LMFDB - Embedded newform 6027.2.a.bo.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.64420 q^{2} +1.00000 q^{3} +0.703405 q^{4} +3.28206 q^{5} +1.64420 q^{6} -2.13187 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.64420 q^{2} +1.00000 q^{3} +0.703405 q^{4} +3.28206 q^{5} +1.64420 q^{6} -2.13187 q^{8} +1.00000 q^{9} +5.39638 q^{10} -3.35789 q^{11} +0.703405 q^{12} +5.75857 q^{13} +3.28206 q^{15} -4.91203 q^{16} +6.12943 q^{17} +1.64420 q^{18} +3.14030 q^{19} +2.30862 q^{20} -5.52106 q^{22} -9.17799 q^{23} -2.13187 q^{24} +5.77193 q^{25} +9.46827 q^{26} +1.00000 q^{27} +0.986050 q^{29} +5.39638 q^{30} -4.50254 q^{31} -3.81265 q^{32} -3.35789 q^{33} +10.0780 q^{34} +0.703405 q^{36} +11.7958 q^{37} +5.16329 q^{38} +5.75857 q^{39} -6.99692 q^{40} -1.00000 q^{41} +7.67969 q^{43} -2.36196 q^{44} +3.28206 q^{45} -15.0905 q^{46} +12.0154 q^{47} -4.91203 q^{48} +9.49023 q^{50} +6.12943 q^{51} +4.05061 q^{52} -2.61317 q^{53} +1.64420 q^{54} -11.0208 q^{55} +3.14030 q^{57} +1.62127 q^{58} +11.2245 q^{59} +2.30862 q^{60} +1.80269 q^{61} -7.40309 q^{62} +3.55530 q^{64} +18.9000 q^{65} -5.52106 q^{66} -13.1550 q^{67} +4.31147 q^{68} -9.17799 q^{69} -5.92317 q^{71} -2.13187 q^{72} -9.66466 q^{73} +19.3947 q^{74} +5.77193 q^{75} +2.20890 q^{76} +9.46827 q^{78} -8.44944 q^{79} -16.1216 q^{80} +1.00000 q^{81} -1.64420 q^{82} +5.92934 q^{83} +20.1172 q^{85} +12.6270 q^{86} +0.986050 q^{87} +7.15857 q^{88} +11.3923 q^{89} +5.39638 q^{90} -6.45584 q^{92} -4.50254 q^{93} +19.7557 q^{94} +10.3067 q^{95} -3.81265 q^{96} -11.7824 q^{97} -3.35789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * 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 $

$2$	1.64420	1.16263	0.581314	−	0.813680i	$-0.302539\pi$
$2$	1.64420	1.16263	0.581314	+	0.813680i	$0.302539\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.703405	0.351702
$5$	3.28206	1.46778	0.733891	−	0.679267i	$-0.237702\pi$
$5$	3.28206	1.46778	0.733891	+	0.679267i	$0.237702\pi$
$6$	1.64420	0.671243
$7$	0	0
$7$	0	0
$8$	−2.13187	−0.753729
$9$	1.00000	0.333333
$10$	5.39638	1.70648
$11$	−3.35789	−1.01244	−0.506221	−	0.862404i	$-0.668958\pi$
$11$	−3.35789	−1.01244	−0.506221	+	0.862404i	$0.668958\pi$
$12$	0.703405	0.203055
$13$	5.75857	1.59714	0.798571	−	0.601901i	$-0.205590\pi$
$13$	5.75857	1.59714	0.798571	+	0.601901i	$0.205590\pi$
$14$	0	0
$15$	3.28206	0.847425
$16$	−4.91203	−1.22801
$17$	6.12943	1.48661	0.743303	−	0.668955i	$-0.233258\pi$
$17$	6.12943	1.48661	0.743303	+	0.668955i	$0.233258\pi$
$18$	1.64420	0.387542
$19$	3.14030	0.720434	0.360217	−	0.932869i	$-0.382703\pi$
$19$	3.14030	0.720434	0.360217	+	0.932869i	$0.382703\pi$
$20$	2.30862	0.516223
$21$	0	0
$22$	−5.52106	−1.17709
$23$	−9.17799	−1.91374	−0.956871	−	0.290512i	$-0.906174\pi$
$23$	−9.17799	−1.91374	−0.956871	+	0.290512i	$0.906174\pi$
$24$	−2.13187	−0.435165
$25$	5.77193	1.15439
$26$	9.46827	1.85688
$27$	1.00000	0.192450
$28$	0	0
$29$	0.986050	0.183105	0.0915524	−	0.995800i	$-0.470817\pi$
$29$	0.986050	0.183105	0.0915524	+	0.995800i	$0.470817\pi$
$30$	5.39638	0.985239
$31$	−4.50254	−0.808680	−0.404340	−	0.914609i	$-0.632499\pi$
$31$	−4.50254	−0.808680	−0.404340	+	0.914609i	$0.632499\pi$
$32$	−3.81265	−0.673987
$33$	−3.35789	−0.584534
$34$	10.0780	1.72837
$35$	0	0
$36$	0.703405	0.117234
$37$	11.7958	1.93922	0.969611	−	0.244651i	$-0.0786733\pi$
$37$	11.7958	1.93922	0.969611	+	0.244651i	$0.0786733\pi$
$38$	5.16329	0.837596
$39$	5.75857	0.922110
$40$	−6.99692	−1.10631
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	7.67969	1.17114	0.585571	−	0.810621i	$-0.300870\pi$
$43$	7.67969	1.17114	0.585571	+	0.810621i	$0.300870\pi$
$44$	−2.36196	−0.356078
$45$	3.28206	0.489261
$46$	−15.0905	−2.22497
$47$	12.0154	1.75262	0.876311	−	0.481746i	$-0.159997\pi$
$47$	12.0154	1.75262	0.876311	+	0.481746i	$0.159997\pi$
$48$	−4.91203	−0.708991
$49$	0	0
$50$	9.49023	1.34212
$51$	6.12943	0.858292
$52$	4.05061	0.561718
$53$	−2.61317	−0.358947	−0.179473	−	0.983763i	$-0.557439\pi$
$53$	−2.61317	−0.358947	−0.179473	+	0.983763i	$0.557439\pi$
$54$	1.64420	0.223748
$55$	−11.0208	−1.48605
$56$	0	0
$57$	3.14030	0.415943
$58$	1.62127	0.212883
$59$	11.2245	1.46131	0.730654	−	0.682748i	$-0.239215\pi$
$59$	11.2245	1.46131	0.730654	+	0.682748i	$0.239215\pi$
$60$	2.30862	0.298041
$61$	1.80269	0.230810	0.115405	−	0.993319i	$-0.463183\pi$
$61$	1.80269	0.230810	0.115405	+	0.993319i	$0.463183\pi$
$62$	−7.40309	−0.940194
$63$	0	0
$64$	3.55530	0.444412
$65$	18.9000	2.34426
$66$	−5.52106	−0.679595
$67$	−13.1550	−1.60714	−0.803571	−	0.595209i	$-0.797069\pi$
$67$	−13.1550	−1.60714	−0.803571	+	0.595209i	$0.797069\pi$
$68$	4.31147	0.522843
$69$	−9.17799	−1.10490
$70$	0	0
$71$	−5.92317	−0.702951	−0.351475	−	0.936197i	$-0.614320\pi$
$71$	−5.92317	−0.702951	−0.351475	+	0.936197i	$0.614320\pi$
$72$	−2.13187	−0.251243
$73$	−9.66466	−1.13116	−0.565581	−	0.824692i	$-0.691348\pi$
$73$	−9.66466	−1.13116	−0.565581	+	0.824692i	$0.691348\pi$
$74$	19.3947	2.25459
$75$	5.77193	0.666485
$76$	2.20890	0.253378
$77$	0	0
$78$	9.46827	1.07207
$79$	−8.44944	−0.950637	−0.475318	−	0.879814i	$-0.657667\pi$
$79$	−8.44944	−0.950637	−0.475318	+	0.879814i	$0.657667\pi$
$80$	−16.1216	−1.80245
$81$	1.00000	0.111111
$82$	−1.64420	−0.181572
$83$	5.92934	0.650830	0.325415	−	0.945571i	$-0.394496\pi$
$83$	5.92934	0.650830	0.325415	+	0.945571i	$0.394496\pi$
$84$	0	0
$85$	20.1172	2.18201
$86$	12.6270	1.36160
$87$	0.986050	0.105716
$88$	7.15857	0.763107
$89$	11.3923	1.20758	0.603788	−	0.797145i	$-0.293657\pi$
$89$	11.3923	1.20758	0.603788	+	0.797145i	$0.293657\pi$
$90$	5.39638	0.568828
$91$	0	0
$92$	−6.45584	−0.673068
$93$	−4.50254	−0.466892
$94$	19.7557	2.03765
$95$	10.3067	1.05744
$96$	−3.81265	−0.389127
$97$	−11.7824	−1.19632	−0.598160	−	0.801377i	$-0.704101\pi$
$97$	−11.7824	−1.19632	−0.598160	+	0.801377i	$0.704101\pi$
$98$	0	0
$99$	−3.35789	−0.337481
$100$	4.06001	0.406001
$101$	−4.37589	−0.435417	−0.217708	−	0.976014i	$-0.569858\pi$
$101$	−4.37589	−0.435417	−0.217708	+	0.976014i	$0.569858\pi$
$102$	10.0780	0.997874
$103$	7.57841	0.746723	0.373361	−	0.927686i	$-0.378205\pi$
$103$	7.57841	0.746723	0.373361	+	0.927686i	$0.378205\pi$
$104$	−12.2765	−1.20381
$105$	0	0
$106$	−4.29659	−0.417321
$107$	20.3029	1.96276	0.981380	−	0.192078i	$-0.0615226\pi$
$107$	20.3029	1.96276	0.981380	+	0.192078i	$0.0615226\pi$
$108$	0.703405	0.0676852
$109$	−6.23589	−0.597290	−0.298645	−	0.954364i	$-0.596535\pi$
$109$	−6.23589	−0.597290	−0.298645	+	0.954364i	$0.596535\pi$
$110$	−18.1204	−1.72772
$111$	11.7958	1.11961
$112$	0	0
$113$	−3.17038	−0.298245	−0.149122	−	0.988819i	$-0.547645\pi$
$113$	−3.17038	−0.298245	−0.149122	+	0.988819i	$0.547645\pi$
$114$	5.16329	0.483586
$115$	−30.1227	−2.80896
$116$	0.693592	0.0643984
$117$	5.75857	0.532380
$118$	18.4554	1.69896
$119$	0	0
$120$	−6.99692	−0.638728
$121$	0.275433	0.0250393
$122$	2.96398	0.268346
$123$	−1.00000	−0.0901670
$124$	−3.16711	−0.284415
$125$	2.53353	0.226606
$126$	0	0
$127$	8.07325	0.716385	0.358193	−	0.933648i	$-0.383393\pi$
$127$	8.07325	0.716385	0.358193	+	0.933648i	$0.383393\pi$
$128$	13.4709	1.19067
$129$	7.67969	0.676159
$130$	31.0754	2.72550
$131$	−9.14130	−0.798679	−0.399340	−	0.916803i	$-0.630761\pi$
$131$	−9.14130	−0.798679	−0.399340	+	0.916803i	$0.630761\pi$
$132$	−2.36196	−0.205582
$133$	0	0
$134$	−21.6295	−1.86851
$135$	3.28206	0.282475
$136$	−13.0671	−1.12050
$137$	−6.53936	−0.558695	−0.279348	−	0.960190i	$-0.590118\pi$
$137$	−6.53936	−0.558695	−0.279348	+	0.960190i	$0.590118\pi$
$138$	−15.0905	−1.28459
$139$	8.98420	0.762030	0.381015	−	0.924569i	$-0.375575\pi$
$139$	8.98420	0.762030	0.381015	+	0.924569i	$0.375575\pi$
$140$	0	0
$141$	12.0154	1.01188
$142$	−9.73890	−0.817270
$143$	−19.3367	−1.61701
$144$	−4.91203	−0.409336
$145$	3.23628	0.268758
$146$	−15.8907	−1.31512
$147$	0	0
$148$	8.29724	0.682029
$149$	0.272952	0.0223611	0.0111805	−	0.999937i	$-0.496441\pi$
$149$	0.272952	0.0223611	0.0111805	+	0.999937i	$0.496441\pi$
$150$	9.49023	0.774874
$151$	−6.62811	−0.539388	−0.269694	−	0.962946i	$-0.586923\pi$
$151$	−6.62811	−0.539388	−0.269694	+	0.962946i	$0.586923\pi$
$152$	−6.69470	−0.543011
$153$	6.12943	0.495535
$154$	0	0
$155$	−14.7776	−1.18697
$156$	4.05061	0.324308
$157$	23.3131	1.86058	0.930292	−	0.366819i	$-0.119553\pi$
$157$	23.3131	1.86058	0.930292	+	0.366819i	$0.119553\pi$
$158$	−13.8926	−1.10524
$159$	−2.61317	−0.207238
$160$	−12.5133	−0.989266
$161$	0	0
$162$	1.64420	0.129181
$163$	−21.0309	−1.64727	−0.823634	−	0.567122i	$-0.808057\pi$
$163$	−21.0309	−1.64727	−0.823634	+	0.567122i	$0.808057\pi$
$164$	−0.703405	−0.0549267
$165$	−11.0208	−0.857969
$166$	9.74905	0.756673
$167$	−3.40709	−0.263648	−0.131824	−	0.991273i	$-0.542083\pi$
$167$	−3.40709	−0.263648	−0.131824	+	0.991273i	$0.542083\pi$
$168$	0	0
$169$	20.1612	1.55086
$170$	33.0767	2.53687
$171$	3.14030	0.240145
$172$	5.40193	0.411893
$173$	4.48482	0.340974	0.170487	−	0.985360i	$-0.445466\pi$
$173$	4.48482	0.340974	0.170487	+	0.985360i	$0.445466\pi$
$174$	1.62127	0.122908
$175$	0	0
$176$	16.4941	1.24329
$177$	11.2245	0.843687
$178$	18.7312	1.40396
$179$	13.9561	1.04313	0.521565	−	0.853211i	$-0.325348\pi$
$179$	13.9561	1.04313	0.521565	+	0.853211i	$0.325348\pi$
$180$	2.30862	0.172074
$181$	−9.21198	−0.684721	−0.342361	−	0.939569i	$-0.611226\pi$
$181$	−9.21198	−0.684721	−0.342361	+	0.939569i	$0.611226\pi$
$182$	0	0
$183$	1.80269	0.133258
$184$	19.5662	1.44244
$185$	38.7147	2.84636
$186$	−7.40309	−0.542821
$187$	−20.5820	−1.50510
$188$	8.45167	0.616401
$189$	0	0
$190$	16.9462	1.22941
$191$	−18.9462	−1.37090	−0.685451	−	0.728119i	$-0.740395\pi$
$191$	−18.9462	−1.37090	−0.685451	+	0.728119i	$0.740395\pi$
$192$	3.55530	0.256581
$193$	−15.5168	−1.11692	−0.558461	−	0.829531i	$-0.688608\pi$
$193$	−15.5168	−1.11692	−0.558461	+	0.829531i	$0.688608\pi$
$194$	−19.3726	−1.39087
$195$	18.9000	1.35346
$196$	0	0
$197$	3.07929	0.219390	0.109695	−	0.993965i	$-0.465013\pi$
$197$	3.07929	0.219390	0.109695	+	0.993965i	$0.465013\pi$
$198$	−5.52106	−0.392364
$199$	5.82235	0.412736	0.206368	−	0.978474i	$-0.433836\pi$
$199$	5.82235	0.412736	0.206368	+	0.978474i	$0.433836\pi$
$200$	−12.3050	−0.870094
$201$	−13.1550	−0.927884
$202$	−7.19485	−0.506228
$203$	0	0
$204$	4.31147	0.301863
$205$	−3.28206	−0.229229
$206$	12.4604	0.868160
$207$	−9.17799	−0.637914
$208$	−28.2863	−1.96130
$209$	−10.5448	−0.729398
$210$	0	0
$211$	−19.1035	−1.31514	−0.657569	−	0.753394i	$-0.728415\pi$
$211$	−19.1035	−1.31514	−0.657569	+	0.753394i	$0.728415\pi$
$212$	−1.83812	−0.126242
$213$	−5.92317	−0.405849
$214$	33.3822	2.28196
$215$	25.2052	1.71898
$216$	−2.13187	−0.145055
$217$	0	0
$218$	−10.2531	−0.694426
$219$	−9.66466	−0.653077
$220$	−7.75209	−0.522646
$221$	35.2968	2.37432
$222$	19.3947	1.30169
$223$	−27.3295	−1.83012	−0.915059	−	0.403320i	$-0.867856\pi$
$223$	−27.3295	−1.83012	−0.915059	+	0.403320i	$0.867856\pi$
$224$	0	0
$225$	5.77193	0.384796
$226$	−5.21275	−0.346747
$227$	6.27102	0.416222	0.208111	−	0.978105i	$-0.433268\pi$
$227$	6.27102	0.416222	0.208111	+	0.978105i	$0.433268\pi$
$228$	2.20890	0.146288
$229$	−7.57515	−0.500580	−0.250290	−	0.968171i	$-0.580526\pi$
$229$	−7.57515	−0.500580	−0.250290	+	0.968171i	$0.580526\pi$
$230$	−49.5279	−3.26577
$231$	0	0
$232$	−2.10213	−0.138011
$233$	−1.10598	−0.0724553	−0.0362276	−	0.999344i	$-0.511534\pi$
$233$	−1.10598	−0.0724553	−0.0362276	+	0.999344i	$0.511534\pi$
$234$	9.46827	0.618960
$235$	39.4352	2.57247
$236$	7.89538	0.513946
$237$	−8.44944	−0.548850
$238$	0	0
$239$	18.1910	1.17668	0.588339	−	0.808615i	$-0.299782\pi$
$239$	18.1910	1.17668	0.588339	+	0.808615i	$0.299782\pi$
$240$	−16.1216	−1.04064
$241$	20.6913	1.33284	0.666422	−	0.745575i	$-0.267825\pi$
$241$	20.6913	1.33284	0.666422	+	0.745575i	$0.267825\pi$
$242$	0.452867	0.0291114
$243$	1.00000	0.0641500
$244$	1.26802	0.0811765
$245$	0	0
$246$	−1.64420	−0.104831
$247$	18.0836	1.15063
$248$	9.59882	0.609525
$249$	5.92934	0.375757
$250$	4.16564	0.263458
$251$	−2.49992	−0.157793	−0.0788967	−	0.996883i	$-0.525140\pi$
$251$	−2.49992	−0.157793	−0.0788967	+	0.996883i	$0.525140\pi$
$252$	0	0
$253$	30.8187	1.93755
$254$	13.2741	0.832889
$255$	20.1172	1.25979
$256$	15.0383	0.939896
$257$	12.6110	0.786650	0.393325	−	0.919400i	$-0.371325\pi$
$257$	12.6110	0.786650	0.393325	+	0.919400i	$0.371325\pi$
$258$	12.6270	0.786121
$259$	0	0
$260$	13.2943	0.824481
$261$	0.986050	0.0610350
$262$	−15.0302	−0.928566
$263$	−21.2852	−1.31250	−0.656250	−	0.754544i	$-0.727858\pi$
$263$	−21.2852	−1.31250	−0.656250	+	0.754544i	$0.727858\pi$
$264$	7.15857	0.440580
$265$	−8.57659	−0.526856
$266$	0	0
$267$	11.3923	0.697195
$268$	−9.25331	−0.565236
$269$	−26.5602	−1.61940	−0.809701	−	0.586842i	$-0.800371\pi$
$269$	−26.5602	−1.61940	−0.809701	+	0.586842i	$0.800371\pi$
$270$	5.39638	0.328413
$271$	11.8390	0.719170	0.359585	−	0.933112i	$-0.382918\pi$
$271$	11.8390	0.719170	0.359585	+	0.933112i	$0.382918\pi$
$272$	−30.1080	−1.82556
$273$	0	0
$274$	−10.7520	−0.649555
$275$	−19.3815	−1.16875
$276$	−6.45584	−0.388596
$277$	−19.3182	−1.16072	−0.580360	−	0.814360i	$-0.697088\pi$
$277$	−19.3182	−1.16072	−0.580360	+	0.814360i	$0.697088\pi$
$278$	14.7718	0.885957
$279$	−4.50254	−0.269560
$280$	0	0
$281$	−17.2205	−1.02729	−0.513645	−	0.858003i	$-0.671705\pi$
$281$	−17.2205	−1.02729	−0.513645	+	0.858003i	$0.671705\pi$
$282$	19.7557	1.17644
$283$	−21.7400	−1.29231	−0.646156	−	0.763206i	$-0.723624\pi$
$283$	−21.7400	−1.29231	−0.646156	+	0.763206i	$0.723624\pi$
$284$	−4.16639	−0.247230
$285$	10.3067	0.610513
$286$	−31.7934	−1.87998
$287$	0	0
$288$	−3.81265	−0.224662
$289$	20.5699	1.20999
$290$	5.32110	0.312466
$291$	−11.7824	−0.690696
$292$	−6.79817	−0.397833
$293$	−3.46874	−0.202646	−0.101323	−	0.994854i	$-0.532308\pi$
$293$	−3.46874	−0.202646	−0.101323	+	0.994854i	$0.532308\pi$
$294$	0	0
$295$	36.8396	2.14488
$296$	−25.1471	−1.46165
$297$	−3.35789	−0.194845
$298$	0.448788	0.0259976
$299$	−52.8521	−3.05652
$300$	4.06001	0.234405
$301$	0	0
$302$	−10.8980	−0.627107
$303$	−4.37589	−0.251388
$304$	−15.4252	−0.884698
$305$	5.91653	0.338779
$306$	10.0780	0.576123
$307$	−26.8694	−1.53352	−0.766758	−	0.641937i	$-0.778131\pi$
$307$	−26.8694	−1.53352	−0.766758	+	0.641937i	$0.778131\pi$
$308$	0	0
$309$	7.57841	0.431121
$310$	−24.2974	−1.38000
$311$	28.0423	1.59013	0.795066	−	0.606523i	$-0.207436\pi$
$311$	28.0423	1.59013	0.795066	+	0.606523i	$0.207436\pi$
$312$	−12.2765	−0.695021
$313$	14.1597	0.800356	0.400178	−	0.916438i	$-0.368948\pi$
$313$	14.1597	0.800356	0.400178	+	0.916438i	$0.368948\pi$
$314$	38.3314	2.16317
$315$	0	0
$316$	−5.94338	−0.334341
$317$	31.4411	1.76591	0.882955	−	0.469458i	$-0.155551\pi$
$317$	31.4411	1.76591	0.882955	+	0.469458i	$0.155551\pi$
$318$	−4.29659	−0.240941
$319$	−3.31105	−0.185383
$320$	11.6687	0.652301
$321$	20.3029	1.13320
$322$	0	0
$323$	19.2482	1.07100
$324$	0.703405	0.0390780
$325$	33.2381	1.84372
$326$	−34.5791	−1.91516
$327$	−6.23589	−0.344845
$328$	2.13187	0.117713
$329$	0	0
$330$	−18.1204	−0.997498
$331$	−13.1862	−0.724778	−0.362389	−	0.932027i	$-0.618039\pi$
$331$	−13.1862	−0.724778	−0.362389	+	0.932027i	$0.618039\pi$
$332$	4.17073	0.228898
$333$	11.7958	0.646408
$334$	−5.60195	−0.306525
$335$	−43.1756	−2.35894
$336$	0	0
$337$	1.19410	0.0650470	0.0325235	−	0.999471i	$-0.489646\pi$
$337$	1.19410	0.0650470	0.0325235	+	0.999471i	$0.489646\pi$
$338$	33.1491	1.80307
$339$	−3.17038	−0.172192
$340$	14.1505	0.767419
$341$	15.1190	0.818742
$342$	5.16329	0.279199
$343$	0	0
$344$	−16.3721	−0.882723
$345$	−30.1227	−1.62175
$346$	7.37395	0.396426
$347$	−1.39245	−0.0747507	−0.0373753	−	0.999301i	$-0.511900\pi$
$347$	−1.39245	−0.0747507	−0.0373753	+	0.999301i	$0.511900\pi$
$348$	0.693592	0.0371804
$349$	1.98813	0.106422	0.0532112	−	0.998583i	$-0.483054\pi$
$349$	1.98813	0.106422	0.0532112	+	0.998583i	$0.483054\pi$
$350$	0	0
$351$	5.75857	0.307370
$352$	12.8024	0.682373
$353$	19.9677	1.06277	0.531387	−	0.847129i	$-0.321671\pi$
$353$	19.9677	1.06277	0.531387	+	0.847129i	$0.321671\pi$
$354$	18.4554	0.980894
$355$	−19.4402	−1.03178
$356$	8.01337	0.424708
$357$	0	0
$358$	22.9467	1.21277
$359$	18.9529	1.00029	0.500147	−	0.865940i	$-0.333279\pi$
$359$	18.9529	1.00029	0.500147	+	0.865940i	$0.333279\pi$
$360$	−6.99692	−0.368770
$361$	−9.13853	−0.480975
$362$	−15.1464	−0.796076
$363$	0.275433	0.0144565
$364$	0	0
$365$	−31.7200	−1.66030
$366$	2.96398	0.154930
$367$	−3.57715	−0.186726	−0.0933630	−	0.995632i	$-0.529762\pi$
$367$	−3.57715	−0.186726	−0.0933630	+	0.995632i	$0.529762\pi$
$368$	45.0826	2.35009
$369$	−1.00000	−0.0520579
$370$	63.6548	3.30925
$371$	0	0
$372$	−3.16711	−0.164207
$373$	22.8399	1.18261	0.591303	−	0.806450i	$-0.298614\pi$
$373$	22.8399	1.18261	0.591303	+	0.806450i	$0.298614\pi$
$374$	−33.8409	−1.74987
$375$	2.53353	0.130831
$376$	−25.6152	−1.32100
$377$	5.67824	0.292444
$378$	0	0
$379$	−24.3056	−1.24849	−0.624247	−	0.781227i	$-0.714594\pi$
$379$	−24.3056	−1.24849	−0.624247	+	0.781227i	$0.714594\pi$
$380$	7.24975	0.371904
$381$	8.07325	0.413605
$382$	−31.1515	−1.59385
$383$	−14.8477	−0.758682	−0.379341	−	0.925257i	$-0.623849\pi$
$383$	−14.8477	−0.758682	−0.379341	+	0.925257i	$0.623849\pi$
$384$	13.4709	0.687435
$385$	0	0
$386$	−25.5127	−1.29856
$387$	7.67969	0.390380
$388$	−8.28779	−0.420749
$389$	−30.2374	−1.53310	−0.766548	−	0.642188i	$-0.778027\pi$
$389$	−30.2374	−1.53310	−0.766548	+	0.642188i	$0.778027\pi$
$390$	31.0754	1.57357
$391$	−56.2558	−2.84498
$392$	0	0
$393$	−9.14130	−0.461118
$394$	5.06298	0.255069
$395$	−27.7316	−1.39533
$396$	−2.36196	−0.118693
$397$	−16.8983	−0.848101	−0.424051	−	0.905639i	$-0.639392\pi$
$397$	−16.8983	−0.848101	−0.424051	+	0.905639i	$0.639392\pi$
$398$	9.57313	0.479858
$399$	0	0
$400$	−28.3519	−1.41760
$401$	−27.9165	−1.39408	−0.697042	−	0.717030i	$-0.745501\pi$
$401$	−27.9165	−1.39408	−0.697042	+	0.717030i	$0.745501\pi$
$402$	−21.6295	−1.07878
$403$	−25.9282	−1.29158
$404$	−3.07802	−0.153137
$405$	3.28206	0.163087
$406$	0	0
$407$	−39.6091	−1.96335
$408$	−13.0671	−0.646919
$409$	29.3409	1.45081	0.725407	−	0.688320i	$-0.241651\pi$
$409$	29.3409	1.45081	0.725407	+	0.688320i	$0.241651\pi$
$410$	−5.39638	−0.266508
$411$	−6.53936	−0.322563
$412$	5.33069	0.262624
$413$	0	0
$414$	−15.0905	−0.741656
$415$	19.4605	0.955277
$416$	−21.9554	−1.07645
$417$	8.98420	0.439958
$418$	−17.3378	−0.848018
$419$	−9.50190	−0.464198	−0.232099	−	0.972692i	$-0.574559\pi$
$419$	−9.50190	−0.464198	−0.232099	+	0.972692i	$0.574559\pi$
$420$	0	0
$421$	−6.34695	−0.309331	−0.154666	−	0.987967i	$-0.549430\pi$
$421$	−6.34695	−0.309331	−0.154666	+	0.987967i	$0.549430\pi$
$422$	−31.4100	−1.52902
$423$	12.0154	0.584207
$424$	5.57093	0.270548
$425$	35.3787	1.71612
$426$	−9.73890	−0.471851
$427$	0	0
$428$	14.2812	0.690307
$429$	−19.3367	−0.933583
$430$	41.4425	1.99853
$431$	5.67814	0.273507	0.136753	−	0.990605i	$-0.456333\pi$
$431$	5.67814	0.273507	0.136753	+	0.990605i	$0.456333\pi$
$432$	−4.91203	−0.236330
$433$	−22.8926	−1.10015	−0.550075	−	0.835116i	$-0.685401\pi$
$433$	−22.8926	−1.10015	−0.550075	+	0.835116i	$0.685401\pi$
$434$	0	0
$435$	3.23628	0.155168
$436$	−4.38635	−0.210068
$437$	−28.8216	−1.37872
$438$	−15.8907	−0.759285
$439$	13.8291	0.660027	0.330014	−	0.943976i	$-0.392947\pi$
$439$	13.8291	0.660027	0.330014	+	0.943976i	$0.392947\pi$
$440$	23.4949	1.12007
$441$	0	0
$442$	58.0351	2.76045
$443$	−20.1776	−0.958669	−0.479334	−	0.877632i	$-0.659122\pi$
$443$	−20.1776	−0.958669	−0.479334	+	0.877632i	$0.659122\pi$
$444$	8.29724	0.393770
$445$	37.3901	1.77246
$446$	−44.9352	−2.12775
$447$	0.272952	0.0129102
$448$	0	0
$449$	2.97663	0.140476	0.0702379	−	0.997530i	$-0.477624\pi$
$449$	2.97663	0.140476	0.0702379	+	0.997530i	$0.477624\pi$
$450$	9.49023	0.447374
$451$	3.35789	0.158117
$452$	−2.23006	−0.104893
$453$	−6.62811	−0.311416
$454$	10.3108	0.483912
$455$	0	0
$456$	−6.69470	−0.313508
$457$	1.48861	0.0696341	0.0348171	−	0.999394i	$-0.488915\pi$
$457$	1.48861	0.0696341	0.0348171	+	0.999394i	$0.488915\pi$
$458$	−12.4551	−0.581988
$459$	6.12943	0.286097
$460$	−21.1885	−0.987917
$461$	26.5341	1.23581	0.617907	−	0.786251i	$-0.287981\pi$
$461$	26.5341	1.23581	0.617907	+	0.786251i	$0.287981\pi$
$462$	0	0
$463$	14.3359	0.666245	0.333123	−	0.942883i	$-0.391898\pi$
$463$	14.3359	0.666245	0.333123	+	0.942883i	$0.391898\pi$
$464$	−4.84351	−0.224854
$465$	−14.7776	−0.685296
$466$	−1.81846	−0.0842385
$467$	−26.7495	−1.23782	−0.618909	−	0.785462i	$-0.712425\pi$
$467$	−26.7495	−1.23782	−0.618909	+	0.785462i	$0.712425\pi$
$468$	4.05061	0.187239
$469$	0	0
$470$	64.8395	2.99082
$471$	23.3131	1.07421
$472$	−23.9292	−1.10143
$473$	−25.7876	−1.18571
$474$	−13.8926	−0.638108
$475$	18.1256	0.831659
$476$	0	0
$477$	−2.61317	−0.119649
$478$	29.9097	1.36804
$479$	−16.7956	−0.767410	−0.383705	−	0.923456i	$-0.625352\pi$
$479$	−16.7956	−0.767410	−0.383705	+	0.923456i	$0.625352\pi$
$480$	−12.5133	−0.571153
$481$	67.9272	3.09721
$482$	34.0207	1.54960
$483$	0	0
$484$	0.193741	0.00880639
$485$	−38.6705	−1.75594
$486$	1.64420	0.0745826
$487$	−11.1089	−0.503392	−0.251696	−	0.967806i	$-0.580988\pi$
$487$	−11.1089	−0.503392	−0.251696	+	0.967806i	$0.580988\pi$
$488$	−3.84309	−0.173968
$489$	−21.0309	−0.951050
$490$	0	0
$491$	−34.5338	−1.55849	−0.779244	−	0.626720i	$-0.784397\pi$
$491$	−34.5338	−1.55849	−0.779244	+	0.626720i	$0.784397\pi$
$492$	−0.703405	−0.0317119
$493$	6.04392	0.272205
$494$	29.7332	1.33776
$495$	−11.0208	−0.495348
$496$	22.1166	0.993066
$497$	0	0
$498$	9.74905	0.436865
$499$	−1.84774	−0.0827161	−0.0413580	−	0.999144i	$-0.513168\pi$
$499$	−1.84774	−0.0827161	−0.0413580	+	0.999144i	$0.513168\pi$
$500$	1.78210	0.0796979
$501$	−3.40709	−0.152218
$502$	−4.11037	−0.183455
$503$	−7.20636	−0.321316	−0.160658	−	0.987010i	$-0.551362\pi$
$503$	−7.20636	−0.321316	−0.160658	+	0.987010i	$0.551362\pi$
$504$	0	0
$505$	−14.3619	−0.639098
$506$	50.6722	2.25265
$507$	20.1612	0.895389
$508$	5.67876	0.251954
$509$	9.61401	0.426134	0.213067	−	0.977038i	$-0.431655\pi$
$509$	9.61401	0.426134	0.213067	+	0.977038i	$0.431655\pi$
$510$	33.0767	1.46466
$511$	0	0
$512$	−2.21575	−0.0979233
$513$	3.14030	0.138648
$514$	20.7350	0.914581
$515$	24.8728	1.09603
$516$	5.40193	0.237807
$517$	−40.3463	−1.77443
$518$	0	0
$519$	4.48482	0.196862
$520$	−40.2923	−1.76693
$521$	−16.5470	−0.724936	−0.362468	−	0.931996i	$-0.618066\pi$
$521$	−16.5470	−0.724936	−0.362468	+	0.931996i	$0.618066\pi$
$522$	1.62127	0.0709609
$523$	26.9120	1.17678	0.588390	−	0.808577i	$-0.299762\pi$
$523$	26.9120	1.17678	0.588390	+	0.808577i	$0.299762\pi$
$524$	−6.43003	−0.280897
$525$	0	0
$526$	−34.9972	−1.52595
$527$	−27.5980	−1.20219
$528$	16.4941	0.717812
$529$	61.2354	2.66241
$530$	−14.1017	−0.612537
$531$	11.2245	0.487103
$532$	0	0
$533$	−5.75857	−0.249432
$534$	18.7312	0.810578
$535$	66.6355	2.88090
$536$	28.0448	1.21135
$537$	13.9561	0.602252
$538$	−43.6703	−1.88276
$539$	0	0
$540$	2.30862	0.0993471
$541$	−22.1189	−0.950965	−0.475483	−	0.879725i	$-0.657727\pi$
$541$	−22.1189	−0.950965	−0.475483	+	0.879725i	$0.657727\pi$
$542$	19.4658	0.836126
$543$	−9.21198	−0.395324
$544$	−23.3693	−1.00195
$545$	−20.4666	−0.876692
$546$	0	0
$547$	9.32996	0.398920	0.199460	−	0.979906i	$-0.436081\pi$
$547$	9.32996	0.398920	0.199460	+	0.979906i	$0.436081\pi$
$548$	−4.59982	−0.196495
$549$	1.80269	0.0769368
$550$	−31.8672	−1.35882
$551$	3.09649	0.131915
$552$	19.5662	0.832795
$553$	0	0
$554$	−31.7631	−1.34948
$555$	38.7147	1.64335
$556$	6.31953	0.268008
$557$	35.5298	1.50545	0.752723	−	0.658338i	$-0.228740\pi$
$557$	35.5298	1.50545	0.752723	+	0.658338i	$0.228740\pi$
$558$	−7.40309	−0.313398
$559$	44.2241	1.87048
$560$	0	0
$561$	−20.5820	−0.868971
$562$	−28.3141	−1.19436
$563$	−11.6691	−0.491795	−0.245897	−	0.969296i	$-0.579083\pi$
$563$	−11.6691	−0.491795	−0.245897	+	0.969296i	$0.579083\pi$
$564$	8.45167	0.355879
$565$	−10.4054	−0.437758
$566$	−35.7450	−1.50248
$567$	0	0
$568$	12.6274	0.529834
$569$	10.1162	0.424095	0.212047	−	0.977259i	$-0.431987\pi$
$569$	10.1162	0.424095	0.212047	+	0.977259i	$0.431987\pi$
$570$	16.9462	0.709800
$571$	−7.08972	−0.296696	−0.148348	−	0.988935i	$-0.547395\pi$
$571$	−7.08972	−0.296696	−0.148348	+	0.988935i	$0.547395\pi$
$572$	−13.6015	−0.568707
$573$	−18.9462	−0.791491
$574$	0	0
$575$	−52.9747	−2.20920
$576$	3.55530	0.148137
$577$	−16.7129	−0.695767	−0.347884	−	0.937538i	$-0.613100\pi$
$577$	−16.7129	−0.695767	−0.347884	+	0.937538i	$0.613100\pi$
$578$	33.8211	1.40677
$579$	−15.5168	−0.644855
$580$	2.27641	0.0945229
$581$	0	0
$582$	−19.3726	−0.803022
$583$	8.77475	0.363413
$584$	20.6038	0.852590
$585$	18.9000	0.781419
$586$	−5.70332	−0.235602
$587$	18.0499	0.745000	0.372500	−	0.928032i	$-0.378501\pi$
$587$	18.0499	0.745000	0.372500	+	0.928032i	$0.378501\pi$
$588$	0	0
$589$	−14.1393	−0.582601
$590$	60.5718	2.49370
$591$	3.07929	0.126665
$592$	−57.9415	−2.38138
$593$	−2.63006	−0.108004	−0.0540018	−	0.998541i	$-0.517198\pi$
$593$	−2.63006	−0.108004	−0.0540018	+	0.998541i	$0.517198\pi$
$594$	−5.52106	−0.226532
$595$	0	0
$596$	0.191996	0.00786444
$597$	5.82235	0.238293
$598$	−86.8996	−3.55359
$599$	−41.3763	−1.69059	−0.845296	−	0.534299i	$-0.820576\pi$
$599$	−41.3763	−1.69059	−0.845296	+	0.534299i	$0.820576\pi$
$600$	−12.3050	−0.502349
$601$	−7.93199	−0.323552	−0.161776	−	0.986827i	$-0.551722\pi$
$601$	−7.93199	−0.323552	−0.161776	+	0.986827i	$0.551722\pi$
$602$	0	0
$603$	−13.1550	−0.535714
$604$	−4.66224	−0.189704
$605$	0.903987	0.0367523
$606$	−7.19485	−0.292271
$607$	25.0957	1.01860	0.509302	−	0.860588i	$-0.329904\pi$
$607$	25.0957	1.01860	0.509302	+	0.860588i	$0.329904\pi$
$608$	−11.9728	−0.485563
$609$	0	0
$610$	9.72798	0.393874
$611$	69.1914	2.79918
$612$	4.31147	0.174281
$613$	39.5202	1.59621	0.798103	−	0.602521i	$-0.205837\pi$
$613$	39.5202	1.59621	0.798103	+	0.602521i	$0.205837\pi$
$614$	−44.1787	−1.78291
$615$	−3.28206	−0.132346
$616$	0	0
$617$	−16.0390	−0.645705	−0.322853	−	0.946449i	$-0.604642\pi$
$617$	−16.0390	−0.645705	−0.322853	+	0.946449i	$0.604642\pi$
$618$	12.4604	0.501233
$619$	−4.05138	−0.162839	−0.0814194	−	0.996680i	$-0.525945\pi$
$619$	−4.05138	−0.162839	−0.0814194	+	0.996680i	$0.525945\pi$
$620$	−10.3946	−0.417459
$621$	−9.17799	−0.368300
$622$	46.1072	1.84873
$623$	0	0
$624$	−28.2863	−1.13236
$625$	−20.5445	−0.821778
$626$	23.2815	0.930515
$627$	−10.5448	−0.421118
$628$	16.3985	0.654372
$629$	72.3017	2.88286
$630$	0	0
$631$	−35.7081	−1.42152	−0.710759	−	0.703436i	$-0.751648\pi$
$631$	−35.7081	−1.42152	−0.710759	+	0.703436i	$0.751648\pi$
$632$	18.0131	0.716522
$633$	−19.1035	−0.759295
$634$	51.6956	2.05310
$635$	26.4969	1.05150
$636$	−1.83812	−0.0728861
$637$	0	0
$638$	−5.44404	−0.215531
$639$	−5.92317	−0.234317
$640$	44.2124	1.74765
$641$	16.1373	0.637383	0.318692	−	0.947858i	$-0.396757\pi$
$641$	16.1373	0.637383	0.318692	+	0.947858i	$0.396757\pi$
$642$	33.3822	1.31749
$643$	−17.6523	−0.696137	−0.348068	−	0.937469i	$-0.613162\pi$
$643$	−17.6523	−0.696137	−0.348068	+	0.937469i	$0.613162\pi$
$644$	0	0
$645$	25.2052	0.992454
$646$	31.6480	1.24517
$647$	−0.0105799	−0.000415939 0	−0.000207970	−	1.00000i	$-0.500066\pi$
$647$	−0.0105799	−0.000415939 0	−0.000207970		1.00000i	$0.500066\pi$
$648$	−2.13187	−0.0837476
$649$	−37.6907	−1.47949
$650$	54.6502	2.14356
$651$	0	0
$652$	−14.7932	−0.579348
$653$	−35.3931	−1.38504	−0.692519	−	0.721399i	$-0.743499\pi$
$653$	−35.3931	−1.38504	−0.692519	+	0.721399i	$0.743499\pi$
$654$	−10.2531	−0.400927
$655$	−30.0023	−1.17229
$656$	4.91203	0.191783
$657$	−9.66466	−0.377054
$658$	0	0
$659$	2.98465	0.116266	0.0581328	−	0.998309i	$-0.481485\pi$
$659$	2.98465	0.116266	0.0581328	+	0.998309i	$0.481485\pi$
$660$	−7.75209	−0.301750
$661$	46.2120	1.79744	0.898718	−	0.438526i	$-0.144499\pi$
$661$	46.2120	1.79744	0.898718	+	0.438526i	$0.144499\pi$
$662$	−21.6807	−0.842646
$663$	35.2968	1.37081
$664$	−12.6406	−0.490549
$665$	0	0
$666$	19.3947	0.751531
$667$	−9.04995	−0.350416
$668$	−2.39656	−0.0927258
$669$	−27.3295	−1.05662
$670$	−70.9895	−2.74256
$671$	−6.05322	−0.233682
$672$	0	0
$673$	−14.0235	−0.540565	−0.270282	−	0.962781i	$-0.587117\pi$
$673$	−14.0235	−0.540565	−0.270282	+	0.962781i	$0.587117\pi$
$674$	1.96335	0.0756254
$675$	5.77193	0.222162
$676$	14.1815	0.545441
$677$	−2.26496	−0.0870497	−0.0435248	−	0.999052i	$-0.513859\pi$
$677$	−2.26496	−0.0870497	−0.0435248	+	0.999052i	$0.513859\pi$
$678$	−5.21275	−0.200195
$679$	0	0
$680$	−42.8871	−1.64465
$681$	6.27102	0.240306
$682$	24.8588	0.951892
$683$	−3.25047	−0.124376	−0.0621879	−	0.998064i	$-0.519808\pi$
$683$	−3.25047	−0.124376	−0.0621879	+	0.998064i	$0.519808\pi$
$684$	2.20890	0.0844594
$685$	−21.4626	−0.820044
$686$	0	0
$687$	−7.57515	−0.289010
$688$	−37.7229	−1.43817
$689$	−15.0481	−0.573289
$690$	−49.5279	−1.88549
$691$	−5.13808	−0.195462	−0.0977309	−	0.995213i	$-0.531158\pi$
$691$	−5.13808	−0.195462	−0.0977309	+	0.995213i	$0.531158\pi$
$692$	3.15464	0.119921
$693$	0	0
$694$	−2.28947	−0.0869072
$695$	29.4867	1.11849
$696$	−2.10213	−0.0796809
$697$	−6.12943	−0.232169
$698$	3.26890	0.123730
$699$	−1.10598	−0.0418321
$700$	0	0
$701$	33.0426	1.24800	0.624001	−	0.781424i	$-0.285506\pi$
$701$	33.0426	1.24800	0.624001	+	0.781424i	$0.285506\pi$
$702$	9.46827	0.357357
$703$	37.0424	1.39708
$704$	−11.9383	−0.449942
$705$	39.4352	1.48522
$706$	32.8310	1.23561
$707$	0	0
$708$	7.89538	0.296727
$709$	−40.5637	−1.52340	−0.761701	−	0.647928i	$-0.775636\pi$
$709$	−40.5637	−1.52340	−0.761701	+	0.647928i	$0.775636\pi$
$710$	−31.9637	−1.19957
$711$	−8.44944	−0.316879
$712$	−24.2868	−0.910185
$713$	41.3243	1.54761
$714$	0	0
$715$	−63.4641	−2.37342
$716$	9.81682	0.366872
$717$	18.1910	0.679355
$718$	31.1624	1.16297
$719$	18.0190	0.671994	0.335997	−	0.941863i	$-0.390927\pi$
$719$	18.0190	0.671994	0.335997	+	0.941863i	$0.390927\pi$
$720$	−16.1216	−0.600816
$721$	0	0
$722$	−15.0256	−0.559195
$723$	20.6913	0.769517
$724$	−6.47975	−0.240818
$725$	5.69141	0.211374
$726$	0.452867	0.0168075
$727$	10.1884	0.377868	0.188934	−	0.981990i	$-0.439497\pi$
$727$	10.1884	0.377868	0.188934	+	0.981990i	$0.439497\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−52.1542	−1.93031
$731$	47.0721	1.74102
$732$	1.26802	0.0468673
$733$	−42.6537	−1.57545	−0.787726	−	0.616026i	$-0.788742\pi$
$733$	−42.6537	−1.57545	−0.787726	+	0.616026i	$0.788742\pi$
$734$	−5.88157	−0.217093
$735$	0	0
$736$	34.9924	1.28984
$737$	44.1731	1.62714
$738$	−1.64420	−0.0605240
$739$	16.1174	0.592887	0.296444	−	0.955050i	$-0.404199\pi$
$739$	16.1174	0.592887	0.296444	+	0.955050i	$0.404199\pi$
$740$	27.2321	1.00107
$741$	18.0836	0.664319
$742$	0	0
$743$	−27.9584	−1.02569	−0.512846	−	0.858480i	$-0.671409\pi$
$743$	−27.9584	−1.02569	−0.512846	+	0.858480i	$0.671409\pi$
$744$	9.59882	0.351910
$745$	0.895844	0.0328212
$746$	37.5534	1.37493
$747$	5.92934	0.216943
$748$	−14.4774	−0.529348
$749$	0	0
$750$	4.16564	0.152108
$751$	17.5578	0.640695	0.320347	−	0.947300i	$-0.396200\pi$
$751$	17.5578	0.640695	0.320347	+	0.947300i	$0.396200\pi$
$752$	−59.0199	−2.15223
$753$	−2.49992	−0.0911020
$754$	9.33618	0.340004
$755$	−21.7539	−0.791704
$756$	0	0
$757$	−5.87592	−0.213564	−0.106782	−	0.994282i	$-0.534055\pi$
$757$	−5.87592	−0.213564	−0.106782	+	0.994282i	$0.534055\pi$
$758$	−39.9633	−1.45153
$759$	30.8187	1.11865
$760$	−21.9724	−0.797023
$761$	26.4642	0.959326	0.479663	−	0.877453i	$-0.340759\pi$
$761$	26.4642	0.959326	0.479663	+	0.877453i	$0.340759\pi$
$762$	13.2741	0.480869
$763$	0	0
$764$	−13.3269	−0.482150
$765$	20.1172	0.727338
$766$	−24.4126	−0.882065
$767$	64.6373	2.33392
$768$	15.0383	0.542649
$769$	30.5496	1.10165	0.550823	−	0.834622i	$-0.314314\pi$
$769$	30.5496	1.10165	0.550823	+	0.834622i	$0.314314\pi$
$770$	0	0
$771$	12.6110	0.454173
$772$	−10.9146	−0.392824
$773$	−33.4890	−1.20452	−0.602258	−	0.798302i	$-0.705732\pi$
$773$	−33.4890	−1.20452	−0.602258	+	0.798302i	$0.705732\pi$
$774$	12.6270	0.453867
$775$	−25.9884	−0.933530
$776$	25.1185	0.901701
$777$	0	0
$778$	−49.7164	−1.78242
$779$	−3.14030	−0.112513
$780$	13.2943	0.476014
$781$	19.8894	0.711697
$782$	−92.4960	−3.30765
$783$	0.986050	0.0352386
$784$	0	0
$785$	76.5149	2.73093
$786$	−15.0302	−0.536108
$787$	6.84173	0.243881	0.121941	−	0.992537i	$-0.461088\pi$
$787$	6.84173	0.243881	0.121941	+	0.992537i	$0.461088\pi$
$788$	2.16599	0.0771601
$789$	−21.2852	−0.757772
$790$	−45.5964	−1.62225
$791$	0	0
$792$	7.15857	0.254369
$793$	10.3809	0.368637
$794$	−27.7842	−0.986026
$795$	−8.57659	−0.304180
$796$	4.09547	0.145160
$797$	−9.72791	−0.344580	−0.172290	−	0.985046i	$-0.555117\pi$
$797$	−9.72791	−0.344580	−0.172290	+	0.985046i	$0.555117\pi$
$798$	0	0
$799$	73.6474	2.60546
$800$	−22.0063	−0.778041
$801$	11.3923	0.402526
$802$	−45.9004	−1.62080
$803$	32.4529	1.14524
$804$	−9.25331	−0.326339
$805$	0	0
$806$	−42.6313	−1.50162
$807$	−26.5602	−0.934963
$808$	9.32880	0.328186
$809$	23.9599	0.842386	0.421193	−	0.906971i	$-0.361611\pi$
$809$	23.9599	0.842386	0.421193	+	0.906971i	$0.361611\pi$
$810$	5.39638	0.189609
$811$	30.6208	1.07524	0.537622	−	0.843186i	$-0.319323\pi$
$811$	30.6208	1.07524	0.537622	+	0.843186i	$0.319323\pi$
$812$	0	0
$813$	11.8390	0.415213
$814$	−65.1254	−2.28265
$815$	−69.0247	−2.41783
$816$	−30.1080	−1.05399
$817$	24.1165	0.843730
$818$	48.2424	1.68676
$819$	0	0
$820$	−2.30862	−0.0806204
$821$	19.7037	0.687662	0.343831	−	0.939031i	$-0.388275\pi$
$821$	19.7037	0.687662	0.343831	+	0.939031i	$0.388275\pi$
$822$	−10.7520	−0.375021
$823$	−26.6490	−0.928926	−0.464463	−	0.885593i	$-0.653753\pi$
$823$	−26.6490	−0.928926	−0.464463	+	0.885593i	$0.653753\pi$
$824$	−16.1562	−0.562826
$825$	−19.3815	−0.674778
$826$	0	0
$827$	2.60475	0.0905761	0.0452881	−	0.998974i	$-0.485579\pi$
$827$	2.60475	0.0905761	0.0452881	+	0.998974i	$0.485579\pi$
$828$	−6.45584	−0.224356
$829$	7.20154	0.250120	0.125060	−	0.992149i	$-0.460088\pi$
$829$	7.20154	0.250120	0.125060	+	0.992149i	$0.460088\pi$
$830$	31.9970	1.11063
$831$	−19.3182	−0.670142
$832$	20.4734	0.709789
$833$	0	0
$834$	14.7718	0.511507
$835$	−11.1823	−0.386979
$836$	−7.41725	−0.256531
$837$	−4.50254	−0.155631
$838$	−15.6231	−0.539689
$839$	−3.36252	−0.116087	−0.0580436	−	0.998314i	$-0.518486\pi$
$839$	−3.36252	−0.116087	−0.0580436	+	0.998314i	$0.518486\pi$
$840$	0	0
$841$	−28.0277	−0.966473
$842$	−10.4357	−0.359637
$843$	−17.2205	−0.593107
$844$	−13.4375	−0.462537
$845$	66.1702	2.27633
$846$	19.7557	0.679215
$847$	0	0
$848$	12.8360	0.440789
$849$	−21.7400	−0.746116
$850$	58.1697	1.99520
$851$	−108.262	−3.71117
$852$	−4.16639	−0.142738
$853$	4.03938	0.138306	0.0691529	−	0.997606i	$-0.477970\pi$
$853$	4.03938	0.138306	0.0691529	+	0.997606i	$0.477970\pi$
$854$	0	0
$855$	10.3067	0.352480
$856$	−43.2832	−1.47939
$857$	21.4868	0.733975	0.366987	−	0.930226i	$-0.380389\pi$
$857$	21.4868	0.733975	0.366987	+	0.930226i	$0.380389\pi$
$858$	−31.7934	−1.08541
$859$	−24.7283	−0.843717	−0.421859	−	0.906662i	$-0.638622\pi$
$859$	−24.7283	−0.843717	−0.421859	+	0.906662i	$0.638622\pi$
$860$	17.7295	0.604570
$861$	0	0
$862$	9.33602	0.317986
$863$	−0.835485	−0.0284402	−0.0142201	−	0.999899i	$-0.504527\pi$
$863$	−0.835485	−0.0284402	−0.0142201	+	0.999899i	$0.504527\pi$
$864$	−3.81265	−0.129709
$865$	14.7194	0.500476
$866$	−37.6401	−1.27906
$867$	20.5699	0.698591
$868$	0	0
$869$	28.3723	0.962465
$870$	5.32110	0.180402
$871$	−75.7542	−2.56683
$872$	13.2941	0.450194
$873$	−11.7824	−0.398774
$874$	−47.3886	−1.60294
$875$	0	0
$876$	−6.79817	−0.229689
$877$	−43.9609	−1.48445	−0.742227	−	0.670148i	$-0.766230\pi$
$877$	−43.9609	−1.48445	−0.742227	+	0.670148i	$0.766230\pi$
$878$	22.7379	0.767366
$879$	−3.46874	−0.116998
$880$	54.1346	1.82488
$881$	49.2250	1.65843	0.829217	−	0.558927i	$-0.188787\pi$
$881$	49.2250	1.65843	0.829217	+	0.558927i	$0.188787\pi$
$882$	0	0
$883$	−28.1493	−0.947300	−0.473650	−	0.880713i	$-0.657064\pi$
$883$	−28.1493	−0.947300	−0.473650	+	0.880713i	$0.657064\pi$
$884$	24.8279	0.835053
$885$	36.8396	1.23835
$886$	−33.1761	−1.11457
$887$	39.1184	1.31347	0.656733	−	0.754123i	$-0.271938\pi$
$887$	39.1184	1.31347	0.656733	+	0.754123i	$0.271938\pi$
$888$	−25.1471	−0.843883
$889$	0	0
$890$	61.4769	2.06071
$891$	−3.35789	−0.112494
$892$	−19.2237	−0.643657
$893$	37.7318	1.26265
$894$	0.448788	0.0150097
$895$	45.8049	1.53109
$896$	0	0
$897$	−52.8521	−1.76468
$898$	4.89418	0.163321
$899$	−4.43973	−0.148073
$900$	4.06001	0.135334
$901$	−16.0173	−0.533612
$902$	5.52106	0.183831
$903$	0	0
$904$	6.75883	0.224795
$905$	−30.2343	−1.00502
$906$	−10.8980	−0.362061
$907$	−35.8670	−1.19094	−0.595472	−	0.803376i	$-0.703035\pi$
$907$	−35.8670	−1.19094	−0.595472	+	0.803376i	$0.703035\pi$
$908$	4.41107	0.146386
$909$	−4.37589	−0.145139
$910$	0	0
$911$	−17.2869	−0.572741	−0.286371	−	0.958119i	$-0.592449\pi$
$911$	−17.2869	−0.572741	−0.286371	+	0.958119i	$0.592449\pi$
$912$	−15.4252	−0.510781
$913$	−19.9101	−0.658928
$914$	2.44757	0.0809585
$915$	5.91653	0.195594
$916$	−5.32840	−0.176055
$917$	0	0
$918$	10.0780	0.332625
$919$	−22.0788	−0.728312	−0.364156	−	0.931338i	$-0.618643\pi$
$919$	−22.0788	−0.728312	−0.364156	+	0.931338i	$0.618643\pi$
$920$	64.2176	2.11719
$921$	−26.8694	−0.885376
$922$	43.6274	1.43679
$923$	−34.1090	−1.12271
$924$	0	0
$925$	68.0847	2.23861
$926$	23.5711	0.774595
$927$	7.57841	0.248908
$928$	−3.75946	−0.123410
$929$	33.4705	1.09813	0.549066	−	0.835779i	$-0.314984\pi$
$929$	33.4705	1.09813	0.549066	+	0.835779i	$0.314984\pi$
$930$	−24.2974	−0.796744
$931$	0	0
$932$	−0.777953	−0.0254827
$933$	28.0423	0.918063
$934$	−43.9816	−1.43912
$935$	−67.5513	−2.20916
$936$	−12.2765	−0.401270
$937$	−34.1088	−1.11429	−0.557143	−	0.830416i	$-0.688103\pi$
$937$	−34.1088	−1.11429	−0.557143	+	0.830416i	$0.688103\pi$
$938$	0	0
$939$	14.1597	0.462086
$940$	27.7389	0.904743
$941$	−2.69587	−0.0878829	−0.0439415	−	0.999034i	$-0.513992\pi$
$941$	−2.69587	−0.0878829	−0.0439415	+	0.999034i	$0.513992\pi$
$942$	38.3314	1.24890
$943$	9.17799	0.298876
$944$	−55.1352	−1.79450
$945$	0	0
$946$	−42.4000	−1.37854
$947$	24.9949	0.812226	0.406113	−	0.913823i	$-0.366884\pi$
$947$	24.9949	0.812226	0.406113	+	0.913823i	$0.366884\pi$
$948$	−5.94338	−0.193032
$949$	−55.6547	−1.80663
$950$	29.8022	0.966910
$951$	31.4411	1.01955
$952$	0	0
$953$	−29.7561	−0.963895	−0.481948	−	0.876200i	$-0.660070\pi$
$953$	−29.7561	−0.963895	−0.481948	+	0.876200i	$0.660070\pi$
$954$	−4.29659	−0.139107
$955$	−62.1828	−2.01219
$956$	12.7956	0.413840
$957$	−3.31105	−0.107031
$958$	−27.6154	−0.892212
$959$	0	0
$960$	11.6687	0.376606
$961$	−10.7271	−0.346036
$962$	111.686	3.60090
$963$	20.3029	0.654253
$964$	14.5544	0.468764
$965$	−50.9270	−1.63940
$966$	0	0
$967$	40.3371	1.29715	0.648577	−	0.761149i	$-0.275364\pi$
$967$	40.3371	1.29715	0.648577	+	0.761149i	$0.275364\pi$
$968$	−0.587185	−0.0188729
$969$	19.2482	0.618342
$970$	−63.5822	−2.04150
$971$	57.5004	1.84527	0.922637	−	0.385669i	$-0.126029\pi$
$971$	57.5004	1.84527	0.922637	+	0.385669i	$0.126029\pi$
$972$	0.703405	0.0225617
$973$	0	0
$974$	−18.2653	−0.585258
$975$	33.2381	1.06447
$976$	−8.85485	−0.283437
$977$	40.1369	1.28409	0.642047	−	0.766665i	$-0.278085\pi$
$977$	40.1369	1.28409	0.642047	+	0.766665i	$0.278085\pi$
$978$	−34.5791	−1.10572
$979$	−38.2540	−1.22260
$980$	0	0
$981$	−6.23589	−0.199097
$982$	−56.7806	−1.81194
$983$	−7.02052	−0.223920	−0.111960	−	0.993713i	$-0.535713\pi$
$983$	−7.02052	−0.223920	−0.111960	+	0.993713i	$0.535713\pi$
$984$	2.13187	0.0679614
$985$	10.1064	0.322017
$986$	9.93744	0.316473
$987$	0	0
$988$	12.7201	0.404681
$989$	−70.4841	−2.24126
$990$	−18.1204	−0.575906
$991$	−1.28810	−0.0409177	−0.0204589	−	0.999791i	$-0.506513\pi$
$991$	−1.28810	−0.0409177	−0.0204589	+	0.999791i	$0.506513\pi$
$992$	17.1666	0.545040
$993$	−13.1862	−0.418450
$994$	0	0
$995$	19.1093	0.605806
$996$	4.17073	0.132155
$997$	−24.1834	−0.765895	−0.382948	−	0.923770i	$-0.625091\pi$
$997$	−24.1834	−0.765895	−0.382948	+	0.923770i	$0.625091\pi$
$998$	−3.03805	−0.0961679
$999$	11.7958	0.373204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.17	yes	24
7.6	odd	2		6027.2.a.bn.1.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.17	✓	24	7.6	odd	2
6027.2.a.bo.1.17	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+1.64420 q^{2} +1.00000 q^{3} +0.703405 q^{4} +3.28206 q^{5} +1.64420 q^{6} -2.13187 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.64420 q^{2} +1.00000 q^{3} +0.703405 q^{4} +3.28206 q^{5} +1.64420 q^{6} -2.13187 q^{8} +1.00000 q^{9} +5.39638 q^{10} -3.35789 q^{11} +0.703405 q^{12} +5.75857 q^{13} +3.28206 q^{15} -4.91203 q^{16} +6.12943 q^{17} +1.64420 q^{18} +3.14030 q^{19} +2.30862 q^{20} -5.52106 q^{22} -9.17799 q^{23} -2.13187 q^{24} +5.77193 q^{25} +9.46827 q^{26} +1.00000 q^{27} +0.986050 q^{29} +5.39638 q^{30} -4.50254 q^{31} -3.81265 q^{32} -3.35789 q^{33} +10.0780 q^{34} +0.703405 q^{36} +11.7958 q^{37} +5.16329 q^{38} +5.75857 q^{39} -6.99692 q^{40} -1.00000 q^{41} +7.67969 q^{43} -2.36196 q^{44} +3.28206 q^{45} -15.0905 q^{46} +12.0154 q^{47} -4.91203 q^{48} +9.49023 q^{50} +6.12943 q^{51} +4.05061 q^{52} -2.61317 q^{53} +1.64420 q^{54} -11.0208 q^{55} +3.14030 q^{57} +1.62127 q^{58} +11.2245 q^{59} +2.30862 q^{60} +1.80269 q^{61} -7.40309 q^{62} +3.55530 q^{64} +18.9000 q^{65} -5.52106 q^{66} -13.1550 q^{67} +4.31147 q^{68} -9.17799 q^{69} -5.92317 q^{71} -2.13187 q^{72} -9.66466 q^{73} +19.3947 q^{74} +5.77193 q^{75} +2.20890 q^{76} +9.46827 q^{78} -8.44944 q^{79} -16.1216 q^{80} +1.00000 q^{81} -1.64420 q^{82} +5.92934 q^{83} +20.1172 q^{85} +12.6270 q^{86} +0.986050 q^{87} +7.15857 q^{88} +11.3923 q^{89} +5.39638 q^{90} -6.45584 q^{92} -4.50254 q^{93} +19.7557 q^{94} +10.3067 q^{95} -3.81265 q^{96} -11.7824 q^{97} -3.35789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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