LMFDB - Embedded newform 605.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.477260$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.477260 q^{2} +0.323071 q^{3} -1.77222 q^{4} -1.00000 q^{5} -0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +O(q^{10})$	\(q-0.477260 q^{2} +0.323071 q^{3} -1.77222 q^{4} -1.00000 q^{5} -0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +0.477260 q^{10} -0.572554 q^{12} +4.66785 q^{13} +1.28155 q^{14} -0.323071 q^{15} +2.68522 q^{16} +4.62632 q^{17} +1.38197 q^{18} +4.34044 q^{19} +1.77222 q^{20} -0.867517 q^{21} +2.77222 q^{23} +0.581635 q^{24} +1.00000 q^{25} -2.22778 q^{26} -1.90471 q^{27} +4.75881 q^{28} +3.01341 q^{29} +0.154189 q^{30} +2.38630 q^{31} -4.88221 q^{32} -2.20796 q^{34} +2.68522 q^{35} +5.13169 q^{36} -10.6429 q^{37} -2.07152 q^{38} +1.50805 q^{39} -1.80033 q^{40} +2.21041 q^{41} +0.414031 q^{42} +7.06719 q^{43} +2.89563 q^{45} -1.32307 q^{46} +4.36215 q^{47} +0.867517 q^{48} +0.210405 q^{49} -0.477260 q^{50} +1.49463 q^{51} -8.27247 q^{52} -6.33404 q^{53} +0.909040 q^{54} -4.83428 q^{56} +1.40227 q^{57} -1.43818 q^{58} +11.7473 q^{59} +0.572554 q^{60} +3.98263 q^{61} -1.13889 q^{62} +7.77539 q^{63} -3.04036 q^{64} -4.66785 q^{65} +7.31984 q^{67} -8.19888 q^{68} +0.895625 q^{69} -1.28155 q^{70} +1.19571 q^{71} -5.21308 q^{72} -1.02171 q^{73} +5.07943 q^{74} +0.323071 q^{75} -7.69223 q^{76} -0.719730 q^{78} -3.50213 q^{79} -2.68522 q^{80} +8.07152 q^{81} -1.05494 q^{82} -11.1158 q^{83} +1.53743 q^{84} -4.62632 q^{85} -3.37289 q^{86} +0.973547 q^{87} +2.76978 q^{89} -1.38197 q^{90} -12.5342 q^{91} -4.91300 q^{92} +0.770945 q^{93} -2.08188 q^{94} -4.34044 q^{95} -1.57730 q^{96} +18.5342 q^{97} -0.100418 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8	$ 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} - q^{10} + 8 q^{12} + q^{13} + 2 q^{14} - 3 q^{16} - q^{17} + 10 q^{18} + 20 q^{19} + q^{20} + 10 q^{21} + 5 q^{23} + 11 q^{24} + 4 q^{25} - 15 q^{26} - 15 q^{27} + 13 q^{28} + 12 q^{29} - q^{30} - 5 q^{31} - 8 q^{32} + 2 q^{34} - 3 q^{35} + 7 q^{37} + 20 q^{38} + 7 q^{39} - 3 q^{40} + 11 q^{41} + 12 q^{42} + 19 q^{43} - 4 q^{46} + 5 q^{47} - 10 q^{48} + 3 q^{49} + q^{50} + 7 q^{51} - 11 q^{52} - 11 q^{53} - 8 q^{54} + 11 q^{56} - 5 q^{57} - 14 q^{58} + 9 q^{59} - 8 q^{60} + 12 q^{61} - 35 q^{62} - 5 q^{63} - 3 q^{64} - q^{65} - 19 q^{67} - 3 q^{68} - 8 q^{69} - 2 q^{70} + 5 q^{71} - 25 q^{72} + 11 q^{73} - 8 q^{78} + 34 q^{79} + 3 q^{80} + 4 q^{81} - 6 q^{82} - 11 q^{83} + 11 q^{84} + q^{85} + q^{86} - 19 q^{87} - 8 q^{89} - 10 q^{90} - 8 q^{91} - 12 q^{92} - 5 q^{93} - q^{94} - 20 q^{95} - 34 q^{96} + 32 q^{97} - 8 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8 - q^10 + 8 * q^12 + q^13 + 2 * q^14 - 3 * q^16 - q^17 + 10 * q^18 + 20 * q^19 + q^20 + 10 * q^21 + 5 * q^23 + 11 * q^24 + 4 * q^25 - 15 * q^26 - 15 * q^27 + 13 * q^28 + 12 * q^29 - q^30 - 5 * q^31 - 8 * q^32 + 2 * q^34 - 3 * q^35 + 7 * q^37 + 20 * q^38 + 7 * q^39 - 3 * q^40 + 11 * q^41 + 12 * q^42 + 19 * q^43 - 4 * q^46 + 5 * q^47 - 10 * q^48 + 3 * q^49 + q^50 + 7 * q^51 - 11 * q^52 - 11 * q^53 - 8 * q^54 + 11 * q^56 - 5 * q^57 - 14 * q^58 + 9 * q^59 - 8 * q^60 + 12 * q^61 - 35 * q^62 - 5 * q^63 - 3 * q^64 - q^65 - 19 * q^67 - 3 * q^68 - 8 * q^69 - 2 * q^70 + 5 * q^71 - 25 * q^72 + 11 * q^73 - 8 * q^78 + 34 * q^79 + 3 * q^80 + 4 * q^81 - 6 * q^82 - 11 * q^83 + 11 * q^84 + q^85 + q^86 - 19 * q^87 - 8 * q^89 - 10 * q^90 - 8 * q^91 - 12 * q^92 - 5 * q^93 - q^94 - 20 * q^95 - 34 * q^96 + 32 * q^97 - 8 * q^98

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 $

$2$	−0.477260	−0.337474	−0.168737	−	0.985661i	$-0.553969\pi$
$2$	−0.477260	−0.337474	−0.168737	+	0.985661i	$0.553969\pi$
$3$	0.323071	0.186525	0.0932626	−	0.995642i	$-0.470270\pi$
$3$	0.323071	0.186525	0.0932626	+	0.995642i	$0.470270\pi$
$4$	−1.77222	−0.886111
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.154189	−0.0629474
$7$	−2.68522	−1.01492	−0.507459	−	0.861676i	$-0.669415\pi$
$7$	−2.68522	−1.01492	−0.507459	+	0.861676i	$0.669415\pi$
$8$	1.80033	0.636513
$9$	−2.89563	−0.965208
$10$	0.477260	0.150923
$11$	0	0
$11$	0	0
$12$	−0.572554	−0.165282
$13$	4.66785	1.29463	0.647314	−	0.762223i	$-0.275892\pi$
$13$	4.66785	1.29463	0.647314	+	0.762223i	$0.275892\pi$
$14$	1.28155	0.342508
$15$	−0.323071	−0.0834166
$16$	2.68522	0.671305
$17$	4.62632	1.12205	0.561024	−	0.827799i	$-0.310407\pi$
$17$	4.62632	1.12205	0.561024	+	0.827799i	$0.310407\pi$
$18$	1.38197	0.325733
$19$	4.34044	0.995766	0.497883	−	0.867244i	$-0.334111\pi$
$19$	4.34044	0.995766	0.497883	+	0.867244i	$0.334111\pi$
$20$	1.77222	0.396281
$21$	−0.867517	−0.189308
$22$	0	0
$23$	2.77222	0.578048	0.289024	−	0.957322i	$-0.406669\pi$
$23$	2.77222	0.578048	0.289024	+	0.957322i	$0.406669\pi$
$24$	0.581635	0.118726
$25$	1.00000	0.200000
$26$	−2.22778	−0.436903
$27$	−1.90471	−0.366561
$28$	4.75881	0.899330
$29$	3.01341	0.559577	0.279789	−	0.960062i	$-0.409736\pi$
$29$	3.01341	0.559577	0.279789	+	0.960062i	$0.409736\pi$
$30$	0.154189	0.0281509
$31$	2.38630	0.428592	0.214296	−	0.976769i	$-0.431254\pi$
$31$	2.38630	0.428592	0.214296	+	0.976769i	$0.431254\pi$
$32$	−4.88221	−0.863061
$33$	0	0
$34$	−2.20796	−0.378662
$35$	2.68522	0.453885
$36$	5.13169	0.855282
$37$	−10.6429	−1.74968	−0.874842	−	0.484409i	$-0.839035\pi$
$37$	−10.6429	−1.74968	−0.874842	+	0.484409i	$0.839035\pi$
$38$	−2.07152	−0.336045
$39$	1.50805	0.241481
$40$	−1.80033	−0.284657
$41$	2.21041	0.345207	0.172604	−	0.984991i	$-0.444782\pi$
$41$	2.21041	0.345207	0.172604	+	0.984991i	$0.444782\pi$
$42$	0.414031	0.0638864
$43$	7.06719	1.07774	0.538868	−	0.842390i	$-0.318852\pi$
$43$	7.06719	1.07774	0.538868	+	0.842390i	$0.318852\pi$
$44$	0	0
$45$	2.89563	0.431654
$46$	−1.32307	−0.195076
$47$	4.36215	0.636285	0.318142	−	0.948043i	$-0.396941\pi$
$47$	4.36215	0.636285	0.318142	+	0.948043i	$0.396941\pi$
$48$	0.867517	0.125215
$49$	0.210405	0.0300579
$50$	−0.477260	−0.0674948
$51$	1.49463	0.209290
$52$	−8.27247	−1.14718
$53$	−6.33404	−0.870047	−0.435024	−	0.900419i	$-0.643260\pi$
$53$	−6.33404	−0.870047	−0.435024	+	0.900419i	$0.643260\pi$
$54$	0.909040	0.123705
$55$	0	0
$56$	−4.83428	−0.646008
$57$	1.40227	0.185735
$58$	−1.43818	−0.188843
$59$	11.7473	1.52937	0.764683	−	0.644407i	$-0.222896\pi$
$59$	11.7473	1.52937	0.764683	+	0.644407i	$0.222896\pi$
$60$	0.572554	0.0739164
$61$	3.98263	0.509923	0.254962	−	0.966951i	$-0.417937\pi$
$61$	3.98263	0.509923	0.254962	+	0.966951i	$0.417937\pi$
$62$	−1.13889	−0.144639
$63$	7.77539	0.979607
$64$	−3.04036	−0.380044
$65$	−4.66785	−0.578975
$66$	0	0
$67$	7.31984	0.894260	0.447130	−	0.894469i	$-0.352446\pi$
$67$	7.31984	0.894260	0.447130	+	0.894469i	$0.352446\pi$
$68$	−8.19888	−0.994260
$69$	0.895625	0.107821
$70$	−1.28155	−0.153174
$71$	1.19571	0.141905	0.0709525	−	0.997480i	$-0.477396\pi$
$71$	1.19571	0.141905	0.0709525	+	0.997480i	$0.477396\pi$
$72$	−5.21308	−0.614368
$73$	−1.02171	−0.119582	−0.0597908	−	0.998211i	$-0.519043\pi$
$73$	−1.02171	−0.119582	−0.0597908	+	0.998211i	$0.519043\pi$
$74$	5.07943	0.590472
$75$	0.323071	0.0373050
$76$	−7.69223	−0.882360
$77$	0	0
$78$	−0.719730	−0.0814934
$79$	−3.50213	−0.394021	−0.197010	−	0.980401i	$-0.563123\pi$
$79$	−3.50213	−0.394021	−0.197010	+	0.980401i	$0.563123\pi$
$80$	−2.68522	−0.300217
$81$	8.07152	0.896836
$82$	−1.05494	−0.116498
$83$	−11.1158	−1.22012	−0.610061	−	0.792355i	$-0.708855\pi$
$83$	−11.1158	−1.22012	−0.610061	+	0.792355i	$0.708855\pi$
$84$	1.53743	0.167748
$85$	−4.62632	−0.501795
$86$	−3.37289	−0.363708
$87$	0.973547	0.104375
$88$	0	0
$89$	2.76978	0.293596	0.146798	−	0.989167i	$-0.453103\pi$
$89$	2.76978	0.293596	0.146798	+	0.989167i	$0.453103\pi$
$90$	−1.38197	−0.145672
$91$	−12.5342	−1.31394
$92$	−4.91300	−0.512215
$93$	0.770945	0.0799432
$94$	−2.08188	−0.214729
$95$	−4.34044	−0.445320
$96$	−1.57730	−0.160983
$97$	18.5342	1.88186	0.940931	−	0.338597i	$-0.109952\pi$
$97$	18.5342	1.88186	0.940931	+	0.338597i	$0.109952\pi$
$98$	−0.100418	−0.0101438
$99$	0	0
$100$	−1.77222	−0.177222
$101$	7.11455	0.707925	0.353962	−	0.935260i	$-0.384834\pi$
$101$	7.11455	0.707925	0.353962	+	0.935260i	$0.384834\pi$
$102$	−0.713328	−0.0706300
$103$	7.52835	0.741791	0.370895	−	0.928675i	$-0.379051\pi$
$103$	7.52835	0.741791	0.370895	+	0.928675i	$0.379051\pi$
$104$	8.40367	0.824048
$105$	0.867517	0.0846610
$106$	3.02298	0.293618
$107$	−18.0292	−1.74295	−0.871475	−	0.490441i	$-0.836836\pi$
$107$	−18.0292	−1.74295	−0.871475	+	0.490441i	$0.836836\pi$
$108$	3.37556	0.324814
$109$	16.3653	1.56751	0.783756	−	0.621068i	$-0.213301\pi$
$109$	16.3653	1.56751	0.783756	+	0.621068i	$0.213301\pi$
$110$	0	0
$111$	−3.43842	−0.326360
$112$	−7.21041	−0.681319
$113$	−2.05377	−0.193203	−0.0966013	−	0.995323i	$-0.530797\pi$
$113$	−2.05377	−0.193203	−0.0966013	+	0.995323i	$0.530797\pi$
$114$	−0.669248	−0.0626808
$115$	−2.77222	−0.258511
$116$	−5.34044	−0.495848
$117$	−13.5163	−1.24959
$118$	−5.60651	−0.516121
$119$	−12.4227	−1.13879
$120$	−0.581635	−0.0530958
$121$	0	0
$122$	−1.90075	−0.172086
$123$	0.714118	0.0643899
$124$	−4.22906	−0.379780
$125$	−1.00000	−0.0894427
$126$	−3.71088	−0.330592
$127$	0.0762667	0.00676758	0.00338379	−	0.999994i	$-0.498923\pi$
$127$	0.0762667	0.00676758	0.00338379	+	0.999994i	$0.498923\pi$
$128$	11.2155	0.991316
$129$	2.28320	0.201025
$130$	2.22778	0.195389
$131$	11.4831	1.00328	0.501642	−	0.865075i	$-0.332730\pi$
$131$	11.4831	1.00328	0.501642	+	0.865075i	$0.332730\pi$
$132$	0	0
$133$	−11.6550	−1.01062
$134$	−3.49346	−0.301789
$135$	1.90471	0.163931
$136$	8.32892	0.714199
$137$	−18.3293	−1.56598	−0.782989	−	0.622036i	$-0.786306\pi$
$137$	−18.3293	−1.56598	−0.782989	+	0.622036i	$0.786306\pi$
$138$	−0.427446	−0.0363866
$139$	23.1874	1.96673	0.983363	−	0.181653i	$-0.0581446\pi$
$139$	23.1874	1.96673	0.983363	+	0.181653i	$0.0581446\pi$
$140$	−4.75881	−0.402193
$141$	1.40928	0.118683
$142$	−0.570666	−0.0478892
$143$	0	0
$144$	−7.77539	−0.647949
$145$	−3.01341	−0.250250
$146$	0.487619	0.0403557
$147$	0.0679759	0.00560655
$148$	18.8616	1.55041
$149$	−14.6646	−1.20137	−0.600686	−	0.799485i	$-0.705106\pi$
$149$	−14.6646	−1.20137	−0.600686	+	0.799485i	$0.705106\pi$
$150$	−0.154189	−0.0125895
$151$	7.51902	0.611889	0.305944	−	0.952049i	$-0.401028\pi$
$151$	7.51902	0.611889	0.305944	+	0.952049i	$0.401028\pi$
$152$	7.81423	0.633818
$153$	−13.3961	−1.08301
$154$	0	0
$155$	−2.38630	−0.191672
$156$	−2.67259	−0.213979
$157$	−13.3819	−1.06799	−0.533996	−	0.845487i	$-0.679310\pi$
$157$	−13.3819	−1.06799	−0.533996	+	0.845487i	$0.679310\pi$
$158$	1.67143	0.132972
$159$	−2.04635	−0.162286
$160$	4.88221	0.385973
$161$	−7.44403	−0.586672
$162$	−3.85221	−0.302658
$163$	−0.771990	−0.0604669	−0.0302335	−	0.999543i	$-0.509625\pi$
$163$	−0.771990	−0.0604669	−0.0302335	+	0.999543i	$0.509625\pi$
$164$	−3.91733	−0.305892
$165$	0	0
$166$	5.30514	0.411759
$167$	8.48232	0.656381	0.328191	−	0.944612i	$-0.393561\pi$
$167$	8.48232	0.656381	0.328191	+	0.944612i	$0.393561\pi$
$168$	−1.56182	−0.120497
$169$	8.78880	0.676062
$170$	2.20796	0.169343
$171$	−12.5683	−0.961122
$172$	−12.5246	−0.954994
$173$	−5.07871	−0.386127	−0.193064	−	0.981186i	$-0.561842\pi$
$173$	−5.07871	−0.386127	−0.193064	+	0.981186i	$0.561842\pi$
$174$	−0.464635	−0.0352239
$175$	−2.68522	−0.202984
$176$	0	0
$177$	3.79521	0.285265
$178$	−1.32190	−0.0990809
$179$	−11.3170	−0.845876	−0.422938	−	0.906159i	$-0.639001\pi$
$179$	−11.3170	−0.845876	−0.422938	+	0.906159i	$0.639001\pi$
$180$	−5.13169	−0.382494
$181$	7.40006	0.550042	0.275021	−	0.961438i	$-0.411315\pi$
$181$	7.40006	0.550042	0.275021	+	0.961438i	$0.411315\pi$
$182$	5.98207	0.443421
$183$	1.28667	0.0951135
$184$	4.99092	0.367935
$185$	10.6429	0.782482
$186$	−0.367941	−0.0269787
$187$	0	0
$188$	−7.73070	−0.563819
$189$	5.11455	0.372029
$190$	2.07152	0.150284
$191$	−5.15608	−0.373081	−0.186540	−	0.982447i	$-0.559728\pi$
$191$	−5.15608	−0.373081	−0.186540	+	0.982447i	$0.559728\pi$
$192$	−0.982251	−0.0708879
$193$	4.03230	0.290251	0.145126	−	0.989413i	$-0.453641\pi$
$193$	4.03230	0.290251	0.145126	+	0.989413i	$0.453641\pi$
$194$	−8.84563	−0.635079
$195$	−1.50805	−0.107993
$196$	−0.372885	−0.0266346
$197$	−11.4176	−0.813469	−0.406734	−	0.913547i	$-0.633333\pi$
$197$	−11.4176	−0.813469	−0.406734	+	0.913547i	$0.633333\pi$
$198$	0	0
$199$	−7.16644	−0.508015	−0.254008	−	0.967202i	$-0.581749\pi$
$199$	−7.16644	−0.508015	−0.254008	+	0.967202i	$0.581749\pi$
$200$	1.80033	0.127303
$201$	2.36483	0.166802
$202$	−3.39549	−0.238906
$203$	−8.09168	−0.567925
$204$	−2.64882	−0.185455
$205$	−2.21041	−0.154381
$206$	−3.59298	−0.250335
$207$	−8.02732	−0.557937
$208$	12.5342	0.869090
$209$	0	0
$210$	−0.414031	−0.0285709
$211$	−3.48359	−0.239820	−0.119910	−	0.992785i	$-0.538261\pi$
$211$	−3.48359	−0.239820	−0.119910	+	0.992785i	$0.538261\pi$
$212$	11.2253	0.770959
$213$	0.386300	0.0264688
$214$	8.60462	0.588200
$215$	−7.06719	−0.481978
$216$	−3.42910	−0.233321
$217$	−6.40774	−0.434986
$218$	−7.81051	−0.528995
$219$	−0.330084	−0.0223050
$220$	0	0
$221$	21.5950	1.45264
$222$	1.64102	0.110138
$223$	10.5449	0.706141	0.353071	−	0.935597i	$-0.385138\pi$
$223$	10.5449	0.706141	0.353071	+	0.935597i	$0.385138\pi$
$224$	13.1098	0.875936
$225$	−2.89563	−0.193042
$226$	0.980183	0.0652008
$227$	−0.216018	−0.0143376	−0.00716880	−	0.999974i	$-0.502282\pi$
$227$	−0.216018	−0.0143376	−0.00716880	+	0.999974i	$0.502282\pi$
$228$	−2.48514	−0.164582
$229$	−0.0757097	−0.00500304	−0.00250152	−	0.999997i	$-0.500796\pi$
$229$	−0.0757097	−0.00500304	−0.00250152	+	0.999997i	$0.500796\pi$
$230$	1.32307	0.0872407
$231$	0	0
$232$	5.42514	0.356178
$233$	−15.1201	−0.990548	−0.495274	−	0.868737i	$-0.664932\pi$
$233$	−15.1201	−0.990548	−0.495274	+	0.868737i	$0.664932\pi$
$234$	6.45081	0.421702
$235$	−4.36215	−0.284555
$236$	−20.8188	−1.35519
$237$	−1.13144	−0.0734948
$238$	5.92886	0.384311
$239$	23.1646	1.49839	0.749197	−	0.662347i	$-0.230439\pi$
$239$	23.1646	1.49839	0.749197	+	0.662347i	$0.230439\pi$
$240$	−0.867517	−0.0559980
$241$	21.3349	1.37430	0.687151	−	0.726515i	$-0.258861\pi$
$241$	21.3349	1.37430	0.687151	+	0.726515i	$0.258861\pi$
$242$	0	0
$243$	8.32179	0.533843
$244$	−7.05810	−0.451849
$245$	−0.210405	−0.0134423
$246$	−0.340820	−0.0217299
$247$	20.2605	1.28915
$248$	4.29613	0.272805
$249$	−3.59120	−0.227583
$250$	0.477260	0.0301846
$251$	−6.22186	−0.392721	−0.196360	−	0.980532i	$-0.562912\pi$
$251$	−6.22186	−0.392721	−0.196360	+	0.980532i	$0.562912\pi$
$252$	−13.7797	−0.868041
$253$	0	0
$254$	−0.0363991	−0.00228388
$255$	−1.49463	−0.0935975
$256$	0.728021	0.0455013
$257$	−14.2903	−0.891406	−0.445703	−	0.895181i	$-0.647046\pi$
$257$	−14.2903	−0.891406	−0.445703	+	0.895181i	$0.647046\pi$
$258$	−1.08968	−0.0678406
$259$	28.5785	1.77578
$260$	8.27247	0.513037
$261$	−8.72572	−0.540108
$262$	−5.48043	−0.338582
$263$	−4.13132	−0.254748	−0.127374	−	0.991855i	$-0.540655\pi$
$263$	−4.13132	−0.254748	−0.127374	+	0.991855i	$0.540655\pi$
$264$	0	0
$265$	6.33404	0.389097
$266$	5.56249	0.341058
$267$	0.894835	0.0547630
$268$	−12.9724	−0.792414
$269$	−1.68394	−0.102672	−0.0513359	−	0.998681i	$-0.516348\pi$
$269$	−1.68394	−0.102672	−0.0513359	+	0.998681i	$0.516348\pi$
$270$	−0.909040	−0.0553224
$271$	18.4310	1.11960	0.559801	−	0.828627i	$-0.310877\pi$
$271$	18.4310	1.11960	0.559801	+	0.828627i	$0.310877\pi$
$272$	12.4227	0.753237
$273$	−4.04944	−0.245083
$274$	8.74784	0.528476
$275$	0	0
$276$	−1.58725	−0.0955411
$277$	3.42745	0.205935	0.102968	−	0.994685i	$-0.467166\pi$
$277$	3.42745	0.205935	0.102968	+	0.994685i	$0.467166\pi$
$278$	−11.0664	−0.663718
$279$	−6.90983	−0.413681
$280$	4.83428	0.288904
$281$	22.8217	1.36143	0.680715	−	0.732548i	$-0.261669\pi$
$281$	22.8217	1.36143	0.680715	+	0.732548i	$0.261669\pi$
$282$	−0.672595	−0.0400524
$283$	29.0991	1.72976	0.864880	−	0.501978i	$-0.167394\pi$
$283$	29.0991	1.72976	0.864880	+	0.501978i	$0.167394\pi$
$284$	−2.11907	−0.125744
$285$	−1.40227	−0.0830634
$286$	0	0
$287$	−5.93542	−0.350357
$288$	14.1371	0.833034
$289$	4.40288	0.258993
$290$	1.43818	0.0844530
$291$	5.98786	0.351015
$292$	1.81069	0.105963
$293$	−21.2136	−1.23931	−0.619655	−	0.784874i	$-0.712727\pi$
$293$	−21.2136	−1.23931	−0.619655	+	0.784874i	$0.712727\pi$
$294$	−0.0324422	−0.00189207
$295$	−11.7473	−0.683953
$296$	−19.1608	−1.11370
$297$	0	0
$298$	6.99883	0.405432
$299$	12.9403	0.748358
$300$	−0.572554	−0.0330564
$301$	−18.9769	−1.09381
$302$	−3.58853	−0.206496
$303$	2.29851	0.132046
$304$	11.6550	0.668463
$305$	−3.98263	−0.228045
$306$	6.39342	0.365488
$307$	6.87520	0.392388	0.196194	−	0.980565i	$-0.437142\pi$
$307$	6.87520	0.392388	0.196194	+	0.980565i	$0.437142\pi$
$308$	0	0
$309$	2.43219	0.138363
$310$	1.13889	0.0646844
$311$	25.1577	1.42656	0.713280	−	0.700879i	$-0.247209\pi$
$311$	25.1577	1.42656	0.713280	+	0.700879i	$0.247209\pi$
$312$	2.71498	0.153706
$313$	−11.5793	−0.654503	−0.327251	−	0.944937i	$-0.606122\pi$
$313$	−11.5793	−0.654503	−0.327251	+	0.944937i	$0.606122\pi$
$314$	6.38664	0.360419
$315$	−7.77539	−0.438094
$316$	6.20656	0.349146
$317$	20.7413	1.16495	0.582473	−	0.812850i	$-0.302085\pi$
$317$	20.7413	1.16495	0.582473	+	0.812850i	$0.302085\pi$
$318$	0.976639	0.0547672
$319$	0	0
$320$	3.04036	0.169961
$321$	−5.82472	−0.325104
$322$	3.55274	0.197986
$323$	20.0803	1.11730
$324$	−14.3045	−0.794696
$325$	4.66785	0.258926
$326$	0.368440	0.0204060
$327$	5.28716	0.292381
$328$	3.97946	0.219729
$329$	−11.7133	−0.645777
$330$	0	0
$331$	−32.1415	−1.76665	−0.883327	−	0.468757i	$-0.844702\pi$
$331$	−32.1415	−1.76665	−0.883327	+	0.468757i	$0.844702\pi$
$332$	19.6997	1.08116
$333$	30.8179	1.68881
$334$	−4.04827	−0.221511
$335$	−7.31984	−0.399925
$336$	−2.32947	−0.127083
$337$	17.9964	0.980326	0.490163	−	0.871631i	$-0.336937\pi$
$337$	17.9964	0.980326	0.490163	+	0.871631i	$0.336937\pi$
$338$	−4.19454	−0.228153
$339$	−0.663514	−0.0360371
$340$	8.19888	0.444647
$341$	0	0
$342$	5.99834	0.324353
$343$	18.2316	0.984411
$344$	12.7233	0.685993
$345$	−0.895625	−0.0482188
$346$	2.42387	0.130308
$347$	8.04981	0.432137	0.216068	−	0.976378i	$-0.430677\pi$
$347$	8.04981	0.432137	0.216068	+	0.976378i	$0.430677\pi$
$348$	−1.72534	−0.0924881
$349$	−19.2294	−1.02932	−0.514662	−	0.857393i	$-0.672083\pi$
$349$	−19.2294	−1.02932	−0.514662	+	0.857393i	$0.672083\pi$
$350$	1.28155	0.0685016
$351$	−8.89088	−0.474560
$352$	0	0
$353$	14.8497	0.790371	0.395186	−	0.918601i	$-0.370680\pi$
$353$	14.8497	0.790371	0.395186	+	0.918601i	$0.370680\pi$
$354$	−1.81130	−0.0962695
$355$	−1.19571	−0.0634618
$356$	−4.90866	−0.260159
$357$	−4.01341	−0.212412
$358$	5.40117	0.285461
$359$	−10.2233	−0.539563	−0.269782	−	0.962922i	$-0.586952\pi$
$359$	−10.2233	−0.539563	−0.269782	+	0.962922i	$0.586952\pi$
$360$	5.21308	0.274754
$361$	−0.160555	−0.00845028
$362$	−3.53175	−0.185625
$363$	0	0
$364$	22.2134	1.16430
$365$	1.02171	0.0534785
$366$	−0.614077	−0.0320983
$367$	14.1434	0.738279	0.369139	−	0.929374i	$-0.379653\pi$
$367$	14.1434	0.738279	0.369139	+	0.929374i	$0.379653\pi$
$368$	7.44403	0.388047
$369$	−6.40050	−0.333197
$370$	−5.07943	−0.264067
$371$	17.0083	0.883026
$372$	−1.36629	−0.0708386
$373$	−12.4600	−0.645154	−0.322577	−	0.946543i	$-0.604549\pi$
$373$	−12.4600	−0.645154	−0.322577	+	0.946543i	$0.604549\pi$
$374$	0	0
$375$	−0.323071	−0.0166833
$376$	7.85331	0.405004
$377$	14.0662	0.724444
$378$	−2.44097	−0.125550
$379$	16.3370	0.839174	0.419587	−	0.907715i	$-0.362175\pi$
$379$	16.3370	0.839174	0.419587	+	0.907715i	$0.362175\pi$
$380$	7.69223	0.394603
$381$	0.0246396	0.00126232
$382$	2.46079	0.125905
$383$	−0.812648	−0.0415244	−0.0207622	−	0.999784i	$-0.506609\pi$
$383$	−0.812648	−0.0415244	−0.0207622	+	0.999784i	$0.506609\pi$
$384$	3.62339	0.184905
$385$	0	0
$386$	−1.92445	−0.0979522
$387$	−20.4639	−1.04024
$388$	−32.8467	−1.66754
$389$	−30.3941	−1.54104	−0.770521	−	0.637414i	$-0.780004\pi$
$389$	−30.3941	−1.54104	−0.770521	+	0.637414i	$0.780004\pi$
$390$	0.719730	0.0364450
$391$	12.8252	0.648598
$392$	0.378799	0.0191322
$393$	3.70986	0.187138
$394$	5.44915	0.274524
$395$	3.50213	0.176211
$396$	0	0
$397$	−14.8996	−0.747789	−0.373894	−	0.927471i	$-0.621978\pi$
$397$	−14.8996	−0.747789	−0.373894	+	0.927471i	$0.621978\pi$
$398$	3.42025	0.171442
$399$	−3.76541	−0.188506
$400$	2.68522	0.134261
$401$	12.1692	0.607700	0.303850	−	0.952720i	$-0.401728\pi$
$401$	12.1692	0.607700	0.303850	+	0.952720i	$0.401728\pi$
$402$	−1.12864	−0.0562913
$403$	11.1389	0.554867
$404$	−12.6086	−0.627300
$405$	−8.07152	−0.401077
$406$	3.86184	0.191660
$407$	0	0
$408$	2.69083	0.133216
$409$	0.262108	0.0129604	0.00648020	−	0.999979i	$-0.497937\pi$
$409$	0.262108	0.0129604	0.00648020	+	0.999979i	$0.497937\pi$
$410$	1.05494	0.0520997
$411$	−5.92166	−0.292094
$412$	−13.3419	−0.657309
$413$	−31.5440	−1.55218
$414$	3.83112	0.188289
$415$	11.1158	0.545655
$416$	−22.7894	−1.11734
$417$	7.49116	0.366844
$418$	0	0
$419$	−1.26916	−0.0620023	−0.0310012	−	0.999519i	$-0.509870\pi$
$419$	−1.26916	−0.0620023	−0.0310012	+	0.999519i	$0.509870\pi$
$420$	−1.53743	−0.0750191
$421$	−29.6655	−1.44581	−0.722903	−	0.690949i	$-0.757193\pi$
$421$	−29.6655	−1.44581	−0.722903	+	0.690949i	$0.757193\pi$
$422$	1.66258	0.0809331
$423$	−12.6311	−0.614147
$424$	−11.4034	−0.553797
$425$	4.62632	0.224410
$426$	−0.184366	−0.00893254
$427$	−10.6942	−0.517530
$428$	31.9518	1.54445
$429$	0	0
$430$	3.37289	0.162655
$431$	−31.3549	−1.51031	−0.755156	−	0.655545i	$-0.772439\pi$
$431$	−31.3549	−1.51031	−0.755156	+	0.655545i	$0.772439\pi$
$432$	−5.11455	−0.246074
$433$	−26.0325	−1.25104	−0.625521	−	0.780207i	$-0.715114\pi$
$433$	−26.0325	−1.25104	−0.625521	+	0.780207i	$0.715114\pi$
$434$	3.05816	0.146796
$435$	−0.973547	−0.0466780
$436$	−29.0030	−1.38899
$437$	12.0327	0.575601
$438$	0.157536	0.00752735
$439$	−14.4191	−0.688185	−0.344093	−	0.938936i	$-0.611813\pi$
$439$	−14.4191	−0.688185	−0.344093	+	0.938936i	$0.611813\pi$
$440$	0	0
$441$	−0.609255	−0.0290121
$442$	−10.3064	−0.490226
$443$	−0.330608	−0.0157077	−0.00785383	−	0.999969i	$-0.502500\pi$
$443$	−0.330608	−0.0157077	−0.00785383	+	0.999969i	$0.502500\pi$
$444$	6.09364	0.289191
$445$	−2.76978	−0.131300
$446$	−5.03268	−0.238304
$447$	−4.73771	−0.224086
$448$	8.16402	0.385714
$449$	8.50828	0.401531	0.200765	−	0.979639i	$-0.435657\pi$
$449$	8.50828	0.401531	0.200765	+	0.979639i	$0.435657\pi$
$450$	1.38197	0.0651465
$451$	0	0
$452$	3.63974	0.171199
$453$	2.42918	0.114133
$454$	0.103097	0.00483856
$455$	12.5342	0.587612
$456$	2.52455	0.118223
$457$	−1.13847	−0.0532555	−0.0266277	−	0.999645i	$-0.508477\pi$
$457$	−1.13847	−0.0532555	−0.0266277	+	0.999645i	$0.508477\pi$
$458$	0.0361332	0.00168839
$459$	−8.81179	−0.411299
$460$	4.91300	0.229070
$461$	−14.5073	−0.675670	−0.337835	−	0.941205i	$-0.609695\pi$
$461$	−14.5073	−0.675670	−0.337835	+	0.941205i	$0.609695\pi$
$462$	0	0
$463$	−4.89739	−0.227601	−0.113801	−	0.993504i	$-0.536302\pi$
$463$	−4.89739	−0.227601	−0.113801	+	0.993504i	$0.536302\pi$
$464$	8.09168	0.375647
$465$	−0.770945	−0.0357517
$466$	7.21620	0.334284
$467$	32.4230	1.50036	0.750180	−	0.661234i	$-0.229967\pi$
$467$	32.4230	1.50036	0.750180	+	0.661234i	$0.229967\pi$
$468$	23.9540	1.10727
$469$	−19.6554	−0.907601
$470$	2.08188	0.0960299
$471$	−4.32330	−0.199207
$472$	21.1490	0.973461
$473$	0	0
$474$	0.539990	0.0248026
$475$	4.34044	0.199153
$476$	22.0158	1.00909
$477$	18.3410	0.839777
$478$	−11.0555	−0.505669
$479$	−17.7354	−0.810352	−0.405176	−	0.914239i	$-0.632790\pi$
$479$	−17.7354	−0.810352	−0.405176	+	0.914239i	$0.632790\pi$
$480$	1.57730	0.0719936
$481$	−49.6795	−2.26519
$482$	−10.1823	−0.463791
$483$	−2.40495	−0.109429
$484$	0	0
$485$	−18.5342	−0.841595
$486$	−3.97166	−0.180158
$487$	−18.4603	−0.836514	−0.418257	−	0.908329i	$-0.637359\pi$
$487$	−18.4603	−0.836514	−0.418257	+	0.908329i	$0.637359\pi$
$488$	7.17005	0.324573
$489$	−0.249408	−0.0112786
$490$	0.100418	0.00453642
$491$	11.4338	0.516002	0.258001	−	0.966145i	$-0.416936\pi$
$491$	11.4338	0.516002	0.258001	+	0.966145i	$0.416936\pi$
$492$	−1.26558	−0.0570566
$493$	13.9410	0.627873
$494$	−9.66954	−0.435053
$495$	0	0
$496$	6.40774	0.287716
$497$	−3.21075	−0.144022
$498$	1.71394	0.0768034
$499$	10.8815	0.487125	0.243562	−	0.969885i	$-0.421684\pi$
$499$	10.8815	0.487125	0.243562	+	0.969885i	$0.421684\pi$
$500$	1.77222	0.0792562
$501$	2.74039	0.122432
$502$	2.96945	0.132533
$503$	−44.7247	−1.99417	−0.997087	−	0.0762683i	$-0.975699\pi$
$503$	−44.7247	−1.99417	−0.997087	+	0.0762683i	$0.975699\pi$
$504$	13.9983	0.623533
$505$	−7.11455	−0.316594
$506$	0	0
$507$	2.83941	0.126103
$508$	−0.135162	−0.00599683
$509$	−13.8093	−0.612088	−0.306044	−	0.952017i	$-0.599006\pi$
$509$	−13.8093	−0.612088	−0.306044	+	0.952017i	$0.599006\pi$
$510$	0.713328	0.0315867
$511$	2.74350	0.121365
$512$	−22.7784	−1.00667
$513$	−8.26727	−0.365009
$514$	6.82020	0.300826
$515$	−7.52835	−0.331739
$516$	−4.04635	−0.178130
$517$	0	0
$518$	−13.6394	−0.599281
$519$	−1.64079	−0.0720225
$520$	−8.40367	−0.368525
$521$	−3.64972	−0.159897	−0.0799486	−	0.996799i	$-0.525476\pi$
$521$	−3.64972	−0.159897	−0.0799486	+	0.996799i	$0.525476\pi$
$522$	4.16444	0.182272
$523$	4.98707	0.218069	0.109035	−	0.994038i	$-0.465224\pi$
$523$	4.98707	0.218069	0.109035	+	0.994038i	$0.465224\pi$
$524$	−20.3506	−0.889021
$525$	−0.867517	−0.0378615
$526$	1.97171	0.0859707
$527$	11.0398	0.480901
$528$	0	0
$529$	−15.3148	−0.665860
$530$	−3.02298	−0.131310
$531$	−34.0157	−1.47616
$532$	20.6553	0.895522
$533$	10.3178	0.446915
$534$	−0.427069	−0.0184811
$535$	18.0292	0.779471
$536$	13.1781	0.569208
$537$	−3.65621	−0.157777
$538$	0.803678	0.0346490
$539$	0	0
$540$	−3.37556	−0.145261
$541$	−0.247594	−0.0106449	−0.00532246	−	0.999986i	$-0.501694\pi$
$541$	−0.247594	−0.0106449	−0.00532246	+	0.999986i	$0.501694\pi$
$542$	−8.79637	−0.377837
$543$	2.39075	0.102597
$544$	−22.5867	−0.968396
$545$	−16.3653	−0.701013
$546$	1.93263	0.0827091
$547$	25.3120	1.08226	0.541132	−	0.840938i	$-0.317996\pi$
$547$	25.3120	1.08226	0.541132	+	0.840938i	$0.317996\pi$
$548$	32.4836	1.38763
$549$	−11.5322	−0.492182
$550$	0	0
$551$	13.0796	0.557208
$552$	1.61242	0.0686292
$553$	9.40400	0.399899
$554$	−1.63578	−0.0694978
$555$	3.43842	0.145953
$556$	−41.0932	−1.74274
$557$	38.6671	1.63838	0.819190	−	0.573523i	$-0.194424\pi$
$557$	38.6671	1.63838	0.819190	+	0.573523i	$0.194424\pi$
$558$	3.29779	0.139606
$559$	32.9885	1.39527
$560$	7.21041	0.304695
$561$	0	0
$562$	−10.8919	−0.459447
$563$	−13.9362	−0.587341	−0.293671	−	0.955907i	$-0.594877\pi$
$563$	−13.9362	−0.587341	−0.293671	+	0.955907i	$0.594877\pi$
$564$	−2.49757	−0.105166
$565$	2.05377	0.0864028
$566$	−13.8878	−0.583749
$567$	−21.6738	−0.910214
$568$	2.15268	0.0903243
$569$	−27.9125	−1.17015	−0.585076	−	0.810979i	$-0.698935\pi$
$569$	−27.9125	−1.17015	−0.585076	+	0.810979i	$0.698935\pi$
$570$	0.669248	0.0280317
$571$	31.4113	1.31452	0.657261	−	0.753663i	$-0.271715\pi$
$571$	31.4113	1.31452	0.657261	+	0.753663i	$0.271715\pi$
$572$	0	0
$573$	−1.66578	−0.0695889
$574$	2.83274	0.118236
$575$	2.77222	0.115610
$576$	8.80373	0.366822
$577$	20.7349	0.863206	0.431603	−	0.902064i	$-0.357948\pi$
$577$	20.7349	0.863206	0.431603	+	0.902064i	$0.357948\pi$
$578$	−2.10132	−0.0874034
$579$	1.30272	0.0541392
$580$	5.34044	0.221750
$581$	29.8485	1.23832
$582$	−2.85777	−0.118458
$583$	0	0
$584$	−1.83941	−0.0761153
$585$	13.5163	0.558832
$586$	10.1244	0.418235
$587$	15.2367	0.628886	0.314443	−	0.949276i	$-0.398182\pi$
$587$	15.2367	0.628886	0.314443	+	0.949276i	$0.398182\pi$
$588$	−0.120468	−0.00496803
$589$	10.3576	0.426777
$590$	5.60651	0.230816
$591$	−3.68869	−0.151732
$592$	−28.5785	−1.17457
$593$	−27.5413	−1.13098	−0.565492	−	0.824754i	$-0.691314\pi$
$593$	−27.5413	−1.13098	−0.565492	+	0.824754i	$0.691314\pi$
$594$	0	0
$595$	12.4227	0.509281
$596$	25.9890	1.06455
$597$	−2.31527	−0.0947576
$598$	−6.17589	−0.252551
$599$	−26.7331	−1.09228	−0.546142	−	0.837693i	$-0.683904\pi$
$599$	−26.7331	−1.09228	−0.546142	+	0.837693i	$0.683904\pi$
$600$	0.581635	0.0237451
$601$	−2.40680	−0.0981753	−0.0490876	−	0.998794i	$-0.515631\pi$
$601$	−2.40680	−0.0981753	−0.0490876	+	0.998794i	$0.515631\pi$
$602$	9.05694	0.369133
$603$	−21.1955	−0.863147
$604$	−13.3254	−0.542202
$605$	0	0
$606$	−1.09699	−0.0445620
$607$	−10.2929	−0.417774	−0.208887	−	0.977940i	$-0.566984\pi$
$607$	−10.2929	−0.417774	−0.208887	+	0.977940i	$0.566984\pi$
$608$	−21.1910	−0.859407
$609$	−2.61419	−0.105932
$610$	1.90075	0.0769591
$611$	20.3618	0.823752
$612$	23.7409	0.959668
$613$	−27.8756	−1.12589	−0.562943	−	0.826496i	$-0.690331\pi$
$613$	−27.8756	−1.12589	−0.562943	+	0.826496i	$0.690331\pi$
$614$	−3.28126	−0.132421
$615$	−0.714118	−0.0287960
$616$	0	0
$617$	−28.7216	−1.15629	−0.578143	−	0.815935i	$-0.696222\pi$
$617$	−28.7216	−1.15629	−0.578143	+	0.815935i	$0.696222\pi$
$618$	−1.16079	−0.0466938
$619$	22.6968	0.912261	0.456131	−	0.889913i	$-0.349235\pi$
$619$	22.6968	0.912261	0.456131	+	0.889913i	$0.349235\pi$
$620$	4.22906	0.169843
$621$	−5.28027	−0.211890
$622$	−12.0067	−0.481427
$623$	−7.43746	−0.297976
$624$	4.04944	0.162107
$625$	1.00000	0.0400000
$626$	5.52635	0.220877
$627$	0	0
$628$	23.7157	0.946360
$629$	−49.2375	−1.96323
$630$	3.71088	0.147845
$631$	28.5364	1.13602	0.568008	−	0.823023i	$-0.307714\pi$
$631$	28.5364	1.13602	0.568008	+	0.823023i	$0.307714\pi$
$632$	−6.30500	−0.250799
$633$	−1.12545	−0.0447326
$634$	−9.89897	−0.393138
$635$	−0.0762667	−0.00302655
$636$	3.62658	0.143803
$637$	0.982140	0.0389138
$638$	0	0
$639$	−3.46233	−0.136968
$640$	−11.2155	−0.443330
$641$	2.37375	0.0937575	0.0468788	−	0.998901i	$-0.485073\pi$
$641$	2.37375	0.0937575	0.0468788	+	0.998901i	$0.485073\pi$
$642$	2.77990	0.109714
$643$	11.3603	0.448007	0.224004	−	0.974588i	$-0.428087\pi$
$643$	11.3603	0.448007	0.224004	+	0.974588i	$0.428087\pi$
$644$	13.1925	0.519856
$645$	−2.28320	−0.0899010
$646$	−9.58352	−0.377059
$647$	−48.4220	−1.90366	−0.951832	−	0.306621i	$-0.900802\pi$
$647$	−48.4220	−1.90366	−0.951832	+	0.306621i	$0.900802\pi$
$648$	14.5314	0.570848
$649$	0	0
$650$	−2.22778	−0.0873806
$651$	−2.07016	−0.0811358
$652$	1.36814	0.0535804
$653$	29.7548	1.16440	0.582198	−	0.813047i	$-0.302193\pi$
$653$	29.7548	1.16440	0.582198	+	0.813047i	$0.302193\pi$
$654$	−2.52335	−0.0986708
$655$	−11.4831	−0.448682
$656$	5.93542	0.231739
$657$	2.95848	0.115421
$658$	5.59030	0.217933
$659$	28.4931	1.10993	0.554966	−	0.831873i	$-0.312731\pi$
$659$	28.4931	1.10993	0.554966	+	0.831873i	$0.312731\pi$
$660$	0	0
$661$	−1.02875	−0.0400139	−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875	−0.0400139	−0.0200070	+	0.999800i	$0.506369\pi$
$662$	15.3398	0.596200
$663$	6.97671	0.270953
$664$	−20.0122	−0.776623
$665$	11.6550	0.451963
$666$	−14.7081	−0.569929
$667$	8.35386	0.323463
$668$	−15.0326	−0.581627
$669$	3.40676	0.131713
$670$	3.49346	0.134964
$671$	0	0
$672$	4.23540	0.163384
$673$	−13.0369	−0.502536	−0.251268	−	0.967918i	$-0.580848\pi$
$673$	−13.0369	−0.502536	−0.251268	+	0.967918i	$0.580848\pi$
$674$	−8.58896	−0.330834
$675$	−1.90471	−0.0733122
$676$	−15.5757	−0.599066
$677$	37.1064	1.42612	0.713058	−	0.701105i	$-0.247310\pi$
$677$	37.1064	1.42612	0.713058	+	0.701105i	$0.247310\pi$
$678$	0.316669	0.0121616
$679$	−49.7684	−1.90994
$680$	−8.32892	−0.319399
$681$	−0.0697890	−0.00267432
$682$	0	0
$683$	−32.8992	−1.25885	−0.629426	−	0.777061i	$-0.716710\pi$
$683$	−32.8992	−1.25885	−0.629426	+	0.777061i	$0.716710\pi$
$684$	22.2738	0.851661
$685$	18.3293	0.700326
$686$	−8.70119	−0.332213
$687$	−0.0244596	−0.000933193 0
$688$	18.9769	0.723489
$689$	−29.5663	−1.12639
$690$	0.427446	0.0162726
$691$	36.6998	1.39613	0.698064	−	0.716035i	$-0.254045\pi$
$691$	36.6998	1.39613	0.698064	+	0.716035i	$0.254045\pi$
$692$	9.00061	0.342152
$693$	0	0
$694$	−3.84185	−0.145835
$695$	−23.1874	−0.879546
$696$	1.75271	0.0664362
$697$	10.2261	0.387339
$698$	9.17741	0.347370
$699$	−4.88485	−0.184762
$700$	4.75881	0.179866
$701$	36.2497	1.36913	0.684566	−	0.728951i	$-0.259992\pi$
$701$	36.2497	1.36913	0.684566	+	0.728951i	$0.259992\pi$
$702$	4.24326	0.160152
$703$	−46.1949	−1.74227
$704$	0	0
$705$	−1.40928	−0.0530767
$706$	−7.08718	−0.266730
$707$	−19.1041	−0.718485
$708$	−6.72595	−0.252777
$709$	−18.6013	−0.698585	−0.349293	−	0.937014i	$-0.613578\pi$
$709$	−18.6013	−0.698585	−0.349293	+	0.937014i	$0.613578\pi$
$710$	0.570666	0.0214167
$711$	10.1409	0.380312
$712$	4.98652	0.186878
$713$	6.61536	0.247747
$714$	1.91544	0.0716836
$715$	0	0
$716$	20.0563	0.749540
$717$	7.48382	0.279488
$718$	4.87915	0.182088
$719$	−37.4280	−1.39583	−0.697914	−	0.716181i	$-0.745888\pi$
$719$	−37.4280	−1.39583	−0.697914	+	0.716181i	$0.745888\pi$
$720$	7.77539	0.289772
$721$	−20.2153	−0.752856
$722$	0.0766267	0.00285175
$723$	6.89269	0.256342
$724$	−13.1146	−0.487399
$725$	3.01341	0.111915
$726$	0	0
$727$	14.6011	0.541526	0.270763	−	0.962646i	$-0.412724\pi$
$727$	14.6011	0.541526	0.270763	+	0.962646i	$0.412724\pi$
$728$	−22.5657	−0.836341
$729$	−21.5260	−0.797260
$730$	−0.487619	−0.0180476
$731$	32.6951	1.20927
$732$	−2.28027	−0.0842812
$733$	−41.8369	−1.54528	−0.772640	−	0.634844i	$-0.781064\pi$
$733$	−41.8369	−1.54528	−0.772640	+	0.634844i	$0.781064\pi$
$734$	−6.75007	−0.249150
$735$	−0.0679759	−0.00250733
$736$	−13.5346	−0.498891
$737$	0	0
$738$	3.05470	0.112445
$739$	11.9299	0.438849	0.219424	−	0.975630i	$-0.429582\pi$
$739$	11.9299	0.438849	0.219424	+	0.975630i	$0.429582\pi$
$740$	−18.8616	−0.693366
$741$	6.54559	0.240458
$742$	−8.11738	−0.297998
$743$	−46.6803	−1.71253	−0.856267	−	0.516534i	$-0.827222\pi$
$743$	−46.6803	−1.71253	−0.856267	+	0.516534i	$0.827222\pi$
$744$	1.38796	0.0508849
$745$	14.6646	0.537270
$746$	5.94666	0.217723
$747$	32.1873	1.17767
$748$	0	0
$749$	48.4124	1.76895
$750$	0.154189	0.00563018
$751$	14.4039	0.525607	0.262803	−	0.964849i	$-0.415353\pi$
$751$	14.4039	0.525607	0.262803	+	0.964849i	$0.415353\pi$
$752$	11.7133	0.427141
$753$	−2.01010	−0.0732523
$754$	−6.71322	−0.244481
$755$	−7.51902	−0.273645
$756$	−9.06413	−0.329659
$757$	−16.0616	−0.583768	−0.291884	−	0.956454i	$-0.594282\pi$
$757$	−16.0616	−0.583768	−0.291884	+	0.956454i	$0.594282\pi$
$758$	−7.79698	−0.283199
$759$	0	0
$760$	−7.81423	−0.283452
$761$	38.8840	1.40954	0.704772	−	0.709433i	$-0.251049\pi$
$761$	38.8840	1.40954	0.704772	+	0.709433i	$0.251049\pi$
$762$	−0.0117595	−0.000426001 0
$763$	−43.9445	−1.59090
$764$	9.13772	0.330591
$765$	13.3961	0.484337
$766$	0.387844	0.0140134
$767$	54.8345	1.97996
$768$	0.235203	0.00848714
$769$	−43.0017	−1.55068	−0.775341	−	0.631543i	$-0.782422\pi$
$769$	−43.0017	−1.55068	−0.775341	+	0.631543i	$0.782422\pi$
$770$	0	0
$771$	−4.61679	−0.166270
$772$	−7.14613	−0.257195
$773$	−7.85462	−0.282511	−0.141256	−	0.989973i	$-0.545114\pi$
$773$	−7.85462	−0.282511	−0.141256	+	0.989973i	$0.545114\pi$
$774$	9.76661	0.351054
$775$	2.38630	0.0857184
$776$	33.3677	1.19783
$777$	9.23290	0.331228
$778$	14.5059	0.520061
$779$	9.59414	0.343746
$780$	2.67259	0.0956942
$781$	0	0
$782$	−6.12096	−0.218885
$783$	−5.73967	−0.205119
$784$	0.564984	0.0201780
$785$	13.3819	0.477620
$786$	−1.77057	−0.0631541
$787$	11.4249	0.407253	0.203627	−	0.979049i	$-0.434727\pi$
$787$	11.4249	0.407253	0.203627	+	0.979049i	$0.434727\pi$
$788$	20.2345	0.720824
$789$	−1.33471	−0.0475169
$790$	−1.67143	−0.0594667
$791$	5.51483	0.196085
$792$	0	0
$793$	18.5903	0.660161
$794$	7.11097	0.252359
$795$	2.04635	0.0725764
$796$	12.7005	0.450158
$797$	−4.28502	−0.151783	−0.0758915	−	0.997116i	$-0.524180\pi$
$797$	−4.28502	−0.151783	−0.0758915	+	0.997116i	$0.524180\pi$
$798$	1.79708	0.0636159
$799$	20.1807	0.713942
$800$	−4.88221	−0.172612
$801$	−8.02024	−0.283381
$802$	−5.80787	−0.205083
$803$	0	0
$804$	−4.19100	−0.147805
$805$	7.44403	0.262368
$806$	−5.31614	−0.187253
$807$	−0.544033	−0.0191509
$808$	12.8086	0.450603
$809$	19.8484	0.697833	0.348917	−	0.937154i	$-0.386550\pi$
$809$	19.8484	0.697833	0.348917	+	0.937154i	$0.386550\pi$
$810$	3.85221	0.135353
$811$	3.13836	0.110203	0.0551014	−	0.998481i	$-0.482452\pi$
$811$	3.13836	0.110203	0.0551014	+	0.998481i	$0.482452\pi$
$812$	14.3403	0.503245
$813$	5.95452	0.208834
$814$	0	0
$815$	0.771990	0.0270416
$816$	4.01341	0.140498
$817$	30.6747	1.07317
$818$	−0.125094	−0.00437379
$819$	36.2943	1.26823
$820$	3.91733	0.136799
$821$	−23.4999	−0.820151	−0.410076	−	0.912052i	$-0.634498\pi$
$821$	−23.4999	−0.820151	−0.410076	+	0.912052i	$0.634498\pi$
$822$	2.82617	0.0985741
$823$	−12.6564	−0.441173	−0.220586	−	0.975367i	$-0.570797\pi$
$823$	−12.6564	−0.441173	−0.220586	+	0.975367i	$0.570797\pi$
$824$	13.5535	0.472159
$825$	0	0
$826$	15.0547	0.523820
$827$	−30.2236	−1.05098	−0.525488	−	0.850801i	$-0.676117\pi$
$827$	−30.2236	−1.05098	−0.525488	+	0.850801i	$0.676117\pi$
$828$	14.2262	0.494395
$829$	2.00166	0.0695204	0.0347602	−	0.999396i	$-0.488933\pi$
$829$	2.00166	0.0695204	0.0347602	+	0.999396i	$0.488933\pi$
$830$	−5.30514	−0.184144
$831$	1.10731	0.0384121
$832$	−14.1919	−0.492016
$833$	0.973403	0.0337264
$834$	−3.57523	−0.123800
$835$	−8.48232	−0.293543
$836$	0	0
$837$	−4.54520	−0.157105
$838$	0.605717	0.0209242
$839$	35.3744	1.22126	0.610629	−	0.791917i	$-0.290917\pi$
$839$	35.3744	1.22126	0.610629	+	0.791917i	$0.290917\pi$
$840$	1.56182	0.0538878
$841$	−19.9193	−0.686873
$842$	14.1581	0.487922
$843$	7.37304	0.253941
$844$	6.17370	0.212508
$845$	−8.78880	−0.302344
$846$	6.02834	0.207259
$847$	0	0
$848$	−17.0083	−0.584067
$849$	9.40107	0.322644
$850$	−2.20796	−0.0757324
$851$	−29.5045	−1.01140
$852$	−0.684610	−0.0234543
$853$	18.2034	0.623272	0.311636	−	0.950202i	$-0.399123\pi$
$853$	18.2034	0.623272	0.311636	+	0.950202i	$0.399123\pi$
$854$	5.10393	0.174653
$855$	12.5683	0.429827
$856$	−32.4585	−1.10941
$857$	29.2837	1.00031	0.500156	−	0.865935i	$-0.333276\pi$
$857$	29.2837	1.00031	0.500156	+	0.865935i	$0.333276\pi$
$858$	0	0
$859$	8.44030	0.287979	0.143990	−	0.989579i	$-0.454007\pi$
$859$	8.44030	0.287979	0.143990	+	0.989579i	$0.454007\pi$
$860$	12.5246	0.427086
$861$	−1.91756	−0.0653504
$862$	14.9644	0.509691
$863$	−19.3487	−0.658636	−0.329318	−	0.944219i	$-0.606819\pi$
$863$	−19.3487	−0.658636	−0.329318	+	0.944219i	$0.606819\pi$
$864$	9.29918	0.316364
$865$	5.07871	0.172681
$866$	12.4243	0.422194
$867$	1.42244	0.0483087
$868$	11.3559	0.385446
$869$	0	0
$870$	0.464635	0.0157526
$871$	34.1679	1.15773
$872$	29.4630	0.997743
$873$	−53.6681	−1.81639
$874$	−5.74271	−0.194250
$875$	2.68522	0.0907770
$876$	0.584982	0.0197647
$877$	−17.5140	−0.591405	−0.295702	−	0.955280i	$-0.595554\pi$
$877$	−17.5140	−0.591405	−0.295702	+	0.955280i	$0.595554\pi$
$878$	6.88165	0.232245
$879$	−6.85349	−0.231163
$880$	0	0
$881$	−20.0575	−0.675754	−0.337877	−	0.941190i	$-0.609709\pi$
$881$	−20.0575	−0.675754	−0.337877	+	0.941190i	$0.609709\pi$
$882$	0.290773	0.00979083
$883$	26.8980	0.905189	0.452594	−	0.891717i	$-0.350499\pi$
$883$	26.8980	0.905189	0.452594	+	0.891717i	$0.350499\pi$
$884$	−38.2711	−1.28720
$885$	−3.79521	−0.127574
$886$	0.157786	0.00530092
$887$	−6.80568	−0.228512	−0.114256	−	0.993451i	$-0.536448\pi$
$887$	−6.80568	−0.228512	−0.114256	+	0.993451i	$0.536448\pi$
$888$	−6.19029	−0.207732
$889$	−0.204793	−0.00686854
$890$	1.32190	0.0443103
$891$	0	0
$892$	−18.6880	−0.625720
$893$	18.9337	0.633591
$894$	2.26112	0.0756232
$895$	11.3170	0.378287
$896$	−30.1160	−1.00610
$897$	4.18064	0.139588
$898$	−4.06066	−0.135506
$899$	7.19091	0.239830
$900$	5.13169	0.171056
$901$	−29.3033	−0.976235
$902$	0	0
$903$	−6.13090	−0.204024
$904$	−3.69747	−0.122976
$905$	−7.40006	−0.245986
$906$	−1.15935	−0.0385168
$907$	−21.3313	−0.708295	−0.354148	−	0.935190i	$-0.615229\pi$
$907$	−21.3313	−0.708295	−0.354148	+	0.935190i	$0.615229\pi$
$908$	0.382831	0.0127047
$909$	−20.6011	−0.683295
$910$	−5.98207	−0.198304
$911$	−27.5888	−0.914059	−0.457029	−	0.889452i	$-0.651087\pi$
$911$	−27.5888	−0.914059	−0.457029	+	0.889452i	$0.651087\pi$
$912$	3.76541	0.124685
$913$	0	0
$914$	0.543347	0.0179723
$915$	−1.28667	−0.0425361
$916$	0.134174	0.00443325
$917$	−30.8347	−1.01825
$918$	4.20551	0.138803
$919$	6.00889	0.198215	0.0991075	−	0.995077i	$-0.468401\pi$
$919$	6.00889	0.198215	0.0991075	+	0.995077i	$0.468401\pi$
$920$	−4.99092	−0.164546
$921$	2.22118	0.0731903
$922$	6.92373	0.228021
$923$	5.58140	0.183714
$924$	0	0
$925$	−10.6429	−0.349937
$926$	2.33733	0.0768094
$927$	−21.7993	−0.715982
$928$	−14.7121	−0.482949
$929$	9.59739	0.314880	0.157440	−	0.987529i	$-0.449676\pi$
$929$	9.59739	0.314880	0.157440	+	0.987529i	$0.449676\pi$
$930$	0.367941	0.0120653
$931$	0.913252	0.0299306
$932$	26.7961	0.877736
$933$	8.12771	0.266089
$934$	−15.4742	−0.506332
$935$	0	0
$936$	−24.3339	−0.795378
$937$	38.5917	1.26074	0.630369	−	0.776296i	$-0.282904\pi$
$937$	38.5917	1.26074	0.630369	+	0.776296i	$0.282904\pi$
$938$	9.38072	0.306291
$939$	−3.74095	−0.122081
$940$	7.73070	0.252148
$941$	29.1846	0.951391	0.475695	−	0.879610i	$-0.342196\pi$
$941$	29.1846	0.951391	0.475695	+	0.879610i	$0.342196\pi$
$942$	2.06334	0.0672273
$943$	6.12774	0.199547
$944$	31.5440	1.02667
$945$	−5.11455	−0.166376
$946$	0	0
$947$	46.7623	1.51957	0.759785	−	0.650174i	$-0.225304\pi$
$947$	46.7623	1.51957	0.759785	+	0.650174i	$0.225304\pi$
$948$	2.00516	0.0651246
$949$	−4.76917	−0.154814
$950$	−2.07152	−0.0672090
$951$	6.70090	0.217292
$952$	−22.3650	−0.724853
$953$	6.15238	0.199295	0.0996475	−	0.995023i	$-0.468228\pi$
$953$	6.15238	0.199295	0.0996475	+	0.995023i	$0.468228\pi$
$954$	−8.75343	−0.283403
$955$	5.15608	0.166847
$956$	−41.0529	−1.32774
$957$	0	0
$958$	8.46440	0.273472
$959$	49.2182	1.58934
$960$	0.982251	0.0317020
$961$	−25.3056	−0.816309
$962$	23.7100	0.764442
$963$	52.2058	1.68231
$964$	−37.8102	−1.21778
$965$	−4.03230	−0.129804
$966$	1.14779	0.0369294
$967$	−3.39625	−0.109216	−0.0546080	−	0.998508i	$-0.517391\pi$
$967$	−3.39625	−0.109216	−0.0546080	+	0.998508i	$0.517391\pi$
$968$	0	0
$969$	6.48736	0.208404
$970$	8.84563	0.284016
$971$	−9.39500	−0.301500	−0.150750	−	0.988572i	$-0.548169\pi$
$971$	−9.39500	−0.301500	−0.150750	+	0.988572i	$0.548169\pi$
$972$	−14.7481	−0.473045
$973$	−62.2631	−1.99606
$974$	8.81035	0.282302
$975$	1.50805	0.0482961
$976$	10.6942	0.342314
$977$	−16.5552	−0.529649	−0.264824	−	0.964297i	$-0.585314\pi$
$977$	−16.5552	−0.529649	−0.264824	+	0.964297i	$0.585314\pi$
$978$	0.119032	0.00380623
$979$	0	0
$980$	0.372885	0.0119114
$981$	−47.3878	−1.51298
$982$	−5.45692	−0.174137
$983$	50.8180	1.62084	0.810421	−	0.585848i	$-0.199238\pi$
$983$	50.8180	1.62084	0.810421	+	0.585848i	$0.199238\pi$
$984$	1.28565	0.0409850
$985$	11.4176	0.363794
$986$	−6.65350	−0.211891
$987$	−3.78424	−0.120454
$988$	−35.9062	−1.14233
$989$	19.5918	0.622983
$990$	0	0
$991$	11.3642	0.360996	0.180498	−	0.983575i	$-0.442229\pi$
$991$	11.3642	0.360996	0.180498	+	0.983575i	$0.442229\pi$
$992$	−11.6504	−0.369901
$993$	−10.3840	−0.329526
$994$	1.53236	0.0486036
$995$	7.16644	0.227191
$996$	6.36441	0.201664
$997$	29.1644	0.923647	0.461824	−	0.886972i	$-0.347195\pi$
$997$	29.1644	0.923647	0.461824	+	0.886972i	$0.347195\pi$
$998$	−5.19332	−0.164392
$999$	20.2716	0.641365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.k.1.2		4
3.2	odd	2		5445.2.a.bi.1.3		4
4.3	odd	2		9680.2.a.cm.1.3		4
5.4	even	2		3025.2.a.w.1.3		4
11.2	odd	10		605.2.g.m.81.1		8
11.3	even	5		605.2.g.k.251.1		8
11.4	even	5		605.2.g.k.511.1		8
11.5	even	5		605.2.g.e.366.2		8
11.6	odd	10		605.2.g.m.366.1		8
11.7	odd	10		55.2.g.b.16.2	✓	8
11.8	odd	10		55.2.g.b.31.2	yes	8
11.9	even	5		605.2.g.e.81.2		8
11.10	odd	2		605.2.a.j.1.3		4
33.8	even	10		495.2.n.e.361.1		8
33.29	even	10		495.2.n.e.181.1		8
33.32	even	2		5445.2.a.bp.1.2		4
44.7	even	10		880.2.bo.h.401.1		8
44.19	even	10		880.2.bo.h.801.1		8
44.43	even	2		9680.2.a.cn.1.3		4
55.7	even	20		275.2.z.a.49.2		16
55.8	even	20		275.2.z.a.174.2		16
55.18	even	20		275.2.z.a.49.3		16
55.19	odd	10		275.2.h.a.251.1		8
55.29	odd	10		275.2.h.a.126.1		8
55.52	even	20		275.2.z.a.174.3		16
55.54	odd	2		3025.2.a.bd.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	11.7	odd	10
55.2.g.b.31.2	yes	8	11.8	odd	10
275.2.h.a.126.1		8	55.29	odd	10
275.2.h.a.251.1		8	55.19	odd	10
275.2.z.a.49.2		16	55.7	even	20
275.2.z.a.49.3		16	55.18	even	20
275.2.z.a.174.2		16	55.8	even	20
275.2.z.a.174.3		16	55.52	even	20
495.2.n.e.181.1		8	33.29	even	10
495.2.n.e.361.1		8	33.8	even	10
605.2.a.j.1.3		4	11.10	odd	2
605.2.a.k.1.2		4	1.1	even	1	trivial
605.2.g.e.81.2		8	11.9	even	5
605.2.g.e.366.2		8	11.5	even	5
605.2.g.k.251.1		8	11.3	even	5
605.2.g.k.511.1		8	11.4	even	5
605.2.g.m.81.1		8	11.2	odd	10
605.2.g.m.366.1		8	11.6	odd	10
880.2.bo.h.401.1		8	44.7	even	10
880.2.bo.h.801.1		8	44.19	even	10
3025.2.a.w.1.3		4	5.4	even	2
3025.2.a.bd.1.2		4	55.54	odd	2
5445.2.a.bi.1.3		4	3.2	odd	2
5445.2.a.bp.1.2		4	33.32	even	2
9680.2.a.cm.1.3		4	4.3	odd	2
9680.2.a.cn.1.3		4	44.43	even	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q-0.477260 q^{2} +0.323071 q^{3} -1.77222 q^{4} -1.00000 q^{5} -0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +O(q^{10})\)	\(q-0.477260 q^{2} +0.323071 q^{3} -1.77222 q^{4} -1.00000 q^{5} -0.154189 q^{6} -2.68522 q^{7} +1.80033 q^{8} -2.89563 q^{9} +0.477260 q^{10} -0.572554 q^{12} +4.66785 q^{13} +1.28155 q^{14} -0.323071 q^{15} +2.68522 q^{16} +4.62632 q^{17} +1.38197 q^{18} +4.34044 q^{19} +1.77222 q^{20} -0.867517 q^{21} +2.77222 q^{23} +0.581635 q^{24} +1.00000 q^{25} -2.22778 q^{26} -1.90471 q^{27} +4.75881 q^{28} +3.01341 q^{29} +0.154189 q^{30} +2.38630 q^{31} -4.88221 q^{32} -2.20796 q^{34} +2.68522 q^{35} +5.13169 q^{36} -10.6429 q^{37} -2.07152 q^{38} +1.50805 q^{39} -1.80033 q^{40} +2.21041 q^{41} +0.414031 q^{42} +7.06719 q^{43} +2.89563 q^{45} -1.32307 q^{46} +4.36215 q^{47} +0.867517 q^{48} +0.210405 q^{49} -0.477260 q^{50} +1.49463 q^{51} -8.27247 q^{52} -6.33404 q^{53} +0.909040 q^{54} -4.83428 q^{56} +1.40227 q^{57} -1.43818 q^{58} +11.7473 q^{59} +0.572554 q^{60} +3.98263 q^{61} -1.13889 q^{62} +7.77539 q^{63} -3.04036 q^{64} -4.66785 q^{65} +7.31984 q^{67} -8.19888 q^{68} +0.895625 q^{69} -1.28155 q^{70} +1.19571 q^{71} -5.21308 q^{72} -1.02171 q^{73} +5.07943 q^{74} +0.323071 q^{75} -7.69223 q^{76} -0.719730 q^{78} -3.50213 q^{79} -2.68522 q^{80} +8.07152 q^{81} -1.05494 q^{82} -11.1158 q^{83} +1.53743 q^{84} -4.62632 q^{85} -3.37289 q^{86} +0.973547 q^{87} +2.76978 q^{89} -1.38197 q^{90} -12.5342 q^{91} -4.91300 q^{92} +0.770945 q^{93} -2.08188 q^{94} -4.34044 q^{95} -1.57730 q^{96} +18.5342 q^{97} -0.100418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8	\( 4 q + q^{2} - q^{4} - 4 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} - q^{10} + 8 q^{12} + q^{13} + 2 q^{14} - 3 q^{16} - q^{17} + 10 q^{18} + 20 q^{19} + q^{20} + 10 q^{21} + 5 q^{23} + 11 q^{24} + 4 q^{25} - 15 q^{26} - 15 q^{27} + 13 q^{28} + 12 q^{29} - q^{30} - 5 q^{31} - 8 q^{32} + 2 q^{34} - 3 q^{35} + 7 q^{37} + 20 q^{38} + 7 q^{39} - 3 q^{40} + 11 q^{41} + 12 q^{42} + 19 q^{43} - 4 q^{46} + 5 q^{47} - 10 q^{48} + 3 q^{49} + q^{50} + 7 q^{51} - 11 q^{52} - 11 q^{53} - 8 q^{54} + 11 q^{56} - 5 q^{57} - 14 q^{58} + 9 q^{59} - 8 q^{60} + 12 q^{61} - 35 q^{62} - 5 q^{63} - 3 q^{64} - q^{65} - 19 q^{67} - 3 q^{68} - 8 q^{69} - 2 q^{70} + 5 q^{71} - 25 q^{72} + 11 q^{73} - 8 q^{78} + 34 q^{79} + 3 q^{80} + 4 q^{81} - 6 q^{82} - 11 q^{83} + 11 q^{84} + q^{85} + q^{86} - 19 q^{87} - 8 q^{89} - 10 q^{90} - 8 q^{91} - 12 q^{92} - 5 q^{93} - q^{94} - 20 q^{95} - 34 q^{96} + 32 q^{97} - 8 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 - 4 * q^5 + q^6 + 3 * q^7 + 3 * q^8 - q^10 + 8 * q^12 + q^13 + 2 * q^14 - 3 * q^16 - q^17 + 10 * q^18 + 20 * q^19 + q^20 + 10 * q^21 + 5 * q^23 + 11 * q^24 + 4 * q^25 - 15 * q^26 - 15 * q^27 + 13 * q^28 + 12 * q^29 - q^30 - 5 * q^31 - 8 * q^32 + 2 * q^34 - 3 * q^35 + 7 * q^37 + 20 * q^38 + 7 * q^39 - 3 * q^40 + 11 * q^41 + 12 * q^42 + 19 * q^43 - 4 * q^46 + 5 * q^47 - 10 * q^48 + 3 * q^49 + q^50 + 7 * q^51 - 11 * q^52 - 11 * q^53 - 8 * q^54 + 11 * q^56 - 5 * q^57 - 14 * q^58 + 9 * q^59 - 8 * q^60 + 12 * q^61 - 35 * q^62 - 5 * q^63 - 3 * q^64 - q^65 - 19 * q^67 - 3 * q^68 - 8 * q^69 - 2 * q^70 + 5 * q^71 - 25 * q^72 + 11 * q^73 - 8 * q^78 + 34 * q^79 + 3 * q^80 + 4 * q^81 - 6 * q^82 - 11 * q^83 + 11 * q^84 + q^85 + q^86 - 19 * q^87 - 8 * q^89 - 10 * q^90 - 8 * q^91 - 12 * q^92 - 5 * q^93 - q^94 - 20 * q^95 - 34 * q^96 + 32 * q^97 - 8 * q^98

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