LMFDB - Embedded newform 6027.2.a.bo.1.10

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			1.10
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)

$f(q)$	$=$	$q-0.308797 q^{2} +1.00000 q^{3} -1.90464 q^{4} -0.898648 q^{5} -0.308797 q^{6} +1.20574 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.308797 q^{2} +1.00000 q^{3} -1.90464 q^{4} -0.898648 q^{5} -0.308797 q^{6} +1.20574 q^{8} +1.00000 q^{9} +0.277499 q^{10} +1.38960 q^{11} -1.90464 q^{12} +6.64217 q^{13} -0.898648 q^{15} +3.43696 q^{16} +6.17243 q^{17} -0.308797 q^{18} +5.46842 q^{19} +1.71160 q^{20} -0.429104 q^{22} +4.76671 q^{23} +1.20574 q^{24} -4.19243 q^{25} -2.05108 q^{26} +1.00000 q^{27} -6.78706 q^{29} +0.277499 q^{30} -6.37461 q^{31} -3.47280 q^{32} +1.38960 q^{33} -1.90603 q^{34} -1.90464 q^{36} +7.16373 q^{37} -1.68863 q^{38} +6.64217 q^{39} -1.08354 q^{40} -1.00000 q^{41} -6.00164 q^{43} -2.64669 q^{44} -0.898648 q^{45} -1.47194 q^{46} +6.21931 q^{47} +3.43696 q^{48} +1.29461 q^{50} +6.17243 q^{51} -12.6510 q^{52} +10.4055 q^{53} -0.308797 q^{54} -1.24876 q^{55} +5.46842 q^{57} +2.09582 q^{58} -4.50432 q^{59} +1.71160 q^{60} +13.3304 q^{61} +1.96846 q^{62} -5.80153 q^{64} -5.96897 q^{65} -0.429104 q^{66} -4.95916 q^{67} -11.7563 q^{68} +4.76671 q^{69} +10.9115 q^{71} +1.20574 q^{72} +4.36211 q^{73} -2.21214 q^{74} -4.19243 q^{75} -10.4154 q^{76} -2.05108 q^{78} -8.63992 q^{79} -3.08862 q^{80} +1.00000 q^{81} +0.308797 q^{82} -9.05009 q^{83} -5.54684 q^{85} +1.85329 q^{86} -6.78706 q^{87} +1.67550 q^{88} -1.29949 q^{89} +0.277499 q^{90} -9.07888 q^{92} -6.37461 q^{93} -1.92050 q^{94} -4.91418 q^{95} -3.47280 q^{96} +7.81362 q^{97} +1.38960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.308797	−0.218352	−0.109176	−	0.994022i	$-0.534821\pi$
$2$	−0.308797	−0.218352	−0.109176	+	0.994022i	$0.534821\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.90464	−0.952322
$5$	−0.898648	−0.401888	−0.200944	−	0.979603i	$-0.564401\pi$
$5$	−0.898648	−0.401888	−0.200944	+	0.979603i	$0.564401\pi$
$6$	−0.308797	−0.126066
$7$	0	0
$7$	0	0
$8$	1.20574	0.426294
$9$	1.00000	0.333333
$10$	0.277499	0.0877530
$11$	1.38960	0.418980	0.209490	−	0.977811i	$-0.432820\pi$
$11$	1.38960	0.418980	0.209490	+	0.977811i	$0.432820\pi$
$12$	−1.90464	−0.549824
$13$	6.64217	1.84221	0.921103	−	0.389319i	$-0.127289\pi$
$13$	6.64217	1.84221	0.921103	+	0.389319i	$0.127289\pi$
$14$	0	0
$15$	−0.898648	−0.232030
$16$	3.43696	0.859240
$17$	6.17243	1.49703	0.748517	−	0.663115i	$-0.230766\pi$
$17$	6.17243	1.49703	0.748517	+	0.663115i	$0.230766\pi$
$18$	−0.308797	−0.0727841
$19$	5.46842	1.25454	0.627271	−	0.778801i	$-0.284172\pi$
$19$	5.46842	1.25454	0.627271	+	0.778801i	$0.284172\pi$
$20$	1.71160	0.382726
$21$	0	0
$22$	−0.429104	−0.0914852
$23$	4.76671	0.993927	0.496964	−	0.867771i	$-0.334448\pi$
$23$	4.76671	0.993927	0.496964	+	0.867771i	$0.334448\pi$
$24$	1.20574	0.246121
$25$	−4.19243	−0.838486
$26$	−2.05108	−0.402250
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.78706	−1.26033	−0.630163	−	0.776463i	$-0.717012\pi$
$29$	−6.78706	−1.26033	−0.630163	+	0.776463i	$0.717012\pi$
$30$	0.277499	0.0506642
$31$	−6.37461	−1.14491	−0.572457	−	0.819935i	$-0.694009\pi$
$31$	−6.37461	−1.14491	−0.572457	+	0.819935i	$0.694009\pi$
$32$	−3.47280	−0.613911
$33$	1.38960	0.241898
$34$	−1.90603	−0.326881
$35$	0	0
$36$	−1.90464	−0.317441
$37$	7.16373	1.17771	0.588855	−	0.808239i	$-0.299579\pi$
$37$	7.16373	1.17771	0.588855	+	0.808239i	$0.299579\pi$
$38$	−1.68863	−0.273932
$39$	6.64217	1.06360
$40$	−1.08354	−0.171322
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−6.00164	−0.915241	−0.457620	−	0.889148i	$-0.651298\pi$
$43$	−6.00164	−0.915241	−0.457620	+	0.889148i	$0.651298\pi$
$44$	−2.64669	−0.399004
$45$	−0.898648	−0.133963
$46$	−1.47194	−0.217026
$47$	6.21931	0.907180	0.453590	−	0.891211i	$-0.350143\pi$
$47$	6.21931	0.907180	0.453590	+	0.891211i	$0.350143\pi$
$48$	3.43696	0.496082
$49$	0	0
$50$	1.29461	0.183085
$51$	6.17243	0.864313
$52$	−12.6510	−1.75437
$53$	10.4055	1.42930	0.714650	−	0.699483i	$-0.246586\pi$
$53$	10.4055	1.42930	0.714650	+	0.699483i	$0.246586\pi$
$54$	−0.308797	−0.0420219
$55$	−1.24876	−0.168383
$56$	0	0
$57$	5.46842	0.724310
$58$	2.09582	0.275195
$59$	−4.50432	−0.586413	−0.293207	−	0.956049i	$-0.594722\pi$
$59$	−4.50432	−0.586413	−0.293207	+	0.956049i	$0.594722\pi$
$60$	1.71160	0.220967
$61$	13.3304	1.70678	0.853391	−	0.521272i	$-0.174542\pi$
$61$	13.3304	1.70678	0.853391	+	0.521272i	$0.174542\pi$
$62$	1.96846	0.249994
$63$	0	0
$64$	−5.80153	−0.725191
$65$	−5.96897	−0.740360
$66$	−0.429104	−0.0528190
$67$	−4.95916	−0.605857	−0.302929	−	0.953013i	$-0.597964\pi$
$67$	−4.95916	−0.605857	−0.302929	+	0.953013i	$0.597964\pi$
$68$	−11.7563	−1.42566
$69$	4.76671	0.573844
$70$	0	0
$71$	10.9115	1.29496	0.647481	−	0.762082i	$-0.275823\pi$
$71$	10.9115	1.29496	0.647481	+	0.762082i	$0.275823\pi$
$72$	1.20574	0.142098
$73$	4.36211	0.510547	0.255273	−	0.966869i	$-0.417835\pi$
$73$	4.36211	0.510547	0.255273	+	0.966869i	$0.417835\pi$
$74$	−2.21214	−0.257156
$75$	−4.19243	−0.484100
$76$	−10.4154	−1.19473
$77$	0	0
$78$	−2.05108	−0.232239
$79$	−8.63992	−0.972067	−0.486034	−	0.873940i	$-0.661557\pi$
$79$	−8.63992	−0.972067	−0.486034	+	0.873940i	$0.661557\pi$
$80$	−3.08862	−0.345318
$81$	1.00000	0.111111
$82$	0.308797	0.0341009
$83$	−9.05009	−0.993376	−0.496688	−	0.867929i	$-0.665451\pi$
$83$	−9.05009	−0.993376	−0.496688	+	0.867929i	$0.665451\pi$
$84$	0	0
$85$	−5.54684	−0.601640
$86$	1.85329	0.199845
$87$	−6.78706	−0.727649
$88$	1.67550	0.178609
$89$	−1.29949	−0.137746	−0.0688729	−	0.997625i	$-0.521940\pi$
$89$	−1.29949	−0.137746	−0.0688729	+	0.997625i	$0.521940\pi$
$90$	0.277499	0.0292510
$91$	0	0
$92$	−9.07888	−0.946539
$93$	−6.37461	−0.661016
$94$	−1.92050	−0.198085
$95$	−4.91418	−0.504184
$96$	−3.47280	−0.354442
$97$	7.81362	0.793353	0.396677	−	0.917958i	$-0.370163\pi$
$97$	7.81362	0.793353	0.396677	+	0.917958i	$0.370163\pi$
$98$	0	0
$99$	1.38960	0.139660
$100$	7.98509	0.798509
$101$	−12.5977	−1.25352	−0.626759	−	0.779213i	$-0.715619\pi$
$101$	−12.5977	−1.25352	−0.626759	+	0.779213i	$0.715619\pi$
$102$	−1.90603	−0.188725
$103$	−18.5097	−1.82381	−0.911906	−	0.410399i	$-0.865389\pi$
$103$	−18.5097	−1.82381	−0.911906	+	0.410399i	$0.865389\pi$
$104$	8.00874	0.785321
$105$	0	0
$106$	−3.21317	−0.312091
$107$	3.77779	0.365213	0.182607	−	0.983186i	$-0.441547\pi$
$107$	3.77779	0.365213	0.182607	+	0.983186i	$0.441547\pi$
$108$	−1.90464	−0.183275
$109$	−5.31301	−0.508894	−0.254447	−	0.967087i	$-0.581893\pi$
$109$	−5.31301	−0.508894	−0.254447	+	0.967087i	$0.581893\pi$
$110$	0.385613	0.0367668
$111$	7.16373	0.679951
$112$	0	0
$113$	−16.6298	−1.56440	−0.782200	−	0.623028i	$-0.785902\pi$
$113$	−16.6298	−1.56440	−0.782200	+	0.623028i	$0.785902\pi$
$114$	−1.68863	−0.158155
$115$	−4.28359	−0.399447
$116$	12.9269	1.20024
$117$	6.64217	0.614069
$118$	1.39092	0.128045
$119$	0	0
$120$	−1.08354	−0.0989129
$121$	−9.06901	−0.824456
$122$	−4.11638	−0.372680
$123$	−1.00000	−0.0901670
$124$	12.1414	1.09033
$125$	8.26076	0.738865
$126$	0	0
$127$	−7.11991	−0.631790	−0.315895	−	0.948794i	$-0.602305\pi$
$127$	−7.11991	−0.631790	−0.315895	+	0.948794i	$0.602305\pi$
$128$	8.73710	0.772258
$129$	−6.00164	−0.528415
$130$	1.84320	0.161659
$131$	−1.76987	−0.154635	−0.0773173	−	0.997007i	$-0.524635\pi$
$131$	−1.76987	−0.154635	−0.0773173	+	0.997007i	$0.524635\pi$
$132$	−2.64669	−0.230365
$133$	0	0
$134$	1.53137	0.132290
$135$	−0.898648	−0.0773433
$136$	7.44236	0.638177
$137$	16.2543	1.38870	0.694348	−	0.719640i	$-0.255693\pi$
$137$	16.2543	1.38870	0.694348	+	0.719640i	$0.255693\pi$
$138$	−1.47194	−0.125300
$139$	10.8156	0.917370	0.458685	−	0.888599i	$-0.348321\pi$
$139$	10.8156	0.917370	0.458685	+	0.888599i	$0.348321\pi$
$140$	0	0
$141$	6.21931	0.523760
$142$	−3.36945	−0.282758
$143$	9.22996	0.771848
$144$	3.43696	0.286413
$145$	6.09918	0.506509
$146$	−1.34701	−0.111479
$147$	0	0
$148$	−13.6444	−1.12156
$149$	6.94118	0.568644	0.284322	−	0.958729i	$-0.408232\pi$
$149$	6.94118	0.568644	0.284322	+	0.958729i	$0.408232\pi$
$150$	1.29461	0.105704
$151$	−15.9874	−1.30103	−0.650516	−	0.759492i	$-0.725447\pi$
$151$	−15.9874	−1.30103	−0.650516	+	0.759492i	$0.725447\pi$
$152$	6.59350	0.534803
$153$	6.17243	0.499012
$154$	0	0
$155$	5.72853	0.460126
$156$	−12.6510	−1.01289
$157$	−7.87899	−0.628812	−0.314406	−	0.949289i	$-0.601805\pi$
$157$	−7.87899	−0.628812	−0.314406	+	0.949289i	$0.601805\pi$
$158$	2.66798	0.212253
$159$	10.4055	0.825206
$160$	3.12083	0.246723
$161$	0	0
$162$	−0.308797	−0.0242614
$163$	23.6380	1.85147	0.925735	−	0.378172i	$-0.123447\pi$
$163$	23.6380	1.85147	0.925735	+	0.378172i	$0.123447\pi$
$164$	1.90464	0.148728
$165$	−1.24876	−0.0972159
$166$	2.79464	0.216906
$167$	13.3089	1.02988	0.514938	−	0.857227i	$-0.327815\pi$
$167$	13.3089	1.02988	0.514938	+	0.857227i	$0.327815\pi$
$168$	0	0
$169$	31.1184	2.39372
$170$	1.71285	0.131369
$171$	5.46842	0.418180
$172$	11.4310	0.871604
$173$	6.99173	0.531571	0.265786	−	0.964032i	$-0.414369\pi$
$173$	6.99173	0.531571	0.265786	+	0.964032i	$0.414369\pi$
$174$	2.09582	0.158884
$175$	0	0
$176$	4.77600	0.360004
$177$	−4.50432	−0.338566
$178$	0.401279	0.0300771
$179$	−6.32731	−0.472925	−0.236463	−	0.971641i	$-0.575988\pi$
$179$	−6.32731	−0.472925	−0.236463	+	0.971641i	$0.575988\pi$
$180$	1.71160	0.127575
$181$	6.94382	0.516130	0.258065	−	0.966128i	$-0.416915\pi$
$181$	6.94382	0.516130	0.258065	+	0.966128i	$0.416915\pi$
$182$	0	0
$183$	13.3304	0.985411
$184$	5.74742	0.423705
$185$	−6.43767	−0.473307
$186$	1.96846	0.144334
$187$	8.57721	0.627228
$188$	−11.8456	−0.863927
$189$	0	0
$190$	1.51748	0.110090
$191$	19.9797	1.44568	0.722842	−	0.691014i	$-0.242836\pi$
$191$	19.9797	1.44568	0.722842	+	0.691014i	$0.242836\pi$
$192$	−5.80153	−0.418689
$193$	10.2929	0.740897	0.370448	−	0.928853i	$-0.379204\pi$
$193$	10.2929	0.740897	0.370448	+	0.928853i	$0.379204\pi$
$194$	−2.41282	−0.173230
$195$	−5.96897	−0.427447
$196$	0	0
$197$	−27.5794	−1.96495	−0.982477	−	0.186383i	$-0.940323\pi$
$197$	−27.5794	−1.96495	−0.982477	+	0.186383i	$0.940323\pi$
$198$	−0.429104	−0.0304951
$199$	15.6115	1.10667	0.553335	−	0.832959i	$-0.313355\pi$
$199$	15.6115	1.10667	0.553335	+	0.832959i	$0.313355\pi$
$200$	−5.05499	−0.357442
$201$	−4.95916	−0.349792
$202$	3.89013	0.273708
$203$	0	0
$204$	−11.7563	−0.823105
$205$	0.898648	0.0627643
$206$	5.71573	0.398233
$207$	4.76671	0.331309
$208$	22.8289	1.58290
$209$	7.59891	0.525628
$210$	0	0
$211$	20.4853	1.41026	0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853	1.41026	0.705132	+	0.709076i	$0.250888\pi$
$212$	−19.8187	−1.36115
$213$	10.9115	0.747646
$214$	−1.16657	−0.0797451
$215$	5.39336	0.367824
$216$	1.20574	0.0820403
$217$	0	0
$218$	1.64064	0.111118
$219$	4.36211	0.294764
$220$	2.37845	0.160355
$221$	40.9983	2.75785
$222$	−2.21214	−0.148469
$223$	−15.7327	−1.05354	−0.526771	−	0.850007i	$-0.676597\pi$
$223$	−15.7327	−1.05354	−0.526771	+	0.850007i	$0.676597\pi$
$224$	0	0
$225$	−4.19243	−0.279495
$226$	5.13523	0.341590
$227$	−14.8282	−0.984183	−0.492092	−	0.870543i	$-0.663768\pi$
$227$	−14.8282	−0.984183	−0.492092	+	0.870543i	$0.663768\pi$
$228$	−10.4154	−0.689776
$229$	−7.20918	−0.476396	−0.238198	−	0.971217i	$-0.576557\pi$
$229$	−7.20918	−0.476396	−0.238198	+	0.971217i	$0.576557\pi$
$230$	1.32276	0.0872201
$231$	0	0
$232$	−8.18344	−0.537269
$233$	4.00163	0.262156	0.131078	−	0.991372i	$-0.458156\pi$
$233$	4.00163	0.262156	0.131078	+	0.991372i	$0.458156\pi$
$234$	−2.05108	−0.134083
$235$	−5.58897	−0.364584
$236$	8.57914	0.558454
$237$	−8.63992	−0.561223
$238$	0	0
$239$	2.64792	0.171280	0.0856399	−	0.996326i	$-0.472707\pi$
$239$	2.64792	0.171280	0.0856399	+	0.996326i	$0.472707\pi$
$240$	−3.08862	−0.199369
$241$	9.68840	0.624085	0.312042	−	0.950068i	$-0.398987\pi$
$241$	9.68840	0.624085	0.312042	+	0.950068i	$0.398987\pi$
$242$	2.80048	0.180022
$243$	1.00000	0.0641500
$244$	−25.3897	−1.62541
$245$	0	0
$246$	0.308797	0.0196882
$247$	36.3222	2.31112
$248$	−7.68613	−0.488070
$249$	−9.05009	−0.573526
$250$	−2.55090	−0.161333
$251$	21.2826	1.34335	0.671674	−	0.740847i	$-0.265576\pi$
$251$	21.2826	1.34335	0.671674	+	0.740847i	$0.265576\pi$
$252$	0	0
$253$	6.62381	0.416436
$254$	2.19861	0.137953
$255$	−5.54684	−0.347357
$256$	8.90507	0.556567
$257$	28.2476	1.76204	0.881019	−	0.473081i	$-0.156858\pi$
$257$	28.2476	1.76204	0.881019	+	0.473081i	$0.156858\pi$
$258$	1.85329	0.115380
$259$	0	0
$260$	11.3688	0.705061
$261$	−6.78706	−0.420109
$262$	0.546531	0.0337648
$263$	−5.67723	−0.350073	−0.175036	−	0.984562i	$-0.556004\pi$
$263$	−5.67723	−0.350073	−0.175036	+	0.984562i	$0.556004\pi$
$264$	1.67550	0.103120
$265$	−9.35084	−0.574418
$266$	0	0
$267$	−1.29949	−0.0795276
$268$	9.44543	0.576971
$269$	−0.465240	−0.0283662	−0.0141831	−	0.999899i	$-0.504515\pi$
$269$	−0.465240	−0.0283662	−0.0141831	+	0.999899i	$0.504515\pi$
$270$	0.277499	0.0168881
$271$	−8.51652	−0.517342	−0.258671	−	0.965965i	$-0.583285\pi$
$271$	−8.51652	−0.517342	−0.258671	+	0.965965i	$0.583285\pi$
$272$	21.2144	1.28631
$273$	0	0
$274$	−5.01926	−0.303225
$275$	−5.82580	−0.351309
$276$	−9.07888	−0.546485
$277$	−0.909276	−0.0546331	−0.0273165	−	0.999627i	$-0.508696\pi$
$277$	−0.909276	−0.0546331	−0.0273165	+	0.999627i	$0.508696\pi$
$278$	−3.33983	−0.200310
$279$	−6.37461	−0.381638
$280$	0	0
$281$	24.6460	1.47026	0.735128	−	0.677928i	$-0.237122\pi$
$281$	24.6460	1.47026	0.735128	+	0.677928i	$0.237122\pi$
$282$	−1.92050	−0.114364
$283$	−27.0805	−1.60977	−0.804885	−	0.593430i	$-0.797773\pi$
$283$	−27.0805	−1.60977	−0.804885	+	0.593430i	$0.797773\pi$
$284$	−20.7826	−1.23322
$285$	−4.91418	−0.291091
$286$	−2.85018	−0.168535
$287$	0	0
$288$	−3.47280	−0.204637
$289$	21.0989	1.24111
$290$	−1.88341	−0.110597
$291$	7.81362	0.458043
$292$	−8.30827	−0.486205
$293$	−31.1849	−1.82184	−0.910921	−	0.412581i	$-0.864627\pi$
$293$	−31.1849	−1.82184	−0.910921	+	0.412581i	$0.864627\pi$
$294$	0	0
$295$	4.04780	0.235672
$296$	8.63761	0.502051
$297$	1.38960	0.0806327
$298$	−2.14341	−0.124165
$299$	31.6613	1.83102
$300$	7.98509	0.461020
$301$	0	0
$302$	4.93684	0.284083
$303$	−12.5977	−0.723719
$304$	18.7947	1.07795
$305$	−11.9793	−0.685934
$306$	−1.90603	−0.108960
$307$	−25.2868	−1.44319	−0.721596	−	0.692314i	$-0.756591\pi$
$307$	−25.2868	−1.44319	−0.721596	+	0.692314i	$0.756591\pi$
$308$	0	0
$309$	−18.5097	−1.05298
$310$	−1.76895	−0.100470
$311$	−8.85487	−0.502113	−0.251057	−	0.967972i	$-0.580778\pi$
$311$	−8.85487	−0.502113	−0.251057	+	0.967972i	$0.580778\pi$
$312$	8.00874	0.453406
$313$	−3.62015	−0.204623	−0.102312	−	0.994752i	$-0.532624\pi$
$313$	−3.62015	−0.204623	−0.102312	+	0.994752i	$0.532624\pi$
$314$	2.43301	0.137303
$315$	0	0
$316$	16.4560	0.925721
$317$	12.1660	0.683312	0.341656	−	0.939825i	$-0.389012\pi$
$317$	12.1660	0.683312	0.341656	+	0.939825i	$0.389012\pi$
$318$	−3.21317	−0.180186
$319$	−9.43130	−0.528051
$320$	5.21353	0.291445
$321$	3.77779	0.210856
$322$	0	0
$323$	33.7534	1.87809
$324$	−1.90464	−0.105814
$325$	−27.8468	−1.54466
$326$	−7.29934	−0.404273
$327$	−5.31301	−0.293810
$328$	−1.20574	−0.0665759
$329$	0	0
$330$	0.385613	0.0212273
$331$	2.91507	0.160227	0.0801135	−	0.996786i	$-0.474472\pi$
$331$	2.91507	0.160227	0.0801135	+	0.996786i	$0.474472\pi$
$332$	17.2372	0.946014
$333$	7.16373	0.392570
$334$	−4.10976	−0.224876
$335$	4.45654	0.243487
$336$	0	0
$337$	14.6448	0.797753	0.398877	−	0.917005i	$-0.369400\pi$
$337$	14.6448	0.797753	0.398877	+	0.917005i	$0.369400\pi$
$338$	−9.60926	−0.522675
$339$	−16.6298	−0.903207
$340$	10.5648	0.572955
$341$	−8.85815	−0.479696
$342$	−1.68863	−0.0913106
$343$	0	0
$344$	−7.23642	−0.390162
$345$	−4.28359	−0.230621
$346$	−2.15902	−0.116070
$347$	26.4588	1.42039	0.710193	−	0.704007i	$-0.248608\pi$
$347$	26.4588	1.42039	0.710193	+	0.704007i	$0.248608\pi$
$348$	12.9269	0.692957
$349$	4.11366	0.220199	0.110099	−	0.993921i	$-0.464883\pi$
$349$	4.11366	0.220199	0.110099	+	0.993921i	$0.464883\pi$
$350$	0	0
$351$	6.64217	0.354533
$352$	−4.82581	−0.257216
$353$	−35.9977	−1.91596	−0.957982	−	0.286829i	$-0.907399\pi$
$353$	−35.9977	−1.91596	−0.957982	+	0.286829i	$0.907399\pi$
$354$	1.39092	0.0739266
$355$	−9.80563	−0.520429
$356$	2.47507	0.131178
$357$	0	0
$358$	1.95385	0.103264
$359$	−14.7022	−0.775951	−0.387976	−	0.921670i	$-0.626826\pi$
$359$	−14.7022	−0.775951	−0.387976	+	0.921670i	$0.626826\pi$
$360$	−1.08354	−0.0571074
$361$	10.9036	0.573874
$362$	−2.14423	−0.112698
$363$	−9.06901	−0.476000
$364$	0	0
$365$	−3.92000	−0.205182
$366$	−4.11638	−0.215167
$367$	4.99355	0.260661	0.130331	−	0.991471i	$-0.458396\pi$
$367$	4.99355	0.260661	0.130331	+	0.991471i	$0.458396\pi$
$368$	16.3830	0.854022
$369$	−1.00000	−0.0520579
$370$	1.98793	0.103348
$371$	0	0
$372$	12.1414	0.629500
$373$	26.6906	1.38199	0.690993	−	0.722862i	$-0.257174\pi$
$373$	26.6906	1.38199	0.690993	+	0.722862i	$0.257174\pi$
$374$	−2.64861	−0.136957
$375$	8.26076	0.426584
$376$	7.49888	0.386725
$377$	−45.0808	−2.32178
$378$	0	0
$379$	1.64461	0.0844778	0.0422389	−	0.999108i	$-0.486551\pi$
$379$	1.64461	0.0844778	0.0422389	+	0.999108i	$0.486551\pi$
$380$	9.35977	0.480146
$381$	−7.11991	−0.364764
$382$	−6.16968	−0.315668
$383$	10.6131	0.542306	0.271153	−	0.962536i	$-0.412595\pi$
$383$	10.6131	0.542306	0.271153	+	0.962536i	$0.412595\pi$
$384$	8.73710	0.445863
$385$	0	0
$386$	−3.17840	−0.161776
$387$	−6.00164	−0.305080
$388$	−14.8822	−0.755528
$389$	26.4309	1.34010	0.670049	−	0.742317i	$-0.266273\pi$
$389$	26.4309	1.34010	0.670049	+	0.742317i	$0.266273\pi$
$390$	1.84320	0.0933340
$391$	29.4222	1.48794
$392$	0	0
$393$	−1.76987	−0.0892783
$394$	8.51644	0.429052
$395$	7.76425	0.390662
$396$	−2.64669	−0.133001
$397$	−14.6264	−0.734080	−0.367040	−	0.930205i	$-0.619629\pi$
$397$	−14.6264	−0.734080	−0.367040	+	0.930205i	$0.619629\pi$
$398$	−4.82078	−0.241644
$399$	0	0
$400$	−14.4092	−0.720461
$401$	−24.7129	−1.23410	−0.617051	−	0.786923i	$-0.711673\pi$
$401$	−24.7129	−1.23410	−0.617051	+	0.786923i	$0.711673\pi$
$402$	1.53137	0.0763778
$403$	−42.3412	−2.10917
$404$	23.9941	1.19375
$405$	−0.898648	−0.0446542
$406$	0	0
$407$	9.95472	0.493437
$408$	7.44236	0.368452
$409$	9.79226	0.484196	0.242098	−	0.970252i	$-0.422164\pi$
$409$	9.79226	0.484196	0.242098	+	0.970252i	$0.422164\pi$
$410$	−0.277499	−0.0137047
$411$	16.2543	0.801764
$412$	35.2543	1.73686
$413$	0	0
$414$	−1.47194	−0.0723421
$415$	8.13284	0.399226
$416$	−23.0670	−1.13095
$417$	10.8156	0.529644
$418$	−2.34652	−0.114772
$419$	1.56318	0.0763662	0.0381831	−	0.999271i	$-0.487843\pi$
$419$	1.56318	0.0763662	0.0381831	+	0.999271i	$0.487843\pi$
$420$	0	0
$421$	−25.0323	−1.22000	−0.610000	−	0.792401i	$-0.708831\pi$
$421$	−25.0323	−1.22000	−0.610000	+	0.792401i	$0.708831\pi$
$422$	−6.32578	−0.307934
$423$	6.21931	0.302393
$424$	12.5463	0.609302
$425$	−25.8775	−1.25524
$426$	−3.36945	−0.163250
$427$	0	0
$428$	−7.19536	−0.347801
$429$	9.22996	0.445626
$430$	−1.66545	−0.0803152
$431$	12.4377	0.599101	0.299550	−	0.954081i	$-0.403163\pi$
$431$	12.4377	0.599101	0.299550	+	0.954081i	$0.403163\pi$
$432$	3.43696	0.165361
$433$	−0.0273710	−0.00131537	−0.000657683	−	1.00000i	$-0.500209\pi$
$433$	−0.0273710	−0.00131537	−0.000657683		1.00000i	$0.500209\pi$
$434$	0	0
$435$	6.09918	0.292433
$436$	10.1194	0.484631
$437$	26.0664	1.24692
$438$	−1.34701	−0.0643624
$439$	−33.9319	−1.61948	−0.809740	−	0.586789i	$-0.800392\pi$
$439$	−33.9319	−1.61948	−0.809740	+	0.586789i	$0.800392\pi$
$440$	−1.50568	−0.0717806
$441$	0	0
$442$	−12.6602	−0.602182
$443$	19.8639	0.943760	0.471880	−	0.881663i	$-0.343575\pi$
$443$	19.8639	0.943760	0.471880	+	0.881663i	$0.343575\pi$
$444$	−13.6444	−0.647533
$445$	1.16779	0.0553583
$446$	4.85822	0.230043
$447$	6.94118	0.328307
$448$	0	0
$449$	14.0360	0.662399	0.331200	−	0.943561i	$-0.392547\pi$
$449$	14.0360	0.662399	0.331200	+	0.943561i	$0.392547\pi$
$450$	1.29461	0.0610285
$451$	−1.38960	−0.0654337
$452$	31.6739	1.48981
$453$	−15.9874	−0.751152
$454$	4.57890	0.214899
$455$	0	0
$456$	6.59350	0.308769
$457$	23.3867	1.09399	0.546993	−	0.837137i	$-0.315773\pi$
$457$	23.3867	1.09399	0.546993	+	0.837137i	$0.315773\pi$
$458$	2.22617	0.104022
$459$	6.17243	0.288104
$460$	8.15872	0.380402
$461$	23.2004	1.08055	0.540275	−	0.841488i	$-0.318320\pi$
$461$	23.2004	1.08055	0.540275	+	0.841488i	$0.318320\pi$
$462$	0	0
$463$	−14.4318	−0.670702	−0.335351	−	0.942093i	$-0.608855\pi$
$463$	−14.4318	−0.670702	−0.335351	+	0.942093i	$0.608855\pi$
$464$	−23.3269	−1.08292
$465$	5.72853	0.265654
$466$	−1.23569	−0.0572423
$467$	−21.6092	−0.999955	−0.499977	−	0.866039i	$-0.666658\pi$
$467$	−21.6092	−0.999955	−0.499977	+	0.866039i	$0.666658\pi$
$468$	−12.6510	−0.584791
$469$	0	0
$470$	1.72586	0.0796078
$471$	−7.87899	−0.363045
$472$	−5.43105	−0.249984
$473$	−8.33987	−0.383468
$474$	2.66798	0.122544
$475$	−22.9260	−1.05192
$476$	0	0
$477$	10.4055	0.476433
$478$	−0.817669	−0.0373993
$479$	−6.91726	−0.316057	−0.158029	−	0.987435i	$-0.550514\pi$
$479$	−6.91726	−0.316057	−0.158029	+	0.987435i	$0.550514\pi$
$480$	3.12083	0.142446
$481$	47.5827	2.16959
$482$	−2.99175	−0.136270
$483$	0	0
$484$	17.2732	0.785148
$485$	−7.02169	−0.318839
$486$	−0.308797	−0.0140073
$487$	15.0820	0.683430	0.341715	−	0.939804i	$-0.388992\pi$
$487$	15.0820	0.683430	0.341715	+	0.939804i	$0.388992\pi$
$488$	16.0730	0.727591
$489$	23.6380	1.06895
$490$	0	0
$491$	24.3627	1.09948	0.549738	−	0.835337i	$-0.314728\pi$
$491$	24.3627	1.09948	0.549738	+	0.835337i	$0.314728\pi$
$492$	1.90464	0.0858680
$493$	−41.8927	−1.88675
$494$	−11.2162	−0.504639
$495$	−1.24876	−0.0561276
$496$	−21.9093	−0.983755
$497$	0	0
$498$	2.79464	0.125231
$499$	1.21709	0.0544843	0.0272421	−	0.999629i	$-0.491327\pi$
$499$	1.21709	0.0544843	0.0272421	+	0.999629i	$0.491327\pi$
$500$	−15.7338	−0.703637
$501$	13.3089	0.594599
$502$	−6.57201	−0.293323
$503$	37.9289	1.69117	0.845583	−	0.533845i	$-0.179253\pi$
$503$	37.9289	1.69117	0.845583	+	0.533845i	$0.179253\pi$
$504$	0	0
$505$	11.3209	0.503773
$506$	−2.04541	−0.0909297
$507$	31.1184	1.38202
$508$	13.5609	0.601668
$509$	27.0118	1.19728	0.598638	−	0.801020i	$-0.295709\pi$
$509$	27.0118	1.19728	0.598638	+	0.801020i	$0.295709\pi$
$510$	1.71285	0.0758461
$511$	0	0
$512$	−20.2241	−0.893786
$513$	5.46842	0.241437
$514$	−8.72277	−0.384745
$515$	16.6337	0.732967
$516$	11.4310	0.503221
$517$	8.64235	0.380090
$518$	0	0
$519$	6.99173	0.306903
$520$	−7.19704	−0.315611
$521$	41.0082	1.79660	0.898300	−	0.439383i	$-0.144803\pi$
$521$	41.0082	1.79660	0.898300	+	0.439383i	$0.144803\pi$
$522$	2.09582	0.0917316
$523$	−37.2325	−1.62807	−0.814033	−	0.580819i	$-0.802732\pi$
$523$	−37.2325	−1.62807	−0.814033	+	0.580819i	$0.802732\pi$
$524$	3.37098	0.147262
$525$	0	0
$526$	1.75311	0.0764392
$527$	−39.3468	−1.71397
$528$	4.77600	0.207849
$529$	−0.278497	−0.0121086
$530$	2.88751	0.125425
$531$	−4.50432	−0.195471
$532$	0	0
$533$	−6.64217	−0.287704
$534$	0.401279	0.0173650
$535$	−3.39491	−0.146775
$536$	−5.97946	−0.258273
$537$	−6.32731	−0.273044
$538$	0.143664	0.00619381
$539$	0	0
$540$	1.71160	0.0736557
$541$	−18.6657	−0.802500	−0.401250	−	0.915969i	$-0.631424\pi$
$541$	−18.6657	−0.802500	−0.401250	+	0.915969i	$0.631424\pi$
$542$	2.62987	0.112963
$543$	6.94382	0.297988
$544$	−21.4357	−0.919046
$545$	4.77452	0.204518
$546$	0	0
$547$	22.4706	0.960775	0.480388	−	0.877056i	$-0.340496\pi$
$547$	22.4706	0.960775	0.480388	+	0.877056i	$0.340496\pi$
$548$	−30.9586	−1.32249
$549$	13.3304	0.568927
$550$	1.79899	0.0767091
$551$	−37.1145	−1.58113
$552$	5.74742	0.244626
$553$	0	0
$554$	0.280781	0.0119293
$555$	−6.43767	−0.273264
$556$	−20.5999	−0.873632
$557$	1.44517	0.0612339	0.0306170	−	0.999531i	$-0.490253\pi$
$557$	1.44517	0.0612339	0.0306170	+	0.999531i	$0.490253\pi$
$558$	1.96846	0.0833314
$559$	−39.8639	−1.68606
$560$	0	0
$561$	8.57721	0.362130
$562$	−7.61060	−0.321034
$563$	−33.4355	−1.40914	−0.704568	−	0.709636i	$-0.748859\pi$
$563$	−33.4355	−1.40914	−0.704568	+	0.709636i	$0.748859\pi$
$564$	−11.8456	−0.498789
$565$	14.9443	0.628713
$566$	8.36238	0.351497
$567$	0	0
$568$	13.1565	0.552034
$569$	32.2954	1.35389	0.676946	−	0.736033i	$-0.263303\pi$
$569$	32.2954	1.35389	0.676946	+	0.736033i	$0.263303\pi$
$570$	1.51748	0.0635604
$571$	−23.7959	−0.995829	−0.497915	−	0.867226i	$-0.665901\pi$
$571$	−23.7959	−0.995829	−0.497915	+	0.867226i	$0.665901\pi$
$572$	−17.5798	−0.735048
$573$	19.9797	0.834666
$574$	0	0
$575$	−19.9841	−0.833394
$576$	−5.80153	−0.241730
$577$	14.7145	0.612574	0.306287	−	0.951939i	$-0.400913\pi$
$577$	14.7145	0.612574	0.306287	+	0.951939i	$0.400913\pi$
$578$	−6.51528	−0.271000
$579$	10.2929	0.427757
$580$	−11.6168	−0.482360
$581$	0	0
$582$	−2.41282	−0.100015
$583$	14.4594	0.598848
$584$	5.25958	0.217643
$585$	−5.96897	−0.246787
$586$	9.62980	0.397803
$587$	3.04010	0.125479	0.0627393	−	0.998030i	$-0.480016\pi$
$587$	3.04010	0.125479	0.0627393	+	0.998030i	$0.480016\pi$
$588$	0	0
$589$	−34.8590	−1.43634
$590$	−1.24995	−0.0514595
$591$	−27.5794	−1.13447
$592$	24.6215	1.01194
$593$	−42.2287	−1.73413	−0.867063	−	0.498198i	$-0.833995\pi$
$593$	−42.2287	−1.73413	−0.867063	+	0.498198i	$0.833995\pi$
$594$	−0.429104	−0.0176063
$595$	0	0
$596$	−13.2205	−0.541532
$597$	15.6115	0.638936
$598$	−9.77690	−0.399807
$599$	−41.9943	−1.71584	−0.857920	−	0.513783i	$-0.828243\pi$
$599$	−41.9943	−1.71584	−0.857920	+	0.513783i	$0.828243\pi$
$600$	−5.05499	−0.206369
$601$	−29.4544	−1.20147	−0.600735	−	0.799448i	$-0.705125\pi$
$601$	−29.4544	−1.20147	−0.600735	+	0.799448i	$0.705125\pi$
$602$	0	0
$603$	−4.95916	−0.201952
$604$	30.4502	1.23900
$605$	8.14985	0.331339
$606$	3.89013	0.158026
$607$	20.7083	0.840526	0.420263	−	0.907402i	$-0.361938\pi$
$607$	20.7083	0.840526	0.420263	+	0.907402i	$0.361938\pi$
$608$	−18.9907	−0.770177
$609$	0	0
$610$	3.69918	0.149775
$611$	41.3097	1.67121
$612$	−11.7563	−0.475220
$613$	−41.4706	−1.67498	−0.837491	−	0.546451i	$-0.815978\pi$
$613$	−41.4706	−1.67498	−0.837491	+	0.546451i	$0.815978\pi$
$614$	7.80847	0.315124
$615$	0.898648	0.0362370
$616$	0	0
$617$	2.76644	0.111373	0.0556863	−	0.998448i	$-0.482265\pi$
$617$	2.76644	0.111373	0.0556863	+	0.998448i	$0.482265\pi$
$618$	5.71573	0.229920
$619$	−0.990969	−0.0398304	−0.0199152	−	0.999802i	$-0.506340\pi$
$619$	−0.990969	−0.0398304	−0.0199152	+	0.999802i	$0.506340\pi$
$620$	−10.9108	−0.438189
$621$	4.76671	0.191281
$622$	2.73435	0.109638
$623$	0	0
$624$	22.8289	0.913886
$625$	13.5386	0.541546
$626$	1.11789	0.0446799
$627$	7.59891	0.303471
$628$	15.0067	0.598832
$629$	44.2177	1.76307
$630$	0	0
$631$	−4.46880	−0.177900	−0.0889500	−	0.996036i	$-0.528351\pi$
$631$	−4.46880	−0.177900	−0.0889500	+	0.996036i	$0.528351\pi$
$632$	−10.4175	−0.414386
$633$	20.4853	0.814217
$634$	−3.75683	−0.149203
$635$	6.39830	0.253909
$636$	−19.8187	−0.785862
$637$	0	0
$638$	2.91235	0.115301
$639$	10.9115	0.431654
$640$	−7.85158	−0.310361
$641$	−30.9202	−1.22127	−0.610637	−	0.791911i	$-0.709086\pi$
$641$	−30.9202	−1.22127	−0.610637	+	0.791911i	$0.709086\pi$
$642$	−1.16657	−0.0460409
$643$	9.54896	0.376574	0.188287	−	0.982114i	$-0.439706\pi$
$643$	9.54896	0.376574	0.188287	+	0.982114i	$0.439706\pi$
$644$	0	0
$645$	5.39336	0.212363
$646$	−10.4230	−0.410086
$647$	38.0623	1.49638	0.748191	−	0.663484i	$-0.230923\pi$
$647$	38.0623	1.49638	0.748191	+	0.663484i	$0.230923\pi$
$648$	1.20574	0.0473660
$649$	−6.25921	−0.245695
$650$	8.59901	0.337281
$651$	0	0
$652$	−45.0220	−1.76320
$653$	27.2830	1.06767	0.533833	−	0.845590i	$-0.320751\pi$
$653$	27.2830	1.06767	0.533833	+	0.845590i	$0.320751\pi$
$654$	1.64064	0.0641540
$655$	1.59049	0.0621457
$656$	−3.43696	−0.134191
$657$	4.36211	0.170182
$658$	0	0
$659$	−9.31532	−0.362873	−0.181437	−	0.983403i	$-0.558075\pi$
$659$	−9.31532	−0.362873	−0.181437	+	0.983403i	$0.558075\pi$
$660$	2.37845	0.0925809
$661$	−14.6419	−0.569502	−0.284751	−	0.958601i	$-0.591911\pi$
$661$	−14.6419	−0.569502	−0.284751	+	0.958601i	$0.591911\pi$
$662$	−0.900165	−0.0349859
$663$	40.9983	1.59224
$664$	−10.9121	−0.423470
$665$	0	0
$666$	−2.21214	−0.0857186
$667$	−32.3519	−1.25267
$668$	−25.3488	−0.980774
$669$	−15.7327	−0.608263
$670$	−1.37616	−0.0531658
$671$	18.5239	0.715107
$672$	0	0
$673$	−28.2730	−1.08984	−0.544921	−	0.838487i	$-0.683441\pi$
$673$	−28.2730	−1.08984	−0.544921	+	0.838487i	$0.683441\pi$
$674$	−4.52227	−0.174191
$675$	−4.19243	−0.161367
$676$	−59.2695	−2.27960
$677$	−25.4582	−0.978437	−0.489218	−	0.872161i	$-0.662718\pi$
$677$	−25.4582	−0.978437	−0.489218	+	0.872161i	$0.662718\pi$
$678$	5.13523	0.197217
$679$	0	0
$680$	−6.68806	−0.256475
$681$	−14.8282	−0.568219
$682$	2.73537	0.104743
$683$	−51.8529	−1.98410	−0.992048	−	0.125861i	$-0.959831\pi$
$683$	−51.8529	−1.98410	−0.992048	+	0.125861i	$0.959831\pi$
$684$	−10.4154	−0.398243
$685$	−14.6069	−0.558099
$686$	0	0
$687$	−7.20918	−0.275048
$688$	−20.6274	−0.786412
$689$	69.1148	2.63306
$690$	1.32276	0.0503566
$691$	−47.1718	−1.79450	−0.897249	−	0.441524i	$-0.854438\pi$
$691$	−47.1718	−1.79450	−0.897249	+	0.441524i	$0.854438\pi$
$692$	−13.3168	−0.506227
$693$	0	0
$694$	−8.17040	−0.310144
$695$	−9.71944	−0.368679
$696$	−8.18344	−0.310193
$697$	−6.17243	−0.233798
$698$	−1.27028	−0.0480809
$699$	4.00163	0.151356
$700$	0	0
$701$	39.7588	1.50167	0.750834	−	0.660491i	$-0.229652\pi$
$701$	39.7588	1.50167	0.750834	+	0.660491i	$0.229652\pi$
$702$	−2.05108	−0.0774130
$703$	39.1743	1.47749
$704$	−8.06180	−0.303841
$705$	−5.58897	−0.210493
$706$	11.1160	0.418355
$707$	0	0
$708$	8.57914	0.322424
$709$	−11.4500	−0.430016	−0.215008	−	0.976612i	$-0.568978\pi$
$709$	−11.4500	−0.430016	−0.215008	+	0.976612i	$0.568978\pi$
$710$	3.02795	0.113637
$711$	−8.63992	−0.324022
$712$	−1.56685	−0.0587202
$713$	−30.3859	−1.13796
$714$	0	0
$715$	−8.29448	−0.310196
$716$	12.0513	0.450377
$717$	2.64792	0.0988884
$718$	4.53998	0.169431
$719$	42.0567	1.56845	0.784226	−	0.620476i	$-0.213060\pi$
$719$	42.0567	1.56845	0.784226	+	0.620476i	$0.213060\pi$
$720$	−3.08862	−0.115106
$721$	0	0
$722$	−3.36700	−0.125307
$723$	9.68840	0.360315
$724$	−13.2255	−0.491522
$725$	28.4543	1.05677
$726$	2.80048	0.103936
$727$	−24.0062	−0.890342	−0.445171	−	0.895446i	$-0.646857\pi$
$727$	−24.0062	−0.890342	−0.445171	+	0.895446i	$0.646857\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.21048	0.0448020
$731$	−37.0447	−1.37015
$732$	−25.3897	−0.938429
$733$	−45.8010	−1.69170	−0.845849	−	0.533423i	$-0.820905\pi$
$733$	−45.8010	−1.69170	−0.845849	+	0.533423i	$0.820905\pi$
$734$	−1.54199	−0.0569159
$735$	0	0
$736$	−16.5538	−0.610183
$737$	−6.89124	−0.253842
$738$	0.308797	0.0113670
$739$	27.6295	1.01637	0.508184	−	0.861248i	$-0.330317\pi$
$739$	27.6295	1.01637	0.508184	+	0.861248i	$0.330317\pi$
$740$	12.2615	0.450741
$741$	36.3222	1.33433
$742$	0	0
$743$	−5.43601	−0.199428	−0.0997139	−	0.995016i	$-0.531793\pi$
$743$	−5.43601	−0.199428	−0.0997139	+	0.995016i	$0.531793\pi$
$744$	−7.68613	−0.281787
$745$	−6.23768	−0.228531
$746$	−8.24196	−0.301760
$747$	−9.05009	−0.331125
$748$	−16.3365	−0.597323
$749$	0	0
$750$	−2.55090	−0.0931455
$751$	2.55797	0.0933416	0.0466708	−	0.998910i	$-0.485139\pi$
$751$	2.55797	0.0933416	0.0466708	+	0.998910i	$0.485139\pi$
$752$	21.3755	0.779485
$753$	21.2826	0.775582
$754$	13.9208	0.506966
$755$	14.3670	0.522869
$756$	0	0
$757$	13.4360	0.488339	0.244170	−	0.969733i	$-0.421485\pi$
$757$	13.4360	0.488339	0.244170	+	0.969733i	$0.421485\pi$
$758$	−0.507849	−0.0184459
$759$	6.62381	0.240429
$760$	−5.92523	−0.214931
$761$	19.8756	0.720489	0.360245	−	0.932858i	$-0.382693\pi$
$761$	19.8756	0.720489	0.360245	+	0.932858i	$0.382693\pi$
$762$	2.19861	0.0796471
$763$	0	0
$764$	−38.0543	−1.37676
$765$	−5.54684	−0.200547
$766$	−3.27730	−0.118414
$767$	−29.9185	−1.08029
$768$	8.90507	0.321334
$769$	−54.3254	−1.95902	−0.979512	−	0.201384i	$-0.935456\pi$
$769$	−54.3254	−1.95902	−0.979512	+	0.201384i	$0.935456\pi$
$770$	0	0
$771$	28.2476	1.01731
$772$	−19.6043	−0.705572
$773$	23.4861	0.844737	0.422368	−	0.906424i	$-0.361199\pi$
$773$	23.4861	0.844737	0.422368	+	0.906424i	$0.361199\pi$
$774$	1.85329	0.0666150
$775$	26.7251	0.959994
$776$	9.42121	0.338202
$777$	0	0
$778$	−8.16176	−0.292613
$779$	−5.46842	−0.195926
$780$	11.3688	0.407067
$781$	15.1627	0.542563
$782$	−9.08547	−0.324896
$783$	−6.78706	−0.242550
$784$	0	0
$785$	7.08044	0.252712
$786$	0.546531	0.0194941
$787$	21.1427	0.753655	0.376828	−	0.926283i	$-0.377015\pi$
$787$	21.1427	0.753655	0.376828	+	0.926283i	$0.377015\pi$
$788$	52.5290	1.87127
$789$	−5.67723	−0.202115
$790$	−2.39757	−0.0853018
$791$	0	0
$792$	1.67550	0.0595362
$793$	88.5427	3.14424
$794$	4.51660	0.160288
$795$	−9.35084	−0.331640
$796$	−29.7343	−1.05391
$797$	31.1992	1.10513	0.552566	−	0.833469i	$-0.313649\pi$
$797$	31.1992	1.10513	0.552566	+	0.833469i	$0.313649\pi$
$798$	0	0
$799$	38.3883	1.35808
$800$	14.5595	0.514756
$801$	−1.29949	−0.0459153
$802$	7.63126	0.269469
$803$	6.06159	0.213909
$804$	9.44543	0.333115
$805$	0	0
$806$	13.0748	0.460541
$807$	−0.465240	−0.0163772
$808$	−15.1896	−0.534367
$809$	−15.7021	−0.552058	−0.276029	−	0.961149i	$-0.589019\pi$
$809$	−15.7021	−0.552058	−0.276029	+	0.961149i	$0.589019\pi$
$810$	0.277499	0.00975034
$811$	23.2522	0.816496	0.408248	−	0.912871i	$-0.366140\pi$
$811$	23.2522	0.816496	0.408248	+	0.912871i	$0.366140\pi$
$812$	0	0
$813$	−8.51652	−0.298687
$814$	−3.07398	−0.107743
$815$	−21.2422	−0.744083
$816$	21.2144	0.742653
$817$	−32.8195	−1.14821
$818$	−3.02382	−0.105725
$819$	0	0
$820$	−1.71160	−0.0597718
$821$	51.4928	1.79711	0.898555	−	0.438861i	$-0.144618\pi$
$821$	51.4928	1.79711	0.898555	+	0.438861i	$0.144618\pi$
$822$	−5.01926	−0.175067
$823$	−7.46987	−0.260383	−0.130192	−	0.991489i	$-0.541559\pi$
$823$	−7.46987	−0.260383	−0.130192	+	0.991489i	$0.541559\pi$
$824$	−22.3179	−0.777480
$825$	−5.82580	−0.202828
$826$	0	0
$827$	−2.08519	−0.0725090	−0.0362545	−	0.999343i	$-0.511543\pi$
$827$	−2.08519	−0.0725090	−0.0362545	+	0.999343i	$0.511543\pi$
$828$	−9.07888	−0.315513
$829$	−35.6611	−1.23856	−0.619280	−	0.785170i	$-0.712575\pi$
$829$	−35.6611	−1.23856	−0.619280	+	0.785170i	$0.712575\pi$
$830$	−2.51140	−0.0871718
$831$	−0.909276	−0.0315424
$832$	−38.5347	−1.33595
$833$	0	0
$834$	−3.33983	−0.115649
$835$	−11.9600	−0.413895
$836$	−14.4732	−0.500567
$837$	−6.37461	−0.220339
$838$	−0.482704	−0.0166747
$839$	28.7416	0.992271	0.496136	−	0.868245i	$-0.334752\pi$
$839$	28.7416	0.992271	0.496136	+	0.868245i	$0.334752\pi$
$840$	0	0
$841$	17.0642	0.588421
$842$	7.72989	0.266390
$843$	24.6460	0.848853
$844$	−39.0172	−1.34303
$845$	−27.9645	−0.962008
$846$	−1.92050	−0.0660282
$847$	0	0
$848$	35.7631	1.22811
$849$	−27.0805	−0.929402
$850$	7.99089	0.274085
$851$	34.1474	1.17056
$852$	−20.7826	−0.712000
$853$	−10.3798	−0.355399	−0.177700	−	0.984085i	$-0.556866\pi$
$853$	−10.3798	−0.355399	−0.177700	+	0.984085i	$0.556866\pi$
$854$	0	0
$855$	−4.91418	−0.168061
$856$	4.55504	0.155688
$857$	−17.1959	−0.587400	−0.293700	−	0.955898i	$-0.594887\pi$
$857$	−17.1959	−0.587400	−0.293700	+	0.955898i	$0.594887\pi$
$858$	−2.85018	−0.0973035
$859$	−20.5963	−0.702738	−0.351369	−	0.936237i	$-0.614284\pi$
$859$	−20.5963	−0.702738	−0.351369	+	0.936237i	$0.614284\pi$
$860$	−10.2724	−0.350287
$861$	0	0
$862$	−3.84071	−0.130815
$863$	−3.01849	−0.102750	−0.0513752	−	0.998679i	$-0.516360\pi$
$863$	−3.01849	−0.102750	−0.0513752	+	0.998679i	$0.516360\pi$
$864$	−3.47280	−0.118147
$865$	−6.28310	−0.213632
$866$	0.00845207	0.000287213 0
$867$	21.0989	0.716557
$868$	0	0
$869$	−12.0060	−0.407277
$870$	−1.88341	−0.0638535
$871$	−32.9396	−1.11611
$872$	−6.40611	−0.216938
$873$	7.81362	0.264451
$874$	−8.04920	−0.272268
$875$	0	0
$876$	−8.30827	−0.280711
$877$	14.5978	0.492933	0.246466	−	0.969151i	$-0.420731\pi$
$877$	14.5978	0.492933	0.246466	+	0.969151i	$0.420731\pi$
$878$	10.4780	0.353617
$879$	−31.1849	−1.05184
$880$	−4.29194	−0.144681
$881$	8.66646	0.291981	0.145990	−	0.989286i	$-0.453363\pi$
$881$	8.66646	0.291981	0.145990	+	0.989286i	$0.453363\pi$
$882$	0	0
$883$	−12.6380	−0.425304	−0.212652	−	0.977128i	$-0.568210\pi$
$883$	−12.6380	−0.425304	−0.212652	+	0.977128i	$0.568210\pi$
$884$	−78.0873	−2.62636
$885$	4.04780	0.136065
$886$	−6.13389	−0.206072
$887$	21.8225	0.732729	0.366364	−	0.930472i	$-0.380602\pi$
$887$	21.8225	0.732729	0.366364	+	0.930472i	$0.380602\pi$
$888$	8.63761	0.289859
$889$	0	0
$890$	−0.360608	−0.0120876
$891$	1.38960	0.0465533
$892$	29.9653	1.00331
$893$	34.0098	1.13809
$894$	−2.14341	−0.0716865
$895$	5.68602	0.190063
$896$	0	0
$897$	31.6613	1.05714
$898$	−4.33427	−0.144636
$899$	43.2648	1.44296
$900$	7.98509	0.266170
$901$	64.2270	2.13971
$902$	0.429104	0.0142876
$903$	0	0
$904$	−20.0512	−0.666894
$905$	−6.24005	−0.207426
$906$	4.93684	0.164016
$907$	8.54997	0.283897	0.141949	−	0.989874i	$-0.454663\pi$
$907$	8.54997	0.283897	0.141949	+	0.989874i	$0.454663\pi$
$908$	28.2425	0.937260
$909$	−12.5977	−0.417839
$910$	0	0
$911$	−4.92067	−0.163029	−0.0815145	−	0.996672i	$-0.525976\pi$
$911$	−4.92067	−0.163029	−0.0815145	+	0.996672i	$0.525976\pi$
$912$	18.7947	0.622356
$913$	−12.5760	−0.416205
$914$	−7.22175	−0.238874
$915$	−11.9793	−0.396024
$916$	13.7309	0.453683
$917$	0	0
$918$	−1.90603	−0.0629083
$919$	−54.5333	−1.79889	−0.899444	−	0.437037i	$-0.856028\pi$
$919$	−54.5333	−1.79889	−0.899444	+	0.437037i	$0.856028\pi$
$920$	−5.16490	−0.170282
$921$	−25.2868	−0.833228
$922$	−7.16420	−0.235941
$923$	72.4763	2.38559
$924$	0	0
$925$	−30.0335	−0.987494
$926$	4.45649	0.146449
$927$	−18.5097	−0.607937
$928$	23.5701	0.773728
$929$	2.13381	0.0700080	0.0350040	−	0.999387i	$-0.488856\pi$
$929$	2.13381	0.0700080	0.0350040	+	0.999387i	$0.488856\pi$
$930$	−1.76895	−0.0580062
$931$	0	0
$932$	−7.62169	−0.249657
$933$	−8.85487	−0.289895
$934$	6.67285	0.218342
$935$	−7.70789	−0.252075
$936$	8.00874	0.261774
$937$	−6.22159	−0.203250	−0.101625	−	0.994823i	$-0.532404\pi$
$937$	−6.22159	−0.203250	−0.101625	+	0.994823i	$0.532404\pi$
$938$	0	0
$939$	−3.62015	−0.118139
$940$	10.6450	0.347202
$941$	10.0787	0.328555	0.164278	−	0.986414i	$-0.447471\pi$
$941$	10.0787	0.328555	0.164278	+	0.986414i	$0.447471\pi$
$942$	2.43301	0.0792716
$943$	−4.76671	−0.155225
$944$	−15.4812	−0.503870
$945$	0	0
$946$	2.57532	0.0837310
$947$	−46.3131	−1.50497	−0.752486	−	0.658608i	$-0.771146\pi$
$947$	−46.3131	−1.50497	−0.752486	+	0.658608i	$0.771146\pi$
$948$	16.4560	0.534465
$949$	28.9739	0.940532
$950$	7.07946	0.229688
$951$	12.1660	0.394510
$952$	0	0
$953$	20.1172	0.651659	0.325829	−	0.945429i	$-0.394356\pi$
$953$	20.1172	0.651659	0.325829	+	0.945429i	$0.394356\pi$
$954$	−3.21317	−0.104030
$955$	−17.9548	−0.581002
$956$	−5.04335	−0.163114
$957$	−9.43130	−0.304871
$958$	2.13603	0.0690119
$959$	0	0
$960$	5.21353	0.168266
$961$	9.63561	0.310826
$962$	−14.6934	−0.473734
$963$	3.77779	0.121738
$964$	−18.4530	−0.594330
$965$	−9.24966	−0.297757
$966$	0	0
$967$	−34.4719	−1.10854	−0.554271	−	0.832336i	$-0.687003\pi$
$967$	−34.4719	−1.10854	−0.554271	+	0.832336i	$0.687003\pi$
$968$	−10.9349	−0.351460
$969$	33.7534	1.08432
$970$	2.16828	0.0696191
$971$	−15.7013	−0.503880	−0.251940	−	0.967743i	$-0.581069\pi$
$971$	−15.7013	−0.503880	−0.251940	+	0.967743i	$0.581069\pi$
$972$	−1.90464	−0.0610915
$973$	0	0
$974$	−4.65727	−0.149229
$975$	−27.8468	−0.891813
$976$	45.8160	1.46653
$977$	−13.7257	−0.439123	−0.219561	−	0.975599i	$-0.570463\pi$
$977$	−13.7257	−0.439123	−0.219561	+	0.975599i	$0.570463\pi$
$978$	−7.29934	−0.233407
$979$	−1.80577	−0.0577127
$980$	0	0
$981$	−5.31301	−0.169631
$982$	−7.52314	−0.240073
$983$	31.3146	0.998781	0.499391	−	0.866377i	$-0.333557\pi$
$983$	31.3146	0.998781	0.499391	+	0.866377i	$0.333557\pi$
$984$	−1.20574	−0.0384376
$985$	24.7842	0.789691
$986$	12.9363	0.411976
$987$	0	0
$988$	−69.1808	−2.20093
$989$	−28.6080	−0.909683
$990$	0.385613	0.0122556
$991$	−4.10511	−0.130403	−0.0652016	−	0.997872i	$-0.520769\pi$
$991$	−4.10511	−0.130403	−0.0652016	+	0.997872i	$0.520769\pi$
$992$	22.1378	0.702875
$993$	2.91507	0.0925071
$994$	0	0
$995$	−14.0292	−0.444757
$996$	17.2372	0.546182
$997$	56.9183	1.80262	0.901311	−	0.433173i	$-0.142606\pi$
$997$	56.9183	1.80262	0.901311	+	0.433173i	$0.142606\pi$
$998$	−0.375832	−0.0118968
$999$	7.16373	0.226650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.10	yes	24
7.6	odd	2		6027.2.a.bn.1.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.10	✓	24	7.6	odd	2
6027.2.a.bo.1.10	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)

\(f(q)\)	\(=\)	\(q-0.308797 q^{2} +1.00000 q^{3} -1.90464 q^{4} -0.898648 q^{5} -0.308797 q^{6} +1.20574 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.308797 q^{2} +1.00000 q^{3} -1.90464 q^{4} -0.898648 q^{5} -0.308797 q^{6} +1.20574 q^{8} +1.00000 q^{9} +0.277499 q^{10} +1.38960 q^{11} -1.90464 q^{12} +6.64217 q^{13} -0.898648 q^{15} +3.43696 q^{16} +6.17243 q^{17} -0.308797 q^{18} +5.46842 q^{19} +1.71160 q^{20} -0.429104 q^{22} +4.76671 q^{23} +1.20574 q^{24} -4.19243 q^{25} -2.05108 q^{26} +1.00000 q^{27} -6.78706 q^{29} +0.277499 q^{30} -6.37461 q^{31} -3.47280 q^{32} +1.38960 q^{33} -1.90603 q^{34} -1.90464 q^{36} +7.16373 q^{37} -1.68863 q^{38} +6.64217 q^{39} -1.08354 q^{40} -1.00000 q^{41} -6.00164 q^{43} -2.64669 q^{44} -0.898648 q^{45} -1.47194 q^{46} +6.21931 q^{47} +3.43696 q^{48} +1.29461 q^{50} +6.17243 q^{51} -12.6510 q^{52} +10.4055 q^{53} -0.308797 q^{54} -1.24876 q^{55} +5.46842 q^{57} +2.09582 q^{58} -4.50432 q^{59} +1.71160 q^{60} +13.3304 q^{61} +1.96846 q^{62} -5.80153 q^{64} -5.96897 q^{65} -0.429104 q^{66} -4.95916 q^{67} -11.7563 q^{68} +4.76671 q^{69} +10.9115 q^{71} +1.20574 q^{72} +4.36211 q^{73} -2.21214 q^{74} -4.19243 q^{75} -10.4154 q^{76} -2.05108 q^{78} -8.63992 q^{79} -3.08862 q^{80} +1.00000 q^{81} +0.308797 q^{82} -9.05009 q^{83} -5.54684 q^{85} +1.85329 q^{86} -6.78706 q^{87} +1.67550 q^{88} -1.29949 q^{89} +0.277499 q^{90} -9.07888 q^{92} -6.37461 q^{93} -1.92050 q^{94} -4.91418 q^{95} -3.47280 q^{96} +7.81362 q^{97} +1.38960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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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