LMFDB - Embedded newform 931.2.a.n.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 4x^{3} - 12x^{2} - x + 1 $ x^7 - 3x^6 - 6x^5 + 18x^4 + 4x^3 - 12*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.350729$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68364 q^{2} +1.11676 q^{3} +5.20193 q^{4} -2.50047 q^{5} +2.99699 q^{6} +8.59284 q^{8} -1.75284 q^{9} +O(q^{10})$	\(q+2.68364 q^{2} +1.11676 q^{3} +5.20193 q^{4} -2.50047 q^{5} +2.99699 q^{6} +8.59284 q^{8} -1.75284 q^{9} -6.71038 q^{10} +3.90997 q^{11} +5.80932 q^{12} +3.81822 q^{13} -2.79243 q^{15} +12.6562 q^{16} +0.499526 q^{17} -4.70400 q^{18} +1.00000 q^{19} -13.0073 q^{20} +10.4930 q^{22} -6.75794 q^{23} +9.59616 q^{24} +1.25237 q^{25} +10.2467 q^{26} -5.30779 q^{27} +1.90902 q^{29} -7.49389 q^{30} -4.15334 q^{31} +16.7791 q^{32} +4.36651 q^{33} +1.34055 q^{34} -9.11817 q^{36} -3.45034 q^{37} +2.68364 q^{38} +4.26404 q^{39} -21.4862 q^{40} -5.36728 q^{41} -5.67960 q^{43} +20.3394 q^{44} +4.38294 q^{45} -18.1359 q^{46} +11.7589 q^{47} +14.1340 q^{48} +3.36091 q^{50} +0.557852 q^{51} +19.8621 q^{52} -0.368058 q^{53} -14.2442 q^{54} -9.77678 q^{55} +1.11676 q^{57} +5.12314 q^{58} -3.72724 q^{59} -14.5261 q^{60} -9.33771 q^{61} -11.1461 q^{62} +19.7167 q^{64} -9.54736 q^{65} +11.7181 q^{66} -8.24577 q^{67} +2.59850 q^{68} -7.54701 q^{69} +0.281828 q^{71} -15.0619 q^{72} -10.8698 q^{73} -9.25948 q^{74} +1.39860 q^{75} +5.20193 q^{76} +11.4432 q^{78} +10.4780 q^{79} -31.6466 q^{80} -0.669016 q^{81} -14.4039 q^{82} +6.71931 q^{83} -1.24905 q^{85} -15.2420 q^{86} +2.13193 q^{87} +33.5978 q^{88} +6.27725 q^{89} +11.7622 q^{90} -35.1543 q^{92} -4.63830 q^{93} +31.5566 q^{94} -2.50047 q^{95} +18.7383 q^{96} -0.490341 q^{97} -6.85356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9	$ 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} - 22 q^{12} + 6 q^{13} + 2 q^{15} + 24 q^{16} + 19 q^{17} - 12 q^{18} + 7 q^{19} - 8 q^{20} - 6 q^{22} - q^{23} + 20 q^{24} - 3 q^{25} + 12 q^{26} - 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} - 14 q^{33} + 6 q^{34} + 46 q^{36} + 8 q^{37} + 2 q^{38} + 16 q^{39} - 10 q^{40} - 4 q^{41} + 4 q^{43} + 26 q^{44} + 14 q^{45} - 16 q^{46} + 5 q^{47} - 28 q^{48} + 16 q^{50} - 4 q^{51} + 42 q^{52} + 20 q^{53} - 24 q^{54} - 30 q^{55} - 2 q^{57} - 16 q^{59} - 44 q^{60} + 5 q^{61} + 24 q^{62} + 32 q^{64} + 26 q^{65} + 68 q^{66} - 4 q^{67} + 22 q^{68} - 36 q^{69} + 12 q^{71} + 3 q^{73} - 4 q^{74} + 18 q^{75} + 10 q^{76} - 14 q^{78} - 20 q^{79} - 4 q^{80} + 27 q^{81} - 48 q^{82} - 11 q^{83} + 26 q^{85} + 36 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} + 32 q^{90} - 30 q^{92} - 4 q^{93} + 16 q^{94} - 2 q^{95} - 12 q^{96} - 4 q^{97} + 15 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 - 22 * q^12 + 6 * q^13 + 2 * q^15 + 24 * q^16 + 19 * q^17 - 12 * q^18 + 7 * q^19 - 8 * q^20 - 6 * q^22 - q^23 + 20 * q^24 - 3 * q^25 + 12 * q^26 - 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 - 14 * q^33 + 6 * q^34 + 46 * q^36 + 8 * q^37 + 2 * q^38 + 16 * q^39 - 10 * q^40 - 4 * q^41 + 4 * q^43 + 26 * q^44 + 14 * q^45 - 16 * q^46 + 5 * q^47 - 28 * q^48 + 16 * q^50 - 4 * q^51 + 42 * q^52 + 20 * q^53 - 24 * q^54 - 30 * q^55 - 2 * q^57 - 16 * q^59 - 44 * q^60 + 5 * q^61 + 24 * q^62 + 32 * q^64 + 26 * q^65 + 68 * q^66 - 4 * q^67 + 22 * q^68 - 36 * q^69 + 12 * q^71 + 3 * q^73 - 4 * q^74 + 18 * q^75 + 10 * q^76 - 14 * q^78 - 20 * q^79 - 4 * q^80 + 27 * q^81 - 48 * q^82 - 11 * q^83 + 26 * q^85 + 36 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 + 32 * q^90 - 30 * q^92 - 4 * q^93 + 16 * q^94 - 2 * q^95 - 12 * q^96 - 4 * q^97 + 15 * 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 $

$2$	2.68364	1.89762	0.948811	−	0.315846i	$-0.102288\pi$
$2$	2.68364	1.89762	0.948811	+	0.315846i	$0.102288\pi$
$3$	1.11676	0.644763	0.322381	−	0.946610i	$-0.395517\pi$
$3$	1.11676	0.644763	0.322381	+	0.946610i	$0.395517\pi$
$4$	5.20193	2.60097
$5$	−2.50047	−1.11825	−0.559123	−	0.829085i	$-0.688862\pi$
$5$	−2.50047	−1.11825	−0.559123	+	0.829085i	$0.688862\pi$
$6$	2.99699	1.22352
$7$	0	0
$7$	0	0
$8$	8.59284	3.03803
$9$	−1.75284	−0.584281
$10$	−6.71038	−2.12201
$11$	3.90997	1.17890	0.589450	−	0.807805i	$-0.299344\pi$
$11$	3.90997	1.17890	0.589450	+	0.807805i	$0.299344\pi$
$12$	5.80932	1.67701
$13$	3.81822	1.05898	0.529492	−	0.848315i	$-0.322383\pi$
$13$	3.81822	1.05898	0.529492	+	0.848315i	$0.322383\pi$
$14$	0	0
$15$	−2.79243	−0.721003
$16$	12.6562	3.16406
$17$	0.499526	0.121153	0.0605765	−	0.998164i	$-0.480706\pi$
$17$	0.499526	0.121153	0.0605765	+	0.998164i	$0.480706\pi$
$18$	−4.70400	−1.10874
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−13.0073	−2.90852
$21$	0	0
$22$	10.4930	2.23711
$23$	−6.75794	−1.40913	−0.704564	−	0.709641i	$-0.748857\pi$
$23$	−6.75794	−1.40913	−0.704564	+	0.709641i	$0.748857\pi$
$24$	9.59616	1.95881
$25$	1.25237	0.250474
$26$	10.2467	2.00955
$27$	−5.30779	−1.02149
$28$	0	0
$29$	1.90902	0.354497	0.177248	−	0.984166i	$-0.443280\pi$
$29$	1.90902	0.354497	0.177248	+	0.984166i	$0.443280\pi$
$30$	−7.49389	−1.36819
$31$	−4.15334	−0.745962	−0.372981	−	0.927839i	$-0.621664\pi$
$31$	−4.15334	−0.745962	−0.372981	+	0.927839i	$0.621664\pi$
$32$	16.7791	2.96616
$33$	4.36651	0.760111
$34$	1.34055	0.229902
$35$	0	0
$36$	−9.11817	−1.51969
$37$	−3.45034	−0.567233	−0.283616	−	0.958938i	$-0.591534\pi$
$37$	−3.45034	−0.567233	−0.283616	+	0.958938i	$0.591534\pi$
$38$	2.68364	0.435344
$39$	4.26404	0.682793
$40$	−21.4862	−3.39726
$41$	−5.36728	−0.838229	−0.419114	−	0.907933i	$-0.637659\pi$
$41$	−5.36728	−0.838229	−0.419114	+	0.907933i	$0.637659\pi$
$42$	0	0
$43$	−5.67960	−0.866131	−0.433066	−	0.901362i	$-0.642568\pi$
$43$	−5.67960	−0.866131	−0.433066	+	0.901362i	$0.642568\pi$
$44$	20.3394	3.06628
$45$	4.38294	0.653370
$46$	−18.1359	−2.67399
$47$	11.7589	1.71521	0.857605	−	0.514309i	$-0.171952\pi$
$47$	11.7589	1.71521	0.857605	+	0.514309i	$0.171952\pi$
$48$	14.1340	2.04007
$49$	0	0
$50$	3.36091	0.475304
$51$	0.557852	0.0781149
$52$	19.8621	2.75438
$53$	−0.368058	−0.0505567	−0.0252783	−	0.999680i	$-0.508047\pi$
$53$	−0.368058	−0.0505567	−0.0252783	+	0.999680i	$0.508047\pi$
$54$	−14.2442	−1.93839
$55$	−9.77678	−1.31830
$56$	0	0
$57$	1.11676	0.147919
$58$	5.12314	0.672701
$59$	−3.72724	−0.485246	−0.242623	−	0.970121i	$-0.578008\pi$
$59$	−3.72724	−0.485246	−0.242623	+	0.970121i	$0.578008\pi$
$60$	−14.5261	−1.87531
$61$	−9.33771	−1.19557	−0.597786	−	0.801656i	$-0.703953\pi$
$61$	−9.33771	−1.19557	−0.597786	+	0.801656i	$0.703953\pi$
$62$	−11.1461	−1.41555
$63$	0	0
$64$	19.7167	2.46458
$65$	−9.54736	−1.18420
$66$	11.7181	1.44240
$67$	−8.24577	−1.00738	−0.503690	−	0.863884i	$-0.668025\pi$
$67$	−8.24577	−1.00738	−0.503690	+	0.863884i	$0.668025\pi$
$68$	2.59850	0.315115
$69$	−7.54701	−0.908553
$70$	0	0
$71$	0.281828	0.0334468	0.0167234	−	0.999860i	$-0.494677\pi$
$71$	0.281828	0.0334468	0.0167234	+	0.999860i	$0.494677\pi$
$72$	−15.0619	−1.77506
$73$	−10.8698	−1.27221	−0.636106	−	0.771602i	$-0.719456\pi$
$73$	−10.8698	−1.27221	−0.636106	+	0.771602i	$0.719456\pi$
$74$	−9.25948	−1.07639
$75$	1.39860	0.161496
$76$	5.20193	0.596703
$77$	0	0
$78$	11.4432	1.29568
$79$	10.4780	1.17887	0.589435	−	0.807816i	$-0.299350\pi$
$79$	10.4780	1.17887	0.589435	+	0.807816i	$0.299350\pi$
$80$	−31.6466	−3.53819
$81$	−0.669016	−0.0743351
$82$	−14.4039	−1.59064
$83$	6.71931	0.737540	0.368770	−	0.929521i	$-0.379779\pi$
$83$	6.71931	0.737540	0.368770	+	0.929521i	$0.379779\pi$
$84$	0	0
$85$	−1.24905	−0.135479
$86$	−15.2420	−1.64359
$87$	2.13193	0.228566
$88$	33.5978	3.58153
$89$	6.27725	0.665388	0.332694	−	0.943035i	$-0.392042\pi$
$89$	6.27725	0.665388	0.332694	+	0.943035i	$0.392042\pi$
$90$	11.7622	1.23985
$91$	0	0
$92$	−35.1543	−3.66509
$93$	−4.63830	−0.480969
$94$	31.5566	3.25482
$95$	−2.50047	−0.256543
$96$	18.7383	1.91247
$97$	−0.490341	−0.0497866	−0.0248933	−	0.999690i	$-0.507925\pi$
$97$	−0.490341	−0.0497866	−0.0248933	+	0.999690i	$0.507925\pi$
$98$	0	0
$99$	−6.85356	−0.688809
$100$	6.51474	0.651474
$101$	5.34737	0.532083	0.266041	−	0.963962i	$-0.414284\pi$
$101$	5.34737	0.532083	0.266041	+	0.963962i	$0.414284\pi$
$102$	1.49707	0.148233
$103$	11.9504	1.17751	0.588755	−	0.808312i	$-0.299618\pi$
$103$	11.9504	1.17751	0.588755	+	0.808312i	$0.299618\pi$
$104$	32.8093	3.21722
$105$	0	0
$106$	−0.987737	−0.0959375
$107$	−7.92619	−0.766254	−0.383127	−	0.923696i	$-0.625153\pi$
$107$	−7.92619	−0.766254	−0.383127	+	0.923696i	$0.625153\pi$
$108$	−27.6108	−2.65685
$109$	−8.95215	−0.857461	−0.428730	−	0.903433i	$-0.641039\pi$
$109$	−8.95215	−0.857461	−0.428730	+	0.903433i	$0.641039\pi$
$110$	−26.2374	−2.50164
$111$	−3.85321	−0.365731
$112$	0	0
$113$	−0.491403	−0.0462273	−0.0231137	−	0.999733i	$-0.507358\pi$
$113$	−0.491403	−0.0462273	−0.0231137	+	0.999733i	$0.507358\pi$
$114$	2.99699	0.280694
$115$	16.8980	1.57575
$116$	9.93061	0.922034
$117$	−6.69274	−0.618744
$118$	−10.0026	−0.920813
$119$	0	0
$120$	−23.9949	−2.19043
$121$	4.28788	0.389807
$122$	−25.0591	−2.26874
$123$	−5.99398	−0.540459
$124$	−21.6054	−1.94022
$125$	9.37085	0.838155
$126$	0	0
$127$	15.2498	1.35320	0.676599	−	0.736352i	$-0.263453\pi$
$127$	15.2498	1.35320	0.676599	+	0.736352i	$0.263453\pi$
$128$	19.3542	1.71069
$129$	−6.34277	−0.558449
$130$	−25.6217	−2.24717
$131$	7.29797	0.637627	0.318813	−	0.947817i	$-0.396716\pi$
$131$	7.29797	0.637627	0.318813	+	0.947817i	$0.396716\pi$
$132$	22.7143	1.97702
$133$	0	0
$134$	−22.1287	−1.91163
$135$	13.2720	1.14227
$136$	4.29235	0.368066
$137$	0.480682	0.0410674	0.0205337	−	0.999789i	$-0.493463\pi$
$137$	0.480682	0.0410674	0.0205337	+	0.999789i	$0.493463\pi$
$138$	−20.2535	−1.72409
$139$	14.5356	1.23289	0.616445	−	0.787398i	$-0.288572\pi$
$139$	14.5356	1.23289	0.616445	+	0.787398i	$0.288572\pi$
$140$	0	0
$141$	13.1319	1.10590
$142$	0.756324	0.0634693
$143$	14.9291	1.24844
$144$	−22.1844	−1.84870
$145$	−4.77346	−0.396415
$146$	−29.1706	−2.41417
$147$	0	0
$148$	−17.9484	−1.47535
$149$	9.02790	0.739594	0.369797	−	0.929113i	$-0.379427\pi$
$149$	9.02790	0.739594	0.369797	+	0.929113i	$0.379427\pi$
$150$	3.75334	0.306459
$151$	15.7057	1.27812	0.639058	−	0.769159i	$-0.279324\pi$
$151$	15.7057	1.27812	0.639058	+	0.769159i	$0.279324\pi$
$152$	8.59284	0.696971
$153$	−0.875591	−0.0707873
$154$	0	0
$155$	10.3853	0.834169
$156$	22.1813	1.77592
$157$	−17.1071	−1.36530	−0.682649	−	0.730747i	$-0.739172\pi$
$157$	−17.1071	−1.36530	−0.682649	+	0.730747i	$0.739172\pi$
$158$	28.1193	2.23705
$159$	−0.411034	−0.0325971
$160$	−41.9557	−3.31689
$161$	0	0
$162$	−1.79540	−0.141060
$163$	−17.2750	−1.35308	−0.676542	−	0.736404i	$-0.736522\pi$
$163$	−17.2750	−1.35308	−0.676542	+	0.736404i	$0.736522\pi$
$164$	−27.9202	−2.18020
$165$	−10.9183	−0.849991
$166$	18.0322	1.39957
$167$	−4.67778	−0.361977	−0.180989	−	0.983485i	$-0.557930\pi$
$167$	−4.67778	−0.361977	−0.180989	+	0.983485i	$0.557930\pi$
$168$	0	0
$169$	1.57881	0.121447
$170$	−3.35201	−0.257087
$171$	−1.75284	−0.134043
$172$	−29.5449	−2.25278
$173$	18.7344	1.42435	0.712176	−	0.702001i	$-0.247710\pi$
$173$	18.7344	1.42435	0.712176	+	0.702001i	$0.247710\pi$
$174$	5.72132	0.433732
$175$	0	0
$176$	49.4855	3.73011
$177$	−4.16245	−0.312869
$178$	16.8459	1.26265
$179$	17.2765	1.29130	0.645652	−	0.763631i	$-0.276586\pi$
$179$	17.2765	1.29130	0.645652	+	0.763631i	$0.276586\pi$
$180$	22.7997	1.69939
$181$	−15.7397	−1.16992	−0.584960	−	0.811062i	$-0.698890\pi$
$181$	−15.7397	−1.16992	−0.584960	+	0.811062i	$0.698890\pi$
$182$	0	0
$183$	−10.4280	−0.770860
$184$	−58.0699	−4.28097
$185$	8.62749	0.634306
$186$	−12.4475	−0.912697
$187$	1.95313	0.142827
$188$	61.1689	4.46120
$189$	0	0
$190$	−6.71038	−0.486822
$191$	1.01980	0.0737901	0.0368951	−	0.999319i	$-0.488253\pi$
$191$	1.01980	0.0737901	0.0368951	+	0.999319i	$0.488253\pi$
$192$	22.0188	1.58907
$193$	20.5861	1.48182	0.740910	−	0.671605i	$-0.234395\pi$
$193$	20.5861	1.48182	0.740910	+	0.671605i	$0.234395\pi$
$194$	−1.31590	−0.0944760
$195$	−10.6621	−0.763531
$196$	0	0
$197$	18.9676	1.35139	0.675693	−	0.737183i	$-0.263845\pi$
$197$	18.9676	1.35139	0.675693	+	0.737183i	$0.263845\pi$
$198$	−18.3925	−1.30710
$199$	22.3297	1.58291	0.791457	−	0.611225i	$-0.209323\pi$
$199$	22.3297	1.58291	0.791457	+	0.611225i	$0.209323\pi$
$200$	10.7614	0.760946
$201$	−9.20856	−0.649522
$202$	14.3504	1.00969
$203$	0	0
$204$	2.90191	0.203174
$205$	13.4208	0.937346
$206$	32.0706	2.23447
$207$	11.8456	0.823326
$208$	48.3243	3.35069
$209$	3.90997	0.270458
$210$	0	0
$211$	−12.3683	−0.851471	−0.425735	−	0.904848i	$-0.639985\pi$
$211$	−12.3683	−0.851471	−0.425735	+	0.904848i	$0.639985\pi$
$212$	−1.91461	−0.131496
$213$	0.314734	0.0215652
$214$	−21.2711	−1.45406
$215$	14.2017	0.968548
$216$	−45.6090	−3.10330
$217$	0	0
$218$	−24.0244	−1.62714
$219$	−12.1390	−0.820275
$220$	−50.8581	−3.42886
$221$	1.90730	0.128299
$222$	−10.3406	−0.694018
$223$	−7.92989	−0.531025	−0.265512	−	0.964107i	$-0.585541\pi$
$223$	−7.92989	−0.531025	−0.265512	+	0.964107i	$0.585541\pi$
$224$	0	0
$225$	−2.19521	−0.146347
$226$	−1.31875	−0.0877219
$227$	−11.4835	−0.762183	−0.381092	−	0.924537i	$-0.624452\pi$
$227$	−11.4835	−0.762183	−0.381092	+	0.924537i	$0.624452\pi$
$228$	5.80932	0.384732
$229$	−7.16879	−0.473727	−0.236864	−	0.971543i	$-0.576119\pi$
$229$	−7.16879	−0.473727	−0.236864	+	0.971543i	$0.576119\pi$
$230$	45.3483	2.99018
$231$	0	0
$232$	16.4039	1.07697
$233$	2.70758	0.177379	0.0886896	−	0.996059i	$-0.471732\pi$
$233$	2.70758	0.177379	0.0886896	+	0.996059i	$0.471732\pi$
$234$	−17.9609	−1.17414
$235$	−29.4028	−1.91803
$236$	−19.3889	−1.26211
$237$	11.7015	0.760091
$238$	0	0
$239$	1.73065	0.111947	0.0559733	−	0.998432i	$-0.482174\pi$
$239$	1.73065	0.111947	0.0559733	+	0.998432i	$0.482174\pi$
$240$	−35.3417	−2.28130
$241$	−13.9741	−0.900151	−0.450076	−	0.892990i	$-0.648603\pi$
$241$	−13.9741	−0.900151	−0.450076	+	0.892990i	$0.648603\pi$
$242$	11.5071	0.739706
$243$	15.1763	0.973557
$244$	−48.5741	−3.10964
$245$	0	0
$246$	−16.0857	−1.02559
$247$	3.81822	0.242948
$248$	−35.6890	−2.26625
$249$	7.50387	0.475539
$250$	25.1480	1.59050
$251$	−19.4746	−1.22923	−0.614613	−	0.788829i	$-0.710688\pi$
$251$	−19.4746	−1.22923	−0.614613	+	0.788829i	$0.710688\pi$
$252$	0	0
$253$	−26.4233	−1.66122
$254$	40.9249	2.56786
$255$	−1.39489	−0.0873517
$256$	12.5065	0.781656
$257$	7.56878	0.472127	0.236064	−	0.971738i	$-0.424143\pi$
$257$	7.56878	0.472127	0.236064	+	0.971738i	$0.424143\pi$
$258$	−17.0217	−1.05973
$259$	0	0
$260$	−49.6647	−3.08007
$261$	−3.34622	−0.207126
$262$	19.5851	1.20997
$263$	−21.8590	−1.34788	−0.673941	−	0.738785i	$-0.735400\pi$
$263$	−21.8590	−1.34788	−0.673941	+	0.738785i	$0.735400\pi$
$264$	37.5207	2.30924
$265$	0.920320	0.0565348
$266$	0	0
$267$	7.01020	0.429017
$268$	−42.8939	−2.62016
$269$	9.06825	0.552901	0.276450	−	0.961028i	$-0.410842\pi$
$269$	9.06825	0.552901	0.276450	+	0.961028i	$0.410842\pi$
$270$	35.6173	2.16760
$271$	−4.19137	−0.254608	−0.127304	−	0.991864i	$-0.540632\pi$
$271$	−4.19137	−0.254608	−0.127304	+	0.991864i	$0.540632\pi$
$272$	6.32212	0.383335
$273$	0	0
$274$	1.28998	0.0779304
$275$	4.89673	0.295284
$276$	−39.2590	−2.36312
$277$	25.9019	1.55629	0.778146	−	0.628083i	$-0.216160\pi$
$277$	25.9019	1.55629	0.778146	+	0.628083i	$0.216160\pi$
$278$	39.0082	2.33956
$279$	7.28016	0.435852
$280$	0	0
$281$	18.8291	1.12325	0.561625	−	0.827392i	$-0.310177\pi$
$281$	18.8291	1.12325	0.561625	+	0.827392i	$0.310177\pi$
$282$	35.2412	2.09859
$283$	−14.3402	−0.852435	−0.426218	−	0.904621i	$-0.640154\pi$
$283$	−14.3402	−0.852435	−0.426218	+	0.904621i	$0.640154\pi$
$284$	1.46605	0.0869940
$285$	−2.79243	−0.165410
$286$	40.0644	2.36906
$287$	0	0
$288$	−29.4111	−1.73307
$289$	−16.7505	−0.985322
$290$	−12.8103	−0.752245
$291$	−0.547594	−0.0321005
$292$	−56.5438	−3.30898
$293$	−24.6224	−1.43845	−0.719227	−	0.694775i	$-0.755504\pi$
$293$	−24.6224	−1.43845	−0.719227	+	0.694775i	$0.755504\pi$
$294$	0	0
$295$	9.31988	0.542624
$296$	−29.6482	−1.72327
$297$	−20.7533	−1.20423
$298$	24.2276	1.40347
$299$	−25.8033	−1.49224
$300$	7.27541	0.420046
$301$	0	0
$302$	42.1486	2.42538
$303$	5.97174	0.343067
$304$	12.6562	0.725885
$305$	23.3487	1.33694
$306$	−2.34977	−0.134328
$307$	15.7711	0.900106	0.450053	−	0.893002i	$-0.351405\pi$
$307$	15.7711	0.900106	0.450053	+	0.893002i	$0.351405\pi$
$308$	0	0
$309$	13.3458	0.759215
$310$	27.8705	1.58294
$311$	1.29333	0.0733380	0.0366690	−	0.999327i	$-0.488325\pi$
$311$	1.29333	0.0733380	0.0366690	+	0.999327i	$0.488325\pi$
$312$	36.6402	2.07434
$313$	−2.52189	−0.142546	−0.0712730	−	0.997457i	$-0.522706\pi$
$313$	−2.52189	−0.142546	−0.0712730	+	0.997457i	$0.522706\pi$
$314$	−45.9094	−2.59082
$315$	0	0
$316$	54.5060	3.06620
$317$	31.4384	1.76576	0.882879	−	0.469601i	$-0.155602\pi$
$317$	31.4384	1.76576	0.882879	+	0.469601i	$0.155602\pi$
$318$	−1.10307	−0.0618569
$319$	7.46423	0.417917
$320$	−49.3010	−2.75601
$321$	−8.85167	−0.494052
$322$	0	0
$323$	0.499526	0.0277944
$324$	−3.48018	−0.193343
$325$	4.78182	0.265248
$326$	−46.3599	−2.56764
$327$	−9.99742	−0.552859
$328$	−46.1202	−2.54656
$329$	0	0
$330$	−29.3009	−1.61296
$331$	−6.06509	−0.333367	−0.166684	−	0.986010i	$-0.553306\pi$
$331$	−6.06509	−0.333367	−0.166684	+	0.986010i	$0.553306\pi$
$332$	34.9534	1.91832
$333$	6.04791	0.331423
$334$	−12.5535	−0.686895
$335$	20.6183	1.12650
$336$	0	0
$337$	5.62125	0.306209	0.153104	−	0.988210i	$-0.451073\pi$
$337$	5.62125	0.306209	0.153104	+	0.988210i	$0.451073\pi$
$338$	4.23695	0.230460
$339$	−0.548780	−0.0298056
$340$	−6.49749	−0.352376
$341$	−16.2395	−0.879416
$342$	−4.70400	−0.254363
$343$	0	0
$344$	−48.8039	−2.63133
$345$	18.8711	1.01599
$346$	50.2765	2.70288
$347$	−8.00977	−0.429987	−0.214994	−	0.976615i	$-0.568973\pi$
$347$	−8.00977	−0.429987	−0.214994	+	0.976615i	$0.568973\pi$
$348$	11.0901	0.594494
$349$	5.41276	0.289739	0.144869	−	0.989451i	$-0.453724\pi$
$349$	5.41276	0.289739	0.144869	+	0.989451i	$0.453724\pi$
$350$	0	0
$351$	−20.2663	−1.08174
$352$	65.6059	3.49680
$353$	−22.0386	−1.17300	−0.586499	−	0.809950i	$-0.699494\pi$
$353$	−22.0386	−1.17300	−0.586499	+	0.809950i	$0.699494\pi$
$354$	−11.1705	−0.593706
$355$	−0.704703	−0.0374017
$356$	32.6539	1.73065
$357$	0	0
$358$	46.3639	2.45041
$359$	−4.45259	−0.234999	−0.117499	−	0.993073i	$-0.537488\pi$
$359$	−4.45259	−0.234999	−0.117499	+	0.993073i	$0.537488\pi$
$360$	37.6619	1.98495
$361$	1.00000	0.0526316
$362$	−42.2396	−2.22006
$363$	4.78854	0.251333
$364$	0	0
$365$	27.1796	1.42264
$366$	−27.9850	−1.46280
$367$	10.9327	0.570684	0.285342	−	0.958426i	$-0.407893\pi$
$367$	10.9327	0.570684	0.285342	+	0.958426i	$0.407893\pi$
$368$	−85.5300	−4.45856
$369$	9.40800	0.489761
$370$	23.1531	1.20367
$371$	0	0
$372$	−24.1281	−1.25098
$373$	23.0077	1.19129	0.595646	−	0.803247i	$-0.296896\pi$
$373$	23.0077	1.19129	0.595646	+	0.803247i	$0.296896\pi$
$374$	5.24151	0.271032
$375$	10.4650	0.540411
$376$	101.042	5.21085
$377$	7.28907	0.375406
$378$	0	0
$379$	7.81693	0.401529	0.200764	−	0.979640i	$-0.435657\pi$
$379$	7.81693	0.401529	0.200764	+	0.979640i	$0.435657\pi$
$380$	−13.0073	−0.667260
$381$	17.0304	0.872492
$382$	2.73678	0.140026
$383$	−30.7796	−1.57276	−0.786382	−	0.617741i	$-0.788048\pi$
$383$	−30.7796	−1.57276	−0.786382	+	0.617741i	$0.788048\pi$
$384$	21.6141	1.10299
$385$	0	0
$386$	55.2457	2.81193
$387$	9.95545	0.506064
$388$	−2.55072	−0.129493
$389$	12.6631	0.642046	0.321023	−	0.947071i	$-0.395973\pi$
$389$	12.6631	0.642046	0.321023	+	0.947071i	$0.395973\pi$
$390$	−28.6133	−1.44889
$391$	−3.37577	−0.170720
$392$	0	0
$393$	8.15010	0.411118
$394$	50.9022	2.56442
$395$	−26.2000	−1.31827
$396$	−35.6518	−1.79157
$397$	−20.3317	−1.02042	−0.510208	−	0.860051i	$-0.670432\pi$
$397$	−20.3317	−1.02042	−0.510208	+	0.860051i	$0.670432\pi$
$398$	59.9250	3.00377
$399$	0	0
$400$	15.8503	0.792514
$401$	12.2297	0.610723	0.305361	−	0.952237i	$-0.401223\pi$
$401$	12.2297	0.610723	0.305361	+	0.952237i	$0.401223\pi$
$402$	−24.7125	−1.23255
$403$	−15.8584	−0.789962
$404$	27.8166	1.38393
$405$	1.67286	0.0831249
$406$	0	0
$407$	−13.4907	−0.668711
$408$	4.79353	0.237315
$409$	−14.6092	−0.722379	−0.361189	−	0.932492i	$-0.617629\pi$
$409$	−14.6092	−0.722379	−0.361189	+	0.932492i	$0.617629\pi$
$410$	36.0165	1.77873
$411$	0.536807	0.0264787
$412$	62.1653	3.06266
$413$	0	0
$414$	31.7893	1.56236
$415$	−16.8015	−0.824751
$416$	64.0664	3.14111
$417$	16.2328	0.794922
$418$	10.4930	0.513228
$419$	5.59493	0.273330	0.136665	−	0.990617i	$-0.456362\pi$
$419$	5.59493	0.273330	0.136665	+	0.990617i	$0.456362\pi$
$420$	0	0
$421$	−29.1506	−1.42071	−0.710356	−	0.703843i	$-0.751466\pi$
$421$	−29.1506	−1.42071	−0.710356	+	0.703843i	$0.751466\pi$
$422$	−33.1922	−1.61577
$423$	−20.6115	−1.00216
$424$	−3.16267	−0.153593
$425$	0.625591	0.0303456
$426$	0.844634	0.0409227
$427$	0	0
$428$	−41.2315	−1.99300
$429$	16.6723	0.804946
$430$	38.1123	1.83794
$431$	15.6691	0.754754	0.377377	−	0.926060i	$-0.376826\pi$
$431$	15.6691	0.754754	0.377377	+	0.926060i	$0.376826\pi$
$432$	−67.1767	−3.23204
$433$	−2.31050	−0.111036	−0.0555178	−	0.998458i	$-0.517681\pi$
$433$	−2.31050	−0.111036	−0.0555178	+	0.998458i	$0.517681\pi$
$434$	0	0
$435$	−5.33082	−0.255593
$436$	−46.5685	−2.23023
$437$	−6.75794	−0.323276
$438$	−32.5766	−1.55657
$439$	−13.7514	−0.656317	−0.328159	−	0.944623i	$-0.606428\pi$
$439$	−13.7514	−0.656317	−0.328159	+	0.944623i	$0.606428\pi$
$440$	−84.0103	−4.00503
$441$	0	0
$442$	5.11851	0.243463
$443$	−21.3326	−1.01354	−0.506771	−	0.862081i	$-0.669161\pi$
$443$	−21.3326	−1.01354	−0.506771	+	0.862081i	$0.669161\pi$
$444$	−20.0441	−0.951253
$445$	−15.6961	−0.744067
$446$	−21.2810	−1.00768
$447$	10.0820	0.476863
$448$	0	0
$449$	−19.9216	−0.940160	−0.470080	−	0.882624i	$-0.655775\pi$
$449$	−19.9216	−0.940160	−0.470080	+	0.882624i	$0.655775\pi$
$450$	−5.89114	−0.277711
$451$	−20.9859	−0.988189
$452$	−2.55624	−0.120236
$453$	17.5396	0.824082
$454$	−30.8175	−1.44634
$455$	0	0
$456$	9.59616	0.449381
$457$	23.0073	1.07623	0.538117	−	0.842870i	$-0.319136\pi$
$457$	23.0073	1.07623	0.538117	+	0.842870i	$0.319136\pi$
$458$	−19.2385	−0.898955
$459$	−2.65138	−0.123756
$460$	87.9025	4.09847
$461$	38.4381	1.79024	0.895121	−	0.445824i	$-0.147089\pi$
$461$	38.4381	1.79024	0.895121	+	0.445824i	$0.147089\pi$
$462$	0	0
$463$	−21.4507	−0.996899	−0.498450	−	0.866919i	$-0.666097\pi$
$463$	−21.4507	−0.996899	−0.498450	+	0.866919i	$0.666097\pi$
$464$	24.1611	1.12165
$465$	11.5979	0.537841
$466$	7.26617	0.336599
$467$	7.30415	0.337996	0.168998	−	0.985616i	$-0.445947\pi$
$467$	7.30415	0.337996	0.168998	+	0.985616i	$0.445947\pi$
$468$	−34.8152	−1.60933
$469$	0	0
$470$	−78.9065	−3.63969
$471$	−19.1046	−0.880293
$472$	−32.0276	−1.47419
$473$	−22.2071	−1.02108
$474$	31.4025	1.44237
$475$	1.25237	0.0574626
$476$	0	0
$477$	0.645148	0.0295393
$478$	4.64445	0.212432
$479$	31.0308	1.41783	0.708917	−	0.705292i	$-0.249184\pi$
$479$	31.0308	1.41783	0.708917	+	0.705292i	$0.249184\pi$
$480$	−46.8546	−2.13861
$481$	−13.1742	−0.600690
$482$	−37.5015	−1.70815
$483$	0	0
$484$	22.3052	1.01387
$485$	1.22608	0.0556736
$486$	40.7276	1.84744
$487$	−9.67618	−0.438469	−0.219235	−	0.975672i	$-0.570356\pi$
$487$	−9.67618	−0.438469	−0.219235	+	0.975672i	$0.570356\pi$
$488$	−80.2374	−3.63218
$489$	−19.2921	−0.872418
$490$	0	0
$491$	1.50591	0.0679607	0.0339803	−	0.999423i	$-0.489182\pi$
$491$	1.50591	0.0679607	0.0339803	+	0.999423i	$0.489182\pi$
$492$	−31.1803	−1.40572
$493$	0.953608	0.0429483
$494$	10.2467	0.461022
$495$	17.1372	0.770258
$496$	−52.5657	−2.36027
$497$	0	0
$498$	20.1377	0.902392
$499$	−3.56223	−0.159467	−0.0797337	−	0.996816i	$-0.525407\pi$
$499$	−3.56223	−0.159467	−0.0797337	+	0.996816i	$0.525407\pi$
$500$	48.7465	2.18001
$501$	−5.22396	−0.233389
$502$	−52.2629	−2.33261
$503$	−7.20185	−0.321115	−0.160557	−	0.987027i	$-0.551329\pi$
$503$	−7.20185	−0.321115	−0.160557	+	0.987027i	$0.551329\pi$
$504$	0	0
$505$	−13.3709	−0.594999
$506$	−70.9108	−3.15237
$507$	1.76315	0.0783043
$508$	79.3282	3.51962
$509$	−14.0302	−0.621880	−0.310940	−	0.950430i	$-0.600644\pi$
$509$	−14.0302	−0.621880	−0.310940	+	0.950430i	$0.600644\pi$
$510$	−3.74340	−0.165760
$511$	0	0
$512$	−5.14551	−0.227401
$513$	−5.30779	−0.234345
$514$	20.3119	0.895919
$515$	−29.8817	−1.31675
$516$	−32.9946	−1.45251
$517$	45.9769	2.02206
$518$	0	0
$519$	20.9219	0.918369
$520$	−82.0389	−3.59764
$521$	−35.5422	−1.55713	−0.778566	−	0.627563i	$-0.784053\pi$
$521$	−35.5422	−1.55713	−0.778566	+	0.627563i	$0.784053\pi$
$522$	−8.98005	−0.393046
$523$	3.86196	0.168872	0.0844358	−	0.996429i	$-0.473091\pi$
$523$	3.86196	0.168872	0.0844358	+	0.996429i	$0.473091\pi$
$524$	37.9636	1.65845
$525$	0	0
$526$	−58.6617	−2.55777
$527$	−2.07470	−0.0903755
$528$	55.2635	2.40504
$529$	22.6697	0.985639
$530$	2.46981	0.107282
$531$	6.53327	0.283520
$532$	0	0
$533$	−20.4935	−0.887671
$534$	18.8129	0.814112
$535$	19.8192	0.856860
$536$	−70.8545	−3.06045
$537$	19.2937	0.832585
$538$	24.3359	1.04920
$539$	0	0
$540$	69.0400	2.97101
$541$	−1.84900	−0.0794946	−0.0397473	−	0.999210i	$-0.512655\pi$
$541$	−1.84900	−0.0794946	−0.0397473	+	0.999210i	$0.512655\pi$
$542$	−11.2481	−0.483149
$543$	−17.5775	−0.754321
$544$	8.38161	0.359359
$545$	22.3846	0.958852
$546$	0	0
$547$	37.8410	1.61796	0.808981	−	0.587834i	$-0.200019\pi$
$547$	37.8410	1.61796	0.808981	+	0.587834i	$0.200019\pi$
$548$	2.50047	0.106815
$549$	16.3675	0.698549
$550$	13.1411	0.560337
$551$	1.90902	0.0813272
$552$	−64.8502	−2.76021
$553$	0	0
$554$	69.5113	2.95325
$555$	9.63485	0.408977
$556$	75.6130	3.20671
$557$	−12.5528	−0.531881	−0.265941	−	0.963989i	$-0.585682\pi$
$557$	−12.5528	−0.531881	−0.265941	+	0.963989i	$0.585682\pi$
$558$	19.5373	0.827081
$559$	−21.6860	−0.917219
$560$	0	0
$561$	2.18119	0.0920897
$562$	50.5305	2.13150
$563$	43.6992	1.84170	0.920852	−	0.389913i	$-0.127495\pi$
$563$	43.6992	1.84170	0.920852	+	0.389913i	$0.127495\pi$
$564$	68.3111	2.87642
$565$	1.22874	0.0516935
$566$	−38.4839	−1.61760
$567$	0	0
$568$	2.42170	0.101612
$569$	13.7685	0.577205	0.288602	−	0.957449i	$-0.406809\pi$
$569$	13.7685	0.577205	0.288602	+	0.957449i	$0.406809\pi$
$570$	−7.49389	−0.313885
$571$	−8.60206	−0.359985	−0.179993	−	0.983668i	$-0.557607\pi$
$571$	−8.60206	−0.359985	−0.179993	+	0.983668i	$0.557607\pi$
$572$	77.6603	3.24714
$573$	1.13887	0.0475771
$574$	0	0
$575$	−8.46343	−0.352949
$576$	−34.5602	−1.44001
$577$	11.0778	0.461174	0.230587	−	0.973052i	$-0.425935\pi$
$577$	11.0778	0.461174	0.230587	+	0.973052i	$0.425935\pi$
$578$	−44.9523	−1.86977
$579$	22.9898	0.955422
$580$	−24.8312	−1.03106
$581$	0	0
$582$	−1.46955	−0.0609146
$583$	−1.43910	−0.0596013
$584$	−93.4022	−3.86501
$585$	16.7350	0.691908
$586$	−66.0776	−2.72964
$587$	−30.8292	−1.27246	−0.636229	−	0.771501i	$-0.719507\pi$
$587$	−30.8292	−1.27246	−0.636229	+	0.771501i	$0.719507\pi$
$588$	0	0
$589$	−4.15334	−0.171136
$590$	25.0112	1.02970
$591$	21.1823	0.871323
$592$	−43.6683	−1.79476
$593$	32.6485	1.34071	0.670356	−	0.742040i	$-0.266141\pi$
$593$	32.6485	1.34071	0.670356	+	0.742040i	$0.266141\pi$
$594$	−55.6945	−2.28517
$595$	0	0
$596$	46.9625	1.92366
$597$	24.9370	1.02060
$598$	−69.2468	−2.83171
$599$	32.4080	1.32415	0.662077	−	0.749436i	$-0.269675\pi$
$599$	32.4080	1.32415	0.662077	+	0.749436i	$0.269675\pi$
$600$	12.0179	0.490630
$601$	30.7942	1.25612	0.628061	−	0.778164i	$-0.283849\pi$
$601$	30.7942	1.25612	0.628061	+	0.778164i	$0.283849\pi$
$602$	0	0
$603$	14.4535	0.588593
$604$	81.7002	3.32434
$605$	−10.7217	−0.435900
$606$	16.0260	0.651012
$607$	16.7270	0.678929	0.339465	−	0.940619i	$-0.389754\pi$
$607$	16.7270	0.678929	0.339465	+	0.940619i	$0.389754\pi$
$608$	16.7791	0.680483
$609$	0	0
$610$	62.6595	2.53701
$611$	44.8980	1.81638
$612$	−4.55476	−0.184115
$613$	12.2408	0.494402	0.247201	−	0.968964i	$-0.420489\pi$
$613$	12.2408	0.494402	0.247201	+	0.968964i	$0.420489\pi$
$614$	42.3241	1.70806
$615$	14.9878	0.604366
$616$	0	0
$617$	−22.1670	−0.892410	−0.446205	−	0.894931i	$-0.647225\pi$
$617$	−22.1670	−0.892410	−0.446205	+	0.894931i	$0.647225\pi$
$618$	35.8153	1.44070
$619$	−11.2957	−0.454014	−0.227007	−	0.973893i	$-0.572894\pi$
$619$	−11.2957	−0.454014	−0.227007	+	0.973893i	$0.572894\pi$
$620$	54.0238	2.16965
$621$	35.8697	1.43940
$622$	3.47084	0.139168
$623$	0	0
$624$	53.9667	2.16040
$625$	−29.6934	−1.18774
$626$	−6.76786	−0.270498
$627$	4.36651	0.174382
$628$	−88.9901	−3.55109
$629$	−1.72354	−0.0687219
$630$	0	0
$631$	−6.41864	−0.255522	−0.127761	−	0.991805i	$-0.540779\pi$
$631$	−6.41864	−0.255522	−0.127761	+	0.991805i	$0.540779\pi$
$632$	90.0360	3.58144
$633$	−13.8125	−0.548997
$634$	84.3694	3.35074
$635$	−38.1316	−1.51321
$636$	−2.13817	−0.0847839
$637$	0	0
$638$	20.0313	0.793047
$639$	−0.493999	−0.0195423
$640$	−48.3948	−1.91297
$641$	−0.425712	−0.0168146	−0.00840731	−	0.999965i	$-0.502676\pi$
$641$	−0.425712	−0.0168146	−0.00840731	+	0.999965i	$0.502676\pi$
$642$	−23.7547	−0.937524
$643$	−1.43665	−0.0566558	−0.0283279	−	0.999599i	$-0.509018\pi$
$643$	−1.43665	−0.0566558	−0.0283279	+	0.999599i	$0.509018\pi$
$644$	0	0
$645$	15.8599	0.624484
$646$	1.34055	0.0527432
$647$	−15.2793	−0.600691	−0.300346	−	0.953830i	$-0.597102\pi$
$647$	−15.2793	−0.600691	−0.300346	+	0.953830i	$0.597102\pi$
$648$	−5.74875	−0.225832
$649$	−14.5734	−0.572057
$650$	12.8327	0.503340
$651$	0	0
$652$	−89.8634	−3.51932
$653$	30.5804	1.19670	0.598352	−	0.801233i	$-0.295822\pi$
$653$	30.5804	1.19670	0.598352	+	0.801233i	$0.295822\pi$
$654$	−26.8295	−1.04912
$655$	−18.2484	−0.713024
$656$	−67.9296	−2.65220
$657$	19.0530	0.743329
$658$	0	0
$659$	20.8936	0.813900	0.406950	−	0.913450i	$-0.366592\pi$
$659$	20.8936	0.813900	0.406950	+	0.913450i	$0.366592\pi$
$660$	−56.7965	−2.21080
$661$	18.8720	0.734036	0.367018	−	0.930214i	$-0.380379\pi$
$661$	18.8720	0.734036	0.367018	+	0.930214i	$0.380379\pi$
$662$	−16.2765	−0.632605
$663$	2.13000	0.0827224
$664$	57.7380	2.24067
$665$	0	0
$666$	16.2304	0.628916
$667$	−12.9011	−0.499531
$668$	−24.3335	−0.941490
$669$	−8.85580	−0.342385
$670$	55.3322	2.13767
$671$	−36.5102	−1.40946
$672$	0	0
$673$	−23.7927	−0.917140	−0.458570	−	0.888658i	$-0.651638\pi$
$673$	−23.7927	−0.917140	−0.458570	+	0.888658i	$0.651638\pi$
$674$	15.0854	0.581068
$675$	−6.64732	−0.255855
$676$	8.21285	0.315879
$677$	4.53271	0.174206	0.0871031	−	0.996199i	$-0.472239\pi$
$677$	4.53271	0.174206	0.0871031	+	0.996199i	$0.472239\pi$
$678$	−1.47273	−0.0565598
$679$	0	0
$680$	−10.7329	−0.411588
$681$	−12.8243	−0.491428
$682$	−43.5809	−1.66880
$683$	24.6042	0.941454	0.470727	−	0.882279i	$-0.343992\pi$
$683$	24.6042	0.941454	0.470727	+	0.882279i	$0.343992\pi$
$684$	−9.11817	−0.348642
$685$	−1.20193	−0.0459235
$686$	0	0
$687$	−8.00584	−0.305442
$688$	−71.8824	−2.74049
$689$	−1.40533	−0.0535387
$690$	50.6432	1.92796
$691$	−31.5197	−1.19907	−0.599534	−	0.800350i	$-0.704647\pi$
$691$	−31.5197	−1.19907	−0.599534	+	0.800350i	$0.704647\pi$
$692$	97.4551	3.70469
$693$	0	0
$694$	−21.4954	−0.815953
$695$	−36.3458	−1.37867
$696$	18.3193	0.694391
$697$	−2.68110	−0.101554
$698$	14.5259	0.549814
$699$	3.02372	0.114368
$700$	0	0
$701$	−22.9853	−0.868145	−0.434072	−	0.900878i	$-0.642924\pi$
$701$	−22.9853	−0.868145	−0.434072	+	0.900878i	$0.642924\pi$
$702$	−54.3876	−2.05273
$703$	−3.45034	−0.130132
$704$	77.0916	2.90550
$705$	−32.8359	−1.23667
$706$	−59.1438	−2.22591
$707$	0	0
$708$	−21.6528	−0.813760
$709$	−14.8812	−0.558876	−0.279438	−	0.960164i	$-0.590148\pi$
$709$	−14.8812	−0.558876	−0.279438	+	0.960164i	$0.590148\pi$
$710$	−1.89117	−0.0709743
$711$	−18.3663	−0.688791
$712$	53.9394	2.02147
$713$	28.0680	1.05116
$714$	0	0
$715$	−37.3299	−1.39606
$716$	89.8711	3.35864
$717$	1.93273	0.0721790
$718$	−11.9491	−0.445938
$719$	18.8456	0.702824	0.351412	−	0.936221i	$-0.385702\pi$
$719$	18.8456	0.702824	0.351412	+	0.936221i	$0.385702\pi$
$720$	55.4715	2.06730
$721$	0	0
$722$	2.68364	0.0998748
$723$	−15.6057	−0.580384
$724$	−81.8766	−3.04292
$725$	2.39080	0.0887922
$726$	12.8507	0.476935
$727$	−30.1414	−1.11788	−0.558942	−	0.829207i	$-0.688792\pi$
$727$	−30.1414	−1.11788	−0.558942	+	0.829207i	$0.688792\pi$
$728$	0	0
$729$	18.9553	0.702049
$730$	72.9403	2.69964
$731$	−2.83711	−0.104934
$732$	−54.2458	−2.00498
$733$	3.85253	0.142296	0.0711481	−	0.997466i	$-0.477334\pi$
$733$	3.85253	0.142296	0.0711481	+	0.997466i	$0.477334\pi$
$734$	29.3396	1.08294
$735$	0	0
$736$	−113.392	−4.17969
$737$	−32.2407	−1.18760
$738$	25.2477	0.929381
$739$	12.4494	0.457957	0.228979	−	0.973431i	$-0.426461\pi$
$739$	12.4494	0.457957	0.228979	+	0.973431i	$0.426461\pi$
$740$	44.8796	1.64981
$741$	4.26404	0.156644
$742$	0	0
$743$	−4.85312	−0.178044	−0.0890219	−	0.996030i	$-0.528374\pi$
$743$	−4.85312	−0.178044	−0.0890219	+	0.996030i	$0.528374\pi$
$744$	−39.8561	−1.46120
$745$	−22.5740	−0.827048
$746$	61.7443	2.26062
$747$	−11.7779	−0.430931
$748$	10.1601	0.371489
$749$	0	0
$750$	28.0843	1.02550
$751$	−46.4340	−1.69440	−0.847200	−	0.531274i	$-0.821714\pi$
$751$	−46.4340	−1.69440	−0.847200	+	0.531274i	$0.821714\pi$
$752$	148.823	5.42702
$753$	−21.7485	−0.792559
$754$	19.5613	0.712379
$755$	−39.2718	−1.42925
$756$	0	0
$757$	1.68974	0.0614145	0.0307073	−	0.999528i	$-0.490224\pi$
$757$	1.68974	0.0614145	0.0307073	+	0.999528i	$0.490224\pi$
$758$	20.9778	0.761950
$759$	−29.5086	−1.07109
$760$	−21.4862	−0.779385
$761$	27.4753	0.995980	0.497990	−	0.867183i	$-0.334072\pi$
$761$	27.4753	0.995980	0.497990	+	0.867183i	$0.334072\pi$
$762$	45.7034	1.65566
$763$	0	0
$764$	5.30493	0.191926
$765$	2.18939	0.0791576
$766$	−82.6014	−2.98451
$767$	−14.2314	−0.513868
$768$	13.9668	0.503983
$769$	40.8806	1.47419	0.737097	−	0.675787i	$-0.236196\pi$
$769$	40.8806	1.47419	0.737097	+	0.675787i	$0.236196\pi$
$770$	0	0
$771$	8.45252	0.304410
$772$	107.087	3.85416
$773$	51.3530	1.84704	0.923520	−	0.383549i	$-0.125298\pi$
$773$	51.3530	1.84704	0.923520	+	0.383549i	$0.125298\pi$
$774$	26.7169	0.960318
$775$	−5.20152	−0.186844
$776$	−4.21342	−0.151253
$777$	0	0
$778$	33.9833	1.21836
$779$	−5.36728	−0.192303
$780$	−55.4637	−1.98592
$781$	1.10194	0.0394304
$782$	−9.05935	−0.323962
$783$	−10.1327	−0.362113
$784$	0	0
$785$	42.7759	1.52674
$786$	21.8720	0.780147
$787$	37.0140	1.31941	0.659703	−	0.751526i	$-0.270682\pi$
$787$	37.0140	1.31941	0.659703	+	0.751526i	$0.270682\pi$
$788$	98.6682	3.51491
$789$	−24.4113	−0.869065
$790$	−70.3115	−2.50157
$791$	0	0
$792$	−58.8916	−2.09262
$793$	−35.6534	−1.26609
$794$	−54.5629	−1.93636
$795$	1.02778	0.0364516
$796$	116.158	4.11710
$797$	−7.22656	−0.255978	−0.127989	−	0.991776i	$-0.540852\pi$
$797$	−7.22656	−0.255978	−0.127989	+	0.991776i	$0.540852\pi$
$798$	0	0
$799$	5.87387	0.207803
$800$	21.0136	0.742944
$801$	−11.0030	−0.388773
$802$	32.8202	1.15892
$803$	−42.5005	−1.49981
$804$	−47.9023	−1.68938
$805$	0	0
$806$	−42.5582	−1.49905
$807$	10.1271	0.356490
$808$	45.9490	1.61648
$809$	−41.7468	−1.46774	−0.733869	−	0.679291i	$-0.762287\pi$
$809$	−41.7468	−1.46774	−0.733869	+	0.679291i	$0.762287\pi$
$810$	4.48935	0.157740
$811$	17.2252	0.604858	0.302429	−	0.953172i	$-0.402202\pi$
$811$	17.2252	0.604858	0.302429	+	0.953172i	$0.402202\pi$
$812$	0	0
$813$	−4.68077	−0.164162
$814$	−36.2043	−1.26896
$815$	43.1957	1.51308
$816$	7.06031	0.247160
$817$	−5.67960	−0.198704
$818$	−39.2059	−1.37080
$819$	0	0
$820$	69.8138	2.43800
$821$	38.9623	1.35979	0.679897	−	0.733308i	$-0.262025\pi$
$821$	38.9623	1.35979	0.679897	+	0.733308i	$0.262025\pi$
$822$	1.44060	0.0502466
$823$	−49.0696	−1.71046	−0.855229	−	0.518251i	$-0.826583\pi$
$823$	−49.0696	−1.71046	−0.855229	+	0.518251i	$0.826583\pi$
$824$	102.688	3.57731
$825$	5.46848	0.190388
$826$	0	0
$827$	−21.1748	−0.736321	−0.368160	−	0.929762i	$-0.620012\pi$
$827$	−21.1748	−0.736321	−0.368160	+	0.929762i	$0.620012\pi$
$828$	61.6200	2.14144
$829$	39.2362	1.36273	0.681364	−	0.731945i	$-0.261387\pi$
$829$	39.2362	1.36273	0.681364	+	0.731945i	$0.261387\pi$
$830$	−45.0891	−1.56507
$831$	28.9262	1.00344
$832$	75.2826	2.60995
$833$	0	0
$834$	43.5629	1.50846
$835$	11.6967	0.404779
$836$	20.3394	0.703453
$837$	22.0451	0.761990
$838$	15.0148	0.518677
$839$	0.378453	0.0130656	0.00653282	−	0.999979i	$-0.497921\pi$
$839$	0.378453	0.0130656	0.00653282	+	0.999979i	$0.497921\pi$
$840$	0	0
$841$	−25.3556	−0.874332
$842$	−78.2297	−2.69597
$843$	21.0276	0.724229
$844$	−64.3392	−2.21465
$845$	−3.94777	−0.135807
$846$	−55.3138	−1.90173
$847$	0	0
$848$	−4.65823	−0.159964
$849$	−16.0146	−0.549619
$850$	1.67886	0.0575845
$851$	23.3172	0.799303
$852$	1.63723	0.0560905
$853$	32.7401	1.12100	0.560500	−	0.828155i	$-0.310609\pi$
$853$	32.7401	1.12100	0.560500	+	0.828155i	$0.310609\pi$
$854$	0	0
$855$	4.38294	0.149893
$856$	−68.1085	−2.32790
$857$	42.1163	1.43867	0.719333	−	0.694666i	$-0.244448\pi$
$857$	42.1163	1.43867	0.719333	+	0.694666i	$0.244448\pi$
$858$	44.7424	1.52748
$859$	−36.3957	−1.24181	−0.620903	−	0.783887i	$-0.713234\pi$
$859$	−36.3957	−1.24181	−0.620903	+	0.783887i	$0.713234\pi$
$860$	73.8763	2.51916
$861$	0	0
$862$	42.0502	1.43224
$863$	−46.5786	−1.58555	−0.792777	−	0.609511i	$-0.791366\pi$
$863$	−46.5786	−1.58555	−0.792777	+	0.609511i	$0.791366\pi$
$864$	−89.0601	−3.02989
$865$	−46.8449	−1.59277
$866$	−6.20056	−0.210704
$867$	−18.7063	−0.635299
$868$	0	0
$869$	40.9688	1.38977
$870$	−14.3060	−0.485020
$871$	−31.4842	−1.06680
$872$	−76.9244	−2.60499
$873$	0.859490	0.0290893
$874$	−18.1359	−0.613455
$875$	0	0
$876$	−63.1460	−2.13351
$877$	−53.1054	−1.79324	−0.896621	−	0.442799i	$-0.853985\pi$
$877$	−53.1054	−1.79324	−0.896621	+	0.442799i	$0.853985\pi$
$878$	−36.9038	−1.24544
$879$	−27.4973	−0.927462
$880$	−123.737	−4.17118
$881$	−42.1837	−1.42120	−0.710602	−	0.703594i	$-0.751577\pi$
$881$	−42.1837	−1.42120	−0.710602	+	0.703594i	$0.751577\pi$
$882$	0	0
$883$	14.9249	0.502261	0.251131	−	0.967953i	$-0.419198\pi$
$883$	14.9249	0.502261	0.251131	+	0.967953i	$0.419198\pi$
$884$	9.92165	0.333701
$885$	10.4081	0.349864
$886$	−57.2491	−1.92332
$887$	−36.5221	−1.22629	−0.613145	−	0.789970i	$-0.710096\pi$
$887$	−36.5221	−1.22629	−0.613145	+	0.789970i	$0.710096\pi$
$888$	−33.1100	−1.11110
$889$	0	0
$890$	−42.1227	−1.41196
$891$	−2.61583	−0.0876337
$892$	−41.2507	−1.38118
$893$	11.7589	0.393496
$894$	27.0565	0.904905
$895$	−43.1994	−1.44400
$896$	0	0
$897$	−28.8161	−0.962143
$898$	−53.4625	−1.78407
$899$	−7.92883	−0.264441
$900$	−11.4193	−0.380644
$901$	−0.183855	−0.00612509
$902$	−56.3187	−1.87521
$903$	0	0
$904$	−4.22255	−0.140440
$905$	39.3566	1.30826
$906$	47.0700	1.56379
$907$	−48.3971	−1.60700	−0.803500	−	0.595305i	$-0.797031\pi$
$907$	−48.3971	−1.60700	−0.803500	+	0.595305i	$0.797031\pi$
$908$	−59.7361	−1.98241
$909$	−9.37309	−0.310886
$910$	0	0
$911$	23.0349	0.763181	0.381591	−	0.924331i	$-0.375376\pi$
$911$	23.0349	0.763181	0.381591	+	0.924331i	$0.375376\pi$
$912$	14.1340	0.468024
$913$	26.2723	0.869487
$914$	61.7432	2.04228
$915$	26.0749	0.862011
$916$	−37.2916	−1.23215
$917$	0	0
$918$	−7.11536	−0.234842
$919$	24.1697	0.797284	0.398642	−	0.917107i	$-0.369482\pi$
$919$	24.1697	0.797284	0.398642	+	0.917107i	$0.369482\pi$
$920$	145.202	4.78717
$921$	17.6126	0.580355
$922$	103.154	3.39720
$923$	1.07608	0.0354196
$924$	0	0
$925$	−4.32110	−0.142077
$926$	−57.5660	−1.89174
$927$	−20.9472	−0.687996
$928$	32.0317	1.05149
$929$	−27.7698	−0.911096	−0.455548	−	0.890211i	$-0.650557\pi$
$929$	−27.7698	−0.911096	−0.455548	+	0.890211i	$0.650557\pi$
$930$	31.1247	1.02062
$931$	0	0
$932$	14.0846	0.461357
$933$	1.44434	0.0472856
$934$	19.6017	0.641388
$935$	−4.88376	−0.159716
$936$	−57.5096	−1.87976
$937$	−33.2550	−1.08639	−0.543196	−	0.839606i	$-0.682786\pi$
$937$	−33.2550	−1.08639	−0.543196	+	0.839606i	$0.682786\pi$
$938$	0	0
$939$	−2.81636	−0.0919083
$940$	−152.951	−4.98872
$941$	−60.4396	−1.97027	−0.985137	−	0.171769i	$-0.945052\pi$
$941$	−60.4396	−1.97027	−0.985137	+	0.171769i	$0.945052\pi$
$942$	−51.2699	−1.67046
$943$	36.2718	1.18117
$944$	−47.1729	−1.53535
$945$	0	0
$946$	−59.5959	−1.93763
$947$	−14.7125	−0.478092	−0.239046	−	0.971008i	$-0.576835\pi$
$947$	−14.7125	−0.478092	−0.239046	+	0.971008i	$0.576835\pi$
$948$	60.8702	1.97697
$949$	−41.5032	−1.34725
$950$	3.36091	0.109042
$951$	35.1092	1.13849
$952$	0	0
$953$	5.03031	0.162948	0.0814738	−	0.996675i	$-0.474037\pi$
$953$	5.03031	0.162948	0.0814738	+	0.996675i	$0.474037\pi$
$954$	1.73135	0.0560544
$955$	−2.54998	−0.0825155
$956$	9.00273	0.291169
$957$	8.33577	0.269457
$958$	83.2756	2.69051
$959$	0	0
$960$	−55.0575	−1.77697
$961$	−13.7497	−0.443540
$962$	−35.3547	−1.13988
$963$	13.8934	0.447708
$964$	−72.6923	−2.34126
$965$	−51.4750	−1.65704
$966$	0	0
$967$	12.4769	0.401229	0.200614	−	0.979670i	$-0.435706\pi$
$967$	12.4769	0.401229	0.200614	+	0.979670i	$0.435706\pi$
$968$	36.8450	1.18424
$969$	0.557852	0.0179208
$970$	3.29037	0.105647
$971$	24.0239	0.770962	0.385481	−	0.922716i	$-0.374035\pi$
$971$	24.0239	0.770962	0.385481	+	0.922716i	$0.374035\pi$
$972$	78.9458	2.53219
$973$	0	0
$974$	−25.9674	−0.832049
$975$	5.34016	0.171022
$976$	−118.180	−3.78286
$977$	56.3027	1.80128	0.900642	−	0.434562i	$-0.143097\pi$
$977$	56.3027	1.80128	0.900642	+	0.434562i	$0.143097\pi$
$978$	−51.7730	−1.65552
$979$	24.5439	0.784426
$980$	0	0
$981$	15.6917	0.500998
$982$	4.04132	0.128964
$983$	−56.6327	−1.80630	−0.903151	−	0.429323i	$-0.858752\pi$
$983$	−56.6327	−1.80630	−0.903151	+	0.429323i	$0.858752\pi$
$984$	−51.5053	−1.64193
$985$	−47.4280	−1.51118
$986$	2.55914	0.0814997
$987$	0	0
$988$	19.8621	0.631898
$989$	38.3824	1.22049
$990$	45.9900	1.46166
$991$	−29.7864	−0.946196	−0.473098	−	0.881010i	$-0.656864\pi$
$991$	−29.7864	−0.946196	−0.473098	+	0.881010i	$0.656864\pi$
$992$	−69.6894	−2.21264
$993$	−6.77326	−0.214943
$994$	0	0
$995$	−55.8349	−1.77009
$996$	39.0346	1.23686
$997$	24.7456	0.783701	0.391851	−	0.920029i	$-0.371835\pi$
$997$	24.7456	0.783701	0.391851	+	0.920029i	$0.371835\pi$
$998$	−9.55975	−0.302609
$999$	18.3137	0.579420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.n.1.7		7
3.2	odd	2		8379.2.a.cl.1.1		7
7.2	even	3		133.2.f.d.39.1	✓	14
7.3	odd	6		931.2.f.p.324.1		14
7.4	even	3		133.2.f.d.58.1	yes	14
7.5	odd	6		931.2.f.p.704.1		14
7.6	odd	2		931.2.a.o.1.7		7
21.2	odd	6		1197.2.j.l.172.7		14
21.11	odd	6		1197.2.j.l.856.7		14
21.20	even	2		8379.2.a.ck.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.1	✓	14	7.2	even	3
133.2.f.d.58.1	yes	14	7.4	even	3
931.2.a.n.1.7		7	1.1	even	1	trivial
931.2.a.o.1.7		7	7.6	odd	2
931.2.f.p.324.1		14	7.3	odd	6
931.2.f.p.704.1		14	7.5	odd	6
1197.2.j.l.172.7		14	21.2	odd	6
1197.2.j.l.856.7		14	21.11	odd	6
8379.2.a.ck.1.1		7	21.20	even	2
8379.2.a.cl.1.1		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68364 q^{2} +1.11676 q^{3} +5.20193 q^{4} -2.50047 q^{5} +2.99699 q^{6} +8.59284 q^{8} -1.75284 q^{9} +O(q^{10})\)	\(q+2.68364 q^{2} +1.11676 q^{3} +5.20193 q^{4} -2.50047 q^{5} +2.99699 q^{6} +8.59284 q^{8} -1.75284 q^{9} -6.71038 q^{10} +3.90997 q^{11} +5.80932 q^{12} +3.81822 q^{13} -2.79243 q^{15} +12.6562 q^{16} +0.499526 q^{17} -4.70400 q^{18} +1.00000 q^{19} -13.0073 q^{20} +10.4930 q^{22} -6.75794 q^{23} +9.59616 q^{24} +1.25237 q^{25} +10.2467 q^{26} -5.30779 q^{27} +1.90902 q^{29} -7.49389 q^{30} -4.15334 q^{31} +16.7791 q^{32} +4.36651 q^{33} +1.34055 q^{34} -9.11817 q^{36} -3.45034 q^{37} +2.68364 q^{38} +4.26404 q^{39} -21.4862 q^{40} -5.36728 q^{41} -5.67960 q^{43} +20.3394 q^{44} +4.38294 q^{45} -18.1359 q^{46} +11.7589 q^{47} +14.1340 q^{48} +3.36091 q^{50} +0.557852 q^{51} +19.8621 q^{52} -0.368058 q^{53} -14.2442 q^{54} -9.77678 q^{55} +1.11676 q^{57} +5.12314 q^{58} -3.72724 q^{59} -14.5261 q^{60} -9.33771 q^{61} -11.1461 q^{62} +19.7167 q^{64} -9.54736 q^{65} +11.7181 q^{66} -8.24577 q^{67} +2.59850 q^{68} -7.54701 q^{69} +0.281828 q^{71} -15.0619 q^{72} -10.8698 q^{73} -9.25948 q^{74} +1.39860 q^{75} +5.20193 q^{76} +11.4432 q^{78} +10.4780 q^{79} -31.6466 q^{80} -0.669016 q^{81} -14.4039 q^{82} +6.71931 q^{83} -1.24905 q^{85} -15.2420 q^{86} +2.13193 q^{87} +33.5978 q^{88} +6.27725 q^{89} +11.7622 q^{90} -35.1543 q^{92} -4.63830 q^{93} +31.5566 q^{94} -2.50047 q^{95} +18.7383 q^{96} -0.490341 q^{97} -6.85356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9	\( 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} - 22 q^{12} + 6 q^{13} + 2 q^{15} + 24 q^{16} + 19 q^{17} - 12 q^{18} + 7 q^{19} - 8 q^{20} - 6 q^{22} - q^{23} + 20 q^{24} - 3 q^{25} + 12 q^{26} - 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} - 14 q^{33} + 6 q^{34} + 46 q^{36} + 8 q^{37} + 2 q^{38} + 16 q^{39} - 10 q^{40} - 4 q^{41} + 4 q^{43} + 26 q^{44} + 14 q^{45} - 16 q^{46} + 5 q^{47} - 28 q^{48} + 16 q^{50} - 4 q^{51} + 42 q^{52} + 20 q^{53} - 24 q^{54} - 30 q^{55} - 2 q^{57} - 16 q^{59} - 44 q^{60} + 5 q^{61} + 24 q^{62} + 32 q^{64} + 26 q^{65} + 68 q^{66} - 4 q^{67} + 22 q^{68} - 36 q^{69} + 12 q^{71} + 3 q^{73} - 4 q^{74} + 18 q^{75} + 10 q^{76} - 14 q^{78} - 20 q^{79} - 4 q^{80} + 27 q^{81} - 48 q^{82} - 11 q^{83} + 26 q^{85} + 36 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} + 32 q^{90} - 30 q^{92} - 4 q^{93} + 16 q^{94} - 2 q^{95} - 12 q^{96} - 4 q^{97} + 15 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 - 22 * q^12 + 6 * q^13 + 2 * q^15 + 24 * q^16 + 19 * q^17 - 12 * q^18 + 7 * q^19 - 8 * q^20 - 6 * q^22 - q^23 + 20 * q^24 - 3 * q^25 + 12 * q^26 - 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 - 14 * q^33 + 6 * q^34 + 46 * q^36 + 8 * q^37 + 2 * q^38 + 16 * q^39 - 10 * q^40 - 4 * q^41 + 4 * q^43 + 26 * q^44 + 14 * q^45 - 16 * q^46 + 5 * q^47 - 28 * q^48 + 16 * q^50 - 4 * q^51 + 42 * q^52 + 20 * q^53 - 24 * q^54 - 30 * q^55 - 2 * q^57 - 16 * q^59 - 44 * q^60 + 5 * q^61 + 24 * q^62 + 32 * q^64 + 26 * q^65 + 68 * q^66 - 4 * q^67 + 22 * q^68 - 36 * q^69 + 12 * q^71 + 3 * q^73 - 4 * q^74 + 18 * q^75 + 10 * q^76 - 14 * q^78 - 20 * q^79 - 4 * q^80 + 27 * q^81 - 48 * q^82 - 11 * q^83 + 26 * q^85 + 36 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 + 32 * q^90 - 30 * q^92 - 4 * q^93 + 16 * q^94 - 2 * q^95 - 12 * q^96 - 4 * q^97 + 15 * q^99

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