LMFDB - Embedded newform 1859.2.a.s.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,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, 2, names="a")

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-0.776244 q^{2} +3.01008 q^{3} -1.39745 q^{4} -0.0164567 q^{5} -2.33656 q^{6} -0.793722 q^{7} +2.63725 q^{8} +6.06060 q^{9} +O(q^{10})$	\(q-0.776244 q^{2} +3.01008 q^{3} -1.39745 q^{4} -0.0164567 q^{5} -2.33656 q^{6} -0.793722 q^{7} +2.63725 q^{8} +6.06060 q^{9} +0.0127744 q^{10} -1.00000 q^{11} -4.20643 q^{12} +0.616122 q^{14} -0.0495361 q^{15} +0.747743 q^{16} +3.12834 q^{17} -4.70450 q^{18} -1.22596 q^{19} +0.0229974 q^{20} -2.38917 q^{21} +0.776244 q^{22} +4.26925 q^{23} +7.93833 q^{24} -4.99973 q^{25} +9.21265 q^{27} +1.10918 q^{28} +8.01948 q^{29} +0.0384521 q^{30} -2.49364 q^{31} -5.85492 q^{32} -3.01008 q^{33} -2.42836 q^{34} +0.0130621 q^{35} -8.46935 q^{36} +8.88674 q^{37} +0.951641 q^{38} -0.0434004 q^{40} +8.43142 q^{41} +1.85458 q^{42} +11.8954 q^{43} +1.39745 q^{44} -0.0997375 q^{45} -3.31398 q^{46} -12.2753 q^{47} +2.25077 q^{48} -6.37001 q^{49} +3.88101 q^{50} +9.41657 q^{51} +4.56675 q^{53} -7.15126 q^{54} +0.0164567 q^{55} -2.09324 q^{56} -3.69023 q^{57} -6.22507 q^{58} -0.265214 q^{59} +0.0692239 q^{60} -4.49240 q^{61} +1.93567 q^{62} -4.81043 q^{63} +3.04936 q^{64} +2.33656 q^{66} -5.31411 q^{67} -4.37169 q^{68} +12.8508 q^{69} -0.0101393 q^{70} +13.1162 q^{71} +15.9833 q^{72} +11.5434 q^{73} -6.89828 q^{74} -15.0496 q^{75} +1.71321 q^{76} +0.793722 q^{77} -9.35606 q^{79} -0.0123054 q^{80} +9.54904 q^{81} -6.54484 q^{82} +4.81647 q^{83} +3.33873 q^{84} -0.0514822 q^{85} -9.23375 q^{86} +24.1393 q^{87} -2.63725 q^{88} +1.66164 q^{89} +0.0774207 q^{90} -5.96605 q^{92} -7.50605 q^{93} +9.52863 q^{94} +0.0201752 q^{95} -17.6238 q^{96} -8.35282 q^{97} +4.94468 q^{98} -6.06060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * 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 $

$2$	−0.776244	−0.548887	−0.274444	−	0.961603i	$-0.588494\pi$
$2$	−0.776244	−0.548887	−0.274444	+	0.961603i	$0.588494\pi$
$3$	3.01008	1.73787	0.868936	−	0.494925i	$-0.164804\pi$
$3$	3.01008	1.73787	0.868936	+	0.494925i	$0.164804\pi$
$4$	−1.39745	−0.698723
$5$	−0.0164567	−0.00735967	−0.00367983	−	0.999993i	$-0.501171\pi$
$5$	−0.0164567	−0.00735967	−0.00367983	+	0.999993i	$0.501171\pi$
$6$	−2.33656	−0.953896
$7$	−0.793722	−0.299999	−0.149999	−	0.988686i	$-0.547927\pi$
$7$	−0.793722	−0.299999	−0.149999	+	0.988686i	$0.547927\pi$
$8$	2.63725	0.932407
$9$	6.06060	2.02020
$10$	0.0127744	0.00403963
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.20643	−1.21429
$13$	0	0
$13$	0	0
$14$	0.616122	0.164665
$15$	−0.0495361	−0.0127902
$16$	0.747743	0.186936
$17$	3.12834	0.758734	0.379367	−	0.925246i	$-0.376142\pi$
$17$	3.12834	0.758734	0.379367	+	0.925246i	$0.376142\pi$
$18$	−4.70450	−1.10886
$19$	−1.22596	−0.281254	−0.140627	−	0.990063i	$-0.544912\pi$
$19$	−1.22596	−0.281254	−0.140627	+	0.990063i	$0.544912\pi$
$20$	0.0229974	0.00514237
$21$	−2.38917	−0.521359
$22$	0.776244	0.165496
$23$	4.26925	0.890201	0.445100	−	0.895481i	$-0.353168\pi$
$23$	4.26925	0.890201	0.445100	+	0.895481i	$0.353168\pi$
$24$	7.93833	1.62040
$25$	−4.99973	−0.999946
$26$	0	0
$27$	9.21265	1.77298
$28$	1.10918	0.209616
$29$	8.01948	1.48918	0.744590	−	0.667522i	$-0.232645\pi$
$29$	8.01948	1.48918	0.744590	+	0.667522i	$0.232645\pi$
$30$	0.0384521	0.00702036
$31$	−2.49364	−0.447870	−0.223935	−	0.974604i	$-0.571890\pi$
$31$	−2.49364	−0.447870	−0.223935	+	0.974604i	$0.571890\pi$
$32$	−5.85492	−1.03501
$33$	−3.01008	−0.523988
$34$	−2.42836	−0.416460
$35$	0.0130621	0.00220789
$36$	−8.46935	−1.41156
$37$	8.88674	1.46097	0.730486	−	0.682928i	$-0.239294\pi$
$37$	8.88674	1.46097	0.730486	+	0.682928i	$0.239294\pi$
$38$	0.951641	0.154377
$39$	0	0
$40$	−0.0434004	−0.00686221
$41$	8.43142	1.31677	0.658384	−	0.752683i	$-0.271240\pi$
$41$	8.43142	1.31677	0.658384	+	0.752683i	$0.271240\pi$
$42$	1.85458	0.286167
$43$	11.8954	1.81404	0.907018	−	0.421092i	$-0.138353\pi$
$43$	11.8954	1.81404	0.907018	+	0.421092i	$0.138353\pi$
$44$	1.39745	0.210673
$45$	−0.0997375	−0.0148680
$46$	−3.31398	−0.488620
$47$	−12.2753	−1.79054	−0.895268	−	0.445528i	$-0.853016\pi$
$47$	−12.2753	−1.79054	−0.895268	+	0.445528i	$0.853016\pi$
$48$	2.25077	0.324871
$49$	−6.37001	−0.910001
$50$	3.88101	0.548858
$51$	9.41657	1.31858
$52$	0	0
$53$	4.56675	0.627292	0.313646	−	0.949540i	$-0.398450\pi$
$53$	4.56675	0.627292	0.313646	+	0.949540i	$0.398450\pi$
$54$	−7.15126	−0.973164
$55$	0.0164567	0.00221902
$56$	−2.09324	−0.279721
$57$	−3.69023	−0.488783
$58$	−6.22507	−0.817392
$59$	−0.265214	−0.0345279	−0.0172639	−	0.999851i	$-0.505496\pi$
$59$	−0.265214	−0.0345279	−0.0172639	+	0.999851i	$0.505496\pi$
$60$	0.0692239	0.00893677
$61$	−4.49240	−0.575192	−0.287596	−	0.957752i	$-0.592856\pi$
$61$	−4.49240	−0.575192	−0.287596	+	0.957752i	$0.592856\pi$
$62$	1.93567	0.245830
$63$	−4.81043	−0.606057
$64$	3.04936	0.381170
$65$	0	0
$66$	2.33656	0.287610
$67$	−5.31411	−0.649221	−0.324611	−	0.945848i	$-0.605233\pi$
$67$	−5.31411	−0.649221	−0.324611	+	0.945848i	$0.605233\pi$
$68$	−4.37169	−0.530145
$69$	12.8508	1.54706
$70$	−0.0101393	−0.00121188
$71$	13.1162	1.55661	0.778304	−	0.627888i	$-0.216080\pi$
$71$	13.1162	1.55661	0.778304	+	0.627888i	$0.216080\pi$
$72$	15.9833	1.88365
$73$	11.5434	1.35106	0.675529	−	0.737333i	$-0.263915\pi$
$73$	11.5434	1.35106	0.675529	+	0.737333i	$0.263915\pi$
$74$	−6.89828	−0.801909
$75$	−15.0496	−1.73778
$76$	1.71321	0.196518
$77$	0.793722	0.0904530
$78$	0	0
$79$	−9.35606	−1.05264	−0.526320	−	0.850287i	$-0.676428\pi$
$79$	−9.35606	−1.05264	−0.526320	+	0.850287i	$0.676428\pi$
$80$	−0.0123054	−0.00137579
$81$	9.54904	1.06100
$82$	−6.54484	−0.722757
$83$	4.81647	0.528677	0.264338	−	0.964430i	$-0.414846\pi$
$83$	4.81647	0.528677	0.264338	+	0.964430i	$0.414846\pi$
$84$	3.33873	0.364285
$85$	−0.0514822	−0.00558403
$86$	−9.23375	−0.995701
$87$	24.1393	2.58800
$88$	−2.63725	−0.281131
$89$	1.66164	0.176134	0.0880668	−	0.996115i	$-0.471931\pi$
$89$	1.66164	0.176134	0.0880668	+	0.996115i	$0.471931\pi$
$90$	0.0774207	0.00816085
$91$	0	0
$92$	−5.96605	−0.622003
$93$	−7.50605	−0.778341
$94$	9.52863	0.982803
$95$	0.0201752	0.00206993
$96$	−17.6238	−1.79872
$97$	−8.35282	−0.848101	−0.424050	−	0.905639i	$-0.639392\pi$
$97$	−8.35282	−0.848101	−0.424050	+	0.905639i	$0.639392\pi$
$98$	4.94468	0.499488
$99$	−6.06060	−0.609113
$100$	6.98685	0.698685
$101$	5.67235	0.564420	0.282210	−	0.959353i	$-0.408933\pi$
$101$	5.67235	0.564420	0.282210	+	0.959353i	$0.408933\pi$
$102$	−7.30955	−0.723754
$103$	16.9225	1.66743	0.833714	−	0.552197i	$-0.186210\pi$
$103$	16.9225	1.66743	0.833714	+	0.552197i	$0.186210\pi$
$104$	0	0
$105$	0.0393178	0.00383703
$106$	−3.54491	−0.344312
$107$	4.36032	0.421528	0.210764	−	0.977537i	$-0.432405\pi$
$107$	4.36032	0.421528	0.210764	+	0.977537i	$0.432405\pi$
$108$	−12.8742	−1.23882
$109$	17.4935	1.67557	0.837787	−	0.545997i	$-0.183849\pi$
$109$	17.4935	1.67557	0.837787	+	0.545997i	$0.183849\pi$
$110$	−0.0127744	−0.00121799
$111$	26.7498	2.53898
$112$	−0.593500	−0.0560805
$113$	1.17709	0.110731	0.0553655	−	0.998466i	$-0.482368\pi$
$113$	1.17709	0.110731	0.0553655	+	0.998466i	$0.482368\pi$
$114$	2.86452	0.268287
$115$	−0.0702579	−0.00655158
$116$	−11.2068	−1.04052
$117$	0	0
$118$	0.205870	0.0189519
$119$	−2.48303	−0.227619
$120$	−0.130639	−0.0119256
$121$	1.00000	0.0909091
$122$	3.48720	0.315716
$123$	25.3793	2.28837
$124$	3.48472	0.312937
$125$	0.164563	0.0147189
$126$	3.73406	0.332657
$127$	−0.134766	−0.0119585	−0.00597926	−	0.999982i	$-0.501903\pi$
$127$	−0.134766	−0.0119585	−0.00597926	+	0.999982i	$0.501903\pi$
$128$	9.34280	0.825795
$129$	35.8062	3.15256
$130$	0	0
$131$	−21.2414	−1.85587	−0.927933	−	0.372746i	$-0.878416\pi$
$131$	−21.2414	−1.85587	−0.927933	+	0.372746i	$0.878416\pi$
$132$	4.20643	0.366122
$133$	0.973068	0.0843757
$134$	4.12504	0.356349
$135$	−0.151610	−0.0130485
$136$	8.25021	0.707450
$137$	−10.7421	−0.917763	−0.458882	−	0.888497i	$-0.651750\pi$
$137$	−10.7421	−0.917763	−0.458882	+	0.888497i	$0.651750\pi$
$138$	−9.97536	−0.849159
$139$	−13.7985	−1.17037	−0.585186	−	0.810899i	$-0.698979\pi$
$139$	−13.7985	−1.17037	−0.585186	+	0.810899i	$0.698979\pi$
$140$	−0.0182535	−0.00154270
$141$	−36.9497	−3.11172
$142$	−10.1814	−0.854402
$143$	0	0
$144$	4.53177	0.377648
$145$	−0.131974	−0.0109599
$146$	−8.96053	−0.741579
$147$	−19.1742	−1.58146
$148$	−12.4187	−1.02081
$149$	12.7827	1.04720	0.523600	−	0.851964i	$-0.324589\pi$
$149$	12.7827	1.04720	0.523600	+	0.851964i	$0.324589\pi$
$150$	11.6822	0.953844
$151$	−8.66190	−0.704895	−0.352448	−	0.935832i	$-0.614651\pi$
$151$	−8.66190	−0.704895	−0.352448	+	0.935832i	$0.614651\pi$
$152$	−3.23315	−0.262243
$153$	18.9596	1.53279
$154$	−0.616122	−0.0496485
$155$	0.0410371	0.00329618
$156$	0	0
$157$	−5.07034	−0.404657	−0.202328	−	0.979318i	$-0.564851\pi$
$157$	−5.07034	−0.404657	−0.202328	+	0.979318i	$0.564851\pi$
$158$	7.26259	0.577780
$159$	13.7463	1.09015
$160$	0.0963528	0.00761736
$161$	−3.38860	−0.267059
$162$	−7.41239	−0.582372
$163$	−18.7754	−1.47060	−0.735300	−	0.677741i	$-0.762959\pi$
$163$	−18.7754	−1.47060	−0.735300	+	0.677741i	$0.762959\pi$
$164$	−11.7825	−0.920055
$165$	0.0495361	0.00385638
$166$	−3.73876	−0.290184
$167$	15.4424	1.19497	0.597483	−	0.801882i	$-0.296168\pi$
$167$	15.4424	1.19497	0.597483	+	0.801882i	$0.296168\pi$
$168$	−6.30082	−0.486119
$169$	0	0
$170$	0.0399628	0.00306500
$171$	−7.43003	−0.568188
$172$	−16.6232	−1.26751
$173$	−7.64125	−0.580953	−0.290477	−	0.956882i	$-0.593814\pi$
$173$	−7.64125	−0.580953	−0.290477	+	0.956882i	$0.593814\pi$
$174$	−18.7380	−1.42052
$175$	3.96839	0.299982
$176$	−0.747743	−0.0563633
$177$	−0.798315	−0.0600050
$178$	−1.28984	−0.0966776
$179$	−21.6699	−1.61968	−0.809841	−	0.586649i	$-0.800447\pi$
$179$	−21.6699	−1.61968	−0.809841	+	0.586649i	$0.800447\pi$
$180$	0.139378	0.0103886
$181$	−11.9637	−0.889252	−0.444626	−	0.895716i	$-0.646663\pi$
$181$	−11.9637	−0.889252	−0.444626	+	0.895716i	$0.646663\pi$
$182$	0	0
$183$	−13.5225	−0.999611
$184$	11.2591	0.830030
$185$	−0.146247	−0.0107523
$186$	5.82653	0.427222
$187$	−3.12834	−0.228767
$188$	17.1541	1.25109
$189$	−7.31228	−0.531890
$190$	−0.0156609	−0.00113616
$191$	−11.5803	−0.837924	−0.418962	−	0.908004i	$-0.637606\pi$
$191$	−11.5803	−0.837924	−0.418962	+	0.908004i	$0.637606\pi$
$192$	9.17884	0.662425
$193$	23.4115	1.68519	0.842597	−	0.538545i	$-0.181026\pi$
$193$	23.4115	1.68519	0.842597	+	0.538545i	$0.181026\pi$
$194$	6.48383	0.465512
$195$	0	0
$196$	8.90173	0.635838
$197$	−6.57290	−0.468300	−0.234150	−	0.972200i	$-0.575231\pi$
$197$	−6.57290	−0.468300	−0.234150	+	0.972200i	$0.575231\pi$
$198$	4.70450	0.334334
$199$	19.8590	1.40777	0.703884	−	0.710315i	$-0.251448\pi$
$199$	19.8590	1.40777	0.703884	+	0.710315i	$0.251448\pi$
$200$	−13.1855	−0.932357
$201$	−15.9959	−1.12826
$202$	−4.40313	−0.309803
$203$	−6.36523	−0.446752
$204$	−13.1591	−0.921324
$205$	−0.138754	−0.00969097
$206$	−13.1360	−0.915230
$207$	25.8742	1.79838
$208$	0	0
$209$	1.22596	0.0848012
$210$	−0.0305202	−0.00210610
$211$	7.79372	0.536542	0.268271	−	0.963343i	$-0.413548\pi$
$211$	7.79372	0.536542	0.268271	+	0.963343i	$0.413548\pi$
$212$	−6.38179	−0.438303
$213$	39.4809	2.70518
$214$	−3.38467	−0.231372
$215$	−0.195760	−0.0133507
$216$	24.2960	1.65314
$217$	1.97925	0.134360
$218$	−13.5792	−0.919702
$219$	34.7467	2.34797
$220$	−0.0229974	−0.00155048
$221$	0	0
$222$	−20.7644	−1.39361
$223$	−4.38266	−0.293485	−0.146742	−	0.989175i	$-0.546879\pi$
$223$	−4.38266	−0.293485	−0.146742	+	0.989175i	$0.546879\pi$
$224$	4.64718	0.310503
$225$	−30.3013	−2.02009
$226$	−0.913707	−0.0607789
$227$	−21.0447	−1.39679	−0.698393	−	0.715714i	$-0.746101\pi$
$227$	−21.0447	−1.39679	−0.698393	+	0.715714i	$0.746101\pi$
$228$	5.15689	0.341524
$229$	12.8810	0.851197	0.425599	−	0.904912i	$-0.360064\pi$
$229$	12.8810	0.851197	0.425599	+	0.904912i	$0.360064\pi$
$230$	0.0545373	0.00359608
$231$	2.38917	0.157196
$232$	21.1493	1.38852
$233$	−13.8170	−0.905185	−0.452592	−	0.891717i	$-0.649501\pi$
$233$	−13.8170	−0.905185	−0.452592	+	0.891717i	$0.649501\pi$
$234$	0	0
$235$	0.202011	0.0131778
$236$	0.370621	0.0241254
$237$	−28.1625	−1.82935
$238$	1.92744	0.124937
$239$	−3.95240	−0.255659	−0.127830	−	0.991796i	$-0.540801\pi$
$239$	−3.95240	−0.255659	−0.127830	+	0.991796i	$0.540801\pi$
$240$	−0.0370403	−0.00239094
$241$	−5.51486	−0.355243	−0.177622	−	0.984099i	$-0.556840\pi$
$241$	−5.51486	−0.355243	−0.177622	+	0.984099i	$0.556840\pi$
$242$	−0.776244	−0.0498989
$243$	1.10546	0.0709152
$244$	6.27788	0.401900
$245$	0.104829	0.00669730
$246$	−19.7005	−1.25606
$247$	0	0
$248$	−6.57633	−0.417598
$249$	14.4980	0.918772
$250$	−0.127741	−0.00807904
$251$	−6.96137	−0.439398	−0.219699	−	0.975568i	$-0.570508\pi$
$251$	−6.96137	−0.439398	−0.219699	+	0.975568i	$0.570508\pi$
$252$	6.72231	0.423466
$253$	−4.26925	−0.268406
$254$	0.104611	0.00656388
$255$	−0.154966	−0.00970433
$256$	−13.3510	−0.834439
$257$	13.5802	0.847108	0.423554	−	0.905871i	$-0.360782\pi$
$257$	13.5802	0.847108	0.423554	+	0.905871i	$0.360782\pi$
$258$	−27.7944	−1.73040
$259$	−7.05360	−0.438289
$260$	0	0
$261$	48.6028	3.00844
$262$	16.4885	1.01866
$263$	−10.5992	−0.653575	−0.326788	−	0.945098i	$-0.605966\pi$
$263$	−10.5992	−0.653575	−0.326788	+	0.945098i	$0.605966\pi$
$264$	−7.93833	−0.488570
$265$	−0.0751537	−0.00461666
$266$	−0.755338	−0.0463128
$267$	5.00168	0.306098
$268$	7.42617	0.453626
$269$	0.00954813	0.000582160 0	0.000291080	−	1.00000i	$-0.499907\pi$
$269$	0.00954813	0.000582160 0	0.000291080		1.00000i	$0.499907\pi$
$270$	0.117686	0.00716216
$271$	3.75212	0.227925	0.113963	−	0.993485i	$-0.463646\pi$
$271$	3.75212	0.227925	0.113963	+	0.993485i	$0.463646\pi$
$272$	2.33920	0.141835
$273$	0	0
$274$	8.33852	0.503749
$275$	4.99973	0.301495
$276$	−17.9583	−1.08096
$277$	13.1876	0.792368	0.396184	−	0.918171i	$-0.370334\pi$
$277$	13.1876	0.792368	0.396184	+	0.918171i	$0.370334\pi$
$278$	10.7110	0.642403
$279$	−15.1129	−0.904787
$280$	0.0344478	0.00205865
$281$	24.7282	1.47516	0.737579	−	0.675261i	$-0.235969\pi$
$281$	24.7282	1.47516	0.737579	+	0.675261i	$0.235969\pi$
$282$	28.6820	1.70799
$283$	−23.1300	−1.37493	−0.687467	−	0.726216i	$-0.741277\pi$
$283$	−23.1300	−1.37493	−0.687467	+	0.726216i	$0.741277\pi$
$284$	−18.3292	−1.08764
$285$	0.0607291	0.00359728
$286$	0	0
$287$	−6.69220	−0.395028
$288$	−35.4843	−2.09093
$289$	−7.21348	−0.424322
$290$	0.102444	0.00601573
$291$	−25.1427	−1.47389
$292$	−16.1313	−0.944015
$293$	−10.9621	−0.640411	−0.320206	−	0.947348i	$-0.603752\pi$
$293$	−10.9621	−0.640411	−0.320206	+	0.947348i	$0.603752\pi$
$294$	14.8839	0.868046
$295$	0.00436454	0.000254114 0
$296$	23.4365	1.36222
$297$	−9.21265	−0.534572
$298$	−9.92249	−0.574795
$299$	0	0
$300$	21.0310	1.21422
$301$	−9.44166	−0.544208
$302$	6.72375	0.386908
$303$	17.0742	0.980889
$304$	−0.916701	−0.0525764
$305$	0.0739301	0.00423322
$306$	−14.7173	−0.841331
$307$	19.6256	1.12009	0.560046	−	0.828462i	$-0.310784\pi$
$307$	19.6256	1.12009	0.560046	+	0.828462i	$0.310784\pi$
$308$	−1.10918	−0.0632015
$309$	50.9382	2.89777
$310$	−0.0318548	−0.00180923
$311$	14.9752	0.849167	0.424583	−	0.905389i	$-0.360421\pi$
$311$	14.9752	0.849167	0.424583	+	0.905389i	$0.360421\pi$
$312$	0	0
$313$	11.5917	0.655201	0.327600	−	0.944816i	$-0.393760\pi$
$313$	11.5917	0.655201	0.327600	+	0.944816i	$0.393760\pi$
$314$	3.93582	0.222111
$315$	0.0791638	0.00446038
$316$	13.0746	0.735503
$317$	−5.55127	−0.311791	−0.155895	−	0.987774i	$-0.549826\pi$
$317$	−5.55127	−0.311791	−0.155895	+	0.987774i	$0.549826\pi$
$318$	−10.6705	−0.598371
$319$	−8.01948	−0.449004
$320$	−0.0501825	−0.00280529
$321$	13.1249	0.732562
$322$	2.63038	0.146585
$323$	−3.83521	−0.213397
$324$	−13.3443	−0.741348
$325$	0	0
$326$	14.5743	0.807194
$327$	52.6569	2.91193
$328$	22.2357	1.22776
$329$	9.74317	0.537158
$330$	−0.0384521	−0.00211672
$331$	−7.04341	−0.387141	−0.193570	−	0.981086i	$-0.562007\pi$
$331$	−7.04341	−0.387141	−0.193570	+	0.981086i	$0.562007\pi$
$332$	−6.73076	−0.369398
$333$	53.8590	2.95145
$334$	−11.9870	−0.655901
$335$	0.0874527	0.00477805
$336$	−1.78648	−0.0974607
$337$	−16.3751	−0.892009	−0.446004	−	0.895031i	$-0.647153\pi$
$337$	−16.3751	−0.892009	−0.446004	+	0.895031i	$0.647153\pi$
$338$	0	0
$339$	3.54313	0.192436
$340$	0.0719436	0.00390169
$341$	2.49364	0.135038
$342$	5.76751	0.311871
$343$	10.6121	0.572997
$344$	31.3712	1.69142
$345$	−0.211482	−0.0113858
$346$	5.93147	0.318878
$347$	11.2716	0.605091	0.302545	−	0.953135i	$-0.402164\pi$
$347$	11.2716	0.605091	0.302545	+	0.953135i	$0.402164\pi$
$348$	−33.7333	−1.80830
$349$	−22.7506	−1.21781	−0.608907	−	0.793242i	$-0.708392\pi$
$349$	−22.7506	−1.21781	−0.608907	+	0.793242i	$0.708392\pi$
$350$	−3.08044	−0.164657
$351$	0	0
$352$	5.85492	0.312069
$353$	−3.24835	−0.172892	−0.0864462	−	0.996257i	$-0.527551\pi$
$353$	−3.24835	−0.172892	−0.0864462	+	0.996257i	$0.527551\pi$
$354$	0.619687	0.0329360
$355$	−0.215850	−0.0114561
$356$	−2.32205	−0.123069
$357$	−7.47413	−0.395573
$358$	16.8211	0.889023
$359$	−31.4679	−1.66081	−0.830405	−	0.557160i	$-0.811891\pi$
$359$	−31.4679	−1.66081	−0.830405	+	0.557160i	$0.811891\pi$
$360$	−0.263032	−0.0138630
$361$	−17.4970	−0.920896
$362$	9.28672	0.488099
$363$	3.01008	0.157988
$364$	0	0
$365$	−0.189967	−0.00994334
$366$	10.4967	0.548674
$367$	23.1155	1.20662	0.603310	−	0.797507i	$-0.293848\pi$
$367$	23.1155	1.20662	0.603310	+	0.797507i	$0.293848\pi$
$368$	3.19231	0.166410
$369$	51.0995	2.66013
$370$	0.113523	0.00590178
$371$	−3.62473	−0.188187
$372$	10.4893	0.543845
$373$	−7.74228	−0.400880	−0.200440	−	0.979706i	$-0.564237\pi$
$373$	−7.74228	−0.400880	−0.200440	+	0.979706i	$0.564237\pi$
$374$	2.42836	0.125567
$375$	0.495347	0.0255796
$376$	−32.3730	−1.66951
$377$	0	0
$378$	5.67611	0.291948
$379$	10.4868	0.538670	0.269335	−	0.963047i	$-0.413196\pi$
$379$	10.4868	0.538670	0.269335	+	0.963047i	$0.413196\pi$
$380$	−0.0281938	−0.00144631
$381$	−0.405656	−0.0207824
$382$	8.98917	0.459926
$383$	−9.84176	−0.502891	−0.251445	−	0.967872i	$-0.580906\pi$
$383$	−9.84176	−0.502891	−0.251445	+	0.967872i	$0.580906\pi$
$384$	28.1226	1.43513
$385$	−0.0130621	−0.000665704 0
$386$	−18.1730	−0.924981
$387$	72.0934	3.66471
$388$	11.6726	0.592587
$389$	−24.0364	−1.21869	−0.609347	−	0.792904i	$-0.708568\pi$
$389$	−24.0364	−1.21869	−0.609347	+	0.792904i	$0.708568\pi$
$390$	0	0
$391$	13.3557	0.675426
$392$	−16.7993	−0.848492
$393$	−63.9383	−3.22526
$394$	5.10218	0.257044
$395$	0.153970	0.00774707
$396$	8.46935	0.425601
$397$	−10.7120	−0.537619	−0.268809	−	0.963193i	$-0.586630\pi$
$397$	−10.7120	−0.537619	−0.268809	+	0.963193i	$0.586630\pi$
$398$	−15.4154	−0.772706
$399$	2.92901	0.146634
$400$	−3.73851	−0.186926
$401$	−10.8191	−0.540281	−0.270140	−	0.962821i	$-0.587070\pi$
$401$	−10.8191	−0.540281	−0.270140	+	0.962821i	$0.587070\pi$
$402$	12.4167	0.619290
$403$	0	0
$404$	−7.92679	−0.394373
$405$	−0.157146	−0.00780864
$406$	4.94097	0.245216
$407$	−8.88674	−0.440499
$408$	24.8338	1.22946
$409$	−29.7938	−1.47321	−0.736604	−	0.676324i	$-0.763572\pi$
$409$	−29.7938	−1.47321	−0.736604	+	0.676324i	$0.763572\pi$
$410$	0.107707	0.00531925
$411$	−32.3347	−1.59495
$412$	−23.6483	−1.16507
$413$	0.210506	0.0103583
$414$	−20.0847	−0.987110
$415$	−0.0792634	−0.00389088
$416$	0	0
$417$	−41.5346	−2.03396
$418$	−0.951641	−0.0465463
$419$	0.335538	0.0163921	0.00819605	−	0.999966i	$-0.497391\pi$
$419$	0.335538	0.0163921	0.00819605	+	0.999966i	$0.497391\pi$
$420$	−0.0549445	−0.00268102
$421$	−34.9448	−1.70311	−0.851554	−	0.524267i	$-0.824339\pi$
$421$	−34.9448	−1.70311	−0.851554	+	0.524267i	$0.824339\pi$
$422$	−6.04983	−0.294501
$423$	−74.3956	−3.61724
$424$	12.0437	0.584891
$425$	−15.6409	−0.758693
$426$	−30.6468	−1.48484
$427$	3.56571	0.172557
$428$	−6.09331	−0.294531
$429$	0	0
$430$	0.151957	0.00732803
$431$	−15.8744	−0.764641	−0.382320	−	0.924030i	$-0.624875\pi$
$431$	−15.8744	−0.764641	−0.382320	+	0.924030i	$0.624875\pi$
$432$	6.88870	0.331433
$433$	−9.59664	−0.461185	−0.230593	−	0.973050i	$-0.574066\pi$
$433$	−9.59664	−0.461185	−0.230593	+	0.973050i	$0.574066\pi$
$434$	−1.53638	−0.0737488
$435$	−0.397253	−0.0190468
$436$	−24.4462	−1.17076
$437$	−5.23392	−0.250372
$438$	−26.9719	−1.28877
$439$	7.77923	0.371283	0.185641	−	0.982618i	$-0.440564\pi$
$439$	7.77923	0.371283	0.185641	+	0.982618i	$0.440564\pi$
$440$	0.0434004	0.00206903
$441$	−38.6060	−1.83838
$442$	0	0
$443$	−23.0476	−1.09503	−0.547513	−	0.836797i	$-0.684425\pi$
$443$	−23.0476	−1.09503	−0.547513	+	0.836797i	$0.684425\pi$
$444$	−37.3814	−1.77404
$445$	−0.0273452	−0.00129629
$446$	3.40201	0.161090
$447$	38.4770	1.81990
$448$	−2.42035	−0.114351
$449$	−29.1978	−1.37793	−0.688964	−	0.724796i	$-0.741934\pi$
$449$	−29.1978	−1.37793	−0.688964	+	0.724796i	$0.741934\pi$
$450$	23.5212	1.10880
$451$	−8.43142	−0.397020
$452$	−1.64491	−0.0773703
$453$	−26.0730	−1.22502
$454$	16.3358	0.766679
$455$	0	0
$456$	−9.73204	−0.455745
$457$	31.1916	1.45908	0.729541	−	0.683937i	$-0.239734\pi$
$457$	31.1916	1.45908	0.729541	+	0.683937i	$0.239734\pi$
$458$	−9.99876	−0.467211
$459$	28.8203	1.34522
$460$	0.0981816	0.00457774
$461$	37.6692	1.75443	0.877215	−	0.480097i	$-0.159399\pi$
$461$	37.6692	1.75443	0.877215	+	0.480097i	$0.159399\pi$
$462$	−1.85458	−0.0862827
$463$	0.988906	0.0459584	0.0229792	−	0.999736i	$-0.492685\pi$
$463$	0.988906	0.0459584	0.0229792	+	0.999736i	$0.492685\pi$
$464$	5.99651	0.278381
$465$	0.123525	0.00572833
$466$	10.7254	0.496845
$467$	11.5156	0.532878	0.266439	−	0.963852i	$-0.414153\pi$
$467$	11.5156	0.532878	0.266439	+	0.963852i	$0.414153\pi$
$468$	0	0
$469$	4.21792	0.194765
$470$	−0.156810	−0.00723310
$471$	−15.2621	−0.703242
$472$	−0.699434	−0.0321940
$473$	−11.8954	−0.546952
$474$	21.8610	1.00411
$475$	6.12945	0.281238
$476$	3.46990	0.159043
$477$	27.6772	1.26725
$478$	3.06803	0.140328
$479$	9.11697	0.416565	0.208283	−	0.978069i	$-0.433213\pi$
$479$	9.11697	0.416565	0.208283	+	0.978069i	$0.433213\pi$
$480$	0.290030	0.0132380
$481$	0	0
$482$	4.28088	0.194989
$483$	−10.2000	−0.464114
$484$	−1.39745	−0.0635202
$485$	0.137460	0.00624174
$486$	−0.858106	−0.0389245
$487$	−18.6189	−0.843704	−0.421852	−	0.906665i	$-0.638620\pi$
$487$	−18.6189	−0.843704	−0.421852	+	0.906665i	$0.638620\pi$
$488$	−11.8476	−0.536314
$489$	−56.5154	−2.55572
$490$	−0.0813732	−0.00367607
$491$	−25.0177	−1.12903	−0.564517	−	0.825421i	$-0.690938\pi$
$491$	−25.0177	−1.12903	−0.564517	+	0.825421i	$0.690938\pi$
$492$	−35.4662	−1.59894
$493$	25.0877	1.12989
$494$	0	0
$495$	0.0997375	0.00448287
$496$	−1.86460	−0.0837230
$497$	−10.4106	−0.466980
$498$	−11.2540	−0.504303
$499$	−6.05960	−0.271265	−0.135632	−	0.990759i	$-0.543307\pi$
$499$	−6.05960	−0.271265	−0.135632	+	0.990759i	$0.543307\pi$
$500$	−0.229967	−0.0102845
$501$	46.4828	2.07670
$502$	5.40372	0.241180
$503$	11.7680	0.524707	0.262354	−	0.964972i	$-0.415501\pi$
$503$	11.7680	0.524707	0.262354	+	0.964972i	$0.415501\pi$
$504$	−12.6863	−0.565092
$505$	−0.0933482	−0.00415394
$506$	3.31398	0.147324
$507$	0	0
$508$	0.188328	0.00835568
$509$	2.42538	0.107503	0.0537515	−	0.998554i	$-0.482882\pi$
$509$	2.42538	0.107503	0.0537515	+	0.998554i	$0.482882\pi$
$510$	0.120291	0.00532659
$511$	−9.16228	−0.405316
$512$	−8.32195	−0.367782
$513$	−11.2943	−0.498656
$514$	−10.5415	−0.464967
$515$	−0.278489	−0.0122717
$516$	−50.0372	−2.20277
$517$	12.2753	0.539867
$518$	5.47531	0.240571
$519$	−23.0008	−1.00962
$520$	0	0
$521$	−25.3612	−1.11109	−0.555547	−	0.831485i	$-0.687491\pi$
$521$	−25.3612	−1.11109	−0.555547	+	0.831485i	$0.687491\pi$
$522$	−37.7276	−1.65129
$523$	8.65849	0.378609	0.189305	−	0.981918i	$-0.439377\pi$
$523$	8.65849	0.378609	0.189305	+	0.981918i	$0.439377\pi$
$524$	29.6836	1.29674
$525$	11.9452	0.521331
$526$	8.22757	0.358739
$527$	−7.80095	−0.339815
$528$	−2.25077	−0.0979522
$529$	−4.77347	−0.207542
$530$	0.0583376	0.00253403
$531$	−1.60735	−0.0697531
$532$	−1.35981	−0.0589552
$533$	0	0
$534$	−3.88252	−0.168013
$535$	−0.0717566	−0.00310231
$536$	−14.0146	−0.605339
$537$	−65.2281	−2.81480
$538$	−0.00741168	−0.000319540 0
$539$	6.37001	0.274376
$540$	0.211867	0.00911729
$541$	−29.9184	−1.28629	−0.643146	−	0.765744i	$-0.722371\pi$
$541$	−29.9184	−1.28629	−0.643146	+	0.765744i	$0.722371\pi$
$542$	−2.91256	−0.125105
$543$	−36.0116	−1.54541
$544$	−18.3162	−0.785301
$545$	−0.287886	−0.0123317
$546$	0	0
$547$	34.8749	1.49114	0.745572	−	0.666425i	$-0.232176\pi$
$547$	34.8749	1.49114	0.745572	+	0.666425i	$0.232176\pi$
$548$	15.0116	0.641262
$549$	−27.2266	−1.16200
$550$	−3.88101	−0.165487
$551$	−9.83153	−0.418837
$552$	33.8907	1.44249
$553$	7.42611	0.315790
$554$	−10.2368	−0.434921
$555$	−0.440214	−0.0186861
$556$	19.2826	0.817766
$557$	−29.4325	−1.24710	−0.623548	−	0.781785i	$-0.714309\pi$
$557$	−29.4325	−1.24710	−0.623548	+	0.781785i	$0.714309\pi$
$558$	11.7313	0.496626
$559$	0	0
$560$	0.00976706	0.000412734 0
$561$	−9.41657	−0.397568
$562$	−19.1951	−0.809696
$563$	−31.9030	−1.34455	−0.672276	−	0.740301i	$-0.734683\pi$
$563$	−31.9030	−1.34455	−0.672276	+	0.740301i	$0.734683\pi$
$564$	51.6351	2.17423
$565$	−0.0193710	−0.000814943 0
$566$	17.9545	0.754684
$567$	−7.57928	−0.318300
$568$	34.5907	1.45139
$569$	1.00569	0.0421605	0.0210803	−	0.999778i	$-0.493289\pi$
$569$	1.00569	0.0421605	0.0210803	+	0.999778i	$0.493289\pi$
$570$	−0.0471406	−0.00197450
$571$	−24.9551	−1.04434	−0.522170	−	0.852841i	$-0.674877\pi$
$571$	−24.9551	−1.04434	−0.522170	+	0.852841i	$0.674877\pi$
$572$	0	0
$573$	−34.8578	−1.45620
$574$	5.19478	0.216826
$575$	−21.3451	−0.890153
$576$	18.4810	0.770040
$577$	37.2141	1.54924	0.774621	−	0.632426i	$-0.217941\pi$
$577$	37.2141	1.54924	0.774621	+	0.632426i	$0.217941\pi$
$578$	5.59942	0.232905
$579$	70.4704	2.92865
$580$	0.184427	0.00765791
$581$	−3.82294	−0.158602
$582$	19.5169	0.809000
$583$	−4.56675	−0.189136
$584$	30.4429	1.25974
$585$	0	0
$586$	8.50924	0.351514
$587$	2.81457	0.116170	0.0580849	−	0.998312i	$-0.481501\pi$
$587$	2.81457	0.116170	0.0580849	+	0.998312i	$0.481501\pi$
$588$	26.7950	1.10501
$589$	3.05709	0.125965
$590$	−0.00338795	−0.000139480 0
$591$	−19.7850	−0.813845
$592$	6.64500	0.273108
$593$	12.7265	0.522614	0.261307	−	0.965256i	$-0.415846\pi$
$593$	12.7265	0.522614	0.261307	+	0.965256i	$0.415846\pi$
$594$	7.15126	0.293420
$595$	0.0408626	0.00167520
$596$	−17.8631	−0.731702
$597$	59.7772	2.44652
$598$	0	0
$599$	−30.9274	−1.26366	−0.631830	−	0.775107i	$-0.717696\pi$
$599$	−30.9274	−1.26366	−0.631830	+	0.775107i	$0.717696\pi$
$600$	−39.6895	−1.62032
$601$	−9.40485	−0.383632	−0.191816	−	0.981431i	$-0.561438\pi$
$601$	−9.40485	−0.383632	−0.191816	+	0.981431i	$0.561438\pi$
$602$	7.32903	0.298709
$603$	−32.2067	−1.31156
$604$	12.1045	0.492526
$605$	−0.0164567	−0.000669061 0
$606$	−13.2538	−0.538398
$607$	37.6487	1.52811	0.764056	−	0.645150i	$-0.223205\pi$
$607$	37.6487	1.52811	0.764056	+	0.645150i	$0.223205\pi$
$608$	7.17788	0.291102
$609$	−19.1599	−0.776397
$610$	−0.0573878	−0.00232356
$611$	0	0
$612$	−26.4950	−1.07100
$613$	8.20597	0.331436	0.165718	−	0.986173i	$-0.447006\pi$
$613$	8.20597	0.331436	0.165718	+	0.986173i	$0.447006\pi$
$614$	−15.2342	−0.614804
$615$	−0.417660	−0.0168417
$616$	2.09324	0.0843390
$617$	−19.7324	−0.794396	−0.397198	−	0.917733i	$-0.630017\pi$
$617$	−19.7324	−0.794396	−0.397198	+	0.917733i	$0.630017\pi$
$618$	−39.5405	−1.59055
$619$	36.5226	1.46797	0.733983	−	0.679168i	$-0.237659\pi$
$619$	36.5226	1.46797	0.733983	+	0.679168i	$0.237659\pi$
$620$	−0.0573470	−0.00230311
$621$	39.3311	1.57830
$622$	−11.6244	−0.466097
$623$	−1.31888	−0.0528399
$624$	0	0
$625$	24.9959	0.999838
$626$	−8.99798	−0.359631
$627$	3.69023	0.147374
$628$	7.08552	0.282743
$629$	27.8008	1.10849
$630$	−0.0614504	−0.00244824
$631$	5.64926	0.224894	0.112447	−	0.993658i	$-0.464131\pi$
$631$	5.64926	0.224894	0.112447	+	0.993658i	$0.464131\pi$
$632$	−24.6742	−0.981489
$633$	23.4597	0.932441
$634$	4.30914	0.171138
$635$	0.00221780	8.80107e−5 0
$636$	−19.2097	−0.761714
$637$	0	0
$638$	6.22507	0.246453
$639$	79.4921	3.14466
$640$	−0.153752	−0.00607757
$641$	−22.5700	−0.891461	−0.445730	−	0.895167i	$-0.647056\pi$
$641$	−22.5700	−0.891461	−0.445730	+	0.895167i	$0.647056\pi$
$642$	−10.1881	−0.402094
$643$	27.0779	1.06785	0.533924	−	0.845532i	$-0.320717\pi$
$643$	27.0779	1.06785	0.533924	+	0.845532i	$0.320717\pi$
$644$	4.73538	0.186600
$645$	−0.589253	−0.0232018
$646$	2.97706	0.117131
$647$	1.96650	0.0773110	0.0386555	−	0.999253i	$-0.487693\pi$
$647$	1.96650	0.0773110	0.0386555	+	0.999253i	$0.487693\pi$
$648$	25.1832	0.989289
$649$	0.265214	0.0104105
$650$	0	0
$651$	5.95771	0.233501
$652$	26.2376	1.02754
$653$	−7.55567	−0.295676	−0.147838	−	0.989012i	$-0.547231\pi$
$653$	−7.55567	−0.295676	−0.147838	+	0.989012i	$0.547231\pi$
$654$	−40.8746	−1.59832
$655$	0.349563	0.0136586
$656$	6.30454	0.246151
$657$	69.9602	2.72941
$658$	−7.56308	−0.294839
$659$	12.1726	0.474178	0.237089	−	0.971488i	$-0.423807\pi$
$659$	12.1726	0.474178	0.237089	+	0.971488i	$0.423807\pi$
$660$	−0.0692239	−0.00269454
$661$	12.8925	0.501459	0.250729	−	0.968057i	$-0.419330\pi$
$661$	12.8925	0.501459	0.250729	+	0.968057i	$0.419330\pi$
$662$	5.46740	0.212497
$663$	0	0
$664$	12.7022	0.492942
$665$	−0.0160135	−0.000620977 0
$666$	−41.8077	−1.62002
$667$	34.2372	1.32567
$668$	−21.5798	−0.834949
$669$	−13.1922	−0.510039
$670$	−0.0678847	−0.00262261
$671$	4.49240	0.173427
$672$	13.9884	0.539614
$673$	−13.8175	−0.532625	−0.266312	−	0.963887i	$-0.585805\pi$
$673$	−13.8175	−0.532625	−0.266312	+	0.963887i	$0.585805\pi$
$674$	12.7111	0.489612
$675$	−46.0607	−1.77288
$676$	0	0
$677$	−28.9663	−1.11326	−0.556632	−	0.830759i	$-0.687907\pi$
$677$	−28.9663	−1.11326	−0.556632	+	0.830759i	$0.687907\pi$
$678$	−2.75033	−0.105626
$679$	6.62982	0.254429
$680$	−0.135771	−0.00520659
$681$	−63.3463	−2.42744
$682$	−1.93567	−0.0741206
$683$	15.3612	0.587782	0.293891	−	0.955839i	$-0.405050\pi$
$683$	15.3612	0.587782	0.293891	+	0.955839i	$0.405050\pi$
$684$	10.3831	0.397006
$685$	0.176780	0.00675443
$686$	−8.23755	−0.314511
$687$	38.7727	1.47927
$688$	8.89473	0.339108
$689$	0	0
$690$	0.164162	0.00624953
$691$	−21.8394	−0.830811	−0.415406	−	0.909636i	$-0.636360\pi$
$691$	−21.8394	−0.830811	−0.415406	+	0.909636i	$0.636360\pi$
$692$	10.6782	0.405925
$693$	4.81043	0.182733
$694$	−8.74950	−0.332127
$695$	0.227078	0.00861355
$696$	63.6613	2.41307
$697$	26.3764	0.999076
$698$	17.6600	0.668443
$699$	−41.5905	−1.57310
$700$	−5.54561	−0.209604
$701$	9.49260	0.358531	0.179265	−	0.983801i	$-0.442628\pi$
$701$	9.49260	0.358531	0.179265	+	0.983801i	$0.442628\pi$
$702$	0	0
$703$	−10.8948	−0.410904
$704$	−3.04936	−0.114927
$705$	0.608070	0.0229012
$706$	2.52152	0.0948985
$707$	−4.50226	−0.169325
$708$	1.11560	0.0419269
$709$	−47.6774	−1.79056	−0.895281	−	0.445501i	$-0.853026\pi$
$709$	−47.6774	−1.79056	−0.895281	+	0.445501i	$0.853026\pi$
$710$	0.167552	0.00628812
$711$	−56.7033	−2.12654
$712$	4.38216	0.164228
$713$	−10.6460	−0.398695
$714$	5.80175	0.217125
$715$	0	0
$716$	30.2825	1.13171
$717$	−11.8970	−0.444303
$718$	24.4267	0.911598
$719$	−46.3833	−1.72981	−0.864903	−	0.501938i	$-0.832620\pi$
$719$	−46.3833	−1.72981	−0.864903	+	0.501938i	$0.832620\pi$
$720$	−0.0745781	−0.00277936
$721$	−13.4318	−0.500226
$722$	13.5820	0.505468
$723$	−16.6002	−0.617367
$724$	16.7186	0.621340
$725$	−40.0952	−1.48910
$726$	−2.33656	−0.0867178
$727$	40.9805	1.51988	0.759942	−	0.649991i	$-0.225228\pi$
$727$	40.9805	1.51988	0.759942	+	0.649991i	$0.225228\pi$
$728$	0	0
$729$	−25.3196	−0.937763
$730$	0.147461	0.00545777
$731$	37.2130	1.37637
$732$	18.8969	0.698450
$733$	35.5052	1.31141	0.655707	−	0.755015i	$-0.272371\pi$
$733$	35.5052	1.31141	0.655707	+	0.755015i	$0.272371\pi$
$734$	−17.9433	−0.662298
$735$	0.315545	0.0116391
$736$	−24.9962	−0.921371
$737$	5.31411	0.195748
$738$	−39.6657	−1.46011
$739$	38.0716	1.40049	0.700243	−	0.713905i	$-0.253075\pi$
$739$	38.0716	1.40049	0.700243	+	0.713905i	$0.253075\pi$
$740$	0.204372	0.00751285
$741$	0	0
$742$	2.81367	0.103293
$743$	11.3244	0.415451	0.207726	−	0.978187i	$-0.433394\pi$
$743$	11.3244	0.415451	0.207726	+	0.978187i	$0.433394\pi$
$744$	−19.7953	−0.725731
$745$	−0.210361	−0.00770704
$746$	6.00990	0.220038
$747$	29.1907	1.06803
$748$	4.37169	0.159845
$749$	−3.46088	−0.126458
$750$	−0.384510	−0.0140403
$751$	1.05097	0.0383506	0.0191753	−	0.999816i	$-0.493896\pi$
$751$	1.05097	0.0383506	0.0191753	+	0.999816i	$0.493896\pi$
$752$	−9.17877	−0.334715
$753$	−20.9543	−0.763617
$754$	0	0
$755$	0.142546	0.00518780
$756$	10.2185	0.371644
$757$	35.2725	1.28200	0.641001	−	0.767540i	$-0.278520\pi$
$757$	35.2725	1.28200	0.641001	+	0.767540i	$0.278520\pi$
$758$	−8.14031	−0.295669
$759$	−12.8508	−0.466455
$760$	0.0532070	0.00193002
$761$	−3.55303	−0.128797	−0.0643986	−	0.997924i	$-0.520513\pi$
$761$	−3.55303	−0.128797	−0.0643986	+	0.997924i	$0.520513\pi$
$762$	0.314888	0.0114072
$763$	−13.8850	−0.502670
$764$	16.1829	0.585476
$765$	−0.312013	−0.0112809
$766$	7.63961	0.276030
$767$	0	0
$768$	−40.1877	−1.45015
$769$	6.79345	0.244978	0.122489	−	0.992470i	$-0.460912\pi$
$769$	6.79345	0.244978	0.122489	+	0.992470i	$0.460912\pi$
$770$	0.0101393	0.000365396 0
$771$	40.8774	1.47216
$772$	−32.7162	−1.17748
$773$	−47.9248	−1.72373	−0.861867	−	0.507135i	$-0.830705\pi$
$773$	−47.9248	−1.72373	−0.861867	+	0.507135i	$0.830705\pi$
$774$	−55.9621	−2.01151
$775$	12.4675	0.447846
$776$	−22.0285	−0.790776
$777$	−21.2319	−0.761691
$778$	18.6581	0.668926
$779$	−10.3366	−0.370346
$780$	0	0
$781$	−13.1162	−0.469335
$782$	−10.3673	−0.370733
$783$	73.8806	2.64028
$784$	−4.76313	−0.170112
$785$	0.0834411	0.00297814
$786$	49.6317	1.77030
$787$	−48.8325	−1.74069	−0.870345	−	0.492442i	$-0.836104\pi$
$787$	−48.8325	−1.74069	−0.870345	+	0.492442i	$0.836104\pi$
$788$	9.18527	0.327212
$789$	−31.9045	−1.13583
$790$	−0.119518	−0.00425227
$791$	−0.934279	−0.0332191
$792$	−15.9833	−0.567941
$793$	0	0
$794$	8.31511	0.295092
$795$	−0.226219	−0.00802316
$796$	−27.7519	−0.983639
$797$	−0.103318	−0.00365971	−0.00182986	−	0.999998i	$-0.500582\pi$
$797$	−0.103318	−0.00365971	−0.00182986	+	0.999998i	$0.500582\pi$
$798$	−2.27363	−0.0804856
$799$	−38.4013	−1.35854
$800$	29.2730	1.03496
$801$	10.0705	0.355825
$802$	8.39827	0.296553
$803$	−11.5434	−0.407359
$804$	22.3534	0.788343
$805$	0.0557652	0.00196547
$806$	0	0
$807$	0.0287407	0.00101172
$808$	14.9594	0.526269
$809$	26.3906	0.927844	0.463922	−	0.885876i	$-0.346442\pi$
$809$	26.3906	0.927844	0.463922	+	0.885876i	$0.346442\pi$
$810$	0.121984	0.00428606
$811$	−34.1395	−1.19880	−0.599399	−	0.800450i	$-0.704594\pi$
$811$	−34.1395	−1.19880	−0.599399	+	0.800450i	$0.704594\pi$
$812$	8.89506	0.312155
$813$	11.2942	0.396105
$814$	6.89828	0.241785
$815$	0.308981	0.0108231
$816$	7.04118	0.246490
$817$	−14.5833	−0.510204
$818$	23.1272	0.808625
$819$	0	0
$820$	0.193900	0.00677130
$821$	10.4146	0.363472	0.181736	−	0.983347i	$-0.441828\pi$
$821$	10.4146	0.363472	0.181736	+	0.983347i	$0.441828\pi$
$822$	25.0996	0.875451
$823$	42.5770	1.48414	0.742070	−	0.670322i	$-0.233844\pi$
$823$	42.5770	1.48414	0.742070	+	0.670322i	$0.233844\pi$
$824$	44.6289	1.55472
$825$	15.0496	0.523960
$826$	−0.163404	−0.00568555
$827$	−26.2465	−0.912680	−0.456340	−	0.889805i	$-0.650840\pi$
$827$	−26.2465	−0.912680	−0.456340	+	0.889805i	$0.650840\pi$
$828$	−36.1578	−1.25657
$829$	28.8072	1.00051	0.500257	−	0.865877i	$-0.333239\pi$
$829$	28.8072	1.00051	0.500257	+	0.865877i	$0.333239\pi$
$830$	0.0615277	0.00213566
$831$	39.6959	1.37703
$832$	0	0
$833$	−19.9276	−0.690449
$834$	32.2410	1.11641
$835$	−0.254130	−0.00879455
$836$	−1.71321	−0.0592525
$837$	−22.9730	−0.794063
$838$	−0.260459	−0.00899741
$839$	−23.6632	−0.816944	−0.408472	−	0.912771i	$-0.633938\pi$
$839$	−23.6632	−0.816944	−0.408472	+	0.912771i	$0.633938\pi$
$840$	0.103691	0.00357767
$841$	35.3120	1.21766
$842$	27.1257	0.934814
$843$	74.4338	2.56364
$844$	−10.8913	−0.374894
$845$	0	0
$846$	57.7492	1.98546
$847$	−0.793722	−0.0272726
$848$	3.41476	0.117263
$849$	−69.6231	−2.38946
$850$	12.1411	0.416437
$851$	37.9398	1.30056
$852$	−55.1724	−1.89017
$853$	46.2856	1.58479	0.792394	−	0.610009i	$-0.208834\pi$
$853$	46.2856	1.58479	0.792394	+	0.610009i	$0.208834\pi$
$854$	−2.76786	−0.0947143
$855$	0.122274	0.00418168
$856$	11.4992	0.393036
$857$	4.37312	0.149383	0.0746915	−	0.997207i	$-0.476203\pi$
$857$	4.37312	0.149383	0.0746915	+	0.997207i	$0.476203\pi$
$858$	0	0
$859$	36.8769	1.25822	0.629112	−	0.777315i	$-0.283419\pi$
$859$	36.8769	1.25822	0.629112	+	0.777315i	$0.283419\pi$
$860$	0.273563	0.00932843
$861$	−20.1441	−0.686509
$862$	12.3224	0.419702
$863$	−8.80418	−0.299698	−0.149849	−	0.988709i	$-0.547879\pi$
$863$	−8.80418	−0.299698	−0.149849	+	0.988709i	$0.547879\pi$
$864$	−53.9394	−1.83505
$865$	0.125750	0.00427562
$866$	7.44934	0.253139
$867$	−21.7132	−0.737418
$868$	−2.76590	−0.0938807
$869$	9.35606	0.317383
$870$	0.308366	0.0104546
$871$	0	0
$872$	46.1347	1.56232
$873$	−50.6231	−1.71333
$874$	4.06280	0.137426
$875$	−0.130617	−0.00441566
$876$	−48.5567	−1.64058
$877$	−0.0731659	−0.00247064	−0.00123532	−	0.999999i	$-0.500393\pi$
$877$	−0.0731659	−0.00247064	−0.00123532	+	0.999999i	$0.500393\pi$
$878$	−6.03858	−0.203792
$879$	−32.9967	−1.11295
$880$	0.0123054	0.000414815 0
$881$	22.5405	0.759407	0.379704	−	0.925108i	$-0.376026\pi$
$881$	22.5405	0.759407	0.379704	+	0.925108i	$0.376026\pi$
$882$	29.9677	1.00907
$883$	−35.3920	−1.19104	−0.595518	−	0.803342i	$-0.703053\pi$
$883$	−35.3920	−1.19104	−0.595518	+	0.803342i	$0.703053\pi$
$884$	0	0
$885$	0.0131376	0.000441617 0
$886$	17.8906	0.601046
$887$	25.3897	0.852502	0.426251	−	0.904605i	$-0.359834\pi$
$887$	25.3897	0.852502	0.426251	+	0.904605i	$0.359834\pi$
$888$	70.5459	2.36737
$889$	0.106966	0.00358754
$890$	0.0212265	0.000711515 0
$891$	−9.54904	−0.319905
$892$	6.12453	0.205064
$893$	15.0490	0.503595
$894$	−29.8675	−0.998919
$895$	0.356615	0.0119203
$896$	−7.41558	−0.247737
$897$	0	0
$898$	22.6646	0.756327
$899$	−19.9977	−0.666959
$900$	42.3445	1.41148
$901$	14.2864	0.475948
$902$	6.54484	0.217919
$903$	−28.4202	−0.945764
$904$	3.10427	0.103246
$905$	0.196882	0.00654460
$906$	20.2390	0.672397
$907$	16.0891	0.534228	0.267114	−	0.963665i	$-0.413930\pi$
$907$	16.0891	0.534228	0.267114	+	0.963665i	$0.413930\pi$
$908$	29.4088	0.975966
$909$	34.3778	1.14024
$910$	0	0
$911$	−10.6061	−0.351396	−0.175698	−	0.984444i	$-0.556218\pi$
$911$	−10.6061	−0.351396	−0.175698	+	0.984444i	$0.556218\pi$
$912$	−2.75934	−0.0913710
$913$	−4.81647	−0.159402
$914$	−24.2123	−0.800872
$915$	0.222536	0.00735680
$916$	−18.0004	−0.594751
$917$	16.8597	0.556757
$918$	−22.3716	−0.738373
$919$	−0.0784038	−0.00258630	−0.00129315	−	0.999999i	$-0.500412\pi$
$919$	−0.0784038	−0.00258630	−0.00129315	+	0.999999i	$0.500412\pi$
$920$	−0.185287	−0.00610874
$921$	59.0746	1.94657
$922$	−29.2405	−0.962985
$923$	0	0
$924$	−3.33873	−0.109836
$925$	−44.4313	−1.46089
$926$	−0.767632	−0.0252260
$927$	102.561	3.36853
$928$	−46.9534	−1.54132
$929$	5.70834	0.187284	0.0936422	−	0.995606i	$-0.470149\pi$
$929$	5.70834	0.187284	0.0936422	+	0.995606i	$0.470149\pi$
$930$	−0.0958855	−0.00314421
$931$	7.80935	0.255941
$932$	19.3086	0.632473
$933$	45.0766	1.47574
$934$	−8.93891	−0.292490
$935$	0.0514822	0.00168365
$936$	0	0
$937$	55.6681	1.81860	0.909299	−	0.416143i	$-0.136619\pi$
$937$	55.6681	1.81860	0.909299	+	0.416143i	$0.136619\pi$
$938$	−3.27414	−0.106904
$939$	34.8919	1.13865
$940$	−0.282299	−0.00920759
$941$	−17.4945	−0.570303	−0.285151	−	0.958482i	$-0.592044\pi$
$941$	−17.4945	−0.570303	−0.285151	+	0.958482i	$0.592044\pi$
$942$	11.8471	0.386001
$943$	35.9959	1.17219
$944$	−0.198312	−0.00645450
$945$	0.120336	0.00391453
$946$	9.23375	0.300215
$947$	−38.2431	−1.24273	−0.621367	−	0.783520i	$-0.713422\pi$
$947$	−38.2431	−1.24273	−0.621367	+	0.783520i	$0.713422\pi$
$948$	39.3556	1.27821
$949$	0	0
$950$	−4.75795	−0.154368
$951$	−16.7098	−0.541852
$952$	−6.54837	−0.212234
$953$	−55.0966	−1.78476	−0.892378	−	0.451289i	$-0.850964\pi$
$953$	−55.0966	−1.78476	−0.892378	+	0.451289i	$0.850964\pi$
$954$	−21.4843	−0.695580
$955$	0.190574	0.00616684
$956$	5.52326	0.178635
$957$	−24.1393	−0.780312
$958$	−7.07700	−0.228647
$959$	8.52627	0.275328
$960$	−0.151053	−0.00487523
$961$	−24.7818	−0.799412
$962$	0	0
$963$	26.4262	0.851571
$964$	7.70671	0.248216
$965$	−0.385276	−0.0124025
$966$	7.91766	0.254747
$967$	−25.7894	−0.829330	−0.414665	−	0.909974i	$-0.636101\pi$
$967$	−25.7894	−0.829330	−0.414665	+	0.909974i	$0.636101\pi$
$968$	2.63725	0.0847643
$969$	−11.5443	−0.370856
$970$	−0.106703	−0.00342601
$971$	42.9387	1.37797	0.688985	−	0.724776i	$-0.258057\pi$
$971$	42.9387	1.37797	0.688985	+	0.724776i	$0.258057\pi$
$972$	−1.54482	−0.0495501
$973$	10.9522	0.351110
$974$	14.4528	0.463099
$975$	0	0
$976$	−3.35916	−0.107524
$977$	−42.1485	−1.34845	−0.674225	−	0.738526i	$-0.735522\pi$
$977$	−42.1485	−1.34845	−0.674225	+	0.738526i	$0.735522\pi$
$978$	43.8698	1.40280
$979$	−1.66164	−0.0531063
$980$	−0.146493	−0.00467956
$981$	106.021	3.38499
$982$	19.4199	0.619713
$983$	51.7672	1.65112	0.825559	−	0.564316i	$-0.190860\pi$
$983$	51.7672	1.65112	0.825559	+	0.564316i	$0.190860\pi$
$984$	66.9314	2.13370
$985$	0.108168	0.00344653
$986$	−19.4741	−0.620183
$987$	29.3277	0.933512
$988$	0	0
$989$	50.7846	1.61486
$990$	−0.0774207	−0.00246059
$991$	33.1031	1.05155	0.525777	−	0.850622i	$-0.323775\pi$
$991$	33.1031	1.05155	0.525777	+	0.850622i	$0.323775\pi$
$992$	14.6001	0.463552
$993$	−21.2012	−0.672801
$994$	8.08118	0.256319
$995$	−0.326814	−0.0103607
$996$	−20.2601	−0.641967
$997$	−10.4149	−0.329842	−0.164921	−	0.986307i	$-0.552737\pi$
$997$	−10.4149	−0.329842	−0.164921	+	0.986307i	$0.552737\pi$
$998$	4.70373	0.148894
$999$	81.8704	2.59027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.9	✓	21
13.12	even	2		1859.2.a.t.1.13	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.9	✓	21	1.1	even	1	trivial
1859.2.a.t.1.13	yes	21	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-0.776244 q^{2} +3.01008 q^{3} -1.39745 q^{4} -0.0164567 q^{5} -2.33656 q^{6} -0.793722 q^{7} +2.63725 q^{8} +6.06060 q^{9} +O(q^{10})\)	\(q-0.776244 q^{2} +3.01008 q^{3} -1.39745 q^{4} -0.0164567 q^{5} -2.33656 q^{6} -0.793722 q^{7} +2.63725 q^{8} +6.06060 q^{9} +0.0127744 q^{10} -1.00000 q^{11} -4.20643 q^{12} +0.616122 q^{14} -0.0495361 q^{15} +0.747743 q^{16} +3.12834 q^{17} -4.70450 q^{18} -1.22596 q^{19} +0.0229974 q^{20} -2.38917 q^{21} +0.776244 q^{22} +4.26925 q^{23} +7.93833 q^{24} -4.99973 q^{25} +9.21265 q^{27} +1.10918 q^{28} +8.01948 q^{29} +0.0384521 q^{30} -2.49364 q^{31} -5.85492 q^{32} -3.01008 q^{33} -2.42836 q^{34} +0.0130621 q^{35} -8.46935 q^{36} +8.88674 q^{37} +0.951641 q^{38} -0.0434004 q^{40} +8.43142 q^{41} +1.85458 q^{42} +11.8954 q^{43} +1.39745 q^{44} -0.0997375 q^{45} -3.31398 q^{46} -12.2753 q^{47} +2.25077 q^{48} -6.37001 q^{49} +3.88101 q^{50} +9.41657 q^{51} +4.56675 q^{53} -7.15126 q^{54} +0.0164567 q^{55} -2.09324 q^{56} -3.69023 q^{57} -6.22507 q^{58} -0.265214 q^{59} +0.0692239 q^{60} -4.49240 q^{61} +1.93567 q^{62} -4.81043 q^{63} +3.04936 q^{64} +2.33656 q^{66} -5.31411 q^{67} -4.37169 q^{68} +12.8508 q^{69} -0.0101393 q^{70} +13.1162 q^{71} +15.9833 q^{72} +11.5434 q^{73} -6.89828 q^{74} -15.0496 q^{75} +1.71321 q^{76} +0.793722 q^{77} -9.35606 q^{79} -0.0123054 q^{80} +9.54904 q^{81} -6.54484 q^{82} +4.81647 q^{83} +3.33873 q^{84} -0.0514822 q^{85} -9.23375 q^{86} +24.1393 q^{87} -2.63725 q^{88} +1.66164 q^{89} +0.0774207 q^{90} -5.96605 q^{92} -7.50605 q^{93} +9.52863 q^{94} +0.0201752 q^{95} -17.6238 q^{96} -8.35282 q^{97} +4.94468 q^{98} -6.06060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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