LMFDB - Embedded newform 755.2.a.k.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [755,2,Mod(1,755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(755, 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("755.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.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:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 32 x^{16} + 64 x^{15} + 417 x^{14} - 839 x^{13} - 2829 x^{12} + 5789 x^{11} + \cdots + 576 $ x^18 - 2x^17 - 32x^16 + 64x^15 + 417x^14 - 839x^13 - 2829x^12 + 5789x^11 + 10562x^10 - 22471x^9 - 20867x^8 + 48611x^7 + 18052x^6 - 54316x^5 - 788x^4 + 25424x^3 - 5248x^2 - 2240*x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-2.74545$ of defining polynomial
Character	$\chi$	$=$	755.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74545 q^{2} -2.37118 q^{3} +5.53751 q^{4} -1.00000 q^{5} -6.50997 q^{6} -0.409554 q^{7} +9.71206 q^{8} +2.62250 q^{9} +O(q^{10})$	\(q+2.74545 q^{2} -2.37118 q^{3} +5.53751 q^{4} -1.00000 q^{5} -6.50997 q^{6} -0.409554 q^{7} +9.71206 q^{8} +2.62250 q^{9} -2.74545 q^{10} +5.72690 q^{11} -13.1304 q^{12} +1.36347 q^{13} -1.12441 q^{14} +2.37118 q^{15} +15.5890 q^{16} +3.94334 q^{17} +7.19996 q^{18} -7.09974 q^{19} -5.53751 q^{20} +0.971127 q^{21} +15.7229 q^{22} -2.57969 q^{23} -23.0291 q^{24} +1.00000 q^{25} +3.74335 q^{26} +0.895110 q^{27} -2.26791 q^{28} +5.12396 q^{29} +6.50997 q^{30} +3.92785 q^{31} +23.3747 q^{32} -13.5795 q^{33} +10.8262 q^{34} +0.409554 q^{35} +14.5221 q^{36} -2.09769 q^{37} -19.4920 q^{38} -3.23304 q^{39} -9.71206 q^{40} +0.147496 q^{41} +2.66618 q^{42} +1.71111 q^{43} +31.7127 q^{44} -2.62250 q^{45} -7.08242 q^{46} -7.21140 q^{47} -36.9643 q^{48} -6.83227 q^{49} +2.74545 q^{50} -9.35037 q^{51} +7.55024 q^{52} -11.1784 q^{53} +2.45748 q^{54} -5.72690 q^{55} -3.97761 q^{56} +16.8348 q^{57} +14.0676 q^{58} -0.776067 q^{59} +13.1304 q^{60} +5.83711 q^{61} +10.7837 q^{62} -1.07406 q^{63} +32.9961 q^{64} -1.36347 q^{65} -37.2819 q^{66} -12.6969 q^{67} +21.8363 q^{68} +6.11692 q^{69} +1.12441 q^{70} +1.98583 q^{71} +25.4699 q^{72} -13.6922 q^{73} -5.75909 q^{74} -2.37118 q^{75} -39.3148 q^{76} -2.34547 q^{77} -8.87616 q^{78} -14.3558 q^{79} -15.5890 q^{80} -9.98998 q^{81} +0.404944 q^{82} +2.08110 q^{83} +5.37762 q^{84} -3.94334 q^{85} +4.69778 q^{86} -12.1498 q^{87} +55.6200 q^{88} +8.84651 q^{89} -7.19996 q^{90} -0.558415 q^{91} -14.2851 q^{92} -9.31364 q^{93} -19.7986 q^{94} +7.09974 q^{95} -55.4256 q^{96} +10.3150 q^{97} -18.7577 q^{98} +15.0188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 2 q^{3} + 32 q^{4} - 18 q^{5} + 10 q^{6} + 4 q^{7} + 32 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 2 * q^3 + 32 * q^4 - 18 * q^5 + 10 * q^6 + 4 * q^7 + 32 * q^9	\( 18 q - 2 q^{2} + 2 q^{3} + 32 q^{4} - 18 q^{5} + 10 q^{6} + 4 q^{7} + 32 q^{9} + 2 q^{10} + 11 q^{11} + 12 q^{13} + q^{14} - 2 q^{15} + 60 q^{16} - 25 q^{17} - 9 q^{18} + 8 q^{19} - 32 q^{20} + 20 q^{21} + 29 q^{22} + 12 q^{23} + 15 q^{24} + 18 q^{25} + 5 q^{26} + 5 q^{27} + 15 q^{28} + 24 q^{29} - 10 q^{30} + 11 q^{31} - 17 q^{32} - 33 q^{33} + 17 q^{34} - 4 q^{35} + 90 q^{36} + 45 q^{37} - 28 q^{38} + 38 q^{39} + 12 q^{41} - 9 q^{42} + 19 q^{43} + 6 q^{44} - 32 q^{45} - 5 q^{46} - 16 q^{47} - 3 q^{48} + 62 q^{49} - 2 q^{50} + 7 q^{51} + q^{52} - 4 q^{53} - 6 q^{54} - 11 q^{55} + 2 q^{56} + 5 q^{57} + 28 q^{58} - 8 q^{59} + 27 q^{61} - 57 q^{62} + 10 q^{63} + 98 q^{64} - 12 q^{65} - 32 q^{66} + 9 q^{67} - 26 q^{68} + 31 q^{69} - q^{70} + 9 q^{71} - 102 q^{72} + 2 q^{73} - 24 q^{74} + 2 q^{75} - 43 q^{76} + 11 q^{77} + 45 q^{78} + 20 q^{79} - 60 q^{80} + 66 q^{81} - 19 q^{82} - 20 q^{83} - 33 q^{84} + 25 q^{85} + 21 q^{86} - 33 q^{87} + 62 q^{88} + 13 q^{89} + 9 q^{90} + 22 q^{91} - 6 q^{92} + 58 q^{93} + 70 q^{94} - 8 q^{95} - 17 q^{96} - 27 q^{97} - 6 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 2 * q^3 + 32 * q^4 - 18 * q^5 + 10 * q^6 + 4 * q^7 + 32 * q^9 + 2 * q^10 + 11 * q^11 + 12 * q^13 + q^14 - 2 * q^15 + 60 * q^16 - 25 * q^17 - 9 * q^18 + 8 * q^19 - 32 * q^20 + 20 * q^21 + 29 * q^22 + 12 * q^23 + 15 * q^24 + 18 * q^25 + 5 * q^26 + 5 * q^27 + 15 * q^28 + 24 * q^29 - 10 * q^30 + 11 * q^31 - 17 * q^32 - 33 * q^33 + 17 * q^34 - 4 * q^35 + 90 * q^36 + 45 * q^37 - 28 * q^38 + 38 * q^39 + 12 * q^41 - 9 * q^42 + 19 * q^43 + 6 * q^44 - 32 * q^45 - 5 * q^46 - 16 * q^47 - 3 * q^48 + 62 * q^49 - 2 * q^50 + 7 * q^51 + q^52 - 4 * q^53 - 6 * q^54 - 11 * q^55 + 2 * q^56 + 5 * q^57 + 28 * q^58 - 8 * q^59 + 27 * q^61 - 57 * q^62 + 10 * q^63 + 98 * q^64 - 12 * q^65 - 32 * q^66 + 9 * q^67 - 26 * q^68 + 31 * q^69 - q^70 + 9 * q^71 - 102 * q^72 + 2 * q^73 - 24 * q^74 + 2 * q^75 - 43 * q^76 + 11 * q^77 + 45 * q^78 + 20 * q^79 - 60 * q^80 + 66 * q^81 - 19 * q^82 - 20 * q^83 - 33 * q^84 + 25 * q^85 + 21 * q^86 - 33 * q^87 + 62 * q^88 + 13 * q^89 + 9 * q^90 + 22 * q^91 - 6 * q^92 + 58 * q^93 + 70 * q^94 - 8 * q^95 - 17 * q^96 - 27 * q^97 - 6 * 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 $

$2$	2.74545	1.94133	0.970664	−	0.240440i	$-0.0772918\pi$
$2$	2.74545	1.94133	0.970664	+	0.240440i	$0.0772918\pi$
$3$	−2.37118	−1.36900	−0.684501	−	0.729012i	$-0.739980\pi$
$3$	−2.37118	−1.36900	−0.684501	+	0.729012i	$0.739980\pi$
$4$	5.53751	2.76875
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.50997	−2.65768
$7$	−0.409554	−0.154797	−0.0773984	−	0.997000i	$-0.524661\pi$
$7$	−0.409554	−0.154797	−0.0773984	+	0.997000i	$0.524661\pi$
$8$	9.71206	3.43373
$9$	2.62250	0.874168
$10$	−2.74545	−0.868188
$11$	5.72690	1.72672	0.863362	−	0.504585i	$-0.168354\pi$
$11$	5.72690	1.72672	0.863362	+	0.504585i	$0.168354\pi$
$12$	−13.1304	−3.79043
$13$	1.36347	0.378159	0.189080	−	0.981962i	$-0.439450\pi$
$13$	1.36347	0.378159	0.189080	+	0.981962i	$0.439450\pi$
$14$	−1.12441	−0.300511
$15$	2.37118	0.612237
$16$	15.5890	3.89724
$17$	3.94334	0.956399	0.478200	−	0.878251i	$-0.341290\pi$
$17$	3.94334	0.956399	0.478200	+	0.878251i	$0.341290\pi$
$18$	7.19996	1.69705
$19$	−7.09974	−1.62879	−0.814396	−	0.580310i	$-0.802931\pi$
$19$	−7.09974	−1.62879	−0.814396	+	0.580310i	$0.802931\pi$
$20$	−5.53751	−1.23822
$21$	0.971127	0.211917
$22$	15.7229	3.35214
$23$	−2.57969	−0.537903	−0.268951	−	0.963154i	$-0.586677\pi$
$23$	−2.57969	−0.537903	−0.268951	+	0.963154i	$0.586677\pi$
$24$	−23.0291	−4.70079
$25$	1.00000	0.200000
$26$	3.74335	0.734131
$27$	0.895110	0.172264
$28$	−2.26791	−0.428594
$29$	5.12396	0.951495	0.475748	−	0.879582i	$-0.342178\pi$
$29$	5.12396	0.951495	0.475748	+	0.879582i	$0.342178\pi$
$30$	6.50997	1.18855
$31$	3.92785	0.705462	0.352731	−	0.935725i	$-0.385253\pi$
$31$	3.92785	0.705462	0.352731	+	0.935725i	$0.385253\pi$
$32$	23.3747	4.13210
$33$	−13.5795	−2.36389
$34$	10.8262	1.85668
$35$	0.409554	0.0692272
$36$	14.5221	2.42036
$37$	−2.09769	−0.344857	−0.172429	−	0.985022i	$-0.555161\pi$
$37$	−2.09769	−0.344857	−0.172429	+	0.985022i	$0.555161\pi$
$38$	−19.4920	−3.16202
$39$	−3.23304	−0.517701
$40$	−9.71206	−1.53561
$41$	0.147496	0.0230350	0.0115175	−	0.999934i	$-0.496334\pi$
$41$	0.147496	0.0230350	0.0115175	+	0.999934i	$0.496334\pi$
$42$	2.66618	0.411401
$43$	1.71111	0.260942	0.130471	−	0.991452i	$-0.458351\pi$
$43$	1.71111	0.260942	0.130471	+	0.991452i	$0.458351\pi$
$44$	31.7127	4.78087
$45$	−2.62250	−0.390940
$46$	−7.08242	−1.04425
$47$	−7.21140	−1.05189	−0.525945	−	0.850518i	$-0.676288\pi$
$47$	−7.21140	−1.05189	−0.525945	+	0.850518i	$0.676288\pi$
$48$	−36.9643	−5.33534
$49$	−6.83227	−0.976038
$50$	2.74545	0.388266
$51$	−9.35037	−1.30931
$52$	7.55024	1.04703
$53$	−11.1784	−1.53547	−0.767737	−	0.640766i	$-0.778617\pi$
$53$	−11.1784	−1.53547	−0.767737	+	0.640766i	$0.778617\pi$
$54$	2.45748	0.334421
$55$	−5.72690	−0.772214
$56$	−3.97761	−0.531531
$57$	16.8348	2.22982
$58$	14.0676	1.84716
$59$	−0.776067	−0.101035	−0.0505177	−	0.998723i	$-0.516087\pi$
$59$	−0.776067	−0.101035	−0.0505177	+	0.998723i	$0.516087\pi$
$60$	13.1304	1.69513
$61$	5.83711	0.747365	0.373683	−	0.927557i	$-0.378095\pi$
$61$	5.83711	0.747365	0.373683	+	0.927557i	$0.378095\pi$
$62$	10.7837	1.36953
$63$	−1.07406	−0.135318
$64$	32.9961	4.12451
$65$	−1.36347	−0.169118
$66$	−37.2819	−4.58909
$67$	−12.6969	−1.55117	−0.775585	−	0.631243i	$-0.782545\pi$
$67$	−12.6969	−1.55117	−0.775585	+	0.631243i	$0.782545\pi$
$68$	21.8363	2.64803
$69$	6.11692	0.736390
$70$	1.12441	0.134393
$71$	1.98583	0.235675	0.117837	−	0.993033i	$-0.462404\pi$
$71$	1.98583	0.235675	0.117837	+	0.993033i	$0.462404\pi$
$72$	25.4699	3.00166
$73$	−13.6922	−1.60255	−0.801274	−	0.598298i	$-0.795844\pi$
$73$	−13.6922	−1.60255	−0.801274	+	0.598298i	$0.795844\pi$
$74$	−5.75909	−0.669481
$75$	−2.37118	−0.273801
$76$	−39.3148	−4.50972
$77$	−2.34547	−0.267291
$78$	−8.87616	−1.00503
$79$	−14.3558	−1.61516	−0.807579	−	0.589760i	$-0.799222\pi$
$79$	−14.3558	−1.61516	−0.807579	+	0.589760i	$0.799222\pi$
$80$	−15.5890	−1.74290
$81$	−9.98998	−1.11000
$82$	0.404944	0.0447185
$83$	2.08110	0.228430	0.114215	−	0.993456i	$-0.463565\pi$
$83$	2.08110	0.228430	0.114215	+	0.993456i	$0.463565\pi$
$84$	5.37762	0.586747
$85$	−3.94334	−0.427715
$86$	4.69778	0.506575
$87$	−12.1498	−1.30260
$88$	55.6200	5.92911
$89$	8.84651	0.937728	0.468864	−	0.883270i	$-0.344663\pi$
$89$	8.84651	0.937728	0.468864	+	0.883270i	$0.344663\pi$
$90$	−7.19996	−0.758943
$91$	−0.558415	−0.0585378
$92$	−14.2851	−1.48932
$93$	−9.31364	−0.965780
$94$	−19.7986	−2.04206
$95$	7.09974	0.728417
$96$	−55.4256	−5.65685
$97$	10.3150	1.04733	0.523663	−	0.851926i	$-0.324565\pi$
$97$	10.3150	1.04733	0.523663	+	0.851926i	$0.324565\pi$
$98$	−18.7577	−1.89481
$99$	15.0188	1.50945
$100$	5.53751	0.553751
$101$	8.21622	0.817544	0.408772	−	0.912636i	$-0.365957\pi$
$101$	8.21622	0.817544	0.408772	+	0.912636i	$0.365957\pi$
$102$	−25.6710	−2.54181
$103$	−15.5311	−1.53032	−0.765161	−	0.643839i	$-0.777341\pi$
$103$	−15.5311	−1.53032	−0.765161	+	0.643839i	$0.777341\pi$
$104$	13.2421	1.29850
$105$	−0.971127	−0.0947723
$106$	−30.6898	−2.98086
$107$	−17.3828	−1.68046	−0.840230	−	0.542231i	$-0.817580\pi$
$107$	−17.3828	−1.68046	−0.840230	+	0.542231i	$0.817580\pi$
$108$	4.95668	0.476956
$109$	8.03341	0.769461	0.384730	−	0.923029i	$-0.374294\pi$
$109$	8.03341	0.769461	0.384730	+	0.923029i	$0.374294\pi$
$110$	−15.7229	−1.49912
$111$	4.97399	0.472111
$112$	−6.38453	−0.603281
$113$	3.31515	0.311863	0.155932	−	0.987768i	$-0.450162\pi$
$113$	3.31515	0.311863	0.155932	+	0.987768i	$0.450162\pi$
$114$	46.2190	4.32881
$115$	2.57969	0.240557
$116$	28.3740	2.63446
$117$	3.57571	0.330575
$118$	−2.13066	−0.196143
$119$	−1.61501	−0.148048
$120$	23.0291	2.10226
$121$	21.7973	1.98158
$122$	16.0255	1.45088
$123$	−0.349740	−0.0315350
$124$	21.7505	1.95325
$125$	−1.00000	−0.0894427
$126$	−2.94877	−0.262698
$127$	20.8447	1.84967	0.924833	−	0.380374i	$-0.124205\pi$
$127$	20.8447	1.84967	0.924833	+	0.380374i	$0.124205\pi$
$128$	43.8399	3.87493
$129$	−4.05736	−0.357231
$130$	−3.74335	−0.328313
$131$	17.3616	1.51689	0.758446	−	0.651736i	$-0.225959\pi$
$131$	17.3616	1.51689	0.758446	+	0.651736i	$0.225959\pi$
$132$	−75.1967	−6.54503
$133$	2.90772	0.252132
$134$	−34.8587	−3.01133
$135$	−0.895110	−0.0770388
$136$	38.2979	3.28402
$137$	−17.4458	−1.49050	−0.745248	−	0.666788i	$-0.767669\pi$
$137$	−17.4458	−1.49050	−0.745248	+	0.666788i	$0.767669\pi$
$138$	16.7937	1.42958
$139$	14.8163	1.25670	0.628349	−	0.777931i	$-0.283731\pi$
$139$	14.8163	1.25670	0.628349	+	0.777931i	$0.283731\pi$
$140$	2.26791	0.191673
$141$	17.0995	1.44004
$142$	5.45200	0.457522
$143$	7.80846	0.652976
$144$	40.8822	3.40685
$145$	−5.12396	−0.425522
$146$	−37.5912	−3.11107
$147$	16.2005	1.33620
$148$	−11.6159	−0.954825
$149$	9.04142	0.740702	0.370351	−	0.928892i	$-0.379237\pi$
$149$	9.04142	0.740702	0.370351	+	0.928892i	$0.379237\pi$
$150$	−6.50997	−0.531537
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−68.9531	−5.59283
$153$	10.3414	0.836054
$154$	−6.43938	−0.518900
$155$	−3.92785	−0.315492
$156$	−17.9030	−1.43339
$157$	11.1420	0.889227	0.444613	−	0.895723i	$-0.353341\pi$
$157$	11.1420	0.889227	0.444613	+	0.895723i	$0.353341\pi$
$158$	−39.4132	−3.13555
$159$	26.5061	2.10207
$160$	−23.3747	−1.84793
$161$	1.05652	0.0832656
$162$	−27.4270	−2.15487
$163$	−13.2605	−1.03864	−0.519321	−	0.854579i	$-0.673815\pi$
$163$	−13.2605	−1.03864	−0.519321	+	0.854579i	$0.673815\pi$
$164$	0.816761	0.0637783
$165$	13.5795	1.05716
$166$	5.71355	0.443458
$167$	−7.09489	−0.549019	−0.274509	−	0.961584i	$-0.588515\pi$
$167$	−7.09489	−0.549019	−0.274509	+	0.961584i	$0.588515\pi$
$168$	9.43164	0.727667
$169$	−11.1409	−0.856996
$170$	−10.8262	−0.830335
$171$	−18.6191	−1.42384
$172$	9.47530	0.722485
$173$	−17.4978	−1.33033	−0.665165	−	0.746697i	$-0.731639\pi$
$173$	−17.4978	−1.33033	−0.665165	+	0.746697i	$0.731639\pi$
$174$	−33.3568	−2.52877
$175$	−0.409554	−0.0309594
$176$	89.2765	6.72947
$177$	1.84020	0.138318
$178$	24.2877	1.82044
$179$	−16.3614	−1.22291	−0.611454	−	0.791280i	$-0.709415\pi$
$179$	−16.3614	−1.22291	−0.611454	+	0.791280i	$0.709415\pi$
$180$	−14.5221	−1.08242
$181$	−10.8496	−0.806441	−0.403220	−	0.915103i	$-0.632109\pi$
$181$	−10.8496	−0.806441	−0.403220	+	0.915103i	$0.632109\pi$
$182$	−1.53310	−0.113641
$183$	−13.8408	−1.02315
$184$	−25.0541	−1.84701
$185$	2.09769	0.154225
$186$	−25.5702	−1.87490
$187$	22.5831	1.65144
$188$	−39.9332	−2.91243
$189$	−0.366596	−0.0266659
$190$	19.4920	1.41410
$191$	−20.1127	−1.45531	−0.727653	−	0.685945i	$-0.759389\pi$
$191$	−20.1127	−1.45531	−0.727653	+	0.685945i	$0.759389\pi$
$192$	−78.2398	−5.64647
$193$	22.6793	1.63249	0.816245	−	0.577706i	$-0.196052\pi$
$193$	22.6793	1.63249	0.816245	+	0.577706i	$0.196052\pi$
$194$	28.3192	2.03320
$195$	3.23304	0.231523
$196$	−37.8337	−2.70241
$197$	10.2683	0.731583	0.365792	−	0.930697i	$-0.380798\pi$
$197$	10.2683	0.731583	0.365792	+	0.930697i	$0.380798\pi$
$198$	41.2334	2.93033
$199$	2.10850	0.149468	0.0747338	−	0.997204i	$-0.476189\pi$
$199$	2.10850	0.149468	0.0747338	+	0.997204i	$0.476189\pi$
$200$	9.71206	0.686746
$201$	30.1066	2.12356
$202$	22.5572	1.58712
$203$	−2.09854	−0.147288
$204$	−51.7777	−3.62517
$205$	−0.147496	−0.0103016
$206$	−42.6398	−2.97086
$207$	−6.76525	−0.470218
$208$	21.2551	1.47378
$209$	−40.6594	−2.81247
$210$	−2.66618	−0.183984
$211$	−5.57718	−0.383949	−0.191974	−	0.981400i	$-0.561489\pi$
$211$	−5.57718	−0.383949	−0.191974	+	0.981400i	$0.561489\pi$
$212$	−61.9006	−4.25135
$213$	−4.70876	−0.322639
$214$	−47.7237	−3.26232
$215$	−1.71111	−0.116697
$216$	8.69336	0.591508
$217$	−1.60867	−0.109203
$218$	22.0553	1.49378
$219$	32.4666	2.19389
$220$	−31.7127	−2.13807
$221$	5.37663	0.361671
$222$	13.6559	0.916521
$223$	0.748241	0.0501059	0.0250530	−	0.999686i	$-0.492025\pi$
$223$	0.748241	0.0501059	0.0250530	+	0.999686i	$0.492025\pi$
$224$	−9.57319	−0.639636
$225$	2.62250	0.174834
$226$	9.10159	0.605429
$227$	−2.87119	−0.190567	−0.0952837	−	0.995450i	$-0.530376\pi$
$227$	−2.87119	−0.190567	−0.0952837	+	0.995450i	$0.530376\pi$
$228$	93.2227	6.17382
$229$	21.0587	1.39160	0.695799	−	0.718236i	$-0.255050\pi$
$229$	21.0587	1.39160	0.695799	+	0.718236i	$0.255050\pi$
$230$	7.08242	0.467001
$231$	5.56154	0.365923
$232$	49.7642	3.26718
$233$	19.6997	1.29057	0.645285	−	0.763942i	$-0.276739\pi$
$233$	19.6997	1.29057	0.645285	+	0.763942i	$0.276739\pi$
$234$	9.81695	0.641754
$235$	7.21140	0.470420
$236$	−4.29748	−0.279742
$237$	34.0403	2.21115
$238$	−4.43393	−0.287409
$239$	4.87975	0.315645	0.157822	−	0.987468i	$-0.449553\pi$
$239$	4.87975	0.315645	0.157822	+	0.987468i	$0.449553\pi$
$240$	36.9643	2.38604
$241$	−5.84024	−0.376203	−0.188102	−	0.982150i	$-0.560233\pi$
$241$	−5.84024	−0.376203	−0.188102	+	0.982150i	$0.560233\pi$
$242$	59.8435	3.84689
$243$	21.0027	1.34733
$244$	32.3230	2.06927
$245$	6.83227	0.436497
$246$	−0.960195	−0.0612198
$247$	−9.68029	−0.615942
$248$	38.1475	2.42237
$249$	−4.93466	−0.312721
$250$	−2.74545	−0.173638
$251$	−10.3099	−0.650755	−0.325378	−	0.945584i	$-0.605491\pi$
$251$	−10.3099	−0.650755	−0.325378	+	0.945584i	$0.605491\pi$
$252$	−5.94760	−0.374664
$253$	−14.7736	−0.928810
$254$	57.2280	3.59081
$255$	9.35037	0.585543
$256$	54.3681	3.39800
$257$	−23.6882	−1.47763	−0.738814	−	0.673909i	$-0.764614\pi$
$257$	−23.6882	−1.47763	−0.738814	+	0.673909i	$0.764614\pi$
$258$	−11.1393	−0.693502
$259$	0.859115	0.0533828
$260$	−7.55024	−0.468246
$261$	13.4376	0.831767
$262$	47.6655	2.94478
$263$	−5.10433	−0.314747	−0.157373	−	0.987539i	$-0.550303\pi$
$263$	−5.10433	−0.314747	−0.157373	+	0.987539i	$0.550303\pi$
$264$	−131.885	−8.11696
$265$	11.1784	0.686684
$266$	7.98302	0.489470
$267$	−20.9767	−1.28375
$268$	−70.3091	−4.29481
$269$	2.11997	0.129257	0.0646285	−	0.997909i	$-0.479414\pi$
$269$	2.11997	0.129257	0.0646285	+	0.997909i	$0.479414\pi$
$270$	−2.45748	−0.149558
$271$	−22.8282	−1.38671	−0.693356	−	0.720595i	$-0.743869\pi$
$271$	−22.8282	−1.38671	−0.693356	+	0.720595i	$0.743869\pi$
$272$	61.4726	3.72732
$273$	1.32410	0.0801384
$274$	−47.8966	−2.89354
$275$	5.72690	0.345345
$276$	33.8725	2.03888
$277$	27.0330	1.62425	0.812127	−	0.583481i	$-0.198310\pi$
$277$	27.0330	1.62425	0.812127	+	0.583481i	$0.198310\pi$
$278$	40.6773	2.43966
$279$	10.3008	0.616693
$280$	3.97761	0.237708
$281$	6.97790	0.416266	0.208133	−	0.978100i	$-0.433261\pi$
$281$	6.97790	0.416266	0.208133	+	0.978100i	$0.433261\pi$
$282$	46.9460	2.79559
$283$	−9.00783	−0.535460	−0.267730	−	0.963494i	$-0.586274\pi$
$283$	−9.00783	−0.535460	−0.267730	+	0.963494i	$0.586274\pi$
$284$	10.9965	0.652525
$285$	−16.8348	−0.997205
$286$	21.4378	1.26764
$287$	−0.0604076	−0.00356575
$288$	61.3002	3.61215
$289$	−1.45011	−0.0853003
$290$	−14.0676	−0.826077
$291$	−24.4587	−1.43379
$292$	−75.8205	−4.43706
$293$	28.4414	1.66156	0.830782	−	0.556598i	$-0.187893\pi$
$293$	28.4414	1.66156	0.830782	+	0.556598i	$0.187893\pi$
$294$	44.4778	2.59400
$295$	0.776067	0.0451844
$296$	−20.3728	−1.18415
$297$	5.12620	0.297452
$298$	24.8228	1.43795
$299$	−3.51734	−0.203413
$300$	−13.1304	−0.758086
$301$	−0.700793	−0.0403930
$302$	2.74545	0.157983
$303$	−19.4822	−1.11922
$304$	−110.678	−6.34780
$305$	−5.83711	−0.334232
$306$	28.3919	1.62305
$307$	−8.39020	−0.478854	−0.239427	−	0.970914i	$-0.576960\pi$
$307$	−8.39020	−0.478854	−0.239427	+	0.970914i	$0.576960\pi$
$308$	−12.9881	−0.740064
$309$	36.8270	2.09502
$310$	−10.7837	−0.612474
$311$	8.70291	0.493497	0.246748	−	0.969080i	$-0.420638\pi$
$311$	8.70291	0.493497	0.246748	+	0.969080i	$0.420638\pi$
$312$	−31.3995	−1.77765
$313$	16.4553	0.930109	0.465055	−	0.885282i	$-0.346035\pi$
$313$	16.4553	0.930109	0.465055	+	0.885282i	$0.346035\pi$
$314$	30.5898	1.72628
$315$	1.07406	0.0605163
$316$	−79.4955	−4.47197
$317$	13.2192	0.742466	0.371233	−	0.928540i	$-0.378935\pi$
$317$	13.2192	0.742466	0.371233	+	0.928540i	$0.378935\pi$
$318$	72.7711	4.08080
$319$	29.3444	1.64297
$320$	−32.9961	−1.84454
$321$	41.2178	2.30055
$322$	2.90063	0.161646
$323$	−27.9966	−1.55777
$324$	−55.3196	−3.07331
$325$	1.36347	0.0756318
$326$	−36.4060	−2.01634
$327$	−19.0487	−1.05339
$328$	1.43249	0.0790961
$329$	2.95346	0.162829
$330$	37.2819	2.05230
$331$	21.9734	1.20777	0.603883	−	0.797073i	$-0.293619\pi$
$331$	21.9734	1.20777	0.603883	+	0.797073i	$0.293619\pi$
$332$	11.5241	0.632467
$333$	−5.50119	−0.301463
$334$	−19.4787	−1.06583
$335$	12.6969	0.693705
$336$	15.1389	0.825893
$337$	8.04206	0.438079	0.219040	−	0.975716i	$-0.429708\pi$
$337$	8.04206	0.438079	0.219040	+	0.975716i	$0.429708\pi$
$338$	−30.5869	−1.66371
$339$	−7.86083	−0.426941
$340$	−21.8363	−1.18424
$341$	22.4944	1.21814
$342$	−51.1178	−2.76414
$343$	5.66506	0.305884
$344$	16.6184	0.896006
$345$	−6.11692	−0.329324
$346$	−48.0392	−2.58261
$347$	−23.5159	−1.26240	−0.631201	−	0.775620i	$-0.717438\pi$
$347$	−23.5159	−1.26240	−0.631201	+	0.775620i	$0.717438\pi$
$348$	−67.2798	−3.60658
$349$	25.8680	1.38468	0.692341	−	0.721570i	$-0.256579\pi$
$349$	25.8680	1.38468	0.692341	+	0.721570i	$0.256579\pi$
$350$	−1.12441	−0.0601023
$351$	1.22046	0.0651432
$352$	133.864	7.13499
$353$	−30.3878	−1.61738	−0.808689	−	0.588236i	$-0.799822\pi$
$353$	−30.3878	−1.61738	−0.808689	+	0.588236i	$0.799822\pi$
$354$	5.05217	0.268520
$355$	−1.98583	−0.105397
$356$	48.9876	2.59634
$357$	3.82948	0.202678
$358$	−44.9194	−2.37407
$359$	−14.7748	−0.779785	−0.389892	−	0.920860i	$-0.627488\pi$
$359$	−14.7748	−0.779785	−0.389892	+	0.920860i	$0.627488\pi$
$360$	−25.4699	−1.34238
$361$	31.4062	1.65296
$362$	−29.7869	−1.56557
$363$	−51.6855	−2.71278
$364$	−3.09223	−0.162077
$365$	13.6922	0.716681
$366$	−37.9994	−1.98626
$367$	−5.94394	−0.310271	−0.155136	−	0.987893i	$-0.549581\pi$
$367$	−5.94394	−0.310271	−0.155136	+	0.987893i	$0.549581\pi$
$368$	−40.2147	−2.09634
$369$	0.386809	0.0201365
$370$	5.75909	0.299401
$371$	4.57816	0.237686
$372$	−51.5744	−2.67401
$373$	29.1043	1.50696	0.753482	−	0.657469i	$-0.228373\pi$
$373$	29.1043	1.50696	0.753482	+	0.657469i	$0.228373\pi$
$374$	62.0007	3.20598
$375$	2.37118	0.122447
$376$	−70.0375	−3.61191
$377$	6.98637	0.359817
$378$	−1.00647	−0.0517673
$379$	−1.66503	−0.0855268	−0.0427634	−	0.999085i	$-0.513616\pi$
$379$	−1.66503	−0.0855268	−0.0427634	+	0.999085i	$0.513616\pi$
$380$	39.3148	2.01681
$381$	−49.4265	−2.53220
$382$	−55.2186	−2.82523
$383$	6.99444	0.357399	0.178700	−	0.983904i	$-0.442811\pi$
$383$	6.99444	0.357399	0.178700	+	0.983904i	$0.442811\pi$
$384$	−103.952	−5.30479
$385$	2.34547	0.119536
$386$	62.2649	3.16920
$387$	4.48740	0.228107
$388$	57.1192	2.89979
$389$	−0.271314	−0.0137562	−0.00687809	−	0.999976i	$-0.502189\pi$
$389$	−0.271314	−0.0137562	−0.00687809	+	0.999976i	$0.502189\pi$
$390$	8.87616	0.449462
$391$	−10.1726	−0.514450
$392$	−66.3554	−3.35145
$393$	−41.1676	−2.07663
$394$	28.1910	1.42024
$395$	14.3558	0.722320
$396$	83.1668	4.17929
$397$	7.26762	0.364751	0.182376	−	0.983229i	$-0.441621\pi$
$397$	7.26762	0.364751	0.182376	+	0.983229i	$0.441621\pi$
$398$	5.78879	0.290166
$399$	−6.89474	−0.345169
$400$	15.5890	0.779449
$401$	−20.7453	−1.03597	−0.517986	−	0.855389i	$-0.673318\pi$
$401$	−20.7453	−1.03597	−0.517986	+	0.855389i	$0.673318\pi$
$402$	82.6563	4.12252
$403$	5.35551	0.266777
$404$	45.4974	2.26358
$405$	9.98998	0.496406
$406$	−5.76143	−0.285935
$407$	−12.0132	−0.595473
$408$	−90.8113	−4.49583
$409$	−17.8601	−0.883127	−0.441564	−	0.897230i	$-0.645576\pi$
$409$	−17.8601	−0.883127	−0.441564	+	0.897230i	$0.645576\pi$
$410$	−0.404944	−0.0199987
$411$	41.3672	2.04049
$412$	−86.0035	−4.23709
$413$	0.317841	0.0156399
$414$	−18.5737	−0.912846
$415$	−2.08110	−0.102157
$416$	31.8707	1.56259
$417$	−35.1321	−1.72042
$418$	−111.629	−5.45993
$419$	7.42282	0.362629	0.181314	−	0.983425i	$-0.441965\pi$
$419$	7.42282	0.362629	0.181314	+	0.983425i	$0.441965\pi$
$420$	−5.37762	−0.262401
$421$	−10.8561	−0.529094	−0.264547	−	0.964373i	$-0.585222\pi$
$421$	−10.8561	−0.529094	−0.264547	+	0.964373i	$0.585222\pi$
$422$	−15.3119	−0.745370
$423$	−18.9119	−0.919529
$424$	−108.565	−5.27240
$425$	3.94334	0.191280
$426$	−12.9277	−0.626348
$427$	−2.39061	−0.115690
$428$	−96.2574	−4.65278
$429$	−18.5153	−0.893926
$430$	−4.69778	−0.226547
$431$	14.1617	0.682147	0.341073	−	0.940037i	$-0.389210\pi$
$431$	14.1617	0.682147	0.341073	+	0.940037i	$0.389210\pi$
$432$	13.9538	0.671355
$433$	−10.6625	−0.512407	−0.256203	−	0.966623i	$-0.582472\pi$
$433$	−10.6625	−0.512407	−0.256203	+	0.966623i	$0.582472\pi$
$434$	−4.41651	−0.211999
$435$	12.1498	0.582540
$436$	44.4851	2.13045
$437$	18.3151	0.876131
$438$	89.1356	4.25906
$439$	−26.0303	−1.24236	−0.621179	−	0.783669i	$-0.713346\pi$
$439$	−26.0303	−1.24236	−0.621179	+	0.783669i	$0.713346\pi$
$440$	−55.6200	−2.65158
$441$	−17.9176	−0.853221
$442$	14.7613	0.702122
$443$	32.4476	1.54163	0.770817	−	0.637057i	$-0.219848\pi$
$443$	32.4476	1.54163	0.770817	+	0.637057i	$0.219848\pi$
$444$	27.5435	1.30716
$445$	−8.84651	−0.419365
$446$	2.05426	0.0972720
$447$	−21.4389	−1.01402
$448$	−13.5137	−0.638462
$449$	−27.7702	−1.31056	−0.655278	−	0.755388i	$-0.727448\pi$
$449$	−27.7702	−1.31056	−0.655278	+	0.755388i	$0.727448\pi$
$450$	7.19996	0.339409
$451$	0.844695	0.0397751
$452$	18.3577	0.863472
$453$	−2.37118	−0.111408
$454$	−7.88271	−0.369954
$455$	0.558415	0.0261789
$456$	163.500	7.65660
$457$	−4.67961	−0.218903	−0.109452	−	0.993992i	$-0.534909\pi$
$457$	−4.67961	−0.218903	−0.109452	+	0.993992i	$0.534909\pi$
$458$	57.8157	2.70155
$459$	3.52972	0.164753
$460$	14.2851	0.666044
$461$	−17.9640	−0.836666	−0.418333	−	0.908294i	$-0.637386\pi$
$461$	−17.9640	−0.836666	−0.418333	+	0.908294i	$0.637386\pi$
$462$	15.2690	0.710376
$463$	−34.6368	−1.60971	−0.804855	−	0.593471i	$-0.797757\pi$
$463$	−34.6368	−1.60971	−0.804855	+	0.593471i	$0.797757\pi$
$464$	79.8773	3.70821
$465$	9.31364	0.431910
$466$	54.0846	2.50542
$467$	4.70383	0.217667	0.108834	−	0.994060i	$-0.465288\pi$
$467$	4.70383	0.217667	0.108834	+	0.994060i	$0.465288\pi$
$468$	19.8005	0.915280
$469$	5.20006	0.240116
$470$	19.7986	0.913239
$471$	−26.4197	−1.21735
$472$	−7.53721	−0.346928
$473$	9.79937	0.450575
$474$	93.4560	4.29258
$475$	−7.09974	−0.325758
$476$	−8.94312	−0.409907
$477$	−29.3154	−1.34226
$478$	13.3971	0.612770
$479$	14.2102	0.649279	0.324640	−	0.945838i	$-0.394757\pi$
$479$	14.2102	0.649279	0.324640	+	0.945838i	$0.394757\pi$
$480$	55.4256	2.52982
$481$	−2.86014	−0.130411
$482$	−16.0341	−0.730334
$483$	−2.50521	−0.113991
$484$	120.703	5.48650
$485$	−10.3150	−0.468378
$486$	57.6620	2.61560
$487$	−11.0703	−0.501642	−0.250821	−	0.968033i	$-0.580701\pi$
$487$	−11.0703	−0.501642	−0.250821	+	0.968033i	$0.580701\pi$
$488$	56.6904	2.56625
$489$	31.4430	1.42190
$490$	18.7577	0.847385
$491$	−15.8004	−0.713062	−0.356531	−	0.934284i	$-0.616041\pi$
$491$	−15.8004	−0.713062	−0.356531	+	0.934284i	$0.616041\pi$
$492$	−1.93669	−0.0873127
$493$	20.2055	0.910009
$494$	−26.5768	−1.19575
$495$	−15.0188	−0.675045
$496$	61.2311	2.74936
$497$	−0.813304	−0.0364817
$498$	−13.5479	−0.607095
$499$	4.30734	0.192823	0.0964115	−	0.995342i	$-0.469264\pi$
$499$	4.30734	0.192823	0.0964115	+	0.995342i	$0.469264\pi$
$500$	−5.53751	−0.247645
$501$	16.8233	0.751608
$502$	−28.3054	−1.26333
$503$	23.2152	1.03511	0.517556	−	0.855649i	$-0.326842\pi$
$503$	23.2152	1.03511	0.517556	+	0.855649i	$0.326842\pi$
$504$	−10.4313	−0.464647
$505$	−8.21622	−0.365617
$506$	−40.5603	−1.80312
$507$	26.4172	1.17323
$508$	115.428	5.12127
$509$	−25.7517	−1.14142	−0.570712	−	0.821150i	$-0.693333\pi$
$509$	−25.7517	−1.14142	−0.570712	+	0.821150i	$0.693333\pi$
$510$	25.6710	1.13673
$511$	5.60768	0.248069
$512$	61.5852	2.72171
$513$	−6.35504	−0.280582
$514$	−65.0348	−2.86856
$515$	15.5311	0.684381
$516$	−22.4677	−0.989084
$517$	−41.2989	−1.81632
$518$	2.35866	0.103634
$519$	41.4904	1.82122
$520$	−13.2421	−0.580705
$521$	−26.0511	−1.14132	−0.570661	−	0.821186i	$-0.693313\pi$
$521$	−26.0511	−1.14132	−0.570661	+	0.821186i	$0.693313\pi$
$522$	36.8923	1.61473
$523$	−16.2781	−0.711790	−0.355895	−	0.934526i	$-0.615824\pi$
$523$	−16.2781	−0.711790	−0.355895	+	0.934526i	$0.615824\pi$
$524$	96.1401	4.19990
$525$	0.971127	0.0423835
$526$	−14.0137	−0.611026
$527$	15.4888	0.674704
$528$	−211.691	−9.21266
$529$	−16.3452	−0.710661
$530$	30.6898	1.33308
$531$	−2.03524	−0.0883219
$532$	16.1015	0.698091
$533$	0.201107	0.00871091
$534$	−57.5905	−2.49218
$535$	17.3828	0.751524
$536$	−123.313	−5.32630
$537$	38.7958	1.67416
$538$	5.82028	0.250930
$539$	−39.1277	−1.68535
$540$	−4.95668	−0.213301
$541$	31.7624	1.36557	0.682785	−	0.730619i	$-0.260768\pi$
$541$	31.7624	1.36557	0.682785	+	0.730619i	$0.260768\pi$
$542$	−62.6737	−2.69206
$543$	25.7263	1.10402
$544$	92.1742	3.95194
$545$	−8.03341	−0.344113
$546$	3.63527	0.155575
$547$	16.3708	0.699967	0.349983	−	0.936756i	$-0.386187\pi$
$547$	16.3708	0.699967	0.349983	+	0.936756i	$0.386187\pi$
$548$	−96.6063	−4.12682
$549$	15.3078	0.653323
$550$	15.7229	0.670428
$551$	−36.3787	−1.54979
$552$	59.4079	2.52857
$553$	5.87949	0.250021
$554$	74.2178	3.15321
$555$	−4.97399	−0.211134
$556$	82.0452	3.47949
$557$	−8.20755	−0.347765	−0.173883	−	0.984766i	$-0.555631\pi$
$557$	−8.20755	−0.347765	−0.173883	+	0.984766i	$0.555631\pi$
$558$	28.2804	1.19720
$559$	2.33305	0.0986777
$560$	6.38453	0.269796
$561$	−53.5486	−2.26082
$562$	19.1575	0.808109
$563$	−14.6402	−0.617010	−0.308505	−	0.951223i	$-0.599829\pi$
$563$	−14.6402	−0.617010	−0.308505	+	0.951223i	$0.599829\pi$
$564$	94.6888	3.98712
$565$	−3.31515	−0.139469
$566$	−24.7306	−1.03950
$567$	4.09144	0.171824
$568$	19.2865	0.809243
$569$	34.6261	1.45160	0.725801	−	0.687905i	$-0.241469\pi$
$569$	34.6261	1.45160	0.725801	+	0.687905i	$0.241469\pi$
$570$	−46.2190	−1.93590
$571$	23.8854	0.999571	0.499786	−	0.866149i	$-0.333412\pi$
$571$	23.8854	0.999571	0.499786	+	0.866149i	$0.333412\pi$
$572$	43.2394	1.80793
$573$	47.6910	1.99232
$574$	−0.165846	−0.00692229
$575$	−2.57969	−0.107581
$576$	86.5324	3.60552
$577$	20.4468	0.851209	0.425605	−	0.904909i	$-0.360061\pi$
$577$	20.4468	0.851209	0.425605	+	0.904909i	$0.360061\pi$
$578$	−3.98120	−0.165596
$579$	−53.7767	−2.23488
$580$	−28.3740	−1.17816
$581$	−0.852321	−0.0353603
$582$	−67.1501	−2.78346
$583$	−64.0176	−2.65134
$584$	−132.979	−5.50272
$585$	−3.57571	−0.147837
$586$	78.0845	3.22564
$587$	6.11666	0.252461	0.126231	−	0.992001i	$-0.459712\pi$
$587$	6.11666	0.252461	0.126231	+	0.992001i	$0.459712\pi$
$588$	89.7107	3.69961
$589$	−27.8867	−1.14905
$590$	2.13066	0.0877177
$591$	−24.3479	−1.00154
$592$	−32.7008	−1.34399
$593$	−28.3186	−1.16290	−0.581452	−	0.813581i	$-0.697515\pi$
$593$	−28.3186	−1.16290	−0.581452	+	0.813581i	$0.697515\pi$
$594$	14.0737	0.577452
$595$	1.61501	0.0662089
$596$	50.0669	2.05082
$597$	−4.99964	−0.204622
$598$	−9.65668	−0.394891
$599$	35.6183	1.45533	0.727663	−	0.685935i	$-0.240607\pi$
$599$	35.6183	1.45533	0.727663	+	0.685935i	$0.240607\pi$
$600$	−23.0291	−0.940158
$601$	31.5191	1.28569	0.642845	−	0.765996i	$-0.277754\pi$
$601$	31.5191	1.28569	0.642845	+	0.765996i	$0.277754\pi$
$602$	−1.92399	−0.0784161
$603$	−33.2976	−1.35598
$604$	5.53751	0.225318
$605$	−21.7973	−0.886188
$606$	−53.4873	−2.17277
$607$	3.32898	0.135119	0.0675596	−	0.997715i	$-0.478479\pi$
$607$	3.32898	0.135119	0.0675596	+	0.997715i	$0.478479\pi$
$608$	−165.954	−6.73032
$609$	4.97601	0.201638
$610$	−16.0255	−0.648854
$611$	−9.83254	−0.397782
$612$	57.2657	2.31483
$613$	−28.8013	−1.16327	−0.581636	−	0.813449i	$-0.697587\pi$
$613$	−28.8013	−1.16327	−0.581636	+	0.813449i	$0.697587\pi$
$614$	−23.0349	−0.929612
$615$	0.349740	0.0141029
$616$	−22.7794	−0.917807
$617$	−33.0710	−1.33139	−0.665694	−	0.746225i	$-0.731864\pi$
$617$	−33.0710	−1.33139	−0.665694	+	0.746225i	$0.731864\pi$
$618$	101.107	4.06711
$619$	−4.02487	−0.161773	−0.0808865	−	0.996723i	$-0.525775\pi$
$619$	−4.02487	−0.161773	−0.0808865	+	0.996723i	$0.525775\pi$
$620$	−21.7505	−0.873521
$621$	−2.30911	−0.0926612
$622$	23.8934	0.958039
$623$	−3.62312	−0.145157
$624$	−50.3998	−2.01761
$625$	1.00000	0.0400000
$626$	45.1773	1.80565
$627$	96.4110	3.85028
$628$	61.6988	2.46205
$629$	−8.27188	−0.329821
$630$	2.94877	0.117482
$631$	34.4434	1.37117	0.685585	−	0.727993i	$-0.259547\pi$
$631$	34.4434	1.37117	0.685585	+	0.727993i	$0.259547\pi$
$632$	−139.425	−5.54602
$633$	13.2245	0.525627
$634$	36.2928	1.44137
$635$	−20.8447	−0.827195
$636$	146.777	5.82011
$637$	−9.31560	−0.369098
$638$	80.5636	3.18954
$639$	5.20785	0.206019
$640$	−43.8399	−1.73292
$641$	−21.5044	−0.849374	−0.424687	−	0.905340i	$-0.639616\pi$
$641$	−21.5044	−0.849374	−0.424687	+	0.905340i	$0.639616\pi$
$642$	113.162	4.46613
$643$	−2.46658	−0.0972723	−0.0486362	−	0.998817i	$-0.515487\pi$
$643$	−2.46658	−0.0972723	−0.0486362	+	0.998817i	$0.515487\pi$
$644$	5.85050	0.230542
$645$	4.05736	0.159758
$646$	−76.8634	−3.02415
$647$	4.94737	0.194501	0.0972506	−	0.995260i	$-0.468995\pi$
$647$	4.94737	0.194501	0.0972506	+	0.995260i	$0.468995\pi$
$648$	−97.0233	−3.81144
$649$	−4.44446	−0.174460
$650$	3.74335	0.146826
$651$	3.81444	0.149500
$652$	−73.4300	−2.87574
$653$	−13.7880	−0.539566	−0.269783	−	0.962921i	$-0.586952\pi$
$653$	−13.7880	−0.539566	−0.269783	+	0.962921i	$0.586952\pi$
$654$	−52.2972	−2.04498
$655$	−17.3616	−0.678375
$656$	2.29931	0.0897731
$657$	−35.9078	−1.40090
$658$	8.10857	0.316105
$659$	4.51603	0.175919	0.0879597	−	0.996124i	$-0.471965\pi$
$659$	4.51603	0.175919	0.0879597	+	0.996124i	$0.471965\pi$
$660$	75.1967	2.92703
$661$	−4.84653	−0.188508	−0.0942541	−	0.995548i	$-0.530047\pi$
$661$	−4.84653	−0.188508	−0.0942541	+	0.995548i	$0.530047\pi$
$662$	60.3268	2.34467
$663$	−12.7490	−0.495129
$664$	20.2117	0.784368
$665$	−2.90772	−0.112757
$666$	−15.1033	−0.585239
$667$	−13.2182	−0.511812
$668$	−39.2880	−1.52010
$669$	−1.77422	−0.0685952
$670$	34.8587	1.34671
$671$	33.4285	1.29049
$672$	22.6998	0.875663
$673$	41.1033	1.58442	0.792208	−	0.610252i	$-0.208932\pi$
$673$	41.1033	1.58442	0.792208	+	0.610252i	$0.208932\pi$
$674$	22.0791	0.850455
$675$	0.895110	0.0344528
$676$	−61.6931	−2.37281
$677$	−4.33170	−0.166481	−0.0832404	−	0.996529i	$-0.526527\pi$
$677$	−4.33170	−0.166481	−0.0832404	+	0.996529i	$0.526527\pi$
$678$	−21.5815	−0.828833
$679$	−4.22453	−0.162123
$680$	−38.2979	−1.46866
$681$	6.80811	0.260887
$682$	61.7572	2.36481
$683$	9.02009	0.345144	0.172572	−	0.984997i	$-0.444792\pi$
$683$	9.02009	0.345144	0.172572	+	0.984997i	$0.444792\pi$
$684$	−103.103	−3.94226
$685$	17.4458	0.666570
$686$	15.5531	0.593822
$687$	−49.9340	−1.90510
$688$	26.6745	1.01696
$689$	−15.2415	−0.580653
$690$	−16.7937	−0.639325
$691$	−14.7051	−0.559407	−0.279704	−	0.960086i	$-0.590236\pi$
$691$	−14.7051	−0.559407	−0.279704	+	0.960086i	$0.590236\pi$
$692$	−96.8939	−3.68336
$693$	−6.15101	−0.233658
$694$	−64.5619	−2.45074
$695$	−14.8163	−0.562013
$696$	−118.000	−4.47278
$697$	0.581627	0.0220307
$698$	71.0193	2.68812
$699$	−46.7116	−1.76679
$700$	−2.26791	−0.0857189
$701$	−12.4801	−0.471369	−0.235684	−	0.971830i	$-0.575733\pi$
$701$	−12.4801	−0.471369	−0.235684	+	0.971830i	$0.575733\pi$
$702$	3.35071	0.126464
$703$	14.8930	0.561700
$704$	188.965	7.12190
$705$	−17.0995	−0.644006
$706$	−83.4282	−3.13986
$707$	−3.36498	−0.126553
$708$	10.1901	0.382968
$709$	13.7565	0.516635	0.258318	−	0.966060i	$-0.416832\pi$
$709$	13.7565	0.516635	0.258318	+	0.966060i	$0.416832\pi$
$710$	−5.45200	−0.204610
$711$	−37.6482	−1.41192
$712$	85.9178	3.21991
$713$	−10.1326	−0.379470
$714$	10.5137	0.393464
$715$	−7.80846	−0.292020
$716$	−90.6013	−3.38593
$717$	−11.5708	−0.432118
$718$	−40.5635	−1.51382
$719$	−13.5291	−0.504551	−0.252275	−	0.967656i	$-0.581179\pi$
$719$	−13.5291	−0.504551	−0.252275	+	0.967656i	$0.581179\pi$
$720$	−40.8822	−1.52359
$721$	6.36081	0.236889
$722$	86.2243	3.20894
$723$	13.8483	0.515023
$724$	−60.0795	−2.23284
$725$	5.12396	0.190299
$726$	−141.900	−5.26640
$727$	6.07544	0.225326	0.112663	−	0.993633i	$-0.464062\pi$
$727$	6.07544	0.225326	0.112663	+	0.993633i	$0.464062\pi$
$728$	−5.42336	−0.201003
$729$	−19.8314	−0.734495
$730$	37.5912	1.39131
$731$	6.74749	0.249565
$732$	−76.6438	−2.83284
$733$	41.7228	1.54107	0.770534	−	0.637399i	$-0.219990\pi$
$733$	41.7228	1.54107	0.770534	+	0.637399i	$0.219990\pi$
$734$	−16.3188	−0.602338
$735$	−16.2005	−0.597566
$736$	−60.2994	−2.22267
$737$	−72.7137	−2.67844
$738$	1.06197	0.0390915
$739$	38.9251	1.43188	0.715942	−	0.698160i	$-0.245998\pi$
$739$	38.9251	1.43188	0.715942	+	0.698160i	$0.245998\pi$
$740$	11.6159	0.427011
$741$	22.9537	0.843226
$742$	12.5691	0.461427
$743$	26.2242	0.962071	0.481036	−	0.876701i	$-0.340261\pi$
$743$	26.2242	0.962071	0.481036	+	0.876701i	$0.340261\pi$
$744$	−90.4546	−3.31623
$745$	−9.04142	−0.331252
$746$	79.9045	2.92551
$747$	5.45769	0.199686
$748$	125.054	4.57242
$749$	7.11920	0.260130
$750$	6.50997	0.237710
$751$	−18.4457	−0.673094	−0.336547	−	0.941667i	$-0.609259\pi$
$751$	−18.4457	−0.673094	−0.336547	+	0.941667i	$0.609259\pi$
$752$	−112.418	−4.09948
$753$	24.4467	0.890886
$754$	19.1808	0.698522
$755$	−1.00000	−0.0363937
$756$	−2.03003	−0.0738313
$757$	36.3116	1.31977	0.659885	−	0.751367i	$-0.270605\pi$
$757$	36.3116	1.31977	0.659885	+	0.751367i	$0.270605\pi$
$758$	−4.57126	−0.166036
$759$	35.0309	1.27154
$760$	68.9531	2.50119
$761$	17.1080	0.620165	0.310083	−	0.950710i	$-0.399643\pi$
$761$	17.1080	0.620165	0.310083	+	0.950710i	$0.399643\pi$
$762$	−135.698	−4.91582
$763$	−3.29011	−0.119110
$764$	−111.374	−4.02939
$765$	−10.3414	−0.373895
$766$	19.2029	0.693829
$767$	−1.05815	−0.0382074
$768$	−128.917	−4.65188
$769$	25.4156	0.916511	0.458256	−	0.888820i	$-0.348474\pi$
$769$	25.4156	0.916511	0.458256	+	0.888820i	$0.348474\pi$
$770$	6.43938	0.232059
$771$	56.1690	2.02288
$772$	125.587	4.51996
$773$	2.14231	0.0770536	0.0385268	−	0.999258i	$-0.487734\pi$
$773$	2.14231	0.0770536	0.0385268	+	0.999258i	$0.487734\pi$
$774$	12.3199	0.442831
$775$	3.92785	0.141092
$776$	100.180	3.59623
$777$	−2.03712	−0.0730812
$778$	−0.744881	−0.0267053
$779$	−1.04718	−0.0375192
$780$	17.9030	0.641030
$781$	11.3726	0.406945
$782$	−27.9284	−0.998716
$783$	4.58650	0.163908
$784$	−106.508	−3.80386
$785$	−11.1420	−0.397674
$786$	−113.024	−4.03142
$787$	−36.0836	−1.28624	−0.643121	−	0.765765i	$-0.722361\pi$
$787$	−36.0836	−1.28624	−0.643121	+	0.765765i	$0.722361\pi$
$788$	56.8606	2.02557
$789$	12.1033	0.430889
$790$	39.4132	1.40226
$791$	−1.35773	−0.0482754
$792$	145.864	5.18304
$793$	7.95874	0.282623
$794$	19.9529	0.708102
$795$	−26.5061	−0.940073
$796$	11.6758	0.413839
$797$	−19.3971	−0.687081	−0.343541	−	0.939138i	$-0.611626\pi$
$797$	−19.3971	−0.687081	−0.343541	+	0.939138i	$0.611626\pi$
$798$	−18.9292	−0.670086
$799$	−28.4370	−1.00603
$800$	23.3747	0.826420
$801$	23.2000	0.819732
$802$	−56.9553	−2.01116
$803$	−78.4136	−2.76716
$804$	166.716	5.87961
$805$	−1.05652	−0.0372375
$806$	14.7033	0.517902
$807$	−5.02684	−0.176953
$808$	79.7964	2.80723
$809$	39.5269	1.38969	0.694846	−	0.719158i	$-0.255472\pi$
$809$	39.5269	1.38969	0.694846	+	0.719158i	$0.255472\pi$
$810$	27.4270	0.963687
$811$	41.5967	1.46066	0.730329	−	0.683095i	$-0.239367\pi$
$811$	41.5967	1.46066	0.730329	+	0.683095i	$0.239367\pi$
$812$	−11.6207	−0.407805
$813$	54.1298	1.89841
$814$	−32.9817	−1.15601
$815$	13.2605	0.464494
$816$	−145.763	−5.10271
$817$	−12.1485	−0.425020
$818$	−49.0342	−1.71444
$819$	−1.46445	−0.0511719
$820$	−0.816761	−0.0285225
$821$	−44.9498	−1.56876	−0.784380	−	0.620280i	$-0.787019\pi$
$821$	−44.9498	−1.56876	−0.784380	+	0.620280i	$0.787019\pi$
$822$	113.572	3.96126
$823$	17.8689	0.622870	0.311435	−	0.950268i	$-0.399190\pi$
$823$	17.8689	0.622870	0.311435	+	0.950268i	$0.399190\pi$
$824$	−150.839	−5.25472
$825$	−13.5795	−0.472778
$826$	0.872618	0.0303623
$827$	24.8985	0.865806	0.432903	−	0.901440i	$-0.357489\pi$
$827$	24.8985	0.865806	0.432903	+	0.901440i	$0.357489\pi$
$828$	−37.4626	−1.30192
$829$	35.1635	1.22128	0.610640	−	0.791909i	$-0.290912\pi$
$829$	35.1635	1.22128	0.610640	+	0.791909i	$0.290912\pi$
$830$	−5.71355	−0.198320
$831$	−64.1001	−2.22361
$832$	44.9893	1.55972
$833$	−26.9419	−0.933482
$834$	−96.4534	−3.33991
$835$	7.09489	0.245529
$836$	−225.152	−7.78704
$837$	3.51585	0.121526
$838$	20.3790	0.703981
$839$	35.9651	1.24165	0.620826	−	0.783948i	$-0.286797\pi$
$839$	35.9651	1.24165	0.620826	+	0.783948i	$0.286797\pi$
$840$	−9.43164	−0.325423
$841$	−2.74506	−0.0946571
$842$	−29.8049	−1.02714
$843$	−16.5459	−0.569870
$844$	−30.8837	−1.06306
$845$	11.1409	0.383260
$846$	−51.9218	−1.78511
$847$	−8.92718	−0.306742
$848$	−174.260	−5.98411
$849$	21.3592	0.733046
$850$	10.8262	0.371337
$851$	5.41138	0.185500
$852$	−26.0748	−0.893308
$853$	−20.1505	−0.689939	−0.344970	−	0.938614i	$-0.612111\pi$
$853$	−20.1505	−0.689939	−0.344970	+	0.938614i	$0.612111\pi$
$854$	−6.56331	−0.224592
$855$	18.6191	0.636759
$856$	−168.823	−5.77025
$857$	32.5725	1.11266	0.556328	−	0.830963i	$-0.312210\pi$
$857$	32.5725	1.11266	0.556328	+	0.830963i	$0.312210\pi$
$858$	−50.8328	−1.73540
$859$	11.5974	0.395698	0.197849	−	0.980233i	$-0.436604\pi$
$859$	11.5974	0.395698	0.197849	+	0.980233i	$0.436604\pi$
$860$	−9.47530	−0.323105
$861$	0.143237	0.00488152
$862$	38.8804	1.32427
$863$	−3.25780	−0.110897	−0.0554485	−	0.998462i	$-0.517659\pi$
$863$	−3.25780	−0.110897	−0.0554485	+	0.998462i	$0.517659\pi$
$864$	20.9229	0.711812
$865$	17.4978	0.594941
$866$	−29.2734	−0.994749
$867$	3.43847	0.116776
$868$	−8.90800	−0.302357
$869$	−82.2143	−2.78893
$870$	33.3568	1.13090
$871$	−17.3118	−0.586589
$872$	78.0209	2.64212
$873$	27.0510	0.915539
$874$	50.2833	1.70086
$875$	0.409554	0.0138454
$876$	179.784	6.07435
$877$	−21.9443	−0.741006	−0.370503	−	0.928831i	$-0.620815\pi$
$877$	−21.9443	−0.741006	−0.370503	+	0.928831i	$0.620815\pi$
$878$	−71.4649	−2.41182
$879$	−67.4397	−2.27469
$880$	−89.2765	−3.00951
$881$	25.0285	0.843233	0.421616	−	0.906774i	$-0.361463\pi$
$881$	25.0285	0.843233	0.421616	+	0.906774i	$0.361463\pi$
$882$	−49.1921	−1.65638
$883$	13.6265	0.458568	0.229284	−	0.973360i	$-0.426361\pi$
$883$	13.6265	0.458568	0.229284	+	0.973360i	$0.426361\pi$
$884$	29.7731	1.00138
$885$	−1.84020	−0.0618575
$886$	89.0834	2.99282
$887$	43.3273	1.45479	0.727394	−	0.686220i	$-0.240731\pi$
$887$	43.3273	1.45479	0.727394	+	0.686220i	$0.240731\pi$
$888$	48.3077	1.62110
$889$	−8.53702	−0.286322
$890$	−24.2877	−0.814125
$891$	−57.2116	−1.91666
$892$	4.14339	0.138731
$893$	51.1990	1.71331
$894$	−58.8594	−1.96855
$895$	16.3614	0.546901
$896$	−17.9548	−0.599827
$897$	8.34025	0.278473
$898$	−76.2417	−2.54422
$899$	20.1261	0.671244
$900$	14.5221	0.484071
$901$	−44.0802	−1.46853
$902$	2.31907	0.0772166
$903$	1.66171	0.0552982
$904$	32.1969	1.07085
$905$	10.8496	0.360651
$906$	−6.50997	−0.216279
$907$	38.2121	1.26881	0.634406	−	0.773000i	$-0.281245\pi$
$907$	38.2121	1.26881	0.634406	+	0.773000i	$0.281245\pi$
$908$	−15.8992	−0.527634
$909$	21.5471	0.714671
$910$	1.53310	0.0508219
$911$	−47.2420	−1.56520	−0.782599	−	0.622526i	$-0.786106\pi$
$911$	−47.2420	−1.56520	−0.782599	+	0.622526i	$0.786106\pi$
$912$	262.437	8.69015
$913$	11.9182	0.394436
$914$	−12.8477	−0.424963
$915$	13.8408	0.457564
$916$	116.613	3.85300
$917$	−7.11052	−0.234810
$918$	9.69067	0.319840
$919$	−20.7803	−0.685480	−0.342740	−	0.939430i	$-0.611355\pi$
$919$	−20.7803	−0.685480	−0.342740	+	0.939430i	$0.611355\pi$
$920$	25.0541	0.826010
$921$	19.8947	0.655552
$922$	−49.3193	−1.62424
$923$	2.70762	0.0891225
$924$	30.7971	1.01315
$925$	−2.09769	−0.0689715
$926$	−95.0938	−3.12498
$927$	−40.7303	−1.33776
$928$	119.771	3.93167
$929$	16.1602	0.530198	0.265099	−	0.964221i	$-0.414595\pi$
$929$	16.1602	0.530198	0.265099	+	0.964221i	$0.414595\pi$
$930$	25.5702	0.838479
$931$	48.5073	1.58976
$932$	109.087	3.57327
$933$	−20.6362	−0.675598
$934$	12.9141	0.422563
$935$	−22.5831	−0.738545
$936$	34.7275	1.13510
$937$	1.67931	0.0548605	0.0274303	−	0.999624i	$-0.491268\pi$
$937$	1.67931	0.0548605	0.0274303	+	0.999624i	$0.491268\pi$
$938$	14.2765	0.466144
$939$	−39.0186	−1.27332
$940$	39.9332	1.30248
$941$	1.66990	0.0544370	0.0272185	−	0.999630i	$-0.491335\pi$
$941$	1.66990	0.0544370	0.0272185	+	0.999630i	$0.491335\pi$
$942$	−72.5339	−2.36328
$943$	−0.380494	−0.0123906
$944$	−12.0981	−0.393759
$945$	0.366596	0.0119254
$946$	26.9037	0.874714
$947$	11.8324	0.384501	0.192251	−	0.981346i	$-0.438421\pi$
$947$	11.8324	0.384501	0.192251	+	0.981346i	$0.438421\pi$
$948$	188.498	6.12214
$949$	−18.6689	−0.606018
$950$	−19.4920	−0.632403
$951$	−31.3452	−1.01644
$952$	−15.6851	−0.508356
$953$	−5.06600	−0.164104	−0.0820519	−	0.996628i	$-0.526147\pi$
$953$	−5.06600	−0.164104	−0.0820519	+	0.996628i	$0.526147\pi$
$954$	−80.4842	−2.60577
$955$	20.1127	0.650833
$956$	27.0216	0.873942
$957$	−69.5809	−2.24923
$958$	39.0133	1.26046
$959$	7.14500	0.230724
$960$	78.2398	2.52518
$961$	−15.5720	−0.502323
$962$	−7.85236	−0.253170
$963$	−45.5865	−1.46900
$964$	−32.3404	−1.04161
$965$	−22.6793	−0.730072
$966$	−6.87793	−0.221294
$967$	28.1196	0.904265	0.452132	−	0.891951i	$-0.350663\pi$
$967$	28.1196	0.904265	0.452132	+	0.891951i	$0.350663\pi$
$968$	211.697	6.80420
$969$	66.3851	2.13260
$970$	−28.3192	−0.909276
$971$	47.2285	1.51563	0.757817	−	0.652468i	$-0.226266\pi$
$971$	47.2285	1.51563	0.757817	+	0.652468i	$0.226266\pi$
$972$	116.303	3.73042
$973$	−6.06806	−0.194533
$974$	−30.3929	−0.973852
$975$	−3.23304	−0.103540
$976$	90.9946	2.91267
$977$	11.8376	0.378718	0.189359	−	0.981908i	$-0.439359\pi$
$977$	11.8376	0.378718	0.189359	+	0.981908i	$0.439359\pi$
$978$	86.3253	2.76038
$979$	50.6630	1.61920
$980$	37.8337	1.20855
$981$	21.0676	0.672638
$982$	−43.3792	−1.38429
$983$	−4.86039	−0.155022	−0.0775112	−	0.996991i	$-0.524697\pi$
$983$	−4.86039	−0.155022	−0.0775112	+	0.996991i	$0.524697\pi$
$984$	−3.39670	−0.108283
$985$	−10.2683	−0.327174
$986$	55.4732	1.76663
$987$	−7.00318	−0.222914
$988$	−53.6047	−1.70539
$989$	−4.41414	−0.140362
$990$	−41.2334	−1.31048
$991$	−39.7600	−1.26302	−0.631508	−	0.775369i	$-0.717564\pi$
$991$	−39.7600	−1.26302	−0.631508	+	0.775369i	$0.717564\pi$
$992$	91.8122	2.91504
$993$	−52.1029	−1.65343
$994$	−2.23289	−0.0708229
$995$	−2.10850	−0.0668439
$996$	−27.3257	−0.865849
$997$	58.7462	1.86051	0.930256	−	0.366912i	$-0.119585\pi$
$997$	58.7462	1.86051	0.930256	+	0.366912i	$0.119585\pi$
$998$	11.8256	0.374333
$999$	−1.87766	−0.0594065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.a.k.1.18	✓	18
3.2	odd	2		6795.2.a.bi.1.1		18
5.4	even	2		3775.2.a.r.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.a.k.1.18	✓	18	1.1	even	1	trivial
3775.2.a.r.1.1		18	5.4	even	2
6795.2.a.bi.1.1		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.a (trivial)

\(f(q)\)	\(=\)	\(q+2.74545 q^{2} -2.37118 q^{3} +5.53751 q^{4} -1.00000 q^{5} -6.50997 q^{6} -0.409554 q^{7} +9.71206 q^{8} +2.62250 q^{9} +O(q^{10})\)	\(q+2.74545 q^{2} -2.37118 q^{3} +5.53751 q^{4} -1.00000 q^{5} -6.50997 q^{6} -0.409554 q^{7} +9.71206 q^{8} +2.62250 q^{9} -2.74545 q^{10} +5.72690 q^{11} -13.1304 q^{12} +1.36347 q^{13} -1.12441 q^{14} +2.37118 q^{15} +15.5890 q^{16} +3.94334 q^{17} +7.19996 q^{18} -7.09974 q^{19} -5.53751 q^{20} +0.971127 q^{21} +15.7229 q^{22} -2.57969 q^{23} -23.0291 q^{24} +1.00000 q^{25} +3.74335 q^{26} +0.895110 q^{27} -2.26791 q^{28} +5.12396 q^{29} +6.50997 q^{30} +3.92785 q^{31} +23.3747 q^{32} -13.5795 q^{33} +10.8262 q^{34} +0.409554 q^{35} +14.5221 q^{36} -2.09769 q^{37} -19.4920 q^{38} -3.23304 q^{39} -9.71206 q^{40} +0.147496 q^{41} +2.66618 q^{42} +1.71111 q^{43} +31.7127 q^{44} -2.62250 q^{45} -7.08242 q^{46} -7.21140 q^{47} -36.9643 q^{48} -6.83227 q^{49} +2.74545 q^{50} -9.35037 q^{51} +7.55024 q^{52} -11.1784 q^{53} +2.45748 q^{54} -5.72690 q^{55} -3.97761 q^{56} +16.8348 q^{57} +14.0676 q^{58} -0.776067 q^{59} +13.1304 q^{60} +5.83711 q^{61} +10.7837 q^{62} -1.07406 q^{63} +32.9961 q^{64} -1.36347 q^{65} -37.2819 q^{66} -12.6969 q^{67} +21.8363 q^{68} +6.11692 q^{69} +1.12441 q^{70} +1.98583 q^{71} +25.4699 q^{72} -13.6922 q^{73} -5.75909 q^{74} -2.37118 q^{75} -39.3148 q^{76} -2.34547 q^{77} -8.87616 q^{78} -14.3558 q^{79} -15.5890 q^{80} -9.98998 q^{81} +0.404944 q^{82} +2.08110 q^{83} +5.37762 q^{84} -3.94334 q^{85} +4.69778 q^{86} -12.1498 q^{87} +55.6200 q^{88} +8.84651 q^{89} -7.19996 q^{90} -0.558415 q^{91} -14.2851 q^{92} -9.31364 q^{93} -19.7986 q^{94} +7.09974 q^{95} -55.4256 q^{96} +10.3150 q^{97} -18.7577 q^{98} +15.0188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 2 q^{3} + 32 q^{4} - 18 q^{5} + 10 q^{6} + 4 q^{7} + 32 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 2 * q^3 + 32 * q^4 - 18 * q^5 + 10 * q^6 + 4 * q^7 + 32 * q^9	\( 18 q - 2 q^{2} + 2 q^{3} + 32 q^{4} - 18 q^{5} + 10 q^{6} + 4 q^{7} + 32 q^{9} + 2 q^{10} + 11 q^{11} + 12 q^{13} + q^{14} - 2 q^{15} + 60 q^{16} - 25 q^{17} - 9 q^{18} + 8 q^{19} - 32 q^{20} + 20 q^{21} + 29 q^{22} + 12 q^{23} + 15 q^{24} + 18 q^{25} + 5 q^{26} + 5 q^{27} + 15 q^{28} + 24 q^{29} - 10 q^{30} + 11 q^{31} - 17 q^{32} - 33 q^{33} + 17 q^{34} - 4 q^{35} + 90 q^{36} + 45 q^{37} - 28 q^{38} + 38 q^{39} + 12 q^{41} - 9 q^{42} + 19 q^{43} + 6 q^{44} - 32 q^{45} - 5 q^{46} - 16 q^{47} - 3 q^{48} + 62 q^{49} - 2 q^{50} + 7 q^{51} + q^{52} - 4 q^{53} - 6 q^{54} - 11 q^{55} + 2 q^{56} + 5 q^{57} + 28 q^{58} - 8 q^{59} + 27 q^{61} - 57 q^{62} + 10 q^{63} + 98 q^{64} - 12 q^{65} - 32 q^{66} + 9 q^{67} - 26 q^{68} + 31 q^{69} - q^{70} + 9 q^{71} - 102 q^{72} + 2 q^{73} - 24 q^{74} + 2 q^{75} - 43 q^{76} + 11 q^{77} + 45 q^{78} + 20 q^{79} - 60 q^{80} + 66 q^{81} - 19 q^{82} - 20 q^{83} - 33 q^{84} + 25 q^{85} + 21 q^{86} - 33 q^{87} + 62 q^{88} + 13 q^{89} + 9 q^{90} + 22 q^{91} - 6 q^{92} + 58 q^{93} + 70 q^{94} - 8 q^{95} - 17 q^{96} - 27 q^{97} - 6 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 2 * q^3 + 32 * q^4 - 18 * q^5 + 10 * q^6 + 4 * q^7 + 32 * q^9 + 2 * q^10 + 11 * q^11 + 12 * q^13 + q^14 - 2 * q^15 + 60 * q^16 - 25 * q^17 - 9 * q^18 + 8 * q^19 - 32 * q^20 + 20 * q^21 + 29 * q^22 + 12 * q^23 + 15 * q^24 + 18 * q^25 + 5 * q^26 + 5 * q^27 + 15 * q^28 + 24 * q^29 - 10 * q^30 + 11 * q^31 - 17 * q^32 - 33 * q^33 + 17 * q^34 - 4 * q^35 + 90 * q^36 + 45 * q^37 - 28 * q^38 + 38 * q^39 + 12 * q^41 - 9 * q^42 + 19 * q^43 + 6 * q^44 - 32 * q^45 - 5 * q^46 - 16 * q^47 - 3 * q^48 + 62 * q^49 - 2 * q^50 + 7 * q^51 + q^52 - 4 * q^53 - 6 * q^54 - 11 * q^55 + 2 * q^56 + 5 * q^57 + 28 * q^58 - 8 * q^59 + 27 * q^61 - 57 * q^62 + 10 * q^63 + 98 * q^64 - 12 * q^65 - 32 * q^66 + 9 * q^67 - 26 * q^68 + 31 * q^69 - q^70 + 9 * q^71 - 102 * q^72 + 2 * q^73 - 24 * q^74 + 2 * q^75 - 43 * q^76 + 11 * q^77 + 45 * q^78 + 20 * q^79 - 60 * q^80 + 66 * q^81 - 19 * q^82 - 20 * q^83 - 33 * q^84 + 25 * q^85 + 21 * q^86 - 33 * q^87 + 62 * q^88 + 13 * q^89 + 9 * q^90 + 22 * q^91 - 6 * q^92 + 58 * q^93 + 70 * q^94 - 8 * q^95 - 17 * q^96 - 27 * q^97 - 6 * q^98 + 11 * q^99

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