LMFDB - Embedded newform 1859.2.a.s.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.17546 q^{2} -1.22926 q^{3} -0.618298 q^{4} +1.06938 q^{5} +1.44494 q^{6} +3.67782 q^{7} +3.07770 q^{8} -1.48892 q^{9} +O(q^{10})$	\(q-1.17546 q^{2} -1.22926 q^{3} -0.618298 q^{4} +1.06938 q^{5} +1.44494 q^{6} +3.67782 q^{7} +3.07770 q^{8} -1.48892 q^{9} -1.25701 q^{10} -1.00000 q^{11} +0.760050 q^{12} -4.32312 q^{14} -1.31454 q^{15} -2.38111 q^{16} +4.61281 q^{17} +1.75016 q^{18} +6.56325 q^{19} -0.661193 q^{20} -4.52100 q^{21} +1.17546 q^{22} +6.89013 q^{23} -3.78330 q^{24} -3.85644 q^{25} +5.51805 q^{27} -2.27399 q^{28} -7.50948 q^{29} +1.54519 q^{30} +4.02002 q^{31} -3.35650 q^{32} +1.22926 q^{33} -5.42216 q^{34} +3.93297 q^{35} +0.920595 q^{36} -4.37781 q^{37} -7.71483 q^{38} +3.29122 q^{40} -7.56827 q^{41} +5.31425 q^{42} +3.03588 q^{43} +0.618298 q^{44} -1.59221 q^{45} -8.09906 q^{46} +2.86516 q^{47} +2.92701 q^{48} +6.52636 q^{49} +4.53308 q^{50} -5.67034 q^{51} +11.3481 q^{53} -6.48624 q^{54} -1.06938 q^{55} +11.3192 q^{56} -8.06795 q^{57} +8.82708 q^{58} -7.28662 q^{59} +0.812779 q^{60} -2.10752 q^{61} -4.72536 q^{62} -5.47597 q^{63} +8.70765 q^{64} -1.44494 q^{66} +6.17708 q^{67} -2.85209 q^{68} -8.46977 q^{69} -4.62304 q^{70} -10.0122 q^{71} -4.58244 q^{72} -7.21487 q^{73} +5.14593 q^{74} +4.74057 q^{75} -4.05805 q^{76} -3.67782 q^{77} -15.1525 q^{79} -2.54630 q^{80} -2.31637 q^{81} +8.89618 q^{82} +3.56754 q^{83} +2.79533 q^{84} +4.93282 q^{85} -3.56855 q^{86} +9.23111 q^{87} -3.07770 q^{88} -3.36383 q^{89} +1.87158 q^{90} -4.26015 q^{92} -4.94165 q^{93} -3.36788 q^{94} +7.01858 q^{95} +4.12602 q^{96} +18.1156 q^{97} -7.67147 q^{98} +1.48892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.17546	−0.831174	−0.415587	−	0.909553i	$-0.636424\pi$
$2$	−1.17546	−0.831174	−0.415587	+	0.909553i	$0.636424\pi$
$3$	−1.22926	−0.709714	−0.354857	−	0.934921i	$-0.615470\pi$
$3$	−1.22926	−0.709714	−0.354857	+	0.934921i	$0.615470\pi$
$4$	−0.618298	−0.309149
$5$	1.06938	0.478239	0.239120	−	0.970990i	$-0.423141\pi$
$5$	1.06938	0.478239	0.239120	+	0.970990i	$0.423141\pi$
$6$	1.44494	0.589896
$7$	3.67782	1.39009	0.695043	−	0.718968i	$-0.255385\pi$
$7$	3.67782	1.39009	0.695043	+	0.718968i	$0.255385\pi$
$8$	3.07770	1.08813
$9$	−1.48892	−0.496306
$10$	−1.25701	−0.397500
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.760050	0.219407
$13$	0	0
$13$	0	0
$14$	−4.32312	−1.15540
$15$	−1.31454	−0.339413
$16$	−2.38111	−0.595278
$17$	4.61281	1.11877	0.559385	−	0.828908i	$-0.311037\pi$
$17$	4.61281	1.11877	0.559385	+	0.828908i	$0.311037\pi$
$18$	1.75016	0.412517
$19$	6.56325	1.50571	0.752857	−	0.658184i	$-0.228675\pi$
$19$	6.56325	1.50571	0.752857	+	0.658184i	$0.228675\pi$
$20$	−0.661193	−0.147847
$21$	−4.52100	−0.986563
$22$	1.17546	0.250609
$23$	6.89013	1.43669	0.718346	−	0.695686i	$-0.244900\pi$
$23$	6.89013	1.43669	0.718346	+	0.695686i	$0.244900\pi$
$24$	−3.78330	−0.772262
$25$	−3.85644	−0.771287
$26$	0	0
$27$	5.51805	1.06195
$28$	−2.27399	−0.429744
$29$	−7.50948	−1.39447	−0.697237	−	0.716840i	$-0.745588\pi$
$29$	−7.50948	−1.39447	−0.697237	+	0.716840i	$0.745588\pi$
$30$	1.54519	0.282112
$31$	4.02002	0.722016	0.361008	−	0.932563i	$-0.382433\pi$
$31$	4.02002	0.722016	0.361008	+	0.932563i	$0.382433\pi$
$32$	−3.35650	−0.593352
$33$	1.22926	0.213987
$34$	−5.42216	−0.929893
$35$	3.93297	0.664793
$36$	0.920595	0.153432
$37$	−4.37781	−0.719707	−0.359854	−	0.933009i	$-0.617173\pi$
$37$	−4.37781	−0.719707	−0.359854	+	0.933009i	$0.617173\pi$
$38$	−7.71483	−1.25151
$39$	0	0
$40$	3.29122	0.520387
$41$	−7.56827	−1.18197	−0.590983	−	0.806684i	$-0.701260\pi$
$41$	−7.56827	−1.18197	−0.590983	+	0.806684i	$0.701260\pi$
$42$	5.31425	0.820006
$43$	3.03588	0.462967	0.231483	−	0.972839i	$-0.425642\pi$
$43$	3.03588	0.462967	0.231483	+	0.972839i	$0.425642\pi$
$44$	0.618298	0.0932120
$45$	−1.59221	−0.237353
$46$	−8.09906	−1.19414
$47$	2.86516	0.417927	0.208963	−	0.977923i	$-0.432991\pi$
$47$	2.86516	0.417927	0.208963	+	0.977923i	$0.432991\pi$
$48$	2.92701	0.422477
$49$	6.52636	0.932338
$50$	4.53308	0.641074
$51$	−5.67034	−0.794007
$52$	0	0
$53$	11.3481	1.55879	0.779393	−	0.626536i	$-0.215528\pi$
$53$	11.3481	1.55879	0.779393	+	0.626536i	$0.215528\pi$
$54$	−6.48624	−0.882665
$55$	−1.06938	−0.144195
$56$	11.3192	1.51260
$57$	−8.06795	−1.06863
$58$	8.82708	1.15905
$59$	−7.28662	−0.948638	−0.474319	−	0.880353i	$-0.657306\pi$
$59$	−7.28662	−0.948638	−0.474319	+	0.880353i	$0.657306\pi$
$60$	0.812779	0.104929
$61$	−2.10752	−0.269841	−0.134920	−	0.990856i	$-0.543078\pi$
$61$	−2.10752	−0.269841	−0.134920	+	0.990856i	$0.543078\pi$
$62$	−4.72536	−0.600121
$63$	−5.47597	−0.689908
$64$	8.70765	1.08846
$65$	0	0
$66$	−1.44494	−0.177860
$67$	6.17708	0.754650	0.377325	−	0.926081i	$-0.376844\pi$
$67$	6.17708	0.754650	0.377325	+	0.926081i	$0.376844\pi$
$68$	−2.85209	−0.345867
$69$	−8.46977	−1.01964
$70$	−4.62304	−0.552559
$71$	−10.0122	−1.18823	−0.594116	−	0.804379i	$-0.702498\pi$
$71$	−10.0122	−1.18823	−0.594116	+	0.804379i	$0.702498\pi$
$72$	−4.58244	−0.540046
$73$	−7.21487	−0.844437	−0.422219	−	0.906494i	$-0.638749\pi$
$73$	−7.21487	−0.844437	−0.422219	+	0.906494i	$0.638749\pi$
$74$	5.14593	0.598202
$75$	4.74057	0.547393
$76$	−4.05805	−0.465490
$77$	−3.67782	−0.419127
$78$	0	0
$79$	−15.1525	−1.70479	−0.852395	−	0.522898i	$-0.824851\pi$
$79$	−15.1525	−1.70479	−0.852395	+	0.522898i	$0.824851\pi$
$80$	−2.54630	−0.284685
$81$	−2.31637	−0.257375
$82$	8.89618	0.982419
$83$	3.56754	0.391588	0.195794	−	0.980645i	$-0.437272\pi$
$83$	3.56754	0.391588	0.195794	+	0.980645i	$0.437272\pi$
$84$	2.79533	0.304995
$85$	4.93282	0.535039
$86$	−3.56855	−0.384806
$87$	9.23111	0.989678
$88$	−3.07770	−0.328084
$89$	−3.36383	−0.356566	−0.178283	−	0.983979i	$-0.557054\pi$
$89$	−3.36383	−0.356566	−0.178283	+	0.983979i	$0.557054\pi$
$90$	1.87158	0.197282
$91$	0	0
$92$	−4.26015	−0.444152
$93$	−4.94165	−0.512425
$94$	−3.36788	−0.347370
$95$	7.01858	0.720091
$96$	4.12602	0.421110
$97$	18.1156	1.83936	0.919679	−	0.392671i	$-0.128449\pi$
$97$	18.1156	1.83936	0.919679	+	0.392671i	$0.128449\pi$
$98$	−7.67147	−0.774935
$99$	1.48892	0.149642
$100$	2.38443	0.238443
$101$	13.1809	1.31155	0.655773	−	0.754958i	$-0.272343\pi$
$101$	13.1809	1.31155	0.655773	+	0.754958i	$0.272343\pi$
$102$	6.66525	0.659958
$103$	5.35159	0.527308	0.263654	−	0.964617i	$-0.415072\pi$
$103$	5.35159	0.527308	0.263654	+	0.964617i	$0.415072\pi$
$104$	0	0
$105$	−4.83465	−0.471813
$106$	−13.3393	−1.29562
$107$	8.40679	0.812715	0.406358	−	0.913714i	$-0.366799\pi$
$107$	8.40679	0.812715	0.406358	+	0.913714i	$0.366799\pi$
$108$	−3.41180	−0.328301
$109$	12.9301	1.23848	0.619240	−	0.785202i	$-0.287441\pi$
$109$	12.9301	1.23848	0.619240	+	0.785202i	$0.287441\pi$
$110$	1.25701	0.119851
$111$	5.38147	0.510786
$112$	−8.75730	−0.827487
$113$	2.38626	0.224480	0.112240	−	0.993681i	$-0.464197\pi$
$113$	2.38626	0.224480	0.112240	+	0.993681i	$0.464197\pi$
$114$	9.48354	0.888215
$115$	7.36814	0.687082
$116$	4.64310	0.431101
$117$	0	0
$118$	8.56512	0.788483
$119$	16.9651	1.55519
$120$	−4.04576	−0.369326
$121$	1.00000	0.0909091
$122$	2.47730	0.224285
$123$	9.30338	0.838857
$124$	−2.48557	−0.223211
$125$	−9.47086	−0.847099
$126$	6.43677	0.573433
$127$	11.3039	1.00306	0.501529	−	0.865141i	$-0.332771\pi$
$127$	11.3039	1.00306	0.501529	+	0.865141i	$0.332771\pi$
$128$	−3.52247	−0.311346
$129$	−3.73188	−0.328574
$130$	0	0
$131$	−8.65899	−0.756540	−0.378270	−	0.925695i	$-0.623481\pi$
$131$	−8.65899	−0.756540	−0.378270	+	0.925695i	$0.623481\pi$
$132$	−0.760050	−0.0661538
$133$	24.1385	2.09307
$134$	−7.26090	−0.627246
$135$	5.90087	0.507866
$136$	14.1968	1.21737
$137$	7.29319	0.623099	0.311550	−	0.950230i	$-0.399152\pi$
$137$	7.29319	0.623099	0.311550	+	0.950230i	$0.399152\pi$
$138$	9.95586	0.847499
$139$	−12.3363	−1.04635	−0.523176	−	0.852225i	$-0.675253\pi$
$139$	−12.3363	−1.04635	−0.523176	+	0.852225i	$0.675253\pi$
$140$	−2.43175	−0.205520
$141$	−3.52203	−0.296608
$142$	11.7689	0.987628
$143$	0	0
$144$	3.54528	0.295440
$145$	−8.03045	−0.666893
$146$	8.48078	0.701874
$147$	−8.02260	−0.661693
$148$	2.70679	0.222497
$149$	−0.138812	−0.0113719	−0.00568597	−	0.999984i	$-0.501810\pi$
$149$	−0.138812	−0.0113719	−0.00568597	+	0.999984i	$0.501810\pi$
$150$	−5.57234	−0.454979
$151$	21.2786	1.73163	0.865813	−	0.500368i	$-0.166802\pi$
$151$	21.2786	1.73163	0.865813	+	0.500368i	$0.166802\pi$
$152$	20.1997	1.63841
$153$	−6.86809	−0.555252
$154$	4.32312	0.348367
$155$	4.29891	0.345296
$156$	0	0
$157$	15.4984	1.23691	0.618453	−	0.785822i	$-0.287760\pi$
$157$	15.4984	1.23691	0.618453	+	0.785822i	$0.287760\pi$
$158$	17.8111	1.41698
$159$	−13.9498	−1.10629
$160$	−3.58936	−0.283764
$161$	25.3407	1.99712
$162$	2.72280	0.213923
$163$	−1.31961	−0.103360	−0.0516799	−	0.998664i	$-0.516458\pi$
$163$	−1.31961	−0.103360	−0.0516799	+	0.998664i	$0.516458\pi$
$164$	4.67945	0.365403
$165$	1.31454	0.102337
$166$	−4.19349	−0.325478
$167$	6.49802	0.502832	0.251416	−	0.967879i	$-0.419104\pi$
$167$	6.49802	0.502832	0.251416	+	0.967879i	$0.419104\pi$
$168$	−13.9143	−1.07351
$169$	0	0
$170$	−5.79832	−0.444711
$171$	−9.77214	−0.747294
$172$	−1.87708	−0.143126
$173$	2.23420	0.169863	0.0849314	−	0.996387i	$-0.472933\pi$
$173$	2.23420	0.169863	0.0849314	+	0.996387i	$0.472933\pi$
$174$	−10.8508	−0.822595
$175$	−14.1833	−1.07216
$176$	2.38111	0.179483
$177$	8.95716	0.673262
$178$	3.95404	0.296368
$179$	12.7708	0.954531	0.477265	−	0.878759i	$-0.341628\pi$
$179$	12.7708	0.954531	0.477265	+	0.878759i	$0.341628\pi$
$180$	0.984462	0.0733774
$181$	15.3012	1.13733	0.568665	−	0.822569i	$-0.307460\pi$
$181$	15.3012	1.13733	0.568665	+	0.822569i	$0.307460\pi$
$182$	0	0
$183$	2.59070	0.191510
$184$	21.2058	1.56331
$185$	−4.68152	−0.344192
$186$	5.80870	0.425915
$187$	−4.61281	−0.337322
$188$	−1.77152	−0.129202
$189$	20.2944	1.47620
$190$	−8.25005	−0.598521
$191$	−10.0060	−0.724010	−0.362005	−	0.932176i	$-0.617908\pi$
$191$	−10.0060	−0.724010	−0.362005	+	0.932176i	$0.617908\pi$
$192$	−10.7040	−0.772493
$193$	10.8911	0.783958	0.391979	−	0.919974i	$-0.371791\pi$
$193$	10.8911	0.783958	0.391979	+	0.919974i	$0.371791\pi$
$194$	−21.2941	−1.52883
$195$	0	0
$196$	−4.03524	−0.288231
$197$	2.41459	0.172033	0.0860163	−	0.996294i	$-0.472586\pi$
$197$	2.41459	0.172033	0.0860163	+	0.996294i	$0.472586\pi$
$198$	−1.75016	−0.124378
$199$	0.0512234	0.00363113	0.00181557	−	0.999998i	$-0.499422\pi$
$199$	0.0512234	0.00363113	0.00181557	+	0.999998i	$0.499422\pi$
$200$	−11.8690	−0.839262
$201$	−7.59324	−0.535586
$202$	−15.4936	−1.09012
$203$	−27.6185	−1.93844
$204$	3.50596	0.245466
$205$	−8.09332	−0.565262
$206$	−6.29057	−0.438285
$207$	−10.2588	−0.713038
$208$	0	0
$209$	−6.56325	−0.453990
$210$	5.68293	0.392159
$211$	25.6713	1.76728	0.883641	−	0.468165i	$-0.155085\pi$
$211$	25.6713	1.76728	0.883641	+	0.468165i	$0.155085\pi$
$212$	−7.01653	−0.481897
$213$	12.3076	0.843305
$214$	−9.88183	−0.675508
$215$	3.24649	0.221409
$216$	16.9829	1.15554
$217$	14.7849	1.00366
$218$	−15.1988	−1.02939
$219$	8.86896	0.599309
$220$	0.661193	0.0445776
$221$	0	0
$222$	−6.32569	−0.424553
$223$	−5.80464	−0.388708	−0.194354	−	0.980931i	$-0.562261\pi$
$223$	−5.80464	−0.388708	−0.194354	+	0.980931i	$0.562261\pi$
$224$	−12.3446	−0.824809
$225$	5.74192	0.382794
$226$	−2.80494	−0.186582
$227$	−3.73623	−0.247983	−0.123991	−	0.992283i	$-0.539569\pi$
$227$	−3.73623	−0.247983	−0.123991	+	0.992283i	$0.539569\pi$
$228$	4.98840	0.330365
$229$	−18.5146	−1.22348	−0.611739	−	0.791060i	$-0.709530\pi$
$229$	−18.5146	−1.22348	−0.611739	+	0.791060i	$0.709530\pi$
$230$	−8.66093	−0.571085
$231$	4.52100	0.297460
$232$	−23.1119	−1.51737
$233$	15.2245	0.997387	0.498694	−	0.866778i	$-0.333813\pi$
$233$	15.2245	0.997387	0.498694	+	0.866778i	$0.333813\pi$
$234$	0	0
$235$	3.06393	0.199869
$236$	4.50531	0.293270
$237$	18.6264	1.20991
$238$	−19.9417	−1.29263
$239$	−24.2441	−1.56822	−0.784110	−	0.620622i	$-0.786880\pi$
$239$	−24.2441	−1.56822	−0.784110	+	0.620622i	$0.786880\pi$
$240$	3.13007	0.202045
$241$	−14.5797	−0.939162	−0.469581	−	0.882889i	$-0.655595\pi$
$241$	−14.5797	−0.939162	−0.469581	+	0.882889i	$0.655595\pi$
$242$	−1.17546	−0.0755613
$243$	−13.7067	−0.879287
$244$	1.30308	0.0834210
$245$	6.97913	0.445880
$246$	−10.9357	−0.697237
$247$	0	0
$248$	12.3724	0.785648
$249$	−4.38544	−0.277916
$250$	11.1326	0.704087
$251$	−20.3766	−1.28616	−0.643079	−	0.765800i	$-0.722343\pi$
$251$	−20.3766	−1.28616	−0.643079	+	0.765800i	$0.722343\pi$
$252$	3.38578	0.213284
$253$	−6.89013	−0.433179
$254$	−13.2872	−0.833715
$255$	−6.06372	−0.379725
$256$	−13.2748	−0.829674
$257$	−2.30300	−0.143657	−0.0718287	−	0.997417i	$-0.522883\pi$
$257$	−2.30300	−0.143657	−0.0718287	+	0.997417i	$0.522883\pi$
$258$	4.38667	0.273102
$259$	−16.1008	−1.00045
$260$	0	0
$261$	11.1810	0.692086
$262$	10.1783	0.628817
$263$	−4.84720	−0.298891	−0.149446	−	0.988770i	$-0.547749\pi$
$263$	−4.84720	−0.298891	−0.149446	+	0.988770i	$0.547749\pi$
$264$	3.78330	0.232846
$265$	12.1354	0.745472
$266$	−28.3738	−1.73971
$267$	4.13503	0.253060
$268$	−3.81928	−0.233299
$269$	25.1720	1.53476	0.767381	−	0.641191i	$-0.221559\pi$
$269$	25.1720	1.53476	0.767381	+	0.641191i	$0.221559\pi$
$270$	−6.93622	−0.422125
$271$	8.88098	0.539481	0.269740	−	0.962933i	$-0.413062\pi$
$271$	8.88098	0.539481	0.269740	+	0.962933i	$0.413062\pi$
$272$	−10.9836	−0.665979
$273$	0	0
$274$	−8.57284	−0.517904
$275$	3.85644	0.232552
$276$	5.23684	0.315221
$277$	19.1219	1.14892	0.574462	−	0.818531i	$-0.305211\pi$
$277$	19.1219	1.14892	0.574462	+	0.818531i	$0.305211\pi$
$278$	14.5008	0.869701
$279$	−5.98547	−0.358341
$280$	12.1045	0.723382
$281$	0.195636	0.0116706	0.00583532	−	0.999983i	$-0.498143\pi$
$281$	0.195636	0.0116706	0.00583532	+	0.999983i	$0.498143\pi$
$282$	4.14000	0.246533
$283$	−9.94140	−0.590955	−0.295478	−	0.955350i	$-0.595479\pi$
$283$	−9.94140	−0.590955	−0.295478	+	0.955350i	$0.595479\pi$
$284$	6.19054	0.367341
$285$	−8.62767	−0.511059
$286$	0	0
$287$	−27.8347	−1.64303
$288$	4.99756	0.294484
$289$	4.27797	0.251645
$290$	9.43946	0.554304
$291$	−22.2688	−1.30542
$292$	4.46094	0.261057
$293$	2.74298	0.160247	0.0801234	−	0.996785i	$-0.474469\pi$
$293$	2.74298	0.160247	0.0801234	+	0.996785i	$0.474469\pi$
$294$	9.43024	0.549983
$295$	−7.79214	−0.453676
$296$	−13.4736	−0.783136
$297$	−5.51805	−0.320190
$298$	0.163168	0.00945207
$299$	0	0
$300$	−2.93108	−0.169226
$301$	11.1654	0.643563
$302$	−25.0121	−1.43928
$303$	−16.2027	−0.930823
$304$	−15.6278	−0.896318
$305$	−2.25373	−0.129048
$306$	8.07315	0.461511
$307$	29.7166	1.69602	0.848008	−	0.529983i	$-0.177802\pi$
$307$	29.7166	1.69602	0.848008	+	0.529983i	$0.177802\pi$
$308$	2.27399	0.129573
$309$	−6.57850	−0.374238
$310$	−5.05318	−0.287002
$311$	12.2907	0.696941	0.348471	−	0.937320i	$-0.386701\pi$
$311$	12.2907	0.696941	0.348471	+	0.937320i	$0.386701\pi$
$312$	0	0
$313$	−0.838781	−0.0474107	−0.0237054	−	0.999719i	$-0.507546\pi$
$313$	−0.838781	−0.0474107	−0.0237054	+	0.999719i	$0.507546\pi$
$314$	−18.2177	−1.02808
$315$	−5.85587	−0.329941
$316$	9.36877	0.527035
$317$	−3.62055	−0.203351	−0.101675	−	0.994818i	$-0.532420\pi$
$317$	−3.62055	−0.203351	−0.101675	+	0.994818i	$0.532420\pi$
$318$	16.3974	0.919522
$319$	7.50948	0.420450
$320$	9.31175	0.520543
$321$	−10.3341	−0.576795
$322$	−29.7869	−1.65996
$323$	30.2750	1.68455
$324$	1.43221	0.0795672
$325$	0	0
$326$	1.55115	0.0859100
$327$	−15.8945	−0.878967
$328$	−23.2929	−1.28613
$329$	10.5375	0.580954
$330$	−1.54519	−0.0850598
$331$	−2.09287	−0.115035	−0.0575174	−	0.998345i	$-0.518318\pi$
$331$	−2.09287	−0.115035	−0.0575174	+	0.998345i	$0.518318\pi$
$332$	−2.20580	−0.121059
$333$	6.51819	0.357195
$334$	−7.63815	−0.417941
$335$	6.60562	0.360903
$336$	10.7650	0.587279
$337$	21.8264	1.18896	0.594479	−	0.804111i	$-0.297358\pi$
$337$	21.8264	1.18896	0.594479	+	0.804111i	$0.297358\pi$
$338$	0	0
$339$	−2.93333	−0.159317
$340$	−3.04995	−0.165407
$341$	−4.02002	−0.217696
$342$	11.4867	0.621132
$343$	−1.74195	−0.0940563
$344$	9.34352	0.503769
$345$	−9.05736	−0.487632
$346$	−2.62620	−0.141186
$347$	−29.8757	−1.60381	−0.801907	−	0.597449i	$-0.796181\pi$
$347$	−29.8757	−1.60381	−0.801907	+	0.597449i	$0.796181\pi$
$348$	−5.70758	−0.305958
$349$	2.72847	0.146052	0.0730259	−	0.997330i	$-0.476734\pi$
$349$	2.72847	0.146052	0.0730259	+	0.997330i	$0.476734\pi$
$350$	16.6719	0.891148
$351$	0	0
$352$	3.35650	0.178902
$353$	−33.1863	−1.76633	−0.883164	−	0.469063i	$-0.844592\pi$
$353$	−33.1863	−1.76633	−0.883164	+	0.469063i	$0.844592\pi$
$354$	−10.5288	−0.559598
$355$	−10.7068	−0.568259
$356$	2.07985	0.110232
$357$	−20.8545	−1.10374
$358$	−15.0115	−0.793382
$359$	−22.1247	−1.16769	−0.583847	−	0.811863i	$-0.698453\pi$
$359$	−22.1247	−1.16769	−0.583847	+	0.811863i	$0.698453\pi$
$360$	−4.90035	−0.258271
$361$	24.0763	1.26717
$362$	−17.9859	−0.945320
$363$	−1.22926	−0.0645195
$364$	0	0
$365$	−7.71541	−0.403843
$366$	−3.04525	−0.159178
$367$	−26.9673	−1.40768	−0.703840	−	0.710358i	$-0.748533\pi$
$367$	−26.9673	−1.40768	−0.703840	+	0.710358i	$0.748533\pi$
$368$	−16.4062	−0.855230
$369$	11.2685	0.586616
$370$	5.50293	0.286084
$371$	41.7364	2.16685
$372$	3.05541	0.158416
$373$	−19.4916	−1.00924	−0.504618	−	0.863343i	$-0.668367\pi$
$373$	−19.4916	−1.00924	−0.504618	+	0.863343i	$0.668367\pi$
$374$	5.42216	0.280373
$375$	11.6422	0.601198
$376$	8.81811	0.454759
$377$	0	0
$378$	−23.8552	−1.22698
$379$	35.8631	1.84216	0.921081	−	0.389370i	$-0.127307\pi$
$379$	35.8631	1.84216	0.921081	+	0.389370i	$0.127307\pi$
$380$	−4.33958	−0.222616
$381$	−13.8954	−0.711884
$382$	11.7617	0.601779
$383$	−30.1820	−1.54223	−0.771114	−	0.636697i	$-0.780300\pi$
$383$	−30.1820	−1.54223	−0.771114	+	0.636697i	$0.780300\pi$
$384$	4.33004	0.220966
$385$	−3.93297	−0.200443
$386$	−12.8020	−0.651606
$387$	−4.52017	−0.229773
$388$	−11.2008	−0.568636
$389$	24.7916	1.25698	0.628492	−	0.777816i	$-0.283673\pi$
$389$	24.7916	1.25698	0.628492	+	0.777816i	$0.283673\pi$
$390$	0	0
$391$	31.7828	1.60733
$392$	20.0862	1.01451
$393$	10.6442	0.536927
$394$	−2.83825	−0.142989
$395$	−16.2037	−0.815298
$396$	−0.920595	−0.0462616
$397$	26.5220	1.33110	0.665550	−	0.746353i	$-0.268197\pi$
$397$	26.5220	1.33110	0.665550	+	0.746353i	$0.268197\pi$
$398$	−0.0602110	−0.00301810
$399$	−29.6725	−1.48548
$400$	9.18260	0.459130
$401$	−10.9423	−0.546432	−0.273216	−	0.961953i	$-0.588087\pi$
$401$	−10.9423	−0.546432	−0.273216	+	0.961953i	$0.588087\pi$
$402$	8.92554	0.445165
$403$	0	0
$404$	−8.14972	−0.405463
$405$	−2.47707	−0.123087
$406$	32.4644	1.61118
$407$	4.37781	0.217000
$408$	−17.4516	−0.863983
$409$	−32.8872	−1.62617	−0.813083	−	0.582147i	$-0.802213\pi$
$409$	−32.8872	−1.62617	−0.813083	+	0.582147i	$0.802213\pi$
$410$	9.51336	0.469831
$411$	−8.96523	−0.442222
$412$	−3.30888	−0.163017
$413$	−26.7989	−1.31869
$414$	12.0588	0.592659
$415$	3.81504	0.187273
$416$	0	0
$417$	15.1645	0.742611
$418$	7.71483	0.377345
$419$	10.4527	0.510650	0.255325	−	0.966855i	$-0.417818\pi$
$419$	10.4527	0.510650	0.255325	+	0.966855i	$0.417818\pi$
$420$	2.98925	0.145861
$421$	−13.9640	−0.680566	−0.340283	−	0.940323i	$-0.610523\pi$
$421$	−13.9640	−0.680566	−0.340283	+	0.940323i	$0.610523\pi$
$422$	−30.1755	−1.46892
$423$	−4.26599	−0.207419
$424$	34.9261	1.69616
$425$	−17.7890	−0.862893
$426$	−14.4671	−0.700934
$427$	−7.75109	−0.375101
$428$	−5.19790	−0.251250
$429$	0	0
$430$	−3.81612	−0.184029
$431$	−11.3165	−0.545097	−0.272549	−	0.962142i	$-0.587867\pi$
$431$	−11.3165	−0.545097	−0.272549	+	0.962142i	$0.587867\pi$
$432$	−13.1391	−0.632155
$433$	−35.6680	−1.71409	−0.857047	−	0.515238i	$-0.827704\pi$
$433$	−35.6680	−1.71409	−0.857047	+	0.515238i	$0.827704\pi$
$434$	−17.3790	−0.834220
$435$	9.87152	0.473303
$436$	−7.99466	−0.382875
$437$	45.2217	2.16325
$438$	−10.4251	−0.498130
$439$	13.2650	0.633104	0.316552	−	0.948575i	$-0.397475\pi$
$439$	13.2650	0.633104	0.316552	+	0.948575i	$0.397475\pi$
$440$	−3.29122	−0.156903
$441$	−9.71722	−0.462725
$442$	0	0
$443$	33.9842	1.61464	0.807319	−	0.590115i	$-0.200917\pi$
$443$	33.9842	1.61464	0.807319	+	0.590115i	$0.200917\pi$
$444$	−3.32735	−0.157909
$445$	−3.59720	−0.170524
$446$	6.82312	0.323084
$447$	0.170637	0.00807083
$448$	32.0252	1.51305
$449$	10.8215	0.510700	0.255350	−	0.966849i	$-0.417809\pi$
$449$	10.8215	0.510700	0.255350	+	0.966849i	$0.417809\pi$
$450$	−6.74938	−0.318169
$451$	7.56827	0.356376
$452$	−1.47542	−0.0693978
$453$	−26.1569	−1.22896
$454$	4.39179	0.206117
$455$	0	0
$456$	−24.8307	−1.16281
$457$	27.7721	1.29912	0.649562	−	0.760308i	$-0.274952\pi$
$457$	27.7721	1.29912	0.649562	+	0.760308i	$0.274952\pi$
$458$	21.7631	1.01692
$459$	25.4537	1.18808
$460$	−4.55570	−0.212411
$461$	−3.29026	−0.153243	−0.0766214	−	0.997060i	$-0.524413\pi$
$461$	−3.29026	−0.153243	−0.0766214	+	0.997060i	$0.524413\pi$
$462$	−5.31425	−0.247241
$463$	14.1359	0.656950	0.328475	−	0.944513i	$-0.393465\pi$
$463$	14.1359	0.656950	0.328475	+	0.944513i	$0.393465\pi$
$464$	17.8809	0.830100
$465$	−5.28448	−0.245062
$466$	−17.8957	−0.829003
$467$	11.3193	0.523796	0.261898	−	0.965096i	$-0.415652\pi$
$467$	11.3193	0.523796	0.261898	+	0.965096i	$0.415652\pi$
$468$	0	0
$469$	22.7182	1.04903
$470$	−3.60152	−0.166126
$471$	−19.0516	−0.877849
$472$	−22.4260	−1.03224
$473$	−3.03588	−0.139590
$474$	−21.8945	−1.00565
$475$	−25.3108	−1.16134
$476$	−10.4895	−0.480784
$477$	−16.8964	−0.773634
$478$	28.4979	1.30346
$479$	−26.9047	−1.22931	−0.614654	−	0.788797i	$-0.710704\pi$
$479$	−26.9047	−1.22931	−0.614654	+	0.788797i	$0.710704\pi$
$480$	4.41226	0.201391
$481$	0	0
$482$	17.1379	0.780608
$483$	−31.1503	−1.41739
$484$	−0.618298	−0.0281045
$485$	19.3724	0.879653
$486$	16.1117	0.730841
$487$	39.8486	1.80571	0.902856	−	0.429944i	$-0.141467\pi$
$487$	39.8486	1.80571	0.902856	+	0.429944i	$0.141467\pi$
$488$	−6.48632	−0.293622
$489$	1.62214	0.0733559
$490$	−8.20368	−0.370604
$491$	−1.66711	−0.0752356	−0.0376178	−	0.999292i	$-0.511977\pi$
$491$	−1.66711	−0.0752356	−0.0376178	+	0.999292i	$0.511977\pi$
$492$	−5.75226	−0.259332
$493$	−34.6398	−1.56010
$494$	0	0
$495$	1.59221	0.0715646
$496$	−9.57210	−0.429800
$497$	−36.8231	−1.65174
$498$	5.15490	0.230996
$499$	−25.1675	−1.12665	−0.563327	−	0.826234i	$-0.690479\pi$
$499$	−25.1675	−1.12665	−0.563327	+	0.826234i	$0.690479\pi$
$500$	5.85581	0.261880
$501$	−7.98776	−0.356867
$502$	23.9518	1.06902
$503$	10.5616	0.470919	0.235459	−	0.971884i	$-0.424341\pi$
$503$	10.5616	0.470919	0.235459	+	0.971884i	$0.424341\pi$
$504$	−16.8534	−0.750710
$505$	14.0953	0.627233
$506$	8.09906	0.360047
$507$	0	0
$508$	−6.98917	−0.310094
$509$	22.9522	1.01734	0.508670	−	0.860962i	$-0.330137\pi$
$509$	22.9522	1.01734	0.508670	+	0.860962i	$0.330137\pi$
$510$	7.12765	0.315618
$511$	−26.5350	−1.17384
$512$	22.6489	1.00095
$513$	36.2164	1.59899
$514$	2.70708	0.119404
$515$	5.72286	0.252179
$516$	2.30742	0.101578
$517$	−2.86516	−0.126010
$518$	18.9258	0.831552
$519$	−2.74641	−0.120554
$520$	0	0
$521$	21.3081	0.933524	0.466762	−	0.884383i	$-0.345420\pi$
$521$	21.3081	0.933524	0.466762	+	0.884383i	$0.345420\pi$
$522$	−13.1428	−0.575244
$523$	22.0155	0.962671	0.481335	−	0.876536i	$-0.340152\pi$
$523$	22.0155	0.962671	0.481335	+	0.876536i	$0.340152\pi$
$524$	5.35384	0.233884
$525$	17.4350	0.760924
$526$	5.69768	0.248431
$527$	18.5435	0.807770
$528$	−2.92701	−0.127382
$529$	24.4739	1.06408
$530$	−14.2647	−0.619618
$531$	10.8492	0.470814
$532$	−14.9248	−0.647071
$533$	0	0
$534$	−4.86055	−0.210337
$535$	8.99001	0.388672
$536$	19.0112	0.821158
$537$	−15.6986	−0.677444
$538$	−29.5886	−1.27566
$539$	−6.52636	−0.281110
$540$	−3.64850	−0.157006
$541$	−25.7702	−1.10795	−0.553975	−	0.832534i	$-0.686890\pi$
$541$	−25.7702	−1.10795	−0.553975	+	0.832534i	$0.686890\pi$
$542$	−10.4392	−0.448403
$543$	−18.8092	−0.807179
$544$	−15.4829	−0.663824
$545$	13.8271	0.592290
$546$	0	0
$547$	26.4584	1.13128	0.565640	−	0.824652i	$-0.308629\pi$
$547$	26.4584	1.13128	0.565640	+	0.824652i	$0.308629\pi$
$548$	−4.50936	−0.192631
$549$	3.13793	0.133923
$550$	−4.53308	−0.193291
$551$	−49.2866	−2.09968
$552$	−26.0674	−1.10950
$553$	−55.7282	−2.36981
$554$	−22.4770	−0.954956
$555$	5.75481	0.244278
$556$	7.62752	0.323479
$557$	−18.4881	−0.783365	−0.391682	−	0.920100i	$-0.628107\pi$
$557$	−18.4881	−0.783365	−0.391682	+	0.920100i	$0.628107\pi$
$558$	7.03567	0.297844
$559$	0	0
$560$	−9.36484	−0.395737
$561$	5.67034	0.239402
$562$	−0.229961	−0.00970034
$563$	12.2594	0.516673	0.258336	−	0.966055i	$-0.416826\pi$
$563$	12.2594	0.516673	0.258336	+	0.966055i	$0.416826\pi$
$564$	2.17767	0.0916962
$565$	2.55180	0.107355
$566$	11.6857	0.491187
$567$	−8.51920	−0.357773
$568$	−30.8146	−1.29295
$569$	−15.0610	−0.631390	−0.315695	−	0.948861i	$-0.602238\pi$
$569$	−15.0610	−0.631390	−0.315695	+	0.948861i	$0.602238\pi$
$570$	10.1415	0.424779
$571$	30.4829	1.27567	0.637834	−	0.770174i	$-0.279830\pi$
$571$	30.4829	1.27567	0.637834	+	0.770174i	$0.279830\pi$
$572$	0	0
$573$	12.3000	0.513840
$574$	32.7186	1.36565
$575$	−26.5713	−1.10810
$576$	−12.9650	−0.540207
$577$	−46.1063	−1.91943	−0.959715	−	0.280975i	$-0.909342\pi$
$577$	−46.1063	−1.91943	−0.959715	+	0.280975i	$0.909342\pi$
$578$	−5.02858	−0.209161
$579$	−13.3880	−0.556386
$580$	4.96521	0.206169
$581$	13.1208	0.544341
$582$	26.1760	1.08503
$583$	−11.3481	−0.469992
$584$	−22.2052	−0.918858
$585$	0	0
$586$	−3.22426	−0.133193
$587$	−23.9638	−0.989090	−0.494545	−	0.869152i	$-0.664665\pi$
$587$	−23.9638	−0.989090	−0.494545	+	0.869152i	$0.664665\pi$
$588$	4.96036	0.204562
$589$	26.3844	1.08715
$590$	9.15933	0.377084
$591$	−2.96817	−0.122094
$592$	10.4240	0.428426
$593$	−39.1542	−1.60787	−0.803936	−	0.594716i	$-0.797265\pi$
$593$	−39.1542	−1.60787	−0.803936	+	0.594716i	$0.797265\pi$
$594$	6.48624	0.266134
$595$	18.1420	0.743751
$596$	0.0858274	0.00351563
$597$	−0.0629669	−0.00257706
$598$	0	0
$599$	−42.5743	−1.73954	−0.869770	−	0.493457i	$-0.835733\pi$
$599$	−42.5743	−1.73954	−0.869770	+	0.493457i	$0.835733\pi$
$600$	14.5900	0.595636
$601$	44.5295	1.81640	0.908198	−	0.418540i	$-0.137458\pi$
$601$	44.5295	1.81640	0.908198	+	0.418540i	$0.137458\pi$
$602$	−13.1245	−0.534914
$603$	−9.19716	−0.374537
$604$	−13.1565	−0.535331
$605$	1.06938	0.0434763
$606$	19.0456	0.773677
$607$	39.1704	1.58988	0.794939	−	0.606690i	$-0.207503\pi$
$607$	39.1704	1.58988	0.794939	+	0.606690i	$0.207503\pi$
$608$	−22.0296	−0.893417
$609$	33.9504	1.37574
$610$	2.64917	0.107262
$611$	0	0
$612$	4.24653	0.171656
$613$	−6.12204	−0.247267	−0.123633	−	0.992328i	$-0.539455\pi$
$613$	−6.12204	−0.247267	−0.123633	+	0.992328i	$0.539455\pi$
$614$	−34.9306	−1.40969
$615$	9.94881	0.401175
$616$	−11.3192	−0.456065
$617$	8.47140	0.341046	0.170523	−	0.985354i	$-0.445454\pi$
$617$	8.47140	0.341046	0.170523	+	0.985354i	$0.445454\pi$
$618$	7.73275	0.311057
$619$	42.4986	1.70816	0.854082	−	0.520139i	$-0.174120\pi$
$619$	42.4986	1.70816	0.854082	+	0.520139i	$0.174120\pi$
$620$	−2.65801	−0.106748
$621$	38.0201	1.52569
$622$	−14.4472	−0.579280
$623$	−12.3716	−0.495657
$624$	0	0
$625$	9.15428	0.366171
$626$	0.985952	0.0394066
$627$	8.06795	0.322203
$628$	−9.58262	−0.382388
$629$	−20.1940	−0.805186
$630$	6.88333	0.274238
$631$	34.2480	1.36339	0.681696	−	0.731636i	$-0.261243\pi$
$631$	34.2480	1.36339	0.681696	+	0.731636i	$0.261243\pi$
$632$	−46.6349	−1.85504
$633$	−31.5567	−1.25427
$634$	4.25581	0.169020
$635$	12.0881	0.479701
$636$	8.62515	0.342009
$637$	0	0
$638$	−8.82708	−0.349467
$639$	14.9074	0.589726
$640$	−3.76685	−0.148898
$641$	14.6005	0.576685	0.288342	−	0.957527i	$-0.406896\pi$
$641$	14.6005	0.576685	0.288342	+	0.957527i	$0.406896\pi$
$642$	12.1473	0.479418
$643$	−1.58929	−0.0626756	−0.0313378	−	0.999509i	$-0.509977\pi$
$643$	−1.58929	−0.0626756	−0.0313378	+	0.999509i	$0.509977\pi$
$644$	−15.6681	−0.617409
$645$	−3.99079	−0.157137
$646$	−35.5870	−1.40015
$647$	−15.5801	−0.612516	−0.306258	−	0.951949i	$-0.599077\pi$
$647$	−15.5801	−0.612516	−0.306258	+	0.951949i	$0.599077\pi$
$648$	−7.12910	−0.280057
$649$	7.28662	0.286025
$650$	0	0
$651$	−18.1745	−0.712315
$652$	0.815912	0.0319536
$653$	−47.8185	−1.87128	−0.935642	−	0.352951i	$-0.885178\pi$
$653$	−47.8185	−1.87128	−0.935642	+	0.352951i	$0.885178\pi$
$654$	18.6833	0.730575
$655$	−9.25972	−0.361807
$656$	18.0209	0.703598
$657$	10.7424	0.419099
$658$	−12.3864	−0.482874
$659$	−16.8762	−0.657405	−0.328703	−	0.944433i	$-0.606611\pi$
$659$	−16.8762	−0.657405	−0.328703	+	0.944433i	$0.606611\pi$
$660$	−0.812779	−0.0316374
$661$	−12.4198	−0.483073	−0.241537	−	0.970392i	$-0.577651\pi$
$661$	−12.4198	−0.483073	−0.241537	+	0.970392i	$0.577651\pi$
$662$	2.46009	0.0956139
$663$	0	0
$664$	10.9798	0.426099
$665$	25.8131	1.00099
$666$	−7.66186	−0.296891
$667$	−51.7413	−2.00343
$668$	−4.01771	−0.155450
$669$	7.13542	0.275871
$670$	−7.76462	−0.299974
$671$	2.10752	0.0813600
$672$	15.1748	0.585379
$673$	1.62677	0.0627072	0.0313536	−	0.999508i	$-0.490018\pi$
$673$	1.62677	0.0627072	0.0313536	+	0.999508i	$0.490018\pi$
$674$	−25.6560	−0.988232
$675$	−21.2800	−0.819068
$676$	0	0
$677$	−21.9960	−0.845377	−0.422688	−	0.906275i	$-0.638914\pi$
$677$	−21.9960	−0.845377	−0.422688	+	0.906275i	$0.638914\pi$
$678$	3.44801	0.132420
$679$	66.6258	2.55687
$680$	15.1817	0.582193
$681$	4.59281	0.175997
$682$	4.72536	0.180943
$683$	15.2134	0.582123	0.291061	−	0.956704i	$-0.405992\pi$
$683$	15.2134	0.582123	0.291061	+	0.956704i	$0.405992\pi$
$684$	6.04210	0.231025
$685$	7.79916	0.297990
$686$	2.04759	0.0781772
$687$	22.7593	0.868320
$688$	−7.22876	−0.275594
$689$	0	0
$690$	10.6465	0.405307
$691$	−31.9585	−1.21576	−0.607879	−	0.794029i	$-0.707980\pi$
$691$	−31.9585	−1.21576	−0.607879	+	0.794029i	$0.707980\pi$
$692$	−1.38140	−0.0525129
$693$	5.47597	0.208015
$694$	35.1177	1.33305
$695$	−13.1921	−0.500407
$696$	28.4106	1.07690
$697$	−34.9110	−1.32235
$698$	−3.20721	−0.121395
$699$	−18.7148	−0.707860
$700$	8.76950	0.331456
$701$	−40.6598	−1.53570	−0.767850	−	0.640630i	$-0.778673\pi$
$701$	−40.6598	−1.53570	−0.767850	+	0.640630i	$0.778673\pi$
$702$	0	0
$703$	−28.7327	−1.08367
$704$	−8.70765	−0.328182
$705$	−3.76637	−0.141850
$706$	39.0091	1.46813
$707$	48.4769	1.82316
$708$	−5.53820	−0.208138
$709$	−41.0918	−1.54324	−0.771618	−	0.636087i	$-0.780552\pi$
$709$	−41.0918	−1.54324	−0.771618	+	0.636087i	$0.780552\pi$
$710$	12.5854	0.472322
$711$	22.5608	0.846098
$712$	−10.3529	−0.387990
$713$	27.6984	1.03731
$714$	24.5136	0.917398
$715$	0	0
$716$	−7.89613	−0.295092
$717$	29.8023	1.11299
$718$	26.0066	0.970558
$719$	18.1968	0.678628	0.339314	−	0.940673i	$-0.389805\pi$
$719$	18.1968	0.678628	0.339314	+	0.940673i	$0.389805\pi$
$720$	3.79123	0.141291
$721$	19.6822	0.733003
$722$	−28.3007	−1.05324
$723$	17.9223	0.666537
$724$	−9.46071	−0.351605
$725$	28.9598	1.07554
$726$	1.44494	0.0536269
$727$	20.6633	0.766360	0.383180	−	0.923674i	$-0.374829\pi$
$727$	20.6633	0.766360	0.383180	+	0.923674i	$0.374829\pi$
$728$	0	0
$729$	23.7983	0.881417
$730$	9.06914	0.335664
$731$	14.0039	0.517953
$732$	−1.60182	−0.0592050
$733$	19.0258	0.702736	0.351368	−	0.936237i	$-0.385717\pi$
$733$	19.0258	0.702736	0.351368	+	0.936237i	$0.385717\pi$
$734$	31.6989	1.17003
$735$	−8.57918	−0.316448
$736$	−23.1267	−0.852463
$737$	−6.17708	−0.227536
$738$	−13.2457	−0.487580
$739$	8.63479	0.317636	0.158818	−	0.987308i	$-0.449232\pi$
$739$	8.63479	0.317636	0.158818	+	0.987308i	$0.449232\pi$
$740$	2.89458	0.106407
$741$	0	0
$742$	−49.0594	−1.80103
$743$	−11.9479	−0.438326	−0.219163	−	0.975688i	$-0.570333\pi$
$743$	−11.9479	−0.438326	−0.219163	+	0.975688i	$0.570333\pi$
$744$	−15.2089	−0.557586
$745$	−0.148442	−0.00543851
$746$	22.9116	0.838852
$747$	−5.31177	−0.194347
$748$	2.85209	0.104283
$749$	30.9187	1.12974
$750$	−13.6849	−0.499701
$751$	15.8146	0.577084	0.288542	−	0.957467i	$-0.406830\pi$
$751$	15.8146	0.577084	0.288542	+	0.957467i	$0.406830\pi$
$752$	−6.82227	−0.248782
$753$	25.0481	0.912804
$754$	0	0
$755$	22.7548	0.828131
$756$	−12.5480	−0.456366
$757$	23.7363	0.862711	0.431356	−	0.902182i	$-0.358035\pi$
$757$	23.7363	0.862711	0.431356	+	0.902182i	$0.358035\pi$
$758$	−42.1556	−1.53116
$759$	8.46977	0.307433
$760$	21.6011	0.783554
$761$	32.2561	1.16928	0.584641	−	0.811292i	$-0.301235\pi$
$761$	32.2561	1.16928	0.584641	+	0.811292i	$0.301235\pi$
$762$	16.3335	0.591700
$763$	47.5546	1.72159
$764$	6.18670	0.223827
$765$	−7.34456	−0.265543
$766$	35.4777	1.28186
$767$	0	0
$768$	16.3182	0.588831
$769$	7.48171	0.269797	0.134899	−	0.990859i	$-0.456929\pi$
$769$	7.48171	0.269797	0.134899	+	0.990859i	$0.456929\pi$
$770$	4.62304	0.166603
$771$	2.83099	0.101956
$772$	−6.73394	−0.242360
$773$	−10.9110	−0.392442	−0.196221	−	0.980560i	$-0.562867\pi$
$773$	−10.9110	−0.392442	−0.196221	+	0.980560i	$0.562867\pi$
$774$	5.31327	0.190982
$775$	−15.5029	−0.556882
$776$	55.7543	2.00146
$777$	19.7921	0.710037
$778$	−29.1415	−1.04477
$779$	−49.6725	−1.77970
$780$	0	0
$781$	10.0122	0.358265
$782$	−37.3594	−1.33597
$783$	−41.4377	−1.48086
$784$	−15.5400	−0.555000
$785$	16.5736	0.591537
$786$	−12.5118	−0.446280
$787$	7.03953	0.250932	0.125466	−	0.992098i	$-0.459957\pi$
$787$	7.03953	0.250932	0.125466	+	0.992098i	$0.459957\pi$
$788$	−1.49294	−0.0531837
$789$	5.95848	0.212127
$790$	19.0468	0.677655
$791$	8.77622	0.312046
$792$	4.58244	0.162830
$793$	0	0
$794$	−31.1755	−1.10638
$795$	−14.9176	−0.529072
$796$	−0.0316713	−0.00112256
$797$	48.7730	1.72763	0.863815	−	0.503810i	$-0.168069\pi$
$797$	48.7730	1.72763	0.863815	+	0.503810i	$0.168069\pi$
$798$	34.8787	1.23469
$799$	13.2164	0.467564
$800$	12.9441	0.457645
$801$	5.00847	0.176966
$802$	12.8622	0.454180
$803$	7.21487	0.254607
$804$	4.69489	0.165576
$805$	27.0987	0.955103
$806$	0	0
$807$	−30.9429	−1.08924
$808$	40.5668	1.42713
$809$	−1.73025	−0.0608323	−0.0304161	−	0.999537i	$-0.509683\pi$
$809$	−1.73025	−0.0608323	−0.0304161	+	0.999537i	$0.509683\pi$
$810$	2.91169	0.102307
$811$	24.2221	0.850555	0.425277	−	0.905063i	$-0.360177\pi$
$811$	24.2221	0.850555	0.425277	+	0.905063i	$0.360177\pi$
$812$	17.0765	0.599267
$813$	−10.9170	−0.382877
$814$	−5.14593	−0.180365
$815$	−1.41116	−0.0494307
$816$	13.5017	0.472654
$817$	19.9252	0.697095
$818$	38.6575	1.35163
$819$	0	0
$820$	5.00409	0.174750
$821$	−13.5810	−0.473980	−0.236990	−	0.971512i	$-0.576161\pi$
$821$	−13.5810	−0.473980	−0.236990	+	0.971512i	$0.576161\pi$
$822$	10.5383	0.367564
$823$	−27.9238	−0.973361	−0.486681	−	0.873580i	$-0.661792\pi$
$823$	−27.9238	−0.973361	−0.486681	+	0.873580i	$0.661792\pi$
$824$	16.4706	0.573780
$825$	−4.74057	−0.165045
$826$	31.5010	1.09606
$827$	−40.2312	−1.39897	−0.699487	−	0.714645i	$-0.746588\pi$
$827$	−40.2312	−1.39897	−0.699487	+	0.714645i	$0.746588\pi$
$828$	6.34302	0.220435
$829$	31.1538	1.08201	0.541007	−	0.841018i	$-0.318043\pi$
$829$	31.1538	1.08201	0.541007	+	0.841018i	$0.318043\pi$
$830$	−4.48442	−0.155656
$831$	−23.5058	−0.815408
$832$	0	0
$833$	30.1048	1.04307
$834$	−17.8253	−0.617239
$835$	6.94882	0.240474
$836$	4.05805	0.140350
$837$	22.1826	0.766744
$838$	−12.2868	−0.424439
$839$	−29.6198	−1.02259	−0.511295	−	0.859405i	$-0.670834\pi$
$839$	−29.6198	−1.02259	−0.511295	+	0.859405i	$0.670834\pi$
$840$	−14.8796	−0.513395
$841$	27.3922	0.944560
$842$	16.4141	0.565669
$843$	−0.240487	−0.00828282
$844$	−15.8725	−0.546354
$845$	0	0
$846$	5.01449	0.172402
$847$	3.67782	0.126371
$848$	−27.0212	−0.927910
$849$	12.2206	0.419409
$850$	20.9102	0.717214
$851$	−30.1637	−1.03400
$852$	−7.60979	−0.260707
$853$	−15.9816	−0.547201	−0.273600	−	0.961843i	$-0.588215\pi$
$853$	−15.9816	−0.547201	−0.273600	+	0.961843i	$0.588215\pi$
$854$	9.11108	0.311775
$855$	−10.4501	−0.357385
$856$	25.8736	0.884341
$857$	−43.4613	−1.48461	−0.742304	−	0.670063i	$-0.766267\pi$
$857$	−43.4613	−1.48461	−0.742304	+	0.670063i	$0.766267\pi$
$858$	0	0
$859$	−12.6283	−0.430873	−0.215436	−	0.976518i	$-0.569117\pi$
$859$	−12.6283	−0.430873	−0.215436	+	0.976518i	$0.569117\pi$
$860$	−2.00730	−0.0684484
$861$	34.2162	1.16608
$862$	13.3021	0.453071
$863$	1.60745	0.0547183	0.0273592	−	0.999626i	$-0.491290\pi$
$863$	1.60745	0.0547183	0.0273592	+	0.999626i	$0.491290\pi$
$864$	−18.5214	−0.630109
$865$	2.38919	0.0812351
$866$	41.9262	1.42471
$867$	−5.25874	−0.178596
$868$	−9.14147	−0.310282
$869$	15.1525	0.514014
$870$	−11.6036	−0.393397
$871$	0	0
$872$	39.7950	1.34763
$873$	−26.9726	−0.912884
$874$	−53.1562	−1.79803
$875$	−34.8321	−1.17754
$876$	−5.48366	−0.185276
$877$	−29.9609	−1.01171	−0.505854	−	0.862619i	$-0.668823\pi$
$877$	−29.9609	−1.01171	−0.505854	+	0.862619i	$0.668823\pi$
$878$	−15.5925	−0.526220
$879$	−3.37184	−0.113729
$880$	2.54630	0.0858358
$881$	−21.5314	−0.725413	−0.362706	−	0.931903i	$-0.618147\pi$
$881$	−21.5314	−0.725413	−0.362706	+	0.931903i	$0.618147\pi$
$882$	11.4222	0.384605
$883$	−18.9850	−0.638897	−0.319449	−	0.947604i	$-0.603498\pi$
$883$	−18.9850	−0.638897	−0.319449	+	0.947604i	$0.603498\pi$
$884$	0	0
$885$	9.57857	0.321980
$886$	−39.9470	−1.34205
$887$	20.3848	0.684454	0.342227	−	0.939617i	$-0.388819\pi$
$887$	20.3848	0.684454	0.342227	+	0.939617i	$0.388819\pi$
$888$	16.5625	0.555803
$889$	41.5736	1.39434
$890$	4.22836	0.141735
$891$	2.31637	0.0776014
$892$	3.58900	0.120169
$893$	18.8048	0.629278
$894$	−0.200576	−0.00670827
$895$	13.6567	0.456494
$896$	−12.9550	−0.432797
$897$	0	0
$898$	−12.7203	−0.424481
$899$	−30.1882	−1.00683
$900$	−3.55022	−0.118341
$901$	52.3467	1.74392
$902$	−8.89618	−0.296211
$903$	−13.7252	−0.456746
$904$	7.34418	0.244264
$905$	16.3627	0.543916
$906$	30.7464	1.02148
$907$	−45.1311	−1.49855	−0.749277	−	0.662257i	$-0.769599\pi$
$907$	−45.1311	−1.49855	−0.749277	+	0.662257i	$0.769599\pi$
$908$	2.31011	0.0766636
$909$	−19.6252	−0.650928
$910$	0	0
$911$	−48.3701	−1.60257	−0.801287	−	0.598281i	$-0.795851\pi$
$911$	−48.3701	−1.60257	−0.801287	+	0.598281i	$0.795851\pi$
$912$	19.2107	0.636129
$913$	−3.56754	−0.118068
$914$	−32.6449	−1.07980
$915$	2.77043	0.0915874
$916$	11.4475	0.378237
$917$	−31.8462	−1.05166
$918$	−29.9198	−0.987499
$919$	−13.2762	−0.437942	−0.218971	−	0.975731i	$-0.570270\pi$
$919$	−13.2762	−0.437942	−0.218971	+	0.975731i	$0.570270\pi$
$920$	22.6769	0.747636
$921$	−36.5295	−1.20369
$922$	3.86757	0.127372
$923$	0	0
$924$	−2.79533	−0.0919595
$925$	16.8827	0.555101
$926$	−16.6161	−0.546040
$927$	−7.96808	−0.261706
$928$	25.2056	0.827414
$929$	−7.34338	−0.240929	−0.120464	−	0.992718i	$-0.538438\pi$
$929$	−7.34338	−0.240929	−0.120464	+	0.992718i	$0.538438\pi$
$930$	6.21168	0.203689
$931$	42.8342	1.40383
$932$	−9.41325	−0.308341
$933$	−15.1085	−0.494629
$934$	−13.3054	−0.435366
$935$	−4.93282	−0.161320
$936$	0	0
$937$	−0.746195	−0.0243771	−0.0121886	−	0.999926i	$-0.503880\pi$
$937$	−0.746195	−0.0243771	−0.0121886	+	0.999926i	$0.503880\pi$
$938$	−26.7043	−0.871925
$939$	1.03108	0.0336481
$940$	−1.89442	−0.0617893
$941$	−9.19693	−0.299811	−0.149906	−	0.988700i	$-0.547897\pi$
$941$	−9.19693	−0.299811	−0.149906	+	0.988700i	$0.547897\pi$
$942$	22.3943	0.729646
$943$	−52.1464	−1.69812
$944$	17.3503	0.564703
$945$	21.7023	0.705977
$946$	3.56855	0.116023
$947$	−6.18127	−0.200864	−0.100432	−	0.994944i	$-0.532023\pi$
$947$	−6.18127	−0.200864	−0.100432	+	0.994944i	$0.532023\pi$
$948$	−11.5167	−0.374044
$949$	0	0
$950$	29.7517	0.965274
$951$	4.45061	0.144321
$952$	52.2134	1.69225
$953$	9.60309	0.311074	0.155537	−	0.987830i	$-0.450289\pi$
$953$	9.60309	0.311074	0.155537	+	0.987830i	$0.450289\pi$
$954$	19.8610	0.643025
$955$	−10.7002	−0.346250
$956$	14.9901	0.484814
$957$	−9.23111	−0.298399
$958$	31.6254	1.02177
$959$	26.8230	0.866161
$960$	−11.4466	−0.369436
$961$	−14.8395	−0.478693
$962$	0	0
$963$	−12.5170	−0.403355
$964$	9.01462	0.290341
$965$	11.6467	0.374919
$966$	36.6159	1.17810
$967$	1.44208	0.0463741	0.0231871	−	0.999731i	$-0.492619\pi$
$967$	1.44208	0.0463741	0.0231871	+	0.999731i	$0.492619\pi$
$968$	3.07770	0.0989210
$969$	−37.2159	−1.19555
$970$	−22.7714	−0.731145
$971$	−1.61534	−0.0518388	−0.0259194	−	0.999664i	$-0.508251\pi$
$971$	−1.61534	−0.0518388	−0.0259194	+	0.999664i	$0.508251\pi$
$972$	8.47484	0.271831
$973$	−45.3707	−1.45452
$974$	−46.8403	−1.50086
$975$	0	0
$976$	5.01824	0.160630
$977$	32.0531	1.02547	0.512734	−	0.858547i	$-0.328633\pi$
$977$	32.0531	1.02547	0.512734	+	0.858547i	$0.328633\pi$
$978$	−1.90676	−0.0609716
$979$	3.36383	0.107509
$980$	−4.31519	−0.137844
$981$	−19.2519	−0.614665
$982$	1.95962	0.0625339
$983$	−11.4865	−0.366362	−0.183181	−	0.983079i	$-0.558639\pi$
$983$	−11.4865	−0.366362	−0.183181	+	0.983079i	$0.558639\pi$
$984$	28.6330	0.912787
$985$	2.58211	0.0822728
$986$	40.7176	1.29671
$987$	−12.9534	−0.412311
$988$	0	0
$989$	20.9176	0.665140
$990$	−1.87158	−0.0594827
$991$	−8.32889	−0.264576	−0.132288	−	0.991211i	$-0.542232\pi$
$991$	−8.32889	−0.264576	−0.132288	+	0.991211i	$0.542232\pi$
$992$	−13.4932	−0.428409
$993$	2.57269	0.0816418
$994$	43.2841	1.37289
$995$	0.0547770	0.00173655
$996$	2.71151	0.0859174
$997$	3.85545	0.122103	0.0610517	−	0.998135i	$-0.480555\pi$
$997$	3.85545	0.122103	0.0610517	+	0.998135i	$0.480555\pi$
$998$	29.5834	0.936446
$999$	−24.1570	−0.764293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.8	✓	21
13.12	even	2		1859.2.a.t.1.14	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.8	✓	21	1.1	even	1	trivial
1859.2.a.t.1.14	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)

\(f(q)\)	\(=\)	\(q-1.17546 q^{2} -1.22926 q^{3} -0.618298 q^{4} +1.06938 q^{5} +1.44494 q^{6} +3.67782 q^{7} +3.07770 q^{8} -1.48892 q^{9} +O(q^{10})\)	\(q-1.17546 q^{2} -1.22926 q^{3} -0.618298 q^{4} +1.06938 q^{5} +1.44494 q^{6} +3.67782 q^{7} +3.07770 q^{8} -1.48892 q^{9} -1.25701 q^{10} -1.00000 q^{11} +0.760050 q^{12} -4.32312 q^{14} -1.31454 q^{15} -2.38111 q^{16} +4.61281 q^{17} +1.75016 q^{18} +6.56325 q^{19} -0.661193 q^{20} -4.52100 q^{21} +1.17546 q^{22} +6.89013 q^{23} -3.78330 q^{24} -3.85644 q^{25} +5.51805 q^{27} -2.27399 q^{28} -7.50948 q^{29} +1.54519 q^{30} +4.02002 q^{31} -3.35650 q^{32} +1.22926 q^{33} -5.42216 q^{34} +3.93297 q^{35} +0.920595 q^{36} -4.37781 q^{37} -7.71483 q^{38} +3.29122 q^{40} -7.56827 q^{41} +5.31425 q^{42} +3.03588 q^{43} +0.618298 q^{44} -1.59221 q^{45} -8.09906 q^{46} +2.86516 q^{47} +2.92701 q^{48} +6.52636 q^{49} +4.53308 q^{50} -5.67034 q^{51} +11.3481 q^{53} -6.48624 q^{54} -1.06938 q^{55} +11.3192 q^{56} -8.06795 q^{57} +8.82708 q^{58} -7.28662 q^{59} +0.812779 q^{60} -2.10752 q^{61} -4.72536 q^{62} -5.47597 q^{63} +8.70765 q^{64} -1.44494 q^{66} +6.17708 q^{67} -2.85209 q^{68} -8.46977 q^{69} -4.62304 q^{70} -10.0122 q^{71} -4.58244 q^{72} -7.21487 q^{73} +5.14593 q^{74} +4.74057 q^{75} -4.05805 q^{76} -3.67782 q^{77} -15.1525 q^{79} -2.54630 q^{80} -2.31637 q^{81} +8.89618 q^{82} +3.56754 q^{83} +2.79533 q^{84} +4.93282 q^{85} -3.56855 q^{86} +9.23111 q^{87} -3.07770 q^{88} -3.36383 q^{89} +1.87158 q^{90} -4.26015 q^{92} -4.94165 q^{93} -3.36788 q^{94} +7.01858 q^{95} +4.12602 q^{96} +18.1156 q^{97} -7.67147 q^{98} +1.48892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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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