LMFDB - Embedded newform 4003.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53975 q^{2} -3.24477 q^{3} +4.45032 q^{4} +3.59171 q^{5} +8.24090 q^{6} +4.74281 q^{7} -6.22319 q^{8} +7.52854 q^{9} +O(q^{10})$	\(q-2.53975 q^{2} -3.24477 q^{3} +4.45032 q^{4} +3.59171 q^{5} +8.24090 q^{6} +4.74281 q^{7} -6.22319 q^{8} +7.52854 q^{9} -9.12202 q^{10} +4.76337 q^{11} -14.4403 q^{12} +3.36742 q^{13} -12.0455 q^{14} -11.6543 q^{15} +6.90469 q^{16} +5.35637 q^{17} -19.1206 q^{18} -2.01798 q^{19} +15.9842 q^{20} -15.3893 q^{21} -12.0978 q^{22} -2.21388 q^{23} +20.1928 q^{24} +7.90035 q^{25} -8.55240 q^{26} -14.6941 q^{27} +21.1070 q^{28} -3.92084 q^{29} +29.5989 q^{30} -6.33401 q^{31} -5.08979 q^{32} -15.4560 q^{33} -13.6038 q^{34} +17.0348 q^{35} +33.5044 q^{36} +9.40711 q^{37} +5.12516 q^{38} -10.9265 q^{39} -22.3519 q^{40} +0.410884 q^{41} +39.0850 q^{42} -10.6813 q^{43} +21.1985 q^{44} +27.0403 q^{45} +5.62270 q^{46} -2.33990 q^{47} -22.4041 q^{48} +15.4942 q^{49} -20.0649 q^{50} -17.3802 q^{51} +14.9861 q^{52} +12.5748 q^{53} +37.3192 q^{54} +17.1086 q^{55} -29.5154 q^{56} +6.54789 q^{57} +9.95796 q^{58} -6.43629 q^{59} -51.8652 q^{60} -9.91875 q^{61} +16.0868 q^{62} +35.7064 q^{63} -0.882591 q^{64} +12.0948 q^{65} +39.2544 q^{66} +13.7899 q^{67} +23.8376 q^{68} +7.18354 q^{69} -43.2640 q^{70} +10.7550 q^{71} -46.8515 q^{72} -3.56896 q^{73} -23.8917 q^{74} -25.6348 q^{75} -8.98065 q^{76} +22.5917 q^{77} +27.7506 q^{78} -1.58288 q^{79} +24.7996 q^{80} +25.0933 q^{81} -1.04354 q^{82} +1.22307 q^{83} -68.4874 q^{84} +19.2385 q^{85} +27.1278 q^{86} +12.7222 q^{87} -29.6433 q^{88} -3.37179 q^{89} -68.6755 q^{90} +15.9710 q^{91} -9.85248 q^{92} +20.5524 q^{93} +5.94275 q^{94} -7.24799 q^{95} +16.5152 q^{96} +2.68050 q^{97} -39.3514 q^{98} +35.8612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.53975	−1.79587	−0.897936	−	0.440125i	$-0.854934\pi$
$2$	−2.53975	−1.79587	−0.897936	+	0.440125i	$0.854934\pi$
$3$	−3.24477	−1.87337	−0.936685	−	0.350174i	$-0.886123\pi$
$3$	−3.24477	−1.87337	−0.936685	+	0.350174i	$0.886123\pi$
$4$	4.45032	2.22516
$5$	3.59171	1.60626	0.803130	−	0.595804i	$-0.203167\pi$
$5$	3.59171	1.60626	0.803130	+	0.595804i	$0.203167\pi$
$6$	8.24090	3.36433
$7$	4.74281	1.79261	0.896306	−	0.443436i	$-0.146241\pi$
$7$	4.74281	1.79261	0.896306	+	0.443436i	$0.146241\pi$
$8$	−6.22319	−2.20023
$9$	7.52854	2.50951
$10$	−9.12202	−2.88464
$11$	4.76337	1.43621	0.718105	−	0.695935i	$-0.245010\pi$
$11$	4.76337	1.43621	0.718105	+	0.695935i	$0.245010\pi$
$12$	−14.4403	−4.16854
$13$	3.36742	0.933954	0.466977	−	0.884269i	$-0.345343\pi$
$13$	3.36742	0.933954	0.466977	+	0.884269i	$0.345343\pi$
$14$	−12.0455	−3.21930
$15$	−11.6543	−3.00912
$16$	6.90469	1.72617
$17$	5.35637	1.29911	0.649555	−	0.760314i	$-0.274955\pi$
$17$	5.35637	1.29911	0.649555	+	0.760314i	$0.274955\pi$
$18$	−19.1206	−4.50677
$19$	−2.01798	−0.462957	−0.231478	−	0.972840i	$-0.574356\pi$
$19$	−2.01798	−0.462957	−0.231478	+	0.972840i	$0.574356\pi$
$20$	15.9842	3.57418
$21$	−15.3893	−3.35823
$22$	−12.0978	−2.57925
$23$	−2.21388	−0.461627	−0.230813	−	0.972998i	$-0.574139\pi$
$23$	−2.21388	−0.461627	−0.230813	+	0.972998i	$0.574139\pi$
$24$	20.1928	4.12184
$25$	7.90035	1.58007
$26$	−8.55240	−1.67726
$27$	−14.6941	−2.82788
$28$	21.1070	3.98885
$29$	−3.92084	−0.728083	−0.364041	−	0.931383i	$-0.618603\pi$
$29$	−3.92084	−0.728083	−0.364041	+	0.931383i	$0.618603\pi$
$30$	29.5989	5.40399
$31$	−6.33401	−1.13762	−0.568811	−	0.822468i	$-0.692596\pi$
$31$	−6.33401	−1.13762	−0.568811	+	0.822468i	$0.692596\pi$
$32$	−5.08979	−0.899757
$33$	−15.4560	−2.69055
$34$	−13.6038	−2.33304
$35$	17.0348	2.87940
$36$	33.5044	5.58407
$37$	9.40711	1.54652	0.773260	−	0.634089i	$-0.218625\pi$
$37$	9.40711	1.54652	0.773260	+	0.634089i	$0.218625\pi$
$38$	5.12516	0.831411
$39$	−10.9265	−1.74964
$40$	−22.3519	−3.53414
$41$	0.410884	0.0641693	0.0320847	−	0.999485i	$-0.489785\pi$
$41$	0.410884	0.0641693	0.0320847	+	0.999485i	$0.489785\pi$
$42$	39.0850	6.03095
$43$	−10.6813	−1.62888	−0.814441	−	0.580246i	$-0.802956\pi$
$43$	−10.6813	−1.62888	−0.814441	+	0.580246i	$0.802956\pi$
$44$	21.1985	3.19579
$45$	27.0403	4.03093
$46$	5.62270	0.829023
$47$	−2.33990	−0.341309	−0.170655	−	0.985331i	$-0.554588\pi$
$47$	−2.33990	−0.341309	−0.170655	+	0.985331i	$0.554588\pi$
$48$	−22.4041	−3.23376
$49$	15.4942	2.21346
$50$	−20.0649	−2.83760
$51$	−17.3802	−2.43371
$52$	14.9861	2.07820
$53$	12.5748	1.72728	0.863642	−	0.504105i	$-0.168177\pi$
$53$	12.5748	1.72728	0.863642	+	0.504105i	$0.168177\pi$
$54$	37.3192	5.07851
$55$	17.1086	2.30693
$56$	−29.5154	−3.94416
$57$	6.54789	0.867289
$58$	9.95796	1.30754
$59$	−6.43629	−0.837934	−0.418967	−	0.908001i	$-0.637608\pi$
$59$	−6.43629	−0.837934	−0.418967	+	0.908001i	$0.637608\pi$
$60$	−51.8652	−6.69576
$61$	−9.91875	−1.26997	−0.634983	−	0.772526i	$-0.718993\pi$
$61$	−9.91875	−1.26997	−0.634983	+	0.772526i	$0.718993\pi$
$62$	16.0868	2.04302
$63$	35.7064	4.49858
$64$	−0.882591	−0.110324
$65$	12.0948	1.50017
$66$	39.2544	4.83189
$67$	13.7899	1.68470	0.842350	−	0.538931i	$-0.181172\pi$
$67$	13.7899	1.68470	0.842350	+	0.538931i	$0.181172\pi$
$68$	23.8376	2.89073
$69$	7.18354	0.864797
$70$	−43.2640	−5.17104
$71$	10.7550	1.27639	0.638193	−	0.769877i	$-0.279682\pi$
$71$	10.7550	1.27639	0.638193	+	0.769877i	$0.279682\pi$
$72$	−46.8515	−5.52150
$73$	−3.56896	−0.417715	−0.208858	−	0.977946i	$-0.566975\pi$
$73$	−3.56896	−0.417715	−0.208858	+	0.977946i	$0.566975\pi$
$74$	−23.8917	−2.77735
$75$	−25.6348	−2.96005
$76$	−8.98065	−1.03015
$77$	22.5917	2.57457
$78$	27.7506	3.14213
$79$	−1.58288	−0.178088	−0.0890442	−	0.996028i	$-0.528381\pi$
$79$	−1.58288	−0.178088	−0.0890442	+	0.996028i	$0.528381\pi$
$80$	24.7996	2.77268
$81$	25.0933	2.78814
$82$	−1.04354	−0.115240
$83$	1.22307	0.134249	0.0671244	−	0.997745i	$-0.478618\pi$
$83$	1.22307	0.134249	0.0671244	+	0.997745i	$0.478618\pi$
$84$	−68.4874	−7.47258
$85$	19.2385	2.08671
$86$	27.1278	2.92526
$87$	12.7222	1.36397
$88$	−29.6433	−3.15999
$89$	−3.37179	−0.357409	−0.178705	−	0.983903i	$-0.557191\pi$
$89$	−3.37179	−0.357409	−0.178705	+	0.983903i	$0.557191\pi$
$90$	−68.6755	−7.23904
$91$	15.9710	1.67422
$92$	−9.85248	−1.02719
$93$	20.5524	2.13119
$94$	5.94275	0.612948
$95$	−7.24799	−0.743628
$96$	16.5152	1.68558
$97$	2.68050	0.272164	0.136082	−	0.990698i	$-0.456549\pi$
$97$	2.68050	0.272164	0.136082	+	0.990698i	$0.456549\pi$
$98$	−39.3514	−3.97509
$99$	35.8612	3.60419
$100$	35.1591	3.51591
$101$	−9.82006	−0.977133	−0.488566	−	0.872527i	$-0.662480\pi$
$101$	−9.82006	−0.977133	−0.488566	+	0.872527i	$0.662480\pi$
$102$	44.1413	4.37064
$103$	−7.58336	−0.747211	−0.373605	−	0.927588i	$-0.621879\pi$
$103$	−7.58336	−0.747211	−0.373605	+	0.927588i	$0.621879\pi$
$104$	−20.9561	−2.05491
$105$	−55.2739	−5.39418
$106$	−31.9369	−3.10198
$107$	15.0921	1.45901	0.729506	−	0.683975i	$-0.239750\pi$
$107$	15.0921	1.45901	0.729506	+	0.683975i	$0.239750\pi$
$108$	−65.3933	−6.29247
$109$	−12.7695	−1.22310	−0.611549	−	0.791206i	$-0.709453\pi$
$109$	−12.7695	−1.22310	−0.611549	+	0.791206i	$0.709453\pi$
$110$	−43.4516	−4.14294
$111$	−30.5239	−2.89720
$112$	32.7476	3.09436
$113$	−8.09113	−0.761149	−0.380575	−	0.924750i	$-0.624274\pi$
$113$	−8.09113	−0.761149	−0.380575	+	0.924750i	$0.624274\pi$
$114$	−16.6300	−1.55754
$115$	−7.95162	−0.741492
$116$	−17.4490	−1.62010
$117$	25.3518	2.34377
$118$	16.3466	1.50482
$119$	25.4042	2.32880
$120$	72.5267	6.62075
$121$	11.6897	1.06270
$122$	25.1911	2.28070
$123$	−1.33323	−0.120213
$124$	−28.1884	−2.53139
$125$	10.4172	0.931742
$126$	−90.6853	−8.07889
$127$	−15.6124	−1.38538	−0.692689	−	0.721236i	$-0.743574\pi$
$127$	−15.6124	−1.38538	−0.692689	+	0.721236i	$0.743574\pi$
$128$	12.4211	1.09788
$129$	34.6584	3.05150
$130$	−30.7177	−2.69412
$131$	11.1016	0.969950	0.484975	−	0.874528i	$-0.338829\pi$
$131$	11.1016	0.969950	0.484975	+	0.874528i	$0.338829\pi$
$132$	−68.7843	−5.98690
$133$	−9.57089	−0.829902
$134$	−35.0228	−3.02551
$135$	−52.7768	−4.54230
$136$	−33.3337	−2.85834
$137$	12.8982	1.10197	0.550984	−	0.834516i	$-0.314252\pi$
$137$	12.8982	1.10197	0.550984	+	0.834516i	$0.314252\pi$
$138$	−18.2444	−1.55307
$139$	−7.25627	−0.615469	−0.307735	−	0.951472i	$-0.599571\pi$
$139$	−7.25627	−0.615469	−0.307735	+	0.951472i	$0.599571\pi$
$140$	75.8101	6.40712
$141$	7.59243	0.639398
$142$	−27.3150	−2.29223
$143$	16.0403	1.34135
$144$	51.9822	4.33185
$145$	−14.0825	−1.16949
$146$	9.06426	0.750163
$147$	−50.2752	−4.14663
$148$	41.8646	3.44125
$149$	−9.21475	−0.754902	−0.377451	−	0.926030i	$-0.623199\pi$
$149$	−9.21475	−0.754902	−0.377451	+	0.926030i	$0.623199\pi$
$150$	65.1060	5.31588
$151$	3.45983	0.281557	0.140778	−	0.990041i	$-0.455040\pi$
$151$	3.45983	0.281557	0.140778	+	0.990041i	$0.455040\pi$
$152$	12.5583	1.01861
$153$	40.3257	3.26014
$154$	−57.3773	−4.62360
$155$	−22.7499	−1.82732
$156$	−48.6264	−3.89323
$157$	22.7776	1.81785	0.908926	−	0.416957i	$-0.136903\pi$
$157$	22.7776	1.81785	0.908926	+	0.416957i	$0.136903\pi$
$158$	4.02013	0.319824
$159$	−40.8024	−3.23584
$160$	−18.2810	−1.44524
$161$	−10.5000	−0.827518
$162$	−63.7306	−5.00715
$163$	9.31838	0.729872	0.364936	−	0.931033i	$-0.381091\pi$
$163$	9.31838	0.729872	0.364936	+	0.931033i	$0.381091\pi$
$164$	1.82856	0.142787
$165$	−55.5136	−4.32172
$166$	−3.10628	−0.241094
$167$	−6.63149	−0.513160	−0.256580	−	0.966523i	$-0.582596\pi$
$167$	−6.63149	−0.513160	−0.256580	+	0.966523i	$0.582596\pi$
$168$	95.7706	7.38886
$169$	−1.66048	−0.127729
$170$	−48.8610	−3.74746
$171$	−15.1924	−1.16180
$172$	−47.5351	−3.62452
$173$	−16.0378	−1.21933	−0.609667	−	0.792658i	$-0.708697\pi$
$173$	−16.0378	−1.21933	−0.609667	+	0.792658i	$0.708697\pi$
$174$	−32.3113	−2.44951
$175$	37.4698	2.83245
$176$	32.8896	2.47915
$177$	20.8843	1.56976
$178$	8.56350	0.641862
$179$	20.3352	1.51992	0.759960	−	0.649969i	$-0.225218\pi$
$179$	20.3352	1.51992	0.759960	+	0.649969i	$0.225218\pi$
$180$	120.338	8.96946
$181$	−9.42876	−0.700835	−0.350417	−	0.936594i	$-0.613960\pi$
$181$	−9.42876	−0.700835	−0.350417	+	0.936594i	$0.613960\pi$
$182$	−40.5624	−3.00668
$183$	32.1841	2.37912
$184$	13.7774	1.01568
$185$	33.7876	2.48411
$186$	−52.1980	−3.82734
$187$	25.5144	1.86580
$188$	−10.4133	−0.759467
$189$	−69.6912	−5.06929
$190$	18.4081	1.33546
$191$	−3.26886	−0.236527	−0.118263	−	0.992982i	$-0.537733\pi$
$191$	−3.26886	−0.236527	−0.118263	+	0.992982i	$0.537733\pi$
$192$	2.86380	0.206677
$193$	−9.31156	−0.670261	−0.335130	−	0.942172i	$-0.608780\pi$
$193$	−9.31156	−0.670261	−0.335130	+	0.942172i	$0.608780\pi$
$194$	−6.80780	−0.488771
$195$	−39.2448	−2.81038
$196$	68.9542	4.92530
$197$	14.2685	1.01659	0.508296	−	0.861183i	$-0.330276\pi$
$197$	14.2685	1.01659	0.508296	+	0.861183i	$0.330276\pi$
$198$	−91.0784	−6.47266
$199$	−5.91968	−0.419635	−0.209817	−	0.977741i	$-0.567287\pi$
$199$	−5.91968	−0.419635	−0.209817	+	0.977741i	$0.567287\pi$
$200$	−49.1653	−3.47651
$201$	−44.7449	−3.15607
$202$	24.9405	1.75481
$203$	−18.5958	−1.30517
$204$	−77.3474	−5.41540
$205$	1.47577	0.103073
$206$	19.2598	1.34190
$207$	−16.6673	−1.15846
$208$	23.2510	1.61217
$209$	−9.61239	−0.664903
$210$	140.382	9.68726
$211$	5.48689	0.377733	0.188866	−	0.982003i	$-0.439519\pi$
$211$	5.48689	0.377733	0.188866	+	0.982003i	$0.439519\pi$
$212$	55.9620	3.84348
$213$	−34.8976	−2.39114
$214$	−38.3302	−2.62020
$215$	−38.3641	−2.61641
$216$	91.4440	6.22198
$217$	−30.0410	−2.03932
$218$	32.4314	2.19653
$219$	11.5805	0.782535
$220$	76.1388	5.13328
$221$	18.0372	1.21331
$222$	77.5231	5.20301
$223$	−14.9949	−1.00414	−0.502068	−	0.864828i	$-0.667427\pi$
$223$	−14.9949	−1.00414	−0.502068	+	0.864828i	$0.667427\pi$
$224$	−24.1399	−1.61292
$225$	59.4781	3.96521
$226$	20.5494	1.36693
$227$	−10.9200	−0.724783	−0.362391	−	0.932026i	$-0.618040\pi$
$227$	−10.9200	−0.724783	−0.362391	+	0.932026i	$0.618040\pi$
$228$	29.1402	1.92985
$229$	−6.08968	−0.402418	−0.201209	−	0.979548i	$-0.564487\pi$
$229$	−6.08968	−0.402418	−0.201209	+	0.979548i	$0.564487\pi$
$230$	20.1951	1.33163
$231$	−73.3050	−4.82312
$232$	24.4002	1.60195
$233$	2.71107	0.177608	0.0888041	−	0.996049i	$-0.471696\pi$
$233$	2.71107	0.177608	0.0888041	+	0.996049i	$0.471696\pi$
$234$	−64.3871	−4.20911
$235$	−8.40422	−0.548231
$236$	−28.6436	−1.86454
$237$	5.13610	0.333625
$238$	−64.5203	−4.18223
$239$	5.81499	0.376140	0.188070	−	0.982156i	$-0.439777\pi$
$239$	5.81499	0.376140	0.188070	+	0.982156i	$0.439777\pi$
$240$	−80.4691	−5.19426
$241$	10.9275	0.703904	0.351952	−	0.936018i	$-0.385518\pi$
$241$	10.9275	0.703904	0.351952	+	0.936018i	$0.385518\pi$
$242$	−29.6889	−1.90847
$243$	−37.3398	−2.39535
$244$	−44.1416	−2.82588
$245$	55.6507	3.55539
$246$	3.38605	0.215887
$247$	−6.79539	−0.432380
$248$	39.4177	2.50303
$249$	−3.96857	−0.251498
$250$	−26.4570	−1.67329
$251$	25.8279	1.63024	0.815121	−	0.579291i	$-0.196671\pi$
$251$	25.8279	1.63024	0.815121	+	0.579291i	$0.196671\pi$
$252$	158.905	10.0101
$253$	−10.5455	−0.662993
$254$	39.6516	2.48796
$255$	−62.4246	−3.90918
$256$	−29.7814	−1.86134
$257$	−8.60565	−0.536805	−0.268403	−	0.963307i	$-0.586496\pi$
$257$	−8.60565	−0.536805	−0.268403	+	0.963307i	$0.586496\pi$
$258$	−88.0235	−5.48010
$259$	44.6161	2.77231
$260$	53.8256	3.33812
$261$	−29.5182	−1.82713
$262$	−28.1952	−1.74191
$263$	10.2459	0.631789	0.315895	−	0.948794i	$-0.397695\pi$
$263$	10.2459	0.631789	0.315895	+	0.948794i	$0.397695\pi$
$264$	96.1858	5.91983
$265$	45.1651	2.77447
$266$	24.3076	1.49040
$267$	10.9407	0.669560
$268$	61.3693	3.74872
$269$	16.7723	1.02262	0.511311	−	0.859396i	$-0.329160\pi$
$269$	16.7723	1.02262	0.511311	+	0.859396i	$0.329160\pi$
$270$	134.040	8.15740
$271$	18.1711	1.10382	0.551908	−	0.833905i	$-0.313900\pi$
$271$	18.1711	1.10382	0.551908	+	0.833905i	$0.313900\pi$
$272$	36.9841	2.24249
$273$	−51.8223	−3.13643
$274$	−32.7582	−1.97900
$275$	37.6323	2.26931
$276$	31.9691	1.92431
$277$	21.1181	1.26886	0.634432	−	0.772979i	$-0.281234\pi$
$277$	21.1181	1.26886	0.634432	+	0.772979i	$0.281234\pi$
$278$	18.4291	1.10530
$279$	−47.6859	−2.85488
$280$	−106.011	−6.33534
$281$	25.3073	1.50971	0.754855	−	0.655892i	$-0.227707\pi$
$281$	25.3073	1.50971	0.754855	+	0.655892i	$0.227707\pi$
$282$	−19.2829	−1.14828
$283$	−3.63388	−0.216012	−0.108006	−	0.994150i	$-0.534447\pi$
$283$	−3.63388	−0.216012	−0.108006	+	0.994150i	$0.534447\pi$
$284$	47.8632	2.84016
$285$	23.5181	1.39309
$286$	−40.7382	−2.40890
$287$	1.94874	0.115031
$288$	−38.3187	−2.25795
$289$	11.6907	0.687689
$290$	35.7660	2.10025
$291$	−8.69762	−0.509863
$292$	−15.8830	−0.929483
$293$	13.2491	0.774020	0.387010	−	0.922075i	$-0.373508\pi$
$293$	13.2491	0.774020	0.387010	+	0.922075i	$0.373508\pi$
$294$	127.686	7.44682
$295$	−23.1173	−1.34594
$296$	−58.5422	−3.40270
$297$	−69.9933	−4.06142
$298$	23.4031	1.35571
$299$	−7.45508	−0.431138
$300$	−114.083	−6.58659
$301$	−50.6593	−2.91995
$302$	−8.78708	−0.505640
$303$	31.8639	1.83053
$304$	−13.9335	−0.799143
$305$	−35.6252	−2.03990
$306$	−102.417	−5.85479
$307$	−3.26910	−0.186578	−0.0932888	−	0.995639i	$-0.529738\pi$
$307$	−3.26910	−0.186578	−0.0932888	+	0.995639i	$0.529738\pi$
$308$	100.540	5.72882
$309$	24.6063	1.39980
$310$	57.7790	3.28163
$311$	−11.3857	−0.645626	−0.322813	−	0.946463i	$-0.604628\pi$
$311$	−11.3857	−0.645626	−0.322813	+	0.946463i	$0.604628\pi$
$312$	67.9977	3.84961
$313$	−3.94201	−0.222815	−0.111408	−	0.993775i	$-0.535536\pi$
$313$	−3.94201	−0.222815	−0.111408	+	0.993775i	$0.535536\pi$
$314$	−57.8494	−3.26463
$315$	128.247	7.22589
$316$	−7.04434	−0.396275
$317$	12.6385	0.709847	0.354924	−	0.934895i	$-0.384507\pi$
$317$	12.6385	0.709847	0.354924	+	0.934895i	$0.384507\pi$
$318$	103.628	5.81116
$319$	−18.6764	−1.04568
$320$	−3.17001	−0.177209
$321$	−48.9705	−2.73327
$322$	26.6674	1.48612
$323$	−10.8091	−0.601432
$324$	111.673	6.20406
$325$	26.6038	1.47571
$326$	−23.6663	−1.31076
$327$	41.4342	2.29132
$328$	−2.55701	−0.141187
$329$	−11.0977	−0.611835
$330$	140.990	7.76127
$331$	−34.4138	−1.89155	−0.945776	−	0.324821i	$-0.894696\pi$
$331$	−34.4138	−1.89155	−0.945776	+	0.324821i	$0.894696\pi$
$332$	5.44303	0.298725
$333$	70.8218	3.88101
$334$	16.8423	0.921571
$335$	49.5291	2.70607
$336$	−106.258	−5.79688
$337$	−11.9311	−0.649927	−0.324963	−	0.945727i	$-0.605352\pi$
$337$	−11.9311	−0.649927	−0.324963	+	0.945727i	$0.605352\pi$
$338$	4.21720	0.229385
$339$	26.2539	1.42591
$340$	85.6175	4.64326
$341$	−30.1712	−1.63386
$342$	38.5850	2.08644
$343$	40.2864	2.17526
$344$	66.4717	3.58391
$345$	25.8012	1.38909
$346$	40.7320	2.18977
$347$	−16.3853	−0.879611	−0.439805	−	0.898093i	$-0.644953\pi$
$347$	−16.3853	−0.879611	−0.439805	+	0.898093i	$0.644953\pi$
$348$	56.6180	3.03504
$349$	−14.7671	−0.790465	−0.395233	−	0.918581i	$-0.629336\pi$
$349$	−14.7671	−0.790465	−0.395233	+	0.918581i	$0.629336\pi$
$350$	−95.1639	−5.08672
$351$	−49.4811	−2.64111
$352$	−24.2446	−1.29224
$353$	−10.5677	−0.562462	−0.281231	−	0.959640i	$-0.590743\pi$
$353$	−10.5677	−0.562462	−0.281231	+	0.959640i	$0.590743\pi$
$354$	−53.0409	−2.81909
$355$	38.6288	2.05021
$356$	−15.0055	−0.795292
$357$	−82.4309	−4.36271
$358$	−51.6462	−2.72958
$359$	0.0478943	0.00252776	0.00126388	−	0.999999i	$-0.499598\pi$
$359$	0.0478943	0.00252776	0.00126388	+	0.999999i	$0.499598\pi$
$360$	−168.277	−8.86897
$361$	−14.9278	−0.785671
$362$	23.9467	1.25861
$363$	−37.9304	−1.99083
$364$	71.0761	3.72540
$365$	−12.8187	−0.670959
$366$	−81.7395	−4.27259
$367$	−17.3593	−0.906146	−0.453073	−	0.891473i	$-0.649672\pi$
$367$	−17.3593	−0.906146	−0.453073	+	0.891473i	$0.649672\pi$
$368$	−15.2862	−0.796847
$369$	3.09336	0.161034
$370$	−85.8119	−4.46115
$371$	59.6400	3.09635
$372$	91.4648	4.74223
$373$	−14.3286	−0.741907	−0.370954	−	0.928651i	$-0.620969\pi$
$373$	−14.3286	−0.741907	−0.370954	+	0.928651i	$0.620969\pi$
$374$	−64.8001	−3.35073
$375$	−33.8014	−1.74550
$376$	14.5616	0.750958
$377$	−13.2031	−0.679996
$378$	176.998	9.10379
$379$	11.1668	0.573599	0.286800	−	0.957991i	$-0.407409\pi$
$379$	11.1668	0.573599	0.286800	+	0.957991i	$0.407409\pi$
$380$	−32.2559	−1.65469
$381$	50.6587	2.59533
$382$	8.30208	0.424772
$383$	0.758264	0.0387455	0.0193727	−	0.999812i	$-0.493833\pi$
$383$	0.758264	0.0387455	0.0193727	+	0.999812i	$0.493833\pi$
$384$	−40.3038	−2.05674
$385$	81.1429	4.13542
$386$	23.6490	1.20370
$387$	−80.4145	−4.08770
$388$	11.9291	0.605607
$389$	8.42979	0.427407	0.213704	−	0.976899i	$-0.431447\pi$
$389$	8.42979	0.427407	0.213704	+	0.976899i	$0.431447\pi$
$390$	99.6719	5.04708
$391$	−11.8584	−0.599704
$392$	−96.4234	−4.87012
$393$	−36.0221	−1.81707
$394$	−36.2385	−1.82567
$395$	−5.68525	−0.286056
$396$	159.594	8.01989
$397$	−10.2386	−0.513858	−0.256929	−	0.966430i	$-0.582711\pi$
$397$	−10.2386	−0.513858	−0.256929	+	0.966430i	$0.582711\pi$
$398$	15.0345	0.753611
$399$	31.0554	1.55471
$400$	54.5494	2.72747
$401$	−17.7390	−0.885846	−0.442923	−	0.896560i	$-0.646058\pi$
$401$	−17.7390	−0.885846	−0.442923	+	0.896560i	$0.646058\pi$
$402$	113.641	5.66789
$403$	−21.3293	−1.06249
$404$	−43.7024	−2.17428
$405$	90.1277	4.47848
$406$	47.2287	2.34392
$407$	44.8096	2.22113
$408$	108.160	5.35473
$409$	25.5946	1.26557	0.632786	−	0.774326i	$-0.281911\pi$
$409$	25.5946	1.26557	0.632786	+	0.774326i	$0.281911\pi$
$410$	−3.74810	−0.185105
$411$	−41.8517	−2.06439
$412$	−33.7484	−1.66266
$413$	−30.5261	−1.50209
$414$	42.3308	2.08044
$415$	4.39289	0.215639
$416$	−17.1395	−0.840332
$417$	23.5449	1.15300
$418$	24.4130	1.19408
$419$	−22.1386	−1.08154	−0.540772	−	0.841169i	$-0.681868\pi$
$419$	−22.1386	−1.08154	−0.540772	+	0.841169i	$0.681868\pi$
$420$	−245.986	−12.0029
$421$	0.347309	0.0169268	0.00846340	−	0.999964i	$-0.497306\pi$
$421$	0.347309	0.0169268	0.00846340	+	0.999964i	$0.497306\pi$
$422$	−13.9353	−0.678360
$423$	−17.6160	−0.856520
$424$	−78.2555	−3.80042
$425$	42.3172	2.05269
$426$	88.6310	4.29419
$427$	−47.0427	−2.27656
$428$	67.1648	3.24653
$429$	−52.0470	−2.51285
$430$	97.4350	4.69873
$431$	21.3345	1.02765	0.513824	−	0.857896i	$-0.328228\pi$
$431$	21.3345	1.02765	0.513824	+	0.857896i	$0.328228\pi$
$432$	−101.458	−4.88140
$433$	8.85380	0.425487	0.212743	−	0.977108i	$-0.431760\pi$
$433$	8.85380	0.425487	0.212743	+	0.977108i	$0.431760\pi$
$434$	76.2966	3.66235
$435$	45.6946	2.19089
$436$	−56.8284	−2.72159
$437$	4.46757	0.213713
$438$	−29.4114	−1.40533
$439$	−9.72648	−0.464219	−0.232110	−	0.972690i	$-0.574563\pi$
$439$	−9.72648	−0.464219	−0.232110	+	0.972690i	$0.574563\pi$
$440$	−106.470	−5.07576
$441$	116.649	5.55471
$442$	−45.8098	−2.17895
$443$	−18.6532	−0.886239	−0.443119	−	0.896463i	$-0.646128\pi$
$443$	−18.6532	−0.886239	−0.443119	+	0.896463i	$0.646128\pi$
$444$	−135.841	−6.44674
$445$	−12.1105	−0.574092
$446$	38.0834	1.80330
$447$	29.8998	1.41421
$448$	−4.18596	−0.197768
$449$	20.6696	0.975461	0.487730	−	0.872994i	$-0.337825\pi$
$449$	20.6696	0.975461	0.487730	+	0.872994i	$0.337825\pi$
$450$	−151.059	−7.12100
$451$	1.95719	0.0921606
$452$	−36.0081	−1.69368
$453$	−11.2263	−0.527460
$454$	27.7339	1.30162
$455$	57.3632	2.68923
$456$	−40.7487	−1.90823
$457$	4.34037	0.203034	0.101517	−	0.994834i	$-0.467630\pi$
$457$	4.34037	0.203034	0.101517	+	0.994834i	$0.467630\pi$
$458$	15.4663	0.722691
$459$	−78.7069	−3.67373
$460$	−35.3872	−1.64994
$461$	20.1046	0.936366	0.468183	−	0.883632i	$-0.344909\pi$
$461$	20.1046	0.936366	0.468183	+	0.883632i	$0.344909\pi$
$462$	186.176	8.66170
$463$	4.90993	0.228184	0.114092	−	0.993470i	$-0.463604\pi$
$463$	4.90993	0.228184	0.114092	+	0.993470i	$0.463604\pi$
$464$	−27.0722	−1.25680
$465$	73.8183	3.42324
$466$	−6.88543	−0.318962
$467$	30.9924	1.43416	0.717078	−	0.696992i	$-0.245479\pi$
$467$	30.9924	1.43416	0.717078	+	0.696992i	$0.245479\pi$
$468$	112.823	5.21526
$469$	65.4027	3.02001
$470$	21.3446	0.984553
$471$	−73.9082	−3.40551
$472$	40.0543	1.84365
$473$	−50.8789	−2.33942
$474$	−13.0444	−0.599149
$475$	−15.9427	−0.731504
$476$	113.057	5.18195
$477$	94.6701	4.33464
$478$	−14.7686	−0.675500
$479$	−39.0254	−1.78312	−0.891559	−	0.452905i	$-0.850388\pi$
$479$	−39.0254	−1.78312	−0.891559	+	0.452905i	$0.850388\pi$
$480$	59.3178	2.70747
$481$	31.6777	1.44438
$482$	−27.7532	−1.26412
$483$	34.0702	1.55025
$484$	52.0228	2.36467
$485$	9.62757	0.437166
$486$	94.8336	4.30174
$487$	−0.560130	−0.0253819	−0.0126909	−	0.999919i	$-0.504040\pi$
$487$	−0.560130	−0.0253819	−0.0126909	+	0.999919i	$0.504040\pi$
$488$	61.7263	2.79422
$489$	−30.2360	−1.36732
$490$	−141.339	−6.38503
$491$	6.53601	0.294966	0.147483	−	0.989065i	$-0.452883\pi$
$491$	6.53601	0.294966	0.147483	+	0.989065i	$0.452883\pi$
$492$	−5.93327	−0.267493
$493$	−21.0015	−0.945860
$494$	17.2586	0.776500
$495$	128.803	5.78926
$496$	−43.7344	−1.96373
$497$	51.0090	2.28806
$498$	10.0792	0.451658
$499$	−9.20441	−0.412046	−0.206023	−	0.978547i	$-0.566052\pi$
$499$	−9.20441	−0.412046	−0.206023	+	0.978547i	$0.566052\pi$
$500$	46.3598	2.07327
$501$	21.5177	0.961339
$502$	−65.5963	−2.92771
$503$	−0.0865584	−0.00385945	−0.00192972	−	0.999998i	$-0.500614\pi$
$503$	−0.0865584	−0.00385945	−0.00192972	+	0.999998i	$0.500614\pi$
$504$	−222.208	−9.89792
$505$	−35.2708	−1.56953
$506$	26.7830	1.19065
$507$	5.38787	0.239284
$508$	−69.4802	−3.08269
$509$	14.9959	0.664680	0.332340	−	0.943160i	$-0.392162\pi$
$509$	14.9959	0.664680	0.332340	+	0.943160i	$0.392162\pi$
$510$	158.543	7.02039
$511$	−16.9269	−0.748801
$512$	50.7949	2.24484
$513$	29.6524	1.30918
$514$	21.8562	0.964034
$515$	−27.2372	−1.20021
$516$	154.241	6.79007
$517$	−11.1458	−0.490192
$518$	−113.314	−4.97872
$519$	52.0391	2.28426
$520$	−75.2681	−3.30072
$521$	−27.1293	−1.18856	−0.594278	−	0.804260i	$-0.702562\pi$
$521$	−27.1293	−1.18856	−0.594278	+	0.804260i	$0.702562\pi$
$522$	74.9689	3.28130
$523$	13.1053	0.573056	0.286528	−	0.958072i	$-0.407499\pi$
$523$	13.1053	0.573056	0.286528	+	0.958072i	$0.407499\pi$
$524$	49.4056	2.15829
$525$	−121.581	−5.30623
$526$	−26.0220	−1.13461
$527$	−33.9273	−1.47790
$528$	−106.719	−4.64436
$529$	−18.0987	−0.786901
$530$	−114.708	−4.98259
$531$	−48.4559	−2.10281
$532$	−42.5935	−1.84666
$533$	1.38362	0.0599312
$534$	−27.7866	−1.20244
$535$	54.2065	2.34355
$536$	−85.8169	−3.70673
$537$	−65.9829	−2.84737
$538$	−42.5973	−1.83650
$539$	73.8047	3.17899
$540$	−234.873	−10.1073
$541$	−27.4875	−1.18178	−0.590890	−	0.806752i	$-0.701223\pi$
$541$	−27.4875	−1.18178	−0.590890	+	0.806752i	$0.701223\pi$
$542$	−46.1500	−1.98231
$543$	30.5942	1.31292
$544$	−27.2628	−1.16888
$545$	−45.8644	−1.96461
$546$	131.616	5.63263
$547$	17.2159	0.736100	0.368050	−	0.929806i	$-0.380026\pi$
$547$	17.2159	0.736100	0.368050	+	0.929806i	$0.380026\pi$
$548$	57.4011	2.45205
$549$	−74.6737	−3.18700
$550$	−95.5765	−4.07539
$551$	7.91219	0.337071
$552$	−44.7045	−1.90275
$553$	−7.50731	−0.319243
$554$	−53.6347	−2.27872
$555$	−109.633	−4.65366
$556$	−32.2927	−1.36952
$557$	44.6026	1.88987	0.944937	−	0.327251i	$-0.106122\pi$
$557$	44.6026	1.88987	0.944937	+	0.327251i	$0.106122\pi$
$558$	121.110	5.12700
$559$	−35.9684	−1.52130
$560$	117.620	4.97034
$561$	−82.7883	−3.49533
$562$	−64.2743	−2.71125
$563$	−23.0818	−0.972780	−0.486390	−	0.873742i	$-0.661687\pi$
$563$	−23.0818	−0.972780	−0.486390	+	0.873742i	$0.661687\pi$
$564$	33.7887	1.42276
$565$	−29.0610	−1.22260
$566$	9.22914	0.387930
$567$	119.013	4.99806
$568$	−66.9305	−2.80834
$569$	14.6720	0.615082	0.307541	−	0.951535i	$-0.400494\pi$
$569$	14.6720	0.615082	0.307541	+	0.951535i	$0.400494\pi$
$570$	−59.7300	−2.50181
$571$	−24.3728	−1.01997	−0.509984	−	0.860184i	$-0.670349\pi$
$571$	−24.3728	−1.01997	−0.509984	+	0.860184i	$0.670349\pi$
$572$	71.3843	2.98473
$573$	10.6067	0.443102
$574$	−4.94932	−0.206581
$575$	−17.4904	−0.729402
$576$	−6.64462	−0.276859
$577$	19.4507	0.809744	0.404872	−	0.914373i	$-0.367316\pi$
$577$	19.4507	0.809744	0.404872	+	0.914373i	$0.367316\pi$
$578$	−29.6915	−1.23500
$579$	30.2139	1.25565
$580$	−62.6717	−2.60230
$581$	5.80076	0.240656
$582$	22.0897	0.915649
$583$	59.8985	2.48074
$584$	22.2103	0.919069
$585$	91.0561	3.76470
$586$	−33.6493	−1.39004
$587$	−17.0384	−0.703250	−0.351625	−	0.936141i	$-0.614371\pi$
$587$	−17.0384	−0.703250	−0.351625	+	0.936141i	$0.614371\pi$
$588$	−223.741	−9.22690
$589$	12.7819	0.526670
$590$	58.7120	2.41714
$591$	−46.2981	−1.90445
$592$	64.9532	2.66956
$593$	−13.0652	−0.536522	−0.268261	−	0.963346i	$-0.586449\pi$
$593$	−13.0652	−0.536522	−0.268261	+	0.963346i	$0.586449\pi$
$594$	177.765	7.29380
$595$	91.2445	3.74066
$596$	−41.0086	−1.67978
$597$	19.2080	0.786131
$598$	18.9340	0.774269
$599$	−47.9088	−1.95750	−0.978750	−	0.205056i	$-0.934262\pi$
$599$	−47.9088	−1.95750	−0.978750	+	0.205056i	$0.934262\pi$
$600$	159.530	6.51280
$601$	23.6529	0.964824	0.482412	−	0.875945i	$-0.339761\pi$
$601$	23.6529	0.964824	0.482412	+	0.875945i	$0.339761\pi$
$602$	128.662	5.24387
$603$	103.818	4.22778
$604$	15.3973	0.626508
$605$	41.9859	1.70697
$606$	−80.9261	−3.28740
$607$	2.59796	0.105448	0.0527240	−	0.998609i	$-0.483210\pi$
$607$	2.59796	0.105448	0.0527240	+	0.998609i	$0.483210\pi$
$608$	10.2711	0.416548
$609$	60.3391	2.44507
$610$	90.4791	3.66339
$611$	−7.87942	−0.318767
$612$	179.462	7.25432
$613$	−35.6594	−1.44027	−0.720135	−	0.693834i	$-0.755920\pi$
$613$	−35.6594	−1.44027	−0.720135	+	0.693834i	$0.755920\pi$
$614$	8.30270	0.335070
$615$	−4.78855	−0.193093
$616$	−140.593	−5.66464
$617$	−41.2502	−1.66067	−0.830335	−	0.557264i	$-0.811851\pi$
$617$	−41.2502	−1.66067	−0.830335	+	0.557264i	$0.811851\pi$
$618$	−62.4937	−2.51387
$619$	−33.0594	−1.32877	−0.664385	−	0.747391i	$-0.731306\pi$
$619$	−33.0594	−1.32877	−0.664385	+	0.747391i	$0.731306\pi$
$620$	−101.244	−4.06607
$621$	32.5310	1.30542
$622$	28.9169	1.15946
$623$	−15.9918	−0.640696
$624$	−75.4441	−3.02018
$625$	−2.08624	−0.0834496
$626$	10.0117	0.400148
$627$	31.1900	1.24561
$628$	101.368	4.04501
$629$	50.3880	2.00910
$630$	−325.715	−12.9768
$631$	−44.0046	−1.75179	−0.875897	−	0.482497i	$-0.839730\pi$
$631$	−44.0046	−1.75179	−0.875897	+	0.482497i	$0.839730\pi$
$632$	9.85058	0.391835
$633$	−17.8037	−0.707633
$634$	−32.0985	−1.27480
$635$	−56.0752	−2.22528
$636$	−181.584	−7.20026
$637$	52.1755	2.06727
$638$	47.4334	1.87791
$639$	80.9696	3.20311
$640$	44.6131	1.76349
$641$	−12.0311	−0.475200	−0.237600	−	0.971363i	$-0.576361\pi$
$641$	−12.0311	−0.475200	−0.237600	+	0.971363i	$0.576361\pi$
$642$	124.373	4.90860
$643$	15.6142	0.615764	0.307882	−	0.951425i	$-0.400380\pi$
$643$	15.6142	0.615764	0.307882	+	0.951425i	$0.400380\pi$
$644$	−46.7284	−1.84136
$645$	124.483	4.90150
$646$	27.4523	1.08010
$647$	−23.3538	−0.918134	−0.459067	−	0.888402i	$-0.651816\pi$
$647$	−23.3538	−0.918134	−0.459067	+	0.888402i	$0.651816\pi$
$648$	−156.160	−6.13455
$649$	−30.6584	−1.20345
$650$	−67.5669	−2.65019
$651$	97.4762	3.82039
$652$	41.4697	1.62408
$653$	23.6841	0.926829	0.463415	−	0.886142i	$-0.346624\pi$
$653$	23.6841	0.926829	0.463415	+	0.886142i	$0.346624\pi$
$654$	−105.232	−4.11491
$655$	39.8736	1.55799
$656$	2.83703	0.110767
$657$	−26.8691	−1.04826
$658$	28.1853	1.09878
$659$	−41.8663	−1.63088	−0.815439	−	0.578843i	$-0.803505\pi$
$659$	−41.8663	−1.63088	−0.815439	+	0.578843i	$0.803505\pi$
$660$	−247.053	−9.61652
$661$	−15.5783	−0.605927	−0.302964	−	0.953002i	$-0.597976\pi$
$661$	−15.5783	−0.605927	−0.302964	+	0.953002i	$0.597976\pi$
$662$	87.4023	3.39699
$663$	−58.5264	−2.27298
$664$	−7.61137	−0.295378
$665$	−34.3758	−1.33304
$666$	−179.870	−6.96980
$667$	8.68029	0.336102
$668$	−29.5122	−1.14186
$669$	48.6552	1.88112
$670$	−125.791	−4.85975
$671$	−47.2467	−1.82394
$672$	78.3285	3.02159
$673$	−28.3857	−1.09419	−0.547095	−	0.837071i	$-0.684266\pi$
$673$	−28.3857	−1.09419	−0.547095	+	0.837071i	$0.684266\pi$
$674$	30.3019	1.16719
$675$	−116.088	−4.46824
$676$	−7.38966	−0.284218
$677$	29.2089	1.12259	0.561294	−	0.827616i	$-0.310304\pi$
$677$	29.2089	1.12259	0.561294	+	0.827616i	$0.310304\pi$
$678$	−66.6782	−2.56076
$679$	12.7131	0.487884
$680$	−119.725	−4.59124
$681$	35.4327	1.35779
$682$	76.6273	2.93421
$683$	−28.0978	−1.07513	−0.537567	−	0.843221i	$-0.680656\pi$
$683$	−28.0978	−1.07513	−0.537567	+	0.843221i	$0.680656\pi$
$684$	−67.6112	−2.58518
$685$	46.3266	1.77005
$686$	−102.317	−3.90649
$687$	19.7596	0.753877
$688$	−73.7510	−2.81173
$689$	42.3447	1.61321
$690$	−65.5285	−2.49463
$691$	15.5707	0.592337	0.296169	−	0.955136i	$-0.404291\pi$
$691$	15.5707	0.592337	0.296169	+	0.955136i	$0.404291\pi$
$692$	−71.3734	−2.71321
$693$	170.083	6.46091
$694$	41.6146	1.57967
$695$	−26.0624	−0.988603
$696$	−79.1729	−3.00104
$697$	2.20085	0.0833631
$698$	37.5047	1.41957
$699$	−8.79680	−0.332726
$700$	166.753	6.30266
$701$	−7.53946	−0.284761	−0.142381	−	0.989812i	$-0.545476\pi$
$701$	−7.53946	−0.284761	−0.142381	+	0.989812i	$0.545476\pi$
$702$	125.670	4.74309
$703$	−18.9834	−0.715971
$704$	−4.20410	−0.158448
$705$	27.2698	1.02704
$706$	26.8393	1.01011
$707$	−46.5747	−1.75162
$708$	92.9418	3.49297
$709$	46.8627	1.75996	0.879982	−	0.475006i	$-0.157554\pi$
$709$	46.8627	1.75996	0.879982	+	0.475006i	$0.157554\pi$
$710$	−98.1075	−3.68191
$711$	−11.9168	−0.446915
$712$	20.9833	0.786382
$713$	14.0228	0.525157
$714$	209.354	7.83487
$715$	57.6119	2.15456
$716$	90.4979	3.38206
$717$	−18.8683	−0.704650
$718$	−0.121639	−0.00453954
$719$	2.55536	0.0952987	0.0476494	−	0.998864i	$-0.484827\pi$
$719$	2.55536	0.0952987	0.0476494	+	0.998864i	$0.484827\pi$
$720$	186.705	6.95808
$721$	−35.9664	−1.33946
$722$	37.9127	1.41097
$723$	−35.4573	−1.31867
$724$	−41.9610	−1.55947
$725$	−30.9760	−1.15042
$726$	96.3335	3.57527
$727$	10.4017	0.385777	0.192889	−	0.981221i	$-0.438214\pi$
$727$	10.4017	0.385777	0.192889	+	0.981221i	$0.438214\pi$
$728$	−99.3907	−3.68366
$729$	45.8791	1.69923
$730$	32.5561	1.20496
$731$	−57.2130	−2.11610
$732$	143.229	5.29391
$733$	−49.7404	−1.83720	−0.918602	−	0.395184i	$-0.870681\pi$
$733$	−49.7404	−1.83720	−0.918602	+	0.395184i	$0.870681\pi$
$734$	44.0881	1.62732
$735$	−180.574	−6.66056
$736$	11.2682	0.415352
$737$	65.6862	2.41958
$738$	−7.85635	−0.289196
$739$	−22.2977	−0.820234	−0.410117	−	0.912033i	$-0.634512\pi$
$739$	−22.2977	−0.820234	−0.410117	+	0.912033i	$0.634512\pi$
$740$	150.365	5.52754
$741$	22.0495	0.810008
$742$	−151.470	−5.56066
$743$	−1.05428	−0.0386777	−0.0193388	−	0.999813i	$-0.506156\pi$
$743$	−1.05428	−0.0386777	−0.0193388	+	0.999813i	$0.506156\pi$
$744$	−127.902	−4.68910
$745$	−33.0967	−1.21257
$746$	36.3910	1.33237
$747$	9.20790	0.336899
$748$	113.547	4.15169
$749$	71.5790	2.61544
$750$	85.8471	3.13469
$751$	26.3770	0.962512	0.481256	−	0.876580i	$-0.340181\pi$
$751$	26.3770	0.962512	0.481256	+	0.876580i	$0.340181\pi$
$752$	−16.1563	−0.589158
$753$	−83.8056	−3.05404
$754$	33.5326	1.22119
$755$	12.4267	0.452253
$756$	−310.148	−11.2800
$757$	13.0679	0.474963	0.237481	−	0.971392i	$-0.423678\pi$
$757$	13.0679	0.474963	0.237481	+	0.971392i	$0.423678\pi$
$758$	−28.3608	−1.03011
$759$	34.2179	1.24203
$760$	45.1056	1.63615
$761$	−4.60361	−0.166881	−0.0834403	−	0.996513i	$-0.526591\pi$
$761$	−4.60361	−0.166881	−0.0834403	+	0.996513i	$0.526591\pi$
$762$	−128.660	−4.66087
$763$	−60.5634	−2.19254
$764$	−14.5475	−0.526309
$765$	144.838	5.23662
$766$	−1.92580	−0.0695819
$767$	−21.6737	−0.782592
$768$	96.6338	3.48697
$769$	33.8700	1.22138	0.610692	−	0.791868i	$-0.290891\pi$
$769$	33.8700	1.22138	0.610692	+	0.791868i	$0.290891\pi$
$770$	−206.082	−7.42669
$771$	27.9234	1.00563
$772$	−41.4394	−1.49144
$773$	−25.0964	−0.902653	−0.451327	−	0.892359i	$-0.649049\pi$
$773$	−25.0964	−0.902653	−0.451327	+	0.892359i	$0.649049\pi$
$774$	204.233	7.34099
$775$	−50.0409	−1.79752
$776$	−16.6813	−0.598822
$777$	−144.769	−5.19356
$778$	−21.4095	−0.767569
$779$	−0.829156	−0.0297076
$780$	−174.652	−6.25354
$781$	51.2301	1.83316
$782$	30.1173	1.07699
$783$	57.6132	2.05893
$784$	106.983	3.82081
$785$	81.8105	2.91994
$786$	91.4870	3.26323
$787$	−14.3551	−0.511705	−0.255852	−	0.966716i	$-0.582356\pi$
$787$	−14.3551	−0.511705	−0.255852	+	0.966716i	$0.582356\pi$
$788$	63.4995	2.26208
$789$	−33.2456	−1.18358
$790$	14.4391	0.513720
$791$	−38.3747	−1.36445
$792$	−223.171	−7.93004
$793$	−33.4006	−1.18609
$794$	26.0033	0.922824
$795$	−146.550	−5.19760
$796$	−26.3444	−0.933754
$797$	47.1912	1.67160	0.835799	−	0.549035i	$-0.185005\pi$
$797$	47.1912	1.67160	0.835799	+	0.549035i	$0.185005\pi$
$798$	−78.8728	−2.79207
$799$	−12.5334	−0.443398
$800$	−40.2111	−1.42168
$801$	−25.3847	−0.896923
$802$	45.0527	1.59087
$803$	−17.0003	−0.599927
$804$	−199.129	−7.02275
$805$	−37.7130	−1.32921
$806$	54.1710	1.90809
$807$	−54.4221	−1.91575
$808$	61.1121	2.14992
$809$	−27.0460	−0.950888	−0.475444	−	0.879746i	$-0.657713\pi$
$809$	−27.0460	−0.950888	−0.475444	+	0.879746i	$0.657713\pi$
$810$	−228.902	−8.04278
$811$	20.4598	0.718442	0.359221	−	0.933253i	$-0.383042\pi$
$811$	20.4598	0.718442	0.359221	+	0.933253i	$0.383042\pi$
$812$	−82.7573	−2.90421
$813$	−58.9610	−2.06785
$814$	−113.805	−3.98886
$815$	33.4689	1.17236
$816$	−120.005	−4.20101
$817$	21.5546	0.754102
$818$	−65.0039	−2.27281
$819$	120.239	4.20147
$820$	6.56767	0.229353
$821$	13.1333	0.458355	0.229178	−	0.973385i	$-0.426396\pi$
$821$	13.1333	0.458355	0.229178	+	0.973385i	$0.426396\pi$
$822$	106.293	3.70739
$823$	45.1745	1.57468	0.787341	−	0.616517i	$-0.211457\pi$
$823$	45.1745	1.57468	0.787341	+	0.616517i	$0.211457\pi$
$824$	47.1927	1.64403
$825$	−122.108	−4.25126
$826$	77.5286	2.69756
$827$	−9.17208	−0.318944	−0.159472	−	0.987202i	$-0.550979\pi$
$827$	−9.17208	−0.318944	−0.159472	+	0.987202i	$0.550979\pi$
$828$	−74.1748	−2.57775
$829$	42.0193	1.45939	0.729695	−	0.683773i	$-0.239662\pi$
$829$	42.0193	1.45939	0.729695	+	0.683773i	$0.239662\pi$
$830$	−11.1568	−0.387259
$831$	−68.5234	−2.37705
$832$	−2.97205	−0.103037
$833$	82.9928	2.87553
$834$	−59.7982	−2.07064
$835$	−23.8184	−0.824269
$836$	−42.7782	−1.47951
$837$	93.0725	3.21706
$838$	56.2265	1.94231
$839$	−14.9279	−0.515367	−0.257683	−	0.966229i	$-0.582959\pi$
$839$	−14.9279	−0.515367	−0.257683	+	0.966229i	$0.582959\pi$
$840$	343.980	11.8684
$841$	−13.6270	−0.469896
$842$	−0.882077	−0.0303984
$843$	−82.1165	−2.82824
$844$	24.4184	0.840515
$845$	−5.96395	−0.205166
$846$	44.7402	1.53820
$847$	55.4419	1.90501
$848$	86.8253	2.98159
$849$	11.7911	0.404670
$850$	−107.475	−3.68636
$851$	−20.8263	−0.713915
$852$	−155.305	−5.32067
$853$	−35.6711	−1.22136	−0.610678	−	0.791879i	$-0.709103\pi$
$853$	−35.6711	−1.22136	−0.610678	+	0.791879i	$0.709103\pi$
$854$	119.477	4.08841
$855$	−54.5668	−1.86615
$856$	−93.9211	−3.21016
$857$	−50.2470	−1.71640	−0.858202	−	0.513312i	$-0.828419\pi$
$857$	−50.2470	−1.71640	−0.858202	+	0.513312i	$0.828419\pi$
$858$	132.186	4.51276
$859$	32.3848	1.10496	0.552478	−	0.833528i	$-0.313682\pi$
$859$	32.3848	1.10496	0.552478	+	0.833528i	$0.313682\pi$
$860$	−170.732	−5.82192
$861$	−6.32323	−0.215495
$862$	−54.1843	−1.84552
$863$	57.2987	1.95047	0.975235	−	0.221172i	$-0.0709881\pi$
$863$	57.2987	1.95047	0.975235	+	0.221172i	$0.0709881\pi$
$864$	74.7898	2.54440
$865$	−57.6032	−1.95857
$866$	−22.4864	−0.764120
$867$	−37.9337	−1.28830
$868$	−133.692	−4.53780
$869$	−7.53986	−0.255772
$870$	−116.053	−3.93455
$871$	46.4363	1.57343
$872$	79.4672	2.69110
$873$	20.1803	0.682998
$874$	−11.3465	−0.383801
$875$	49.4068	1.67025
$876$	51.5367	1.74126
$877$	1.71786	0.0580079	0.0290039	−	0.999579i	$-0.490766\pi$
$877$	1.71786	0.0580079	0.0290039	+	0.999579i	$0.490766\pi$
$878$	24.7028	0.833679
$879$	−42.9903	−1.45003
$880$	118.130	3.98215
$881$	39.4879	1.33038	0.665190	−	0.746674i	$-0.268350\pi$
$881$	39.4879	1.33038	0.665190	+	0.746674i	$0.268350\pi$
$882$	−296.259	−9.97555
$883$	5.17124	0.174026	0.0870131	−	0.996207i	$-0.472268\pi$
$883$	5.17124	0.174026	0.0870131	+	0.996207i	$0.472268\pi$
$884$	80.2711	2.69981
$885$	75.0103	2.52144
$886$	47.3743	1.59157
$887$	0.218500	0.00733652	0.00366826	−	0.999993i	$-0.498832\pi$
$887$	0.218500	0.00733652	0.00366826	+	0.999993i	$0.498832\pi$
$888$	189.956	6.37451
$889$	−74.0467	−2.48345
$890$	30.7576	1.03100
$891$	119.529	4.00436
$892$	−66.7322	−2.23436
$893$	4.72187	0.158011
$894$	−75.9378	−2.53974
$895$	73.0379	2.44139
$896$	58.9111	1.96808
$897$	24.1900	0.807681
$898$	−52.4957	−1.75180
$899$	24.8347	0.828283
$900$	264.696	8.82321
$901$	67.3554	2.24393
$902$	−4.97078	−0.165509
$903$	164.378	5.47015
$904$	50.3526	1.67470
$905$	−33.8653	−1.12572
$906$	28.5121	0.947250
$907$	11.6504	0.386846	0.193423	−	0.981115i	$-0.438041\pi$
$907$	11.6504	0.386846	0.193423	+	0.981115i	$0.438041\pi$
$908$	−48.5973	−1.61276
$909$	−73.9307	−2.45213
$910$	−145.688	−4.82951
$911$	6.79986	0.225289	0.112645	−	0.993635i	$-0.464068\pi$
$911$	6.79986	0.225289	0.112645	+	0.993635i	$0.464068\pi$
$912$	45.2111	1.49709
$913$	5.82591	0.192810
$914$	−11.0234	−0.364623
$915$	115.596	3.82148
$916$	−27.1010	−0.895443
$917$	52.6527	1.73874
$918$	199.896	6.59754
$919$	31.4247	1.03661	0.518303	−	0.855197i	$-0.326564\pi$
$919$	31.4247	1.03661	0.518303	+	0.855197i	$0.326564\pi$
$920$	49.4844	1.63145
$921$	10.6075	0.349529
$922$	−51.0607	−1.68159
$923$	36.2167	1.19209
$924$	−326.231	−10.7322
$925$	74.3195	2.44361
$926$	−12.4700	−0.409789
$927$	−57.0916	−1.87514
$928$	19.9563	0.655097
$929$	−13.9089	−0.456336	−0.228168	−	0.973622i	$-0.573273\pi$
$929$	−13.9089	−0.456336	−0.228168	+	0.973622i	$0.573273\pi$
$930$	−187.480	−6.14770
$931$	−31.2670	−1.02474
$932$	12.0651	0.395206
$933$	36.9441	1.20950
$934$	−78.7129	−2.57556
$935$	91.6401	2.99695
$936$	−157.769	−5.15683
$937$	−48.5608	−1.58641	−0.793205	−	0.608954i	$-0.791589\pi$
$937$	−48.5608	−1.58641	−0.793205	+	0.608954i	$0.791589\pi$
$938$	−166.106	−5.42356
$939$	12.7909	0.417416
$940$	−37.4015	−1.21990
$941$	25.5561	0.833105	0.416552	−	0.909112i	$-0.363238\pi$
$941$	25.5561	0.833105	0.416552	+	0.909112i	$0.363238\pi$
$942$	187.708	6.11586
$943$	−0.909650	−0.0296223
$944$	−44.4406	−1.44642
$945$	−250.310	−8.14259
$946$	129.220	4.20129
$947$	51.3532	1.66875	0.834377	−	0.551194i	$-0.185828\pi$
$947$	51.3532	1.66875	0.834377	+	0.551194i	$0.185828\pi$
$948$	22.8573	0.742369
$949$	−12.0182	−0.390127
$950$	40.4906	1.31369
$951$	−41.0089	−1.32981
$952$	−158.095	−5.12390
$953$	51.9020	1.68127	0.840635	−	0.541602i	$-0.182182\pi$
$953$	51.9020	1.68127	0.840635	+	0.541602i	$0.182182\pi$
$954$	−240.438	−7.78447
$955$	−11.7408	−0.379923
$956$	25.8785	0.836972
$957$	60.6007	1.95894
$958$	99.1148	3.20225
$959$	61.1737	1.97540
$960$	10.2859	0.331977
$961$	9.11972	0.294185
$962$	−80.4534	−2.59392
$963$	113.622	3.66141
$964$	48.6310	1.56630
$965$	−33.4444	−1.07661
$966$	−86.5296	−2.78404
$967$	1.40827	0.0452869	0.0226434	−	0.999744i	$-0.492792\pi$
$967$	1.40827	0.0452869	0.0226434	+	0.999744i	$0.492792\pi$
$968$	−72.7471	−2.33818
$969$	35.0729	1.12670
$970$	−24.4516	−0.785094
$971$	−33.5172	−1.07562	−0.537810	−	0.843066i	$-0.680748\pi$
$971$	−33.5172	−1.07562	−0.537810	+	0.843066i	$0.680748\pi$
$972$	−166.174	−5.33003
$973$	−34.4151	−1.10330
$974$	1.42259	0.0455826
$975$	−86.3232	−2.76456
$976$	−68.4859	−2.19218
$977$	8.04807	0.257481	0.128740	−	0.991678i	$-0.458907\pi$
$977$	8.04807	0.257481	0.128740	+	0.991678i	$0.458907\pi$
$978$	76.7918	2.45553
$979$	−16.0611	−0.513315
$980$	247.663	7.91131
$981$	−96.1359	−3.06938
$982$	−16.5998	−0.529722
$983$	−34.2212	−1.09149	−0.545743	−	0.837953i	$-0.683752\pi$
$983$	−34.2212	−1.09149	−0.545743	+	0.837953i	$0.683752\pi$
$984$	8.29691	0.264496
$985$	51.2484	1.63291
$986$	53.3385	1.69864
$987$	36.0094	1.14619
$988$	−30.2416	−0.962115
$989$	23.6471	0.751935
$990$	−327.127	−10.3968
$991$	−39.9411	−1.26877	−0.634386	−	0.773017i	$-0.718747\pi$
$991$	−39.9411	−1.26877	−0.634386	+	0.773017i	$0.718747\pi$
$992$	32.2388	1.02358
$993$	111.665	3.54357
$994$	−129.550	−4.10907
$995$	−21.2617	−0.674042
$996$	−17.6614	−0.559622
$997$	−28.6697	−0.907980	−0.453990	−	0.891007i	$-0.650000\pi$
$997$	−28.6697	−0.907980	−0.453990	+	0.891007i	$0.650000\pi$
$998$	23.3769	0.739982
$999$	−138.229	−4.37337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.11	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.11	✓	179	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53975 q^{2} -3.24477 q^{3} +4.45032 q^{4} +3.59171 q^{5} +8.24090 q^{6} +4.74281 q^{7} -6.22319 q^{8} +7.52854 q^{9} +O(q^{10})\)	\(q-2.53975 q^{2} -3.24477 q^{3} +4.45032 q^{4} +3.59171 q^{5} +8.24090 q^{6} +4.74281 q^{7} -6.22319 q^{8} +7.52854 q^{9} -9.12202 q^{10} +4.76337 q^{11} -14.4403 q^{12} +3.36742 q^{13} -12.0455 q^{14} -11.6543 q^{15} +6.90469 q^{16} +5.35637 q^{17} -19.1206 q^{18} -2.01798 q^{19} +15.9842 q^{20} -15.3893 q^{21} -12.0978 q^{22} -2.21388 q^{23} +20.1928 q^{24} +7.90035 q^{25} -8.55240 q^{26} -14.6941 q^{27} +21.1070 q^{28} -3.92084 q^{29} +29.5989 q^{30} -6.33401 q^{31} -5.08979 q^{32} -15.4560 q^{33} -13.6038 q^{34} +17.0348 q^{35} +33.5044 q^{36} +9.40711 q^{37} +5.12516 q^{38} -10.9265 q^{39} -22.3519 q^{40} +0.410884 q^{41} +39.0850 q^{42} -10.6813 q^{43} +21.1985 q^{44} +27.0403 q^{45} +5.62270 q^{46} -2.33990 q^{47} -22.4041 q^{48} +15.4942 q^{49} -20.0649 q^{50} -17.3802 q^{51} +14.9861 q^{52} +12.5748 q^{53} +37.3192 q^{54} +17.1086 q^{55} -29.5154 q^{56} +6.54789 q^{57} +9.95796 q^{58} -6.43629 q^{59} -51.8652 q^{60} -9.91875 q^{61} +16.0868 q^{62} +35.7064 q^{63} -0.882591 q^{64} +12.0948 q^{65} +39.2544 q^{66} +13.7899 q^{67} +23.8376 q^{68} +7.18354 q^{69} -43.2640 q^{70} +10.7550 q^{71} -46.8515 q^{72} -3.56896 q^{73} -23.8917 q^{74} -25.6348 q^{75} -8.98065 q^{76} +22.5917 q^{77} +27.7506 q^{78} -1.58288 q^{79} +24.7996 q^{80} +25.0933 q^{81} -1.04354 q^{82} +1.22307 q^{83} -68.4874 q^{84} +19.2385 q^{85} +27.1278 q^{86} +12.7222 q^{87} -29.6433 q^{88} -3.37179 q^{89} -68.6755 q^{90} +15.9710 q^{91} -9.85248 q^{92} +20.5524 q^{93} +5.94275 q^{94} -7.24799 q^{95} +16.5152 q^{96} +2.68050 q^{97} -39.3514 q^{98} +35.8612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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