LMFDB - Embedded newform 275.4.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,4,Mod(1,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("275.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	275.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:	$16.2255252516$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.732051 q^{2} -5.92820 q^{3} -7.46410 q^{4} -4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +O(q^{10})$	\(q+0.732051 q^{2} -5.92820 q^{3} -7.46410 q^{4} -4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} -11.0000 q^{11} +44.2487 q^{12} -74.6410 q^{13} -12.3923 q^{14} +51.4256 q^{16} +82.7846 q^{17} +5.96152 q^{18} -67.9230 q^{19} +100.354 q^{21} -8.05256 q^{22} -13.3538 q^{23} +67.1103 q^{24} -54.6410 q^{26} +111.785 q^{27} +126.354 q^{28} +168.995 q^{29} -65.4974 q^{31} +128.210 q^{32} +65.2102 q^{33} +60.6025 q^{34} -60.7846 q^{36} -40.8564 q^{37} -49.7231 q^{38} +442.487 q^{39} +274.928 q^{41} +73.4641 q^{42} +2.28719 q^{43} +82.1051 q^{44} -9.77568 q^{46} -71.8461 q^{47} -304.862 q^{48} -56.4359 q^{49} -490.764 q^{51} +557.128 q^{52} +149.005 q^{53} +81.8320 q^{54} +191.636 q^{56} +402.662 q^{57} +123.713 q^{58} +545.631 q^{59} +101.303 q^{61} -47.9474 q^{62} -137.856 q^{63} -317.549 q^{64} +47.7372 q^{66} -411.641 q^{67} -617.913 q^{68} +79.1642 q^{69} -470.636 q^{71} -92.1896 q^{72} -610.600 q^{73} -29.9090 q^{74} +506.985 q^{76} +186.210 q^{77} +323.923 q^{78} -978.225 q^{79} -882.559 q^{81} +201.261 q^{82} -26.1539 q^{83} -749.051 q^{84} +1.67434 q^{86} -1001.84 q^{87} +124.526 q^{88} -352.887 q^{89} +1263.54 q^{91} +99.6743 q^{92} +388.282 q^{93} -52.5950 q^{94} -760.056 q^{96} -847.585 q^{97} -41.3140 q^{98} -89.5795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} - 8 q^{4} - 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 - 8 * q^4 - 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} - 8 q^{4} - 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9} - 22 q^{11} + 40 q^{12} - 80 q^{13} - 4 q^{14} - 8 q^{16} + 124 q^{17} - 92 q^{18} + 72 q^{19} + 76 q^{21} + 22 q^{22} + 98 q^{23} + 252 q^{24} - 40 q^{26} + 182 q^{27} + 128 q^{28} + 144 q^{29} - 34 q^{31} + 104 q^{32} - 22 q^{33} - 52 q^{34} - 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} + 536 q^{41} + 140 q^{42} + 60 q^{43} + 88 q^{44} - 314 q^{46} + 272 q^{47} - 776 q^{48} - 390 q^{49} - 164 q^{51} + 560 q^{52} + 492 q^{53} - 110 q^{54} + 120 q^{56} + 1512 q^{57} + 192 q^{58} + 634 q^{59} + 840 q^{61} - 134 q^{62} - 248 q^{63} + 224 q^{64} + 286 q^{66} - 754 q^{67} - 640 q^{68} + 962 q^{69} - 678 q^{71} + 744 q^{72} + 400 q^{73} + 6 q^{74} + 432 q^{76} + 220 q^{77} + 440 q^{78} + 316 q^{79} - 1294 q^{81} - 512 q^{82} - 468 q^{83} - 736 q^{84} - 156 q^{86} - 1200 q^{87} - 132 q^{88} - 1842 q^{89} + 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} - 952 q^{96} - 2194 q^{97} + 870 q^{98} - 484 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 - 8 * q^4 - 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9 - 22 * q^11 + 40 * q^12 - 80 * q^13 - 4 * q^14 - 8 * q^16 + 124 * q^17 - 92 * q^18 + 72 * q^19 + 76 * q^21 + 22 * q^22 + 98 * q^23 + 252 * q^24 - 40 * q^26 + 182 * q^27 + 128 * q^28 + 144 * q^29 - 34 * q^31 + 104 * q^32 - 22 * q^33 - 52 * q^34 - 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 + 536 * q^41 + 140 * q^42 + 60 * q^43 + 88 * q^44 - 314 * q^46 + 272 * q^47 - 776 * q^48 - 390 * q^49 - 164 * q^51 + 560 * q^52 + 492 * q^53 - 110 * q^54 + 120 * q^56 + 1512 * q^57 + 192 * q^58 + 634 * q^59 + 840 * q^61 - 134 * q^62 - 248 * q^63 + 224 * q^64 + 286 * q^66 - 754 * q^67 - 640 * q^68 + 962 * q^69 - 678 * q^71 + 744 * q^72 + 400 * q^73 + 6 * q^74 + 432 * q^76 + 220 * q^77 + 440 * q^78 + 316 * q^79 - 1294 * q^81 - 512 * q^82 - 468 * q^83 - 736 * q^84 - 156 * q^86 - 1200 * q^87 - 132 * q^88 - 1842 * q^89 + 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 - 952 * q^96 - 2194 * q^97 + 870 * q^98 - 484 * 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 $

$2$	0.732051	0.258819	0.129410	−	0.991591i	$-0.458692\pi$
$2$	0.732051	0.258819	0.129410	+	0.991591i	$0.458692\pi$
$3$	−5.92820	−1.14088	−0.570442	−	0.821338i	$-0.693228\pi$
$3$	−5.92820	−1.14088	−0.570442	+	0.821338i	$0.693228\pi$
$4$	−7.46410	−0.933013
$5$	0	0
$5$	0	0
$6$	−4.33975	−0.295282
$7$	−16.9282	−0.914037	−0.457019	−	0.889457i	$-0.651083\pi$
$7$	−16.9282	−0.914037	−0.457019	+	0.889457i	$0.651083\pi$
$8$	−11.3205	−0.500301
$9$	8.14359	0.301615
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	44.2487	1.06446
$13$	−74.6410	−1.59244	−0.796219	−	0.605009i	$-0.793170\pi$
$13$	−74.6410	−1.59244	−0.796219	+	0.605009i	$0.793170\pi$
$14$	−12.3923	−0.236570
$15$	0	0
$16$	51.4256	0.803525
$17$	82.7846	1.18107	0.590536	−	0.807011i	$-0.298916\pi$
$17$	82.7846	1.18107	0.590536	+	0.807011i	$0.298916\pi$
$18$	5.96152	0.0780636
$19$	−67.9230	−0.820138	−0.410069	−	0.912055i	$-0.634495\pi$
$19$	−67.9230	−0.820138	−0.410069	+	0.912055i	$0.634495\pi$
$20$	0	0
$21$	100.354	1.04281
$22$	−8.05256	−0.0780369
$23$	−13.3538	−0.121064	−0.0605319	−	0.998166i	$-0.519280\pi$
$23$	−13.3538	−0.121064	−0.0605319	+	0.998166i	$0.519280\pi$
$24$	67.1103	0.570784
$25$	0	0
$26$	−54.6410	−0.412153
$27$	111.785	0.796776
$28$	126.354	0.852808
$29$	168.995	1.08212	0.541061	−	0.840983i	$-0.318023\pi$
$29$	168.995	1.08212	0.541061	+	0.840983i	$0.318023\pi$
$30$	0	0
$31$	−65.4974	−0.379474	−0.189737	−	0.981835i	$-0.560763\pi$
$31$	−65.4974	−0.379474	−0.189737	+	0.981835i	$0.560763\pi$
$32$	128.210	0.708268
$33$	65.2102	0.343989
$34$	60.6025	0.305684
$35$	0	0
$36$	−60.7846	−0.281410
$37$	−40.8564	−0.181534	−0.0907669	−	0.995872i	$-0.528932\pi$
$37$	−40.8564	−0.181534	−0.0907669	+	0.995872i	$0.528932\pi$
$38$	−49.7231	−0.212267
$39$	442.487	1.81679
$40$	0	0
$41$	274.928	1.04723	0.523617	−	0.851954i	$-0.324582\pi$
$41$	274.928	1.04723	0.523617	+	0.851954i	$0.324582\pi$
$42$	73.4641	0.269899
$43$	2.28719	0.00811146	0.00405573	−	0.999992i	$-0.498709\pi$
$43$	2.28719	0.00811146	0.00405573	+	0.999992i	$0.498709\pi$
$44$	82.1051	0.281314
$45$	0	0
$46$	−9.77568	−0.0313336
$47$	−71.8461	−0.222975	−0.111488	−	0.993766i	$-0.535562\pi$
$47$	−71.8461	−0.222975	−0.111488	+	0.993766i	$0.535562\pi$
$48$	−304.862	−0.916729
$49$	−56.4359	−0.164536
$50$	0	0
$51$	−490.764	−1.34746
$52$	557.128	1.48576
$53$	149.005	0.386178	0.193089	−	0.981181i	$-0.438149\pi$
$53$	149.005	0.386178	0.193089	+	0.981181i	$0.438149\pi$
$54$	81.8320	0.206221
$55$	0	0
$56$	191.636	0.457293
$57$	402.662	0.935681
$58$	123.713	0.280074
$59$	545.631	1.20398	0.601992	−	0.798502i	$-0.294374\pi$
$59$	545.631	1.20398	0.601992	+	0.798502i	$0.294374\pi$
$60$	0	0
$61$	101.303	0.212631	0.106315	−	0.994332i	$-0.466095\pi$
$61$	101.303	0.212631	0.106315	+	0.994332i	$0.466095\pi$
$62$	−47.9474	−0.0982150
$63$	−137.856	−0.275687
$64$	−317.549	−0.620212
$65$	0	0
$66$	47.7372	0.0890310
$67$	−411.641	−0.750596	−0.375298	−	0.926904i	$-0.622460\pi$
$67$	−411.641	−0.750596	−0.375298	+	0.926904i	$0.622460\pi$
$68$	−617.913	−1.10195
$69$	79.1642	0.138120
$70$	0	0
$71$	−470.636	−0.786679	−0.393339	−	0.919393i	$-0.628680\pi$
$71$	−470.636	−0.786679	−0.393339	+	0.919393i	$0.628680\pi$
$72$	−92.1896	−0.150898
$73$	−610.600	−0.978977	−0.489488	−	0.872010i	$-0.662816\pi$
$73$	−610.600	−0.978977	−0.489488	+	0.872010i	$0.662816\pi$
$74$	−29.9090	−0.0469844
$75$	0	0
$76$	506.985	0.765199
$77$	186.210	0.275593
$78$	323.923	0.470219
$79$	−978.225	−1.39315	−0.696576	−	0.717483i	$-0.745294\pi$
$79$	−978.225	−1.39315	−0.696576	+	0.717483i	$0.745294\pi$
$80$	0	0
$81$	−882.559	−1.21064
$82$	201.261	0.271044
$83$	−26.1539	−0.0345875	−0.0172938	−	0.999850i	$-0.505505\pi$
$83$	−26.1539	−0.0345875	−0.0172938	+	0.999850i	$0.505505\pi$
$84$	−749.051	−0.972955
$85$	0	0
$86$	1.67434	0.00209940
$87$	−1001.84	−1.23458
$88$	124.526	0.150846
$89$	−352.887	−0.420292	−0.210146	−	0.977670i	$-0.567394\pi$
$89$	−352.887	−0.420292	−0.210146	+	0.977670i	$0.567394\pi$
$90$	0	0
$91$	1263.54	1.45555
$92$	99.6743	0.112954
$93$	388.282	0.432935
$94$	−52.5950	−0.0577102
$95$	0	0
$96$	−760.056	−0.808051
$97$	−847.585	−0.887208	−0.443604	−	0.896223i	$-0.646300\pi$
$97$	−847.585	−0.887208	−0.443604	+	0.896223i	$0.646300\pi$
$98$	−41.3140	−0.0425851
$99$	−89.5795	−0.0909402
$100$	0	0
$101$	1293.46	1.27430	0.637150	−	0.770740i	$-0.280113\pi$
$101$	1293.46	1.27430	0.637150	+	0.770740i	$0.280113\pi$
$102$	−359.264	−0.348750
$103$	1725.24	1.65042	0.825209	−	0.564828i	$-0.191057\pi$
$103$	1725.24	1.65042	0.825209	+	0.564828i	$0.191057\pi$
$104$	844.974	0.796697
$105$	0	0
$106$	109.079	0.0999502
$107$	484.179	0.437452	0.218726	−	0.975786i	$-0.429810\pi$
$107$	484.179	0.437452	0.218726	+	0.975786i	$0.429810\pi$
$108$	−834.372	−0.743402
$109$	−64.2563	−0.0564645	−0.0282323	−	0.999601i	$-0.508988\pi$
$109$	−64.2563	−0.0564645	−0.0282323	+	0.999601i	$0.508988\pi$
$110$	0	0
$111$	242.205	0.207109
$112$	−870.543	−0.734452
$113$	2005.08	1.66922	0.834612	−	0.550839i	$-0.185692\pi$
$113$	2005.08	1.66922	0.834612	+	0.550839i	$0.185692\pi$
$114$	294.769	0.242172
$115$	0	0
$116$	−1261.39	−1.00963
$117$	−607.846	−0.480302
$118$	399.429	0.311614
$119$	−1401.39	−1.07954
$120$	0	0
$121$	121.000	0.0909091
$122$	74.1587	0.0550329
$123$	−1629.83	−1.19477
$124$	488.879	0.354054
$125$	0	0
$126$	−100.918	−0.0713530
$127$	−109.605	−0.0765816	−0.0382908	−	0.999267i	$-0.512191\pi$
$127$	−109.605	−0.0765816	−0.0382908	+	0.999267i	$0.512191\pi$
$128$	−1258.14	−0.868791
$129$	−13.5589	−0.00925423
$130$	0	0
$131$	1156.71	0.771469	0.385734	−	0.922610i	$-0.373948\pi$
$131$	1156.71	0.771469	0.385734	+	0.922610i	$0.373948\pi$
$132$	−486.736	−0.320946
$133$	1149.82	0.749636
$134$	−301.342	−0.194269
$135$	0	0
$136$	−937.164	−0.590891
$137$	−198.323	−0.123678	−0.0618391	−	0.998086i	$-0.519697\pi$
$137$	−198.323	−0.123678	−0.0618391	+	0.998086i	$0.519697\pi$
$138$	57.9522	0.0357480
$139$	−2900.14	−1.76969	−0.884844	−	0.465888i	$-0.845735\pi$
$139$	−2900.14	−1.76969	−0.884844	+	0.465888i	$0.845735\pi$
$140$	0	0
$141$	425.918	0.254389
$142$	−344.529	−0.203607
$143$	821.051	0.480138
$144$	418.789	0.242355
$145$	0	0
$146$	−446.990	−0.253378
$147$	334.564	0.187717
$148$	304.956	0.169373
$149$	3488.34	1.91796	0.958980	−	0.283472i	$-0.0914864\pi$
$149$	3488.34	1.91796	0.958980	+	0.283472i	$0.0914864\pi$
$150$	0	0
$151$	−1163.32	−0.626953	−0.313477	−	0.949596i	$-0.601494\pi$
$151$	−1163.32	−0.626953	−0.313477	+	0.949596i	$0.601494\pi$
$152$	768.923	0.410315
$153$	674.164	0.356228
$154$	136.315	0.0713286
$155$	0	0
$156$	−3302.77	−1.69508
$157$	−342.057	−0.173880	−0.0869398	−	0.996214i	$-0.527709\pi$
$157$	−342.057	−0.173880	−0.0869398	+	0.996214i	$0.527709\pi$
$158$	−716.111	−0.360574
$159$	−883.333	−0.440584
$160$	0	0
$161$	226.056	0.110657
$162$	−646.078	−0.313338
$163$	1394.89	0.670285	0.335142	−	0.942167i	$-0.391216\pi$
$163$	1394.89	0.670285	0.335142	+	0.942167i	$0.391216\pi$
$164$	−2052.09	−0.977082
$165$	0	0
$166$	−19.1460	−0.00895191
$167$	−478.703	−0.221815	−0.110908	−	0.993831i	$-0.535376\pi$
$167$	−478.703	−0.221815	−0.110908	+	0.993831i	$0.535376\pi$
$168$	−1136.06	−0.521718
$169$	3374.28	1.53586
$170$	0	0
$171$	−553.138	−0.247365
$172$	−17.0718	−0.00756809
$173$	−1808.58	−0.794822	−0.397411	−	0.917641i	$-0.630091\pi$
$173$	−1808.58	−0.794822	−0.397411	+	0.917641i	$0.630091\pi$
$174$	−733.395	−0.319532
$175$	0	0
$176$	−565.682	−0.242272
$177$	−3234.61	−1.37361
$178$	−258.331	−0.108780
$179$	−4429.85	−1.84973	−0.924867	−	0.380292i	$-0.875824\pi$
$179$	−4429.85	−1.84973	−0.924867	+	0.380292i	$0.875824\pi$
$180$	0	0
$181$	3409.17	1.40001	0.700005	−	0.714138i	$-0.253181\pi$
$181$	3409.17	1.40001	0.700005	+	0.714138i	$0.253181\pi$
$182$	924.974	0.376723
$183$	−600.543	−0.242587
$184$	151.172	0.0605682
$185$	0	0
$186$	284.242	0.112052
$187$	−910.631	−0.356106
$188$	536.267	0.208039
$189$	−1892.31	−0.728283
$190$	0	0
$191$	2923.75	1.10762	0.553810	−	0.832643i	$-0.313173\pi$
$191$	2923.75	1.10762	0.553810	+	0.832643i	$0.313173\pi$
$192$	1882.49	0.707590
$193$	2484.18	0.926505	0.463253	−	0.886226i	$-0.346682\pi$
$193$	2484.18	0.926505	0.463253	+	0.886226i	$0.346682\pi$
$194$	−620.475	−0.229626
$195$	0	0
$196$	421.244	0.153514
$197$	5125.67	1.85375	0.926876	−	0.375369i	$-0.122484\pi$
$197$	5125.67	1.85375	0.926876	+	0.375369i	$0.122484\pi$
$198$	−65.5768	−0.0235371
$199$	−7.69219	−0.00274013	−0.00137006	−	0.999999i	$-0.500436\pi$
$199$	−7.69219	−0.00274013	−0.00137006	+	0.999999i	$0.500436\pi$
$200$	0	0
$201$	2440.29	0.856343
$202$	946.879	0.329813
$203$	−2860.78	−0.989100
$204$	3663.11	1.25720
$205$	0	0
$206$	1262.96	0.427160
$207$	−108.748	−0.0365146
$208$	−3838.46	−1.27956
$209$	747.154	0.247281
$210$	0	0
$211$	3107.34	1.01383	0.506915	−	0.861996i	$-0.330786\pi$
$211$	3107.34	1.01383	0.506915	+	0.861996i	$0.330786\pi$
$212$	−1112.19	−0.360309
$213$	2790.03	0.897509
$214$	354.444	0.113221
$215$	0	0
$216$	−1265.46	−0.398628
$217$	1108.75	0.346853
$218$	−47.0388	−0.0146141
$219$	3619.76	1.11690
$220$	0	0
$221$	−6179.13	−1.88078
$222$	177.306	0.0536037
$223$	12.3185	0.00369913	0.00184957	−	0.999998i	$-0.499411\pi$
$223$	12.3185	0.00369913	0.00184957	+	0.999998i	$0.499411\pi$
$224$	−2170.37	−0.647383
$225$	0	0
$226$	1467.82	0.432027
$227$	−4615.90	−1.34964	−0.674820	−	0.737983i	$-0.735779\pi$
$227$	−4615.90	−1.34964	−0.674820	+	0.737983i	$0.735779\pi$
$228$	−3005.51	−0.873003
$229$	5074.63	1.46437	0.732186	−	0.681105i	$-0.238500\pi$
$229$	5074.63	1.46437	0.732186	+	0.681105i	$0.238500\pi$
$230$	0	0
$231$	−1103.89	−0.314419
$232$	−1913.11	−0.541386
$233$	−211.683	−0.0595184	−0.0297592	−	0.999557i	$-0.509474\pi$
$233$	−211.683	−0.0595184	−0.0297592	+	0.999557i	$0.509474\pi$
$234$	−444.974	−0.124311
$235$	0	0
$236$	−4072.64	−1.12333
$237$	5799.12	1.58942
$238$	−1025.89	−0.279406
$239$	4312.49	1.16716	0.583581	−	0.812055i	$-0.301651\pi$
$239$	4312.49	1.16716	0.583581	+	0.812055i	$0.301651\pi$
$240$	0	0
$241$	−996.584	−0.266372	−0.133186	−	0.991091i	$-0.542521\pi$
$241$	−996.584	−0.266372	−0.133186	+	0.991091i	$0.542521\pi$
$242$	88.5781	0.0235290
$243$	2213.80	0.584426
$244$	−756.133	−0.198387
$245$	0	0
$246$	−1193.12	−0.309230
$247$	5069.85	1.30602
$248$	741.464	0.189851
$249$	155.046	0.0394603
$250$	0	0
$251$	−276.892	−0.0696306	−0.0348153	−	0.999394i	$-0.511084\pi$
$251$	−276.892	−0.0696306	−0.0348153	+	0.999394i	$0.511084\pi$
$252$	1028.97	0.257219
$253$	146.892	0.0365021
$254$	−80.2364	−0.0198208
$255$	0	0
$256$	1619.36	0.395352
$257$	3235.18	0.785233	0.392617	−	0.919702i	$-0.371570\pi$
$257$	3235.18	0.785233	0.392617	+	0.919702i	$0.371570\pi$
$258$	−9.92581	−0.00239517
$259$	691.626	0.165929
$260$	0	0
$261$	1376.23	0.326384
$262$	846.772	0.199671
$263$	−207.944	−0.0487544	−0.0243772	−	0.999703i	$-0.507760\pi$
$263$	−207.944	−0.0487544	−0.0243772	+	0.999703i	$0.507760\pi$
$264$	−738.213	−0.172098
$265$	0	0
$266$	841.723	0.194020
$267$	2091.99	0.479504
$268$	3072.53	0.700316
$269$	5033.04	1.14078	0.570390	−	0.821374i	$-0.306792\pi$
$269$	5033.04	1.14078	0.570390	+	0.821374i	$0.306792\pi$
$270$	0	0
$271$	1487.01	0.333319	0.166660	−	0.986015i	$-0.446702\pi$
$271$	1487.01	0.333319	0.166660	+	0.986015i	$0.446702\pi$
$272$	4257.25	0.949021
$273$	−7490.51	−1.66061
$274$	−145.183	−0.0320102
$275$	0	0
$276$	−590.890	−0.128867
$277$	235.836	0.0511552	0.0255776	−	0.999673i	$-0.491858\pi$
$277$	235.836	0.0511552	0.0255776	+	0.999673i	$0.491858\pi$
$278$	−2123.05	−0.458029
$279$	−533.384	−0.114455
$280$	0	0
$281$	−4915.01	−1.04343	−0.521717	−	0.853118i	$-0.674708\pi$
$281$	−4915.01	−1.04343	−0.521717	+	0.853118i	$0.674708\pi$
$282$	311.794	0.0658406
$283$	5199.56	1.09216	0.546081	−	0.837733i	$-0.316119\pi$
$283$	5199.56	1.09216	0.546081	+	0.837733i	$0.316119\pi$
$284$	3512.87	0.733981
$285$	0	0
$286$	601.051	0.124269
$287$	−4654.04	−0.957210
$288$	1044.09	0.213624
$289$	1940.29	0.394930
$290$	0	0
$291$	5024.65	1.01220
$292$	4557.58	0.913398
$293$	8880.92	1.77075	0.885373	−	0.464881i	$-0.153903\pi$
$293$	8880.92	1.77075	0.885373	+	0.464881i	$0.153903\pi$
$294$	244.918	0.0485846
$295$	0	0
$296$	462.515	0.0908215
$297$	−1229.63	−0.240237
$298$	2553.64	0.496405
$299$	996.743	0.192786
$300$	0	0
$301$	−38.7180	−0.00741417
$302$	−851.612	−0.162267
$303$	−7667.90	−1.45383
$304$	−3492.99	−0.659001
$305$	0	0
$306$	493.522	0.0921987
$307$	1497.93	0.278474	0.139237	−	0.990259i	$-0.455535\pi$
$307$	1497.93	0.278474	0.139237	+	0.990259i	$0.455535\pi$
$308$	−1389.89	−0.257131
$309$	−10227.6	−1.88293
$310$	0	0
$311$	−7484.71	−1.36469	−0.682345	−	0.731030i	$-0.739040\pi$
$311$	−7484.71	−1.36469	−0.682345	+	0.731030i	$0.739040\pi$
$312$	−5009.18	−0.908939
$313$	658.363	0.118891	0.0594455	−	0.998232i	$-0.481067\pi$
$313$	658.363	0.118891	0.0594455	+	0.998232i	$0.481067\pi$
$314$	−250.403	−0.0450034
$315$	0	0
$316$	7301.57	1.29983
$317$	−233.708	−0.0414080	−0.0207040	−	0.999786i	$-0.506591\pi$
$317$	−233.708	−0.0414080	−0.0207040	+	0.999786i	$0.506591\pi$
$318$	−646.645	−0.114032
$319$	−1858.94	−0.326272
$320$	0	0
$321$	−2870.31	−0.499082
$322$	165.485	0.0286401
$323$	−5622.98	−0.968641
$324$	6587.51	1.12955
$325$	0	0
$326$	1021.13	0.173482
$327$	380.924	0.0644194
$328$	−3112.33	−0.523931
$329$	1216.23	0.203808
$330$	0	0
$331$	8532.95	1.41696	0.708480	−	0.705731i	$-0.249381\pi$
$331$	8532.95	1.41696	0.708480	+	0.705731i	$0.249381\pi$
$332$	195.215	0.0322706
$333$	−332.718	−0.0547533
$334$	−350.435	−0.0574100
$335$	0	0
$336$	5160.76	0.837924
$337$	−11691.2	−1.88979	−0.944895	−	0.327373i	$-0.893837\pi$
$337$	−11691.2	−1.88979	−0.944895	+	0.327373i	$0.893837\pi$
$338$	2470.15	0.397509
$339$	−11886.5	−1.90439
$340$	0	0
$341$	720.472	0.114416
$342$	−404.925	−0.0640229
$343$	6761.73	1.06443
$344$	−25.8921	−0.00405817
$345$	0	0
$346$	−1323.98	−0.205715
$347$	−4598.79	−0.711459	−0.355729	−	0.934589i	$-0.615768\pi$
$347$	−4598.79	−0.711459	−0.355729	+	0.934589i	$0.615768\pi$
$348$	7477.80	1.15187
$349$	6720.27	1.03074	0.515369	−	0.856968i	$-0.327655\pi$
$349$	6720.27	1.03074	0.515369	+	0.856968i	$0.327655\pi$
$350$	0	0
$351$	−8343.72	−1.26882
$352$	−1410.31	−0.213551
$353$	−5738.70	−0.865270	−0.432635	−	0.901569i	$-0.642416\pi$
$353$	−5738.70	−0.865270	−0.432635	+	0.901569i	$0.642416\pi$
$354$	−2367.90	−0.355515
$355$	0	0
$356$	2633.99	0.392138
$357$	8307.75	1.23163
$358$	−3242.87	−0.478746
$359$	−4115.27	−0.605001	−0.302501	−	0.953149i	$-0.597821\pi$
$359$	−4115.27	−0.605001	−0.302501	+	0.953149i	$0.597821\pi$
$360$	0	0
$361$	−2245.46	−0.327374
$362$	2495.69	0.362349
$363$	−717.313	−0.103717
$364$	−9431.18	−1.35804
$365$	0	0
$366$	−439.628	−0.0627861
$367$	−9662.99	−1.37440	−0.687199	−	0.726469i	$-0.741160\pi$
$367$	−9662.99	−1.37440	−0.687199	+	0.726469i	$0.741160\pi$
$368$	−686.729	−0.0972778
$369$	2238.90	0.315861
$370$	0	0
$371$	−2522.39	−0.352981
$372$	−2898.18	−0.403934
$373$	141.780	0.0196812	0.00984062	−	0.999952i	$-0.496868\pi$
$373$	141.780	0.0196812	0.00984062	+	0.999952i	$0.496868\pi$
$374$	−666.628	−0.0921671
$375$	0	0
$376$	813.334	0.111555
$377$	−12613.9	−1.72321
$378$	−1385.27	−0.188494
$379$	−2819.73	−0.382163	−0.191082	−	0.981574i	$-0.561200\pi$
$379$	−2819.73	−0.382163	−0.191082	+	0.981574i	$0.561200\pi$
$380$	0	0
$381$	649.760	0.0873707
$382$	2140.34	0.286673
$383$	6337.84	0.845557	0.422778	−	0.906233i	$-0.361055\pi$
$383$	6337.84	0.845557	0.422778	+	0.906233i	$0.361055\pi$
$384$	7458.53	0.991189
$385$	0	0
$386$	1818.55	0.239797
$387$	18.6259	0.00244653
$388$	6326.46	0.827776
$389$	−8805.25	−1.14767	−0.573836	−	0.818970i	$-0.694545\pi$
$389$	−8805.25	−1.14767	−0.573836	+	0.818970i	$0.694545\pi$
$390$	0	0
$391$	−1105.49	−0.142985
$392$	638.883	0.0823176
$393$	−6857.23	−0.880156
$394$	3752.25	0.479786
$395$	0	0
$396$	668.631	0.0848484
$397$	−4315.26	−0.545534	−0.272767	−	0.962080i	$-0.587939\pi$
$397$	−4315.26	−0.545534	−0.272767	+	0.962080i	$0.587939\pi$
$398$	−5.63108	−0.000709197 0
$399$	−6816.34	−0.855247
$400$	0	0
$401$	361.681	0.0450411	0.0225206	−	0.999746i	$-0.492831\pi$
$401$	361.681	0.0450411	0.0225206	+	0.999746i	$0.492831\pi$
$402$	1786.42	0.221638
$403$	4888.79	0.604288
$404$	−9654.53	−1.18894
$405$	0	0
$406$	−2094.24	−0.255998
$407$	449.420	0.0547345
$408$	5555.70	0.674137
$409$	9220.50	1.11473	0.557365	−	0.830268i	$-0.311812\pi$
$409$	9220.50	1.11473	0.557365	+	0.830268i	$0.311812\pi$
$410$	0	0
$411$	1175.70	0.141102
$412$	−12877.4	−1.53986
$413$	−9236.55	−1.10049
$414$	−79.6092	−0.00945067
$415$	0	0
$416$	−9569.74	−1.12787
$417$	17192.6	2.01901
$418$	546.954	0.0640010
$419$	−14912.9	−1.73876	−0.869380	−	0.494144i	$-0.835481\pi$
$419$	−14912.9	−1.73876	−0.869380	+	0.494144i	$0.835481\pi$
$420$	0	0
$421$	−13486.0	−1.56121	−0.780603	−	0.625027i	$-0.785088\pi$
$421$	−13486.0	−1.56121	−0.780603	+	0.625027i	$0.785088\pi$
$422$	2274.73	0.262399
$423$	−585.085	−0.0672525
$424$	−1686.81	−0.193205
$425$	0	0
$426$	2042.44	0.232292
$427$	−1714.87	−0.194352
$428$	−3613.96	−0.408148
$429$	−4867.36	−0.547782
$430$	0	0
$431$	406.334	0.0454116	0.0227058	−	0.999742i	$-0.492772\pi$
$431$	406.334	0.0454116	0.0227058	+	0.999742i	$0.492772\pi$
$432$	5748.59	0.640230
$433$	1766.69	0.196078	0.0980391	−	0.995183i	$-0.468743\pi$
$433$	1766.69	0.196078	0.0980391	+	0.995183i	$0.468743\pi$
$434$	811.664	0.0897722
$435$	0	0
$436$	479.615	0.0526821
$437$	907.033	0.0992889
$438$	2649.85	0.289075
$439$	7824.19	0.850634	0.425317	−	0.905044i	$-0.360163\pi$
$439$	7824.19	0.850634	0.425317	+	0.905044i	$0.360163\pi$
$440$	0	0
$441$	−459.591	−0.0496265
$442$	−4523.44	−0.486783
$443$	−11667.9	−1.25137	−0.625686	−	0.780075i	$-0.715181\pi$
$443$	−11667.9	−1.25137	−0.625686	+	0.780075i	$0.715181\pi$
$444$	−1807.84	−0.193235
$445$	0	0
$446$	9.01776	0.000957406 0
$447$	−20679.6	−2.18817
$448$	5375.53	0.566897
$449$	16975.3	1.78421	0.892107	−	0.451825i	$-0.149227\pi$
$449$	16975.3	1.78421	0.892107	+	0.451825i	$0.149227\pi$
$450$	0	0
$451$	−3024.21	−0.315753
$452$	−14966.1	−1.55741
$453$	6896.42	0.715280
$454$	−3379.07	−0.349312
$455$	0	0
$456$	−4558.33	−0.468122
$457$	16192.9	1.65748	0.828741	−	0.559632i	$-0.189057\pi$
$457$	16192.9	1.65748	0.828741	+	0.559632i	$0.189057\pi$
$458$	3714.89	0.379007
$459$	9254.05	0.941050
$460$	0	0
$461$	8586.04	0.867444	0.433722	−	0.901047i	$-0.357200\pi$
$461$	8586.04	0.867444	0.433722	+	0.901047i	$0.357200\pi$
$462$	−808.105	−0.0813776
$463$	7917.20	0.794694	0.397347	−	0.917668i	$-0.369931\pi$
$463$	7917.20	0.794694	0.397347	+	0.917668i	$0.369931\pi$
$464$	8690.67	0.869513
$465$	0	0
$466$	−154.962	−0.0154045
$467$	15155.0	1.50169	0.750844	−	0.660480i	$-0.229647\pi$
$467$	15155.0	1.50169	0.750844	+	0.660480i	$0.229647\pi$
$468$	4537.03	0.448128
$469$	6968.34	0.686073
$470$	0	0
$471$	2027.78	0.198376
$472$	−6176.82	−0.602354
$473$	−25.1591	−0.00244570
$474$	4245.25	0.411373
$475$	0	0
$476$	10460.2	1.00723
$477$	1213.44	0.116477
$478$	3156.96	0.302084
$479$	10001.1	0.953993	0.476996	−	0.878905i	$-0.341725\pi$
$479$	10001.1	0.953993	0.476996	+	0.878905i	$0.341725\pi$
$480$	0	0
$481$	3049.56	0.289081
$482$	−729.550	−0.0689421
$483$	−1340.11	−0.126246
$484$	−903.156	−0.0848193
$485$	0	0
$486$	1620.62	0.151261
$487$	−7044.54	−0.655480	−0.327740	−	0.944768i	$-0.606287\pi$
$487$	−7044.54	−0.655480	−0.327740	+	0.944768i	$0.606287\pi$
$488$	−1146.80	−0.106379
$489$	−8269.21	−0.764717
$490$	0	0
$491$	−13326.4	−1.22487	−0.612437	−	0.790520i	$-0.709811\pi$
$491$	−13326.4	−1.22487	−0.612437	+	0.790520i	$0.709811\pi$
$492$	12165.2	1.11474
$493$	13990.2	1.27806
$494$	3711.38	0.338022
$495$	0	0
$496$	−3368.25	−0.304917
$497$	7967.02	0.719054
$498$	113.501	0.0102131
$499$	−20069.1	−1.80044	−0.900218	−	0.435440i	$-0.856593\pi$
$499$	−20069.1	−1.80044	−0.900218	+	0.435440i	$0.856593\pi$
$500$	0	0
$501$	2837.85	0.253065
$502$	−202.699	−0.0180217
$503$	−7782.35	−0.689856	−0.344928	−	0.938629i	$-0.612097\pi$
$503$	−7782.35	−0.689856	−0.344928	+	0.938629i	$0.612097\pi$
$504$	1560.60	0.137926
$505$	0	0
$506$	107.532	0.00944744
$507$	−20003.4	−1.75224
$508$	818.102	0.0714516
$509$	−1475.93	−0.128526	−0.0642628	−	0.997933i	$-0.520470\pi$
$509$	−1475.93	−0.128526	−0.0642628	+	0.997933i	$0.520470\pi$
$510$	0	0
$511$	10336.4	0.894821
$512$	11250.6	0.971116
$513$	−7592.75	−0.653466
$514$	2368.32	0.203233
$515$	0	0
$516$	101.205	0.00863431
$517$	790.307	0.0672295
$518$	506.305	0.0429455
$519$	10721.7	0.906799
$520$	0	0
$521$	7609.43	0.639875	0.319938	−	0.947439i	$-0.396338\pi$
$521$	7609.43	0.639875	0.319938	+	0.947439i	$0.396338\pi$
$522$	1007.47	0.0844744
$523$	−12452.9	−1.04116	−0.520581	−	0.853812i	$-0.674285\pi$
$523$	−12452.9	−1.04116	−0.520581	+	0.853812i	$0.674285\pi$
$524$	−8633.82	−0.719790
$525$	0	0
$526$	−152.226	−0.0126186
$527$	−5422.18	−0.448186
$528$	3353.48	0.276404
$529$	−11988.7	−0.985344
$530$	0	0
$531$	4443.39	0.363139
$532$	−8582.34	−0.699420
$533$	−20520.9	−1.66765
$534$	1531.44	0.124105
$535$	0	0
$536$	4659.99	0.375524
$537$	26261.0	2.11033
$538$	3684.44	0.295255
$539$	620.795	0.0496095
$540$	0	0
$541$	9312.17	0.740039	0.370020	−	0.929024i	$-0.379351\pi$
$541$	9312.17	0.740039	0.370020	+	0.929024i	$0.379351\pi$
$542$	1088.57	0.0862693
$543$	−20210.3	−1.59725
$544$	10613.8	0.836515
$545$	0	0
$546$	−5483.44	−0.429797
$547$	11018.6	0.861278	0.430639	−	0.902524i	$-0.358288\pi$
$547$	11018.6	0.861278	0.430639	+	0.902524i	$0.358288\pi$
$548$	1480.31	0.115393
$549$	824.968	0.0641325
$550$	0	0
$551$	−11478.6	−0.887490
$552$	−896.179	−0.0691013
$553$	16559.6	1.27339
$554$	172.644	0.0132399
$555$	0	0
$556$	21646.9	1.65114
$557$	12018.4	0.914250	0.457125	−	0.889403i	$-0.348879\pi$
$557$	12018.4	0.914250	0.457125	+	0.889403i	$0.348879\pi$
$558$	−390.464	−0.0296231
$559$	−170.718	−0.0129170
$560$	0	0
$561$	5398.40	0.406276
$562$	−3598.04	−0.270061
$563$	8763.89	0.656046	0.328023	−	0.944670i	$-0.393618\pi$
$563$	8763.89	0.656046	0.328023	+	0.944670i	$0.393618\pi$
$564$	−3179.10	−0.237348
$565$	0	0
$566$	3806.34	0.282672
$567$	14940.1	1.10657
$568$	5327.84	0.393576
$569$	−10273.2	−0.756895	−0.378447	−	0.925623i	$-0.623542\pi$
$569$	−10273.2	−0.756895	−0.378447	+	0.925623i	$0.623542\pi$
$570$	0	0
$571$	2602.62	0.190747	0.0953734	−	0.995442i	$-0.469596\pi$
$571$	2602.62	0.190747	0.0953734	+	0.995442i	$0.469596\pi$
$572$	−6128.41	−0.447975
$573$	−17332.6	−1.26366
$574$	−3406.99	−0.247744
$575$	0	0
$576$	−2585.99	−0.187065
$577$	19727.0	1.42331	0.711653	−	0.702532i	$-0.247947\pi$
$577$	19727.0	1.42331	0.711653	+	0.702532i	$0.247947\pi$
$578$	1420.39	0.102215
$579$	−14726.7	−1.05703
$580$	0	0
$581$	442.739	0.0316143
$582$	3678.30	0.261977
$583$	−1639.06	−0.116437
$584$	6912.30	0.489783
$585$	0	0
$586$	6501.28	0.458303
$587$	10116.2	0.711309	0.355654	−	0.934618i	$-0.384258\pi$
$587$	10116.2	0.711309	0.355654	+	0.934618i	$0.384258\pi$
$588$	−2497.22	−0.175142
$589$	4448.78	0.311221
$590$	0	0
$591$	−30386.0	−2.11491
$592$	−2101.07	−0.145867
$593$	−3130.32	−0.216774	−0.108387	−	0.994109i	$-0.534569\pi$
$593$	−3130.32	−0.216774	−0.108387	+	0.994109i	$0.534569\pi$
$594$	−900.152	−0.0621779
$595$	0	0
$596$	−26037.3	−1.78948
$597$	45.6009	0.00312616
$598$	729.667	0.0498968
$599$	10080.1	0.687581	0.343790	−	0.939046i	$-0.388289\pi$
$599$	10080.1	0.687581	0.343790	+	0.939046i	$0.388289\pi$
$600$	0	0
$601$	4777.02	0.324224	0.162112	−	0.986772i	$-0.448169\pi$
$601$	4777.02	0.324224	0.162112	+	0.986772i	$0.448169\pi$
$602$	−28.3435	−0.00191893
$603$	−3352.24	−0.226391
$604$	8683.16	0.584955
$605$	0	0
$606$	−5613.29	−0.376278
$607$	2571.35	0.171941	0.0859703	−	0.996298i	$-0.472601\pi$
$607$	2571.35	0.171941	0.0859703	+	0.996298i	$0.472601\pi$
$608$	−8708.43	−0.580877
$609$	16959.3	1.12845
$610$	0	0
$611$	5362.67	0.355074
$612$	−5032.03	−0.332366
$613$	−12711.9	−0.837564	−0.418782	−	0.908087i	$-0.637543\pi$
$613$	−12711.9	−0.837564	−0.418782	+	0.908087i	$0.637543\pi$
$614$	1096.56	0.0720744
$615$	0	0
$616$	−2107.99	−0.137879
$617$	−16236.1	−1.05939	−0.529693	−	0.848189i	$-0.677693\pi$
$617$	−16236.1	−1.05939	−0.529693	+	0.848189i	$0.677693\pi$
$618$	−7487.11	−0.487339
$619$	12657.3	0.821874	0.410937	−	0.911664i	$-0.365202\pi$
$619$	12657.3	0.821874	0.410937	+	0.911664i	$0.365202\pi$
$620$	0	0
$621$	−1492.75	−0.0964607
$622$	−5479.19	−0.353208
$623$	5973.75	0.384162
$624$	22755.2	1.45983
$625$	0	0
$626$	481.955	0.0307713
$627$	−4429.28	−0.282119
$628$	2553.15	0.162232
$629$	−3382.28	−0.214404
$630$	0	0
$631$	−3949.97	−0.249201	−0.124600	−	0.992207i	$-0.539765\pi$
$631$	−3949.97	−0.249201	−0.124600	+	0.992207i	$0.539765\pi$
$632$	11074.0	0.696994
$633$	−18421.0	−1.15666
$634$	−171.086	−0.0107172
$635$	0	0
$636$	6593.29	0.411070
$637$	4212.44	0.262014
$638$	−1360.84	−0.0844455
$639$	−3832.67	−0.237274
$640$	0	0
$641$	−7398.27	−0.455872	−0.227936	−	0.973676i	$-0.573198\pi$
$641$	−7398.27	−0.455872	−0.227936	+	0.973676i	$0.573198\pi$
$642$	−2101.22	−0.129172
$643$	12491.7	0.766134	0.383067	−	0.923721i	$-0.374868\pi$
$643$	12491.7	0.766134	0.383067	+	0.923721i	$0.374868\pi$
$644$	−1687.31	−0.103244
$645$	0	0
$646$	−4116.31	−0.250703
$647$	10472.0	0.636315	0.318158	−	0.948038i	$-0.396936\pi$
$647$	10472.0	0.636315	0.318158	+	0.948038i	$0.396936\pi$
$648$	9991.02	0.605685
$649$	−6001.94	−0.363015
$650$	0	0
$651$	−6572.92	−0.395719
$652$	−10411.6	−0.625384
$653$	−6337.94	−0.379820	−0.189910	−	0.981801i	$-0.560820\pi$
$653$	−6337.94	−0.379820	−0.189910	+	0.981801i	$0.560820\pi$
$654$	278.856	0.0166730
$655$	0	0
$656$	14138.4	0.841479
$657$	−4972.48	−0.295274
$658$	890.339	0.0527493
$659$	15196.7	0.898302	0.449151	−	0.893456i	$-0.351726\pi$
$659$	15196.7	0.898302	0.449151	+	0.893456i	$0.351726\pi$
$660$	0	0
$661$	2298.17	0.135232	0.0676161	−	0.997711i	$-0.478461\pi$
$661$	2298.17	0.135232	0.0676161	+	0.997711i	$0.478461\pi$
$662$	6246.55	0.366736
$663$	36631.1	2.14575
$664$	296.075	0.0173042
$665$	0	0
$666$	−243.566	−0.0141712
$667$	−2256.73	−0.131006
$668$	3573.09	0.206956
$669$	−73.0265	−0.00422028
$670$	0	0
$671$	−1114.33	−0.0641106
$672$	12866.4	0.738589
$673$	−23199.6	−1.32880	−0.664398	−	0.747379i	$-0.731312\pi$
$673$	−23199.6	−1.32880	−0.664398	+	0.747379i	$0.731312\pi$
$674$	−8558.54	−0.489114
$675$	0	0
$676$	−25186.0	−1.43298
$677$	2145.38	0.121793	0.0608963	−	0.998144i	$-0.480604\pi$
$677$	2145.38	0.121793	0.0608963	+	0.998144i	$0.480604\pi$
$678$	−8701.55	−0.492892
$679$	14348.1	0.810941
$680$	0	0
$681$	27364.0	1.53978
$682$	527.422	0.0296129
$683$	29544.6	1.65519	0.827593	−	0.561329i	$-0.189710\pi$
$683$	29544.6	1.65519	0.827593	+	0.561329i	$0.189710\pi$
$684$	4128.68	0.230795
$685$	0	0
$686$	4949.93	0.275495
$687$	−30083.4	−1.67068
$688$	117.620	0.00651776
$689$	−11121.9	−0.614964
$690$	0	0
$691$	27803.1	1.53065	0.765325	−	0.643644i	$-0.222578\pi$
$691$	27803.1	1.53065	0.765325	+	0.643644i	$0.222578\pi$
$692$	13499.5	0.741579
$693$	1516.42	0.0831227
$694$	−3366.55	−0.184139
$695$	0	0
$696$	11341.3	0.617659
$697$	22759.8	1.23686
$698$	4919.58	0.266775
$699$	1254.90	0.0679036
$700$	0	0
$701$	−19697.8	−1.06130	−0.530652	−	0.847590i	$-0.678053\pi$
$701$	−19697.8	−1.06130	−0.530652	+	0.847590i	$0.678053\pi$
$702$	−6108.02	−0.328394
$703$	2775.09	0.148883
$704$	3493.03	0.187001
$705$	0	0
$706$	−4201.02	−0.223948
$707$	−21896.0	−1.16476
$708$	24143.5	1.28159
$709$	19122.5	1.01292	0.506460	−	0.862263i	$-0.330954\pi$
$709$	19122.5	1.01292	0.506460	+	0.862263i	$0.330954\pi$
$710$	0	0
$711$	−7966.27	−0.420195
$712$	3994.86	0.210272
$713$	874.641	0.0459405
$714$	6081.70	0.318770
$715$	0	0
$716$	33064.8	1.72582
$717$	−25565.3	−1.33160
$718$	−3012.59	−0.156586
$719$	1837.44	0.0953060	0.0476530	−	0.998864i	$-0.484826\pi$
$719$	1837.44	0.0953060	0.0476530	+	0.998864i	$0.484826\pi$
$720$	0	0
$721$	−29205.2	−1.50854
$722$	−1643.79	−0.0847307
$723$	5907.95	0.303899
$724$	−25446.4	−1.30623
$725$	0	0
$726$	−525.109	−0.0268438
$727$	7555.46	0.385442	0.192721	−	0.981254i	$-0.438269\pi$
$727$	7555.46	0.385442	0.192721	+	0.981254i	$0.438269\pi$
$728$	−14303.9	−0.728211
$729$	10705.2	0.543881
$730$	0	0
$731$	189.344	0.00958021
$732$	4482.51	0.226337
$733$	−11984.6	−0.603905	−0.301952	−	0.953323i	$-0.597638\pi$
$733$	−11984.6	−0.603905	−0.301952	+	0.953323i	$0.597638\pi$
$734$	−7073.80	−0.355720
$735$	0	0
$736$	−1712.10	−0.0857456
$737$	4528.05	0.226313
$738$	1638.99	0.0817508
$739$	−27142.5	−1.35109	−0.675543	−	0.737321i	$-0.736091\pi$
$739$	−27142.5	−1.35109	−0.675543	+	0.737321i	$0.736091\pi$
$740$	0	0
$741$	−30055.1	−1.49001
$742$	−1846.52	−0.0913582
$743$	29222.6	1.44290	0.721450	−	0.692467i	$-0.243476\pi$
$743$	29222.6	1.44290	0.721450	+	0.692467i	$0.243476\pi$
$744$	−4395.55	−0.216598
$745$	0	0
$746$	103.790	0.00509388
$747$	−212.987	−0.0104321
$748$	6797.04	0.332252
$749$	−8196.29	−0.399847
$750$	0	0
$751$	−8859.39	−0.430471	−0.215236	−	0.976562i	$-0.569052\pi$
$751$	−8859.39	−0.430471	−0.215236	+	0.976562i	$0.569052\pi$
$752$	−3694.73	−0.179166
$753$	1641.47	0.0794404
$754$	−9234.05	−0.446000
$755$	0	0
$756$	14124.4	0.679497
$757$	−35734.4	−1.71571	−0.857853	−	0.513896i	$-0.828202\pi$
$757$	−35734.4	−1.71571	−0.857853	+	0.513896i	$0.828202\pi$
$758$	−2064.19	−0.0989112
$759$	−870.806	−0.0416446
$760$	0	0
$761$	34394.7	1.63838	0.819189	−	0.573524i	$-0.194424\pi$
$761$	34394.7	1.63838	0.819189	+	0.573524i	$0.194424\pi$
$762$	475.658	0.0226132
$763$	1087.74	0.0516107
$764$	−21823.2	−1.03342
$765$	0	0
$766$	4639.62	0.218846
$767$	−40726.4	−1.91727
$768$	−9599.92	−0.451051
$769$	−11602.7	−0.544091	−0.272045	−	0.962284i	$-0.587700\pi$
$769$	−11602.7	−0.544091	−0.272045	+	0.962284i	$0.587700\pi$
$770$	0	0
$771$	−19178.8	−0.895859
$772$	−18542.2	−0.864441
$773$	12680.6	0.590026	0.295013	−	0.955493i	$-0.404676\pi$
$773$	12680.6	0.590026	0.295013	+	0.955493i	$0.404676\pi$
$774$	13.6351	0.000633210 0
$775$	0	0
$776$	9595.09	0.443871
$777$	−4100.10	−0.189305
$778$	−6445.89	−0.297039
$779$	−18674.0	−0.858876
$780$	0	0
$781$	5176.99	0.237193
$782$	−809.276	−0.0370072
$783$	18891.0	0.862210
$784$	−2902.25	−0.132209
$785$	0	0
$786$	−5019.84	−0.227801
$787$	4417.61	0.200090	0.100045	−	0.994983i	$-0.468101\pi$
$787$	4417.61	0.200090	0.100045	+	0.994983i	$0.468101\pi$
$788$	−38258.5	−1.72957
$789$	1232.74	0.0556231
$790$	0	0
$791$	−33942.4	−1.52573
$792$	1014.09	0.0454974
$793$	−7561.33	−0.338601
$794$	−3158.99	−0.141194
$795$	0	0
$796$	57.4153	0.00255657
$797$	27030.1	1.20132	0.600661	−	0.799504i	$-0.294904\pi$
$797$	27030.1	1.20132	0.600661	+	0.799504i	$0.294904\pi$
$798$	−4989.91	−0.221354
$799$	−5947.75	−0.263350
$800$	0	0
$801$	−2873.77	−0.126766
$802$	264.769	0.0116575
$803$	6716.60	0.295173
$804$	−18214.6	−0.798979
$805$	0	0
$806$	3578.85	0.156401
$807$	−29836.9	−1.30150
$808$	−14642.6	−0.637533
$809$	23647.0	1.02767	0.513835	−	0.857889i	$-0.328224\pi$
$809$	23647.0	1.02767	0.513835	+	0.857889i	$0.328224\pi$
$810$	0	0
$811$	33486.1	1.44988	0.724941	−	0.688811i	$-0.241867\pi$
$811$	33486.1	1.44988	0.724941	+	0.688811i	$0.241867\pi$
$812$	21353.1	0.922843
$813$	−8815.30	−0.380278
$814$	328.999	0.0141663
$815$	0	0
$816$	−25237.8	−1.08272
$817$	−155.353	−0.00665251
$818$	6749.88	0.288513
$819$	10289.7	0.439014
$820$	0	0
$821$	2605.69	0.110766	0.0553832	−	0.998465i	$-0.482362\pi$
$821$	2605.69	0.110766	0.0553832	+	0.998465i	$0.482362\pi$
$822$	860.673	0.0365200
$823$	−31976.2	−1.35434	−0.677169	−	0.735828i	$-0.736793\pi$
$823$	−31976.2	−1.35434	−0.677169	+	0.735828i	$0.736793\pi$
$824$	−19530.6	−0.825705
$825$	0	0
$826$	−6761.62	−0.284827
$827$	37759.0	1.58768	0.793839	−	0.608128i	$-0.208079\pi$
$827$	37759.0	1.58768	0.793839	+	0.608128i	$0.208079\pi$
$828$	811.707	0.0340686
$829$	−1137.55	−0.0476584	−0.0238292	−	0.999716i	$-0.507586\pi$
$829$	−1137.55	−0.0476584	−0.0238292	+	0.999716i	$0.507586\pi$
$830$	0	0
$831$	−1398.08	−0.0583621
$832$	23702.2	0.987649
$833$	−4672.03	−0.194329
$834$	12585.9	0.522557
$835$	0	0
$836$	−5576.83	−0.230716
$837$	−7321.60	−0.302356
$838$	−10917.0	−0.450024
$839$	−37372.2	−1.53782	−0.768911	−	0.639356i	$-0.779201\pi$
$839$	−37372.2	−1.53782	−0.768911	+	0.639356i	$0.779201\pi$
$840$	0	0
$841$	4170.26	0.170989
$842$	−9872.44	−0.404070
$843$	29137.2	1.19044
$844$	−23193.5	−0.945917
$845$	0	0
$846$	−428.312	−0.0174062
$847$	−2048.31	−0.0830943
$848$	7662.68	0.310304
$849$	−30824.0	−1.24603
$850$	0	0
$851$	545.589	0.0219772
$852$	−20825.0	−0.837387
$853$	22490.8	0.902780	0.451390	−	0.892327i	$-0.350928\pi$
$853$	22490.8	0.902780	0.451390	+	0.892327i	$0.350928\pi$
$854$	−1255.37	−0.0503021
$855$	0	0
$856$	−5481.16	−0.218858
$857$	−43409.5	−1.73027	−0.865135	−	0.501539i	$-0.832767\pi$
$857$	−43409.5	−1.73027	−0.865135	+	0.501539i	$0.832767\pi$
$858$	−3563.15	−0.141776
$859$	29533.2	1.17306	0.586532	−	0.809926i	$-0.300493\pi$
$859$	29533.2	1.17306	0.586532	+	0.809926i	$0.300493\pi$
$860$	0	0
$861$	27590.1	1.09207
$862$	297.457	0.0117534
$863$	−14351.6	−0.566090	−0.283045	−	0.959107i	$-0.591345\pi$
$863$	−14351.6	−0.566090	−0.283045	+	0.959107i	$0.591345\pi$
$864$	14331.9	0.564331
$865$	0	0
$866$	1293.31	0.0507488
$867$	−11502.4	−0.450569
$868$	−8275.85	−0.323618
$869$	10760.5	0.420051
$870$	0	0
$871$	30725.3	1.19528
$872$	727.413	0.0282492
$873$	−6902.39	−0.267595
$874$	663.994	0.0256979
$875$	0	0
$876$	−27018.3	−1.04208
$877$	43248.7	1.66523	0.832614	−	0.553854i	$-0.186844\pi$
$877$	43248.7	1.66523	0.832614	+	0.553854i	$0.186844\pi$
$878$	5727.71	0.220160
$879$	−52647.9	−2.02021
$880$	0	0
$881$	3816.13	0.145935	0.0729675	−	0.997334i	$-0.476753\pi$
$881$	3816.13	0.145935	0.0729675	+	0.997334i	$0.476753\pi$
$882$	−336.444	−0.0128443
$883$	−48787.6	−1.85938	−0.929690	−	0.368343i	$-0.879925\pi$
$883$	−48787.6	−1.85938	−0.929690	+	0.368343i	$0.879925\pi$
$884$	46121.6	1.75479
$885$	0	0
$886$	−8541.49	−0.323879
$887$	−41495.1	−1.57077	−0.785384	−	0.619009i	$-0.787534\pi$
$887$	−41495.1	−1.57077	−0.785384	+	0.619009i	$0.787534\pi$
$888$	−2741.88	−0.103617
$889$	1855.41	0.0699984
$890$	0	0
$891$	9708.15	0.365023
$892$	−91.9464	−0.00345134
$893$	4880.01	0.182870
$894$	−15138.5	−0.566340
$895$	0	0
$896$	21298.1	0.794107
$897$	−5908.90	−0.219947
$898$	12426.7	0.461788
$899$	−11068.7	−0.410637
$900$	0	0
$901$	12335.3	0.456104
$902$	−2213.88	−0.0817228
$903$	229.528	0.00845871
$904$	−22698.5	−0.835113
$905$	0	0
$906$	5048.53	0.185128
$907$	−21615.3	−0.791316	−0.395658	−	0.918398i	$-0.629483\pi$
$907$	−21615.3	−0.791316	−0.395658	+	0.918398i	$0.629483\pi$
$908$	34453.6	1.25923
$909$	10533.4	0.384347
$910$	0	0
$911$	3646.35	0.132611	0.0663057	−	0.997799i	$-0.478879\pi$
$911$	3646.35	0.132611	0.0663057	+	0.997799i	$0.478879\pi$
$912$	20707.1	0.751844
$913$	287.693	0.0104285
$914$	11854.0	0.428988
$915$	0	0
$916$	−37877.6	−1.36628
$917$	−19581.1	−0.705151
$918$	6774.43	0.243562
$919$	31280.0	1.12278	0.561388	−	0.827553i	$-0.310267\pi$
$919$	31280.0	1.12278	0.561388	+	0.827553i	$0.310267\pi$
$920$	0	0
$921$	−8880.05	−0.317707
$922$	6285.42	0.224511
$923$	35128.7	1.25274
$924$	8239.56	0.293357
$925$	0	0
$926$	5795.79	0.205682
$927$	14049.7	0.497790
$928$	21666.9	0.766433
$929$	6557.92	0.231602	0.115801	−	0.993272i	$-0.463056\pi$
$929$	6557.92	0.231602	0.115801	+	0.993272i	$0.463056\pi$
$930$	0	0
$931$	3833.30	0.134942
$932$	1580.02	0.0555314
$933$	44370.9	1.55695
$934$	11094.2	0.388665
$935$	0	0
$936$	6881.13	0.240296
$937$	24473.3	0.853265	0.426632	−	0.904425i	$-0.359700\pi$
$937$	24473.3	0.853265	0.426632	+	0.904425i	$0.359700\pi$
$938$	5101.18	0.177569
$939$	−3902.91	−0.135641
$940$	0	0
$941$	15420.8	0.534224	0.267112	−	0.963665i	$-0.413931\pi$
$941$	15420.8	0.534224	0.267112	+	0.963665i	$0.413931\pi$
$942$	1484.44	0.0513436
$943$	−3671.34	−0.126782
$944$	28059.4	0.967432
$945$	0	0
$946$	−18.4177	−0.000632993 0
$947$	33141.2	1.13722	0.568608	−	0.822609i	$-0.307482\pi$
$947$	33141.2	1.13722	0.568608	+	0.822609i	$0.307482\pi$
$948$	−43285.2	−1.48295
$949$	45575.8	1.55896
$950$	0	0
$951$	1385.47	0.0472417
$952$	15864.5	0.540096
$953$	20735.4	0.704813	0.352406	−	0.935847i	$-0.385363\pi$
$953$	20735.4	0.704813	0.352406	+	0.935847i	$0.385363\pi$
$954$	888.298	0.0301464
$955$	0	0
$956$	−32188.9	−1.08898
$957$	11020.2	0.372239
$958$	7321.32	0.246911
$959$	3357.26	0.113046
$960$	0	0
$961$	−25501.1	−0.856000
$962$	2232.44	0.0748198
$963$	3942.96	0.131942
$964$	7438.60	0.248528
$965$	0	0
$966$	−981.027	−0.0326750
$967$	8178.87	0.271990	0.135995	−	0.990710i	$-0.456577\pi$
$967$	8178.87	0.271990	0.135995	+	0.990710i	$0.456577\pi$
$968$	−1369.78	−0.0454819
$969$	33334.2	1.10511
$970$	0	0
$971$	−20576.1	−0.680039	−0.340020	−	0.940418i	$-0.610434\pi$
$971$	−20576.1	−0.680039	−0.340020	+	0.940418i	$0.610434\pi$
$972$	−16524.1	−0.545277
$973$	49094.1	1.61756
$974$	−5156.96	−0.169651
$975$	0	0
$976$	5209.55	0.170854
$977$	−14541.9	−0.476188	−0.238094	−	0.971242i	$-0.576523\pi$
$977$	−14541.9	−0.476188	−0.238094	+	0.971242i	$0.576523\pi$
$978$	−6053.48	−0.197923
$979$	3881.76	0.126723
$980$	0	0
$981$	−523.277	−0.0170305
$982$	−9755.62	−0.317021
$983$	29285.7	0.950223	0.475111	−	0.879926i	$-0.342408\pi$
$983$	29285.7	0.950223	0.475111	+	0.879926i	$0.342408\pi$
$984$	18450.5	0.597745
$985$	0	0
$986$	10241.5	0.330787
$987$	−7210.03	−0.232521
$988$	−37841.8	−1.21853
$989$	−30.5427	−0.000982004 0
$990$	0	0
$991$	−38085.9	−1.22083	−0.610413	−	0.792083i	$-0.708997\pi$
$991$	−38085.9	−1.22083	−0.610413	+	0.792083i	$0.708997\pi$
$992$	−8397.44	−0.268769
$993$	−50585.1	−1.61658
$994$	5832.26	0.186105
$995$	0	0
$996$	−1157.28	−0.0368170
$997$	26803.6	0.851434	0.425717	−	0.904856i	$-0.360022\pi$
$997$	26803.6	0.851434	0.425717	+	0.904856i	$0.360022\pi$
$998$	−14691.6	−0.465987
$999$	−4567.12	−0.144642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.4.a.b.1.2		2
3.2	odd	2		2475.4.a.q.1.1		2
5.2	odd	4		275.4.b.c.199.3		4
5.3	odd	4		275.4.b.c.199.2		4
5.4	even	2		11.4.a.a.1.1	✓	2
15.14	odd	2		99.4.a.c.1.2		2
20.19	odd	2		176.4.a.i.1.1		2
35.34	odd	2		539.4.a.e.1.1		2
40.19	odd	2		704.4.a.n.1.2		2
40.29	even	2		704.4.a.p.1.1		2
55.4	even	10		121.4.c.c.27.1		8
55.9	even	10		121.4.c.c.81.2		8
55.14	even	10		121.4.c.c.9.1		8
55.19	odd	10		121.4.c.f.9.2		8
55.24	odd	10		121.4.c.f.81.1		8
55.29	odd	10		121.4.c.f.27.2		8
55.39	odd	10		121.4.c.f.3.1		8
55.49	even	10		121.4.c.c.3.2		8
55.54	odd	2		121.4.a.c.1.2		2
60.59	even	2		1584.4.a.bc.1.2		2
65.64	even	2		1859.4.a.a.1.2		2
165.164	even	2		1089.4.a.v.1.1		2
220.219	even	2		1936.4.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.a.a.1.1	✓	2	5.4	even	2
99.4.a.c.1.2		2	15.14	odd	2
121.4.a.c.1.2		2	55.54	odd	2
121.4.c.c.3.2		8	55.49	even	10
121.4.c.c.9.1		8	55.14	even	10
121.4.c.c.27.1		8	55.4	even	10
121.4.c.c.81.2		8	55.9	even	10
121.4.c.f.3.1		8	55.39	odd	10
121.4.c.f.9.2		8	55.19	odd	10
121.4.c.f.27.2		8	55.29	odd	10
121.4.c.f.81.1		8	55.24	odd	10
176.4.a.i.1.1		2	20.19	odd	2
275.4.a.b.1.2		2	1.1	even	1	trivial
275.4.b.c.199.2		4	5.3	odd	4
275.4.b.c.199.3		4	5.2	odd	4
539.4.a.e.1.1		2	35.34	odd	2
704.4.a.n.1.2		2	40.19	odd	2
704.4.a.p.1.1		2	40.29	even	2
1089.4.a.v.1.1		2	165.164	even	2
1584.4.a.bc.1.2		2	60.59	even	2
1859.4.a.a.1.2		2	65.64	even	2
1936.4.a.w.1.1		2	220.219	even	2
2475.4.a.q.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	275.a (trivial)

\(f(q)\)	\(=\)	\(q+0.732051 q^{2} -5.92820 q^{3} -7.46410 q^{4} -4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} +O(q^{10})\)	\(q+0.732051 q^{2} -5.92820 q^{3} -7.46410 q^{4} -4.33975 q^{6} -16.9282 q^{7} -11.3205 q^{8} +8.14359 q^{9} -11.0000 q^{11} +44.2487 q^{12} -74.6410 q^{13} -12.3923 q^{14} +51.4256 q^{16} +82.7846 q^{17} +5.96152 q^{18} -67.9230 q^{19} +100.354 q^{21} -8.05256 q^{22} -13.3538 q^{23} +67.1103 q^{24} -54.6410 q^{26} +111.785 q^{27} +126.354 q^{28} +168.995 q^{29} -65.4974 q^{31} +128.210 q^{32} +65.2102 q^{33} +60.6025 q^{34} -60.7846 q^{36} -40.8564 q^{37} -49.7231 q^{38} +442.487 q^{39} +274.928 q^{41} +73.4641 q^{42} +2.28719 q^{43} +82.1051 q^{44} -9.77568 q^{46} -71.8461 q^{47} -304.862 q^{48} -56.4359 q^{49} -490.764 q^{51} +557.128 q^{52} +149.005 q^{53} +81.8320 q^{54} +191.636 q^{56} +402.662 q^{57} +123.713 q^{58} +545.631 q^{59} +101.303 q^{61} -47.9474 q^{62} -137.856 q^{63} -317.549 q^{64} +47.7372 q^{66} -411.641 q^{67} -617.913 q^{68} +79.1642 q^{69} -470.636 q^{71} -92.1896 q^{72} -610.600 q^{73} -29.9090 q^{74} +506.985 q^{76} +186.210 q^{77} +323.923 q^{78} -978.225 q^{79} -882.559 q^{81} +201.261 q^{82} -26.1539 q^{83} -749.051 q^{84} +1.67434 q^{86} -1001.84 q^{87} +124.526 q^{88} -352.887 q^{89} +1263.54 q^{91} +99.6743 q^{92} +388.282 q^{93} -52.5950 q^{94} -760.056 q^{96} -847.585 q^{97} -41.3140 q^{98} -89.5795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} - 8 q^{4} - 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 - 8 * q^4 - 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} - 8 q^{4} - 26 q^{6} - 20 q^{7} + 12 q^{8} + 44 q^{9} - 22 q^{11} + 40 q^{12} - 80 q^{13} - 4 q^{14} - 8 q^{16} + 124 q^{17} - 92 q^{18} + 72 q^{19} + 76 q^{21} + 22 q^{22} + 98 q^{23} + 252 q^{24} - 40 q^{26} + 182 q^{27} + 128 q^{28} + 144 q^{29} - 34 q^{31} + 104 q^{32} - 22 q^{33} - 52 q^{34} - 80 q^{36} - 54 q^{37} - 432 q^{38} + 400 q^{39} + 536 q^{41} + 140 q^{42} + 60 q^{43} + 88 q^{44} - 314 q^{46} + 272 q^{47} - 776 q^{48} - 390 q^{49} - 164 q^{51} + 560 q^{52} + 492 q^{53} - 110 q^{54} + 120 q^{56} + 1512 q^{57} + 192 q^{58} + 634 q^{59} + 840 q^{61} - 134 q^{62} - 248 q^{63} + 224 q^{64} + 286 q^{66} - 754 q^{67} - 640 q^{68} + 962 q^{69} - 678 q^{71} + 744 q^{72} + 400 q^{73} + 6 q^{74} + 432 q^{76} + 220 q^{77} + 440 q^{78} + 316 q^{79} - 1294 q^{81} - 512 q^{82} - 468 q^{83} - 736 q^{84} - 156 q^{86} - 1200 q^{87} - 132 q^{88} - 1842 q^{89} + 1280 q^{91} + 40 q^{92} + 638 q^{93} - 992 q^{94} - 952 q^{96} - 2194 q^{97} + 870 q^{98} - 484 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 - 8 * q^4 - 26 * q^6 - 20 * q^7 + 12 * q^8 + 44 * q^9 - 22 * q^11 + 40 * q^12 - 80 * q^13 - 4 * q^14 - 8 * q^16 + 124 * q^17 - 92 * q^18 + 72 * q^19 + 76 * q^21 + 22 * q^22 + 98 * q^23 + 252 * q^24 - 40 * q^26 + 182 * q^27 + 128 * q^28 + 144 * q^29 - 34 * q^31 + 104 * q^32 - 22 * q^33 - 52 * q^34 - 80 * q^36 - 54 * q^37 - 432 * q^38 + 400 * q^39 + 536 * q^41 + 140 * q^42 + 60 * q^43 + 88 * q^44 - 314 * q^46 + 272 * q^47 - 776 * q^48 - 390 * q^49 - 164 * q^51 + 560 * q^52 + 492 * q^53 - 110 * q^54 + 120 * q^56 + 1512 * q^57 + 192 * q^58 + 634 * q^59 + 840 * q^61 - 134 * q^62 - 248 * q^63 + 224 * q^64 + 286 * q^66 - 754 * q^67 - 640 * q^68 + 962 * q^69 - 678 * q^71 + 744 * q^72 + 400 * q^73 + 6 * q^74 + 432 * q^76 + 220 * q^77 + 440 * q^78 + 316 * q^79 - 1294 * q^81 - 512 * q^82 - 468 * q^83 - 736 * q^84 - 156 * q^86 - 1200 * q^87 - 132 * q^88 - 1842 * q^89 + 1280 * q^91 + 40 * q^92 + 638 * q^93 - 992 * q^94 - 952 * q^96 - 2194 * q^97 + 870 * q^98 - 484 * q^99

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