LMFDB - Embedded newform 8025.2.a.bf.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 49 x^{9} + 71 x^{8} - 278 x^{7} - 92 x^{6} + 649 x^{5} - 127 x^{4} + \cdots - 6 $ x^12 - 3x^11 - 15x^10 + 49x^9 + 71x^8 - 278x^7 - 92x^6 + 649x^5 - 127x^4 - 529x^3 + 267x^2 + 15*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1605)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.73551$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73551 q^{2} -1.00000 q^{3} +1.01200 q^{4} -1.73551 q^{6} +4.69063 q^{7} -1.71469 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.73551 q^{2} -1.00000 q^{3} +1.01200 q^{4} -1.73551 q^{6} +4.69063 q^{7} -1.71469 q^{8} +1.00000 q^{9} +2.19066 q^{11} -1.01200 q^{12} -2.63307 q^{13} +8.14063 q^{14} -4.99986 q^{16} -1.38890 q^{17} +1.73551 q^{18} +0.215496 q^{19} -4.69063 q^{21} +3.80191 q^{22} -2.79261 q^{23} +1.71469 q^{24} -4.56973 q^{26} -1.00000 q^{27} +4.74690 q^{28} -7.70002 q^{29} -4.81186 q^{31} -5.24792 q^{32} -2.19066 q^{33} -2.41045 q^{34} +1.01200 q^{36} -7.41620 q^{37} +0.373996 q^{38} +2.63307 q^{39} -7.32360 q^{41} -8.14063 q^{42} -9.15677 q^{43} +2.21694 q^{44} -4.84660 q^{46} -1.99062 q^{47} +4.99986 q^{48} +15.0020 q^{49} +1.38890 q^{51} -2.66466 q^{52} +5.83030 q^{53} -1.73551 q^{54} -8.04298 q^{56} -0.215496 q^{57} -13.3635 q^{58} +10.7619 q^{59} -0.552233 q^{61} -8.35102 q^{62} +4.69063 q^{63} +0.891893 q^{64} -3.80191 q^{66} -8.35384 q^{67} -1.40556 q^{68} +2.79261 q^{69} +4.85111 q^{71} -1.71469 q^{72} -5.48768 q^{73} -12.8709 q^{74} +0.218081 q^{76} +10.2756 q^{77} +4.56973 q^{78} +5.30027 q^{79} +1.00000 q^{81} -12.7102 q^{82} -8.87948 q^{83} -4.74690 q^{84} -15.8917 q^{86} +7.70002 q^{87} -3.75630 q^{88} -3.68952 q^{89} -12.3508 q^{91} -2.82611 q^{92} +4.81186 q^{93} -3.45475 q^{94} +5.24792 q^{96} -3.01913 q^{97} +26.0361 q^{98} +2.19066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9	$ 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9} + 4 q^{11} - 15 q^{12} - 13 q^{13} + 4 q^{14} + 13 q^{16} + 4 q^{17} - 3 q^{18} + 14 q^{19} + 7 q^{21} - 15 q^{22} - 11 q^{23} + 3 q^{24} - 8 q^{26} - 12 q^{27} - 16 q^{28} - 7 q^{29} + 4 q^{31} - 4 q^{32} - 4 q^{33} + q^{34} + 15 q^{36} - 24 q^{37} + 11 q^{38} + 13 q^{39} + 13 q^{41} - 4 q^{42} - 25 q^{43} + 10 q^{44} - 22 q^{46} - 19 q^{47} - 13 q^{48} + 9 q^{49} - 4 q^{51} - 20 q^{52} - 11 q^{53} + 3 q^{54} - 37 q^{56} - 14 q^{57} + 2 q^{58} + 8 q^{59} + 7 q^{61} + 11 q^{62} - 7 q^{63} - 19 q^{64} + 15 q^{66} - 33 q^{67} + 24 q^{68} + 11 q^{69} - 3 q^{72} - 34 q^{73} - 27 q^{74} - 9 q^{76} + 29 q^{77} + 8 q^{78} + 12 q^{81} - q^{82} + 24 q^{83} + 16 q^{84} - 36 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} + 30 q^{91} + 28 q^{92} - 4 q^{93} - 8 q^{94} + 4 q^{96} - 16 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9 + 4 * q^11 - 15 * q^12 - 13 * q^13 + 4 * q^14 + 13 * q^16 + 4 * q^17 - 3 * q^18 + 14 * q^19 + 7 * q^21 - 15 * q^22 - 11 * q^23 + 3 * q^24 - 8 * q^26 - 12 * q^27 - 16 * q^28 - 7 * q^29 + 4 * q^31 - 4 * q^32 - 4 * q^33 + q^34 + 15 * q^36 - 24 * q^37 + 11 * q^38 + 13 * q^39 + 13 * q^41 - 4 * q^42 - 25 * q^43 + 10 * q^44 - 22 * q^46 - 19 * q^47 - 13 * q^48 + 9 * q^49 - 4 * q^51 - 20 * q^52 - 11 * q^53 + 3 * q^54 - 37 * q^56 - 14 * q^57 + 2 * q^58 + 8 * q^59 + 7 * q^61 + 11 * q^62 - 7 * q^63 - 19 * q^64 + 15 * q^66 - 33 * q^67 + 24 * q^68 + 11 * q^69 - 3 * q^72 - 34 * q^73 - 27 * q^74 - 9 * q^76 + 29 * q^77 + 8 * q^78 + 12 * q^81 - q^82 + 24 * q^83 + 16 * q^84 - 36 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 + 30 * q^91 + 28 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^96 - 16 * q^97 + 36 * 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 $

$2$	1.73551	1.22719	0.613596	−	0.789620i	$-0.289723\pi$
$2$	1.73551	1.22719	0.613596	+	0.789620i	$0.289723\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.01200	0.505998
$5$	0	0
$5$	0	0
$6$	−1.73551	−0.708519
$7$	4.69063	1.77289	0.886445	−	0.462834i	$-0.153167\pi$
$7$	4.69063	1.77289	0.886445	+	0.462834i	$0.153167\pi$
$8$	−1.71469	−0.606235
$9$	1.00000	0.333333
$10$	0	0
$11$	2.19066	0.660508	0.330254	−	0.943892i	$-0.392866\pi$
$11$	2.19066	0.660508	0.330254	+	0.943892i	$0.392866\pi$
$12$	−1.01200	−0.292138
$13$	−2.63307	−0.730283	−0.365142	−	0.930952i	$-0.618979\pi$
$13$	−2.63307	−0.730283	−0.365142	+	0.930952i	$0.618979\pi$
$14$	8.14063	2.17568
$15$	0	0
$16$	−4.99986	−1.24996
$17$	−1.38890	−0.336858	−0.168429	−	0.985714i	$-0.553869\pi$
$17$	−1.38890	−0.336858	−0.168429	+	0.985714i	$0.553869\pi$
$18$	1.73551	0.409064
$19$	0.215496	0.0494382	0.0247191	−	0.999694i	$-0.492131\pi$
$19$	0.215496	0.0494382	0.0247191	+	0.999694i	$0.492131\pi$
$20$	0	0
$21$	−4.69063	−1.02358
$22$	3.80191	0.810569
$23$	−2.79261	−0.582299	−0.291150	−	0.956678i	$-0.594038\pi$
$23$	−2.79261	−0.582299	−0.291150	+	0.956678i	$0.594038\pi$
$24$	1.71469	0.350010
$25$	0	0
$26$	−4.56973	−0.896197
$27$	−1.00000	−0.192450
$28$	4.74690	0.897079
$29$	−7.70002	−1.42986	−0.714929	−	0.699198i	$-0.753541\pi$
$29$	−7.70002	−1.42986	−0.714929	+	0.699198i	$0.753541\pi$
$30$	0	0
$31$	−4.81186	−0.864235	−0.432117	−	0.901817i	$-0.642233\pi$
$31$	−4.81186	−0.864235	−0.432117	+	0.901817i	$0.642233\pi$
$32$	−5.24792	−0.927710
$33$	−2.19066	−0.381344
$34$	−2.41045	−0.413389
$35$	0	0
$36$	1.01200	0.168666
$37$	−7.41620	−1.21922	−0.609608	−	0.792703i	$-0.708673\pi$
$37$	−7.41620	−1.21922	−0.609608	+	0.792703i	$0.708673\pi$
$38$	0.373996	0.0606701
$39$	2.63307	0.421629
$40$	0	0
$41$	−7.32360	−1.14375	−0.571877	−	0.820339i	$-0.693785\pi$
$41$	−7.32360	−1.14375	−0.571877	+	0.820339i	$0.693785\pi$
$42$	−8.14063	−1.25613
$43$	−9.15677	−1.39639	−0.698197	−	0.715906i	$-0.746014\pi$
$43$	−9.15677	−1.39639	−0.698197	+	0.715906i	$0.746014\pi$
$44$	2.21694	0.334216
$45$	0	0
$46$	−4.84660	−0.714592
$47$	−1.99062	−0.290362	−0.145181	−	0.989405i	$-0.546376\pi$
$47$	−1.99062	−0.290362	−0.145181	+	0.989405i	$0.546376\pi$
$48$	4.99986	0.721667
$49$	15.0020	2.14314
$50$	0	0
$51$	1.38890	0.194485
$52$	−2.66466	−0.369522
$53$	5.83030	0.800853	0.400427	−	0.916329i	$-0.368862\pi$
$53$	5.83030	0.800853	0.400427	+	0.916329i	$0.368862\pi$
$54$	−1.73551	−0.236173
$55$	0	0
$56$	−8.04298	−1.07479
$57$	−0.215496	−0.0285432
$58$	−13.3635	−1.75471
$59$	10.7619	1.40108	0.700542	−	0.713611i	$-0.252942\pi$
$59$	10.7619	1.40108	0.700542	+	0.713611i	$0.252942\pi$
$60$	0	0
$61$	−0.552233	−0.0707062	−0.0353531	−	0.999375i	$-0.511256\pi$
$61$	−0.552233	−0.0707062	−0.0353531	+	0.999375i	$0.511256\pi$
$62$	−8.35102	−1.06058
$63$	4.69063	0.590963
$64$	0.891893	0.111487
$65$	0	0
$66$	−3.80191	−0.467982
$67$	−8.35384	−1.02058	−0.510292	−	0.860001i	$-0.670463\pi$
$67$	−8.35384	−1.02058	−0.510292	+	0.860001i	$0.670463\pi$
$68$	−1.40556	−0.170449
$69$	2.79261	0.336190
$70$	0	0
$71$	4.85111	0.575721	0.287860	−	0.957672i	$-0.407056\pi$
$71$	4.85111	0.575721	0.287860	+	0.957672i	$0.407056\pi$
$72$	−1.71469	−0.202078
$73$	−5.48768	−0.642284	−0.321142	−	0.947031i	$-0.604067\pi$
$73$	−5.48768	−0.642284	−0.321142	+	0.947031i	$0.604067\pi$
$74$	−12.8709	−1.49621
$75$	0	0
$76$	0.218081	0.0250156
$77$	10.2756	1.17101
$78$	4.56973	0.517420
$79$	5.30027	0.596327	0.298164	−	0.954515i	$-0.403626\pi$
$79$	5.30027	0.596327	0.298164	+	0.954515i	$0.403626\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−12.7102	−1.40360
$83$	−8.87948	−0.974649	−0.487325	−	0.873221i	$-0.662027\pi$
$83$	−8.87948	−0.974649	−0.487325	+	0.873221i	$0.662027\pi$
$84$	−4.74690	−0.517929
$85$	0	0
$86$	−15.8917	−1.71364
$87$	7.70002	0.825528
$88$	−3.75630	−0.400423
$89$	−3.68952	−0.391089	−0.195544	−	0.980695i	$-0.562647\pi$
$89$	−3.68952	−0.391089	−0.195544	+	0.980695i	$0.562647\pi$
$90$	0	0
$91$	−12.3508	−1.29471
$92$	−2.82611	−0.294642
$93$	4.81186	0.498966
$94$	−3.45475	−0.356330
$95$	0	0
$96$	5.24792	0.535614
$97$	−3.01913	−0.306546	−0.153273	−	0.988184i	$-0.548981\pi$
$97$	−3.01913	−0.306546	−0.153273	+	0.988184i	$0.548981\pi$
$98$	26.0361	2.63004
$99$	2.19066	0.220169
$100$	0	0
$101$	−5.05765	−0.503255	−0.251628	−	0.967824i	$-0.580966\pi$
$101$	−5.05765	−0.503255	−0.251628	+	0.967824i	$0.580966\pi$
$102$	2.41045	0.238670
$103$	1.01788	0.100294	0.0501471	−	0.998742i	$-0.484031\pi$
$103$	1.01788	0.100294	0.0501471	+	0.998742i	$0.484031\pi$
$104$	4.51491	0.442723
$105$	0	0
$106$	10.1185	0.982800
$107$	−1.00000	−0.0966736
$107$	−1.00000	−0.0966736
$108$	−1.01200	−0.0973794
$109$	−3.13292	−0.300079	−0.150040	−	0.988680i	$-0.547940\pi$
$109$	−3.13292	−0.300079	−0.150040	+	0.988680i	$0.547940\pi$
$110$	0	0
$111$	7.41620	0.703915
$112$	−23.4525	−2.21605
$113$	−18.5160	−1.74184	−0.870920	−	0.491426i	$-0.836476\pi$
$113$	−18.5160	−1.74184	−0.870920	+	0.491426i	$0.836476\pi$
$114$	−0.373996	−0.0350279
$115$	0	0
$116$	−7.79239	−0.723505
$117$	−2.63307	−0.243428
$118$	18.6774	1.71940
$119$	−6.51481	−0.597212
$120$	0	0
$121$	−6.20102	−0.563729
$122$	−0.958406	−0.0867700
$123$	7.32360	0.660347
$124$	−4.86958	−0.437301
$125$	0	0
$126$	8.14063	0.725225
$127$	9.53839	0.846395	0.423198	−	0.906037i	$-0.360908\pi$
$127$	9.53839	0.846395	0.423198	+	0.906037i	$0.360908\pi$
$128$	12.0437	1.06453
$129$	9.15677	0.806208
$130$	0	0
$131$	15.1827	1.32652	0.663258	−	0.748391i	$-0.269173\pi$
$131$	15.1827	1.32652	0.663258	+	0.748391i	$0.269173\pi$
$132$	−2.21694	−0.192960
$133$	1.01081	0.0876485
$134$	−14.4982	−1.25245
$135$	0	0
$136$	2.38153	0.204215
$137$	13.1819	1.12620	0.563102	−	0.826387i	$-0.309608\pi$
$137$	13.1819	1.12620	0.563102	+	0.826387i	$0.309608\pi$
$138$	4.84660	0.412570
$139$	15.6248	1.32528	0.662641	−	0.748938i	$-0.269436\pi$
$139$	15.6248	1.32528	0.662641	+	0.748938i	$0.269436\pi$
$140$	0	0
$141$	1.99062	0.167641
$142$	8.41915	0.706519
$143$	−5.76816	−0.482358
$144$	−4.99986	−0.416655
$145$	0	0
$146$	−9.52392	−0.788206
$147$	−15.0020	−1.23734
$148$	−7.50517	−0.616921
$149$	−0.363978	−0.0298182	−0.0149091	−	0.999889i	$-0.504746\pi$
$149$	−0.363978	−0.0298182	−0.0149091	+	0.999889i	$0.504746\pi$
$150$	0	0
$151$	21.8364	1.77702	0.888509	−	0.458859i	$-0.151742\pi$
$151$	21.8364	1.77702	0.888509	+	0.458859i	$0.151742\pi$
$152$	−0.369509	−0.0299712
$153$	−1.38890	−0.112286
$154$	17.8333	1.43705
$155$	0	0
$156$	2.66466	0.213344
$157$	−16.3597	−1.30565	−0.652824	−	0.757510i	$-0.726416\pi$
$157$	−16.3597	−1.30565	−0.652824	+	0.757510i	$0.726416\pi$
$158$	9.19868	0.731808
$159$	−5.83030	−0.462373
$160$	0	0
$161$	−13.0991	−1.03235
$162$	1.73551	0.136355
$163$	−4.38626	−0.343558	−0.171779	−	0.985136i	$-0.554952\pi$
$163$	−4.38626	−0.343558	−0.171779	+	0.985136i	$0.554952\pi$
$164$	−7.41145	−0.578737
$165$	0	0
$166$	−15.4104	−1.19608
$167$	−19.5427	−1.51226	−0.756131	−	0.654421i	$-0.772913\pi$
$167$	−19.5427	−1.51226	−0.756131	+	0.654421i	$0.772913\pi$
$168$	8.04298	0.620529
$169$	−6.06693	−0.466687
$170$	0	0
$171$	0.215496	0.0164794
$172$	−9.26661	−0.706573
$173$	14.4078	1.09540	0.547702	−	0.836674i	$-0.315503\pi$
$173$	14.4078	1.09540	0.547702	+	0.836674i	$0.315503\pi$
$174$	13.3635	1.01308
$175$	0	0
$176$	−10.9530	−0.825611
$177$	−10.7619	−0.808916
$178$	−6.40321	−0.479941
$179$	19.7077	1.47303	0.736513	−	0.676423i	$-0.236471\pi$
$179$	19.7077	1.47303	0.736513	+	0.676423i	$0.236471\pi$
$180$	0	0
$181$	4.55282	0.338409	0.169204	−	0.985581i	$-0.445880\pi$
$181$	4.55282	0.338409	0.169204	+	0.985581i	$0.445880\pi$
$182$	−21.4349	−1.58886
$183$	0.552233	0.0408222
$184$	4.78846	0.353010
$185$	0	0
$186$	8.35102	0.612327
$187$	−3.04260	−0.222497
$188$	−2.01450	−0.146923
$189$	−4.69063	−0.341193
$190$	0	0
$191$	8.23672	0.595988	0.297994	−	0.954568i	$-0.403682\pi$
$191$	8.23672	0.595988	0.297994	+	0.954568i	$0.403682\pi$
$192$	−0.891893	−0.0643668
$193$	−17.3735	−1.25057	−0.625286	−	0.780396i	$-0.715018\pi$
$193$	−17.3735	−1.25057	−0.625286	+	0.780396i	$0.715018\pi$
$194$	−5.23973	−0.376190
$195$	0	0
$196$	15.1819	1.08442
$197$	3.81741	0.271979	0.135989	−	0.990710i	$-0.456579\pi$
$197$	3.81741	0.271979	0.135989	+	0.990710i	$0.456579\pi$
$198$	3.80191	0.270190
$199$	−0.987724	−0.0700179	−0.0350090	−	0.999387i	$-0.511146\pi$
$199$	−0.987724	−0.0700179	−0.0350090	+	0.999387i	$0.511146\pi$
$200$	0	0
$201$	8.35384	0.589234
$202$	−8.77761	−0.617590
$203$	−36.1179	−2.53498
$204$	1.40556	0.0984090
$205$	0	0
$206$	1.76653	0.123080
$207$	−2.79261	−0.194100
$208$	13.1650	0.912828
$209$	0.472078	0.0326543
$210$	0	0
$211$	−6.14274	−0.422883	−0.211442	−	0.977391i	$-0.567816\pi$
$211$	−6.14274	−0.422883	−0.211442	+	0.977391i	$0.567816\pi$
$212$	5.90024	0.405230
$213$	−4.85111	−0.332392
$214$	−1.73551	−0.118637
$215$	0	0
$216$	1.71469	0.116670
$217$	−22.5706	−1.53219
$218$	−5.43721	−0.368255
$219$	5.48768	0.370823
$220$	0	0
$221$	3.65708	0.246002
$222$	12.8709	0.863838
$223$	−24.4314	−1.63605	−0.818024	−	0.575184i	$-0.804931\pi$
$223$	−24.4314	−1.63605	−0.818024	+	0.575184i	$0.804931\pi$
$224$	−24.6160	−1.64473
$225$	0	0
$226$	−32.1347	−2.13757
$227$	25.5518	1.69593	0.847965	−	0.530052i	$-0.177827\pi$
$227$	25.5518	1.69593	0.847965	+	0.530052i	$0.177827\pi$
$228$	−0.218081	−0.0144428
$229$	6.28372	0.415240	0.207620	−	0.978210i	$-0.433428\pi$
$229$	6.28372	0.415240	0.207620	+	0.978210i	$0.433428\pi$
$230$	0	0
$231$	−10.2756	−0.676082
$232$	13.2031	0.866829
$233$	−7.63191	−0.499983	−0.249992	−	0.968248i	$-0.580428\pi$
$233$	−7.63191	−0.499983	−0.249992	+	0.968248i	$0.580428\pi$
$234$	−4.56973	−0.298732
$235$	0	0
$236$	10.8910	0.708946
$237$	−5.30027	−0.344290
$238$	−11.3065	−0.732893
$239$	−18.9375	−1.22496	−0.612481	−	0.790485i	$-0.709828\pi$
$239$	−18.9375	−1.22496	−0.612481	+	0.790485i	$0.709828\pi$
$240$	0	0
$241$	−6.01729	−0.387608	−0.193804	−	0.981040i	$-0.562083\pi$
$241$	−6.01729	−0.387608	−0.193804	+	0.981040i	$0.562083\pi$
$242$	−10.7619	−0.691804
$243$	−1.00000	−0.0641500
$244$	−0.558857	−0.0357772
$245$	0	0
$246$	12.7102	0.810371
$247$	−0.567417	−0.0361039
$248$	8.25084	0.523929
$249$	8.87948	0.562714
$250$	0	0
$251$	−23.3493	−1.47380	−0.736898	−	0.676004i	$-0.763710\pi$
$251$	−23.3493	−1.47380	−0.736898	+	0.676004i	$0.763710\pi$
$252$	4.74690	0.299026
$253$	−6.11765	−0.384613
$254$	16.5540	1.03869
$255$	0	0
$256$	19.1182	1.19489
$257$	−9.80843	−0.611833	−0.305916	−	0.952058i	$-0.598963\pi$
$257$	−9.80843	−0.611833	−0.305916	+	0.952058i	$0.598963\pi$
$258$	15.8917	0.989372
$259$	−34.7866	−2.16154
$260$	0	0
$261$	−7.70002	−0.476619
$262$	26.3497	1.62789
$263$	−5.59190	−0.344811	−0.172406	−	0.985026i	$-0.555154\pi$
$263$	−5.59190	−0.344811	−0.172406	+	0.985026i	$0.555154\pi$
$264$	3.75630	0.231184
$265$	0	0
$266$	1.75427	0.107561
$267$	3.68952	0.225795
$268$	−8.45405	−0.516413
$269$	−0.393247	−0.0239767	−0.0119884	−	0.999928i	$-0.503816\pi$
$269$	−0.393247	−0.0239767	−0.0119884	+	0.999928i	$0.503816\pi$
$270$	0	0
$271$	−5.34982	−0.324979	−0.162489	−	0.986710i	$-0.551952\pi$
$271$	−5.34982	−0.324979	−0.162489	+	0.986710i	$0.551952\pi$
$272$	6.94430	0.421060
$273$	12.3508	0.747502
$274$	22.8773	1.38207
$275$	0	0
$276$	2.82611	0.170112
$277$	−2.03649	−0.122361	−0.0611804	−	0.998127i	$-0.519486\pi$
$277$	−2.03649	−0.122361	−0.0611804	+	0.998127i	$0.519486\pi$
$278$	27.1171	1.62637
$279$	−4.81186	−0.288078
$280$	0	0
$281$	−30.9269	−1.84494	−0.922472	−	0.386063i	$-0.873835\pi$
$281$	−30.9269	−1.84494	−0.922472	+	0.386063i	$0.873835\pi$
$282$	3.45475	0.205727
$283$	−11.0298	−0.655651	−0.327826	−	0.944738i	$-0.606316\pi$
$283$	−11.0298	−0.655651	−0.327826	+	0.944738i	$0.606316\pi$
$284$	4.90930	0.291313
$285$	0	0
$286$	−10.0107	−0.591945
$287$	−34.3523	−2.02775
$288$	−5.24792	−0.309237
$289$	−15.0710	−0.886527
$290$	0	0
$291$	3.01913	0.176984
$292$	−5.55351	−0.324995
$293$	15.0271	0.877893	0.438947	−	0.898513i	$-0.355352\pi$
$293$	15.0271	0.877893	0.438947	+	0.898513i	$0.355352\pi$
$294$	−26.0361	−1.51846
$295$	0	0
$296$	12.7165	0.739131
$297$	−2.19066	−0.127115
$298$	−0.631687	−0.0365926
$299$	7.35314	0.425243
$300$	0	0
$301$	−42.9510	−2.47565
$302$	37.8972	2.18074
$303$	5.05765	0.290554
$304$	−1.07745	−0.0617960
$305$	0	0
$306$	−2.41045	−0.137796
$307$	−23.3647	−1.33349	−0.666746	−	0.745285i	$-0.732313\pi$
$307$	−23.3647	−1.33349	−0.666746	+	0.745285i	$0.732313\pi$
$308$	10.3988	0.592528
$309$	−1.01788	−0.0579049
$310$	0	0
$311$	11.9330	0.676656	0.338328	−	0.941028i	$-0.390139\pi$
$311$	11.9330	0.676656	0.338328	+	0.941028i	$0.390139\pi$
$312$	−4.51491	−0.255606
$313$	28.5301	1.61262	0.806308	−	0.591495i	$-0.201462\pi$
$313$	28.5301	1.61262	0.806308	+	0.591495i	$0.201462\pi$
$314$	−28.3925	−1.60228
$315$	0	0
$316$	5.36386	0.301741
$317$	13.5617	0.761699	0.380849	−	0.924637i	$-0.375632\pi$
$317$	13.5617	0.761699	0.380849	+	0.924637i	$0.375632\pi$
$318$	−10.1185	−0.567420
$319$	−16.8681	−0.944432
$320$	0	0
$321$	1.00000	0.0558146
$322$	−22.7336	−1.26689
$323$	−0.299303	−0.0166536
$324$	1.01200	0.0562220
$325$	0	0
$326$	−7.61239	−0.421611
$327$	3.13292	0.173251
$328$	12.5577	0.693383
$329$	−9.33727	−0.514780
$330$	0	0
$331$	29.4602	1.61928	0.809639	−	0.586928i	$-0.199663\pi$
$331$	29.4602	1.61928	0.809639	+	0.586928i	$0.199663\pi$
$332$	−8.98600	−0.493171
$333$	−7.41620	−0.406405
$334$	−33.9166	−1.85583
$335$	0	0
$336$	23.4525	1.27944
$337$	−23.5737	−1.28414	−0.642072	−	0.766645i	$-0.721925\pi$
$337$	−23.5737	−1.28414	−0.642072	+	0.766645i	$0.721925\pi$
$338$	−10.5292	−0.572714
$339$	18.5160	1.00565
$340$	0	0
$341$	−10.5411	−0.570834
$342$	0.373996	0.0202234
$343$	37.5343	2.02666
$344$	15.7010	0.846543
$345$	0	0
$346$	25.0049	1.34427
$347$	34.8687	1.87185	0.935926	−	0.352196i	$-0.114565\pi$
$347$	34.8687	1.87185	0.935926	+	0.352196i	$0.114565\pi$
$348$	7.79239	0.417716
$349$	−8.99851	−0.481679	−0.240840	−	0.970565i	$-0.577423\pi$
$349$	−8.99851	−0.481679	−0.240840	+	0.970565i	$0.577423\pi$
$350$	0	0
$351$	2.63307	0.140543
$352$	−11.4964	−0.612760
$353$	−24.6248	−1.31065	−0.655324	−	0.755348i	$-0.727468\pi$
$353$	−24.6248	−1.31065	−0.655324	+	0.755348i	$0.727468\pi$
$354$	−18.6774	−0.992695
$355$	0	0
$356$	−3.73378	−0.197890
$357$	6.51481	0.344800
$358$	34.2030	1.80768
$359$	−3.55702	−0.187733	−0.0938663	−	0.995585i	$-0.529923\pi$
$359$	−3.55702	−0.187733	−0.0938663	+	0.995585i	$0.529923\pi$
$360$	0	0
$361$	−18.9536	−0.997556
$362$	7.90147	0.415292
$363$	6.20102	0.325469
$364$	−12.4989	−0.655122
$365$	0	0
$366$	0.958406	0.0500967
$367$	2.41794	0.126215	0.0631077	−	0.998007i	$-0.479899\pi$
$367$	2.41794	0.126215	0.0631077	+	0.998007i	$0.479899\pi$
$368$	13.9626	0.727853
$369$	−7.32360	−0.381251
$370$	0	0
$371$	27.3478	1.41983
$372$	4.86958	0.252476
$373$	23.6293	1.22348	0.611739	−	0.791060i	$-0.290470\pi$
$373$	23.6293	1.22348	0.611739	+	0.791060i	$0.290470\pi$
$374$	−5.28047	−0.273047
$375$	0	0
$376$	3.41330	0.176028
$377$	20.2747	1.04420
$378$	−8.14063	−0.418709
$379$	−16.7055	−0.858101	−0.429051	−	0.903280i	$-0.641152\pi$
$379$	−16.7055	−0.858101	−0.429051	+	0.903280i	$0.641152\pi$
$380$	0	0
$381$	−9.53839	−0.488666
$382$	14.2949	0.731392
$383$	3.46608	0.177109	0.0885543	−	0.996071i	$-0.471775\pi$
$383$	3.46608	0.177109	0.0885543	+	0.996071i	$0.471775\pi$
$384$	−12.0437	−0.614604
$385$	0	0
$386$	−30.1519	−1.53469
$387$	−9.15677	−0.465465
$388$	−3.05534	−0.155112
$389$	14.7372	0.747206	0.373603	−	0.927589i	$-0.378122\pi$
$389$	14.7372	0.747206	0.373603	+	0.927589i	$0.378122\pi$
$390$	0	0
$391$	3.87865	0.196152
$392$	−25.7238	−1.29925
$393$	−15.1827	−0.765864
$394$	6.62515	0.333770
$395$	0	0
$396$	2.21694	0.111405
$397$	−15.4823	−0.777035	−0.388518	−	0.921441i	$-0.627013\pi$
$397$	−15.4823	−0.777035	−0.388518	+	0.921441i	$0.627013\pi$
$398$	−1.71421	−0.0859254
$399$	−1.01081	−0.0506039
$400$	0	0
$401$	22.6681	1.13199	0.565995	−	0.824408i	$-0.308492\pi$
$401$	22.6681	1.13199	0.565995	+	0.824408i	$0.308492\pi$
$402$	14.4982	0.723103
$403$	12.6700	0.631136
$404$	−5.11832	−0.254646
$405$	0	0
$406$	−62.6830	−3.11091
$407$	−16.2464	−0.805302
$408$	−2.38153	−0.117904
$409$	−22.5448	−1.11477	−0.557385	−	0.830254i	$-0.688195\pi$
$409$	−22.5448	−1.11477	−0.557385	+	0.830254i	$0.688195\pi$
$410$	0	0
$411$	−13.1819	−0.650214
$412$	1.03009	0.0507487
$413$	50.4802	2.48397
$414$	−4.84660	−0.238197
$415$	0	0
$416$	13.8182	0.677491
$417$	−15.6248	−0.765151
$418$	0.819296	0.0400731
$419$	−25.0781	−1.22515	−0.612573	−	0.790414i	$-0.709866\pi$
$419$	−25.0781	−1.22515	−0.612573	+	0.790414i	$0.709866\pi$
$420$	0	0
$421$	−14.4964	−0.706512	−0.353256	−	0.935527i	$-0.614926\pi$
$421$	−14.4964	−0.706512	−0.353256	+	0.935527i	$0.614926\pi$
$422$	−10.6608	−0.518959
$423$	−1.99062	−0.0967874
$424$	−9.99716	−0.485505
$425$	0	0
$426$	−8.41915	−0.407909
$427$	−2.59032	−0.125354
$428$	−1.01200	−0.0489167
$429$	5.76816	0.278489
$430$	0	0
$431$	4.27036	0.205696	0.102848	−	0.994697i	$-0.467204\pi$
$431$	4.27036	0.205696	0.102848	+	0.994697i	$0.467204\pi$
$432$	4.99986	0.240556
$433$	−5.78696	−0.278104	−0.139052	−	0.990285i	$-0.544405\pi$
$433$	−5.78696	−0.278104	−0.139052	+	0.990285i	$0.544405\pi$
$434$	−39.1715	−1.88029
$435$	0	0
$436$	−3.17050	−0.151840
$437$	−0.601796	−0.0287878
$438$	9.52392	0.455071
$439$	−33.3602	−1.59220	−0.796098	−	0.605168i	$-0.793106\pi$
$439$	−33.3602	−1.59220	−0.796098	+	0.605168i	$0.793106\pi$
$440$	0	0
$441$	15.0020	0.714380
$442$	6.34689	0.301891
$443$	19.4605	0.924597	0.462299	−	0.886724i	$-0.347025\pi$
$443$	19.4605	0.924597	0.462299	+	0.886724i	$0.347025\pi$
$444$	7.50517	0.356179
$445$	0	0
$446$	−42.4010	−2.00774
$447$	0.363978	0.0172155
$448$	4.18354	0.197654
$449$	−7.12147	−0.336083	−0.168041	−	0.985780i	$-0.553744\pi$
$449$	−7.12147	−0.336083	−0.168041	+	0.985780i	$0.553744\pi$
$450$	0	0
$451$	−16.0435	−0.755458
$452$	−18.7381	−0.881367
$453$	−21.8364	−1.02596
$454$	44.3454	2.08123
$455$	0	0
$456$	0.369509	0.0173039
$457$	−14.9036	−0.697163	−0.348581	−	0.937279i	$-0.613337\pi$
$457$	−14.9036	−0.697163	−0.348581	+	0.937279i	$0.613337\pi$
$458$	10.9055	0.509579
$459$	1.38890	0.0648283
$460$	0	0
$461$	0.409261	0.0190612	0.00953060	−	0.999955i	$-0.496966\pi$
$461$	0.409261	0.0190612	0.00953060	+	0.999955i	$0.496966\pi$
$462$	−17.8333	−0.829682
$463$	16.4368	0.763883	0.381942	−	0.924186i	$-0.375256\pi$
$463$	16.4368	0.763883	0.381942	+	0.924186i	$0.375256\pi$
$464$	38.4990	1.78727
$465$	0	0
$466$	−13.2453	−0.613575
$467$	32.9064	1.52273	0.761364	−	0.648325i	$-0.224530\pi$
$467$	32.9064	1.52273	0.761364	+	0.648325i	$0.224530\pi$
$468$	−2.66466	−0.123174
$469$	−39.1847	−1.80938
$470$	0	0
$471$	16.3597	0.753816
$472$	−18.4534	−0.849386
$473$	−20.0593	−0.922329
$474$	−9.19868	−0.422509
$475$	0	0
$476$	−6.59297	−0.302188
$477$	5.83030	0.266951
$478$	−32.8662	−1.50326
$479$	32.5555	1.48750	0.743749	−	0.668459i	$-0.233046\pi$
$479$	32.5555	1.48750	0.743749	+	0.668459i	$0.233046\pi$
$480$	0	0
$481$	19.5274	0.890373
$482$	−10.4431	−0.475669
$483$	13.0991	0.596029
$484$	−6.27541	−0.285246
$485$	0	0
$486$	−1.73551	−0.0787243
$487$	−0.578014	−0.0261923	−0.0130962	−	0.999914i	$-0.504169\pi$
$487$	−0.578014	−0.0261923	−0.0130962	+	0.999914i	$0.504169\pi$
$488$	0.946908	0.0428645
$489$	4.38626	0.198353
$490$	0	0
$491$	−14.0182	−0.632631	−0.316316	−	0.948654i	$-0.602446\pi$
$491$	−14.0182	−0.632631	−0.316316	+	0.948654i	$0.602446\pi$
$492$	7.41145	0.334134
$493$	10.6946	0.481658
$494$	−0.984758	−0.0443064
$495$	0	0
$496$	24.0586	1.08026
$497$	22.7547	1.02069
$498$	15.4104	0.690558
$499$	25.7061	1.15076	0.575382	−	0.817885i	$-0.304854\pi$
$499$	25.7061	1.15076	0.575382	+	0.817885i	$0.304854\pi$
$500$	0	0
$501$	19.5427	0.873104
$502$	−40.5230	−1.80863
$503$	−10.0865	−0.449733	−0.224866	−	0.974390i	$-0.572195\pi$
$503$	−10.0865	−0.449733	−0.224866	+	0.974390i	$0.572195\pi$
$504$	−8.04298	−0.358263
$505$	0	0
$506$	−10.6172	−0.471994
$507$	6.06693	0.269442
$508$	9.65281	0.428274
$509$	13.6288	0.604087	0.302044	−	0.953294i	$-0.402331\pi$
$509$	13.6288	0.604087	0.302044	+	0.953294i	$0.402331\pi$
$510$	0	0
$511$	−25.7407	−1.13870
$512$	9.09243	0.401832
$513$	−0.215496	−0.00951439
$514$	−17.0226	−0.750836
$515$	0	0
$516$	9.26661	0.407940
$517$	−4.36077	−0.191787
$518$	−60.3726	−2.65262
$519$	−14.4078	−0.632431
$520$	0	0
$521$	10.0578	0.440639	0.220319	−	0.975428i	$-0.429290\pi$
$521$	10.0578	0.440639	0.220319	+	0.975428i	$0.429290\pi$
$522$	−13.3635	−0.584903
$523$	30.2988	1.32487	0.662437	−	0.749118i	$-0.269522\pi$
$523$	30.2988	1.32487	0.662437	+	0.749118i	$0.269522\pi$
$524$	15.3648	0.671214
$525$	0	0
$526$	−9.70480	−0.423149
$527$	6.68319	0.291124
$528$	10.9530	0.476667
$529$	−15.2013	−0.660928
$530$	0	0
$531$	10.7619	0.467028
$532$	1.02294	0.0443500
$533$	19.2836	0.835264
$534$	6.40321	0.277094
$535$	0	0
$536$	14.3242	0.618713
$537$	−19.7077	−0.850452
$538$	−0.682484	−0.0294240
$539$	32.8642	1.41556
$540$	0	0
$541$	−18.1896	−0.782030	−0.391015	−	0.920384i	$-0.627876\pi$
$541$	−18.1896	−0.782030	−0.391015	+	0.920384i	$0.627876\pi$
$542$	−9.28467	−0.398811
$543$	−4.55282	−0.195380
$544$	7.28884	0.312506
$545$	0	0
$546$	21.4349	0.917328
$547$	−11.3421	−0.484953	−0.242476	−	0.970157i	$-0.577960\pi$
$547$	−11.3421	−0.484953	−0.242476	+	0.970157i	$0.577960\pi$
$548$	13.3400	0.569857
$549$	−0.552233	−0.0235687
$550$	0	0
$551$	−1.65932	−0.0706896
$552$	−4.78846	−0.203810
$553$	24.8616	1.05722
$554$	−3.53435	−0.150160
$555$	0	0
$556$	15.8123	0.670590
$557$	11.1633	0.473002	0.236501	−	0.971631i	$-0.423999\pi$
$557$	11.1633	0.473002	0.236501	+	0.971631i	$0.423999\pi$
$558$	−8.35102	−0.353527
$559$	24.1104	1.01976
$560$	0	0
$561$	3.04260	0.128459
$562$	−53.6740	−2.26410
$563$	−4.91211	−0.207021	−0.103510	−	0.994628i	$-0.533007\pi$
$563$	−4.91211	−0.207021	−0.103510	+	0.994628i	$0.533007\pi$
$564$	2.01450	0.0848259
$565$	0	0
$566$	−19.1423	−0.804610
$567$	4.69063	0.196988
$568$	−8.31815	−0.349022
$569$	−16.6229	−0.696867	−0.348433	−	0.937334i	$-0.613286\pi$
$569$	−16.6229	−0.696867	−0.348433	+	0.937334i	$0.613286\pi$
$570$	0	0
$571$	0.524040	0.0219304	0.0109652	−	0.999940i	$-0.496510\pi$
$571$	0.524040	0.0219304	0.0109652	+	0.999940i	$0.496510\pi$
$572$	−5.83736	−0.244072
$573$	−8.23672	−0.344094
$574$	−59.6187	−2.48844
$575$	0	0
$576$	0.891893	0.0371622
$577$	−30.5562	−1.27207	−0.636035	−	0.771660i	$-0.719427\pi$
$577$	−30.5562	−1.27207	−0.636035	+	0.771660i	$0.719427\pi$
$578$	−26.1558	−1.08794
$579$	17.3735	0.722018
$580$	0	0
$581$	−41.6503	−1.72795
$582$	5.23973	0.217194
$583$	12.7722	0.528970
$584$	9.40967	0.389375
$585$	0	0
$586$	26.0797	1.07734
$587$	29.5470	1.21953	0.609767	−	0.792580i	$-0.291263\pi$
$587$	29.5470	1.21953	0.609767	+	0.792580i	$0.291263\pi$
$588$	−15.1819	−0.626093
$589$	−1.03694	−0.0427262
$590$	0	0
$591$	−3.81741	−0.157027
$592$	37.0799	1.52398
$593$	30.0003	1.23196	0.615982	−	0.787760i	$-0.288759\pi$
$593$	30.0003	1.23196	0.615982	+	0.787760i	$0.288759\pi$
$594$	−3.80191	−0.155994
$595$	0	0
$596$	−0.368344	−0.0150880
$597$	0.987724	0.0404249
$598$	12.7615	0.521855
$599$	−6.95391	−0.284129	−0.142065	−	0.989857i	$-0.545374\pi$
$599$	−6.95391	−0.284129	−0.142065	+	0.989857i	$0.545374\pi$
$600$	0	0
$601$	27.3021	1.11368	0.556839	−	0.830621i	$-0.312014\pi$
$601$	27.3021	1.11368	0.556839	+	0.830621i	$0.312014\pi$
$602$	−74.5419	−3.03810
$603$	−8.35384	−0.340195
$604$	22.0983	0.899168
$605$	0	0
$606$	8.77761	0.356566
$607$	40.7525	1.65409	0.827047	−	0.562132i	$-0.190019\pi$
$607$	40.7525	1.65409	0.827047	+	0.562132i	$0.190019\pi$
$608$	−1.13091	−0.0458643
$609$	36.1179	1.46357
$610$	0	0
$611$	5.24146	0.212047
$612$	−1.40556	−0.0568165
$613$	−38.1944	−1.54266	−0.771328	−	0.636438i	$-0.780407\pi$
$613$	−38.1944	−1.54266	−0.771328	+	0.636438i	$0.780407\pi$
$614$	−40.5496	−1.63645
$615$	0	0
$616$	−17.6194	−0.709906
$617$	−22.4393	−0.903373	−0.451686	−	0.892177i	$-0.649177\pi$
$617$	−22.4393	−0.903373	−0.451686	+	0.892177i	$0.649177\pi$
$618$	−1.76653	−0.0710604
$619$	39.5413	1.58930	0.794650	−	0.607068i	$-0.207654\pi$
$619$	39.5413	1.58930	0.794650	+	0.607068i	$0.207654\pi$
$620$	0	0
$621$	2.79261	0.112063
$622$	20.7098	0.830386
$623$	−17.3062	−0.693358
$624$	−13.1650	−0.527021
$625$	0	0
$626$	49.5143	1.97899
$627$	−0.472078	−0.0188530
$628$	−16.5560	−0.660655
$629$	10.3004	0.410702
$630$	0	0
$631$	−2.14648	−0.0854498	−0.0427249	−	0.999087i	$-0.513604\pi$
$631$	−2.14648	−0.0854498	−0.0427249	+	0.999087i	$0.513604\pi$
$632$	−9.08833	−0.361514
$633$	6.14274	0.244152
$634$	23.5364	0.934750
$635$	0	0
$636$	−5.90024	−0.233960
$637$	−39.5013	−1.56510
$638$	−29.2747	−1.15900
$639$	4.85111	0.191907
$640$	0	0
$641$	−22.8115	−0.901000	−0.450500	−	0.892777i	$-0.648754\pi$
$641$	−22.8115	−0.901000	−0.450500	+	0.892777i	$0.648754\pi$
$642$	1.73551	0.0684951
$643$	20.5494	0.810390	0.405195	−	0.914230i	$-0.367204\pi$
$643$	20.5494	0.810390	0.405195	+	0.914230i	$0.367204\pi$
$644$	−13.2562	−0.522368
$645$	0	0
$646$	−0.519443	−0.0204372
$647$	36.3986	1.43098	0.715489	−	0.698624i	$-0.246204\pi$
$647$	36.3986	1.43098	0.715489	+	0.698624i	$0.246204\pi$
$648$	−1.71469	−0.0673594
$649$	23.5757	0.925427
$650$	0	0
$651$	22.5706	0.884612
$652$	−4.43887	−0.173840
$653$	−20.4785	−0.801387	−0.400694	−	0.916212i	$-0.631231\pi$
$653$	−20.4785	−0.801387	−0.400694	+	0.916212i	$0.631231\pi$
$654$	5.43721	0.212612
$655$	0	0
$656$	36.6169	1.42965
$657$	−5.48768	−0.214095
$658$	−16.2049	−0.631734
$659$	−31.3294	−1.22042	−0.610209	−	0.792240i	$-0.708915\pi$
$659$	−31.3294	−1.22042	−0.610209	+	0.792240i	$0.708915\pi$
$660$	0	0
$661$	35.4116	1.37735	0.688676	−	0.725069i	$-0.258192\pi$
$661$	35.4116	1.37735	0.688676	+	0.725069i	$0.258192\pi$
$662$	51.1285	1.98716
$663$	−3.65708	−0.142029
$664$	15.2256	0.590866
$665$	0	0
$666$	−12.8709	−0.498737
$667$	21.5031	0.832604
$668$	−19.7772	−0.765201
$669$	24.4314	0.944573
$670$	0	0
$671$	−1.20975	−0.0467020
$672$	24.6160	0.949584
$673$	−46.9118	−1.80832	−0.904158	−	0.427198i	$-0.859501\pi$
$673$	−46.9118	−1.80832	−0.904158	+	0.427198i	$0.859501\pi$
$674$	−40.9125	−1.57589
$675$	0	0
$676$	−6.13970	−0.236142
$677$	24.8631	0.955567	0.477783	−	0.878478i	$-0.341440\pi$
$677$	24.8631	0.955567	0.477783	+	0.878478i	$0.341440\pi$
$678$	32.1347	1.23413
$679$	−14.1616	−0.543472
$680$	0	0
$681$	−25.5518	−0.979146
$682$	−18.2942	−0.700522
$683$	7.09417	0.271451	0.135725	−	0.990746i	$-0.456664\pi$
$683$	7.09417	0.271451	0.135725	+	0.990746i	$0.456664\pi$
$684$	0.218081	0.00833854
$685$	0	0
$686$	65.1412	2.48710
$687$	−6.28372	−0.239739
$688$	45.7825	1.74544
$689$	−15.3516	−0.584850
$690$	0	0
$691$	−2.59409	−0.0986838	−0.0493419	−	0.998782i	$-0.515712\pi$
$691$	−2.59409	−0.0986838	−0.0493419	+	0.998782i	$0.515712\pi$
$692$	14.5806	0.554272
$693$	10.2756	0.390336
$694$	60.5151	2.29712
$695$	0	0
$696$	−13.2031	−0.500464
$697$	10.1717	0.385282
$698$	−15.6170	−0.591112
$699$	7.63191	0.288665
$700$	0	0
$701$	−2.71769	−0.102646	−0.0513229	−	0.998682i	$-0.516344\pi$
$701$	−2.71769	−0.102646	−0.0513229	+	0.998682i	$0.516344\pi$
$702$	4.56973	0.172473
$703$	−1.59816	−0.0602758
$704$	1.95383	0.0736378
$705$	0	0
$706$	−42.7367	−1.60842
$707$	−23.7236	−0.892216
$708$	−10.8910	−0.409310
$709$	−4.33561	−0.162827	−0.0814136	−	0.996680i	$-0.525943\pi$
$709$	−4.33561	−0.162827	−0.0814136	+	0.996680i	$0.525943\pi$
$710$	0	0
$711$	5.30027	0.198776
$712$	6.32639	0.237092
$713$	13.4376	0.503243
$714$	11.3065	0.423136
$715$	0	0
$716$	19.9442	0.745348
$717$	18.9375	0.707232
$718$	−6.17325	−0.230384
$719$	−40.4200	−1.50741	−0.753705	−	0.657213i	$-0.771735\pi$
$719$	−40.4200	−1.50741	−0.753705	+	0.657213i	$0.771735\pi$
$720$	0	0
$721$	4.77447	0.177811
$722$	−32.8941	−1.22419
$723$	6.01729	0.223785
$724$	4.60744	0.171234
$725$	0	0
$726$	10.7619	0.399413
$727$	−12.6228	−0.468155	−0.234078	−	0.972218i	$-0.575207\pi$
$727$	−12.6228	−0.468155	−0.234078	+	0.972218i	$0.575207\pi$
$728$	21.1777	0.784899
$729$	1.00000	0.0370370
$730$	0	0
$731$	12.7178	0.470386
$732$	0.558857	0.0206560
$733$	37.4973	1.38500	0.692498	−	0.721420i	$-0.256510\pi$
$733$	37.4973	1.38500	0.692498	+	0.721420i	$0.256510\pi$
$734$	4.19636	0.154891
$735$	0	0
$736$	14.6554	0.540205
$737$	−18.3004	−0.674103
$738$	−12.7102	−0.467868
$739$	−9.57866	−0.352357	−0.176178	−	0.984358i	$-0.556374\pi$
$739$	−9.57866	−0.352357	−0.176178	+	0.984358i	$0.556374\pi$
$740$	0	0
$741$	0.567417	0.0208446
$742$	47.4623	1.74240
$743$	−11.3735	−0.417252	−0.208626	−	0.977995i	$-0.566899\pi$
$743$	−11.3735	−0.417252	−0.208626	+	0.977995i	$0.566899\pi$
$744$	−8.25084	−0.302491
$745$	0	0
$746$	41.0089	1.50144
$747$	−8.87948	−0.324883
$748$	−3.07910	−0.112583
$749$	−4.69063	−0.171392
$750$	0	0
$751$	−0.721272	−0.0263196	−0.0131598	−	0.999913i	$-0.504189\pi$
$751$	−0.721272	−0.0263196	−0.0131598	+	0.999913i	$0.504189\pi$
$752$	9.95283	0.362942
$753$	23.3493	0.850896
$754$	35.1870	1.28143
$755$	0	0
$756$	−4.74690	−0.172643
$757$	46.0256	1.67283	0.836415	−	0.548097i	$-0.184648\pi$
$757$	46.0256	1.67283	0.836415	+	0.548097i	$0.184648\pi$
$758$	−28.9925	−1.05305
$759$	6.11765	0.222056
$760$	0	0
$761$	−8.05330	−0.291932	−0.145966	−	0.989290i	$-0.546629\pi$
$761$	−8.05330	−0.291932	−0.145966	+	0.989290i	$0.546629\pi$
$762$	−16.5540	−0.599687
$763$	−14.6954	−0.532008
$764$	8.33553	0.301569
$765$	0	0
$766$	6.01543	0.217346
$767$	−28.3370	−1.02319
$768$	−19.1182	−0.689870
$769$	24.8950	0.897738	0.448869	−	0.893598i	$-0.351827\pi$
$769$	24.8950	0.897738	0.448869	+	0.893598i	$0.351827\pi$
$770$	0	0
$771$	9.80843	0.353242
$772$	−17.5819	−0.632787
$773$	−50.9293	−1.83180	−0.915899	−	0.401408i	$-0.868521\pi$
$773$	−50.9293	−1.83180	−0.915899	+	0.401408i	$0.868521\pi$
$774$	−15.8917	−0.571214
$775$	0	0
$776$	5.17687	0.185839
$777$	34.7866	1.24796
$778$	25.5766	0.916965
$779$	−1.57821	−0.0565451
$780$	0	0
$781$	10.6271	0.380268
$782$	6.73144	0.240716
$783$	7.70002	0.275176
$784$	−75.0078	−2.67885
$785$	0	0
$786$	−26.3497	−0.939861
$787$	−22.7639	−0.811446	−0.405723	−	0.913996i	$-0.632980\pi$
$787$	−22.7639	−0.811446	−0.405723	+	0.913996i	$0.632980\pi$
$788$	3.86320	0.137621
$789$	5.59190	0.199077
$790$	0	0
$791$	−86.8517	−3.08809
$792$	−3.75630	−0.133474
$793$	1.45407	0.0516355
$794$	−26.8697	−0.953571
$795$	0	0
$796$	−0.999573	−0.0354289
$797$	53.0229	1.87817	0.939083	−	0.343690i	$-0.111677\pi$
$797$	53.0229	1.87817	0.939083	+	0.343690i	$0.111677\pi$
$798$	−1.75427	−0.0621006
$799$	2.76478	0.0978108
$800$	0	0
$801$	−3.68952	−0.130363
$802$	39.3407	1.38917
$803$	−12.0216	−0.424234
$804$	8.45405	0.298151
$805$	0	0
$806$	21.9889	0.774525
$807$	0.393247	0.0138430
$808$	8.67231	0.305091
$809$	24.4401	0.859267	0.429634	−	0.903003i	$-0.358643\pi$
$809$	24.4401	0.859267	0.429634	+	0.903003i	$0.358643\pi$
$810$	0	0
$811$	16.9695	0.595879	0.297940	−	0.954585i	$-0.403701\pi$
$811$	16.9695	0.595879	0.297940	+	0.954585i	$0.403701\pi$
$812$	−36.5512	−1.28269
$813$	5.34982	0.187626
$814$	−28.1957	−0.988259
$815$	0	0
$816$	−6.94430	−0.243099
$817$	−1.97325	−0.0690352
$818$	−39.1267	−1.36803
$819$	−12.3508	−0.431571
$820$	0	0
$821$	−50.2029	−1.75209	−0.876047	−	0.482226i	$-0.839828\pi$
$821$	−50.2029	−1.75209	−0.876047	+	0.482226i	$0.839828\pi$
$822$	−22.8773	−0.797937
$823$	14.9669	0.521714	0.260857	−	0.965378i	$-0.415995\pi$
$823$	14.9669	0.521714	0.260857	+	0.965378i	$0.415995\pi$
$824$	−1.74534	−0.0608018
$825$	0	0
$826$	87.6089	3.04831
$827$	20.0549	0.697377	0.348688	−	0.937239i	$-0.386627\pi$
$827$	20.0549	0.697377	0.348688	+	0.937239i	$0.386627\pi$
$828$	−2.82611	−0.0982141
$829$	25.6887	0.892204	0.446102	−	0.894982i	$-0.352812\pi$
$829$	25.6887	0.892204	0.446102	+	0.894982i	$0.352812\pi$
$830$	0	0
$831$	2.03649	0.0706450
$832$	−2.34842	−0.0814168
$833$	−20.8363	−0.721934
$834$	−27.1171	−0.938987
$835$	0	0
$836$	0.477741	0.0165230
$837$	4.81186	0.166322
$838$	−43.5233	−1.50349
$839$	−7.79708	−0.269185	−0.134593	−	0.990901i	$-0.542973\pi$
$839$	−7.79708	−0.269185	−0.134593	+	0.990901i	$0.542973\pi$
$840$	0	0
$841$	30.2903	1.04449
$842$	−25.1587	−0.867025
$843$	30.9269	1.06518
$844$	−6.21642	−0.213978
$845$	0	0
$846$	−3.45475	−0.118777
$847$	−29.0867	−0.999430
$848$	−29.1507	−1.00104
$849$	11.0298	0.378541
$850$	0	0
$851$	20.7105	0.709948
$852$	−4.90930	−0.168190
$853$	−17.2109	−0.589291	−0.294646	−	0.955607i	$-0.595202\pi$
$853$	−17.2109	−0.589291	−0.294646	+	0.955607i	$0.595202\pi$
$854$	−4.49552	−0.153834
$855$	0	0
$856$	1.71469	0.0586069
$857$	−46.6226	−1.59260	−0.796300	−	0.604903i	$-0.793212\pi$
$857$	−46.6226	−1.59260	−0.796300	+	0.604903i	$0.793212\pi$
$858$	10.0107	0.341760
$859$	−11.7077	−0.399460	−0.199730	−	0.979851i	$-0.564007\pi$
$859$	−11.7077	−0.399460	−0.199730	+	0.979851i	$0.564007\pi$
$860$	0	0
$861$	34.3523	1.17072
$862$	7.41125	0.252428
$863$	−55.0794	−1.87492	−0.937462	−	0.348086i	$-0.886832\pi$
$863$	−55.0794	−1.87492	−0.937462	+	0.348086i	$0.886832\pi$
$864$	5.24792	0.178538
$865$	0	0
$866$	−10.0433	−0.341286
$867$	15.0710	0.511837
$868$	−22.8414	−0.775287
$869$	11.6111	0.393879
$870$	0	0
$871$	21.9963	0.745315
$872$	5.37199	0.181919
$873$	−3.01913	−0.102182
$874$	−1.04442	−0.0353281
$875$	0	0
$876$	5.55351	0.187636
$877$	15.2004	0.513280	0.256640	−	0.966507i	$-0.417385\pi$
$877$	15.2004	0.513280	0.256640	+	0.966507i	$0.417385\pi$
$878$	−57.8970	−1.95393
$879$	−15.0271	−0.506852
$880$	0	0
$881$	55.4683	1.86878	0.934388	−	0.356257i	$-0.115947\pi$
$881$	55.4683	1.86878	0.934388	+	0.356257i	$0.115947\pi$
$882$	26.0361	0.876681
$883$	−55.6704	−1.87346	−0.936730	−	0.350054i	$-0.886163\pi$
$883$	−55.6704	−1.87346	−0.936730	+	0.350054i	$0.886163\pi$
$884$	3.70095	0.124476
$885$	0	0
$886$	33.7739	1.13466
$887$	−7.96895	−0.267571	−0.133786	−	0.991010i	$-0.542713\pi$
$887$	−7.96895	−0.267571	−0.133786	+	0.991010i	$0.542713\pi$
$888$	−12.7165	−0.426738
$889$	44.7410	1.50057
$890$	0	0
$891$	2.19066	0.0733898
$892$	−24.7245	−0.827837
$893$	−0.428972	−0.0143550
$894$	0.631687	0.0211268
$895$	0	0
$896$	56.4926	1.88729
$897$	−7.35314	−0.245514
$898$	−12.3594	−0.412438
$899$	37.0514	1.23573
$900$	0	0
$901$	−8.09771	−0.269774
$902$	−27.8436	−0.927092
$903$	42.9510	1.42932
$904$	31.7492	1.05596
$905$	0	0
$906$	−37.8972	−1.25905
$907$	24.9363	0.827997	0.413999	−	0.910277i	$-0.364132\pi$
$907$	24.9363	0.827997	0.413999	+	0.910277i	$0.364132\pi$
$908$	25.8583	0.858138
$909$	−5.05765	−0.167752
$910$	0	0
$911$	8.02446	0.265862	0.132931	−	0.991125i	$-0.457561\pi$
$911$	8.02446	0.265862	0.132931	+	0.991125i	$0.457561\pi$
$912$	1.07745	0.0356779
$913$	−19.4519	−0.643764
$914$	−25.8654	−0.855552
$915$	0	0
$916$	6.35910	0.210111
$917$	71.2162	2.35177
$918$	2.41045	0.0795567
$919$	3.47063	0.114485	0.0572427	−	0.998360i	$-0.481769\pi$
$919$	3.47063	0.114485	0.0572427	+	0.998360i	$0.481769\pi$
$920$	0	0
$921$	23.3647	0.769892
$922$	0.710277	0.0233917
$923$	−12.7733	−0.420439
$924$	−10.3988	−0.342096
$925$	0	0
$926$	28.5263	0.937431
$927$	1.01788	0.0334314
$928$	40.4091	1.32649
$929$	40.0950	1.31547	0.657737	−	0.753248i	$-0.271514\pi$
$929$	40.0950	1.31547	0.657737	+	0.753248i	$0.271514\pi$
$930$	0	0
$931$	3.23287	0.105953
$932$	−7.72346	−0.252990
$933$	−11.9330	−0.390667
$934$	57.1095	1.86868
$935$	0	0
$936$	4.51491	0.147574
$937$	−53.8498	−1.75920	−0.879599	−	0.475717i	$-0.842189\pi$
$937$	−53.8498	−1.75920	−0.879599	+	0.475717i	$0.842189\pi$
$938$	−68.0055	−2.22046
$939$	−28.5301	−0.931045
$940$	0	0
$941$	11.8771	0.387181	0.193590	−	0.981082i	$-0.437987\pi$
$941$	11.8771	0.387181	0.193590	+	0.981082i	$0.437987\pi$
$942$	28.3925	0.925076
$943$	20.4519	0.666007
$944$	−53.8081	−1.75131
$945$	0	0
$946$	−34.8132	−1.13187
$947$	44.1478	1.43461	0.717306	−	0.696759i	$-0.245375\pi$
$947$	44.1478	1.43461	0.717306	+	0.696759i	$0.245375\pi$
$948$	−5.36386	−0.174210
$949$	14.4495	0.469049
$950$	0	0
$951$	−13.5617	−0.439767
$952$	11.1709	0.362051
$953$	20.1072	0.651337	0.325668	−	0.945484i	$-0.394411\pi$
$953$	20.1072	0.651337	0.325668	+	0.945484i	$0.394411\pi$
$954$	10.1185	0.327600
$955$	0	0
$956$	−19.1646	−0.619829
$957$	16.8681	0.545268
$958$	56.5004	1.82544
$959$	61.8313	1.99664
$960$	0	0
$961$	−7.84605	−0.253098
$962$	33.8900	1.09266
$963$	−1.00000	−0.0322245
$964$	−6.08947	−0.196129
$965$	0	0
$966$	22.7336	0.731441
$967$	48.0211	1.54425	0.772127	−	0.635468i	$-0.219193\pi$
$967$	48.0211	1.54425	0.772127	+	0.635468i	$0.219193\pi$
$968$	10.6328	0.341752
$969$	0.299303	0.00961498
$970$	0	0
$971$	−28.6487	−0.919381	−0.459690	−	0.888079i	$-0.652040\pi$
$971$	−28.6487	−0.919381	−0.459690	+	0.888079i	$0.652040\pi$
$972$	−1.01200	−0.0324598
$973$	73.2903	2.34958
$974$	−1.00315	−0.0321430
$975$	0	0
$976$	2.76108	0.0883801
$977$	17.7864	0.569039	0.284519	−	0.958670i	$-0.408166\pi$
$977$	17.7864	0.569039	0.284519	+	0.958670i	$0.408166\pi$
$978$	7.61239	0.243417
$979$	−8.08248	−0.258317
$980$	0	0
$981$	−3.13292	−0.100026
$982$	−24.3287	−0.776360
$983$	−28.4687	−0.908011	−0.454005	−	0.890999i	$-0.650005\pi$
$983$	−28.4687	−0.908011	−0.454005	+	0.890999i	$0.650005\pi$
$984$	−12.5577	−0.400325
$985$	0	0
$986$	18.5605	0.591087
$987$	9.33727	0.297209
$988$	−0.574224	−0.0182685
$989$	25.5713	0.813119
$990$	0	0
$991$	22.6326	0.718947	0.359474	−	0.933155i	$-0.382956\pi$
$991$	22.6326	0.718947	0.359474	+	0.933155i	$0.382956\pi$
$992$	25.2522	0.801759
$993$	−29.4602	−0.934891
$994$	39.4911	1.25258
$995$	0	0
$996$	8.98600	0.284732
$997$	18.0862	0.572795	0.286398	−	0.958111i	$-0.407542\pi$
$997$	18.0862	0.572795	0.286398	+	0.958111i	$0.407542\pi$
$998$	44.6132	1.41221
$999$	7.41620	0.234638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.bf.1.10		12
5.4	even	2		1605.2.a.n.1.3	✓	12
15.14	odd	2		4815.2.a.u.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1605.2.a.n.1.3	✓	12	5.4	even	2
4815.2.a.u.1.10		12	15.14	odd	2
8025.2.a.bf.1.10		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.73551 q^{2} -1.00000 q^{3} +1.01200 q^{4} -1.73551 q^{6} +4.69063 q^{7} -1.71469 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.73551 q^{2} -1.00000 q^{3} +1.01200 q^{4} -1.73551 q^{6} +4.69063 q^{7} -1.71469 q^{8} +1.00000 q^{9} +2.19066 q^{11} -1.01200 q^{12} -2.63307 q^{13} +8.14063 q^{14} -4.99986 q^{16} -1.38890 q^{17} +1.73551 q^{18} +0.215496 q^{19} -4.69063 q^{21} +3.80191 q^{22} -2.79261 q^{23} +1.71469 q^{24} -4.56973 q^{26} -1.00000 q^{27} +4.74690 q^{28} -7.70002 q^{29} -4.81186 q^{31} -5.24792 q^{32} -2.19066 q^{33} -2.41045 q^{34} +1.01200 q^{36} -7.41620 q^{37} +0.373996 q^{38} +2.63307 q^{39} -7.32360 q^{41} -8.14063 q^{42} -9.15677 q^{43} +2.21694 q^{44} -4.84660 q^{46} -1.99062 q^{47} +4.99986 q^{48} +15.0020 q^{49} +1.38890 q^{51} -2.66466 q^{52} +5.83030 q^{53} -1.73551 q^{54} -8.04298 q^{56} -0.215496 q^{57} -13.3635 q^{58} +10.7619 q^{59} -0.552233 q^{61} -8.35102 q^{62} +4.69063 q^{63} +0.891893 q^{64} -3.80191 q^{66} -8.35384 q^{67} -1.40556 q^{68} +2.79261 q^{69} +4.85111 q^{71} -1.71469 q^{72} -5.48768 q^{73} -12.8709 q^{74} +0.218081 q^{76} +10.2756 q^{77} +4.56973 q^{78} +5.30027 q^{79} +1.00000 q^{81} -12.7102 q^{82} -8.87948 q^{83} -4.74690 q^{84} -15.8917 q^{86} +7.70002 q^{87} -3.75630 q^{88} -3.68952 q^{89} -12.3508 q^{91} -2.82611 q^{92} +4.81186 q^{93} -3.45475 q^{94} +5.24792 q^{96} -3.01913 q^{97} +26.0361 q^{98} +2.19066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9	\( 12 q - 3 q^{2} - 12 q^{3} + 15 q^{4} + 3 q^{6} - 7 q^{7} - 3 q^{8} + 12 q^{9} + 4 q^{11} - 15 q^{12} - 13 q^{13} + 4 q^{14} + 13 q^{16} + 4 q^{17} - 3 q^{18} + 14 q^{19} + 7 q^{21} - 15 q^{22} - 11 q^{23} + 3 q^{24} - 8 q^{26} - 12 q^{27} - 16 q^{28} - 7 q^{29} + 4 q^{31} - 4 q^{32} - 4 q^{33} + q^{34} + 15 q^{36} - 24 q^{37} + 11 q^{38} + 13 q^{39} + 13 q^{41} - 4 q^{42} - 25 q^{43} + 10 q^{44} - 22 q^{46} - 19 q^{47} - 13 q^{48} + 9 q^{49} - 4 q^{51} - 20 q^{52} - 11 q^{53} + 3 q^{54} - 37 q^{56} - 14 q^{57} + 2 q^{58} + 8 q^{59} + 7 q^{61} + 11 q^{62} - 7 q^{63} - 19 q^{64} + 15 q^{66} - 33 q^{67} + 24 q^{68} + 11 q^{69} - 3 q^{72} - 34 q^{73} - 27 q^{74} - 9 q^{76} + 29 q^{77} + 8 q^{78} + 12 q^{81} - q^{82} + 24 q^{83} + 16 q^{84} - 36 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} + 30 q^{91} + 28 q^{92} - 4 q^{93} - 8 q^{94} + 4 q^{96} - 16 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 12 * q^3 + 15 * q^4 + 3 * q^6 - 7 * q^7 - 3 * q^8 + 12 * q^9 + 4 * q^11 - 15 * q^12 - 13 * q^13 + 4 * q^14 + 13 * q^16 + 4 * q^17 - 3 * q^18 + 14 * q^19 + 7 * q^21 - 15 * q^22 - 11 * q^23 + 3 * q^24 - 8 * q^26 - 12 * q^27 - 16 * q^28 - 7 * q^29 + 4 * q^31 - 4 * q^32 - 4 * q^33 + q^34 + 15 * q^36 - 24 * q^37 + 11 * q^38 + 13 * q^39 + 13 * q^41 - 4 * q^42 - 25 * q^43 + 10 * q^44 - 22 * q^46 - 19 * q^47 - 13 * q^48 + 9 * q^49 - 4 * q^51 - 20 * q^52 - 11 * q^53 + 3 * q^54 - 37 * q^56 - 14 * q^57 + 2 * q^58 + 8 * q^59 + 7 * q^61 + 11 * q^62 - 7 * q^63 - 19 * q^64 + 15 * q^66 - 33 * q^67 + 24 * q^68 + 11 * q^69 - 3 * q^72 - 34 * q^73 - 27 * q^74 - 9 * q^76 + 29 * q^77 + 8 * q^78 + 12 * q^81 - q^82 + 24 * q^83 + 16 * q^84 - 36 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 + 30 * q^91 + 28 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^96 - 16 * q^97 + 36 * q^98 + 4 * q^99

Introduction

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