LMFDB - Embedded newform 950.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.76156$ of defining polynomial
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.76156 q^{3} +1.00000 q^{4} +2.76156 q^{6} -0.761557 q^{7} +1.00000 q^{8} +4.62620 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.76156 q^{3} +1.00000 q^{4} +2.76156 q^{6} -0.761557 q^{7} +1.00000 q^{8} +4.62620 q^{9} -0.864641 q^{11} +2.76156 q^{12} +5.62620 q^{13} -0.761557 q^{14} +1.00000 q^{16} -3.62620 q^{17} +4.62620 q^{18} +1.00000 q^{19} -2.10308 q^{21} -0.864641 q^{22} -8.01395 q^{23} +2.76156 q^{24} +5.62620 q^{26} +4.49084 q^{27} -0.761557 q^{28} -7.35548 q^{29} +8.11704 q^{31} +1.00000 q^{32} -2.38776 q^{33} -3.62620 q^{34} +4.62620 q^{36} +0.476886 q^{37} +1.00000 q^{38} +15.5371 q^{39} -2.65847 q^{41} -2.10308 q^{42} +6.86464 q^{43} -0.864641 q^{44} -8.01395 q^{46} +1.25240 q^{47} +2.76156 q^{48} -6.42003 q^{49} -10.0140 q^{51} +5.62620 q^{52} +2.37380 q^{53} +4.49084 q^{54} -0.761557 q^{56} +2.76156 q^{57} -7.35548 q^{58} +4.49084 q^{59} -10.8646 q^{61} +8.11704 q^{62} -3.52311 q^{63} +1.00000 q^{64} -2.38776 q^{66} +1.03228 q^{67} -3.62620 q^{68} -22.1310 q^{69} -10.1816 q^{71} +4.62620 q^{72} +16.4017 q^{73} +0.476886 q^{74} +1.00000 q^{76} +0.658473 q^{77} +15.5371 q^{78} -12.5693 q^{79} -1.47689 q^{81} -2.65847 q^{82} -0.270718 q^{83} -2.10308 q^{84} +6.86464 q^{86} -20.3126 q^{87} -0.864641 q^{88} +0.387755 q^{89} -4.28467 q^{91} -8.01395 q^{92} +22.4157 q^{93} +1.25240 q^{94} +2.76156 q^{96} -8.50479 q^{97} -6.42003 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{12} + 8 q^{13} + 4 q^{14} + 3 q^{16} - 2 q^{17} + 5 q^{18} + 3 q^{19} - 10 q^{21} + 2 q^{24} + 8 q^{26} + 2 q^{27} + 4 q^{28} - 8 q^{29} + 4 q^{31} + 3 q^{32} + 8 q^{33} - 2 q^{34} + 5 q^{36} + 14 q^{37} + 3 q^{38} + 10 q^{39} + 2 q^{41} - 10 q^{42} + 18 q^{43} - 14 q^{47} + 2 q^{48} - 3 q^{49} - 6 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} + 4 q^{56} + 2 q^{57} - 8 q^{58} + 2 q^{59} - 30 q^{61} + 4 q^{62} + 2 q^{63} + 3 q^{64} + 8 q^{66} + 2 q^{67} - 2 q^{68} - 22 q^{69} - 8 q^{71} + 5 q^{72} + 10 q^{73} + 14 q^{74} + 3 q^{76} - 8 q^{77} + 10 q^{78} - 17 q^{81} + 2 q^{82} - 6 q^{83} - 10 q^{84} + 18 q^{86} + 6 q^{87} - 14 q^{89} + 6 q^{91} + 4 q^{93} - 14 q^{94} + 2 q^{96} + 10 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^12 + 8 * q^13 + 4 * q^14 + 3 * q^16 - 2 * q^17 + 5 * q^18 + 3 * q^19 - 10 * q^21 + 2 * q^24 + 8 * q^26 + 2 * q^27 + 4 * q^28 - 8 * q^29 + 4 * q^31 + 3 * q^32 + 8 * q^33 - 2 * q^34 + 5 * q^36 + 14 * q^37 + 3 * q^38 + 10 * q^39 + 2 * q^41 - 10 * q^42 + 18 * q^43 - 14 * q^47 + 2 * q^48 - 3 * q^49 - 6 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 + 4 * q^56 + 2 * q^57 - 8 * q^58 + 2 * q^59 - 30 * q^61 + 4 * q^62 + 2 * q^63 + 3 * q^64 + 8 * q^66 + 2 * q^67 - 2 * q^68 - 22 * q^69 - 8 * q^71 + 5 * q^72 + 10 * q^73 + 14 * q^74 + 3 * q^76 - 8 * q^77 + 10 * q^78 - 17 * q^81 + 2 * q^82 - 6 * q^83 - 10 * q^84 + 18 * q^86 + 6 * q^87 - 14 * q^89 + 6 * q^91 + 4 * q^93 - 14 * q^94 + 2 * q^96 + 10 * q^97 - 3 * q^98 - 12 * 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
$3$	2.76156	1.59439	0.797193	−	0.603725i	$-0.206317\pi$
$3$	2.76156	1.59439	0.797193	+	0.603725i	$0.206317\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.76156	1.12740
$7$	−0.761557	−0.287842	−0.143921	−	0.989589i	$-0.545971\pi$
$7$	−0.761557	−0.287842	−0.143921	+	0.989589i	$0.545971\pi$
$8$	1.00000	0.353553
$9$	4.62620	1.54207
$10$	0	0
$11$	−0.864641	−0.260699	−0.130350	−	0.991468i	$-0.541610\pi$
$11$	−0.864641	−0.260699	−0.130350	+	0.991468i	$0.541610\pi$
$12$	2.76156	0.797193
$13$	5.62620	1.56043	0.780213	−	0.625514i	$-0.215111\pi$
$13$	5.62620	1.56043	0.780213	+	0.625514i	$0.215111\pi$
$14$	−0.761557	−0.203535
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.62620	−0.879482	−0.439741	−	0.898125i	$-0.644930\pi$
$17$	−3.62620	−0.879482	−0.439741	+	0.898125i	$0.644930\pi$
$18$	4.62620	1.09041
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−2.10308	−0.458930
$22$	−0.864641	−0.184342
$23$	−8.01395	−1.67102	−0.835512	−	0.549472i	$-0.814829\pi$
$23$	−8.01395	−1.67102	−0.835512	+	0.549472i	$0.814829\pi$
$24$	2.76156	0.563700
$25$	0	0
$26$	5.62620	1.10339
$27$	4.49084	0.864262
$28$	−0.761557	−0.143921
$29$	−7.35548	−1.36588	−0.682939	−	0.730475i	$-0.739299\pi$
$29$	−7.35548	−1.36588	−0.682939	+	0.730475i	$0.739299\pi$
$30$	0	0
$31$	8.11704	1.45786	0.728931	−	0.684587i	$-0.240017\pi$
$31$	8.11704	1.45786	0.728931	+	0.684587i	$0.240017\pi$
$32$	1.00000	0.176777
$33$	−2.38776	−0.415655
$34$	−3.62620	−0.621888
$35$	0	0
$36$	4.62620	0.771033
$37$	0.476886	0.0783995	0.0391998	−	0.999231i	$-0.487519\pi$
$37$	0.476886	0.0783995	0.0391998	+	0.999231i	$0.487519\pi$
$38$	1.00000	0.162221
$39$	15.5371	2.48792
$40$	0	0
$41$	−2.65847	−0.415184	−0.207592	−	0.978216i	$-0.566563\pi$
$41$	−2.65847	−0.415184	−0.207592	+	0.978216i	$0.566563\pi$
$42$	−2.10308	−0.324513
$43$	6.86464	1.04685	0.523424	−	0.852072i	$-0.324654\pi$
$43$	6.86464	1.04685	0.523424	+	0.852072i	$0.324654\pi$
$44$	−0.864641	−0.130350
$45$	0	0
$46$	−8.01395	−1.18159
$47$	1.25240	0.182681	0.0913404	−	0.995820i	$-0.470885\pi$
$47$	1.25240	0.182681	0.0913404	+	0.995820i	$0.470885\pi$
$48$	2.76156	0.398596
$49$	−6.42003	−0.917147
$50$	0	0
$51$	−10.0140	−1.40223
$52$	5.62620	0.780213
$53$	2.37380	0.326067	0.163033	−	0.986621i	$-0.447872\pi$
$53$	2.37380	0.326067	0.163033	+	0.986621i	$0.447872\pi$
$54$	4.49084	0.611126
$55$	0	0
$56$	−0.761557	−0.101767
$57$	2.76156	0.365777
$58$	−7.35548	−0.965822
$59$	4.49084	0.584657	0.292329	−	0.956318i	$-0.405570\pi$
$59$	4.49084	0.584657	0.292329	+	0.956318i	$0.405570\pi$
$60$	0	0
$61$	−10.8646	−1.39107	−0.695537	−	0.718490i	$-0.744834\pi$
$61$	−10.8646	−1.39107	−0.695537	+	0.718490i	$0.744834\pi$
$62$	8.11704	1.03086
$63$	−3.52311	−0.443871
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.38776	−0.293912
$67$	1.03228	0.126113	0.0630563	−	0.998010i	$-0.479915\pi$
$67$	1.03228	0.126113	0.0630563	+	0.998010i	$0.479915\pi$
$68$	−3.62620	−0.439741
$69$	−22.1310	−2.66426
$70$	0	0
$71$	−10.1816	−1.20833	−0.604166	−	0.796858i	$-0.706494\pi$
$71$	−10.1816	−1.20833	−0.604166	+	0.796858i	$0.706494\pi$
$72$	4.62620	0.545203
$73$	16.4017	1.91967	0.959837	−	0.280557i	$-0.0905191\pi$
$73$	16.4017	1.91967	0.959837	+	0.280557i	$0.0905191\pi$
$74$	0.476886	0.0554368
$75$	0	0
$76$	1.00000	0.114708
$77$	0.658473	0.0750400
$78$	15.5371	1.75923
$79$	−12.5693	−1.41416	−0.707081	−	0.707133i	$-0.749988\pi$
$79$	−12.5693	−1.41416	−0.707081	+	0.707133i	$0.749988\pi$
$80$	0	0
$81$	−1.47689	−0.164098
$82$	−2.65847	−0.293579
$83$	−0.270718	−0.0297152	−0.0148576	−	0.999890i	$-0.504729\pi$
$83$	−0.270718	−0.0297152	−0.0148576	+	0.999890i	$0.504729\pi$
$84$	−2.10308	−0.229465
$85$	0	0
$86$	6.86464	0.740233
$87$	−20.3126	−2.17774
$88$	−0.864641	−0.0921710
$89$	0.387755	0.0411020	0.0205510	−	0.999789i	$-0.493458\pi$
$89$	0.387755	0.0411020	0.0205510	+	0.999789i	$0.493458\pi$
$90$	0	0
$91$	−4.28467	−0.449156
$92$	−8.01395	−0.835512
$93$	22.4157	2.32440
$94$	1.25240	0.129175
$95$	0	0
$96$	2.76156	0.281850
$97$	−8.50479	−0.863531	−0.431765	−	0.901986i	$-0.642109\pi$
$97$	−8.50479	−0.863531	−0.431765	+	0.901986i	$0.642109\pi$
$98$	−6.42003	−0.648521
$99$	−4.00000	−0.402015
$100$	0	0
$101$	16.4157	1.63342	0.816710	−	0.577049i	$-0.195796\pi$
$101$	16.4157	1.63342	0.816710	+	0.577049i	$0.195796\pi$
$102$	−10.0140	−0.991529
$103$	−9.64015	−0.949872	−0.474936	−	0.880020i	$-0.657529\pi$
$103$	−9.64015	−0.949872	−0.474936	+	0.880020i	$0.657529\pi$
$104$	5.62620	0.551694
$105$	0	0
$106$	2.37380	0.230564
$107$	4.28467	0.414215	0.207107	−	0.978318i	$-0.433595\pi$
$107$	4.28467	0.414215	0.207107	+	0.978318i	$0.433595\pi$
$108$	4.49084	0.432131
$109$	−13.4200	−1.28541	−0.642703	−	0.766116i	$-0.722187\pi$
$109$	−13.4200	−1.28541	−0.642703	+	0.766116i	$0.722187\pi$
$110$	0	0
$111$	1.31695	0.124999
$112$	−0.761557	−0.0719604
$113$	−10.3232	−0.971125	−0.485563	−	0.874202i	$-0.661385\pi$
$113$	−10.3232	−0.971125	−0.485563	+	0.874202i	$0.661385\pi$
$114$	2.76156	0.258644
$115$	0	0
$116$	−7.35548	−0.682939
$117$	26.0279	2.40628
$118$	4.49084	0.413415
$119$	2.76156	0.253152
$120$	0	0
$121$	−10.2524	−0.932036
$122$	−10.8646	−0.983638
$123$	−7.34153	−0.661963
$124$	8.11704	0.728931
$125$	0	0
$126$	−3.52311	−0.313864
$127$	16.9817	1.50688	0.753440	−	0.657517i	$-0.228393\pi$
$127$	16.9817	1.50688	0.753440	+	0.657517i	$0.228393\pi$
$128$	1.00000	0.0883883
$129$	18.9571	1.66908
$130$	0	0
$131$	0.541436	0.0473055	0.0236528	−	0.999720i	$-0.492470\pi$
$131$	0.541436	0.0473055	0.0236528	+	0.999720i	$0.492470\pi$
$132$	−2.38776	−0.207827
$133$	−0.761557	−0.0660354
$134$	1.03228	0.0891750
$135$	0	0
$136$	−3.62620	−0.310944
$137$	2.87859	0.245935	0.122967	−	0.992411i	$-0.460759\pi$
$137$	2.87859	0.245935	0.122967	+	0.992411i	$0.460759\pi$
$138$	−22.1310	−1.88392
$139$	3.58767	0.304302	0.152151	−	0.988357i	$-0.451380\pi$
$139$	3.58767	0.304302	0.152151	+	0.988357i	$0.451380\pi$
$140$	0	0
$141$	3.45856	0.291264
$142$	−10.1816	−0.854420
$143$	−4.86464	−0.406802
$144$	4.62620	0.385517
$145$	0	0
$146$	16.4017	1.35742
$147$	−17.7293	−1.46229
$148$	0.476886	0.0391998
$149$	−16.8401	−1.37959	−0.689796	−	0.724004i	$-0.742300\pi$
$149$	−16.8401	−1.37959	−0.689796	+	0.724004i	$0.742300\pi$
$150$	0	0
$151$	−16.9817	−1.38195	−0.690975	−	0.722879i	$-0.742818\pi$
$151$	−16.9817	−1.38195	−0.690975	+	0.722879i	$0.742818\pi$
$152$	1.00000	0.0811107
$153$	−16.7755	−1.35622
$154$	0.658473	0.0530613
$155$	0	0
$156$	15.5371	1.24396
$157$	14.8401	1.18437	0.592183	−	0.805804i	$-0.298266\pi$
$157$	14.8401	1.18437	0.592183	+	0.805804i	$0.298266\pi$
$158$	−12.5693	−0.999963
$159$	6.55539	0.519876
$160$	0	0
$161$	6.10308	0.480990
$162$	−1.47689	−0.116035
$163$	13.3694	1.04717	0.523587	−	0.851972i	$-0.324593\pi$
$163$	13.3694	1.04717	0.523587	+	0.851972i	$0.324593\pi$
$164$	−2.65847	−0.207592
$165$	0	0
$166$	−0.270718	−0.0210118
$167$	9.84632	0.761931	0.380966	−	0.924589i	$-0.375592\pi$
$167$	9.84632	0.761931	0.380966	+	0.924589i	$0.375592\pi$
$168$	−2.10308	−0.162256
$169$	18.6541	1.43493
$170$	0	0
$171$	4.62620	0.353774
$172$	6.86464	0.523424
$173$	2.98168	0.226693	0.113346	−	0.993556i	$-0.463843\pi$
$173$	2.98168	0.226693	0.113346	+	0.993556i	$0.463843\pi$
$174$	−20.3126	−1.53989
$175$	0	0
$176$	−0.864641	−0.0651748
$177$	12.4017	0.932169
$178$	0.387755	0.0290635
$179$	11.7938	0.881512	0.440756	−	0.897627i	$-0.354710\pi$
$179$	11.7938	0.881512	0.440756	+	0.897627i	$0.354710\pi$
$180$	0	0
$181$	14.5693	1.08293	0.541465	−	0.840723i	$-0.317870\pi$
$181$	14.5693	1.08293	0.541465	+	0.840723i	$0.317870\pi$
$182$	−4.28467	−0.317601
$183$	−30.0033	−2.21791
$184$	−8.01395	−0.590796
$185$	0	0
$186$	22.4157	1.64360
$187$	3.13536	0.229280
$188$	1.25240	0.0913404
$189$	−3.42003	−0.248771
$190$	0	0
$191$	13.2384	0.957900	0.478950	−	0.877842i	$-0.341017\pi$
$191$	13.2384	0.957900	0.478950	+	0.877842i	$0.341017\pi$
$192$	2.76156	0.199298
$193$	2.54144	0.182937	0.0914683	−	0.995808i	$-0.470844\pi$
$193$	2.54144	0.182937	0.0914683	+	0.995808i	$0.470844\pi$
$194$	−8.50479	−0.610609
$195$	0	0
$196$	−6.42003	−0.458574
$197$	−19.9109	−1.41859	−0.709295	−	0.704911i	$-0.750987\pi$
$197$	−19.9109	−1.41859	−0.709295	+	0.704911i	$0.750987\pi$
$198$	−4.00000	−0.284268
$199$	−20.3126	−1.43992	−0.719960	−	0.694015i	$-0.755840\pi$
$199$	−20.3126	−1.43992	−0.719960	+	0.694015i	$0.755840\pi$
$200$	0	0
$201$	2.85069	0.201072
$202$	16.4157	1.15500
$203$	5.60162	0.393157
$204$	−10.0140	−0.701117
$205$	0	0
$206$	−9.64015	−0.671661
$207$	−37.0741	−2.57683
$208$	5.62620	0.390107
$209$	−0.864641	−0.0598085
$210$	0	0
$211$	18.0419	1.24205	0.621026	−	0.783790i	$-0.286716\pi$
$211$	18.0419	1.24205	0.621026	+	0.783790i	$0.286716\pi$
$212$	2.37380	0.163033
$213$	−28.1170	−1.92655
$214$	4.28467	0.292894
$215$	0	0
$216$	4.49084	0.305563
$217$	−6.18159	−0.419634
$218$	−13.4200	−0.908919
$219$	45.2943	3.06070
$220$	0	0
$221$	−20.4017	−1.37237
$222$	1.31695	0.0883877
$223$	−13.5231	−0.905575	−0.452787	−	0.891619i	$-0.649570\pi$
$223$	−13.5231	−0.905575	−0.452787	+	0.891619i	$0.649570\pi$
$224$	−0.761557	−0.0508837
$225$	0	0
$226$	−10.3232	−0.686689
$227$	13.6016	0.902771	0.451386	−	0.892329i	$-0.350930\pi$
$227$	13.6016	0.902771	0.451386	+	0.892329i	$0.350930\pi$
$228$	2.76156	0.182889
$229$	13.5877	0.897898	0.448949	−	0.893557i	$-0.351798\pi$
$229$	13.5877	0.897898	0.448949	+	0.893557i	$0.351798\pi$
$230$	0	0
$231$	1.81841	0.119643
$232$	−7.35548	−0.482911
$233$	25.5510	1.67390	0.836952	−	0.547277i	$-0.184336\pi$
$233$	25.5510	1.67390	0.836952	+	0.547277i	$0.184336\pi$
$234$	26.0279	1.70150
$235$	0	0
$236$	4.49084	0.292329
$237$	−34.7110	−2.25472
$238$	2.76156	0.179005
$239$	−11.3309	−0.732935	−0.366468	−	0.930431i	$-0.619433\pi$
$239$	−11.3309	−0.732935	−0.366468	+	0.930431i	$0.619433\pi$
$240$	0	0
$241$	−1.25240	−0.0806739	−0.0403370	−	0.999186i	$-0.512843\pi$
$241$	−1.25240	−0.0806739	−0.0403370	+	0.999186i	$0.512843\pi$
$242$	−10.2524	−0.659049
$243$	−17.5510	−1.12590
$244$	−10.8646	−0.695537
$245$	0	0
$246$	−7.34153	−0.468079
$247$	5.62620	0.357986
$248$	8.11704	0.515432
$249$	−0.747604	−0.0473775
$250$	0	0
$251$	10.5939	0.668682	0.334341	−	0.942452i	$-0.391486\pi$
$251$	10.5939	0.668682	0.334341	+	0.942452i	$0.391486\pi$
$252$	−3.52311	−0.221935
$253$	6.92919	0.435635
$254$	16.9817	1.06553
$255$	0	0
$256$	1.00000	0.0625000
$257$	−0.153681	−0.00958637	−0.00479319	−	0.999989i	$-0.501526\pi$
$257$	−0.153681	−0.00958637	−0.00479319	+	0.999989i	$0.501526\pi$
$258$	18.9571	1.18022
$259$	−0.363176	−0.0225666
$260$	0	0
$261$	−34.0279	−2.10627
$262$	0.541436	0.0334501
$263$	0.504792	0.0311268	0.0155634	−	0.999879i	$-0.495046\pi$
$263$	0.504792	0.0311268	0.0155634	+	0.999879i	$0.495046\pi$
$264$	−2.38776	−0.146956
$265$	0	0
$266$	−0.761557	−0.0466941
$267$	1.07081	0.0655324
$268$	1.03228	0.0630563
$269$	−3.49521	−0.213107	−0.106553	−	0.994307i	$-0.533981\pi$
$269$	−3.49521	−0.213107	−0.106553	+	0.994307i	$0.533981\pi$
$270$	0	0
$271$	5.47252	0.332432	0.166216	−	0.986089i	$-0.446845\pi$
$271$	5.47252	0.332432	0.166216	+	0.986089i	$0.446845\pi$
$272$	−3.62620	−0.219871
$273$	−11.8324	−0.716127
$274$	2.87859	0.173902
$275$	0	0
$276$	−22.1310	−1.33213
$277$	12.9538	0.778317	0.389158	−	0.921171i	$-0.372766\pi$
$277$	12.9538	0.778317	0.389158	+	0.921171i	$0.372766\pi$
$278$	3.58767	0.215174
$279$	37.5510	2.24812
$280$	0	0
$281$	0.153681	0.00916785	0.00458393	−	0.999989i	$-0.498541\pi$
$281$	0.153681	0.00916785	0.00458393	+	0.999989i	$0.498541\pi$
$282$	3.45856	0.205954
$283$	−18.2341	−1.08390	−0.541952	−	0.840410i	$-0.682314\pi$
$283$	−18.2341	−1.08390	−0.541952	+	0.840410i	$0.682314\pi$
$284$	−10.1816	−0.604166
$285$	0	0
$286$	−4.86464	−0.287652
$287$	2.02458	0.119507
$288$	4.62620	0.272601
$289$	−3.85069	−0.226511
$290$	0	0
$291$	−23.4865	−1.37680
$292$	16.4017	0.959837
$293$	2.03853	0.119092	0.0595462	−	0.998226i	$-0.481035\pi$
$293$	2.03853	0.119092	0.0595462	+	0.998226i	$0.481035\pi$
$294$	−17.7293	−1.03399
$295$	0	0
$296$	0.476886	0.0277184
$297$	−3.88296	−0.225312
$298$	−16.8401	−0.975519
$299$	−45.0881	−2.60751
$300$	0	0
$301$	−5.22782	−0.301326
$302$	−16.9817	−0.977186
$303$	45.3328	2.60430
$304$	1.00000	0.0573539
$305$	0	0
$306$	−16.7755	−0.958992
$307$	16.5414	0.944070	0.472035	−	0.881580i	$-0.343520\pi$
$307$	16.5414	0.944070	0.472035	+	0.881580i	$0.343520\pi$
$308$	0.658473	0.0375200
$309$	−26.6218	−1.51446
$310$	0	0
$311$	−21.4725	−1.21759	−0.608797	−	0.793326i	$-0.708348\pi$
$311$	−21.4725	−1.21759	−0.608797	+	0.793326i	$0.708348\pi$
$312$	15.5371	0.879613
$313$	−1.12141	−0.0633856	−0.0316928	−	0.999498i	$-0.510090\pi$
$313$	−1.12141	−0.0633856	−0.0316928	+	0.999498i	$0.510090\pi$
$314$	14.8401	0.837473
$315$	0	0
$316$	−12.5693	−0.707081
$317$	−29.8882	−1.67869	−0.839344	−	0.543601i	$-0.817060\pi$
$317$	−29.8882	−1.67869	−0.839344	+	0.543601i	$0.817060\pi$
$318$	6.55539	0.367608
$319$	6.35985	0.356083
$320$	0	0
$321$	11.8324	0.660418
$322$	6.10308	0.340112
$323$	−3.62620	−0.201767
$324$	−1.47689	−0.0820492
$325$	0	0
$326$	13.3694	0.740464
$327$	−37.0602	−2.04943
$328$	−2.65847	−0.146790
$329$	−0.953771	−0.0525831
$330$	0	0
$331$	32.3126	1.77606	0.888030	−	0.459786i	$-0.152074\pi$
$331$	32.3126	1.77606	0.888030	+	0.459786i	$0.152074\pi$
$332$	−0.270718	−0.0148576
$333$	2.20617	0.120897
$334$	9.84632	0.538767
$335$	0	0
$336$	−2.10308	−0.114733
$337$	26.3511	1.43544	0.717718	−	0.696334i	$-0.245187\pi$
$337$	26.3511	1.43544	0.717718	+	0.696334i	$0.245187\pi$
$338$	18.6541	1.01465
$339$	−28.5081	−1.54835
$340$	0	0
$341$	−7.01832	−0.380063
$342$	4.62620	0.250156
$343$	10.2201	0.551835
$344$	6.86464	0.370117
$345$	0	0
$346$	2.98168	0.160296
$347$	−2.77551	−0.148997	−0.0744986	−	0.997221i	$-0.523736\pi$
$347$	−2.77551	−0.148997	−0.0744986	+	0.997221i	$0.523736\pi$
$348$	−20.3126	−1.08887
$349$	11.5510	0.618312	0.309156	−	0.951011i	$-0.399953\pi$
$349$	11.5510	0.618312	0.309156	+	0.951011i	$0.399953\pi$
$350$	0	0
$351$	25.2663	1.34862
$352$	−0.864641	−0.0460855
$353$	−8.40171	−0.447178	−0.223589	−	0.974684i	$-0.571777\pi$
$353$	−8.40171	−0.447178	−0.223589	+	0.974684i	$0.571777\pi$
$354$	12.4017	0.659143
$355$	0	0
$356$	0.387755	0.0205510
$357$	7.62620	0.403621
$358$	11.7938	0.623323
$359$	22.7895	1.20278	0.601391	−	0.798955i	$-0.294613\pi$
$359$	22.7895	1.20278	0.601391	+	0.798955i	$0.294613\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	14.5693	0.765748
$363$	−28.3126	−1.48602
$364$	−4.28467	−0.224578
$365$	0	0
$366$	−30.0033	−1.56830
$367$	4.06455	0.212168	0.106084	−	0.994357i	$-0.466169\pi$
$367$	4.06455	0.212168	0.106084	+	0.994357i	$0.466169\pi$
$368$	−8.01395	−0.417756
$369$	−12.2986	−0.640241
$370$	0	0
$371$	−1.80779	−0.0938556
$372$	22.4157	1.16220
$373$	−18.4017	−0.952804	−0.476402	−	0.879227i	$-0.658059\pi$
$373$	−18.4017	−0.952804	−0.476402	+	0.879227i	$0.658059\pi$
$374$	3.13536	0.162126
$375$	0	0
$376$	1.25240	0.0645874
$377$	−41.3834	−2.13135
$378$	−3.42003	−0.175907
$379$	1.23844	0.0636145	0.0318073	−	0.999494i	$-0.489874\pi$
$379$	1.23844	0.0636145	0.0318073	+	0.999494i	$0.489874\pi$
$380$	0	0
$381$	46.8959	2.40255
$382$	13.2384	0.677338
$383$	16.8646	0.861743	0.430871	−	0.902413i	$-0.358206\pi$
$383$	16.8646	0.861743	0.430871	+	0.902413i	$0.358206\pi$
$384$	2.76156	0.140925
$385$	0	0
$386$	2.54144	0.129356
$387$	31.7572	1.61431
$388$	−8.50479	−0.431765
$389$	8.59392	0.435729	0.217865	−	0.975979i	$-0.430091\pi$
$389$	8.59392	0.435729	0.217865	+	0.975979i	$0.430091\pi$
$390$	0	0
$391$	29.0602	1.46964
$392$	−6.42003	−0.324261
$393$	1.49521	0.0754233
$394$	−19.9109	−1.00310
$395$	0	0
$396$	−4.00000	−0.201008
$397$	16.0558	0.805818	0.402909	−	0.915240i	$-0.367999\pi$
$397$	16.0558	0.805818	0.402909	+	0.915240i	$0.367999\pi$
$398$	−20.3126	−1.01818
$399$	−2.10308	−0.105286
$400$	0	0
$401$	−14.8925	−0.743698	−0.371849	−	0.928293i	$-0.621276\pi$
$401$	−14.8925	−0.743698	−0.371849	+	0.928293i	$0.621276\pi$
$402$	2.85069	0.142179
$403$	45.6681	2.27489
$404$	16.4157	0.816710
$405$	0	0
$406$	5.60162	0.278004
$407$	−0.412335	−0.0204387
$408$	−10.0140	−0.495765
$409$	−18.3511	−0.907404	−0.453702	−	0.891153i	$-0.649897\pi$
$409$	−18.3511	−0.907404	−0.453702	+	0.891153i	$0.649897\pi$
$410$	0	0
$411$	7.94940	0.392115
$412$	−9.64015	−0.474936
$413$	−3.42003	−0.168289
$414$	−37.0741	−1.82209
$415$	0	0
$416$	5.62620	0.275847
$417$	9.90754	0.485174
$418$	−0.864641	−0.0422910
$419$	34.7509	1.69769	0.848847	−	0.528639i	$-0.177297\pi$
$419$	34.7509	1.69769	0.848847	+	0.528639i	$0.177297\pi$
$420$	0	0
$421$	−40.1589	−1.95722	−0.978612	−	0.205713i	$-0.934049\pi$
$421$	−40.1589	−1.95722	−0.978612	+	0.205713i	$0.934049\pi$
$422$	18.0419	0.878264
$423$	5.79383	0.281706
$424$	2.37380	0.115282
$425$	0	0
$426$	−28.1170	−1.36227
$427$	8.27405	0.400409
$428$	4.28467	0.207107
$429$	−13.4340	−0.648599
$430$	0	0
$431$	34.9571	1.68382	0.841912	−	0.539615i	$-0.181430\pi$
$431$	34.9571	1.68382	0.841912	+	0.539615i	$0.181430\pi$
$432$	4.49084	0.216066
$433$	1.13536	0.0545619	0.0272809	−	0.999628i	$-0.491315\pi$
$433$	1.13536	0.0545619	0.0272809	+	0.999628i	$0.491315\pi$
$434$	−6.18159	−0.296726
$435$	0	0
$436$	−13.4200	−0.642703
$437$	−8.01395	−0.383359
$438$	45.2943	2.16424
$439$	−6.80009	−0.324551	−0.162275	−	0.986746i	$-0.551883\pi$
$439$	−6.80009	−0.324551	−0.162275	+	0.986746i	$0.551883\pi$
$440$	0	0
$441$	−29.7003	−1.41430
$442$	−20.4017	−0.970410
$443$	38.0679	1.80866	0.904330	−	0.426835i	$-0.140371\pi$
$443$	38.0679	1.80866	0.904330	+	0.426835i	$0.140371\pi$
$444$	1.31695	0.0624995
$445$	0	0
$446$	−13.5231	−0.640338
$447$	−46.5048	−2.19960
$448$	−0.761557	−0.0359802
$449$	−18.5414	−0.875024	−0.437512	−	0.899212i	$-0.644140\pi$
$449$	−18.5414	−0.875024	−0.437512	+	0.899212i	$0.644140\pi$
$450$	0	0
$451$	2.29862	0.108238
$452$	−10.3232	−0.485563
$453$	−46.8959	−2.20336
$454$	13.6016	0.638356
$455$	0	0
$456$	2.76156	0.129322
$457$	16.3738	0.765934	0.382967	−	0.923762i	$-0.374902\pi$
$457$	16.3738	0.765934	0.382967	+	0.923762i	$0.374902\pi$
$458$	13.5877	0.634910
$459$	−16.2847	−0.760103
$460$	0	0
$461$	1.70470	0.0793959	0.0396979	−	0.999212i	$-0.487360\pi$
$461$	1.70470	0.0793959	0.0396979	+	0.999212i	$0.487360\pi$
$462$	1.81841	0.0846002
$463$	−10.0279	−0.466036	−0.233018	−	0.972472i	$-0.574860\pi$
$463$	−10.0279	−0.466036	−0.233018	+	0.972472i	$0.574860\pi$
$464$	−7.35548	−0.341470
$465$	0	0
$466$	25.5510	1.18363
$467$	32.7509	1.51553	0.757766	−	0.652526i	$-0.226291\pi$
$467$	32.7509	1.51553	0.757766	+	0.652526i	$0.226291\pi$
$468$	26.0279	1.20314
$469$	−0.786137	−0.0363004
$470$	0	0
$471$	40.9817	1.88834
$472$	4.49084	0.206708
$473$	−5.93545	−0.272912
$474$	−34.7110	−1.59433
$475$	0	0
$476$	2.76156	0.126576
$477$	10.9817	0.502816
$478$	−11.3309	−0.518263
$479$	27.2803	1.24647	0.623234	−	0.782035i	$-0.285818\pi$
$479$	27.2803	1.24647	0.623234	+	0.782035i	$0.285818\pi$
$480$	0	0
$481$	2.68305	0.122337
$482$	−1.25240	−0.0570451
$483$	16.8540	0.766884
$484$	−10.2524	−0.466018
$485$	0	0
$486$	−17.5510	−0.796130
$487$	−11.0741	−0.501817	−0.250908	−	0.968011i	$-0.580729\pi$
$487$	−11.0741	−0.501817	−0.250908	+	0.968011i	$0.580729\pi$
$488$	−10.8646	−0.491819
$489$	36.9205	1.66960
$490$	0	0
$491$	8.11704	0.366317	0.183158	−	0.983083i	$-0.441368\pi$
$491$	8.11704	0.366317	0.183158	+	0.983083i	$0.441368\pi$
$492$	−7.34153	−0.330982
$493$	26.6724	1.20127
$494$	5.62620	0.253135
$495$	0	0
$496$	8.11704	0.364466
$497$	7.75386	0.347808
$498$	−0.747604	−0.0335009
$499$	0.295298	0.0132193	0.00660967	−	0.999978i	$-0.497896\pi$
$499$	0.295298	0.0132193	0.00660967	+	0.999978i	$0.497896\pi$
$500$	0	0
$501$	27.1912	1.21481
$502$	10.5939	0.472830
$503$	19.6016	0.873993	0.436996	−	0.899463i	$-0.356042\pi$
$503$	19.6016	0.873993	0.436996	+	0.899463i	$0.356042\pi$
$504$	−3.52311	−0.156932
$505$	0	0
$506$	6.92919	0.308040
$507$	51.5144	2.28783
$508$	16.9817	0.753440
$509$	−1.79383	−0.0795102	−0.0397551	−	0.999209i	$-0.512658\pi$
$509$	−1.79383	−0.0795102	−0.0397551	+	0.999209i	$0.512658\pi$
$510$	0	0
$511$	−12.4908	−0.552562
$512$	1.00000	0.0441942
$513$	4.49084	0.198275
$514$	−0.153681	−0.00677859
$515$	0	0
$516$	18.9571	0.834540
$517$	−1.08287	−0.0476247
$518$	−0.363176	−0.0159570
$519$	8.23407	0.361436
$520$	0	0
$521$	−2.61850	−0.114719	−0.0573593	−	0.998354i	$-0.518268\pi$
$521$	−2.61850	−0.114719	−0.0573593	+	0.998354i	$0.518268\pi$
$522$	−34.0279	−1.48936
$523$	14.9956	0.655713	0.327857	−	0.944728i	$-0.393674\pi$
$523$	14.9956	0.655713	0.327857	+	0.944728i	$0.393674\pi$
$524$	0.541436	0.0236528
$525$	0	0
$526$	0.504792	0.0220100
$527$	−29.4340	−1.28216
$528$	−2.38776	−0.103914
$529$	41.2234	1.79232
$530$	0	0
$531$	20.7755	0.901580
$532$	−0.761557	−0.0330177
$533$	−14.9571	−0.647864
$534$	1.07081	0.0463384
$535$	0	0
$536$	1.03228	0.0445875
$537$	32.5693	1.40547
$538$	−3.49521	−0.150689
$539$	5.55102	0.239099
$540$	0	0
$541$	3.40608	0.146439	0.0732194	−	0.997316i	$-0.476673\pi$
$541$	3.40608	0.146439	0.0732194	+	0.997316i	$0.476673\pi$
$542$	5.47252	0.235065
$543$	40.2341	1.72661
$544$	−3.62620	−0.155472
$545$	0	0
$546$	−11.8324	−0.506378
$547$	4.74760	0.202993	0.101496	−	0.994836i	$-0.467637\pi$
$547$	4.74760	0.202993	0.101496	+	0.994836i	$0.467637\pi$
$548$	2.87859	0.122967
$549$	−50.2620	−2.14513
$550$	0	0
$551$	−7.35548	−0.313354
$552$	−22.1310	−0.941958
$553$	9.57227	0.407054
$554$	12.9538	0.550353
$555$	0	0
$556$	3.58767	0.152151
$557$	43.0462	1.82393	0.911964	−	0.410271i	$-0.134566\pi$
$557$	43.0462	1.82393	0.911964	+	0.410271i	$0.134566\pi$
$558$	37.5510	1.58966
$559$	38.6218	1.63353
$560$	0	0
$561$	8.65847	0.365561
$562$	0.153681	0.00648265
$563$	17.0096	0.716869	0.358434	−	0.933555i	$-0.383311\pi$
$563$	17.0096	0.716869	0.358434	+	0.933555i	$0.383311\pi$
$564$	3.45856	0.145632
$565$	0	0
$566$	−18.2341	−0.766435
$567$	1.12473	0.0472343
$568$	−10.1816	−0.427210
$569$	−19.7572	−0.828264	−0.414132	−	0.910217i	$-0.635915\pi$
$569$	−19.7572	−0.828264	−0.414132	+	0.910217i	$0.635915\pi$
$570$	0	0
$571$	−11.3973	−0.476964	−0.238482	−	0.971147i	$-0.576650\pi$
$571$	−11.3973	−0.476964	−0.238482	+	0.971147i	$0.576650\pi$
$572$	−4.86464	−0.203401
$573$	36.5587	1.52726
$574$	2.02458	0.0845043
$575$	0	0
$576$	4.62620	0.192758
$577$	−18.3372	−0.763386	−0.381693	−	0.924289i	$-0.624659\pi$
$577$	−18.3372	−0.763386	−0.381693	+	0.924289i	$0.624659\pi$
$578$	−3.85069	−0.160167
$579$	7.01832	0.291672
$580$	0	0
$581$	0.206167	0.00855327
$582$	−23.4865	−0.973546
$583$	−2.05249	−0.0850053
$584$	16.4017	0.678708
$585$	0	0
$586$	2.03853	0.0842110
$587$	−11.9475	−0.493127	−0.246563	−	0.969127i	$-0.579301\pi$
$587$	−11.9475	−0.493127	−0.246563	+	0.969127i	$0.579301\pi$
$588$	−17.7293	−0.731143
$589$	8.11704	0.334457
$590$	0	0
$591$	−54.9850	−2.26178
$592$	0.476886	0.0195999
$593$	−24.3911	−1.00162	−0.500811	−	0.865557i	$-0.666965\pi$
$593$	−24.3911	−1.00162	−0.500811	+	0.865557i	$0.666965\pi$
$594$	−3.88296	−0.159320
$595$	0	0
$596$	−16.8401	−0.689796
$597$	−56.0943	−2.29579
$598$	−45.0881	−1.84379
$599$	−21.0708	−0.860930	−0.430465	−	0.902607i	$-0.641650\pi$
$599$	−21.0708	−0.860930	−0.430465	+	0.902607i	$0.641650\pi$
$600$	0	0
$601$	32.3878	1.32112	0.660562	−	0.750771i	$-0.270318\pi$
$601$	32.3878	1.32112	0.660562	+	0.750771i	$0.270318\pi$
$602$	−5.22782	−0.213070
$603$	4.77551	0.194474
$604$	−16.9817	−0.690975
$605$	0	0
$606$	45.3328	1.84152
$607$	19.0183	0.771930	0.385965	−	0.922513i	$-0.373869\pi$
$607$	19.0183	0.771930	0.385965	+	0.922513i	$0.373869\pi$
$608$	1.00000	0.0405554
$609$	15.4692	0.626843
$610$	0	0
$611$	7.04623	0.285060
$612$	−16.7755	−0.678110
$613$	−23.5756	−0.952210	−0.476105	−	0.879389i	$-0.657952\pi$
$613$	−23.5756	−0.952210	−0.476105	+	0.879389i	$0.657952\pi$
$614$	16.5414	0.667558
$615$	0	0
$616$	0.658473	0.0265307
$617$	−26.2707	−1.05762	−0.528810	−	0.848740i	$-0.677361\pi$
$617$	−26.2707	−1.05762	−0.528810	+	0.848740i	$0.677361\pi$
$618$	−26.6218	−1.07089
$619$	11.4985	0.462165	0.231083	−	0.972934i	$-0.425773\pi$
$619$	11.4985	0.462165	0.231083	+	0.972934i	$0.425773\pi$
$620$	0	0
$621$	−35.9894	−1.44420
$622$	−21.4725	−0.860969
$623$	−0.295298	−0.0118309
$624$	15.5371	0.621980
$625$	0	0
$626$	−1.12141	−0.0448204
$627$	−2.38776	−0.0953578
$628$	14.8401	0.592183
$629$	−1.72928	−0.0689510
$630$	0	0
$631$	−45.8130	−1.82379	−0.911893	−	0.410427i	$-0.865380\pi$
$631$	−45.8130	−1.82379	−0.911893	+	0.410427i	$0.865380\pi$
$632$	−12.5693	−0.499982
$633$	49.8236	1.98031
$634$	−29.8882	−1.18701
$635$	0	0
$636$	6.55539	0.259938
$637$	−36.1204	−1.43114
$638$	6.35985	0.251789
$639$	−47.1020	−1.86333
$640$	0	0
$641$	1.36943	0.0540894	0.0270447	−	0.999634i	$-0.491390\pi$
$641$	1.36943	0.0540894	0.0270447	+	0.999634i	$0.491390\pi$
$642$	11.8324	0.466986
$643$	−24.7389	−0.975606	−0.487803	−	0.872954i	$-0.662201\pi$
$643$	−24.7389	−0.975606	−0.487803	+	0.872954i	$0.662201\pi$
$644$	6.10308	0.240495
$645$	0	0
$646$	−3.62620	−0.142671
$647$	−6.82611	−0.268362	−0.134181	−	0.990957i	$-0.542840\pi$
$647$	−6.82611	−0.268362	−0.134181	+	0.990957i	$0.542840\pi$
$648$	−1.47689	−0.0580175
$649$	−3.88296	−0.152420
$650$	0	0
$651$	−17.0708	−0.669058
$652$	13.3694	0.523587
$653$	6.91713	0.270688	0.135344	−	0.990799i	$-0.456786\pi$
$653$	6.91713	0.270688	0.135344	+	0.990799i	$0.456786\pi$
$654$	−37.0602	−1.44917
$655$	0	0
$656$	−2.65847	−0.103796
$657$	75.8776	2.96027
$658$	−0.953771	−0.0371819
$659$	9.44461	0.367910	0.183955	−	0.982935i	$-0.441110\pi$
$659$	9.44461	0.367910	0.183955	+	0.982935i	$0.441110\pi$
$660$	0	0
$661$	−22.1955	−0.863306	−0.431653	−	0.902040i	$-0.642070\pi$
$661$	−22.1955	−0.863306	−0.431653	+	0.902040i	$0.642070\pi$
$662$	32.3126	1.25586
$663$	−56.3405	−2.18808
$664$	−0.270718	−0.0105059
$665$	0	0
$666$	2.20617	0.0854873
$667$	58.9465	2.28242
$668$	9.84632	0.380966
$669$	−37.3449	−1.44384
$670$	0	0
$671$	9.39401	0.362652
$672$	−2.10308	−0.0811282
$673$	12.2986	0.474077	0.237039	−	0.971500i	$-0.423823\pi$
$673$	12.2986	0.474077	0.237039	+	0.971500i	$0.423823\pi$
$674$	26.3511	1.01501
$675$	0	0
$676$	18.6541	0.717466
$677$	−35.9527	−1.38178	−0.690888	−	0.722962i	$-0.742780\pi$
$677$	−35.9527	−1.38178	−0.690888	+	0.722962i	$0.742780\pi$
$678$	−28.5081	−1.09485
$679$	6.47689	0.248560
$680$	0	0
$681$	37.5616	1.43937
$682$	−7.01832	−0.268745
$683$	−9.00958	−0.344742	−0.172371	−	0.985032i	$-0.555143\pi$
$683$	−9.00958	−0.344742	−0.172371	+	0.985032i	$0.555143\pi$
$684$	4.62620	0.176887
$685$	0	0
$686$	10.2201	0.390206
$687$	37.5231	1.43160
$688$	6.86464	0.261712
$689$	13.3555	0.508803
$690$	0	0
$691$	−9.11078	−0.346590	−0.173295	−	0.984870i	$-0.555441\pi$
$691$	−9.11078	−0.346590	−0.173295	+	0.984870i	$0.555441\pi$
$692$	2.98168	0.113346
$693$	3.04623	0.115717
$694$	−2.77551	−0.105357
$695$	0	0
$696$	−20.3126	−0.769946
$697$	9.64015	0.365147
$698$	11.5510	0.437213
$699$	70.5606	2.66885
$700$	0	0
$701$	−14.7476	−0.557009	−0.278505	−	0.960435i	$-0.589839\pi$
$701$	−14.7476	−0.557009	−0.278505	+	0.960435i	$0.589839\pi$
$702$	25.2663	0.953617
$703$	0.476886	0.0179861
$704$	−0.864641	−0.0325874
$705$	0	0
$706$	−8.40171	−0.316202
$707$	−12.5015	−0.470166
$708$	12.4017	0.466085
$709$	−8.63389	−0.324253	−0.162126	−	0.986770i	$-0.551835\pi$
$709$	−8.63389	−0.324253	−0.162126	+	0.986770i	$0.551835\pi$
$710$	0	0
$711$	−58.1483	−2.18073
$712$	0.387755	0.0145317
$713$	−65.0496	−2.43613
$714$	7.62620	0.285403
$715$	0	0
$716$	11.7938	0.440756
$717$	−31.2909	−1.16858
$718$	22.7895	0.850495
$719$	−38.2759	−1.42745	−0.713726	−	0.700425i	$-0.752994\pi$
$719$	−38.2759	−1.42745	−0.713726	+	0.700425i	$0.752994\pi$
$720$	0	0
$721$	7.34153	0.273413
$722$	1.00000	0.0372161
$723$	−3.45856	−0.128625
$724$	14.5693	0.541465
$725$	0	0
$726$	−28.3126	−1.05078
$727$	−31.1893	−1.15675	−0.578373	−	0.815772i	$-0.696312\pi$
$727$	−31.1893	−1.15675	−0.578373	+	0.815772i	$0.696312\pi$
$728$	−4.28467	−0.158800
$729$	−44.0375	−1.63102
$730$	0	0
$731$	−24.8925	−0.920684
$732$	−30.0033	−1.10895
$733$	−13.9634	−0.515748	−0.257874	−	0.966179i	$-0.583022\pi$
$733$	−13.9634	−0.515748	−0.257874	+	0.966179i	$0.583022\pi$
$734$	4.06455	0.150025
$735$	0	0
$736$	−8.01395	−0.295398
$737$	−0.892548	−0.0328774
$738$	−12.2986	−0.452719
$739$	9.02165	0.331867	0.165933	−	0.986137i	$-0.446936\pi$
$739$	9.02165	0.331867	0.165933	+	0.986137i	$0.446936\pi$
$740$	0	0
$741$	15.5371	0.570768
$742$	−1.80779	−0.0663659
$743$	−15.0342	−0.551550	−0.275775	−	0.961222i	$-0.588934\pi$
$743$	−15.0342	−0.551550	−0.275775	+	0.961222i	$0.588934\pi$
$744$	22.4157	0.821798
$745$	0	0
$746$	−18.4017	−0.673734
$747$	−1.25240	−0.0458228
$748$	3.13536	0.114640
$749$	−3.26302	−0.119228
$750$	0	0
$751$	29.6681	1.08260	0.541301	−	0.840829i	$-0.317932\pi$
$751$	29.6681	1.08260	0.541301	+	0.840829i	$0.317932\pi$
$752$	1.25240	0.0456702
$753$	29.2557	1.06614
$754$	−41.3834	−1.50709
$755$	0	0
$756$	−3.42003	−0.124385
$757$	10.5819	0.384604	0.192302	−	0.981336i	$-0.438405\pi$
$757$	10.5819	0.384604	0.192302	+	0.981336i	$0.438405\pi$
$758$	1.23844	0.0449823
$759$	19.1354	0.694570
$760$	0	0
$761$	−0.979789	−0.0355173	−0.0177587	−	0.999842i	$-0.505653\pi$
$761$	−0.979789	−0.0355173	−0.0177587	+	0.999842i	$0.505653\pi$
$762$	46.8959	1.69886
$763$	10.2201	0.369993
$764$	13.2384	0.478950
$765$	0	0
$766$	16.8646	0.609344
$767$	25.2663	0.912315
$768$	2.76156	0.0996491
$769$	43.1772	1.55701	0.778505	−	0.627638i	$-0.215978\pi$
$769$	43.1772	1.55701	0.778505	+	0.627638i	$0.215978\pi$
$770$	0	0
$771$	−0.424399	−0.0152844
$772$	2.54144	0.0914683
$773$	37.5250	1.34968	0.674840	−	0.737964i	$-0.264213\pi$
$773$	37.5250	1.34968	0.674840	+	0.737964i	$0.264213\pi$
$774$	31.7572	1.14149
$775$	0	0
$776$	−8.50479	−0.305304
$777$	−1.00293	−0.0359799
$778$	8.59392	0.308107
$779$	−2.65847	−0.0952497
$780$	0	0
$781$	8.80342	0.315011
$782$	29.0602	1.03919
$783$	−33.0323	−1.18048
$784$	−6.42003	−0.229287
$785$	0	0
$786$	1.49521	0.0533323
$787$	22.5833	0.805008	0.402504	−	0.915418i	$-0.368140\pi$
$787$	22.5833	0.805008	0.402504	+	0.915418i	$0.368140\pi$
$788$	−19.9109	−0.709295
$789$	1.39401	0.0496282
$790$	0	0
$791$	7.86171	0.279530
$792$	−4.00000	−0.142134
$793$	−61.1266	−2.17067
$794$	16.0558	0.569799
$795$	0	0
$796$	−20.3126	−0.719960
$797$	35.9806	1.27450	0.637250	−	0.770657i	$-0.280072\pi$
$797$	35.9806	1.27450	0.637250	+	0.770657i	$0.280072\pi$
$798$	−2.10308	−0.0744484
$799$	−4.54144	−0.160664
$800$	0	0
$801$	1.79383	0.0633820
$802$	−14.8925	−0.525874
$803$	−14.1816	−0.500457
$804$	2.85069	0.100536
$805$	0	0
$806$	45.6681	1.60859
$807$	−9.65222	−0.339774
$808$	16.4157	0.577501
$809$	−0.955660	−0.0335992	−0.0167996	−	0.999859i	$-0.505348\pi$
$809$	−0.955660	−0.0335992	−0.0167996	+	0.999859i	$0.505348\pi$
$810$	0	0
$811$	−7.53707	−0.264662	−0.132331	−	0.991206i	$-0.542246\pi$
$811$	−7.53707	−0.264662	−0.132331	+	0.991206i	$0.542246\pi$
$812$	5.60162	0.196578
$813$	15.1127	0.530024
$814$	−0.412335	−0.0144523
$815$	0	0
$816$	−10.0140	−0.350558
$817$	6.86464	0.240163
$818$	−18.3511	−0.641632
$819$	−19.8217	−0.692628
$820$	0	0
$821$	13.3082	0.464460	0.232230	−	0.972661i	$-0.425398\pi$
$821$	13.3082	0.464460	0.232230	+	0.972661i	$0.425398\pi$
$822$	7.94940	0.277267
$823$	24.4050	0.850706	0.425353	−	0.905028i	$-0.360150\pi$
$823$	24.4050	0.850706	0.425353	+	0.905028i	$0.360150\pi$
$824$	−9.64015	−0.335831
$825$	0	0
$826$	−3.42003	−0.118998
$827$	−11.6874	−0.406411	−0.203206	−	0.979136i	$-0.565136\pi$
$827$	−11.6874	−0.406411	−0.203206	+	0.979136i	$0.565136\pi$
$828$	−37.0741	−1.28842
$829$	25.6541	0.891004	0.445502	−	0.895281i	$-0.353025\pi$
$829$	25.6541	0.891004	0.445502	+	0.895281i	$0.353025\pi$
$830$	0	0
$831$	35.7726	1.24094
$832$	5.62620	0.195053
$833$	23.2803	0.806615
$834$	9.90754	0.343070
$835$	0	0
$836$	−0.864641	−0.0299042
$837$	36.4523	1.25998
$838$	34.7509	1.20045
$839$	−2.91713	−0.100710	−0.0503552	−	0.998731i	$-0.516035\pi$
$839$	−2.91713	−0.100710	−0.0503552	+	0.998731i	$0.516035\pi$
$840$	0	0
$841$	25.1031	0.865624
$842$	−40.1589	−1.38397
$843$	0.424399	0.0146171
$844$	18.0419	0.621026
$845$	0	0
$846$	5.79383	0.199196
$847$	7.80779	0.268279
$848$	2.37380	0.0815167
$849$	−50.3544	−1.72816
$850$	0	0
$851$	−3.82174	−0.131008
$852$	−28.1170	−0.963274
$853$	−6.24281	−0.213750	−0.106875	−	0.994272i	$-0.534084\pi$
$853$	−6.24281	−0.213750	−0.106875	+	0.994272i	$0.534084\pi$
$854$	8.27405	0.283132
$855$	0	0
$856$	4.28467	0.146447
$857$	−23.2158	−0.793035	−0.396517	−	0.918027i	$-0.629781\pi$
$857$	−23.2158	−0.793035	−0.396517	+	0.918027i	$0.629781\pi$
$858$	−13.4340	−0.458629
$859$	−7.13536	−0.243455	−0.121728	−	0.992564i	$-0.538843\pi$
$859$	−7.13536	−0.243455	−0.121728	+	0.992564i	$0.538843\pi$
$860$	0	0
$861$	5.59099	0.190541
$862$	34.9571	1.19064
$863$	−7.31362	−0.248959	−0.124479	−	0.992222i	$-0.539726\pi$
$863$	−7.31362	−0.248959	−0.124479	+	0.992222i	$0.539726\pi$
$864$	4.49084	0.152781
$865$	0	0
$866$	1.13536	0.0385811
$867$	−10.6339	−0.361146
$868$	−6.18159	−0.209817
$869$	10.8680	0.368671
$870$	0	0
$871$	5.80779	0.196789
$872$	−13.4200	−0.454460
$873$	−39.3449	−1.33162
$874$	−8.01395	−0.271076
$875$	0	0
$876$	45.2943	1.53035
$877$	−22.0173	−0.743471	−0.371735	−	0.928339i	$-0.621237\pi$
$877$	−22.0173	−0.743471	−0.371735	+	0.928339i	$0.621237\pi$
$878$	−6.80009	−0.229492
$879$	5.62953	0.189879
$880$	0	0
$881$	11.7572	0.396110	0.198055	−	0.980191i	$-0.436538\pi$
$881$	11.7572	0.396110	0.198055	+	0.980191i	$0.436538\pi$
$882$	−29.7003	−1.00006
$883$	55.6560	1.87297	0.936487	−	0.350703i	$-0.114057\pi$
$883$	55.6560	1.87297	0.936487	+	0.350703i	$0.114057\pi$
$884$	−20.4017	−0.686184
$885$	0	0
$886$	38.0679	1.27892
$887$	−6.41566	−0.215417	−0.107708	−	0.994183i	$-0.534351\pi$
$887$	−6.41566	−0.215417	−0.107708	+	0.994183i	$0.534351\pi$
$888$	1.31695	0.0441938
$889$	−12.9325	−0.433743
$890$	0	0
$891$	1.27698	0.0427803
$892$	−13.5231	−0.452787
$893$	1.25240	0.0419098
$894$	−46.5048	−1.55535
$895$	0	0
$896$	−0.761557	−0.0254418
$897$	−124.513	−4.15738
$898$	−18.5414	−0.618736
$899$	−59.7047	−1.99126
$900$	0	0
$901$	−8.60788	−0.286770
$902$	2.29862	0.0765358
$903$	−14.4369	−0.480430
$904$	−10.3232	−0.343345
$905$	0	0
$906$	−46.8959	−1.55801
$907$	−57.1160	−1.89651	−0.948253	−	0.317516i	$-0.897151\pi$
$907$	−57.1160	−1.89651	−0.948253	+	0.317516i	$0.897151\pi$
$908$	13.6016	0.451386
$909$	75.9421	2.51884
$910$	0	0
$911$	−26.6339	−0.882420	−0.441210	−	0.897404i	$-0.645451\pi$
$911$	−26.6339	−0.882420	−0.441210	+	0.897404i	$0.645451\pi$
$912$	2.76156	0.0914443
$913$	0.234074	0.00774672
$914$	16.3738	0.541597
$915$	0	0
$916$	13.5877	0.448949
$917$	−0.412335	−0.0136165
$918$	−16.2847	−0.537474
$919$	6.63246	0.218785	0.109392	−	0.993999i	$-0.465110\pi$
$919$	6.63246	0.218785	0.109392	+	0.993999i	$0.465110\pi$
$920$	0	0
$921$	45.6801	1.50521
$922$	1.70470	0.0561414
$923$	−57.2836	−1.88551
$924$	1.81841	0.0598214
$925$	0	0
$926$	−10.0279	−0.329537
$927$	−44.5972	−1.46477
$928$	−7.35548	−0.241455
$929$	−50.0173	−1.64101	−0.820507	−	0.571637i	$-0.806309\pi$
$929$	−50.0173	−1.64101	−0.820507	+	0.571637i	$0.806309\pi$
$930$	0	0
$931$	−6.42003	−0.210408
$932$	25.5510	0.836952
$933$	−59.2976	−1.94132
$934$	32.7509	1.07164
$935$	0	0
$936$	26.0279	0.850749
$937$	−39.8882	−1.30309	−0.651545	−	0.758610i	$-0.725879\pi$
$937$	−39.8882	−1.30309	−0.651545	+	0.758610i	$0.725879\pi$
$938$	−0.786137	−0.0256683
$939$	−3.09683	−0.101061
$940$	0	0
$941$	−5.59829	−0.182499	−0.0912495	−	0.995828i	$-0.529086\pi$
$941$	−5.59829	−0.182499	−0.0912495	+	0.995828i	$0.529086\pi$
$942$	40.9817	1.33526
$943$	21.3049	0.693782
$944$	4.49084	0.146164
$945$	0	0
$946$	−5.93545	−0.192978
$947$	12.7110	0.413051	0.206525	−	0.978441i	$-0.433784\pi$
$947$	12.7110	0.413051	0.206525	+	0.978441i	$0.433784\pi$
$948$	−34.7110	−1.12736
$949$	92.2793	2.99551
$950$	0	0
$951$	−82.5379	−2.67648
$952$	2.76156	0.0895026
$953$	−57.0129	−1.84683	−0.923415	−	0.383804i	$-0.874614\pi$
$953$	−57.0129	−1.84683	−0.923415	+	0.383804i	$0.874614\pi$
$954$	10.9817	0.355545
$955$	0	0
$956$	−11.3309	−0.366468
$957$	17.5631	0.567734
$958$	27.2803	0.881387
$959$	−2.19221	−0.0707903
$960$	0	0
$961$	34.8863	1.12536
$962$	2.68305	0.0865051
$963$	19.8217	0.638747
$964$	−1.25240	−0.0403370
$965$	0	0
$966$	16.8540	0.542269
$967$	−33.0183	−1.06180	−0.530899	−	0.847435i	$-0.678146\pi$
$967$	−33.0183	−1.06180	−0.530899	+	0.847435i	$0.678146\pi$
$968$	−10.2524	−0.329524
$969$	−10.0140	−0.321695
$970$	0	0
$971$	−3.04623	−0.0977581	−0.0488791	−	0.998805i	$-0.515565\pi$
$971$	−3.04623	−0.0977581	−0.0488791	+	0.998805i	$0.515565\pi$
$972$	−17.5510	−0.562949
$973$	−2.73221	−0.0875907
$974$	−11.0741	−0.354838
$975$	0	0
$976$	−10.8646	−0.347769
$977$	13.4465	0.430192	0.215096	−	0.976593i	$-0.430994\pi$
$977$	13.4465	0.430192	0.215096	+	0.976593i	$0.430994\pi$
$978$	36.9205	1.18059
$979$	−0.335269	−0.0107152
$980$	0	0
$981$	−62.0837	−1.98218
$982$	8.11704	0.259025
$983$	−22.0646	−0.703750	−0.351875	−	0.936047i	$-0.614456\pi$
$983$	−22.0646	−0.703750	−0.351875	+	0.936047i	$0.614456\pi$
$984$	−7.34153	−0.234039
$985$	0	0
$986$	26.6724	0.849423
$987$	−2.63389	−0.0838378
$988$	5.62620	0.178993
$989$	−55.0129	−1.74931
$990$	0	0
$991$	51.9946	1.65166	0.825831	−	0.563917i	$-0.190706\pi$
$991$	51.9946	1.65166	0.825831	+	0.563917i	$0.190706\pi$
$992$	8.11704	0.257716
$993$	89.2330	2.83172
$994$	7.75386	0.245938
$995$	0	0
$996$	−0.747604	−0.0236887
$997$	−37.7693	−1.19616	−0.598082	−	0.801435i	$-0.704070\pi$
$997$	−37.7693	−1.19616	−0.598082	+	0.801435i	$0.704070\pi$
$998$	0.295298	0.00934749
$999$	2.14162	0.0677578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.a.n.1.3		3
3.2	odd	2		8550.2.a.ck.1.1		3
4.3	odd	2		7600.2.a.bi.1.1		3
5.2	odd	4		190.2.b.b.39.4	yes	6
5.3	odd	4		190.2.b.b.39.3	✓	6
5.4	even	2		950.2.a.i.1.1		3
15.2	even	4		1710.2.d.d.1369.3		6
15.8	even	4		1710.2.d.d.1369.6		6
15.14	odd	2		8550.2.a.cl.1.3		3
20.3	even	4		1520.2.d.j.609.1		6
20.7	even	4		1520.2.d.j.609.6		6
20.19	odd	2		7600.2.a.cd.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.b.39.3	✓	6	5.3	odd	4
190.2.b.b.39.4	yes	6	5.2	odd	4
950.2.a.i.1.1		3	5.4	even	2
950.2.a.n.1.3		3	1.1	even	1	trivial
1520.2.d.j.609.1		6	20.3	even	4
1520.2.d.j.609.6		6	20.7	even	4
1710.2.d.d.1369.3		6	15.2	even	4
1710.2.d.d.1369.6		6	15.8	even	4
7600.2.a.bi.1.1		3	4.3	odd	2
7600.2.a.cd.1.3		3	20.19	odd	2
8550.2.a.ck.1.1		3	3.2	odd	2
8550.2.a.cl.1.3		3	15.14	odd	2

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.76156 q^{3} +1.00000 q^{4} +2.76156 q^{6} -0.761557 q^{7} +1.00000 q^{8} +4.62620 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.76156 q^{3} +1.00000 q^{4} +2.76156 q^{6} -0.761557 q^{7} +1.00000 q^{8} +4.62620 q^{9} -0.864641 q^{11} +2.76156 q^{12} +5.62620 q^{13} -0.761557 q^{14} +1.00000 q^{16} -3.62620 q^{17} +4.62620 q^{18} +1.00000 q^{19} -2.10308 q^{21} -0.864641 q^{22} -8.01395 q^{23} +2.76156 q^{24} +5.62620 q^{26} +4.49084 q^{27} -0.761557 q^{28} -7.35548 q^{29} +8.11704 q^{31} +1.00000 q^{32} -2.38776 q^{33} -3.62620 q^{34} +4.62620 q^{36} +0.476886 q^{37} +1.00000 q^{38} +15.5371 q^{39} -2.65847 q^{41} -2.10308 q^{42} +6.86464 q^{43} -0.864641 q^{44} -8.01395 q^{46} +1.25240 q^{47} +2.76156 q^{48} -6.42003 q^{49} -10.0140 q^{51} +5.62620 q^{52} +2.37380 q^{53} +4.49084 q^{54} -0.761557 q^{56} +2.76156 q^{57} -7.35548 q^{58} +4.49084 q^{59} -10.8646 q^{61} +8.11704 q^{62} -3.52311 q^{63} +1.00000 q^{64} -2.38776 q^{66} +1.03228 q^{67} -3.62620 q^{68} -22.1310 q^{69} -10.1816 q^{71} +4.62620 q^{72} +16.4017 q^{73} +0.476886 q^{74} +1.00000 q^{76} +0.658473 q^{77} +15.5371 q^{78} -12.5693 q^{79} -1.47689 q^{81} -2.65847 q^{82} -0.270718 q^{83} -2.10308 q^{84} +6.86464 q^{86} -20.3126 q^{87} -0.864641 q^{88} +0.387755 q^{89} -4.28467 q^{91} -8.01395 q^{92} +22.4157 q^{93} +1.25240 q^{94} +2.76156 q^{96} -8.50479 q^{97} -6.42003 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{12} + 8 q^{13} + 4 q^{14} + 3 q^{16} - 2 q^{17} + 5 q^{18} + 3 q^{19} - 10 q^{21} + 2 q^{24} + 8 q^{26} + 2 q^{27} + 4 q^{28} - 8 q^{29} + 4 q^{31} + 3 q^{32} + 8 q^{33} - 2 q^{34} + 5 q^{36} + 14 q^{37} + 3 q^{38} + 10 q^{39} + 2 q^{41} - 10 q^{42} + 18 q^{43} - 14 q^{47} + 2 q^{48} - 3 q^{49} - 6 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} + 4 q^{56} + 2 q^{57} - 8 q^{58} + 2 q^{59} - 30 q^{61} + 4 q^{62} + 2 q^{63} + 3 q^{64} + 8 q^{66} + 2 q^{67} - 2 q^{68} - 22 q^{69} - 8 q^{71} + 5 q^{72} + 10 q^{73} + 14 q^{74} + 3 q^{76} - 8 q^{77} + 10 q^{78} - 17 q^{81} + 2 q^{82} - 6 q^{83} - 10 q^{84} + 18 q^{86} + 6 q^{87} - 14 q^{89} + 6 q^{91} + 4 q^{93} - 14 q^{94} + 2 q^{96} + 10 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^12 + 8 * q^13 + 4 * q^14 + 3 * q^16 - 2 * q^17 + 5 * q^18 + 3 * q^19 - 10 * q^21 + 2 * q^24 + 8 * q^26 + 2 * q^27 + 4 * q^28 - 8 * q^29 + 4 * q^31 + 3 * q^32 + 8 * q^33 - 2 * q^34 + 5 * q^36 + 14 * q^37 + 3 * q^38 + 10 * q^39 + 2 * q^41 - 10 * q^42 + 18 * q^43 - 14 * q^47 + 2 * q^48 - 3 * q^49 - 6 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 + 4 * q^56 + 2 * q^57 - 8 * q^58 + 2 * q^59 - 30 * q^61 + 4 * q^62 + 2 * q^63 + 3 * q^64 + 8 * q^66 + 2 * q^67 - 2 * q^68 - 22 * q^69 - 8 * q^71 + 5 * q^72 + 10 * q^73 + 14 * q^74 + 3 * q^76 - 8 * q^77 + 10 * q^78 - 17 * q^81 + 2 * q^82 - 6 * q^83 - 10 * q^84 + 18 * q^86 + 6 * q^87 - 14 * q^89 + 6 * q^91 + 4 * q^93 - 14 * q^94 + 2 * q^96 + 10 * q^97 - 3 * q^98 - 12 * q^99

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