LMFDB - Embedded newform 1859.4.a.g.1.2

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			1.2
Root			$5.08131$ 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)

$f(q)$	$=$	$q-5.08131 q^{2} -7.39360 q^{3} +17.8197 q^{4} +8.39690 q^{5} +37.5692 q^{6} -14.1925 q^{7} -49.8972 q^{8} +27.6653 q^{9} +O(q^{10})$	\(q-5.08131 q^{2} -7.39360 q^{3} +17.8197 q^{4} +8.39690 q^{5} +37.5692 q^{6} -14.1925 q^{7} -49.8972 q^{8} +27.6653 q^{9} -42.6673 q^{10} +11.0000 q^{11} -131.752 q^{12} +72.1166 q^{14} -62.0833 q^{15} +110.985 q^{16} -16.9156 q^{17} -140.576 q^{18} -41.1173 q^{19} +149.631 q^{20} +104.934 q^{21} -55.8944 q^{22} +131.744 q^{23} +368.920 q^{24} -54.4921 q^{25} -4.91923 q^{27} -252.907 q^{28} -97.3789 q^{29} +315.465 q^{30} -14.2202 q^{31} -164.774 q^{32} -81.3296 q^{33} +85.9535 q^{34} -119.173 q^{35} +492.989 q^{36} +364.630 q^{37} +208.930 q^{38} -418.982 q^{40} -114.491 q^{41} -533.202 q^{42} +507.029 q^{43} +196.017 q^{44} +232.303 q^{45} -669.430 q^{46} -316.377 q^{47} -820.581 q^{48} -141.572 q^{49} +276.891 q^{50} +125.067 q^{51} -456.545 q^{53} +24.9961 q^{54} +92.3659 q^{55} +708.167 q^{56} +304.005 q^{57} +494.813 q^{58} -600.903 q^{59} -1106.31 q^{60} +665.804 q^{61} +72.2572 q^{62} -392.641 q^{63} -50.6164 q^{64} +413.261 q^{66} -808.411 q^{67} -301.432 q^{68} -974.059 q^{69} +605.556 q^{70} -495.396 q^{71} -1380.42 q^{72} +494.502 q^{73} -1852.80 q^{74} +402.893 q^{75} -732.700 q^{76} -156.118 q^{77} -643.276 q^{79} +931.932 q^{80} -710.593 q^{81} +581.762 q^{82} +814.591 q^{83} +1869.89 q^{84} -142.039 q^{85} -2576.37 q^{86} +719.980 q^{87} -548.869 q^{88} -701.144 q^{89} -1180.40 q^{90} +2347.64 q^{92} +105.138 q^{93} +1607.61 q^{94} -345.258 q^{95} +1218.27 q^{96} -810.294 q^{97} +719.374 q^{98} +304.319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.08131	−1.79652	−0.898258	−	0.439469i	$-0.855167\pi$
$2$	−5.08131	−1.79652	−0.898258	+	0.439469i	$0.855167\pi$
$3$	−7.39360	−1.42290	−0.711450	−	0.702737i	$-0.751961\pi$
$3$	−7.39360	−1.42290	−0.711450	+	0.702737i	$0.751961\pi$
$4$	17.8197	2.22747
$5$	8.39690	0.751042	0.375521	−	0.926814i	$-0.377464\pi$
$5$	8.39690	0.751042	0.375521	+	0.926814i	$0.377464\pi$
$6$	37.5692	2.55626
$7$	−14.1925	−0.766324	−0.383162	−	0.923681i	$-0.625165\pi$
$7$	−14.1925	−0.766324	−0.383162	+	0.923681i	$0.625165\pi$
$8$	−49.8972	−2.20517
$9$	27.6653	1.02464
$10$	−42.6673	−1.34926
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−131.752	−3.16946
$13$	0	0
$13$	0	0
$14$	72.1166	1.37671
$15$	−62.0833	−1.06866
$16$	110.985	1.73415
$17$	−16.9156	−0.241332	−0.120666	−	0.992693i	$-0.538503\pi$
$17$	−16.9156	−0.241332	−0.120666	+	0.992693i	$0.538503\pi$
$18$	−140.576	−1.84079
$19$	−41.1173	−0.496471	−0.248236	−	0.968700i	$-0.579851\pi$
$19$	−41.1173	−0.496471	−0.248236	+	0.968700i	$0.579851\pi$
$20$	149.631	1.67292
$21$	104.934	1.09040
$22$	−55.8944	−0.541670
$23$	131.744	1.19437	0.597183	−	0.802105i	$-0.296286\pi$
$23$	131.744	1.19437	0.597183	+	0.802105i	$0.296286\pi$
$24$	368.920	3.13773
$25$	−54.4921	−0.435937
$26$	0	0
$27$	−4.91923	−0.0350632
$28$	−252.907	−1.70696
$29$	−97.3789	−0.623545	−0.311772	−	0.950157i	$-0.600923\pi$
$29$	−97.3789	−0.623545	−0.311772	+	0.950157i	$0.600923\pi$
$30$	315.465	1.91986
$31$	−14.2202	−0.0823878	−0.0411939	−	0.999151i	$-0.513116\pi$
$31$	−14.2202	−0.0823878	−0.0411939	+	0.999151i	$0.513116\pi$
$32$	−164.774	−0.910254
$33$	−81.3296	−0.429020
$34$	85.9535	0.433556
$35$	−119.173	−0.575541
$36$	492.989	2.28236
$37$	364.630	1.62013	0.810066	−	0.586339i	$-0.199431\pi$
$37$	364.630	1.62013	0.810066	+	0.586339i	$0.199431\pi$
$38$	208.930	0.891919
$39$	0	0
$40$	−418.982	−1.65617
$41$	−114.491	−0.436108	−0.218054	−	0.975937i	$-0.569971\pi$
$41$	−114.491	−0.436108	−0.218054	+	0.975937i	$0.569971\pi$
$42$	−533.202	−1.95892
$43$	507.029	1.79817	0.899084	−	0.437776i	$-0.144234\pi$
$43$	507.029	1.79817	0.899084	+	0.437776i	$0.144234\pi$
$44$	196.017	0.671607
$45$	232.303	0.769549
$46$	−669.430	−2.14570
$47$	−316.377	−0.981879	−0.490939	−	0.871194i	$-0.663346\pi$
$47$	−316.377	−0.981879	−0.490939	+	0.871194i	$0.663346\pi$
$48$	−820.581	−2.46751
$49$	−141.572	−0.412748
$50$	276.891	0.783167
$51$	125.067	0.343391
$52$	0	0
$53$	−456.545	−1.18323	−0.591616	−	0.806220i	$-0.701510\pi$
$53$	−456.545	−1.18323	−0.591616	+	0.806220i	$0.701510\pi$
$54$	24.9961	0.0629915
$55$	92.3659	0.226448
$56$	708.167	1.68987
$57$	304.005	0.706429
$58$	494.813	1.12021
$59$	−600.903	−1.32595	−0.662974	−	0.748643i	$-0.730706\pi$
$59$	−600.903	−1.32595	−0.662974	+	0.748643i	$0.730706\pi$
$60$	−1106.31	−2.38040
$61$	665.804	1.39750	0.698749	−	0.715367i	$-0.253740\pi$
$61$	665.804	1.39750	0.698749	+	0.715367i	$0.253740\pi$
$62$	72.2572	0.148011
$63$	−392.641	−0.785208
$64$	−50.6164	−0.0988601
$65$	0	0
$66$	413.261	0.770742
$67$	−808.411	−1.47408	−0.737038	−	0.675851i	$-0.763776\pi$
$67$	−808.411	−1.47408	−0.737038	+	0.675851i	$0.763776\pi$
$68$	−301.432	−0.537559
$69$	−974.059	−1.69946
$70$	605.556	1.03397
$71$	−495.396	−0.828066	−0.414033	−	0.910262i	$-0.635880\pi$
$71$	−495.396	−0.828066	−0.414033	+	0.910262i	$0.635880\pi$
$72$	−1380.42	−2.25950
$73$	494.502	0.792837	0.396419	−	0.918070i	$-0.370253\pi$
$73$	494.502	0.792837	0.396419	+	0.918070i	$0.370253\pi$
$74$	−1852.80	−2.91059
$75$	402.893	0.620294
$76$	−732.700	−1.10587
$77$	−156.118	−0.231055
$78$	0	0
$79$	−643.276	−0.916130	−0.458065	−	0.888919i	$-0.651457\pi$
$79$	−643.276	−0.916130	−0.458065	+	0.888919i	$0.651457\pi$
$80$	931.932	1.30242
$81$	−710.593	−0.974751
$82$	581.762	0.783474
$83$	814.591	1.07727	0.538633	−	0.842541i	$-0.318941\pi$
$83$	814.591	1.07727	0.538633	+	0.842541i	$0.318941\pi$
$84$	1869.89	2.42883
$85$	−142.039	−0.181250
$86$	−2576.37	−3.23044
$87$	719.980	0.887242
$88$	−548.869	−0.664882
$89$	−701.144	−0.835069	−0.417535	−	0.908661i	$-0.637106\pi$
$89$	−701.144	−0.835069	−0.417535	+	0.908661i	$0.637106\pi$
$90$	−1180.40	−1.38251
$91$	0	0
$92$	2347.64	2.66041
$93$	105.138	0.117230
$94$	1607.61	1.76396
$95$	−345.258	−0.372871
$96$	1218.27	1.29520
$97$	−810.294	−0.848174	−0.424087	−	0.905622i	$-0.639405\pi$
$97$	−810.294	−0.848174	−0.424087	+	0.905622i	$0.639405\pi$
$98$	719.374	0.741507
$99$	304.319	0.308941
$100$	−971.035	−0.971035
$101$	707.340	0.696861	0.348430	−	0.937335i	$-0.386715\pi$
$101$	707.340	0.696861	0.348430	+	0.937335i	$0.386715\pi$
$102$	−635.506	−0.616907
$103$	1849.13	1.76893	0.884467	−	0.466602i	$-0.154522\pi$
$103$	1849.13	1.76893	0.884467	+	0.466602i	$0.154522\pi$
$104$	0	0
$105$	881.119	0.818937
$106$	2319.85	2.12570
$107$	2010.06	1.81607	0.908036	−	0.418892i	$-0.137582\pi$
$107$	2010.06	1.81607	0.908036	+	0.418892i	$0.137582\pi$
$108$	−87.6594	−0.0781021
$109$	−1655.72	−1.45495	−0.727475	−	0.686134i	$-0.759307\pi$
$109$	−1655.72	−1.45495	−0.727475	+	0.686134i	$0.759307\pi$
$110$	−469.340	−0.406817
$111$	−2695.93	−2.30528
$112$	−1575.16	−1.32892
$113$	169.236	0.140888	0.0704441	−	0.997516i	$-0.477558\pi$
$113$	169.236	0.140888	0.0704441	+	0.997516i	$0.477558\pi$
$114$	−1544.74	−1.26911
$115$	1106.24	0.897019
$116$	−1735.27	−1.38893
$117$	0	0
$118$	3053.38	2.38209
$119$	240.075	0.184938
$120$	3097.78	2.35656
$121$	121.000	0.0909091
$122$	−3383.16	−2.51063
$123$	846.497	0.620537
$124$	−253.400	−0.183516
$125$	−1507.18	−1.07845
$126$	1995.13	1.41064
$127$	598.018	0.417839	0.208919	−	0.977933i	$-0.433005\pi$
$127$	598.018	0.417839	0.208919	+	0.977933i	$0.433005\pi$
$128$	1575.39	1.08786
$129$	−3748.77	−2.55861
$130$	0	0
$131$	2576.77	1.71858	0.859288	−	0.511493i	$-0.170907\pi$
$131$	2576.77	1.71858	0.859288	+	0.511493i	$0.170907\pi$
$132$	−1449.27	−0.955629
$133$	583.558	0.380458
$134$	4107.79	2.64820
$135$	−41.3063	−0.0263339
$136$	844.042	0.532176
$137$	2146.54	1.33862	0.669312	−	0.742981i	$-0.266589\pi$
$137$	2146.54	1.33862	0.669312	+	0.742981i	$0.266589\pi$
$138$	4949.50	3.05311
$139$	172.147	0.105045	0.0525226	−	0.998620i	$-0.483274\pi$
$139$	172.147	0.105045	0.0525226	+	0.998620i	$0.483274\pi$
$140$	−2123.63	−1.28200
$141$	2339.16	1.39711
$142$	2517.26	1.48763
$143$	0	0
$144$	3070.45	1.77688
$145$	−817.681	−0.468308
$146$	−2512.72	−1.42434
$147$	1046.73	0.587298
$148$	6497.62	3.60879
$149$	2002.03	1.10076	0.550379	−	0.834915i	$-0.314483\pi$
$149$	2002.03	1.10076	0.550379	+	0.834915i	$0.314483\pi$
$150$	−2047.22	−1.11437
$151$	805.224	0.433962	0.216981	−	0.976176i	$-0.430379\pi$
$151$	805.224	0.433962	0.216981	+	0.976176i	$0.430379\pi$
$152$	2051.64	1.09480
$153$	−467.976	−0.247279
$154$	793.283	0.415095
$155$	−119.405	−0.0618766
$156$	0	0
$157$	−868.349	−0.441413	−0.220706	−	0.975340i	$-0.570836\pi$
$157$	−868.349	−0.441413	−0.220706	+	0.975340i	$0.570836\pi$
$158$	3268.69	1.64584
$159$	3375.51	1.68362
$160$	−1383.59	−0.683639
$161$	−1869.77	−0.915272
$162$	3610.75	1.75115
$163$	−1387.71	−0.666835	−0.333417	−	0.942779i	$-0.608202\pi$
$163$	−1387.71	−0.666835	−0.333417	+	0.942779i	$0.608202\pi$
$164$	−2040.19	−0.971416
$165$	−682.917	−0.322212
$166$	−4139.19	−1.93532
$167$	353.259	0.163689	0.0818443	−	0.996645i	$-0.473919\pi$
$167$	353.259	0.163689	0.0818443	+	0.996645i	$0.473919\pi$
$168$	−5235.90	−2.40452
$169$	0	0
$170$	721.743	0.325619
$171$	−1137.52	−0.508705
$172$	9035.13	4.00536
$173$	−854.066	−0.375338	−0.187669	−	0.982232i	$-0.560093\pi$
$173$	−854.066	−0.375338	−0.187669	+	0.982232i	$0.560093\pi$
$174$	−3658.45	−1.59394
$175$	773.380	0.334069
$176$	1220.84	0.522865
$177$	4442.84	1.88669
$178$	3562.73	1.50021
$179$	2038.19	0.851069	0.425534	−	0.904942i	$-0.360086\pi$
$179$	2038.19	0.851069	0.425534	+	0.904942i	$0.360086\pi$
$180$	4139.58	1.71415
$181$	3743.92	1.53748	0.768738	−	0.639564i	$-0.220885\pi$
$181$	3743.92	1.53748	0.768738	+	0.639564i	$0.220885\pi$
$182$	0	0
$183$	−4922.69	−1.98850
$184$	−6573.63	−2.63378
$185$	3061.76	1.21679
$186$	−534.241	−0.210605
$187$	−186.072	−0.0727642
$188$	−5637.75	−2.18710
$189$	69.8162	0.0268698
$190$	1754.36	0.669868
$191$	−1154.72	−0.437449	−0.218725	−	0.975787i	$-0.570190\pi$
$191$	−1154.72	−0.437449	−0.218725	+	0.975787i	$0.570190\pi$
$192$	374.237	0.140668
$193$	−4247.90	−1.58430	−0.792151	−	0.610325i	$-0.791039\pi$
$193$	−4247.90	−1.58430	−0.792151	+	0.610325i	$0.791039\pi$
$194$	4117.36	1.52376
$195$	0	0
$196$	−2522.78	−0.919382
$197$	−530.359	−0.191810	−0.0959048	−	0.995391i	$-0.530574\pi$
$197$	−530.359	−0.191810	−0.0959048	+	0.995391i	$0.530574\pi$
$198$	−1546.34	−0.555018
$199$	−2627.30	−0.935902	−0.467951	−	0.883754i	$-0.655008\pi$
$199$	−2627.30	−0.935902	−0.467951	+	0.883754i	$0.655008\pi$
$200$	2719.00	0.961312
$201$	5977.07	2.09746
$202$	−3594.21	−1.25192
$203$	1382.05	0.477837
$204$	2228.67	0.764892
$205$	−961.365	−0.327535
$206$	−9396.01	−3.17792
$207$	3644.73	1.22380
$208$	0	0
$209$	−452.290	−0.149692
$210$	−4477.24	−1.47123
$211$	149.531	0.0487874	0.0243937	−	0.999702i	$-0.492234\pi$
$211$	149.531	0.0487874	0.0243937	+	0.999702i	$0.492234\pi$
$212$	−8135.52	−2.63561
$213$	3662.76	1.17825
$214$	−10213.7	−3.26260
$215$	4257.47	1.35050
$216$	245.456	0.0773201
$217$	201.820	0.0631357
$218$	8413.26	2.61384
$219$	−3656.15	−1.12813
$220$	1645.94	0.504405
$221$	0	0
$222$	13698.9	4.14148
$223$	−516.482	−0.155095	−0.0775475	−	0.996989i	$-0.524709\pi$
$223$	−516.482	−0.155095	−0.0775475	+	0.996989i	$0.524709\pi$
$224$	2338.55	0.697549
$225$	−1507.54	−0.446679
$226$	−859.940	−0.253108
$227$	5213.26	1.52430	0.762150	−	0.647401i	$-0.224144\pi$
$227$	5213.26	1.52430	0.762150	+	0.647401i	$0.224144\pi$
$228$	5417.29	1.57355
$229$	879.485	0.253790	0.126895	−	0.991916i	$-0.459499\pi$
$229$	879.485	0.253790	0.126895	+	0.991916i	$0.459499\pi$
$230$	−5621.14	−1.61151
$231$	1154.27	0.328768
$232$	4858.93	1.37502
$233$	5310.87	1.49325	0.746624	−	0.665246i	$-0.231673\pi$
$233$	5310.87	1.49325	0.746624	+	0.665246i	$0.231673\pi$
$234$	0	0
$235$	−2656.58	−0.737432
$236$	−10707.9	−2.95351
$237$	4756.13	1.30356
$238$	−1219.90	−0.332244
$239$	−2999.57	−0.811825	−0.405913	−	0.913912i	$-0.633046\pi$
$239$	−2999.57	−0.811825	−0.405913	+	0.913912i	$0.633046\pi$
$240$	−6890.34	−1.85321
$241$	363.128	0.0970587	0.0485294	−	0.998822i	$-0.484547\pi$
$241$	363.128	0.0970587	0.0485294	+	0.998822i	$0.484547\pi$
$242$	−614.839	−0.163320
$243$	5386.66	1.42204
$244$	11864.4	3.11288
$245$	−1188.77	−0.309991
$246$	−4301.32	−1.11480
$247$	0	0
$248$	709.547	0.181679
$249$	−6022.76	−1.53284
$250$	7658.44	1.93745
$251$	2666.24	0.670484	0.335242	−	0.942132i	$-0.391182\pi$
$251$	2666.24	0.670484	0.335242	+	0.942132i	$0.391182\pi$
$252$	−6996.76	−1.74903
$253$	1449.18	0.360115
$254$	−3038.72	−0.750654
$255$	1050.18	0.257901
$256$	−7600.10	−1.85549
$257$	−322.343	−0.0782382	−0.0391191	−	0.999235i	$-0.512455\pi$
$257$	−322.343	−0.0782382	−0.0391191	+	0.999235i	$0.512455\pi$
$258$	19048.7	4.59659
$259$	−5175.02	−1.24155
$260$	0	0
$261$	−2694.02	−0.638910
$262$	−13093.4	−3.08745
$263$	3062.65	0.718064	0.359032	−	0.933325i	$-0.383107\pi$
$263$	3062.65	0.718064	0.359032	+	0.933325i	$0.383107\pi$
$264$	4058.12	0.946060
$265$	−3833.56	−0.888657
$266$	−2965.24	−0.683499
$267$	5183.98	1.18822
$268$	−14405.7	−3.28346
$269$	3911.44	0.886560	0.443280	−	0.896383i	$-0.353815\pi$
$269$	3911.44	0.886560	0.443280	+	0.896383i	$0.353815\pi$
$270$	209.890	0.0473093
$271$	−3909.86	−0.876410	−0.438205	−	0.898875i	$-0.644386\pi$
$271$	−3909.86	−0.876410	−0.438205	+	0.898875i	$0.644386\pi$
$272$	−1877.38	−0.418504
$273$	0	0
$274$	−10907.3	−2.40486
$275$	−599.413	−0.131440
$276$	−17357.5	−3.78550
$277$	−749.619	−0.162600	−0.0813001	−	0.996690i	$-0.525907\pi$
$277$	−749.619	−0.162600	−0.0813001	+	0.996690i	$0.525907\pi$
$278$	−874.731	−0.188715
$279$	−393.406	−0.0844180
$280$	5946.41	1.26916
$281$	4479.67	0.951014	0.475507	−	0.879712i	$-0.342265\pi$
$281$	4479.67	0.951014	0.475507	+	0.879712i	$0.342265\pi$
$282$	−11886.0	−2.50994
$283$	−2689.55	−0.564938	−0.282469	−	0.959276i	$-0.591153\pi$
$283$	−2689.55	−0.564938	−0.282469	+	0.959276i	$0.591153\pi$
$284$	−8827.83	−1.84449
$285$	2552.70	0.530557
$286$	0	0
$287$	1624.91	0.334200
$288$	−4558.52	−0.932684
$289$	−4626.86	−0.941759
$290$	4154.89	0.841323
$291$	5990.99	1.20687
$292$	8811.91	1.76602
$293$	1565.76	0.312192	0.156096	−	0.987742i	$-0.450109\pi$
$293$	1565.76	0.312192	0.156096	+	0.987742i	$0.450109\pi$
$294$	−5318.76	−1.05509
$295$	−5045.72	−0.995842
$296$	−18194.0	−3.57266
$297$	−54.1115	−0.0105719
$298$	−10173.0	−1.97753
$299$	0	0
$300$	7179.44	1.38168
$301$	−7196.02	−1.37798
$302$	−4091.60	−0.779619
$303$	−5229.79	−0.991562
$304$	−4563.42	−0.860954
$305$	5590.69	1.04958
$306$	2377.93	0.444240
$307$	−4583.91	−0.852174	−0.426087	−	0.904682i	$-0.640108\pi$
$307$	−4583.91	−0.852174	−0.426087	+	0.904682i	$0.640108\pi$
$308$	−2781.98	−0.514668
$309$	−13671.7	−2.51702
$310$	606.737	0.111162
$311$	−8238.96	−1.50221	−0.751107	−	0.660181i	$-0.770480\pi$
$311$	−8238.96	−1.50221	−0.751107	+	0.660181i	$0.770480\pi$
$312$	0	0
$313$	−768.625	−0.138803	−0.0694014	−	0.997589i	$-0.522109\pi$
$313$	−768.625	−0.138803	−0.0694014	+	0.997589i	$0.522109\pi$
$314$	4412.35	0.793005
$315$	−3296.97	−0.589724
$316$	−11463.0	−2.04065
$317$	−7760.24	−1.37495	−0.687474	−	0.726209i	$-0.741281\pi$
$317$	−7760.24	−1.37495	−0.687474	+	0.726209i	$0.741281\pi$
$318$	−17152.0	−3.02465
$319$	−1071.17	−0.188006
$320$	−425.021	−0.0742480
$321$	−14861.6	−2.58409
$322$	9500.90	1.64430
$323$	695.524	0.119814
$324$	−12662.6	−2.17123
$325$	0	0
$326$	7051.40	1.19798
$327$	12241.8	2.07025
$328$	5712.76	0.961689
$329$	4490.18	0.752437
$330$	3470.11	0.578859
$331$	6840.82	1.13597	0.567984	−	0.823040i	$-0.307724\pi$
$331$	6840.82	1.13597	0.567984	+	0.823040i	$0.307724\pi$
$332$	14515.8	2.39957
$333$	10087.6	1.66005
$334$	−1795.02	−0.294069
$335$	−6788.15	−1.10709
$336$	11646.1	1.89092
$337$	−8919.67	−1.44180	−0.720898	−	0.693041i	$-0.756271\pi$
$337$	−8919.67	−1.44180	−0.720898	+	0.693041i	$0.756271\pi$
$338$	0	0
$339$	−1251.26	−0.200470
$340$	−2531.09	−0.403729
$341$	−156.422	−0.0248409
$342$	5780.12	0.913897
$343$	6877.30	1.08262
$344$	−25299.3	−3.96526
$345$	−8179.08	−1.27637
$346$	4339.78	0.674300
$347$	−1123.04	−0.173741	−0.0868704	−	0.996220i	$-0.527687\pi$
$347$	−1123.04	−0.173741	−0.0868704	+	0.996220i	$0.527687\pi$
$348$	12829.9	1.97630
$349$	−8686.32	−1.33229	−0.666143	−	0.745824i	$-0.732056\pi$
$349$	−8686.32	−1.33229	−0.666143	+	0.745824i	$0.732056\pi$
$350$	−3929.78	−0.600160
$351$	0	0
$352$	−1812.51	−0.274452
$353$	7042.07	1.06179	0.530895	−	0.847438i	$-0.321856\pi$
$353$	7042.07	1.06179	0.530895	+	0.847438i	$0.321856\pi$
$354$	−22575.4	−3.38947
$355$	−4159.79	−0.621912
$356$	−12494.2	−1.86009
$357$	−1775.02	−0.263148
$358$	−10356.7	−1.52896
$359$	3511.01	0.516167	0.258083	−	0.966123i	$-0.416909\pi$
$359$	3511.01	0.516167	0.258083	+	0.966123i	$0.416909\pi$
$360$	−11591.3	−1.69698
$361$	−5168.37	−0.753516
$362$	−19024.0	−2.76210
$363$	−894.626	−0.129354
$364$	0	0
$365$	4152.29	0.595454
$366$	25013.7	3.57237
$367$	9087.30	1.29252	0.646258	−	0.763119i	$-0.276333\pi$
$367$	9087.30	1.29252	0.646258	+	0.763119i	$0.276333\pi$
$368$	14621.6	2.07121
$369$	−3167.42	−0.446854
$370$	−15557.8	−2.18598
$371$	6479.53	0.906739
$372$	1873.54	0.261125
$373$	1078.96	0.149775	0.0748877	−	0.997192i	$-0.476140\pi$
$373$	1078.96	0.149775	0.0748877	+	0.997192i	$0.476140\pi$
$374$	945.489	0.130722
$375$	11143.5	1.53452
$376$	15786.3	2.16520
$377$	0	0
$378$	−354.758	−0.0482719
$379$	7331.45	0.993644	0.496822	−	0.867852i	$-0.334500\pi$
$379$	7331.45	0.993644	0.496822	+	0.867852i	$0.334500\pi$
$380$	−6152.41	−0.830557
$381$	−4421.51	−0.594543
$382$	5867.51	0.785884
$383$	−13121.8	−1.75063	−0.875314	−	0.483555i	$-0.839345\pi$
$383$	−13121.8	−1.75063	−0.875314	+	0.483555i	$0.839345\pi$
$384$	−11647.8	−1.54791
$385$	−1310.90	−0.173532
$386$	21584.9	2.84622
$387$	14027.1	1.84248
$388$	−14439.2	−1.88928
$389$	−10391.2	−1.35439	−0.677193	−	0.735805i	$-0.736804\pi$
$389$	−10391.2	−1.35439	−0.677193	+	0.735805i	$0.736804\pi$
$390$	0	0
$391$	−2228.52	−0.288239
$392$	7064.07	0.910177
$393$	−19051.6	−2.44536
$394$	2694.92	0.344589
$395$	−5401.53	−0.688051
$396$	5422.88	0.688157
$397$	−1816.57	−0.229651	−0.114825	−	0.993386i	$-0.536631\pi$
$397$	−1816.57	−0.229651	−0.114825	+	0.993386i	$0.536631\pi$
$398$	13350.1	1.68136
$399$	−4314.60	−0.541353
$400$	−6047.82	−0.755977
$401$	4316.84	0.537587	0.268794	−	0.963198i	$-0.413375\pi$
$401$	4316.84	0.537587	0.268794	+	0.963198i	$0.413375\pi$
$402$	−30371.4	−3.76812
$403$	0	0
$404$	12604.6	1.55223
$405$	−5966.78	−0.732078
$406$	−7022.64	−0.858442
$407$	4010.93	0.488488
$408$	−6240.51	−0.757233
$409$	−5210.61	−0.629946	−0.314973	−	0.949101i	$-0.601995\pi$
$409$	−5210.61	−0.629946	−0.314973	+	0.949101i	$0.601995\pi$
$410$	4885.00	0.588422
$411$	−15870.7	−1.90473
$412$	32951.0	3.94024
$413$	8528.33	1.01611
$414$	−18520.0	−2.19857
$415$	6840.04	0.809071
$416$	0	0
$417$	−1272.78	−0.149469
$418$	2298.23	0.268924
$419$	15135.7	1.76474	0.882371	−	0.470555i	$-0.155946\pi$
$419$	15135.7	1.76474	0.882371	+	0.470555i	$0.155946\pi$
$420$	15701.3	1.82416
$421$	9138.85	1.05796	0.528979	−	0.848635i	$-0.322575\pi$
$421$	9138.85	1.05796	0.528979	+	0.848635i	$0.322575\pi$
$422$	−759.814	−0.0876473
$423$	−8752.67	−1.00607
$424$	22780.3	2.60922
$425$	921.767	0.105205
$426$	−18611.6	−2.11675
$427$	−9449.43	−1.07094
$428$	35818.7	4.04524
$429$	0	0
$430$	−21633.6	−2.42619
$431$	16132.4	1.80294	0.901471	−	0.432839i	$-0.142488\pi$
$431$	16132.4	1.80294	0.901471	+	0.432839i	$0.142488\pi$
$432$	−545.962	−0.0608046
$433$	−13220.2	−1.46726	−0.733631	−	0.679549i	$-0.762176\pi$
$433$	−13220.2	−1.46726	−0.733631	+	0.679549i	$0.762176\pi$
$434$	−1025.51	−0.113424
$435$	6045.60	0.666355
$436$	−29504.6	−3.24086
$437$	−5416.94	−0.592969
$438$	18578.1	2.02670
$439$	1977.15	0.214953	0.107476	−	0.994208i	$-0.465723\pi$
$439$	1977.15	0.214953	0.107476	+	0.994208i	$0.465723\pi$
$440$	−4608.80	−0.499354
$441$	−3916.65	−0.422919
$442$	0	0
$443$	−8193.35	−0.878731	−0.439366	−	0.898308i	$-0.644797\pi$
$443$	−8193.35	−0.878731	−0.439366	+	0.898308i	$0.644797\pi$
$444$	−48040.8	−5.13495
$445$	−5887.44	−0.627172
$446$	2624.41	0.278631
$447$	−14802.2	−1.56627
$448$	718.374	0.0757589
$449$	9442.32	0.992451	0.496225	−	0.868194i	$-0.334719\pi$
$449$	9442.32	0.992451	0.496225	+	0.868194i	$0.334719\pi$
$450$	7660.29	0.802466
$451$	−1259.40	−0.131491
$452$	3015.74	0.313824
$453$	−5953.51	−0.617484
$454$	−26490.2	−2.73843
$455$	0	0
$456$	−15169.0	−1.55779
$457$	−13134.0	−1.34439	−0.672193	−	0.740376i	$-0.734648\pi$
$457$	−13134.0	−1.34439	−0.672193	+	0.740376i	$0.734648\pi$
$458$	−4468.94	−0.455938
$459$	83.2117	0.00846186
$460$	19712.9	1.99808
$461$	7792.44	0.787267	0.393634	−	0.919267i	$-0.371218\pi$
$461$	7792.44	0.787267	0.393634	+	0.919267i	$0.371218\pi$
$462$	−5865.22	−0.590638
$463$	4945.75	0.496433	0.248216	−	0.968705i	$-0.420156\pi$
$463$	4945.75	0.496433	0.248216	+	0.968705i	$0.420156\pi$
$464$	−10807.6	−1.08132
$465$	882.837	0.0880442
$466$	−26986.2	−2.68264
$467$	2325.45	0.230427	0.115213	−	0.993341i	$-0.463245\pi$
$467$	2325.45	0.230427	0.115213	+	0.993341i	$0.463245\pi$
$468$	0	0
$469$	11473.4	1.12962
$470$	13498.9	1.32481
$471$	6420.23	0.628086
$472$	29983.4	2.92393
$473$	5577.32	0.542168
$474$	−24167.4	−2.34187
$475$	2240.57	0.216430
$476$	4278.08	0.411944
$477$	−12630.5	−1.21239
$478$	15241.8	1.45846
$479$	2177.89	0.207746	0.103873	−	0.994591i	$-0.466876\pi$
$479$	2177.89	0.207746	0.103873	+	0.994591i	$0.466876\pi$
$480$	10229.7	0.972749
$481$	0	0
$482$	−1845.17	−0.174367
$483$	13824.4	1.30234
$484$	2156.19	0.202497
$485$	−6803.95	−0.637014
$486$	−27371.3	−2.55471
$487$	8702.68	0.809766	0.404883	−	0.914368i	$-0.367312\pi$
$487$	8702.68	0.809766	0.404883	+	0.914368i	$0.367312\pi$
$488$	−33221.7	−3.08172
$489$	10260.2	0.948839
$490$	6040.51	0.556903
$491$	−9808.25	−0.901508	−0.450754	−	0.892648i	$-0.648845\pi$
$491$	−9808.25	−0.901508	−0.450754	+	0.892648i	$0.648845\pi$
$492$	15084.4	1.38223
$493$	1647.22	0.150481
$494$	0	0
$495$	2555.33	0.232028
$496$	−1578.23	−0.142872
$497$	7030.92	0.634567
$498$	30603.5	2.75377
$499$	−38.4379	−0.00344833	−0.00172417	−	0.999999i	$-0.500549\pi$
$499$	−38.4379	−0.00344833	−0.00172417	+	0.999999i	$0.500549\pi$
$500$	−26857.5	−2.40221
$501$	−2611.85	−0.232912
$502$	−13548.0	−1.20453
$503$	14505.4	1.28581	0.642907	−	0.765944i	$-0.277728\pi$
$503$	14505.4	1.28581	0.642907	+	0.765944i	$0.277728\pi$
$504$	19591.7	1.73151
$505$	5939.46	0.523371
$506$	−7363.73	−0.646952
$507$	0	0
$508$	10656.5	0.930723
$509$	−4567.56	−0.397748	−0.198874	−	0.980025i	$-0.563728\pi$
$509$	−4567.56	−0.397748	−0.198874	+	0.980025i	$0.563728\pi$
$510$	−5336.28	−0.463323
$511$	−7018.23	−0.607570
$512$	26015.4	2.24556
$513$	202.265	0.0174079
$514$	1637.93	0.140556
$515$	15527.0	1.32854
$516$	−66802.1	−5.69923
$517$	−3480.14	−0.296048
$518$	26295.9	2.23046
$519$	6314.62	0.534068
$520$	0	0
$521$	−15441.2	−1.29845	−0.649224	−	0.760597i	$-0.724906\pi$
$521$	−15441.2	−1.29845	−0.649224	+	0.760597i	$0.724906\pi$
$522$	13689.2	1.14781
$523$	−14503.6	−1.21262	−0.606308	−	0.795230i	$-0.707350\pi$
$523$	−14503.6	−1.21262	−0.606308	+	0.795230i	$0.707350\pi$
$524$	45917.4	3.82807
$525$	−5718.06	−0.475346
$526$	−15562.3	−1.29001
$527$	240.543	0.0198828
$528$	−9026.39	−0.743983
$529$	5189.37	0.426512
$530$	19479.5	1.59649
$531$	−16624.2	−1.35862
$532$	10398.9	0.847458
$533$	0	0
$534$	−26341.4	−2.13465
$535$	16878.3	1.36395
$536$	40337.4	3.25058
$537$	−15069.5	−1.21098
$538$	−19875.2	−1.59272
$539$	−1557.30	−0.124448
$540$	−736.067	−0.0586579
$541$	4920.22	0.391010	0.195505	−	0.980703i	$-0.437365\pi$
$541$	4920.22	0.391010	0.195505	+	0.980703i	$0.437365\pi$
$542$	19867.2	1.57448
$543$	−27681.0	−2.18767
$544$	2787.25	0.219673
$545$	−13903.0	−1.09273
$546$	0	0
$547$	9165.27	0.716415	0.358207	−	0.933642i	$-0.383388\pi$
$547$	9165.27	0.716415	0.358207	+	0.933642i	$0.383388\pi$
$548$	38250.8	2.98174
$549$	18419.7	1.43194
$550$	3045.80	0.236134
$551$	4003.96	0.309572
$552$	48602.8	3.74760
$553$	9129.71	0.702052
$554$	3809.05	0.292114
$555$	−22637.5	−1.73136
$556$	3067.61	0.233985
$557$	−11716.1	−0.891248	−0.445624	−	0.895220i	$-0.647018\pi$
$557$	−11716.1	−0.891248	−0.445624	+	0.895220i	$0.647018\pi$
$558$	1999.02	0.151658
$559$	0	0
$560$	−13226.5	−0.998072
$561$	1375.74	0.103536
$562$	−22762.6	−1.70851
$563$	−17926.4	−1.34194	−0.670968	−	0.741487i	$-0.734121\pi$
$563$	−17926.4	−1.34194	−0.670968	+	0.741487i	$0.734121\pi$
$564$	41683.3	3.11203
$565$	1421.06	0.105813
$566$	13666.5	1.01492
$567$	10085.1	0.746975
$568$	24718.9	1.82602
$569$	−17003.8	−1.25279	−0.626394	−	0.779507i	$-0.715470\pi$
$569$	−17003.8	−1.25279	−0.626394	+	0.779507i	$0.715470\pi$
$570$	−12971.1	−0.953154
$571$	17442.2	1.27834	0.639169	−	0.769066i	$-0.279278\pi$
$571$	17442.2	1.27834	0.639169	+	0.769066i	$0.279278\pi$
$572$	0	0
$573$	8537.56	0.622446
$574$	−8256.67	−0.600395
$575$	−7178.98	−0.520668
$576$	−1400.32	−0.101296
$577$	−3667.47	−0.264608	−0.132304	−	0.991209i	$-0.542237\pi$
$577$	−3667.47	−0.264608	−0.132304	+	0.991209i	$0.542237\pi$
$578$	23510.5	1.69188
$579$	31407.3	2.25430
$580$	−14570.9	−1.04314
$581$	−11561.1	−0.825534
$582$	−30442.1	−2.16815
$583$	−5022.00	−0.356758
$584$	−24674.3	−1.74834
$585$	0	0
$586$	−7956.09	−0.560859
$587$	16869.3	1.18615	0.593077	−	0.805146i	$-0.297913\pi$
$587$	16869.3	1.18615	0.593077	+	0.805146i	$0.297913\pi$
$588$	18652.5	1.30819
$589$	584.696	0.0409032
$590$	25638.9	1.78905
$591$	3921.26	0.272926
$592$	40468.6	2.80954
$593$	−19768.3	−1.36895	−0.684475	−	0.729036i	$-0.739969\pi$
$593$	−19768.3	−1.36895	−0.684475	+	0.729036i	$0.739969\pi$
$594$	274.957	0.0189927
$595$	2015.89	0.138896
$596$	35675.7	2.45190
$597$	19425.2	1.33169
$598$	0	0
$599$	6521.14	0.444819	0.222409	−	0.974953i	$-0.428608\pi$
$599$	6521.14	0.444819	0.222409	+	0.974953i	$0.428608\pi$
$600$	−20103.2	−1.36785
$601$	6399.99	0.434378	0.217189	−	0.976130i	$-0.430311\pi$
$601$	6399.99	0.434378	0.217189	+	0.976130i	$0.430311\pi$
$602$	36565.2	2.47556
$603$	−22365.0	−1.51040
$604$	14348.9	0.966636
$605$	1016.02	0.0682765
$606$	26574.2	1.78136
$607$	−9363.06	−0.626087	−0.313044	−	0.949739i	$-0.601349\pi$
$607$	−9363.06	−0.626087	−0.313044	+	0.949739i	$0.601349\pi$
$608$	6775.04	0.451915
$609$	−10218.3	−0.679914
$610$	−28408.0	−1.88559
$611$	0	0
$612$	−8339.21	−0.550805
$613$	−14967.1	−0.986160	−0.493080	−	0.869984i	$-0.664129\pi$
$613$	−14967.1	−0.986160	−0.493080	+	0.869984i	$0.664129\pi$
$614$	23292.3	1.53094
$615$	7107.95	0.466049
$616$	7789.83	0.509515
$617$	−14849.8	−0.968930	−0.484465	−	0.874811i	$-0.660986\pi$
$617$	−14849.8	−0.968930	−0.484465	+	0.874811i	$0.660986\pi$
$618$	69470.4	4.52186
$619$	−17698.2	−1.14919	−0.574597	−	0.818437i	$-0.694841\pi$
$619$	−17698.2	−1.14919	−0.574597	+	0.818437i	$0.694841\pi$
$620$	−2127.78	−0.137828
$621$	−648.077	−0.0418783
$622$	41864.7	2.69875
$623$	9951.01	0.639934
$624$	0	0
$625$	−5844.10	−0.374023
$626$	3905.63	0.249361
$627$	3344.05	0.212996
$628$	−15473.8	−0.983232
$629$	−6167.95	−0.390989
$630$	16752.9	1.05945
$631$	−8430.46	−0.531872	−0.265936	−	0.963991i	$-0.585681\pi$
$631$	−8430.46	−0.531872	−0.265936	+	0.963991i	$0.585681\pi$
$632$	32097.7	2.02022
$633$	−1105.57	−0.0694195
$634$	39432.2	2.47012
$635$	5021.50	0.313814
$636$	60150.8	3.75021
$637$	0	0
$638$	5442.94	0.337755
$639$	−13705.3	−0.848471
$640$	13228.4	0.817026
$641$	−19579.1	−1.20644	−0.603219	−	0.797575i	$-0.706116\pi$
$641$	−19579.1	−1.20644	−0.603219	+	0.797575i	$0.706116\pi$
$642$	75516.3	4.64235
$643$	−518.879	−0.0318236	−0.0159118	−	0.999873i	$-0.505065\pi$
$643$	−518.879	−0.0318236	−0.0159118	+	0.999873i	$0.505065\pi$
$644$	−33318.9	−2.03874
$645$	−31478.1	−1.92162
$646$	−3534.18	−0.215248
$647$	−16661.0	−1.01238	−0.506192	−	0.862421i	$-0.668947\pi$
$647$	−16661.0	−1.01238	−0.506192	+	0.862421i	$0.668947\pi$
$648$	35456.6	2.14949
$649$	−6609.93	−0.399788
$650$	0	0
$651$	−1492.18	−0.0898358
$652$	−24728.7	−1.48535
$653$	−6807.96	−0.407988	−0.203994	−	0.978972i	$-0.565392\pi$
$653$	−6807.96	−0.407988	−0.203994	+	0.978972i	$0.565392\pi$
$654$	−62204.3	−3.71923
$655$	21636.9	1.29072
$656$	−12706.8	−0.756274
$657$	13680.6	0.812375
$658$	−22816.0	−1.35176
$659$	−19175.5	−1.13349	−0.566746	−	0.823893i	$-0.691798\pi$
$659$	−19175.5	−1.13349	−0.566746	+	0.823893i	$0.691798\pi$
$660$	−12169.4	−0.717717
$661$	−14298.3	−0.841359	−0.420680	−	0.907209i	$-0.638208\pi$
$661$	−14298.3	−0.841359	−0.420680	+	0.907209i	$0.638208\pi$
$662$	−34760.3	−2.04078
$663$	0	0
$664$	−40645.8	−2.37555
$665$	4900.08	0.285740
$666$	−51258.4	−2.98231
$667$	−12829.0	−0.744741
$668$	6294.98	0.364611
$669$	3818.66	0.220685
$670$	34492.7	1.98891
$671$	7323.84	0.421362
$672$	−17290.3	−0.992542
$673$	−17468.7	−1.00055	−0.500274	−	0.865867i	$-0.666768\pi$
$673$	−17468.7	−1.00055	−0.500274	+	0.865867i	$0.666768\pi$
$674$	45323.7	2.59021
$675$	268.059	0.0152853
$676$	0	0
$677$	−6157.18	−0.349542	−0.174771	−	0.984609i	$-0.555918\pi$
$677$	−6157.18	−0.349542	−0.174771	+	0.984609i	$0.555918\pi$
$678$	6358.06	0.360147
$679$	11500.1	0.649976
$680$	7087.33	0.399686
$681$	−38544.7	−2.16892
$682$	794.830	0.0446270
$683$	2532.80	0.141896	0.0709479	−	0.997480i	$-0.477398\pi$
$683$	2532.80	0.141896	0.0709479	+	0.997480i	$0.477398\pi$
$684$	−20270.4	−1.13313
$685$	18024.3	1.00536
$686$	−34945.7	−1.94495
$687$	−6502.56	−0.361118
$688$	56272.8	3.11828
$689$	0	0
$690$	41560.5	2.29301
$691$	1721.58	0.0947787	0.0473894	−	0.998876i	$-0.484910\pi$
$691$	1721.58	0.0947787	0.0473894	+	0.998876i	$0.484910\pi$
$692$	−15219.2	−0.836053
$693$	−4319.05	−0.236749
$694$	5706.53	0.312128
$695$	1445.50	0.0788933
$696$	−35925.0	−1.95651
$697$	1936.68	0.105247
$698$	44137.9	2.39347
$699$	−39266.5	−2.12474
$700$	13781.4	0.744127
$701$	−4583.86	−0.246976	−0.123488	−	0.992346i	$-0.539408\pi$
$701$	−4583.86	−0.246976	−0.123488	+	0.992346i	$0.539408\pi$
$702$	0	0
$703$	−14992.6	−0.804349
$704$	−556.780	−0.0298074
$705$	19641.7	1.04929
$706$	−35783.0	−1.90752
$707$	−10038.9	−0.534021
$708$	79170.2	4.20254
$709$	−23542.7	−1.24706	−0.623528	−	0.781801i	$-0.714301\pi$
$709$	−23542.7	−1.24706	−0.623528	+	0.781801i	$0.714301\pi$
$710$	21137.2	1.11727
$711$	−17796.5	−0.938705
$712$	34985.1	1.84147
$713$	−1873.42	−0.0984012
$714$	9019.43	0.472750
$715$	0	0
$716$	36320.0	1.89573
$717$	22177.6	1.15515
$718$	−17840.5	−0.927301
$719$	−27921.8	−1.44827	−0.724135	−	0.689658i	$-0.757761\pi$
$719$	−27921.8	−1.44827	−0.724135	+	0.689658i	$0.757761\pi$
$720$	25782.2	1.33451
$721$	−26243.8	−1.35558
$722$	26262.1	1.35370
$723$	−2684.83	−0.138105
$724$	66715.6	3.42468
$725$	5306.38	0.271826
$726$	4545.87	0.232387
$727$	−13436.0	−0.685440	−0.342720	−	0.939438i	$-0.611348\pi$
$727$	−13436.0	−0.685440	−0.342720	+	0.939438i	$0.611348\pi$
$728$	0	0
$729$	−20640.8	−1.04866
$730$	−21099.1	−1.06974
$731$	−8576.71	−0.433955
$732$	−87721.0	−4.42932
$733$	31785.9	1.60169	0.800846	−	0.598871i	$-0.204384\pi$
$733$	31785.9	1.60169	0.800846	+	0.598871i	$0.204384\pi$
$734$	−46175.4	−2.32202
$735$	8789.29	0.441085
$736$	−21707.9	−1.08718
$737$	−8892.52	−0.444451
$738$	16094.6	0.802781
$739$	−37446.3	−1.86398	−0.931992	−	0.362480i	$-0.881930\pi$
$739$	−37446.3	−1.86398	−0.931992	+	0.362480i	$0.881930\pi$
$740$	54559.9	2.71035
$741$	0	0
$742$	−32924.5	−1.62897
$743$	−22478.5	−1.10990	−0.554949	−	0.831884i	$-0.687262\pi$
$743$	−22478.5	−1.10990	−0.554949	+	0.831884i	$0.687262\pi$
$744$	−5246.11	−0.258510
$745$	16810.9	0.826715
$746$	−5482.51	−0.269074
$747$	22535.9	1.10381
$748$	−3315.75	−0.162080
$749$	−28527.8	−1.39170
$750$	−56623.4	−2.75679
$751$	38290.4	1.86050	0.930250	−	0.366926i	$-0.119590\pi$
$751$	38290.4	1.86050	0.930250	+	0.366926i	$0.119590\pi$
$752$	−35113.2	−1.70272
$753$	−19713.1	−0.954031
$754$	0	0
$755$	6761.39	0.325923
$756$	1244.11	0.0598515
$757$	31162.8	1.49621	0.748105	−	0.663581i	$-0.230964\pi$
$757$	31162.8	1.49621	0.748105	+	0.663581i	$0.230964\pi$
$758$	−37253.4	−1.78510
$759$	−10714.7	−0.512407
$760$	17227.4	0.822241
$761$	−6940.98	−0.330631	−0.165316	−	0.986241i	$-0.552864\pi$
$761$	−6940.98	−0.330631	−0.165316	+	0.986241i	$0.552864\pi$
$762$	22467.1	1.06811
$763$	23498.9	1.11496
$764$	−20576.9	−0.974404
$765$	−3929.55	−0.185716
$766$	66675.8	3.14503
$767$	0	0
$768$	56192.1	2.64018
$769$	−29642.8	−1.39005	−0.695024	−	0.718987i	$-0.744606\pi$
$769$	−29642.8	−1.39005	−0.695024	+	0.718987i	$0.744606\pi$
$770$	6661.12	0.311753
$771$	2383.28	0.111325
$772$	−75696.5	−3.52898
$773$	−12259.8	−0.570447	−0.285224	−	0.958461i	$-0.592068\pi$
$773$	−12259.8	−0.570447	−0.285224	+	0.958461i	$0.592068\pi$
$774$	−71276.2	−3.31004
$775$	774.888	0.0359158
$776$	40431.4	1.87036
$777$	38262.1	1.76659
$778$	52801.1	2.43318
$779$	4707.54	0.216515
$780$	0	0
$781$	−5449.36	−0.249671
$782$	11323.8	0.517825
$783$	479.029	0.0218635
$784$	−15712.5	−0.715764
$785$	−7291.44	−0.331519
$786$	96807.2	4.39313
$787$	−29131.5	−1.31947	−0.659737	−	0.751497i	$-0.729332\pi$
$787$	−29131.5	−1.31947	−0.659737	+	0.751497i	$0.729332\pi$
$788$	−9450.86	−0.427250
$789$	−22644.0	−1.02173
$790$	27446.8	1.23609
$791$	−2401.88	−0.107966
$792$	−15184.6	−0.681266
$793$	0	0
$794$	9230.58	0.412571
$795$	28343.8	1.26447
$796$	−46817.9	−2.08469
$797$	−9788.43	−0.435036	−0.217518	−	0.976056i	$-0.569796\pi$
$797$	−9788.43	−0.435036	−0.217518	+	0.976056i	$0.569796\pi$
$798$	21923.8	0.972549
$799$	5351.71	0.236958
$800$	8978.85	0.396813
$801$	−19397.4	−0.855647
$802$	−21935.2	−0.965784
$803$	5439.53	0.239049
$804$	106510.	4.67203
$805$	−15700.3	−0.687407
$806$	0	0
$807$	−28919.6	−1.26149
$808$	−35294.3	−1.53669
$809$	33510.8	1.45634	0.728169	−	0.685398i	$-0.240372\pi$
$809$	33510.8	1.45634	0.728169	+	0.685398i	$0.240372\pi$
$810$	30319.1	1.31519
$811$	−25368.7	−1.09842	−0.549208	−	0.835686i	$-0.685070\pi$
$811$	−25368.7	−1.09842	−0.549208	+	0.835686i	$0.685070\pi$
$812$	24627.8	1.06437
$813$	28907.9	1.24704
$814$	−20380.8	−0.877576
$815$	−11652.5	−0.500821
$816$	13880.6	0.595489
$817$	−20847.7	−0.892739
$818$	26476.7	1.13171
$819$	0	0
$820$	−17131.3	−0.729574
$821$	6865.71	0.291857	0.145929	−	0.989295i	$-0.453383\pi$
$821$	6865.71	0.291857	0.145929	+	0.989295i	$0.453383\pi$
$822$	80643.9	3.42187
$823$	23632.8	1.00096	0.500478	−	0.865750i	$-0.333158\pi$
$823$	23632.8	1.00096	0.500478	+	0.865750i	$0.333158\pi$
$824$	−92266.4	−3.90079
$825$	4431.82	0.187026
$826$	−43335.1	−1.82545
$827$	16496.1	0.693621	0.346810	−	0.937935i	$-0.387265\pi$
$827$	16496.1	0.693621	0.346810	+	0.937935i	$0.387265\pi$
$828$	64948.2	2.72597
$829$	−14914.3	−0.624845	−0.312422	−	0.949943i	$-0.601140\pi$
$829$	−14914.3	−0.624845	−0.312422	+	0.949943i	$0.601140\pi$
$830$	−34756.4	−1.45351
$831$	5542.38	0.231364
$832$	0	0
$833$	2394.78	0.0996091
$834$	6467.41	0.268523
$835$	2966.28	0.122937
$836$	−8059.70	−0.333434
$837$	69.9523	0.00288878
$838$	−76909.2	−3.17038
$839$	−31648.1	−1.30228	−0.651140	−	0.758957i	$-0.725709\pi$
$839$	−31648.1	−1.30228	−0.651140	+	0.758957i	$0.725709\pi$
$840$	−43965.3	−1.80589
$841$	−14906.4	−0.611192
$842$	−46437.4	−1.90064
$843$	−33120.9	−1.35320
$844$	2664.60	0.108672
$845$	0	0
$846$	44475.1	1.80743
$847$	−1717.29	−0.0696658
$848$	−50669.8	−2.05190
$849$	19885.5	0.803850
$850$	−4683.79	−0.189003
$851$	48037.7	1.93503
$852$	65269.4	2.62452
$853$	−18058.9	−0.724883	−0.362442	−	0.932006i	$-0.618057\pi$
$853$	−18058.9	−0.724883	−0.362442	+	0.932006i	$0.618057\pi$
$854$	48015.5	1.92395
$855$	−9551.67	−0.382059
$856$	−100296.	−4.00474
$857$	−1170.83	−0.0466682	−0.0233341	−	0.999728i	$-0.507428\pi$
$857$	−1170.83	−0.0466682	−0.0233341	+	0.999728i	$0.507428\pi$
$858$	0	0
$859$	29295.1	1.16360	0.581802	−	0.813330i	$-0.302348\pi$
$859$	29295.1	1.16360	0.581802	+	0.813330i	$0.302348\pi$
$860$	75867.1	3.00819
$861$	−12013.9	−0.475533
$862$	−81973.6	−3.23901
$863$	40519.5	1.59826	0.799131	−	0.601156i	$-0.205293\pi$
$863$	40519.5	1.59826	0.799131	+	0.601156i	$0.205293\pi$
$864$	810.559	0.0319164
$865$	−7171.50	−0.281894
$866$	67176.2	2.63596
$867$	34209.2	1.34003
$868$	3596.39	0.140633
$869$	−7076.04	−0.276223
$870$	−30719.6	−1.19712
$871$	0	0
$872$	82616.0	3.20841
$873$	−22417.0	−0.869074
$874$	27525.2	1.06528
$875$	21390.6	0.826441
$876$	−65151.7	−2.51287
$877$	14885.6	0.573148	0.286574	−	0.958058i	$-0.407483\pi$
$877$	14885.6	0.573148	0.286574	+	0.958058i	$0.407483\pi$
$878$	−10046.5	−0.386166
$879$	−11576.6	−0.444218
$880$	10251.3	0.392693
$881$	−48555.5	−1.85684	−0.928421	−	0.371530i	$-0.878833\pi$
$881$	−48555.5	−1.85684	−0.928421	+	0.371530i	$0.878833\pi$
$882$	19901.7	0.759780
$883$	44627.8	1.70084	0.850422	−	0.526101i	$-0.176346\pi$
$883$	44627.8	1.70084	0.850422	+	0.526101i	$0.176346\pi$
$884$	0	0
$885$	37306.1	1.41698
$886$	41633.0	1.57865
$887$	393.094	0.0148803	0.00744015	−	0.999972i	$-0.497632\pi$
$887$	393.094	0.0148803	0.00744015	+	0.999972i	$0.497632\pi$
$888$	134519.	5.08353
$889$	−8487.39	−0.320200
$890$	29915.9	1.12672
$891$	−7816.53	−0.293898
$892$	−9203.58	−0.345469
$893$	13008.6	0.487475
$894$	75214.8	2.81382
$895$	17114.5	0.639188
$896$	−22358.7	−0.833651
$897$	0	0
$898$	−47979.4	−1.78295
$899$	1384.75	0.0513725
$900$	−26864.0	−0.994963
$901$	7722.74	0.285551
$902$	6399.38	0.236226
$903$	53204.5	1.96073
$904$	−8444.39	−0.310682
$905$	31437.3	1.15471
$906$	30251.6	1.10932
$907$	37844.4	1.38545	0.692725	−	0.721201i	$-0.256410\pi$
$907$	37844.4	1.38545	0.692725	+	0.721201i	$0.256410\pi$
$908$	92898.9	3.39533
$909$	19568.8	0.714033
$910$	0	0
$911$	−18091.5	−0.657957	−0.328978	−	0.944337i	$-0.606704\pi$
$911$	−18091.5	−0.657957	−0.328978	+	0.944337i	$0.606704\pi$
$912$	33740.1	1.22505
$913$	8960.50	0.324808
$914$	66738.2	2.41521
$915$	−41335.3	−1.49345
$916$	15672.2	0.565310
$917$	−36570.8	−1.31699
$918$	−422.825	−0.0152019
$919$	−6008.42	−0.215669	−0.107834	−	0.994169i	$-0.534392\pi$
$919$	−6008.42	−0.215669	−0.107834	+	0.994169i	$0.534392\pi$
$920$	−55198.1	−1.97807
$921$	33891.6	1.21256
$922$	−39595.8	−1.41434
$923$	0	0
$924$	20568.8	0.732321
$925$	−19869.5	−0.706275
$926$	−25130.9	−0.891849
$927$	51156.8	1.81252
$928$	16045.5	0.567584
$929$	47476.7	1.67671	0.838354	−	0.545127i	$-0.183519\pi$
$929$	47476.7	1.67671	0.838354	+	0.545127i	$0.183519\pi$
$930$	−4485.97	−0.158173
$931$	5821.08	0.204917
$932$	94638.4	3.32616
$933$	60915.6	2.13750
$934$	−11816.4	−0.413965
$935$	−1562.43	−0.0546490
$936$	0	0
$937$	−21379.3	−0.745390	−0.372695	−	0.927954i	$-0.621566\pi$
$937$	−21379.3	−0.745390	−0.372695	+	0.927954i	$0.621566\pi$
$938$	−58299.9	−2.02938
$939$	5682.91	0.197502
$940$	−47339.6	−1.64261
$941$	−348.879	−0.0120862	−0.00604312	−	0.999982i	$-0.501924\pi$
$941$	−348.879	−0.0120862	−0.00604312	+	0.999982i	$0.501924\pi$
$942$	−32623.2	−1.12837
$943$	−15083.4	−0.520872
$944$	−66691.4	−2.29939
$945$	586.240	0.0201803
$946$	−28340.1	−0.974013
$947$	−10328.3	−0.354408	−0.177204	−	0.984174i	$-0.556705\pi$
$947$	−10328.3	−0.354408	−0.177204	+	0.984174i	$0.556705\pi$
$948$	84753.0	2.90364
$949$	0	0
$950$	−11385.0	−0.388820
$951$	57376.1	1.95641
$952$	−11979.1	−0.407819
$953$	5551.10	0.188686	0.0943431	−	0.995540i	$-0.469925\pi$
$953$	5551.10	0.188686	0.0943431	+	0.995540i	$0.469925\pi$
$954$	64179.4	2.17808
$955$	−9696.09	−0.328543
$956$	−53451.6	−1.80832
$957$	7919.79	0.267513
$958$	−11066.5	−0.373219
$959$	−30464.8	−1.02582
$960$	3142.43	0.105647
$961$	−29588.8	−0.993212
$962$	0	0
$963$	55608.9	1.86082
$964$	6470.85	0.216195
$965$	−35669.2	−1.18988
$966$	−70245.9	−2.33967
$967$	37547.1	1.24864	0.624320	−	0.781169i	$-0.285376\pi$
$967$	37547.1	1.24864	0.624320	+	0.781169i	$0.285376\pi$
$968$	−6037.56	−0.200470
$969$	−5142.43	−0.170484
$970$	34573.0	1.14441
$971$	30583.4	1.01078	0.505390	−	0.862891i	$-0.331349\pi$
$971$	30583.4	1.01078	0.505390	+	0.862891i	$0.331349\pi$
$972$	95988.9	3.16754
$973$	−2443.19	−0.0804987
$974$	−44221.1	−1.45476
$975$	0	0
$976$	73894.4	2.42347
$977$	9018.83	0.295330	0.147665	−	0.989037i	$-0.452824\pi$
$977$	9018.83	0.295330	0.147665	+	0.989037i	$0.452824\pi$
$978$	−52135.3	−1.70460
$979$	−7712.59	−0.251783
$980$	−21183.6	−0.690494
$981$	−45806.2	−1.49080
$982$	49838.8	1.61957
$983$	−31169.0	−1.01133	−0.505665	−	0.862730i	$-0.668753\pi$
$983$	−31169.0	−1.01133	−0.505665	+	0.862730i	$0.668753\pi$
$984$	−42237.8	−1.36839
$985$	−4453.37	−0.144057
$986$	−8370.06	−0.270342
$987$	−33198.6	−1.07064
$988$	0	0
$989$	66797.8	2.14767
$990$	−12984.5	−0.416841
$991$	−55395.4	−1.77568	−0.887838	−	0.460157i	$-0.847793\pi$
$991$	−55395.4	−1.77568	−0.887838	+	0.460157i	$0.847793\pi$
$992$	2343.11	0.0749938
$993$	−50578.3	−1.61637
$994$	−35726.3	−1.14001
$995$	−22061.2	−0.702901
$996$	−107324.	−3.41435
$997$	−42485.7	−1.34958	−0.674792	−	0.738008i	$-0.735767\pi$
$997$	−42485.7	−1.34958	−0.674792	+	0.738008i	$0.735767\pi$
$998$	195.315	0.00619498
$999$	−1793.70	−0.0568070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.2		17
13.3	even	3		143.4.e.b.100.16	✓	34
13.9	even	3		143.4.e.b.133.16	yes	34
13.12	even	2		1859.4.a.h.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.16	✓	34	13.3	even	3
143.4.e.b.133.16	yes	34	13.9	even	3
1859.4.a.g.1.2		17	1.1	even	1	trivial
1859.4.a.h.1.16		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)

\(f(q)\)	\(=\)	\(q-5.08131 q^{2} -7.39360 q^{3} +17.8197 q^{4} +8.39690 q^{5} +37.5692 q^{6} -14.1925 q^{7} -49.8972 q^{8} +27.6653 q^{9} +O(q^{10})\)	\(q-5.08131 q^{2} -7.39360 q^{3} +17.8197 q^{4} +8.39690 q^{5} +37.5692 q^{6} -14.1925 q^{7} -49.8972 q^{8} +27.6653 q^{9} -42.6673 q^{10} +11.0000 q^{11} -131.752 q^{12} +72.1166 q^{14} -62.0833 q^{15} +110.985 q^{16} -16.9156 q^{17} -140.576 q^{18} -41.1173 q^{19} +149.631 q^{20} +104.934 q^{21} -55.8944 q^{22} +131.744 q^{23} +368.920 q^{24} -54.4921 q^{25} -4.91923 q^{27} -252.907 q^{28} -97.3789 q^{29} +315.465 q^{30} -14.2202 q^{31} -164.774 q^{32} -81.3296 q^{33} +85.9535 q^{34} -119.173 q^{35} +492.989 q^{36} +364.630 q^{37} +208.930 q^{38} -418.982 q^{40} -114.491 q^{41} -533.202 q^{42} +507.029 q^{43} +196.017 q^{44} +232.303 q^{45} -669.430 q^{46} -316.377 q^{47} -820.581 q^{48} -141.572 q^{49} +276.891 q^{50} +125.067 q^{51} -456.545 q^{53} +24.9961 q^{54} +92.3659 q^{55} +708.167 q^{56} +304.005 q^{57} +494.813 q^{58} -600.903 q^{59} -1106.31 q^{60} +665.804 q^{61} +72.2572 q^{62} -392.641 q^{63} -50.6164 q^{64} +413.261 q^{66} -808.411 q^{67} -301.432 q^{68} -974.059 q^{69} +605.556 q^{70} -495.396 q^{71} -1380.42 q^{72} +494.502 q^{73} -1852.80 q^{74} +402.893 q^{75} -732.700 q^{76} -156.118 q^{77} -643.276 q^{79} +931.932 q^{80} -710.593 q^{81} +581.762 q^{82} +814.591 q^{83} +1869.89 q^{84} -142.039 q^{85} -2576.37 q^{86} +719.980 q^{87} -548.869 q^{88} -701.144 q^{89} -1180.40 q^{90} +2347.64 q^{92} +105.138 q^{93} +1607.61 q^{94} -345.258 q^{95} +1218.27 q^{96} -810.294 q^{97} +719.374 q^{98} +304.319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 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

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