LMFDB - Embedded newform 2738.2.a.q.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2738,2,Mod(1,2738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2738.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2738, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-6,0,6,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$21.8630400734$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.37902897.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} - x^{3} + 60x^{2} - 64 $ x^6 - 15x^4 - x^3 + 60x^2 - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.18117$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +2.18117 q^{3} +1.00000 q^{4} +1.87939 q^{5} -2.18117 q^{6} -4.09926 q^{7} -1.00000 q^{8} +1.75751 q^{9} -1.87939 q^{10} +3.34175 q^{11} +2.18117 q^{12} -1.93869 q^{13} +4.09926 q^{14} +4.09926 q^{15} +1.00000 q^{16} -4.44656 q^{17} -1.75751 q^{18} +0.0992633 q^{19} +1.87939 q^{20} -8.94120 q^{21} -3.34175 q^{22} -9.52292 q^{23} -2.18117 q^{24} -1.46791 q^{25} +1.93869 q^{26} -2.71008 q^{27} -4.09926 q^{28} -0.774576 q^{29} -4.09926 q^{30} -10.3914 q^{31} -1.00000 q^{32} +7.28893 q^{33} +4.44656 q^{34} -7.70409 q^{35} +1.75751 q^{36} -0.0992633 q^{38} -4.22861 q^{39} -1.87939 q^{40} +5.69443 q^{41} +8.94120 q^{42} +1.11986 q^{43} +3.34175 q^{44} +3.30304 q^{45} +9.52292 q^{46} -7.11448 q^{47} +2.18117 q^{48} +9.80396 q^{49} +1.46791 q^{50} -9.69871 q^{51} -1.93869 q^{52} +0.818828 q^{53} +2.71008 q^{54} +6.28044 q^{55} +4.09926 q^{56} +0.216510 q^{57} +0.774576 q^{58} -8.09926 q^{59} +4.09926 q^{60} +10.7009 q^{61} +10.3914 q^{62} -7.20451 q^{63} +1.00000 q^{64} -3.64354 q^{65} -7.28893 q^{66} +13.1663 q^{67} -4.44656 q^{68} -20.7711 q^{69} +7.70409 q^{70} -2.97316 q^{71} -1.75751 q^{72} -2.55740 q^{73} -3.20177 q^{75} +0.0992633 q^{76} -13.6987 q^{77} +4.22861 q^{78} +5.43563 q^{79} +1.87939 q^{80} -11.1837 q^{81} -5.69443 q^{82} +0.658250 q^{83} -8.94120 q^{84} -8.35680 q^{85} -1.11986 q^{86} -1.68948 q^{87} -3.34175 q^{88} -3.52523 q^{89} -3.30304 q^{90} +7.94718 q^{91} -9.52292 q^{92} -22.6655 q^{93} +7.11448 q^{94} +0.186554 q^{95} -2.18117 q^{96} -3.62024 q^{97} -9.80396 q^{98} +5.87317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - 3 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{11} + 3 q^{14} + 3 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 21 q^{19} + 6 q^{21} + 3 q^{22} - 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28}+ \cdots - 36 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^11 + 3 * q^14 + 3 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 21 * q^19 + 6 * q^21 + 3 * q^22 - 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 + 6 * q^29 - 3 * q^30 - 21 * q^31 - 6 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^35 + 12 * q^36 + 21 * q^38 - 27 * q^39 + 18 * q^41 - 6 * q^42 - 18 * q^43 - 3 * q^44 - 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 + 18 * q^50 + 18 * q^53 + 3 * q^54 + 3 * q^55 + 3 * q^56 - 6 * q^57 - 6 * q^58 - 27 * q^59 + 3 * q^60 + 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 + 3 * q^66 + 9 * q^67 - 3 * q^68 - 27 * q^69 - 3 * q^70 - 12 * q^72 + 27 * q^73 - 3 * q^75 - 21 * q^76 - 24 * q^77 + 27 * q^78 - 21 * q^79 - 6 * q^81 - 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 + 3 * q^88 + 21 * q^89 + 6 * q^90 + 24 * q^91 - 21 * q^92 - 54 * q^93 + 9 * q^94 - 3 * q^95 - 42 * q^97 - 15 * q^98 - 36 * q^99

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.18117	1.25930	0.629650	−	0.776879i	$-0.283198\pi$
$3$	2.18117	1.25930	0.629650	+	0.776879i	$0.283198\pi$
$4$	1.00000	0.500000
$5$	1.87939	0.840487	0.420243	−	0.907411i	$-0.361945\pi$
$5$	1.87939	0.840487	0.420243	+	0.907411i	$0.361945\pi$
$6$	−2.18117	−0.890460
$7$	−4.09926	−1.54938	−0.774688	−	0.632344i	$-0.782093\pi$
$7$	−4.09926	−1.54938	−0.774688	+	0.632344i	$0.782093\pi$
$8$	−1.00000	−0.353553
$9$	1.75751	0.585838
$10$	−1.87939	−0.594314
$11$	3.34175	1.00758	0.503788	−	0.863827i	$-0.331939\pi$
$11$	3.34175	1.00758	0.503788	+	0.863827i	$0.331939\pi$
$12$	2.18117	0.629650
$13$	−1.93869	−0.537695	−0.268847	−	0.963183i	$-0.586643\pi$
$13$	−1.93869	−0.537695	−0.268847	+	0.963183i	$0.586643\pi$
$14$	4.09926	1.09557
$15$	4.09926	1.05843
$16$	1.00000	0.250000
$17$	−4.44656	−1.07845	−0.539225	−	0.842162i	$-0.681283\pi$
$17$	−4.44656	−1.07845	−0.539225	+	0.842162i	$0.681283\pi$
$18$	−1.75751	−0.414250
$19$	0.0992633	0.0227726	0.0113863	−	0.999935i	$-0.496376\pi$
$19$	0.0992633	0.0227726	0.0113863	+	0.999935i	$0.496376\pi$
$20$	1.87939	0.420243
$21$	−8.94120	−1.95113
$22$	−3.34175	−0.712464
$23$	−9.52292	−1.98567	−0.992833	−	0.119507i	$-0.961868\pi$
$23$	−9.52292	−1.98567	−0.992833	+	0.119507i	$0.961868\pi$
$24$	−2.18117	−0.445230
$25$	−1.46791	−0.293582
$26$	1.93869	0.380208
$27$	−2.71008	−0.521555
$28$	−4.09926	−0.774688
$29$	−0.774576	−0.143835	−0.0719175	−	0.997411i	$-0.522912\pi$
$29$	−0.774576	−0.143835	−0.0719175	+	0.997411i	$0.522912\pi$
$30$	−4.09926	−0.748420
$31$	−10.3914	−1.86636	−0.933179	−	0.359413i	$-0.882977\pi$
$31$	−10.3914	−1.86636	−0.933179	+	0.359413i	$0.882977\pi$
$32$	−1.00000	−0.176777
$33$	7.28893	1.26884
$34$	4.44656	0.762579
$35$	−7.70409	−1.30223
$36$	1.75751	0.292919
$37$	0	0
$37$	0	0
$38$	−0.0992633	−0.0161026
$39$	−4.22861	−0.677119
$40$	−1.87939	−0.297157
$41$	5.69443	0.889320	0.444660	−	0.895699i	$-0.353324\pi$
$41$	5.69443	0.889320	0.444660	+	0.895699i	$0.353324\pi$
$42$	8.94120	1.37966
$43$	1.11986	0.170777	0.0853884	−	0.996348i	$-0.472787\pi$
$43$	1.11986	0.170777	0.0853884	+	0.996348i	$0.472787\pi$
$44$	3.34175	0.503788
$45$	3.30304	0.492389
$46$	9.52292	1.40408
$47$	−7.11448	−1.03775	−0.518877	−	0.854849i	$-0.673650\pi$
$47$	−7.11448	−1.03775	−0.518877	+	0.854849i	$0.673650\pi$
$48$	2.18117	0.314825
$49$	9.80396	1.40057
$50$	1.46791	0.207594
$51$	−9.69871	−1.35809
$52$	−1.93869	−0.268847
$53$	0.818828	0.112475	0.0562373	−	0.998417i	$-0.482090\pi$
$53$	0.818828	0.112475	0.0562373	+	0.998417i	$0.482090\pi$
$54$	2.71008	0.368795
$55$	6.28044	0.846854
$56$	4.09926	0.547787
$57$	0.216510	0.0286775
$58$	0.774576	0.101707
$59$	−8.09926	−1.05443	−0.527217	−	0.849731i	$-0.676765\pi$
$59$	−8.09926	−1.05443	−0.527217	+	0.849731i	$0.676765\pi$
$60$	4.09926	0.529213
$61$	10.7009	1.37011	0.685056	−	0.728491i	$-0.259778\pi$
$61$	10.7009	1.37011	0.685056	+	0.728491i	$0.259778\pi$
$62$	10.3914	1.31971
$63$	−7.20451	−0.907683
$64$	1.00000	0.125000
$65$	−3.64354	−0.451925
$66$	−7.28893	−0.897206
$67$	13.1663	1.60852	0.804260	−	0.594278i	$-0.202562\pi$
$67$	13.1663	1.60852	0.804260	+	0.594278i	$0.202562\pi$
$68$	−4.44656	−0.539225
$69$	−20.7711	−2.50055
$70$	7.70409	0.920815
$71$	−2.97316	−0.352849	−0.176425	−	0.984314i	$-0.556453\pi$
$71$	−2.97316	−0.352849	−0.176425	+	0.984314i	$0.556453\pi$
$72$	−1.75751	−0.207125
$73$	−2.55740	−0.299321	−0.149660	−	0.988737i	$-0.547818\pi$
$73$	−2.55740	−0.299321	−0.149660	+	0.988737i	$0.547818\pi$
$74$	0	0
$75$	−3.20177	−0.369708
$76$	0.0992633	0.0113863
$77$	−13.6987	−1.56111
$78$	4.22861	0.478796
$79$	5.43563	0.611556	0.305778	−	0.952103i	$-0.401083\pi$
$79$	5.43563	0.611556	0.305778	+	0.952103i	$0.401083\pi$
$80$	1.87939	0.210122
$81$	−11.1837	−1.24263
$82$	−5.69443	−0.628844
$83$	0.658250	0.0722523	0.0361262	−	0.999347i	$-0.488498\pi$
$83$	0.658250	0.0722523	0.0361262	+	0.999347i	$0.488498\pi$
$84$	−8.94120	−0.975565
$85$	−8.35680	−0.906422
$86$	−1.11986	−0.120757
$87$	−1.68948	−0.181132
$88$	−3.34175	−0.356232
$89$	−3.52523	−0.373673	−0.186837	−	0.982391i	$-0.559824\pi$
$89$	−3.52523	−0.373673	−0.186837	+	0.982391i	$0.559824\pi$
$90$	−3.30304	−0.348171
$91$	7.94718	0.833091
$92$	−9.52292	−0.992833
$93$	−22.6655	−2.35030
$94$	7.11448	0.733802
$95$	0.186554	0.0191400
$96$	−2.18117	−0.222615
$97$	−3.62024	−0.367580	−0.183790	−	0.982966i	$-0.558837\pi$
$97$	−3.62024	−0.367580	−0.183790	+	0.982966i	$0.558837\pi$
$98$	−9.80396	−0.990349
$99$	5.87317	0.590276
$100$	−1.46791	−0.146791
$101$	3.94811	0.392852	0.196426	−	0.980519i	$-0.437066\pi$
$101$	3.94811	0.392852	0.196426	+	0.980519i	$0.437066\pi$
$102$	9.69871	0.960316
$103$	1.97880	0.194977	0.0974887	−	0.995237i	$-0.468919\pi$
$103$	1.97880	0.194977	0.0974887	+	0.995237i	$0.468919\pi$
$104$	1.93869	0.190104
$105$	−16.8040	−1.63990
$106$	−0.818828	−0.0795316
$107$	8.24882	0.797443	0.398722	−	0.917072i	$-0.369454\pi$
$107$	8.24882	0.797443	0.398722	+	0.917072i	$0.369454\pi$
$108$	−2.71008	−0.260777
$109$	8.78453	0.841406	0.420703	−	0.907198i	$-0.361783\pi$
$109$	8.78453	0.841406	0.420703	+	0.907198i	$0.361783\pi$
$110$	−6.28044	−0.598816
$111$	0	0
$112$	−4.09926	−0.387344
$113$	−9.97690	−0.938548	−0.469274	−	0.883053i	$-0.655484\pi$
$113$	−9.97690	−0.938548	−0.469274	+	0.883053i	$0.655484\pi$
$114$	−0.216510	−0.0202781
$115$	−17.8972	−1.66893
$116$	−0.774576	−0.0719175
$117$	−3.40727	−0.315002
$118$	8.09926	0.745598
$119$	18.2276	1.67092
$120$	−4.09926	−0.374210
$121$	0.167293	0.0152085
$122$	−10.7009	−0.968815
$123$	12.4205	1.11992
$124$	−10.3914	−0.933179
$125$	−12.1557	−1.08724
$126$	7.20451	0.641829
$127$	−16.7774	−1.48875	−0.744376	−	0.667761i	$-0.767253\pi$
$127$	−16.7774	−1.48875	−0.744376	+	0.667761i	$0.767253\pi$
$128$	−1.00000	−0.0883883
$129$	2.44260	0.215059
$130$	3.64354	0.319559
$131$	−1.40367	−0.122639	−0.0613194	−	0.998118i	$-0.519531\pi$
$131$	−1.40367	−0.122639	−0.0613194	+	0.998118i	$0.519531\pi$
$132$	7.28893	0.634420
$133$	−0.406906	−0.0352833
$134$	−13.1663	−1.13740
$135$	−5.09328	−0.438360
$136$	4.44656	0.381289
$137$	12.4193	1.06105	0.530525	−	0.847669i	$-0.321995\pi$
$137$	12.4193	1.06105	0.530525	+	0.847669i	$0.321995\pi$
$138$	20.7711	1.76816
$139$	18.3996	1.56063	0.780315	−	0.625386i	$-0.215059\pi$
$139$	18.3996	1.56063	0.780315	+	0.625386i	$0.215059\pi$
$140$	−7.70409	−0.651115
$141$	−15.5179	−1.30684
$142$	2.97316	0.249502
$143$	−6.47860	−0.541768
$144$	1.75751	0.146459
$145$	−1.45573	−0.120891
$146$	2.55740	0.211652
$147$	21.3841	1.76373
$148$	0	0
$149$	12.4068	1.01640	0.508201	−	0.861238i	$-0.330311\pi$
$149$	12.4068	1.01640	0.508201	+	0.861238i	$0.330311\pi$
$150$	3.20177	0.261423
$151$	−12.5489	−1.02121	−0.510607	−	0.859814i	$-0.670579\pi$
$151$	−12.5489	−1.02121	−0.510607	+	0.859814i	$0.670579\pi$
$152$	−0.0992633	−0.00805132
$153$	−7.81489	−0.631796
$154$	13.6987	1.10387
$155$	−19.5295	−1.56865
$156$	−4.22861	−0.338560
$157$	3.51326	0.280388	0.140194	−	0.990124i	$-0.455227\pi$
$157$	3.51326	0.280388	0.140194	+	0.990124i	$0.455227\pi$
$158$	−5.43563	−0.432436
$159$	1.78600	0.141639
$160$	−1.87939	−0.148578
$161$	39.0370	3.07654
$162$	11.1837	0.878673
$163$	2.39144	0.187312	0.0936559	−	0.995605i	$-0.470145\pi$
$163$	2.39144	0.187312	0.0936559	+	0.995605i	$0.470145\pi$
$164$	5.69443	0.444660
$165$	13.6987	1.06644
$166$	−0.658250	−0.0510901
$167$	15.5840	1.20592	0.602962	−	0.797770i	$-0.293987\pi$
$167$	15.5840	1.20592	0.602962	+	0.797770i	$0.293987\pi$
$168$	8.94120	0.689829
$169$	−9.24150	−0.710884
$170$	8.35680	0.640937
$171$	0.174457	0.0133410
$172$	1.11986	0.0853884
$173$	−17.8772	−1.35918	−0.679589	−	0.733593i	$-0.737842\pi$
$173$	−17.8772	−1.35918	−0.679589	+	0.733593i	$0.737842\pi$
$174$	1.68948	0.128079
$175$	6.01735	0.454869
$176$	3.34175	0.251894
$177$	−17.6659	−1.32785
$178$	3.52523	0.264227
$179$	20.4063	1.52524	0.762619	−	0.646848i	$-0.223913\pi$
$179$	20.4063	1.52524	0.762619	+	0.646848i	$0.223913\pi$
$180$	3.30304	0.246194
$181$	−18.2764	−1.35848	−0.679238	−	0.733918i	$-0.737690\pi$
$181$	−18.2764	−1.35848	−0.679238	+	0.733918i	$0.737690\pi$
$182$	−7.94718	−0.589084
$183$	23.3405	1.72538
$184$	9.52292	0.702039
$185$	0	0
$186$	22.6655	1.66192
$187$	−14.8593	−1.08662
$188$	−7.11448	−0.518877
$189$	11.1093	0.808084
$190$	−0.186554	−0.0135340
$191$	−5.76567	−0.417189	−0.208595	−	0.978002i	$-0.566889\pi$
$191$	−5.76567	−0.417189	−0.208595	+	0.978002i	$0.566889\pi$
$192$	2.18117	0.157413
$193$	0.359424	0.0258719	0.0129360	−	0.999916i	$-0.495882\pi$
$193$	0.359424	0.0258719	0.0129360	+	0.999916i	$0.495882\pi$
$194$	3.62024	0.259918
$195$	−7.94718	−0.569110
$196$	9.80396	0.700283
$197$	6.96601	0.496307	0.248154	−	0.968721i	$-0.420176\pi$
$197$	6.96601	0.496307	0.248154	+	0.968721i	$0.420176\pi$
$198$	−5.87317	−0.417388
$199$	−11.1779	−0.792383	−0.396191	−	0.918168i	$-0.629668\pi$
$199$	−11.1779	−0.792383	−0.396191	+	0.918168i	$0.629668\pi$
$200$	1.46791	0.103797
$201$	28.7180	2.02561
$202$	−3.94811	−0.277788
$203$	3.17519	0.222855
$204$	−9.69871	−0.679046
$205$	10.7020	0.747462
$206$	−1.97880	−0.137870
$207$	−16.7367	−1.16328
$208$	−1.93869	−0.134424
$209$	0.331713	0.0229451
$210$	16.8040	1.15958
$211$	−12.2103	−0.840589	−0.420295	−	0.907388i	$-0.638073\pi$
$211$	−12.2103	−0.840589	−0.420295	+	0.907388i	$0.638073\pi$
$212$	0.818828	0.0562373
$213$	−6.48497	−0.444343
$214$	−8.24882	−0.563877
$215$	2.10464	0.143536
$216$	2.71008	0.184397
$217$	42.5972	2.89169
$218$	−8.78453	−0.594964
$219$	−5.57812	−0.376935
$220$	6.28044	0.423427
$221$	8.62048	0.579876
$222$	0	0
$223$	−10.7545	−0.720177	−0.360088	−	0.932918i	$-0.617253\pi$
$223$	−10.7545	−0.720177	−0.360088	+	0.932918i	$0.617253\pi$
$224$	4.09926	0.273894
$225$	−2.57987	−0.171992
$226$	9.97690	0.663653
$227$	2.96526	0.196811	0.0984057	−	0.995146i	$-0.468626\pi$
$227$	2.96526	0.196811	0.0984057	+	0.995146i	$0.468626\pi$
$228$	0.216510	0.0143388
$229$	−3.03262	−0.200401	−0.100201	−	0.994967i	$-0.531949\pi$
$229$	−3.03262	−0.200401	−0.100201	+	0.994967i	$0.531949\pi$
$230$	17.8972	1.18011
$231$	−29.8793	−1.96591
$232$	0.774576	0.0508534
$233$	−0.288806	−0.0189203	−0.00946016	−	0.999955i	$-0.503011\pi$
$233$	−0.288806	−0.0189203	−0.00946016	+	0.999955i	$0.503011\pi$
$234$	3.40727	0.222740
$235$	−13.3708	−0.872218
$236$	−8.09926	−0.527217
$237$	11.8561	0.770133
$238$	−18.2276	−1.18152
$239$	5.03510	0.325693	0.162847	−	0.986651i	$-0.447932\pi$
$239$	5.03510	0.325693	0.162847	+	0.986651i	$0.447932\pi$
$240$	4.09926	0.264606
$241$	17.3760	1.11928	0.559642	−	0.828734i	$-0.310939\pi$
$241$	17.3760	1.11928	0.559642	+	0.828734i	$0.310939\pi$
$242$	−0.167293	−0.0107540
$243$	−16.2633	−1.04329
$244$	10.7009	0.685056
$245$	18.4254	1.17716
$246$	−12.4205	−0.791904
$247$	−0.192440	−0.0122447
$248$	10.3914	0.659857
$249$	1.43576	0.0909874
$250$	12.1557	0.768794
$251$	1.75569	0.110818	0.0554090	−	0.998464i	$-0.482354\pi$
$251$	1.75569	0.110818	0.0554090	+	0.998464i	$0.482354\pi$
$252$	−7.20451	−0.453841
$253$	−31.8232	−2.00071
$254$	16.7774	1.05271
$255$	−18.2276	−1.14146
$256$	1.00000	0.0625000
$257$	12.7541	0.795577	0.397789	−	0.917477i	$-0.369778\pi$
$257$	12.7541	0.795577	0.397789	+	0.917477i	$0.369778\pi$
$258$	−2.44260	−0.152070
$259$	0	0
$260$	−3.64354	−0.225963
$261$	−1.36133	−0.0842640
$262$	1.40367	0.0867188
$263$	−26.3651	−1.62574	−0.812871	−	0.582444i	$-0.802096\pi$
$263$	−26.3651	−1.62574	−0.812871	+	0.582444i	$0.802096\pi$
$264$	−7.28893	−0.448603
$265$	1.53889	0.0945334
$266$	0.406906	0.0249490
$267$	−7.68913	−0.470567
$268$	13.1663	0.804260
$269$	13.6058	0.829559	0.414779	−	0.909922i	$-0.363859\pi$
$269$	13.6058	0.829559	0.414779	+	0.909922i	$0.363859\pi$
$270$	5.09328	0.309967
$271$	−4.31590	−0.262172	−0.131086	−	0.991371i	$-0.541846\pi$
$271$	−4.31590	−0.262172	−0.131086	+	0.991371i	$0.541846\pi$
$272$	−4.44656	−0.269612
$273$	17.3342	1.04911
$274$	−12.4193	−0.750275
$275$	−4.90539	−0.295806
$276$	−20.7711	−1.25028
$277$	3.49344	0.209900	0.104950	−	0.994477i	$-0.466532\pi$
$277$	3.49344	0.209900	0.104950	+	0.994477i	$0.466532\pi$
$278$	−18.3996	−1.10353
$279$	−18.2631	−1.09338
$280$	7.70409	0.460408
$281$	7.33775	0.437734	0.218867	−	0.975755i	$-0.429764\pi$
$281$	7.33775	0.437734	0.218867	+	0.975755i	$0.429764\pi$
$282$	15.5179	0.924078
$283$	−14.0029	−0.832384	−0.416192	−	0.909277i	$-0.636636\pi$
$283$	−14.0029	−0.832384	−0.416192	+	0.909277i	$0.636636\pi$
$284$	−2.97316	−0.176425
$285$	0.406906	0.0241031
$286$	6.47860	0.383088
$287$	−23.3430	−1.37789
$288$	−1.75751	−0.103562
$289$	2.77189	0.163053
$290$	1.45573	0.0854832
$291$	−7.89638	−0.462894
$292$	−2.55740	−0.149660
$293$	−25.2747	−1.47657	−0.738283	−	0.674491i	$-0.764363\pi$
$293$	−25.2747	−1.47657	−0.738283	+	0.674491i	$0.764363\pi$
$294$	−21.3841	−1.24715
$295$	−15.2216	−0.886238
$296$	0	0
$297$	−9.05640	−0.525506
$298$	−12.4068	−0.718705
$299$	18.4620	1.06768
$300$	−3.20177	−0.184854
$301$	−4.59059	−0.264597
$302$	12.5489	0.722108
$303$	8.61152	0.494719
$304$	0.0992633	0.00569314
$305$	20.1111	1.15156
$306$	7.81489	0.446747
$307$	−24.5991	−1.40394	−0.701972	−	0.712205i	$-0.747697\pi$
$307$	−24.5991	−1.40394	−0.701972	+	0.712205i	$0.747697\pi$
$308$	−13.6987	−0.780557
$309$	4.31611	0.245535
$310$	19.5295	1.10920
$311$	−5.20715	−0.295270	−0.147635	−	0.989042i	$-0.547166\pi$
$311$	−5.20715	−0.295270	−0.147635	+	0.989042i	$0.547166\pi$
$312$	4.22861	0.239398
$313$	−7.23640	−0.409025	−0.204513	−	0.978864i	$-0.565561\pi$
$313$	−7.23640	−0.409025	−0.204513	+	0.978864i	$0.565561\pi$
$314$	−3.51326	−0.198264
$315$	−13.5400	−0.762895
$316$	5.43563	0.305778
$317$	−13.3490	−0.749755	−0.374878	−	0.927074i	$-0.622315\pi$
$317$	−13.3490	−0.749755	−0.374878	+	0.927074i	$0.622315\pi$
$318$	−1.78600	−0.100154
$319$	−2.58844	−0.144925
$320$	1.87939	0.105061
$321$	17.9921	1.00422
$322$	−39.0370	−2.17545
$323$	−0.441380	−0.0245591
$324$	−11.1837	−0.621316
$325$	2.84582	0.157858
$326$	−2.39144	−0.132449
$327$	19.1606	1.05958
$328$	−5.69443	−0.314422
$329$	29.1641	1.60787
$330$	−13.6987	−0.754089
$331$	4.57313	0.251362	0.125681	−	0.992071i	$-0.459888\pi$
$331$	4.57313	0.251362	0.125681	+	0.992071i	$0.459888\pi$
$332$	0.658250	0.0361262
$333$	0	0
$334$	−15.5840	−0.852717
$335$	24.7446	1.35194
$336$	−8.94120	−0.487782
$337$	3.25330	0.177219	0.0886094	−	0.996066i	$-0.471758\pi$
$337$	3.25330	0.177219	0.0886094	+	0.996066i	$0.471758\pi$
$338$	9.24150	0.502671
$339$	−21.7613	−1.18191
$340$	−8.35680	−0.453211
$341$	−34.7256	−1.88050
$342$	−0.174457	−0.00943353
$343$	−11.4942	−0.620627
$344$	−1.11986	−0.0603787
$345$	−39.0370	−2.10168
$346$	17.8772	0.961084
$347$	−24.4774	−1.31402	−0.657008	−	0.753884i	$-0.728178\pi$
$347$	−24.4774	−1.31402	−0.657008	+	0.753884i	$0.728178\pi$
$348$	−1.68948	−0.0905658
$349$	5.70239	0.305242	0.152621	−	0.988285i	$-0.451229\pi$
$349$	5.70239	0.305242	0.152621	+	0.988285i	$0.451229\pi$
$350$	−6.01735	−0.321641
$351$	5.25399	0.280437
$352$	−3.34175	−0.178116
$353$	−24.4340	−1.30049	−0.650245	−	0.759725i	$-0.725334\pi$
$353$	−24.4340	−1.30049	−0.650245	+	0.759725i	$0.725334\pi$
$354$	17.6659	0.938931
$355$	−5.58771	−0.296565
$356$	−3.52523	−0.186837
$357$	39.7576	2.10419
$358$	−20.4063	−1.07851
$359$	18.7092	0.987435	0.493717	−	0.869622i	$-0.335638\pi$
$359$	18.7092	0.987435	0.493717	+	0.869622i	$0.335638\pi$
$360$	−3.30304	−0.174086
$361$	−18.9901	−0.999481
$362$	18.2764	0.960588
$363$	0.364896	0.0191521
$364$	7.94718	0.416546
$365$	−4.80633	−0.251575
$366$	−23.3405	−1.22003
$367$	33.7230	1.76032	0.880162	−	0.474673i	$-0.157434\pi$
$367$	33.7230	1.76032	0.880162	+	0.474673i	$0.157434\pi$
$368$	−9.52292	−0.496417
$369$	10.0080	0.520997
$370$	0	0
$371$	−3.35659	−0.174265
$372$	−22.6655	−1.17515
$373$	31.4347	1.62763	0.813813	−	0.581127i	$-0.197388\pi$
$373$	31.4347	1.62763	0.813813	+	0.581127i	$0.197388\pi$
$374$	14.8593	0.768356
$375$	−26.5137	−1.36916
$376$	7.11448	0.366901
$377$	1.50166	0.0773394
$378$	−11.1093	−0.571402
$379$	6.96691	0.357866	0.178933	−	0.983861i	$-0.442735\pi$
$379$	6.96691	0.357866	0.178933	+	0.983861i	$0.442735\pi$
$380$	0.186554	0.00957002
$381$	−36.5944	−1.87479
$382$	5.76567	0.294997
$383$	2.87727	0.147022	0.0735109	−	0.997294i	$-0.476580\pi$
$383$	2.87727	0.147022	0.0735109	+	0.997294i	$0.476580\pi$
$384$	−2.18117	−0.111307
$385$	−25.7452	−1.31209
$386$	−0.359424	−0.0182942
$387$	1.96817	0.100047
$388$	−3.62024	−0.183790
$389$	11.8116	0.598873	0.299436	−	0.954116i	$-0.403201\pi$
$389$	11.8116	0.598873	0.299436	+	0.954116i	$0.403201\pi$
$390$	7.94718	0.402421
$391$	42.3442	2.14144
$392$	−9.80396	−0.495175
$393$	−3.06164	−0.154439
$394$	−6.96601	−0.350942
$395$	10.2156	0.514005
$396$	5.87317	0.295138
$397$	−31.3125	−1.57153	−0.785765	−	0.618525i	$-0.787730\pi$
$397$	−31.3125	−1.57153	−0.785765	+	0.618525i	$0.787730\pi$
$398$	11.1779	0.560299
$399$	−0.887533	−0.0444322
$400$	−1.46791	−0.0733956
$401$	14.0281	0.700531	0.350266	−	0.936650i	$-0.386091\pi$
$401$	14.0281	0.700531	0.350266	+	0.936650i	$0.386091\pi$
$402$	−28.7180	−1.43232
$403$	20.1457	1.00353
$404$	3.94811	0.196426
$405$	−21.0185	−1.04442
$406$	−3.17519	−0.157582
$407$	0	0
$408$	9.69871	0.480158
$409$	0.0810699	0.00400865	0.00200432	−	0.999998i	$-0.499362\pi$
$409$	0.0810699	0.00400865	0.00200432	+	0.999998i	$0.499362\pi$
$410$	−10.7020	−0.528535
$411$	27.0886	1.33618
$412$	1.97880	0.0974887
$413$	33.2010	1.63372
$414$	16.7367	0.822562
$415$	1.23711	0.0607271
$416$	1.93869	0.0950519
$417$	40.1326	1.96530
$418$	−0.331713	−0.0162246
$419$	4.63611	0.226489	0.113244	−	0.993567i	$-0.463876\pi$
$419$	4.63611	0.226489	0.113244	+	0.993567i	$0.463876\pi$
$420$	−16.8040	−0.819949
$421$	19.3222	0.941706	0.470853	−	0.882212i	$-0.343946\pi$
$421$	19.3222	0.941706	0.470853	+	0.882212i	$0.343946\pi$
$422$	12.2103	0.594386
$423$	−12.5038	−0.607955
$424$	−0.818828	−0.0397658
$425$	6.52715	0.316613
$426$	6.48497	0.314198
$427$	−43.8659	−2.12282
$428$	8.24882	0.398722
$429$	−14.1310	−0.682249
$430$	−2.10464	−0.101495
$431$	−7.54172	−0.363272	−0.181636	−	0.983366i	$-0.558139\pi$
$431$	−7.54172	−0.363272	−0.181636	+	0.983366i	$0.558139\pi$
$432$	−2.71008	−0.130389
$433$	29.8339	1.43373	0.716863	−	0.697214i	$-0.245577\pi$
$433$	29.8339	1.43373	0.716863	+	0.697214i	$0.245577\pi$
$434$	−42.5972	−2.04473
$435$	−3.17519	−0.152239
$436$	8.78453	0.420703
$437$	−0.945277	−0.0452187
$438$	5.57812	0.266533
$439$	−21.9541	−1.04781	−0.523906	−	0.851776i	$-0.675526\pi$
$439$	−21.9541	−1.04781	−0.523906	+	0.851776i	$0.675526\pi$
$440$	−6.28044	−0.299408
$441$	17.2306	0.820504
$442$	−8.62048	−0.410034
$443$	−34.6241	−1.64504	−0.822520	−	0.568736i	$-0.807433\pi$
$443$	−34.6241	−1.64504	−0.822520	+	0.568736i	$0.807433\pi$
$444$	0	0
$445$	−6.62526	−0.314068
$446$	10.7545	0.509242
$447$	27.0613	1.27996
$448$	−4.09926	−0.193672
$449$	19.9414	0.941093	0.470547	−	0.882375i	$-0.344057\pi$
$449$	19.9414	0.941093	0.470547	+	0.882375i	$0.344057\pi$
$450$	2.57987	0.121616
$451$	19.0294	0.896057
$452$	−9.97690	−0.469274
$453$	−27.3713	−1.28602
$454$	−2.96526	−0.139167
$455$	14.9358	0.700202
$456$	−0.216510	−0.0101390
$457$	−32.2388	−1.50807	−0.754034	−	0.656835i	$-0.771895\pi$
$457$	−32.2388	−1.50807	−0.754034	+	0.656835i	$0.771895\pi$
$458$	3.03262	0.141705
$459$	12.0505	0.562470
$460$	−17.8972	−0.834463
$461$	−7.32821	−0.341309	−0.170654	−	0.985331i	$-0.554588\pi$
$461$	−7.32821	−0.341309	−0.170654	+	0.985331i	$0.554588\pi$
$462$	29.8793	1.39011
$463$	−6.48631	−0.301444	−0.150722	−	0.988576i	$-0.548160\pi$
$463$	−6.48631	−0.301444	−0.150722	+	0.988576i	$0.548160\pi$
$464$	−0.774576	−0.0359588
$465$	−42.5972	−1.97540
$466$	0.288806	0.0133787
$467$	11.9858	0.554635	0.277317	−	0.960778i	$-0.410555\pi$
$467$	11.9858	0.554635	0.277317	+	0.960778i	$0.410555\pi$
$468$	−3.40727	−0.157501
$469$	−53.9721	−2.49220
$470$	13.3708	0.616751
$471$	7.66302	0.353093
$472$	8.09926	0.372799
$473$	3.74229	0.172070
$474$	−11.8561	−0.544566
$475$	−0.145710	−0.00668562
$476$	18.2276	0.835462
$477$	1.43910	0.0658919
$478$	−5.03510	−0.230300
$479$	−22.6922	−1.03683	−0.518417	−	0.855128i	$-0.673478\pi$
$479$	−22.6922	−1.03683	−0.518417	+	0.855128i	$0.673478\pi$
$480$	−4.09926	−0.187105
$481$	0	0
$482$	−17.3760	−0.791454
$483$	85.1464	3.87429
$484$	0.167293	0.00760425
$485$	−6.80383	−0.308946
$486$	16.2633	0.737719
$487$	−12.3108	−0.557856	−0.278928	−	0.960312i	$-0.589979\pi$
$487$	−12.3108	−0.557856	−0.278928	+	0.960312i	$0.589979\pi$
$488$	−10.7009	−0.484408
$489$	5.21614	0.235882
$490$	−18.4254	−0.832375
$491$	1.15080	0.0519347	0.0259674	−	0.999663i	$-0.491733\pi$
$491$	1.15080	0.0519347	0.0259674	+	0.999663i	$0.491733\pi$
$492$	12.4205	0.559961
$493$	3.44420	0.155119
$494$	0.192440	0.00865830
$495$	11.0379	0.496119
$496$	−10.3914	−0.466589
$497$	12.1878	0.546696
$498$	−1.43576	−0.0643378
$499$	−27.9156	−1.24967	−0.624837	−	0.780755i	$-0.714834\pi$
$499$	−27.9156	−1.24967	−0.624837	+	0.780755i	$0.714834\pi$
$500$	−12.1557	−0.543619
$501$	33.9913	1.51862
$502$	−1.75569	−0.0783602
$503$	16.3677	0.729800	0.364900	−	0.931047i	$-0.381103\pi$
$503$	16.3677	0.729800	0.364900	+	0.931047i	$0.381103\pi$
$504$	7.20451	0.320914
$505$	7.42003	0.330187
$506$	31.8232	1.41471
$507$	−20.1573	−0.895217
$508$	−16.7774	−0.744376
$509$	4.33404	0.192103	0.0960514	−	0.995376i	$-0.469379\pi$
$509$	4.33404	0.192103	0.0960514	+	0.995376i	$0.469379\pi$
$510$	18.2276	0.807133
$511$	10.4834	0.463760
$512$	−1.00000	−0.0441942
$513$	−0.269011	−0.0118771
$514$	−12.7541	−0.562558
$515$	3.71893	0.163876
$516$	2.44260	0.107530
$517$	−23.7748	−1.04561
$518$	0	0
$519$	−38.9932	−1.71161
$520$	3.64354	0.159780
$521$	1.87292	0.0820542	0.0410271	−	0.999158i	$-0.486937\pi$
$521$	1.87292	0.0820542	0.0410271	+	0.999158i	$0.486937\pi$
$522$	1.36133	0.0595837
$523$	−37.0562	−1.62035	−0.810177	−	0.586186i	$-0.800629\pi$
$523$	−37.0562	−1.62035	−0.810177	+	0.586186i	$0.800629\pi$
$524$	−1.40367	−0.0613194
$525$	13.1249	0.572817
$526$	26.3651	1.14957
$527$	46.2061	2.01277
$528$	7.28893	0.317210
$529$	67.6861	2.94287
$530$	−1.53889	−0.0668452
$531$	−14.2346	−0.617727
$532$	−0.406906	−0.0176416
$533$	−11.0397	−0.478183
$534$	7.68913	0.332741
$535$	15.5027	0.670240
$536$	−13.1663	−0.568698
$537$	44.5096	1.92073
$538$	−13.6058	−0.586587
$539$	32.7624	1.41118
$540$	−5.09328	−0.219180
$541$	−15.5062	−0.666665	−0.333332	−	0.942809i	$-0.608173\pi$
$541$	−15.5062	−0.666665	−0.333332	+	0.942809i	$0.608173\pi$
$542$	4.31590	0.185384
$543$	−39.8641	−1.71073
$544$	4.44656	0.190645
$545$	16.5095	0.707190
$546$	−17.3342	−0.741834
$547$	41.1850	1.76094	0.880472	−	0.474099i	$-0.157226\pi$
$547$	41.1850	1.76094	0.880472	+	0.474099i	$0.157226\pi$
$548$	12.4193	0.530525
$549$	18.8070	0.802663
$550$	4.90539	0.209167
$551$	−0.0768869	−0.00327549
$552$	20.7711	0.884078
$553$	−22.2821	−0.947531
$554$	−3.49344	−0.148422
$555$	0	0
$556$	18.3996	0.780315
$557$	12.2046	0.517126	0.258563	−	0.965994i	$-0.416751\pi$
$557$	12.2046	0.517126	0.258563	+	0.965994i	$0.416751\pi$
$558$	18.2631	0.773138
$559$	−2.17105	−0.0918258
$560$	−7.70409	−0.325557
$561$	−32.4107	−1.36838
$562$	−7.33775	−0.309524
$563$	11.4193	0.481266	0.240633	−	0.970616i	$-0.422645\pi$
$563$	11.4193	0.481266	0.240633	+	0.970616i	$0.422645\pi$
$564$	−15.5179	−0.653421
$565$	−18.7504	−0.788837
$566$	14.0029	0.588585
$567$	45.8449	1.92530
$568$	2.97316	0.124751
$569$	22.3465	0.936812	0.468406	−	0.883513i	$-0.344828\pi$
$569$	22.3465	0.936812	0.468406	+	0.883513i	$0.344828\pi$
$570$	−0.406906	−0.0170434
$571$	−13.2022	−0.552494	−0.276247	−	0.961087i	$-0.589091\pi$
$571$	−13.2022	−0.552494	−0.276247	+	0.961087i	$0.589091\pi$
$572$	−6.47860	−0.270884
$573$	−12.5759	−0.525367
$574$	23.3430	0.974316
$575$	13.9788	0.582956
$576$	1.75751	0.0732297
$577$	−29.3529	−1.22198	−0.610989	−	0.791639i	$-0.709228\pi$
$577$	−29.3529	−1.22198	−0.610989	+	0.791639i	$0.709228\pi$
$578$	−2.77189	−0.115296
$579$	0.783966	0.0325805
$580$	−1.45573	−0.0604457
$581$	−2.69834	−0.111946
$582$	7.89638	0.327315
$583$	2.73632	0.113327
$584$	2.55740	0.105826
$585$	−6.40356	−0.264755
$586$	25.2747	1.04409
$587$	21.2405	0.876690	0.438345	−	0.898807i	$-0.355565\pi$
$587$	21.2405	0.876690	0.438345	+	0.898807i	$0.355565\pi$
$588$	21.3841	0.881867
$589$	−1.03149	−0.0425017
$590$	15.2216	0.626665
$591$	15.1941	0.625000
$592$	0	0
$593$	31.4119	1.28993	0.644965	−	0.764212i	$-0.276872\pi$
$593$	31.4119	1.28993	0.644965	+	0.764212i	$0.276872\pi$
$594$	9.05640	0.371589
$595$	34.2567	1.40439
$596$	12.4068	0.508201
$597$	−24.3810	−0.997848
$598$	−18.4620	−0.754965
$599$	−20.3033	−0.829570	−0.414785	−	0.909919i	$-0.636143\pi$
$599$	−20.3033	−0.829570	−0.414785	+	0.909919i	$0.636143\pi$
$600$	3.20177	0.130712
$601$	−44.5828	−1.81857	−0.909286	−	0.416171i	$-0.863372\pi$
$601$	−44.5828	−1.81857	−0.909286	+	0.416171i	$0.863372\pi$
$602$	4.59059	0.187099
$603$	23.1400	0.942332
$604$	−12.5489	−0.510607
$605$	0.314409	0.0127825
$606$	−8.61152	−0.349819
$607$	20.1087	0.816188	0.408094	−	0.912940i	$-0.366194\pi$
$607$	20.1087	0.816188	0.408094	+	0.912940i	$0.366194\pi$
$608$	−0.0992633	−0.00402566
$609$	6.92564	0.280641
$610$	−20.1111	−0.814276
$611$	13.7927	0.557994
$612$	−7.81489	−0.315898
$613$	32.2195	1.30133	0.650667	−	0.759363i	$-0.274489\pi$
$613$	32.2195	1.30133	0.650667	+	0.759363i	$0.274489\pi$
$614$	24.5991	0.992738
$615$	23.3430	0.941279
$616$	13.6987	0.551937
$617$	38.9312	1.56731	0.783656	−	0.621195i	$-0.213353\pi$
$617$	38.9312	1.56731	0.783656	+	0.621195i	$0.213353\pi$
$618$	−4.31611	−0.173619
$619$	−26.3624	−1.05959	−0.529796	−	0.848125i	$-0.677732\pi$
$619$	−26.3624	−1.05959	−0.529796	+	0.848125i	$0.677732\pi$
$620$	−19.5295	−0.784324
$621$	25.8079	1.03563
$622$	5.20715	0.208788
$623$	14.4508	0.578961
$624$	−4.22861	−0.169280
$625$	−15.5057	−0.620227
$626$	7.23640	0.289225
$627$	0.723524	0.0288947
$628$	3.51326	0.140194
$629$	0	0
$630$	13.5400	0.539448
$631$	−41.3133	−1.64466	−0.822328	−	0.569013i	$-0.807325\pi$
$631$	−41.3133	−1.64466	−0.822328	+	0.569013i	$0.807325\pi$
$632$	−5.43563	−0.216218
$633$	−26.6327	−1.05855
$634$	13.3490	0.530157
$635$	−31.5312	−1.25128
$636$	1.78600	0.0708197
$637$	−19.0068	−0.753077
$638$	2.58844	0.102477
$639$	−5.22537	−0.206712
$640$	−1.87939	−0.0742892
$641$	−43.7391	−1.72759	−0.863795	−	0.503844i	$-0.831919\pi$
$641$	−43.7391	−1.72759	−0.863795	+	0.503844i	$0.831919\pi$
$642$	−17.9921	−0.710091
$643$	3.31553	0.130752	0.0653759	−	0.997861i	$-0.479175\pi$
$643$	3.31553	0.130752	0.0653759	+	0.997861i	$0.479175\pi$
$644$	39.0370	1.53827
$645$	4.59059	0.180754
$646$	0.441380	0.0173659
$647$	22.8404	0.897950	0.448975	−	0.893544i	$-0.351789\pi$
$647$	22.8404	0.897950	0.448975	+	0.893544i	$0.351789\pi$
$648$	11.1837	0.439337
$649$	−27.0657	−1.06242
$650$	−2.84582	−0.111622
$651$	92.9119	3.64151
$652$	2.39144	0.0936559
$653$	−2.12737	−0.0832505	−0.0416252	−	0.999133i	$-0.513254\pi$
$653$	−2.12737	−0.0832505	−0.0416252	+	0.999133i	$0.513254\pi$
$654$	−19.1606	−0.749238
$655$	−2.63803	−0.103076
$656$	5.69443	0.222330
$657$	−4.49466	−0.175353
$658$	−29.1641	−1.13694
$659$	−8.56624	−0.333693	−0.166847	−	0.985983i	$-0.553358\pi$
$659$	−8.56624	−0.333693	−0.166847	+	0.985983i	$0.553358\pi$
$660$	13.6987	0.533222
$661$	−0.801614	−0.0311792	−0.0155896	−	0.999878i	$-0.504963\pi$
$661$	−0.801614	−0.0311792	−0.0155896	+	0.999878i	$0.504963\pi$
$662$	−4.57313	−0.177740
$663$	18.8028	0.730239
$664$	−0.658250	−0.0255451
$665$	−0.764734	−0.0296551
$666$	0	0
$667$	7.37622	0.285609
$668$	15.5840	0.602962
$669$	−23.4575	−0.906919
$670$	−24.7446	−0.955966
$671$	35.7598	1.38049
$672$	8.94120	0.344914
$673$	43.0383	1.65901	0.829503	−	0.558502i	$-0.188624\pi$
$673$	43.0383	1.65901	0.829503	+	0.558502i	$0.188624\pi$
$674$	−3.25330	−0.125313
$675$	3.97815	0.153119
$676$	−9.24150	−0.355442
$677$	19.9943	0.768444	0.384222	−	0.923241i	$-0.374470\pi$
$677$	19.9943	0.768444	0.384222	+	0.923241i	$0.374470\pi$
$678$	21.7613	0.835739
$679$	14.8403	0.569520
$680$	8.35680	0.320469
$681$	6.46775	0.247845
$682$	34.7256	1.32971
$683$	−36.8290	−1.40922	−0.704611	−	0.709594i	$-0.748878\pi$
$683$	−36.8290	−1.40922	−0.704611	+	0.709594i	$0.748878\pi$
$684$	0.174457	0.00667051
$685$	23.3406	0.891798
$686$	11.4942	0.438849
$687$	−6.61468	−0.252366
$688$	1.11986	0.0426942
$689$	−1.58745	−0.0604770
$690$	39.0370	1.48611
$691$	0.878837	0.0334325	0.0167163	−	0.999860i	$-0.494679\pi$
$691$	0.878837	0.0334325	0.0167163	+	0.999860i	$0.494679\pi$
$692$	−17.8772	−0.679589
$693$	−24.0757	−0.914559
$694$	24.4774	0.929149
$695$	34.5799	1.31169
$696$	1.68948	0.0640397
$697$	−25.3206	−0.959087
$698$	−5.70239	−0.215839
$699$	−0.629936	−0.0238264
$700$	6.01735	0.227435
$701$	20.8420	0.787193	0.393596	−	0.919283i	$-0.371231\pi$
$701$	20.8420	0.787193	0.393596	+	0.919283i	$0.371231\pi$
$702$	−5.25399	−0.198299
$703$	0	0
$704$	3.34175	0.125947
$705$	−29.1641	−1.09838
$706$	24.4340	0.919585
$707$	−16.1844	−0.608676
$708$	−17.6659	−0.663925
$709$	21.6348	0.812512	0.406256	−	0.913759i	$-0.366834\pi$
$709$	21.6348	0.812512	0.406256	+	0.913759i	$0.366834\pi$
$710$	5.58771	0.209703
$711$	9.55319	0.358273
$712$	3.52523	0.132114
$713$	98.9569	3.70596
$714$	−39.7576	−1.48789
$715$	−12.1758	−0.455349
$716$	20.4063	0.762619
$717$	10.9824	0.410146
$718$	−18.7092	−0.698222
$719$	25.6877	0.957991	0.478996	−	0.877817i	$-0.341001\pi$
$719$	25.6877	0.957991	0.478996	+	0.877817i	$0.341001\pi$
$720$	3.30304	0.123097
$721$	−8.11164	−0.302093
$722$	18.9901	0.706740
$723$	37.9000	1.40952
$724$	−18.2764	−0.679238
$725$	1.13701	0.0422274
$726$	−0.364896	−0.0135426
$727$	−26.6751	−0.989326	−0.494663	−	0.869085i	$-0.664709\pi$
$727$	−26.6751	−0.989326	−0.494663	+	0.869085i	$0.664709\pi$
$728$	−7.94718	−0.294542
$729$	−1.92204	−0.0711865
$730$	4.80633	0.177890
$731$	−4.97952	−0.184174
$732$	23.3405	0.862691
$733$	−11.3802	−0.420336	−0.210168	−	0.977665i	$-0.567401\pi$
$733$	−11.3802	−0.420336	−0.210168	+	0.977665i	$0.567401\pi$
$734$	−33.7230	−1.24474
$735$	40.1890	1.48239
$736$	9.52292	0.351020
$737$	43.9985	1.62071
$738$	−10.0080	−0.368401
$739$	3.18059	0.117000	0.0584999	−	0.998287i	$-0.481368\pi$
$739$	3.18059	0.117000	0.0584999	+	0.998287i	$0.481368\pi$
$740$	0	0
$741$	−0.419746	−0.0154197
$742$	3.35659	0.123224
$743$	−52.9609	−1.94295	−0.971473	−	0.237151i	$-0.923786\pi$
$743$	−52.9609	−1.94295	−0.971473	+	0.237151i	$0.923786\pi$
$744$	22.6655	0.830958
$745$	23.3171	0.854273
$746$	−31.4347	−1.15091
$747$	1.15688	0.0423281
$748$	−14.8593	−0.543309
$749$	−33.8141	−1.23554
$750$	26.5137	0.968142
$751$	−6.42966	−0.234621	−0.117311	−	0.993095i	$-0.537427\pi$
$751$	−6.42966	−0.234621	−0.117311	+	0.993095i	$0.537427\pi$
$752$	−7.11448	−0.259438
$753$	3.82946	0.139553
$754$	−1.50166	−0.0546872
$755$	−23.5842	−0.858317
$756$	11.1093	0.404042
$757$	31.7443	1.15377	0.576883	−	0.816827i	$-0.304269\pi$
$757$	31.7443	1.15377	0.576883	+	0.816827i	$0.304269\pi$
$758$	−6.96691	−0.253050
$759$	−69.4119	−2.51949
$760$	−0.186554	−0.00676702
$761$	−23.0835	−0.836778	−0.418389	−	0.908268i	$-0.637405\pi$
$761$	−23.0835	−0.836778	−0.418389	+	0.908268i	$0.637405\pi$
$762$	36.5944	1.32567
$763$	−36.0101	−1.30365
$764$	−5.76567	−0.208595
$765$	−14.6872	−0.531016
$766$	−2.87727	−0.103960
$767$	15.7019	0.566964
$768$	2.18117	0.0787063
$769$	−47.1598	−1.70062	−0.850312	−	0.526278i	$-0.823587\pi$
$769$	−47.1598	−1.70062	−0.850312	+	0.526278i	$0.823587\pi$
$770$	25.7452	0.927791
$771$	27.8188	1.00187
$772$	0.359424	0.0129360
$773$	−4.00160	−0.143927	−0.0719637	−	0.997407i	$-0.522927\pi$
$773$	−4.00160	−0.143927	−0.0719637	+	0.997407i	$0.522927\pi$
$774$	−1.96817	−0.0707442
$775$	15.2537	0.547929
$776$	3.62024	0.129959
$777$	0	0
$778$	−11.8116	−0.423467
$779$	0.565248	0.0202521
$780$	−7.94718	−0.284555
$781$	−9.93556	−0.355522
$782$	−42.3442	−1.51423
$783$	2.09916	0.0750179
$784$	9.80396	0.350141
$785$	6.60276	0.235663
$786$	3.06164	0.109205
$787$	11.5669	0.412315	0.206157	−	0.978519i	$-0.433904\pi$
$787$	11.5669	0.412315	0.206157	+	0.978519i	$0.433904\pi$
$788$	6.96601	0.248154
$789$	−57.5068	−2.04730
$790$	−10.2156	−0.363456
$791$	40.8979	1.45416
$792$	−5.87317	−0.208694
$793$	−20.7457	−0.736702
$794$	31.3125	1.11124
$795$	3.35659	0.119046
$796$	−11.1779	−0.396191
$797$	36.6547	1.29838	0.649189	−	0.760627i	$-0.275109\pi$
$797$	36.6547	1.29838	0.649189	+	0.760627i	$0.275109\pi$
$798$	0.887533	0.0314183
$799$	31.6349	1.11916
$800$	1.46791	0.0518985
$801$	−6.19564	−0.218912
$802$	−14.0281	−0.495351
$803$	−8.54618	−0.301588
$804$	28.7180	1.01281
$805$	73.3655	2.58579
$806$	−20.1457	−0.709603
$807$	29.6765	1.04466
$808$	−3.94811	−0.138894
$809$	7.79653	0.274112	0.137056	−	0.990563i	$-0.456236\pi$
$809$	7.79653	0.274112	0.137056	+	0.990563i	$0.456236\pi$
$810$	21.0185	0.738513
$811$	−29.7682	−1.04530	−0.522652	−	0.852546i	$-0.675057\pi$
$811$	−29.7682	−1.04530	−0.522652	+	0.852546i	$0.675057\pi$
$812$	3.17519	0.111427
$813$	−9.41372	−0.330154
$814$	0	0
$815$	4.49443	0.157433
$816$	−9.69871	−0.339523
$817$	0.111161	0.00388902
$818$	−0.0810699	−0.00283454
$819$	13.9673	0.488056
$820$	10.7020	0.373731
$821$	39.2154	1.36863	0.684313	−	0.729188i	$-0.260102\pi$
$821$	39.2154	1.36863	0.684313	+	0.729188i	$0.260102\pi$
$822$	−27.0886	−0.944822
$823$	−12.1146	−0.422288	−0.211144	−	0.977455i	$-0.567719\pi$
$823$	−12.1146	−0.422288	−0.211144	+	0.977455i	$0.567719\pi$
$824$	−1.97880	−0.0689349
$825$	−10.6995	−0.372509
$826$	−33.2010	−1.15521
$827$	14.0447	0.488384	0.244192	−	0.969727i	$-0.421477\pi$
$827$	14.0447	0.488384	0.244192	+	0.969727i	$0.421477\pi$
$828$	−16.7367	−0.581639
$829$	−32.0629	−1.11359	−0.556796	−	0.830649i	$-0.687969\pi$
$829$	−32.0629	−1.11359	−0.556796	+	0.830649i	$0.687969\pi$
$830$	−1.23711	−0.0429405
$831$	7.61980	0.264328
$832$	−1.93869	−0.0672118
$833$	−43.5939	−1.51044
$834$	−40.1326	−1.38968
$835$	29.2883	1.01356
$836$	0.331713	0.0114725
$837$	28.1616	0.973407
$838$	−4.63611	−0.160152
$839$	−11.0541	−0.381631	−0.190815	−	0.981626i	$-0.561113\pi$
$839$	−11.0541	−0.381631	−0.190815	+	0.981626i	$0.561113\pi$
$840$	16.8040	0.579792
$841$	−28.4000	−0.979311
$842$	−19.3222	−0.665887
$843$	16.0049	0.551238
$844$	−12.2103	−0.420295
$845$	−17.3683	−0.597489
$846$	12.5038	0.429889
$847$	−0.685780	−0.0235637
$848$	0.818828	0.0281187
$849$	−30.5427	−1.04822
$850$	−6.52715	−0.223880
$851$	0	0
$852$	−6.48497	−0.222172
$853$	−51.1448	−1.75116	−0.875582	−	0.483070i	$-0.839522\pi$
$853$	−51.1448	−1.75116	−0.875582	+	0.483070i	$0.839522\pi$
$854$	43.8659	1.50106
$855$	0.327871	0.0112130
$856$	−8.24882	−0.281939
$857$	11.4315	0.390493	0.195246	−	0.980754i	$-0.437449\pi$
$857$	11.4315	0.390493	0.195246	+	0.980754i	$0.437449\pi$
$858$	14.1310	0.482423
$859$	10.9927	0.375066	0.187533	−	0.982258i	$-0.439951\pi$
$859$	10.9927	0.375066	0.187533	+	0.982258i	$0.439951\pi$
$860$	2.10464	0.0717678
$861$	−50.9150	−1.73518
$862$	7.54172	0.256872
$863$	−15.0332	−0.511737	−0.255869	−	0.966712i	$-0.582361\pi$
$863$	−15.0332	−0.511737	−0.255869	+	0.966712i	$0.582361\pi$
$864$	2.71008	0.0921987
$865$	−33.5981	−1.14237
$866$	−29.8339	−1.01380
$867$	6.04598	0.205332
$868$	42.5972	1.44584
$869$	18.1645	0.616189
$870$	3.17519	0.107649
$871$	−25.5253	−0.864893
$872$	−8.78453	−0.297482
$873$	−6.36263	−0.215342
$874$	0.945277	0.0319745
$875$	49.8294	1.68454
$876$	−5.57812	−0.188467
$877$	−29.4471	−0.994360	−0.497180	−	0.867648i	$-0.665631\pi$
$877$	−29.4471	−0.994360	−0.497180	+	0.867648i	$0.665631\pi$
$878$	21.9541	0.740915
$879$	−55.1286	−1.85944
$880$	6.28044	0.211713
$881$	18.3789	0.619200	0.309600	−	0.950867i	$-0.399805\pi$
$881$	18.3789	0.619200	0.309600	+	0.950867i	$0.399805\pi$
$882$	−17.2306	−0.580184
$883$	−29.1969	−0.982555	−0.491278	−	0.871003i	$-0.663470\pi$
$883$	−29.1969	−0.982555	−0.491278	+	0.871003i	$0.663470\pi$
$884$	8.62048	0.289938
$885$	−33.2010	−1.11604
$886$	34.6241	1.16322
$887$	−36.5446	−1.22705	−0.613524	−	0.789676i	$-0.710249\pi$
$887$	−36.5446	−1.22705	−0.613524	+	0.789676i	$0.710249\pi$
$888$	0	0
$889$	68.7749	2.30664
$890$	6.62526	0.222079
$891$	−37.3731	−1.25205
$892$	−10.7545	−0.360088
$893$	−0.706206	−0.0236323
$894$	−27.0613	−0.905066
$895$	38.3513	1.28194
$896$	4.09926	0.136947
$897$	40.2687	1.34453
$898$	−19.9414	−0.665453
$899$	8.04895	0.268448
$900$	−2.57987	−0.0859958
$901$	−3.64097	−0.121298
$902$	−19.0294	−0.633608
$903$	−10.0129	−0.333208
$904$	9.97690	0.331827
$905$	−34.3485	−1.14178
$906$	27.3713	0.909351
$907$	−18.2228	−0.605080	−0.302540	−	0.953137i	$-0.597835\pi$
$907$	−18.2228	−0.605080	−0.302540	+	0.953137i	$0.597835\pi$
$908$	2.96526	0.0984057
$909$	6.93886	0.230148
$910$	−14.9358	−0.495118
$911$	52.4746	1.73856	0.869280	−	0.494319i	$-0.164583\pi$
$911$	52.4746	1.73856	0.869280	+	0.494319i	$0.164583\pi$
$912$	0.216510	0.00716938
$913$	2.19971	0.0727997
$914$	32.2388	1.06637
$915$	43.8659	1.45016
$916$	−3.03262	−0.100201
$917$	5.75400	0.190014
$918$	−12.0505	−0.397727
$919$	44.3955	1.46447	0.732236	−	0.681051i	$-0.238477\pi$
$919$	44.3955	1.46447	0.732236	+	0.681051i	$0.238477\pi$
$920$	17.8972	0.590055
$921$	−53.6548	−1.76799
$922$	7.32821	0.241342
$923$	5.76402	0.189725
$924$	−29.8793	−0.982955
$925$	0	0
$926$	6.48631	0.213153
$927$	3.47777	0.114225
$928$	0.774576	0.0254267
$929$	29.9244	0.981787	0.490893	−	0.871220i	$-0.336670\pi$
$929$	29.9244	0.981787	0.490893	+	0.871220i	$0.336670\pi$
$930$	42.5972	1.39682
$931$	0.973173	0.0318945
$932$	−0.288806	−0.00946016
$933$	−11.3577	−0.371834
$934$	−11.9858	−0.392186
$935$	−27.9263	−0.913289
$936$	3.40727	0.111370
$937$	9.94451	0.324873	0.162436	−	0.986719i	$-0.448065\pi$
$937$	9.94451	0.324873	0.162436	+	0.986719i	$0.448065\pi$
$938$	53.9721	1.76225
$939$	−15.7838	−0.515086
$940$	−13.3708	−0.436109
$941$	12.3569	0.402824	0.201412	−	0.979507i	$-0.435447\pi$
$941$	12.3569	0.402824	0.201412	+	0.979507i	$0.435447\pi$
$942$	−7.66302	−0.249675
$943$	−54.2276	−1.76589
$944$	−8.09926	−0.263609
$945$	20.8787	0.679184
$946$	−3.74229	−0.121672
$947$	27.9971	0.909784	0.454892	−	0.890547i	$-0.349678\pi$
$947$	27.9971	0.909784	0.454892	+	0.890547i	$0.349678\pi$
$948$	11.8561	0.385067
$949$	4.95799	0.160943
$950$	0.145710	0.00472745
$951$	−29.1165	−0.944167
$952$	−18.2276	−0.590761
$953$	43.8032	1.41893	0.709463	−	0.704743i	$-0.248938\pi$
$953$	43.8032	1.41893	0.709463	+	0.704743i	$0.248938\pi$
$954$	−1.43910	−0.0465926
$955$	−10.8359	−0.350642
$956$	5.03510	0.162847
$957$	−5.64583	−0.182504
$958$	22.6922	0.733152
$959$	−50.9099	−1.64396
$960$	4.09926	0.132303
$961$	76.9820	2.48329
$962$	0	0
$963$	14.4974	0.467172
$964$	17.3760	0.559642
$965$	0.675497	0.0217450
$966$	−85.1464	−2.73954
$967$	55.3082	1.77859	0.889295	−	0.457334i	$-0.151195\pi$
$967$	55.3082	1.77859	0.889295	+	0.457334i	$0.151195\pi$
$968$	−0.167293	−0.00537702
$969$	−0.962726	−0.0309272
$970$	6.80383	0.218458
$971$	−55.1799	−1.77081	−0.885404	−	0.464822i	$-0.846118\pi$
$971$	−55.1799	−1.77081	−0.885404	+	0.464822i	$0.846118\pi$
$972$	−16.2633	−0.521646
$973$	−75.4247	−2.41800
$974$	12.3108	0.394464
$975$	6.20722	0.198790
$976$	10.7009	0.342528
$977$	25.5345	0.816920	0.408460	−	0.912776i	$-0.366066\pi$
$977$	25.5345	0.816920	0.408460	+	0.912776i	$0.366066\pi$
$978$	−5.21614	−0.166794
$979$	−11.7804	−0.376504
$980$	18.4254	0.588578
$981$	15.4389	0.492927
$982$	−1.15080	−0.0367234
$983$	−31.2734	−0.997465	−0.498733	−	0.866756i	$-0.666201\pi$
$983$	−31.2734	−0.997465	−0.498733	+	0.866756i	$0.666201\pi$
$984$	−12.4205	−0.395952
$985$	13.0918	0.417140
$986$	−3.44420	−0.109686
$987$	63.6120	2.02479
$988$	−0.192440	−0.00612234
$989$	−10.6643	−0.339106
$990$	−11.0379	−0.350809
$991$	7.61348	0.241850	0.120925	−	0.992662i	$-0.461414\pi$
$991$	7.61348	0.241850	0.120925	+	0.992662i	$0.461414\pi$
$992$	10.3914	0.329928
$993$	9.97478	0.316540
$994$	−12.1878	−0.386572
$995$	−21.0076	−0.665987
$996$	1.43576	0.0454937
$997$	−15.6027	−0.494143	−0.247071	−	0.968997i	$-0.579468\pi$
$997$	−15.6027	−0.494143	−0.247071	+	0.968997i	$0.579468\pi$
$998$	27.9156	0.883653
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.q.1.5		6
37.4	even	18		74.2.f.b.53.1	yes	12
37.28	even	18		74.2.f.b.7.1	✓	12
37.36	even	2		2738.2.a.t.1.5		6
111.41	odd	18		666.2.x.g.127.1		12
111.65	odd	18		666.2.x.g.451.1		12
148.115	odd	18		592.2.bc.d.497.2		12
148.139	odd	18		592.2.bc.d.81.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.7.1	✓	12	37.28	even	18
74.2.f.b.53.1	yes	12	37.4	even	18
592.2.bc.d.81.2		12	148.139	odd	18
592.2.bc.d.497.2		12	148.115	odd	18
666.2.x.g.127.1		12	111.41	odd	18
666.2.x.g.451.1		12	111.65	odd	18
2738.2.a.q.1.5		6	1.1	even	1	trivial
2738.2.a.t.1.5		6	37.36	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.18117 q^{3} +1.00000 q^{4} +1.87939 q^{5} -2.18117 q^{6} -4.09926 q^{7} -1.00000 q^{8} +1.75751 q^{9} -1.87939 q^{10} +3.34175 q^{11} +2.18117 q^{12} -1.93869 q^{13} +4.09926 q^{14} +4.09926 q^{15} +1.00000 q^{16} -4.44656 q^{17} -1.75751 q^{18} +0.0992633 q^{19} +1.87939 q^{20} -8.94120 q^{21} -3.34175 q^{22} -9.52292 q^{23} -2.18117 q^{24} -1.46791 q^{25} +1.93869 q^{26} -2.71008 q^{27} -4.09926 q^{28} -0.774576 q^{29} -4.09926 q^{30} -10.3914 q^{31} -1.00000 q^{32} +7.28893 q^{33} +4.44656 q^{34} -7.70409 q^{35} +1.75751 q^{36} -0.0992633 q^{38} -4.22861 q^{39} -1.87939 q^{40} +5.69443 q^{41} +8.94120 q^{42} +1.11986 q^{43} +3.34175 q^{44} +3.30304 q^{45} +9.52292 q^{46} -7.11448 q^{47} +2.18117 q^{48} +9.80396 q^{49} +1.46791 q^{50} -9.69871 q^{51} -1.93869 q^{52} +0.818828 q^{53} +2.71008 q^{54} +6.28044 q^{55} +4.09926 q^{56} +0.216510 q^{57} +0.774576 q^{58} -8.09926 q^{59} +4.09926 q^{60} +10.7009 q^{61} +10.3914 q^{62} -7.20451 q^{63} +1.00000 q^{64} -3.64354 q^{65} -7.28893 q^{66} +13.1663 q^{67} -4.44656 q^{68} -20.7711 q^{69} +7.70409 q^{70} -2.97316 q^{71} -1.75751 q^{72} -2.55740 q^{73} -3.20177 q^{75} +0.0992633 q^{76} -13.6987 q^{77} +4.22861 q^{78} +5.43563 q^{79} +1.87939 q^{80} -11.1837 q^{81} -5.69443 q^{82} +0.658250 q^{83} -8.94120 q^{84} -8.35680 q^{85} -1.11986 q^{86} -1.68948 q^{87} -3.34175 q^{88} -3.52523 q^{89} -3.30304 q^{90} +7.94718 q^{91} -9.52292 q^{92} -22.6655 q^{93} +7.11448 q^{94} +0.186554 q^{95} -2.18117 q^{96} -3.62024 q^{97} -9.80396 q^{98} +5.87317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 3 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{11} + 3 q^{14} + 3 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 21 q^{19} + 6 q^{21} + 3 q^{22} - 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28}+ \cdots - 36 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^11 + 3 * q^14 + 3 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 21 * q^19 + 6 * q^21 + 3 * q^22 - 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 + 6 * q^29 - 3 * q^30 - 21 * q^31 - 6 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^35 + 12 * q^36 + 21 * q^38 - 27 * q^39 + 18 * q^41 - 6 * q^42 - 18 * q^43 - 3 * q^44 - 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 + 18 * q^50 + 18 * q^53 + 3 * q^54 + 3 * q^55 + 3 * q^56 - 6 * q^57 - 6 * q^58 - 27 * q^59 + 3 * q^60 + 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 + 3 * q^66 + 9 * q^67 - 3 * q^68 - 27 * q^69 - 3 * q^70 - 12 * q^72 + 27 * q^73 - 3 * q^75 - 21 * q^76 - 24 * q^77 + 27 * q^78 - 21 * q^79 - 6 * q^81 - 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 + 3 * q^88 + 21 * q^89 + 6 * q^90 + 24 * q^91 - 21 * q^92 - 54 * q^93 + 9 * q^94 - 3 * q^95 - 42 * q^97 - 15 * q^98 - 36 * q^99

Introduction

L-functions

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