LMFDB - Embedded newform 1175.2.a.k.1.7

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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 23 x^{11} - x^{10} + 200 x^{9} + 11 x^{8} - 816 x^{7} - 19 x^{6} + 1581 x^{5} - 102 x^{4} + \cdots - 117 $ x^13 - 23x^11 - x^10 + 200x^9 + 11x^8 - 816x^7 - 19x^6 + 1581x^5 - 102x^4 - 1309x^3 + 300x^2 + 341x - 117
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.452387$ 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)

$f(q)$	$=$	$q-0.452387 q^{2} +0.461453 q^{3} -1.79535 q^{4} -0.208755 q^{6} +1.59927 q^{7} +1.71697 q^{8} -2.78706 q^{9} +O(q^{10})$	\(q-0.452387 q^{2} +0.461453 q^{3} -1.79535 q^{4} -0.208755 q^{6} +1.59927 q^{7} +1.71697 q^{8} -2.78706 q^{9} -0.580808 q^{11} -0.828467 q^{12} +4.75272 q^{13} -0.723491 q^{14} +2.81396 q^{16} -6.34890 q^{17} +1.26083 q^{18} +6.21796 q^{19} +0.737989 q^{21} +0.262750 q^{22} -5.12274 q^{23} +0.792298 q^{24} -2.15007 q^{26} -2.67045 q^{27} -2.87125 q^{28} -2.57536 q^{29} +8.34089 q^{31} -4.70693 q^{32} -0.268015 q^{33} +2.87216 q^{34} +5.00374 q^{36} +7.48617 q^{37} -2.81293 q^{38} +2.19315 q^{39} +10.9109 q^{41} -0.333857 q^{42} +5.38559 q^{43} +1.04275 q^{44} +2.31746 q^{46} -1.00000 q^{47} +1.29851 q^{48} -4.44232 q^{49} -2.92971 q^{51} -8.53277 q^{52} +6.26826 q^{53} +1.20808 q^{54} +2.74590 q^{56} +2.86929 q^{57} +1.16506 q^{58} +6.74665 q^{59} +2.24547 q^{61} -3.77331 q^{62} -4.45728 q^{63} -3.49856 q^{64} +0.121247 q^{66} +7.71459 q^{67} +11.3985 q^{68} -2.36390 q^{69} -4.87459 q^{71} -4.78529 q^{72} -11.6433 q^{73} -3.38665 q^{74} -11.1634 q^{76} -0.928871 q^{77} -0.992155 q^{78} +16.8273 q^{79} +7.12890 q^{81} -4.93596 q^{82} +13.1327 q^{83} -1.32495 q^{84} -2.43637 q^{86} -1.18841 q^{87} -0.997227 q^{88} +16.0157 q^{89} +7.60090 q^{91} +9.19708 q^{92} +3.84892 q^{93} +0.452387 q^{94} -2.17202 q^{96} -1.71756 q^{97} +2.00965 q^{98} +1.61875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9}+O(q^{10}) $ 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9	$ 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9} + 9 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 34 q^{16} - 5 q^{17} + 7 q^{18} + 16 q^{19} + 26 q^{21} - 15 q^{22} + 10 q^{23} - 8 q^{24} + 3 q^{26} - 15 q^{27} + 30 q^{28} + 10 q^{29} + 15 q^{31} - 36 q^{32} + 22 q^{33} + q^{34} + 57 q^{36} - 5 q^{37} + 42 q^{38} - 2 q^{39} + 24 q^{41} - 62 q^{42} + 2 q^{43} - 6 q^{44} + 50 q^{46} - 13 q^{47} + 67 q^{48} + 39 q^{49} + 9 q^{51} - 36 q^{52} - 4 q^{53} - 34 q^{54} - 9 q^{56} + 5 q^{57} + 27 q^{58} - 25 q^{59} + 22 q^{61} - 2 q^{62} + 7 q^{63} + 53 q^{64} + 2 q^{66} + 4 q^{67} - 5 q^{68} + 5 q^{69} - 6 q^{71} - 66 q^{72} + 3 q^{73} - 49 q^{74} + 63 q^{76} + 8 q^{77} + 59 q^{78} + 37 q^{79} + 49 q^{81} - 48 q^{82} - 27 q^{83} - 2 q^{84} + 3 q^{86} + 35 q^{87} + 44 q^{88} + 32 q^{89} + 12 q^{91} - 29 q^{92} - 56 q^{93} - 11 q^{96} - 25 q^{97} + 61 q^{98} + 36 q^{99}+O(q^{100}) $ 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9 + 9 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 34 * q^16 - 5 * q^17 + 7 * q^18 + 16 * q^19 + 26 * q^21 - 15 * q^22 + 10 * q^23 - 8 * q^24 + 3 * q^26 - 15 * q^27 + 30 * q^28 + 10 * q^29 + 15 * q^31 - 36 * q^32 + 22 * q^33 + q^34 + 57 * q^36 - 5 * q^37 + 42 * q^38 - 2 * q^39 + 24 * q^41 - 62 * q^42 + 2 * q^43 - 6 * q^44 + 50 * q^46 - 13 * q^47 + 67 * q^48 + 39 * q^49 + 9 * q^51 - 36 * q^52 - 4 * q^53 - 34 * q^54 - 9 * q^56 + 5 * q^57 + 27 * q^58 - 25 * q^59 + 22 * q^61 - 2 * q^62 + 7 * q^63 + 53 * q^64 + 2 * q^66 + 4 * q^67 - 5 * q^68 + 5 * q^69 - 6 * q^71 - 66 * q^72 + 3 * q^73 - 49 * q^74 + 63 * q^76 + 8 * q^77 + 59 * q^78 + 37 * q^79 + 49 * q^81 - 48 * q^82 - 27 * q^83 - 2 * q^84 + 3 * q^86 + 35 * q^87 + 44 * q^88 + 32 * q^89 + 12 * q^91 - 29 * q^92 - 56 * q^93 - 11 * q^96 - 25 * q^97 + 61 * q^98 + 36 * 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 $

$2$	−0.452387	−0.319886	−0.159943	−	0.987126i	$-0.551131\pi$
$2$	−0.452387	−0.319886	−0.159943	+	0.987126i	$0.551131\pi$
$3$	0.461453	0.266420	0.133210	−	0.991088i	$-0.457472\pi$
$3$	0.461453	0.266420	0.133210	+	0.991088i	$0.457472\pi$
$4$	−1.79535	−0.897673
$5$	0	0
$5$	0	0
$6$	−0.208755	−0.0852239
$7$	1.59927	0.604469	0.302234	−	0.953234i	$-0.402267\pi$
$7$	1.59927	0.604469	0.302234	+	0.953234i	$0.402267\pi$
$8$	1.71697	0.607039
$9$	−2.78706	−0.929021
$10$	0	0
$11$	−0.580808	−0.175120	−0.0875601	−	0.996159i	$-0.527907\pi$
$11$	−0.580808	−0.175120	−0.0875601	+	0.996159i	$0.527907\pi$
$12$	−0.828467	−0.239158
$13$	4.75272	1.31817	0.659083	−	0.752070i	$-0.270944\pi$
$13$	4.75272	1.31817	0.659083	+	0.752070i	$0.270944\pi$
$14$	−0.723491	−0.193361
$15$	0	0
$16$	2.81396	0.703490
$17$	−6.34890	−1.53983	−0.769917	−	0.638144i	$-0.779702\pi$
$17$	−6.34890	−1.53983	−0.769917	+	0.638144i	$0.779702\pi$
$18$	1.26083	0.297181
$19$	6.21796	1.42650	0.713249	−	0.700911i	$-0.247223\pi$
$19$	6.21796	1.42650	0.713249	+	0.700911i	$0.247223\pi$
$20$	0	0
$21$	0.737989	0.161042
$22$	0.262750	0.0560185
$23$	−5.12274	−1.06816	−0.534082	−	0.845433i	$-0.679343\pi$
$23$	−5.12274	−1.06816	−0.534082	+	0.845433i	$0.679343\pi$
$24$	0.792298	0.161727
$25$	0	0
$26$	−2.15007	−0.421663
$27$	−2.67045	−0.513929
$28$	−2.87125	−0.542615
$29$	−2.57536	−0.478233	−0.239117	−	0.970991i	$-0.576858\pi$
$29$	−2.57536	−0.478233	−0.239117	+	0.970991i	$0.576858\pi$
$30$	0	0
$31$	8.34089	1.49807	0.749034	−	0.662532i	$-0.230518\pi$
$31$	8.34089	1.49807	0.749034	+	0.662532i	$0.230518\pi$
$32$	−4.70693	−0.832075
$33$	−0.268015	−0.0466555
$34$	2.87216	0.492571
$35$	0	0
$36$	5.00374	0.833957
$37$	7.48617	1.23072	0.615360	−	0.788247i	$-0.289011\pi$
$37$	7.48617	1.23072	0.615360	+	0.788247i	$0.289011\pi$
$38$	−2.81293	−0.456317
$39$	2.19315	0.351186
$40$	0	0
$41$	10.9109	1.70400	0.852001	−	0.523541i	$-0.175389\pi$
$41$	10.9109	1.70400	0.852001	+	0.523541i	$0.175389\pi$
$42$	−0.333857	−0.0515152
$43$	5.38559	0.821294	0.410647	−	0.911794i	$-0.365303\pi$
$43$	5.38559	0.821294	0.410647	+	0.911794i	$0.365303\pi$
$44$	1.04275	0.157201
$45$	0	0
$46$	2.31746	0.341691
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	1.29851	0.187424
$49$	−4.44232	−0.634617
$50$	0	0
$51$	−2.92971	−0.410242
$52$	−8.53277	−1.18328
$53$	6.26826	0.861012	0.430506	−	0.902588i	$-0.358335\pi$
$53$	6.26826	0.861012	0.430506	+	0.902588i	$0.358335\pi$
$54$	1.20808	0.164399
$55$	0	0
$56$	2.74590	0.366936
$57$	2.86929	0.380047
$58$	1.16506	0.152980
$59$	6.74665	0.878339	0.439169	−	0.898404i	$-0.355273\pi$
$59$	6.74665	0.878339	0.439169	+	0.898404i	$0.355273\pi$
$60$	0	0
$61$	2.24547	0.287503	0.143751	−	0.989614i	$-0.454083\pi$
$61$	2.24547	0.287503	0.143751	+	0.989614i	$0.454083\pi$
$62$	−3.77331	−0.479211
$63$	−4.45728	−0.561564
$64$	−3.49856	−0.437320
$65$	0	0
$66$	0.121247	0.0149244
$67$	7.71459	0.942487	0.471243	−	0.882003i	$-0.343805\pi$
$67$	7.71459	0.942487	0.471243	+	0.882003i	$0.343805\pi$
$68$	11.3985	1.38227
$69$	−2.36390	−0.284580
$70$	0	0
$71$	−4.87459	−0.578507	−0.289253	−	0.957253i	$-0.593407\pi$
$71$	−4.87459	−0.578507	−0.289253	+	0.957253i	$0.593407\pi$
$72$	−4.78529	−0.563952
$73$	−11.6433	−1.36275	−0.681373	−	0.731936i	$-0.738617\pi$
$73$	−11.6433	−1.36275	−0.681373	+	0.731936i	$0.738617\pi$
$74$	−3.38665	−0.393690
$75$	0	0
$76$	−11.1634	−1.28053
$77$	−0.928871	−0.105855
$78$	−0.992155	−0.112339
$79$	16.8273	1.89322	0.946608	−	0.322387i	$-0.104485\pi$
$79$	16.8273	1.89322	0.946608	+	0.322387i	$0.104485\pi$
$80$	0	0
$81$	7.12890	0.792100
$82$	−4.93596	−0.545086
$83$	13.1327	1.44150	0.720749	−	0.693196i	$-0.243798\pi$
$83$	13.1327	1.44150	0.720749	+	0.693196i	$0.243798\pi$
$84$	−1.32495	−0.144563
$85$	0	0
$86$	−2.43637	−0.262721
$87$	−1.18841	−0.127411
$88$	−0.997227	−0.106305
$89$	16.0157	1.69766	0.848828	−	0.528668i	$-0.177309\pi$
$89$	16.0157	1.69766	0.848828	+	0.528668i	$0.177309\pi$
$90$	0	0
$91$	7.60090	0.796791
$92$	9.19708	0.958862
$93$	3.84892	0.399115
$94$	0.452387	0.0466602
$95$	0	0
$96$	−2.17202	−0.221681
$97$	−1.71756	−0.174392	−0.0871959	−	0.996191i	$-0.527791\pi$
$97$	−1.71756	−0.174392	−0.0871959	+	0.996191i	$0.527791\pi$
$98$	2.00965	0.203005
$99$	1.61875	0.162690
$100$	0	0
$101$	13.9225	1.38534	0.692670	−	0.721254i	$-0.256434\pi$
$101$	13.9225	1.38534	0.692670	+	0.721254i	$0.256434\pi$
$102$	1.32536	0.131231
$103$	−4.65406	−0.458578	−0.229289	−	0.973358i	$-0.573640\pi$
$103$	−4.65406	−0.458578	−0.229289	+	0.973358i	$0.573640\pi$
$104$	8.16025	0.800179
$105$	0	0
$106$	−2.83568	−0.275426
$107$	−6.26668	−0.605822	−0.302911	−	0.953019i	$-0.597959\pi$
$107$	−6.26668	−0.605822	−0.302911	+	0.953019i	$0.597959\pi$
$108$	4.79439	0.461340
$109$	−10.5395	−1.00950	−0.504752	−	0.863264i	$-0.668416\pi$
$109$	−10.5395	−1.00950	−0.504752	+	0.863264i	$0.668416\pi$
$110$	0	0
$111$	3.45451	0.327888
$112$	4.50029	0.425238
$113$	−15.8508	−1.49111	−0.745557	−	0.666442i	$-0.767816\pi$
$113$	−15.8508	−1.49111	−0.745557	+	0.666442i	$0.767816\pi$
$114$	−1.29803	−0.121572
$115$	0	0
$116$	4.62367	0.429297
$117$	−13.2461	−1.22460
$118$	−3.05210	−0.280968
$119$	−10.1536	−0.930781
$120$	0	0
$121$	−10.6627	−0.969333
$122$	−1.01582	−0.0919681
$123$	5.03488	0.453980
$124$	−14.9748	−1.34478
$125$	0	0
$126$	2.01641	0.179636
$127$	18.1456	1.61016	0.805080	−	0.593167i	$-0.202123\pi$
$127$	18.1456	1.61016	0.805080	+	0.593167i	$0.202123\pi$
$128$	10.9966	0.971968
$129$	2.48519	0.218809
$130$	0	0
$131$	−7.75531	−0.677584	−0.338792	−	0.940861i	$-0.610018\pi$
$131$	−7.75531	−0.677584	−0.338792	+	0.940861i	$0.610018\pi$
$132$	0.481180	0.0418814
$133$	9.94423	0.862274
$134$	−3.48998	−0.301488
$135$	0	0
$136$	−10.9008	−0.934739
$137$	−15.9120	−1.35945	−0.679726	−	0.733466i	$-0.737901\pi$
$137$	−15.9120	−1.35945	−0.679726	+	0.733466i	$0.737901\pi$
$138$	1.06940	0.0910332
$139$	8.99853	0.763245	0.381623	−	0.924318i	$-0.375365\pi$
$139$	8.99853	0.763245	0.381623	+	0.924318i	$0.375365\pi$
$140$	0	0
$141$	−0.461453	−0.0388613
$142$	2.20520	0.185056
$143$	−2.76042	−0.230838
$144$	−7.84268	−0.653556
$145$	0	0
$146$	5.26728	0.435924
$147$	−2.04992	−0.169075
$148$	−13.4403	−1.10478
$149$	12.3626	1.01279	0.506394	−	0.862302i	$-0.330978\pi$
$149$	12.3626	1.01279	0.506394	+	0.862302i	$0.330978\pi$
$150$	0	0
$151$	−7.92803	−0.645174	−0.322587	−	0.946540i	$-0.604553\pi$
$151$	−7.92803	−0.645174	−0.322587	+	0.946540i	$0.604553\pi$
$152$	10.6760	0.865940
$153$	17.6948	1.43054
$154$	0.420209	0.0338614
$155$	0	0
$156$	−3.93747	−0.315250
$157$	6.99954	0.558624	0.279312	−	0.960200i	$-0.409894\pi$
$157$	6.99954	0.558624	0.279312	+	0.960200i	$0.409894\pi$
$158$	−7.61244	−0.605613
$159$	2.89250	0.229391
$160$	0	0
$161$	−8.19266	−0.645672
$162$	−3.22502	−0.253382
$163$	−10.9524	−0.857856	−0.428928	−	0.903339i	$-0.641109\pi$
$163$	−10.9524	−0.857856	−0.428928	+	0.903339i	$0.641109\pi$
$164$	−19.5889	−1.52964
$165$	0	0
$166$	−5.94105	−0.461115
$167$	6.23095	0.482166	0.241083	−	0.970505i	$-0.422497\pi$
$167$	6.23095	0.482166	0.241083	+	0.970505i	$0.422497\pi$
$168$	1.26710	0.0977590
$169$	9.58833	0.737564
$170$	0	0
$171$	−17.3298	−1.32525
$172$	−9.66899	−0.737254
$173$	8.70832	0.662081	0.331041	−	0.943617i	$-0.392600\pi$
$173$	8.70832	0.662081	0.331041	+	0.943617i	$0.392600\pi$
$174$	0.537621	0.0407569
$175$	0	0
$176$	−1.63437	−0.123195
$177$	3.11326	0.234007
$178$	−7.24528	−0.543057
$179$	−15.9073	−1.18897	−0.594485	−	0.804107i	$-0.702644\pi$
$179$	−15.9073	−1.18897	−0.594485	+	0.804107i	$0.702644\pi$
$180$	0	0
$181$	24.6840	1.83475	0.917373	−	0.398029i	$-0.130306\pi$
$181$	24.6840	1.83475	0.917373	+	0.398029i	$0.130306\pi$
$182$	−3.43855	−0.254882
$183$	1.03618	0.0765964
$184$	−8.79556	−0.648417
$185$	0	0
$186$	−1.74120	−0.127671
$187$	3.68749	0.269656
$188$	1.79535	0.130939
$189$	−4.27079	−0.310654
$190$	0	0
$191$	−9.45140	−0.683879	−0.341940	−	0.939722i	$-0.611084\pi$
$191$	−9.45140	−0.683879	−0.341940	+	0.939722i	$0.611084\pi$
$192$	−1.61442	−0.116511
$193$	−19.8375	−1.42794	−0.713968	−	0.700178i	$-0.753104\pi$
$193$	−19.8375	−1.42794	−0.713968	+	0.700178i	$0.753104\pi$
$194$	0.777002	0.0557855
$195$	0	0
$196$	7.97550	0.569679
$197$	4.84658	0.345305	0.172652	−	0.984983i	$-0.444766\pi$
$197$	4.84658	0.345305	0.172652	+	0.984983i	$0.444766\pi$
$198$	−0.732301	−0.0520423
$199$	−5.82105	−0.412643	−0.206321	−	0.978484i	$-0.566149\pi$
$199$	−5.82105	−0.412643	−0.206321	+	0.978484i	$0.566149\pi$
$200$	0	0
$201$	3.55992	0.251097
$202$	−6.29836	−0.443151
$203$	−4.11871	−0.289077
$204$	5.25985	0.368263
$205$	0	0
$206$	2.10544	0.146693
$207$	14.2774	0.992347
$208$	13.3740	0.927317
$209$	−3.61144	−0.249809
$210$	0	0
$211$	5.25267	0.361609	0.180804	−	0.983519i	$-0.442130\pi$
$211$	5.25267	0.361609	0.180804	+	0.983519i	$0.442130\pi$
$212$	−11.2537	−0.772907
$213$	−2.24939	−0.154126
$214$	2.83496	0.193794
$215$	0	0
$216$	−4.58508	−0.311975
$217$	13.3394	0.905535
$218$	4.76795	0.322926
$219$	−5.37284	−0.363063
$220$	0	0
$221$	−30.1745	−2.02976
$222$	−1.56278	−0.104887
$223$	−12.9362	−0.866275	−0.433137	−	0.901328i	$-0.642594\pi$
$223$	−12.9362	−0.866275	−0.433137	+	0.901328i	$0.642594\pi$
$224$	−7.52767	−0.502964
$225$	0	0
$226$	7.17068	0.476986
$227$	−0.0742918	−0.00493092	−0.00246546	−	0.999997i	$-0.500785\pi$
$227$	−0.0742918	−0.00493092	−0.00246546	+	0.999997i	$0.500785\pi$
$228$	−5.15138	−0.341158
$229$	5.16238	0.341140	0.170570	−	0.985346i	$-0.445439\pi$
$229$	5.16238	0.341140	0.170570	+	0.985346i	$0.445439\pi$
$230$	0	0
$231$	−0.428630	−0.0282018
$232$	−4.42181	−0.290306
$233$	−12.0798	−0.791377	−0.395688	−	0.918385i	$-0.629494\pi$
$233$	−12.0798	−0.791377	−0.395688	+	0.918385i	$0.629494\pi$
$234$	5.99237	0.391734
$235$	0	0
$236$	−12.1126	−0.788461
$237$	7.76499	0.504390
$238$	4.59337	0.297744
$239$	−11.6130	−0.751184	−0.375592	−	0.926785i	$-0.622561\pi$
$239$	−11.6130	−0.751184	−0.375592	+	0.926785i	$0.622561\pi$
$240$	0	0
$241$	−20.7509	−1.33668	−0.668342	−	0.743854i	$-0.732996\pi$
$241$	−20.7509	−1.33668	−0.668342	+	0.743854i	$0.732996\pi$
$242$	4.82365	0.310076
$243$	11.3010	0.724960
$244$	−4.03139	−0.258083
$245$	0	0
$246$	−2.27771	−0.145222
$247$	29.5522	1.88036
$248$	14.3210	0.909386
$249$	6.06011	0.384044
$250$	0	0
$251$	9.63604	0.608221	0.304111	−	0.952637i	$-0.401641\pi$
$251$	9.63604	0.608221	0.304111	+	0.952637i	$0.401641\pi$
$252$	8.00235	0.504101
$253$	2.97533	0.187057
$254$	−8.20882	−0.515067
$255$	0	0
$256$	2.02242	0.126402
$257$	1.08735	0.0678269	0.0339134	−	0.999425i	$-0.489203\pi$
$257$	1.08735	0.0678269	0.0339134	+	0.999425i	$0.489203\pi$
$258$	−1.12427	−0.0699939
$259$	11.9724	0.743931
$260$	0	0
$261$	7.17770	0.444288
$262$	3.50840	0.216750
$263$	−22.0302	−1.35844	−0.679219	−	0.733936i	$-0.737681\pi$
$263$	−22.0302	−1.35844	−0.679219	+	0.733936i	$0.737681\pi$
$264$	−0.460173	−0.0283217
$265$	0	0
$266$	−4.49864	−0.275829
$267$	7.39047	0.452289
$268$	−13.8504	−0.846045
$269$	25.4061	1.54904	0.774520	−	0.632549i	$-0.217991\pi$
$269$	25.4061	1.54904	0.774520	+	0.632549i	$0.217991\pi$
$270$	0	0
$271$	−7.90253	−0.480044	−0.240022	−	0.970767i	$-0.577155\pi$
$271$	−7.90253	−0.480044	−0.240022	+	0.970767i	$0.577155\pi$
$272$	−17.8655	−1.08326
$273$	3.50745	0.212281
$274$	7.19837	0.434870
$275$	0	0
$276$	4.24402	0.255460
$277$	4.52011	0.271587	0.135794	−	0.990737i	$-0.456642\pi$
$277$	4.52011	0.271587	0.135794	+	0.990737i	$0.456642\pi$
$278$	−4.07082	−0.244152
$279$	−23.2466	−1.39174
$280$	0	0
$281$	−10.0249	−0.598035	−0.299018	−	0.954248i	$-0.596659\pi$
$281$	−10.0249	−0.598035	−0.299018	+	0.954248i	$0.596659\pi$
$282$	0.208755	0.0124312
$283$	−20.6987	−1.23041	−0.615206	−	0.788367i	$-0.710927\pi$
$283$	−20.6987	−1.23041	−0.615206	+	0.788367i	$0.710927\pi$
$284$	8.75157	0.519310
$285$	0	0
$286$	1.24878	0.0738417
$287$	17.4496	1.03002
$288$	13.1185	0.773015
$289$	23.3085	1.37109
$290$	0	0
$291$	−0.792573	−0.0464614
$292$	20.9038	1.22330
$293$	−11.0402	−0.644973	−0.322487	−	0.946574i	$-0.604519\pi$
$293$	−11.0402	−0.644973	−0.322487	+	0.946574i	$0.604519\pi$
$294$	0.927358	0.0540846
$295$	0	0
$296$	12.8535	0.747094
$297$	1.55102	0.0899994
$298$	−5.59270	−0.323976
$299$	−24.3469	−1.40802
$300$	0	0
$301$	8.61303	0.496447
$302$	3.58654	0.206382
$303$	6.42457	0.369082
$304$	17.4971	1.00353
$305$	0	0
$306$	−8.00488	−0.457609
$307$	−12.8283	−0.732149	−0.366074	−	0.930586i	$-0.619298\pi$
$307$	−12.8283	−0.732149	−0.366074	+	0.930586i	$0.619298\pi$
$308$	1.66765	0.0950229
$309$	−2.14763	−0.122174
$310$	0	0
$311$	16.4724	0.934064	0.467032	−	0.884240i	$-0.345323\pi$
$311$	16.4724	0.934064	0.467032	+	0.884240i	$0.345323\pi$
$312$	3.76557	0.213183
$313$	−16.3625	−0.924861	−0.462430	−	0.886656i	$-0.653022\pi$
$313$	−16.3625	−0.924861	−0.462430	+	0.886656i	$0.653022\pi$
$314$	−3.16650	−0.178696
$315$	0	0
$316$	−30.2108	−1.69949
$317$	11.8904	0.667833	0.333917	−	0.942603i	$-0.391630\pi$
$317$	11.8904	0.667833	0.333917	+	0.942603i	$0.391630\pi$
$318$	−1.30853	−0.0733788
$319$	1.49579	0.0837483
$320$	0	0
$321$	−2.89177	−0.161403
$322$	3.70625	0.206541
$323$	−39.4772	−2.19657
$324$	−12.7988	−0.711046
$325$	0	0
$326$	4.95471	0.274416
$327$	−4.86349	−0.268952
$328$	18.7337	1.03440
$329$	−1.59927	−0.0881708
$330$	0	0
$331$	−10.4116	−0.572275	−0.286137	−	0.958189i	$-0.592371\pi$
$331$	−10.4116	−0.572275	−0.286137	+	0.958189i	$0.592371\pi$
$332$	−23.5777	−1.29399
$333$	−20.8644	−1.14336
$334$	−2.81880	−0.154238
$335$	0	0
$336$	2.07667	0.113292
$337$	−26.7089	−1.45493	−0.727463	−	0.686147i	$-0.759301\pi$
$337$	−26.7089	−1.45493	−0.727463	+	0.686147i	$0.759301\pi$
$338$	−4.33764	−0.235936
$339$	−7.31437	−0.397262
$340$	0	0
$341$	−4.84446	−0.262342
$342$	7.83980	0.423928
$343$	−18.2994	−0.988075
$344$	9.24687	0.498558
$345$	0	0
$346$	−3.93953	−0.211790
$347$	3.97664	0.213477	0.106739	−	0.994287i	$-0.465959\pi$
$347$	3.97664	0.213477	0.106739	+	0.994287i	$0.465959\pi$
$348$	2.13360	0.114373
$349$	29.9896	1.60531	0.802653	−	0.596446i	$-0.203421\pi$
$349$	29.9896	1.60531	0.802653	+	0.596446i	$0.203421\pi$
$350$	0	0
$351$	−12.6919	−0.677444
$352$	2.73382	0.145713
$353$	4.53276	0.241254	0.120627	−	0.992698i	$-0.461509\pi$
$353$	4.53276	0.241254	0.120627	+	0.992698i	$0.461509\pi$
$354$	−1.40840	−0.0748555
$355$	0	0
$356$	−28.7537	−1.52394
$357$	−4.68542	−0.247979
$358$	7.19627	0.380335
$359$	−4.59045	−0.242275	−0.121137	−	0.992636i	$-0.538654\pi$
$359$	−4.59045	−0.242275	−0.121137	+	0.992636i	$0.538654\pi$
$360$	0	0
$361$	19.6631	1.03490
$362$	−11.1667	−0.586909
$363$	−4.92031	−0.258249
$364$	−13.6462	−0.715258
$365$	0	0
$366$	−0.468753	−0.0245021
$367$	−14.8859	−0.777036	−0.388518	−	0.921441i	$-0.627013\pi$
$367$	−14.8859	−0.777036	−0.388518	+	0.921441i	$0.627013\pi$
$368$	−14.4152	−0.751443
$369$	−30.4094	−1.58305
$370$	0	0
$371$	10.0247	0.520455
$372$	−6.91015	−0.358275
$373$	15.4296	0.798914	0.399457	−	0.916752i	$-0.369199\pi$
$373$	15.4296	0.798914	0.399457	+	0.916752i	$0.369199\pi$
$374$	−1.66817	−0.0862592
$375$	0	0
$376$	−1.71697	−0.0885457
$377$	−12.2400	−0.630391
$378$	1.93205	0.0993739
$379$	5.33338	0.273957	0.136979	−	0.990574i	$-0.456261\pi$
$379$	5.33338	0.273957	0.136979	+	0.990574i	$0.456261\pi$
$380$	0	0
$381$	8.37332	0.428978
$382$	4.27569	0.218763
$383$	25.1311	1.28414	0.642069	−	0.766647i	$-0.278076\pi$
$383$	25.1311	1.28414	0.642069	+	0.766647i	$0.278076\pi$
$384$	5.07439	0.258952
$385$	0	0
$386$	8.97424	0.456777
$387$	−15.0100	−0.762999
$388$	3.08362	0.156547
$389$	−24.2602	−1.23004	−0.615020	−	0.788512i	$-0.710852\pi$
$389$	−24.2602	−1.23004	−0.615020	+	0.788512i	$0.710852\pi$
$390$	0	0
$391$	32.5237	1.64479
$392$	−7.62731	−0.385237
$393$	−3.57871	−0.180522
$394$	−2.19253	−0.110458
$395$	0	0
$396$	−2.90621	−0.146043
$397$	1.67235	0.0839330	0.0419665	−	0.999119i	$-0.486638\pi$
$397$	1.67235	0.0839330	0.0419665	+	0.999119i	$0.486638\pi$
$398$	2.63337	0.131999
$399$	4.58879	0.229727
$400$	0	0
$401$	−3.54676	−0.177117	−0.0885583	−	0.996071i	$-0.528226\pi$
$401$	−3.54676	−0.177117	−0.0885583	+	0.996071i	$0.528226\pi$
$402$	−1.61046	−0.0803224
$403$	39.6419	1.97470
$404$	−24.9957	−1.24358
$405$	0	0
$406$	1.86325	0.0924717
$407$	−4.34803	−0.215524
$408$	−5.03022	−0.249033
$409$	−3.05268	−0.150945	−0.0754727	−	0.997148i	$-0.524047\pi$
$409$	−3.05268	−0.150945	−0.0754727	+	0.997148i	$0.524047\pi$
$410$	0	0
$411$	−7.34262	−0.362185
$412$	8.35565	0.411653
$413$	10.7897	0.530928
$414$	−6.45890	−0.317438
$415$	0	0
$416$	−22.3707	−1.09681
$417$	4.15240	0.203344
$418$	1.63377	0.0799103
$419$	31.5206	1.53988	0.769942	−	0.638114i	$-0.220285\pi$
$419$	31.5206	1.53988	0.769942	+	0.638114i	$0.220285\pi$
$420$	0	0
$421$	−8.32065	−0.405523	−0.202762	−	0.979228i	$-0.564992\pi$
$421$	−8.32065	−0.405523	−0.202762	+	0.979228i	$0.564992\pi$
$422$	−2.37624	−0.115674
$423$	2.78706	0.135512
$424$	10.7624	0.522668
$425$	0	0
$426$	1.01760	0.0493026
$427$	3.59112	0.173786
$428$	11.2509	0.543830
$429$	−1.27380	−0.0614997
$430$	0	0
$431$	−32.5478	−1.56777	−0.783886	−	0.620905i	$-0.786765\pi$
$431$	−32.5478	−1.56777	−0.783886	+	0.620905i	$0.786765\pi$
$432$	−7.51455	−0.361544
$433$	10.4552	0.502444	0.251222	−	0.967929i	$-0.419168\pi$
$433$	10.4552	0.502444	0.251222	+	0.967929i	$0.419168\pi$
$434$	−6.03456	−0.289668
$435$	0	0
$436$	18.9221	0.906204
$437$	−31.8530	−1.52373
$438$	2.43060	0.116139
$439$	−18.7482	−0.894804	−0.447402	−	0.894333i	$-0.647651\pi$
$439$	−18.7482	−0.894804	−0.447402	+	0.894333i	$0.647651\pi$
$440$	0	0
$441$	12.3810	0.589573
$442$	13.6506	0.649291
$443$	3.05537	0.145165	0.0725825	−	0.997362i	$-0.476876\pi$
$443$	3.05537	0.145165	0.0725825	+	0.997362i	$0.476876\pi$
$444$	−6.20205	−0.294336
$445$	0	0
$446$	5.85219	0.277109
$447$	5.70477	0.269827
$448$	−5.59516	−0.264347
$449$	4.90473	0.231468	0.115734	−	0.993280i	$-0.463078\pi$
$449$	4.90473	0.231468	0.115734	+	0.993280i	$0.463078\pi$
$450$	0	0
$451$	−6.33716	−0.298405
$452$	28.4576	1.33853
$453$	−3.65841	−0.171887
$454$	0.0336086	0.00157733
$455$	0	0
$456$	4.92648	0.230704
$457$	27.7987	1.30037	0.650183	−	0.759778i	$-0.274692\pi$
$457$	27.7987	1.30037	0.650183	+	0.759778i	$0.274692\pi$
$458$	−2.33539	−0.109126
$459$	16.9544	0.791365
$460$	0	0
$461$	−9.31718	−0.433944	−0.216972	−	0.976178i	$-0.569618\pi$
$461$	−9.31718	−0.433944	−0.216972	+	0.976178i	$0.569618\pi$
$462$	0.193907	0.00902136
$463$	4.29955	0.199817	0.0999085	−	0.994997i	$-0.468145\pi$
$463$	4.29955	0.199817	0.0999085	+	0.994997i	$0.468145\pi$
$464$	−7.24697	−0.336432
$465$	0	0
$466$	5.46476	0.253150
$467$	37.8343	1.75076	0.875381	−	0.483433i	$-0.160610\pi$
$467$	37.8343	1.75076	0.875381	+	0.483433i	$0.160610\pi$
$468$	23.7814	1.09929
$469$	12.3377	0.569704
$470$	0	0
$471$	3.22996	0.148829
$472$	11.5838	0.533186
$473$	−3.12799	−0.143825
$474$	−3.51278	−0.161347
$475$	0	0
$476$	18.2293	0.835537
$477$	−17.4700	−0.799897
$478$	5.25358	0.240293
$479$	−16.6107	−0.758964	−0.379482	−	0.925199i	$-0.623898\pi$
$479$	−16.6107	−0.758964	−0.379482	+	0.925199i	$0.623898\pi$
$480$	0	0
$481$	35.5797	1.62229
$482$	9.38745	0.427586
$483$	−3.78052	−0.172020
$484$	19.1432	0.870144
$485$	0	0
$486$	−5.11243	−0.231905
$487$	−0.494434	−0.0224050	−0.0112025	−	0.999937i	$-0.503566\pi$
$487$	−0.494434	−0.0224050	−0.0112025	+	0.999937i	$0.503566\pi$
$488$	3.85539	0.174525
$489$	−5.05400	−0.228550
$490$	0	0
$491$	5.39195	0.243335	0.121668	−	0.992571i	$-0.461176\pi$
$491$	5.39195	0.243335	0.121668	+	0.992571i	$0.461176\pi$
$492$	−9.03935	−0.407525
$493$	16.3507	0.736399
$494$	−13.3690	−0.601502
$495$	0	0
$496$	23.4709	1.05388
$497$	−7.79580	−0.349689
$498$	−2.74151	−0.122850
$499$	23.0771	1.03307	0.516537	−	0.856265i	$-0.327221\pi$
$499$	23.0771	1.03307	0.516537	+	0.856265i	$0.327221\pi$
$500$	0	0
$501$	2.87529	0.128458
$502$	−4.35922	−0.194562
$503$	−0.840156	−0.0374607	−0.0187304	−	0.999825i	$-0.505962\pi$
$503$	−0.840156	−0.0374607	−0.0187304	+	0.999825i	$0.505962\pi$
$504$	−7.65299	−0.340891
$505$	0	0
$506$	−1.34600	−0.0598370
$507$	4.42456	0.196502
$508$	−32.5776	−1.44540
$509$	12.0150	0.532554	0.266277	−	0.963896i	$-0.414206\pi$
$509$	12.0150	0.532554	0.266277	+	0.963896i	$0.414206\pi$
$510$	0	0
$511$	−18.6209	−0.823738
$512$	−22.9080	−1.01240
$513$	−16.6048	−0.733119
$514$	−0.491902	−0.0216969
$515$	0	0
$516$	−4.46178	−0.196419
$517$	0.580808	0.0255439
$518$	−5.41618	−0.237973
$519$	4.01848	0.176392
$520$	0	0
$521$	35.5532	1.55761	0.778806	−	0.627265i	$-0.215826\pi$
$521$	35.5532	1.55761	0.778806	+	0.627265i	$0.215826\pi$
$522$	−3.24710	−0.142122
$523$	−31.1596	−1.36251	−0.681256	−	0.732045i	$-0.738566\pi$
$523$	−31.1596	−1.36251	−0.681256	+	0.732045i	$0.738566\pi$
$524$	13.9235	0.608249
$525$	0	0
$526$	9.96616	0.434545
$527$	−52.9554	−2.30677
$528$	−0.754184	−0.0328217
$529$	3.24243	0.140975
$530$	0	0
$531$	−18.8033	−0.815995
$532$	−17.8533	−0.774040
$533$	51.8566	2.24616
$534$	−3.34335	−0.144681
$535$	0	0
$536$	13.2457	0.572126
$537$	−7.34048	−0.316765
$538$	−11.4934	−0.495516
$539$	2.58014	0.111134
$540$	0	0
$541$	10.1171	0.434970	0.217485	−	0.976064i	$-0.430215\pi$
$541$	10.1171	0.434970	0.217485	+	0.976064i	$0.430215\pi$
$542$	3.57500	0.153559
$543$	11.3905	0.488813
$544$	29.8838	1.28126
$545$	0	0
$546$	−1.58673	−0.0679057
$547$	−19.7996	−0.846570	−0.423285	−	0.905997i	$-0.639123\pi$
$547$	−19.7996	−0.846570	−0.423285	+	0.905997i	$0.639123\pi$
$548$	28.5675	1.22034
$549$	−6.25826	−0.267096
$550$	0	0
$551$	−16.0135	−0.682199
$552$	−4.05873	−0.172751
$553$	26.9114	1.14439
$554$	−2.04484	−0.0868769
$555$	0	0
$556$	−16.1555	−0.685145
$557$	−21.5981	−0.915142	−0.457571	−	0.889173i	$-0.651281\pi$
$557$	−21.5981	−0.915142	−0.457571	+	0.889173i	$0.651281\pi$
$558$	10.5164	0.445197
$559$	25.5962	1.08260
$560$	0	0
$561$	1.70160	0.0718417
$562$	4.53513	0.191303
$563$	37.5005	1.58046	0.790230	−	0.612811i	$-0.209961\pi$
$563$	37.5005	1.58046	0.790230	+	0.612811i	$0.209961\pi$
$564$	0.828467	0.0348848
$565$	0	0
$566$	9.36383	0.393591
$567$	11.4011	0.478800
$568$	−8.36950	−0.351176
$569$	23.7979	0.997661	0.498831	−	0.866699i	$-0.333763\pi$
$569$	23.7979	0.997661	0.498831	+	0.866699i	$0.333763\pi$
$570$	0	0
$571$	−25.9076	−1.08420	−0.542100	−	0.840314i	$-0.682371\pi$
$571$	−25.9076	−1.08420	−0.542100	+	0.840314i	$0.682371\pi$
$572$	4.95590	0.207217
$573$	−4.36137	−0.182199
$574$	−7.89396	−0.329488
$575$	0	0
$576$	9.75071	0.406280
$577$	4.25610	0.177184	0.0885919	−	0.996068i	$-0.471763\pi$
$577$	4.25610	0.177184	0.0885919	+	0.996068i	$0.471763\pi$
$578$	−10.5444	−0.438591
$579$	−9.15408	−0.380430
$580$	0	0
$581$	21.0028	0.871341
$582$	0.358550	0.0148624
$583$	−3.64066	−0.150781
$584$	−19.9912	−0.827240
$585$	0	0
$586$	4.99443	0.206318
$587$	34.6297	1.42932	0.714660	−	0.699472i	$-0.246581\pi$
$587$	34.6297	1.42932	0.714660	+	0.699472i	$0.246581\pi$
$588$	3.68032	0.151774
$589$	51.8633	2.13699
$590$	0	0
$591$	2.23647	0.0919960
$592$	21.0658	0.865798
$593$	14.2119	0.583613	0.291807	−	0.956477i	$-0.405744\pi$
$593$	14.2119	0.583613	0.291807	+	0.956477i	$0.405744\pi$
$594$	−0.701662	−0.0287895
$595$	0	0
$596$	−22.1952	−0.909152
$597$	−2.68614	−0.109936
$598$	11.0142	0.450405
$599$	8.38848	0.342744	0.171372	−	0.985206i	$-0.445180\pi$
$599$	8.38848	0.342744	0.171372	+	0.985206i	$0.445180\pi$
$600$	0	0
$601$	16.0945	0.656509	0.328255	−	0.944589i	$-0.393540\pi$
$601$	16.0945	0.656509	0.328255	+	0.944589i	$0.393540\pi$
$602$	−3.89642	−0.158806
$603$	−21.5010	−0.875590
$604$	14.2336	0.579156
$605$	0	0
$606$	−2.90639	−0.118064
$607$	−36.4635	−1.48001	−0.740004	−	0.672602i	$-0.765176\pi$
$607$	−36.4635	−1.48001	−0.740004	+	0.672602i	$0.765176\pi$
$608$	−29.2675	−1.18695
$609$	−1.90059	−0.0770158
$610$	0	0
$611$	−4.75272	−0.192274
$612$	−31.7682	−1.28415
$613$	9.15182	0.369638	0.184819	−	0.982773i	$-0.440830\pi$
$613$	9.15182	0.369638	0.184819	+	0.982773i	$0.440830\pi$
$614$	5.80335	0.234204
$615$	0	0
$616$	−1.59484	−0.0642579
$617$	28.5245	1.14835	0.574177	−	0.818731i	$-0.305322\pi$
$617$	28.5245	1.14835	0.574177	+	0.818731i	$0.305322\pi$
$618$	0.971559	0.0390818
$619$	−21.0566	−0.846338	−0.423169	−	0.906051i	$-0.639082\pi$
$619$	−21.0566	−0.846338	−0.423169	+	0.906051i	$0.639082\pi$
$620$	0	0
$621$	13.6800	0.548961
$622$	−7.45190	−0.298794
$623$	25.6134	1.02618
$624$	6.17145	0.247056
$625$	0	0
$626$	7.40216	0.295850
$627$	−1.66651	−0.0665540
$628$	−12.5666	−0.501462
$629$	−47.5289	−1.89510
$630$	0	0
$631$	45.7928	1.82298	0.911492	−	0.411317i	$-0.134931\pi$
$631$	45.7928	1.82298	0.911492	+	0.411317i	$0.134931\pi$
$632$	28.8918	1.14926
$633$	2.42386	0.0963397
$634$	−5.37908	−0.213630
$635$	0	0
$636$	−5.19305	−0.205918
$637$	−21.1131	−0.836532
$638$	−0.676677	−0.0267899
$639$	13.5858	0.537445
$640$	0	0
$641$	−14.8338	−0.585899	−0.292950	−	0.956128i	$-0.594637\pi$
$641$	−14.8338	−0.585899	−0.292950	+	0.956128i	$0.594637\pi$
$642$	1.30820	0.0516306
$643$	−36.5239	−1.44036	−0.720181	−	0.693786i	$-0.755941\pi$
$643$	−36.5239	−1.44036	−0.720181	+	0.693786i	$0.755941\pi$
$644$	14.7087	0.579602
$645$	0	0
$646$	17.8590	0.702652
$647$	23.5431	0.925577	0.462788	−	0.886469i	$-0.346849\pi$
$647$	23.5431	0.925577	0.462788	+	0.886469i	$0.346849\pi$
$648$	12.2401	0.480835
$649$	−3.91851	−0.153815
$650$	0	0
$651$	6.15549	0.241253
$652$	19.6633	0.770075
$653$	30.2332	1.18312	0.591558	−	0.806262i	$-0.298513\pi$
$653$	30.2332	1.18312	0.591558	+	0.806262i	$0.298513\pi$
$654$	2.20018	0.0860339
$655$	0	0
$656$	30.7029	1.19875
$657$	32.4506	1.26602
$658$	0.723491	0.0282046
$659$	−36.1590	−1.40856	−0.704278	−	0.709924i	$-0.748729\pi$
$659$	−36.1590	−1.40856	−0.704278	+	0.709924i	$0.748729\pi$
$660$	0	0
$661$	35.2063	1.36936	0.684682	−	0.728842i	$-0.259941\pi$
$661$	35.2063	1.36936	0.684682	+	0.728842i	$0.259941\pi$
$662$	4.71008	0.183063
$663$	−13.9241	−0.540767
$664$	22.5484	0.875046
$665$	0	0
$666$	9.43879	0.365746
$667$	13.1929	0.510832
$668$	−11.1867	−0.432827
$669$	−5.96946	−0.230793
$670$	0	0
$671$	−1.30419	−0.0503476
$672$	−3.47366	−0.133999
$673$	7.00921	0.270185	0.135093	−	0.990833i	$-0.456867\pi$
$673$	7.00921	0.270185	0.135093	+	0.990833i	$0.456867\pi$
$674$	12.0827	0.465410
$675$	0	0
$676$	−17.2144	−0.662091
$677$	−26.0291	−1.00038	−0.500191	−	0.865915i	$-0.666737\pi$
$677$	−26.0291	−1.00038	−0.500191	+	0.865915i	$0.666737\pi$
$678$	3.30893	0.127079
$679$	−2.74685	−0.105414
$680$	0	0
$681$	−0.0342821	−0.00131369
$682$	2.19157	0.0839195
$683$	13.2884	0.508466	0.254233	−	0.967143i	$-0.418177\pi$
$683$	13.2884	0.508466	0.254233	+	0.967143i	$0.418177\pi$
$684$	31.1131	1.18964
$685$	0	0
$686$	8.27842	0.316071
$687$	2.38219	0.0908864
$688$	15.1548	0.577772
$689$	29.7913	1.13496
$690$	0	0
$691$	19.5086	0.742141	0.371071	−	0.928605i	$-0.378991\pi$
$691$	19.5086	0.742141	0.371071	+	0.928605i	$0.378991\pi$
$692$	−15.6344	−0.594332
$693$	2.58882	0.0983412
$694$	−1.79898	−0.0682884
$695$	0	0
$696$	−2.04046	−0.0773433
$697$	−69.2724	−2.62388
$698$	−13.5669	−0.513515
$699$	−5.57427	−0.210838
$700$	0	0
$701$	18.9165	0.714466	0.357233	−	0.934015i	$-0.383720\pi$
$701$	18.9165	0.714466	0.357233	+	0.934015i	$0.383720\pi$
$702$	5.74166	0.216705
$703$	46.5487	1.75562
$704$	2.03199	0.0765837
$705$	0	0
$706$	−2.05056	−0.0771739
$707$	22.2659	0.837395
$708$	−5.58938	−0.210062
$709$	−1.15079	−0.0432188	−0.0216094	−	0.999766i	$-0.506879\pi$
$709$	−1.15079	−0.0432188	−0.0216094	+	0.999766i	$0.506879\pi$
$710$	0	0
$711$	−46.8986	−1.75884
$712$	27.4983	1.03054
$713$	−42.7282	−1.60018
$714$	2.11962	0.0793249
$715$	0	0
$716$	28.5592	1.06731
$717$	−5.35886	−0.200130
$718$	2.07666	0.0775003
$719$	−16.7484	−0.624610	−0.312305	−	0.949982i	$-0.601101\pi$
$719$	−16.7484	−0.624610	−0.312305	+	0.949982i	$0.601101\pi$
$720$	0	0
$721$	−7.44312	−0.277196
$722$	−8.89531	−0.331049
$723$	−9.57556	−0.356119
$724$	−44.3163	−1.64700
$725$	0	0
$726$	2.22589	0.0826104
$727$	−4.74664	−0.176043	−0.0880216	−	0.996119i	$-0.528054\pi$
$727$	−4.74664	−0.176043	−0.0880216	+	0.996119i	$0.528054\pi$
$728$	13.0505	0.483683
$729$	−16.1718	−0.598956
$730$	0	0
$731$	−34.1925	−1.26466
$732$	−1.86030	−0.0687585
$733$	−9.59701	−0.354474	−0.177237	−	0.984168i	$-0.556716\pi$
$733$	−9.59701	−0.354474	−0.177237	+	0.984168i	$0.556716\pi$
$734$	6.73417	0.248563
$735$	0	0
$736$	24.1124	0.888793
$737$	−4.48070	−0.165049
$738$	13.7568	0.506396
$739$	−51.9719	−1.91182	−0.955908	−	0.293666i	$-0.905125\pi$
$739$	−51.9719	−1.91182	−0.955908	+	0.293666i	$0.905125\pi$
$740$	0	0
$741$	13.6369	0.500966
$742$	−4.53503	−0.166486
$743$	−23.5092	−0.862470	−0.431235	−	0.902240i	$-0.641922\pi$
$743$	−23.5092	−0.862470	−0.431235	+	0.902240i	$0.641922\pi$
$744$	6.60847	0.242278
$745$	0	0
$746$	−6.98015	−0.255561
$747$	−36.6016	−1.33918
$748$	−6.62032	−0.242063
$749$	−10.0221	−0.366201
$750$	0	0
$751$	6.14017	0.224058	0.112029	−	0.993705i	$-0.464265\pi$
$751$	6.14017	0.224058	0.112029	+	0.993705i	$0.464265\pi$
$752$	−2.81396	−0.102615
$753$	4.44658	0.162042
$754$	5.53721	0.201653
$755$	0	0
$756$	7.66754	0.278866
$757$	−32.8249	−1.19304	−0.596521	−	0.802597i	$-0.703451\pi$
$757$	−32.8249	−1.19304	−0.596521	+	0.802597i	$0.703451\pi$
$758$	−2.41275	−0.0876352
$759$	1.37297	0.0498357
$760$	0	0
$761$	48.4200	1.75523	0.877613	−	0.479370i	$-0.159135\pi$
$761$	48.4200	1.75523	0.877613	+	0.479370i	$0.159135\pi$
$762$	−3.78798	−0.137224
$763$	−16.8556	−0.610214
$764$	16.9685	0.613900
$765$	0	0
$766$	−11.3690	−0.410778
$767$	32.0649	1.15780
$768$	0.933253	0.0336759
$769$	30.9255	1.11520	0.557600	−	0.830110i	$-0.311722\pi$
$769$	30.9255	1.11520	0.557600	+	0.830110i	$0.311722\pi$
$770$	0	0
$771$	0.501759	0.0180704
$772$	35.6152	1.28182
$773$	3.49412	0.125675	0.0628373	−	0.998024i	$-0.479985\pi$
$773$	3.49412	0.125675	0.0628373	+	0.998024i	$0.479985\pi$
$774$	6.79031	0.244073
$775$	0	0
$776$	−2.94899	−0.105863
$777$	5.52471	0.198198
$778$	10.9750	0.393472
$779$	67.8438	2.43076
$780$	0	0
$781$	2.83120	0.101308
$782$	−14.7133	−0.526147
$783$	6.87739	0.245778
$784$	−12.5005	−0.446447
$785$	0	0
$786$	1.61896	0.0577464
$787$	14.9113	0.531532	0.265766	−	0.964038i	$-0.414375\pi$
$787$	14.9113	0.531532	0.265766	+	0.964038i	$0.414375\pi$
$788$	−8.70129	−0.309971
$789$	−10.1659	−0.361915
$790$	0	0
$791$	−25.3497	−0.901332
$792$	2.77933	0.0987593
$793$	10.6721	0.378977
$794$	−0.756551	−0.0268490
$795$	0	0
$796$	10.4508	0.370418
$797$	−43.5762	−1.54355	−0.771774	−	0.635897i	$-0.780630\pi$
$797$	−43.5762	−1.54355	−0.771774	+	0.635897i	$0.780630\pi$
$798$	−2.07591	−0.0734864
$799$	6.34890	0.224608
$800$	0	0
$801$	−44.6366	−1.57716
$802$	1.60451	0.0566571
$803$	6.76253	0.238645
$804$	−6.39128	−0.225403
$805$	0	0
$806$	−17.9335	−0.631680
$807$	11.7237	0.412695
$808$	23.9045	0.840956
$809$	3.51877	0.123713	0.0618567	−	0.998085i	$-0.480298\pi$
$809$	3.51877	0.123713	0.0618567	+	0.998085i	$0.480298\pi$
$810$	0	0
$811$	39.2945	1.37982	0.689909	−	0.723896i	$-0.257651\pi$
$811$	39.2945	1.37982	0.689909	+	0.723896i	$0.257651\pi$
$812$	7.39452	0.259497
$813$	−3.64664	−0.127893
$814$	1.96699	0.0689430
$815$	0	0
$816$	−8.24410	−0.288601
$817$	33.4874	1.17158
$818$	1.38099	0.0482853
$819$	−21.1842	−0.740235
$820$	0	0
$821$	−38.8984	−1.35756	−0.678781	−	0.734341i	$-0.737491\pi$
$821$	−38.8984	−1.35756	−0.678781	+	0.734341i	$0.737491\pi$
$822$	3.32171	0.115858
$823$	−24.2893	−0.846672	−0.423336	−	0.905973i	$-0.639141\pi$
$823$	−24.2893	−0.846672	−0.423336	+	0.905973i	$0.639141\pi$
$824$	−7.99086	−0.278375
$825$	0	0
$826$	−4.88114	−0.169837
$827$	−52.0230	−1.80902	−0.904509	−	0.426454i	$-0.859762\pi$
$827$	−52.0230	−1.80902	−0.904509	+	0.426454i	$0.859762\pi$
$828$	−25.6328	−0.890803
$829$	29.9135	1.03894	0.519469	−	0.854489i	$-0.326130\pi$
$829$	29.9135	1.03894	0.519469	+	0.854489i	$0.326130\pi$
$830$	0	0
$831$	2.08582	0.0723562
$832$	−16.6277	−0.576461
$833$	28.2038	0.977205
$834$	−1.87849	−0.0650468
$835$	0	0
$836$	6.48379	0.224247
$837$	−22.2740	−0.769901
$838$	−14.2595	−0.492587
$839$	−13.5110	−0.466453	−0.233227	−	0.972422i	$-0.574928\pi$
$839$	−13.5110	−0.466453	−0.233227	+	0.972422i	$0.574928\pi$
$840$	0	0
$841$	−22.3675	−0.771293
$842$	3.76415	0.129721
$843$	−4.62601	−0.159328
$844$	−9.43036	−0.324606
$845$	0	0
$846$	−1.26083	−0.0433482
$847$	−17.0525	−0.585932
$848$	17.6386	0.605713
$849$	−9.55148	−0.327806
$850$	0	0
$851$	−38.3497	−1.31461
$852$	4.03843	0.138354
$853$	16.4979	0.564879	0.282439	−	0.959285i	$-0.408856\pi$
$853$	16.4979	0.564879	0.282439	+	0.959285i	$0.408856\pi$
$854$	−1.62458	−0.0555919
$855$	0	0
$856$	−10.7597	−0.367758
$857$	28.8540	0.985634	0.492817	−	0.870133i	$-0.335967\pi$
$857$	28.8540	0.985634	0.492817	+	0.870133i	$0.335967\pi$
$858$	0.576251	0.0196729
$859$	14.5946	0.497963	0.248981	−	0.968508i	$-0.419904\pi$
$859$	14.5946	0.497963	0.248981	+	0.968508i	$0.419904\pi$
$860$	0	0
$861$	8.05215	0.274417
$862$	14.7242	0.501508
$863$	−23.0031	−0.783035	−0.391518	−	0.920171i	$-0.628050\pi$
$863$	−23.0031	−0.783035	−0.391518	+	0.920171i	$0.628050\pi$
$864$	12.5696	0.427628
$865$	0	0
$866$	−4.72979	−0.160725
$867$	10.7558	0.365285
$868$	−23.9488	−0.812875
$869$	−9.77342	−0.331540
$870$	0	0
$871$	36.6653	1.24235
$872$	−18.0960	−0.612808
$873$	4.78695	0.162014
$874$	14.4099	0.487421
$875$	0	0
$876$	9.64610	0.325912
$877$	48.4915	1.63744	0.818720	−	0.574193i	$-0.194684\pi$
$877$	48.4915	1.63744	0.818720	+	0.574193i	$0.194684\pi$
$878$	8.48145	0.286235
$879$	−5.09451	−0.171834
$880$	0	0
$881$	−5.31191	−0.178963	−0.0894813	−	0.995988i	$-0.528521\pi$
$881$	−5.31191	−0.178963	−0.0894813	+	0.995988i	$0.528521\pi$
$882$	−5.60102	−0.188596
$883$	38.2325	1.28663	0.643313	−	0.765603i	$-0.277559\pi$
$883$	38.2325	1.28663	0.643313	+	0.765603i	$0.277559\pi$
$884$	54.1737	1.82206
$885$	0	0
$886$	−1.38221	−0.0464363
$887$	−0.713185	−0.0239464	−0.0119732	−	0.999928i	$-0.503811\pi$
$887$	−0.713185	−0.0239464	−0.0119732	+	0.999928i	$0.503811\pi$
$888$	5.93128	0.199041
$889$	29.0197	0.973291
$890$	0	0
$891$	−4.14052	−0.138713
$892$	23.2250	0.777632
$893$	−6.21796	−0.208076
$894$	−2.58077	−0.0863137
$895$	0	0
$896$	17.5865	0.587524
$897$	−11.2349	−0.375124
$898$	−2.21884	−0.0740435
$899$	−21.4808	−0.716426
$900$	0	0
$901$	−39.7965	−1.32581
$902$	2.86685	0.0954556
$903$	3.97451	0.132263
$904$	−27.2152	−0.905164
$905$	0	0
$906$	1.65502	0.0549843
$907$	−53.8244	−1.78721	−0.893605	−	0.448854i	$-0.851832\pi$
$907$	−53.8244	−1.78721	−0.893605	+	0.448854i	$0.851832\pi$
$908$	0.133379	0.00442635
$909$	−38.8029	−1.28701
$910$	0	0
$911$	−42.8707	−1.42037	−0.710185	−	0.704015i	$-0.751389\pi$
$911$	−42.8707	−1.42037	−0.710185	+	0.704015i	$0.751389\pi$
$912$	8.07408	0.267359
$913$	−7.62757	−0.252436
$914$	−12.5758	−0.415969
$915$	0	0
$916$	−9.26826	−0.306232
$917$	−12.4029	−0.409579
$918$	−7.66997	−0.253147
$919$	−34.0735	−1.12398	−0.561991	−	0.827143i	$-0.689965\pi$
$919$	−34.0735	−1.12398	−0.561991	+	0.827143i	$0.689965\pi$
$920$	0	0
$921$	−5.91964	−0.195059
$922$	4.21497	0.138813
$923$	−23.1675	−0.762569
$924$	0.769539	0.0253160
$925$	0	0
$926$	−1.94506	−0.0639187
$927$	12.9712	0.426028
$928$	12.1221	0.397926
$929$	−54.7822	−1.79735	−0.898673	−	0.438619i	$-0.855468\pi$
$929$	−54.7822	−1.79735	−0.898673	+	0.438619i	$0.855468\pi$
$930$	0	0
$931$	−27.6222	−0.905281
$932$	21.6875	0.710397
$933$	7.60123	0.248853
$934$	−17.1158	−0.560044
$935$	0	0
$936$	−22.7431	−0.743382
$937$	30.8250	1.00701	0.503504	−	0.863993i	$-0.332044\pi$
$937$	30.8250	1.00701	0.503504	+	0.863993i	$0.332044\pi$
$938$	−5.58143	−0.182240
$939$	−7.55050	−0.246401
$940$	0	0
$941$	4.16848	0.135889	0.0679443	−	0.997689i	$-0.478356\pi$
$941$	4.16848	0.135889	0.0679443	+	0.997689i	$0.478356\pi$
$942$	−1.46119	−0.0476082
$943$	−55.8938	−1.82015
$944$	18.9848	0.617902
$945$	0	0
$946$	1.41506	0.0460077
$947$	−38.1130	−1.23850	−0.619252	−	0.785192i	$-0.712564\pi$
$947$	−38.1130	−1.23850	−0.619252	+	0.785192i	$0.712564\pi$
$948$	−13.9408	−0.452777
$949$	−55.3374	−1.79633
$950$	0	0
$951$	5.48687	0.177924
$952$	−17.4334	−0.565020
$953$	25.3518	0.821226	0.410613	−	0.911810i	$-0.365315\pi$
$953$	25.3518	0.821226	0.410613	+	0.911810i	$0.365315\pi$
$954$	7.90321	0.255876
$955$	0	0
$956$	20.8494	0.674318
$957$	0.690237	0.0223122
$958$	7.51448	0.242782
$959$	−25.4476	−0.821746
$960$	0	0
$961$	38.5704	1.24421
$962$	−16.0958	−0.518949
$963$	17.4656	0.562821
$964$	37.2551	1.19990
$965$	0	0
$966$	1.71026	0.0550267
$967$	−51.1659	−1.64538	−0.822692	−	0.568487i	$-0.807529\pi$
$967$	−51.1659	−1.64538	−0.822692	+	0.568487i	$0.807529\pi$
$968$	−18.3074	−0.588423
$969$	−18.2169	−0.585210
$970$	0	0
$971$	−47.2586	−1.51660	−0.758300	−	0.651906i	$-0.773970\pi$
$971$	−47.2586	−1.51660	−0.758300	+	0.651906i	$0.773970\pi$
$972$	−20.2892	−0.650777
$973$	14.3911	0.461358
$974$	0.223676	0.00716703
$975$	0	0
$976$	6.31866	0.202255
$977$	44.5517	1.42533	0.712667	−	0.701503i	$-0.247487\pi$
$977$	44.5517	1.42533	0.712667	+	0.701503i	$0.247487\pi$
$978$	2.28637	0.0731099
$979$	−9.30203	−0.297294
$980$	0	0
$981$	29.3743	0.937850
$982$	−2.43925	−0.0778396
$983$	−11.5188	−0.367393	−0.183697	−	0.982983i	$-0.558806\pi$
$983$	−11.5188	−0.367393	−0.183697	+	0.982983i	$0.558806\pi$
$984$	8.64471	0.275583
$985$	0	0
$986$	−7.39685	−0.235564
$987$	−0.737989	−0.0234905
$988$	−53.0565	−1.68795
$989$	−27.5889	−0.877277
$990$	0	0
$991$	22.4320	0.712576	0.356288	−	0.934376i	$-0.384042\pi$
$991$	22.4320	0.712576	0.356288	+	0.934376i	$0.384042\pi$
$992$	−39.2600	−1.24651
$993$	−4.80447	−0.152465
$994$	3.52672	0.111861
$995$	0	0
$996$	−10.8800	−0.344746
$997$	2.92578	0.0926605	0.0463302	−	0.998926i	$-0.485247\pi$
$997$	2.92578	0.0926605	0.0463302	+	0.998926i	$0.485247\pi$
$998$	−10.4398	−0.330466
$999$	−19.9915	−0.632503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.k.1.7	✓	13
5.2	odd	4		1175.2.c.h.424.13		26
5.3	odd	4		1175.2.c.h.424.14		26
5.4	even	2		1175.2.a.l.1.7	yes	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1175.2.a.k.1.7	✓	13	1.1	even	1	trivial
1175.2.a.l.1.7	yes	13	5.4	even	2
1175.2.c.h.424.13		26	5.2	odd	4
1175.2.c.h.424.14		26	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-0.452387 q^{2} +0.461453 q^{3} -1.79535 q^{4} -0.208755 q^{6} +1.59927 q^{7} +1.71697 q^{8} -2.78706 q^{9} +O(q^{10})\)	\(q-0.452387 q^{2} +0.461453 q^{3} -1.79535 q^{4} -0.208755 q^{6} +1.59927 q^{7} +1.71697 q^{8} -2.78706 q^{9} -0.580808 q^{11} -0.828467 q^{12} +4.75272 q^{13} -0.723491 q^{14} +2.81396 q^{16} -6.34890 q^{17} +1.26083 q^{18} +6.21796 q^{19} +0.737989 q^{21} +0.262750 q^{22} -5.12274 q^{23} +0.792298 q^{24} -2.15007 q^{26} -2.67045 q^{27} -2.87125 q^{28} -2.57536 q^{29} +8.34089 q^{31} -4.70693 q^{32} -0.268015 q^{33} +2.87216 q^{34} +5.00374 q^{36} +7.48617 q^{37} -2.81293 q^{38} +2.19315 q^{39} +10.9109 q^{41} -0.333857 q^{42} +5.38559 q^{43} +1.04275 q^{44} +2.31746 q^{46} -1.00000 q^{47} +1.29851 q^{48} -4.44232 q^{49} -2.92971 q^{51} -8.53277 q^{52} +6.26826 q^{53} +1.20808 q^{54} +2.74590 q^{56} +2.86929 q^{57} +1.16506 q^{58} +6.74665 q^{59} +2.24547 q^{61} -3.77331 q^{62} -4.45728 q^{63} -3.49856 q^{64} +0.121247 q^{66} +7.71459 q^{67} +11.3985 q^{68} -2.36390 q^{69} -4.87459 q^{71} -4.78529 q^{72} -11.6433 q^{73} -3.38665 q^{74} -11.1634 q^{76} -0.928871 q^{77} -0.992155 q^{78} +16.8273 q^{79} +7.12890 q^{81} -4.93596 q^{82} +13.1327 q^{83} -1.32495 q^{84} -2.43637 q^{86} -1.18841 q^{87} -0.997227 q^{88} +16.0157 q^{89} +7.60090 q^{91} +9.19708 q^{92} +3.84892 q^{93} +0.452387 q^{94} -2.17202 q^{96} -1.71756 q^{97} +2.00965 q^{98} +1.61875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9}+O(q^{10}) \) 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9	\( 13 q + 20 q^{4} + 5 q^{6} - 3 q^{8} + 27 q^{9} + 9 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 34 q^{16} - 5 q^{17} + 7 q^{18} + 16 q^{19} + 26 q^{21} - 15 q^{22} + 10 q^{23} - 8 q^{24} + 3 q^{26} - 15 q^{27} + 30 q^{28} + 10 q^{29} + 15 q^{31} - 36 q^{32} + 22 q^{33} + q^{34} + 57 q^{36} - 5 q^{37} + 42 q^{38} - 2 q^{39} + 24 q^{41} - 62 q^{42} + 2 q^{43} - 6 q^{44} + 50 q^{46} - 13 q^{47} + 67 q^{48} + 39 q^{49} + 9 q^{51} - 36 q^{52} - 4 q^{53} - 34 q^{54} - 9 q^{56} + 5 q^{57} + 27 q^{58} - 25 q^{59} + 22 q^{61} - 2 q^{62} + 7 q^{63} + 53 q^{64} + 2 q^{66} + 4 q^{67} - 5 q^{68} + 5 q^{69} - 6 q^{71} - 66 q^{72} + 3 q^{73} - 49 q^{74} + 63 q^{76} + 8 q^{77} + 59 q^{78} + 37 q^{79} + 49 q^{81} - 48 q^{82} - 27 q^{83} - 2 q^{84} + 3 q^{86} + 35 q^{87} + 44 q^{88} + 32 q^{89} + 12 q^{91} - 29 q^{92} - 56 q^{93} - 11 q^{96} - 25 q^{97} + 61 q^{98} + 36 q^{99}+O(q^{100}) \) 13 * q + 20 * q^4 + 5 * q^6 - 3 * q^8 + 27 * q^9 + 9 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 34 * q^16 - 5 * q^17 + 7 * q^18 + 16 * q^19 + 26 * q^21 - 15 * q^22 + 10 * q^23 - 8 * q^24 + 3 * q^26 - 15 * q^27 + 30 * q^28 + 10 * q^29 + 15 * q^31 - 36 * q^32 + 22 * q^33 + q^34 + 57 * q^36 - 5 * q^37 + 42 * q^38 - 2 * q^39 + 24 * q^41 - 62 * q^42 + 2 * q^43 - 6 * q^44 + 50 * q^46 - 13 * q^47 + 67 * q^48 + 39 * q^49 + 9 * q^51 - 36 * q^52 - 4 * q^53 - 34 * q^54 - 9 * q^56 + 5 * q^57 + 27 * q^58 - 25 * q^59 + 22 * q^61 - 2 * q^62 + 7 * q^63 + 53 * q^64 + 2 * q^66 + 4 * q^67 - 5 * q^68 + 5 * q^69 - 6 * q^71 - 66 * q^72 + 3 * q^73 - 49 * q^74 + 63 * q^76 + 8 * q^77 + 59 * q^78 + 37 * q^79 + 49 * q^81 - 48 * q^82 - 27 * q^83 - 2 * q^84 + 3 * q^86 + 35 * q^87 + 44 * q^88 + 32 * q^89 + 12 * q^91 - 29 * q^92 - 56 * q^93 - 11 * q^96 - 25 * q^97 + 61 * q^98 + 36 * q^99

Introduction

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