LMFDB - Embedded newform 1075.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.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:	$8.58391821729$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 13x^{4} + 15x^{3} - 7x^{2} - 4x + 1 $ x^7 - 3x^6 - 6x^5 + 13x^4 + 15x^3 - 7x^2 - 4x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.55799$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55799 q^{2} -2.90146 q^{3} +4.54331 q^{4} +7.42190 q^{6} +4.65360 q^{7} -6.50577 q^{8} +5.41847 q^{9} +O(q^{10})$	\(q-2.55799 q^{2} -2.90146 q^{3} +4.54331 q^{4} +7.42190 q^{6} +4.65360 q^{7} -6.50577 q^{8} +5.41847 q^{9} -2.75214 q^{11} -13.1822 q^{12} -2.87515 q^{13} -11.9039 q^{14} +7.55506 q^{16} -1.25800 q^{17} -13.8604 q^{18} -3.50233 q^{19} -13.5022 q^{21} +7.03995 q^{22} +2.67807 q^{23} +18.8762 q^{24} +7.35462 q^{26} -7.01708 q^{27} +21.1428 q^{28} +1.51167 q^{29} +0.856373 q^{31} -6.31424 q^{32} +7.98523 q^{33} +3.21796 q^{34} +24.6178 q^{36} +2.17758 q^{37} +8.95892 q^{38} +8.34215 q^{39} -7.54514 q^{41} +34.5386 q^{42} +1.00000 q^{43} -12.5038 q^{44} -6.85049 q^{46} -1.61715 q^{47} -21.9207 q^{48} +14.6560 q^{49} +3.65004 q^{51} -13.0627 q^{52} -12.8513 q^{53} +17.9496 q^{54} -30.2752 q^{56} +10.1619 q^{57} -3.86684 q^{58} -6.51889 q^{59} +6.88801 q^{61} -2.19059 q^{62} +25.2154 q^{63} +1.04163 q^{64} -20.4261 q^{66} +5.90371 q^{67} -5.71550 q^{68} -7.77032 q^{69} +10.8888 q^{71} -35.2513 q^{72} +2.57151 q^{73} -5.57022 q^{74} -15.9122 q^{76} -12.8074 q^{77} -21.3391 q^{78} -5.67849 q^{79} +4.10438 q^{81} +19.3004 q^{82} -3.97451 q^{83} -61.3449 q^{84} -2.55799 q^{86} -4.38606 q^{87} +17.9048 q^{88} -3.39656 q^{89} -13.3798 q^{91} +12.1673 q^{92} -2.48473 q^{93} +4.13666 q^{94} +18.3205 q^{96} -10.6929 q^{97} -37.4899 q^{98} -14.9124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 4 q^{2} - 5 q^{3} + 8 q^{4} + 4 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 7 * q - 4 * q^2 - 5 * q^3 + 8 * q^4 + 4 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9	$ 7 q - 4 q^{2} - 5 q^{3} + 8 q^{4} + 4 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9} + q^{11} - 23 q^{12} - 14 q^{13} - 17 q^{14} + 2 q^{16} - 12 q^{17} - 15 q^{18} - 4 q^{21} + 17 q^{22} - 18 q^{23} + 17 q^{24} + 12 q^{26} - 8 q^{27} + 2 q^{28} + 10 q^{29} - 15 q^{31} - 15 q^{32} - 20 q^{33} - 8 q^{34} + 32 q^{36} - 5 q^{37} - 4 q^{38} + 10 q^{39} - 21 q^{41} + 47 q^{42} + 7 q^{43} + 13 q^{44} + 4 q^{46} - 2 q^{47} - 33 q^{48} + 16 q^{49} + 16 q^{51} - 2 q^{52} - 42 q^{53} + 3 q^{54} - 28 q^{56} + 8 q^{57} - 30 q^{58} + 9 q^{59} + 4 q^{61} - 35 q^{62} + 8 q^{63} - 11 q^{64} - 24 q^{66} + 28 q^{67} - 30 q^{68} - 38 q^{69} + 2 q^{71} - 9 q^{72} - 11 q^{73} - 17 q^{74} - 36 q^{76} - 58 q^{77} + 2 q^{78} - 9 q^{79} - 25 q^{81} + 28 q^{82} - 12 q^{83} - 46 q^{84} - 4 q^{86} - 20 q^{87} + 14 q^{88} + 6 q^{89} + 42 q^{93} + 20 q^{94} + 40 q^{96} - 26 q^{97} - 13 q^{98} + 7 q^{99}+O(q^{100}) $ 7 * q - 4 * q^2 - 5 * q^3 + 8 * q^4 + 4 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9 + q^11 - 23 * q^12 - 14 * q^13 - 17 * q^14 + 2 * q^16 - 12 * q^17 - 15 * q^18 - 4 * q^21 + 17 * q^22 - 18 * q^23 + 17 * q^24 + 12 * q^26 - 8 * q^27 + 2 * q^28 + 10 * q^29 - 15 * q^31 - 15 * q^32 - 20 * q^33 - 8 * q^34 + 32 * q^36 - 5 * q^37 - 4 * q^38 + 10 * q^39 - 21 * q^41 + 47 * q^42 + 7 * q^43 + 13 * q^44 + 4 * q^46 - 2 * q^47 - 33 * q^48 + 16 * q^49 + 16 * q^51 - 2 * q^52 - 42 * q^53 + 3 * q^54 - 28 * q^56 + 8 * q^57 - 30 * q^58 + 9 * q^59 + 4 * q^61 - 35 * q^62 + 8 * q^63 - 11 * q^64 - 24 * q^66 + 28 * q^67 - 30 * q^68 - 38 * q^69 + 2 * q^71 - 9 * q^72 - 11 * q^73 - 17 * q^74 - 36 * q^76 - 58 * q^77 + 2 * q^78 - 9 * q^79 - 25 * q^81 + 28 * q^82 - 12 * q^83 - 46 * q^84 - 4 * q^86 - 20 * q^87 + 14 * q^88 + 6 * q^89 + 42 * q^93 + 20 * q^94 + 40 * q^96 - 26 * q^97 - 13 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.55799	−1.80877	−0.904386	−	0.426715i	$-0.859671\pi$
$2$	−2.55799	−1.80877	−0.904386	+	0.426715i	$0.859671\pi$
$3$	−2.90146	−1.67516	−0.837579	−	0.546316i	$-0.816030\pi$
$3$	−2.90146	−1.67516	−0.837579	+	0.546316i	$0.816030\pi$
$4$	4.54331	2.27166
$5$	0	0
$5$	0	0
$6$	7.42190	3.02998
$7$	4.65360	1.75890	0.879448	−	0.475995i	$-0.157912\pi$
$7$	4.65360	1.75890	0.879448	+	0.475995i	$0.157912\pi$
$8$	−6.50577	−2.30014
$9$	5.41847	1.80616
$10$	0	0
$11$	−2.75214	−0.829802	−0.414901	−	0.909867i	$-0.636184\pi$
$11$	−2.75214	−0.829802	−0.414901	+	0.909867i	$0.636184\pi$
$12$	−13.1822	−3.80538
$13$	−2.87515	−0.797424	−0.398712	−	0.917076i	$-0.630543\pi$
$13$	−2.87515	−0.797424	−0.398712	+	0.917076i	$0.630543\pi$
$14$	−11.9039	−3.18144
$15$	0	0
$16$	7.55506	1.88877
$17$	−1.25800	−0.305110	−0.152555	−	0.988295i	$-0.548750\pi$
$17$	−1.25800	−0.305110	−0.152555	+	0.988295i	$0.548750\pi$
$18$	−13.8604	−3.26692
$19$	−3.50233	−0.803490	−0.401745	−	0.915752i	$-0.631596\pi$
$19$	−3.50233	−0.803490	−0.401745	+	0.915752i	$0.631596\pi$
$20$	0	0
$21$	−13.5022	−2.94643
$22$	7.03995	1.50092
$23$	2.67807	0.558417	0.279208	−	0.960231i	$-0.409928\pi$
$23$	2.67807	0.558417	0.279208	+	0.960231i	$0.409928\pi$
$24$	18.8762	3.85309
$25$	0	0
$26$	7.35462	1.44236
$27$	−7.01708	−1.35044
$28$	21.1428	3.99561
$29$	1.51167	0.280711	0.140355	−	0.990101i	$-0.455176\pi$
$29$	1.51167	0.280711	0.140355	+	0.990101i	$0.455176\pi$
$30$	0	0
$31$	0.856373	0.153809	0.0769046	−	0.997038i	$-0.475496\pi$
$31$	0.856373	0.153809	0.0769046	+	0.997038i	$0.475496\pi$
$32$	−6.31424	−1.11621
$33$	7.98523	1.39005
$34$	3.21796	0.551875
$35$	0	0
$36$	24.6178	4.10296
$37$	2.17758	0.357991	0.178996	−	0.983850i	$-0.442715\pi$
$37$	2.17758	0.357991	0.178996	+	0.983850i	$0.442715\pi$
$38$	8.95892	1.45333
$39$	8.34215	1.33581
$40$	0	0
$41$	−7.54514	−1.17835	−0.589177	−	0.808004i	$-0.700548\pi$
$41$	−7.54514	−1.17835	−0.589177	+	0.808004i	$0.700548\pi$
$42$	34.5386	5.32942
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−12.5038	−1.88502
$45$	0	0
$46$	−6.85049	−1.01005
$47$	−1.61715	−0.235886	−0.117943	−	0.993020i	$-0.537630\pi$
$47$	−1.61715	−0.235886	−0.117943	+	0.993020i	$0.537630\pi$
$48$	−21.9207	−3.16398
$49$	14.6560	2.09372
$50$	0	0
$51$	3.65004	0.511108
$52$	−13.0627	−1.81147
$53$	−12.8513	−1.76526	−0.882628	−	0.470072i	$-0.844228\pi$
$53$	−12.8513	−1.76526	−0.882628	+	0.470072i	$0.844228\pi$
$54$	17.9496	2.44264
$55$	0	0
$56$	−30.2752	−4.04570
$57$	10.1619	1.34597
$58$	−3.86684	−0.507741
$59$	−6.51889	−0.848687	−0.424343	−	0.905501i	$-0.639495\pi$
$59$	−6.51889	−0.848687	−0.424343	+	0.905501i	$0.639495\pi$
$60$	0	0
$61$	6.88801	0.881920	0.440960	−	0.897527i	$-0.354638\pi$
$61$	6.88801	0.881920	0.440960	+	0.897527i	$0.354638\pi$
$62$	−2.19059	−0.278206
$63$	25.2154	3.17684
$64$	1.04163	0.130204
$65$	0	0
$66$	−20.4261	−2.51428
$67$	5.90371	0.721253	0.360627	−	0.932710i	$-0.382563\pi$
$67$	5.90371	0.721253	0.360627	+	0.932710i	$0.382563\pi$
$68$	−5.71550	−0.693106
$69$	−7.77032	−0.935437
$70$	0	0
$71$	10.8888	1.29227	0.646133	−	0.763225i	$-0.276385\pi$
$71$	10.8888	1.29227	0.646133	+	0.763225i	$0.276385\pi$
$72$	−35.2513	−4.15440
$73$	2.57151	0.300973	0.150487	−	0.988612i	$-0.451916\pi$
$73$	2.57151	0.300973	0.150487	+	0.988612i	$0.451916\pi$
$74$	−5.57022	−0.647525
$75$	0	0
$76$	−15.9122	−1.82525
$77$	−12.8074	−1.45954
$78$	−21.3391	−2.41618
$79$	−5.67849	−0.638880	−0.319440	−	0.947607i	$-0.603495\pi$
$79$	−5.67849	−0.638880	−0.319440	+	0.947607i	$0.603495\pi$
$80$	0	0
$81$	4.10438	0.456043
$82$	19.3004	2.13137
$83$	−3.97451	−0.436259	−0.218130	−	0.975920i	$-0.569996\pi$
$83$	−3.97451	−0.436259	−0.218130	+	0.975920i	$0.569996\pi$
$84$	−61.3449	−6.69327
$85$	0	0
$86$	−2.55799	−0.275835
$87$	−4.38606	−0.470235
$88$	17.9048	1.90866
$89$	−3.39656	−0.360034	−0.180017	−	0.983663i	$-0.557615\pi$
$89$	−3.39656	−0.360034	−0.180017	+	0.983663i	$0.557615\pi$
$90$	0	0
$91$	−13.3798	−1.40259
$92$	12.1673	1.26853
$93$	−2.48473	−0.257655
$94$	4.13666	0.426664
$95$	0	0
$96$	18.3205	1.86983
$97$	−10.6929	−1.08570	−0.542850	−	0.839830i	$-0.682655\pi$
$97$	−10.6929	−1.08570	−0.542850	+	0.839830i	$0.682655\pi$
$98$	−37.4899	−3.78705
$99$	−14.9124	−1.49875
$100$	0	0
$101$	7.24172	0.720578	0.360289	−	0.932841i	$-0.382678\pi$
$101$	7.24172	0.720578	0.360289	+	0.932841i	$0.382678\pi$
$102$	−9.33677	−0.924478
$103$	1.80537	0.177888	0.0889441	−	0.996037i	$-0.471651\pi$
$103$	1.80537	0.177888	0.0889441	+	0.996037i	$0.471651\pi$
$104$	18.7051	1.83418
$105$	0	0
$106$	32.8734	3.19295
$107$	19.8455	1.91854	0.959269	−	0.282495i	$-0.0911619\pi$
$107$	19.8455	1.91854	0.959269	+	0.282495i	$0.0911619\pi$
$108$	−31.8808	−3.06773
$109$	−2.83608	−0.271648	−0.135824	−	0.990733i	$-0.543368\pi$
$109$	−2.83608	−0.271648	−0.135824	+	0.990733i	$0.543368\pi$
$110$	0	0
$111$	−6.31815	−0.599692
$112$	35.1582	3.32214
$113$	−12.9747	−1.22056	−0.610279	−	0.792187i	$-0.708943\pi$
$113$	−12.9747	−1.22056	−0.610279	+	0.792187i	$0.708943\pi$
$114$	−25.9940	−2.43456
$115$	0	0
$116$	6.86800	0.637678
$117$	−15.5789	−1.44027
$118$	16.6752	1.53508
$119$	−5.85424	−0.536657
$120$	0	0
$121$	−3.42571	−0.311429
$122$	−17.6195	−1.59519
$123$	21.8919	1.97393
$124$	3.89077	0.349401
$125$	0	0
$126$	−64.5007	−5.74618
$127$	−16.6902	−1.48101	−0.740506	−	0.672050i	$-0.765414\pi$
$127$	−16.6902	−1.48101	−0.740506	+	0.672050i	$0.765414\pi$
$128$	9.96399	0.880701
$129$	−2.90146	−0.255459
$130$	0	0
$131$	−18.6341	−1.62807	−0.814036	−	0.580814i	$-0.802734\pi$
$131$	−18.6341	−1.62807	−0.814036	+	0.580814i	$0.802734\pi$
$132$	36.2794	3.15772
$133$	−16.2984	−1.41325
$134$	−15.1016	−1.30458
$135$	0	0
$136$	8.18427	0.701795
$137$	4.13604	0.353366	0.176683	−	0.984268i	$-0.443463\pi$
$137$	4.13604	0.353366	0.176683	+	0.984268i	$0.443463\pi$
$138$	19.8764	1.69199
$139$	5.03294	0.426888	0.213444	−	0.976955i	$-0.431532\pi$
$139$	5.03294	0.426888	0.213444	+	0.976955i	$0.431532\pi$
$140$	0	0
$141$	4.69210	0.395146
$142$	−27.8535	−2.33742
$143$	7.91283	0.661704
$144$	40.9368	3.41140
$145$	0	0
$146$	−6.57791	−0.544392
$147$	−42.5238	−3.50730
$148$	9.89341	0.813233
$149$	5.21136	0.426931	0.213466	−	0.976951i	$-0.431525\pi$
$149$	5.21136	0.426931	0.213466	+	0.976951i	$0.431525\pi$
$150$	0	0
$151$	16.2335	1.32106	0.660531	−	0.750798i	$-0.270331\pi$
$151$	16.2335	1.32106	0.660531	+	0.750798i	$0.270331\pi$
$152$	22.7853	1.84814
$153$	−6.81644	−0.551077
$154$	32.7611	2.63997
$155$	0	0
$156$	37.9010	3.03451
$157$	−17.5417	−1.39998	−0.699991	−	0.714151i	$-0.746813\pi$
$157$	−17.5417	−1.39998	−0.699991	+	0.714151i	$0.746813\pi$
$158$	14.5255	1.15559
$159$	37.2874	2.95708
$160$	0	0
$161$	12.4627	0.982197
$162$	−10.4990	−0.824877
$163$	−22.0049	−1.72356	−0.861779	−	0.507284i	$-0.830649\pi$
$163$	−22.0049	−1.72356	−0.861779	+	0.507284i	$0.830649\pi$
$164$	−34.2799	−2.67681
$165$	0	0
$166$	10.1668	0.789093
$167$	14.6571	1.13420	0.567102	−	0.823648i	$-0.308065\pi$
$167$	14.6571	1.13420	0.567102	+	0.823648i	$0.308065\pi$
$168$	87.8424	6.77719
$169$	−4.73348	−0.364114
$170$	0	0
$171$	−18.9773	−1.45123
$172$	4.54331	0.346424
$173$	−22.9175	−1.74239	−0.871194	−	0.490938i	$-0.836654\pi$
$173$	−22.9175	−1.74239	−0.871194	+	0.490938i	$0.836654\pi$
$174$	11.2195	0.850547
$175$	0	0
$176$	−20.7926	−1.56730
$177$	18.9143	1.42169
$178$	8.68836	0.651220
$179$	8.88351	0.663984	0.331992	−	0.943282i	$-0.392279\pi$
$179$	8.88351	0.663984	0.331992	+	0.943282i	$0.392279\pi$
$180$	0	0
$181$	−17.0565	−1.26780	−0.633899	−	0.773416i	$-0.718547\pi$
$181$	−17.0565	−1.26780	−0.633899	+	0.773416i	$0.718547\pi$
$182$	34.2255	2.53696
$183$	−19.9853	−1.47736
$184$	−17.4229	−1.28443
$185$	0	0
$186$	6.35592	0.466039
$187$	3.46220	0.253181
$188$	−7.34723	−0.535852
$189$	−32.6547	−2.37528
$190$	0	0
$191$	3.68117	0.266360	0.133180	−	0.991092i	$-0.457481\pi$
$191$	3.68117	0.266360	0.133180	+	0.991092i	$0.457481\pi$
$192$	−3.02225	−0.218112
$193$	−7.19136	−0.517646	−0.258823	−	0.965925i	$-0.583335\pi$
$193$	−7.19136	−0.517646	−0.258823	+	0.965925i	$0.583335\pi$
$194$	27.3523	1.96378
$195$	0	0
$196$	66.5868	4.75620
$197$	−21.9741	−1.56559	−0.782794	−	0.622281i	$-0.786206\pi$
$197$	−21.9741	−1.56559	−0.782794	+	0.622281i	$0.786206\pi$
$198$	38.1457	2.71090
$199$	−9.72508	−0.689393	−0.344696	−	0.938714i	$-0.612018\pi$
$199$	−9.72508	−0.689393	−0.344696	+	0.938714i	$0.612018\pi$
$200$	0	0
$201$	−17.1294	−1.20821
$202$	−18.5242	−1.30336
$203$	7.03472	0.493741
$204$	16.5833	1.16106
$205$	0	0
$206$	−4.61811	−0.321759
$207$	14.5111	1.00859
$208$	−21.7220	−1.50615
$209$	9.63891	0.666737
$210$	0	0
$211$	−15.0232	−1.03424	−0.517121	−	0.855912i	$-0.672996\pi$
$211$	−15.0232	−1.03424	−0.517121	+	0.855912i	$0.672996\pi$
$212$	−58.3873	−4.01005
$213$	−31.5935	−2.16475
$214$	−50.7646	−3.47020
$215$	0	0
$216$	45.6515	3.10619
$217$	3.98522	0.270534
$218$	7.25467	0.491349
$219$	−7.46115	−0.504178
$220$	0	0
$221$	3.61695	0.243302
$222$	16.1618	1.08471
$223$	−1.30864	−0.0876329	−0.0438164	−	0.999040i	$-0.513952\pi$
$223$	−1.30864	−0.0876329	−0.0438164	+	0.999040i	$0.513952\pi$
$224$	−29.3839	−1.96330
$225$	0	0
$226$	33.1892	2.20771
$227$	−10.7175	−0.711346	−0.355673	−	0.934610i	$-0.615748\pi$
$227$	−10.7175	−0.711346	−0.355673	+	0.934610i	$0.615748\pi$
$228$	46.1685	3.05759
$229$	5.90649	0.390312	0.195156	−	0.980772i	$-0.437479\pi$
$229$	5.90649	0.390312	0.195156	+	0.980772i	$0.437479\pi$
$230$	0	0
$231$	37.1601	2.44495
$232$	−9.83459	−0.645672
$233$	15.6980	1.02841	0.514205	−	0.857668i	$-0.328087\pi$
$233$	15.6980	1.02841	0.514205	+	0.857668i	$0.328087\pi$
$234$	39.8507	2.60512
$235$	0	0
$236$	−29.6173	−1.92792
$237$	16.4759	1.07023
$238$	14.9751	0.970691
$239$	−4.30394	−0.278399	−0.139199	−	0.990264i	$-0.544453\pi$
$239$	−4.30394	−0.278399	−0.139199	+	0.990264i	$0.544453\pi$
$240$	0	0
$241$	−12.6935	−0.817658	−0.408829	−	0.912611i	$-0.634063\pi$
$241$	−12.6935	−0.817658	−0.408829	+	0.912611i	$0.634063\pi$
$242$	8.76294	0.563303
$243$	9.14255	0.586495
$244$	31.2944	2.00342
$245$	0	0
$246$	−55.9993	−3.57039
$247$	10.0697	0.640722
$248$	−5.57136	−0.353782
$249$	11.5319	0.730803
$250$	0	0
$251$	13.8300	0.872944	0.436472	−	0.899718i	$-0.356228\pi$
$251$	13.8300	0.872944	0.436472	+	0.899718i	$0.356228\pi$
$252$	114.561	7.21669
$253$	−7.37044	−0.463376
$254$	42.6933	2.67881
$255$	0	0
$256$	−27.5711	−1.72319
$257$	−17.6694	−1.10219	−0.551093	−	0.834444i	$-0.685789\pi$
$257$	−17.6694	−1.10219	−0.551093	+	0.834444i	$0.685789\pi$
$258$	7.42190	0.462068
$259$	10.1336	0.629670
$260$	0	0
$261$	8.19095	0.507007
$262$	47.6659	2.94481
$263$	23.8786	1.47242	0.736210	−	0.676753i	$-0.236614\pi$
$263$	23.8786	1.47242	0.736210	+	0.676753i	$0.236614\pi$
$264$	−51.9500	−3.19730
$265$	0	0
$266$	41.6913	2.55626
$267$	9.85497	0.603114
$268$	26.8224	1.63844
$269$	−13.6155	−0.830150	−0.415075	−	0.909787i	$-0.636245\pi$
$269$	−13.6155	−0.830150	−0.415075	+	0.909787i	$0.636245\pi$
$270$	0	0
$271$	27.3758	1.66296	0.831481	−	0.555553i	$-0.187493\pi$
$271$	27.3758	1.66296	0.831481	+	0.555553i	$0.187493\pi$
$272$	−9.50428	−0.576282
$273$	38.8210	2.34956
$274$	−10.5800	−0.639158
$275$	0	0
$276$	−35.3030	−2.12499
$277$	18.7350	1.12568	0.562838	−	0.826568i	$-0.309710\pi$
$277$	18.7350	1.12568	0.562838	+	0.826568i	$0.309710\pi$
$278$	−12.8742	−0.772143
$279$	4.64023	0.277803
$280$	0	0
$281$	−32.6216	−1.94604	−0.973021	−	0.230716i	$-0.925893\pi$
$281$	−32.6216	−1.94604	−0.973021	+	0.230716i	$0.925893\pi$
$282$	−12.0024	−0.714730
$283$	−24.2837	−1.44352	−0.721759	−	0.692145i	$-0.756666\pi$
$283$	−24.2837	−1.44352	−0.721759	+	0.692145i	$0.756666\pi$
$284$	49.4714	2.93559
$285$	0	0
$286$	−20.2410	−1.19687
$287$	−35.1121	−2.07260
$288$	−34.2135	−2.01605
$289$	−15.4174	−0.906908
$290$	0	0
$291$	31.0250	1.81872
$292$	11.6832	0.683707
$293$	−9.28516	−0.542445	−0.271222	−	0.962517i	$-0.587428\pi$
$293$	−9.28516	−0.542445	−0.271222	+	0.962517i	$0.587428\pi$
$294$	108.775	6.34391
$295$	0	0
$296$	−14.1668	−0.823429
$297$	19.3120	1.12060
$298$	−13.3306	−0.772221
$299$	−7.69988	−0.445295
$300$	0	0
$301$	4.65360	0.268229
$302$	−41.5251	−2.38950
$303$	−21.0116	−1.20708
$304$	−26.4603	−1.51760
$305$	0	0
$306$	17.4364	0.996772
$307$	9.60835	0.548378	0.274189	−	0.961676i	$-0.411591\pi$
$307$	9.60835	0.548378	0.274189	+	0.961676i	$0.411591\pi$
$308$	−58.1879	−3.31556
$309$	−5.23820	−0.297991
$310$	0	0
$311$	3.76181	0.213313	0.106656	−	0.994296i	$-0.465986\pi$
$311$	3.76181	0.213313	0.106656	+	0.994296i	$0.465986\pi$
$312$	−54.2721	−3.07255
$313$	5.88340	0.332549	0.166275	−	0.986079i	$-0.446826\pi$
$313$	5.88340	0.332549	0.166275	+	0.986079i	$0.446826\pi$
$314$	44.8716	2.53225
$315$	0	0
$316$	−25.7992	−1.45132
$317$	20.8714	1.17225	0.586126	−	0.810220i	$-0.300652\pi$
$317$	20.8714	1.17225	0.586126	+	0.810220i	$0.300652\pi$
$318$	−95.3808	−5.34869
$319$	−4.16034	−0.232934
$320$	0	0
$321$	−57.5809	−3.21385
$322$	−31.8794	−1.77657
$323$	4.40594	0.245153
$324$	18.6475	1.03597
$325$	0	0
$326$	56.2883	3.11752
$327$	8.22878	0.455053
$328$	49.0870	2.71037
$329$	−7.52558	−0.414899
$330$	0	0
$331$	−9.34602	−0.513704	−0.256852	−	0.966451i	$-0.582685\pi$
$331$	−9.34602	−0.513704	−0.256852	+	0.966451i	$0.582685\pi$
$332$	−18.0574	−0.991031
$333$	11.7991	0.646588
$334$	−37.4928	−2.05151
$335$	0	0
$336$	−102.010	−5.56511
$337$	−21.5829	−1.17570	−0.587848	−	0.808971i	$-0.700025\pi$
$337$	−21.5829	−1.17570	−0.587848	+	0.808971i	$0.700025\pi$
$338$	12.1082	0.658600
$339$	37.6456	2.04463
$340$	0	0
$341$	−2.35686	−0.127631
$342$	48.5436	2.62494
$343$	35.6280	1.92373
$344$	−6.50577	−0.350767
$345$	0	0
$346$	58.6229	3.15158
$347$	−20.0841	−1.07817	−0.539086	−	0.842251i	$-0.681230\pi$
$347$	−20.0841	−1.07817	−0.539086	+	0.842251i	$0.681230\pi$
$348$	−19.9272	−1.06821
$349$	−35.9199	−1.92275	−0.961373	−	0.275248i	$-0.911240\pi$
$349$	−35.9199	−1.92275	−0.961373	+	0.275248i	$0.911240\pi$
$350$	0	0
$351$	20.1752	1.07687
$352$	17.3777	0.926233
$353$	−8.36282	−0.445108	−0.222554	−	0.974920i	$-0.571439\pi$
$353$	−8.36282	−0.445108	−0.222554	+	0.974920i	$0.571439\pi$
$354$	−48.3826	−2.57150
$355$	0	0
$356$	−15.4316	−0.817874
$357$	16.9858	0.898986
$358$	−22.7239	−1.20100
$359$	−20.4233	−1.07790	−0.538951	−	0.842337i	$-0.681179\pi$
$359$	−20.4233	−1.07790	−0.538951	+	0.842337i	$0.681179\pi$
$360$	0	0
$361$	−6.73369	−0.354405
$362$	43.6303	2.29316
$363$	9.93957	0.521692
$364$	−60.7887	−3.18619
$365$	0	0
$366$	51.1222	2.67220
$367$	−16.1639	−0.843748	−0.421874	−	0.906655i	$-0.638627\pi$
$367$	−16.1639	−0.843748	−0.421874	+	0.906655i	$0.638627\pi$
$368$	20.2330	1.05472
$369$	−40.8831	−2.12829
$370$	0	0
$371$	−59.8046	−3.10490
$372$	−11.2889	−0.585303
$373$	20.6324	1.06831	0.534154	−	0.845387i	$-0.320630\pi$
$373$	20.6324	1.06831	0.534154	+	0.845387i	$0.320630\pi$
$374$	−8.85628	−0.457947
$375$	0	0
$376$	10.5208	0.542570
$377$	−4.34629	−0.223845
$378$	83.5304	4.29634
$379$	0.610264	0.0313471	0.0156736	−	0.999877i	$-0.495011\pi$
$379$	0.610264	0.0313471	0.0156736	+	0.999877i	$0.495011\pi$
$380$	0	0
$381$	48.4258	2.48093
$382$	−9.41640	−0.481785
$383$	−3.66771	−0.187411	−0.0937056	−	0.995600i	$-0.529871\pi$
$383$	−3.66771	−0.187411	−0.0937056	+	0.995600i	$0.529871\pi$
$384$	−28.9101	−1.47531
$385$	0	0
$386$	18.3954	0.936303
$387$	5.41847	0.275436
$388$	−48.5812	−2.46634
$389$	15.5873	0.790308	0.395154	−	0.918615i	$-0.370691\pi$
$389$	15.5873	0.790308	0.395154	+	0.918615i	$0.370691\pi$
$390$	0	0
$391$	−3.36902	−0.170379
$392$	−95.3486	−4.81583
$393$	54.0662	2.72728
$394$	56.2094	2.83179
$395$	0	0
$396$	−67.7516	−3.40465
$397$	11.9679	0.600653	0.300327	−	0.953836i	$-0.402904\pi$
$397$	11.9679	0.600653	0.300327	+	0.953836i	$0.402904\pi$
$398$	24.8767	1.24695
$399$	47.2893	2.36743
$400$	0	0
$401$	18.4292	0.920308	0.460154	−	0.887839i	$-0.347794\pi$
$401$	18.4292	0.920308	0.460154	+	0.887839i	$0.347794\pi$
$402$	43.8168	2.18538
$403$	−2.46220	−0.122651
$404$	32.9014	1.63691
$405$	0	0
$406$	−17.9947	−0.893064
$407$	−5.99300	−0.297062
$408$	−23.7463	−1.17562
$409$	19.5080	0.964608	0.482304	−	0.876004i	$-0.339800\pi$
$409$	19.5080	0.964608	0.482304	+	0.876004i	$0.339800\pi$
$410$	0	0
$411$	−12.0006	−0.591944
$412$	8.20235	0.404101
$413$	−30.3363	−1.49275
$414$	−37.1191	−1.82431
$415$	0	0
$416$	18.1544	0.890093
$417$	−14.6029	−0.715105
$418$	−24.6562	−1.20598
$419$	−4.62480	−0.225936	−0.112968	−	0.993599i	$-0.536036\pi$
$419$	−4.62480	−0.225936	−0.112968	+	0.993599i	$0.536036\pi$
$420$	0	0
$421$	−14.2290	−0.693479	−0.346739	−	0.937962i	$-0.612711\pi$
$421$	−14.2290	−0.693479	−0.346739	+	0.937962i	$0.612711\pi$
$422$	38.4293	1.87071
$423$	−8.76249	−0.426047
$424$	83.6073	4.06033
$425$	0	0
$426$	80.8159	3.91554
$427$	32.0541	1.55121
$428$	90.1643	4.35826
$429$	−22.9588	−1.10846
$430$	0	0
$431$	−6.16609	−0.297010	−0.148505	−	0.988912i	$-0.547446\pi$
$431$	−6.16609	−0.297010	−0.148505	+	0.988912i	$0.547446\pi$
$432$	−53.0145	−2.55066
$433$	7.06948	0.339738	0.169869	−	0.985467i	$-0.445666\pi$
$433$	7.06948	0.339738	0.169869	+	0.985467i	$0.445666\pi$
$434$	−10.1941	−0.489335
$435$	0	0
$436$	−12.8852	−0.617090
$437$	−9.37950	−0.448682
$438$	19.0855	0.911942
$439$	−20.1260	−0.960561	−0.480280	−	0.877115i	$-0.659465\pi$
$439$	−20.1260	−0.960561	−0.480280	+	0.877115i	$0.659465\pi$
$440$	0	0
$441$	79.4131	3.78158
$442$	−9.25213	−0.440079
$443$	13.8121	0.656230	0.328115	−	0.944638i	$-0.393587\pi$
$443$	13.8121	0.656230	0.328115	+	0.944638i	$0.393587\pi$
$444$	−28.7053	−1.36229
$445$	0	0
$446$	3.34748	0.158508
$447$	−15.1205	−0.715177
$448$	4.84733	0.229015
$449$	−26.8611	−1.26765	−0.633827	−	0.773475i	$-0.718517\pi$
$449$	−26.8611	−1.26765	−0.633827	+	0.773475i	$0.718517\pi$
$450$	0	0
$451$	20.7653	0.977800
$452$	−58.9482	−2.77269
$453$	−47.1008	−2.21299
$454$	27.4153	1.28666
$455$	0	0
$456$	−66.1107	−3.09592
$457$	−1.21693	−0.0569255	−0.0284627	−	0.999595i	$-0.509061\pi$
$457$	−1.21693	−0.0569255	−0.0284627	+	0.999595i	$0.509061\pi$
$458$	−15.1087	−0.705985
$459$	8.82751	0.412033
$460$	0	0
$461$	−7.23850	−0.337130	−0.168565	−	0.985691i	$-0.553913\pi$
$461$	−7.23850	−0.337130	−0.168565	+	0.985691i	$0.553913\pi$
$462$	−95.0551	−4.42236
$463$	−12.3759	−0.575155	−0.287577	−	0.957757i	$-0.592850\pi$
$463$	−12.3759	−0.575155	−0.287577	+	0.957757i	$0.592850\pi$
$464$	11.4208	0.530196
$465$	0	0
$466$	−40.1553	−1.86016
$467$	−31.3868	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$467$	−31.3868	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$468$	−70.7799	−3.27180
$469$	27.4735	1.26861
$470$	0	0
$471$	50.8966	2.34519
$472$	42.4104	1.95210
$473$	−2.75214	−0.126544
$474$	−42.1452	−1.93579
$475$	0	0
$476$	−26.5976	−1.21910
$477$	−69.6341	−3.18833
$478$	11.0094	0.503560
$479$	−17.7452	−0.810799	−0.405400	−	0.914140i	$-0.632868\pi$
$479$	−17.7452	−0.810799	−0.405400	+	0.914140i	$0.632868\pi$
$480$	0	0
$481$	−6.26087	−0.285471
$482$	32.4697	1.47896
$483$	−36.1600	−1.64534
$484$	−15.5641	−0.707458
$485$	0	0
$486$	−23.3865	−1.06084
$487$	27.0534	1.22591	0.612953	−	0.790119i	$-0.289981\pi$
$487$	27.0534	1.22591	0.612953	+	0.790119i	$0.289981\pi$
$488$	−44.8118	−2.02854
$489$	63.8463	2.88723
$490$	0	0
$491$	36.8983	1.66520	0.832600	−	0.553875i	$-0.186852\pi$
$491$	36.8983	1.66520	0.832600	+	0.553875i	$0.186852\pi$
$492$	99.4619	4.48409
$493$	−1.90169	−0.0856477
$494$	−25.7583	−1.15892
$495$	0	0
$496$	6.46995	0.290509
$497$	50.6723	2.27296
$498$	−29.4984	−1.32186
$499$	−32.6895	−1.46338	−0.731692	−	0.681635i	$-0.761269\pi$
$499$	−32.6895	−1.46338	−0.731692	+	0.681635i	$0.761269\pi$
$500$	0	0
$501$	−42.5271	−1.89997
$502$	−35.3771	−1.57896
$503$	−11.2556	−0.501862	−0.250931	−	0.968005i	$-0.580737\pi$
$503$	−11.2556	−0.501862	−0.250931	+	0.968005i	$0.580737\pi$
$504$	−164.045	−7.30716
$505$	0	0
$506$	18.8535	0.838141
$507$	13.7340	0.609949
$508$	−75.8286	−3.36435
$509$	14.6760	0.650504	0.325252	−	0.945627i	$-0.394551\pi$
$509$	14.6760	0.650504	0.325252	+	0.945627i	$0.394551\pi$
$510$	0	0
$511$	11.9668	0.529380
$512$	50.5985	2.23616
$513$	24.5761	1.08506
$514$	45.1981	1.99360
$515$	0	0
$516$	−13.1822	−0.580316
$517$	4.45063	0.195739
$518$	−25.9216	−1.13893
$519$	66.4943	2.91878
$520$	0	0
$521$	9.27997	0.406563	0.203281	−	0.979120i	$-0.434839\pi$
$521$	9.27997	0.406563	0.203281	+	0.979120i	$0.434839\pi$
$522$	−20.9524	−0.917060
$523$	−6.98066	−0.305243	−0.152621	−	0.988285i	$-0.548771\pi$
$523$	−6.98066	−0.305243	−0.152621	+	0.988285i	$0.548771\pi$
$524$	−84.6607	−3.69842
$525$	0	0
$526$	−61.0813	−2.66327
$527$	−1.07732	−0.0469288
$528$	60.3289	2.62548
$529$	−15.8279	−0.688170
$530$	0	0
$531$	−35.3224	−1.53286
$532$	−74.0489	−3.21043
$533$	21.6935	0.939648
$534$	−25.2089	−1.09090
$535$	0	0
$536$	−38.4082	−1.65898
$537$	−25.7751	−1.11228
$538$	34.8282	1.50155
$539$	−40.3354	−1.73737
$540$	0	0
$541$	−6.41182	−0.275666	−0.137833	−	0.990456i	$-0.544014\pi$
$541$	−6.41182	−0.275666	−0.137833	+	0.990456i	$0.544014\pi$
$542$	−70.0271	−3.00792
$543$	49.4887	2.12376
$544$	7.94332	0.340567
$545$	0	0
$546$	−99.3038	−4.24981
$547$	25.6911	1.09847	0.549236	−	0.835667i	$-0.314919\pi$
$547$	25.6911	1.09847	0.549236	+	0.835667i	$0.314919\pi$
$548$	18.7913	0.802726
$549$	37.3225	1.59288
$550$	0	0
$551$	−5.29438	−0.225548
$552$	50.5519	2.15163
$553$	−26.4254	−1.12372
$554$	−47.9239	−2.03609
$555$	0	0
$556$	22.8662	0.969743
$557$	40.8999	1.73298	0.866492	−	0.499191i	$-0.166369\pi$
$557$	40.8999	1.73298	0.866492	+	0.499191i	$0.166369\pi$
$558$	−11.8697	−0.502483
$559$	−2.87515	−0.121606
$560$	0	0
$561$	−10.0454	−0.424119
$562$	83.4458	3.51995
$563$	22.9717	0.968142	0.484071	−	0.875029i	$-0.339158\pi$
$563$	22.9717	0.968142	0.484071	+	0.875029i	$0.339158\pi$
$564$	21.3177	0.897637
$565$	0	0
$566$	62.1175	2.61099
$567$	19.1002	0.802132
$568$	−70.8402	−2.97239
$569$	0.0964183	0.00404206	0.00202103	−	0.999998i	$-0.499357\pi$
$569$	0.0964183	0.00404206	0.00202103	+	0.999998i	$0.499357\pi$
$570$	0	0
$571$	6.86506	0.287294	0.143647	−	0.989629i	$-0.454117\pi$
$571$	6.86506	0.287294	0.143647	+	0.989629i	$0.454117\pi$
$572$	35.9505	1.50317
$573$	−10.6808	−0.446196
$574$	89.8164	3.74886
$575$	0	0
$576$	5.64404	0.235168
$577$	−29.9093	−1.24514	−0.622569	−	0.782565i	$-0.713911\pi$
$577$	−29.9093	−1.24514	−0.622569	+	0.782565i	$0.713911\pi$
$578$	39.4376	1.64039
$579$	20.8655	0.867139
$580$	0	0
$581$	−18.4958	−0.767335
$582$	−79.3617	−3.28965
$583$	35.3685	1.46481
$584$	−16.7297	−0.692279
$585$	0	0
$586$	23.7513	0.981159
$587$	5.78012	0.238571	0.119285	−	0.992860i	$-0.461940\pi$
$587$	5.78012	0.238571	0.119285	+	0.992860i	$0.461940\pi$
$588$	−193.199	−7.96739
$589$	−2.99930	−0.123584
$590$	0	0
$591$	63.7569	2.62261
$592$	16.4517	0.676162
$593$	2.92510	0.120119	0.0600597	−	0.998195i	$-0.480871\pi$
$593$	2.92510	0.120119	0.0600597	+	0.998195i	$0.480871\pi$
$594$	−49.3999	−2.02690
$595$	0	0
$596$	23.6768	0.969841
$597$	28.2169	1.15484
$598$	19.6962	0.805438
$599$	41.9315	1.71327	0.856637	−	0.515919i	$-0.172550\pi$
$599$	41.9315	1.71327	0.856637	+	0.515919i	$0.172550\pi$
$600$	0	0
$601$	−22.7550	−0.928195	−0.464098	−	0.885784i	$-0.653621\pi$
$601$	−22.7550	−0.928195	−0.464098	+	0.885784i	$0.653621\pi$
$602$	−11.9039	−0.485165
$603$	31.9891	1.30270
$604$	73.7538	3.00100
$605$	0	0
$606$	53.7473	2.18334
$607$	9.01085	0.365739	0.182870	−	0.983137i	$-0.441461\pi$
$607$	9.01085	0.365739	0.182870	+	0.983137i	$0.441461\pi$
$608$	22.1145	0.896863
$609$	−20.4110	−0.827094
$610$	0	0
$611$	4.64956	0.188101
$612$	−30.9692	−1.25186
$613$	6.67725	0.269692	0.134846	−	0.990867i	$-0.456946\pi$
$613$	6.67725	0.269692	0.134846	+	0.990867i	$0.456946\pi$
$614$	−24.5781	−0.991890
$615$	0	0
$616$	83.3218	3.35713
$617$	6.89464	0.277568	0.138784	−	0.990323i	$-0.455681\pi$
$617$	6.89464	0.277568	0.138784	+	0.990323i	$0.455681\pi$
$618$	13.3993	0.538998
$619$	−12.2209	−0.491200	−0.245600	−	0.969371i	$-0.578985\pi$
$619$	−12.2209	−0.491200	−0.245600	+	0.969371i	$0.578985\pi$
$620$	0	0
$621$	−18.7923	−0.754108
$622$	−9.62267	−0.385834
$623$	−15.8062	−0.633263
$624$	63.0254	2.52304
$625$	0	0
$626$	−15.0497	−0.601506
$627$	−27.9669	−1.11689
$628$	−79.6976	−3.18028
$629$	−2.73940	−0.109227
$630$	0	0
$631$	35.8386	1.42671	0.713357	−	0.700801i	$-0.247174\pi$
$631$	35.8386	1.42671	0.713357	+	0.700801i	$0.247174\pi$
$632$	36.9429	1.46951
$633$	43.5893	1.73252
$634$	−53.3887	−2.12034
$635$	0	0
$636$	169.408	6.71748
$637$	−42.1383	−1.66958
$638$	10.6421	0.421325
$639$	59.0008	2.33403
$640$	0	0
$641$	26.5290	1.04783	0.523916	−	0.851770i	$-0.324470\pi$
$641$	26.5290	1.04783	0.523916	+	0.851770i	$0.324470\pi$
$642$	147.291	5.81313
$643$	−9.69986	−0.382525	−0.191263	−	0.981539i	$-0.561258\pi$
$643$	−9.69986	−0.382525	−0.191263	+	0.981539i	$0.561258\pi$
$644$	56.6219	2.23121
$645$	0	0
$646$	−11.2703	−0.443426
$647$	−12.6694	−0.498086	−0.249043	−	0.968492i	$-0.580116\pi$
$647$	−12.6694	−0.498086	−0.249043	+	0.968492i	$0.580116\pi$
$648$	−26.7022	−1.04896
$649$	17.9409	0.704242
$650$	0	0
$651$	−11.5630	−0.453188
$652$	−99.9752	−3.91533
$653$	−12.0318	−0.470841	−0.235420	−	0.971894i	$-0.575647\pi$
$653$	−12.0318	−0.470841	−0.235420	+	0.971894i	$0.575647\pi$
$654$	−21.0491	−0.823087
$655$	0	0
$656$	−57.0040	−2.22563
$657$	13.9337	0.543604
$658$	19.2504	0.750457
$659$	−35.2538	−1.37329	−0.686646	−	0.726992i	$-0.740918\pi$
$659$	−35.2538	−1.37329	−0.686646	+	0.726992i	$0.740918\pi$
$660$	0	0
$661$	8.66493	0.337027	0.168513	−	0.985699i	$-0.446103\pi$
$661$	8.66493	0.337027	0.168513	+	0.985699i	$0.446103\pi$
$662$	23.9070	0.929173
$663$	−10.4944	−0.407570
$664$	25.8572	1.00346
$665$	0	0
$666$	−30.1820	−1.16953
$667$	4.04837	0.156754
$668$	66.5919	2.57652
$669$	3.79696	0.146799
$670$	0	0
$671$	−18.9568	−0.731819
$672$	85.2563	3.28883
$673$	−45.6857	−1.76105	−0.880527	−	0.473997i	$-0.842811\pi$
$673$	−45.6857	−1.76105	−0.880527	+	0.473997i	$0.842811\pi$
$674$	55.2089	2.12657
$675$	0	0
$676$	−21.5057	−0.827142
$677$	14.1652	0.544413	0.272206	−	0.962239i	$-0.412247\pi$
$677$	14.1652	0.544413	0.272206	+	0.962239i	$0.412247\pi$
$678$	−96.2971	−3.69827
$679$	−49.7605	−1.90963
$680$	0	0
$681$	31.0964	1.19162
$682$	6.02882	0.230856
$683$	−5.23815	−0.200432	−0.100216	−	0.994966i	$-0.531953\pi$
$683$	−5.23815	−0.200432	−0.100216	+	0.994966i	$0.531953\pi$
$684$	−86.2196	−3.29669
$685$	0	0
$686$	−91.1361	−3.47959
$687$	−17.1374	−0.653834
$688$	7.55506	0.288034
$689$	36.9494	1.40766
$690$	0	0
$691$	1.63216	0.0620905	0.0310452	−	0.999518i	$-0.490116\pi$
$691$	1.63216	0.0620905	0.0310452	+	0.999518i	$0.490116\pi$
$692$	−104.122	−3.95811
$693$	−69.3963	−2.63615
$694$	51.3750	1.95017
$695$	0	0
$696$	28.5347	1.08160
$697$	9.49181	0.359528
$698$	91.8827	3.47781
$699$	−45.5471	−1.72275
$700$	0	0
$701$	18.2179	0.688079	0.344040	−	0.938955i	$-0.388205\pi$
$701$	18.2179	0.688079	0.344040	+	0.938955i	$0.388205\pi$
$702$	−51.6080	−1.94782
$703$	−7.62659	−0.287642
$704$	−2.86671	−0.108043
$705$	0	0
$706$	21.3920	0.805098
$707$	33.7001	1.26742
$708$	85.9335	3.22958
$709$	−30.5091	−1.14579	−0.572896	−	0.819628i	$-0.694180\pi$
$709$	−30.5091	−1.14579	−0.572896	+	0.819628i	$0.694180\pi$
$710$	0	0
$711$	−30.7687	−1.15392
$712$	22.0972	0.828128
$713$	2.29343	0.0858896
$714$	−43.4496	−1.62606
$715$	0	0
$716$	40.3605	1.50834
$717$	12.4877	0.466362
$718$	52.2427	1.94968
$719$	48.5741	1.81151	0.905754	−	0.423805i	$-0.139306\pi$
$719$	48.5741	1.81151	0.905754	+	0.423805i	$0.139306\pi$
$720$	0	0
$721$	8.40146	0.312887
$722$	17.2247	0.641037
$723$	36.8296	1.36971
$724$	−77.4929	−2.88000
$725$	0	0
$726$	−25.4253	−0.943622
$727$	−8.33888	−0.309272	−0.154636	−	0.987972i	$-0.549420\pi$
$727$	−8.33888	−0.309272	−0.154636	+	0.987972i	$0.549420\pi$
$728$	87.0460	3.22614
$729$	−38.8399	−1.43851
$730$	0	0
$731$	−1.25800	−0.0465289
$732$	−90.7994	−3.35604
$733$	49.9810	1.84609	0.923046	−	0.384689i	$-0.125691\pi$
$733$	49.9810	1.84609	0.923046	+	0.384689i	$0.125691\pi$
$734$	41.3470	1.52615
$735$	0	0
$736$	−16.9100	−0.623311
$737$	−16.2479	−0.598498
$738$	104.579	3.84959
$739$	−41.3151	−1.51980	−0.759900	−	0.650040i	$-0.774752\pi$
$739$	−41.3151	−1.51980	−0.759900	+	0.650040i	$0.774752\pi$
$740$	0	0
$741$	−29.2169	−1.07331
$742$	152.980	5.61606
$743$	−16.9386	−0.621418	−0.310709	−	0.950505i	$-0.600566\pi$
$743$	−16.9386	−0.621418	−0.310709	+	0.950505i	$0.600566\pi$
$744$	16.1651	0.592641
$745$	0	0
$746$	−52.7776	−1.93232
$747$	−21.5358	−0.787952
$748$	15.7299	0.575141
$749$	92.3531	3.37451
$750$	0	0
$751$	30.8293	1.12498	0.562488	−	0.826805i	$-0.309844\pi$
$751$	30.8293	1.12498	0.562488	+	0.826805i	$0.309844\pi$
$752$	−12.2177	−0.445533
$753$	−40.1273	−1.46232
$754$	11.1178	0.404885
$755$	0	0
$756$	−148.361	−5.39582
$757$	−1.56967	−0.0570508	−0.0285254	−	0.999593i	$-0.509081\pi$
$757$	−1.56967	−0.0570508	−0.0285254	+	0.999593i	$0.509081\pi$
$758$	−1.56105	−0.0566998
$759$	21.3850	0.776227
$760$	0	0
$761$	22.5245	0.816514	0.408257	−	0.912867i	$-0.366137\pi$
$761$	22.5245	0.816514	0.408257	+	0.912867i	$0.366137\pi$
$762$	−123.873	−4.48744
$763$	−13.1980	−0.477800
$764$	16.7247	0.605079
$765$	0	0
$766$	9.38196	0.338984
$767$	18.7428	0.676764
$768$	79.9963	2.88662
$769$	36.8069	1.32729	0.663645	−	0.748048i	$-0.269009\pi$
$769$	36.8069	1.32729	0.663645	+	0.748048i	$0.269009\pi$
$770$	0	0
$771$	51.2670	1.84634
$772$	−32.6726	−1.17591
$773$	6.39415	0.229982	0.114991	−	0.993367i	$-0.463316\pi$
$773$	6.39415	0.229982	0.114991	+	0.993367i	$0.463316\pi$
$774$	−13.8604	−0.498201
$775$	0	0
$776$	69.5655	2.49726
$777$	−29.4022	−1.05480
$778$	−39.8722	−1.42949
$779$	26.4256	0.946795
$780$	0	0
$781$	−29.9676	−1.07233
$782$	8.61793	0.308176
$783$	−10.6075	−0.379082
$784$	110.727	3.95454
$785$	0	0
$786$	−138.301	−4.93303
$787$	19.0986	0.680792	0.340396	−	0.940282i	$-0.389439\pi$
$787$	19.0986	0.680792	0.340396	+	0.940282i	$0.389439\pi$
$788$	−99.8350	−3.55648
$789$	−69.2829	−2.46654
$790$	0	0
$791$	−60.3791	−2.14683
$792$	97.0165	3.44733
$793$	−19.8041	−0.703264
$794$	−30.6138	−1.08644
$795$	0	0
$796$	−44.1841	−1.56606
$797$	−22.8838	−0.810587	−0.405293	−	0.914187i	$-0.632831\pi$
$797$	−22.8838	−0.810587	−0.405293	+	0.914187i	$0.632831\pi$
$798$	−120.966	−4.28213
$799$	2.03438	0.0719712
$800$	0	0
$801$	−18.4041	−0.650278
$802$	−47.1416	−1.66463
$803$	−7.07717	−0.249748
$804$	−77.8241	−2.74465
$805$	0	0
$806$	6.29830	0.221848
$807$	39.5047	1.39063
$808$	−47.1129	−1.65743
$809$	25.3820	0.892385	0.446192	−	0.894937i	$-0.352780\pi$
$809$	25.3820	0.892385	0.446192	+	0.894937i	$0.352780\pi$
$810$	0	0
$811$	34.9031	1.22561	0.612807	−	0.790232i	$-0.290040\pi$
$811$	34.9031	1.22561	0.612807	+	0.790232i	$0.290040\pi$
$812$	31.9609	1.12161
$813$	−79.4298	−2.78573
$814$	15.3300	0.537317
$815$	0	0
$816$	27.5763	0.965363
$817$	−3.50233	−0.122531
$818$	−49.9012	−1.74476
$819$	−72.4981	−2.53329
$820$	0	0
$821$	−8.81110	−0.307510	−0.153755	−	0.988109i	$-0.549137\pi$
$821$	−8.81110	−0.307510	−0.153755	+	0.988109i	$0.549137\pi$
$822$	30.6973	1.07069
$823$	53.6465	1.87000	0.935000	−	0.354647i	$-0.115399\pi$
$823$	53.6465	1.87000	0.935000	+	0.354647i	$0.115399\pi$
$824$	−11.7453	−0.409167
$825$	0	0
$826$	77.6000	2.70005
$827$	−26.1870	−0.910610	−0.455305	−	0.890335i	$-0.650470\pi$
$827$	−26.1870	−0.910610	−0.455305	+	0.890335i	$0.650470\pi$
$828$	65.9282	2.29117
$829$	−20.7768	−0.721609	−0.360805	−	0.932641i	$-0.617498\pi$
$829$	−20.7768	−0.721609	−0.360805	+	0.932641i	$0.617498\pi$
$830$	0	0
$831$	−54.3587	−1.88568
$832$	−2.99485	−0.103828
$833$	−18.4373	−0.638814
$834$	37.3540	1.29346
$835$	0	0
$836$	43.7926	1.51460
$837$	−6.00924	−0.207710
$838$	11.8302	0.408667
$839$	6.69341	0.231082	0.115541	−	0.993303i	$-0.463140\pi$
$839$	6.69341	0.231082	0.115541	+	0.993303i	$0.463140\pi$
$840$	0	0
$841$	−26.7148	−0.921202
$842$	36.3976	1.25434
$843$	94.6503	3.25993
$844$	−68.2553	−2.34944
$845$	0	0
$846$	22.4144	0.770621
$847$	−15.9419	−0.547770
$848$	−97.0920	−3.33415
$849$	70.4582	2.41812
$850$	0	0
$851$	5.83171	0.199908
$852$	−143.539	−4.91757
$853$	−1.30907	−0.0448216	−0.0224108	−	0.999749i	$-0.507134\pi$
$853$	−1.30907	−0.0448216	−0.0224108	+	0.999749i	$0.507134\pi$
$854$	−81.9940	−2.80578
$855$	0	0
$856$	−129.110	−4.41290
$857$	−44.3888	−1.51629	−0.758146	−	0.652085i	$-0.773894\pi$
$857$	−44.3888	−1.51629	−0.758146	+	0.652085i	$0.773894\pi$
$858$	58.7283	2.00495
$859$	45.0433	1.53686	0.768429	−	0.639934i	$-0.221039\pi$
$859$	45.0433	1.53686	0.768429	+	0.639934i	$0.221039\pi$
$860$	0	0
$861$	101.876	3.47194
$862$	15.7728	0.537224
$863$	−11.9618	−0.407185	−0.203593	−	0.979056i	$-0.565262\pi$
$863$	−11.9618	−0.407185	−0.203593	+	0.979056i	$0.565262\pi$
$864$	44.3075	1.50737
$865$	0	0
$866$	−18.0837	−0.614508
$867$	44.7330	1.51921
$868$	18.1061	0.614561
$869$	15.6280	0.530144
$870$	0	0
$871$	−16.9741	−0.575145
$872$	18.4509	0.624826
$873$	−57.9392	−1.96094
$874$	23.9927	0.811564
$875$	0	0
$876$	−33.8983	−1.14532
$877$	43.8462	1.48058	0.740290	−	0.672288i	$-0.234688\pi$
$877$	43.8462	1.48058	0.740290	+	0.672288i	$0.234688\pi$
$878$	51.4821	1.73744
$879$	26.9405	0.908681
$880$	0	0
$881$	−47.3980	−1.59688	−0.798440	−	0.602075i	$-0.794341\pi$
$881$	−47.3980	−1.59688	−0.798440	+	0.602075i	$0.794341\pi$
$882$	−203.138	−6.84001
$883$	−30.3462	−1.02123	−0.510616	−	0.859809i	$-0.670583\pi$
$883$	−30.3462	−1.02123	−0.510616	+	0.859809i	$0.670583\pi$
$884$	16.4329	0.552700
$885$	0	0
$886$	−35.3311	−1.18697
$887$	32.2182	1.08178	0.540891	−	0.841093i	$-0.318087\pi$
$887$	32.2182	1.08178	0.540891	+	0.841093i	$0.318087\pi$
$888$	41.1044	1.37937
$889$	−77.6694	−2.60495
$890$	0	0
$891$	−11.2958	−0.378425
$892$	−5.94555	−0.199072
$893$	5.66380	0.189532
$894$	38.6782	1.29359
$895$	0	0
$896$	46.3685	1.54906
$897$	22.3409	0.745940
$898$	68.7105	2.29290
$899$	1.29456	0.0431758
$900$	0	0
$901$	16.1669	0.538598
$902$	−53.1175	−1.76862
$903$	−13.5022	−0.449326
$904$	84.4104	2.80745
$905$	0	0
$906$	120.483	4.00279
$907$	0.236166	0.00784178	0.00392089	−	0.999992i	$-0.498752\pi$
$907$	0.236166	0.00784178	0.00392089	+	0.999992i	$0.498752\pi$
$908$	−48.6930	−1.61593
$909$	39.2390	1.30148
$910$	0	0
$911$	8.55551	0.283457	0.141728	−	0.989906i	$-0.454734\pi$
$911$	8.55551	0.283457	0.141728	+	0.989906i	$0.454734\pi$
$912$	76.7735	2.54223
$913$	10.9384	0.362009
$914$	3.11289	0.102965
$915$	0	0
$916$	26.8350	0.886654
$917$	−86.7159	−2.86361
$918$	−22.5807	−0.745273
$919$	4.60285	0.151834	0.0759170	−	0.997114i	$-0.475812\pi$
$919$	4.60285	0.151834	0.0759170	+	0.997114i	$0.475812\pi$
$920$	0	0
$921$	−27.8782	−0.918619
$922$	18.5160	0.609792
$923$	−31.3071	−1.03049
$924$	168.830	5.55409
$925$	0	0
$926$	31.6573	1.04032
$927$	9.78233	0.321294
$928$	−9.54506	−0.313332
$929$	−3.94258	−0.129352	−0.0646759	−	0.997906i	$-0.520601\pi$
$929$	−3.94258	−0.129352	−0.0646759	+	0.997906i	$0.520601\pi$
$930$	0	0
$931$	−51.3302	−1.68228
$932$	71.3208	2.33619
$933$	−10.9147	−0.357332
$934$	80.2871	2.62708
$935$	0	0
$936$	101.353	3.31282
$937$	−56.0563	−1.83128	−0.915640	−	0.401998i	$-0.868316\pi$
$937$	−56.0563	−1.83128	−0.915640	+	0.401998i	$0.868316\pi$
$938$	−70.2770	−2.29463
$939$	−17.0704	−0.557073
$940$	0	0
$941$	43.3453	1.41301	0.706507	−	0.707706i	$-0.250270\pi$
$941$	43.3453	1.41301	0.706507	+	0.707706i	$0.250270\pi$
$942$	−130.193	−4.24192
$943$	−20.2065	−0.658013
$944$	−49.2506	−1.60297
$945$	0	0
$946$	7.03995	0.228889
$947$	13.9452	0.453158	0.226579	−	0.973993i	$-0.427246\pi$
$947$	13.9452	0.453158	0.226579	+	0.973993i	$0.427246\pi$
$948$	74.8552	2.43118
$949$	−7.39350	−0.240003
$950$	0	0
$951$	−60.5574	−1.96371
$952$	38.0863	1.23439
$953$	−50.4348	−1.63374	−0.816872	−	0.576819i	$-0.804294\pi$
$953$	−50.4348	−1.63374	−0.816872	+	0.576819i	$0.804294\pi$
$954$	178.123	5.76696
$955$	0	0
$956$	−19.5541	−0.632426
$957$	12.0711	0.390202
$958$	45.3921	1.46655
$959$	19.2475	0.621534
$960$	0	0
$961$	−30.2666	−0.976343
$962$	16.0152	0.516352
$963$	107.532	3.46518
$964$	−57.6704	−1.85744
$965$	0	0
$966$	92.4969	2.97604
$967$	41.3945	1.33116	0.665579	−	0.746328i	$-0.268185\pi$
$967$	41.3945	1.33116	0.665579	+	0.746328i	$0.268185\pi$
$968$	22.2869	0.716328
$969$	−12.7837	−0.410670
$970$	0	0
$971$	−24.3121	−0.780211	−0.390106	−	0.920770i	$-0.627562\pi$
$971$	−24.3121	−0.780211	−0.390106	+	0.920770i	$0.627562\pi$
$972$	41.5375	1.33231
$973$	23.4213	0.750852
$974$	−69.2023	−2.21739
$975$	0	0
$976$	52.0394	1.66574
$977$	25.4964	0.815701	0.407851	−	0.913049i	$-0.366278\pi$
$977$	25.4964	0.815701	0.407851	+	0.913049i	$0.366278\pi$
$978$	−163.318	−5.22234
$979$	9.34780	0.298757
$980$	0	0
$981$	−15.3672	−0.490638
$982$	−94.3856	−3.01197
$983$	6.55969	0.209221	0.104611	−	0.994513i	$-0.466640\pi$
$983$	6.55969	0.209221	0.104611	+	0.994513i	$0.466640\pi$
$984$	−142.424	−4.54030
$985$	0	0
$986$	4.86450	0.154917
$987$	21.8352	0.695021
$988$	45.7500	1.45550
$989$	2.67807	0.0851578
$990$	0	0
$991$	−15.7361	−0.499875	−0.249938	−	0.968262i	$-0.580410\pi$
$991$	−15.7361	−0.499875	−0.249938	+	0.968262i	$0.580410\pi$
$992$	−5.40734	−0.171683
$993$	27.1171	0.860535
$994$	−129.619	−4.11127
$995$	0	0
$996$	52.3929	1.66013
$997$	32.6204	1.03310	0.516550	−	0.856257i	$-0.327216\pi$
$997$	32.6204	1.03310	0.516550	+	0.856257i	$0.327216\pi$
$998$	83.6195	2.64693
$999$	−15.2802	−0.483445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.a.s.1.1		7
3.2	odd	2		9675.2.a.cn.1.7		7
5.2	odd	4		215.2.b.b.44.1	✓	14
5.3	odd	4		215.2.b.b.44.14	yes	14
5.4	even	2		1075.2.a.t.1.7		7
15.2	even	4		1935.2.b.d.1549.14		14
15.8	even	4		1935.2.b.d.1549.1		14
15.14	odd	2		9675.2.a.cm.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.b.b.44.1	✓	14	5.2	odd	4
215.2.b.b.44.14	yes	14	5.3	odd	4
1075.2.a.s.1.1		7	1.1	even	1	trivial
1075.2.a.t.1.7		7	5.4	even	2
1935.2.b.d.1549.1		14	15.8	even	4
1935.2.b.d.1549.14		14	15.2	even	4
9675.2.a.cm.1.1		7	15.14	odd	2
9675.2.a.cn.1.7		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55799 q^{2} -2.90146 q^{3} +4.54331 q^{4} +7.42190 q^{6} +4.65360 q^{7} -6.50577 q^{8} +5.41847 q^{9} +O(q^{10})\)	\(q-2.55799 q^{2} -2.90146 q^{3} +4.54331 q^{4} +7.42190 q^{6} +4.65360 q^{7} -6.50577 q^{8} +5.41847 q^{9} -2.75214 q^{11} -13.1822 q^{12} -2.87515 q^{13} -11.9039 q^{14} +7.55506 q^{16} -1.25800 q^{17} -13.8604 q^{18} -3.50233 q^{19} -13.5022 q^{21} +7.03995 q^{22} +2.67807 q^{23} +18.8762 q^{24} +7.35462 q^{26} -7.01708 q^{27} +21.1428 q^{28} +1.51167 q^{29} +0.856373 q^{31} -6.31424 q^{32} +7.98523 q^{33} +3.21796 q^{34} +24.6178 q^{36} +2.17758 q^{37} +8.95892 q^{38} +8.34215 q^{39} -7.54514 q^{41} +34.5386 q^{42} +1.00000 q^{43} -12.5038 q^{44} -6.85049 q^{46} -1.61715 q^{47} -21.9207 q^{48} +14.6560 q^{49} +3.65004 q^{51} -13.0627 q^{52} -12.8513 q^{53} +17.9496 q^{54} -30.2752 q^{56} +10.1619 q^{57} -3.86684 q^{58} -6.51889 q^{59} +6.88801 q^{61} -2.19059 q^{62} +25.2154 q^{63} +1.04163 q^{64} -20.4261 q^{66} +5.90371 q^{67} -5.71550 q^{68} -7.77032 q^{69} +10.8888 q^{71} -35.2513 q^{72} +2.57151 q^{73} -5.57022 q^{74} -15.9122 q^{76} -12.8074 q^{77} -21.3391 q^{78} -5.67849 q^{79} +4.10438 q^{81} +19.3004 q^{82} -3.97451 q^{83} -61.3449 q^{84} -2.55799 q^{86} -4.38606 q^{87} +17.9048 q^{88} -3.39656 q^{89} -13.3798 q^{91} +12.1673 q^{92} -2.48473 q^{93} +4.13666 q^{94} +18.3205 q^{96} -10.6929 q^{97} -37.4899 q^{98} -14.9124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 4 q^{2} - 5 q^{3} + 8 q^{4} + 4 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 7 * q - 4 * q^2 - 5 * q^3 + 8 * q^4 + 4 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9	\( 7 q - 4 q^{2} - 5 q^{3} + 8 q^{4} + 4 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9} + q^{11} - 23 q^{12} - 14 q^{13} - 17 q^{14} + 2 q^{16} - 12 q^{17} - 15 q^{18} - 4 q^{21} + 17 q^{22} - 18 q^{23} + 17 q^{24} + 12 q^{26} - 8 q^{27} + 2 q^{28} + 10 q^{29} - 15 q^{31} - 15 q^{32} - 20 q^{33} - 8 q^{34} + 32 q^{36} - 5 q^{37} - 4 q^{38} + 10 q^{39} - 21 q^{41} + 47 q^{42} + 7 q^{43} + 13 q^{44} + 4 q^{46} - 2 q^{47} - 33 q^{48} + 16 q^{49} + 16 q^{51} - 2 q^{52} - 42 q^{53} + 3 q^{54} - 28 q^{56} + 8 q^{57} - 30 q^{58} + 9 q^{59} + 4 q^{61} - 35 q^{62} + 8 q^{63} - 11 q^{64} - 24 q^{66} + 28 q^{67} - 30 q^{68} - 38 q^{69} + 2 q^{71} - 9 q^{72} - 11 q^{73} - 17 q^{74} - 36 q^{76} - 58 q^{77} + 2 q^{78} - 9 q^{79} - 25 q^{81} + 28 q^{82} - 12 q^{83} - 46 q^{84} - 4 q^{86} - 20 q^{87} + 14 q^{88} + 6 q^{89} + 42 q^{93} + 20 q^{94} + 40 q^{96} - 26 q^{97} - 13 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 5 * q^3 + 8 * q^4 + 4 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9 + q^11 - 23 * q^12 - 14 * q^13 - 17 * q^14 + 2 * q^16 - 12 * q^17 - 15 * q^18 - 4 * q^21 + 17 * q^22 - 18 * q^23 + 17 * q^24 + 12 * q^26 - 8 * q^27 + 2 * q^28 + 10 * q^29 - 15 * q^31 - 15 * q^32 - 20 * q^33 - 8 * q^34 + 32 * q^36 - 5 * q^37 - 4 * q^38 + 10 * q^39 - 21 * q^41 + 47 * q^42 + 7 * q^43 + 13 * q^44 + 4 * q^46 - 2 * q^47 - 33 * q^48 + 16 * q^49 + 16 * q^51 - 2 * q^52 - 42 * q^53 + 3 * q^54 - 28 * q^56 + 8 * q^57 - 30 * q^58 + 9 * q^59 + 4 * q^61 - 35 * q^62 + 8 * q^63 - 11 * q^64 - 24 * q^66 + 28 * q^67 - 30 * q^68 - 38 * q^69 + 2 * q^71 - 9 * q^72 - 11 * q^73 - 17 * q^74 - 36 * q^76 - 58 * q^77 + 2 * q^78 - 9 * q^79 - 25 * q^81 + 28 * q^82 - 12 * q^83 - 46 * q^84 - 4 * q^86 - 20 * q^87 + 14 * q^88 + 6 * q^89 + 42 * q^93 + 20 * q^94 + 40 * q^96 - 26 * q^97 - 13 * q^98 + 7 * q^99

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