LMFDB - Embedded newform 1339.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.660355 q^{2} +0.482681 q^{3} -1.56393 q^{4} -1.20794 q^{5} -0.318741 q^{6} +3.96472 q^{7} +2.35346 q^{8} -2.76702 q^{9} +O(q^{10})$	\(q-0.660355 q^{2} +0.482681 q^{3} -1.56393 q^{4} -1.20794 q^{5} -0.318741 q^{6} +3.96472 q^{7} +2.35346 q^{8} -2.76702 q^{9} +0.797669 q^{10} +2.71768 q^{11} -0.754880 q^{12} -1.00000 q^{13} -2.61812 q^{14} -0.583050 q^{15} +1.57374 q^{16} +6.47204 q^{17} +1.82721 q^{18} -4.68054 q^{19} +1.88914 q^{20} +1.91369 q^{21} -1.79463 q^{22} -8.31202 q^{23} +1.13597 q^{24} -3.54088 q^{25} +0.660355 q^{26} -2.78363 q^{27} -6.20055 q^{28} +6.39874 q^{29} +0.385020 q^{30} +7.65256 q^{31} -5.74615 q^{32} +1.31177 q^{33} -4.27384 q^{34} -4.78914 q^{35} +4.32743 q^{36} +9.32428 q^{37} +3.09082 q^{38} -0.482681 q^{39} -2.84284 q^{40} -7.20013 q^{41} -1.26372 q^{42} +2.87183 q^{43} -4.25026 q^{44} +3.34239 q^{45} +5.48889 q^{46} +6.15864 q^{47} +0.759616 q^{48} +8.71899 q^{49} +2.33824 q^{50} +3.12393 q^{51} +1.56393 q^{52} -0.927464 q^{53} +1.83818 q^{54} -3.28279 q^{55} +9.33080 q^{56} -2.25921 q^{57} -4.22544 q^{58} +10.1431 q^{59} +0.911849 q^{60} -8.07223 q^{61} -5.05340 q^{62} -10.9705 q^{63} +0.647009 q^{64} +1.20794 q^{65} -0.866234 q^{66} +10.8317 q^{67} -10.1218 q^{68} -4.01205 q^{69} +3.16253 q^{70} +11.3894 q^{71} -6.51207 q^{72} +14.9878 q^{73} -6.15733 q^{74} -1.70912 q^{75} +7.32005 q^{76} +10.7748 q^{77} +0.318741 q^{78} -3.55621 q^{79} -1.90099 q^{80} +6.95745 q^{81} +4.75464 q^{82} +11.1477 q^{83} -2.99289 q^{84} -7.81784 q^{85} -1.89643 q^{86} +3.08855 q^{87} +6.39594 q^{88} +0.729999 q^{89} -2.20717 q^{90} -3.96472 q^{91} +12.9994 q^{92} +3.69374 q^{93} -4.06689 q^{94} +5.65381 q^{95} -2.77356 q^{96} -4.43564 q^{97} -5.75763 q^{98} -7.51986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) $ 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * 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 $

$2$	−0.660355	−0.466941	−0.233471	−	0.972364i	$-0.575008\pi$
$2$	−0.660355	−0.466941	−0.233471	+	0.972364i	$0.575008\pi$
$3$	0.482681	0.278676	0.139338	−	0.990245i	$-0.455503\pi$
$3$	0.482681	0.278676	0.139338	+	0.990245i	$0.455503\pi$
$4$	−1.56393	−0.781966
$5$	−1.20794	−0.540207	−0.270104	−	0.962831i	$-0.587058\pi$
$5$	−1.20794	−0.540207	−0.270104	+	0.962831i	$0.587058\pi$
$6$	−0.318741	−0.130125
$7$	3.96472	1.49852	0.749261	−	0.662274i	$-0.230409\pi$
$7$	3.96472	1.49852	0.749261	+	0.662274i	$0.230409\pi$
$8$	2.35346	0.832074
$9$	−2.76702	−0.922340
$10$	0.797669	0.252245
$11$	2.71768	0.819410	0.409705	−	0.912218i	$-0.365632\pi$
$11$	2.71768	0.819410	0.409705	+	0.912218i	$0.365632\pi$
$12$	−0.754880	−0.217915
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.61812	−0.699722
$15$	−0.583050	−0.150543
$16$	1.57374	0.393436
$17$	6.47204	1.56970	0.784850	−	0.619685i	$-0.212740\pi$
$17$	6.47204	1.56970	0.784850	+	0.619685i	$0.212740\pi$
$18$	1.82721	0.430679
$19$	−4.68054	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$19$	−4.68054	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$20$	1.88914	0.422424
$21$	1.91369	0.417602
$22$	−1.79463	−0.382617
$23$	−8.31202	−1.73318	−0.866588	−	0.499024i	$-0.833692\pi$
$23$	−8.31202	−1.73318	−0.866588	+	0.499024i	$0.833692\pi$
$24$	1.13597	0.231879
$25$	−3.54088	−0.708176
$26$	0.660355	0.129506
$27$	−2.78363	−0.535710
$28$	−6.20055	−1.17179
$29$	6.39874	1.18822	0.594108	−	0.804386i	$-0.297505\pi$
$29$	6.39874	1.18822	0.594108	+	0.804386i	$0.297505\pi$
$30$	0.385020	0.0702946
$31$	7.65256	1.37444	0.687220	−	0.726449i	$-0.258831\pi$
$31$	7.65256	1.37444	0.687220	+	0.726449i	$0.258831\pi$
$32$	−5.74615	−1.01579
$33$	1.31177	0.228350
$34$	−4.27384	−0.732958
$35$	−4.78914	−0.809513
$36$	4.32743	0.721238
$37$	9.32428	1.53290	0.766451	−	0.642303i	$-0.222021\pi$
$37$	9.32428	1.53290	0.766451	+	0.642303i	$0.222021\pi$
$38$	3.09082	0.501397
$39$	−0.482681	−0.0772908
$40$	−2.84284	−0.449492
$41$	−7.20013	−1.12447	−0.562236	−	0.826977i	$-0.690059\pi$
$41$	−7.20013	−1.12447	−0.562236	+	0.826977i	$0.690059\pi$
$42$	−1.26372	−0.194996
$43$	2.87183	0.437951	0.218975	−	0.975730i	$-0.429729\pi$
$43$	2.87183	0.437951	0.218975	+	0.975730i	$0.429729\pi$
$44$	−4.25026	−0.640751
$45$	3.34239	0.498255
$46$	5.48889	0.809292
$47$	6.15864	0.898329	0.449165	−	0.893449i	$-0.351722\pi$
$47$	6.15864	0.898329	0.449165	+	0.893449i	$0.351722\pi$
$48$	0.759616	0.109641
$49$	8.71899	1.24557
$50$	2.33824	0.330677
$51$	3.12393	0.437438
$52$	1.56393	0.216878
$53$	−0.927464	−0.127397	−0.0636985	−	0.997969i	$-0.520290\pi$
$53$	−0.927464	−0.127397	−0.0636985	+	0.997969i	$0.520290\pi$
$54$	1.83818	0.250145
$55$	−3.28279	−0.442651
$56$	9.33080	1.24688
$57$	−2.25921	−0.299239
$58$	−4.22544	−0.554827
$59$	10.1431	1.32052	0.660259	−	0.751038i	$-0.270447\pi$
$59$	10.1431	1.32052	0.660259	+	0.751038i	$0.270447\pi$
$60$	0.911849	0.117719
$61$	−8.07223	−1.03354	−0.516771	−	0.856124i	$-0.672866\pi$
$61$	−8.07223	−1.03354	−0.516771	+	0.856124i	$0.672866\pi$
$62$	−5.05340	−0.641783
$63$	−10.9705	−1.38215
$64$	0.647009	0.0808762
$65$	1.20794	0.149827
$66$	−0.866234	−0.106626
$67$	10.8317	1.32330	0.661651	−	0.749812i	$-0.269856\pi$
$67$	10.8317	1.32330	0.661651	+	0.749812i	$0.269856\pi$
$68$	−10.1218	−1.22745
$69$	−4.01205	−0.482995
$70$	3.16253	0.377995
$71$	11.3894	1.35167	0.675836	−	0.737052i	$-0.263783\pi$
$71$	11.3894	1.35167	0.675836	+	0.737052i	$0.263783\pi$
$72$	−6.51207	−0.767455
$73$	14.9878	1.75419	0.877094	−	0.480319i	$-0.159479\pi$
$73$	14.9878	1.75419	0.877094	+	0.480319i	$0.159479\pi$
$74$	−6.15733	−0.715775
$75$	−1.70912	−0.197352
$76$	7.32005	0.839667
$77$	10.7748	1.22791
$78$	0.318741	0.0360903
$79$	−3.55621	−0.400105	−0.200052	−	0.979785i	$-0.564111\pi$
$79$	−3.55621	−0.400105	−0.200052	+	0.979785i	$0.564111\pi$
$80$	−1.90099	−0.212537
$81$	6.95745	0.773050
$82$	4.75464	0.525062
$83$	11.1477	1.22362	0.611812	−	0.791003i	$-0.290441\pi$
$83$	11.1477	1.22362	0.611812	+	0.791003i	$0.290441\pi$
$84$	−2.99289	−0.326551
$85$	−7.81784	−0.847964
$86$	−1.89643	−0.204497
$87$	3.08855	0.331127
$88$	6.39594	0.681810
$89$	0.729999	0.0773798	0.0386899	−	0.999251i	$-0.487682\pi$
$89$	0.729999	0.0773798	0.0386899	+	0.999251i	$0.487682\pi$
$90$	−2.20717	−0.232656
$91$	−3.96472	−0.415615
$92$	12.9994	1.35528
$93$	3.69374	0.383023
$94$	−4.06689	−0.419467
$95$	5.65381	0.580069
$96$	−2.77356	−0.283075
$97$	−4.43564	−0.450371	−0.225186	−	0.974316i	$-0.572299\pi$
$97$	−4.43564	−0.450371	−0.225186	+	0.974316i	$0.572299\pi$
$98$	−5.75763	−0.581608
$99$	−7.51986	−0.755775
$100$	5.53769	0.553769
$101$	0.551181	0.0548445	0.0274223	−	0.999624i	$-0.491270\pi$
$101$	0.551181	0.0548445	0.0274223	+	0.999624i	$0.491270\pi$
$102$	−2.06290	−0.204258
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.35346	−0.230776
$105$	−2.31163	−0.225592
$106$	0.612456	0.0594869
$107$	13.9944	1.35289	0.676447	−	0.736491i	$-0.263519\pi$
$107$	13.9944	1.35289	0.676447	+	0.736491i	$0.263519\pi$
$108$	4.35341	0.418907
$109$	−17.8480	−1.70953	−0.854764	−	0.519017i	$-0.826298\pi$
$109$	−17.8480	−1.70953	−0.854764	+	0.519017i	$0.826298\pi$
$110$	2.16781	0.206692
$111$	4.50065	0.427183
$112$	6.23945	0.589573
$113$	5.03133	0.473307	0.236654	−	0.971594i	$-0.423949\pi$
$113$	5.03133	0.473307	0.236654	+	0.971594i	$0.423949\pi$
$114$	1.49188	0.139727
$115$	10.0404	0.936275
$116$	−10.0072	−0.929144
$117$	2.76702	0.255811
$118$	−6.69804	−0.616604
$119$	25.6598	2.35223
$120$	−1.37218	−0.125263
$121$	−3.61423	−0.328567
$122$	5.33053	0.482604
$123$	−3.47536	−0.313363
$124$	−11.9681	−1.07477
$125$	10.3169	0.922769
$126$	7.24439	0.645382
$127$	2.14384	0.190235	0.0951175	−	0.995466i	$-0.469677\pi$
$127$	2.14384	0.190235	0.0951175	+	0.995466i	$0.469677\pi$
$128$	11.0650	0.978021
$129$	1.38618	0.122046
$130$	−0.797669	−0.0699602
$131$	−9.76344	−0.853035	−0.426518	−	0.904479i	$-0.640260\pi$
$131$	−9.76344	−0.853035	−0.426518	+	0.904479i	$0.640260\pi$
$132$	−2.05152	−0.178562
$133$	−18.5570	−1.60910
$134$	−7.15276	−0.617905
$135$	3.36246	0.289394
$136$	15.2317	1.30611
$137$	6.29174	0.537539	0.268770	−	0.963204i	$-0.413383\pi$
$137$	6.29174	0.537539	0.268770	+	0.963204i	$0.413383\pi$
$138$	2.64938	0.225530
$139$	13.1002	1.11115	0.555573	−	0.831468i	$-0.312499\pi$
$139$	13.1002	1.11115	0.555573	+	0.831468i	$0.312499\pi$
$140$	7.48989	0.633011
$141$	2.97266	0.250343
$142$	−7.52103	−0.631151
$143$	−2.71768	−0.227264
$144$	−4.35458	−0.362882
$145$	−7.72929	−0.641883
$146$	−9.89726	−0.819103
$147$	4.20849	0.347110
$148$	−14.5825	−1.19868
$149$	−10.0500	−0.823329	−0.411665	−	0.911335i	$-0.635052\pi$
$149$	−10.0500	−0.823329	−0.411665	+	0.911335i	$0.635052\pi$
$150$	1.12862	0.0921517
$151$	2.77417	0.225759	0.112880	−	0.993609i	$-0.463993\pi$
$151$	2.77417	0.225759	0.112880	+	0.993609i	$0.463993\pi$
$152$	−11.0155	−0.893472
$153$	−17.9083	−1.44780
$154$	−7.11521	−0.573360
$155$	−9.24383	−0.742483
$156$	0.754880	0.0604387
$157$	−4.82362	−0.384967	−0.192483	−	0.981300i	$-0.561654\pi$
$157$	−4.82362	−0.384967	−0.192483	+	0.981300i	$0.561654\pi$
$158$	2.34836	0.186826
$159$	−0.447669	−0.0355025
$160$	6.94100	0.548735
$161$	−32.9548	−2.59720
$162$	−4.59439	−0.360969
$163$	−24.8357	−1.94528	−0.972640	−	0.232319i	$-0.925369\pi$
$163$	−24.8357	−1.94528	−0.972640	+	0.232319i	$0.925369\pi$
$164$	11.2605	0.879298
$165$	−1.58454	−0.123356
$166$	−7.36147	−0.571361
$167$	−7.17488	−0.555209	−0.277605	−	0.960695i	$-0.589541\pi$
$167$	−7.17488	−0.555209	−0.277605	+	0.960695i	$0.589541\pi$
$168$	4.50380	0.347476
$169$	1.00000	0.0769231
$170$	5.16255	0.395949
$171$	12.9512	0.990399
$172$	−4.49135	−0.342462
$173$	18.9456	1.44041	0.720204	−	0.693762i	$-0.244048\pi$
$173$	18.9456	1.44041	0.720204	+	0.693762i	$0.244048\pi$
$174$	−2.03954	−0.154617
$175$	−14.0386	−1.06122
$176$	4.27693	0.322386
$177$	4.89587	0.367996
$178$	−0.482059	−0.0361318
$179$	−6.21013	−0.464167	−0.232083	−	0.972696i	$-0.574554\pi$
$179$	−6.21013	−0.464167	−0.232083	+	0.972696i	$0.574554\pi$
$180$	−5.22727	−0.389618
$181$	−4.15115	−0.308552	−0.154276	−	0.988028i	$-0.549305\pi$
$181$	−4.15115	−0.308552	−0.154276	+	0.988028i	$0.549305\pi$
$182$	2.61812	0.194068
$183$	−3.89631	−0.288023
$184$	−19.5620	−1.44213
$185$	−11.2632	−0.828085
$186$	−2.43918	−0.178849
$187$	17.5889	1.28623
$188$	−9.63168	−0.702463
$189$	−11.0363	−0.802773
$190$	−3.73352	−0.270858
$191$	20.2522	1.46540	0.732700	−	0.680552i	$-0.238260\pi$
$191$	20.2522	1.46540	0.732700	+	0.680552i	$0.238260\pi$
$192$	0.312299	0.0225382
$193$	18.0044	1.29599	0.647994	−	0.761646i	$-0.275608\pi$
$193$	18.0044	1.29599	0.647994	+	0.761646i	$0.275608\pi$
$194$	2.92910	0.210297
$195$	0.583050	0.0417530
$196$	−13.6359	−0.973993
$197$	10.5791	0.753730	0.376865	−	0.926268i	$-0.377002\pi$
$197$	10.5791	0.753730	0.376865	+	0.926268i	$0.377002\pi$
$198$	4.96578	0.352903
$199$	−19.7761	−1.40189	−0.700946	−	0.713214i	$-0.747239\pi$
$199$	−19.7761	−1.40189	−0.700946	+	0.713214i	$0.747239\pi$
$200$	−8.33332	−0.589255
$201$	5.22825	0.368772
$202$	−0.363975	−0.0256092
$203$	25.3692	1.78057
$204$	−4.88561	−0.342061
$205$	8.69733	0.607448
$206$	−0.660355	−0.0460091
$207$	22.9995	1.59858
$208$	−1.57374	−0.109120
$209$	−12.7202	−0.879875
$210$	1.52649	0.105338
$211$	−3.03126	−0.208680	−0.104340	−	0.994542i	$-0.533273\pi$
$211$	−3.03126	−0.208680	−0.104340	+	0.994542i	$0.533273\pi$
$212$	1.45049	0.0996201
$213$	5.49744	0.376678
$214$	−9.24130	−0.631722
$215$	−3.46900	−0.236584
$216$	−6.55116	−0.445750
$217$	30.3402	2.05963
$218$	11.7860	0.798249
$219$	7.23432	0.488850
$220$	5.13406	0.346138
$221$	−6.47204	−0.435357
$222$	−2.97203	−0.199469
$223$	−4.45426	−0.298279	−0.149140	−	0.988816i	$-0.547650\pi$
$223$	−4.45426	−0.298279	−0.149140	+	0.988816i	$0.547650\pi$
$224$	−22.7819	−1.52218
$225$	9.79768	0.653179
$226$	−3.32246	−0.221007
$227$	7.71607	0.512134	0.256067	−	0.966659i	$-0.417573\pi$
$227$	7.71607	0.512134	0.256067	+	0.966659i	$0.417573\pi$
$228$	3.53325	0.233995
$229$	−21.8584	−1.44444	−0.722220	−	0.691663i	$-0.756878\pi$
$229$	−21.8584	−1.44444	−0.722220	+	0.691663i	$0.756878\pi$
$230$	−6.63024	−0.437185
$231$	5.20080	0.342188
$232$	15.0592	0.988683
$233$	−1.05931	−0.0693976	−0.0346988	−	0.999398i	$-0.511047\pi$
$233$	−1.05931	−0.0693976	−0.0346988	+	0.999398i	$0.511047\pi$
$234$	−1.82721	−0.119449
$235$	−7.43926	−0.485284
$236$	−15.8631	−1.03260
$237$	−1.71651	−0.111500
$238$	−16.9446	−1.09835
$239$	22.4690	1.45340	0.726701	−	0.686954i	$-0.241053\pi$
$239$	22.4690	1.45340	0.726701	+	0.686954i	$0.241053\pi$
$240$	−0.917571	−0.0592289
$241$	−25.3391	−1.63223	−0.816117	−	0.577886i	$-0.803878\pi$
$241$	−25.3391	−1.63223	−0.816117	+	0.577886i	$0.803878\pi$
$242$	2.38668	0.153421
$243$	11.7091	0.751140
$244$	12.6244	0.808195
$245$	−10.5320	−0.672866
$246$	2.29497	0.146322
$247$	4.68054	0.297816
$248$	18.0100	1.14364
$249$	5.38080	0.340995
$250$	−6.81280	−0.430879
$251$	5.25745	0.331847	0.165924	−	0.986139i	$-0.446939\pi$
$251$	5.25745	0.331847	0.165924	+	0.986139i	$0.446939\pi$
$252$	17.1570	1.08079
$253$	−22.5894	−1.42018
$254$	−1.41569	−0.0888286
$255$	−3.77352	−0.236307
$256$	−8.60087	−0.537555
$257$	0.419041	0.0261391	0.0130695	−	0.999915i	$-0.495840\pi$
$257$	0.419041	0.0261391	0.0130695	+	0.999915i	$0.495840\pi$
$258$	−0.915370	−0.0569885
$259$	36.9681	2.29709
$260$	−1.88914	−0.117159
$261$	−17.7054	−1.09594
$262$	6.44733	0.398318
$263$	11.6395	0.717722	0.358861	−	0.933391i	$-0.383165\pi$
$263$	11.6395	0.717722	0.358861	+	0.933391i	$0.383165\pi$
$264$	3.08720	0.190004
$265$	1.12032	0.0688208
$266$	12.2542	0.751355
$267$	0.352357	0.0215639
$268$	−16.9400	−1.03478
$269$	−3.96389	−0.241682	−0.120841	−	0.992672i	$-0.538559\pi$
$269$	−3.96389	−0.241682	−0.120841	+	0.992672i	$0.538559\pi$
$270$	−2.22042	−0.135130
$271$	4.00104	0.243046	0.121523	−	0.992589i	$-0.461222\pi$
$271$	4.00104	0.243046	0.121523	+	0.992589i	$0.461222\pi$
$272$	10.1853	0.617577
$273$	−1.91369	−0.115822
$274$	−4.15478	−0.250999
$275$	−9.62297	−0.580287
$276$	6.27458	0.377685
$277$	26.7352	1.60636	0.803181	−	0.595735i	$-0.203139\pi$
$277$	26.7352	1.60636	0.803181	+	0.595735i	$0.203139\pi$
$278$	−8.65079	−0.518840
$279$	−21.1748	−1.26770
$280$	−11.2711	−0.673574
$281$	−19.1311	−1.14127	−0.570633	−	0.821205i	$-0.693302\pi$
$281$	−19.1311	−1.14127	−0.570633	+	0.821205i	$0.693302\pi$
$282$	−1.96301	−0.116895
$283$	1.46951	0.0873534	0.0436767	−	0.999046i	$-0.486093\pi$
$283$	1.46951	0.0873534	0.0436767	+	0.999046i	$0.486093\pi$
$284$	−17.8122	−1.05696
$285$	2.72899	0.161651
$286$	1.79463	0.106119
$287$	−28.5465	−1.68505
$288$	15.8997	0.936899
$289$	24.8873	1.46396
$290$	5.10407	0.299722
$291$	−2.14100	−0.125508
$292$	−23.4399	−1.37171
$293$	−19.9016	−1.16266	−0.581332	−	0.813667i	$-0.697468\pi$
$293$	−19.9016	−1.16266	−0.581332	+	0.813667i	$0.697468\pi$
$294$	−2.77910	−0.162080
$295$	−12.2522	−0.713353
$296$	21.9443	1.27549
$297$	−7.56501	−0.438966
$298$	6.63658	0.384447
$299$	8.31202	0.480697
$300$	2.67294	0.154322
$301$	11.3860	0.656279
$302$	−1.83194	−0.105416
$303$	0.266044	0.0152839
$304$	−7.36598	−0.422468
$305$	9.75077	0.558327
$306$	11.8258	0.676037
$307$	−16.7504	−0.955998	−0.477999	−	0.878360i	$-0.658638\pi$
$307$	−16.7504	−0.955998	−0.477999	+	0.878360i	$0.658638\pi$
$308$	−16.8511	−0.960180
$309$	0.482681	0.0274588
$310$	6.10421	0.346696
$311$	−23.0803	−1.30877	−0.654383	−	0.756163i	$-0.727072\pi$
$311$	−23.0803	−1.30877	−0.654383	+	0.756163i	$0.727072\pi$
$312$	−1.13597	−0.0643116
$313$	−0.444838	−0.0251437	−0.0125719	−	0.999921i	$-0.504002\pi$
$313$	−0.444838	−0.0251437	−0.0125719	+	0.999921i	$0.504002\pi$
$314$	3.18530	0.179757
$315$	13.2516	0.746646
$316$	5.56167	0.312868
$317$	−9.85899	−0.553736	−0.276868	−	0.960908i	$-0.589297\pi$
$317$	−9.85899	−0.553736	−0.276868	+	0.960908i	$0.589297\pi$
$318$	0.295621	0.0165776
$319$	17.3897	0.973636
$320$	−0.781549	−0.0436899
$321$	6.75485	0.377019
$322$	21.7619	1.21274
$323$	−30.2927	−1.68553
$324$	−10.8810	−0.604499
$325$	3.54088	0.196413
$326$	16.4004	0.908331
$327$	−8.61488	−0.476404
$328$	−16.9452	−0.935643
$329$	24.4173	1.34617
$330$	1.04636	0.0576002
$331$	0.417427	0.0229439	0.0114719	−	0.999934i	$-0.496348\pi$
$331$	0.417427	0.0229439	0.0114719	+	0.999934i	$0.496348\pi$
$332$	−17.4343	−0.956832
$333$	−25.8005	−1.41386
$334$	4.73797	0.259250
$335$	−13.0840	−0.714857
$336$	3.01166	0.164300
$337$	−27.5333	−1.49983	−0.749917	−	0.661532i	$-0.769907\pi$
$337$	−27.5333	−1.49983	−0.749917	+	0.661532i	$0.769907\pi$
$338$	−0.660355	−0.0359186
$339$	2.42852	0.131899
$340$	12.2266	0.663078
$341$	20.7972	1.12623
$342$	−8.55236	−0.462458
$343$	6.81532	0.367993
$344$	6.75874	0.364407
$345$	4.84632	0.260917
$346$	−12.5108	−0.672586
$347$	−11.4328	−0.613744	−0.306872	−	0.951751i	$-0.599282\pi$
$347$	−11.4328	−0.613744	−0.306872	+	0.951751i	$0.599282\pi$
$348$	−4.83028	−0.258930
$349$	22.9441	1.22817	0.614084	−	0.789240i	$-0.289525\pi$
$349$	22.9441	1.22817	0.614084	+	0.789240i	$0.289525\pi$
$350$	9.27045	0.495527
$351$	2.78363	0.148579
$352$	−15.6162	−0.832345
$353$	18.9001	1.00595	0.502974	−	0.864301i	$-0.332239\pi$
$353$	18.9001	1.00595	0.502974	+	0.864301i	$0.332239\pi$
$354$	−3.23301	−0.171833
$355$	−13.7577	−0.730183
$356$	−1.14167	−0.0605083
$357$	12.3855	0.655510
$358$	4.10089	0.216739
$359$	−31.8587	−1.68144	−0.840718	−	0.541473i	$-0.817867\pi$
$359$	−31.8587	−1.68144	−0.840718	+	0.541473i	$0.817867\pi$
$360$	7.86619	0.414585
$361$	2.90748	0.153025
$362$	2.74123	0.144076
$363$	−1.74452	−0.0915636
$364$	6.20055	0.324997
$365$	−18.1043	−0.947625
$366$	2.57295	0.134490
$367$	−0.203290	−0.0106117	−0.00530584	−	0.999986i	$-0.501689\pi$
$367$	−0.203290	−0.0106117	−0.00530584	+	0.999986i	$0.501689\pi$
$368$	−13.0810	−0.681894
$369$	19.9229	1.03714
$370$	7.43769	0.386667
$371$	−3.67713	−0.190907
$372$	−5.77676	−0.299511
$373$	18.1433	0.939424	0.469712	−	0.882820i	$-0.344358\pi$
$373$	18.1433	0.939424	0.469712	+	0.882820i	$0.344358\pi$
$374$	−11.6149	−0.600594
$375$	4.97976	0.257154
$376$	14.4941	0.747476
$377$	−6.39874	−0.329552
$378$	7.28788	0.374848
$379$	−0.370562	−0.0190345	−0.00951726	−	0.999955i	$-0.503029\pi$
$379$	−0.370562	−0.0190345	−0.00951726	+	0.999955i	$0.503029\pi$
$380$	−8.84218	−0.453594
$381$	1.03479	0.0530139
$382$	−13.3737	−0.684256
$383$	4.37402	0.223502	0.111751	−	0.993736i	$-0.464354\pi$
$383$	4.37402	0.223502	0.111751	+	0.993736i	$0.464354\pi$
$384$	5.34088	0.272551
$385$	−13.0153	−0.663323
$386$	−11.8893	−0.605150
$387$	−7.94642	−0.403939
$388$	6.93704	0.352175
$389$	23.4726	1.19011	0.595055	−	0.803685i	$-0.297130\pi$
$389$	23.4726	1.19011	0.595055	+	0.803685i	$0.297130\pi$
$390$	−0.385020	−0.0194962
$391$	−53.7958	−2.72057
$392$	20.5198	1.03641
$393$	−4.71262	−0.237720
$394$	−6.98596	−0.351948
$395$	4.29569	0.216140
$396$	11.7606	0.590990
$397$	−3.86119	−0.193787	−0.0968937	−	0.995295i	$-0.530891\pi$
$397$	−3.86119	−0.193787	−0.0968937	+	0.995295i	$0.530891\pi$
$398$	13.0593	0.654602
$399$	−8.95712	−0.448417
$400$	−5.57244	−0.278622
$401$	−26.1874	−1.30774	−0.653868	−	0.756609i	$-0.726855\pi$
$401$	−26.1874	−1.30774	−0.653868	+	0.756609i	$0.726855\pi$
$402$	−3.45250	−0.172195
$403$	−7.65256	−0.381201
$404$	−0.862009	−0.0428866
$405$	−8.40419	−0.417607
$406$	−16.7527	−0.831421
$407$	25.3404	1.25608
$408$	7.35204	0.363980
$409$	12.2687	0.606647	0.303323	−	0.952888i	$-0.401904\pi$
$409$	12.2687	0.606647	0.303323	+	0.952888i	$0.401904\pi$
$410$	−5.74332	−0.283642
$411$	3.03690	0.149799
$412$	−1.56393	−0.0770494
$413$	40.2145	1.97882
$414$	−15.1879	−0.746442
$415$	−13.4658	−0.661011
$416$	5.74615	0.281728
$417$	6.32322	0.309650
$418$	8.39985	0.410850
$419$	−0.160461	−0.00783905	−0.00391952	−	0.999992i	$-0.501248\pi$
$419$	−0.160461	−0.00783905	−0.00391952	+	0.999992i	$0.501248\pi$
$420$	3.61523	0.176405
$421$	−32.5116	−1.58452	−0.792258	−	0.610186i	$-0.791095\pi$
$421$	−32.5116	−1.58452	−0.792258	+	0.610186i	$0.791095\pi$
$422$	2.00171	0.0974415
$423$	−17.0411	−0.828565
$424$	−2.18275	−0.106004
$425$	−22.9167	−1.11162
$426$	−3.63026	−0.175887
$427$	−32.0041	−1.54879
$428$	−21.8864	−1.05792
$429$	−1.31177	−0.0633329
$430$	2.29077	0.110471
$431$	−4.71712	−0.227216	−0.113608	−	0.993526i	$-0.536241\pi$
$431$	−4.71712	−0.227216	−0.113608	+	0.993526i	$0.536241\pi$
$432$	−4.38072	−0.210768
$433$	−3.36865	−0.161887	−0.0809434	−	0.996719i	$-0.525793\pi$
$433$	−3.36865	−0.161887	−0.0809434	+	0.996719i	$0.525793\pi$
$434$	−20.0353	−0.961727
$435$	−3.73078	−0.178877
$436$	27.9130	1.33679
$437$	38.9048	1.86107
$438$	−4.77722	−0.228264
$439$	−19.8332	−0.946587	−0.473294	−	0.880905i	$-0.656935\pi$
$439$	−19.8332	−0.946587	−0.473294	+	0.880905i	$0.656935\pi$
$440$	−7.72592	−0.368319
$441$	−24.1256	−1.14884
$442$	4.27384	0.203286
$443$	18.7757	0.892059	0.446029	−	0.895018i	$-0.352838\pi$
$443$	18.7757	0.892059	0.446029	+	0.895018i	$0.352838\pi$
$444$	−7.03871	−0.334042
$445$	−0.881795	−0.0418011
$446$	2.94139	0.139279
$447$	−4.85095	−0.229442
$448$	2.56521	0.121195
$449$	−28.6769	−1.35335	−0.676673	−	0.736284i	$-0.736579\pi$
$449$	−28.6769	−1.35335	−0.676673	+	0.736284i	$0.736579\pi$
$450$	−6.46995	−0.304996
$451$	−19.5676	−0.921404
$452$	−7.86865	−0.370110
$453$	1.33904	0.0629136
$454$	−5.09535	−0.239136
$455$	4.78914	0.224518
$456$	−5.31695	−0.248989
$457$	−28.4377	−1.33026	−0.665129	−	0.746729i	$-0.731623\pi$
$457$	−28.4377	−1.33026	−0.665129	+	0.746729i	$0.731623\pi$
$458$	14.4343	0.674469
$459$	−18.0158	−0.840904
$460$	−15.7025	−0.732135
$461$	32.3210	1.50534	0.752670	−	0.658398i	$-0.228766\pi$
$461$	32.3210	1.50534	0.752670	+	0.658398i	$0.228766\pi$
$462$	−3.43437	−0.159782
$463$	−25.5305	−1.18650	−0.593252	−	0.805017i	$-0.702156\pi$
$463$	−25.5305	−1.18650	−0.593252	+	0.805017i	$0.702156\pi$
$464$	10.0700	0.467487
$465$	−4.46182	−0.206912
$466$	0.699519	0.0324046
$467$	10.3375	0.478362	0.239181	−	0.970975i	$-0.423121\pi$
$467$	10.3375	0.478362	0.239181	+	0.970975i	$0.423121\pi$
$468$	−4.32743	−0.200035
$469$	42.9446	1.98300
$470$	4.91255	0.226599
$471$	−2.32827	−0.107281
$472$	23.8713	1.09877
$473$	7.80472	0.358861
$474$	1.13351	0.0520638
$475$	16.5732	0.760432
$476$	−40.1302	−1.83936
$477$	2.56631	0.117503
$478$	−14.8375	−0.678654
$479$	7.74989	0.354102	0.177051	−	0.984202i	$-0.443344\pi$
$479$	7.74989	0.354102	0.177051	+	0.984202i	$0.443344\pi$
$480$	3.35029	0.152919
$481$	−9.32428	−0.425151
$482$	16.7328	0.762158
$483$	−15.9067	−0.723778
$484$	5.65241	0.256928
$485$	5.35799	0.243294
$486$	−7.73217	−0.350739
$487$	−32.6922	−1.48142	−0.740712	−	0.671823i	$-0.765512\pi$
$487$	−32.6922	−1.48142	−0.740712	+	0.671823i	$0.765512\pi$
$488$	−18.9977	−0.859983
$489$	−11.9877	−0.542102
$490$	6.95487	0.314189
$491$	33.5136	1.51245	0.756225	−	0.654312i	$-0.227042\pi$
$491$	33.5136	1.51245	0.756225	+	0.654312i	$0.227042\pi$
$492$	5.43523	0.245039
$493$	41.4129	1.86514
$494$	−3.09082	−0.139063
$495$	9.08355	0.408275
$496$	12.0432	0.540754
$497$	45.1557	2.02551
$498$	−3.55324	−0.159225
$499$	−4.94095	−0.221187	−0.110594	−	0.993866i	$-0.535275\pi$
$499$	−4.94095	−0.221187	−0.110594	+	0.993866i	$0.535275\pi$
$500$	−16.1349	−0.721574
$501$	−3.46318	−0.154723
$502$	−3.47178	−0.154953
$503$	−27.2946	−1.21701	−0.608503	−	0.793552i	$-0.708230\pi$
$503$	−27.2946	−1.21701	−0.608503	+	0.793552i	$0.708230\pi$
$504$	−25.8185	−1.15005
$505$	−0.665793	−0.0296274
$506$	14.9170	0.663142
$507$	0.482681	0.0214366
$508$	−3.35282	−0.148757
$509$	34.8693	1.54555	0.772776	−	0.634679i	$-0.218867\pi$
$509$	34.8693	1.54555	0.772776	+	0.634679i	$0.218867\pi$
$510$	2.49186	0.110342
$511$	59.4224	2.62869
$512$	−16.4505	−0.727014
$513$	13.0289	0.575240
$514$	−0.276716	−0.0122054
$515$	−1.20794	−0.0532282
$516$	−2.16789	−0.0954360
$517$	16.7372	0.736100
$518$	−24.4121	−1.07261
$519$	9.14468	0.401407
$520$	2.84284	0.124667
$521$	−18.9592	−0.830618	−0.415309	−	0.909680i	$-0.636327\pi$
$521$	−18.9592	−0.830618	−0.415309	+	0.909680i	$0.636327\pi$
$522$	11.6919	0.511739
$523$	−38.9217	−1.70193	−0.850963	−	0.525225i	$-0.823981\pi$
$523$	−38.9217	−1.70193	−0.850963	+	0.525225i	$0.823981\pi$
$524$	15.2693	0.667044
$525$	−6.77616	−0.295736
$526$	−7.68619	−0.335134
$527$	49.5277	2.15746
$528$	2.06439	0.0898411
$529$	46.0897	2.00390
$530$	−0.739810	−0.0321353
$531$	−28.0661	−1.21797
$532$	29.0219	1.25826
$533$	7.20013	0.311872
$534$	−0.232680	−0.0100691
$535$	−16.9045	−0.730843
$536$	25.4920	1.10108
$537$	−2.99751	−0.129352
$538$	2.61757	0.112852
$539$	23.6954	1.02063
$540$	−5.25865	−0.226296
$541$	−1.70202	−0.0731756	−0.0365878	−	0.999330i	$-0.511649\pi$
$541$	−1.70202	−0.0731756	−0.0365878	+	0.999330i	$0.511649\pi$
$542$	−2.64211	−0.113488
$543$	−2.00368	−0.0859861
$544$	−37.1893	−1.59448
$545$	21.5593	0.923499
$546$	1.26372	0.0540821
$547$	−10.6570	−0.455661	−0.227830	−	0.973701i	$-0.573163\pi$
$547$	−10.6570	−0.455661	−0.227830	+	0.973701i	$0.573163\pi$
$548$	−9.83984	−0.420337
$549$	22.3360	0.953277
$550$	6.35457	0.270960
$551$	−29.9496	−1.27589
$552$	−9.44221	−0.401887
$553$	−14.0994	−0.599566
$554$	−17.6547	−0.750077
$555$	−5.43652	−0.230767
$556$	−20.4878	−0.868878
$557$	5.67379	0.240406	0.120203	−	0.992749i	$-0.461645\pi$
$557$	5.67379	0.240406	0.120203	+	0.992749i	$0.461645\pi$
$558$	13.9829	0.591942
$559$	−2.87183	−0.121466
$560$	−7.53689	−0.318492
$561$	8.48983	0.358441
$562$	12.6333	0.532904
$563$	4.29318	0.180936	0.0904681	−	0.995899i	$-0.471164\pi$
$563$	4.29318	0.180936	0.0904681	+	0.995899i	$0.471164\pi$
$564$	−4.64903	−0.195759
$565$	−6.07754	−0.255684
$566$	−0.970400	−0.0407889
$567$	27.5843	1.15843
$568$	26.8045	1.12469
$569$	31.7667	1.33173	0.665864	−	0.746073i	$-0.268063\pi$
$569$	31.7667	1.33173	0.665864	+	0.746073i	$0.268063\pi$
$570$	−1.80210	−0.0754817
$571$	1.79492	0.0751150	0.0375575	−	0.999294i	$-0.488042\pi$
$571$	1.79492	0.0751150	0.0375575	+	0.999294i	$0.488042\pi$
$572$	4.25026	0.177712
$573$	9.77536	0.408372
$574$	18.8508	0.786818
$575$	29.4319	1.22739
$576$	−1.79029	−0.0745953
$577$	−2.35312	−0.0979618	−0.0489809	−	0.998800i	$-0.515597\pi$
$577$	−2.35312	−0.0979618	−0.0489809	+	0.998800i	$0.515597\pi$
$578$	−16.4345	−0.683584
$579$	8.69040	0.361161
$580$	12.0881	0.501930
$581$	44.1977	1.83363
$582$	1.41382	0.0586047
$583$	−2.52055	−0.104390
$584$	35.2732	1.45961
$585$	−3.34239	−0.138191
$586$	13.1421	0.542896
$587$	−6.26999	−0.258790	−0.129395	−	0.991593i	$-0.541304\pi$
$587$	−6.26999	−0.258790	−0.129395	+	0.991593i	$0.541304\pi$
$588$	−6.58179	−0.271428
$589$	−35.8181	−1.47586
$590$	8.09083	0.333094
$591$	5.10633	0.210046
$592$	14.6740	0.603099
$593$	7.15872	0.293973	0.146987	−	0.989138i	$-0.453043\pi$
$593$	7.15872	0.293973	0.146987	+	0.989138i	$0.453043\pi$
$594$	4.99559	0.204971
$595$	−30.9955	−1.27069
$596$	15.7175	0.643815
$597$	−9.54556	−0.390674
$598$	−5.48889	−0.224457
$599$	−7.47913	−0.305589	−0.152794	−	0.988258i	$-0.548827\pi$
$599$	−7.47913	−0.305589	−0.152794	+	0.988258i	$0.548827\pi$
$600$	−4.02233	−0.164211
$601$	18.1436	0.740092	0.370046	−	0.929013i	$-0.379342\pi$
$601$	18.1436	0.740092	0.370046	+	0.929013i	$0.379342\pi$
$602$	−7.51881	−0.306444
$603$	−29.9715	−1.22053
$604$	−4.33862	−0.176536
$605$	4.36578	0.177494
$606$	−0.175684	−0.00713666
$607$	39.8808	1.61871	0.809355	−	0.587319i	$-0.199817\pi$
$607$	39.8808	1.61871	0.809355	+	0.587319i	$0.199817\pi$
$608$	26.8951	1.09074
$609$	12.2452	0.496201
$610$	−6.43897	−0.260706
$611$	−6.15864	−0.249152
$612$	28.0073	1.13213
$613$	5.56440	0.224744	0.112372	−	0.993666i	$-0.464155\pi$
$613$	5.56440	0.224744	0.112372	+	0.993666i	$0.464155\pi$
$614$	11.0612	0.446395
$615$	4.19803	0.169281
$616$	25.3581	1.02171
$617$	−16.7470	−0.674208	−0.337104	−	0.941467i	$-0.609447\pi$
$617$	−16.7470	−0.674208	−0.337104	+	0.941467i	$0.609447\pi$
$618$	−0.318741	−0.0128216
$619$	11.1598	0.448549	0.224274	−	0.974526i	$-0.427999\pi$
$619$	11.1598	0.448549	0.224274	+	0.974526i	$0.427999\pi$
$620$	14.4567	0.580596
$621$	23.1376	0.928480
$622$	15.2412	0.611117
$623$	2.89424	0.115955
$624$	−0.759616	−0.0304090
$625$	5.24224	0.209690
$626$	0.293751	0.0117407
$627$	−6.13980	−0.245200
$628$	7.54381	0.301031
$629$	60.3471	2.40620
$630$	−8.75079	−0.348640
$631$	34.5547	1.37560	0.687801	−	0.725899i	$-0.258576\pi$
$631$	34.5547	1.37560	0.687801	+	0.725899i	$0.258576\pi$
$632$	−8.36939	−0.332917
$633$	−1.46313	−0.0581542
$634$	6.51043	0.258562
$635$	−2.58963	−0.102766
$636$	0.700124	0.0277617
$637$	−8.71899	−0.345459
$638$	−11.4834	−0.454631
$639$	−31.5146	−1.24670
$640$	−13.3659	−0.528334
$641$	−38.7772	−1.53161	−0.765805	−	0.643073i	$-0.777659\pi$
$641$	−38.7772	−1.53161	−0.765805	+	0.643073i	$0.777659\pi$
$642$	−4.46060	−0.176046
$643$	24.6726	0.972991	0.486496	−	0.873683i	$-0.338275\pi$
$643$	24.6726	0.972991	0.486496	+	0.873683i	$0.338275\pi$
$644$	51.5391	2.03092
$645$	−1.67442	−0.0659303
$646$	20.0039	0.787043
$647$	8.80294	0.346079	0.173040	−	0.984915i	$-0.444641\pi$
$647$	8.80294	0.346079	0.173040	+	0.984915i	$0.444641\pi$
$648$	16.3741	0.643235
$649$	27.5656	1.08205
$650$	−2.33824	−0.0917132
$651$	14.6447	0.573969
$652$	38.8413	1.52114
$653$	33.3414	1.30475	0.652374	−	0.757897i	$-0.273773\pi$
$653$	33.3414	1.30475	0.652374	+	0.757897i	$0.273773\pi$
$654$	5.68888	0.222453
$655$	11.7936	0.460816
$656$	−11.3312	−0.442408
$657$	−41.4715	−1.61796
$658$	−16.1241	−0.628581
$659$	−12.0166	−0.468101	−0.234050	−	0.972224i	$-0.575198\pi$
$659$	−12.0166	−0.468101	−0.234050	+	0.972224i	$0.575198\pi$
$660$	2.47811	0.0964604
$661$	35.7756	1.39151	0.695755	−	0.718279i	$-0.255070\pi$
$661$	35.7756	1.39151	0.695755	+	0.718279i	$0.255070\pi$
$662$	−0.275650	−0.0107134
$663$	−3.12393	−0.121323
$664$	26.2358	1.01815
$665$	22.4158	0.869247
$666$	17.0375	0.660188
$667$	−53.1864	−2.05939
$668$	11.2210	0.434155
$669$	−2.14999	−0.0831232
$670$	8.64011	0.333797
$671$	−21.9377	−0.846895
$672$	−10.9964	−0.424194
$673$	29.7768	1.14781	0.573906	−	0.818921i	$-0.305427\pi$
$673$	29.7768	1.14781	0.573906	+	0.818921i	$0.305427\pi$
$674$	18.1817	0.700335
$675$	9.85650	0.379377
$676$	−1.56393	−0.0601512
$677$	−44.2689	−1.70139	−0.850697	−	0.525657i	$-0.823820\pi$
$677$	−44.2689	−1.70139	−0.850697	+	0.525657i	$0.823820\pi$
$678$	−1.60369	−0.0615893
$679$	−17.5861	−0.674892
$680$	−18.3990	−0.705568
$681$	3.72440	0.142719
$682$	−13.7335	−0.525884
$683$	−19.6093	−0.750328	−0.375164	−	0.926959i	$-0.622414\pi$
$683$	−19.6093	−0.750328	−0.375164	+	0.926959i	$0.622414\pi$
$684$	−20.2547	−0.774458
$685$	−7.60004	−0.290383
$686$	−4.50053	−0.171831
$687$	−10.5506	−0.402531
$688$	4.51953	0.172306
$689$	0.927464	0.0353336
$690$	−3.20029	−0.121833
$691$	3.14272	0.119555	0.0597774	−	0.998212i	$-0.480961\pi$
$691$	3.14272	0.119555	0.0597774	+	0.998212i	$0.480961\pi$
$692$	−29.6296	−1.12635
$693$	−29.8141	−1.13255
$694$	7.54970	0.286583
$695$	−15.8243	−0.600249
$696$	7.26877	0.275522
$697$	−46.5995	−1.76508
$698$	−15.1512	−0.573483
$699$	−0.511308	−0.0193394
$700$	21.9554	0.829836
$701$	−22.5081	−0.850117	−0.425059	−	0.905166i	$-0.639747\pi$
$701$	−22.5081	−0.850117	−0.425059	+	0.905166i	$0.639747\pi$
$702$	−1.83818	−0.0693778
$703$	−43.6427	−1.64601
$704$	1.75836	0.0662708
$705$	−3.59079	−0.135237
$706$	−12.4807	−0.469719
$707$	2.18528	0.0821858
$708$	−7.65681	−0.287760
$709$	−5.64765	−0.212102	−0.106051	−	0.994361i	$-0.533821\pi$
$709$	−5.64765	−0.212102	−0.106051	+	0.994361i	$0.533821\pi$
$710$	9.08496	0.340952
$711$	9.84010	0.369033
$712$	1.71802	0.0643857
$713$	−63.6082	−2.38215
$714$	−8.17883	−0.306085
$715$	3.28279	0.122769
$716$	9.71221	0.362962
$717$	10.8454	0.405028
$718$	21.0380	0.785132
$719$	6.35907	0.237153	0.118577	−	0.992945i	$-0.462167\pi$
$719$	6.35907	0.237153	0.118577	+	0.992945i	$0.462167\pi$
$720$	5.26007	0.196031
$721$	3.96472	0.147654
$722$	−1.91997	−0.0714537
$723$	−12.2307	−0.454865
$724$	6.49211	0.241277
$725$	−22.6572	−0.841466
$726$	1.15200	0.0427548
$727$	−32.3295	−1.19904	−0.599518	−	0.800361i	$-0.704641\pi$
$727$	−32.3295	−1.19904	−0.599518	+	0.800361i	$0.704641\pi$
$728$	−9.33080	−0.345823
$729$	−15.2206	−0.563726
$730$	11.9553	0.442485
$731$	18.5866	0.687451
$732$	6.09356	0.225224
$733$	−8.86175	−0.327316	−0.163658	−	0.986517i	$-0.552329\pi$
$733$	−8.86175	−0.327316	−0.163658	+	0.986517i	$0.552329\pi$
$734$	0.134244	0.00495503
$735$	−5.08360	−0.187512
$736$	47.7621	1.76054
$737$	29.4370	1.08433
$738$	−13.1562	−0.484286
$739$	−28.5800	−1.05133	−0.525667	−	0.850690i	$-0.676184\pi$
$739$	−28.5800	−1.05133	−0.525667	+	0.850690i	$0.676184\pi$
$740$	17.6148	0.647534
$741$	2.25921	0.0829941
$742$	2.42821	0.0891425
$743$	19.7685	0.725236	0.362618	−	0.931938i	$-0.381883\pi$
$743$	19.7685	0.725236	0.362618	+	0.931938i	$0.381883\pi$
$744$	8.69308	0.318704
$745$	12.1398	0.444768
$746$	−11.9810	−0.438656
$747$	−30.8460	−1.12860
$748$	−27.5079	−1.00579
$749$	55.4840	2.02734
$750$	−3.28841	−0.120076
$751$	−34.5288	−1.25997	−0.629987	−	0.776606i	$-0.716940\pi$
$751$	−34.5288	−1.25997	−0.629987	+	0.776606i	$0.716940\pi$
$752$	9.69212	0.353435
$753$	2.53767	0.0924778
$754$	4.22544	0.153881
$755$	−3.35104	−0.121957
$756$	17.2600	0.627741
$757$	46.8992	1.70458	0.852291	−	0.523068i	$-0.175213\pi$
$757$	46.8992	1.70458	0.852291	+	0.523068i	$0.175213\pi$
$758$	0.244703	0.00888800
$759$	−10.9035	−0.395771
$760$	13.3060	0.482660
$761$	43.1198	1.56309	0.781546	−	0.623848i	$-0.214432\pi$
$761$	43.1198	1.56309	0.781546	+	0.623848i	$0.214432\pi$
$762$	−0.683329	−0.0247544
$763$	−70.7623	−2.56177
$764$	−31.6731	−1.14589
$765$	21.6321	0.782111
$766$	−2.88840	−0.104362
$767$	−10.1431	−0.366246
$768$	−4.15148	−0.149804
$769$	−13.4752	−0.485927	−0.242963	−	0.970035i	$-0.578119\pi$
$769$	−13.4752	−0.485927	−0.242963	+	0.970035i	$0.578119\pi$
$770$	8.59474	0.309733
$771$	0.202263	0.00728433
$772$	−28.1577	−1.01342
$773$	12.7875	0.459935	0.229968	−	0.973198i	$-0.426138\pi$
$773$	12.7875	0.459935	0.229968	+	0.973198i	$0.426138\pi$
$774$	5.24746	0.188616
$775$	−27.0968	−0.973346
$776$	−10.4391	−0.374742
$777$	17.8438	0.640143
$778$	−15.5003	−0.555712
$779$	33.7005	1.20745
$780$	−0.911849	−0.0326494
$781$	30.9527	1.10757
$782$	35.5243	1.27035
$783$	−17.8117	−0.636539
$784$	13.7215	0.490052
$785$	5.82664	0.207962
$786$	3.11200	0.111001
$787$	−41.4462	−1.47740	−0.738698	−	0.674036i	$-0.764559\pi$
$787$	−41.4462	−1.47740	−0.738698	+	0.674036i	$0.764559\pi$
$788$	−16.5450	−0.589391
$789$	5.61816	0.200012
$790$	−2.83668	−0.100924
$791$	19.9478	0.709262
$792$	−17.6977	−0.628860
$793$	8.07223	0.286653
$794$	2.54975	0.0904874
$795$	0.540758	0.0191787
$796$	30.9285	1.09623
$797$	2.87954	0.101998	0.0509992	−	0.998699i	$-0.483759\pi$
$797$	2.87954	0.101998	0.0509992	+	0.998699i	$0.483759\pi$
$798$	5.91488	0.209385
$799$	39.8589	1.41011
$800$	20.3464	0.719355
$801$	−2.01992	−0.0713704
$802$	17.2930	0.610636
$803$	40.7320	1.43740
$804$	−8.17663	−0.288367
$805$	39.8075	1.40303
$806$	5.05340	0.177999
$807$	−1.91329	−0.0673511
$808$	1.29718	0.0456347
$809$	−20.3116	−0.714117	−0.357058	−	0.934082i	$-0.616220\pi$
$809$	−20.3116	−0.714117	−0.357058	+	0.934082i	$0.616220\pi$
$810$	5.54975	0.194998
$811$	21.4940	0.754755	0.377378	−	0.926059i	$-0.376826\pi$
$811$	21.4940	0.754755	0.377378	+	0.926059i	$0.376826\pi$
$812$	−39.6757	−1.39234
$813$	1.93123	0.0677310
$814$	−16.7336	−0.586514
$815$	30.0000	1.05085
$816$	4.91627	0.172104
$817$	−13.4417	−0.470267
$818$	−8.10168	−0.283269
$819$	10.9705	0.383339
$820$	−13.6020	−0.475003
$821$	1.56739	0.0547023	0.0273511	−	0.999626i	$-0.491293\pi$
$821$	1.56739	0.0547023	0.0273511	+	0.999626i	$0.491293\pi$
$822$	−2.00543	−0.0699475
$823$	23.6355	0.823883	0.411941	−	0.911210i	$-0.364851\pi$
$823$	23.6355	0.823883	0.411941	+	0.911210i	$0.364851\pi$
$824$	2.35346	0.0819867
$825$	−4.64482	−0.161712
$826$	−26.5558	−0.923995
$827$	39.3961	1.36994	0.684968	−	0.728573i	$-0.259816\pi$
$827$	39.3961	1.36994	0.684968	+	0.728573i	$0.259816\pi$
$828$	−35.9697	−1.25003
$829$	−49.5334	−1.72037	−0.860183	−	0.509985i	$-0.829651\pi$
$829$	−49.5334	−1.72037	−0.860183	+	0.509985i	$0.829651\pi$
$830$	8.89222	0.308653
$831$	12.9046	0.447654
$832$	−0.647009	−0.0224310
$833$	56.4297	1.95517
$834$	−4.17557	−0.144588
$835$	8.66683	0.299928
$836$	19.8935	0.688032
$837$	−21.3019	−0.736301
$838$	0.105961	0.00366038
$839$	−5.74434	−0.198317	−0.0991584	−	0.995072i	$-0.531615\pi$
$839$	−5.74434	−0.198317	−0.0991584	+	0.995072i	$0.531615\pi$
$840$	−5.44032	−0.187709
$841$	11.9438	0.411856
$842$	21.4692	0.739876
$843$	−9.23421	−0.318043
$844$	4.74068	0.163181
$845$	−1.20794	−0.0415544
$846$	11.2532	0.386891
$847$	−14.3294	−0.492365
$848$	−1.45959	−0.0501226
$849$	0.709305	0.0243433
$850$	15.1332	0.519064
$851$	−77.5036	−2.65679
$852$	−8.59761	−0.294549
$853$	−2.63622	−0.0902624	−0.0451312	−	0.998981i	$-0.514371\pi$
$853$	−2.63622	−0.0902624	−0.0451312	+	0.998981i	$0.514371\pi$
$854$	21.1341	0.723193
$855$	−15.6442	−0.535021
$856$	32.9354	1.12571
$857$	5.26089	0.179709	0.0898543	−	0.995955i	$-0.471360\pi$
$857$	5.26089	0.179709	0.0898543	+	0.995955i	$0.471360\pi$
$858$	0.866234	0.0295727
$859$	−17.1978	−0.586780	−0.293390	−	0.955993i	$-0.594783\pi$
$859$	−17.1978	−0.586780	−0.293390	+	0.955993i	$0.594783\pi$
$860$	5.42528	0.185001
$861$	−13.7788	−0.469582
$862$	3.11498	0.106097
$863$	17.6302	0.600139	0.300069	−	0.953917i	$-0.402990\pi$
$863$	17.6302	0.600139	0.300069	+	0.953917i	$0.402990\pi$
$864$	15.9952	0.544166
$865$	−22.8852	−0.778119
$866$	2.22450	0.0755917
$867$	12.0126	0.407970
$868$	−47.4501	−1.61056
$869$	−9.66463	−0.327850
$870$	2.46364	0.0835252
$871$	−10.8317	−0.367018
$872$	−42.0045	−1.42245
$873$	12.2735	0.415395
$874$	−25.6910	−0.869010
$875$	40.9035	1.38279
$876$	−11.3140	−0.382264
$877$	29.5996	0.999507	0.499753	−	0.866168i	$-0.333424\pi$
$877$	29.5996	0.999507	0.499753	+	0.866168i	$0.333424\pi$
$878$	13.0970	0.442001
$879$	−9.60612	−0.324006
$880$	−5.16627	−0.174155
$881$	2.06792	0.0696700	0.0348350	−	0.999393i	$-0.488909\pi$
$881$	2.06792	0.0696700	0.0348350	+	0.999393i	$0.488909\pi$
$882$	15.9315	0.536441
$883$	−33.2151	−1.11778	−0.558888	−	0.829243i	$-0.688772\pi$
$883$	−33.2151	−1.11778	−0.558888	+	0.829243i	$0.688772\pi$
$884$	10.1218	0.340434
$885$	−5.91392	−0.198794
$886$	−12.3986	−0.416539
$887$	30.3257	1.01824	0.509118	−	0.860696i	$-0.329972\pi$
$887$	30.3257	1.01824	0.509118	+	0.860696i	$0.329972\pi$
$888$	10.5921	0.355448
$889$	8.49972	0.285071
$890$	0.582298	0.0195187
$891$	18.9081	0.633445
$892$	6.96615	0.233244
$893$	−28.8258	−0.964617
$894$	3.20335	0.107136
$895$	7.50146	0.250746
$896$	43.8698	1.46559
$897$	4.01205	0.133959
$898$	18.9369	0.631933
$899$	48.9667	1.63313
$900$	−15.3229	−0.510764
$901$	−6.00259	−0.199975
$902$	12.9216	0.430242
$903$	5.49581	0.182889
$904$	11.8410	0.393827
$905$	5.01434	0.166682
$906$	−0.884242	−0.0293770
$907$	−0.938423	−0.0311598	−0.0155799	−	0.999879i	$-0.504959\pi$
$907$	−0.938423	−0.0311598	−0.0155799	+	0.999879i	$0.504959\pi$
$908$	−12.0674	−0.400471
$909$	−1.52513	−0.0505853
$910$	−3.16253	−0.104837
$911$	−37.9998	−1.25899	−0.629495	−	0.777005i	$-0.716738\pi$
$911$	−37.9998	−1.25899	−0.629495	+	0.777005i	$0.716738\pi$
$912$	−3.55542	−0.117732
$913$	30.2960	1.00265
$914$	18.7789	0.621152
$915$	4.70651	0.155592
$916$	34.1850	1.12950
$917$	−38.7093	−1.27829
$918$	11.8968	0.392653
$919$	−11.8415	−0.390614	−0.195307	−	0.980742i	$-0.562570\pi$
$919$	−11.8415	−0.390614	−0.195307	+	0.980742i	$0.562570\pi$
$920$	23.6297	0.779049
$921$	−8.08512	−0.266414
$922$	−21.3433	−0.702906
$923$	−11.3894	−0.374886
$924$	−8.13370	−0.267579
$925$	−33.0162	−1.08556
$926$	16.8592	0.554028
$927$	−2.76702	−0.0908808
$928$	−36.7681	−1.20697
$929$	28.9711	0.950512	0.475256	−	0.879848i	$-0.342356\pi$
$929$	28.9711	0.950512	0.475256	+	0.879848i	$0.342356\pi$
$930$	2.94639	0.0966158
$931$	−40.8096	−1.33748
$932$	1.65669	0.0542665
$933$	−11.1404	−0.364721
$934$	−6.82641	−0.223367
$935$	−21.2464	−0.694830
$936$	6.51207	0.212854
$937$	−40.5115	−1.32345	−0.661727	−	0.749745i	$-0.730176\pi$
$937$	−40.5115	−1.32345	−0.661727	+	0.749745i	$0.730176\pi$
$938$	−28.3587	−0.925944
$939$	−0.214715	−0.00700695
$940$	11.6345	0.379475
$941$	−20.1834	−0.657960	−0.328980	−	0.944337i	$-0.606705\pi$
$941$	−20.1834	−0.657960	−0.328980	+	0.944337i	$0.606705\pi$
$942$	1.53748	0.0500939
$943$	59.8476	1.94891
$944$	15.9626	0.519539
$945$	13.3312	0.433664
$946$	−5.15388	−0.167567
$947$	3.40069	0.110508	0.0552538	−	0.998472i	$-0.482403\pi$
$947$	3.40069	0.110508	0.0552538	+	0.998472i	$0.482403\pi$
$948$	2.68451	0.0871888
$949$	−14.9878	−0.486524
$950$	−10.9442	−0.355077
$951$	−4.75875	−0.154313
$952$	60.3894	1.95723
$953$	−11.9424	−0.386851	−0.193426	−	0.981115i	$-0.561960\pi$
$953$	−11.9424	−0.386851	−0.193426	+	0.981115i	$0.561960\pi$
$954$	−1.69468	−0.0548672
$955$	−24.4635	−0.791620
$956$	−35.1400	−1.13651
$957$	8.39367	0.271329
$958$	−5.11768	−0.165345
$959$	24.9450	0.805515
$960$	−0.377239	−0.0121753
$961$	27.5617	0.889086
$962$	6.15733	0.198520
$963$	−38.7229	−1.24783
$964$	39.6286	1.27635
$965$	−21.7483	−0.700102
$966$	10.5040	0.337962
$967$	−19.9105	−0.640280	−0.320140	−	0.947370i	$-0.603730\pi$
$967$	−19.9105	−0.640280	−0.320140	+	0.947370i	$0.603730\pi$
$968$	−8.50595	−0.273392
$969$	−14.6217	−0.469716
$970$	−3.53818	−0.113604
$971$	59.9560	1.92408	0.962040	−	0.272908i	$-0.0879856\pi$
$971$	59.9560	1.92408	0.962040	+	0.272908i	$0.0879856\pi$
$972$	−18.3123	−0.587366
$973$	51.9387	1.66508
$974$	21.5884	0.691738
$975$	1.70912	0.0547355
$976$	−12.7036	−0.406633
$977$	−43.2833	−1.38475	−0.692377	−	0.721536i	$-0.743436\pi$
$977$	−43.2833	−1.38475	−0.692377	+	0.721536i	$0.743436\pi$
$978$	7.91614	0.253130
$979$	1.98390	0.0634058
$980$	16.4714	0.526158
$981$	49.3857	1.57677
$982$	−22.1309	−0.706225
$983$	−5.29865	−0.169001	−0.0845003	−	0.996423i	$-0.526929\pi$
$983$	−5.29865	−0.169001	−0.0845003	+	0.996423i	$0.526929\pi$
$984$	−8.17913	−0.260741
$985$	−12.7789	−0.407170
$986$	−27.3472	−0.870912
$987$	11.7857	0.375144
$988$	−7.32005	−0.232882
$989$	−23.8707	−0.759046
$990$	−5.99836	−0.190641
$991$	15.8149	0.502377	0.251189	−	0.967938i	$-0.419179\pi$
$991$	15.8149	0.502377	0.251189	+	0.967938i	$0.419179\pi$
$992$	−43.9727	−1.39614
$993$	0.201484	0.00639391
$994$	−29.8188	−0.945794
$995$	23.8884	0.757313
$996$	−8.41521	−0.266646
$997$	−18.1893	−0.576062	−0.288031	−	0.957621i	$-0.593001\pi$
$997$	−18.1893	−0.576062	−0.288031	+	0.957621i	$0.593001\pi$
$998$	3.26278	0.103281
$999$	−25.9553	−0.821191

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.13	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.13	✓	30	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-0.660355 q^{2} +0.482681 q^{3} -1.56393 q^{4} -1.20794 q^{5} -0.318741 q^{6} +3.96472 q^{7} +2.35346 q^{8} -2.76702 q^{9} +O(q^{10})\)	\(q-0.660355 q^{2} +0.482681 q^{3} -1.56393 q^{4} -1.20794 q^{5} -0.318741 q^{6} +3.96472 q^{7} +2.35346 q^{8} -2.76702 q^{9} +0.797669 q^{10} +2.71768 q^{11} -0.754880 q^{12} -1.00000 q^{13} -2.61812 q^{14} -0.583050 q^{15} +1.57374 q^{16} +6.47204 q^{17} +1.82721 q^{18} -4.68054 q^{19} +1.88914 q^{20} +1.91369 q^{21} -1.79463 q^{22} -8.31202 q^{23} +1.13597 q^{24} -3.54088 q^{25} +0.660355 q^{26} -2.78363 q^{27} -6.20055 q^{28} +6.39874 q^{29} +0.385020 q^{30} +7.65256 q^{31} -5.74615 q^{32} +1.31177 q^{33} -4.27384 q^{34} -4.78914 q^{35} +4.32743 q^{36} +9.32428 q^{37} +3.09082 q^{38} -0.482681 q^{39} -2.84284 q^{40} -7.20013 q^{41} -1.26372 q^{42} +2.87183 q^{43} -4.25026 q^{44} +3.34239 q^{45} +5.48889 q^{46} +6.15864 q^{47} +0.759616 q^{48} +8.71899 q^{49} +2.33824 q^{50} +3.12393 q^{51} +1.56393 q^{52} -0.927464 q^{53} +1.83818 q^{54} -3.28279 q^{55} +9.33080 q^{56} -2.25921 q^{57} -4.22544 q^{58} +10.1431 q^{59} +0.911849 q^{60} -8.07223 q^{61} -5.05340 q^{62} -10.9705 q^{63} +0.647009 q^{64} +1.20794 q^{65} -0.866234 q^{66} +10.8317 q^{67} -10.1218 q^{68} -4.01205 q^{69} +3.16253 q^{70} +11.3894 q^{71} -6.51207 q^{72} +14.9878 q^{73} -6.15733 q^{74} -1.70912 q^{75} +7.32005 q^{76} +10.7748 q^{77} +0.318741 q^{78} -3.55621 q^{79} -1.90099 q^{80} +6.95745 q^{81} +4.75464 q^{82} +11.1477 q^{83} -2.99289 q^{84} -7.81784 q^{85} -1.89643 q^{86} +3.08855 q^{87} +6.39594 q^{88} +0.729999 q^{89} -2.20717 q^{90} -3.96472 q^{91} +12.9994 q^{92} +3.69374 q^{93} -4.06689 q^{94} +5.65381 q^{95} -2.77356 q^{96} -4.43564 q^{97} -5.75763 q^{98} -7.51986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

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