LMFDB - Embedded newform 671.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 $ x^19 - 5x^18 - 18x^17 + 122x^16 + 78x^15 - 1177x^14 + 387x^13 + 5755x^12 - 4673x^11 - 15053x^10 + 16875x^9 + 20141x^8 - 28019x^7 - 11589x^6 + 21077x^5 + 1674x^4 - 6404x^3 + 241x^2 + 643x - 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.04293$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.04293 q^{2} +0.810410 q^{3} +2.17358 q^{4} +0.258135 q^{5} +1.65561 q^{6} +3.70333 q^{7} +0.354615 q^{8} -2.34324 q^{9} +O(q^{10})$	\(q+2.04293 q^{2} +0.810410 q^{3} +2.17358 q^{4} +0.258135 q^{5} +1.65561 q^{6} +3.70333 q^{7} +0.354615 q^{8} -2.34324 q^{9} +0.527352 q^{10} +1.00000 q^{11} +1.76149 q^{12} -0.00787872 q^{13} +7.56566 q^{14} +0.209195 q^{15} -3.62271 q^{16} +1.30910 q^{17} -4.78708 q^{18} +5.50424 q^{19} +0.561077 q^{20} +3.00121 q^{21} +2.04293 q^{22} +5.32776 q^{23} +0.287383 q^{24} -4.93337 q^{25} -0.0160957 q^{26} -4.33021 q^{27} +8.04948 q^{28} -9.36018 q^{29} +0.427372 q^{30} +5.66655 q^{31} -8.11018 q^{32} +0.810410 q^{33} +2.67440 q^{34} +0.955958 q^{35} -5.09321 q^{36} -8.19092 q^{37} +11.2448 q^{38} -0.00638500 q^{39} +0.0915384 q^{40} -6.86058 q^{41} +6.13128 q^{42} -10.4500 q^{43} +2.17358 q^{44} -0.604870 q^{45} +10.8843 q^{46} +7.67253 q^{47} -2.93588 q^{48} +6.71464 q^{49} -10.0785 q^{50} +1.06090 q^{51} -0.0171250 q^{52} +3.79668 q^{53} -8.84634 q^{54} +0.258135 q^{55} +1.31326 q^{56} +4.46069 q^{57} -19.1222 q^{58} -1.40324 q^{59} +0.454702 q^{60} -1.00000 q^{61} +11.5764 q^{62} -8.67777 q^{63} -9.32316 q^{64} -0.00203377 q^{65} +1.65561 q^{66} +9.44385 q^{67} +2.84542 q^{68} +4.31767 q^{69} +1.95296 q^{70} -2.38488 q^{71} -0.830946 q^{72} +7.22936 q^{73} -16.7335 q^{74} -3.99805 q^{75} +11.9639 q^{76} +3.70333 q^{77} -0.0130441 q^{78} +13.3586 q^{79} -0.935147 q^{80} +3.52046 q^{81} -14.0157 q^{82} -16.1053 q^{83} +6.52338 q^{84} +0.337923 q^{85} -21.3486 q^{86} -7.58559 q^{87} +0.354615 q^{88} -1.11606 q^{89} -1.23571 q^{90} -0.0291775 q^{91} +11.5803 q^{92} +4.59223 q^{93} +15.6745 q^{94} +1.42084 q^{95} -6.57258 q^{96} +3.08628 q^{97} +13.7176 q^{98} -2.34324 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * 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 $

$2$	2.04293	1.44457	0.722286	−	0.691594i	$-0.243091\pi$
$2$	2.04293	1.44457	0.722286	+	0.691594i	$0.243091\pi$
$3$	0.810410	0.467891	0.233945	−	0.972250i	$-0.424836\pi$
$3$	0.810410	0.467891	0.233945	+	0.972250i	$0.424836\pi$
$4$	2.17358	1.08679
$5$	0.258135	0.115441	0.0577207	−	0.998333i	$-0.481617\pi$
$5$	0.258135	0.115441	0.0577207	+	0.998333i	$0.481617\pi$
$6$	1.65561	0.675902
$7$	3.70333	1.39973	0.699863	−	0.714277i	$-0.253244\pi$
$7$	3.70333	1.39973	0.699863	+	0.714277i	$0.253244\pi$
$8$	0.354615	0.125375
$9$	−2.34324	−0.781078
$10$	0.527352	0.166763
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.76149	0.508499
$13$	−0.00787872	−0.00218516	−0.00109258	−	0.999999i	$-0.500348\pi$
$13$	−0.00787872	−0.00218516	−0.00109258	+	0.999999i	$0.500348\pi$
$14$	7.56566	2.02201
$15$	0.209195	0.0540139
$16$	−3.62271	−0.905677
$17$	1.30910	0.317502	0.158751	−	0.987319i	$-0.449253\pi$
$17$	1.30910	0.317502	0.158751	+	0.987319i	$0.449253\pi$
$18$	−4.78708	−1.12832
$19$	5.50424	1.26276	0.631380	−	0.775474i	$-0.282489\pi$
$19$	5.50424	1.26276	0.631380	+	0.775474i	$0.282489\pi$
$20$	0.561077	0.125461
$21$	3.00121	0.654919
$22$	2.04293	0.435555
$23$	5.32776	1.11092	0.555458	−	0.831545i	$-0.312543\pi$
$23$	5.32776	1.11092	0.555458	+	0.831545i	$0.312543\pi$
$24$	0.287383	0.0586619
$25$	−4.93337	−0.986673
$26$	−0.0160957	−0.00315663
$27$	−4.33021	−0.833350
$28$	8.04948	1.52121
$29$	−9.36018	−1.73814	−0.869071	−	0.494688i	$-0.835283\pi$
$29$	−9.36018	−1.73814	−0.869071	+	0.494688i	$0.835283\pi$
$30$	0.427372	0.0780270
$31$	5.66655	1.01774	0.508871	−	0.860843i	$-0.330063\pi$
$31$	5.66655	1.01774	0.508871	+	0.860843i	$0.330063\pi$
$32$	−8.11018	−1.43369
$33$	0.810410	0.141074
$34$	2.67440	0.458655
$35$	0.955958	0.161586
$36$	−5.09321	−0.848869
$37$	−8.19092	−1.34658	−0.673289	−	0.739379i	$-0.735119\pi$
$37$	−8.19092	−1.34658	−0.673289	+	0.739379i	$0.735119\pi$
$38$	11.2448	1.82415
$39$	−0.00638500	−0.00102242
$40$	0.0915384	0.0144735
$41$	−6.86058	−1.07144	−0.535721	−	0.844395i	$-0.679960\pi$
$41$	−6.86058	−1.07144	−0.535721	+	0.844395i	$0.679960\pi$
$42$	6.13128	0.946078
$43$	−10.4500	−1.59360	−0.796802	−	0.604241i	$-0.793477\pi$
$43$	−10.4500	−1.59360	−0.796802	+	0.604241i	$0.793477\pi$
$44$	2.17358	0.327680
$45$	−0.604870	−0.0901688
$46$	10.8843	1.60480
$47$	7.67253	1.11915	0.559577	−	0.828779i	$-0.310964\pi$
$47$	7.67253	1.11915	0.559577	+	0.828779i	$0.310964\pi$
$48$	−2.93588	−0.423758
$49$	6.71464	0.959234
$50$	−10.0785	−1.42532
$51$	1.06090	0.148556
$52$	−0.0171250	−0.00237482
$53$	3.79668	0.521515	0.260757	−	0.965404i	$-0.416028\pi$
$53$	3.79668	0.521515	0.260757	+	0.965404i	$0.416028\pi$
$54$	−8.84634	−1.20383
$55$	0.258135	0.0348069
$56$	1.31326	0.175491
$57$	4.46069	0.590833
$58$	−19.1222	−2.51087
$59$	−1.40324	−0.182687	−0.0913434	−	0.995819i	$-0.529116\pi$
$59$	−1.40324	−0.182687	−0.0913434	+	0.995819i	$0.529116\pi$
$60$	0.454702	0.0587018
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	11.5764	1.47020
$63$	−8.67777	−1.09330
$64$	−9.32316	−1.16539
$65$	−0.00203377	−0.000252258 0
$66$	1.65561	0.203792
$67$	9.44385	1.15375	0.576875	−	0.816832i	$-0.304272\pi$
$67$	9.44385	1.15375	0.576875	+	0.816832i	$0.304272\pi$
$68$	2.84542	0.345058
$69$	4.31767	0.519787
$70$	1.95296	0.233423
$71$	−2.38488	−0.283033	−0.141516	−	0.989936i	$-0.545198\pi$
$71$	−2.38488	−0.283033	−0.141516	+	0.989936i	$0.545198\pi$
$72$	−0.830946	−0.0979279
$73$	7.22936	0.846133	0.423066	−	0.906099i	$-0.360954\pi$
$73$	7.22936	0.846133	0.423066	+	0.906099i	$0.360954\pi$
$74$	−16.7335	−1.94523
$75$	−3.99805	−0.461655
$76$	11.9639	1.37235
$77$	3.70333	0.422033
$78$	−0.0130441	−0.00147696
$79$	13.3586	1.50297	0.751483	−	0.659753i	$-0.229339\pi$
$79$	13.3586	1.50297	0.751483	+	0.659753i	$0.229339\pi$
$80$	−0.935147	−0.104553
$81$	3.52046	0.391162
$82$	−14.0157	−1.54778
$83$	−16.1053	−1.76778	−0.883892	−	0.467691i	$-0.845086\pi$
$83$	−16.1053	−1.76778	−0.883892	+	0.467691i	$0.845086\pi$
$84$	6.52338	0.711759
$85$	0.337923	0.0366529
$86$	−21.3486	−2.30208
$87$	−7.58559	−0.813260
$88$	0.354615	0.0378021
$89$	−1.11606	−0.118302	−0.0591510	−	0.998249i	$-0.518839\pi$
$89$	−1.11606	−0.118302	−0.0591510	+	0.998249i	$0.518839\pi$
$90$	−1.23571	−0.130255
$91$	−0.0291775	−0.00305863
$92$	11.5803	1.20733
$93$	4.59223	0.476192
$94$	15.6745	1.61670
$95$	1.42084	0.145775
$96$	−6.57258	−0.670811
$97$	3.08628	0.313365	0.156682	−	0.987649i	$-0.449920\pi$
$97$	3.08628	0.313365	0.156682	+	0.987649i	$0.449920\pi$
$98$	13.7176	1.38568
$99$	−2.34324	−0.235504
$100$	−10.7231	−1.07231
$101$	−15.6491	−1.55714	−0.778571	−	0.627556i	$-0.784055\pi$
$101$	−15.6491	−1.55714	−0.778571	+	0.627556i	$0.784055\pi$
$102$	2.16736	0.214600
$103$	−13.4795	−1.32818	−0.664090	−	0.747653i	$-0.731181\pi$
$103$	−13.4795	−1.32818	−0.664090	+	0.747653i	$0.731181\pi$
$104$	−0.00279391	−0.000273966 0
$105$	0.774718	0.0756047
$106$	7.75638	0.753366
$107$	6.95103	0.671981	0.335991	−	0.941865i	$-0.390929\pi$
$107$	6.95103	0.671981	0.335991	+	0.941865i	$0.390929\pi$
$108$	−9.41207	−0.905677
$109$	−6.12951	−0.587101	−0.293550	−	0.955944i	$-0.594837\pi$
$109$	−6.12951	−0.587101	−0.293550	+	0.955944i	$0.594837\pi$
$110$	0.527352	0.0502811
$111$	−6.63800	−0.630051
$112$	−13.4161	−1.26770
$113$	−8.08811	−0.760866	−0.380433	−	0.924809i	$-0.624225\pi$
$113$	−8.08811	−0.760866	−0.380433	+	0.924809i	$0.624225\pi$
$114$	9.11290	0.853501
$115$	1.37528	0.128246
$116$	−20.3451	−1.88900
$117$	0.0184617	0.00170678
$118$	−2.86673	−0.263904
$119$	4.84801	0.444416
$120$	0.0741837	0.00677201
$121$	1.00000	0.0909091
$122$	−2.04293	−0.184959
$123$	−5.55988	−0.501318
$124$	12.3167	1.10607
$125$	−2.56415	−0.229344
$126$	−17.7281	−1.57935
$127$	13.4117	1.19009	0.595046	−	0.803691i	$-0.297134\pi$
$127$	13.4117	1.19009	0.595046	+	0.803691i	$0.297134\pi$
$128$	−2.82623	−0.249806
$129$	−8.46875	−0.745632
$130$	−0.00415486	−0.000364406 0
$131$	−20.8568	−1.82227	−0.911134	−	0.412110i	$-0.864792\pi$
$131$	−20.8568	−1.82227	−0.911134	+	0.412110i	$0.864792\pi$
$132$	1.76149	0.153318
$133$	20.3840	1.76752
$134$	19.2932	1.66668
$135$	−1.11778	−0.0962030
$136$	0.464225	0.0398069
$137$	−18.1777	−1.55303	−0.776514	−	0.630100i	$-0.783014\pi$
$137$	−18.1777	−1.55303	−0.776514	+	0.630100i	$0.783014\pi$
$138$	8.82072	0.750870
$139$	15.8671	1.34583	0.672915	−	0.739720i	$-0.265042\pi$
$139$	15.8671	1.34583	0.672915	+	0.739720i	$0.265042\pi$
$140$	2.07785	0.175610
$141$	6.21790	0.523641
$142$	−4.87215	−0.408861
$143$	−0.00787872	−0.000658852 0
$144$	8.48886	0.707405
$145$	−2.41619	−0.200653
$146$	14.7691	1.22230
$147$	5.44161	0.448816
$148$	−17.8036	−1.46345
$149$	14.2587	1.16811	0.584057	−	0.811712i	$-0.301464\pi$
$149$	14.2587	1.16811	0.584057	+	0.811712i	$0.301464\pi$
$150$	−8.16775	−0.666894
$151$	−5.05638	−0.411482	−0.205741	−	0.978606i	$-0.565960\pi$
$151$	−5.05638	−0.411482	−0.205741	+	0.978606i	$0.565960\pi$
$152$	1.95189	0.158319
$153$	−3.06752	−0.247994
$154$	7.56566	0.609658
$155$	1.46273	0.117490
$156$	−0.0138783	−0.00111115
$157$	10.6739	0.851866	0.425933	−	0.904755i	$-0.359946\pi$
$157$	10.6739	0.851866	0.425933	+	0.904755i	$0.359946\pi$
$158$	27.2908	2.17114
$159$	3.07687	0.244012
$160$	−2.09352	−0.165507
$161$	19.7305	1.55498
$162$	7.19206	0.565062
$163$	21.2742	1.66633	0.833163	−	0.553027i	$-0.186527\pi$
$163$	21.2742	1.66633	0.833163	+	0.553027i	$0.186527\pi$
$164$	−14.9120	−1.16443
$165$	0.209195	0.0162858
$166$	−32.9020	−2.55369
$167$	24.7792	1.91747	0.958736	−	0.284296i	$-0.0917600\pi$
$167$	24.7792	1.91747	0.958736	+	0.284296i	$0.0917600\pi$
$168$	1.06428	0.0821106
$169$	−12.9999	−0.999995
$170$	0.690354	0.0529478
$171$	−12.8977	−0.986314
$172$	−22.7138	−1.73191
$173$	14.4780	1.10074	0.550372	−	0.834920i	$-0.314486\pi$
$173$	14.4780	1.10074	0.550372	+	0.834920i	$0.314486\pi$
$174$	−15.4969	−1.17481
$175$	−18.2699	−1.38107
$176$	−3.62271	−0.273072
$177$	−1.13720	−0.0854774
$178$	−2.28004	−0.170896
$179$	15.6344	1.16857	0.584286	−	0.811548i	$-0.301375\pi$
$179$	15.6344	1.16857	0.584286	+	0.811548i	$0.301375\pi$
$180$	−1.31473	−0.0979946
$181$	−17.0567	−1.26781	−0.633907	−	0.773410i	$-0.718550\pi$
$181$	−17.0567	−1.26781	−0.633907	+	0.773410i	$0.718550\pi$
$182$	−0.0596077	−0.00441842
$183$	−0.810410	−0.0599072
$184$	1.88930	0.139281
$185$	−2.11436	−0.155451
$186$	9.38163	0.687894
$187$	1.30910	0.0957305
$188$	16.6769	1.21629
$189$	−16.0362	−1.16646
$190$	2.90267	0.210582
$191$	5.93707	0.429591	0.214796	−	0.976659i	$-0.431091\pi$
$191$	5.93707	0.429591	0.214796	+	0.976659i	$0.431091\pi$
$192$	−7.55558	−0.545277
$193$	−8.74432	−0.629430	−0.314715	−	0.949186i	$-0.601909\pi$
$193$	−8.74432	−0.629430	−0.314715	+	0.949186i	$0.601909\pi$
$194$	6.30507	0.452678
$195$	−0.00164819	−0.000118029 0
$196$	14.5948	1.04249
$197$	12.3241	0.878058	0.439029	−	0.898473i	$-0.355323\pi$
$197$	12.3241	0.878058	0.439029	+	0.898473i	$0.355323\pi$
$198$	−4.78708	−0.340203
$199$	−4.55083	−0.322600	−0.161300	−	0.986905i	$-0.551569\pi$
$199$	−4.55083	−0.322600	−0.161300	+	0.986905i	$0.551569\pi$
$200$	−1.74945	−0.123704
$201$	7.65340	0.539829
$202$	−31.9701	−2.24941
$203$	−34.6638	−2.43292
$204$	2.30596	0.161450
$205$	−1.77095	−0.123689
$206$	−27.5378	−1.91865
$207$	−12.4842	−0.867712
$208$	0.0285423	0.00197905
$209$	5.50424	0.380736
$210$	1.58270	0.109217
$211$	18.6369	1.28302	0.641510	−	0.767115i	$-0.278308\pi$
$211$	18.6369	1.28302	0.641510	+	0.767115i	$0.278308\pi$
$212$	8.25240	0.566777
$213$	−1.93273	−0.132428
$214$	14.2005	0.970726
$215$	−2.69750	−0.183968
$216$	−1.53556	−0.104481
$217$	20.9851	1.42456
$218$	−12.5222	−0.848110
$219$	5.85875	0.395898
$220$	0.561077	0.0378278
$221$	−0.0103140	−0.000693794 0
$222$	−13.5610	−0.910155
$223$	−7.51298	−0.503107	−0.251553	−	0.967843i	$-0.580941\pi$
$223$	−7.51298	−0.503107	−0.251553	+	0.967843i	$0.580941\pi$
$224$	−30.0347	−2.00678
$225$	11.5600	0.770669
$226$	−16.5235	−1.09913
$227$	13.7165	0.910397	0.455199	−	0.890390i	$-0.349568\pi$
$227$	13.7165	0.910397	0.455199	+	0.890390i	$0.349568\pi$
$228$	9.69567	0.642112
$229$	15.9667	1.05511	0.527555	−	0.849521i	$-0.323109\pi$
$229$	15.9667	1.05511	0.527555	+	0.849521i	$0.323109\pi$
$230$	2.80961	0.185260
$231$	3.00121	0.197465
$232$	−3.31926	−0.217920
$233$	2.12028	0.138904	0.0694522	−	0.997585i	$-0.477875\pi$
$233$	2.12028	0.138904	0.0694522	+	0.997585i	$0.477875\pi$
$234$	0.0377160	0.00246557
$235$	1.98055	0.129197
$236$	−3.05006	−0.198542
$237$	10.8260	0.703223
$238$	9.90416	0.641992
$239$	19.8029	1.28094	0.640472	−	0.767982i	$-0.278739\pi$
$239$	19.8029	1.28094	0.640472	+	0.767982i	$0.278739\pi$
$240$	−0.757852	−0.0489192
$241$	25.0484	1.61351	0.806755	−	0.590886i	$-0.201222\pi$
$241$	25.0484	1.61351	0.806755	+	0.590886i	$0.201222\pi$
$242$	2.04293	0.131325
$243$	15.8437	1.01637
$244$	−2.17358	−0.139149
$245$	1.73328	0.110735
$246$	−11.3585	−0.724190
$247$	−0.0433664	−0.00275934
$248$	2.00944	0.127600
$249$	−13.0519	−0.827130
$250$	−5.23838	−0.331304
$251$	−5.56763	−0.351426	−0.175713	−	0.984441i	$-0.556223\pi$
$251$	−5.56763	−0.351426	−0.175713	+	0.984441i	$0.556223\pi$
$252$	−18.8618	−1.18818
$253$	5.32776	0.334954
$254$	27.3991	1.71918
$255$	0.273856	0.0171495
$256$	12.8725	0.804532
$257$	14.5336	0.906581	0.453290	−	0.891363i	$-0.350250\pi$
$257$	14.5336	0.906581	0.453290	+	0.891363i	$0.350250\pi$
$258$	−17.3011	−1.07712
$259$	−30.3337	−1.88484
$260$	−0.00442057	−0.000274152 0
$261$	21.9331	1.35763
$262$	−42.6091	−2.63240
$263$	1.40712	0.0867665	0.0433833	−	0.999059i	$-0.486186\pi$
$263$	1.40712	0.0867665	0.0433833	+	0.999059i	$0.486186\pi$
$264$	0.287383	0.0176872
$265$	0.980056	0.0602044
$266$	41.6432	2.55331
$267$	−0.904466	−0.0553524
$268$	20.5270	1.25389
$269$	−17.4391	−1.06328	−0.531641	−	0.846970i	$-0.678425\pi$
$269$	−17.4391	−1.06328	−0.531641	+	0.846970i	$0.678425\pi$
$270$	−2.28355	−0.138972
$271$	8.55281	0.519546	0.259773	−	0.965670i	$-0.416352\pi$
$271$	8.55281	0.519546	0.259773	+	0.965670i	$0.416352\pi$
$272$	−4.74247	−0.287554
$273$	−0.0236457	−0.00143110
$274$	−37.1359	−2.24346
$275$	−4.93337	−0.297493
$276$	9.38481	0.564899
$277$	24.0213	1.44330	0.721649	−	0.692259i	$-0.243384\pi$
$277$	24.0213	1.44330	0.721649	+	0.692259i	$0.243384\pi$
$278$	32.4155	1.94415
$279$	−13.2781	−0.794937
$280$	0.338997	0.0202589
$281$	−13.7518	−0.820363	−0.410182	−	0.912004i	$-0.634535\pi$
$281$	−13.7518	−0.820363	−0.410182	+	0.912004i	$0.634535\pi$
$282$	12.7028	0.756438
$283$	13.3219	0.791904	0.395952	−	0.918271i	$-0.370415\pi$
$283$	13.3219	0.791904	0.395952	+	0.918271i	$0.370415\pi$
$284$	−5.18372	−0.307597
$285$	1.15146	0.0682066
$286$	−0.0160957	−0.000951759 0
$287$	−25.4070	−1.49973
$288$	19.0041	1.11983
$289$	−15.2863	−0.899192
$290$	−4.93611	−0.289859
$291$	2.50116	0.146620
$292$	15.7136	0.919569
$293$	−2.73244	−0.159631	−0.0798153	−	0.996810i	$-0.525433\pi$
$293$	−2.73244	−0.159631	−0.0798153	+	0.996810i	$0.525433\pi$
$294$	11.1169	0.648348
$295$	−0.362226	−0.0210896
$296$	−2.90462	−0.168828
$297$	−4.33021	−0.251264
$298$	29.1295	1.68743
$299$	−0.0419760	−0.00242753
$300$	−8.69009	−0.501722
$301$	−38.6996	−2.23061
$302$	−10.3298	−0.594416
$303$	−12.6822	−0.728572
$304$	−19.9402	−1.14365
$305$	−0.258135	−0.0147808
$306$	−6.26674	−0.358246
$307$	−4.26245	−0.243271	−0.121636	−	0.992575i	$-0.538814\pi$
$307$	−4.26245	−0.243271	−0.121636	+	0.992575i	$0.538814\pi$
$308$	8.04948	0.458662
$309$	−10.9240	−0.621442
$310$	2.98827	0.169722
$311$	−22.4144	−1.27101	−0.635503	−	0.772098i	$-0.719207\pi$
$311$	−22.4144	−1.27101	−0.635503	+	0.772098i	$0.719207\pi$
$312$	−0.00226421	−0.000128186 0
$313$	16.6893	0.943338	0.471669	−	0.881776i	$-0.343652\pi$
$313$	16.6893	0.943338	0.471669	+	0.881776i	$0.343652\pi$
$314$	21.8060	1.23058
$315$	−2.24003	−0.126212
$316$	29.0361	1.63341
$317$	1.55846	0.0875321	0.0437661	−	0.999042i	$-0.486064\pi$
$317$	1.55846	0.0875321	0.0437661	+	0.999042i	$0.486064\pi$
$318$	6.28585	0.352493
$319$	−9.36018	−0.524069
$320$	−2.40663	−0.134535
$321$	5.63318	0.314414
$322$	40.3080	2.24628
$323$	7.20557	0.400929
$324$	7.65200	0.425111
$325$	0.0388686	0.00215604
$326$	43.4619	2.40713
$327$	−4.96742	−0.274699
$328$	−2.43286	−0.134332
$329$	28.4139	1.56651
$330$	0.427372	0.0235260
$331$	−35.1122	−1.92994	−0.964970	−	0.262359i	$-0.915500\pi$
$331$	−35.1122	−1.92994	−0.964970	+	0.262359i	$0.915500\pi$
$332$	−35.0061	−1.92121
$333$	19.1932	1.05178
$334$	50.6223	2.76993
$335$	2.43779	0.133191
$336$	−10.8725	−0.593145
$337$	−4.77141	−0.259915	−0.129958	−	0.991520i	$-0.541484\pi$
$337$	−4.77141	−0.259915	−0.129958	+	0.991520i	$0.541484\pi$
$338$	−26.5580	−1.44457
$339$	−6.55469	−0.356002
$340$	0.734503	0.0398340
$341$	5.66655	0.306861
$342$	−26.3492	−1.42480
$343$	−1.05679	−0.0570613
$344$	−3.70571	−0.199799
$345$	1.11454	0.0600049
$346$	29.5777	1.59010
$347$	−29.6463	−1.59150	−0.795748	−	0.605628i	$-0.792922\pi$
$347$	−29.6463	−1.59150	−0.795748	+	0.605628i	$0.792922\pi$
$348$	−16.4879	−0.883843
$349$	−20.4772	−1.09612	−0.548061	−	0.836439i	$-0.684634\pi$
$349$	−20.4772	−1.09612	−0.548061	+	0.836439i	$0.684634\pi$
$350$	−37.3242	−1.99506
$351$	0.0341165	0.00182101
$352$	−8.11018	−0.432274
$353$	13.5176	0.719467	0.359734	−	0.933055i	$-0.382868\pi$
$353$	13.5176	0.719467	0.359734	+	0.933055i	$0.382868\pi$
$354$	−2.32323	−0.123478
$355$	−0.615620	−0.0326737
$356$	−2.42585	−0.128570
$357$	3.92888	0.207938
$358$	31.9401	1.68809
$359$	−29.2780	−1.54523	−0.772617	−	0.634873i	$-0.781053\pi$
$359$	−29.2780	−1.54523	−0.772617	+	0.634873i	$0.781053\pi$
$360$	−0.214496	−0.0113049
$361$	11.2966	0.594560
$362$	−34.8457	−1.83145
$363$	0.810410	0.0425355
$364$	−0.0634196	−0.00332409
$365$	1.86615	0.0976787
$366$	−1.65561	−0.0865404
$367$	29.5168	1.54076	0.770382	−	0.637583i	$-0.220066\pi$
$367$	29.5168	1.54076	0.770382	+	0.637583i	$0.220066\pi$
$368$	−19.3009	−1.00613
$369$	16.0759	0.836880
$370$	−4.31950	−0.224560
$371$	14.0604	0.729978
$372$	9.98159	0.517521
$373$	−1.71187	−0.0886372	−0.0443186	−	0.999017i	$-0.514112\pi$
$373$	−1.71187	−0.0886372	−0.0443186	+	0.999017i	$0.514112\pi$
$374$	2.67440	0.138290
$375$	−2.07801	−0.107308
$376$	2.72079	0.140314
$377$	0.0737463	0.00379813
$378$	−32.7609	−1.68504
$379$	2.38593	0.122557	0.0612785	−	0.998121i	$-0.480482\pi$
$379$	2.38593	0.122557	0.0612785	+	0.998121i	$0.480482\pi$
$380$	3.08830	0.158426
$381$	10.8689	0.556833
$382$	12.1290	0.620576
$383$	−26.0429	−1.33073	−0.665365	−	0.746519i	$-0.731724\pi$
$383$	−26.0429	−1.33073	−0.665365	+	0.746519i	$0.731724\pi$
$384$	−2.29041	−0.116882
$385$	0.955958	0.0487201
$386$	−17.8641	−0.909257
$387$	24.4867	1.24473
$388$	6.70829	0.340562
$389$	29.8371	1.51280	0.756401	−	0.654108i	$-0.226956\pi$
$389$	29.8371	1.51280	0.756401	+	0.654108i	$0.226956\pi$
$390$	−0.00336714	−0.000170502 0
$391$	6.97455	0.352718
$392$	2.38111	0.120264
$393$	−16.9026	−0.852622
$394$	25.1774	1.26842
$395$	3.44833	0.173504
$396$	−5.09321	−0.255944
$397$	−8.40866	−0.422019	−0.211009	−	0.977484i	$-0.567675\pi$
$397$	−8.40866	−0.422019	−0.211009	+	0.977484i	$0.567675\pi$
$398$	−9.29704	−0.466019
$399$	16.5194	0.827005
$400$	17.8721	0.893607
$401$	3.53907	0.176733	0.0883663	−	0.996088i	$-0.471835\pi$
$401$	3.53907	0.176733	0.0883663	+	0.996088i	$0.471835\pi$
$402$	15.6354	0.779822
$403$	−0.0446452	−0.00222393
$404$	−34.0146	−1.69229
$405$	0.908752	0.0451563
$406$	−70.8159	−3.51453
$407$	−8.19092	−0.406009
$408$	0.376212	0.0186253
$409$	27.3518	1.35246	0.676230	−	0.736690i	$-0.263612\pi$
$409$	27.3518	1.35246	0.676230	+	0.736690i	$0.263612\pi$
$410$	−3.61794	−0.178677
$411$	−14.7314	−0.726647
$412$	−29.2989	−1.44345
$413$	−5.19667	−0.255712
$414$	−25.5044	−1.25347
$415$	−4.15733	−0.204075
$416$	0.0638979	0.00313285
$417$	12.8589	0.629701
$418$	11.2448	0.550001
$419$	1.75179	0.0855807	0.0427904	−	0.999084i	$-0.486375\pi$
$419$	1.75179	0.0855807	0.0427904	+	0.999084i	$0.486375\pi$
$420$	1.68391	0.0821665
$421$	23.3908	1.14000	0.569999	−	0.821646i	$-0.306944\pi$
$421$	23.3908	1.14000	0.569999	+	0.821646i	$0.306944\pi$
$422$	38.0741	1.85342
$423$	−17.9785	−0.874147
$424$	1.34636	0.0653850
$425$	−6.45825	−0.313271
$426$	−3.94844	−0.191302
$427$	−3.70333	−0.179217
$428$	15.1086	0.730303
$429$	−0.00638500	−0.000308271 0
$430$	−5.51081	−0.265755
$431$	−4.31680	−0.207933	−0.103966	−	0.994581i	$-0.533153\pi$
$431$	−4.31680	−0.207933	−0.103966	+	0.994581i	$0.533153\pi$
$432$	15.6871	0.754746
$433$	−13.9306	−0.669460	−0.334730	−	0.942314i	$-0.608645\pi$
$433$	−13.9306	−0.669460	−0.334730	+	0.942314i	$0.608645\pi$
$434$	42.8712	2.05788
$435$	−1.95810	−0.0938839
$436$	−13.3230	−0.638056
$437$	29.3253	1.40282
$438$	11.9690	0.571903
$439$	32.4433	1.54843	0.774217	−	0.632920i	$-0.218144\pi$
$439$	32.4433	1.54843	0.774217	+	0.632920i	$0.218144\pi$
$440$	0.0915384	0.00436392
$441$	−15.7340	−0.749237
$442$	−0.0210708	−0.00100224
$443$	8.90538	0.423108	0.211554	−	0.977366i	$-0.432148\pi$
$443$	8.90538	0.423108	0.211554	+	0.977366i	$0.432148\pi$
$444$	−14.4282	−0.684734
$445$	−0.288094	−0.0136569
$446$	−15.3485	−0.726774
$447$	11.5554	0.546550
$448$	−34.5267	−1.63123
$449$	−9.99183	−0.471543	−0.235772	−	0.971808i	$-0.575762\pi$
$449$	−9.99183	−0.471543	−0.235772	+	0.971808i	$0.575762\pi$
$450$	23.6164	1.11329
$451$	−6.86058	−0.323052
$452$	−17.5802	−0.826901
$453$	−4.09774	−0.192529
$454$	28.0219	1.31514
$455$	−0.00753172	−0.000353093 0
$456$	1.58183	0.0740759
$457$	−6.77456	−0.316901	−0.158450	−	0.987367i	$-0.550650\pi$
$457$	−6.77456	−0.316901	−0.158450	+	0.987367i	$0.550650\pi$
$458$	32.6190	1.52418
$459$	−5.66866	−0.264590
$460$	2.98928	0.139376
$461$	−30.4830	−1.41974	−0.709869	−	0.704334i	$-0.751246\pi$
$461$	−30.4830	−1.41974	−0.709869	+	0.704334i	$0.751246\pi$
$462$	6.13128	0.285253
$463$	30.5875	1.42152	0.710762	−	0.703433i	$-0.248350\pi$
$463$	30.5875	1.42152	0.710762	+	0.703433i	$0.248350\pi$
$464$	33.9092	1.57419
$465$	1.18541	0.0549723
$466$	4.33160	0.200657
$467$	−7.82628	−0.362157	−0.181079	−	0.983469i	$-0.557959\pi$
$467$	−7.82628	−0.362157	−0.181079	+	0.983469i	$0.557959\pi$
$468$	0.0401280	0.00185492
$469$	34.9737	1.61493
$470$	4.04613	0.186634
$471$	8.65020	0.398580
$472$	−0.497611	−0.0229044
$473$	−10.4500	−0.480490
$474$	22.1168	1.01586
$475$	−27.1544	−1.24593
$476$	10.5375	0.482987
$477$	−8.89652	−0.407344
$478$	40.4560	1.85042
$479$	−26.1714	−1.19580	−0.597900	−	0.801570i	$-0.703998\pi$
$479$	−26.1714	−1.19580	−0.597900	+	0.801570i	$0.703998\pi$
$480$	−1.69661	−0.0774393
$481$	0.0645340	0.00294250
$482$	51.1723	2.33083
$483$	15.9898	0.727559
$484$	2.17358	0.0987991
$485$	0.796677	0.0361752
$486$	32.3675	1.46822
$487$	−21.4184	−0.970558	−0.485279	−	0.874359i	$-0.661282\pi$
$487$	−21.4184	−0.970558	−0.485279	+	0.874359i	$0.661282\pi$
$488$	−0.354615	−0.0160527
$489$	17.2409	0.779658
$490$	3.54098	0.159965
$491$	18.5600	0.837602	0.418801	−	0.908078i	$-0.362451\pi$
$491$	18.5600	0.837602	0.418801	+	0.908078i	$0.362451\pi$
$492$	−12.0849	−0.544827
$493$	−12.2534	−0.551864
$494$	−0.0885946	−0.00398606
$495$	−0.604870	−0.0271869
$496$	−20.5283	−0.921746
$497$	−8.83198	−0.396168
$498$	−26.6641	−1.19485
$499$	4.28745	0.191933	0.0959664	−	0.995385i	$-0.469406\pi$
$499$	4.28745	0.191933	0.0959664	+	0.995385i	$0.469406\pi$
$500$	−5.57338	−0.249249
$501$	20.0813	0.897167
$502$	−11.3743	−0.507660
$503$	23.9445	1.06763	0.533817	−	0.845600i	$-0.320757\pi$
$503$	23.9445	1.06763	0.533817	+	0.845600i	$0.320757\pi$
$504$	−3.07727	−0.137072
$505$	−4.03957	−0.179759
$506$	10.8843	0.483865
$507$	−10.5353	−0.467888
$508$	29.1513	1.29338
$509$	−7.67997	−0.340409	−0.170204	−	0.985409i	$-0.554443\pi$
$509$	−7.67997	−0.340409	−0.170204	+	0.985409i	$0.554443\pi$
$510$	0.559470	0.0247738
$511$	26.7727	1.18435
$512$	31.9502	1.41201
$513$	−23.8345	−1.05232
$514$	29.6912	1.30962
$515$	−3.47954	−0.153327
$516$	−18.4075	−0.810346
$517$	7.67253	0.337437
$518$	−61.9697	−2.72279
$519$	11.7331	0.515028
$520$	−0.000721206 0	−3.16270e−5 0
$521$	5.64205	0.247183	0.123591	−	0.992333i	$-0.460559\pi$
$521$	5.64205	0.247183	0.123591	+	0.992333i	$0.460559\pi$
$522$	44.8079	1.96119
$523$	−29.6807	−1.29785	−0.648923	−	0.760854i	$-0.724780\pi$
$523$	−29.6807	−1.29785	−0.648923	+	0.760854i	$0.724780\pi$
$524$	−45.3340	−1.98042
$525$	−14.8061	−0.646191
$526$	2.87465	0.125341
$527$	7.41805	0.323136
$528$	−2.93588	−0.127768
$529$	5.38506	0.234133
$530$	2.00219	0.0869696
$531$	3.28813	0.142693
$532$	44.3063	1.92092
$533$	0.0540526	0.00234128
$534$	−1.84776	−0.0799606
$535$	1.79430	0.0775744
$536$	3.34893	0.144652
$537$	12.6703	0.546764
$538$	−35.6270	−1.53599
$539$	6.71464	0.289220
$540$	−2.42958	−0.104553
$541$	−22.9640	−0.987299	−0.493649	−	0.869661i	$-0.664337\pi$
$541$	−22.9640	−0.987299	−0.493649	+	0.869661i	$0.664337\pi$
$542$	17.4728	0.750522
$543$	−13.8229	−0.593198
$544$	−10.6170	−0.455200
$545$	−1.58224	−0.0677757
$546$	−0.0483067	−0.00206734
$547$	4.53664	0.193973	0.0969864	−	0.995286i	$-0.469080\pi$
$547$	4.53664	0.193973	0.0969864	+	0.995286i	$0.469080\pi$
$548$	−39.5108	−1.68782
$549$	2.34324	0.100007
$550$	−10.0785	−0.429751
$551$	−51.5207	−2.19485
$552$	1.53111	0.0651684
$553$	49.4715	2.10374
$554$	49.0739	2.08495
$555$	−1.71350	−0.0727340
$556$	34.4884	1.46264
$557$	−22.3000	−0.944883	−0.472441	−	0.881362i	$-0.656627\pi$
$557$	−22.3000	−0.944883	−0.472441	+	0.881362i	$0.656627\pi$
$558$	−27.1262	−1.14834
$559$	0.0823323	0.00348229
$560$	−3.46315	−0.146345
$561$	1.06090	0.0447914
$562$	−28.0940	−1.18507
$563$	−35.5125	−1.49667	−0.748337	−	0.663319i	$-0.769147\pi$
$563$	−35.5125	−1.49667	−0.748337	+	0.663319i	$0.769147\pi$
$564$	13.5151	0.569088
$565$	−2.08782	−0.0878353
$566$	27.2158	1.14396
$567$	13.0374	0.547520
$568$	−0.845713	−0.0354853
$569$	8.27466	0.346892	0.173446	−	0.984843i	$-0.444510\pi$
$569$	8.27466	0.346892	0.173446	+	0.984843i	$0.444510\pi$
$570$	2.35236	0.0985294
$571$	24.1399	1.01022	0.505111	−	0.863054i	$-0.331452\pi$
$571$	24.1399	1.01022	0.505111	+	0.863054i	$0.331452\pi$
$572$	−0.0171250	−0.000716034 0
$573$	4.81146	0.201002
$574$	−51.9048	−2.16646
$575$	−26.2838	−1.09611
$576$	21.8464	0.910265
$577$	11.0843	0.461443	0.230722	−	0.973020i	$-0.425891\pi$
$577$	11.0843	0.461443	0.230722	+	0.973020i	$0.425891\pi$
$578$	−31.2288	−1.29895
$579$	−7.08648	−0.294504
$580$	−5.25178	−0.218068
$581$	−59.6431	−2.47441
$582$	5.10970	0.211804
$583$	3.79668	0.157243
$584$	2.56364	0.106084
$585$	0.00476561	0.000197034 0
$586$	−5.58219	−0.230598
$587$	−37.2506	−1.53750	−0.768748	−	0.639552i	$-0.779120\pi$
$587$	−37.2506	−1.53750	−0.768748	+	0.639552i	$0.779120\pi$
$588$	11.8278	0.487770
$589$	31.1901	1.28516
$590$	−0.740004	−0.0304655
$591$	9.98760	0.410835
$592$	29.6733	1.21957
$593$	5.45566	0.224037	0.112018	−	0.993706i	$-0.464268\pi$
$593$	5.45566	0.224037	0.112018	+	0.993706i	$0.464268\pi$
$594$	−8.84634	−0.362970
$595$	1.25144	0.0513040
$596$	30.9923	1.26950
$597$	−3.68804	−0.150941
$598$	−0.0857541	−0.00350675
$599$	−7.85153	−0.320805	−0.160402	−	0.987052i	$-0.551279\pi$
$599$	−7.85153	−0.320805	−0.160402	+	0.987052i	$0.551279\pi$
$600$	−1.41777	−0.0578801
$601$	−5.45245	−0.222410	−0.111205	−	0.993797i	$-0.535471\pi$
$601$	−5.45245	−0.222410	−0.111205	+	0.993797i	$0.535471\pi$
$602$	−79.0608	−3.22228
$603$	−22.1292	−0.901170
$604$	−10.9904	−0.447195
$605$	0.258135	0.0104947
$606$	−25.9089	−1.05248
$607$	26.4522	1.07366	0.536832	−	0.843689i	$-0.319621\pi$
$607$	26.4522	1.07366	0.536832	+	0.843689i	$0.319621\pi$
$608$	−44.6404	−1.81041
$609$	−28.0919	−1.13834
$610$	−0.527352	−0.0213519
$611$	−0.0604497	−0.00244553
$612$	−6.66750	−0.269518
$613$	−37.7627	−1.52522	−0.762610	−	0.646858i	$-0.776082\pi$
$613$	−37.7627	−1.52522	−0.762610	+	0.646858i	$0.776082\pi$
$614$	−8.70791	−0.351423
$615$	−1.43520	−0.0578728
$616$	1.31326	0.0529126
$617$	6.90176	0.277854	0.138927	−	0.990303i	$-0.455635\pi$
$617$	6.90176	0.277854	0.138927	+	0.990303i	$0.455635\pi$
$618$	−22.3169	−0.897719
$619$	−9.60723	−0.386147	−0.193074	−	0.981184i	$-0.561846\pi$
$619$	−9.60723	−0.386147	−0.193074	+	0.981184i	$0.561846\pi$
$620$	3.17937	0.127687
$621$	−23.0703	−0.925781
$622$	−45.7912	−1.83606
$623$	−4.13313	−0.165591
$624$	0.0231310	0.000925980 0
$625$	24.0049	0.960197
$626$	34.0952	1.36272
$627$	4.46069	0.178143
$628$	23.2005	0.925800
$629$	−10.7227	−0.427542
$630$	−4.57624	−0.182322
$631$	3.53921	0.140894	0.0704470	−	0.997516i	$-0.477557\pi$
$631$	3.53921	0.140894	0.0704470	+	0.997516i	$0.477557\pi$
$632$	4.73718	0.188435
$633$	15.1036	0.600313
$634$	3.18384	0.126447
$635$	3.46202	0.137386
$636$	6.68783	0.265190
$637$	−0.0529028	−0.00209608
$638$	−19.1222	−0.757057
$639$	5.58833	0.221071
$640$	−0.729549	−0.0288380
$641$	1.01070	0.0399202	0.0199601	−	0.999801i	$-0.493646\pi$
$641$	1.01070	0.0399202	0.0199601	+	0.999801i	$0.493646\pi$
$642$	11.5082	0.454193
$643$	−1.65064	−0.0650949	−0.0325474	−	0.999470i	$-0.510362\pi$
$643$	−1.65064	−0.0650949	−0.0325474	+	0.999470i	$0.510362\pi$
$644$	42.8857	1.68993
$645$	−2.18608	−0.0860768
$646$	14.7205	0.579171
$647$	−7.49452	−0.294640	−0.147320	−	0.989089i	$-0.547065\pi$
$647$	−7.49452	−0.294640	−0.147320	+	0.989089i	$0.547065\pi$
$648$	1.24841	0.0490420
$649$	−1.40324	−0.0550821
$650$	0.0794060	0.00311456
$651$	17.0065	0.666539
$652$	46.2413	1.81095
$653$	−19.4359	−0.760586	−0.380293	−	0.924866i	$-0.624177\pi$
$653$	−19.4359	−0.760586	−0.380293	+	0.924866i	$0.624177\pi$
$654$	−10.1481	−0.396823
$655$	−5.38387	−0.210365
$656$	24.8539	0.970380
$657$	−16.9401	−0.660896
$658$	58.0477	2.26294
$659$	22.1175	0.861575	0.430787	−	0.902454i	$-0.358236\pi$
$659$	22.1175	0.861575	0.430787	+	0.902454i	$0.358236\pi$
$660$	0.454702	0.0176993
$661$	−23.6575	−0.920170	−0.460085	−	0.887875i	$-0.652181\pi$
$661$	−23.6575	−0.920170	−0.460085	+	0.887875i	$0.652181\pi$
$662$	−71.7319	−2.78794
$663$	−0.00835857	−0.000324620 0
$664$	−5.71117	−0.221636
$665$	5.26182	0.204045
$666$	39.2105	1.51938
$667$	−49.8688	−1.93093
$668$	53.8596	2.08389
$669$	−6.08860	−0.235399
$670$	4.98024	0.192403
$671$	−1.00000	−0.0386046
$672$	−24.3404	−0.938951
$673$	46.7560	1.80231	0.901156	−	0.433495i	$-0.142720\pi$
$673$	46.7560	1.80231	0.901156	+	0.433495i	$0.142720\pi$
$674$	−9.74768	−0.375466
$675$	21.3625	0.822244
$676$	−28.2564	−1.08679
$677$	−31.5062	−1.21088	−0.605441	−	0.795891i	$-0.707003\pi$
$677$	−31.5062	−1.21088	−0.605441	+	0.795891i	$0.707003\pi$
$678$	−13.3908	−0.514270
$679$	11.4295	0.438625
$680$	0.119832	0.00459537
$681$	11.1160	0.425966
$682$	11.5764	0.443283
$683$	−2.41783	−0.0925158	−0.0462579	−	0.998930i	$-0.514730\pi$
$683$	−2.41783	−0.0925158	−0.0462579	+	0.998930i	$0.514730\pi$
$684$	−28.0343	−1.07192
$685$	−4.69230	−0.179284
$686$	−2.15895	−0.0824292
$687$	12.9396	0.493676
$688$	37.8571	1.44329
$689$	−0.0299130	−0.00113960
$690$	2.27694	0.0866814
$691$	−14.7015	−0.559272	−0.279636	−	0.960106i	$-0.590214\pi$
$691$	−14.7015	−0.559272	−0.279636	+	0.960106i	$0.590214\pi$
$692$	31.4692	1.19628
$693$	−8.67777	−0.329641
$694$	−60.5654	−2.29903
$695$	4.09585	0.155365
$696$	−2.68996	−0.101963
$697$	−8.98115	−0.340185
$698$	−41.8336	−1.58343
$699$	1.71830	0.0649920
$700$	−39.7111	−1.50094
$701$	−25.7270	−0.971696	−0.485848	−	0.874043i	$-0.661489\pi$
$701$	−25.7270	−0.971696	−0.485848	+	0.874043i	$0.661489\pi$
$702$	0.0696978	0.00263058
$703$	−45.0848	−1.70040
$704$	−9.32316	−0.351380
$705$	1.60505	0.0604499
$706$	27.6155	1.03932
$707$	−57.9537	−2.17957
$708$	−2.47180	−0.0928960
$709$	−25.1540	−0.944678	−0.472339	−	0.881417i	$-0.656590\pi$
$709$	−25.1540	−0.944678	−0.472339	+	0.881417i	$0.656590\pi$
$710$	−1.25767	−0.0471995
$711$	−31.3025	−1.17393
$712$	−0.395771	−0.0148322
$713$	30.1900	1.13063
$714$	8.02643	0.300382
$715$	−0.00203377	−7.60587e−5 0
$716$	33.9827	1.26999
$717$	16.0485	0.599341
$718$	−59.8130	−2.23220
$719$	−38.5325	−1.43702	−0.718511	−	0.695516i	$-0.755176\pi$
$719$	−38.5325	−1.43702	−0.718511	+	0.695516i	$0.755176\pi$
$720$	2.19127	0.0816638
$721$	−49.9192	−1.85909
$722$	23.0783	0.858886
$723$	20.2995	0.754946
$724$	−37.0741	−1.37785
$725$	46.1772	1.71498
$726$	1.65561	0.0614456
$727$	4.84428	0.179664	0.0898321	−	0.995957i	$-0.471367\pi$
$727$	4.84428	0.179664	0.0898321	+	0.995957i	$0.471367\pi$
$728$	−0.0103468	−0.000383477 0
$729$	2.27848	0.0843882
$730$	3.81242	0.141104
$731$	−13.6800	−0.505973
$732$	−1.76149	−0.0651066
$733$	−19.4064	−0.716791	−0.358396	−	0.933570i	$-0.616676\pi$
$733$	−19.4064	−0.716791	−0.358396	+	0.933570i	$0.616676\pi$
$734$	60.3009	2.22575
$735$	1.40467	0.0518120
$736$	−43.2091	−1.59271
$737$	9.44385	0.347869
$738$	32.8421	1.20893
$739$	−38.4782	−1.41544	−0.707721	−	0.706492i	$-0.750277\pi$
$739$	−38.4782	−1.41544	−0.707721	+	0.706492i	$0.750277\pi$
$740$	−4.59573	−0.168943
$741$	−0.0351445	−0.00129107
$742$	28.7244	1.05451
$743$	33.7312	1.23748	0.618739	−	0.785597i	$-0.287644\pi$
$743$	33.7312	1.23748	0.618739	+	0.785597i	$0.287644\pi$
$744$	1.62847	0.0597027
$745$	3.68065	0.134849
$746$	−3.49724	−0.128043
$747$	37.7385	1.38078
$748$	2.84542	0.104039
$749$	25.7419	0.940590
$750$	−4.24524	−0.155014
$751$	−5.71247	−0.208451	−0.104225	−	0.994554i	$-0.533236\pi$
$751$	−5.71247	−0.208451	−0.104225	+	0.994554i	$0.533236\pi$
$752$	−27.7953	−1.01359
$753$	−4.51206	−0.164429
$754$	0.150659	0.00548667
$755$	−1.30523	−0.0475020
$756$	−34.8560	−1.26770
$757$	−21.7395	−0.790137	−0.395068	−	0.918652i	$-0.629279\pi$
$757$	−21.7395	−0.790137	−0.395068	+	0.918652i	$0.629279\pi$
$758$	4.87430	0.177042
$759$	4.31767	0.156722
$760$	0.503849	0.0182765
$761$	−23.7043	−0.859280	−0.429640	−	0.903000i	$-0.641360\pi$
$761$	−23.7043	−0.859280	−0.429640	+	0.903000i	$0.641360\pi$
$762$	22.2045	0.804386
$763$	−22.6996	−0.821780
$764$	12.9047	0.466876
$765$	−0.791833	−0.0286288
$766$	−53.2039	−1.92234
$767$	0.0110558	0.000399201 0
$768$	10.4320	0.376433
$769$	−20.0877	−0.724382	−0.362191	−	0.932104i	$-0.617971\pi$
$769$	−20.0877	−0.724382	−0.362191	+	0.932104i	$0.617971\pi$
$770$	1.95296	0.0703797
$771$	11.7782	0.424181
$772$	−19.0065	−0.684058
$773$	−10.5928	−0.380997	−0.190499	−	0.981687i	$-0.561010\pi$
$773$	−10.5928	−0.380997	−0.190499	+	0.981687i	$0.561010\pi$
$774$	50.0248	1.79810
$775$	−27.9552	−1.00418
$776$	1.09444	0.0392882
$777$	−24.5827	−0.881900
$778$	60.9553	2.18535
$779$	−37.7622	−1.35297
$780$	−0.00358247	−0.000128273 0
$781$	−2.38488	−0.0853376
$782$	14.2485	0.509527
$783$	40.5316	1.44848
$784$	−24.3252	−0.868756
$785$	2.75529	0.0983406
$786$	−34.5308	−1.23167
$787$	36.4962	1.30095	0.650474	−	0.759529i	$-0.274570\pi$
$787$	36.4962	1.30095	0.650474	+	0.759529i	$0.274570\pi$
$788$	26.7875	0.954265
$789$	1.14034	0.0405972
$790$	7.04471	0.250640
$791$	−29.9529	−1.06500
$792$	−0.830946	−0.0295264
$793$	0.00787872	0.000279782 0
$794$	−17.1783	−0.609637
$795$	0.794247	0.0281690
$796$	−9.89159	−0.350598
$797$	−37.3176	−1.32186	−0.660928	−	0.750449i	$-0.729837\pi$
$797$	−37.3176	−1.32186	−0.660928	+	0.750449i	$0.729837\pi$
$798$	33.7481	1.19467
$799$	10.0441	0.355334
$800$	40.0105	1.41459
$801$	2.61519	0.0924032
$802$	7.23008	0.255303
$803$	7.22936	0.255119
$804$	16.6353	0.586681
$805$	5.09312	0.179509
$806$	−0.0912072	−0.00321264
$807$	−14.1329	−0.497500
$808$	−5.54940	−0.195227
$809$	3.35331	0.117896	0.0589481	−	0.998261i	$-0.481225\pi$
$809$	3.35331	0.117896	0.0589481	+	0.998261i	$0.481225\pi$
$810$	1.85652	0.0652315
$811$	45.4775	1.59693	0.798466	−	0.602040i	$-0.205645\pi$
$811$	45.4775	1.59693	0.798466	+	0.602040i	$0.205645\pi$
$812$	−75.3446	−2.64408
$813$	6.93129	0.243091
$814$	−16.7335	−0.586509
$815$	5.49162	0.192363
$816$	−3.84334	−0.134544
$817$	−57.5191	−2.01234
$818$	55.8780	1.95373
$819$	0.0683697	0.00238903
$820$	−3.84931	−0.134424
$821$	40.0896	1.39914	0.699569	−	0.714566i	$-0.253376\pi$
$821$	40.0896	1.39914	0.699569	+	0.714566i	$0.253376\pi$
$822$	−30.0953	−1.04969
$823$	39.0760	1.36211	0.681053	−	0.732235i	$-0.261523\pi$
$823$	39.0760	1.36211	0.681053	+	0.732235i	$0.261523\pi$
$824$	−4.78005	−0.166521
$825$	−3.99805	−0.139194
$826$	−10.6165	−0.369394
$827$	36.3950	1.26558	0.632790	−	0.774324i	$-0.281910\pi$
$827$	36.3950	1.26558	0.632790	+	0.774324i	$0.281910\pi$
$828$	−27.1354	−0.943021
$829$	15.1932	0.527682	0.263841	−	0.964566i	$-0.415011\pi$
$829$	15.1932	0.527682	0.263841	+	0.964566i	$0.415011\pi$
$830$	−8.49316	−0.294802
$831$	19.4671	0.675306
$832$	0.0734546	0.00254658
$833$	8.79010	0.304559
$834$	26.2698	0.909649
$835$	6.39637	0.221356
$836$	11.9639	0.413780
$837$	−24.5374	−0.848136
$838$	3.57880	0.123628
$839$	−44.7668	−1.54552	−0.772760	−	0.634698i	$-0.781124\pi$
$839$	−44.7668	−1.54552	−0.772760	+	0.634698i	$0.781124\pi$
$840$	0.274726	0.00947896
$841$	58.6130	2.02114
$842$	47.7859	1.64681
$843$	−11.1446	−0.383840
$844$	40.5089	1.39437
$845$	−3.35574	−0.115441
$846$	−36.7290	−1.26277
$847$	3.70333	0.127248
$848$	−13.7543	−0.472324
$849$	10.7962	0.370525
$850$	−13.1938	−0.452543
$851$	−43.6393	−1.49593
$852$	−4.20094	−0.143922
$853$	−15.9365	−0.545655	−0.272828	−	0.962063i	$-0.587959\pi$
$853$	−15.9365	−0.545655	−0.272828	+	0.962063i	$0.587959\pi$
$854$	−7.56566	−0.258891
$855$	−3.32935	−0.113861
$856$	2.46494	0.0842498
$857$	16.0604	0.548613	0.274306	−	0.961642i	$-0.411552\pi$
$857$	16.0604	0.548613	0.274306	+	0.961642i	$0.411552\pi$
$858$	−0.0130441	−0.000445319 0
$859$	10.4010	0.354879	0.177439	−	0.984132i	$-0.443219\pi$
$859$	10.4010	0.354879	0.177439	+	0.984132i	$0.443219\pi$
$860$	−5.86323	−0.199934
$861$	−20.5901	−0.701707
$862$	−8.81893	−0.300374
$863$	7.63100	0.259762	0.129881	−	0.991530i	$-0.458540\pi$
$863$	7.63100	0.259762	0.129881	+	0.991530i	$0.458540\pi$
$864$	35.1188	1.19477
$865$	3.73728	0.127071
$866$	−28.4592	−0.967084
$867$	−12.3881	−0.420724
$868$	45.6128	1.54820
$869$	13.3586	0.453161
$870$	−4.00028	−0.135622
$871$	−0.0744055	−0.00252113
$872$	−2.17362	−0.0736079
$873$	−7.23189	−0.244762
$874$	59.9096	2.02647
$875$	−9.49588	−0.321019
$876$	12.7345	0.430258
$877$	20.0264	0.676243	0.338121	−	0.941103i	$-0.390209\pi$
$877$	20.0264	0.676243	0.338121	+	0.941103i	$0.390209\pi$
$878$	66.2795	2.23683
$879$	−2.21439	−0.0746897
$880$	−0.935147	−0.0315238
$881$	−28.9606	−0.975707	−0.487854	−	0.872925i	$-0.662220\pi$
$881$	−28.9606	−0.975707	−0.487854	+	0.872925i	$0.662220\pi$
$882$	−32.1435	−1.08233
$883$	−5.61907	−0.189097	−0.0945483	−	0.995520i	$-0.530141\pi$
$883$	−5.61907	−0.189097	−0.0945483	+	0.995520i	$0.530141\pi$
$884$	−0.0224183	−0.000754009 0
$885$	−0.293552	−0.00986763
$886$	18.1931	0.611210
$887$	−25.4708	−0.855227	−0.427614	−	0.903962i	$-0.640646\pi$
$887$	−25.4708	−0.855227	−0.427614	+	0.903962i	$0.640646\pi$
$888$	−2.35393	−0.0789929
$889$	49.6678	1.66580
$890$	−0.588556	−0.0197285
$891$	3.52046	0.117940
$892$	−16.3301	−0.546772
$893$	42.2314	1.41322
$894$	23.6068	0.789531
$895$	4.03579	0.134902
$896$	−10.4665	−0.349660
$897$	−0.0340177	−0.00113582
$898$	−20.4126	−0.681179
$899$	−53.0399	−1.76898
$900$	25.1267	0.837556
$901$	4.97022	0.165582
$902$	−14.0157	−0.466672
$903$	−31.3626	−1.04368
$904$	−2.86816	−0.0953937
$905$	−4.40292	−0.146358
$906$	−8.37141	−0.278121
$907$	17.8521	0.592769	0.296384	−	0.955069i	$-0.404219\pi$
$907$	17.8521	0.592769	0.296384	+	0.955069i	$0.404219\pi$
$908$	29.8140	0.989411
$909$	36.6695	1.21625
$910$	−0.0153868	−0.000510068 0
$911$	8.27741	0.274243	0.137121	−	0.990554i	$-0.456215\pi$
$911$	8.27741	0.274243	0.137121	+	0.990554i	$0.456215\pi$
$912$	−16.1598	−0.535104
$913$	−16.1053	−0.533007
$914$	−13.8400	−0.457786
$915$	−0.209195	−0.00691577
$916$	34.7050	1.14668
$917$	−77.2396	−2.55068
$918$	−11.5807	−0.382220
$919$	34.4100	1.13508	0.567541	−	0.823345i	$-0.307895\pi$
$919$	34.4100	1.13508	0.567541	+	0.823345i	$0.307895\pi$
$920$	0.487695	0.0160788
$921$	−3.45434	−0.113824
$922$	−62.2749	−2.05091
$923$	0.0187898	0.000618473 0
$924$	6.52338	0.214604
$925$	40.4088	1.32863
$926$	62.4883	2.05349
$927$	31.5858	1.03741
$928$	75.9128	2.49196
$929$	−4.44967	−0.145989	−0.0729945	−	0.997332i	$-0.523256\pi$
$929$	−4.44967	−0.145989	−0.0729945	+	0.997332i	$0.523256\pi$
$930$	2.42172	0.0794115
$931$	36.9590	1.21128
$932$	4.60861	0.150960
$933$	−18.1649	−0.594692
$934$	−15.9886	−0.523162
$935$	0.337923	0.0110513
$936$	0.00654679	0.000213989 0
$937$	12.1561	0.397121	0.198561	−	0.980089i	$-0.436373\pi$
$937$	12.1561	0.397121	0.198561	+	0.980089i	$0.436373\pi$
$938$	71.4490	2.33289
$939$	13.5252	0.441379
$940$	4.30488	0.140410
$941$	−6.21548	−0.202619	−0.101310	−	0.994855i	$-0.532303\pi$
$941$	−6.21548	−0.202619	−0.101310	+	0.994855i	$0.532303\pi$
$942$	17.6718	0.575778
$943$	−36.5515	−1.19028
$944$	5.08354	0.165455
$945$	−4.13950	−0.134658
$946$	−21.3486	−0.694102
$947$	−6.30385	−0.204848	−0.102424	−	0.994741i	$-0.532660\pi$
$947$	−6.30385	−0.204848	−0.102424	+	0.994741i	$0.532660\pi$
$948$	23.5312	0.764256
$949$	−0.0569581	−0.00184894
$950$	−55.4747	−1.79984
$951$	1.26300	0.0409554
$952$	1.71918	0.0557188
$953$	7.96427	0.257988	0.128994	−	0.991645i	$-0.458825\pi$
$953$	7.96427	0.257988	0.128994	+	0.991645i	$0.458825\pi$
$954$	−18.1750	−0.588438
$955$	1.53256	0.0495926
$956$	43.0432	1.39212
$957$	−7.58559	−0.245207
$958$	−53.4664	−1.72742
$959$	−67.3181	−2.17381
$960$	−1.95036	−0.0629475
$961$	1.10981	0.0358002
$962$	0.131839	0.00425065
$963$	−16.2879	−0.524870
$964$	54.4448	1.75355
$965$	−2.25721	−0.0726622
$966$	32.6660	1.05101
$967$	−1.30919	−0.0421007	−0.0210503	−	0.999778i	$-0.506701\pi$
$967$	−1.30919	−0.0421007	−0.0210503	+	0.999778i	$0.506701\pi$
$968$	0.354615	0.0113978
$969$	5.83947	0.187591
$970$	1.62756	0.0522578
$971$	−4.43427	−0.142303	−0.0711513	−	0.997466i	$-0.522667\pi$
$971$	−4.43427	−0.142303	−0.0711513	+	0.997466i	$0.522667\pi$
$972$	34.4375	1.10458
$973$	58.7611	1.88379
$974$	−43.7563	−1.40204
$975$	0.0314995	0.00100879
$976$	3.62271	0.115960
$977$	11.8370	0.378700	0.189350	−	0.981910i	$-0.439362\pi$
$977$	11.8370	0.378700	0.189350	+	0.981910i	$0.439362\pi$
$978$	35.2219	1.12627
$979$	−1.11606	−0.0356694
$980$	3.76743	0.120346
$981$	14.3629	0.458572
$982$	37.9169	1.20998
$983$	33.6534	1.07338	0.536689	−	0.843780i	$-0.319675\pi$
$983$	33.6534	1.07338	0.536689	+	0.843780i	$0.319675\pi$
$984$	−1.97162	−0.0628528
$985$	3.18129	0.101364
$986$	−25.0328	−0.797208
$987$	23.0269	0.732954
$988$	−0.0942603	−0.00299882
$989$	−55.6749	−1.77036
$990$	−1.23571	−0.0392735
$991$	−50.9965	−1.61996	−0.809979	−	0.586459i	$-0.800521\pi$
$991$	−50.9965	−1.61996	−0.809979	+	0.586459i	$0.800521\pi$
$992$	−45.9568	−1.45913
$993$	−28.4553	−0.903001
$994$	−18.0432	−0.572294
$995$	−1.17473	−0.0372413
$996$	−28.3693	−0.898917
$997$	−1.72155	−0.0545219	−0.0272610	−	0.999628i	$-0.508679\pi$
$997$	−1.72155	−0.0545219	−0.0272610	+	0.999628i	$0.508679\pi$
$998$	8.75899	0.277261
$999$	35.4684	1.12217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.15	✓	19
3.2	odd	2		6039.2.a.k.1.5		19
11.10	odd	2		7381.2.a.i.1.5		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.15	✓	19	1.1	even	1	trivial
6039.2.a.k.1.5		19	3.2	odd	2
7381.2.a.i.1.5		19	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+2.04293 q^{2} +0.810410 q^{3} +2.17358 q^{4} +0.258135 q^{5} +1.65561 q^{6} +3.70333 q^{7} +0.354615 q^{8} -2.34324 q^{9} +O(q^{10})\)	\(q+2.04293 q^{2} +0.810410 q^{3} +2.17358 q^{4} +0.258135 q^{5} +1.65561 q^{6} +3.70333 q^{7} +0.354615 q^{8} -2.34324 q^{9} +0.527352 q^{10} +1.00000 q^{11} +1.76149 q^{12} -0.00787872 q^{13} +7.56566 q^{14} +0.209195 q^{15} -3.62271 q^{16} +1.30910 q^{17} -4.78708 q^{18} +5.50424 q^{19} +0.561077 q^{20} +3.00121 q^{21} +2.04293 q^{22} +5.32776 q^{23} +0.287383 q^{24} -4.93337 q^{25} -0.0160957 q^{26} -4.33021 q^{27} +8.04948 q^{28} -9.36018 q^{29} +0.427372 q^{30} +5.66655 q^{31} -8.11018 q^{32} +0.810410 q^{33} +2.67440 q^{34} +0.955958 q^{35} -5.09321 q^{36} -8.19092 q^{37} +11.2448 q^{38} -0.00638500 q^{39} +0.0915384 q^{40} -6.86058 q^{41} +6.13128 q^{42} -10.4500 q^{43} +2.17358 q^{44} -0.604870 q^{45} +10.8843 q^{46} +7.67253 q^{47} -2.93588 q^{48} +6.71464 q^{49} -10.0785 q^{50} +1.06090 q^{51} -0.0171250 q^{52} +3.79668 q^{53} -8.84634 q^{54} +0.258135 q^{55} +1.31326 q^{56} +4.46069 q^{57} -19.1222 q^{58} -1.40324 q^{59} +0.454702 q^{60} -1.00000 q^{61} +11.5764 q^{62} -8.67777 q^{63} -9.32316 q^{64} -0.00203377 q^{65} +1.65561 q^{66} +9.44385 q^{67} +2.84542 q^{68} +4.31767 q^{69} +1.95296 q^{70} -2.38488 q^{71} -0.830946 q^{72} +7.22936 q^{73} -16.7335 q^{74} -3.99805 q^{75} +11.9639 q^{76} +3.70333 q^{77} -0.0130441 q^{78} +13.3586 q^{79} -0.935147 q^{80} +3.52046 q^{81} -14.0157 q^{82} -16.1053 q^{83} +6.52338 q^{84} +0.337923 q^{85} -21.3486 q^{86} -7.58559 q^{87} +0.354615 q^{88} -1.11606 q^{89} -1.23571 q^{90} -0.0291775 q^{91} +11.5803 q^{92} +4.59223 q^{93} +15.6745 q^{94} +1.42084 q^{95} -6.57258 q^{96} +3.08628 q^{97} +13.7176 q^{98} -2.34324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * q^99

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