LMFDB - Embedded newform 4013.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$1$
Dimension:	$157$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47196 q^{2} +3.17720 q^{3} +4.11056 q^{4} +1.49907 q^{5} -7.85391 q^{6} +0.578951 q^{7} -5.21722 q^{8} +7.09463 q^{9} +O(q^{10})$	\(q-2.47196 q^{2} +3.17720 q^{3} +4.11056 q^{4} +1.49907 q^{5} -7.85391 q^{6} +0.578951 q^{7} -5.21722 q^{8} +7.09463 q^{9} -3.70563 q^{10} -3.62820 q^{11} +13.0601 q^{12} -5.86699 q^{13} -1.43114 q^{14} +4.76285 q^{15} +4.67561 q^{16} +0.953941 q^{17} -17.5376 q^{18} -2.12315 q^{19} +6.16202 q^{20} +1.83945 q^{21} +8.96875 q^{22} -7.14598 q^{23} -16.5762 q^{24} -2.75279 q^{25} +14.5029 q^{26} +13.0095 q^{27} +2.37982 q^{28} -7.91699 q^{29} -11.7735 q^{30} -10.1236 q^{31} -1.12345 q^{32} -11.5275 q^{33} -2.35810 q^{34} +0.867887 q^{35} +29.1629 q^{36} +9.62322 q^{37} +5.24834 q^{38} -18.6406 q^{39} -7.82097 q^{40} -3.68038 q^{41} -4.54703 q^{42} -6.35709 q^{43} -14.9139 q^{44} +10.6353 q^{45} +17.6645 q^{46} +8.52677 q^{47} +14.8554 q^{48} -6.66482 q^{49} +6.80478 q^{50} +3.03087 q^{51} -24.1166 q^{52} +4.31509 q^{53} -32.1588 q^{54} -5.43892 q^{55} -3.02051 q^{56} -6.74570 q^{57} +19.5704 q^{58} -10.2964 q^{59} +19.5780 q^{60} -4.64279 q^{61} +25.0251 q^{62} +4.10744 q^{63} -6.57409 q^{64} -8.79502 q^{65} +28.4955 q^{66} +1.76436 q^{67} +3.92123 q^{68} -22.7042 q^{69} -2.14538 q^{70} +3.02266 q^{71} -37.0142 q^{72} -1.36938 q^{73} -23.7882 q^{74} -8.74619 q^{75} -8.72736 q^{76} -2.10055 q^{77} +46.0788 q^{78} +10.0069 q^{79} +7.00906 q^{80} +20.0499 q^{81} +9.09774 q^{82} -3.15643 q^{83} +7.56116 q^{84} +1.43002 q^{85} +15.7145 q^{86} -25.1539 q^{87} +18.9291 q^{88} +17.9657 q^{89} -26.2901 q^{90} -3.39670 q^{91} -29.3740 q^{92} -32.1648 q^{93} -21.0778 q^{94} -3.18276 q^{95} -3.56944 q^{96} -0.134843 q^{97} +16.4751 q^{98} -25.7407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) $ 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * 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 $

$2$	−2.47196	−1.74794	−0.873968	−	0.485983i	$-0.838462\pi$
$2$	−2.47196	−1.74794	−0.873968	+	0.485983i	$0.838462\pi$
$3$	3.17720	1.83436	0.917180	−	0.398473i	$-0.130460\pi$
$3$	3.17720	1.83436	0.917180	+	0.398473i	$0.130460\pi$
$4$	4.11056	2.05528
$5$	1.49907	0.670404	0.335202	−	0.942146i	$-0.391195\pi$
$5$	1.49907	0.670404	0.335202	+	0.942146i	$0.391195\pi$
$6$	−7.85391	−3.20634
$7$	0.578951	0.218823	0.109411	−	0.993997i	$-0.465103\pi$
$7$	0.578951	0.218823	0.109411	+	0.993997i	$0.465103\pi$
$8$	−5.21722	−1.84457
$9$	7.09463	2.36488
$10$	−3.70563	−1.17182
$11$	−3.62820	−1.09394	−0.546972	−	0.837151i	$-0.684219\pi$
$11$	−3.62820	−1.09394	−0.546972	+	0.837151i	$0.684219\pi$
$12$	13.0601	3.77013
$13$	−5.86699	−1.62721	−0.813605	−	0.581418i	$-0.802498\pi$
$13$	−5.86699	−1.62721	−0.813605	+	0.581418i	$0.802498\pi$
$14$	−1.43114	−0.382489
$15$	4.76285	1.22976
$16$	4.67561	1.16890
$17$	0.953941	0.231365	0.115682	−	0.993286i	$-0.463095\pi$
$17$	0.953941	0.231365	0.115682	+	0.993286i	$0.463095\pi$
$18$	−17.5376	−4.13365
$19$	−2.12315	−0.487085	−0.243543	−	0.969890i	$-0.578310\pi$
$19$	−2.12315	−0.487085	−0.243543	+	0.969890i	$0.578310\pi$
$20$	6.16202	1.37787
$21$	1.83945	0.401400
$22$	8.96875	1.91214
$23$	−7.14598	−1.49004	−0.745020	−	0.667043i	$-0.767560\pi$
$23$	−7.14598	−1.49004	−0.745020	+	0.667043i	$0.767560\pi$
$24$	−16.5762	−3.38360
$25$	−2.75279	−0.550559
$26$	14.5029	2.84426
$27$	13.0095	2.50367
$28$	2.37982	0.449743
$29$	−7.91699	−1.47015	−0.735074	−	0.677987i	$-0.762852\pi$
$29$	−7.91699	−1.47015	−0.735074	+	0.677987i	$0.762852\pi$
$30$	−11.7735	−2.14955
$31$	−10.1236	−1.81826	−0.909128	−	0.416518i	$-0.863250\pi$
$31$	−10.1236	−1.81826	−0.909128	+	0.416518i	$0.863250\pi$
$32$	−1.12345	−0.198600
$33$	−11.5275	−2.00669
$34$	−2.35810	−0.404411
$35$	0.867887	0.146700
$36$	29.1629	4.86049
$37$	9.62322	1.58205	0.791024	−	0.611785i	$-0.209548\pi$
$37$	9.62322	1.58205	0.791024	+	0.611785i	$0.209548\pi$
$38$	5.24834	0.851394
$39$	−18.6406	−2.98489
$40$	−7.82097	−1.23660
$41$	−3.68038	−0.574779	−0.287390	−	0.957814i	$-0.592787\pi$
$41$	−3.68038	−0.574779	−0.287390	+	0.957814i	$0.592787\pi$
$42$	−4.54703	−0.701622
$43$	−6.35709	−0.969448	−0.484724	−	0.874667i	$-0.661080\pi$
$43$	−6.35709	−0.969448	−0.484724	+	0.874667i	$0.661080\pi$
$44$	−14.9139	−2.24836
$45$	10.6353	1.58542
$46$	17.6645	2.60449
$47$	8.52677	1.24376	0.621878	−	0.783114i	$-0.286370\pi$
$47$	8.52677	1.24376	0.621878	+	0.783114i	$0.286370\pi$
$48$	14.8554	2.14419
$49$	−6.66482	−0.952117
$50$	6.80478	0.962341
$51$	3.03087	0.424406
$52$	−24.1166	−3.34438
$53$	4.31509	0.592723	0.296361	−	0.955076i	$-0.404227\pi$
$53$	4.31509	0.592723	0.296361	+	0.955076i	$0.404227\pi$
$54$	−32.1588	−4.37626
$55$	−5.43892	−0.733384
$56$	−3.02051	−0.403633
$57$	−6.74570	−0.893489
$58$	19.5704	2.56972
$59$	−10.2964	−1.34048	−0.670238	−	0.742146i	$-0.733808\pi$
$59$	−10.2964	−1.34048	−0.670238	+	0.742146i	$0.733808\pi$
$60$	19.5780	2.52751
$61$	−4.64279	−0.594448	−0.297224	−	0.954808i	$-0.596061\pi$
$61$	−4.64279	−0.594448	−0.297224	+	0.954808i	$0.596061\pi$
$62$	25.0251	3.17819
$63$	4.10744	0.517489
$64$	−6.57409	−0.821761
$65$	−8.79502	−1.09089
$66$	28.4955	3.50756
$67$	1.76436	0.215551	0.107776	−	0.994175i	$-0.465627\pi$
$67$	1.76436	0.215551	0.107776	+	0.994175i	$0.465627\pi$
$68$	3.92123	0.475520
$69$	−22.7042	−2.73327
$70$	−2.14538	−0.256422
$71$	3.02266	0.358724	0.179362	−	0.983783i	$-0.442597\pi$
$71$	3.02266	0.358724	0.179362	+	0.983783i	$0.442597\pi$
$72$	−37.0142	−4.36217
$73$	−1.36938	−0.160274	−0.0801369	−	0.996784i	$-0.525536\pi$
$73$	−1.36938	−0.160274	−0.0801369	+	0.996784i	$0.525536\pi$
$74$	−23.7882	−2.76532
$75$	−8.74619	−1.00992
$76$	−8.72736	−1.00110
$77$	−2.10055	−0.239380
$78$	46.0788	5.21740
$79$	10.0069	1.12587	0.562933	−	0.826502i	$-0.309673\pi$
$79$	10.0069	1.12587	0.562933	+	0.826502i	$0.309673\pi$
$80$	7.00906	0.783636
$81$	20.0499	2.22776
$82$	9.09774	1.00468
$83$	−3.15643	−0.346463	−0.173232	−	0.984881i	$-0.555421\pi$
$83$	−3.15643	−0.346463	−0.173232	+	0.984881i	$0.555421\pi$
$84$	7.56116	0.824990
$85$	1.43002	0.155108
$86$	15.7145	1.69453
$87$	−25.1539	−2.69678
$88$	18.9291	2.01785
$89$	17.9657	1.90436	0.952181	−	0.305536i	$-0.0988356\pi$
$89$	17.9657	1.90436	0.952181	+	0.305536i	$0.0988356\pi$
$90$	−26.2901	−2.77122
$91$	−3.39670	−0.356071
$92$	−29.3740	−3.06245
$93$	−32.1648	−3.33533
$94$	−21.0778	−2.17401
$95$	−3.18276	−0.326544
$96$	−3.56944	−0.364304
$97$	−0.134843	−0.0136913	−0.00684563	−	0.999977i	$-0.502179\pi$
$97$	−0.134843	−0.0136913	−0.00684563	+	0.999977i	$0.502179\pi$
$98$	16.4751	1.66424
$99$	−25.7407	−2.58704
$100$	−11.3155	−1.13155
$101$	8.34191	0.830051	0.415026	−	0.909810i	$-0.363773\pi$
$101$	8.34191	0.830051	0.415026	+	0.909810i	$0.363773\pi$
$102$	−7.49216	−0.741835
$103$	−3.40494	−0.335499	−0.167750	−	0.985830i	$-0.553650\pi$
$103$	−3.40494	−0.335499	−0.167750	+	0.985830i	$0.553650\pi$
$104$	30.6094	3.00150
$105$	2.75746	0.269100
$106$	−10.6667	−1.03604
$107$	−1.27847	−0.123595	−0.0617974	−	0.998089i	$-0.519683\pi$
$107$	−1.27847	−0.123595	−0.0617974	+	0.998089i	$0.519683\pi$
$108$	53.4763	5.14576
$109$	−6.70652	−0.642368	−0.321184	−	0.947017i	$-0.604081\pi$
$109$	−6.70652	−0.642368	−0.321184	+	0.947017i	$0.604081\pi$
$110$	13.4448	1.28191
$111$	30.5750	2.90205
$112$	2.70695	0.255782
$113$	7.82515	0.736128	0.368064	−	0.929800i	$-0.380021\pi$
$113$	7.82515	0.736128	0.368064	+	0.929800i	$0.380021\pi$
$114$	16.6751	1.56176
$115$	−10.7123	−0.998928
$116$	−32.5433	−3.02157
$117$	−41.6241	−3.84815
$118$	25.4522	2.34307
$119$	0.552285	0.0506279
$120$	−24.8488	−2.26838
$121$	2.16383	0.196712
$122$	11.4768	1.03906
$123$	−11.6933	−1.05435
$124$	−41.6138	−3.73703
$125$	−11.6220	−1.03950
$126$	−10.1534	−0.904538
$127$	4.79010	0.425053	0.212526	−	0.977155i	$-0.431831\pi$
$127$	4.79010	0.425053	0.212526	+	0.977155i	$0.431831\pi$
$128$	18.4978	1.63499
$129$	−20.1978	−1.77832
$130$	21.7409	1.90680
$131$	−14.0423	−1.22688	−0.613442	−	0.789739i	$-0.710216\pi$
$131$	−14.0423	−1.22688	−0.613442	+	0.789739i	$0.710216\pi$
$132$	−47.3847	−4.12430
$133$	−1.22920	−0.106585
$134$	−4.36143	−0.376770
$135$	19.5021	1.67847
$136$	−4.97692	−0.426767
$137$	9.09311	0.776877	0.388438	−	0.921475i	$-0.373015\pi$
$137$	9.09311	0.776877	0.388438	+	0.921475i	$0.373015\pi$
$138$	56.1238	4.77758
$139$	−11.8603	−1.00598	−0.502988	−	0.864293i	$-0.667766\pi$
$139$	−11.8603	−1.00598	−0.502988	+	0.864293i	$0.667766\pi$
$140$	3.56751	0.301509
$141$	27.0913	2.28150
$142$	−7.47189	−0.627027
$143$	21.2866	1.78008
$144$	33.1717	2.76431
$145$	−11.8681	−0.985593
$146$	3.38505	0.280148
$147$	−21.1755	−1.74652
$148$	39.5569	3.25156
$149$	−21.5887	−1.76861	−0.884307	−	0.466906i	$-0.845368\pi$
$149$	−21.5887	−1.76861	−0.884307	+	0.466906i	$0.845368\pi$
$150$	21.6202	1.76528
$151$	−4.54011	−0.369469	−0.184734	−	0.982788i	$-0.559142\pi$
$151$	−4.54011	−0.369469	−0.184734	+	0.982788i	$0.559142\pi$
$152$	11.0770	0.898461
$153$	6.76786	0.547149
$154$	5.19247	0.418421
$155$	−15.1760	−1.21897
$156$	−76.6235	−6.13479
$157$	−5.18490	−0.413800	−0.206900	−	0.978362i	$-0.566337\pi$
$157$	−5.18490	−0.413800	−0.206900	+	0.978362i	$0.566337\pi$
$158$	−24.7367	−1.96794
$159$	13.7099	1.08727
$160$	−1.68413	−0.133142
$161$	−4.13717	−0.326055
$162$	−49.5624	−3.89399
$163$	−15.4552	−1.21054	−0.605272	−	0.796018i	$-0.706936\pi$
$163$	−15.4552	−1.21054	−0.605272	+	0.796018i	$0.706936\pi$
$164$	−15.1285	−1.18133
$165$	−17.2806	−1.34529
$166$	7.80255	0.605595
$167$	6.06231	0.469116	0.234558	−	0.972102i	$-0.424636\pi$
$167$	6.06231	0.469116	0.234558	+	0.972102i	$0.424636\pi$
$168$	−9.59679	−0.740409
$169$	21.4216	1.64781
$170$	−3.53495	−0.271119
$171$	−15.0630	−1.15190
$172$	−26.1312	−1.99249
$173$	−9.10593	−0.692311	−0.346156	−	0.938177i	$-0.612513\pi$
$173$	−9.10593	−0.692311	−0.346156	+	0.938177i	$0.612513\pi$
$174$	62.1793	4.71380
$175$	−1.59373	−0.120475
$176$	−16.9640	−1.27871
$177$	−32.7138	−2.45892
$178$	−44.4104	−3.32870
$179$	16.6365	1.24347	0.621735	−	0.783228i	$-0.286428\pi$
$179$	16.6365	1.24347	0.621735	+	0.783228i	$0.286428\pi$
$180$	43.7172	3.25849
$181$	−3.58419	−0.266411	−0.133205	−	0.991088i	$-0.542527\pi$
$181$	−3.58419	−0.266411	−0.133205	+	0.991088i	$0.542527\pi$
$182$	8.39649	0.622389
$183$	−14.7511	−1.09043
$184$	37.2821	2.74848
$185$	14.4259	1.06061
$186$	79.5100	5.82995
$187$	−3.46109	−0.253100
$188$	35.0498	2.55627
$189$	7.53185	0.547861
$190$	7.86763	0.570778
$191$	20.7986	1.50494	0.752468	−	0.658629i	$-0.228863\pi$
$191$	20.7986	1.50494	0.752468	+	0.658629i	$0.228863\pi$
$192$	−20.8872	−1.50741
$193$	21.3070	1.53371	0.766856	−	0.641819i	$-0.221820\pi$
$193$	21.3070	1.53371	0.766856	+	0.641819i	$0.221820\pi$
$194$	0.333326	0.0239314
$195$	−27.9436	−2.00108
$196$	−27.3961	−1.95687
$197$	27.6771	1.97191	0.985955	−	0.167010i	$-0.0534113\pi$
$197$	27.6771	1.97191	0.985955	+	0.167010i	$0.0534113\pi$
$198$	63.6299	4.52198
$199$	−10.5391	−0.747097	−0.373549	−	0.927611i	$-0.621859\pi$
$199$	−10.5391	−0.747097	−0.373549	+	0.927611i	$0.621859\pi$
$200$	14.3619	1.01554
$201$	5.60574	0.395398
$202$	−20.6208	−1.45088
$203$	−4.58355	−0.321702
$204$	12.4586	0.872274
$205$	−5.51715	−0.385334
$206$	8.41687	0.586431
$207$	−50.6981	−3.52376
$208$	−27.4317	−1.90205
$209$	7.70323	0.532844
$210$	−6.81631	−0.470370
$211$	14.1610	0.974880	0.487440	−	0.873156i	$-0.337931\pi$
$211$	14.1610	0.974880	0.487440	+	0.873156i	$0.337931\pi$
$212$	17.7374	1.21821
$213$	9.60362	0.658029
$214$	3.16033	0.216036
$215$	−9.52972	−0.649922
$216$	−67.8733	−4.61819
$217$	−5.86108	−0.397876
$218$	16.5782	1.12282
$219$	−4.35080	−0.294000
$220$	−22.3570	−1.50731
$221$	−5.59676	−0.376479
$222$	−75.5799	−5.07259
$223$	1.18469	0.0793327	0.0396664	−	0.999213i	$-0.487370\pi$
$223$	1.18469	0.0793327	0.0396664	+	0.999213i	$0.487370\pi$
$224$	−0.650424	−0.0434583
$225$	−19.5300	−1.30200
$226$	−19.3434	−1.28670
$227$	−22.8977	−1.51977	−0.759886	−	0.650057i	$-0.774745\pi$
$227$	−22.8977	−1.51977	−0.759886	+	0.650057i	$0.774745\pi$
$228$	−27.7286	−1.83637
$229$	20.0150	1.32263	0.661313	−	0.750110i	$-0.269999\pi$
$229$	20.0150	1.32263	0.661313	+	0.750110i	$0.269999\pi$
$230$	26.4804	1.74606
$231$	−6.67388	−0.439109
$232$	41.3047	2.71178
$233$	−7.46751	−0.489213	−0.244606	−	0.969622i	$-0.578659\pi$
$233$	−7.46751	−0.489213	−0.244606	+	0.969622i	$0.578659\pi$
$234$	102.893	6.72632
$235$	12.7822	0.833820
$236$	−42.3240	−2.75506
$237$	31.7940	2.06524
$238$	−1.36522	−0.0884943
$239$	20.6462	1.33549	0.667745	−	0.744390i	$-0.267260\pi$
$239$	20.6462	1.33549	0.667745	+	0.744390i	$0.267260\pi$
$240$	22.2692	1.43747
$241$	4.53419	0.292073	0.146036	−	0.989279i	$-0.453348\pi$
$241$	4.53419	0.292073	0.146036	+	0.989279i	$0.453348\pi$
$242$	−5.34890	−0.343840
$243$	24.6741	1.58285
$244$	−19.0845	−1.22176
$245$	−9.99102	−0.638303
$246$	28.9054	1.84294
$247$	12.4565	0.792590
$248$	52.8171	3.35389
$249$	−10.0286	−0.635538
$250$	28.7290	1.81698
$251$	13.8865	0.876506	0.438253	−	0.898852i	$-0.355597\pi$
$251$	13.8865	0.876506	0.438253	+	0.898852i	$0.355597\pi$
$252$	16.8839	1.06359
$253$	25.9270	1.63002
$254$	−11.8409	−0.742965
$255$	4.54348	0.284523
$256$	−32.5775	−2.03609
$257$	2.78642	0.173812	0.0869060	−	0.996217i	$-0.472302\pi$
$257$	2.78642	0.173812	0.0869060	+	0.996217i	$0.472302\pi$
$258$	49.9280	3.10838
$259$	5.57138	0.346188
$260$	−36.1525	−2.24208
$261$	−56.1681	−3.47672
$262$	34.7120	2.14452
$263$	5.47237	0.337441	0.168720	−	0.985664i	$-0.446036\pi$
$263$	5.47237	0.337441	0.168720	+	0.985664i	$0.446036\pi$
$264$	60.1417	3.70146
$265$	6.46861	0.397364
$266$	3.03853	0.186305
$267$	57.0807	3.49328
$268$	7.25252	0.443018
$269$	15.9910	0.974991	0.487495	−	0.873126i	$-0.337911\pi$
$269$	15.9910	0.974991	0.487495	+	0.873126i	$0.337911\pi$
$270$	−48.2083	−2.93386
$271$	7.87921	0.478628	0.239314	−	0.970942i	$-0.423078\pi$
$271$	7.87921	0.478628	0.239314	+	0.970942i	$0.423078\pi$
$272$	4.46025	0.270443
$273$	−10.7920	−0.653162
$274$	−22.4778	−1.35793
$275$	9.98768	0.602280
$276$	−93.3272	−5.61764
$277$	13.9030	0.835350	0.417675	−	0.908597i	$-0.362845\pi$
$277$	13.9030	0.835350	0.417675	+	0.908597i	$0.362845\pi$
$278$	29.3181	1.75838
$279$	−71.8233	−4.29995
$280$	−4.52796	−0.270597
$281$	21.7003	1.29453	0.647265	−	0.762265i	$-0.275913\pi$
$281$	21.7003	1.29453	0.647265	+	0.762265i	$0.275913\pi$
$282$	−66.9685	−3.98791
$283$	−24.5177	−1.45743	−0.728714	−	0.684818i	$-0.759882\pi$
$283$	−24.5177	−1.45743	−0.728714	+	0.684818i	$0.759882\pi$
$284$	12.4249	0.737280
$285$	−10.1123	−0.598999
$286$	−52.6195	−3.11146
$287$	−2.13076	−0.125775
$288$	−7.97048	−0.469665
$289$	−16.0900	−0.946470
$290$	29.3374	1.72275
$291$	−0.428424	−0.0251147
$292$	−5.62892	−0.329408
$293$	−0.935697	−0.0546640	−0.0273320	−	0.999626i	$-0.508701\pi$
$293$	−0.935697	−0.0546640	−0.0273320	+	0.999626i	$0.508701\pi$
$294$	52.3448	3.05281
$295$	−15.4350	−0.898661
$296$	−50.2065	−2.91819
$297$	−47.2010	−2.73888
$298$	53.3663	3.09142
$299$	41.9254	2.42461
$300$	−35.9518	−2.07568
$301$	−3.68045	−0.212137
$302$	11.2229	0.645808
$303$	26.5040	1.52261
$304$	−9.92704	−0.569355
$305$	−6.95986	−0.398520
$306$	−16.7298	−0.956381
$307$	−14.6801	−0.837840	−0.418920	−	0.908023i	$-0.637591\pi$
$307$	−14.6801	−0.837840	−0.418920	+	0.908023i	$0.637591\pi$
$308$	−8.63444	−0.491993
$309$	−10.8182	−0.615426
$310$	37.5144	2.13067
$311$	33.6434	1.90774	0.953870	−	0.300221i	$-0.0970604\pi$
$311$	33.6434	1.90774	0.953870	+	0.300221i	$0.0970604\pi$
$312$	97.2522	5.50582
$313$	−31.3554	−1.77231	−0.886156	−	0.463386i	$-0.846634\pi$
$313$	−31.3554	−1.77231	−0.886156	+	0.463386i	$0.846634\pi$
$314$	12.8168	0.723296
$315$	6.15734	0.346927
$316$	41.1341	2.31397
$317$	−17.5945	−0.988207	−0.494104	−	0.869403i	$-0.664504\pi$
$317$	−17.5945	−0.988207	−0.494104	+	0.869403i	$0.664504\pi$
$318$	−33.8903	−1.90047
$319$	28.7244	1.60826
$320$	−9.85501	−0.550912
$321$	−4.06197	−0.226717
$322$	10.2269	0.569923
$323$	−2.02536	−0.112694
$324$	82.4163	4.57868
$325$	16.1506	0.895874
$326$	38.2046	2.11596
$327$	−21.3080	−1.17833
$328$	19.2014	1.06022
$329$	4.93658	0.272163
$330$	42.7168	2.35148
$331$	13.8002	0.758530	0.379265	−	0.925288i	$-0.376177\pi$
$331$	13.8002	0.758530	0.379265	+	0.925288i	$0.376177\pi$
$332$	−12.9747	−0.712079
$333$	68.2732	3.74135
$334$	−14.9858	−0.819984
$335$	2.64490	0.144506
$336$	8.60053	0.469197
$337$	11.8316	0.644507	0.322254	−	0.946653i	$-0.395560\pi$
$337$	11.8316	0.644507	0.322254	+	0.946653i	$0.395560\pi$
$338$	−52.9531	−2.88027
$339$	24.8621	1.35032
$340$	5.87820	0.318790
$341$	36.7305	1.98907
$342$	37.2351	2.01344
$343$	−7.91126	−0.427168
$344$	33.1664	1.78821
$345$	−34.0352	−1.83239
$346$	22.5095	1.21012
$347$	27.3047	1.46579	0.732896	−	0.680340i	$-0.238168\pi$
$347$	27.3047	1.46579	0.732896	+	0.680340i	$0.238168\pi$
$348$	−103.397	−5.54264
$349$	16.6400	0.890721	0.445361	−	0.895351i	$-0.353076\pi$
$349$	16.6400	0.890721	0.445361	+	0.895351i	$0.353076\pi$
$350$	3.93964	0.210582
$351$	−76.3264	−4.07400
$352$	4.07611	0.217257
$353$	−33.3952	−1.77745	−0.888724	−	0.458443i	$-0.848407\pi$
$353$	−33.3952	−1.77745	−0.888724	+	0.458443i	$0.848407\pi$
$354$	80.8670	4.29803
$355$	4.53118	0.240490
$356$	73.8492	3.91400
$357$	1.75472	0.0928698
$358$	−41.1247	−2.17351
$359$	15.5338	0.819844	0.409922	−	0.912121i	$-0.365556\pi$
$359$	15.5338	0.819844	0.409922	+	0.912121i	$0.365556\pi$
$360$	−55.4869	−2.92442
$361$	−14.4922	−0.762748
$362$	8.85996	0.465669
$363$	6.87494	0.360841
$364$	−13.9623	−0.731826
$365$	−2.05280	−0.107448
$366$	36.4640	1.90600
$367$	−7.70214	−0.402048	−0.201024	−	0.979586i	$-0.564427\pi$
$367$	−7.70214	−0.402048	−0.201024	+	0.979586i	$0.564427\pi$
$368$	−33.4118	−1.74171
$369$	−26.1110	−1.35928
$370$	−35.6601	−1.85388
$371$	2.49822	0.129701
$372$	−132.215	−6.85505
$373$	−7.41571	−0.383971	−0.191985	−	0.981398i	$-0.561493\pi$
$373$	−7.41571	−0.383971	−0.191985	+	0.981398i	$0.561493\pi$
$374$	8.55566	0.442402
$375$	−36.9254	−1.90682
$376$	−44.4860	−2.29419
$377$	46.4489	2.39224
$378$	−18.6184	−0.957627
$379$	18.6723	0.959131	0.479566	−	0.877506i	$-0.340794\pi$
$379$	18.6723	0.959131	0.479566	+	0.877506i	$0.340794\pi$
$380$	−13.0829	−0.671140
$381$	15.2191	0.779699
$382$	−51.4133	−2.63053
$383$	1.89151	0.0966518	0.0483259	−	0.998832i	$-0.484611\pi$
$383$	1.89151	0.0966518	0.0483259	+	0.998832i	$0.484611\pi$
$384$	58.7712	2.99915
$385$	−3.14887	−0.160481
$386$	−52.6700	−2.68083
$387$	−45.1012	−2.29262
$388$	−0.554282	−0.0281394
$389$	26.8722	1.36247	0.681236	−	0.732064i	$-0.261443\pi$
$389$	26.8722	1.36247	0.681236	+	0.732064i	$0.261443\pi$
$390$	69.0753	3.49776
$391$	−6.81684	−0.344742
$392$	34.7718	1.75624
$393$	−44.6154	−2.25055
$394$	−68.4165	−3.44677
$395$	15.0011	0.754785
$396$	−105.809	−5.31710
$397$	−7.08411	−0.355541	−0.177771	−	0.984072i	$-0.556889\pi$
$397$	−7.08411	−0.355541	−0.177771	+	0.984072i	$0.556889\pi$
$398$	26.0522	1.30588
$399$	−3.90543	−0.195516
$400$	−12.8710	−0.643549
$401$	29.5212	1.47422	0.737109	−	0.675774i	$-0.236190\pi$
$401$	29.5212	1.47422	0.737109	+	0.675774i	$0.236190\pi$
$402$	−13.8571	−0.691131
$403$	59.3951	2.95868
$404$	34.2900	1.70599
$405$	30.0561	1.49350
$406$	11.3303	0.562315
$407$	−34.9150	−1.73067
$408$	−15.8127	−0.782845
$409$	−18.7609	−0.927668	−0.463834	−	0.885922i	$-0.653527\pi$
$409$	−18.7609	−0.927668	−0.463834	+	0.885922i	$0.653527\pi$
$410$	13.6381	0.673540
$411$	28.8907	1.42507
$412$	−13.9962	−0.689545
$413$	−5.96111	−0.293327
$414$	125.323	6.15931
$415$	−4.73170	−0.232270
$416$	6.59128	0.323164
$417$	−37.6825	−1.84532
$418$	−19.0420	−0.931377
$419$	−27.5001	−1.34347	−0.671734	−	0.740792i	$-0.734450\pi$
$419$	−27.5001	−1.34347	−0.671734	+	0.740792i	$0.734450\pi$
$420$	11.3347	0.553077
$421$	16.2618	0.792554	0.396277	−	0.918131i	$-0.370302\pi$
$421$	16.2618	0.792554	0.396277	+	0.918131i	$0.370302\pi$
$422$	−35.0052	−1.70403
$423$	60.4943	2.94133
$424$	−22.5128	−1.09332
$425$	−2.62600	−0.127380
$426$	−23.7397	−1.15019
$427$	−2.68795	−0.130079
$428$	−5.25525	−0.254022
$429$	67.6319	3.26530
$430$	23.5570	1.13602
$431$	−7.02795	−0.338524	−0.169262	−	0.985571i	$-0.554138\pi$
$431$	−7.02795	−0.338524	−0.169262	+	0.985571i	$0.554138\pi$
$432$	60.8272	2.92655
$433$	1.62769	0.0782219	0.0391109	−	0.999235i	$-0.487547\pi$
$433$	1.62769	0.0782219	0.0391109	+	0.999235i	$0.487547\pi$
$434$	14.4883	0.695462
$435$	−37.7074	−1.80793
$436$	−27.5676	−1.32025
$437$	15.1720	0.725776
$438$	10.7550	0.513893
$439$	−29.6434	−1.41480	−0.707401	−	0.706812i	$-0.750133\pi$
$439$	−29.6434	−1.41480	−0.707401	+	0.706812i	$0.750133\pi$
$440$	28.3760	1.35277
$441$	−47.2844	−2.25164
$442$	13.8349	0.658061
$443$	−32.9947	−1.56763	−0.783814	−	0.620996i	$-0.786728\pi$
$443$	−32.9947	−1.56763	−0.783814	+	0.620996i	$0.786728\pi$
$444$	125.680	5.96452
$445$	26.9318	1.27669
$446$	−2.92850	−0.138669
$447$	−68.5916	−3.24427
$448$	−3.80608	−0.179820
$449$	3.76701	0.177776	0.0888881	−	0.996042i	$-0.471669\pi$
$449$	3.76701	0.177776	0.0888881	+	0.996042i	$0.471669\pi$
$450$	48.2774	2.27582
$451$	13.3532	0.628776
$452$	32.1658	1.51295
$453$	−14.4249	−0.677739
$454$	56.6020	2.65646
$455$	−5.09189	−0.238711
$456$	35.1938	1.64810
$457$	5.97676	0.279581	0.139791	−	0.990181i	$-0.455357\pi$
$457$	5.97676	0.279581	0.139791	+	0.990181i	$0.455357\pi$
$458$	−49.4761	−2.31187
$459$	12.4103	0.579262
$460$	−44.0336	−2.05308
$461$	9.67375	0.450551	0.225276	−	0.974295i	$-0.427672\pi$
$461$	9.67375	0.450551	0.225276	+	0.974295i	$0.427672\pi$
$462$	16.4975	0.767534
$463$	13.1378	0.610567	0.305283	−	0.952262i	$-0.401249\pi$
$463$	13.1378	0.610567	0.305283	+	0.952262i	$0.401249\pi$
$464$	−37.0167	−1.71846
$465$	−48.2172	−2.23602
$466$	18.4594	0.855113
$467$	−36.7750	−1.70174	−0.850872	−	0.525372i	$-0.823926\pi$
$467$	−36.7750	−1.70174	−0.850872	+	0.525372i	$0.823926\pi$
$468$	−171.099	−7.90903
$469$	1.02148	0.0471675
$470$	−31.5971	−1.45746
$471$	−16.4735	−0.759058
$472$	53.7186	2.47260
$473$	23.0648	1.06052
$474$	−78.5934	−3.60992
$475$	5.84461	0.268169
$476$	2.27020	0.104055
$477$	30.6139	1.40172
$478$	−51.0364	−2.33435
$479$	−37.1383	−1.69689	−0.848445	−	0.529283i	$-0.822461\pi$
$479$	−37.1383	−1.69689	−0.848445	+	0.529283i	$0.822461\pi$
$480$	−5.35083	−0.244231
$481$	−56.4594	−2.57432
$482$	−11.2083	−0.510524
$483$	−13.1446	−0.598102
$484$	8.89457	0.404299
$485$	−0.202139	−0.00917867
$486$	−60.9933	−2.76671
$487$	−6.21335	−0.281554	−0.140777	−	0.990041i	$-0.544960\pi$
$487$	−6.21335	−0.281554	−0.140777	+	0.990041i	$0.544960\pi$
$488$	24.2224	1.09650
$489$	−49.1043	−2.22057
$490$	24.6973	1.11571
$491$	−15.7514	−0.710849	−0.355425	−	0.934705i	$-0.615664\pi$
$491$	−15.7514	−0.710849	−0.355425	+	0.934705i	$0.615664\pi$
$492$	−48.0662	−2.16699
$493$	−7.55234	−0.340140
$494$	−30.7920	−1.38540
$495$	−38.5871	−1.73436
$496$	−47.3340	−2.12536
$497$	1.74997	0.0784971
$498$	24.7903	1.11088
$499$	−39.2954	−1.75910	−0.879551	−	0.475804i	$-0.842157\pi$
$499$	−39.2954	−1.75910	−0.879551	+	0.475804i	$0.842157\pi$
$500$	−47.7728	−2.13647
$501$	19.2612	0.860527
$502$	−34.3267	−1.53208
$503$	−8.08960	−0.360698	−0.180349	−	0.983603i	$-0.557723\pi$
$503$	−8.08960	−0.360698	−0.180349	+	0.983603i	$0.557723\pi$
$504$	−21.4294	−0.954543
$505$	12.5051	0.556470
$506$	−64.0905	−2.84917
$507$	68.0607	3.02268
$508$	19.6900	0.873603
$509$	−27.6853	−1.22713	−0.613565	−	0.789644i	$-0.710265\pi$
$509$	−27.6853	−1.22713	−0.613565	+	0.789644i	$0.710265\pi$
$510$	−11.2313	−0.497329
$511$	−0.792804	−0.0350716
$512$	43.5345	1.92397
$513$	−27.6211	−1.21950
$514$	−6.88791	−0.303812
$515$	−5.10425	−0.224920
$516$	−83.0243	−3.65494
$517$	−30.9368	−1.36060
$518$	−13.7722	−0.605115
$519$	−28.9314	−1.26995
$520$	45.8856	2.01221
$521$	−29.6714	−1.29993	−0.649963	−	0.759966i	$-0.725216\pi$
$521$	−29.6714	−1.29993	−0.649963	+	0.759966i	$0.725216\pi$
$522$	138.845	6.07708
$523$	−38.3633	−1.67751	−0.838756	−	0.544507i	$-0.816717\pi$
$523$	−38.3633	−1.67751	−0.838756	+	0.544507i	$0.816717\pi$
$524$	−57.7219	−2.52159
$525$	−5.06361	−0.220994
$526$	−13.5275	−0.589825
$527$	−9.65733	−0.420680
$528$	−53.8982	−2.34562
$529$	28.0650	1.22022
$530$	−15.9901	−0.694567
$531$	−73.0491	−3.17006
$532$	−5.05272	−0.219063
$533$	21.5928	0.935287
$534$	−141.101	−6.10604
$535$	−1.91652	−0.0828584
$536$	−9.20507	−0.397598
$537$	52.8576	2.28097
$538$	−39.5291	−1.70422
$539$	24.1813	1.04156
$540$	80.1646	3.44974
$541$	6.15372	0.264569	0.132284	−	0.991212i	$-0.457769\pi$
$541$	6.15372	0.264569	0.132284	+	0.991212i	$0.457769\pi$
$542$	−19.4770	−0.836611
$543$	−11.3877	−0.488694
$544$	−1.07171	−0.0459491
$545$	−10.0535	−0.430646
$546$	26.6774	1.14169
$547$	−37.2158	−1.59123	−0.795616	−	0.605802i	$-0.792852\pi$
$547$	−37.2158	−1.59123	−0.795616	+	0.605802i	$0.792852\pi$
$548$	37.3778	1.59670
$549$	−32.9388	−1.40580
$550$	−24.6891	−1.05275
$551$	16.8090	0.716087
$552$	118.453	5.04169
$553$	5.79352	0.246365
$554$	−34.3676	−1.46014
$555$	45.8340	1.94554
$556$	−48.7524	−2.06756
$557$	−27.3622	−1.15937	−0.579687	−	0.814840i	$-0.696825\pi$
$557$	−27.3622	−1.15937	−0.579687	+	0.814840i	$0.696825\pi$
$558$	177.544	7.51604
$559$	37.2970	1.57749
$560$	4.05790	0.171478
$561$	−10.9966	−0.464276
$562$	−53.6421	−2.26276
$563$	−30.1597	−1.27108	−0.635539	−	0.772068i	$-0.719222\pi$
$563$	−30.1597	−1.27108	−0.635539	+	0.772068i	$0.719222\pi$
$564$	111.360	4.68912
$565$	11.7304	0.493503
$566$	60.6067	2.54749
$567$	11.6079	0.487486
$568$	−15.7699	−0.661690
$569$	−27.7906	−1.16504	−0.582521	−	0.812816i	$-0.697933\pi$
$569$	−27.7906	−1.16504	−0.582521	+	0.812816i	$0.697933\pi$
$570$	24.9971	1.04701
$571$	−32.4428	−1.35769	−0.678844	−	0.734282i	$-0.737519\pi$
$571$	−32.4428	−1.35769	−0.678844	+	0.734282i	$0.737519\pi$
$572$	87.5000	3.65856
$573$	66.0815	2.76059
$574$	5.26715	0.219847
$575$	19.6714	0.820354
$576$	−46.6407	−1.94336
$577$	−0.372015	−0.0154872	−0.00774359	−	0.999970i	$-0.502465\pi$
$577$	−0.372015	−0.0154872	−0.00774359	+	0.999970i	$0.502465\pi$
$578$	39.7738	1.65437
$579$	67.6967	2.81338
$580$	−48.7846	−2.02567
$581$	−1.82742	−0.0758140
$582$	1.05905	0.0438989
$583$	−15.6560	−0.648405
$584$	7.14436	0.295636
$585$	−62.3974	−2.57981
$586$	2.31300	0.0955492
$587$	−1.39218	−0.0574613	−0.0287306	−	0.999587i	$-0.509147\pi$
$587$	−1.39218	−0.0574613	−0.0287306	+	0.999587i	$0.509147\pi$
$588$	−87.0432	−3.58960
$589$	21.4940	0.885645
$590$	38.1547	1.57080
$591$	87.9357	3.61719
$592$	44.9944	1.84926
$593$	40.6707	1.67015	0.835073	−	0.550139i	$-0.185425\pi$
$593$	40.6707	1.67015	0.835073	+	0.550139i	$0.185425\pi$
$594$	116.679	4.78738
$595$	0.827913	0.0339411
$596$	−88.7416	−3.63500
$597$	−33.4849	−1.37045
$598$	−103.638	−4.23806
$599$	20.5979	0.841607	0.420804	−	0.907152i	$-0.361748\pi$
$599$	20.5979	0.841607	0.420804	+	0.907152i	$0.361748\pi$
$600$	45.6308	1.86287
$601$	−4.24414	−0.173122	−0.0865611	−	0.996247i	$-0.527588\pi$
$601$	−4.24414	−0.173122	−0.0865611	+	0.996247i	$0.527588\pi$
$602$	9.09790	0.370803
$603$	12.5175	0.509752
$604$	−18.6624	−0.759362
$605$	3.24373	0.131877
$606$	−65.5166	−2.66143
$607$	3.20624	0.130137	0.0650687	−	0.997881i	$-0.479273\pi$
$607$	3.20624	0.130137	0.0650687	+	0.997881i	$0.479273\pi$
$608$	2.38526	0.0967352
$609$	−14.5629	−0.590117
$610$	17.2045	0.696588
$611$	−50.0265	−2.02385
$612$	27.8197	1.12454
$613$	−3.91734	−0.158220	−0.0791099	−	0.996866i	$-0.525208\pi$
$613$	−3.91734	−0.158220	−0.0791099	+	0.996866i	$0.525208\pi$
$614$	36.2886	1.46449
$615$	−17.5291	−0.706842
$616$	10.9590	0.441552
$617$	38.2986	1.54184	0.770921	−	0.636931i	$-0.219796\pi$
$617$	38.2986	1.54184	0.770921	+	0.636931i	$0.219796\pi$
$618$	26.7421	1.07573
$619$	15.9178	0.639792	0.319896	−	0.947453i	$-0.396352\pi$
$619$	15.9178	0.639792	0.319896	+	0.947453i	$0.396352\pi$
$620$	−62.3819	−2.50532
$621$	−92.9654	−3.73057
$622$	−83.1649	−3.33461
$623$	10.4013	0.416718
$624$	−87.1562	−3.48904
$625$	−3.65817	−0.146327
$626$	77.5092	3.09789
$627$	24.4747	0.977427
$628$	−21.3128	−0.850475
$629$	9.17999	0.366030
$630$	−15.2207	−0.606406
$631$	−23.1825	−0.922881	−0.461441	−	0.887171i	$-0.652667\pi$
$631$	−23.1825	−0.922881	−0.461441	+	0.887171i	$0.652667\pi$
$632$	−52.2083	−2.07673
$633$	44.9922	1.78828
$634$	43.4929	1.72732
$635$	7.18069	0.284957
$636$	56.3555	2.23464
$637$	39.1024	1.54929
$638$	−71.0055	−2.81113
$639$	21.4447	0.848339
$640$	27.7294	1.09610
$641$	8.77047	0.346413	0.173206	−	0.984886i	$-0.444587\pi$
$641$	8.77047	0.346413	0.173206	+	0.984886i	$0.444587\pi$
$642$	10.0410	0.396287
$643$	−5.88172	−0.231952	−0.115976	−	0.993252i	$-0.537000\pi$
$643$	−5.88172	−0.231952	−0.115976	+	0.993252i	$0.537000\pi$
$644$	−17.0061	−0.670134
$645$	−30.2779	−1.19219
$646$	5.00661	0.196982
$647$	13.9110	0.546898	0.273449	−	0.961887i	$-0.411836\pi$
$647$	13.9110	0.546898	0.273449	+	0.961887i	$0.411836\pi$
$648$	−104.605	−4.10926
$649$	37.3574	1.46641
$650$	−39.9236	−1.56593
$651$	−18.6218	−0.729848
$652$	−63.5296	−2.48801
$653$	−46.7109	−1.82794	−0.913969	−	0.405785i	$-0.866998\pi$
$653$	−46.7109	−1.82794	−0.913969	+	0.405785i	$0.866998\pi$
$654$	52.6724	2.05965
$655$	−21.0504	−0.822509
$656$	−17.2080	−0.671861
$657$	−9.71524	−0.379028
$658$	−12.2030	−0.475723
$659$	−12.6538	−0.492923	−0.246461	−	0.969153i	$-0.579268\pi$
$659$	−12.6538	−0.492923	−0.246461	+	0.969153i	$0.579268\pi$
$660$	−71.0329	−2.76495
$661$	−31.0586	−1.20804	−0.604020	−	0.796969i	$-0.706435\pi$
$661$	−31.0586	−1.20804	−0.604020	+	0.796969i	$0.706435\pi$
$662$	−34.1136	−1.32586
$663$	−17.7821	−0.690598
$664$	16.4678	0.639074
$665$	−1.84266	−0.0714553
$666$	−168.768	−6.53964
$667$	56.5746	2.19058
$668$	24.9195	0.964165
$669$	3.76400	0.145525
$670$	−6.53808	−0.252588
$671$	16.8450	0.650292
$672$	−2.06653	−0.0797181
$673$	20.5950	0.793880	0.396940	−	0.917845i	$-0.370072\pi$
$673$	20.5950	0.793880	0.396940	+	0.917845i	$0.370072\pi$
$674$	−29.2471	−1.12656
$675$	−35.8124	−1.37842
$676$	88.0547	3.38672
$677$	47.0781	1.80936	0.904679	−	0.426095i	$-0.140111\pi$
$677$	47.0781	1.80936	0.904679	+	0.426095i	$0.140111\pi$
$678$	−61.4580	−2.36028
$679$	−0.0780676	−0.00299596
$680$	−7.46074	−0.286106
$681$	−72.7506	−2.78781
$682$	−90.7962	−3.47676
$683$	−19.9289	−0.762560	−0.381280	−	0.924460i	$-0.624517\pi$
$683$	−19.9289	−0.762560	−0.381280	+	0.924460i	$0.624517\pi$
$684$	−61.9174	−2.36747
$685$	13.6312	0.520821
$686$	19.5563	0.746662
$687$	63.5916	2.42617
$688$	−29.7233	−1.13319
$689$	−25.3166	−0.964485
$690$	84.1335	3.20291
$691$	38.9652	1.48230	0.741152	−	0.671337i	$-0.234280\pi$
$691$	38.9652	1.48230	0.741152	+	0.671337i	$0.234280\pi$
$692$	−37.4305	−1.42289
$693$	−14.9026	−0.566104
$694$	−67.4960	−2.56211
$695$	−17.7794	−0.674410
$696$	131.233	4.97439
$697$	−3.51087	−0.132984
$698$	−41.1334	−1.55692
$699$	−23.7258	−0.897392
$700$	−6.55114	−0.247610
$701$	−3.77527	−0.142590	−0.0712951	−	0.997455i	$-0.522713\pi$
$701$	−3.77527	−0.142590	−0.0712951	+	0.997455i	$0.522713\pi$
$702$	188.676	7.12110
$703$	−20.4316	−0.770592
$704$	23.8521	0.898960
$705$	40.6117	1.52953
$706$	82.5515	3.10687
$707$	4.82956	0.181634
$708$	−134.472	−5.05377
$709$	−27.1323	−1.01897	−0.509487	−	0.860478i	$-0.670165\pi$
$709$	−27.1323	−1.01897	−0.509487	+	0.860478i	$0.670165\pi$
$710$	−11.2009	−0.420362
$711$	70.9954	2.66254
$712$	−93.7310	−3.51272
$713$	72.3431	2.70927
$714$	−4.33760	−0.162330
$715$	31.9101	1.19337
$716$	68.3854	2.55568
$717$	65.5971	2.44977
$718$	−38.3989	−1.43304
$719$	49.9102	1.86134	0.930669	−	0.365863i	$-0.119226\pi$
$719$	49.9102	1.86134	0.930669	+	0.365863i	$0.119226\pi$
$720$	49.7266	1.85320
$721$	−1.97130	−0.0734149
$722$	35.8241	1.33324
$723$	14.4060	0.535766
$724$	−14.7331	−0.547550
$725$	21.7938	0.809402
$726$	−16.9945	−0.630727
$727$	−3.44505	−0.127770	−0.0638849	−	0.997957i	$-0.520349\pi$
$727$	−3.44505	−0.127770	−0.0638849	+	0.997957i	$0.520349\pi$
$728$	17.7213	0.656796
$729$	18.2451	0.675745
$730$	5.07442	0.187813
$731$	−6.06429	−0.224296
$732$	−60.6353	−2.24114
$733$	−19.6327	−0.725150	−0.362575	−	0.931955i	$-0.618102\pi$
$733$	−19.6327	−0.725150	−0.362575	+	0.931955i	$0.618102\pi$
$734$	19.0393	0.702755
$735$	−31.7435	−1.17088
$736$	8.02817	0.295922
$737$	−6.40146	−0.235801
$738$	64.5451	2.37594
$739$	11.7317	0.431558	0.215779	−	0.976442i	$-0.430771\pi$
$739$	11.7317	0.431558	0.215779	+	0.976442i	$0.430771\pi$
$740$	59.2985	2.17986
$741$	39.5769	1.45389
$742$	−6.17550	−0.226710
$743$	−6.09704	−0.223679	−0.111839	−	0.993726i	$-0.535674\pi$
$743$	−6.09704	−0.223679	−0.111839	+	0.993726i	$0.535674\pi$
$744$	167.811	6.15224
$745$	−32.3629	−1.18569
$746$	18.3313	0.671157
$747$	−22.3937	−0.819342
$748$	−14.2270	−0.520191
$749$	−0.740174	−0.0270454
$750$	91.2779	3.33300
$751$	−4.02071	−0.146718	−0.0733589	−	0.997306i	$-0.523372\pi$
$751$	−4.02071	−0.146718	−0.0733589	+	0.997306i	$0.523372\pi$
$752$	39.8678	1.45383
$753$	44.1201	1.60783
$754$	−114.820	−4.18148
$755$	−6.80593	−0.247693
$756$	30.9601	1.12601
$757$	−34.4026	−1.25038	−0.625192	−	0.780471i	$-0.714979\pi$
$757$	−34.4026	−1.25038	−0.625192	+	0.780471i	$0.714979\pi$
$758$	−46.1571	−1.67650
$759$	82.3755	2.99004
$760$	16.6051	0.602331
$761$	−17.8805	−0.648166	−0.324083	−	0.946029i	$-0.605056\pi$
$761$	−17.8805	−0.648166	−0.324083	+	0.946029i	$0.605056\pi$
$762$	−37.6210	−1.36286
$763$	−3.88275	−0.140565
$764$	85.4941	3.09307
$765$	10.1455	0.366811
$766$	−4.67573	−0.168941
$767$	60.4089	2.18124
$768$	−103.505	−3.73492
$769$	−36.4840	−1.31565	−0.657823	−	0.753173i	$-0.728522\pi$
$769$	−36.4840	−1.31565	−0.657823	+	0.753173i	$0.728522\pi$
$770$	7.78386	0.280511
$771$	8.85302	0.318834
$772$	87.5838	3.15221
$773$	1.12758	0.0405564	0.0202782	−	0.999794i	$-0.493545\pi$
$773$	1.12758	0.0405564	0.0202782	+	0.999794i	$0.493545\pi$
$774$	111.488	4.00736
$775$	27.8682	1.00106
$776$	0.703507	0.0252544
$777$	17.7014	0.635034
$778$	−66.4268	−2.38152
$779$	7.81402	0.279966
$780$	−114.864	−4.11279
$781$	−10.9668	−0.392424
$782$	16.8509	0.602588
$783$	−102.996	−3.68077
$784$	−31.1621	−1.11293
$785$	−7.77251	−0.277413
$786$	110.287	3.93382
$787$	−10.9951	−0.391933	−0.195967	−	0.980611i	$-0.562784\pi$
$787$	−10.9951	−0.391933	−0.195967	+	0.980611i	$0.562784\pi$
$788$	113.768	4.05283
$789$	17.3868	0.618988
$790$	−37.0820	−1.31932
$791$	4.53038	0.161082
$792$	134.295	4.77197
$793$	27.2392	0.967292
$794$	17.5116	0.621463
$795$	20.5521	0.728908
$796$	−43.3217	−1.53550
$797$	−10.5273	−0.372896	−0.186448	−	0.982465i	$-0.559698\pi$
$797$	−10.5273	−0.372896	−0.186448	+	0.982465i	$0.559698\pi$
$798$	9.65405	0.341750
$799$	8.13403	0.287761
$800$	3.09263	0.109341
$801$	127.460	4.50358
$802$	−72.9751	−2.57684
$803$	4.96838	0.175330
$804$	23.0428	0.812655
$805$	−6.20190	−0.218588
$806$	−146.822	−5.17159
$807$	50.8068	1.78848
$808$	−43.5216	−1.53108
$809$	−51.3387	−1.80497	−0.902486	−	0.430720i	$-0.858260\pi$
$809$	−51.3387	−1.80497	−0.902486	+	0.430720i	$0.858260\pi$
$810$	−74.2974	−2.61055
$811$	12.1354	0.426133	0.213066	−	0.977038i	$-0.431655\pi$
$811$	12.1354	0.426133	0.213066	+	0.977038i	$0.431655\pi$
$812$	−18.8410	−0.661188
$813$	25.0338	0.877975
$814$	86.3083	3.02510
$815$	−23.1684	−0.811554
$816$	14.1711	0.496089
$817$	13.4971	0.472204
$818$	46.3761	1.62150
$819$	−24.0983	−0.842063
$820$	−22.6786	−0.791971
$821$	21.3498	0.745112	0.372556	−	0.928010i	$-0.378481\pi$
$821$	21.3498	0.745112	0.372556	+	0.928010i	$0.378481\pi$
$822$	−71.4164	−2.49093
$823$	−34.1383	−1.18998	−0.594992	−	0.803731i	$-0.702845\pi$
$823$	−34.1383	−1.18998	−0.594992	+	0.803731i	$0.702845\pi$
$824$	17.7643	0.618850
$825$	31.7329	1.10480
$826$	14.7356	0.512717
$827$	10.2165	0.355264	0.177632	−	0.984097i	$-0.443156\pi$
$827$	10.2165	0.355264	0.177632	+	0.984097i	$0.443156\pi$
$828$	−208.398	−7.24232
$829$	−5.74960	−0.199692	−0.0998459	−	0.995003i	$-0.531835\pi$
$829$	−5.74960	−0.199692	−0.0998459	+	0.995003i	$0.531835\pi$
$830$	11.6966	0.405993
$831$	44.1726	1.53233
$832$	38.5701	1.33718
$833$	−6.35784	−0.220286
$834$	93.1495	3.22550
$835$	9.08782	0.314497
$836$	31.6646	1.09514
$837$	−131.703	−4.55232
$838$	67.9791	2.34830
$839$	−7.97767	−0.275420	−0.137710	−	0.990473i	$-0.543974\pi$
$839$	−7.97767	−0.275420	−0.137710	+	0.990473i	$0.543974\pi$
$840$	−14.3863	−0.496373
$841$	33.6787	1.16133
$842$	−40.1985	−1.38533
$843$	68.9462	2.37463
$844$	58.2095	2.00365
$845$	32.1124	1.10470
$846$	−149.539	−5.14126
$847$	1.25275	0.0430451
$848$	20.1757	0.692835
$849$	−77.8979	−2.67345
$850$	6.49136	0.222652
$851$	−68.7673	−2.35731
$852$	39.4763	1.35244
$853$	3.06088	0.104802	0.0524012	−	0.998626i	$-0.483313\pi$
$853$	3.06088	0.104802	0.0524012	+	0.998626i	$0.483313\pi$
$854$	6.64448	0.227370
$855$	−22.5805	−0.772236
$856$	6.67008	0.227979
$857$	26.1636	0.893731	0.446866	−	0.894601i	$-0.352540\pi$
$857$	26.1636	0.893731	0.446866	+	0.894601i	$0.352540\pi$
$858$	−167.183	−5.70754
$859$	2.55609	0.0872126	0.0436063	−	0.999049i	$-0.486115\pi$
$859$	2.55609	0.0872126	0.0436063	+	0.999049i	$0.486115\pi$
$860$	−39.1725	−1.33577
$861$	−6.76987	−0.230716
$862$	17.3728	0.591719
$863$	−28.2968	−0.963233	−0.481617	−	0.876382i	$-0.659950\pi$
$863$	−28.2968	−0.963233	−0.481617	+	0.876382i	$0.659950\pi$
$864$	−14.6155	−0.497230
$865$	−13.6504	−0.464128
$866$	−4.02358	−0.136727
$867$	−51.1212	−1.73617
$868$	−24.0923	−0.817747
$869$	−36.3071	−1.23163
$870$	93.2110	3.16015
$871$	−10.3515	−0.350747
$872$	34.9894	1.18489
$873$	−0.956663	−0.0323781
$874$	−37.5045	−1.26861
$875$	−6.72855	−0.227467
$876$	−17.8842	−0.604253
$877$	4.65678	0.157248	0.0786242	−	0.996904i	$-0.474947\pi$
$877$	4.65678	0.157248	0.0786242	+	0.996904i	$0.474947\pi$
$878$	73.2772	2.47298
$879$	−2.97290	−0.100273
$880$	−25.4303	−0.857254
$881$	−46.6024	−1.57007	−0.785037	−	0.619448i	$-0.787356\pi$
$881$	−46.6024	−1.57007	−0.785037	+	0.619448i	$0.787356\pi$
$882$	116.885	3.93572
$883$	45.8130	1.54173	0.770866	−	0.636998i	$-0.219824\pi$
$883$	45.8130	1.54173	0.770866	+	0.636998i	$0.219824\pi$
$884$	−23.0058	−0.773770
$885$	−49.0402	−1.64847
$886$	81.5615	2.74011
$887$	−37.5599	−1.26114	−0.630569	−	0.776134i	$-0.717178\pi$
$887$	−37.5599	−1.26114	−0.630569	+	0.776134i	$0.717178\pi$
$888$	−159.516	−5.35301
$889$	2.77323	0.0930112
$890$	−66.5743	−2.23158
$891$	−72.7449	−2.43705
$892$	4.86974	0.163051
$893$	−18.1036	−0.605816
$894$	169.555	5.67078
$895$	24.9393	0.833627
$896$	10.7093	0.357773
$897$	133.205	4.44760
$898$	−9.31188	−0.310741
$899$	80.1485	2.67310
$900$	−80.2795	−2.67598
$901$	4.11634	0.137135
$902$	−33.0084	−1.09906
$903$	−11.6935	−0.389136
$904$	−40.8255	−1.35784
$905$	−5.37295	−0.178603
$906$	35.6576	1.18464
$907$	−25.4936	−0.846502	−0.423251	−	0.906012i	$-0.639111\pi$
$907$	−25.4936	−0.846502	−0.423251	+	0.906012i	$0.639111\pi$
$908$	−94.1223	−3.12356
$909$	59.1828	1.96297
$910$	12.5869	0.417252
$911$	−3.73544	−0.123761	−0.0618803	−	0.998084i	$-0.519710\pi$
$911$	−3.73544	−0.123761	−0.0618803	+	0.998084i	$0.519710\pi$
$912$	−31.5402	−1.04440
$913$	11.4522	0.379011
$914$	−14.7743	−0.488690
$915$	−22.1129	−0.731030
$916$	82.2728	2.71837
$917$	−8.12983	−0.268471
$918$	−30.6776	−1.01251
$919$	−33.4955	−1.10491	−0.552457	−	0.833542i	$-0.686309\pi$
$919$	−33.4955	−1.10491	−0.552457	+	0.833542i	$0.686309\pi$
$920$	55.8885	1.84259
$921$	−46.6418	−1.53690
$922$	−23.9131	−0.787535
$923$	−17.7339	−0.583720
$924$	−27.4334	−0.902492
$925$	−26.4907	−0.871010
$926$	−32.4761	−1.06723
$927$	−24.1568	−0.793414
$928$	8.89436	0.291972
$929$	48.2896	1.58433	0.792166	−	0.610306i	$-0.208954\pi$
$929$	48.2896	1.58433	0.792166	+	0.610306i	$0.208954\pi$
$930$	119.191	3.90842
$931$	14.1504	0.463762
$932$	−30.6957	−1.00547
$933$	106.892	3.49948
$934$	90.9062	2.97454
$935$	−5.18841	−0.169679
$936$	217.162	7.09817
$937$	10.5823	0.345708	0.172854	−	0.984947i	$-0.444701\pi$
$937$	10.5823	0.345708	0.172854	+	0.984947i	$0.444701\pi$
$938$	−2.52505	−0.0824459
$939$	−99.6226	−3.25106
$940$	52.5421	1.71373
$941$	6.10937	0.199160	0.0995799	−	0.995030i	$-0.468250\pi$
$941$	6.10937	0.199160	0.0995799	+	0.995030i	$0.468250\pi$
$942$	40.7217	1.32678
$943$	26.2999	0.856444
$944$	−48.1419	−1.56689
$945$	11.2908	0.367288
$946$	−57.0152	−1.85372
$947$	44.5554	1.44786	0.723928	−	0.689875i	$-0.242335\pi$
$947$	44.5554	1.44786	0.723928	+	0.689875i	$0.242335\pi$
$948$	130.691	4.24466
$949$	8.03414	0.260799
$950$	−14.4476	−0.468742
$951$	−55.9014	−1.81273
$952$	−2.88139	−0.0933865
$953$	3.81730	0.123654	0.0618272	−	0.998087i	$-0.480307\pi$
$953$	3.81730	0.123654	0.0618272	+	0.998087i	$0.480307\pi$
$954$	−75.6763	−2.45011
$955$	31.1786	1.00891
$956$	84.8674	2.74481
$957$	91.2633	2.95012
$958$	91.8041	2.96606
$959$	5.26447	0.169998
$960$	−31.3114	−1.01057
$961$	71.4876	2.30605
$962$	139.565	4.49976
$963$	−9.07030	−0.292286
$964$	18.6381	0.600292
$965$	31.9407	1.02821
$966$	32.4930	1.04544
$967$	57.1517	1.83787	0.918937	−	0.394403i	$-0.129049\pi$
$967$	57.1517	1.83787	0.918937	+	0.394403i	$0.129049\pi$
$968$	−11.2892	−0.362848
$969$	−6.43500	−0.206722
$970$	0.499679	0.0160437
$971$	18.8629	0.605340	0.302670	−	0.953095i	$-0.402122\pi$
$971$	18.8629	0.605340	0.302670	+	0.953095i	$0.402122\pi$
$972$	101.425	3.25319
$973$	−6.86652	−0.220131
$974$	15.3591	0.492138
$975$	51.3138	1.64336
$976$	−21.7078	−0.694851
$977$	−39.2511	−1.25575	−0.627877	−	0.778313i	$-0.716076\pi$
$977$	−39.2511	−1.25575	−0.627877	+	0.778313i	$0.716076\pi$
$978$	121.384	3.88142
$979$	−65.1832	−2.08326
$980$	−41.0687	−1.31189
$981$	−47.5803	−1.51912
$982$	38.9367	1.24252
$983$	−40.5373	−1.29294	−0.646469	−	0.762940i	$-0.723755\pi$
$983$	−40.5373	−1.29294	−0.646469	+	0.762940i	$0.723755\pi$
$984$	61.0067	1.94482
$985$	41.4898	1.32198
$986$	18.6690	0.594543
$987$	15.6845	0.499244
$988$	51.2033	1.62900
$989$	45.4276	1.44452
$990$	95.3857	3.03155
$991$	−15.0486	−0.478036	−0.239018	−	0.971015i	$-0.576825\pi$
$991$	−15.0486	−0.478036	−0.239018	+	0.971015i	$0.576825\pi$
$992$	11.3734	0.361106
$993$	43.8462	1.39142
$994$	−4.32586	−0.137208
$995$	−15.7988	−0.500857
$996$	−41.2233	−1.30621
$997$	−22.7197	−0.719540	−0.359770	−	0.933041i	$-0.617145\pi$
$997$	−22.7197	−0.719540	−0.359770	+	0.933041i	$0.617145\pi$
$998$	97.1364	3.07480
$999$	125.193	3.96093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.b.1.14	✓	157

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.b.1.14	✓	157	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47196 q^{2} +3.17720 q^{3} +4.11056 q^{4} +1.49907 q^{5} -7.85391 q^{6} +0.578951 q^{7} -5.21722 q^{8} +7.09463 q^{9} +O(q^{10})\)	\(q-2.47196 q^{2} +3.17720 q^{3} +4.11056 q^{4} +1.49907 q^{5} -7.85391 q^{6} +0.578951 q^{7} -5.21722 q^{8} +7.09463 q^{9} -3.70563 q^{10} -3.62820 q^{11} +13.0601 q^{12} -5.86699 q^{13} -1.43114 q^{14} +4.76285 q^{15} +4.67561 q^{16} +0.953941 q^{17} -17.5376 q^{18} -2.12315 q^{19} +6.16202 q^{20} +1.83945 q^{21} +8.96875 q^{22} -7.14598 q^{23} -16.5762 q^{24} -2.75279 q^{25} +14.5029 q^{26} +13.0095 q^{27} +2.37982 q^{28} -7.91699 q^{29} -11.7735 q^{30} -10.1236 q^{31} -1.12345 q^{32} -11.5275 q^{33} -2.35810 q^{34} +0.867887 q^{35} +29.1629 q^{36} +9.62322 q^{37} +5.24834 q^{38} -18.6406 q^{39} -7.82097 q^{40} -3.68038 q^{41} -4.54703 q^{42} -6.35709 q^{43} -14.9139 q^{44} +10.6353 q^{45} +17.6645 q^{46} +8.52677 q^{47} +14.8554 q^{48} -6.66482 q^{49} +6.80478 q^{50} +3.03087 q^{51} -24.1166 q^{52} +4.31509 q^{53} -32.1588 q^{54} -5.43892 q^{55} -3.02051 q^{56} -6.74570 q^{57} +19.5704 q^{58} -10.2964 q^{59} +19.5780 q^{60} -4.64279 q^{61} +25.0251 q^{62} +4.10744 q^{63} -6.57409 q^{64} -8.79502 q^{65} +28.4955 q^{66} +1.76436 q^{67} +3.92123 q^{68} -22.7042 q^{69} -2.14538 q^{70} +3.02266 q^{71} -37.0142 q^{72} -1.36938 q^{73} -23.7882 q^{74} -8.74619 q^{75} -8.72736 q^{76} -2.10055 q^{77} +46.0788 q^{78} +10.0069 q^{79} +7.00906 q^{80} +20.0499 q^{81} +9.09774 q^{82} -3.15643 q^{83} +7.56116 q^{84} +1.43002 q^{85} +15.7145 q^{86} -25.1539 q^{87} +18.9291 q^{88} +17.9657 q^{89} -26.2901 q^{90} -3.39670 q^{91} -29.3740 q^{92} -32.1648 q^{93} -21.0778 q^{94} -3.18276 q^{95} -3.56944 q^{96} -0.134843 q^{97} +16.4751 q^{98} -25.7407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * q^99

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