LMFDB - Embedded newform 6027.2.a.bo.1.11

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			1.11
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)

$f(q)$	$=$	$q-0.0650408 q^{2} +1.00000 q^{3} -1.99577 q^{4} -2.65358 q^{5} -0.0650408 q^{6} +0.259888 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0650408 q^{2} +1.00000 q^{3} -1.99577 q^{4} -2.65358 q^{5} -0.0650408 q^{6} +0.259888 q^{8} +1.00000 q^{9} +0.172591 q^{10} -5.47071 q^{11} -1.99577 q^{12} -3.40299 q^{13} -2.65358 q^{15} +3.97464 q^{16} -6.28311 q^{17} -0.0650408 q^{18} -4.25848 q^{19} +5.29593 q^{20} +0.355819 q^{22} -1.06746 q^{23} +0.259888 q^{24} +2.04147 q^{25} +0.221333 q^{26} +1.00000 q^{27} -6.10576 q^{29} +0.172591 q^{30} -10.4918 q^{31} -0.778289 q^{32} -5.47071 q^{33} +0.408658 q^{34} -1.99577 q^{36} +3.83754 q^{37} +0.276975 q^{38} -3.40299 q^{39} -0.689632 q^{40} -1.00000 q^{41} -4.68577 q^{43} +10.9183 q^{44} -2.65358 q^{45} +0.0694285 q^{46} +11.1163 q^{47} +3.97464 q^{48} -0.132779 q^{50} -6.28311 q^{51} +6.79158 q^{52} +8.14739 q^{53} -0.0650408 q^{54} +14.5169 q^{55} -4.25848 q^{57} +0.397124 q^{58} +14.0580 q^{59} +5.29593 q^{60} -14.1386 q^{61} +0.682395 q^{62} -7.89865 q^{64} +9.03008 q^{65} +0.355819 q^{66} -6.51962 q^{67} +12.5396 q^{68} -1.06746 q^{69} -10.1718 q^{71} +0.259888 q^{72} -4.82870 q^{73} -0.249597 q^{74} +2.04147 q^{75} +8.49894 q^{76} +0.221333 q^{78} +9.32274 q^{79} -10.5470 q^{80} +1.00000 q^{81} +0.0650408 q^{82} -5.03523 q^{83} +16.6727 q^{85} +0.304766 q^{86} -6.10576 q^{87} -1.42177 q^{88} +8.62706 q^{89} +0.172591 q^{90} +2.13041 q^{92} -10.4918 q^{93} -0.723014 q^{94} +11.3002 q^{95} -0.778289 q^{96} -16.5259 q^{97} -5.47071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.0650408	−0.0459908	−0.0229954	−	0.999736i	$-0.507320\pi$
$2$	−0.0650408	−0.0459908	−0.0229954	+	0.999736i	$0.507320\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.99577	−0.997885
$5$	−2.65358	−1.18672	−0.593358	−	0.804939i	$-0.702198\pi$
$5$	−2.65358	−1.18672	−0.593358	+	0.804939i	$0.702198\pi$
$6$	−0.0650408	−0.0265528
$7$	0	0
$7$	0	0
$8$	0.259888	0.0918843
$9$	1.00000	0.333333
$10$	0.172591	0.0545779
$11$	−5.47071	−1.64948	−0.824740	−	0.565512i	$-0.808678\pi$
$11$	−5.47071	−1.64948	−0.824740	+	0.565512i	$0.808678\pi$
$12$	−1.99577	−0.576129
$13$	−3.40299	−0.943819	−0.471909	−	0.881647i	$-0.656435\pi$
$13$	−3.40299	−0.943819	−0.471909	+	0.881647i	$0.656435\pi$
$14$	0	0
$15$	−2.65358	−0.685150
$16$	3.97464	0.993659
$17$	−6.28311	−1.52388	−0.761939	−	0.647649i	$-0.775752\pi$
$17$	−6.28311	−1.52388	−0.761939	+	0.647649i	$0.775752\pi$
$18$	−0.0650408	−0.0153303
$19$	−4.25848	−0.976962	−0.488481	−	0.872574i	$-0.662449\pi$
$19$	−4.25848	−0.976962	−0.488481	+	0.872574i	$0.662449\pi$
$20$	5.29593	1.18421
$21$	0	0
$22$	0.355819	0.0758608
$23$	−1.06746	−0.222581	−0.111291	−	0.993788i	$-0.535498\pi$
$23$	−1.06746	−0.222581	−0.111291	+	0.993788i	$0.535498\pi$
$24$	0.259888	0.0530494
$25$	2.04147	0.408293
$26$	0.221333	0.0434069
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.10576	−1.13381	−0.566906	−	0.823783i	$-0.691860\pi$
$29$	−6.10576	−1.13381	−0.566906	+	0.823783i	$0.691860\pi$
$30$	0.172591	0.0315106
$31$	−10.4918	−1.88438	−0.942192	−	0.335072i	$-0.891239\pi$
$31$	−10.4918	−1.88438	−0.942192	+	0.335072i	$0.891239\pi$
$32$	−0.778289	−0.137583
$33$	−5.47071	−0.952328
$34$	0.408658	0.0700843
$35$	0	0
$36$	−1.99577	−0.332628
$37$	3.83754	0.630888	0.315444	−	0.948944i	$-0.397847\pi$
$37$	3.83754	0.630888	0.315444	+	0.948944i	$0.397847\pi$
$38$	0.276975	0.0449312
$39$	−3.40299	−0.544914
$40$	−0.689632	−0.109040
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−4.68577	−0.714573	−0.357286	−	0.933995i	$-0.616298\pi$
$43$	−4.68577	−0.714573	−0.357286	+	0.933995i	$0.616298\pi$
$44$	10.9183	1.64599
$45$	−2.65358	−0.395572
$46$	0.0694285	0.0102367
$47$	11.1163	1.62148	0.810741	−	0.585405i	$-0.199064\pi$
$47$	11.1163	1.62148	0.810741	+	0.585405i	$0.199064\pi$
$48$	3.97464	0.573689
$49$	0	0
$50$	−0.132779	−0.0187777
$51$	−6.28311	−0.879811
$52$	6.79158	0.941822
$53$	8.14739	1.11913	0.559565	−	0.828786i	$-0.310968\pi$
$53$	8.14739	1.11913	0.559565	+	0.828786i	$0.310968\pi$
$54$	−0.0650408	−0.00885093
$55$	14.5169	1.95746
$56$	0	0
$57$	−4.25848	−0.564049
$58$	0.397124	0.0521449
$59$	14.0580	1.83020	0.915100	−	0.403228i	$-0.132112\pi$
$59$	14.0580	1.83020	0.915100	+	0.403228i	$0.132112\pi$
$60$	5.29593	0.683701
$61$	−14.1386	−1.81027	−0.905133	−	0.425128i	$-0.860229\pi$
$61$	−14.1386	−1.81027	−0.905133	+	0.425128i	$0.860229\pi$
$62$	0.682395	0.0866643
$63$	0	0
$64$	−7.89865	−0.987331
$65$	9.03008	1.12004
$66$	0.355819	0.0437983
$67$	−6.51962	−0.796498	−0.398249	−	0.917277i	$-0.630382\pi$
$67$	−6.51962	−0.796498	−0.398249	+	0.917277i	$0.630382\pi$
$68$	12.5396	1.52065
$69$	−1.06746	−0.128507
$70$	0	0
$71$	−10.1718	−1.20717	−0.603587	−	0.797297i	$-0.706262\pi$
$71$	−10.1718	−1.20717	−0.603587	+	0.797297i	$0.706262\pi$
$72$	0.259888	0.0306281
$73$	−4.82870	−0.565157	−0.282578	−	0.959244i	$-0.591190\pi$
$73$	−4.82870	−0.565157	−0.282578	+	0.959244i	$0.591190\pi$
$74$	−0.249597	−0.0290150
$75$	2.04147	0.235728
$76$	8.49894	0.974896
$77$	0	0
$78$	0.221333	0.0250610
$79$	9.32274	1.04889	0.524445	−	0.851444i	$-0.324273\pi$
$79$	9.32274	1.04889	0.524445	+	0.851444i	$0.324273\pi$
$80$	−10.5470	−1.17919
$81$	1.00000	0.111111
$82$	0.0650408	0.00718255
$83$	−5.03523	−0.552688	−0.276344	−	0.961059i	$-0.589123\pi$
$83$	−5.03523	−0.552688	−0.276344	+	0.961059i	$0.589123\pi$
$84$	0	0
$85$	16.6727	1.80841
$86$	0.304766	0.0328637
$87$	−6.10576	−0.654607
$88$	−1.42177	−0.151561
$89$	8.62706	0.914466	0.457233	−	0.889347i	$-0.348841\pi$
$89$	8.62706	0.914466	0.457233	+	0.889347i	$0.348841\pi$
$90$	0.172591	0.0181926
$91$	0	0
$92$	2.13041	0.222110
$93$	−10.4918	−1.08795
$94$	−0.723014	−0.0745732
$95$	11.3002	1.15938
$96$	−0.778289	−0.0794338
$97$	−16.5259	−1.67795	−0.838977	−	0.544167i	$-0.816846\pi$
$97$	−16.5259	−1.67795	−0.838977	+	0.544167i	$0.816846\pi$
$98$	0	0
$99$	−5.47071	−0.549827
$100$	−4.07430	−0.407430
$101$	−12.2461	−1.21853	−0.609264	−	0.792968i	$-0.708535\pi$
$101$	−12.2461	−1.21853	−0.609264	+	0.792968i	$0.708535\pi$
$102$	0.408658	0.0404632
$103$	−4.18464	−0.412325	−0.206163	−	0.978518i	$-0.566098\pi$
$103$	−4.18464	−0.412325	−0.206163	+	0.978518i	$0.566098\pi$
$104$	−0.884395	−0.0867221
$105$	0	0
$106$	−0.529913	−0.0514697
$107$	4.55230	0.440087	0.220044	−	0.975490i	$-0.429380\pi$
$107$	4.55230	0.440087	0.220044	+	0.975490i	$0.429380\pi$
$108$	−1.99577	−0.192043
$109$	−9.25158	−0.886141	−0.443070	−	0.896487i	$-0.646111\pi$
$109$	−9.25158	−0.886141	−0.443070	+	0.896487i	$0.646111\pi$
$110$	−0.944192	−0.0900252
$111$	3.83754	0.364243
$112$	0	0
$113$	6.81242	0.640858	0.320429	−	0.947272i	$-0.396173\pi$
$113$	6.81242	0.640858	0.320429	+	0.947272i	$0.396173\pi$
$114$	0.276975	0.0259411
$115$	2.83259	0.264140
$116$	12.1857	1.13141
$117$	−3.40299	−0.314606
$118$	−0.914345	−0.0841723
$119$	0	0
$120$	−0.689632	−0.0629545
$121$	18.9286	1.72078
$122$	0.919587	0.0832555
$123$	−1.00000	−0.0901670
$124$	20.9392	1.88040
$125$	7.85069	0.702187
$126$	0	0
$127$	−13.5337	−1.20092	−0.600461	−	0.799654i	$-0.705016\pi$
$127$	−13.5337	−1.20092	−0.600461	+	0.799654i	$0.705016\pi$
$128$	2.07031	0.182992
$129$	−4.68577	−0.412559
$130$	−0.587324	−0.0515117
$131$	4.69146	0.409895	0.204948	−	0.978773i	$-0.434298\pi$
$131$	4.69146	0.409895	0.204948	+	0.978773i	$0.434298\pi$
$132$	10.9183	0.950313
$133$	0	0
$134$	0.424041	0.0366316
$135$	−2.65358	−0.228383
$136$	−1.63290	−0.140020
$137$	−12.7773	−1.09164	−0.545818	−	0.837904i	$-0.683781\pi$
$137$	−12.7773	−1.09164	−0.545818	+	0.837904i	$0.683781\pi$
$138$	0.0694285	0.00591015
$139$	−12.5370	−1.06338	−0.531688	−	0.846940i	$-0.678442\pi$
$139$	−12.5370	−1.06338	−0.531688	+	0.846940i	$0.678442\pi$
$140$	0	0
$141$	11.1163	0.936163
$142$	0.661584	0.0555189
$143$	18.6167	1.55681
$144$	3.97464	0.331220
$145$	16.2021	1.34551
$146$	0.314063	0.0259920
$147$	0	0
$148$	−7.65885	−0.629553
$149$	2.62732	0.215238	0.107619	−	0.994192i	$-0.465677\pi$
$149$	2.62732	0.215238	0.107619	+	0.994192i	$0.465677\pi$
$150$	−0.132779	−0.0108413
$151$	−5.95876	−0.484917	−0.242458	−	0.970162i	$-0.577954\pi$
$151$	−5.95876	−0.484917	−0.242458	+	0.970162i	$0.577954\pi$
$152$	−1.10673	−0.0897675
$153$	−6.28311	−0.507959
$154$	0	0
$155$	27.8408	2.23623
$156$	6.79158	0.543761
$157$	13.8828	1.10797	0.553983	−	0.832528i	$-0.313107\pi$
$157$	13.8828	1.10797	0.553983	+	0.832528i	$0.313107\pi$
$158$	−0.606358	−0.0482393
$159$	8.14739	0.646130
$160$	2.06525	0.163272
$161$	0	0
$162$	−0.0650408	−0.00511009
$163$	−0.962223	−0.0753671	−0.0376836	−	0.999290i	$-0.511998\pi$
$163$	−0.962223	−0.0753671	−0.0376836	+	0.999290i	$0.511998\pi$
$164$	1.99577	0.155843
$165$	14.5169	1.13014
$166$	0.327495	0.0254185
$167$	−10.9165	−0.844743	−0.422371	−	0.906423i	$-0.638802\pi$
$167$	−10.9165	−0.844743	−0.422371	+	0.906423i	$0.638802\pi$
$168$	0	0
$169$	−1.41969	−0.109207
$170$	−1.08441	−0.0831701
$171$	−4.25848	−0.325654
$172$	9.35171	0.713061
$173$	−18.1821	−1.38236	−0.691182	−	0.722681i	$-0.742910\pi$
$173$	−18.1821	−1.38236	−0.691182	+	0.722681i	$0.742910\pi$
$174$	0.397124	0.0301059
$175$	0	0
$176$	−21.7441	−1.63902
$177$	14.0580	1.05667
$178$	−0.561110	−0.0420570
$179$	14.3377	1.07165	0.535823	−	0.844330i	$-0.320001\pi$
$179$	14.3377	1.07165	0.535823	+	0.844330i	$0.320001\pi$
$180$	5.29593	0.394735
$181$	26.4209	1.96385	0.981925	−	0.189272i	$-0.0606128\pi$
$181$	26.4209	1.96385	0.981925	+	0.189272i	$0.0606128\pi$
$182$	0	0
$183$	−14.1386	−1.04516
$184$	−0.277420	−0.0204517
$185$	−10.1832	−0.748684
$186$	0.682395	0.0500357
$187$	34.3730	2.51360
$188$	−22.1856	−1.61805
$189$	0	0
$190$	−0.734974	−0.0533206
$191$	4.42857	0.320440	0.160220	−	0.987081i	$-0.448780\pi$
$191$	4.42857	0.320440	0.160220	+	0.987081i	$0.448780\pi$
$192$	−7.89865	−0.570036
$193$	4.70814	0.338899	0.169450	−	0.985539i	$-0.445801\pi$
$193$	4.70814	0.338899	0.169450	+	0.985539i	$0.445801\pi$
$194$	1.07486	0.0771704
$195$	9.03008	0.646658
$196$	0	0
$197$	25.9342	1.84774	0.923868	−	0.382712i	$-0.125010\pi$
$197$	25.9342	1.84774	0.923868	+	0.382712i	$0.125010\pi$
$198$	0.355819	0.0252869
$199$	−14.9384	−1.05896	−0.529479	−	0.848323i	$-0.677612\pi$
$199$	−14.9384	−1.05896	−0.529479	+	0.848323i	$0.677612\pi$
$200$	0.530552	0.0375157
$201$	−6.51962	−0.459859
$202$	0.796493	0.0560410
$203$	0	0
$204$	12.5396	0.877950
$205$	2.65358	0.185334
$206$	0.272172	0.0189632
$207$	−1.06746	−0.0741937
$208$	−13.5256	−0.937834
$209$	23.2969	1.61148
$210$	0	0
$211$	12.7550	0.878091	0.439045	−	0.898465i	$-0.355317\pi$
$211$	12.7550	0.878091	0.439045	+	0.898465i	$0.355317\pi$
$212$	−16.2603	−1.11676
$213$	−10.1718	−0.696962
$214$	−0.296085	−0.0202400
$215$	12.4340	0.847994
$216$	0.259888	0.0176831
$217$	0	0
$218$	0.601730	0.0407543
$219$	−4.82870	−0.326294
$220$	−28.9725	−1.95332
$221$	21.3813	1.43826
$222$	−0.249597	−0.0167518
$223$	7.54896	0.505515	0.252758	−	0.967530i	$-0.418662\pi$
$223$	7.54896	0.505515	0.252758	+	0.967530i	$0.418662\pi$
$224$	0	0
$225$	2.04147	0.136098
$226$	−0.443085	−0.0294736
$227$	−7.98410	−0.529923	−0.264962	−	0.964259i	$-0.585359\pi$
$227$	−7.98410	−0.529923	−0.264962	+	0.964259i	$0.585359\pi$
$228$	8.49894	0.562856
$229$	−15.2575	−1.00825	−0.504123	−	0.863632i	$-0.668184\pi$
$229$	−15.2575	−1.00825	−0.504123	+	0.863632i	$0.668184\pi$
$230$	−0.184234	−0.0121480
$231$	0	0
$232$	−1.58681	−0.104179
$233$	−13.1497	−0.861468	−0.430734	−	0.902479i	$-0.641745\pi$
$233$	−13.1497	−0.861468	−0.430734	+	0.902479i	$0.641745\pi$
$234$	0.221333	0.0144690
$235$	−29.4980	−1.92424
$236$	−28.0566	−1.82633
$237$	9.32274	0.605577
$238$	0	0
$239$	24.1988	1.56529	0.782645	−	0.622469i	$-0.213870\pi$
$239$	24.1988	1.56529	0.782645	+	0.622469i	$0.213870\pi$
$240$	−10.5470	−0.680806
$241$	15.7240	1.01287	0.506436	−	0.862278i	$-0.330963\pi$
$241$	15.7240	1.01287	0.506436	+	0.862278i	$0.330963\pi$
$242$	−1.23113	−0.0791401
$243$	1.00000	0.0641500
$244$	28.2175	1.80644
$245$	0	0
$246$	0.0650408	0.00414685
$247$	14.4915	0.922075
$248$	−2.72669	−0.173145
$249$	−5.03523	−0.319095
$250$	−0.510615	−0.0322941
$251$	2.62369	0.165606	0.0828028	−	0.996566i	$-0.473613\pi$
$251$	2.62369	0.165606	0.0828028	+	0.996566i	$0.473613\pi$
$252$	0	0
$253$	5.83977	0.367143
$254$	0.880243	0.0552313
$255$	16.6727	1.04409
$256$	15.6626	0.978916
$257$	−19.5935	−1.22221	−0.611104	−	0.791550i	$-0.709274\pi$
$257$	−19.5935	−1.22221	−0.611104	+	0.791550i	$0.709274\pi$
$258$	0.304766	0.0189739
$259$	0	0
$260$	−18.0220	−1.11767
$261$	−6.10576	−0.377937
$262$	−0.305136	−0.0188514
$263$	1.27756	0.0787776	0.0393888	−	0.999224i	$-0.487459\pi$
$263$	1.27756	0.0787776	0.0393888	+	0.999224i	$0.487459\pi$
$264$	−1.42177	−0.0875039
$265$	−21.6197	−1.32809
$266$	0	0
$267$	8.62706	0.527967
$268$	13.0117	0.794814
$269$	−10.3127	−0.628779	−0.314389	−	0.949294i	$-0.601800\pi$
$269$	−10.3127	−0.628779	−0.314389	+	0.949294i	$0.601800\pi$
$270$	0.172591	0.0105035
$271$	−6.53411	−0.396919	−0.198459	−	0.980109i	$-0.563594\pi$
$271$	−6.53411	−0.396919	−0.198459	+	0.980109i	$0.563594\pi$
$272$	−24.9731	−1.51421
$273$	0	0
$274$	0.831044	0.0502052
$275$	−11.1683	−0.673471
$276$	2.13041	0.128235
$277$	−14.7541	−0.886486	−0.443243	−	0.896401i	$-0.646172\pi$
$277$	−14.7541	−0.886486	−0.443243	+	0.896401i	$0.646172\pi$
$278$	0.815417	0.0489055
$279$	−10.4918	−0.628128
$280$	0	0
$281$	−9.67355	−0.577075	−0.288538	−	0.957469i	$-0.593169\pi$
$281$	−9.67355	−0.577075	−0.288538	+	0.957469i	$0.593169\pi$
$282$	−0.723014	−0.0430549
$283$	−18.0256	−1.07151	−0.535756	−	0.844373i	$-0.679973\pi$
$283$	−18.0256	−1.07151	−0.535756	+	0.844373i	$0.679973\pi$
$284$	20.3006	1.20462
$285$	11.3002	0.669366
$286$	−1.21085	−0.0715989
$287$	0	0
$288$	−0.778289	−0.0458611
$289$	22.4774	1.32220
$290$	−1.05380	−0.0618811
$291$	−16.5259	−0.968767
$292$	9.63698	0.563962
$293$	30.2323	1.76619	0.883094	−	0.469195i	$-0.155456\pi$
$293$	30.2323	1.76619	0.883094	+	0.469195i	$0.155456\pi$
$294$	0	0
$295$	−37.3040	−2.17193
$296$	0.997330	0.0579686
$297$	−5.47071	−0.317443
$298$	−0.170883	−0.00989898
$299$	3.63256	0.210076
$300$	−4.07430	−0.235230
$301$	0	0
$302$	0.387562	0.0223017
$303$	−12.2461	−0.703517
$304$	−16.9259	−0.970767
$305$	37.5179	2.14827
$306$	0.408658	0.0233614
$307$	−5.59004	−0.319040	−0.159520	−	0.987195i	$-0.550995\pi$
$307$	−5.59004	−0.319040	−0.159520	+	0.987195i	$0.550995\pi$
$308$	0	0
$309$	−4.18464	−0.238056
$310$	−1.81079	−0.102846
$311$	−2.84702	−0.161440	−0.0807200	−	0.996737i	$-0.525722\pi$
$311$	−2.84702	−0.161440	−0.0807200	+	0.996737i	$0.525722\pi$
$312$	−0.884395	−0.0500690
$313$	7.97569	0.450813	0.225406	−	0.974265i	$-0.427629\pi$
$313$	7.97569	0.450813	0.225406	+	0.974265i	$0.427629\pi$
$314$	−0.902947	−0.0509562
$315$	0	0
$316$	−18.6060	−1.04667
$317$	−9.27505	−0.520939	−0.260469	−	0.965482i	$-0.583877\pi$
$317$	−9.27505	−0.520939	−0.260469	+	0.965482i	$0.583877\pi$
$318$	−0.529913	−0.0297160
$319$	33.4028	1.87020
$320$	20.9597	1.17168
$321$	4.55230	0.254085
$322$	0	0
$323$	26.7565	1.48877
$324$	−1.99577	−0.110876
$325$	−6.94708	−0.385355
$326$	0.0625837	0.00346619
$327$	−9.25158	−0.511613
$328$	−0.259888	−0.0143499
$329$	0	0
$330$	−0.944192	−0.0519761
$331$	14.6322	0.804257	0.402129	−	0.915583i	$-0.368270\pi$
$331$	14.6322	0.804257	0.402129	+	0.915583i	$0.368270\pi$
$332$	10.0492	0.551519
$333$	3.83754	0.210296
$334$	0.710016	0.0388504
$335$	17.3003	0.945217
$336$	0	0
$337$	14.1264	0.769517	0.384758	−	0.923017i	$-0.374285\pi$
$337$	14.1264	0.769517	0.384758	+	0.923017i	$0.374285\pi$
$338$	0.0923374	0.00502249
$339$	6.81242	0.370000
$340$	−33.2749	−1.80458
$341$	57.3976	3.10825
$342$	0.276975	0.0149771
$343$	0	0
$344$	−1.21777	−0.0656580
$345$	2.83259	0.152502
$346$	1.18258	0.0635759
$347$	20.2540	1.08729	0.543645	−	0.839315i	$-0.317044\pi$
$347$	20.2540	1.08729	0.543645	+	0.839315i	$0.317044\pi$
$348$	12.1857	0.653222
$349$	−23.8877	−1.27868	−0.639339	−	0.768925i	$-0.720792\pi$
$349$	−23.8877	−1.27868	−0.639339	+	0.768925i	$0.720792\pi$
$350$	0	0
$351$	−3.40299	−0.181638
$352$	4.25779	0.226941
$353$	19.9546	1.06208	0.531039	−	0.847347i	$-0.321802\pi$
$353$	19.9546	1.06208	0.531039	+	0.847347i	$0.321802\pi$
$354$	−0.914345	−0.0485969
$355$	26.9917	1.43257
$356$	−17.2176	−0.912532
$357$	0	0
$358$	−0.932532	−0.0492859
$359$	−4.70206	−0.248165	−0.124082	−	0.992272i	$-0.539599\pi$
$359$	−4.70206	−0.248165	−0.124082	+	0.992272i	$0.539599\pi$
$360$	−0.689632	−0.0363468
$361$	−0.865350	−0.0455448
$362$	−1.71844	−0.0903189
$363$	18.9286	0.993495
$364$	0	0
$365$	12.8133	0.670680
$366$	0.919587	0.0480676
$367$	−12.9579	−0.676398	−0.338199	−	0.941075i	$-0.609818\pi$
$367$	−12.9579	−0.676398	−0.338199	+	0.941075i	$0.609818\pi$
$368$	−4.24277	−0.221170
$369$	−1.00000	−0.0520579
$370$	0.662323	0.0344326
$371$	0	0
$372$	20.9392	1.08565
$373$	24.5509	1.27120	0.635599	−	0.772019i	$-0.280753\pi$
$373$	24.5509	1.27120	0.635599	+	0.772019i	$0.280753\pi$
$374$	−2.23565	−0.115603
$375$	7.85069	0.405408
$376$	2.88900	0.148989
$377$	20.7778	1.07011
$378$	0	0
$379$	33.8102	1.73671	0.868356	−	0.495941i	$-0.165177\pi$
$379$	33.8102	1.73671	0.868356	+	0.495941i	$0.165177\pi$
$380$	−22.5526	−1.15692
$381$	−13.5337	−0.693353
$382$	−0.288038	−0.0147373
$383$	−23.0463	−1.17761	−0.588805	−	0.808275i	$-0.700401\pi$
$383$	−23.0463	−1.17761	−0.588805	+	0.808275i	$0.700401\pi$
$384$	2.07031	0.105650
$385$	0	0
$386$	−0.306221	−0.0155862
$387$	−4.68577	−0.238191
$388$	32.9820	1.67440
$389$	−4.13177	−0.209489	−0.104745	−	0.994499i	$-0.533402\pi$
$389$	−4.13177	−0.209489	−0.104745	+	0.994499i	$0.533402\pi$
$390$	−0.587324	−0.0297403
$391$	6.70697	0.339186
$392$	0	0
$393$	4.69146	0.236653
$394$	−1.68678	−0.0849788
$395$	−24.7386	−1.24473
$396$	10.9183	0.548664
$397$	25.3153	1.27054	0.635268	−	0.772292i	$-0.280890\pi$
$397$	25.3153	1.27054	0.635268	+	0.772292i	$0.280890\pi$
$398$	0.971607	0.0487023
$399$	0	0
$400$	8.11409	0.405704
$401$	27.0679	1.35171	0.675853	−	0.737037i	$-0.263776\pi$
$401$	27.0679	1.35171	0.675853	+	0.737037i	$0.263776\pi$
$402$	0.424041	0.0211492
$403$	35.7035	1.77852
$404$	24.4403	1.21595
$405$	−2.65358	−0.131857
$406$	0	0
$407$	−20.9941	−1.04064
$408$	−1.63290	−0.0808408
$409$	−36.0335	−1.78174	−0.890870	−	0.454258i	$-0.849904\pi$
$409$	−36.0335	−1.78174	−0.890870	+	0.454258i	$0.849904\pi$
$410$	−0.172591	−0.00852364
$411$	−12.7773	−0.630256
$412$	8.35159	0.411453
$413$	0	0
$414$	0.0694285	0.00341223
$415$	13.3614	0.655883
$416$	2.64851	0.129854
$417$	−12.5370	−0.613940
$418$	−1.51525	−0.0741132
$419$	28.2596	1.38057	0.690287	−	0.723536i	$-0.257484\pi$
$419$	28.2596	1.38057	0.690287	+	0.723536i	$0.257484\pi$
$420$	0	0
$421$	18.5570	0.904415	0.452207	−	0.891913i	$-0.350637\pi$
$421$	18.5570	0.904415	0.452207	+	0.891913i	$0.350637\pi$
$422$	−0.829595	−0.0403841
$423$	11.1163	0.540494
$424$	2.11741	0.102830
$425$	−12.8268	−0.622189
$426$	0.661584	0.0320538
$427$	0	0
$428$	−9.08534	−0.439157
$429$	18.6167	0.898824
$430$	−0.808719	−0.0389999
$431$	−1.77967	−0.0857239	−0.0428619	−	0.999081i	$-0.513648\pi$
$431$	−1.77967	−0.0857239	−0.0428619	+	0.999081i	$0.513648\pi$
$432$	3.97464	0.191230
$433$	−28.5720	−1.37308	−0.686541	−	0.727092i	$-0.740872\pi$
$433$	−28.5720	−1.37308	−0.686541	+	0.727092i	$0.740872\pi$
$434$	0	0
$435$	16.2021	0.776832
$436$	18.4640	0.884266
$437$	4.54576	0.217453
$438$	0.314063	0.0150065
$439$	−6.39885	−0.305400	−0.152700	−	0.988273i	$-0.548797\pi$
$439$	−6.39885	−0.305400	−0.152700	+	0.988273i	$0.548797\pi$
$440$	3.77278	0.179860
$441$	0	0
$442$	−1.39066	−0.0661468
$443$	−25.5094	−1.21199	−0.605995	−	0.795468i	$-0.707225\pi$
$443$	−25.5094	−1.21199	−0.605995	+	0.795468i	$0.707225\pi$
$444$	−7.65885	−0.363473
$445$	−22.8925	−1.08521
$446$	−0.490990	−0.0232490
$447$	2.62732	0.124268
$448$	0	0
$449$	−15.3343	−0.723671	−0.361835	−	0.932242i	$-0.617850\pi$
$449$	−15.3343	−0.723671	−0.361835	+	0.932242i	$0.617850\pi$
$450$	−0.132779	−0.00625924
$451$	5.47071	0.257605
$452$	−13.5960	−0.639503
$453$	−5.95876	−0.279967
$454$	0.519292	0.0243716
$455$	0	0
$456$	−1.10673	−0.0518273
$457$	−12.4509	−0.582430	−0.291215	−	0.956658i	$-0.594059\pi$
$457$	−12.4509	−0.582430	−0.291215	+	0.956658i	$0.594059\pi$
$458$	0.992361	0.0463700
$459$	−6.28311	−0.293270
$460$	−5.65320	−0.263582
$461$	−37.9754	−1.76869	−0.884345	−	0.466833i	$-0.845395\pi$
$461$	−37.9754	−1.76869	−0.884345	+	0.466833i	$0.845395\pi$
$462$	0	0
$463$	7.28313	0.338476	0.169238	−	0.985575i	$-0.445869\pi$
$463$	7.28313	0.338476	0.169238	+	0.985575i	$0.445869\pi$
$464$	−24.2682	−1.12662
$465$	27.8408	1.29109
$466$	0.855269	0.0396196
$467$	−12.6148	−0.583743	−0.291871	−	0.956458i	$-0.594278\pi$
$467$	−12.6148	−0.583743	−0.291871	+	0.956458i	$0.594278\pi$
$468$	6.79158	0.313941
$469$	0	0
$470$	1.91857	0.0884972
$471$	13.8828	0.639685
$472$	3.65351	0.168166
$473$	25.6344	1.17867
$474$	−0.606358	−0.0278509
$475$	−8.69354	−0.398887
$476$	0	0
$477$	8.14739	0.373043
$478$	−1.57391	−0.0719888
$479$	−42.8999	−1.96015	−0.980073	−	0.198638i	$-0.936348\pi$
$479$	−42.8999	−1.96015	−0.980073	+	0.198638i	$0.936348\pi$
$480$	2.06525	0.0942653
$481$	−13.0591	−0.595443
$482$	−1.02270	−0.0465827
$483$	0	0
$484$	−37.7772	−1.71714
$485$	43.8528	1.99125
$486$	−0.0650408	−0.00295031
$487$	−31.2404	−1.41564	−0.707819	−	0.706394i	$-0.750321\pi$
$487$	−31.2404	−1.41564	−0.707819	+	0.706394i	$0.750321\pi$
$488$	−3.67446	−0.166335
$489$	−0.962223	−0.0435132
$490$	0	0
$491$	39.3972	1.77797	0.888985	−	0.457936i	$-0.151411\pi$
$491$	39.3972	1.77797	0.888985	+	0.457936i	$0.151411\pi$
$492$	1.99577	0.0899762
$493$	38.3632	1.72779
$494$	−0.942541	−0.0424069
$495$	14.5169	0.652488
$496$	−41.7011	−1.87244
$497$	0	0
$498$	0.327495	0.0146754
$499$	11.5175	0.515594	0.257797	−	0.966199i	$-0.417003\pi$
$499$	11.5175	0.515594	0.257797	+	0.966199i	$0.417003\pi$
$500$	−15.6682	−0.700702
$501$	−10.9165	−0.487712
$502$	−0.170647	−0.00761633
$503$	−4.15133	−0.185099	−0.0925494	−	0.995708i	$-0.529502\pi$
$503$	−4.15133	−0.185099	−0.0925494	+	0.995708i	$0.529502\pi$
$504$	0	0
$505$	32.4958	1.44605
$506$	−0.379823	−0.0168852
$507$	−1.41969	−0.0630505
$508$	27.0102	1.19838
$509$	5.60204	0.248306	0.124153	−	0.992263i	$-0.460379\pi$
$509$	5.60204	0.248306	0.124153	+	0.992263i	$0.460379\pi$
$510$	−1.08441	−0.0480183
$511$	0	0
$512$	−5.15934	−0.228013
$513$	−4.25848	−0.188016
$514$	1.27437	0.0562103
$515$	11.1043	0.489313
$516$	9.35171	0.411686
$517$	−60.8141	−2.67460
$518$	0	0
$519$	−18.1821	−0.798108
$520$	2.34681	0.102914
$521$	−6.60586	−0.289408	−0.144704	−	0.989475i	$-0.546223\pi$
$521$	−6.60586	−0.289408	−0.144704	+	0.989475i	$0.546223\pi$
$522$	0.397124	0.0173816
$523$	−14.2512	−0.623163	−0.311581	−	0.950219i	$-0.600859\pi$
$523$	−14.2512	−0.623163	−0.311581	+	0.950219i	$0.600859\pi$
$524$	−9.36308	−0.409028
$525$	0	0
$526$	−0.0830934	−0.00362304
$527$	65.9212	2.87157
$528$	−21.7441	−0.946289
$529$	−21.8605	−0.950458
$530$	1.40616	0.0610798
$531$	14.0580	0.610066
$532$	0	0
$533$	3.40299	0.147400
$534$	−0.561110	−0.0242816
$535$	−12.0799	−0.522259
$536$	−1.69437	−0.0731857
$537$	14.3377	0.618715
$538$	0.670748	0.0289180
$539$	0	0
$540$	5.29593	0.227900
$541$	40.0215	1.72066	0.860329	−	0.509738i	$-0.170258\pi$
$541$	40.0215	1.72066	0.860329	+	0.509738i	$0.170258\pi$
$542$	0.424983	0.0182546
$543$	26.4209	1.13383
$544$	4.89007	0.209660
$545$	24.5498	1.05160
$546$	0	0
$547$	−12.9488	−0.553651	−0.276826	−	0.960920i	$-0.589282\pi$
$547$	−12.9488	−0.553651	−0.276826	+	0.960920i	$0.589282\pi$
$548$	25.5005	1.08933
$549$	−14.1386	−0.603422
$550$	0.726392	0.0309735
$551$	26.0013	1.10769
$552$	−0.277420	−0.0118078
$553$	0	0
$554$	0.959616	0.0407702
$555$	−10.1832	−0.432253
$556$	25.0210	1.06113
$557$	−11.4145	−0.483648	−0.241824	−	0.970320i	$-0.577746\pi$
$557$	−11.4145	−0.483648	−0.241824	+	0.970320i	$0.577746\pi$
$558$	0.682395	0.0288881
$559$	15.9456	0.674427
$560$	0	0
$561$	34.3730	1.45123
$562$	0.629175	0.0265401
$563$	−34.8335	−1.46806	−0.734028	−	0.679119i	$-0.762362\pi$
$563$	−34.8335	−1.46806	−0.734028	+	0.679119i	$0.762362\pi$
$564$	−22.1856	−0.934183
$565$	−18.0773	−0.760516
$566$	1.17240	0.0492796
$567$	0	0
$568$	−2.64354	−0.110920
$569$	−41.6149	−1.74459	−0.872294	−	0.488982i	$-0.837369\pi$
$569$	−41.6149	−1.74459	−0.872294	+	0.488982i	$0.837369\pi$
$570$	−0.734974	−0.0307847
$571$	−40.2264	−1.68342	−0.841711	−	0.539929i	$-0.818451\pi$
$571$	−40.2264	−1.68342	−0.841711	+	0.539929i	$0.818451\pi$
$572$	−37.1547	−1.55352
$573$	4.42857	0.185006
$574$	0	0
$575$	−2.17919	−0.0908784
$576$	−7.89865	−0.329110
$577$	22.0329	0.917242	0.458621	−	0.888632i	$-0.348343\pi$
$577$	22.0329	0.917242	0.458621	+	0.888632i	$0.348343\pi$
$578$	−1.46195	−0.0608091
$579$	4.70814	0.195664
$580$	−32.3357	−1.34267
$581$	0	0
$582$	1.07486	0.0445544
$583$	−44.5720	−1.84598
$584$	−1.25492	−0.0519290
$585$	9.03008	0.373348
$586$	−1.96633	−0.0812284
$587$	−14.1762	−0.585116	−0.292558	−	0.956248i	$-0.594506\pi$
$587$	−14.1762	−0.585116	−0.292558	+	0.956248i	$0.594506\pi$
$588$	0	0
$589$	44.6792	1.84097
$590$	2.42628	0.0998885
$591$	25.9342	1.06679
$592$	15.2528	0.626887
$593$	−0.457779	−0.0187987	−0.00939936	−	0.999956i	$-0.502992\pi$
$593$	−0.457779	−0.0187987	−0.00939936	+	0.999956i	$0.502992\pi$
$594$	0.355819	0.0145994
$595$	0	0
$596$	−5.24352	−0.214783
$597$	−14.9384	−0.611389
$598$	−0.236264	−0.00966156
$599$	−27.7858	−1.13530	−0.567648	−	0.823271i	$-0.692147\pi$
$599$	−27.7858	−1.13530	−0.567648	+	0.823271i	$0.692147\pi$
$600$	0.530552	0.0216597
$601$	−30.0070	−1.22401	−0.612007	−	0.790853i	$-0.709637\pi$
$601$	−30.0070	−1.22401	−0.612007	+	0.790853i	$0.709637\pi$
$602$	0	0
$603$	−6.51962	−0.265499
$604$	11.8923	0.483891
$605$	−50.2285	−2.04208
$606$	0.796493	0.0323553
$607$	−24.6437	−1.00026	−0.500129	−	0.865951i	$-0.666714\pi$
$607$	−24.6437	−1.00026	−0.500129	+	0.865951i	$0.666714\pi$
$608$	3.31433	0.134414
$609$	0	0
$610$	−2.44020	−0.0988006
$611$	−37.8287	−1.53038
$612$	12.5396	0.506885
$613$	31.1894	1.25973	0.629865	−	0.776705i	$-0.283110\pi$
$613$	31.1894	1.25973	0.629865	+	0.776705i	$0.283110\pi$
$614$	0.363580	0.0146729
$615$	2.65358	0.107003
$616$	0	0
$617$	−35.2034	−1.41724	−0.708619	−	0.705592i	$-0.750681\pi$
$617$	−35.2034	−1.41724	−0.708619	+	0.705592i	$0.750681\pi$
$618$	0.272172	0.0109484
$619$	−32.5283	−1.30742	−0.653711	−	0.756744i	$-0.726789\pi$
$619$	−32.5283	−1.30742	−0.653711	+	0.756744i	$0.726789\pi$
$620$	−55.5639	−2.23150
$621$	−1.06746	−0.0428358
$622$	0.185173	0.00742475
$623$	0	0
$624$	−13.5256	−0.541459
$625$	−31.0397	−1.24159
$626$	−0.518745	−0.0207332
$627$	23.2969	0.930388
$628$	−27.7068	−1.10562
$629$	−24.1117	−0.961395
$630$	0	0
$631$	1.97175	0.0784943	0.0392471	−	0.999230i	$-0.487504\pi$
$631$	1.97175	0.0784943	0.0392471	+	0.999230i	$0.487504\pi$
$632$	2.42287	0.0963765
$633$	12.7550	0.506966
$634$	0.603257	0.0239584
$635$	35.9127	1.42515
$636$	−16.2603	−0.644764
$637$	0	0
$638$	−2.17255	−0.0860119
$639$	−10.1718	−0.402391
$640$	−5.49373	−0.217159
$641$	5.94124	0.234665	0.117333	−	0.993093i	$-0.462566\pi$
$641$	5.94124	0.234665	0.117333	+	0.993093i	$0.462566\pi$
$642$	−0.296085	−0.0116855
$643$	−0.918004	−0.0362025	−0.0181013	−	0.999836i	$-0.505762\pi$
$643$	−0.918004	−0.0362025	−0.0181013	+	0.999836i	$0.505762\pi$
$644$	0	0
$645$	12.4340	0.489590
$646$	−1.74026	−0.0684697
$647$	41.6269	1.63652	0.818260	−	0.574848i	$-0.194939\pi$
$647$	41.6269	1.63652	0.818260	+	0.574848i	$0.194939\pi$
$648$	0.259888	0.0102094
$649$	−76.9073	−3.01888
$650$	0.451844	0.0177228
$651$	0	0
$652$	1.92038	0.0752077
$653$	−16.7700	−0.656260	−0.328130	−	0.944633i	$-0.606418\pi$
$653$	−16.7700	−0.656260	−0.328130	+	0.944633i	$0.606418\pi$
$654$	0.601730	0.0235295
$655$	−12.4492	−0.486429
$656$	−3.97464	−0.155183
$657$	−4.82870	−0.188386
$658$	0	0
$659$	30.2319	1.17767	0.588833	−	0.808255i	$-0.299588\pi$
$659$	30.2319	1.17767	0.588833	+	0.808255i	$0.299588\pi$
$660$	−28.9725	−1.12775
$661$	1.62355	0.0631488	0.0315744	−	0.999501i	$-0.489948\pi$
$661$	1.62355	0.0631488	0.0315744	+	0.999501i	$0.489948\pi$
$662$	−0.951688	−0.0369884
$663$	21.3813	0.830382
$664$	−1.30859	−0.0507833
$665$	0	0
$666$	−0.249597	−0.00967167
$667$	6.51767	0.252365
$668$	21.7868	0.842956
$669$	7.54896	0.291859
$670$	−1.12523	−0.0434712
$671$	77.3483	2.98600
$672$	0	0
$673$	−28.1360	−1.08456	−0.542282	−	0.840196i	$-0.682440\pi$
$673$	−28.1360	−1.08456	−0.542282	+	0.840196i	$0.682440\pi$
$674$	−0.918795	−0.0353907
$675$	2.04147	0.0785761
$676$	2.83337	0.108976
$677$	−17.6912	−0.679929	−0.339964	−	0.940438i	$-0.610415\pi$
$677$	−17.6912	−0.679929	−0.339964	+	0.940438i	$0.610415\pi$
$678$	−0.443085	−0.0170166
$679$	0	0
$680$	4.33303	0.166164
$681$	−7.98410	−0.305951
$682$	−3.73318	−0.142951
$683$	3.62028	0.138526	0.0692630	−	0.997598i	$-0.477935\pi$
$683$	3.62028	0.138526	0.0692630	+	0.997598i	$0.477935\pi$
$684$	8.49894	0.324965
$685$	33.9055	1.29546
$686$	0	0
$687$	−15.2575	−0.582111
$688$	−18.6242	−0.710042
$689$	−27.7255	−1.05626
$690$	−0.184234	−0.00701366
$691$	−10.5745	−0.402273	−0.201136	−	0.979563i	$-0.564463\pi$
$691$	−10.5745	−0.402273	−0.201136	+	0.979563i	$0.564463\pi$
$692$	36.2874	1.37944
$693$	0	0
$694$	−1.31733	−0.0500053
$695$	33.2679	1.26192
$696$	−1.58681	−0.0601480
$697$	6.28311	0.237990
$698$	1.55367	0.0588073
$699$	−13.1497	−0.497369
$700$	0	0
$701$	−38.8486	−1.46729	−0.733645	−	0.679533i	$-0.762182\pi$
$701$	−38.8486	−1.46729	−0.733645	+	0.679533i	$0.762182\pi$
$702$	0.221333	0.00835367
$703$	−16.3421	−0.616353
$704$	43.2112	1.62858
$705$	−29.4980	−1.11096
$706$	−1.29786	−0.0488458
$707$	0	0
$708$	−28.0566	−1.05443
$709$	29.2915	1.10006	0.550032	−	0.835144i	$-0.314616\pi$
$709$	29.2915	1.10006	0.550032	+	0.835144i	$0.314616\pi$
$710$	−1.75556	−0.0658851
$711$	9.32274	0.349630
$712$	2.24207	0.0840250
$713$	11.1996	0.419428
$714$	0	0
$715$	−49.4009	−1.84749
$716$	−28.6147	−1.06938
$717$	24.1988	0.903720
$718$	0.305825	0.0114133
$719$	−8.04364	−0.299977	−0.149989	−	0.988688i	$-0.547924\pi$
$719$	−8.04364	−0.299977	−0.149989	+	0.988688i	$0.547924\pi$
$720$	−10.5470	−0.393063
$721$	0	0
$722$	0.0562831	0.00209464
$723$	15.7240	0.584782
$724$	−52.7300	−1.95970
$725$	−12.4647	−0.462928
$726$	−1.23113	−0.0456916
$727$	45.4403	1.68529	0.842643	−	0.538472i	$-0.180998\pi$
$727$	45.4403	1.68529	0.842643	+	0.538472i	$0.180998\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.833389	−0.0308451
$731$	29.4412	1.08892
$732$	28.2175	1.04295
$733$	−36.2630	−1.33940	−0.669702	−	0.742630i	$-0.733578\pi$
$733$	−36.2630	−1.33940	−0.669702	+	0.742630i	$0.733578\pi$
$734$	0.842794	0.0311081
$735$	0	0
$736$	0.830794	0.0306235
$737$	35.6669	1.31381
$738$	0.0650408	0.00239418
$739$	−34.1511	−1.25627	−0.628134	−	0.778105i	$-0.716181\pi$
$739$	−34.1511	−1.25627	−0.628134	+	0.778105i	$0.716181\pi$
$740$	20.3233	0.747101
$741$	14.4915	0.532360
$742$	0	0
$743$	19.8077	0.726673	0.363337	−	0.931658i	$-0.381637\pi$
$743$	19.8077	0.726673	0.363337	+	0.931658i	$0.381637\pi$
$744$	−2.72669	−0.0999655
$745$	−6.97179	−0.255427
$746$	−1.59681	−0.0584634
$747$	−5.03523	−0.184229
$748$	−68.6006	−2.50829
$749$	0	0
$750$	−0.510615	−0.0186450
$751$	22.2356	0.811387	0.405694	−	0.914009i	$-0.367030\pi$
$751$	22.2356	0.811387	0.405694	+	0.914009i	$0.367030\pi$
$752$	44.1833	1.61120
$753$	2.62369	0.0956124
$754$	−1.35141	−0.0492153
$755$	15.8120	0.575458
$756$	0	0
$757$	−38.0167	−1.38174	−0.690870	−	0.722979i	$-0.742772\pi$
$757$	−38.0167	−1.38174	−0.690870	+	0.722979i	$0.742772\pi$
$758$	−2.19904	−0.0798727
$759$	5.83977	0.211970
$760$	2.93679	0.106528
$761$	−18.8243	−0.682382	−0.341191	−	0.939994i	$-0.610830\pi$
$761$	−18.8243	−0.682382	−0.341191	+	0.939994i	$0.610830\pi$
$762$	0.880243	0.0318878
$763$	0	0
$764$	−8.83841	−0.319762
$765$	16.6727	0.602803
$766$	1.49895	0.0541591
$767$	−47.8393	−1.72738
$768$	15.6626	0.565177
$769$	−2.09557	−0.0755682	−0.0377841	−	0.999286i	$-0.512030\pi$
$769$	−2.09557	−0.0755682	−0.0377841	+	0.999286i	$0.512030\pi$
$770$	0	0
$771$	−19.5935	−0.705642
$772$	−9.39637	−0.338183
$773$	6.12334	0.220241	0.110121	−	0.993918i	$-0.464876\pi$
$773$	6.12334	0.220241	0.110121	+	0.993918i	$0.464876\pi$
$774$	0.304766	0.0109546
$775$	−21.4187	−0.769382
$776$	−4.29489	−0.154178
$777$	0	0
$778$	0.268734	0.00963456
$779$	4.25848	0.152576
$780$	−18.0220	−0.645290
$781$	55.6471	1.99121
$782$	−0.436227	−0.0155994
$783$	−6.10576	−0.218202
$784$	0	0
$785$	−36.8390	−1.31484
$786$	−0.305136	−0.0108839
$787$	25.8179	0.920310	0.460155	−	0.887839i	$-0.347794\pi$
$787$	25.8179	0.920310	0.460155	+	0.887839i	$0.347794\pi$
$788$	−51.7587	−1.84383
$789$	1.27756	0.0454823
$790$	1.60902	0.0572463
$791$	0	0
$792$	−1.42177	−0.0505204
$793$	48.1136	1.70856
$794$	−1.64652	−0.0584329
$795$	−21.6197	−0.766773
$796$	29.8137	1.05672
$797$	17.1847	0.608714	0.304357	−	0.952558i	$-0.401558\pi$
$797$	17.1847	0.608714	0.304357	+	0.952558i	$0.401558\pi$
$798$	0	0
$799$	−69.8450	−2.47094
$800$	−1.58885	−0.0561744
$801$	8.62706	0.304822
$802$	−1.76052	−0.0621660
$803$	26.4164	0.932215
$804$	13.0117	0.458886
$805$	0	0
$806$	−2.32218	−0.0817954
$807$	−10.3127	−0.363026
$808$	−3.18260	−0.111964
$809$	−4.69562	−0.165089	−0.0825446	−	0.996587i	$-0.526305\pi$
$809$	−4.69562	−0.165089	−0.0825446	+	0.996587i	$0.526305\pi$
$810$	0.172591	0.00606422
$811$	18.8630	0.662371	0.331185	−	0.943566i	$-0.392551\pi$
$811$	18.8630	0.662371	0.331185	+	0.943566i	$0.392551\pi$
$812$	0	0
$813$	−6.53411	−0.229161
$814$	1.36547	0.0478597
$815$	2.55333	0.0894393
$816$	−24.9731	−0.874232
$817$	19.9542	0.698110
$818$	2.34364	0.0819436
$819$	0	0
$820$	−5.29593	−0.184942
$821$	37.6024	1.31233	0.656167	−	0.754616i	$-0.272177\pi$
$821$	37.6024	1.31233	0.656167	+	0.754616i	$0.272177\pi$
$822$	0.831044	0.0289860
$823$	−45.6703	−1.59197	−0.795983	−	0.605320i	$-0.793045\pi$
$823$	−45.6703	−1.59197	−0.795983	+	0.605320i	$0.793045\pi$
$824$	−1.08754	−0.0378862
$825$	−11.1683	−0.388829
$826$	0	0
$827$	−23.4857	−0.816678	−0.408339	−	0.912830i	$-0.633892\pi$
$827$	−23.4857	−0.816678	−0.408339	+	0.912830i	$0.633892\pi$
$828$	2.13041	0.0740368
$829$	−27.5826	−0.957982	−0.478991	−	0.877820i	$-0.658997\pi$
$829$	−27.5826	−0.957982	−0.478991	+	0.877820i	$0.658997\pi$
$830$	−0.869033	−0.0301646
$831$	−14.7541	−0.511813
$832$	26.8790	0.931862
$833$	0	0
$834$	0.815417	0.0282356
$835$	28.9677	1.00247
$836$	−46.4952	−1.60807
$837$	−10.4918	−0.362650
$838$	−1.83803	−0.0634937
$839$	11.7966	0.407263	0.203631	−	0.979048i	$-0.434726\pi$
$839$	11.7966	0.407263	0.203631	+	0.979048i	$0.434726\pi$
$840$	0	0
$841$	8.28036	0.285530
$842$	−1.20696	−0.0415947
$843$	−9.67355	−0.333175
$844$	−25.4561	−0.876233
$845$	3.76724	0.129597
$846$	−0.723014	−0.0248577
$847$	0	0
$848$	32.3829	1.11203
$849$	−18.0256	−0.618637
$850$	0.834262	0.0286149
$851$	−4.09643	−0.140424
$852$	20.3006	0.695488
$853$	−6.50215	−0.222629	−0.111315	−	0.993785i	$-0.535506\pi$
$853$	−6.50215	−0.222629	−0.111315	+	0.993785i	$0.535506\pi$
$854$	0	0
$855$	11.3002	0.386459
$856$	1.18309	0.0404371
$857$	50.2945	1.71803	0.859014	−	0.511952i	$-0.171078\pi$
$857$	50.2945	1.71803	0.859014	+	0.511952i	$0.171078\pi$
$858$	−1.21085	−0.0413376
$859$	0.973780	0.0332249	0.0166125	−	0.999862i	$-0.494712\pi$
$859$	0.973780	0.0332249	0.0166125	+	0.999862i	$0.494712\pi$
$860$	−24.8155	−0.846201
$861$	0	0
$862$	0.115751	0.00394251
$863$	−40.4421	−1.37667	−0.688333	−	0.725395i	$-0.741657\pi$
$863$	−40.4421	−1.37667	−0.688333	+	0.725395i	$0.741657\pi$
$864$	−0.778289	−0.0264779
$865$	48.2477	1.64047
$866$	1.85834	0.0631491
$867$	22.4774	0.763373
$868$	0	0
$869$	−51.0019	−1.73012
$870$	−1.05380	−0.0357271
$871$	22.1862	0.751750
$872$	−2.40437	−0.0814224
$873$	−16.5259	−0.559318
$874$	−0.295660	−0.0100008
$875$	0	0
$876$	9.63698	0.325603
$877$	−35.9374	−1.21352	−0.606760	−	0.794885i	$-0.707531\pi$
$877$	−35.9374	−1.21352	−0.606760	+	0.794885i	$0.707531\pi$
$878$	0.416186	0.0140456
$879$	30.2323	1.01971
$880$	57.6995	1.94505
$881$	4.34713	0.146459	0.0732293	−	0.997315i	$-0.476669\pi$
$881$	4.34713	0.146459	0.0732293	+	0.997315i	$0.476669\pi$
$882$	0	0
$883$	24.4854	0.824000	0.412000	−	0.911184i	$-0.364830\pi$
$883$	24.4854	0.824000	0.412000	+	0.911184i	$0.364830\pi$
$884$	−42.6722	−1.43522
$885$	−37.3040	−1.25396
$886$	1.65915	0.0557404
$887$	−5.39213	−0.181050	−0.0905250	−	0.995894i	$-0.528854\pi$
$887$	−5.39213	−0.181050	−0.0905250	+	0.995894i	$0.528854\pi$
$888$	0.997330	0.0334682
$889$	0	0
$890$	1.48895	0.0499097
$891$	−5.47071	−0.183276
$892$	−15.0660	−0.504446
$893$	−47.3386	−1.58413
$894$	−0.170883	−0.00571518
$895$	−38.0461	−1.27174
$896$	0	0
$897$	3.63256	0.121288
$898$	0.997355	0.0332822
$899$	64.0605	2.13654
$900$	−4.07430	−0.135810
$901$	−51.1909	−1.70542
$902$	−0.355819	−0.0118475
$903$	0	0
$904$	1.77046	0.0588848
$905$	−70.1098	−2.33053
$906$	0.387562	0.0128759
$907$	25.2422	0.838154	0.419077	−	0.907951i	$-0.362354\pi$
$907$	25.2422	0.838154	0.419077	+	0.907951i	$0.362354\pi$
$908$	15.9344	0.528802
$909$	−12.2461	−0.406176
$910$	0	0
$911$	−7.07772	−0.234495	−0.117248	−	0.993103i	$-0.537407\pi$
$911$	−7.07772	−0.234495	−0.117248	+	0.993103i	$0.537407\pi$
$912$	−16.9259	−0.560473
$913$	27.5462	0.911648
$914$	0.809818	0.0267864
$915$	37.5179	1.24030
$916$	30.4505	1.00611
$917$	0	0
$918$	0.408658	0.0134877
$919$	−9.66161	−0.318707	−0.159353	−	0.987222i	$-0.550941\pi$
$919$	−9.66161	−0.318707	−0.159353	+	0.987222i	$0.550941\pi$
$920$	0.736156	0.0242703
$921$	−5.59004	−0.184198
$922$	2.46995	0.0813435
$923$	34.6146	1.13935
$924$	0	0
$925$	7.83421	0.257587
$926$	−0.473700	−0.0155668
$927$	−4.18464	−0.137442
$928$	4.75205	0.155994
$929$	−11.2288	−0.368404	−0.184202	−	0.982888i	$-0.558970\pi$
$929$	−11.2288	−0.368404	−0.184202	+	0.982888i	$0.558970\pi$
$930$	−1.81079	−0.0593781
$931$	0	0
$932$	26.2438	0.859646
$933$	−2.84702	−0.0932074
$934$	0.820475	0.0268468
$935$	−91.2114	−2.98293
$936$	−0.884395	−0.0289074
$937$	34.3993	1.12378	0.561888	−	0.827214i	$-0.310075\pi$
$937$	34.3993	1.12378	0.561888	+	0.827214i	$0.310075\pi$
$938$	0	0
$939$	7.97569	0.260277
$940$	58.8712	1.92017
$941$	28.0008	0.912801	0.456401	−	0.889774i	$-0.349138\pi$
$941$	28.0008	0.912801	0.456401	+	0.889774i	$0.349138\pi$
$942$	−0.902947	−0.0294196
$943$	1.06746	0.0347613
$944$	55.8755	1.81859
$945$	0	0
$946$	−1.66728	−0.0542081
$947$	−1.50126	−0.0487845	−0.0243922	−	0.999702i	$-0.507765\pi$
$947$	−1.50126	−0.0487845	−0.0243922	+	0.999702i	$0.507765\pi$
$948$	−18.6060	−0.604296
$949$	16.4320	0.533406
$950$	0.565435	0.0183451
$951$	−9.27505	−0.300764
$952$	0	0
$953$	26.3166	0.852479	0.426240	−	0.904610i	$-0.359838\pi$
$953$	26.3166	0.852479	0.426240	+	0.904610i	$0.359838\pi$
$954$	−0.529913	−0.0171566
$955$	−11.7516	−0.380271
$956$	−48.2952	−1.56198
$957$	33.4028	1.07976
$958$	2.79024	0.0901486
$959$	0	0
$960$	20.9597	0.676471
$961$	79.0781	2.55091
$962$	0.849374	0.0273849
$963$	4.55230	0.146696
$964$	−31.3815	−1.01073
$965$	−12.4934	−0.402177
$966$	0	0
$967$	−20.1209	−0.647045	−0.323523	−	0.946220i	$-0.604867\pi$
$967$	−20.1209	−0.647045	−0.323523	+	0.946220i	$0.604867\pi$
$968$	4.91932	0.158113
$969$	26.7565	0.859542
$970$	−2.85222	−0.0915793
$971$	−24.1292	−0.774341	−0.387171	−	0.922008i	$-0.626548\pi$
$971$	−24.1292	−0.774341	−0.387171	+	0.922008i	$0.626548\pi$
$972$	−1.99577	−0.0640143
$973$	0	0
$974$	2.03190	0.0651063
$975$	−6.94708	−0.222485
$976$	−56.1959	−1.79879
$977$	29.1755	0.933408	0.466704	−	0.884414i	$-0.345441\pi$
$977$	29.1755	0.933408	0.466704	+	0.884414i	$0.345441\pi$
$978$	0.0625837	0.00200121
$979$	−47.1961	−1.50839
$980$	0	0
$981$	−9.25158	−0.295380
$982$	−2.56242	−0.0817702
$983$	−7.77819	−0.248086	−0.124043	−	0.992277i	$-0.539586\pi$
$983$	−7.77819	−0.248086	−0.124043	+	0.992277i	$0.539586\pi$
$984$	−0.259888	−0.00828492
$985$	−68.8184	−2.19274
$986$	−2.49517	−0.0794624
$987$	0	0
$988$	−28.9218	−0.920125
$989$	5.00187	0.159050
$990$	−0.944192	−0.0300084
$991$	−24.9735	−0.793310	−0.396655	−	0.917968i	$-0.629829\pi$
$991$	−24.9735	−0.793310	−0.396655	+	0.917968i	$0.629829\pi$
$992$	8.16566	0.259260
$993$	14.6322	0.464338
$994$	0	0
$995$	39.6403	1.25668
$996$	10.0492	0.318420
$997$	−38.1977	−1.20973	−0.604866	−	0.796327i	$-0.706773\pi$
$997$	−38.1977	−1.20973	−0.604866	+	0.796327i	$0.706773\pi$
$998$	−0.749106	−0.0237125
$999$	3.83754	0.121414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.11	yes	24
7.6	odd	2		6027.2.a.bn.1.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.11	✓	24	7.6	odd	2
6027.2.a.bo.1.11	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)

\(f(q)\)	\(=\)	\(q-0.0650408 q^{2} +1.00000 q^{3} -1.99577 q^{4} -2.65358 q^{5} -0.0650408 q^{6} +0.259888 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0650408 q^{2} +1.00000 q^{3} -1.99577 q^{4} -2.65358 q^{5} -0.0650408 q^{6} +0.259888 q^{8} +1.00000 q^{9} +0.172591 q^{10} -5.47071 q^{11} -1.99577 q^{12} -3.40299 q^{13} -2.65358 q^{15} +3.97464 q^{16} -6.28311 q^{17} -0.0650408 q^{18} -4.25848 q^{19} +5.29593 q^{20} +0.355819 q^{22} -1.06746 q^{23} +0.259888 q^{24} +2.04147 q^{25} +0.221333 q^{26} +1.00000 q^{27} -6.10576 q^{29} +0.172591 q^{30} -10.4918 q^{31} -0.778289 q^{32} -5.47071 q^{33} +0.408658 q^{34} -1.99577 q^{36} +3.83754 q^{37} +0.276975 q^{38} -3.40299 q^{39} -0.689632 q^{40} -1.00000 q^{41} -4.68577 q^{43} +10.9183 q^{44} -2.65358 q^{45} +0.0694285 q^{46} +11.1163 q^{47} +3.97464 q^{48} -0.132779 q^{50} -6.28311 q^{51} +6.79158 q^{52} +8.14739 q^{53} -0.0650408 q^{54} +14.5169 q^{55} -4.25848 q^{57} +0.397124 q^{58} +14.0580 q^{59} +5.29593 q^{60} -14.1386 q^{61} +0.682395 q^{62} -7.89865 q^{64} +9.03008 q^{65} +0.355819 q^{66} -6.51962 q^{67} +12.5396 q^{68} -1.06746 q^{69} -10.1718 q^{71} +0.259888 q^{72} -4.82870 q^{73} -0.249597 q^{74} +2.04147 q^{75} +8.49894 q^{76} +0.221333 q^{78} +9.32274 q^{79} -10.5470 q^{80} +1.00000 q^{81} +0.0650408 q^{82} -5.03523 q^{83} +16.6727 q^{85} +0.304766 q^{86} -6.10576 q^{87} -1.42177 q^{88} +8.62706 q^{89} +0.172591 q^{90} +2.13041 q^{92} -10.4918 q^{93} -0.723014 q^{94} +11.3002 q^{95} -0.778289 q^{96} -16.5259 q^{97} -5.47071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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

Varieties

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Groups

Database

Properties

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