LMFDB - Embedded newform 1045.2.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 8x^{4} + 27x^{3} - 16x^{2} - 18x + 11 $ x^7 - x^6 - 10x^5 + 8x^4 + 27x^3 - 16x^2 - 18*x + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.97792$ of defining polynomial
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.97792 q^{2} +2.65412 q^{3} +1.91218 q^{4} -1.00000 q^{5} +5.24965 q^{6} +1.06653 q^{7} -0.173707 q^{8} +4.04436 q^{9} +O(q^{10})$	\(q+1.97792 q^{2} +2.65412 q^{3} +1.91218 q^{4} -1.00000 q^{5} +5.24965 q^{6} +1.06653 q^{7} -0.173707 q^{8} +4.04436 q^{9} -1.97792 q^{10} +1.00000 q^{11} +5.07515 q^{12} +0.939291 q^{13} +2.10952 q^{14} -2.65412 q^{15} -4.16793 q^{16} +3.65839 q^{17} +7.99944 q^{18} -1.00000 q^{19} -1.91218 q^{20} +2.83071 q^{21} +1.97792 q^{22} +5.35035 q^{23} -0.461041 q^{24} +1.00000 q^{25} +1.85784 q^{26} +2.77187 q^{27} +2.03940 q^{28} -4.46966 q^{29} -5.24965 q^{30} -2.71979 q^{31} -7.89643 q^{32} +2.65412 q^{33} +7.23600 q^{34} -1.06653 q^{35} +7.73354 q^{36} +0.932050 q^{37} -1.97792 q^{38} +2.49299 q^{39} +0.173707 q^{40} -1.21816 q^{41} +5.59893 q^{42} -3.58402 q^{43} +1.91218 q^{44} -4.04436 q^{45} +10.5826 q^{46} -4.30223 q^{47} -11.0622 q^{48} -5.86250 q^{49} +1.97792 q^{50} +9.70980 q^{51} +1.79609 q^{52} -12.1575 q^{53} +5.48254 q^{54} -1.00000 q^{55} -0.185265 q^{56} -2.65412 q^{57} -8.84063 q^{58} -6.15610 q^{59} -5.07515 q^{60} +2.13701 q^{61} -5.37953 q^{62} +4.31345 q^{63} -7.28267 q^{64} -0.939291 q^{65} +5.24965 q^{66} +4.93275 q^{67} +6.99548 q^{68} +14.2005 q^{69} -2.10952 q^{70} +7.32299 q^{71} -0.702536 q^{72} +1.14496 q^{73} +1.84352 q^{74} +2.65412 q^{75} -1.91218 q^{76} +1.06653 q^{77} +4.93095 q^{78} -6.71067 q^{79} +4.16793 q^{80} -4.77622 q^{81} -2.40943 q^{82} +2.82737 q^{83} +5.41282 q^{84} -3.65839 q^{85} -7.08891 q^{86} -11.8630 q^{87} -0.173707 q^{88} -8.77091 q^{89} -7.99944 q^{90} +1.00179 q^{91} +10.2308 q^{92} -7.21866 q^{93} -8.50948 q^{94} +1.00000 q^{95} -20.9581 q^{96} +13.3420 q^{97} -11.5956 q^{98} +4.04436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9	\( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9} - q^{10} + 7 q^{11} + 13 q^{12} + q^{13} + 12 q^{14} - 3 q^{15} + 3 q^{16} + q^{17} + 7 q^{18} - 7 q^{19} - 7 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 25 q^{24} + 7 q^{25} + 12 q^{27} + 4 q^{28} + 11 q^{29} - 8 q^{30} + 7 q^{31} + 12 q^{32} + 3 q^{33} - 14 q^{34} + q^{35} + 7 q^{36} - 17 q^{37} - q^{38} + 30 q^{39} - 3 q^{40} + 17 q^{41} + 33 q^{42} - 3 q^{43} + 7 q^{44} - 2 q^{45} + 18 q^{46} + 14 q^{47} - 12 q^{48} + 6 q^{49} + q^{50} + 8 q^{51} - 17 q^{52} + 7 q^{53} - 27 q^{54} - 7 q^{55} + 36 q^{56} - 3 q^{57} - 15 q^{58} + 35 q^{59} - 13 q^{60} + 17 q^{61} + 46 q^{62} - 22 q^{63} + 5 q^{64} - q^{65} + 8 q^{66} + 4 q^{67} - 35 q^{68} - 4 q^{69} - 12 q^{70} + 10 q^{71} + 12 q^{72} + 22 q^{73} - 11 q^{74} + 3 q^{75} - 7 q^{76} - q^{77} - 41 q^{78} + 11 q^{79} - 3 q^{80} - 21 q^{81} - 14 q^{82} + 39 q^{83} + 21 q^{84} - q^{85} - 24 q^{86} - 2 q^{87} + 3 q^{88} + 18 q^{89} - 7 q^{90} - 22 q^{91} - 51 q^{92} + 10 q^{93} + 14 q^{94} + 7 q^{95} - 11 q^{96} - 4 q^{97} - 26 q^{98} + 2 q^{99}+O(q^{100}) \) 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9 - q^10 + 7 * q^11 + 13 * q^12 + q^13 + 12 * q^14 - 3 * q^15 + 3 * q^16 + q^17 + 7 * q^18 - 7 * q^19 - 7 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 25 * q^24 + 7 * q^25 + 12 * q^27 + 4 * q^28 + 11 * q^29 - 8 * q^30 + 7 * q^31 + 12 * q^32 + 3 * q^33 - 14 * q^34 + q^35 + 7 * q^36 - 17 * q^37 - q^38 + 30 * q^39 - 3 * q^40 + 17 * q^41 + 33 * q^42 - 3 * q^43 + 7 * q^44 - 2 * q^45 + 18 * q^46 + 14 * q^47 - 12 * q^48 + 6 * q^49 + q^50 + 8 * q^51 - 17 * q^52 + 7 * q^53 - 27 * q^54 - 7 * q^55 + 36 * q^56 - 3 * q^57 - 15 * q^58 + 35 * q^59 - 13 * q^60 + 17 * q^61 + 46 * q^62 - 22 * q^63 + 5 * q^64 - q^65 + 8 * q^66 + 4 * q^67 - 35 * q^68 - 4 * q^69 - 12 * q^70 + 10 * q^71 + 12 * q^72 + 22 * q^73 - 11 * q^74 + 3 * q^75 - 7 * q^76 - q^77 - 41 * q^78 + 11 * q^79 - 3 * q^80 - 21 * q^81 - 14 * q^82 + 39 * q^83 + 21 * q^84 - q^85 - 24 * q^86 - 2 * q^87 + 3 * q^88 + 18 * q^89 - 7 * q^90 - 22 * q^91 - 51 * q^92 + 10 * q^93 + 14 * q^94 + 7 * q^95 - 11 * q^96 - 4 * q^97 - 26 * q^98 + 2 * 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 $

$2$	1.97792	1.39860	0.699301	−	0.714827i	$-0.253495\pi$
$2$	1.97792	1.39860	0.699301	+	0.714827i	$0.253495\pi$
$3$	2.65412	1.53236	0.766179	−	0.642627i	$-0.222156\pi$
$3$	2.65412	1.53236	0.766179	+	0.642627i	$0.222156\pi$
$4$	1.91218	0.956088
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.24965	2.14316
$7$	1.06653	0.403112	0.201556	−	0.979477i	$-0.435400\pi$
$7$	1.06653	0.403112	0.201556	+	0.979477i	$0.435400\pi$
$8$	−0.173707	−0.0614148
$9$	4.04436	1.34812
$10$	−1.97792	−0.625474
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.07515	1.46507
$13$	0.939291	0.260512	0.130256	−	0.991480i	$-0.458420\pi$
$13$	0.939291	0.260512	0.130256	+	0.991480i	$0.458420\pi$
$14$	2.10952	0.563794
$15$	−2.65412	−0.685291
$16$	−4.16793	−1.04198
$17$	3.65839	0.887289	0.443645	−	0.896203i	$-0.353685\pi$
$17$	3.65839	0.887289	0.443645	+	0.896203i	$0.353685\pi$
$18$	7.99944	1.88549
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.91218	−0.427576
$21$	2.83071	0.617712
$22$	1.97792	0.421694
$23$	5.35035	1.11563	0.557813	−	0.829967i	$-0.311641\pi$
$23$	5.35035	1.11563	0.557813	+	0.829967i	$0.311641\pi$
$24$	−0.461041	−0.0941095
$25$	1.00000	0.200000
$26$	1.85784	0.364353
$27$	2.77187	0.533446
$28$	2.03940	0.385411
$29$	−4.46966	−0.829994	−0.414997	−	0.909823i	$-0.636217\pi$
$29$	−4.46966	−0.829994	−0.414997	+	0.909823i	$0.636217\pi$
$30$	−5.24965	−0.958450
$31$	−2.71979	−0.488489	−0.244244	−	0.969714i	$-0.578540\pi$
$31$	−2.71979	−0.488489	−0.244244	+	0.969714i	$0.578540\pi$
$32$	−7.89643	−1.39591
$33$	2.65412	0.462023
$34$	7.23600	1.24096
$35$	−1.06653	−0.180277
$36$	7.73354	1.28892
$37$	0.932050	0.153228	0.0766141	−	0.997061i	$-0.475589\pi$
$37$	0.932050	0.153228	0.0766141	+	0.997061i	$0.475589\pi$
$38$	−1.97792	−0.320861
$39$	2.49299	0.399198
$40$	0.173707	0.0274656
$41$	−1.21816	−0.190245	−0.0951227	−	0.995466i	$-0.530324\pi$
$41$	−1.21816	−0.190245	−0.0951227	+	0.995466i	$0.530324\pi$
$42$	5.59893	0.863934
$43$	−3.58402	−0.546558	−0.273279	−	0.961935i	$-0.588108\pi$
$43$	−3.58402	−0.546558	−0.273279	+	0.961935i	$0.588108\pi$
$44$	1.91218	0.288272
$45$	−4.04436	−0.602898
$46$	10.5826	1.56032
$47$	−4.30223	−0.627545	−0.313772	−	0.949498i	$-0.601593\pi$
$47$	−4.30223	−0.627545	−0.313772	+	0.949498i	$0.601593\pi$
$48$	−11.0622	−1.59669
$49$	−5.86250	−0.837501
$50$	1.97792	0.279720
$51$	9.70980	1.35964
$52$	1.79609	0.249073
$53$	−12.1575	−1.66996	−0.834980	−	0.550280i	$-0.814521\pi$
$53$	−12.1575	−1.66996	−0.834980	+	0.550280i	$0.814521\pi$
$54$	5.48254	0.746079
$55$	−1.00000	−0.134840
$56$	−0.185265	−0.0247571
$57$	−2.65412	−0.351547
$58$	−8.84063	−1.16083
$59$	−6.15610	−0.801456	−0.400728	−	0.916197i	$-0.631243\pi$
$59$	−6.15610	−0.801456	−0.400728	+	0.916197i	$0.631243\pi$
$60$	−5.07515	−0.655199
$61$	2.13701	0.273616	0.136808	−	0.990598i	$-0.456316\pi$
$61$	2.13701	0.273616	0.136808	+	0.990598i	$0.456316\pi$
$62$	−5.37953	−0.683202
$63$	4.31345	0.543444
$64$	−7.28267	−0.910333
$65$	−0.939291	−0.116505
$66$	5.24965	0.646187
$67$	4.93275	0.602631	0.301315	−	0.953525i	$-0.402574\pi$
$67$	4.93275	0.602631	0.301315	+	0.953525i	$0.402574\pi$
$68$	6.99548	0.848327
$69$	14.2005	1.70954
$70$	−2.10952	−0.252136
$71$	7.32299	0.869079	0.434539	−	0.900653i	$-0.356911\pi$
$71$	7.32299	0.869079	0.434539	+	0.900653i	$0.356911\pi$
$72$	−0.702536	−0.0827946
$73$	1.14496	0.134008	0.0670038	−	0.997753i	$-0.478656\pi$
$73$	1.14496	0.134008	0.0670038	+	0.997753i	$0.478656\pi$
$74$	1.84352	0.214305
$75$	2.65412	0.306472
$76$	−1.91218	−0.219342
$77$	1.06653	0.121543
$78$	4.93095	0.558320
$79$	−6.71067	−0.755009	−0.377505	−	0.926008i	$-0.623218\pi$
$79$	−6.71067	−0.755009	−0.377505	+	0.926008i	$0.623218\pi$
$80$	4.16793	0.465989
$81$	−4.77622	−0.530691
$82$	−2.40943	−0.266078
$83$	2.82737	0.310344	0.155172	−	0.987887i	$-0.450407\pi$
$83$	2.82737	0.310344	0.155172	+	0.987887i	$0.450407\pi$
$84$	5.41282	0.590588
$85$	−3.65839	−0.396808
$86$	−7.08891	−0.764417
$87$	−11.8630	−1.27185
$88$	−0.173707	−0.0185173
$89$	−8.77091	−0.929714	−0.464857	−	0.885386i	$-0.653894\pi$
$89$	−8.77091	−0.929714	−0.464857	+	0.885386i	$0.653894\pi$
$90$	−7.99944	−0.843215
$91$	1.00179	0.105016
$92$	10.2308	1.06664
$93$	−7.21866	−0.748540
$94$	−8.50948	−0.877686
$95$	1.00000	0.102598
$96$	−20.9581	−2.13903
$97$	13.3420	1.35468	0.677339	−	0.735671i	$-0.263133\pi$
$97$	13.3420	1.35468	0.677339	+	0.735671i	$0.263133\pi$
$98$	−11.5956	−1.17133
$99$	4.04436	0.406474
$100$	1.91218	0.191218
$101$	−0.926286	−0.0921689	−0.0460845	−	0.998938i	$-0.514674\pi$
$101$	−0.926286	−0.0921689	−0.0460845	+	0.998938i	$0.514674\pi$
$102$	19.2052	1.90160
$103$	−10.4344	−1.02814	−0.514068	−	0.857749i	$-0.671862\pi$
$103$	−10.4344	−1.02814	−0.514068	+	0.857749i	$0.671862\pi$
$104$	−0.163162	−0.0159993
$105$	−2.83071	−0.276249
$106$	−24.0466	−2.33561
$107$	13.5595	1.31085	0.655426	−	0.755260i	$-0.272489\pi$
$107$	13.5595	1.31085	0.655426	+	0.755260i	$0.272489\pi$
$108$	5.30030	0.510022
$109$	5.85440	0.560750	0.280375	−	0.959891i	$-0.409541\pi$
$109$	5.85440	0.560750	0.280375	+	0.959891i	$0.409541\pi$
$110$	−1.97792	−0.188587
$111$	2.47378	0.234800
$112$	−4.44525	−0.420036
$113$	8.68686	0.817191	0.408595	−	0.912716i	$-0.366019\pi$
$113$	8.68686	0.817191	0.408595	+	0.912716i	$0.366019\pi$
$114$	−5.24965	−0.491674
$115$	−5.35035	−0.498923
$116$	−8.54677	−0.793548
$117$	3.79883	0.351202
$118$	−12.1763	−1.12092
$119$	3.90180	0.357677
$120$	0.461041	0.0420871
$121$	1.00000	0.0909091
$122$	4.22684	0.382680
$123$	−3.23316	−0.291524
$124$	−5.20072	−0.467039
$125$	−1.00000	−0.0894427
$126$	8.53168	0.760062
$127$	−15.9545	−1.41573	−0.707866	−	0.706347i	$-0.750342\pi$
$127$	−15.9545	−1.41573	−0.707866	+	0.706347i	$0.750342\pi$
$128$	1.38832	0.122711
$129$	−9.51242	−0.837522
$130$	−1.85784	−0.162944
$131$	5.20014	0.454338	0.227169	−	0.973855i	$-0.427053\pi$
$131$	5.20014	0.454338	0.227169	+	0.973855i	$0.427053\pi$
$132$	5.07515	0.441735
$133$	−1.06653	−0.0924803
$134$	9.75659	0.842841
$135$	−2.77187	−0.238564
$136$	−0.635489	−0.0544927
$137$	7.54419	0.644544	0.322272	−	0.946647i	$-0.395553\pi$
$137$	7.54419	0.644544	0.322272	+	0.946647i	$0.395553\pi$
$138$	28.0875	2.39096
$139$	0.357301	0.0303059	0.0151529	−	0.999885i	$-0.495176\pi$
$139$	0.357301	0.0303059	0.0151529	+	0.999885i	$0.495176\pi$
$140$	−2.03940	−0.172361
$141$	−11.4186	−0.961624
$142$	14.4843	1.21550
$143$	0.939291	0.0785475
$144$	−16.8566	−1.40472
$145$	4.46966	0.371185
$146$	2.26465	0.187423
$147$	−15.5598	−1.28335
$148$	1.78224	0.146500
$149$	−10.7634	−0.881769	−0.440884	−	0.897564i	$-0.645335\pi$
$149$	−10.7634	−0.881769	−0.440884	+	0.897564i	$0.645335\pi$
$150$	5.24965	0.428632
$151$	7.13976	0.581025	0.290513	−	0.956871i	$-0.406174\pi$
$151$	7.13976	0.581025	0.290513	+	0.956871i	$0.406174\pi$
$152$	0.173707	0.0140895
$153$	14.7958	1.19617
$154$	2.10952	0.169990
$155$	2.71979	0.218459
$156$	4.76704	0.381669
$157$	12.7164	1.01488	0.507440	−	0.861687i	$-0.330592\pi$
$157$	12.7164	1.01488	0.507440	+	0.861687i	$0.330592\pi$
$158$	−13.2732	−1.05596
$159$	−32.2675	−2.55898
$160$	7.89643	0.624268
$161$	5.70633	0.449722
$162$	−9.44699	−0.742225
$163$	−4.45308	−0.348792	−0.174396	−	0.984676i	$-0.555797\pi$
$163$	−4.45308	−0.348792	−0.174396	+	0.984676i	$0.555797\pi$
$164$	−2.32935	−0.181891
$165$	−2.65412	−0.206623
$166$	5.59231	0.434047
$167$	10.0911	0.780874	0.390437	−	0.920630i	$-0.372324\pi$
$167$	10.0911	0.780874	0.390437	+	0.920630i	$0.372324\pi$
$168$	−0.491716	−0.0379367
$169$	−12.1177	−0.932133
$170$	−7.23600	−0.554976
$171$	−4.04436	−0.309280
$172$	−6.85328	−0.522558
$173$	23.8006	1.80952	0.904762	−	0.425917i	$-0.140048\pi$
$173$	23.8006	1.80952	0.904762	+	0.425917i	$0.140048\pi$
$174$	−23.4641	−1.77881
$175$	1.06653	0.0806224
$176$	−4.16793	−0.314170
$177$	−16.3390	−1.22812
$178$	−17.3482	−1.30030
$179$	20.0682	1.49997	0.749985	−	0.661455i	$-0.230061\pi$
$179$	20.0682	1.49997	0.749985	+	0.661455i	$0.230061\pi$
$180$	−7.73354	−0.576424
$181$	7.49807	0.557327	0.278663	−	0.960389i	$-0.410109\pi$
$181$	7.49807	0.557327	0.278663	+	0.960389i	$0.410109\pi$
$182$	1.98146	0.146875
$183$	5.67188	0.419278
$184$	−0.929396	−0.0685160
$185$	−0.932050	−0.0685257
$186$	−14.2779	−1.04691
$187$	3.65839	0.267528
$188$	−8.22663	−0.599988
$189$	2.95629	0.215039
$190$	1.97792	0.143494
$191$	−4.21863	−0.305250	−0.152625	−	0.988284i	$-0.548773\pi$
$191$	−4.21863	−0.305250	−0.152625	+	0.988284i	$0.548773\pi$
$192$	−19.3291	−1.39496
$193$	7.70714	0.554772	0.277386	−	0.960759i	$-0.410532\pi$
$193$	7.70714	0.554772	0.277386	+	0.960759i	$0.410532\pi$
$194$	26.3895	1.89465
$195$	−2.49299	−0.178527
$196$	−11.2101	−0.800725
$197$	18.4285	1.31298	0.656489	−	0.754336i	$-0.272041\pi$
$197$	18.4285	1.31298	0.656489	+	0.754336i	$0.272041\pi$
$198$	7.99944	0.568495
$199$	−21.6489	−1.53465	−0.767324	−	0.641260i	$-0.778412\pi$
$199$	−21.6489	−1.53465	−0.767324	+	0.641260i	$0.778412\pi$
$200$	−0.173707	−0.0122830
$201$	13.0921	0.923446
$202$	−1.83212	−0.128908
$203$	−4.76704	−0.334581
$204$	18.5669	1.29994
$205$	1.21816	0.0850803
$206$	−20.6385	−1.43795
$207$	21.6388	1.50400
$208$	−3.91490	−0.271450
$209$	−1.00000	−0.0691714
$210$	−5.59893	−0.386363
$211$	23.9164	1.64647	0.823235	−	0.567700i	$-0.192167\pi$
$211$	23.9164	1.64647	0.823235	+	0.567700i	$0.192167\pi$
$212$	−23.2473	−1.59663
$213$	19.4361	1.33174
$214$	26.8197	1.83336
$215$	3.58402	0.244428
$216$	−0.481494	−0.0327615
$217$	−2.90075	−0.196916
$218$	11.5795	0.784266
$219$	3.03887	0.205348
$220$	−1.91218	−0.128919
$221$	3.43629	0.231150
$222$	4.89294	0.328392
$223$	4.18886	0.280506	0.140253	−	0.990116i	$-0.455208\pi$
$223$	4.18886	0.280506	0.140253	+	0.990116i	$0.455208\pi$
$224$	−8.42182	−0.562707
$225$	4.04436	0.269624
$226$	17.1819	1.14292
$227$	−8.74816	−0.580636	−0.290318	−	0.956930i	$-0.593761\pi$
$227$	−8.74816	−0.580636	−0.290318	+	0.956930i	$0.593761\pi$
$228$	−5.07515	−0.336110
$229$	−16.8146	−1.11114	−0.555571	−	0.831469i	$-0.687500\pi$
$229$	−16.8146	−1.11114	−0.555571	+	0.831469i	$0.687500\pi$
$230$	−10.5826	−0.697795
$231$	2.83071	0.186247
$232$	0.776412	0.0509740
$233$	−7.41167	−0.485554	−0.242777	−	0.970082i	$-0.578058\pi$
$233$	−7.41167	−0.485554	−0.242777	+	0.970082i	$0.578058\pi$
$234$	7.51380	0.491192
$235$	4.30223	0.280647
$236$	−11.7716	−0.766263
$237$	−17.8109	−1.15694
$238$	7.71745	0.500248
$239$	−19.7326	−1.27640	−0.638199	−	0.769871i	$-0.720320\pi$
$239$	−19.7326	−1.27640	−0.638199	+	0.769871i	$0.720320\pi$
$240$	11.0622	0.714062
$241$	15.0994	0.972640	0.486320	−	0.873781i	$-0.338339\pi$
$241$	15.0994	0.972640	0.486320	+	0.873781i	$0.338339\pi$
$242$	1.97792	0.127146
$243$	−20.9923	−1.34665
$244$	4.08634	0.261601
$245$	5.86250	0.374542
$246$	−6.39493	−0.407726
$247$	−0.939291	−0.0597657
$248$	0.472448	0.0300005
$249$	7.50417	0.475558
$250$	−1.97792	−0.125095
$251$	12.3858	0.781782	0.390891	−	0.920437i	$-0.372167\pi$
$251$	12.3858	0.781782	0.390891	+	0.920437i	$0.372167\pi$
$252$	8.24809	0.519581
$253$	5.35035	0.336374
$254$	−31.5567	−1.98005
$255$	−9.70980	−0.608052
$256$	17.3113	1.08196
$257$	26.5496	1.65612	0.828060	−	0.560639i	$-0.189445\pi$
$257$	26.5496	1.65612	0.828060	+	0.560639i	$0.189445\pi$
$258$	−18.8148	−1.17136
$259$	0.994064	0.0617681
$260$	−1.79609	−0.111389
$261$	−18.0769	−1.11893
$262$	10.2855	0.635438
$263$	15.0108	0.925604	0.462802	−	0.886462i	$-0.346844\pi$
$263$	15.0108	0.925604	0.462802	+	0.886462i	$0.346844\pi$
$264$	−0.461041	−0.0283751
$265$	12.1575	0.746829
$266$	−2.10952	−0.129343
$267$	−23.2791	−1.42466
$268$	9.43228	0.576168
$269$	11.8307	0.721329	0.360664	−	0.932696i	$-0.382550\pi$
$269$	11.8307	0.721329	0.360664	+	0.932696i	$0.382550\pi$
$270$	−5.48254	−0.333657
$271$	−13.4154	−0.814927	−0.407464	−	0.913221i	$-0.633587\pi$
$271$	−13.4154	−0.814927	−0.407464	+	0.913221i	$0.633587\pi$
$272$	−15.2479	−0.924540
$273$	2.65886	0.160922
$274$	14.9218	0.901461
$275$	1.00000	0.0603023
$276$	27.1538	1.63447
$277$	−0.515992	−0.0310030	−0.0155015	−	0.999880i	$-0.504934\pi$
$277$	−0.515992	−0.0310030	−0.0155015	+	0.999880i	$0.504934\pi$
$278$	0.706713	0.0423859
$279$	−10.9998	−0.658542
$280$	0.185265	0.0110717
$281$	21.9281	1.30812	0.654061	−	0.756441i	$-0.273064\pi$
$281$	21.9281	1.30812	0.654061	+	0.756441i	$0.273064\pi$
$282$	−22.5852	−1.34493
$283$	18.6023	1.10579	0.552896	−	0.833250i	$-0.313522\pi$
$283$	18.6023	1.10579	0.552896	+	0.833250i	$0.313522\pi$
$284$	14.0028	0.830916
$285$	2.65412	0.157217
$286$	1.85784	0.109857
$287$	−1.29921	−0.0766902
$288$	−31.9360	−1.88185
$289$	−3.61621	−0.212718
$290$	8.84063	0.519140
$291$	35.4114	2.07585
$292$	2.18937	0.128123
$293$	−5.87287	−0.343097	−0.171548	−	0.985176i	$-0.554877\pi$
$293$	−5.87287	−0.343097	−0.171548	+	0.985176i	$0.554877\pi$
$294$	−30.7761	−1.79490
$295$	6.15610	0.358422
$296$	−0.161904	−0.00941048
$297$	2.77187	0.160840
$298$	−21.2891	−1.23324
$299$	5.02554	0.290634
$300$	5.07515	0.293014
$301$	−3.82248	−0.220324
$302$	14.1219	0.812623
$303$	−2.45848	−0.141236
$304$	4.16793	0.239047
$305$	−2.13701	−0.122365
$306$	29.2650	1.67297
$307$	0.566566	0.0323356	0.0161678	−	0.999869i	$-0.494853\pi$
$307$	0.566566	0.0323356	0.0161678	+	0.999869i	$0.494853\pi$
$308$	2.03940	0.116206
$309$	−27.6943	−1.57547
$310$	5.37953	0.305537
$311$	−22.1715	−1.25723	−0.628616	−	0.777716i	$-0.716378\pi$
$311$	−22.1715	−1.25723	−0.628616	+	0.777716i	$0.716378\pi$
$312$	−0.433051	−0.0245167
$313$	−30.3230	−1.71396	−0.856979	−	0.515351i	$-0.827662\pi$
$313$	−30.3230	−1.71396	−0.856979	+	0.515351i	$0.827662\pi$
$314$	25.1521	1.41941
$315$	−4.31345	−0.243036
$316$	−12.8320	−0.721856
$317$	−13.6662	−0.767569	−0.383785	−	0.923423i	$-0.625379\pi$
$317$	−13.6662	−0.767569	−0.383785	+	0.923423i	$0.625379\pi$
$318$	−63.8225	−3.57899
$319$	−4.46966	−0.250253
$320$	7.28267	0.407113
$321$	35.9887	2.00869
$322$	11.2867	0.628982
$323$	−3.65839	−0.203558
$324$	−9.13297	−0.507387
$325$	0.939291	0.0521025
$326$	−8.80785	−0.487822
$327$	15.5383	0.859269
$328$	0.211604	0.0116839
$329$	−4.58848	−0.252971
$330$	−5.24965	−0.288984
$331$	1.04337	0.0573489	0.0286745	−	0.999589i	$-0.490871\pi$
$331$	1.04337	0.0573489	0.0286745	+	0.999589i	$0.490871\pi$
$332$	5.40642	0.296716
$333$	3.76955	0.206570
$334$	19.9595	1.09213
$335$	−4.93275	−0.269505
$336$	−11.7982	−0.643646
$337$	−32.3936	−1.76459	−0.882296	−	0.470696i	$-0.844003\pi$
$337$	−32.3936	−1.76459	−0.882296	+	0.470696i	$0.844003\pi$
$338$	−23.9679	−1.30368
$339$	23.0560	1.25223
$340$	−6.99548	−0.379383
$341$	−2.71979	−0.147285
$342$	−7.99944	−0.432560
$343$	−13.7183	−0.740719
$344$	0.622571	0.0335668
$345$	−14.2005	−0.764528
$346$	47.0757	2.53081
$347$	0.837115	0.0449387	0.0224693	−	0.999748i	$-0.492847\pi$
$347$	0.837115	0.0449387	0.0224693	+	0.999748i	$0.492847\pi$
$348$	−22.6842	−1.21600
$349$	−1.98491	−0.106250	−0.0531250	−	0.998588i	$-0.516918\pi$
$349$	−1.98491	−0.106250	−0.0531250	+	0.998588i	$0.516918\pi$
$350$	2.10952	0.112759
$351$	2.60359	0.138969
$352$	−7.89643	−0.420881
$353$	0.0707574	0.00376604	0.00188302	−	0.999998i	$-0.499401\pi$
$353$	0.0707574	0.00376604	0.00188302	+	0.999998i	$0.499401\pi$
$354$	−32.3174	−1.71765
$355$	−7.32299	−0.388664
$356$	−16.7715	−0.888889
$357$	10.3558	0.548089
$358$	39.6934	2.09786
$359$	−23.4992	−1.24024	−0.620120	−	0.784507i	$-0.712916\pi$
$359$	−23.4992	−1.24024	−0.620120	+	0.784507i	$0.712916\pi$
$360$	0.702536	0.0370269
$361$	1.00000	0.0526316
$362$	14.8306	0.779479
$363$	2.65412	0.139305
$364$	1.91559	0.100404
$365$	−1.14496	−0.0599301
$366$	11.2185	0.586403
$367$	−16.4763	−0.860057	−0.430029	−	0.902815i	$-0.641497\pi$
$367$	−16.4763	−0.860057	−0.430029	+	0.902815i	$0.641497\pi$
$368$	−22.2999	−1.16246
$369$	−4.92670	−0.256474
$370$	−1.84352	−0.0958402
$371$	−12.9664	−0.673181
$372$	−13.8033	−0.715670
$373$	1.92401	0.0996217	0.0498108	−	0.998759i	$-0.484138\pi$
$373$	1.92401	0.0996217	0.0498108	+	0.998759i	$0.484138\pi$
$374$	7.23600	0.374165
$375$	−2.65412	−0.137058
$376$	0.747330	0.0385406
$377$	−4.19831	−0.216224
$378$	5.84732	0.300753
$379$	−29.8162	−1.53156	−0.765779	−	0.643104i	$-0.777646\pi$
$379$	−29.8162	−1.53156	−0.765779	+	0.643104i	$0.777646\pi$
$380$	1.91218	0.0980926
$381$	−42.3452	−2.16941
$382$	−8.34413	−0.426923
$383$	−19.4719	−0.994969	−0.497484	−	0.867473i	$-0.665743\pi$
$383$	−19.4719	−0.994969	−0.497484	+	0.867473i	$0.665743\pi$
$384$	3.68477	0.188038
$385$	−1.06653	−0.0543556
$386$	15.2441	0.775906
$387$	−14.4951	−0.736826
$388$	25.5123	1.29519
$389$	−11.7829	−0.597415	−0.298708	−	0.954345i	$-0.596556\pi$
$389$	−11.7829	−0.597415	−0.298708	+	0.954345i	$0.596556\pi$
$390$	−4.93095	−0.249688
$391$	19.5737	0.989882
$392$	1.01836	0.0514350
$393$	13.8018	0.696208
$394$	36.4502	1.83633
$395$	6.71067	0.337650
$396$	7.73354	0.388625
$397$	35.1177	1.76251	0.881254	−	0.472643i	$-0.156700\pi$
$397$	35.1177	1.76251	0.881254	+	0.472643i	$0.156700\pi$
$398$	−42.8198	−2.14636
$399$	−2.83071	−0.141713
$400$	−4.16793	−0.208397
$401$	27.0103	1.34883	0.674414	−	0.738353i	$-0.264396\pi$
$401$	27.0103	1.34883	0.674414	+	0.738353i	$0.264396\pi$
$402$	25.8952	1.29153
$403$	−2.55468	−0.127257
$404$	−1.77122	−0.0881216
$405$	4.77622	0.237332
$406$	−9.42884	−0.467946
$407$	0.932050	0.0462000
$408$	−1.68667	−0.0835024
$409$	33.0664	1.63503	0.817515	−	0.575907i	$-0.195351\pi$
$409$	33.0664	1.63503	0.817515	+	0.575907i	$0.195351\pi$
$410$	2.40943	0.118994
$411$	20.0232	0.987672
$412$	−19.9525	−0.982989
$413$	−6.56570	−0.323077
$414$	42.7998	2.10349
$415$	−2.82737	−0.138790
$416$	−7.41705	−0.363651
$417$	0.948320	0.0464394
$418$	−1.97792	−0.0967433
$419$	7.98503	0.390094	0.195047	−	0.980794i	$-0.437514\pi$
$419$	7.98503	0.390094	0.195047	+	0.980794i	$0.437514\pi$
$420$	−5.41282	−0.264119
$421$	−28.8735	−1.40721	−0.703604	−	0.710592i	$-0.748427\pi$
$421$	−28.8735	−1.40721	−0.703604	+	0.710592i	$0.748427\pi$
$422$	47.3047	2.30276
$423$	−17.3998	−0.846007
$424$	2.11185	0.102560
$425$	3.65839	0.177458
$426$	38.4431	1.86257
$427$	2.27919	0.110298
$428$	25.9283	1.25329
$429$	2.49299	0.120363
$430$	7.08891	0.341858
$431$	27.5088	1.32505	0.662527	−	0.749038i	$-0.269484\pi$
$431$	27.5088	1.32505	0.662527	+	0.749038i	$0.269484\pi$
$432$	−11.5530	−0.555842
$433$	−33.5624	−1.61291	−0.806453	−	0.591299i	$-0.798615\pi$
$433$	−33.5624	−1.61291	−0.806453	+	0.591299i	$0.798615\pi$
$434$	−5.73746	−0.275407
$435$	11.8630	0.568788
$436$	11.1946	0.536126
$437$	−5.35035	−0.255942
$438$	6.01065	0.287200
$439$	25.8608	1.23427	0.617134	−	0.786858i	$-0.288294\pi$
$439$	25.8608	1.23427	0.617134	+	0.786858i	$0.288294\pi$
$440$	0.173707	0.00828118
$441$	−23.7101	−1.12905
$442$	6.79672	0.323287
$443$	2.34708	0.111513	0.0557566	−	0.998444i	$-0.482243\pi$
$443$	2.34708	0.111513	0.0557566	+	0.998444i	$0.482243\pi$
$444$	4.73030	0.224490
$445$	8.77091	0.415781
$446$	8.28523	0.392317
$447$	−28.5673	−1.35119
$448$	−7.76722	−0.366966
$449$	18.4815	0.872195	0.436097	−	0.899899i	$-0.356360\pi$
$449$	18.4815	0.872195	0.436097	+	0.899899i	$0.356360\pi$
$450$	7.99944	0.377097
$451$	−1.21816	−0.0573611
$452$	16.6108	0.781307
$453$	18.9498	0.890339
$454$	−17.3032	−0.812079
$455$	−1.00179	−0.0469645
$456$	0.461041	0.0215902
$457$	17.1365	0.801612	0.400806	−	0.916163i	$-0.368730\pi$
$457$	17.1365	0.801612	0.400806	+	0.916163i	$0.368730\pi$
$458$	−33.2581	−1.55405
$459$	10.1406	0.473321
$460$	−10.2308	−0.477014
$461$	−16.3205	−0.760122	−0.380061	−	0.924961i	$-0.624097\pi$
$461$	−16.3205	−0.760122	−0.380061	+	0.924961i	$0.624097\pi$
$462$	5.59893	0.260486
$463$	−18.2993	−0.850441	−0.425220	−	0.905090i	$-0.639803\pi$
$463$	−18.2993	−0.850441	−0.425220	+	0.905090i	$0.639803\pi$
$464$	18.6292	0.864840
$465$	7.21866	0.334757
$466$	−14.6597	−0.679098
$467$	3.89977	0.180460	0.0902299	−	0.995921i	$-0.471240\pi$
$467$	3.89977	0.180460	0.0902299	+	0.995921i	$0.471240\pi$
$468$	7.26404	0.335780
$469$	5.26094	0.242928
$470$	8.50948	0.392513
$471$	33.7509	1.55516
$472$	1.06936	0.0492213
$473$	−3.58402	−0.164793
$474$	−35.2286	−1.61811
$475$	−1.00000	−0.0458831
$476$	7.46092	0.341971
$477$	−49.1693	−2.25131
$478$	−39.0296	−1.78517
$479$	16.4447	0.751377	0.375688	−	0.926746i	$-0.377406\pi$
$479$	16.4447	0.751377	0.375688	+	0.926746i	$0.377406\pi$
$480$	20.9581	0.956602
$481$	0.875467	0.0399178
$482$	29.8655	1.36034
$483$	15.1453	0.689135
$484$	1.91218	0.0869171
$485$	−13.3420	−0.605830
$486$	−41.5211	−1.88343
$487$	−28.4329	−1.28842	−0.644209	−	0.764849i	$-0.722813\pi$
$487$	−28.4329	−1.28842	−0.644209	+	0.764849i	$0.722813\pi$
$488$	−0.371214	−0.0168041
$489$	−11.8190	−0.534475
$490$	11.5956	0.523835
$491$	−6.25955	−0.282490	−0.141245	−	0.989975i	$-0.545110\pi$
$491$	−6.25955	−0.282490	−0.141245	+	0.989975i	$0.545110\pi$
$492$	−6.18237	−0.278723
$493$	−16.3517	−0.736445
$494$	−1.85784	−0.0835884
$495$	−4.04436	−0.181781
$496$	11.3359	0.508997
$497$	7.81022	0.350336
$498$	14.8427	0.665116
$499$	−10.4851	−0.469378	−0.234689	−	0.972070i	$-0.575407\pi$
$499$	−10.4851	−0.469378	−0.234689	+	0.972070i	$0.575407\pi$
$500$	−1.91218	−0.0855151
$501$	26.7831	1.19658
$502$	24.4981	1.09340
$503$	18.4277	0.821651	0.410825	−	0.911714i	$-0.365241\pi$
$503$	18.4277	0.821651	0.410825	+	0.911714i	$0.365241\pi$
$504$	−0.749279	−0.0333755
$505$	0.926286	0.0412192
$506$	10.5826	0.470453
$507$	−32.1619	−1.42836
$508$	−30.5078	−1.35357
$509$	14.0013	0.620596	0.310298	−	0.950639i	$-0.399571\pi$
$509$	14.0013	0.620596	0.310298	+	0.950639i	$0.399571\pi$
$510$	−19.2052	−0.850422
$511$	1.22114	0.0540201
$512$	31.4638	1.39052
$513$	−2.77187	−0.122381
$514$	52.5131	2.31625
$515$	10.4344	0.459796
$516$	−18.1894	−0.800745
$517$	−4.30223	−0.189212
$518$	1.96618	0.0863891
$519$	63.1696	2.77284
$520$	0.163162	0.00715512
$521$	−36.3013	−1.59039	−0.795195	−	0.606353i	$-0.792632\pi$
$521$	−36.3013	−1.59039	−0.795195	+	0.606353i	$0.792632\pi$
$522$	−35.7547	−1.56494
$523$	23.2657	1.01734	0.508669	−	0.860962i	$-0.330138\pi$
$523$	23.2657	1.01734	0.508669	+	0.860962i	$0.330138\pi$
$524$	9.94358	0.434387
$525$	2.83071	0.123542
$526$	29.6901	1.29455
$527$	−9.95005	−0.433431
$528$	−11.0622	−0.481421
$529$	5.62625	0.244620
$530$	24.0466	1.04452
$531$	−24.8975	−1.08046
$532$	−2.03940	−0.0884193
$533$	−1.14421	−0.0495613
$534$	−46.0442	−1.99253
$535$	−13.5595	−0.586230
$536$	−0.856854	−0.0370105
$537$	53.2635	2.29849
$538$	23.4001	1.00885
$539$	−5.86250	−0.252516
$540$	−5.30030	−0.228089
$541$	30.6302	1.31689	0.658447	−	0.752627i	$-0.271214\pi$
$541$	30.6302	1.31689	0.658447	+	0.752627i	$0.271214\pi$
$542$	−26.5346	−1.13976
$543$	19.9008	0.854024
$544$	−28.8882	−1.23857
$545$	−5.85440	−0.250775
$546$	5.25903	0.225066
$547$	−14.9225	−0.638040	−0.319020	−	0.947748i	$-0.603354\pi$
$547$	−14.9225	−0.638040	−0.319020	+	0.947748i	$0.603354\pi$
$548$	14.4258	0.616241
$549$	8.64284	0.368867
$550$	1.97792	0.0843389
$551$	4.46966	0.190414
$552$	−2.46673	−0.104991
$553$	−7.15716	−0.304354
$554$	−1.02059	−0.0433608
$555$	−2.47378	−0.105006
$556$	0.683222	0.0289751
$557$	8.54485	0.362057	0.181028	−	0.983478i	$-0.442057\pi$
$557$	8.54485	0.362057	0.181028	+	0.983478i	$0.442057\pi$
$558$	−21.7568	−0.921038
$559$	−3.36644	−0.142385
$560$	4.44525	0.187846
$561$	9.70980	0.409948
$562$	43.3721	1.82954
$563$	17.7855	0.749571	0.374786	−	0.927111i	$-0.377716\pi$
$563$	17.7855	0.749571	0.374786	+	0.927111i	$0.377716\pi$
$564$	−21.8345	−0.919397
$565$	−8.68686	−0.365459
$566$	36.7939	1.54656
$567$	−5.09400	−0.213928
$568$	−1.27206	−0.0533743
$569$	−29.7657	−1.24785	−0.623923	−	0.781486i	$-0.714462\pi$
$569$	−29.7657	−1.24785	−0.623923	+	0.781486i	$0.714462\pi$
$570$	5.24965	0.219884
$571$	22.2184	0.929810	0.464905	−	0.885360i	$-0.346088\pi$
$571$	22.2184	0.929810	0.464905	+	0.885360i	$0.346088\pi$
$572$	1.79609	0.0750983
$573$	−11.1968	−0.467752
$574$	−2.56975	−0.107259
$575$	5.35035	0.223125
$576$	−29.4537	−1.22724
$577$	−12.0936	−0.503464	−0.251732	−	0.967797i	$-0.581000\pi$
$577$	−12.0936	−0.503464	−0.251732	+	0.967797i	$0.581000\pi$
$578$	−7.15258	−0.297508
$579$	20.4557	0.850110
$580$	8.54677	0.354885
$581$	3.01548	0.125103
$582$	70.0409	2.90329
$583$	−12.1575	−0.503512
$584$	−0.198888	−0.00823006
$585$	−3.79883	−0.157062
$586$	−11.6161	−0.479856
$587$	−14.3554	−0.592510	−0.296255	−	0.955109i	$-0.595738\pi$
$587$	−14.3554	−0.592510	−0.296255	+	0.955109i	$0.595738\pi$
$588$	−29.7531	−1.22700
$589$	2.71979	0.112067
$590$	12.1763	0.501290
$591$	48.9115	2.01195
$592$	−3.88472	−0.159661
$593$	7.64570	0.313971	0.156986	−	0.987601i	$-0.449822\pi$
$593$	7.64570	0.313971	0.156986	+	0.987601i	$0.449822\pi$
$594$	5.48254	0.224951
$595$	−3.90180	−0.159958
$596$	−20.5814	−0.843049
$597$	−57.4587	−2.35163
$598$	9.94012	0.406482
$599$	22.5450	0.921165	0.460583	−	0.887617i	$-0.347641\pi$
$599$	22.5450	0.921165	0.460583	+	0.887617i	$0.347641\pi$
$600$	−0.461041	−0.0188219
$601$	8.27574	0.337574	0.168787	−	0.985653i	$-0.446015\pi$
$601$	8.27574	0.337574	0.168787	+	0.985653i	$0.446015\pi$
$602$	−7.56057	−0.308146
$603$	19.9498	0.812419
$604$	13.6525	0.555511
$605$	−1.00000	−0.0406558
$606$	−4.86267	−0.197533
$607$	−12.8552	−0.521778	−0.260889	−	0.965369i	$-0.584016\pi$
$607$	−12.8552	−0.521778	−0.260889	+	0.965369i	$0.584016\pi$
$608$	7.89643	0.320243
$609$	−12.6523	−0.512698
$610$	−4.22684	−0.171140
$611$	−4.04105	−0.163483
$612$	28.2923	1.14365
$613$	−17.0191	−0.687394	−0.343697	−	0.939081i	$-0.611679\pi$
$613$	−17.0191	−0.687394	−0.343697	+	0.939081i	$0.611679\pi$
$614$	1.12062	0.0452247
$615$	3.23316	0.130373
$616$	−0.185265	−0.00746454
$617$	21.5265	0.866625	0.433313	−	0.901244i	$-0.357345\pi$
$617$	21.5265	0.866625	0.433313	+	0.901244i	$0.357345\pi$
$618$	−54.7771	−2.20346
$619$	34.9987	1.40672	0.703359	−	0.710835i	$-0.251683\pi$
$619$	34.9987	1.40672	0.703359	+	0.710835i	$0.251683\pi$
$620$	5.20072	0.208866
$621$	14.8305	0.595126
$622$	−43.8536	−1.75837
$623$	−9.35448	−0.374779
$624$	−10.3906	−0.415958
$625$	1.00000	0.0400000
$626$	−59.9766	−2.39715
$627$	−2.65412	−0.105995
$628$	24.3160	0.970315
$629$	3.40980	0.135958
$630$	−8.53168	−0.339910
$631$	26.6365	1.06038	0.530191	−	0.847878i	$-0.322120\pi$
$631$	26.6365	1.06038	0.530191	+	0.847878i	$0.322120\pi$
$632$	1.16569	0.0463688
$633$	63.4769	2.52298
$634$	−27.0306	−1.07352
$635$	15.9545	0.633135
$636$	−61.7011	−2.44661
$637$	−5.50660	−0.218179
$638$	−8.84063	−0.350004
$639$	29.6168	1.17162
$640$	−1.38832	−0.0548781
$641$	−18.3904	−0.726376	−0.363188	−	0.931716i	$-0.618312\pi$
$641$	−18.3904	−0.726376	−0.363188	+	0.931716i	$0.618312\pi$
$642$	71.1828	2.80936
$643$	10.1583	0.400603	0.200302	−	0.979734i	$-0.435808\pi$
$643$	10.1583	0.400603	0.200302	+	0.979734i	$0.435808\pi$
$644$	10.9115	0.429974
$645$	9.51242	0.374551
$646$	−7.23600	−0.284697
$647$	24.9283	0.980034	0.490017	−	0.871713i	$-0.336991\pi$
$647$	24.9283	0.980034	0.490017	+	0.871713i	$0.336991\pi$
$648$	0.829664	0.0325923
$649$	−6.15610	−0.241648
$650$	1.85784	0.0728707
$651$	−7.69895	−0.301746
$652$	−8.51508	−0.333476
$653$	3.18346	0.124579	0.0622893	−	0.998058i	$-0.480160\pi$
$653$	3.18346	0.124579	0.0622893	+	0.998058i	$0.480160\pi$
$654$	30.7335	1.20178
$655$	−5.20014	−0.203186
$656$	5.07723	0.198232
$657$	4.63064	0.180659
$658$	−9.07566	−0.353806
$659$	44.5078	1.73378	0.866888	−	0.498503i	$-0.166117\pi$
$659$	44.5078	1.73378	0.866888	+	0.498503i	$0.166117\pi$
$660$	−5.07515	−0.197550
$661$	5.31054	0.206556	0.103278	−	0.994653i	$-0.467067\pi$
$661$	5.31054	0.206556	0.103278	+	0.994653i	$0.467067\pi$
$662$	2.06371	0.0802083
$663$	9.12033	0.354204
$664$	−0.491134	−0.0190597
$665$	1.06653	0.0413584
$666$	7.45588	0.288909
$667$	−23.9142	−0.925963
$668$	19.2960	0.746585
$669$	11.1177	0.429836
$670$	−9.75659	−0.376930
$671$	2.13701	0.0824983
$672$	−22.3525	−0.862268
$673$	−27.9535	−1.07753	−0.538765	−	0.842456i	$-0.681109\pi$
$673$	−27.9535	−1.07753	−0.538765	+	0.842456i	$0.681109\pi$
$674$	−64.0720	−2.46796
$675$	2.77187	0.106689
$676$	−23.1712	−0.891202
$677$	−41.9276	−1.61141	−0.805704	−	0.592319i	$-0.798213\pi$
$677$	−41.9276	−1.61141	−0.805704	+	0.592319i	$0.798213\pi$
$678$	45.6029	1.75137
$679$	14.2297	0.546087
$680$	0.635489	0.0243699
$681$	−23.2187	−0.889742
$682$	−5.37953	−0.205993
$683$	21.6527	0.828516	0.414258	−	0.910159i	$-0.364041\pi$
$683$	21.6527	0.828516	0.414258	+	0.910159i	$0.364041\pi$
$684$	−7.73354	−0.295699
$685$	−7.54419	−0.288249
$686$	−27.1337	−1.03597
$687$	−44.6281	−1.70267
$688$	14.9380	0.569504
$689$	−11.4194	−0.435045
$690$	−28.0875	−1.06927
$691$	45.5121	1.73136	0.865681	−	0.500597i	$-0.166886\pi$
$691$	45.5121	1.73136	0.865681	+	0.500597i	$0.166886\pi$
$692$	45.5109	1.73007
$693$	4.31345	0.163855
$694$	1.65575	0.0628514
$695$	−0.357301	−0.0135532
$696$	2.06069	0.0781104
$697$	−4.45652	−0.168803
$698$	−3.92601	−0.148602
$699$	−19.6715	−0.744043
$700$	2.03940	0.0770822
$701$	−27.3430	−1.03273	−0.516365	−	0.856369i	$-0.672715\pi$
$701$	−27.3430	−1.03273	−0.516365	+	0.856369i	$0.672715\pi$
$702$	5.14970	0.194363
$703$	−0.932050	−0.0351529
$704$	−7.28267	−0.274476
$705$	11.4186	0.430051
$706$	0.139953	0.00526719
$707$	−0.987916	−0.0371544
$708$	−31.2431	−1.17419
$709$	3.38760	0.127224	0.0636120	−	0.997975i	$-0.479738\pi$
$709$	3.38760	0.127224	0.0636120	+	0.997975i	$0.479738\pi$
$710$	−14.4843	−0.543586
$711$	−27.1404	−1.01784
$712$	1.52357	0.0570983
$713$	−14.5518	−0.544970
$714$	20.4831	0.766559
$715$	−0.939291	−0.0351275
$716$	38.3740	1.43410
$717$	−52.3728	−1.95590
$718$	−46.4796	−1.73460
$719$	33.5021	1.24942	0.624709	−	0.780858i	$-0.285218\pi$
$719$	33.5021	1.24942	0.624709	+	0.780858i	$0.285218\pi$
$720$	16.8566	0.628210
$721$	−11.1287	−0.414454
$722$	1.97792	0.0736106
$723$	40.0757	1.49043
$724$	14.3376	0.532854
$725$	−4.46966	−0.165999
$726$	5.24965	0.194833
$727$	−45.5324	−1.68871	−0.844353	−	0.535788i	$-0.820015\pi$
$727$	−45.5324	−1.68871	−0.844353	+	0.535788i	$0.820015\pi$
$728$	−0.174018	−0.00644953
$729$	−41.3874	−1.53287
$730$	−2.26465	−0.0838183
$731$	−13.1117	−0.484955
$732$	10.8456	0.400866
$733$	−4.71433	−0.174128	−0.0870640	−	0.996203i	$-0.527748\pi$
$733$	−4.71433	−0.174128	−0.0870640	+	0.996203i	$0.527748\pi$
$734$	−32.5889	−1.20288
$735$	15.5598	0.573932
$736$	−42.2487	−1.55731
$737$	4.93275	0.181700
$738$	−9.74463	−0.358705
$739$	35.7265	1.31422	0.657110	−	0.753795i	$-0.271779\pi$
$739$	35.7265	1.31422	0.657110	+	0.753795i	$0.271779\pi$
$740$	−1.78224	−0.0655166
$741$	−2.49299	−0.0915824
$742$	−25.6465	−0.941513
$743$	−26.9341	−0.988118	−0.494059	−	0.869428i	$-0.664487\pi$
$743$	−26.9341	−0.988118	−0.494059	+	0.869428i	$0.664487\pi$
$744$	1.25393	0.0459715
$745$	10.7634	0.394339
$746$	3.80555	0.139331
$747$	11.4349	0.418381
$748$	6.99548	0.255780
$749$	14.4617	0.528420
$750$	−5.24965	−0.191690
$751$	−27.7767	−1.01358	−0.506792	−	0.862068i	$-0.669169\pi$
$751$	−27.7767	−1.01358	−0.506792	+	0.862068i	$0.669169\pi$
$752$	17.9314	0.653891
$753$	32.8733	1.19797
$754$	−8.30393	−0.302411
$755$	−7.13976	−0.259842
$756$	5.65295	0.205596
$757$	−23.4521	−0.852380	−0.426190	−	0.904634i	$-0.640145\pi$
$757$	−23.4521	−0.852380	−0.426190	+	0.904634i	$0.640145\pi$
$758$	−58.9742	−2.14204
$759$	14.2005	0.515445
$760$	−0.173707	−0.00630103
$761$	−15.9940	−0.579783	−0.289892	−	0.957059i	$-0.593619\pi$
$761$	−15.9940	−0.579783	−0.289892	+	0.957059i	$0.593619\pi$
$762$	−83.7554	−3.03414
$763$	6.24392	0.226045
$764$	−8.06678	−0.291846
$765$	−14.7958	−0.534945
$766$	−38.5139	−1.39157
$767$	−5.78237	−0.208789
$768$	45.9464	1.65795
$769$	19.9815	0.720552	0.360276	−	0.932846i	$-0.382683\pi$
$769$	19.9815	0.720552	0.360276	+	0.932846i	$0.382683\pi$
$770$	−2.10952	−0.0760219
$771$	70.4659	2.53777
$772$	14.7374	0.530411
$773$	53.4366	1.92198	0.960991	−	0.276581i	$-0.0892013\pi$
$773$	53.4366	1.92198	0.960991	+	0.276581i	$0.0892013\pi$
$774$	−28.6701	−1.03053
$775$	−2.71979	−0.0976978
$776$	−2.31761	−0.0831973
$777$	2.63837	0.0946509
$778$	−23.3056	−0.835546
$779$	1.21816	0.0436453
$780$	−4.76704	−0.170688
$781$	7.32299	0.262037
$782$	38.7152	1.38445
$783$	−12.3893	−0.442757
$784$	24.4345	0.872662
$785$	−12.7164	−0.453868
$786$	27.2989	0.973719
$787$	6.90402	0.246102	0.123051	−	0.992400i	$-0.460732\pi$
$787$	6.90402	0.246102	0.123051	+	0.992400i	$0.460732\pi$
$788$	35.2386	1.25532
$789$	39.8404	1.41836
$790$	13.2732	0.472239
$791$	9.26484	0.329420
$792$	−0.702536	−0.0249635
$793$	2.00727	0.0712804
$794$	69.4601	2.46505
$795$	32.2675	1.14441
$796$	−41.3965	−1.46726
$797$	28.5820	1.01243	0.506213	−	0.862409i	$-0.331045\pi$
$797$	28.5820	1.01243	0.506213	+	0.862409i	$0.331045\pi$
$798$	−5.59893	−0.198200
$799$	−15.7392	−0.556814
$800$	−7.89643	−0.279181
$801$	−35.4727	−1.25337
$802$	53.4242	1.88647
$803$	1.14496	0.0404048
$804$	25.0344	0.882896
$805$	−5.70633	−0.201122
$806$	−5.05295	−0.177983
$807$	31.4000	1.10533
$808$	0.160903	0.00566054
$809$	45.3303	1.59373	0.796864	−	0.604158i	$-0.206491\pi$
$809$	45.3303	1.59373	0.796864	+	0.604158i	$0.206491\pi$
$810$	9.44699	0.331933
$811$	11.1668	0.392119	0.196060	−	0.980592i	$-0.437185\pi$
$811$	11.1668	0.392119	0.196060	+	0.980592i	$0.437185\pi$
$812$	−9.11543	−0.319889
$813$	−35.6061	−1.24876
$814$	1.84352	0.0646155
$815$	4.45308	0.155985
$816$	−40.4698	−1.41673
$817$	3.58402	0.125389
$818$	65.4029	2.28676
$819$	4.05159	0.141574
$820$	2.32935	0.0813443
$821$	−23.2715	−0.812180	−0.406090	−	0.913833i	$-0.633108\pi$
$821$	−23.2715	−0.812180	−0.406090	+	0.913833i	$0.633108\pi$
$822$	39.6044	1.38136
$823$	−36.1529	−1.26021	−0.630105	−	0.776510i	$-0.716988\pi$
$823$	−36.1529	−1.26021	−0.630105	+	0.776510i	$0.716988\pi$
$824$	1.81254	0.0631428
$825$	2.65412	0.0924047
$826$	−12.9864	−0.451856
$827$	10.7797	0.374848	0.187424	−	0.982279i	$-0.439986\pi$
$827$	10.7797	0.374848	0.187424	+	0.982279i	$0.439986\pi$
$828$	41.3771	1.43795
$829$	−42.2859	−1.46865	−0.734326	−	0.678797i	$-0.762501\pi$
$829$	−42.2859	−1.46865	−0.734326	+	0.678797i	$0.762501\pi$
$830$	−5.59231	−0.194112
$831$	−1.36951	−0.0475076
$832$	−6.84054	−0.237153
$833$	−21.4473	−0.743105
$834$	1.87570	0.0649503
$835$	−10.0911	−0.349218
$836$	−1.91218	−0.0661340
$837$	−7.53890	−0.260582
$838$	15.7938	0.545587
$839$	27.2267	0.939971	0.469986	−	0.882674i	$-0.344259\pi$
$839$	27.2267	0.939971	0.469986	+	0.882674i	$0.344259\pi$
$840$	0.491716	0.0169658
$841$	−9.02217	−0.311109
$842$	−57.1095	−1.96812
$843$	58.1999	2.00451
$844$	45.7323	1.57417
$845$	12.1177	0.416863
$846$	−34.4154	−1.18323
$847$	1.06653	0.0366466
$848$	50.6716	1.74007
$849$	49.3728	1.69447
$850$	7.23600	0.248193
$851$	4.98680	0.170945
$852$	37.1653	1.27326
$853$	−11.3022	−0.386981	−0.193490	−	0.981102i	$-0.561981\pi$
$853$	−11.3022	−0.386981	−0.193490	+	0.981102i	$0.561981\pi$
$854$	4.50807	0.154263
$855$	4.04436	0.138314
$856$	−2.35539	−0.0805057
$857$	1.20558	0.0411817	0.0205908	−	0.999788i	$-0.493445\pi$
$857$	1.20558	0.0411817	0.0205908	+	0.999788i	$0.493445\pi$
$858$	4.93095	0.168340
$859$	28.1617	0.960865	0.480432	−	0.877032i	$-0.340480\pi$
$859$	28.1617	0.960865	0.480432	+	0.877032i	$0.340480\pi$
$860$	6.85328	0.233695
$861$	−3.44827	−0.117517
$862$	54.4103	1.85322
$863$	8.48764	0.288923	0.144461	−	0.989510i	$-0.453855\pi$
$863$	8.48764	0.288923	0.144461	+	0.989510i	$0.453855\pi$
$864$	−21.8879	−0.744640
$865$	−23.8006	−0.809244
$866$	−66.3838	−2.25581
$867$	−9.59785	−0.325960
$868$	−5.54675	−0.188269
$869$	−6.71067	−0.227644
$870$	23.4641	0.795508
$871$	4.63328	0.156993
$872$	−1.01695	−0.0344383
$873$	53.9600	1.82627
$874$	−10.5826	−0.357961
$875$	−1.06653	−0.0360555
$876$	5.81086	0.196331
$877$	34.1439	1.15296	0.576478	−	0.817112i	$-0.304427\pi$
$877$	34.1439	1.15296	0.576478	+	0.817112i	$0.304427\pi$
$878$	51.1506	1.72625
$879$	−15.5873	−0.525747
$880$	4.16793	0.140501
$881$	−42.0557	−1.41689	−0.708446	−	0.705765i	$-0.750603\pi$
$881$	−42.0557	−1.41689	−0.708446	+	0.705765i	$0.750603\pi$
$882$	−46.8967	−1.57909
$883$	−12.9984	−0.437430	−0.218715	−	0.975789i	$-0.570187\pi$
$883$	−12.9984	−0.437430	−0.218715	+	0.975789i	$0.570187\pi$
$884$	6.57079	0.221000
$885$	16.3390	0.549231
$886$	4.64235	0.155963
$887$	58.3513	1.95925	0.979623	−	0.200847i	$-0.0643695\pi$
$887$	58.3513	1.95925	0.979623	+	0.200847i	$0.0643695\pi$
$888$	−0.429713	−0.0144202
$889$	−17.0160	−0.570699
$890$	17.3482	0.581512
$891$	−4.77622	−0.160009
$892$	8.00983	0.268189
$893$	4.30223	0.143969
$894$	−56.5038	−1.88977
$895$	−20.0682	−0.670807
$896$	1.48069	0.0494664
$897$	13.3384	0.445356
$898$	36.5549	1.21985
$899$	12.1565	0.405443
$900$	7.73354	0.257785
$901$	−44.4768	−1.48174
$902$	−2.40943	−0.0802254
$903$	−10.1453	−0.337615
$904$	−1.50897	−0.0501876
$905$	−7.49807	−0.249244
$906$	37.4812	1.24523
$907$	−58.8388	−1.95371	−0.976855	−	0.213904i	$-0.931382\pi$
$907$	−58.8388	−1.95371	−0.976855	+	0.213904i	$0.931382\pi$
$908$	−16.7280	−0.555139
$909$	−3.74624	−0.124255
$910$	−1.98146	−0.0656846
$911$	−23.1241	−0.766137	−0.383068	−	0.923720i	$-0.625133\pi$
$911$	−23.1241	−0.766137	−0.383068	+	0.923720i	$0.625133\pi$
$912$	11.0622	0.366306
$913$	2.82737	0.0935721
$914$	33.8947	1.12114
$915$	−5.67188	−0.187507
$916$	−32.1526	−1.06235
$917$	5.54613	0.183149
$918$	20.0572	0.661988
$919$	−32.2210	−1.06287	−0.531437	−	0.847098i	$-0.678348\pi$
$919$	−32.2210	−1.06287	−0.531437	+	0.847098i	$0.678348\pi$
$920$	0.929396	0.0306413
$921$	1.50374	0.0495498
$922$	−32.2807	−1.06311
$923$	6.87842	0.226406
$924$	5.41282	0.178069
$925$	0.932050	0.0306456
$926$	−36.1946	−1.18943
$927$	−42.2007	−1.38605
$928$	35.2943	1.15859
$929$	−0.527392	−0.0173032	−0.00865158	−	0.999963i	$-0.502754\pi$
$929$	−0.527392	−0.0173032	−0.00865158	+	0.999963i	$0.502754\pi$
$930$	14.2779	0.468192
$931$	5.86250	0.192136
$932$	−14.1724	−0.464233
$933$	−58.8459	−1.92653
$934$	7.71344	0.252392
$935$	−3.65839	−0.119642
$936$	−0.659886	−0.0215690
$937$	−41.3338	−1.35032	−0.675158	−	0.737673i	$-0.735925\pi$
$937$	−41.3338	−1.35032	−0.675158	+	0.737673i	$0.735925\pi$
$938$	10.4057	0.339759
$939$	−80.4810	−2.62640
$940$	8.22663	0.268323
$941$	25.4253	0.828840	0.414420	−	0.910086i	$-0.363984\pi$
$941$	25.4253	0.828840	0.414420	+	0.910086i	$0.363984\pi$
$942$	66.7567	2.17505
$943$	−6.51761	−0.212242
$944$	25.6582	0.835104
$945$	−2.95629	−0.0961682
$946$	−7.08891	−0.230480
$947$	−13.9372	−0.452897	−0.226448	−	0.974023i	$-0.572711\pi$
$947$	−13.9372	−0.452897	−0.226448	+	0.974023i	$0.572711\pi$
$948$	−34.0577	−1.10614
$949$	1.07545	0.0349107
$950$	−1.97792	−0.0641723
$951$	−36.2717	−1.17619
$952$	−0.677771	−0.0219667
$953$	40.7458	1.31989	0.659943	−	0.751316i	$-0.270580\pi$
$953$	40.7458	1.31989	0.659943	+	0.751316i	$0.270580\pi$
$954$	−97.2531	−3.14868
$955$	4.21863	0.136512
$956$	−37.7323	−1.22035
$957$	−11.8630	−0.383477
$958$	32.5263	1.05088
$959$	8.04614	0.259824
$960$	19.3291	0.623843
$961$	−23.6027	−0.761379
$962$	1.73160	0.0558292
$963$	54.8397	1.76719
$964$	28.8728	0.929930
$965$	−7.70714	−0.248102
$966$	29.9562	0.963826
$967$	−21.5806	−0.693985	−0.346993	−	0.937868i	$-0.612797\pi$
$967$	−21.5806	−0.693985	−0.346993	+	0.937868i	$0.612797\pi$
$968$	−0.173707	−0.00558317
$969$	−9.70980	−0.311924
$970$	−26.3895	−0.847315
$971$	−40.5213	−1.30039	−0.650194	−	0.759768i	$-0.725313\pi$
$971$	−40.5213	−1.30039	−0.650194	+	0.759768i	$0.725313\pi$
$972$	−40.1409	−1.28752
$973$	0.381074	0.0122167
$974$	−56.2381	−1.80199
$975$	2.49299	0.0798397
$976$	−8.90691	−0.285103
$977$	−51.7112	−1.65439	−0.827194	−	0.561917i	$-0.810064\pi$
$977$	−51.7112	−1.65439	−0.827194	+	0.561917i	$0.810064\pi$
$978$	−23.3771	−0.747518
$979$	−8.77091	−0.280319
$980$	11.2101	0.358095
$981$	23.6773	0.755958
$982$	−12.3809	−0.395090
$983$	39.5850	1.26256	0.631282	−	0.775553i	$-0.282529\pi$
$983$	39.5850	1.26256	0.631282	+	0.775553i	$0.282529\pi$
$984$	0.561623	0.0179039
$985$	−18.4285	−0.587181
$986$	−32.3425	−1.02999
$987$	−12.1784	−0.387642
$988$	−1.79609	−0.0571413
$989$	−19.1758	−0.609754
$990$	−7.99944	−0.254239
$991$	42.2901	1.34339	0.671694	−	0.740828i	$-0.265567\pi$
$991$	42.2901	1.34339	0.671694	+	0.740828i	$0.265567\pi$
$992$	21.4766	0.681884
$993$	2.76924	0.0878791
$994$	15.4480	0.489981
$995$	21.6489	0.686315
$996$	14.3493	0.454675
$997$	−40.6774	−1.28827	−0.644133	−	0.764914i	$-0.722782\pi$
$997$	−40.6774	−1.28827	−0.644133	+	0.764914i	$0.722782\pi$
$998$	−20.7387	−0.656473
$999$	2.58352	0.0817389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.a.h.1.6	✓	7
3.2	odd	2		9405.2.a.bd.1.2		7
5.4	even	2		5225.2.a.m.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.a.h.1.6	✓	7	1.1	even	1	trivial
5225.2.a.m.1.2		7	5.4	even	2
9405.2.a.bd.1.2		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+1.97792 q^{2} +2.65412 q^{3} +1.91218 q^{4} -1.00000 q^{5} +5.24965 q^{6} +1.06653 q^{7} -0.173707 q^{8} +4.04436 q^{9} +O(q^{10})\)	\(q+1.97792 q^{2} +2.65412 q^{3} +1.91218 q^{4} -1.00000 q^{5} +5.24965 q^{6} +1.06653 q^{7} -0.173707 q^{8} +4.04436 q^{9} -1.97792 q^{10} +1.00000 q^{11} +5.07515 q^{12} +0.939291 q^{13} +2.10952 q^{14} -2.65412 q^{15} -4.16793 q^{16} +3.65839 q^{17} +7.99944 q^{18} -1.00000 q^{19} -1.91218 q^{20} +2.83071 q^{21} +1.97792 q^{22} +5.35035 q^{23} -0.461041 q^{24} +1.00000 q^{25} +1.85784 q^{26} +2.77187 q^{27} +2.03940 q^{28} -4.46966 q^{29} -5.24965 q^{30} -2.71979 q^{31} -7.89643 q^{32} +2.65412 q^{33} +7.23600 q^{34} -1.06653 q^{35} +7.73354 q^{36} +0.932050 q^{37} -1.97792 q^{38} +2.49299 q^{39} +0.173707 q^{40} -1.21816 q^{41} +5.59893 q^{42} -3.58402 q^{43} +1.91218 q^{44} -4.04436 q^{45} +10.5826 q^{46} -4.30223 q^{47} -11.0622 q^{48} -5.86250 q^{49} +1.97792 q^{50} +9.70980 q^{51} +1.79609 q^{52} -12.1575 q^{53} +5.48254 q^{54} -1.00000 q^{55} -0.185265 q^{56} -2.65412 q^{57} -8.84063 q^{58} -6.15610 q^{59} -5.07515 q^{60} +2.13701 q^{61} -5.37953 q^{62} +4.31345 q^{63} -7.28267 q^{64} -0.939291 q^{65} +5.24965 q^{66} +4.93275 q^{67} +6.99548 q^{68} +14.2005 q^{69} -2.10952 q^{70} +7.32299 q^{71} -0.702536 q^{72} +1.14496 q^{73} +1.84352 q^{74} +2.65412 q^{75} -1.91218 q^{76} +1.06653 q^{77} +4.93095 q^{78} -6.71067 q^{79} +4.16793 q^{80} -4.77622 q^{81} -2.40943 q^{82} +2.82737 q^{83} +5.41282 q^{84} -3.65839 q^{85} -7.08891 q^{86} -11.8630 q^{87} -0.173707 q^{88} -8.77091 q^{89} -7.99944 q^{90} +1.00179 q^{91} +10.2308 q^{92} -7.21866 q^{93} -8.50948 q^{94} +1.00000 q^{95} -20.9581 q^{96} +13.3420 q^{97} -11.5956 q^{98} +4.04436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9	\( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9} - q^{10} + 7 q^{11} + 13 q^{12} + q^{13} + 12 q^{14} - 3 q^{15} + 3 q^{16} + q^{17} + 7 q^{18} - 7 q^{19} - 7 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 25 q^{24} + 7 q^{25} + 12 q^{27} + 4 q^{28} + 11 q^{29} - 8 q^{30} + 7 q^{31} + 12 q^{32} + 3 q^{33} - 14 q^{34} + q^{35} + 7 q^{36} - 17 q^{37} - q^{38} + 30 q^{39} - 3 q^{40} + 17 q^{41} + 33 q^{42} - 3 q^{43} + 7 q^{44} - 2 q^{45} + 18 q^{46} + 14 q^{47} - 12 q^{48} + 6 q^{49} + q^{50} + 8 q^{51} - 17 q^{52} + 7 q^{53} - 27 q^{54} - 7 q^{55} + 36 q^{56} - 3 q^{57} - 15 q^{58} + 35 q^{59} - 13 q^{60} + 17 q^{61} + 46 q^{62} - 22 q^{63} + 5 q^{64} - q^{65} + 8 q^{66} + 4 q^{67} - 35 q^{68} - 4 q^{69} - 12 q^{70} + 10 q^{71} + 12 q^{72} + 22 q^{73} - 11 q^{74} + 3 q^{75} - 7 q^{76} - q^{77} - 41 q^{78} + 11 q^{79} - 3 q^{80} - 21 q^{81} - 14 q^{82} + 39 q^{83} + 21 q^{84} - q^{85} - 24 q^{86} - 2 q^{87} + 3 q^{88} + 18 q^{89} - 7 q^{90} - 22 q^{91} - 51 q^{92} + 10 q^{93} + 14 q^{94} + 7 q^{95} - 11 q^{96} - 4 q^{97} - 26 q^{98} + 2 q^{99}+O(q^{100}) \) 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9 - q^10 + 7 * q^11 + 13 * q^12 + q^13 + 12 * q^14 - 3 * q^15 + 3 * q^16 + q^17 + 7 * q^18 - 7 * q^19 - 7 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 25 * q^24 + 7 * q^25 + 12 * q^27 + 4 * q^28 + 11 * q^29 - 8 * q^30 + 7 * q^31 + 12 * q^32 + 3 * q^33 - 14 * q^34 + q^35 + 7 * q^36 - 17 * q^37 - q^38 + 30 * q^39 - 3 * q^40 + 17 * q^41 + 33 * q^42 - 3 * q^43 + 7 * q^44 - 2 * q^45 + 18 * q^46 + 14 * q^47 - 12 * q^48 + 6 * q^49 + q^50 + 8 * q^51 - 17 * q^52 + 7 * q^53 - 27 * q^54 - 7 * q^55 + 36 * q^56 - 3 * q^57 - 15 * q^58 + 35 * q^59 - 13 * q^60 + 17 * q^61 + 46 * q^62 - 22 * q^63 + 5 * q^64 - q^65 + 8 * q^66 + 4 * q^67 - 35 * q^68 - 4 * q^69 - 12 * q^70 + 10 * q^71 + 12 * q^72 + 22 * q^73 - 11 * q^74 + 3 * q^75 - 7 * q^76 - q^77 - 41 * q^78 + 11 * q^79 - 3 * q^80 - 21 * q^81 - 14 * q^82 + 39 * q^83 + 21 * q^84 - q^85 - 24 * q^86 - 2 * q^87 + 3 * q^88 + 18 * q^89 - 7 * q^90 - 22 * q^91 - 51 * q^92 + 10 * q^93 + 14 * q^94 + 7 * q^95 - 11 * q^96 - 4 * q^97 - 26 * q^98 + 2 * q^99

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