LMFDB - Embedded newform 1441.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83773 q^{2} -0.0182258 q^{3} +1.37726 q^{4} +1.49121 q^{5} -0.0334942 q^{6} -3.57754 q^{7} -1.14443 q^{8} -2.99967 q^{9} +O(q^{10})$	\(q+1.83773 q^{2} -0.0182258 q^{3} +1.37726 q^{4} +1.49121 q^{5} -0.0334942 q^{6} -3.57754 q^{7} -1.14443 q^{8} -2.99967 q^{9} +2.74044 q^{10} -1.00000 q^{11} -0.0251017 q^{12} -1.26798 q^{13} -6.57456 q^{14} -0.0271785 q^{15} -4.85767 q^{16} -4.58956 q^{17} -5.51259 q^{18} +3.55015 q^{19} +2.05378 q^{20} +0.0652036 q^{21} -1.83773 q^{22} -3.11470 q^{23} +0.0208581 q^{24} -2.77630 q^{25} -2.33021 q^{26} +0.109349 q^{27} -4.92721 q^{28} +5.18886 q^{29} -0.0499468 q^{30} -5.58235 q^{31} -6.63825 q^{32} +0.0182258 q^{33} -8.43438 q^{34} -5.33485 q^{35} -4.13133 q^{36} +10.2685 q^{37} +6.52423 q^{38} +0.0231100 q^{39} -1.70658 q^{40} +0.879208 q^{41} +0.119827 q^{42} -0.823570 q^{43} -1.37726 q^{44} -4.47313 q^{45} -5.72399 q^{46} +0.232773 q^{47} +0.0885351 q^{48} +5.79878 q^{49} -5.10209 q^{50} +0.0836484 q^{51} -1.74634 q^{52} -2.76986 q^{53} +0.200954 q^{54} -1.49121 q^{55} +4.09423 q^{56} -0.0647044 q^{57} +9.53574 q^{58} -1.50065 q^{59} -0.0374319 q^{60} +4.67579 q^{61} -10.2589 q^{62} +10.7314 q^{63} -2.48399 q^{64} -1.89082 q^{65} +0.0334942 q^{66} -6.86847 q^{67} -6.32102 q^{68} +0.0567679 q^{69} -9.80404 q^{70} +1.57085 q^{71} +3.43290 q^{72} +2.77266 q^{73} +18.8708 q^{74} +0.0506003 q^{75} +4.88949 q^{76} +3.57754 q^{77} +0.0424700 q^{78} -9.48090 q^{79} -7.24380 q^{80} +8.99701 q^{81} +1.61575 q^{82} +3.47830 q^{83} +0.0898024 q^{84} -6.84398 q^{85} -1.51350 q^{86} -0.0945712 q^{87} +1.14443 q^{88} -11.3872 q^{89} -8.22042 q^{90} +4.53625 q^{91} -4.28976 q^{92} +0.101743 q^{93} +0.427774 q^{94} +5.29401 q^{95} +0.120988 q^{96} +3.52175 q^{97} +10.6566 q^{98} +2.99967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.83773	1.29947	0.649737	−	0.760159i	$-0.274879\pi$
$2$	1.83773	1.29947	0.649737	+	0.760159i	$0.274879\pi$
$3$	−0.0182258	−0.0105227	−0.00526134	−	0.999986i	$-0.501675\pi$
$3$	−0.0182258	−0.0105227	−0.00526134	+	0.999986i	$0.501675\pi$
$4$	1.37726	0.688631
$5$	1.49121	0.666889	0.333444	−	0.942770i	$-0.391789\pi$
$5$	1.49121	0.666889	0.333444	+	0.942770i	$0.391789\pi$
$6$	−0.0334942	−0.0136739
$7$	−3.57754	−1.35218	−0.676091	−	0.736818i	$-0.736327\pi$
$7$	−3.57754	−1.35218	−0.676091	+	0.736818i	$0.736327\pi$
$8$	−1.14443	−0.404616
$9$	−2.99967	−0.999889
$10$	2.74044	0.866604
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.0251017	−0.00724624
$13$	−1.26798	−0.351675	−0.175837	−	0.984419i	$-0.556263\pi$
$13$	−1.26798	−0.351675	−0.175837	+	0.984419i	$0.556263\pi$
$14$	−6.57456	−1.75713
$15$	−0.0271785	−0.00701745
$16$	−4.85767	−1.21442
$17$	−4.58956	−1.11313	−0.556565	−	0.830804i	$-0.687881\pi$
$17$	−4.58956	−1.11313	−0.556565	+	0.830804i	$0.687881\pi$
$18$	−5.51259	−1.29933
$19$	3.55015	0.814460	0.407230	−	0.913326i	$-0.366495\pi$
$19$	3.55015	0.814460	0.407230	+	0.913326i	$0.366495\pi$
$20$	2.05378	0.459240
$21$	0.0652036	0.0142286
$22$	−1.83773	−0.391806
$23$	−3.11470	−0.649460	−0.324730	−	0.945807i	$-0.605273\pi$
$23$	−3.11470	−0.649460	−0.324730	+	0.945807i	$0.605273\pi$
$24$	0.0208581	0.00425764
$25$	−2.77630	−0.555260
$26$	−2.33021	−0.456992
$27$	0.109349	0.0210442
$28$	−4.92721	−0.931155
$29$	5.18886	0.963547	0.481773	−	0.876296i	$-0.339993\pi$
$29$	5.18886	0.963547	0.481773	+	0.876296i	$0.339993\pi$
$30$	−0.0499468	−0.00911900
$31$	−5.58235	−1.00262	−0.501310	−	0.865268i	$-0.667148\pi$
$31$	−5.58235	−1.00262	−0.501310	+	0.865268i	$0.667148\pi$
$32$	−6.63825	−1.17349
$33$	0.0182258	0.00317271
$34$	−8.43438	−1.44648
$35$	−5.33485	−0.901755
$36$	−4.13133	−0.688555
$37$	10.2685	1.68813	0.844066	−	0.536239i	$-0.180156\pi$
$37$	10.2685	1.68813	0.844066	+	0.536239i	$0.180156\pi$
$38$	6.52423	1.05837
$39$	0.0231100	0.00370056
$40$	−1.70658	−0.269834
$41$	0.879208	0.137309	0.0686546	−	0.997640i	$-0.478129\pi$
$41$	0.879208	0.137309	0.0686546	+	0.997640i	$0.478129\pi$
$42$	0.119827	0.0184897
$43$	−0.823570	−0.125593	−0.0627967	−	0.998026i	$-0.520002\pi$
$43$	−0.823570	−0.125593	−0.0627967	+	0.998026i	$0.520002\pi$
$44$	−1.37726	−0.207630
$45$	−4.47313	−0.666815
$46$	−5.72399	−0.843956
$47$	0.232773	0.0339534	0.0169767	−	0.999856i	$-0.494596\pi$
$47$	0.232773	0.0339534	0.0169767	+	0.999856i	$0.494596\pi$
$48$	0.0885351	0.0127789
$49$	5.79878	0.828398
$50$	−5.10209	−0.721545
$51$	0.0836484	0.0117131
$52$	−1.74634	−0.242174
$53$	−2.76986	−0.380469	−0.190235	−	0.981739i	$-0.560925\pi$
$53$	−2.76986	−0.380469	−0.190235	+	0.981739i	$0.560925\pi$
$54$	0.200954	0.0273464
$55$	−1.49121	−0.201074
$56$	4.09423	0.547114
$57$	−0.0647044	−0.00857030
$58$	9.53574	1.25210
$59$	−1.50065	−0.195368	−0.0976840	−	0.995217i	$-0.531143\pi$
$59$	−1.50065	−0.195368	−0.0976840	+	0.995217i	$0.531143\pi$
$60$	−0.0374319	−0.00483244
$61$	4.67579	0.598674	0.299337	−	0.954148i	$-0.403235\pi$
$61$	4.67579	0.598674	0.299337	+	0.954148i	$0.403235\pi$
$62$	−10.2589	−1.30288
$63$	10.7314	1.35203
$64$	−2.48399	−0.310499
$65$	−1.89082	−0.234528
$66$	0.0334942	0.00412285
$67$	−6.86847	−0.839117	−0.419558	−	0.907728i	$-0.637815\pi$
$67$	−6.86847	−0.839117	−0.419558	+	0.907728i	$0.637815\pi$
$68$	−6.32102	−0.766536
$69$	0.0567679	0.00683406
$70$	−9.80404	−1.17181
$71$	1.57085	0.186426	0.0932131	−	0.995646i	$-0.470286\pi$
$71$	1.57085	0.186426	0.0932131	+	0.995646i	$0.470286\pi$
$72$	3.43290	0.404571
$73$	2.77266	0.324515	0.162257	−	0.986748i	$-0.448122\pi$
$73$	2.77266	0.324515	0.162257	+	0.986748i	$0.448122\pi$
$74$	18.8708	2.19368
$75$	0.0506003	0.00584282
$76$	4.88949	0.560863
$77$	3.57754	0.407698
$78$	0.0424700	0.00480878
$79$	−9.48090	−1.06668	−0.533342	−	0.845900i	$-0.679064\pi$
$79$	−9.48090	−1.06668	−0.533342	+	0.845900i	$0.679064\pi$
$80$	−7.24380	−0.809882
$81$	8.99701	0.999668
$82$	1.61575	0.178430
$83$	3.47830	0.381794	0.190897	−	0.981610i	$-0.438860\pi$
$83$	3.47830	0.381794	0.190897	+	0.981610i	$0.438860\pi$
$84$	0.0898024	0.00979824
$85$	−6.84398	−0.742334
$86$	−1.51350	−0.163205
$87$	−0.0945712	−0.0101391
$88$	1.14443	0.121996
$89$	−11.3872	−1.20704	−0.603518	−	0.797349i	$-0.706235\pi$
$89$	−11.3872	−1.20704	−0.603518	+	0.797349i	$0.706235\pi$
$90$	−8.22042	−0.866508
$91$	4.53625	0.475528
$92$	−4.28976	−0.447238
$93$	0.101743	0.0105502
$94$	0.427774	0.0441216
$95$	5.29401	0.543154
$96$	0.120988	0.0123482
$97$	3.52175	0.357579	0.178790	−	0.983887i	$-0.442782\pi$
$97$	3.52175	0.357579	0.178790	+	0.983887i	$0.442782\pi$
$98$	10.6566	1.07648
$99$	2.99967	0.301478
$100$	−3.82369	−0.382369
$101$	−13.2580	−1.31922	−0.659610	−	0.751608i	$-0.729278\pi$
$101$	−13.2580	−1.31922	−0.659610	+	0.751608i	$0.729278\pi$
$102$	0.153723	0.0152209
$103$	10.6634	1.05070	0.525349	−	0.850887i	$-0.323935\pi$
$103$	10.6634	1.05070	0.525349	+	0.850887i	$0.323935\pi$
$104$	1.45111	0.142293
$105$	0.0972321	0.00948888
$106$	−5.09026	−0.494410
$107$	−8.26534	−0.799041	−0.399520	−	0.916724i	$-0.630823\pi$
$107$	−8.26534	−0.799041	−0.399520	+	0.916724i	$0.630823\pi$
$108$	0.150602	0.0144917
$109$	−6.51124	−0.623663	−0.311832	−	0.950137i	$-0.600943\pi$
$109$	−6.51124	−0.623663	−0.311832	+	0.950137i	$0.600943\pi$
$110$	−2.74044	−0.261291
$111$	−0.187152	−0.0177637
$112$	17.3785	1.64212
$113$	−0.171830	−0.0161644	−0.00808222	−	0.999967i	$-0.502573\pi$
$113$	−0.171830	−0.0161644	−0.00808222	+	0.999967i	$0.502573\pi$
$114$	−0.118909	−0.0111369
$115$	−4.64467	−0.433117
$116$	7.14642	0.663528
$117$	3.80352	0.351636
$118$	−2.75779	−0.253876
$119$	16.4193	1.50516
$120$	0.0311038	0.00283937
$121$	1.00000	0.0909091
$122$	8.59285	0.777961
$123$	−0.0160243	−0.00144486
$124$	−7.68835	−0.690435
$125$	−11.5961	−1.03718
$126$	19.7215	1.75693
$127$	10.4674	0.928832	0.464416	−	0.885617i	$-0.346264\pi$
$127$	10.4674	0.928832	0.464416	+	0.885617i	$0.346264\pi$
$128$	8.71160	0.770004
$129$	0.0150102	0.00132158
$130$	−3.47483	−0.304763
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	0.0251017	0.00218482
$133$	−12.7008	−1.10130
$134$	−12.6224	−1.09041
$135$	0.163062	0.0140341
$136$	5.25241	0.450390
$137$	17.8689	1.52664	0.763322	−	0.646018i	$-0.223567\pi$
$137$	17.8689	1.52664	0.763322	+	0.646018i	$0.223567\pi$
$138$	0.104324	0.00888068
$139$	−19.5652	−1.65950	−0.829751	−	0.558133i	$-0.811518\pi$
$139$	−19.5652	−1.65950	−0.829751	+	0.558133i	$0.811518\pi$
$140$	−7.34749	−0.620977
$141$	−0.00424248	−0.000357281 0
$142$	2.88681	0.242256
$143$	1.26798	0.106034
$144$	14.5714	1.21428
$145$	7.73767	0.642578
$146$	5.09540	0.421699
$147$	−0.105688	−0.00871696
$148$	14.1424	1.16250
$149$	12.1407	0.994608	0.497304	−	0.867576i	$-0.334323\pi$
$149$	12.1407	0.994608	0.497304	+	0.867576i	$0.334323\pi$
$150$	0.0929898	0.00759259
$151$	20.6099	1.67721	0.838607	−	0.544737i	$-0.183371\pi$
$151$	20.6099	1.67721	0.838607	+	0.544737i	$0.183371\pi$
$152$	−4.06288	−0.329543
$153$	13.7671	1.11301
$154$	6.57456	0.529793
$155$	−8.32444	−0.668635
$156$	0.0318285	0.00254832
$157$	−19.7760	−1.57830	−0.789150	−	0.614201i	$-0.789479\pi$
$157$	−19.7760	−1.57830	−0.789150	+	0.614201i	$0.789479\pi$
$158$	−17.4234	−1.38613
$159$	0.0504829	0.00400356
$160$	−9.89902	−0.782586
$161$	11.1430	0.878188
$162$	16.5341	1.29904
$163$	−7.45866	−0.584208	−0.292104	−	0.956387i	$-0.594355\pi$
$163$	−7.45866	−0.584208	−0.292104	+	0.956387i	$0.594355\pi$
$164$	1.21090	0.0945554
$165$	0.0271785	0.00211584
$166$	6.39220	0.496131
$167$	−11.7277	−0.907517	−0.453759	−	0.891125i	$-0.649917\pi$
$167$	−11.7277	−0.907517	−0.453759	+	0.891125i	$0.649917\pi$
$168$	−0.0746206	−0.00575711
$169$	−11.3922	−0.876325
$170$	−12.5774	−0.964644
$171$	−10.6493	−0.814370
$172$	−1.13427	−0.0864874
$173$	14.3954	1.09446	0.547232	−	0.836981i	$-0.315682\pi$
$173$	14.3954	1.09446	0.547232	+	0.836981i	$0.315682\pi$
$174$	−0.173797	−0.0131755
$175$	9.93231	0.750812
$176$	4.85767	0.366161
$177$	0.0273506	0.00205579
$178$	−20.9266	−1.56851
$179$	−15.5880	−1.16510	−0.582549	−	0.812796i	$-0.697945\pi$
$179$	−15.5880	−1.16510	−0.582549	+	0.812796i	$0.697945\pi$
$180$	−6.16067	−0.459189
$181$	−26.4123	−1.96321	−0.981604	−	0.190926i	$-0.938851\pi$
$181$	−26.4123	−1.96321	−0.981604	+	0.190926i	$0.938851\pi$
$182$	8.33642	0.617936
$183$	−0.0852201	−0.00629965
$184$	3.56454	0.262782
$185$	15.3125	1.12580
$186$	0.186976	0.0137098
$187$	4.58956	0.335622
$188$	0.320589	0.0233814
$189$	−0.391200	−0.0284556
$190$	9.72898	0.705814
$191$	−16.6390	−1.20395	−0.601977	−	0.798514i	$-0.705620\pi$
$191$	−16.6390	−1.20395	−0.601977	+	0.798514i	$0.705620\pi$
$192$	0.0452727	0.00326728
$193$	−22.8907	−1.64771	−0.823853	−	0.566804i	$-0.808180\pi$
$193$	−22.8907	−1.64771	−0.823853	+	0.566804i	$0.808180\pi$
$194$	6.47203	0.464665
$195$	0.0344618	0.00246786
$196$	7.98644	0.570460
$197$	−5.27453	−0.375795	−0.187897	−	0.982189i	$-0.560167\pi$
$197$	−5.27453	−0.375795	−0.187897	+	0.982189i	$0.560167\pi$
$198$	5.51259	0.391763
$199$	−13.7827	−0.977028	−0.488514	−	0.872556i	$-0.662461\pi$
$199$	−13.7827	−0.977028	−0.488514	+	0.872556i	$0.662461\pi$
$200$	3.17727	0.224667
$201$	0.125183	0.00882975
$202$	−24.3647	−1.71429
$203$	−18.5633	−1.30289
$204$	0.115206	0.00806602
$205$	1.31108	0.0915700
$206$	19.5965	1.36535
$207$	9.34307	0.649388
$208$	6.15944	0.427080
$209$	−3.55015	−0.245569
$210$	0.178687	0.0123305
$211$	−6.28007	−0.432338	−0.216169	−	0.976356i	$-0.569356\pi$
$211$	−6.28007	−0.432338	−0.216169	+	0.976356i	$0.569356\pi$
$212$	−3.81482	−0.262003
$213$	−0.0286301	−0.00196170
$214$	−15.1895	−1.03833
$215$	−1.22811	−0.0837567
$216$	−0.125142	−0.00851481
$217$	19.9711	1.35572
$218$	−11.9659	−0.810434
$219$	−0.0505339	−0.00341477
$220$	−2.05378	−0.138466
$221$	5.81947	0.391460
$222$	−0.343935	−0.0230834
$223$	3.15020	0.210953	0.105477	−	0.994422i	$-0.466363\pi$
$223$	3.15020	0.210953	0.105477	+	0.994422i	$0.466363\pi$
$224$	23.7486	1.58677
$225$	8.32797	0.555198
$226$	−0.315778	−0.0210053
$227$	14.6514	0.972445	0.486223	−	0.873835i	$-0.338374\pi$
$227$	14.6514	0.972445	0.486223	+	0.873835i	$0.338374\pi$
$228$	−0.0891149	−0.00590178
$229$	20.9777	1.38625	0.693123	−	0.720819i	$-0.256234\pi$
$229$	20.9777	1.38625	0.693123	+	0.720819i	$0.256234\pi$
$230$	−8.53566	−0.562824
$231$	−0.0652036	−0.00429008
$232$	−5.93826	−0.389866
$233$	24.7513	1.62151	0.810757	−	0.585383i	$-0.199056\pi$
$233$	24.7513	1.62151	0.810757	+	0.585383i	$0.199056\pi$
$234$	6.98986	0.456941
$235$	0.347113	0.0226431
$236$	−2.06679	−0.134536
$237$	0.172797	0.0112244
$238$	30.1743	1.95591
$239$	1.92746	0.124677	0.0623385	−	0.998055i	$-0.480144\pi$
$239$	1.92746	0.124677	0.0623385	+	0.998055i	$0.480144\pi$
$240$	0.132024	0.00852213
$241$	−13.2651	−0.854479	−0.427239	−	0.904139i	$-0.640514\pi$
$241$	−13.2651	−0.854479	−0.427239	+	0.904139i	$0.640514\pi$
$242$	1.83773	0.118134
$243$	−0.492024	−0.0315634
$244$	6.43979	0.412265
$245$	8.64719	0.552449
$246$	−0.0294484	−0.00187756
$247$	−4.50152	−0.286425
$248$	6.38858	0.405675
$249$	−0.0633949	−0.00401749
$250$	−21.3105	−1.34779
$251$	−3.02268	−0.190790	−0.0953948	−	0.995440i	$-0.530411\pi$
$251$	−3.02268	−0.190790	−0.0953948	+	0.995440i	$0.530411\pi$
$252$	14.7800	0.931052
$253$	3.11470	0.195820
$254$	19.2363	1.20699
$255$	0.124737	0.00781135
$256$	20.9776	1.31110
$257$	9.72955	0.606913	0.303456	−	0.952845i	$-0.401859\pi$
$257$	9.72955	0.606913	0.303456	+	0.952845i	$0.401859\pi$
$258$	0.0275848	0.00171736
$259$	−36.7360	−2.28266
$260$	−2.60416	−0.161503
$261$	−15.5649	−0.963440
$262$	−1.83773	−0.113536
$263$	−19.0214	−1.17291	−0.586454	−	0.809983i	$-0.699476\pi$
$263$	−19.0214	−1.17291	−0.586454	+	0.809983i	$0.699476\pi$
$264$	−0.0208581	−0.00128373
$265$	−4.13043	−0.253731
$266$	−23.3407	−1.43111
$267$	0.207540	0.0127013
$268$	−9.45968	−0.577842
$269$	1.21572	0.0741236	0.0370618	−	0.999313i	$-0.488200\pi$
$269$	1.21572	0.0741236	0.0370618	+	0.999313i	$0.488200\pi$
$270$	0.299664	0.0182370
$271$	−5.59463	−0.339850	−0.169925	−	0.985457i	$-0.554353\pi$
$271$	−5.59463	−0.339850	−0.169925	+	0.985457i	$0.554353\pi$
$272$	22.2946	1.35181
$273$	−0.0826769	−0.00500383
$274$	32.8383	1.98383
$275$	2.77630	0.167417
$276$	0.0781843	0.00470614
$277$	18.0011	1.08158	0.540791	−	0.841157i	$-0.318125\pi$
$277$	18.0011	1.08158	0.540791	+	0.841157i	$0.318125\pi$
$278$	−35.9557	−2.15648
$279$	16.7452	1.00251
$280$	6.10535	0.364864
$281$	21.0667	1.25674	0.628368	−	0.777916i	$-0.283723\pi$
$281$	21.0667	1.25674	0.628368	+	0.777916i	$0.283723\pi$
$282$	−0.00779654	−0.000464277 0
$283$	11.2307	0.667594	0.333797	−	0.942645i	$-0.391670\pi$
$283$	11.2307	0.667594	0.333797	+	0.942645i	$0.391670\pi$
$284$	2.16348	0.128379
$285$	−0.0964877	−0.00571544
$286$	2.33021	0.137788
$287$	−3.14540	−0.185667
$288$	19.9126	1.17336
$289$	4.06403	0.239060
$290$	14.2198	0.835013
$291$	−0.0641867	−0.00376269
$292$	3.81868	0.223471
$293$	30.8664	1.80324	0.901618	−	0.432532i	$-0.142380\pi$
$293$	30.8664	1.80324	0.901618	+	0.432532i	$0.142380\pi$
$294$	−0.194225	−0.0113275
$295$	−2.23778	−0.130289
$296$	−11.7515	−0.683045
$297$	−0.109349	−0.00634506
$298$	22.3114	1.29247
$299$	3.94938	0.228399
$300$	0.0696899	0.00402355
$301$	2.94635	0.169825
$302$	37.8756	2.17949
$303$	0.241638	0.0138817
$304$	−17.2455	−0.989095
$305$	6.97258	0.399249
$306$	25.3003	1.44632
$307$	1.52703	0.0871521	0.0435761	−	0.999050i	$-0.486125\pi$
$307$	1.52703	0.0871521	0.0435761	+	0.999050i	$0.486125\pi$
$308$	4.92721	0.280754
$309$	−0.194350	−0.0110562
$310$	−15.2981	−0.868874
$311$	28.3783	1.60918	0.804592	−	0.593829i	$-0.202384\pi$
$311$	28.3783	1.60918	0.804592	+	0.593829i	$0.202384\pi$
$312$	−0.0264477	−0.00149730
$313$	6.43125	0.363516	0.181758	−	0.983343i	$-0.441821\pi$
$313$	6.43125	0.363516	0.181758	+	0.983343i	$0.441821\pi$
$314$	−36.3431	−2.05096
$315$	16.0028	0.901655
$316$	−13.0577	−0.734552
$317$	6.29619	0.353629	0.176815	−	0.984244i	$-0.443421\pi$
$317$	6.29619	0.353629	0.176815	+	0.984244i	$0.443421\pi$
$318$	0.0927741	0.00520251
$319$	−5.18886	−0.290520
$320$	−3.70415	−0.207068
$321$	0.150643	0.00840805
$322$	20.4778	1.14118
$323$	−16.2936	−0.906601
$324$	12.3912	0.688402
$325$	3.52029	0.195271
$326$	−13.7070	−0.759162
$327$	0.118673	0.00656261
$328$	−1.00619	−0.0555575
$329$	−0.832754	−0.0459112
$330$	0.0499468	0.00274948
$331$	−1.59392	−0.0876098	−0.0438049	−	0.999040i	$-0.513948\pi$
$331$	−1.59392	−0.0876098	−0.0438049	+	0.999040i	$0.513948\pi$
$332$	4.79054	0.262915
$333$	−30.8021	−1.68795
$334$	−21.5524	−1.17929
$335$	−10.2423	−0.559597
$336$	−0.316738	−0.0172795
$337$	23.5506	1.28288	0.641440	−	0.767173i	$-0.278337\pi$
$337$	23.5506	1.28288	0.641440	+	0.767173i	$0.278337\pi$
$338$	−20.9359	−1.13876
$339$	0.00313175	0.000170093 0
$340$	−9.42596	−0.511194
$341$	5.58235	0.302301
$342$	−19.5705	−1.05825
$343$	4.29740	0.232038
$344$	0.942515	0.0508170
$345$	0.0846528	0.00455755
$346$	26.4549	1.42223
$347$	9.11703	0.489428	0.244714	−	0.969595i	$-0.421306\pi$
$347$	9.11703	0.489428	0.244714	+	0.969595i	$0.421306\pi$
$348$	−0.130249	−0.00698209
$349$	16.7880	0.898642	0.449321	−	0.893370i	$-0.351666\pi$
$349$	16.7880	0.898642	0.449321	+	0.893370i	$0.351666\pi$
$350$	18.2529	0.975661
$351$	−0.138652	−0.00740071
$352$	6.63825	0.353820
$353$	−21.6887	−1.15437	−0.577186	−	0.816612i	$-0.695849\pi$
$353$	−21.6887	−1.15437	−0.577186	+	0.816612i	$0.695849\pi$
$354$	0.0502630	0.00267145
$355$	2.34247	0.124325
$356$	−15.6831	−0.831203
$357$	−0.299255	−0.0158383
$358$	−28.6465	−1.51401
$359$	−26.8914	−1.41927	−0.709636	−	0.704569i	$-0.751140\pi$
$359$	−26.8914	−1.41927	−0.709636	+	0.704569i	$0.751140\pi$
$360$	5.11917	0.269804
$361$	−6.39644	−0.336655
$362$	−48.5387	−2.55114
$363$	−0.0182258	−0.000956607 0
$364$	6.24761	0.327464
$365$	4.13461	0.216415
$366$	−0.156612	−0.00818623
$367$	−16.1821	−0.844697	−0.422349	−	0.906433i	$-0.638794\pi$
$367$	−16.1821	−0.844697	−0.422349	+	0.906433i	$0.638794\pi$
$368$	15.1302	0.788716
$369$	−2.63733	−0.137294
$370$	28.1402	1.46294
$371$	9.90927	0.514464
$372$	0.140127	0.00726522
$373$	9.45912	0.489775	0.244887	−	0.969552i	$-0.421249\pi$
$373$	9.45912	0.489775	0.244887	+	0.969552i	$0.421249\pi$
$374$	8.43438	0.436131
$375$	0.211348	0.0109140
$376$	−0.266391	−0.0137381
$377$	−6.57937	−0.338855
$378$	−0.718920	−0.0369773
$379$	−18.0593	−0.927645	−0.463822	−	0.885928i	$-0.653522\pi$
$379$	−18.0593	−0.927645	−0.463822	+	0.885928i	$0.653522\pi$
$380$	7.29124	0.374033
$381$	−0.190777	−0.00977380
$382$	−30.5780	−1.56451
$383$	−16.4271	−0.839388	−0.419694	−	0.907666i	$-0.637863\pi$
$383$	−16.4271	−0.839388	−0.419694	+	0.907666i	$0.637863\pi$
$384$	−0.158776	−0.00810250
$385$	5.33485	0.271889
$386$	−42.0669	−2.14115
$387$	2.47044	0.125579
$388$	4.85037	0.246240
$389$	−19.9608	−1.01205	−0.506026	−	0.862518i	$-0.668886\pi$
$389$	−19.9608	−1.01205	−0.506026	+	0.862518i	$0.668886\pi$
$390$	0.0633316	0.00320692
$391$	14.2951	0.722934
$392$	−6.63628	−0.335183
$393$	0.0182258	0.000919371 0
$394$	−9.69318	−0.488336
$395$	−14.1380	−0.711360
$396$	4.13133	0.207607
$397$	−21.9444	−1.10136	−0.550679	−	0.834717i	$-0.685631\pi$
$397$	−21.9444	−1.10136	−0.550679	+	0.834717i	$0.685631\pi$
$398$	−25.3289	−1.26962
$399$	0.231482	0.0115886
$400$	13.4863	0.674317
$401$	13.3119	0.664763	0.332381	−	0.943145i	$-0.392148\pi$
$401$	13.3119	0.664763	0.332381	+	0.943145i	$0.392148\pi$
$402$	0.230054	0.0114740
$403$	7.07831	0.352596
$404$	−18.2597	−0.908456
$405$	13.4164	0.666667
$406$	−34.1145	−1.69307
$407$	−10.2685	−0.508991
$408$	−0.0957294	−0.00473931
$409$	20.4919	1.01326	0.506629	−	0.862164i	$-0.330892\pi$
$409$	20.4919	1.01326	0.506629	+	0.862164i	$0.330892\pi$
$410$	2.40942	0.118993
$411$	−0.325675	−0.0160644
$412$	14.6863	0.723543
$413$	5.36863	0.264173
$414$	17.1701	0.843862
$415$	5.18688	0.254614
$416$	8.41718	0.412686
$417$	0.356593	0.0174624
$418$	−6.52423	−0.319110
$419$	−37.4876	−1.83139	−0.915694	−	0.401875i	$-0.868359\pi$
$419$	−37.4876	−1.83139	−0.915694	+	0.401875i	$0.868359\pi$
$420$	0.133914	0.00653434
$421$	33.7783	1.64625	0.823127	−	0.567857i	$-0.192227\pi$
$421$	33.7783	1.64625	0.823127	+	0.567857i	$0.192227\pi$
$422$	−11.5411	−0.561812
$423$	−0.698241	−0.0339497
$424$	3.16990	0.153944
$425$	12.7420	0.618077
$426$	−0.0526145	−0.00254918
$427$	−16.7278	−0.809516
$428$	−11.3835	−0.550244
$429$	−0.0231100	−0.00111576
$430$	−2.25695	−0.108840
$431$	−29.6131	−1.42641	−0.713206	−	0.700955i	$-0.752758\pi$
$431$	−29.6131	−1.42641	−0.713206	+	0.700955i	$0.752758\pi$
$432$	−0.531181	−0.0255565
$433$	8.47070	0.407076	0.203538	−	0.979067i	$-0.434756\pi$
$433$	8.47070	0.407076	0.203538	+	0.979067i	$0.434756\pi$
$434$	36.7015	1.76173
$435$	−0.141025	−0.00676165
$436$	−8.96768	−0.429474
$437$	−11.0577	−0.528959
$438$	−0.0928679	−0.00443740
$439$	−9.93599	−0.474219	−0.237110	−	0.971483i	$-0.576200\pi$
$439$	−9.93599	−0.474219	−0.237110	+	0.971483i	$0.576200\pi$
$440$	1.70658	0.0813579
$441$	−17.3944	−0.828306
$442$	10.6946	0.508692
$443$	−13.2908	−0.631467	−0.315734	−	0.948848i	$-0.602251\pi$
$443$	−13.2908	−0.631467	−0.315734	+	0.948848i	$0.602251\pi$
$444$	−0.257757	−0.0122326
$445$	−16.9806	−0.804959
$446$	5.78923	0.274128
$447$	−0.221275	−0.0104659
$448$	8.88657	0.419851
$449$	17.7446	0.837418	0.418709	−	0.908120i	$-0.362483\pi$
$449$	17.7446	0.837418	0.418709	+	0.908120i	$0.362483\pi$
$450$	15.3046	0.721465
$451$	−0.879208	−0.0414003
$452$	−0.236655	−0.0111313
$453$	−0.375633	−0.0176488
$454$	26.9253	1.26367
$455$	6.76449	0.317124
$456$	0.0740494	0.00346768
$457$	−11.3996	−0.533252	−0.266626	−	0.963800i	$-0.585909\pi$
$457$	−11.3996	−0.533252	−0.266626	+	0.963800i	$0.585909\pi$
$458$	38.5514	1.80139
$459$	−0.501863	−0.0234249
$460$	−6.39692	−0.298258
$461$	−10.0996	−0.470384	−0.235192	−	0.971949i	$-0.575572\pi$
$461$	−10.0996	−0.470384	−0.235192	+	0.971949i	$0.575572\pi$
$462$	−0.119827	−0.00557484
$463$	−7.51056	−0.349045	−0.174523	−	0.984653i	$-0.555838\pi$
$463$	−7.51056	−0.349045	−0.174523	+	0.984653i	$0.555838\pi$
$464$	−25.2058	−1.17015
$465$	0.151720	0.00703583
$466$	45.4864	2.10711
$467$	20.8541	0.965013	0.482507	−	0.875892i	$-0.339726\pi$
$467$	20.8541	0.965013	0.482507	+	0.875892i	$0.339726\pi$
$468$	5.23845	0.242147
$469$	24.5722	1.13464
$470$	0.637901	0.0294242
$471$	0.360434	0.0166079
$472$	1.71738	0.0790490
$473$	0.823570	0.0378678
$474$	0.317555	0.0145858
$475$	−9.85627	−0.452237
$476$	22.6137	1.03650
$477$	8.30865	0.380427
$478$	3.54215	0.162014
$479$	−18.8295	−0.860343	−0.430172	−	0.902747i	$-0.641547\pi$
$479$	−18.8295	−0.860343	−0.430172	+	0.902747i	$0.641547\pi$
$480$	0.180418	0.00823490
$481$	−13.0203	−0.593673
$482$	−24.3777	−1.11037
$483$	−0.203090	−0.00924089
$484$	1.37726	0.0626028
$485$	5.25166	0.238466
$486$	−0.904209	−0.0410158
$487$	−33.8488	−1.53384	−0.766918	−	0.641745i	$-0.778211\pi$
$487$	−33.8488	−1.53384	−0.766918	+	0.641745i	$0.778211\pi$
$488$	−5.35110	−0.242233
$489$	0.135940	0.00614743
$490$	15.8912	0.717893
$491$	17.8304	0.804674	0.402337	−	0.915492i	$-0.368198\pi$
$491$	17.8304	0.804674	0.402337	+	0.915492i	$0.368198\pi$
$492$	−0.0220696	−0.000994976 0
$493$	−23.8146	−1.07255
$494$	−8.27260	−0.372202
$495$	4.47313	0.201052
$496$	27.1172	1.21760
$497$	−5.61979	−0.252082
$498$	−0.116503	−0.00522062
$499$	−22.5938	−1.01144	−0.505719	−	0.862698i	$-0.668773\pi$
$499$	−22.5938	−1.01144	−0.505719	+	0.862698i	$0.668773\pi$
$500$	−15.9708	−0.714238
$501$	0.213747	0.00954951
$502$	−5.55487	−0.247926
$503$	13.6560	0.608890	0.304445	−	0.952530i	$-0.401529\pi$
$503$	13.6560	0.608890	0.304445	+	0.952530i	$0.401529\pi$
$504$	−12.2813	−0.547054
$505$	−19.7704	−0.879773
$506$	5.72399	0.254462
$507$	0.207633	0.00922129
$508$	14.4164	0.639623
$509$	−31.1936	−1.38263	−0.691316	−	0.722553i	$-0.742969\pi$
$509$	−31.1936	−1.38263	−0.691316	+	0.722553i	$0.742969\pi$
$510$	0.229234	0.0101506
$511$	−9.91929	−0.438803
$512$	21.1280	0.933733
$513$	0.388205	0.0171397
$514$	17.8803	0.788667
$515$	15.9014	0.700699
$516$	0.0206730	0.000910080 0
$517$	−0.232773	−0.0102373
$518$	−67.5109	−2.96626
$519$	−0.262368	−0.0115167
$520$	2.16391	0.0948936
$521$	5.47439	0.239837	0.119919	−	0.992784i	$-0.461737\pi$
$521$	5.47439	0.239837	0.119919	+	0.992784i	$0.461737\pi$
$522$	−28.6040	−1.25196
$523$	−14.2591	−0.623509	−0.311754	−	0.950163i	$-0.600917\pi$
$523$	−14.2591	−0.623509	−0.311754	+	0.950163i	$0.600917\pi$
$524$	−1.37726	−0.0601660
$525$	−0.181025	−0.00790056
$526$	−34.9562	−1.52416
$527$	25.6205	1.11605
$528$	−0.0885351	−0.00385299
$529$	−13.2986	−0.578202
$530$	−7.59064	−0.329716
$531$	4.50145	0.195346
$532$	−17.4923	−0.758388
$533$	−1.11482	−0.0482882
$534$	0.381404	0.0165050
$535$	−12.3253	−0.532871
$536$	7.86045	0.339520
$537$	0.284103	0.0122600
$538$	2.23416	0.0963216
$539$	−5.79878	−0.249771
$540$	0.224579	0.00966434
$541$	2.84357	0.122254	0.0611272	−	0.998130i	$-0.480530\pi$
$541$	2.84357	0.122254	0.0611272	+	0.998130i	$0.480530\pi$
$542$	−10.2814	−0.441626
$543$	0.481385	0.0206582
$544$	30.4666	1.30625
$545$	−9.70961	−0.415914
$546$	−0.151938	−0.00650235
$547$	−28.0768	−1.20048	−0.600240	−	0.799820i	$-0.704928\pi$
$547$	−28.0768	−1.20048	−0.600240	+	0.799820i	$0.704928\pi$
$548$	24.6102	1.05129
$549$	−14.0258	−0.598607
$550$	5.10209	0.217554
$551$	18.4212	0.784770
$552$	−0.0649667	−0.00276517
$553$	33.9183	1.44235
$554$	33.0812	1.40549
$555$	−0.279082	−0.0118464
$556$	−26.9465	−1.14278
$557$	−23.4296	−0.992743	−0.496372	−	0.868110i	$-0.665335\pi$
$557$	−23.4296	−0.992743	−0.496372	+	0.868110i	$0.665335\pi$
$558$	30.7732	1.30273
$559$	1.04427	0.0441680
$560$	25.9150	1.09511
$561$	−0.0836484	−0.00353164
$562$	38.7150	1.63310
$563$	−31.2549	−1.31724	−0.658618	−	0.752477i	$-0.728859\pi$
$563$	−31.2549	−1.31724	−0.658618	+	0.752477i	$0.728859\pi$
$564$	−0.00584300	−0.000246035 0
$565$	−0.256235	−0.0107799
$566$	20.6390	0.867521
$567$	−32.1872	−1.35173
$568$	−1.79773	−0.0754309
$569$	−29.5173	−1.23743	−0.618715	−	0.785616i	$-0.712346\pi$
$569$	−29.5173	−1.23743	−0.618715	+	0.785616i	$0.712346\pi$
$570$	−0.177319	−0.00742706
$571$	3.07839	0.128826	0.0644132	−	0.997923i	$-0.479482\pi$
$571$	3.07839	0.128826	0.0644132	+	0.997923i	$0.479482\pi$
$572$	1.74634	0.0730182
$573$	0.303259	0.0126688
$574$	−5.78041	−0.241269
$575$	8.64734	0.360619
$576$	7.45115	0.310464
$577$	9.86301	0.410603	0.205301	−	0.978699i	$-0.434183\pi$
$577$	9.86301	0.410603	0.205301	+	0.978699i	$0.434183\pi$
$578$	7.46859	0.310653
$579$	0.417201	0.0173383
$580$	10.6568	0.442499
$581$	−12.4438	−0.516255
$582$	−0.117958	−0.00488952
$583$	2.76986	0.114716
$584$	−3.17310	−0.131304
$585$	5.67184	0.234502
$586$	56.7243	2.34326
$587$	15.2444	0.629204	0.314602	−	0.949224i	$-0.398129\pi$
$587$	15.2444	0.629204	0.314602	+	0.949224i	$0.398129\pi$
$588$	−0.145559	−0.00600277
$589$	−19.8182	−0.816593
$590$	−4.11245	−0.169307
$591$	0.0961327	0.00395437
$592$	−49.8810	−2.05010
$593$	16.1735	0.664168	0.332084	−	0.943250i	$-0.392248\pi$
$593$	16.1735	0.664168	0.332084	+	0.943250i	$0.392248\pi$
$594$	−0.200954	−0.00824524
$595$	24.4846	1.00377
$596$	16.7210	0.684918
$597$	0.251200	0.0102809
$598$	7.25791	0.296798
$599$	11.4551	0.468044	0.234022	−	0.972231i	$-0.424811\pi$
$599$	11.4551	0.468044	0.234022	+	0.972231i	$0.424811\pi$
$600$	−0.0579083	−0.00236410
$601$	−1.51823	−0.0619298	−0.0309649	−	0.999520i	$-0.509858\pi$
$601$	−1.51823	−0.0619298	−0.0309649	+	0.999520i	$0.509858\pi$
$602$	5.41461	0.220683
$603$	20.6031	0.839024
$604$	28.3853	1.15498
$605$	1.49121	0.0606262
$606$	0.444066	0.0180389
$607$	28.8915	1.17267	0.586336	−	0.810068i	$-0.300570\pi$
$607$	28.8915	1.17267	0.586336	+	0.810068i	$0.300570\pi$
$608$	−23.5668	−0.955760
$609$	0.338332	0.0137099
$610$	12.8137	0.518813
$611$	−0.295152	−0.0119406
$612$	18.9610	0.766452
$613$	16.6014	0.670523	0.335261	−	0.942125i	$-0.391175\pi$
$613$	16.6014	0.670523	0.335261	+	0.942125i	$0.391175\pi$
$614$	2.80627	0.113252
$615$	−0.0238955	−0.000963561 0
$616$	−4.09423	−0.164961
$617$	−17.9838	−0.724000	−0.362000	−	0.932178i	$-0.617906\pi$
$617$	−17.9838	−0.724000	−0.362000	+	0.932178i	$0.617906\pi$
$618$	−0.357163	−0.0143672
$619$	4.13158	0.166062	0.0830312	−	0.996547i	$-0.473540\pi$
$619$	4.13158	0.166062	0.0830312	+	0.996547i	$0.473540\pi$
$620$	−11.4649	−0.460443
$621$	−0.340589	−0.0136674
$622$	52.1516	2.09109
$623$	40.7380	1.63213
$624$	−0.112261	−0.00449403
$625$	−3.41068	−0.136427
$626$	11.8189	0.472379
$627$	0.0647044	0.00258404
$628$	−27.2368	−1.08687
$629$	−47.1279	−1.87911
$630$	29.4089	1.17168
$631$	21.3008	0.847970	0.423985	−	0.905669i	$-0.360631\pi$
$631$	21.3008	0.847970	0.423985	+	0.905669i	$0.360631\pi$
$632$	10.8502	0.431597
$633$	0.114459	0.00454935
$634$	11.5707	0.459532
$635$	15.6091	0.619428
$636$	0.0695282	0.00275697
$637$	−7.35275	−0.291326
$638$	−9.53574	−0.377523
$639$	−4.71204	−0.186406
$640$	12.9908	0.513507
$641$	−20.7169	−0.818270	−0.409135	−	0.912474i	$-0.634170\pi$
$641$	−20.7169	−0.818270	−0.409135	+	0.912474i	$0.634170\pi$
$642$	0.276841	0.0109260
$643$	6.59414	0.260048	0.130024	−	0.991511i	$-0.458495\pi$
$643$	6.59414	0.260048	0.130024	+	0.991511i	$0.458495\pi$
$644$	15.3468	0.604748
$645$	0.0223834	0.000881345 0
$646$	−29.9433	−1.17810
$647$	−33.2987	−1.30911	−0.654553	−	0.756016i	$-0.727143\pi$
$647$	−33.2987	−1.30911	−0.654553	+	0.756016i	$0.727143\pi$
$648$	−10.2964	−0.404481
$649$	1.50065	0.0589057
$650$	6.46936	0.253749
$651$	−0.363989	−0.0142658
$652$	−10.2725	−0.402303
$653$	−27.7402	−1.08556	−0.542780	−	0.839875i	$-0.682628\pi$
$653$	−27.7402	−1.08556	−0.542780	+	0.839875i	$0.682628\pi$
$654$	0.218089	0.00852794
$655$	−1.49121	−0.0582663
$656$	−4.27091	−0.166751
$657$	−8.31705	−0.324479
$658$	−1.53038	−0.0596604
$659$	−39.7988	−1.55034	−0.775171	−	0.631752i	$-0.782336\pi$
$659$	−39.7988	−1.55034	−0.775171	+	0.631752i	$0.782336\pi$
$660$	0.0374319	0.00145703
$661$	11.2725	0.438450	0.219225	−	0.975674i	$-0.429647\pi$
$661$	11.2725	0.438450	0.219225	+	0.975674i	$0.429647\pi$
$662$	−2.92920	−0.113847
$663$	−0.106065	−0.00411921
$664$	−3.98066	−0.154480
$665$	−18.9395	−0.734444
$666$	−56.6060	−2.19344
$667$	−16.1617	−0.625785
$668$	−16.1521	−0.624944
$669$	−0.0574150	−0.00221979
$670$	−18.8226	−0.727182
$671$	−4.67579	−0.180507
$672$	−0.432838	−0.0166971
$673$	32.3303	1.24624	0.623120	−	0.782126i	$-0.285865\pi$
$673$	32.3303	1.24624	0.623120	+	0.782126i	$0.285865\pi$
$674$	43.2796	1.66707
$675$	−0.303585	−0.0116850
$676$	−15.6901	−0.603465
$677$	−35.5873	−1.36773	−0.683866	−	0.729607i	$-0.739703\pi$
$677$	−35.5873	−1.36773	−0.683866	+	0.729607i	$0.739703\pi$
$678$	0.00575531	0.000221032 0
$679$	−12.5992	−0.483513
$680$	7.83243	0.300360
$681$	−0.267033	−0.0102327
$682$	10.2589	0.392832
$683$	13.9433	0.533526	0.266763	−	0.963762i	$-0.414046\pi$
$683$	13.9433	0.533526	0.266763	+	0.963762i	$0.414046\pi$
$684$	−14.6668	−0.560800
$685$	26.6463	1.01810
$686$	7.89748	0.301527
$687$	−0.382336	−0.0145870
$688$	4.00064	0.152523
$689$	3.51213	0.133801
$690$	0.155569	0.00592242
$691$	38.2345	1.45451	0.727254	−	0.686369i	$-0.240796\pi$
$691$	38.2345	1.45451	0.727254	+	0.686369i	$0.240796\pi$
$692$	19.8263	0.753681
$693$	−10.7314	−0.407653
$694$	16.7547	0.635998
$695$	−29.1759	−1.10670
$696$	0.108230	0.00410244
$697$	−4.03517	−0.152843
$698$	30.8519	1.16776
$699$	−0.451113	−0.0170627
$700$	13.6794	0.517033
$701$	−33.5133	−1.26578	−0.632889	−	0.774242i	$-0.718131\pi$
$701$	−33.5133	−1.26578	−0.632889	+	0.774242i	$0.718131\pi$
$702$	−0.254806	−0.00961702
$703$	36.4547	1.37492
$704$	2.48399	0.0936189
$705$	−0.00632642	−0.000238267 0
$706$	−39.8580	−1.50008
$707$	47.4310	1.78383
$708$	0.0376689	0.00141568
$709$	5.42967	0.203915	0.101958	−	0.994789i	$-0.467489\pi$
$709$	5.42967	0.203915	0.101958	+	0.994789i	$0.467489\pi$
$710$	4.30484	0.161558
$711$	28.4395	1.06657
$712$	13.0318	0.488386
$713$	17.3873	0.651161
$714$	−0.549951	−0.0205814
$715$	1.89082	0.0707128
$716$	−21.4687	−0.802323
$717$	−0.0351295	−0.00131194
$718$	−49.4191	−1.84431
$719$	−26.8037	−0.999609	−0.499804	−	0.866138i	$-0.666595\pi$
$719$	−26.8037	−0.999609	−0.499804	+	0.866138i	$0.666595\pi$
$720$	21.7290	0.809792
$721$	−38.1488	−1.42074
$722$	−11.7549	−0.437474
$723$	0.241767	0.00899141
$724$	−36.3766	−1.35193
$725$	−14.4058	−0.535019
$726$	−0.0334942	−0.00124309
$727$	−3.36631	−0.124850	−0.0624248	−	0.998050i	$-0.519883\pi$
$727$	−3.36631	−0.124850	−0.0624248	+	0.998050i	$0.519883\pi$
$728$	−5.19140	−0.192406
$729$	−26.9821	−0.999336
$730$	7.59831	0.281226
$731$	3.77982	0.139802
$732$	−0.117370	−0.00433813
$733$	25.8138	0.953454	0.476727	−	0.879051i	$-0.341823\pi$
$733$	25.8138	0.953454	0.476727	+	0.879051i	$0.341823\pi$
$734$	−29.7383	−1.09766
$735$	−0.157602	−0.00581324
$736$	20.6762	0.762134
$737$	6.86847	0.253003
$738$	−4.84671	−0.178410
$739$	−40.0047	−1.47160	−0.735798	−	0.677201i	$-0.763193\pi$
$739$	−40.0047	−1.47160	−0.735798	+	0.677201i	$0.763193\pi$
$740$	21.0893	0.775258
$741$	0.0820439	0.00301396
$742$	18.2106	0.668532
$743$	18.7804	0.688985	0.344492	−	0.938789i	$-0.388051\pi$
$743$	18.7804	0.688985	0.344492	+	0.938789i	$0.388051\pi$
$744$	−0.116437	−0.00426879
$745$	18.1044	0.663293
$746$	17.3833	0.636449
$747$	−10.4338	−0.381751
$748$	6.32102	0.231119
$749$	29.5696	1.08045
$750$	0.388401	0.0141824
$751$	−46.5255	−1.69774	−0.848870	−	0.528602i	$-0.822716\pi$
$751$	−46.5255	−1.69774	−0.848870	+	0.528602i	$0.822716\pi$
$752$	−1.13073	−0.0412337
$753$	0.0550907	0.00200762
$754$	−12.0911	−0.440333
$755$	30.7337	1.11851
$756$	−0.538784	−0.0195954
$757$	−4.22171	−0.153441	−0.0767204	−	0.997053i	$-0.524445\pi$
$757$	−4.22171	−0.153441	−0.0767204	+	0.997053i	$0.524445\pi$
$758$	−33.1882	−1.20545
$759$	−0.0567679	−0.00206055
$760$	−6.05861	−0.219769
$761$	32.0311	1.16113	0.580563	−	0.814215i	$-0.302833\pi$
$761$	32.0311	1.16113	0.580563	+	0.814215i	$0.302833\pi$
$762$	−0.350597	−0.0127008
$763$	23.2942	0.843307
$764$	−22.9162	−0.829080
$765$	20.5297	0.742252
$766$	−30.1887	−1.09076
$767$	1.90280	0.0687060
$768$	−0.382333	−0.0137963
$769$	19.6483	0.708537	0.354268	−	0.935144i	$-0.384730\pi$
$769$	19.6483	0.708537	0.354268	+	0.935144i	$0.384730\pi$
$770$	9.80404	0.353313
$771$	−0.177329	−0.00638635
$772$	−31.5264	−1.13466
$773$	3.66392	0.131782	0.0658909	−	0.997827i	$-0.479011\pi$
$773$	3.66392	0.131782	0.0658909	+	0.997827i	$0.479011\pi$
$774$	4.54000	0.163187
$775$	15.4983	0.556714
$776$	−4.03038	−0.144682
$777$	0.669543	0.0240197
$778$	−36.6826	−1.31514
$779$	3.12132	0.111833
$780$	0.0474629	0.00169945
$781$	−1.57085	−0.0562096
$782$	26.2706	0.939433
$783$	0.567396	0.0202771
$784$	−28.1686	−1.00602
$785$	−29.4902	−1.05255
$786$	0.0334942	0.00119470
$787$	−2.15771	−0.0769140	−0.0384570	−	0.999260i	$-0.512244\pi$
$787$	−2.15771	−0.0769140	−0.0384570	+	0.999260i	$0.512244\pi$
$788$	−7.26441	−0.258784
$789$	0.346680	0.0123421
$790$	−25.9819	−0.924393
$791$	0.614730	0.0218573
$792$	−3.43290	−0.121983
$793$	−5.92881	−0.210538
$794$	−40.3280	−1.43119
$795$	0.0752805	0.00266993
$796$	−18.9824	−0.672812
$797$	31.1678	1.10402	0.552011	−	0.833837i	$-0.313861\pi$
$797$	31.1678	1.10402	0.552011	+	0.833837i	$0.313861\pi$
$798$	0.425403	0.0150591
$799$	−1.06832	−0.0377946
$800$	18.4298	0.651591
$801$	34.1577	1.20690
$802$	24.4637	0.863842
$803$	−2.77266	−0.0978449
$804$	0.172410	0.00608044
$805$	16.6165	0.585654
$806$	13.0080	0.458189
$807$	−0.0221574	−0.000779979 0
$808$	15.1728	0.533777
$809$	−4.39744	−0.154606	−0.0773029	−	0.997008i	$-0.524631\pi$
$809$	−4.39744	−0.154606	−0.0773029	+	0.997008i	$0.524631\pi$
$810$	24.6558	0.866316
$811$	32.4575	1.13974	0.569869	−	0.821736i	$-0.306994\pi$
$811$	32.4575	1.13974	0.569869	+	0.821736i	$0.306994\pi$
$812$	−25.5666	−0.897211
$813$	0.101967	0.00357613
$814$	−18.8708	−0.661420
$815$	−11.1224	−0.389601
$816$	−0.406337	−0.0142246
$817$	−2.92380	−0.102291
$818$	37.6586	1.31670
$819$	−13.6072	−0.475476
$820$	1.80570	0.0630579
$821$	−17.5239	−0.611588	−0.305794	−	0.952098i	$-0.598922\pi$
$821$	−17.5239	−0.611588	−0.305794	+	0.952098i	$0.598922\pi$
$822$	−0.598504	−0.0208752
$823$	36.1452	1.25994	0.629972	−	0.776618i	$-0.283067\pi$
$823$	36.1452	1.25994	0.629972	+	0.776618i	$0.283067\pi$
$824$	−12.2035	−0.425129
$825$	−0.0506003	−0.00176168
$826$	9.86612	0.343286
$827$	8.59747	0.298963	0.149482	−	0.988764i	$-0.452239\pi$
$827$	8.59747	0.298963	0.149482	+	0.988764i	$0.452239\pi$
$828$	12.8678	0.447189
$829$	−31.9912	−1.11110	−0.555550	−	0.831483i	$-0.687492\pi$
$829$	−31.9912	−1.11110	−0.555550	+	0.831483i	$0.687492\pi$
$830$	9.53209	0.330864
$831$	−0.328085	−0.0113811
$832$	3.14965	0.109195
$833$	−26.6138	−0.922115
$834$	0.655322	0.0226919
$835$	−17.4885	−0.605213
$836$	−4.88949	−0.169106
$837$	−0.610423	−0.0210993
$838$	−68.8922	−2.37984
$839$	−20.4839	−0.707181	−0.353591	−	0.935400i	$-0.615039\pi$
$839$	−20.4839	−0.707181	−0.353591	+	0.935400i	$0.615039\pi$
$840$	−0.111275	−0.00383935
$841$	−2.07575	−0.0715776
$842$	62.0755	2.13926
$843$	−0.383959	−0.0132242
$844$	−8.64931	−0.297721
$845$	−16.9882	−0.584411
$846$	−1.28318	−0.0441167
$847$	−3.57754	−0.122926
$848$	13.4551	0.462049
$849$	−0.204688	−0.00702488
$850$	23.4163	0.803174
$851$	−31.9833	−1.09637
$852$	−0.0394312	−0.00135089
$853$	45.3915	1.55418	0.777088	−	0.629392i	$-0.216696\pi$
$853$	45.3915	1.55418	0.777088	+	0.629392i	$0.216696\pi$
$854$	−30.7413	−1.05194
$855$	−15.8803	−0.543094
$856$	9.45907	0.323304
$857$	−47.6433	−1.62746	−0.813732	−	0.581241i	$-0.802567\pi$
$857$	−47.6433	−1.62746	−0.813732	+	0.581241i	$0.802567\pi$
$858$	−0.0424700	−0.00144990
$859$	48.8222	1.66579	0.832895	−	0.553431i	$-0.186682\pi$
$859$	48.8222	1.66579	0.832895	+	0.553431i	$0.186682\pi$
$860$	−1.69144	−0.0576775
$861$	0.0573275	0.00195372
$862$	−54.4209	−1.85358
$863$	−36.0064	−1.22567	−0.612836	−	0.790210i	$-0.709971\pi$
$863$	−36.0064	−1.22567	−0.612836	+	0.790210i	$0.709971\pi$
$864$	−0.725885	−0.0246951
$865$	21.4666	0.729885
$866$	15.5669	0.528984
$867$	−0.0740702	−0.00251556
$868$	27.5054	0.933594
$869$	9.48090	0.321617
$870$	−0.259167	−0.00878658
$871$	8.70908	0.295096
$872$	7.45163	0.252344
$873$	−10.5641	−0.357540
$874$	−20.3210	−0.687368
$875$	41.4854	1.40246
$876$	−0.0695985	−0.00235151
$877$	17.4270	0.588469	0.294235	−	0.955733i	$-0.404935\pi$
$877$	17.4270	0.588469	0.294235	+	0.955733i	$0.404935\pi$
$878$	−18.2597	−0.616235
$879$	−0.562566	−0.0189749
$880$	7.24380	0.244189
$881$	43.7235	1.47308	0.736541	−	0.676393i	$-0.236458\pi$
$881$	43.7235	1.47308	0.736541	+	0.676393i	$0.236458\pi$
$882$	−31.9663	−1.07636
$883$	−38.6497	−1.30067	−0.650334	−	0.759649i	$-0.725371\pi$
$883$	−38.6497	−1.30067	−0.650334	+	0.759649i	$0.725371\pi$
$884$	8.01494	0.269571
$885$	0.0407854	0.00137099
$886$	−24.4250	−0.820575
$887$	39.0616	1.31156	0.655779	−	0.754953i	$-0.272340\pi$
$887$	39.0616	1.31156	0.655779	+	0.754953i	$0.272340\pi$
$888$	0.214181	0.00718746
$889$	−37.4476	−1.25595
$890$	−31.2059	−1.04602
$891$	−8.99701	−0.301411
$892$	4.33865	0.145269
$893$	0.826379	0.0276537
$894$	−0.406644	−0.0136002
$895$	−23.2449	−0.776991
$896$	−31.1661	−1.04119
$897$	−0.0719807	−0.00240336
$898$	32.6098	1.08820
$899$	−28.9660	−0.966070
$900$	11.4698	0.382327
$901$	12.7124	0.423512
$902$	−1.61575	−0.0537986
$903$	−0.0536997	−0.00178701
$904$	0.196647	0.00654038
$905$	−39.3862	−1.30924
$906$	−0.690313	−0.0229341
$907$	−32.6498	−1.08412	−0.542059	−	0.840340i	$-0.682355\pi$
$907$	−32.6498	−1.08412	−0.542059	+	0.840340i	$0.682355\pi$
$908$	20.1788	0.669656
$909$	39.7696	1.31907
$910$	12.4313	0.412095
$911$	−15.6287	−0.517802	−0.258901	−	0.965904i	$-0.583360\pi$
$911$	−15.6287	−0.517802	−0.258901	+	0.965904i	$0.583360\pi$
$912$	0.314313	0.0104079
$913$	−3.47830	−0.115115
$914$	−20.9495	−0.692947
$915$	−0.127081	−0.00420117
$916$	28.8918	0.954612
$917$	3.57754	0.118141
$918$	−0.922289	−0.0304401
$919$	29.2614	0.965246	0.482623	−	0.875828i	$-0.339684\pi$
$919$	29.2614	0.965246	0.482623	+	0.875828i	$0.339684\pi$
$920$	5.31548	0.175246
$921$	−0.0278313	−0.000917074 0
$922$	−18.5603	−0.611252
$923$	−1.99181	−0.0655614
$924$	−0.0898024	−0.00295428
$925$	−28.5084	−0.937351
$926$	−13.8024	−0.453575
$927$	−31.9867	−1.05058
$928$	−34.4450	−1.13071
$929$	41.2545	1.35352	0.676759	−	0.736205i	$-0.263384\pi$
$929$	41.2545	1.35352	0.676759	+	0.736205i	$0.263384\pi$
$930$	0.278820	0.00914288
$931$	20.5865	0.674697
$932$	34.0891	1.11663
$933$	−0.517217	−0.0169329
$934$	38.3243	1.25401
$935$	6.84398	0.223822
$936$	−4.35285	−0.142277
$937$	2.16729	0.0708024	0.0354012	−	0.999373i	$-0.488729\pi$
$937$	2.16729	0.0708024	0.0354012	+	0.999373i	$0.488729\pi$
$938$	45.1571	1.47443
$939$	−0.117215	−0.00382516
$940$	0.478065	0.0155928
$941$	6.90113	0.224970	0.112485	−	0.993653i	$-0.464119\pi$
$941$	6.90113	0.224970	0.112485	+	0.993653i	$0.464119\pi$
$942$	0.662382	0.0215816
$943$	−2.73847	−0.0891768
$944$	7.28967	0.237259
$945$	−0.583360	−0.0189767
$946$	1.51350	0.0492082
$947$	48.5107	1.57639	0.788194	−	0.615427i	$-0.211016\pi$
$947$	48.5107	1.57639	0.788194	+	0.615427i	$0.211016\pi$
$948$	0.237987	0.00772945
$949$	−3.51568	−0.114124
$950$	−18.1132	−0.587670
$951$	−0.114753	−0.00372113
$952$	−18.7907	−0.609010
$953$	32.9776	1.06825	0.534124	−	0.845406i	$-0.320641\pi$
$953$	32.9776	1.06825	0.534124	+	0.845406i	$0.320641\pi$
$954$	15.2691	0.494355
$955$	−24.8122	−0.802903
$956$	2.65462	0.0858564
$957$	0.0945712	0.00305705
$958$	−34.6036	−1.11799
$959$	−63.9267	−2.06430
$960$	0.0675111	0.00217891
$961$	0.162600	0.00524516
$962$	−23.9278	−0.771463
$963$	24.7933	0.798952
$964$	−18.2695	−0.588421
$965$	−34.1347	−1.09884
$966$	−0.373224	−0.0120083
$967$	−47.4409	−1.52560	−0.762798	−	0.646637i	$-0.776175\pi$
$967$	−47.4409	−1.52560	−0.762798	+	0.646637i	$0.776175\pi$
$968$	−1.14443	−0.0367832
$969$	0.296964	0.00953987
$970$	9.65115	0.309880
$971$	14.8923	0.477916	0.238958	−	0.971030i	$-0.423194\pi$
$971$	14.8923	0.477916	0.238958	+	0.971030i	$0.423194\pi$
$972$	−0.677646	−0.0217355
$973$	69.9954	2.24395
$974$	−62.2051	−1.99318
$975$	−0.0641602	−0.00205477
$976$	−22.7135	−0.727040
$977$	4.66310	0.149186	0.0745928	−	0.997214i	$-0.476234\pi$
$977$	4.66310	0.149186	0.0745928	+	0.997214i	$0.476234\pi$
$978$	0.249822	0.00798842
$979$	11.3872	0.363935
$980$	11.9094	0.380433
$981$	19.5316	0.623594
$982$	32.7675	1.04565
$983$	34.2240	1.09158	0.545788	−	0.837923i	$-0.316230\pi$
$983$	34.2240	1.09158	0.545788	+	0.837923i	$0.316230\pi$
$984$	0.0183386	0.000584613 0
$985$	−7.86543	−0.250613
$986$	−43.7648	−1.39375
$987$	0.0151776	0.000483109 0
$988$	−6.19978	−0.197241
$989$	2.56517	0.0815678
$990$	8.22042	0.261262
$991$	−0.981225	−0.0311696	−0.0155848	−	0.999879i	$-0.504961\pi$
$991$	−0.981225	−0.0311696	−0.0155848	+	0.999879i	$0.504961\pi$
$992$	37.0570	1.17656
$993$	0.0290505	0.000921889 0
$994$	−10.3277	−0.327574
$995$	−20.5528	−0.651569
$996$	−0.0873114	−0.00276657
$997$	−38.9310	−1.23296	−0.616479	−	0.787371i	$-0.711442\pi$
$997$	−38.9310	−1.23296	−0.616479	+	0.787371i	$0.711442\pi$
$998$	−41.5214	−1.31434
$999$	1.12285	0.0355254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.d.1.20	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.d.1.20	✓	23	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83773 q^{2} -0.0182258 q^{3} +1.37726 q^{4} +1.49121 q^{5} -0.0334942 q^{6} -3.57754 q^{7} -1.14443 q^{8} -2.99967 q^{9} +O(q^{10})\)	\(q+1.83773 q^{2} -0.0182258 q^{3} +1.37726 q^{4} +1.49121 q^{5} -0.0334942 q^{6} -3.57754 q^{7} -1.14443 q^{8} -2.99967 q^{9} +2.74044 q^{10} -1.00000 q^{11} -0.0251017 q^{12} -1.26798 q^{13} -6.57456 q^{14} -0.0271785 q^{15} -4.85767 q^{16} -4.58956 q^{17} -5.51259 q^{18} +3.55015 q^{19} +2.05378 q^{20} +0.0652036 q^{21} -1.83773 q^{22} -3.11470 q^{23} +0.0208581 q^{24} -2.77630 q^{25} -2.33021 q^{26} +0.109349 q^{27} -4.92721 q^{28} +5.18886 q^{29} -0.0499468 q^{30} -5.58235 q^{31} -6.63825 q^{32} +0.0182258 q^{33} -8.43438 q^{34} -5.33485 q^{35} -4.13133 q^{36} +10.2685 q^{37} +6.52423 q^{38} +0.0231100 q^{39} -1.70658 q^{40} +0.879208 q^{41} +0.119827 q^{42} -0.823570 q^{43} -1.37726 q^{44} -4.47313 q^{45} -5.72399 q^{46} +0.232773 q^{47} +0.0885351 q^{48} +5.79878 q^{49} -5.10209 q^{50} +0.0836484 q^{51} -1.74634 q^{52} -2.76986 q^{53} +0.200954 q^{54} -1.49121 q^{55} +4.09423 q^{56} -0.0647044 q^{57} +9.53574 q^{58} -1.50065 q^{59} -0.0374319 q^{60} +4.67579 q^{61} -10.2589 q^{62} +10.7314 q^{63} -2.48399 q^{64} -1.89082 q^{65} +0.0334942 q^{66} -6.86847 q^{67} -6.32102 q^{68} +0.0567679 q^{69} -9.80404 q^{70} +1.57085 q^{71} +3.43290 q^{72} +2.77266 q^{73} +18.8708 q^{74} +0.0506003 q^{75} +4.88949 q^{76} +3.57754 q^{77} +0.0424700 q^{78} -9.48090 q^{79} -7.24380 q^{80} +8.99701 q^{81} +1.61575 q^{82} +3.47830 q^{83} +0.0898024 q^{84} -6.84398 q^{85} -1.51350 q^{86} -0.0945712 q^{87} +1.14443 q^{88} -11.3872 q^{89} -8.22042 q^{90} +4.53625 q^{91} -4.28976 q^{92} +0.101743 q^{93} +0.427774 q^{94} +5.29401 q^{95} +0.120988 q^{96} +3.52175 q^{97} +10.6566 q^{98} +2.99967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

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