LMFDB - Embedded newform 1175.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, 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("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 47)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.06150$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.673363 q^{2} +0.188279 q^{3} -1.54658 q^{4} -0.126780 q^{6} +3.31128 q^{7} +2.38814 q^{8} -2.96455 q^{9} +O(q^{10})$	\(q-0.673363 q^{2} +0.188279 q^{3} -1.54658 q^{4} -0.126780 q^{6} +3.31128 q^{7} +2.38814 q^{8} -2.96455 q^{9} -1.02983 q^{11} -0.291189 q^{12} -6.49956 q^{13} -2.22969 q^{14} +1.48508 q^{16} +3.28144 q^{17} +1.99622 q^{18} +4.12300 q^{19} +0.623443 q^{21} +0.693450 q^{22} -3.46972 q^{23} +0.449635 q^{24} +4.37656 q^{26} -1.12300 q^{27} -5.12116 q^{28} -2.97017 q^{29} -6.49956 q^{31} -5.77627 q^{32} -0.193895 q^{33} -2.20960 q^{34} +4.58492 q^{36} +0.964551 q^{37} -2.77627 q^{38} -1.22373 q^{39} +0.653275 q^{41} -0.419803 q^{42} -1.72328 q^{43} +1.59272 q^{44} +2.33638 q^{46} -1.00000 q^{47} +0.279610 q^{48} +3.96455 q^{49} +0.617826 q^{51} +10.0521 q^{52} +7.03456 q^{53} +0.756185 q^{54} +7.90778 q^{56} +0.776272 q^{57} +2.00000 q^{58} -11.5573 q^{59} +2.71767 q^{61} +4.37656 q^{62} -9.81645 q^{63} +0.919358 q^{64} +0.130562 q^{66} -13.4585 q^{67} -5.07503 q^{68} -0.653275 q^{69} -10.1174 q^{71} -7.07975 q^{72} -8.39972 q^{73} -0.649493 q^{74} -6.37656 q^{76} -3.41006 q^{77} +0.824012 q^{78} -2.11738 q^{79} +8.68222 q^{81} -0.439891 q^{82} +2.30566 q^{83} -0.964206 q^{84} +1.16039 q^{86} -0.559219 q^{87} -2.45938 q^{88} -14.5274 q^{89} -21.5218 q^{91} +5.36621 q^{92} -1.22373 q^{93} +0.673363 q^{94} -1.08755 q^{96} -10.4008 q^{97} -2.66958 q^{98} +3.05299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9	$ 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9} - 6 q^{11} + 11 q^{12} - 8 q^{13} - 5 q^{14} + 5 q^{16} - 6 q^{17} - 16 q^{18} + 4 q^{21} - 4 q^{22} + 6 q^{23} - 13 q^{24} + 16 q^{26} + 12 q^{27} - 16 q^{28} - 10 q^{29} - 8 q^{31} - 10 q^{32} - 12 q^{33} - 10 q^{34} + 11 q^{36} - 10 q^{37} + 2 q^{38} - 18 q^{39} + 6 q^{41} + 15 q^{42} - 2 q^{43} - 30 q^{44} + 18 q^{46} - 4 q^{47} - 6 q^{48} + 2 q^{49} - 8 q^{51} - 4 q^{52} + 6 q^{53} - 5 q^{54} + 2 q^{56} - 10 q^{57} + 8 q^{58} + 4 q^{59} - 6 q^{61} + 16 q^{62} - 16 q^{63} - 31 q^{64} + 32 q^{66} - 10 q^{67} - 43 q^{68} - 6 q^{69} - 12 q^{71} - 27 q^{72} - 22 q^{73} + 18 q^{74} - 24 q^{76} + 10 q^{77} + 28 q^{78} + 20 q^{79} + 4 q^{81} + 20 q^{82} - 20 q^{83} - 19 q^{84} + 38 q^{86} + 12 q^{87} - 2 q^{88} - 6 q^{89} - 22 q^{91} + 32 q^{92} - 18 q^{93} + q^{94} + 26 q^{96} - 30 q^{97} + 15 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9 - 6 * q^11 + 11 * q^12 - 8 * q^13 - 5 * q^14 + 5 * q^16 - 6 * q^17 - 16 * q^18 + 4 * q^21 - 4 * q^22 + 6 * q^23 - 13 * q^24 + 16 * q^26 + 12 * q^27 - 16 * q^28 - 10 * q^29 - 8 * q^31 - 10 * q^32 - 12 * q^33 - 10 * q^34 + 11 * q^36 - 10 * q^37 + 2 * q^38 - 18 * q^39 + 6 * q^41 + 15 * q^42 - 2 * q^43 - 30 * q^44 + 18 * q^46 - 4 * q^47 - 6 * q^48 + 2 * q^49 - 8 * q^51 - 4 * q^52 + 6 * q^53 - 5 * q^54 + 2 * q^56 - 10 * q^57 + 8 * q^58 + 4 * q^59 - 6 * q^61 + 16 * q^62 - 16 * q^63 - 31 * q^64 + 32 * q^66 - 10 * q^67 - 43 * q^68 - 6 * q^69 - 12 * q^71 - 27 * q^72 - 22 * q^73 + 18 * q^74 - 24 * q^76 + 10 * q^77 + 28 * q^78 + 20 * q^79 + 4 * q^81 + 20 * q^82 - 20 * q^83 - 19 * q^84 + 38 * q^86 + 12 * q^87 - 2 * q^88 - 6 * q^89 - 22 * q^91 + 32 * q^92 - 18 * q^93 + q^94 + 26 * q^96 - 30 * q^97 + 15 * q^98 + 4 * 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 $

$2$	−0.673363	−0.476139	−0.238070	−	0.971248i	$-0.576515\pi$
$2$	−0.673363	−0.476139	−0.238070	+	0.971248i	$0.576515\pi$
$3$	0.188279	0.108703	0.0543514	−	0.998522i	$-0.482691\pi$
$3$	0.188279	0.108703	0.0543514	+	0.998522i	$0.482691\pi$
$4$	−1.54658	−0.773291
$5$	0	0
$5$	0	0
$6$	−0.126780	−0.0517576
$7$	3.31128	1.25154	0.625772	−	0.780006i	$-0.284784\pi$
$7$	3.31128	1.25154	0.625772	+	0.780006i	$0.284784\pi$
$8$	2.38814	0.844334
$9$	−2.96455	−0.988184
$10$	0	0
$11$	−1.02983	−0.310506	−0.155253	−	0.987875i	$-0.549619\pi$
$11$	−1.02983	−0.310506	−0.155253	+	0.987875i	$0.549619\pi$
$12$	−0.291189	−0.0840589
$13$	−6.49956	−1.80265	−0.901326	−	0.433141i	$-0.857405\pi$
$13$	−6.49956	−1.80265	−0.901326	+	0.433141i	$0.857405\pi$
$14$	−2.22969	−0.595910
$15$	0	0
$16$	1.48508	0.371271
$17$	3.28144	0.795867	0.397934	−	0.917414i	$-0.369727\pi$
$17$	3.28144	0.795867	0.397934	+	0.917414i	$0.369727\pi$
$18$	1.99622	0.470513
$19$	4.12300	0.945881	0.472940	−	0.881094i	$-0.343193\pi$
$19$	4.12300	0.945881	0.472940	+	0.881094i	$0.343193\pi$
$20$	0	0
$21$	0.623443	0.136046
$22$	0.693450	0.147844
$23$	−3.46972	−0.723487	−0.361744	−	0.932278i	$-0.617818\pi$
$23$	−3.46972	−0.723487	−0.361744	+	0.932278i	$0.617818\pi$
$24$	0.449635	0.0917814
$25$	0	0
$26$	4.37656	0.858314
$27$	−1.12300	−0.216121
$28$	−5.12116	−0.967809
$29$	−2.97017	−0.551546	−0.275773	−	0.961223i	$-0.588934\pi$
$29$	−2.97017	−0.551546	−0.275773	+	0.961223i	$0.588934\pi$
$30$	0	0
$31$	−6.49956	−1.16735	−0.583677	−	0.811986i	$-0.698387\pi$
$31$	−6.49956	−1.16735	−0.583677	+	0.811986i	$0.698387\pi$
$32$	−5.77627	−1.02111
$33$	−0.193895	−0.0337529
$34$	−2.20960	−0.378944
$35$	0	0
$36$	4.58492	0.764154
$37$	0.964551	0.158571	0.0792856	−	0.996852i	$-0.474736\pi$
$37$	0.964551	0.158571	0.0792856	+	0.996852i	$0.474736\pi$
$38$	−2.77627	−0.450371
$39$	−1.22373	−0.195953
$40$	0	0
$41$	0.653275	0.102024	0.0510122	−	0.998698i	$-0.483755\pi$
$41$	0.653275	0.102024	0.0510122	+	0.998698i	$0.483755\pi$
$42$	−0.419803	−0.0647770
$43$	−1.72328	−0.262798	−0.131399	−	0.991330i	$-0.541947\pi$
$43$	−1.72328	−0.262798	−0.131399	+	0.991330i	$0.541947\pi$
$44$	1.59272	0.240112
$45$	0	0
$46$	2.33638	0.344481
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	0.279610	0.0403582
$49$	3.96455	0.566364
$50$	0	0
$51$	0.617826	0.0865129
$52$	10.0521	1.39398
$53$	7.03456	0.966271	0.483135	−	0.875546i	$-0.339498\pi$
$53$	7.03456	0.966271	0.483135	+	0.875546i	$0.339498\pi$
$54$	0.756185	0.102904
$55$	0	0
$56$	7.90778	1.05672
$57$	0.776272	0.102820
$58$	2.00000	0.262613
$59$	−11.5573	−1.50463	−0.752314	−	0.658804i	$-0.771063\pi$
$59$	−11.5573	−1.50463	−0.752314	+	0.658804i	$0.771063\pi$
$60$	0	0
$61$	2.71767	0.347961	0.173981	−	0.984749i	$-0.444337\pi$
$61$	2.71767	0.347961	0.173981	+	0.984749i	$0.444337\pi$
$62$	4.37656	0.555823
$63$	−9.81645	−1.23676
$64$	0.919358	0.114920
$65$	0	0
$66$	0.130562	0.0160711
$67$	−13.4585	−1.64422	−0.822108	−	0.569331i	$-0.807202\pi$
$67$	−13.4585	−1.64422	−0.822108	+	0.569331i	$0.807202\pi$
$68$	−5.07503	−0.615437
$69$	−0.653275	−0.0786450
$70$	0	0
$71$	−10.1174	−1.20071	−0.600356	−	0.799733i	$-0.704974\pi$
$71$	−10.1174	−1.20071	−0.600356	+	0.799733i	$0.704974\pi$
$72$	−7.07975	−0.834357
$73$	−8.39972	−0.983112	−0.491556	−	0.870846i	$-0.663572\pi$
$73$	−8.39972	−0.983112	−0.491556	+	0.870846i	$0.663572\pi$
$74$	−0.649493	−0.0755020
$75$	0	0
$76$	−6.37656	−0.731441
$77$	−3.41006	−0.388612
$78$	0.824012	0.0933010
$79$	−2.11738	−0.238224	−0.119112	−	0.992881i	$-0.538005\pi$
$79$	−2.11738	−0.238224	−0.119112	+	0.992881i	$0.538005\pi$
$80$	0	0
$81$	8.68222	0.964691
$82$	−0.439891	−0.0485778
$83$	2.30566	0.253079	0.126540	−	0.991962i	$-0.459613\pi$
$83$	2.30566	0.253079	0.126540	+	0.991962i	$0.459613\pi$
$84$	−0.964206	−0.105203
$85$	0	0
$86$	1.16039	0.125129
$87$	−0.559219	−0.0599546
$88$	−2.45938	−0.262171
$89$	−14.5274	−1.53991	−0.769953	−	0.638101i	$-0.779720\pi$
$89$	−14.5274	−1.53991	−0.769953	+	0.638101i	$0.779720\pi$
$90$	0	0
$91$	−21.5218	−2.25610
$92$	5.36621	0.559466
$93$	−1.22373	−0.126895
$94$	0.673363	0.0694521
$95$	0	0
$96$	−1.08755	−0.110997
$97$	−10.4008	−1.05604	−0.528019	−	0.849232i	$-0.677065\pi$
$97$	−10.4008	−1.05604	−0.528019	+	0.849232i	$0.677065\pi$
$98$	−2.66958	−0.269668
$99$	3.05299	0.306837
$100$	0	0
$101$	7.90400	0.786477	0.393239	−	0.919436i	$-0.371355\pi$
$101$	7.90400	0.786477	0.393239	+	0.919436i	$0.371355\pi$
$102$	−0.416021	−0.0411922
$103$	−2.11738	−0.208632	−0.104316	−	0.994544i	$-0.533265\pi$
$103$	−2.11738	−0.208632	−0.104316	+	0.994544i	$0.533265\pi$
$104$	−15.5218	−1.52204
$105$	0	0
$106$	−4.73681	−0.460080
$107$	−12.5629	−1.21450	−0.607250	−	0.794511i	$-0.707727\pi$
$107$	−12.5629	−1.21450	−0.607250	+	0.794511i	$0.707727\pi$
$108$	1.73681	0.167125
$109$	−7.01860	−0.672260	−0.336130	−	0.941816i	$-0.609118\pi$
$109$	−7.01860	−0.672260	−0.336130	+	0.941816i	$0.609118\pi$
$110$	0	0
$111$	0.181604	0.0172371
$112$	4.91752	0.464662
$113$	4.93578	0.464319	0.232159	−	0.972678i	$-0.425421\pi$
$113$	4.93578	0.464319	0.232159	+	0.972678i	$0.425421\pi$
$114$	−0.522713	−0.0489565
$115$	0	0
$116$	4.59361	0.426506
$117$	19.2683	1.78135
$118$	7.78223	0.716413
$119$	10.8658	0.996063
$120$	0	0
$121$	−9.93945	−0.903586
$122$	−1.82997	−0.165678
$123$	0.122998	0.0110903
$124$	10.0521	0.902705
$125$	0	0
$126$	6.61003	0.588868
$127$	−8.02316	−0.711940	−0.355970	−	0.934497i	$-0.615849\pi$
$127$	−8.02316	−0.711940	−0.355970	+	0.934497i	$0.615849\pi$
$128$	10.9335	0.966393
$129$	−0.324457	−0.0285669
$130$	0	0
$131$	19.5573	1.70873	0.854363	−	0.519676i	$-0.173947\pi$
$131$	19.5573	1.70873	0.854363	+	0.519676i	$0.173947\pi$
$132$	0.299875	0.0261008
$133$	13.6524	1.18381
$134$	9.06244	0.782876
$135$	0	0
$136$	7.83654	0.671977
$137$	−6.57045	−0.561352	−0.280676	−	0.959803i	$-0.590559\pi$
$137$	−6.57045	−0.561352	−0.280676	+	0.959803i	$0.590559\pi$
$138$	0.439891	0.0374460
$139$	−6.82768	−0.579116	−0.289558	−	0.957160i	$-0.593508\pi$
$139$	−6.82768	−0.579116	−0.289558	+	0.957160i	$0.593508\pi$
$140$	0	0
$141$	−0.188279	−0.0158559
$142$	6.81267	0.571706
$143$	6.69345	0.559734
$144$	−4.40261	−0.366884
$145$	0	0
$146$	5.65605	0.468098
$147$	0.746440	0.0615654
$148$	−1.49176	−0.122622
$149$	−6.09422	−0.499258	−0.249629	−	0.968342i	$-0.580309\pi$
$149$	−6.09422	−0.499258	−0.249629	+	0.968342i	$0.580309\pi$
$150$	0	0
$151$	10.1118	0.822884	0.411442	−	0.911436i	$-0.365025\pi$
$151$	10.1118	0.822884	0.411442	+	0.911436i	$0.365025\pi$
$152$	9.84628	0.798639
$153$	−9.72801	−0.786463
$154$	2.29621	0.185034
$155$	0	0
$156$	1.89260	0.151529
$157$	4.34111	0.346458	0.173229	−	0.984882i	$-0.444580\pi$
$157$	4.34111	0.346458	0.173229	+	0.984882i	$0.444580\pi$
$158$	1.42577	0.113428
$159$	1.32446	0.105036
$160$	0	0
$161$	−11.4892	−0.905477
$162$	−5.84628	−0.459327
$163$	−1.40639	−0.110157	−0.0550785	−	0.998482i	$-0.517541\pi$
$163$	−1.40639	−0.110157	−0.0550785	+	0.998482i	$0.517541\pi$
$164$	−1.01034	−0.0788946
$165$	0	0
$166$	−1.55254	−0.120501
$167$	3.84628	0.297634	0.148817	−	0.988865i	$-0.452453\pi$
$167$	3.84628	0.297634	0.148817	+	0.988865i	$0.452453\pi$
$168$	1.48887	0.114869
$169$	29.2442	2.24956
$170$	0	0
$171$	−12.2228	−0.934704
$172$	2.66520	0.203220
$173$	−0.270211	−0.0205437	−0.0102719	−	0.999947i	$-0.503270\pi$
$173$	−0.270211	−0.0205437	−0.0102719	+	0.999947i	$0.503270\pi$
$174$	0.376557	0.0285467
$175$	0	0
$176$	−1.52939	−0.115282
$177$	−2.17599	−0.163557
$178$	9.78223	0.733209
$179$	17.6926	1.32240	0.661202	−	0.750208i	$-0.270047\pi$
$179$	17.6926	1.32240	0.661202	+	0.750208i	$0.270047\pi$
$180$	0	0
$181$	−14.4399	−1.07331	−0.536654	−	0.843802i	$-0.680312\pi$
$181$	−14.4399	−1.07331	−0.536654	+	0.843802i	$0.680312\pi$
$182$	14.4920	1.07422
$183$	0.511678	0.0378244
$184$	−8.28617	−0.610865
$185$	0	0
$186$	0.824012	0.0604195
$187$	−3.37934	−0.247122
$188$	1.54658	0.112796
$189$	−3.71856	−0.270485
$190$	0	0
$191$	−3.05877	−0.221325	−0.110663	−	0.993858i	$-0.535297\pi$
$191$	−3.05877	−0.221325	−0.110663	+	0.993858i	$0.535297\pi$
$192$	0.173095	0.0124921
$193$	−4.13056	−0.297324	−0.148662	−	0.988888i	$-0.547497\pi$
$193$	−4.13056	−0.297324	−0.148662	+	0.988888i	$0.547497\pi$
$194$	7.00349	0.502821
$195$	0	0
$196$	−6.13151	−0.437965
$197$	21.9386	1.56306	0.781529	−	0.623869i	$-0.214440\pi$
$197$	21.9386	1.56306	0.781529	+	0.623869i	$0.214440\pi$
$198$	−2.05577	−0.146097
$199$	−8.08861	−0.573386	−0.286693	−	0.958022i	$-0.592556\pi$
$199$	−8.08861	−0.573386	−0.286693	+	0.958022i	$0.592556\pi$
$200$	0	0
$201$	−2.53395	−0.178731
$202$	−5.32226	−0.374473
$203$	−9.83505	−0.690285
$204$	−0.955519	−0.0668997
$205$	0	0
$206$	1.42577	0.0993378
$207$	10.2862	0.714938
$208$	−9.65238	−0.669272
$209$	−4.24600	−0.293702
$210$	0	0
$211$	21.2107	1.46021	0.730103	−	0.683337i	$-0.239472\pi$
$211$	21.2107	1.46021	0.730103	+	0.683337i	$0.239472\pi$
$212$	−10.8795	−0.747209
$213$	−1.90489	−0.130521
$214$	8.45938	0.578271
$215$	0	0
$216$	−2.68187	−0.182478
$217$	−21.5218	−1.46100
$218$	4.72606	0.320089
$219$	−1.58149	−0.106867
$220$	0	0
$221$	−21.3279	−1.43467
$222$	−0.122286	−0.00820727
$223$	7.69503	0.515297	0.257649	−	0.966239i	$-0.417052\pi$
$223$	7.69503	0.515297	0.257649	+	0.966239i	$0.417052\pi$
$224$	−19.1268	−1.27797
$225$	0	0
$226$	−3.32357	−0.221080
$227$	−2.59939	−0.172528	−0.0862639	−	0.996272i	$-0.527493\pi$
$227$	−2.59939	−0.172528	−0.0862639	+	0.996272i	$0.527493\pi$
$228$	−1.20057	−0.0795097
$229$	26.9721	1.78236	0.891182	−	0.453646i	$-0.149877\pi$
$229$	26.9721	1.78236	0.891182	+	0.453646i	$0.149877\pi$
$230$	0	0
$231$	−0.642041	−0.0422432
$232$	−7.09317	−0.465689
$233$	6.52271	0.427317	0.213659	−	0.976908i	$-0.431462\pi$
$233$	6.52271	0.427317	0.213659	+	0.976908i	$0.431462\pi$
$234$	−12.9745	−0.848171
$235$	0	0
$236$	17.8743	1.16352
$237$	−0.398658	−0.0258956
$238$	−7.31660	−0.474265
$239$	25.4222	1.64442	0.822211	−	0.569183i	$-0.192740\pi$
$239$	25.4222	1.64442	0.822211	+	0.569183i	$0.192740\pi$
$240$	0	0
$241$	5.89454	0.379701	0.189850	−	0.981813i	$-0.439200\pi$
$241$	5.89454	0.379701	0.189850	+	0.981813i	$0.439200\pi$
$242$	6.69285	0.430233
$243$	5.00367	0.320986
$244$	−4.20310	−0.269076
$245$	0	0
$246$	−0.0828221	−0.00528054
$247$	−26.7977	−1.70509
$248$	−15.5218	−0.985637
$249$	0.434107	0.0275104
$250$	0	0
$251$	8.00017	0.504966	0.252483	−	0.967601i	$-0.418753\pi$
$251$	8.00017	0.504966	0.252483	+	0.967601i	$0.418753\pi$
$252$	15.1819	0.956373
$253$	3.57323	0.224647
$254$	5.40249	0.338983
$255$	0	0
$256$	−9.20092	−0.575057
$257$	−1.88646	−0.117674	−0.0588369	−	0.998268i	$-0.518739\pi$
$257$	−1.88646	−0.117674	−0.0588369	+	0.998268i	$0.518739\pi$
$258$	0.218477	0.0136018
$259$	3.19390	0.198459
$260$	0	0
$261$	8.80521	0.545029
$262$	−13.1691	−0.813592
$263$	25.7436	1.58742	0.793709	−	0.608297i	$-0.208147\pi$
$263$	25.7436	1.58742	0.793709	+	0.608297i	$0.208147\pi$
$264$	−0.463049	−0.0284987
$265$	0	0
$266$	−9.19301	−0.563659
$267$	−2.73521	−0.167392
$268$	20.8147	1.27146
$269$	14.3653	0.875869	0.437935	−	0.899007i	$-0.355710\pi$
$269$	14.3653	0.875869	0.437935	+	0.899007i	$0.355710\pi$
$270$	0	0
$271$	−23.7615	−1.44341	−0.721704	−	0.692201i	$-0.756641\pi$
$271$	−23.7615	−1.44341	−0.721704	+	0.692201i	$0.756641\pi$
$272$	4.87322	0.295482
$273$	−4.05210	−0.245244
$274$	4.42430	0.267282
$275$	0	0
$276$	1.01034	0.0608155
$277$	5.46044	0.328086	0.164043	−	0.986453i	$-0.447546\pi$
$277$	5.46044	0.328086	0.164043	+	0.986453i	$0.447546\pi$
$278$	4.59751	0.275740
$279$	19.2683	1.15356
$280$	0	0
$281$	−3.14160	−0.187412	−0.0937060	−	0.995600i	$-0.529871\pi$
$281$	−3.14160	−0.187412	−0.0937060	+	0.995600i	$0.529871\pi$
$282$	0.126780	0.00754963
$283$	23.6766	1.40743	0.703714	−	0.710483i	$-0.251524\pi$
$283$	23.6766	1.40743	0.703714	+	0.710483i	$0.251524\pi$
$284$	15.6474	0.928500
$285$	0	0
$286$	−4.50712	−0.266512
$287$	2.16317	0.127688
$288$	17.1241	1.00904
$289$	−6.23212	−0.366596
$290$	0	0
$291$	−1.95824	−0.114794
$292$	12.9909	0.760232
$293$	−14.9029	−0.870639	−0.435320	−	0.900276i	$-0.643365\pi$
$293$	−14.9029	−0.870639	−0.435320	+	0.900276i	$0.643365\pi$
$294$	−0.502625	−0.0293137
$295$	0	0
$296$	2.30348	0.133887
$297$	1.15650	0.0671069
$298$	4.10362	0.237716
$299$	22.5517	1.30420
$300$	0	0
$301$	−5.70626	−0.328904
$302$	−6.80888	−0.391807
$303$	1.48815	0.0854922
$304$	6.12300	0.351178
$305$	0	0
$306$	6.55048	0.374466
$307$	−11.0586	−0.631148	−0.315574	−	0.948901i	$-0.602197\pi$
$307$	−11.0586	−0.631148	−0.315574	+	0.948901i	$0.602197\pi$
$308$	5.27394	0.300511
$309$	−0.398658	−0.0226788
$310$	0	0
$311$	−29.0744	−1.64866	−0.824328	−	0.566112i	$-0.808447\pi$
$311$	−29.0744	−1.64866	−0.824328	+	0.566112i	$0.808447\pi$
$312$	−2.92243	−0.165450
$313$	−15.8387	−0.895257	−0.447629	−	0.894220i	$-0.647731\pi$
$313$	−15.8387	−0.895257	−0.447629	+	0.894220i	$0.647731\pi$
$314$	−2.92314	−0.164962
$315$	0	0
$316$	3.27470	0.184217
$317$	1.94401	0.109186	0.0545931	−	0.998509i	$-0.482614\pi$
$317$	1.94401	0.109186	0.0545931	+	0.998509i	$0.482614\pi$
$318$	−0.891840	−0.0500119
$319$	3.05877	0.171258
$320$	0	0
$321$	−2.36532	−0.132020
$322$	7.73641	0.431133
$323$	13.5294	0.752795
$324$	−13.4278	−0.745987
$325$	0	0
$326$	0.947010	0.0524500
$327$	−1.32145	−0.0730765
$328$	1.56011	0.0861426
$329$	−3.31128	−0.182557
$330$	0	0
$331$	−24.8638	−1.36664	−0.683320	−	0.730119i	$-0.739464\pi$
$331$	−24.8638	−1.36664	−0.683320	+	0.730119i	$0.739464\pi$
$332$	−3.56589	−0.195704
$333$	−2.85946	−0.156698
$334$	−2.58994	−0.141715
$335$	0	0
$336$	0.925865	0.0505101
$337$	−17.7186	−0.965191	−0.482596	−	0.875843i	$-0.660306\pi$
$337$	−17.7186	−0.965191	−0.482596	+	0.875843i	$0.660306\pi$
$338$	−19.6920	−1.07110
$339$	0.929301	0.0504727
$340$	0	0
$341$	6.69345	0.362471
$342$	8.23040	0.445049
$343$	−10.0512	−0.542714
$344$	−4.11543	−0.221889
$345$	0	0
$346$	0.181950	0.00978168
$347$	24.7884	1.33071	0.665355	−	0.746527i	$-0.268280\pi$
$347$	24.7884	1.33071	0.665355	+	0.746527i	$0.268280\pi$
$348$	0.864879	0.0463624
$349$	−17.1340	−0.917164	−0.458582	−	0.888652i	$-0.651642\pi$
$349$	−17.1340	−0.917164	−0.458582	+	0.888652i	$0.651642\pi$
$350$	0	0
$351$	7.29899	0.389591
$352$	5.94859	0.317061
$353$	20.1530	1.07264	0.536318	−	0.844016i	$-0.319815\pi$
$353$	20.1530	1.07264	0.536318	+	0.844016i	$0.319815\pi$
$354$	1.46523	0.0778760
$355$	0	0
$356$	22.4679	1.19080
$357$	2.04579	0.108275
$358$	−11.9135	−0.629648
$359$	21.3681	1.12777	0.563883	−	0.825855i	$-0.309307\pi$
$359$	21.3681	1.12777	0.563883	+	0.825855i	$0.309307\pi$
$360$	0	0
$361$	−2.00089	−0.105310
$362$	9.72328	0.511044
$363$	−1.87139	−0.0982223
$364$	33.2853	1.74462
$365$	0	0
$366$	−0.344545	−0.0180097
$367$	19.1854	1.00147	0.500736	−	0.865600i	$-0.333063\pi$
$367$	19.1854	1.00147	0.500736	+	0.865600i	$0.333063\pi$
$368$	−5.15283	−0.268610
$369$	−1.93667	−0.100819
$370$	0	0
$371$	23.2934	1.20933
$372$	1.89260	0.0981265
$373$	−16.8628	−0.873121	−0.436560	−	0.899675i	$-0.643803\pi$
$373$	−16.8628	−0.873121	−0.436560	+	0.899675i	$0.643803\pi$
$374$	2.27552	0.117664
$375$	0	0
$376$	−2.38814	−0.123159
$377$	19.3048	0.994246
$378$	2.50394	0.128789
$379$	−8.61783	−0.442668	−0.221334	−	0.975198i	$-0.571041\pi$
$379$	−8.61783	−0.442668	−0.221334	+	0.975198i	$0.571041\pi$
$380$	0	0
$381$	−1.51059	−0.0773898
$382$	2.05966	0.105382
$383$	−13.5639	−0.693085	−0.346543	−	0.938034i	$-0.612644\pi$
$383$	−13.5639	−0.693085	−0.346543	+	0.938034i	$0.612644\pi$
$384$	2.05854	0.105050
$385$	0	0
$386$	2.78137	0.141568
$387$	5.10876	0.259693
$388$	16.0857	0.816625
$389$	−29.7045	−1.50608	−0.753039	−	0.657976i	$-0.771413\pi$
$389$	−29.7045	−1.50608	−0.753039	+	0.657976i	$0.771413\pi$
$390$	0	0
$391$	−11.3857	−0.575800
$392$	9.46789	0.478201
$393$	3.68222	0.185743
$394$	−14.7726	−0.744233
$395$	0	0
$396$	−4.72170	−0.237274
$397$	14.6589	0.735709	0.367854	−	0.929883i	$-0.380093\pi$
$397$	14.6589	0.735709	0.367854	+	0.929883i	$0.380093\pi$
$398$	5.44657	0.273012
$399$	2.57045	0.128684
$400$	0	0
$401$	−22.3978	−1.11849	−0.559246	−	0.829002i	$-0.688909\pi$
$401$	−22.3978	−1.11849	−0.559246	+	0.829002i	$0.688909\pi$
$402$	1.70626	0.0851007
$403$	42.2442	2.10433
$404$	−12.2242	−0.608176
$405$	0	0
$406$	6.62255	0.328672
$407$	−0.993326	−0.0492373
$408$	1.47545	0.0730458
$409$	26.2442	1.29769	0.648846	−	0.760919i	$-0.275252\pi$
$409$	26.2442	1.29769	0.648846	+	0.760919i	$0.275252\pi$
$410$	0	0
$411$	−1.23708	−0.0610205
$412$	3.27470	0.161333
$413$	−38.2693	−1.88311
$414$	−6.92632	−0.340410
$415$	0	0
$416$	37.5432	1.84071
$417$	−1.28551	−0.0629515
$418$	2.85909	0.139843
$419$	−14.7626	−0.721199	−0.360599	−	0.932721i	$-0.617428\pi$
$419$	−14.7626	−0.721199	−0.360599	+	0.932721i	$0.617428\pi$
$420$	0	0
$421$	9.21616	0.449168	0.224584	−	0.974455i	$-0.427898\pi$
$421$	9.21616	0.449168	0.224584	+	0.974455i	$0.427898\pi$
$422$	−14.2825	−0.695261
$423$	2.96455	0.144141
$424$	16.7995	0.815855
$425$	0	0
$426$	1.28268	0.0621460
$427$	8.99894	0.435489
$428$	19.4295	0.939163
$429$	1.26023	0.0608447
$430$	0	0
$431$	36.1780	1.74264	0.871318	−	0.490720i	$-0.163266\pi$
$431$	36.1780	1.74264	0.871318	+	0.490720i	$0.163266\pi$
$432$	−1.66775	−0.0802395
$433$	8.15194	0.391757	0.195879	−	0.980628i	$-0.437244\pi$
$433$	8.15194	0.391757	0.195879	+	0.980628i	$0.437244\pi$
$434$	14.4920	0.695638
$435$	0	0
$436$	10.8548	0.519853
$437$	−14.3057	−0.684333
$438$	1.06491	0.0508836
$439$	−27.7968	−1.32667	−0.663333	−	0.748324i	$-0.730859\pi$
$439$	−27.7968	−1.32667	−0.663333	+	0.748324i	$0.730859\pi$
$440$	0	0
$441$	−11.7531	−0.559672
$442$	14.3614	0.683104
$443$	−1.57203	−0.0746896	−0.0373448	−	0.999302i	$-0.511890\pi$
$443$	−1.57203	−0.0746896	−0.0373448	+	0.999302i	$0.511890\pi$
$444$	−0.280866	−0.0133293
$445$	0	0
$446$	−5.18155	−0.245353
$447$	−1.14741	−0.0542707
$448$	3.04425	0.143827
$449$	−22.7261	−1.07251	−0.536255	−	0.844056i	$-0.680161\pi$
$449$	−22.7261	−1.07251	−0.536255	+	0.844056i	$0.680161\pi$
$450$	0	0
$451$	−0.672763	−0.0316792
$452$	−7.63359	−0.359054
$453$	1.90383	0.0894497
$454$	1.75034	0.0821473
$455$	0	0
$456$	1.85384	0.0868142
$457$	−38.4669	−1.79941	−0.899703	−	0.436504i	$-0.856217\pi$
$457$	−38.4669	−1.79941	−0.899703	+	0.436504i	$0.856217\pi$
$458$	−18.1620	−0.848653
$459$	−3.68505	−0.172004
$460$	0	0
$461$	18.1060	0.843280	0.421640	−	0.906763i	$-0.361455\pi$
$461$	18.1060	0.843280	0.421640	+	0.906763i	$0.361455\pi$
$462$	0.432327	0.0201137
$463$	−41.3837	−1.92326	−0.961632	−	0.274344i	$-0.911539\pi$
$463$	−41.3837	−1.92326	−0.961632	+	0.274344i	$0.911539\pi$
$464$	−4.41095	−0.204773
$465$	0	0
$466$	−4.39215	−0.203462
$467$	17.9849	0.832241	0.416120	−	0.909310i	$-0.363390\pi$
$467$	17.9849	0.832241	0.416120	+	0.909310i	$0.363390\pi$
$468$	−29.8000	−1.37750
$469$	−44.5648	−2.05781
$470$	0	0
$471$	0.817338	0.0376610
$472$	−27.6003	−1.27041
$473$	1.77469	0.0816004
$474$	0.268441	0.0123299
$475$	0	0
$476$	−16.8048	−0.770247
$477$	−20.8543	−0.954853
$478$	−17.1183	−0.782974
$479$	7.50884	0.343088	0.171544	−	0.985176i	$-0.445124\pi$
$479$	7.50884	0.343088	0.171544	+	0.985176i	$0.445124\pi$
$480$	0	0
$481$	−6.26915	−0.285849
$482$	−3.96917	−0.180791
$483$	−2.16317	−0.0984278
$484$	15.3722	0.698735
$485$	0	0
$486$	−3.36928	−0.152834
$487$	9.79854	0.444014	0.222007	−	0.975045i	$-0.428739\pi$
$487$	9.79854	0.444014	0.222007	+	0.975045i	$0.428739\pi$
$488$	6.49016	0.293796
$489$	−0.264793	−0.0119744
$490$	0	0
$491$	15.1695	0.684589	0.342295	−	0.939593i	$-0.388796\pi$
$491$	15.1695	0.684589	0.342295	+	0.939593i	$0.388796\pi$
$492$	−0.190226	−0.00857606
$493$	−9.74644	−0.438958
$494$	18.0445	0.811862
$495$	0	0
$496$	−9.65238	−0.433405
$497$	−33.5014	−1.50275
$498$	−0.292311	−0.0130988
$499$	12.5592	0.562228	0.281114	−	0.959674i	$-0.409296\pi$
$499$	12.5592	0.562228	0.281114	+	0.959674i	$0.409296\pi$
$500$	0	0
$501$	0.724172	0.0323536
$502$	−5.38701	−0.240434
$503$	33.6253	1.49928	0.749640	−	0.661846i	$-0.230227\pi$
$503$	33.6253	1.49928	0.749640	+	0.661846i	$0.230227\pi$
$504$	−23.4430	−1.04423
$505$	0	0
$506$	−2.40608	−0.106963
$507$	5.50606	0.244533
$508$	12.4085	0.550537
$509$	−2.11933	−0.0939376	−0.0469688	−	0.998896i	$-0.514956\pi$
$509$	−2.11933	−0.0939376	−0.0469688	+	0.998896i	$0.514956\pi$
$510$	0	0
$511$	−27.8138	−1.23041
$512$	−15.6714	−0.692585
$513$	−4.63012	−0.204425
$514$	1.27027	0.0560292
$515$	0	0
$516$	0.501800	0.0220905
$517$	1.02983	0.0452920
$518$	−2.15065	−0.0944941
$519$	−0.0508749	−0.00223316
$520$	0	0
$521$	−0.786784	−0.0344696	−0.0172348	−	0.999851i	$-0.505486\pi$
$521$	−0.786784	−0.0344696	−0.0172348	+	0.999851i	$0.505486\pi$
$522$	−5.92910	−0.259510
$523$	0.0803513	0.00351352	0.00175676	−	0.999998i	$-0.499441\pi$
$523$	0.0803513	0.00351352	0.00175676	+	0.999998i	$0.499441\pi$
$524$	−30.2469	−1.32134
$525$	0	0
$526$	−17.3348	−0.755832
$527$	−21.3279	−0.929059
$528$	−0.287951	−0.0125315
$529$	−10.9610	−0.476566
$530$	0	0
$531$	34.2621	1.48685
$532$	−21.1145	−0.915432
$533$	−4.24600	−0.183914
$534$	1.84179	0.0797019
$535$	0	0
$536$	−32.1407	−1.38827
$537$	3.33113	0.143749
$538$	−9.67307	−0.417036
$539$	−4.08282	−0.175860
$540$	0	0
$541$	32.7717	1.40896	0.704482	−	0.709722i	$-0.251179\pi$
$541$	32.7717	1.40896	0.704482	+	0.709722i	$0.251179\pi$
$542$	16.0001	0.687264
$543$	−2.71872	−0.116672
$544$	−18.9545	−0.812668
$545$	0	0
$546$	2.72853	0.116770
$547$	3.20882	0.137199	0.0685997	−	0.997644i	$-0.478147\pi$
$547$	3.20882	0.137199	0.0685997	+	0.997644i	$0.478147\pi$
$548$	10.1617	0.434088
$549$	−8.05666	−0.343850
$550$	0	0
$551$	−12.2460	−0.521697
$552$	−1.56011	−0.0664027
$553$	−7.01123	−0.298148
$554$	−3.67685	−0.156215
$555$	0	0
$556$	10.5596	0.447826
$557$	9.06491	0.384093	0.192046	−	0.981386i	$-0.438488\pi$
$557$	9.06491	0.384093	0.192046	+	0.981386i	$0.438488\pi$
$558$	−12.9745	−0.549256
$559$	11.2006	0.473734
$560$	0	0
$561$	−0.636257	−0.0268628
$562$	2.11543	0.0892342
$563$	17.3681	0.731978	0.365989	−	0.930619i	$-0.380731\pi$
$563$	17.3681	0.731978	0.365989	+	0.930619i	$0.380731\pi$
$564$	0.291189	0.0122612
$565$	0	0
$566$	−15.9429	−0.670132
$567$	28.7492	1.20735
$568$	−24.1617	−1.01380
$569$	1.19301	0.0500134	0.0250067	−	0.999687i	$-0.492039\pi$
$569$	1.19301	0.0500134	0.0250067	+	0.999687i	$0.492039\pi$
$570$	0	0
$571$	7.43516	0.311152	0.155576	−	0.987824i	$-0.450277\pi$
$571$	7.43516	0.311152	0.155576	+	0.987824i	$0.450277\pi$
$572$	−10.3520	−0.432838
$573$	−0.575902	−0.0240586
$574$	−1.45660	−0.0607973
$575$	0	0
$576$	−2.72548	−0.113562
$577$	4.71294	0.196202	0.0981011	−	0.995176i	$-0.468723\pi$
$577$	4.71294	0.196202	0.0981011	+	0.995176i	$0.468723\pi$
$578$	4.19648	0.174551
$579$	−0.777697	−0.0323200
$580$	0	0
$581$	7.63468	0.316740
$582$	1.31861	0.0546581
$583$	−7.24441	−0.300033
$584$	−20.0597	−0.830075
$585$	0	0
$586$	10.0351	0.414545
$587$	−33.9179	−1.39994	−0.699970	−	0.714172i	$-0.746803\pi$
$587$	−33.9179	−1.39994	−0.699970	+	0.714172i	$0.746803\pi$
$588$	−1.15443	−0.0476080
$589$	−26.7977	−1.10418
$590$	0	0
$591$	4.13056	0.169909
$592$	1.43244	0.0588729
$593$	−3.38937	−0.139185	−0.0695924	−	0.997576i	$-0.522170\pi$
$593$	−3.38937	−0.139185	−0.0695924	+	0.997576i	$0.522170\pi$
$594$	−0.778743	−0.0319522
$595$	0	0
$596$	9.42522	0.386072
$597$	−1.52291	−0.0623286
$598$	−15.1854	−0.620979
$599$	−21.9775	−0.897978	−0.448989	−	0.893537i	$-0.648216\pi$
$599$	−21.9775	−0.897978	−0.448989	+	0.893537i	$0.648216\pi$
$600$	0	0
$601$	−9.45743	−0.385777	−0.192888	−	0.981221i	$-0.561786\pi$
$601$	−9.45743	−0.385777	−0.192888	+	0.981221i	$0.561786\pi$
$602$	3.84239	0.156604
$603$	39.8984	1.62479
$604$	−15.6387	−0.636329
$605$	0	0
$606$	−1.00207	−0.0407062
$607$	10.9014	0.442474	0.221237	−	0.975220i	$-0.428991\pi$
$607$	10.9014	0.442474	0.221237	+	0.975220i	$0.428991\pi$
$608$	−23.8156	−0.965848
$609$	−1.85173	−0.0750359
$610$	0	0
$611$	6.49956	0.262944
$612$	15.0452	0.608165
$613$	6.65622	0.268842	0.134421	−	0.990924i	$-0.457083\pi$
$613$	6.65622	0.268842	0.134421	+	0.990924i	$0.457083\pi$
$614$	7.44645	0.300514
$615$	0	0
$616$	−8.14368	−0.328118
$617$	−24.5957	−0.990184	−0.495092	−	0.868840i	$-0.664866\pi$
$617$	−24.5957	−0.990184	−0.495092	+	0.868840i	$0.664866\pi$
$618$	0.268441	0.0107983
$619$	−0.872443	−0.0350664	−0.0175332	−	0.999846i	$-0.505581\pi$
$619$	−0.872443	−0.0350664	−0.0175332	+	0.999846i	$0.505581\pi$
$620$	0	0
$621$	3.89649	0.156361
$622$	19.5776	0.784990
$623$	−48.1044	−1.92726
$624$	−1.81734	−0.0727517
$625$	0	0
$626$	10.6652	0.426267
$627$	−0.799430	−0.0319262
$628$	−6.71388	−0.267913
$629$	3.16512	0.126202
$630$	0	0
$631$	−8.64783	−0.344265	−0.172132	−	0.985074i	$-0.555066\pi$
$631$	−8.64783	−0.344265	−0.172132	+	0.985074i	$0.555066\pi$
$632$	−5.05659	−0.201141
$633$	3.99352	0.158728
$634$	−1.30902	−0.0519878
$635$	0	0
$636$	−2.04838	−0.0812237
$637$	−25.7678	−1.02096
$638$	−2.05966	−0.0815429
$639$	29.9935	1.18652
$640$	0	0
$641$	39.4781	1.55929	0.779645	−	0.626221i	$-0.215399\pi$
$641$	39.4781	1.55929	0.779645	+	0.626221i	$0.215399\pi$
$642$	1.59272	0.0628597
$643$	−43.5906	−1.71904	−0.859522	−	0.511098i	$-0.829239\pi$
$643$	−43.5906	−1.71904	−0.859522	+	0.511098i	$0.829239\pi$
$644$	17.7690	0.700197
$645$	0	0
$646$	−9.11018	−0.358435
$647$	0.539590	0.0212135	0.0106067	−	0.999944i	$-0.496624\pi$
$647$	0.539590	0.0212135	0.0106067	+	0.999944i	$0.496624\pi$
$648$	20.7343	0.814521
$649$	11.9020	0.467196
$650$	0	0
$651$	−4.05210	−0.158814
$652$	2.17510	0.0851834
$653$	30.7168	1.20204	0.601020	−	0.799234i	$-0.294761\pi$
$653$	30.7168	1.20204	0.601020	+	0.799234i	$0.294761\pi$
$654$	0.889817	0.0347946
$655$	0	0
$656$	0.970168	0.0378787
$657$	24.9014	0.971496
$658$	2.22969	0.0869224
$659$	9.12950	0.355635	0.177817	−	0.984063i	$-0.443096\pi$
$659$	9.12950	0.355635	0.177817	+	0.984063i	$0.443096\pi$
$660$	0	0
$661$	19.7384	0.767733	0.383866	−	0.923389i	$-0.374592\pi$
$661$	19.7384	0.767733	0.383866	+	0.923389i	$0.374592\pi$
$662$	16.7424	0.650711
$663$	−4.01559	−0.155953
$664$	5.50623	0.213683
$665$	0	0
$666$	1.92545	0.0746098
$667$	10.3057	0.399037
$668$	−5.94859	−0.230158
$669$	1.44881	0.0560142
$670$	0	0
$671$	−2.79874	−0.108044
$672$	−3.60117	−0.138918
$673$	−29.6599	−1.14331	−0.571654	−	0.820495i	$-0.693698\pi$
$673$	−29.6599	−1.14331	−0.571654	+	0.820495i	$0.693698\pi$
$674$	11.9310	0.459565
$675$	0	0
$676$	−45.2286	−1.73956
$677$	14.9373	0.574088	0.287044	−	0.957917i	$-0.407327\pi$
$677$	14.9373	0.574088	0.287044	+	0.957917i	$0.407327\pi$
$678$	−0.625757	−0.0240320
$679$	−34.4398	−1.32168
$680$	0	0
$681$	−0.489411	−0.0187543
$682$	−4.50712	−0.172587
$683$	17.7363	0.678659	0.339330	−	0.940668i	$-0.389800\pi$
$683$	17.7363	0.678659	0.339330	+	0.940668i	$0.389800\pi$
$684$	18.9036	0.722798
$685$	0	0
$686$	6.76811	0.258408
$687$	5.07826	0.193748
$688$	−2.55922	−0.0975693
$689$	−45.7215	−1.74185
$690$	0	0
$691$	−11.4062	−0.433911	−0.216955	−	0.976182i	$-0.569613\pi$
$691$	−11.4062	−0.433911	−0.216955	+	0.976182i	$0.569613\pi$
$692$	0.417903	0.0158863
$693$	10.1093	0.384020
$694$	−16.6916	−0.633603
$695$	0	0
$696$	−1.33549	−0.0506217
$697$	2.14368	0.0811979
$698$	11.5374	0.436698
$699$	1.22809	0.0464505
$700$	0	0
$701$	36.5936	1.38212	0.691061	−	0.722797i	$-0.257144\pi$
$701$	36.5936	1.38212	0.691061	+	0.722797i	$0.257144\pi$
$702$	−4.91486	−0.185500
$703$	3.97684	0.149989
$704$	−0.946784	−0.0356833
$705$	0	0
$706$	−13.5703	−0.510724
$707$	26.1723	0.984311
$708$	3.36535	0.126477
$709$	6.89276	0.258863	0.129432	−	0.991588i	$-0.458685\pi$
$709$	6.89276	0.258863	0.129432	+	0.991588i	$0.458685\pi$
$710$	0	0
$711$	6.27708	0.235409
$712$	−34.6935	−1.30019
$713$	22.5517	0.844566
$714$	−1.37756	−0.0515539
$715$	0	0
$716$	−27.3630	−1.02260
$717$	4.78645	0.178753
$718$	−14.3885	−0.536973
$719$	−14.3925	−0.536750	−0.268375	−	0.963314i	$-0.586487\pi$
$719$	−14.3925	−0.536750	−0.268375	+	0.963314i	$0.586487\pi$
$720$	0	0
$721$	−7.01123	−0.261112
$722$	1.34732	0.0501422
$723$	1.10982	0.0412745
$724$	22.3325	0.829980
$725$	0	0
$726$	1.26012	0.0467675
$727$	−28.2525	−1.04783	−0.523913	−	0.851772i	$-0.675528\pi$
$727$	−28.2525	−1.04783	−0.523913	+	0.851772i	$0.675528\pi$
$728$	−51.3970	−1.90490
$729$	−25.1046	−0.929799
$730$	0	0
$731$	−5.65486	−0.209152
$732$	−0.791353	−0.0292493
$733$	31.0782	1.14790	0.573950	−	0.818890i	$-0.305410\pi$
$733$	31.0782	1.14790	0.573950	+	0.818890i	$0.305410\pi$
$734$	−12.9188	−0.476840
$735$	0	0
$736$	20.0421	0.738760
$737$	13.8600	0.510539
$738$	1.30408	0.0480038
$739$	21.3558	0.785586	0.392793	−	0.919627i	$-0.371509\pi$
$739$	21.3558	0.785586	0.392793	+	0.919627i	$0.371509\pi$
$740$	0	0
$741$	−5.04543	−0.185348
$742$	−15.6849	−0.575810
$743$	19.3608	0.710278	0.355139	−	0.934814i	$-0.384434\pi$
$743$	19.3608	0.710278	0.355139	+	0.934814i	$0.384434\pi$
$744$	−2.92243	−0.107141
$745$	0	0
$746$	11.3548	0.415727
$747$	−6.83525	−0.250089
$748$	5.22642	0.191097
$749$	−41.5992	−1.52000
$750$	0	0
$751$	−35.7617	−1.30496	−0.652481	−	0.757805i	$-0.726272\pi$
$751$	−35.7617	−1.30496	−0.652481	+	0.757805i	$0.726272\pi$
$752$	−1.48508	−0.0541554
$753$	1.50626	0.0548912
$754$	−12.9991	−0.473400
$755$	0	0
$756$	5.75105	0.209164
$757$	−41.5565	−1.51040	−0.755199	−	0.655495i	$-0.772460\pi$
$757$	−41.5565	−1.51040	−0.755199	+	0.655495i	$0.772460\pi$
$758$	5.80292	0.210772
$759$	0.672763	0.0244198
$760$	0	0
$761$	−6.43411	−0.233236	−0.116618	−	0.993177i	$-0.537205\pi$
$761$	−6.43411	−0.233236	−0.116618	+	0.993177i	$0.537205\pi$
$762$	1.01717	0.0368483
$763$	−23.2405	−0.841363
$764$	4.73065	0.171149
$765$	0	0
$766$	9.13345	0.330005
$767$	75.1171	2.71232
$768$	−1.73234	−0.0625103
$769$	−10.4367	−0.376359	−0.188179	−	0.982135i	$-0.560259\pi$
$769$	−10.4367	−0.376359	−0.188179	+	0.982135i	$0.560259\pi$
$770$	0	0
$771$	−0.355179	−0.0127915
$772$	6.38826	0.229918
$773$	−50.5472	−1.81806	−0.909029	−	0.416733i	$-0.863175\pi$
$773$	−50.5472	−1.81806	−0.909029	+	0.416733i	$0.863175\pi$
$774$	−3.44005	−0.123650
$775$	0	0
$776$	−24.8385	−0.891649
$777$	0.601342	0.0215730
$778$	20.0019	0.717102
$779$	2.69345	0.0965029
$780$	0	0
$781$	10.4192	0.372828
$782$	7.66671	0.274161
$783$	3.33549	0.119201
$784$	5.88769	0.210275
$785$	0	0
$786$	−2.47947	−0.0884397
$787$	9.37722	0.334262	0.167131	−	0.985935i	$-0.446550\pi$
$787$	9.37722	0.334262	0.167131	+	0.985935i	$0.446550\pi$
$788$	−33.9298	−1.20870
$789$	4.84697	0.172557
$790$	0	0
$791$	16.3437	0.581116
$792$	7.29096	0.259073
$793$	−17.6636	−0.627253
$794$	−9.87075	−0.350300
$795$	0	0
$796$	12.5097	0.443395
$797$	−52.2349	−1.85025	−0.925127	−	0.379658i	$-0.876042\pi$
$797$	−52.2349	−1.85025	−0.925127	+	0.379658i	$0.876042\pi$
$798$	−1.73085	−0.0612713
$799$	−3.28144	−0.116089
$800$	0	0
$801$	43.0673	1.52171
$802$	15.0818	0.532558
$803$	8.65030	0.305262
$804$	3.91896	0.138211
$805$	0	0
$806$	−28.4457	−1.00196
$807$	2.70468	0.0952094
$808$	18.8758	0.664049
$809$	47.8218	1.68133	0.840663	−	0.541559i	$-0.182166\pi$
$809$	47.8218	1.68133	0.840663	+	0.541559i	$0.182166\pi$
$810$	0	0
$811$	−50.7827	−1.78322	−0.891611	−	0.452803i	$-0.850424\pi$
$811$	−50.7827	−1.78322	−0.891611	+	0.452803i	$0.850424\pi$
$812$	15.2107	0.533791
$813$	−4.47379	−0.156903
$814$	0.668868	0.0234438
$815$	0	0
$816$	0.917523	0.0321197
$817$	−7.10509	−0.248576
$818$	−17.6719	−0.617883
$819$	63.8025	2.22944
$820$	0	0
$821$	−21.3544	−0.745274	−0.372637	−	0.927977i	$-0.621546\pi$
$821$	−21.3544	−0.745274	−0.372637	+	0.927977i	$0.621546\pi$
$822$	0.833001	0.0290542
$823$	−25.5641	−0.891109	−0.445554	−	0.895255i	$-0.646993\pi$
$823$	−25.5641	−0.891109	−0.445554	+	0.895255i	$0.646993\pi$
$824$	−5.05659	−0.176155
$825$	0	0
$826$	25.7691	0.896623
$827$	17.4029	0.605157	0.302578	−	0.953125i	$-0.402153\pi$
$827$	17.4029	0.605157	0.302578	+	0.953125i	$0.402153\pi$
$828$	−15.9084	−0.552856
$829$	−36.5097	−1.26803	−0.634017	−	0.773319i	$-0.718595\pi$
$829$	−36.5097	−1.26803	−0.634017	+	0.773319i	$0.718595\pi$
$830$	0	0
$831$	1.02808	0.0356638
$832$	−5.97542	−0.207160
$833$	13.0095	0.450751
$834$	0.865612	0.0299737
$835$	0	0
$836$	6.56678	0.227117
$837$	7.29899	0.252290
$838$	9.94056	0.343391
$839$	41.5069	1.43298	0.716489	−	0.697598i	$-0.245748\pi$
$839$	41.5069	1.43298	0.716489	+	0.697598i	$0.245748\pi$
$840$	0	0
$841$	−20.1781	−0.695797
$842$	−6.20582	−0.213867
$843$	−0.591496	−0.0203722
$844$	−32.8041	−1.12916
$845$	0	0
$846$	−1.99622	−0.0686314
$847$	−32.9123	−1.13088
$848$	10.4469	0.358748
$849$	4.45780	0.152991
$850$	0	0
$851$	−3.34673	−0.114724
$852$	2.94607	0.100931
$853$	25.8833	0.886228	0.443114	−	0.896465i	$-0.353874\pi$
$853$	25.8833	0.886228	0.443114	+	0.896465i	$0.353874\pi$
$854$	−6.05955	−0.207354
$855$	0	0
$856$	−30.0019	−1.02544
$857$	15.2712	0.521656	0.260828	−	0.965385i	$-0.416005\pi$
$857$	15.2712	0.521656	0.260828	+	0.965385i	$0.416005\pi$
$858$	−0.848594	−0.0289705
$859$	−3.00856	−0.102651	−0.0513254	−	0.998682i	$-0.516345\pi$
$859$	−3.00856	−0.102651	−0.0513254	+	0.998682i	$0.516345\pi$
$860$	0	0
$861$	0.407279	0.0138800
$862$	−24.3609	−0.829737
$863$	−18.6708	−0.635562	−0.317781	−	0.948164i	$-0.602938\pi$
$863$	−18.6708	−0.635562	−0.317781	+	0.948164i	$0.602938\pi$
$864$	6.48674	0.220683
$865$	0	0
$866$	−5.48921	−0.186531
$867$	−1.17338	−0.0398499
$868$	33.2853	1.12978
$869$	2.18055	0.0739700
$870$	0	0
$871$	87.4742	2.96395
$872$	−16.7614	−0.567612
$873$	30.8336	1.04356
$874$	9.63290	0.325838
$875$	0	0
$876$	2.44590	0.0826393
$877$	13.5982	0.459178	0.229589	−	0.973288i	$-0.426262\pi$
$877$	13.5982	0.459178	0.229589	+	0.973288i	$0.426262\pi$
$878$	18.7173	0.631678
$879$	−2.80591	−0.0946408
$880$	0	0
$881$	18.6439	0.628130	0.314065	−	0.949401i	$-0.398309\pi$
$881$	18.6439	0.628130	0.314065	+	0.949401i	$0.398309\pi$
$882$	7.91411	0.266482
$883$	−12.6048	−0.424186	−0.212093	−	0.977250i	$-0.568028\pi$
$883$	−12.6048	−0.424186	−0.212093	+	0.977250i	$0.568028\pi$
$884$	32.9854	1.10942
$885$	0	0
$886$	1.05855	0.0355626
$887$	−35.2879	−1.18485	−0.592425	−	0.805625i	$-0.701829\pi$
$887$	−35.2879	−1.18485	−0.592425	+	0.805625i	$0.701829\pi$
$888$	0.433696	0.0145539
$889$	−26.5669	−0.891025
$890$	0	0
$891$	−8.94123	−0.299542
$892$	−11.9010	−0.398475
$893$	−4.12300	−0.137971
$894$	0.772624	0.0258404
$895$	0	0
$896$	36.2038	1.20948
$897$	4.24600	0.141770
$898$	15.3029	0.510664
$899$	19.3048	0.643850
$900$	0	0
$901$	23.0835	0.769023
$902$	0.453014	0.0150837
$903$	−1.07437	−0.0357527
$904$	11.7873	0.392040
$905$	0	0
$906$	−1.28197	−0.0425905
$907$	32.7155	1.08630	0.543150	−	0.839635i	$-0.317231\pi$
$907$	32.7155	1.08630	0.543150	+	0.839635i	$0.317231\pi$
$908$	4.02018	0.133414
$909$	−23.4318	−0.777184
$910$	0	0
$911$	0.151799	0.00502932	0.00251466	−	0.999997i	$-0.499200\pi$
$911$	0.151799	0.00502932	0.00251466	+	0.999997i	$0.499200\pi$
$912$	1.15283	0.0381740
$913$	−2.37444	−0.0785826
$914$	25.9022	0.856767
$915$	0	0
$916$	−41.7145	−1.37829
$917$	64.7595	2.13855
$918$	2.48138	0.0818977
$919$	6.69167	0.220738	0.110369	−	0.993891i	$-0.464797\pi$
$919$	6.69167	0.220738	0.110369	+	0.993891i	$0.464797\pi$
$920$	0	0
$921$	−2.08210	−0.0686075
$922$	−12.1919	−0.401519
$923$	65.7585	2.16447
$924$	0.992970	0.0326663
$925$	0	0
$926$	27.8662	0.915741
$927$	6.27708	0.206166
$928$	17.1565	0.563190
$929$	−20.0082	−0.656448	−0.328224	−	0.944600i	$-0.606450\pi$
$929$	−20.0082	−0.656448	−0.328224	+	0.944600i	$0.606450\pi$
$930$	0	0
$931$	16.3458	0.535713
$932$	−10.0879	−0.330441
$933$	−5.47408	−0.179213
$934$	−12.1103	−0.396262
$935$	0	0
$936$	46.0152	1.50406
$937$	45.2245	1.47742	0.738710	−	0.674023i	$-0.235435\pi$
$937$	45.2245	1.47742	0.738710	+	0.674023i	$0.235435\pi$
$938$	30.0083	0.979804
$939$	−2.98209	−0.0973169
$940$	0	0
$941$	8.29268	0.270334	0.135167	−	0.990823i	$-0.456843\pi$
$941$	8.29268	0.270334	0.135167	+	0.990823i	$0.456843\pi$
$942$	−0.550365	−0.0179319
$943$	−2.26668	−0.0738133
$944$	−17.1635	−0.558625
$945$	0	0
$946$	−1.19501	−0.0388532
$947$	−44.4232	−1.44356	−0.721780	−	0.692122i	$-0.756676\pi$
$947$	−44.4232	−1.44356	−0.721780	+	0.692122i	$0.756676\pi$
$948$	0.616557	0.0200248
$949$	54.5944	1.77221
$950$	0	0
$951$	0.366015	0.0118688
$952$	25.9489	0.841010
$953$	−21.2201	−0.687385	−0.343693	−	0.939082i	$-0.611678\pi$
$953$	−21.2201	−0.687385	−0.343693	+	0.939082i	$0.611678\pi$
$954$	14.0425	0.454643
$955$	0	0
$956$	−39.3175	−1.27162
$957$	0.575902	0.0186163
$958$	−5.05617	−0.163358
$959$	−21.7566	−0.702557
$960$	0	0
$961$	11.2442	0.362717
$962$	4.22141	0.136104
$963$	37.2433	1.20015
$964$	−9.11640	−0.293619
$965$	0	0
$966$	1.45660	0.0468653
$967$	19.4401	0.625150	0.312575	−	0.949893i	$-0.398808\pi$
$967$	19.4401	0.625150	0.312575	+	0.949893i	$0.398808\pi$
$968$	−23.7368	−0.762928
$969$	2.54729	0.0818309
$970$	0	0
$971$	9.63835	0.309309	0.154655	−	0.987969i	$-0.450574\pi$
$971$	9.63835	0.309309	0.154655	+	0.987969i	$0.450574\pi$
$972$	−7.73859	−0.248215
$973$	−22.6083	−0.724790
$974$	−6.59797	−0.211413
$975$	0	0
$976$	4.03596	0.129188
$977$	−48.3635	−1.54729	−0.773643	−	0.633621i	$-0.781568\pi$
$977$	−48.3635	−1.54729	−0.773643	+	0.633621i	$0.781568\pi$
$978$	0.178302	0.00570146
$979$	14.9608	0.478150
$980$	0	0
$981$	20.8070	0.664316
$982$	−10.2146	−0.325960
$983$	58.9782	1.88111	0.940556	−	0.339638i	$-0.110305\pi$
$983$	58.9782	1.88111	0.940556	+	0.339638i	$0.110305\pi$
$984$	0.293735	0.00936394
$985$	0	0
$986$	6.56289	0.209005
$987$	−0.623443	−0.0198444
$988$	41.4448	1.31853
$989$	5.97931	0.190131
$990$	0	0
$991$	−1.41726	−0.0450206	−0.0225103	−	0.999747i	$-0.507166\pi$
$991$	−1.41726	−0.0450206	−0.0225103	+	0.999747i	$0.507166\pi$
$992$	37.5432	1.19200
$993$	−4.68133	−0.148557
$994$	22.5586	0.715516
$995$	0	0
$996$	−0.671382	−0.0212735
$997$	25.8810	0.819660	0.409830	−	0.912162i	$-0.365588\pi$
$997$	25.8810	0.819660	0.409830	+	0.912162i	$0.365588\pi$
$998$	−8.45691	−0.267699
$999$	−1.08319	−0.0342706

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.f.1.2		4
5.2	odd	4		1175.2.c.e.424.3		8
5.3	odd	4		1175.2.c.e.424.6		8
5.4	even	2		47.2.a.a.1.3	✓	4
15.14	odd	2		423.2.a.k.1.2		4
20.19	odd	2		752.2.a.h.1.3		4
35.34	odd	2		2303.2.a.h.1.3		4
40.19	odd	2		3008.2.a.p.1.2		4
40.29	even	2		3008.2.a.q.1.3		4
55.54	odd	2		5687.2.a.s.1.2		4
60.59	even	2		6768.2.a.bv.1.1		4
65.64	even	2		7943.2.a.h.1.2		4
235.234	odd	2		2209.2.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.2.a.a.1.3	✓	4	5.4	even	2
423.2.a.k.1.2		4	15.14	odd	2
752.2.a.h.1.3		4	20.19	odd	2
1175.2.a.f.1.2		4	1.1	even	1	trivial
1175.2.c.e.424.3		8	5.2	odd	4
1175.2.c.e.424.6		8	5.3	odd	4
2209.2.a.e.1.3		4	235.234	odd	2
2303.2.a.h.1.3		4	35.34	odd	2
3008.2.a.p.1.2		4	40.19	odd	2
3008.2.a.q.1.3		4	40.29	even	2
5687.2.a.s.1.2		4	55.54	odd	2
6768.2.a.bv.1.1		4	60.59	even	2
7943.2.a.h.1.2		4	65.64	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:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-0.673363 q^{2} +0.188279 q^{3} -1.54658 q^{4} -0.126780 q^{6} +3.31128 q^{7} +2.38814 q^{8} -2.96455 q^{9} +O(q^{10})\)	\(q-0.673363 q^{2} +0.188279 q^{3} -1.54658 q^{4} -0.126780 q^{6} +3.31128 q^{7} +2.38814 q^{8} -2.96455 q^{9} -1.02983 q^{11} -0.291189 q^{12} -6.49956 q^{13} -2.22969 q^{14} +1.48508 q^{16} +3.28144 q^{17} +1.99622 q^{18} +4.12300 q^{19} +0.623443 q^{21} +0.693450 q^{22} -3.46972 q^{23} +0.449635 q^{24} +4.37656 q^{26} -1.12300 q^{27} -5.12116 q^{28} -2.97017 q^{29} -6.49956 q^{31} -5.77627 q^{32} -0.193895 q^{33} -2.20960 q^{34} +4.58492 q^{36} +0.964551 q^{37} -2.77627 q^{38} -1.22373 q^{39} +0.653275 q^{41} -0.419803 q^{42} -1.72328 q^{43} +1.59272 q^{44} +2.33638 q^{46} -1.00000 q^{47} +0.279610 q^{48} +3.96455 q^{49} +0.617826 q^{51} +10.0521 q^{52} +7.03456 q^{53} +0.756185 q^{54} +7.90778 q^{56} +0.776272 q^{57} +2.00000 q^{58} -11.5573 q^{59} +2.71767 q^{61} +4.37656 q^{62} -9.81645 q^{63} +0.919358 q^{64} +0.130562 q^{66} -13.4585 q^{67} -5.07503 q^{68} -0.653275 q^{69} -10.1174 q^{71} -7.07975 q^{72} -8.39972 q^{73} -0.649493 q^{74} -6.37656 q^{76} -3.41006 q^{77} +0.824012 q^{78} -2.11738 q^{79} +8.68222 q^{81} -0.439891 q^{82} +2.30566 q^{83} -0.964206 q^{84} +1.16039 q^{86} -0.559219 q^{87} -2.45938 q^{88} -14.5274 q^{89} -21.5218 q^{91} +5.36621 q^{92} -1.22373 q^{93} +0.673363 q^{94} -1.08755 q^{96} -10.4008 q^{97} -2.66958 q^{98} +3.05299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9	\( 4 q - q^{2} + 3 q^{4} - 8 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9} - 6 q^{11} + 11 q^{12} - 8 q^{13} - 5 q^{14} + 5 q^{16} - 6 q^{17} - 16 q^{18} + 4 q^{21} - 4 q^{22} + 6 q^{23} - 13 q^{24} + 16 q^{26} + 12 q^{27} - 16 q^{28} - 10 q^{29} - 8 q^{31} - 10 q^{32} - 12 q^{33} - 10 q^{34} + 11 q^{36} - 10 q^{37} + 2 q^{38} - 18 q^{39} + 6 q^{41} + 15 q^{42} - 2 q^{43} - 30 q^{44} + 18 q^{46} - 4 q^{47} - 6 q^{48} + 2 q^{49} - 8 q^{51} - 4 q^{52} + 6 q^{53} - 5 q^{54} + 2 q^{56} - 10 q^{57} + 8 q^{58} + 4 q^{59} - 6 q^{61} + 16 q^{62} - 16 q^{63} - 31 q^{64} + 32 q^{66} - 10 q^{67} - 43 q^{68} - 6 q^{69} - 12 q^{71} - 27 q^{72} - 22 q^{73} + 18 q^{74} - 24 q^{76} + 10 q^{77} + 28 q^{78} + 20 q^{79} + 4 q^{81} + 20 q^{82} - 20 q^{83} - 19 q^{84} + 38 q^{86} + 12 q^{87} - 2 q^{88} - 6 q^{89} - 22 q^{91} + 32 q^{92} - 18 q^{93} + q^{94} + 26 q^{96} - 30 q^{97} + 15 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - q^2 + 3 * q^4 - 8 * q^6 - 4 * q^7 + 3 * q^8 + 2 * q^9 - 6 * q^11 + 11 * q^12 - 8 * q^13 - 5 * q^14 + 5 * q^16 - 6 * q^17 - 16 * q^18 + 4 * q^21 - 4 * q^22 + 6 * q^23 - 13 * q^24 + 16 * q^26 + 12 * q^27 - 16 * q^28 - 10 * q^29 - 8 * q^31 - 10 * q^32 - 12 * q^33 - 10 * q^34 + 11 * q^36 - 10 * q^37 + 2 * q^38 - 18 * q^39 + 6 * q^41 + 15 * q^42 - 2 * q^43 - 30 * q^44 + 18 * q^46 - 4 * q^47 - 6 * q^48 + 2 * q^49 - 8 * q^51 - 4 * q^52 + 6 * q^53 - 5 * q^54 + 2 * q^56 - 10 * q^57 + 8 * q^58 + 4 * q^59 - 6 * q^61 + 16 * q^62 - 16 * q^63 - 31 * q^64 + 32 * q^66 - 10 * q^67 - 43 * q^68 - 6 * q^69 - 12 * q^71 - 27 * q^72 - 22 * q^73 + 18 * q^74 - 24 * q^76 + 10 * q^77 + 28 * q^78 + 20 * q^79 + 4 * q^81 + 20 * q^82 - 20 * q^83 - 19 * q^84 + 38 * q^86 + 12 * q^87 - 2 * q^88 - 6 * q^89 - 22 * q^91 + 32 * q^92 - 18 * q^93 + q^94 + 26 * q^96 - 30 * q^97 + 15 * q^98 + 4 * q^99

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