LMFDB - Embedded newform 4033.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77942 q^{2} -0.824598 q^{3} +5.72520 q^{4} +1.36321 q^{5} +2.29191 q^{6} +0.958419 q^{7} -10.3539 q^{8} -2.32004 q^{9} +O(q^{10})$	\(q-2.77942 q^{2} -0.824598 q^{3} +5.72520 q^{4} +1.36321 q^{5} +2.29191 q^{6} +0.958419 q^{7} -10.3539 q^{8} -2.32004 q^{9} -3.78894 q^{10} +4.89198 q^{11} -4.72099 q^{12} +2.13403 q^{13} -2.66385 q^{14} -1.12410 q^{15} +17.3275 q^{16} +0.837569 q^{17} +6.44837 q^{18} -3.09218 q^{19} +7.80466 q^{20} -0.790311 q^{21} -13.5969 q^{22} -5.75639 q^{23} +8.53782 q^{24} -3.14165 q^{25} -5.93139 q^{26} +4.38689 q^{27} +5.48714 q^{28} -5.18087 q^{29} +3.12436 q^{30} +6.00005 q^{31} -27.4527 q^{32} -4.03391 q^{33} -2.32796 q^{34} +1.30653 q^{35} -13.2827 q^{36} +1.00000 q^{37} +8.59449 q^{38} -1.75972 q^{39} -14.1146 q^{40} -0.796596 q^{41} +2.19661 q^{42} +0.0513828 q^{43} +28.0076 q^{44} -3.16270 q^{45} +15.9994 q^{46} +3.24631 q^{47} -14.2882 q^{48} -6.08143 q^{49} +8.73199 q^{50} -0.690658 q^{51} +12.2178 q^{52} -7.63203 q^{53} -12.1930 q^{54} +6.66880 q^{55} -9.92339 q^{56} +2.54981 q^{57} +14.3998 q^{58} +4.07640 q^{59} -6.43571 q^{60} +9.04914 q^{61} -16.6767 q^{62} -2.22357 q^{63} +41.6477 q^{64} +2.90914 q^{65} +11.2120 q^{66} -9.72569 q^{67} +4.79525 q^{68} +4.74670 q^{69} -3.63140 q^{70} -15.8755 q^{71} +24.0215 q^{72} -12.2726 q^{73} -2.77942 q^{74} +2.59060 q^{75} -17.7034 q^{76} +4.68857 q^{77} +4.89101 q^{78} +0.151525 q^{79} +23.6211 q^{80} +3.34269 q^{81} +2.21408 q^{82} -14.0084 q^{83} -4.52469 q^{84} +1.14178 q^{85} -0.142815 q^{86} +4.27214 q^{87} -50.6511 q^{88} -7.24068 q^{89} +8.79049 q^{90} +2.04530 q^{91} -32.9565 q^{92} -4.94763 q^{93} -9.02287 q^{94} -4.21530 q^{95} +22.6375 q^{96} +4.48748 q^{97} +16.9029 q^{98} -11.3496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) $ 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * 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 $

$2$	−2.77942	−1.96535	−0.982675	−	0.185337i	$-0.940662\pi$
$2$	−2.77942	−1.96535	−0.982675	+	0.185337i	$0.940662\pi$
$3$	−0.824598	−0.476082	−0.238041	−	0.971255i	$-0.576505\pi$
$3$	−0.824598	−0.476082	−0.238041	+	0.971255i	$0.576505\pi$
$4$	5.72520	2.86260
$5$	1.36321	0.609647	0.304823	−	0.952409i	$-0.401403\pi$
$5$	1.36321	0.609647	0.304823	+	0.952409i	$0.401403\pi$
$6$	2.29191	0.935667
$7$	0.958419	0.362248	0.181124	−	0.983460i	$-0.442026\pi$
$7$	0.958419	0.362248	0.181124	+	0.983460i	$0.442026\pi$
$8$	−10.3539	−3.66066
$9$	−2.32004	−0.773346
$10$	−3.78894	−1.19817
$11$	4.89198	1.47499	0.737493	−	0.675355i	$-0.236009\pi$
$11$	4.89198	1.47499	0.737493	+	0.675355i	$0.236009\pi$
$12$	−4.72099	−1.36283
$13$	2.13403	0.591875	0.295937	−	0.955207i	$-0.404368\pi$
$13$	2.13403	0.591875	0.295937	+	0.955207i	$0.404368\pi$
$14$	−2.66385	−0.711945
$15$	−1.12410	−0.290242
$16$	17.3275	4.33188
$17$	0.837569	0.203140	0.101570	−	0.994828i	$-0.467613\pi$
$17$	0.837569	0.203140	0.101570	+	0.994828i	$0.467613\pi$
$18$	6.44837	1.51990
$19$	−3.09218	−0.709395	−0.354698	−	0.934981i	$-0.615416\pi$
$19$	−3.09218	−0.709395	−0.354698	+	0.934981i	$0.615416\pi$
$20$	7.80466	1.74518
$21$	−0.790311	−0.172460
$22$	−13.5969	−2.89886
$23$	−5.75639	−1.20029	−0.600145	−	0.799891i	$-0.704890\pi$
$23$	−5.75639	−1.20029	−0.600145	+	0.799891i	$0.704890\pi$
$24$	8.53782	1.74277
$25$	−3.14165	−0.628331
$26$	−5.93139	−1.16324
$27$	4.38689	0.844258
$28$	5.48714	1.03697
$29$	−5.18087	−0.962064	−0.481032	−	0.876703i	$-0.659738\pi$
$29$	−5.18087	−0.962064	−0.481032	+	0.876703i	$0.659738\pi$
$30$	3.12436	0.570427
$31$	6.00005	1.07764	0.538820	−	0.842421i	$-0.318870\pi$
$31$	6.00005	1.07764	0.538820	+	0.842421i	$0.318870\pi$
$32$	−27.4527	−4.85300
$33$	−4.03391	−0.702214
$34$	−2.32796	−0.399242
$35$	1.30653	0.220844
$36$	−13.2827	−2.21378
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	8.59449	1.39421
$39$	−1.75972	−0.281781
$40$	−14.1146	−2.23171
$41$	−0.796596	−0.124407	−0.0622037	−	0.998063i	$-0.519813\pi$
$41$	−0.796596	−0.124407	−0.0622037	+	0.998063i	$0.519813\pi$
$42$	2.19661	0.338944
$43$	0.0513828	0.00783580	0.00391790	−	0.999992i	$-0.498753\pi$
$43$	0.0513828	0.00783580	0.00391790	+	0.999992i	$0.498753\pi$
$44$	28.0076	4.22230
$45$	−3.16270	−0.471468
$46$	15.9994	2.35899
$47$	3.24631	0.473523	0.236761	−	0.971568i	$-0.423914\pi$
$47$	3.24631	0.473523	0.236761	+	0.971568i	$0.423914\pi$
$48$	−14.2882	−2.06233
$49$	−6.08143	−0.868776
$50$	8.73199	1.23489
$51$	−0.690658	−0.0967115
$52$	12.2178	1.69430
$53$	−7.63203	−1.04834	−0.524170	−	0.851614i	$-0.675624\pi$
$53$	−7.63203	−1.04834	−0.524170	+	0.851614i	$0.675624\pi$
$54$	−12.1930	−1.65926
$55$	6.66880	0.899221
$56$	−9.92339	−1.32607
$57$	2.54981	0.337730
$58$	14.3998	1.89079
$59$	4.07640	0.530702	0.265351	−	0.964152i	$-0.414512\pi$
$59$	4.07640	0.530702	0.265351	+	0.964152i	$0.414512\pi$
$60$	−6.43571	−0.830846
$61$	9.04914	1.15862	0.579312	−	0.815106i	$-0.303321\pi$
$61$	9.04914	1.15862	0.579312	+	0.815106i	$0.303321\pi$
$62$	−16.6767	−2.11794
$63$	−2.22357	−0.280143
$64$	41.6477	5.20596
$65$	2.90914	0.360834
$66$	11.2120	1.38010
$67$	−9.72569	−1.18818	−0.594091	−	0.804398i	$-0.702488\pi$
$67$	−9.72569	−1.18818	−0.594091	+	0.804398i	$0.702488\pi$
$68$	4.79525	0.581510
$69$	4.74670	0.571436
$70$	−3.63140	−0.434035
$71$	−15.8755	−1.88408	−0.942039	−	0.335503i	$-0.891094\pi$
$71$	−15.8755	−1.88408	−0.942039	+	0.335503i	$0.891094\pi$
$72$	24.0215	2.83096
$73$	−12.2726	−1.43640	−0.718201	−	0.695836i	$-0.755034\pi$
$73$	−12.2726	−1.43640	−0.718201	+	0.695836i	$0.755034\pi$
$74$	−2.77942	−0.323102
$75$	2.59060	0.299137
$76$	−17.7034	−2.03072
$77$	4.68857	0.534312
$78$	4.89101	0.553798
$79$	0.151525	0.0170479	0.00852396	−	0.999964i	$-0.497287\pi$
$79$	0.151525	0.0170479	0.00852396	+	0.999964i	$0.497287\pi$
$80$	23.6211	2.64092
$81$	3.34269	0.371410
$82$	2.21408	0.244504
$83$	−14.0084	−1.53762	−0.768810	−	0.639477i	$-0.779151\pi$
$83$	−14.0084	−1.53762	−0.768810	+	0.639477i	$0.779151\pi$
$84$	−4.52469	−0.493684
$85$	1.14178	0.123844
$86$	−0.142815	−0.0154001
$87$	4.27214	0.458021
$88$	−50.6511	−5.39943
$89$	−7.24068	−0.767511	−0.383756	−	0.923435i	$-0.625369\pi$
$89$	−7.24068	−0.767511	−0.383756	+	0.923435i	$0.625369\pi$
$90$	8.79049	0.926599
$91$	2.04530	0.214406
$92$	−32.9565	−3.43595
$93$	−4.94763	−0.513045
$94$	−9.02287	−0.930638
$95$	−4.21530	−0.432481
$96$	22.6375	2.31043
$97$	4.48748	0.455634	0.227817	−	0.973704i	$-0.426841\pi$
$97$	4.48748	0.455634	0.227817	+	0.973704i	$0.426841\pi$
$98$	16.9029	1.70745
$99$	−11.3496	−1.14067
$100$	−17.9866	−1.79866
$101$	−13.9496	−1.38804	−0.694018	−	0.719957i	$-0.744161\pi$
$101$	−13.9496	−1.38804	−0.694018	+	0.719957i	$0.744161\pi$
$102$	1.91963	0.190072
$103$	−5.24280	−0.516589	−0.258294	−	0.966066i	$-0.583160\pi$
$103$	−5.24280	−0.516589	−0.258294	+	0.966066i	$0.583160\pi$
$104$	−22.0956	−2.16665
$105$	−1.07736	−0.105140
$106$	21.2126	2.06035
$107$	−7.68517	−0.742954	−0.371477	−	0.928442i	$-0.621148\pi$
$107$	−7.68517	−0.742954	−0.371477	+	0.928442i	$0.621148\pi$
$108$	25.1158	2.41677
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−18.5354	−1.76728
$111$	−0.824598	−0.0782674
$112$	16.6070	1.56922
$113$	10.7760	1.01372	0.506860	−	0.862028i	$-0.330806\pi$
$113$	10.7760	1.01372	0.506860	+	0.862028i	$0.330806\pi$
$114$	−7.08700	−0.663758
$115$	−7.84717	−0.731753
$116$	−29.6615	−2.75400
$117$	−4.95104	−0.457724
$118$	−11.3300	−1.04302
$119$	0.802743	0.0735873
$120$	11.6389	1.06248
$121$	12.9314	1.17559
$122$	−25.1514	−2.27710
$123$	0.656871	0.0592281
$124$	34.3515	3.08486
$125$	−11.0988	−0.992707
$126$	6.18024	0.550580
$127$	1.04430	0.0926669	0.0463335	−	0.998926i	$-0.485246\pi$
$127$	1.04430	0.0926669	0.0463335	+	0.998926i	$0.485246\pi$
$128$	−60.8512	−5.37854
$129$	−0.0423701	−0.00373048
$130$	−8.08574	−0.709166
$131$	16.1917	1.41468	0.707338	−	0.706876i	$-0.249896\pi$
$131$	16.1917	1.41468	0.707338	+	0.706876i	$0.249896\pi$
$132$	−23.0950	−2.01016
$133$	−2.96361	−0.256977
$134$	27.0318	2.33519
$135$	5.98026	0.514699
$136$	−8.67212	−0.743628
$137$	−5.86488	−0.501070	−0.250535	−	0.968108i	$-0.580607\pi$
$137$	−5.86488	−0.501070	−0.250535	+	0.968108i	$0.580607\pi$
$138$	−13.1931	−1.12307
$139$	12.3628	1.04860	0.524298	−	0.851535i	$-0.324328\pi$
$139$	12.3628	1.04860	0.524298	+	0.851535i	$0.324328\pi$
$140$	7.48014	0.632187
$141$	−2.67690	−0.225436
$142$	44.1248	3.70287
$143$	10.4396	0.873007
$144$	−40.2005	−3.35004
$145$	−7.06262	−0.586519
$146$	34.1108	2.82303
$147$	5.01474	0.413609
$148$	5.72520	0.470609
$149$	9.06874	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$149$	9.06874	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$150$	−7.20038	−0.587909
$151$	0.462075	0.0376031	0.0188016	−	0.999823i	$-0.494015\pi$
$151$	0.462075	0.0376031	0.0188016	+	0.999823i	$0.494015\pi$
$152$	32.0162	2.59686
$153$	−1.94319	−0.157098
$154$	−13.0315	−1.05011
$155$	8.17934	0.656980
$156$	−10.0748	−0.806626
$157$	0.693985	0.0553861	0.0276930	−	0.999616i	$-0.491184\pi$
$157$	0.693985	0.0553861	0.0276930	+	0.999616i	$0.491184\pi$
$158$	−0.421153	−0.0335051
$159$	6.29335	0.499095
$160$	−37.4239	−2.95862
$161$	−5.51703	−0.434803
$162$	−9.29076	−0.729951
$163$	−4.75616	−0.372531	−0.186265	−	0.982499i	$-0.559638\pi$
$163$	−4.75616	−0.372531	−0.186265	+	0.982499i	$0.559638\pi$
$164$	−4.56067	−0.356129
$165$	−5.49908	−0.428103
$166$	38.9353	3.02196
$167$	7.43172	0.575084	0.287542	−	0.957768i	$-0.407162\pi$
$167$	7.43172	0.575084	0.287542	+	0.957768i	$0.407162\pi$
$168$	8.18281	0.631318
$169$	−8.44590	−0.649684
$170$	−3.17350	−0.243397
$171$	7.17398	0.548608
$172$	0.294177	0.0224308
$173$	−21.2862	−1.61836	−0.809180	−	0.587560i	$-0.800089\pi$
$173$	−21.2862	−1.61836	−0.809180	+	0.587560i	$0.800089\pi$
$174$	−11.8741	−0.900172
$175$	−3.01102	−0.227612
$176$	84.7658	6.38947
$177$	−3.36139	−0.252658
$178$	20.1249	1.50843
$179$	−19.5904	−1.46426	−0.732129	−	0.681166i	$-0.761473\pi$
$179$	−19.5904	−1.46426	−0.732129	+	0.681166i	$0.761473\pi$
$180$	−18.1071	−1.34962
$181$	2.20280	0.163733	0.0818663	−	0.996643i	$-0.473912\pi$
$181$	2.20280	0.163733	0.0818663	+	0.996643i	$0.473912\pi$
$182$	−5.68476	−0.421382
$183$	−7.46191	−0.551600
$184$	59.6011	4.39385
$185$	1.36321	0.100225
$186$	13.7516	1.00831
$187$	4.09737	0.299629
$188$	18.5858	1.35551
$189$	4.20448	0.305831
$190$	11.7161	0.849976
$191$	−3.10676	−0.224797	−0.112399	−	0.993663i	$-0.535853\pi$
$191$	−3.10676	−0.224797	−0.112399	+	0.993663i	$0.535853\pi$
$192$	−34.3426	−2.47846
$193$	−23.2882	−1.67632	−0.838162	−	0.545421i	$-0.816370\pi$
$193$	−23.2882	−1.67632	−0.838162	+	0.545421i	$0.816370\pi$
$194$	−12.4726	−0.895481
$195$	−2.39887	−0.171787
$196$	−34.8174	−2.48696
$197$	20.9738	1.49432	0.747160	−	0.664644i	$-0.231417\pi$
$197$	20.9738	1.49432	0.747160	+	0.664644i	$0.231417\pi$
$198$	31.5453	2.24183
$199$	21.3056	1.51031	0.755157	−	0.655544i	$-0.227561\pi$
$199$	21.3056	1.51031	0.755157	+	0.655544i	$0.227561\pi$
$200$	32.5284	2.30011
$201$	8.01979	0.565672
$202$	38.7718	2.72798
$203$	−4.96545	−0.348506
$204$	−3.95416	−0.276846
$205$	−1.08593	−0.0758445
$206$	14.5720	1.01528
$207$	13.3550	0.928239
$208$	36.9775	2.56393
$209$	−15.1269	−1.04635
$210$	2.99444	0.206636
$211$	20.5998	1.41815	0.709075	−	0.705133i	$-0.249113\pi$
$211$	20.5998	1.41815	0.709075	+	0.705133i	$0.249113\pi$
$212$	−43.6949	−3.00098
$213$	13.0909	0.896976
$214$	21.3604	1.46016
$215$	0.0700456	0.00477707
$216$	−45.4215	−3.09054
$217$	5.75056	0.390374
$218$	−2.77942	−0.188246
$219$	10.1200	0.683845
$220$	38.1802	2.57411
$221$	1.78740	0.120234
$222$	2.29191	0.153823
$223$	0.646910	0.0433203	0.0216602	−	0.999765i	$-0.493105\pi$
$223$	0.646910	0.0433203	0.0216602	+	0.999765i	$0.493105\pi$
$224$	−26.3112	−1.75799
$225$	7.28876	0.485917
$226$	−29.9511	−1.99232
$227$	−2.09178	−0.138836	−0.0694182	−	0.997588i	$-0.522114\pi$
$227$	−2.09178	−0.138836	−0.0694182	+	0.997588i	$0.522114\pi$
$228$	14.5982	0.966787
$229$	21.9908	1.45319	0.726597	−	0.687064i	$-0.241101\pi$
$229$	21.9908	1.45319	0.726597	+	0.687064i	$0.241101\pi$
$230$	21.8106	1.43815
$231$	−3.86618	−0.254376
$232$	53.6423	3.52179
$233$	−18.5442	−1.21487	−0.607434	−	0.794370i	$-0.707801\pi$
$233$	−18.5442	−1.21487	−0.607434	+	0.794370i	$0.707801\pi$
$234$	13.7610	0.899588
$235$	4.42540	0.288682
$236$	23.3382	1.51919
$237$	−0.124947	−0.00811620
$238$	−2.23116	−0.144625
$239$	26.5452	1.71707	0.858534	−	0.512756i	$-0.171375\pi$
$239$	26.5452	1.71707	0.858534	+	0.512756i	$0.171375\pi$
$240$	−19.4779	−1.25729
$241$	23.1876	1.49365	0.746823	−	0.665023i	$-0.231578\pi$
$241$	23.1876	1.49365	0.746823	+	0.665023i	$0.231578\pi$
$242$	−35.9420	−2.31044
$243$	−15.9171	−1.02108
$244$	51.8082	3.31668
$245$	−8.29028	−0.529646
$246$	−1.82572	−0.116404
$247$	−6.59882	−0.419873
$248$	−62.1240	−3.94488
$249$	11.5513	0.732033
$250$	30.8483	1.95102
$251$	1.84392	0.116388	0.0581938	−	0.998305i	$-0.481466\pi$
$251$	1.84392	0.116388	0.0581938	+	0.998305i	$0.481466\pi$
$252$	−12.7304	−0.801939
$253$	−28.1601	−1.77041
$254$	−2.90256	−0.182123
$255$	−0.941513	−0.0589598
$256$	85.8360	5.36475
$257$	18.9300	1.18082	0.590409	−	0.807104i	$-0.298966\pi$
$257$	18.9300	1.18082	0.590409	+	0.807104i	$0.298966\pi$
$258$	0.117765	0.00733170
$259$	0.958419	0.0595533
$260$	16.6554	1.03292
$261$	12.0198	0.744008
$262$	−45.0036	−2.78033
$263$	−23.3573	−1.44027	−0.720136	−	0.693833i	$-0.755921\pi$
$263$	−23.3573	−1.44027	−0.720136	+	0.693833i	$0.755921\pi$
$264$	41.7668	2.57057
$265$	−10.4041	−0.639117
$266$	8.23713	0.505051
$267$	5.97065	0.365398
$268$	−55.6815	−3.40129
$269$	−23.0203	−1.40357	−0.701786	−	0.712388i	$-0.747614\pi$
$269$	−23.0203	−1.40357	−0.701786	+	0.712388i	$0.747614\pi$
$270$	−16.6217	−1.01156
$271$	−3.72034	−0.225994	−0.112997	−	0.993595i	$-0.536045\pi$
$271$	−3.72034	−0.225994	−0.112997	+	0.993595i	$0.536045\pi$
$272$	14.5130	0.879980
$273$	−1.68655	−0.102075
$274$	16.3010	0.984779
$275$	−15.3689	−0.926780
$276$	27.1758	1.63579
$277$	−8.45163	−0.507809	−0.253905	−	0.967229i	$-0.581715\pi$
$277$	−8.45163	−0.507809	−0.253905	+	0.967229i	$0.581715\pi$
$278$	−34.3614	−2.06086
$279$	−13.9203	−0.833389
$280$	−13.5277	−0.808434
$281$	18.0965	1.07955	0.539773	−	0.841810i	$-0.318510\pi$
$281$	18.0965	1.07955	0.539773	+	0.841810i	$0.318510\pi$
$282$	7.44024	0.443060
$283$	24.9428	1.48269	0.741347	−	0.671122i	$-0.234187\pi$
$283$	24.9428	1.48269	0.741347	+	0.671122i	$0.234187\pi$
$284$	−90.8906	−5.39336
$285$	3.47593	0.205896
$286$	−29.0162	−1.71576
$287$	−0.763473	−0.0450664
$288$	63.6913	3.75305
$289$	−16.2985	−0.958734
$290$	19.6300	1.15272
$291$	−3.70036	−0.216919
$292$	−70.2632	−4.11184
$293$	−27.8267	−1.62565	−0.812826	−	0.582507i	$-0.802072\pi$
$293$	−27.8267	−1.62565	−0.812826	+	0.582507i	$0.802072\pi$
$294$	−13.9381	−0.812885
$295$	5.55700	0.323541
$296$	−10.3539	−0.601809
$297$	21.4606	1.24527
$298$	−25.2059	−1.46014
$299$	−12.2843	−0.710421
$300$	14.8317	0.856310
$301$	0.0492462	0.00283851
$302$	−1.28430	−0.0739033
$303$	11.5028	0.660819
$304$	−53.5799	−3.07302
$305$	12.3359	0.706351
$306$	5.40096	0.308752
$307$	−29.6512	−1.69228	−0.846140	−	0.532960i	$-0.821080\pi$
$307$	−29.6512	−1.69228	−0.846140	+	0.532960i	$0.821080\pi$
$308$	26.8430	1.52952
$309$	4.32321	0.245939
$310$	−22.7339	−1.29120
$311$	14.6888	0.832925	0.416462	−	0.909153i	$-0.363270\pi$
$311$	14.6888	0.832925	0.416462	+	0.909153i	$0.363270\pi$
$312$	18.2200	1.03150
$313$	18.1796	1.02757	0.513786	−	0.857918i	$-0.328243\pi$
$313$	18.1796	1.02757	0.513786	+	0.857918i	$0.328243\pi$
$314$	−1.92888	−0.108853
$315$	−3.03120	−0.170789
$316$	0.867512	0.0488014
$317$	16.5169	0.927684	0.463842	−	0.885918i	$-0.346471\pi$
$317$	16.5169	0.927684	0.463842	+	0.885918i	$0.346471\pi$
$318$	−17.4919	−0.980897
$319$	−25.3447	−1.41903
$320$	56.7746	3.17380
$321$	6.33718	0.353707
$322$	15.3342	0.854540
$323$	−2.58992	−0.144107
$324$	19.1376	1.06320
$325$	−6.70440	−0.371893
$326$	13.2194	0.732154
$327$	−0.824598	−0.0456004
$328$	8.24789	0.455413
$329$	3.11132	0.171533
$330$	15.2843	0.841372
$331$	−18.8681	−1.03708	−0.518542	−	0.855052i	$-0.673525\pi$
$331$	−18.8681	−1.03708	−0.518542	+	0.855052i	$0.673525\pi$
$332$	−80.2009	−4.40159
$333$	−2.32004	−0.127137
$334$	−20.6559	−1.13024
$335$	−13.2582	−0.724371
$336$	−13.6941	−0.747076
$337$	17.6262	0.960160	0.480080	−	0.877225i	$-0.340608\pi$
$337$	17.6262	0.960160	0.480080	+	0.877225i	$0.340608\pi$
$338$	23.4747	1.27686
$339$	−8.88586	−0.482614
$340$	6.53694	0.354516
$341$	29.3521	1.58951
$342$	−19.9395	−1.07821
$343$	−12.5375	−0.676961
$344$	−0.532013	−0.0286842
$345$	6.47076	0.348374
$346$	59.1634	3.18065
$347$	−21.9925	−1.18062	−0.590311	−	0.807176i	$-0.700995\pi$
$347$	−21.9925	−1.18062	−0.590311	+	0.807176i	$0.700995\pi$
$348$	24.4588	1.31113
$349$	28.0938	1.50383	0.751913	−	0.659262i	$-0.229131\pi$
$349$	28.0938	1.50383	0.751913	+	0.659262i	$0.229131\pi$
$350$	8.36891	0.447337
$351$	9.36178	0.499695
$352$	−134.298	−7.15811
$353$	−10.2693	−0.546579	−0.273290	−	0.961932i	$-0.588112\pi$
$353$	−10.2693	−0.546579	−0.273290	+	0.961932i	$0.588112\pi$
$354$	9.34273	0.496561
$355$	−21.6417	−1.14862
$356$	−41.4544	−2.19708
$357$	−0.661940	−0.0350336
$358$	54.4501	2.87778
$359$	−20.1559	−1.06379	−0.531894	−	0.846811i	$-0.678519\pi$
$359$	−20.1559	−1.06379	−0.531894	+	0.846811i	$0.678519\pi$
$360$	32.7464	1.72588
$361$	−9.43840	−0.496758
$362$	−6.12250	−0.321792
$363$	−10.6632	−0.559675
$364$	11.7098	0.613758
$365$	−16.7302	−0.875698
$366$	20.7398	1.08409
$367$	2.99594	0.156387	0.0781933	−	0.996938i	$-0.475085\pi$
$367$	2.99594	0.156387	0.0781933	+	0.996938i	$0.475085\pi$
$368$	−99.7439	−5.19951
$369$	1.84813	0.0962099
$370$	−3.78894	−0.196978
$371$	−7.31468	−0.379759
$372$	−28.3262	−1.46864
$373$	21.6692	1.12199	0.560994	−	0.827820i	$-0.310419\pi$
$373$	21.6692	1.12199	0.560994	+	0.827820i	$0.310419\pi$
$374$	−11.3883	−0.588877
$375$	9.15205	0.472610
$376$	−33.6120	−1.73341
$377$	−11.0562	−0.569421
$378$	−11.6860	−0.601065
$379$	−25.7115	−1.32071	−0.660355	−	0.750953i	$-0.729594\pi$
$379$	−25.7115	−1.32071	−0.660355	+	0.750953i	$0.729594\pi$
$380$	−24.1334	−1.23802
$381$	−0.861130	−0.0441170
$382$	8.63500	0.441805
$383$	−25.7078	−1.31361	−0.656805	−	0.754061i	$-0.728092\pi$
$383$	−25.7078	−1.31361	−0.656805	+	0.754061i	$0.728092\pi$
$384$	50.1778	2.56063
$385$	6.39151	0.325741
$386$	64.7279	3.29456
$387$	−0.119210	−0.00605978
$388$	25.6917	1.30430
$389$	−13.7766	−0.698502	−0.349251	−	0.937029i	$-0.613564\pi$
$389$	−13.7766	−0.698502	−0.349251	+	0.937029i	$0.613564\pi$
$390$	6.66748	0.337621
$391$	−4.82137	−0.243827
$392$	62.9666	3.18030
$393$	−13.3516	−0.673501
$394$	−58.2951	−2.93686
$395$	0.206561	0.0103932
$396$	−64.9786	−3.26530
$397$	−13.7140	−0.688286	−0.344143	−	0.938917i	$-0.611830\pi$
$397$	−13.7140	−0.688286	−0.344143	+	0.938917i	$0.611830\pi$
$398$	−59.2173	−2.96829
$399$	2.44379	0.122342
$400$	−54.4371	−2.72185
$401$	−10.2756	−0.513140	−0.256570	−	0.966526i	$-0.582592\pi$
$401$	−10.2756	−0.513140	−0.256570	+	0.966526i	$0.582592\pi$
$402$	−22.2904	−1.11174
$403$	12.8043	0.637828
$404$	−79.8642	−3.97339
$405$	4.55680	0.226429
$406$	13.8011	0.684937
$407$	4.89198	0.242486
$408$	7.15101	0.354028
$409$	−18.1949	−0.899679	−0.449839	−	0.893109i	$-0.648519\pi$
$409$	−18.1949	−0.899679	−0.449839	+	0.893109i	$0.648519\pi$
$410$	3.01826	0.149061
$411$	4.83617	0.238550
$412$	−30.0161	−1.47879
$413$	3.90690	0.192246
$414$	−37.1193	−1.82431
$415$	−19.0964	−0.937405
$416$	−58.5850	−2.87237
$417$	−10.1943	−0.499217
$418$	42.0440	2.05644
$419$	−16.5703	−0.809511	−0.404755	−	0.914425i	$-0.632643\pi$
$419$	−16.5703	−0.809511	−0.404755	+	0.914425i	$0.632643\pi$
$420$	−6.16811	−0.300973
$421$	−34.4202	−1.67754	−0.838769	−	0.544488i	$-0.816724\pi$
$421$	−34.4202	−1.67754	−0.838769	+	0.544488i	$0.816724\pi$
$422$	−57.2557	−2.78716
$423$	−7.53156	−0.366197
$424$	79.0214	3.83762
$425$	−2.63135	−0.127639
$426$	−36.3852	−1.76287
$427$	8.67288	0.419710
$428$	−43.9992	−2.12678
$429$	−8.60851	−0.415623
$430$	−0.194686	−0.00938861
$431$	−0.553127	−0.0266432	−0.0133216	−	0.999911i	$-0.504241\pi$
$431$	−0.553127	−0.0266432	−0.0133216	+	0.999911i	$0.504241\pi$
$432$	76.0140	3.65722
$433$	34.5293	1.65937	0.829685	−	0.558231i	$-0.188520\pi$
$433$	34.5293	1.65937	0.829685	+	0.558231i	$0.188520\pi$
$434$	−15.9833	−0.767221
$435$	5.82383	0.279231
$436$	5.72520	0.274187
$437$	17.7998	0.851480
$438$	−28.1277	−1.34399
$439$	−12.8301	−0.612348	−0.306174	−	0.951975i	$-0.599049\pi$
$439$	−12.8301	−0.612348	−0.306174	+	0.951975i	$0.599049\pi$
$440$	−69.0482	−3.29174
$441$	14.1092	0.671865
$442$	−4.96795	−0.236301
$443$	26.2525	1.24730	0.623648	−	0.781705i	$-0.285650\pi$
$443$	26.2525	1.24730	0.623648	+	0.781705i	$0.285650\pi$
$444$	−4.72099	−0.224048
$445$	−9.87059	−0.467911
$446$	−1.79804	−0.0851396
$447$	−7.47807	−0.353700
$448$	39.9160	1.88585
$449$	6.83854	0.322731	0.161365	−	0.986895i	$-0.448410\pi$
$449$	6.83854	0.322731	0.161365	+	0.986895i	$0.448410\pi$
$450$	−20.2586	−0.954997
$451$	−3.89693	−0.183499
$452$	61.6947	2.90188
$453$	−0.381026	−0.0179022
$454$	5.81395	0.272862
$455$	2.78818	0.130712
$456$	−26.4005	−1.23632
$457$	−3.89460	−0.182182	−0.0910909	−	0.995843i	$-0.529035\pi$
$457$	−3.89460	−0.182182	−0.0910909	+	0.995843i	$0.529035\pi$
$458$	−61.1218	−2.85603
$459$	3.67433	0.171503
$460$	−44.9266	−2.09472
$461$	−6.74154	−0.313985	−0.156992	−	0.987600i	$-0.550180\pi$
$461$	−6.74154	−0.313985	−0.156992	+	0.987600i	$0.550180\pi$
$462$	10.7458	0.499938
$463$	34.0679	1.58327	0.791634	−	0.610995i	$-0.209231\pi$
$463$	34.0679	1.58327	0.791634	+	0.610995i	$0.209231\pi$
$464$	−89.7717	−4.16755
$465$	−6.74467	−0.312776
$466$	51.5421	2.38764
$467$	−2.19907	−0.101761	−0.0508805	−	0.998705i	$-0.516203\pi$
$467$	−2.19907	−0.101761	−0.0508805	+	0.998705i	$0.516203\pi$
$468$	−28.3457	−1.31028
$469$	−9.32129	−0.430417
$470$	−12.3001	−0.567360
$471$	−0.572259	−0.0263683
$472$	−42.2067	−1.94272
$473$	0.251363	0.0115577
$474$	0.347282	0.0159512
$475$	9.71457	0.445735
$476$	4.59586	0.210651
$477$	17.7066	0.810729
$478$	−73.7805	−3.37464
$479$	5.90296	0.269713	0.134856	−	0.990865i	$-0.456943\pi$
$479$	5.90296	0.269713	0.134856	+	0.990865i	$0.456943\pi$
$480$	30.8596	1.40854
$481$	2.13403	0.0973036
$482$	−64.4482	−2.93554
$483$	4.54933	0.207002
$484$	74.0351	3.36523
$485$	6.11738	0.277776
$486$	44.2403	2.00678
$487$	−39.8364	−1.80516	−0.902581	−	0.430520i	$-0.858330\pi$
$487$	−39.8364	−1.80516	−0.902581	+	0.430520i	$0.858330\pi$
$488$	−93.6941	−4.24133
$489$	3.92192	0.177355
$490$	23.0422	1.04094
$491$	−26.8172	−1.21024	−0.605122	−	0.796133i	$-0.706876\pi$
$491$	−26.8172	−1.21024	−0.605122	+	0.796133i	$0.706876\pi$
$492$	3.76072	0.169546
$493$	−4.33934	−0.195434
$494$	18.3409	0.825198
$495$	−15.4719	−0.695409
$496$	103.966	4.66821
$497$	−15.2154	−0.682505
$498$	−32.1059	−1.43870
$499$	−18.8754	−0.844979	−0.422490	−	0.906368i	$-0.638844\pi$
$499$	−18.8754	−0.844979	−0.422490	+	0.906368i	$0.638844\pi$
$500$	−63.5428	−2.84172
$501$	−6.12818	−0.273787
$502$	−5.12505	−0.228742
$503$	14.3552	0.640068	0.320034	−	0.947406i	$-0.396306\pi$
$503$	14.3552	0.640068	0.320034	+	0.947406i	$0.396306\pi$
$504$	23.0227	1.02551
$505$	−19.0162	−0.846212
$506$	78.2689	3.47948
$507$	6.96447	0.309303
$508$	5.97885	0.265268
$509$	31.5817	1.39983	0.699917	−	0.714225i	$-0.253221\pi$
$509$	31.5817	1.39983	0.699917	+	0.714225i	$0.253221\pi$
$510$	2.61686	0.115877
$511$	−11.7623	−0.520334
$512$	−116.872	−5.16507
$513$	−13.5651	−0.598913
$514$	−52.6144	−2.32072
$515$	−7.14705	−0.314937
$516$	−0.242578	−0.0106789
$517$	15.8809	0.698440
$518$	−2.66385	−0.117043
$519$	17.5526	0.770472
$520$	−30.1210	−1.32089
$521$	9.00651	0.394582	0.197291	−	0.980345i	$-0.436786\pi$
$521$	9.00651	0.394582	0.197291	+	0.980345i	$0.436786\pi$
$522$	−33.4082	−1.46224
$523$	23.6816	1.03553	0.517763	−	0.855524i	$-0.326765\pi$
$523$	23.6816	1.03553	0.517763	+	0.855524i	$0.326765\pi$
$524$	92.7007	4.04965
$525$	2.48288	0.108362
$526$	64.9199	2.83064
$527$	5.02546	0.218912
$528$	−69.8977	−3.04191
$529$	10.1360	0.440695
$530$	28.9173	1.25609
$531$	−9.45740	−0.410416
$532$	−16.9673	−0.735624
$533$	−1.69996	−0.0736336
$534$	−16.5950	−0.718135
$535$	−10.4765	−0.452939
$536$	100.699	4.34953
$537$	16.1542	0.697106
$538$	63.9832	2.75851
$539$	−29.7502	−1.28143
$540$	34.2382	1.47338
$541$	14.7575	0.634475	0.317237	−	0.948346i	$-0.397245\pi$
$541$	14.7575	0.634475	0.317237	+	0.948346i	$0.397245\pi$
$542$	10.3404	0.444158
$543$	−1.81642	−0.0779501
$544$	−22.9936	−0.985840
$545$	1.36321	0.0583936
$546$	4.68764	0.200612
$547$	−21.7780	−0.931162	−0.465581	−	0.885005i	$-0.654155\pi$
$547$	−21.7780	−0.931162	−0.465581	+	0.885005i	$0.654155\pi$
$548$	−33.5776	−1.43436
$549$	−20.9944	−0.896017
$550$	42.7167	1.82145
$551$	16.0202	0.682484
$552$	−49.1470	−2.09183
$553$	0.145225	0.00617558
$554$	23.4907	0.998023
$555$	−1.12410	−0.0477155
$556$	70.7793	3.00171
$557$	6.40499	0.271388	0.135694	−	0.990751i	$-0.456674\pi$
$557$	6.40499	0.271388	0.135694	+	0.990751i	$0.456674\pi$
$558$	38.6906	1.63790
$559$	0.109653	0.00463781
$560$	22.6389	0.956668
$561$	−3.37868	−0.142648
$562$	−50.2979	−2.12169
$563$	−26.4236	−1.11362	−0.556812	−	0.830639i	$-0.687976\pi$
$563$	−26.4236	−1.11362	−0.556812	+	0.830639i	$0.687976\pi$
$564$	−15.3258	−0.645332
$565$	14.6900	0.618011
$566$	−69.3266	−2.91401
$567$	3.20370	0.134543
$568$	164.374	6.89697
$569$	30.5528	1.28084	0.640420	−	0.768025i	$-0.278760\pi$
$569$	30.5528	1.28084	0.640420	+	0.768025i	$0.278760\pi$
$570$	−9.66108	−0.404658
$571$	−5.01143	−0.209722	−0.104861	−	0.994487i	$-0.533440\pi$
$571$	−5.01143	−0.209722	−0.104861	+	0.994487i	$0.533440\pi$
$572$	59.7691	2.49907
$573$	2.56183	0.107022
$574$	2.12202	0.0885712
$575$	18.0846	0.754179
$576$	−96.6243	−4.02601
$577$	−3.02799	−0.126057	−0.0630285	−	0.998012i	$-0.520076\pi$
$577$	−3.02799	−0.126057	−0.0630285	+	0.998012i	$0.520076\pi$
$578$	45.3004	1.88425
$579$	19.2034	0.798068
$580$	−40.4349	−1.67897
$581$	−13.4259	−0.557001
$582$	10.2849	0.426322
$583$	−37.3357	−1.54629
$584$	127.070	5.25818
$585$	−6.74932	−0.279050
$586$	77.3421	3.19497
$587$	−1.42811	−0.0589443	−0.0294722	−	0.999566i	$-0.509383\pi$
$587$	−1.42811	−0.0589443	−0.0294722	+	0.999566i	$0.509383\pi$
$588$	28.7104	1.18400
$589$	−18.5533	−0.764473
$590$	−15.4453	−0.635871
$591$	−17.2949	−0.711419
$592$	17.3275	0.712157
$593$	12.8450	0.527479	0.263740	−	0.964594i	$-0.415044\pi$
$593$	12.8450	0.527479	0.263740	+	0.964594i	$0.415044\pi$
$594$	−59.6481	−2.44739
$595$	1.09431	0.0448623
$596$	51.9204	2.12674
$597$	−17.5685	−0.719033
$598$	34.1434	1.39623
$599$	1.02222	0.0417668	0.0208834	−	0.999782i	$-0.493352\pi$
$599$	1.02222	0.0417668	0.0208834	+	0.999782i	$0.493352\pi$
$600$	−26.8229	−1.09504
$601$	11.9178	0.486135	0.243068	−	0.970009i	$-0.421846\pi$
$601$	11.9178	0.486135	0.243068	+	0.970009i	$0.421846\pi$
$602$	−0.136876	−0.00557866
$603$	22.5640	0.918876
$604$	2.64547	0.107643
$605$	17.6283	0.716692
$606$	−31.9712	−1.29874
$607$	15.6216	0.634062	0.317031	−	0.948415i	$-0.397314\pi$
$607$	15.6216	0.634062	0.317031	+	0.948415i	$0.397314\pi$
$608$	84.8888	3.44270
$609$	4.09450	0.165917
$610$	−34.2867	−1.38823
$611$	6.92773	0.280266
$612$	−11.1252	−0.449708
$613$	−10.7373	−0.433674	−0.216837	−	0.976208i	$-0.569574\pi$
$613$	−10.7373	−0.433674	−0.216837	+	0.976208i	$0.569574\pi$
$614$	82.4131	3.32592
$615$	0.895455	0.0361082
$616$	−48.5450	−1.95593
$617$	12.5871	0.506739	0.253369	−	0.967370i	$-0.418461\pi$
$617$	12.5871	0.506739	0.253369	+	0.967370i	$0.418461\pi$
$618$	−12.0160	−0.483355
$619$	−19.7886	−0.795372	−0.397686	−	0.917521i	$-0.630187\pi$
$619$	−19.7886	−0.795372	−0.397686	+	0.917521i	$0.630187\pi$
$620$	46.8284	1.88067
$621$	−25.2527	−1.01335
$622$	−40.8264	−1.63699
$623$	−6.93961	−0.278030
$624$	−30.4916	−1.22064
$625$	0.578263	0.0231305
$626$	−50.5288	−2.01954
$627$	12.4736	0.498148
$628$	3.97321	0.158548
$629$	0.837569	0.0333961
$630$	8.42498	0.335659
$631$	−24.9605	−0.993663	−0.496832	−	0.867847i	$-0.665503\pi$
$631$	−24.9605	−0.993663	−0.496832	+	0.867847i	$0.665503\pi$
$632$	−1.56888	−0.0624066
$633$	−16.9866	−0.675156
$634$	−45.9076	−1.82322
$635$	1.42361	0.0564941
$636$	36.0307	1.42871
$637$	−12.9780	−0.514206
$638$	70.4437	2.78889
$639$	36.8318	1.45704
$640$	−82.9531	−3.27901
$641$	−37.0545	−1.46356	−0.731782	−	0.681539i	$-0.761311\pi$
$641$	−37.0545	−1.46356	−0.731782	+	0.681539i	$0.761311\pi$
$642$	−17.6137	−0.695158
$643$	−32.2352	−1.27123	−0.635616	−	0.772006i	$-0.719254\pi$
$643$	−32.2352	−1.27123	−0.635616	+	0.772006i	$0.719254\pi$
$644$	−31.5861	−1.24467
$645$	−0.0577595	−0.00227428
$646$	7.19848	0.283220
$647$	−26.3248	−1.03493	−0.517467	−	0.855703i	$-0.673125\pi$
$647$	−26.3248	−1.03493	−0.517467	+	0.855703i	$0.673125\pi$
$648$	−34.6099	−1.35961
$649$	19.9417	0.782778
$650$	18.6344	0.730900
$651$	−4.74190	−0.185850
$652$	−27.2300	−1.06641
$653$	8.20088	0.320925	0.160463	−	0.987042i	$-0.448701\pi$
$653$	8.20088	0.320925	0.160463	+	0.987042i	$0.448701\pi$
$654$	2.29191	0.0896207
$655$	22.0727	0.862452
$656$	−13.8030	−0.538918
$657$	28.4730	1.11084
$658$	−8.64769	−0.337122
$659$	−2.71242	−0.105661	−0.0528305	−	0.998603i	$-0.516824\pi$
$659$	−2.71242	−0.105661	−0.0528305	+	0.998603i	$0.516824\pi$
$660$	−31.4833	−1.22549
$661$	−35.2852	−1.37244	−0.686218	−	0.727396i	$-0.740730\pi$
$661$	−35.2852	−1.37244	−0.686218	+	0.727396i	$0.740730\pi$
$662$	52.4425	2.03823
$663$	−1.47389	−0.0572411
$664$	145.042	5.62871
$665$	−4.04003	−0.156665
$666$	6.44837	0.249869
$667$	29.8231	1.15476
$668$	42.5481	1.64624
$669$	−0.533441	−0.0206240
$670$	36.8501	1.42364
$671$	44.2682	1.70896
$672$	21.6962	0.836948
$673$	−45.1104	−1.73888	−0.869440	−	0.494039i	$-0.835520\pi$
$673$	−45.1104	−1.73888	−0.869440	+	0.494039i	$0.835520\pi$
$674$	−48.9907	−1.88705
$675$	−13.7821	−0.530473
$676$	−48.3545	−1.85979
$677$	−5.58911	−0.214807	−0.107404	−	0.994216i	$-0.534254\pi$
$677$	−5.58911	−0.214807	−0.107404	+	0.994216i	$0.534254\pi$
$678$	24.6976	0.948505
$679$	4.30088	0.165053
$680$	−11.8219	−0.453351
$681$	1.72488	0.0660975
$682$	−81.5820	−3.12393
$683$	−45.6573	−1.74703	−0.873515	−	0.486798i	$-0.838165\pi$
$683$	−45.6573	−1.74703	−0.873515	+	0.486798i	$0.838165\pi$
$684$	41.0725	1.57045
$685$	−7.99507	−0.305476
$686$	34.8470	1.33047
$687$	−18.1336	−0.691839
$688$	0.890336	0.0339438
$689$	−16.2870	−0.620486
$690$	−17.9850	−0.684677
$691$	11.5645	0.439935	0.219967	−	0.975507i	$-0.429405\pi$
$691$	11.5645	0.439935	0.219967	+	0.975507i	$0.429405\pi$
$692$	−121.868	−4.63272
$693$	−10.8777	−0.413208
$694$	61.1266	2.32033
$695$	16.8531	0.639273
$696$	−44.2333	−1.67666
$697$	−0.667204	−0.0252722
$698$	−78.0846	−2.95555
$699$	15.2915	0.578377
$700$	−17.2387	−0.651562
$701$	−26.2875	−0.992867	−0.496433	−	0.868075i	$-0.665357\pi$
$701$	−26.2875	−0.992867	−0.496433	+	0.868075i	$0.665357\pi$
$702$	−26.0204	−0.982075
$703$	−3.09218	−0.116624
$704$	203.740	7.67873
$705$	−3.64918	−0.137436
$706$	28.5427	1.07422
$707$	−13.3696	−0.502814
$708$	−19.2446	−0.723258
$709$	−23.7303	−0.891209	−0.445604	−	0.895230i	$-0.647011\pi$
$709$	−23.7303	−0.891209	−0.445604	+	0.895230i	$0.647011\pi$
$710$	60.1515	2.25744
$711$	−0.351544	−0.0131839
$712$	74.9694	2.80960
$713$	−34.5386	−1.29348
$714$	1.83981	0.0688532
$715$	14.2314	0.532226
$716$	−112.159	−4.19158
$717$	−21.8892	−0.817465
$718$	56.0218	2.09072
$719$	2.85840	0.106600	0.0533002	−	0.998579i	$-0.483026\pi$
$719$	2.85840	0.106600	0.0533002	+	0.998579i	$0.483026\pi$
$720$	−54.8018	−2.04234
$721$	−5.02480	−0.187134
$722$	26.2333	0.976304
$723$	−19.1205	−0.711097
$724$	12.6114	0.468701
$725$	16.2765	0.604494
$726$	29.6377	1.09996
$727$	4.72668	0.175303	0.0876514	−	0.996151i	$-0.472064\pi$
$727$	4.72668	0.175303	0.0876514	+	0.996151i	$0.472064\pi$
$728$	−21.1769	−0.784867
$729$	3.09710	0.114707
$730$	46.5003	1.72105
$731$	0.0430366	0.00159177
$732$	−42.7209	−1.57901
$733$	−22.1404	−0.817774	−0.408887	−	0.912585i	$-0.634083\pi$
$733$	−22.1404	−0.817774	−0.408887	+	0.912585i	$0.634083\pi$
$734$	−8.32698	−0.307354
$735$	6.83615	0.252155
$736$	158.028	5.82501
$737$	−47.5779	−1.75255
$738$	−5.13675	−0.189086
$739$	−16.1363	−0.593585	−0.296792	−	0.954942i	$-0.595917\pi$
$739$	−16.1363	−0.593585	−0.296792	+	0.954942i	$0.595917\pi$
$740$	7.80466	0.286905
$741$	5.44138	0.199894
$742$	20.3306	0.746360
$743$	−44.6789	−1.63911	−0.819554	−	0.573002i	$-0.805779\pi$
$743$	−44.6789	−1.63911	−0.819554	+	0.573002i	$0.805779\pi$
$744$	51.2273	1.87809
$745$	12.3626	0.452931
$746$	−60.2279	−2.20510
$747$	32.5000	1.18911
$748$	23.4583	0.857719
$749$	−7.36562	−0.269134
$750$	−25.4374	−0.928843
$751$	−28.2527	−1.03095	−0.515477	−	0.856903i	$-0.672385\pi$
$751$	−28.2527	−1.03095	−0.515477	+	0.856903i	$0.672385\pi$
$752$	56.2505	2.05124
$753$	−1.52050	−0.0554100
$754$	30.7298	1.11911
$755$	0.629906	0.0229246
$756$	24.0715	0.875472
$757$	−8.09378	−0.294173	−0.147087	−	0.989124i	$-0.546990\pi$
$757$	−8.09378	−0.294173	−0.147087	+	0.989124i	$0.546990\pi$
$758$	71.4631	2.59566
$759$	23.2208	0.842861
$760$	43.6449	1.58317
$761$	17.9860	0.651993	0.325997	−	0.945371i	$-0.394300\pi$
$761$	17.9860	0.651993	0.325997	+	0.945371i	$0.394300\pi$
$762$	2.39345	0.0867054
$763$	0.958419	0.0346971
$764$	−17.7868	−0.643504
$765$	−2.64898	−0.0957742
$766$	71.4530	2.58170
$767$	8.69918	0.314109
$768$	−70.7802	−2.55406
$769$	24.6813	0.890032	0.445016	−	0.895523i	$-0.353198\pi$
$769$	24.6813	0.890032	0.445016	+	0.895523i	$0.353198\pi$
$770$	−17.7647	−0.640196
$771$	−15.6096	−0.562166
$772$	−133.330	−4.79865
$773$	−17.5954	−0.632862	−0.316431	−	0.948615i	$-0.602485\pi$
$773$	−17.5954	−0.632862	−0.316431	+	0.948615i	$0.602485\pi$
$774$	0.331335	0.0119096
$775$	−18.8501	−0.677115
$776$	−46.4629	−1.66792
$777$	−0.790311	−0.0283522
$778$	38.2911	1.37280
$779$	2.46322	0.0882540
$780$	−13.7340	−0.491757
$781$	−77.6627	−2.77899
$782$	13.4006	0.479206
$783$	−22.7279	−0.812230
$784$	−105.376	−3.76343
$785$	0.946049	0.0337659
$786$	37.1099	1.32367
$787$	17.4938	0.623586	0.311793	−	0.950150i	$-0.399071\pi$
$787$	17.4938	0.623586	0.311793	+	0.950150i	$0.399071\pi$
$788$	120.079	4.27764
$789$	19.2604	0.685688
$790$	−0.574120	−0.0204263
$791$	10.3279	0.367219
$792$	117.513	4.17563
$793$	19.3112	0.685760
$794$	38.1170	1.35272
$795$	8.57917	0.304272
$796$	121.979	4.32342
$797$	13.5190	0.478867	0.239434	−	0.970913i	$-0.423038\pi$
$797$	13.5190	0.478867	0.239434	+	0.970913i	$0.423038\pi$
$798$	−6.79232	−0.240445
$799$	2.71901	0.0961916
$800$	86.2469	3.04929
$801$	16.7987	0.593552
$802$	28.5603	1.00850
$803$	−60.0374	−2.11867
$804$	45.9149	1.61929
$805$	−7.52088	−0.265076
$806$	−35.5886	−1.25356
$807$	18.9825	0.668215
$808$	144.433	5.08113
$809$	−46.1882	−1.62389	−0.811946	−	0.583733i	$-0.801591\pi$
$809$	−46.1882	−1.62389	−0.811946	+	0.583733i	$0.801591\pi$
$810$	−12.6653	−0.445012
$811$	−24.5661	−0.862632	−0.431316	−	0.902201i	$-0.641951\pi$
$811$	−24.5661	−0.862632	−0.431316	+	0.902201i	$0.641951\pi$
$812$	−28.4282	−0.997634
$813$	3.06778	0.107592
$814$	−13.5969	−0.476570
$815$	−6.48365	−0.227112
$816$	−11.9674	−0.418943
$817$	−0.158885	−0.00555868
$818$	50.5713	1.76818
$819$	−4.74517	−0.165810
$820$	−6.21716	−0.217113
$821$	−22.9485	−0.800908	−0.400454	−	0.916317i	$-0.631148\pi$
$821$	−22.9485	−0.800908	−0.400454	+	0.916317i	$0.631148\pi$
$822$	−13.4418	−0.468835
$823$	25.4225	0.886173	0.443087	−	0.896479i	$-0.353883\pi$
$823$	25.4225	0.886173	0.443087	+	0.896479i	$0.353883\pi$
$824$	54.2835	1.89106
$825$	12.6732	0.441223
$826$	−10.8589	−0.377831
$827$	33.5647	1.16716	0.583579	−	0.812056i	$-0.301652\pi$
$827$	33.5647	1.16716	0.583579	+	0.812056i	$0.301652\pi$
$828$	76.4603	2.65718
$829$	17.1300	0.594950	0.297475	−	0.954730i	$-0.403855\pi$
$829$	17.1300	0.594950	0.297475	+	0.954730i	$0.403855\pi$
$830$	53.0770	1.84233
$831$	6.96919	0.241759
$832$	88.8776	3.08128
$833$	−5.09362	−0.176484
$834$	28.3343	0.981137
$835$	10.1310	0.350598
$836$	−86.6045	−2.99528
$837$	26.3216	0.909807
$838$	46.0558	1.59097
$839$	37.4511	1.29296	0.646478	−	0.762933i	$-0.276241\pi$
$839$	37.4511	1.29296	0.646478	+	0.762933i	$0.276241\pi$
$840$	11.1549	0.384881
$841$	−2.15857	−0.0744334
$842$	95.6683	3.29695
$843$	−14.9223	−0.513953
$844$	117.938	4.05960
$845$	−11.5135	−0.396078
$846$	20.9334	0.719705
$847$	12.3937	0.425854
$848$	−132.244	−4.54128
$849$	−20.5678	−0.705884
$850$	7.31365	0.250856
$851$	−5.75639	−0.197326
$852$	74.9482	2.56768
$853$	42.2196	1.44557	0.722786	−	0.691071i	$-0.242861\pi$
$853$	42.2196	1.44557	0.722786	+	0.691071i	$0.242861\pi$
$854$	−24.1056	−0.824877
$855$	9.77966	0.334457
$856$	79.5716	2.71970
$857$	−17.1302	−0.585158	−0.292579	−	0.956241i	$-0.594513\pi$
$857$	−17.1302	−0.585158	−0.292579	+	0.956241i	$0.594513\pi$
$858$	23.9267	0.816844
$859$	−1.44406	−0.0492707	−0.0246353	−	0.999697i	$-0.507842\pi$
$859$	−1.44406	−0.0492707	−0.0246353	+	0.999697i	$0.507842\pi$
$860$	0.401025	0.0136748
$861$	0.629558	0.0214553
$862$	1.53737	0.0523632
$863$	−38.9721	−1.32663	−0.663313	−	0.748342i	$-0.730850\pi$
$863$	−38.9721	−1.32663	−0.663313	+	0.748342i	$0.730850\pi$
$864$	−120.432	−4.09718
$865$	−29.0176	−0.986628
$866$	−95.9715	−3.26124
$867$	13.4397	0.456436
$868$	32.9231	1.11748
$869$	0.741258	0.0251454
$870$	−16.1869	−0.548787
$871$	−20.7550	−0.703255
$872$	−10.3539	−0.350628
$873$	−10.4111	−0.352363
$874$	−49.4732	−1.67346
$875$	−10.6373	−0.359606
$876$	57.9389	1.95757
$877$	23.7225	0.801052	0.400526	−	0.916285i	$-0.368827\pi$
$877$	23.7225	0.801052	0.400526	+	0.916285i	$0.368827\pi$
$878$	35.6604	1.20348
$879$	22.9458	0.773943
$880$	115.554	3.89532
$881$	41.5469	1.39975	0.699875	−	0.714265i	$-0.253239\pi$
$881$	41.5469	1.39975	0.699875	+	0.714265i	$0.253239\pi$
$882$	−39.2153	−1.32045
$883$	−13.2556	−0.446087	−0.223043	−	0.974809i	$-0.571599\pi$
$883$	−13.2556	−0.446087	−0.223043	+	0.974809i	$0.571599\pi$
$884$	10.2332	0.344181
$885$	−4.58229	−0.154032
$886$	−72.9670	−2.45137
$887$	7.78856	0.261514	0.130757	−	0.991414i	$-0.458259\pi$
$887$	7.78856	0.261514	0.130757	+	0.991414i	$0.458259\pi$
$888$	8.53782	0.286510
$889$	1.00088	0.0335685
$890$	27.4345	0.919608
$891$	16.3524	0.547825
$892$	3.70369	0.124009
$893$	−10.0382	−0.335915
$894$	20.7847	0.695145
$895$	−26.7059	−0.892680
$896$	−58.3210	−1.94837
$897$	10.1296	0.338219
$898$	−19.0072	−0.634279
$899$	−31.0855	−1.03676
$900$	41.7296	1.39099
$901$	−6.39235	−0.212960
$902$	10.8312	0.360640
$903$	−0.0406084	−0.00135136
$904$	−111.574	−3.71089
$905$	3.00288	0.0998190
$906$	1.05903	0.0351840
$907$	−43.0535	−1.42957	−0.714783	−	0.699346i	$-0.753475\pi$
$907$	−43.0535	−1.42957	−0.714783	+	0.699346i	$0.753475\pi$
$908$	−11.9759	−0.397433
$909$	32.3636	1.07343
$910$	−7.74953	−0.256894
$911$	−41.3839	−1.37111	−0.685555	−	0.728021i	$-0.740440\pi$
$911$	−41.3839	−1.37111	−0.685555	+	0.728021i	$0.740440\pi$
$912$	44.1819	1.46301
$913$	−68.5287	−2.26797
$914$	10.8248	0.358051
$915$	−10.1722	−0.336281
$916$	125.902	4.15991
$917$	15.5184	0.512464
$918$	−10.2125	−0.337063
$919$	0.174815	0.00576663	0.00288332	−	0.999996i	$-0.499082\pi$
$919$	0.174815	0.00576663	0.00288332	+	0.999996i	$0.499082\pi$
$920$	81.2490	2.67870
$921$	24.4503	0.805664
$922$	18.7376	0.617090
$923$	−33.8789	−1.11514
$924$	−22.1347	−0.728177
$925$	−3.14165	−0.103297
$926$	−94.6891	−3.11168
$927$	12.1635	0.399502
$928$	142.229	4.66890
$929$	57.4546	1.88503	0.942513	−	0.334170i	$-0.108456\pi$
$929$	57.4546	1.88503	0.942513	+	0.334170i	$0.108456\pi$
$930$	18.7463	0.614715
$931$	18.8049	0.616306
$932$	−106.169	−3.47768
$933$	−12.1123	−0.396540
$934$	6.11215	0.199996
$935$	5.58558	0.182668
$936$	51.2627	1.67557
$937$	49.9136	1.63061	0.815303	−	0.579035i	$-0.196571\pi$
$937$	49.9136	1.63061	0.815303	+	0.579035i	$0.196571\pi$
$938$	25.9078	0.845921
$939$	−14.9909	−0.489208
$940$	25.3363	0.826380
$941$	37.2740	1.21510	0.607549	−	0.794283i	$-0.292153\pi$
$941$	37.2740	1.21510	0.607549	+	0.794283i	$0.292153\pi$
$942$	1.59055	0.0518229
$943$	4.58551	0.149325
$944$	70.6339	2.29894
$945$	5.73160	0.186449
$946$	−0.698645	−0.0227149
$947$	−54.3767	−1.76700	−0.883502	−	0.468427i	$-0.844821\pi$
$947$	−54.3767	−1.76700	−0.883502	+	0.468427i	$0.844821\pi$
$948$	−0.715349	−0.0232334
$949$	−26.1902	−0.850170
$950$	−27.0009	−0.876025
$951$	−13.6198	−0.441654
$952$	−8.31153	−0.269378
$953$	26.8201	0.868788	0.434394	−	0.900723i	$-0.356963\pi$
$953$	26.8201	0.868788	0.434394	+	0.900723i	$0.356963\pi$
$954$	−49.2141	−1.59337
$955$	−4.23517	−0.137047
$956$	151.977	4.91528
$957$	20.8992	0.675575
$958$	−16.4068	−0.530080
$959$	−5.62101	−0.181512
$960$	−46.8162	−1.51099
$961$	5.00060	0.161310
$962$	−5.93139	−0.191236
$963$	17.8299	0.574560
$964$	132.754	4.27571
$965$	−31.7468	−1.02197
$966$	−12.6445	−0.406831
$967$	9.93219	0.319398	0.159699	−	0.987166i	$-0.448948\pi$
$967$	9.93219	0.319398	0.159699	+	0.987166i	$0.448948\pi$
$968$	−133.891	−4.30342
$969$	2.13564	0.0686067
$970$	−17.0028	−0.545927
$971$	36.0063	1.15550	0.577748	−	0.816215i	$-0.303932\pi$
$971$	36.0063	1.15550	0.577748	+	0.816215i	$0.303932\pi$
$972$	−91.1283	−2.92294
$973$	11.8487	0.379852
$974$	110.722	3.54777
$975$	5.52843	0.177052
$976$	156.799	5.01902
$977$	−14.9530	−0.478390	−0.239195	−	0.970972i	$-0.576883\pi$
$977$	−14.9530	−0.478390	−0.239195	+	0.970972i	$0.576883\pi$
$978$	−10.9007	−0.348565
$979$	−35.4213	−1.13207
$980$	−47.4635	−1.51617
$981$	−2.32004	−0.0740731
$982$	74.5365	2.37855
$983$	14.7271	0.469723	0.234861	−	0.972029i	$-0.424536\pi$
$983$	14.7271	0.469723	0.234861	+	0.972029i	$0.424536\pi$
$984$	−6.80119	−0.216814
$985$	28.5917	0.911008
$986$	12.0609	0.384096
$987$	−2.56559	−0.0816637
$988$	−37.7796	−1.20193
$989$	−0.295779	−0.00940523
$990$	43.0029	1.36672
$991$	−13.4199	−0.426298	−0.213149	−	0.977020i	$-0.568372\pi$
$991$	−13.4199	−0.426298	−0.213149	+	0.977020i	$0.568372\pi$
$992$	−164.718	−5.22979
$993$	15.5586	0.493737
$994$	42.2901	1.34136
$995$	29.0440	0.920758
$996$	66.1335	2.09552
$997$	−20.7497	−0.657148	−0.328574	−	0.944478i	$-0.606568\pi$
$997$	−20.7497	−0.657148	−0.328574	+	0.944478i	$0.606568\pi$
$998$	52.4628	1.66068
$999$	4.38689	0.138795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.1	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.1	✓	77	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77942 q^{2} -0.824598 q^{3} +5.72520 q^{4} +1.36321 q^{5} +2.29191 q^{6} +0.958419 q^{7} -10.3539 q^{8} -2.32004 q^{9} +O(q^{10})\)	\(q-2.77942 q^{2} -0.824598 q^{3} +5.72520 q^{4} +1.36321 q^{5} +2.29191 q^{6} +0.958419 q^{7} -10.3539 q^{8} -2.32004 q^{9} -3.78894 q^{10} +4.89198 q^{11} -4.72099 q^{12} +2.13403 q^{13} -2.66385 q^{14} -1.12410 q^{15} +17.3275 q^{16} +0.837569 q^{17} +6.44837 q^{18} -3.09218 q^{19} +7.80466 q^{20} -0.790311 q^{21} -13.5969 q^{22} -5.75639 q^{23} +8.53782 q^{24} -3.14165 q^{25} -5.93139 q^{26} +4.38689 q^{27} +5.48714 q^{28} -5.18087 q^{29} +3.12436 q^{30} +6.00005 q^{31} -27.4527 q^{32} -4.03391 q^{33} -2.32796 q^{34} +1.30653 q^{35} -13.2827 q^{36} +1.00000 q^{37} +8.59449 q^{38} -1.75972 q^{39} -14.1146 q^{40} -0.796596 q^{41} +2.19661 q^{42} +0.0513828 q^{43} +28.0076 q^{44} -3.16270 q^{45} +15.9994 q^{46} +3.24631 q^{47} -14.2882 q^{48} -6.08143 q^{49} +8.73199 q^{50} -0.690658 q^{51} +12.2178 q^{52} -7.63203 q^{53} -12.1930 q^{54} +6.66880 q^{55} -9.92339 q^{56} +2.54981 q^{57} +14.3998 q^{58} +4.07640 q^{59} -6.43571 q^{60} +9.04914 q^{61} -16.6767 q^{62} -2.22357 q^{63} +41.6477 q^{64} +2.90914 q^{65} +11.2120 q^{66} -9.72569 q^{67} +4.79525 q^{68} +4.74670 q^{69} -3.63140 q^{70} -15.8755 q^{71} +24.0215 q^{72} -12.2726 q^{73} -2.77942 q^{74} +2.59060 q^{75} -17.7034 q^{76} +4.68857 q^{77} +4.89101 q^{78} +0.151525 q^{79} +23.6211 q^{80} +3.34269 q^{81} +2.21408 q^{82} -14.0084 q^{83} -4.52469 q^{84} +1.14178 q^{85} -0.142815 q^{86} +4.27214 q^{87} -50.6511 q^{88} -7.24068 q^{89} +8.79049 q^{90} +2.04530 q^{91} -32.9565 q^{92} -4.94763 q^{93} -9.02287 q^{94} -4.21530 q^{95} +22.6375 q^{96} +4.48748 q^{97} +16.9029 q^{98} -11.3496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * q^99

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