LMFDB - Embedded newform 1550.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1550,2,Mod(1,1550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1550, 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("1550.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1550 = 2 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1550.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:	$12.3768123133$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.6224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 2x + 5 $ x^4 - 6x^2 - 2x + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 310)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.796815$ of defining polynomial
Character	$\chi$	$=$	1550.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.79682 q^{3} +1.00000 q^{4} -1.79682 q^{6} +3.47817 q^{7} +1.00000 q^{8} +0.228545 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.79682 q^{3} +1.00000 q^{4} -1.79682 q^{6} +3.47817 q^{7} +1.00000 q^{8} +0.228545 q^{9} -2.47063 q^{11} -1.79682 q^{12} -7.00754 q^{13} +3.47817 q^{14} +1.00000 q^{16} -5.40399 q^{17} +0.228545 q^{18} +0.480550 q^{19} -6.24962 q^{21} -2.47063 q^{22} +0.365086 q^{23} -1.79682 q^{24} -7.00754 q^{26} +4.97979 q^{27} +3.47817 q^{28} -0.00991953 q^{29} -1.00000 q^{31} +1.00000 q^{32} +4.43927 q^{33} -5.40399 q^{34} +0.228545 q^{36} -10.5270 q^{37} +0.480550 q^{38} +12.5912 q^{39} +9.63015 q^{41} -6.24962 q^{42} -5.72264 q^{43} -2.47063 q^{44} +0.365086 q^{46} -2.94328 q^{47} -1.79682 q^{48} +5.09764 q^{49} +9.70996 q^{51} -7.00754 q^{52} -6.60117 q^{53} +4.97979 q^{54} +3.47817 q^{56} -0.863459 q^{57} -0.00991953 q^{58} -10.9563 q^{59} +8.31388 q^{61} -1.00000 q^{62} +0.794916 q^{63} +1.00000 q^{64} +4.43927 q^{66} -7.01544 q^{67} -5.40399 q^{68} -0.655991 q^{69} +0.632531 q^{71} +0.228545 q^{72} -3.20871 q^{73} -10.5270 q^{74} +0.480550 q^{76} -8.59326 q^{77} +12.5912 q^{78} -13.5111 q^{79} -9.63340 q^{81} +9.63015 q^{82} +9.56589 q^{83} -6.24962 q^{84} -5.72264 q^{86} +0.0178236 q^{87} -2.47063 q^{88} +15.1516 q^{89} -24.3734 q^{91} +0.365086 q^{92} +1.79682 q^{93} -2.94328 q^{94} -1.79682 q^{96} -5.32981 q^{97} +5.09764 q^{98} -0.564649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 8 q^{11} - 4 q^{12} - 10 q^{13} - 6 q^{14} + 4 q^{16} - 4 q^{17} + 4 q^{18} + 6 q^{19} - 2 q^{21} - 8 q^{22} - 8 q^{23} - 4 q^{24} - 10 q^{26} - 22 q^{27} - 6 q^{28} - 6 q^{29} - 4 q^{31} + 4 q^{32} + 6 q^{33} - 4 q^{34} + 4 q^{36} - 20 q^{37} + 6 q^{38} + 20 q^{39} - 2 q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{46} - 2 q^{47} - 4 q^{48} + 16 q^{49} - 22 q^{51} - 10 q^{52} - 2 q^{53} - 22 q^{54} - 6 q^{56} - 16 q^{57} - 6 q^{58} - 4 q^{59} + 2 q^{61} - 4 q^{62} - 2 q^{63} + 4 q^{64} + 6 q^{66} - 22 q^{67} - 4 q^{68} + 14 q^{69} - 12 q^{71} + 4 q^{72} - 4 q^{73} - 20 q^{74} + 6 q^{76} + 2 q^{77} + 20 q^{78} - 16 q^{79} + 44 q^{81} + 8 q^{83} - 2 q^{84} - 22 q^{86} + 18 q^{87} - 8 q^{88} + 12 q^{89} - 10 q^{91} - 8 q^{92} + 4 q^{93} - 2 q^{94} - 4 q^{96} - 6 q^{97} + 16 q^{98} - 10 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 8 * q^11 - 4 * q^12 - 10 * q^13 - 6 * q^14 + 4 * q^16 - 4 * q^17 + 4 * q^18 + 6 * q^19 - 2 * q^21 - 8 * q^22 - 8 * q^23 - 4 * q^24 - 10 * q^26 - 22 * q^27 - 6 * q^28 - 6 * q^29 - 4 * q^31 + 4 * q^32 + 6 * q^33 - 4 * q^34 + 4 * q^36 - 20 * q^37 + 6 * q^38 + 20 * q^39 - 2 * q^42 - 22 * q^43 - 8 * q^44 - 8 * q^46 - 2 * q^47 - 4 * q^48 + 16 * q^49 - 22 * q^51 - 10 * q^52 - 2 * q^53 - 22 * q^54 - 6 * q^56 - 16 * q^57 - 6 * q^58 - 4 * q^59 + 2 * q^61 - 4 * q^62 - 2 * q^63 + 4 * q^64 + 6 * q^66 - 22 * q^67 - 4 * q^68 + 14 * q^69 - 12 * q^71 + 4 * q^72 - 4 * q^73 - 20 * q^74 + 6 * q^76 + 2 * q^77 + 20 * q^78 - 16 * q^79 + 44 * q^81 + 8 * q^83 - 2 * q^84 - 22 * q^86 + 18 * q^87 - 8 * q^88 + 12 * q^89 - 10 * q^91 - 8 * q^92 + 4 * q^93 - 2 * q^94 - 4 * q^96 - 6 * q^97 + 16 * q^98 - 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.79682	−1.03739	−0.518696	−	0.854959i	$-0.673582\pi$
$3$	−1.79682	−1.03739	−0.518696	+	0.854959i	$0.673582\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.79682	−0.733547
$7$	3.47817	1.31462	0.657312	−	0.753619i	$-0.271694\pi$
$7$	3.47817	1.31462	0.657312	+	0.753619i	$0.271694\pi$
$8$	1.00000	0.353553
$9$	0.228545	0.0761815
$10$	0	0
$11$	−2.47063	−0.744923	−0.372462	−	0.928048i	$-0.621486\pi$
$11$	−2.47063	−0.744923	−0.372462	+	0.928048i	$0.621486\pi$
$12$	−1.79682	−0.518696
$13$	−7.00754	−1.94354	−0.971770	−	0.235929i	$-0.924187\pi$
$13$	−7.00754	−1.94354	−0.971770	+	0.235929i	$0.924187\pi$
$14$	3.47817	0.929579
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.40399	−1.31066	−0.655330	−	0.755343i	$-0.727470\pi$
$17$	−5.40399	−1.31066	−0.655330	+	0.755343i	$0.727470\pi$
$18$	0.228545	0.0538685
$19$	0.480550	0.110246	0.0551228	−	0.998480i	$-0.482445\pi$
$19$	0.480550	0.110246	0.0551228	+	0.998480i	$0.482445\pi$
$20$	0	0
$21$	−6.24962	−1.36378
$22$	−2.47063	−0.526740
$23$	0.365086	0.0761256	0.0380628	−	0.999275i	$-0.487881\pi$
$23$	0.365086	0.0761256	0.0380628	+	0.999275i	$0.487881\pi$
$24$	−1.79682	−0.366773
$25$	0	0
$26$	−7.00754	−1.37429
$27$	4.97979	0.958362
$28$	3.47817	0.657312
$29$	−0.00991953	−0.00184201	−0.000921005	−	1.00000i	$-0.500293\pi$
$29$	−0.00991953	−0.00184201	−0.000921005		1.00000i	$0.500293\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	4.43927	0.772777
$34$	−5.40399	−0.926776
$35$	0	0
$36$	0.228545	0.0380908
$37$	−10.5270	−1.73063	−0.865313	−	0.501232i	$-0.832880\pi$
$37$	−10.5270	−1.73063	−0.865313	+	0.501232i	$0.832880\pi$
$38$	0.480550	0.0779554
$39$	12.5912	2.01621
$40$	0	0
$41$	9.63015	1.50398	0.751988	−	0.659177i	$-0.229095\pi$
$41$	9.63015	1.50398	0.751988	+	0.659177i	$0.229095\pi$
$42$	−6.24962	−0.964338
$43$	−5.72264	−0.872694	−0.436347	−	0.899779i	$-0.643728\pi$
$43$	−5.72264	−0.872694	−0.436347	+	0.899779i	$0.643728\pi$
$44$	−2.47063	−0.372462
$45$	0	0
$46$	0.365086	0.0538289
$47$	−2.94328	−0.429321	−0.214660	−	0.976689i	$-0.568864\pi$
$47$	−2.94328	−0.429321	−0.214660	+	0.976689i	$0.568864\pi$
$48$	−1.79682	−0.259348
$49$	5.09764	0.728234
$50$	0	0
$51$	9.70996	1.35967
$52$	−7.00754	−0.971770
$53$	−6.60117	−0.906740	−0.453370	−	0.891322i	$-0.649778\pi$
$53$	−6.60117	−0.906740	−0.453370	+	0.891322i	$0.649778\pi$
$54$	4.97979	0.677664
$55$	0	0
$56$	3.47817	0.464790
$57$	−0.863459	−0.114368
$58$	−0.00991953	−0.00130250
$59$	−10.9563	−1.42639	−0.713196	−	0.700964i	$-0.752753\pi$
$59$	−10.9563	−1.42639	−0.713196	+	0.700964i	$0.752753\pi$
$60$	0	0
$61$	8.31388	1.06448	0.532242	−	0.846592i	$-0.321350\pi$
$61$	8.31388	1.06448	0.532242	+	0.846592i	$0.321350\pi$
$62$	−1.00000	−0.127000
$63$	0.794916	0.100150
$64$	1.00000	0.125000
$65$	0	0
$66$	4.43927	0.546436
$67$	−7.01544	−0.857072	−0.428536	−	0.903525i	$-0.640971\pi$
$67$	−7.01544	−0.857072	−0.428536	+	0.903525i	$0.640971\pi$
$68$	−5.40399	−0.655330
$69$	−0.655991	−0.0789721
$70$	0	0
$71$	0.632531	0.0750676	0.0375338	−	0.999295i	$-0.488050\pi$
$71$	0.632531	0.0750676	0.0375338	+	0.999295i	$0.488050\pi$
$72$	0.228545	0.0269342
$73$	−3.20871	−0.375551	−0.187775	−	0.982212i	$-0.560128\pi$
$73$	−3.20871	−0.375551	−0.187775	+	0.982212i	$0.560128\pi$
$74$	−10.5270	−1.22374
$75$	0	0
$76$	0.480550	0.0551228
$77$	−8.59326	−0.979293
$78$	12.5912	1.42568
$79$	−13.5111	−1.52011	−0.760057	−	0.649857i	$-0.774829\pi$
$79$	−13.5111	−1.52011	−0.760057	+	0.649857i	$0.774829\pi$
$80$	0	0
$81$	−9.63340	−1.07038
$82$	9.63015	1.06347
$83$	9.56589	1.04999	0.524996	−	0.851105i	$-0.324067\pi$
$83$	9.56589	1.04999	0.524996	+	0.851105i	$0.324067\pi$
$84$	−6.24962	−0.681890
$85$	0	0
$86$	−5.72264	−0.617088
$87$	0.0178236	0.00191089
$88$	−2.47063	−0.263370
$89$	15.1516	1.60607	0.803034	−	0.595933i	$-0.203218\pi$
$89$	15.1516	1.60607	0.803034	+	0.595933i	$0.203218\pi$
$90$	0	0
$91$	−24.3734	−2.55502
$92$	0.365086	0.0380628
$93$	1.79682	0.186321
$94$	−2.94328	−0.303576
$95$	0	0
$96$	−1.79682	−0.183387
$97$	−5.32981	−0.541160	−0.270580	−	0.962698i	$-0.587215\pi$
$97$	−5.32981	−0.541160	−0.270580	+	0.962698i	$0.587215\pi$
$98$	5.09764	0.514939
$99$	−0.564649	−0.0567494
$100$	0	0
$101$	−0.300341	−0.0298851	−0.0149425	−	0.999888i	$-0.504757\pi$
$101$	−0.300341	−0.0298851	−0.0149425	+	0.999888i	$0.504757\pi$
$102$	9.70996	0.961430
$103$	−2.50401	−0.246727	−0.123364	−	0.992362i	$-0.539368\pi$
$103$	−2.50401	−0.246727	−0.123364	+	0.992362i	$0.539368\pi$
$104$	−7.00754	−0.687145
$105$	0	0
$106$	−6.60117	−0.641162
$107$	−13.4369	−1.29899	−0.649496	−	0.760365i	$-0.725020\pi$
$107$	−13.4369	−1.29899	−0.649496	+	0.760365i	$0.725020\pi$
$108$	4.97979	0.479181
$109$	−0.706711	−0.0676906	−0.0338453	−	0.999427i	$-0.510775\pi$
$109$	−0.706711	−0.0676906	−0.0338453	+	0.999427i	$0.510775\pi$
$110$	0	0
$111$	18.9150	1.79534
$112$	3.47817	0.328656
$113$	7.55597	0.710806	0.355403	−	0.934713i	$-0.384344\pi$
$113$	7.55597	0.710806	0.355403	+	0.934713i	$0.384344\pi$
$114$	−0.863459	−0.0808703
$115$	0	0
$116$	−0.00991953	−0.000921005 0
$117$	−1.60153	−0.148062
$118$	−10.9563	−1.00861
$119$	−18.7960	−1.72302
$120$	0	0
$121$	−4.89599	−0.445090
$122$	8.31388	0.752704
$123$	−17.3036	−1.56021
$124$	−1.00000	−0.0898027
$125$	0	0
$126$	0.794916	0.0708167
$127$	−17.9389	−1.59182	−0.795909	−	0.605416i	$-0.793007\pi$
$127$	−17.9389	−1.59182	−0.795909	+	0.605416i	$0.793007\pi$
$128$	1.00000	0.0883883
$129$	10.2825	0.905325
$130$	0	0
$131$	2.15198	0.188019	0.0940097	−	0.995571i	$-0.470032\pi$
$131$	2.15198	0.188019	0.0940097	+	0.995571i	$0.470032\pi$
$132$	4.43927	0.386388
$133$	1.67143	0.144932
$134$	−7.01544	−0.606042
$135$	0	0
$136$	−5.40399	−0.463388
$137$	10.3651	0.885549	0.442775	−	0.896633i	$-0.353994\pi$
$137$	10.3651	0.885549	0.442775	+	0.896633i	$0.353994\pi$
$138$	−0.655991	−0.0558417
$139$	14.0250	1.18958	0.594792	−	0.803880i	$-0.297234\pi$
$139$	14.0250	1.18958	0.594792	+	0.803880i	$0.297234\pi$
$140$	0	0
$141$	5.28852	0.445374
$142$	0.632531	0.0530808
$143$	17.3130	1.44779
$144$	0.228545	0.0190454
$145$	0	0
$146$	−3.20871	−0.265554
$147$	−9.15952	−0.755464
$148$	−10.5270	−0.865313
$149$	−20.5301	−1.68189	−0.840947	−	0.541118i	$-0.818001\pi$
$149$	−20.5301	−1.68189	−0.840947	+	0.541118i	$0.818001\pi$
$150$	0	0
$151$	−11.0849	−0.902073	−0.451036	−	0.892506i	$-0.648946\pi$
$151$	−11.0849	−0.902073	−0.451036	+	0.892506i	$0.648946\pi$
$152$	0.480550	0.0389777
$153$	−1.23505	−0.0998480
$154$	−8.59326	−0.692465
$155$	0	0
$156$	12.5912	1.00811
$157$	15.3976	1.22886	0.614432	−	0.788970i	$-0.289385\pi$
$157$	15.3976	1.22886	0.614432	+	0.788970i	$0.289385\pi$
$158$	−13.5111	−1.07488
$159$	11.8611	0.940644
$160$	0	0
$161$	1.26983	0.100077
$162$	−9.63340	−0.756871
$163$	−17.9325	−1.40458	−0.702291	−	0.711890i	$-0.747839\pi$
$163$	−17.9325	−1.40458	−0.702291	+	0.711890i	$0.747839\pi$
$164$	9.63015	0.751988
$165$	0	0
$166$	9.56589	0.742457
$167$	12.9658	1.00332	0.501661	−	0.865065i	$-0.332723\pi$
$167$	12.9658	1.00332	0.501661	+	0.865065i	$0.332723\pi$
$168$	−6.24962	−0.482169
$169$	36.1056	2.77735
$170$	0	0
$171$	0.109827	0.00839868
$172$	−5.72264	−0.436347
$173$	6.51908	0.495637	0.247818	−	0.968807i	$-0.420286\pi$
$173$	6.51908	0.495637	0.247818	+	0.968807i	$0.420286\pi$
$174$	0.0178236	0.00135120
$175$	0	0
$176$	−2.47063	−0.186231
$177$	19.6865	1.47973
$178$	15.1516	1.13566
$179$	14.2820	1.06749	0.533745	−	0.845646i	$-0.320784\pi$
$179$	14.2820	1.06749	0.533745	+	0.845646i	$0.320784\pi$
$180$	0	0
$181$	−6.92295	−0.514579	−0.257290	−	0.966334i	$-0.582829\pi$
$181$	−6.92295	−0.514579	−0.257290	+	0.966334i	$0.582829\pi$
$182$	−24.3734	−1.80667
$183$	−14.9385	−1.10429
$184$	0.365086	0.0269145
$185$	0	0
$186$	1.79682	0.131749
$187$	13.3513	0.976340
$188$	−2.94328	−0.214660
$189$	17.3205	1.25988
$190$	0	0
$191$	−7.17783	−0.519369	−0.259685	−	0.965693i	$-0.583619\pi$
$191$	−7.17783	−0.519369	−0.259685	+	0.965693i	$0.583619\pi$
$192$	−1.79682	−0.129674
$193$	9.63958	0.693872	0.346936	−	0.937889i	$-0.387222\pi$
$193$	9.63958	0.693872	0.346936	+	0.937889i	$0.387222\pi$
$194$	−5.32981	−0.382658
$195$	0	0
$196$	5.09764	0.364117
$197$	14.8309	1.05666	0.528331	−	0.849039i	$-0.322818\pi$
$197$	14.8309	1.05666	0.528331	+	0.849039i	$0.322818\pi$
$198$	−0.564649	−0.0401279
$199$	9.18726	0.651268	0.325634	−	0.945496i	$-0.394422\pi$
$199$	9.18726	0.651268	0.325634	+	0.945496i	$0.394422\pi$
$200$	0	0
$201$	12.6054	0.889120
$202$	−0.300341	−0.0211319
$203$	−0.0345018	−0.00242155
$204$	9.70996	0.679833
$205$	0	0
$206$	−2.50401	−0.174463
$207$	0.0834383	0.00579937
$208$	−7.00754	−0.485885
$209$	−1.18726	−0.0821245
$210$	0	0
$211$	7.97177	0.548799	0.274400	−	0.961616i	$-0.411521\pi$
$211$	7.97177	0.548799	0.274400	+	0.961616i	$0.411521\pi$
$212$	−6.60117	−0.453370
$213$	−1.13654	−0.0778745
$214$	−13.4369	−0.918526
$215$	0	0
$216$	4.97979	0.338832
$217$	−3.47817	−0.236113
$218$	−0.706711	−0.0478645
$219$	5.76545	0.389593
$220$	0	0
$221$	37.8686	2.54732
$222$	18.9150	1.26949
$223$	23.2190	1.55486	0.777430	−	0.628969i	$-0.216523\pi$
$223$	23.2190	1.55486	0.777430	+	0.628969i	$0.216523\pi$
$224$	3.47817	0.232395
$225$	0	0
$226$	7.55597	0.502615
$227$	1.88252	0.124947	0.0624736	−	0.998047i	$-0.480101\pi$
$227$	1.88252	0.124947	0.0624736	+	0.998047i	$0.480101\pi$
$228$	−0.863459	−0.0571840
$229$	−11.9472	−0.789493	−0.394746	−	0.918790i	$-0.629168\pi$
$229$	−11.9472	−0.789493	−0.394746	+	0.918790i	$0.629168\pi$
$230$	0	0
$231$	15.4405	1.01591
$232$	−0.00991953	−0.000651249 0
$233$	10.4393	0.683899	0.341950	−	0.939718i	$-0.388913\pi$
$233$	10.4393	0.683899	0.341950	+	0.939718i	$0.388913\pi$
$234$	−1.60153	−0.104696
$235$	0	0
$236$	−10.9563	−0.713196
$237$	24.2769	1.57695
$238$	−18.7960	−1.21836
$239$	5.47615	0.354223	0.177111	−	0.984191i	$-0.443325\pi$
$239$	5.47615	0.354223	0.177111	+	0.984191i	$0.443325\pi$
$240$	0	0
$241$	5.73722	0.369567	0.184784	−	0.982779i	$-0.440842\pi$
$241$	5.73722	0.369567	0.184784	+	0.982779i	$0.440842\pi$
$242$	−4.89599	−0.314726
$243$	2.37006	0.152040
$244$	8.31388	0.532242
$245$	0	0
$246$	−17.3036	−1.10324
$247$	−3.36747	−0.214267
$248$	−1.00000	−0.0635001
$249$	−17.1881	−1.08925
$250$	0	0
$251$	0.881767	0.0556566	0.0278283	−	0.999613i	$-0.491141\pi$
$251$	0.881767	0.0556566	0.0278283	+	0.999613i	$0.491141\pi$
$252$	0.794916	0.0500750
$253$	−0.901992	−0.0567077
$254$	−17.9389	−1.12559
$255$	0	0
$256$	1.00000	0.0625000
$257$	−24.6079	−1.53500	−0.767500	−	0.641049i	$-0.778500\pi$
$257$	−24.6079	−1.53500	−0.767500	+	0.641049i	$0.778500\pi$
$258$	10.2825	0.640162
$259$	−36.6146	−2.27512
$260$	0	0
$261$	−0.00226705	−0.000140327 0
$262$	2.15198	0.132950
$263$	12.9818	0.800493	0.400246	−	0.916408i	$-0.368925\pi$
$263$	12.9818	0.800493	0.400246	+	0.916408i	$0.368925\pi$
$264$	4.43927	0.273218
$265$	0	0
$266$	1.67143	0.102482
$267$	−27.2246	−1.66612
$268$	−7.01544	−0.428536
$269$	12.6611	0.771964	0.385982	−	0.922506i	$-0.373863\pi$
$269$	12.6611	0.771964	0.385982	+	0.922506i	$0.373863\pi$
$270$	0	0
$271$	−4.60165	−0.279530	−0.139765	−	0.990185i	$-0.544635\pi$
$271$	−4.60165	−0.279530	−0.139765	+	0.990185i	$0.544635\pi$
$272$	−5.40399	−0.327665
$273$	43.7944	2.65056
$274$	10.3651	0.626178
$275$	0	0
$276$	−0.655991	−0.0394860
$277$	11.7734	0.707392	0.353696	−	0.935360i	$-0.384925\pi$
$277$	11.7734	0.707392	0.353696	+	0.935360i	$0.384925\pi$
$278$	14.0250	0.841163
$279$	−0.228545	−0.0136826
$280$	0	0
$281$	−28.3293	−1.68999	−0.844993	−	0.534777i	$-0.820396\pi$
$281$	−28.3293	−1.68999	−0.844993	+	0.534777i	$0.820396\pi$
$282$	5.28852	0.314927
$283$	−22.2992	−1.32555	−0.662775	−	0.748819i	$-0.730621\pi$
$283$	−22.2992	−1.32555	−0.662775	+	0.748819i	$0.730621\pi$
$284$	0.632531	0.0375338
$285$	0	0
$286$	17.3130	1.02374
$287$	33.4953	1.97716
$288$	0.228545	0.0134671
$289$	12.2031	0.717828
$290$	0	0
$291$	9.57668	0.561395
$292$	−3.20871	−0.187775
$293$	−10.5227	−0.614743	−0.307371	−	0.951590i	$-0.599449\pi$
$293$	−10.5227	−0.614743	−0.307371	+	0.951590i	$0.599449\pi$
$294$	−9.15952	−0.534194
$295$	0	0
$296$	−10.5270	−0.611869
$297$	−12.3032	−0.713906
$298$	−20.5301	−1.18928
$299$	−2.55835	−0.147953
$300$	0	0
$301$	−19.9043	−1.14726
$302$	−11.0849	−0.637862
$303$	0.539657	0.0310025
$304$	0.480550	0.0275614
$305$	0	0
$306$	−1.23505	−0.0706032
$307$	−25.5955	−1.46082	−0.730408	−	0.683012i	$-0.760670\pi$
$307$	−25.5955	−1.46082	−0.730408	+	0.683012i	$0.760670\pi$
$308$	−8.59326	−0.489647
$309$	4.49924	0.255953
$310$	0	0
$311$	21.0492	1.19359	0.596795	−	0.802393i	$-0.296440\pi$
$311$	21.0492	1.19359	0.596795	+	0.802393i	$0.296440\pi$
$312$	12.5912	0.712839
$313$	−15.6658	−0.885483	−0.442742	−	0.896649i	$-0.645994\pi$
$313$	−15.6658	−0.885483	−0.442742	+	0.896649i	$0.645994\pi$
$314$	15.3976	0.868938
$315$	0	0
$316$	−13.5111	−0.760057
$317$	23.8928	1.34195	0.670977	−	0.741478i	$-0.265875\pi$
$317$	23.8928	1.34195	0.670977	+	0.741478i	$0.265875\pi$
$318$	11.8611	0.665136
$319$	0.0245075	0.00137216
$320$	0	0
$321$	24.1436	1.34756
$322$	1.26983	0.0707648
$323$	−2.59688	−0.144494
$324$	−9.63340	−0.535189
$325$	0	0
$326$	−17.9325	−0.993190
$327$	1.26983	0.0702217
$328$	9.63015	0.531736
$329$	−10.2372	−0.564395
$330$	0	0
$331$	0.617845	0.0339598	0.0169799	−	0.999856i	$-0.494595\pi$
$331$	0.617845	0.0339598	0.0169799	+	0.999856i	$0.494595\pi$
$332$	9.56589	0.524996
$333$	−2.40589	−0.131842
$334$	12.9658	0.709455
$335$	0	0
$336$	−6.24962	−0.340945
$337$	20.6992	1.12756	0.563778	−	0.825926i	$-0.309347\pi$
$337$	20.6992	1.12756	0.563778	+	0.825926i	$0.309347\pi$
$338$	36.1056	1.96388
$339$	−13.5767	−0.737384
$340$	0	0
$341$	2.47063	0.133792
$342$	0.109827	0.00593876
$343$	−6.61672	−0.357269
$344$	−5.72264	−0.308544
$345$	0	0
$346$	6.51908	0.350468
$347$	33.0611	1.77482	0.887408	−	0.460986i	$-0.152504\pi$
$347$	33.0611	1.77482	0.887408	+	0.460986i	$0.152504\pi$
$348$	0.0178236	0.000955443 0
$349$	7.31198	0.391401	0.195701	−	0.980664i	$-0.437302\pi$
$349$	7.31198	0.391401	0.195701	+	0.980664i	$0.437302\pi$
$350$	0	0
$351$	−34.8961	−1.86261
$352$	−2.47063	−0.131685
$353$	21.7429	1.15726	0.578628	−	0.815592i	$-0.303588\pi$
$353$	21.7429	1.15726	0.578628	+	0.815592i	$0.303588\pi$
$354$	19.6865	1.04633
$355$	0	0
$356$	15.1516	0.803034
$357$	33.7729	1.78745
$358$	14.2820	0.754829
$359$	−7.72054	−0.407475	−0.203737	−	0.979026i	$-0.565309\pi$
$359$	−7.72054	−0.407475	−0.203737	+	0.979026i	$0.565309\pi$
$360$	0	0
$361$	−18.7691	−0.987846
$362$	−6.92295	−0.363862
$363$	8.79718	0.461732
$364$	−24.3734	−1.27751
$365$	0	0
$366$	−14.9385	−0.780848
$367$	−23.0325	−1.20229	−0.601144	−	0.799141i	$-0.705288\pi$
$367$	−23.0325	−1.20229	−0.601144	+	0.799141i	$0.705288\pi$
$368$	0.365086	0.0190314
$369$	2.20092	0.114575
$370$	0	0
$371$	−22.9600	−1.19202
$372$	1.79682	0.0931605
$373$	7.35528	0.380842	0.190421	−	0.981703i	$-0.439015\pi$
$373$	7.35528	0.380842	0.190421	+	0.981703i	$0.439015\pi$
$374$	13.3513	0.690377
$375$	0	0
$376$	−2.94328	−0.151788
$377$	0.0695115	0.00358002
$378$	17.3205	0.890873
$379$	19.3928	0.996144	0.498072	−	0.867136i	$-0.334042\pi$
$379$	19.3928	0.996144	0.498072	+	0.867136i	$0.334042\pi$
$380$	0	0
$381$	32.2328	1.65134
$382$	−7.17783	−0.367249
$383$	13.1111	0.669944	0.334972	−	0.942228i	$-0.391273\pi$
$383$	13.1111	0.669944	0.334972	+	0.942228i	$0.391273\pi$
$384$	−1.79682	−0.0916933
$385$	0	0
$386$	9.63958	0.490642
$387$	−1.30788	−0.0664831
$388$	−5.32981	−0.270580
$389$	−8.76355	−0.444330	−0.222165	−	0.975009i	$-0.571312\pi$
$389$	−8.76355	−0.444330	−0.222165	+	0.975009i	$0.571312\pi$
$390$	0	0
$391$	−1.97292	−0.0997748
$392$	5.09764	0.257470
$393$	−3.86671	−0.195050
$394$	14.8309	0.747172
$395$	0	0
$396$	−0.564649	−0.0283747
$397$	−22.2056	−1.11447	−0.557233	−	0.830356i	$-0.688137\pi$
$397$	−22.2056	−1.11447	−0.557233	+	0.830356i	$0.688137\pi$
$398$	9.18726	0.460516
$399$	−3.00325	−0.150351
$400$	0	0
$401$	−5.65942	−0.282618	−0.141309	−	0.989966i	$-0.545131\pi$
$401$	−5.65942	−0.282618	−0.141309	+	0.989966i	$0.545131\pi$
$402$	12.6054	0.628703
$403$	7.00754	0.349070
$404$	−0.300341	−0.0149425
$405$	0	0
$406$	−0.0345018	−0.00171229
$407$	26.0083	1.28918
$408$	9.70996	0.480715
$409$	−13.2801	−0.656660	−0.328330	−	0.944563i	$-0.606486\pi$
$409$	−13.2801	−0.656660	−0.328330	+	0.944563i	$0.606486\pi$
$410$	0	0
$411$	−18.6241	−0.918661
$412$	−2.50401	−0.123364
$413$	−38.1079	−1.87517
$414$	0.0834383	0.00410077
$415$	0	0
$416$	−7.00754	−0.343573
$417$	−25.2003	−1.23406
$418$	−1.18726	−0.0580708
$419$	18.8268	0.919751	0.459876	−	0.887983i	$-0.347894\pi$
$419$	18.8268	0.919751	0.459876	+	0.887983i	$0.347894\pi$
$420$	0	0
$421$	16.6627	0.812089	0.406045	−	0.913853i	$-0.366908\pi$
$421$	16.6627	0.812089	0.406045	+	0.913853i	$0.366908\pi$
$422$	7.97177	0.388060
$423$	−0.672670	−0.0327063
$424$	−6.60117	−0.320581
$425$	0	0
$426$	−1.13654	−0.0550656
$427$	28.9171	1.39939
$428$	−13.4369	−0.649496
$429$	−31.1083	−1.50192
$430$	0	0
$431$	−30.2936	−1.45919	−0.729595	−	0.683880i	$-0.760291\pi$
$431$	−30.2936	−1.45919	−0.729595	+	0.683880i	$0.760291\pi$
$432$	4.97979	0.239590
$433$	−10.7913	−0.518597	−0.259298	−	0.965797i	$-0.583491\pi$
$433$	−10.7913	−0.518597	−0.259298	+	0.965797i	$0.583491\pi$
$434$	−3.47817	−0.166957
$435$	0	0
$436$	−0.706711	−0.0338453
$437$	0.175442	0.00839252
$438$	5.76545	0.275484
$439$	8.47303	0.404396	0.202198	−	0.979345i	$-0.435192\pi$
$439$	8.47303	0.404396	0.202198	+	0.979345i	$0.435192\pi$
$440$	0	0
$441$	1.16504	0.0554780
$442$	37.8686	1.80123
$443$	−35.8921	−1.70528	−0.852642	−	0.522495i	$-0.825001\pi$
$443$	−35.8921	−1.70528	−0.852642	+	0.522495i	$0.825001\pi$
$444$	18.9150	0.897668
$445$	0	0
$446$	23.2190	1.09945
$447$	36.8888	1.74478
$448$	3.47817	0.164328
$449$	−17.3271	−0.817714	−0.408857	−	0.912598i	$-0.634073\pi$
$449$	−17.3271	−0.817714	−0.408857	+	0.912598i	$0.634073\pi$
$450$	0	0
$451$	−23.7925	−1.12035
$452$	7.55597	0.355403
$453$	19.9174	0.935803
$454$	1.88252	0.0883511
$455$	0	0
$456$	−0.863459	−0.0404352
$457$	20.0674	0.938713	0.469357	−	0.883009i	$-0.344486\pi$
$457$	20.0674	0.938713	0.469357	+	0.883009i	$0.344486\pi$
$458$	−11.9472	−0.558256
$459$	−26.9107	−1.25609
$460$	0	0
$461$	−10.2586	−0.477789	−0.238895	−	0.971045i	$-0.576785\pi$
$461$	−10.2586	−0.477789	−0.238895	+	0.971045i	$0.576785\pi$
$462$	15.4405	0.718357
$463$	0.766689	0.0356310	0.0178155	−	0.999841i	$-0.494329\pi$
$463$	0.766689	0.0356310	0.0178155	+	0.999841i	$0.494329\pi$
$464$	−0.00991953	−0.000460503 0
$465$	0	0
$466$	10.4393	0.483590
$467$	−21.4273	−0.991539	−0.495770	−	0.868454i	$-0.665114\pi$
$467$	−21.4273	−0.991539	−0.495770	+	0.868454i	$0.665114\pi$
$468$	−1.60153	−0.0740309
$469$	−24.4009	−1.12673
$470$	0	0
$471$	−27.6667	−1.27481
$472$	−10.9563	−0.504306
$473$	14.1385	0.650090
$474$	24.2769	1.11507
$475$	0	0
$476$	−18.7960	−0.861512
$477$	−1.50866	−0.0690768
$478$	5.47615	0.250473
$479$	−29.6667	−1.35550	−0.677752	−	0.735290i	$-0.737046\pi$
$479$	−29.6667	−1.35550	−0.677752	+	0.735290i	$0.737046\pi$
$480$	0	0
$481$	73.7682	3.36354
$482$	5.73722	0.261323
$483$	−2.28165	−0.103819
$484$	−4.89599	−0.222545
$485$	0	0
$486$	2.37006	0.107508
$487$	25.8096	1.16955	0.584773	−	0.811197i	$-0.301184\pi$
$487$	25.8096	1.16955	0.584773	+	0.811197i	$0.301184\pi$
$488$	8.31388	0.376352
$489$	32.2214	1.45710
$490$	0	0
$491$	−18.7250	−0.845048	−0.422524	−	0.906352i	$-0.638856\pi$
$491$	−18.7250	−0.845048	−0.422524	+	0.906352i	$0.638856\pi$
$492$	−17.3036	−0.780106
$493$	0.0536050	0.00241425
$494$	−3.36747	−0.151510
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	2.20005	0.0986856
$498$	−17.1881	−0.770219
$499$	41.9722	1.87893	0.939466	−	0.342642i	$-0.111322\pi$
$499$	41.9722	1.87893	0.939466	+	0.342642i	$0.111322\pi$
$500$	0	0
$501$	−23.2971	−1.04084
$502$	0.881767	0.0393552
$503$	30.3436	1.35296	0.676478	−	0.736463i	$-0.263505\pi$
$503$	30.3436	1.35296	0.676478	+	0.736463i	$0.263505\pi$
$504$	0.794916	0.0354084
$505$	0	0
$506$	−0.901992	−0.0400984
$507$	−64.8750	−2.88120
$508$	−17.9389	−0.795909
$509$	−25.3183	−1.12221	−0.561107	−	0.827744i	$-0.689624\pi$
$509$	−25.3183	−1.12221	−0.561107	+	0.827744i	$0.689624\pi$
$510$	0	0
$511$	−11.1604	−0.493708
$512$	1.00000	0.0441942
$513$	2.39304	0.105655
$514$	−24.6079	−1.08541
$515$	0	0
$516$	10.2825	0.452663
$517$	7.27175	0.319811
$518$	−36.6146	−1.60875
$519$	−11.7136	−0.514169
$520$	0	0
$521$	7.15235	0.313350	0.156675	−	0.987650i	$-0.449922\pi$
$521$	7.15235	0.313350	0.156675	+	0.987650i	$0.449922\pi$
$522$	−0.00226705	−9.92263e−5 0
$523$	−20.5035	−0.896557	−0.448278	−	0.893894i	$-0.647963\pi$
$523$	−20.5035	−0.896557	−0.448278	+	0.893894i	$0.647963\pi$
$524$	2.15198	0.0940097
$525$	0	0
$526$	12.9818	0.566034
$527$	5.40399	0.235401
$528$	4.43927	0.193194
$529$	−22.8667	−0.994205
$530$	0	0
$531$	−2.50401	−0.108665
$532$	1.67143	0.0724658
$533$	−67.4836	−2.92304
$534$	−27.2246	−1.17813
$535$	0	0
$536$	−7.01544	−0.303021
$537$	−25.6622	−1.10740
$538$	12.6611	0.545861
$539$	−12.5944	−0.542479
$540$	0	0
$541$	17.0504	0.733052	0.366526	−	0.930408i	$-0.380547\pi$
$541$	17.0504	0.733052	0.366526	+	0.930408i	$0.380547\pi$
$542$	−4.60165	−0.197658
$543$	12.4393	0.533820
$544$	−5.40399	−0.231694
$545$	0	0
$546$	43.7944	1.87423
$547$	−19.3000	−0.825207	−0.412604	−	0.910911i	$-0.635381\pi$
$547$	−19.3000	−0.825207	−0.412604	+	0.910911i	$0.635381\pi$
$548$	10.3651	0.442775
$549$	1.90009	0.0810940
$550$	0	0
$551$	−0.00476683	−0.000203074 0
$552$	−0.655991	−0.0279209
$553$	−46.9937	−1.99838
$554$	11.7734	0.500202
$555$	0	0
$556$	14.0250	0.594792
$557$	−12.9913	−0.550460	−0.275230	−	0.961378i	$-0.588754\pi$
$557$	−12.9913	−0.550460	−0.275230	+	0.961378i	$0.588754\pi$
$558$	−0.228545	−0.00967506
$559$	40.1016	1.69612
$560$	0	0
$561$	−23.9897	−1.01285
$562$	−28.3293	−1.19500
$563$	−17.6480	−0.743773	−0.371887	−	0.928278i	$-0.621289\pi$
$563$	−17.6480	−0.743773	−0.371887	+	0.928278i	$0.621289\pi$
$564$	5.28852	0.222687
$565$	0	0
$566$	−22.2992	−0.937305
$567$	−33.5066	−1.40714
$568$	0.632531	0.0265404
$569$	16.5151	0.692347	0.346173	−	0.938171i	$-0.387481\pi$
$569$	16.5151	0.692347	0.346173	+	0.938171i	$0.387481\pi$
$570$	0	0
$571$	−34.8517	−1.45850	−0.729248	−	0.684249i	$-0.760130\pi$
$571$	−34.8517	−1.45850	−0.729248	+	0.684249i	$0.760130\pi$
$572$	17.3130	0.723894
$573$	12.8972	0.538789
$574$	33.4953	1.39806
$575$	0	0
$576$	0.228545	0.00952269
$577$	14.2440	0.592985	0.296492	−	0.955035i	$-0.404183\pi$
$577$	14.2440	0.592985	0.296492	+	0.955035i	$0.404183\pi$
$578$	12.2031	0.507581
$579$	−17.3205	−0.719817
$580$	0	0
$581$	33.2717	1.38034
$582$	9.57668	0.396966
$583$	16.3090	0.675451
$584$	−3.20871	−0.132777
$585$	0	0
$586$	−10.5227	−0.434689
$587$	12.2766	0.506711	0.253355	−	0.967373i	$-0.418466\pi$
$587$	12.2766	0.506711	0.253355	+	0.967373i	$0.418466\pi$
$588$	−9.15952	−0.377732
$589$	−0.480550	−0.0198007
$590$	0	0
$591$	−26.6485	−1.09617
$592$	−10.5270	−0.432656
$593$	42.1988	1.73290	0.866449	−	0.499266i	$-0.166397\pi$
$593$	42.1988	1.73290	0.866449	+	0.499266i	$0.166397\pi$
$594$	−12.3032	−0.504808
$595$	0	0
$596$	−20.5301	−0.840947
$597$	−16.5078	−0.675620
$598$	−2.55835	−0.104619
$599$	−8.14997	−0.332999	−0.166499	−	0.986042i	$-0.553246\pi$
$599$	−8.14997	−0.332999	−0.166499	+	0.986042i	$0.553246\pi$
$600$	0	0
$601$	14.6953	0.599432	0.299716	−	0.954028i	$-0.403108\pi$
$601$	14.6953	0.599432	0.299716	+	0.954028i	$0.403108\pi$
$602$	−19.9043	−0.811238
$603$	−1.60334	−0.0652931
$604$	−11.0849	−0.451036
$605$	0	0
$606$	0.539657	0.0219221
$607$	−7.18249	−0.291528	−0.145764	−	0.989319i	$-0.546564\pi$
$607$	−7.18249	−0.291528	−0.145764	+	0.989319i	$0.546564\pi$
$608$	0.480550	0.0194889
$609$	0.0619933	0.00251210
$610$	0	0
$611$	20.6251	0.834403
$612$	−1.23505	−0.0499240
$613$	4.55787	0.184091	0.0920453	−	0.995755i	$-0.470660\pi$
$613$	4.55787	0.184091	0.0920453	+	0.995755i	$0.470660\pi$
$614$	−25.5955	−1.03295
$615$	0	0
$616$	−8.59326	−0.346232
$617$	−12.5698	−0.506041	−0.253021	−	0.967461i	$-0.581424\pi$
$617$	−12.5698	−0.506041	−0.253021	+	0.967461i	$0.581424\pi$
$618$	4.49924	0.180986
$619$	−12.3888	−0.497948	−0.248974	−	0.968510i	$-0.580093\pi$
$619$	−12.3888	−0.497948	−0.248974	+	0.968510i	$0.580093\pi$
$620$	0	0
$621$	1.81805	0.0729559
$622$	21.0492	0.843996
$623$	52.6998	2.11137
$624$	12.5912	0.504053
$625$	0	0
$626$	−15.6658	−0.626131
$627$	2.13329	0.0851953
$628$	15.3976	0.614432
$629$	56.8877	2.26826
$630$	0	0
$631$	24.3238	0.968315	0.484158	−	0.874981i	$-0.339126\pi$
$631$	24.3238	0.968315	0.484158	+	0.874981i	$0.339126\pi$
$632$	−13.5111	−0.537441
$633$	−14.3238	−0.569320
$634$	23.8928	0.948905
$635$	0	0
$636$	11.8611	0.470322
$637$	−35.7219	−1.41535
$638$	0.0245075	0.000970261 0
$639$	0.144562	0.00571876
$640$	0	0
$641$	−20.1238	−0.794840	−0.397420	−	0.917637i	$-0.630094\pi$
$641$	−20.1238	−0.794840	−0.397420	+	0.917637i	$0.630094\pi$
$642$	24.1436	0.952872
$643$	14.7682	0.582402	0.291201	−	0.956662i	$-0.405945\pi$
$643$	14.7682	0.582402	0.291201	+	0.956662i	$0.405945\pi$
$644$	1.26983	0.0500383
$645$	0	0
$646$	−2.59688	−0.102173
$647$	−11.4557	−0.450369	−0.225185	−	0.974316i	$-0.572298\pi$
$647$	−11.4557	−0.450369	−0.225185	+	0.974316i	$0.572298\pi$
$648$	−9.63340	−0.378436
$649$	27.0690	1.06255
$650$	0	0
$651$	6.24962	0.244942
$652$	−17.9325	−0.702291
$653$	6.14168	0.240342	0.120171	−	0.992753i	$-0.461656\pi$
$653$	6.14168	0.240342	0.120171	+	0.992753i	$0.461656\pi$
$654$	1.26983	0.0496542
$655$	0	0
$656$	9.63015	0.375994
$657$	−0.733332	−0.0286100
$658$	−10.2372	−0.399088
$659$	−23.6164	−0.919963	−0.459981	−	0.887929i	$-0.652144\pi$
$659$	−23.6164	−0.919963	−0.459981	+	0.887929i	$0.652144\pi$
$660$	0	0
$661$	36.5330	1.42097	0.710485	−	0.703713i	$-0.248476\pi$
$661$	36.5330	1.42097	0.710485	+	0.703713i	$0.248476\pi$
$662$	0.617845	0.0240132
$663$	−68.0429	−2.64257
$664$	9.56589	0.371228
$665$	0	0
$666$	−2.40589	−0.0932262
$667$	−0.00362148	−0.000140224 0
$668$	12.9658	0.501661
$669$	−41.7203	−1.61300
$670$	0	0
$671$	−20.5405	−0.792958
$672$	−6.24962	−0.241084
$673$	11.1721	0.430652	0.215326	−	0.976542i	$-0.430919\pi$
$673$	11.1721	0.430652	0.215326	+	0.976542i	$0.430919\pi$
$674$	20.6992	0.797303
$675$	0	0
$676$	36.1056	1.38868
$677$	−14.4172	−0.554096	−0.277048	−	0.960856i	$-0.589356\pi$
$677$	−14.4172	−0.554096	−0.277048	+	0.960856i	$0.589356\pi$
$678$	−13.5767	−0.521409
$679$	−18.5380	−0.711421
$680$	0	0
$681$	−3.38254	−0.129619
$682$	2.47063	0.0946053
$683$	42.5368	1.62763	0.813813	−	0.581127i	$-0.197388\pi$
$683$	42.5368	1.62763	0.813813	+	0.581127i	$0.197388\pi$
$684$	0.109827	0.00419934
$685$	0	0
$686$	−6.61672	−0.252628
$687$	21.4669	0.819013
$688$	−5.72264	−0.218173
$689$	46.2579	1.76229
$690$	0	0
$691$	−44.3143	−1.68579	−0.842897	−	0.538075i	$-0.819152\pi$
$691$	−44.3143	−1.68579	−0.842897	+	0.538075i	$0.819152\pi$
$692$	6.51908	0.247818
$693$	−1.96394	−0.0746040
$694$	33.0611	1.25498
$695$	0	0
$696$	0.0178236	0.000675600 0
$697$	−52.0412	−1.97120
$698$	7.31198	0.276763
$699$	−18.7574	−0.709471
$700$	0	0
$701$	23.8627	0.901281	0.450641	−	0.892706i	$-0.351196\pi$
$701$	23.8627	0.901281	0.450641	+	0.892706i	$0.351196\pi$
$702$	−34.8961	−1.31707
$703$	−5.05874	−0.190794
$704$	−2.47063	−0.0931154
$705$	0	0
$706$	21.7429	0.818303
$707$	−1.04464	−0.0392876
$708$	19.6865	0.739864
$709$	−46.3627	−1.74119	−0.870594	−	0.492002i	$-0.836265\pi$
$709$	−46.3627	−1.74119	−0.870594	+	0.492002i	$0.836265\pi$
$710$	0	0
$711$	−3.08788	−0.115805
$712$	15.1516	0.567831
$713$	−0.365086	−0.0136726
$714$	33.7729	1.26392
$715$	0	0
$716$	14.2820	0.533745
$717$	−9.83963	−0.367468
$718$	−7.72054	−0.288128
$719$	−6.20252	−0.231315	−0.115658	−	0.993289i	$-0.536898\pi$
$719$	−6.20252	−0.231315	−0.115658	+	0.993289i	$0.536898\pi$
$720$	0	0
$721$	−8.70936	−0.324354
$722$	−18.7691	−0.698513
$723$	−10.3087	−0.383386
$724$	−6.92295	−0.257290
$725$	0	0
$726$	8.79718	0.326494
$727$	−19.6556	−0.728987	−0.364493	−	0.931206i	$-0.618758\pi$
$727$	−19.6556	−0.728987	−0.364493	+	0.931206i	$0.618758\pi$
$728$	−24.3734	−0.903337
$729$	24.6416	0.912653
$730$	0	0
$731$	30.9250	1.14380
$732$	−14.9385	−0.552143
$733$	26.8898	0.993198	0.496599	−	0.867980i	$-0.334582\pi$
$733$	26.8898	0.993198	0.496599	+	0.867980i	$0.334582\pi$
$734$	−23.0325	−0.850146
$735$	0	0
$736$	0.365086	0.0134572
$737$	17.3326	0.638453
$738$	2.20092	0.0810169
$739$	−31.8249	−1.17070	−0.585350	−	0.810781i	$-0.699043\pi$
$739$	−31.8249	−1.17070	−0.585350	+	0.810781i	$0.699043\pi$
$740$	0	0
$741$	6.05072	0.222279
$742$	−22.9600	−0.842886
$743$	−11.7373	−0.430601	−0.215300	−	0.976548i	$-0.569073\pi$
$743$	−11.7373	−0.430601	−0.215300	+	0.976548i	$0.569073\pi$
$744$	1.79682	0.0658744
$745$	0	0
$746$	7.35528	0.269296
$747$	2.18623	0.0799900
$748$	13.3513	0.488170
$749$	−46.7357	−1.70769
$750$	0	0
$751$	0.486363	0.0177477	0.00887383	−	0.999961i	$-0.497175\pi$
$751$	0.486363	0.0177477	0.00887383	+	0.999961i	$0.497175\pi$
$752$	−2.94328	−0.107330
$753$	−1.58437	−0.0577377
$754$	0.0695115	0.00253146
$755$	0	0
$756$	17.3205	0.629942
$757$	30.9080	1.12337	0.561685	−	0.827351i	$-0.310153\pi$
$757$	30.9080	1.12337	0.561685	+	0.827351i	$0.310153\pi$
$758$	19.3928	0.704380
$759$	1.62071	0.0588281
$760$	0	0
$761$	22.4602	0.814180	0.407090	−	0.913388i	$-0.366544\pi$
$761$	22.4602	0.814180	0.407090	+	0.913388i	$0.366544\pi$
$762$	32.2328	1.16767
$763$	−2.45806	−0.0889877
$764$	−7.17783	−0.259685
$765$	0	0
$766$	13.1111	0.473722
$767$	76.7769	2.77225
$768$	−1.79682	−0.0648370
$769$	4.70873	0.169801	0.0849005	−	0.996389i	$-0.472943\pi$
$769$	4.70873	0.169801	0.0849005	+	0.996389i	$0.472943\pi$
$770$	0	0
$771$	44.2159	1.59240
$772$	9.63958	0.346936
$773$	−23.9122	−0.860061	−0.430031	−	0.902814i	$-0.641497\pi$
$773$	−23.9122	−0.860061	−0.430031	+	0.902814i	$0.641497\pi$
$774$	−1.30788	−0.0470107
$775$	0	0
$776$	−5.32981	−0.191329
$777$	65.7897	2.36019
$778$	−8.76355	−0.314189
$779$	4.62776	0.165807
$780$	0	0
$781$	−1.56275	−0.0559196
$782$	−1.97292	−0.0705514
$783$	−0.0493972	−0.00176531
$784$	5.09764	0.182059
$785$	0	0
$786$	−3.86671	−0.137921
$787$	−12.6874	−0.452255	−0.226128	−	0.974098i	$-0.572607\pi$
$787$	−12.6874	−0.452255	−0.226128	+	0.974098i	$0.572607\pi$
$788$	14.8309	0.528331
$789$	−23.3259	−0.830424
$790$	0	0
$791$	26.2809	0.934442
$792$	−0.564649	−0.0200639
$793$	−58.2598	−2.06887
$794$	−22.2056	−0.788047
$795$	0	0
$796$	9.18726	0.325634
$797$	−30.6460	−1.08554	−0.542768	−	0.839883i	$-0.682624\pi$
$797$	−30.6460	−1.08554	−0.542768	+	0.839883i	$0.682624\pi$
$798$	−3.00325	−0.106314
$799$	15.9054	0.562693
$800$	0	0
$801$	3.46282	0.122353
$802$	−5.65942	−0.199841
$803$	7.92752	0.279756
$804$	12.6054	0.444560
$805$	0	0
$806$	7.00754	0.246830
$807$	−22.7497	−0.800829
$808$	−0.300341	−0.0105660
$809$	53.8848	1.89449	0.947245	−	0.320510i	$-0.103854\pi$
$809$	53.8848	1.89449	0.947245	+	0.320510i	$0.103854\pi$
$810$	0	0
$811$	−6.42547	−0.225629	−0.112814	−	0.993616i	$-0.535987\pi$
$811$	−6.42547	−0.225629	−0.112814	+	0.993616i	$0.535987\pi$
$812$	−0.0345018	−0.00121077
$813$	8.26832	0.289982
$814$	26.0083	0.911590
$815$	0	0
$816$	9.70996	0.339917
$817$	−2.75001	−0.0962107
$818$	−13.2801	−0.464329
$819$	−5.57040	−0.194646
$820$	0	0
$821$	−12.2283	−0.426769	−0.213384	−	0.976968i	$-0.568449\pi$
$821$	−12.2283	−0.426769	−0.213384	+	0.976968i	$0.568449\pi$
$822$	−18.6241	−0.649592
$823$	−33.0905	−1.15346	−0.576731	−	0.816934i	$-0.695672\pi$
$823$	−33.0905	−1.15346	−0.576731	+	0.816934i	$0.695672\pi$
$824$	−2.50401	−0.0872313
$825$	0	0
$826$	−38.1079	−1.32595
$827$	−21.6099	−0.751451	−0.375725	−	0.926731i	$-0.622606\pi$
$827$	−21.6099	−0.751451	−0.375725	+	0.926731i	$0.622606\pi$
$828$	0.0834383	0.00289968
$829$	−2.19681	−0.0762984	−0.0381492	−	0.999272i	$-0.512146\pi$
$829$	−2.19681	−0.0762984	−0.0381492	+	0.999272i	$0.512146\pi$
$830$	0	0
$831$	−21.1545	−0.733843
$832$	−7.00754	−0.242943
$833$	−27.5476	−0.954467
$834$	−25.2003	−0.872616
$835$	0	0
$836$	−1.18726	−0.0410623
$837$	−4.97979	−0.172127
$838$	18.8268	0.650363
$839$	23.3786	0.807120	0.403560	−	0.914953i	$-0.367773\pi$
$839$	23.3786	0.807120	0.403560	+	0.914953i	$0.367773\pi$
$840$	0	0
$841$	−28.9999	−0.999997
$842$	16.6627	0.574234
$843$	50.9026	1.75318
$844$	7.97177	0.274400
$845$	0	0
$846$	−0.672670	−0.0231269
$847$	−17.0291	−0.585125
$848$	−6.60117	−0.226685
$849$	40.0675	1.37511
$850$	0	0
$851$	−3.84325	−0.131745
$852$	−1.13654	−0.0389373
$853$	13.8395	0.473854	0.236927	−	0.971527i	$-0.423860\pi$
$853$	13.8395	0.473854	0.236927	+	0.971527i	$0.423860\pi$
$854$	28.9171	0.989522
$855$	0	0
$856$	−13.4369	−0.459263
$857$	−4.45306	−0.152114	−0.0760568	−	0.997103i	$-0.524233\pi$
$857$	−4.45306	−0.152114	−0.0760568	+	0.997103i	$0.524233\pi$
$858$	−31.1083	−1.06202
$859$	39.0357	1.33188	0.665940	−	0.746005i	$-0.268031\pi$
$859$	39.0357	1.33188	0.665940	+	0.746005i	$0.268031\pi$
$860$	0	0
$861$	−60.1848	−2.05109
$862$	−30.2936	−1.03180
$863$	2.85709	0.0972563	0.0486282	−	0.998817i	$-0.484515\pi$
$863$	2.85709	0.0972563	0.0486282	+	0.998817i	$0.484515\pi$
$864$	4.97979	0.169416
$865$	0	0
$866$	−10.7913	−0.366703
$867$	−21.9267	−0.744668
$868$	−3.47817	−0.118057
$869$	33.3808	1.13237
$870$	0	0
$871$	49.1610	1.66576
$872$	−0.706711	−0.0239322
$873$	−1.21810	−0.0412264
$874$	0.175442	0.00593441
$875$	0	0
$876$	5.76545	0.194797
$877$	−8.39130	−0.283354	−0.141677	−	0.989913i	$-0.545249\pi$
$877$	−8.39130	−0.283354	−0.141677	+	0.989913i	$0.545249\pi$
$878$	8.47303	0.285951
$879$	18.9074	0.637729
$880$	0	0
$881$	11.8276	0.398483	0.199241	−	0.979950i	$-0.436152\pi$
$881$	11.8276	0.398483	0.199241	+	0.979950i	$0.436152\pi$
$882$	1.16504	0.0392289
$883$	−13.6326	−0.458775	−0.229388	−	0.973335i	$-0.573672\pi$
$883$	−13.6326	−0.458775	−0.229388	+	0.973335i	$0.573672\pi$
$884$	37.8686	1.27366
$885$	0	0
$886$	−35.8921	−1.20582
$887$	−0.478944	−0.0160814	−0.00804068	−	0.999968i	$-0.502559\pi$
$887$	−0.478944	−0.0160814	−0.00804068	+	0.999968i	$0.502559\pi$
$888$	18.9150	0.634747
$889$	−62.3944	−2.09264
$890$	0	0
$891$	23.8006	0.797349
$892$	23.2190	0.777430
$893$	−1.41439	−0.0473308
$894$	36.8888	1.23375
$895$	0	0
$896$	3.47817	0.116197
$897$	4.59688	0.153485
$898$	−17.3271	−0.578211
$899$	0.00991953	0.000330835 0
$900$	0	0
$901$	35.6726	1.18843
$902$	−23.7925	−0.792205
$903$	35.7643	1.19016
$904$	7.55597	0.251308
$905$	0	0
$906$	19.9174	0.661712
$907$	−18.7958	−0.624104	−0.312052	−	0.950065i	$-0.601016\pi$
$907$	−18.7958	−0.624104	−0.312052	+	0.950065i	$0.601016\pi$
$908$	1.88252	0.0624736
$909$	−0.0686413	−0.00227669
$910$	0	0
$911$	9.54043	0.316089	0.158044	−	0.987432i	$-0.449481\pi$
$911$	9.54043	0.316089	0.158044	+	0.987432i	$0.449481\pi$
$912$	−0.863459	−0.0285920
$913$	−23.6338	−0.782164
$914$	20.0674	0.663771
$915$	0	0
$916$	−11.9472	−0.394746
$917$	7.48495	0.247175
$918$	−26.9107	−0.888187
$919$	0.788134	0.0259981	0.0129991	−	0.999916i	$-0.495862\pi$
$919$	0.788134	0.0259981	0.0129991	+	0.999916i	$0.495862\pi$
$920$	0	0
$921$	45.9905	1.51544
$922$	−10.2586	−0.337848
$923$	−4.43248	−0.145897
$924$	15.4405	0.507955
$925$	0	0
$926$	0.766689	0.0251950
$927$	−0.572278	−0.0187961
$928$	−0.00991953	−0.000325625 0
$929$	−25.3062	−0.830271	−0.415136	−	0.909760i	$-0.636266\pi$
$929$	−25.3062	−0.830271	−0.415136	+	0.909760i	$0.636266\pi$
$930$	0	0
$931$	2.44967	0.0802847
$932$	10.4393	0.341950
$933$	−37.8215	−1.23822
$934$	−21.4273	−0.701124
$935$	0	0
$936$	−1.60153	−0.0523478
$937$	−51.1730	−1.67175	−0.835874	−	0.548922i	$-0.815039\pi$
$937$	−51.1730	−1.67175	−0.835874	+	0.548922i	$0.815039\pi$
$938$	−24.4009	−0.796717
$939$	28.1485	0.918593
$940$	0	0
$941$	−37.4102	−1.21954	−0.609769	−	0.792579i	$-0.708738\pi$
$941$	−37.4102	−1.21954	−0.609769	+	0.792579i	$0.708738\pi$
$942$	−27.6667	−0.901429
$943$	3.51583	0.114491
$944$	−10.9563	−0.356598
$945$	0	0
$946$	14.1385	0.459683
$947$	−38.3159	−1.24510	−0.622550	−	0.782580i	$-0.713903\pi$
$947$	−38.3159	−1.24510	−0.622550	+	0.782580i	$0.713903\pi$
$948$	24.2769	0.788476
$949$	22.4851	0.729898
$950$	0	0
$951$	−42.9310	−1.39213
$952$	−18.7960	−0.609181
$953$	7.42383	0.240481	0.120241	−	0.992745i	$-0.461633\pi$
$953$	7.42383	0.240481	0.120241	+	0.992745i	$0.461633\pi$
$954$	−1.50866	−0.0488447
$955$	0	0
$956$	5.47615	0.177111
$957$	−0.0440354	−0.00142346
$958$	−29.6667	−0.958486
$959$	36.0515	1.16416
$960$	0	0
$961$	1.00000	0.0322581
$962$	73.7682	2.37838
$963$	−3.07093	−0.0989592
$964$	5.73722	0.184784
$965$	0	0
$966$	−2.28165	−0.0734108
$967$	7.13090	0.229314	0.114657	−	0.993405i	$-0.463423\pi$
$967$	7.13090	0.229314	0.114657	+	0.993405i	$0.463423\pi$
$968$	−4.89599	−0.157363
$969$	4.66612	0.149897
$970$	0	0
$971$	28.9403	0.928738	0.464369	−	0.885642i	$-0.346281\pi$
$971$	28.9403	0.928738	0.464369	+	0.885642i	$0.346281\pi$
$972$	2.37006	0.0760198
$973$	48.7813	1.56386
$974$	25.8096	0.826994
$975$	0	0
$976$	8.31388	0.266121
$977$	33.7944	1.08118	0.540590	−	0.841286i	$-0.318201\pi$
$977$	33.7944	1.08118	0.540590	+	0.841286i	$0.318201\pi$
$978$	32.2214	1.03033
$979$	−37.4340	−1.19640
$980$	0	0
$981$	−0.161515	−0.00515677
$982$	−18.7250	−0.597539
$983$	19.8142	0.631973	0.315987	−	0.948764i	$-0.397665\pi$
$983$	19.8142	0.631973	0.315987	+	0.948764i	$0.397665\pi$
$984$	−17.3036	−0.551618
$985$	0	0
$986$	0.0536050	0.00170713
$987$	18.3944	0.585499
$988$	−3.36747	−0.107133
$989$	−2.08925	−0.0664344
$990$	0	0
$991$	−60.3261	−1.91632	−0.958161	−	0.286229i	$-0.907598\pi$
$991$	−60.3261	−1.91632	−0.958161	+	0.286229i	$0.907598\pi$
$992$	−1.00000	−0.0317500
$993$	−1.11015	−0.0352296
$994$	2.20005	0.0697813
$995$	0	0
$996$	−17.1881	−0.544627
$997$	21.3759	0.676980	0.338490	−	0.940970i	$-0.390084\pi$
$997$	21.3759	0.676980	0.338490	+	0.940970i	$0.390084\pi$
$998$	41.9722	1.32861
$999$	−52.4222	−1.65857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1550.2.a.p.1.2		4
5.2	odd	4		310.2.b.a.249.7	yes	8
5.3	odd	4		310.2.b.a.249.2	✓	8
5.4	even	2		1550.2.a.o.1.3		4
15.2	even	4		2790.2.d.m.559.1		8
15.8	even	4		2790.2.d.m.559.5		8
20.3	even	4		2480.2.d.d.1489.7		8
20.7	even	4		2480.2.d.d.1489.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.a.249.2	✓	8	5.3	odd	4
310.2.b.a.249.7	yes	8	5.2	odd	4
1550.2.a.o.1.3		4	5.4	even	2
1550.2.a.p.1.2		4	1.1	even	1	trivial
2480.2.d.d.1489.2		8	20.7	even	4
2480.2.d.d.1489.7		8	20.3	even	4
2790.2.d.m.559.1		8	15.2	even	4
2790.2.d.m.559.5		8	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1550.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.79682 q^{3} +1.00000 q^{4} -1.79682 q^{6} +3.47817 q^{7} +1.00000 q^{8} +0.228545 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.79682 q^{3} +1.00000 q^{4} -1.79682 q^{6} +3.47817 q^{7} +1.00000 q^{8} +0.228545 q^{9} -2.47063 q^{11} -1.79682 q^{12} -7.00754 q^{13} +3.47817 q^{14} +1.00000 q^{16} -5.40399 q^{17} +0.228545 q^{18} +0.480550 q^{19} -6.24962 q^{21} -2.47063 q^{22} +0.365086 q^{23} -1.79682 q^{24} -7.00754 q^{26} +4.97979 q^{27} +3.47817 q^{28} -0.00991953 q^{29} -1.00000 q^{31} +1.00000 q^{32} +4.43927 q^{33} -5.40399 q^{34} +0.228545 q^{36} -10.5270 q^{37} +0.480550 q^{38} +12.5912 q^{39} +9.63015 q^{41} -6.24962 q^{42} -5.72264 q^{43} -2.47063 q^{44} +0.365086 q^{46} -2.94328 q^{47} -1.79682 q^{48} +5.09764 q^{49} +9.70996 q^{51} -7.00754 q^{52} -6.60117 q^{53} +4.97979 q^{54} +3.47817 q^{56} -0.863459 q^{57} -0.00991953 q^{58} -10.9563 q^{59} +8.31388 q^{61} -1.00000 q^{62} +0.794916 q^{63} +1.00000 q^{64} +4.43927 q^{66} -7.01544 q^{67} -5.40399 q^{68} -0.655991 q^{69} +0.632531 q^{71} +0.228545 q^{72} -3.20871 q^{73} -10.5270 q^{74} +0.480550 q^{76} -8.59326 q^{77} +12.5912 q^{78} -13.5111 q^{79} -9.63340 q^{81} +9.63015 q^{82} +9.56589 q^{83} -6.24962 q^{84} -5.72264 q^{86} +0.0178236 q^{87} -2.47063 q^{88} +15.1516 q^{89} -24.3734 q^{91} +0.365086 q^{92} +1.79682 q^{93} -2.94328 q^{94} -1.79682 q^{96} -5.32981 q^{97} +5.09764 q^{98} -0.564649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 8 q^{11} - 4 q^{12} - 10 q^{13} - 6 q^{14} + 4 q^{16} - 4 q^{17} + 4 q^{18} + 6 q^{19} - 2 q^{21} - 8 q^{22} - 8 q^{23} - 4 q^{24} - 10 q^{26} - 22 q^{27} - 6 q^{28} - 6 q^{29} - 4 q^{31} + 4 q^{32} + 6 q^{33} - 4 q^{34} + 4 q^{36} - 20 q^{37} + 6 q^{38} + 20 q^{39} - 2 q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{46} - 2 q^{47} - 4 q^{48} + 16 q^{49} - 22 q^{51} - 10 q^{52} - 2 q^{53} - 22 q^{54} - 6 q^{56} - 16 q^{57} - 6 q^{58} - 4 q^{59} + 2 q^{61} - 4 q^{62} - 2 q^{63} + 4 q^{64} + 6 q^{66} - 22 q^{67} - 4 q^{68} + 14 q^{69} - 12 q^{71} + 4 q^{72} - 4 q^{73} - 20 q^{74} + 6 q^{76} + 2 q^{77} + 20 q^{78} - 16 q^{79} + 44 q^{81} + 8 q^{83} - 2 q^{84} - 22 q^{86} + 18 q^{87} - 8 q^{88} + 12 q^{89} - 10 q^{91} - 8 q^{92} + 4 q^{93} - 2 q^{94} - 4 q^{96} - 6 q^{97} + 16 q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 8 * q^11 - 4 * q^12 - 10 * q^13 - 6 * q^14 + 4 * q^16 - 4 * q^17 + 4 * q^18 + 6 * q^19 - 2 * q^21 - 8 * q^22 - 8 * q^23 - 4 * q^24 - 10 * q^26 - 22 * q^27 - 6 * q^28 - 6 * q^29 - 4 * q^31 + 4 * q^32 + 6 * q^33 - 4 * q^34 + 4 * q^36 - 20 * q^37 + 6 * q^38 + 20 * q^39 - 2 * q^42 - 22 * q^43 - 8 * q^44 - 8 * q^46 - 2 * q^47 - 4 * q^48 + 16 * q^49 - 22 * q^51 - 10 * q^52 - 2 * q^53 - 22 * q^54 - 6 * q^56 - 16 * q^57 - 6 * q^58 - 4 * q^59 + 2 * q^61 - 4 * q^62 - 2 * q^63 + 4 * q^64 + 6 * q^66 - 22 * q^67 - 4 * q^68 + 14 * q^69 - 12 * q^71 + 4 * q^72 - 4 * q^73 - 20 * q^74 + 6 * q^76 + 2 * q^77 + 20 * q^78 - 16 * q^79 + 44 * q^81 + 8 * q^83 - 2 * q^84 - 22 * q^86 + 18 * q^87 - 8 * q^88 + 12 * q^89 - 10 * q^91 - 8 * q^92 + 4 * q^93 - 2 * q^94 - 4 * q^96 - 6 * q^97 + 16 * q^98 - 10 * q^99

Introduction

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