LMFDB - Embedded newform 4719.2.a.bp.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4719,2,Mod(1,4719)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4719, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4719.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4719 = 3 \cdot 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4719.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:	$37.6814047138$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 17 x^{12} + 53 x^{11} + 105 x^{10} - 347 x^{9} - 296 x^{8} + 1059 x^{7} + 404 x^{6} + \cdots + 11 $ x^14 - 3x^13 - 17x^12 + 53x^11 + 105x^10 - 347x^9 - 296x^8 + 1059x^7 + 404x^6 - 1547x^5 - 275x^4 + 948x^3 + 97x^2 - 138*x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.29581$ of defining polynomial
Character	$\chi$	$=$	4719.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.29581 q^{2} -1.00000 q^{3} -0.320873 q^{4} -1.33560 q^{5} -1.29581 q^{6} +5.13358 q^{7} -3.00741 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.29581 q^{2} -1.00000 q^{3} -0.320873 q^{4} -1.33560 q^{5} -1.29581 q^{6} +5.13358 q^{7} -3.00741 q^{8} +1.00000 q^{9} -1.73068 q^{10} +0.320873 q^{12} +1.00000 q^{13} +6.65215 q^{14} +1.33560 q^{15} -3.25529 q^{16} +5.19730 q^{17} +1.29581 q^{18} -4.23896 q^{19} +0.428557 q^{20} -5.13358 q^{21} +3.46218 q^{23} +3.00741 q^{24} -3.21618 q^{25} +1.29581 q^{26} -1.00000 q^{27} -1.64723 q^{28} +4.70827 q^{29} +1.73068 q^{30} +4.24350 q^{31} +1.79658 q^{32} +6.73472 q^{34} -6.85639 q^{35} -0.320873 q^{36} -8.46260 q^{37} -5.49289 q^{38} -1.00000 q^{39} +4.01669 q^{40} +7.86990 q^{41} -6.65215 q^{42} +2.51675 q^{43} -1.33560 q^{45} +4.48633 q^{46} -11.5344 q^{47} +3.25529 q^{48} +19.3537 q^{49} -4.16757 q^{50} -5.19730 q^{51} -0.320873 q^{52} -11.0282 q^{53} -1.29581 q^{54} -15.4388 q^{56} +4.23896 q^{57} +6.10103 q^{58} -1.03395 q^{59} -0.428557 q^{60} -0.549443 q^{61} +5.49877 q^{62} +5.13358 q^{63} +8.83862 q^{64} -1.33560 q^{65} -7.62437 q^{67} -1.66767 q^{68} -3.46218 q^{69} -8.88459 q^{70} +4.34984 q^{71} -3.00741 q^{72} +10.5117 q^{73} -10.9659 q^{74} +3.21618 q^{75} +1.36017 q^{76} -1.29581 q^{78} +15.1417 q^{79} +4.34776 q^{80} +1.00000 q^{81} +10.1979 q^{82} +7.47118 q^{83} +1.64723 q^{84} -6.94149 q^{85} +3.26123 q^{86} -4.70827 q^{87} +7.64133 q^{89} -1.73068 q^{90} +5.13358 q^{91} -1.11092 q^{92} -4.24350 q^{93} -14.9464 q^{94} +5.66154 q^{95} -1.79658 q^{96} -5.88642 q^{97} +25.0787 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} - 14 q^{3} + 15 q^{4} + 8 q^{5} - 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q + 3 * q^2 - 14 * q^3 + 15 * q^4 + 8 * q^5 - 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	$ 14 q + 3 q^{2} - 14 q^{3} + 15 q^{4} + 8 q^{5} - 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - q^{10} - 15 q^{12} + 14 q^{13} + 18 q^{14} - 8 q^{15} + 13 q^{16} - q^{17} + 3 q^{18} - 10 q^{19} + 32 q^{20} - 3 q^{21} + 15 q^{23} - 9 q^{24} + 24 q^{25} + 3 q^{26} - 14 q^{27} + 4 q^{28} + 18 q^{29} + q^{30} + 8 q^{31} + 11 q^{32} - 12 q^{34} - 23 q^{35} + 15 q^{36} + q^{37} + 14 q^{38} - 14 q^{39} + 46 q^{40} - 18 q^{42} - 6 q^{43} + 8 q^{45} + 26 q^{47} - 13 q^{48} + 23 q^{49} + 4 q^{50} + q^{51} + 15 q^{52} + 8 q^{53} - 3 q^{54} + 24 q^{56} + 10 q^{57} + 10 q^{59} - 32 q^{60} + 14 q^{61} + 65 q^{62} + 3 q^{63} + 43 q^{64} + 8 q^{65} - 44 q^{67} - 38 q^{68} - 15 q^{69} + 67 q^{70} + 37 q^{71} + 9 q^{72} + 13 q^{73} - 58 q^{74} - 24 q^{75} - 62 q^{76} - 3 q^{78} - 14 q^{79} + 56 q^{80} + 14 q^{81} - 14 q^{82} + 36 q^{83} - 4 q^{84} + 5 q^{85} + 25 q^{86} - 18 q^{87} + 63 q^{89} - q^{90} + 3 q^{91} + 34 q^{92} - 8 q^{93} - 41 q^{94} + 9 q^{95} - 11 q^{96} + 26 q^{97} - 33 q^{98}+O(q^{100}) $ 14 * q + 3 * q^2 - 14 * q^3 + 15 * q^4 + 8 * q^5 - 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - q^10 - 15 * q^12 + 14 * q^13 + 18 * q^14 - 8 * q^15 + 13 * q^16 - q^17 + 3 * q^18 - 10 * q^19 + 32 * q^20 - 3 * q^21 + 15 * q^23 - 9 * q^24 + 24 * q^25 + 3 * q^26 - 14 * q^27 + 4 * q^28 + 18 * q^29 + q^30 + 8 * q^31 + 11 * q^32 - 12 * q^34 - 23 * q^35 + 15 * q^36 + q^37 + 14 * q^38 - 14 * q^39 + 46 * q^40 - 18 * q^42 - 6 * q^43 + 8 * q^45 + 26 * q^47 - 13 * q^48 + 23 * q^49 + 4 * q^50 + q^51 + 15 * q^52 + 8 * q^53 - 3 * q^54 + 24 * q^56 + 10 * q^57 + 10 * q^59 - 32 * q^60 + 14 * q^61 + 65 * q^62 + 3 * q^63 + 43 * q^64 + 8 * q^65 - 44 * q^67 - 38 * q^68 - 15 * q^69 + 67 * q^70 + 37 * q^71 + 9 * q^72 + 13 * q^73 - 58 * q^74 - 24 * q^75 - 62 * q^76 - 3 * q^78 - 14 * q^79 + 56 * q^80 + 14 * q^81 - 14 * q^82 + 36 * q^83 - 4 * q^84 + 5 * q^85 + 25 * q^86 - 18 * q^87 + 63 * q^89 - q^90 + 3 * q^91 + 34 * q^92 - 8 * q^93 - 41 * q^94 + 9 * q^95 - 11 * q^96 + 26 * q^97 - 33 * 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 $

$2$	1.29581	0.916277	0.458138	−	0.888881i	$-0.348516\pi$
$2$	1.29581	0.916277	0.458138	+	0.888881i	$0.348516\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.320873	−0.160437
$5$	−1.33560	−0.597297	−0.298648	−	0.954363i	$-0.596536\pi$
$5$	−1.33560	−0.597297	−0.298648	+	0.954363i	$0.596536\pi$
$6$	−1.29581	−0.529013
$7$	5.13358	1.94031	0.970156	−	0.242481i	$-0.0779613\pi$
$7$	5.13358	1.94031	0.970156	+	0.242481i	$0.0779613\pi$
$8$	−3.00741	−1.06328
$9$	1.00000	0.333333
$10$	−1.73068	−0.547289
$11$	0	0
$11$	0	0
$12$	0.320873	0.0926281
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	6.65215	1.77786
$15$	1.33560	0.344849
$16$	−3.25529	−0.813823
$17$	5.19730	1.26053	0.630265	−	0.776380i	$-0.282946\pi$
$17$	5.19730	1.26053	0.630265	+	0.776380i	$0.282946\pi$
$18$	1.29581	0.305426
$19$	−4.23896	−0.972484	−0.486242	−	0.873824i	$-0.661633\pi$
$19$	−4.23896	−0.972484	−0.486242	+	0.873824i	$0.661633\pi$
$20$	0.428557	0.0958283
$21$	−5.13358	−1.12024
$22$	0	0
$23$	3.46218	0.721914	0.360957	−	0.932582i	$-0.382450\pi$
$23$	3.46218	0.721914	0.360957	+	0.932582i	$0.382450\pi$
$24$	3.00741	0.613886
$25$	−3.21618	−0.643237
$26$	1.29581	0.254129
$27$	−1.00000	−0.192450
$28$	−1.64723	−0.311297
$29$	4.70827	0.874304	0.437152	−	0.899388i	$-0.355987\pi$
$29$	4.70827	0.874304	0.437152	+	0.899388i	$0.355987\pi$
$30$	1.73068	0.315978
$31$	4.24350	0.762155	0.381077	−	0.924543i	$-0.375553\pi$
$31$	4.24350	0.762155	0.381077	+	0.924543i	$0.375553\pi$
$32$	1.79658	0.317594
$33$	0	0
$34$	6.73472	1.15499
$35$	−6.85639	−1.15894
$36$	−0.320873	−0.0534789
$37$	−8.46260	−1.39124	−0.695621	−	0.718409i	$-0.744871\pi$
$37$	−8.46260	−1.39124	−0.695621	+	0.718409i	$0.744871\pi$
$38$	−5.49289	−0.891065
$39$	−1.00000	−0.160128
$40$	4.01669	0.635094
$41$	7.86990	1.22907	0.614536	−	0.788889i	$-0.289343\pi$
$41$	7.86990	1.22907	0.614536	+	0.788889i	$0.289343\pi$
$42$	−6.65215	−1.02645
$43$	2.51675	0.383801	0.191900	−	0.981414i	$-0.438535\pi$
$43$	2.51675	0.383801	0.191900	+	0.981414i	$0.438535\pi$
$44$	0	0
$45$	−1.33560	−0.199099
$46$	4.48633	0.661473
$47$	−11.5344	−1.68247	−0.841234	−	0.540671i	$-0.818170\pi$
$47$	−11.5344	−1.68247	−0.841234	+	0.540671i	$0.818170\pi$
$48$	3.25529	0.469861
$49$	19.3537	2.76481
$50$	−4.16757	−0.589383
$51$	−5.19730	−0.727768
$52$	−0.320873	−0.0444971
$53$	−11.0282	−1.51483	−0.757417	−	0.652932i	$-0.773539\pi$
$53$	−11.0282	−1.51483	−0.757417	+	0.652932i	$0.773539\pi$
$54$	−1.29581	−0.176338
$55$	0	0
$56$	−15.4388	−2.06310
$57$	4.23896	0.561464
$58$	6.10103	0.801104
$59$	−1.03395	−0.134609	−0.0673044	−	0.997732i	$-0.521440\pi$
$59$	−1.03395	−0.134609	−0.0673044	+	0.997732i	$0.521440\pi$
$60$	−0.428557	−0.0553265
$61$	−0.549443	−0.0703490	−0.0351745	−	0.999381i	$-0.511199\pi$
$61$	−0.549443	−0.0703490	−0.0351745	+	0.999381i	$0.511199\pi$
$62$	5.49877	0.698345
$63$	5.13358	0.646771
$64$	8.83862	1.10483
$65$	−1.33560	−0.165660
$66$	0	0
$67$	−7.62437	−0.931465	−0.465732	−	0.884926i	$-0.654209\pi$
$67$	−7.62437	−0.931465	−0.465732	+	0.884926i	$0.654209\pi$
$68$	−1.66767	−0.202235
$69$	−3.46218	−0.416797
$70$	−8.88459	−1.06191
$71$	4.34984	0.516232	0.258116	−	0.966114i	$-0.416898\pi$
$71$	4.34984	0.516232	0.258116	+	0.966114i	$0.416898\pi$
$72$	−3.00741	−0.354427
$73$	10.5117	1.23030	0.615148	−	0.788412i	$-0.289096\pi$
$73$	10.5117	1.23030	0.615148	+	0.788412i	$0.289096\pi$
$74$	−10.9659	−1.27476
$75$	3.21618	0.371373
$76$	1.36017	0.156022
$77$	0	0
$78$	−1.29581	−0.146722
$79$	15.1417	1.70357	0.851786	−	0.523890i	$-0.175520\pi$
$79$	15.1417	1.70357	0.851786	+	0.523890i	$0.175520\pi$
$80$	4.34776	0.486094
$81$	1.00000	0.111111
$82$	10.1979	1.12617
$83$	7.47118	0.820068	0.410034	−	0.912070i	$-0.365517\pi$
$83$	7.47118	0.820068	0.410034	+	0.912070i	$0.365517\pi$
$84$	1.64723	0.179727
$85$	−6.94149	−0.752911
$86$	3.26123	0.351668
$87$	−4.70827	−0.504779
$88$	0	0
$89$	7.64133	0.809979	0.404990	−	0.914321i	$-0.367275\pi$
$89$	7.64133	0.809979	0.404990	+	0.914321i	$0.367275\pi$
$90$	−1.73068	−0.182430
$91$	5.13358	0.538146
$92$	−1.11092	−0.115822
$93$	−4.24350	−0.440030
$94$	−14.9464	−1.54161
$95$	5.66154	0.580861
$96$	−1.79658	−0.183363
$97$	−5.88642	−0.597675	−0.298837	−	0.954304i	$-0.596599\pi$
$97$	−5.88642	−0.597675	−0.298837	+	0.954304i	$0.596599\pi$
$98$	25.0787	2.53333
$99$	0	0
$100$	1.03199	0.103199
$101$	6.72479	0.669141	0.334571	−	0.942371i	$-0.391409\pi$
$101$	6.72479	0.669141	0.334571	+	0.942371i	$0.391409\pi$
$102$	−6.73472	−0.666837
$103$	−16.8169	−1.65702	−0.828510	−	0.559974i	$-0.810811\pi$
$103$	−16.8169	−1.65702	−0.828510	+	0.559974i	$0.810811\pi$
$104$	−3.00741	−0.294901
$105$	6.85639	0.669115
$106$	−14.2904	−1.38801
$107$	5.66441	0.547599	0.273800	−	0.961787i	$-0.411719\pi$
$107$	5.66441	0.547599	0.273800	+	0.961787i	$0.411719\pi$
$108$	0.320873	0.0308760
$109$	6.40035	0.613043	0.306521	−	0.951864i	$-0.400835\pi$
$109$	6.40035	0.613043	0.306521	+	0.951864i	$0.400835\pi$
$110$	0	0
$111$	8.46260	0.803234
$112$	−16.7113	−1.57907
$113$	17.5587	1.65179	0.825893	−	0.563826i	$-0.190671\pi$
$113$	17.5587	1.65179	0.825893	+	0.563826i	$0.190671\pi$
$114$	5.49289	0.514456
$115$	−4.62407	−0.431197
$116$	−1.51076	−0.140270
$117$	1.00000	0.0924500
$118$	−1.33980	−0.123339
$119$	26.6808	2.44582
$120$	−4.01669	−0.366672
$121$	0	0
$122$	−0.711975	−0.0644592
$123$	−7.86990	−0.709605
$124$	−1.36163	−0.122278
$125$	10.9735	0.981500
$126$	6.65215	0.592621
$127$	−2.07315	−0.183962	−0.0919811	−	0.995761i	$-0.529320\pi$
$127$	−2.07315	−0.183962	−0.0919811	+	0.995761i	$0.529320\pi$
$128$	7.86002	0.694734
$129$	−2.51675	−0.221588
$130$	−1.73068	−0.151791
$131$	4.14790	0.362404	0.181202	−	0.983446i	$-0.442001\pi$
$131$	4.14790	0.362404	0.181202	+	0.983446i	$0.442001\pi$
$132$	0	0
$133$	−21.7610	−1.88692
$134$	−9.87974	−0.853480
$135$	1.33560	0.114950
$136$	−15.6304	−1.34030
$137$	−2.43972	−0.208440	−0.104220	−	0.994554i	$-0.533235\pi$
$137$	−2.43972	−0.208440	−0.104220	+	0.994554i	$0.533235\pi$
$138$	−4.48633	−0.381902
$139$	1.90794	0.161829	0.0809145	−	0.996721i	$-0.474216\pi$
$139$	1.90794	0.161829	0.0809145	+	0.996721i	$0.474216\pi$
$140$	2.20003	0.185937
$141$	11.5344	0.971374
$142$	5.63658	0.473011
$143$	0	0
$144$	−3.25529	−0.271274
$145$	−6.28834	−0.522219
$146$	13.6211	1.12729
$147$	−19.3537	−1.59626
$148$	2.71542	0.223206
$149$	11.4691	0.939585	0.469793	−	0.882777i	$-0.344329\pi$
$149$	11.4691	0.939585	0.469793	+	0.882777i	$0.344329\pi$
$150$	4.16757	0.340280
$151$	20.2241	1.64582	0.822909	−	0.568174i	$-0.192350\pi$
$151$	20.2241	1.64582	0.822909	+	0.568174i	$0.192350\pi$
$152$	12.7483	1.03402
$153$	5.19730	0.420177
$154$	0	0
$155$	−5.66760	−0.455233
$156$	0.320873	0.0256904
$157$	−12.2158	−0.974930	−0.487465	−	0.873143i	$-0.662078\pi$
$157$	−12.2158	−0.974930	−0.487465	+	0.873143i	$0.662078\pi$
$158$	19.6208	1.56094
$159$	11.0282	0.874589
$160$	−2.39951	−0.189698
$161$	17.7734	1.40074
$162$	1.29581	0.101809
$163$	8.68702	0.680420	0.340210	−	0.940350i	$-0.389502\pi$
$163$	8.68702	0.680420	0.340210	+	0.940350i	$0.389502\pi$
$164$	−2.52524	−0.197188
$165$	0	0
$166$	9.68124	0.751410
$167$	−4.05267	−0.313605	−0.156803	−	0.987630i	$-0.550119\pi$
$167$	−4.05267	−0.313605	−0.156803	+	0.987630i	$0.550119\pi$
$168$	15.4388	1.19113
$169$	1.00000	0.0769231
$170$	−8.99486	−0.689875
$171$	−4.23896	−0.324161
$172$	−0.807558	−0.0615757
$173$	−3.40566	−0.258927	−0.129464	−	0.991584i	$-0.541326\pi$
$173$	−3.40566	−0.258927	−0.129464	+	0.991584i	$0.541326\pi$
$174$	−6.10103	−0.462518
$175$	−16.5105	−1.24808
$176$	0	0
$177$	1.03395	0.0777164
$178$	9.90172	0.742165
$179$	22.3266	1.66877	0.834385	−	0.551183i	$-0.185823\pi$
$179$	22.3266	1.66877	0.834385	+	0.551183i	$0.185823\pi$
$180$	0.428557	0.0319428
$181$	−1.98276	−0.147378	−0.0736888	−	0.997281i	$-0.523477\pi$
$181$	−1.98276	−0.147378	−0.0736888	+	0.997281i	$0.523477\pi$
$182$	6.65215	0.493091
$183$	0.549443	0.0406160
$184$	−10.4122	−0.767598
$185$	11.3026	0.830985
$186$	−5.49877	−0.403190
$187$	0	0
$188$	3.70109	0.269930
$189$	−5.13358	−0.373413
$190$	7.33628	0.532230
$191$	−6.67868	−0.483252	−0.241626	−	0.970369i	$-0.577681\pi$
$191$	−6.67868	−0.483252	−0.241626	+	0.970369i	$0.577681\pi$
$192$	−8.83862	−0.637872
$193$	11.8732	0.854650	0.427325	−	0.904098i	$-0.359456\pi$
$193$	11.8732	0.854650	0.427325	+	0.904098i	$0.359456\pi$
$194$	−7.62768	−0.547636
$195$	1.33560	0.0956440
$196$	−6.21008	−0.443577
$197$	−0.795388	−0.0566690	−0.0283345	−	0.999598i	$-0.509020\pi$
$197$	−0.795388	−0.0566690	−0.0283345	+	0.999598i	$0.509020\pi$
$198$	0	0
$199$	−13.3224	−0.944400	−0.472200	−	0.881491i	$-0.656540\pi$
$199$	−13.3224	−0.944400	−0.472200	+	0.881491i	$0.656540\pi$
$200$	9.67240	0.683942
$201$	7.62437	0.537781
$202$	8.71405	0.613119
$203$	24.1703	1.69642
$204$	1.66767	0.116761
$205$	−10.5110	−0.734120
$206$	−21.7916	−1.51829
$207$	3.46218	0.240638
$208$	−3.25529	−0.225714
$209$	0	0
$210$	8.88459	0.613095
$211$	18.8513	1.29778	0.648889	−	0.760883i	$-0.275234\pi$
$211$	18.8513	1.29778	0.648889	+	0.760883i	$0.275234\pi$
$212$	3.53864	0.243035
$213$	−4.34984	−0.298046
$214$	7.34001	0.501753
$215$	−3.36136	−0.229243
$216$	3.00741	0.204629
$217$	21.7844	1.47882
$218$	8.29365	0.561717
$219$	−10.5117	−0.710312
$220$	0	0
$221$	5.19730	0.349608
$222$	10.9659	0.735985
$223$	24.1955	1.62025	0.810124	−	0.586258i	$-0.199400\pi$
$223$	24.1955	1.62025	0.810124	+	0.586258i	$0.199400\pi$
$224$	9.22290	0.616231
$225$	−3.21618	−0.214412
$226$	22.7528	1.51349
$227$	−7.16660	−0.475664	−0.237832	−	0.971306i	$-0.576437\pi$
$227$	−7.16660	−0.475664	−0.237832	+	0.971306i	$0.576437\pi$
$228$	−1.36017	−0.0900794
$229$	4.48292	0.296240	0.148120	−	0.988969i	$-0.452678\pi$
$229$	4.48292	0.296240	0.148120	+	0.988969i	$0.452678\pi$
$230$	−5.99193	−0.395096
$231$	0	0
$232$	−14.1597	−0.929631
$233$	3.45289	0.226206	0.113103	−	0.993583i	$-0.463921\pi$
$233$	3.45289	0.226206	0.113103	+	0.993583i	$0.463921\pi$
$234$	1.29581	0.0847098
$235$	15.4053	1.00493
$236$	0.331767	0.0215962
$237$	−15.1417	−0.983558
$238$	34.5732	2.24105
$239$	−2.40303	−0.155439	−0.0777196	−	0.996975i	$-0.524764\pi$
$239$	−2.40303	−0.155439	−0.0777196	+	0.996975i	$0.524764\pi$
$240$	−4.34776	−0.280646
$241$	−12.4843	−0.804186	−0.402093	−	0.915599i	$-0.631717\pi$
$241$	−12.4843	−0.804186	−0.402093	+	0.915599i	$0.631717\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0.176302	0.0112866
$245$	−25.8487	−1.65141
$246$	−10.1979	−0.650195
$247$	−4.23896	−0.269719
$248$	−12.7620	−0.810385
$249$	−7.47118	−0.473467
$250$	14.2196	0.899326
$251$	10.8086	0.682234	0.341117	−	0.940021i	$-0.389195\pi$
$251$	10.8086	0.682234	0.341117	+	0.940021i	$0.389195\pi$
$252$	−1.64723	−0.103766
$253$	0	0
$254$	−2.68641	−0.168560
$255$	6.94149	0.434693
$256$	−7.49214	−0.468258
$257$	15.2512	0.951343	0.475671	−	0.879623i	$-0.342205\pi$
$257$	15.2512	0.951343	0.475671	+	0.879623i	$0.342205\pi$
$258$	−3.26123	−0.203036
$259$	−43.4435	−2.69945
$260$	0.428557	0.0265780
$261$	4.70827	0.291435
$262$	5.37490	0.332063
$263$	−2.09170	−0.128980	−0.0644898	−	0.997918i	$-0.520542\pi$
$263$	−2.09170	−0.128980	−0.0644898	+	0.997918i	$0.520542\pi$
$264$	0	0
$265$	14.7292	0.904805
$266$	−28.1982	−1.72894
$267$	−7.64133	−0.467642
$268$	2.44646	0.149441
$269$	9.69422	0.591067	0.295534	−	0.955332i	$-0.404503\pi$
$269$	9.69422	0.591067	0.295534	+	0.955332i	$0.404503\pi$
$270$	1.73068	0.105326
$271$	13.6672	0.830226	0.415113	−	0.909770i	$-0.363742\pi$
$271$	13.6672	0.830226	0.415113	+	0.909770i	$0.363742\pi$
$272$	−16.9187	−1.02585
$273$	−5.13358	−0.310699
$274$	−3.16142	−0.190989
$275$	0	0
$276$	1.11092	0.0668696
$277$	−22.7582	−1.36741	−0.683704	−	0.729760i	$-0.739632\pi$
$277$	−22.7582	−1.36741	−0.683704	+	0.729760i	$0.739632\pi$
$278$	2.47233	0.148280
$279$	4.24350	0.254052
$280$	20.6200	1.23228
$281$	13.1755	0.785982	0.392991	−	0.919542i	$-0.371440\pi$
$281$	13.1755	0.785982	0.392991	+	0.919542i	$0.371440\pi$
$282$	14.9464	0.890047
$283$	−6.52134	−0.387653	−0.193827	−	0.981036i	$-0.562090\pi$
$283$	−6.52134	−0.387653	−0.193827	+	0.981036i	$0.562090\pi$
$284$	−1.39575	−0.0828225
$285$	−5.66154	−0.335360
$286$	0	0
$287$	40.4008	2.38478
$288$	1.79658	0.105865
$289$	10.0119	0.588937
$290$	−8.14851	−0.478497
$291$	5.88642	0.345068
$292$	−3.37291	−0.197385
$293$	14.6163	0.853896	0.426948	−	0.904276i	$-0.359589\pi$
$293$	14.6163	0.853896	0.426948	+	0.904276i	$0.359589\pi$
$294$	−25.0787	−1.46262
$295$	1.38094	0.0804014
$296$	25.4505	1.47928
$297$	0	0
$298$	14.8618	0.860920
$299$	3.46218	0.200223
$300$	−1.03199	−0.0595818
$301$	12.9199	0.744694
$302$	26.2067	1.50802
$303$	−6.72479	−0.386329
$304$	13.7991	0.791430
$305$	0.733834	0.0420192
$306$	6.73472	0.384998
$307$	23.2249	1.32552	0.662758	−	0.748834i	$-0.269386\pi$
$307$	23.2249	1.32552	0.662758	+	0.748834i	$0.269386\pi$
$308$	0	0
$309$	16.8169	0.956681
$310$	−7.34414	−0.417119
$311$	−29.4051	−1.66741	−0.833706	−	0.552209i	$-0.813785\pi$
$311$	−29.4051	−1.66741	−0.833706	+	0.552209i	$0.813785\pi$
$312$	3.00741	0.170261
$313$	−2.84405	−0.160755	−0.0803776	−	0.996764i	$-0.525613\pi$
$313$	−2.84405	−0.160755	−0.0803776	+	0.996764i	$0.525613\pi$
$314$	−15.8294	−0.893306
$315$	−6.85639	−0.386314
$316$	−4.85856	−0.273315
$317$	−13.5296	−0.759900	−0.379950	−	0.925007i	$-0.624059\pi$
$317$	−13.5296	−0.759900	−0.379950	+	0.925007i	$0.624059\pi$
$318$	14.2904	0.801366
$319$	0	0
$320$	−11.8048	−0.659910
$321$	−5.66441	−0.316157
$322$	23.0310	1.28347
$323$	−22.0311	−1.22585
$324$	−0.320873	−0.0178263
$325$	−3.21618	−0.178402
$326$	11.2567	0.623453
$327$	−6.40035	−0.353940
$328$	−23.6680	−1.30685
$329$	−59.2129	−3.26451
$330$	0	0
$331$	−29.8070	−1.63834	−0.819170	−	0.573551i	$-0.805565\pi$
$331$	−29.8070	−1.63834	−0.819170	+	0.573551i	$0.805565\pi$
$332$	−2.39730	−0.131569
$333$	−8.46260	−0.463748
$334$	−5.25150	−0.287349
$335$	10.1831	0.556361
$336$	16.7113	0.911677
$337$	−30.2024	−1.64523	−0.822614	−	0.568601i	$-0.807485\pi$
$337$	−30.2024	−1.64523	−0.822614	+	0.568601i	$0.807485\pi$
$338$	1.29581	0.0704828
$339$	−17.5587	−0.953660
$340$	2.22734	0.120794
$341$	0	0
$342$	−5.49289	−0.297022
$343$	63.4186	3.42428
$344$	−7.56891	−0.408088
$345$	4.62407	0.248952
$346$	−4.41309	−0.237249
$347$	14.3920	0.772604	0.386302	−	0.922372i	$-0.373752\pi$
$347$	14.3920	0.772604	0.386302	+	0.922372i	$0.373752\pi$
$348$	1.51076	0.0809851
$349$	−7.48287	−0.400549	−0.200274	−	0.979740i	$-0.564183\pi$
$349$	−7.48287	−0.400549	−0.200274	+	0.979740i	$0.564183\pi$
$350$	−21.3946	−1.14359
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	16.9258	0.900867	0.450433	−	0.892810i	$-0.351269\pi$
$353$	16.9258	0.900867	0.450433	+	0.892810i	$0.351269\pi$
$354$	1.33980	0.0712098
$355$	−5.80963	−0.308343
$356$	−2.45190	−0.129950
$357$	−26.6808	−1.41210
$358$	28.9311	1.52905
$359$	22.5281	1.18899	0.594493	−	0.804101i	$-0.297353\pi$
$359$	22.5281	1.18899	0.594493	+	0.804101i	$0.297353\pi$
$360$	4.01669	0.211698
$361$	−1.03123	−0.0542750
$362$	−2.56929	−0.135039
$363$	0	0
$364$	−1.64723	−0.0863383
$365$	−14.0393	−0.734852
$366$	0.711975	0.0372155
$367$	−9.23495	−0.482061	−0.241030	−	0.970518i	$-0.577485\pi$
$367$	−9.23495	−0.482061	−0.241030	+	0.970518i	$0.577485\pi$
$368$	−11.2704	−0.587511
$369$	7.86990	0.409691
$370$	14.6461	0.761412
$371$	−56.6139	−2.93925
$372$	1.36163	0.0705970
$373$	−34.1084	−1.76607	−0.883034	−	0.469309i	$-0.844503\pi$
$373$	−34.1084	−1.76607	−0.883034	+	0.469309i	$0.844503\pi$
$374$	0	0
$375$	−10.9735	−0.566669
$376$	34.6888	1.78894
$377$	4.70827	0.242488
$378$	−6.65215	−0.342150
$379$	−3.19487	−0.164110	−0.0820548	−	0.996628i	$-0.526148\pi$
$379$	−3.19487	−0.164110	−0.0820548	+	0.996628i	$0.526148\pi$
$380$	−1.81664	−0.0931914
$381$	2.07315	0.106211
$382$	−8.65430	−0.442793
$383$	13.8676	0.708602	0.354301	−	0.935131i	$-0.384719\pi$
$383$	13.8676	0.708602	0.354301	+	0.935131i	$0.384719\pi$
$384$	−7.86002	−0.401105
$385$	0	0
$386$	15.3854	0.783096
$387$	2.51675	0.127934
$388$	1.88879	0.0958890
$389$	13.3531	0.677031	0.338515	−	0.940961i	$-0.390075\pi$
$389$	13.3531	0.677031	0.338515	+	0.940961i	$0.390075\pi$
$390$	1.73068	0.0876364
$391$	17.9940	0.909995
$392$	−58.2045	−2.93977
$393$	−4.14790	−0.209234
$394$	−1.03067	−0.0519245
$395$	−20.2232	−1.01754
$396$	0	0
$397$	4.18951	0.210266	0.105133	−	0.994458i	$-0.466473\pi$
$397$	4.18951	0.210266	0.105133	+	0.994458i	$0.466473\pi$
$398$	−17.2633	−0.865332
$399$	21.7610	1.08942
$400$	10.4696	0.523481
$401$	23.9379	1.19540	0.597701	−	0.801719i	$-0.296081\pi$
$401$	23.9379	1.19540	0.597701	+	0.801719i	$0.296081\pi$
$402$	9.87974	0.492757
$403$	4.24350	0.211384
$404$	−2.15780	−0.107355
$405$	−1.33560	−0.0663663
$406$	31.3201	1.55439
$407$	0	0
$408$	15.6304	0.773822
$409$	4.02972	0.199257	0.0996285	−	0.995025i	$-0.468235\pi$
$409$	4.02972	0.199257	0.0996285	+	0.995025i	$0.468235\pi$
$410$	−13.6203	−0.672658
$411$	2.43972	0.120343
$412$	5.39610	0.265847
$413$	−5.30787	−0.261183
$414$	4.48633	0.220491
$415$	−9.97847	−0.489824
$416$	1.79658	0.0880846
$417$	−1.90794	−0.0934320
$418$	0	0
$419$	2.08844	0.102027	0.0510136	−	0.998698i	$-0.483755\pi$
$419$	2.08844	0.102027	0.0510136	+	0.998698i	$0.483755\pi$
$420$	−2.20003	−0.107351
$421$	5.72072	0.278811	0.139405	−	0.990235i	$-0.455481\pi$
$421$	5.72072	0.278811	0.139405	+	0.990235i	$0.455481\pi$
$422$	24.4277	1.18912
$423$	−11.5344	−0.560823
$424$	33.1662	1.61069
$425$	−16.7155	−0.810820
$426$	−5.63658	−0.273093
$427$	−2.82061	−0.136499
$428$	−1.81756	−0.0878550
$429$	0	0
$430$	−4.35569	−0.210050
$431$	−3.27779	−0.157886	−0.0789429	−	0.996879i	$-0.525154\pi$
$431$	−3.27779	−0.157886	−0.0789429	+	0.996879i	$0.525154\pi$
$432$	3.25529	0.156620
$433$	−16.3007	−0.783364	−0.391682	−	0.920101i	$-0.628107\pi$
$433$	−16.3007	−0.783364	−0.391682	+	0.920101i	$0.628107\pi$
$434$	28.2284	1.35501
$435$	6.28834	0.301503
$436$	−2.05370	−0.0983545
$437$	−14.6760	−0.702050
$438$	−13.6211	−0.650842
$439$	−8.36438	−0.399210	−0.199605	−	0.979876i	$-0.563966\pi$
$439$	−8.36438	−0.399210	−0.199605	+	0.979876i	$0.563966\pi$
$440$	0	0
$441$	19.3537	0.921604
$442$	6.73472	0.320338
$443$	21.5276	1.02281	0.511405	−	0.859340i	$-0.329125\pi$
$443$	21.5276	1.02281	0.511405	+	0.859340i	$0.329125\pi$
$444$	−2.71542	−0.128868
$445$	−10.2057	−0.483798
$446$	31.3528	1.48460
$447$	−11.4691	−0.542470
$448$	45.3738	2.14371
$449$	10.0017	0.472009	0.236005	−	0.971752i	$-0.424162\pi$
$449$	10.0017	0.472009	0.236005	+	0.971752i	$0.424162\pi$
$450$	−4.16757	−0.196461
$451$	0	0
$452$	−5.63413	−0.265007
$453$	−20.2241	−0.950213
$454$	−9.28656	−0.435840
$455$	−6.85639	−0.321433
$456$	−12.7483	−0.596994
$457$	20.4575	0.956961	0.478480	−	0.878098i	$-0.341188\pi$
$457$	20.4575	0.956961	0.478480	+	0.878098i	$0.341188\pi$
$458$	5.80902	0.271438
$459$	−5.19730	−0.242589
$460$	1.48374	0.0691798
$461$	17.0646	0.794776	0.397388	−	0.917651i	$-0.369917\pi$
$461$	17.0646	0.794776	0.397388	+	0.917651i	$0.369917\pi$
$462$	0	0
$463$	2.88792	0.134213	0.0671065	−	0.997746i	$-0.478623\pi$
$463$	2.88792	0.134213	0.0671065	+	0.997746i	$0.478623\pi$
$464$	−15.3268	−0.711529
$465$	5.66760	0.262829
$466$	4.47429	0.207267
$467$	17.9572	0.830958	0.415479	−	0.909603i	$-0.363614\pi$
$467$	17.9572	0.830958	0.415479	+	0.909603i	$0.363614\pi$
$468$	−0.320873	−0.0148324
$469$	−39.1403	−1.80733
$470$	19.9624	0.920797
$471$	12.2158	0.562876
$472$	3.10951	0.143127
$473$	0	0
$474$	−19.6208	−0.901211
$475$	13.6333	0.625537
$476$	−8.56115	−0.392400
$477$	−11.0282	−0.504944
$478$	−3.11388	−0.142425
$479$	−4.84099	−0.221191	−0.110595	−	0.993866i	$-0.535276\pi$
$479$	−4.84099	−0.221191	−0.110595	+	0.993866i	$0.535276\pi$
$480$	2.39951	0.109522
$481$	−8.46260	−0.385861
$482$	−16.1773	−0.736857
$483$	−17.7734	−0.808717
$484$	0	0
$485$	7.86187	0.356989
$486$	−1.29581	−0.0587792
$487$	−36.0541	−1.63377	−0.816884	−	0.576802i	$-0.804300\pi$
$487$	−36.0541	−1.63377	−0.816884	+	0.576802i	$0.804300\pi$
$488$	1.65240	0.0748008
$489$	−8.68702	−0.392840
$490$	−33.4950	−1.51315
$491$	1.06957	0.0482691	0.0241346	−	0.999709i	$-0.492317\pi$
$491$	1.06957	0.0482691	0.0241346	+	0.999709i	$0.492317\pi$
$492$	2.52524	0.113847
$493$	24.4703	1.10209
$494$	−5.49289	−0.247137
$495$	0	0
$496$	−13.8138	−0.620260
$497$	22.3303	1.00165
$498$	−9.68124	−0.433827
$499$	0.0986671	0.00441695	0.00220847	−	0.999998i	$-0.499297\pi$
$499$	0.0986671	0.00441695	0.00220847	+	0.999998i	$0.499297\pi$
$500$	−3.52110	−0.157469
$501$	4.05267	0.181060
$502$	14.0059	0.625116
$503$	−1.31032	−0.0584244	−0.0292122	−	0.999573i	$-0.509300\pi$
$503$	−1.31032	−0.0584244	−0.0292122	+	0.999573i	$0.509300\pi$
$504$	−15.4388	−0.687699
$505$	−8.98160	−0.399676
$506$	0	0
$507$	−1.00000	−0.0444116
$508$	0.665218	0.0295143
$509$	−33.6313	−1.49068	−0.745340	−	0.666684i	$-0.767713\pi$
$509$	−33.6313	−1.49068	−0.745340	+	0.666684i	$0.767713\pi$
$510$	8.99486	0.398299
$511$	53.9625	2.38716
$512$	−25.4284	−1.12379
$513$	4.23896	0.187155
$514$	19.7627	0.871693
$515$	22.4606	0.989733
$516$	0.807558	0.0355508
$517$	0	0
$518$	−56.2945	−2.47344
$519$	3.40566	0.149492
$520$	4.01669	0.176143
$521$	38.4482	1.68444	0.842222	−	0.539130i	$-0.181247\pi$
$521$	38.4482	1.68444	0.842222	+	0.539130i	$0.181247\pi$
$522$	6.10103	0.267035
$523$	38.1775	1.66939	0.834693	−	0.550715i	$-0.185645\pi$
$523$	38.1775	1.66939	0.834693	+	0.550715i	$0.185645\pi$
$524$	−1.33095	−0.0581429
$525$	16.5105	0.720579
$526$	−2.71044	−0.118181
$527$	22.0547	0.960720
$528$	0	0
$529$	−11.0133	−0.478840
$530$	19.0862	0.829052
$531$	−1.03395	−0.0448696
$532$	6.98254	0.302731
$533$	7.86990	0.340883
$534$	−9.90172	−0.428489
$535$	−7.56537	−0.327079
$536$	22.9296	0.990409
$537$	−22.3266	−0.963464
$538$	12.5619	0.541581
$539$	0	0
$540$	−0.428557	−0.0184422
$541$	−45.5341	−1.95767	−0.978833	−	0.204662i	$-0.934390\pi$
$541$	−45.5341	−1.95767	−0.978833	+	0.204662i	$0.934390\pi$
$542$	17.7102	0.760717
$543$	1.98276	0.0850886
$544$	9.33737	0.400336
$545$	−8.54829	−0.366168
$546$	−6.65215	−0.284686
$547$	−15.0021	−0.641445	−0.320722	−	0.947173i	$-0.603926\pi$
$547$	−15.0021	−0.641445	−0.320722	+	0.947173i	$0.603926\pi$
$548$	0.782842	0.0334414
$549$	−0.549443	−0.0234497
$550$	0	0
$551$	−19.9582	−0.850246
$552$	10.4122	0.443173
$553$	77.7311	3.30546
$554$	−29.4903	−1.25292
$555$	−11.3026	−0.479769
$556$	−0.612206	−0.0259633
$557$	−26.5233	−1.12383	−0.561914	−	0.827195i	$-0.689935\pi$
$557$	−26.5233	−1.12383	−0.561914	+	0.827195i	$0.689935\pi$
$558$	5.49877	0.232782
$559$	2.51675	0.106447
$560$	22.3196	0.943174
$561$	0	0
$562$	17.0729	0.720177
$563$	−5.05144	−0.212893	−0.106446	−	0.994318i	$-0.533947\pi$
$563$	−5.05144	−0.212893	−0.106446	+	0.994318i	$0.533947\pi$
$564$	−3.70109	−0.155844
$565$	−23.4514	−0.986607
$566$	−8.45042	−0.355198
$567$	5.13358	0.215590
$568$	−13.0818	−0.548899
$569$	−43.2405	−1.81273	−0.906367	−	0.422491i	$-0.861156\pi$
$569$	−43.2405	−1.81273	−0.906367	+	0.422491i	$0.861156\pi$
$570$	−7.33628	−0.307283
$571$	−42.7566	−1.78931	−0.894653	−	0.446761i	$-0.852577\pi$
$571$	−42.7566	−1.78931	−0.894653	+	0.446761i	$0.852577\pi$
$572$	0	0
$573$	6.67868	0.279006
$574$	52.3518	2.18512
$575$	−11.1350	−0.464362
$576$	8.83862	0.368276
$577$	−33.3622	−1.38889	−0.694443	−	0.719547i	$-0.744349\pi$
$577$	−33.3622	−1.38889	−0.694443	+	0.719547i	$0.744349\pi$
$578$	12.9736	0.539629
$579$	−11.8732	−0.493433
$580$	2.01776	0.0837830
$581$	38.3539	1.59119
$582$	7.62768	0.316178
$583$	0	0
$584$	−31.6129	−1.30815
$585$	−1.33560	−0.0552201
$586$	18.9400	0.782405
$587$	−11.6006	−0.478809	−0.239404	−	0.970920i	$-0.576952\pi$
$587$	−11.6006	−0.478809	−0.239404	+	0.970920i	$0.576952\pi$
$588$	6.21008	0.256099
$589$	−17.9880	−0.741183
$590$	1.78944	0.0736699
$591$	0.795388	0.0327179
$592$	27.5482	1.13223
$593$	−6.47910	−0.266065	−0.133032	−	0.991112i	$-0.542471\pi$
$593$	−6.47910	−0.266065	−0.133032	+	0.991112i	$0.542471\pi$
$594$	0	0
$595$	−35.6347	−1.46088
$596$	−3.68013	−0.150744
$597$	13.3224	0.545250
$598$	4.48633	0.183460
$599$	−29.3566	−1.19948	−0.599739	−	0.800195i	$-0.704729\pi$
$599$	−29.3566	−1.19948	−0.599739	+	0.800195i	$0.704729\pi$
$600$	−9.67240	−0.394874
$601$	−27.7592	−1.13232	−0.566161	−	0.824295i	$-0.691572\pi$
$601$	−27.7592	−1.13232	−0.566161	+	0.824295i	$0.691572\pi$
$602$	16.7418	0.682345
$603$	−7.62437	−0.310488
$604$	−6.48939	−0.264049
$605$	0	0
$606$	−8.71405	−0.353984
$607$	3.83550	0.155678	0.0778391	−	0.996966i	$-0.475198\pi$
$607$	3.83550	0.155678	0.0778391	+	0.996966i	$0.475198\pi$
$608$	−7.61563	−0.308855
$609$	−24.1703	−0.979430
$610$	0.950910	0.0385012
$611$	−11.5344	−0.466633
$612$	−1.66767	−0.0674118
$613$	0.861210	0.0347840	0.0173920	−	0.999849i	$-0.494464\pi$
$613$	0.861210	0.0347840	0.0173920	+	0.999849i	$0.494464\pi$
$614$	30.0951	1.21454
$615$	10.5110	0.423845
$616$	0	0
$617$	−1.66906	−0.0671939	−0.0335970	−	0.999435i	$-0.510696\pi$
$617$	−1.66906	−0.0671939	−0.0335970	+	0.999435i	$0.510696\pi$
$618$	21.7916	0.876585
$619$	−23.3574	−0.938812	−0.469406	−	0.882982i	$-0.655532\pi$
$619$	−23.3574	−0.938812	−0.469406	+	0.882982i	$0.655532\pi$
$620$	1.81858	0.0730360
$621$	−3.46218	−0.138932
$622$	−38.1035	−1.52781
$623$	39.2274	1.57161
$624$	3.25529	0.130316
$625$	1.42476	0.0569903
$626$	−3.68535	−0.147296
$627$	0	0
$628$	3.91974	0.156414
$629$	−43.9827	−1.75370
$630$	−8.88459	−0.353971
$631$	−32.0889	−1.27744	−0.638719	−	0.769440i	$-0.720535\pi$
$631$	−32.0889	−1.27744	−0.638719	+	0.769440i	$0.720535\pi$
$632$	−45.5373	−1.81138
$633$	−18.8513	−0.749272
$634$	−17.5319	−0.696279
$635$	2.76889	0.109880
$636$	−3.53864	−0.140316
$637$	19.3537	0.766821
$638$	0	0
$639$	4.34984	0.172077
$640$	−10.4978	−0.414962
$641$	−29.6097	−1.16951	−0.584756	−	0.811209i	$-0.698810\pi$
$641$	−29.6097	−1.16951	−0.584756	+	0.811209i	$0.698810\pi$
$642$	−7.34001	−0.289687
$643$	−9.49762	−0.374549	−0.187275	−	0.982308i	$-0.559965\pi$
$643$	−9.49762	−0.374549	−0.187275	+	0.982308i	$0.559965\pi$
$644$	−5.70300	−0.224730
$645$	3.36136	0.132353
$646$	−28.5482	−1.12321
$647$	3.28992	0.129340	0.0646701	−	0.997907i	$-0.479400\pi$
$647$	3.28992	0.129340	0.0646701	+	0.997907i	$0.479400\pi$
$648$	−3.00741	−0.118142
$649$	0	0
$650$	−4.16757	−0.163465
$651$	−21.7844	−0.853796
$652$	−2.78743	−0.109164
$653$	22.3605	0.875034	0.437517	−	0.899210i	$-0.355858\pi$
$653$	22.3605	0.875034	0.437517	+	0.899210i	$0.355858\pi$
$654$	−8.29365	−0.324307
$655$	−5.53992	−0.216463
$656$	−25.6188	−1.00025
$657$	10.5117	0.410099
$658$	−76.7288	−2.99120
$659$	−32.2194	−1.25509	−0.627544	−	0.778581i	$-0.715940\pi$
$659$	−32.2194	−1.25509	−0.627544	+	0.778581i	$0.715940\pi$
$660$	0	0
$661$	29.0822	1.13117	0.565583	−	0.824692i	$-0.308651\pi$
$661$	29.0822	1.13117	0.565583	+	0.824692i	$0.308651\pi$
$662$	−38.6242	−1.50117
$663$	−5.19730	−0.201846
$664$	−22.4689	−0.871963
$665$	29.0640	1.12705
$666$	−10.9659	−0.424921
$667$	16.3009	0.631172
$668$	1.30039	0.0503137
$669$	−24.1955	−0.935451
$670$	13.1953	0.509781
$671$	0	0
$672$	−9.22290	−0.355781
$673$	10.2029	0.393293	0.196646	−	0.980474i	$-0.436995\pi$
$673$	10.2029	0.393293	0.196646	+	0.980474i	$0.436995\pi$
$674$	−39.1366	−1.50748
$675$	3.21618	0.123791
$676$	−0.320873	−0.0123413
$677$	−20.7299	−0.796715	−0.398358	−	0.917230i	$-0.630420\pi$
$677$	−20.7299	−0.796715	−0.398358	+	0.917230i	$0.630420\pi$
$678$	−22.7528	−0.873816
$679$	−30.2184	−1.15968
$680$	20.8759	0.800556
$681$	7.16660	0.274625
$682$	0	0
$683$	−36.6034	−1.40059	−0.700296	−	0.713853i	$-0.746949\pi$
$683$	−36.6034	−1.40059	−0.700296	+	0.713853i	$0.746949\pi$
$684$	1.36017	0.0520073
$685$	3.25849	0.124500
$686$	82.1786	3.13759
$687$	−4.48292	−0.171034
$688$	−8.19276	−0.312346
$689$	−11.0282	−0.420139
$690$	5.99193	0.228109
$691$	−30.0259	−1.14224	−0.571119	−	0.820867i	$-0.693490\pi$
$691$	−30.0259	−1.14224	−0.571119	+	0.820867i	$0.693490\pi$
$692$	1.09278	0.0415414
$693$	0	0
$694$	18.6493	0.707919
$695$	−2.54823	−0.0966599
$696$	14.1597	0.536723
$697$	40.9022	1.54928
$698$	−9.69638	−0.367013
$699$	−3.45289	−0.130600
$700$	5.29779	0.200238
$701$	16.4374	0.620833	0.310417	−	0.950601i	$-0.399531\pi$
$701$	16.4374	0.620833	0.310417	+	0.950601i	$0.399531\pi$
$702$	−1.29581	−0.0489072
$703$	35.8726	1.35296
$704$	0	0
$705$	−15.4053	−0.580198
$706$	21.9326	0.825444
$707$	34.5222	1.29834
$708$	−0.331767	−0.0124686
$709$	24.6359	0.925219	0.462610	−	0.886562i	$-0.346913\pi$
$709$	24.6359	0.925219	0.462610	+	0.886562i	$0.346913\pi$
$710$	−7.52819	−0.282528
$711$	15.1417	0.567857
$712$	−22.9806	−0.861236
$713$	14.6918	0.550211
$714$	−34.5732	−1.29387
$715$	0	0
$716$	−7.16401	−0.267732
$717$	2.40303	0.0897429
$718$	29.1921	1.08944
$719$	−0.410144	−0.0152958	−0.00764789	−	0.999971i	$-0.502434\pi$
$719$	−0.410144	−0.0152958	−0.00764789	+	0.999971i	$0.502434\pi$
$720$	4.34776	0.162031
$721$	−86.3311	−3.21514
$722$	−1.33627	−0.0497309
$723$	12.4843	0.464297
$724$	0.636216	0.0236448
$725$	−15.1427	−0.562384
$726$	0	0
$727$	16.4301	0.609359	0.304679	−	0.952455i	$-0.401451\pi$
$727$	16.4301	0.609359	0.304679	+	0.952455i	$0.401451\pi$
$728$	−15.4388	−0.572200
$729$	1.00000	0.0370370
$730$	−18.1923	−0.673328
$731$	13.0803	0.483793
$732$	−0.176302	−0.00651630
$733$	−13.8678	−0.512220	−0.256110	−	0.966648i	$-0.582441\pi$
$733$	−13.8678	−0.512220	−0.256110	+	0.966648i	$0.582441\pi$
$734$	−11.9668	−0.441701
$735$	25.8487	0.953443
$736$	6.22009	0.229275
$737$	0	0
$738$	10.1979	0.375390
$739$	−14.3545	−0.528040	−0.264020	−	0.964517i	$-0.585048\pi$
$739$	−14.3545	−0.528040	−0.264020	+	0.964517i	$0.585048\pi$
$740$	−3.62671	−0.133320
$741$	4.23896	0.155722
$742$	−73.3610	−2.69317
$743$	−35.4031	−1.29881	−0.649406	−	0.760442i	$-0.724982\pi$
$743$	−35.4031	−1.29881	−0.649406	+	0.760442i	$0.724982\pi$
$744$	12.7620	0.467876
$745$	−15.3181	−0.561211
$746$	−44.1981	−1.61821
$747$	7.47118	0.273356
$748$	0	0
$749$	29.0787	1.06251
$750$	−14.2196	−0.519226
$751$	3.07915	0.112360	0.0561799	−	0.998421i	$-0.482108\pi$
$751$	3.07915	0.112360	0.0561799	+	0.998421i	$0.482108\pi$
$752$	37.5479	1.36923
$753$	−10.8086	−0.393888
$754$	6.10103	0.222186
$755$	−27.0113	−0.983041
$756$	1.64723	0.0599092
$757$	−46.0065	−1.67213	−0.836067	−	0.548628i	$-0.815150\pi$
$757$	−46.0065	−1.67213	−0.836067	+	0.548628i	$0.815150\pi$
$758$	−4.13995	−0.150370
$759$	0	0
$760$	−17.0266	−0.617619
$761$	−4.97927	−0.180498	−0.0902492	−	0.995919i	$-0.528766\pi$
$761$	−4.97927	−0.180498	−0.0902492	+	0.995919i	$0.528766\pi$
$762$	2.68641	0.0973183
$763$	32.8568	1.18949
$764$	2.14301	0.0775313
$765$	−6.94149	−0.250970
$766$	17.9698	0.649276
$767$	−1.03395	−0.0373338
$768$	7.49214	0.270349
$769$	4.13404	0.149077	0.0745387	−	0.997218i	$-0.476252\pi$
$769$	4.13404	0.149077	0.0745387	+	0.997218i	$0.476252\pi$
$770$	0	0
$771$	−15.2512	−0.549258
$772$	−3.80979	−0.137117
$773$	30.0912	1.08231	0.541153	−	0.840924i	$-0.317988\pi$
$773$	30.0912	1.08231	0.541153	+	0.840924i	$0.317988\pi$
$774$	3.26123	0.117223
$775$	−13.6479	−0.490246
$776$	17.7029	0.635497
$777$	43.4435	1.55853
$778$	17.3031	0.620348
$779$	−33.3602	−1.19525
$780$	−0.428557	−0.0153448
$781$	0	0
$782$	23.3168	0.833807
$783$	−4.70827	−0.168260
$784$	−63.0019	−2.25007
$785$	16.3154	0.582322
$786$	−5.37490	−0.191716
$787$	29.8884	1.06541	0.532703	−	0.846302i	$-0.321176\pi$
$787$	29.8884	1.06541	0.532703	+	0.846302i	$0.321176\pi$
$788$	0.255219	0.00909179
$789$	2.09170	0.0744664
$790$	−26.2054	−0.932346
$791$	90.1392	3.20498
$792$	0	0
$793$	−0.549443	−0.0195113
$794$	5.42882	0.192661
$795$	−14.7292	−0.522389
$796$	4.27480	0.151516
$797$	19.8653	0.703664	0.351832	−	0.936063i	$-0.385559\pi$
$797$	19.8653	0.703664	0.351832	+	0.936063i	$0.385559\pi$
$798$	28.1982	0.998206
$799$	−59.9479	−2.12080
$800$	−5.77813	−0.204288
$801$	7.64133	0.269993
$802$	31.0190	1.09532
$803$	0	0
$804$	−2.44646	−0.0862798
$805$	−23.7381	−0.836657
$806$	5.49877	0.193686
$807$	−9.69422	−0.341253
$808$	−20.2242	−0.711485
$809$	33.7736	1.18742	0.593709	−	0.804680i	$-0.297663\pi$
$809$	33.7736	1.18742	0.593709	+	0.804680i	$0.297663\pi$
$810$	−1.73068	−0.0608099
$811$	34.5492	1.21319	0.606593	−	0.795012i	$-0.292536\pi$
$811$	34.5492	1.21319	0.606593	+	0.795012i	$0.292536\pi$
$812$	−7.75560	−0.272168
$813$	−13.6672	−0.479331
$814$	0	0
$815$	−11.6023	−0.406412
$816$	16.9187	0.592274
$817$	−10.6684	−0.373240
$818$	5.22176	0.182575
$819$	5.13358	0.179382
$820$	3.37270	0.117780
$821$	34.3473	1.19873	0.599364	−	0.800477i	$-0.295420\pi$
$821$	34.3473	1.19873	0.599364	+	0.800477i	$0.295420\pi$
$822$	3.16142	0.110267
$823$	−8.96775	−0.312596	−0.156298	−	0.987710i	$-0.549956\pi$
$823$	−8.96775	−0.312596	−0.156298	+	0.987710i	$0.549956\pi$
$824$	50.5754	1.76188
$825$	0	0
$826$	−6.87799	−0.239316
$827$	−38.3717	−1.33431	−0.667157	−	0.744917i	$-0.732489\pi$
$827$	−38.3717	−1.33431	−0.667157	+	0.744917i	$0.732489\pi$
$828$	−1.11092	−0.0386072
$829$	−26.5545	−0.922277	−0.461139	−	0.887328i	$-0.652559\pi$
$829$	−26.5545	−0.922277	−0.461139	+	0.887328i	$0.652559\pi$
$830$	−12.9302	−0.448814
$831$	22.7582	0.789473
$832$	8.83862	0.306424
$833$	100.587	3.48513
$834$	−2.47233	−0.0856096
$835$	5.41273	0.187315
$836$	0	0
$837$	−4.24350	−0.146677
$838$	2.70623	0.0934851
$839$	23.1373	0.798787	0.399394	−	0.916780i	$-0.369221\pi$
$839$	23.1373	0.798787	0.399394	+	0.916780i	$0.369221\pi$
$840$	−20.6200	−0.711458
$841$	−6.83220	−0.235593
$842$	7.41297	0.255468
$843$	−13.1755	−0.453787
$844$	−6.04888	−0.208211
$845$	−1.33560	−0.0459459
$846$	−14.9464	−0.513869
$847$	0	0
$848$	35.8999	1.23281
$849$	6.52134	0.223812
$850$	−21.6601	−0.742935
$851$	−29.2990	−1.00436
$852$	1.39575	0.0478176
$853$	29.6243	1.01432	0.507158	−	0.861853i	$-0.330696\pi$
$853$	29.6243	1.01432	0.507158	+	0.861853i	$0.330696\pi$
$854$	−3.65498	−0.125071
$855$	5.66154	0.193620
$856$	−17.0352	−0.582252
$857$	43.2426	1.47714	0.738570	−	0.674177i	$-0.235502\pi$
$857$	43.2426	1.47714	0.738570	+	0.674177i	$0.235502\pi$
$858$	0	0
$859$	30.7817	1.05026	0.525129	−	0.851023i	$-0.324017\pi$
$859$	30.7817	1.05026	0.525129	+	0.851023i	$0.324017\pi$
$860$	1.07857	0.0367790
$861$	−40.4008	−1.37685
$862$	−4.24740	−0.144667
$863$	−46.6596	−1.58831	−0.794155	−	0.607715i	$-0.792086\pi$
$863$	−46.6596	−1.58831	−0.794155	+	0.607715i	$0.792086\pi$
$864$	−1.79658	−0.0611209
$865$	4.54858	0.154656
$866$	−21.1227	−0.717778
$867$	−10.0119	−0.340023
$868$	−6.99002	−0.237257
$869$	0	0
$870$	8.14851	0.276260
$871$	−7.62437	−0.258342
$872$	−19.2485	−0.651837
$873$	−5.88642	−0.199225
$874$	−19.0174	−0.643272
$875$	56.3334	1.90442
$876$	3.37291	0.113960
$877$	7.61016	0.256977	0.128488	−	0.991711i	$-0.458987\pi$
$877$	7.61016	0.256977	0.128488	+	0.991711i	$0.458987\pi$
$878$	−10.8387	−0.365787
$879$	−14.6163	−0.492997
$880$	0	0
$881$	25.4044	0.855897	0.427949	−	0.903803i	$-0.359236\pi$
$881$	25.4044	0.855897	0.427949	+	0.903803i	$0.359236\pi$
$882$	25.0787	0.844444
$883$	−35.4094	−1.19162	−0.595811	−	0.803125i	$-0.703169\pi$
$883$	−35.4094	−1.19162	−0.595811	+	0.803125i	$0.703169\pi$
$884$	−1.66767	−0.0560900
$885$	−1.38094	−0.0464198
$886$	27.8958	0.937176
$887$	−43.0717	−1.44620	−0.723102	−	0.690741i	$-0.757285\pi$
$887$	−43.0717	−1.44620	−0.723102	+	0.690741i	$0.757285\pi$
$888$	−25.4505	−0.854064
$889$	−10.6427	−0.356944
$890$	−13.2247	−0.443293
$891$	0	0
$892$	−7.76368	−0.259947
$893$	48.8939	1.63617
$894$	−14.8618	−0.497053
$895$	−29.8193	−0.996750
$896$	40.3501	1.34800
$897$	−3.46218	−0.115599
$898$	12.9603	0.432491
$899$	19.9795	0.666355
$900$	1.03199	0.0343996
$901$	−57.3166	−1.90949
$902$	0	0
$903$	−12.9199	−0.429949
$904$	−52.8064	−1.75631
$905$	2.64817	0.0880282
$906$	−26.2067	−0.870658
$907$	17.8656	0.593219	0.296609	−	0.954999i	$-0.404144\pi$
$907$	17.8656	0.593219	0.296609	+	0.954999i	$0.404144\pi$
$908$	2.29957	0.0763139
$909$	6.72479	0.223047
$910$	−8.88459	−0.294521
$911$	−14.8251	−0.491178	−0.245589	−	0.969374i	$-0.578981\pi$
$911$	−14.8251	−0.491178	−0.245589	+	0.969374i	$0.578981\pi$
$912$	−13.7991	−0.456932
$913$	0	0
$914$	26.5090	0.876841
$915$	−0.733834	−0.0242598
$916$	−1.43845	−0.0475277
$917$	21.2936	0.703177
$918$	−6.73472	−0.222279
$919$	14.8434	0.489639	0.244820	−	0.969569i	$-0.421271\pi$
$919$	14.8434	0.489639	0.244820	+	0.969569i	$0.421271\pi$
$920$	13.9065	0.458484
$921$	−23.2249	−0.765287
$922$	22.1124	0.728234
$923$	4.34984	0.143177
$924$	0	0
$925$	27.2173	0.894898
$926$	3.74220	0.122976
$927$	−16.8169	−0.552340
$928$	8.45879	0.277673
$929$	−43.2453	−1.41883	−0.709416	−	0.704790i	$-0.751041\pi$
$929$	−43.2453	−1.41883	−0.709416	+	0.704790i	$0.751041\pi$
$930$	7.34414	0.240824
$931$	−82.0394	−2.68873
$932$	−1.10794	−0.0362917
$933$	29.4051	0.962681
$934$	23.2691	0.761388
$935$	0	0
$936$	−3.00741	−0.0983004
$937$	−20.6216	−0.673678	−0.336839	−	0.941562i	$-0.609358\pi$
$937$	−20.6216	−0.673678	−0.336839	+	0.941562i	$0.609358\pi$
$938$	−50.7185	−1.65602
$939$	2.84405	0.0928121
$940$	−4.94316	−0.161228
$941$	34.8141	1.13491	0.567453	−	0.823406i	$-0.307929\pi$
$941$	34.8141	1.13491	0.567453	+	0.823406i	$0.307929\pi$
$942$	15.8294	0.515750
$943$	27.2470	0.887285
$944$	3.36581	0.109548
$945$	6.85639	0.223038
$946$	0	0
$947$	−30.0683	−0.977089	−0.488544	−	0.872539i	$-0.662472\pi$
$947$	−30.0683	−0.977089	−0.488544	+	0.872539i	$0.662472\pi$
$948$	4.85856	0.157799
$949$	10.5117	0.341223
$950$	17.6661	0.573165
$951$	13.5296	0.438729
$952$	−80.2401	−2.60060
$953$	25.6609	0.831238	0.415619	−	0.909539i	$-0.363565\pi$
$953$	25.6609	0.831238	0.415619	+	0.909539i	$0.363565\pi$
$954$	−14.2904	−0.462669
$955$	8.92001	0.288645
$956$	0.771069	0.0249381
$957$	0	0
$958$	−6.27301	−0.202672
$959$	−12.5245	−0.404438
$960$	11.8048	0.380999
$961$	−12.9927	−0.419120
$962$	−10.9659	−0.353556
$963$	5.66441	0.182533
$964$	4.00588	0.129021
$965$	−15.8578	−0.510480
$966$	−23.0310	−0.741009
$967$	−29.4759	−0.947883	−0.473941	−	0.880556i	$-0.657169\pi$
$967$	−29.4759	−0.947883	−0.473941	+	0.880556i	$0.657169\pi$
$968$	0	0
$969$	22.0311	0.707742
$970$	10.1875	0.327101
$971$	29.5543	0.948444	0.474222	−	0.880405i	$-0.342729\pi$
$971$	29.5543	0.948444	0.474222	+	0.880405i	$0.342729\pi$
$972$	0.320873	0.0102920
$973$	9.79455	0.313999
$974$	−46.7193	−1.49698
$975$	3.21618	0.103000
$976$	1.78860	0.0572517
$977$	−47.4089	−1.51675	−0.758373	−	0.651821i	$-0.774006\pi$
$977$	−47.4089	−1.51675	−0.758373	+	0.651821i	$0.774006\pi$
$978$	−11.2567	−0.359951
$979$	0	0
$980$	8.29415	0.264947
$981$	6.40035	0.204348
$982$	1.38596	0.0442279
$983$	−17.7968	−0.567630	−0.283815	−	0.958879i	$-0.591600\pi$
$983$	−17.7968	−0.567630	−0.283815	+	0.958879i	$0.591600\pi$
$984$	23.6680	0.754510
$985$	1.06232	0.0338482
$986$	31.7089	1.00982
$987$	59.2129	1.88477
$988$	1.36017	0.0432727
$989$	8.71344	0.277071
$990$	0	0
$991$	9.33646	0.296582	0.148291	−	0.988944i	$-0.452623\pi$
$991$	9.33646	0.296582	0.148291	+	0.988944i	$0.452623\pi$
$992$	7.62379	0.242056
$993$	29.8070	0.945896
$994$	28.9358	0.917789
$995$	17.7934	0.564087
$996$	2.39730	0.0759614
$997$	−2.58572	−0.0818907	−0.0409453	−	0.999161i	$-0.513037\pi$
$997$	−2.58572	−0.0818907	−0.0409453	+	0.999161i	$0.513037\pi$
$998$	0.127854	0.00404715
$999$	8.46260	0.267745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4719.2.a.bp.1.9		14
11.3	even	5		429.2.n.c.196.5	✓	28
11.4	even	5		429.2.n.c.313.5	yes	28
11.10	odd	2		4719.2.a.bo.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.196.5	✓	28	11.3	even	5
429.2.n.c.313.5	yes	28	11.4	even	5
4719.2.a.bo.1.6		14	11.10	odd	2
4719.2.a.bp.1.9		14	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:	\( N \)	\(=\)	\( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4719.a (trivial)

\(f(q)\)	\(=\)	\(q+1.29581 q^{2} -1.00000 q^{3} -0.320873 q^{4} -1.33560 q^{5} -1.29581 q^{6} +5.13358 q^{7} -3.00741 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.29581 q^{2} -1.00000 q^{3} -0.320873 q^{4} -1.33560 q^{5} -1.29581 q^{6} +5.13358 q^{7} -3.00741 q^{8} +1.00000 q^{9} -1.73068 q^{10} +0.320873 q^{12} +1.00000 q^{13} +6.65215 q^{14} +1.33560 q^{15} -3.25529 q^{16} +5.19730 q^{17} +1.29581 q^{18} -4.23896 q^{19} +0.428557 q^{20} -5.13358 q^{21} +3.46218 q^{23} +3.00741 q^{24} -3.21618 q^{25} +1.29581 q^{26} -1.00000 q^{27} -1.64723 q^{28} +4.70827 q^{29} +1.73068 q^{30} +4.24350 q^{31} +1.79658 q^{32} +6.73472 q^{34} -6.85639 q^{35} -0.320873 q^{36} -8.46260 q^{37} -5.49289 q^{38} -1.00000 q^{39} +4.01669 q^{40} +7.86990 q^{41} -6.65215 q^{42} +2.51675 q^{43} -1.33560 q^{45} +4.48633 q^{46} -11.5344 q^{47} +3.25529 q^{48} +19.3537 q^{49} -4.16757 q^{50} -5.19730 q^{51} -0.320873 q^{52} -11.0282 q^{53} -1.29581 q^{54} -15.4388 q^{56} +4.23896 q^{57} +6.10103 q^{58} -1.03395 q^{59} -0.428557 q^{60} -0.549443 q^{61} +5.49877 q^{62} +5.13358 q^{63} +8.83862 q^{64} -1.33560 q^{65} -7.62437 q^{67} -1.66767 q^{68} -3.46218 q^{69} -8.88459 q^{70} +4.34984 q^{71} -3.00741 q^{72} +10.5117 q^{73} -10.9659 q^{74} +3.21618 q^{75} +1.36017 q^{76} -1.29581 q^{78} +15.1417 q^{79} +4.34776 q^{80} +1.00000 q^{81} +10.1979 q^{82} +7.47118 q^{83} +1.64723 q^{84} -6.94149 q^{85} +3.26123 q^{86} -4.70827 q^{87} +7.64133 q^{89} -1.73068 q^{90} +5.13358 q^{91} -1.11092 q^{92} -4.24350 q^{93} -14.9464 q^{94} +5.66154 q^{95} -1.79658 q^{96} -5.88642 q^{97} +25.0787 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} - 14 q^{3} + 15 q^{4} + 8 q^{5} - 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q + 3 * q^2 - 14 * q^3 + 15 * q^4 + 8 * q^5 - 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 14 q + 3 q^{2} - 14 q^{3} + 15 q^{4} + 8 q^{5} - 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - q^{10} - 15 q^{12} + 14 q^{13} + 18 q^{14} - 8 q^{15} + 13 q^{16} - q^{17} + 3 q^{18} - 10 q^{19} + 32 q^{20} - 3 q^{21} + 15 q^{23} - 9 q^{24} + 24 q^{25} + 3 q^{26} - 14 q^{27} + 4 q^{28} + 18 q^{29} + q^{30} + 8 q^{31} + 11 q^{32} - 12 q^{34} - 23 q^{35} + 15 q^{36} + q^{37} + 14 q^{38} - 14 q^{39} + 46 q^{40} - 18 q^{42} - 6 q^{43} + 8 q^{45} + 26 q^{47} - 13 q^{48} + 23 q^{49} + 4 q^{50} + q^{51} + 15 q^{52} + 8 q^{53} - 3 q^{54} + 24 q^{56} + 10 q^{57} + 10 q^{59} - 32 q^{60} + 14 q^{61} + 65 q^{62} + 3 q^{63} + 43 q^{64} + 8 q^{65} - 44 q^{67} - 38 q^{68} - 15 q^{69} + 67 q^{70} + 37 q^{71} + 9 q^{72} + 13 q^{73} - 58 q^{74} - 24 q^{75} - 62 q^{76} - 3 q^{78} - 14 q^{79} + 56 q^{80} + 14 q^{81} - 14 q^{82} + 36 q^{83} - 4 q^{84} + 5 q^{85} + 25 q^{86} - 18 q^{87} + 63 q^{89} - q^{90} + 3 q^{91} + 34 q^{92} - 8 q^{93} - 41 q^{94} + 9 q^{95} - 11 q^{96} + 26 q^{97} - 33 q^{98}+O(q^{100}) \) 14 * q + 3 * q^2 - 14 * q^3 + 15 * q^4 + 8 * q^5 - 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - q^10 - 15 * q^12 + 14 * q^13 + 18 * q^14 - 8 * q^15 + 13 * q^16 - q^17 + 3 * q^18 - 10 * q^19 + 32 * q^20 - 3 * q^21 + 15 * q^23 - 9 * q^24 + 24 * q^25 + 3 * q^26 - 14 * q^27 + 4 * q^28 + 18 * q^29 + q^30 + 8 * q^31 + 11 * q^32 - 12 * q^34 - 23 * q^35 + 15 * q^36 + q^37 + 14 * q^38 - 14 * q^39 + 46 * q^40 - 18 * q^42 - 6 * q^43 + 8 * q^45 + 26 * q^47 - 13 * q^48 + 23 * q^49 + 4 * q^50 + q^51 + 15 * q^52 + 8 * q^53 - 3 * q^54 + 24 * q^56 + 10 * q^57 + 10 * q^59 - 32 * q^60 + 14 * q^61 + 65 * q^62 + 3 * q^63 + 43 * q^64 + 8 * q^65 - 44 * q^67 - 38 * q^68 - 15 * q^69 + 67 * q^70 + 37 * q^71 + 9 * q^72 + 13 * q^73 - 58 * q^74 - 24 * q^75 - 62 * q^76 - 3 * q^78 - 14 * q^79 + 56 * q^80 + 14 * q^81 - 14 * q^82 + 36 * q^83 - 4 * q^84 + 5 * q^85 + 25 * q^86 - 18 * q^87 + 63 * q^89 - q^90 + 3 * q^91 + 34 * q^92 - 8 * q^93 - 41 * q^94 + 9 * q^95 - 11 * q^96 + 26 * q^97 - 33 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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