LMFDB - Embedded newform 6027.2.a.bo.1.16

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			1.16
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.50751 q^{2} +1.00000 q^{3} +0.272577 q^{4} +1.10903 q^{5} +1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.50751 q^{2} +1.00000 q^{3} +0.272577 q^{4} +1.10903 q^{5} +1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} +1.67187 q^{10} +3.74096 q^{11} +0.272577 q^{12} +4.04957 q^{13} +1.10903 q^{15} -4.47086 q^{16} -1.28562 q^{17} +1.50751 q^{18} +2.77400 q^{19} +0.302296 q^{20} +5.63953 q^{22} +8.14553 q^{23} -2.60410 q^{24} -3.77005 q^{25} +6.10476 q^{26} +1.00000 q^{27} -1.13225 q^{29} +1.67187 q^{30} +3.06661 q^{31} -1.53164 q^{32} +3.74096 q^{33} -1.93807 q^{34} +0.272577 q^{36} -8.99346 q^{37} +4.18183 q^{38} +4.04957 q^{39} -2.88803 q^{40} -1.00000 q^{41} +5.07578 q^{43} +1.01970 q^{44} +1.10903 q^{45} +12.2794 q^{46} -1.77524 q^{47} -4.47086 q^{48} -5.68338 q^{50} -1.28562 q^{51} +1.10382 q^{52} -1.43908 q^{53} +1.50751 q^{54} +4.14884 q^{55} +2.77400 q^{57} -1.70688 q^{58} -11.8133 q^{59} +0.302296 q^{60} +6.29435 q^{61} +4.62294 q^{62} +6.63275 q^{64} +4.49110 q^{65} +5.63953 q^{66} +1.53411 q^{67} -0.350429 q^{68} +8.14553 q^{69} +12.4191 q^{71} -2.60410 q^{72} +7.32700 q^{73} -13.5577 q^{74} -3.77005 q^{75} +0.756129 q^{76} +6.10476 q^{78} +3.06259 q^{79} -4.95832 q^{80} +1.00000 q^{81} -1.50751 q^{82} -10.5895 q^{83} -1.42579 q^{85} +7.65178 q^{86} -1.13225 q^{87} -9.74185 q^{88} -0.862204 q^{89} +1.67187 q^{90} +2.22028 q^{92} +3.06661 q^{93} -2.67619 q^{94} +3.07645 q^{95} -1.53164 q^{96} -2.95888 q^{97} +3.74096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.50751	1.06597	0.532984	−	0.846125i	$-0.321071\pi$
$2$	1.50751	1.06597	0.532984	+	0.846125i	$0.321071\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.272577	0.136288
$5$	1.10903	0.495973	0.247987	−	0.968763i	$-0.420231\pi$
$5$	1.10903	0.495973	0.247987	+	0.968763i	$0.420231\pi$
$6$	1.50751	0.615437
$7$	0	0
$7$	0	0
$8$	−2.60410	−0.920689
$9$	1.00000	0.333333
$10$	1.67187	0.528692
$11$	3.74096	1.12794	0.563971	−	0.825794i	$-0.309273\pi$
$11$	3.74096	1.12794	0.563971	+	0.825794i	$0.309273\pi$
$12$	0.272577	0.0786862
$13$	4.04957	1.12315	0.561575	−	0.827426i	$-0.310196\pi$
$13$	4.04957	1.12315	0.561575	+	0.827426i	$0.310196\pi$
$14$	0	0
$15$	1.10903	0.286350
$16$	−4.47086	−1.11771
$17$	−1.28562	−0.311808	−0.155904	−	0.987772i	$-0.549829\pi$
$17$	−1.28562	−0.311808	−0.155904	+	0.987772i	$0.549829\pi$
$18$	1.50751	0.355323
$19$	2.77400	0.636400	0.318200	−	0.948024i	$-0.396922\pi$
$19$	2.77400	0.636400	0.318200	+	0.948024i	$0.396922\pi$
$20$	0.302296	0.0675955
$21$	0	0
$22$	5.63953	1.20235
$23$	8.14553	1.69846	0.849230	−	0.528023i	$-0.177067\pi$
$23$	8.14553	1.69846	0.849230	+	0.528023i	$0.177067\pi$
$24$	−2.60410	−0.531560
$25$	−3.77005	−0.754010
$26$	6.10476	1.19724
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.13225	−0.210254	−0.105127	−	0.994459i	$-0.533525\pi$
$29$	−1.13225	−0.210254	−0.105127	+	0.994459i	$0.533525\pi$
$30$	1.67187	0.305240
$31$	3.06661	0.550779	0.275390	−	0.961333i	$-0.411193\pi$
$31$	3.06661	0.550779	0.275390	+	0.961333i	$0.411193\pi$
$32$	−1.53164	−0.270758
$33$	3.74096	0.651218
$34$	−1.93807	−0.332377
$35$	0	0
$36$	0.272577	0.0454295
$37$	−8.99346	−1.47852	−0.739258	−	0.673423i	$-0.764823\pi$
$37$	−8.99346	−1.47852	−0.739258	+	0.673423i	$0.764823\pi$
$38$	4.18183	0.678382
$39$	4.04957	0.648450
$40$	−2.88803	−0.456637
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	5.07578	0.774050	0.387025	−	0.922069i	$-0.373503\pi$
$43$	5.07578	0.774050	0.387025	+	0.922069i	$0.373503\pi$
$44$	1.01970	0.153726
$45$	1.10903	0.165324
$46$	12.2794	1.81050
$47$	−1.77524	−0.258946	−0.129473	−	0.991583i	$-0.541329\pi$
$47$	−1.77524	−0.258946	−0.129473	+	0.991583i	$0.541329\pi$
$48$	−4.47086	−0.645312
$49$	0	0
$50$	−5.68338	−0.803751
$51$	−1.28562	−0.180022
$52$	1.10382	0.153072
$53$	−1.43908	−0.197673	−0.0988365	−	0.995104i	$-0.531512\pi$
$53$	−1.43908	−0.197673	−0.0988365	+	0.995104i	$0.531512\pi$
$54$	1.50751	0.205146
$55$	4.14884	0.559430
$56$	0	0
$57$	2.77400	0.367425
$58$	−1.70688	−0.224124
$59$	−11.8133	−1.53796	−0.768980	−	0.639273i	$-0.779235\pi$
$59$	−11.8133	−1.53796	−0.768980	+	0.639273i	$0.779235\pi$
$60$	0.302296	0.0390263
$61$	6.29435	0.805908	0.402954	−	0.915220i	$-0.367983\pi$
$61$	6.29435	0.805908	0.402954	+	0.915220i	$0.367983\pi$
$62$	4.62294	0.587113
$63$	0	0
$64$	6.63275	0.829094
$65$	4.49110	0.557052
$66$	5.63953	0.694178
$67$	1.53411	0.187421	0.0937107	−	0.995599i	$-0.470127\pi$
$67$	1.53411	0.187421	0.0937107	+	0.995599i	$0.470127\pi$
$68$	−0.350429	−0.0424958
$69$	8.14553	0.980606
$70$	0	0
$71$	12.4191	1.47388	0.736938	−	0.675960i	$-0.236271\pi$
$71$	12.4191	1.47388	0.736938	+	0.675960i	$0.236271\pi$
$72$	−2.60410	−0.306896
$73$	7.32700	0.857561	0.428780	−	0.903409i	$-0.358943\pi$
$73$	7.32700	0.857561	0.428780	+	0.903409i	$0.358943\pi$
$74$	−13.5577	−1.57605
$75$	−3.77005	−0.435328
$76$	0.756129	0.0867339
$77$	0	0
$78$	6.10476	0.691228
$79$	3.06259	0.344568	0.172284	−	0.985047i	$-0.444885\pi$
$79$	3.06259	0.344568	0.172284	+	0.985047i	$0.444885\pi$
$80$	−4.95832	−0.554356
$81$	1.00000	0.111111
$82$	−1.50751	−0.166476
$83$	−10.5895	−1.16235	−0.581175	−	0.813778i	$-0.697407\pi$
$83$	−10.5895	−1.16235	−0.581175	+	0.813778i	$0.697407\pi$
$84$	0	0
$85$	−1.42579	−0.154648
$86$	7.65178	0.825112
$87$	−1.13225	−0.121390
$88$	−9.74185	−1.03848
$89$	−0.862204	−0.0913935	−0.0456967	−	0.998955i	$-0.514551\pi$
$89$	−0.862204	−0.0913935	−0.0456967	+	0.998955i	$0.514551\pi$
$90$	1.67187	0.176231
$91$	0	0
$92$	2.22028	0.231480
$93$	3.06661	0.317993
$94$	−2.67619	−0.276028
$95$	3.07645	0.315637
$96$	−1.53164	−0.156322
$97$	−2.95888	−0.300428	−0.150214	−	0.988653i	$-0.547996\pi$
$97$	−2.95888	−0.300428	−0.150214	+	0.988653i	$0.547996\pi$
$98$	0	0
$99$	3.74096	0.375981
$100$	−1.02763	−0.102763
$101$	9.78581	0.973724	0.486862	−	0.873479i	$-0.338141\pi$
$101$	9.78581	0.973724	0.486862	+	0.873479i	$0.338141\pi$
$102$	−1.93807	−0.191898
$103$	5.64685	0.556400	0.278200	−	0.960523i	$-0.410262\pi$
$103$	5.64685	0.556400	0.278200	+	0.960523i	$0.410262\pi$
$104$	−10.5455	−1.03407
$105$	0	0
$106$	−2.16942	−0.210713
$107$	14.2514	1.37773	0.688866	−	0.724889i	$-0.258109\pi$
$107$	14.2514	1.37773	0.688866	+	0.724889i	$0.258109\pi$
$108$	0.272577	0.0262287
$109$	−1.98301	−0.189938	−0.0949689	−	0.995480i	$-0.530275\pi$
$109$	−1.98301	−0.189938	−0.0949689	+	0.995480i	$0.530275\pi$
$110$	6.25441	0.596334
$111$	−8.99346	−0.853621
$112$	0	0
$113$	1.92257	0.180860	0.0904302	−	0.995903i	$-0.471176\pi$
$113$	1.92257	0.180860	0.0904302	+	0.995903i	$0.471176\pi$
$114$	4.18183	0.391664
$115$	9.03364	0.842391
$116$	−0.308626	−0.0286552
$117$	4.04957	0.374383
$118$	−17.8086	−1.63942
$119$	0	0
$120$	−2.88803	−0.263640
$121$	2.99480	0.272255
$122$	9.48877	0.859073
$123$	−1.00000	−0.0901670
$124$	0.835887	0.0750649
$125$	−9.72625	−0.869943
$126$	0	0
$127$	6.05248	0.537071	0.268536	−	0.963270i	$-0.413460\pi$
$127$	6.05248	0.537071	0.268536	+	0.963270i	$0.413460\pi$
$128$	13.0622	1.15455
$129$	5.07578	0.446898
$130$	6.77036	0.593800
$131$	10.1642	0.888055	0.444027	−	0.896013i	$-0.353549\pi$
$131$	10.1642	0.888055	0.444027	+	0.896013i	$0.353549\pi$
$132$	1.01970	0.0887535
$133$	0	0
$134$	2.31268	0.199785
$135$	1.10903	0.0954501
$136$	3.34788	0.287078
$137$	10.4749	0.894928	0.447464	−	0.894302i	$-0.352327\pi$
$137$	10.4749	0.894928	0.447464	+	0.894302i	$0.352327\pi$
$138$	12.2794	1.04530
$139$	−5.03683	−0.427219	−0.213609	−	0.976919i	$-0.568522\pi$
$139$	−5.03683	−0.427219	−0.213609	+	0.976919i	$0.568522\pi$
$140$	0	0
$141$	−1.77524	−0.149503
$142$	18.7219	1.57110
$143$	15.1493	1.26685
$144$	−4.47086	−0.372571
$145$	−1.25570	−0.104280
$146$	11.0455	0.914132
$147$	0	0
$148$	−2.45141	−0.201505
$149$	12.4511	1.02003	0.510016	−	0.860165i	$-0.329640\pi$
$149$	12.4511	1.02003	0.510016	+	0.860165i	$0.329640\pi$
$150$	−5.68338	−0.464046
$151$	1.01228	0.0823779	0.0411889	−	0.999151i	$-0.486885\pi$
$151$	1.01228	0.0823779	0.0411889	+	0.999151i	$0.486885\pi$
$152$	−7.22378	−0.585926
$153$	−1.28562	−0.103936
$154$	0	0
$155$	3.40096	0.273172
$156$	1.10382	0.0883763
$157$	−3.97214	−0.317011	−0.158506	−	0.987358i	$-0.550668\pi$
$157$	−3.97214	−0.317011	−0.158506	+	0.987358i	$0.550668\pi$
$158$	4.61688	0.367299
$159$	−1.43908	−0.114127
$160$	−1.69864	−0.134289
$161$	0	0
$162$	1.50751	0.118441
$163$	22.6056	1.77061	0.885304	−	0.465013i	$-0.153950\pi$
$163$	22.6056	1.77061	0.885304	+	0.465013i	$0.153950\pi$
$164$	−0.272577	−0.0212847
$165$	4.14884	0.322987
$166$	−15.9638	−1.23903
$167$	−10.2870	−0.796035	−0.398017	−	0.917378i	$-0.630302\pi$
$167$	−10.2870	−0.796035	−0.398017	+	0.917378i	$0.630302\pi$
$168$	0	0
$169$	3.39903	0.261464
$170$	−2.14938	−0.164850
$171$	2.77400	0.212133
$172$	1.38354	0.105494
$173$	−8.31332	−0.632050	−0.316025	−	0.948751i	$-0.602348\pi$
$173$	−8.31332	−0.632050	−0.316025	+	0.948751i	$0.602348\pi$
$174$	−1.70688	−0.129398
$175$	0	0
$176$	−16.7253	−1.26072
$177$	−11.8133	−0.887942
$178$	−1.29978	−0.0974225
$179$	5.82288	0.435222	0.217611	−	0.976036i	$-0.430174\pi$
$179$	5.82288	0.435222	0.217611	+	0.976036i	$0.430174\pi$
$180$	0.302296	0.0225318
$181$	−16.9447	−1.25949	−0.629746	−	0.776801i	$-0.716841\pi$
$181$	−16.9447	−1.25949	−0.629746	+	0.776801i	$0.716841\pi$
$182$	0	0
$183$	6.29435	0.465291
$184$	−21.2118	−1.56375
$185$	−9.97402	−0.733304
$186$	4.62294	0.338970
$187$	−4.80944	−0.351701
$188$	−0.483891	−0.0352913
$189$	0	0
$190$	4.63777	0.336459
$191$	12.9496	0.937001	0.468501	−	0.883463i	$-0.344794\pi$
$191$	12.9496	0.937001	0.468501	+	0.883463i	$0.344794\pi$
$192$	6.63275	0.478678
$193$	−1.53674	−0.110617	−0.0553084	−	0.998469i	$-0.517614\pi$
$193$	−1.53674	−0.110617	−0.0553084	+	0.998469i	$0.517614\pi$
$194$	−4.46053	−0.320247
$195$	4.49110	0.321614
$196$	0	0
$197$	14.6537	1.04403	0.522017	−	0.852935i	$-0.325180\pi$
$197$	14.6537	1.04403	0.522017	+	0.852935i	$0.325180\pi$
$198$	5.63953	0.400784
$199$	−15.9626	−1.13156	−0.565780	−	0.824556i	$-0.691425\pi$
$199$	−15.9626	−1.13156	−0.565780	+	0.824556i	$0.691425\pi$
$200$	9.81760	0.694209
$201$	1.53411	0.108208
$202$	14.7522	1.03796
$203$	0	0
$204$	−0.350429	−0.0245350
$205$	−1.10903	−0.0774580
$206$	8.51266	0.593105
$207$	8.14553	0.566153
$208$	−18.1050	−1.25536
$209$	10.3774	0.717822
$210$	0	0
$211$	23.5174	1.61901	0.809503	−	0.587116i	$-0.199737\pi$
$211$	23.5174	1.61901	0.809503	+	0.587116i	$0.199737\pi$
$212$	−0.392260	−0.0269405
$213$	12.4191	0.850943
$214$	21.4840	1.46862
$215$	5.62920	0.383908
$216$	−2.60410	−0.177187
$217$	0	0
$218$	−2.98940	−0.202468
$219$	7.32700	0.495113
$220$	1.13088	0.0762438
$221$	−5.20619	−0.350206
$222$	−13.5577	−0.909933
$223$	−22.1230	−1.48146	−0.740732	−	0.671801i	$-0.765521\pi$
$223$	−22.1230	−1.48146	−0.740732	+	0.671801i	$0.765521\pi$
$224$	0	0
$225$	−3.77005	−0.251337
$226$	2.89829	0.192791
$227$	21.8654	1.45126	0.725630	−	0.688085i	$-0.241549\pi$
$227$	21.8654	1.45126	0.725630	+	0.688085i	$0.241549\pi$
$228$	0.756129	0.0500758
$229$	−14.7855	−0.977054	−0.488527	−	0.872549i	$-0.662466\pi$
$229$	−14.7855	−0.977054	−0.488527	+	0.872549i	$0.662466\pi$
$230$	13.6183	0.897962
$231$	0	0
$232$	2.94850	0.193578
$233$	−27.2105	−1.78262	−0.891310	−	0.453394i	$-0.850213\pi$
$233$	−27.2105	−1.78262	−0.891310	+	0.453394i	$0.850213\pi$
$234$	6.10476	0.399080
$235$	−1.96880	−0.128430
$236$	−3.22003	−0.209606
$237$	3.06259	0.198937
$238$	0	0
$239$	−23.9634	−1.55006	−0.775031	−	0.631924i	$-0.782266\pi$
$239$	−23.9634	−1.55006	−0.775031	+	0.631924i	$0.782266\pi$
$240$	−4.95832	−0.320058
$241$	12.9104	0.831632	0.415816	−	0.909449i	$-0.363496\pi$
$241$	12.9104	0.831632	0.415816	+	0.909449i	$0.363496\pi$
$242$	4.51468	0.290215
$243$	1.00000	0.0641500
$244$	1.71569	0.109836
$245$	0	0
$246$	−1.50751	−0.0961151
$247$	11.2335	0.714772
$248$	−7.98577	−0.507097
$249$	−10.5895	−0.671083
$250$	−14.6624	−0.927331
$251$	−13.4903	−0.851497	−0.425749	−	0.904841i	$-0.639989\pi$
$251$	−13.4903	−0.851497	−0.425749	+	0.904841i	$0.639989\pi$
$252$	0	0
$253$	30.4721	1.91577
$254$	9.12416	0.572501
$255$	−1.42579	−0.0892863
$256$	6.42585	0.401616
$257$	−4.35831	−0.271864	−0.135932	−	0.990718i	$-0.543403\pi$
$257$	−4.35831	−0.271864	−0.135932	+	0.990718i	$0.543403\pi$
$258$	7.65178	0.476379
$259$	0	0
$260$	1.22417	0.0759198
$261$	−1.13225	−0.0700846
$262$	15.3227	0.946638
$263$	−14.2904	−0.881182	−0.440591	−	0.897708i	$-0.645231\pi$
$263$	−14.2904	−0.881182	−0.440591	+	0.897708i	$0.645231\pi$
$264$	−9.74185	−0.599569
$265$	−1.59598	−0.0980405
$266$	0	0
$267$	−0.862204	−0.0527660
$268$	0.418163	0.0255434
$269$	−20.3295	−1.23951	−0.619755	−	0.784795i	$-0.712768\pi$
$269$	−20.3295	−1.23951	−0.619755	+	0.784795i	$0.712768\pi$
$270$	1.67187	0.101747
$271$	21.1831	1.28678	0.643392	−	0.765537i	$-0.277527\pi$
$271$	21.1831	1.28678	0.643392	+	0.765537i	$0.277527\pi$
$272$	5.74780	0.348512
$273$	0	0
$274$	15.7909	0.953965
$275$	−14.1036	−0.850480
$276$	2.22028	0.133645
$277$	3.20291	0.192444	0.0962221	−	0.995360i	$-0.469324\pi$
$277$	3.20291	0.192444	0.0962221	+	0.995360i	$0.469324\pi$
$278$	−7.59306	−0.455401
$279$	3.06661	0.183593
$280$	0	0
$281$	−16.8668	−1.00619	−0.503094	−	0.864231i	$-0.667805\pi$
$281$	−16.8668	−1.00619	−0.503094	+	0.864231i	$0.667805\pi$
$282$	−2.67619	−0.159365
$283$	29.0207	1.72510	0.862551	−	0.505971i	$-0.168866\pi$
$283$	29.0207	1.72510	0.862551	+	0.505971i	$0.168866\pi$
$284$	3.38516	0.200872
$285$	3.07645	0.182233
$286$	22.8377	1.35042
$287$	0	0
$288$	−1.53164	−0.0902528
$289$	−15.3472	−0.902776
$290$	−1.89298	−0.111160
$291$	−2.95888	−0.173452
$292$	1.99717	0.116876
$293$	−33.4645	−1.95502	−0.977509	−	0.210896i	$-0.932362\pi$
$293$	−33.4645	−1.95502	−0.977509	+	0.210896i	$0.932362\pi$
$294$	0	0
$295$	−13.1013	−0.762787
$296$	23.4199	1.36125
$297$	3.74096	0.217073
$298$	18.7701	1.08732
$299$	32.9859	1.90762
$300$	−1.02763	−0.0593302
$301$	0	0
$302$	1.52601	0.0878122
$303$	9.78581	0.562180
$304$	−12.4022	−0.711313
$305$	6.98062	0.399709
$306$	−1.93807	−0.110792
$307$	−12.0971	−0.690419	−0.345209	−	0.938526i	$-0.612192\pi$
$307$	−12.0971	−0.690419	−0.345209	+	0.938526i	$0.612192\pi$
$308$	0	0
$309$	5.64685	0.321238
$310$	5.12698	0.291193
$311$	−4.23825	−0.240329	−0.120165	−	0.992754i	$-0.538342\pi$
$311$	−4.23825	−0.240329	−0.120165	+	0.992754i	$0.538342\pi$
$312$	−10.5455	−0.597021
$313$	23.4002	1.32266	0.661329	−	0.750096i	$-0.269993\pi$
$313$	23.4002	1.32266	0.661329	+	0.750096i	$0.269993\pi$
$314$	−5.98802	−0.337924
$315$	0	0
$316$	0.834792	0.0469607
$317$	7.71467	0.433299	0.216650	−	0.976249i	$-0.430487\pi$
$317$	7.71467	0.433299	0.216650	+	0.976249i	$0.430487\pi$
$318$	−2.16942	−0.121655
$319$	−4.23571	−0.237154
$320$	7.35592	0.411209
$321$	14.2514	0.795434
$322$	0	0
$323$	−3.56630	−0.198434
$324$	0.272577	0.0151432
$325$	−15.2671	−0.846866
$326$	34.0781	1.88741
$327$	−1.98301	−0.109661
$328$	2.60410	0.143787
$329$	0	0
$330$	6.25441	0.344294
$331$	0.784765	0.0431346	0.0215673	−	0.999767i	$-0.493134\pi$
$331$	0.784765	0.0431346	0.0215673	+	0.999767i	$0.493134\pi$
$332$	−2.88646	−0.158415
$333$	−8.99346	−0.492838
$334$	−15.5078	−0.848548
$335$	1.70138	0.0929561
$336$	0	0
$337$	−11.6836	−0.636447	−0.318224	−	0.948016i	$-0.603086\pi$
$337$	−11.6836	−0.636447	−0.318224	+	0.948016i	$0.603086\pi$
$338$	5.12406	0.278712
$339$	1.92257	0.104420
$340$	−0.388637	−0.0210768
$341$	11.4721	0.621248
$342$	4.18183	0.226127
$343$	0	0
$344$	−13.2179	−0.712659
$345$	9.03364	0.486355
$346$	−12.5324	−0.673745
$347$	1.28541	0.0690042	0.0345021	−	0.999405i	$-0.489015\pi$
$347$	1.28541	0.0690042	0.0345021	+	0.999405i	$0.489015\pi$
$348$	−0.308626	−0.0165441
$349$	−30.6569	−1.64103	−0.820513	−	0.571628i	$-0.806312\pi$
$349$	−30.6569	−1.64103	−0.820513	+	0.571628i	$0.806312\pi$
$350$	0	0
$351$	4.04957	0.216150
$352$	−5.72981	−0.305400
$353$	−0.656222	−0.0349271	−0.0174636	−	0.999848i	$-0.505559\pi$
$353$	−0.656222	−0.0349271	−0.0174636	+	0.999848i	$0.505559\pi$
$354$	−17.8086	−0.946518
$355$	13.7732	0.731003
$356$	−0.235017	−0.0124559
$357$	0	0
$358$	8.77803	0.463933
$359$	−0.670115	−0.0353673	−0.0176837	−	0.999844i	$-0.505629\pi$
$359$	−0.670115	−0.0353673	−0.0176837	+	0.999844i	$0.505629\pi$
$360$	−2.88803	−0.152212
$361$	−11.3049	−0.594996
$362$	−25.5443	−1.34258
$363$	2.99480	0.157186
$364$	0	0
$365$	8.12587	0.425327
$366$	9.48877	0.495986
$367$	−24.0081	−1.25321	−0.626607	−	0.779335i	$-0.715557\pi$
$367$	−24.0081	−1.25321	−0.626607	+	0.779335i	$0.715557\pi$
$368$	−36.4175	−1.89839
$369$	−1.00000	−0.0520579
$370$	−15.0359	−0.781679
$371$	0	0
$372$	0.835887	0.0433387
$373$	−3.48977	−0.180694	−0.0903468	−	0.995910i	$-0.528798\pi$
$373$	−3.48977	−0.180694	−0.0903468	+	0.995910i	$0.528798\pi$
$374$	−7.25027	−0.374902
$375$	−9.72625	−0.502262
$376$	4.62292	0.238409
$377$	−4.58513	−0.236146
$378$	0	0
$379$	29.7705	1.52921	0.764603	−	0.644501i	$-0.222935\pi$
$379$	29.7705	1.52921	0.764603	+	0.644501i	$0.222935\pi$
$380$	0.838570	0.0430177
$381$	6.05248	0.310078
$382$	19.5216	0.998814
$383$	−9.44326	−0.482528	−0.241264	−	0.970460i	$-0.577562\pi$
$383$	−9.44326	−0.482528	−0.241264	+	0.970460i	$0.577562\pi$
$384$	13.0622	0.666578
$385$	0	0
$386$	−2.31664	−0.117914
$387$	5.07578	0.258017
$388$	−0.806521	−0.0409449
$389$	31.9855	1.62173	0.810864	−	0.585235i	$-0.198998\pi$
$389$	31.9855	1.62173	0.810864	+	0.585235i	$0.198998\pi$
$390$	6.77036	0.342831
$391$	−10.4720	−0.529593
$392$	0	0
$393$	10.1642	0.512719
$394$	22.0906	1.11291
$395$	3.39651	0.170897
$396$	1.01970	0.0512419
$397$	−21.0779	−1.05787	−0.528934	−	0.848663i	$-0.677408\pi$
$397$	−21.0779	−1.05787	−0.528934	+	0.848663i	$0.677408\pi$
$398$	−24.0638	−1.20621
$399$	0	0
$400$	16.8554	0.842768
$401$	−21.5312	−1.07522	−0.537609	−	0.843194i	$-0.680672\pi$
$401$	−21.5312	−1.07522	−0.537609	+	0.843194i	$0.680672\pi$
$402$	2.31268	0.115346
$403$	12.4185	0.618607
$404$	2.66739	0.132707
$405$	1.10903	0.0551082
$406$	0	0
$407$	−33.6442	−1.66768
$408$	3.34788	0.165745
$409$	35.8518	1.77276	0.886379	−	0.462961i	$-0.153213\pi$
$409$	35.8518	1.77276	0.886379	+	0.462961i	$0.153213\pi$
$410$	−1.67187	−0.0825678
$411$	10.4749	0.516687
$412$	1.53920	0.0758310
$413$	0	0
$414$	12.2794	0.603501
$415$	−11.7441	−0.576495
$416$	−6.20249	−0.304102
$417$	−5.03683	−0.246655
$418$	15.6441	0.765176
$419$	−9.75270	−0.476451	−0.238225	−	0.971210i	$-0.576566\pi$
$419$	−9.75270	−0.476451	−0.238225	+	0.971210i	$0.576566\pi$
$420$	0	0
$421$	0.117163	0.00571015	0.00285508	−	0.999996i	$-0.499091\pi$
$421$	0.117163	0.00571015	0.00285508	+	0.999996i	$0.499091\pi$
$422$	35.4527	1.72581
$423$	−1.77524	−0.0863153
$424$	3.74751	0.181995
$425$	4.84684	0.235106
$426$	18.7219	0.907078
$427$	0	0
$428$	3.88459	0.187769
$429$	15.1493	0.731415
$430$	8.48605	0.409234
$431$	21.1818	1.02029	0.510146	−	0.860088i	$-0.329591\pi$
$431$	21.1818	1.02029	0.510146	+	0.860088i	$0.329591\pi$
$432$	−4.47086	−0.215104
$433$	−23.6911	−1.13852	−0.569260	−	0.822157i	$-0.692770\pi$
$433$	−23.6911	−1.13852	−0.569260	+	0.822157i	$0.692770\pi$
$434$	0	0
$435$	−1.25570	−0.0602063
$436$	−0.540523	−0.0258863
$437$	22.5957	1.08090
$438$	11.0455	0.527775
$439$	−17.5444	−0.837349	−0.418675	−	0.908136i	$-0.637505\pi$
$439$	−17.5444	−0.837349	−0.418675	+	0.908136i	$0.637505\pi$
$440$	−10.8040	−0.515061
$441$	0	0
$442$	−7.84837	−0.373309
$443$	4.89678	0.232653	0.116327	−	0.993211i	$-0.462888\pi$
$443$	4.89678	0.232653	0.116327	+	0.993211i	$0.462888\pi$
$444$	−2.45141	−0.116339
$445$	−0.956211	−0.0453287
$446$	−33.3505	−1.57919
$447$	12.4511	0.588915
$448$	0	0
$449$	−25.8031	−1.21772	−0.608862	−	0.793276i	$-0.708374\pi$
$449$	−25.8031	−1.21772	−0.608862	+	0.793276i	$0.708374\pi$
$450$	−5.68338	−0.267917
$451$	−3.74096	−0.176155
$452$	0.524049	0.0246492
$453$	1.01228	0.0475609
$454$	32.9623	1.54700
$455$	0	0
$456$	−7.22378	−0.338285
$457$	−10.7604	−0.503349	−0.251675	−	0.967812i	$-0.580981\pi$
$457$	−10.7604	−0.503349	−0.251675	+	0.967812i	$0.580981\pi$
$458$	−22.2893	−1.04151
$459$	−1.28562	−0.0600074
$460$	2.46236	0.114808
$461$	4.73851	0.220694	0.110347	−	0.993893i	$-0.464804\pi$
$461$	4.73851	0.220694	0.110347	+	0.993893i	$0.464804\pi$
$462$	0	0
$463$	−13.8446	−0.643413	−0.321707	−	0.946839i	$-0.604256\pi$
$463$	−13.8446	−0.643413	−0.321707	+	0.946839i	$0.604256\pi$
$464$	5.06213	0.235004
$465$	3.40096	0.157716
$466$	−41.0200	−1.90022
$467$	11.5666	0.535238	0.267619	−	0.963525i	$-0.413763\pi$
$467$	11.5666	0.535238	0.267619	+	0.963525i	$0.413763\pi$
$468$	1.10382	0.0510241
$469$	0	0
$470$	−2.96798	−0.136903
$471$	−3.97214	−0.183026
$472$	30.7630	1.41598
$473$	18.9883	0.873084
$474$	4.61688	0.212060
$475$	−10.4581	−0.479852
$476$	0	0
$477$	−1.43908	−0.0658910
$478$	−36.1249	−1.65232
$479$	11.9744	0.547123	0.273562	−	0.961854i	$-0.411798\pi$
$479$	11.9744	0.547123	0.273562	+	0.961854i	$0.411798\pi$
$480$	−1.69864	−0.0775318
$481$	−36.4196	−1.66059
$482$	19.4625	0.886494
$483$	0	0
$484$	0.816313	0.0371052
$485$	−3.28148	−0.149004
$486$	1.50751	0.0683819
$487$	−11.7895	−0.534235	−0.267118	−	0.963664i	$-0.586071\pi$
$487$	−11.7895	−0.534235	−0.267118	+	0.963664i	$0.586071\pi$
$488$	−16.3911	−0.741991
$489$	22.6056	1.02226
$490$	0	0
$491$	−41.8155	−1.88711	−0.943553	−	0.331222i	$-0.892539\pi$
$491$	−41.8155	−1.88711	−0.943553	+	0.331222i	$0.892539\pi$
$492$	−0.272577	−0.0122887
$493$	1.45564	0.0655588
$494$	16.9346	0.761924
$495$	4.14884	0.186477
$496$	−13.7104	−0.615614
$497$	0	0
$498$	−15.9638	−0.715354
$499$	−18.7923	−0.841260	−0.420630	−	0.907232i	$-0.638191\pi$
$499$	−18.7923	−0.841260	−0.420630	+	0.907232i	$0.638191\pi$
$500$	−2.65115	−0.118563
$501$	−10.2870	−0.459591
$502$	−20.3367	−0.907669
$503$	5.66329	0.252514	0.126257	−	0.991998i	$-0.459704\pi$
$503$	5.66329	0.252514	0.126257	+	0.991998i	$0.459704\pi$
$504$	0	0
$505$	10.8528	0.482941
$506$	45.9369	2.04215
$507$	3.39903	0.150956
$508$	1.64977	0.0731966
$509$	−16.0628	−0.711970	−0.355985	−	0.934492i	$-0.615855\pi$
$509$	−16.0628	−0.711970	−0.355985	+	0.934492i	$0.615855\pi$
$510$	−2.14938	−0.0951763
$511$	0	0
$512$	−16.4374	−0.726437
$513$	2.77400	0.122475
$514$	−6.57018	−0.289798
$515$	6.26253	0.275960
$516$	1.38354	0.0609070
$517$	−6.64112	−0.292076
$518$	0	0
$519$	−8.31332	−0.364914
$520$	−11.6953	−0.512872
$521$	−29.4204	−1.28893	−0.644465	−	0.764634i	$-0.722920\pi$
$521$	−29.4204	−1.28893	−0.644465	+	0.764634i	$0.722920\pi$
$522$	−1.70688	−0.0747080
$523$	1.46912	0.0642401	0.0321201	−	0.999484i	$-0.489774\pi$
$523$	1.46912	0.0642401	0.0321201	+	0.999484i	$0.489774\pi$
$524$	2.77054	0.121032
$525$	0	0
$526$	−21.5428	−0.939312
$527$	−3.94248	−0.171737
$528$	−16.7253	−0.727875
$529$	43.3496	1.88477
$530$	−2.40596	−0.104508
$531$	−11.8133	−0.512653
$532$	0	0
$533$	−4.04957	−0.175406
$534$	−1.29978	−0.0562469
$535$	15.8052	0.683318
$536$	−3.99498	−0.172557
$537$	5.82288	0.251276
$538$	−30.6468	−1.32128
$539$	0	0
$540$	0.302296	0.0130088
$541$	14.1541	0.608534	0.304267	−	0.952587i	$-0.401588\pi$
$541$	14.1541	0.608534	0.304267	+	0.952587i	$0.401588\pi$
$542$	31.9337	1.37167
$543$	−16.9447	−0.727168
$544$	1.96910	0.0844246
$545$	−2.19922	−0.0942042
$546$	0	0
$547$	−36.1112	−1.54401	−0.772003	−	0.635619i	$-0.780745\pi$
$547$	−36.1112	−1.54401	−0.772003	+	0.635619i	$0.780745\pi$
$548$	2.85521	0.121968
$549$	6.29435	0.268636
$550$	−21.2613	−0.906585
$551$	−3.14087	−0.133805
$552$	−21.2118	−0.902834
$553$	0	0
$554$	4.82841	0.205139
$555$	−9.97402	−0.423373
$556$	−1.37292	−0.0582250
$557$	−28.3038	−1.19927	−0.599635	−	0.800274i	$-0.704687\pi$
$557$	−28.3038	−1.19927	−0.599635	+	0.800274i	$0.704687\pi$
$558$	4.62294	0.195704
$559$	20.5547	0.869373
$560$	0	0
$561$	−4.80944	−0.203055
$562$	−25.4268	−1.07257
$563$	−28.6819	−1.20880	−0.604399	−	0.796682i	$-0.706587\pi$
$563$	−28.6819	−1.20880	−0.604399	+	0.796682i	$0.706587\pi$
$564$	−0.483891	−0.0203755
$565$	2.13219	0.0897019
$566$	43.7489	1.83890
$567$	0	0
$568$	−32.3406	−1.35698
$569$	−25.3316	−1.06195	−0.530977	−	0.847386i	$-0.678175\pi$
$569$	−25.3316	−1.06195	−0.530977	+	0.847386i	$0.678175\pi$
$570$	4.63777	0.194255
$571$	−44.5188	−1.86305	−0.931526	−	0.363674i	$-0.881522\pi$
$571$	−44.5188	−1.86305	−0.931526	+	0.363674i	$0.881522\pi$
$572$	4.12935	0.172657
$573$	12.9496	0.540978
$574$	0	0
$575$	−30.7091	−1.28066
$576$	6.63275	0.276365
$577$	8.77810	0.365437	0.182718	−	0.983165i	$-0.441510\pi$
$577$	8.77810	0.365437	0.182718	+	0.983165i	$0.441510\pi$
$578$	−23.1360	−0.962331
$579$	−1.53674	−0.0638646
$580$	−0.342275	−0.0142122
$581$	0	0
$582$	−4.46053	−0.184895
$583$	−5.38355	−0.222964
$584$	−19.0803	−0.789547
$585$	4.49110	0.185684
$586$	−50.4480	−2.08399
$587$	8.35115	0.344689	0.172344	−	0.985037i	$-0.444866\pi$
$587$	8.35115	0.344689	0.172344	+	0.985037i	$0.444866\pi$
$588$	0	0
$589$	8.50678	0.350516
$590$	−19.7503	−0.813107
$591$	14.6537	0.602773
$592$	40.2084	1.65256
$593$	6.68553	0.274542	0.137271	−	0.990534i	$-0.456167\pi$
$593$	6.68553	0.274542	0.137271	+	0.990534i	$0.456167\pi$
$594$	5.63953	0.231393
$595$	0	0
$596$	3.39387	0.139018
$597$	−15.9626	−0.653306
$598$	49.7265	2.03347
$599$	6.46648	0.264213	0.132107	−	0.991236i	$-0.457826\pi$
$599$	6.46648	0.264213	0.132107	+	0.991236i	$0.457826\pi$
$600$	9.81760	0.400802
$601$	40.0959	1.63554	0.817772	−	0.575542i	$-0.195209\pi$
$601$	40.0959	1.63554	0.817772	+	0.575542i	$0.195209\pi$
$602$	0	0
$603$	1.53411	0.0624738
$604$	0.275923	0.0112272
$605$	3.32132	0.135031
$606$	14.7522	0.599266
$607$	2.40461	0.0976000	0.0488000	−	0.998809i	$-0.484460\pi$
$607$	2.40461	0.0976000	0.0488000	+	0.998809i	$0.484460\pi$
$608$	−4.24877	−0.172311
$609$	0	0
$610$	10.5233	0.426077
$611$	−7.18898	−0.290835
$612$	−0.350429	−0.0141653
$613$	−21.6500	−0.874435	−0.437218	−	0.899356i	$-0.644036\pi$
$613$	−21.6500	−0.874435	−0.437218	+	0.899356i	$0.644036\pi$
$614$	−18.2365	−0.735964
$615$	−1.10903	−0.0447204
$616$	0	0
$617$	−5.55725	−0.223726	−0.111863	−	0.993724i	$-0.535682\pi$
$617$	−5.55725	−0.223726	−0.111863	+	0.993724i	$0.535682\pi$
$618$	8.51266	0.342429
$619$	−39.3059	−1.57984	−0.789918	−	0.613212i	$-0.789877\pi$
$619$	−39.3059	−1.57984	−0.789918	+	0.613212i	$0.789877\pi$
$620$	0.927024	0.0372302
$621$	8.14553	0.326869
$622$	−6.38920	−0.256183
$623$	0	0
$624$	−18.1050	−0.724782
$625$	8.06355	0.322542
$626$	35.2760	1.40991
$627$	10.3774	0.414435
$628$	−1.08271	−0.0432049
$629$	11.5621	0.461012
$630$	0	0
$631$	−1.34175	−0.0534142	−0.0267071	−	0.999643i	$-0.508502\pi$
$631$	−1.34175	−0.0534142	−0.0267071	+	0.999643i	$0.508502\pi$
$632$	−7.97530	−0.317240
$633$	23.5174	0.934733
$634$	11.6299	0.461883
$635$	6.71239	0.266373
$636$	−0.392260	−0.0155541
$637$	0	0
$638$	−6.38536	−0.252799
$639$	12.4191	0.491292
$640$	14.4864	0.572624
$641$	21.6189	0.853894	0.426947	−	0.904277i	$-0.359589\pi$
$641$	21.6189	0.853894	0.426947	+	0.904277i	$0.359589\pi$
$642$	21.4840	0.847907
$643$	−24.8621	−0.980465	−0.490233	−	0.871592i	$-0.663088\pi$
$643$	−24.8621	−0.980465	−0.490233	+	0.871592i	$0.663088\pi$
$644$	0	0
$645$	5.62920	0.221649
$646$	−5.37622	−0.211525
$647$	−29.3258	−1.15292	−0.576459	−	0.817126i	$-0.695566\pi$
$647$	−29.3258	−1.15292	−0.576459	+	0.817126i	$0.695566\pi$
$648$	−2.60410	−0.102299
$649$	−44.1931	−1.73473
$650$	−23.0152	−0.902732
$651$	0	0
$652$	6.16177	0.241313
$653$	40.3928	1.58069	0.790346	−	0.612661i	$-0.209901\pi$
$653$	40.3928	1.58069	0.790346	+	0.612661i	$0.209901\pi$
$654$	−2.98940	−0.116895
$655$	11.2725	0.440452
$656$	4.47086	0.174558
$657$	7.32700	0.285854
$658$	0	0
$659$	36.6015	1.42579	0.712895	−	0.701271i	$-0.247384\pi$
$659$	36.6015	1.42579	0.712895	+	0.701271i	$0.247384\pi$
$660$	1.13088	0.0440194
$661$	35.4309	1.37810	0.689050	−	0.724714i	$-0.258028\pi$
$661$	35.4309	1.37810	0.689050	+	0.724714i	$0.258028\pi$
$662$	1.18304	0.0459801
$663$	−5.20619	−0.202192
$664$	27.5762	1.07016
$665$	0	0
$666$	−13.5577	−0.525350
$667$	−9.22279	−0.357108
$668$	−2.80401	−0.108490
$669$	−22.1230	−0.855323
$670$	2.56484	0.0990882
$671$	23.5469	0.909018
$672$	0	0
$673$	4.09653	0.157910	0.0789549	−	0.996878i	$-0.474842\pi$
$673$	4.09653	0.157910	0.0789549	+	0.996878i	$0.474842\pi$
$674$	−17.6131	−0.678432
$675$	−3.77005	−0.145109
$676$	0.926497	0.0356345
$677$	46.9399	1.80405	0.902023	−	0.431687i	$-0.142081\pi$
$677$	46.9399	1.80405	0.902023	+	0.431687i	$0.142081\pi$
$678$	2.89829	0.111308
$679$	0	0
$680$	3.71290	0.142383
$681$	21.8654	0.837885
$682$	17.2942	0.662230
$683$	43.8835	1.67916	0.839578	−	0.543239i	$-0.182802\pi$
$683$	43.8835	1.67916	0.839578	+	0.543239i	$0.182802\pi$
$684$	0.756129	0.0289113
$685$	11.6169	0.443861
$686$	0	0
$687$	−14.7855	−0.564103
$688$	−22.6931	−0.865166
$689$	−5.82766	−0.222016
$690$	13.6183	0.518439
$691$	13.1815	0.501446	0.250723	−	0.968059i	$-0.419332\pi$
$691$	13.1815	0.501446	0.250723	+	0.968059i	$0.419332\pi$
$692$	−2.26602	−0.0861411
$693$	0	0
$694$	1.93776	0.0735563
$695$	−5.58600	−0.211889
$696$	2.94850	0.111763
$697$	1.28562	0.0486962
$698$	−46.2155	−1.74928
$699$	−27.2105	−1.02920
$700$	0	0
$701$	−21.8416	−0.824945	−0.412472	−	0.910970i	$-0.635335\pi$
$701$	−21.8416	−0.824945	−0.412472	+	0.910970i	$0.635335\pi$
$702$	6.10476	0.230409
$703$	−24.9479	−0.940926
$704$	24.8129	0.935170
$705$	−1.96880	−0.0741493
$706$	−0.989258	−0.0372312
$707$	0	0
$708$	−3.22003	−0.121016
$709$	−23.7312	−0.891243	−0.445622	−	0.895221i	$-0.647017\pi$
$709$	−23.7312	−0.891243	−0.445622	+	0.895221i	$0.647017\pi$
$710$	20.7631	0.779226
$711$	3.06259	0.114856
$712$	2.24527	0.0841450
$713$	24.9792	0.935477
$714$	0	0
$715$	16.8010	0.628323
$716$	1.58718	0.0593158
$717$	−23.9634	−0.894928
$718$	−1.01020	−0.0377005
$719$	−14.4356	−0.538358	−0.269179	−	0.963090i	$-0.586752\pi$
$719$	−14.4356	−0.538358	−0.269179	+	0.963090i	$0.586752\pi$
$720$	−4.95832	−0.184785
$721$	0	0
$722$	−17.0422	−0.634246
$723$	12.9104	0.480143
$724$	−4.61874	−0.171654
$725$	4.26865	0.158534
$726$	4.51468	0.167556
$727$	−7.96786	−0.295512	−0.147756	−	0.989024i	$-0.547205\pi$
$727$	−7.96786	−0.295512	−0.147756	+	0.989024i	$0.547205\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.2498	0.453385
$731$	−6.52551	−0.241355
$732$	1.71569	0.0634138
$733$	33.3492	1.23178	0.615890	−	0.787832i	$-0.288796\pi$
$733$	33.3492	1.23178	0.615890	+	0.787832i	$0.288796\pi$
$734$	−36.1924	−1.33589
$735$	0	0
$736$	−12.4760	−0.459872
$737$	5.73905	0.211401
$738$	−1.50751	−0.0554921
$739$	−14.8315	−0.545584	−0.272792	−	0.962073i	$-0.587947\pi$
$739$	−14.8315	−0.545584	−0.272792	+	0.962073i	$0.587947\pi$
$740$	−2.71869	−0.0999409
$741$	11.2335	0.412674
$742$	0	0
$743$	31.1321	1.14213	0.571063	−	0.820906i	$-0.306531\pi$
$743$	31.1321	1.14213	0.571063	+	0.820906i	$0.306531\pi$
$744$	−7.98577	−0.292772
$745$	13.8086	0.505908
$746$	−5.26086	−0.192614
$747$	−10.5895	−0.387450
$748$	−1.31094	−0.0479328
$749$	0	0
$750$	−14.6624	−0.535395
$751$	3.96823	0.144803	0.0724014	−	0.997376i	$-0.476934\pi$
$751$	3.96823	0.144803	0.0724014	+	0.997376i	$0.476934\pi$
$752$	7.93686	0.289427
$753$	−13.4903	−0.491612
$754$	−6.91212	−0.251725
$755$	1.12265	0.0408572
$756$	0	0
$757$	−28.9528	−1.05231	−0.526153	−	0.850390i	$-0.676366\pi$
$757$	−28.9528	−1.05231	−0.526153	+	0.850390i	$0.676366\pi$
$758$	44.8792	1.63009
$759$	30.4721	1.10607
$760$	−8.01139	−0.290604
$761$	12.6480	0.458490	0.229245	−	0.973369i	$-0.426374\pi$
$761$	12.6480	0.458490	0.229245	+	0.973369i	$0.426374\pi$
$762$	9.12416	0.330533
$763$	0	0
$764$	3.52977	0.127702
$765$	−1.42579	−0.0515494
$766$	−14.2358	−0.514359
$767$	−47.8388	−1.72736
$768$	6.42585	0.231873
$769$	22.8838	0.825210	0.412605	−	0.910910i	$-0.364619\pi$
$769$	22.8838	0.825210	0.412605	+	0.910910i	$0.364619\pi$
$770$	0	0
$771$	−4.35831	−0.156961
$772$	−0.418879	−0.0150758
$773$	−0.777954	−0.0279811	−0.0139905	−	0.999902i	$-0.504453\pi$
$773$	−0.777954	−0.0279811	−0.0139905	+	0.999902i	$0.504453\pi$
$774$	7.65178	0.275037
$775$	−11.5613	−0.415293
$776$	7.70521	0.276601
$777$	0	0
$778$	48.2183	1.72871
$779$	−2.77400	−0.0993889
$780$	1.22417	0.0438323
$781$	46.4594	1.66245
$782$	−15.7866	−0.564529
$783$	−1.13225	−0.0404634
$784$	0	0
$785$	−4.40522	−0.157229
$786$	15.3227	0.546542
$787$	−29.3699	−1.04692	−0.523462	−	0.852049i	$-0.675360\pi$
$787$	−29.3699	−1.04692	−0.523462	+	0.852049i	$0.675360\pi$
$788$	3.99426	0.142290
$789$	−14.2904	−0.508751
$790$	5.12026	0.182171
$791$	0	0
$792$	−9.74185	−0.346162
$793$	25.4894	0.905155
$794$	−31.7750	−1.12765
$795$	−1.59598	−0.0566037
$796$	−4.35104	−0.154219
$797$	−22.5919	−0.800247	−0.400124	−	0.916461i	$-0.631033\pi$
$797$	−22.5919	−0.800247	−0.400124	+	0.916461i	$0.631033\pi$
$798$	0	0
$799$	2.28228	0.0807413
$800$	5.77437	0.204155
$801$	−0.862204	−0.0304645
$802$	−32.4585	−1.14615
$803$	27.4100	0.967279
$804$	0.418163	0.0147475
$805$	0	0
$806$	18.7209	0.659416
$807$	−20.3295	−0.715632
$808$	−25.4832	−0.896497
$809$	31.0716	1.09242	0.546209	−	0.837649i	$-0.316070\pi$
$809$	31.0716	1.09242	0.546209	+	0.837649i	$0.316070\pi$
$810$	1.67187	0.0587436
$811$	−32.1947	−1.13051	−0.565254	−	0.824917i	$-0.691222\pi$
$811$	−32.1947	−1.13051	−0.565254	+	0.824917i	$0.691222\pi$
$812$	0	0
$813$	21.1831	0.742925
$814$	−50.7188	−1.77769
$815$	25.0703	0.878175
$816$	5.74780	0.201213
$817$	14.0802	0.492605
$818$	54.0468	1.88970
$819$	0	0
$820$	−0.302296	−0.0105566
$821$	−21.4757	−0.749509	−0.374754	−	0.927124i	$-0.622273\pi$
$821$	−21.4757	−0.749509	−0.374754	+	0.927124i	$0.622273\pi$
$822$	15.7909	0.550772
$823$	27.4356	0.956345	0.478172	−	0.878266i	$-0.341299\pi$
$823$	27.4356	0.956345	0.478172	+	0.878266i	$0.341299\pi$
$824$	−14.7050	−0.512272
$825$	−14.1036	−0.491025
$826$	0	0
$827$	5.26418	0.183053	0.0915267	−	0.995803i	$-0.470825\pi$
$827$	5.26418	0.183053	0.0915267	+	0.995803i	$0.470825\pi$
$828$	2.22028	0.0771602
$829$	36.4033	1.26434	0.632169	−	0.774831i	$-0.282165\pi$
$829$	36.4033	1.26434	0.632169	+	0.774831i	$0.282165\pi$
$830$	−17.7043	−0.614525
$831$	3.20291	0.111108
$832$	26.8598	0.931196
$833$	0	0
$834$	−7.59306	−0.262926
$835$	−11.4086	−0.394812
$836$	2.82865	0.0978309
$837$	3.06661	0.105998
$838$	−14.7023	−0.507881
$839$	35.5047	1.22576	0.612880	−	0.790176i	$-0.290011\pi$
$839$	35.5047	1.22576	0.612880	+	0.790176i	$0.290011\pi$
$840$	0	0
$841$	−27.7180	−0.955793
$842$	0.176623	0.00608684
$843$	−16.8668	−0.580923
$844$	6.41030	0.220652
$845$	3.76963	0.129679
$846$	−2.67619	−0.0920094
$847$	0	0
$848$	6.43392	0.220942
$849$	29.0207	0.995988
$850$	7.30664	0.250616
$851$	−73.2564	−2.51120
$852$	3.38516	0.115974
$853$	−28.0973	−0.962035	−0.481017	−	0.876711i	$-0.659733\pi$
$853$	−28.0973	−0.962035	−0.481017	+	0.876711i	$0.659733\pi$
$854$	0	0
$855$	3.07645	0.105212
$856$	−37.1120	−1.26846
$857$	45.0276	1.53811	0.769056	−	0.639181i	$-0.220727\pi$
$857$	45.0276	1.53811	0.769056	+	0.639181i	$0.220727\pi$
$858$	22.8377	0.779665
$859$	19.7121	0.672568	0.336284	−	0.941761i	$-0.390830\pi$
$859$	19.7121	0.672568	0.336284	+	0.941761i	$0.390830\pi$
$860$	1.53439	0.0523222
$861$	0	0
$862$	31.9317	1.08760
$863$	−8.30927	−0.282851	−0.141425	−	0.989949i	$-0.545169\pi$
$863$	−8.30927	−0.282851	−0.141425	+	0.989949i	$0.545169\pi$
$864$	−1.53164	−0.0521075
$865$	−9.21972	−0.313480
$866$	−35.7145	−1.21363
$867$	−15.3472	−0.521218
$868$	0	0
$869$	11.4570	0.388653
$870$	−1.89298	−0.0641780
$871$	6.21249	0.210502
$872$	5.16396	0.174874
$873$	−2.95888	−0.100143
$874$	34.0632	1.15220
$875$	0	0
$876$	1.99717	0.0674782
$877$	36.4096	1.22947	0.614733	−	0.788735i	$-0.289264\pi$
$877$	36.4096	1.22947	0.614733	+	0.788735i	$0.289264\pi$
$878$	−26.4483	−0.892588
$879$	−33.4645	−1.12873
$880$	−18.5489	−0.625282
$881$	−41.2925	−1.39118	−0.695590	−	0.718439i	$-0.744857\pi$
$881$	−41.2925	−1.39118	−0.695590	+	0.718439i	$0.744857\pi$
$882$	0	0
$883$	−27.7916	−0.935261	−0.467631	−	0.883924i	$-0.654892\pi$
$883$	−27.7916	−0.935261	−0.467631	+	0.883924i	$0.654892\pi$
$884$	−1.41909	−0.0477291
$885$	−13.1013	−0.440395
$886$	7.38193	0.248001
$887$	−22.4719	−0.754534	−0.377267	−	0.926105i	$-0.623136\pi$
$887$	−22.4719	−0.754534	−0.377267	+	0.926105i	$0.623136\pi$
$888$	23.4199	0.785920
$889$	0	0
$890$	−1.44149	−0.0483190
$891$	3.74096	0.125327
$892$	−6.03021	−0.201906
$893$	−4.92453	−0.164793
$894$	18.7701	0.627765
$895$	6.45775	0.215859
$896$	0	0
$897$	32.9859	1.10137
$898$	−38.8984	−1.29806
$899$	−3.47217	−0.115803
$900$	−1.02763	−0.0342543
$901$	1.85010	0.0616359
$902$	−5.63953	−0.187776
$903$	0	0
$904$	−5.00657	−0.166516
$905$	−18.7922	−0.624675
$906$	1.52601	0.0506984
$907$	−48.2992	−1.60375	−0.801875	−	0.597492i	$-0.796164\pi$
$907$	−48.2992	−1.60375	−0.801875	+	0.597492i	$0.796164\pi$
$908$	5.96001	0.197790
$909$	9.78581	0.324575
$910$	0	0
$911$	37.4429	1.24054	0.620269	−	0.784389i	$-0.287023\pi$
$911$	37.4429	1.24054	0.620269	+	0.784389i	$0.287023\pi$
$912$	−12.4022	−0.410677
$913$	−39.6150	−1.31106
$914$	−16.2213	−0.536554
$915$	6.98062	0.230772
$916$	−4.03019	−0.133161
$917$	0	0
$918$	−1.93807	−0.0639660
$919$	−11.5498	−0.380992	−0.190496	−	0.981688i	$-0.561010\pi$
$919$	−11.5498	−0.380992	−0.190496	+	0.981688i	$0.561010\pi$
$920$	−23.5245	−0.775580
$921$	−12.0971	−0.398613
$922$	7.14334	0.235253
$923$	50.2920	1.65538
$924$	0	0
$925$	33.9058	1.11482
$926$	−20.8708	−0.685858
$927$	5.64685	0.185467
$928$	1.73420	0.0569280
$929$	2.48031	0.0813764	0.0406882	−	0.999172i	$-0.487045\pi$
$929$	2.48031	0.0813764	0.0406882	+	0.999172i	$0.487045\pi$
$930$	5.12698	0.168120
$931$	0	0
$932$	−7.41696	−0.242951
$933$	−4.23825	−0.138754
$934$	17.4367	0.570547
$935$	−5.33382	−0.174434
$936$	−10.5455	−0.344690
$937$	−20.6957	−0.676098	−0.338049	−	0.941128i	$-0.609767\pi$
$937$	−20.6957	−0.676098	−0.338049	+	0.941128i	$0.609767\pi$
$938$	0	0
$939$	23.4002	0.763637
$940$	−0.536649	−0.0175036
$941$	−19.6088	−0.639230	−0.319615	−	0.947547i	$-0.603554\pi$
$941$	−19.6088	−0.639230	−0.319615	+	0.947547i	$0.603554\pi$
$942$	−5.98802	−0.195100
$943$	−8.14553	−0.265255
$944$	52.8155	1.71900
$945$	0	0
$946$	28.6250	0.930679
$947$	51.2866	1.66659	0.833296	−	0.552828i	$-0.186451\pi$
$947$	51.2866	1.66659	0.833296	+	0.552828i	$0.186451\pi$
$948$	0.834792	0.0271128
$949$	29.6712	0.963168
$950$	−15.7657	−0.511507
$951$	7.71467	0.250165
$952$	0	0
$953$	49.5293	1.60441	0.802205	−	0.597048i	$-0.203660\pi$
$953$	49.5293	1.60441	0.802205	+	0.597048i	$0.203660\pi$
$954$	−2.16942	−0.0702377
$955$	14.3615	0.464728
$956$	−6.53186	−0.211255
$957$	−4.23571	−0.136921
$958$	18.0515	0.583216
$959$	0	0
$960$	7.35592	0.237411
$961$	−21.5959	−0.696642
$962$	−54.9029	−1.77014
$963$	14.2514	0.459244
$964$	3.51908	0.113342
$965$	−1.70429	−0.0548630
$966$	0	0
$967$	−22.8164	−0.733727	−0.366863	−	0.930275i	$-0.619568\pi$
$967$	−22.8164	−0.733727	−0.366863	+	0.930275i	$0.619568\pi$
$968$	−7.79877	−0.250662
$969$	−3.56630	−0.114566
$970$	−4.94686	−0.158834
$971$	24.2347	0.777729	0.388864	−	0.921295i	$-0.372867\pi$
$971$	24.2347	0.777729	0.388864	+	0.921295i	$0.372867\pi$
$972$	0.272577	0.00874291
$973$	0	0
$974$	−17.7728	−0.569478
$975$	−15.2671	−0.488938
$976$	−28.1411	−0.900775
$977$	−33.0385	−1.05700	−0.528498	−	0.848934i	$-0.677245\pi$
$977$	−33.0385	−1.05700	−0.528498	+	0.848934i	$0.677245\pi$
$978$	34.0781	1.08970
$979$	−3.22547	−0.103087
$980$	0	0
$981$	−1.98301	−0.0633126
$982$	−63.0371	−2.01159
$983$	21.3362	0.680518	0.340259	−	0.940332i	$-0.389485\pi$
$983$	21.3362	0.680518	0.340259	+	0.940332i	$0.389485\pi$
$984$	2.60410	0.0830157
$985$	16.2514	0.517813
$986$	2.19439	0.0698836
$987$	0	0
$988$	3.06200	0.0974151
$989$	41.3449	1.31469
$990$	6.25441	0.198778
$991$	6.34983	0.201709	0.100854	−	0.994901i	$-0.467842\pi$
$991$	6.34983	0.201709	0.100854	+	0.994901i	$0.467842\pi$
$992$	−4.69695	−0.149128
$993$	0.784765	0.0249038
$994$	0	0
$995$	−17.7030	−0.561224
$996$	−2.88646	−0.0914609
$997$	−39.8519	−1.26212	−0.631061	−	0.775733i	$-0.717380\pi$
$997$	−39.8519	−1.26212	−0.631061	+	0.775733i	$0.717380\pi$
$998$	−28.3296	−0.896757
$999$	−8.99346	−0.284540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.16	yes	24
7.6	odd	2		6027.2.a.bn.1.16	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.16	✓	24	7.6	odd	2
6027.2.a.bo.1.16	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.50751 q^{2} +1.00000 q^{3} +0.272577 q^{4} +1.10903 q^{5} +1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.50751 q^{2} +1.00000 q^{3} +0.272577 q^{4} +1.10903 q^{5} +1.50751 q^{6} -2.60410 q^{8} +1.00000 q^{9} +1.67187 q^{10} +3.74096 q^{11} +0.272577 q^{12} +4.04957 q^{13} +1.10903 q^{15} -4.47086 q^{16} -1.28562 q^{17} +1.50751 q^{18} +2.77400 q^{19} +0.302296 q^{20} +5.63953 q^{22} +8.14553 q^{23} -2.60410 q^{24} -3.77005 q^{25} +6.10476 q^{26} +1.00000 q^{27} -1.13225 q^{29} +1.67187 q^{30} +3.06661 q^{31} -1.53164 q^{32} +3.74096 q^{33} -1.93807 q^{34} +0.272577 q^{36} -8.99346 q^{37} +4.18183 q^{38} +4.04957 q^{39} -2.88803 q^{40} -1.00000 q^{41} +5.07578 q^{43} +1.01970 q^{44} +1.10903 q^{45} +12.2794 q^{46} -1.77524 q^{47} -4.47086 q^{48} -5.68338 q^{50} -1.28562 q^{51} +1.10382 q^{52} -1.43908 q^{53} +1.50751 q^{54} +4.14884 q^{55} +2.77400 q^{57} -1.70688 q^{58} -11.8133 q^{59} +0.302296 q^{60} +6.29435 q^{61} +4.62294 q^{62} +6.63275 q^{64} +4.49110 q^{65} +5.63953 q^{66} +1.53411 q^{67} -0.350429 q^{68} +8.14553 q^{69} +12.4191 q^{71} -2.60410 q^{72} +7.32700 q^{73} -13.5577 q^{74} -3.77005 q^{75} +0.756129 q^{76} +6.10476 q^{78} +3.06259 q^{79} -4.95832 q^{80} +1.00000 q^{81} -1.50751 q^{82} -10.5895 q^{83} -1.42579 q^{85} +7.65178 q^{86} -1.13225 q^{87} -9.74185 q^{88} -0.862204 q^{89} +1.67187 q^{90} +2.22028 q^{92} +3.06661 q^{93} -2.67619 q^{94} +3.07645 q^{95} -1.53164 q^{96} -2.95888 q^{97} +3.74096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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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Database

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