LMFDB - Embedded newform 8007.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74837 q^{2} +1.00000 q^{3} +5.55354 q^{4} +2.55432 q^{5} -2.74837 q^{6} -2.04110 q^{7} -9.76645 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.74837 q^{2} +1.00000 q^{3} +5.55354 q^{4} +2.55432 q^{5} -2.74837 q^{6} -2.04110 q^{7} -9.76645 q^{8} +1.00000 q^{9} -7.02023 q^{10} -5.80879 q^{11} +5.55354 q^{12} -2.32772 q^{13} +5.60969 q^{14} +2.55432 q^{15} +15.7347 q^{16} -1.00000 q^{17} -2.74837 q^{18} -6.67248 q^{19} +14.1855 q^{20} -2.04110 q^{21} +15.9647 q^{22} -6.56568 q^{23} -9.76645 q^{24} +1.52457 q^{25} +6.39743 q^{26} +1.00000 q^{27} -11.3353 q^{28} +7.29762 q^{29} -7.02023 q^{30} -7.67579 q^{31} -23.7120 q^{32} -5.80879 q^{33} +2.74837 q^{34} -5.21362 q^{35} +5.55354 q^{36} -1.60860 q^{37} +18.3385 q^{38} -2.32772 q^{39} -24.9467 q^{40} +9.34316 q^{41} +5.60969 q^{42} +2.76403 q^{43} -32.2594 q^{44} +2.55432 q^{45} +18.0449 q^{46} +12.4009 q^{47} +15.7347 q^{48} -2.83393 q^{49} -4.19009 q^{50} -1.00000 q^{51} -12.9271 q^{52} +9.12560 q^{53} -2.74837 q^{54} -14.8375 q^{55} +19.9343 q^{56} -6.67248 q^{57} -20.0566 q^{58} +9.89996 q^{59} +14.1855 q^{60} +4.09796 q^{61} +21.0959 q^{62} -2.04110 q^{63} +33.6999 q^{64} -5.94575 q^{65} +15.9647 q^{66} +4.77678 q^{67} -5.55354 q^{68} -6.56568 q^{69} +14.3290 q^{70} -9.97371 q^{71} -9.76645 q^{72} +2.31790 q^{73} +4.42103 q^{74} +1.52457 q^{75} -37.0559 q^{76} +11.8563 q^{77} +6.39743 q^{78} -5.04106 q^{79} +40.1916 q^{80} +1.00000 q^{81} -25.6785 q^{82} -15.9263 q^{83} -11.3353 q^{84} -2.55432 q^{85} -7.59658 q^{86} +7.29762 q^{87} +56.7313 q^{88} -6.49694 q^{89} -7.02023 q^{90} +4.75110 q^{91} -36.4628 q^{92} -7.67579 q^{93} -34.0823 q^{94} -17.0437 q^{95} -23.7120 q^{96} +9.01662 q^{97} +7.78869 q^{98} -5.80879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * 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 $

$2$	−2.74837	−1.94339	−0.971696	−	0.236236i	$-0.924086\pi$
$2$	−2.74837	−1.94339	−0.971696	+	0.236236i	$0.924086\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.55354	2.77677
$5$	2.55432	1.14233	0.571164	−	0.820836i	$-0.306492\pi$
$5$	2.55432	1.14233	0.571164	+	0.820836i	$0.306492\pi$
$6$	−2.74837	−1.12202
$7$	−2.04110	−0.771462	−0.385731	−	0.922611i	$-0.626051\pi$
$7$	−2.04110	−0.771462	−0.385731	+	0.922611i	$0.626051\pi$
$8$	−9.76645	−3.45296
$9$	1.00000	0.333333
$10$	−7.02023	−2.21999
$11$	−5.80879	−1.75142	−0.875708	−	0.482840i	$-0.839605\pi$
$11$	−5.80879	−1.75142	−0.875708	+	0.482840i	$0.839605\pi$
$12$	5.55354	1.60317
$13$	−2.32772	−0.645593	−0.322796	−	0.946468i	$-0.604623\pi$
$13$	−2.32772	−0.645593	−0.322796	+	0.946468i	$0.604623\pi$
$14$	5.60969	1.49925
$15$	2.55432	0.659524
$16$	15.7347	3.93369
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.74837	−0.647797
$19$	−6.67248	−1.53077	−0.765386	−	0.643571i	$-0.777452\pi$
$19$	−6.67248	−1.53077	−0.765386	+	0.643571i	$0.777452\pi$
$20$	14.1855	3.17198
$21$	−2.04110	−0.445404
$22$	15.9647	3.40369
$23$	−6.56568	−1.36904	−0.684519	−	0.728995i	$-0.739988\pi$
$23$	−6.56568	−1.36904	−0.684519	+	0.728995i	$0.739988\pi$
$24$	−9.76645	−1.99357
$25$	1.52457	0.304914
$26$	6.39743	1.25464
$27$	1.00000	0.192450
$28$	−11.3353	−2.14217
$29$	7.29762	1.35513	0.677567	−	0.735461i	$-0.263034\pi$
$29$	7.29762	1.35513	0.677567	+	0.735461i	$0.263034\pi$
$30$	−7.02023	−1.28171
$31$	−7.67579	−1.37861	−0.689306	−	0.724470i	$-0.742085\pi$
$31$	−7.67579	−1.37861	−0.689306	+	0.724470i	$0.742085\pi$
$32$	−23.7120	−4.19173
$33$	−5.80879	−1.01118
$34$	2.74837	0.471342
$35$	−5.21362	−0.881263
$36$	5.55354	0.925590
$37$	−1.60860	−0.264452	−0.132226	−	0.991220i	$-0.542213\pi$
$37$	−1.60860	−0.264452	−0.132226	+	0.991220i	$0.542213\pi$
$38$	18.3385	2.97489
$39$	−2.32772	−0.372733
$40$	−24.9467	−3.94442
$41$	9.34316	1.45916	0.729578	−	0.683898i	$-0.239717\pi$
$41$	9.34316	1.45916	0.729578	+	0.683898i	$0.239717\pi$
$42$	5.60969	0.865594
$43$	2.76403	0.421511	0.210755	−	0.977539i	$-0.432408\pi$
$43$	2.76403	0.421511	0.210755	+	0.977539i	$0.432408\pi$
$44$	−32.2594	−4.86328
$45$	2.55432	0.380776
$46$	18.0449	2.66058
$47$	12.4009	1.80886	0.904430	−	0.426622i	$-0.140297\pi$
$47$	12.4009	1.80886	0.904430	+	0.426622i	$0.140297\pi$
$48$	15.7347	2.27112
$49$	−2.83393	−0.404847
$50$	−4.19009	−0.592568
$51$	−1.00000	−0.140028
$52$	−12.9271	−1.79266
$53$	9.12560	1.25350	0.626749	−	0.779221i	$-0.284385\pi$
$53$	9.12560	1.25350	0.626749	+	0.779221i	$0.284385\pi$
$54$	−2.74837	−0.374006
$55$	−14.8375	−2.00069
$56$	19.9343	2.66383
$57$	−6.67248	−0.883792
$58$	−20.0566	−2.63356
$59$	9.89996	1.28886	0.644432	−	0.764661i	$-0.277094\pi$
$59$	9.89996	1.28886	0.644432	+	0.764661i	$0.277094\pi$
$60$	14.1855	1.83135
$61$	4.09796	0.524690	0.262345	−	0.964974i	$-0.415504\pi$
$61$	4.09796	0.524690	0.262345	+	0.964974i	$0.415504\pi$
$62$	21.0959	2.67918
$63$	−2.04110	−0.257154
$64$	33.6999	4.21249
$65$	−5.94575	−0.737479
$66$	15.9647	1.96512
$67$	4.77678	0.583576	0.291788	−	0.956483i	$-0.405750\pi$
$67$	4.77678	0.583576	0.291788	+	0.956483i	$0.405750\pi$
$68$	−5.55354	−0.673466
$69$	−6.56568	−0.790415
$70$	14.3290	1.71264
$71$	−9.97371	−1.18366	−0.591831	−	0.806062i	$-0.701595\pi$
$71$	−9.97371	−1.18366	−0.591831	+	0.806062i	$0.701595\pi$
$72$	−9.76645	−1.15099
$73$	2.31790	0.271290	0.135645	−	0.990758i	$-0.456689\pi$
$73$	2.31790	0.271290	0.135645	+	0.990758i	$0.456689\pi$
$74$	4.42103	0.513934
$75$	1.52457	0.176042
$76$	−37.0559	−4.25060
$77$	11.8563	1.35115
$78$	6.39743	0.724367
$79$	−5.04106	−0.567164	−0.283582	−	0.958948i	$-0.591523\pi$
$79$	−5.04106	−0.567164	−0.283582	+	0.958948i	$0.591523\pi$
$80$	40.1916	4.49356
$81$	1.00000	0.111111
$82$	−25.6785	−2.83571
$83$	−15.9263	−1.74814	−0.874068	−	0.485803i	$-0.838527\pi$
$83$	−15.9263	−1.74814	−0.874068	+	0.485803i	$0.838527\pi$
$84$	−11.3353	−1.23678
$85$	−2.55432	−0.277055
$86$	−7.59658	−0.819160
$87$	7.29762	0.782387
$88$	56.7313	6.04758
$89$	−6.49694	−0.688674	−0.344337	−	0.938846i	$-0.611896\pi$
$89$	−6.49694	−0.688674	−0.344337	+	0.938846i	$0.611896\pi$
$90$	−7.02023	−0.739997
$91$	4.75110	0.498050
$92$	−36.4628	−3.80151
$93$	−7.67579	−0.795943
$94$	−34.0823	−3.51532
$95$	−17.0437	−1.74864
$96$	−23.7120	−2.42010
$97$	9.01662	0.915499	0.457750	−	0.889081i	$-0.348656\pi$
$97$	9.01662	0.915499	0.457750	+	0.889081i	$0.348656\pi$
$98$	7.78869	0.786776
$99$	−5.80879	−0.583806
$100$	8.46677	0.846677
$101$	−8.87768	−0.883362	−0.441681	−	0.897172i	$-0.645618\pi$
$101$	−8.87768	−0.883362	−0.441681	+	0.897172i	$0.645618\pi$
$102$	2.74837	0.272129
$103$	0.896354	0.0883204	0.0441602	−	0.999024i	$-0.485939\pi$
$103$	0.896354	0.0883204	0.0441602	+	0.999024i	$0.485939\pi$
$104$	22.7335	2.22921
$105$	−5.21362	−0.508797
$106$	−25.0805	−2.43604
$107$	8.56843	0.828341	0.414171	−	0.910199i	$-0.364072\pi$
$107$	8.56843	0.828341	0.414171	+	0.910199i	$0.364072\pi$
$108$	5.55354	0.534390
$109$	−18.2364	−1.74673	−0.873363	−	0.487070i	$-0.838066\pi$
$109$	−18.2364	−1.74673	−0.873363	+	0.487070i	$0.838066\pi$
$110$	40.7791	3.88813
$111$	−1.60860	−0.152682
$112$	−32.1161	−3.03469
$113$	6.72522	0.632656	0.316328	−	0.948650i	$-0.397550\pi$
$113$	6.72522	0.632656	0.316328	+	0.948650i	$0.397550\pi$
$114$	18.3385	1.71755
$115$	−16.7709	−1.56389
$116$	40.5276	3.76290
$117$	−2.32772	−0.215198
$118$	−27.2088	−2.50477
$119$	2.04110	0.187107
$120$	−24.9467	−2.27731
$121$	22.7421	2.06746
$122$	−11.2627	−1.01968
$123$	9.34316	0.842444
$124$	−42.6278	−3.82809
$125$	−8.87737	−0.794016
$126$	5.60969	0.499751
$127$	7.86963	0.698317	0.349159	−	0.937064i	$-0.386467\pi$
$127$	7.86963	0.698317	0.349159	+	0.937064i	$0.386467\pi$
$128$	−45.1958	−3.99479
$129$	2.76403	0.243359
$130$	16.3411	1.43321
$131$	9.15693	0.800045	0.400022	−	0.916505i	$-0.369002\pi$
$131$	9.15693	0.800045	0.400022	+	0.916505i	$0.369002\pi$
$132$	−32.2594	−2.80782
$133$	13.6192	1.18093
$134$	−13.1284	−1.13412
$135$	2.55432	0.219841
$136$	9.76645	0.837466
$137$	4.75217	0.406005	0.203003	−	0.979178i	$-0.434930\pi$
$137$	4.75217	0.406005	0.203003	+	0.979178i	$0.434930\pi$
$138$	18.0449	1.53609
$139$	−16.8487	−1.42909	−0.714545	−	0.699589i	$-0.753366\pi$
$139$	−16.8487	−1.42909	−0.714545	+	0.699589i	$0.753366\pi$
$140$	−28.9541	−2.44706
$141$	12.4009	1.04435
$142$	27.4115	2.30032
$143$	13.5212	1.13070
$144$	15.7347	1.31123
$145$	18.6405	1.54801
$146$	−6.37045	−0.527222
$147$	−2.83393	−0.233738
$148$	−8.93343	−0.734324
$149$	−14.3578	−1.17623	−0.588117	−	0.808776i	$-0.700131\pi$
$149$	−14.3578	−1.17623	−0.588117	+	0.808776i	$0.700131\pi$
$150$	−4.19009	−0.342119
$151$	12.2007	0.992876	0.496438	−	0.868072i	$-0.334641\pi$
$151$	12.2007	0.992876	0.496438	+	0.868072i	$0.334641\pi$
$152$	65.1665	5.28570
$153$	−1.00000	−0.0808452
$154$	−32.5855	−2.62582
$155$	−19.6065	−1.57483
$156$	−12.9271	−1.03499
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	13.8547	1.10222
$159$	9.12560	0.723707
$160$	−60.5682	−4.78833
$161$	13.4012	1.05616
$162$	−2.74837	−0.215932
$163$	−19.6490	−1.53903	−0.769513	−	0.638631i	$-0.779501\pi$
$163$	−19.6490	−1.53903	−0.769513	+	0.638631i	$0.779501\pi$
$164$	51.8876	4.05174
$165$	−14.8375	−1.15510
$166$	43.7713	3.39731
$167$	7.48811	0.579447	0.289724	−	0.957110i	$-0.406437\pi$
$167$	7.48811	0.579447	0.289724	+	0.957110i	$0.406437\pi$
$168$	19.9343	1.53796
$169$	−7.58173	−0.583210
$170$	7.02023	0.538427
$171$	−6.67248	−0.510258
$172$	15.3502	1.17044
$173$	1.73853	0.132178	0.0660889	−	0.997814i	$-0.478948\pi$
$173$	1.73853	0.132178	0.0660889	+	0.997814i	$0.478948\pi$
$174$	−20.0566	−1.52048
$175$	−3.11179	−0.235230
$176$	−91.3999	−6.88952
$177$	9.89996	0.744126
$178$	17.8560	1.33836
$179$	24.9035	1.86137	0.930687	−	0.365816i	$-0.119210\pi$
$179$	24.9035	1.86137	0.930687	+	0.365816i	$0.119210\pi$
$180$	14.1855	1.05733
$181$	16.6820	1.23996	0.619980	−	0.784617i	$-0.287141\pi$
$181$	16.6820	1.23996	0.619980	+	0.784617i	$0.287141\pi$
$182$	−13.0578	−0.967906
$183$	4.09796	0.302930
$184$	64.1234	4.72724
$185$	−4.10889	−0.302091
$186$	21.0959	1.54683
$187$	5.80879	0.424781
$188$	68.8690	5.02279
$189$	−2.04110	−0.148468
$190$	46.8424	3.39830
$191$	7.16781	0.518645	0.259322	−	0.965791i	$-0.416501\pi$
$191$	7.16781	0.518645	0.259322	+	0.965791i	$0.416501\pi$
$192$	33.6999	2.43208
$193$	−3.06501	−0.220624	−0.110312	−	0.993897i	$-0.535185\pi$
$193$	−3.06501	−0.220624	−0.110312	+	0.993897i	$0.535185\pi$
$194$	−24.7810	−1.77917
$195$	−5.94575	−0.425784
$196$	−15.7383	−1.12417
$197$	22.3273	1.59076	0.795378	−	0.606114i	$-0.207273\pi$
$197$	22.3273	1.59076	0.795378	+	0.606114i	$0.207273\pi$
$198$	15.9647	1.13456
$199$	22.8546	1.62012	0.810058	−	0.586350i	$-0.199435\pi$
$199$	22.8546	1.62012	0.810058	+	0.586350i	$0.199435\pi$
$200$	−14.8896	−1.05286
$201$	4.77678	0.336928
$202$	24.3991	1.71672
$203$	−14.8951	−1.04543
$204$	−5.55354	−0.388826
$205$	23.8654	1.66684
$206$	−2.46351	−0.171641
$207$	−6.56568	−0.456346
$208$	−36.6261	−2.53956
$209$	38.7591	2.68102
$210$	14.3290	0.988792
$211$	−23.5919	−1.62414	−0.812068	−	0.583562i	$-0.801658\pi$
$211$	−23.5919	−1.62414	−0.812068	+	0.583562i	$0.801658\pi$
$212$	50.6794	3.48068
$213$	−9.97371	−0.683388
$214$	−23.5492	−1.60979
$215$	7.06023	0.481504
$216$	−9.76645	−0.664523
$217$	15.6670	1.06355
$218$	50.1203	3.39457
$219$	2.31790	0.156629
$220$	−82.4009	−5.55547
$221$	2.32772	0.156579
$222$	4.42103	0.296720
$223$	−1.95000	−0.130581	−0.0652907	−	0.997866i	$-0.520797\pi$
$223$	−1.95000	−0.130581	−0.0652907	+	0.997866i	$0.520797\pi$
$224$	48.3985	3.23376
$225$	1.52457	0.101638
$226$	−18.4834	−1.22950
$227$	17.1686	1.13952	0.569762	−	0.821810i	$-0.307036\pi$
$227$	17.1686	1.13952	0.569762	+	0.821810i	$0.307036\pi$
$228$	−37.0559	−2.45409
$229$	10.2477	0.677185	0.338593	−	0.940933i	$-0.390049\pi$
$229$	10.2477	0.677185	0.338593	+	0.940933i	$0.390049\pi$
$230$	46.0926	3.03925
$231$	11.8563	0.780087
$232$	−71.2718	−4.67922
$233$	27.8663	1.82558	0.912789	−	0.408431i	$-0.133924\pi$
$233$	27.8663	1.82558	0.912789	+	0.408431i	$0.133924\pi$
$234$	6.39743	0.418213
$235$	31.6760	2.06631
$236$	54.9798	3.57888
$237$	−5.04106	−0.327452
$238$	−5.60969	−0.363622
$239$	−26.6938	−1.72668	−0.863339	−	0.504625i	$-0.831631\pi$
$239$	−26.6938	−1.72668	−0.863339	+	0.504625i	$0.831631\pi$
$240$	40.1916	2.59436
$241$	5.29337	0.340976	0.170488	−	0.985360i	$-0.445466\pi$
$241$	5.29337	0.340976	0.170488	+	0.985360i	$0.445466\pi$
$242$	−62.5036	−4.01789
$243$	1.00000	0.0641500
$244$	22.7582	1.45694
$245$	−7.23877	−0.462468
$246$	−25.6785	−1.63720
$247$	15.5317	0.988256
$248$	74.9653	4.76030
$249$	−15.9263	−1.00929
$250$	24.3983	1.54308
$251$	15.0828	0.952015	0.476008	−	0.879441i	$-0.342083\pi$
$251$	15.0828	0.952015	0.476008	+	0.879441i	$0.342083\pi$
$252$	−11.3353	−0.714058
$253$	38.1387	2.39776
$254$	−21.6287	−1.35710
$255$	−2.55432	−0.159958
$256$	56.8151	3.55094
$257$	−1.17061	−0.0730209	−0.0365104	−	0.999333i	$-0.511624\pi$
$257$	−1.17061	−0.0730209	−0.0365104	+	0.999333i	$0.511624\pi$
$258$	−7.59658	−0.472942
$259$	3.28331	0.204015
$260$	−33.0199	−2.04781
$261$	7.29762	0.451711
$262$	−25.1666	−1.55480
$263$	−27.0225	−1.66628	−0.833138	−	0.553065i	$-0.813458\pi$
$263$	−27.0225	−1.66628	−0.833138	+	0.553065i	$0.813458\pi$
$264$	56.7313	3.49157
$265$	23.3097	1.43191
$266$	−37.4305	−2.29501
$267$	−6.49694	−0.397606
$268$	26.5280	1.62046
$269$	−13.3311	−0.812809	−0.406404	−	0.913693i	$-0.633218\pi$
$269$	−13.3311	−0.812809	−0.406404	+	0.913693i	$0.633218\pi$
$270$	−7.02023	−0.427238
$271$	6.05912	0.368065	0.184033	−	0.982920i	$-0.441085\pi$
$271$	6.05912	0.368065	0.184033	+	0.982920i	$0.441085\pi$
$272$	−15.7347	−0.954059
$273$	4.75110	0.287549
$274$	−13.0607	−0.789027
$275$	−8.85591	−0.534032
$276$	−36.4628	−2.19480
$277$	−7.42038	−0.445847	−0.222924	−	0.974836i	$-0.571560\pi$
$277$	−7.42038	−0.445847	−0.222924	+	0.974836i	$0.571560\pi$
$278$	46.3066	2.77728
$279$	−7.67579	−0.459538
$280$	50.9186	3.04297
$281$	−17.8702	−1.06605	−0.533023	−	0.846100i	$-0.678944\pi$
$281$	−17.8702	−1.06605	−0.533023	+	0.846100i	$0.678944\pi$
$282$	−34.0823	−2.02957
$283$	−9.81438	−0.583404	−0.291702	−	0.956509i	$-0.594222\pi$
$283$	−9.81438	−0.583404	−0.291702	+	0.956509i	$0.594222\pi$
$284$	−55.3894	−3.28676
$285$	−17.0437	−1.00958
$286$	−37.1614	−2.19740
$287$	−19.0703	−1.12568
$288$	−23.7120	−1.39724
$289$	1.00000	0.0588235
$290$	−51.2309	−3.00838
$291$	9.01662	0.528564
$292$	12.8726	0.753309
$293$	28.5326	1.66689	0.833447	−	0.552599i	$-0.186364\pi$
$293$	28.5326	1.66689	0.833447	+	0.552599i	$0.186364\pi$
$294$	7.78869	0.454245
$295$	25.2877	1.47231
$296$	15.7103	0.913144
$297$	−5.80879	−0.337060
$298$	39.4605	2.28588
$299$	15.2830	0.883841
$300$	8.46677	0.488829
$301$	−5.64165	−0.325179
$302$	−33.5319	−1.92955
$303$	−8.87768	−0.510009
$304$	−104.990	−6.02158
$305$	10.4675	0.599368
$306$	2.74837	0.157114
$307$	0.195445	0.0111547	0.00557733	−	0.999984i	$-0.498225\pi$
$307$	0.195445	0.0111547	0.00557733	+	0.999984i	$0.498225\pi$
$308$	65.8445	3.75184
$309$	0.896354	0.0509918
$310$	53.8858	3.06051
$311$	−11.2345	−0.637049	−0.318525	−	0.947915i	$-0.603187\pi$
$311$	−11.2345	−0.637049	−0.318525	+	0.947915i	$0.603187\pi$
$312$	22.7335	1.28703
$313$	11.1660	0.631137	0.315569	−	0.948903i	$-0.397805\pi$
$313$	11.1660	0.631137	0.315569	+	0.948903i	$0.397805\pi$
$314$	2.74837	0.155100
$315$	−5.21362	−0.293754
$316$	−27.9958	−1.57488
$317$	30.7138	1.72506	0.862529	−	0.506008i	$-0.168879\pi$
$317$	30.7138	1.72506	0.862529	+	0.506008i	$0.168879\pi$
$318$	−25.0805	−1.40645
$319$	−42.3903	−2.37340
$320$	86.0805	4.81205
$321$	8.56843	0.478243
$322$	−36.8314	−2.05253
$323$	6.67248	0.371267
$324$	5.55354	0.308530
$325$	−3.54877	−0.196850
$326$	54.0027	2.99093
$327$	−18.2364	−1.00847
$328$	−91.2495	−5.03841
$329$	−25.3115	−1.39547
$330$	40.7791	2.24481
$331$	19.1659	1.05345	0.526727	−	0.850034i	$-0.323419\pi$
$331$	19.1659	1.05345	0.526727	+	0.850034i	$0.323419\pi$
$332$	−88.4473	−4.85417
$333$	−1.60860	−0.0881508
$334$	−20.5801	−1.12609
$335$	12.2014	0.666636
$336$	−32.1161	−1.75208
$337$	12.1009	0.659180	0.329590	−	0.944124i	$-0.393089\pi$
$337$	12.1009	0.659180	0.329590	+	0.944124i	$0.393089\pi$
$338$	20.8374	1.13341
$339$	6.72522	0.365264
$340$	−14.1855	−0.769319
$341$	44.5871	2.41453
$342$	18.3385	0.991630
$343$	20.0720	1.08379
$344$	−26.9948	−1.45546
$345$	−16.7709	−0.902913
$346$	−4.77812	−0.256873
$347$	18.6905	1.00336	0.501679	−	0.865054i	$-0.332716\pi$
$347$	18.6905	1.00336	0.501679	+	0.865054i	$0.332716\pi$
$348$	40.5276	2.17251
$349$	−33.2505	−1.77986	−0.889928	−	0.456101i	$-0.849246\pi$
$349$	−33.2505	−1.77986	−0.889928	+	0.456101i	$0.849246\pi$
$350$	8.55237	0.457143
$351$	−2.32772	−0.124244
$352$	137.738	7.34147
$353$	12.4333	0.661760	0.330880	−	0.943673i	$-0.392655\pi$
$353$	12.4333	0.661760	0.330880	+	0.943673i	$0.392655\pi$
$354$	−27.2088	−1.44613
$355$	−25.4761	−1.35213
$356$	−36.0810	−1.91229
$357$	2.04110	0.108026
$358$	−68.4440	−3.61738
$359$	4.67969	0.246985	0.123492	−	0.992346i	$-0.460591\pi$
$359$	4.67969	0.246985	0.123492	+	0.992346i	$0.460591\pi$
$360$	−24.9467	−1.31481
$361$	25.5220	1.34326
$362$	−45.8482	−2.40973
$363$	22.7421	1.19365
$364$	26.3854	1.38297
$365$	5.92067	0.309902
$366$	−11.2627	−0.588712
$367$	10.3997	0.542858	0.271429	−	0.962458i	$-0.412504\pi$
$367$	10.3997	0.542858	0.271429	+	0.962458i	$0.412504\pi$
$368$	−103.309	−5.38537
$369$	9.34316	0.486385
$370$	11.2927	0.587082
$371$	−18.6262	−0.967025
$372$	−42.6278	−2.21015
$373$	2.05401	0.106352	0.0531762	−	0.998585i	$-0.483066\pi$
$373$	2.05401	0.106352	0.0531762	+	0.998585i	$0.483066\pi$
$374$	−15.9647	−0.825516
$375$	−8.87737	−0.458426
$376$	−121.113	−6.24592
$377$	−16.9868	−0.874864
$378$	5.60969	0.288531
$379$	27.9222	1.43427	0.717134	−	0.696936i	$-0.245454\pi$
$379$	27.9222	1.43427	0.717134	+	0.696936i	$0.245454\pi$
$380$	−94.6528	−4.85559
$381$	7.86963	0.403174
$382$	−19.6998	−1.00793
$383$	7.87763	0.402528	0.201264	−	0.979537i	$-0.435495\pi$
$383$	7.87763	0.402528	0.201264	+	0.979537i	$0.435495\pi$
$384$	−45.1958	−2.30639
$385$	30.2848	1.54346
$386$	8.42377	0.428759
$387$	2.76403	0.140504
$388$	50.0742	2.54213
$389$	28.7655	1.45847	0.729233	−	0.684265i	$-0.239877\pi$
$389$	28.7655	1.45847	0.729233	+	0.684265i	$0.239877\pi$
$390$	16.3411	0.827464
$391$	6.56568	0.332041
$392$	27.6774	1.39792
$393$	9.15693	0.461906
$394$	−61.3637	−3.09146
$395$	−12.8765	−0.647887
$396$	−32.2594	−1.62109
$397$	−0.449869	−0.0225783	−0.0112891	−	0.999936i	$-0.503594\pi$
$397$	−0.449869	−0.0225783	−0.0112891	+	0.999936i	$0.503594\pi$
$398$	−62.8128	−3.14852
$399$	13.6192	0.681812
$400$	23.9887	1.19944
$401$	28.8283	1.43962	0.719809	−	0.694172i	$-0.244229\pi$
$401$	28.8283	1.43962	0.719809	+	0.694172i	$0.244229\pi$
$402$	−13.1284	−0.654783
$403$	17.8671	0.890023
$404$	−49.3025	−2.45289
$405$	2.55432	0.126925
$406$	40.9374	2.03169
$407$	9.34403	0.463166
$408$	9.76645	0.483511
$409$	−23.2766	−1.15095	−0.575476	−	0.817818i	$-0.695183\pi$
$409$	−23.2766	−1.15095	−0.575476	+	0.817818i	$0.695183\pi$
$410$	−65.5911	−3.23931
$411$	4.75217	0.234407
$412$	4.97794	0.245246
$413$	−20.2068	−0.994310
$414$	18.0449	0.886859
$415$	−40.6809	−1.99695
$416$	55.1949	2.70615
$417$	−16.8487	−0.825086
$418$	−106.524	−5.21027
$419$	−1.65295	−0.0807517	−0.0403759	−	0.999185i	$-0.512856\pi$
$419$	−1.65295	−0.0807517	−0.0403759	+	0.999185i	$0.512856\pi$
$420$	−28.9541	−1.41281
$421$	11.1658	0.544186	0.272093	−	0.962271i	$-0.412284\pi$
$421$	11.1658	0.544186	0.272093	+	0.962271i	$0.412284\pi$
$422$	64.8394	3.15633
$423$	12.4009	0.602953
$424$	−89.1247	−4.32828
$425$	−1.52457	−0.0739525
$426$	27.4115	1.32809
$427$	−8.36433	−0.404778
$428$	47.5851	2.30011
$429$	13.5212	0.652811
$430$	−19.4041	−0.935750
$431$	−19.9562	−0.961255	−0.480628	−	0.876925i	$-0.659591\pi$
$431$	−19.9562	−0.961255	−0.480628	+	0.876925i	$0.659591\pi$
$432$	15.7347	0.757038
$433$	−1.30912	−0.0629125	−0.0314562	−	0.999505i	$-0.510014\pi$
$433$	−1.30912	−0.0629125	−0.0314562	+	0.999505i	$0.510014\pi$
$434$	−43.0588	−2.06689
$435$	18.6405	0.893743
$436$	−101.276	−4.85026
$437$	43.8094	2.09569
$438$	−6.37045	−0.304392
$439$	14.5352	0.693729	0.346865	−	0.937915i	$-0.387246\pi$
$439$	14.5352	0.693729	0.346865	+	0.937915i	$0.387246\pi$
$440$	144.910	6.90832
$441$	−2.83393	−0.134949
$442$	−6.39743	−0.304295
$443$	−35.3545	−1.67974	−0.839871	−	0.542786i	$-0.817369\pi$
$443$	−35.3545	−1.67974	−0.839871	+	0.542786i	$0.817369\pi$
$444$	−8.93343	−0.423962
$445$	−16.5953	−0.786692
$446$	5.35932	0.253771
$447$	−14.3578	−0.679099
$448$	−68.7848	−3.24977
$449$	31.5624	1.48952	0.744762	−	0.667330i	$-0.232563\pi$
$449$	31.5624	1.48952	0.744762	+	0.667330i	$0.232563\pi$
$450$	−4.19009	−0.197523
$451$	−54.2725	−2.55559
$452$	37.3488	1.75674
$453$	12.2007	0.573237
$454$	−47.1858	−2.21454
$455$	12.1358	0.568937
$456$	65.1665	3.05170
$457$	−37.5099	−1.75464	−0.877320	−	0.479907i	$-0.840671\pi$
$457$	−37.5099	−1.75464	−0.877320	+	0.479907i	$0.840671\pi$
$458$	−28.1644	−1.31604
$459$	−1.00000	−0.0466760
$460$	−93.1377	−4.34257
$461$	3.17135	0.147705	0.0738523	−	0.997269i	$-0.476471\pi$
$461$	3.17135	0.147705	0.0738523	+	0.997269i	$0.476471\pi$
$462$	−32.5855	−1.51602
$463$	41.4362	1.92570	0.962851	−	0.270033i	$-0.0870347\pi$
$463$	41.4362	1.92570	0.962851	+	0.270033i	$0.0870347\pi$
$464$	114.826	5.33067
$465$	−19.6065	−0.909228
$466$	−76.5868	−3.54781
$467$	29.5881	1.36917	0.684587	−	0.728931i	$-0.259983\pi$
$467$	29.5881	1.36917	0.684587	+	0.728931i	$0.259983\pi$
$468$	−12.9271	−0.597554
$469$	−9.74986	−0.450207
$470$	−87.0573	−4.01565
$471$	−1.00000	−0.0460776
$472$	−96.6874	−4.45040
$473$	−16.0557	−0.738241
$474$	13.8547	0.636368
$475$	−10.1727	−0.466754
$476$	11.3353	0.519553
$477$	9.12560	0.417832
$478$	73.3644	3.35561
$479$	22.4777	1.02703	0.513517	−	0.858079i	$-0.328342\pi$
$479$	22.4777	1.02703	0.513517	+	0.858079i	$0.328342\pi$
$480$	−60.5682	−2.76455
$481$	3.74437	0.170729
$482$	−14.5481	−0.662649
$483$	13.4012	0.609775
$484$	126.299	5.74087
$485$	23.0314	1.04580
$486$	−2.74837	−0.124669
$487$	−32.6605	−1.47999	−0.739994	−	0.672614i	$-0.765171\pi$
$487$	−32.6605	−1.47999	−0.739994	+	0.672614i	$0.765171\pi$
$488$	−40.0225	−1.81174
$489$	−19.6490	−0.888557
$490$	19.8948	0.898757
$491$	−25.7223	−1.16083	−0.580417	−	0.814320i	$-0.697110\pi$
$491$	−25.7223	−1.16083	−0.580417	+	0.814320i	$0.697110\pi$
$492$	51.8876	2.33927
$493$	−7.29762	−0.328668
$494$	−42.6868	−1.92057
$495$	−14.8375	−0.666898
$496$	−120.777	−5.42303
$497$	20.3573	0.913150
$498$	43.7713	1.96144
$499$	−12.7070	−0.568843	−0.284422	−	0.958699i	$-0.591802\pi$
$499$	−12.7070	−0.568843	−0.284422	+	0.958699i	$0.591802\pi$
$500$	−49.3009	−2.20480
$501$	7.48811	0.334544
$502$	−41.4530	−1.85014
$503$	−0.325153	−0.0144978	−0.00724892	−	0.999974i	$-0.502307\pi$
$503$	−0.325153	−0.0144978	−0.00724892	+	0.999974i	$0.502307\pi$
$504$	19.9343	0.887943
$505$	−22.6765	−1.00909
$506$	−104.819	−4.65978
$507$	−7.58173	−0.336716
$508$	43.7043	1.93907
$509$	−27.8027	−1.23233	−0.616166	−	0.787616i	$-0.711315\pi$
$509$	−27.8027	−1.23233	−0.616166	+	0.787616i	$0.711315\pi$
$510$	7.02023	0.310861
$511$	−4.73105	−0.209290
$512$	−65.7573	−2.90609
$513$	−6.67248	−0.294597
$514$	3.21728	0.141908
$515$	2.28958	0.100891
$516$	15.3502	0.675753
$517$	−72.0343	−3.16807
$518$	−9.02375	−0.396481
$519$	1.73853	0.0763129
$520$	58.0688	2.54649
$521$	3.09881	0.135761	0.0678807	−	0.997693i	$-0.478376\pi$
$521$	3.09881	0.135761	0.0678807	+	0.997693i	$0.478376\pi$
$522$	−20.0566	−0.877852
$523$	28.1590	1.23131	0.615654	−	0.788017i	$-0.288892\pi$
$523$	28.1590	1.23131	0.615654	+	0.788017i	$0.288892\pi$
$524$	50.8534	2.22154
$525$	−3.11179	−0.135810
$526$	74.2677	3.23823
$527$	7.67579	0.334363
$528$	−91.3999	−3.97767
$529$	20.1081	0.874266
$530$	−64.0638	−2.78275
$531$	9.89996	0.429622
$532$	75.6347	3.27918
$533$	−21.7482	−0.942020
$534$	17.8560	0.772704
$535$	21.8865	0.946238
$536$	−46.6522	−2.01507
$537$	24.9035	1.07466
$538$	36.6387	1.57961
$539$	16.4617	0.709056
$540$	14.1855	0.610449
$541$	16.6156	0.714359	0.357179	−	0.934036i	$-0.383739\pi$
$541$	16.6156	0.714359	0.357179	+	0.934036i	$0.383739\pi$
$542$	−16.6527	−0.715295
$543$	16.6820	0.715892
$544$	23.7120	1.01664
$545$	−46.5816	−1.99533
$546$	−13.0578	−0.558821
$547$	−40.1020	−1.71464	−0.857319	−	0.514785i	$-0.827872\pi$
$547$	−40.1020	−1.71464	−0.857319	+	0.514785i	$0.827872\pi$
$548$	26.3914	1.12738
$549$	4.09796	0.174897
$550$	24.3393	1.03783
$551$	−48.6932	−2.07440
$552$	64.1234	2.72927
$553$	10.2893	0.437545
$554$	20.3940	0.866456
$555$	−4.10889	−0.174413
$556$	−93.5701	−3.96826
$557$	20.3359	0.861661	0.430831	−	0.902433i	$-0.358221\pi$
$557$	20.3359	0.861661	0.430831	+	0.902433i	$0.358221\pi$
$558$	21.0959	0.893062
$559$	−6.43388	−0.272124
$560$	−82.0350	−3.46661
$561$	5.80879	0.245247
$562$	49.1139	2.07175
$563$	45.4525	1.91559	0.957797	−	0.287444i	$-0.0928056\pi$
$563$	45.4525	1.91559	0.957797	+	0.287444i	$0.0928056\pi$
$564$	68.8690	2.89991
$565$	17.1784	0.722700
$566$	26.9736	1.13378
$567$	−2.04110	−0.0857180
$568$	97.4078	4.08714
$569$	0.698823	0.0292962	0.0146481	−	0.999893i	$-0.495337\pi$
$569$	0.698823	0.0292962	0.0146481	+	0.999893i	$0.495337\pi$
$570$	46.8424	1.96201
$571$	0.193151	0.00808310	0.00404155	−	0.999992i	$-0.498714\pi$
$571$	0.193151	0.00808310	0.00404155	+	0.999992i	$0.498714\pi$
$572$	75.0907	3.13970
$573$	7.16781	0.299440
$574$	52.4122	2.18764
$575$	−10.0098	−0.417439
$576$	33.6999	1.40416
$577$	6.91838	0.288016	0.144008	−	0.989577i	$-0.454001\pi$
$577$	6.91838	0.288016	0.144008	+	0.989577i	$0.454001\pi$
$578$	−2.74837	−0.114317
$579$	−3.06501	−0.127377
$580$	103.521	4.29846
$581$	32.5071	1.34862
$582$	−24.7810	−1.02721
$583$	−53.0087	−2.19540
$584$	−22.6377	−0.936753
$585$	−5.94575	−0.245826
$586$	−78.4183	−3.23943
$587$	−32.9160	−1.35859	−0.679295	−	0.733865i	$-0.737714\pi$
$587$	−32.9160	−1.35859	−0.679295	+	0.733865i	$0.737714\pi$
$588$	−15.7383	−0.649038
$589$	51.2166	2.11034
$590$	−69.5000	−2.86127
$591$	22.3273	0.918423
$592$	−25.3109	−1.04027
$593$	−17.1145	−0.702807	−0.351404	−	0.936224i	$-0.614295\pi$
$593$	−17.1145	−0.702807	−0.351404	+	0.936224i	$0.614295\pi$
$594$	15.9647	0.655040
$595$	5.21362	0.213738
$596$	−79.7365	−3.26613
$597$	22.8546	0.935375
$598$	−42.0035	−1.71765
$599$	0.945369	0.0386267	0.0193134	−	0.999813i	$-0.493852\pi$
$599$	0.945369	0.0386267	0.0193134	+	0.999813i	$0.493852\pi$
$600$	−14.8896	−0.607867
$601$	4.01531	0.163788	0.0818940	−	0.996641i	$-0.473903\pi$
$601$	4.01531	0.163788	0.0818940	+	0.996641i	$0.473903\pi$
$602$	15.5053	0.631951
$603$	4.77678	0.194525
$604$	67.7569	2.75699
$605$	58.0906	2.36172
$606$	24.3991	0.991147
$607$	18.5856	0.754365	0.377183	−	0.926139i	$-0.376893\pi$
$607$	18.5856	0.754365	0.377183	+	0.926139i	$0.376893\pi$
$608$	158.218	6.41659
$609$	−14.8951	−0.603581
$610$	−28.7686	−1.16481
$611$	−28.8658	−1.16779
$612$	−5.55354	−0.224489
$613$	36.0349	1.45544	0.727718	−	0.685877i	$-0.240581\pi$
$613$	36.0349	1.45544	0.727718	+	0.685877i	$0.240581\pi$
$614$	−0.537157	−0.0216779
$615$	23.8654	0.962348
$616$	−115.794	−4.66547
$617$	−4.15823	−0.167404	−0.0837020	−	0.996491i	$-0.526674\pi$
$617$	−4.15823	−0.167404	−0.0837020	+	0.996491i	$0.526674\pi$
$618$	−2.46351	−0.0990970
$619$	44.1944	1.77632	0.888160	−	0.459533i	$-0.151983\pi$
$619$	44.1944	1.77632	0.888160	+	0.459533i	$0.151983\pi$
$620$	−108.885	−4.37294
$621$	−6.56568	−0.263472
$622$	30.8765	1.23804
$623$	13.2609	0.531286
$624$	−36.6261	−1.46622
$625$	−30.2985	−1.21194
$626$	−30.6882	−1.22655
$627$	38.7591	1.54789
$628$	−5.55354	−0.221610
$629$	1.60860	0.0641391
$630$	14.3290	0.570879
$631$	−6.31677	−0.251467	−0.125733	−	0.992064i	$-0.540128\pi$
$631$	−6.31677	−0.251467	−0.125733	+	0.992064i	$0.540128\pi$
$632$	49.2333	1.95840
$633$	−23.5919	−0.937696
$634$	−84.4129	−3.35246
$635$	20.1016	0.797707
$636$	50.6794	2.00957
$637$	6.59659	0.261366
$638$	116.504	4.61245
$639$	−9.97371	−0.394554
$640$	−115.445	−4.56336
$641$	−14.1678	−0.559594	−0.279797	−	0.960059i	$-0.590267\pi$
$641$	−14.1678	−0.559594	−0.279797	+	0.960059i	$0.590267\pi$
$642$	−23.5492	−0.929413
$643$	−37.8184	−1.49141	−0.745705	−	0.666276i	$-0.767887\pi$
$643$	−37.8184	−1.49141	−0.745705	+	0.666276i	$0.767887\pi$
$644$	74.4240	2.93272
$645$	7.06023	0.277996
$646$	−18.3385	−0.721517
$647$	3.31170	0.130196	0.0650981	−	0.997879i	$-0.479264\pi$
$647$	3.31170	0.130196	0.0650981	+	0.997879i	$0.479264\pi$
$648$	−9.76645	−0.383662
$649$	−57.5068	−2.25734
$650$	9.75334	0.382557
$651$	15.6670	0.614039
$652$	−109.121	−4.27352
$653$	21.2759	0.832590	0.416295	−	0.909230i	$-0.363328\pi$
$653$	21.2759	0.832590	0.416295	+	0.909230i	$0.363328\pi$
$654$	50.1203	1.95986
$655$	23.3898	0.913914
$656$	147.012	5.73986
$657$	2.31790	0.0904299
$658$	69.5653	2.71194
$659$	−17.7219	−0.690347	−0.345174	−	0.938539i	$-0.612180\pi$
$659$	−17.7219	−0.690347	−0.345174	+	0.938539i	$0.612180\pi$
$660$	−82.4009	−3.20745
$661$	−26.1958	−1.01890	−0.509449	−	0.860501i	$-0.670151\pi$
$661$	−26.1958	−1.01890	−0.509449	+	0.860501i	$0.670151\pi$
$662$	−52.6751	−2.04727
$663$	2.32772	0.0904011
$664$	155.543	6.03625
$665$	34.7878	1.34901
$666$	4.42103	0.171311
$667$	−47.9138	−1.85523
$668$	41.5855	1.60899
$669$	−1.95000	−0.0753913
$670$	−33.5341	−1.29553
$671$	−23.8042	−0.918951
$672$	48.3985	1.86701
$673$	−33.9239	−1.30767	−0.653835	−	0.756638i	$-0.726841\pi$
$673$	−33.9239	−1.30767	−0.653835	+	0.756638i	$0.726841\pi$
$674$	−33.2579	−1.28105
$675$	1.52457	0.0586808
$676$	−42.1055	−1.61944
$677$	26.2180	1.00764	0.503820	−	0.863809i	$-0.331927\pi$
$677$	26.2180	1.00764	0.503820	+	0.863809i	$0.331927\pi$
$678$	−18.4834	−0.709851
$679$	−18.4038	−0.706272
$680$	24.9467	0.956662
$681$	17.1686	0.657904
$682$	−122.542	−4.69237
$683$	−15.0005	−0.573978	−0.286989	−	0.957934i	$-0.592654\pi$
$683$	−15.0005	−0.573978	−0.286989	+	0.957934i	$0.592654\pi$
$684$	−37.0559	−1.41687
$685$	12.1386	0.463791
$686$	−55.1653	−2.10622
$687$	10.2477	0.390973
$688$	43.4913	1.65809
$689$	−21.2418	−0.809249
$690$	46.0926	1.75471
$691$	27.3259	1.03953	0.519764	−	0.854310i	$-0.326020\pi$
$691$	27.3259	1.03953	0.519764	+	0.854310i	$0.326020\pi$
$692$	9.65498	0.367027
$693$	11.8563	0.450384
$694$	−51.3684	−1.94992
$695$	−43.0371	−1.63249
$696$	−71.2718	−2.70155
$697$	−9.34316	−0.353897
$698$	91.3846	3.45896
$699$	27.8663	1.05400
$700$	−17.2815	−0.653179
$701$	−27.2266	−1.02834	−0.514168	−	0.857689i	$-0.671899\pi$
$701$	−27.2266	−1.02834	−0.514168	+	0.857689i	$0.671899\pi$
$702$	6.39743	0.241456
$703$	10.7334	0.404816
$704$	−195.756	−7.37783
$705$	31.6760	1.19299
$706$	−34.1714	−1.28606
$707$	18.1202	0.681480
$708$	54.9798	2.06627
$709$	6.36757	0.239139	0.119569	−	0.992826i	$-0.461849\pi$
$709$	6.36757	0.239139	0.119569	+	0.992826i	$0.461849\pi$
$710$	70.0178	2.62772
$711$	−5.04106	−0.189055
$712$	63.4520	2.37797
$713$	50.3968	1.88737
$714$	−5.60969	−0.209937
$715$	34.5376	1.29163
$716$	138.303	5.16861
$717$	−26.6938	−0.996898
$718$	−12.8615	−0.479988
$719$	14.4770	0.539900	0.269950	−	0.962874i	$-0.412993\pi$
$719$	14.4770	0.539900	0.269950	+	0.962874i	$0.412993\pi$
$720$	40.1916	1.49785
$721$	−1.82954	−0.0681358
$722$	−70.1440	−2.61049
$723$	5.29337	0.196862
$724$	92.6440	3.44309
$725$	11.1257	0.413199
$726$	−62.5036	−2.31973
$727$	24.3487	0.903043	0.451522	−	0.892260i	$-0.350881\pi$
$727$	24.3487	0.903043	0.451522	+	0.892260i	$0.350881\pi$
$728$	−46.4013	−1.71975
$729$	1.00000	0.0370370
$730$	−16.2722	−0.602261
$731$	−2.76403	−0.102231
$732$	22.7582	0.841167
$733$	11.0638	0.408650	0.204325	−	0.978903i	$-0.434500\pi$
$733$	11.0638	0.408650	0.204325	+	0.978903i	$0.434500\pi$
$734$	−28.5821	−1.05499
$735$	−7.23877	−0.267006
$736$	155.685	5.73864
$737$	−27.7473	−1.02209
$738$	−25.6785	−0.945237
$739$	49.5529	1.82283	0.911417	−	0.411485i	$-0.134990\pi$
$739$	49.5529	1.82283	0.911417	+	0.411485i	$0.134990\pi$
$740$	−22.8189	−0.838839
$741$	15.5317	0.570570
$742$	51.1918	1.87931
$743$	0.567673	0.0208259	0.0104130	−	0.999946i	$-0.496685\pi$
$743$	0.567673	0.0208259	0.0104130	+	0.999946i	$0.496685\pi$
$744$	74.9653	2.74836
$745$	−36.6744	−1.34365
$746$	−5.64517	−0.206684
$747$	−15.9263	−0.582712
$748$	32.2594	1.17952
$749$	−17.4890	−0.639033
$750$	24.3983	0.890900
$751$	−34.6706	−1.26515	−0.632575	−	0.774499i	$-0.718002\pi$
$751$	−34.6706	−1.26515	−0.632575	+	0.774499i	$0.718002\pi$
$752$	195.125	7.11549
$753$	15.0828	0.549646
$754$	46.6860	1.70020
$755$	31.1644	1.13419
$756$	−11.3353	−0.412261
$757$	−38.7354	−1.40786	−0.703931	−	0.710269i	$-0.748574\pi$
$757$	−38.7354	−1.40786	−0.703931	+	0.710269i	$0.748574\pi$
$758$	−76.7406	−2.78734
$759$	38.1387	1.38435
$760$	166.456	6.03800
$761$	22.7903	0.826146	0.413073	−	0.910698i	$-0.364455\pi$
$761$	22.7903	0.826146	0.413073	+	0.910698i	$0.364455\pi$
$762$	−21.6287	−0.783524
$763$	37.2221	1.34753
$764$	39.8068	1.44016
$765$	−2.55432	−0.0923518
$766$	−21.6507	−0.782270
$767$	−23.0443	−0.832082
$768$	56.8151	2.05014
$769$	31.4610	1.13451	0.567256	−	0.823541i	$-0.308005\pi$
$769$	31.4610	1.13451	0.567256	+	0.823541i	$0.308005\pi$
$770$	−83.2340	−2.99954
$771$	−1.17061	−0.0421586
$772$	−17.0216	−0.612622
$773$	−33.9744	−1.22197	−0.610987	−	0.791640i	$-0.709227\pi$
$773$	−33.9744	−1.22197	−0.610987	+	0.791640i	$0.709227\pi$
$774$	−7.59658	−0.273053
$775$	−11.7023	−0.420359
$776$	−88.0604	−3.16118
$777$	3.28331	0.117788
$778$	−79.0581	−2.83437
$779$	−62.3420	−2.23364
$780$	−33.0199	−1.18230
$781$	57.9352	2.07309
$782$	−18.0449	−0.645285
$783$	7.29762	0.260796
$784$	−44.5911	−1.59254
$785$	−2.55432	−0.0911677
$786$	−25.1666	−0.897664
$787$	−26.2513	−0.935759	−0.467879	−	0.883792i	$-0.654982\pi$
$787$	−26.2513	−0.935759	−0.467879	+	0.883792i	$0.654982\pi$
$788$	123.996	4.41716
$789$	−27.0225	−0.962025
$790$	35.3894	1.25910
$791$	−13.7268	−0.488070
$792$	56.7313	2.01586
$793$	−9.53890	−0.338736
$794$	1.23641	0.0438784
$795$	23.3097	0.826711
$796$	126.924	4.49869
$797$	20.7100	0.733585	0.366792	−	0.930303i	$-0.380456\pi$
$797$	20.7100	0.733585	0.366792	+	0.930303i	$0.380456\pi$
$798$	−37.4305	−1.32503
$799$	−12.4009	−0.438713
$800$	−36.1506	−1.27812
$801$	−6.49694	−0.229558
$802$	−79.2310	−2.79774
$803$	−13.4642	−0.475141
$804$	26.5280	0.935572
$805$	34.2309	1.20648
$806$	−49.1054	−1.72966
$807$	−13.3311	−0.469275
$808$	86.7034	3.05021
$809$	19.7478	0.694297	0.347148	−	0.937810i	$-0.387150\pi$
$809$	19.7478	0.694297	0.347148	+	0.937810i	$0.387150\pi$
$810$	−7.02023	−0.246666
$811$	−12.1231	−0.425698	−0.212849	−	0.977085i	$-0.568274\pi$
$811$	−12.1231	−0.425698	−0.212849	+	0.977085i	$0.568274\pi$
$812$	−82.7208	−2.90293
$813$	6.05912	0.212503
$814$	−25.6809	−0.900113
$815$	−50.1898	−1.75807
$816$	−15.7347	−0.550826
$817$	−18.4429	−0.645237
$818$	63.9727	2.23675
$819$	4.75110	0.166017
$820$	132.538	4.62842
$821$	−20.7455	−0.724024	−0.362012	−	0.932173i	$-0.617910\pi$
$821$	−20.7455	−0.724024	−0.362012	+	0.932173i	$0.617910\pi$
$822$	−13.0607	−0.455545
$823$	9.74260	0.339606	0.169803	−	0.985478i	$-0.445687\pi$
$823$	9.74260	0.339606	0.169803	+	0.985478i	$0.445687\pi$
$824$	−8.75420	−0.304967
$825$	−8.85591	−0.308323
$826$	55.5357	1.93233
$827$	−42.3542	−1.47280	−0.736400	−	0.676547i	$-0.763476\pi$
$827$	−42.3542	−1.47280	−0.736400	+	0.676547i	$0.763476\pi$
$828$	−36.4628	−1.26717
$829$	−26.0893	−0.906119	−0.453060	−	0.891480i	$-0.649668\pi$
$829$	−26.0893	−0.906119	−0.453060	+	0.891480i	$0.649668\pi$
$830$	111.806	3.88085
$831$	−7.42038	−0.257410
$832$	−78.4439	−2.71955
$833$	2.83393	0.0981898
$834$	46.3066	1.60347
$835$	19.1271	0.661919
$836$	215.250	7.44458
$837$	−7.67579	−0.265314
$838$	4.54291	0.156932
$839$	21.2546	0.733789	0.366894	−	0.930263i	$-0.380421\pi$
$839$	21.2546	0.733789	0.366894	+	0.930263i	$0.380421\pi$
$840$	50.9186	1.75686
$841$	24.2552	0.836387
$842$	−30.6876	−1.05757
$843$	−17.8702	−0.615482
$844$	−131.019	−4.50986
$845$	−19.3662	−0.666217
$846$	−34.0823	−1.17177
$847$	−46.4187	−1.59497
$848$	143.589	4.93087
$849$	−9.81438	−0.336829
$850$	4.19009	0.143719
$851$	10.5616	0.362045
$852$	−55.3894	−1.89761
$853$	26.2844	0.899962	0.449981	−	0.893038i	$-0.351431\pi$
$853$	26.2844	0.899962	0.449981	+	0.893038i	$0.351431\pi$
$854$	22.9883	0.786643
$855$	−17.0437	−0.582882
$856$	−83.6831	−2.86023
$857$	−4.22891	−0.144457	−0.0722285	−	0.997388i	$-0.523011\pi$
$857$	−4.22891	−0.144457	−0.0722285	+	0.997388i	$0.523011\pi$
$858$	−37.1614	−1.26867
$859$	15.2998	0.522021	0.261011	−	0.965336i	$-0.415944\pi$
$859$	15.2998	0.522021	0.261011	+	0.965336i	$0.415944\pi$
$860$	39.2093	1.33703
$861$	−19.0703	−0.649913
$862$	54.8470	1.86810
$863$	−31.1438	−1.06015	−0.530074	−	0.847951i	$-0.677836\pi$
$863$	−31.1438	−1.06015	−0.530074	+	0.847951i	$0.677836\pi$
$864$	−23.7120	−0.806699
$865$	4.44076	0.150990
$866$	3.59796	0.122264
$867$	1.00000	0.0339618
$868$	87.0075	2.95323
$869$	29.2825	0.993340
$870$	−51.2309	−1.73689
$871$	−11.1190	−0.376753
$872$	178.104	6.03138
$873$	9.01662	0.305166
$874$	−120.404	−4.07274
$875$	18.1196	0.612553
$876$	12.8726	0.434923
$877$	20.6346	0.696780	0.348390	−	0.937350i	$-0.386728\pi$
$877$	20.6346	0.696780	0.348390	+	0.937350i	$0.386728\pi$
$878$	−39.9482	−1.34819
$879$	28.5326	0.962382
$880$	−233.465	−7.87010
$881$	−38.2108	−1.28736	−0.643678	−	0.765297i	$-0.722592\pi$
$881$	−38.2108	−1.28736	−0.643678	+	0.765297i	$0.722592\pi$
$882$	7.78869	0.262259
$883$	39.9989	1.34607	0.673034	−	0.739611i	$-0.264991\pi$
$883$	39.9989	1.34607	0.673034	+	0.739611i	$0.264991\pi$
$884$	12.9271	0.434785
$885$	25.2877	0.850037
$886$	97.1672	3.26440
$887$	−27.0900	−0.909594	−0.454797	−	0.890595i	$-0.650288\pi$
$887$	−27.0900	−0.909594	−0.454797	+	0.890595i	$0.650288\pi$
$888$	15.7103	0.527204
$889$	−16.0627	−0.538725
$890$	45.6100	1.52885
$891$	−5.80879	−0.194602
$892$	−10.8294	−0.362595
$893$	−82.7449	−2.76895
$894$	39.4605	1.31976
$895$	63.6116	2.12630
$896$	92.2490	3.08182
$897$	15.2830	0.510286
$898$	−86.7453	−2.89473
$899$	−56.0150	−1.86820
$900$	8.46677	0.282226
$901$	−9.12560	−0.304018
$902$	149.161	4.96651
$903$	−5.64165	−0.187742
$904$	−65.6816	−2.18454
$905$	42.6112	1.41644
$906$	−33.5319	−1.11402
$907$	42.4487	1.40949	0.704743	−	0.709463i	$-0.251062\pi$
$907$	42.4487	1.40949	0.704743	+	0.709463i	$0.251062\pi$
$908$	95.3468	3.16420
$909$	−8.87768	−0.294454
$910$	−33.3538	−1.10567
$911$	41.1238	1.36249	0.681245	−	0.732055i	$-0.261439\pi$
$911$	41.1238	1.36249	0.681245	+	0.732055i	$0.261439\pi$
$912$	−104.990	−3.47656
$913$	92.5124	3.06172
$914$	103.091	3.40995
$915$	10.4675	0.346046
$916$	56.9109	1.88039
$917$	−18.6902	−0.617204
$918$	2.74837	0.0907098
$919$	3.90559	0.128834	0.0644168	−	0.997923i	$-0.479481\pi$
$919$	3.90559	0.128834	0.0644168	+	0.997923i	$0.479481\pi$
$920$	163.792	5.40006
$921$	0.195445	0.00644015
$922$	−8.71606	−0.287048
$923$	23.2160	0.764164
$924$	65.8445	2.16612
$925$	−2.45243	−0.0806353
$926$	−113.882	−3.74239
$927$	0.896354	0.0294401
$928$	−173.041	−5.68036
$929$	9.28197	0.304532	0.152266	−	0.988340i	$-0.451343\pi$
$929$	9.28197	0.304532	0.152266	+	0.988340i	$0.451343\pi$
$930$	53.8858	1.76699
$931$	18.9093	0.619728
$932$	154.756	5.06921
$933$	−11.2345	−0.367801
$934$	−81.3190	−2.66084
$935$	14.8375	0.485239
$936$	22.7335	0.743069
$937$	−19.1420	−0.625342	−0.312671	−	0.949861i	$-0.601224\pi$
$937$	−19.1420	−0.625342	−0.312671	+	0.949861i	$0.601224\pi$
$938$	26.7962	0.874928
$939$	11.1660	0.364387
$940$	175.914	5.73767
$941$	11.9882	0.390806	0.195403	−	0.980723i	$-0.437399\pi$
$941$	11.9882	0.390806	0.195403	+	0.980723i	$0.437399\pi$
$942$	2.74837	0.0895468
$943$	−61.3442	−1.99764
$944$	155.773	5.06999
$945$	−5.21362	−0.169599
$946$	44.1269	1.43469
$947$	−22.0296	−0.715866	−0.357933	−	0.933747i	$-0.616518\pi$
$947$	−22.0296	−0.715866	−0.357933	+	0.933747i	$0.616518\pi$
$948$	−27.9958	−0.909260
$949$	−5.39542	−0.175143
$950$	27.9583	0.907086
$951$	30.7138	0.995963
$952$	−19.9343	−0.646073
$953$	19.6992	0.638119	0.319060	−	0.947735i	$-0.396633\pi$
$953$	19.6992	0.638119	0.319060	+	0.947735i	$0.396633\pi$
$954$	−25.0805	−0.812012
$955$	18.3089	0.592463
$956$	−148.245	−4.79459
$957$	−42.3903	−1.37029
$958$	−61.7772	−1.99593
$959$	−9.69964	−0.313218
$960$	86.0805	2.77824
$961$	27.9178	0.900574
$962$	−10.2909	−0.331792
$963$	8.56843	0.276114
$964$	29.3969	0.946812
$965$	−7.82902	−0.252025
$966$	−36.8314	−1.18503
$967$	53.1241	1.70836	0.854178	−	0.519980i	$-0.174061\pi$
$967$	53.1241	1.70836	0.854178	+	0.519980i	$0.174061\pi$
$968$	−222.109	−7.13886
$969$	6.67248	0.214351
$970$	−63.2987	−2.03240
$971$	17.0137	0.545996	0.272998	−	0.962015i	$-0.411985\pi$
$971$	17.0137	0.545996	0.272998	+	0.962015i	$0.411985\pi$
$972$	5.55354	0.178130
$973$	34.3899	1.10249
$974$	89.7631	2.87619
$975$	−3.54877	−0.113652
$976$	64.4804	2.06397
$977$	6.12295	0.195890	0.0979452	−	0.995192i	$-0.468773\pi$
$977$	6.12295	0.195890	0.0979452	+	0.995192i	$0.468773\pi$
$978$	54.0027	1.72681
$979$	37.7394	1.20616
$980$	−40.2008	−1.28417
$981$	−18.2364	−0.582242
$982$	70.6945	2.25595
$983$	0.537123	0.0171316	0.00856578	−	0.999963i	$-0.497273\pi$
$983$	0.537123	0.0171316	0.00856578	+	0.999963i	$0.497273\pi$
$984$	−91.2495	−2.90893
$985$	57.0312	1.81716
$986$	20.0566	0.638731
$987$	−25.3115	−0.805673
$988$	86.2557	2.74416
$989$	−18.1477	−0.577064
$990$	40.7791	1.29604
$991$	−18.7623	−0.596005	−0.298003	−	0.954565i	$-0.596320\pi$
$991$	−18.7623	−0.596005	−0.298003	+	0.954565i	$0.596320\pi$
$992$	182.008	5.77878
$993$	19.1659	0.608212
$994$	−55.9494	−1.77461
$995$	58.3779	1.85070
$996$	−88.4473	−2.80256
$997$	44.4058	1.40635	0.703173	−	0.711019i	$-0.251766\pi$
$997$	44.4058	1.40635	0.703173	+	0.711019i	$0.251766\pi$
$998$	34.9235	1.10548
$999$	−1.60860	−0.0508939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.1	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74837 q^{2} +1.00000 q^{3} +5.55354 q^{4} +2.55432 q^{5} -2.74837 q^{6} -2.04110 q^{7} -9.76645 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.74837 q^{2} +1.00000 q^{3} +5.55354 q^{4} +2.55432 q^{5} -2.74837 q^{6} -2.04110 q^{7} -9.76645 q^{8} +1.00000 q^{9} -7.02023 q^{10} -5.80879 q^{11} +5.55354 q^{12} -2.32772 q^{13} +5.60969 q^{14} +2.55432 q^{15} +15.7347 q^{16} -1.00000 q^{17} -2.74837 q^{18} -6.67248 q^{19} +14.1855 q^{20} -2.04110 q^{21} +15.9647 q^{22} -6.56568 q^{23} -9.76645 q^{24} +1.52457 q^{25} +6.39743 q^{26} +1.00000 q^{27} -11.3353 q^{28} +7.29762 q^{29} -7.02023 q^{30} -7.67579 q^{31} -23.7120 q^{32} -5.80879 q^{33} +2.74837 q^{34} -5.21362 q^{35} +5.55354 q^{36} -1.60860 q^{37} +18.3385 q^{38} -2.32772 q^{39} -24.9467 q^{40} +9.34316 q^{41} +5.60969 q^{42} +2.76403 q^{43} -32.2594 q^{44} +2.55432 q^{45} +18.0449 q^{46} +12.4009 q^{47} +15.7347 q^{48} -2.83393 q^{49} -4.19009 q^{50} -1.00000 q^{51} -12.9271 q^{52} +9.12560 q^{53} -2.74837 q^{54} -14.8375 q^{55} +19.9343 q^{56} -6.67248 q^{57} -20.0566 q^{58} +9.89996 q^{59} +14.1855 q^{60} +4.09796 q^{61} +21.0959 q^{62} -2.04110 q^{63} +33.6999 q^{64} -5.94575 q^{65} +15.9647 q^{66} +4.77678 q^{67} -5.55354 q^{68} -6.56568 q^{69} +14.3290 q^{70} -9.97371 q^{71} -9.76645 q^{72} +2.31790 q^{73} +4.42103 q^{74} +1.52457 q^{75} -37.0559 q^{76} +11.8563 q^{77} +6.39743 q^{78} -5.04106 q^{79} +40.1916 q^{80} +1.00000 q^{81} -25.6785 q^{82} -15.9263 q^{83} -11.3353 q^{84} -2.55432 q^{85} -7.59658 q^{86} +7.29762 q^{87} +56.7313 q^{88} -6.49694 q^{89} -7.02023 q^{90} +4.75110 q^{91} -36.4628 q^{92} -7.67579 q^{93} -34.0823 q^{94} -17.0437 q^{95} -23.7120 q^{96} +9.01662 q^{97} +7.78869 q^{98} -5.80879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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