LMFDB - Embedded newform 2671.2.a.b.1.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.57809 q^{2} -3.26225 q^{3} +0.490374 q^{4} +1.75402 q^{5} +5.14812 q^{6} -4.57822 q^{7} +2.38233 q^{8} +7.64225 q^{9} +O(q^{10})$	\(q-1.57809 q^{2} -3.26225 q^{3} +0.490374 q^{4} +1.75402 q^{5} +5.14812 q^{6} -4.57822 q^{7} +2.38233 q^{8} +7.64225 q^{9} -2.76801 q^{10} -3.30987 q^{11} -1.59972 q^{12} -4.85355 q^{13} +7.22485 q^{14} -5.72206 q^{15} -4.74028 q^{16} +5.91332 q^{17} -12.0602 q^{18} +5.00340 q^{19} +0.860127 q^{20} +14.9353 q^{21} +5.22329 q^{22} -6.05137 q^{23} -7.77174 q^{24} -1.92340 q^{25} +7.65935 q^{26} -15.1442 q^{27} -2.24504 q^{28} -1.14495 q^{29} +9.02993 q^{30} +0.334227 q^{31} +2.71594 q^{32} +10.7976 q^{33} -9.33175 q^{34} -8.03031 q^{35} +3.74756 q^{36} +5.34195 q^{37} -7.89582 q^{38} +15.8335 q^{39} +4.17866 q^{40} -3.22586 q^{41} -23.5692 q^{42} +5.43550 q^{43} -1.62308 q^{44} +13.4047 q^{45} +9.54962 q^{46} -4.51196 q^{47} +15.4640 q^{48} +13.9601 q^{49} +3.03530 q^{50} -19.2907 q^{51} -2.38006 q^{52} -14.1105 q^{53} +23.8989 q^{54} -5.80560 q^{55} -10.9068 q^{56} -16.3223 q^{57} +1.80684 q^{58} -5.94093 q^{59} -2.80595 q^{60} -9.41839 q^{61} -0.527441 q^{62} -34.9879 q^{63} +5.19456 q^{64} -8.51325 q^{65} -17.0396 q^{66} +3.98765 q^{67} +2.89973 q^{68} +19.7411 q^{69} +12.6726 q^{70} -1.79621 q^{71} +18.2064 q^{72} -8.95577 q^{73} -8.43008 q^{74} +6.27460 q^{75} +2.45353 q^{76} +15.1533 q^{77} -24.9867 q^{78} -15.7932 q^{79} -8.31457 q^{80} +26.4772 q^{81} +5.09070 q^{82} -14.1456 q^{83} +7.32387 q^{84} +10.3721 q^{85} -8.57772 q^{86} +3.73512 q^{87} -7.88521 q^{88} +16.1259 q^{89} -21.1538 q^{90} +22.2206 q^{91} -2.96743 q^{92} -1.09033 q^{93} +7.12029 q^{94} +8.77608 q^{95} -8.86007 q^{96} -16.7400 q^{97} -22.0303 q^{98} -25.2949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.57809	−1.11588	−0.557940	−	0.829881i	$-0.688408\pi$
$2$	−1.57809	−1.11588	−0.557940	+	0.829881i	$0.688408\pi$
$3$	−3.26225	−1.88346	−0.941729	−	0.336372i	$-0.890800\pi$
$3$	−3.26225	−1.88346	−0.941729	+	0.336372i	$0.890800\pi$
$4$	0.490374	0.245187
$5$	1.75402	0.784424	0.392212	−	0.919875i	$-0.371710\pi$
$5$	1.75402	0.784424	0.392212	+	0.919875i	$0.371710\pi$
$6$	5.14812	2.10171
$7$	−4.57822	−1.73040	−0.865202	−	0.501423i	$-0.832810\pi$
$7$	−4.57822	−1.73040	−0.865202	+	0.501423i	$0.832810\pi$
$8$	2.38233	0.842280
$9$	7.64225	2.54742
$10$	−2.76801	−0.875322
$11$	−3.30987	−0.997965	−0.498982	−	0.866612i	$-0.666293\pi$
$11$	−3.30987	−0.997965	−0.498982	+	0.866612i	$0.666293\pi$
$12$	−1.59972	−0.461799
$13$	−4.85355	−1.34613	−0.673067	−	0.739582i	$-0.735023\pi$
$13$	−4.85355	−1.34613	−0.673067	+	0.739582i	$0.735023\pi$
$14$	7.22485	1.93092
$15$	−5.72206	−1.47743
$16$	−4.74028	−1.18507
$17$	5.91332	1.43419	0.717095	−	0.696976i	$-0.245471\pi$
$17$	5.91332	1.43419	0.717095	+	0.696976i	$0.245471\pi$
$18$	−12.0602	−2.84261
$19$	5.00340	1.14786	0.573929	−	0.818905i	$-0.305419\pi$
$19$	5.00340	1.14786	0.573929	+	0.818905i	$0.305419\pi$
$20$	0.860127	0.192330
$21$	14.9353	3.25914
$22$	5.22329	1.11361
$23$	−6.05137	−1.26180	−0.630899	−	0.775865i	$-0.717314\pi$
$23$	−6.05137	−1.26180	−0.630899	+	0.775865i	$0.717314\pi$
$24$	−7.77174	−1.58640
$25$	−1.92340	−0.384680
$26$	7.65935	1.50212
$27$	−15.1442	−2.91450
$28$	−2.24504	−0.424272
$29$	−1.14495	−0.212613	−0.106306	−	0.994333i	$-0.533902\pi$
$29$	−1.14495	−0.212613	−0.106306	+	0.994333i	$0.533902\pi$
$30$	9.02993	1.64863
$31$	0.334227	0.0600289	0.0300145	−	0.999549i	$-0.490445\pi$
$31$	0.334227	0.0600289	0.0300145	+	0.999549i	$0.490445\pi$
$32$	2.71594	0.480115
$33$	10.7976	1.87963
$34$	−9.33175	−1.60038
$35$	−8.03031	−1.35737
$36$	3.74756	0.624593
$37$	5.34195	0.878211	0.439105	−	0.898436i	$-0.355295\pi$
$37$	5.34195	0.878211	0.439105	+	0.898436i	$0.355295\pi$
$38$	−7.89582	−1.28087
$39$	15.8335	2.53539
$40$	4.17866	0.660705
$41$	−3.22586	−0.503794	−0.251897	−	0.967754i	$-0.581054\pi$
$41$	−3.22586	−0.503794	−0.251897	+	0.967754i	$0.581054\pi$
$42$	−23.5692	−3.63681
$43$	5.43550	0.828906	0.414453	−	0.910071i	$-0.363973\pi$
$43$	5.43550	0.828906	0.414453	+	0.910071i	$0.363973\pi$
$44$	−1.62308	−0.244688
$45$	13.4047	1.99825
$46$	9.54962	1.40802
$47$	−4.51196	−0.658138	−0.329069	−	0.944306i	$-0.606735\pi$
$47$	−4.51196	−0.658138	−0.329069	+	0.944306i	$0.606735\pi$
$48$	15.4640	2.23203
$49$	13.9601	1.99430
$50$	3.03530	0.429256
$51$	−19.2907	−2.70124
$52$	−2.38006	−0.330054
$53$	−14.1105	−1.93823	−0.969113	−	0.246617i	$-0.920681\pi$
$53$	−14.1105	−1.93823	−0.969113	+	0.246617i	$0.920681\pi$
$54$	23.8989	3.25223
$55$	−5.80560	−0.782827
$56$	−10.9068	−1.45749
$57$	−16.3223	−2.16194
$58$	1.80684	0.237250
$59$	−5.94093	−0.773443	−0.386722	−	0.922197i	$-0.626393\pi$
$59$	−5.94093	−0.773443	−0.386722	+	0.922197i	$0.626393\pi$
$60$	−2.80595	−0.362246
$61$	−9.41839	−1.20590	−0.602951	−	0.797779i	$-0.706008\pi$
$61$	−9.41839	−1.20590	−0.602951	+	0.797779i	$0.706008\pi$
$62$	−0.527441	−0.0669850
$63$	−34.9879	−4.40806
$64$	5.19456	0.649320
$65$	−8.51325	−1.05594
$66$	−17.0396	−2.09744
$67$	3.98765	0.487169	0.243584	−	0.969880i	$-0.421677\pi$
$67$	3.98765	0.487169	0.243584	+	0.969880i	$0.421677\pi$
$68$	2.89973	0.351644
$69$	19.7411	2.37655
$70$	12.6726	1.51466
$71$	−1.79621	−0.213171	−0.106585	−	0.994304i	$-0.533992\pi$
$71$	−1.79621	−0.213171	−0.106585	+	0.994304i	$0.533992\pi$
$72$	18.2064	2.14564
$73$	−8.95577	−1.04819	−0.524097	−	0.851659i	$-0.675597\pi$
$73$	−8.95577	−1.04819	−0.524097	+	0.851659i	$0.675597\pi$
$74$	−8.43008	−0.979977
$75$	6.27460	0.724528
$76$	2.45353	0.281440
$77$	15.1533	1.72688
$78$	−24.9867	−2.82919
$79$	−15.7932	−1.77687	−0.888437	−	0.458998i	$-0.848208\pi$
$79$	−15.7932	−1.77687	−0.888437	+	0.458998i	$0.848208\pi$
$80$	−8.31457	−0.929597
$81$	26.4772	2.94192
$82$	5.09070	0.562173
$83$	−14.1456	−1.55268	−0.776338	−	0.630317i	$-0.782925\pi$
$83$	−14.1456	−1.55268	−0.776338	+	0.630317i	$0.782925\pi$
$84$	7.32387	0.799099
$85$	10.3721	1.12501
$86$	−8.57772	−0.924960
$87$	3.73512	0.400447
$88$	−7.88521	−0.840566
$89$	16.1259	1.70934	0.854669	−	0.519173i	$-0.173760\pi$
$89$	16.1259	1.70934	0.854669	+	0.519173i	$0.173760\pi$
$90$	−21.1538	−2.22981
$91$	22.2206	2.32936
$92$	−2.96743	−0.309376
$93$	−1.09033	−0.113062
$94$	7.12029	0.734402
$95$	8.77608	0.900407
$96$	−8.86007	−0.904277
$97$	−16.7400	−1.69969	−0.849847	−	0.527030i	$-0.823306\pi$
$97$	−16.7400	−1.69969	−0.849847	+	0.527030i	$0.823306\pi$
$98$	−22.0303	−2.22540
$99$	−25.2949	−2.54223
$100$	−0.943184	−0.0943184
$101$	−12.0492	−1.19894	−0.599471	−	0.800396i	$-0.704623\pi$
$101$	−12.0492	−1.19894	−0.599471	+	0.800396i	$0.704623\pi$
$102$	30.4425	3.01425
$103$	−0.842821	−0.0830457	−0.0415228	−	0.999138i	$-0.513221\pi$
$103$	−0.842821	−0.0830457	−0.0415228	+	0.999138i	$0.513221\pi$
$104$	−11.5628	−1.13382
$105$	26.1968	2.55655
$106$	22.2677	2.16283
$107$	4.62718	0.447326	0.223663	−	0.974667i	$-0.428198\pi$
$107$	4.62718	0.447326	0.223663	+	0.974667i	$0.428198\pi$
$108$	−7.42630	−0.714596
$109$	11.3913	1.09109	0.545545	−	0.838081i	$-0.316323\pi$
$109$	11.3913	1.09109	0.545545	+	0.838081i	$0.316323\pi$
$110$	9.16177	0.873541
$111$	−17.4267	−1.65407
$112$	21.7020	2.05065
$113$	−10.7592	−1.01214	−0.506072	−	0.862491i	$-0.668903\pi$
$113$	−10.7592	−1.01214	−0.506072	+	0.862491i	$0.668903\pi$
$114$	25.7581	2.41247
$115$	−10.6143	−0.989784
$116$	−0.561455	−0.0521298
$117$	−37.0921	−3.42916
$118$	9.37533	0.863069
$119$	−27.0725	−2.48173
$120$	−13.6318	−1.24441
$121$	−0.0447306	−0.00406642
$122$	14.8631	1.34564
$123$	10.5235	0.948875
$124$	0.163896	0.0147183
$125$	−12.1438	−1.08618
$126$	55.2141	4.91886
$127$	−16.5307	−1.46686	−0.733429	−	0.679766i	$-0.762081\pi$
$127$	−16.5307	−1.46686	−0.733429	+	0.679766i	$0.762081\pi$
$128$	−13.6294	−1.20468
$129$	−17.7319	−1.56121
$130$	13.4347	1.17830
$131$	6.70495	0.585814	0.292907	−	0.956141i	$-0.405377\pi$
$131$	6.70495	0.585814	0.292907	+	0.956141i	$0.405377\pi$
$132$	5.29487	0.460859
$133$	−22.9066	−1.98626
$134$	−6.29287	−0.543621
$135$	−26.5632	−2.28620
$136$	14.0875	1.20799
$137$	10.8289	0.925177	0.462588	−	0.886573i	$-0.346921\pi$
$137$	10.8289	0.925177	0.462588	+	0.886573i	$0.346921\pi$
$138$	−31.1532	−2.65194
$139$	−1.95959	−0.166210	−0.0831052	−	0.996541i	$-0.526484\pi$
$139$	−1.95959	−0.166210	−0.0831052	+	0.996541i	$0.526484\pi$
$140$	−3.93785	−0.332809
$141$	14.7191	1.23958
$142$	2.83458	0.237873
$143$	16.0647	1.34339
$144$	−36.2264	−3.01887
$145$	−2.00828	−0.166778
$146$	14.1330	1.16966
$147$	−45.5412	−3.75618
$148$	2.61955	0.215326
$149$	3.90362	0.319797	0.159898	−	0.987133i	$-0.448883\pi$
$149$	3.90362	0.319797	0.159898	+	0.987133i	$0.448883\pi$
$150$	−9.90189	−0.808486
$151$	12.4152	1.01034	0.505169	−	0.863021i	$-0.331430\pi$
$151$	12.4152	1.01034	0.505169	+	0.863021i	$0.331430\pi$
$152$	11.9197	0.966818
$153$	45.1910	3.65348
$154$	−23.9133	−1.92699
$155$	0.586242	0.0470881
$156$	7.76433	0.621644
$157$	14.2051	1.13369	0.566847	−	0.823823i	$-0.308163\pi$
$157$	14.2051	1.13369	0.566847	+	0.823823i	$0.308163\pi$
$158$	24.9231	1.98278
$159$	46.0319	3.65057
$160$	4.76383	0.376614
$161$	27.7045	2.18342
$162$	−41.7835	−3.28282
$163$	−20.9932	−1.64432	−0.822159	−	0.569258i	$-0.807231\pi$
$163$	−20.9932	−1.64432	−0.822159	+	0.569258i	$0.807231\pi$
$164$	−1.58187	−0.123524
$165$	18.9393	1.47442
$166$	22.3230	1.73260
$167$	14.7732	1.14319	0.571593	−	0.820538i	$-0.306326\pi$
$167$	14.7732	1.14319	0.571593	+	0.820538i	$0.306326\pi$
$168$	35.5807	2.74511
$169$	10.5570	0.812076
$170$	−16.3681	−1.25538
$171$	38.2372	2.92407
$172$	2.66543	0.203237
$173$	3.43212	0.260939	0.130469	−	0.991452i	$-0.458352\pi$
$173$	3.43212	0.260939	0.130469	+	0.991452i	$0.458352\pi$
$174$	−5.89436	−0.446851
$175$	8.80574	0.665651
$176$	15.6897	1.18266
$177$	19.3808	1.45675
$178$	−25.4481	−1.90742
$179$	−1.24768	−0.0932557	−0.0466278	−	0.998912i	$-0.514847\pi$
$179$	−1.24768	−0.0932557	−0.0466278	+	0.998912i	$0.514847\pi$
$180$	6.57331	0.489946
$181$	−7.52330	−0.559203	−0.279601	−	0.960116i	$-0.590202\pi$
$181$	−7.52330	−0.559203	−0.279601	+	0.960116i	$0.590202\pi$
$182$	−35.0662	−2.59928
$183$	30.7251	2.27126
$184$	−14.4164	−1.06279
$185$	9.36990	0.688889
$186$	1.72064	0.126164
$187$	−19.5723	−1.43127
$188$	−2.21255	−0.161367
$189$	69.3333	5.04325
$190$	−13.8495	−1.00475
$191$	11.0510	0.799622	0.399811	−	0.916598i	$-0.369076\pi$
$191$	11.0510	0.799622	0.399811	+	0.916598i	$0.369076\pi$
$192$	−16.9459	−1.22297
$193$	19.3693	1.39423	0.697115	−	0.716959i	$-0.254467\pi$
$193$	19.3693	1.39423	0.697115	+	0.716959i	$0.254467\pi$
$194$	26.4173	1.89665
$195$	27.7723	1.98882
$196$	6.84566	0.488976
$197$	−1.12271	−0.0799896	−0.0399948	−	0.999200i	$-0.512734\pi$
$197$	−1.12271	−0.0799896	−0.0399948	+	0.999200i	$0.512734\pi$
$198$	39.9177	2.83682
$199$	18.6926	1.32508	0.662540	−	0.749026i	$-0.269478\pi$
$199$	18.6926	1.32508	0.662540	+	0.749026i	$0.269478\pi$
$200$	−4.58217	−0.324008
$201$	−13.0087	−0.917562
$202$	19.0148	1.33788
$203$	5.24185	0.367906
$204$	−9.45965	−0.662308
$205$	−5.65823	−0.395188
$206$	1.33005	0.0926689
$207$	−46.2461	−3.21433
$208$	23.0072	1.59526
$209$	−16.5606	−1.14552
$210$	−41.3410	−2.85280
$211$	6.64967	0.457782	0.228891	−	0.973452i	$-0.426490\pi$
$211$	6.64967	0.457782	0.228891	+	0.973452i	$0.426490\pi$
$212$	−6.91942	−0.475228
$213$	5.85967	0.401498
$214$	−7.30211	−0.499162
$215$	9.53400	0.650214
$216$	−36.0784	−2.45482
$217$	−1.53016	−0.103874
$218$	−17.9765	−1.21753
$219$	29.2159	1.97423
$220$	−2.84691	−0.191939
$221$	−28.7006	−1.93061
$222$	27.5010	1.84575
$223$	18.7417	1.25503	0.627517	−	0.778603i	$-0.284071\pi$
$223$	18.7417	1.25503	0.627517	+	0.778603i	$0.284071\pi$
$224$	−12.4342	−0.830793
$225$	−14.6991	−0.979940
$226$	16.9791	1.12943
$227$	8.41415	0.558467	0.279233	−	0.960223i	$-0.409920\pi$
$227$	8.41415	0.558467	0.279233	+	0.960223i	$0.409920\pi$
$228$	−8.00403	−0.530080
$229$	−12.1206	−0.800953	−0.400477	−	0.916307i	$-0.631155\pi$
$229$	−12.1206	−0.800953	−0.400477	+	0.916307i	$0.631155\pi$
$230$	16.7503	1.10448
$231$	−49.4339	−3.25251
$232$	−2.72766	−0.179079
$233$	−9.80022	−0.642034	−0.321017	−	0.947074i	$-0.604025\pi$
$233$	−9.80022	−0.642034	−0.321017	+	0.947074i	$0.604025\pi$
$234$	58.5347	3.82653
$235$	−7.91410	−0.516259
$236$	−2.91328	−0.189638
$237$	51.5213	3.34667
$238$	42.7228	2.76931
$239$	−0.371294	−0.0240170	−0.0120085	−	0.999928i	$-0.503823\pi$
$239$	−0.371294	−0.0240170	−0.0120085	+	0.999928i	$0.503823\pi$
$240$	27.1242	1.75086
$241$	11.4092	0.734931	0.367466	−	0.930037i	$-0.380226\pi$
$241$	11.4092	0.734931	0.367466	+	0.930037i	$0.380226\pi$
$242$	0.0705890	0.00453763
$243$	−40.9428	−2.62648
$244$	−4.61853	−0.295671
$245$	24.4863	1.56437
$246$	−16.6071	−1.05883
$247$	−24.2843	−1.54517
$248$	0.796238	0.0505612
$249$	46.1463	2.92440
$250$	19.1640	1.21204
$251$	17.5664	1.10878	0.554391	−	0.832256i	$-0.312951\pi$
$251$	17.5664	1.10878	0.554391	+	0.832256i	$0.312951\pi$
$252$	−17.1571	−1.08080
$253$	20.0293	1.25923
$254$	26.0869	1.63684
$255$	−33.8363	−2.11891
$256$	11.1193	0.694955
$257$	−0.767498	−0.0478752	−0.0239376	−	0.999713i	$-0.507620\pi$
$257$	−0.767498	−0.0478752	−0.0239376	+	0.999713i	$0.507620\pi$
$258$	27.9826	1.74212
$259$	−24.4566	−1.51966
$260$	−4.17468	−0.258902
$261$	−8.75002	−0.541613
$262$	−10.5810	−0.653698
$263$	8.07374	0.497848	0.248924	−	0.968523i	$-0.419923\pi$
$263$	8.07374	0.497848	0.248924	+	0.968523i	$0.419923\pi$
$264$	25.7235	1.58317
$265$	−24.7502	−1.52039
$266$	36.1488	2.21642
$267$	−52.6065	−3.21947
$268$	1.95544	0.119447
$269$	21.0537	1.28367	0.641835	−	0.766843i	$-0.278174\pi$
$269$	21.0537	1.28367	0.641835	+	0.766843i	$0.278174\pi$
$270$	41.9192	2.55112
$271$	−26.7179	−1.62300	−0.811498	−	0.584356i	$-0.801347\pi$
$271$	−26.7179	−1.62300	−0.811498	+	0.584356i	$0.801347\pi$
$272$	−28.0308	−1.69962
$273$	−72.4892	−4.38724
$274$	−17.0890	−1.03239
$275$	6.36621	0.383897
$276$	9.68050	0.582698
$277$	22.6444	1.36057	0.680285	−	0.732948i	$-0.261856\pi$
$277$	22.6444	1.36057	0.680285	+	0.732948i	$0.261856\pi$
$278$	3.09242	0.185471
$279$	2.55425	0.152919
$280$	−19.1308	−1.14329
$281$	21.9713	1.31070	0.655348	−	0.755327i	$-0.272522\pi$
$281$	21.9713	1.31070	0.655348	+	0.755327i	$0.272522\pi$
$282$	−23.2282	−1.38322
$283$	−13.9224	−0.827603	−0.413801	−	0.910367i	$-0.635799\pi$
$283$	−13.9224	−0.827603	−0.413801	+	0.910367i	$0.635799\pi$
$284$	−0.880813	−0.0522666
$285$	−28.6297	−1.69588
$286$	−25.3515	−1.49907
$287$	14.7687	0.871767
$288$	20.7559	1.22305
$289$	17.9673	1.05690
$290$	3.16925	0.186105
$291$	54.6101	3.20130
$292$	−4.39167	−0.257003
$293$	−17.7734	−1.03834	−0.519168	−	0.854672i	$-0.673758\pi$
$293$	−17.7734	−1.03834	−0.519168	+	0.854672i	$0.673758\pi$
$294$	71.8683	4.19144
$295$	−10.4205	−0.606707
$296$	12.7263	0.739700
$297$	50.1253	2.90856
$298$	−6.16027	−0.356855
$299$	29.3707	1.69855
$300$	3.07690	0.177645
$301$	−24.8849	−1.43434
$302$	−19.5924	−1.12741
$303$	39.3075	2.25816
$304$	−23.7175	−1.36029
$305$	−16.5201	−0.945937
$306$	−71.3156	−4.07684
$307$	−16.4024	−0.936134	−0.468067	−	0.883693i	$-0.655049\pi$
$307$	−16.4024	−0.936134	−0.468067	+	0.883693i	$0.655049\pi$
$308$	7.43079	0.423409
$309$	2.74949	0.156413
$310$	−0.925144	−0.0525446
$311$	−0.0898297	−0.00509377	−0.00254689	−	0.999997i	$-0.500811\pi$
$311$	−0.0898297	−0.00509377	−0.00254689	+	0.999997i	$0.500811\pi$
$312$	37.7206	2.13551
$313$	11.7919	0.666517	0.333259	−	0.942835i	$-0.391852\pi$
$313$	11.7919	0.666517	0.333259	+	0.942835i	$0.391852\pi$
$314$	−22.4170	−1.26507
$315$	−61.3696	−3.45779
$316$	−7.74457	−0.435666
$317$	0.848362	0.0476488	0.0238244	−	0.999716i	$-0.492416\pi$
$317$	0.848362	0.0476488	0.0238244	+	0.999716i	$0.492416\pi$
$318$	−72.6426	−4.07359
$319$	3.78965	0.212180
$320$	9.11138	0.509342
$321$	−15.0950	−0.842521
$322$	−43.7203	−2.43643
$323$	29.5867	1.64625
$324$	12.9837	0.721319
$325$	9.33532	0.517830
$326$	33.1293	1.83486
$327$	−37.1613	−2.05502
$328$	−7.68505	−0.424336
$329$	20.6568	1.13884
$330$	−29.8880	−1.64528
$331$	−8.54449	−0.469648	−0.234824	−	0.972038i	$-0.575451\pi$
$331$	−8.54449	−0.469648	−0.234824	+	0.972038i	$0.575451\pi$
$332$	−6.93661	−0.380696
$333$	40.8245	2.23717
$334$	−23.3135	−1.27566
$335$	6.99443	0.382147
$336$	−70.7974	−3.86232
$337$	−19.4692	−1.06055	−0.530277	−	0.847824i	$-0.677912\pi$
$337$	−19.4692	−1.06055	−0.530277	+	0.847824i	$0.677912\pi$
$338$	−16.6599	−0.906179
$339$	35.0993	1.90633
$340$	5.08620	0.275838
$341$	−1.10625	−0.0599067
$342$	−60.3418	−3.26291
$343$	−31.8648	−1.72054
$344$	12.9492	0.698172
$345$	34.6263	1.86422
$346$	−5.41619	−0.291176
$347$	−23.6837	−1.27141	−0.635703	−	0.771934i	$-0.719290\pi$
$347$	−23.6837	−1.27141	−0.635703	+	0.771934i	$0.719290\pi$
$348$	1.83161	0.0981844
$349$	−19.2180	−1.02871	−0.514357	−	0.857576i	$-0.671970\pi$
$349$	−19.2180	−1.02871	−0.514357	+	0.857576i	$0.671970\pi$
$350$	−13.8963	−0.742787
$351$	73.5030	3.92330
$352$	−8.98942	−0.479138
$353$	−33.7685	−1.79732	−0.898658	−	0.438650i	$-0.855457\pi$
$353$	−33.7685	−1.79732	−0.898658	+	0.438650i	$0.855457\pi$
$354$	−30.5846	−1.62556
$355$	−3.15059	−0.167216
$356$	7.90770	0.419107
$357$	88.3170	4.67423
$358$	1.96895	0.104062
$359$	13.4617	0.710479	0.355239	−	0.934775i	$-0.384399\pi$
$359$	13.4617	0.710479	0.355239	+	0.934775i	$0.384399\pi$
$360$	31.9344	1.68309
$361$	6.03398	0.317578
$362$	11.8725	0.624003
$363$	0.145922	0.00765893
$364$	10.8964	0.571127
$365$	−15.7086	−0.822228
$366$	−48.4870	−2.53446
$367$	36.2169	1.89051	0.945253	−	0.326338i	$-0.105815\pi$
$367$	36.2169	1.89051	0.945253	+	0.326338i	$0.105815\pi$
$368$	28.6852	1.49532
$369$	−24.6528	−1.28337
$370$	−14.7866	−0.768717
$371$	64.6009	3.35391
$372$	−0.534669	−0.0277213
$373$	16.3885	0.848562	0.424281	−	0.905531i	$-0.360527\pi$
$373$	16.3885	0.848562	0.424281	+	0.905531i	$0.360527\pi$
$374$	30.8869	1.59713
$375$	39.6161	2.04577
$376$	−10.7490	−0.554337
$377$	5.55710	0.286205
$378$	−109.414	−5.62766
$379$	−21.9011	−1.12498	−0.562492	−	0.826802i	$-0.690157\pi$
$379$	−21.9011	−1.12498	−0.562492	+	0.826802i	$0.690157\pi$
$380$	4.30356	0.220768
$381$	53.9271	2.76277
$382$	−17.4395	−0.892281
$383$	−7.90382	−0.403866	−0.201933	−	0.979399i	$-0.564722\pi$
$383$	−7.90382	−0.403866	−0.201933	+	0.979399i	$0.564722\pi$
$384$	44.4624	2.26896
$385$	26.5793	1.35461
$386$	−30.5665	−1.55579
$387$	41.5395	2.11157
$388$	−8.20888	−0.416743
$389$	13.0908	0.663729	0.331864	−	0.943327i	$-0.392322\pi$
$389$	13.0908	0.663729	0.331864	+	0.943327i	$0.392322\pi$
$390$	−43.8273	−2.21928
$391$	−35.7837	−1.80966
$392$	33.2575	1.67976
$393$	−21.8732	−1.10336
$394$	1.77174	0.0892587
$395$	−27.7017	−1.39382
$396$	−12.4039	−0.623322
$397$	−5.34097	−0.268055	−0.134028	−	0.990978i	$-0.542791\pi$
$397$	−5.34097	−0.268055	−0.134028	+	0.990978i	$0.542791\pi$
$398$	−29.4986	−1.47863
$399$	74.7271	3.74103
$400$	9.11745	0.455873
$401$	4.91082	0.245235	0.122617	−	0.992454i	$-0.460871\pi$
$401$	4.91082	0.245235	0.122617	+	0.992454i	$0.460871\pi$
$402$	20.5289	1.02389
$403$	−1.62219	−0.0808070
$404$	−5.90862	−0.293965
$405$	46.4417	2.30771
$406$	−8.27212	−0.410538
$407$	−17.6812	−0.876423
$408$	−45.9568	−2.27520
$409$	3.73105	0.184488	0.0922442	−	0.995736i	$-0.470596\pi$
$409$	3.73105	0.184488	0.0922442	+	0.995736i	$0.470596\pi$
$410$	8.92920	0.440982
$411$	−35.3266	−1.74253
$412$	−0.413297	−0.0203617
$413$	27.1989	1.33837
$414$	72.9806	3.58680
$415$	−24.8116	−1.21796
$416$	−13.1820	−0.646299
$417$	6.39267	0.313050
$418$	26.1342	1.27826
$419$	5.59589	0.273377	0.136689	−	0.990614i	$-0.456354\pi$
$419$	5.59589	0.273377	0.136689	+	0.990614i	$0.456354\pi$
$420$	12.8462	0.626832
$421$	−16.1497	−0.787087	−0.393544	−	0.919306i	$-0.628751\pi$
$421$	−16.1497	−0.787087	−0.393544	+	0.919306i	$0.628751\pi$
$422$	−10.4938	−0.510830
$423$	−34.4816	−1.67655
$424$	−33.6158	−1.63253
$425$	−11.3737	−0.551704
$426$	−9.24710	−0.448023
$427$	43.1194	2.08670
$428$	2.26905	0.109679
$429$	−52.4069	−2.53023
$430$	−15.0455	−0.725560
$431$	−33.1628	−1.59740	−0.798699	−	0.601731i	$-0.794478\pi$
$431$	−33.1628	−1.59740	−0.798699	+	0.601731i	$0.794478\pi$
$432$	71.7876	3.45388
$433$	17.4773	0.839906	0.419953	−	0.907546i	$-0.362047\pi$
$433$	17.4773	0.839906	0.419953	+	0.907546i	$0.362047\pi$
$434$	2.41474	0.115911
$435$	6.55149	0.314120
$436$	5.58600	0.267521
$437$	−30.2774	−1.44837
$438$	−46.1054	−2.20300
$439$	−5.65634	−0.269963	−0.134981	−	0.990848i	$-0.543097\pi$
$439$	−5.65634	−0.269963	−0.134981	+	0.990848i	$0.543097\pi$
$440$	−13.8308	−0.659360
$441$	106.686	5.08031
$442$	45.2922	2.15433
$443$	−7.95604	−0.378003	−0.189001	−	0.981977i	$-0.560525\pi$
$443$	−7.95604	−0.378003	−0.189001	+	0.981977i	$0.560525\pi$
$444$	−8.54562	−0.405557
$445$	28.2852	1.34084
$446$	−29.5760	−1.40047
$447$	−12.7346	−0.602324
$448$	−23.7818	−1.12359
$449$	−30.9594	−1.46106	−0.730532	−	0.682879i	$-0.760728\pi$
$449$	−30.9594	−1.46106	−0.730532	+	0.682879i	$0.760728\pi$
$450$	23.1965	1.09349
$451$	10.6772	0.502769
$452$	−5.27605	−0.248164
$453$	−40.5016	−1.90293
$454$	−13.2783	−0.623182
$455$	38.9755	1.82720
$456$	−38.8851	−1.82096
$457$	27.5039	1.28658	0.643290	−	0.765622i	$-0.277569\pi$
$457$	27.5039	1.28658	0.643290	+	0.765622i	$0.277569\pi$
$458$	19.1275	0.893767
$459$	−89.5522	−4.17994
$460$	−5.20495	−0.242682
$461$	−18.4996	−0.861611	−0.430806	−	0.902445i	$-0.641771\pi$
$461$	−18.4996	−0.861611	−0.430806	+	0.902445i	$0.641771\pi$
$462$	78.0112	3.62941
$463$	24.4158	1.13470	0.567349	−	0.823477i	$-0.307969\pi$
$463$	24.4158	1.13470	0.567349	+	0.823477i	$0.307969\pi$
$464$	5.42740	0.251961
$465$	−1.91247	−0.0886885
$466$	15.4656	0.716432
$467$	12.0251	0.556454	0.278227	−	0.960515i	$-0.410253\pi$
$467$	12.0251	0.556454	0.278227	+	0.960515i	$0.410253\pi$
$468$	−18.1890	−0.840786
$469$	−18.2563	−0.842999
$470$	12.4892	0.576082
$471$	−46.3407	−2.13527
$472$	−14.1532	−0.651456
$473$	−17.9908	−0.827219
$474$	−81.3054	−3.73448
$475$	−9.62353	−0.441558
$476$	−13.2756	−0.608487
$477$	−107.836	−4.93747
$478$	0.585935	0.0268001
$479$	1.45417	0.0664426	0.0332213	−	0.999448i	$-0.489423\pi$
$479$	1.45417	0.0664426	0.0332213	+	0.999448i	$0.489423\pi$
$480$	−15.5408	−0.709336
$481$	−25.9274	−1.18219
$482$	−18.0048	−0.820095
$483$	−90.3789	−4.11238
$484$	−0.0219347	−0.000997032 0
$485$	−29.3624	−1.33328
$486$	64.6115	2.93084
$487$	33.1667	1.50293	0.751463	−	0.659775i	$-0.229348\pi$
$487$	33.1667	1.50293	0.751463	+	0.659775i	$0.229348\pi$
$488$	−22.4377	−1.01571
$489$	68.4851	3.09700
$490$	−38.6417	−1.74565
$491$	39.2796	1.77266	0.886332	−	0.463051i	$-0.153245\pi$
$491$	39.2796	1.77266	0.886332	+	0.463051i	$0.153245\pi$
$492$	5.16046	0.232652
$493$	−6.77047	−0.304927
$494$	38.3228	1.72422
$495$	−44.3678	−1.99419
$496$	−1.58433	−0.0711385
$497$	8.22343	0.368871
$498$	−72.8231	−3.26328
$499$	1.89976	0.0850451	0.0425226	−	0.999096i	$-0.486461\pi$
$499$	1.89976	0.0850451	0.0425226	+	0.999096i	$0.486461\pi$
$500$	−5.95501	−0.266316
$501$	−48.1938	−2.15314
$502$	−27.7214	−1.23727
$503$	11.5291	0.514058	0.257029	−	0.966404i	$-0.417256\pi$
$503$	11.5291	0.514058	0.257029	+	0.966404i	$0.417256\pi$
$504$	−83.3527	−3.71282
$505$	−21.1346	−0.940479
$506$	−31.6081	−1.40515
$507$	−34.4395	−1.52951
$508$	−8.10620	−0.359654
$509$	28.5578	1.26580	0.632902	−	0.774232i	$-0.281864\pi$
$509$	28.5578	1.26580	0.632902	+	0.774232i	$0.281864\pi$
$510$	53.3969	2.36445
$511$	41.0015	1.81380
$512$	9.71149	0.429191
$513$	−75.7723	−3.34543
$514$	1.21118	0.0534230
$515$	−1.47833	−0.0651430
$516$	−8.69528	−0.382788
$517$	14.9340	0.656798
$518$	38.5948	1.69576
$519$	−11.1964	−0.491468
$520$	−20.2814	−0.889397
$521$	−0.850199	−0.0372479	−0.0186240	−	0.999827i	$-0.505929\pi$
$521$	−0.850199	−0.0372479	−0.0186240	+	0.999827i	$0.505929\pi$
$522$	13.8083	0.604375
$523$	25.6198	1.12027	0.560137	−	0.828400i	$-0.310749\pi$
$523$	25.6198	1.12027	0.560137	+	0.828400i	$0.310749\pi$
$524$	3.28793	0.143634
$525$	−28.7265	−1.25373
$526$	−12.7411	−0.555538
$527$	1.97639	0.0860929
$528$	−51.1838	−2.22749
$529$	13.6191	0.592136
$530$	39.0580	1.69657
$531$	−45.4021	−1.97028
$532$	−11.2328	−0.487004
$533$	15.6569	0.678174
$534$	83.0179	3.59254
$535$	8.11618	0.350893
$536$	9.49989	0.410333
$537$	4.07023	0.175643
$538$	−33.2247	−1.43242
$539$	−46.2061	−1.99024
$540$	−13.0259	−0.560546
$541$	−3.81666	−0.164091	−0.0820454	−	0.996629i	$-0.526145\pi$
$541$	−3.81666	−0.164091	−0.0820454	+	0.996629i	$0.526145\pi$
$542$	42.1633	1.81107
$543$	24.5429	1.05324
$544$	16.0602	0.688576
$545$	19.9806	0.855877
$546$	114.395	4.89564
$547$	30.2495	1.29338	0.646688	−	0.762755i	$-0.276154\pi$
$547$	30.2495	1.29338	0.646688	+	0.762755i	$0.276154\pi$
$548$	5.31022	0.226841
$549$	−71.9777	−3.07193
$550$	−10.0465	−0.428383
$551$	−5.72866	−0.244049
$552$	47.0297	2.00172
$553$	72.3047	3.07471
$554$	−35.7349	−1.51823
$555$	−30.5669	−1.29749
$556$	−0.960932	−0.0407526
$557$	−24.2721	−1.02844	−0.514220	−	0.857658i	$-0.671919\pi$
$557$	−24.2721	−1.02844	−0.514220	+	0.857658i	$0.671919\pi$
$558$	−4.03083	−0.170639
$559$	−26.3815	−1.11582
$560$	38.0659	1.60858
$561$	63.8498	2.69574
$562$	−34.6727	−1.46258
$563$	21.3705	0.900661	0.450330	−	0.892862i	$-0.351306\pi$
$563$	21.3705	0.900661	0.450330	+	0.892862i	$0.351306\pi$
$564$	7.21788	0.303928
$565$	−18.8720	−0.793949
$566$	21.9709	0.923505
$567$	−121.219	−5.09070
$568$	−4.27916	−0.179549
$569$	33.3598	1.39852	0.699258	−	0.714870i	$-0.253514\pi$
$569$	33.3598	1.39852	0.699258	+	0.714870i	$0.253514\pi$
$570$	45.1803	1.89240
$571$	−6.59658	−0.276058	−0.138029	−	0.990428i	$-0.544077\pi$
$571$	−6.59658	−0.276058	−0.138029	+	0.990428i	$0.544077\pi$
$572$	7.87769	0.329383
$573$	−36.0511	−1.50605
$574$	−23.3063	−0.972787
$575$	11.6392	0.485388
$576$	39.6981	1.65409
$577$	−26.6680	−1.11020	−0.555101	−	0.831783i	$-0.687320\pi$
$577$	−26.6680	−1.11020	−0.555101	+	0.831783i	$0.687320\pi$
$578$	−28.3540	−1.17937
$579$	−63.1873	−2.62598
$580$	−0.984806	−0.0408919
$581$	64.7614	2.68676
$582$	−86.1798	−3.57227
$583$	46.7040	1.93428
$584$	−21.3356	−0.882873
$585$	−65.0604	−2.68992
$586$	28.0481	1.15866
$587$	24.9007	1.02776	0.513880	−	0.857862i	$-0.328207\pi$
$587$	24.9007	1.02776	0.513880	+	0.857862i	$0.328207\pi$
$588$	−22.3322	−0.920965
$589$	1.67227	0.0689047
$590$	16.4446	0.677012
$591$	3.66255	0.150657
$592$	−25.3223	−1.04074
$593$	25.9980	1.06761	0.533805	−	0.845608i	$-0.320762\pi$
$593$	25.9980	1.06761	0.533805	+	0.845608i	$0.320762\pi$
$594$	−79.1023	−3.24561
$595$	−47.4857	−1.94673
$596$	1.91423	0.0784100
$597$	−60.9797	−2.49573
$598$	−46.3496	−1.89538
$599$	35.3062	1.44257	0.721287	−	0.692637i	$-0.243551\pi$
$599$	35.3062	1.44257	0.721287	+	0.692637i	$0.243551\pi$
$600$	14.9482	0.610256
$601$	40.9734	1.67134	0.835671	−	0.549231i	$-0.185079\pi$
$601$	40.9734	1.67134	0.835671	+	0.549231i	$0.185079\pi$
$602$	39.2707	1.60055
$603$	30.4746	1.24102
$604$	6.08811	0.247722
$605$	−0.0784585	−0.00318979
$606$	−62.0309	−2.51983
$607$	−27.1536	−1.10213	−0.551066	−	0.834462i	$-0.685779\pi$
$607$	−27.1536	−1.10213	−0.551066	+	0.834462i	$0.685779\pi$
$608$	13.5889	0.551104
$609$	−17.1002	−0.692935
$610$	26.0702	1.05555
$611$	21.8991	0.885941
$612$	22.1605	0.895785
$613$	−29.1665	−1.17802	−0.589011	−	0.808125i	$-0.700483\pi$
$613$	−29.1665	−1.17802	−0.589011	+	0.808125i	$0.700483\pi$
$614$	25.8845	1.04461
$615$	18.4585	0.744320
$616$	36.1002	1.45452
$617$	−9.09491	−0.366147	−0.183074	−	0.983099i	$-0.558605\pi$
$617$	−9.09491	−0.366147	−0.183074	+	0.983099i	$0.558605\pi$
$618$	−4.33895	−0.174538
$619$	4.70485	0.189104	0.0945520	−	0.995520i	$-0.469858\pi$
$619$	4.70485	0.189104	0.0945520	+	0.995520i	$0.469858\pi$
$620$	0.287478	0.0115454
$621$	91.6430	3.67751
$622$	0.141759	0.00568404
$623$	−73.8277	−2.95785
$624$	−75.0552	−3.00461
$625$	−11.6835	−0.467342
$626$	−18.6087	−0.743753
$627$	54.0248	2.15754
$628$	6.96583	0.277967
$629$	31.5886	1.25952
$630$	96.8469	3.85847
$631$	39.0607	1.55498	0.777492	−	0.628893i	$-0.216492\pi$
$631$	39.0607	1.55498	0.777492	+	0.628893i	$0.216492\pi$
$632$	−37.6246	−1.49663
$633$	−21.6929	−0.862214
$634$	−1.33879	−0.0531703
$635$	−28.9952	−1.15064
$636$	22.5728	0.895072
$637$	−67.7560	−2.68459
$638$	−5.98042	−0.236767
$639$	−13.7271	−0.543034
$640$	−23.9062	−0.944977
$641$	−11.2938	−0.446078	−0.223039	−	0.974809i	$-0.571598\pi$
$641$	−11.2938	−0.446078	−0.223039	+	0.974809i	$0.571598\pi$
$642$	23.8213	0.940151
$643$	−11.7637	−0.463913	−0.231957	−	0.972726i	$-0.574513\pi$
$643$	−11.7637	−0.463913	−0.231957	+	0.972726i	$0.574513\pi$
$644$	13.5856	0.535346
$645$	−31.1023	−1.22465
$646$	−46.6905	−1.83701
$647$	−5.66524	−0.222724	−0.111362	−	0.993780i	$-0.535521\pi$
$647$	−5.66524	−0.222724	−0.111362	+	0.993780i	$0.535521\pi$
$648$	63.0775	2.47792
$649$	19.6637	0.771869
$650$	−14.7320	−0.577836
$651$	4.99177	0.195643
$652$	−10.2945	−0.403165
$653$	−7.55407	−0.295614	−0.147807	−	0.989016i	$-0.547221\pi$
$653$	−7.55407	−0.295614	−0.147807	+	0.989016i	$0.547221\pi$
$654$	58.6439	2.29316
$655$	11.7606	0.459526
$656$	15.2915	0.597031
$657$	−68.4422	−2.67019
$658$	−32.5983	−1.27081
$659$	−28.2988	−1.10237	−0.551183	−	0.834385i	$-0.685823\pi$
$659$	−28.2988	−1.10237	−0.551183	+	0.834385i	$0.685823\pi$
$660$	9.28733	0.361509
$661$	−18.5845	−0.722852	−0.361426	−	0.932401i	$-0.617710\pi$
$661$	−18.5845	−0.722852	−0.361426	+	0.932401i	$0.617710\pi$
$662$	13.4840	0.524070
$663$	93.6284	3.63623
$664$	−33.6994	−1.30779
$665$	−40.1788	−1.55807
$666$	−64.4248	−2.49641
$667$	6.92854	0.268274
$668$	7.24439	0.280294
$669$	−61.1399	−2.36380
$670$	−11.0379	−0.426429
$671$	31.1737	1.20345
$672$	40.5633	1.56476
$673$	37.0730	1.42906	0.714530	−	0.699605i	$-0.246641\pi$
$673$	37.0730	1.42906	0.714530	+	0.699605i	$0.246641\pi$
$674$	30.7242	1.18345
$675$	29.1283	1.12115
$676$	5.17687	0.199110
$677$	−9.51246	−0.365593	−0.182797	−	0.983151i	$-0.558515\pi$
$677$	−9.51246	−0.365593	−0.182797	+	0.983151i	$0.558515\pi$
$678$	−55.3899	−2.12724
$679$	76.6396	2.94116
$680$	24.7098	0.947576
$681$	−27.4490	−1.05185
$682$	1.74576	0.0668487
$683$	−3.89436	−0.149014	−0.0745068	−	0.997221i	$-0.523738\pi$
$683$	−3.89436	−0.149014	−0.0745068	+	0.997221i	$0.523738\pi$
$684$	18.7505	0.716944
$685$	18.9942	0.725730
$686$	50.2856	1.91991
$687$	39.5405	1.50856
$688$	−25.7658	−0.982312
$689$	68.4861	2.60911
$690$	−54.6435	−2.08024
$691$	16.2346	0.617594	0.308797	−	0.951128i	$-0.400074\pi$
$691$	16.2346	0.617594	0.308797	+	0.951128i	$0.400074\pi$
$692$	1.68302	0.0639788
$693$	115.806	4.39909
$694$	37.3750	1.41874
$695$	−3.43717	−0.130379
$696$	8.89829	0.337289
$697$	−19.0755	−0.722536
$698$	30.3277	1.14792
$699$	31.9707	1.20924
$700$	4.31810	0.163209
$701$	−5.98455	−0.226033	−0.113017	−	0.993593i	$-0.536051\pi$
$701$	−5.98455	−0.226033	−0.113017	+	0.993593i	$0.536051\pi$
$702$	−115.995	−4.37793
$703$	26.7279	1.00806
$704$	−17.1933	−0.647998
$705$	25.8177	0.972352
$706$	53.2898	2.00559
$707$	55.1640	2.07466
$708$	9.50382	0.357176
$709$	−47.3409	−1.77792	−0.888962	−	0.457980i	$-0.848573\pi$
$709$	−47.3409	−1.77792	−0.888962	+	0.457980i	$0.848573\pi$
$710$	4.97192	0.186593
$711$	−120.696	−4.52644
$712$	38.4171	1.43974
$713$	−2.02253	−0.0757444
$714$	−139.372	−5.21588
$715$	28.1778	1.05379
$716$	−0.611827	−0.0228651
$717$	1.21125	0.0452350
$718$	−21.2437	−0.792809
$719$	−22.2809	−0.830936	−0.415468	−	0.909608i	$-0.636382\pi$
$719$	−22.2809	−0.830936	−0.415468	+	0.909608i	$0.636382\pi$
$720$	−63.5420	−2.36807
$721$	3.85862	0.143703
$722$	−9.52217	−0.354379
$723$	−37.2196	−1.38421
$724$	−3.68923	−0.137109
$725$	2.20220	0.0817878
$726$	−0.230279	−0.00854644
$727$	−37.5848	−1.39394	−0.696972	−	0.717099i	$-0.745470\pi$
$727$	−37.5848	−1.39394	−0.696972	+	0.717099i	$0.745470\pi$
$728$	52.9369	1.96197
$729$	54.1337	2.00495
$730$	24.7897	0.917507
$731$	32.1418	1.18881
$732$	15.0668	0.556884
$733$	−15.2856	−0.564588	−0.282294	−	0.959328i	$-0.591095\pi$
$733$	−15.2856	−0.564588	−0.282294	+	0.959328i	$0.591095\pi$
$734$	−57.1536	−2.10958
$735$	−79.8804	−2.94643
$736$	−16.4352	−0.605809
$737$	−13.1986	−0.486177
$738$	38.9044	1.43209
$739$	−13.1782	−0.484769	−0.242384	−	0.970180i	$-0.577930\pi$
$739$	−13.1782	−0.484769	−0.242384	+	0.970180i	$0.577930\pi$
$740$	4.59476	0.168907
$741$	79.2212	2.91026
$742$	−101.946	−3.74256
$743$	−13.5671	−0.497729	−0.248865	−	0.968538i	$-0.580057\pi$
$743$	−13.5671	−0.497729	−0.248865	+	0.968538i	$0.580057\pi$
$744$	−2.59753	−0.0952299
$745$	6.84704	0.250856
$746$	−25.8625	−0.946893
$747$	−108.104	−3.95531
$748$	−9.59776	−0.350929
$749$	−21.1842	−0.774055
$750$	−62.5178	−2.28283
$751$	−33.5696	−1.22497	−0.612487	−	0.790481i	$-0.709831\pi$
$751$	−33.5696	−1.22497	−0.612487	+	0.790481i	$0.709831\pi$
$752$	21.3880	0.779939
$753$	−57.3060	−2.08835
$754$	−8.76961	−0.319370
$755$	21.7766	0.792533
$756$	33.9992	1.23654
$757$	14.5816	0.529976	0.264988	−	0.964252i	$-0.414632\pi$
$757$	14.5816	0.529976	0.264988	+	0.964252i	$0.414632\pi$
$758$	34.5620	1.25535
$759$	−65.3405	−2.37171
$760$	20.9075	0.758395
$761$	42.2884	1.53295	0.766476	−	0.642273i	$-0.222008\pi$
$761$	42.2884	1.53295	0.766476	+	0.642273i	$0.222008\pi$
$762$	−85.1019	−3.08291
$763$	−52.1519	−1.88803
$764$	5.41912	0.196057
$765$	79.2662	2.86587
$766$	12.4729	0.450666
$767$	28.8346	1.04116
$768$	−36.2738	−1.30892
$769$	23.0676	0.831839	0.415919	−	0.909401i	$-0.363460\pi$
$769$	23.0676	0.831839	0.415919	+	0.909401i	$0.363460\pi$
$770$	−41.9446	−1.51158
$771$	2.50377	0.0901710
$772$	9.49818	0.341847
$773$	11.3048	0.406607	0.203303	−	0.979116i	$-0.434832\pi$
$773$	11.3048	0.406607	0.203303	+	0.979116i	$0.434832\pi$
$774$	−65.5531	−2.35626
$775$	−0.642852	−0.0230919
$776$	−39.8803	−1.43162
$777$	79.7835	2.86222
$778$	−20.6585	−0.740641
$779$	−16.1402	−0.578284
$780$	13.6188	0.487632
$781$	5.94522	0.212737
$782$	56.4699	2.01936
$783$	17.3394	0.619658
$784$	−66.1747	−2.36338
$785$	24.9162	0.889296
$786$	34.5179	1.23121
$787$	23.1246	0.824301	0.412151	−	0.911116i	$-0.364778\pi$
$787$	23.1246	0.824301	0.412151	+	0.911116i	$0.364778\pi$
$788$	−0.550546	−0.0196124
$789$	−26.3385	−0.937676
$790$	43.7158	1.55534
$791$	49.2581	1.75142
$792$	−60.2607	−2.14127
$793$	45.7127	1.62330
$794$	8.42853	0.299117
$795$	80.7411	2.86359
$796$	9.16634	0.324892
$797$	−0.569104	−0.0201587	−0.0100793	−	0.999949i	$-0.503208\pi$
$797$	−0.569104	−0.0201587	−0.0100793	+	0.999949i	$0.503208\pi$
$798$	−117.926	−4.17454
$799$	−26.6807	−0.943894
$800$	−5.22384	−0.184691
$801$	123.238	4.35440
$802$	−7.74973	−0.273652
$803$	29.6425	1.04606
$804$	−6.37912	−0.224974
$805$	48.5944	1.71273
$806$	2.55996	0.0901708
$807$	−68.6825	−2.41774
$808$	−28.7052	−1.00985
$809$	−20.9629	−0.737017	−0.368508	−	0.929624i	$-0.620131\pi$
$809$	−20.9629	−0.737017	−0.368508	+	0.929624i	$0.620131\pi$
$810$	−73.2893	−2.57512
$811$	−51.3851	−1.80438	−0.902188	−	0.431343i	$-0.858040\pi$
$811$	−51.3851	−1.80438	−0.902188	+	0.431343i	$0.858040\pi$
$812$	2.57047	0.0902056
$813$	87.1603	3.05684
$814$	27.9025	0.977983
$815$	−36.8227	−1.28984
$816$	91.4433	3.20116
$817$	27.1960	0.951467
$818$	−5.88794	−0.205867
$819$	169.816	5.93384
$820$	−2.77465	−0.0968949
$821$	−37.8881	−1.32230	−0.661152	−	0.750252i	$-0.729932\pi$
$821$	−37.8881	−1.32230	−0.661152	+	0.750252i	$0.729932\pi$
$822$	55.7486	1.94446
$823$	42.6253	1.48583	0.742913	−	0.669388i	$-0.233444\pi$
$823$	42.6253	1.48583	0.742913	+	0.669388i	$0.233444\pi$
$824$	−2.00788	−0.0699477
$825$	−20.7681	−0.723054
$826$	−42.9223	−1.49346
$827$	29.3468	1.02049	0.510244	−	0.860029i	$-0.329555\pi$
$827$	29.3468	1.02049	0.510244	+	0.860029i	$0.329555\pi$
$828$	−22.6779	−0.788111
$829$	38.0589	1.32184	0.660920	−	0.750457i	$-0.270166\pi$
$829$	38.0589	1.32184	0.660920	+	0.750457i	$0.270166\pi$
$830$	39.1550	1.35909
$831$	−73.8716	−2.56258
$832$	−25.2121	−0.874071
$833$	82.5504	2.86020
$834$	−10.0882	−0.349327
$835$	25.9126	0.896741
$836$	−8.12089	−0.280867
$837$	−5.06159	−0.174954
$838$	−8.83083	−0.305056
$839$	4.60879	0.159113	0.0795566	−	0.996830i	$-0.474650\pi$
$839$	4.60879	0.159113	0.0795566	+	0.996830i	$0.474650\pi$
$840$	62.4095	2.15333
$841$	−27.6891	−0.954796
$842$	25.4857	0.878295
$843$	−71.6757	−2.46864
$844$	3.26082	0.112242
$845$	18.5172	0.637012
$846$	54.4151	1.87083
$847$	0.204786	0.00703654
$848$	66.8877	2.29693
$849$	45.4184	1.55876
$850$	17.9487	0.615635
$851$	−32.3261	−1.10812
$852$	2.87343	0.0984420
$853$	−0.735905	−0.0251969	−0.0125985	−	0.999921i	$-0.504010\pi$
$853$	−0.735905	−0.0251969	−0.0125985	+	0.999921i	$0.504010\pi$
$854$	−68.0464	−2.32850
$855$	67.0690	2.29371
$856$	11.0235	0.376774
$857$	−3.45687	−0.118084	−0.0590422	−	0.998255i	$-0.518805\pi$
$857$	−3.45687	−0.118084	−0.0590422	+	0.998255i	$0.518805\pi$
$858$	82.7028	2.82343
$859$	−23.9575	−0.817418	−0.408709	−	0.912665i	$-0.634021\pi$
$859$	−23.9575	−0.817418	−0.408709	+	0.912665i	$0.634021\pi$
$860$	4.67523	0.159424
$861$	−48.1790	−1.64194
$862$	52.3340	1.78250
$863$	−18.5562	−0.631659	−0.315830	−	0.948816i	$-0.602283\pi$
$863$	−18.5562	−0.631659	−0.315830	+	0.948816i	$0.602283\pi$
$864$	−41.1307	−1.39929
$865$	6.02001	0.204687
$866$	−27.5808	−0.937233
$867$	−58.6137	−1.99063
$868$	−0.750352	−0.0254686
$869$	52.2735	1.77326
$870$	−10.3389	−0.350520
$871$	−19.3543	−0.655794
$872$	27.1379	0.919004
$873$	−127.932	−4.32983
$874$	47.7806	1.61620
$875$	55.5970	1.87952
$876$	14.3267	0.484055
$877$	6.91944	0.233653	0.116826	−	0.993152i	$-0.462728\pi$
$877$	6.91944	0.233653	0.116826	+	0.993152i	$0.462728\pi$
$878$	8.92623	0.301246
$879$	57.9813	1.95566
$880$	27.5202	0.927705
$881$	38.3038	1.29049	0.645243	−	0.763977i	$-0.276756\pi$
$881$	38.3038	1.29049	0.645243	+	0.763977i	$0.276756\pi$
$882$	−168.361	−5.66901
$883$	13.0194	0.438136	0.219068	−	0.975710i	$-0.429698\pi$
$883$	13.0194	0.438136	0.219068	+	0.975710i	$0.429698\pi$
$884$	−14.0740	−0.473360
$885$	33.9944	1.14271
$886$	12.5554	0.421806
$887$	17.9624	0.603118	0.301559	−	0.953448i	$-0.402493\pi$
$887$	17.9624	0.603118	0.301559	+	0.953448i	$0.402493\pi$
$888$	−41.5162	−1.39319
$889$	75.6809	2.53826
$890$	−44.6366	−1.49622
$891$	−87.6363	−2.93593
$892$	9.19041	0.307718
$893$	−22.5752	−0.755449
$894$	20.0963	0.672121
$895$	−2.18845	−0.0731519
$896$	62.3982	2.08458
$897$	−95.8144	−3.19915
$898$	48.8567	1.63037
$899$	−0.382674	−0.0127629
$900$	−7.20805	−0.240268
$901$	−83.4398	−2.77978
$902$	−16.8496	−0.561029
$903$	81.1807	2.70153
$904$	−25.6320	−0.852509
$905$	−13.1961	−0.438652
$906$	63.9152	2.12344
$907$	5.48629	0.182169	0.0910846	−	0.995843i	$-0.470967\pi$
$907$	5.48629	0.182169	0.0910846	+	0.995843i	$0.470967\pi$
$908$	4.12608	0.136929
$909$	−92.0832	−3.05421
$910$	−61.5070	−2.03894
$911$	14.6574	0.485621	0.242810	−	0.970074i	$-0.421931\pi$
$911$	14.6574	0.485621	0.242810	+	0.970074i	$0.421931\pi$
$912$	77.3723	2.56205
$913$	46.8200	1.54952
$914$	−43.4038	−1.43567
$915$	53.8926	1.78163
$916$	−5.94364	−0.196383
$917$	−30.6967	−1.01370
$918$	141.322	4.66431
$919$	23.7931	0.784863	0.392432	−	0.919781i	$-0.371634\pi$
$919$	23.7931	0.784863	0.392432	+	0.919781i	$0.371634\pi$
$920$	−25.2866	−0.833676
$921$	53.5086	1.76317
$922$	29.1940	0.961454
$923$	8.71799	0.286956
$924$	−24.2411	−0.797473
$925$	−10.2747	−0.337830
$926$	−38.5304	−1.26619
$927$	−6.44105	−0.211552
$928$	−3.10963	−0.102079
$929$	4.71133	0.154574	0.0772869	−	0.997009i	$-0.475374\pi$
$929$	4.71133	0.154574	0.0772869	+	0.997009i	$0.475374\pi$
$930$	3.01805	0.0989657
$931$	69.8478	2.28917
$932$	−4.80577	−0.157418
$933$	0.293046	0.00959391
$934$	−18.9767	−0.620936
$935$	−34.3303	−1.12272
$936$	−88.3655	−2.88832
$937$	28.3190	0.925142	0.462571	−	0.886582i	$-0.346927\pi$
$937$	28.3190	0.925142	0.462571	+	0.886582i	$0.346927\pi$
$938$	28.8101	0.940685
$939$	−38.4681	−1.25536
$940$	−3.88086	−0.126580
$941$	−26.6165	−0.867673	−0.433837	−	0.900992i	$-0.642840\pi$
$941$	−26.6165	−0.867673	−0.433837	+	0.900992i	$0.642840\pi$
$942$	73.1298	2.38270
$943$	19.5209	0.635686
$944$	28.1617	0.916585
$945$	121.612	3.95605
$946$	28.3912	0.923077
$947$	33.6128	1.09227	0.546135	−	0.837697i	$-0.316099\pi$
$947$	33.6128	1.09227	0.546135	+	0.837697i	$0.316099\pi$
$948$	25.2647	0.820559
$949$	43.4673	1.41101
$950$	15.1868	0.492725
$951$	−2.76757	−0.0897445
$952$	−64.4955	−2.09031
$953$	37.6360	1.21915	0.609575	−	0.792729i	$-0.291340\pi$
$953$	37.6360	1.21915	0.609575	+	0.792729i	$0.291340\pi$
$954$	170.175	5.50962
$955$	19.3837	0.627242
$956$	−0.182073	−0.00588865
$957$	−12.3628	−0.399632
$958$	−2.29481	−0.0741419
$959$	−49.5772	−1.60093
$960$	−29.7236	−0.959324
$961$	−30.8883	−0.996397
$962$	40.9159	1.31918
$963$	35.3621	1.13953
$964$	5.59477	0.180196
$965$	33.9742	1.09367
$966$	142.626	4.58892
$967$	−46.6775	−1.50105	−0.750524	−	0.660843i	$-0.770199\pi$
$967$	−46.6775	−1.50105	−0.750524	+	0.660843i	$0.770199\pi$
$968$	−0.106563	−0.00342506
$969$	−96.5190	−3.10064
$970$	46.3366	1.48778
$971$	27.9752	0.897768	0.448884	−	0.893590i	$-0.351822\pi$
$971$	27.9752	0.897768	0.448884	+	0.893590i	$0.351822\pi$
$972$	−20.0773	−0.643978
$973$	8.97144	0.287611
$974$	−52.3401	−1.67708
$975$	−30.4541	−0.975312
$976$	44.6458	1.42908
$977$	28.8738	0.923754	0.461877	−	0.886944i	$-0.347176\pi$
$977$	28.8738	0.923754	0.461877	+	0.886944i	$0.347176\pi$
$978$	−108.076	−3.45588
$979$	−53.3746	−1.70586
$980$	12.0075	0.383564
$981$	87.0553	2.77946
$982$	−61.9868	−1.97808
$983$	10.1594	0.324033	0.162017	−	0.986788i	$-0.448200\pi$
$983$	10.1594	0.324033	0.162017	+	0.986788i	$0.448200\pi$
$984$	25.0705	0.799219
$985$	−1.96926	−0.0627457
$986$	10.6844	0.340262
$987$	−67.3874	−2.14497
$988$	−11.9084	−0.378855
$989$	−32.8923	−1.04591
$990$	70.0165	2.22527
$991$	−9.98005	−0.317027	−0.158513	−	0.987357i	$-0.550670\pi$
$991$	−9.98005	−0.317027	−0.158513	+	0.987357i	$0.550670\pi$
$992$	0.907740	0.0288208
$993$	27.8742	0.884562
$994$	−12.9773	−0.411616
$995$	32.7872	1.03942
$996$	22.6289	0.717025
$997$	1.63893	0.0519056	0.0259528	−	0.999663i	$-0.491738\pi$
$997$	1.63893	0.0519056	0.0259528	+	0.999663i	$0.491738\pi$
$998$	−2.99800	−0.0949001
$999$	−80.8993	−2.55954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.27	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.27	✓	122	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-1.57809 q^{2} -3.26225 q^{3} +0.490374 q^{4} +1.75402 q^{5} +5.14812 q^{6} -4.57822 q^{7} +2.38233 q^{8} +7.64225 q^{9} +O(q^{10})\)	\(q-1.57809 q^{2} -3.26225 q^{3} +0.490374 q^{4} +1.75402 q^{5} +5.14812 q^{6} -4.57822 q^{7} +2.38233 q^{8} +7.64225 q^{9} -2.76801 q^{10} -3.30987 q^{11} -1.59972 q^{12} -4.85355 q^{13} +7.22485 q^{14} -5.72206 q^{15} -4.74028 q^{16} +5.91332 q^{17} -12.0602 q^{18} +5.00340 q^{19} +0.860127 q^{20} +14.9353 q^{21} +5.22329 q^{22} -6.05137 q^{23} -7.77174 q^{24} -1.92340 q^{25} +7.65935 q^{26} -15.1442 q^{27} -2.24504 q^{28} -1.14495 q^{29} +9.02993 q^{30} +0.334227 q^{31} +2.71594 q^{32} +10.7976 q^{33} -9.33175 q^{34} -8.03031 q^{35} +3.74756 q^{36} +5.34195 q^{37} -7.89582 q^{38} +15.8335 q^{39} +4.17866 q^{40} -3.22586 q^{41} -23.5692 q^{42} +5.43550 q^{43} -1.62308 q^{44} +13.4047 q^{45} +9.54962 q^{46} -4.51196 q^{47} +15.4640 q^{48} +13.9601 q^{49} +3.03530 q^{50} -19.2907 q^{51} -2.38006 q^{52} -14.1105 q^{53} +23.8989 q^{54} -5.80560 q^{55} -10.9068 q^{56} -16.3223 q^{57} +1.80684 q^{58} -5.94093 q^{59} -2.80595 q^{60} -9.41839 q^{61} -0.527441 q^{62} -34.9879 q^{63} +5.19456 q^{64} -8.51325 q^{65} -17.0396 q^{66} +3.98765 q^{67} +2.89973 q^{68} +19.7411 q^{69} +12.6726 q^{70} -1.79621 q^{71} +18.2064 q^{72} -8.95577 q^{73} -8.43008 q^{74} +6.27460 q^{75} +2.45353 q^{76} +15.1533 q^{77} -24.9867 q^{78} -15.7932 q^{79} -8.31457 q^{80} +26.4772 q^{81} +5.09070 q^{82} -14.1456 q^{83} +7.32387 q^{84} +10.3721 q^{85} -8.57772 q^{86} +3.73512 q^{87} -7.88521 q^{88} +16.1259 q^{89} -21.1538 q^{90} +22.2206 q^{91} -2.96743 q^{92} -1.09033 q^{93} +7.12029 q^{94} +8.77608 q^{95} -8.86007 q^{96} -16.7400 q^{97} -22.0303 q^{98} -25.2949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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