LMFDB - Embedded newform 1005.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1005,2,Mod(1,1005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1005 = 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1005.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.02496540314$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.772525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 5x^{2} + 4x - 1 $ x^5 - x^4 - 6x^3 + 5x^2 + 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.37272$ of defining polynomial
Character	$\chi$	$=$	1005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37272 q^{2} +1.00000 q^{3} +3.62978 q^{4} -1.00000 q^{5} +2.37272 q^{6} +1.95126 q^{7} +3.86701 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.37272 q^{2} +1.00000 q^{3} +3.62978 q^{4} -1.00000 q^{5} +2.37272 q^{6} +1.95126 q^{7} +3.86701 q^{8} +1.00000 q^{9} -2.37272 q^{10} +2.67852 q^{11} +3.62978 q^{12} -2.75136 q^{13} +4.62978 q^{14} -1.00000 q^{15} +1.91575 q^{16} +1.08425 q^{17} +2.37272 q^{18} +1.42146 q^{19} -3.62978 q^{20} +1.95126 q^{21} +6.35538 q^{22} -3.64551 q^{23} +3.86701 q^{24} +1.00000 q^{25} -6.52819 q^{26} +1.00000 q^{27} +7.08264 q^{28} +0.505707 q^{29} -2.37272 q^{30} -1.03551 q^{31} -3.18849 q^{32} +2.67852 q^{33} +2.57262 q^{34} -1.95126 q^{35} +3.62978 q^{36} -1.29988 q^{37} +3.37272 q^{38} -2.75136 q^{39} -3.86701 q^{40} +5.95308 q^{41} +4.62978 q^{42} -5.95376 q^{43} +9.72245 q^{44} -1.00000 q^{45} -8.64977 q^{46} -0.237227 q^{47} +1.91575 q^{48} -3.19259 q^{49} +2.37272 q^{50} +1.08425 q^{51} -9.98683 q^{52} -5.59495 q^{53} +2.37272 q^{54} -2.67852 q^{55} +7.54553 q^{56} +1.42146 q^{57} +1.19990 q^{58} +10.1397 q^{59} -3.62978 q^{60} -3.65276 q^{61} -2.45697 q^{62} +1.95126 q^{63} -11.3969 q^{64} +2.75136 q^{65} +6.35538 q^{66} -1.00000 q^{67} +3.93559 q^{68} -3.64551 q^{69} -4.62978 q^{70} -3.54371 q^{71} +3.86701 q^{72} -2.02964 q^{73} -3.08425 q^{74} +1.00000 q^{75} +5.15958 q^{76} +5.22649 q^{77} -6.52819 q^{78} -12.6282 q^{79} -1.91575 q^{80} +1.00000 q^{81} +14.1250 q^{82} +3.94715 q^{83} +7.08264 q^{84} -1.08425 q^{85} -14.1266 q^{86} +0.505707 q^{87} +10.3579 q^{88} +5.47270 q^{89} -2.37272 q^{90} -5.36861 q^{91} -13.2324 q^{92} -1.03551 q^{93} -0.562873 q^{94} -1.42146 q^{95} -3.18849 q^{96} +12.7407 q^{97} -7.57511 q^{98} +2.67852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{7} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^7 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{7} + 5 q^{9} - q^{10} + 11 q^{11} + 3 q^{12} - q^{13} + 8 q^{14} - 5 q^{15} + 3 q^{16} + 12 q^{17} + q^{18} + 9 q^{19} - 3 q^{20} - 3 q^{21} - 5 q^{22} + 4 q^{23} + 5 q^{25} + 15 q^{26} + 5 q^{27} + 9 q^{28} + 11 q^{29} - q^{30} + q^{31} + q^{32} + 11 q^{33} + 2 q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{38} - q^{39} + 19 q^{41} + 8 q^{42} + 9 q^{43} + 23 q^{44} - 5 q^{45} + 2 q^{46} + 3 q^{47} + 3 q^{48} - 6 q^{49} + q^{50} + 12 q^{51} - 30 q^{52} + 9 q^{53} + q^{54} - 11 q^{55} + 16 q^{56} + 9 q^{57} + 6 q^{58} + 21 q^{59} - 3 q^{60} - 7 q^{61} - 8 q^{62} - 3 q^{63} - 22 q^{64} + q^{65} - 5 q^{66} - 5 q^{67} + 13 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 6 q^{73} - 22 q^{74} + 5 q^{75} - 4 q^{76} - 23 q^{77} + 15 q^{78} - 15 q^{79} - 3 q^{80} + 5 q^{81} - 12 q^{82} + 9 q^{84} - 12 q^{85} - 21 q^{86} + 11 q^{87} - 11 q^{88} + 16 q^{89} - q^{90} - 9 q^{91} - 26 q^{92} + q^{93} - 7 q^{94} - 9 q^{95} + q^{96} + 5 q^{97} - q^{98} + 11 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^7 + 5 * q^9 - q^10 + 11 * q^11 + 3 * q^12 - q^13 + 8 * q^14 - 5 * q^15 + 3 * q^16 + 12 * q^17 + q^18 + 9 * q^19 - 3 * q^20 - 3 * q^21 - 5 * q^22 + 4 * q^23 + 5 * q^25 + 15 * q^26 + 5 * q^27 + 9 * q^28 + 11 * q^29 - q^30 + q^31 + q^32 + 11 * q^33 + 2 * q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 + 6 * q^38 - q^39 + 19 * q^41 + 8 * q^42 + 9 * q^43 + 23 * q^44 - 5 * q^45 + 2 * q^46 + 3 * q^47 + 3 * q^48 - 6 * q^49 + q^50 + 12 * q^51 - 30 * q^52 + 9 * q^53 + q^54 - 11 * q^55 + 16 * q^56 + 9 * q^57 + 6 * q^58 + 21 * q^59 - 3 * q^60 - 7 * q^61 - 8 * q^62 - 3 * q^63 - 22 * q^64 + q^65 - 5 * q^66 - 5 * q^67 + 13 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 6 * q^73 - 22 * q^74 + 5 * q^75 - 4 * q^76 - 23 * q^77 + 15 * q^78 - 15 * q^79 - 3 * q^80 + 5 * q^81 - 12 * q^82 + 9 * q^84 - 12 * q^85 - 21 * q^86 + 11 * q^87 - 11 * q^88 + 16 * q^89 - q^90 - 9 * q^91 - 26 * q^92 + q^93 - 7 * q^94 - 9 * q^95 + q^96 + 5 * q^97 - q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.37272	1.67776	0.838882	−	0.544314i	$-0.183210\pi$
$2$	2.37272	1.67776	0.838882	+	0.544314i	$0.183210\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.62978	1.81489
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.37272	0.968657
$7$	1.95126	0.737506	0.368753	−	0.929527i	$-0.379785\pi$
$7$	1.95126	0.737506	0.368753	+	0.929527i	$0.379785\pi$
$8$	3.86701	1.36719
$9$	1.00000	0.333333
$10$	−2.37272	−0.750319
$11$	2.67852	0.807605	0.403803	−	0.914846i	$-0.367688\pi$
$11$	2.67852	0.807605	0.403803	+	0.914846i	$0.367688\pi$
$12$	3.62978	1.04783
$13$	−2.75136	−0.763089	−0.381545	−	0.924350i	$-0.624608\pi$
$13$	−2.75136	−0.763089	−0.381545	+	0.924350i	$0.624608\pi$
$14$	4.62978	1.23736
$15$	−1.00000	−0.258199
$16$	1.91575	0.478938
$17$	1.08425	0.262969	0.131485	−	0.991318i	$-0.458026\pi$
$17$	1.08425	0.262969	0.131485	+	0.991318i	$0.458026\pi$
$18$	2.37272	0.559255
$19$	1.42146	0.326105	0.163052	−	0.986617i	$-0.447866\pi$
$19$	1.42146	0.326105	0.163052	+	0.986617i	$0.447866\pi$
$20$	−3.62978	−0.811644
$21$	1.95126	0.425799
$22$	6.35538	1.35497
$23$	−3.64551	−0.760142	−0.380071	−	0.924957i	$-0.624100\pi$
$23$	−3.64551	−0.760142	−0.380071	+	0.924957i	$0.624100\pi$
$24$	3.86701	0.789350
$25$	1.00000	0.200000
$26$	−6.52819	−1.28028
$27$	1.00000	0.192450
$28$	7.08264	1.33849
$29$	0.505707	0.0939075	0.0469538	−	0.998897i	$-0.485049\pi$
$29$	0.505707	0.0939075	0.0469538	+	0.998897i	$0.485049\pi$
$30$	−2.37272	−0.433197
$31$	−1.03551	−0.185983	−0.0929913	−	0.995667i	$-0.529643\pi$
$31$	−1.03551	−0.185983	−0.0929913	+	0.995667i	$0.529643\pi$
$32$	−3.18849	−0.563650
$33$	2.67852	0.466271
$34$	2.57262	0.441200
$35$	−1.95126	−0.329823
$36$	3.62978	0.604964
$37$	−1.29988	−0.213699	−0.106850	−	0.994275i	$-0.534076\pi$
$37$	−1.29988	−0.213699	−0.106850	+	0.994275i	$0.534076\pi$
$38$	3.37272	0.547127
$39$	−2.75136	−0.440570
$40$	−3.86701	−0.611428
$41$	5.95308	0.929715	0.464857	−	0.885386i	$-0.346106\pi$
$41$	5.95308	0.929715	0.464857	+	0.885386i	$0.346106\pi$
$42$	4.62978	0.714391
$43$	−5.95376	−0.907939	−0.453970	−	0.891017i	$-0.649993\pi$
$43$	−5.95376	−0.907939	−0.453970	+	0.891017i	$0.649993\pi$
$44$	9.72245	1.46572
$45$	−1.00000	−0.149071
$46$	−8.64977	−1.27534
$47$	−0.237227	−0.0346031	−0.0173016	−	0.999850i	$-0.505508\pi$
$47$	−0.237227	−0.0346031	−0.0173016	+	0.999850i	$0.505508\pi$
$48$	1.91575	0.276515
$49$	−3.19259	−0.456085
$50$	2.37272	0.335553
$51$	1.08425	0.151825
$52$	−9.98683	−1.38492
$53$	−5.59495	−0.768526	−0.384263	−	0.923224i	$-0.625544\pi$
$53$	−5.59495	−0.768526	−0.384263	+	0.923224i	$0.625544\pi$
$54$	2.37272	0.322886
$55$	−2.67852	−0.361172
$56$	7.54553	1.00831
$57$	1.42146	0.188277
$58$	1.19990	0.157555
$59$	10.1397	1.32008	0.660041	−	0.751230i	$-0.270539\pi$
$59$	10.1397	1.32008	0.660041	+	0.751230i	$0.270539\pi$
$60$	−3.62978	−0.468603
$61$	−3.65276	−0.467688	−0.233844	−	0.972274i	$-0.575130\pi$
$61$	−3.65276	−0.467688	−0.233844	+	0.972274i	$0.575130\pi$
$62$	−2.45697	−0.312035
$63$	1.95126	0.245835
$64$	−11.3969	−1.42461
$65$	2.75136	0.341264
$66$	6.35538	0.782293
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	3.93559	0.477260
$69$	−3.64551	−0.438868
$70$	−4.62978	−0.553365
$71$	−3.54371	−0.420561	−0.210281	−	0.977641i	$-0.567438\pi$
$71$	−3.54371	−0.420561	−0.210281	+	0.977641i	$0.567438\pi$
$72$	3.86701	0.455731
$73$	−2.02964	−0.237552	−0.118776	−	0.992921i	$-0.537897\pi$
$73$	−2.02964	−0.237552	−0.118776	+	0.992921i	$0.537897\pi$
$74$	−3.08425	−0.358537
$75$	1.00000	0.115470
$76$	5.15958	0.591845
$77$	5.22649	0.595614
$78$	−6.52819	−0.739172
$79$	−12.6282	−1.42078	−0.710390	−	0.703808i	$-0.751482\pi$
$79$	−12.6282	−1.42078	−0.710390	+	0.703808i	$0.751482\pi$
$80$	−1.91575	−0.214187
$81$	1.00000	0.111111
$82$	14.1250	1.55984
$83$	3.94715	0.433256	0.216628	−	0.976254i	$-0.430494\pi$
$83$	3.94715	0.433256	0.216628	+	0.976254i	$0.430494\pi$
$84$	7.08264	0.772779
$85$	−1.08425	−0.117603
$86$	−14.1266	−1.52331
$87$	0.505707	0.0542175
$88$	10.3579	1.10415
$89$	5.47270	0.580105	0.290052	−	0.957011i	$-0.406327\pi$
$89$	5.47270	0.580105	0.290052	+	0.957011i	$0.406327\pi$
$90$	−2.37272	−0.250106
$91$	−5.36861	−0.562783
$92$	−13.2324	−1.37957
$93$	−1.03551	−0.107377
$94$	−0.562873	−0.0580559
$95$	−1.42146	−0.145839
$96$	−3.18849	−0.325423
$97$	12.7407	1.29362	0.646810	−	0.762651i	$-0.276103\pi$
$97$	12.7407	1.29362	0.646810	+	0.762651i	$0.276103\pi$
$98$	−7.57511	−0.765202
$99$	2.67852	0.269202
$100$	3.62978	0.362978
$101$	−3.70832	−0.368991	−0.184496	−	0.982833i	$-0.559065\pi$
$101$	−3.70832	−0.368991	−0.184496	+	0.982833i	$0.559065\pi$
$102$	2.57262	0.254727
$103$	−12.2597	−1.20799	−0.603993	−	0.796990i	$-0.706424\pi$
$103$	−12.2597	−1.20799	−0.603993	+	0.796990i	$0.706424\pi$
$104$	−10.6395	−1.04329
$105$	−1.95126	−0.190423
$106$	−13.2752	−1.28940
$107$	−11.3506	−1.09730	−0.548650	−	0.836052i	$-0.684858\pi$
$107$	−11.3506	−1.09730	−0.548650	+	0.836052i	$0.684858\pi$
$108$	3.62978	0.349276
$109$	11.2067	1.07341	0.536704	−	0.843770i	$-0.319669\pi$
$109$	11.2067	1.07341	0.536704	+	0.843770i	$0.319669\pi$
$110$	−6.35538	−0.605961
$111$	−1.29988	−0.123379
$112$	3.73812	0.353219
$113$	−3.61426	−0.340001	−0.170000	−	0.985444i	$-0.554377\pi$
$113$	−3.61426	−0.340001	−0.170000	+	0.985444i	$0.554377\pi$
$114$	3.37272	0.315884
$115$	3.64551	0.339946
$116$	1.83561	0.170432
$117$	−2.75136	−0.254363
$118$	24.0587	2.21479
$119$	2.11565	0.193941
$120$	−3.86701	−0.353008
$121$	−3.82551	−0.347774
$122$	−8.66696	−0.784670
$123$	5.95308	0.536771
$124$	−3.75867	−0.337538
$125$	−1.00000	−0.0894427
$126$	4.62978	0.412454
$127$	−5.40273	−0.479415	−0.239708	−	0.970845i	$-0.577052\pi$
$127$	−5.40273	−0.479415	−0.239708	+	0.970845i	$0.577052\pi$
$128$	−20.6646	−1.82651
$129$	−5.95376	−0.524199
$130$	6.52819	0.572560
$131$	0.484487	0.0423298	0.0211649	−	0.999776i	$-0.493263\pi$
$131$	0.484487	0.0423298	0.0211649	+	0.999776i	$0.493263\pi$
$132$	9.72245	0.846231
$133$	2.77363	0.240504
$134$	−2.37272	−0.204971
$135$	−1.00000	−0.0860663
$136$	4.19280	0.359530
$137$	−0.221558	−0.0189290	−0.00946448	−	0.999955i	$-0.503013\pi$
$137$	−0.221558	−0.0189290	−0.00946448	+	0.999955i	$0.503013\pi$
$138$	−8.64977	−0.736317
$139$	5.20583	0.441552	0.220776	−	0.975324i	$-0.429141\pi$
$139$	5.20583	0.441552	0.220776	+	0.975324i	$0.429141\pi$
$140$	−7.08264	−0.598592
$141$	−0.237227	−0.0199781
$142$	−8.40822	−0.705602
$143$	−7.36958	−0.616275
$144$	1.91575	0.159646
$145$	−0.505707	−0.0419967
$146$	−4.81577	−0.398556
$147$	−3.19259	−0.263321
$148$	−4.71829	−0.387841
$149$	19.0895	1.56387	0.781935	−	0.623361i	$-0.214233\pi$
$149$	19.0895	1.56387	0.781935	+	0.623361i	$0.214233\pi$
$150$	2.37272	0.193731
$151$	−19.0521	−1.55044	−0.775218	−	0.631694i	$-0.782360\pi$
$151$	−19.0521	−1.55044	−0.775218	+	0.631694i	$0.782360\pi$
$152$	5.49679	0.445849
$153$	1.08425	0.0876564
$154$	12.4010	0.999299
$155$	1.03551	0.0831740
$156$	−9.98683	−0.799586
$157$	3.45110	0.275428	0.137714	−	0.990472i	$-0.456025\pi$
$157$	3.45110	0.275428	0.137714	+	0.990472i	$0.456025\pi$
$158$	−29.9631	−2.38373
$159$	−5.59495	−0.443709
$160$	3.18849	0.252072
$161$	−7.11334	−0.560610
$162$	2.37272	0.186418
$163$	−0.582649	−0.0456366	−0.0228183	−	0.999740i	$-0.507264\pi$
$163$	−0.582649	−0.0456366	−0.0228183	+	0.999740i	$0.507264\pi$
$164$	21.6084	1.68733
$165$	−2.67852	−0.208523
$166$	9.36547	0.726901
$167$	14.5078	1.12265	0.561323	−	0.827597i	$-0.310293\pi$
$167$	14.5078	1.12265	0.561323	+	0.827597i	$0.310293\pi$
$168$	7.54553	0.582150
$169$	−5.43003	−0.417695
$170$	−2.57262	−0.197311
$171$	1.42146	0.108702
$172$	−21.6108	−1.64781
$173$	5.56713	0.423261	0.211630	−	0.977350i	$-0.432123\pi$
$173$	5.56713	0.423261	0.211630	+	0.977350i	$0.432123\pi$
$174$	1.19990	0.0909642
$175$	1.95126	0.147501
$176$	5.13138	0.386793
$177$	10.1397	0.762150
$178$	12.9852	0.973279
$179$	−0.506596	−0.0378648	−0.0189324	−	0.999821i	$-0.506027\pi$
$179$	−0.506596	−0.0378648	−0.0189324	+	0.999821i	$0.506027\pi$
$180$	−3.62978	−0.270548
$181$	−9.49078	−0.705444	−0.352722	−	0.935728i	$-0.614744\pi$
$181$	−9.49078	−0.705444	−0.352722	+	0.935728i	$0.614744\pi$
$182$	−12.7382	−0.944217
$183$	−3.65276	−0.270020
$184$	−14.0972	−1.03926
$185$	1.29988	0.0955692
$186$	−2.45697	−0.180153
$187$	2.90419	0.212375
$188$	−0.861083	−0.0628009
$189$	1.95126	0.141933
$190$	−3.37272	−0.244683
$191$	4.35843	0.315365	0.157682	−	0.987490i	$-0.449598\pi$
$191$	4.35843	0.315365	0.157682	+	0.987490i	$0.449598\pi$
$192$	−11.3969	−0.822498
$193$	25.3768	1.82666	0.913330	−	0.407220i	$-0.133502\pi$
$193$	25.3768	1.82666	0.913330	+	0.407220i	$0.133502\pi$
$194$	30.2300	2.17039
$195$	2.75136	0.197029
$196$	−11.5884	−0.827744
$197$	9.87194	0.703347	0.351673	−	0.936123i	$-0.385613\pi$
$197$	9.87194	0.703347	0.351673	+	0.936123i	$0.385613\pi$
$198$	6.35538	0.451657
$199$	18.6656	1.32317	0.661586	−	0.749869i	$-0.269884\pi$
$199$	18.6656	1.32317	0.661586	+	0.749869i	$0.269884\pi$
$200$	3.86701	0.273439
$201$	−1.00000	−0.0705346
$202$	−8.79878	−0.619080
$203$	0.986766	0.0692574
$204$	3.93559	0.275546
$205$	−5.95308	−0.415781
$206$	−29.0888	−2.02671
$207$	−3.64551	−0.253381
$208$	−5.27092	−0.365472
$209$	3.80741	0.263364
$210$	−4.62978	−0.319485
$211$	9.79186	0.674099	0.337050	−	0.941487i	$-0.390571\pi$
$211$	9.79186	0.674099	0.337050	+	0.941487i	$0.390571\pi$
$212$	−20.3085	−1.39479
$213$	−3.54371	−0.242811
$214$	−26.9317	−1.84101
$215$	5.95376	0.406043
$216$	3.86701	0.263117
$217$	−2.02054	−0.137163
$218$	26.5904	1.80093
$219$	−2.02964	−0.137151
$220$	−9.72245	−0.655488
$221$	−2.98316	−0.200669
$222$	−3.08425	−0.207001
$223$	25.9827	1.73993	0.869964	−	0.493114i	$-0.164142\pi$
$223$	25.9827	1.73993	0.869964	+	0.493114i	$0.164142\pi$
$224$	−6.22156	−0.415695
$225$	1.00000	0.0666667
$226$	−8.57561	−0.570441
$227$	2.59070	0.171951	0.0859753	−	0.996297i	$-0.472599\pi$
$227$	2.59070	0.171951	0.0859753	+	0.996297i	$0.472599\pi$
$228$	5.15958	0.341702
$229$	11.8859	0.785443	0.392722	−	0.919657i	$-0.371534\pi$
$229$	11.8859	0.785443	0.392722	+	0.919657i	$0.371534\pi$
$230$	8.64977	0.570349
$231$	5.22649	0.343878
$232$	1.95558	0.128390
$233$	−8.22825	−0.539050	−0.269525	−	0.962993i	$-0.586867\pi$
$233$	−8.22825	−0.539050	−0.269525	+	0.962993i	$0.586867\pi$
$234$	−6.52819	−0.426761
$235$	0.237227	0.0154750
$236$	36.8051	2.39580
$237$	−12.6282	−0.820288
$238$	5.01984	0.325388
$239$	14.8231	0.958823	0.479412	−	0.877590i	$-0.340850\pi$
$239$	14.8231	0.958823	0.479412	+	0.877590i	$0.340850\pi$
$240$	−1.91575	−0.123661
$241$	−20.4686	−1.31850	−0.659248	−	0.751926i	$-0.729125\pi$
$241$	−20.4686	−1.31850	−0.659248	+	0.751926i	$0.729125\pi$
$242$	−9.07686	−0.583482
$243$	1.00000	0.0641500
$244$	−13.2587	−0.848802
$245$	3.19259	0.203967
$246$	14.1250	0.900575
$247$	−3.91094	−0.248847
$248$	−4.00432	−0.254274
$249$	3.94715	0.250141
$250$	−2.37272	−0.150064
$251$	−4.53060	−0.285969	−0.142985	−	0.989725i	$-0.545670\pi$
$251$	−4.53060	−0.285969	−0.142985	+	0.989725i	$0.545670\pi$
$252$	7.08264	0.446164
$253$	−9.76459	−0.613895
$254$	−12.8192	−0.804345
$255$	−1.08425	−0.0678983
$256$	−26.2374	−1.63984
$257$	10.3827	0.647657	0.323829	−	0.946116i	$-0.395030\pi$
$257$	10.3827	0.647657	0.323829	+	0.946116i	$0.395030\pi$
$258$	−14.1266	−0.879482
$259$	−2.53640	−0.157604
$260$	9.98683	0.619357
$261$	0.505707	0.0313025
$262$	1.14955	0.0710194
$263$	−0.218936	−0.0135001	−0.00675007	−	0.999977i	$-0.502149\pi$
$263$	−0.218936	−0.0135001	−0.00675007	+	0.999977i	$0.502149\pi$
$264$	10.3579	0.637483
$265$	5.59495	0.343695
$266$	6.58104	0.403509
$267$	5.47270	0.334924
$268$	−3.62978	−0.221724
$269$	−0.644216	−0.0392786	−0.0196393	−	0.999807i	$-0.506252\pi$
$269$	−0.644216	−0.0392786	−0.0196393	+	0.999807i	$0.506252\pi$
$270$	−2.37272	−0.144399
$271$	−3.58271	−0.217634	−0.108817	−	0.994062i	$-0.534706\pi$
$271$	−3.58271	−0.217634	−0.108817	+	0.994062i	$0.534706\pi$
$272$	2.07715	0.125946
$273$	−5.36861	−0.324923
$274$	−0.525694	−0.0317583
$275$	2.67852	0.161521
$276$	−13.2324	−0.796498
$277$	−28.9786	−1.74115	−0.870577	−	0.492032i	$-0.836254\pi$
$277$	−28.9786	−1.74115	−0.870577	+	0.492032i	$0.836254\pi$
$278$	12.3519	0.740821
$279$	−1.03551	−0.0619942
$280$	−7.54553	−0.450932
$281$	20.3499	1.21398	0.606988	−	0.794711i	$-0.292378\pi$
$281$	20.3499	1.21398	0.606988	+	0.794711i	$0.292378\pi$
$282$	−0.562873	−0.0335186
$283$	9.85606	0.585882	0.292941	−	0.956131i	$-0.405366\pi$
$283$	9.85606	0.585882	0.292941	+	0.956131i	$0.405366\pi$
$284$	−12.8629	−0.763273
$285$	−1.42146	−0.0841999
$286$	−17.4859	−1.03396
$287$	11.6160	0.685670
$288$	−3.18849	−0.187883
$289$	−15.8244	−0.930847
$290$	−1.19990	−0.0704606
$291$	12.7407	0.746872
$292$	−7.36716	−0.431131
$293$	−13.1658	−0.769155	−0.384577	−	0.923093i	$-0.625653\pi$
$293$	−13.1658	−0.769155	−0.384577	+	0.923093i	$0.625653\pi$
$294$	−7.57511	−0.441790
$295$	−10.1397	−0.590359
$296$	−5.02665	−0.292168
$297$	2.67852	0.155424
$298$	45.2939	2.62380
$299$	10.0301	0.580056
$300$	3.62978	0.209566
$301$	−11.6173	−0.669611
$302$	−45.2051	−2.60126
$303$	−3.70832	−0.213037
$304$	2.72316	0.156184
$305$	3.65276	0.209156
$306$	2.57262	0.147067
$307$	12.6254	0.720570	0.360285	−	0.932842i	$-0.382679\pi$
$307$	12.6254	0.720570	0.360285	+	0.932842i	$0.382679\pi$
$308$	18.9710	1.08097
$309$	−12.2597	−0.697431
$310$	2.45697	0.139546
$311$	26.5275	1.50423	0.752117	−	0.659029i	$-0.229033\pi$
$311$	26.5275	1.50423	0.752117	+	0.659029i	$0.229033\pi$
$312$	−10.6395	−0.602344
$313$	3.99563	0.225846	0.112923	−	0.993604i	$-0.463979\pi$
$313$	3.99563	0.225846	0.112923	+	0.993604i	$0.463979\pi$
$314$	8.18849	0.462103
$315$	−1.95126	−0.109941
$316$	−45.8375	−2.57856
$317$	17.6218	0.989736	0.494868	−	0.868968i	$-0.335216\pi$
$317$	17.6218	0.989736	0.494868	+	0.868968i	$0.335216\pi$
$318$	−13.2752	−0.744438
$319$	1.35455	0.0758402
$320$	11.3969	0.637104
$321$	−11.3506	−0.633527
$322$	−16.8779	−0.940570
$323$	1.54122	0.0857555
$324$	3.62978	0.201655
$325$	−2.75136	−0.152618
$326$	−1.38246	−0.0765674
$327$	11.2067	0.619733
$328$	23.0206	1.27110
$329$	−0.462891	−0.0255200
$330$	−6.35538	−0.349852
$331$	−6.44511	−0.354255	−0.177128	−	0.984188i	$-0.556681\pi$
$331$	−6.44511	−0.354255	−0.177128	+	0.984188i	$0.556681\pi$
$332$	14.3273	0.786313
$333$	−1.29988	−0.0712331
$334$	34.4228	1.88353
$335$	1.00000	0.0546358
$336$	3.73812	0.203931
$337$	3.60029	0.196120	0.0980600	−	0.995181i	$-0.468736\pi$
$337$	3.60029	0.196120	0.0980600	+	0.995181i	$0.468736\pi$
$338$	−12.8839	−0.700793
$339$	−3.61426	−0.196300
$340$	−3.93559	−0.213437
$341$	−2.77363	−0.150201
$342$	3.37272	0.182376
$343$	−19.8884	−1.07387
$344$	−23.0232	−1.24133
$345$	3.64551	0.196268
$346$	13.2092	0.710132
$347$	20.7501	1.11392	0.556961	−	0.830538i	$-0.311967\pi$
$347$	20.7501	1.11392	0.556961	+	0.830538i	$0.311967\pi$
$348$	1.83561	0.0983989
$349$	3.28124	0.175641	0.0878205	−	0.996136i	$-0.472010\pi$
$349$	3.28124	0.175641	0.0878205	+	0.996136i	$0.472010\pi$
$350$	4.62978	0.247472
$351$	−2.75136	−0.146857
$352$	−8.54043	−0.455207
$353$	11.7190	0.623741	0.311870	−	0.950125i	$-0.399045\pi$
$353$	11.7190	0.623741	0.311870	+	0.950125i	$0.399045\pi$
$354$	24.0587	1.27871
$355$	3.54371	0.188081
$356$	19.8647	1.05283
$357$	2.11565	0.111972
$358$	−1.20201	−0.0635281
$359$	2.93286	0.154791	0.0773953	−	0.997000i	$-0.475340\pi$
$359$	2.93286	0.154791	0.0773953	+	0.997000i	$0.475340\pi$
$360$	−3.86701	−0.203809
$361$	−16.9795	−0.893656
$362$	−22.5189	−1.18357
$363$	−3.82551	−0.200787
$364$	−19.4869	−1.02139
$365$	2.02964	0.106236
$366$	−8.66696	−0.453029
$367$	−33.5937	−1.75358	−0.876788	−	0.480878i	$-0.840318\pi$
$367$	−33.5937	−1.75358	−0.876788	+	0.480878i	$0.840318\pi$
$368$	−6.98389	−0.364061
$369$	5.95308	0.309905
$370$	3.08425	0.160342
$371$	−10.9172	−0.566793
$372$	−3.75867	−0.194878
$373$	21.7590	1.12664	0.563319	−	0.826239i	$-0.309524\pi$
$373$	21.7590	1.12664	0.563319	+	0.826239i	$0.309524\pi$
$374$	6.89081	0.356315
$375$	−1.00000	−0.0516398
$376$	−0.917359	−0.0473092
$377$	−1.39138	−0.0716598
$378$	4.62978	0.238130
$379$	33.3833	1.71479	0.857394	−	0.514661i	$-0.172082\pi$
$379$	33.3833	1.71479	0.857394	+	0.514661i	$0.172082\pi$
$380$	−5.15958	−0.264681
$381$	−5.40273	−0.276790
$382$	10.3413	0.529108
$383$	−14.0277	−0.716784	−0.358392	−	0.933571i	$-0.616675\pi$
$383$	−14.0277	−0.716784	−0.358392	+	0.933571i	$0.616675\pi$
$384$	−20.6646	−1.05453
$385$	−5.22649	−0.266367
$386$	60.2119	3.06470
$387$	−5.95376	−0.302646
$388$	46.2459	2.34778
$389$	26.9402	1.36592	0.682961	−	0.730455i	$-0.260692\pi$
$389$	26.9402	1.36592	0.682961	+	0.730455i	$0.260692\pi$
$390$	6.52819	0.330568
$391$	−3.95265	−0.199894
$392$	−12.3458	−0.623556
$393$	0.484487	0.0244391
$394$	23.4233	1.18005
$395$	12.6282	0.635392
$396$	9.72245	0.488572
$397$	−21.0908	−1.05852	−0.529258	−	0.848461i	$-0.677530\pi$
$397$	−21.0908	−1.05852	−0.529258	+	0.848461i	$0.677530\pi$
$398$	44.2883	2.21997
$399$	2.77363	0.138855
$400$	1.91575	0.0957875
$401$	12.6788	0.633150	0.316575	−	0.948567i	$-0.397467\pi$
$401$	12.6788	0.633150	0.316575	+	0.948567i	$0.397467\pi$
$402$	−2.37272	−0.118340
$403$	2.84905	0.141921
$404$	−13.4604	−0.669679
$405$	−1.00000	−0.0496904
$406$	2.34131	0.116198
$407$	−3.48176	−0.172585
$408$	4.19280	0.207575
$409$	−6.57130	−0.324930	−0.162465	−	0.986714i	$-0.551944\pi$
$409$	−6.57130	−0.324930	−0.162465	+	0.986714i	$0.551944\pi$
$410$	−14.1250	−0.697582
$411$	−0.221558	−0.0109286
$412$	−44.5001	−2.19236
$413$	19.7853	0.973569
$414$	−8.64977	−0.425113
$415$	−3.94715	−0.193758
$416$	8.77266	0.430115
$417$	5.20583	0.254930
$418$	9.03390	0.441862
$419$	4.89077	0.238930	0.119465	−	0.992838i	$-0.461882\pi$
$419$	4.89077	0.238930	0.119465	+	0.992838i	$0.461882\pi$
$420$	−7.08264	−0.345597
$421$	9.33671	0.455044	0.227522	−	0.973773i	$-0.426938\pi$
$421$	9.33671	0.455044	0.227522	+	0.973773i	$0.426938\pi$
$422$	23.2333	1.13098
$423$	−0.237227	−0.0115344
$424$	−21.6357	−1.05072
$425$	1.08425	0.0525938
$426$	−8.40822	−0.407380
$427$	−7.12748	−0.344923
$428$	−41.2001	−1.99148
$429$	−7.36958	−0.355807
$430$	14.1266	0.681244
$431$	−15.0863	−0.726682	−0.363341	−	0.931656i	$-0.618364\pi$
$431$	−15.0863	−0.726682	−0.363341	+	0.931656i	$0.618364\pi$
$432$	1.91575	0.0921716
$433$	−12.1778	−0.585228	−0.292614	−	0.956231i	$-0.594525\pi$
$433$	−12.1778	−0.585228	−0.292614	+	0.956231i	$0.594525\pi$
$434$	−4.79417	−0.230128
$435$	−0.505707	−0.0242468
$436$	40.6779	1.94812
$437$	−5.18194	−0.247886
$438$	−4.81577	−0.230106
$439$	17.9850	0.858375	0.429187	−	0.903215i	$-0.358800\pi$
$439$	17.9850	0.858375	0.429187	+	0.903215i	$0.358800\pi$
$440$	−10.3579	−0.493792
$441$	−3.19259	−0.152028
$442$	−7.07819	−0.336675
$443$	0.495493	0.0235416	0.0117708	−	0.999931i	$-0.496253\pi$
$443$	0.495493	0.0235416	0.0117708	+	0.999931i	$0.496253\pi$
$444$	−4.71829	−0.223920
$445$	−5.47270	−0.259431
$446$	61.6495	2.91919
$447$	19.0895	0.902900
$448$	−22.2382	−1.05066
$449$	−0.122811	−0.00579581	−0.00289790	−	0.999996i	$-0.500922\pi$
$449$	−0.122811	−0.00579581	−0.00289790	+	0.999996i	$0.500922\pi$
$450$	2.37272	0.111851
$451$	15.9455	0.750842
$452$	−13.1190	−0.617065
$453$	−19.0521	−0.895144
$454$	6.14699	0.288493
$455$	5.36861	0.251684
$456$	5.49679	0.257411
$457$	−30.1100	−1.40849	−0.704243	−	0.709959i	$-0.748713\pi$
$457$	−30.1100	−1.40849	−0.704243	+	0.709959i	$0.748713\pi$
$458$	28.2019	1.31779
$459$	1.08425	0.0506084
$460$	13.2324	0.616965
$461$	13.3180	0.620279	0.310140	−	0.950691i	$-0.399624\pi$
$461$	13.3180	0.620279	0.310140	+	0.950691i	$0.399624\pi$
$462$	12.4010	0.576946
$463$	−5.79215	−0.269184	−0.134592	−	0.990901i	$-0.542972\pi$
$463$	−5.79215	−0.269184	−0.134592	+	0.990901i	$0.542972\pi$
$464$	0.968809	0.0449758
$465$	1.03551	0.0480205
$466$	−19.5233	−0.904399
$467$	−10.3019	−0.476714	−0.238357	−	0.971178i	$-0.576609\pi$
$467$	−10.3019	−0.476714	−0.238357	+	0.971178i	$0.576609\pi$
$468$	−9.98683	−0.461641
$469$	−1.95126	−0.0901007
$470$	0.562873	0.0259634
$471$	3.45110	0.159018
$472$	39.2105	1.80481
$473$	−15.9473	−0.733256
$474$	−29.9631	−1.37625
$475$	1.42146	0.0652210
$476$	7.67935	0.351982
$477$	−5.59495	−0.256175
$478$	35.1709	1.60868
$479$	17.5699	0.802790	0.401395	−	0.915905i	$-0.368525\pi$
$479$	17.5699	0.802790	0.401395	+	0.915905i	$0.368525\pi$
$480$	3.18849	0.145534
$481$	3.57644	0.163072
$482$	−48.5661	−2.21212
$483$	−7.11334	−0.323668
$484$	−13.8858	−0.631172
$485$	−12.7407	−0.578525
$486$	2.37272	0.107629
$487$	−16.8404	−0.763110	−0.381555	−	0.924346i	$-0.624611\pi$
$487$	−16.8404	−0.763110	−0.381555	+	0.924346i	$0.624611\pi$
$488$	−14.1253	−0.639420
$489$	−0.582649	−0.0263483
$490$	7.57511	0.342209
$491$	19.0245	0.858566	0.429283	−	0.903170i	$-0.358766\pi$
$491$	19.0245	0.858566	0.429283	+	0.903170i	$0.358766\pi$
$492$	21.6084	0.974181
$493$	0.548313	0.0246948
$494$	−9.27955	−0.417507
$495$	−2.67852	−0.120391
$496$	−1.98377	−0.0890741
$497$	−6.91470	−0.310167
$498$	9.36547	0.419677
$499$	20.8840	0.934898	0.467449	−	0.884020i	$-0.345173\pi$
$499$	20.8840	0.934898	0.467449	+	0.884020i	$0.345173\pi$
$500$	−3.62978	−0.162329
$501$	14.5078	0.648160
$502$	−10.7498	−0.479789
$503$	−30.9759	−1.38115	−0.690574	−	0.723262i	$-0.742642\pi$
$503$	−30.9759	−1.38115	−0.690574	+	0.723262i	$0.742642\pi$
$504$	7.54553	0.336105
$505$	3.70832	0.165018
$506$	−23.1686	−1.02997
$507$	−5.43003	−0.241156
$508$	−19.6107	−0.870086
$509$	−31.7866	−1.40892	−0.704459	−	0.709745i	$-0.748810\pi$
$509$	−31.7866	−1.40892	−0.704459	+	0.709745i	$0.748810\pi$
$510$	−2.57262	−0.113917
$511$	−3.96036	−0.175196
$512$	−20.9248	−0.924754
$513$	1.42146	0.0627589
$514$	24.6353	1.08662
$515$	12.2597	0.540227
$516$	−21.6108	−0.951364
$517$	−0.635418	−0.0279457
$518$	−6.01817	−0.264423
$519$	5.56713	0.244370
$520$	10.6395	0.466574
$521$	15.0006	0.657189	0.328594	−	0.944471i	$-0.393425\pi$
$521$	15.0006	0.657189	0.328594	+	0.944471i	$0.393425\pi$
$522$	1.19990	0.0525182
$523$	−28.4077	−1.24218	−0.621092	−	0.783738i	$-0.713311\pi$
$523$	−28.4077	−1.24218	−0.621092	+	0.783738i	$0.713311\pi$
$524$	1.75858	0.0768240
$525$	1.95126	0.0851599
$526$	−0.519472	−0.0226500
$527$	−1.12275	−0.0489077
$528$	5.13138	0.223315
$529$	−9.71023	−0.422184
$530$	13.2752	0.576639
$531$	10.1397	0.440027
$532$	10.0677	0.436489
$533$	−16.3790	−0.709455
$534$	12.9852	0.561923
$535$	11.3506	0.490728
$536$	−3.86701	−0.167029
$537$	−0.506596	−0.0218612
$538$	−1.52854	−0.0659001
$539$	−8.55143	−0.368336
$540$	−3.62978	−0.156201
$541$	−26.4317	−1.13639	−0.568193	−	0.822895i	$-0.692357\pi$
$541$	−26.4317	−1.13639	−0.568193	+	0.822895i	$0.692357\pi$
$542$	−8.50076	−0.365139
$543$	−9.49078	−0.407288
$544$	−3.45711	−0.148223
$545$	−11.2067	−0.480043
$546$	−12.7382	−0.545144
$547$	1.18766	0.0507806	0.0253903	−	0.999678i	$-0.491917\pi$
$547$	1.18766	0.0507806	0.0253903	+	0.999678i	$0.491917\pi$
$548$	−0.804206	−0.0343540
$549$	−3.65276	−0.155896
$550$	6.35538	0.270994
$551$	0.718842	0.0306237
$552$	−14.0972	−0.600018
$553$	−24.6408	−1.04783
$554$	−68.7580	−2.92125
$555$	1.29988	0.0551769
$556$	18.8960	0.801369
$557$	−10.8424	−0.459409	−0.229705	−	0.973260i	$-0.573776\pi$
$557$	−10.8424	−0.459409	−0.229705	+	0.973260i	$0.573776\pi$
$558$	−2.45697	−0.104012
$559$	16.3809	0.692839
$560$	−3.73812	−0.157965
$561$	2.90419	0.122615
$562$	48.2846	2.03677
$563$	−26.3683	−1.11129	−0.555646	−	0.831419i	$-0.687529\pi$
$563$	−26.3683	−1.11129	−0.555646	+	0.831419i	$0.687529\pi$
$564$	−0.861083	−0.0362581
$565$	3.61426	0.152053
$566$	23.3856	0.982972
$567$	1.95126	0.0819451
$568$	−13.7036	−0.574989
$569$	1.23359	0.0517149	0.0258575	−	0.999666i	$-0.491768\pi$
$569$	1.23359	0.0517149	0.0258575	+	0.999666i	$0.491768\pi$
$570$	−3.37272	−0.141268
$571$	39.9629	1.67239	0.836197	−	0.548430i	$-0.184774\pi$
$571$	39.9629	1.67239	0.836197	+	0.548430i	$0.184774\pi$
$572$	−26.7500	−1.11847
$573$	4.35843	0.182076
$574$	27.5614	1.15039
$575$	−3.64551	−0.152028
$576$	−11.3969	−0.474870
$577$	−6.33542	−0.263747	−0.131873	−	0.991267i	$-0.542099\pi$
$577$	−6.33542	−0.263747	−0.131873	+	0.991267i	$0.542099\pi$
$578$	−37.5468	−1.56174
$579$	25.3768	1.05462
$580$	−1.83561	−0.0762195
$581$	7.70191	0.319529
$582$	30.2300	1.25307
$583$	−14.9862	−0.620665
$584$	−7.84865	−0.324780
$585$	2.75136	0.113755
$586$	−31.2387	−1.29046
$587$	32.6259	1.34661	0.673307	−	0.739363i	$-0.264873\pi$
$587$	32.6259	1.34661	0.673307	+	0.739363i	$0.264873\pi$
$588$	−11.5884	−0.477898
$589$	−1.47193	−0.0606498
$590$	−24.0587	−0.990482
$591$	9.87194	0.406077
$592$	−2.49025	−0.102349
$593$	−14.3168	−0.587919	−0.293959	−	0.955818i	$-0.594973\pi$
$593$	−14.3168	−0.587919	−0.293959	+	0.955818i	$0.594973\pi$
$594$	6.35538	0.260764
$595$	−2.11565	−0.0867332
$596$	69.2905	2.83825
$597$	18.6656	0.763934
$598$	23.7986	0.973197
$599$	2.19627	0.0897370	0.0448685	−	0.998993i	$-0.485713\pi$
$599$	2.19627	0.0897370	0.0448685	+	0.998993i	$0.485713\pi$
$600$	3.86701	0.157870
$601$	10.4237	0.425191	0.212595	−	0.977140i	$-0.431808\pi$
$601$	10.4237	0.425191	0.212595	+	0.977140i	$0.431808\pi$
$602$	−27.5646	−1.12345
$603$	−1.00000	−0.0407231
$604$	−69.1548	−2.81387
$605$	3.82551	0.155529
$606$	−8.79878	−0.357426
$607$	−5.62239	−0.228206	−0.114103	−	0.993469i	$-0.536399\pi$
$607$	−5.62239	−0.228206	−0.114103	+	0.993469i	$0.536399\pi$
$608$	−4.53230	−0.183809
$609$	0.986766	0.0399858
$610$	8.66696	0.350915
$611$	0.652697	0.0264053
$612$	3.93559	0.159087
$613$	−13.8504	−0.559412	−0.279706	−	0.960086i	$-0.590237\pi$
$613$	−13.8504	−0.559412	−0.279706	+	0.960086i	$0.590237\pi$
$614$	29.9565	1.20895
$615$	−5.95308	−0.240051
$616$	20.2109	0.814320
$617$	29.6146	1.19224	0.596119	−	0.802896i	$-0.296709\pi$
$617$	29.6146	1.19224	0.596119	+	0.802896i	$0.296709\pi$
$618$	−29.0888	−1.17012
$619$	18.7983	0.755568	0.377784	−	0.925894i	$-0.376686\pi$
$619$	18.7983	0.755568	0.377784	+	0.925894i	$0.376686\pi$
$620$	3.75867	0.150952
$621$	−3.64551	−0.146289
$622$	62.9422	2.52375
$623$	10.6786	0.427831
$624$	−5.27092	−0.211005
$625$	1.00000	0.0400000
$626$	9.48049	0.378916
$627$	3.80741	0.152053
$628$	12.5267	0.499872
$629$	−1.40940	−0.0561963
$630$	−4.62978	−0.184455
$631$	6.94277	0.276387	0.138194	−	0.990405i	$-0.455870\pi$
$631$	6.94277	0.276387	0.138194	+	0.990405i	$0.455870\pi$
$632$	−48.8333	−1.94248
$633$	9.79186	0.389192
$634$	41.8114	1.66054
$635$	5.40273	0.214401
$636$	−20.3085	−0.805283
$637$	8.78396	0.348033
$638$	3.21396	0.127242
$639$	−3.54371	−0.140187
$640$	20.6646	0.816839
$641$	3.01036	0.118902	0.0594511	−	0.998231i	$-0.481065\pi$
$641$	3.01036	0.118902	0.0594511	+	0.998231i	$0.481065\pi$
$642$	−26.9317	−1.06291
$643$	37.6154	1.48341	0.741704	−	0.670727i	$-0.234018\pi$
$643$	37.6154	1.48341	0.741704	+	0.670727i	$0.234018\pi$
$644$	−25.8199	−1.01745
$645$	5.95376	0.234429
$646$	3.65687	0.143877
$647$	37.6958	1.48198	0.740988	−	0.671518i	$-0.234358\pi$
$647$	37.6958	1.48198	0.740988	+	0.671518i	$0.234358\pi$
$648$	3.86701	0.151910
$649$	27.1595	1.06611
$650$	−6.52819	−0.256057
$651$	−2.02054	−0.0791913
$652$	−2.11489	−0.0828254
$653$	−44.6305	−1.74653	−0.873263	−	0.487249i	$-0.838001\pi$
$653$	−44.6305	−1.74653	−0.873263	+	0.487249i	$0.838001\pi$
$654$	26.5904	1.03977
$655$	−0.484487	−0.0189305
$656$	11.4046	0.445275
$657$	−2.02964	−0.0791840
$658$	−1.09831	−0.0428166
$659$	16.2673	0.633683	0.316841	−	0.948479i	$-0.397378\pi$
$659$	16.2673	0.633683	0.316841	+	0.948479i	$0.397378\pi$
$660$	−9.72245	−0.378446
$661$	39.7086	1.54449	0.772243	−	0.635328i	$-0.219135\pi$
$661$	39.7086	1.54449	0.772243	+	0.635328i	$0.219135\pi$
$662$	−15.2924	−0.594357
$663$	−2.98316	−0.115856
$664$	15.2637	0.592345
$665$	−2.77363	−0.107557
$666$	−3.08425	−0.119512
$667$	−1.84356	−0.0713830
$668$	52.6600	2.03748
$669$	25.9827	1.00455
$670$	2.37272	0.0916660
$671$	−9.78400	−0.377707
$672$	−6.22156	−0.240002
$673$	−36.2897	−1.39886	−0.699432	−	0.714699i	$-0.746564\pi$
$673$	−36.2897	−1.39886	−0.699432	+	0.714699i	$0.746564\pi$
$674$	8.54245	0.329043
$675$	1.00000	0.0384900
$676$	−19.7098	−0.758070
$677$	−10.0824	−0.387498	−0.193749	−	0.981051i	$-0.562065\pi$
$677$	−10.0824	−0.387498	−0.193749	+	0.981051i	$0.562065\pi$
$678$	−8.57561	−0.329344
$679$	24.8604	0.954053
$680$	−4.19280	−0.160787
$681$	2.59070	0.0992757
$682$	−6.58104	−0.252001
$683$	−50.8236	−1.94471	−0.972355	−	0.233509i	$-0.924979\pi$
$683$	−50.8236	−1.94471	−0.972355	+	0.233509i	$0.924979\pi$
$684$	5.15958	0.197282
$685$	0.221558	0.00846529
$686$	−47.1895	−1.80170
$687$	11.8859	0.453476
$688$	−11.4059	−0.434846
$689$	15.3937	0.586454
$690$	8.64977	0.329291
$691$	42.3954	1.61280	0.806399	−	0.591372i	$-0.201413\pi$
$691$	42.3954	1.61280	0.806399	+	0.591372i	$0.201413\pi$
$692$	20.2075	0.768172
$693$	5.22649	0.198538
$694$	49.2341	1.86890
$695$	−5.20583	−0.197468
$696$	1.95558	0.0741259
$697$	6.45462	0.244486
$698$	7.78546	0.294684
$699$	−8.22825	−0.311221
$700$	7.08264	0.267699
$701$	21.1944	0.800501	0.400251	−	0.916406i	$-0.368923\pi$
$701$	21.1944	0.800501	0.400251	+	0.916406i	$0.368923\pi$
$702$	−6.52819	−0.246391
$703$	−1.84773	−0.0696883
$704$	−30.5268	−1.15052
$705$	0.237227	0.00893449
$706$	27.8059	1.04649
$707$	−7.23588	−0.272133
$708$	36.8051	1.38322
$709$	0.220959	0.00829829	0.00414915	−	0.999991i	$-0.498679\pi$
$709$	0.220959	0.00829829	0.00414915	+	0.999991i	$0.498679\pi$
$710$	8.40822	0.315555
$711$	−12.6282	−0.473593
$712$	21.1630	0.793116
$713$	3.77496	0.141373
$714$	5.01984	0.187863
$715$	7.36958	0.275607
$716$	−1.83883	−0.0687204
$717$	14.8231	0.553577
$718$	6.95886	0.259702
$719$	−3.77886	−0.140928	−0.0704639	−	0.997514i	$-0.522448\pi$
$719$	−3.77886	−0.140928	−0.0704639	+	0.997514i	$0.522448\pi$
$720$	−1.91575	−0.0713958
$721$	−23.9219	−0.890897
$722$	−40.2874	−1.49934
$723$	−20.4686	−0.761234
$724$	−34.4495	−1.28030
$725$	0.505707	0.0187815
$726$	−9.07686	−0.336874
$727$	11.4854	0.425970	0.212985	−	0.977055i	$-0.431681\pi$
$727$	11.4854	0.425970	0.212985	+	0.977055i	$0.431681\pi$
$728$	−20.7605	−0.769434
$729$	1.00000	0.0370370
$730$	4.81577	0.178240
$731$	−6.45536	−0.238760
$732$	−13.2587	−0.490056
$733$	−14.7533	−0.544924	−0.272462	−	0.962167i	$-0.587838\pi$
$733$	−14.7533	−0.544924	−0.272462	+	0.962167i	$0.587838\pi$
$734$	−79.7083	−2.94209
$735$	3.19259	0.117761
$736$	11.6237	0.428454
$737$	−2.67852	−0.0986647
$738$	14.1250	0.519947
$739$	−25.1486	−0.925108	−0.462554	−	0.886591i	$-0.653067\pi$
$739$	−25.1486	−0.925108	−0.462554	+	0.886591i	$0.653067\pi$
$740$	4.71829	0.173448
$741$	−3.91094	−0.143672
$742$	−25.9034	−0.950944
$743$	−19.8349	−0.727670	−0.363835	−	0.931463i	$-0.618533\pi$
$743$	−19.8349	−0.727670	−0.363835	+	0.931463i	$0.618533\pi$
$744$	−4.00432	−0.146805
$745$	−19.0895	−0.699384
$746$	51.6279	1.89023
$747$	3.94715	0.144419
$748$	10.5416	0.385438
$749$	−22.1479	−0.809266
$750$	−2.37272	−0.0866393
$751$	46.1168	1.68283	0.841413	−	0.540392i	$-0.181724\pi$
$751$	46.1168	1.68283	0.841413	+	0.540392i	$0.181724\pi$
$752$	−0.454468	−0.0165727
$753$	−4.53060	−0.165104
$754$	−3.30135	−0.120228
$755$	19.0521	0.693376
$756$	7.08264	0.257593
$757$	36.1244	1.31297	0.656483	−	0.754341i	$-0.272044\pi$
$757$	36.1244	1.31297	0.656483	+	0.754341i	$0.272044\pi$
$758$	79.2092	2.87701
$759$	−9.76459	−0.354432
$760$	−5.49679	−0.199390
$761$	16.4280	0.595516	0.297758	−	0.954641i	$-0.403761\pi$
$761$	16.4280	0.595516	0.297758	+	0.954641i	$0.403761\pi$
$762$	−12.8192	−0.464389
$763$	21.8672	0.791646
$764$	15.8201	0.572353
$765$	−1.08425	−0.0392011
$766$	−33.2838	−1.20259
$767$	−27.8981	−1.00734
$768$	−26.2374	−0.946761
$769$	−5.66144	−0.204157	−0.102078	−	0.994776i	$-0.532549\pi$
$769$	−5.66144	−0.204157	−0.102078	+	0.994776i	$0.532549\pi$
$770$	−12.4010	−0.446900
$771$	10.3827	0.373925
$772$	92.1122	3.31519
$773$	−12.0599	−0.433765	−0.216883	−	0.976198i	$-0.569589\pi$
$773$	−12.0599	−0.433765	−0.216883	+	0.976198i	$0.569589\pi$
$774$	−14.1266	−0.507769
$775$	−1.03551	−0.0371965
$776$	49.2683	1.76863
$777$	−2.53640	−0.0909930
$778$	63.9214	2.29169
$779$	8.46205	0.303184
$780$	9.98683	0.357586
$781$	−9.49192	−0.339647
$782$	−9.37851	−0.335375
$783$	0.505707	0.0180725
$784$	−6.11621	−0.218436
$785$	−3.45110	−0.123175
$786$	1.14955	0.0410031
$787$	−25.0872	−0.894264	−0.447132	−	0.894468i	$-0.647554\pi$
$787$	−25.0872	−0.894264	−0.447132	+	0.894468i	$0.647554\pi$
$788$	35.8330	1.27650
$789$	−0.218936	−0.00779431
$790$	29.9631	1.06604
$791$	−7.05235	−0.250753
$792$	10.3579	0.368051
$793$	10.0500	0.356888
$794$	−50.0424	−1.77594
$795$	5.59495	0.198432
$796$	67.7522	2.40141
$797$	40.4715	1.43357	0.716786	−	0.697293i	$-0.245612\pi$
$797$	40.4715	1.43357	0.716786	+	0.697293i	$0.245612\pi$
$798$	6.58104	0.232966
$799$	−0.257213	−0.00909956
$800$	−3.18849	−0.112730
$801$	5.47270	0.193368
$802$	30.0833	1.06228
$803$	−5.43645	−0.191848
$804$	−3.62978	−0.128013
$805$	7.11334	0.250712
$806$	6.75999	0.238111
$807$	−0.644216	−0.0226775
$808$	−14.3401	−0.504483
$809$	−47.6668	−1.67588	−0.837938	−	0.545766i	$-0.816239\pi$
$809$	−47.6668	−1.67588	−0.837938	+	0.545766i	$0.816239\pi$
$810$	−2.37272	−0.0833687
$811$	−0.0516995	−0.00181542	−0.000907708	−	1.00000i	$-0.500289\pi$
$811$	−0.0516995	−0.00181542	−0.000907708		1.00000i	$0.500289\pi$
$812$	3.58174	0.125695
$813$	−3.58271	−0.125651
$814$	−8.26123	−0.289556
$815$	0.582649	0.0204093
$816$	2.07715	0.0727148
$817$	−8.46301	−0.296083
$818$	−15.5918	−0.545155
$819$	−5.36861	−0.187594
$820$	−21.6084	−0.754597
$821$	−8.19398	−0.285972	−0.142986	−	0.989725i	$-0.545670\pi$
$821$	−8.19398	−0.285972	−0.142986	+	0.989725i	$0.545670\pi$
$822$	−0.525694	−0.0183357
$823$	0.198532	0.00692041	0.00346020	−	0.999994i	$-0.498899\pi$
$823$	0.198532	0.00692041	0.00346020	+	0.999994i	$0.498899\pi$
$824$	−47.4084	−1.65155
$825$	2.67852	0.0932542
$826$	46.9448	1.63342
$827$	43.6483	1.51780	0.758900	−	0.651207i	$-0.225737\pi$
$827$	43.6483	1.51780	0.758900	+	0.651207i	$0.225737\pi$
$828$	−13.2324	−0.459858
$829$	−25.8047	−0.896234	−0.448117	−	0.893975i	$-0.647905\pi$
$829$	−25.8047	−0.896234	−0.448117	+	0.893975i	$0.647905\pi$
$830$	−9.36547	−0.325080
$831$	−28.9786	−1.00526
$832$	31.3569	1.08710
$833$	−3.46157	−0.119936
$834$	12.3519	0.427713
$835$	−14.5078	−0.502062
$836$	13.8201	0.477977
$837$	−1.03551	−0.0357924
$838$	11.6044	0.400868
$839$	−15.5692	−0.537510	−0.268755	−	0.963209i	$-0.586612\pi$
$839$	−15.5692	−0.537510	−0.268755	+	0.963209i	$0.586612\pi$
$840$	−7.54553	−0.260346
$841$	−28.7443	−0.991181
$842$	22.1534	0.763456
$843$	20.3499	0.700889
$844$	35.5423	1.22342
$845$	5.43003	0.186799
$846$	−0.562873	−0.0193520
$847$	−7.46456	−0.256485
$848$	−10.7185	−0.368076
$849$	9.85606	0.338259
$850$	2.57262	0.0882400
$851$	4.73873	0.162442
$852$	−12.8629	−0.440676
$853$	−57.0267	−1.95256	−0.976278	−	0.216519i	$-0.930530\pi$
$853$	−57.0267	−1.95256	−0.976278	+	0.216519i	$0.930530\pi$
$854$	−16.9115	−0.578699
$855$	−1.42146	−0.0486128
$856$	−43.8927	−1.50022
$857$	−7.15460	−0.244397	−0.122198	−	0.992506i	$-0.538994\pi$
$857$	−7.15460	−0.244397	−0.122198	+	0.992506i	$0.538994\pi$
$858$	−17.4859	−0.596959
$859$	−11.9723	−0.408490	−0.204245	−	0.978920i	$-0.565474\pi$
$859$	−11.9723	−0.408490	−0.204245	+	0.978920i	$0.565474\pi$
$860$	21.6108	0.736923
$861$	11.6160	0.395872
$862$	−35.7955	−1.21920
$863$	27.9251	0.950582	0.475291	−	0.879829i	$-0.342343\pi$
$863$	27.9251	0.950582	0.475291	+	0.879829i	$0.342343\pi$
$864$	−3.18849	−0.108474
$865$	−5.56713	−0.189288
$866$	−28.8945	−0.981875
$867$	−15.8244	−0.537425
$868$	−7.33413	−0.248937
$869$	−33.8249	−1.14743
$870$	−1.19990	−0.0406804
$871$	2.75136	0.0932262
$872$	43.3365	1.46756
$873$	12.7407	0.431207
$874$	−12.2953	−0.415894
$875$	−1.95126	−0.0659646
$876$	−7.36716	−0.248913
$877$	−8.14791	−0.275136	−0.137568	−	0.990492i	$-0.543928\pi$
$877$	−8.14791	−0.275136	−0.137568	+	0.990492i	$0.543928\pi$
$878$	42.6732	1.44015
$879$	−13.1658	−0.444072
$880$	−5.13138	−0.172979
$881$	−40.6826	−1.37063	−0.685316	−	0.728246i	$-0.740336\pi$
$881$	−40.6826	−1.37063	−0.685316	+	0.728246i	$0.740336\pi$
$882$	−7.57511	−0.255067
$883$	−10.3181	−0.347231	−0.173615	−	0.984814i	$-0.555545\pi$
$883$	−10.3181	−0.347231	−0.173615	+	0.984814i	$0.555545\pi$
$884$	−10.8282	−0.364192
$885$	−10.1397	−0.340844
$886$	1.17566	0.0394972
$887$	−2.20975	−0.0741960	−0.0370980	−	0.999312i	$-0.511811\pi$
$887$	−2.20975	−0.0741960	−0.0370980	+	0.999312i	$0.511811\pi$
$888$	−5.02665	−0.168683
$889$	−10.5421	−0.353572
$890$	−12.9852	−0.435263
$891$	2.67852	0.0897339
$892$	94.3114	3.15778
$893$	−0.337208	−0.0112842
$894$	45.2939	1.51485
$895$	0.506596	0.0169336
$896$	−40.3219	−1.34706
$897$	10.0301	0.334896
$898$	−0.291396	−0.00972400
$899$	−0.523664	−0.0174652
$900$	3.62978	0.120993
$901$	−6.06632	−0.202099
$902$	37.8340	1.25974
$903$	−11.6173	−0.386600
$904$	−13.9764	−0.464847
$905$	9.49078	0.315484
$906$	−45.2051	−1.50184
$907$	−49.9572	−1.65880	−0.829400	−	0.558655i	$-0.811318\pi$
$907$	−49.9572	−1.65880	−0.829400	+	0.558655i	$0.811318\pi$
$908$	9.40367	0.312072
$909$	−3.70832	−0.122997
$910$	12.7382	0.422267
$911$	−1.46368	−0.0484939	−0.0242470	−	0.999706i	$-0.507719\pi$
$911$	−1.46368	−0.0484939	−0.0242470	+	0.999706i	$0.507719\pi$
$912$	2.72316	0.0901728
$913$	10.5725	0.349900
$914$	−71.4424	−2.36310
$915$	3.65276	0.120756
$916$	43.1433	1.42549
$917$	0.945359	0.0312185
$918$	2.57262	0.0849090
$919$	33.6083	1.10864	0.554318	−	0.832305i	$-0.312979\pi$
$919$	33.6083	1.10864	0.554318	+	0.832305i	$0.312979\pi$
$920$	14.0972	0.464772
$921$	12.6254	0.416021
$922$	31.5997	1.04068
$923$	9.75002	0.320926
$924$	18.9710	0.624101
$925$	−1.29988	−0.0427398
$926$	−13.7431	−0.451627
$927$	−12.2597	−0.402662
$928$	−1.61244	−0.0529310
$929$	−56.2208	−1.84455	−0.922273	−	0.386539i	$-0.873670\pi$
$929$	−56.2208	−1.84455	−0.922273	+	0.386539i	$0.873670\pi$
$930$	2.45697	0.0805671
$931$	−4.53813	−0.148731
$932$	−29.8667	−0.978318
$933$	26.5275	0.868470
$934$	−24.4434	−0.799814
$935$	−2.90419	−0.0949771
$936$	−10.6395	−0.347764
$937$	6.22741	0.203441	0.101720	−	0.994813i	$-0.467565\pi$
$937$	6.22741	0.203441	0.101720	+	0.994813i	$0.467565\pi$
$938$	−4.62978	−0.151168
$939$	3.99563	0.130392
$940$	0.861083	0.0280854
$941$	48.5144	1.58152	0.790762	−	0.612124i	$-0.209685\pi$
$941$	48.5144	1.58152	0.790762	+	0.612124i	$0.209685\pi$
$942$	8.18849	0.266795
$943$	−21.7020	−0.706715
$944$	19.4252	0.632237
$945$	−1.95126	−0.0634744
$946$	−37.8384	−1.23023
$947$	−48.4503	−1.57442	−0.787211	−	0.616684i	$-0.788476\pi$
$947$	−48.4503	−1.57442	−0.787211	+	0.616684i	$0.788476\pi$
$948$	−45.8375	−1.48873
$949$	5.58428	0.181273
$950$	3.37272	0.109425
$951$	17.6218	0.571424
$952$	8.18124	0.265155
$953$	32.0576	1.03845	0.519223	−	0.854639i	$-0.326221\pi$
$953$	32.0576	1.03845	0.519223	+	0.854639i	$0.326221\pi$
$954$	−13.2752	−0.429802
$955$	−4.35843	−0.141035
$956$	53.8044	1.74016
$957$	1.35455	0.0437864
$958$	41.6884	1.34689
$959$	−0.432316	−0.0139602
$960$	11.3969	0.367832
$961$	−29.9277	−0.965410
$962$	8.48587	0.273596
$963$	−11.3506	−0.365767
$964$	−74.2964	−2.39293
$965$	−25.3768	−0.816907
$966$	−16.8779	−0.543038
$967$	−52.0257	−1.67303	−0.836516	−	0.547942i	$-0.815411\pi$
$967$	−52.0257	−1.67303	−0.836516	+	0.547942i	$0.815411\pi$
$968$	−14.7933	−0.475474
$969$	1.54122	0.0495110
$970$	−30.2300	−0.970628
$971$	1.82629	0.0586085	0.0293043	−	0.999571i	$-0.490671\pi$
$971$	1.82629	0.0586085	0.0293043	+	0.999571i	$0.490671\pi$
$972$	3.62978	0.116425
$973$	10.1579	0.325648
$974$	−39.9574	−1.28032
$975$	−2.75136	−0.0881140
$976$	−6.99778	−0.223993
$977$	−54.1568	−1.73263	−0.866314	−	0.499500i	$-0.833517\pi$
$977$	−54.1568	−1.73263	−0.866314	+	0.499500i	$0.833517\pi$
$978$	−1.38246	−0.0442062
$979$	14.6587	0.468496
$980$	11.5884	0.370178
$981$	11.2067	0.357803
$982$	45.1398	1.44047
$983$	−58.0499	−1.85150	−0.925752	−	0.378131i	$-0.876567\pi$
$983$	−58.0499	−1.85150	−0.925752	+	0.378131i	$0.876567\pi$
$984$	23.0206	0.733870
$985$	−9.87194	−0.314546
$986$	1.30099	0.0414320
$987$	−0.462891	−0.0147340
$988$	−14.1959	−0.451630
$989$	21.7045	0.690163
$990$	−6.35538	−0.201987
$991$	3.30069	0.104850	0.0524249	−	0.998625i	$-0.483305\pi$
$991$	3.30069	0.104850	0.0524249	+	0.998625i	$0.483305\pi$
$992$	3.30170	0.104829
$993$	−6.44511	−0.204530
$994$	−16.4066	−0.520386
$995$	−18.6656	−0.591741
$996$	14.3273	0.453978
$997$	54.2891	1.71935	0.859677	−	0.510838i	$-0.170665\pi$
$997$	54.2891	1.71935	0.859677	+	0.510838i	$0.170665\pi$
$998$	49.5519	1.56854
$999$	−1.29988	−0.0411264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1005.2.a.h.1.5	✓	5
3.2	odd	2		3015.2.a.j.1.1		5
5.4	even	2		5025.2.a.w.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1005.2.a.h.1.5	✓	5	1.1	even	1	trivial
3015.2.a.j.1.1		5	3.2	odd	2
5025.2.a.w.1.1		5	5.4	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:	\( N \)	\(=\)	\( 1005 = 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1005.a (trivial)

\(f(q)\)	\(=\)	\(q+2.37272 q^{2} +1.00000 q^{3} +3.62978 q^{4} -1.00000 q^{5} +2.37272 q^{6} +1.95126 q^{7} +3.86701 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.37272 q^{2} +1.00000 q^{3} +3.62978 q^{4} -1.00000 q^{5} +2.37272 q^{6} +1.95126 q^{7} +3.86701 q^{8} +1.00000 q^{9} -2.37272 q^{10} +2.67852 q^{11} +3.62978 q^{12} -2.75136 q^{13} +4.62978 q^{14} -1.00000 q^{15} +1.91575 q^{16} +1.08425 q^{17} +2.37272 q^{18} +1.42146 q^{19} -3.62978 q^{20} +1.95126 q^{21} +6.35538 q^{22} -3.64551 q^{23} +3.86701 q^{24} +1.00000 q^{25} -6.52819 q^{26} +1.00000 q^{27} +7.08264 q^{28} +0.505707 q^{29} -2.37272 q^{30} -1.03551 q^{31} -3.18849 q^{32} +2.67852 q^{33} +2.57262 q^{34} -1.95126 q^{35} +3.62978 q^{36} -1.29988 q^{37} +3.37272 q^{38} -2.75136 q^{39} -3.86701 q^{40} +5.95308 q^{41} +4.62978 q^{42} -5.95376 q^{43} +9.72245 q^{44} -1.00000 q^{45} -8.64977 q^{46} -0.237227 q^{47} +1.91575 q^{48} -3.19259 q^{49} +2.37272 q^{50} +1.08425 q^{51} -9.98683 q^{52} -5.59495 q^{53} +2.37272 q^{54} -2.67852 q^{55} +7.54553 q^{56} +1.42146 q^{57} +1.19990 q^{58} +10.1397 q^{59} -3.62978 q^{60} -3.65276 q^{61} -2.45697 q^{62} +1.95126 q^{63} -11.3969 q^{64} +2.75136 q^{65} +6.35538 q^{66} -1.00000 q^{67} +3.93559 q^{68} -3.64551 q^{69} -4.62978 q^{70} -3.54371 q^{71} +3.86701 q^{72} -2.02964 q^{73} -3.08425 q^{74} +1.00000 q^{75} +5.15958 q^{76} +5.22649 q^{77} -6.52819 q^{78} -12.6282 q^{79} -1.91575 q^{80} +1.00000 q^{81} +14.1250 q^{82} +3.94715 q^{83} +7.08264 q^{84} -1.08425 q^{85} -14.1266 q^{86} +0.505707 q^{87} +10.3579 q^{88} +5.47270 q^{89} -2.37272 q^{90} -5.36861 q^{91} -13.2324 q^{92} -1.03551 q^{93} -0.562873 q^{94} -1.42146 q^{95} -3.18849 q^{96} +12.7407 q^{97} -7.57511 q^{98} +2.67852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{7} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^7 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{7} + 5 q^{9} - q^{10} + 11 q^{11} + 3 q^{12} - q^{13} + 8 q^{14} - 5 q^{15} + 3 q^{16} + 12 q^{17} + q^{18} + 9 q^{19} - 3 q^{20} - 3 q^{21} - 5 q^{22} + 4 q^{23} + 5 q^{25} + 15 q^{26} + 5 q^{27} + 9 q^{28} + 11 q^{29} - q^{30} + q^{31} + q^{32} + 11 q^{33} + 2 q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{38} - q^{39} + 19 q^{41} + 8 q^{42} + 9 q^{43} + 23 q^{44} - 5 q^{45} + 2 q^{46} + 3 q^{47} + 3 q^{48} - 6 q^{49} + q^{50} + 12 q^{51} - 30 q^{52} + 9 q^{53} + q^{54} - 11 q^{55} + 16 q^{56} + 9 q^{57} + 6 q^{58} + 21 q^{59} - 3 q^{60} - 7 q^{61} - 8 q^{62} - 3 q^{63} - 22 q^{64} + q^{65} - 5 q^{66} - 5 q^{67} + 13 q^{68} + 4 q^{69} - 8 q^{70} + 6 q^{71} + 6 q^{73} - 22 q^{74} + 5 q^{75} - 4 q^{76} - 23 q^{77} + 15 q^{78} - 15 q^{79} - 3 q^{80} + 5 q^{81} - 12 q^{82} + 9 q^{84} - 12 q^{85} - 21 q^{86} + 11 q^{87} - 11 q^{88} + 16 q^{89} - q^{90} - 9 q^{91} - 26 q^{92} + q^{93} - 7 q^{94} - 9 q^{95} + q^{96} + 5 q^{97} - q^{98} + 11 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^7 + 5 * q^9 - q^10 + 11 * q^11 + 3 * q^12 - q^13 + 8 * q^14 - 5 * q^15 + 3 * q^16 + 12 * q^17 + q^18 + 9 * q^19 - 3 * q^20 - 3 * q^21 - 5 * q^22 + 4 * q^23 + 5 * q^25 + 15 * q^26 + 5 * q^27 + 9 * q^28 + 11 * q^29 - q^30 + q^31 + q^32 + 11 * q^33 + 2 * q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 + 6 * q^38 - q^39 + 19 * q^41 + 8 * q^42 + 9 * q^43 + 23 * q^44 - 5 * q^45 + 2 * q^46 + 3 * q^47 + 3 * q^48 - 6 * q^49 + q^50 + 12 * q^51 - 30 * q^52 + 9 * q^53 + q^54 - 11 * q^55 + 16 * q^56 + 9 * q^57 + 6 * q^58 + 21 * q^59 - 3 * q^60 - 7 * q^61 - 8 * q^62 - 3 * q^63 - 22 * q^64 + q^65 - 5 * q^66 - 5 * q^67 + 13 * q^68 + 4 * q^69 - 8 * q^70 + 6 * q^71 + 6 * q^73 - 22 * q^74 + 5 * q^75 - 4 * q^76 - 23 * q^77 + 15 * q^78 - 15 * q^79 - 3 * q^80 + 5 * q^81 - 12 * q^82 + 9 * q^84 - 12 * q^85 - 21 * q^86 + 11 * q^87 - 11 * q^88 + 16 * q^89 - q^90 - 9 * q^91 - 26 * q^92 + q^93 - 7 * q^94 - 9 * q^95 + q^96 + 5 * q^97 - q^98 + 11 * q^99

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