LMFDB - Embedded newform 5915.2.a.bg.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5915,2,Mod(1,5915)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5915, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5915.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5915 = 5 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5915.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:	$47.2315127956$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} + 3 x^{13} + 76 x^{12} - 125 x^{11} - 299 x^{10} + 716 x^{9} + 496 x^{8} - 1774 x^{7} + \cdots - 1 $ x^15 - 7x^14 + 3x^13 + 76x^12 - 125x^11 - 299x^10 + 716x^9 + 496x^8 - 1774x^7 - 244x^6 + 2131x^5 - 143x^4 - 1178x^3 + 98x^2 + 243x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.22367$ of defining polynomial
Character	$\chi$	$=$	5915.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22367 q^{2} -1.20005 q^{3} +2.94470 q^{4} +1.00000 q^{5} +2.66851 q^{6} +1.00000 q^{7} -2.10070 q^{8} -1.55988 q^{9} +O(q^{10})$	\(q-2.22367 q^{2} -1.20005 q^{3} +2.94470 q^{4} +1.00000 q^{5} +2.66851 q^{6} +1.00000 q^{7} -2.10070 q^{8} -1.55988 q^{9} -2.22367 q^{10} +1.88956 q^{11} -3.53378 q^{12} -2.22367 q^{14} -1.20005 q^{15} -1.21815 q^{16} -4.06355 q^{17} +3.46866 q^{18} -8.50313 q^{19} +2.94470 q^{20} -1.20005 q^{21} -4.20175 q^{22} -0.247744 q^{23} +2.52094 q^{24} +1.00000 q^{25} +5.47208 q^{27} +2.94470 q^{28} +6.30044 q^{29} +2.66851 q^{30} +7.59811 q^{31} +6.91014 q^{32} -2.26756 q^{33} +9.03598 q^{34} +1.00000 q^{35} -4.59339 q^{36} +2.16041 q^{37} +18.9081 q^{38} -2.10070 q^{40} -7.49604 q^{41} +2.66851 q^{42} +6.02456 q^{43} +5.56418 q^{44} -1.55988 q^{45} +0.550901 q^{46} -6.33141 q^{47} +1.46183 q^{48} +1.00000 q^{49} -2.22367 q^{50} +4.87645 q^{51} +5.92445 q^{53} -12.1681 q^{54} +1.88956 q^{55} -2.10070 q^{56} +10.2042 q^{57} -14.0101 q^{58} +10.3305 q^{59} -3.53378 q^{60} -5.68993 q^{61} -16.8957 q^{62} -1.55988 q^{63} -12.9296 q^{64} +5.04230 q^{66} -7.75830 q^{67} -11.9659 q^{68} +0.297305 q^{69} -2.22367 q^{70} -13.2525 q^{71} +3.27684 q^{72} +11.4297 q^{73} -4.80403 q^{74} -1.20005 q^{75} -25.0392 q^{76} +1.88956 q^{77} +9.85820 q^{79} -1.21815 q^{80} -1.88712 q^{81} +16.6687 q^{82} -11.0480 q^{83} -3.53378 q^{84} -4.06355 q^{85} -13.3966 q^{86} -7.56084 q^{87} -3.96939 q^{88} -9.03643 q^{89} +3.46866 q^{90} -0.729532 q^{92} -9.11811 q^{93} +14.0790 q^{94} -8.50313 q^{95} -8.29251 q^{96} -3.16108 q^{97} -2.22367 q^{98} -2.94749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 7 q^{2} - 7 q^{3} + 13 q^{4} + 15 q^{5} - 4 q^{6} + 15 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 7 * q^2 - 7 * q^3 + 13 * q^4 + 15 * q^5 - 4 * q^6 + 15 * q^7 - 24 * q^8 + 2 * q^9	\( 15 q - 7 q^{2} - 7 q^{3} + 13 q^{4} + 15 q^{5} - 4 q^{6} + 15 q^{7} - 24 q^{8} + 2 q^{9} - 7 q^{10} - 6 q^{11} + q^{12} - 7 q^{14} - 7 q^{15} + 5 q^{16} - 6 q^{17} + 9 q^{18} - 14 q^{19} + 13 q^{20} - 7 q^{21} + 5 q^{22} + 6 q^{23} + 3 q^{24} + 15 q^{25} - 25 q^{27} + 13 q^{28} - 26 q^{29} - 4 q^{30} - 12 q^{31} - 35 q^{32} + 19 q^{33} - 22 q^{34} + 15 q^{35} - 11 q^{36} - 60 q^{37} + 42 q^{38} - 24 q^{40} - 5 q^{41} - 4 q^{42} + q^{43} - 11 q^{44} + 2 q^{45} - 13 q^{46} - 20 q^{47} + 19 q^{48} + 15 q^{49} - 7 q^{50} - 12 q^{51} - 4 q^{53} + 7 q^{54} - 6 q^{55} - 24 q^{56} + 18 q^{57} - 35 q^{58} - 15 q^{59} + q^{60} - 23 q^{61} + 17 q^{62} + 2 q^{63} + 62 q^{64} - 20 q^{66} - 30 q^{67} + 17 q^{68} - 35 q^{69} - 7 q^{70} + 5 q^{71} - q^{72} - 44 q^{73} + 39 q^{74} - 7 q^{75} - 54 q^{76} - 6 q^{77} - 6 q^{79} + 5 q^{80} - 25 q^{81} + 32 q^{82} - 21 q^{83} + q^{84} - 6 q^{85} - 6 q^{86} + 59 q^{87} - 2 q^{88} - 18 q^{89} + 9 q^{90} + 41 q^{92} - 46 q^{93} - 29 q^{94} - 14 q^{95} - 32 q^{96} - 15 q^{97} - 7 q^{98} - 34 q^{99}+O(q^{100}) \) 15 * q - 7 * q^2 - 7 * q^3 + 13 * q^4 + 15 * q^5 - 4 * q^6 + 15 * q^7 - 24 * q^8 + 2 * q^9 - 7 * q^10 - 6 * q^11 + q^12 - 7 * q^14 - 7 * q^15 + 5 * q^16 - 6 * q^17 + 9 * q^18 - 14 * q^19 + 13 * q^20 - 7 * q^21 + 5 * q^22 + 6 * q^23 + 3 * q^24 + 15 * q^25 - 25 * q^27 + 13 * q^28 - 26 * q^29 - 4 * q^30 - 12 * q^31 - 35 * q^32 + 19 * q^33 - 22 * q^34 + 15 * q^35 - 11 * q^36 - 60 * q^37 + 42 * q^38 - 24 * q^40 - 5 * q^41 - 4 * q^42 + q^43 - 11 * q^44 + 2 * q^45 - 13 * q^46 - 20 * q^47 + 19 * q^48 + 15 * q^49 - 7 * q^50 - 12 * q^51 - 4 * q^53 + 7 * q^54 - 6 * q^55 - 24 * q^56 + 18 * q^57 - 35 * q^58 - 15 * q^59 + q^60 - 23 * q^61 + 17 * q^62 + 2 * q^63 + 62 * q^64 - 20 * q^66 - 30 * q^67 + 17 * q^68 - 35 * q^69 - 7 * q^70 + 5 * q^71 - q^72 - 44 * q^73 + 39 * q^74 - 7 * q^75 - 54 * q^76 - 6 * q^77 - 6 * q^79 + 5 * q^80 - 25 * q^81 + 32 * q^82 - 21 * q^83 + q^84 - 6 * q^85 - 6 * q^86 + 59 * q^87 - 2 * q^88 - 18 * q^89 + 9 * q^90 + 41 * q^92 - 46 * q^93 - 29 * q^94 - 14 * q^95 - 32 * q^96 - 15 * q^97 - 7 * q^98 - 34 * 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 $

$2$	−2.22367	−1.57237	−0.786185	−	0.617991i	$-0.787947\pi$
$2$	−2.22367	−1.57237	−0.786185	+	0.617991i	$0.787947\pi$
$3$	−1.20005	−0.692849	−0.346424	−	0.938078i	$-0.612604\pi$
$3$	−1.20005	−0.692849	−0.346424	+	0.938078i	$0.612604\pi$
$4$	2.94470	1.47235
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.66851	1.08941
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.10070	−0.742709
$9$	−1.55988	−0.519961
$10$	−2.22367	−0.703186
$11$	1.88956	0.569723	0.284861	−	0.958569i	$-0.408052\pi$
$11$	1.88956	0.569723	0.284861	+	0.958569i	$0.408052\pi$
$12$	−3.53378	−1.02012
$13$	0	0
$13$	0	0
$14$	−2.22367	−0.594300
$15$	−1.20005	−0.309851
$16$	−1.21815	−0.304536
$17$	−4.06355	−0.985555	−0.492777	−	0.870155i	$-0.664018\pi$
$17$	−4.06355	−0.985555	−0.492777	+	0.870155i	$0.664018\pi$
$18$	3.46866	0.817571
$19$	−8.50313	−1.95075	−0.975376	−	0.220546i	$-0.929216\pi$
$19$	−8.50313	−1.95075	−0.975376	+	0.220546i	$0.929216\pi$
$20$	2.94470	0.658455
$21$	−1.20005	−0.261872
$22$	−4.20175	−0.895815
$23$	−0.247744	−0.0516583	−0.0258291	−	0.999666i	$-0.508223\pi$
$23$	−0.247744	−0.0516583	−0.0258291	+	0.999666i	$0.508223\pi$
$24$	2.52094	0.514585
$25$	1.00000	0.200000
$26$	0	0
$27$	5.47208	1.05310
$28$	2.94470	0.556496
$29$	6.30044	1.16996	0.584981	−	0.811047i	$-0.301102\pi$
$29$	6.30044	1.16996	0.584981	+	0.811047i	$0.301102\pi$
$30$	2.66851	0.487201
$31$	7.59811	1.36466	0.682331	−	0.731044i	$-0.260966\pi$
$31$	7.59811	1.36466	0.682331	+	0.731044i	$0.260966\pi$
$32$	6.91014	1.22155
$33$	−2.26756	−0.394732
$34$	9.03598	1.54966
$35$	1.00000	0.169031
$36$	−4.59339	−0.765564
$37$	2.16041	0.355169	0.177585	−	0.984106i	$-0.443172\pi$
$37$	2.16041	0.355169	0.177585	+	0.984106i	$0.443172\pi$
$38$	18.9081	3.06731
$39$	0	0
$40$	−2.10070	−0.332149
$41$	−7.49604	−1.17069	−0.585343	−	0.810786i	$-0.699040\pi$
$41$	−7.49604	−1.17069	−0.585343	+	0.810786i	$0.699040\pi$
$42$	2.66851	0.411760
$43$	6.02456	0.918737	0.459369	−	0.888246i	$-0.348076\pi$
$43$	6.02456	0.918737	0.459369	+	0.888246i	$0.348076\pi$
$44$	5.56418	0.838831
$45$	−1.55988	−0.232534
$46$	0.550901	0.0812259
$47$	−6.33141	−0.923531	−0.461766	−	0.887002i	$-0.652784\pi$
$47$	−6.33141	−0.923531	−0.461766	+	0.887002i	$0.652784\pi$
$48$	1.46183	0.210998
$49$	1.00000	0.142857
$50$	−2.22367	−0.314474
$51$	4.87645	0.682840
$52$	0	0
$53$	5.92445	0.813786	0.406893	−	0.913476i	$-0.366612\pi$
$53$	5.92445	0.813786	0.406893	+	0.913476i	$0.366612\pi$
$54$	−12.1681	−1.65587
$55$	1.88956	0.254788
$56$	−2.10070	−0.280717
$57$	10.2042	1.35158
$58$	−14.0101	−1.83961
$59$	10.3305	1.34492	0.672458	−	0.740135i	$-0.265239\pi$
$59$	10.3305	1.34492	0.672458	+	0.740135i	$0.265239\pi$
$60$	−3.53378	−0.456209
$61$	−5.68993	−0.728521	−0.364261	−	0.931297i	$-0.618678\pi$
$61$	−5.68993	−0.728521	−0.364261	+	0.931297i	$0.618678\pi$
$62$	−16.8957	−2.14575
$63$	−1.55988	−0.196527
$64$	−12.9296	−1.61620
$65$	0	0
$66$	5.04230	0.620664
$67$	−7.75830	−0.947827	−0.473913	−	0.880571i	$-0.657159\pi$
$67$	−7.75830	−0.947827	−0.473913	+	0.880571i	$0.657159\pi$
$68$	−11.9659	−1.45108
$69$	0.297305	0.0357913
$70$	−2.22367	−0.265779
$71$	−13.2525	−1.57278	−0.786391	−	0.617729i	$-0.788053\pi$
$71$	−13.2525	−1.57278	−0.786391	+	0.617729i	$0.788053\pi$
$72$	3.27684	0.386179
$73$	11.4297	1.33774	0.668871	−	0.743378i	$-0.266778\pi$
$73$	11.4297	1.33774	0.668871	+	0.743378i	$0.266778\pi$
$74$	−4.80403	−0.558457
$75$	−1.20005	−0.138570
$76$	−25.0392	−2.87219
$77$	1.88956	0.215335
$78$	0	0
$79$	9.85820	1.10913	0.554567	−	0.832139i	$-0.312884\pi$
$79$	9.85820	1.10913	0.554567	+	0.832139i	$0.312884\pi$
$80$	−1.21815	−0.136193
$81$	−1.88712	−0.209680
$82$	16.6687	1.84075
$83$	−11.0480	−1.21267	−0.606337	−	0.795208i	$-0.707362\pi$
$83$	−11.0480	−1.21267	−0.606337	+	0.795208i	$0.707362\pi$
$84$	−3.53378	−0.385567
$85$	−4.06355	−0.440753
$86$	−13.3966	−1.44460
$87$	−7.56084	−0.810607
$88$	−3.96939	−0.423138
$89$	−9.03643	−0.957859	−0.478930	−	0.877853i	$-0.658975\pi$
$89$	−9.03643	−0.957859	−0.478930	+	0.877853i	$0.658975\pi$
$90$	3.46866	0.365629
$91$	0	0
$92$	−0.729532	−0.0760590
$93$	−9.11811	−0.945504
$94$	14.0790	1.45213
$95$	−8.50313	−0.872403
$96$	−8.29251	−0.846351
$97$	−3.16108	−0.320959	−0.160480	−	0.987039i	$-0.551304\pi$
$97$	−3.16108	−0.320959	−0.160480	+	0.987039i	$0.551304\pi$
$98$	−2.22367	−0.224624
$99$	−2.94749	−0.296234
$100$	2.94470	0.294470
$101$	−4.22511	−0.420414	−0.210207	−	0.977657i	$-0.567414\pi$
$101$	−4.22511	−0.420414	−0.210207	+	0.977657i	$0.567414\pi$
$102$	−10.8436	−1.07368
$103$	2.25849	0.222535	0.111268	−	0.993790i	$-0.464509\pi$
$103$	2.25849	0.222535	0.111268	+	0.993790i	$0.464509\pi$
$104$	0	0
$105$	−1.20005	−0.117113
$106$	−13.1740	−1.27957
$107$	6.14758	0.594309	0.297155	−	0.954829i	$-0.403962\pi$
$107$	6.14758	0.594309	0.297155	+	0.954829i	$0.403962\pi$
$108$	16.1136	1.55054
$109$	−1.66622	−0.159595	−0.0797977	−	0.996811i	$-0.525427\pi$
$109$	−1.66622	−0.159595	−0.0797977	+	0.996811i	$0.525427\pi$
$110$	−4.20175	−0.400621
$111$	−2.59260	−0.246078
$112$	−1.21815	−0.115104
$113$	18.8431	1.77261	0.886303	−	0.463106i	$-0.153265\pi$
$113$	18.8431	1.77261	0.886303	+	0.463106i	$0.153265\pi$
$114$	−22.6907	−2.12518
$115$	−0.247744	−0.0231023
$116$	18.5529	1.72259
$117$	0	0
$118$	−22.9716	−2.11471
$119$	−4.06355	−0.372505
$120$	2.52094	0.230129
$121$	−7.42958	−0.675416
$122$	12.6525	1.14551
$123$	8.99562	0.811108
$124$	22.3742	2.00926
$125$	1.00000	0.0894427
$126$	3.46866	0.309013
$127$	15.5727	1.38185	0.690926	−	0.722925i	$-0.257203\pi$
$127$	15.5727	1.38185	0.690926	+	0.722925i	$0.257203\pi$
$128$	14.9308	1.31971
$129$	−7.22977	−0.636546
$130$	0	0
$131$	−6.60678	−0.577237	−0.288619	−	0.957444i	$-0.593196\pi$
$131$	−6.60678	−0.577237	−0.288619	+	0.957444i	$0.593196\pi$
$132$	−6.67728	−0.581183
$133$	−8.50313	−0.737315
$134$	17.2519	1.49033
$135$	5.47208	0.470962
$136$	8.53628	0.731980
$137$	−7.39243	−0.631578	−0.315789	−	0.948830i	$-0.602269\pi$
$137$	−7.39243	−0.631578	−0.315789	+	0.948830i	$0.602269\pi$
$138$	−0.661108	−0.0562773
$139$	−16.6163	−1.40938	−0.704689	−	0.709516i	$-0.748914\pi$
$139$	−16.6163	−1.40938	−0.704689	+	0.709516i	$0.748914\pi$
$140$	2.94470	0.248873
$141$	7.59800	0.639867
$142$	29.4691	2.47300
$143$	0	0
$144$	1.90016	0.158347
$145$	6.30044	0.523223
$146$	−25.4158	−2.10343
$147$	−1.20005	−0.0989784
$148$	6.36176	0.522933
$149$	12.6633	1.03742	0.518710	−	0.854950i	$-0.326412\pi$
$149$	12.6633	1.03742	0.518710	+	0.854950i	$0.326412\pi$
$150$	2.66851	0.217883
$151$	−22.3121	−1.81573	−0.907866	−	0.419260i	$-0.862290\pi$
$151$	−22.3121	−1.81573	−0.907866	+	0.419260i	$0.862290\pi$
$152$	17.8625	1.44884
$153$	6.33866	0.512450
$154$	−4.20175	−0.338586
$155$	7.59811	0.610295
$156$	0	0
$157$	−8.56721	−0.683738	−0.341869	−	0.939748i	$-0.611060\pi$
$157$	−8.56721	−0.683738	−0.341869	+	0.939748i	$0.611060\pi$
$158$	−21.9214	−1.74397
$159$	−7.10963	−0.563830
$160$	6.91014	0.546295
$161$	−0.247744	−0.0195250
$162$	4.19632	0.329694
$163$	7.20791	0.564567	0.282283	−	0.959331i	$-0.408908\pi$
$163$	7.20791	0.564567	0.282283	+	0.959331i	$0.408908\pi$
$164$	−22.0736	−1.72366
$165$	−2.26756	−0.176529
$166$	24.5671	1.90677
$167$	10.3398	0.800115	0.400057	−	0.916490i	$-0.368990\pi$
$167$	10.3398	0.800115	0.400057	+	0.916490i	$0.368990\pi$
$168$	2.52094	0.194495
$169$	0	0
$170$	9.03598	0.693028
$171$	13.2639	1.01432
$172$	17.7405	1.35270
$173$	13.2420	1.00677	0.503384	−	0.864063i	$-0.332088\pi$
$173$	13.2420	1.00677	0.503384	+	0.864063i	$0.332088\pi$
$174$	16.8128	1.27457
$175$	1.00000	0.0755929
$176$	−2.30175	−0.173501
$177$	−12.3971	−0.931823
$178$	20.0940	1.50611
$179$	16.4738	1.23131	0.615655	−	0.788016i	$-0.288892\pi$
$179$	16.4738	1.23131	0.615655	+	0.788016i	$0.288892\pi$
$180$	−4.59339	−0.342371
$181$	0.708825	0.0526866	0.0263433	−	0.999653i	$-0.491614\pi$
$181$	0.708825	0.0526866	0.0263433	+	0.999653i	$0.491614\pi$
$182$	0	0
$183$	6.82820	0.504755
$184$	0.520436	0.0383670
$185$	2.16041	0.158836
$186$	20.2756	1.48668
$187$	−7.67830	−0.561493
$188$	−18.6441	−1.35976
$189$	5.47208	0.398035
$190$	18.9081	1.37174
$191$	−8.16011	−0.590445	−0.295222	−	0.955429i	$-0.595394\pi$
$191$	−8.16011	−0.590445	−0.295222	+	0.955429i	$0.595394\pi$
$192$	15.5161	1.11978
$193$	−5.46032	−0.393043	−0.196521	−	0.980500i	$-0.562964\pi$
$193$	−5.46032	−0.393043	−0.196521	+	0.980500i	$0.562964\pi$
$194$	7.02920	0.504667
$195$	0	0
$196$	2.94470	0.210336
$197$	−14.0218	−0.999015	−0.499508	−	0.866309i	$-0.666486\pi$
$197$	−14.0218	−0.999015	−0.499508	+	0.866309i	$0.666486\pi$
$198$	6.55423	0.465789
$199$	−20.7830	−1.47327	−0.736634	−	0.676291i	$-0.763586\pi$
$199$	−20.7830	−1.47327	−0.736634	+	0.676291i	$0.763586\pi$
$200$	−2.10070	−0.148542
$201$	9.31033	0.656700
$202$	9.39523	0.661046
$203$	6.30044	0.442204
$204$	14.3597	1.00538
$205$	−7.49604	−0.523546
$206$	−5.02213	−0.349908
$207$	0.386452	0.0268603
$208$	0	0
$209$	−16.0672	−1.11139
$210$	2.66851	0.184145
$211$	−14.0684	−0.968506	−0.484253	−	0.874928i	$-0.660909\pi$
$211$	−14.0684	−0.968506	−0.484253	+	0.874928i	$0.660909\pi$
$212$	17.4457	1.19818
$213$	15.9036	1.08970
$214$	−13.6702	−0.934475
$215$	6.02456	0.410872
$216$	−11.4952	−0.782148
$217$	7.59811	0.515794
$218$	3.70513	0.250943
$219$	−13.7162	−0.926853
$220$	5.56418	0.375137
$221$	0	0
$222$	5.76507	0.386926
$223$	−14.9206	−0.999154	−0.499577	−	0.866269i	$-0.666511\pi$
$223$	−14.9206	−0.999154	−0.499577	+	0.866269i	$0.666511\pi$
$224$	6.91014	0.461703
$225$	−1.55988	−0.103992
$226$	−41.9007	−2.78719
$227$	16.4967	1.09493	0.547463	−	0.836830i	$-0.315594\pi$
$227$	16.4967	1.09493	0.547463	+	0.836830i	$0.315594\pi$
$228$	30.0482	1.98999
$229$	−6.10883	−0.403683	−0.201841	−	0.979418i	$-0.564693\pi$
$229$	−6.10883	−0.403683	−0.201841	+	0.979418i	$0.564693\pi$
$230$	0.550901	0.0363253
$231$	−2.26756	−0.149195
$232$	−13.2353	−0.868941
$233$	18.3172	1.20000	0.600001	−	0.799999i	$-0.295167\pi$
$233$	18.3172	1.20000	0.600001	+	0.799999i	$0.295167\pi$
$234$	0	0
$235$	−6.33141	−0.413016
$236$	30.4202	1.98019
$237$	−11.8303	−0.768462
$238$	9.03598	0.585715
$239$	19.0642	1.23316	0.616581	−	0.787292i	$-0.288517\pi$
$239$	19.0642	1.23316	0.616581	+	0.787292i	$0.288517\pi$
$240$	1.46183	0.0943610
$241$	−7.40537	−0.477022	−0.238511	−	0.971140i	$-0.576659\pi$
$241$	−7.40537	−0.477022	−0.238511	+	0.971140i	$0.576659\pi$
$242$	16.5209	1.06200
$243$	−14.1516	−0.907826
$244$	−16.7551	−1.07264
$245$	1.00000	0.0638877
$246$	−20.0033	−1.27536
$247$	0	0
$248$	−15.9613	−1.01355
$249$	13.2581	0.840200
$250$	−2.22367	−0.140637
$251$	2.44835	0.154538	0.0772691	−	0.997010i	$-0.475380\pi$
$251$	2.44835	0.154538	0.0772691	+	0.997010i	$0.475380\pi$
$252$	−4.59339	−0.289356
$253$	−0.468127	−0.0294309
$254$	−34.6285	−2.17278
$255$	4.87645	0.305375
$256$	−7.34198	−0.458874
$257$	−2.38290	−0.148641	−0.0743205	−	0.997234i	$-0.523679\pi$
$257$	−2.38290	−0.148641	−0.0743205	+	0.997234i	$0.523679\pi$
$258$	16.0766	1.00089
$259$	2.16041	0.134241
$260$	0	0
$261$	−9.82795	−0.608335
$262$	14.6913	0.907631
$263$	−14.2680	−0.879803	−0.439902	−	0.898046i	$-0.644987\pi$
$263$	−14.2680	−0.879803	−0.439902	+	0.898046i	$0.644987\pi$
$264$	4.76346	0.293171
$265$	5.92445	0.363936
$266$	18.9081	1.15933
$267$	10.8442	0.663652
$268$	−22.8458	−1.39553
$269$	0.00656097	0.000400030 0	0.000200015	−	1.00000i	$-0.499936\pi$
$269$	0.00656097	0.000400030 0	0.000200015		1.00000i	$0.499936\pi$
$270$	−12.1681	−0.740527
$271$	−27.9930	−1.70046	−0.850228	−	0.526414i	$-0.823536\pi$
$271$	−27.9930	−1.70046	−0.850228	+	0.526414i	$0.823536\pi$
$272$	4.94999	0.300137
$273$	0	0
$274$	16.4383	0.993074
$275$	1.88956	0.113945
$276$	0.875474	0.0526974
$277$	7.50898	0.451171	0.225586	−	0.974223i	$-0.427570\pi$
$277$	7.50898	0.451171	0.225586	+	0.974223i	$0.427570\pi$
$278$	36.9492	2.21607
$279$	−11.8522	−0.709571
$280$	−2.10070	−0.125541
$281$	−5.16175	−0.307924	−0.153962	−	0.988077i	$-0.549203\pi$
$281$	−5.16175	−0.307924	−0.153962	+	0.988077i	$0.549203\pi$
$282$	−16.8954	−1.00611
$283$	29.4260	1.74919	0.874596	−	0.484853i	$-0.161127\pi$
$283$	29.4260	1.74919	0.874596	+	0.484853i	$0.161127\pi$
$284$	−39.0246	−2.31568
$285$	10.2042	0.604443
$286$	0	0
$287$	−7.49604	−0.442478
$288$	−10.7790	−0.635160
$289$	−0.487595	−0.0286820
$290$	−14.0101	−0.822701
$291$	3.79345	0.222376
$292$	33.6570	1.96962
$293$	9.09643	0.531419	0.265709	−	0.964053i	$-0.414394\pi$
$293$	9.09643	0.531419	0.265709	+	0.964053i	$0.414394\pi$
$294$	2.66851	0.155631
$295$	10.3305	0.601465
$296$	−4.53837	−0.263787
$297$	10.3398	0.599977
$298$	−28.1590	−1.63121
$299$	0	0
$300$	−3.53378	−0.204023
$301$	6.02456	0.347250
$302$	49.6147	2.85500
$303$	5.07033	0.291283
$304$	10.3581	0.594075
$305$	−5.68993	−0.325805
$306$	−14.0951	−0.805761
$307$	−11.7805	−0.672349	−0.336175	−	0.941800i	$-0.609133\pi$
$307$	−11.7805	−0.672349	−0.336175	+	0.941800i	$0.609133\pi$
$308$	5.56418	0.317048
$309$	−2.71030	−0.154183
$310$	−16.8957	−0.959610
$311$	1.52307	0.0863652	0.0431826	−	0.999067i	$-0.486250\pi$
$311$	1.52307	0.0863652	0.0431826	+	0.999067i	$0.486250\pi$
$312$	0	0
$313$	−32.7225	−1.84959	−0.924794	−	0.380469i	$-0.875762\pi$
$313$	−32.7225	−1.84959	−0.924794	+	0.380469i	$0.875762\pi$
$314$	19.0506	1.07509
$315$	−1.55988	−0.0878894
$316$	29.0294	1.63303
$317$	9.14324	0.513535	0.256768	−	0.966473i	$-0.417342\pi$
$317$	9.14324	0.513535	0.256768	+	0.966473i	$0.417342\pi$
$318$	15.8095	0.886550
$319$	11.9050	0.666554
$320$	−12.9296	−0.722785
$321$	−7.37740	−0.411766
$322$	0.550901	0.0307005
$323$	34.5529	1.92257
$324$	−5.55699	−0.308722
$325$	0	0
$326$	−16.0280	−0.887708
$327$	1.99955	0.110575
$328$	15.7469	0.869478
$329$	−6.33141	−0.349062
$330$	5.04230	0.277570
$331$	−2.73470	−0.150313	−0.0751563	−	0.997172i	$-0.523946\pi$
$331$	−2.73470	−0.150313	−0.0751563	+	0.997172i	$0.523946\pi$
$332$	−32.5330	−1.78548
$333$	−3.36998	−0.184674
$334$	−22.9922	−1.25808
$335$	−7.75830	−0.423881
$336$	1.46183	0.0797496
$337$	−30.3119	−1.65119	−0.825596	−	0.564261i	$-0.809161\pi$
$337$	−30.3119	−1.65119	−0.825596	+	0.564261i	$0.809161\pi$
$338$	0	0
$339$	−22.6126	−1.22815
$340$	−11.9659	−0.648943
$341$	14.3571	0.777479
$342$	−29.4945	−1.59488
$343$	1.00000	0.0539949
$344$	−12.6558	−0.682354
$345$	0.297305	0.0160064
$346$	−29.4458	−1.58301
$347$	−9.57542	−0.514035	−0.257018	−	0.966407i	$-0.582740\pi$
$347$	−9.57542	−0.514035	−0.257018	+	0.966407i	$0.582740\pi$
$348$	−22.2644	−1.19350
$349$	−29.3392	−1.57049	−0.785245	−	0.619185i	$-0.787463\pi$
$349$	−29.3392	−1.57049	−0.785245	+	0.619185i	$0.787463\pi$
$350$	−2.22367	−0.118860
$351$	0	0
$352$	13.0571	0.695946
$353$	−10.6218	−0.565343	−0.282672	−	0.959217i	$-0.591221\pi$
$353$	−10.6218	−0.565343	−0.282672	+	0.959217i	$0.591221\pi$
$354$	27.5670	1.46517
$355$	−13.2525	−0.703369
$356$	−26.6096	−1.41030
$357$	4.87645	0.258089
$358$	−36.6323	−1.93608
$359$	24.3605	1.28570	0.642848	−	0.765994i	$-0.277753\pi$
$359$	24.3605	1.28570	0.642848	+	0.765994i	$0.277753\pi$
$360$	3.27684	0.172705
$361$	53.3033	2.80544
$362$	−1.57619	−0.0828428
$363$	8.91585	0.467961
$364$	0	0
$365$	11.4297	0.598257
$366$	−15.1836	−0.793662
$367$	24.1195	1.25903	0.629515	−	0.776989i	$-0.283254\pi$
$367$	24.1195	1.25903	0.629515	+	0.776989i	$0.283254\pi$
$368$	0.301788	0.0157318
$369$	11.6930	0.608711
$370$	−4.80403	−0.249750
$371$	5.92445	0.307582
$372$	−26.8501	−1.39211
$373$	27.5122	1.42453	0.712265	−	0.701911i	$-0.247670\pi$
$373$	27.5122	1.42453	0.712265	+	0.701911i	$0.247670\pi$
$374$	17.0740	0.882875
$375$	−1.20005	−0.0619703
$376$	13.3004	0.685915
$377$	0	0
$378$	−12.1681	−0.625859
$379$	−27.4490	−1.40996	−0.704981	−	0.709227i	$-0.749044\pi$
$379$	−27.4490	−1.40996	−0.704981	+	0.709227i	$0.749044\pi$
$380$	−25.0392	−1.28448
$381$	−18.6880	−0.957414
$382$	18.1454	0.928398
$383$	20.4062	1.04271	0.521353	−	0.853341i	$-0.325427\pi$
$383$	20.4062	1.04271	0.521353	+	0.853341i	$0.325427\pi$
$384$	−17.9177	−0.914358
$385$	1.88956	0.0963007
$386$	12.1419	0.618009
$387$	−9.39761	−0.477707
$388$	−9.30844	−0.472564
$389$	−15.3374	−0.777635	−0.388818	−	0.921315i	$-0.627116\pi$
$389$	−15.3374	−0.777635	−0.388818	+	0.921315i	$0.627116\pi$
$390$	0	0
$391$	1.00672	0.0509120
$392$	−2.10070	−0.106101
$393$	7.92846	0.399938
$394$	31.1799	1.57082
$395$	9.85820	0.496020
$396$	−8.67946	−0.436159
$397$	−7.57370	−0.380113	−0.190057	−	0.981773i	$-0.560867\pi$
$397$	−7.57370	−0.380113	−0.190057	+	0.981773i	$0.560867\pi$
$398$	46.2145	2.31652
$399$	10.2042	0.510848
$400$	−1.21815	−0.0609073
$401$	13.5353	0.675918	0.337959	−	0.941161i	$-0.390263\pi$
$401$	13.5353	0.675918	0.337959	+	0.941161i	$0.390263\pi$
$402$	−20.7031	−1.03258
$403$	0	0
$404$	−12.4417	−0.618996
$405$	−1.88712	−0.0937716
$406$	−14.0101	−0.695309
$407$	4.08222	0.202348
$408$	−10.2440	−0.507151
$409$	−9.93411	−0.491210	−0.245605	−	0.969370i	$-0.578987\pi$
$409$	−9.93411	−0.491210	−0.245605	+	0.969370i	$0.578987\pi$
$410$	16.6687	0.823209
$411$	8.87127	0.437588
$412$	6.65057	0.327650
$413$	10.3305	0.508330
$414$	−0.859341	−0.0422343
$415$	−11.0480	−0.542324
$416$	0	0
$417$	19.9404	0.976486
$418$	35.7280	1.74751
$419$	0.866261	0.0423196	0.0211598	−	0.999776i	$-0.493264\pi$
$419$	0.866261	0.0423196	0.0211598	+	0.999776i	$0.493264\pi$
$420$	−3.53378	−0.172431
$421$	−6.05345	−0.295027	−0.147513	−	0.989060i	$-0.547127\pi$
$421$	−6.05345	−0.295027	−0.147513	+	0.989060i	$0.547127\pi$
$422$	31.2834	1.52285
$423$	9.87626	0.480200
$424$	−12.4455	−0.604406
$425$	−4.06355	−0.197111
$426$	−35.3644	−1.71341
$427$	−5.68993	−0.275355
$428$	18.1028	0.875031
$429$	0	0
$430$	−13.3966	−0.646043
$431$	−8.12547	−0.391390	−0.195695	−	0.980665i	$-0.562696\pi$
$431$	−8.12547	−0.391390	−0.195695	+	0.980665i	$0.562696\pi$
$432$	−6.66579	−0.320708
$433$	−6.04963	−0.290727	−0.145363	−	0.989378i	$-0.546435\pi$
$433$	−6.04963	−0.290727	−0.145363	+	0.989378i	$0.546435\pi$
$434$	−16.8957	−0.811019
$435$	−7.56084	−0.362514
$436$	−4.90653	−0.234980
$437$	2.10660	0.100772
$438$	30.5002	1.45736
$439$	14.7939	0.706076	0.353038	−	0.935609i	$-0.385149\pi$
$439$	14.7939	0.706076	0.353038	+	0.935609i	$0.385149\pi$
$440$	−3.96939	−0.189233
$441$	−1.55988	−0.0742801
$442$	0	0
$443$	−29.2129	−1.38795	−0.693974	−	0.720000i	$-0.744142\pi$
$443$	−29.2129	−1.38795	−0.693974	+	0.720000i	$0.744142\pi$
$444$	−7.63442	−0.362313
$445$	−9.03643	−0.428368
$446$	33.1784	1.57104
$447$	−15.1966	−0.718775
$448$	−12.9296	−0.610865
$449$	−13.2010	−0.622992	−0.311496	−	0.950248i	$-0.600830\pi$
$449$	−13.2010	−0.622992	−0.311496	+	0.950248i	$0.600830\pi$
$450$	3.46866	0.163514
$451$	−14.1642	−0.666966
$452$	55.4871	2.60990
$453$	26.7756	1.25803
$454$	−36.6833	−1.72163
$455$	0	0
$456$	−21.4359	−1.00383
$457$	−33.0914	−1.54795	−0.773976	−	0.633215i	$-0.781735\pi$
$457$	−33.0914	−1.54795	−0.773976	+	0.633215i	$0.781735\pi$
$458$	13.5840	0.634739
$459$	−22.2361	−1.03789
$460$	−0.729532	−0.0340146
$461$	34.9412	1.62737	0.813687	−	0.581303i	$-0.197457\pi$
$461$	34.9412	1.62737	0.813687	+	0.581303i	$0.197457\pi$
$462$	5.04230	0.234589
$463$	7.61790	0.354034	0.177017	−	0.984208i	$-0.443355\pi$
$463$	7.61790	0.354034	0.177017	+	0.984208i	$0.443355\pi$
$464$	−7.67485	−0.356296
$465$	−9.11811	−0.422842
$466$	−40.7314	−1.88685
$467$	−11.5468	−0.534324	−0.267162	−	0.963652i	$-0.586086\pi$
$467$	−11.5468	−0.534324	−0.267162	+	0.963652i	$0.586086\pi$
$468$	0	0
$469$	−7.75830	−0.358245
$470$	14.0790	0.649414
$471$	10.2811	0.473727
$472$	−21.7012	−0.998880
$473$	11.3838	0.523426
$474$	26.3067	1.20831
$475$	−8.50313	−0.390151
$476$	−11.9659	−0.548457
$477$	−9.24145	−0.423137
$478$	−42.3925	−1.93899
$479$	14.9928	0.685038	0.342519	−	0.939511i	$-0.388720\pi$
$479$	14.9928	0.685038	0.342519	+	0.939511i	$0.388720\pi$
$480$	−8.29251	−0.378500
$481$	0	0
$482$	16.4671	0.750055
$483$	0.297305	0.0135279
$484$	−21.8779	−0.994448
$485$	−3.16108	−0.143537
$486$	31.4685	1.42744
$487$	−6.10050	−0.276440	−0.138220	−	0.990402i	$-0.544138\pi$
$487$	−6.10050	−0.276440	−0.138220	+	0.990402i	$0.544138\pi$
$488$	11.9528	0.541079
$489$	−8.64984	−0.391159
$490$	−2.22367	−0.100455
$491$	33.7705	1.52404	0.762021	−	0.647552i	$-0.224207\pi$
$491$	33.7705	1.52404	0.762021	+	0.647552i	$0.224207\pi$
$492$	26.4894	1.19423
$493$	−25.6021	−1.15306
$494$	0	0
$495$	−2.94749	−0.132480
$496$	−9.25561	−0.415589
$497$	−13.2525	−0.594456
$498$	−29.4817	−1.32111
$499$	−17.8342	−0.798370	−0.399185	−	0.916870i	$-0.630707\pi$
$499$	−17.8342	−0.798370	−0.399185	+	0.916870i	$0.630707\pi$
$500$	2.94470	0.131691
$501$	−12.4082	−0.554358
$502$	−5.44431	−0.242991
$503$	18.0767	0.805998	0.402999	−	0.915200i	$-0.367968\pi$
$503$	18.0767	0.805998	0.402999	+	0.915200i	$0.367968\pi$
$504$	3.27684	0.145962
$505$	−4.22511	−0.188015
$506$	1.04096	0.0462763
$507$	0	0
$508$	45.8569	2.03457
$509$	13.4375	0.595607	0.297804	−	0.954627i	$-0.403746\pi$
$509$	13.4375	0.595607	0.297804	+	0.954627i	$0.403746\pi$
$510$	−10.8436	−0.480163
$511$	11.4297	0.505619
$512$	−13.5355	−0.598189
$513$	−46.5299	−2.05434
$514$	5.29877	0.233719
$515$	2.25849	0.0995209
$516$	−21.2895	−0.937218
$517$	−11.9636	−0.526157
$518$	−4.80403	−0.211077
$519$	−15.8910	−0.697538
$520$	0	0
$521$	−11.5052	−0.504051	−0.252026	−	0.967721i	$-0.581097\pi$
$521$	−11.5052	−0.504051	−0.252026	+	0.967721i	$0.581097\pi$
$522$	21.8541	0.956528
$523$	−36.3237	−1.58832	−0.794162	−	0.607705i	$-0.792090\pi$
$523$	−36.3237	−1.58832	−0.794162	+	0.607705i	$0.792090\pi$
$524$	−19.4550	−0.849895
$525$	−1.20005	−0.0523744
$526$	31.7273	1.38338
$527$	−30.8753	−1.34495
$528$	2.76222	0.120210
$529$	−22.9386	−0.997331
$530$	−13.1740	−0.572242
$531$	−16.1144	−0.699304
$532$	−25.0392	−1.08559
$533$	0	0
$534$	−24.1138	−1.04351
$535$	6.14758	0.265783
$536$	16.2978	0.703959
$537$	−19.7694	−0.853111
$538$	−0.0145894	−0.000628995 0
$539$	1.88956	0.0813890
$540$	16.1136	0.693420
$541$	18.8788	0.811664	0.405832	−	0.913948i	$-0.366982\pi$
$541$	18.8788	0.811664	0.405832	+	0.913948i	$0.366982\pi$
$542$	62.2472	2.67375
$543$	−0.850625	−0.0365038
$544$	−28.0797	−1.20391
$545$	−1.66622	−0.0713732
$546$	0	0
$547$	15.3945	0.658220	0.329110	−	0.944292i	$-0.393251\pi$
$547$	15.3945	0.658220	0.329110	+	0.944292i	$0.393251\pi$
$548$	−21.7685	−0.929903
$549$	8.87563	0.378803
$550$	−4.20175	−0.179163
$551$	−53.5735	−2.28231
$552$	−0.624548	−0.0265825
$553$	9.85820	0.419213
$554$	−16.6975	−0.709408
$555$	−2.59260	−0.110050
$556$	−48.9301	−2.07510
$557$	−28.5575	−1.21002	−0.605010	−	0.796218i	$-0.706831\pi$
$557$	−28.5575	−1.21002	−0.605010	+	0.796218i	$0.706831\pi$
$558$	26.3553	1.11571
$559$	0	0
$560$	−1.21815	−0.0514760
$561$	9.21434	0.389030
$562$	11.4780	0.484171
$563$	−17.6752	−0.744922	−0.372461	−	0.928048i	$-0.621486\pi$
$563$	−17.6752	−0.744922	−0.372461	+	0.928048i	$0.621486\pi$
$564$	22.3738	0.942109
$565$	18.8431	0.792733
$566$	−65.4336	−2.75038
$567$	−1.88712	−0.0792515
$568$	27.8395	1.16812
$569$	−30.5675	−1.28146	−0.640728	−	0.767768i	$-0.721368\pi$
$569$	−30.5675	−1.28146	−0.640728	+	0.767768i	$0.721368\pi$
$570$	−22.6907	−0.950409
$571$	18.2914	0.765473	0.382737	−	0.923857i	$-0.374982\pi$
$571$	18.2914	0.765473	0.382737	+	0.923857i	$0.374982\pi$
$572$	0	0
$573$	9.79253	0.409089
$574$	16.6687	0.695739
$575$	−0.247744	−0.0103317
$576$	20.1686	0.840359
$577$	−39.0132	−1.62414	−0.812071	−	0.583558i	$-0.801660\pi$
$577$	−39.0132	−1.62414	−0.812071	+	0.583558i	$0.801660\pi$
$578$	1.08425	0.0450988
$579$	6.55265	0.272319
$580$	18.5529	0.770367
$581$	−11.0480	−0.458348
$582$	−8.43538	−0.349658
$583$	11.1946	0.463632
$584$	−24.0103	−0.993553
$585$	0	0
$586$	−20.2274	−0.835588
$587$	−27.7061	−1.14355	−0.571777	−	0.820409i	$-0.693746\pi$
$587$	−27.7061	−1.14355	−0.571777	+	0.820409i	$0.693746\pi$
$588$	−3.53378	−0.145731
$589$	−64.6078	−2.66212
$590$	−22.9716	−0.945725
$591$	16.8269	0.692166
$592$	−2.63169	−0.108162
$593$	−29.5542	−1.21364	−0.606822	−	0.794838i	$-0.707556\pi$
$593$	−29.5542	−1.21364	−0.606822	+	0.794838i	$0.707556\pi$
$594$	−22.9923	−0.943386
$595$	−4.06355	−0.166589
$596$	37.2897	1.52745
$597$	24.9406	1.02075
$598$	0	0
$599$	−13.9899	−0.571611	−0.285805	−	0.958288i	$-0.592261\pi$
$599$	−13.9899	−0.571611	−0.285805	+	0.958288i	$0.592261\pi$
$600$	2.52094	0.102917
$601$	23.0233	0.939138	0.469569	−	0.882896i	$-0.344409\pi$
$601$	23.0233	0.939138	0.469569	+	0.882896i	$0.344409\pi$
$602$	−13.3966	−0.546006
$603$	12.1020	0.492833
$604$	−65.7024	−2.67339
$605$	−7.42958	−0.302055
$606$	−11.2747	−0.458005
$607$	5.17372	0.209995	0.104997	−	0.994472i	$-0.466517\pi$
$607$	5.17372	0.209995	0.104997	+	0.994472i	$0.466517\pi$
$608$	−58.7579	−2.38295
$609$	−7.56084	−0.306381
$610$	12.6525	0.512286
$611$	0	0
$612$	18.6654	0.754505
$613$	−23.3273	−0.942181	−0.471091	−	0.882085i	$-0.656140\pi$
$613$	−23.3273	−0.942181	−0.471091	+	0.882085i	$0.656140\pi$
$614$	26.1959	1.05718
$615$	8.99562	0.362738
$616$	−3.96939	−0.159931
$617$	−44.8587	−1.80594	−0.902972	−	0.429700i	$-0.858619\pi$
$617$	−44.8587	−1.80594	−0.902972	+	0.429700i	$0.858619\pi$
$618$	6.02680	0.242433
$619$	−5.96323	−0.239682	−0.119841	−	0.992793i	$-0.538239\pi$
$619$	−5.96323	−0.239682	−0.119841	+	0.992793i	$0.538239\pi$
$620$	22.3742	0.898568
$621$	−1.35568	−0.0544014
$622$	−3.38680	−0.135798
$623$	−9.03643	−0.362037
$624$	0	0
$625$	1.00000	0.0400000
$626$	72.7641	2.90824
$627$	19.2814	0.770024
$628$	−25.2279	−1.00670
$629$	−8.77892	−0.350039
$630$	3.46866	0.138195
$631$	−40.4942	−1.61205	−0.806024	−	0.591883i	$-0.798385\pi$
$631$	−40.4942	−1.61205	−0.806024	+	0.591883i	$0.798385\pi$
$632$	−20.7091	−0.823764
$633$	16.8827	0.671028
$634$	−20.3315	−0.807468
$635$	15.5727	0.617983
$636$	−20.9357	−0.830155
$637$	0	0
$638$	−26.4729	−1.04807
$639$	20.6723	0.817785
$640$	14.9308	0.590192
$641$	−39.4108	−1.55663	−0.778316	−	0.627872i	$-0.783926\pi$
$641$	−39.4108	−1.55663	−0.778316	+	0.627872i	$0.783926\pi$
$642$	16.4049	0.647449
$643$	31.8299	1.25525	0.627624	−	0.778517i	$-0.284028\pi$
$643$	31.8299	1.25525	0.627624	+	0.778517i	$0.284028\pi$
$644$	−0.729532	−0.0287476
$645$	−7.22977	−0.284672
$646$	−76.8341	−3.02300
$647$	32.2306	1.26712	0.633558	−	0.773696i	$-0.281594\pi$
$647$	32.2306	1.26712	0.633558	+	0.773696i	$0.281594\pi$
$648$	3.96426	0.155731
$649$	19.5201	0.766229
$650$	0	0
$651$	−9.11811	−0.357367
$652$	21.2251	0.831240
$653$	−41.0838	−1.60773	−0.803867	−	0.594810i	$-0.797227\pi$
$653$	−41.0838	−1.60773	−0.803867	+	0.594810i	$0.797227\pi$
$654$	−4.44634	−0.173866
$655$	−6.60678	−0.258148
$656$	9.13127	0.356516
$657$	−17.8290	−0.695574
$658$	14.0790	0.548855
$659$	−36.1492	−1.40817	−0.704087	−	0.710114i	$-0.748643\pi$
$659$	−36.1492	−1.40817	−0.704087	+	0.710114i	$0.748643\pi$
$660$	−6.67728	−0.259913
$661$	−12.3339	−0.479733	−0.239867	−	0.970806i	$-0.577104\pi$
$661$	−12.3339	−0.479733	−0.239867	+	0.970806i	$0.577104\pi$
$662$	6.08106	0.236347
$663$	0	0
$664$	23.2085	0.900664
$665$	−8.50313	−0.329737
$666$	7.49373	0.290376
$667$	−1.56090	−0.0604382
$668$	30.4475	1.17805
$669$	17.9054	0.692262
$670$	17.2519	0.666498
$671$	−10.7515	−0.415055
$672$	−8.29251	−0.319891
$673$	−12.8677	−0.496013	−0.248006	−	0.968758i	$-0.579775\pi$
$673$	−12.8677	−0.496013	−0.248006	+	0.968758i	$0.579775\pi$
$674$	67.4035	2.59629
$675$	5.47208	0.210621
$676$	0	0
$677$	−3.72009	−0.142975	−0.0714873	−	0.997442i	$-0.522775\pi$
$677$	−3.72009	−0.142975	−0.0714873	+	0.997442i	$0.522775\pi$
$678$	50.2829	1.93110
$679$	−3.16108	−0.121311
$680$	8.53628	0.327351
$681$	−19.7969	−0.758618
$682$	−31.9254	−1.22248
$683$	17.3489	0.663836	0.331918	−	0.943308i	$-0.392304\pi$
$683$	17.3489	0.663836	0.331918	+	0.943308i	$0.392304\pi$
$684$	39.0582	1.49343
$685$	−7.39243	−0.282450
$686$	−2.22367	−0.0849000
$687$	7.33090	0.279691
$688$	−7.33879	−0.279789
$689$	0	0
$690$	−0.661108	−0.0251680
$691$	−19.9380	−0.758478	−0.379239	−	0.925299i	$-0.623814\pi$
$691$	−19.9380	−0.758478	−0.379239	+	0.925299i	$0.623814\pi$
$692$	38.9936	1.48232
$693$	−2.94749	−0.111966
$694$	21.2926	0.808254
$695$	−16.6163	−0.630293
$696$	15.8830	0.602045
$697$	30.4605	1.15377
$698$	65.2406	2.46939
$699$	−21.9816	−0.831419
$700$	2.94470	0.111299
$701$	−20.2346	−0.764251	−0.382126	−	0.924110i	$-0.624808\pi$
$701$	−20.2346	−0.764251	−0.382126	+	0.924110i	$0.624808\pi$
$702$	0	0
$703$	−18.3703	−0.692847
$704$	−24.4312	−0.920784
$705$	7.59800	0.286157
$706$	23.6194	0.888929
$707$	−4.22511	−0.158901
$708$	−36.5057	−1.37197
$709$	−25.2407	−0.947934	−0.473967	−	0.880543i	$-0.657178\pi$
$709$	−25.2407	−0.947934	−0.473967	+	0.880543i	$0.657178\pi$
$710$	29.4691	1.10596
$711$	−15.3776	−0.576707
$712$	18.9828	0.711411
$713$	−1.88239	−0.0704960
$714$	−10.8436	−0.405812
$715$	0	0
$716$	48.5104	1.81292
$717$	−22.8780	−0.854394
$718$	−54.1696	−2.02159
$719$	10.1468	0.378410	0.189205	−	0.981938i	$-0.439409\pi$
$719$	10.1468	0.378410	0.189205	+	0.981938i	$0.439409\pi$
$720$	1.90016	0.0708149
$721$	2.25849	0.0841105
$722$	−118.529	−4.41119
$723$	8.88680	0.330504
$724$	2.08728	0.0775730
$725$	6.30044	0.233992
$726$	−19.8259	−0.735808
$727$	−23.5932	−0.875024	−0.437512	−	0.899213i	$-0.644140\pi$
$727$	−23.5932	−0.875024	−0.437512	+	0.899213i	$0.644140\pi$
$728$	0	0
$729$	22.6440	0.838666
$730$	−25.4158	−0.940681
$731$	−24.4811	−0.905466
$732$	20.1070	0.743176
$733$	17.1266	0.632586	0.316293	−	0.948662i	$-0.397562\pi$
$733$	17.1266	0.632586	0.316293	+	0.948662i	$0.397562\pi$
$734$	−53.6338	−1.97966
$735$	−1.20005	−0.0442645
$736$	−1.71195	−0.0631033
$737$	−14.6597	−0.539998
$738$	−26.0012	−0.957119
$739$	53.8808	1.98204	0.991018	−	0.133725i	$-0.0426939\pi$
$739$	53.8808	1.98204	0.991018	+	0.133725i	$0.0426939\pi$
$740$	6.36176	0.233863
$741$	0	0
$742$	−13.1740	−0.483633
$743$	18.1802	0.666969	0.333484	−	0.942756i	$-0.391776\pi$
$743$	18.1802	0.666969	0.333484	+	0.942756i	$0.391776\pi$
$744$	19.1544	0.702234
$745$	12.6633	0.463949
$746$	−61.1781	−2.23989
$747$	17.2336	0.630543
$748$	−22.6103	−0.826714
$749$	6.14758	0.224628
$750$	2.66851	0.0974402
$751$	−39.4197	−1.43844	−0.719222	−	0.694780i	$-0.755502\pi$
$751$	−39.4197	−1.43844	−0.719222	+	0.694780i	$0.755502\pi$
$752$	7.71258	0.281249
$753$	−2.93813	−0.107072
$754$	0	0
$755$	−22.3121	−0.812020
$756$	16.1136	0.586047
$757$	37.6686	1.36909	0.684544	−	0.728972i	$-0.260002\pi$
$757$	37.6686	1.36909	0.684544	+	0.728972i	$0.260002\pi$
$758$	61.0375	2.21698
$759$	0.561775	0.0203911
$760$	17.8625	0.647941
$761$	21.0799	0.764145	0.382072	−	0.924132i	$-0.375210\pi$
$761$	21.0799	0.764145	0.382072	+	0.924132i	$0.375210\pi$
$762$	41.5559	1.50541
$763$	−1.66622	−0.0603214
$764$	−24.0291	−0.869341
$765$	6.33866	0.229175
$766$	−45.3765	−1.63952
$767$	0	0
$768$	8.81074	0.317930
$769$	7.33346	0.264451	0.132226	−	0.991220i	$-0.457788\pi$
$769$	7.33346	0.264451	0.132226	+	0.991220i	$0.457788\pi$
$770$	−4.20175	−0.151420
$771$	2.85959	0.102986
$772$	−16.0790	−0.578696
$773$	−22.0871	−0.794417	−0.397209	−	0.917728i	$-0.630021\pi$
$773$	−22.0871	−0.794417	−0.397209	+	0.917728i	$0.630021\pi$
$774$	20.8972	0.751133
$775$	7.59811	0.272932
$776$	6.64048	0.238379
$777$	−2.59260	−0.0930089
$778$	34.1052	1.22273
$779$	63.7399	2.28372
$780$	0	0
$781$	−25.0413	−0.896050
$782$	−2.23861	−0.0800526
$783$	34.4765	1.23209
$784$	−1.21815	−0.0435052
$785$	−8.56721	−0.305777
$786$	−17.6303	−0.628851
$787$	3.74597	0.133529	0.0667647	−	0.997769i	$-0.478732\pi$
$787$	3.74597	0.133529	0.0667647	+	0.997769i	$0.478732\pi$
$788$	−41.2901	−1.47090
$789$	17.1223	0.609570
$790$	−21.9214	−0.779927
$791$	18.8431	0.669982
$792$	6.19178	0.220015
$793$	0	0
$794$	16.8414	0.597679
$795$	−7.10963	−0.252153
$796$	−61.1997	−2.16917
$797$	−6.73673	−0.238627	−0.119314	−	0.992857i	$-0.538069\pi$
$797$	−6.73673	−0.238627	−0.119314	+	0.992857i	$0.538069\pi$
$798$	−22.6907	−0.803242
$799$	25.7280	0.910191
$800$	6.91014	0.244311
$801$	14.0958	0.498049
$802$	−30.0979	−1.06279
$803$	21.5970	0.762142
$804$	27.4161	0.966892
$805$	−0.247744	−0.00873184
$806$	0	0
$807$	−0.00787349	−0.000277160 0
$808$	8.87567	0.312245
$809$	−25.2059	−0.886194	−0.443097	−	0.896474i	$-0.646120\pi$
$809$	−25.2059	−0.886194	−0.443097	+	0.896474i	$0.646120\pi$
$810$	4.19632	0.147444
$811$	−53.7622	−1.88785	−0.943923	−	0.330166i	$-0.892895\pi$
$811$	−53.7622	−1.88785	−0.943923	+	0.330166i	$0.892895\pi$
$812$	18.5529	0.651079
$813$	33.5930	1.17816
$814$	−9.07749	−0.318166
$815$	7.20791	0.252482
$816$	−5.94023	−0.207950
$817$	−51.2277	−1.79223
$818$	22.0902	0.772364
$819$	0	0
$820$	−22.0736	−0.770843
$821$	−15.6351	−0.545670	−0.272835	−	0.962061i	$-0.587961\pi$
$821$	−15.6351	−0.545670	−0.272835	+	0.962061i	$0.587961\pi$
$822$	−19.7268	−0.688050
$823$	26.0337	0.907479	0.453739	−	0.891134i	$-0.350090\pi$
$823$	26.0337	0.907479	0.453739	+	0.891134i	$0.350090\pi$
$824$	−4.74440	−0.165279
$825$	−2.26756	−0.0789463
$826$	−22.9716	−0.799284
$827$	33.7759	1.17450	0.587251	−	0.809405i	$-0.300210\pi$
$827$	33.7759	1.17450	0.587251	+	0.809405i	$0.300210\pi$
$828$	1.13798	0.0395477
$829$	23.3157	0.809788	0.404894	−	0.914364i	$-0.367308\pi$
$829$	23.3157	0.809788	0.404894	+	0.914364i	$0.367308\pi$
$830$	24.5671	0.852735
$831$	−9.01115	−0.312593
$832$	0	0
$833$	−4.06355	−0.140794
$834$	−44.3408	−1.53540
$835$	10.3398	0.357822
$836$	−47.3129	−1.63635
$837$	41.5775	1.43713
$838$	−1.92628	−0.0665421
$839$	−2.89916	−0.100090	−0.0500451	−	0.998747i	$-0.515937\pi$
$839$	−2.89916	−0.100090	−0.0500451	+	0.998747i	$0.515937\pi$
$840$	2.52094	0.0869807
$841$	10.6955	0.368812
$842$	13.4609	0.463892
$843$	6.19435	0.213345
$844$	−41.4271	−1.42598
$845$	0	0
$846$	−21.9615	−0.755053
$847$	−7.42958	−0.255283
$848$	−7.21684	−0.247827
$849$	−35.3126	−1.21192
$850$	9.03598	0.309931
$851$	−0.535229	−0.0183474
$852$	46.8314	1.60442
$853$	44.1505	1.51168	0.755842	−	0.654754i	$-0.227228\pi$
$853$	44.1505	1.51168	0.755842	+	0.654754i	$0.227228\pi$
$854$	12.6525	0.432960
$855$	13.2639	0.453616
$856$	−12.9142	−0.441399
$857$	50.1138	1.71185	0.855927	−	0.517096i	$-0.172987\pi$
$857$	50.1138	1.71185	0.855927	+	0.517096i	$0.172987\pi$
$858$	0	0
$859$	−2.41237	−0.0823089	−0.0411544	−	0.999153i	$-0.513104\pi$
$859$	−2.41237	−0.0823089	−0.0411544	+	0.999153i	$0.513104\pi$
$860$	17.7405	0.604947
$861$	8.99562	0.306570
$862$	18.0684	0.615411
$863$	−45.0444	−1.53333	−0.766664	−	0.642048i	$-0.778085\pi$
$863$	−45.0444	−1.53333	−0.766664	+	0.642048i	$0.778085\pi$
$864$	37.8129	1.28642
$865$	13.2420	0.450241
$866$	13.4524	0.457130
$867$	0.585138	0.0198723
$868$	22.3742	0.759428
$869$	18.6276	0.631899
$870$	16.8128	0.570007
$871$	0	0
$872$	3.50023	0.118533
$873$	4.93092	0.166886
$874$	−4.68439	−0.158452
$875$	1.00000	0.0338062
$876$	−40.3900	−1.36465
$877$	−35.2115	−1.18901	−0.594503	−	0.804093i	$-0.702651\pi$
$877$	−35.2115	−1.18901	−0.594503	+	0.804093i	$0.702651\pi$
$878$	−32.8968	−1.11021
$879$	−10.9162	−0.368193
$880$	−2.30175	−0.0775921
$881$	−25.1069	−0.845874	−0.422937	−	0.906159i	$-0.639001\pi$
$881$	−25.1069	−0.845874	−0.422937	+	0.906159i	$0.639001\pi$
$882$	3.46866	0.116796
$883$	−4.32891	−0.145680	−0.0728398	−	0.997344i	$-0.523206\pi$
$883$	−4.32891	−0.145680	−0.0728398	+	0.997344i	$0.523206\pi$
$884$	0	0
$885$	−12.3971	−0.416724
$886$	64.9599	2.18237
$887$	−35.3745	−1.18776	−0.593879	−	0.804554i	$-0.702404\pi$
$887$	−35.3745	−1.18776	−0.593879	+	0.804554i	$0.702404\pi$
$888$	5.44626	0.182765
$889$	15.5727	0.522291
$890$	20.0940	0.673553
$891$	−3.56582	−0.119459
$892$	−43.9365	−1.47110
$893$	53.8369	1.80158
$894$	33.7922	1.13018
$895$	16.4738	0.550659
$896$	14.9308	0.498803
$897$	0	0
$898$	29.3545	0.979574
$899$	47.8715	1.59660
$900$	−4.59339	−0.153113
$901$	−24.0743	−0.802030
$902$	31.4965	1.04872
$903$	−7.22977	−0.240592
$904$	−39.5836	−1.31653
$905$	0.708825	0.0235621
$906$	−59.5401	−1.97809
$907$	−51.6060	−1.71355	−0.856775	−	0.515690i	$-0.827536\pi$
$907$	−51.6060	−1.71355	−0.856775	+	0.515690i	$0.827536\pi$
$908$	48.5779	1.61211
$909$	6.59067	0.218599
$910$	0	0
$911$	43.5829	1.44396	0.721982	−	0.691911i	$-0.243231\pi$
$911$	43.5829	1.44396	0.721982	+	0.691911i	$0.243231\pi$
$912$	−12.4302	−0.411604
$913$	−20.8758	−0.690888
$914$	73.5843	2.43395
$915$	6.82820	0.225733
$916$	−17.9887	−0.594362
$917$	−6.60678	−0.218175
$918$	49.4456	1.63195
$919$	46.6150	1.53769	0.768843	−	0.639438i	$-0.220833\pi$
$919$	46.6150	1.53769	0.768843	+	0.639438i	$0.220833\pi$
$920$	0.520436	0.0171583
$921$	14.1372	0.465836
$922$	−77.6976	−2.55884
$923$	0	0
$924$	−6.67728	−0.219666
$925$	2.16041	0.0710338
$926$	−16.9397	−0.556672
$927$	−3.52298	−0.115710
$928$	43.5370	1.42917
$929$	38.4956	1.26300	0.631500	−	0.775376i	$-0.282439\pi$
$929$	38.4956	1.26300	0.631500	+	0.775376i	$0.282439\pi$
$930$	20.2756	0.664865
$931$	−8.50313	−0.278679
$932$	53.9387	1.76682
$933$	−1.82776	−0.0598380
$934$	25.6764	0.840156
$935$	−7.67830	−0.251107
$936$	0	0
$937$	3.47305	0.113460	0.0567298	−	0.998390i	$-0.481933\pi$
$937$	3.47305	0.113460	0.0567298	+	0.998390i	$0.481933\pi$
$938$	17.2519	0.563294
$939$	39.2686	1.28148
$940$	−18.6441	−0.608104
$941$	−4.15931	−0.135590	−0.0677949	−	0.997699i	$-0.521596\pi$
$941$	−4.15931	−0.135590	−0.0677949	+	0.997699i	$0.521596\pi$
$942$	−22.8617	−0.744874
$943$	1.85710	0.0604756
$944$	−12.5840	−0.409576
$945$	5.47208	0.178007
$946$	−25.3137	−0.823019
$947$	45.0918	1.46529	0.732643	−	0.680613i	$-0.238287\pi$
$947$	45.0918	1.46529	0.732643	+	0.680613i	$0.238287\pi$
$948$	−34.8368	−1.13145
$949$	0	0
$950$	18.9081	0.613461
$951$	−10.9723	−0.355802
$952$	8.53628	0.276662
$953$	−18.4195	−0.596666	−0.298333	−	0.954462i	$-0.596431\pi$
$953$	−18.4195	−0.596666	−0.298333	+	0.954462i	$0.596431\pi$
$954$	20.5499	0.665328
$955$	−8.16011	−0.264055
$956$	56.1384	1.81564
$957$	−14.2866	−0.461821
$958$	−33.3390	−1.07713
$959$	−7.39243	−0.238714
$960$	15.5161	0.500781
$961$	26.7313	0.862301
$962$	0	0
$963$	−9.58951	−0.309018
$964$	−21.8066	−0.702343
$965$	−5.46032	−0.175774
$966$	−0.661108	−0.0212708
$967$	−19.1704	−0.616479	−0.308240	−	0.951309i	$-0.599740\pi$
$967$	−19.1704	−0.616479	−0.308240	+	0.951309i	$0.599740\pi$
$968$	15.6073	0.501637
$969$	−41.4651	−1.33205
$970$	7.02920	0.225694
$971$	−4.63074	−0.148607	−0.0743037	−	0.997236i	$-0.523673\pi$
$971$	−4.63074	−0.148607	−0.0743037	+	0.997236i	$0.523673\pi$
$972$	−41.6722	−1.33664
$973$	−16.6163	−0.532695
$974$	13.5655	0.434666
$975$	0	0
$976$	6.93117	0.221861
$977$	−0.874735	−0.0279852	−0.0139926	−	0.999902i	$-0.504454\pi$
$977$	−0.874735	−0.0279852	−0.0139926	+	0.999902i	$0.504454\pi$
$978$	19.2344	0.615047
$979$	−17.0748	−0.545714
$980$	2.94470	0.0940650
$981$	2.59912	0.0829834
$982$	−75.0944	−2.39636
$983$	−7.25632	−0.231441	−0.115720	−	0.993282i	$-0.536918\pi$
$983$	−7.25632	−0.231441	−0.115720	+	0.993282i	$0.536918\pi$
$984$	−18.8971	−0.602417
$985$	−14.0218	−0.446773
$986$	56.9306	1.81304
$987$	7.59800	0.241847
$988$	0	0
$989$	−1.49255	−0.0474604
$990$	6.55423	0.208307
$991$	45.4115	1.44254	0.721272	−	0.692651i	$-0.243558\pi$
$991$	45.4115	1.44254	0.721272	+	0.692651i	$0.243558\pi$
$992$	52.5041	1.66701
$993$	3.28177	0.104144
$994$	29.4691	0.934705
$995$	−20.7830	−0.658866
$996$	39.0412	1.23707
$997$	2.84406	0.0900722	0.0450361	−	0.998985i	$-0.485660\pi$
$997$	2.84406	0.0900722	0.0450361	+	0.998985i	$0.485660\pi$
$998$	39.6574	1.25533
$999$	11.8219	0.374030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5915.2.a.bg.1.3	✓	15
13.12	even	2		5915.2.a.bl.1.13	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5915.2.a.bg.1.3	✓	15	1.1	even	1	trivial
5915.2.a.bl.1.13	yes	15	13.12	even	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:	\( N \)	\(=\)	\( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5915.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22367 q^{2} -1.20005 q^{3} +2.94470 q^{4} +1.00000 q^{5} +2.66851 q^{6} +1.00000 q^{7} -2.10070 q^{8} -1.55988 q^{9} +O(q^{10})\)	\(q-2.22367 q^{2} -1.20005 q^{3} +2.94470 q^{4} +1.00000 q^{5} +2.66851 q^{6} +1.00000 q^{7} -2.10070 q^{8} -1.55988 q^{9} -2.22367 q^{10} +1.88956 q^{11} -3.53378 q^{12} -2.22367 q^{14} -1.20005 q^{15} -1.21815 q^{16} -4.06355 q^{17} +3.46866 q^{18} -8.50313 q^{19} +2.94470 q^{20} -1.20005 q^{21} -4.20175 q^{22} -0.247744 q^{23} +2.52094 q^{24} +1.00000 q^{25} +5.47208 q^{27} +2.94470 q^{28} +6.30044 q^{29} +2.66851 q^{30} +7.59811 q^{31} +6.91014 q^{32} -2.26756 q^{33} +9.03598 q^{34} +1.00000 q^{35} -4.59339 q^{36} +2.16041 q^{37} +18.9081 q^{38} -2.10070 q^{40} -7.49604 q^{41} +2.66851 q^{42} +6.02456 q^{43} +5.56418 q^{44} -1.55988 q^{45} +0.550901 q^{46} -6.33141 q^{47} +1.46183 q^{48} +1.00000 q^{49} -2.22367 q^{50} +4.87645 q^{51} +5.92445 q^{53} -12.1681 q^{54} +1.88956 q^{55} -2.10070 q^{56} +10.2042 q^{57} -14.0101 q^{58} +10.3305 q^{59} -3.53378 q^{60} -5.68993 q^{61} -16.8957 q^{62} -1.55988 q^{63} -12.9296 q^{64} +5.04230 q^{66} -7.75830 q^{67} -11.9659 q^{68} +0.297305 q^{69} -2.22367 q^{70} -13.2525 q^{71} +3.27684 q^{72} +11.4297 q^{73} -4.80403 q^{74} -1.20005 q^{75} -25.0392 q^{76} +1.88956 q^{77} +9.85820 q^{79} -1.21815 q^{80} -1.88712 q^{81} +16.6687 q^{82} -11.0480 q^{83} -3.53378 q^{84} -4.06355 q^{85} -13.3966 q^{86} -7.56084 q^{87} -3.96939 q^{88} -9.03643 q^{89} +3.46866 q^{90} -0.729532 q^{92} -9.11811 q^{93} +14.0790 q^{94} -8.50313 q^{95} -8.29251 q^{96} -3.16108 q^{97} -2.22367 q^{98} -2.94749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 7 q^{2} - 7 q^{3} + 13 q^{4} + 15 q^{5} - 4 q^{6} + 15 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 7 * q^2 - 7 * q^3 + 13 * q^4 + 15 * q^5 - 4 * q^6 + 15 * q^7 - 24 * q^8 + 2 * q^9	\( 15 q - 7 q^{2} - 7 q^{3} + 13 q^{4} + 15 q^{5} - 4 q^{6} + 15 q^{7} - 24 q^{8} + 2 q^{9} - 7 q^{10} - 6 q^{11} + q^{12} - 7 q^{14} - 7 q^{15} + 5 q^{16} - 6 q^{17} + 9 q^{18} - 14 q^{19} + 13 q^{20} - 7 q^{21} + 5 q^{22} + 6 q^{23} + 3 q^{24} + 15 q^{25} - 25 q^{27} + 13 q^{28} - 26 q^{29} - 4 q^{30} - 12 q^{31} - 35 q^{32} + 19 q^{33} - 22 q^{34} + 15 q^{35} - 11 q^{36} - 60 q^{37} + 42 q^{38} - 24 q^{40} - 5 q^{41} - 4 q^{42} + q^{43} - 11 q^{44} + 2 q^{45} - 13 q^{46} - 20 q^{47} + 19 q^{48} + 15 q^{49} - 7 q^{50} - 12 q^{51} - 4 q^{53} + 7 q^{54} - 6 q^{55} - 24 q^{56} + 18 q^{57} - 35 q^{58} - 15 q^{59} + q^{60} - 23 q^{61} + 17 q^{62} + 2 q^{63} + 62 q^{64} - 20 q^{66} - 30 q^{67} + 17 q^{68} - 35 q^{69} - 7 q^{70} + 5 q^{71} - q^{72} - 44 q^{73} + 39 q^{74} - 7 q^{75} - 54 q^{76} - 6 q^{77} - 6 q^{79} + 5 q^{80} - 25 q^{81} + 32 q^{82} - 21 q^{83} + q^{84} - 6 q^{85} - 6 q^{86} + 59 q^{87} - 2 q^{88} - 18 q^{89} + 9 q^{90} + 41 q^{92} - 46 q^{93} - 29 q^{94} - 14 q^{95} - 32 q^{96} - 15 q^{97} - 7 q^{98} - 34 q^{99}+O(q^{100}) \) 15 * q - 7 * q^2 - 7 * q^3 + 13 * q^4 + 15 * q^5 - 4 * q^6 + 15 * q^7 - 24 * q^8 + 2 * q^9 - 7 * q^10 - 6 * q^11 + q^12 - 7 * q^14 - 7 * q^15 + 5 * q^16 - 6 * q^17 + 9 * q^18 - 14 * q^19 + 13 * q^20 - 7 * q^21 + 5 * q^22 + 6 * q^23 + 3 * q^24 + 15 * q^25 - 25 * q^27 + 13 * q^28 - 26 * q^29 - 4 * q^30 - 12 * q^31 - 35 * q^32 + 19 * q^33 - 22 * q^34 + 15 * q^35 - 11 * q^36 - 60 * q^37 + 42 * q^38 - 24 * q^40 - 5 * q^41 - 4 * q^42 + q^43 - 11 * q^44 + 2 * q^45 - 13 * q^46 - 20 * q^47 + 19 * q^48 + 15 * q^49 - 7 * q^50 - 12 * q^51 - 4 * q^53 + 7 * q^54 - 6 * q^55 - 24 * q^56 + 18 * q^57 - 35 * q^58 - 15 * q^59 + q^60 - 23 * q^61 + 17 * q^62 + 2 * q^63 + 62 * q^64 - 20 * q^66 - 30 * q^67 + 17 * q^68 - 35 * q^69 - 7 * q^70 + 5 * q^71 - q^72 - 44 * q^73 + 39 * q^74 - 7 * q^75 - 54 * q^76 - 6 * q^77 - 6 * q^79 + 5 * q^80 - 25 * q^81 + 32 * q^82 - 21 * q^83 + q^84 - 6 * q^85 - 6 * q^86 + 59 * q^87 - 2 * q^88 - 18 * q^89 + 9 * q^90 + 41 * q^92 - 46 * q^93 - 29 * q^94 - 14 * q^95 - 32 * q^96 - 15 * q^97 - 7 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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