.477914	−0.238957	−	0.971030i	$-0.576806\pi$
$643$	−12.1187	−0.477914	−0.238957	+	0.971030i	$0.576806\pi$
$644$	1.27044	0.0500624
$645$	0	0
$646$	−5.69456	−0.224050
$647$	−20.2287	−0.795271	−0.397635	−	0.917543i	$-0.630169\pi$
$647$	−20.2287	−0.795271	−0.397635	+	0.917543i	$0.630169\pi$
$648$	−1.00000	−0.0392837
$649$	68.4982	2.68879
$650$	0	0
$651$	1.04841	0.0410904
$652$	−18.3753	−0.719632
$653$	−33.3838	−1.30641	−0.653204	−	0.757182i	$-0.726576\pi$
$653$	−33.3838	−1.30641	−0.653204	+	0.757182i	$0.726576\pi$
$654$	9.80609	0.383448
$655$	0	0
$656$	−7.58064	−0.295974
$657$	1.78112	0.0694880
$658$	−0.324883	−0.0126653
$659$	−30.3942	−1.18399	−0.591995	−	0.805941i	$-0.701660\pi$
$659$	−30.3942	−1.18399	−0.591995	+	0.805941i	$0.701660\pi$
$660$	0	0
$661$	24.9370	0.969935	0.484968	−	0.874532i	$-0.338831\pi$
$661$	24.9370	0.969935	0.484968	+	0.874532i	$0.338831\pi$
$662$	−14.5094	−0.563924
$663$	3.27816	0.127313
$664$	15.1392	0.587516
$665$	0	0
$666$	−9.00947	−0.349110
$667$	42.2175	1.63467
$668$	8.94427	0.346064
$669$	13.0539	0.504694
$670$	0	0
$671$	24.6933	0.953276
$672$	−0.273457	−0.0105489
$673$	−46.0697	−1.77586	−0.887928	−	0.459983i	$-0.847855\pi$
$673$	−46.0697	−1.77586	−0.887928	+	0.459983i	$0.847855\pi$
$674$	−11.0676	−0.426307
$675$	0	0
$676$	−9.99634	−0.384475
$677$	28.5921	1.09888	0.549442	−	0.835532i	$-0.314840\pi$
$677$	28.5921	1.09888	0.549442	+	0.835532i	$0.314840\pi$
$678$	17.3291	0.665522
$679$	−1.60956	−0.0617693
$680$	0	0
$681$	7.06154	0.270599
$682$	18.3782	0.703737
$683$	8.92741	0.341598	0.170799	−	0.985306i	$-0.445365\pi$
$683$	8.92741	0.341598	0.170799	+	0.985306i	$0.445365\pi$
$684$	−3.01062	−0.115114
$685$	0	0
$686$	3.80796	0.145388
$687$	−12.5771	−0.479847
$688$	2.88963	0.110166
$689$	20.1301	0.766894
$690$	0	0
$691$	−1.31278	−0.0499406	−0.0249703	−	0.999688i	$-0.507949\pi$
$691$	−1.31278	−0.0499406	−0.0249703	+	0.999688i	$0.507949\pi$
$692$	11.9151	0.452945
$693$	−1.31085	−0.0497950
$694$	−1.01062	−0.0383627
$695$	0	0
$696$	−9.08715	−0.344448
$697$	14.3387	0.543118
$698$	−30.4268	−1.15167
$699$	−9.80527	−0.370869
$700$	0	0
$701$	22.5267	0.850822	0.425411	−	0.905000i	$-0.360130\pi$
$701$	22.5267	0.850822	0.425411	+	0.905000i	$0.360130\pi$
$702$	1.73311	0.0654119
$703$	−27.1241	−1.02300
$704$	−4.79360	−0.180666
$705$	0	0
$706$	−15.6597	−0.589360
$707$	1.32238	0.0497331
$708$	−14.2895	−0.537032
$709$	−6.89619	−0.258992	−0.129496	−	0.991580i	$-0.541336\pi$
$709$	−6.89619	−0.258992	−0.129496	+	0.991580i	$0.541336\pi$
$710$	0	0
$711$	−16.0593	−0.602272
$712$	14.8273	0.555678
$713$	17.8117	0.667053
$714$	0.517242	0.0193573
$715$	0	0
$716$	−3.75621	−0.140376
$717$	5.04029	0.188233
$718$	−4.37321	−0.163207
$719$	28.3423	1.05699	0.528495	−	0.848936i	$-0.322756\pi$
$719$	28.3423	1.05699	0.528495	+	0.848936i	$0.322756\pi$
$720$	0	0
$721$	−0.0199580	−0.000743274 0
$722$	9.93616	0.369786
$723$	6.84097	0.254419
$724$	−18.0626	−0.671290
$725$	0	0
$726$	−11.9786	−0.444569
$727$	17.0802	0.633469	0.316735	−	0.948514i	$-0.397414\pi$
$727$	17.0802	0.633469	0.316735	+	0.948514i	$0.397414\pi$
$728$	0.473931	0.0175651
$729$	1.00000	0.0370370
$730$	0	0
$731$	−5.46570	−0.202156
$732$	−5.15131	−0.190398
$733$	−11.8923	−0.439251	−0.219626	−	0.975584i	$-0.570484\pi$
$733$	−11.8923	−0.439251	−0.219626	+	0.975584i	$0.570484\pi$
$734$	−21.8334	−0.805885
$735$	0	0
$736$	−4.64584	−0.171248
$737$	−30.1518	−1.11065
$738$	7.58064	0.279047
$739$	11.4605	0.421581	0.210791	−	0.977531i	$-0.432396\pi$
$739$	11.4605	0.421581	0.210791	+	0.977531i	$0.432396\pi$
$740$	0	0
$741$	5.21773	0.191678
$742$	3.17621	0.116602
$743$	8.64114	0.317013	0.158506	−	0.987358i	$-0.449332\pi$
$743$	8.64114	0.317013	0.158506	+	0.987358i	$0.449332\pi$
$744$	−3.83390	−0.140558
$745$	0	0
$746$	1.41871	0.0519428
$747$	−15.1392	−0.553915
$748$	9.06706	0.331525
$749$	1.59905	0.0584281
$750$	0	0
$751$	−8.45998	−0.308709	−0.154354	−	0.988016i	$-0.549330\pi$
$751$	−8.45998	−0.308709	−0.154354	+	0.988016i	$0.549330\pi$
$752$	1.18806	0.0433240
$753$	−7.07549	−0.257845
$754$	15.7490	0.573545
$755$	0	0
$756$	0.273457	0.00994555
$757$	−53.6675	−1.95058	−0.975289	−	0.220932i	$-0.929090\pi$
$757$	−53.6675	−1.95058	−0.975289	+	0.220932i	$0.929090\pi$
$758$	26.0806	0.947290
$759$	−22.2703	−0.808362
$760$	0	0
$761$	11.7714	0.426713	0.213357	−	0.976974i	$-0.431560\pi$
$761$	11.7714	0.426713	0.213357	+	0.976974i	$0.431560\pi$
$762$	−18.3677	−0.665391
$763$	−2.68155	−0.0970786
$764$	−16.6007	−0.600594
$765$	0	0
$766$	32.7645	1.18383
$767$	24.7652	0.894220
$768$	1.00000	0.0360844
$769$	5.09591	0.183763	0.0918816	−	0.995770i	$-0.470712\pi$
$769$	5.09591	0.183763	0.0918816	+	0.995770i	$0.470712\pi$
$770$	0	0
$771$	4.47318	0.161097
$772$	3.84858	0.138513
$773$	−12.6222	−0.453990	−0.226995	−	0.973896i	$-0.572890\pi$
$773$	−12.6222	−0.453990	−0.226995	+	0.973896i	$0.572890\pi$
$774$	−2.88963	−0.103865
$775$	0	0
$776$	5.88597	0.211294
$777$	2.46371	0.0883850
$778$	4.46133	0.159946
$779$	22.8225	0.817699
$780$	0	0
$781$	6.72145	0.240512
$782$	8.78757	0.314243
$783$	9.08715	0.324748
$784$	−6.92522	−0.247329
$785$	0	0
$786$	7.57357	0.270140
$787$	−44.2098	−1.57591	−0.787954	−	0.615734i	$-0.788860\pi$
$787$	−44.2098	−1.57591	−0.787954	+	0.615734i	$0.788860\pi$
$788$	10.7432	0.382711
$789$	2.50232	0.0890849
$790$	0	0
$791$	−4.73878	−0.168492
$792$	4.79360	0.170333
$793$	8.92777	0.317034
$794$	2.11727	0.0751389
$795$	0	0
$796$	2.49808	0.0885421
$797$	−46.3400	−1.64145	−0.820723	−	0.571326i	$-0.806429\pi$
$797$	−46.3400	−1.64145	−0.820723	+	0.571326i	$0.806429\pi$
$798$	0.823277	0.0291437
$799$	−2.24720	−0.0795002
$800$	0	0
$801$	−14.8273	−0.523898
$802$	28.6530	1.01177
$803$	−8.53798	−0.301299
$804$	6.29000	0.221831
$805$	0	0
$806$	6.64456	0.234045
$807$	6.18870	0.217853
$808$	−4.83576	−0.170122
$809$	49.4913	1.74002	0.870011	−	0.493033i	$-0.164112\pi$
$809$	49.4913	1.74002	0.870011	+	0.493033i	$0.164112\pi$
$810$	0	0
$811$	−2.80756	−0.0985867	−0.0492934	−	0.998784i	$-0.515697\pi$
$811$	−2.80756	−0.0985867	−0.0492934	+	0.998784i	$0.515697\pi$
$812$	2.48495	0.0872046
$813$	13.1689	0.461853
$814$	43.1878	1.51373
$815$	0	0
$816$	−1.89149	−0.0662154
$817$	−8.69957	−0.304360
$818$	−39.3546	−1.37600
$819$	−0.473931	−0.0165605
$820$	0	0
$821$	−37.3643	−1.30402	−0.652011	−	0.758209i	$-0.726075\pi$
$821$	−37.3643	−1.30402	−0.652011	+	0.758209i	$0.726075\pi$
$822$	19.6095	0.683960
$823$	−22.8380	−0.796082	−0.398041	−	0.917368i	$-0.630310\pi$
$823$	−22.8380	−0.796082	−0.398041	+	0.917368i	$0.630310\pi$
$824$	0.0729839	0.00254251
$825$	0	0
$826$	3.90757	0.135962
$827$	10.7107	0.372448	0.186224	−	0.982507i	$-0.440375\pi$
$827$	10.7107	0.372448	0.186224	+	0.982507i	$0.440375\pi$
$828$	4.64584	0.161454
$829$	−27.5959	−0.958445	−0.479223	−	0.877693i	$-0.659081\pi$
$829$	−27.5959	−0.958445	−0.479223	+	0.877693i	$0.659081\pi$
$830$	0	0
$831$	−5.16714	−0.179246
$832$	−1.73311	−0.0600847
$833$	13.0990	0.453853
$834$	−9.56514	−0.331214
$835$	0	0
$836$	14.4317	0.499132
$837$	3.83390	0.132519
$838$	−14.1068	−0.487313
$839$	−9.93655	−0.343048	−0.171524	−	0.985180i	$-0.554869\pi$
$839$	−9.93655	−0.343048	−0.171524	+	0.985180i	$0.554869\pi$
$840$	0	0
$841$	53.5763	1.84746
$842$	−16.3046	−0.561892
$843$	−0.0469714	−0.00161778
$844$	24.2741	0.835547
$845$	0	0
$846$	−1.18806	−0.0408462
$847$	3.27565	0.112553
$848$	−11.6150	−0.398861
$849$	−21.8712	−0.750617
$850$	0	0
$851$	41.8566	1.43482
$852$	−1.40217	−0.0480375
$853$	45.0081	1.54105	0.770524	−	0.637412i	$-0.219995\pi$
$853$	45.0081	1.54105	0.770524	+	0.637412i	$0.219995\pi$
$854$	1.40866	0.0482035
$855$	0	0
$856$	−5.84754	−0.199865
$857$	24.6986	0.843686	0.421843	−	0.906669i	$-0.361383\pi$
$857$	24.6986	0.843686	0.421843	+	0.906669i	$0.361383\pi$
$858$	−8.30783	−0.283625
$859$	−17.3400	−0.591632	−0.295816	−	0.955245i	$-0.595592\pi$
$859$	−17.3400	−0.591632	−0.295816	+	0.955245i	$0.595592\pi$
$860$	0	0
$861$	−2.07298	−0.0706471
$862$	1.98217	0.0675130
$863$	−25.8867	−0.881195	−0.440598	−	0.897705i	$-0.645233\pi$
$863$	−25.8867	−0.881195	−0.440598	+	0.897705i	$0.645233\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	4.48943	0.152557
$867$	−13.4223	−0.455844
$868$	1.04841	0.0355853
$869$	76.9821	2.61144
$870$	0	0
$871$	−10.9012	−0.369375
$872$	9.80609	0.332076
$873$	−5.88597	−0.199210
$874$	13.9869	0.473113
$875$	0	0
$876$	1.78112	0.0601784
$877$	20.1898	0.681761	0.340881	−	0.940107i	$-0.389275\pi$
$877$	20.1898	0.681761	0.340881	+	0.940107i	$0.389275\pi$
$878$	−25.7158	−0.867866
$879$	8.35289	0.281736
$880$	0	0
$881$	23.7732	0.800940	0.400470	−	0.916310i	$-0.368847\pi$
$881$	23.7732	0.800940	0.400470	+	0.916310i	$0.368847\pi$
$882$	6.92522	0.233184
$883$	32.5787	1.09636	0.548180	−	0.836361i	$-0.315321\pi$
$883$	32.5787	1.09636	0.548180	+	0.836361i	$0.315321\pi$
$884$	3.27816	0.110256
$885$	0	0
$886$	29.1477	0.979234
$887$	56.3177	1.89096	0.945481	−	0.325678i	$-0.105592\pi$
$887$	56.3177	1.89096	0.945481	+	0.325678i	$0.105592\pi$
$888$	−9.00947	−0.302338
$889$	5.02278	0.168459
$890$	0	0
$891$	−4.79360	−0.160592
$892$	13.0539	0.437078
$893$	−3.57679	−0.119693
$894$	4.64398	0.155318
$895$	0	0
$896$	−0.273457	−0.00913557
$897$	−8.05174	−0.268840
$898$	5.14037	0.171536
$899$	34.8392	1.16195
$900$	0	0
$901$	21.9697	0.731917
$902$	−36.3386	−1.20994
$903$	0.790190	0.0262959
$904$	17.3291	0.576359
$905$	0	0
$906$	16.7881	0.557747
$907$	46.7617	1.55270	0.776349	−	0.630304i	$-0.217070\pi$
$907$	46.7617	1.55270	0.776349	+	0.630304i	$0.217070\pi$
$908$	7.06154	0.234345
$909$	4.83576	0.160392
$910$	0	0
$911$	−16.7472	−0.554858	−0.277429	−	0.960746i	$-0.589482\pi$
$911$	−16.7472	−0.554858	−0.277429	+	0.960746i	$0.589482\pi$
$912$	−3.01062	−0.0996916
$913$	72.5714	2.40176
$914$	−20.8445	−0.689475
$915$	0	0
$916$	−12.5771	−0.415560
$917$	−2.07105	−0.0683921
$918$	1.89149	0.0624285
$919$	−5.12507	−0.169061	−0.0845303	−	0.996421i	$-0.526939\pi$
$919$	−5.12507	−0.169061	−0.0845303	+	0.996421i	$0.526939\pi$
$920$	0	0
$921$	−2.28918	−0.0754309
$922$	4.96989	0.163675
$923$	2.43011	0.0799880
$924$	−1.31085	−0.0431237
$925$	0	0
$926$	−7.10664	−0.233539
$927$	−0.0729839	−0.00239711
$928$	−9.08715	−0.298300
$929$	45.3434	1.48767	0.743834	−	0.668364i	$-0.233005\pi$
$929$	45.3434	1.48767	0.743834	+	0.668364i	$0.233005\pi$
$930$	0	0
$931$	20.8492	0.683306
$932$	−9.80527	−0.321182
$933$	25.6673	0.840309
$934$	30.1821	0.987590
$935$	0	0
$936$	1.73311	0.0566484
$937$	31.0119	1.01311	0.506557	−	0.862207i	$-0.330918\pi$
$937$	31.0119	1.01311	0.506557	+	0.862207i	$0.330918\pi$
$938$	−1.72005	−0.0561616
$939$	30.2110	0.985898
$940$	0	0
$941$	−48.3113	−1.57490	−0.787452	−	0.616377i	$-0.788600\pi$
$941$	−48.3113	−1.57490	−0.787452	+	0.616377i	$0.788600\pi$
$942$	−5.57763	−0.181729
$943$	−35.2185	−1.14687
$944$	−14.2895	−0.465083
$945$	0	0
$946$	13.8517	0.450358
$947$	33.3872	1.08494	0.542470	−	0.840075i	$-0.317489\pi$
$947$	33.3872	1.08494	0.542470	+	0.840075i	$0.317489\pi$
$948$	−16.0593	−0.521583
$949$	−3.08687	−0.100204
$950$	0	0
$951$	−25.8613	−0.838609
$952$	0.517242	0.0167639
$953$	21.8525	0.707872	0.353936	−	0.935270i	$-0.384843\pi$
$953$	21.8525	0.707872	0.353936	+	0.935270i	$0.384843\pi$
$954$	11.6150	0.376050
$955$	0	0
$956$	5.04029	0.163015
$957$	−43.5602	−1.40810
$958$	−27.8415	−0.899518
$959$	−5.36236	−0.173160
$960$	0	0
$961$	−16.3012	−0.525846
$962$	15.6144	0.503428
$963$	5.84754	0.188434
$964$	6.84097	0.220333
$965$	0	0
$966$	−1.27044	−0.0408757
$967$	−32.2205	−1.03614	−0.518071	−	0.855338i	$-0.673350\pi$
$967$	−32.2205	−1.03614	−0.518071	+	0.855338i	$0.673350\pi$
$968$	−11.9786	−0.385008
$969$	5.69456	0.182936
$970$	0	0
$971$	35.6114	1.14282	0.571411	−	0.820664i	$-0.306396\pi$
$971$	35.6114	1.14282	0.571411	+	0.820664i	$0.306396\pi$
$972$	1.00000	0.0320750
$973$	2.61566	0.0838542
$974$	1.29951	0.0416391
$975$	0	0
$976$	−5.15131	−0.164889
$977$	−9.85880	−0.315411	−0.157706	−	0.987486i	$-0.550410\pi$
$977$	−9.85880	−0.315411	−0.157706	+	0.987486i	$0.550410\pi$
$978$	18.3753	0.587577
$979$	71.0764	2.27161
$980$	0	0
$981$	−9.80609	−0.313084
$982$	−19.1650	−0.611580
$983$	30.4129	0.970020	0.485010	−	0.874509i	$-0.338816\pi$
$983$	30.4129	0.970020	0.485010	+	0.874509i	$0.338816\pi$
$984$	7.58064	0.241662
$985$	0	0
$986$	17.1883	0.547386
$987$	0.324883	0.0103411
$988$	5.21773	0.165998
$989$	13.4247	0.426882
$990$	0	0
$991$	−41.0077	−1.30265	−0.651327	−	0.758798i	$-0.725787\pi$
$991$	−41.0077	−1.30265	−0.651327	+	0.758798i	$0.725787\pi$
$992$	−3.83390	−0.121726
$993$	14.5094	0.460442
$994$	0.383434	0.0121618
$995$	0	0
$996$	−15.1392	−0.479705
$997$	8.00811	0.253620	0.126810	−	0.991927i	$-0.459526\pi$
$997$	8.00811	0.253620	0.126810	+	0.991927i	$0.459526\pi$
$998$	−6.41339	−0.203012
$999$	9.00947	0.285047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.m.1.2		4
5.2	odd	4		3750.2.c.e.1249.2		8
5.3	odd	4		3750.2.c.e.1249.7		8
5.4	even	2		3750.2.a.o.1.3		4
25.3	odd	20		750.2.h.c.49.2		8
25.4	even	10		750.2.g.c.451.2		8
25.6	even	5		750.2.g.e.301.1		8
25.8	odd	20		150.2.h.a.139.1	yes	8
25.17	odd	20		750.2.h.c.199.2		8
25.19	even	10		750.2.g.c.301.2		8
25.21	even	5		750.2.g.e.451.1		8
25.22	odd	20		150.2.h.a.109.1	✓	8
75.8	even	20		450.2.l.a.289.2		8
75.47	even	20		450.2.l.a.109.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.109.1	✓	8	25.22	odd	20
150.2.h.a.139.1	yes	8	25.8	odd	20
450.2.l.a.109.2		8	75.47	even	20
450.2.l.a.289.2		8	75.8	even	20
750.2.g.c.301.2		8	25.19	even	10
750.2.g.c.451.2		8	25.4	even	10
750.2.g.e.301.1		8	25.6	even	5
750.2.g.e.451.1		8	25.21	even	5
750.2.h.c.49.2		8	25.3	odd	20
750.2.h.c.199.2		8	25.17	odd	20
3750.2.a.m.1.2		4	1.1	even	1	trivial
3750.2.a.o.1.3		4	5.4	even	2
3750.2.c.e.1249.2		8	5.2	odd	4
3750.2.c.e.1249.7		8	5.3	odd	4

Overview	Random
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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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.273457 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.273457 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.79360 q^{11} +1.00000 q^{12} -1.73311 q^{13} -0.273457 q^{14} +1.00000 q^{16} -1.89149 q^{17} -1.00000 q^{18} -3.01062 q^{19} +0.273457 q^{21} +4.79360 q^{22} +4.64584 q^{23} -1.00000 q^{24} +1.73311 q^{26} +1.00000 q^{27} +0.273457 q^{28} +9.08715 q^{29} +3.83390 q^{31} -1.00000 q^{32} -4.79360 q^{33} +1.89149 q^{34} +1.00000 q^{36} +9.00947 q^{37} +3.01062 q^{38} -1.73311 q^{39} -7.58064 q^{41} -0.273457 q^{42} +2.88963 q^{43} -4.79360 q^{44} -4.64584 q^{46} +1.18806 q^{47} +1.00000 q^{48} -6.92522 q^{49} -1.89149 q^{51} -1.73311 q^{52} -11.6150 q^{53} -1.00000 q^{54} -0.273457 q^{56} -3.01062 q^{57} -9.08715 q^{58} -14.2895 q^{59} -5.15131 q^{61} -3.83390 q^{62} +0.273457 q^{63} +1.00000 q^{64} +4.79360 q^{66} +6.29000 q^{67} -1.89149 q^{68} +4.64584 q^{69} -1.40217 q^{71} -1.00000 q^{72} +1.78112 q^{73} -9.00947 q^{74} -3.01062 q^{76} -1.31085 q^{77} +1.73311 q^{78} -16.0593 q^{79} +1.00000 q^{81} +7.58064 q^{82} -15.1392 q^{83} +0.273457 q^{84} -2.88963 q^{86} +9.08715 q^{87} +4.79360 q^{88} -14.8273 q^{89} -0.473931 q^{91} +4.64584 q^{92} +3.83390 q^{93} -1.18806 q^{94} -1.00000 q^{96} -5.88597 q^{97} +6.92522 q^{98} -4.79360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} - 10 q^{11} + 4 q^{12} - 2 q^{13} - 4 q^{14} + 4 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 4 q^{21} + 10 q^{22} - 4 q^{24} + 2 q^{26} + 4 q^{27} + 4 q^{28} - 14 q^{29} - 18 q^{31} - 4 q^{32} - 10 q^{33} + 6 q^{34} + 4 q^{36} - 2 q^{37} + 6 q^{38} - 2 q^{39} - 14 q^{41} - 4 q^{42} + 14 q^{43} - 10 q^{44} - 10 q^{47} + 4 q^{48} - 4 q^{49} - 6 q^{51} - 2 q^{52} - 14 q^{53} - 4 q^{54} - 4 q^{56} - 6 q^{57} + 14 q^{58} - 20 q^{59} + 18 q^{62} + 4 q^{63} + 4 q^{64} + 10 q^{66} + 14 q^{67} - 6 q^{68} - 30 q^{71} - 4 q^{72} + 8 q^{73} + 2 q^{74} - 6 q^{76} - 20 q^{77} + 2 q^{78} - 28 q^{79} + 4 q^{81} + 14 q^{82} - 12 q^{83} + 4 q^{84} - 14 q^{86} - 14 q^{87} + 10 q^{88} - 28 q^{89} - 22 q^{91} - 18 q^{93} + 10 q^{94} - 4 q^{96} + 8 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 - 10 * q^11 + 4 * q^12 - 2 * q^13 - 4 * q^14 + 4 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 + 4 * q^21 + 10 * q^22 - 4 * q^24 + 2 * q^26 + 4 * q^27 + 4 * q^28 - 14 * q^29 - 18 * q^31 - 4 * q^32 - 10 * q^33 + 6 * q^34 + 4 * q^36 - 2 * q^37 + 6 * q^38 - 2 * q^39 - 14 * q^41 - 4 * q^42 + 14 * q^43 - 10 * q^44 - 10 * q^47 + 4 * q^48 - 4 * q^49 - 6 * q^51 - 2 * q^52 - 14 * q^53 - 4 * q^54 - 4 * q^56 - 6 * q^57 + 14 * q^58 - 20 * q^59 + 18 * q^62 + 4 * q^63 + 4 * q^64 + 10 * q^66 + 14 * q^67 - 6 * q^68 - 30 * q^71 - 4 * q^72 + 8 * q^73 + 2 * q^74 - 6 * q^76 - 20 * q^77 + 2 * q^78 - 28 * q^79 + 4 * q^81 + 14 * q^82 - 12 * q^83 + 4 * q^84 - 14 * q^86 - 14 * q^87 + 10 * q^88 - 28 * q^89 - 22 * q^91 - 18 * q^93 + 10 * q^94 - 4 * q^96 + 8 * q^97 + 4 * q^98 - 10 * q^99

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