LMFDB - Embedded newform 4025.2.a.z.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.30520$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30520 q^{2} -0.930494 q^{3} +3.31395 q^{4} +2.14497 q^{6} -1.00000 q^{7} -3.02891 q^{8} -2.13418 q^{9} +O(q^{10})$	\(q-2.30520 q^{2} -0.930494 q^{3} +3.31395 q^{4} +2.14497 q^{6} -1.00000 q^{7} -3.02891 q^{8} -2.13418 q^{9} +0.709352 q^{11} -3.08361 q^{12} -3.91757 q^{13} +2.30520 q^{14} +0.354347 q^{16} -4.79009 q^{17} +4.91971 q^{18} +2.72673 q^{19} +0.930494 q^{21} -1.63520 q^{22} -1.00000 q^{23} +2.81838 q^{24} +9.03077 q^{26} +4.77732 q^{27} -3.31395 q^{28} +9.19789 q^{29} +4.59512 q^{31} +5.24098 q^{32} -0.660048 q^{33} +11.0421 q^{34} -7.07256 q^{36} -0.806689 q^{37} -6.28566 q^{38} +3.64527 q^{39} -5.49453 q^{41} -2.14497 q^{42} +11.2721 q^{43} +2.35076 q^{44} +2.30520 q^{46} -3.17718 q^{47} -0.329718 q^{48} +1.00000 q^{49} +4.45715 q^{51} -12.9826 q^{52} +14.0152 q^{53} -11.0127 q^{54} +3.02891 q^{56} -2.53721 q^{57} -21.2030 q^{58} -12.6497 q^{59} -4.77144 q^{61} -10.5927 q^{62} +2.13418 q^{63} -12.7902 q^{64} +1.52154 q^{66} -13.6404 q^{67} -15.8741 q^{68} +0.930494 q^{69} +16.5093 q^{71} +6.46424 q^{72} -8.26175 q^{73} +1.85958 q^{74} +9.03624 q^{76} -0.709352 q^{77} -8.40308 q^{78} +14.9425 q^{79} +1.95727 q^{81} +12.6660 q^{82} +3.90233 q^{83} +3.08361 q^{84} -25.9845 q^{86} -8.55858 q^{87} -2.14856 q^{88} +14.7492 q^{89} +3.91757 q^{91} -3.31395 q^{92} -4.27573 q^{93} +7.32404 q^{94} -4.87670 q^{96} -14.9733 q^{97} -2.30520 q^{98} -1.51389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * 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 $

$2$	−2.30520	−1.63002	−0.815011	−	0.579445i	$-0.803269\pi$
$2$	−2.30520	−1.63002	−0.815011	+	0.579445i	$0.803269\pi$
$3$	−0.930494	−0.537221	−0.268610	−	0.963249i	$-0.586564\pi$
$3$	−0.930494	−0.537221	−0.268610	+	0.963249i	$0.586564\pi$
$4$	3.31395	1.65697
$5$	0	0
$5$	0	0
$6$	2.14497	0.875682
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.02891	−1.07088
$9$	−2.13418	−0.711394
$10$	0	0
$11$	0.709352	0.213878	0.106939	−	0.994266i	$-0.465895\pi$
$11$	0.709352	0.213878	0.106939	+	0.994266i	$0.465895\pi$
$12$	−3.08361	−0.890160
$13$	−3.91757	−1.08654	−0.543269	−	0.839559i	$-0.682814\pi$
$13$	−3.91757	−1.08654	−0.543269	+	0.839559i	$0.682814\pi$
$14$	2.30520	0.616091
$15$	0	0
$16$	0.354347	0.0885869
$17$	−4.79009	−1.16177	−0.580884	−	0.813986i	$-0.697293\pi$
$17$	−4.79009	−1.16177	−0.580884	+	0.813986i	$0.697293\pi$
$18$	4.91971	1.15959
$19$	2.72673	0.625555	0.312777	−	0.949826i	$-0.398741\pi$
$19$	2.72673	0.625555	0.312777	+	0.949826i	$0.398741\pi$
$20$	0	0
$21$	0.930494	0.203050
$22$	−1.63520	−0.348626
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.81838	0.575300
$25$	0	0
$26$	9.03077	1.77108
$27$	4.77732	0.919396
$28$	−3.31395	−0.626277
$29$	9.19789	1.70801	0.854003	−	0.520268i	$-0.174168\pi$
$29$	9.19789	1.70801	0.854003	+	0.520268i	$0.174168\pi$
$30$	0	0
$31$	4.59512	0.825309	0.412654	−	0.910888i	$-0.364602\pi$
$31$	4.59512	0.825309	0.412654	+	0.910888i	$0.364602\pi$
$32$	5.24098	0.926482
$33$	−0.660048	−0.114900
$34$	11.0421	1.89371
$35$	0	0
$36$	−7.07256	−1.17876
$37$	−0.806689	−0.132619	−0.0663095	−	0.997799i	$-0.521122\pi$
$37$	−0.806689	−0.132619	−0.0663095	+	0.997799i	$0.521122\pi$
$38$	−6.28566	−1.01967
$39$	3.64527	0.583711
$40$	0	0
$41$	−5.49453	−0.858102	−0.429051	−	0.903280i	$-0.641152\pi$
$41$	−5.49453	−0.858102	−0.429051	+	0.903280i	$0.641152\pi$
$42$	−2.14497	−0.330977
$43$	11.2721	1.71898	0.859492	−	0.511149i	$-0.170780\pi$
$43$	11.2721	1.71898	0.859492	+	0.511149i	$0.170780\pi$
$44$	2.35076	0.354390
$45$	0	0
$46$	2.30520	0.339883
$47$	−3.17718	−0.463440	−0.231720	−	0.972783i	$-0.574435\pi$
$47$	−3.17718	−0.463440	−0.231720	+	0.972783i	$0.574435\pi$
$48$	−0.329718	−0.0475907
$49$	1.00000	0.142857
$50$	0	0
$51$	4.45715	0.624126
$52$	−12.9826	−1.80036
$53$	14.0152	1.92514	0.962568	−	0.271042i	$-0.0873682\pi$
$53$	14.0152	1.92514	0.962568	+	0.271042i	$0.0873682\pi$
$54$	−11.0127	−1.49864
$55$	0	0
$56$	3.02891	0.404755
$57$	−2.53721	−0.336061
$58$	−21.2030	−2.78409
$59$	−12.6497	−1.64685	−0.823425	−	0.567425i	$-0.807940\pi$
$59$	−12.6497	−1.64685	−0.823425	+	0.567425i	$0.807940\pi$
$60$	0	0
$61$	−4.77144	−0.610921	−0.305460	−	0.952205i	$-0.598810\pi$
$61$	−4.77144	−0.610921	−0.305460	+	0.952205i	$0.598810\pi$
$62$	−10.5927	−1.34527
$63$	2.13418	0.268882
$64$	−12.7902	−1.59877
$65$	0	0
$66$	1.52154	0.187289
$67$	−13.6404	−1.66644	−0.833218	−	0.552944i	$-0.813504\pi$
$67$	−13.6404	−1.66644	−0.833218	+	0.552944i	$0.813504\pi$
$68$	−15.8741	−1.92502
$69$	0.930494	0.112018
$70$	0	0
$71$	16.5093	1.95929	0.979646	−	0.200732i	$-0.0643320\pi$
$71$	16.5093	1.95929	0.979646	+	0.200732i	$0.0643320\pi$
$72$	6.46424	0.761818
$73$	−8.26175	−0.966964	−0.483482	−	0.875354i	$-0.660628\pi$
$73$	−8.26175	−0.966964	−0.483482	+	0.875354i	$0.660628\pi$
$74$	1.85958	0.216172
$75$	0	0
$76$	9.03624	1.03653
$77$	−0.709352	−0.0808382
$78$	−8.40308	−0.951461
$79$	14.9425	1.68117	0.840584	−	0.541682i	$-0.182212\pi$
$79$	14.9425	1.68117	0.840584	+	0.541682i	$0.182212\pi$
$80$	0	0
$81$	1.95727	0.217475
$82$	12.6660	1.39873
$83$	3.90233	0.428337	0.214168	−	0.976797i	$-0.431296\pi$
$83$	3.90233	0.428337	0.214168	+	0.976797i	$0.431296\pi$
$84$	3.08361	0.336449
$85$	0	0
$86$	−25.9845	−2.80198
$87$	−8.55858	−0.917576
$88$	−2.14856	−0.229038
$89$	14.7492	1.56341	0.781704	−	0.623649i	$-0.214351\pi$
$89$	14.7492	1.56341	0.781704	+	0.623649i	$0.214351\pi$
$90$	0	0
$91$	3.91757	0.410673
$92$	−3.31395	−0.345503
$93$	−4.27573	−0.443373
$94$	7.32404	0.755417
$95$	0	0
$96$	−4.87670	−0.497726
$97$	−14.9733	−1.52031	−0.760155	−	0.649741i	$-0.774877\pi$
$97$	−14.9733	−1.52031	−0.760155	+	0.649741i	$0.774877\pi$
$98$	−2.30520	−0.232860
$99$	−1.51389	−0.152151
$100$	0	0
$101$	1.93634	0.192673	0.0963365	−	0.995349i	$-0.469288\pi$
$101$	1.93634	0.192673	0.0963365	+	0.995349i	$0.469288\pi$
$102$	−10.2746	−1.01734
$103$	2.08106	0.205053	0.102526	−	0.994730i	$-0.467307\pi$
$103$	2.08106	0.205053	0.102526	+	0.994730i	$0.467307\pi$
$104$	11.8660	1.16355
$105$	0	0
$106$	−32.3078	−3.13801
$107$	−4.86119	−0.469949	−0.234974	−	0.972002i	$-0.575501\pi$
$107$	−4.86119	−0.469949	−0.234974	+	0.972002i	$0.575501\pi$
$108$	15.8318	1.52342
$109$	−6.18163	−0.592093	−0.296046	−	0.955174i	$-0.595668\pi$
$109$	−6.18163	−0.592093	−0.296046	+	0.955174i	$0.595668\pi$
$110$	0	0
$111$	0.750619	0.0712456
$112$	−0.354347	−0.0334827
$113$	2.56109	0.240927	0.120463	−	0.992718i	$-0.461562\pi$
$113$	2.56109	0.240927	0.120463	+	0.992718i	$0.461562\pi$
$114$	5.84877	0.547787
$115$	0	0
$116$	30.4813	2.83012
$117$	8.36080	0.772956
$118$	29.1601	2.68440
$119$	4.79009	0.439107
$120$	0	0
$121$	−10.4968	−0.954256
$122$	10.9991	0.995814
$123$	5.11263	0.460990
$124$	15.2280	1.36751
$125$	0	0
$126$	−4.91971	−0.438283
$127$	7.51001	0.666406	0.333203	−	0.942855i	$-0.391871\pi$
$127$	7.51001	0.666406	0.333203	+	0.942855i	$0.391871\pi$
$128$	19.0020	1.67956
$129$	−10.4886	−0.923474
$130$	0	0
$131$	−19.6300	−1.71509	−0.857543	−	0.514413i	$-0.828010\pi$
$131$	−19.6300	−1.71509	−0.857543	+	0.514413i	$0.828010\pi$
$132$	−2.18736	−0.190386
$133$	−2.72673	−0.236438
$134$	31.4438	2.71633
$135$	0	0
$136$	14.5088	1.24412
$137$	−15.6513	−1.33718	−0.668592	−	0.743630i	$-0.733103\pi$
$137$	−15.6513	−1.33718	−0.668592	+	0.743630i	$0.733103\pi$
$138$	−2.14497	−0.182592
$139$	−1.70351	−0.144489	−0.0722447	−	0.997387i	$-0.523016\pi$
$139$	−1.70351	−0.144489	−0.0722447	+	0.997387i	$0.523016\pi$
$140$	0	0
$141$	2.95635	0.248970
$142$	−38.0572	−3.19369
$143$	−2.77893	−0.232386
$144$	−0.756242	−0.0630201
$145$	0	0
$146$	19.0450	1.57617
$147$	−0.930494	−0.0767458
$148$	−2.67333	−0.219746
$149$	−23.7205	−1.94326	−0.971631	−	0.236501i	$-0.923999\pi$
$149$	−23.7205	−1.94326	−0.971631	+	0.236501i	$0.923999\pi$
$150$	0	0
$151$	−8.33717	−0.678469	−0.339235	−	0.940702i	$-0.610168\pi$
$151$	−8.33717	−0.678469	−0.339235	+	0.940702i	$0.610168\pi$
$152$	−8.25902	−0.669895
$153$	10.2229	0.826475
$154$	1.63520	0.131768
$155$	0	0
$156$	12.0802	0.967193
$157$	16.1332	1.28757	0.643786	−	0.765205i	$-0.277363\pi$
$157$	16.1332	1.28757	0.643786	+	0.765205i	$0.277363\pi$
$158$	−34.4455	−2.74034
$159$	−13.0411	−1.03422
$160$	0	0
$161$	1.00000	0.0788110
$162$	−4.51191	−0.354489
$163$	2.98990	0.234187	0.117093	−	0.993121i	$-0.462642\pi$
$163$	2.98990	0.234187	0.117093	+	0.993121i	$0.462642\pi$
$164$	−18.2086	−1.42185
$165$	0	0
$166$	−8.99566	−0.698199
$167$	16.9421	1.31102	0.655510	−	0.755186i	$-0.272454\pi$
$167$	16.9421	1.31102	0.655510	+	0.755186i	$0.272454\pi$
$168$	−2.81838	−0.217443
$169$	2.34733	0.180564
$170$	0	0
$171$	−5.81934	−0.445016
$172$	37.3552	2.84831
$173$	25.8095	1.96226	0.981132	−	0.193340i	$-0.0619321\pi$
$173$	25.8095	1.96226	0.981132	+	0.193340i	$0.0619321\pi$
$174$	19.7292	1.49567
$175$	0	0
$176$	0.251357	0.0189468
$177$	11.7705	0.884722
$178$	−33.9998	−2.54839
$179$	19.7074	1.47300	0.736499	−	0.676439i	$-0.236478\pi$
$179$	19.7074	1.47300	0.736499	+	0.676439i	$0.236478\pi$
$180$	0	0
$181$	−16.7299	−1.24352	−0.621761	−	0.783207i	$-0.713583\pi$
$181$	−16.7299	−1.24352	−0.621761	+	0.783207i	$0.713583\pi$
$182$	−9.03077	−0.669405
$183$	4.43980	0.328199
$184$	3.02891	0.223294
$185$	0	0
$186$	9.85642	0.722708
$187$	−3.39786	−0.248476
$188$	−10.5290	−0.767907
$189$	−4.77732	−0.347499
$190$	0	0
$191$	−0.000216850 0	−1.56907e−5 0	−7.84536e−6	−	1.00000i	$-0.500002\pi$
$191$	−0.000216850 0	−1.56907e−5 0	−7.84536e−6		1.00000i	$0.500002\pi$
$192$	11.9012	0.858895
$193$	4.11572	0.296256	0.148128	−	0.988968i	$-0.452675\pi$
$193$	4.11572	0.296256	0.148128	+	0.988968i	$0.452675\pi$
$194$	34.5165	2.47814
$195$	0	0
$196$	3.31395	0.236710
$197$	3.37351	0.240353	0.120176	−	0.992753i	$-0.461654\pi$
$197$	3.37351	0.240353	0.120176	+	0.992753i	$0.461654\pi$
$198$	3.48981	0.248010
$199$	11.3857	0.807110	0.403555	−	0.914955i	$-0.367774\pi$
$199$	11.3857	0.807110	0.403555	+	0.914955i	$0.367774\pi$
$200$	0	0
$201$	12.6923	0.895244
$202$	−4.46365	−0.314061
$203$	−9.19789	−0.645566
$204$	14.7708	1.03416
$205$	0	0
$206$	−4.79725	−0.334240
$207$	2.13418	0.148336
$208$	−1.38818	−0.0962529
$209$	1.93421	0.133792
$210$	0	0
$211$	−7.81930	−0.538303	−0.269152	−	0.963098i	$-0.586743\pi$
$211$	−7.81930	−0.538303	−0.269152	+	0.963098i	$0.586743\pi$
$212$	46.4456	3.18990
$213$	−15.3618	−1.05257
$214$	11.2060	0.766027
$215$	0	0
$216$	−14.4701	−0.984564
$217$	−4.59512	−0.311937
$218$	14.2499	0.965124
$219$	7.68750	0.519473
$220$	0	0
$221$	18.7655	1.26230
$222$	−1.73033	−0.116132
$223$	13.9469	0.933956	0.466978	−	0.884269i	$-0.345343\pi$
$223$	13.9469	0.933956	0.466978	+	0.884269i	$0.345343\pi$
$224$	−5.24098	−0.350177
$225$	0	0
$226$	−5.90382	−0.392716
$227$	−2.91510	−0.193482	−0.0967411	−	0.995310i	$-0.530842\pi$
$227$	−2.91510	−0.193482	−0.0967411	+	0.995310i	$0.530842\pi$
$228$	−8.40816	−0.556844
$229$	−8.49122	−0.561115	−0.280558	−	0.959837i	$-0.590519\pi$
$229$	−8.49122	−0.561115	−0.280558	+	0.959837i	$0.590519\pi$
$230$	0	0
$231$	0.660048	0.0434280
$232$	−27.8596	−1.82907
$233$	−16.3911	−1.07382	−0.536910	−	0.843640i	$-0.680408\pi$
$233$	−16.3911	−1.07382	−0.536910	+	0.843640i	$0.680408\pi$
$234$	−19.2733	−1.25994
$235$	0	0
$236$	−41.9204	−2.72879
$237$	−13.9039	−0.903158
$238$	−11.0421	−0.715754
$239$	13.2165	0.854904	0.427452	−	0.904038i	$-0.359411\pi$
$239$	13.2165	0.854904	0.427452	+	0.904038i	$0.359411\pi$
$240$	0	0
$241$	3.98974	0.257002	0.128501	−	0.991709i	$-0.458984\pi$
$241$	3.98974	0.257002	0.128501	+	0.991709i	$0.458984\pi$
$242$	24.1973	1.55546
$243$	−16.1532	−1.03623
$244$	−15.8123	−1.01228
$245$	0	0
$246$	−11.7856	−0.751424
$247$	−10.6821	−0.679689
$248$	−13.9182	−0.883807
$249$	−3.63110	−0.230111
$250$	0	0
$251$	−28.3197	−1.78753	−0.893763	−	0.448540i	$-0.851944\pi$
$251$	−28.3197	−1.78753	−0.893763	+	0.448540i	$0.851944\pi$
$252$	7.07256	0.445530
$253$	−0.709352	−0.0445966
$254$	−17.3121	−1.08626
$255$	0	0
$256$	−18.2230	−1.13894
$257$	10.6757	0.665930	0.332965	−	0.942939i	$-0.391951\pi$
$257$	10.6757	0.665930	0.332965	+	0.942939i	$0.391951\pi$
$258$	24.1784	1.50528
$259$	0.806689	0.0501252
$260$	0	0
$261$	−19.6300	−1.21506
$262$	45.2512	2.79563
$263$	6.86062	0.423044	0.211522	−	0.977373i	$-0.432158\pi$
$263$	6.86062	0.423044	0.211522	+	0.977373i	$0.432158\pi$
$264$	1.99922	0.123044
$265$	0	0
$266$	6.28566	0.385398
$267$	−13.7240	−0.839896
$268$	−45.2035	−2.76124
$269$	−24.4928	−1.49335	−0.746676	−	0.665188i	$-0.768352\pi$
$269$	−24.4928	−1.49335	−0.746676	+	0.665188i	$0.768352\pi$
$270$	0	0
$271$	−24.9077	−1.51303	−0.756517	−	0.653974i	$-0.773100\pi$
$271$	−24.9077	−1.51303	−0.756517	+	0.653974i	$0.773100\pi$
$272$	−1.69736	−0.102917
$273$	−3.64527	−0.220622
$274$	36.0795	2.17964
$275$	0	0
$276$	3.08361	0.185611
$277$	−8.34715	−0.501532	−0.250766	−	0.968048i	$-0.580682\pi$
$277$	−8.34715	−0.501532	−0.250766	+	0.968048i	$0.580682\pi$
$278$	3.92692	0.235521
$279$	−9.80683	−0.587119
$280$	0	0
$281$	−2.02096	−0.120561	−0.0602803	−	0.998181i	$-0.519199\pi$
$281$	−2.02096	−0.120561	−0.0602803	+	0.998181i	$0.519199\pi$
$282$	−6.81498	−0.405826
$283$	−6.65672	−0.395701	−0.197850	−	0.980232i	$-0.563396\pi$
$283$	−6.65672	−0.395701	−0.197850	+	0.980232i	$0.563396\pi$
$284$	54.7109	3.24649
$285$	0	0
$286$	6.40600	0.378795
$287$	5.49453	0.324332
$288$	−11.1852	−0.659094
$289$	5.94499	0.349706
$290$	0	0
$291$	13.9326	0.816743
$292$	−27.3790	−1.60223
$293$	23.0991	1.34947	0.674733	−	0.738062i	$-0.264259\pi$
$293$	23.0991	1.34947	0.674733	+	0.738062i	$0.264259\pi$
$294$	2.14497	0.125097
$295$	0	0
$296$	2.44339	0.142019
$297$	3.38881	0.196638
$298$	54.6806	3.16756
$299$	3.91757	0.226559
$300$	0	0
$301$	−11.2721	−0.649715
$302$	19.2188	1.10592
$303$	−1.80175	−0.103508
$304$	0.966210	0.0554159
$305$	0	0
$306$	−23.5659	−1.34717
$307$	12.4205	0.708873	0.354436	−	0.935080i	$-0.384673\pi$
$307$	12.4205	0.708873	0.354436	+	0.935080i	$0.384673\pi$
$308$	−2.35076	−0.133947
$309$	−1.93641	−0.110159
$310$	0	0
$311$	31.3617	1.77836	0.889179	−	0.457559i	$-0.151276\pi$
$311$	31.3617	1.77836	0.889179	+	0.457559i	$0.151276\pi$
$312$	−11.0412	−0.625084
$313$	−20.9153	−1.18220	−0.591101	−	0.806597i	$-0.701307\pi$
$313$	−20.9153	−1.18220	−0.591101	+	0.806597i	$0.701307\pi$
$314$	−37.1903	−2.09877
$315$	0	0
$316$	49.5188	2.78565
$317$	0.597601	0.0335646	0.0167823	−	0.999859i	$-0.494658\pi$
$317$	0.597601	0.0335646	0.0167823	+	0.999859i	$0.494658\pi$
$318$	30.0622	1.68581
$319$	6.52455	0.365304
$320$	0	0
$321$	4.52330	0.252466
$322$	−2.30520	−0.128464
$323$	−13.0613	−0.726750
$324$	6.48630	0.360350
$325$	0	0
$326$	−6.89231	−0.381730
$327$	5.75197	0.318085
$328$	16.6424	0.918925
$329$	3.17718	0.175164
$330$	0	0
$331$	−25.4744	−1.40020	−0.700099	−	0.714046i	$-0.746861\pi$
$331$	−25.4744	−1.40020	−0.700099	+	0.714046i	$0.746861\pi$
$332$	12.9321	0.709742
$333$	1.72162	0.0943443
$334$	−39.0550	−2.13699
$335$	0	0
$336$	0.329718	0.0179876
$337$	−14.5255	−0.791254	−0.395627	−	0.918411i	$-0.629473\pi$
$337$	−14.5255	−0.791254	−0.395627	+	0.918411i	$0.629473\pi$
$338$	−5.41106	−0.294323
$339$	−2.38308	−0.129431
$340$	0	0
$341$	3.25956	0.176515
$342$	13.4147	0.725386
$343$	−1.00000	−0.0539949
$344$	−34.1423	−1.84083
$345$	0	0
$346$	−59.4962	−3.19853
$347$	0.842635	0.0452350	0.0226175	−	0.999744i	$-0.492800\pi$
$347$	0.842635	0.0452350	0.0226175	+	0.999744i	$0.492800\pi$
$348$	−28.3627	−1.52040
$349$	−15.8934	−0.850756	−0.425378	−	0.905016i	$-0.639859\pi$
$349$	−15.8934	−0.850756	−0.425378	+	0.905016i	$0.639859\pi$
$350$	0	0
$351$	−18.7155	−0.998959
$352$	3.71770	0.198154
$353$	22.4359	1.19414	0.597071	−	0.802188i	$-0.296331\pi$
$353$	22.4359	1.19414	0.597071	+	0.802188i	$0.296331\pi$
$354$	−27.1333	−1.44212
$355$	0	0
$356$	48.8779	2.59053
$357$	−4.45715	−0.235897
$358$	−45.4294	−2.40102
$359$	−22.2373	−1.17364	−0.586820	−	0.809717i	$-0.699621\pi$
$359$	−22.2373	−1.17364	−0.586820	+	0.809717i	$0.699621\pi$
$360$	0	0
$361$	−11.5649	−0.608681
$362$	38.5657	2.02697
$363$	9.76722	0.512646
$364$	12.9826	0.680473
$365$	0	0
$366$	−10.2346	−0.534972
$367$	−10.1232	−0.528428	−0.264214	−	0.964464i	$-0.585112\pi$
$367$	−10.1232	−0.528428	−0.264214	+	0.964464i	$0.585112\pi$
$368$	−0.354347	−0.0184716
$369$	11.7263	0.610448
$370$	0	0
$371$	−14.0152	−0.727633
$372$	−14.1696	−0.734657
$373$	−5.50875	−0.285232	−0.142616	−	0.989778i	$-0.545551\pi$
$373$	−5.50875	−0.285232	−0.142616	+	0.989778i	$0.545551\pi$
$374$	7.83275	0.405022
$375$	0	0
$376$	9.62340	0.496289
$377$	−36.0334	−1.85581
$378$	11.0127	0.566431
$379$	20.6238	1.05937	0.529687	−	0.848193i	$-0.322309\pi$
$379$	20.6238	1.05937	0.529687	+	0.848193i	$0.322309\pi$
$380$	0	0
$381$	−6.98802	−0.358007
$382$	0.000499883 0	2.55762e−5 0
$383$	−8.06269	−0.411984	−0.205992	−	0.978554i	$-0.566042\pi$
$383$	−8.06269	−0.411984	−0.205992	+	0.978554i	$0.566042\pi$
$384$	−17.6812	−0.902292
$385$	0	0
$386$	−9.48755	−0.482904
$387$	−24.0568	−1.22287
$388$	−49.6208	−2.51911
$389$	17.9274	0.908953	0.454477	−	0.890759i	$-0.349826\pi$
$389$	17.9274	0.908953	0.454477	+	0.890759i	$0.349826\pi$
$390$	0	0
$391$	4.79009	0.242245
$392$	−3.02891	−0.152983
$393$	18.2656	0.921380
$394$	−7.77662	−0.391781
$395$	0	0
$396$	−5.01694	−0.252111
$397$	−29.2823	−1.46963	−0.734817	−	0.678265i	$-0.762732\pi$
$397$	−29.2823	−1.46963	−0.734817	+	0.678265i	$0.762732\pi$
$398$	−26.2463	−1.31561
$399$	2.53721	0.127019
$400$	0	0
$401$	4.35453	0.217455	0.108727	−	0.994072i	$-0.465322\pi$
$401$	4.35453	0.217455	0.108727	+	0.994072i	$0.465322\pi$
$402$	−29.2582	−1.45927
$403$	−18.0017	−0.896729
$404$	6.41693	0.319254
$405$	0	0
$406$	21.2030	1.05229
$407$	−0.572227	−0.0283642
$408$	−13.5003	−0.668365
$409$	−30.1195	−1.48932	−0.744658	−	0.667447i	$-0.767387\pi$
$409$	−30.1195	−1.48932	−0.744658	+	0.667447i	$0.767387\pi$
$410$	0	0
$411$	14.5635	0.718363
$412$	6.89651	0.339767
$413$	12.6497	0.622451
$414$	−4.91971	−0.241791
$415$	0	0
$416$	−20.5319	−1.00666
$417$	1.58510	0.0776227
$418$	−4.45875	−0.218084
$419$	−19.6444	−0.959690	−0.479845	−	0.877353i	$-0.659307\pi$
$419$	−19.6444	−0.959690	−0.479845	+	0.877353i	$0.659307\pi$
$420$	0	0
$421$	−10.4256	−0.508114	−0.254057	−	0.967189i	$-0.581765\pi$
$421$	−10.4256	−0.508114	−0.254057	+	0.967189i	$0.581765\pi$
$422$	18.0251	0.877446
$423$	6.78069	0.329688
$424$	−42.4507	−2.06159
$425$	0	0
$426$	35.4120	1.71572
$427$	4.77144	0.230906
$428$	−16.1097	−0.778692
$429$	2.58578	0.124843
$430$	0	0
$431$	−12.3810	−0.596370	−0.298185	−	0.954508i	$-0.596381\pi$
$431$	−12.3810	−0.596370	−0.298185	+	0.954508i	$0.596381\pi$
$432$	1.69283	0.0814464
$433$	−31.6045	−1.51882	−0.759409	−	0.650614i	$-0.774512\pi$
$433$	−31.6045	−1.51882	−0.759409	+	0.650614i	$0.774512\pi$
$434$	10.5927	0.508465
$435$	0	0
$436$	−20.4856	−0.981082
$437$	−2.72673	−0.130437
$438$	−17.7212	−0.846753
$439$	−21.9482	−1.04753	−0.523766	−	0.851862i	$-0.675473\pi$
$439$	−21.9482	−1.04753	−0.523766	+	0.851862i	$0.675473\pi$
$440$	0	0
$441$	−2.13418	−0.101628
$442$	−43.2582	−2.05758
$443$	−36.6972	−1.74354	−0.871768	−	0.489919i	$-0.837026\pi$
$443$	−36.6972	−1.74354	−0.871768	+	0.489919i	$0.837026\pi$
$444$	2.48751	0.118052
$445$	0	0
$446$	−32.1505	−1.52237
$447$	22.0718	1.04396
$448$	12.7902	0.604280
$449$	−13.5442	−0.639192	−0.319596	−	0.947554i	$-0.603547\pi$
$449$	−13.5442	−0.639192	−0.319596	+	0.947554i	$0.603547\pi$
$450$	0	0
$451$	−3.89756	−0.183529
$452$	8.48730	0.399209
$453$	7.75768	0.364488
$454$	6.71990	0.315380
$455$	0	0
$456$	7.68496	0.359881
$457$	20.7225	0.969358	0.484679	−	0.874692i	$-0.338936\pi$
$457$	20.7225	0.969358	0.484679	+	0.874692i	$0.338936\pi$
$458$	19.5739	0.914631
$459$	−22.8838	−1.06813
$460$	0	0
$461$	30.4075	1.41622	0.708110	−	0.706102i	$-0.249548\pi$
$461$	30.4075	1.41622	0.708110	+	0.706102i	$0.249548\pi$
$462$	−1.52154	−0.0707885
$463$	−2.56874	−0.119379	−0.0596896	−	0.998217i	$-0.519011\pi$
$463$	−2.56874	−0.119379	−0.0596896	+	0.998217i	$0.519011\pi$
$464$	3.25925	0.151307
$465$	0	0
$466$	37.7849	1.75035
$467$	−10.3342	−0.478211	−0.239105	−	0.970994i	$-0.576854\pi$
$467$	−10.3342	−0.478211	−0.239105	+	0.970994i	$0.576854\pi$
$468$	27.7072	1.28077
$469$	13.6404	0.629854
$470$	0	0
$471$	−15.0119	−0.691711
$472$	38.3148	1.76358
$473$	7.99591	0.367652
$474$	32.0514	1.47217
$475$	0	0
$476$	15.8741	0.727589
$477$	−29.9110	−1.36953
$478$	−30.4667	−1.39351
$479$	−3.13603	−0.143289	−0.0716444	−	0.997430i	$-0.522825\pi$
$479$	−3.13603	−0.143289	−0.0716444	+	0.997430i	$0.522825\pi$
$480$	0	0
$481$	3.16026	0.144095
$482$	−9.19714	−0.418918
$483$	−0.930494	−0.0423389
$484$	−34.7859	−1.58118
$485$	0	0
$486$	37.2364	1.68908
$487$	−21.1409	−0.957987	−0.478993	−	0.877818i	$-0.658998\pi$
$487$	−21.1409	−0.957987	−0.478993	+	0.877818i	$0.658998\pi$
$488$	14.4523	0.654223
$489$	−2.78208	−0.125810
$490$	0	0
$491$	−30.5820	−1.38015	−0.690073	−	0.723740i	$-0.742422\pi$
$491$	−30.5820	−1.38015	−0.690073	+	0.723740i	$0.742422\pi$
$492$	16.9430	0.763848
$493$	−44.0588	−1.98431
$494$	24.6245	1.10791
$495$	0	0
$496$	1.62827	0.0731115
$497$	−16.5093	−0.740543
$498$	8.37040	0.375087
$499$	−2.28112	−0.102117	−0.0510586	−	0.998696i	$-0.516260\pi$
$499$	−2.28112	−0.102117	−0.0510586	+	0.998696i	$0.516260\pi$
$500$	0	0
$501$	−15.7645	−0.704308
$502$	65.2826	2.91371
$503$	15.2047	0.677943	0.338971	−	0.940797i	$-0.389921\pi$
$503$	15.2047	0.677943	0.338971	+	0.940797i	$0.389921\pi$
$504$	−6.46424	−0.287940
$505$	0	0
$506$	1.63520	0.0726934
$507$	−2.18417	−0.0970025
$508$	24.8878	1.10422
$509$	−31.9407	−1.41575	−0.707874	−	0.706338i	$-0.750346\pi$
$509$	−31.9407	−1.41575	−0.707874	+	0.706338i	$0.750346\pi$
$510$	0	0
$511$	8.26175	0.365478
$512$	4.00370	0.176940
$513$	13.0265	0.575133
$514$	−24.6095	−1.08548
$515$	0	0
$516$	−34.7588	−1.53017
$517$	−2.25374	−0.0991195
$518$	−1.85958	−0.0817053
$519$	−24.0156	−1.05417
$520$	0	0
$521$	41.6912	1.82652	0.913261	−	0.407374i	$-0.133556\pi$
$521$	41.6912	1.82652	0.913261	+	0.407374i	$0.133556\pi$
$522$	45.2510	1.98058
$523$	−22.0295	−0.963281	−0.481641	−	0.876369i	$-0.659959\pi$
$523$	−22.0295	−0.963281	−0.481641	+	0.876369i	$0.659959\pi$
$524$	−65.0529	−2.84185
$525$	0	0
$526$	−15.8151	−0.689571
$527$	−22.0111	−0.958817
$528$	−0.233886	−0.0101786
$529$	1.00000	0.0434783
$530$	0	0
$531$	26.9967	1.17156
$532$	−9.03624	−0.391771
$533$	21.5252	0.932360
$534$	31.6366	1.36905
$535$	0	0
$536$	41.3154	1.78456
$537$	−18.3376	−0.791325
$538$	56.4608	2.43420
$539$	0.709352	0.0305540
$540$	0	0
$541$	13.7712	0.592068	0.296034	−	0.955177i	$-0.404336\pi$
$541$	13.7712	0.592068	0.296034	+	0.955177i	$0.404336\pi$
$542$	57.4172	2.46628
$543$	15.5671	0.668046
$544$	−25.1048	−1.07636
$545$	0	0
$546$	8.40308	0.359619
$547$	−26.4745	−1.13197	−0.565984	−	0.824416i	$-0.691504\pi$
$547$	−26.4745	−1.13197	−0.565984	+	0.824416i	$0.691504\pi$
$548$	−51.8677	−2.21568
$549$	10.1831	0.434605
$550$	0	0
$551$	25.0802	1.06845
$552$	−2.81838	−0.119958
$553$	−14.9425	−0.635422
$554$	19.2419	0.817508
$555$	0	0
$556$	−5.64533	−0.239415
$557$	−5.83619	−0.247287	−0.123644	−	0.992327i	$-0.539458\pi$
$557$	−5.83619	−0.247287	−0.123644	+	0.992327i	$0.539458\pi$
$558$	22.6067	0.957018
$559$	−44.1593	−1.86774
$560$	0	0
$561$	3.16169	0.133487
$562$	4.65873	0.196516
$563$	7.24108	0.305175	0.152588	−	0.988290i	$-0.451239\pi$
$563$	7.24108	0.305175	0.152588	+	0.988290i	$0.451239\pi$
$564$	9.79718	0.412536
$565$	0	0
$566$	15.3451	0.645001
$567$	−1.95727	−0.0821978
$568$	−50.0051	−2.09817
$569$	23.9768	1.00516	0.502580	−	0.864531i	$-0.332384\pi$
$569$	23.9768	1.00516	0.502580	+	0.864531i	$0.332384\pi$
$570$	0	0
$571$	−16.1798	−0.677104	−0.338552	−	0.940948i	$-0.609937\pi$
$571$	−16.1798	−0.677104	−0.338552	+	0.940948i	$0.609937\pi$
$572$	−9.20924	−0.385058
$573$	0.000201778 0	8.42938e−6 0
$574$	−12.6660	−0.528668
$575$	0	0
$576$	27.2966	1.13736
$577$	−1.21253	−0.0504782	−0.0252391	−	0.999681i	$-0.508035\pi$
$577$	−1.21253	−0.0504782	−0.0252391	+	0.999681i	$0.508035\pi$
$578$	−13.7044	−0.570028
$579$	−3.82965	−0.159155
$580$	0	0
$581$	−3.90233	−0.161896
$582$	−32.1174	−1.33131
$583$	9.94171	0.411744
$584$	25.0241	1.03550
$585$	0	0
$586$	−53.2481	−2.19966
$587$	31.6048	1.30447	0.652235	−	0.758017i	$-0.273831\pi$
$587$	31.6048	1.30447	0.652235	+	0.758017i	$0.273831\pi$
$588$	−3.08361	−0.127166
$589$	12.5297	0.516276
$590$	0	0
$591$	−3.13903	−0.129123
$592$	−0.285848	−0.0117483
$593$	12.7135	0.522080	0.261040	−	0.965328i	$-0.415935\pi$
$593$	12.7135	0.522080	0.261040	+	0.965328i	$0.415935\pi$
$594$	−7.81187	−0.320525
$595$	0	0
$596$	−78.6086	−3.21993
$597$	−10.5943	−0.433597
$598$	−9.03077	−0.369296
$599$	−4.67856	−0.191161	−0.0955804	−	0.995422i	$-0.530471\pi$
$599$	−4.67856	−0.191161	−0.0955804	+	0.995422i	$0.530471\pi$
$600$	0	0
$601$	40.3668	1.64659	0.823297	−	0.567611i	$-0.192132\pi$
$601$	40.3668	1.64659	0.823297	+	0.567611i	$0.192132\pi$
$602$	25.9845	1.05905
$603$	29.1110	1.18549
$604$	−27.6289	−1.12421
$605$	0	0
$606$	4.15340	0.168720
$607$	−19.3976	−0.787325	−0.393662	−	0.919255i	$-0.628792\pi$
$607$	−19.3976	−0.787325	−0.393662	+	0.919255i	$0.628792\pi$
$608$	14.2907	0.579566
$609$	8.55858	0.346811
$610$	0	0
$611$	12.4468	0.503545
$612$	33.8782	1.36945
$613$	−14.0340	−0.566830	−0.283415	−	0.958997i	$-0.591467\pi$
$613$	−14.0340	−0.566830	−0.283415	+	0.958997i	$0.591467\pi$
$614$	−28.6316	−1.15548
$615$	0	0
$616$	2.14856	0.0865681
$617$	29.0055	1.16772	0.583860	−	0.811855i	$-0.301542\pi$
$617$	29.0055	1.16772	0.583860	+	0.811855i	$0.301542\pi$
$618$	4.46381	0.179561
$619$	−9.40330	−0.377950	−0.188975	−	0.981982i	$-0.560517\pi$
$619$	−9.40330	−0.377950	−0.188975	+	0.981982i	$0.560517\pi$
$620$	0	0
$621$	−4.77732	−0.191707
$622$	−72.2950	−2.89876
$623$	−14.7492	−0.590913
$624$	1.29169	0.0517091
$625$	0	0
$626$	48.2139	1.92702
$627$	−1.79977	−0.0718760
$628$	53.4647	2.13347
$629$	3.86412	0.154072
$630$	0	0
$631$	−14.3553	−0.571474	−0.285737	−	0.958308i	$-0.592238\pi$
$631$	−14.3553	−0.571474	−0.285737	+	0.958308i	$0.592238\pi$
$632$	−45.2596	−1.80033
$633$	7.27581	0.289188
$634$	−1.37759	−0.0547110
$635$	0	0
$636$	−43.2173	−1.71368
$637$	−3.91757	−0.155220
$638$	−15.0404	−0.595455
$639$	−35.2338	−1.39383
$640$	0	0
$641$	34.2916	1.35444	0.677218	−	0.735782i	$-0.263185\pi$
$641$	34.2916	1.35444	0.677218	+	0.735782i	$0.263185\pi$
$642$	−10.4271	−0.411526
$643$	13.1024	0.516707	0.258353	−	0.966050i	$-0.416820\pi$
$643$	13.1024	0.516707	0.258353	+	0.966050i	$0.416820\pi$
$644$	3.31395	0.130588
$645$	0	0
$646$	30.1089	1.18462
$647$	−13.4922	−0.530435	−0.265217	−	0.964189i	$-0.585444\pi$
$647$	−13.4922	−0.530435	−0.265217	+	0.964189i	$0.585444\pi$
$648$	−5.92841	−0.232890
$649$	−8.97309	−0.352224
$650$	0	0
$651$	4.27573	0.167579
$652$	9.90836	0.388041
$653$	26.3357	1.03060	0.515298	−	0.857011i	$-0.327681\pi$
$653$	26.3357	1.03060	0.515298	+	0.857011i	$0.327681\pi$
$654$	−13.2594	−0.518485
$655$	0	0
$656$	−1.94697	−0.0760165
$657$	17.6321	0.687892
$658$	−7.32404	−0.285521
$659$	30.7155	1.19651	0.598253	−	0.801307i	$-0.295862\pi$
$659$	30.7155	1.19651	0.598253	+	0.801307i	$0.295862\pi$
$660$	0	0
$661$	−14.5710	−0.566745	−0.283372	−	0.959010i	$-0.591453\pi$
$661$	−14.5710	−0.566745	−0.283372	+	0.959010i	$0.591453\pi$
$662$	58.7235	2.28235
$663$	−17.4612	−0.678136
$664$	−11.8198	−0.458698
$665$	0	0
$666$	−3.96868	−0.153783
$667$	−9.19789	−0.356144
$668$	56.1453	2.17233
$669$	−12.9775	−0.501740
$670$	0	0
$671$	−3.38463	−0.130662
$672$	4.87670	0.188123
$673$	14.3211	0.552038	0.276019	−	0.961152i	$-0.410985\pi$
$673$	14.3211	0.552038	0.276019	+	0.961152i	$0.410985\pi$
$674$	33.4842	1.28976
$675$	0	0
$676$	7.77891	0.299189
$677$	−28.3658	−1.09019	−0.545094	−	0.838375i	$-0.683506\pi$
$677$	−28.3658	−1.09019	−0.545094	+	0.838375i	$0.683506\pi$
$678$	5.49346	0.210975
$679$	14.9733	0.574623
$680$	0	0
$681$	2.71249	0.103943
$682$	−7.51394	−0.287724
$683$	−3.53372	−0.135214	−0.0676071	−	0.997712i	$-0.521536\pi$
$683$	−3.53372	−0.135214	−0.0676071	+	0.997712i	$0.521536\pi$
$684$	−19.2850	−0.737379
$685$	0	0
$686$	2.30520	0.0880129
$687$	7.90102	0.301443
$688$	3.99425	0.152279
$689$	−54.9055	−2.09173
$690$	0	0
$691$	21.9959	0.836764	0.418382	−	0.908271i	$-0.362597\pi$
$691$	21.9959	0.836764	0.418382	+	0.908271i	$0.362597\pi$
$692$	85.5315	3.25142
$693$	1.51389	0.0575078
$694$	−1.94244	−0.0737341
$695$	0	0
$696$	25.9232	0.982615
$697$	26.3193	0.996915
$698$	36.6376	1.38675
$699$	15.2519	0.576878
$700$	0	0
$701$	33.0978	1.25009	0.625043	−	0.780591i	$-0.285082\pi$
$701$	33.0978	1.25009	0.625043	+	0.780591i	$0.285082\pi$
$702$	43.1429	1.62832
$703$	−2.19962	−0.0829604
$704$	−9.07275	−0.341942
$705$	0	0
$706$	−51.7192	−1.94648
$707$	−1.93634	−0.0728236
$708$	39.0067	1.46596
$709$	32.1089	1.20588	0.602938	−	0.797788i	$-0.293997\pi$
$709$	32.1089	1.20588	0.602938	+	0.797788i	$0.293997\pi$
$710$	0	0
$711$	−31.8901	−1.19597
$712$	−44.6739	−1.67422
$713$	−4.59512	−0.172089
$714$	10.2746	0.384518
$715$	0	0
$716$	65.3092	2.44072
$717$	−12.2979	−0.459272
$718$	51.2615	1.91306
$719$	−35.4855	−1.32339	−0.661694	−	0.749774i	$-0.730162\pi$
$719$	−35.4855	−1.32339	−0.661694	+	0.749774i	$0.730162\pi$
$720$	0	0
$721$	−2.08106	−0.0775026
$722$	26.6595	0.992164
$723$	−3.71243	−0.138067
$724$	−55.4420	−2.06048
$725$	0	0
$726$	−22.5154	−0.835625
$727$	−17.0021	−0.630574	−0.315287	−	0.948996i	$-0.602101\pi$
$727$	−17.0021	−0.630574	−0.315287	+	0.948996i	$0.602101\pi$
$728$	−11.8660	−0.439781
$729$	9.15863	0.339209
$730$	0	0
$731$	−53.9946	−1.99706
$732$	14.7132	0.543817
$733$	−53.1566	−1.96339	−0.981693	−	0.190472i	$-0.938998\pi$
$733$	−53.1566	−1.96339	−0.981693	+	0.190472i	$0.938998\pi$
$734$	23.3360	0.861349
$735$	0	0
$736$	−5.24098	−0.193185
$737$	−9.67583	−0.356414
$738$	−27.0315	−0.995044
$739$	0.0204752	0.000753191 0	0.000376596	−	1.00000i	$-0.499880\pi$
$739$	0.0204752	0.000753191 0	0.000376596		1.00000i	$0.499880\pi$
$740$	0	0
$741$	9.93967	0.365143
$742$	32.3078	1.18606
$743$	−41.1435	−1.50941	−0.754704	−	0.656065i	$-0.772220\pi$
$743$	−41.1435	−1.50941	−0.754704	+	0.656065i	$0.772220\pi$
$744$	12.9508	0.474800
$745$	0	0
$746$	12.6988	0.464935
$747$	−8.32829	−0.304716
$748$	−11.2603	−0.411719
$749$	4.86119	0.177624
$750$	0	0
$751$	46.5976	1.70037	0.850186	−	0.526483i	$-0.176490\pi$
$751$	46.5976	1.70037	0.850186	+	0.526483i	$0.176490\pi$
$752$	−1.12583	−0.0410547
$753$	26.3513	0.960296
$754$	83.0641	3.02502
$755$	0	0
$756$	−15.8318	−0.575797
$757$	−33.1567	−1.20510	−0.602550	−	0.798081i	$-0.705849\pi$
$757$	−33.1567	−1.20510	−0.602550	+	0.798081i	$0.705849\pi$
$758$	−47.5420	−1.72680
$759$	0.660048	0.0239582
$760$	0	0
$761$	10.0225	0.363316	0.181658	−	0.983362i	$-0.441854\pi$
$761$	10.0225	0.363316	0.181658	+	0.983362i	$0.441854\pi$
$762$	16.1088	0.583560
$763$	6.18163	0.223790
$764$	−0.000718629 0	−2.59991e−5 0
$765$	0	0
$766$	18.5861	0.671543
$767$	49.5560	1.78936
$768$	16.9564	0.611861
$769$	−9.36109	−0.337570	−0.168785	−	0.985653i	$-0.553984\pi$
$769$	−9.36109	−0.337570	−0.168785	+	0.985653i	$0.553984\pi$
$770$	0	0
$771$	−9.93364	−0.357751
$772$	13.6393	0.490888
$773$	−3.48472	−0.125337	−0.0626684	−	0.998034i	$-0.519961\pi$
$773$	−3.48472	−0.125337	−0.0626684	+	0.998034i	$0.519961\pi$
$774$	55.4557	1.99331
$775$	0	0
$776$	45.3528	1.62807
$777$	−0.750619	−0.0269283
$778$	−41.3261	−1.48161
$779$	−14.9821	−0.536790
$780$	0	0
$781$	11.7109	0.419049
$782$	−11.0421	−0.394865
$783$	43.9413	1.57033
$784$	0.354347	0.0126553
$785$	0	0
$786$	−42.1059	−1.50187
$787$	−32.7487	−1.16736	−0.583682	−	0.811982i	$-0.698389\pi$
$787$	−32.7487	−1.16736	−0.583682	+	0.811982i	$0.698389\pi$
$788$	11.1796	0.398258
$789$	−6.38376	−0.227268
$790$	0	0
$791$	−2.56109	−0.0910618
$792$	4.58542	0.162936
$793$	18.6924	0.663788
$794$	67.5014	2.39554
$795$	0	0
$796$	37.7316	1.33736
$797$	21.2625	0.753158	0.376579	−	0.926385i	$-0.377100\pi$
$797$	21.2625	0.753158	0.376579	+	0.926385i	$0.377100\pi$
$798$	−5.84877	−0.207044
$799$	15.2190	0.538410
$800$	0	0
$801$	−31.4774	−1.11220
$802$	−10.0381	−0.354456
$803$	−5.86049	−0.206812
$804$	42.0615	1.48340
$805$	0	0
$806$	41.4975	1.46169
$807$	22.7904	0.802260
$808$	−5.86500	−0.206330
$809$	−21.5257	−0.756803	−0.378402	−	0.925641i	$-0.623526\pi$
$809$	−21.5257	−0.756803	−0.378402	+	0.925641i	$0.623526\pi$
$810$	0	0
$811$	−0.613016	−0.0215259	−0.0107630	−	0.999942i	$-0.503426\pi$
$811$	−0.613016	−0.0215259	−0.0107630	+	0.999942i	$0.503426\pi$
$812$	−30.4813	−1.06968
$813$	23.1764	0.812833
$814$	1.31910	0.0462343
$815$	0	0
$816$	1.57938	0.0552894
$817$	30.7361	1.07532
$818$	69.4315	2.42762
$819$	−8.36080	−0.292150
$820$	0	0
$821$	8.87035	0.309577	0.154789	−	0.987948i	$-0.450530\pi$
$821$	8.87035	0.309577	0.154789	+	0.987948i	$0.450530\pi$
$822$	−33.5717	−1.17095
$823$	7.92495	0.276246	0.138123	−	0.990415i	$-0.455893\pi$
$823$	7.92495	0.276246	0.138123	+	0.990415i	$0.455893\pi$
$824$	−6.30333	−0.219587
$825$	0	0
$826$	−29.1601	−1.01461
$827$	−36.0984	−1.25526	−0.627632	−	0.778510i	$-0.715976\pi$
$827$	−36.0984	−1.25526	−0.627632	+	0.778510i	$0.715976\pi$
$828$	7.07256	0.245789
$829$	−0.675531	−0.0234622	−0.0117311	−	0.999931i	$-0.503734\pi$
$829$	−0.675531	−0.0234622	−0.0117311	+	0.999931i	$0.503734\pi$
$830$	0	0
$831$	7.76697	0.269433
$832$	50.1064	1.73713
$833$	−4.79009	−0.165967
$834$	−3.65398	−0.126527
$835$	0	0
$836$	6.40988	0.221690
$837$	21.9524	0.758786
$838$	45.2842	1.56432
$839$	−29.8282	−1.02979	−0.514893	−	0.857255i	$-0.672168\pi$
$839$	−29.8282	−1.02979	−0.514893	+	0.857255i	$0.672168\pi$
$840$	0	0
$841$	55.6013	1.91728
$842$	24.0331	0.828237
$843$	1.88049	0.0647677
$844$	−25.9128	−0.891954
$845$	0	0
$846$	−15.6308	−0.537399
$847$	10.4968	0.360675
$848$	4.96625	0.170542
$849$	6.19404	0.212579
$850$	0	0
$851$	0.806689	0.0276530
$852$	−50.9082	−1.74408
$853$	43.2041	1.47928	0.739639	−	0.673004i	$-0.234996\pi$
$853$	43.2041	1.47928	0.739639	+	0.673004i	$0.234996\pi$
$854$	−10.9991	−0.376382
$855$	0	0
$856$	14.7241	0.503259
$857$	11.0759	0.378346	0.189173	−	0.981944i	$-0.439419\pi$
$857$	11.0759	0.378346	0.189173	+	0.981944i	$0.439419\pi$
$858$	−5.96074	−0.203496
$859$	34.7012	1.18399	0.591995	−	0.805942i	$-0.298340\pi$
$859$	34.7012	1.18399	0.591995	+	0.805942i	$0.298340\pi$
$860$	0	0
$861$	−5.11263	−0.174238
$862$	28.5406	0.972097
$863$	−53.4387	−1.81907	−0.909537	−	0.415623i	$-0.863564\pi$
$863$	−53.4387	−1.81907	−0.909537	+	0.415623i	$0.863564\pi$
$864$	25.0378	0.851805
$865$	0	0
$866$	72.8548	2.47571
$867$	−5.53178	−0.187869
$868$	−15.2280	−0.516872
$869$	10.5995	0.359564
$870$	0	0
$871$	53.4371	1.81065
$872$	18.7236	0.634061
$873$	31.9558	1.08154
$874$	6.28566	0.212616
$875$	0	0
$876$	25.4760	0.860753
$877$	10.2527	0.346208	0.173104	−	0.984904i	$-0.444620\pi$
$877$	10.2527	0.346208	0.173104	+	0.984904i	$0.444620\pi$
$878$	50.5950	1.70750
$879$	−21.4936	−0.724961
$880$	0	0
$881$	−21.7396	−0.732424	−0.366212	−	0.930531i	$-0.619346\pi$
$881$	−21.7396	−0.732424	−0.366212	+	0.930531i	$0.619346\pi$
$882$	4.91971	0.165655
$883$	16.1632	0.543935	0.271968	−	0.962306i	$-0.412326\pi$
$883$	16.1632	0.543935	0.271968	+	0.962306i	$0.412326\pi$
$884$	62.1879	2.09160
$885$	0	0
$886$	84.5944	2.84200
$887$	−3.60774	−0.121136	−0.0605681	−	0.998164i	$-0.519291\pi$
$887$	−3.60774	−0.121136	−0.0605681	+	0.998164i	$0.519291\pi$
$888$	−2.27356	−0.0762956
$889$	−7.51001	−0.251878
$890$	0	0
$891$	1.38840	0.0465130
$892$	46.2194	1.54754
$893$	−8.66332	−0.289907
$894$	−50.8799	−1.70168
$895$	0	0
$896$	−19.0020	−0.634812
$897$	−3.64527	−0.121712
$898$	31.2222	1.04190
$899$	42.2655	1.40963
$900$	0	0
$901$	−67.1341	−2.23656
$902$	8.98465	0.299156
$903$	10.4886	0.349040
$904$	−7.75730	−0.258004
$905$	0	0
$906$	−17.8830	−0.594123
$907$	−11.8255	−0.392659	−0.196330	−	0.980538i	$-0.562902\pi$
$907$	−11.8255	−0.392659	−0.196330	+	0.980538i	$0.562902\pi$
$908$	−9.66050	−0.320595
$909$	−4.13250	−0.137066
$910$	0	0
$911$	−48.1231	−1.59439	−0.797195	−	0.603722i	$-0.793684\pi$
$911$	−48.1231	−1.59439	−0.797195	+	0.603722i	$0.793684\pi$
$912$	−0.899052	−0.0297706
$913$	2.76813	0.0916117
$914$	−47.7695	−1.58007
$915$	0	0
$916$	−28.1394	−0.929753
$917$	19.6300	0.648241
$918$	52.7518	1.74107
$919$	36.8685	1.21618	0.608089	−	0.793869i	$-0.291936\pi$
$919$	36.8685	1.21618	0.608089	+	0.793869i	$0.291936\pi$
$920$	0	0
$921$	−11.5572	−0.380821
$922$	−70.0954	−2.30847
$923$	−64.6762	−2.12884
$924$	2.18736	0.0719590
$925$	0	0
$926$	5.92145	0.194591
$927$	−4.44135	−0.145873
$928$	48.2059	1.58244
$929$	−27.5807	−0.904893	−0.452446	−	0.891792i	$-0.649449\pi$
$929$	−27.5807	−0.904893	−0.452446	+	0.891792i	$0.649449\pi$
$930$	0	0
$931$	2.72673	0.0893650
$932$	−54.3194	−1.77929
$933$	−29.1819	−0.955371
$934$	23.8224	0.779494
$935$	0	0
$936$	−25.3241	−0.827744
$937$	−26.5360	−0.866892	−0.433446	−	0.901180i	$-0.642703\pi$
$937$	−26.5360	−0.866892	−0.433446	+	0.901180i	$0.642703\pi$
$938$	−31.4438	−1.02668
$939$	19.4615	0.635104
$940$	0	0
$941$	39.9295	1.30166	0.650832	−	0.759222i	$-0.274420\pi$
$941$	39.9295	1.30166	0.650832	+	0.759222i	$0.274420\pi$
$942$	34.6054	1.12750
$943$	5.49453	0.178927
$944$	−4.48239	−0.145889
$945$	0	0
$946$	−18.4322	−0.599282
$947$	−5.28432	−0.171717	−0.0858586	−	0.996307i	$-0.527363\pi$
$947$	−5.28432	−0.171717	−0.0858586	+	0.996307i	$0.527363\pi$
$948$	−46.0769	−1.49651
$949$	32.3659	1.05064
$950$	0	0
$951$	−0.556064	−0.0180316
$952$	−14.5088	−0.470231
$953$	−43.2605	−1.40134	−0.700672	−	0.713483i	$-0.747116\pi$
$953$	−43.2605	−1.40134	−0.700672	+	0.713483i	$0.747116\pi$
$954$	68.9508	2.23236
$955$	0	0
$956$	43.7988	1.41655
$957$	−6.07105	−0.196249
$958$	7.22917	0.233564
$959$	15.6513	0.505408
$960$	0	0
$961$	−9.88484	−0.318866
$962$	−7.28503	−0.234879
$963$	10.3747	0.334319
$964$	13.2218	0.425845
$965$	0	0
$966$	2.14497	0.0690134
$967$	15.3544	0.493766	0.246883	−	0.969045i	$-0.420594\pi$
$967$	15.3544	0.493766	0.246883	+	0.969045i	$0.420594\pi$
$968$	31.7939	1.02189
$969$	12.1535	0.390425
$970$	0	0
$971$	−41.9060	−1.34483	−0.672414	−	0.740175i	$-0.734743\pi$
$971$	−41.9060	−1.34483	−0.672414	+	0.740175i	$0.734743\pi$
$972$	−53.5308	−1.71700
$973$	1.70351	0.0546119
$974$	48.7341	1.56154
$975$	0	0
$976$	−1.69075	−0.0541195
$977$	35.8935	1.14833	0.574167	−	0.818738i	$-0.305326\pi$
$977$	35.8935	1.14833	0.574167	+	0.818738i	$0.305326\pi$
$978$	6.41325	0.205073
$979$	10.4624	0.334378
$980$	0	0
$981$	13.1927	0.421211
$982$	70.4976	2.24967
$983$	−36.1916	−1.15433	−0.577167	−	0.816626i	$-0.695842\pi$
$983$	−36.1916	−1.15433	−0.577167	+	0.816626i	$0.695842\pi$
$984$	−15.4857	−0.493666
$985$	0	0
$986$	101.564	3.23447
$987$	−2.95635	−0.0941016
$988$	−35.4001	−1.12623
$989$	−11.2721	−0.358433
$990$	0	0
$991$	−23.6677	−0.751829	−0.375914	−	0.926654i	$-0.622671\pi$
$991$	−23.6677	−0.751829	−0.375914	+	0.926654i	$0.622671\pi$
$992$	24.0829	0.764634
$993$	23.7037	0.752215
$994$	38.0572	1.20710
$995$	0	0
$996$	−12.0333	−0.381288
$997$	−47.9363	−1.51816	−0.759078	−	0.650999i	$-0.774350\pi$
$997$	−47.9363	−1.51816	−0.759078	+	0.650999i	$0.774350\pi$
$998$	5.25845	0.166453
$999$	−3.85382	−0.121929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.z.1.3	✓	14
5.4	even	2		4025.2.a.bc.1.12	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.3	✓	14	1.1	even	1	trivial
4025.2.a.bc.1.12	yes	14	5.4	even	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30520 q^{2} -0.930494 q^{3} +3.31395 q^{4} +2.14497 q^{6} -1.00000 q^{7} -3.02891 q^{8} -2.13418 q^{9} +O(q^{10})\)	\(q-2.30520 q^{2} -0.930494 q^{3} +3.31395 q^{4} +2.14497 q^{6} -1.00000 q^{7} -3.02891 q^{8} -2.13418 q^{9} +0.709352 q^{11} -3.08361 q^{12} -3.91757 q^{13} +2.30520 q^{14} +0.354347 q^{16} -4.79009 q^{17} +4.91971 q^{18} +2.72673 q^{19} +0.930494 q^{21} -1.63520 q^{22} -1.00000 q^{23} +2.81838 q^{24} +9.03077 q^{26} +4.77732 q^{27} -3.31395 q^{28} +9.19789 q^{29} +4.59512 q^{31} +5.24098 q^{32} -0.660048 q^{33} +11.0421 q^{34} -7.07256 q^{36} -0.806689 q^{37} -6.28566 q^{38} +3.64527 q^{39} -5.49453 q^{41} -2.14497 q^{42} +11.2721 q^{43} +2.35076 q^{44} +2.30520 q^{46} -3.17718 q^{47} -0.329718 q^{48} +1.00000 q^{49} +4.45715 q^{51} -12.9826 q^{52} +14.0152 q^{53} -11.0127 q^{54} +3.02891 q^{56} -2.53721 q^{57} -21.2030 q^{58} -12.6497 q^{59} -4.77144 q^{61} -10.5927 q^{62} +2.13418 q^{63} -12.7902 q^{64} +1.52154 q^{66} -13.6404 q^{67} -15.8741 q^{68} +0.930494 q^{69} +16.5093 q^{71} +6.46424 q^{72} -8.26175 q^{73} +1.85958 q^{74} +9.03624 q^{76} -0.709352 q^{77} -8.40308 q^{78} +14.9425 q^{79} +1.95727 q^{81} +12.6660 q^{82} +3.90233 q^{83} +3.08361 q^{84} -25.9845 q^{86} -8.55858 q^{87} -2.14856 q^{88} +14.7492 q^{89} +3.91757 q^{91} -3.31395 q^{92} -4.27573 q^{93} +7.32404 q^{94} -4.87670 q^{96} -14.9733 q^{97} -2.30520 q^{98} -1.51389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

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