LMFDB - Embedded newform 7942.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.66908$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.66908 q^{3} +1.00000 q^{4} -4.12398 q^{5} -2.66908 q^{6} -4.21417 q^{7} +1.00000 q^{8} +4.12398 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.66908 q^{3} +1.00000 q^{4} -4.12398 q^{5} -2.66908 q^{6} -4.21417 q^{7} +1.00000 q^{8} +4.12398 q^{9} -4.12398 q^{10} -1.00000 q^{11} -2.66908 q^{12} +2.21417 q^{13} -4.21417 q^{14} +11.0072 q^{15} +1.00000 q^{16} -3.45490 q^{17} +4.12398 q^{18} -4.12398 q^{20} +11.2480 q^{21} -1.00000 q^{22} -5.45490 q^{23} -2.66908 q^{24} +12.0072 q^{25} +2.21417 q^{26} -3.00000 q^{27} -4.21417 q^{28} -5.57889 q^{29} +11.0072 q^{30} -7.00724 q^{31} +1.00000 q^{32} +2.66908 q^{33} -3.45490 q^{34} +17.3792 q^{35} +4.12398 q^{36} +2.90981 q^{37} -5.90981 q^{39} -4.12398 q^{40} +11.9170 q^{41} +11.2480 q^{42} +1.46214 q^{43} -1.00000 q^{44} -17.0072 q^{45} -5.45490 q^{46} +7.58612 q^{47} -2.66908 q^{48} +10.7593 q^{49} +12.0072 q^{50} +9.22141 q^{51} +2.21417 q^{52} +13.2214 q^{53} -3.00000 q^{54} +4.12398 q^{55} -4.21417 q^{56} -5.57889 q^{58} -4.79306 q^{59} +11.0072 q^{60} +8.90981 q^{61} -7.00724 q^{62} -17.3792 q^{63} +1.00000 q^{64} -9.13122 q^{65} +2.66908 q^{66} -1.30437 q^{67} -3.45490 q^{68} +14.5596 q^{69} +17.3792 q^{70} +6.80030 q^{71} +4.12398 q^{72} -1.45490 q^{73} +2.90981 q^{74} -32.0483 q^{75} +4.21417 q^{77} -5.90981 q^{78} +9.15777 q^{79} -4.12398 q^{80} -4.36471 q^{81} +11.9170 q^{82} -13.2142 q^{83} +11.2480 q^{84} +14.2480 q^{85} +1.46214 q^{86} +14.8905 q^{87} -1.00000 q^{88} -8.24797 q^{89} -17.0072 q^{90} -9.33092 q^{91} -5.45490 q^{92} +18.7029 q^{93} +7.58612 q^{94} -2.66908 q^{96} -2.18038 q^{97} +10.7593 q^{98} -4.12398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 6 q^{14} + 9 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} + 15 q^{21} - 3 q^{22} - 15 q^{23} + 12 q^{25} - 9 q^{27} - 6 q^{28} - 6 q^{29} + 9 q^{30} + 3 q^{31} + 3 q^{32} - 9 q^{34} + 3 q^{36} + 6 q^{37} - 15 q^{39} - 3 q^{40} + 9 q^{41} + 15 q^{42} - 21 q^{43} - 3 q^{44} - 27 q^{45} - 15 q^{46} - 12 q^{47} + 27 q^{49} + 12 q^{50} - 3 q^{51} + 9 q^{53} - 9 q^{54} + 3 q^{55} - 6 q^{56} - 6 q^{58} + 3 q^{59} + 9 q^{60} + 24 q^{61} + 3 q^{62} + 3 q^{64} + 6 q^{65} - 9 q^{68} - 3 q^{69} - 21 q^{71} + 3 q^{72} - 3 q^{73} + 6 q^{74} - 36 q^{75} + 6 q^{77} - 15 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} - 33 q^{83} + 15 q^{84} + 24 q^{85} - 21 q^{86} + 6 q^{87} - 3 q^{88} - 6 q^{89} - 27 q^{90} - 36 q^{91} - 15 q^{92} + 36 q^{93} - 12 q^{94} - 12 q^{97} + 27 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 6 * q^14 + 9 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 + 15 * q^21 - 3 * q^22 - 15 * q^23 + 12 * q^25 - 9 * q^27 - 6 * q^28 - 6 * q^29 + 9 * q^30 + 3 * q^31 + 3 * q^32 - 9 * q^34 + 3 * q^36 + 6 * q^37 - 15 * q^39 - 3 * q^40 + 9 * q^41 + 15 * q^42 - 21 * q^43 - 3 * q^44 - 27 * q^45 - 15 * q^46 - 12 * q^47 + 27 * q^49 + 12 * q^50 - 3 * q^51 + 9 * q^53 - 9 * q^54 + 3 * q^55 - 6 * q^56 - 6 * q^58 + 3 * q^59 + 9 * q^60 + 24 * q^61 + 3 * q^62 + 3 * q^64 + 6 * q^65 - 9 * q^68 - 3 * q^69 - 21 * q^71 + 3 * q^72 - 3 * q^73 + 6 * q^74 - 36 * q^75 + 6 * q^77 - 15 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 - 33 * q^83 + 15 * q^84 + 24 * q^85 - 21 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 27 * q^90 - 36 * q^91 - 15 * q^92 + 36 * q^93 - 12 * q^94 - 12 * q^97 + 27 * q^98 - 3 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.66908	−1.54099	−0.770497	−	0.637444i	$-0.779992\pi$
$3$	−2.66908	−1.54099	−0.770497	+	0.637444i	$0.779992\pi$
$4$	1.00000	0.500000
$5$	−4.12398	−1.84430	−0.922151	−	0.386831i	$-0.873570\pi$
$5$	−4.12398	−1.84430	−0.922151	+	0.386831i	$0.873570\pi$
$6$	−2.66908	−1.08965
$7$	−4.21417	−1.59281	−0.796404	−	0.604765i	$-0.793267\pi$
$7$	−4.21417	−1.59281	−0.796404	+	0.604765i	$0.793267\pi$
$8$	1.00000	0.353553
$9$	4.12398	1.37466
$10$	−4.12398	−1.30412
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.66908	−0.770497
$13$	2.21417	0.614102	0.307051	−	0.951693i	$-0.400658\pi$
$13$	2.21417	0.614102	0.307051	+	0.951693i	$0.400658\pi$
$14$	−4.21417	−1.12629
$15$	11.0072	2.84206
$16$	1.00000	0.250000
$17$	−3.45490	−0.837937	−0.418969	−	0.908001i	$-0.637608\pi$
$17$	−3.45490	−0.837937	−0.418969	+	0.908001i	$0.637608\pi$
$18$	4.12398	0.972032
$19$	0	0
$19$	0	0
$20$	−4.12398	−0.922151
$21$	11.2480	2.45451
$22$	−1.00000	−0.213201
$23$	−5.45490	−1.13743	−0.568713	−	0.822536i	$-0.692559\pi$
$23$	−5.45490	−1.13743	−0.568713	+	0.822536i	$0.692559\pi$
$24$	−2.66908	−0.544823
$25$	12.0072	2.40145
$26$	2.21417	0.434235
$27$	−3.00000	−0.577350
$28$	−4.21417	−0.796404
$29$	−5.57889	−1.03597	−0.517987	−	0.855389i	$-0.673318\pi$
$29$	−5.57889	−1.03597	−0.517987	+	0.855389i	$0.673318\pi$
$30$	11.0072	2.00964
$31$	−7.00724	−1.25854	−0.629268	−	0.777188i	$-0.716645\pi$
$31$	−7.00724	−1.25854	−0.629268	+	0.777188i	$0.716645\pi$
$32$	1.00000	0.176777
$33$	2.66908	0.464627
$34$	−3.45490	−0.592511
$35$	17.3792	2.93762
$36$	4.12398	0.687331
$37$	2.90981	0.478370	0.239185	−	0.970974i	$-0.423120\pi$
$37$	2.90981	0.478370	0.239185	+	0.970974i	$0.423120\pi$
$38$	0	0
$39$	−5.90981	−0.946327
$40$	−4.12398	−0.652059
$41$	11.9170	1.86113	0.930565	−	0.366127i	$-0.119316\pi$
$41$	11.9170	1.86113	0.930565	+	0.366127i	$0.119316\pi$
$42$	11.2480	1.73560
$43$	1.46214	0.222974	0.111487	−	0.993766i	$-0.464439\pi$
$43$	1.46214	0.222974	0.111487	+	0.993766i	$0.464439\pi$
$44$	−1.00000	−0.150756
$45$	−17.0072	−2.53529
$46$	−5.45490	−0.804282
$47$	7.58612	1.10655	0.553275	−	0.832999i	$-0.313378\pi$
$47$	7.58612	1.10655	0.553275	+	0.832999i	$0.313378\pi$
$48$	−2.66908	−0.385248
$49$	10.7593	1.53704
$50$	12.0072	1.69808
$51$	9.22141	1.29126
$52$	2.21417	0.307051
$53$	13.2214	1.81610	0.908050	−	0.418861i	$-0.137571\pi$
$53$	13.2214	1.81610	0.908050	+	0.418861i	$0.137571\pi$
$54$	−3.00000	−0.408248
$55$	4.12398	0.556078
$56$	−4.21417	−0.563143
$57$	0	0
$58$	−5.57889	−0.732544
$59$	−4.79306	−0.624004	−0.312002	−	0.950082i	$-0.600999\pi$
$59$	−4.79306	−0.624004	−0.312002	+	0.950082i	$0.600999\pi$
$60$	11.0072	1.42103
$61$	8.90981	1.14078	0.570392	−	0.821373i	$-0.306791\pi$
$61$	8.90981	1.14078	0.570392	+	0.821373i	$0.306791\pi$
$62$	−7.00724	−0.889920
$63$	−17.3792	−2.18957
$64$	1.00000	0.125000
$65$	−9.13122	−1.13259
$66$	2.66908	0.328541
$67$	−1.30437	−0.159354	−0.0796769	−	0.996821i	$-0.525389\pi$
$67$	−1.30437	−0.159354	−0.0796769	+	0.996821i	$0.525389\pi$
$68$	−3.45490	−0.418969
$69$	14.5596	1.75277
$70$	17.3792	2.07721
$71$	6.80030	0.807047	0.403524	−	0.914969i	$-0.367785\pi$
$71$	6.80030	0.807047	0.403524	+	0.914969i	$0.367785\pi$
$72$	4.12398	0.486016
$73$	−1.45490	−0.170284	−0.0851418	−	0.996369i	$-0.527134\pi$
$73$	−1.45490	−0.170284	−0.0851418	+	0.996369i	$0.527134\pi$
$74$	2.90981	0.338258
$75$	−32.0483	−3.70061
$76$	0	0
$77$	4.21417	0.480250
$78$	−5.90981	−0.669154
$79$	9.15777	1.03033	0.515165	−	0.857091i	$-0.327731\pi$
$79$	9.15777	1.03033	0.515165	+	0.857091i	$0.327731\pi$
$80$	−4.12398	−0.461075
$81$	−4.36471	−0.484968
$82$	11.9170	1.31602
$83$	−13.2142	−1.45044	−0.725222	−	0.688515i	$-0.758263\pi$
$83$	−13.2142	−1.45044	−0.725222	+	0.688515i	$0.758263\pi$
$84$	11.2480	1.22725
$85$	14.2480	1.54541
$86$	1.46214	0.157667
$87$	14.8905	1.59643
$88$	−1.00000	−0.106600
$89$	−8.24797	−0.874283	−0.437141	−	0.899393i	$-0.644009\pi$
$89$	−8.24797	−0.874283	−0.437141	+	0.899393i	$0.644009\pi$
$90$	−17.0072	−1.79272
$91$	−9.33092	−0.978146
$92$	−5.45490	−0.568713
$93$	18.7029	1.93940
$94$	7.58612	0.782449
$95$	0	0
$96$	−2.66908	−0.272412
$97$	−2.18038	−0.221384	−0.110692	−	0.993855i	$-0.535307\pi$
$97$	−2.18038	−0.221384	−0.110692	+	0.993855i	$0.535307\pi$
$98$	10.7593	1.08685
$99$	−4.12398	−0.414476
$100$	12.0072	1.20072
$101$	−6.24797	−0.621696	−0.310848	−	0.950460i	$-0.600613\pi$
$101$	−6.24797	−0.621696	−0.310848	+	0.950460i	$0.600613\pi$
$102$	9.22141	0.913056
$103$	−0.605441	−0.0596559	−0.0298280	−	0.999555i	$-0.509496\pi$
$103$	−0.605441	−0.0596559	−0.0298280	+	0.999555i	$0.509496\pi$
$104$	2.21417	0.217118
$105$	−46.3864	−4.52685
$106$	13.2214	1.28418
$107$	−3.88325	−0.375408	−0.187704	−	0.982226i	$-0.560105\pi$
$107$	−3.88325	−0.375408	−0.187704	+	0.982226i	$0.560105\pi$
$108$	−3.00000	−0.288675
$109$	4.97345	0.476370	0.238185	−	0.971220i	$-0.423448\pi$
$109$	4.97345	0.476370	0.238185	+	0.971220i	$0.423448\pi$
$110$	4.12398	0.393206
$111$	−7.76651	−0.737164
$112$	−4.21417	−0.398202
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	0	0
$115$	22.4959	2.09776
$116$	−5.57889	−0.517987
$117$	9.13122	0.844182
$118$	−4.79306	−0.441237
$119$	14.5596	1.33467
$120$	11.0072	1.00482
$121$	1.00000	0.0909091
$122$	8.90981	0.806656
$123$	−31.8075	−2.86799
$124$	−7.00724	−0.629268
$125$	−28.8977	−2.58469
$126$	−17.3792	−1.54826
$127$	2.48146	0.220194	0.110097	−	0.993921i	$-0.464884\pi$
$127$	2.48146	0.220194	0.110097	+	0.993921i	$0.464884\pi$
$128$	1.00000	0.0883883
$129$	−3.90257	−0.343602
$130$	−9.13122	−0.800861
$131$	11.0072	0.961707	0.480853	−	0.876801i	$-0.340327\pi$
$131$	11.0072	0.961707	0.480853	+	0.876801i	$0.340327\pi$
$132$	2.66908	0.232314
$133$	0	0
$134$	−1.30437	−0.112680
$135$	12.3719	1.06481
$136$	−3.45490	−0.296256
$137$	6.94360	0.593232	0.296616	−	0.954997i	$-0.404142\pi$
$137$	6.94360	0.593232	0.296616	+	0.954997i	$0.404142\pi$
$138$	14.5596	1.23939
$139$	−4.37195	−0.370824	−0.185412	−	0.982661i	$-0.559362\pi$
$139$	−4.37195	−0.370824	−0.185412	+	0.982661i	$0.559362\pi$
$140$	17.3792	1.46881
$141$	−20.2480	−1.70519
$142$	6.80030	0.570668
$143$	−2.21417	−0.185159
$144$	4.12398	0.343665
$145$	23.0072	1.91065
$146$	−1.45490	−0.120409
$147$	−28.7173	−2.36857
$148$	2.90981	0.239185
$149$	11.7665	0.963950	0.481975	−	0.876185i	$-0.339920\pi$
$149$	11.7665	0.963950	0.481975	+	0.876185i	$0.339920\pi$
$150$	−32.0483	−2.61673
$151$	19.5861	1.59390	0.796948	−	0.604048i	$-0.206446\pi$
$151$	19.5861	1.59390	0.796948	+	0.604048i	$0.206446\pi$
$152$	0	0
$153$	−14.2480	−1.15188
$154$	4.21417	0.339588
$155$	28.8977	2.32112
$156$	−5.90981	−0.473163
$157$	20.6199	1.64565	0.822824	−	0.568296i	$-0.192397\pi$
$157$	20.6199	1.64565	0.822824	+	0.568296i	$0.192397\pi$
$158$	9.15777	0.728553
$159$	−35.2890	−2.79860
$160$	−4.12398	−0.326029
$161$	22.9879	1.81170
$162$	−4.36471	−0.342924
$163$	−17.8341	−1.39687	−0.698437	−	0.715672i	$-0.746121\pi$
$163$	−17.8341	−1.39687	−0.698437	+	0.715672i	$0.746121\pi$
$164$	11.9170	0.930565
$165$	−11.0072	−0.856912
$166$	−13.2142	−1.02562
$167$	−4.18038	−0.323488	−0.161744	−	0.986833i	$-0.551712\pi$
$167$	−4.18038	−0.323488	−0.161744	+	0.986833i	$0.551712\pi$
$168$	11.2480	0.867799
$169$	−8.09743	−0.622879
$170$	14.2480	1.09277
$171$	0	0
$172$	1.46214	0.111487
$173$	−23.7101	−1.80265	−0.901323	−	0.433147i	$-0.857403\pi$
$173$	−23.7101	−1.80265	−0.901323	+	0.433147i	$0.857403\pi$
$174$	14.8905	1.12885
$175$	−50.6006	−3.82505
$176$	−1.00000	−0.0753778
$177$	12.7931	0.961585
$178$	−8.24797	−0.618211
$179$	10.8269	0.809237	0.404619	−	0.914486i	$-0.367404\pi$
$179$	10.8269	0.809237	0.404619	+	0.914486i	$0.367404\pi$
$180$	−17.0072	−1.26764
$181$	17.8341	1.32560	0.662799	−	0.748798i	$-0.269368\pi$
$181$	17.8341	1.32560	0.662799	+	0.748798i	$0.269368\pi$
$182$	−9.33092	−0.691654
$183$	−23.7810	−1.75794
$184$	−5.45490	−0.402141
$185$	−12.0000	−0.882258
$186$	18.7029	1.37136
$187$	3.45490	0.252648
$188$	7.58612	0.553275
$189$	12.6425	0.919608
$190$	0	0
$191$	0.612679	0.0443319	0.0221659	−	0.999754i	$-0.492944\pi$
$191$	0.612679	0.0443319	0.0221659	+	0.999754i	$0.492944\pi$
$192$	−2.66908	−0.192624
$193$	−11.6425	−0.838047	−0.419024	−	0.907975i	$-0.637628\pi$
$193$	−11.6425	−0.838047	−0.419024	+	0.907975i	$0.637628\pi$
$194$	−2.18038	−0.156542
$195$	24.3719	1.74531
$196$	10.7593	0.768519
$197$	−12.9098	−0.919786	−0.459893	−	0.887974i	$-0.652112\pi$
$197$	−12.9098	−0.919786	−0.459893	+	0.887974i	$0.652112\pi$
$198$	−4.12398	−0.293079
$199$	−18.3647	−1.30184	−0.650920	−	0.759146i	$-0.725617\pi$
$199$	−18.3647	−1.30184	−0.650920	+	0.759146i	$0.725617\pi$
$200$	12.0072	0.849040
$201$	3.48146	0.245563
$202$	−6.24797	−0.439605
$203$	23.5104	1.65011
$204$	9.22141	0.645628
$205$	−49.1457	−3.43248
$206$	−0.605441	−0.0421831
$207$	−22.4959	−1.56358
$208$	2.21417	0.153525
$209$	0	0
$210$	−46.3864	−3.20097
$211$	−2.13122	−0.146719	−0.0733596	−	0.997306i	$-0.523372\pi$
$211$	−2.13122	−0.146719	−0.0733596	+	0.997306i	$0.523372\pi$
$212$	13.2214	0.908050
$213$	−18.1505	−1.24365
$214$	−3.88325	−0.265454
$215$	−6.02985	−0.411232
$216$	−3.00000	−0.204124
$217$	29.5297	2.00461
$218$	4.97345	0.336844
$219$	3.88325	0.262406
$220$	4.12398	0.278039
$221$	−7.64976	−0.514579
$222$	−7.76651	−0.521254
$223$	−6.90981	−0.462715	−0.231357	−	0.972869i	$-0.574317\pi$
$223$	−6.90981	−0.462715	−0.231357	+	0.972869i	$0.574317\pi$
$224$	−4.21417	−0.281571
$225$	49.5176	3.30118
$226$	8.00000	0.532152
$227$	2.72548	0.180896	0.0904482	−	0.995901i	$-0.471170\pi$
$227$	2.72548	0.180896	0.0904482	+	0.995901i	$0.471170\pi$
$228$	0	0
$229$	3.48870	0.230539	0.115270	−	0.993334i	$-0.463227\pi$
$229$	3.48870	0.230539	0.115270	+	0.993334i	$0.463227\pi$
$230$	22.4959	1.48334
$231$	−11.2480	−0.740062
$232$	−5.57889	−0.366272
$233$	−17.0902	−1.11962	−0.559808	−	0.828622i	$-0.689125\pi$
$233$	−17.0902	−1.11962	−0.559808	+	0.828622i	$0.689125\pi$
$234$	9.13122	0.596927
$235$	−31.2850	−2.04081
$236$	−4.79306	−0.312002
$237$	−24.4428	−1.58773
$238$	14.5596	0.943757
$239$	6.06035	0.392011	0.196006	−	0.980603i	$-0.437203\pi$
$239$	6.06035	0.392011	0.196006	+	0.980603i	$0.437203\pi$
$240$	11.0072	0.710514
$241$	−4.85341	−0.312635	−0.156318	−	0.987707i	$-0.549962\pi$
$241$	−4.85341	−0.312635	−0.156318	+	0.987707i	$0.549962\pi$
$242$	1.00000	0.0642824
$243$	20.6498	1.32468
$244$	8.90981	0.570392
$245$	−44.3711	−2.83476
$246$	−31.8075	−2.02797
$247$	0	0
$248$	−7.00724	−0.444960
$249$	35.2697	2.23513
$250$	−28.8977	−1.82765
$251$	−1.58612	−0.100115	−0.0500576	−	0.998746i	$-0.515941\pi$
$251$	−1.58612	−0.100115	−0.0500576	+	0.998746i	$0.515941\pi$
$252$	−17.3792	−1.09479
$253$	5.45490	0.342947
$254$	2.48146	0.155701
$255$	−38.0289	−2.38147
$256$	1.00000	0.0625000
$257$	−19.5185	−1.21753	−0.608767	−	0.793349i	$-0.708335\pi$
$257$	−19.5185	−1.21753	−0.608767	+	0.793349i	$0.708335\pi$
$258$	−3.90257	−0.242963
$259$	−12.2624	−0.761951
$260$	−9.13122	−0.566294
$261$	−23.0072	−1.42411
$262$	11.0072	0.680029
$263$	−13.0483	−0.804591	−0.402295	−	0.915510i	$-0.631787\pi$
$263$	−13.0483	−0.804591	−0.402295	+	0.915510i	$0.631787\pi$
$264$	2.66908	0.164270
$265$	−54.5249	−3.34944
$266$	0	0
$267$	22.0145	1.34726
$268$	−1.30437	−0.0796769
$269$	−23.6006	−1.43895	−0.719477	−	0.694516i	$-0.755618\pi$
$269$	−23.6006	−1.43895	−0.719477	+	0.694516i	$0.755618\pi$
$270$	12.3719	0.752933
$271$	−16.4090	−0.996778	−0.498389	−	0.866954i	$-0.666075\pi$
$271$	−16.4090	−0.996778	−0.498389	+	0.866954i	$0.666075\pi$
$272$	−3.45490	−0.209484
$273$	24.9050	1.50732
$274$	6.94360	0.419478
$275$	−12.0072	−0.724064
$276$	14.5596	0.876383
$277$	−11.5861	−0.696143	−0.348071	−	0.937468i	$-0.613163\pi$
$277$	−11.5861	−0.696143	−0.348071	+	0.937468i	$0.613163\pi$
$278$	−4.37195	−0.262212
$279$	−28.8977	−1.73006
$280$	17.3792	1.03861
$281$	−7.03379	−0.419601	−0.209800	−	0.977744i	$-0.567281\pi$
$281$	−7.03379	−0.419601	−0.209800	+	0.977744i	$0.567281\pi$
$282$	−20.2480	−1.20575
$283$	8.33092	0.495222	0.247611	−	0.968860i	$-0.420355\pi$
$283$	8.33092	0.495222	0.247611	+	0.968860i	$0.420355\pi$
$284$	6.80030	0.403524
$285$	0	0
$286$	−2.21417	−0.130927
$287$	−50.2205	−2.96442
$288$	4.12398	0.243008
$289$	−5.06364	−0.297861
$290$	23.0072	1.35103
$291$	5.81962	0.341152
$292$	−1.45490	−0.0851418
$293$	−10.2142	−0.596718	−0.298359	−	0.954454i	$-0.596439\pi$
$293$	−10.2142	−0.596718	−0.298359	+	0.954454i	$0.596439\pi$
$294$	−28.7173	−1.67483
$295$	19.7665	1.15085
$296$	2.90981	0.169129
$297$	3.00000	0.174078
$298$	11.7665	0.681616
$299$	−12.0781	−0.698495
$300$	−32.0483	−1.85031
$301$	−6.16172	−0.355156
$302$	19.5861	1.12705
$303$	16.6763	0.958029
$304$	0	0
$305$	−36.7439	−2.10395
$306$	−14.2480	−0.814502
$307$	1.93242	0.110289	0.0551444	−	0.998478i	$-0.482438\pi$
$307$	1.93242	0.110289	0.0551444	+	0.998478i	$0.482438\pi$
$308$	4.21417	0.240125
$309$	1.61597	0.0919294
$310$	28.8977	1.64128
$311$	−27.7173	−1.57171	−0.785853	−	0.618413i	$-0.787776\pi$
$311$	−27.7173	−1.57171	−0.785853	+	0.618413i	$0.787776\pi$
$312$	−5.90981	−0.334577
$313$	11.5258	0.651476	0.325738	−	0.945460i	$-0.394387\pi$
$313$	11.5258	0.651476	0.325738	+	0.945460i	$0.394387\pi$
$314$	20.6199	1.16365
$315$	71.6715	4.03823
$316$	9.15777	0.515165
$317$	33.8977	1.90389	0.951943	−	0.306275i	$-0.0990827\pi$
$317$	33.8977	1.90389	0.951943	+	0.306275i	$0.0990827\pi$
$318$	−35.2890	−1.97891
$319$	5.57889	0.312358
$320$	−4.12398	−0.230538
$321$	10.3647	0.578502
$322$	22.9879	1.28107
$323$	0	0
$324$	−4.36471	−0.242484
$325$	26.5861	1.47473
$326$	−17.8341	−0.987739
$327$	−13.2745	−0.734083
$328$	11.9170	0.658009
$329$	−31.9693	−1.76252
$330$	−11.0072	−0.605928
$331$	16.2697	0.894262	0.447131	−	0.894468i	$-0.352446\pi$
$331$	16.2697	0.894262	0.447131	+	0.894468i	$0.352446\pi$
$332$	−13.2142	−0.725222
$333$	12.0000	0.657596
$334$	−4.18038	−0.228740
$335$	5.37919	0.293896
$336$	11.2480	0.613627
$337$	6.82685	0.371882	0.185941	−	0.982561i	$-0.440467\pi$
$337$	6.82685	0.371882	0.185941	+	0.982561i	$0.440467\pi$
$338$	−8.09743	−0.440442
$339$	−21.3526	−1.15972
$340$	14.2480	0.772704
$341$	7.00724	0.379463
$342$	0	0
$343$	−15.8422	−0.855400
$344$	1.46214	0.0788334
$345$	−60.0434	−3.23263
$346$	−23.7101	−1.27466
$347$	−5.09019	−0.273256	−0.136628	−	0.990622i	$-0.543626\pi$
$347$	−5.09019	−0.273256	−0.136628	+	0.990622i	$0.543626\pi$
$348$	14.8905	0.798214
$349$	30.9919	1.65896	0.829478	−	0.558539i	$-0.188638\pi$
$349$	30.9919	1.65896	0.829478	+	0.558539i	$0.188638\pi$
$350$	−50.6006	−2.70472
$351$	−6.64252	−0.354552
$352$	−1.00000	−0.0533002
$353$	−17.8301	−0.949003	−0.474501	−	0.880255i	$-0.657372\pi$
$353$	−17.8301	−0.949003	−0.474501	+	0.880255i	$0.657372\pi$
$354$	12.7931	0.679944
$355$	−28.0443	−1.48844
$356$	−8.24797	−0.437141
$357$	−38.8606	−2.05672
$358$	10.8269	0.572217
$359$	24.4090	1.28826	0.644130	−	0.764916i	$-0.277220\pi$
$359$	24.4090	1.28826	0.644130	+	0.764916i	$0.277220\pi$
$360$	−17.0072	−0.896360
$361$	0	0
$362$	17.8341	0.937339
$363$	−2.66908	−0.140090
$364$	−9.33092	−0.489073
$365$	6.00000	0.314054
$366$	−23.7810	−1.24305
$367$	−26.6232	−1.38972	−0.694860	−	0.719145i	$-0.744534\pi$
$367$	−26.6232	−1.38972	−0.694860	+	0.719145i	$0.744534\pi$
$368$	−5.45490	−0.284357
$369$	49.1457	2.55842
$370$	−12.0000	−0.623850
$371$	−55.7173	−2.89270
$372$	18.7029	0.969699
$373$	12.6160	0.653230	0.326615	−	0.945157i	$-0.394092\pi$
$373$	12.6160	0.653230	0.326615	+	0.945157i	$0.394092\pi$
$374$	3.45490	0.178649
$375$	77.1303	3.98299
$376$	7.58612	0.391225
$377$	−12.3526	−0.636193
$378$	12.6425	0.650261
$379$	22.8905	1.17581	0.587903	−	0.808932i	$-0.299954\pi$
$379$	22.8905	1.17581	0.587903	+	0.808932i	$0.299954\pi$
$380$	0	0
$381$	−6.62321	−0.339317
$382$	0.612679	0.0313474
$383$	0.0298464	0.00152508	0.000762539	−	1.00000i	$-0.499757\pi$
$383$	0.0298464	0.00152508	0.000762539		1.00000i	$0.499757\pi$
$384$	−2.66908	−0.136206
$385$	−17.3792	−0.885725
$386$	−11.6425	−0.592589
$387$	6.02985	0.306514
$388$	−2.18038	−0.110692
$389$	9.22865	0.467911	0.233956	−	0.972247i	$-0.424833\pi$
$389$	9.22865	0.467911	0.233956	+	0.972247i	$0.424833\pi$
$390$	24.3719	1.23412
$391$	18.8462	0.953092
$392$	10.7593	0.543425
$393$	−29.3792	−1.48198
$394$	−12.9098	−0.650387
$395$	−37.7665	−1.90024
$396$	−4.12398	−0.207238
$397$	17.2697	0.866740	0.433370	−	0.901216i	$-0.357324\pi$
$397$	17.2697	0.866740	0.433370	+	0.901216i	$0.357324\pi$
$398$	−18.3647	−0.920540
$399$	0	0
$400$	12.0072	0.600362
$401$	13.2850	0.663424	0.331712	−	0.943381i	$-0.392374\pi$
$401$	13.2850	0.663424	0.331712	+	0.943381i	$0.392374\pi$
$402$	3.48146	0.173639
$403$	−15.5152	−0.772870
$404$	−6.24797	−0.310848
$405$	18.0000	0.894427
$406$	23.5104	1.16680
$407$	−2.90981	−0.144234
$408$	9.22141	0.456528
$409$	−1.94360	−0.0961048	−0.0480524	−	0.998845i	$-0.515301\pi$
$409$	−1.94360	−0.0961048	−0.0480524	+	0.998845i	$0.515301\pi$
$410$	−49.1457	−2.42713
$411$	−18.5330	−0.914166
$412$	−0.605441	−0.0298280
$413$	20.1988	0.993918
$414$	−22.4959	−1.10561
$415$	54.4950	2.67506
$416$	2.21417	0.108559
$417$	11.6691	0.571437
$418$	0	0
$419$	−2.49593	−0.121934	−0.0609671	−	0.998140i	$-0.519418\pi$
$419$	−2.49593	−0.121934	−0.0609671	+	0.998140i	$0.519418\pi$
$420$	−46.3864	−2.26343
$421$	−15.6353	−0.762017	−0.381009	−	0.924571i	$-0.624423\pi$
$421$	−15.6353	−0.762017	−0.381009	+	0.924571i	$0.624423\pi$
$422$	−2.13122	−0.103746
$423$	31.2850	1.52113
$424$	13.2214	0.642089
$425$	−41.4839	−2.01226
$426$	−18.1505	−0.879396
$427$	−37.5475	−1.81705
$428$	−3.88325	−0.187704
$429$	5.90981	0.285328
$430$	−6.02985	−0.290785
$431$	−0.262441	−0.0126413	−0.00632067	−	0.999980i	$-0.502012\pi$
$431$	−0.262441	−0.0126413	−0.00632067	+	0.999980i	$0.502012\pi$
$432$	−3.00000	−0.144338
$433$	32.2769	1.55113	0.775565	−	0.631268i	$-0.217465\pi$
$433$	32.2769	1.55113	0.775565	+	0.631268i	$0.217465\pi$
$434$	29.5297	1.41747
$435$	−61.4081	−2.94429
$436$	4.97345	0.238185
$437$	0	0
$438$	3.88325	0.185549
$439$	17.0902	0.815670	0.407835	−	0.913056i	$-0.366284\pi$
$439$	17.0902	0.815670	0.407835	+	0.913056i	$0.366284\pi$
$440$	4.12398	0.196603
$441$	44.3711	2.11291
$442$	−7.64976	−0.363862
$443$	16.2624	0.772652	0.386326	−	0.922362i	$-0.373744\pi$
$443$	16.2624	0.772652	0.386326	+	0.922362i	$0.373744\pi$
$444$	−7.76651	−0.368582
$445$	34.0145	1.61244
$446$	−6.90981	−0.327189
$447$	−31.4057	−1.48544
$448$	−4.21417	−0.199101
$449$	27.3382	1.29017	0.645084	−	0.764112i	$-0.276822\pi$
$449$	27.3382	1.29017	0.645084	+	0.764112i	$0.276822\pi$
$450$	49.5176	2.33428
$451$	−11.9170	−0.561152
$452$	8.00000	0.376288
$453$	−52.2769	−2.45618
$454$	2.72548	0.127913
$455$	38.4806	1.80400
$456$	0	0
$457$	10.4920	0.490794	0.245397	−	0.969423i	$-0.421082\pi$
$457$	10.4920	0.490794	0.245397	+	0.969423i	$0.421082\pi$
$458$	3.48870	0.163016
$459$	10.3647	0.483783
$460$	22.4959	1.04888
$461$	6.18038	0.287849	0.143925	−	0.989589i	$-0.454028\pi$
$461$	6.18038	0.287849	0.143925	+	0.989589i	$0.454028\pi$
$462$	−11.2480	−0.523303
$463$	−11.1433	−0.517873	−0.258937	−	0.965894i	$-0.583372\pi$
$463$	−11.1433	−0.517873	−0.258937	+	0.965894i	$0.583372\pi$
$464$	−5.57889	−0.258993
$465$	−77.1303	−3.57683
$466$	−17.0902	−0.791688
$467$	−34.5104	−1.59695	−0.798476	−	0.602027i	$-0.794360\pi$
$467$	−34.5104	−1.59695	−0.798476	+	0.602027i	$0.794360\pi$
$468$	9.13122	0.422091
$469$	5.49683	0.253820
$470$	−31.2850	−1.44307
$471$	−55.0362	−2.53593
$472$	−4.79306	−0.220619
$473$	−1.46214	−0.0672293
$474$	−24.4428	−1.12270
$475$	0	0
$476$	14.5596	0.667337
$477$	54.5249	2.49652
$478$	6.06035	0.277194
$479$	41.6980	1.90523	0.952616	−	0.304176i	$-0.0983812\pi$
$479$	41.6980	1.90523	0.952616	+	0.304176i	$0.0983812\pi$
$480$	11.0072	0.502409
$481$	6.44282	0.293768
$482$	−4.85341	−0.221067
$483$	−61.3566	−2.79182
$484$	1.00000	0.0454545
$485$	8.99187	0.408300
$486$	20.6498	0.936692
$487$	−9.10137	−0.412423	−0.206211	−	0.978507i	$-0.566113\pi$
$487$	−9.10137	−0.412423	−0.206211	+	0.978507i	$0.566113\pi$
$488$	8.90981	0.403328
$489$	47.6006	2.15257
$490$	−44.3711	−2.00448
$491$	−30.8413	−1.39185	−0.695925	−	0.718115i	$-0.745005\pi$
$491$	−30.8413	−1.39185	−0.695925	+	0.718115i	$0.745005\pi$
$492$	−31.8075	−1.43399
$493$	19.2745	0.868081
$494$	0	0
$495$	17.0072	0.764418
$496$	−7.00724	−0.314634
$497$	−28.6577	−1.28547
$498$	35.2697	1.58047
$499$	21.7665	0.974403	0.487201	−	0.873290i	$-0.338018\pi$
$499$	21.7665	0.974403	0.487201	+	0.873290i	$0.338018\pi$
$500$	−28.8977	−1.29235
$501$	11.1578	0.498493
$502$	−1.58612	−0.0707922
$503$	38.0893	1.69832	0.849159	−	0.528138i	$-0.177109\pi$
$503$	38.0893	1.69832	0.849159	+	0.528138i	$0.177109\pi$
$504$	−17.3792	−0.774131
$505$	25.7665	1.14659
$506$	5.45490	0.242500
$507$	21.6127	0.959853
$508$	2.48146	0.110097
$509$	−14.9388	−0.662149	−0.331074	−	0.943605i	$-0.607411\pi$
$509$	−14.9388	−0.662149	−0.331074	+	0.943605i	$0.607411\pi$
$510$	−38.0289	−1.68395
$511$	6.13122	0.271229
$512$	1.00000	0.0441942
$513$	0	0
$514$	−19.5185	−0.860926
$515$	2.49683	0.110023
$516$	−3.90257	−0.171801
$517$	−7.58612	−0.333637
$518$	−12.2624	−0.538781
$519$	63.2842	2.77787
$520$	−9.13122	−0.400431
$521$	−7.22536	−0.316549	−0.158274	−	0.987395i	$-0.550593\pi$
$521$	−7.22536	−0.316549	−0.158274	+	0.987395i	$0.550593\pi$
$522$	−23.0072	−1.00700
$523$	−4.90586	−0.214518	−0.107259	−	0.994231i	$-0.534207\pi$
$523$	−4.90586	−0.214518	−0.107259	+	0.994231i	$0.534207\pi$
$524$	11.0072	0.480853
$525$	135.057	5.89437
$526$	−13.0483	−0.568931
$527$	24.2093	1.05458
$528$	2.66908	0.116157
$529$	6.75598	0.293738
$530$	−54.5249	−2.36841
$531$	−19.7665	−0.857793
$532$	0	0
$533$	26.3864	1.14292
$534$	22.0145	0.952659
$535$	16.0145	0.692366
$536$	−1.30437	−0.0563401
$537$	−28.8977	−1.24703
$538$	−23.6006	−1.01749
$539$	−10.7593	−0.463435
$540$	12.3719	0.532404
$541$	30.8712	1.32726	0.663628	−	0.748063i	$-0.269016\pi$
$541$	30.8712	1.32726	0.663628	+	0.748063i	$0.269016\pi$
$542$	−16.4090	−0.704828
$543$	−47.6006	−2.04274
$544$	−3.45490	−0.148128
$545$	−20.5104	−0.878569
$546$	24.9050	1.06583
$547$	−2.54115	−0.108652	−0.0543259	−	0.998523i	$-0.517301\pi$
$547$	−2.54115	−0.108652	−0.0543259	+	0.998523i	$0.517301\pi$
$548$	6.94360	0.296616
$549$	36.7439	1.56819
$550$	−12.0072	−0.511990
$551$	0	0
$552$	14.5596	0.619696
$553$	−38.5925	−1.64112
$554$	−11.5861	−0.492247
$555$	32.0289	1.35955
$556$	−4.37195	−0.185412
$557$	23.9017	1.01275	0.506373	−	0.862314i	$-0.330986\pi$
$557$	23.9017	1.01275	0.506373	+	0.862314i	$0.330986\pi$
$558$	−28.8977	−1.22334
$559$	3.23744	0.136929
$560$	17.3792	0.734405
$561$	−9.22141	−0.389328
$562$	−7.03379	−0.296703
$563$	10.6232	0.447715	0.223857	−	0.974622i	$-0.428135\pi$
$563$	10.6232	0.447715	0.223857	+	0.974622i	$0.428135\pi$
$564$	−20.2480	−0.852593
$565$	−32.9919	−1.38798
$566$	8.33092	0.350175
$567$	18.3937	0.772461
$568$	6.80030	0.285334
$569$	−29.3373	−1.22988	−0.614941	−	0.788573i	$-0.710820\pi$
$569$	−29.3373	−1.22988	−0.614941	+	0.788573i	$0.710820\pi$
$570$	0	0
$571$	19.8639	0.831280	0.415640	−	0.909529i	$-0.363558\pi$
$571$	19.8639	0.831280	0.415640	+	0.909529i	$0.363558\pi$
$572$	−2.21417	−0.0925793
$573$	−1.63529	−0.0683151
$574$	−50.2205	−2.09616
$575$	−65.4983	−2.73147
$576$	4.12398	0.171833
$577$	−3.17709	−0.132264	−0.0661320	−	0.997811i	$-0.521066\pi$
$577$	−3.17709	−0.132264	−0.0661320	+	0.997811i	$0.521066\pi$
$578$	−5.06364	−0.210620
$579$	31.0748	1.29143
$580$	23.0072	0.955324
$581$	55.6868	2.31028
$582$	5.81962	0.241231
$583$	−13.2214	−0.547575
$584$	−1.45490	−0.0602044
$585$	−37.6570	−1.55693
$586$	−10.2142	−0.421944
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	−28.7173	−1.18428
$589$	0	0
$590$	19.7665	0.813774
$591$	34.4573	1.41738
$592$	2.90981	0.119592
$593$	−3.45885	−0.142038	−0.0710190	−	0.997475i	$-0.522625\pi$
$593$	−3.45885	−0.142038	−0.0710190	+	0.997475i	$0.522625\pi$
$594$	3.00000	0.123091
$595$	−60.0434	−2.46154
$596$	11.7665	0.481975
$597$	49.0169	2.00613
$598$	−12.0781	−0.493911
$599$	−40.3864	−1.65014	−0.825072	−	0.565027i	$-0.808866\pi$
$599$	−40.3864	−1.65014	−0.825072	+	0.565027i	$0.808866\pi$
$600$	−32.0483	−1.30836
$601$	−18.3309	−0.747734	−0.373867	−	0.927482i	$-0.621968\pi$
$601$	−18.3309	−0.747734	−0.373867	+	0.927482i	$0.621968\pi$
$602$	−6.16172	−0.251133
$603$	−5.37919	−0.219057
$604$	19.5861	0.796948
$605$	−4.12398	−0.167664
$606$	16.6763	0.677429
$607$	−12.4283	−0.504451	−0.252226	−	0.967668i	$-0.581162\pi$
$607$	−12.4283	−0.504451	−0.252226	+	0.967668i	$0.581162\pi$
$608$	0	0
$609$	−62.7511	−2.54280
$610$	−36.7439	−1.48772
$611$	16.7970	0.679534
$612$	−14.2480	−0.575940
$613$	−0.0531082	−0.00214502	−0.00107251	−	0.999999i	$-0.500341\pi$
$613$	−0.0531082	−0.00214502	−0.00107251	+	0.999999i	$0.500341\pi$
$614$	1.93242	0.0779860
$615$	131.174	5.28944
$616$	4.21417	0.169794
$617$	−17.4887	−0.704068	−0.352034	−	0.935987i	$-0.614510\pi$
$617$	−17.4887	−0.704068	−0.352034	+	0.935987i	$0.614510\pi$
$618$	1.61597	0.0650039
$619$	25.2995	1.01687	0.508437	−	0.861099i	$-0.330224\pi$
$619$	25.2995	1.01687	0.508437	+	0.861099i	$0.330224\pi$
$620$	28.8977	1.16056
$621$	16.3647	0.656693
$622$	−27.7173	−1.11136
$623$	34.7584	1.39256
$624$	−5.90981	−0.236582
$625$	59.1376	2.36550
$626$	11.5258	0.460663
$627$	0	0
$628$	20.6199	0.822824
$629$	−10.0531	−0.400844
$630$	71.6715	2.85546
$631$	9.02261	0.359184	0.179592	−	0.983741i	$-0.442522\pi$
$631$	9.02261	0.359184	0.179592	+	0.983741i	$0.442522\pi$
$632$	9.15777	0.364277
$633$	5.68840	0.226093
$634$	33.8977	1.34625
$635$	−10.2335	−0.406104
$636$	−35.2890	−1.39930
$637$	23.8229	0.943898
$638$	5.57889	0.220870
$639$	28.0443	1.10942
$640$	−4.12398	−0.163015
$641$	−30.4573	−1.20299	−0.601495	−	0.798876i	$-0.705428\pi$
$641$	−30.4573	−1.20299	−0.601495	+	0.798876i	$0.705428\pi$
$642$	10.3647	0.409063
$643$	−36.7584	−1.44961	−0.724804	−	0.688955i	$-0.758070\pi$
$643$	−36.7584	−1.44961	−0.724804	+	0.688955i	$0.758070\pi$
$644$	22.9879	0.905851
$645$	16.0941	0.633706
$646$	0	0
$647$	−41.0700	−1.61463	−0.807314	−	0.590122i	$-0.799079\pi$
$647$	−41.0700	−1.61463	−0.807314	+	0.590122i	$0.799079\pi$
$648$	−4.36471	−0.171462
$649$	4.79306	0.188144
$650$	26.5861	1.04279
$651$	−78.8172	−3.08909
$652$	−17.8341	−0.698437
$653$	28.4806	1.11453	0.557265	−	0.830335i	$-0.311851\pi$
$653$	28.4806	1.11453	0.557265	+	0.830335i	$0.311851\pi$
$654$	−13.2745	−0.519075
$655$	−45.3937	−1.77368
$656$	11.9170	0.465282
$657$	−6.00000	−0.234082
$658$	−31.9693	−1.24629
$659$	10.5740	0.411906	0.205953	−	0.978562i	$-0.433971\pi$
$659$	10.5740	0.411906	0.205953	+	0.978562i	$0.433971\pi$
$660$	−11.0072	−0.428456
$661$	−7.70287	−0.299607	−0.149803	−	0.988716i	$-0.547864\pi$
$661$	−7.70287	−0.299607	−0.149803	+	0.988716i	$0.547864\pi$
$662$	16.2697	0.632339
$663$	20.4178	0.792962
$664$	−13.2142	−0.512809
$665$	0	0
$666$	12.0000	0.464991
$667$	30.4323	1.17834
$668$	−4.18038	−0.161744
$669$	18.4428	0.713041
$670$	5.37919	0.207816
$671$	−8.90981	−0.343959
$672$	11.2480	0.433900
$673$	31.5176	1.21492	0.607458	−	0.794352i	$-0.292189\pi$
$673$	31.5176	1.21492	0.607458	+	0.794352i	$0.292189\pi$
$674$	6.82685	0.262961
$675$	−36.0217	−1.38648
$676$	−8.09743	−0.311440
$677$	−11.9928	−0.460919	−0.230460	−	0.973082i	$-0.574023\pi$
$677$	−11.9928	−0.460919	−0.230460	+	0.973082i	$0.574023\pi$
$678$	−21.3526	−0.820043
$679$	9.18852	0.352623
$680$	14.2480	0.546385
$681$	−7.27452	−0.278760
$682$	7.00724	0.268321
$683$	−39.1722	−1.49888	−0.749442	−	0.662070i	$-0.769678\pi$
$683$	−39.1722	−1.49888	−0.749442	+	0.662070i	$0.769678\pi$
$684$	0	0
$685$	−28.6353	−1.09410
$686$	−15.8422	−0.604859
$687$	−9.31160	−0.355260
$688$	1.46214	0.0557436
$689$	29.2745	1.11527
$690$	−60.0434	−2.28581
$691$	−49.1722	−1.87060	−0.935300	−	0.353855i	$-0.884871\pi$
$691$	−49.1722	−1.87060	−0.935300	+	0.353855i	$0.884871\pi$
$692$	−23.7101	−0.901323
$693$	17.3792	0.660181
$694$	−5.09019	−0.193221
$695$	18.0298	0.683911
$696$	14.8905	0.564423
$697$	−41.1722	−1.55951
$698$	30.9919	1.17306
$699$	45.6151	1.72532
$700$	−50.6006	−1.91252
$701$	37.8486	1.42952	0.714760	−	0.699370i	$-0.246536\pi$
$701$	37.8486	1.42952	0.714760	+	0.699370i	$0.246536\pi$
$702$	−6.64252	−0.250706
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	83.5023	3.14488
$706$	−17.8301	−0.671046
$707$	26.3300	0.990242
$708$	12.7931	0.480793
$709$	27.7511	1.04222	0.521108	−	0.853491i	$-0.325519\pi$
$709$	27.7511	1.04222	0.521108	+	0.853491i	$0.325519\pi$
$710$	−28.0443	−1.05248
$711$	37.7665	1.41635
$712$	−8.24797	−0.309106
$713$	38.2238	1.43149
$714$	−38.8606	−1.45432
$715$	9.13122	0.341488
$716$	10.8269	0.404619
$717$	−16.1755	−0.604087
$718$	24.4090	0.910937
$719$	−17.0410	−0.635523	−0.317762	−	0.948171i	$-0.602931\pi$
$719$	−17.0410	−0.635523	−0.317762	+	0.948171i	$0.602931\pi$
$720$	−17.0072	−0.633822
$721$	2.55144	0.0950204
$722$	0	0
$723$	12.9541	0.481769
$724$	17.8341	0.662799
$725$	−66.9870	−2.48784
$726$	−2.66908	−0.0990588
$727$	13.5225	0.501521	0.250761	−	0.968049i	$-0.419319\pi$
$727$	13.5225	0.501521	0.250761	+	0.968049i	$0.419319\pi$
$728$	−9.33092	−0.345827
$729$	−42.0217	−1.55636
$730$	6.00000	0.222070
$731$	−5.05156	−0.186839
$732$	−23.7810	−0.878970
$733$	−25.6682	−0.948076	−0.474038	−	0.880504i	$-0.657204\pi$
$733$	−25.6682	−0.948076	−0.474038	+	0.880504i	$0.657204\pi$
$734$	−26.6232	−0.982681
$735$	118.430	4.36835
$736$	−5.45490	−0.201070
$737$	1.30437	0.0480470
$738$	49.1457	1.80908
$739$	21.3493	0.785348	0.392674	−	0.919678i	$-0.371550\pi$
$739$	21.3493	0.785348	0.392674	+	0.919678i	$0.371550\pi$
$740$	−12.0000	−0.441129
$741$	0	0
$742$	−55.7173	−2.04545
$743$	7.55718	0.277246	0.138623	−	0.990345i	$-0.455732\pi$
$743$	7.55718	0.277246	0.138623	+	0.990345i	$0.455732\pi$
$744$	18.7029	0.685680
$745$	−48.5249	−1.77781
$746$	12.6160	0.461904
$747$	−54.4950	−1.99387
$748$	3.45490	0.126324
$749$	16.3647	0.597954
$750$	77.1303	2.81640
$751$	53.5861	1.95539	0.977693	−	0.210040i	$-0.0673595\pi$
$751$	53.5861	1.95539	0.977693	+	0.210040i	$0.0673595\pi$
$752$	7.58612	0.276637
$753$	4.23349	0.154277
$754$	−12.3526	−0.449856
$755$	−80.7728	−2.93962
$756$	12.6425	0.459804
$757$	−13.9436	−0.506789	−0.253394	−	0.967363i	$-0.581547\pi$
$757$	−13.9436	−0.506789	−0.253394	+	0.967363i	$0.581547\pi$
$758$	22.8905	0.831420
$759$	−14.5596	−0.528479
$760$	0	0
$761$	−45.7994	−1.66023	−0.830114	−	0.557594i	$-0.811724\pi$
$761$	−45.7994	−1.66023	−0.830114	+	0.557594i	$0.811724\pi$
$762$	−6.62321	−0.239934
$763$	−20.9590	−0.758766
$764$	0.612679	0.0221659
$765$	58.7584	2.12441
$766$	0.0298464	0.00107839
$767$	−10.6127	−0.383202
$768$	−2.66908	−0.0963121
$769$	−40.8751	−1.47399	−0.736997	−	0.675896i	$-0.763757\pi$
$769$	−40.8751	−1.47399	−0.736997	+	0.675896i	$0.763757\pi$
$770$	−17.3792	−0.626302
$771$	52.0965	1.87621
$772$	−11.6425	−0.419024
$773$	−37.4983	−1.34872	−0.674361	−	0.738402i	$-0.735581\pi$
$773$	−37.4983	−1.34872	−0.674361	+	0.738402i	$0.735581\pi$
$774$	6.02985	0.216738
$775$	−84.1376	−3.02231
$776$	−2.18038	−0.0782712
$777$	32.7294	1.17416
$778$	9.22865	0.330863
$779$	0	0
$780$	24.3719	0.872656
$781$	−6.80030	−0.243334
$782$	18.8462	0.673938
$783$	16.7367	0.598119
$784$	10.7593	0.384260
$785$	−85.0362	−3.03507
$786$	−29.3792	−1.04792
$787$	−8.80754	−0.313955	−0.156977	−	0.987602i	$-0.550175\pi$
$787$	−8.80754	−0.313955	−0.156977	+	0.987602i	$0.550175\pi$
$788$	−12.9098	−0.459893
$789$	34.8269	1.23987
$790$	−37.7665	−1.34367
$791$	−33.7134	−1.19871
$792$	−4.12398	−0.146539
$793$	19.7279	0.700557
$794$	17.2697	0.612878
$795$	145.531	5.16146
$796$	−18.3647	−0.650920
$797$	26.1312	0.925615	0.462808	−	0.886459i	$-0.346842\pi$
$797$	26.1312	0.925615	0.462808	+	0.886459i	$0.346842\pi$
$798$	0	0
$799$	−26.2093	−0.927220
$800$	12.0072	0.424520
$801$	−34.0145	−1.20184
$802$	13.2850	0.469111
$803$	1.45490	0.0513425
$804$	3.48146	0.122782
$805$	−94.8018	−3.34132
$806$	−15.5152	−0.546501
$807$	62.9919	2.21742
$808$	−6.24797	−0.219803
$809$	−6.01053	−0.211319	−0.105659	−	0.994402i	$-0.533695\pi$
$809$	−6.01053	−0.211319	−0.105659	+	0.994402i	$0.533695\pi$
$810$	18.0000	0.632456
$811$	40.2809	1.41445	0.707226	−	0.706987i	$-0.249946\pi$
$811$	40.2809	1.41445	0.707226	+	0.706987i	$0.249946\pi$
$812$	23.5104	0.825054
$813$	43.7970	1.53603
$814$	−2.90981	−0.101989
$815$	73.5475	2.57626
$816$	9.22141	0.322814
$817$	0	0
$818$	−1.94360	−0.0679564
$819$	−38.4806	−1.34462
$820$	−49.1457	−1.71624
$821$	50.1496	1.75023	0.875117	−	0.483911i	$-0.160784\pi$
$821$	50.1496	1.75023	0.875117	+	0.483911i	$0.160784\pi$
$822$	−18.5330	−0.646413
$823$	−42.7400	−1.48982	−0.744911	−	0.667164i	$-0.767508\pi$
$823$	−42.7400	−1.48982	−0.744911	+	0.667164i	$0.767508\pi$
$824$	−0.605441	−0.0210915
$825$	32.0483	1.11578
$826$	20.1988	0.702806
$827$	−49.0555	−1.70583	−0.852913	−	0.522052i	$-0.825167\pi$
$827$	−49.0555	−1.70583	−0.852913	+	0.522052i	$0.825167\pi$
$828$	−22.4959	−0.781788
$829$	−49.9653	−1.73537	−0.867683	−	0.497117i	$-0.834392\pi$
$829$	−49.9653	−1.73537	−0.867683	+	0.497117i	$0.834392\pi$
$830$	54.4950	1.89155
$831$	30.9243	1.07275
$832$	2.21417	0.0767627
$833$	−37.1722	−1.28794
$834$	11.6691	0.404067
$835$	17.2398	0.596609
$836$	0	0
$837$	21.0217	0.726617
$838$	−2.49593	−0.0862206
$839$	52.0257	1.79613	0.898063	−	0.439868i	$-0.144975\pi$
$839$	52.0257	1.79613	0.898063	+	0.439868i	$0.144975\pi$
$840$	−46.3864	−1.60048
$841$	2.12398	0.0732408
$842$	−15.6353	−0.538828
$843$	18.7737	0.646602
$844$	−2.13122	−0.0733596
$845$	33.3937	1.14878
$846$	31.2850	1.07560
$847$	−4.21417	−0.144801
$848$	13.2214	0.454025
$849$	−22.2359	−0.763134
$850$	−41.4839	−1.42288
$851$	−15.8727	−0.544110
$852$	−18.1505	−0.621827
$853$	16.2335	0.555824	0.277912	−	0.960607i	$-0.410358\pi$
$853$	16.2335	0.555824	0.277912	+	0.960607i	$0.410358\pi$
$854$	−37.5475	−1.28485
$855$	0	0
$856$	−3.88325	−0.132727
$857$	−9.60150	−0.327981	−0.163990	−	0.986462i	$-0.552437\pi$
$857$	−9.60150	−0.327981	−0.163990	+	0.986462i	$0.552437\pi$
$858$	5.90981	0.201758
$859$	19.4057	0.662115	0.331058	−	0.943611i	$-0.392595\pi$
$859$	19.4057	0.662115	0.331058	+	0.943611i	$0.392595\pi$
$860$	−6.02985	−0.205616
$861$	134.043	4.56816
$862$	−0.262441	−0.00893877
$863$	−1.54839	−0.0527077	−0.0263539	−	0.999653i	$-0.508390\pi$
$863$	−1.54839	−0.0527077	−0.0263539	+	0.999653i	$0.508390\pi$
$864$	−3.00000	−0.102062
$865$	97.7801	3.32462
$866$	32.2769	1.09681
$867$	13.5152	0.459002
$868$	29.5297	1.00230
$869$	−9.15777	−0.310656
$870$	−61.4081	−2.08193
$871$	−2.88810	−0.0978594
$872$	4.97345	0.168422
$873$	−8.99187	−0.304329
$874$	0	0
$875$	121.780	4.11692
$876$	3.88325	0.131203
$877$	12.1200	0.409265	0.204632	−	0.978839i	$-0.434400\pi$
$877$	12.1200	0.409265	0.204632	+	0.978839i	$0.434400\pi$
$878$	17.0902	0.576766
$879$	27.2624	0.919539
$880$	4.12398	0.139019
$881$	53.6836	1.80864	0.904322	−	0.426850i	$-0.140377\pi$
$881$	53.6836	1.80864	0.904322	+	0.426850i	$0.140377\pi$
$882$	44.3711	1.49405
$883$	34.4283	1.15861	0.579303	−	0.815112i	$-0.303325\pi$
$883$	34.4283	1.15861	0.579303	+	0.815112i	$0.303325\pi$
$884$	−7.64976	−0.257289
$885$	−52.7584	−1.77345
$886$	16.2624	0.546347
$887$	27.5330	0.924468	0.462234	−	0.886758i	$-0.347048\pi$
$887$	27.5330	0.924468	0.462234	+	0.886758i	$0.347048\pi$
$888$	−7.76651	−0.260627
$889$	−10.4573	−0.350727
$890$	34.0145	1.14017
$891$	4.36471	0.146223
$892$	−6.90981	−0.231357
$893$	0	0
$894$	−31.4057	−1.05037
$895$	−44.6498	−1.49248
$896$	−4.21417	−0.140786
$897$	32.2374	1.07638
$898$	27.3382	0.912286
$899$	39.0926	1.30381
$900$	49.5176	1.65059
$901$	−45.6787	−1.52178
$902$	−11.9170	−0.396794
$903$	16.4461	0.547292
$904$	8.00000	0.266076
$905$	−73.5475	−2.44480
$906$	−52.2769	−1.73678
$907$	−15.5677	−0.516917	−0.258459	−	0.966022i	$-0.583215\pi$
$907$	−15.5677	−0.516917	−0.258459	+	0.966022i	$0.583215\pi$
$908$	2.72548	0.0904482
$909$	−25.7665	−0.854621
$910$	38.4806	1.27562
$911$	0.623208	0.0206478	0.0103239	−	0.999947i	$-0.496714\pi$
$911$	0.623208	0.0206478	0.0103239	+	0.999947i	$0.496714\pi$
$912$	0	0
$913$	13.2142	0.437325
$914$	10.4920	0.347044
$915$	98.0724	3.24217
$916$	3.48870	0.115270
$917$	−46.3864	−1.53181
$918$	10.3647	0.342086
$919$	−44.4887	−1.46755	−0.733773	−	0.679394i	$-0.762243\pi$
$919$	−44.4887	−1.46755	−0.733773	+	0.679394i	$0.762243\pi$
$920$	22.4959	0.741669
$921$	−5.15777	−0.169954
$922$	6.18038	0.203540
$923$	15.0571	0.495609
$924$	−11.2480	−0.370031
$925$	34.9388	1.14878
$926$	−11.1433	−0.366192
$927$	−2.49683	−0.0820067
$928$	−5.57889	−0.183136
$929$	44.1224	1.44761	0.723805	−	0.690005i	$-0.242391\pi$
$929$	44.1224	1.44761	0.723805	+	0.690005i	$0.242391\pi$
$930$	−77.1303	−2.52920
$931$	0	0
$932$	−17.0902	−0.559808
$933$	73.9798	2.42199
$934$	−34.5104	−1.12922
$935$	−14.2480	−0.465958
$936$	9.13122	0.298463
$937$	24.8672	0.812377	0.406188	−	0.913789i	$-0.366858\pi$
$937$	24.8672	0.812377	0.406188	+	0.913789i	$0.366858\pi$
$938$	5.49683	0.179478
$939$	−30.7632	−1.00392
$940$	−31.2850	−1.02041
$941$	−29.8301	−0.972435	−0.486217	−	0.873838i	$-0.661624\pi$
$941$	−29.8301	−0.972435	−0.486217	+	0.873838i	$0.661624\pi$
$942$	−55.0362	−1.79318
$943$	−65.0063	−2.11690
$944$	−4.79306	−0.156001
$945$	−52.1376	−1.69603
$946$	−1.46214	−0.0475383
$947$	9.07572	0.294921	0.147461	−	0.989068i	$-0.452890\pi$
$947$	9.07572	0.294921	0.147461	+	0.989068i	$0.452890\pi$
$948$	−24.4428	−0.793866
$949$	−3.22141	−0.104571
$950$	0	0
$951$	−90.4757	−2.93388
$952$	14.5596	0.471878
$953$	−1.27058	−0.0411580	−0.0205790	−	0.999788i	$-0.506551\pi$
$953$	−1.27058	−0.0411580	−0.0205790	+	0.999788i	$0.506551\pi$
$954$	54.5249	1.76531
$955$	−2.52668	−0.0817613
$956$	6.06035	0.196006
$957$	−14.8905	−0.481341
$958$	41.6980	1.34720
$959$	−29.2615	−0.944905
$960$	11.0072	0.355257
$961$	18.1014	0.583915
$962$	6.44282	0.207725
$963$	−16.0145	−0.516059
$964$	−4.85341	−0.156318
$965$	48.0136	1.54561
$966$	−61.3566	−1.97412
$967$	6.67632	0.214696	0.107348	−	0.994222i	$-0.465764\pi$
$967$	6.67632	0.214696	0.107348	+	0.994222i	$0.465764\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	8.99187	0.288711
$971$	0.191566	0.00614764	0.00307382	−	0.999995i	$-0.499022\pi$
$971$	0.191566	0.00614764	0.00307382	+	0.999995i	$0.499022\pi$
$972$	20.6498	0.662341
$973$	18.4242	0.590651
$974$	−9.10137	−0.291627
$975$	−70.9605	−2.27255
$976$	8.90981	0.285196
$977$	−16.4959	−0.527752	−0.263876	−	0.964557i	$-0.585001\pi$
$977$	−16.4959	−0.527752	−0.263876	+	0.964557i	$0.585001\pi$
$978$	47.6006	1.52210
$979$	8.24797	0.263606
$980$	−44.3711	−1.41738
$981$	20.5104	0.654847
$982$	−30.8413	−0.984186
$983$	35.0072	1.11656	0.558279	−	0.829653i	$-0.311462\pi$
$983$	35.0072	1.11656	0.558279	+	0.829653i	$0.311462\pi$
$984$	−31.8075	−1.01399
$985$	53.2398	1.69636
$986$	19.2745	0.613826
$987$	85.3285	2.71604
$988$	0	0
$989$	−7.97584	−0.253617
$990$	17.0072	0.540525
$991$	11.3759	0.361367	0.180684	−	0.983541i	$-0.442169\pi$
$991$	11.3759	0.361367	0.180684	+	0.983541i	$0.442169\pi$
$992$	−7.00724	−0.222480
$993$	−43.4251	−1.37805
$994$	−28.6577	−0.908966
$995$	75.7358	2.40099
$996$	35.2697	1.11756
$997$	8.89533	0.281718	0.140859	−	0.990030i	$-0.455014\pi$
$997$	8.89533	0.281718	0.140859	+	0.990030i	$0.455014\pi$
$998$	21.7665	0.689007
$999$	−8.72942	−0.276187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bi.1.1		3
19.18	odd	2		418.2.a.g.1.3	✓	3
57.56	even	2		3762.2.a.bg.1.3		3
76.75	even	2		3344.2.a.q.1.1		3
209.208	even	2		4598.2.a.bo.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.g.1.3	✓	3	19.18	odd	2
3344.2.a.q.1.1		3	76.75	even	2
3762.2.a.bg.1.3		3	57.56	even	2
4598.2.a.bo.1.3		3	209.208	even	2
7942.2.a.bi.1.1		3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.66908 q^{3} +1.00000 q^{4} -4.12398 q^{5} -2.66908 q^{6} -4.21417 q^{7} +1.00000 q^{8} +4.12398 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.66908 q^{3} +1.00000 q^{4} -4.12398 q^{5} -2.66908 q^{6} -4.21417 q^{7} +1.00000 q^{8} +4.12398 q^{9} -4.12398 q^{10} -1.00000 q^{11} -2.66908 q^{12} +2.21417 q^{13} -4.21417 q^{14} +11.0072 q^{15} +1.00000 q^{16} -3.45490 q^{17} +4.12398 q^{18} -4.12398 q^{20} +11.2480 q^{21} -1.00000 q^{22} -5.45490 q^{23} -2.66908 q^{24} +12.0072 q^{25} +2.21417 q^{26} -3.00000 q^{27} -4.21417 q^{28} -5.57889 q^{29} +11.0072 q^{30} -7.00724 q^{31} +1.00000 q^{32} +2.66908 q^{33} -3.45490 q^{34} +17.3792 q^{35} +4.12398 q^{36} +2.90981 q^{37} -5.90981 q^{39} -4.12398 q^{40} +11.9170 q^{41} +11.2480 q^{42} +1.46214 q^{43} -1.00000 q^{44} -17.0072 q^{45} -5.45490 q^{46} +7.58612 q^{47} -2.66908 q^{48} +10.7593 q^{49} +12.0072 q^{50} +9.22141 q^{51} +2.21417 q^{52} +13.2214 q^{53} -3.00000 q^{54} +4.12398 q^{55} -4.21417 q^{56} -5.57889 q^{58} -4.79306 q^{59} +11.0072 q^{60} +8.90981 q^{61} -7.00724 q^{62} -17.3792 q^{63} +1.00000 q^{64} -9.13122 q^{65} +2.66908 q^{66} -1.30437 q^{67} -3.45490 q^{68} +14.5596 q^{69} +17.3792 q^{70} +6.80030 q^{71} +4.12398 q^{72} -1.45490 q^{73} +2.90981 q^{74} -32.0483 q^{75} +4.21417 q^{77} -5.90981 q^{78} +9.15777 q^{79} -4.12398 q^{80} -4.36471 q^{81} +11.9170 q^{82} -13.2142 q^{83} +11.2480 q^{84} +14.2480 q^{85} +1.46214 q^{86} +14.8905 q^{87} -1.00000 q^{88} -8.24797 q^{89} -17.0072 q^{90} -9.33092 q^{91} -5.45490 q^{92} +18.7029 q^{93} +7.58612 q^{94} -2.66908 q^{96} -2.18038 q^{97} +10.7593 q^{98} -4.12398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 6 q^{14} + 9 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} + 15 q^{21} - 3 q^{22} - 15 q^{23} + 12 q^{25} - 9 q^{27} - 6 q^{28} - 6 q^{29} + 9 q^{30} + 3 q^{31} + 3 q^{32} - 9 q^{34} + 3 q^{36} + 6 q^{37} - 15 q^{39} - 3 q^{40} + 9 q^{41} + 15 q^{42} - 21 q^{43} - 3 q^{44} - 27 q^{45} - 15 q^{46} - 12 q^{47} + 27 q^{49} + 12 q^{50} - 3 q^{51} + 9 q^{53} - 9 q^{54} + 3 q^{55} - 6 q^{56} - 6 q^{58} + 3 q^{59} + 9 q^{60} + 24 q^{61} + 3 q^{62} + 3 q^{64} + 6 q^{65} - 9 q^{68} - 3 q^{69} - 21 q^{71} + 3 q^{72} - 3 q^{73} + 6 q^{74} - 36 q^{75} + 6 q^{77} - 15 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} - 33 q^{83} + 15 q^{84} + 24 q^{85} - 21 q^{86} + 6 q^{87} - 3 q^{88} - 6 q^{89} - 27 q^{90} - 36 q^{91} - 15 q^{92} + 36 q^{93} - 12 q^{94} - 12 q^{97} + 27 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 6 * q^14 + 9 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 + 15 * q^21 - 3 * q^22 - 15 * q^23 + 12 * q^25 - 9 * q^27 - 6 * q^28 - 6 * q^29 + 9 * q^30 + 3 * q^31 + 3 * q^32 - 9 * q^34 + 3 * q^36 + 6 * q^37 - 15 * q^39 - 3 * q^40 + 9 * q^41 + 15 * q^42 - 21 * q^43 - 3 * q^44 - 27 * q^45 - 15 * q^46 - 12 * q^47 + 27 * q^49 + 12 * q^50 - 3 * q^51 + 9 * q^53 - 9 * q^54 + 3 * q^55 - 6 * q^56 - 6 * q^58 + 3 * q^59 + 9 * q^60 + 24 * q^61 + 3 * q^62 + 3 * q^64 + 6 * q^65 - 9 * q^68 - 3 * q^69 - 21 * q^71 + 3 * q^72 - 3 * q^73 + 6 * q^74 - 36 * q^75 + 6 * q^77 - 15 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 - 33 * q^83 + 15 * q^84 + 24 * q^85 - 21 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 27 * q^90 - 36 * q^91 - 15 * q^92 + 36 * q^93 - 12 * q^94 - 12 * q^97 + 27 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more