LMFDB - Embedded newform 575.2.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(1,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, 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("575.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.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:	$4.59139811622$
Analytic rank:	$0$
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} - x^{6} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 $ x^7 - x^6 - 12x^5 + 9x^4 + 43x^3 - 14x^2 - 49*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.202227$ of defining polynomial
Character	$\chi$	$=$	575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.202227 q^{2} -2.69619 q^{3} -1.95910 q^{4} -0.545243 q^{6} -2.81698 q^{7} -0.800639 q^{8} +4.26945 q^{9} +O(q^{10})$	\(q+0.202227 q^{2} -2.69619 q^{3} -1.95910 q^{4} -0.545243 q^{6} -2.81698 q^{7} -0.800639 q^{8} +4.26945 q^{9} -1.84786 q^{11} +5.28212 q^{12} -6.49089 q^{13} -0.569670 q^{14} +3.75630 q^{16} +7.06930 q^{17} +0.863400 q^{18} -0.252319 q^{19} +7.59513 q^{21} -0.373689 q^{22} -1.00000 q^{23} +2.15868 q^{24} -1.31263 q^{26} -3.42269 q^{27} +5.51876 q^{28} +4.12351 q^{29} +3.54811 q^{31} +2.36090 q^{32} +4.98220 q^{33} +1.42961 q^{34} -8.36430 q^{36} -7.91248 q^{37} -0.0510258 q^{38} +17.5007 q^{39} +6.53833 q^{41} +1.53594 q^{42} +4.93835 q^{43} +3.62016 q^{44} -0.202227 q^{46} -0.851917 q^{47} -10.1277 q^{48} +0.935388 q^{49} -19.0602 q^{51} +12.7163 q^{52} +12.5831 q^{53} -0.692161 q^{54} +2.25538 q^{56} +0.680301 q^{57} +0.833886 q^{58} -10.3616 q^{59} +1.01207 q^{61} +0.717524 q^{62} -12.0270 q^{63} -7.03516 q^{64} +1.00754 q^{66} -3.37930 q^{67} -13.8495 q^{68} +2.69619 q^{69} -0.851917 q^{71} -3.41829 q^{72} +9.75748 q^{73} -1.60012 q^{74} +0.494319 q^{76} +5.20540 q^{77} +3.53911 q^{78} -16.5320 q^{79} -3.58013 q^{81} +1.32223 q^{82} -0.696772 q^{83} -14.8796 q^{84} +0.998669 q^{86} -11.1178 q^{87} +1.47947 q^{88} +13.1835 q^{89} +18.2847 q^{91} +1.95910 q^{92} -9.56638 q^{93} -0.172281 q^{94} -6.36545 q^{96} +5.48684 q^{97} +0.189161 q^{98} -7.88937 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	$ 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) $ 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.202227	0.142996	0.0714981	−	0.997441i	$-0.477222\pi$
$2$	0.202227	0.142996	0.0714981	+	0.997441i	$0.477222\pi$
$3$	−2.69619	−1.55665	−0.778324	−	0.627863i	$-0.783930\pi$
$3$	−2.69619	−1.55665	−0.778324	+	0.627863i	$0.783930\pi$
$4$	−1.95910	−0.979552
$5$	0	0
$5$	0	0
$6$	−0.545243	−0.222595
$7$	−2.81698	−1.06472	−0.532360	−	0.846518i	$-0.678695\pi$
$7$	−2.81698	−1.06472	−0.532360	+	0.846518i	$0.678695\pi$
$8$	−0.800639	−0.283069
$9$	4.26945	1.42315
$10$	0	0
$11$	−1.84786	−0.557152	−0.278576	−	0.960414i	$-0.589862\pi$
$11$	−1.84786	−0.557152	−0.278576	+	0.960414i	$0.589862\pi$
$12$	5.28212	1.52482
$13$	−6.49089	−1.80025	−0.900124	−	0.435633i	$-0.856525\pi$
$13$	−6.49089	−1.80025	−0.900124	+	0.435633i	$0.856525\pi$
$14$	−0.569670	−0.152251
$15$	0	0
$16$	3.75630	0.939074
$17$	7.06930	1.71456	0.857279	−	0.514853i	$-0.172153\pi$
$17$	7.06930	1.71456	0.857279	+	0.514853i	$0.172153\pi$
$18$	0.863400	0.203505
$19$	−0.252319	−0.0578860	−0.0289430	−	0.999581i	$-0.509214\pi$
$19$	−0.252319	−0.0578860	−0.0289430	+	0.999581i	$0.509214\pi$
$20$	0	0
$21$	7.59513	1.65739
$22$	−0.373689	−0.0796707
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.15868	0.440638
$25$	0	0
$26$	−1.31263	−0.257429
$27$	−3.42269	−0.658696
$28$	5.51876	1.04295
$29$	4.12351	0.765717	0.382858	−	0.923807i	$-0.374940\pi$
$29$	4.12351	0.765717	0.382858	+	0.923807i	$0.374940\pi$
$30$	0	0
$31$	3.54811	0.637259	0.318630	−	0.947879i	$-0.396777\pi$
$31$	3.54811	0.637259	0.318630	+	0.947879i	$0.396777\pi$
$32$	2.36090	0.417353
$33$	4.98220	0.867289
$34$	1.42961	0.245175
$35$	0	0
$36$	−8.36430	−1.39405
$37$	−7.91248	−1.30080	−0.650402	−	0.759591i	$-0.725399\pi$
$37$	−7.91248	−1.30080	−0.650402	+	0.759591i	$0.725399\pi$
$38$	−0.0510258	−0.00827748
$39$	17.5007	2.80235
$40$	0	0
$41$	6.53833	1.02111	0.510557	−	0.859844i	$-0.329439\pi$
$41$	6.53833	1.02111	0.510557	+	0.859844i	$0.329439\pi$
$42$	1.53594	0.237001
$43$	4.93835	0.753092	0.376546	−	0.926398i	$-0.377112\pi$
$43$	4.93835	0.753092	0.376546	+	0.926398i	$0.377112\pi$
$44$	3.62016	0.545760
$45$	0	0
$46$	−0.202227	−0.0298168
$47$	−0.851917	−0.124265	−0.0621324	−	0.998068i	$-0.519790\pi$
$47$	−0.851917	−0.124265	−0.0621324	+	0.998068i	$0.519790\pi$
$48$	−10.1277	−1.46181
$49$	0.935388	0.133627
$50$	0	0
$51$	−19.0602	−2.66896
$52$	12.7163	1.76344
$53$	12.5831	1.72842	0.864208	−	0.503135i	$-0.167820\pi$
$53$	12.5831	1.72842	0.864208	+	0.503135i	$0.167820\pi$
$54$	−0.692161	−0.0941911
$55$	0	0
$56$	2.25538	0.301388
$57$	0.680301	0.0901080
$58$	0.833886	0.109495
$59$	−10.3616	−1.34897	−0.674484	−	0.738290i	$-0.735634\pi$
$59$	−10.3616	−1.34897	−0.674484	+	0.738290i	$0.735634\pi$
$60$	0	0
$61$	1.01207	0.129582	0.0647911	−	0.997899i	$-0.479362\pi$
$61$	1.01207	0.129582	0.0647911	+	0.997899i	$0.479362\pi$
$62$	0.717524	0.0911257
$63$	−12.0270	−1.51526
$64$	−7.03516	−0.879394
$65$	0	0
$66$	1.00754	0.124019
$67$	−3.37930	−0.412848	−0.206424	−	0.978463i	$-0.566183\pi$
$67$	−3.37930	−0.412848	−0.206424	+	0.978463i	$0.566183\pi$
$68$	−13.8495	−1.67950
$69$	2.69619	0.324583
$70$	0	0
$71$	−0.851917	−0.101104	−0.0505520	−	0.998721i	$-0.516098\pi$
$71$	−0.851917	−0.101104	−0.0505520	+	0.998721i	$0.516098\pi$
$72$	−3.41829	−0.402849
$73$	9.75748	1.14203	0.571013	−	0.820941i	$-0.306551\pi$
$73$	9.75748	1.14203	0.571013	+	0.820941i	$0.306551\pi$
$74$	−1.60012	−0.186010
$75$	0	0
$76$	0.494319	0.0567023
$77$	5.20540	0.593211
$78$	3.53911	0.400726
$79$	−16.5320	−1.86000	−0.929999	−	0.367561i	$-0.880193\pi$
$79$	−16.5320	−1.86000	−0.929999	+	0.367561i	$0.880193\pi$
$80$	0	0
$81$	−3.58013	−0.397793
$82$	1.32223	0.146016
$83$	−0.696772	−0.0764806	−0.0382403	−	0.999269i	$-0.512175\pi$
$83$	−0.696772	−0.0764806	−0.0382403	+	0.999269i	$0.512175\pi$
$84$	−14.8796	−1.62350
$85$	0	0
$86$	0.998669	0.107689
$87$	−11.1178	−1.19195
$88$	1.47947	0.157712
$89$	13.1835	1.39745	0.698724	−	0.715392i	$-0.253752\pi$
$89$	13.1835	1.39745	0.698724	+	0.715392i	$0.253752\pi$
$90$	0	0
$91$	18.2847	1.91676
$92$	1.95910	0.204251
$93$	−9.56638	−0.991988
$94$	−0.172281	−0.0177694
$95$	0	0
$96$	−6.36545	−0.649671
$97$	5.48684	0.557104	0.278552	−	0.960421i	$-0.410146\pi$
$97$	5.48684	0.557104	0.278552	+	0.960421i	$0.410146\pi$
$98$	0.189161	0.0191081
$99$	−7.88937	−0.792911
$100$	0	0
$101$	−9.56925	−0.952176	−0.476088	−	0.879398i	$-0.657946\pi$
$101$	−9.56925	−0.952176	−0.476088	+	0.879398i	$0.657946\pi$
$102$	−3.85449	−0.381651
$103$	9.10123	0.896770	0.448385	−	0.893840i	$-0.351999\pi$
$103$	9.10123	0.896770	0.448385	+	0.893840i	$0.351999\pi$
$104$	5.19686	0.509594
$105$	0	0
$106$	2.54464	0.247157
$107$	−11.7093	−1.13198	−0.565991	−	0.824411i	$-0.691506\pi$
$107$	−11.7093	−1.13198	−0.565991	+	0.824411i	$0.691506\pi$
$108$	6.70540	0.645228
$109$	1.46844	0.140651	0.0703257	−	0.997524i	$-0.477596\pi$
$109$	1.46844	0.140651	0.0703257	+	0.997524i	$0.477596\pi$
$110$	0	0
$111$	21.3336	2.02489
$112$	−10.5814	−0.999850
$113$	−1.62939	−0.153280	−0.0766401	−	0.997059i	$-0.524419\pi$
$113$	−1.62939	−0.153280	−0.0766401	+	0.997059i	$0.524419\pi$
$114$	0.137575	0.0128851
$115$	0	0
$116$	−8.07839	−0.750060
$117$	−27.7125	−2.56203
$118$	−2.09540	−0.192897
$119$	−19.9141	−1.82552
$120$	0	0
$121$	−7.58540	−0.689581
$122$	0.204668	0.0185298
$123$	−17.6286	−1.58952
$124$	−6.95112	−0.624229
$125$	0	0
$126$	−2.43218	−0.216676
$127$	8.59258	0.762468	0.381234	−	0.924479i	$-0.375499\pi$
$127$	8.59258	0.762468	0.381234	+	0.924479i	$0.375499\pi$
$128$	−6.14451	−0.543103
$129$	−13.3147	−1.17230
$130$	0	0
$131$	2.93777	0.256674	0.128337	−	0.991731i	$-0.459036\pi$
$131$	2.93777	0.256674	0.128337	+	0.991731i	$0.459036\pi$
$132$	−9.76064	−0.849555
$133$	0.710778	0.0616323
$134$	−0.683387	−0.0590357
$135$	0	0
$136$	−5.65996	−0.485337
$137$	21.9366	1.87417	0.937085	−	0.349101i	$-0.113513\pi$
$137$	21.9366	1.87417	0.937085	+	0.349101i	$0.113513\pi$
$138$	0.545243	0.0464142
$139$	15.3324	1.30048	0.650239	−	0.759730i	$-0.274669\pi$
$139$	15.3324	1.30048	0.650239	+	0.759730i	$0.274669\pi$
$140$	0	0
$141$	2.29693	0.193437
$142$	−0.172281	−0.0144575
$143$	11.9943	1.00301
$144$	16.0373	1.33644
$145$	0	0
$146$	1.97323	0.163305
$147$	−2.52199	−0.208010
$148$	15.5014	1.27420
$149$	−15.0218	−1.23063	−0.615316	−	0.788281i	$-0.710972\pi$
$149$	−15.0218	−1.23063	−0.615316	+	0.788281i	$0.710972\pi$
$150$	0	0
$151$	17.5294	1.42652	0.713262	−	0.700897i	$-0.247217\pi$
$151$	17.5294	1.42652	0.713262	+	0.700897i	$0.247217\pi$
$152$	0.202016	0.0163857
$153$	30.1820	2.44007
$154$	1.05267	0.0848269
$155$	0	0
$156$	−34.2857	−2.74505
$157$	−7.10315	−0.566893	−0.283446	−	0.958988i	$-0.591478\pi$
$157$	−7.10315	−0.566893	−0.283446	+	0.958988i	$0.591478\pi$
$158$	−3.34323	−0.265973
$159$	−33.9263	−2.69053
$160$	0	0
$161$	2.81698	0.222009
$162$	−0.724001	−0.0568829
$163$	14.5905	1.14282	0.571408	−	0.820666i	$-0.306397\pi$
$163$	14.5905	1.14282	0.571408	+	0.820666i	$0.306397\pi$
$164$	−12.8093	−1.00024
$165$	0	0
$166$	−0.140906	−0.0109364
$167$	9.45066	0.731314	0.365657	−	0.930750i	$-0.380844\pi$
$167$	9.45066	0.731314	0.365657	+	0.930750i	$0.380844\pi$
$168$	−6.08095	−0.469156
$169$	29.1316	2.24090
$170$	0	0
$171$	−1.07726	−0.0823805
$172$	−9.67475	−0.737692
$173$	23.3055	1.77188	0.885940	−	0.463799i	$-0.153514\pi$
$173$	23.3055	1.77188	0.885940	+	0.463799i	$0.153514\pi$
$174$	−2.24832	−0.170445
$175$	0	0
$176$	−6.94113	−0.523207
$177$	27.9369	2.09987
$178$	2.66606	0.199830
$179$	23.5562	1.76068	0.880338	−	0.474347i	$-0.157316\pi$
$179$	23.5562	1.76068	0.880338	+	0.474347i	$0.157316\pi$
$180$	0	0
$181$	0.505059	0.0375407	0.0187704	−	0.999824i	$-0.494025\pi$
$181$	0.505059	0.0375407	0.0187704	+	0.999824i	$0.494025\pi$
$182$	3.69767	0.274089
$183$	−2.72874	−0.201714
$184$	0.800639	0.0590239
$185$	0	0
$186$	−1.93458	−0.141851
$187$	−13.0631	−0.955269
$188$	1.66899	0.121724
$189$	9.64165	0.701327
$190$	0	0
$191$	2.51313	0.181844	0.0909219	−	0.995858i	$-0.471019\pi$
$191$	2.51313	0.181844	0.0909219	+	0.995858i	$0.471019\pi$
$192$	18.9681	1.36891
$193$	4.17037	0.300190	0.150095	−	0.988672i	$-0.452042\pi$
$193$	4.17037	0.300190	0.150095	+	0.988672i	$0.452042\pi$
$194$	1.10959	0.0796638
$195$	0	0
$196$	−1.83252	−0.130894
$197$	6.60102	0.470303	0.235151	−	0.971959i	$-0.424441\pi$
$197$	6.60102	0.470303	0.235151	+	0.971959i	$0.424441\pi$
$198$	−1.59545	−0.113383
$199$	−9.91175	−0.702626	−0.351313	−	0.936258i	$-0.614265\pi$
$199$	−9.91175	−0.702626	−0.351313	+	0.936258i	$0.614265\pi$
$200$	0	0
$201$	9.11125	0.642658
$202$	−1.93516	−0.136158
$203$	−11.6159	−0.815273
$204$	37.3409	2.61439
$205$	0	0
$206$	1.84052	0.128235
$207$	−4.26945	−0.296747
$208$	−24.3817	−1.69057
$209$	0.466251	0.0322513
$210$	0	0
$211$	8.33546	0.573837	0.286918	−	0.957955i	$-0.407369\pi$
$211$	8.33546	0.573837	0.286918	+	0.957955i	$0.407369\pi$
$212$	−24.6515	−1.69307
$213$	2.29693	0.157383
$214$	−2.36794	−0.161869
$215$	0	0
$216$	2.74034	0.186456
$217$	−9.99496	−0.678502
$218$	0.296959	0.0201126
$219$	−26.3080	−1.77773
$220$	0	0
$221$	−45.8860	−3.08663
$222$	4.31423	0.289552
$223$	−13.4909	−0.903420	−0.451710	−	0.892165i	$-0.649186\pi$
$223$	−13.4909	−0.903420	−0.451710	+	0.892165i	$0.649186\pi$
$224$	−6.65062	−0.444363
$225$	0	0
$226$	−0.329507	−0.0219185
$227$	5.77415	0.383244	0.191622	−	0.981469i	$-0.438625\pi$
$227$	5.77415	0.383244	0.191622	+	0.981469i	$0.438625\pi$
$228$	−1.33278	−0.0882655
$229$	22.3181	1.47482	0.737412	−	0.675444i	$-0.236048\pi$
$229$	22.3181	1.47482	0.737412	+	0.675444i	$0.236048\pi$
$230$	0	0
$231$	−14.0348	−0.923420
$232$	−3.30144	−0.216750
$233$	−21.8227	−1.42965	−0.714825	−	0.699303i	$-0.753494\pi$
$233$	−21.8227	−1.42965	−0.714825	+	0.699303i	$0.753494\pi$
$234$	−5.60423	−0.366360
$235$	0	0
$236$	20.2995	1.32138
$237$	44.5735	2.89536
$238$	−4.02717	−0.261043
$239$	−26.7115	−1.72782	−0.863912	−	0.503644i	$-0.831993\pi$
$239$	−26.7115	−1.72782	−0.863912	+	0.503644i	$0.831993\pi$
$240$	0	0
$241$	15.1565	0.976318	0.488159	−	0.872755i	$-0.337669\pi$
$241$	15.1565	0.976318	0.488159	+	0.872755i	$0.337669\pi$
$242$	−1.53397	−0.0986076
$243$	19.9208	1.27792
$244$	−1.98275	−0.126933
$245$	0	0
$246$	−3.56498	−0.227295
$247$	1.63778	0.104209
$248$	−2.84075	−0.180388
$249$	1.87863	0.119053
$250$	0	0
$251$	−13.2026	−0.833340	−0.416670	−	0.909058i	$-0.636803\pi$
$251$	−13.2026	−0.833340	−0.416670	+	0.909058i	$0.636803\pi$
$252$	23.5621	1.48427
$253$	1.84786	0.116174
$254$	1.73765	0.109030
$255$	0	0
$256$	12.8277	0.801733
$257$	−13.9450	−0.869866	−0.434933	−	0.900463i	$-0.643228\pi$
$257$	−13.9450	−0.869866	−0.434933	+	0.900463i	$0.643228\pi$
$258$	−2.69260	−0.167634
$259$	22.2893	1.38499
$260$	0	0
$261$	17.6051	1.08973
$262$	0.594097	0.0367035
$263$	−21.7883	−1.34352	−0.671762	−	0.740767i	$-0.734462\pi$
$263$	−21.7883	−1.34352	−0.671762	+	0.740767i	$0.734462\pi$
$264$	−3.98894	−0.245502
$265$	0	0
$266$	0.143739	0.00881319
$267$	−35.5452	−2.17533
$268$	6.62041	0.404406
$269$	10.2596	0.625540	0.312770	−	0.949829i	$-0.398743\pi$
$269$	10.2596	0.625540	0.312770	+	0.949829i	$0.398743\pi$
$270$	0	0
$271$	4.11888	0.250204	0.125102	−	0.992144i	$-0.460074\pi$
$271$	4.11888	0.250204	0.125102	+	0.992144i	$0.460074\pi$
$272$	26.5544	1.61010
$273$	−49.2991	−2.98372
$274$	4.43618	0.267999
$275$	0	0
$276$	−5.28212	−0.317946
$277$	−9.62736	−0.578452	−0.289226	−	0.957261i	$-0.593398\pi$
$277$	−9.62736	−0.578452	−0.289226	+	0.957261i	$0.593398\pi$
$278$	3.10063	0.185964
$279$	15.1485	0.906916
$280$	0	0
$281$	16.9191	1.00931	0.504654	−	0.863322i	$-0.331620\pi$
$281$	16.9191	1.00931	0.504654	+	0.863322i	$0.331620\pi$
$282$	0.464502	0.0276607
$283$	7.51375	0.446646	0.223323	−	0.974744i	$-0.428309\pi$
$283$	7.51375	0.446646	0.223323	+	0.974744i	$0.428309\pi$
$284$	1.66899	0.0990366
$285$	0	0
$286$	2.42557	0.143427
$287$	−18.4183	−1.08720
$288$	10.0798	0.593956
$289$	32.9750	1.93971
$290$	0	0
$291$	−14.7936	−0.867214
$292$	−19.1159	−1.11867
$293$	−15.7923	−0.922596	−0.461298	−	0.887245i	$-0.652616\pi$
$293$	−15.7923	−0.922596	−0.461298	+	0.887245i	$0.652616\pi$
$294$	−0.510014	−0.0297446
$295$	0	0
$296$	6.33503	0.368216
$297$	6.32466	0.366994
$298$	−3.03781	−0.175976
$299$	6.49089	0.375378
$300$	0	0
$301$	−13.9112	−0.801831
$302$	3.54493	0.203988
$303$	25.8005	1.48220
$304$	−0.947785	−0.0543592
$305$	0	0
$306$	6.10363	0.348921
$307$	25.0861	1.43174	0.715870	−	0.698234i	$-0.246030\pi$
$307$	25.0861	1.43174	0.715870	+	0.698234i	$0.246030\pi$
$308$	−10.1979	−0.581081
$309$	−24.5387	−1.39596
$310$	0	0
$311$	18.2599	1.03542	0.517711	−	0.855555i	$-0.326784\pi$
$311$	18.2599	1.03542	0.517711	+	0.855555i	$0.326784\pi$
$312$	−14.0117	−0.793258
$313$	−11.3712	−0.642738	−0.321369	−	0.946954i	$-0.604143\pi$
$313$	−11.3712	−0.642738	−0.321369	+	0.946954i	$0.604143\pi$
$314$	−1.43645	−0.0810636
$315$	0	0
$316$	32.3880	1.82197
$317$	−15.7315	−0.883570	−0.441785	−	0.897121i	$-0.645655\pi$
$317$	−15.7315	−0.883570	−0.441785	+	0.897121i	$0.645655\pi$
$318$	−6.86083	−0.384736
$319$	−7.61969	−0.426621
$320$	0	0
$321$	31.5706	1.76210
$322$	0.569670	0.0317465
$323$	−1.78372	−0.0992488
$324$	7.01386	0.389659
$325$	0	0
$326$	2.95059	0.163418
$327$	−3.95921	−0.218945
$328$	−5.23484	−0.289045
$329$	2.39984	0.132307
$330$	0	0
$331$	12.5991	0.692507	0.346253	−	0.938141i	$-0.387454\pi$
$331$	12.5991	0.692507	0.346253	+	0.938141i	$0.387454\pi$
$332$	1.36505	0.0749168
$333$	−33.7819	−1.85124
$334$	1.91118	0.104575
$335$	0	0
$336$	28.5295	1.55641
$337$	16.5473	0.901388	0.450694	−	0.892679i	$-0.351177\pi$
$337$	16.5473	0.901388	0.450694	+	0.892679i	$0.351177\pi$
$338$	5.89121	0.320440
$339$	4.39315	0.238603
$340$	0	0
$341$	−6.55643	−0.355050
$342$	−0.217852	−0.0117801
$343$	17.0839	0.922444
$344$	−3.95384	−0.213177
$345$	0	0
$346$	4.71300	0.253372
$347$	−8.43461	−0.452794	−0.226397	−	0.974035i	$-0.572695\pi$
$347$	−8.43461	−0.452794	−0.226397	+	0.974035i	$0.572695\pi$
$348$	21.7809	1.16758
$349$	−13.2201	−0.707658	−0.353829	−	0.935310i	$-0.615121\pi$
$349$	−13.2201	−0.707658	−0.353829	+	0.935310i	$0.615121\pi$
$350$	0	0
$351$	22.2163	1.18582
$352$	−4.36263	−0.232529
$353$	1.28663	0.0684803	0.0342401	−	0.999414i	$-0.489099\pi$
$353$	1.28663	0.0684803	0.0342401	+	0.999414i	$0.489099\pi$
$354$	5.64960	0.300273
$355$	0	0
$356$	−25.8278	−1.36887
$357$	53.6922	2.84169
$358$	4.76371	0.251770
$359$	14.7493	0.778438	0.389219	−	0.921145i	$-0.372745\pi$
$359$	14.7493	0.778438	0.389219	+	0.921145i	$0.372745\pi$
$360$	0	0
$361$	−18.9363	−0.996649
$362$	0.102137	0.00536818
$363$	20.4517	1.07344
$364$	−35.8217	−1.87757
$365$	0	0
$366$	−0.551825	−0.0288443
$367$	25.9403	1.35407	0.677036	−	0.735950i	$-0.263264\pi$
$367$	25.9403	1.35407	0.677036	+	0.735950i	$0.263264\pi$
$368$	−3.75630	−0.195811
$369$	27.9151	1.45320
$370$	0	0
$371$	−35.4462	−1.84028
$372$	18.7415	0.971704
$373$	−13.1177	−0.679209	−0.339604	−	0.940568i	$-0.610293\pi$
$373$	−13.1177	−0.679209	−0.339604	+	0.940568i	$0.610293\pi$
$374$	−2.64172	−0.136600
$375$	0	0
$376$	0.682078	0.0351755
$377$	−26.7653	−1.37848
$378$	1.94980	0.100287
$379$	9.63674	0.495006	0.247503	−	0.968887i	$-0.420390\pi$
$379$	9.63674	0.495006	0.247503	+	0.968887i	$0.420390\pi$
$380$	0	0
$381$	−23.1672	−1.18689
$382$	0.508224	0.0260030
$383$	16.1595	0.825711	0.412856	−	0.910797i	$-0.364531\pi$
$383$	16.1595	0.825711	0.412856	+	0.910797i	$0.364531\pi$
$384$	16.5668	0.845419
$385$	0	0
$386$	0.843362	0.0429260
$387$	21.0841	1.07176
$388$	−10.7493	−0.545712
$389$	27.6271	1.40075	0.700374	−	0.713776i	$-0.253017\pi$
$389$	27.6271	1.40075	0.700374	+	0.713776i	$0.253017\pi$
$390$	0	0
$391$	−7.06930	−0.357510
$392$	−0.748908	−0.0378256
$393$	−7.92080	−0.399551
$394$	1.33491	0.0672516
$395$	0	0
$396$	15.4561	0.776698
$397$	−10.7707	−0.540565	−0.270282	−	0.962781i	$-0.587117\pi$
$397$	−10.7707	−0.540565	−0.270282	+	0.962781i	$0.587117\pi$
$398$	−2.00443	−0.100473
$399$	−1.91639	−0.0959397
$400$	0	0
$401$	−31.5635	−1.57621	−0.788104	−	0.615542i	$-0.788937\pi$
$401$	−31.5635	−1.57621	−0.788104	+	0.615542i	$0.788937\pi$
$402$	1.84254	0.0918977
$403$	−23.0304	−1.14723
$404$	18.7472	0.932706
$405$	0	0
$406$	−2.34904	−0.116581
$407$	14.6212	0.724745
$408$	15.2603	0.755499
$409$	15.6426	0.773479	0.386740	−	0.922189i	$-0.373601\pi$
$409$	15.6426	0.773479	0.386740	+	0.922189i	$0.373601\pi$
$410$	0	0
$411$	−59.1453	−2.91742
$412$	−17.8303	−0.878433
$413$	29.1885	1.43627
$414$	−0.863400	−0.0424338
$415$	0	0
$416$	−15.3244	−0.751338
$417$	−41.3391	−2.02439
$418$	0.0942887	0.00461181
$419$	−11.1799	−0.546175	−0.273088	−	0.961989i	$-0.588045\pi$
$419$	−11.1799	−0.546175	−0.273088	+	0.961989i	$0.588045\pi$
$420$	0	0
$421$	0.661200	0.0322249	0.0161125	−	0.999870i	$-0.494871\pi$
$421$	0.661200	0.0322249	0.0161125	+	0.999870i	$0.494871\pi$
$422$	1.68566	0.0820565
$423$	−3.63722	−0.176848
$424$	−10.0745	−0.489260
$425$	0	0
$426$	0.464502	0.0225052
$427$	−2.85098	−0.137969
$428$	22.9398	1.10884
$429$	−32.3389	−1.56134
$430$	0	0
$431$	−15.2276	−0.733488	−0.366744	−	0.930322i	$-0.619527\pi$
$431$	−15.2276	−0.733488	−0.366744	+	0.930322i	$0.619527\pi$
$432$	−12.8566	−0.618565
$433$	22.2662	1.07005	0.535023	−	0.844838i	$-0.320303\pi$
$433$	22.2662	1.07005	0.535023	+	0.844838i	$0.320303\pi$
$434$	−2.02125	−0.0970233
$435$	0	0
$436$	−2.87684	−0.137775
$437$	0.252319	0.0120701
$438$	−5.32020	−0.254209
$439$	21.1491	1.00939	0.504695	−	0.863298i	$-0.331605\pi$
$439$	21.1491	1.00939	0.504695	+	0.863298i	$0.331605\pi$
$440$	0	0
$441$	3.99359	0.190171
$442$	−9.27941	−0.441376
$443$	9.94721	0.472606	0.236303	−	0.971679i	$-0.424064\pi$
$443$	9.94721	0.472606	0.236303	+	0.971679i	$0.424064\pi$
$444$	−41.7947	−1.98349
$445$	0	0
$446$	−2.72824	−0.129186
$447$	40.5016	1.91566
$448$	19.8179	0.936308
$449$	−8.32870	−0.393056	−0.196528	−	0.980498i	$-0.562967\pi$
$449$	−8.32870	−0.393056	−0.196528	+	0.980498i	$0.562967\pi$
$450$	0	0
$451$	−12.0819	−0.568916
$452$	3.19215	0.150146
$453$	−47.2627	−2.22060
$454$	1.16769	0.0548024
$455$	0	0
$456$	−0.544675	−0.0255067
$457$	−33.2599	−1.55583	−0.777916	−	0.628369i	$-0.783723\pi$
$457$	−33.2599	−1.55583	−0.777916	+	0.628369i	$0.783723\pi$
$458$	4.51333	0.210894
$459$	−24.1960	−1.12937
$460$	0	0
$461$	14.8481	0.691544	0.345772	−	0.938318i	$-0.387617\pi$
$461$	14.8481	0.691544	0.345772	+	0.938318i	$0.387617\pi$
$462$	−2.83821	−0.132046
$463$	−15.6422	−0.726956	−0.363478	−	0.931603i	$-0.618411\pi$
$463$	−15.6422	−0.726956	−0.363478	+	0.931603i	$0.618411\pi$
$464$	15.4891	0.719065
$465$	0	0
$466$	−4.41314	−0.204435
$467$	−5.26987	−0.243861	−0.121930	−	0.992539i	$-0.538908\pi$
$467$	−5.26987	−0.243861	−0.121930	+	0.992539i	$0.538908\pi$
$468$	54.2918	2.50964
$469$	9.51944	0.439567
$470$	0	0
$471$	19.1514	0.882452
$472$	8.29591	0.381850
$473$	−9.12541	−0.419587
$474$	9.01398	0.414026
$475$	0	0
$476$	39.0138	1.78819
$477$	53.7228	2.45980
$478$	−5.40179	−0.247072
$479$	0.404422	0.0184785	0.00923927	−	0.999957i	$-0.497059\pi$
$479$	0.404422	0.0184785	0.00923927	+	0.999957i	$0.497059\pi$
$480$	0	0
$481$	51.3590	2.34177
$482$	3.06506	0.139610
$483$	−7.59513	−0.345590
$484$	14.8606	0.675481
$485$	0	0
$486$	4.02853	0.182738
$487$	−17.0409	−0.772198	−0.386099	−	0.922457i	$-0.626178\pi$
$487$	−17.0409	−0.772198	−0.386099	+	0.922457i	$0.626178\pi$
$488$	−0.810302	−0.0366807
$489$	−39.3388	−1.77896
$490$	0	0
$491$	−9.42821	−0.425489	−0.212745	−	0.977108i	$-0.568240\pi$
$491$	−9.42821	−0.425489	−0.212745	+	0.977108i	$0.568240\pi$
$492$	34.5362	1.55701
$493$	29.1503	1.31287
$494$	0.331203	0.0149015
$495$	0	0
$496$	13.3278	0.598434
$497$	2.39984	0.107647
$498$	0.379910	0.0170242
$499$	−25.7959	−1.15478	−0.577391	−	0.816468i	$-0.695929\pi$
$499$	−25.7959	−1.15478	−0.577391	+	0.816468i	$0.695929\pi$
$500$	0	0
$501$	−25.4808	−1.13840
$502$	−2.66992	−0.119165
$503$	21.6111	0.963589	0.481795	−	0.876284i	$-0.339985\pi$
$503$	21.6111	0.963589	0.481795	+	0.876284i	$0.339985\pi$
$504$	9.62926	0.428921
$505$	0	0
$506$	0.373689	0.0166125
$507$	−78.5445	−3.48828
$508$	−16.8338	−0.746877
$509$	−6.13182	−0.271788	−0.135894	−	0.990723i	$-0.543391\pi$
$509$	−6.13182	−0.271788	−0.135894	+	0.990723i	$0.543391\pi$
$510$	0	0
$511$	−27.4866	−1.21594
$512$	14.8831	0.657748
$513$	0.863609	0.0381293
$514$	−2.82006	−0.124388
$515$	0	0
$516$	26.0850	1.14833
$517$	1.57423	0.0692345
$518$	4.50750	0.198048
$519$	−62.8360	−2.75819
$520$	0	0
$521$	22.4021	0.981454	0.490727	−	0.871313i	$-0.336731\pi$
$521$	22.4021	0.981454	0.490727	+	0.871313i	$0.336731\pi$
$522$	3.56024	0.155827
$523$	8.25468	0.360952	0.180476	−	0.983579i	$-0.442236\pi$
$523$	8.25468	0.360952	0.180476	+	0.983579i	$0.442236\pi$
$524$	−5.75540	−0.251426
$525$	0	0
$526$	−4.40619	−0.192119
$527$	25.0827	1.09262
$528$	18.7146	0.814449
$529$	1.00000	0.0434783
$530$	0	0
$531$	−44.2384	−1.91978
$532$	−1.39249	−0.0603720
$533$	−42.4395	−1.83826
$534$	−7.18821	−0.311064
$535$	0	0
$536$	2.70560	0.116864
$537$	−63.5121	−2.74075
$538$	2.07477	0.0894498
$539$	−1.72847	−0.0744505
$540$	0	0
$541$	24.9079	1.07087	0.535437	−	0.844575i	$-0.320147\pi$
$541$	24.9079	1.07087	0.535437	+	0.844575i	$0.320147\pi$
$542$	0.832950	0.0357782
$543$	−1.36174	−0.0584376
$544$	16.6899	0.715575
$545$	0	0
$546$	−9.96962	−0.426660
$547$	−19.8049	−0.846795	−0.423398	−	0.905944i	$-0.639163\pi$
$547$	−19.8049	−0.846795	−0.423398	+	0.905944i	$0.639163\pi$
$548$	−42.9761	−1.83585
$549$	4.32098	0.184415
$550$	0	0
$551$	−1.04044	−0.0443243
$552$	−2.15868	−0.0918793
$553$	46.5704	1.98038
$554$	−1.94692	−0.0827165
$555$	0	0
$556$	−30.0378	−1.27389
$557$	−36.6380	−1.55240	−0.776201	−	0.630486i	$-0.782856\pi$
$557$	−36.6380	−1.55240	−0.776201	+	0.630486i	$0.782856\pi$
$558$	3.06344	0.129686
$559$	−32.0543	−1.35575
$560$	0	0
$561$	35.2207	1.48702
$562$	3.42150	0.144327
$563$	19.0783	0.804054	0.402027	−	0.915628i	$-0.368306\pi$
$563$	19.0783	0.804054	0.402027	+	0.915628i	$0.368306\pi$
$564$	−4.49993	−0.189481
$565$	0	0
$566$	1.51949	0.0638687
$567$	10.0852	0.423537
$568$	0.682078	0.0286194
$569$	4.50086	0.188686	0.0943429	−	0.995540i	$-0.469925\pi$
$569$	4.50086	0.188686	0.0943429	+	0.995540i	$0.469925\pi$
$570$	0	0
$571$	1.25913	0.0526930	0.0263465	−	0.999653i	$-0.491613\pi$
$571$	1.25913	0.0526930	0.0263465	+	0.999653i	$0.491613\pi$
$572$	−23.4981	−0.982503
$573$	−6.77589	−0.283067
$574$	−3.72469	−0.155466
$575$	0	0
$576$	−30.0363	−1.25151
$577$	1.33814	0.0557077	0.0278539	−	0.999612i	$-0.491133\pi$
$577$	1.33814	0.0557077	0.0278539	+	0.999612i	$0.491133\pi$
$578$	6.66845	0.277371
$579$	−11.2441	−0.467289
$580$	0	0
$581$	1.96279	0.0814304
$582$	−2.99166	−0.124008
$583$	−23.2518	−0.962990
$584$	−7.81221	−0.323272
$585$	0	0
$586$	−3.19363	−0.131928
$587$	−22.4997	−0.928664	−0.464332	−	0.885661i	$-0.653705\pi$
$587$	−22.4997	−0.928664	−0.464332	+	0.885661i	$0.653705\pi$
$588$	4.94083	0.203757
$589$	−0.895256	−0.0368884
$590$	0	0
$591$	−17.7976	−0.732096
$592$	−29.7216	−1.22155
$593$	−30.8988	−1.26886	−0.634432	−	0.772979i	$-0.718766\pi$
$593$	−30.8988	−1.26886	−0.634432	+	0.772979i	$0.718766\pi$
$594$	1.27902	0.0524788
$595$	0	0
$596$	29.4292	1.20547
$597$	26.7240	1.09374
$598$	1.31263	0.0536776
$599$	−7.34413	−0.300073	−0.150036	−	0.988680i	$-0.547939\pi$
$599$	−7.34413	−0.300073	−0.150036	+	0.988680i	$0.547939\pi$
$600$	0	0
$601$	−5.10253	−0.208136	−0.104068	−	0.994570i	$-0.533186\pi$
$601$	−5.10253	−0.208136	−0.104068	+	0.994570i	$0.533186\pi$
$602$	−2.81323	−0.114659
$603$	−14.4278	−0.587544
$604$	−34.3420	−1.39735
$605$	0	0
$606$	5.21757	0.211949
$607$	21.4965	0.872518	0.436259	−	0.899821i	$-0.356303\pi$
$607$	21.4965	0.872518	0.436259	+	0.899821i	$0.356303\pi$
$608$	−0.595701	−0.0241589
$609$	31.3186	1.26909
$610$	0	0
$611$	5.52970	0.223708
$612$	−59.1298	−2.39018
$613$	−44.4369	−1.79479	−0.897396	−	0.441227i	$-0.854543\pi$
$613$	−44.4369	−1.79479	−0.897396	+	0.441227i	$0.854543\pi$
$614$	5.07310	0.204733
$615$	0	0
$616$	−4.16765	−0.167919
$617$	25.0662	1.00913	0.504564	−	0.863375i	$-0.331653\pi$
$617$	25.0662	1.00913	0.504564	+	0.863375i	$0.331653\pi$
$618$	−4.96238	−0.199616
$619$	−11.6002	−0.466252	−0.233126	−	0.972447i	$-0.574895\pi$
$619$	−11.6002	−0.466252	−0.233126	+	0.972447i	$0.574895\pi$
$620$	0	0
$621$	3.42269	0.137348
$622$	3.69265	0.148062
$623$	−37.1377	−1.48789
$624$	65.7378	2.63162
$625$	0	0
$626$	−2.29957	−0.0919091
$627$	−1.25710	−0.0502039
$628$	13.9158	0.555301
$629$	−55.9357	−2.23030
$630$	0	0
$631$	−9.17437	−0.365226	−0.182613	−	0.983185i	$-0.558456\pi$
$631$	−9.17437	−0.365226	−0.182613	+	0.983185i	$0.558456\pi$
$632$	13.2362	0.526507
$633$	−22.4740	−0.893261
$634$	−3.18134	−0.126347
$635$	0	0
$636$	66.4652	2.63552
$637$	−6.07150	−0.240562
$638$	−1.54091	−0.0610052
$639$	−3.63722	−0.143886
$640$	0	0
$641$	3.98400	0.157359	0.0786793	−	0.996900i	$-0.474930\pi$
$641$	3.98400	0.157359	0.0786793	+	0.996900i	$0.474930\pi$
$642$	6.38443	0.251973
$643$	13.3005	0.524520	0.262260	−	0.964997i	$-0.415532\pi$
$643$	13.3005	0.524520	0.262260	+	0.964997i	$0.415532\pi$
$644$	−5.51876	−0.217470
$645$	0	0
$646$	−0.360717	−0.0141922
$647$	3.02871	0.119071	0.0595354	−	0.998226i	$-0.481038\pi$
$647$	3.02871	0.119071	0.0595354	+	0.998226i	$0.481038\pi$
$648$	2.86639	0.112603
$649$	19.1469	0.751580
$650$	0	0
$651$	26.9483	1.05619
$652$	−28.5843	−1.11945
$653$	24.8569	0.972727	0.486363	−	0.873757i	$-0.338323\pi$
$653$	24.8569	0.972727	0.486363	+	0.873757i	$0.338323\pi$
$654$	−0.800660	−0.0313083
$655$	0	0
$656$	24.5599	0.958903
$657$	41.6591	1.62528
$658$	0.485312	0.0189194
$659$	30.2901	1.17994	0.589968	−	0.807427i	$-0.299140\pi$
$659$	30.2901	1.17994	0.589968	+	0.807427i	$0.299140\pi$
$660$	0	0
$661$	−41.7574	−1.62418	−0.812088	−	0.583535i	$-0.801669\pi$
$661$	−41.7574	−1.62418	−0.812088	+	0.583535i	$0.801669\pi$
$662$	2.54787	0.0990259
$663$	123.718	4.80479
$664$	0.557862	0.0216493
$665$	0	0
$666$	−6.83163	−0.264720
$667$	−4.12351	−0.159663
$668$	−18.5148	−0.716360
$669$	36.3742	1.40631
$670$	0	0
$671$	−1.87017	−0.0721971
$672$	17.9314	0.691717
$673$	−18.1446	−0.699424	−0.349712	−	0.936857i	$-0.613721\pi$
$673$	−18.1446	−0.699424	−0.349712	+	0.936857i	$0.613721\pi$
$674$	3.34631	0.128895
$675$	0	0
$676$	−57.0719	−2.19507
$677$	16.4647	0.632790	0.316395	−	0.948627i	$-0.397527\pi$
$677$	16.4647	0.632790	0.316395	+	0.948627i	$0.397527\pi$
$678$	0.888415	0.0341194
$679$	−15.4563	−0.593159
$680$	0	0
$681$	−15.5682	−0.596575
$682$	−1.32589	−0.0507709
$683$	46.7050	1.78712	0.893558	−	0.448948i	$-0.148201\pi$
$683$	46.7050	1.78712	0.893558	+	0.448948i	$0.148201\pi$
$684$	2.11047	0.0806959
$685$	0	0
$686$	3.45483	0.131906
$687$	−60.1740	−2.29578
$688$	18.5499	0.707209
$689$	−81.6752	−3.11158
$690$	0	0
$691$	−11.5366	−0.438872	−0.219436	−	0.975627i	$-0.570422\pi$
$691$	−11.5366	−0.438872	−0.219436	+	0.975627i	$0.570422\pi$
$692$	−45.6578	−1.73565
$693$	22.2242	0.844228
$694$	−1.70571	−0.0647478
$695$	0	0
$696$	8.90132	0.337404
$697$	46.2214	1.75076
$698$	−2.67347	−0.101192
$699$	58.8381	2.22546
$700$	0	0
$701$	31.8694	1.20369	0.601845	−	0.798613i	$-0.294432\pi$
$701$	31.8694	1.20369	0.601845	+	0.798613i	$0.294432\pi$
$702$	4.49274	0.169567
$703$	1.99647	0.0752982
$704$	13.0000	0.489957
$705$	0	0
$706$	0.260191	0.00979243
$707$	26.9564	1.01380
$708$	−54.7313	−2.05693
$709$	5.06884	0.190364	0.0951822	−	0.995460i	$-0.469657\pi$
$709$	5.06884	0.190364	0.0951822	+	0.995460i	$0.469657\pi$
$710$	0	0
$711$	−70.5827	−2.64706
$712$	−10.5552	−0.395573
$713$	−3.54811	−0.132878
$714$	10.8580	0.406352
$715$	0	0
$716$	−46.1491	−1.72467
$717$	72.0193	2.68961
$718$	2.98271	0.111314
$719$	6.53346	0.243657	0.121828	−	0.992551i	$-0.461124\pi$
$719$	6.53346	0.243657	0.121828	+	0.992551i	$0.461124\pi$
$720$	0	0
$721$	−25.6380	−0.954809
$722$	−3.82944	−0.142517
$723$	−40.8649	−1.51978
$724$	−0.989462	−0.0367731
$725$	0	0
$726$	4.13589	0.153497
$727$	46.2193	1.71418	0.857089	−	0.515169i	$-0.172271\pi$
$727$	46.2193	1.71418	0.857089	+	0.515169i	$0.172271\pi$
$728$	−14.6395	−0.542574
$729$	−42.9699	−1.59148
$730$	0	0
$731$	34.9107	1.29122
$732$	5.34588	0.197589
$733$	20.2561	0.748177	0.374089	−	0.927393i	$-0.377956\pi$
$733$	20.2561	0.748177	0.374089	+	0.927393i	$0.377956\pi$
$734$	5.24583	0.193627
$735$	0	0
$736$	−2.36090	−0.0870240
$737$	6.24450	0.230019
$738$	5.64519	0.207802
$739$	0.454209	0.0167083	0.00835417	−	0.999965i	$-0.497341\pi$
$739$	0.454209	0.0167083	0.00835417	+	0.999965i	$0.497341\pi$
$740$	0	0
$741$	−4.41576	−0.162217
$742$	−7.16820	−0.263153
$743$	17.9525	0.658614	0.329307	−	0.944223i	$-0.393185\pi$
$743$	17.9525	0.658614	0.329307	+	0.944223i	$0.393185\pi$
$744$	7.65922	0.280801
$745$	0	0
$746$	−2.65276	−0.0971243
$747$	−2.97483	−0.108843
$748$	25.5920	0.935736
$749$	32.9849	1.20524
$750$	0	0
$751$	14.8866	0.543219	0.271610	−	0.962408i	$-0.412444\pi$
$751$	14.8866	0.543219	0.271610	+	0.962408i	$0.412444\pi$
$752$	−3.20005	−0.116694
$753$	35.5967	1.29722
$754$	−5.41266	−0.197118
$755$	0	0
$756$	−18.8890	−0.686986
$757$	31.7028	1.15226	0.576129	−	0.817358i	$-0.304562\pi$
$757$	31.7028	1.15226	0.576129	+	0.817358i	$0.304562\pi$
$758$	1.94881	0.0707840
$759$	−4.98220	−0.180842
$760$	0	0
$761$	−6.80194	−0.246570	−0.123285	−	0.992371i	$-0.539343\pi$
$761$	−6.80194	−0.246570	−0.123285	+	0.992371i	$0.539343\pi$
$762$	−4.68505	−0.169721
$763$	−4.13658	−0.149754
$764$	−4.92349	−0.178126
$765$	0	0
$766$	3.26789	0.118074
$767$	67.2561	2.42848
$768$	−34.5860	−1.24802
$769$	19.2067	0.692612	0.346306	−	0.938122i	$-0.387436\pi$
$769$	19.2067	0.692612	0.346306	+	0.938122i	$0.387436\pi$
$770$	0	0
$771$	37.5985	1.35408
$772$	−8.17019	−0.294051
$773$	−27.6037	−0.992835	−0.496418	−	0.868084i	$-0.665351\pi$
$773$	−27.6037	−0.992835	−0.496418	+	0.868084i	$0.665351\pi$
$774$	4.26377	0.153258
$775$	0	0
$776$	−4.39297	−0.157699
$777$	−60.0962	−2.15594
$778$	5.58694	0.200302
$779$	−1.64974	−0.0591082
$780$	0	0
$781$	1.57423	0.0563303
$782$	−1.42961	−0.0511226
$783$	−14.1135	−0.504375
$784$	3.51360	0.125486
$785$	0	0
$786$	−1.60180	−0.0571344
$787$	35.6271	1.26997	0.634984	−	0.772525i	$-0.281007\pi$
$787$	35.6271	1.26997	0.634984	+	0.772525i	$0.281007\pi$
$788$	−12.9321	−0.460686
$789$	58.7455	2.09139
$790$	0	0
$791$	4.58997	0.163200
$792$	6.31653	0.224448
$793$	−6.56923	−0.233280
$794$	−2.17812	−0.0772987
$795$	0	0
$796$	19.4182	0.688258
$797$	−9.85579	−0.349110	−0.174555	−	0.984647i	$-0.555849\pi$
$797$	−9.85579	−0.349110	−0.174555	+	0.984647i	$0.555849\pi$
$798$	−0.387547	−0.0137190
$799$	−6.02246	−0.213059
$800$	0	0
$801$	56.2863	1.98878
$802$	−6.38301	−0.225392
$803$	−18.0305	−0.636282
$804$	−17.8499	−0.629517
$805$	0	0
$806$	−4.65737	−0.164049
$807$	−27.6619	−0.973745
$808$	7.66151	0.269531
$809$	35.4171	1.24520	0.622599	−	0.782541i	$-0.286077\pi$
$809$	35.4171	1.24520	0.622599	+	0.782541i	$0.286077\pi$
$810$	0	0
$811$	−23.6023	−0.828790	−0.414395	−	0.910097i	$-0.636007\pi$
$811$	−23.6023	−0.828790	−0.414395	+	0.910097i	$0.636007\pi$
$812$	22.7567	0.798603
$813$	−11.1053	−0.389480
$814$	2.95680	0.103636
$815$	0	0
$816$	−71.5958	−2.50635
$817$	−1.24604	−0.0435934
$818$	3.16337	0.110605
$819$	78.0657	2.72784
$820$	0	0
$821$	−21.1904	−0.739548	−0.369774	−	0.929122i	$-0.620565\pi$
$821$	−21.1904	−0.739548	−0.369774	+	0.929122i	$0.620565\pi$
$822$	−11.9608	−0.417180
$823$	−28.8463	−1.00552	−0.502759	−	0.864427i	$-0.667682\pi$
$823$	−28.8463	−1.00552	−0.502759	+	0.864427i	$0.667682\pi$
$824$	−7.28679	−0.253847
$825$	0	0
$826$	5.90271	0.205381
$827$	−7.85313	−0.273080	−0.136540	−	0.990635i	$-0.543598\pi$
$827$	−7.85313	−0.273080	−0.136540	+	0.990635i	$0.543598\pi$
$828$	8.36430	0.290680
$829$	−7.58148	−0.263316	−0.131658	−	0.991295i	$-0.542030\pi$
$829$	−7.58148	−0.263316	−0.131658	+	0.991295i	$0.542030\pi$
$830$	0	0
$831$	25.9572	0.900446
$832$	45.6644	1.58313
$833$	6.61254	0.229111
$834$	−8.35990	−0.289480
$835$	0	0
$836$	−0.913435	−0.0315918
$837$	−12.1441	−0.419760
$838$	−2.26089	−0.0781010
$839$	33.2424	1.14765	0.573827	−	0.818977i	$-0.305458\pi$
$839$	33.2424	1.14765	0.573827	+	0.818977i	$0.305458\pi$
$840$	0	0
$841$	−11.9967	−0.413678
$842$	0.133713	0.00460804
$843$	−45.6171	−1.57114
$844$	−16.3300	−0.562103
$845$	0	0
$846$	−0.735545	−0.0252886
$847$	21.3679	0.734211
$848$	47.2657	1.62311
$849$	−20.2585	−0.695271
$850$	0	0
$851$	7.91248	0.271236
$852$	−4.49993	−0.154165
$853$	−21.1798	−0.725183	−0.362591	−	0.931948i	$-0.618108\pi$
$853$	−21.1798	−0.725183	−0.362591	+	0.931948i	$0.618108\pi$
$854$	−0.576546	−0.0197290
$855$	0	0
$856$	9.37493	0.320429
$857$	13.2340	0.452066	0.226033	−	0.974120i	$-0.427424\pi$
$857$	13.2340	0.452066	0.226033	+	0.974120i	$0.427424\pi$
$858$	−6.53980	−0.223265
$859$	−31.6863	−1.08112	−0.540561	−	0.841305i	$-0.681788\pi$
$859$	−31.6863	−1.08112	−0.540561	+	0.841305i	$0.681788\pi$
$860$	0	0
$861$	49.6594	1.69239
$862$	−3.07944	−0.104886
$863$	1.12760	0.0383840	0.0191920	−	0.999816i	$-0.493891\pi$
$863$	1.12760	0.0383840	0.0191920	+	0.999816i	$0.493891\pi$
$864$	−8.08063	−0.274909
$865$	0	0
$866$	4.50283	0.153013
$867$	−88.9070	−3.01944
$868$	19.5812	0.664628
$869$	30.5490	1.03630
$870$	0	0
$871$	21.9347	0.743228
$872$	−1.17569	−0.0398140
$873$	23.4258	0.792843
$874$	0.0510258	0.00172597
$875$	0	0
$876$	51.5402	1.74138
$877$	30.9499	1.04510	0.522552	−	0.852608i	$-0.324980\pi$
$877$	30.9499	1.04510	0.522552	+	0.852608i	$0.324980\pi$
$878$	4.27692	0.144339
$879$	42.5791	1.43616
$880$	0	0
$881$	45.9333	1.54753	0.773765	−	0.633472i	$-0.218371\pi$
$881$	45.9333	1.54753	0.773765	+	0.633472i	$0.218371\pi$
$882$	0.807614	0.0271938
$883$	14.0404	0.472496	0.236248	−	0.971693i	$-0.424082\pi$
$883$	14.0404	0.472496	0.236248	+	0.971693i	$0.424082\pi$
$884$	89.8955	3.02351
$885$	0	0
$886$	2.01160	0.0675809
$887$	−33.4833	−1.12426	−0.562129	−	0.827049i	$-0.690018\pi$
$887$	−33.4833	−1.12426	−0.562129	+	0.827049i	$0.690018\pi$
$888$	−17.0805	−0.573183
$889$	−24.2051	−0.811814
$890$	0	0
$891$	6.61560	0.221631
$892$	26.4302	0.884947
$893$	0.214955	0.00719319
$894$	8.19053	0.273932
$895$	0	0
$896$	17.3090	0.578252
$897$	−17.5007	−0.584331
$898$	−1.68429	−0.0562055
$899$	14.6307	0.487960
$900$	0	0
$901$	88.9534	2.96347
$902$	−2.44330	−0.0813529
$903$	37.5074	1.24817
$904$	1.30455	0.0433888
$905$	0	0
$906$	−9.55780	−0.317537
$907$	22.0732	0.732929	0.366464	−	0.930432i	$-0.380568\pi$
$907$	22.0732	0.732929	0.366464	+	0.930432i	$0.380568\pi$
$908$	−11.3122	−0.375407
$909$	−40.8555	−1.35509
$910$	0	0
$911$	−29.9624	−0.992699	−0.496349	−	0.868123i	$-0.665327\pi$
$911$	−29.9624	−0.992699	−0.496349	+	0.868123i	$0.665327\pi$
$912$	2.55541	0.0846181
$913$	1.28754	0.0426113
$914$	−6.72605	−0.222478
$915$	0	0
$916$	−43.7235	−1.44467
$917$	−8.27565	−0.273286
$918$	−4.89309	−0.161496
$919$	27.8980	0.920269	0.460134	−	0.887849i	$-0.347801\pi$
$919$	27.8980	0.920269	0.460134	+	0.887849i	$0.347801\pi$
$920$	0	0
$921$	−67.6370	−2.22871
$922$	3.00269	0.0988883
$923$	5.52970	0.182012
$924$	27.4956	0.904538
$925$	0	0
$926$	−3.16328	−0.103952
$927$	38.8573	1.27624
$928$	9.73521	0.319574
$929$	−25.6063	−0.840115	−0.420057	−	0.907498i	$-0.637990\pi$
$929$	−25.6063	−0.840115	−0.420057	+	0.907498i	$0.637990\pi$
$930$	0	0
$931$	−0.236016	−0.00773512
$932$	42.7529	1.40042
$933$	−49.2322	−1.61179
$934$	−1.06571	−0.0348711
$935$	0	0
$936$	22.1877	0.725229
$937$	−23.1946	−0.757736	−0.378868	−	0.925451i	$-0.623687\pi$
$937$	−23.1946	−0.757736	−0.378868	+	0.925451i	$0.623687\pi$
$938$	1.92509	0.0628564
$939$	30.6589	1.00052
$940$	0	0
$941$	8.04530	0.262269	0.131135	−	0.991365i	$-0.458138\pi$
$941$	8.04530	0.262269	0.131135	+	0.991365i	$0.458138\pi$
$942$	3.87294	0.126187
$943$	−6.53833	−0.212917
$944$	−38.9213	−1.26678
$945$	0	0
$946$	−1.84541	−0.0599993
$947$	−42.2271	−1.37220	−0.686098	−	0.727509i	$-0.740678\pi$
$947$	−42.2271	−1.37220	−0.686098	+	0.727509i	$0.740678\pi$
$948$	−87.3242	−2.83616
$949$	−63.3347	−2.05593
$950$	0	0
$951$	42.4152	1.37541
$952$	15.9440	0.516748
$953$	13.3175	0.431396	0.215698	−	0.976460i	$-0.430797\pi$
$953$	13.3175	0.431396	0.215698	+	0.976460i	$0.430797\pi$
$954$	10.8642	0.351742
$955$	0	0
$956$	52.3306	1.69249
$957$	20.5442	0.664098
$958$	0.0817852	0.00264236
$959$	−61.7950	−1.99546
$960$	0	0
$961$	−18.4109	−0.593901
$962$	10.3862	0.334864
$963$	−49.9924	−1.61098
$964$	−29.6932	−0.956355
$965$	0	0
$966$	−1.53594	−0.0494181
$967$	−42.9969	−1.38269	−0.691344	−	0.722526i	$-0.742981\pi$
$967$	−42.9969	−1.38269	−0.691344	+	0.722526i	$0.742981\pi$
$968$	6.07316	0.195199
$969$	4.80925	0.154495
$970$	0	0
$971$	−9.01250	−0.289225	−0.144612	−	0.989488i	$-0.546194\pi$
$971$	−9.01250	−0.289225	−0.144612	+	0.989488i	$0.546194\pi$
$972$	−39.0269	−1.25179
$973$	−43.1911	−1.38464
$974$	−3.44614	−0.110421
$975$	0	0
$976$	3.80164	0.121687
$977$	−41.1074	−1.31514	−0.657571	−	0.753392i	$-0.728416\pi$
$977$	−41.1074	−1.31514	−0.657571	+	0.753392i	$0.728416\pi$
$978$	−7.95537	−0.254385
$979$	−24.3613	−0.778591
$980$	0	0
$981$	6.26945	0.200168
$982$	−1.90664	−0.0608434
$983$	59.8861	1.91007	0.955035	−	0.296493i	$-0.0958173\pi$
$983$	59.8861	1.91007	0.955035	+	0.296493i	$0.0958173\pi$
$984$	14.1141	0.449942
$985$	0	0
$986$	5.89499	0.187735
$987$	−6.47042	−0.205956
$988$	−3.20857	−0.102078
$989$	−4.93835	−0.157030
$990$	0	0
$991$	20.8275	0.661607	0.330804	−	0.943700i	$-0.392680\pi$
$991$	20.8275	0.661607	0.330804	+	0.943700i	$0.392680\pi$
$992$	8.37674	0.265962
$993$	−33.9695	−1.07799
$994$	0.485312	0.0153932
$995$	0	0
$996$	−3.68043	−0.116619
$997$	12.7634	0.404222	0.202111	−	0.979363i	$-0.435220\pi$
$997$	12.7634	0.404222	0.202111	+	0.979363i	$0.435220\pi$
$998$	−5.21662	−0.165129
$999$	27.0819	0.856834

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.a.k.1.4	✓	7
3.2	odd	2		5175.2.a.cg.1.4		7
4.3	odd	2		9200.2.a.da.1.6		7
5.2	odd	4		575.2.b.f.24.8		14
5.3	odd	4		575.2.b.f.24.7		14
5.4	even	2		575.2.a.l.1.4	yes	7
15.14	odd	2		5175.2.a.cb.1.4		7
20.19	odd	2		9200.2.a.db.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.k.1.4	✓	7	1.1	even	1	trivial
575.2.a.l.1.4	yes	7	5.4	even	2
575.2.b.f.24.7		14	5.3	odd	4
575.2.b.f.24.8		14	5.2	odd	4
5175.2.a.cb.1.4		7	15.14	odd	2
5175.2.a.cg.1.4		7	3.2	odd	2
9200.2.a.da.1.6		7	4.3	odd	2
9200.2.a.db.1.2		7	20.19	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.a (trivial)

\(f(q)\)	\(=\)	\(q+0.202227 q^{2} -2.69619 q^{3} -1.95910 q^{4} -0.545243 q^{6} -2.81698 q^{7} -0.800639 q^{8} +4.26945 q^{9} +O(q^{10})\)	\(q+0.202227 q^{2} -2.69619 q^{3} -1.95910 q^{4} -0.545243 q^{6} -2.81698 q^{7} -0.800639 q^{8} +4.26945 q^{9} -1.84786 q^{11} +5.28212 q^{12} -6.49089 q^{13} -0.569670 q^{14} +3.75630 q^{16} +7.06930 q^{17} +0.863400 q^{18} -0.252319 q^{19} +7.59513 q^{21} -0.373689 q^{22} -1.00000 q^{23} +2.15868 q^{24} -1.31263 q^{26} -3.42269 q^{27} +5.51876 q^{28} +4.12351 q^{29} +3.54811 q^{31} +2.36090 q^{32} +4.98220 q^{33} +1.42961 q^{34} -8.36430 q^{36} -7.91248 q^{37} -0.0510258 q^{38} +17.5007 q^{39} +6.53833 q^{41} +1.53594 q^{42} +4.93835 q^{43} +3.62016 q^{44} -0.202227 q^{46} -0.851917 q^{47} -10.1277 q^{48} +0.935388 q^{49} -19.0602 q^{51} +12.7163 q^{52} +12.5831 q^{53} -0.692161 q^{54} +2.25538 q^{56} +0.680301 q^{57} +0.833886 q^{58} -10.3616 q^{59} +1.01207 q^{61} +0.717524 q^{62} -12.0270 q^{63} -7.03516 q^{64} +1.00754 q^{66} -3.37930 q^{67} -13.8495 q^{68} +2.69619 q^{69} -0.851917 q^{71} -3.41829 q^{72} +9.75748 q^{73} -1.60012 q^{74} +0.494319 q^{76} +5.20540 q^{77} +3.53911 q^{78} -16.5320 q^{79} -3.58013 q^{81} +1.32223 q^{82} -0.696772 q^{83} -14.8796 q^{84} +0.998669 q^{86} -11.1178 q^{87} +1.47947 q^{88} +13.1835 q^{89} +18.2847 q^{91} +1.95910 q^{92} -9.56638 q^{93} -0.172281 q^{94} -6.36545 q^{96} +5.48684 q^{97} +0.189161 q^{98} -7.88937 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9	\( 7 q - q^{2} + 11 q^{4} + 5 q^{6} + 3 q^{7} - 6 q^{8} + 15 q^{9} - q^{11} + 6 q^{12} - 3 q^{13} + 7 q^{14} + 7 q^{16} + 10 q^{17} - 24 q^{18} + 15 q^{19} + 2 q^{21} + 21 q^{22} - 7 q^{23} + 18 q^{24} - 20 q^{26} - 11 q^{28} + 3 q^{29} + 14 q^{31} + 17 q^{32} + 6 q^{33} + 20 q^{34} - 10 q^{37} - 31 q^{38} - 8 q^{39} + 19 q^{41} + 44 q^{42} + 5 q^{43} - 3 q^{44} + q^{46} - 14 q^{47} - 27 q^{48} + 40 q^{49} + 2 q^{51} + 16 q^{52} + 4 q^{53} - q^{54} - 9 q^{56} - 4 q^{57} - 13 q^{58} - 16 q^{59} + 40 q^{61} - 12 q^{62} + 53 q^{63} - 4 q^{64} - 54 q^{66} - 4 q^{67} + 20 q^{68} - 14 q^{71} - 6 q^{72} - 3 q^{73} - 18 q^{74} + 35 q^{76} - 17 q^{77} + 23 q^{78} - q^{79} + 47 q^{81} - 22 q^{82} + 17 q^{83} - 60 q^{84} - 35 q^{86} - 56 q^{87} + 57 q^{88} + 16 q^{89} + 25 q^{91} - 11 q^{92} + 14 q^{93} + 7 q^{94} - 19 q^{96} - 24 q^{97} - 46 q^{98} - 53 q^{99}+O(q^{100}) \) 7 * q - q^2 + 11 * q^4 + 5 * q^6 + 3 * q^7 - 6 * q^8 + 15 * q^9 - q^11 + 6 * q^12 - 3 * q^13 + 7 * q^14 + 7 * q^16 + 10 * q^17 - 24 * q^18 + 15 * q^19 + 2 * q^21 + 21 * q^22 - 7 * q^23 + 18 * q^24 - 20 * q^26 - 11 * q^28 + 3 * q^29 + 14 * q^31 + 17 * q^32 + 6 * q^33 + 20 * q^34 - 10 * q^37 - 31 * q^38 - 8 * q^39 + 19 * q^41 + 44 * q^42 + 5 * q^43 - 3 * q^44 + q^46 - 14 * q^47 - 27 * q^48 + 40 * q^49 + 2 * q^51 + 16 * q^52 + 4 * q^53 - q^54 - 9 * q^56 - 4 * q^57 - 13 * q^58 - 16 * q^59 + 40 * q^61 - 12 * q^62 + 53 * q^63 - 4 * q^64 - 54 * q^66 - 4 * q^67 + 20 * q^68 - 14 * q^71 - 6 * q^72 - 3 * q^73 - 18 * q^74 + 35 * q^76 - 17 * q^77 + 23 * q^78 - q^79 + 47 * q^81 - 22 * q^82 + 17 * q^83 - 60 * q^84 - 35 * q^86 - 56 * q^87 + 57 * q^88 + 16 * q^89 + 25 * q^91 - 11 * q^92 + 14 * q^93 + 7 * q^94 - 19 * q^96 - 24 * q^97 - 46 * q^98 - 53 * q^99

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