LMFDB - Embedded newform 197.4.a.b.1.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.29462 q^{2} +2.94855 q^{3} +20.0330 q^{4} -9.33457 q^{5} +15.6115 q^{6} +18.0311 q^{7} +63.7099 q^{8} -18.3060 q^{9} -49.4229 q^{10} -4.05739 q^{11} +59.0683 q^{12} +69.1707 q^{13} +95.4676 q^{14} -27.5235 q^{15} +177.056 q^{16} -71.9052 q^{17} -96.9234 q^{18} -14.1894 q^{19} -186.999 q^{20} +53.1656 q^{21} -21.4823 q^{22} -42.4299 q^{23} +187.852 q^{24} -37.8659 q^{25} +366.233 q^{26} -133.587 q^{27} +361.216 q^{28} -71.4476 q^{29} -145.726 q^{30} +80.1079 q^{31} +427.764 q^{32} -11.9634 q^{33} -380.710 q^{34} -168.312 q^{35} -366.724 q^{36} -42.2617 q^{37} -75.1275 q^{38} +203.954 q^{39} -594.705 q^{40} -378.750 q^{41} +281.492 q^{42} -157.510 q^{43} -81.2815 q^{44} +170.879 q^{45} -224.650 q^{46} +286.857 q^{47} +522.059 q^{48} -17.8803 q^{49} -200.485 q^{50} -212.016 q^{51} +1385.70 q^{52} +543.696 q^{53} -707.293 q^{54} +37.8740 q^{55} +1148.76 q^{56} -41.8382 q^{57} -378.288 q^{58} -709.668 q^{59} -551.377 q^{60} +697.029 q^{61} +424.141 q^{62} -330.077 q^{63} +848.398 q^{64} -645.679 q^{65} -63.3418 q^{66} -148.766 q^{67} -1440.47 q^{68} -125.107 q^{69} -891.149 q^{70} -120.024 q^{71} -1166.28 q^{72} +1099.31 q^{73} -223.759 q^{74} -111.650 q^{75} -284.256 q^{76} -73.1591 q^{77} +1079.86 q^{78} +641.422 q^{79} -1652.74 q^{80} +100.373 q^{81} -2005.34 q^{82} -1036.30 q^{83} +1065.06 q^{84} +671.203 q^{85} -833.956 q^{86} -210.667 q^{87} -258.496 q^{88} +1308.32 q^{89} +904.738 q^{90} +1247.22 q^{91} -849.997 q^{92} +236.203 q^{93} +1518.80 q^{94} +132.452 q^{95} +1261.29 q^{96} +1133.62 q^{97} -94.6693 q^{98} +74.2747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100}) $ 27 * q + 4 * q^2 + 32 * q^3 + 128 * q^4 + 29 * q^5 + 36 * q^6 + 122 * q^7 + 27 * q^8 + 287 * q^9 + 127 * q^10 + 98 * q^11 + 256 * q^12 + 193 * q^13 + 113 * q^14 + 194 * q^15 + 672 * q^16 + 124 * q^17 + 61 * q^18 + 535 * q^19 + 279 * q^20 + 188 * q^21 + 165 * q^22 + 344 * q^23 + 165 * q^24 + 910 * q^25 - 44 * q^26 + 1382 * q^27 + 1038 * q^28 + 346 * q^29 + 115 * q^30 + 599 * q^31 + 100 * q^32 + 794 * q^33 + 886 * q^34 + 12 * q^35 + 1714 * q^36 + 1428 * q^37 + 1108 * q^38 + 568 * q^39 + 1206 * q^40 + 549 * q^41 + 355 * q^42 + 2091 * q^43 + 586 * q^44 + 1167 * q^45 + 469 * q^46 + 1270 * q^47 + 2258 * q^48 + 2165 * q^49 - 353 * q^50 - 128 * q^51 + 1000 * q^52 - 208 * q^53 - 2945 * q^54 + 810 * q^55 - 5592 * q^56 - 1006 * q^57 + 287 * q^58 + 603 * q^59 - 2211 * q^60 - 314 * q^61 - 1347 * q^62 + 2416 * q^63 + 5 * q^64 - 1958 * q^65 - 8706 * q^66 + 4372 * q^67 - 6709 * q^68 - 306 * q^69 - 4329 * q^70 - 871 * q^71 - 7589 * q^72 + 942 * q^73 - 5237 * q^74 - 1530 * q^75 - 2470 * q^76 - 1868 * q^77 - 10179 * q^78 - 197 * q^79 - 1882 * q^80 + 1083 * q^81 - 961 * q^82 - 799 * q^83 - 3140 * q^84 - 1444 * q^85 - 7066 * q^86 - 794 * q^87 - 2409 * q^88 - 572 * q^89 - 10939 * q^90 + 3872 * q^91 - 6154 * q^92 - 1506 * q^93 + 1231 * q^94 - 756 * q^95 - 10975 * q^96 + 6335 * q^97 - 5330 * q^98 + 1940 * 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 $

$2$	5.29462	1.87193	0.935965	−	0.352094i	$-0.114530\pi$
$2$	5.29462	1.87193	0.935965	+	0.352094i	$0.114530\pi$
$3$	2.94855	0.567450	0.283725	−	0.958906i	$-0.408430\pi$
$3$	2.94855	0.567450	0.283725	+	0.958906i	$0.408430\pi$
$4$	20.0330	2.50412
$5$	−9.33457	−0.834909	−0.417454	−	0.908698i	$-0.637078\pi$
$5$	−9.33457	−0.834909	−0.417454	+	0.908698i	$0.637078\pi$
$6$	15.6115	1.06223
$7$	18.0311	0.973587	0.486793	−	0.873517i	$-0.338166\pi$
$7$	18.0311	0.973587	0.486793	+	0.873517i	$0.338166\pi$
$8$	63.7099	2.81561
$9$	−18.3060	−0.678001
$10$	−49.4229	−1.56289
$11$	−4.05739	−0.111214	−0.0556068	−	0.998453i	$-0.517709\pi$
$11$	−4.05739	−0.111214	−0.0556068	+	0.998453i	$0.517709\pi$
$12$	59.0683	1.42096
$13$	69.1707	1.47573	0.737866	−	0.674947i	$-0.235834\pi$
$13$	69.1707	1.47573	0.737866	+	0.674947i	$0.235834\pi$
$14$	95.4676	1.82249
$15$	−27.5235	−0.473769
$16$	177.056	2.76650
$17$	−71.9052	−1.02586	−0.512928	−	0.858431i	$-0.671439\pi$
$17$	−71.9052	−1.02586	−0.512928	+	0.858431i	$0.671439\pi$
$18$	−96.9234	−1.26917
$19$	−14.1894	−0.171330	−0.0856651	−	0.996324i	$-0.527302\pi$
$19$	−14.1894	−0.171330	−0.0856651	+	0.996324i	$0.527302\pi$
$20$	−186.999	−2.09071
$21$	53.1656	0.552461
$22$	−21.4823	−0.208184
$23$	−42.4299	−0.384663	−0.192332	−	0.981330i	$-0.561605\pi$
$23$	−42.4299	−0.384663	−0.192332	+	0.981330i	$0.561605\pi$
$24$	187.852	1.59772
$25$	−37.8659	−0.302927
$26$	366.233	2.76247
$27$	−133.587	−0.952181
$28$	361.216	2.43798
$29$	−71.4476	−0.457500	−0.228750	−	0.973485i	$-0.573464\pi$
$29$	−71.4476	−0.457500	−0.228750	+	0.973485i	$0.573464\pi$
$30$	−145.726	−0.886862
$31$	80.1079	0.464123	0.232061	−	0.972701i	$-0.425453\pi$
$31$	80.1079	0.464123	0.232061	+	0.972701i	$0.425453\pi$
$32$	427.764	2.36308
$33$	−11.9634	−0.0631081
$34$	−380.710	−1.92033
$35$	−168.312	−0.812856
$36$	−366.724	−1.69780
$37$	−42.2617	−0.187778	−0.0938889	−	0.995583i	$-0.529930\pi$
$37$	−42.2617	−0.187778	−0.0938889	+	0.995583i	$0.529930\pi$
$38$	−75.1275	−0.320718
$39$	203.954	0.837403
$40$	−594.705	−2.35078
$41$	−378.750	−1.44270	−0.721351	−	0.692569i	$-0.756479\pi$
$41$	−378.750	−1.44270	−0.721351	+	0.692569i	$0.756479\pi$
$42$	281.492	1.03417
$43$	−157.510	−0.558606	−0.279303	−	0.960203i	$-0.590103\pi$
$43$	−157.510	−0.558606	−0.279303	+	0.960203i	$0.590103\pi$
$44$	−81.2815	−0.278492
$45$	170.879	0.566069
$46$	−224.650	−0.720062
$47$	286.857	0.890263	0.445132	−	0.895465i	$-0.353157\pi$
$47$	286.857	0.890263	0.445132	+	0.895465i	$0.353157\pi$
$48$	522.059	1.56985
$49$	−17.8803	−0.0521291
$50$	−200.485	−0.567058
$51$	−212.016	−0.582122
$52$	1385.70	3.69541
$53$	543.696	1.40910	0.704551	−	0.709654i	$-0.251149\pi$
$53$	543.696	1.40910	0.704551	+	0.709654i	$0.251149\pi$
$54$	−707.293	−1.78242
$55$	37.8740	0.0928532
$56$	1148.76	2.74124
$57$	−41.8382	−0.0972212
$58$	−378.288	−0.856407
$59$	−709.668	−1.56595	−0.782974	−	0.622055i	$-0.786298\pi$
$59$	−709.668	−1.56595	−0.782974	+	0.622055i	$0.786298\pi$
$60$	−551.377	−1.18637
$61$	697.029	1.46304	0.731520	−	0.681820i	$-0.238811\pi$
$61$	697.029	1.46304	0.731520	+	0.681820i	$0.238811\pi$
$62$	424.141	0.868805
$63$	−330.077	−0.660093
$64$	848.398	1.65703
$65$	−645.679	−1.23210
$66$	−63.3418	−0.118134
$67$	−148.766	−0.271263	−0.135632	−	0.990759i	$-0.543306\pi$
$67$	−148.766	−0.271263	−0.135632	+	0.990759i	$0.543306\pi$
$68$	−1440.47	−2.56887
$69$	−125.107	−0.218277
$70$	−891.149	−1.52161
$71$	−120.024	−0.200623	−0.100312	−	0.994956i	$-0.531984\pi$
$71$	−120.024	−0.200623	−0.100312	+	0.994956i	$0.531984\pi$
$72$	−1166.28	−1.90898
$73$	1099.31	1.76253	0.881263	−	0.472626i	$-0.156694\pi$
$73$	1099.31	1.76253	0.881263	+	0.472626i	$0.156694\pi$
$74$	−223.759	−0.351507
$75$	−111.650	−0.171896
$76$	−284.256	−0.429031
$77$	−73.1591	−0.108276
$78$	1079.86	1.56756
$79$	641.422	0.913489	0.456745	−	0.889598i	$-0.349015\pi$
$79$	641.422	0.913489	0.456745	+	0.889598i	$0.349015\pi$
$80$	−1652.74	−2.30977
$81$	100.373	0.137686
$82$	−2005.34	−2.70064
$83$	−1036.30	−1.37046	−0.685232	−	0.728325i	$-0.740299\pi$
$83$	−1036.30	−1.37046	−0.685232	+	0.728325i	$0.740299\pi$
$84$	1065.06	1.38343
$85$	671.203	0.856497
$86$	−833.956	−1.04567
$87$	−210.667	−0.259608
$88$	−258.496	−0.313134
$89$	1308.32	1.55822	0.779112	−	0.626885i	$-0.215670\pi$
$89$	1308.32	1.55822	0.779112	+	0.626885i	$0.215670\pi$
$90$	904.738	1.05964
$91$	1247.22	1.43675
$92$	−849.997	−0.963243
$93$	236.203	0.263366
$94$	1518.80	1.66651
$95$	132.452	0.143045
$96$	1261.29	1.34093
$97$	1133.62	1.18662	0.593310	−	0.804974i	$-0.297821\pi$
$97$	1133.62	1.18662	0.593310	+	0.804974i	$0.297821\pi$
$98$	−94.6693	−0.0975821
$99$	74.2747	0.0754029
$100$	−758.566	−0.758566
$101$	−620.803	−0.611606	−0.305803	−	0.952095i	$-0.598925\pi$
$101$	−620.803	−0.611606	−0.305803	+	0.952095i	$0.598925\pi$
$102$	−1122.54	−1.08969
$103$	150.910	0.144365	0.0721824	−	0.997391i	$-0.477004\pi$
$103$	150.910	0.144365	0.0721824	+	0.997391i	$0.477004\pi$
$104$	4406.86	4.15508
$105$	−496.278	−0.461255
$106$	2878.66	2.63774
$107$	−1234.84	−1.11567	−0.557835	−	0.829952i	$-0.688368\pi$
$107$	−1234.84	−1.11567	−0.557835	+	0.829952i	$0.688368\pi$
$108$	−2676.15	−2.38438
$109$	−1255.65	−1.10339	−0.551694	−	0.834047i	$-0.686018\pi$
$109$	−1255.65	−1.10339	−0.551694	+	0.834047i	$0.686018\pi$
$110$	200.528	0.173815
$111$	−124.611	−0.106554
$112$	3192.51	2.69343
$113$	793.103	0.660256	0.330128	−	0.943936i	$-0.392908\pi$
$113$	793.103	0.660256	0.330128	+	0.943936i	$0.392908\pi$
$114$	−221.517	−0.181991
$115$	396.065	0.321159
$116$	−1431.31	−1.14563
$117$	−1266.24	−1.00055
$118$	−3757.42	−2.93134
$119$	−1296.53	−0.998760
$120$	−1753.52	−1.33395
$121$	−1314.54	−0.987632
$122$	3690.50	2.73871
$123$	−1116.77	−0.818661
$124$	1604.80	1.16222
$125$	1520.28	1.08783
$126$	−1747.63	−1.23565
$127$	−462.966	−0.323477	−0.161738	−	0.986834i	$-0.551710\pi$
$127$	−462.966	−0.323477	−0.161738	+	0.986834i	$0.551710\pi$
$128$	1069.83	0.738755
$129$	−464.427	−0.316981
$130$	−3418.62	−2.30641
$131$	1012.79	0.675480	0.337740	−	0.941240i	$-0.390338\pi$
$131$	1012.79	0.675480	0.337740	+	0.941240i	$0.390338\pi$
$132$	−239.663	−0.158030
$133$	−255.850	−0.166805
$134$	−787.658	−0.507786
$135$	1246.98	0.794984
$136$	−4581.07	−2.88841
$137$	−228.045	−0.142213	−0.0711066	−	0.997469i	$-0.522653\pi$
$137$	−228.045	−0.142213	−0.0711066	+	0.997469i	$0.522653\pi$
$138$	−662.394	−0.408599
$139$	3185.35	1.94373	0.971864	−	0.235543i	$-0.0756867\pi$
$139$	3185.35	1.94373	0.971864	+	0.235543i	$0.0756867\pi$
$140$	−3371.79	−2.03549
$141$	845.813	0.505180
$142$	−635.482	−0.375553
$143$	−280.653	−0.164121
$144$	−3241.19	−1.87569
$145$	666.932	0.381971
$146$	5820.42	3.29933
$147$	−52.7210	−0.0295807
$148$	−846.627	−0.470218
$149$	3379.30	1.85801	0.929003	−	0.370071i	$-0.120667\pi$
$149$	3379.30	1.85801	0.929003	+	0.370071i	$0.120667\pi$
$150$	−591.142	−0.321777
$151$	−668.749	−0.360411	−0.180205	−	0.983629i	$-0.557676\pi$
$151$	−668.749	−0.360411	−0.180205	+	0.983629i	$0.557676\pi$
$152$	−904.006	−0.482399
$153$	1316.30	0.695532
$154$	−387.349	−0.202685
$155$	−747.773	−0.387500
$156$	4085.80	2.09696
$157$	−1534.41	−0.779997	−0.389999	−	0.920815i	$-0.627525\pi$
$157$	−1534.41	−0.779997	−0.389999	+	0.920815i	$0.627525\pi$
$158$	3396.09	1.70999
$159$	1603.12	0.799594
$160$	−3992.99	−1.97296
$161$	−765.057	−0.374503
$162$	531.438	0.257739
$163$	−3198.04	−1.53675	−0.768374	−	0.640001i	$-0.778934\pi$
$163$	−3198.04	−1.53675	−0.768374	+	0.640001i	$0.778934\pi$
$164$	−7587.49	−3.61270
$165$	111.673	0.0526895
$166$	−5486.80	−2.56541
$167$	2983.50	1.38245	0.691227	−	0.722637i	$-0.257070\pi$
$167$	2983.50	1.38245	0.691227	+	0.722637i	$0.257070\pi$
$168$	3387.18	1.55551
$169$	2587.59	1.17778
$170$	3553.76	1.60330
$171$	259.752	0.116162
$172$	−3155.40	−1.39882
$173$	−554.568	−0.243717	−0.121859	−	0.992547i	$-0.538885\pi$
$173$	−554.568	−0.243717	−0.121859	+	0.992547i	$0.538885\pi$
$174$	−1115.40	−0.485968
$175$	−682.763	−0.294926
$176$	−718.385	−0.307672
$177$	−2092.50	−0.888596
$178$	6927.07	2.91689
$179$	−288.419	−0.120433	−0.0602163	−	0.998185i	$-0.519179\pi$
$179$	−288.419	−0.120433	−0.0602163	+	0.998185i	$0.519179\pi$
$180$	3423.21	1.41751
$181$	−556.784	−0.228649	−0.114324	−	0.993443i	$-0.536470\pi$
$181$	−556.784	−0.228649	−0.114324	+	0.993443i	$0.536470\pi$
$182$	6603.57	2.68950
$183$	2055.23	0.830201
$184$	−2703.21	−1.08306
$185$	394.494	0.156777
$186$	1250.60	0.493003
$187$	291.747	0.114089
$188$	5746.59	2.22933
$189$	−2408.72	−0.927031
$190$	701.282	0.267770
$191$	3369.03	1.27631	0.638153	−	0.769910i	$-0.279699\pi$
$191$	3369.03	1.27631	0.638153	+	0.769910i	$0.279699\pi$
$192$	2501.55	0.940280
$193$	1299.26	0.484574	0.242287	−	0.970205i	$-0.422102\pi$
$193$	1299.26	0.484574	0.242287	+	0.970205i	$0.422102\pi$
$194$	6002.11	2.22127
$195$	−1903.82	−0.699156
$196$	−358.195	−0.130538
$197$	−197.000	−0.0712470
$197$	−197.000	−0.0712470
$198$	393.256	0.141149
$199$	5005.03	1.78290	0.891451	−	0.453118i	$-0.149688\pi$
$199$	5005.03	1.78290	0.891451	+	0.453118i	$0.149688\pi$
$200$	−2412.43	−0.852924
$201$	−438.644	−0.153928
$202$	−3286.91	−1.14488
$203$	−1288.28	−0.445415
$204$	−4247.31	−1.45770
$205$	3535.47	1.20453
$206$	799.009	0.270241
$207$	776.723	0.260802
$208$	12247.1	4.08261
$209$	57.5719	0.0190542
$210$	−2627.60	−0.863437
$211$	2362.15	0.770698	0.385349	−	0.922771i	$-0.374081\pi$
$211$	2362.15	0.770698	0.385349	+	0.922771i	$0.374081\pi$
$212$	10891.8	3.52856
$213$	−353.898	−0.113844
$214$	−6538.01	−2.08845
$215$	1470.29	0.466385
$216$	−8510.84	−2.68097
$217$	1444.43	0.451864
$218$	−6648.18	−2.06546
$219$	3241.37	1.00014
$220$	758.728	0.232516
$221$	−4973.73	−1.51389
$222$	−659.767	−0.199462
$223$	2327.09	0.698806	0.349403	−	0.936973i	$-0.386384\pi$
$223$	2327.09	0.698806	0.349403	+	0.936973i	$0.386384\pi$
$224$	7713.04	2.30067
$225$	693.174	0.205385
$226$	4199.18	1.23595
$227$	4923.79	1.43966	0.719832	−	0.694148i	$-0.244219\pi$
$227$	4923.79	1.43966	0.719832	+	0.694148i	$0.244219\pi$
$228$	−838.144	−0.243454
$229$	−499.330	−0.144090	−0.0720451	−	0.997401i	$-0.522953\pi$
$229$	−499.330	−0.144090	−0.0720451	+	0.997401i	$0.522953\pi$
$230$	2097.01	0.601187
$231$	−215.714	−0.0614412
$232$	−4551.92	−1.28814
$233$	−5763.06	−1.62039	−0.810195	−	0.586161i	$-0.800639\pi$
$233$	−5763.06	−1.62039	−0.810195	+	0.586161i	$0.800639\pi$
$234$	−6704.26	−1.87295
$235$	−2677.68	−0.743289
$236$	−14216.8	−3.92132
$237$	1891.27	0.518359
$238$	−6864.61	−1.86961
$239$	1756.24	0.475320	0.237660	−	0.971348i	$-0.423620\pi$
$239$	1756.24	0.475320	0.237660	+	0.971348i	$0.423620\pi$
$240$	−4873.20	−1.31068
$241$	−3771.03	−1.00794	−0.503970	−	0.863721i	$-0.668128\pi$
$241$	−3771.03	−1.00794	−0.503970	+	0.863721i	$0.668128\pi$
$242$	−6959.97	−1.84878
$243$	3902.81	1.03031
$244$	13963.6	3.66363
$245$	166.905	0.0435231
$246$	−5912.84	−1.53248
$247$	−981.492	−0.252837
$248$	5103.67	1.30679
$249$	−3055.58	−0.777669
$250$	8049.31	2.03633
$251$	−1425.89	−0.358572	−0.179286	−	0.983797i	$-0.557379\pi$
$251$	−1425.89	−0.358572	−0.179286	+	0.983797i	$0.557379\pi$
$252$	−6612.43	−1.65295
$253$	172.155	0.0427798
$254$	−2451.23	−0.605526
$255$	1979.08	0.486019
$256$	−1122.84	−0.274130
$257$	−693.244	−0.168262	−0.0841311	−	0.996455i	$-0.526811\pi$
$257$	−693.244	−0.168262	−0.0841311	+	0.996455i	$0.526811\pi$
$258$	−2458.96	−0.593366
$259$	−762.023	−0.182818
$260$	−12934.9	−3.08533
$261$	1307.92	0.310185
$262$	5362.33	1.26445
$263$	−4031.93	−0.945321	−0.472660	−	0.881245i	$-0.656706\pi$
$263$	−4031.93	−0.945321	−0.472660	+	0.881245i	$0.656706\pi$
$264$	−762.190	−0.177688
$265$	−5075.17	−1.17647
$266$	−1354.63	−0.312247
$267$	3857.66	0.884213
$268$	−2980.22	−0.679276
$269$	6789.40	1.53887	0.769437	−	0.638723i	$-0.220537\pi$
$269$	6789.40	1.53887	0.769437	+	0.638723i	$0.220537\pi$
$270$	6602.28	1.48815
$271$	−8700.77	−1.95031	−0.975155	−	0.221524i	$-0.928897\pi$
$271$	−8700.77	−1.95031	−0.975155	+	0.221524i	$0.928897\pi$
$272$	−12731.2	−2.83803
$273$	3677.51	0.815285
$274$	−1207.41	−0.266213
$275$	153.637	0.0336896
$276$	−2506.26	−0.546592
$277$	−7379.87	−1.60077	−0.800385	−	0.599486i	$-0.795372\pi$
$277$	−7379.87	−1.60077	−0.800385	+	0.599486i	$0.795372\pi$
$278$	16865.2	3.63852
$279$	−1466.46	−0.314676
$280$	−10723.2	−2.28868
$281$	−1700.09	−0.360921	−0.180461	−	0.983582i	$-0.557759\pi$
$281$	−1700.09	−0.360921	−0.180461	+	0.983582i	$0.557759\pi$
$282$	4478.26	0.945661
$283$	6412.86	1.34701	0.673507	−	0.739181i	$-0.264787\pi$
$283$	6412.86	1.34701	0.673507	+	0.739181i	$0.264787\pi$
$284$	−2404.44	−0.502385
$285$	390.542	0.0811709
$286$	−1485.95	−0.307224
$287$	−6829.27	−1.40460
$288$	−7830.66	−1.60217
$289$	257.351	0.0523816
$290$	3531.15	0.715022
$291$	3342.55	0.673347
$292$	22022.4	4.41358
$293$	5779.05	1.15227	0.576136	−	0.817354i	$-0.304560\pi$
$293$	5779.05	1.15227	0.576136	+	0.817354i	$0.304560\pi$
$294$	−279.138	−0.0553729
$295$	6624.44	1.30742
$296$	−2692.49	−0.528708
$297$	542.016	0.105895
$298$	17892.1	3.47806
$299$	−2934.91	−0.567660
$300$	−2236.67	−0.430448
$301$	−2840.08	−0.543852
$302$	−3540.77	−0.674663
$303$	−1830.47	−0.347055
$304$	−2512.32	−0.473985
$305$	−6506.46	−1.22151
$306$	6969.29	1.30199
$307$	−6036.78	−1.12227	−0.561136	−	0.827724i	$-0.689635\pi$
$307$	−6036.78	−1.12227	−0.561136	+	0.827724i	$0.689635\pi$
$308$	−1465.59	−0.271136
$309$	444.965	0.0819197
$310$	−3959.17	−0.725373
$311$	−3061.92	−0.558281	−0.279141	−	0.960250i	$-0.590050\pi$
$311$	−3061.92	−0.558281	−0.279141	+	0.960250i	$0.590050\pi$
$312$	12993.9	2.35780
$313$	−4879.17	−0.881108	−0.440554	−	0.897726i	$-0.645218\pi$
$313$	−4879.17	−0.881108	−0.440554	+	0.897726i	$0.645218\pi$
$314$	−8124.13	−1.46010
$315$	3081.13	0.551117
$316$	12849.6	2.28749
$317$	−10748.1	−1.90433	−0.952165	−	0.305585i	$-0.901148\pi$
$317$	−10748.1	−1.90433	−0.952165	+	0.305585i	$0.901148\pi$
$318$	8487.89	1.49678
$319$	289.891	0.0508801
$320$	−7919.43	−1.38347
$321$	−3641.00	−0.633086
$322$	−4050.69	−0.701043
$323$	1020.29	0.175760
$324$	2010.77	0.344783
$325$	−2619.21	−0.447039
$326$	−16932.4	−2.87668
$327$	−3702.35	−0.626117
$328$	−24130.1	−4.06209
$329$	5172.34	0.866748
$330$	591.268	0.0986310
$331$	7559.89	1.25538	0.627688	−	0.778465i	$-0.284001\pi$
$331$	7559.89	1.25538	0.627688	+	0.778465i	$0.284001\pi$
$332$	−20760.1	−3.43181
$333$	773.643	0.127313
$334$	15796.5	2.58786
$335$	1388.66	0.226480
$336$	9413.29	1.52838
$337$	−5154.75	−0.833227	−0.416613	−	0.909084i	$-0.636783\pi$
$337$	−5154.75	−0.833227	−0.416613	+	0.909084i	$0.636783\pi$
$338$	13700.3	2.20473
$339$	2338.51	0.374662
$340$	13446.2	2.14477
$341$	−325.029	−0.0516167
$342$	1375.29	0.217447
$343$	−6507.06	−1.02434
$344$	−10035.0	−1.57282
$345$	1167.82	0.182241
$346$	−2936.23	−0.456221
$347$	−10446.8	−1.61618	−0.808092	−	0.589057i	$-0.799499\pi$
$347$	−10446.8	−1.61618	−0.808092	+	0.589057i	$0.799499\pi$
$348$	−4220.29	−0.650090
$349$	842.221	0.129178	0.0645889	−	0.997912i	$-0.479426\pi$
$349$	842.221	0.129178	0.0645889	+	0.997912i	$0.479426\pi$
$350$	−3614.97	−0.552080
$351$	−9240.33	−1.40516
$352$	−1735.60	−0.262807
$353$	−3595.84	−0.542174	−0.271087	−	0.962555i	$-0.587383\pi$
$353$	−3595.84	−0.542174	−0.271087	+	0.962555i	$0.587383\pi$
$354$	−11079.0	−1.66339
$355$	1120.37	0.167502
$356$	26209.6	3.90198
$357$	−3822.88	−0.566746
$358$	−1527.07	−0.225441
$359$	−8095.55	−1.19016	−0.595079	−	0.803667i	$-0.702879\pi$
$359$	−8095.55	−1.19016	−0.595079	+	0.803667i	$0.702879\pi$
$360$	10886.7	1.59383
$361$	−6657.66	−0.970646
$362$	−2947.96	−0.428014
$363$	−3875.99	−0.560431
$364$	24985.6	3.59780
$365$	−10261.6	−1.47155
$366$	10881.6	1.55408
$367$	−5170.03	−0.735350	−0.367675	−	0.929954i	$-0.619846\pi$
$367$	−5170.03	−0.735350	−0.367675	+	0.929954i	$0.619846\pi$
$368$	−7512.47	−1.06417
$369$	6933.41	0.978154
$370$	2088.70	0.293476
$371$	9803.42	1.37188
$372$	4731.84	0.659501
$373$	5606.06	0.778205	0.389103	−	0.921194i	$-0.372785\pi$
$373$	5606.06	0.778205	0.389103	+	0.921194i	$0.372785\pi$
$374$	1544.69	0.213567
$375$	4482.64	0.617286
$376$	18275.6	2.50663
$377$	−4942.08	−0.675147
$378$	−12753.3	−1.73534
$379$	5523.87	0.748659	0.374330	−	0.927296i	$-0.377873\pi$
$379$	5523.87	0.748659	0.374330	+	0.927296i	$0.377873\pi$
$380$	2653.41	0.358202
$381$	−1365.08	−0.183557
$382$	17837.7	2.38915
$383$	−9491.97	−1.26636	−0.633182	−	0.774003i	$-0.718251\pi$
$383$	−9491.97	−1.26636	−0.633182	+	0.774003i	$0.718251\pi$
$384$	3154.46	0.419206
$385$	682.908	0.0904006
$386$	6879.08	0.907088
$387$	2883.38	0.378736
$388$	22709.9	2.97144
$389$	8344.60	1.08763	0.543815	−	0.839205i	$-0.316979\pi$
$389$	8344.60	1.08763	0.543815	+	0.839205i	$0.316979\pi$
$390$	−10080.0	−1.30877
$391$	3050.93	0.394609
$392$	−1139.15	−0.146775
$393$	2986.27	0.383301
$394$	−1043.04	−0.133369
$395$	−5987.40	−0.762680
$396$	1487.94	0.188818
$397$	2024.81	0.255975	0.127988	−	0.991776i	$-0.459148\pi$
$397$	2024.81	0.255975	0.127988	+	0.991776i	$0.459148\pi$
$398$	26499.7	3.33747
$399$	−754.389	−0.0946533
$400$	−6704.38	−0.838047
$401$	−4974.85	−0.619532	−0.309766	−	0.950813i	$-0.600251\pi$
$401$	−4974.85	−0.619532	−0.309766	+	0.950813i	$0.600251\pi$
$402$	−2322.45	−0.288143
$403$	5541.12	0.684921
$404$	−12436.5	−1.53153
$405$	−936.941	−0.114955
$406$	−6820.93	−0.833786
$407$	171.472	0.0208834
$408$	−13507.5	−1.63903
$409$	−1716.52	−0.207522	−0.103761	−	0.994602i	$-0.533088\pi$
$409$	−1716.52	−0.207522	−0.103761	+	0.994602i	$0.533088\pi$
$410$	18718.9	2.25479
$411$	−672.403	−0.0806988
$412$	3023.17	0.361507
$413$	−12796.1	−1.52459
$414$	4112.45	0.488203
$415$	9673.39	1.14421
$416$	29588.7	3.48728
$417$	9392.19	1.10297
$418$	304.821	0.0356682
$419$	−6697.71	−0.780918	−0.390459	−	0.920620i	$-0.627684\pi$
$419$	−6697.71	−0.780918	−0.390459	+	0.920620i	$0.627684\pi$
$420$	−9941.92	−1.15504
$421$	9411.47	1.08952	0.544759	−	0.838593i	$-0.316621\pi$
$421$	9411.47	1.08952	0.544759	+	0.838593i	$0.316621\pi$
$422$	12506.7	1.44269
$423$	−5251.21	−0.603599
$424$	34638.8	3.96748
$425$	2722.75	0.310760
$426$	−1873.75	−0.213107
$427$	12568.2	1.42440
$428$	−24737.5	−2.79377
$429$	−827.520	−0.0931306
$430$	7784.62	0.873041
$431$	1139.75	0.127378	0.0636892	−	0.997970i	$-0.479713\pi$
$431$	1139.75	0.127378	0.0636892	+	0.997970i	$0.479713\pi$
$432$	−23652.4	−2.63421
$433$	537.848	0.0596936	0.0298468	−	0.999554i	$-0.490498\pi$
$433$	537.848	0.0596936	0.0298468	+	0.999554i	$0.490498\pi$
$434$	7647.71	0.845857
$435$	1966.49	0.216749
$436$	−25154.4	−2.76302
$437$	602.056	0.0659044
$438$	17161.8	1.87220
$439$	−2870.16	−0.312039	−0.156020	−	0.987754i	$-0.549866\pi$
$439$	−2870.16	−0.312039	−0.156020	+	0.987754i	$0.549866\pi$
$440$	2412.95	0.261438
$441$	327.317	0.0353436
$442$	−26334.0	−2.83389
$443$	7916.90	0.849082	0.424541	−	0.905409i	$-0.360436\pi$
$443$	7916.90	0.849082	0.424541	+	0.905409i	$0.360436\pi$
$444$	−2496.32	−0.266825
$445$	−12212.6	−1.30097
$446$	12321.1	1.30812
$447$	9964.05	1.05433
$448$	15297.5	1.61326
$449$	−13391.9	−1.40758	−0.703792	−	0.710407i	$-0.748511\pi$
$449$	−13391.9	−1.40758	−0.703792	+	0.710407i	$0.748511\pi$
$450$	3670.09	0.384466
$451$	1536.74	0.160448
$452$	15888.2	1.65336
$453$	−1971.84	−0.204515
$454$	26069.6	2.69495
$455$	−11642.3	−1.19956
$456$	−2665.51	−0.273737
$457$	3193.74	0.326908	0.163454	−	0.986551i	$-0.447736\pi$
$457$	3193.74	0.326908	0.163454	+	0.986551i	$0.447736\pi$
$458$	−2643.76	−0.269727
$459$	9605.61	0.976801
$460$	7934.36	0.804220
$461$	10163.1	1.02677	0.513387	−	0.858157i	$-0.328390\pi$
$461$	10163.1	1.02677	0.513387	+	0.858157i	$0.328390\pi$
$462$	−1142.12	−0.115014
$463$	−16399.4	−1.64610	−0.823051	−	0.567968i	$-0.807730\pi$
$463$	−16399.4	−1.64610	−0.823051	+	0.567968i	$0.807730\pi$
$464$	−12650.2	−1.26567
$465$	−2204.85	−0.219887
$466$	−30513.2	−3.03325
$467$	−2083.20	−0.206422	−0.103211	−	0.994659i	$-0.532912\pi$
$467$	−2083.20	−0.206422	−0.103211	+	0.994659i	$0.532912\pi$
$468$	−25366.6	−2.50549
$469$	−2682.41	−0.264098
$470$	−14177.3	−1.39138
$471$	−4524.30	−0.442609
$472$	−45212.9	−4.40909
$473$	639.080	0.0621246
$474$	10013.5	0.970332
$475$	537.294	0.0519005
$476$	−25973.3	−2.50102
$477$	−9952.91	−0.955372
$478$	9298.60	0.889766
$479$	−1493.90	−0.142501	−0.0712503	−	0.997458i	$-0.522699\pi$
$479$	−1493.90	−0.142501	−0.0712503	+	0.997458i	$0.522699\pi$
$480$	−11773.5	−1.11956
$481$	−2923.27	−0.277110
$482$	−19966.2	−1.88679
$483$	−2255.81	−0.212512
$484$	−26334.1	−2.47315
$485$	−10581.9	−0.990720
$486$	20663.9	1.92867
$487$	14720.7	1.36973	0.684865	−	0.728670i	$-0.259861\pi$
$487$	14720.7	1.36973	0.684865	+	0.728670i	$0.259861\pi$
$488$	44407.7	4.11935
$489$	−9429.60	−0.872027
$490$	883.697	0.0814721
$491$	11111.7	1.02131	0.510656	−	0.859785i	$-0.329402\pi$
$491$	11111.7	1.02131	0.510656	+	0.859785i	$0.329402\pi$
$492$	−22372.1	−2.05003
$493$	5137.45	0.469329
$494$	−5196.62	−0.473294
$495$	−693.322	−0.0629545
$496$	14183.6	1.28400
$497$	−2164.17	−0.195324
$498$	−16178.1	−1.45574
$499$	6406.98	0.574781	0.287390	−	0.957814i	$-0.407212\pi$
$499$	6406.98	0.574781	0.287390	+	0.957814i	$0.407212\pi$
$500$	30455.8	2.72405
$501$	8797.00	0.784473
$502$	−7549.56	−0.671222
$503$	16931.4	1.50086	0.750432	−	0.660947i	$-0.229845\pi$
$503$	16931.4	1.50086	0.750432	+	0.660947i	$0.229845\pi$
$504$	−21029.2	−1.85856
$505$	5794.92	0.510635
$506$	911.493	0.0800807
$507$	7629.66	0.668333
$508$	−9274.57	−0.810025
$509$	−1272.26	−0.110789	−0.0553947	−	0.998465i	$-0.517642\pi$
$509$	−1272.26	−0.110789	−0.0553947	+	0.998465i	$0.517642\pi$
$510$	10478.5	0.909793
$511$	19821.7	1.71597
$512$	−14503.6	−1.25191
$513$	1895.52	0.163137
$514$	−3670.46	−0.314975
$515$	−1408.68	−0.120531
$516$	−9303.86	−0.793759
$517$	−1163.89	−0.0990093
$518$	−4034.62	−0.342222
$519$	−1635.18	−0.138297
$520$	−41136.2	−3.46911
$521$	5329.98	0.448197	0.224099	−	0.974566i	$-0.428056\pi$
$521$	5329.98	0.448197	0.224099	+	0.974566i	$0.428056\pi$
$522$	6924.94	0.580645
$523$	−2352.66	−0.196701	−0.0983506	−	0.995152i	$-0.531357\pi$
$523$	−2352.66	−0.196701	−0.0983506	+	0.995152i	$0.531357\pi$
$524$	20289.2	1.69148
$525$	−2013.16	−0.167355
$526$	−21347.5	−1.76957
$527$	−5760.17	−0.476123
$528$	−2118.20	−0.174588
$529$	−10366.7	−0.852034
$530$	−26871.1	−2.20227
$531$	12991.2	1.06171
$532$	−5125.44	−0.417699
$533$	−26198.4	−2.12904
$534$	20424.8	1.65519
$535$	11526.7	0.931482
$536$	−9477.86	−0.763771
$537$	−850.419	−0.0683394
$538$	35947.3	2.88066
$539$	72.5473	0.00579747
$540$	24980.7	1.99074
$541$	446.967	0.0355205	0.0177603	−	0.999842i	$-0.494346\pi$
$541$	446.967	0.0355205	0.0177603	+	0.999842i	$0.494346\pi$
$542$	−46067.2	−3.65084
$543$	−1641.71	−0.129747
$544$	−30758.4	−2.42419
$545$	11720.9	0.921228
$546$	19471.0	1.52616
$547$	6496.73	0.507824	0.253912	−	0.967227i	$-0.418283\pi$
$547$	6496.73	0.507824	0.253912	+	0.967227i	$0.418283\pi$
$548$	−4568.42	−0.356119
$549$	−12759.8	−0.991942
$550$	813.447	0.0630645
$551$	1013.80	0.0783835
$552$	−7970.56	−0.614582
$553$	11565.5	0.889361
$554$	−39073.6	−2.99653
$555$	1163.19	0.0889632
$556$	63812.1	4.86733
$557$	−3929.02	−0.298883	−0.149442	−	0.988771i	$-0.547748\pi$
$557$	−3929.02	−0.298883	−0.149442	+	0.988771i	$0.547748\pi$
$558$	−7764.33	−0.589051
$559$	−10895.1	−0.824353
$560$	−29800.7	−2.24877
$561$	860.233	0.0647398
$562$	−9001.33	−0.675619
$563$	8042.66	0.602056	0.301028	−	0.953615i	$-0.402670\pi$
$563$	8042.66	0.602056	0.301028	+	0.953615i	$0.402670\pi$
$564$	16944.1	1.26503
$565$	−7403.28	−0.551253
$566$	33953.7	2.52152
$567$	1809.84	0.134049
$568$	−7646.73	−0.564876
$569$	9979.73	0.735276	0.367638	−	0.929969i	$-0.380167\pi$
$569$	9979.73	0.735276	0.367638	+	0.929969i	$0.380167\pi$
$570$	2067.77	0.151946
$571$	14222.8	1.04239	0.521196	−	0.853437i	$-0.325486\pi$
$571$	14222.8	1.04239	0.521196	+	0.853437i	$0.325486\pi$
$572$	−5622.30	−0.410980
$573$	9933.76	0.724239
$574$	−36158.4	−2.62931
$575$	1606.65	0.116525
$576$	−15530.8	−1.12347
$577$	−8627.75	−0.622492	−0.311246	−	0.950329i	$-0.600746\pi$
$577$	−8627.75	−0.622492	−0.311246	+	0.950329i	$0.600746\pi$
$578$	1362.57	0.0980547
$579$	3830.94	0.274971
$580$	13360.6	0.956500
$581$	−18685.6	−1.33427
$582$	17697.5	1.26046
$583$	−2205.99	−0.156711
$584$	70036.9	4.96258
$585$	11819.8	0.835366
$586$	30597.8	2.15697
$587$	−26249.5	−1.84571	−0.922857	−	0.385142i	$-0.874152\pi$
$587$	−26249.5	−1.84571	−0.922857	+	0.385142i	$0.874152\pi$
$588$	−1056.16	−0.0740735
$589$	−1136.68	−0.0795182
$590$	35073.9	2.44741
$591$	−580.865	−0.0404291
$592$	−7482.68	−0.519487
$593$	−11900.4	−0.824097	−0.412048	−	0.911162i	$-0.635187\pi$
$593$	−11900.4	−0.824097	−0.412048	+	0.911162i	$0.635187\pi$
$594$	2869.76	0.198229
$595$	12102.5	0.833874
$596$	67697.4	4.65267
$597$	14757.6	1.01171
$598$	−15539.2	−1.06262
$599$	23284.4	1.58827	0.794135	−	0.607741i	$-0.207924\pi$
$599$	23284.4	1.58827	0.794135	+	0.607741i	$0.207924\pi$
$600$	−7113.19	−0.483991
$601$	18057.7	1.22561	0.612804	−	0.790235i	$-0.290041\pi$
$601$	18057.7	1.22561	0.612804	+	0.790235i	$0.290041\pi$
$602$	−15037.1	−1.01805
$603$	2723.31	0.183917
$604$	−13397.0	−0.902512
$605$	12270.6	0.824582
$606$	−9691.64	−0.649663
$607$	14117.2	0.943987	0.471993	−	0.881602i	$-0.343535\pi$
$607$	14117.2	0.943987	0.471993	+	0.881602i	$0.343535\pi$
$608$	−6069.72	−0.404868
$609$	−3798.56	−0.252751
$610$	−34449.2	−2.28657
$611$	19842.1	1.31379
$612$	26369.3	1.74170
$613$	15003.2	0.988538	0.494269	−	0.869309i	$-0.335436\pi$
$613$	15003.2	0.988538	0.494269	+	0.869309i	$0.335436\pi$
$614$	−31962.5	−2.10081
$615$	10424.5	0.683508
$616$	−4660.96	−0.304863
$617$	5683.75	0.370858	0.185429	−	0.982658i	$-0.440633\pi$
$617$	5683.75	0.370858	0.185429	+	0.982658i	$0.440633\pi$
$618$	2355.92	0.153348
$619$	−22819.0	−1.48170	−0.740849	−	0.671672i	$-0.765577\pi$
$619$	−22819.0	−1.48170	−0.740849	+	0.671672i	$0.765577\pi$
$620$	−14980.1	−0.970347
$621$	5668.10	0.366269
$622$	−16211.7	−1.04506
$623$	23590.5	1.51707
$624$	36111.2	2.31668
$625$	−9457.94	−0.605308
$626$	−25833.3	−1.64937
$627$	169.754	0.0108123
$628$	−30738.9	−1.95321
$629$	3038.83	0.192633
$630$	16313.4	1.03165
$631$	−19171.0	−1.20949	−0.604743	−	0.796421i	$-0.706724\pi$
$631$	−19171.0	−1.20949	−0.604743	+	0.796421i	$0.706724\pi$
$632$	40865.0	2.57203
$633$	6964.94	0.437332
$634$	−56907.0	−3.56477
$635$	4321.58	0.270074
$636$	32115.2	2.00228
$637$	−1236.79	−0.0769286
$638$	1534.86	0.0952440
$639$	2197.17	0.136023
$640$	−9986.41	−0.616793
$641$	−18464.3	−1.13775	−0.568873	−	0.822425i	$-0.692620\pi$
$641$	−18464.3	−1.13775	−0.568873	+	0.822425i	$0.692620\pi$
$642$	−19277.7	−1.18509
$643$	20320.1	1.24626	0.623131	−	0.782118i	$-0.285861\pi$
$643$	20320.1	1.24626	0.623131	+	0.782118i	$0.285861\pi$
$644$	−15326.4	−0.937800
$645$	4335.23	0.264650
$646$	5402.05	0.329011
$647$	−19838.1	−1.20543	−0.602717	−	0.797955i	$-0.705915\pi$
$647$	−19838.1	−1.20543	−0.602717	+	0.797955i	$0.705915\pi$
$648$	6394.77	0.387670
$649$	2879.40	0.174155
$650$	−13867.7	−0.836826
$651$	4258.99	0.256410
$652$	−64066.2	−3.84820
$653$	−14882.7	−0.891889	−0.445944	−	0.895061i	$-0.647132\pi$
$653$	−14882.7	−0.891889	−0.445944	+	0.895061i	$0.647132\pi$
$654$	−19602.5	−1.17205
$655$	−9453.95	−0.563964
$656$	−67059.9	−3.99124
$657$	−20124.0	−1.19499
$658$	27385.5	1.62249
$659$	1822.35	0.107722	0.0538608	−	0.998548i	$-0.482847\pi$
$659$	1822.35	0.107722	0.0538608	+	0.998548i	$0.482847\pi$
$660$	2237.15	0.131941
$661$	−13294.9	−0.782316	−0.391158	−	0.920324i	$-0.627925\pi$
$661$	−13294.9	−0.782316	−0.391158	+	0.920324i	$0.627925\pi$
$662$	40026.7	2.34997
$663$	−14665.3	−0.859056
$664$	−66022.5	−3.85869
$665$	2388.25	0.139267
$666$	4096.14	0.238322
$667$	3031.52	0.175983
$668$	59768.3	3.46183
$669$	6861.56	0.396537
$670$	7352.45	0.423955
$671$	−2828.12	−0.162710
$672$	22742.3	1.30551
$673$	26371.5	1.51047	0.755235	−	0.655454i	$-0.227523\pi$
$673$	26371.5	1.51047	0.755235	+	0.655454i	$0.227523\pi$
$674$	−27292.4	−1.55974
$675$	5058.40	0.288441
$676$	51837.1	2.94931
$677$	−3293.49	−0.186971	−0.0934853	−	0.995621i	$-0.529801\pi$
$677$	−3293.49	−0.186971	−0.0934853	+	0.995621i	$0.529801\pi$
$678$	12381.5	0.701341
$679$	20440.5	1.15528
$680$	42762.3	2.41156
$681$	14518.1	0.816937
$682$	−1720.90	−0.0966229
$683$	1265.50	0.0708977	0.0354489	−	0.999371i	$-0.488714\pi$
$683$	1265.50	0.0708977	0.0354489	+	0.999371i	$0.488714\pi$
$684$	5203.60	0.290884
$685$	2128.70	0.118735
$686$	−34452.4	−1.91749
$687$	−1472.30	−0.0817640
$688$	−27888.1	−1.54538
$689$	37607.9	2.07946
$690$	6183.16	0.341143
$691$	2745.08	0.151125	0.0755627	−	0.997141i	$-0.475925\pi$
$691$	2745.08	0.151125	0.0755627	+	0.997141i	$0.475925\pi$
$692$	−11109.6	−0.610297
$693$	1339.25	0.0734112
$694$	−55312.0	−3.02538
$695$	−29733.9	−1.62284
$696$	−13421.6	−0.730954
$697$	27234.1	1.48001
$698$	4459.24	0.241812
$699$	−16992.7	−0.919489
$700$	−13677.8	−0.738530
$701$	11610.0	0.625540	0.312770	−	0.949829i	$-0.398743\pi$
$701$	11610.0	0.625540	0.312770	+	0.949829i	$0.398743\pi$
$702$	−48924.0	−2.63037
$703$	599.668	0.0321720
$704$	−3442.28	−0.184284
$705$	−7895.30	−0.421779
$706$	−19038.6	−1.01491
$707$	−11193.7	−0.595451
$708$	−41918.9	−2.22515
$709$	−21016.4	−1.11324	−0.556620	−	0.830767i	$-0.687902\pi$
$709$	−21016.4	−1.11324	−0.556620	+	0.830767i	$0.687902\pi$
$710$	5931.95	0.313552
$711$	−11741.9	−0.619347
$712$	83353.1	4.38735
$713$	−3398.97	−0.178531
$714$	−20240.7	−1.06091
$715$	2619.77	0.137026
$716$	−5777.88	−0.301578
$717$	5178.36	0.269720
$718$	−42862.8	−2.22789
$719$	−15546.0	−0.806352	−0.403176	−	0.915122i	$-0.632094\pi$
$719$	−15546.0	−0.806352	−0.403176	+	0.915122i	$0.632094\pi$
$720$	30255.1	1.56603
$721$	2721.06	0.140552
$722$	−35249.8	−1.81698
$723$	−11119.1	−0.571955
$724$	−11154.0	−0.572564
$725$	2705.43	0.138589
$726$	−20521.9	−1.04909
$727$	29761.3	1.51827	0.759136	−	0.650932i	$-0.225622\pi$
$727$	29761.3	1.51827	0.759136	+	0.650932i	$0.225622\pi$
$728$	79460.5	4.04533
$729$	8797.58	0.446963
$730$	−54331.1	−2.75464
$731$	11325.8	0.573050
$732$	41172.3	2.07892
$733$	−6134.71	−0.309128	−0.154564	−	0.987983i	$-0.549397\pi$
$733$	−6134.71	−0.309128	−0.154564	+	0.987983i	$0.549397\pi$
$734$	−27373.3	−1.37652
$735$	492.128	0.0246972
$736$	−18150.0	−0.908991
$737$	603.601	0.0301681
$738$	36709.7	1.83104
$739$	9420.97	0.468953	0.234476	−	0.972122i	$-0.424662\pi$
$739$	9420.97	0.468953	0.234476	+	0.972122i	$0.424662\pi$
$740$	7902.89	0.392589
$741$	−2893.98	−0.143472
$742$	51905.4	2.56807
$743$	24198.2	1.19481	0.597407	−	0.801938i	$-0.296198\pi$
$743$	24198.2	1.19481	0.597407	+	0.801938i	$0.296198\pi$
$744$	15048.5	0.741536
$745$	−31544.3	−1.55127
$746$	29681.9	1.45675
$747$	18970.5	0.929176
$748$	5844.56	0.285693
$749$	−22265.5	−1.08620
$750$	23733.8	1.15552
$751$	−6822.49	−0.331500	−0.165750	−	0.986168i	$-0.553004\pi$
$751$	−6822.49	−0.331500	−0.165750	+	0.986168i	$0.553004\pi$
$752$	50789.7	2.46291
$753$	−4204.33	−0.203472
$754$	−26166.4	−1.26383
$755$	6242.48	0.300910
$756$	−48253.9	−2.32140
$757$	31702.0	1.52210	0.761048	−	0.648695i	$-0.224685\pi$
$757$	31702.0	1.52210	0.761048	+	0.648695i	$0.224685\pi$
$758$	29246.8	1.40144
$759$	507.608	0.0242754
$760$	8438.51	0.402759
$761$	−6180.40	−0.294401	−0.147201	−	0.989107i	$-0.547026\pi$
$761$	−6180.40	−0.294401	−0.147201	+	0.989107i	$0.547026\pi$
$762$	−7227.57	−0.343605
$763$	−22640.7	−1.07424
$764$	67491.6	3.19602
$765$	−12287.1	−0.580706
$766$	−50256.3	−2.37054
$767$	−49088.3	−2.31092
$768$	−3310.74	−0.155555
$769$	−16944.4	−0.794578	−0.397289	−	0.917693i	$-0.630049\pi$
$769$	−16944.4	−0.794578	−0.397289	+	0.917693i	$0.630049\pi$
$770$	3615.74	0.169224
$771$	−2044.07	−0.0954803
$772$	26028.0	1.21343
$773$	1442.45	0.0671169	0.0335585	−	0.999437i	$-0.489316\pi$
$773$	1442.45	0.0671169	0.0335585	+	0.999437i	$0.489316\pi$
$774$	15266.4	0.708966
$775$	−3033.36	−0.140595
$776$	72223.1	3.34106
$777$	−2246.87	−0.103740
$778$	44181.5	2.03597
$779$	5374.24	0.247179
$780$	−38139.1	−1.75077
$781$	486.985	0.0223120
$782$	16153.5	0.738681
$783$	9544.49	0.435622
$784$	−3165.81	−0.144215
$785$	14323.1	0.651227
$786$	15811.1	0.717512
$787$	−22188.4	−1.00499	−0.502497	−	0.864579i	$-0.667585\pi$
$787$	−22188.4	−1.00499	−0.502497	+	0.864579i	$0.667585\pi$
$788$	−3946.49	−0.178411
$789$	−11888.4	−0.536422
$790$	−31701.0	−1.42768
$791$	14300.5	0.642816
$792$	4732.03	0.212305
$793$	48214.0	2.15905
$794$	10720.6	0.479168
$795$	−14964.4	−0.667588
$796$	100266.	4.46460
$797$	−33481.1	−1.48803	−0.744017	−	0.668161i	$-0.767082\pi$
$797$	−33481.1	−1.48803	−0.744017	+	0.668161i	$0.767082\pi$
$798$	−3994.20	−0.177184
$799$	−20626.5	−0.913282
$800$	−16197.7	−0.715842
$801$	−23950.2	−1.05648
$802$	−26339.9	−1.15972
$803$	−4460.33	−0.196017
$804$	−8787.34	−0.385455
$805$	7141.48	0.312676
$806$	29338.1	1.28212
$807$	20018.9	0.873233
$808$	−39551.3	−1.72204
$809$	16181.1	0.703210	0.351605	−	0.936148i	$-0.385636\pi$
$809$	16181.1	0.703210	0.351605	+	0.936148i	$0.385636\pi$
$810$	−4960.74	−0.215188
$811$	1746.49	0.0756195	0.0378098	−	0.999285i	$-0.487962\pi$
$811$	1746.49	0.0756195	0.0378098	+	0.999285i	$0.487962\pi$
$812$	−25808.0	−1.11537
$813$	−25654.7	−1.10670
$814$	907.879	0.0390923
$815$	29852.3	1.28304
$816$	−37538.7	−1.61044
$817$	2234.98	0.0957061
$818$	−9088.31	−0.388466
$819$	−22831.7	−0.974120
$820$	70825.9	3.01628
$821$	22960.3	0.976031	0.488016	−	0.872835i	$-0.337721\pi$
$821$	22960.3	0.976031	0.488016	+	0.872835i	$0.337721\pi$
$822$	−3560.12	−0.151062
$823$	2006.60	0.0849887	0.0424943	−	0.999097i	$-0.486470\pi$
$823$	2006.60	0.0849887	0.0424943	+	0.999097i	$0.486470\pi$
$824$	9614.44	0.406474
$825$	453.006	0.0191171
$826$	−67750.3	−2.85392
$827$	−2070.21	−0.0870475	−0.0435237	−	0.999052i	$-0.513858\pi$
$827$	−2070.21	−0.0870475	−0.0435237	+	0.999052i	$0.513858\pi$
$828$	15560.1	0.653080
$829$	−44977.7	−1.88437	−0.942183	−	0.335099i	$-0.891230\pi$
$829$	−44977.7	−1.88437	−0.942183	+	0.335099i	$0.891230\pi$
$830$	51216.9	2.14189
$831$	−21759.9	−0.908356
$832$	58684.3	2.44533
$833$	1285.69	0.0534770
$834$	49728.0	2.06468
$835$	−27849.6	−1.15422
$836$	1153.34	0.0477141
$837$	−10701.4	−0.441929
$838$	−35461.8	−1.46182
$839$	27362.0	1.12591	0.562957	−	0.826486i	$-0.309663\pi$
$839$	27362.0	1.12591	0.562957	+	0.826486i	$0.309663\pi$
$840$	−31617.8	−1.29871
$841$	−19284.2	−0.790694
$842$	49830.1	2.03950
$843$	−5012.81	−0.204805
$844$	47320.9	1.92992
$845$	−24154.0	−0.983343
$846$	−27803.1	−1.12990
$847$	−23702.5	−0.961545
$848$	96264.6	3.89828
$849$	18908.7	0.764363
$850$	14415.9	0.581720
$851$	1793.16	0.0722312
$852$	−7089.62	−0.285078
$853$	45411.8	1.82282	0.911412	−	0.411494i	$-0.134993\pi$
$853$	45411.8	1.82282	0.911412	+	0.411494i	$0.134993\pi$
$854$	66543.7	2.66637
$855$	−2424.67	−0.0969847
$856$	−78671.7	−3.14129
$857$	−29755.1	−1.18601	−0.593007	−	0.805197i	$-0.702059\pi$
$857$	−29755.1	−1.18601	−0.593007	+	0.805197i	$0.702059\pi$
$858$	−4381.40	−0.174334
$859$	23109.5	0.917913	0.458957	−	0.888459i	$-0.348223\pi$
$859$	23109.5	0.917913	0.458957	+	0.888459i	$0.348223\pi$
$860$	29454.2	1.16789
$861$	−20136.5	−0.797038
$862$	6034.57	0.238443
$863$	−25242.5	−0.995671	−0.497836	−	0.867271i	$-0.665872\pi$
$863$	−25242.5	−0.995671	−0.497836	+	0.867271i	$0.665872\pi$
$864$	−57143.8	−2.25008
$865$	5176.65	0.203482
$866$	2847.70	0.111742
$867$	758.813	0.0297239
$868$	28936.3	1.13152
$869$	−2602.50	−0.101592
$870$	10411.8	0.405739
$871$	−10290.2	−0.400312
$872$	−79997.3	−3.10671
$873$	−20752.2	−0.804529
$874$	3187.65	0.123368
$875$	27412.3	1.05909
$876$	64934.3	2.50448
$877$	−19445.4	−0.748718	−0.374359	−	0.927284i	$-0.622137\pi$
$877$	−19445.4	−0.748718	−0.374359	+	0.927284i	$0.622137\pi$
$878$	−15196.4	−0.584115
$879$	17039.8	0.653856
$880$	6705.81	0.256878
$881$	−15716.2	−0.601013	−0.300507	−	0.953780i	$-0.597156\pi$
$881$	−15716.2	−0.601013	−0.300507	+	0.953780i	$0.597156\pi$
$882$	1733.02	0.0661607
$883$	19809.6	0.754980	0.377490	−	0.926014i	$-0.376787\pi$
$883$	19809.6	0.754980	0.377490	+	0.926014i	$0.376787\pi$
$884$	−99638.6	−3.79096
$885$	19532.5	0.741897
$886$	41916.9	1.58942
$887$	27287.4	1.03294	0.516471	−	0.856304i	$-0.327245\pi$
$887$	27287.4	1.03294	0.516471	+	0.856304i	$0.327245\pi$
$888$	−7938.95	−0.300015
$889$	−8347.77	−0.314933
$890$	−64661.2	−2.43533
$891$	−407.253	−0.0153126
$892$	46618.6	1.74989
$893$	−4070.33	−0.152529
$894$	52755.8	1.97362
$895$	2692.26	0.100550
$896$	19290.2	0.719242
$897$	−8653.74	−0.322118
$898$	−70905.2	−2.63490
$899$	−5723.52	−0.212336
$900$	13886.3	0.514308
$901$	−39094.5	−1.44554
$902$	8136.43	0.300347
$903$	−8374.12	−0.308608
$904$	50528.6	1.85902
$905$	5197.34	0.190901
$906$	−10440.1	−0.382837
$907$	12684.3	0.464361	0.232180	−	0.972673i	$-0.425414\pi$
$907$	12684.3	0.464361	0.232180	+	0.972673i	$0.425414\pi$
$908$	98638.2	3.60509
$909$	11364.4	0.414669
$910$	−61641.4	−2.24549
$911$	−37986.2	−1.38149	−0.690746	−	0.723097i	$-0.742718\pi$
$911$	−37986.2	−1.38149	−0.690746	+	0.723097i	$0.742718\pi$
$912$	−7407.71	−0.268962
$913$	4204.67	0.152414
$914$	16909.6	0.611949
$915$	−19184.7	−0.693143
$916$	−10003.1	−0.360819
$917$	18261.7	0.657638
$918$	50858.0	1.82850
$919$	14608.2	0.524353	0.262177	−	0.965020i	$-0.415560\pi$
$919$	14608.2	0.524353	0.262177	+	0.965020i	$0.415560\pi$
$920$	25233.3	0.904257
$921$	−17799.8	−0.636833
$922$	53809.8	1.92205
$923$	−8302.16	−0.296066
$924$	−4321.38	−0.153856
$925$	1600.28	0.0568830
$926$	−86828.6	−3.08139
$927$	−2762.56	−0.0978794
$928$	−30562.7	−1.08111
$929$	46330.5	1.63623	0.818114	−	0.575056i	$-0.195020\pi$
$929$	46330.5	1.63623	0.818114	+	0.575056i	$0.195020\pi$
$930$	−11673.8	−0.411613
$931$	253.711	0.00893129
$932$	−115451.	−4.05765
$933$	−9028.23	−0.316796
$934$	−11029.7	−0.386407
$935$	−2723.33	−0.0952540
$936$	−80672.2	−2.81715
$937$	36210.9	1.26249	0.631247	−	0.775582i	$-0.282543\pi$
$937$	36210.9	1.26249	0.631247	+	0.775582i	$0.282543\pi$
$938$	−14202.3	−0.494373
$939$	−14386.5	−0.499984
$940$	−53642.0	−1.86128
$941$	−48013.8	−1.66334	−0.831672	−	0.555268i	$-0.812616\pi$
$941$	−48013.8	−1.66334	−0.831672	+	0.555268i	$0.812616\pi$
$942$	−23954.5	−0.828533
$943$	16070.3	0.554955
$944$	−125651.	−4.33219
$945$	22484.4	0.773986
$946$	3383.68	0.116293
$947$	48383.6	1.66025	0.830124	−	0.557579i	$-0.188270\pi$
$947$	48383.6	1.66025	0.830124	+	0.557579i	$0.188270\pi$
$948$	37887.7	1.29803
$949$	76040.0	2.60102
$950$	2844.77	0.0971542
$951$	−31691.3	−1.08061
$952$	−82601.7	−2.81212
$953$	21420.9	0.728111	0.364056	−	0.931377i	$-0.381392\pi$
$953$	21420.9	0.728111	0.364056	+	0.931377i	$0.381392\pi$
$954$	−52696.9	−1.78839
$955$	−31448.4	−1.06560
$956$	35182.6	1.19026
$957$	854.759	0.0288719
$958$	−7909.60	−0.266751
$959$	−4111.90	−0.138457
$960$	−23350.9	−0.785048
$961$	−23373.7	−0.784590
$962$	−15477.6	−0.518730
$963$	22605.0	0.756425
$964$	−75544.9	−2.52400
$965$	−12128.0	−0.404575
$966$	−11943.7	−0.397807
$967$	27808.7	0.924786	0.462393	−	0.886675i	$-0.346991\pi$
$967$	27808.7	0.924786	0.462393	+	0.886675i	$0.346991\pi$
$968$	−83749.1	−2.78078
$969$	3008.39	0.0997350
$970$	−56027.1	−1.85456
$971$	30783.5	1.01739	0.508697	−	0.860946i	$-0.330127\pi$
$971$	30783.5	1.01739	0.508697	+	0.860946i	$0.330127\pi$
$972$	78184.9	2.58002
$973$	57435.4	1.89239
$974$	77940.4	2.56404
$975$	−7722.89	−0.253672
$976$	123413.	4.04750
$977$	−55303.0	−1.81095	−0.905476	−	0.424398i	$-0.860486\pi$
$977$	−55303.0	−1.81095	−0.905476	+	0.424398i	$0.860486\pi$
$978$	−49926.1	−1.63237
$979$	−5308.37	−0.173296
$980$	3343.60	0.108987
$981$	22985.9	0.748098
$982$	58832.3	1.91183
$983$	−44404.1	−1.44077	−0.720383	−	0.693577i	$-0.756034\pi$
$983$	−44404.1	−1.44077	−0.720383	+	0.693577i	$0.756034\pi$
$984$	−71149.0	−2.30503
$985$	1838.91	0.0594848
$986$	27200.8	0.878551
$987$	15250.9	0.491836
$988$	−19662.2	−0.633135
$989$	6683.15	0.214875
$990$	−3670.87	−0.117846
$991$	20571.6	0.659412	0.329706	−	0.944084i	$-0.393050\pi$
$991$	20571.6	0.659412	0.329706	+	0.944084i	$0.393050\pi$
$992$	34267.3	1.09676
$993$	22290.8	0.712362
$994$	−11458.4	−0.365633
$995$	−46719.8	−1.48856
$996$	−61212.4	−1.94738
$997$	18008.7	0.572057	0.286029	−	0.958221i	$-0.407665\pi$
$997$	18008.7	0.572057	0.286029	+	0.958221i	$0.407665\pi$
$998$	33922.5	1.07595
$999$	5645.62	0.178798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.b.1.27	✓	27
3.2	odd	2		1773.4.a.d.1.1		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.b.1.27	✓	27	1.1	even	1	trivial
1773.4.a.d.1.1		27	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q+5.29462 q^{2} +2.94855 q^{3} +20.0330 q^{4} -9.33457 q^{5} +15.6115 q^{6} +18.0311 q^{7} +63.7099 q^{8} -18.3060 q^{9} -49.4229 q^{10} -4.05739 q^{11} +59.0683 q^{12} +69.1707 q^{13} +95.4676 q^{14} -27.5235 q^{15} +177.056 q^{16} -71.9052 q^{17} -96.9234 q^{18} -14.1894 q^{19} -186.999 q^{20} +53.1656 q^{21} -21.4823 q^{22} -42.4299 q^{23} +187.852 q^{24} -37.8659 q^{25} +366.233 q^{26} -133.587 q^{27} +361.216 q^{28} -71.4476 q^{29} -145.726 q^{30} +80.1079 q^{31} +427.764 q^{32} -11.9634 q^{33} -380.710 q^{34} -168.312 q^{35} -366.724 q^{36} -42.2617 q^{37} -75.1275 q^{38} +203.954 q^{39} -594.705 q^{40} -378.750 q^{41} +281.492 q^{42} -157.510 q^{43} -81.2815 q^{44} +170.879 q^{45} -224.650 q^{46} +286.857 q^{47} +522.059 q^{48} -17.8803 q^{49} -200.485 q^{50} -212.016 q^{51} +1385.70 q^{52} +543.696 q^{53} -707.293 q^{54} +37.8740 q^{55} +1148.76 q^{56} -41.8382 q^{57} -378.288 q^{58} -709.668 q^{59} -551.377 q^{60} +697.029 q^{61} +424.141 q^{62} -330.077 q^{63} +848.398 q^{64} -645.679 q^{65} -63.3418 q^{66} -148.766 q^{67} -1440.47 q^{68} -125.107 q^{69} -891.149 q^{70} -120.024 q^{71} -1166.28 q^{72} +1099.31 q^{73} -223.759 q^{74} -111.650 q^{75} -284.256 q^{76} -73.1591 q^{77} +1079.86 q^{78} +641.422 q^{79} -1652.74 q^{80} +100.373 q^{81} -2005.34 q^{82} -1036.30 q^{83} +1065.06 q^{84} +671.203 q^{85} -833.956 q^{86} -210.667 q^{87} -258.496 q^{88} +1308.32 q^{89} +904.738 q^{90} +1247.22 q^{91} -849.997 q^{92} +236.203 q^{93} +1518.80 q^{94} +132.452 q^{95} +1261.29 q^{96} +1133.62 q^{97} -94.6693 q^{98} +74.2747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100}) \) 27 * q + 4 * q^2 + 32 * q^3 + 128 * q^4 + 29 * q^5 + 36 * q^6 + 122 * q^7 + 27 * q^8 + 287 * q^9 + 127 * q^10 + 98 * q^11 + 256 * q^12 + 193 * q^13 + 113 * q^14 + 194 * q^15 + 672 * q^16 + 124 * q^17 + 61 * q^18 + 535 * q^19 + 279 * q^20 + 188 * q^21 + 165 * q^22 + 344 * q^23 + 165 * q^24 + 910 * q^25 - 44 * q^26 + 1382 * q^27 + 1038 * q^28 + 346 * q^29 + 115 * q^30 + 599 * q^31 + 100 * q^32 + 794 * q^33 + 886 * q^34 + 12 * q^35 + 1714 * q^36 + 1428 * q^37 + 1108 * q^38 + 568 * q^39 + 1206 * q^40 + 549 * q^41 + 355 * q^42 + 2091 * q^43 + 586 * q^44 + 1167 * q^45 + 469 * q^46 + 1270 * q^47 + 2258 * q^48 + 2165 * q^49 - 353 * q^50 - 128 * q^51 + 1000 * q^52 - 208 * q^53 - 2945 * q^54 + 810 * q^55 - 5592 * q^56 - 1006 * q^57 + 287 * q^58 + 603 * q^59 - 2211 * q^60 - 314 * q^61 - 1347 * q^62 + 2416 * q^63 + 5 * q^64 - 1958 * q^65 - 8706 * q^66 + 4372 * q^67 - 6709 * q^68 - 306 * q^69 - 4329 * q^70 - 871 * q^71 - 7589 * q^72 + 942 * q^73 - 5237 * q^74 - 1530 * q^75 - 2470 * q^76 - 1868 * q^77 - 10179 * q^78 - 197 * q^79 - 1882 * q^80 + 1083 * q^81 - 961 * q^82 - 799 * q^83 - 3140 * q^84 - 1444 * q^85 - 7066 * q^86 - 794 * q^87 - 2409 * q^88 - 572 * q^89 - 10939 * q^90 + 3872 * q^91 - 6154 * q^92 - 1506 * q^93 + 1231 * q^94 - 756 * q^95 - 10975 * q^96 + 6335 * q^97 - 5330 * q^98 + 1940 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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