LMFDB - Embedded newform 605.2.a.i.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
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			$-0.777484$ 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)

$f(q)$	$=$	$q-2.25800 q^{2} +0.777484 q^{3} +3.09855 q^{4} +1.00000 q^{5} -1.75556 q^{6} -0.123970 q^{7} -2.48051 q^{8} -2.39552 q^{9} +O(q^{10})$	\(q-2.25800 q^{2} +0.777484 q^{3} +3.09855 q^{4} +1.00000 q^{5} -1.75556 q^{6} -0.123970 q^{7} -2.48051 q^{8} -2.39552 q^{9} -2.25800 q^{10} +2.40907 q^{12} -5.49406 q^{13} +0.279924 q^{14} +0.777484 q^{15} -0.596106 q^{16} -0.519488 q^{17} +5.40907 q^{18} -3.15945 q^{19} +3.09855 q^{20} -0.0963848 q^{21} -7.92856 q^{23} -1.92856 q^{24} +1.00000 q^{25} +12.4056 q^{26} -4.19493 q^{27} -0.384127 q^{28} +4.07662 q^{29} -1.75556 q^{30} +7.04903 q^{31} +6.30703 q^{32} +1.17300 q^{34} -0.123970 q^{35} -7.42262 q^{36} -8.78754 q^{37} +7.13403 q^{38} -4.27155 q^{39} -2.48051 q^{40} +7.55147 q^{41} +0.217636 q^{42} -3.42310 q^{43} -2.39552 q^{45} +17.9027 q^{46} +0.456423 q^{47} -0.463463 q^{48} -6.98463 q^{49} -2.25800 q^{50} -0.403894 q^{51} -17.0236 q^{52} +0.0354802 q^{53} +9.47214 q^{54} +0.307509 q^{56} -2.45642 q^{57} -9.20499 q^{58} -5.47485 q^{59} +2.40907 q^{60} -7.68899 q^{61} -15.9167 q^{62} +0.296973 q^{63} -13.0490 q^{64} -5.49406 q^{65} -2.53792 q^{67} -1.60966 q^{68} -6.16433 q^{69} +0.279924 q^{70} +12.2732 q^{71} +5.94211 q^{72} -8.52117 q^{73} +19.8422 q^{74} +0.777484 q^{75} -9.78970 q^{76} +9.64514 q^{78} -6.27371 q^{79} -0.596106 q^{80} +3.92506 q^{81} -17.0512 q^{82} -0.626410 q^{83} -0.298653 q^{84} -0.519488 q^{85} +7.72935 q^{86} +3.16951 q^{87} -10.1852 q^{89} +5.40907 q^{90} +0.681099 q^{91} -24.5670 q^{92} +5.48051 q^{93} -1.03060 q^{94} -3.15945 q^{95} +4.90362 q^{96} -1.83489 q^{97} +15.7713 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} + q^{6} - 11 q^{7} - 9 q^{8}+O(q^{10}) $ 4 * q - 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 + q^6 - 11 * q^7 - 9 * q^8	$ 4 q - 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} + q^{6} - 11 q^{7} - 9 q^{8} - 3 q^{10} - 14 q^{12} - 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} - 3 q^{17} - 2 q^{18} - 12 q^{19} + 7 q^{20} + 6 q^{21} - 9 q^{23} + 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} - 7 q^{28} + 8 q^{29} + q^{30} + 3 q^{31} - 6 q^{32} - 10 q^{34} - 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} + 3 q^{39} - 9 q^{40} + 7 q^{41} + 2 q^{42} - 21 q^{43} - 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} - 3 q^{50} - 9 q^{51} - 27 q^{52} - 11 q^{53} + 20 q^{54} + 15 q^{56} - 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} - 4 q^{61} - 11 q^{62} - 3 q^{63} - 27 q^{64} - 7 q^{65} - q^{67} + 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} - 13 q^{72} + 9 q^{73} + 36 q^{74} - 2 q^{75} - 8 q^{76} + 6 q^{78} - 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} - 15 q^{83} + 47 q^{84} - 3 q^{85} - 3 q^{86} - 15 q^{87} - 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} + 11 q^{94} - 12 q^{95} + 26 q^{96} + 6 q^{97} + 42 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 + q^6 - 11 * q^7 - 9 * q^8 - 3 * q^10 - 14 * q^12 - 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 - 3 * q^17 - 2 * q^18 - 12 * q^19 + 7 * q^20 + 6 * q^21 - 9 * q^23 + 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 - 7 * q^28 + 8 * q^29 + q^30 + 3 * q^31 - 6 * q^32 - 10 * q^34 - 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 + 3 * q^39 - 9 * q^40 + 7 * q^41 + 2 * q^42 - 21 * q^43 - 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 - 3 * q^50 - 9 * q^51 - 27 * q^52 - 11 * q^53 + 20 * q^54 + 15 * q^56 - 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 - 4 * q^61 - 11 * q^62 - 3 * q^63 - 27 * q^64 - 7 * q^65 - q^67 + 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 - 13 * q^72 + 9 * q^73 + 36 * q^74 - 2 * q^75 - 8 * q^76 + 6 * q^78 - 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 - 15 * q^83 + 47 * q^84 - 3 * q^85 - 3 * q^86 - 15 * q^87 - 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 + 11 * q^94 - 12 * q^95 + 26 * q^96 + 6 * q^97 + 42 * 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 $

$2$	−2.25800	−1.59664	−0.798322	−	0.602231i	$-0.794279\pi$
$2$	−2.25800	−1.59664	−0.798322	+	0.602231i	$0.794279\pi$
$3$	0.777484	0.448881	0.224440	−	0.974488i	$-0.427945\pi$
$3$	0.777484	0.448881	0.224440	+	0.974488i	$0.427945\pi$
$4$	3.09855	1.54927
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.75556	−0.716703
$7$	−0.123970	−0.0468563	−0.0234281	−	0.999726i	$-0.507458\pi$
$7$	−0.123970	−0.0468563	−0.0234281	+	0.999726i	$0.507458\pi$
$8$	−2.48051	−0.876993
$9$	−2.39552	−0.798506
$10$	−2.25800	−0.714041
$11$	0	0
$11$	0	0
$12$	2.40907	0.695439
$13$	−5.49406	−1.52378	−0.761890	−	0.647707i	$-0.775728\pi$
$13$	−5.49406	−1.52378	−0.761890	+	0.647707i	$0.775728\pi$
$14$	0.279924	0.0748128
$15$	0.777484	0.200746
$16$	−0.596106	−0.149027
$17$	−0.519488	−0.125994	−0.0629972	−	0.998014i	$-0.520066\pi$
$17$	−0.519488	−0.125994	−0.0629972	+	0.998014i	$0.520066\pi$
$18$	5.40907	1.27493
$19$	−3.15945	−0.724828	−0.362414	−	0.932017i	$-0.618047\pi$
$19$	−3.15945	−0.724828	−0.362414	+	0.932017i	$0.618047\pi$
$20$	3.09855	0.692856
$21$	−0.0963848	−0.0210329
$22$	0	0
$23$	−7.92856	−1.65322	−0.826609	−	0.562776i	$-0.809733\pi$
$23$	−7.92856	−1.65322	−0.826609	+	0.562776i	$0.809733\pi$
$24$	−1.92856	−0.393665
$25$	1.00000	0.200000
$26$	12.4056	2.43293
$27$	−4.19493	−0.807315
$28$	−0.384127	−0.0725932
$29$	4.07662	0.757009	0.378504	−	0.925599i	$-0.376438\pi$
$29$	4.07662	0.757009	0.378504	+	0.925599i	$0.376438\pi$
$30$	−1.75556	−0.320519
$31$	7.04903	1.26604	0.633022	−	0.774134i	$-0.281814\pi$
$31$	7.04903	1.26604	0.633022	+	0.774134i	$0.281814\pi$
$32$	6.30703	1.11494
$33$	0	0
$34$	1.17300	0.201168
$35$	−0.123970	−0.0209548
$36$	−7.42262	−1.23710
$37$	−8.78754	−1.44466	−0.722331	−	0.691547i	$-0.756929\pi$
$37$	−8.78754	−1.44466	−0.722331	+	0.691547i	$0.756929\pi$
$38$	7.13403	1.15729
$39$	−4.27155	−0.683995
$40$	−2.48051	−0.392203
$41$	7.55147	1.17934	0.589671	−	0.807644i	$-0.299257\pi$
$41$	7.55147	1.17934	0.589671	+	0.807644i	$0.299257\pi$
$42$	0.217636	0.0335820
$43$	−3.42310	−0.522018	−0.261009	−	0.965336i	$-0.584055\pi$
$43$	−3.42310	−0.522018	−0.261009	+	0.965336i	$0.584055\pi$
$44$	0	0
$45$	−2.39552	−0.357103
$46$	17.9027	2.63960
$47$	0.456423	0.0665761	0.0332881	−	0.999446i	$-0.489402\pi$
$47$	0.456423	0.0665761	0.0332881	+	0.999446i	$0.489402\pi$
$48$	−0.463463	−0.0668951
$49$	−6.98463	−0.997804
$50$	−2.25800	−0.319329
$51$	−0.403894	−0.0565565
$52$	−17.0236	−2.36075
$53$	0.0354802	0.00487358	0.00243679	−	0.999997i	$-0.499224\pi$
$53$	0.0354802	0.00487358	0.00243679	+	0.999997i	$0.499224\pi$
$54$	9.47214	1.28899
$55$	0	0
$56$	0.307509	0.0410926
$57$	−2.45642	−0.325361
$58$	−9.20499	−1.20867
$59$	−5.47485	−0.712765	−0.356383	−	0.934340i	$-0.615990\pi$
$59$	−5.47485	−0.712765	−0.356383	+	0.934340i	$0.615990\pi$
$60$	2.40907	0.311010
$61$	−7.68899	−0.984475	−0.492237	−	0.870461i	$-0.663821\pi$
$61$	−7.68899	−0.984475	−0.492237	+	0.870461i	$0.663821\pi$
$62$	−15.9167	−2.02142
$63$	0.296973	0.0374150
$64$	−13.0490	−1.63113
$65$	−5.49406	−0.681455
$66$	0	0
$67$	−2.53792	−0.310056	−0.155028	−	0.987910i	$-0.549547\pi$
$67$	−2.53792	−0.310056	−0.155028	+	0.987910i	$0.549547\pi$
$68$	−1.60966	−0.195200
$69$	−6.16433	−0.742098
$70$	0.279924	0.0334573
$71$	12.2732	1.45656	0.728282	−	0.685277i	$-0.240319\pi$
$71$	12.2732	1.45656	0.728282	+	0.685277i	$0.240319\pi$
$72$	5.94211	0.700284
$73$	−8.52117	−0.997327	−0.498664	−	0.866796i	$-0.666176\pi$
$73$	−8.52117	−0.997327	−0.498664	+	0.866796i	$0.666176\pi$
$74$	19.8422	2.30661
$75$	0.777484	0.0897761
$76$	−9.78970	−1.12296
$77$	0	0
$78$	9.64514	1.09210
$79$	−6.27371	−0.705847	−0.352924	−	0.935652i	$-0.614812\pi$
$79$	−6.27371	−0.705847	−0.352924	+	0.935652i	$0.614812\pi$
$80$	−0.596106	−0.0666467
$81$	3.92506	0.436118
$82$	−17.0512	−1.88299
$83$	−0.626410	−0.0687574	−0.0343787	−	0.999409i	$-0.510945\pi$
$83$	−0.626410	−0.0687574	−0.0343787	+	0.999409i	$0.510945\pi$
$84$	−0.298653	−0.0325857
$85$	−0.519488	−0.0563464
$86$	7.72935	0.833478
$87$	3.16951	0.339807
$88$	0	0
$89$	−10.1852	−1.07963	−0.539816	−	0.841783i	$-0.681506\pi$
$89$	−10.1852	−1.07963	−0.539816	+	0.841783i	$0.681506\pi$
$90$	5.40907	0.570166
$91$	0.681099	0.0713986
$92$	−24.5670	−2.56129
$93$	5.48051	0.568303
$94$	−1.03060	−0.106298
$95$	−3.15945	−0.324153
$96$	4.90362	0.500473
$97$	−1.83489	−0.186305	−0.0931525	−	0.995652i	$-0.529694\pi$
$97$	−1.83489	−0.186305	−0.0931525	+	0.995652i	$0.529694\pi$
$98$	15.7713	1.59314
$99$	0	0
$100$	3.09855	0.309855
$101$	−1.22769	−0.122160	−0.0610800	−	0.998133i	$-0.519454\pi$
$101$	−1.22769	−0.122160	−0.0610800	+	0.998133i	$0.519454\pi$
$102$	0.911991	0.0903006
$103$	−2.35788	−0.232329	−0.116164	−	0.993230i	$-0.537060\pi$
$103$	−2.35788	−0.232329	−0.116164	+	0.993230i	$0.537060\pi$
$104$	13.6281	1.33634
$105$	−0.0963848	−0.00940619
$106$	−0.0801141	−0.00778137
$107$	−5.78181	−0.558948	−0.279474	−	0.960153i	$-0.590160\pi$
$107$	−5.78181	−0.558948	−0.279474	+	0.960153i	$0.590160\pi$
$108$	−12.9982	−1.25075
$109$	−4.21902	−0.404109	−0.202054	−	0.979374i	$-0.564762\pi$
$109$	−4.21902	−0.404109	−0.202054	+	0.979374i	$0.564762\pi$
$110$	0	0
$111$	−6.83217	−0.648481
$112$	0.0738993	0.00698283
$113$	15.1187	1.42224	0.711122	−	0.703069i	$-0.248187\pi$
$113$	15.1187	1.42224	0.711122	+	0.703069i	$0.248187\pi$
$114$	5.54659	0.519486
$115$	−7.92856	−0.739342
$116$	12.6316	1.17281
$117$	13.1611	1.21675
$118$	12.3622	1.13803
$119$	0.0644010	0.00590363
$120$	−1.92856	−0.176053
$121$	0	0
$122$	17.3617	1.57186
$123$	5.87115	0.529384
$124$	21.8417	1.96145
$125$	1.00000	0.0894427
$126$	−0.670563	−0.0597385
$127$	10.7099	0.950349	0.475174	−	0.879892i	$-0.342385\pi$
$127$	10.7099	0.950349	0.475174	+	0.879892i	$0.342385\pi$
$128$	16.8506	1.48940
$129$	−2.66141	−0.234324
$130$	12.4056	1.08804
$131$	−6.56014	−0.573163	−0.286581	−	0.958056i	$-0.592519\pi$
$131$	−6.56014	−0.573163	−0.286581	+	0.958056i	$0.592519\pi$
$132$	0	0
$133$	0.391677	0.0339627
$134$	5.73061	0.495050
$135$	−4.19493	−0.361042
$136$	1.28860	0.110496
$137$	8.37527	0.715548	0.357774	−	0.933808i	$-0.383536\pi$
$137$	8.37527	0.715548	0.357774	+	0.933808i	$0.383536\pi$
$138$	13.9190	1.18487
$139$	16.0074	1.35773	0.678866	−	0.734263i	$-0.262472\pi$
$139$	16.0074	1.35773	0.678866	+	0.734263i	$0.262472\pi$
$140$	−0.384127	−0.0324646
$141$	0.354862	0.0298847
$142$	−27.7129	−2.32561
$143$	0	0
$144$	1.42798	0.118999
$145$	4.07662	0.338545
$146$	19.2408	1.59238
$147$	−5.43044	−0.447895
$148$	−27.2286	−2.23818
$149$	13.8874	1.13770	0.568851	−	0.822441i	$-0.307388\pi$
$149$	13.8874	1.13770	0.568851	+	0.822441i	$0.307388\pi$
$150$	−1.75556	−0.143341
$151$	−8.24962	−0.671345	−0.335672	−	0.941979i	$-0.608963\pi$
$151$	−8.24962	−0.671345	−0.335672	+	0.941979i	$0.608963\pi$
$152$	7.83705	0.635669
$153$	1.24444	0.100607
$154$	0	0
$155$	7.04903	0.566192
$156$	−13.2356	−1.05970
$157$	10.2851	0.820840	0.410420	−	0.911897i	$-0.365382\pi$
$157$	10.2851	0.820840	0.410420	+	0.911897i	$0.365382\pi$
$158$	14.1660	1.12699
$159$	0.0275853	0.00218766
$160$	6.30703	0.498614
$161$	0.982904	0.0774637
$162$	−8.86277	−0.696325
$163$	−2.08849	−0.163583	−0.0817916	−	0.996649i	$-0.526064\pi$
$163$	−2.08849	−0.163583	−0.0817916	+	0.996649i	$0.526064\pi$
$164$	23.3986	1.82712
$165$	0	0
$166$	1.41443	0.109781
$167$	−16.6281	−1.28672	−0.643360	−	0.765564i	$-0.722460\pi$
$167$	−16.6281	−1.28672	−0.643360	+	0.765564i	$0.722460\pi$
$168$	0.239084	0.0184457
$169$	17.1847	1.32190
$170$	1.17300	0.0899652
$171$	7.56852	0.578779
$172$	−10.6066	−0.808749
$173$	19.3244	1.46921	0.734604	−	0.678496i	$-0.237368\pi$
$173$	19.3244	1.46921	0.734604	+	0.678496i	$0.237368\pi$
$174$	−7.15673	−0.542550
$175$	−0.123970	−0.00937126
$176$	0	0
$177$	−4.25661	−0.319947
$178$	22.9982	1.72379
$179$	−2.90097	−0.216829	−0.108414	−	0.994106i	$-0.534577\pi$
$179$	−2.90097	−0.216829	−0.108414	+	0.994106i	$0.534577\pi$
$180$	−7.42262	−0.553250
$181$	10.0170	0.744561	0.372281	−	0.928120i	$-0.378576\pi$
$181$	10.0170	0.744561	0.372281	+	0.928120i	$0.378576\pi$
$182$	−1.53792	−0.113998
$183$	−5.97807	−0.441912
$184$	19.6669	1.44986
$185$	−8.78754	−0.646073
$186$	−12.3750	−0.907377
$187$	0	0
$188$	1.41425	0.103145
$189$	0.520046	0.0378278
$190$	7.13403	0.517557
$191$	−13.5645	−0.981490	−0.490745	−	0.871303i	$-0.663275\pi$
$191$	−13.5645	−0.981490	−0.490745	+	0.871303i	$0.663275\pi$
$192$	−10.1454	−0.732182
$193$	−13.6925	−0.985607	−0.492804	−	0.870141i	$-0.664028\pi$
$193$	−13.6925	−0.985607	−0.492804	+	0.870141i	$0.664028\pi$
$194$	4.14318	0.297463
$195$	−4.27155	−0.305892
$196$	−21.6422	−1.54587
$197$	−2.59965	−0.185217	−0.0926087	−	0.995703i	$-0.529521\pi$
$197$	−2.59965	−0.185217	−0.0926087	+	0.995703i	$0.529521\pi$
$198$	0	0
$199$	17.6907	1.25406	0.627029	−	0.778996i	$-0.284271\pi$
$199$	17.6907	1.25406	0.627029	+	0.778996i	$0.284271\pi$
$200$	−2.48051	−0.175399
$201$	−1.97319	−0.139178
$202$	2.77212	0.195046
$203$	−0.505379	−0.0354706
$204$	−1.25148	−0.0876214
$205$	7.55147	0.527418
$206$	5.32408	0.370946
$207$	18.9930	1.32011
$208$	3.27504	0.227083
$209$	0	0
$210$	0.217636	0.0150183
$211$	−18.3679	−1.26450	−0.632250	−	0.774764i	$-0.717869\pi$
$211$	−18.3679	−1.26450	−0.632250	+	0.774764i	$0.717869\pi$
$212$	0.109937	0.00755050
$213$	9.54224	0.653824
$214$	13.0553	0.892442
$215$	−3.42310	−0.233454
$216$	10.4056	0.708010
$217$	−0.873869	−0.0593221
$218$	9.52653	0.645218
$219$	−6.62507	−0.447681
$220$	0	0
$221$	2.85410	0.191988
$222$	15.4270	1.03539
$223$	1.92904	0.129178	0.0645890	−	0.997912i	$-0.479426\pi$
$223$	1.92904	0.129178	0.0645890	+	0.997912i	$0.479426\pi$
$224$	−0.781883	−0.0522417
$225$	−2.39552	−0.159701
$226$	−34.1379	−2.27082
$227$	−29.3867	−1.95046	−0.975231	−	0.221191i	$-0.929006\pi$
$227$	−29.3867	−1.95046	−0.975231	+	0.221191i	$0.929006\pi$
$228$	−7.61134	−0.504073
$229$	−19.6319	−1.29731	−0.648656	−	0.761082i	$-0.724668\pi$
$229$	−19.6319	−1.29731	−0.648656	+	0.761082i	$0.724668\pi$
$230$	17.9027	1.18047
$231$	0	0
$232$	−10.1121	−0.663892
$233$	−5.06824	−0.332032	−0.166016	−	0.986123i	$-0.553090\pi$
$233$	−5.06824	−0.332032	−0.166016	+	0.986123i	$0.553090\pi$
$234$	−29.7178	−1.94271
$235$	0.456423	0.0297737
$236$	−16.9641	−1.10427
$237$	−4.87771	−0.316841
$238$	−0.145417	−0.00942600
$239$	−22.5031	−1.45560	−0.727802	−	0.685788i	$-0.759458\pi$
$239$	−22.5031	−1.45560	−0.727802	+	0.685788i	$0.759458\pi$
$240$	−0.463463	−0.0299164
$241$	27.6924	1.78382	0.891911	−	0.452212i	$-0.149365\pi$
$241$	27.6924	1.78382	0.891911	+	0.452212i	$0.149365\pi$
$242$	0	0
$243$	15.6365	1.00308
$244$	−23.8247	−1.52522
$245$	−6.98463	−0.446232
$246$	−13.2570	−0.845238
$247$	17.3582	1.10448
$248$	−17.4852	−1.11031
$249$	−0.487024	−0.0308639
$250$	−2.25800	−0.142808
$251$	−4.36932	−0.275789	−0.137894	−	0.990447i	$-0.544033\pi$
$251$	−4.36932	−0.275789	−0.137894	+	0.990447i	$0.544033\pi$
$252$	0.920183	0.0579661
$253$	0	0
$254$	−24.1829	−1.51737
$255$	−0.403894	−0.0252928
$256$	−11.9505	−0.746908
$257$	18.0629	1.12673	0.563367	−	0.826207i	$-0.309506\pi$
$257$	18.0629	1.12673	0.563367	+	0.826207i	$0.309506\pi$
$258$	6.00945	0.374132
$259$	1.08939	0.0676915
$260$	−17.0236	−1.05576
$261$	−9.76561	−0.604476
$262$	14.8128	0.915137
$263$	−13.4340	−0.828377	−0.414188	−	0.910191i	$-0.635935\pi$
$263$	−13.4340	−0.828377	−0.414188	+	0.910191i	$0.635935\pi$
$264$	0	0
$265$	0.0354802	0.00217953
$266$	−0.884406	−0.0542264
$267$	−7.91885	−0.484626
$268$	−7.86386	−0.480362
$269$	−4.25800	−0.259615	−0.129807	−	0.991539i	$-0.541436\pi$
$269$	−4.25800	−0.259615	−0.129807	+	0.991539i	$0.541436\pi$
$270$	9.47214	0.576456
$271$	−12.6509	−0.768486	−0.384243	−	0.923232i	$-0.625537\pi$
$271$	−12.6509	−0.768486	−0.384243	+	0.923232i	$0.625537\pi$
$272$	0.309670	0.0187765
$273$	0.529544	0.0320495
$274$	−18.9113	−1.14248
$275$	0	0
$276$	−19.1005	−1.14971
$277$	31.9772	1.92132	0.960661	−	0.277725i	$-0.0895804\pi$
$277$	31.9772	1.92132	0.960661	+	0.277725i	$0.0895804\pi$
$278$	−36.1447	−2.16781
$279$	−16.8861	−1.01094
$280$	0.307509	0.0183772
$281$	28.8829	1.72301	0.861504	−	0.507750i	$-0.169523\pi$
$281$	28.8829	1.72301	0.861504	+	0.507750i	$0.169523\pi$
$282$	−0.801276	−0.0477153
$283$	4.85229	0.288438	0.144219	−	0.989546i	$-0.453933\pi$
$283$	4.85229	0.288438	0.144219	+	0.989546i	$0.453933\pi$
$284$	38.0292	2.25662
$285$	−2.45642	−0.145506
$286$	0	0
$287$	−0.936157	−0.0552596
$288$	−15.1086	−0.890283
$289$	−16.7301	−0.984125
$290$	−9.20499	−0.540535
$291$	−1.42660	−0.0836288
$292$	−26.4032	−1.54513
$293$	−4.00760	−0.234126	−0.117063	−	0.993124i	$-0.537348\pi$
$293$	−4.00760	−0.234126	−0.117063	+	0.993124i	$0.537348\pi$
$294$	12.2619	0.715129
$295$	−5.47485	−0.318758
$296$	21.7976	1.26696
$297$	0	0
$298$	−31.3577	−1.81651
$299$	43.5600	2.51914
$300$	2.40907	0.139088
$301$	0.424362	0.0244598
$302$	18.6276	1.07190
$303$	−0.954511	−0.0548352
$304$	1.88337	0.108019
$305$	−7.68899	−0.440271
$306$	−2.80995	−0.160634
$307$	−3.68515	−0.210323	−0.105161	−	0.994455i	$-0.533536\pi$
$307$	−3.68515	−0.210323	−0.105161	+	0.994455i	$0.533536\pi$
$308$	0	0
$309$	−1.83321	−0.104288
$310$	−15.9167	−0.904007
$311$	−9.96754	−0.565207	−0.282604	−	0.959237i	$-0.591198\pi$
$311$	−9.96754	−0.565207	−0.282604	+	0.959237i	$0.591198\pi$
$312$	10.5956	0.599859
$313$	18.8612	1.06610	0.533050	−	0.846084i	$-0.321046\pi$
$313$	18.8612	1.06610	0.533050	+	0.846084i	$0.321046\pi$
$314$	−23.2237	−1.31059
$315$	0.296973	0.0167325
$316$	−19.4394	−1.09355
$317$	3.89446	0.218735	0.109367	−	0.994001i	$-0.465118\pi$
$317$	3.89446	0.218735	0.109367	+	0.994001i	$0.465118\pi$
$318$	−0.0622875	−0.00349291
$319$	0	0
$320$	−13.0490	−0.729463
$321$	−4.49526	−0.250901
$322$	−2.21939	−0.123682
$323$	1.64130	0.0913242
$324$	12.1620	0.675666
$325$	−5.49406	−0.304756
$326$	4.71580	0.261184
$327$	−3.28022	−0.181397
$328$	−18.7315	−1.03427
$329$	−0.0565828	−0.00311951
$330$	0	0
$331$	7.97626	0.438415	0.219207	−	0.975678i	$-0.429653\pi$
$331$	7.97626	0.438415	0.219207	+	0.975678i	$0.429653\pi$
$332$	−1.94096	−0.106524
$333$	21.0507	1.15357
$334$	37.5462	2.05443
$335$	−2.53792	−0.138661
$336$	0.0574555	0.00313446
$337$	13.7323	0.748046	0.374023	−	0.927419i	$-0.377978\pi$
$337$	13.7323	0.748046	0.374023	+	0.927419i	$0.377978\pi$
$338$	−38.8031	−2.11061
$339$	11.7545	0.638418
$340$	−1.60966	−0.0872960
$341$	0	0
$342$	−17.0897	−0.924105
$343$	1.73368	0.0936097
$344$	8.49105	0.457807
$345$	−6.16433	−0.331876
$346$	−43.6345	−2.34580
$347$	−0.162947	−0.00874744	−0.00437372	−	0.999990i	$-0.501392\pi$
$347$	−0.162947	−0.00874744	−0.00437372	+	0.999990i	$0.501392\pi$
$348$	9.82086	0.526453
$349$	2.74145	0.146746	0.0733731	−	0.997305i	$-0.476624\pi$
$349$	2.74145	0.146746	0.0733731	+	0.997305i	$0.476624\pi$
$350$	0.279924	0.0149626
$351$	23.0472	1.23017
$352$	0	0
$353$	−5.13584	−0.273353	−0.136677	−	0.990616i	$-0.543642\pi$
$353$	−5.13584	−0.273353	−0.136677	+	0.990616i	$0.543642\pi$
$354$	9.61141	0.510841
$355$	12.2732	0.651395
$356$	−31.5594	−1.67264
$357$	0.0500708	0.00265003
$358$	6.55039	0.346199
$359$	15.1760	0.800960	0.400480	−	0.916306i	$-0.368843\pi$
$359$	15.1760	0.800960	0.400480	+	0.916306i	$0.368843\pi$
$360$	5.94211	0.313177
$361$	−9.01787	−0.474625
$362$	−22.6185	−1.18880
$363$	0	0
$364$	2.11042	0.110616
$365$	−8.52117	−0.446018
$366$	13.4985	0.705576
$367$	20.1643	1.05257	0.526285	−	0.850308i	$-0.323585\pi$
$367$	20.1643	1.05257	0.526285	+	0.850308i	$0.323585\pi$
$368$	4.72626	0.246373
$369$	−18.0897	−0.941712
$370$	19.8422	1.03155
$371$	−0.00439848	−0.000228358 0
$372$	16.9816	0.880456
$373$	−11.2539	−0.582707	−0.291354	−	0.956615i	$-0.594106\pi$
$373$	−11.2539	−0.582707	−0.291354	+	0.956615i	$0.594106\pi$
$374$	0	0
$375$	0.777484	0.0401491
$376$	−1.13216	−0.0583868
$377$	−22.3972	−1.15351
$378$	−1.17426	−0.0603975
$379$	−20.9522	−1.07624	−0.538120	−	0.842868i	$-0.680865\pi$
$379$	−20.9522	−1.07624	−0.538120	+	0.842868i	$0.680865\pi$
$380$	−9.78970	−0.502201
$381$	8.32677	0.426593
$382$	30.6285	1.56709
$383$	16.8308	0.860016	0.430008	−	0.902825i	$-0.358511\pi$
$383$	16.8308	0.860016	0.430008	+	0.902825i	$0.358511\pi$
$384$	13.1011	0.668562
$385$	0	0
$386$	30.9176	1.57366
$387$	8.20011	0.416835
$388$	−5.68550	−0.288637
$389$	15.7630	0.799214	0.399607	−	0.916686i	$-0.369147\pi$
$389$	15.7630	0.799214	0.399607	+	0.916686i	$0.369147\pi$
$390$	9.64514	0.488401
$391$	4.11879	0.208296
$392$	17.3255	0.875068
$393$	−5.10041	−0.257282
$394$	5.87000	0.295726
$395$	−6.27371	−0.315665
$396$	0	0
$397$	6.85466	0.344025	0.172013	−	0.985095i	$-0.444973\pi$
$397$	6.85466	0.344025	0.172013	+	0.985095i	$0.444973\pi$
$398$	−39.9455	−2.00229
$399$	0.304523	0.0152452
$400$	−0.596106	−0.0298053
$401$	−0.141095	−0.00704597	−0.00352298	−	0.999994i	$-0.501121\pi$
$401$	−0.141095	−0.00704597	−0.00352298	+	0.999994i	$0.501121\pi$
$402$	4.45546	0.222218
$403$	−38.7278	−1.92917
$404$	−3.80406	−0.189259
$405$	3.92506	0.195038
$406$	1.14114	0.0566340
$407$	0	0
$408$	1.00186	0.0495996
$409$	−28.7486	−1.42153	−0.710764	−	0.703430i	$-0.751651\pi$
$409$	−28.7486	−1.42153	−0.710764	+	0.703430i	$0.751651\pi$
$410$	−17.0512	−0.842098
$411$	6.51164	0.321196
$412$	−7.30599	−0.359940
$413$	0.678718	0.0333975
$414$	−42.8861	−2.10774
$415$	−0.626410	−0.0307492
$416$	−34.6512	−1.69892
$417$	12.4455	0.609459
$418$	0	0
$419$	−11.0837	−0.541472	−0.270736	−	0.962654i	$-0.587267\pi$
$419$	−11.0837	−0.541472	−0.270736	+	0.962654i	$0.587267\pi$
$420$	−0.298653	−0.0145728
$421$	−3.40334	−0.165868	−0.0829342	−	0.996555i	$-0.526429\pi$
$421$	−3.40334	−0.165868	−0.0829342	+	0.996555i	$0.526429\pi$
$422$	41.4747	2.01896
$423$	−1.09337	−0.0531614
$424$	−0.0880090	−0.00427410
$425$	−0.519488	−0.0251989
$426$	−21.5463	−1.04392
$427$	0.953205	0.0461288
$428$	−17.9152	−0.865963
$429$	0	0
$430$	7.72935	0.372743
$431$	13.6727	0.658592	0.329296	−	0.944227i	$-0.393189\pi$
$431$	13.6727	0.658592	0.329296	+	0.944227i	$0.393189\pi$
$432$	2.50062	0.120311
$433$	−15.4446	−0.742220	−0.371110	−	0.928589i	$-0.621023\pi$
$433$	−15.4446	−0.742220	−0.371110	+	0.928589i	$0.621023\pi$
$434$	1.97319	0.0947163
$435$	3.16951	0.151966
$436$	−13.0728	−0.626075
$437$	25.0499	1.19830
$438$	14.9594	0.714787
$439$	−9.87042	−0.471089	−0.235545	−	0.971864i	$-0.575687\pi$
$439$	−9.87042	−0.471089	−0.235545	+	0.971864i	$0.575687\pi$
$440$	0	0
$441$	16.7318	0.796753
$442$	−6.44455	−0.306536
$443$	31.3000	1.48711	0.743554	−	0.668676i	$-0.233139\pi$
$443$	31.3000	1.48711	0.743554	+	0.668676i	$0.233139\pi$
$444$	−21.1698	−1.00467
$445$	−10.1852	−0.482826
$446$	−4.35576	−0.206251
$447$	10.7973	0.510692
$448$	1.61769	0.0764286
$449$	−12.7272	−0.600633	−0.300317	−	0.953840i	$-0.597092\pi$
$449$	−12.7272	−0.600633	−0.300317	+	0.953840i	$0.597092\pi$
$450$	5.40907	0.254986
$451$	0	0
$452$	46.8459	2.20344
$453$	−6.41395	−0.301354
$454$	66.3550	3.11419
$455$	0.681099	0.0319304
$456$	6.09319	0.285340
$457$	4.31156	0.201686	0.100843	−	0.994902i	$-0.467846\pi$
$457$	4.31156	0.201686	0.100843	+	0.994902i	$0.467846\pi$
$458$	44.3287	2.07134
$459$	2.17922	0.101717
$460$	−24.5670	−1.14544
$461$	17.7315	0.825837	0.412918	−	0.910768i	$-0.364509\pi$
$461$	17.7315	0.825837	0.412918	+	0.910768i	$0.364509\pi$
$462$	0	0
$463$	3.43092	0.159448	0.0797242	−	0.996817i	$-0.474596\pi$
$463$	3.43092	0.159448	0.0797242	+	0.996817i	$0.474596\pi$
$464$	−2.43010	−0.112814
$465$	5.48051	0.254153
$466$	11.4441	0.530136
$467$	−15.6381	−0.723647	−0.361824	−	0.932247i	$-0.617846\pi$
$467$	−15.6381	−0.723647	−0.361824	+	0.932247i	$0.617846\pi$
$468$	40.7804	1.88507
$469$	0.314626	0.0145281
$470$	−1.03060	−0.0475381
$471$	7.99650	0.368459
$472$	13.5804	0.625090
$473$	0	0
$474$	11.0138	0.505883
$475$	−3.15945	−0.144966
$476$	0.199549	0.00914633
$477$	−0.0849935	−0.00389158
$478$	50.8119	2.32408
$479$	38.5074	1.75945	0.879724	−	0.475485i	$-0.157727\pi$
$479$	38.5074	1.75945	0.879724	+	0.475485i	$0.157727\pi$
$480$	4.90362	0.223818
$481$	48.2793	2.20135
$482$	−62.5292	−2.84813
$483$	0.764192	0.0347720
$484$	0	0
$485$	−1.83489	−0.0833182
$486$	−35.3071	−1.60156
$487$	−9.02055	−0.408760	−0.204380	−	0.978892i	$-0.565518\pi$
$487$	−9.02055	−0.408760	−0.204380	+	0.978892i	$0.565518\pi$
$488$	19.0726	0.863378
$489$	−1.62377	−0.0734293
$490$	15.7713	0.712473
$491$	4.73069	0.213493	0.106747	−	0.994286i	$-0.465957\pi$
$491$	4.73069	0.213493	0.106747	+	0.994286i	$0.465957\pi$
$492$	18.1920	0.820160
$493$	−2.11776	−0.0953789
$494$	−39.1948	−1.76346
$495$	0	0
$496$	−4.20197	−0.188674
$497$	−1.52151	−0.0682492
$498$	1.09970	0.0492786
$499$	1.14512	0.0512626	0.0256313	−	0.999671i	$-0.491840\pi$
$499$	1.14512	0.0512626	0.0256313	+	0.999671i	$0.491840\pi$
$500$	3.09855	0.138571
$501$	−12.9281	−0.577584
$502$	9.86590	0.440337
$503$	−16.6416	−0.742014	−0.371007	−	0.928630i	$-0.620987\pi$
$503$	−16.6416	−0.742014	−0.371007	+	0.928630i	$0.620987\pi$
$504$	−0.736644	−0.0328127
$505$	−1.22769	−0.0546316
$506$	0	0
$507$	13.3609	0.593377
$508$	33.1851	1.47235
$509$	−29.5778	−1.31101	−0.655506	−	0.755190i	$-0.727545\pi$
$509$	−29.5778	−1.31101	−0.655506	+	0.755190i	$0.727545\pi$
$510$	0.911991	0.0403836
$511$	1.05637	0.0467310
$512$	−6.71695	−0.296850
$513$	13.2537	0.585164
$514$	−40.7860	−1.79899
$515$	−2.35788	−0.103900
$516$	−8.24650	−0.363032
$517$	0	0
$518$	−2.45984	−0.108079
$519$	15.0244	0.659499
$520$	13.6281	0.597631
$521$	−6.61566	−0.289837	−0.144919	−	0.989444i	$-0.546292\pi$
$521$	−6.61566	−0.289837	−0.144919	+	0.989444i	$0.546292\pi$
$522$	22.0507	0.965133
$523$	−36.2733	−1.58612	−0.793060	−	0.609143i	$-0.791514\pi$
$523$	−36.2733	−1.58612	−0.793060	+	0.609143i	$0.791514\pi$
$524$	−20.3269	−0.887985
$525$	−0.0963848	−0.00420658
$526$	30.3339	1.32262
$527$	−3.66189	−0.159514
$528$	0	0
$529$	39.8620	1.73313
$530$	−0.0801141	−0.00347994
$531$	13.1151	0.569147
$532$	1.21363	0.0526175
$533$	−41.4883	−1.79706
$534$	17.8807	0.773775
$535$	−5.78181	−0.249969
$536$	6.29534	0.271917
$537$	−2.25546	−0.0973303
$538$	9.61454	0.414512
$539$	0	0
$540$	−12.9982	−0.559353
$541$	8.90399	0.382812	0.191406	−	0.981511i	$-0.438695\pi$
$541$	8.90399	0.382812	0.191406	+	0.981511i	$0.438695\pi$
$542$	28.5656	1.22700
$543$	7.78810	0.334219
$544$	−3.27643	−0.140476
$545$	−4.21902	−0.180723
$546$	−1.19571	−0.0511716
$547$	−17.0610	−0.729475	−0.364737	−	0.931110i	$-0.618841\pi$
$547$	−17.0610	−0.729475	−0.364737	+	0.931110i	$0.618841\pi$
$548$	25.9512	1.10858
$549$	18.4191	0.786109
$550$	0	0
$551$	−12.8799	−0.548701
$552$	15.2907	0.650815
$553$	0.777752	0.0330734
$554$	−72.2043	−3.06767
$555$	−6.83217	−0.290010
$556$	49.5997	2.10350
$557$	29.0945	1.23277	0.616387	−	0.787443i	$-0.288596\pi$
$557$	29.0945	1.23277	0.616387	+	0.787443i	$0.288596\pi$
$558$	38.1287	1.61412
$559$	18.8067	0.795441
$560$	0.0738993	0.00312282
$561$	0	0
$562$	−65.2174	−2.75103
$563$	11.0593	0.466094	0.233047	−	0.972465i	$-0.425130\pi$
$563$	11.0593	0.466094	0.233047	+	0.972465i	$0.425130\pi$
$564$	1.09955	0.0462996
$565$	15.1187	0.636047
$566$	−10.9564	−0.460534
$567$	−0.486590	−0.0204349
$568$	−30.4439	−1.27740
$569$	3.11962	0.130781	0.0653906	−	0.997860i	$-0.479171\pi$
$569$	3.11962	0.130781	0.0653906	+	0.997860i	$0.479171\pi$
$570$	5.54659	0.232321
$571$	−9.68683	−0.405381	−0.202691	−	0.979243i	$-0.564969\pi$
$571$	−9.68683	−0.405381	−0.202691	+	0.979243i	$0.564969\pi$
$572$	0	0
$573$	−10.5462	−0.440572
$574$	2.11384	0.0882299
$575$	−7.92856	−0.330644
$576$	31.2592	1.30247
$577$	3.02547	0.125952	0.0629760	−	0.998015i	$-0.479941\pi$
$577$	3.02547	0.125952	0.0629760	+	0.998015i	$0.479941\pi$
$578$	37.7766	1.57130
$579$	−10.6457	−0.442420
$580$	12.6316	0.524498
$581$	0.0776561	0.00322172
$582$	3.22126	0.133525
$583$	0	0
$584$	21.1369	0.874649
$585$	13.1611	0.544146
$586$	9.04914	0.373817
$587$	−44.0302	−1.81732	−0.908661	−	0.417534i	$-0.862894\pi$
$587$	−44.0302	−1.81732	−0.908661	+	0.417534i	$0.862894\pi$
$588$	−16.8265	−0.693912
$589$	−22.2711	−0.917663
$590$	12.3622	0.508944
$591$	−2.02119	−0.0831405
$592$	5.23831	0.215293
$593$	6.60880	0.271391	0.135696	−	0.990751i	$-0.456673\pi$
$593$	6.60880	0.271391	0.135696	+	0.990751i	$0.456673\pi$
$594$	0	0
$595$	0.0644010	0.00264018
$596$	43.0308	1.76261
$597$	13.7542	0.562923
$598$	−98.3583	−4.02217
$599$	−28.2085	−1.15257	−0.576284	−	0.817250i	$-0.695498\pi$
$599$	−28.2085	−1.15257	−0.576284	+	0.817250i	$0.695498\pi$
$600$	−1.92856	−0.0787331
$601$	−4.17737	−0.170399	−0.0851993	−	0.996364i	$-0.527153\pi$
$601$	−4.17737	−0.170399	−0.0851993	+	0.996364i	$0.527153\pi$
$602$	−0.958209	−0.0390537
$603$	6.07963	0.247582
$604$	−25.5618	−1.04010
$605$	0	0
$606$	2.15528	0.0875524
$607$	−13.6779	−0.555171	−0.277585	−	0.960701i	$-0.589534\pi$
$607$	−13.6779	−0.555171	−0.277585	+	0.960701i	$0.589534\pi$
$608$	−19.9267	−0.808136
$609$	−0.392924	−0.0159221
$610$	17.3617	0.702955
$611$	−2.50762	−0.101447
$612$	3.85597	0.155868
$613$	32.4116	1.30909	0.654546	−	0.756022i	$-0.272860\pi$
$613$	32.4116	1.30909	0.654546	+	0.756022i	$0.272860\pi$
$614$	8.32106	0.335811
$615$	5.87115	0.236748
$616$	0	0
$617$	−37.0480	−1.49150	−0.745749	−	0.666227i	$-0.767908\pi$
$617$	−37.0480	−1.49150	−0.745749	+	0.666227i	$0.767908\pi$
$618$	4.13939	0.166511
$619$	19.8463	0.797691	0.398846	−	0.917018i	$-0.369411\pi$
$619$	19.8463	0.797691	0.398846	+	0.917018i	$0.369411\pi$
$620$	21.8417	0.877186
$621$	33.2598	1.33467
$622$	22.5067	0.902435
$623$	1.26266	0.0505875
$624$	2.54630	0.101933
$625$	1.00000	0.0400000
$626$	−42.5886	−1.70218
$627$	0	0
$628$	31.8689	1.27171
$629$	4.56502	0.182019
$630$	−0.670563	−0.0267159
$631$	−46.8648	−1.86566	−0.932829	−	0.360319i	$-0.882668\pi$
$631$	−46.8648	−1.86566	−0.932829	+	0.360319i	$0.882668\pi$
$632$	15.5620	0.619023
$633$	−14.2808	−0.567610
$634$	−8.79368	−0.349242
$635$	10.7099	0.425009
$636$	0.0854743	0.00338928
$637$	38.3740	1.52043
$638$	0	0
$639$	−29.4007	−1.16308
$640$	16.8506	0.666079
$641$	−14.8870	−0.588001	−0.294000	−	0.955805i	$-0.594987\pi$
$641$	−14.8870	−0.588001	−0.294000	+	0.955805i	$0.594987\pi$
$642$	10.1503	0.400600
$643$	−33.0647	−1.30395	−0.651973	−	0.758242i	$-0.726059\pi$
$643$	−33.0647	−1.30395	−0.651973	+	0.758242i	$0.726059\pi$
$644$	3.04557	0.120012
$645$	−2.66141	−0.104793
$646$	−3.70604	−0.145812
$647$	−43.8706	−1.72473	−0.862365	−	0.506287i	$-0.831018\pi$
$647$	−43.8706	−1.72473	−0.862365	+	0.506287i	$0.831018\pi$
$648$	−9.73616	−0.382473
$649$	0	0
$650$	12.4056	0.486587
$651$	−0.679419	−0.0266285
$652$	−6.47128	−0.253435
$653$	34.1285	1.33555	0.667775	−	0.744363i	$-0.267247\pi$
$653$	34.1285	1.33555	0.667775	+	0.744363i	$0.267247\pi$
$654$	7.40673	0.289626
$655$	−6.56014	−0.256326
$656$	−4.50148	−0.175753
$657$	20.4126	0.796372
$658$	0.127764	0.00498075
$659$	−10.4408	−0.406716	−0.203358	−	0.979104i	$-0.565185\pi$
$659$	−10.4408	−0.406716	−0.203358	+	0.979104i	$0.565185\pi$
$660$	0	0
$661$	−45.6827	−1.77685	−0.888426	−	0.459020i	$-0.848201\pi$
$661$	−45.6827	−1.77685	−0.888426	+	0.459020i	$0.848201\pi$
$662$	−18.0104	−0.699992
$663$	2.21902	0.0861796
$664$	1.55382	0.0602998
$665$	0.391677	0.0151886
$666$	−47.5324	−1.84184
$667$	−32.3217	−1.25150
$668$	−51.5229	−1.99348
$669$	1.49980	0.0579855
$670$	5.73061	0.221393
$671$	0	0
$672$	−0.607902	−0.0234503
$673$	29.1150	1.12230	0.561150	−	0.827714i	$-0.310359\pi$
$673$	29.1150	1.12230	0.561150	+	0.827714i	$0.310359\pi$
$674$	−31.0075	−1.19436
$675$	−4.19493	−0.161463
$676$	53.2477	2.04799
$677$	32.2351	1.23890	0.619448	−	0.785038i	$-0.287357\pi$
$677$	32.2351	1.23890	0.619448	+	0.785038i	$0.287357\pi$
$678$	−26.5417	−1.01933
$679$	0.227472	0.00872956
$680$	1.28860	0.0494154
$681$	−22.8477	−0.875524
$682$	0	0
$683$	−11.0364	−0.422295	−0.211148	−	0.977454i	$-0.567720\pi$
$683$	−11.0364	−0.422295	−0.211148	+	0.977454i	$0.567720\pi$
$684$	23.4514	0.896687
$685$	8.37527	0.320003
$686$	−3.91463	−0.149461
$687$	−15.2635	−0.582338
$688$	2.04053	0.0777946
$689$	−0.194930	−0.00742626
$690$	13.9190	0.529888
$691$	36.1610	1.37563	0.687815	−	0.725886i	$-0.258570\pi$
$691$	36.1610	1.37563	0.687815	+	0.725886i	$0.258570\pi$
$692$	59.8776	2.27620
$693$	0	0
$694$	0.367933	0.0139665
$695$	16.0074	0.607196
$696$	−7.86200	−0.298008
$697$	−3.92290	−0.148590
$698$	−6.19018	−0.234302
$699$	−3.94048	−0.149043
$700$	−0.384127	−0.0145186
$701$	−14.1471	−0.534327	−0.267164	−	0.963651i	$-0.586086\pi$
$701$	−14.1471	−0.534327	−0.267164	+	0.963651i	$0.586086\pi$
$702$	−52.0405	−1.96414
$703$	27.7638	1.04713
$704$	0	0
$705$	0.354862	0.0133649
$706$	11.5967	0.436448
$707$	0.152197	0.00572396
$708$	−13.1893	−0.495685
$709$	17.1628	0.644563	0.322281	−	0.946644i	$-0.395550\pi$
$709$	17.1628	0.644563	0.322281	+	0.946644i	$0.395550\pi$
$710$	−27.7129	−1.04005
$711$	15.0288	0.563623
$712$	25.2646	0.946829
$713$	−55.8887	−2.09305
$714$	−0.113060	−0.00423115
$715$	0	0
$716$	−8.98880	−0.335927
$717$	−17.4958	−0.653392
$718$	−34.2674	−1.27885
$719$	−18.3547	−0.684516	−0.342258	−	0.939606i	$-0.611192\pi$
$719$	−18.3547	−0.684516	−0.342258	+	0.939606i	$0.611192\pi$
$720$	1.42798	0.0532178
$721$	0.292306	0.0108861
$722$	20.3623	0.757807
$723$	21.5304	0.800723
$724$	31.0383	1.15353
$725$	4.07662	0.151402
$726$	0	0
$727$	47.2976	1.75417	0.877085	−	0.480336i	$-0.159485\pi$
$727$	47.2976	1.75417	0.877085	+	0.480336i	$0.159485\pi$
$728$	−1.68948	−0.0626161
$729$	0.381919	0.0141451
$730$	19.2408	0.712133
$731$	1.77826	0.0657714
$732$	−18.5233	−0.684642
$733$	−28.7470	−1.06179	−0.530897	−	0.847437i	$-0.678145\pi$
$733$	−28.7470	−1.06179	−0.530897	+	0.847437i	$0.678145\pi$
$734$	−45.5310	−1.68058
$735$	−5.43044	−0.200305
$736$	−50.0056	−1.84323
$737$	0	0
$738$	40.8464	1.50358
$739$	−34.4205	−1.26618	−0.633089	−	0.774079i	$-0.718213\pi$
$739$	−34.4205	−1.26618	−0.633089	+	0.774079i	$0.718213\pi$
$740$	−27.2286	−1.00094
$741$	13.4957	0.495779
$742$	0.00993175	0.000364606 0
$743$	−12.1830	−0.446951	−0.223476	−	0.974710i	$-0.571740\pi$
$743$	−12.1830	−0.446951	−0.223476	+	0.974710i	$0.571740\pi$
$744$	−13.5945	−0.498398
$745$	13.8874	0.508796
$746$	25.4114	0.930376
$747$	1.50058	0.0549032
$748$	0	0
$749$	0.716771	0.0261902
$750$	−1.75556	−0.0641039
$751$	−51.5867	−1.88243	−0.941213	−	0.337813i	$-0.890313\pi$
$751$	−51.5867	−1.88243	−0.941213	+	0.337813i	$0.890313\pi$
$752$	−0.272076	−0.00992161
$753$	−3.39707	−0.123796
$754$	50.5728	1.84175
$755$	−8.24962	−0.300234
$756$	1.61139	0.0586055
$757$	11.0817	0.402772	0.201386	−	0.979512i	$-0.435455\pi$
$757$	11.0817	0.402772	0.201386	+	0.979512i	$0.435455\pi$
$758$	47.3099	1.71837
$759$	0	0
$760$	7.83705	0.284280
$761$	−1.29719	−0.0470232	−0.0235116	−	0.999724i	$-0.507485\pi$
$761$	−1.29719	−0.0470232	−0.0235116	+	0.999724i	$0.507485\pi$
$762$	−18.8018	−0.681118
$763$	0.523032	0.0189350
$764$	−42.0301	−1.52060
$765$	1.24444	0.0449930
$766$	−38.0040	−1.37314
$767$	30.0792	1.08610
$768$	−9.29135	−0.335273
$769$	24.2693	0.875173	0.437587	−	0.899176i	$-0.355833\pi$
$769$	24.2693	0.875173	0.437587	+	0.899176i	$0.355833\pi$
$770$	0	0
$771$	14.0436	0.505769
$772$	−42.4268	−1.52697
$773$	−26.5761	−0.955877	−0.477938	−	0.878393i	$-0.658616\pi$
$773$	−26.5761	−0.955877	−0.477938	+	0.878393i	$0.658616\pi$
$774$	−18.5158	−0.665537
$775$	7.04903	0.253209
$776$	4.55147	0.163388
$777$	0.846985	0.0303854
$778$	−35.5927	−1.27606
$779$	−23.8585	−0.854819
$780$	−13.2356	−0.473910
$781$	0	0
$782$	−9.30022	−0.332575
$783$	−17.1011	−0.611144
$784$	4.16358	0.148699
$785$	10.2851	0.367091
$786$	11.5167	0.410787
$787$	−54.2836	−1.93500	−0.967501	−	0.252866i	$-0.918627\pi$
$787$	−54.2836	−1.93500	−0.967501	+	0.252866i	$0.918627\pi$
$788$	−8.05513	−0.286952
$789$	−10.4447	−0.371842
$790$	14.1660	0.504004
$791$	−1.87426	−0.0666410
$792$	0	0
$793$	42.2438	1.50012
$794$	−15.4778	−0.549286
$795$	0.0275853	0.000978350 0
$796$	54.8154	1.94288
$797$	7.59926	0.269180	0.134590	−	0.990901i	$-0.457028\pi$
$797$	7.59926	0.269180	0.134590	+	0.990901i	$0.457028\pi$
$798$	−0.687611	−0.0243412
$799$	−0.237106	−0.00838822
$800$	6.30703	0.222987
$801$	24.3989	0.862092
$802$	0.318593	0.0112499
$803$	0	0
$804$	−6.11403	−0.215625
$805$	0.982904	0.0346428
$806$	87.4473	3.08020
$807$	−3.31052	−0.116536
$808$	3.04530	0.107133
$809$	−52.5660	−1.84812	−0.924061	−	0.382244i	$-0.875151\pi$
$809$	−52.5660	−1.84812	−0.924061	+	0.382244i	$0.875151\pi$
$810$	−8.86277	−0.311406
$811$	−26.5189	−0.931206	−0.465603	−	0.884994i	$-0.654162\pi$
$811$	−26.5189	−0.931206	−0.465603	+	0.884994i	$0.654162\pi$
$812$	−1.56594	−0.0549537
$813$	−9.83585	−0.344958
$814$	0	0
$815$	−2.08849	−0.0731566
$816$	0.240764	0.00842841
$817$	10.8151	0.378373
$818$	64.9143	2.26968
$819$	−1.63159	−0.0570122
$820$	23.3986	0.817114
$821$	30.4008	1.06100	0.530498	−	0.847686i	$-0.322005\pi$
$821$	30.4008	1.06100	0.530498	+	0.847686i	$0.322005\pi$
$822$	−14.7033	−0.512835
$823$	24.6095	0.857834	0.428917	−	0.903344i	$-0.358895\pi$
$823$	24.6095	0.857834	0.428917	+	0.903344i	$0.358895\pi$
$824$	5.84874	0.203751
$825$	0	0
$826$	−1.53254	−0.0533240
$827$	−16.0101	−0.556725	−0.278363	−	0.960476i	$-0.589792\pi$
$827$	−16.0101	−0.556725	−0.278363	+	0.960476i	$0.589792\pi$
$828$	58.8507	2.04520
$829$	−16.6462	−0.578147	−0.289073	−	0.957307i	$-0.593347\pi$
$829$	−16.6462	−0.578147	−0.289073	+	0.957307i	$0.593347\pi$
$830$	1.41443	0.0490956
$831$	24.8617	0.862444
$832$	71.6922	2.48548
$833$	3.62843	0.125718
$834$	−28.1019	−0.973090
$835$	−16.6281	−0.575439
$836$	0	0
$837$	−29.5702	−1.02210
$838$	25.0269	0.864538
$839$	2.04740	0.0706841	0.0353420	−	0.999375i	$-0.488748\pi$
$839$	2.04740	0.0706841	0.0353420	+	0.999375i	$0.488748\pi$
$840$	0.239084	0.00824917
$841$	−12.3812	−0.426938
$842$	7.68472	0.264833
$843$	22.4560	0.773425
$844$	−56.9139	−1.95906
$845$	17.1847	0.591173
$846$	2.46882	0.0848799
$847$	0	0
$848$	−0.0211500	−0.000726293 0
$849$	3.77258	0.129474
$850$	1.17300	0.0402337
$851$	69.6725	2.38834
$852$	29.5671	1.01295
$853$	35.2057	1.20542	0.602710	−	0.797960i	$-0.294088\pi$
$853$	35.2057	1.20542	0.602710	+	0.797960i	$0.294088\pi$
$854$	−2.15233	−0.0736513
$855$	7.56852	0.258838
$856$	14.3418	0.490194
$857$	−21.9827	−0.750915	−0.375458	−	0.926840i	$-0.622514\pi$
$857$	−21.9827	−0.750915	−0.375458	+	0.926840i	$0.622514\pi$
$858$	0	0
$859$	−13.4218	−0.457945	−0.228972	−	0.973433i	$-0.573537\pi$
$859$	−13.4218	−0.457945	−0.228972	+	0.973433i	$0.573537\pi$
$860$	−10.6066	−0.361684
$861$	−0.727847	−0.0248050
$862$	−30.8730	−1.05154
$863$	−16.0817	−0.547426	−0.273713	−	0.961811i	$-0.588252\pi$
$863$	−16.0817	−0.547426	−0.273713	+	0.961811i	$0.588252\pi$
$864$	−26.4575	−0.900104
$865$	19.3244	0.657050
$866$	34.8738	1.18506
$867$	−13.0074	−0.441755
$868$	−2.70772	−0.0919061
$869$	0	0
$870$	−7.15673	−0.242636
$871$	13.9435	0.472457
$872$	10.4653	0.354401
$873$	4.39552	0.148766
$874$	−56.5625	−1.91326
$875$	−0.123970	−0.00419095
$876$	−20.5281	−0.693580
$877$	−34.3403	−1.15959	−0.579794	−	0.814763i	$-0.696867\pi$
$877$	−34.3403	−1.15959	−0.579794	+	0.814763i	$0.696867\pi$
$878$	22.2874	0.752162
$879$	−3.11584	−0.105095
$880$	0	0
$881$	6.08507	0.205011	0.102506	−	0.994732i	$-0.467314\pi$
$881$	6.08507	0.205011	0.102506	+	0.994732i	$0.467314\pi$
$882$	−37.7804	−1.27213
$883$	4.65731	0.156731	0.0783654	−	0.996925i	$-0.475030\pi$
$883$	4.65731	0.156731	0.0783654	+	0.996925i	$0.475030\pi$
$884$	8.84357	0.297441
$885$	−4.25661	−0.143084
$886$	−70.6752	−2.37438
$887$	22.1457	0.743580	0.371790	−	0.928317i	$-0.378744\pi$
$887$	22.1457	0.743580	0.371790	+	0.928317i	$0.378744\pi$
$888$	16.9473	0.568714
$889$	−1.32771	−0.0445298
$890$	22.9982	0.770901
$891$	0	0
$892$	5.97722	0.200132
$893$	−1.44205	−0.0482562
$894$	−24.3801	−0.815394
$895$	−2.90097	−0.0969688
$896$	−2.08897	−0.0697876
$897$	33.8672	1.13079
$898$	28.7380	0.958998
$899$	28.7362	0.958406
$900$	−7.42262	−0.247421
$901$	−0.0184315	−0.000614044 0
$902$	0	0
$903$	0.329935	0.0109796
$904$	−37.5020	−1.24730
$905$	10.0170	0.332978
$906$	14.4827	0.481155
$907$	36.8607	1.22394	0.611970	−	0.790881i	$-0.290377\pi$
$907$	36.8607	1.22394	0.611970	+	0.790881i	$0.290377\pi$
$908$	−91.0559	−3.02180
$909$	2.94096	0.0975455
$910$	−1.53792	−0.0509815
$911$	16.6589	0.551933	0.275967	−	0.961167i	$-0.411002\pi$
$911$	16.6589	0.551933	0.275967	+	0.961167i	$0.411002\pi$
$912$	1.46429	0.0484874
$913$	0	0
$914$	−9.73549	−0.322021
$915$	−5.97807	−0.197629
$916$	−60.8303	−2.00989
$917$	0.813262	0.0268563
$918$	−4.92066	−0.162406
$919$	50.2970	1.65914	0.829572	−	0.558400i	$-0.188585\pi$
$919$	50.2970	1.65914	0.829572	+	0.558400i	$0.188585\pi$
$920$	19.6669	0.648398
$921$	−2.86515	−0.0944099
$922$	−40.0376	−1.31857
$923$	−67.4299	−2.21948
$924$	0	0
$925$	−8.78754	−0.288933
$926$	−7.74701	−0.254582
$927$	5.64834	0.185516
$928$	25.7113	0.844016
$929$	38.7533	1.27146	0.635728	−	0.771913i	$-0.280700\pi$
$929$	38.7533	1.27146	0.635728	+	0.771913i	$0.280700\pi$
$930$	−12.3750	−0.405791
$931$	22.0676	0.723236
$932$	−15.7042	−0.514407
$933$	−7.74960	−0.253711
$934$	35.3109	1.15541
$935$	0	0
$936$	−32.6463	−1.06708
$937$	−15.6727	−0.512004	−0.256002	−	0.966676i	$-0.582405\pi$
$937$	−15.6727	−0.512004	−0.256002	+	0.966676i	$0.582405\pi$
$938$	−0.710424	−0.0231962
$939$	14.6643	0.478551
$940$	1.41425	0.0461276
$941$	28.3188	0.923167	0.461583	−	0.887097i	$-0.347281\pi$
$941$	28.3188	0.923167	0.461583	+	0.887097i	$0.347281\pi$
$942$	−18.0561	−0.588299
$943$	−59.8723	−1.94971
$944$	3.26359	0.106221
$945$	0.520046	0.0169171
$946$	0	0
$947$	10.1955	0.331309	0.165654	−	0.986184i	$-0.447026\pi$
$947$	10.1955	0.331309	0.165654	+	0.986184i	$0.447026\pi$
$948$	−15.1138	−0.490874
$949$	46.8158	1.51971
$950$	7.13403	0.231458
$951$	3.02788	0.0981858
$952$	−0.159747	−0.00517744
$953$	−4.64256	−0.150387	−0.0751936	−	0.997169i	$-0.523957\pi$
$953$	−4.64256	−0.150387	−0.0751936	+	0.997169i	$0.523957\pi$
$954$	0.191915	0.00621347
$955$	−13.5645	−0.438936
$956$	−69.7268	−2.25513
$957$	0	0
$958$	−86.9496	−2.80921
$959$	−1.03828	−0.0335279
$960$	−10.1454	−0.327442
$961$	18.6889	0.602866
$962$	−109.014	−3.51477
$963$	13.8504	0.446324
$964$	85.8060	2.76363
$965$	−13.6925	−0.440777
$966$	−1.72554	−0.0555184
$967$	38.0543	1.22374	0.611872	−	0.790957i	$-0.290417\pi$
$967$	38.0543	1.22374	0.611872	+	0.790957i	$0.290417\pi$
$968$	0	0
$969$	1.27608	0.0409937
$970$	4.14318	0.133029
$971$	31.6838	1.01678	0.508391	−	0.861126i	$-0.330240\pi$
$971$	31.6838	1.01678	0.508391	+	0.861126i	$0.330240\pi$
$972$	48.4503	1.55404
$973$	−1.98444	−0.0636182
$974$	20.3684	0.652644
$975$	−4.27155	−0.136799
$976$	4.58346	0.146713
$977$	40.5180	1.29628	0.648142	−	0.761519i	$-0.275546\pi$
$977$	40.5180	1.29628	0.648142	+	0.761519i	$0.275546\pi$
$978$	3.66646	0.117241
$979$	0	0
$980$	−21.6422	−0.691335
$981$	10.1067	0.322683
$982$	−10.6819	−0.340872
$983$	−18.8379	−0.600836	−0.300418	−	0.953808i	$-0.597126\pi$
$983$	−18.8379	−0.600836	−0.300418	+	0.953808i	$0.597126\pi$
$984$	−14.5635	−0.464266
$985$	−2.59965	−0.0828317
$986$	4.78188	0.152286
$987$	−0.0439922	−0.00140029
$988$	53.7852	1.71114
$989$	27.1403	0.863011
$990$	0	0
$991$	4.63565	0.147256	0.0736281	−	0.997286i	$-0.476542\pi$
$991$	4.63565	0.147256	0.0736281	+	0.997286i	$0.476542\pi$
$992$	44.4584	1.41156
$993$	6.20141	0.196796
$994$	3.43557	0.108970
$995$	17.6907	0.560832
$996$	−1.50907	−0.0478166
$997$	−20.1940	−0.639549	−0.319775	−	0.947494i	$-0.603607\pi$
$997$	−20.1940	−0.639549	−0.319775	+	0.947494i	$0.603607\pi$
$998$	−2.58568	−0.0818482
$999$	36.8631	1.16630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.i.1.2		4
3.2	odd	2		5445.2.a.bu.1.3		4
4.3	odd	2		9680.2.a.cv.1.2		4
5.4	even	2		3025.2.a.be.1.3		4
11.2	odd	10		605.2.g.j.81.1		8
11.3	even	5		605.2.g.n.251.1		8
11.4	even	5		605.2.g.n.511.1		8
11.5	even	5		605.2.g.g.366.2		8
11.6	odd	10		605.2.g.j.366.1		8
11.7	odd	10		55.2.g.a.16.2	✓	8
11.8	odd	10		55.2.g.a.31.2	yes	8
11.9	even	5		605.2.g.g.81.2		8
11.10	odd	2		605.2.a.l.1.3		4
33.8	even	10		495.2.n.f.361.1		8
33.29	even	10		495.2.n.f.181.1		8
33.32	even	2		5445.2.a.bg.1.2		4
44.7	even	10		880.2.bo.e.401.2		8
44.19	even	10		880.2.bo.e.801.2		8
44.43	even	2		9680.2.a.cs.1.2		4
55.7	even	20		275.2.z.b.49.1		16
55.8	even	20		275.2.z.b.174.1		16
55.18	even	20		275.2.z.b.49.4		16
55.19	odd	10		275.2.h.b.251.1		8
55.29	odd	10		275.2.h.b.126.1		8
55.52	even	20		275.2.z.b.174.4		16
55.54	odd	2		3025.2.a.v.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.16.2	✓	8	11.7	odd	10
55.2.g.a.31.2	yes	8	11.8	odd	10
275.2.h.b.126.1		8	55.29	odd	10
275.2.h.b.251.1		8	55.19	odd	10
275.2.z.b.49.1		16	55.7	even	20
275.2.z.b.49.4		16	55.18	even	20
275.2.z.b.174.1		16	55.8	even	20
275.2.z.b.174.4		16	55.52	even	20
495.2.n.f.181.1		8	33.29	even	10
495.2.n.f.361.1		8	33.8	even	10
605.2.a.i.1.2		4	1.1	even	1	trivial
605.2.a.l.1.3		4	11.10	odd	2
605.2.g.g.81.2		8	11.9	even	5
605.2.g.g.366.2		8	11.5	even	5
605.2.g.j.81.1		8	11.2	odd	10
605.2.g.j.366.1		8	11.6	odd	10
605.2.g.n.251.1		8	11.3	even	5
605.2.g.n.511.1		8	11.4	even	5
880.2.bo.e.401.2		8	44.7	even	10
880.2.bo.e.801.2		8	44.19	even	10
3025.2.a.v.1.2		4	55.54	odd	2
3025.2.a.be.1.3		4	5.4	even	2
5445.2.a.bg.1.2		4	33.32	even	2
5445.2.a.bu.1.3		4	3.2	odd	2
9680.2.a.cs.1.2		4	44.43	even	2
9680.2.a.cv.1.2		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25800 q^{2} +0.777484 q^{3} +3.09855 q^{4} +1.00000 q^{5} -1.75556 q^{6} -0.123970 q^{7} -2.48051 q^{8} -2.39552 q^{9} +O(q^{10})\)	\(q-2.25800 q^{2} +0.777484 q^{3} +3.09855 q^{4} +1.00000 q^{5} -1.75556 q^{6} -0.123970 q^{7} -2.48051 q^{8} -2.39552 q^{9} -2.25800 q^{10} +2.40907 q^{12} -5.49406 q^{13} +0.279924 q^{14} +0.777484 q^{15} -0.596106 q^{16} -0.519488 q^{17} +5.40907 q^{18} -3.15945 q^{19} +3.09855 q^{20} -0.0963848 q^{21} -7.92856 q^{23} -1.92856 q^{24} +1.00000 q^{25} +12.4056 q^{26} -4.19493 q^{27} -0.384127 q^{28} +4.07662 q^{29} -1.75556 q^{30} +7.04903 q^{31} +6.30703 q^{32} +1.17300 q^{34} -0.123970 q^{35} -7.42262 q^{36} -8.78754 q^{37} +7.13403 q^{38} -4.27155 q^{39} -2.48051 q^{40} +7.55147 q^{41} +0.217636 q^{42} -3.42310 q^{43} -2.39552 q^{45} +17.9027 q^{46} +0.456423 q^{47} -0.463463 q^{48} -6.98463 q^{49} -2.25800 q^{50} -0.403894 q^{51} -17.0236 q^{52} +0.0354802 q^{53} +9.47214 q^{54} +0.307509 q^{56} -2.45642 q^{57} -9.20499 q^{58} -5.47485 q^{59} +2.40907 q^{60} -7.68899 q^{61} -15.9167 q^{62} +0.296973 q^{63} -13.0490 q^{64} -5.49406 q^{65} -2.53792 q^{67} -1.60966 q^{68} -6.16433 q^{69} +0.279924 q^{70} +12.2732 q^{71} +5.94211 q^{72} -8.52117 q^{73} +19.8422 q^{74} +0.777484 q^{75} -9.78970 q^{76} +9.64514 q^{78} -6.27371 q^{79} -0.596106 q^{80} +3.92506 q^{81} -17.0512 q^{82} -0.626410 q^{83} -0.298653 q^{84} -0.519488 q^{85} +7.72935 q^{86} +3.16951 q^{87} -10.1852 q^{89} +5.40907 q^{90} +0.681099 q^{91} -24.5670 q^{92} +5.48051 q^{93} -1.03060 q^{94} -3.15945 q^{95} +4.90362 q^{96} -1.83489 q^{97} +15.7713 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} + q^{6} - 11 q^{7} - 9 q^{8}+O(q^{10}) \) 4 * q - 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 + q^6 - 11 * q^7 - 9 * q^8	\( 4 q - 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} + q^{6} - 11 q^{7} - 9 q^{8} - 3 q^{10} - 14 q^{12} - 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} - 3 q^{17} - 2 q^{18} - 12 q^{19} + 7 q^{20} + 6 q^{21} - 9 q^{23} + 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} - 7 q^{28} + 8 q^{29} + q^{30} + 3 q^{31} - 6 q^{32} - 10 q^{34} - 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} + 3 q^{39} - 9 q^{40} + 7 q^{41} + 2 q^{42} - 21 q^{43} - 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} - 3 q^{50} - 9 q^{51} - 27 q^{52} - 11 q^{53} + 20 q^{54} + 15 q^{56} - 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} - 4 q^{61} - 11 q^{62} - 3 q^{63} - 27 q^{64} - 7 q^{65} - q^{67} + 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} - 13 q^{72} + 9 q^{73} + 36 q^{74} - 2 q^{75} - 8 q^{76} + 6 q^{78} - 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} - 15 q^{83} + 47 q^{84} - 3 q^{85} - 3 q^{86} - 15 q^{87} - 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} + 11 q^{94} - 12 q^{95} + 26 q^{96} + 6 q^{97} + 42 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 + q^6 - 11 * q^7 - 9 * q^8 - 3 * q^10 - 14 * q^12 - 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 - 3 * q^17 - 2 * q^18 - 12 * q^19 + 7 * q^20 + 6 * q^21 - 9 * q^23 + 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 - 7 * q^28 + 8 * q^29 + q^30 + 3 * q^31 - 6 * q^32 - 10 * q^34 - 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 + 3 * q^39 - 9 * q^40 + 7 * q^41 + 2 * q^42 - 21 * q^43 - 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 - 3 * q^50 - 9 * q^51 - 27 * q^52 - 11 * q^53 + 20 * q^54 + 15 * q^56 - 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 - 4 * q^61 - 11 * q^62 - 3 * q^63 - 27 * q^64 - 7 * q^65 - q^67 + 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 - 13 * q^72 + 9 * q^73 + 36 * q^74 - 2 * q^75 - 8 * q^76 + 6 * q^78 - 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 - 15 * q^83 + 47 * q^84 - 3 * q^85 - 3 * q^86 - 15 * q^87 - 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 + 11 * q^94 - 12 * q^95 + 26 * q^96 + 6 * q^97 + 42 * q^98

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