LMFDB - Embedded newform 575.2.a.l.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	$-0.522778\pi$
$2$	−0.202227	−0.142996	−0.0714981	+	0.997441i	$0.522778\pi$
$3$	2.69619	1.55665	0.778324	−	0.627863i	$-0.216070\pi$
$3$	2.69619	1.55665	0.778324	+	0.627863i	$0.216070\pi$
$4$	−1.95910	−0.979552
$5$	0	0
$5$	0	0
$6$	−0.545243	−0.222595
$7$	2.81698	1.06472	0.532360	−	0.846518i	$-0.321305\pi$
$7$	2.81698	1.06472	0.532360	+	0.846518i	$0.321305\pi$
$8$	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	$-0.143475\pi$
$13$	6.49089	1.80025	0.900124	+	0.435633i	$0.143475\pi$
$14$	−0.569670	−0.152251
$15$	0	0
$16$	3.75630	0.939074
$17$	−7.06930	−1.71456	−0.857279	−	0.514853i	$-0.827847\pi$
$17$	−7.06930	−1.71456	−0.857279	+	0.514853i	$0.827847\pi$
$18$	−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	$-0.274601\pi$
$37$	7.91248	1.30080	0.650402	+	0.759591i	$0.274601\pi$
$38$	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	$-0.622888\pi$
$43$	−4.93835	−0.753092	−0.376546	+	0.926398i	$0.622888\pi$
$44$	3.62016	0.545760
$45$	0	0
$46$	−0.202227	−0.0298168
$47$	0.851917	0.124265	0.0621324	−	0.998068i	$-0.480210\pi$
$47$	0.851917	0.124265	0.0621324	+	0.998068i	$0.480210\pi$
$48$	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	$-0.832180\pi$
$53$	−12.5831	−1.72842	−0.864208	+	0.503135i	$0.832180\pi$
$54$	−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	$-0.433817\pi$
$67$	3.37930	0.412848	0.206424	+	0.978463i	$0.433817\pi$
$68$	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	$-0.693449\pi$
$73$	−9.75748	−1.14203	−0.571013	+	0.820941i	$0.693449\pi$
$74$	−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	$-0.487825\pi$
$83$	0.696772	0.0764806	0.0382403	+	0.999269i	$0.487825\pi$
$84$	−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	$-0.589854\pi$
$97$	−5.48684	−0.557104	−0.278552	+	0.960421i	$0.589854\pi$
$98$	−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	$-0.648001\pi$
$103$	−9.10123	−0.896770	−0.448385	+	0.893840i	$0.648001\pi$
$104$	5.19686	0.509594
$105$	0	0
$106$	2.54464	0.247157
$107$	11.7093	1.13198	0.565991	−	0.824411i	$-0.308494\pi$
$107$	11.7093	1.13198	0.565991	+	0.824411i	$0.308494\pi$
$108$	−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	$-0.475581\pi$
$113$	1.62939	0.153280	0.0766401	+	0.997059i	$0.475581\pi$
$114$	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	$-0.624501\pi$
$127$	−8.59258	−0.762468	−0.381234	+	0.924479i	$0.624501\pi$
$128$	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	$-0.886487\pi$
$137$	−21.9366	−1.87417	−0.937085	+	0.349101i	$0.886487\pi$
$138$	−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	$-0.408522\pi$
$157$	7.10315	0.566893	0.283446	+	0.958988i	$0.408522\pi$
$158$	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	$-0.693603\pi$
$163$	−14.5905	−1.14282	−0.571408	+	0.820666i	$0.693603\pi$
$164$	−12.8093	−1.00024
$165$	0	0
$166$	−0.140906	−0.0109364
$167$	−9.45066	−0.731314	−0.365657	−	0.930750i	$-0.619156\pi$
$167$	−9.45066	−0.731314	−0.365657	+	0.930750i	$0.619156\pi$
$168$	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	$-0.846486\pi$
$173$	−23.3055	−1.77188	−0.885940	+	0.463799i	$0.846486\pi$
$174$	−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	$-0.547958\pi$
$193$	−4.17037	−0.300190	−0.150095	+	0.988672i	$0.547958\pi$
$194$	1.10959	0.0796638
$195$	0	0
$196$	−1.83252	−0.130894
$197$	−6.60102	−0.470303	−0.235151	−	0.971959i	$-0.575559\pi$
$197$	−6.60102	−0.470303	−0.235151	+	0.971959i	$0.575559\pi$
$198$	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	$-0.350814\pi$
$223$	13.4909	0.903420	0.451710	+	0.892165i	$0.350814\pi$
$224$	−6.65062	−0.444363
$225$	0	0
$226$	−0.329507	−0.0219185
$227$	−5.77415	−0.383244	−0.191622	−	0.981469i	$-0.561375\pi$
$227$	−5.77415	−0.383244	−0.191622	+	0.981469i	$0.561375\pi$
$228$	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	$-0.246506\pi$
$233$	21.8227	1.42965	0.714825	+	0.699303i	$0.246506\pi$
$234$	−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	$-0.356772\pi$
$257$	13.9450	0.869866	0.434933	+	0.900463i	$0.356772\pi$
$258$	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	$-0.265538\pi$
$263$	21.7883	1.34352	0.671762	+	0.740767i	$0.265538\pi$
$264$	−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	$-0.406602\pi$
$277$	9.62736	0.578452	0.289226	+	0.957261i	$0.406602\pi$
$278$	−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	$-0.571691\pi$
$283$	−7.51375	−0.446646	−0.223323	+	0.974744i	$0.571691\pi$
$284$	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	$-0.347384\pi$
$293$	15.7923	0.922596	0.461298	+	0.887245i	$0.347384\pi$
$294$	−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	$-0.753970\pi$
$307$	−25.0861	−1.43174	−0.715870	+	0.698234i	$0.753970\pi$
$308$	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	$-0.395857\pi$
$313$	11.3712	0.642738	0.321369	+	0.946954i	$0.395857\pi$
$314$	−1.43645	−0.0810636
$315$	0	0
$316$	32.3880	1.82197
$317$	15.7315	0.883570	0.441785	−	0.897121i	$-0.354345\pi$
$317$	15.7315	0.883570	0.441785	+	0.897121i	$0.354345\pi$
$318$	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	$-0.648823\pi$
$337$	−16.5473	−0.901388	−0.450694	+	0.892679i	$0.648823\pi$
$338$	−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	$-0.427305\pi$
$347$	8.43461	0.452794	0.226397	+	0.974035i	$0.427305\pi$
$348$	−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	$-0.510901\pi$
$353$	−1.28663	−0.0684803	−0.0342401	+	0.999414i	$0.510901\pi$
$354$	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	$-0.736736\pi$
$367$	−25.9403	−1.35407	−0.677036	+	0.735950i	$0.736736\pi$
$368$	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	$-0.389707\pi$
$373$	13.1177	0.679209	0.339604	+	0.940568i	$0.389707\pi$
$374$	−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	$-0.635469\pi$
$383$	−16.1595	−0.825711	−0.412856	+	0.910797i	$0.635469\pi$
$384$	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	$-0.412883\pi$
$397$	10.7707	0.540565	0.270282	+	0.962781i	$0.412883\pi$
$398$	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	$-0.679697\pi$
$433$	−22.2662	−1.07005	−0.535023	+	0.844838i	$0.679697\pi$
$434$	−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	$-0.575936\pi$
$443$	−9.94721	−0.472606	−0.236303	+	0.971679i	$0.575936\pi$
$444$	−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	$-0.216277\pi$
$457$	33.2599	1.55583	0.777916	+	0.628369i	$0.216277\pi$
$458$	−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	$-0.381589\pi$
$463$	15.6422	0.726956	0.363478	+	0.931603i	$0.381589\pi$
$464$	15.4891	0.719065
$465$	0	0
$466$	−4.41314	−0.204435
$467$	5.26987	0.243861	0.121930	−	0.992539i	$-0.461092\pi$
$467$	5.26987	0.243861	0.121930	+	0.992539i	$0.461092\pi$
$468$	−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	$-0.373822\pi$
$487$	17.0409	0.772198	0.386099	+	0.922457i	$0.373822\pi$
$488$	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	$-0.660015\pi$
$503$	−21.6111	−0.963589	−0.481795	+	0.876284i	$0.660015\pi$
$504$	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	$-0.557764\pi$
$523$	−8.25468	−0.360952	−0.180476	+	0.983579i	$0.557764\pi$
$524$	−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	$-0.360837\pi$
$547$	19.8049	0.846795	0.423398	+	0.905944i	$0.360837\pi$
$548$	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	$-0.217144\pi$
$557$	36.6380	1.55240	0.776201	+	0.630486i	$0.217144\pi$
$558$	−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	$-0.631694\pi$
$563$	−19.0783	−0.804054	−0.402027	+	0.915628i	$0.631694\pi$
$564$	−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	$-0.508867\pi$
$577$	−1.33814	−0.0557077	−0.0278539	+	0.999612i	$0.508867\pi$
$578$	−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	$-0.346295\pi$
$587$	22.4997	0.928664	0.464332	+	0.885661i	$0.346295\pi$
$588$	−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	$-0.281234\pi$
$593$	30.8988	1.26886	0.634432	+	0.772979i	$0.281234\pi$
$594$	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	$-0.643697\pi$
$607$	−21.4965	−0.872518	−0.436259	+	0.899821i	$0.643697\pi$
$608$	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	$-0.145457\pi$
$613$	44.4369	1.79479	0.897396	+	0.441227i	$0.145457\pi$
$614$	5.07310	0.204733
$615$	0	0
$616$	−4.16765	−0.167919
$617$	−25.0662	−1.00913	−0.504564	−	0.863375i	$-0.668347\pi$
$617$	−25.0662	−1.00913	−0.504564	+	0.863375i	$0.668347\pi$
$618$	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	$-0.584468\pi$
$643$	−13.3005	−0.524520	−0.262260	+	0.964997i	$0.584468\pi$
$644$	−5.51876	−0.217470
$645$	0	0
$646$	−0.360717	−0.0141922
$647$	−3.02871	−0.119071	−0.0595354	−	0.998226i	$-0.518962\pi$
$647$	−3.02871	−0.119071	−0.0595354	+	0.998226i	$0.518962\pi$
$648$	−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	$-0.661677\pi$
$653$	−24.8569	−0.972727	−0.486363	+	0.873757i	$0.661677\pi$
$654$	−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	$-0.386279\pi$
$673$	18.1446	0.699424	0.349712	+	0.936857i	$0.386279\pi$
$674$	3.34631	0.128895
$675$	0	0
$676$	−57.0719	−2.19507
$677$	−16.4647	−0.632790	−0.316395	−	0.948627i	$-0.602473\pi$
$677$	−16.4647	−0.632790	−0.316395	+	0.948627i	$0.602473\pi$
$678$	−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	$-0.851799\pi$
$683$	−46.7050	−1.78712	−0.893558	+	0.448948i	$0.851799\pi$
$684$	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	$-0.827729\pi$
$727$	−46.2193	−1.71418	−0.857089	+	0.515169i	$0.827729\pi$
$728$	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	$-0.622044\pi$
$733$	−20.2561	−0.748177	−0.374089	+	0.927393i	$0.622044\pi$
$734$	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	$-0.606815\pi$
$743$	−17.9525	−0.658614	−0.329307	+	0.944223i	$0.606815\pi$
$744$	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	$-0.695438\pi$
$757$	−31.7028	−1.15226	−0.576129	+	0.817358i	$0.695438\pi$
$758$	−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	$-0.334649\pi$
$773$	27.6037	0.992835	0.496418	+	0.868084i	$0.334649\pi$
$774$	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	$-0.718993\pi$
$787$	−35.6271	−1.26997	−0.634984	+	0.772525i	$0.718993\pi$
$788$	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	$-0.444151\pi$
$797$	9.85579	0.349110	0.174555	+	0.984647i	$0.444151\pi$
$798$	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	$-0.332318\pi$
$823$	28.8463	1.00552	0.502759	+	0.864427i	$0.332318\pi$
$824$	−7.28679	−0.253847
$825$	0	0
$826$	5.90271	0.205381
$827$	7.85313	0.273080	0.136540	−	0.990635i	$-0.456402\pi$
$827$	7.85313	0.273080	0.136540	+	0.990635i	$0.456402\pi$
$828$	−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	$-0.381892\pi$
$853$	21.1798	0.725183	0.362591	+	0.931948i	$0.381892\pi$
$854$	−0.576546	−0.0197290
$855$	0	0
$856$	9.37493	0.320429
$857$	−13.2340	−0.452066	−0.226033	−	0.974120i	$-0.572576\pi$
$857$	−13.2340	−0.452066	−0.226033	+	0.974120i	$0.572576\pi$
$858$	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	$-0.506109\pi$
$863$	−1.12760	−0.0383840	−0.0191920	+	0.999816i	$0.506109\pi$
$864$	−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	$-0.675020\pi$
$877$	−30.9499	−1.04510	−0.522552	+	0.852608i	$0.675020\pi$
$878$	−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	$-0.575918\pi$
$883$	−14.0404	−0.472496	−0.236248	+	0.971693i	$0.575918\pi$
$884$	89.8955	3.02351
$885$	0	0
$886$	2.01160	0.0675809
$887$	33.4833	1.12426	0.562129	−	0.827049i	$-0.309982\pi$
$887$	33.4833	1.12426	0.562129	+	0.827049i	$0.309982\pi$
$888$	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	$-0.619432\pi$
$907$	−22.0732	−0.732929	−0.366464	+	0.930432i	$0.619432\pi$
$908$	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	$-0.376313\pi$
$937$	23.1946	0.757736	0.378868	+	0.925451i	$0.376313\pi$
$938$	−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	$-0.259322\pi$
$947$	42.2271	1.37220	0.686098	+	0.727509i	$0.259322\pi$
$948$	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	$-0.569203\pi$
$953$	−13.3175	−0.431396	−0.215698	+	0.976460i	$0.569203\pi$
$954$	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	$-0.257019\pi$
$967$	42.9969	1.38269	0.691344	+	0.722526i	$0.257019\pi$
$968$	−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	$-0.271584\pi$
$977$	41.1074	1.31514	0.657571	+	0.753392i	$0.271584\pi$
$978$	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	$-0.904183\pi$
$983$	−59.8861	−1.91007	−0.955035	+	0.296493i	$0.904183\pi$
$984$	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	$-0.564780\pi$
$997$	−12.7634	−0.404222	−0.202111	+	0.979363i	$0.564780\pi$
$998$	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.l.1.4	yes	7
3.2	odd	2		5175.2.a.cb.1.4		7
4.3	odd	2		9200.2.a.db.1.2		7
5.2	odd	4		575.2.b.f.24.7		14
5.3	odd	4		575.2.b.f.24.8		14
5.4	even	2		575.2.a.k.1.4	✓	7
15.14	odd	2		5175.2.a.cg.1.4		7
20.19	odd	2		9200.2.a.da.1.6		7

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