LMFDB - Embedded newform 1859.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.10562$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.10562 q^{2} +4.57504 q^{3} +18.0674 q^{4} -15.4387 q^{5} -23.3584 q^{6} -16.7622 q^{7} -51.4001 q^{8} -6.06900 q^{9} +O(q^{10})$	\(q-5.10562 q^{2} +4.57504 q^{3} +18.0674 q^{4} -15.4387 q^{5} -23.3584 q^{6} -16.7622 q^{7} -51.4001 q^{8} -6.06900 q^{9} +78.8244 q^{10} +11.0000 q^{11} +82.6589 q^{12} +85.5815 q^{14} -70.6329 q^{15} +117.891 q^{16} -14.0217 q^{17} +30.9860 q^{18} +75.4650 q^{19} -278.937 q^{20} -76.6878 q^{21} -56.1618 q^{22} +185.110 q^{23} -235.158 q^{24} +113.355 q^{25} -151.292 q^{27} -302.849 q^{28} -133.329 q^{29} +360.625 q^{30} -251.441 q^{31} -190.704 q^{32} +50.3254 q^{33} +71.5893 q^{34} +258.788 q^{35} -109.651 q^{36} -75.7614 q^{37} -385.296 q^{38} +793.553 q^{40} +166.386 q^{41} +391.539 q^{42} -31.1238 q^{43} +198.741 q^{44} +93.6978 q^{45} -945.101 q^{46} +136.902 q^{47} +539.354 q^{48} -62.0282 q^{49} -578.747 q^{50} -64.1497 q^{51} +493.058 q^{53} +772.440 q^{54} -169.826 q^{55} +861.580 q^{56} +345.256 q^{57} +680.728 q^{58} +96.1632 q^{59} -1276.15 q^{60} +626.028 q^{61} +1283.76 q^{62} +101.730 q^{63} +30.5359 q^{64} -256.943 q^{66} +992.625 q^{67} -253.334 q^{68} +846.886 q^{69} -1321.27 q^{70} -142.008 q^{71} +311.947 q^{72} -997.470 q^{73} +386.809 q^{74} +518.603 q^{75} +1363.45 q^{76} -184.384 q^{77} +1201.94 q^{79} -1820.08 q^{80} -528.304 q^{81} -849.503 q^{82} +1123.45 q^{83} -1385.55 q^{84} +216.477 q^{85} +158.906 q^{86} -609.986 q^{87} -565.401 q^{88} +853.302 q^{89} -478.385 q^{90} +3344.45 q^{92} -1150.35 q^{93} -698.969 q^{94} -1165.09 q^{95} -872.477 q^{96} -715.772 q^{97} +316.693 q^{98} -66.7590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.10562	−1.80511	−0.902555	−	0.430575i	$-0.858311\pi$
$2$	−5.10562	−1.80511	−0.902555	+	0.430575i	$0.858311\pi$
$3$	4.57504	0.880467	0.440233	−	0.897883i	$-0.354896\pi$
$3$	4.57504	0.880467	0.440233	+	0.897883i	$0.354896\pi$
$4$	18.0674	2.25842
$5$	−15.4387	−1.38088	−0.690442	−	0.723388i	$-0.742584\pi$
$5$	−15.4387	−1.38088	−0.690442	+	0.723388i	$0.742584\pi$
$6$	−23.3584	−1.58934
$7$	−16.7622	−0.905074	−0.452537	−	0.891746i	$-0.649481\pi$
$7$	−16.7622	−0.905074	−0.452537	+	0.891746i	$0.649481\pi$
$8$	−51.4001	−2.27159
$9$	−6.06900	−0.224778
$10$	78.8244	2.49265
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	82.6589	1.98846
$13$	0	0
$13$	0	0
$14$	85.5815	1.63376
$15$	−70.6329	−1.21582
$16$	117.891	1.84204
$17$	−14.0217	−0.200044	−0.100022	−	0.994985i	$-0.531891\pi$
$17$	−14.0217	−0.200044	−0.100022	+	0.994985i	$0.531891\pi$
$18$	30.9860	0.405749
$19$	75.4650	0.911204	0.455602	−	0.890184i	$-0.349424\pi$
$19$	75.4650	0.911204	0.455602	+	0.890184i	$0.349424\pi$
$20$	−278.937	−3.11861
$21$	−76.6878	−0.796888
$22$	−56.1618	−0.544261
$23$	185.110	1.67818	0.839089	−	0.543994i	$-0.183088\pi$
$23$	185.110	1.67818	0.839089	+	0.543994i	$0.183088\pi$
$24$	−235.158	−2.00006
$25$	113.355	0.906839
$26$	0	0
$27$	−151.292	−1.07838
$28$	−302.849	−2.04404
$29$	−133.329	−0.853744	−0.426872	−	0.904312i	$-0.640385\pi$
$29$	−133.329	−0.853744	−0.426872	+	0.904312i	$0.640385\pi$
$30$	360.625	2.19469
$31$	−251.441	−1.45678	−0.728390	−	0.685163i	$-0.759731\pi$
$31$	−251.441	−1.45678	−0.728390	+	0.685163i	$0.759731\pi$
$32$	−190.704	−1.05350
$33$	50.3254	0.265471
$34$	71.5893	0.361102
$35$	258.788	1.24980
$36$	−109.651	−0.507643
$37$	−75.7614	−0.336624	−0.168312	−	0.985734i	$-0.553832\pi$
$37$	−75.7614	−0.336624	−0.168312	+	0.985734i	$0.553832\pi$
$38$	−385.296	−1.64482
$39$	0	0
$40$	793.553	3.13679
$41$	166.386	0.633783	0.316892	−	0.948462i	$-0.397361\pi$
$41$	166.386	0.633783	0.316892	+	0.948462i	$0.397361\pi$
$42$	391.539	1.43847
$43$	−31.1238	−0.110380	−0.0551899	−	0.998476i	$-0.517576\pi$
$43$	−31.1238	−0.110380	−0.0551899	+	0.998476i	$0.517576\pi$
$44$	198.741	0.680939
$45$	93.6978	0.310392
$46$	−945.101	−3.02930
$47$	136.902	0.424876	0.212438	−	0.977175i	$-0.431860\pi$
$47$	136.902	0.424876	0.212438	+	0.977175i	$0.431860\pi$
$48$	539.354	1.62186
$49$	−62.0282	−0.180840
$50$	−578.747	−1.63694
$51$	−64.1497	−0.176132
$52$	0	0
$53$	493.058	1.27786	0.638932	−	0.769263i	$-0.279377\pi$
$53$	493.058	1.27786	0.638932	+	0.769263i	$0.279377\pi$
$54$	772.440	1.94659
$55$	−169.826	−0.416352
$56$	861.580	2.05595
$57$	345.256	0.802285
$58$	680.728	1.54110
$59$	96.1632	0.212193	0.106097	−	0.994356i	$-0.466165\pi$
$59$	96.1632	0.212193	0.106097	+	0.994356i	$0.466165\pi$
$60$	−1276.15	−2.74584
$61$	626.028	1.31401	0.657005	−	0.753886i	$-0.271823\pi$
$61$	626.028	1.31401	0.657005	+	0.753886i	$0.271823\pi$
$62$	1283.76	2.62965
$63$	101.730	0.203441
$64$	30.5359	0.0596404
$65$	0	0
$66$	−256.943	−0.479204
$67$	992.625	1.80998	0.904988	−	0.425436i	$-0.139879\pi$
$67$	992.625	1.80998	0.904988	+	0.425436i	$0.139879\pi$
$68$	−253.334	−0.451784
$69$	846.886	1.47758
$70$	−1321.27	−2.25603
$71$	−142.008	−0.237370	−0.118685	−	0.992932i	$-0.537868\pi$
$71$	−142.008	−0.237370	−0.118685	+	0.992932i	$0.537868\pi$
$72$	311.947	0.510602
$73$	−997.470	−1.59925	−0.799624	−	0.600501i	$-0.794968\pi$
$73$	−997.470	−1.59925	−0.799624	+	0.600501i	$0.794968\pi$
$74$	386.809	0.607644
$75$	518.603	0.798442
$76$	1363.45	2.05788
$77$	−184.384	−0.272890
$78$	0	0
$79$	1201.94	1.71176	0.855879	−	0.517176i	$-0.173017\pi$
$79$	1201.94	1.71176	0.855879	+	0.517176i	$0.173017\pi$
$80$	−1820.08	−2.54364
$81$	−528.304	−0.724697
$82$	−849.503	−1.14405
$83$	1123.45	1.48572	0.742862	−	0.669445i	$-0.233468\pi$
$83$	1123.45	1.48572	0.742862	+	0.669445i	$0.233468\pi$
$84$	−1385.55	−1.79971
$85$	216.477	0.276238
$86$	158.906	0.199248
$87$	−609.986	−0.751694
$88$	−565.401	−0.684909
$89$	853.302	1.01629	0.508145	−	0.861271i	$-0.330331\pi$
$89$	853.302	1.01629	0.508145	+	0.861271i	$0.330331\pi$
$90$	−478.385	−0.560292
$91$	0	0
$92$	3344.45	3.79003
$93$	−1150.35	−1.28265
$94$	−698.969	−0.766948
$95$	−1165.09	−1.25827
$96$	−872.477	−0.927571
$97$	−715.772	−0.749233	−0.374616	−	0.927180i	$-0.622226\pi$
$97$	−715.772	−0.749233	−0.374616	+	0.927180i	$0.622226\pi$
$98$	316.693	0.326437
$99$	−66.7590	−0.0677731
$100$	2048.02	2.04802
$101$	20.0289	0.0197322	0.00986611	−	0.999951i	$-0.496859\pi$
$101$	20.0289	0.0197322	0.00986611	+	0.999951i	$0.496859\pi$
$102$	327.524	0.317938
$103$	−1645.07	−1.57372	−0.786861	−	0.617130i	$-0.788295\pi$
$103$	−1645.07	−1.57372	−0.786861	+	0.617130i	$0.788295\pi$
$104$	0	0
$105$	1183.96	1.10041
$106$	−2517.37	−2.30668
$107$	−492.744	−0.445190	−0.222595	−	0.974911i	$-0.571453\pi$
$107$	−492.744	−0.445190	−0.222595	+	0.974911i	$0.571453\pi$
$108$	−2733.45	−2.43543
$109$	1112.05	0.977204	0.488602	−	0.872507i	$-0.337507\pi$
$109$	1112.05	0.977204	0.488602	+	0.872507i	$0.337507\pi$
$110$	867.068	0.751561
$111$	−346.612	−0.296387
$112$	−1976.11	−1.66718
$113$	−2030.32	−1.69023	−0.845116	−	0.534582i	$-0.820469\pi$
$113$	−2030.32	−1.69023	−0.845116	+	0.534582i	$0.820469\pi$
$114$	−1762.74	−1.44821
$115$	−2857.87	−2.31737
$116$	−2408.90	−1.92811
$117$	0	0
$118$	−490.973	−0.383032
$119$	235.034	0.181055
$120$	3630.54	2.76184
$121$	121.000	0.0909091
$122$	−3196.26	−2.37193
$123$	761.222	0.558025
$124$	−4542.88	−3.29002
$125$	179.786	0.128644
$126$	−519.394	−0.367233
$127$	−89.5366	−0.0625598	−0.0312799	−	0.999511i	$-0.509958\pi$
$127$	−89.5366	−0.0625598	−0.0312799	+	0.999511i	$0.509958\pi$
$128$	1369.72	0.945841
$129$	−142.393	−0.0971858
$130$	0	0
$131$	1458.38	0.972666	0.486333	−	0.873774i	$-0.338334\pi$
$131$	1458.38	0.972666	0.486333	+	0.873774i	$0.338334\pi$
$132$	909.248	0.599544
$133$	−1264.96	−0.824707
$134$	−5067.97	−3.26721
$135$	2335.76	1.48911
$136$	720.715	0.454418
$137$	611.956	0.381627	0.190814	−	0.981626i	$-0.438887\pi$
$137$	611.956	0.381627	0.190814	+	0.981626i	$0.438887\pi$
$138$	−4323.88	−2.66719
$139$	−644.002	−0.392975	−0.196488	−	0.980506i	$-0.562954\pi$
$139$	−644.002	−0.392975	−0.196488	+	0.980506i	$0.562954\pi$
$140$	4675.61	2.82258
$141$	626.332	0.374090
$142$	725.040	0.428479
$143$	0	0
$144$	−715.478	−0.414050
$145$	2058.43	1.17892
$146$	5092.71	2.88682
$147$	−283.782	−0.159224
$148$	−1368.81	−0.760239
$149$	2611.22	1.43570	0.717851	−	0.696197i	$-0.245126\pi$
$149$	2611.22	1.43570	0.717851	+	0.696197i	$0.245126\pi$
$150$	−2647.79	−1.44128
$151$	−2285.24	−1.23159	−0.615795	−	0.787906i	$-0.711165\pi$
$151$	−2285.24	−1.23159	−0.615795	+	0.787906i	$0.711165\pi$
$152$	−3878.91	−2.06988
$153$	85.0975	0.0449655
$154$	941.396	0.492597
$155$	3881.94	2.01164
$156$	0	0
$157$	−2923.64	−1.48619	−0.743096	−	0.669185i	$-0.766643\pi$
$157$	−2923.64	−1.48619	−0.743096	+	0.669185i	$0.766643\pi$
$158$	−6136.65	−3.08991
$159$	2255.76	1.12512
$160$	2944.23	1.45476
$161$	−3102.85	−1.51888
$162$	2697.32	1.30816
$163$	2631.52	1.26452	0.632259	−	0.774757i	$-0.282128\pi$
$163$	2631.52	1.26452	0.632259	+	0.774757i	$0.282128\pi$
$164$	3006.15	1.43135
$165$	−776.962	−0.366584
$166$	−5735.93	−2.68189
$167$	−2436.11	−1.12882	−0.564408	−	0.825496i	$-0.690895\pi$
$167$	−2436.11	−1.12882	−0.564408	+	0.825496i	$0.690895\pi$
$168$	3941.76	1.81020
$169$	0	0
$170$	−1105.25	−0.498640
$171$	−457.998	−0.204818
$172$	−562.325	−0.249284
$173$	99.1829	0.0435881	0.0217940	−	0.999762i	$-0.493062\pi$
$173$	99.1829	0.0435881	0.0217940	+	0.999762i	$0.493062\pi$
$174$	3114.36	1.35689
$175$	−1900.08	−0.820757
$176$	1296.80	0.555396
$177$	439.951	0.186829
$178$	−4356.64	−1.83451
$179$	2671.11	1.11535	0.557676	−	0.830059i	$-0.311693\pi$
$179$	2671.11	1.11535	0.557676	+	0.830059i	$0.311693\pi$
$180$	1692.87	0.700996
$181$	−483.437	−0.198528	−0.0992640	−	0.995061i	$-0.531649\pi$
$181$	−483.437	−0.198528	−0.0992640	+	0.995061i	$0.531649\pi$
$182$	0	0
$183$	2864.10	1.15694
$184$	−9514.68	−3.81213
$185$	1169.66	0.464839
$186$	5873.27	2.31532
$187$	−154.238	−0.0603156
$188$	2473.46	0.959549
$189$	2535.99	0.976011
$190$	5948.49	2.27131
$191$	−1955.90	−0.740964	−0.370482	−	0.928840i	$-0.620808\pi$
$191$	−1955.90	−0.740964	−0.370482	+	0.928840i	$0.620808\pi$
$192$	139.703	0.0525114
$193$	1829.04	0.682161	0.341080	−	0.940034i	$-0.389207\pi$
$193$	1829.04	0.682161	0.341080	+	0.940034i	$0.389207\pi$
$194$	3654.46	1.35245
$195$	0	0
$196$	−1120.69	−0.408413
$197$	2152.79	0.778579	0.389290	−	0.921115i	$-0.372721\pi$
$197$	2152.79	0.778579	0.389290	+	0.921115i	$0.372721\pi$
$198$	340.846	0.122338
$199$	−3064.40	−1.09160	−0.545802	−	0.837914i	$-0.683775\pi$
$199$	−3064.40	−1.09160	−0.545802	+	0.837914i	$0.683775\pi$
$200$	−5826.46	−2.05996
$201$	4541.30	1.59362
$202$	−102.260	−0.0356188
$203$	2234.89	0.772702
$204$	−1159.02	−0.397781
$205$	−2568.79	−0.875181
$206$	8399.10	2.84074
$207$	−1123.43	−0.377217
$208$	0	0
$209$	830.115	0.274738
$210$	−6044.87	−1.98636
$211$	1795.75	0.585897	0.292949	−	0.956128i	$-0.405363\pi$
$211$	1795.75	0.585897	0.292949	+	0.956128i	$0.405363\pi$
$212$	8908.26	2.88595
$213$	−649.693	−0.208996
$214$	2515.76	0.803617
$215$	480.513	0.152422
$216$	7776.43	2.44962
$217$	4214.71	1.31849
$218$	−5677.71	−1.76396
$219$	−4563.47	−1.40808
$220$	−3068.31	−0.940298
$221$	0	0
$222$	1769.67	0.535010
$223$	954.996	0.286777	0.143389	−	0.989666i	$-0.454200\pi$
$223$	954.996	0.286777	0.143389	+	0.989666i	$0.454200\pi$
$224$	3196.62	0.953495
$225$	−687.951	−0.203837
$226$	10366.0	3.05105
$227$	−2511.69	−0.734392	−0.367196	−	0.930144i	$-0.619682\pi$
$227$	−2511.69	−0.734392	−0.367196	+	0.930144i	$0.619682\pi$
$228$	6237.86	1.81190
$229$	−4793.13	−1.38314	−0.691570	−	0.722309i	$-0.743081\pi$
$229$	−4793.13	−1.38314	−0.691570	+	0.722309i	$0.743081\pi$
$230$	14591.2	4.18310
$231$	−843.566	−0.240271
$232$	6853.13	1.93935
$233$	−751.366	−0.211260	−0.105630	−	0.994405i	$-0.533686\pi$
$233$	−751.366	−0.211260	−0.105630	+	0.994405i	$0.533686\pi$
$234$	0	0
$235$	−2113.59	−0.586705
$236$	1737.42	0.479221
$237$	5498.93	1.50715
$238$	−1199.99	−0.326824
$239$	−3847.96	−1.04144	−0.520719	−	0.853728i	$-0.674336\pi$
$239$	−3847.96	−1.04144	−0.520719	+	0.853728i	$0.674336\pi$
$240$	−8326.95	−2.23959
$241$	−6592.39	−1.76205	−0.881023	−	0.473073i	$-0.843145\pi$
$241$	−6592.39	−1.76205	−0.881023	+	0.473073i	$0.843145\pi$
$242$	−617.780	−0.164101
$243$	1667.87	0.440305
$244$	11310.7	2.96759
$245$	957.638	0.249719
$246$	−3886.51	−1.00730
$247$	0	0
$248$	12924.1	3.30920
$249$	5139.85	1.30813
$250$	−917.917	−0.232217
$251$	−4351.00	−1.09415	−0.547077	−	0.837082i	$-0.684259\pi$
$251$	−4351.00	−1.09415	−0.547077	+	0.837082i	$0.684259\pi$
$252$	1837.99	0.459455
$253$	2036.21	0.505990
$254$	457.140	0.112927
$255$	990.391	0.243218
$256$	−7237.58	−1.76699
$257$	2325.96	0.564550	0.282275	−	0.959334i	$-0.408911\pi$
$257$	2325.96	0.564550	0.282275	+	0.959334i	$0.408911\pi$
$258$	727.003	0.175431
$259$	1269.93	0.304670
$260$	0	0
$261$	809.175	0.191903
$262$	−7445.93	−1.75577
$263$	2441.87	0.572519	0.286259	−	0.958152i	$-0.407588\pi$
$263$	2441.87	0.572519	0.286259	+	0.958152i	$0.407588\pi$
$264$	−2586.73	−0.603040
$265$	−7612.20	−1.76458
$266$	6458.41	1.48869
$267$	3903.89	0.894810
$268$	17934.1	4.08769
$269$	136.438	0.0309248	0.0154624	−	0.999880i	$-0.495078\pi$
$269$	136.438	0.0309248	0.0154624	+	0.999880i	$0.495078\pi$
$270$	−11925.5	−2.68801
$271$	−3845.43	−0.861967	−0.430983	−	0.902360i	$-0.641833\pi$
$271$	−3845.43	−0.861967	−0.430983	+	0.902360i	$0.641833\pi$
$272$	−1653.02	−0.368490
$273$	0	0
$274$	−3124.42	−0.688879
$275$	1246.90	0.273422
$276$	15301.0	3.33700
$277$	2423.81	0.525751	0.262875	−	0.964830i	$-0.415329\pi$
$277$	2423.81	0.525751	0.262875	+	0.964830i	$0.415329\pi$
$278$	3288.03	0.709363
$279$	1526.00	0.327452
$280$	−13301.7	−2.83903
$281$	−5767.52	−1.22442	−0.612209	−	0.790696i	$-0.709719\pi$
$281$	−5767.52	−1.22442	−0.612209	+	0.790696i	$0.709719\pi$
$282$	−3197.81	−0.675273
$283$	3332.07	0.699898	0.349949	−	0.936769i	$-0.386199\pi$
$283$	3332.07	0.699898	0.349949	+	0.936769i	$0.386199\pi$
$284$	−2565.71	−0.536081
$285$	−5330.31	−1.10786
$286$	0	0
$287$	−2789.00	−0.573621
$288$	1157.38	0.236803
$289$	−4716.39	−0.959982
$290$	−10509.6	−2.12808
$291$	−3274.68	−0.659675
$292$	−18021.7	−3.61177
$293$	6306.14	1.25737	0.628683	−	0.777662i	$-0.283594\pi$
$293$	6306.14	1.25737	0.628683	+	0.777662i	$0.283594\pi$
$294$	1448.88	0.287417
$295$	−1484.64	−0.293014
$296$	3894.15	0.764671
$297$	−1664.21	−0.325143
$298$	−13331.9	−2.59160
$299$	0	0
$300$	9369.79	1.80322
$301$	521.704	0.0999020
$302$	11667.6	2.22315
$303$	91.6332	0.0173736
$304$	8896.62	1.67847
$305$	−9665.09	−1.81450
$306$	−434.476	−0.0811677
$307$	322.272	0.0599122	0.0299561	−	0.999551i	$-0.490463\pi$
$307$	322.272	0.0599122	0.0299561	+	0.999551i	$0.490463\pi$
$308$	−3331.34	−0.616301
$309$	−7526.26	−1.38561
$310$	−19819.7	−3.63123
$311$	1110.60	0.202497	0.101248	−	0.994861i	$-0.467716\pi$
$311$	1110.60	0.202497	0.101248	+	0.994861i	$0.467716\pi$
$312$	0	0
$313$	−3338.03	−0.602801	−0.301400	−	0.953498i	$-0.597454\pi$
$313$	−3338.03	−0.602801	−0.301400	+	0.953498i	$0.597454\pi$
$314$	14927.0	2.68274
$315$	−1570.58	−0.280928
$316$	21715.9	3.86587
$317$	−780.195	−0.138234	−0.0691169	−	0.997609i	$-0.522018\pi$
$317$	−780.195	−0.138234	−0.0691169	+	0.997609i	$0.522018\pi$
$318$	−11517.1	−2.03096
$319$	−1466.62	−0.257414
$320$	−471.436	−0.0823565
$321$	−2254.32	−0.391975
$322$	15842.0	2.74174
$323$	−1058.15	−0.182281
$324$	−9545.06	−1.63667
$325$	0	0
$326$	−13435.5	−2.28259
$327$	5087.68	0.860396
$328$	−8552.26	−1.43969
$329$	−2294.78	−0.384545
$330$	3966.87	0.661725
$331$	−6569.96	−1.09099	−0.545495	−	0.838114i	$-0.683658\pi$
$331$	−6569.96	−1.09099	−0.545495	+	0.838114i	$0.683658\pi$
$332$	20297.8	3.35539
$333$	459.796	0.0756657
$334$	12437.9	2.03764
$335$	−15324.9	−2.49937
$336$	−9040.77	−1.46790
$337$	8378.64	1.35434	0.677172	−	0.735825i	$-0.263205\pi$
$337$	8378.64	1.35434	0.677172	+	0.735825i	$0.263205\pi$
$338$	0	0
$339$	−9288.79	−1.48819
$340$	3911.17	0.623861
$341$	−2765.85	−0.439235
$342$	2338.36	0.369720
$343$	6789.17	1.06875
$344$	1599.77	0.250737
$345$	−13074.9	−2.04037
$346$	−506.390	−0.0786812
$347$	−8210.63	−1.27023	−0.635115	−	0.772418i	$-0.719047\pi$
$347$	−8210.63	−1.27023	−0.635115	+	0.772418i	$0.719047\pi$
$348$	−11020.8	−1.69764
$349$	−1019.42	−0.156356	−0.0781779	−	0.996939i	$-0.524910\pi$
$349$	−1019.42	−0.156356	−0.0781779	+	0.996939i	$0.524910\pi$
$350$	9701.08	1.48156
$351$	0	0
$352$	−2097.74	−0.317642
$353$	1584.97	0.238979	0.119490	−	0.992835i	$-0.461874\pi$
$353$	1584.97	0.238979	0.119490	+	0.992835i	$0.461874\pi$
$354$	−2246.22	−0.337247
$355$	2192.43	0.327780
$356$	15416.9	2.29521
$357$	1075.29	0.159413
$358$	−13637.7	−2.01333
$359$	−12592.1	−1.85122	−0.925610	−	0.378478i	$-0.876447\pi$
$359$	−12592.1	−1.85122	−0.925610	+	0.378478i	$0.876447\pi$
$360$	−4816.08	−0.705082
$361$	−1164.03	−0.169708
$362$	2468.25	0.358365
$363$	553.580	0.0800425
$364$	0	0
$365$	15399.7	2.20837
$366$	−14623.0	−2.08841
$367$	−8708.30	−1.23861	−0.619304	−	0.785151i	$-0.712585\pi$
$367$	−8708.30	−1.23861	−0.619304	+	0.785151i	$0.712585\pi$
$368$	21822.7	3.09127
$369$	−1009.80	−0.142461
$370$	−5971.85	−0.839085
$371$	−8264.75	−1.15656
$372$	−20783.8	−2.89675
$373$	4512.63	0.626421	0.313211	−	0.949684i	$-0.398595\pi$
$373$	4512.63	0.626421	0.313211	+	0.949684i	$0.398595\pi$
$374$	787.482	0.108876
$375$	822.526	0.113267
$376$	−7036.77	−0.965143
$377$	0	0
$378$	−12947.8	−1.76181
$379$	−10825.4	−1.46719	−0.733595	−	0.679587i	$-0.762159\pi$
$379$	−10825.4	−1.46719	−0.733595	+	0.679587i	$0.762159\pi$
$380$	−21050.0	−2.84169
$381$	−409.634	−0.0550818
$382$	9986.10	1.33752
$383$	−12433.9	−1.65886	−0.829429	−	0.558612i	$-0.811334\pi$
$383$	−12433.9	−1.65886	−0.829429	+	0.558612i	$0.811334\pi$
$384$	6266.55	0.832782
$385$	2846.66	0.376830
$386$	−9338.37	−1.23137
$387$	188.890	0.0248110
$388$	−12932.1	−1.69208
$389$	−7665.34	−0.999096	−0.499548	−	0.866286i	$-0.666500\pi$
$389$	−7665.34	−0.999096	−0.499548	+	0.866286i	$0.666500\pi$
$390$	0	0
$391$	−2595.55	−0.335710
$392$	3188.26	0.410794
$393$	6672.15	0.856400
$394$	−10991.3	−1.40542
$395$	−18556.5	−2.36374
$396$	−1206.16	−0.153060
$397$	−7542.02	−0.953459	−0.476729	−	0.879050i	$-0.658178\pi$
$397$	−7542.02	−0.953459	−0.476729	+	0.879050i	$0.658178\pi$
$398$	15645.7	1.97047
$399$	−5787.25	−0.726127
$400$	13363.5	1.67043
$401$	−8284.12	−1.03164	−0.515822	−	0.856696i	$-0.672513\pi$
$401$	−8284.12	−1.03164	−0.515822	+	0.856696i	$0.672513\pi$
$402$	−23186.2	−2.87667
$403$	0	0
$404$	361.870	0.0445636
$405$	8156.35	1.00072
$406$	−11410.5	−1.39481
$407$	−833.376	−0.101496
$408$	3297.30	0.400100
$409$	14536.5	1.75742	0.878710	−	0.477357i	$-0.158405\pi$
$409$	14536.5	1.75742	0.878710	+	0.477357i	$0.158405\pi$
$410$	13115.3	1.57980
$411$	2799.73	0.336010
$412$	−29722.0	−3.55413
$413$	−1611.91	−0.192050
$414$	5735.82	0.680919
$415$	−17344.7	−2.05161
$416$	0	0
$417$	−2946.34	−0.346002
$418$	−4238.25	−0.495933
$419$	5373.60	0.626534	0.313267	−	0.949665i	$-0.398577\pi$
$419$	5373.60	0.626534	0.313267	+	0.949665i	$0.398577\pi$
$420$	21391.1	2.48519
$421$	−13114.5	−1.51820	−0.759101	−	0.650973i	$-0.774361\pi$
$421$	−13114.5	−1.51820	−0.759101	+	0.650973i	$0.774361\pi$
$422$	−9168.41	−1.05761
$423$	−830.858	−0.0955028
$424$	−25343.3	−2.90278
$425$	−1589.42	−0.181408
$426$	3317.09	0.377261
$427$	−10493.6	−1.18928
$428$	−8902.58	−1.00543
$429$	0	0
$430$	−2453.31	−0.275138
$431$	11992.2	1.34024	0.670119	−	0.742254i	$-0.266243\pi$
$431$	11992.2	1.34024	0.670119	+	0.742254i	$0.266243\pi$
$432$	−17835.9	−1.98641
$433$	−9211.62	−1.02236	−0.511181	−	0.859473i	$-0.670792\pi$
$433$	−9211.62	−1.02236	−0.511181	+	0.859473i	$0.670792\pi$
$434$	−21518.7	−2.38003
$435$	9417.42	1.03800
$436$	20091.8	2.20694
$437$	13969.3	1.52916
$438$	23299.3	2.54175
$439$	7568.74	0.822862	0.411431	−	0.911441i	$-0.365029\pi$
$439$	7568.74	0.822862	0.411431	+	0.911441i	$0.365029\pi$
$440$	8729.09	0.945779
$441$	376.450	0.0406489
$442$	0	0
$443$	9427.11	1.01105	0.505525	−	0.862812i	$-0.331299\pi$
$443$	9427.11	1.01105	0.505525	+	0.862812i	$0.331299\pi$
$444$	−6262.36	−0.669365
$445$	−13173.9	−1.40338
$446$	−4875.85	−0.517664
$447$	11946.4	1.26409
$448$	−511.849	−0.0539790
$449$	7110.58	0.747369	0.373685	−	0.927556i	$-0.378094\pi$
$449$	7110.58	0.747369	0.373685	+	0.927556i	$0.378094\pi$
$450$	3512.42	0.367949
$451$	1830.25	0.191093
$452$	−36682.5	−3.81725
$453$	−10455.1	−1.08437
$454$	12823.8	1.32566
$455$	0	0
$456$	−17746.2	−1.82246
$457$	−2822.62	−0.288920	−0.144460	−	0.989511i	$-0.546145\pi$
$457$	−2822.62	−0.288920	−0.144460	+	0.989511i	$0.546145\pi$
$458$	24471.9	2.49672
$459$	2121.37	0.215723
$460$	−51634.1	−5.23359
$461$	−1614.06	−0.163068	−0.0815339	−	0.996671i	$-0.525982\pi$
$461$	−1614.06	−0.163068	−0.0815339	+	0.996671i	$0.525982\pi$
$462$	4306.93	0.433715
$463$	−6426.71	−0.645085	−0.322543	−	0.946555i	$-0.604538\pi$
$463$	−6426.71	−0.645085	−0.322543	+	0.946555i	$0.604538\pi$
$464$	−15718.2	−1.57263
$465$	17760.0	1.77118
$466$	3836.19	0.381348
$467$	10217.8	1.01247	0.506234	−	0.862396i	$-0.331037\pi$
$467$	10217.8	1.01247	0.506234	+	0.862396i	$0.331037\pi$
$468$	0	0
$469$	−16638.6	−1.63816
$470$	10791.2	1.05907
$471$	−13375.8	−1.30854
$472$	−4942.80	−0.482015
$473$	−342.362	−0.0332808
$474$	−28075.4	−2.72056
$475$	8554.33	0.826315
$476$	4246.45	0.408898
$477$	−2992.37	−0.287236
$478$	19646.2	1.87991
$479$	687.522	0.0655818	0.0327909	−	0.999462i	$-0.489560\pi$
$479$	687.522	0.0655818	0.0327909	+	0.999462i	$0.489560\pi$
$480$	13470.0	1.28087
$481$	0	0
$482$	33658.2	3.18069
$483$	−14195.7	−1.33732
$484$	2186.15	0.205311
$485$	11050.6	1.03460
$486$	−8515.52	−0.794798
$487$	15427.5	1.43550	0.717749	−	0.696302i	$-0.245173\pi$
$487$	15427.5	1.43550	0.717749	+	0.696302i	$0.245173\pi$
$488$	−32177.9	−2.98489
$489$	12039.3	1.11337
$490$	−4889.34	−0.450771
$491$	11935.4	1.09702	0.548509	−	0.836145i	$-0.315196\pi$
$491$	11935.4	1.09702	0.548509	+	0.836145i	$0.315196\pi$
$492$	13753.3	1.26026
$493$	1869.50	0.170787
$494$	0	0
$495$	1030.68	0.0935867
$496$	−29642.5	−2.68345
$497$	2380.37	0.214837
$498$	−26242.1	−2.36132
$499$	16986.6	1.52390	0.761948	−	0.647638i	$-0.224243\pi$
$499$	16986.6	1.52390	0.761948	+	0.647638i	$0.224243\pi$
$500$	3248.25	0.290532
$501$	−11145.3	−0.993885
$502$	22214.5	1.97507
$503$	−16896.3	−1.49775	−0.748877	−	0.662710i	$-0.769406\pi$
$503$	−16896.3	−1.49775	−0.748877	+	0.662710i	$0.769406\pi$
$504$	−5228.93	−0.462133
$505$	−309.222	−0.0272479
$506$	−10396.1	−0.913367
$507$	0	0
$508$	−1617.69	−0.141286
$509$	−8711.47	−0.758604	−0.379302	−	0.925273i	$-0.623836\pi$
$509$	−8711.47	−0.758604	−0.379302	+	0.925273i	$0.623836\pi$
$510$	−5056.56	−0.439036
$511$	16719.8	1.44744
$512$	25994.5	2.24376
$513$	−11417.3	−0.982621
$514$	−11875.5	−1.01907
$515$	25397.8	2.17313
$516$	−2572.66	−0.219486
$517$	1505.92	0.128105
$518$	−6483.77	−0.549963
$519$	453.766	0.0383779
$520$	0	0
$521$	−6558.64	−0.551515	−0.275758	−	0.961227i	$-0.588929\pi$
$521$	−6558.64	−0.551515	−0.275758	+	0.961227i	$0.588929\pi$
$522$	−4131.34	−0.346406
$523$	−13366.6	−1.11756	−0.558778	−	0.829317i	$-0.688730\pi$
$523$	−13366.6	−1.11756	−0.558778	+	0.829317i	$0.688730\pi$
$524$	26349.1	2.19669
$525$	−8692.94	−0.722649
$526$	−12467.3	−1.03346
$527$	3525.62	0.291420
$528$	5932.90	0.489008
$529$	22098.7	1.81628
$530$	38865.0	3.18526
$531$	−583.615	−0.0476963
$532$	−22854.5	−1.86253
$533$	0	0
$534$	−19931.8	−1.61523
$535$	7607.35	0.614756
$536$	−51021.0	−4.11152
$537$	12220.4	0.982030
$538$	−696.601	−0.0558227
$539$	−682.311	−0.0545254
$540$	42201.0	3.36304
$541$	−13872.5	−1.10245	−0.551223	−	0.834358i	$-0.685839\pi$
$541$	−13872.5	−1.10245	−0.551223	+	0.834358i	$0.685839\pi$
$542$	19633.3	1.55594
$543$	−2211.74	−0.174797
$544$	2673.98	0.210746
$545$	−17168.7	−1.34940
$546$	0	0
$547$	10265.2	0.802394	0.401197	−	0.915992i	$-0.368594\pi$
$547$	10265.2	0.802394	0.401197	+	0.915992i	$0.368594\pi$
$548$	11056.4	0.861875
$549$	−3799.37	−0.295361
$550$	−6366.22	−0.493557
$551$	−10061.7	−0.777935
$552$	−43530.0	−3.35645
$553$	−20147.2	−1.54927
$554$	−12375.1	−0.949037
$555$	5351.25	0.409275
$556$	−11635.4	−0.887503
$557$	−6191.03	−0.470956	−0.235478	−	0.971880i	$-0.575666\pi$
$557$	−6191.03	−0.470956	−0.235478	+	0.971880i	$0.575666\pi$
$558$	−7791.16	−0.591086
$559$	0	0
$560$	30508.6	2.30219
$561$	−705.646	−0.0531059
$562$	29446.7	2.21021
$563$	−7821.88	−0.585529	−0.292765	−	0.956185i	$-0.594575\pi$
$563$	−7821.88	−0.585529	−0.292765	+	0.956185i	$0.594575\pi$
$564$	11316.2	0.844851
$565$	31345.6	2.33401
$566$	−17012.3	−1.26339
$567$	8855.55	0.655905
$568$	7299.23	0.539206
$569$	−17053.4	−1.25644	−0.628222	−	0.778034i	$-0.716217\pi$
$569$	−17053.4	−1.25644	−0.628222	+	0.778034i	$0.716217\pi$
$570$	27214.6	1.99981
$571$	14574.5	1.06817	0.534083	−	0.845432i	$-0.320657\pi$
$571$	14574.5	1.06817	0.534083	+	0.845432i	$0.320657\pi$
$572$	0	0
$573$	−8948.34	−0.652395
$574$	14239.6	1.03545
$575$	20983.1	1.52184
$576$	−185.322	−0.0134058
$577$	14203.7	1.02480	0.512398	−	0.858748i	$-0.328757\pi$
$577$	14203.7	1.02480	0.512398	+	0.858748i	$0.328757\pi$
$578$	24080.1	1.73287
$579$	8367.92	0.600620
$580$	37190.5	2.66250
$581$	−18831.6	−1.34469
$582$	16719.3	1.19079
$583$	5423.64	0.385290
$584$	51270.1	3.63283
$585$	0	0
$586$	−32196.7	−2.26968
$587$	−11810.8	−0.830466	−0.415233	−	0.909715i	$-0.636300\pi$
$587$	−11810.8	−0.830466	−0.415233	+	0.909715i	$0.636300\pi$
$588$	−5127.19	−0.359595
$589$	−18975.0	−1.32742
$590$	7580.01	0.528922
$591$	9849.11	0.685513
$592$	−8931.56	−0.620076
$593$	16422.5	1.13725	0.568626	−	0.822596i	$-0.307475\pi$
$593$	16422.5	1.13725	0.568626	+	0.822596i	$0.307475\pi$
$594$	8496.84	0.586918
$595$	−3628.63	−0.250016
$596$	47177.9	3.24242
$597$	−14019.7	−0.961122
$598$	0	0
$599$	−14254.2	−0.972306	−0.486153	−	0.873874i	$-0.661600\pi$
$599$	−14254.2	−0.972306	−0.486153	+	0.873874i	$0.661600\pi$
$600$	−26656.3	−1.81373
$601$	11015.1	0.747613	0.373806	−	0.927507i	$-0.378052\pi$
$601$	11015.1	0.747613	0.373806	+	0.927507i	$0.378052\pi$
$602$	−2663.62	−0.180334
$603$	−6024.24	−0.406843
$604$	−41288.2	−2.78145
$605$	−1868.09	−0.125535
$606$	−467.844	−0.0313612
$607$	−23040.6	−1.54067	−0.770336	−	0.637638i	$-0.779911\pi$
$607$	−23040.6	−1.54067	−0.770336	+	0.637638i	$0.779911\pi$
$608$	−14391.5	−0.959952
$609$	10224.7	0.680339
$610$	49346.3	3.27536
$611$	0	0
$612$	1537.49	0.101551
$613$	9960.55	0.656285	0.328143	−	0.944628i	$-0.393577\pi$
$613$	9960.55	0.656285	0.328143	+	0.944628i	$0.393577\pi$
$614$	−1645.40	−0.108148
$615$	−11752.3	−0.770568
$616$	9477.38	0.619893
$617$	23895.4	1.55915	0.779574	−	0.626310i	$-0.215436\pi$
$617$	23895.4	1.55915	0.779574	+	0.626310i	$0.215436\pi$
$618$	38426.2	2.50118
$619$	−19474.1	−1.26451	−0.632253	−	0.774762i	$-0.717870\pi$
$619$	−19474.1	−1.26451	−0.632253	+	0.774762i	$0.717870\pi$
$620$	70136.3	4.54313
$621$	−28005.7	−1.80971
$622$	−5670.31	−0.365529
$623$	−14303.2	−0.919818
$624$	0	0
$625$	−16945.0	−1.08448
$626$	17042.7	1.08812
$627$	3797.81	0.241898
$628$	−52822.5	−3.35644
$629$	1062.30	0.0673398
$630$	8018.80	0.507106
$631$	759.157	0.0478947	0.0239473	−	0.999713i	$-0.492377\pi$
$631$	759.157	0.0478947	0.0239473	+	0.999713i	$0.492377\pi$
$632$	−61779.9	−3.88841
$633$	8215.62	0.515863
$634$	3983.38	0.249527
$635$	1382.33	0.0863877
$636$	40755.7	2.54099
$637$	0	0
$638$	7488.00	0.464660
$639$	861.848	0.0533555
$640$	−21146.8	−1.30610
$641$	−4117.87	−0.253738	−0.126869	−	0.991919i	$-0.540493\pi$
$641$	−4117.87	−0.253738	−0.126869	+	0.991919i	$0.540493\pi$
$642$	11509.7	0.707558
$643$	2947.79	0.180793	0.0903963	−	0.995906i	$-0.471187\pi$
$643$	2947.79	0.180793	0.0903963	+	0.995906i	$0.471187\pi$
$644$	−56060.4	−3.43026
$645$	2198.36	0.134202
$646$	5402.49	0.329037
$647$	9323.63	0.566537	0.283269	−	0.959041i	$-0.408581\pi$
$647$	9323.63	0.566537	0.283269	+	0.959041i	$0.408581\pi$
$648$	27154.9	1.64621
$649$	1057.80	0.0639786
$650$	0	0
$651$	19282.5	1.16089
$652$	47544.6	2.85581
$653$	13312.4	0.797786	0.398893	−	0.916997i	$-0.369394\pi$
$653$	13312.4	0.797786	0.398893	+	0.916997i	$0.369394\pi$
$654$	−25975.8	−1.55311
$655$	−22515.6	−1.34314
$656$	19615.3	1.16745
$657$	6053.65	0.359476
$658$	11716.3	0.694145
$659$	−9406.59	−0.556038	−0.278019	−	0.960576i	$-0.589678\pi$
$659$	−9406.59	−0.556038	−0.278019	+	0.960576i	$0.589678\pi$
$660$	−14037.6	−0.827901
$661$	−27983.2	−1.64663	−0.823315	−	0.567585i	$-0.807878\pi$
$661$	−27983.2	−1.64663	−0.823315	+	0.567585i	$0.807878\pi$
$662$	33543.7	1.96936
$663$	0	0
$664$	−57745.6	−3.37495
$665$	19529.4	1.13882
$666$	−2347.55	−0.136585
$667$	−24680.5	−1.43274
$668$	−44014.1	−2.54934
$669$	4369.15	0.252498
$670$	78243.0	4.51163
$671$	6886.31	0.396189
$672$	14624.6	0.839521
$673$	3628.69	0.207839	0.103919	−	0.994586i	$-0.466862\pi$
$673$	3628.69	0.207839	0.103919	+	0.994586i	$0.466862\pi$
$674$	−42778.2	−2.44474
$675$	−17149.7	−0.977914
$676$	0	0
$677$	−3329.76	−0.189030	−0.0945148	−	0.995523i	$-0.530130\pi$
$677$	−3329.76	−0.189030	−0.0945148	+	0.995523i	$0.530130\pi$
$678$	47425.0	2.68635
$679$	11997.9	0.678111
$680$	−11126.9	−0.627498
$681$	−11491.1	−0.646608
$682$	14121.4	0.792868
$683$	−381.389	−0.0213667	−0.0106834	−	0.999943i	$-0.503401\pi$
$683$	−381.389	−0.0213667	−0.0106834	+	0.999943i	$0.503401\pi$
$684$	−8274.81	−0.462566
$685$	−9447.84	−0.526983
$686$	−34662.9	−1.92921
$687$	−21928.8	−1.21781
$688$	−3669.20	−0.203324
$689$	0	0
$690$	66755.3	3.68309
$691$	−5090.80	−0.280265	−0.140133	−	0.990133i	$-0.544753\pi$
$691$	−5090.80	−0.280265	−0.140133	+	0.990133i	$0.544753\pi$
$692$	1791.97	0.0984402
$693$	1119.03	0.0613397
$694$	41920.4	2.29290
$695$	9942.59	0.542653
$696$	31353.3	1.70754
$697$	−2333.01	−0.126785
$698$	5204.76	0.282239
$699$	−3437.53	−0.186008
$700$	−34329.4	−1.85361
$701$	1034.50	0.0557381	0.0278691	−	0.999612i	$-0.491128\pi$
$701$	1034.50	0.0557381	0.0278691	+	0.999612i	$0.491128\pi$
$702$	0	0
$703$	−5717.34	−0.306733
$704$	335.895	0.0179823
$705$	−9669.78	−0.516574
$706$	−8092.27	−0.431383
$707$	−335.729	−0.0178591
$708$	7948.75	0.421938
$709$	−19430.4	−1.02923	−0.514614	−	0.857422i	$-0.672065\pi$
$709$	−19430.4	−1.02923	−0.514614	+	0.857422i	$0.672065\pi$
$710$	−11193.7	−0.591679
$711$	−7294.58	−0.384766
$712$	−43859.8	−2.30859
$713$	−46544.3	−2.44474
$714$	−5490.02	−0.287758
$715$	0	0
$716$	48259.8	2.51893
$717$	−17604.6	−0.916952
$718$	64290.7	3.34165
$719$	−6580.59	−0.341328	−0.170664	−	0.985329i	$-0.554591\pi$
$719$	−6580.59	−0.341328	−0.170664	+	0.985329i	$0.554591\pi$
$720$	11046.1	0.571755
$721$	27575.0	1.42434
$722$	5943.08	0.306342
$723$	−30160.4	−1.55142
$724$	−8734.43	−0.448360
$725$	−15113.5	−0.774209
$726$	−2826.37	−0.144485
$727$	−25169.7	−1.28404	−0.642018	−	0.766690i	$-0.721902\pi$
$727$	−25169.7	−1.28404	−0.642018	+	0.766690i	$0.721902\pi$
$728$	0	0
$729$	21894.8	1.11237
$730$	−78625.0	−3.98636
$731$	436.407	0.0220809
$732$	51746.8	2.61286
$733$	−29052.5	−1.46395	−0.731977	−	0.681329i	$-0.761402\pi$
$733$	−29052.5	−1.46395	−0.731977	+	0.681329i	$0.761402\pi$
$734$	44461.3	2.23582
$735$	4381.23	0.219870
$736$	−35301.2	−1.76796
$737$	10918.9	0.545729
$738$	5155.64	0.257157
$739$	10052.9	0.500406	0.250203	−	0.968193i	$-0.419503\pi$
$739$	10052.9	0.500406	0.250203	+	0.968193i	$0.419503\pi$
$740$	21132.7	1.04980
$741$	0	0
$742$	42196.7	2.08772
$743$	−25934.0	−1.28052	−0.640261	−	0.768157i	$-0.721174\pi$
$743$	−25934.0	−1.28052	−0.640261	+	0.768157i	$0.721174\pi$
$744$	59128.3	2.91364
$745$	−40314.0	−1.98254
$746$	−23039.8	−1.13076
$747$	−6818.24	−0.333958
$748$	−2786.68	−0.136218
$749$	8259.47	0.402930
$750$	−4199.51	−0.204459
$751$	−6924.41	−0.336452	−0.168226	−	0.985748i	$-0.553804\pi$
$751$	−6924.41	−0.336452	−0.168226	+	0.985748i	$0.553804\pi$
$752$	16139.4	0.782640
$753$	−19906.0	−0.963366
$754$	0	0
$755$	35281.2	1.70068
$756$	45818.6	2.20424
$757$	24615.3	1.18185	0.590923	−	0.806728i	$-0.298764\pi$
$757$	24615.3	1.18185	0.590923	+	0.806728i	$0.298764\pi$
$758$	55270.5	2.64844
$759$	9315.74	0.445507
$760$	59885.5	2.85826
$761$	5348.89	0.254793	0.127396	−	0.991852i	$-0.459338\pi$
$761$	5348.89	0.254793	0.127396	+	0.991852i	$0.459338\pi$
$762$	2091.43	0.0994287
$763$	−18640.4	−0.884442
$764$	−35338.0	−1.67341
$765$	−1313.80	−0.0620922
$766$	63482.8	2.99442
$767$	0	0
$768$	−33112.2	−1.55577
$769$	34914.1	1.63723	0.818617	−	0.574340i	$-0.194741\pi$
$769$	34914.1	1.63723	0.818617	+	0.574340i	$0.194741\pi$
$770$	−14534.0	−0.680219
$771$	10641.4	0.497067
$772$	33045.9	1.54061
$773$	20104.4	0.935454	0.467727	−	0.883873i	$-0.345073\pi$
$773$	20104.4	0.935454	0.467727	+	0.883873i	$0.345073\pi$
$774$	−964.403	−0.0447865
$775$	−28502.1	−1.32106
$776$	36790.7	1.70195
$777$	5809.98	0.268252
$778$	39136.3	1.80348
$779$	12556.3	0.577506
$780$	0	0
$781$	−1562.09	−0.0715697
$782$	13251.9	0.605993
$783$	20171.6	0.920658
$784$	−7312.55	−0.333115
$785$	45137.4	2.05226
$786$	−34065.4	−1.54590
$787$	−4433.53	−0.200811	−0.100406	−	0.994947i	$-0.532014\pi$
$787$	−4433.53	−0.200811	−0.100406	+	0.994947i	$0.532014\pi$
$788$	38895.3	1.75836
$789$	11171.7	0.504084
$790$	94742.3	4.26681
$791$	34032.6	1.52979
$792$	3431.42	0.153952
$793$	0	0
$794$	38506.7	1.72110
$795$	−34826.1	−1.55366
$796$	−55365.6	−2.46530
$797$	36378.0	1.61678	0.808392	−	0.588645i	$-0.200338\pi$
$797$	36378.0	1.61678	0.808392	+	0.588645i	$0.200338\pi$
$798$	29547.5	1.31074
$799$	−1919.59	−0.0849941
$800$	−21617.2	−0.955354
$801$	−5178.69	−0.228440
$802$	42295.6	1.86223
$803$	−10972.2	−0.482191
$804$	82049.3	3.59907
$805$	47904.2	2.09739
$806$	0	0
$807$	624.210	0.0272283
$808$	−1029.49	−0.0448234
$809$	18976.7	0.824705	0.412353	−	0.911024i	$-0.364707\pi$
$809$	18976.7	0.824705	0.412353	+	0.911024i	$0.364707\pi$
$810$	−41643.2	−1.80641
$811$	−26212.5	−1.13495	−0.567476	−	0.823390i	$-0.692080\pi$
$811$	−26212.5	−1.13495	−0.567476	+	0.823390i	$0.692080\pi$
$812$	40378.6	1.74509
$813$	−17593.0	−0.758933
$814$	4254.90	0.183211
$815$	−40627.4	−1.74615
$816$	−7562.64	−0.324443
$817$	−2348.76	−0.100579
$818$	−74217.9	−3.17233
$819$	0	0
$820$	−46411.3	−1.97653
$821$	−919.299	−0.0390789	−0.0195394	−	0.999809i	$-0.506220\pi$
$821$	−919.299	−0.0390789	−0.0195394	+	0.999809i	$0.506220\pi$
$822$	−14294.3	−0.606535
$823$	586.176	0.0248272	0.0124136	−	0.999923i	$-0.496049\pi$
$823$	586.176	0.0248272	0.0124136	+	0.999923i	$0.496049\pi$
$824$	84556.7	3.57485
$825$	5704.64	0.240739
$826$	8229.79	0.346672
$827$	−10277.1	−0.432126	−0.216063	−	0.976379i	$-0.569322\pi$
$827$	−10277.1	−0.432126	−0.216063	+	0.976379i	$0.569322\pi$
$828$	−20297.5	−0.851915
$829$	−6669.14	−0.279407	−0.139704	−	0.990193i	$-0.544615\pi$
$829$	−6669.14	−0.279407	−0.139704	+	0.990193i	$0.544615\pi$
$830$	88555.5	3.70338
$831$	11089.1	0.462906
$832$	0	0
$833$	869.739	0.0361761
$834$	15042.9	0.624571
$835$	37610.5	1.55876
$836$	14998.0	0.620474
$837$	38041.0	1.57096
$838$	−27435.6	−1.13096
$839$	−22302.1	−0.917704	−0.458852	−	0.888513i	$-0.651739\pi$
$839$	−22302.1	−0.917704	−0.458852	+	0.888513i	$0.651739\pi$
$840$	−60855.9	−2.49967
$841$	−6612.36	−0.271121
$842$	66957.8	2.74052
$843$	−26386.6	−1.07806
$844$	32444.4	1.32320
$845$	0	0
$846$	4242.05	0.172393
$847$	−2028.23	−0.0822795
$848$	58126.9	2.35388
$849$	15244.4	0.616237
$850$	8115.00	0.327461
$851$	−14024.2	−0.564916
$852$	−11738.2	−0.472002
$853$	−30009.1	−1.20456	−0.602281	−	0.798284i	$-0.705741\pi$
$853$	−30009.1	−1.20456	−0.602281	+	0.798284i	$0.705741\pi$
$854$	53576.4	2.14678
$855$	7070.91	0.282830
$856$	25327.1	1.01129
$857$	11017.4	0.439145	0.219572	−	0.975596i	$-0.429534\pi$
$857$	11017.4	0.439145	0.219572	+	0.975596i	$0.429534\pi$
$858$	0	0
$859$	−43496.1	−1.72767	−0.863835	−	0.503774i	$-0.831944\pi$
$859$	−43496.1	−1.72767	−0.863835	+	0.503774i	$0.831944\pi$
$860$	8681.59	0.344232
$861$	−12759.8	−0.505054
$862$	−61227.5	−2.41928
$863$	5170.97	0.203965	0.101983	−	0.994786i	$-0.467481\pi$
$863$	5170.97	0.203965	0.101983	+	0.994786i	$0.467481\pi$
$864$	28851.9	1.13607
$865$	−1531.26	−0.0601900
$866$	47031.1	1.84547
$867$	−21577.7	−0.845233
$868$	76148.7	2.97771
$869$	13221.4	0.516115
$870$	−48081.8	−1.87371
$871$	0	0
$872$	−57159.6	−2.21980
$873$	4344.02	0.168411
$874$	−71322.1	−2.76031
$875$	−3013.60	−0.116432
$876$	−82449.8	−3.18005
$877$	−11286.9	−0.434584	−0.217292	−	0.976107i	$-0.569722\pi$
$877$	−11286.9	−0.434584	−0.217292	+	0.976107i	$0.569722\pi$
$878$	−38643.1	−1.48536
$879$	28850.8	1.10707
$880$	−20020.9	−0.766937
$881$	−19065.6	−0.729098	−0.364549	−	0.931184i	$-0.618777\pi$
$881$	−19065.6	−0.729098	−0.364549	+	0.931184i	$0.618777\pi$
$882$	−1922.01	−0.0733758
$883$	−1138.17	−0.0433777	−0.0216889	−	0.999765i	$-0.506904\pi$
$883$	−1138.17	−0.0433777	−0.0216889	+	0.999765i	$0.506904\pi$
$884$	0	0
$885$	−6792.29	−0.257989
$886$	−48131.2	−1.82506
$887$	3526.66	0.133499	0.0667495	−	0.997770i	$-0.478737\pi$
$887$	3526.66	0.133499	0.0667495	+	0.997770i	$0.478737\pi$
$888$	17815.9	0.673267
$889$	1500.83	0.0566212
$890$	67261.0	2.53325
$891$	−5811.35	−0.218504
$892$	17254.3	0.647663
$893$	10331.3	0.387149
$894$	−60994.0	−2.28182
$895$	−41238.5	−1.54017
$896$	−22959.6	−0.856057
$897$	0	0
$898$	−36303.9	−1.34908
$899$	33524.4	1.24372
$900$	−12429.5	−0.460351
$901$	−6913.50	−0.255629
$902$	−9344.54	−0.344944
$903$	2386.82	0.0879604
$904$	104359.	3.83951
$905$	7463.66	0.274144
$906$	53379.6	1.95741
$907$	28678.3	1.04989	0.524944	−	0.851137i	$-0.324086\pi$
$907$	28678.3	1.04989	0.524944	+	0.851137i	$0.324086\pi$
$908$	−45379.7	−1.65857
$909$	−121.556	−0.00443537
$910$	0	0
$911$	483.164	0.0175718	0.00878591	−	0.999961i	$-0.497203\pi$
$911$	483.164	0.0175718	0.00878591	+	0.999961i	$0.497203\pi$
$912$	40702.4	1.47784
$913$	12358.0	0.447962
$914$	14411.2	0.521533
$915$	−44218.2	−1.59760
$916$	−86599.2	−3.12371
$917$	−24445.7	−0.880335
$918$	−10830.9	−0.389404
$919$	4137.12	0.148499	0.0742497	−	0.997240i	$-0.476344\pi$
$919$	4137.12	0.148499	0.0742497	+	0.997240i	$0.476344\pi$
$920$	146895.	5.26410
$921$	1474.41	0.0527507
$922$	8240.77	0.294355
$923$	0	0
$924$	−15241.0	−0.542632
$925$	−8587.93	−0.305264
$926$	32812.3	1.16445
$927$	9983.93	0.353738
$928$	25426.3	0.899419
$929$	−26880.6	−0.949326	−0.474663	−	0.880168i	$-0.657430\pi$
$929$	−26880.6	−0.949326	−0.474663	+	0.880168i	$0.657430\pi$
$930$	−90675.9	−3.19718
$931$	−4680.96	−0.164782
$932$	−13575.2	−0.477114
$933$	5081.05	0.178292
$934$	−52168.1	−1.82762
$935$	2381.25	0.0832888
$936$	0	0
$937$	54046.4	1.88433	0.942165	−	0.335149i	$-0.108787\pi$
$937$	54046.4	1.88433	0.942165	+	0.335149i	$0.108787\pi$
$938$	84950.3	2.95706
$939$	−15271.6	−0.530746
$940$	−38187.1	−1.32503
$941$	20813.2	0.721030	0.360515	−	0.932753i	$-0.382601\pi$
$941$	20813.2	0.721030	0.360515	+	0.932753i	$0.382601\pi$
$942$	68291.7	2.36206
$943$	30799.7	1.06360
$944$	11336.7	0.390868
$945$	−39152.5	−1.34776
$946$	1747.97	0.0600755
$947$	14509.2	0.497875	0.248937	−	0.968520i	$-0.419919\pi$
$947$	14509.2	0.497875	0.248937	+	0.968520i	$0.419919\pi$
$948$	99351.1	3.40377
$949$	0	0
$950$	−43675.2	−1.49159
$951$	−3569.42	−0.121710
$952$	−12080.8	−0.411282
$953$	−7481.09	−0.254288	−0.127144	−	0.991884i	$-0.540581\pi$
$953$	−7481.09	−0.254288	−0.127144	+	0.991884i	$0.540581\pi$
$954$	15277.9	0.518492
$955$	30196.7	1.02319
$956$	−69522.4	−2.35200
$957$	−6709.84	−0.226644
$958$	−3510.23	−0.118382
$959$	−10257.7	−0.345401
$960$	−2156.84	−0.0725121
$961$	33431.6	1.12221
$962$	0	0
$963$	2990.46	0.100069
$964$	−119107.	−3.97944
$965$	−28238.0	−0.941984
$966$	72477.8	2.41401
$967$	27135.3	0.902392	0.451196	−	0.892425i	$-0.350997\pi$
$967$	27135.3	0.902392	0.451196	+	0.892425i	$0.350997\pi$
$968$	−6219.41	−0.206508
$969$	−4841.06	−0.160492
$970$	−56420.2	−1.86757
$971$	37071.3	1.22521	0.612603	−	0.790390i	$-0.290122\pi$
$971$	37071.3	1.22521	0.612603	+	0.790390i	$0.290122\pi$
$972$	30134.0	0.994393
$973$	10794.9	0.355672
$974$	−78767.0	−2.59123
$975$	0	0
$976$	73802.8	2.42046
$977$	26866.4	0.879767	0.439884	−	0.898055i	$-0.355020\pi$
$977$	26866.4	0.879767	0.439884	+	0.898055i	$0.355020\pi$
$978$	−61468.2	−2.00975
$979$	9386.32	0.306423
$980$	17302.0	0.563971
$981$	−6749.04	−0.219654
$982$	−60937.5	−1.98024
$983$	−47014.2	−1.52545	−0.762727	−	0.646721i	$-0.776140\pi$
$983$	−47014.2	−1.52545	−0.762727	+	0.646721i	$0.776140\pi$
$984$	−39126.9	−1.26760
$985$	−33236.4	−1.07513
$986$	−9544.93	−0.308289
$987$	−10498.7	−0.338579
$988$	0	0
$989$	−5761.33	−0.185237
$990$	−5262.24	−0.168934
$991$	−42911.3	−1.37550	−0.687751	−	0.725947i	$-0.741402\pi$
$991$	−42911.3	−1.37550	−0.687751	+	0.725947i	$0.741402\pi$
$992$	47950.7	1.53472
$993$	−30057.8	−0.960581
$994$	−12153.3	−0.387805
$995$	47310.5	1.50738
$996$	92863.4	2.95431
$997$	23772.8	0.755157	0.377578	−	0.925978i	$-0.376757\pi$
$997$	23772.8	0.755157	0.377578	+	0.925978i	$0.376757\pi$
$998$	−86727.1	−2.75080
$999$	11462.1	0.363008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.1		17
13.3	even	3		143.4.e.b.100.17	✓	34
13.9	even	3		143.4.e.b.133.17	yes	34
13.12	even	2		1859.4.a.h.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.17	✓	34	13.3	even	3
143.4.e.b.133.17	yes	34	13.9	even	3
1859.4.a.g.1.1		17	1.1	even	1	trivial
1859.4.a.h.1.17		17	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-5.10562 q^{2} +4.57504 q^{3} +18.0674 q^{4} -15.4387 q^{5} -23.3584 q^{6} -16.7622 q^{7} -51.4001 q^{8} -6.06900 q^{9} +O(q^{10})\)	\(q-5.10562 q^{2} +4.57504 q^{3} +18.0674 q^{4} -15.4387 q^{5} -23.3584 q^{6} -16.7622 q^{7} -51.4001 q^{8} -6.06900 q^{9} +78.8244 q^{10} +11.0000 q^{11} +82.6589 q^{12} +85.5815 q^{14} -70.6329 q^{15} +117.891 q^{16} -14.0217 q^{17} +30.9860 q^{18} +75.4650 q^{19} -278.937 q^{20} -76.6878 q^{21} -56.1618 q^{22} +185.110 q^{23} -235.158 q^{24} +113.355 q^{25} -151.292 q^{27} -302.849 q^{28} -133.329 q^{29} +360.625 q^{30} -251.441 q^{31} -190.704 q^{32} +50.3254 q^{33} +71.5893 q^{34} +258.788 q^{35} -109.651 q^{36} -75.7614 q^{37} -385.296 q^{38} +793.553 q^{40} +166.386 q^{41} +391.539 q^{42} -31.1238 q^{43} +198.741 q^{44} +93.6978 q^{45} -945.101 q^{46} +136.902 q^{47} +539.354 q^{48} -62.0282 q^{49} -578.747 q^{50} -64.1497 q^{51} +493.058 q^{53} +772.440 q^{54} -169.826 q^{55} +861.580 q^{56} +345.256 q^{57} +680.728 q^{58} +96.1632 q^{59} -1276.15 q^{60} +626.028 q^{61} +1283.76 q^{62} +101.730 q^{63} +30.5359 q^{64} -256.943 q^{66} +992.625 q^{67} -253.334 q^{68} +846.886 q^{69} -1321.27 q^{70} -142.008 q^{71} +311.947 q^{72} -997.470 q^{73} +386.809 q^{74} +518.603 q^{75} +1363.45 q^{76} -184.384 q^{77} +1201.94 q^{79} -1820.08 q^{80} -528.304 q^{81} -849.503 q^{82} +1123.45 q^{83} -1385.55 q^{84} +216.477 q^{85} +158.906 q^{86} -609.986 q^{87} -565.401 q^{88} +853.302 q^{89} -478.385 q^{90} +3344.45 q^{92} -1150.35 q^{93} -698.969 q^{94} -1165.09 q^{95} -872.477 q^{96} -715.772 q^{97} +316.693 q^{98} -66.7590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more