LMFDB - Embedded newform 9295.2.a.bb.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9295,2,Mod(1,9295)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9295, 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("9295.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9295 = 5 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9295.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:	$74.2209486788$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 21 x^{11} + 186 x^{10} - 172 x^{9} - 755 x^{8} + 690 x^{7} + 1489 x^{6} + \cdots - 3 $ x^14 - x^13 - 22x^12 + 21x^11 + 186x^10 - 172x^9 - 755x^8 + 690x^7 + 1489x^6 - 1372x^5 - 1226x^4 + 1169x^3 + 206x^2 - 212x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 715)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.43626$ of defining polynomial
Character	$\chi$	$=$	9295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.43626 q^{2} -3.39685 q^{3} +0.0628427 q^{4} +1.00000 q^{5} +4.87876 q^{6} -0.0323629 q^{7} +2.78226 q^{8} +8.53859 q^{9} +O(q^{10})$	\(q-1.43626 q^{2} -3.39685 q^{3} +0.0628427 q^{4} +1.00000 q^{5} +4.87876 q^{6} -0.0323629 q^{7} +2.78226 q^{8} +8.53859 q^{9} -1.43626 q^{10} -1.00000 q^{11} -0.213467 q^{12} +0.0464815 q^{14} -3.39685 q^{15} -4.12174 q^{16} +3.78377 q^{17} -12.2636 q^{18} -6.83572 q^{19} +0.0628427 q^{20} +0.109932 q^{21} +1.43626 q^{22} -6.58463 q^{23} -9.45093 q^{24} +1.00000 q^{25} -18.8138 q^{27} -0.00203377 q^{28} +2.81175 q^{29} +4.87876 q^{30} -10.2724 q^{31} +0.355362 q^{32} +3.39685 q^{33} -5.43448 q^{34} -0.0323629 q^{35} +0.536588 q^{36} -1.79565 q^{37} +9.81787 q^{38} +2.78226 q^{40} -5.87396 q^{41} -0.157891 q^{42} -0.0423789 q^{43} -0.0628427 q^{44} +8.53859 q^{45} +9.45724 q^{46} +0.474764 q^{47} +14.0009 q^{48} -6.99895 q^{49} -1.43626 q^{50} -12.8529 q^{51} -13.0978 q^{53} +27.0215 q^{54} -1.00000 q^{55} -0.0900420 q^{56} +23.2199 q^{57} -4.03840 q^{58} -0.226853 q^{59} -0.213467 q^{60} -4.37466 q^{61} +14.7539 q^{62} -0.276334 q^{63} +7.73308 q^{64} -4.87876 q^{66} +10.2112 q^{67} +0.237782 q^{68} +22.3670 q^{69} +0.0464815 q^{70} +2.20469 q^{71} +23.7566 q^{72} +4.47066 q^{73} +2.57902 q^{74} -3.39685 q^{75} -0.429575 q^{76} +0.0323629 q^{77} +10.1953 q^{79} -4.12174 q^{80} +38.2918 q^{81} +8.43653 q^{82} -8.39914 q^{83} +0.00690841 q^{84} +3.78377 q^{85} +0.0608671 q^{86} -9.55109 q^{87} -2.78226 q^{88} -13.1205 q^{89} -12.2636 q^{90} -0.413796 q^{92} +34.8939 q^{93} -0.681885 q^{94} -6.83572 q^{95} -1.20711 q^{96} +7.36967 q^{97} +10.0523 q^{98} -8.53859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9}+O(q^{10}) $ 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9	$ 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9} + q^{10} - 14 q^{11} - 9 q^{12} + 12 q^{14} + q^{15} + 15 q^{16} + 17 q^{17} + 23 q^{18} + 3 q^{19} + 17 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} - 13 q^{24} + 14 q^{25} + 10 q^{27} + 27 q^{28} + 21 q^{29} + 2 q^{30} - 9 q^{31} + 26 q^{32} - q^{33} - 56 q^{34} + 5 q^{35} + 51 q^{36} + 8 q^{37} + 5 q^{38} + q^{41} - 42 q^{42} + 23 q^{43} - 17 q^{44} + 27 q^{45} - q^{46} - 18 q^{47} - 14 q^{48} + 41 q^{49} + q^{50} + 18 q^{53} + 8 q^{54} - 14 q^{55} + 80 q^{56} + 44 q^{57} + 22 q^{58} + 8 q^{59} - 9 q^{60} + 16 q^{61} - 5 q^{62} + 50 q^{63} + 10 q^{64} - 2 q^{66} + q^{67} - 8 q^{68} + 34 q^{69} + 12 q^{70} - 20 q^{71} + 117 q^{72} - 15 q^{73} + 49 q^{74} + q^{75} + 10 q^{76} - 5 q^{77} + 5 q^{79} + 15 q^{80} + 82 q^{81} + 32 q^{82} - 18 q^{83} - 50 q^{84} + 17 q^{85} - 74 q^{86} + 2 q^{87} - 16 q^{89} + 23 q^{90} + 7 q^{92} + 33 q^{93} + 34 q^{94} + 3 q^{95} + 56 q^{96} - 5 q^{97} + 34 q^{98} - 27 q^{99}+O(q^{100}) $ 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9 + q^10 - 14 * q^11 - 9 * q^12 + 12 * q^14 + q^15 + 15 * q^16 + 17 * q^17 + 23 * q^18 + 3 * q^19 + 17 * q^20 - 16 * q^21 - q^22 + 4 * q^23 - 13 * q^24 + 14 * q^25 + 10 * q^27 + 27 * q^28 + 21 * q^29 + 2 * q^30 - 9 * q^31 + 26 * q^32 - q^33 - 56 * q^34 + 5 * q^35 + 51 * q^36 + 8 * q^37 + 5 * q^38 + q^41 - 42 * q^42 + 23 * q^43 - 17 * q^44 + 27 * q^45 - q^46 - 18 * q^47 - 14 * q^48 + 41 * q^49 + q^50 + 18 * q^53 + 8 * q^54 - 14 * q^55 + 80 * q^56 + 44 * q^57 + 22 * q^58 + 8 * q^59 - 9 * q^60 + 16 * q^61 - 5 * q^62 + 50 * q^63 + 10 * q^64 - 2 * q^66 + q^67 - 8 * q^68 + 34 * q^69 + 12 * q^70 - 20 * q^71 + 117 * q^72 - 15 * q^73 + 49 * q^74 + q^75 + 10 * q^76 - 5 * q^77 + 5 * q^79 + 15 * q^80 + 82 * q^81 + 32 * q^82 - 18 * q^83 - 50 * q^84 + 17 * q^85 - 74 * q^86 + 2 * q^87 - 16 * q^89 + 23 * q^90 + 7 * q^92 + 33 * q^93 + 34 * q^94 + 3 * q^95 + 56 * q^96 - 5 * q^97 + 34 * q^98 - 27 * 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 $

$2$	−1.43626	−1.01559	−0.507795	−	0.861478i	$-0.669539\pi$
$2$	−1.43626	−1.01559	−0.507795	+	0.861478i	$0.669539\pi$
$3$	−3.39685	−1.96117	−0.980586	−	0.196089i	$-0.937176\pi$
$3$	−3.39685	−1.96117	−0.980586	+	0.196089i	$0.937176\pi$
$4$	0.0628427	0.0314213
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.87876	1.99175
$7$	−0.0323629	−0.0122320	−0.00611601	−	0.999981i	$-0.501947\pi$
$7$	−0.0323629	−0.0122320	−0.00611601	+	0.999981i	$0.501947\pi$
$8$	2.78226	0.983678
$9$	8.53859	2.84620
$10$	−1.43626	−0.454185
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.213467	−0.0616227
$13$	0	0
$13$	0	0
$14$	0.0464815	0.0124227
$15$	−3.39685	−0.877063
$16$	−4.12174	−1.03043
$17$	3.78377	0.917699	0.458849	−	0.888514i	$-0.348262\pi$
$17$	3.78377	0.917699	0.458849	+	0.888514i	$0.348262\pi$
$18$	−12.2636	−2.89057
$19$	−6.83572	−1.56822	−0.784111	−	0.620621i	$-0.786881\pi$
$19$	−6.83572	−1.56822	−0.784111	+	0.620621i	$0.786881\pi$
$20$	0.0628427	0.0140520
$21$	0.109932	0.0239891
$22$	1.43626	0.306212
$23$	−6.58463	−1.37299	−0.686495	−	0.727134i	$-0.740852\pi$
$23$	−6.58463	−1.37299	−0.686495	+	0.727134i	$0.740852\pi$
$24$	−9.45093	−1.92916
$25$	1.00000	0.200000
$26$	0	0
$27$	−18.8138	−3.62071
$28$	−0.00203377	−0.000384347 0
$29$	2.81175	0.522129	0.261064	−	0.965321i	$-0.415926\pi$
$29$	2.81175	0.522129	0.261064	+	0.965321i	$0.415926\pi$
$30$	4.87876	0.890736
$31$	−10.2724	−1.84498	−0.922491	−	0.386018i	$-0.873850\pi$
$31$	−10.2724	−1.84498	−0.922491	+	0.386018i	$0.873850\pi$
$32$	0.355362	0.0628196
$33$	3.39685	0.591316
$34$	−5.43448	−0.932005
$35$	−0.0323629	−0.00547033
$36$	0.536588	0.0894313
$37$	−1.79565	−0.295203	−0.147602	−	0.989047i	$-0.547155\pi$
$37$	−1.79565	−0.295203	−0.147602	+	0.989047i	$0.547155\pi$
$38$	9.81787	1.59267
$39$	0	0
$40$	2.78226	0.439914
$41$	−5.87396	−0.917359	−0.458679	−	0.888602i	$-0.651677\pi$
$41$	−5.87396	−0.917359	−0.458679	+	0.888602i	$0.651677\pi$
$42$	−0.157891	−0.0243631
$43$	−0.0423789	−0.00646272	−0.00323136	−	0.999995i	$-0.501029\pi$
$43$	−0.0423789	−0.00646272	−0.00323136	+	0.999995i	$0.501029\pi$
$44$	−0.0628427	−0.00947389
$45$	8.53859	1.27286
$46$	9.45724	1.39439
$47$	0.474764	0.0692515	0.0346257	−	0.999400i	$-0.488976\pi$
$47$	0.474764	0.0692515	0.0346257	+	0.999400i	$0.488976\pi$
$48$	14.0009	2.02086
$49$	−6.99895	−0.999850
$50$	−1.43626	−0.203118
$51$	−12.8529	−1.79977
$52$	0	0
$53$	−13.0978	−1.79912	−0.899561	−	0.436795i	$-0.856113\pi$
$53$	−13.0978	−1.79912	−0.899561	+	0.436795i	$0.856113\pi$
$54$	27.0215	3.67715
$55$	−1.00000	−0.134840
$56$	−0.0900420	−0.0120324
$57$	23.2199	3.07555
$58$	−4.03840	−0.530268
$59$	−0.226853	−0.0295337	−0.0147668	−	0.999891i	$-0.504701\pi$
$59$	−0.226853	−0.0295337	−0.0147668	+	0.999891i	$0.504701\pi$
$60$	−0.213467	−0.0275585
$61$	−4.37466	−0.560118	−0.280059	−	0.959983i	$-0.590354\pi$
$61$	−4.37466	−0.560118	−0.280059	+	0.959983i	$0.590354\pi$
$62$	14.7539	1.87374
$63$	−0.276334	−0.0348148
$64$	7.73308	0.966635
$65$	0	0
$66$	−4.87876	−0.600534
$67$	10.2112	1.24750	0.623748	−	0.781626i	$-0.285609\pi$
$67$	10.2112	1.24750	0.623748	+	0.781626i	$0.285609\pi$
$68$	0.237782	0.0288353
$69$	22.3670	2.69267
$70$	0.0464815	0.00555561
$71$	2.20469	0.261648	0.130824	−	0.991406i	$-0.458238\pi$
$71$	2.20469	0.261648	0.130824	+	0.991406i	$0.458238\pi$
$72$	23.7566	2.79974
$73$	4.47066	0.523251	0.261626	−	0.965169i	$-0.415741\pi$
$73$	4.47066	0.523251	0.261626	+	0.965169i	$0.415741\pi$
$74$	2.57902	0.299805
$75$	−3.39685	−0.392234
$76$	−0.429575	−0.0492756
$77$	0.0323629	0.00368809
$78$	0	0
$79$	10.1953	1.14706	0.573529	−	0.819185i	$-0.305574\pi$
$79$	10.1953	1.14706	0.573529	+	0.819185i	$0.305574\pi$
$80$	−4.12174	−0.460824
$81$	38.2918	4.25464
$82$	8.43653	0.931659
$83$	−8.39914	−0.921926	−0.460963	−	0.887419i	$-0.652496\pi$
$83$	−8.39914	−0.921926	−0.460963	+	0.887419i	$0.652496\pi$
$84$	0.00690841	0.000753770 0
$85$	3.78377	0.410407
$86$	0.0608671	0.00656347
$87$	−9.55109	−1.02398
$88$	−2.78226	−0.296590
$89$	−13.1205	−1.39078	−0.695388	−	0.718635i	$-0.744767\pi$
$89$	−13.1205	−1.39078	−0.695388	+	0.718635i	$0.744767\pi$
$90$	−12.2636	−1.29270
$91$	0	0
$92$	−0.413796	−0.0431412
$93$	34.8939	3.61833
$94$	−0.681885	−0.0703310
$95$	−6.83572	−0.701330
$96$	−1.20711	−0.123200
$97$	7.36967	0.748276	0.374138	−	0.927373i	$-0.377939\pi$
$97$	7.36967	0.748276	0.374138	+	0.927373i	$0.377939\pi$
$98$	10.0523	1.01544
$99$	−8.53859	−0.858161
$100$	0.0628427	0.00628427
$101$	−14.8701	−1.47963	−0.739815	−	0.672811i	$-0.765087\pi$
$101$	−14.8701	−1.47963	−0.739815	+	0.672811i	$0.765087\pi$
$102$	18.4601	1.82782
$103$	0.980375	0.0965993	0.0482996	−	0.998833i	$-0.484620\pi$
$103$	0.980375	0.0965993	0.0482996	+	0.998833i	$0.484620\pi$
$104$	0	0
$105$	0.109932	0.0107283
$106$	18.8119	1.82717
$107$	−7.77737	−0.751867	−0.375934	−	0.926647i	$-0.622678\pi$
$107$	−7.77737	−0.751867	−0.375934	+	0.926647i	$0.622678\pi$
$108$	−1.18231	−0.113768
$109$	−6.92455	−0.663251	−0.331626	−	0.943411i	$-0.607597\pi$
$109$	−6.92455	−0.663251	−0.331626	+	0.943411i	$0.607597\pi$
$110$	1.43626	0.136942
$111$	6.09956	0.578944
$112$	0.133391	0.0126043
$113$	12.4113	1.16756	0.583780	−	0.811912i	$-0.301573\pi$
$113$	12.4113	1.16756	0.583780	+	0.811912i	$0.301573\pi$
$114$	−33.3498	−3.12350
$115$	−6.58463	−0.614020
$116$	0.176698	0.0164060
$117$	0	0
$118$	0.325819	0.0299941
$119$	−0.122454	−0.0112253
$120$	−9.45093	−0.862748
$121$	1.00000	0.0909091
$122$	6.28315	0.568850
$123$	19.9530	1.79910
$124$	−0.645547	−0.0579718
$125$	1.00000	0.0894427
$126$	0.396887	0.0353575
$127$	−8.28581	−0.735247	−0.367623	−	0.929975i	$-0.619828\pi$
$127$	−8.28581	−0.735247	−0.367623	+	0.929975i	$0.619828\pi$
$128$	−11.8174	−1.04452
$129$	0.143955	0.0126745
$130$	0	0
$131$	−9.09524	−0.794655	−0.397327	−	0.917677i	$-0.630062\pi$
$131$	−9.09524	−0.794655	−0.397327	+	0.917677i	$0.630062\pi$
$132$	0.213467	0.0185799
$133$	0.221224	0.0191825
$134$	−14.6659	−1.26694
$135$	−18.8138	−1.61923
$136$	10.5274	0.902720
$137$	4.58452	0.391682	0.195841	−	0.980636i	$-0.437256\pi$
$137$	4.58452	0.391682	0.195841	+	0.980636i	$0.437256\pi$
$138$	−32.1248	−2.73465
$139$	−14.4750	−1.22775	−0.613875	−	0.789403i	$-0.710390\pi$
$139$	−14.4750	−1.22775	−0.613875	+	0.789403i	$0.710390\pi$
$140$	−0.00203377	−0.000171885 0
$141$	−1.61270	−0.135814
$142$	−3.16650	−0.265727
$143$	0	0
$144$	−35.1938	−2.93282
$145$	2.81175	0.233503
$146$	−6.42103	−0.531408
$147$	23.7744	1.96088
$148$	−0.112844	−0.00927568
$149$	−5.64653	−0.462582	−0.231291	−	0.972885i	$-0.574295\pi$
$149$	−5.64653	−0.462582	−0.231291	+	0.972885i	$0.574295\pi$
$150$	4.87876	0.398349
$151$	13.7821	1.12157	0.560784	−	0.827962i	$-0.310500\pi$
$151$	13.7821	1.12157	0.560784	+	0.827962i	$0.310500\pi$
$152$	−19.0188	−1.54263
$153$	32.3081	2.61195
$154$	−0.0464815	−0.00374559
$155$	−10.2724	−0.825101
$156$	0	0
$157$	19.8650	1.58540	0.792700	−	0.609612i	$-0.208675\pi$
$157$	19.8650	1.58540	0.792700	+	0.609612i	$0.208675\pi$
$158$	−14.6431	−1.16494
$159$	44.4913	3.52839
$160$	0.355362	0.0280938
$161$	0.213098	0.0167945
$162$	−54.9969	−4.32097
$163$	−11.5453	−0.904300	−0.452150	−	0.891942i	$-0.649343\pi$
$163$	−11.5453	−0.904300	−0.452150	+	0.891942i	$0.649343\pi$
$164$	−0.369135	−0.0288246
$165$	3.39685	0.264444
$166$	12.0634	0.936298
$167$	12.7687	0.988076	0.494038	−	0.869440i	$-0.335520\pi$
$167$	12.7687	0.988076	0.494038	+	0.869440i	$0.335520\pi$
$168$	0.305859	0.0235976
$169$	0	0
$170$	−5.43448	−0.416805
$171$	−58.3674	−4.46347
$172$	−0.00266320	−0.000203067 0
$173$	16.3692	1.24453	0.622264	−	0.782807i	$-0.286213\pi$
$173$	16.3692	1.24453	0.622264	+	0.782807i	$0.286213\pi$
$174$	13.7179	1.03995
$175$	−0.0323629	−0.00244641
$176$	4.12174	0.310688
$177$	0.770584	0.0579207
$178$	18.8445	1.41246
$179$	8.70330	0.650515	0.325258	−	0.945625i	$-0.394549\pi$
$179$	8.70330	0.650515	0.325258	+	0.945625i	$0.394549\pi$
$180$	0.536588	0.0399949
$181$	−0.898664	−0.0667972	−0.0333986	−	0.999442i	$-0.510633\pi$
$181$	−0.898664	−0.0667972	−0.0333986	+	0.999442i	$0.510633\pi$
$182$	0	0
$183$	14.8601	1.09849
$184$	−18.3202	−1.35058
$185$	−1.79565	−0.132019
$186$	−50.1167	−3.67474
$187$	−3.78377	−0.276697
$188$	0.0298354	0.00217597
$189$	0.608868	0.0442886
$190$	9.81787	0.712263
$191$	3.27954	0.237299	0.118650	−	0.992936i	$-0.462143\pi$
$191$	3.27954	0.237299	0.118650	+	0.992936i	$0.462143\pi$
$192$	−26.2681	−1.89574
$193$	−0.223483	−0.0160867	−0.00804334	−	0.999968i	$-0.502560\pi$
$193$	−0.223483	−0.0160867	−0.00804334	+	0.999968i	$0.502560\pi$
$194$	−10.5848	−0.759941
$195$	0	0
$196$	−0.439833	−0.0314166
$197$	−13.3815	−0.953392	−0.476696	−	0.879068i	$-0.658166\pi$
$197$	−13.3815	−0.953392	−0.476696	+	0.879068i	$0.658166\pi$
$198$	12.2636	0.871539
$199$	−15.8343	−1.12246	−0.561231	−	0.827659i	$-0.689672\pi$
$199$	−15.8343	−1.12246	−0.561231	+	0.827659i	$0.689672\pi$
$200$	2.78226	0.196736
$201$	−34.6859	−2.44655
$202$	21.3573	1.50270
$203$	−0.0909964	−0.00638669
$204$	−0.807710	−0.0565510
$205$	−5.87396	−0.410255
$206$	−1.40807	−0.0981052
$207$	−56.2235	−3.90780
$208$	0	0
$209$	6.83572	0.472837
$210$	−0.157891	−0.0108955
$211$	−2.48452	−0.171041	−0.0855206	−	0.996336i	$-0.527255\pi$
$211$	−2.48452	−0.171041	−0.0855206	+	0.996336i	$0.527255\pi$
$212$	−0.823101	−0.0565308
$213$	−7.48899	−0.513137
$214$	11.1703	0.763588
$215$	−0.0423789	−0.00289022
$216$	−52.3448	−3.56161
$217$	0.332446	0.0225679
$218$	9.94545	0.673591
$219$	−15.1862	−1.02619
$220$	−0.0628427	−0.00423685
$221$	0	0
$222$	−8.76055	−0.587970
$223$	3.73645	0.250211	0.125106	−	0.992143i	$-0.460073\pi$
$223$	3.73645	0.250211	0.125106	+	0.992143i	$0.460073\pi$
$224$	−0.0115005	−0.000768411 0
$225$	8.53859	0.569239
$226$	−17.8259	−1.18576
$227$	−17.6287	−1.17006	−0.585030	−	0.811011i	$-0.698917\pi$
$227$	−17.6287	−1.17006	−0.585030	+	0.811011i	$0.698917\pi$
$228$	1.45920	0.0966380
$229$	15.9712	1.05541	0.527705	−	0.849428i	$-0.323053\pi$
$229$	15.9712	1.05541	0.527705	+	0.849428i	$0.323053\pi$
$230$	9.45724	0.623592
$231$	−0.109932	−0.00723299
$232$	7.82302	0.513607
$233$	26.7821	1.75455	0.877277	−	0.479985i	$-0.159358\pi$
$233$	26.7821	1.75455	0.877277	+	0.479985i	$0.159358\pi$
$234$	0	0
$235$	0.474764	0.0309702
$236$	−0.0142560	−0.000927988 0
$237$	−34.6318	−2.24958
$238$	0.175875	0.0114003
$239$	−17.1388	−1.10862	−0.554308	−	0.832312i	$-0.687017\pi$
$239$	−17.1388	−1.10862	−0.554308	+	0.832312i	$0.687017\pi$
$240$	14.0009	0.903756
$241$	−10.9505	−0.705387	−0.352693	−	0.935739i	$-0.614734\pi$
$241$	−10.9505	−0.705387	−0.352693	+	0.935739i	$0.614734\pi$
$242$	−1.43626	−0.0923263
$243$	−73.6301	−4.72337
$244$	−0.274915	−0.0175997
$245$	−6.99895	−0.447147
$246$	−28.6576	−1.82714
$247$	0	0
$248$	−28.5806	−1.81487
$249$	28.5306	1.80806
$250$	−1.43626	−0.0908371
$251$	−14.3208	−0.903921	−0.451960	−	0.892038i	$-0.649275\pi$
$251$	−14.3208	−0.903921	−0.451960	+	0.892038i	$0.649275\pi$
$252$	−0.0173655	−0.00109393
$253$	6.58463	0.413972
$254$	11.9006	0.746709
$255$	−12.8529	−0.804880
$256$	1.50675	0.0941719
$257$	1.67114	0.104243	0.0521214	−	0.998641i	$-0.483402\pi$
$257$	1.67114	0.104243	0.0521214	+	0.998641i	$0.483402\pi$
$258$	−0.206756	−0.0128721
$259$	0.0581125	0.00361093
$260$	0	0
$261$	24.0084	1.48608
$262$	13.0631	0.807043
$263$	14.5497	0.897175	0.448588	−	0.893739i	$-0.351927\pi$
$263$	14.5497	0.897175	0.448588	+	0.893739i	$0.351927\pi$
$264$	9.45093	0.581664
$265$	−13.0978	−0.804592
$266$	−0.317735	−0.0194816
$267$	44.5685	2.72755
$268$	0.641699	0.0391980
$269$	4.01107	0.244559	0.122280	−	0.992496i	$-0.460980\pi$
$269$	4.01107	0.244559	0.122280	+	0.992496i	$0.460980\pi$
$270$	27.0215	1.64447
$271$	1.32347	0.0803948	0.0401974	−	0.999192i	$-0.487201\pi$
$271$	1.32347	0.0803948	0.0401974	+	0.999192i	$0.487201\pi$
$272$	−15.5957	−0.945628
$273$	0	0
$274$	−6.58457	−0.397788
$275$	−1.00000	−0.0603023
$276$	1.40560	0.0846073
$277$	−7.21030	−0.433225	−0.216612	−	0.976258i	$-0.569501\pi$
$277$	−7.21030	−0.433225	−0.216612	+	0.976258i	$0.569501\pi$
$278$	20.7898	1.24689
$279$	−87.7121	−5.25118
$280$	−0.0900420	−0.00538104
$281$	−17.6974	−1.05574	−0.527868	−	0.849326i	$-0.677008\pi$
$281$	−17.6974	−1.05574	−0.527868	+	0.849326i	$0.677008\pi$
$282$	2.31626	0.137931
$283$	6.29262	0.374057	0.187029	−	0.982354i	$-0.440114\pi$
$283$	6.29262	0.374057	0.187029	+	0.982354i	$0.440114\pi$
$284$	0.138548	0.00822133
$285$	23.2199	1.37543
$286$	0	0
$287$	0.190098	0.0112212
$288$	3.03429	0.178797
$289$	−2.68309	−0.157829
$290$	−4.03840	−0.237143
$291$	−25.0336	−1.46750
$292$	0.280948	0.0164413
$293$	−13.5561	−0.791956	−0.395978	−	0.918260i	$-0.629594\pi$
$293$	−13.5561	−0.791956	−0.395978	+	0.918260i	$0.629594\pi$
$294$	−34.1462	−1.99145
$295$	−0.226853	−0.0132079
$296$	−4.99597	−0.290385
$297$	18.8138	1.09169
$298$	8.10988	0.469793
$299$	0	0
$300$	−0.213467	−0.0123245
$301$	0.00137150	7.90521e−5 0
$302$	−19.7946	−1.13905
$303$	50.5115	2.90181
$304$	28.1750	1.61595
$305$	−4.37466	−0.250492
$306$	−46.4028	−2.65267
$307$	19.9436	1.13824	0.569121	−	0.822254i	$-0.307284\pi$
$307$	19.9436	1.13824	0.569121	+	0.822254i	$0.307284\pi$
$308$	0.00203377	0.000115885 0
$309$	−3.33019	−0.189448
$310$	14.7539	0.837964
$311$	−7.76978	−0.440584	−0.220292	−	0.975434i	$-0.570701\pi$
$311$	−7.76978	−0.440584	−0.220292	+	0.975434i	$0.570701\pi$
$312$	0	0
$313$	−13.7181	−0.775395	−0.387697	−	0.921787i	$-0.626729\pi$
$313$	−13.7181	−0.775395	−0.387697	+	0.921787i	$0.626729\pi$
$314$	−28.5313	−1.61011
$315$	−0.276334	−0.0155696
$316$	0.640698	0.0360421
$317$	10.5307	0.591464	0.295732	−	0.955271i	$-0.404437\pi$
$317$	10.5307	0.591464	0.295732	+	0.955271i	$0.404437\pi$
$318$	−63.9011	−3.58339
$319$	−2.81175	−0.157428
$320$	7.73308	0.432292
$321$	26.4186	1.47454
$322$	−0.306064	−0.0170563
$323$	−25.8648	−1.43916
$324$	2.40636	0.133686
$325$	0	0
$326$	16.5821	0.918397
$327$	23.5216	1.30075
$328$	−16.3429	−0.902385
$329$	−0.0153647	−0.000847086 0
$330$	−4.87876	−0.268567
$331$	−23.5357	−1.29364	−0.646819	−	0.762644i	$-0.723901\pi$
$331$	−23.5357	−1.29364	−0.646819	+	0.762644i	$0.723901\pi$
$332$	−0.527824	−0.0289681
$333$	−15.3323	−0.840207
$334$	−18.3392	−1.00348
$335$	10.2112	0.557897
$336$	−0.453110	−0.0247192
$337$	30.9661	1.68683	0.843416	−	0.537262i	$-0.180541\pi$
$337$	30.9661	1.68683	0.843416	+	0.537262i	$0.180541\pi$
$338$	0	0
$339$	−42.1594	−2.28978
$340$	0.237782	0.0128955
$341$	10.2724	0.556283
$342$	83.8308	4.53305
$343$	0.453047	0.0244622
$344$	−0.117909	−0.00635723
$345$	22.3670	1.20420
$346$	−23.5105	−1.26393
$347$	10.9473	0.587680	0.293840	−	0.955855i	$-0.405067\pi$
$347$	10.9473	0.587680	0.293840	+	0.955855i	$0.405067\pi$
$348$	−0.600216	−0.0321750
$349$	18.4165	0.985814	0.492907	−	0.870082i	$-0.335934\pi$
$349$	18.4165	0.985814	0.492907	+	0.870082i	$0.335934\pi$
$350$	0.0464815	0.00248454
$351$	0	0
$352$	−0.355362	−0.0189408
$353$	−3.73356	−0.198718	−0.0993588	−	0.995052i	$-0.531679\pi$
$353$	−3.73356	−0.198718	−0.0993588	+	0.995052i	$0.531679\pi$
$354$	−1.10676	−0.0588236
$355$	2.20469	0.117013
$356$	−0.824530	−0.0437000
$357$	0.415957	0.0220148
$358$	−12.5002	−0.660656
$359$	−20.4059	−1.07698	−0.538491	−	0.842631i	$-0.681005\pi$
$359$	−20.4059	−1.07698	−0.538491	+	0.842631i	$0.681005\pi$
$360$	23.7566	1.25208
$361$	27.7271	1.45932
$362$	1.29072	0.0678385
$363$	−3.39685	−0.178288
$364$	0	0
$365$	4.47066	0.234005
$366$	−21.3429	−1.11561
$367$	−1.28509	−0.0670812	−0.0335406	−	0.999437i	$-0.510678\pi$
$367$	−1.28509	−0.0670812	−0.0335406	+	0.999437i	$0.510678\pi$
$368$	27.1401	1.41478
$369$	−50.1553	−2.61098
$370$	2.57902	0.134077
$371$	0.423883	0.0220069
$372$	2.19283	0.113693
$373$	−6.93720	−0.359195	−0.179597	−	0.983740i	$-0.557480\pi$
$373$	−6.93720	−0.359195	−0.179597	+	0.983740i	$0.557480\pi$
$374$	5.43448	0.281010
$375$	−3.39685	−0.175413
$376$	1.32092	0.0681212
$377$	0	0
$378$	−0.874493	−0.0449790
$379$	17.4849	0.898140	0.449070	−	0.893497i	$-0.351755\pi$
$379$	17.4849	0.898140	0.449070	+	0.893497i	$0.351755\pi$
$380$	−0.429575	−0.0220367
$381$	28.1457	1.44195
$382$	−4.71027	−0.240998
$383$	4.70391	0.240359	0.120179	−	0.992752i	$-0.461653\pi$
$383$	4.70391	0.240359	0.120179	+	0.992752i	$0.461653\pi$
$384$	40.1421	2.04849
$385$	0.0323629	0.00164937
$386$	0.320980	0.0163375
$387$	−0.361856	−0.0183942
$388$	0.463129	0.0235118
$389$	20.6511	1.04705	0.523527	−	0.852009i	$-0.324616\pi$
$389$	20.6511	1.04705	0.523527	+	0.852009i	$0.324616\pi$
$390$	0	0
$391$	−24.9147	−1.25999
$392$	−19.4729	−0.983531
$393$	30.8952	1.55845
$394$	19.2193	0.968254
$395$	10.1953	0.512980
$396$	−0.536588	−0.0269646
$397$	−36.7469	−1.84427	−0.922137	−	0.386863i	$-0.873559\pi$
$397$	−36.7469	−1.84427	−0.922137	+	0.386863i	$0.873559\pi$
$398$	22.7421	1.13996
$399$	−0.751464	−0.0376202
$400$	−4.12174	−0.206087
$401$	−0.537341	−0.0268335	−0.0134168	−	0.999910i	$-0.504271\pi$
$401$	−0.537341	−0.0268335	−0.0134168	+	0.999910i	$0.504271\pi$
$402$	49.8180	2.48469
$403$	0	0
$404$	−0.934476	−0.0464919
$405$	38.2918	1.90273
$406$	0.130694	0.00648626
$407$	1.79565	0.0890071
$408$	−35.7601	−1.77039
$409$	−20.4298	−1.01019	−0.505094	−	0.863064i	$-0.668542\pi$
$409$	−20.4298	−1.01019	−0.505094	+	0.863064i	$0.668542\pi$
$410$	8.43653	0.416651
$411$	−15.5729	−0.768156
$412$	0.0616094	0.00303528
$413$	0.00734161	0.000361257 0
$414$	80.7515	3.96872
$415$	−8.39914	−0.412298
$416$	0	0
$417$	49.1693	2.40783
$418$	−9.81787	−0.480208
$419$	8.96631	0.438033	0.219016	−	0.975721i	$-0.429715\pi$
$419$	8.96631	0.438033	0.219016	+	0.975721i	$0.429715\pi$
$420$	0.00690841	0.000337096 0
$421$	0.759279	0.0370050	0.0185025	−	0.999829i	$-0.494110\pi$
$421$	0.759279	0.0370050	0.0185025	+	0.999829i	$0.494110\pi$
$422$	3.56841	0.173708
$423$	4.05382	0.197103
$424$	−36.4415	−1.76976
$425$	3.78377	0.183540
$426$	10.7561	0.521136
$427$	0.141577	0.00685138
$428$	−0.488751	−0.0236247
$429$	0	0
$430$	0.0608671	0.00293527
$431$	20.6585	0.995085	0.497543	−	0.867439i	$-0.334236\pi$
$431$	20.6585	0.995085	0.497543	+	0.867439i	$0.334236\pi$
$432$	77.5454	3.73090
$433$	13.4093	0.644410	0.322205	−	0.946670i	$-0.395576\pi$
$433$	13.4093	0.644410	0.322205	+	0.946670i	$0.395576\pi$
$434$	−0.477478	−0.0229197
$435$	−9.55109	−0.457940
$436$	−0.435157	−0.0208402
$437$	45.0107	2.15315
$438$	21.8113	1.04218
$439$	−0.991852	−0.0473385	−0.0236692	−	0.999720i	$-0.507535\pi$
$439$	−0.991852	−0.0473385	−0.0236692	+	0.999720i	$0.507535\pi$
$440$	−2.78226	−0.132639
$441$	−59.7612	−2.84577
$442$	0	0
$443$	15.2898	0.726439	0.363219	−	0.931704i	$-0.381678\pi$
$443$	15.2898	0.726439	0.363219	+	0.931704i	$0.381678\pi$
$444$	0.383313	0.0181912
$445$	−13.1205	−0.621974
$446$	−5.36651	−0.254112
$447$	19.1804	0.907203
$448$	−0.250265	−0.0118239
$449$	−14.6365	−0.690741	−0.345371	−	0.938466i	$-0.612247\pi$
$449$	−14.6365	−0.690741	−0.345371	+	0.938466i	$0.612247\pi$
$450$	−12.2636	−0.578113
$451$	5.87396	0.276594
$452$	0.779961	0.0366863
$453$	−46.8156	−2.19959
$454$	25.3195	1.18830
$455$	0	0
$456$	64.6039	3.02535
$457$	−23.4374	−1.09636	−0.548179	−	0.836361i	$-0.684679\pi$
$457$	−23.4374	−1.09636	−0.548179	+	0.836361i	$0.684679\pi$
$458$	−22.9389	−1.07186
$459$	−71.1869	−3.32272
$460$	−0.413796	−0.0192933
$461$	16.9841	0.791027	0.395514	−	0.918460i	$-0.370567\pi$
$461$	16.9841	0.791027	0.395514	+	0.918460i	$0.370567\pi$
$462$	0.157891	0.00734575
$463$	27.4560	1.27599	0.637995	−	0.770041i	$-0.279764\pi$
$463$	27.4560	1.27599	0.637995	+	0.770041i	$0.279764\pi$
$464$	−11.5893	−0.538019
$465$	34.8939	1.61817
$466$	−38.4660	−1.78191
$467$	31.9733	1.47955	0.739774	−	0.672856i	$-0.234933\pi$
$467$	31.9733	1.47955	0.739774	+	0.672856i	$0.234933\pi$
$468$	0	0
$469$	−0.330464	−0.0152594
$470$	−0.681885	−0.0314530
$471$	−67.4784	−3.10924
$472$	−0.631163	−0.0290516
$473$	0.0423789	0.00194858
$474$	49.7403	2.28465
$475$	−6.83572	−0.313644
$476$	−0.00769532	−0.000352714 0
$477$	−111.837	−5.12066
$478$	24.6157	1.12590
$479$	−8.85074	−0.404401	−0.202200	−	0.979344i	$-0.564809\pi$
$479$	−8.85074	−0.404401	−0.202200	+	0.979344i	$0.564809\pi$
$480$	−1.20711	−0.0550968
$481$	0	0
$482$	15.7278	0.716383
$483$	−0.723861	−0.0329368
$484$	0.0628427	0.00285648
$485$	7.36967	0.334639
$486$	105.752	4.79701
$487$	−1.96533	−0.0890577	−0.0445288	−	0.999008i	$-0.514179\pi$
$487$	−1.96533	−0.0890577	−0.0445288	+	0.999008i	$0.514179\pi$
$488$	−12.1715	−0.550976
$489$	39.2177	1.77349
$490$	10.0523	0.454117
$491$	1.14590	0.0517137	0.0258569	−	0.999666i	$-0.491769\pi$
$491$	1.14590	0.0517137	0.0258569	+	0.999666i	$0.491769\pi$
$492$	1.25390	0.0565301
$493$	10.6390	0.479157
$494$	0	0
$495$	−8.53859	−0.383781
$496$	42.3402	1.90113
$497$	−0.0713500	−0.00320048
$498$	−40.9774	−1.83624
$499$	15.6260	0.699514	0.349757	−	0.936841i	$-0.386264\pi$
$499$	15.6260	0.699514	0.349757	+	0.936841i	$0.386264\pi$
$500$	0.0628427	0.00281041
$501$	−43.3735	−1.93779
$502$	20.5684	0.918012
$503$	40.6360	1.81187	0.905935	−	0.423417i	$-0.139169\pi$
$503$	40.6360	1.81187	0.905935	+	0.423417i	$0.139169\pi$
$504$	−0.768832	−0.0342465
$505$	−14.8701	−0.661710
$506$	−9.45724	−0.420426
$507$	0	0
$508$	−0.520702	−0.0231024
$509$	42.7320	1.89406	0.947030	−	0.321144i	$-0.104067\pi$
$509$	42.7320	1.89406	0.947030	+	0.321144i	$0.104067\pi$
$510$	18.4601	0.817427
$511$	−0.144684	−0.00640042
$512$	21.4708	0.948884
$513$	128.606	5.67808
$514$	−2.40019	−0.105868
$515$	0.980375	0.0432005
$516$	0.00904650	0.000398250 0
$517$	−0.474764	−0.0208801
$518$	−0.0834646	−0.00366722
$519$	−55.6038	−2.44074
$520$	0	0
$521$	−41.7385	−1.82860	−0.914300	−	0.405039i	$-0.867258\pi$
$521$	−41.7385	−1.82860	−0.914300	+	0.405039i	$0.867258\pi$
$522$	−34.4823	−1.50925
$523$	−22.5208	−0.984767	−0.492384	−	0.870378i	$-0.663874\pi$
$523$	−22.5208	−0.984767	−0.492384	+	0.870378i	$0.663874\pi$
$524$	−0.571569	−0.0249691
$525$	0.109932	0.00479782
$526$	−20.8972	−0.911161
$527$	−38.8685	−1.69314
$528$	−14.0009	−0.609312
$529$	20.3574	0.885102
$530$	18.8119	0.817135
$531$	−1.93700	−0.0840587
$532$	0.0139023	0.000602741 0
$533$	0	0
$534$	−64.0120	−2.77007
$535$	−7.77737	−0.336245
$536$	28.4102	1.22713
$537$	−29.5638	−1.27577
$538$	−5.76094	−0.248372
$539$	6.99895	0.301466
$540$	−1.18231	−0.0508784
$541$	−32.7539	−1.40820	−0.704100	−	0.710101i	$-0.748649\pi$
$541$	−32.7539	−1.40820	−0.704100	+	0.710101i	$0.748649\pi$
$542$	−1.90084	−0.0816481
$543$	3.05263	0.131001
$544$	1.34461	0.0576495
$545$	−6.92455	−0.296615
$546$	0	0
$547$	−11.7532	−0.502531	−0.251266	−	0.967918i	$-0.580847\pi$
$547$	−11.7532	−0.502531	−0.251266	+	0.967918i	$0.580847\pi$
$548$	0.288104	0.0123072
$549$	−37.3535	−1.59421
$550$	1.43626	0.0612423
$551$	−19.2203	−0.818814
$552$	62.2309	2.64872
$553$	−0.329949	−0.0140308
$554$	10.3559	0.439978
$555$	6.09956	0.258912
$556$	−0.909645	−0.0385775
$557$	−28.5211	−1.20848	−0.604239	−	0.796803i	$-0.706523\pi$
$557$	−28.5211	−1.20848	−0.604239	+	0.796803i	$0.706523\pi$
$558$	125.977	5.33304
$559$	0	0
$560$	0.133391	0.00563681
$561$	12.8529	0.542650
$562$	25.4180	1.07219
$563$	12.1272	0.511102	0.255551	−	0.966796i	$-0.417743\pi$
$563$	12.1272	0.511102	0.255551	+	0.966796i	$0.417743\pi$
$564$	−0.101347	−0.00426746
$565$	12.4113	0.522148
$566$	−9.03784	−0.379889
$567$	−1.23923	−0.0520429
$568$	6.13401	0.257377
$569$	40.6458	1.70396	0.851981	−	0.523573i	$-0.175401\pi$
$569$	40.6458	1.70396	0.851981	+	0.523573i	$0.175401\pi$
$570$	−33.3498	−1.39687
$571$	0.816244	0.0341587	0.0170794	−	0.999854i	$-0.494563\pi$
$571$	0.816244	0.0341587	0.0170794	+	0.999854i	$0.494563\pi$
$572$	0	0
$573$	−11.1401	−0.465384
$574$	−0.273031	−0.0113961
$575$	−6.58463	−0.274598
$576$	66.0296	2.75123
$577$	−31.2553	−1.30118	−0.650588	−	0.759431i	$-0.725478\pi$
$577$	−31.2553	−1.30118	−0.650588	+	0.759431i	$0.725478\pi$
$578$	3.85362	0.160290
$579$	0.759139	0.0315487
$580$	0.176698	0.00733698
$581$	0.271821	0.0112770
$582$	35.9548	1.49038
$583$	13.0978	0.542456
$584$	12.4385	0.514711
$585$	0	0
$586$	19.4701	0.804302
$587$	−29.2665	−1.20796	−0.603978	−	0.797001i	$-0.706419\pi$
$587$	−29.2665	−1.20796	−0.603978	+	0.797001i	$0.706419\pi$
$588$	1.49405	0.0616134
$589$	70.2194	2.89334
$590$	0.325819	0.0134138
$591$	45.4549	1.86977
$592$	7.40120	0.304187
$593$	−19.5516	−0.802889	−0.401445	−	0.915883i	$-0.631492\pi$
$593$	−19.5516	−0.802889	−0.401445	+	0.915883i	$0.631492\pi$
$594$	−27.0215	−1.10870
$595$	−0.122454	−0.00502011
$596$	−0.354843	−0.0145349
$597$	53.7867	2.20134
$598$	0	0
$599$	19.7201	0.805740	0.402870	−	0.915257i	$-0.368013\pi$
$599$	19.7201	0.805740	0.402870	+	0.915257i	$0.368013\pi$
$600$	−9.45093	−0.385832
$601$	3.69310	0.150645	0.0753224	−	0.997159i	$-0.476001\pi$
$601$	3.69310	0.150645	0.0753224	+	0.997159i	$0.476001\pi$
$602$	−0.00196984	−8.02845e−5 0
$603$	87.1892	3.55062
$604$	0.866101	0.0352412
$605$	1.00000	0.0406558
$606$	−72.5476	−2.94705
$607$	−3.08558	−0.125240	−0.0626200	−	0.998037i	$-0.519946\pi$
$607$	−3.08558	−0.125240	−0.0626200	+	0.998037i	$0.519946\pi$
$608$	−2.42915	−0.0985151
$609$	0.309101	0.0125254
$610$	6.28315	0.254397
$611$	0	0
$612$	2.03032	0.0820710
$613$	−42.1866	−1.70390	−0.851951	−	0.523622i	$-0.824581\pi$
$613$	−42.1866	−1.70390	−0.851951	+	0.523622i	$0.824581\pi$
$614$	−28.6442	−1.15599
$615$	19.9530	0.804581
$616$	0.0900420	0.00362790
$617$	23.7618	0.956615	0.478308	−	0.878192i	$-0.341250\pi$
$617$	23.7618	0.956615	0.478308	+	0.878192i	$0.341250\pi$
$618$	4.78302	0.192401
$619$	31.9825	1.28548	0.642742	−	0.766083i	$-0.277797\pi$
$619$	31.9825	1.28548	0.642742	+	0.766083i	$0.277797\pi$
$620$	−0.645547	−0.0259258
$621$	123.882	4.97120
$622$	11.1594	0.447452
$623$	0.424619	0.0170120
$624$	0	0
$625$	1.00000	0.0400000
$626$	19.7028	0.787482
$627$	−23.2199	−0.927314
$628$	1.24837	0.0498154
$629$	−6.79433	−0.270908
$630$	0.396887	0.0158123
$631$	18.8952	0.752206	0.376103	−	0.926578i	$-0.377264\pi$
$631$	18.8952	0.752206	0.376103	+	0.926578i	$0.377264\pi$
$632$	28.3659	1.12834
$633$	8.43954	0.335441
$634$	−15.1248	−0.600684
$635$	−8.28581	−0.328812
$636$	2.79595	0.110867
$637$	0	0
$638$	4.03840	0.159882
$639$	18.8249	0.744702
$640$	−11.8174	−0.467125
$641$	2.98633	0.117953	0.0589764	−	0.998259i	$-0.481216\pi$
$641$	2.98633	0.117953	0.0589764	+	0.998259i	$0.481216\pi$
$642$	−37.9439	−1.49753
$643$	−3.88631	−0.153261	−0.0766306	−	0.997060i	$-0.524416\pi$
$643$	−3.88631	−0.153261	−0.0766306	+	0.997060i	$0.524416\pi$
$644$	0.0133916	0.000527704 0
$645$	0.143955	0.00566821
$646$	37.1486	1.46159
$647$	−4.72477	−0.185750	−0.0928749	−	0.995678i	$-0.529606\pi$
$647$	−4.72477	−0.185750	−0.0928749	+	0.995678i	$0.529606\pi$
$648$	106.538	4.18520
$649$	0.226853	0.00890474
$650$	0	0
$651$	−1.12927	−0.0442595
$652$	−0.725539	−0.0284143
$653$	20.5210	0.803050	0.401525	−	0.915848i	$-0.368480\pi$
$653$	20.5210	0.803050	0.401525	+	0.915848i	$0.368480\pi$
$654$	−33.7832	−1.32103
$655$	−9.09524	−0.355380
$656$	24.2109	0.945277
$657$	38.1732	1.48928
$658$	0.0220678	0.000860291 0
$659$	4.01428	0.156374	0.0781870	−	0.996939i	$-0.475087\pi$
$659$	4.01428	0.156374	0.0781870	+	0.996939i	$0.475087\pi$
$660$	0.213467	0.00830920
$661$	7.13527	0.277530	0.138765	−	0.990325i	$-0.455687\pi$
$661$	7.13527	0.277530	0.138765	+	0.990325i	$0.455687\pi$
$662$	33.8033	1.31380
$663$	0	0
$664$	−23.3686	−0.906878
$665$	0.221224	0.00857869
$666$	22.0212	0.853305
$667$	−18.5143	−0.716878
$668$	0.802422	0.0310467
$669$	−12.6922	−0.490707
$670$	−14.6659	−0.566594
$671$	4.37466	0.168882
$672$	0.0390656	0.00150699
$673$	15.9075	0.613188	0.306594	−	0.951840i	$-0.400811\pi$
$673$	15.9075	0.613188	0.306594	+	0.951840i	$0.400811\pi$
$674$	−44.4754	−1.71313
$675$	−18.8138	−0.724142
$676$	0	0
$677$	−43.5391	−1.67335	−0.836673	−	0.547703i	$-0.815502\pi$
$677$	−43.5391	−1.67335	−0.836673	+	0.547703i	$0.815502\pi$
$678$	60.5519	2.32548
$679$	−0.238504	−0.00915293
$680$	10.5274	0.403709
$681$	59.8822	2.29469
$682$	−14.7539	−0.564955
$683$	36.7668	1.40684	0.703421	−	0.710773i	$-0.251655\pi$
$683$	36.7668	1.40684	0.703421	+	0.710773i	$0.251655\pi$
$684$	−3.66796	−0.140248
$685$	4.58452	0.175166
$686$	−0.650693	−0.0248436
$687$	−54.2519	−2.06984
$688$	0.174675	0.00665941
$689$	0	0
$690$	−32.1248	−1.22297
$691$	−32.5538	−1.23841	−0.619203	−	0.785231i	$-0.712544\pi$
$691$	−32.5538	−1.23841	−0.619203	+	0.785231i	$0.712544\pi$
$692$	1.02869	0.0391047
$693$	0.276334	0.0104970
$694$	−15.7231	−0.596841
$695$	−14.4750	−0.549066
$696$	−26.5736	−1.00727
$697$	−22.2257	−0.841859
$698$	−26.4509	−1.00118
$699$	−90.9748	−3.44098
$700$	−0.00203377	−7.68693e−5 0
$701$	39.5223	1.49274	0.746368	−	0.665533i	$-0.231796\pi$
$701$	39.5223	1.49274	0.746368	+	0.665533i	$0.231796\pi$
$702$	0	0
$703$	12.2746	0.462944
$704$	−7.73308	−0.291451
$705$	−1.61270	−0.0607379
$706$	5.36237	0.201815
$707$	0.481239	0.0180989
$708$	0.0484256	0.00181994
$709$	−11.4701	−0.430770	−0.215385	−	0.976529i	$-0.569101\pi$
$709$	−11.4701	−0.430770	−0.215385	+	0.976529i	$0.569101\pi$
$710$	−3.16650	−0.118837
$711$	87.0533	3.26475
$712$	−36.5048	−1.36808
$713$	67.6401	2.53314
$714$	−0.597422	−0.0223580
$715$	0	0
$716$	0.546939	0.0204401
$717$	58.2179	2.17419
$718$	29.3082	1.09377
$719$	−6.60114	−0.246181	−0.123091	−	0.992395i	$-0.539281\pi$
$719$	−6.60114	−0.246181	−0.123091	+	0.992395i	$0.539281\pi$
$720$	−35.1938	−1.31160
$721$	−0.0317278	−0.00118160
$722$	−39.8233	−1.48207
$723$	37.1974	1.38339
$724$	−0.0564744	−0.00209886
$725$	2.81175	0.104426
$726$	4.87876	0.181068
$727$	−16.2708	−0.603450	−0.301725	−	0.953395i	$-0.597562\pi$
$727$	−16.2708	−0.603450	−0.301725	+	0.953395i	$0.597562\pi$
$728$	0	0
$729$	135.235	5.00871
$730$	−6.42103	−0.237653
$731$	−0.160352	−0.00593083
$732$	0.933847	0.0345160
$733$	16.9647	0.626604	0.313302	−	0.949653i	$-0.398565\pi$
$733$	16.9647	0.626604	0.313302	+	0.949653i	$0.398565\pi$
$734$	1.84573	0.0681270
$735$	23.7744	0.876932
$736$	−2.33992	−0.0862508
$737$	−10.2112	−0.376134
$738$	72.0361	2.65169
$739$	16.6880	0.613877	0.306939	−	0.951729i	$-0.400695\pi$
$739$	16.6880	0.613877	0.306939	+	0.951729i	$0.400695\pi$
$740$	−0.112844	−0.00414821
$741$	0	0
$742$	−0.608806	−0.0223500
$743$	23.0315	0.844942	0.422471	−	0.906376i	$-0.361163\pi$
$743$	23.0315	0.844942	0.422471	+	0.906376i	$0.361163\pi$
$744$	97.0839	3.55927
$745$	−5.64653	−0.206873
$746$	9.96363	0.364794
$747$	−71.7168	−2.62398
$748$	−0.237782	−0.00869418
$749$	0.251698	0.00919686
$750$	4.87876	0.178147
$751$	15.3734	0.560982	0.280491	−	0.959857i	$-0.409503\pi$
$751$	15.3734	0.560982	0.280491	+	0.959857i	$0.409503\pi$
$752$	−1.95685	−0.0713591
$753$	48.6456	1.77274
$754$	0	0
$755$	13.7821	0.501581
$756$	0.0382629	0.00139161
$757$	0.0669676	0.00243398	0.00121699	−	0.999999i	$-0.499613\pi$
$757$	0.0669676	0.00243398	0.00121699	+	0.999999i	$0.499613\pi$
$758$	−25.1129	−0.912141
$759$	−22.3670	−0.811871
$760$	−19.0188	−0.689883
$761$	−23.1896	−0.840624	−0.420312	−	0.907380i	$-0.638079\pi$
$761$	−23.1896	−0.840624	−0.420312	+	0.907380i	$0.638079\pi$
$762$	−40.4245	−1.46442
$763$	0.224098	0.00811291
$764$	0.206095	0.00745625
$765$	32.3081	1.16810
$766$	−6.75604	−0.244106
$767$	0	0
$768$	−5.11821	−0.184687
$769$	−10.6054	−0.382441	−0.191221	−	0.981547i	$-0.561245\pi$
$769$	−10.6054	−0.382441	−0.191221	+	0.981547i	$0.561245\pi$
$770$	−0.0464815	−0.00167508
$771$	−5.67661	−0.204438
$772$	−0.0140443	−0.000505465 0
$773$	2.96258	0.106557	0.0532783	−	0.998580i	$-0.483033\pi$
$773$	2.96258	0.106557	0.0532783	+	0.998580i	$0.483033\pi$
$774$	0.519719	0.0186809
$775$	−10.2724	−0.368996
$776$	20.5043	0.736063
$777$	−0.197399	−0.00708166
$778$	−29.6604	−1.06338
$779$	40.1528	1.43862
$780$	0	0
$781$	−2.20469	−0.0788898
$782$	35.7840	1.27963
$783$	−52.8996	−1.89048
$784$	28.8478	1.03028
$785$	19.8650	0.709012
$786$	−44.3735	−1.58275
$787$	7.35471	0.262167	0.131084	−	0.991371i	$-0.458154\pi$
$787$	7.35471	0.262167	0.131084	+	0.991371i	$0.458154\pi$
$788$	−0.840929	−0.0299568
$789$	−49.4233	−1.75951
$790$	−14.6431	−0.520977
$791$	−0.401666	−0.0142816
$792$	−23.7566	−0.844154
$793$	0	0
$794$	52.7781	1.87302
$795$	44.4913	1.57794
$796$	−0.995068	−0.0352693
$797$	−21.2594	−0.753045	−0.376523	−	0.926407i	$-0.622880\pi$
$797$	−21.2594	−0.753045	−0.376523	+	0.926407i	$0.622880\pi$
$798$	1.07930	0.0382067
$799$	1.79640	0.0635520
$800$	0.355362	0.0125639
$801$	−112.031	−3.95842
$802$	0.771762	0.0272519
$803$	−4.47066	−0.157766
$804$	−2.17975	−0.0768740
$805$	0.213098	0.00751071
$806$	0	0
$807$	−13.6250	−0.479623
$808$	−41.3725	−1.45548
$809$	−29.6507	−1.04246	−0.521232	−	0.853415i	$-0.674527\pi$
$809$	−29.6507	−1.04246	−0.521232	+	0.853415i	$0.674527\pi$
$810$	−54.9969	−1.93240
$811$	45.3447	1.59227	0.796133	−	0.605121i	$-0.206875\pi$
$811$	45.3447	1.59227	0.796133	+	0.605121i	$0.206875\pi$
$812$	−0.00571846	−0.000200678 0
$813$	−4.49561	−0.157668
$814$	−2.57902	−0.0903947
$815$	−11.5453	−0.404415
$816$	52.9762	1.85454
$817$	0.289690	0.0101350
$818$	29.3425	1.02594
$819$	0	0
$820$	−0.369135	−0.0128908
$821$	−1.53819	−0.0536831	−0.0268415	−	0.999640i	$-0.508545\pi$
$821$	−1.53819	−0.0536831	−0.0268415	+	0.999640i	$0.508545\pi$
$822$	22.3668	0.780131
$823$	−1.67643	−0.0584366	−0.0292183	−	0.999573i	$-0.509302\pi$
$823$	−1.67643	−0.0584366	−0.0292183	+	0.999573i	$0.509302\pi$
$824$	2.72766	0.0950226
$825$	3.39685	0.118263
$826$	−0.0105445	−0.000366889 0
$827$	35.5845	1.23739	0.618697	−	0.785630i	$-0.287661\pi$
$827$	35.5845	1.23739	0.618697	+	0.785630i	$0.287661\pi$
$828$	−3.53323	−0.122788
$829$	34.6678	1.20406	0.602032	−	0.798472i	$-0.294358\pi$
$829$	34.6678	1.20406	0.602032	+	0.798472i	$0.294358\pi$
$830$	12.0634	0.418725
$831$	24.4923	0.849628
$832$	0	0
$833$	−26.4824	−0.917561
$834$	−70.6198	−2.44536
$835$	12.7687	0.441881
$836$	0.429575	0.0148572
$837$	193.263	6.68015
$838$	−12.8779	−0.444861
$839$	−20.2879	−0.700418	−0.350209	−	0.936672i	$-0.613889\pi$
$839$	−20.2879	−0.700418	−0.350209	+	0.936672i	$0.613889\pi$
$840$	0.305859	0.0105531
$841$	−21.0941	−0.727381
$842$	−1.09052	−0.0375819
$843$	60.1153	2.07048
$844$	−0.156134	−0.00537435
$845$	0	0
$846$	−5.82234	−0.200176
$847$	−0.0323629	−0.00111200
$848$	53.9857	1.85388
$849$	−21.3751	−0.733591
$850$	−5.43448	−0.186401
$851$	11.8237	0.405311
$852$	−0.470628	−0.0161234
$853$	46.4858	1.59164	0.795822	−	0.605531i	$-0.207039\pi$
$853$	46.4858	1.59164	0.795822	+	0.605531i	$0.207039\pi$
$854$	−0.203341	−0.00695819
$855$	−58.3674	−1.99612
$856$	−21.6387	−0.739595
$857$	42.5327	1.45289	0.726445	−	0.687224i	$-0.241171\pi$
$857$	42.5327	1.45289	0.726445	+	0.687224i	$0.241171\pi$
$858$	0	0
$859$	−9.29072	−0.316995	−0.158498	−	0.987359i	$-0.550665\pi$
$859$	−9.29072	−0.316995	−0.158498	+	0.987359i	$0.550665\pi$
$860$	−0.00266320	−9.08144e−5 0
$861$	−0.645736	−0.0220066
$862$	−29.6710	−1.01060
$863$	−26.3585	−0.897254	−0.448627	−	0.893719i	$-0.648087\pi$
$863$	−26.3585	−0.897254	−0.448627	+	0.893719i	$0.648087\pi$
$864$	−6.68569	−0.227452
$865$	16.3692	0.556570
$866$	−19.2592	−0.654456
$867$	9.11407	0.309530
$868$	0.0208918	0.000709113 0
$869$	−10.1953	−0.345851
$870$	13.7179	0.465079
$871$	0	0
$872$	−19.2659	−0.652426
$873$	62.9266	2.12974
$874$	−64.6471	−2.18672
$875$	−0.0323629	−0.00109407
$876$	−0.954339	−0.0322441
$877$	−36.4666	−1.23139	−0.615694	−	0.787985i	$-0.711124\pi$
$877$	−36.4666	−1.23139	−0.615694	+	0.787985i	$0.711124\pi$
$878$	1.42456	0.0480765
$879$	46.0481	1.55316
$880$	4.12174	0.138944
$881$	−20.2922	−0.683662	−0.341831	−	0.939761i	$-0.611047\pi$
$881$	−20.2922	−0.683662	−0.341831	+	0.939761i	$0.611047\pi$
$882$	85.8326	2.89013
$883$	−10.8379	−0.364723	−0.182362	−	0.983232i	$-0.558374\pi$
$883$	−10.8379	−0.364723	−0.182362	+	0.983232i	$0.558374\pi$
$884$	0	0
$885$	0.770584	0.0259029
$886$	−21.9601	−0.737763
$887$	−4.75595	−0.159689	−0.0798446	−	0.996807i	$-0.525442\pi$
$887$	−4.75595	−0.159689	−0.0798446	+	0.996807i	$0.525442\pi$
$888$	16.9706	0.569495
$889$	0.268153	0.00899356
$890$	18.8445	0.631670
$891$	−38.2918	−1.28282
$892$	0.234808	0.00786197
$893$	−3.24536	−0.108602
$894$	−27.5481	−0.921345
$895$	8.70330	0.290919
$896$	0.382447	0.0127766
$897$	0	0
$898$	21.0219	0.701509
$899$	−28.8835	−0.963319
$900$	0.536588	0.0178863
$901$	−49.5591	−1.65105
$902$	−8.43653	−0.280906
$903$	−0.00465879	−0.000155035 0
$904$	34.5315	1.14850
$905$	−0.898664	−0.0298726
$906$	67.2394	2.23388
$907$	−54.5647	−1.81179	−0.905896	−	0.423501i	$-0.860801\pi$
$907$	−54.5647	−1.81179	−0.905896	+	0.423501i	$0.860801\pi$
$908$	−1.10784	−0.0367649
$909$	−126.970	−4.21132
$910$	0	0
$911$	−10.2481	−0.339535	−0.169768	−	0.985484i	$-0.554302\pi$
$911$	−10.2481	−0.339535	−0.169768	+	0.985484i	$0.554302\pi$
$912$	−95.7064	−3.16915
$913$	8.39914	0.277971
$914$	33.6623	1.11345
$915$	14.8601	0.491259
$916$	1.00368	0.0331624
$917$	0.294348	0.00972024
$918$	102.243	3.37452
$919$	−8.92111	−0.294280	−0.147140	−	0.989116i	$-0.547007\pi$
$919$	−8.92111	−0.294280	−0.147140	+	0.989116i	$0.547007\pi$
$920$	−18.3202	−0.603998
$921$	−67.7455	−2.23229
$922$	−24.3936	−0.803359
$923$	0	0
$924$	−0.00690841	−0.000227270 0
$925$	−1.79565	−0.0590406
$926$	−39.4340	−1.29588
$927$	8.37103	0.274941
$928$	0.999188	0.0328000
$929$	−0.639983	−0.0209971	−0.0104986	−	0.999945i	$-0.503342\pi$
$929$	−0.639983	−0.0209971	−0.0104986	+	0.999945i	$0.503342\pi$
$930$	−50.1167	−1.64339
$931$	47.8429	1.56799
$932$	1.68306	0.0551304
$933$	26.3928	0.864060
$934$	−45.9220	−1.50261
$935$	−3.78377	−0.123742
$936$	0	0
$937$	6.59986	0.215608	0.107804	−	0.994172i	$-0.465618\pi$
$937$	6.59986	0.215608	0.107804	+	0.994172i	$0.465618\pi$
$938$	0.474632	0.0154973
$939$	46.5984	1.52068
$940$	0.0298354	0.000973125 0
$941$	−12.1757	−0.396917	−0.198459	−	0.980109i	$-0.563594\pi$
$941$	−12.1757	−0.396917	−0.198459	+	0.980109i	$0.563594\pi$
$942$	96.9166	3.15771
$943$	38.6779	1.25952
$944$	0.935027	0.0304325
$945$	0.608868	0.0198065
$946$	−0.0608671	−0.00197896
$947$	−23.1115	−0.751023	−0.375512	−	0.926818i	$-0.622533\pi$
$947$	−23.1115	−0.751023	−0.375512	+	0.926818i	$0.622533\pi$
$948$	−2.17636	−0.0706848
$949$	0	0
$950$	9.81787	0.318534
$951$	−35.7712	−1.15996
$952$	−0.340698	−0.0110421
$953$	34.1508	1.10625	0.553127	−	0.833097i	$-0.313435\pi$
$953$	34.1508	1.10625	0.553127	+	0.833097i	$0.313435\pi$
$954$	160.627	5.20048
$955$	3.27954	0.106123
$956$	−1.07705	−0.0348342
$957$	9.55109	0.308743
$958$	12.7120	0.410705
$959$	−0.148368	−0.00479107
$960$	−26.2681	−0.847800
$961$	74.5228	2.40396
$962$	0	0
$963$	−66.4078	−2.13996
$964$	−0.688162	−0.0221642
$965$	−0.223483	−0.00719418
$966$	1.03965	0.0334503
$967$	−16.9482	−0.545018	−0.272509	−	0.962153i	$-0.587854\pi$
$967$	−16.9482	−0.545018	−0.272509	+	0.962153i	$0.587854\pi$
$968$	2.78226	0.0894253
$969$	87.8588	2.82243
$970$	−10.5848	−0.339856
$971$	−59.5985	−1.91261	−0.956304	−	0.292376i	$-0.905554\pi$
$971$	−59.5985	−1.91261	−0.956304	+	0.292376i	$0.905554\pi$
$972$	−4.62711	−0.148415
$973$	0.468452	0.0150179
$974$	2.82273	0.0904460
$975$	0	0
$976$	18.0312	0.577165
$977$	0.765200	0.0244809	0.0122405	−	0.999925i	$-0.496104\pi$
$977$	0.765200	0.0244809	0.0122405	+	0.999925i	$0.496104\pi$
$978$	−56.3269	−1.80113
$979$	13.1205	0.419335
$980$	−0.439833	−0.0140499
$981$	−59.1259	−1.88774
$982$	−1.64581	−0.0525199
$983$	13.1827	0.420463	0.210232	−	0.977652i	$-0.432578\pi$
$983$	13.1827	0.420463	0.210232	+	0.977652i	$0.432578\pi$
$984$	55.5144	1.76973
$985$	−13.3815	−0.426370
$986$	−15.2804	−0.486627
$987$	0.0521917	0.00166128
$988$	0	0
$989$	0.279049	0.00887325
$990$	12.2636	0.389764
$991$	−14.7525	−0.468629	−0.234315	−	0.972161i	$-0.575285\pi$
$991$	−14.7525	−0.468629	−0.234315	+	0.972161i	$0.575285\pi$
$992$	−3.65043	−0.115901
$993$	79.9472	2.53705
$994$	0.102477	0.00325038
$995$	−15.8343	−0.501980
$996$	1.79294	0.0568115
$997$	−39.0746	−1.23751	−0.618753	−	0.785586i	$-0.712362\pi$
$997$	−39.0746	−1.23751	−0.618753	+	0.785586i	$0.712362\pi$
$998$	−22.4429	−0.710419
$999$	33.7830	1.06885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9295.2.a.bb.1.5		14
13.4	even	6		715.2.i.e.276.5	✓	28
13.10	even	6		715.2.i.e.386.5	yes	28
13.12	even	2		9295.2.a.ba.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
715.2.i.e.276.5	✓	28	13.4	even	6
715.2.i.e.386.5	yes	28	13.10	even	6
9295.2.a.ba.1.10		14	13.12	even	2
9295.2.a.bb.1.5		14	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:	\( N \)	\(=\)	\( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9295.a (trivial)

\(f(q)\)	\(=\)	\(q-1.43626 q^{2} -3.39685 q^{3} +0.0628427 q^{4} +1.00000 q^{5} +4.87876 q^{6} -0.0323629 q^{7} +2.78226 q^{8} +8.53859 q^{9} +O(q^{10})\)	\(q-1.43626 q^{2} -3.39685 q^{3} +0.0628427 q^{4} +1.00000 q^{5} +4.87876 q^{6} -0.0323629 q^{7} +2.78226 q^{8} +8.53859 q^{9} -1.43626 q^{10} -1.00000 q^{11} -0.213467 q^{12} +0.0464815 q^{14} -3.39685 q^{15} -4.12174 q^{16} +3.78377 q^{17} -12.2636 q^{18} -6.83572 q^{19} +0.0628427 q^{20} +0.109932 q^{21} +1.43626 q^{22} -6.58463 q^{23} -9.45093 q^{24} +1.00000 q^{25} -18.8138 q^{27} -0.00203377 q^{28} +2.81175 q^{29} +4.87876 q^{30} -10.2724 q^{31} +0.355362 q^{32} +3.39685 q^{33} -5.43448 q^{34} -0.0323629 q^{35} +0.536588 q^{36} -1.79565 q^{37} +9.81787 q^{38} +2.78226 q^{40} -5.87396 q^{41} -0.157891 q^{42} -0.0423789 q^{43} -0.0628427 q^{44} +8.53859 q^{45} +9.45724 q^{46} +0.474764 q^{47} +14.0009 q^{48} -6.99895 q^{49} -1.43626 q^{50} -12.8529 q^{51} -13.0978 q^{53} +27.0215 q^{54} -1.00000 q^{55} -0.0900420 q^{56} +23.2199 q^{57} -4.03840 q^{58} -0.226853 q^{59} -0.213467 q^{60} -4.37466 q^{61} +14.7539 q^{62} -0.276334 q^{63} +7.73308 q^{64} -4.87876 q^{66} +10.2112 q^{67} +0.237782 q^{68} +22.3670 q^{69} +0.0464815 q^{70} +2.20469 q^{71} +23.7566 q^{72} +4.47066 q^{73} +2.57902 q^{74} -3.39685 q^{75} -0.429575 q^{76} +0.0323629 q^{77} +10.1953 q^{79} -4.12174 q^{80} +38.2918 q^{81} +8.43653 q^{82} -8.39914 q^{83} +0.00690841 q^{84} +3.78377 q^{85} +0.0608671 q^{86} -9.55109 q^{87} -2.78226 q^{88} -13.1205 q^{89} -12.2636 q^{90} -0.413796 q^{92} +34.8939 q^{93} -0.681885 q^{94} -6.83572 q^{95} -1.20711 q^{96} +7.36967 q^{97} +10.0523 q^{98} -8.53859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9}+O(q^{10}) \) 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9	\( 14 q + q^{2} + q^{3} + 17 q^{4} + 14 q^{5} + 2 q^{6} + 5 q^{7} + 27 q^{9} + q^{10} - 14 q^{11} - 9 q^{12} + 12 q^{14} + q^{15} + 15 q^{16} + 17 q^{17} + 23 q^{18} + 3 q^{19} + 17 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} - 13 q^{24} + 14 q^{25} + 10 q^{27} + 27 q^{28} + 21 q^{29} + 2 q^{30} - 9 q^{31} + 26 q^{32} - q^{33} - 56 q^{34} + 5 q^{35} + 51 q^{36} + 8 q^{37} + 5 q^{38} + q^{41} - 42 q^{42} + 23 q^{43} - 17 q^{44} + 27 q^{45} - q^{46} - 18 q^{47} - 14 q^{48} + 41 q^{49} + q^{50} + 18 q^{53} + 8 q^{54} - 14 q^{55} + 80 q^{56} + 44 q^{57} + 22 q^{58} + 8 q^{59} - 9 q^{60} + 16 q^{61} - 5 q^{62} + 50 q^{63} + 10 q^{64} - 2 q^{66} + q^{67} - 8 q^{68} + 34 q^{69} + 12 q^{70} - 20 q^{71} + 117 q^{72} - 15 q^{73} + 49 q^{74} + q^{75} + 10 q^{76} - 5 q^{77} + 5 q^{79} + 15 q^{80} + 82 q^{81} + 32 q^{82} - 18 q^{83} - 50 q^{84} + 17 q^{85} - 74 q^{86} + 2 q^{87} - 16 q^{89} + 23 q^{90} + 7 q^{92} + 33 q^{93} + 34 q^{94} + 3 q^{95} + 56 q^{96} - 5 q^{97} + 34 q^{98} - 27 q^{99}+O(q^{100}) \) 14 * q + q^2 + q^3 + 17 * q^4 + 14 * q^5 + 2 * q^6 + 5 * q^7 + 27 * q^9 + q^10 - 14 * q^11 - 9 * q^12 + 12 * q^14 + q^15 + 15 * q^16 + 17 * q^17 + 23 * q^18 + 3 * q^19 + 17 * q^20 - 16 * q^21 - q^22 + 4 * q^23 - 13 * q^24 + 14 * q^25 + 10 * q^27 + 27 * q^28 + 21 * q^29 + 2 * q^30 - 9 * q^31 + 26 * q^32 - q^33 - 56 * q^34 + 5 * q^35 + 51 * q^36 + 8 * q^37 + 5 * q^38 + q^41 - 42 * q^42 + 23 * q^43 - 17 * q^44 + 27 * q^45 - q^46 - 18 * q^47 - 14 * q^48 + 41 * q^49 + q^50 + 18 * q^53 + 8 * q^54 - 14 * q^55 + 80 * q^56 + 44 * q^57 + 22 * q^58 + 8 * q^59 - 9 * q^60 + 16 * q^61 - 5 * q^62 + 50 * q^63 + 10 * q^64 - 2 * q^66 + q^67 - 8 * q^68 + 34 * q^69 + 12 * q^70 - 20 * q^71 + 117 * q^72 - 15 * q^73 + 49 * q^74 + q^75 + 10 * q^76 - 5 * q^77 + 5 * q^79 + 15 * q^80 + 82 * q^81 + 32 * q^82 - 18 * q^83 - 50 * q^84 + 17 * q^85 - 74 * q^86 + 2 * q^87 - 16 * q^89 + 23 * q^90 + 7 * q^92 + 33 * q^93 + 34 * q^94 + 3 * q^95 + 56 * q^96 - 5 * q^97 + 34 * q^98 - 27 * q^99

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