LMFDB - Embedded newform 8041.2.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55392 q^{2} +1.24868 q^{3} +4.52253 q^{4} +4.26646 q^{5} -3.18904 q^{6} -0.595052 q^{7} -6.44234 q^{8} -1.44079 q^{9} +O(q^{10})$	\(q-2.55392 q^{2} +1.24868 q^{3} +4.52253 q^{4} +4.26646 q^{5} -3.18904 q^{6} -0.595052 q^{7} -6.44234 q^{8} -1.44079 q^{9} -10.8962 q^{10} +1.00000 q^{11} +5.64721 q^{12} +1.58644 q^{13} +1.51972 q^{14} +5.32746 q^{15} +7.40820 q^{16} -1.00000 q^{17} +3.67967 q^{18} -2.73257 q^{19} +19.2952 q^{20} -0.743032 q^{21} -2.55392 q^{22} -0.638262 q^{23} -8.04445 q^{24} +13.2027 q^{25} -4.05164 q^{26} -5.54514 q^{27} -2.69114 q^{28} -0.508293 q^{29} -13.6059 q^{30} +4.45197 q^{31} -6.03530 q^{32} +1.24868 q^{33} +2.55392 q^{34} -2.53876 q^{35} -6.51601 q^{36} +9.71491 q^{37} +6.97878 q^{38} +1.98096 q^{39} -27.4860 q^{40} +5.39922 q^{41} +1.89765 q^{42} -1.00000 q^{43} +4.52253 q^{44} -6.14707 q^{45} +1.63007 q^{46} +11.5968 q^{47} +9.25050 q^{48} -6.64591 q^{49} -33.7186 q^{50} -1.24868 q^{51} +7.17470 q^{52} +5.13116 q^{53} +14.1619 q^{54} +4.26646 q^{55} +3.83353 q^{56} -3.41212 q^{57} +1.29814 q^{58} +8.62988 q^{59} +24.0936 q^{60} +5.67358 q^{61} -11.3700 q^{62} +0.857344 q^{63} +0.597286 q^{64} +6.76847 q^{65} -3.18904 q^{66} +2.15243 q^{67} -4.52253 q^{68} -0.796988 q^{69} +6.48381 q^{70} +0.352619 q^{71} +9.28206 q^{72} +8.40716 q^{73} -24.8111 q^{74} +16.4860 q^{75} -12.3581 q^{76} -0.595052 q^{77} -5.05921 q^{78} -3.55050 q^{79} +31.6068 q^{80} -2.60176 q^{81} -13.7892 q^{82} -12.3025 q^{83} -3.36038 q^{84} -4.26646 q^{85} +2.55392 q^{86} -0.634697 q^{87} -6.44234 q^{88} -11.1373 q^{89} +15.6991 q^{90} -0.944012 q^{91} -2.88656 q^{92} +5.55911 q^{93} -29.6174 q^{94} -11.6584 q^{95} -7.53618 q^{96} -12.0254 q^{97} +16.9732 q^{98} -1.44079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−2.55392	−1.80590	−0.902948	−	0.429749i	$-0.858602\pi$
$2$	−2.55392	−1.80590	−0.902948	+	0.429749i	$0.858602\pi$
$3$	1.24868	0.720928	0.360464	−	0.932773i	$-0.382618\pi$
$3$	1.24868	0.720928	0.360464	+	0.932773i	$0.382618\pi$
$4$	4.52253	2.26126
$5$	4.26646	1.90802	0.954009	−	0.299777i	$-0.0969123\pi$
$5$	4.26646	1.90802	0.954009	+	0.299777i	$0.0969123\pi$
$6$	−3.18904	−1.30192
$7$	−0.595052	−0.224908	−0.112454	−	0.993657i	$-0.535871\pi$
$7$	−0.595052	−0.224908	−0.112454	+	0.993657i	$0.535871\pi$
$8$	−6.44234	−2.27771
$9$	−1.44079	−0.480263
$10$	−10.8962	−3.44569
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.64721	1.63021
$13$	1.58644	0.439998	0.219999	−	0.975500i	$-0.429395\pi$
$13$	1.58644	0.439998	0.219999	+	0.975500i	$0.429395\pi$
$14$	1.51972	0.406162
$15$	5.32746	1.37554
$16$	7.40820	1.85205
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.67967	0.867306
$19$	−2.73257	−0.626895	−0.313448	−	0.949606i	$-0.601484\pi$
$19$	−2.73257	−0.626895	−0.313448	+	0.949606i	$0.601484\pi$
$20$	19.2952	4.31453
$21$	−0.743032	−0.162143
$22$	−2.55392	−0.544498
$23$	−0.638262	−0.133087	−0.0665435	−	0.997784i	$-0.521197\pi$
$23$	−0.638262	−0.133087	−0.0665435	+	0.997784i	$0.521197\pi$
$24$	−8.04445	−1.64207
$25$	13.2027	2.64053
$26$	−4.05164	−0.794592
$27$	−5.54514	−1.06716
$28$	−2.69114	−0.508577
$29$	−0.508293	−0.0943877	−0.0471938	−	0.998886i	$-0.515028\pi$
$29$	−0.508293	−0.0943877	−0.0471938	+	0.998886i	$0.515028\pi$
$30$	−13.6059	−2.48409
$31$	4.45197	0.799598	0.399799	−	0.916603i	$-0.369080\pi$
$31$	4.45197	0.799598	0.399799	+	0.916603i	$0.369080\pi$
$32$	−6.03530	−1.06690
$33$	1.24868	0.217368
$34$	2.55392	0.437994
$35$	−2.53876	−0.429130
$36$	−6.51601	−1.08600
$37$	9.71491	1.59712	0.798561	−	0.601914i	$-0.205595\pi$
$37$	9.71491	1.59712	0.798561	+	0.601914i	$0.205595\pi$
$38$	6.97878	1.13211
$39$	1.98096	0.317207
$40$	−27.4860	−4.34592
$41$	5.39922	0.843216	0.421608	−	0.906778i	$-0.361466\pi$
$41$	5.39922	0.843216	0.421608	+	0.906778i	$0.361466\pi$
$42$	1.89765	0.292813
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	4.52253	0.681797
$45$	−6.14707	−0.916351
$46$	1.63007	0.240341
$47$	11.5968	1.69157	0.845786	−	0.533523i	$-0.179132\pi$
$47$	11.5968	1.69157	0.845786	+	0.533523i	$0.179132\pi$
$48$	9.25050	1.33519
$49$	−6.64591	−0.949416
$50$	−33.7186	−4.76853
$51$	−1.24868	−0.174851
$52$	7.17470	0.994952
$53$	5.13116	0.704819	0.352409	−	0.935846i	$-0.385362\pi$
$53$	5.13116	0.704819	0.352409	+	0.935846i	$0.385362\pi$
$54$	14.1619	1.92719
$55$	4.26646	0.575289
$56$	3.83353	0.512277
$57$	−3.41212	−0.451946
$58$	1.29814	0.170454
$59$	8.62988	1.12352	0.561758	−	0.827302i	$-0.310125\pi$
$59$	8.62988	1.12352	0.561758	+	0.827302i	$0.310125\pi$
$60$	24.0936	3.11047
$61$	5.67358	0.726428	0.363214	−	0.931706i	$-0.381679\pi$
$61$	5.67358	0.726428	0.363214	+	0.931706i	$0.381679\pi$
$62$	−11.3700	−1.44399
$63$	0.857344	0.108015
$64$	0.597286	0.0746608
$65$	6.76847	0.839525
$66$	−3.18904	−0.392544
$67$	2.15243	0.262962	0.131481	−	0.991319i	$-0.458027\pi$
$67$	2.15243	0.262962	0.131481	+	0.991319i	$0.458027\pi$
$68$	−4.52253	−0.548437
$69$	−0.796988	−0.0959461
$70$	6.48381	0.774964
$71$	0.352619	0.0418482	0.0209241	−	0.999781i	$-0.493339\pi$
$71$	0.352619	0.0418482	0.0209241	+	0.999781i	$0.493339\pi$
$72$	9.28206	1.09390
$73$	8.40716	0.983984	0.491992	−	0.870600i	$-0.336269\pi$
$73$	8.40716	0.983984	0.491992	+	0.870600i	$0.336269\pi$
$74$	−24.8111	−2.88424
$75$	16.4860	1.90364
$76$	−12.3581	−1.41758
$77$	−0.595052	−0.0678125
$78$	−5.05921	−0.572843
$79$	−3.55050	−0.399462	−0.199731	−	0.979851i	$-0.564007\pi$
$79$	−3.55050	−0.399462	−0.199731	+	0.979851i	$0.564007\pi$
$80$	31.6068	3.53375
$81$	−2.60176	−0.289084
$82$	−13.7892	−1.52276
$83$	−12.3025	−1.35038	−0.675189	−	0.737645i	$-0.735938\pi$
$83$	−12.3025	−1.35038	−0.675189	+	0.737645i	$0.735938\pi$
$84$	−3.36038	−0.366648
$85$	−4.26646	−0.462762
$86$	2.55392	0.275397
$87$	−0.634697	−0.0680467
$88$	−6.44234	−0.686756
$89$	−11.1373	−1.18056	−0.590278	−	0.807200i	$-0.700982\pi$
$89$	−11.1373	−1.18056	−0.590278	+	0.807200i	$0.700982\pi$
$90$	15.6991	1.65484
$91$	−0.944012	−0.0989593
$92$	−2.88656	−0.300945
$93$	5.55911	0.576452
$94$	−29.6174	−3.05480
$95$	−11.6584	−1.19613
$96$	−7.53618	−0.769158
$97$	−12.0254	−1.22099	−0.610497	−	0.792019i	$-0.709030\pi$
$97$	−12.0254	−1.22099	−0.610497	+	0.792019i	$0.709030\pi$
$98$	16.9732	1.71455
$99$	−1.44079	−0.144805
$100$	59.7095	5.97095
$101$	−13.9464	−1.38772	−0.693861	−	0.720109i	$-0.744092\pi$
$101$	−13.9464	−1.38772	−0.693861	+	0.720109i	$0.744092\pi$
$102$	3.18904	0.315762
$103$	−1.41604	−0.139527	−0.0697634	−	0.997564i	$-0.522224\pi$
$103$	−1.41604	−0.139527	−0.0697634	+	0.997564i	$0.522224\pi$
$104$	−10.2204	−1.00219
$105$	−3.17011	−0.309371
$106$	−13.1046	−1.27283
$107$	9.06893	0.876727	0.438364	−	0.898798i	$-0.355558\pi$
$107$	9.06893	0.876727	0.438364	+	0.898798i	$0.355558\pi$
$108$	−25.0781	−2.41314
$109$	−15.4803	−1.48275	−0.741373	−	0.671094i	$-0.765825\pi$
$109$	−15.4803	−1.48275	−0.741373	+	0.671094i	$0.765825\pi$
$110$	−10.8962	−1.03891
$111$	12.1309	1.15141
$112$	−4.40827	−0.416542
$113$	−6.29118	−0.591825	−0.295912	−	0.955215i	$-0.595624\pi$
$113$	−6.29118	−0.591825	−0.295912	+	0.955215i	$0.595624\pi$
$114$	8.71429	0.816168
$115$	−2.72312	−0.253932
$116$	−2.29877	−0.213435
$117$	−2.28572	−0.211315
$118$	−22.0401	−2.02895
$119$	0.595052	0.0545483
$120$	−34.3213	−3.13309
$121$	1.00000	0.0909091
$122$	−14.4899	−1.31185
$123$	6.74192	0.607898
$124$	20.1342	1.80810
$125$	34.9964	3.13017
$126$	−2.18959	−0.195064
$127$	21.8289	1.93700	0.968502	−	0.249006i	$-0.0801039\pi$
$127$	21.8289	1.93700	0.968502	+	0.249006i	$0.0801039\pi$
$128$	10.5452	0.932070
$129$	−1.24868	−0.109940
$130$	−17.2861	−1.51610
$131$	−4.02160	−0.351369	−0.175685	−	0.984447i	$-0.556214\pi$
$131$	−4.02160	−0.351369	−0.175685	+	0.984447i	$0.556214\pi$
$132$	5.64721	0.491526
$133$	1.62602	0.140994
$134$	−5.49715	−0.474882
$135$	−23.6581	−2.03617
$136$	6.44234	0.552426
$137$	−10.5552	−0.901790	−0.450895	−	0.892577i	$-0.648895\pi$
$137$	−10.5552	−0.901790	−0.450895	+	0.892577i	$0.648895\pi$
$138$	2.03545	0.173269
$139$	17.3534	1.47190	0.735949	−	0.677037i	$-0.236737\pi$
$139$	17.3534	1.47190	0.735949	+	0.677037i	$0.236737\pi$
$140$	−11.4816	−0.970375
$141$	14.4808	1.21950
$142$	−0.900563	−0.0755736
$143$	1.58644	0.132664
$144$	−10.6737	−0.889472
$145$	−2.16861	−0.180093
$146$	−21.4712	−1.77697
$147$	−8.29864	−0.684461
$148$	43.9360	3.61151
$149$	19.4491	1.59334	0.796668	−	0.604417i	$-0.206594\pi$
$149$	19.4491	1.59334	0.796668	+	0.604417i	$0.206594\pi$
$150$	−42.1039	−3.43777
$151$	−22.1832	−1.80524	−0.902622	−	0.430434i	$-0.858361\pi$
$151$	−22.1832	−1.80524	−0.902622	+	0.430434i	$0.858361\pi$
$152$	17.6042	1.42789
$153$	1.44079	0.116481
$154$	1.51972	0.122462
$155$	18.9942	1.52565
$156$	8.95893	0.717289
$157$	9.59826	0.766025	0.383012	−	0.923743i	$-0.374887\pi$
$157$	9.59826	0.766025	0.383012	+	0.923743i	$0.374887\pi$
$158$	9.06769	0.721387
$159$	6.40719	0.508123
$160$	−25.7494	−2.03566
$161$	0.379799	0.0299324
$162$	6.64469	0.522056
$163$	−5.44017	−0.426107	−0.213054	−	0.977041i	$-0.568341\pi$
$163$	−5.44017	−0.426107	−0.213054	+	0.977041i	$0.568341\pi$
$164$	24.4181	1.90673
$165$	5.32746	0.414742
$166$	31.4197	2.43864
$167$	−6.29256	−0.486933	−0.243466	−	0.969909i	$-0.578285\pi$
$167$	−6.29256	−0.486933	−0.243466	+	0.969909i	$0.578285\pi$
$168$	4.78687	0.369315
$169$	−10.4832	−0.806402
$170$	10.8962	0.835701
$171$	3.93706	0.301075
$172$	−4.52253	−0.344840
$173$	−20.7720	−1.57926	−0.789632	−	0.613581i	$-0.789728\pi$
$173$	−20.7720	−1.57926	−0.789632	+	0.613581i	$0.789728\pi$
$174$	1.62097	0.122885
$175$	−7.85628	−0.593879
$176$	7.40820	0.558414
$177$	10.7760	0.809973
$178$	28.4439	2.13196
$179$	8.18288	0.611617	0.305808	−	0.952093i	$-0.401073\pi$
$179$	8.18288	0.611617	0.305808	+	0.952093i	$0.401073\pi$
$180$	−27.8003	−2.07211
$181$	5.18879	0.385679	0.192840	−	0.981230i	$-0.438230\pi$
$181$	5.18879	0.385679	0.192840	+	0.981230i	$0.438230\pi$
$182$	2.41093	0.178710
$183$	7.08451	0.523702
$184$	4.11191	0.303134
$185$	41.4483	3.04734
$186$	−14.1975	−1.04101
$187$	−1.00000	−0.0731272
$188$	52.4470	3.82509
$189$	3.29965	0.240014
$190$	29.7747	2.16008
$191$	5.34058	0.386431	0.193215	−	0.981156i	$-0.438108\pi$
$191$	5.34058	0.386431	0.193215	+	0.981156i	$0.438108\pi$
$192$	0.745822	0.0538250
$193$	−6.21263	−0.447195	−0.223597	−	0.974682i	$-0.571780\pi$
$193$	−6.21263	−0.447195	−0.223597	+	0.974682i	$0.571780\pi$
$194$	30.7120	2.20499
$195$	8.45167	0.605237
$196$	−30.0563	−2.14688
$197$	−20.5423	−1.46358	−0.731791	−	0.681530i	$-0.761315\pi$
$197$	−20.5423	−1.46358	−0.731791	+	0.681530i	$0.761315\pi$
$198$	3.67967	0.261502
$199$	15.9326	1.12943	0.564717	−	0.825284i	$-0.308985\pi$
$199$	15.9326	1.12943	0.564717	+	0.825284i	$0.308985\pi$
$200$	−85.0562	−6.01438
$201$	2.68771	0.189576
$202$	35.6181	2.50608
$203$	0.302461	0.0212286
$204$	−5.64721	−0.395384
$205$	23.0355	1.60887
$206$	3.61646	0.251971
$207$	0.919602	0.0639167
$208$	11.7526	0.814899
$209$	−2.73257	−0.189016
$210$	8.09623	0.558693
$211$	19.8004	1.36312	0.681558	−	0.731764i	$-0.261303\pi$
$211$	19.8004	1.36312	0.681558	+	0.731764i	$0.261303\pi$
$212$	23.2058	1.59378
$213$	0.440310	0.0301695
$214$	−23.1614	−1.58328
$215$	−4.26646	−0.290970
$216$	35.7237	2.43069
$217$	−2.64916	−0.179836
$218$	39.5355	2.67768
$219$	10.4979	0.709381
$220$	19.2952	1.30088
$221$	−1.58644	−0.106715
$222$	−30.9813	−2.07933
$223$	−4.48898	−0.300604	−0.150302	−	0.988640i	$-0.548025\pi$
$223$	−4.48898	−0.300604	−0.150302	+	0.988640i	$0.548025\pi$
$224$	3.59132	0.239955
$225$	−19.0223	−1.26815
$226$	16.0672	1.06877
$227$	18.5039	1.22815	0.614073	−	0.789249i	$-0.289530\pi$
$227$	18.5039	1.22815	0.614073	+	0.789249i	$0.289530\pi$
$228$	−15.4314	−1.02197
$229$	−7.34625	−0.485454	−0.242727	−	0.970095i	$-0.578042\pi$
$229$	−7.34625	−0.485454	−0.242727	+	0.970095i	$0.578042\pi$
$230$	6.95464	0.458576
$231$	−0.743032	−0.0488879
$232$	3.27460	0.214988
$233$	5.20187	0.340786	0.170393	−	0.985376i	$-0.445496\pi$
$233$	5.20187	0.340786	0.170393	+	0.985376i	$0.445496\pi$
$234$	5.83756	0.381613
$235$	49.4774	3.22755
$236$	39.0289	2.54056
$237$	−4.43345	−0.287983
$238$	−1.51972	−0.0985086
$239$	19.1790	1.24058	0.620292	−	0.784371i	$-0.287014\pi$
$239$	19.1790	1.24058	0.620292	+	0.784371i	$0.287014\pi$
$240$	39.4669	2.54758
$241$	11.0632	0.712642	0.356321	−	0.934364i	$-0.384031\pi$
$241$	11.0632	0.712642	0.356321	+	0.934364i	$0.384031\pi$
$242$	−2.55392	−0.164172
$243$	13.3866	0.858754
$244$	25.6589	1.64264
$245$	−28.3545	−1.81150
$246$	−17.2183	−1.09780
$247$	−4.33505	−0.275833
$248$	−28.6811	−1.82125
$249$	−15.3620	−0.973525
$250$	−89.3781	−5.65277
$251$	31.1560	1.96655	0.983275	−	0.182129i	$-0.0582989\pi$
$251$	31.1560	1.96655	0.983275	+	0.182129i	$0.0582989\pi$
$252$	3.87736	0.244251
$253$	−0.638262	−0.0401272
$254$	−55.7494	−3.49803
$255$	−5.32746	−0.333618
$256$	−28.1261	−1.75788
$257$	9.88820	0.616809	0.308405	−	0.951255i	$-0.400205\pi$
$257$	9.88820	0.616809	0.308405	+	0.951255i	$0.400205\pi$
$258$	3.18904	0.198541
$259$	−5.78088	−0.359206
$260$	30.6106	1.89839
$261$	0.732343	0.0453309
$262$	10.2709	0.634536
$263$	−6.21163	−0.383026	−0.191513	−	0.981490i	$-0.561339\pi$
$263$	−6.21163	−0.383026	−0.191513	+	0.981490i	$0.561339\pi$
$264$	−8.04445	−0.495102
$265$	21.8919	1.34481
$266$	−4.15274	−0.254621
$267$	−13.9070	−0.851095
$268$	9.73444	0.594626
$269$	20.9420	1.27686	0.638429	−	0.769681i	$-0.279585\pi$
$269$	20.9420	1.27686	0.638429	+	0.769681i	$0.279585\pi$
$270$	60.4210	3.67711
$271$	23.6343	1.43568	0.717841	−	0.696207i	$-0.245131\pi$
$271$	23.6343	1.43568	0.717841	+	0.696207i	$0.245131\pi$
$272$	−7.40820	−0.449188
$273$	−1.17877	−0.0713425
$274$	26.9571	1.62854
$275$	13.2027	0.796151
$276$	−3.60440	−0.216959
$277$	−14.3862	−0.864384	−0.432192	−	0.901782i	$-0.642260\pi$
$277$	−14.3862	−0.864384	−0.432192	+	0.901782i	$0.642260\pi$
$278$	−44.3193	−2.65809
$279$	−6.41436	−0.384017
$280$	16.3556	0.977434
$281$	22.1269	1.31998	0.659989	−	0.751275i	$-0.270561\pi$
$281$	22.1269	1.31998	0.659989	+	0.751275i	$0.270561\pi$
$282$	−36.9828	−2.20229
$283$	5.55430	0.330169	0.165084	−	0.986279i	$-0.447210\pi$
$283$	5.55430	0.330169	0.165084	+	0.986279i	$0.447210\pi$
$284$	1.59473	0.0946299
$285$	−14.5577	−0.862322
$286$	−4.05164	−0.239578
$287$	−3.21282	−0.189647
$288$	8.69559	0.512393
$289$	1.00000	0.0588235
$290$	5.53847	0.325230
$291$	−15.0159	−0.880249
$292$	38.0216	2.22505
$293$	−23.8437	−1.39296	−0.696481	−	0.717575i	$-0.745252\pi$
$293$	−23.8437	−1.39296	−0.696481	+	0.717575i	$0.745252\pi$
$294$	21.1941	1.23607
$295$	36.8190	2.14369
$296$	−62.5868	−3.63778
$297$	−5.54514	−0.321762
$298$	−49.6716	−2.87740
$299$	−1.01256	−0.0585580
$300$	74.5582	4.30462
$301$	0.595052	0.0342982
$302$	56.6542	3.26009
$303$	−17.4147	−1.00045
$304$	−20.2434	−1.16104
$305$	24.2061	1.38604
$306$	−3.67967	−0.210353
$307$	−16.2035	−0.924780	−0.462390	−	0.886677i	$-0.653008\pi$
$307$	−16.2035	−0.924780	−0.462390	+	0.886677i	$0.653008\pi$
$308$	−2.69114	−0.153342
$309$	−1.76819	−0.100589
$310$	−48.5096	−2.75516
$311$	−7.70219	−0.436751	−0.218376	−	0.975865i	$-0.570076\pi$
$311$	−7.70219	−0.436751	−0.218376	+	0.975865i	$0.570076\pi$
$312$	−12.7620	−0.722506
$313$	4.43924	0.250921	0.125460	−	0.992099i	$-0.459959\pi$
$313$	4.43924	0.250921	0.125460	+	0.992099i	$0.459959\pi$
$314$	−24.5132	−1.38336
$315$	3.65782	0.206095
$316$	−16.0572	−0.903289
$317$	13.8184	0.776116	0.388058	−	0.921635i	$-0.373146\pi$
$317$	13.8184	0.776116	0.388058	+	0.921635i	$0.373146\pi$
$318$	−16.3635	−0.917618
$319$	−0.508293	−0.0284590
$320$	2.54830	0.142454
$321$	11.3242	0.632057
$322$	−0.969978	−0.0540548
$323$	2.73257	0.152044
$324$	−11.7665	−0.653696
$325$	20.9452	1.16183
$326$	13.8938	0.769506
$327$	−19.3300	−1.06895
$328$	−34.7836	−1.92060
$329$	−6.90072	−0.380449
$330$	−13.6059	−0.748981
$331$	−20.3626	−1.11923	−0.559614	−	0.828753i	$-0.689051\pi$
$331$	−20.3626	−1.11923	−0.559614	+	0.828753i	$0.689051\pi$
$332$	−55.6385	−3.05356
$333$	−13.9971	−0.767039
$334$	16.0707	0.879350
$335$	9.18327	0.501736
$336$	−5.50453	−0.300297
$337$	7.51500	0.409368	0.204684	−	0.978828i	$-0.434383\pi$
$337$	7.51500	0.409368	0.204684	+	0.978828i	$0.434383\pi$
$338$	26.7733	1.45628
$339$	−7.85569	−0.426663
$340$	−19.2952	−1.04643
$341$	4.45197	0.241088
$342$	−10.0550	−0.543710
$343$	8.12003	0.438440
$344$	6.44234	0.347348
$345$	−3.40032	−0.183067
$346$	53.0500	2.85199
$347$	−15.2044	−0.816213	−0.408107	−	0.912934i	$-0.633811\pi$
$347$	−15.2044	−0.816213	−0.408107	+	0.912934i	$0.633811\pi$
$348$	−2.87044	−0.153872
$349$	25.2028	1.34908	0.674538	−	0.738240i	$-0.264343\pi$
$349$	25.2028	1.34908	0.674538	+	0.738240i	$0.264343\pi$
$350$	20.0643	1.07248
$351$	−8.79701	−0.469550
$352$	−6.03530	−0.321682
$353$	−1.73988	−0.0926047	−0.0463024	−	0.998927i	$-0.514744\pi$
$353$	−1.73988	−0.0926047	−0.0463024	+	0.998927i	$0.514744\pi$
$354$	−27.5211	−1.46273
$355$	1.50444	0.0798472
$356$	−50.3689	−2.66955
$357$	0.743032	0.0393254
$358$	−20.8984	−1.10452
$359$	−1.08977	−0.0575157	−0.0287578	−	0.999586i	$-0.509155\pi$
$359$	−1.08977	−0.0575157	−0.0287578	+	0.999586i	$0.509155\pi$
$360$	39.6015	2.08718
$361$	−11.5330	−0.607003
$362$	−13.2518	−0.696497
$363$	1.24868	0.0655389
$364$	−4.26932	−0.223773
$365$	35.8688	1.87746
$366$	−18.0933	−0.945752
$367$	16.1938	0.845311	0.422655	−	0.906290i	$-0.361098\pi$
$367$	16.1938	0.845311	0.422655	+	0.906290i	$0.361098\pi$
$368$	−4.72838	−0.246484
$369$	−7.77914	−0.404966
$370$	−105.856	−5.50318
$371$	−3.05330	−0.158520
$372$	25.1412	1.30351
$373$	13.8301	0.716096	0.358048	−	0.933703i	$-0.383442\pi$
$373$	13.8301	0.716096	0.358048	+	0.933703i	$0.383442\pi$
$374$	2.55392	0.132060
$375$	43.6994	2.25663
$376$	−74.7108	−3.85291
$377$	−0.806375	−0.0415304
$378$	−8.42705	−0.433440
$379$	9.47920	0.486914	0.243457	−	0.969912i	$-0.421719\pi$
$379$	9.47920	0.486914	0.243457	+	0.969912i	$0.421719\pi$
$380$	−52.7255	−2.70476
$381$	27.2574	1.39644
$382$	−13.6394	−0.697854
$383$	28.8688	1.47513	0.737563	−	0.675278i	$-0.235977\pi$
$383$	28.8688	1.47513	0.737563	+	0.675278i	$0.235977\pi$
$384$	13.1676	0.671955
$385$	−2.53876	−0.129387
$386$	15.8666	0.807587
$387$	1.44079	0.0732394
$388$	−54.3852	−2.76099
$389$	9.35289	0.474210	0.237105	−	0.971484i	$-0.423801\pi$
$389$	9.35289	0.474210	0.237105	+	0.971484i	$0.423801\pi$
$390$	−21.5849	−1.09300
$391$	0.638262	0.0322783
$392$	42.8153	2.16250
$393$	−5.02171	−0.253312
$394$	52.4636	2.64308
$395$	−15.1480	−0.762181
$396$	−6.51601	−0.327442
$397$	−28.0321	−1.40689	−0.703446	−	0.710748i	$-0.748356\pi$
$397$	−28.0321	−1.40689	−0.703446	+	0.710748i	$0.748356\pi$
$398$	−40.6908	−2.03964
$399$	2.03039	0.101647
$400$	97.8081	4.89040
$401$	11.4546	0.572017	0.286008	−	0.958227i	$-0.407671\pi$
$401$	11.4546	0.572017	0.286008	+	0.958227i	$0.407671\pi$
$402$	−6.86421	−0.342355
$403$	7.06277	0.351822
$404$	−63.0732	−3.13801
$405$	−11.1003	−0.551578
$406$	−0.772462	−0.0383366
$407$	9.71491	0.481550
$408$	8.04445	0.398260
$409$	−19.6097	−0.969636	−0.484818	−	0.874615i	$-0.661114\pi$
$409$	−19.6097	−0.969636	−0.484818	+	0.874615i	$0.661114\pi$
$410$	−58.8310	−2.90546
$411$	−13.1801	−0.650126
$412$	−6.40409	−0.315507
$413$	−5.13523	−0.252688
$414$	−2.34859	−0.115427
$415$	−52.4882	−2.57655
$416$	−9.57462	−0.469434
$417$	21.6689	1.06113
$418$	6.97878	0.341343
$419$	13.6030	0.664550	0.332275	−	0.943182i	$-0.392184\pi$
$419$	13.6030	0.664550	0.332275	+	0.943182i	$0.392184\pi$
$420$	−14.3369	−0.699570
$421$	−20.7130	−1.00949	−0.504745	−	0.863268i	$-0.668414\pi$
$421$	−20.7130	−1.00949	−0.504745	+	0.863268i	$0.668414\pi$
$422$	−50.5687	−2.46165
$423$	−16.7086	−0.812399
$424$	−33.0567	−1.60537
$425$	−13.2027	−0.640424
$426$	−1.12452	−0.0544831
$427$	−3.37608	−0.163380
$428$	41.0145	1.98251
$429$	1.98096	0.0956415
$430$	10.8962	0.525462
$431$	24.4660	1.17849	0.589243	−	0.807956i	$-0.299426\pi$
$431$	24.4660	1.17849	0.589243	+	0.807956i	$0.299426\pi$
$432$	−41.0795	−1.97644
$433$	−35.1203	−1.68777	−0.843886	−	0.536523i	$-0.819738\pi$
$433$	−35.1203	−1.68777	−0.843886	+	0.536523i	$0.819738\pi$
$434$	6.76574	0.324766
$435$	−2.70791	−0.129834
$436$	−70.0101	−3.35288
$437$	1.74410	0.0834315
$438$	−26.8108	−1.28107
$439$	29.2098	1.39411	0.697055	−	0.717018i	$-0.254493\pi$
$439$	29.2098	1.39411	0.697055	+	0.717018i	$0.254493\pi$
$440$	−27.4860	−1.31034
$441$	9.57536	0.455970
$442$	4.05164	0.192717
$443$	30.2757	1.43844	0.719220	−	0.694783i	$-0.244499\pi$
$443$	30.2757	1.43844	0.719220	+	0.694783i	$0.244499\pi$
$444$	54.8621	2.60364
$445$	−47.5170	−2.25252
$446$	11.4645	0.542860
$447$	24.2858	1.14868
$448$	−0.355416	−0.0167918
$449$	−9.82167	−0.463513	−0.231757	−	0.972774i	$-0.574447\pi$
$449$	−9.82167	−0.463513	−0.231757	+	0.972774i	$0.574447\pi$
$450$	48.5814	2.29015
$451$	5.39922	0.254239
$452$	−28.4520	−1.33827
$453$	−27.6998	−1.30145
$454$	−47.2575	−2.21790
$455$	−4.02759	−0.188816
$456$	21.9820	1.02940
$457$	19.5742	0.915643	0.457822	−	0.889044i	$-0.348630\pi$
$457$	19.5742	0.915643	0.457822	+	0.889044i	$0.348630\pi$
$458$	18.7618	0.876679
$459$	5.54514	0.258825
$460$	−12.3154	−0.574208
$461$	−1.20202	−0.0559836	−0.0279918	−	0.999608i	$-0.508911\pi$
$461$	−1.20202	−0.0559836	−0.0279918	+	0.999608i	$0.508911\pi$
$462$	1.89765	0.0882865
$463$	14.1508	0.657643	0.328821	−	0.944392i	$-0.393349\pi$
$463$	14.1508	0.657643	0.328821	+	0.944392i	$0.393349\pi$
$464$	−3.76554	−0.174811
$465$	23.7177	1.09988
$466$	−13.2852	−0.615424
$467$	−19.5043	−0.902552	−0.451276	−	0.892384i	$-0.649031\pi$
$467$	−19.5043	−0.902552	−0.451276	+	0.892384i	$0.649031\pi$
$468$	−10.3372	−0.477839
$469$	−1.28081	−0.0591423
$470$	−126.362	−5.82862
$471$	11.9852	0.552249
$472$	−55.5967	−2.55904
$473$	−1.00000	−0.0459800
$474$	11.3227	0.520068
$475$	−36.0773	−1.65534
$476$	2.69114	0.123348
$477$	−7.39292	−0.338498
$478$	−48.9816	−2.24037
$479$	−9.90090	−0.452384	−0.226192	−	0.974083i	$-0.572628\pi$
$479$	−9.90090	−0.452384	−0.226192	+	0.974083i	$0.572628\pi$
$480$	−32.1528	−1.46757
$481$	15.4121	0.702731
$482$	−28.2545	−1.28696
$483$	0.474249	0.0215791
$484$	4.52253	0.205569
$485$	−51.3059	−2.32968
$486$	−34.1885	−1.55082
$487$	−24.3005	−1.10116	−0.550580	−	0.834783i	$-0.685593\pi$
$487$	−24.3005	−1.10116	−0.550580	+	0.834783i	$0.685593\pi$
$488$	−36.5512	−1.65459
$489$	−6.79305	−0.307193
$490$	72.4153	3.27139
$491$	23.3672	1.05454	0.527272	−	0.849696i	$-0.323215\pi$
$491$	23.3672	1.05454	0.527272	+	0.849696i	$0.323215\pi$
$492$	30.4905	1.37462
$493$	0.508293	0.0228924
$494$	11.0714	0.498126
$495$	−6.14707	−0.276290
$496$	32.9811	1.48090
$497$	−0.209827	−0.00941202
$498$	39.2333	1.75809
$499$	−15.4943	−0.693619	−0.346809	−	0.937936i	$-0.612735\pi$
$499$	−15.4943	−0.693619	−0.346809	+	0.937936i	$0.612735\pi$
$500$	158.272	7.07814
$501$	−7.85741	−0.351043
$502$	−79.5701	−3.55139
$503$	1.57361	0.0701640	0.0350820	−	0.999384i	$-0.488831\pi$
$503$	1.57361	0.0701640	0.0350820	+	0.999384i	$0.488831\pi$
$504$	−5.52331	−0.246028
$505$	−59.5019	−2.64780
$506$	1.63007	0.0724656
$507$	−13.0902	−0.581357
$508$	98.7219	4.38008
$509$	−6.85295	−0.303752	−0.151876	−	0.988400i	$-0.548531\pi$
$509$	−6.85295	−0.303752	−0.151876	+	0.988400i	$0.548531\pi$
$510$	13.6059	0.602480
$511$	−5.00270	−0.221306
$512$	50.7417	2.24249
$513$	15.1525	0.668999
$514$	−25.2537	−1.11389
$515$	−6.04149	−0.266220
$516$	−5.64721	−0.248604
$517$	11.5968	0.510028
$518$	14.7639	0.648689
$519$	−25.9376	−1.13853
$520$	−43.6048	−1.91220
$521$	2.96156	0.129748	0.0648742	−	0.997893i	$-0.479335\pi$
$521$	2.96156	0.129748	0.0648742	+	0.997893i	$0.479335\pi$
$522$	−1.87035	−0.0818630
$523$	1.03749	0.0453661	0.0226830	−	0.999743i	$-0.492779\pi$
$523$	1.03749	0.0453661	0.0226830	+	0.999743i	$0.492779\pi$
$524$	−18.1878	−0.794538
$525$	−9.81000	−0.428144
$526$	15.8640	0.691705
$527$	−4.45197	−0.193931
$528$	9.25050	0.402576
$529$	−22.5926	−0.982288
$530$	−55.9102	−2.42858
$531$	−12.4338	−0.539583
$532$	7.35373	0.318825
$533$	8.56552	0.371014
$534$	35.5175	1.53699
$535$	38.6922	1.67281
$536$	−13.8667	−0.598951
$537$	10.2178	0.440932
$538$	−53.4843	−2.30587
$539$	−6.64591	−0.286260
$540$	−106.994	−4.60431
$541$	−33.4088	−1.43636	−0.718178	−	0.695859i	$-0.755024\pi$
$541$	−33.4088	−1.43636	−0.718178	+	0.695859i	$0.755024\pi$
$542$	−60.3602	−2.59269
$543$	6.47915	0.278047
$544$	6.03530	0.258761
$545$	−66.0461	−2.82911
$546$	3.01049	0.128837
$547$	−34.8133	−1.48851	−0.744254	−	0.667896i	$-0.767195\pi$
$547$	−34.8133	−1.48851	−0.744254	+	0.667896i	$0.767195\pi$
$548$	−47.7361	−2.03919
$549$	−8.17444	−0.348876
$550$	−33.7186	−1.43777
$551$	1.38895	0.0591712
$552$	5.13447	0.218538
$553$	2.11273	0.0898424
$554$	36.7413	1.56099
$555$	51.7558	2.19691
$556$	78.4813	3.32835
$557$	2.39432	0.101450	0.0507252	−	0.998713i	$-0.483847\pi$
$557$	2.39432	0.101450	0.0507252	+	0.998713i	$0.483847\pi$
$558$	16.3818	0.693496
$559$	−1.58644	−0.0670991
$560$	−18.8077	−0.794770
$561$	−1.24868	−0.0527195
$562$	−56.5104	−2.38375
$563$	−11.6365	−0.490418	−0.245209	−	0.969470i	$-0.578857\pi$
$563$	−11.6365	−0.490418	−0.245209	+	0.969470i	$0.578857\pi$
$564$	65.4897	2.75761
$565$	−26.8411	−1.12921
$566$	−14.1853	−0.596251
$567$	1.54818	0.0650175
$568$	−2.27170	−0.0953182
$569$	18.2554	0.765305	0.382653	−	0.923892i	$-0.375011\pi$
$569$	18.2554	0.765305	0.382653	+	0.923892i	$0.375011\pi$
$570$	37.1792	1.55726
$571$	46.6660	1.95291	0.976455	−	0.215722i	$-0.0692104\pi$
$571$	46.6660	1.95291	0.976455	+	0.215722i	$0.0692104\pi$
$572$	7.17470	0.299989
$573$	6.66869	0.278589
$574$	8.20529	0.342482
$575$	−8.42677	−0.351421
$576$	−0.860564	−0.0358568
$577$	3.14319	0.130853	0.0654264	−	0.997857i	$-0.479159\pi$
$577$	3.14319	0.130853	0.0654264	+	0.997857i	$0.479159\pi$
$578$	−2.55392	−0.106229
$579$	−7.75761	−0.322395
$580$	−9.80761	−0.407239
$581$	7.32064	0.303712
$582$	38.3495	1.58964
$583$	5.13116	0.212511
$584$	−54.1618	−2.24123
$585$	−9.75193	−0.403193
$586$	60.8950	2.51555
$587$	26.0128	1.07366	0.536832	−	0.843689i	$-0.319621\pi$
$587$	26.0128	1.07366	0.536832	+	0.843689i	$0.319621\pi$
$588$	−37.5308	−1.54775
$589$	−12.1653	−0.501264
$590$	−94.0331	−3.87128
$591$	−25.6509	−1.05514
$592$	71.9700	2.95795
$593$	18.3272	0.752606	0.376303	−	0.926497i	$-0.377195\pi$
$593$	18.3272	0.752606	0.376303	+	0.926497i	$0.377195\pi$
$594$	14.1619	0.581068
$595$	2.53876	0.104079
$596$	87.9593	3.60295
$597$	19.8948	0.814241
$598$	2.58601	0.105750
$599$	−12.2063	−0.498735	−0.249368	−	0.968409i	$-0.580223\pi$
$599$	−12.2063	−0.498735	−0.249368	+	0.968409i	$0.580223\pi$
$600$	−106.208	−4.33593
$601$	43.2061	1.76241	0.881206	−	0.472732i	$-0.156732\pi$
$601$	43.2061	1.76241	0.881206	+	0.472732i	$0.156732\pi$
$602$	−1.51972	−0.0619391
$603$	−3.10120	−0.126291
$604$	−100.324	−4.08213
$605$	4.26646	0.173456
$606$	44.4758	1.80671
$607$	−0.416530	−0.0169065	−0.00845323	−	0.999964i	$-0.502691\pi$
$607$	−0.416530	−0.0169065	−0.00845323	+	0.999964i	$0.502691\pi$
$608$	16.4919	0.668834
$609$	0.377678	0.0153043
$610$	−61.8206	−2.50304
$611$	18.3976	0.744289
$612$	6.51601	0.263394
$613$	−34.2794	−1.38453	−0.692266	−	0.721642i	$-0.743387\pi$
$613$	−34.2794	−1.38453	−0.692266	+	0.721642i	$0.743387\pi$
$614$	41.3824	1.67006
$615$	28.7641	1.15988
$616$	3.83353	0.154457
$617$	36.2627	1.45988	0.729941	−	0.683511i	$-0.239548\pi$
$617$	36.2627	1.45988	0.729941	+	0.683511i	$0.239548\pi$
$618$	4.51582	0.181653
$619$	12.5451	0.504229	0.252115	−	0.967697i	$-0.418874\pi$
$619$	12.5451	0.504229	0.252115	+	0.967697i	$0.418874\pi$
$620$	85.9016	3.44989
$621$	3.53925	0.142025
$622$	19.6708	0.788728
$623$	6.62729	0.265517
$624$	14.6753	0.587483
$625$	83.2972	3.33189
$626$	−11.3375	−0.453137
$627$	−3.41212	−0.136267
$628$	43.4084	1.73218
$629$	−9.71491	−0.387359
$630$	−9.34181	−0.372186
$631$	−44.7652	−1.78208	−0.891038	−	0.453928i	$-0.850022\pi$
$631$	−44.7652	−1.78208	−0.891038	+	0.453928i	$0.850022\pi$
$632$	22.8735	0.909859
$633$	24.7244	0.982708
$634$	−35.2910	−1.40159
$635$	93.1322	3.69584
$636$	28.9767	1.14900
$637$	−10.5433	−0.417741
$638$	1.29814	0.0513939
$639$	−0.508050	−0.0200982
$640$	44.9905	1.77841
$641$	10.3472	0.408690	0.204345	−	0.978899i	$-0.434493\pi$
$641$	10.3472	0.408690	0.204345	+	0.978899i	$0.434493\pi$
$642$	−28.9212	−1.14143
$643$	33.5277	1.32220	0.661101	−	0.750297i	$-0.270089\pi$
$643$	33.5277	1.32220	0.661101	+	0.750297i	$0.270089\pi$
$644$	1.71765	0.0676850
$645$	−5.32746	−0.209768
$646$	−6.97878	−0.274577
$647$	49.0109	1.92682	0.963408	−	0.268040i	$-0.0863759\pi$
$647$	49.0109	1.92682	0.963408	+	0.268040i	$0.0863759\pi$
$648$	16.7614	0.658451
$649$	8.62988	0.338753
$650$	−53.4925	−2.09815
$651$	−3.30796	−0.129649
$652$	−24.6033	−0.963541
$653$	0.500721	0.0195947	0.00979737	−	0.999952i	$-0.496881\pi$
$653$	0.500721	0.0195947	0.00979737	+	0.999952i	$0.496881\pi$
$654$	49.3674	1.93042
$655$	−17.1580	−0.670419
$656$	39.9985	1.56168
$657$	−12.1129	−0.472571
$658$	17.6239	0.687051
$659$	−17.1235	−0.667035	−0.333518	−	0.942744i	$-0.608236\pi$
$659$	−17.1235	−0.667035	−0.333518	+	0.942744i	$0.608236\pi$
$660$	24.0936	0.937841
$661$	−4.75895	−0.185102	−0.0925508	−	0.995708i	$-0.529502\pi$
$661$	−4.75895	−0.185102	−0.0925508	+	0.995708i	$0.529502\pi$
$662$	52.0045	2.02121
$663$	−1.98096	−0.0769340
$664$	79.2571	3.07577
$665$	6.93736	0.269019
$666$	35.7476	1.38519
$667$	0.324424	0.0125618
$668$	−28.4583	−1.10108
$669$	−5.60531	−0.216714
$670$	−23.4534	−0.906083
$671$	5.67358	0.219026
$672$	4.48442	0.172990
$673$	−6.84253	−0.263760	−0.131880	−	0.991266i	$-0.542101\pi$
$673$	−6.84253	−0.263760	−0.131880	+	0.991266i	$0.542101\pi$
$674$	−19.1927	−0.739276
$675$	−73.2107	−2.81788
$676$	−47.4107	−1.82349
$677$	12.6953	0.487920	0.243960	−	0.969785i	$-0.421553\pi$
$677$	12.6953	0.487920	0.243960	+	0.969785i	$0.421553\pi$
$678$	20.0628	0.770509
$679$	7.15574	0.274612
$680$	27.4860	1.05404
$681$	23.1055	0.885404
$682$	−11.3700	−0.435380
$683$	34.5924	1.32364	0.661820	−	0.749663i	$-0.269784\pi$
$683$	34.5924	1.32364	0.661820	+	0.749663i	$0.269784\pi$
$684$	17.8055	0.680809
$685$	−45.0333	−1.72063
$686$	−20.7379	−0.791778
$687$	−9.17314	−0.349977
$688$	−7.40820	−0.282435
$689$	8.14025	0.310119
$690$	8.68415	0.330600
$691$	−12.0188	−0.457218	−0.228609	−	0.973518i	$-0.573418\pi$
$691$	−12.0188	−0.457218	−0.228609	+	0.973518i	$0.573418\pi$
$692$	−93.9418	−3.57113
$693$	0.857344	0.0325678
$694$	38.8308	1.47400
$695$	74.0376	2.80841
$696$	4.08894	0.154991
$697$	−5.39922	−0.204510
$698$	−64.3661	−2.43629
$699$	6.49549	0.245682
$700$	−35.5302	−1.34292
$701$	−4.43916	−0.167665	−0.0838325	−	0.996480i	$-0.526716\pi$
$701$	−4.43916	−0.167665	−0.0838325	+	0.996480i	$0.526716\pi$
$702$	22.4669	0.847959
$703$	−26.5467	−1.00123
$704$	0.597286	0.0225111
$705$	61.7816	2.32683
$706$	4.44353	0.167235
$707$	8.29885	0.312111
$708$	48.7347	1.83156
$709$	25.3573	0.952314	0.476157	−	0.879360i	$-0.342029\pi$
$709$	25.3573	0.952314	0.476157	+	0.879360i	$0.342029\pi$
$710$	−3.84221	−0.144196
$711$	5.11552	0.191847
$712$	71.7506	2.68897
$713$	−2.84153	−0.106416
$714$	−1.89765	−0.0710176
$715$	6.76847	0.253126
$716$	37.0073	1.38303
$717$	23.9485	0.894372
$718$	2.78318	0.103867
$719$	13.9187	0.519080	0.259540	−	0.965732i	$-0.416429\pi$
$719$	13.9187	0.519080	0.259540	+	0.965732i	$0.416429\pi$
$720$	−45.5387	−1.69713
$721$	0.842618	0.0313808
$722$	29.4545	1.09618
$723$	13.8144	0.513763
$724$	23.4664	0.872123
$725$	−6.71083	−0.249234
$726$	−3.18904	−0.118356
$727$	−48.9187	−1.81430	−0.907148	−	0.420812i	$-0.861745\pi$
$727$	−48.9187	−1.81430	−0.907148	+	0.420812i	$0.861745\pi$
$728$	6.08165	0.225401
$729$	24.5210	0.908184
$730$	−91.6062	−3.39050
$731$	1.00000	0.0369863
$732$	32.0399	1.18423
$733$	−40.9840	−1.51378	−0.756890	−	0.653543i	$-0.773282\pi$
$733$	−40.9840	−1.51378	−0.756890	+	0.653543i	$0.773282\pi$
$734$	−41.3578	−1.52654
$735$	−35.4058	−1.30596
$736$	3.85210	0.141990
$737$	2.15243	0.0792859
$738$	19.8673	0.731326
$739$	0.342822	0.0126109	0.00630546	−	0.999980i	$-0.497993\pi$
$739$	0.342822	0.0126109	0.00630546	+	0.999980i	$0.497993\pi$
$740$	187.451	6.89083
$741$	−5.41311	−0.198856
$742$	7.79791	0.286270
$743$	−20.4319	−0.749574	−0.374787	−	0.927111i	$-0.622284\pi$
$743$	−20.4319	−0.749574	−0.374787	+	0.927111i	$0.622284\pi$
$744$	−35.8137	−1.31299
$745$	82.9790	3.04012
$746$	−35.3211	−1.29320
$747$	17.7254	0.648537
$748$	−4.52253	−0.165360
$749$	−5.39649	−0.197183
$750$	−111.605	−4.07524
$751$	9.27015	0.338273	0.169136	−	0.985593i	$-0.445902\pi$
$751$	9.27015	0.338273	0.169136	+	0.985593i	$0.445902\pi$
$752$	85.9117	3.13288
$753$	38.9040	1.41774
$754$	2.05942	0.0749996
$755$	−94.6438	−3.44444
$756$	14.9227	0.542735
$757$	32.0377	1.16443	0.582215	−	0.813035i	$-0.302186\pi$
$757$	32.0377	1.16443	0.582215	+	0.813035i	$0.302186\pi$
$758$	−24.2092	−0.879316
$759$	−0.796988	−0.0289288
$760$	75.1075	2.72443
$761$	−2.99035	−0.108400	−0.0542000	−	0.998530i	$-0.517261\pi$
$761$	−2.99035	−0.108400	−0.0542000	+	0.998530i	$0.517261\pi$
$762$	−69.6134	−2.52183
$763$	9.21159	0.333482
$764$	24.1529	0.873822
$765$	6.14707	0.222248
$766$	−73.7287	−2.66393
$767$	13.6908	0.494345
$768$	−35.1206	−1.26731
$769$	55.1837	1.98997	0.994987	−	0.100007i	$-0.0318866\pi$
$769$	55.1837	1.98997	0.994987	+	0.100007i	$0.0318866\pi$
$770$	6.48381	0.233660
$771$	12.3472	0.444675
$772$	−28.0968	−1.01123
$773$	3.11539	0.112053	0.0560264	−	0.998429i	$-0.482157\pi$
$773$	3.11539	0.112053	0.0560264	+	0.998429i	$0.482157\pi$
$774$	−3.67967	−0.132263
$775$	58.7780	2.11137
$776$	77.4718	2.78107
$777$	−7.21849	−0.258962
$778$	−23.8866	−0.856375
$779$	−14.7538	−0.528608
$780$	38.2229	1.36860
$781$	0.352619	0.0126177
$782$	−1.63007	−0.0582913
$783$	2.81856	0.100727
$784$	−49.2343	−1.75837
$785$	40.9506	1.46159
$786$	12.8251	0.457455
$787$	17.7449	0.632537	0.316269	−	0.948670i	$-0.397570\pi$
$787$	17.7449	0.632537	0.316269	+	0.948670i	$0.397570\pi$
$788$	−92.9033	−3.30954
$789$	−7.75636	−0.276134
$790$	38.6870	1.37642
$791$	3.74358	0.133106
$792$	9.28206	0.329824
$793$	9.00078	0.319627
$794$	71.5920	2.54070
$795$	27.3360	0.969509
$796$	72.0558	2.55395
$797$	35.7188	1.26522	0.632612	−	0.774469i	$-0.281983\pi$
$797$	35.7188	1.26522	0.632612	+	0.774469i	$0.281983\pi$
$798$	−5.18546	−0.183563
$799$	−11.5968	−0.410266
$800$	−79.6821	−2.81719
$801$	16.0466	0.566977
$802$	−29.2542	−1.03300
$803$	8.40716	0.296682
$804$	12.1552	0.428682
$805$	1.62040	0.0571115
$806$	−18.0378	−0.635354
$807$	26.1500	0.920522
$808$	89.8478	3.16083
$809$	−13.8715	−0.487695	−0.243848	−	0.969814i	$-0.578410\pi$
$809$	−13.8715	−0.487695	−0.243848	+	0.969814i	$0.578410\pi$
$810$	28.3493	0.996093
$811$	−46.5306	−1.63391	−0.816955	−	0.576701i	$-0.804340\pi$
$811$	−46.5306	−1.63391	−0.816955	+	0.576701i	$0.804340\pi$
$812$	1.36789	0.0480034
$813$	29.5118	1.03502
$814$	−24.8111	−0.869630
$815$	−23.2103	−0.813020
$816$	−9.25050	−0.323832
$817$	2.73257	0.0956006
$818$	50.0816	1.75106
$819$	1.36012	0.0475265
$820$	104.179	3.63809
$821$	−8.74519	−0.305209	−0.152605	−	0.988287i	$-0.548766\pi$
$821$	−8.74519	−0.305209	−0.152605	+	0.988287i	$0.548766\pi$
$822$	33.6609	1.17406
$823$	−40.8917	−1.42540	−0.712698	−	0.701471i	$-0.752527\pi$
$823$	−40.8917	−1.42540	−0.712698	+	0.701471i	$0.752527\pi$
$824$	9.12263	0.317802
$825$	16.4860	0.573968
$826$	13.1150	0.456329
$827$	−25.2317	−0.877393	−0.438696	−	0.898635i	$-0.644560\pi$
$827$	−25.2317	−0.877393	−0.438696	+	0.898635i	$0.644560\pi$
$828$	4.15892	0.144533
$829$	−7.05098	−0.244891	−0.122445	−	0.992475i	$-0.539074\pi$
$829$	−7.05098	−0.244891	−0.122445	+	0.992475i	$0.539074\pi$
$830$	134.051	4.65298
$831$	−17.9638	−0.623158
$832$	0.947557	0.0328506
$833$	6.64591	0.230267
$834$	−55.3408	−1.91629
$835$	−26.8469	−0.929076
$836$	−12.3581	−0.427415
$837$	−24.6868	−0.853301
$838$	−34.7410	−1.20011
$839$	−32.1303	−1.10926	−0.554630	−	0.832097i	$-0.687140\pi$
$839$	−32.1303	−1.10926	−0.554630	+	0.832097i	$0.687140\pi$
$840$	20.4230	0.704659
$841$	−28.7416	−0.991091
$842$	52.8995	1.82304
$843$	27.6295	0.951609
$844$	89.5479	3.08237
$845$	−44.7262	−1.53863
$846$	42.6725	1.46711
$847$	−0.595052	−0.0204462
$848$	38.0127	1.30536
$849$	6.93557	0.238028
$850$	33.7186	1.15654
$851$	−6.20066	−0.212556
$852$	1.99131	0.0682213
$853$	−27.8399	−0.953221	−0.476610	−	0.879115i	$-0.658135\pi$
$853$	−27.8399	−0.953221	−0.476610	+	0.879115i	$0.658135\pi$
$854$	8.62224	0.295047
$855$	16.7973	0.574456
$856$	−58.4252	−1.99693
$857$	30.5580	1.04384	0.521921	−	0.852994i	$-0.325215\pi$
$857$	30.5580	1.04384	0.521921	+	0.852994i	$0.325215\pi$
$858$	−5.05921	−0.172719
$859$	−18.3811	−0.627156	−0.313578	−	0.949563i	$-0.601528\pi$
$859$	−18.3811	−0.627156	−0.313578	+	0.949563i	$0.601528\pi$
$860$	−19.2952	−0.657960
$861$	−4.01179	−0.136721
$862$	−62.4843	−2.12822
$863$	15.7089	0.534738	0.267369	−	0.963594i	$-0.413846\pi$
$863$	15.7089	0.534738	0.267369	+	0.963594i	$0.413846\pi$
$864$	33.4666	1.13856
$865$	−88.6227	−3.01326
$866$	89.6945	3.04794
$867$	1.24868	0.0424075
$868$	−11.9809	−0.406657
$869$	−3.55050	−0.120442
$870$	6.91580	0.234467
$871$	3.41470	0.115703
$872$	99.7295	3.37727
$873$	17.3261	0.586398
$874$	−4.45429	−0.150669
$875$	−20.8247	−0.704002
$876$	47.4770	1.60410
$877$	28.9421	0.977307	0.488653	−	0.872478i	$-0.337488\pi$
$877$	28.9421	0.977307	0.488653	+	0.872478i	$0.337488\pi$
$878$	−74.5997	−2.51762
$879$	−29.7732	−1.00423
$880$	31.6068	1.06546
$881$	31.9419	1.07615	0.538074	−	0.842897i	$-0.319152\pi$
$881$	31.9419	1.07615	0.538074	+	0.842897i	$0.319152\pi$
$882$	−24.4547	−0.823434
$883$	−57.2850	−1.92780	−0.963898	−	0.266273i	$-0.914208\pi$
$883$	−57.2850	−1.92780	−0.963898	+	0.266273i	$0.914208\pi$
$884$	−7.17470	−0.241311
$885$	45.9753	1.54544
$886$	−77.3217	−2.59767
$887$	25.5219	0.856943	0.428471	−	0.903555i	$-0.359052\pi$
$887$	25.5219	0.856943	0.428471	+	0.903555i	$0.359052\pi$
$888$	−78.1511	−2.62258
$889$	−12.9893	−0.435649
$890$	121.355	4.06782
$891$	−2.60176	−0.0871622
$892$	−20.3015	−0.679745
$893$	−31.6892	−1.06044
$894$	−62.0242	−2.07440
$895$	34.9119	1.16698
$896$	−6.27492	−0.209631
$897$	−1.26437	−0.0422161
$898$	25.0838	0.837057
$899$	−2.26291	−0.0754722
$900$	−86.0288	−2.86763
$901$	−5.13116	−0.170944
$902$	−13.7892	−0.459130
$903$	0.743032	0.0247265
$904$	40.5300	1.34801
$905$	22.1377	0.735884
$906$	70.7432	2.35029
$907$	−35.4369	−1.17666	−0.588332	−	0.808620i	$-0.700215\pi$
$907$	−35.4369	−1.17666	−0.588332	+	0.808620i	$0.700215\pi$
$908$	83.6843	2.77716
$909$	20.0939	0.666472
$910$	10.2862	0.340983
$911$	−20.2300	−0.670250	−0.335125	−	0.942174i	$-0.608779\pi$
$911$	−20.2300	−0.670250	−0.335125	+	0.942174i	$0.608779\pi$
$912$	−25.2777	−0.837027
$913$	−12.3025	−0.407154
$914$	−49.9911	−1.65356
$915$	30.2258	0.999233
$916$	−33.2236	−1.09774
$917$	2.39306	0.0790259
$918$	−14.1619	−0.467411
$919$	17.9108	0.590822	0.295411	−	0.955370i	$-0.404543\pi$
$919$	17.9108	0.590822	0.295411	+	0.955370i	$0.404543\pi$
$920$	17.5433	0.578385
$921$	−20.2330	−0.666700
$922$	3.06987	0.101101
$923$	0.559408	0.0184131
$924$	−3.36038	−0.110548
$925$	128.263	4.21726
$926$	−36.1400	−1.18764
$927$	2.04022	0.0670096
$928$	3.06770	0.100702
$929$	−38.8923	−1.27601	−0.638007	−	0.770031i	$-0.720241\pi$
$929$	−38.8923	−1.27601	−0.638007	+	0.770031i	$0.720241\pi$
$930$	−60.5732	−1.98627
$931$	18.1604	0.595184
$932$	23.5256	0.770607
$933$	−9.61760	−0.314866
$934$	49.8126	1.62992
$935$	−4.26646	−0.139528
$936$	14.7254	0.481315
$937$	32.2995	1.05518	0.527589	−	0.849500i	$-0.323096\pi$
$937$	32.2995	1.05518	0.527589	+	0.849500i	$0.323096\pi$
$938$	3.27109	0.106805
$939$	5.54321	0.180896
$940$	223.763	7.29834
$941$	30.8418	1.00541	0.502707	−	0.864457i	$-0.332337\pi$
$941$	30.8418	1.00541	0.502707	+	0.864457i	$0.332337\pi$
$942$	−30.6093	−0.997304
$943$	−3.44612	−0.112221
$944$	63.9319	2.08081
$945$	14.0778	0.457951
$946$	2.55392	0.0830352
$947$	−4.39935	−0.142960	−0.0714799	−	0.997442i	$-0.522772\pi$
$947$	−4.39935	−0.142960	−0.0714799	+	0.997442i	$0.522772\pi$
$948$	−20.0504	−0.651206
$949$	13.3374	0.432951
$950$	92.1386	2.98937
$951$	17.2548	0.559524
$952$	−3.83353	−0.124245
$953$	−19.2614	−0.623940	−0.311970	−	0.950092i	$-0.600989\pi$
$953$	−19.2614	−0.623940	−0.311970	+	0.950092i	$0.600989\pi$
$954$	18.8809	0.611293
$955$	22.7854	0.737317
$956$	86.7374	2.80529
$957$	−0.634697	−0.0205168
$958$	25.2861	0.816958
$959$	6.28088	0.202820
$960$	3.18202	0.102699
$961$	−11.1799	−0.360643
$962$	−39.3613	−1.26906
$963$	−13.0664	−0.421060
$964$	50.0335	1.61147
$965$	−26.5059	−0.853256
$966$	−1.21120	−0.0389696
$967$	−17.6122	−0.566371	−0.283185	−	0.959065i	$-0.591391\pi$
$967$	−17.6122	−0.566371	−0.283185	+	0.959065i	$0.591391\pi$
$968$	−6.44234	−0.207065
$969$	3.41212	0.109613
$970$	131.031	4.20716
$971$	−15.8140	−0.507496	−0.253748	−	0.967270i	$-0.581663\pi$
$971$	−15.8140	−0.507496	−0.253748	+	0.967270i	$0.581663\pi$
$972$	60.5415	1.94187
$973$	−10.3262	−0.331042
$974$	62.0616	1.98858
$975$	26.1539	0.837596
$976$	42.0310	1.34538
$977$	−30.3631	−0.971401	−0.485701	−	0.874125i	$-0.661435\pi$
$977$	−30.3631	−0.971401	−0.485701	+	0.874125i	$0.661435\pi$
$978$	17.3489	0.554758
$979$	−11.1373	−0.355951
$980$	−128.234	−4.09629
$981$	22.3039	0.712108
$982$	−59.6779	−1.90440
$983$	−2.59855	−0.0828810	−0.0414405	−	0.999141i	$-0.513195\pi$
$983$	−2.59855	−0.0828810	−0.0414405	+	0.999141i	$0.513195\pi$
$984$	−43.4338	−1.38462
$985$	−87.6431	−2.79254
$986$	−1.29814	−0.0413413
$987$	−8.61681	−0.274276
$988$	−19.6054	−0.623731
$989$	0.638262	0.0202956
$990$	15.6991	0.498952
$991$	−42.3759	−1.34611	−0.673057	−	0.739591i	$-0.735019\pi$
$991$	−42.3759	−1.34611	−0.673057	+	0.739591i	$0.735019\pi$
$992$	−26.8690	−0.853091
$993$	−25.4264	−0.806883
$994$	0.535882	0.0169971
$995$	67.9760	2.15498
$996$	−69.4749	−2.20140
$997$	4.92344	0.155927	0.0779634	−	0.996956i	$-0.475158\pi$
$997$	4.92344	0.155927	0.0779634	+	0.996956i	$0.475158\pi$
$998$	39.5712	1.25260
$999$	−53.8705	−1.70439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.5	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.5	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55392 q^{2} +1.24868 q^{3} +4.52253 q^{4} +4.26646 q^{5} -3.18904 q^{6} -0.595052 q^{7} -6.44234 q^{8} -1.44079 q^{9} +O(q^{10})\)	\(q-2.55392 q^{2} +1.24868 q^{3} +4.52253 q^{4} +4.26646 q^{5} -3.18904 q^{6} -0.595052 q^{7} -6.44234 q^{8} -1.44079 q^{9} -10.8962 q^{10} +1.00000 q^{11} +5.64721 q^{12} +1.58644 q^{13} +1.51972 q^{14} +5.32746 q^{15} +7.40820 q^{16} -1.00000 q^{17} +3.67967 q^{18} -2.73257 q^{19} +19.2952 q^{20} -0.743032 q^{21} -2.55392 q^{22} -0.638262 q^{23} -8.04445 q^{24} +13.2027 q^{25} -4.05164 q^{26} -5.54514 q^{27} -2.69114 q^{28} -0.508293 q^{29} -13.6059 q^{30} +4.45197 q^{31} -6.03530 q^{32} +1.24868 q^{33} +2.55392 q^{34} -2.53876 q^{35} -6.51601 q^{36} +9.71491 q^{37} +6.97878 q^{38} +1.98096 q^{39} -27.4860 q^{40} +5.39922 q^{41} +1.89765 q^{42} -1.00000 q^{43} +4.52253 q^{44} -6.14707 q^{45} +1.63007 q^{46} +11.5968 q^{47} +9.25050 q^{48} -6.64591 q^{49} -33.7186 q^{50} -1.24868 q^{51} +7.17470 q^{52} +5.13116 q^{53} +14.1619 q^{54} +4.26646 q^{55} +3.83353 q^{56} -3.41212 q^{57} +1.29814 q^{58} +8.62988 q^{59} +24.0936 q^{60} +5.67358 q^{61} -11.3700 q^{62} +0.857344 q^{63} +0.597286 q^{64} +6.76847 q^{65} -3.18904 q^{66} +2.15243 q^{67} -4.52253 q^{68} -0.796988 q^{69} +6.48381 q^{70} +0.352619 q^{71} +9.28206 q^{72} +8.40716 q^{73} -24.8111 q^{74} +16.4860 q^{75} -12.3581 q^{76} -0.595052 q^{77} -5.05921 q^{78} -3.55050 q^{79} +31.6068 q^{80} -2.60176 q^{81} -13.7892 q^{82} -12.3025 q^{83} -3.36038 q^{84} -4.26646 q^{85} +2.55392 q^{86} -0.634697 q^{87} -6.44234 q^{88} -11.1373 q^{89} +15.6991 q^{90} -0.944012 q^{91} -2.88656 q^{92} +5.55911 q^{93} -29.6174 q^{94} -11.6584 q^{95} -7.53618 q^{96} -12.0254 q^{97} +16.9732 q^{98} -1.44079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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