LMFDB - Embedded newform 4114.2.a.bk.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4114,2,Mod(1,4114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4114, 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("4114.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4114 = 2 \cdot 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4114.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:	$32.8504553916$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 33x^{7} + 114x^{6} - 152x^{5} - 294x^{4} + 248x^{3} + 346x^{2} - 125x - 145 $ x^10 - 2x^9 - 19x^8 + 33x^7 + 114x^6 - 152x^5 - 294x^4 + 248x^3 + 346x^2 - 125*x - 145
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 374)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$3.40194$ of defining polynomial
Character	$\chi$	$=$	4114.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.40194 q^{3} +1.00000 q^{4} -2.96940 q^{5} -3.40194 q^{6} -1.03413 q^{7} -1.00000 q^{8} +8.57319 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.40194 q^{3} +1.00000 q^{4} -2.96940 q^{5} -3.40194 q^{6} -1.03413 q^{7} -1.00000 q^{8} +8.57319 q^{9} +2.96940 q^{10} +3.40194 q^{12} +0.179416 q^{13} +1.03413 q^{14} -10.1017 q^{15} +1.00000 q^{16} -1.00000 q^{17} -8.57319 q^{18} -4.96908 q^{19} -2.96940 q^{20} -3.51804 q^{21} -5.81120 q^{23} -3.40194 q^{24} +3.81736 q^{25} -0.179416 q^{26} +18.9597 q^{27} -1.03413 q^{28} -7.93856 q^{29} +10.1017 q^{30} +4.71542 q^{31} -1.00000 q^{32} +1.00000 q^{34} +3.07074 q^{35} +8.57319 q^{36} -8.14024 q^{37} +4.96908 q^{38} +0.610363 q^{39} +2.96940 q^{40} -8.88832 q^{41} +3.51804 q^{42} +8.71354 q^{43} -25.4573 q^{45} +5.81120 q^{46} -1.81721 q^{47} +3.40194 q^{48} -5.93058 q^{49} -3.81736 q^{50} -3.40194 q^{51} +0.179416 q^{52} +1.98966 q^{53} -18.9597 q^{54} +1.03413 q^{56} -16.9045 q^{57} +7.93856 q^{58} +1.01628 q^{59} -10.1017 q^{60} -1.47254 q^{61} -4.71542 q^{62} -8.86577 q^{63} +1.00000 q^{64} -0.532759 q^{65} +2.61461 q^{67} -1.00000 q^{68} -19.7693 q^{69} -3.07074 q^{70} -7.73054 q^{71} -8.57319 q^{72} -9.19909 q^{73} +8.14024 q^{74} +12.9864 q^{75} -4.96908 q^{76} -0.610363 q^{78} +6.33727 q^{79} -2.96940 q^{80} +38.7801 q^{81} +8.88832 q^{82} -10.2796 q^{83} -3.51804 q^{84} +2.96940 q^{85} -8.71354 q^{86} -27.0065 q^{87} +2.64124 q^{89} +25.4573 q^{90} -0.185539 q^{91} -5.81120 q^{92} +16.0416 q^{93} +1.81721 q^{94} +14.7552 q^{95} -3.40194 q^{96} +5.24171 q^{97} +5.93058 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9	$ 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9} + 2 q^{12} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 10 q^{17} - 12 q^{18} - 9 q^{19} - 19 q^{21} - 6 q^{23} - 2 q^{24} + 4 q^{25} + 11 q^{27} - 2 q^{28} - 20 q^{29} + 5 q^{30} - q^{31} - 10 q^{32} + 10 q^{34} - 13 q^{35} + 12 q^{36} + 17 q^{37} + 9 q^{38} - 11 q^{39} - 39 q^{41} + 19 q^{42} - 16 q^{43} - 26 q^{45} + 6 q^{46} - 14 q^{47} + 2 q^{48} + 18 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{53} - 11 q^{54} + 2 q^{56} - 24 q^{57} + 20 q^{58} - 4 q^{59} - 5 q^{60} - 22 q^{61} + q^{62} - 29 q^{63} + 10 q^{64} - 52 q^{65} - 13 q^{67} - 10 q^{68} - 30 q^{69} + 13 q^{70} - 7 q^{71} - 12 q^{72} + 6 q^{73} - 17 q^{74} + 45 q^{75} - 9 q^{76} + 11 q^{78} - 19 q^{79} + 34 q^{81} + 39 q^{82} - 19 q^{83} - 19 q^{84} + 16 q^{86} - 29 q^{87} - 8 q^{89} + 26 q^{90} + 9 q^{91} - 6 q^{92} + 3 q^{93} + 14 q^{94} + 27 q^{95} - 2 q^{96} + 39 q^{97} - 18 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9 + 2 * q^12 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 10 * q^17 - 12 * q^18 - 9 * q^19 - 19 * q^21 - 6 * q^23 - 2 * q^24 + 4 * q^25 + 11 * q^27 - 2 * q^28 - 20 * q^29 + 5 * q^30 - q^31 - 10 * q^32 + 10 * q^34 - 13 * q^35 + 12 * q^36 + 17 * q^37 + 9 * q^38 - 11 * q^39 - 39 * q^41 + 19 * q^42 - 16 * q^43 - 26 * q^45 + 6 * q^46 - 14 * q^47 + 2 * q^48 + 18 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^53 - 11 * q^54 + 2 * q^56 - 24 * q^57 + 20 * q^58 - 4 * q^59 - 5 * q^60 - 22 * q^61 + q^62 - 29 * q^63 + 10 * q^64 - 52 * q^65 - 13 * q^67 - 10 * q^68 - 30 * q^69 + 13 * q^70 - 7 * q^71 - 12 * q^72 + 6 * q^73 - 17 * q^74 + 45 * q^75 - 9 * q^76 + 11 * q^78 - 19 * q^79 + 34 * q^81 + 39 * q^82 - 19 * q^83 - 19 * q^84 + 16 * q^86 - 29 * q^87 - 8 * q^89 + 26 * q^90 + 9 * q^91 - 6 * q^92 + 3 * q^93 + 14 * q^94 + 27 * q^95 - 2 * q^96 + 39 * q^97 - 18 * q^98

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
$3$	3.40194	1.96411	0.982055	−	0.188593i	$-0.0603926\pi$
$3$	3.40194	1.96411	0.982055	+	0.188593i	$0.0603926\pi$
$4$	1.00000	0.500000
$5$	−2.96940	−1.32796	−0.663979	−	0.747751i	$-0.731134\pi$
$5$	−2.96940	−1.32796	−0.663979	+	0.747751i	$0.731134\pi$
$6$	−3.40194	−1.38884
$7$	−1.03413	−0.390863	−0.195432	−	0.980717i	$-0.562611\pi$
$7$	−1.03413	−0.390863	−0.195432	+	0.980717i	$0.562611\pi$
$8$	−1.00000	−0.353553
$9$	8.57319	2.85773
$10$	2.96940	0.939008
$11$	0	0
$11$	0	0
$12$	3.40194	0.982055
$13$	0.179416	0.0497611	0.0248806	−	0.999690i	$-0.492079\pi$
$13$	0.179416	0.0497611	0.0248806	+	0.999690i	$0.492079\pi$
$14$	1.03413	0.276382
$15$	−10.1017	−2.60826
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−8.57319	−2.02072
$19$	−4.96908	−1.13999	−0.569993	−	0.821650i	$-0.693054\pi$
$19$	−4.96908	−1.13999	−0.569993	+	0.821650i	$0.693054\pi$
$20$	−2.96940	−0.663979
$21$	−3.51804	−0.767699
$22$	0	0
$23$	−5.81120	−1.21172	−0.605859	−	0.795572i	$-0.707171\pi$
$23$	−5.81120	−1.21172	−0.605859	+	0.795572i	$0.707171\pi$
$24$	−3.40194	−0.694418
$25$	3.81736	0.763472
$26$	−0.179416	−0.0351864
$27$	18.9597	3.64879
$28$	−1.03413	−0.195432
$29$	−7.93856	−1.47415	−0.737077	−	0.675809i	$-0.763795\pi$
$29$	−7.93856	−1.47415	−0.737077	+	0.675809i	$0.763795\pi$
$30$	10.1017	1.84432
$31$	4.71542	0.846915	0.423458	−	0.905916i	$-0.360816\pi$
$31$	4.71542	0.846915	0.423458	+	0.905916i	$0.360816\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	3.07074	0.519050
$36$	8.57319	1.42887
$37$	−8.14024	−1.33825	−0.669124	−	0.743151i	$-0.733330\pi$
$37$	−8.14024	−1.33825	−0.669124	+	0.743151i	$0.733330\pi$
$38$	4.96908	0.806092
$39$	0.610363	0.0977363
$40$	2.96940	0.469504
$41$	−8.88832	−1.38812	−0.694061	−	0.719916i	$-0.744180\pi$
$41$	−8.88832	−1.38812	−0.694061	+	0.719916i	$0.744180\pi$
$42$	3.51804	0.542845
$43$	8.71354	1.32880	0.664401	−	0.747376i	$-0.268687\pi$
$43$	8.71354	1.32880	0.664401	+	0.747376i	$0.268687\pi$
$44$	0	0
$45$	−25.4573	−3.79495
$46$	5.81120	0.856814
$47$	−1.81721	−0.265067	−0.132534	−	0.991179i	$-0.542311\pi$
$47$	−1.81721	−0.265067	−0.132534	+	0.991179i	$0.542311\pi$
$48$	3.40194	0.491028
$49$	−5.93058	−0.847226
$50$	−3.81736	−0.539856
$51$	−3.40194	−0.476367
$52$	0.179416	0.0248806
$53$	1.98966	0.273301	0.136650	−	0.990619i	$-0.456366\pi$
$53$	1.98966	0.273301	0.136650	+	0.990619i	$0.456366\pi$
$54$	−18.9597	−2.58008
$55$	0	0
$56$	1.03413	0.138191
$57$	−16.9045	−2.23906
$58$	7.93856	1.04238
$59$	1.01628	0.132308	0.0661539	−	0.997809i	$-0.478927\pi$
$59$	1.01628	0.132308	0.0661539	+	0.997809i	$0.478927\pi$
$60$	−10.1017	−1.30413
$61$	−1.47254	−0.188540	−0.0942698	−	0.995547i	$-0.530052\pi$
$61$	−1.47254	−0.188540	−0.0942698	+	0.995547i	$0.530052\pi$
$62$	−4.71542	−0.598859
$63$	−8.86577	−1.11698
$64$	1.00000	0.125000
$65$	−0.532759	−0.0660807
$66$	0	0
$67$	2.61461	0.319426	0.159713	−	0.987164i	$-0.448943\pi$
$67$	2.61461	0.319426	0.159713	+	0.987164i	$0.448943\pi$
$68$	−1.00000	−0.121268
$69$	−19.7693	−2.37995
$70$	−3.07074	−0.367024
$71$	−7.73054	−0.917446	−0.458723	−	0.888579i	$-0.651693\pi$
$71$	−7.73054	−0.917446	−0.458723	+	0.888579i	$0.651693\pi$
$72$	−8.57319	−1.01036
$73$	−9.19909	−1.07667	−0.538336	−	0.842730i	$-0.680947\pi$
$73$	−9.19909	−1.07667	−0.538336	+	0.842730i	$0.680947\pi$
$74$	8.14024	0.946284
$75$	12.9864	1.49954
$76$	−4.96908	−0.569993
$77$	0	0
$78$	−0.610363	−0.0691100
$79$	6.33727	0.712998	0.356499	−	0.934296i	$-0.383970\pi$
$79$	6.33727	0.712998	0.356499	+	0.934296i	$0.383970\pi$
$80$	−2.96940	−0.331989
$81$	38.7801	4.30890
$82$	8.88832	0.981550
$83$	−10.2796	−1.12833	−0.564167	−	0.825660i	$-0.690803\pi$
$83$	−10.2796	−1.12833	−0.564167	+	0.825660i	$0.690803\pi$
$84$	−3.51804	−0.383849
$85$	2.96940	0.322077
$86$	−8.71354	−0.939605
$87$	−27.0065	−2.89540
$88$	0	0
$89$	2.64124	0.279971	0.139986	−	0.990154i	$-0.455294\pi$
$89$	2.64124	0.279971	0.139986	+	0.990154i	$0.455294\pi$
$90$	25.4573	2.68343
$91$	−0.185539	−0.0194498
$92$	−5.81120	−0.605859
$93$	16.0416	1.66343
$94$	1.81721	0.187431
$95$	14.7552	1.51385
$96$	−3.40194	−0.347209
$97$	5.24171	0.532215	0.266107	−	0.963943i	$-0.414262\pi$
$97$	5.24171	0.532215	0.266107	+	0.963943i	$0.414262\pi$
$98$	5.93058	0.599079
$99$	0	0
$100$	3.81736	0.381736
$101$	−8.72686	−0.868355	−0.434178	−	0.900827i	$-0.642961\pi$
$101$	−8.72686	−0.868355	−0.434178	+	0.900827i	$0.642961\pi$
$102$	3.40194	0.336842
$103$	−9.33573	−0.919876	−0.459938	−	0.887951i	$-0.652128\pi$
$103$	−9.33573	−0.919876	−0.459938	+	0.887951i	$0.652128\pi$
$104$	−0.179416	−0.0175932
$105$	10.4465	1.01947
$106$	−1.98966	−0.193253
$107$	8.84405	0.854987	0.427493	−	0.904018i	$-0.359397\pi$
$107$	8.84405	0.854987	0.427493	+	0.904018i	$0.359397\pi$
$108$	18.9597	1.82439
$109$	9.37998	0.898440	0.449220	−	0.893421i	$-0.351702\pi$
$109$	9.37998	0.898440	0.449220	+	0.893421i	$0.351702\pi$
$110$	0	0
$111$	−27.6926	−2.62847
$112$	−1.03413	−0.0977158
$113$	15.2877	1.43815	0.719075	−	0.694932i	$-0.244566\pi$
$113$	15.2877	1.43815	0.719075	+	0.694932i	$0.244566\pi$
$114$	16.9045	1.58325
$115$	17.2558	1.60911
$116$	−7.93856	−0.737077
$117$	1.53817	0.142204
$118$	−1.01628	−0.0935557
$119$	1.03413	0.0947983
$120$	10.1017	0.922158
$121$	0	0
$122$	1.47254	0.133318
$123$	−30.2375	−2.72643
$124$	4.71542	0.423458
$125$	3.51174	0.314099
$126$	8.86577	0.789826
$127$	−1.74992	−0.155281	−0.0776403	−	0.996981i	$-0.524739\pi$
$127$	−1.74992	−0.155281	−0.0776403	+	0.996981i	$0.524739\pi$
$128$	−1.00000	−0.0883883
$129$	29.6429	2.60992
$130$	0.532759	0.0467261
$131$	3.46716	0.302927	0.151463	−	0.988463i	$-0.451601\pi$
$131$	3.46716	0.302927	0.151463	+	0.988463i	$0.451601\pi$
$132$	0	0
$133$	5.13866	0.445579
$134$	−2.61461	−0.225868
$135$	−56.2989	−4.84544
$136$	1.00000	0.0857493
$137$	−12.3297	−1.05339	−0.526697	−	0.850053i	$-0.676570\pi$
$137$	−12.3297	−1.05339	−0.526697	+	0.850053i	$0.676570\pi$
$138$	19.7693	1.68288
$139$	8.33547	0.707005	0.353503	−	0.935434i	$-0.384991\pi$
$139$	8.33547	0.707005	0.353503	+	0.935434i	$0.384991\pi$
$140$	3.07074	0.259525
$141$	−6.18203	−0.520621
$142$	7.73054	0.648732
$143$	0	0
$144$	8.57319	0.714433
$145$	23.5728	1.95761
$146$	9.19909	0.761322
$147$	−20.1755	−1.66405
$148$	−8.14024	−0.669124
$149$	−11.6877	−0.957494	−0.478747	−	0.877953i	$-0.658909\pi$
$149$	−11.6877	−0.957494	−0.478747	+	0.877953i	$0.658909\pi$
$150$	−12.9864	−1.06034
$151$	5.96270	0.485237	0.242619	−	0.970122i	$-0.421994\pi$
$151$	5.96270	0.485237	0.242619	+	0.970122i	$0.421994\pi$
$152$	4.96908	0.403046
$153$	−8.57319	−0.693102
$154$	0	0
$155$	−14.0020	−1.12467
$156$	0.610363	0.0488682
$157$	−16.5166	−1.31817	−0.659084	−	0.752069i	$-0.729056\pi$
$157$	−16.5166	−1.31817	−0.659084	+	0.752069i	$0.729056\pi$
$158$	−6.33727	−0.504166
$159$	6.76870	0.536793
$160$	2.96940	0.234752
$161$	6.00952	0.473616
$162$	−38.7801	−3.04685
$163$	−24.8824	−1.94894	−0.974470	−	0.224518i	$-0.927919\pi$
$163$	−24.8824	−1.94894	−0.974470	+	0.224518i	$0.927919\pi$
$164$	−8.88832	−0.694061
$165$	0	0
$166$	10.2796	0.797853
$167$	6.65037	0.514621	0.257310	−	0.966329i	$-0.417164\pi$
$167$	6.65037	0.514621	0.257310	+	0.966329i	$0.417164\pi$
$168$	3.51804	0.271423
$169$	−12.9678	−0.997524
$170$	−2.96940	−0.227743
$171$	−42.6009	−3.25777
$172$	8.71354	0.664401
$173$	−15.1170	−1.14932	−0.574661	−	0.818391i	$-0.694866\pi$
$173$	−15.1170	−1.14932	−0.574661	+	0.818391i	$0.694866\pi$
$174$	27.0065	2.04736
$175$	−3.94764	−0.298413
$176$	0	0
$177$	3.45731	0.259867
$178$	−2.64124	−0.197969
$179$	5.47852	0.409484	0.204742	−	0.978816i	$-0.434364\pi$
$179$	5.47852	0.409484	0.204742	+	0.978816i	$0.434364\pi$
$180$	−25.4573	−1.89747
$181$	−4.46598	−0.331953	−0.165977	−	0.986130i	$-0.553078\pi$
$181$	−4.46598	−0.331953	−0.165977	+	0.986130i	$0.553078\pi$
$182$	0.185539	0.0137531
$183$	−5.00950	−0.370313
$184$	5.81120	0.428407
$185$	24.1717	1.77714
$186$	−16.0416	−1.17623
$187$	0	0
$188$	−1.81721	−0.132534
$189$	−19.6067	−1.42618
$190$	−14.7552	−1.07046
$191$	−17.5388	−1.26906	−0.634530	−	0.772898i	$-0.718806\pi$
$191$	−17.5388	−1.26906	−0.634530	+	0.772898i	$0.718806\pi$
$192$	3.40194	0.245514
$193$	1.55089	0.111636	0.0558178	−	0.998441i	$-0.482223\pi$
$193$	1.55089	0.111636	0.0558178	+	0.998441i	$0.482223\pi$
$194$	−5.24171	−0.376333
$195$	−1.81242	−0.129790
$196$	−5.93058	−0.423613
$197$	−9.43598	−0.672286	−0.336143	−	0.941811i	$-0.609123\pi$
$197$	−9.43598	−0.672286	−0.336143	+	0.941811i	$0.609123\pi$
$198$	0	0
$199$	16.5432	1.17272	0.586359	−	0.810051i	$-0.300561\pi$
$199$	16.5432	1.17272	0.586359	+	0.810051i	$0.300561\pi$
$200$	−3.81736	−0.269928
$201$	8.89475	0.627387
$202$	8.72686	0.614020
$203$	8.20948	0.576193
$204$	−3.40194	−0.238183
$205$	26.3930	1.84337
$206$	9.33573	0.650451
$207$	−49.8205	−3.46277
$208$	0.179416	0.0124403
$209$	0	0
$210$	−10.4465	−0.720875
$211$	−14.1080	−0.971232	−0.485616	−	0.874172i	$-0.661405\pi$
$211$	−14.1080	−0.971232	−0.485616	+	0.874172i	$0.661405\pi$
$212$	1.98966	0.136650
$213$	−26.2988	−1.80197
$214$	−8.84405	−0.604567
$215$	−25.8740	−1.76459
$216$	−18.9597	−1.29004
$217$	−4.87635	−0.331028
$218$	−9.37998	−0.635293
$219$	−31.2947	−2.11470
$220$	0	0
$221$	−0.179416	−0.0120688
$222$	27.6926	1.85861
$223$	−27.3805	−1.83353	−0.916765	−	0.399426i	$-0.869209\pi$
$223$	−27.3805	−1.83353	−0.916765	+	0.399426i	$0.869209\pi$
$224$	1.03413	0.0690955
$225$	32.7270	2.18180
$226$	−15.2877	−1.01693
$227$	21.6175	1.43481	0.717403	−	0.696658i	$-0.245330\pi$
$227$	21.6175	1.43481	0.717403	+	0.696658i	$0.245330\pi$
$228$	−16.9045	−1.11953
$229$	−0.199868	−0.0132076	−0.00660381	−	0.999978i	$-0.502102\pi$
$229$	−0.199868	−0.0132076	−0.00660381	+	0.999978i	$0.502102\pi$
$230$	−17.2558	−1.13781
$231$	0	0
$232$	7.93856	0.521192
$233$	−20.1453	−1.31976	−0.659881	−	0.751370i	$-0.729393\pi$
$233$	−20.1453	−1.31976	−0.659881	+	0.751370i	$0.729393\pi$
$234$	−1.53817	−0.100553
$235$	5.39603	0.351998
$236$	1.01628	0.0661539
$237$	21.5590	1.40041
$238$	−1.03413	−0.0670325
$239$	−17.3055	−1.11940	−0.559699	−	0.828696i	$-0.689083\pi$
$239$	−17.3055	−1.11940	−0.559699	+	0.828696i	$0.689083\pi$
$240$	−10.1017	−0.652064
$241$	−2.19153	−0.141169	−0.0705843	−	0.997506i	$-0.522486\pi$
$241$	−2.19153	−0.141169	−0.0705843	+	0.997506i	$0.522486\pi$
$242$	0	0
$243$	75.0484	4.81436
$244$	−1.47254	−0.0942698
$245$	17.6103	1.12508
$246$	30.2375	1.92787
$247$	−0.891534	−0.0567270
$248$	−4.71542	−0.299430
$249$	−34.9706	−2.21617
$250$	−3.51174	−0.222102
$251$	−15.9874	−1.00912	−0.504559	−	0.863377i	$-0.668345\pi$
$251$	−15.9874	−1.00912	−0.504559	+	0.863377i	$0.668345\pi$
$252$	−8.86577	−0.558491
$253$	0	0
$254$	1.74992	0.109800
$255$	10.1017	0.632595
$256$	1.00000	0.0625000
$257$	−14.6112	−0.911424	−0.455712	−	0.890127i	$-0.650615\pi$
$257$	−14.6112	−0.911424	−0.455712	+	0.890127i	$0.650615\pi$
$258$	−29.6429	−1.84549
$259$	8.41804	0.523072
$260$	−0.532759	−0.0330403
$261$	−68.0588	−4.21274
$262$	−3.46716	−0.214202
$263$	16.2499	1.00201	0.501004	−	0.865445i	$-0.332964\pi$
$263$	16.2499	1.00201	0.501004	+	0.865445i	$0.332964\pi$
$264$	0	0
$265$	−5.90810	−0.362932
$266$	−5.13866	−0.315072
$267$	8.98534	0.549894
$268$	2.61461	0.159713
$269$	1.45111	0.0884759	0.0442379	−	0.999021i	$-0.485914\pi$
$269$	1.45111	0.0884759	0.0442379	+	0.999021i	$0.485914\pi$
$270$	56.2989	3.42624
$271$	20.8966	1.26938	0.634690	−	0.772767i	$-0.281128\pi$
$271$	20.8966	1.26938	0.634690	+	0.772767i	$0.281128\pi$
$272$	−1.00000	−0.0606339
$273$	−0.631193	−0.0382016
$274$	12.3297	0.744862
$275$	0	0
$276$	−19.7693	−1.18997
$277$	24.1899	1.45343	0.726714	−	0.686940i	$-0.241046\pi$
$277$	24.1899	1.45343	0.726714	+	0.686940i	$0.241046\pi$
$278$	−8.33547	−0.499928
$279$	40.4262	2.42026
$280$	−3.07074	−0.183512
$281$	20.1922	1.20457	0.602284	−	0.798282i	$-0.294257\pi$
$281$	20.1922	1.20457	0.602284	+	0.798282i	$0.294257\pi$
$282$	6.18203	0.368135
$283$	21.6188	1.28510	0.642551	−	0.766243i	$-0.277876\pi$
$283$	21.6188	1.28510	0.642551	+	0.766243i	$0.277876\pi$
$284$	−7.73054	−0.458723
$285$	50.1963	2.97338
$286$	0	0
$287$	9.19165	0.542566
$288$	−8.57319	−0.505180
$289$	1.00000	0.0588235
$290$	−23.5728	−1.38424
$291$	17.8320	1.04533
$292$	−9.19909	−0.538336
$293$	8.21460	0.479902	0.239951	−	0.970785i	$-0.422869\pi$
$293$	8.21460	0.479902	0.239951	+	0.970785i	$0.422869\pi$
$294$	20.1755	1.17666
$295$	−3.01773	−0.175699
$296$	8.14024	0.473142
$297$	0	0
$298$	11.6877	0.677050
$299$	−1.04262	−0.0602965
$300$	12.9864	0.749772
$301$	−9.01091	−0.519380
$302$	−5.96270	−0.343115
$303$	−29.6883	−1.70555
$304$	−4.96908	−0.284996
$305$	4.37257	0.250373
$306$	8.57319	0.490097
$307$	−18.4000	−1.05014	−0.525071	−	0.851058i	$-0.675961\pi$
$307$	−18.4000	−1.05014	−0.525071	+	0.851058i	$0.675961\pi$
$308$	0	0
$309$	−31.7596	−1.80674
$310$	14.0020	0.795260
$311$	22.5527	1.27884	0.639422	−	0.768856i	$-0.279174\pi$
$311$	22.5527	1.27884	0.639422	+	0.768856i	$0.279174\pi$
$312$	−0.610363	−0.0345550
$313$	−1.62957	−0.0921088	−0.0460544	−	0.998939i	$-0.514665\pi$
$313$	−1.62957	−0.0921088	−0.0460544	+	0.998939i	$0.514665\pi$
$314$	16.5166	0.932085
$315$	26.3261	1.48331
$316$	6.33727	0.356499
$317$	0.199905	0.0112278	0.00561389	−	0.999984i	$-0.498213\pi$
$317$	0.199905	0.0112278	0.00561389	+	0.999984i	$0.498213\pi$
$318$	−6.76870	−0.379570
$319$	0	0
$320$	−2.96940	−0.165995
$321$	30.0869	1.67929
$322$	−6.00952	−0.334897
$323$	4.96908	0.276487
$324$	38.7801	2.15445
$325$	0.684896	0.0379912
$326$	24.8824	1.37811
$327$	31.9101	1.76463
$328$	8.88832	0.490775
$329$	1.87922	0.103605
$330$	0	0
$331$	1.12826	0.0620145	0.0310073	−	0.999519i	$-0.490128\pi$
$331$	1.12826	0.0620145	0.0310073	+	0.999519i	$0.490128\pi$
$332$	−10.2796	−0.564167
$333$	−69.7878	−3.82435
$334$	−6.65037	−0.363892
$335$	−7.76384	−0.424184
$336$	−3.51804	−0.191925
$337$	13.3481	0.727118	0.363559	−	0.931571i	$-0.381561\pi$
$337$	13.3481	0.727118	0.363559	+	0.931571i	$0.381561\pi$
$338$	12.9678	0.705356
$339$	52.0080	2.82469
$340$	2.96940	0.161039
$341$	0	0
$342$	42.6009	2.30359
$343$	13.3719	0.722013
$344$	−8.71354	−0.469803
$345$	58.7032	3.16047
$346$	15.1170	0.812694
$347$	20.2778	1.08857	0.544284	−	0.838901i	$-0.316802\pi$
$347$	20.2778	1.08857	0.544284	+	0.838901i	$0.316802\pi$
$348$	−27.0065	−1.44770
$349$	18.7385	1.00305	0.501524	−	0.865143i	$-0.332773\pi$
$349$	18.7385	1.00305	0.501524	+	0.865143i	$0.332773\pi$
$350$	3.94764	0.211010
$351$	3.40167	0.181568
$352$	0	0
$353$	−8.99084	−0.478534	−0.239267	−	0.970954i	$-0.576907\pi$
$353$	−8.99084	−0.478534	−0.239267	+	0.970954i	$0.576907\pi$
$354$	−3.45731	−0.183754
$355$	22.9551	1.21833
$356$	2.64124	0.139986
$357$	3.51804	0.186194
$358$	−5.47852	−0.289549
$359$	−27.6183	−1.45764	−0.728819	−	0.684707i	$-0.759930\pi$
$359$	−27.6183	−1.45764	−0.728819	+	0.684707i	$0.759930\pi$
$360$	25.4573	1.34172
$361$	5.69179	0.299568
$362$	4.46598	0.234727
$363$	0	0
$364$	−0.185539	−0.00972490
$365$	27.3158	1.42977
$366$	5.00950	0.261851
$367$	21.9765	1.14717	0.573583	−	0.819148i	$-0.305553\pi$
$367$	21.9765	1.14717	0.573583	+	0.819148i	$0.305553\pi$
$368$	−5.81120	−0.302930
$369$	−76.2013	−3.96688
$370$	−24.1717	−1.25662
$371$	−2.05756	−0.106823
$372$	16.0416	0.831717
$373$	−36.1420	−1.87136	−0.935681	−	0.352847i	$-0.885214\pi$
$373$	−36.1420	−1.87136	−0.935681	+	0.352847i	$0.885214\pi$
$374$	0	0
$375$	11.9467	0.616926
$376$	1.81721	0.0937154
$377$	−1.42431	−0.0733556
$378$	19.6067	1.00846
$379$	−4.30792	−0.221283	−0.110641	−	0.993860i	$-0.535291\pi$
$379$	−4.30792	−0.221283	−0.110641	+	0.993860i	$0.535291\pi$
$380$	14.7552	0.756927
$381$	−5.95313	−0.304988
$382$	17.5388	0.897361
$383$	10.3865	0.530725	0.265363	−	0.964149i	$-0.414508\pi$
$383$	10.3865	0.530725	0.265363	+	0.964149i	$0.414508\pi$
$384$	−3.40194	−0.173605
$385$	0	0
$386$	−1.55089	−0.0789383
$387$	74.7029	3.79736
$388$	5.24171	0.266107
$389$	−35.1345	−1.78139	−0.890694	−	0.454603i	$-0.849781\pi$
$389$	−35.1345	−1.78139	−0.890694	+	0.454603i	$0.849781\pi$
$390$	1.81242	0.0917752
$391$	5.81120	0.293885
$392$	5.93058	0.299540
$393$	11.7951	0.594982
$394$	9.43598	0.475378
$395$	−18.8179	−0.946832
$396$	0	0
$397$	11.8880	0.596642	0.298321	−	0.954466i	$-0.403573\pi$
$397$	11.8880	0.596642	0.298321	+	0.954466i	$0.403573\pi$
$398$	−16.5432	−0.829237
$399$	17.4814	0.875166
$400$	3.81736	0.190868
$401$	−25.7788	−1.28733	−0.643667	−	0.765306i	$-0.722588\pi$
$401$	−25.7788	−1.28733	−0.643667	+	0.765306i	$0.722588\pi$
$402$	−8.89475	−0.443630
$403$	0.846024	0.0421434
$404$	−8.72686	−0.434178
$405$	−115.154	−5.72203
$406$	−8.20948	−0.407430
$407$	0	0
$408$	3.40194	0.168421
$409$	6.48849	0.320835	0.160418	−	0.987049i	$-0.448716\pi$
$409$	6.48849	0.320835	0.160418	+	0.987049i	$0.448716\pi$
$410$	−26.3930	−1.30346
$411$	−41.9447	−2.06898
$412$	−9.33573	−0.459938
$413$	−1.05096	−0.0517142
$414$	49.8205	2.44855
$415$	30.5243	1.49838
$416$	−0.179416	−0.00879661
$417$	28.3568	1.38864
$418$	0	0
$419$	8.81450	0.430617	0.215308	−	0.976546i	$-0.430924\pi$
$419$	8.81450	0.430617	0.215308	+	0.976546i	$0.430924\pi$
$420$	10.4465	0.509736
$421$	15.7022	0.765276	0.382638	−	0.923898i	$-0.375016\pi$
$421$	15.7022	0.765276	0.382638	+	0.923898i	$0.375016\pi$
$422$	14.1080	0.686765
$423$	−15.5793	−0.757490
$424$	−1.98966	−0.0966264
$425$	−3.81736	−0.185169
$426$	26.2988	1.27418
$427$	1.52279	0.0736932
$428$	8.84405	0.427493
$429$	0	0
$430$	25.8740	1.24776
$431$	−8.87761	−0.427619	−0.213810	−	0.976875i	$-0.568587\pi$
$431$	−8.87761	−0.427619	−0.213810	+	0.976875i	$0.568587\pi$
$432$	18.9597	0.912197
$433$	−13.5937	−0.653270	−0.326635	−	0.945151i	$-0.605915\pi$
$433$	−13.5937	−0.653270	−0.326635	+	0.945151i	$0.605915\pi$
$434$	4.87635	0.234072
$435$	80.1932	3.84497
$436$	9.37998	0.449220
$437$	28.8763	1.38134
$438$	31.2947	1.49532
$439$	8.31914	0.397051	0.198525	−	0.980096i	$-0.436385\pi$
$439$	8.31914	0.397051	0.198525	+	0.980096i	$0.436385\pi$
$440$	0	0
$441$	−50.8440	−2.42114
$442$	0.179416	0.00853396
$443$	−20.9190	−0.993894	−0.496947	−	0.867781i	$-0.665546\pi$
$443$	−20.9190	−0.993894	−0.496947	+	0.867781i	$0.665546\pi$
$444$	−27.6926	−1.31423
$445$	−7.84291	−0.371790
$446$	27.3805	1.29650
$447$	−39.7609	−1.88062
$448$	−1.03413	−0.0488579
$449$	13.2982	0.627582	0.313791	−	0.949492i	$-0.398401\pi$
$449$	13.2982	0.627582	0.313791	+	0.949492i	$0.398401\pi$
$450$	−32.7270	−1.54276
$451$	0	0
$452$	15.2877	0.719075
$453$	20.2847	0.953060
$454$	−21.6175	−1.01456
$455$	0.550941	0.0258285
$456$	16.9045	0.791627
$457$	31.9301	1.49363	0.746814	−	0.665033i	$-0.231583\pi$
$457$	31.9301	1.49363	0.746814	+	0.665033i	$0.231583\pi$
$458$	0.199868	0.00933920
$459$	−18.9597	−0.884961
$460$	17.2558	0.804556
$461$	−8.33972	−0.388419	−0.194210	−	0.980960i	$-0.562214\pi$
$461$	−8.33972	−0.388419	−0.194210	+	0.980960i	$0.562214\pi$
$462$	0	0
$463$	2.42117	0.112521	0.0562607	−	0.998416i	$-0.482082\pi$
$463$	2.42117	0.112521	0.0562607	+	0.998416i	$0.482082\pi$
$464$	−7.93856	−0.368539
$465$	−47.6339	−2.20897
$466$	20.1453	0.933213
$467$	−6.52943	−0.302146	−0.151073	−	0.988523i	$-0.548273\pi$
$467$	−6.52943	−0.302146	−0.151073	+	0.988523i	$0.548273\pi$
$468$	1.53817	0.0711019
$469$	−2.70384	−0.124852
$470$	−5.39603	−0.248900
$471$	−56.1885	−2.58903
$472$	−1.01628	−0.0467779
$473$	0	0
$474$	−21.5590	−0.990238
$475$	−18.9688	−0.870347
$476$	1.03413	0.0473991
$477$	17.0577	0.781020
$478$	17.3055	0.791535
$479$	−11.4595	−0.523597	−0.261798	−	0.965123i	$-0.584316\pi$
$479$	−11.4595	−0.523597	−0.261798	+	0.965123i	$0.584316\pi$
$480$	10.1017	0.461079
$481$	−1.46049	−0.0665927
$482$	2.19153	0.0998213
$483$	20.4440	0.930235
$484$	0	0
$485$	−15.5647	−0.706759
$486$	−75.0484	−3.40427
$487$	−0.572833	−0.0259576	−0.0129788	−	0.999916i	$-0.504131\pi$
$487$	−0.572833	−0.0259576	−0.0129788	+	0.999916i	$0.504131\pi$
$488$	1.47254	0.0666588
$489$	−84.6484	−3.82793
$490$	−17.6103	−0.795552
$491$	22.8998	1.03345	0.516726	−	0.856151i	$-0.327150\pi$
$491$	22.8998	1.03345	0.516726	+	0.856151i	$0.327150\pi$
$492$	−30.2375	−1.36321
$493$	7.93856	0.357535
$494$	0.891534	0.0401120
$495$	0	0
$496$	4.71542	0.211729
$497$	7.99436	0.358596
$498$	34.9706	1.56707
$499$	1.54080	0.0689755	0.0344878	−	0.999405i	$-0.489020\pi$
$499$	1.54080	0.0689755	0.0344878	+	0.999405i	$0.489020\pi$
$500$	3.51174	0.157050
$501$	22.6241	1.01077
$502$	15.9874	0.713554
$503$	11.7734	0.524952	0.262476	−	0.964939i	$-0.415461\pi$
$503$	11.7734	0.524952	0.262476	+	0.964939i	$0.415461\pi$
$504$	8.86577	0.394913
$505$	25.9136	1.15314
$506$	0	0
$507$	−44.1157	−1.95925
$508$	−1.74992	−0.0776403
$509$	−29.9293	−1.32659	−0.663295	−	0.748358i	$-0.730843\pi$
$509$	−29.9293	−1.32659	−0.663295	+	0.748358i	$0.730843\pi$
$510$	−10.1017	−0.447312
$511$	9.51302	0.420831
$512$	−1.00000	−0.0441942
$513$	−94.2122	−4.15957
$514$	14.6112	0.644474
$515$	27.7215	1.22156
$516$	29.6429	1.30496
$517$	0	0
$518$	−8.41804	−0.369868
$519$	−51.4270	−2.25740
$520$	0.532759	0.0233630
$521$	11.0724	0.485091	0.242546	−	0.970140i	$-0.422018\pi$
$521$	11.0724	0.485091	0.242546	+	0.970140i	$0.422018\pi$
$522$	68.0588	2.97885
$523$	20.5680	0.899374	0.449687	−	0.893186i	$-0.351536\pi$
$523$	20.5680	0.899374	0.449687	+	0.893186i	$0.351536\pi$
$524$	3.46716	0.151463
$525$	−13.4296	−0.586117
$526$	−16.2499	−0.708527
$527$	−4.71542	−0.205407
$528$	0	0
$529$	10.7700	0.468262
$530$	5.90810	0.256632
$531$	8.71272	0.378100
$532$	5.13866	0.222789
$533$	−1.59471	−0.0690745
$534$	−8.98534	−0.388834
$535$	−26.2616	−1.13539
$536$	−2.61461	−0.112934
$537$	18.6376	0.804272
$538$	−1.45111	−0.0625619
$539$	0	0
$540$	−56.2989	−2.42272
$541$	25.6002	1.10064	0.550319	−	0.834954i	$-0.314506\pi$
$541$	25.6002	1.10064	0.550319	+	0.834954i	$0.314506\pi$
$542$	−20.8966	−0.897587
$543$	−15.1930	−0.651993
$544$	1.00000	0.0428746
$545$	−27.8530	−1.19309
$546$	0.631193	0.0270126
$547$	−11.5680	−0.494612	−0.247306	−	0.968937i	$-0.579545\pi$
$547$	−11.5680	−0.494612	−0.247306	+	0.968937i	$0.579545\pi$
$548$	−12.3297	−0.526697
$549$	−12.6244	−0.538795
$550$	0	0
$551$	39.4474	1.68051
$552$	19.7693	0.841439
$553$	−6.55354	−0.278685
$554$	−24.1899	−1.02773
$555$	82.2305	3.49049
$556$	8.33547	0.353503
$557$	−13.1655	−0.557838	−0.278919	−	0.960315i	$-0.589976\pi$
$557$	−13.1655	−0.557838	−0.278919	+	0.960315i	$0.589976\pi$
$558$	−40.4262	−1.71138
$559$	1.56335	0.0661227
$560$	3.07074	0.129763
$561$	0	0
$562$	−20.1922	−0.851759
$563$	−14.0659	−0.592808	−0.296404	−	0.955063i	$-0.595787\pi$
$563$	−14.0659	−0.592808	−0.296404	+	0.955063i	$0.595787\pi$
$564$	−6.18203	−0.260311
$565$	−45.3955	−1.90980
$566$	−21.6188	−0.908704
$567$	−40.1035	−1.68419
$568$	7.73054	0.324366
$569$	−15.4212	−0.646488	−0.323244	−	0.946316i	$-0.604774\pi$
$569$	−15.4212	−0.646488	−0.323244	+	0.946316i	$0.604774\pi$
$570$	−50.1963	−2.10249
$571$	10.4252	0.436280	0.218140	−	0.975917i	$-0.430001\pi$
$571$	10.4252	0.436280	0.218140	+	0.975917i	$0.430001\pi$
$572$	0	0
$573$	−59.6658	−2.49257
$574$	−9.19165	−0.383652
$575$	−22.1834	−0.925113
$576$	8.57319	0.357216
$577$	25.6015	1.06580	0.532902	−	0.846177i	$-0.321101\pi$
$577$	25.6015	1.06580	0.532902	+	0.846177i	$0.321101\pi$
$578$	−1.00000	−0.0415945
$579$	5.27604	0.219265
$580$	23.5728	0.978807
$581$	10.6304	0.441025
$582$	−17.8320	−0.739159
$583$	0	0
$584$	9.19909	0.380661
$585$	−4.56745	−0.188841
$586$	−8.21460	−0.339342
$587$	24.6134	1.01590	0.507952	−	0.861385i	$-0.330403\pi$
$587$	24.6134	1.01590	0.507952	+	0.861385i	$0.330403\pi$
$588$	−20.1755	−0.832023
$589$	−23.4313	−0.965471
$590$	3.01773	0.124238
$591$	−32.1006	−1.32044
$592$	−8.14024	−0.334562
$593$	8.11056	0.333061	0.166530	−	0.986036i	$-0.446744\pi$
$593$	8.11056	0.333061	0.166530	+	0.986036i	$0.446744\pi$
$594$	0	0
$595$	−3.07074	−0.125888
$596$	−11.6877	−0.478747
$597$	56.2791	2.30335
$598$	1.04262	0.0426360
$599$	7.61997	0.311343	0.155672	−	0.987809i	$-0.450246\pi$
$599$	7.61997	0.311343	0.155672	+	0.987809i	$0.450246\pi$
$600$	−12.9864	−0.530169
$601$	11.1380	0.454330	0.227165	−	0.973856i	$-0.427054\pi$
$601$	11.1380	0.454330	0.227165	+	0.973856i	$0.427054\pi$
$602$	9.01091	0.367257
$603$	22.4156	0.912833
$604$	5.96270	0.242619
$605$	0	0
$606$	29.6883	1.20600
$607$	−11.4541	−0.464907	−0.232453	−	0.972608i	$-0.574675\pi$
$607$	−11.4541	−0.464907	−0.232453	+	0.972608i	$0.574675\pi$
$608$	4.96908	0.201523
$609$	27.9282	1.13171
$610$	−4.37257	−0.177040
$611$	−0.326037	−0.0131900
$612$	−8.57319	−0.346551
$613$	40.8357	1.64934	0.824670	−	0.565614i	$-0.191361\pi$
$613$	40.8357	1.64934	0.824670	+	0.565614i	$0.191361\pi$
$614$	18.4000	0.742563
$615$	89.7874	3.62058
$616$	0	0
$617$	41.2484	1.66060	0.830300	−	0.557317i	$-0.188169\pi$
$617$	41.2484	1.66060	0.830300	+	0.557317i	$0.188169\pi$
$618$	31.7596	1.27756
$619$	44.3904	1.78420	0.892101	−	0.451837i	$-0.149231\pi$
$619$	44.3904	1.78420	0.892101	+	0.451837i	$0.149231\pi$
$620$	−14.0020	−0.562334
$621$	−110.178	−4.42131
$622$	−22.5527	−0.904279
$623$	−2.73138	−0.109430
$624$	0.610363	0.0244341
$625$	−29.5146	−1.18058
$626$	1.62957	0.0651308
$627$	0	0
$628$	−16.5166	−0.659084
$629$	8.14024	0.324573
$630$	−26.3261	−1.04886
$631$	25.6393	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$631$	25.6393	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$632$	−6.33727	−0.252083
$633$	−47.9944	−1.90761
$634$	−0.199905	−0.00793924
$635$	5.19623	0.206206
$636$	6.76870	0.268396
$637$	−1.06404	−0.0421589
$638$	0	0
$639$	−66.2754	−2.62181
$640$	2.96940	0.117376
$641$	37.1067	1.46563	0.732814	−	0.680430i	$-0.238207\pi$
$641$	37.1067	1.46563	0.732814	+	0.680430i	$0.238207\pi$
$642$	−30.0869	−1.18744
$643$	11.5374	0.454991	0.227495	−	0.973779i	$-0.426946\pi$
$643$	11.5374	0.454991	0.227495	+	0.973779i	$0.426946\pi$
$644$	6.00952	0.236808
$645$	−88.0219	−3.46586
$646$	−4.96908	−0.195506
$647$	−7.95434	−0.312717	−0.156359	−	0.987700i	$-0.549976\pi$
$647$	−7.95434	−0.312717	−0.156359	+	0.987700i	$0.549976\pi$
$648$	−38.7801	−1.52342
$649$	0	0
$650$	−0.684896	−0.0268638
$651$	−16.5890	−0.650176
$652$	−24.8824	−0.974470
$653$	3.31799	0.129843	0.0649214	−	0.997890i	$-0.479320\pi$
$653$	3.31799	0.129843	0.0649214	+	0.997890i	$0.479320\pi$
$654$	−31.9101	−1.24779
$655$	−10.2954	−0.402274
$656$	−8.88832	−0.347030
$657$	−78.8655	−3.07684
$658$	−1.87922	−0.0732598
$659$	9.50486	0.370257	0.185128	−	0.982714i	$-0.440730\pi$
$659$	9.50486	0.370257	0.185128	+	0.982714i	$0.440730\pi$
$660$	0	0
$661$	40.4029	1.57149	0.785746	−	0.618549i	$-0.212279\pi$
$661$	40.4029	1.57149	0.785746	+	0.618549i	$0.212279\pi$
$662$	−1.12826	−0.0438509
$663$	−0.610363	−0.0237045
$664$	10.2796	0.398927
$665$	−15.2588	−0.591710
$666$	69.7878	2.70422
$667$	46.1326	1.78626
$668$	6.65037	0.257310
$669$	−93.1466	−3.60126
$670$	7.76384	0.299943
$671$	0	0
$672$	3.51804	0.135711
$673$	21.9659	0.846725	0.423362	−	0.905960i	$-0.360850\pi$
$673$	21.9659	0.846725	0.423362	+	0.905960i	$0.360850\pi$
$674$	−13.3481	−0.514150
$675$	72.3759	2.78575
$676$	−12.9678	−0.498762
$677$	41.1677	1.58220	0.791102	−	0.611685i	$-0.209508\pi$
$677$	41.1677	1.58220	0.791102	+	0.611685i	$0.209508\pi$
$678$	−52.0080	−1.99735
$679$	−5.42059	−0.208023
$680$	−2.96940	−0.113871
$681$	73.5416	2.81812
$682$	0	0
$683$	−12.0070	−0.459435	−0.229717	−	0.973257i	$-0.573780\pi$
$683$	−12.0070	−0.459435	−0.229717	+	0.973257i	$0.573780\pi$
$684$	−42.6009	−1.62889
$685$	36.6117	1.39886
$686$	−13.3719	−0.510540
$687$	−0.679938	−0.0259412
$688$	8.71354	0.332201
$689$	0.356977	0.0135997
$690$	−58.7032	−2.23479
$691$	−2.31198	−0.0879519	−0.0439759	−	0.999033i	$-0.514002\pi$
$691$	−2.31198	−0.0879519	−0.0439759	+	0.999033i	$0.514002\pi$
$692$	−15.1170	−0.574661
$693$	0	0
$694$	−20.2778	−0.769733
$695$	−24.7514	−0.938873
$696$	27.0065	1.02368
$697$	8.88832	0.336669
$698$	−18.7385	−0.709263
$699$	−68.5331	−2.59216
$700$	−3.94764	−0.149207
$701$	−43.9185	−1.65878	−0.829389	−	0.558672i	$-0.811311\pi$
$701$	−43.9185	−1.65878	−0.829389	+	0.558672i	$0.811311\pi$
$702$	−3.40167	−0.128388
$703$	40.4495	1.52558
$704$	0	0
$705$	18.3570	0.691363
$706$	8.99084	0.338375
$707$	9.02468	0.339408
$708$	3.45731	0.129934
$709$	7.70101	0.289217	0.144609	−	0.989489i	$-0.453808\pi$
$709$	7.70101	0.289217	0.144609	+	0.989489i	$0.453808\pi$
$710$	−22.9551	−0.861489
$711$	54.3306	2.03756
$712$	−2.64124	−0.0989847
$713$	−27.4023	−1.02622
$714$	−3.51804	−0.131659
$715$	0	0
$716$	5.47852	0.204742
$717$	−58.8722	−2.19862
$718$	27.6183	1.03071
$719$	−5.95757	−0.222180	−0.111090	−	0.993810i	$-0.535434\pi$
$719$	−5.95757	−0.222180	−0.111090	+	0.993810i	$0.535434\pi$
$720$	−25.4573	−0.948737
$721$	9.65433	0.359546
$722$	−5.69179	−0.211826
$723$	−7.45544	−0.277271
$724$	−4.46598	−0.165977
$725$	−30.3044	−1.12548
$726$	0	0
$727$	−33.5391	−1.24389	−0.621947	−	0.783059i	$-0.713658\pi$
$727$	−33.5391	−1.24389	−0.621947	+	0.783059i	$0.713658\pi$
$728$	0.185539	0.00687654
$729$	138.970	5.14704
$730$	−27.3158	−1.01100
$731$	−8.71354	−0.322282
$732$	−5.00950	−0.185156
$733$	31.8413	1.17609	0.588043	−	0.808830i	$-0.299899\pi$
$733$	31.8413	1.17609	0.588043	+	0.808830i	$0.299899\pi$
$734$	−21.9765	−0.811168
$735$	59.9091	2.20978
$736$	5.81120	0.214204
$737$	0	0
$738$	76.2013	2.80501
$739$	−31.1196	−1.14475	−0.572377	−	0.819990i	$-0.693979\pi$
$739$	−31.1196	−1.14475	−0.572377	+	0.819990i	$0.693979\pi$
$740$	24.1717	0.888568
$741$	−3.03295	−0.111418
$742$	2.05756	0.0755354
$743$	−21.1501	−0.775921	−0.387961	−	0.921676i	$-0.626820\pi$
$743$	−21.1501	−0.775921	−0.387961	+	0.921676i	$0.626820\pi$
$744$	−16.0416	−0.588113
$745$	34.7055	1.27151
$746$	36.1420	1.32325
$747$	−88.1292	−3.22448
$748$	0	0
$749$	−9.14587	−0.334183
$750$	−11.9467	−0.436232
$751$	−12.7657	−0.465827	−0.232914	−	0.972497i	$-0.574826\pi$
$751$	−12.7657	−0.465827	−0.232914	+	0.972497i	$0.574826\pi$
$752$	−1.81721	−0.0662668
$753$	−54.3883	−1.98202
$754$	1.42431	0.0518702
$755$	−17.7057	−0.644375
$756$	−19.6067	−0.713089
$757$	−3.64017	−0.132304	−0.0661521	−	0.997810i	$-0.521072\pi$
$757$	−3.64017	−0.132304	−0.0661521	+	0.997810i	$0.521072\pi$
$758$	4.30792	0.156471
$759$	0	0
$760$	−14.7552	−0.535228
$761$	−26.7423	−0.969407	−0.484703	−	0.874679i	$-0.661072\pi$
$761$	−26.7423	−0.969407	−0.484703	+	0.874679i	$0.661072\pi$
$762$	5.95313	0.215659
$763$	−9.70010	−0.351167
$764$	−17.5388	−0.634530
$765$	25.4573	0.920410
$766$	−10.3865	−0.375280
$767$	0.182336	0.00658378
$768$	3.40194	0.122757
$769$	2.04734	0.0738289	0.0369145	−	0.999318i	$-0.488247\pi$
$769$	2.04734	0.0738289	0.0369145	+	0.999318i	$0.488247\pi$
$770$	0	0
$771$	−49.7065	−1.79014
$772$	1.55089	0.0558178
$773$	9.50257	0.341784	0.170892	−	0.985290i	$-0.445335\pi$
$773$	9.50257	0.341784	0.170892	+	0.985290i	$0.445335\pi$
$774$	−74.7029	−2.68514
$775$	18.0005	0.646596
$776$	−5.24171	−0.188166
$777$	28.6377	1.02737
$778$	35.1345	1.25963
$779$	44.1668	1.58244
$780$	−1.81242	−0.0648949
$781$	0	0
$782$	−5.81120	−0.207808
$783$	−150.512	−5.37888
$784$	−5.93058	−0.211806
$785$	49.0444	1.75047
$786$	−11.7951	−0.420716
$787$	−28.2198	−1.00593	−0.502964	−	0.864307i	$-0.667757\pi$
$787$	−28.2198	−1.00593	−0.502964	+	0.864307i	$0.667757\pi$
$788$	−9.43598	−0.336143
$789$	55.2810	1.96806
$790$	18.8179	0.669511
$791$	−15.8095	−0.562120
$792$	0	0
$793$	−0.264198	−0.00938194
$794$	−11.8880	−0.421889
$795$	−20.0990	−0.712838
$796$	16.5432	0.586359
$797$	−16.9580	−0.600683	−0.300342	−	0.953832i	$-0.597101\pi$
$797$	−16.9580	−0.600683	−0.300342	+	0.953832i	$0.597101\pi$
$798$	−17.4814	−0.618836
$799$	1.81721	0.0642882
$800$	−3.81736	−0.134964
$801$	22.6439	0.800082
$802$	25.7788	0.910282
$803$	0	0
$804$	8.89475	0.313694
$805$	−17.8447	−0.628943
$806$	−0.846024	−0.0297999
$807$	4.93660	0.173776
$808$	8.72686	0.307010
$809$	−34.3761	−1.20860	−0.604299	−	0.796758i	$-0.706547\pi$
$809$	−34.3761	−1.20860	−0.604299	+	0.796758i	$0.706547\pi$
$810$	115.154	4.04609
$811$	−52.0910	−1.82916	−0.914581	−	0.404402i	$-0.867480\pi$
$811$	−52.0910	−1.82916	−0.914581	+	0.404402i	$0.867480\pi$
$812$	8.20948	0.288096
$813$	71.0890	2.49320
$814$	0	0
$815$	73.8859	2.58811
$816$	−3.40194	−0.119092
$817$	−43.2983	−1.51482
$818$	−6.48849	−0.226865
$819$	−1.59066	−0.0555823
$820$	26.3930	0.921684
$821$	−43.8738	−1.53121	−0.765604	−	0.643313i	$-0.777560\pi$
$821$	−43.8738	−1.53121	−0.765604	+	0.643313i	$0.777560\pi$
$822$	41.9447	1.46299
$823$	15.8347	0.551963	0.275982	−	0.961163i	$-0.410997\pi$
$823$	15.8347	0.551963	0.275982	+	0.961163i	$0.410997\pi$
$824$	9.33573	0.325225
$825$	0	0
$826$	1.05096	0.0365675
$827$	27.5832	0.959162	0.479581	−	0.877498i	$-0.340789\pi$
$827$	27.5832	0.959162	0.479581	+	0.877498i	$0.340789\pi$
$828$	−49.8205	−1.73138
$829$	−31.7237	−1.10181	−0.550905	−	0.834568i	$-0.685717\pi$
$829$	−31.7237	−1.10181	−0.550905	+	0.834568i	$0.685717\pi$
$830$	−30.5243	−1.05952
$831$	82.2925	2.85469
$832$	0.179416	0.00622014
$833$	5.93058	0.205482
$834$	−28.3568	−0.981914
$835$	−19.7476	−0.683395
$836$	0	0
$837$	89.4029	3.09021
$838$	−8.81450	−0.304492
$839$	10.3170	0.356183	0.178092	−	0.984014i	$-0.443008\pi$
$839$	10.3170	0.356183	0.178092	+	0.984014i	$0.443008\pi$
$840$	−10.4465	−0.360438
$841$	34.0208	1.17313
$842$	−15.7022	−0.541132
$843$	68.6928	2.36591
$844$	−14.1080	−0.485616
$845$	38.5067	1.32467
$846$	15.5793	0.535627
$847$	0	0
$848$	1.98966	0.0683252
$849$	73.5457	2.52408
$850$	3.81736	0.130934
$851$	47.3045	1.62158
$852$	−26.2988	−0.900983
$853$	−17.9072	−0.613132	−0.306566	−	0.951849i	$-0.599180\pi$
$853$	−17.9072	−0.613132	−0.306566	+	0.951849i	$0.599180\pi$
$854$	−1.52279	−0.0521090
$855$	126.499	4.32618
$856$	−8.84405	−0.302283
$857$	−36.9569	−1.26242	−0.631212	−	0.775611i	$-0.717442\pi$
$857$	−36.9569	−1.26242	−0.631212	+	0.775611i	$0.717442\pi$
$858$	0	0
$859$	7.41745	0.253080	0.126540	−	0.991961i	$-0.459613\pi$
$859$	7.41745	0.253080	0.126540	+	0.991961i	$0.459613\pi$
$860$	−25.8740	−0.882297
$861$	31.2694	1.06566
$862$	8.87761	0.302372
$863$	−8.23741	−0.280405	−0.140202	−	0.990123i	$-0.544775\pi$
$863$	−8.23741	−0.280405	−0.140202	+	0.990123i	$0.544775\pi$
$864$	−18.9597	−0.645021
$865$	44.8884	1.52625
$866$	13.5937	0.461932
$867$	3.40194	0.115536
$868$	−4.87635	−0.165514
$869$	0	0
$870$	−80.1932	−2.71881
$871$	0.469104	0.0158950
$872$	−9.37998	−0.317646
$873$	44.9382	1.52093
$874$	−28.8763	−0.976756
$875$	−3.63158	−0.122770
$876$	−31.2947	−1.05735
$877$	1.72050	0.0580972	0.0290486	−	0.999578i	$-0.490752\pi$
$877$	1.72050	0.0580972	0.0290486	+	0.999578i	$0.490752\pi$
$878$	−8.31914	−0.280757
$879$	27.9456	0.942581
$880$	0	0
$881$	−35.5789	−1.19868	−0.599341	−	0.800494i	$-0.704571\pi$
$881$	−35.5789	−1.19868	−0.599341	+	0.800494i	$0.704571\pi$
$882$	50.8440	1.71201
$883$	39.0363	1.31368	0.656838	−	0.754031i	$-0.271893\pi$
$883$	39.0363	1.31368	0.656838	+	0.754031i	$0.271893\pi$
$884$	−0.179416	−0.00603442
$885$	−10.2661	−0.345092
$886$	20.9190	0.702789
$887$	46.9450	1.57626	0.788129	−	0.615510i	$-0.211050\pi$
$887$	46.9450	1.57626	0.788129	+	0.615510i	$0.211050\pi$
$888$	27.6926	0.929303
$889$	1.80964	0.0606935
$890$	7.84291	0.262895
$891$	0	0
$892$	−27.3805	−0.916765
$893$	9.02986	0.302173
$894$	39.7609	1.32980
$895$	−16.2679	−0.543777
$896$	1.03413	0.0345478
$897$	−3.54694	−0.118429
$898$	−13.2982	−0.443768
$899$	−37.4337	−1.24848
$900$	32.7270	1.09090
$901$	−1.98966	−0.0662852
$902$	0	0
$903$	−30.6546	−1.02012
$904$	−15.2877	−0.508463
$905$	13.2613	0.440820
$906$	−20.2847	−0.673915
$907$	21.6290	0.718178	0.359089	−	0.933303i	$-0.383087\pi$
$907$	21.6290	0.718178	0.359089	+	0.933303i	$0.383087\pi$
$908$	21.6175	0.717403
$909$	−74.8171	−2.48153
$910$	−0.550941	−0.0182635
$911$	−1.25841	−0.0416930	−0.0208465	−	0.999783i	$-0.506636\pi$
$911$	−1.25841	−0.0416930	−0.0208465	+	0.999783i	$0.506636\pi$
$912$	−16.9045	−0.559765
$913$	0	0
$914$	−31.9301	−1.05615
$915$	14.8752	0.491759
$916$	−0.199868	−0.00660381
$917$	−3.58548	−0.118403
$918$	18.9597	0.625762
$919$	−27.6762	−0.912953	−0.456476	−	0.889735i	$-0.650889\pi$
$919$	−27.6762	−0.912953	−0.456476	+	0.889735i	$0.650889\pi$
$920$	−17.2558	−0.568907
$921$	−62.5956	−2.06260
$922$	8.33972	0.274654
$923$	−1.38698	−0.0456531
$924$	0	0
$925$	−31.0742	−1.02171
$926$	−2.42117	−0.0795647
$927$	−80.0370	−2.62876
$928$	7.93856	0.260596
$929$	−22.2362	−0.729546	−0.364773	−	0.931096i	$-0.618853\pi$
$929$	−22.2362	−0.729546	−0.364773	+	0.931096i	$0.618853\pi$
$930$	47.6339	1.56198
$931$	29.4695	0.965825
$932$	−20.1453	−0.659881
$933$	76.7228	2.51179
$934$	6.52943	0.213649
$935$	0	0
$936$	−1.53817	−0.0502767
$937$	16.9860	0.554908	0.277454	−	0.960739i	$-0.410509\pi$
$937$	16.9860	0.554908	0.277454	+	0.960739i	$0.410509\pi$
$938$	2.70384	0.0882835
$939$	−5.54370	−0.180912
$940$	5.39603	0.175999
$941$	44.4457	1.44889	0.724443	−	0.689334i	$-0.242097\pi$
$941$	44.4457	1.44889	0.724443	+	0.689334i	$0.242097\pi$
$942$	56.1885	1.83072
$943$	51.6518	1.68201
$944$	1.01628	0.0330769
$945$	58.2202	1.89390
$946$	0	0
$947$	34.7136	1.12804	0.564021	−	0.825761i	$-0.309254\pi$
$947$	34.7136	1.12804	0.564021	+	0.825761i	$0.309254\pi$
$948$	21.5590	0.700204
$949$	−1.65047	−0.0535764
$950$	18.9688	0.615428
$951$	0.680065	0.0220526
$952$	−1.03413	−0.0335163
$953$	−13.4477	−0.435612	−0.217806	−	0.975992i	$-0.569890\pi$
$953$	−13.4477	−0.435612	−0.217806	+	0.975992i	$0.569890\pi$
$954$	−17.0577	−0.552264
$955$	52.0797	1.68526
$956$	−17.3055	−0.559699
$957$	0	0
$958$	11.4595	0.370239
$959$	12.7504	0.411733
$960$	−10.1017	−0.326032
$961$	−8.76478	−0.282735
$962$	1.46049	0.0470881
$963$	75.8218	2.44332
$964$	−2.19153	−0.0705843
$965$	−4.60522	−0.148247
$966$	−20.4440	−0.657775
$967$	−15.5224	−0.499166	−0.249583	−	0.968353i	$-0.580294\pi$
$967$	−15.5224	−0.499166	−0.249583	+	0.968353i	$0.580294\pi$
$968$	0	0
$969$	16.9045	0.543051
$970$	15.5647	0.499754
$971$	44.2673	1.42060	0.710302	−	0.703897i	$-0.248558\pi$
$971$	44.2673	1.42060	0.710302	+	0.703897i	$0.248558\pi$
$972$	75.0484	2.40718
$973$	−8.61994	−0.276342
$974$	0.572833	0.0183548
$975$	2.32998	0.0746190
$976$	−1.47254	−0.0471349
$977$	0.174932	0.00559658	0.00279829	−	0.999996i	$-0.499109\pi$
$977$	0.174932	0.00559658	0.00279829	+	0.999996i	$0.499109\pi$
$978$	84.6484	2.70676
$979$	0	0
$980$	17.6103	0.562540
$981$	80.4164	2.56750
$982$	−22.8998	−0.730761
$983$	7.91116	0.252327	0.126163	−	0.992009i	$-0.459734\pi$
$983$	7.91116	0.252327	0.126163	+	0.992009i	$0.459734\pi$
$984$	30.2375	0.963937
$985$	28.0192	0.892767
$986$	−7.93856	−0.252815
$987$	6.39301	0.203492
$988$	−0.891534	−0.0283635
$989$	−50.6361	−1.61013
$990$	0	0
$991$	−41.0588	−1.30428	−0.652138	−	0.758100i	$-0.726128\pi$
$991$	−41.0588	−1.30428	−0.652138	+	0.758100i	$0.726128\pi$
$992$	−4.71542	−0.149715
$993$	3.83826	0.121803
$994$	−7.99436	−0.253566
$995$	−49.1235	−1.55732
$996$	−34.9706	−1.10809
$997$	26.2922	0.832681	0.416341	−	0.909209i	$-0.363312\pi$
$997$	26.2922	0.832681	0.416341	+	0.909209i	$0.363312\pi$
$998$	−1.54080	−0.0487731
$999$	−154.336	−4.88298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4114.2.a.bk.1.10		10
11.3	even	5		374.2.g.g.273.1	yes	20
11.4	even	5		374.2.g.g.137.1	✓	20
11.10	odd	2		4114.2.a.bl.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.g.137.1	✓	20	11.4	even	5
374.2.g.g.273.1	yes	20	11.3	even	5
4114.2.a.bk.1.10		10	1.1	even	1	trivial
4114.2.a.bl.1.10		10	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4114 = 2 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4114.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.40194 q^{3} +1.00000 q^{4} -2.96940 q^{5} -3.40194 q^{6} -1.03413 q^{7} -1.00000 q^{8} +8.57319 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.40194 q^{3} +1.00000 q^{4} -2.96940 q^{5} -3.40194 q^{6} -1.03413 q^{7} -1.00000 q^{8} +8.57319 q^{9} +2.96940 q^{10} +3.40194 q^{12} +0.179416 q^{13} +1.03413 q^{14} -10.1017 q^{15} +1.00000 q^{16} -1.00000 q^{17} -8.57319 q^{18} -4.96908 q^{19} -2.96940 q^{20} -3.51804 q^{21} -5.81120 q^{23} -3.40194 q^{24} +3.81736 q^{25} -0.179416 q^{26} +18.9597 q^{27} -1.03413 q^{28} -7.93856 q^{29} +10.1017 q^{30} +4.71542 q^{31} -1.00000 q^{32} +1.00000 q^{34} +3.07074 q^{35} +8.57319 q^{36} -8.14024 q^{37} +4.96908 q^{38} +0.610363 q^{39} +2.96940 q^{40} -8.88832 q^{41} +3.51804 q^{42} +8.71354 q^{43} -25.4573 q^{45} +5.81120 q^{46} -1.81721 q^{47} +3.40194 q^{48} -5.93058 q^{49} -3.81736 q^{50} -3.40194 q^{51} +0.179416 q^{52} +1.98966 q^{53} -18.9597 q^{54} +1.03413 q^{56} -16.9045 q^{57} +7.93856 q^{58} +1.01628 q^{59} -10.1017 q^{60} -1.47254 q^{61} -4.71542 q^{62} -8.86577 q^{63} +1.00000 q^{64} -0.532759 q^{65} +2.61461 q^{67} -1.00000 q^{68} -19.7693 q^{69} -3.07074 q^{70} -7.73054 q^{71} -8.57319 q^{72} -9.19909 q^{73} +8.14024 q^{74} +12.9864 q^{75} -4.96908 q^{76} -0.610363 q^{78} +6.33727 q^{79} -2.96940 q^{80} +38.7801 q^{81} +8.88832 q^{82} -10.2796 q^{83} -3.51804 q^{84} +2.96940 q^{85} -8.71354 q^{86} -27.0065 q^{87} +2.64124 q^{89} +25.4573 q^{90} -0.185539 q^{91} -5.81120 q^{92} +16.0416 q^{93} +1.81721 q^{94} +14.7552 q^{95} -3.40194 q^{96} +5.24171 q^{97} +5.93058 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9	\( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 12 q^{9} + 2 q^{12} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 10 q^{17} - 12 q^{18} - 9 q^{19} - 19 q^{21} - 6 q^{23} - 2 q^{24} + 4 q^{25} + 11 q^{27} - 2 q^{28} - 20 q^{29} + 5 q^{30} - q^{31} - 10 q^{32} + 10 q^{34} - 13 q^{35} + 12 q^{36} + 17 q^{37} + 9 q^{38} - 11 q^{39} - 39 q^{41} + 19 q^{42} - 16 q^{43} - 26 q^{45} + 6 q^{46} - 14 q^{47} + 2 q^{48} + 18 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{53} - 11 q^{54} + 2 q^{56} - 24 q^{57} + 20 q^{58} - 4 q^{59} - 5 q^{60} - 22 q^{61} + q^{62} - 29 q^{63} + 10 q^{64} - 52 q^{65} - 13 q^{67} - 10 q^{68} - 30 q^{69} + 13 q^{70} - 7 q^{71} - 12 q^{72} + 6 q^{73} - 17 q^{74} + 45 q^{75} - 9 q^{76} + 11 q^{78} - 19 q^{79} + 34 q^{81} + 39 q^{82} - 19 q^{83} - 19 q^{84} + 16 q^{86} - 29 q^{87} - 8 q^{89} + 26 q^{90} + 9 q^{91} - 6 q^{92} + 3 q^{93} + 14 q^{94} + 27 q^{95} - 2 q^{96} + 39 q^{97} - 18 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^6 - 2 * q^7 - 10 * q^8 + 12 * q^9 + 2 * q^12 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 10 * q^17 - 12 * q^18 - 9 * q^19 - 19 * q^21 - 6 * q^23 - 2 * q^24 + 4 * q^25 + 11 * q^27 - 2 * q^28 - 20 * q^29 + 5 * q^30 - q^31 - 10 * q^32 + 10 * q^34 - 13 * q^35 + 12 * q^36 + 17 * q^37 + 9 * q^38 - 11 * q^39 - 39 * q^41 + 19 * q^42 - 16 * q^43 - 26 * q^45 + 6 * q^46 - 14 * q^47 + 2 * q^48 + 18 * q^49 - 4 * q^50 - 2 * q^51 + 8 * q^53 - 11 * q^54 + 2 * q^56 - 24 * q^57 + 20 * q^58 - 4 * q^59 - 5 * q^60 - 22 * q^61 + q^62 - 29 * q^63 + 10 * q^64 - 52 * q^65 - 13 * q^67 - 10 * q^68 - 30 * q^69 + 13 * q^70 - 7 * q^71 - 12 * q^72 + 6 * q^73 - 17 * q^74 + 45 * q^75 - 9 * q^76 + 11 * q^78 - 19 * q^79 + 34 * q^81 + 39 * q^82 - 19 * q^83 - 19 * q^84 + 16 * q^86 - 29 * q^87 - 8 * q^89 + 26 * q^90 + 9 * q^91 - 6 * q^92 + 3 * q^93 + 14 * q^94 + 27 * q^95 - 2 * q^96 + 39 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

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Database

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