LMFDB - Embedded newform 8029.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69962 q^{2} +2.88270 q^{3} +5.28797 q^{4} +3.78908 q^{5} -7.78221 q^{6} +1.00000 q^{7} -8.87628 q^{8} +5.30996 q^{9} +O(q^{10})$	\(q-2.69962 q^{2} +2.88270 q^{3} +5.28797 q^{4} +3.78908 q^{5} -7.78221 q^{6} +1.00000 q^{7} -8.87628 q^{8} +5.30996 q^{9} -10.2291 q^{10} -1.34754 q^{11} +15.2436 q^{12} -0.0860043 q^{13} -2.69962 q^{14} +10.9228 q^{15} +13.3867 q^{16} -0.365486 q^{17} -14.3349 q^{18} -6.43846 q^{19} +20.0366 q^{20} +2.88270 q^{21} +3.63786 q^{22} +1.68540 q^{23} -25.5877 q^{24} +9.35715 q^{25} +0.232179 q^{26} +6.65892 q^{27} +5.28797 q^{28} -0.986289 q^{29} -29.4874 q^{30} +1.00000 q^{31} -18.3864 q^{32} -3.88456 q^{33} +0.986674 q^{34} +3.78908 q^{35} +28.0789 q^{36} +1.00000 q^{37} +17.3814 q^{38} -0.247925 q^{39} -33.6330 q^{40} +1.92341 q^{41} -7.78221 q^{42} +0.0771143 q^{43} -7.12577 q^{44} +20.1199 q^{45} -4.54995 q^{46} +12.0217 q^{47} +38.5898 q^{48} +1.00000 q^{49} -25.2608 q^{50} -1.05359 q^{51} -0.454788 q^{52} +1.84165 q^{53} -17.9766 q^{54} -5.10595 q^{55} -8.87628 q^{56} -18.5601 q^{57} +2.66261 q^{58} +12.3760 q^{59} +57.7594 q^{60} -0.385245 q^{61} -2.69962 q^{62} +5.30996 q^{63} +22.8631 q^{64} -0.325877 q^{65} +10.4869 q^{66} +11.8040 q^{67} -1.93268 q^{68} +4.85851 q^{69} -10.2291 q^{70} -1.23361 q^{71} -47.1327 q^{72} +9.57275 q^{73} -2.69962 q^{74} +26.9738 q^{75} -34.0464 q^{76} -1.34754 q^{77} +0.669303 q^{78} +16.6113 q^{79} +50.7232 q^{80} +3.26579 q^{81} -5.19249 q^{82} -11.0185 q^{83} +15.2436 q^{84} -1.38486 q^{85} -0.208180 q^{86} -2.84318 q^{87} +11.9612 q^{88} -10.0854 q^{89} -54.3161 q^{90} -0.0860043 q^{91} +8.91235 q^{92} +2.88270 q^{93} -32.4540 q^{94} -24.3959 q^{95} -53.0026 q^{96} -8.42154 q^{97} -2.69962 q^{98} -7.15540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) $ 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * 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 $

$2$	−2.69962	−1.90892	−0.954461	−	0.298335i	$-0.903569\pi$
$2$	−2.69962	−1.90892	−0.954461	+	0.298335i	$0.903569\pi$
$3$	2.88270	1.66433	0.832164	−	0.554530i	$-0.187102\pi$
$3$	2.88270	1.66433	0.832164	+	0.554530i	$0.187102\pi$
$4$	5.28797	2.64398
$5$	3.78908	1.69453	0.847265	−	0.531171i	$-0.178248\pi$
$5$	3.78908	1.69453	0.847265	+	0.531171i	$0.178248\pi$
$6$	−7.78221	−3.17707
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.87628	−3.13824
$9$	5.30996	1.76999
$10$	−10.2291	−3.23472
$11$	−1.34754	−0.406300	−0.203150	−	0.979148i	$-0.565118\pi$
$11$	−1.34754	−0.406300	−0.203150	+	0.979148i	$0.565118\pi$
$12$	15.2436	4.40046
$13$	−0.0860043	−0.0238533	−0.0119266	−	0.999929i	$-0.503796\pi$
$13$	−0.0860043	−0.0238533	−0.0119266	+	0.999929i	$0.503796\pi$
$14$	−2.69962	−0.721505
$15$	10.9228	2.82025
$16$	13.3867	3.34667
$17$	−0.365486	−0.0886433	−0.0443217	−	0.999017i	$-0.514113\pi$
$17$	−0.365486	−0.0886433	−0.0443217	+	0.999017i	$0.514113\pi$
$18$	−14.3349	−3.37877
$19$	−6.43846	−1.47708	−0.738542	−	0.674207i	$-0.764485\pi$
$19$	−6.43846	−1.47708	−0.738542	+	0.674207i	$0.764485\pi$
$20$	20.0366	4.48031
$21$	2.88270	0.629057
$22$	3.63786	0.775594
$23$	1.68540	0.351431	0.175715	−	0.984441i	$-0.443776\pi$
$23$	1.68540	0.351431	0.175715	+	0.984441i	$0.443776\pi$
$24$	−25.5877	−5.22306
$25$	9.35715	1.87143
$26$	0.232179	0.0455341
$27$	6.65892	1.28151
$28$	5.28797	0.999332
$29$	−0.986289	−0.183149	−0.0915746	−	0.995798i	$-0.529190\pi$
$29$	−0.986289	−0.183149	−0.0915746	+	0.995798i	$0.529190\pi$
$30$	−29.4874	−5.38364
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−18.3864	−3.25029
$33$	−3.88456	−0.676216
$34$	0.986674	0.169213
$35$	3.78908	0.640472
$36$	28.0789	4.67982
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	17.3814	2.81964
$39$	−0.247925	−0.0396997
$40$	−33.6330	−5.31784
$41$	1.92341	0.300387	0.150193	−	0.988657i	$-0.452010\pi$
$41$	1.92341	0.300387	0.150193	+	0.988657i	$0.452010\pi$
$42$	−7.78221	−1.20082
$43$	0.0771143	0.0117598	0.00587991	−	0.999983i	$-0.498128\pi$
$43$	0.0771143	0.0117598	0.00587991	+	0.999983i	$0.498128\pi$
$44$	−7.12577	−1.07425
$45$	20.1199	2.99929
$46$	−4.54995	−0.670854
$47$	12.0217	1.75354	0.876771	−	0.480908i	$-0.159693\pi$
$47$	12.0217	1.75354	0.876771	+	0.480908i	$0.159693\pi$
$48$	38.5898	5.56995
$49$	1.00000	0.142857
$50$	−25.2608	−3.57241
$51$	−1.05359	−0.147532
$52$	−0.454788	−0.0630678
$53$	1.84165	0.252970	0.126485	−	0.991969i	$-0.459630\pi$
$53$	1.84165	0.252970	0.126485	+	0.991969i	$0.459630\pi$
$54$	−17.9766	−2.44630
$55$	−5.10595	−0.688486
$56$	−8.87628	−1.18614
$57$	−18.5601	−2.45835
$58$	2.66261	0.349618
$59$	12.3760	1.61122	0.805612	−	0.592444i	$-0.201837\pi$
$59$	12.3760	1.61122	0.805612	+	0.592444i	$0.201837\pi$
$60$	57.7594	7.45670
$61$	−0.385245	−0.0493255	−0.0246628	−	0.999696i	$-0.507851\pi$
$61$	−0.385245	−0.0493255	−0.0246628	+	0.999696i	$0.507851\pi$
$62$	−2.69962	−0.342853
$63$	5.30996	0.668992
$64$	22.8631	2.85789
$65$	−0.325877	−0.0404201
$66$	10.4869	1.29084
$67$	11.8040	1.44209	0.721043	−	0.692891i	$-0.243663\pi$
$67$	11.8040	1.44209	0.721043	+	0.692891i	$0.243663\pi$
$68$	−1.93268	−0.234372
$69$	4.85851	0.584896
$70$	−10.2291	−1.22261
$71$	−1.23361	−0.146403	−0.0732015	−	0.997317i	$-0.523322\pi$
$71$	−1.23361	−0.146403	−0.0732015	+	0.997317i	$0.523322\pi$
$72$	−47.1327	−5.55464
$73$	9.57275	1.12041	0.560203	−	0.828355i	$-0.310723\pi$
$73$	9.57275	1.12041	0.560203	+	0.828355i	$0.310723\pi$
$74$	−2.69962	−0.313825
$75$	26.9738	3.11467
$76$	−34.0464	−3.90539
$77$	−1.34754	−0.153567
$78$	0.669303	0.0757837
$79$	16.6113	1.86891	0.934456	−	0.356079i	$-0.115887\pi$
$79$	16.6113	1.86891	0.934456	+	0.356079i	$0.115887\pi$
$80$	50.7232	5.67103
$81$	3.26579	0.362865
$82$	−5.19249	−0.573415
$83$	−11.0185	−1.20944	−0.604718	−	0.796440i	$-0.706714\pi$
$83$	−11.0185	−1.20944	−0.604718	+	0.796440i	$0.706714\pi$
$84$	15.2436	1.66322
$85$	−1.38486	−0.150209
$86$	−0.208180	−0.0224486
$87$	−2.84318	−0.304820
$88$	11.9612	1.27507
$89$	−10.0854	−1.06905	−0.534523	−	0.845154i	$-0.679509\pi$
$89$	−10.0854	−1.06905	−0.534523	+	0.845154i	$0.679509\pi$
$90$	−54.3161	−5.72542
$91$	−0.0860043	−0.00901570
$92$	8.91235	0.929177
$93$	2.88270	0.298922
$94$	−32.4540	−3.34738
$95$	−24.3959	−2.50296
$96$	−53.0026	−5.40955
$97$	−8.42154	−0.855078	−0.427539	−	0.903997i	$-0.640619\pi$
$97$	−8.42154	−0.855078	−0.427539	+	0.903997i	$0.640619\pi$
$98$	−2.69962	−0.272703
$99$	−7.15540	−0.719145
$100$	49.4803	4.94803
$101$	0.259479	0.0258191	0.0129095	−	0.999917i	$-0.495891\pi$
$101$	0.259479	0.0258191	0.0129095	+	0.999917i	$0.495891\pi$
$102$	2.84429	0.281626
$103$	−5.79645	−0.571141	−0.285571	−	0.958358i	$-0.592183\pi$
$103$	−5.79645	−0.571141	−0.285571	+	0.958358i	$0.592183\pi$
$104$	0.763398	0.0748574
$105$	10.9228	1.06595
$106$	−4.97177	−0.482901
$107$	6.99023	0.675771	0.337886	−	0.941187i	$-0.390288\pi$
$107$	6.99023	0.675771	0.337886	+	0.941187i	$0.390288\pi$
$108$	35.2122	3.38829
$109$	8.18325	0.783813	0.391907	−	0.920005i	$-0.371816\pi$
$109$	8.18325	0.783813	0.391907	+	0.920005i	$0.371816\pi$
$110$	13.7842	1.31427
$111$	2.88270	0.273614
$112$	13.3867	1.26492
$113$	7.53628	0.708954	0.354477	−	0.935065i	$-0.384659\pi$
$113$	7.53628	0.708954	0.354477	+	0.935065i	$0.384659\pi$
$114$	50.1054	4.69280
$115$	6.38613	0.595509
$116$	−5.21547	−0.484244
$117$	−0.456679	−0.0422200
$118$	−33.4107	−3.07570
$119$	−0.365486	−0.0335040
$120$	−96.9537	−8.85062
$121$	−9.18413	−0.834921
$122$	1.04002	0.0941586
$123$	5.54463	0.499942
$124$	5.28797	0.474874
$125$	16.5096	1.47666
$126$	−14.3349	−1.27705
$127$	−4.08307	−0.362314	−0.181157	−	0.983454i	$-0.557984\pi$
$127$	−4.08307	−0.362314	−0.181157	+	0.983454i	$0.557984\pi$
$128$	−24.9489	−2.20519
$129$	0.222297	0.0195722
$130$	0.879746	0.0771589
$131$	−15.2328	−1.33090	−0.665448	−	0.746444i	$-0.731759\pi$
$131$	−15.2328	−1.33090	−0.665448	+	0.746444i	$0.731759\pi$
$132$	−20.5414	−1.78790
$133$	−6.43846	−0.558285
$134$	−31.8663	−2.75283
$135$	25.2312	2.17155
$136$	3.24415	0.278184
$137$	12.8711	1.09965	0.549827	−	0.835279i	$-0.314694\pi$
$137$	12.8711	1.09965	0.549827	+	0.835279i	$0.314694\pi$
$138$	−13.1161	−1.11652
$139$	−9.54380	−0.809495	−0.404747	−	0.914428i	$-0.632641\pi$
$139$	−9.54380	−0.809495	−0.404747	+	0.914428i	$0.632641\pi$
$140$	20.0366	1.69340
$141$	34.6549	2.91847
$142$	3.33029	0.279472
$143$	0.115895	0.00969159
$144$	71.0827	5.92356
$145$	−3.73713	−0.310352
$146$	−25.8428	−2.13877
$147$	2.88270	0.237761
$148$	5.28797	0.434668
$149$	22.9020	1.87620	0.938102	−	0.346360i	$-0.112582\pi$
$149$	22.9020	1.87620	0.938102	+	0.346360i	$0.112582\pi$
$150$	−72.8192	−5.94567
$151$	8.94128	0.727631	0.363815	−	0.931471i	$-0.381474\pi$
$151$	8.94128	0.727631	0.363815	+	0.931471i	$0.381474\pi$
$152$	57.1496	4.63544
$153$	−1.94071	−0.156897
$154$	3.63786	0.293147
$155$	3.78908	0.304346
$156$	−1.31102	−0.104965
$157$	−6.76029	−0.539530	−0.269765	−	0.962926i	$-0.586946\pi$
$157$	−6.76029	−0.539530	−0.269765	+	0.962926i	$0.586946\pi$
$158$	−44.8441	−3.56761
$159$	5.30893	0.421025
$160$	−69.6677	−5.50772
$161$	1.68540	0.132828
$162$	−8.81639	−0.692681
$163$	−18.1853	−1.42439	−0.712193	−	0.701984i	$-0.752298\pi$
$163$	−18.1853	−1.42439	−0.712193	+	0.701984i	$0.752298\pi$
$164$	10.1710	0.794218
$165$	−14.7189	−1.14587
$166$	29.7458	2.30872
$167$	−8.84795	−0.684675	−0.342337	−	0.939577i	$-0.611219\pi$
$167$	−8.84795	−0.684675	−0.342337	+	0.939577i	$0.611219\pi$
$168$	−25.5877	−1.97413
$169$	−12.9926	−0.999431
$170$	3.73859	0.286737
$171$	−34.1880	−2.61442
$172$	0.407778	0.0310928
$173$	22.7158	1.72705	0.863524	−	0.504307i	$-0.168252\pi$
$173$	22.7158	1.72705	0.863524	+	0.504307i	$0.168252\pi$
$174$	7.67550	0.581878
$175$	9.35715	0.707334
$176$	−18.0391	−1.35975
$177$	35.6764	2.68160
$178$	27.2267	2.04072
$179$	−23.3056	−1.74194	−0.870970	−	0.491336i	$-0.836509\pi$
$179$	−23.3056	−1.74194	−0.870970	+	0.491336i	$0.836509\pi$
$180$	106.393	7.93009
$181$	−23.1521	−1.72089	−0.860443	−	0.509547i	$-0.829813\pi$
$181$	−23.1521	−1.72089	−0.860443	+	0.509547i	$0.829813\pi$
$182$	0.232179	0.0172103
$183$	−1.11054	−0.0820938
$184$	−14.9601	−1.10287
$185$	3.78908	0.278579
$186$	−7.78221	−0.570619
$187$	0.492508	0.0360157
$188$	63.5703	4.63634
$189$	6.65892	0.484365
$190$	65.8596	4.77796
$191$	5.95886	0.431168	0.215584	−	0.976485i	$-0.430834\pi$
$191$	5.95886	0.431168	0.215584	+	0.976485i	$0.430834\pi$
$192$	65.9075	4.75646
$193$	−19.1353	−1.37739	−0.688695	−	0.725051i	$-0.741816\pi$
$193$	−19.1353	−1.37739	−0.688695	+	0.725051i	$0.741816\pi$
$194$	22.7350	1.63228
$195$	−0.939407	−0.0672723
$196$	5.28797	0.377712
$197$	10.3329	0.736186	0.368093	−	0.929789i	$-0.380011\pi$
$197$	10.3329	0.736186	0.368093	+	0.929789i	$0.380011\pi$
$198$	19.3169	1.37279
$199$	26.8881	1.90604	0.953022	−	0.302900i	$-0.0979549\pi$
$199$	26.8881	1.90604	0.953022	+	0.302900i	$0.0979549\pi$
$200$	−83.0567	−5.87299
$201$	34.0273	2.40010
$202$	−0.700495	−0.0492866
$203$	−0.986289	−0.0692239
$204$	−5.57133	−0.390071
$205$	7.28797	0.509014
$206$	15.6482	1.09026
$207$	8.94941	0.622027
$208$	−1.15131	−0.0798291
$209$	8.67610	0.600139
$210$	−29.4874	−2.03483
$211$	6.23576	0.429287	0.214644	−	0.976692i	$-0.431141\pi$
$211$	6.23576	0.429287	0.214644	+	0.976692i	$0.431141\pi$
$212$	9.73860	0.668850
$213$	−3.55614	−0.243663
$214$	−18.8710	−1.28999
$215$	0.292192	0.0199274
$216$	−59.1064	−4.02168
$217$	1.00000	0.0678844
$218$	−22.0917	−1.49624
$219$	27.5954	1.86472
$220$	−27.0001	−1.82035
$221$	0.0314333	0.00211444
$222$	−7.78221	−0.522307
$223$	9.34364	0.625697	0.312848	−	0.949803i	$-0.398717\pi$
$223$	9.34364	0.625697	0.312848	+	0.949803i	$0.398717\pi$
$224$	−18.3864	−1.22850
$225$	49.6861	3.31240
$226$	−20.3451	−1.35334
$227$	24.4969	1.62592	0.812959	−	0.582321i	$-0.197855\pi$
$227$	24.4969	1.62592	0.812959	+	0.582321i	$0.197855\pi$
$228$	−98.1455	−6.49984
$229$	1.79894	0.118877	0.0594387	−	0.998232i	$-0.481069\pi$
$229$	1.79894	0.118877	0.0594387	+	0.998232i	$0.481069\pi$
$230$	−17.2401	−1.13678
$231$	−3.88456	−0.255585
$232$	8.75458	0.574766
$233$	0.173227	0.0113485	0.00567425	−	0.999984i	$-0.498194\pi$
$233$	0.173227	0.0113485	0.00567425	+	0.999984i	$0.498194\pi$
$234$	1.23286	0.0805947
$235$	45.5511	2.97143
$236$	65.4441	4.26005
$237$	47.8853	3.11048
$238$	0.986674	0.0639566
$239$	5.76697	0.373034	0.186517	−	0.982452i	$-0.440280\pi$
$239$	5.76697	0.373034	0.186517	+	0.982452i	$0.440280\pi$
$240$	146.220	9.43845
$241$	−7.00406	−0.451171	−0.225586	−	0.974223i	$-0.572430\pi$
$241$	−7.00406	−0.451171	−0.225586	+	0.974223i	$0.572430\pi$
$242$	24.7937	1.59380
$243$	−10.5625	−0.677583
$244$	−2.03716	−0.130416
$245$	3.78908	0.242076
$246$	−14.9684	−0.954351
$247$	0.553735	0.0352333
$248$	−8.87628	−0.563644
$249$	−31.7630	−2.01290
$250$	−44.5697	−2.81883
$251$	18.6130	1.17484	0.587420	−	0.809282i	$-0.300144\pi$
$251$	18.6130	1.17484	0.587420	+	0.809282i	$0.300144\pi$
$252$	28.0789	1.76880
$253$	−2.27115	−0.142786
$254$	11.0227	0.691628
$255$	−3.99212	−0.249996
$256$	21.6265	1.35166
$257$	0.703290	0.0438700	0.0219350	−	0.999759i	$-0.493017\pi$
$257$	0.703290	0.0438700	0.0219350	+	0.999759i	$0.493017\pi$
$258$	−0.600119	−0.0373618
$259$	1.00000	0.0621370
$260$	−1.72323	−0.106870
$261$	−5.23715	−0.324172
$262$	41.1228	2.54058
$263$	−8.28787	−0.511052	−0.255526	−	0.966802i	$-0.582249\pi$
$263$	−8.28787	−0.511052	−0.255526	+	0.966802i	$0.582249\pi$
$264$	34.4805	2.12213
$265$	6.97817	0.428666
$266$	17.3814	1.06572
$267$	−29.0731	−1.77924
$268$	62.4191	3.81285
$269$	21.3997	1.30476	0.652381	−	0.757891i	$-0.273770\pi$
$269$	21.3997	1.30476	0.652381	+	0.757891i	$0.273770\pi$
$270$	−68.1147	−4.14533
$271$	−2.71245	−0.164770	−0.0823848	−	0.996601i	$-0.526254\pi$
$271$	−2.71245	−0.164770	−0.0823848	+	0.996601i	$0.526254\pi$
$272$	−4.89264	−0.296660
$273$	−0.247925	−0.0150051
$274$	−34.7472	−2.09915
$275$	−12.6092	−0.760361
$276$	25.6916	1.54646
$277$	−7.47944	−0.449396	−0.224698	−	0.974428i	$-0.572140\pi$
$277$	−7.47944	−0.449396	−0.224698	+	0.974428i	$0.572140\pi$
$278$	25.7647	1.54526
$279$	5.30996	0.317899
$280$	−33.6330	−2.00995
$281$	17.2131	1.02685	0.513425	−	0.858134i	$-0.328376\pi$
$281$	17.2131	1.02685	0.513425	+	0.858134i	$0.328376\pi$
$282$	−93.5552	−5.57113
$283$	−9.17331	−0.545296	−0.272648	−	0.962114i	$-0.587900\pi$
$283$	−9.17331	−0.545296	−0.272648	+	0.962114i	$0.587900\pi$
$284$	−6.52331	−0.387087
$285$	−70.3259	−4.16575
$286$	−0.312872	−0.0185005
$287$	1.92341	0.113536
$288$	−97.6312	−5.75298
$289$	−16.8664	−0.992142
$290$	10.0888	0.592437
$291$	−24.2768	−1.42313
$292$	50.6204	2.96234
$293$	0.841654	0.0491699	0.0245850	−	0.999698i	$-0.492174\pi$
$293$	0.841654	0.0491699	0.0245850	+	0.999698i	$0.492174\pi$
$294$	−7.78221	−0.453867
$295$	46.8938	2.73027
$296$	−8.87628	−0.515923
$297$	−8.97318	−0.520677
$298$	−61.8267	−3.58153
$299$	−0.144952	−0.00838278
$300$	142.637	8.23514
$301$	0.0771143	0.00444479
$302$	−24.1381	−1.38899
$303$	0.747999	0.0429714
$304$	−86.1896	−4.94331
$305$	−1.45972	−0.0835835
$306$	5.23920	0.299505
$307$	13.9831	0.798057	0.399029	−	0.916938i	$-0.369347\pi$
$307$	13.9831	0.798057	0.399029	+	0.916938i	$0.369347\pi$
$308$	−7.12577	−0.406028
$309$	−16.7094	−0.950566
$310$	−10.2291	−0.580974
$311$	−6.99790	−0.396814	−0.198407	−	0.980120i	$-0.563577\pi$
$311$	−6.99790	−0.396814	−0.198407	+	0.980120i	$0.563577\pi$
$312$	2.20065	0.124587
$313$	11.7218	0.662556	0.331278	−	0.943533i	$-0.392520\pi$
$313$	11.7218	0.662556	0.331278	+	0.943533i	$0.392520\pi$
$314$	18.2502	1.02992
$315$	20.1199	1.13363
$316$	87.8398	4.94137
$317$	−12.1632	−0.683151	−0.341576	−	0.939854i	$-0.610961\pi$
$317$	−12.1632	−0.683151	−0.341576	+	0.939854i	$0.610961\pi$
$318$	−14.3321	−0.803705
$319$	1.32907	0.0744135
$320$	86.6302	4.84278
$321$	20.1507	1.12470
$322$	−4.54995	−0.253559
$323$	2.35317	0.130934
$324$	17.2694	0.959410
$325$	−0.804755	−0.0446398
$326$	49.0936	2.71904
$327$	23.5899	1.30452
$328$	−17.0728	−0.942686
$329$	12.0217	0.662776
$330$	39.7356	2.18737
$331$	20.2297	1.11193	0.555964	−	0.831207i	$-0.312349\pi$
$331$	20.2297	1.11193	0.555964	+	0.831207i	$0.312349\pi$
$332$	−58.2654	−3.19773
$333$	5.30996	0.290984
$334$	23.8861	1.30699
$335$	44.7263	2.44366
$336$	38.5898	2.10525
$337$	4.22927	0.230383	0.115192	−	0.993343i	$-0.463252\pi$
$337$	4.22927	0.230383	0.115192	+	0.993343i	$0.463252\pi$
$338$	35.0751	1.90784
$339$	21.7248	1.17993
$340$	−7.32307	−0.397149
$341$	−1.34754	−0.0729736
$342$	92.2946	4.99072
$343$	1.00000	0.0539949
$344$	−0.684488	−0.0369051
$345$	18.4093	0.991123
$346$	−61.3241	−3.29680
$347$	−13.8808	−0.745160	−0.372580	−	0.928000i	$-0.621527\pi$
$347$	−13.8808	−0.745160	−0.372580	+	0.928000i	$0.621527\pi$
$348$	−15.0346	−0.805940
$349$	−27.3434	−1.46366	−0.731829	−	0.681489i	$-0.761333\pi$
$349$	−27.3434	−1.46366	−0.731829	+	0.681489i	$0.761333\pi$
$350$	−25.2608	−1.35025
$351$	−0.572696	−0.0305682
$352$	24.7765	1.32059
$353$	10.5363	0.560793	0.280396	−	0.959884i	$-0.409534\pi$
$353$	10.5363	0.560793	0.280396	+	0.959884i	$0.409534\pi$
$354$	−96.3129	−5.11897
$355$	−4.67426	−0.248084
$356$	−53.3310	−2.82654
$357$	−1.05359	−0.0557617
$358$	62.9163	3.32523
$359$	10.1900	0.537805	0.268903	−	0.963167i	$-0.413339\pi$
$359$	10.1900	0.537805	0.268903	+	0.963167i	$0.413339\pi$
$360$	−178.590	−9.41250
$361$	22.4538	1.18178
$362$	62.5021	3.28504
$363$	−26.4751	−1.38958
$364$	−0.454788	−0.0238374
$365$	36.2720	1.89856
$366$	2.99805	0.156711
$367$	23.4608	1.22464	0.612321	−	0.790609i	$-0.290236\pi$
$367$	23.4608	1.22464	0.612321	+	0.790609i	$0.290236\pi$
$368$	22.5619	1.17612
$369$	10.2132	0.531681
$370$	−10.2291	−0.531785
$371$	1.84165	0.0956138
$372$	15.2436	0.790345
$373$	−19.8038	−1.02540	−0.512702	−	0.858567i	$-0.671355\pi$
$373$	−19.8038	−1.02540	−0.512702	+	0.858567i	$0.671355\pi$
$374$	−1.32959	−0.0687513
$375$	47.5922	2.45765
$376$	−106.708	−5.50303
$377$	0.0848251	0.00436871
$378$	−17.9766	−0.924615
$379$	−5.59183	−0.287233	−0.143617	−	0.989633i	$-0.545873\pi$
$379$	−5.59183	−0.287233	−0.143617	+	0.989633i	$0.545873\pi$
$380$	−129.005	−6.61779
$381$	−11.7703	−0.603008
$382$	−16.0867	−0.823066
$383$	−29.1559	−1.48980	−0.744898	−	0.667178i	$-0.767502\pi$
$383$	−29.1559	−1.48980	−0.744898	+	0.667178i	$0.767502\pi$
$384$	−71.9203	−3.67017
$385$	−5.10595	−0.260223
$386$	51.6582	2.62933
$387$	0.409474	0.0208147
$388$	−44.5329	−2.26081
$389$	−31.0057	−1.57205	−0.786025	−	0.618195i	$-0.787864\pi$
$389$	−31.0057	−1.57205	−0.786025	+	0.618195i	$0.787864\pi$
$390$	2.53604	0.128418
$391$	−0.615990	−0.0311520
$392$	−8.87628	−0.448320
$393$	−43.9116	−2.21505
$394$	−27.8948	−1.40532
$395$	62.9414	3.16693
$396$	−37.8375	−1.90141
$397$	13.5140	0.678248	0.339124	−	0.940742i	$-0.389869\pi$
$397$	13.5140	0.678248	0.339124	+	0.940742i	$0.389869\pi$
$398$	−72.5877	−3.63849
$399$	−18.5601	−0.929170
$400$	125.261	6.26306
$401$	5.10175	0.254769	0.127385	−	0.991853i	$-0.459342\pi$
$401$	5.10175	0.254769	0.127385	+	0.991853i	$0.459342\pi$
$402$	−91.8610	−4.58161
$403$	−0.0860043	−0.00428418
$404$	1.37211	0.0682653
$405$	12.3743	0.614885
$406$	2.66261	0.132143
$407$	−1.34754	−0.0667952
$408$	9.35192	0.462989
$409$	11.8550	0.586194	0.293097	−	0.956083i	$-0.405314\pi$
$409$	11.8550	0.586194	0.293097	+	0.956083i	$0.405314\pi$
$410$	−19.6748	−0.971669
$411$	37.1036	1.83018
$412$	−30.6514	−1.51009
$413$	12.3760	0.608985
$414$	−24.1601	−1.18740
$415$	−41.7499	−2.04942
$416$	1.58131	0.0775302
$417$	−27.5119	−1.34726
$418$	−23.4222	−1.14562
$419$	−13.7499	−0.671728	−0.335864	−	0.941911i	$-0.609028\pi$
$419$	−13.7499	−0.671728	−0.335864	+	0.941911i	$0.609028\pi$
$420$	57.7594	2.81837
$421$	−25.9049	−1.26253	−0.631263	−	0.775569i	$-0.717463\pi$
$421$	−25.9049	−1.26253	−0.631263	+	0.775569i	$0.717463\pi$
$422$	−16.8342	−0.819476
$423$	63.8346	3.10374
$424$	−16.3470	−0.793881
$425$	−3.41990	−0.165890
$426$	9.60023	0.465133
$427$	−0.385245	−0.0186433
$428$	36.9641	1.78673
$429$	0.334089	0.0161300
$430$	−0.788810	−0.0380398
$431$	18.1703	0.875234	0.437617	−	0.899162i	$-0.355823\pi$
$431$	18.1703	0.875234	0.437617	+	0.899162i	$0.355823\pi$
$432$	89.1408	4.28879
$433$	−14.7446	−0.708580	−0.354290	−	0.935136i	$-0.615277\pi$
$433$	−14.7446	−0.708580	−0.354290	+	0.935136i	$0.615277\pi$
$434$	−2.69962	−0.129586
$435$	−10.7730	−0.516527
$436$	43.2728	2.07239
$437$	−10.8514	−0.519093
$438$	−74.4971	−3.55961
$439$	−15.3442	−0.732339	−0.366169	−	0.930548i	$-0.619331\pi$
$439$	−15.3442	−0.732339	−0.366169	+	0.930548i	$0.619331\pi$
$440$	45.3219	2.16064
$441$	5.30996	0.252855
$442$	−0.0848582	−0.00403629
$443$	−29.1675	−1.38579	−0.692894	−	0.721039i	$-0.743665\pi$
$443$	−29.1675	−1.38579	−0.692894	+	0.721039i	$0.743665\pi$
$444$	15.2436	0.723431
$445$	−38.2142	−1.81153
$446$	−25.2243	−1.19441
$447$	66.0195	3.12262
$448$	22.8631	1.08018
$449$	21.5717	1.01803	0.509016	−	0.860757i	$-0.330010\pi$
$449$	21.5717	1.01803	0.509016	+	0.860757i	$0.330010\pi$
$450$	−134.134	−6.32312
$451$	−2.59188	−0.122047
$452$	39.8516	1.87446
$453$	25.7750	1.21102
$454$	−66.1325	−3.10375
$455$	−0.325877	−0.0152774
$456$	164.745	7.71490
$457$	−21.4836	−1.00496	−0.502479	−	0.864589i	$-0.667579\pi$
$457$	−21.4836	−1.00496	−0.502479	+	0.864589i	$0.667579\pi$
$458$	−4.85647	−0.226928
$459$	−2.43374	−0.113597
$460$	33.7696	1.57452
$461$	9.56287	0.445387	0.222694	−	0.974888i	$-0.428515\pi$
$461$	9.56287	0.445387	0.222694	+	0.974888i	$0.428515\pi$
$462$	10.4869	0.487893
$463$	−5.97948	−0.277890	−0.138945	−	0.990300i	$-0.544371\pi$
$463$	−5.97948	−0.277890	−0.138945	+	0.990300i	$0.544371\pi$
$464$	−13.2031	−0.612940
$465$	10.9228	0.506532
$466$	−0.467648	−0.0216634
$467$	−17.9498	−0.830616	−0.415308	−	0.909681i	$-0.636326\pi$
$467$	−17.9498	−0.830616	−0.415308	+	0.909681i	$0.636326\pi$
$468$	−2.41491	−0.111629
$469$	11.8040	0.545057
$470$	−122.971	−5.67222
$471$	−19.4879	−0.897954
$472$	−109.853	−5.05640
$473$	−0.103915	−0.00477801
$474$	−129.272	−5.93767
$475$	−60.2456	−2.76426
$476$	−1.93268	−0.0885841
$477$	9.77909	0.447754
$478$	−15.5686	−0.712093
$479$	−14.6197	−0.667990	−0.333995	−	0.942575i	$-0.608397\pi$
$479$	−14.6197	−0.667990	−0.333995	+	0.942575i	$0.608397\pi$
$480$	−200.831	−9.16665
$481$	−0.0860043	−0.00392146
$482$	18.9083	0.861251
$483$	4.85851	0.221070
$484$	−48.5654	−2.20752
$485$	−31.9099	−1.44896
$486$	28.5147	1.29345
$487$	−38.4394	−1.74185	−0.870927	−	0.491413i	$-0.836481\pi$
$487$	−38.4394	−1.74185	−0.870927	+	0.491413i	$0.836481\pi$
$488$	3.41954	0.154795
$489$	−52.4229	−2.37064
$490$	−10.2291	−0.462104
$491$	−10.1330	−0.457298	−0.228649	−	0.973509i	$-0.573431\pi$
$491$	−10.1330	−0.457298	−0.228649	+	0.973509i	$0.573431\pi$
$492$	29.3198	1.32184
$493$	0.360475	0.0162350
$494$	−1.49488	−0.0672577
$495$	−27.1124	−1.21861
$496$	13.3867	0.601080
$497$	−1.23361	−0.0553351
$498$	85.7481	3.84246
$499$	17.6714	0.791082	0.395541	−	0.918448i	$-0.370557\pi$
$499$	17.6714	0.791082	0.395541	+	0.918448i	$0.370557\pi$
$500$	87.3022	3.90427
$501$	−25.5060	−1.13952
$502$	−50.2480	−2.24268
$503$	10.6069	0.472938	0.236469	−	0.971639i	$-0.424010\pi$
$503$	10.6069	0.472938	0.236469	+	0.971639i	$0.424010\pi$
$504$	−47.1327	−2.09946
$505$	0.983186	0.0437512
$506$	6.13126	0.272568
$507$	−37.4538	−1.66338
$508$	−21.5911	−0.957951
$509$	23.4101	1.03763	0.518817	−	0.854885i	$-0.326373\pi$
$509$	23.4101	1.03763	0.518817	+	0.854885i	$0.326373\pi$
$510$	10.7772	0.477224
$511$	9.57275	0.423474
$512$	−8.48554	−0.375012
$513$	−42.8732	−1.89290
$514$	−1.89862	−0.0837444
$515$	−21.9632	−0.967815
$516$	1.17550	0.0517486
$517$	−16.1997	−0.712463
$518$	−2.69962	−0.118615
$519$	65.4828	2.87437
$520$	2.89258	0.126848
$521$	−39.6763	−1.73825	−0.869126	−	0.494591i	$-0.835318\pi$
$521$	−39.6763	−1.73825	−0.869126	+	0.494591i	$0.835318\pi$
$522$	14.1383	0.618819
$523$	17.3820	0.760063	0.380031	−	0.924974i	$-0.375913\pi$
$523$	17.3820	0.760063	0.380031	+	0.924974i	$0.375913\pi$
$524$	−80.5506	−3.51887
$525$	26.9738	1.17724
$526$	22.3741	0.975558
$527$	−0.365486	−0.0159208
$528$	−52.0014	−2.26307
$529$	−20.1594	−0.876497
$530$	−18.8384	−0.818289
$531$	65.7163	2.85184
$532$	−34.0464	−1.47610
$533$	−0.165422	−0.00716522
$534$	78.4863	3.39643
$535$	26.4866	1.14511
$536$	−104.775	−4.52561
$537$	−67.1830	−2.89916
$538$	−57.7711	−2.49069
$539$	−1.34754	−0.0580428
$540$	133.422	5.74156
$541$	−12.1671	−0.523105	−0.261553	−	0.965189i	$-0.584235\pi$
$541$	−12.1671	−0.523105	−0.261553	+	0.965189i	$0.584235\pi$
$542$	7.32259	0.314532
$543$	−66.7407	−2.86412
$544$	6.71998	0.288117
$545$	31.0070	1.32819
$546$	0.669303	0.0286435
$547$	−8.46074	−0.361755	−0.180878	−	0.983506i	$-0.557894\pi$
$547$	−8.46074	−0.361755	−0.180878	+	0.983506i	$0.557894\pi$
$548$	68.0621	2.90747
$549$	−2.04563	−0.0873055
$550$	34.0400	1.45147
$551$	6.35018	0.270527
$552$	−43.1255	−1.83554
$553$	16.6113	0.706382
$554$	20.1917	0.857863
$555$	10.9228	0.463647
$556$	−50.4673	−2.14029
$557$	−39.3365	−1.66674	−0.833370	−	0.552715i	$-0.813592\pi$
$557$	−39.3365	−1.66674	−0.833370	+	0.552715i	$0.813592\pi$
$558$	−14.3349	−0.606844
$559$	−0.00663216	−0.000280510 0
$560$	50.7232	2.14345
$561$	1.41975	0.0599420
$562$	−46.4690	−1.96018
$563$	33.1483	1.39703	0.698517	−	0.715593i	$-0.253843\pi$
$563$	33.1483	1.39703	0.698517	+	0.715593i	$0.253843\pi$
$564$	183.254	7.71638
$565$	28.5556	1.20134
$566$	24.7645	1.04093
$567$	3.26579	0.137150
$568$	10.9499	0.459448
$569$	−4.26487	−0.178793	−0.0893963	−	0.995996i	$-0.528494\pi$
$569$	−4.26487	−0.178793	−0.0893963	+	0.995996i	$0.528494\pi$
$570$	189.854	7.95209
$571$	−12.3694	−0.517642	−0.258821	−	0.965925i	$-0.583334\pi$
$571$	−12.3694	−0.517642	−0.258821	+	0.965925i	$0.583334\pi$
$572$	0.612847	0.0256244
$573$	17.1776	0.717605
$574$	−5.19249	−0.216731
$575$	15.7706	0.657678
$576$	121.402	5.05842
$577$	−21.3099	−0.887142	−0.443571	−	0.896239i	$-0.646289\pi$
$577$	−21.3099	−0.887142	−0.443571	+	0.896239i	$0.646289\pi$
$578$	45.5330	1.89392
$579$	−55.1614	−2.29243
$580$	−19.7618	−0.820565
$581$	−11.0185	−0.457124
$582$	65.5382	2.71665
$583$	−2.48170	−0.102782
$584$	−84.9704	−3.51610
$585$	−1.73040	−0.0715430
$586$	−2.27215	−0.0938616
$587$	19.2270	0.793585	0.396792	−	0.917908i	$-0.370123\pi$
$587$	19.2270	0.793585	0.396792	+	0.917908i	$0.370123\pi$
$588$	15.2436	0.628637
$589$	−6.43846	−0.265292
$590$	−126.596	−5.21186
$591$	29.7865	1.22525
$592$	13.3867	0.550189
$593$	6.91558	0.283989	0.141994	−	0.989867i	$-0.454649\pi$
$593$	6.91558	0.283989	0.141994	+	0.989867i	$0.454649\pi$
$594$	24.2242	0.993931
$595$	−1.38486	−0.0567736
$596$	121.105	4.96065
$597$	77.5102	3.17228
$598$	0.391315	0.0160021
$599$	−18.4081	−0.752135	−0.376068	−	0.926592i	$-0.622724\pi$
$599$	−18.4081	−0.752135	−0.376068	+	0.926592i	$0.622724\pi$
$600$	−239.427	−9.77458
$601$	−10.3124	−0.420650	−0.210325	−	0.977632i	$-0.567452\pi$
$601$	−10.3124	−0.420650	−0.210325	+	0.977632i	$0.567452\pi$
$602$	−0.208180	−0.00848477
$603$	62.6786	2.55247
$604$	47.2812	1.92384
$605$	−34.7994	−1.41480
$606$	−2.01932	−0.0820291
$607$	−15.0601	−0.611269	−0.305635	−	0.952149i	$-0.598869\pi$
$607$	−15.0601	−0.611269	−0.305635	+	0.952149i	$0.598869\pi$
$608$	118.380	4.80096
$609$	−2.84318	−0.115211
$610$	3.94070	0.159554
$611$	−1.03392	−0.0418278
$612$	−10.2624	−0.414834
$613$	12.4650	0.503455	0.251728	−	0.967798i	$-0.419001\pi$
$613$	12.4650	0.503455	0.251728	+	0.967798i	$0.419001\pi$
$614$	−37.7491	−1.52343
$615$	21.0090	0.847166
$616$	11.9612	0.481929
$617$	−26.3207	−1.05963	−0.529815	−	0.848113i	$-0.677739\pi$
$617$	−26.3207	−1.05963	−0.529815	+	0.848113i	$0.677739\pi$
$618$	45.1092	1.81456
$619$	−14.6053	−0.587035	−0.293518	−	0.955954i	$-0.594826\pi$
$619$	−14.6053	−0.587035	−0.293518	+	0.955954i	$0.594826\pi$
$620$	20.0366	0.804687
$621$	11.2230	0.450362
$622$	18.8917	0.757488
$623$	−10.0854	−0.404061
$624$	−3.31889	−0.132862
$625$	15.7705	0.630818
$626$	−31.6445	−1.26477
$627$	25.0106	0.998827
$628$	−35.7482	−1.42651
$629$	−0.365486	−0.0145729
$630$	−54.3161	−2.16400
$631$	1.78544	0.0710771	0.0355385	−	0.999368i	$-0.488685\pi$
$631$	1.78544	0.0710771	0.0355385	+	0.999368i	$0.488685\pi$
$632$	−147.446	−5.86509
$633$	17.9758	0.714474
$634$	32.8360	1.30408
$635$	−15.4711	−0.613951
$636$	28.0735	1.11318
$637$	−0.0860043	−0.00340761
$638$	−3.58798	−0.142050
$639$	−6.55044	−0.259131
$640$	−94.5335	−3.73677
$641$	34.1195	1.34764	0.673820	−	0.738895i	$-0.264652\pi$
$641$	34.1195	1.34764	0.673820	+	0.738895i	$0.264652\pi$
$642$	−54.3994	−2.14697
$643$	−11.3521	−0.447682	−0.223841	−	0.974626i	$-0.571860\pi$
$643$	−11.3521	−0.447682	−0.223841	+	0.974626i	$0.571860\pi$
$644$	8.91235	0.351196
$645$	0.842303	0.0331656
$646$	−6.35266	−0.249942
$647$	43.7153	1.71862	0.859312	−	0.511451i	$-0.170892\pi$
$647$	43.7153	1.71862	0.859312	+	0.511451i	$0.170892\pi$
$648$	−28.9880	−1.13876
$649$	−16.6773	−0.654639
$650$	2.17254	0.0852138
$651$	2.88270	0.112982
$652$	−96.1635	−3.76605
$653$	−2.58215	−0.101047	−0.0505236	−	0.998723i	$-0.516089\pi$
$653$	−2.58215	−0.101047	−0.0505236	+	0.998723i	$0.516089\pi$
$654$	−63.6837	−2.49023
$655$	−57.7183	−2.25524
$656$	25.7481	1.00530
$657$	50.8309	1.98310
$658$	−32.4540	−1.26519
$659$	−5.33624	−0.207870	−0.103935	−	0.994584i	$-0.533143\pi$
$659$	−5.33624	−0.207870	−0.103935	+	0.994584i	$0.533143\pi$
$660$	−77.8332	−3.02965
$661$	−40.9699	−1.59354	−0.796772	−	0.604280i	$-0.793461\pi$
$661$	−40.9699	−1.59354	−0.796772	+	0.604280i	$0.793461\pi$
$662$	−54.6127	−2.12258
$663$	0.0906129	0.00351911
$664$	97.8031	3.79550
$665$	−24.3959	−0.946031
$666$	−14.3349	−0.555466
$667$	−1.66229	−0.0643643
$668$	−46.7877	−1.81027
$669$	26.9349	1.04136
$670$	−120.744	−4.66475
$671$	0.519134	0.0200409
$672$	−53.0026	−2.04462
$673$	−7.92612	−0.305530	−0.152765	−	0.988263i	$-0.548818\pi$
$673$	−7.92612	−0.305530	−0.152765	+	0.988263i	$0.548818\pi$
$674$	−11.4174	−0.439783
$675$	62.3085	2.39825
$676$	−68.7045	−2.64248
$677$	25.5238	0.980961	0.490481	−	0.871452i	$-0.336821\pi$
$677$	25.5238	0.980961	0.490481	+	0.871452i	$0.336821\pi$
$678$	−58.6489	−2.25240
$679$	−8.42154	−0.323189
$680$	12.2924	0.471391
$681$	70.6173	2.70606
$682$	3.63786	0.139301
$683$	−43.4716	−1.66339	−0.831697	−	0.555230i	$-0.812630\pi$
$683$	−43.4716	−1.66339	−0.831697	+	0.555230i	$0.812630\pi$
$684$	−180.785	−6.91248
$685$	48.7697	1.86340
$686$	−2.69962	−0.103072
$687$	5.18581	0.197851
$688$	1.03230	0.0393562
$689$	−0.158390	−0.00603418
$690$	−49.6982	−1.89198
$691$	−7.62651	−0.290126	−0.145063	−	0.989422i	$-0.546339\pi$
$691$	−7.62651	−0.290126	−0.145063	+	0.989422i	$0.546339\pi$
$692$	120.120	4.56629
$693$	−7.15540	−0.271811
$694$	37.4729	1.42245
$695$	−36.1623	−1.37171
$696$	25.2368	0.956599
$697$	−0.702980	−0.0266273
$698$	73.8168	2.79401
$699$	0.499362	0.0188876
$700$	49.4803	1.87018
$701$	−18.1552	−0.685712	−0.342856	−	0.939388i	$-0.611394\pi$
$701$	−18.1552	−0.685712	−0.342856	+	0.939388i	$0.611394\pi$
$702$	1.54606	0.0583524
$703$	−6.43846	−0.242831
$704$	−30.8090	−1.16116
$705$	131.310	4.94543
$706$	−28.4442	−1.07051
$707$	0.259479	0.00975870
$708$	188.656	7.09012
$709$	14.5881	0.547866	0.273933	−	0.961749i	$-0.411675\pi$
$709$	14.5881	0.547866	0.273933	+	0.961749i	$0.411675\pi$
$710$	12.6188	0.473573
$711$	88.2051	3.30795
$712$	89.5204	3.35492
$713$	1.68540	0.0631188
$714$	2.84429	0.106445
$715$	0.439134	0.0164227
$716$	−123.239	−4.60566
$717$	16.6244	0.620851
$718$	−27.5090	−1.02663
$719$	−13.7535	−0.512918	−0.256459	−	0.966555i	$-0.582556\pi$
$719$	−13.7535	−0.512918	−0.256459	+	0.966555i	$0.582556\pi$
$720$	269.338	10.0376
$721$	−5.79645	−0.215871
$722$	−60.6167	−2.25592
$723$	−20.1906	−0.750897
$724$	−122.428	−4.54999
$725$	−9.22885	−0.342751
$726$	71.4728	2.65260
$727$	19.9226	0.738890	0.369445	−	0.929253i	$-0.379548\pi$
$727$	19.9226	0.738890	0.369445	+	0.929253i	$0.379548\pi$
$728$	0.763398	0.0282934
$729$	−40.2458	−1.49059
$730$	−97.9206	−3.62421
$731$	−0.0281842	−0.00104243
$732$	−5.87253	−0.217055
$733$	0.0295068	0.00108986	0.000544929	−	1.00000i	$-0.499827\pi$
$733$	0.0295068	0.00108986	0.000544929		1.00000i	$0.499827\pi$
$734$	−63.3352	−2.33775
$735$	10.9228	0.402893
$736$	−30.9885	−1.14225
$737$	−15.9064	−0.585919
$738$	−27.5719	−1.01494
$739$	51.8789	1.90840	0.954199	−	0.299173i	$-0.0967108\pi$
$739$	51.8789	1.90840	0.954199	+	0.299173i	$0.0967108\pi$
$740$	20.0366	0.736558
$741$	1.59625	0.0586398
$742$	−4.97177	−0.182519
$743$	33.4917	1.22869	0.614346	−	0.789037i	$-0.289420\pi$
$743$	33.4917	1.22869	0.614346	+	0.789037i	$0.289420\pi$
$744$	−25.5877	−0.938089
$745$	86.7775	3.17928
$746$	53.4629	1.95742
$747$	−58.5077	−2.14068
$748$	2.60437	0.0952251
$749$	6.99023	0.255417
$750$	−128.481	−4.69146
$751$	34.4839	1.25834	0.629168	−	0.777270i	$-0.283396\pi$
$751$	34.4839	1.25834	0.629168	+	0.777270i	$0.283396\pi$
$752$	160.930	5.86853
$753$	53.6556	1.95532
$754$	−0.228996	−0.00833954
$755$	33.8792	1.23299
$756$	35.2122	1.28065
$757$	−32.5981	−1.18480	−0.592399	−	0.805645i	$-0.701819\pi$
$757$	−32.5981	−1.18480	−0.592399	+	0.805645i	$0.701819\pi$
$758$	15.0958	0.548306
$759$	−6.54705	−0.237643
$760$	216.544	7.85489
$761$	−7.35675	−0.266682	−0.133341	−	0.991070i	$-0.542571\pi$
$761$	−7.35675	−0.266682	−0.133341	+	0.991070i	$0.542571\pi$
$762$	31.7753	1.15110
$763$	8.18325	0.296254
$764$	31.5103	1.14000
$765$	−7.35353	−0.265867
$766$	78.7099	2.84391
$767$	−1.06439	−0.0384330
$768$	62.3427	2.24960
$769$	−40.4823	−1.45983	−0.729915	−	0.683538i	$-0.760440\pi$
$769$	−40.4823	−1.45983	−0.729915	+	0.683538i	$0.760440\pi$
$770$	13.7842	0.496746
$771$	2.02737	0.0730140
$772$	−101.187	−3.64180
$773$	−0.0947192	−0.00340681	−0.00170341	−	0.999999i	$-0.500542\pi$
$773$	−0.0947192	−0.00340681	−0.00170341	+	0.999999i	$0.500542\pi$
$774$	−1.10542	−0.0397337
$775$	9.35715	0.336119
$776$	74.7520	2.68344
$777$	2.88270	0.103416
$778$	83.7036	3.00092
$779$	−12.3838	−0.443697
$780$	−4.96755	−0.177867
$781$	1.66235	0.0594835
$782$	1.66294	0.0594667
$783$	−6.56762	−0.234707
$784$	13.3867	0.478096
$785$	−25.6153	−0.914249
$786$	118.545	4.22835
$787$	14.2740	0.508813	0.254406	−	0.967097i	$-0.418120\pi$
$787$	14.2740	0.508813	0.254406	+	0.967097i	$0.418120\pi$
$788$	54.6398	1.94646
$789$	−23.8914	−0.850557
$790$	−169.918	−6.04541
$791$	7.53628	0.267959
$792$	63.5133	2.25685
$793$	0.0331327	0.00117658
$794$	−36.4827	−1.29472
$795$	20.1160	0.713440
$796$	142.183	5.03955
$797$	−46.1433	−1.63448	−0.817239	−	0.576299i	$-0.804497\pi$
$797$	−46.1433	−1.63448	−0.817239	+	0.576299i	$0.804497\pi$
$798$	50.1054	1.77371
$799$	−4.39375	−0.155440
$800$	−172.045	−6.08270
$801$	−53.5528	−1.89220
$802$	−13.7728	−0.486335
$803$	−12.8997	−0.455220
$804$	179.935	6.34583
$805$	6.38613	0.225081
$806$	0.232179	0.00817817
$807$	61.6889	2.17155
$808$	−2.30320	−0.0810265
$809$	31.8675	1.12040	0.560201	−	0.828357i	$-0.310724\pi$
$809$	31.8675	1.12040	0.560201	+	0.828357i	$0.310724\pi$
$810$	−33.4060	−1.17377
$811$	30.2816	1.06333	0.531666	−	0.846954i	$-0.321566\pi$
$811$	30.2816	1.06333	0.531666	+	0.846954i	$0.321566\pi$
$812$	−5.21547	−0.183027
$813$	−7.81917	−0.274230
$814$	3.63786	0.127507
$815$	−68.9057	−2.41366
$816$	−14.1040	−0.493739
$817$	−0.496497	−0.0173702
$818$	−32.0042	−1.11900
$819$	−0.456679	−0.0159577
$820$	38.5386	1.34583
$821$	41.0878	1.43397	0.716987	−	0.697086i	$-0.245521\pi$
$821$	41.0878	1.43397	0.716987	+	0.697086i	$0.245521\pi$
$822$	−100.166	−3.49368
$823$	−51.6109	−1.79904	−0.899521	−	0.436878i	$-0.856084\pi$
$823$	−51.6109	−1.79904	−0.899521	+	0.436878i	$0.856084\pi$
$824$	51.4509	1.79238
$825$	−36.3484	−1.26549
$826$	−33.4107	−1.16251
$827$	20.0877	0.698517	0.349259	−	0.937026i	$-0.386433\pi$
$827$	20.0877	0.698517	0.349259	+	0.937026i	$0.386433\pi$
$828$	47.3242	1.64463
$829$	−0.871984	−0.0302853	−0.0151426	−	0.999885i	$-0.504820\pi$
$829$	−0.871984	−0.0302853	−0.0151426	+	0.999885i	$0.504820\pi$
$830$	112.709	3.91219
$831$	−21.5610	−0.747943
$832$	−1.96633	−0.0681701
$833$	−0.365486	−0.0126633
$834$	74.2719	2.57182
$835$	−33.5256	−1.16020
$836$	45.8790	1.58676
$837$	6.65892	0.230166
$838$	37.1196	1.28228
$839$	−37.0375	−1.27868	−0.639339	−	0.768925i	$-0.720792\pi$
$839$	−37.0375	−1.27868	−0.639339	+	0.768925i	$0.720792\pi$
$840$	−96.9537	−3.34522
$841$	−28.0272	−0.966456
$842$	69.9334	2.41006
$843$	49.6203	1.70901
$844$	32.9745	1.13503
$845$	−49.2300	−1.69357
$846$	−172.329	−5.92481
$847$	−9.18413	−0.315570
$848$	24.6536	0.846608
$849$	−26.4439	−0.907552
$850$	9.23245	0.316671
$851$	1.68540	0.0577748
$852$	−18.8047	−0.644240
$853$	7.41719	0.253960	0.126980	−	0.991905i	$-0.459472\pi$
$853$	7.41719	0.253960	0.126980	+	0.991905i	$0.459472\pi$
$854$	1.04002	0.0355886
$855$	−129.541	−4.43021
$856$	−62.0473	−2.12073
$857$	−36.4694	−1.24577	−0.622885	−	0.782314i	$-0.714039\pi$
$857$	−36.4694	−1.24577	−0.622885	+	0.782314i	$0.714039\pi$
$858$	−0.901915	−0.0307909
$859$	−23.1427	−0.789619	−0.394810	−	0.918763i	$-0.629189\pi$
$859$	−23.1427	−0.789619	−0.394810	+	0.918763i	$0.629189\pi$
$860$	1.54510	0.0526876
$861$	5.54463	0.188960
$862$	−49.0530	−1.67075
$863$	7.51439	0.255793	0.127896	−	0.991788i	$-0.459177\pi$
$863$	7.51439	0.255793	0.127896	+	0.991788i	$0.459177\pi$
$864$	−122.434	−4.16528
$865$	86.0720	2.92653
$866$	39.8049	1.35262
$867$	−48.6208	−1.65125
$868$	5.28797	0.179485
$869$	−22.3844	−0.759338
$870$	29.0831	0.986010
$871$	−1.01519	−0.0343985
$872$	−72.6368	−2.45979
$873$	−44.7181	−1.51348
$874$	29.2947	0.990907
$875$	16.5096	0.558126
$876$	145.923	4.93030
$877$	4.92210	0.166208	0.0831038	−	0.996541i	$-0.473517\pi$
$877$	4.92210	0.166208	0.0831038	+	0.996541i	$0.473517\pi$
$878$	41.4236	1.39798
$879$	2.42624	0.0818349
$880$	−68.3517	−2.30414
$881$	−7.07393	−0.238327	−0.119163	−	0.992875i	$-0.538021\pi$
$881$	−7.07393	−0.238327	−0.119163	+	0.992875i	$0.538021\pi$
$882$	−14.3349	−0.482681
$883$	−54.7925	−1.84391	−0.921957	−	0.387293i	$-0.873410\pi$
$883$	−54.7925	−1.84391	−0.921957	+	0.387293i	$0.873410\pi$
$884$	0.166219	0.00559054
$885$	135.181	4.54406
$886$	78.7412	2.64536
$887$	18.7429	0.629324	0.314662	−	0.949204i	$-0.398109\pi$
$887$	18.7429	0.629324	0.314662	+	0.949204i	$0.398109\pi$
$888$	−25.5877	−0.858665
$889$	−4.08307	−0.136942
$890$	103.164	3.45807
$891$	−4.40079	−0.147432
$892$	49.4089	1.65433
$893$	−77.4011	−2.59013
$894$	−178.228	−5.96083
$895$	−88.3067	−2.95177
$896$	−24.9489	−0.833485
$897$	−0.417853	−0.0139517
$898$	−58.2355	−1.94334
$899$	−0.986289	−0.0328946
$900$	262.738	8.75795
$901$	−0.673097	−0.0224241
$902$	6.99711	0.232978
$903$	0.222297	0.00739759
$904$	−66.8942	−2.22487
$905$	−87.7254	−2.91609
$906$	−69.5828	−2.31174
$907$	−22.8840	−0.759852	−0.379926	−	0.925017i	$-0.624050\pi$
$907$	−22.8840	−0.759852	−0.379926	+	0.925017i	$0.624050\pi$
$908$	129.539	4.29890
$909$	1.37782	0.0456994
$910$	0.879746	0.0291633
$911$	−26.0849	−0.864232	−0.432116	−	0.901818i	$-0.642233\pi$
$911$	−26.0849	−0.864232	−0.432116	+	0.901818i	$0.642233\pi$
$912$	−248.459	−8.22729
$913$	14.8479	0.491393
$914$	57.9975	1.91839
$915$	−4.20795	−0.139110
$916$	9.51275	0.314310
$917$	−15.2328	−0.503031
$918$	6.57018	0.216848
$919$	31.3499	1.03414	0.517070	−	0.855943i	$-0.327023\pi$
$919$	31.3499	1.03414	0.517070	+	0.855943i	$0.327023\pi$
$920$	−56.6851	−1.86885
$921$	40.3091	1.32823
$922$	−25.8161	−0.850209
$923$	0.106096	0.00349219
$924$	−20.5414	−0.675764
$925$	9.35715	0.307661
$926$	16.1423	0.530470
$927$	−30.7789	−1.01091
$928$	18.1343	0.595289
$929$	−13.6937	−0.449276	−0.224638	−	0.974442i	$-0.572120\pi$
$929$	−13.6937	−0.449276	−0.224638	+	0.974442i	$0.572120\pi$
$930$	−29.4874	−0.966931
$931$	−6.43846	−0.211012
$932$	0.916020	0.0300052
$933$	−20.1728	−0.660429
$934$	48.4576	1.58558
$935$	1.86615	0.0610297
$936$	4.05361	0.132496
$937$	−47.4276	−1.54939	−0.774697	−	0.632333i	$-0.782097\pi$
$937$	−47.4276	−1.54939	−0.774697	+	0.632333i	$0.782097\pi$
$938$	−31.8663	−1.04047
$939$	33.7905	1.10271
$940$	240.873	7.85641
$941$	58.2791	1.89984	0.949922	−	0.312488i	$-0.101162\pi$
$941$	58.2791	1.89984	0.949922	+	0.312488i	$0.101162\pi$
$942$	52.6100	1.71413
$943$	3.24173	0.105565
$944$	165.674	5.39223
$945$	25.2312	0.820771
$946$	0.280531	0.00912085
$947$	−22.1487	−0.719736	−0.359868	−	0.933003i	$-0.617178\pi$
$947$	−22.1487	−0.719736	−0.359868	+	0.933003i	$0.617178\pi$
$948$	253.216	8.22406
$949$	−0.823298	−0.0267254
$950$	162.641	5.27675
$951$	−35.0627	−1.13699
$952$	3.24415	0.105144
$953$	27.1148	0.878334	0.439167	−	0.898405i	$-0.355274\pi$
$953$	27.1148	0.878334	0.439167	+	0.898405i	$0.355274\pi$
$954$	−26.3999	−0.854727
$955$	22.5786	0.730627
$956$	30.4955	0.986297
$957$	3.83130	0.123848
$958$	39.4676	1.27514
$959$	12.8711	0.415630
$960$	249.729	8.05997
$961$	1.00000	0.0322581
$962$	0.232179	0.00748576
$963$	37.1178	1.19611
$964$	−37.0373	−1.19289
$965$	−72.5053	−2.33403
$966$	−13.1161	−0.422005
$967$	56.1274	1.80493	0.902467	−	0.430758i	$-0.141754\pi$
$967$	56.1274	1.80493	0.902467	+	0.430758i	$0.141754\pi$
$968$	81.5209	2.62018
$969$	6.78347	0.217916
$970$	86.1448	2.76594
$971$	39.5408	1.26892	0.634462	−	0.772954i	$-0.281222\pi$
$971$	39.5408	1.26892	0.634462	+	0.772954i	$0.281222\pi$
$972$	−55.8540	−1.79152
$973$	−9.54380	−0.305960
$974$	103.772	3.32506
$975$	−2.31987	−0.0742952
$976$	−5.15715	−0.165076
$977$	−51.1101	−1.63516	−0.817579	−	0.575817i	$-0.804684\pi$
$977$	−51.1101	−1.63516	−0.817579	+	0.575817i	$0.804684\pi$
$978$	141.522	4.52537
$979$	13.5905	0.434353
$980$	20.0366	0.640044
$981$	43.4527	1.38734
$982$	27.3554	0.872946
$983$	22.4892	0.717293	0.358647	−	0.933473i	$-0.383238\pi$
$983$	22.4892	0.717293	0.358647	+	0.933473i	$0.383238\pi$
$984$	−49.2156	−1.56894
$985$	39.1521	1.24749
$986$	−0.973146	−0.0309913
$987$	34.6549	1.10308
$988$	2.92813	0.0931564
$989$	0.129969	0.00413276
$990$	73.1933	2.32623
$991$	−18.1881	−0.577763	−0.288882	−	0.957365i	$-0.593283\pi$
$991$	−18.1881	−0.577763	−0.288882	+	0.957365i	$0.593283\pi$
$992$	−18.3864	−0.583770
$993$	58.3163	1.85061
$994$	3.33029	0.105630
$995$	101.881	3.22985
$996$	−167.962	−5.32207
$997$	−54.8304	−1.73650	−0.868249	−	0.496129i	$-0.834754\pi$
$997$	−54.8304	−1.73650	−0.868249	+	0.496129i	$0.834754\pi$
$998$	−47.7062	−1.51011
$999$	6.65892	0.210679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.g.1.3	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.g.1.3	✓	70	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69962 q^{2} +2.88270 q^{3} +5.28797 q^{4} +3.78908 q^{5} -7.78221 q^{6} +1.00000 q^{7} -8.87628 q^{8} +5.30996 q^{9} +O(q^{10})\)	\(q-2.69962 q^{2} +2.88270 q^{3} +5.28797 q^{4} +3.78908 q^{5} -7.78221 q^{6} +1.00000 q^{7} -8.87628 q^{8} +5.30996 q^{9} -10.2291 q^{10} -1.34754 q^{11} +15.2436 q^{12} -0.0860043 q^{13} -2.69962 q^{14} +10.9228 q^{15} +13.3867 q^{16} -0.365486 q^{17} -14.3349 q^{18} -6.43846 q^{19} +20.0366 q^{20} +2.88270 q^{21} +3.63786 q^{22} +1.68540 q^{23} -25.5877 q^{24} +9.35715 q^{25} +0.232179 q^{26} +6.65892 q^{27} +5.28797 q^{28} -0.986289 q^{29} -29.4874 q^{30} +1.00000 q^{31} -18.3864 q^{32} -3.88456 q^{33} +0.986674 q^{34} +3.78908 q^{35} +28.0789 q^{36} +1.00000 q^{37} +17.3814 q^{38} -0.247925 q^{39} -33.6330 q^{40} +1.92341 q^{41} -7.78221 q^{42} +0.0771143 q^{43} -7.12577 q^{44} +20.1199 q^{45} -4.54995 q^{46} +12.0217 q^{47} +38.5898 q^{48} +1.00000 q^{49} -25.2608 q^{50} -1.05359 q^{51} -0.454788 q^{52} +1.84165 q^{53} -17.9766 q^{54} -5.10595 q^{55} -8.87628 q^{56} -18.5601 q^{57} +2.66261 q^{58} +12.3760 q^{59} +57.7594 q^{60} -0.385245 q^{61} -2.69962 q^{62} +5.30996 q^{63} +22.8631 q^{64} -0.325877 q^{65} +10.4869 q^{66} +11.8040 q^{67} -1.93268 q^{68} +4.85851 q^{69} -10.2291 q^{70} -1.23361 q^{71} -47.1327 q^{72} +9.57275 q^{73} -2.69962 q^{74} +26.9738 q^{75} -34.0464 q^{76} -1.34754 q^{77} +0.669303 q^{78} +16.6113 q^{79} +50.7232 q^{80} +3.26579 q^{81} -5.19249 q^{82} -11.0185 q^{83} +15.2436 q^{84} -1.38486 q^{85} -0.208180 q^{86} -2.84318 q^{87} +11.9612 q^{88} -10.0854 q^{89} -54.3161 q^{90} -0.0860043 q^{91} +8.91235 q^{92} +2.88270 q^{93} -32.4540 q^{94} -24.3959 q^{95} -53.0026 q^{96} -8.42154 q^{97} -2.69962 q^{98} -7.15540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

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