LMFDB - Embedded newform 169.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(1,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("169.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.24698 q^{2} -0.554958 q^{3} +3.04892 q^{4} +1.44504 q^{5} -1.24698 q^{6} -2.04892 q^{7} +2.35690 q^{8} -2.69202 q^{9} +3.24698 q^{10} +2.55496 q^{11} -1.69202 q^{12} -4.60388 q^{14} -0.801938 q^{15} -0.801938 q^{16} -5.29590 q^{17} -6.04892 q^{18} +5.85086 q^{19} +4.40581 q^{20} +1.13706 q^{21} +5.74094 q^{22} -1.89008 q^{23} -1.30798 q^{24} -2.91185 q^{25} +3.15883 q^{27} -6.24698 q^{28} +2.26875 q^{29} -1.80194 q^{30} +4.26875 q^{31} -6.51573 q^{32} -1.41789 q^{33} -11.8998 q^{34} -2.96077 q^{35} -8.20775 q^{36} -5.35690 q^{37} +13.1468 q^{38} +3.40581 q^{40} -1.27413 q^{41} +2.55496 q^{42} +6.13706 q^{43} +7.78986 q^{44} -3.89008 q^{45} -4.24698 q^{46} +2.95108 q^{47} +0.445042 q^{48} -2.80194 q^{49} -6.54288 q^{50} +2.93900 q^{51} +5.52111 q^{53} +7.09783 q^{54} +3.69202 q^{55} -4.82908 q^{56} -3.24698 q^{57} +5.09783 q^{58} +12.2078 q^{59} -2.44504 q^{60} +8.56465 q^{61} +9.59179 q^{62} +5.51573 q^{63} -13.0368 q^{64} -3.18598 q^{66} -0.576728 q^{67} -16.1468 q^{68} +1.04892 q^{69} -6.65279 q^{70} +4.59419 q^{71} -6.34481 q^{72} +10.5526 q^{73} -12.0368 q^{74} +1.61596 q^{75} +17.8388 q^{76} -5.23490 q^{77} -15.7778 q^{79} -1.15883 q^{80} +6.32304 q^{81} -2.86294 q^{82} -7.72348 q^{83} +3.46681 q^{84} -7.65279 q^{85} +13.7899 q^{86} -1.25906 q^{87} +6.02177 q^{88} -6.61356 q^{89} -8.74094 q^{90} -5.76271 q^{92} -2.36898 q^{93} +6.63102 q^{94} +8.45473 q^{95} +3.61596 q^{96} -11.9269 q^{97} -6.29590 q^{98} -6.87800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 2 q^{3} + 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9} + 5 q^{10} + 8 q^{11} - 5 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 9 q^{18} + 4 q^{19} - 2 q^{21} + 3 q^{22} - 5 q^{23} - 9 q^{24}+ \cdots - q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 - 2 * q^3 + 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9 + 5 * q^10 + 8 * q^11 - 5 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 9 * q^18 + 4 * q^19 - 2 * q^21 + 3 * q^22 - 5 * q^23 - 9 * q^24 - 5 * q^25 + q^27 - 14 * q^28 - q^29 - q^30 + 5 * q^31 - 7 * q^32 - 10 * q^33 - 13 * q^34 + 4 * q^35 - 7 * q^36 - 12 * q^37 + 12 * q^38 - 3 * q^40 + 7 * q^41 + 8 * q^42 + 13 * q^43 - 11 * q^45 - 8 * q^46 + 18 * q^47 + q^48 - 4 * q^49 - q^50 - q^51 + q^53 + 3 * q^54 + 6 * q^55 - 4 * q^56 - 5 * q^57 - 3 * q^58 + 19 * q^59 - 7 * q^60 + 4 * q^61 + q^62 + 4 * q^63 - 11 * q^64 + 5 * q^66 + q^67 - 21 * q^68 - 6 * q^69 - 2 * q^70 + 27 * q^71 + 4 * q^72 - 9 * q^73 - 8 * q^74 + 15 * q^75 + 21 * q^76 + 8 * q^77 - 5 * q^79 + 5 * q^80 - q^81 - 14 * q^82 + 7 * q^83 + 7 * q^84 - 5 * q^85 + 18 * q^86 - 18 * q^87 + 15 * q^88 + 11 * q^89 - 12 * q^90 - 22 * q^93 + 5 * q^94 + 3 * q^95 + 21 * q^96 - 7 * q^97 - 5 * q^98 - q^99

Coefficient data

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

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

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

$2$	2.24698	1.58885	0.794427	−	0.607359i	$-0.207771\pi$
$2$	2.24698	1.58885	0.794427	+	0.607359i	$0.207771\pi$
$3$	−0.554958	−0.320405	−0.160203	−	0.987084i	$-0.551215\pi$
$3$	−0.554958	−0.320405	−0.160203	+	0.987084i	$0.551215\pi$
$4$	3.04892	1.52446
$5$	1.44504	0.646242	0.323121	−	0.946358i	$-0.395268\pi$
$5$	1.44504	0.646242	0.323121	+	0.946358i	$0.395268\pi$
$6$	−1.24698	−0.509077
$7$	−2.04892	−0.774418	−0.387209	−	0.921992i	$-0.626561\pi$
$7$	−2.04892	−0.774418	−0.387209	+	0.921992i	$0.626561\pi$
$8$	2.35690	0.833289
$9$	−2.69202	−0.897340
$10$	3.24698	1.02679
$11$	2.55496	0.770349	0.385174	−	0.922844i	$-0.374141\pi$
$11$	2.55496	0.770349	0.385174	+	0.922844i	$0.374141\pi$
$12$	−1.69202	−0.488445
$13$	0	0
$13$	0	0
$14$	−4.60388	−1.23044
$15$	−0.801938	−0.207059
$16$	−0.801938	−0.200484
$17$	−5.29590	−1.28444	−0.642222	−	0.766519i	$-0.721987\pi$
$17$	−5.29590	−1.28444	−0.642222	+	0.766519i	$0.721987\pi$
$18$	−6.04892	−1.42574
$19$	5.85086	1.34228	0.671139	−	0.741331i	$-0.265805\pi$
$19$	5.85086	1.34228	0.671139	+	0.741331i	$0.265805\pi$
$20$	4.40581	0.985170
$21$	1.13706	0.248128
$22$	5.74094	1.22397
$23$	−1.89008	−0.394110	−0.197055	−	0.980392i	$-0.563138\pi$
$23$	−1.89008	−0.394110	−0.197055	+	0.980392i	$0.563138\pi$
$24$	−1.30798	−0.266990
$25$	−2.91185	−0.582371
$26$	0	0
$27$	3.15883	0.607918
$28$	−6.24698	−1.18057
$29$	2.26875	0.421296	0.210648	−	0.977562i	$-0.432443\pi$
$29$	2.26875	0.421296	0.210648	+	0.977562i	$0.432443\pi$
$30$	−1.80194	−0.328987
$31$	4.26875	0.766690	0.383345	−	0.923605i	$-0.374772\pi$
$31$	4.26875	0.766690	0.383345	+	0.923605i	$0.374772\pi$
$32$	−6.51573	−1.15183
$33$	−1.41789	−0.246824
$34$	−11.8998	−2.04079
$35$	−2.96077	−0.500462
$36$	−8.20775	−1.36796
$37$	−5.35690	−0.880668	−0.440334	−	0.897834i	$-0.645140\pi$
$37$	−5.35690	−0.880668	−0.440334	+	0.897834i	$0.645140\pi$
$38$	13.1468	2.13268
$39$	0	0
$40$	3.40581	0.538506
$41$	−1.27413	−0.198985	−0.0994926	−	0.995038i	$-0.531722\pi$
$41$	−1.27413	−0.198985	−0.0994926	+	0.995038i	$0.531722\pi$
$42$	2.55496	0.394239
$43$	6.13706	0.935893	0.467947	−	0.883757i	$-0.344994\pi$
$43$	6.13706	0.935893	0.467947	+	0.883757i	$0.344994\pi$
$44$	7.78986	1.17437
$45$	−3.89008	−0.579899
$46$	−4.24698	−0.626183
$47$	2.95108	0.430460	0.215230	−	0.976563i	$-0.430950\pi$
$47$	2.95108	0.430460	0.215230	+	0.976563i	$0.430950\pi$
$48$	0.445042	0.0642363
$49$	−2.80194	−0.400277
$50$	−6.54288	−0.925302
$51$	2.93900	0.411542
$52$	0	0
$53$	5.52111	0.758382	0.379191	−	0.925318i	$-0.376202\pi$
$53$	5.52111	0.758382	0.379191	+	0.925318i	$0.376202\pi$
$54$	7.09783	0.965893
$55$	3.69202	0.497832
$56$	−4.82908	−0.645314
$57$	−3.24698	−0.430073
$58$	5.09783	0.669378
$59$	12.2078	1.58931	0.794657	−	0.607059i	$-0.207651\pi$
$59$	12.2078	1.58931	0.794657	+	0.607059i	$0.207651\pi$
$60$	−2.44504	−0.315654
$61$	8.56465	1.09659	0.548295	−	0.836285i	$-0.315277\pi$
$61$	8.56465	1.09659	0.548295	+	0.836285i	$0.315277\pi$
$62$	9.59179	1.21816
$63$	5.51573	0.694917
$64$	−13.0368	−1.62960
$65$	0	0
$66$	−3.18598	−0.392167
$67$	−0.576728	−0.0704586	−0.0352293	−	0.999379i	$-0.511216\pi$
$67$	−0.576728	−0.0704586	−0.0352293	+	0.999379i	$0.511216\pi$
$68$	−16.1468	−1.95808
$69$	1.04892	0.126275
$70$	−6.65279	−0.795161
$71$	4.59419	0.545230	0.272615	−	0.962123i	$-0.412112\pi$
$71$	4.59419	0.545230	0.272615	+	0.962123i	$0.412112\pi$
$72$	−6.34481	−0.747744
$73$	10.5526	1.23508	0.617542	−	0.786538i	$-0.288128\pi$
$73$	10.5526	1.23508	0.617542	+	0.786538i	$0.288128\pi$
$74$	−12.0368	−1.39925
$75$	1.61596	0.186595
$76$	17.8388	2.04625
$77$	−5.23490	−0.596572
$78$	0	0
$79$	−15.7778	−1.77514	−0.887569	−	0.460674i	$-0.847608\pi$
$79$	−15.7778	−1.77514	−0.887569	+	0.460674i	$0.847608\pi$
$80$	−1.15883	−0.129562
$81$	6.32304	0.702560
$82$	−2.86294	−0.316158
$83$	−7.72348	−0.847762	−0.423881	−	0.905718i	$-0.639333\pi$
$83$	−7.72348	−0.847762	−0.423881	+	0.905718i	$0.639333\pi$
$84$	3.46681	0.378260
$85$	−7.65279	−0.830062
$86$	13.7899	1.48700
$87$	−1.25906	−0.134986
$88$	6.02177	0.641923
$89$	−6.61356	−0.701036	−0.350518	−	0.936556i	$-0.613995\pi$
$89$	−6.61356	−0.701036	−0.350518	+	0.936556i	$0.613995\pi$
$90$	−8.74094	−0.921376
$91$	0	0
$92$	−5.76271	−0.600804
$93$	−2.36898	−0.245652
$94$	6.63102	0.683938
$95$	8.45473	0.867437
$96$	3.61596	0.369052
$97$	−11.9269	−1.21100	−0.605498	−	0.795847i	$-0.707026\pi$
$97$	−11.9269	−1.21100	−0.605498	+	0.795847i	$0.707026\pi$
$98$	−6.29590	−0.635982
$99$	−6.87800	−0.691265
$100$	−8.87800	−0.887800
$101$	13.0640	1.29991	0.649957	−	0.759971i	$-0.274787\pi$
$101$	13.0640	1.29991	0.649957	+	0.759971i	$0.274787\pi$
$102$	6.60388	0.653881
$103$	9.16852	0.903401	0.451701	−	0.892170i	$-0.350818\pi$
$103$	9.16852	0.903401	0.451701	+	0.892170i	$0.350818\pi$
$104$	0	0
$105$	1.64310	0.160351
$106$	12.4058	1.20496
$107$	−6.89977	−0.667026	−0.333513	−	0.942745i	$-0.608234\pi$
$107$	−6.89977	−0.667026	−0.333513	+	0.942745i	$0.608234\pi$
$108$	9.63102	0.926746
$109$	−0.121998	−0.0116853	−0.00584264	−	0.999983i	$-0.501860\pi$
$109$	−0.121998	−0.0116853	−0.00584264	+	0.999983i	$0.501860\pi$
$110$	8.29590	0.790983
$111$	2.97285	0.282171
$112$	1.64310	0.155259
$113$	7.30798	0.687477	0.343738	−	0.939065i	$-0.388307\pi$
$113$	7.30798	0.687477	0.343738	+	0.939065i	$0.388307\pi$
$114$	−7.29590	−0.683323
$115$	−2.73125	−0.254690
$116$	6.91723	0.642249
$117$	0	0
$118$	27.4306	2.52519
$119$	10.8509	0.994696
$120$	−1.89008	−0.172540
$121$	−4.47219	−0.406563
$122$	19.2446	1.74232
$123$	0.707087	0.0637559
$124$	13.0151	1.16879
$125$	−11.4330	−1.02260
$126$	12.3937	1.10412
$127$	−18.9705	−1.68336	−0.841678	−	0.539980i	$-0.818432\pi$
$127$	−18.9705	−1.68336	−0.841678	+	0.539980i	$0.818432\pi$
$128$	−16.2620	−1.43738
$129$	−3.40581	−0.299865
$130$	0	0
$131$	3.25667	0.284536	0.142268	−	0.989828i	$-0.454560\pi$
$131$	3.25667	0.284536	0.142268	+	0.989828i	$0.454560\pi$
$132$	−4.32304	−0.376273
$133$	−11.9879	−1.03948
$134$	−1.29590	−0.111948
$135$	4.56465	0.392862
$136$	−12.4819	−1.07031
$137$	−0.792249	−0.0676864	−0.0338432	−	0.999427i	$-0.510775\pi$
$137$	−0.792249	−0.0676864	−0.0338432	+	0.999427i	$0.510775\pi$
$138$	2.35690	0.200632
$139$	−11.3394	−0.961799	−0.480899	−	0.876776i	$-0.659690\pi$
$139$	−11.3394	−0.961799	−0.480899	+	0.876776i	$0.659690\pi$
$140$	−9.02715	−0.762933
$141$	−1.63773	−0.137922
$142$	10.3230	0.866291
$143$	0	0
$144$	2.15883	0.179903
$145$	3.27844	0.272260
$146$	23.7114	1.96237
$147$	1.55496	0.128251
$148$	−16.3327	−1.34254
$149$	−8.40581	−0.688631	−0.344316	−	0.938854i	$-0.611889\pi$
$149$	−8.40581	−0.688631	−0.344316	+	0.938854i	$0.611889\pi$
$150$	3.63102	0.296472
$151$	−14.1293	−1.14983	−0.574913	−	0.818215i	$-0.694964\pi$
$151$	−14.1293	−1.14983	−0.574913	+	0.818215i	$0.694964\pi$
$152$	13.7899	1.11851
$153$	14.2567	1.15258
$154$	−11.7627	−0.947866
$155$	6.16852	0.495468
$156$	0	0
$157$	−9.43296	−0.752832	−0.376416	−	0.926451i	$-0.622844\pi$
$157$	−9.43296	−0.752832	−0.376416	+	0.926451i	$0.622844\pi$
$158$	−35.4523	−2.82044
$159$	−3.06398	−0.242990
$160$	−9.41550	−0.744361
$161$	3.87263	0.305206
$162$	14.2078	1.11627
$163$	−8.70410	−0.681758	−0.340879	−	0.940107i	$-0.610725\pi$
$163$	−8.70410	−0.681758	−0.340879	+	0.940107i	$0.610725\pi$
$164$	−3.88471	−0.303345
$165$	−2.04892	−0.159508
$166$	−17.3545	−1.34697
$167$	23.8538	1.84587	0.922933	−	0.384961i	$-0.125785\pi$
$167$	23.8538	1.84587	0.922933	+	0.384961i	$0.125785\pi$
$168$	2.67994	0.206762
$169$	0	0
$170$	−17.1957	−1.31885
$171$	−15.7506	−1.20448
$172$	18.7114	1.42673
$173$	−18.8552	−1.43353	−0.716766	−	0.697314i	$-0.754378\pi$
$173$	−18.8552	−1.43353	−0.716766	+	0.697314i	$0.754378\pi$
$174$	−2.82908	−0.214472
$175$	5.96615	0.450998
$176$	−2.04892	−0.154443
$177$	−6.77479	−0.509224
$178$	−14.8605	−1.11384
$179$	6.02177	0.450088	0.225044	−	0.974349i	$-0.427747\pi$
$179$	6.02177	0.450088	0.225044	+	0.974349i	$0.427747\pi$
$180$	−11.8605	−0.884033
$181$	−4.77777	−0.355129	−0.177565	−	0.984109i	$-0.556822\pi$
$181$	−4.77777	−0.355129	−0.177565	+	0.984109i	$0.556822\pi$
$182$	0	0
$183$	−4.75302	−0.351353
$184$	−4.45473	−0.328407
$185$	−7.74094	−0.569125
$186$	−5.32304	−0.390305
$187$	−13.5308	−0.989470
$188$	8.99761	0.656218
$189$	−6.47219	−0.470782
$190$	18.9976	1.37823
$191$	18.4306	1.33359	0.666795	−	0.745242i	$-0.267666\pi$
$191$	18.4306	1.33359	0.666795	+	0.745242i	$0.267666\pi$
$192$	7.23490	0.522134
$193$	−6.05429	−0.435798	−0.217899	−	0.975971i	$-0.569920\pi$
$193$	−6.05429	−0.435798	−0.217899	+	0.975971i	$0.569920\pi$
$194$	−26.7995	−1.92410
$195$	0	0
$196$	−8.54288	−0.610205
$197$	11.4155	0.813321	0.406660	−	0.913579i	$-0.366693\pi$
$197$	11.4155	0.813321	0.406660	+	0.913579i	$0.366693\pi$
$198$	−15.4547	−1.09832
$199$	−13.9051	−0.985710	−0.492855	−	0.870111i	$-0.664047\pi$
$199$	−13.9051	−0.985710	−0.492855	+	0.870111i	$0.664047\pi$
$200$	−6.86294	−0.485283
$201$	0.320060	0.0225753
$202$	29.3545	2.06538
$203$	−4.64848	−0.326259
$204$	8.96077	0.627379
$205$	−1.84117	−0.128593
$206$	20.6015	1.43537
$207$	5.08815	0.353651
$208$	0	0
$209$	14.9487	1.03402
$210$	3.69202	0.254774
$211$	−13.2446	−0.911795	−0.455897	−	0.890032i	$-0.650682\pi$
$211$	−13.2446	−0.911795	−0.455897	+	0.890032i	$0.650682\pi$
$212$	16.8334	1.15612
$213$	−2.54958	−0.174694
$214$	−15.5036	−1.05981
$215$	8.86831	0.604814
$216$	7.44504	0.506571
$217$	−8.74632	−0.593739
$218$	−0.274127	−0.0185662
$219$	−5.85623	−0.395727
$220$	11.2567	0.758924
$221$	0	0
$222$	6.67994	0.448328
$223$	7.33513	0.491196	0.245598	−	0.969372i	$-0.421016\pi$
$223$	7.33513	0.491196	0.245598	+	0.969372i	$0.421016\pi$
$224$	13.3502	0.891997
$225$	7.83877	0.522585
$226$	16.4209	1.09230
$227$	8.67456	0.575751	0.287875	−	0.957668i	$-0.407051\pi$
$227$	8.67456	0.575751	0.287875	+	0.957668i	$0.407051\pi$
$228$	−9.89977	−0.655628
$229$	13.6866	0.904439	0.452219	−	0.891907i	$-0.350632\pi$
$229$	13.6866	0.904439	0.452219	+	0.891907i	$0.350632\pi$
$230$	−6.13706	−0.404666
$231$	2.90515	0.191145
$232$	5.34721	0.351061
$233$	−5.08815	−0.333336	−0.166668	−	0.986013i	$-0.553301\pi$
$233$	−5.08815	−0.333336	−0.166668	+	0.986013i	$0.553301\pi$
$234$	0	0
$235$	4.26444	0.278181
$236$	37.2204	2.42284
$237$	8.75600	0.568764
$238$	24.3817	1.58043
$239$	10.9239	0.706611	0.353305	−	0.935508i	$-0.385058\pi$
$239$	10.9239	0.706611	0.353305	+	0.935508i	$0.385058\pi$
$240$	0.643104	0.0415122
$241$	−11.9148	−0.767502	−0.383751	−	0.923437i	$-0.625368\pi$
$241$	−11.9148	−0.767502	−0.383751	+	0.923437i	$0.625368\pi$
$242$	−10.0489	−0.645969
$243$	−12.9855	−0.833022
$244$	26.1129	1.67171
$245$	−4.04892	−0.258676
$246$	1.58881	0.101299
$247$	0	0
$248$	10.0610	0.638874
$249$	4.28621	0.271627
$250$	−25.6896	−1.62475
$251$	22.3478	1.41058	0.705290	−	0.708919i	$-0.250817\pi$
$251$	22.3478	1.41058	0.705290	+	0.708919i	$0.250817\pi$
$252$	16.8170	1.05937
$253$	−4.82908	−0.303602
$254$	−42.6262	−2.67461
$255$	4.24698	0.265956
$256$	−10.4668	−0.654176
$257$	−18.6601	−1.16398	−0.581992	−	0.813194i	$-0.697727\pi$
$257$	−18.6601	−1.16398	−0.581992	+	0.813194i	$0.697727\pi$
$258$	−7.65279	−0.476442
$259$	10.9758	0.682005
$260$	0	0
$261$	−6.10752	−0.378046
$262$	7.31767	0.452087
$263$	14.3991	0.887887	0.443944	−	0.896055i	$-0.353579\pi$
$263$	14.3991	0.887887	0.443944	+	0.896055i	$0.353579\pi$
$264$	−3.34183	−0.205675
$265$	7.97823	0.490099
$266$	−26.9366	−1.65159
$267$	3.67025	0.224616
$268$	−1.75840	−0.107411
$269$	0.652793	0.0398015	0.0199007	−	0.999802i	$-0.493665\pi$
$269$	0.652793	0.0398015	0.0199007	+	0.999802i	$0.493665\pi$
$270$	10.2567	0.624201
$271$	1.99569	0.121229	0.0606147	−	0.998161i	$-0.480694\pi$
$271$	1.99569	0.121229	0.0606147	+	0.998161i	$0.480694\pi$
$272$	4.24698	0.257511
$273$	0	0
$274$	−1.78017	−0.107544
$275$	−7.43967	−0.448629
$276$	3.19806	0.192501
$277$	11.7845	0.708061	0.354030	−	0.935234i	$-0.384811\pi$
$277$	11.7845	0.708061	0.354030	+	0.935234i	$0.384811\pi$
$278$	−25.4795	−1.52816
$279$	−11.4916	−0.687982
$280$	−6.97823	−0.417029
$281$	6.47219	0.386098	0.193049	−	0.981189i	$-0.438162\pi$
$281$	6.47219	0.386098	0.193049	+	0.981189i	$0.438162\pi$
$282$	−3.67994	−0.219137
$283$	6.58104	0.391202	0.195601	−	0.980684i	$-0.437334\pi$
$283$	6.58104	0.391202	0.195601	+	0.980684i	$0.437334\pi$
$284$	14.0073	0.831180
$285$	−4.69202	−0.277931
$286$	0	0
$287$	2.61058	0.154098
$288$	17.5405	1.03358
$289$	11.0465	0.649796
$290$	7.36658	0.432581
$291$	6.61894	0.388009
$292$	32.1739	1.88284
$293$	24.3381	1.42185	0.710924	−	0.703269i	$-0.248277\pi$
$293$	24.3381	1.42185	0.710924	+	0.703269i	$0.248277\pi$
$294$	3.49396	0.203772
$295$	17.6407	1.02708
$296$	−12.6256	−0.733851
$297$	8.07069	0.468309
$298$	−18.8877	−1.09413
$299$	0	0
$300$	4.92692	0.284456
$301$	−12.5743	−0.724773
$302$	−31.7482	−1.82691
$303$	−7.24996	−0.416500
$304$	−4.69202	−0.269106
$305$	12.3763	0.708663
$306$	32.0344	1.83129
$307$	14.0737	0.803227	0.401613	−	0.915809i	$-0.368450\pi$
$307$	14.0737	0.803227	0.401613	+	0.915809i	$0.368450\pi$
$308$	−15.9608	−0.909449
$309$	−5.08815	−0.289455
$310$	13.8605	0.787226
$311$	−29.7700	−1.68810	−0.844051	−	0.536263i	$-0.819836\pi$
$311$	−29.7700	−1.68810	−0.844051	+	0.536263i	$0.819836\pi$
$312$	0	0
$313$	−7.47889	−0.422732	−0.211366	−	0.977407i	$-0.567791\pi$
$313$	−7.47889	−0.422732	−0.211366	+	0.977407i	$0.567791\pi$
$314$	−21.1957	−1.19614
$315$	7.97046	0.449085
$316$	−48.1051	−2.70613
$317$	−30.0301	−1.68666	−0.843330	−	0.537396i	$-0.819408\pi$
$317$	−30.0301	−1.68666	−0.843330	+	0.537396i	$0.819408\pi$
$318$	−6.88471	−0.386075
$319$	5.79656	0.324545
$320$	−18.8388	−1.05312
$321$	3.82908	0.213719
$322$	8.70171	0.484927
$323$	−30.9855	−1.72408
$324$	19.2784	1.07102
$325$	0	0
$326$	−19.5579	−1.08321
$327$	0.0677037	0.00374402
$328$	−3.00298	−0.165812
$329$	−6.04652	−0.333356
$330$	−4.60388	−0.253435
$331$	15.7168	0.863872	0.431936	−	0.901904i	$-0.357831\pi$
$331$	15.7168	0.863872	0.431936	+	0.901904i	$0.357831\pi$
$332$	−23.5483	−1.29238
$333$	14.4209	0.790259
$334$	53.5991	2.93281
$335$	−0.833397	−0.0455333
$336$	−0.911854	−0.0497457
$337$	1.95407	0.106445	0.0532224	−	0.998583i	$-0.483051\pi$
$337$	1.95407	0.106445	0.0532224	+	0.998583i	$0.483051\pi$
$338$	0	0
$339$	−4.05562	−0.220271
$340$	−23.3327	−1.26540
$341$	10.9065	0.590619
$342$	−35.3913	−1.91374
$343$	20.0834	1.08440
$344$	14.4644	0.779869
$345$	1.51573	0.0816041
$346$	−42.3672	−2.27767
$347$	−17.1250	−0.919317	−0.459659	−	0.888096i	$-0.652028\pi$
$347$	−17.1250	−0.919317	−0.459659	+	0.888096i	$0.652028\pi$
$348$	−3.83877	−0.205780
$349$	10.4668	0.560276	0.280138	−	0.959960i	$-0.409620\pi$
$349$	10.4668	0.560276	0.280138	+	0.959960i	$0.409620\pi$
$350$	13.4058	0.716571
$351$	0	0
$352$	−16.6474	−0.887310
$353$	−15.5308	−0.826621	−0.413310	−	0.910590i	$-0.635628\pi$
$353$	−15.5308	−0.826621	−0.413310	+	0.910590i	$0.635628\pi$
$354$	−15.2228	−0.809084
$355$	6.63879	0.352351
$356$	−20.1642	−1.06870
$357$	−6.02177	−0.318706
$358$	13.5308	0.715125
$359$	21.4263	1.13083	0.565417	−	0.824805i	$-0.308715\pi$
$359$	21.4263	1.13083	0.565417	+	0.824805i	$0.308715\pi$
$360$	−9.16852	−0.483224
$361$	15.2325	0.801711
$362$	−10.7356	−0.564249
$363$	2.48188	0.130265
$364$	0	0
$365$	15.2489	0.798164
$366$	−10.6799	−0.558249
$367$	34.3032	1.79061	0.895306	−	0.445452i	$-0.146957\pi$
$367$	34.3032	1.79061	0.895306	+	0.445452i	$0.146957\pi$
$368$	1.51573	0.0790129
$369$	3.42998	0.178557
$370$	−17.3937	−0.904257
$371$	−11.3123	−0.587305
$372$	−7.22282	−0.374486
$373$	−12.5961	−0.652202	−0.326101	−	0.945335i	$-0.605735\pi$
$373$	−12.5961	−0.652202	−0.326101	+	0.945335i	$0.605735\pi$
$374$	−30.4034	−1.57212
$375$	6.34481	0.327645
$376$	6.95539	0.358697
$377$	0	0
$378$	−14.5429	−0.748005
$379$	−16.5386	−0.849529	−0.424765	−	0.905304i	$-0.639643\pi$
$379$	−16.5386	−0.849529	−0.424765	+	0.905304i	$0.639643\pi$
$380$	25.7778	1.32237
$381$	10.5278	0.539356
$382$	41.4131	2.11888
$383$	−7.53617	−0.385080	−0.192540	−	0.981289i	$-0.561673\pi$
$383$	−7.53617	−0.385080	−0.192540	+	0.981289i	$0.561673\pi$
$384$	9.02475	0.460543
$385$	−7.56465	−0.385530
$386$	−13.6039	−0.692419
$387$	−16.5211	−0.839815
$388$	−36.3642	−1.84611
$389$	35.5555	1.80274	0.901369	−	0.433052i	$-0.142563\pi$
$389$	35.5555	1.80274	0.901369	+	0.433052i	$0.142563\pi$
$390$	0	0
$391$	10.0097	0.506212
$392$	−6.60388	−0.333546
$393$	−1.80731	−0.0911670
$394$	25.6504	1.29225
$395$	−22.7995	−1.14717
$396$	−20.9705	−1.05381
$397$	−1.35152	−0.0678308	−0.0339154	−	0.999425i	$-0.510798\pi$
$397$	−1.35152	−0.0678308	−0.0339154	+	0.999425i	$0.510798\pi$
$398$	−31.2446	−1.56615
$399$	6.65279	0.333056
$400$	2.33513	0.116756
$401$	−0.579121	−0.0289199	−0.0144600	−	0.999895i	$-0.504603\pi$
$401$	−0.579121	−0.0289199	−0.0144600	+	0.999895i	$0.504603\pi$
$402$	0.719169	0.0358689
$403$	0	0
$404$	39.8310	1.98167
$405$	9.13706	0.454024
$406$	−10.4450	−0.518379
$407$	−13.6866	−0.678422
$408$	6.92692	0.342934
$409$	15.1575	0.749490	0.374745	−	0.927128i	$-0.377730\pi$
$409$	15.1575	0.749490	0.374745	+	0.927128i	$0.377730\pi$
$410$	−4.13706	−0.204315
$411$	0.439665	0.0216871
$412$	27.9541	1.37720
$413$	−25.0127	−1.23079
$414$	11.4330	0.561899
$415$	−11.1608	−0.547860
$416$	0	0
$417$	6.29291	0.308165
$418$	33.5894	1.64291
$419$	−35.7235	−1.74521	−0.872603	−	0.488430i	$-0.837570\pi$
$419$	−35.7235	−1.74521	−0.872603	+	0.488430i	$0.837570\pi$
$420$	5.00969	0.244448
$421$	35.0465	1.70806	0.854032	−	0.520221i	$-0.174151\pi$
$421$	35.0465	1.70806	0.854032	+	0.520221i	$0.174151\pi$
$422$	−29.7603	−1.44871
$423$	−7.94438	−0.386269
$424$	13.0127	0.631951
$425$	15.4209	0.748022
$426$	−5.72886	−0.277564
$427$	−17.5483	−0.849220
$428$	−21.0368	−1.01685
$429$	0	0
$430$	19.9269	0.960961
$431$	34.2814	1.65128	0.825639	−	0.564199i	$-0.190815\pi$
$431$	34.2814	1.65128	0.825639	+	0.564199i	$0.190815\pi$
$432$	−2.53319	−0.121878
$433$	13.7385	0.660232	0.330116	−	0.943940i	$-0.392912\pi$
$433$	13.7385	0.660232	0.330116	+	0.943940i	$0.392912\pi$
$434$	−19.6528	−0.943364
$435$	−1.81940	−0.0872334
$436$	−0.371961	−0.0178137
$437$	−11.0586	−0.529005
$438$	−13.1588	−0.628753
$439$	10.2403	0.488742	0.244371	−	0.969682i	$-0.421419\pi$
$439$	10.2403	0.488742	0.244371	+	0.969682i	$0.421419\pi$
$440$	8.70171	0.414838
$441$	7.54288	0.359185
$442$	0	0
$443$	12.1763	0.578513	0.289257	−	0.957252i	$-0.406592\pi$
$443$	12.1763	0.578513	0.289257	+	0.957252i	$0.406592\pi$
$444$	9.06398	0.430158
$445$	−9.55688	−0.453039
$446$	16.4819	0.780440
$447$	4.66487	0.220641
$448$	26.7114	1.26199
$449$	12.9051	0.609032	0.304516	−	0.952507i	$-0.401505\pi$
$449$	12.9051	0.609032	0.304516	+	0.952507i	$0.401505\pi$
$450$	17.6136	0.830311
$451$	−3.25534	−0.153288
$452$	22.2814	1.04803
$453$	7.84117	0.368410
$454$	19.4916	0.914785
$455$	0	0
$456$	−7.65279	−0.358375
$457$	−4.65710	−0.217850	−0.108925	−	0.994050i	$-0.534741\pi$
$457$	−4.65710	−0.217850	−0.108925	+	0.994050i	$0.534741\pi$
$458$	30.7536	1.43702
$459$	−16.7289	−0.780836
$460$	−8.32736	−0.388265
$461$	31.5405	1.46899	0.734493	−	0.678616i	$-0.237420\pi$
$461$	31.5405	1.46899	0.734493	+	0.678616i	$0.237420\pi$
$462$	6.52781	0.303701
$463$	−17.6504	−0.820284	−0.410142	−	0.912022i	$-0.634521\pi$
$463$	−17.6504	−0.820284	−0.410142	+	0.912022i	$0.634521\pi$
$464$	−1.81940	−0.0844633
$465$	−3.42327	−0.158750
$466$	−11.4330	−0.529622
$467$	−32.1726	−1.48877	−0.744385	−	0.667751i	$-0.767257\pi$
$467$	−32.1726	−1.48877	−0.744385	+	0.667751i	$0.767257\pi$
$468$	0	0
$469$	1.18167	0.0545644
$470$	9.58211	0.441990
$471$	5.23490	0.241211
$472$	28.7724	1.32436
$473$	15.6799	0.720964
$474$	19.6746	0.903683
$475$	−17.0368	−0.781704
$476$	33.0834	1.51637
$477$	−14.8629	−0.680527
$478$	24.5459	1.12270
$479$	34.8998	1.59461	0.797306	−	0.603576i	$-0.206258\pi$
$479$	34.8998	1.59461	0.797306	+	0.603576i	$0.206258\pi$
$480$	5.22521	0.238497
$481$	0	0
$482$	−26.7724	−1.21945
$483$	−2.14914	−0.0977895
$484$	−13.6353	−0.619788
$485$	−17.2349	−0.782596
$486$	−29.1782	−1.32355
$487$	−41.8351	−1.89573	−0.947864	−	0.318676i	$-0.896762\pi$
$487$	−41.8351	−1.89573	−0.947864	+	0.318676i	$0.896762\pi$
$488$	20.1860	0.913776
$489$	4.83041	0.218439
$490$	−9.09783	−0.410998
$491$	21.8455	0.985873	0.492936	−	0.870065i	$-0.335924\pi$
$491$	21.8455	0.985873	0.492936	+	0.870065i	$0.335924\pi$
$492$	2.15585	0.0971932
$493$	−12.0151	−0.541131
$494$	0	0
$495$	−9.93900	−0.446725
$496$	−3.42327	−0.153709
$497$	−9.41311	−0.422236
$498$	9.63102	0.431576
$499$	−23.5472	−1.05412	−0.527058	−	0.849829i	$-0.676705\pi$
$499$	−23.5472	−1.05412	−0.527058	+	0.849829i	$0.676705\pi$
$500$	−34.8582	−1.55890
$501$	−13.2379	−0.591425
$502$	50.2150	2.24121
$503$	−7.08682	−0.315986	−0.157993	−	0.987440i	$-0.550502\pi$
$503$	−7.08682	−0.315986	−0.157993	+	0.987440i	$0.550502\pi$
$504$	13.0000	0.579066
$505$	18.8780	0.840060
$506$	−10.8509	−0.482379
$507$	0	0
$508$	−57.8394	−2.56621
$509$	−7.61894	−0.337704	−0.168852	−	0.985641i	$-0.554006\pi$
$509$	−7.61894	−0.337704	−0.168852	+	0.985641i	$0.554006\pi$
$510$	9.54288	0.422566
$511$	−21.6213	−0.956471
$512$	9.00538	0.397985
$513$	18.4819	0.815995
$514$	−41.9288	−1.84940
$515$	13.2489	0.583816
$516$	−10.3840	−0.457132
$517$	7.53989	0.331604
$518$	24.6625	1.08361
$519$	10.4638	0.459311
$520$	0	0
$521$	−39.5133	−1.73111	−0.865555	−	0.500813i	$-0.833034\pi$
$521$	−39.5133	−1.73111	−0.865555	+	0.500813i	$0.833034\pi$
$522$	−13.7235	−0.600660
$523$	−15.8194	−0.691734	−0.345867	−	0.938284i	$-0.612415\pi$
$523$	−15.8194	−0.691734	−0.345867	+	0.938284i	$0.612415\pi$
$524$	9.92931	0.433764
$525$	−3.31096	−0.144502
$526$	32.3545	1.41072
$527$	−22.6069	−0.984770
$528$	1.13706	0.0494843
$529$	−19.4276	−0.844678
$530$	17.9269	0.778696
$531$	−32.8635	−1.42616
$532$	−36.5502	−1.58465
$533$	0	0
$534$	8.24698	0.356882
$535$	−9.97046	−0.431061
$536$	−1.35929	−0.0587123
$537$	−3.34183	−0.144211
$538$	1.46681	0.0632388
$539$	−7.15883	−0.308353
$540$	13.9172	0.598902
$541$	−34.4819	−1.48249	−0.741246	−	0.671234i	$-0.765765\pi$
$541$	−34.4819	−1.48249	−0.741246	+	0.671234i	$0.765765\pi$
$542$	4.48427	0.192616
$543$	2.65146	0.113785
$544$	34.5066	1.47946
$545$	−0.176292	−0.00755152
$546$	0	0
$547$	36.8582	1.57594	0.787970	−	0.615713i	$-0.211132\pi$
$547$	36.8582	1.57594	0.787970	+	0.615713i	$0.211132\pi$
$548$	−2.41550	−0.103185
$549$	−23.0562	−0.984015
$550$	−16.7168	−0.712806
$551$	13.2741	0.565497
$552$	2.47219	0.105223
$553$	32.3274	1.37470
$554$	26.4795	1.12501
$555$	4.29590	0.182351
$556$	−34.5730	−1.46622
$557$	−1.27652	−0.0540879	−0.0270439	−	0.999634i	$-0.508609\pi$
$557$	−1.27652	−0.0540879	−0.0270439	+	0.999634i	$0.508609\pi$
$558$	−25.8213	−1.09310
$559$	0	0
$560$	2.37435	0.100335
$561$	7.50902	0.317031
$562$	14.5429	0.613454
$563$	−9.12737	−0.384673	−0.192336	−	0.981329i	$-0.561607\pi$
$563$	−9.12737	−0.384673	−0.192336	+	0.981329i	$0.561607\pi$
$564$	−4.99330	−0.210256
$565$	10.5603	0.444277
$566$	14.7875	0.621563
$567$	−12.9554	−0.544075
$568$	10.8280	0.454334
$569$	−5.72156	−0.239860	−0.119930	−	0.992782i	$-0.538267\pi$
$569$	−5.72156	−0.239860	−0.119930	+	0.992782i	$0.538267\pi$
$570$	−10.5429	−0.441593
$571$	7.60148	0.318112	0.159056	−	0.987270i	$-0.449155\pi$
$571$	7.60148	0.318112	0.159056	+	0.987270i	$0.449155\pi$
$572$	0	0
$573$	−10.2282	−0.427289
$574$	5.86592	0.244839
$575$	5.50365	0.229518
$576$	35.0954	1.46231
$577$	−45.1564	−1.87989	−0.939944	−	0.341330i	$-0.889123\pi$
$577$	−45.1564	−1.87989	−0.939944	+	0.341330i	$0.889123\pi$
$578$	24.8213	1.03243
$579$	3.35988	0.139632
$580$	9.99569	0.415048
$581$	15.8248	0.656522
$582$	14.8726	0.616490
$583$	14.1062	0.584219
$584$	24.8713	1.02918
$585$	0	0
$586$	54.6872	2.25911
$587$	32.4040	1.33746	0.668728	−	0.743507i	$-0.266839\pi$
$587$	32.4040	1.33746	0.668728	+	0.743507i	$0.266839\pi$
$588$	4.74094	0.195513
$589$	24.9758	1.02911
$590$	39.6383	1.63188
$591$	−6.33513	−0.260592
$592$	4.29590	0.176560
$593$	−36.6848	−1.50647	−0.753233	−	0.657754i	$-0.771507\pi$
$593$	−36.6848	−1.50647	−0.753233	+	0.657754i	$0.771507\pi$
$594$	18.1347	0.744075
$595$	15.6799	0.642815
$596$	−25.6286	−1.04979
$597$	7.71678	0.315827
$598$	0	0
$599$	−9.99223	−0.408271	−0.204136	−	0.978943i	$-0.565438\pi$
$599$	−9.99223	−0.408271	−0.204136	+	0.978943i	$0.565438\pi$
$600$	3.80864	0.155487
$601$	−1.81163	−0.0738978	−0.0369489	−	0.999317i	$-0.511764\pi$
$601$	−1.81163	−0.0738978	−0.0369489	+	0.999317i	$0.511764\pi$
$602$	−28.2543	−1.15156
$603$	1.55257	0.0632253
$604$	−43.0790	−1.75286
$605$	−6.46250	−0.262738
$606$	−16.2905	−0.661757
$607$	11.2161	0.455248	0.227624	−	0.973749i	$-0.426904\pi$
$607$	11.2161	0.455248	0.227624	+	0.973749i	$0.426904\pi$
$608$	−38.1226	−1.54608
$609$	2.57971	0.104535
$610$	27.8092	1.12596
$611$	0	0
$612$	43.4674	1.75707
$613$	20.8944	0.843917	0.421958	−	0.906615i	$-0.361343\pi$
$613$	20.8944	0.843917	0.421958	+	0.906615i	$0.361343\pi$
$614$	31.6233	1.27621
$615$	1.02177	0.0412018
$616$	−12.3381	−0.497117
$617$	−12.0992	−0.487094	−0.243547	−	0.969889i	$-0.578311\pi$
$617$	−12.0992	−0.487094	−0.243547	+	0.969889i	$0.578311\pi$
$618$	−11.4330	−0.459901
$619$	10.5526	0.424143	0.212072	−	0.977254i	$-0.431979\pi$
$619$	10.5526	0.424143	0.212072	+	0.977254i	$0.431979\pi$
$620$	18.8073	0.755320
$621$	−5.97046	−0.239586
$622$	−66.8926	−2.68215
$623$	13.5506	0.542895
$624$	0	0
$625$	−1.96184	−0.0784735
$626$	−16.8049	−0.671660
$627$	−8.29590	−0.331306
$628$	−28.7603	−1.14766
$629$	28.3696	1.13117
$630$	17.9095	0.713530
$631$	13.8514	0.551417	0.275709	−	0.961241i	$-0.411087\pi$
$631$	13.8514	0.551417	0.275709	+	0.961241i	$0.411087\pi$
$632$	−37.1866	−1.47920
$633$	7.35019	0.292144
$634$	−67.4771	−2.67986
$635$	−27.4131	−1.08786
$636$	−9.34183	−0.370428
$637$	0	0
$638$	13.0248	0.515655
$639$	−12.3676	−0.489257
$640$	−23.4993	−0.928893
$641$	34.9608	1.38087	0.690434	−	0.723396i	$-0.257420\pi$
$641$	34.9608	1.38087	0.690434	+	0.723396i	$0.257420\pi$
$642$	8.60388	0.339568
$643$	−33.3980	−1.31709	−0.658545	−	0.752541i	$-0.728828\pi$
$643$	−33.3980	−1.31709	−0.658545	+	0.752541i	$0.728828\pi$
$644$	11.8073	0.465273
$645$	−4.92154	−0.193786
$646$	−69.6238	−2.73931
$647$	2.32842	0.0915397	0.0457698	−	0.998952i	$-0.485426\pi$
$647$	2.32842	0.0915397	0.0457698	+	0.998952i	$0.485426\pi$
$648$	14.9028	0.585436
$649$	31.1903	1.22433
$650$	0	0
$651$	4.85384	0.190237
$652$	−26.5381	−1.03931
$653$	14.5714	0.570221	0.285111	−	0.958495i	$-0.407970\pi$
$653$	14.5714	0.570221	0.285111	+	0.958495i	$0.407970\pi$
$654$	0.152129	0.00594871
$655$	4.70602	0.183879
$656$	1.02177	0.0398934
$657$	−28.4077	−1.10829
$658$	−13.5864	−0.529654
$659$	11.1395	0.433932	0.216966	−	0.976179i	$-0.430384\pi$
$659$	11.1395	0.433932	0.216966	+	0.976179i	$0.430384\pi$
$660$	−6.24698	−0.243163
$661$	13.8498	0.538694	0.269347	−	0.963043i	$-0.413192\pi$
$661$	13.8498	0.538694	0.269347	+	0.963043i	$0.413192\pi$
$662$	35.3153	1.37257
$663$	0	0
$664$	−18.2034	−0.706430
$665$	−17.3230	−0.671759
$666$	32.4034	1.25561
$667$	−4.28813	−0.166037
$668$	72.7284	2.81395
$669$	−4.07069	−0.157382
$670$	−1.87263	−0.0723458
$671$	21.8823	0.844757
$672$	−7.40880	−0.285801
$673$	−6.52973	−0.251703	−0.125851	−	0.992049i	$-0.540166\pi$
$673$	−6.52973	−0.251703	−0.125851	+	0.992049i	$0.540166\pi$
$674$	4.39075	0.169125
$675$	−9.19806	−0.354034
$676$	0	0
$677$	−11.3104	−0.434693	−0.217346	−	0.976095i	$-0.569740\pi$
$677$	−11.3104	−0.434693	−0.217346	+	0.976095i	$0.569740\pi$
$678$	−9.11290	−0.349979
$679$	24.4373	0.937816
$680$	−18.0368	−0.691681
$681$	−4.81402	−0.184474
$682$	24.5066	0.938407
$683$	−14.1793	−0.542555	−0.271277	−	0.962501i	$-0.587446\pi$
$683$	−14.1793	−0.542555	−0.271277	+	0.962501i	$0.587446\pi$
$684$	−48.0224	−1.83618
$685$	−1.14483	−0.0437418
$686$	45.1269	1.72295
$687$	−7.59551	−0.289787
$688$	−4.92154	−0.187632
$689$	0	0
$690$	3.40581	0.129657
$691$	−30.7952	−1.17151	−0.585753	−	0.810490i	$-0.699201\pi$
$691$	−30.7952	−1.17151	−0.585753	+	0.810490i	$0.699201\pi$
$692$	−57.4878	−2.18536
$693$	14.0925	0.535328
$694$	−38.4795	−1.46066
$695$	−16.3860	−0.621555
$696$	−2.96748	−0.112482
$697$	6.74764	0.255585
$698$	23.5187	0.890196
$699$	2.82371	0.106802
$700$	18.1903	0.687528
$701$	6.73184	0.254258	0.127129	−	0.991886i	$-0.459424\pi$
$701$	6.73184	0.254258	0.127129	+	0.991886i	$0.459424\pi$
$702$	0	0
$703$	−31.3424	−1.18210
$704$	−33.3086	−1.25536
$705$	−2.36658	−0.0891307
$706$	−34.8974	−1.31338
$707$	−26.7670	−1.00668
$708$	−20.6558	−0.776292
$709$	47.6252	1.78860	0.894300	−	0.447467i	$-0.147674\pi$
$709$	47.6252	1.78860	0.894300	+	0.447467i	$0.147674\pi$
$710$	14.9172	0.559834
$711$	42.4741	1.59290
$712$	−15.5875	−0.584166
$713$	−8.06829	−0.302160
$714$	−13.5308	−0.506377
$715$	0	0
$716$	18.3599	0.686141
$717$	−6.06233	−0.226402
$718$	48.1444	1.79673
$719$	−5.99330	−0.223512	−0.111756	−	0.993736i	$-0.535648\pi$
$719$	−5.99330	−0.223512	−0.111756	+	0.993736i	$0.535648\pi$
$720$	3.11960	0.116261
$721$	−18.7855	−0.699610
$722$	34.2271	1.27380
$723$	6.61224	0.245912
$724$	−14.5670	−0.541380
$725$	−6.60627	−0.245351
$726$	5.57673	0.206972
$727$	−24.1226	−0.894657	−0.447329	−	0.894370i	$-0.647625\pi$
$727$	−24.1226	−0.894657	−0.447329	+	0.894370i	$0.647625\pi$
$728$	0	0
$729$	−11.7627	−0.435656
$730$	34.2640	1.26817
$731$	−32.5013	−1.20210
$732$	−14.4916	−0.535624
$733$	−36.0646	−1.33208	−0.666038	−	0.745918i	$-0.732011\pi$
$733$	−36.0646	−1.33208	−0.666038	+	0.745918i	$0.732011\pi$
$734$	77.0786	2.84502
$735$	2.24698	0.0828811
$736$	12.3153	0.453947
$737$	−1.47352	−0.0542777
$738$	7.70709	0.283702
$739$	−27.5254	−1.01254	−0.506269	−	0.862375i	$-0.668976\pi$
$739$	−27.5254	−1.01254	−0.506269	+	0.862375i	$0.668976\pi$
$740$	−23.6015	−0.867608
$741$	0	0
$742$	−25.4185	−0.933142
$743$	10.4692	0.384078	0.192039	−	0.981387i	$-0.438490\pi$
$743$	10.4692	0.384078	0.192039	+	0.981387i	$0.438490\pi$
$744$	−5.58343	−0.204699
$745$	−12.1468	−0.445023
$746$	−28.3032	−1.03625
$747$	20.7918	0.760731
$748$	−41.2543	−1.50841
$749$	14.1371	0.516557
$750$	14.2567	0.520580
$751$	4.06770	0.148433	0.0742163	−	0.997242i	$-0.476354\pi$
$751$	4.06770	0.148433	0.0742163	+	0.997242i	$0.476354\pi$
$752$	−2.36658	−0.0863005
$753$	−12.4021	−0.451957
$754$	0	0
$755$	−20.4174	−0.743066
$756$	−19.7332	−0.717688
$757$	20.4336	0.742670	0.371335	−	0.928499i	$-0.378900\pi$
$757$	20.4336	0.742670	0.371335	+	0.928499i	$0.378900\pi$
$758$	−37.1618	−1.34978
$759$	2.67994	0.0972757
$760$	19.9269	0.722825
$761$	27.0237	0.979608	0.489804	−	0.871833i	$-0.337068\pi$
$761$	27.0237	0.979608	0.489804	+	0.871833i	$0.337068\pi$
$762$	23.6558	0.856958
$763$	0.249964	0.00904929
$764$	56.1933	2.03300
$765$	20.6015	0.744848
$766$	−16.9336	−0.611837
$767$	0	0
$768$	5.80864	0.209601
$769$	37.9407	1.36818	0.684088	−	0.729400i	$-0.260201\pi$
$769$	37.9407	1.36818	0.684088	+	0.729400i	$0.260201\pi$
$770$	−16.9976	−0.612551
$771$	10.3556	0.372947
$772$	−18.4590	−0.664355
$773$	16.3375	0.587620	0.293810	−	0.955864i	$-0.405077\pi$
$773$	16.3375	0.587620	0.293810	+	0.955864i	$0.405077\pi$
$774$	−37.1226	−1.33434
$775$	−12.4300	−0.446498
$776$	−28.1105	−1.00911
$777$	−6.09113	−0.218518
$778$	79.8926	2.86429
$779$	−7.45473	−0.267093
$780$	0	0
$781$	11.7380	0.420017
$782$	22.4916	0.804297
$783$	7.16660	0.256114
$784$	2.24698	0.0802493
$785$	−13.6310	−0.486512
$786$	−4.06100	−0.144851
$787$	18.6907	0.666251	0.333126	−	0.942882i	$-0.391897\pi$
$787$	18.6907	0.666251	0.333126	+	0.942882i	$0.391897\pi$
$788$	34.8049	1.23987
$789$	−7.99090	−0.284484
$790$	−51.2301	−1.82269
$791$	−14.9734	−0.532394
$792$	−16.2107	−0.576023
$793$	0	0
$794$	−3.03684	−0.107773
$795$	−4.42758	−0.157030
$796$	−42.3957	−1.50267
$797$	29.2519	1.03615	0.518077	−	0.855334i	$-0.326648\pi$
$797$	29.2519	1.03615	0.518077	+	0.855334i	$0.326648\pi$
$798$	14.9487	0.529178
$799$	−15.6286	−0.552901
$800$	18.9729	0.670792
$801$	17.8039	0.629068
$802$	−1.30127	−0.0459496
$803$	26.9614	0.951446
$804$	0.975837	0.0344151
$805$	5.59611	0.197237
$806$	0	0
$807$	−0.362273	−0.0127526
$808$	30.7904	1.08320
$809$	−6.65087	−0.233832	−0.116916	−	0.993142i	$-0.537301\pi$
$809$	−6.65087	−0.233832	−0.116916	+	0.993142i	$0.537301\pi$
$810$	20.5308	0.721379
$811$	−3.89200	−0.136667	−0.0683333	−	0.997663i	$-0.521768\pi$
$811$	−3.89200	−0.136667	−0.0683333	+	0.997663i	$0.521768\pi$
$812$	−14.1728	−0.497369
$813$	−1.10752	−0.0388425
$814$	−30.7536	−1.07791
$815$	−12.5778	−0.440581
$816$	−2.35690	−0.0825079
$817$	35.9071	1.25623
$818$	34.0586	1.19083
$819$	0	0
$820$	−5.61356	−0.196034
$821$	−45.9982	−1.60535	−0.802674	−	0.596418i	$-0.796590\pi$
$821$	−45.9982	−1.60535	−0.802674	+	0.596418i	$0.796590\pi$
$822$	0.987918	0.0344576
$823$	7.95300	0.277224	0.138612	−	0.990347i	$-0.455736\pi$
$823$	7.95300	0.277224	0.138612	+	0.990347i	$0.455736\pi$
$824$	21.6093	0.752794
$825$	4.12870	0.143743
$826$	−56.2030	−1.95555
$827$	−27.9648	−0.972432	−0.486216	−	0.873839i	$-0.661623\pi$
$827$	−27.9648	−0.972432	−0.486216	+	0.873839i	$0.661623\pi$
$828$	15.5133	0.539126
$829$	27.6310	0.959665	0.479833	−	0.877360i	$-0.340697\pi$
$829$	27.6310	0.959665	0.479833	+	0.877360i	$0.340697\pi$
$830$	−25.0780	−0.870470
$831$	−6.53989	−0.226866
$832$	0	0
$833$	14.8388	0.514133
$834$	14.1400	0.489630
$835$	34.4698	1.19288
$836$	45.5773	1.57632
$837$	13.4843	0.466085
$838$	−80.2699	−2.77288
$839$	−28.6848	−0.990311	−0.495155	−	0.868804i	$-0.664889\pi$
$839$	−28.6848	−0.990311	−0.495155	+	0.868804i	$0.664889\pi$
$840$	3.87263	0.133618
$841$	−23.8528	−0.822509
$842$	78.7488	2.71386
$843$	−3.59179	−0.123708
$844$	−40.3817	−1.38999
$845$	0	0
$846$	−17.8509	−0.613725
$847$	9.16315	0.314849
$848$	−4.42758	−0.152044
$849$	−3.65220	−0.125343
$850$	34.6504	1.18850
$851$	10.1250	0.347080
$852$	−7.77346	−0.266314
$853$	43.2078	1.47941	0.739703	−	0.672934i	$-0.234966\pi$
$853$	43.2078	1.47941	0.739703	+	0.672934i	$0.234966\pi$
$854$	−39.4306	−1.34929
$855$	−22.7603	−0.778386
$856$	−16.2620	−0.555825
$857$	35.1685	1.20133	0.600667	−	0.799499i	$-0.294902\pi$
$857$	35.1685	1.20133	0.600667	+	0.799499i	$0.294902\pi$
$858$	0	0
$859$	27.3793	0.934168	0.467084	−	0.884213i	$-0.345305\pi$
$859$	27.3793	0.934168	0.467084	+	0.884213i	$0.345305\pi$
$860$	27.0388	0.922014
$861$	−1.44876	−0.0493737
$862$	77.0297	2.62364
$863$	41.3913	1.40898	0.704489	−	0.709715i	$-0.251176\pi$
$863$	41.3913	1.40898	0.704489	+	0.709715i	$0.251176\pi$
$864$	−20.5821	−0.700217
$865$	−27.2465	−0.926409
$866$	30.8702	1.04901
$867$	−6.13036	−0.208198
$868$	−26.6668	−0.905130
$869$	−40.3116	−1.36748
$870$	−4.08815	−0.138601
$871$	0	0
$872$	−0.287536	−0.00973721
$873$	32.1075	1.08668
$874$	−24.8485	−0.840512
$875$	23.4252	0.791916
$876$	−17.8552	−0.603270
$877$	24.7472	0.835653	0.417826	−	0.908527i	$-0.362792\pi$
$877$	24.7472	0.835653	0.417826	+	0.908527i	$0.362792\pi$
$878$	23.0097	0.776539
$879$	−13.5066	−0.455567
$880$	−2.96077	−0.0998076
$881$	−28.5875	−0.963137	−0.481568	−	0.876409i	$-0.659933\pi$
$881$	−28.5875	−0.963137	−0.481568	+	0.876409i	$0.659933\pi$
$882$	16.9487	0.570692
$883$	9.61702	0.323639	0.161819	−	0.986820i	$-0.448264\pi$
$883$	9.61702	0.323639	0.161819	+	0.986820i	$0.448264\pi$
$884$	0	0
$885$	−9.78986	−0.329082
$886$	27.3599	0.919173
$887$	15.9661	0.536091	0.268045	−	0.963406i	$-0.413622\pi$
$887$	15.9661	0.536091	0.268045	+	0.963406i	$0.413622\pi$
$888$	7.00670	0.235130
$889$	38.8689	1.30362
$890$	−21.4741	−0.719814
$891$	16.1551	0.541217
$892$	22.3642	0.748809
$893$	17.2664	0.577797
$894$	10.4819	0.350566
$895$	8.70171	0.290866
$896$	33.3196	1.11313
$897$	0	0
$898$	28.9976	0.967663
$899$	9.68473	0.323004
$900$	23.8998	0.796659
$901$	−29.2392	−0.974099
$902$	−7.31468	−0.243552
$903$	6.97823	0.232221
$904$	17.2241	0.572867
$905$	−6.90408	−0.229500
$906$	17.6189	0.585350
$907$	−28.8364	−0.957496	−0.478748	−	0.877952i	$-0.658909\pi$
$907$	−28.8364	−0.957496	−0.478748	+	0.877952i	$0.658909\pi$
$908$	26.4480	0.877709
$909$	−35.1685	−1.16647
$910$	0	0
$911$	38.5633	1.27766	0.638830	−	0.769348i	$-0.279419\pi$
$911$	38.5633	1.27766	0.638830	+	0.769348i	$0.279419\pi$
$912$	2.60388	0.0862229
$913$	−19.7332	−0.653073
$914$	−10.4644	−0.346132
$915$	−6.86831	−0.227059
$916$	41.7294	1.37878
$917$	−6.67264	−0.220350
$918$	−37.5894	−1.24064
$919$	8.87502	0.292760	0.146380	−	0.989228i	$-0.453238\pi$
$919$	8.87502	0.292760	0.146380	+	0.989228i	$0.453238\pi$
$920$	−6.43727	−0.212231
$921$	−7.81030	−0.257358
$922$	70.8708	2.33401
$923$	0	0
$924$	8.85756	0.291392
$925$	15.5985	0.512875
$926$	−39.6601	−1.30331
$927$	−24.6819	−0.810659
$928$	−14.7826	−0.485261
$929$	−24.2295	−0.794945	−0.397472	−	0.917614i	$-0.630113\pi$
$929$	−24.2295	−0.794945	−0.397472	+	0.917614i	$0.630113\pi$
$930$	−7.69202	−0.252231
$931$	−16.3937	−0.537283
$932$	−15.5133	−0.508156
$933$	16.5211	0.540877
$934$	−72.2911	−2.36544
$935$	−19.5526	−0.639437
$936$	0	0
$937$	17.2644	0.564005	0.282002	−	0.959414i	$-0.409001\pi$
$937$	17.2644	0.564005	0.282002	+	0.959414i	$0.409001\pi$
$938$	2.65519	0.0866949
$939$	4.15047	0.135446
$940$	13.0019	0.424076
$941$	−4.34050	−0.141496	−0.0707482	−	0.997494i	$-0.522539\pi$
$941$	−4.34050	−0.141496	−0.0707482	+	0.997494i	$0.522539\pi$
$942$	11.7627	0.383250
$943$	2.40821	0.0784220
$944$	−9.78986	−0.318633
$945$	−9.35258	−0.304240
$946$	35.2325	1.14551
$947$	45.0146	1.46278	0.731389	−	0.681961i	$-0.238872\pi$
$947$	45.0146	1.46278	0.731389	+	0.681961i	$0.238872\pi$
$948$	26.6963	0.867057
$949$	0	0
$950$	−38.2814	−1.24201
$951$	16.6655	0.540415
$952$	25.5743	0.828869
$953$	−46.8859	−1.51878	−0.759391	−	0.650634i	$-0.774503\pi$
$953$	−46.8859	−1.51878	−0.759391	+	0.650634i	$0.774503\pi$
$954$	−33.3967	−1.08126
$955$	26.6329	0.861822
$956$	33.3062	1.07720
$957$	−3.21685	−0.103986
$958$	78.4191	2.53361
$959$	1.62325	0.0524176
$960$	10.4547	0.337425
$961$	−12.7778	−0.412186
$962$	0	0
$963$	18.5743	0.598550
$964$	−36.3274	−1.17003
$965$	−8.74871	−0.281631
$966$	−4.82908	−0.155373
$967$	−6.29457	−0.202420	−0.101210	−	0.994865i	$-0.532271\pi$
$967$	−6.29457	−0.202420	−0.101210	+	0.994865i	$0.532271\pi$
$968$	−10.5405	−0.338784
$969$	17.1957	0.552404
$970$	−38.7265	−1.24343
$971$	−41.8068	−1.34165	−0.670823	−	0.741618i	$-0.734059\pi$
$971$	−41.8068	−1.34165	−0.670823	+	0.741618i	$0.734059\pi$
$972$	−39.5918	−1.26991
$973$	23.2336	0.744834
$974$	−94.0025	−3.01203
$975$	0	0
$976$	−6.86831	−0.219849
$977$	−23.7530	−0.759926	−0.379963	−	0.925002i	$-0.624063\pi$
$977$	−23.7530	−0.759926	−0.379963	+	0.925002i	$0.624063\pi$
$978$	10.8538	0.347067
$979$	−16.8974	−0.540043
$980$	−12.3448	−0.394341
$981$	0.328421	0.0104857
$982$	49.0863	1.56641
$983$	55.7251	1.77736	0.888678	−	0.458532i	$-0.151625\pi$
$983$	55.7251	1.77736	0.888678	+	0.458532i	$0.151625\pi$
$984$	1.66653	0.0531270
$985$	16.4959	0.525602
$986$	−26.9976	−0.859779
$987$	3.35557	0.106809
$988$	0	0
$989$	−11.5996	−0.368845
$990$	−22.3327	−0.709781
$991$	−35.5512	−1.12932	−0.564661	−	0.825323i	$-0.690993\pi$
$991$	−35.5512	−1.12932	−0.564661	+	0.825323i	$0.690993\pi$
$992$	−27.8140	−0.883096
$993$	−8.72215	−0.276789
$994$	−21.1511	−0.670871
$995$	−20.0935	−0.637007
$996$	13.0683	0.414085
$997$	6.61058	0.209359	0.104680	−	0.994506i	$-0.466618\pi$
$997$	6.61058	0.209359	0.104680	+	0.994506i	$0.466618\pi$
$998$	−52.9101	−1.67484
$999$	−16.9215	−0.535374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.a.c.1.3	yes	3
3.2	odd	2		1521.2.a.o.1.1		3
4.3	odd	2		2704.2.a.ba.1.2		3
5.4	even	2		4225.2.a.bb.1.1		3
7.6	odd	2		8281.2.a.bj.1.3		3
13.2	odd	12		169.2.e.b.147.6		12
13.3	even	3		169.2.c.b.22.1		6
13.4	even	6		169.2.c.c.146.3		6
13.5	odd	4		169.2.b.b.168.1		6
13.6	odd	12		169.2.e.b.23.1		12
13.7	odd	12		169.2.e.b.23.6		12
13.8	odd	4		169.2.b.b.168.6		6
13.9	even	3		169.2.c.b.146.1		6
13.10	even	6		169.2.c.c.22.3		6
13.11	odd	12		169.2.e.b.147.1		12
13.12	even	2		169.2.a.b.1.1	✓	3
39.5	even	4		1521.2.b.l.1351.6		6
39.8	even	4		1521.2.b.l.1351.1		6
39.38	odd	2		1521.2.a.r.1.3		3
52.31	even	4		2704.2.f.o.337.3		6
52.47	even	4		2704.2.f.o.337.4		6
52.51	odd	2		2704.2.a.z.1.2		3
65.64	even	2		4225.2.a.bg.1.3		3
91.90	odd	2		8281.2.a.bf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.a.b.1.1	✓	3	13.12	even	2
169.2.a.c.1.3	yes	3	1.1	even	1	trivial
169.2.b.b.168.1		6	13.5	odd	4
169.2.b.b.168.6		6	13.8	odd	4
169.2.c.b.22.1		6	13.3	even	3
169.2.c.b.146.1		6	13.9	even	3
169.2.c.c.22.3		6	13.10	even	6
169.2.c.c.146.3		6	13.4	even	6
169.2.e.b.23.1		12	13.6	odd	12
169.2.e.b.23.6		12	13.7	odd	12
169.2.e.b.147.1		12	13.11	odd	12
169.2.e.b.147.6		12	13.2	odd	12
1521.2.a.o.1.1		3	3.2	odd	2
1521.2.a.r.1.3		3	39.38	odd	2
1521.2.b.l.1351.1		6	39.8	even	4
1521.2.b.l.1351.6		6	39.5	even	4
2704.2.a.z.1.2		3	52.51	odd	2
2704.2.a.ba.1.2		3	4.3	odd	2
2704.2.f.o.337.3		6	52.31	even	4
2704.2.f.o.337.4		6	52.47	even	4
4225.2.a.bb.1.1		3	5.4	even	2
4225.2.a.bg.1.3		3	65.64	even	2
8281.2.a.bf.1.1		3	91.90	odd	2
8281.2.a.bj.1.3		3	7.6	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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24698 q^{2} -0.554958 q^{3} +3.04892 q^{4} +1.44504 q^{5} -1.24698 q^{6} -2.04892 q^{7} +2.35690 q^{8} -2.69202 q^{9} +3.24698 q^{10} +2.55496 q^{11} -1.69202 q^{12} -4.60388 q^{14} -0.801938 q^{15} -0.801938 q^{16} -5.29590 q^{17} -6.04892 q^{18} +5.85086 q^{19} +4.40581 q^{20} +1.13706 q^{21} +5.74094 q^{22} -1.89008 q^{23} -1.30798 q^{24} -2.91185 q^{25} +3.15883 q^{27} -6.24698 q^{28} +2.26875 q^{29} -1.80194 q^{30} +4.26875 q^{31} -6.51573 q^{32} -1.41789 q^{33} -11.8998 q^{34} -2.96077 q^{35} -8.20775 q^{36} -5.35690 q^{37} +13.1468 q^{38} +3.40581 q^{40} -1.27413 q^{41} +2.55496 q^{42} +6.13706 q^{43} +7.78986 q^{44} -3.89008 q^{45} -4.24698 q^{46} +2.95108 q^{47} +0.445042 q^{48} -2.80194 q^{49} -6.54288 q^{50} +2.93900 q^{51} +5.52111 q^{53} +7.09783 q^{54} +3.69202 q^{55} -4.82908 q^{56} -3.24698 q^{57} +5.09783 q^{58} +12.2078 q^{59} -2.44504 q^{60} +8.56465 q^{61} +9.59179 q^{62} +5.51573 q^{63} -13.0368 q^{64} -3.18598 q^{66} -0.576728 q^{67} -16.1468 q^{68} +1.04892 q^{69} -6.65279 q^{70} +4.59419 q^{71} -6.34481 q^{72} +10.5526 q^{73} -12.0368 q^{74} +1.61596 q^{75} +17.8388 q^{76} -5.23490 q^{77} -15.7778 q^{79} -1.15883 q^{80} +6.32304 q^{81} -2.86294 q^{82} -7.72348 q^{83} +3.46681 q^{84} -7.65279 q^{85} +13.7899 q^{86} -1.25906 q^{87} +6.02177 q^{88} -6.61356 q^{89} -8.74094 q^{90} -5.76271 q^{92} -2.36898 q^{93} +6.63102 q^{94} +8.45473 q^{95} +3.61596 q^{96} -11.9269 q^{97} -6.29590 q^{98} -6.87800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 2 q^{3} + 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} - 3 q^{9} + 5 q^{10} + 8 q^{11} - 5 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 9 q^{18} + 4 q^{19} - 2 q^{21} + 3 q^{22} - 5 q^{23} - 9 q^{24}+ \cdots - q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 2 * q^3 + 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8 - 3 * q^9 + 5 * q^10 + 8 * q^11 - 5 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 9 * q^18 + 4 * q^19 - 2 * q^21 + 3 * q^22 - 5 * q^23 - 9 * q^24 - 5 * q^25 + q^27 - 14 * q^28 - q^29 - q^30 + 5 * q^31 - 7 * q^32 - 10 * q^33 - 13 * q^34 + 4 * q^35 - 7 * q^36 - 12 * q^37 + 12 * q^38 - 3 * q^40 + 7 * q^41 + 8 * q^42 + 13 * q^43 - 11 * q^45 - 8 * q^46 + 18 * q^47 + q^48 - 4 * q^49 - q^50 - q^51 + q^53 + 3 * q^54 + 6 * q^55 - 4 * q^56 - 5 * q^57 - 3 * q^58 + 19 * q^59 - 7 * q^60 + 4 * q^61 + q^62 + 4 * q^63 - 11 * q^64 + 5 * q^66 + q^67 - 21 * q^68 - 6 * q^69 - 2 * q^70 + 27 * q^71 + 4 * q^72 - 9 * q^73 - 8 * q^74 + 15 * q^75 + 21 * q^76 + 8 * q^77 - 5 * q^79 + 5 * q^80 - q^81 - 14 * q^82 + 7 * q^83 + 7 * q^84 - 5 * q^85 + 18 * q^86 - 18 * q^87 + 15 * q^88 + 11 * q^89 - 12 * q^90 - 22 * q^93 + 5 * q^94 + 3 * q^95 + 21 * q^96 - 7 * q^97 - 5 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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