LMFDB - Embedded newform 4033.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79445 q^{2} -3.46032 q^{3} +1.22004 q^{4} +0.638539 q^{5} +6.20936 q^{6} -3.14453 q^{7} +1.39960 q^{8} +8.97380 q^{9} +O(q^{10})$	\(q-1.79445 q^{2} -3.46032 q^{3} +1.22004 q^{4} +0.638539 q^{5} +6.20936 q^{6} -3.14453 q^{7} +1.39960 q^{8} +8.97380 q^{9} -1.14582 q^{10} +4.04630 q^{11} -4.22172 q^{12} +1.21584 q^{13} +5.64269 q^{14} -2.20955 q^{15} -4.95158 q^{16} +4.08941 q^{17} -16.1030 q^{18} +2.63464 q^{19} +0.779042 q^{20} +10.8811 q^{21} -7.26087 q^{22} -5.20650 q^{23} -4.84306 q^{24} -4.59227 q^{25} -2.18175 q^{26} -20.6713 q^{27} -3.83645 q^{28} +1.86432 q^{29} +3.96491 q^{30} -0.258488 q^{31} +6.08615 q^{32} -14.0015 q^{33} -7.33822 q^{34} -2.00791 q^{35} +10.9484 q^{36} -1.00000 q^{37} -4.72772 q^{38} -4.20718 q^{39} +0.893699 q^{40} -3.22464 q^{41} -19.5255 q^{42} -3.72099 q^{43} +4.93664 q^{44} +5.73012 q^{45} +9.34279 q^{46} +7.73073 q^{47} +17.1341 q^{48} +2.88808 q^{49} +8.24058 q^{50} -14.1507 q^{51} +1.48337 q^{52} +1.70538 q^{53} +37.0935 q^{54} +2.58372 q^{55} -4.40109 q^{56} -9.11669 q^{57} -3.34542 q^{58} +0.238157 q^{59} -2.69573 q^{60} -9.30387 q^{61} +0.463844 q^{62} -28.2184 q^{63} -1.01810 q^{64} +0.776359 q^{65} +25.1249 q^{66} -12.7784 q^{67} +4.98923 q^{68} +18.0162 q^{69} +3.60308 q^{70} +0.997540 q^{71} +12.5597 q^{72} -2.23889 q^{73} +1.79445 q^{74} +15.8907 q^{75} +3.21436 q^{76} -12.7237 q^{77} +7.54956 q^{78} +9.38330 q^{79} -3.16178 q^{80} +44.6077 q^{81} +5.78644 q^{82} +9.05619 q^{83} +13.2753 q^{84} +2.61125 q^{85} +6.67712 q^{86} -6.45114 q^{87} +5.66320 q^{88} +13.6724 q^{89} -10.2824 q^{90} -3.82324 q^{91} -6.35213 q^{92} +0.894452 q^{93} -13.8724 q^{94} +1.68232 q^{95} -21.0600 q^{96} -5.63517 q^{97} -5.18251 q^{98} +36.3107 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.79445	−1.26887	−0.634433	−	0.772978i	$-0.718766\pi$
$2$	−1.79445	−1.26887	−0.634433	+	0.772978i	$0.718766\pi$
$3$	−3.46032	−1.99782	−0.998908	−	0.0467243i	$-0.985122\pi$
$3$	−3.46032	−1.99782	−0.998908	+	0.0467243i	$0.985122\pi$
$4$	1.22004	0.610019
$5$	0.638539	0.285563	0.142782	−	0.989754i	$-0.454395\pi$
$5$	0.638539	0.285563	0.142782	+	0.989754i	$0.454395\pi$
$6$	6.20936	2.53496
$7$	−3.14453	−1.18852	−0.594261	−	0.804272i	$-0.702555\pi$
$7$	−3.14453	−1.18852	−0.594261	+	0.804272i	$0.702555\pi$
$8$	1.39960	0.494833
$9$	8.97380	2.99127
$10$	−1.14582	−0.362341
$11$	4.04630	1.22001	0.610003	−	0.792399i	$-0.291168\pi$
$11$	4.04630	1.22001	0.610003	+	0.792399i	$0.291168\pi$
$12$	−4.22172	−1.21871
$13$	1.21584	0.337213	0.168606	−	0.985683i	$-0.446073\pi$
$13$	1.21584	0.337213	0.168606	+	0.985683i	$0.446073\pi$
$14$	5.64269	1.50807
$15$	−2.20955	−0.570503
$16$	−4.95158	−1.23790
$17$	4.08941	0.991827	0.495913	−	0.868372i	$-0.334833\pi$
$17$	4.08941	0.991827	0.495913	+	0.868372i	$0.334833\pi$
$18$	−16.1030	−3.79552
$19$	2.63464	0.604428	0.302214	−	0.953240i	$-0.402274\pi$
$19$	2.63464	0.604428	0.302214	+	0.953240i	$0.402274\pi$
$20$	0.779042	0.174199
$21$	10.8811	2.37445
$22$	−7.26087	−1.54802
$23$	−5.20650	−1.08563	−0.542815	−	0.839852i	$-0.682642\pi$
$23$	−5.20650	−1.08563	−0.542815	+	0.839852i	$0.682642\pi$
$24$	−4.84306	−0.988586
$25$	−4.59227	−0.918454
$26$	−2.18175	−0.427877
$27$	−20.6713	−3.97819
$28$	−3.83645	−0.725021
$29$	1.86432	0.346195	0.173098	−	0.984905i	$-0.444622\pi$
$29$	1.86432	0.346195	0.173098	+	0.984905i	$0.444622\pi$
$30$	3.96491	0.723891
$31$	−0.258488	−0.0464259	−0.0232130	−	0.999731i	$-0.507390\pi$
$31$	−0.258488	−0.0464259	−0.0232130	+	0.999731i	$0.507390\pi$
$32$	6.08615	1.07589
$33$	−14.0015	−2.43735
$34$	−7.33822	−1.25849
$35$	−2.00791	−0.339398
$36$	10.9484	1.82473
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−4.72772	−0.766938
$39$	−4.20718	−0.673688
$40$	0.893699	0.141306
$41$	−3.22464	−0.503604	−0.251802	−	0.967779i	$-0.581023\pi$
$41$	−3.22464	−0.503604	−0.251802	+	0.967779i	$0.581023\pi$
$42$	−19.5255	−3.01285
$43$	−3.72099	−0.567446	−0.283723	−	0.958906i	$-0.591570\pi$
$43$	−3.72099	−0.567446	−0.283723	+	0.958906i	$0.591570\pi$
$44$	4.93664	0.744226
$45$	5.73012	0.854196
$46$	9.34279	1.37752
$47$	7.73073	1.12764	0.563821	−	0.825897i	$-0.309331\pi$
$47$	7.73073	1.12764	0.563821	+	0.825897i	$0.309331\pi$
$48$	17.1341	2.47309
$49$	2.88808	0.412583
$50$	8.24058	1.16539
$51$	−14.1507	−1.98149
$52$	1.48337	0.205706
$53$	1.70538	0.234252	0.117126	−	0.993117i	$-0.462632\pi$
$53$	1.70538	0.234252	0.117126	+	0.993117i	$0.462632\pi$
$54$	37.0935	5.04778
$55$	2.58372	0.348389
$56$	−4.40109	−0.588120
$57$	−9.11669	−1.20754
$58$	−3.34542	−0.439275
$59$	0.238157	0.0310054	0.0155027	−	0.999880i	$-0.495065\pi$
$59$	0.238157	0.0310054	0.0155027	+	0.999880i	$0.495065\pi$
$60$	−2.69573	−0.348017
$61$	−9.30387	−1.19124	−0.595619	−	0.803267i	$-0.703093\pi$
$61$	−9.30387	−1.19124	−0.595619	+	0.803267i	$0.703093\pi$
$62$	0.463844	0.0589082
$63$	−28.2184	−3.55519
$64$	−1.01810	−0.127263
$65$	0.776359	0.0962955
$66$	25.1249	3.09266
$67$	−12.7784	−1.56113	−0.780567	−	0.625072i	$-0.785069\pi$
$67$	−12.7784	−1.56113	−0.780567	+	0.625072i	$0.785069\pi$
$68$	4.98923	0.605033
$69$	18.0162	2.16889
$70$	3.60308	0.430650
$71$	0.997540	0.118386	0.0591931	−	0.998247i	$-0.481147\pi$
$71$	0.997540	0.118386	0.0591931	+	0.998247i	$0.481147\pi$
$72$	12.5597	1.48018
$73$	−2.23889	−0.262042	−0.131021	−	0.991380i	$-0.541826\pi$
$73$	−2.23889	−0.262042	−0.131021	+	0.991380i	$0.541826\pi$
$74$	1.79445	0.208600
$75$	15.8907	1.83490
$76$	3.21436	0.368712
$77$	−12.7237	−1.45000
$78$	7.54956	0.854820
$79$	9.38330	1.05570	0.527852	−	0.849336i	$-0.322998\pi$
$79$	9.38330	1.05570	0.527852	+	0.849336i	$0.322998\pi$
$80$	−3.16178	−0.353498
$81$	44.6077	4.95641
$82$	5.78644	0.639006
$83$	9.05619	0.994046	0.497023	−	0.867737i	$-0.334426\pi$
$83$	9.05619	0.994046	0.497023	+	0.867737i	$0.334426\pi$
$84$	13.2753	1.44846
$85$	2.61125	0.283229
$86$	6.67712	0.720013
$87$	−6.45114	−0.691635
$88$	5.66320	0.603699
$89$	13.6724	1.44927	0.724634	−	0.689134i	$-0.242009\pi$
$89$	13.6724	1.44927	0.724634	+	0.689134i	$0.242009\pi$
$90$	−10.2824	−1.08386
$91$	−3.82324	−0.400784
$92$	−6.35213	−0.662255
$93$	0.894452	0.0927504
$94$	−13.8724	−1.43083
$95$	1.68232	0.172602
$96$	−21.0600	−2.14943
$97$	−5.63517	−0.572165	−0.286082	−	0.958205i	$-0.592353\pi$
$97$	−5.63517	−0.572165	−0.286082	+	0.958205i	$0.592353\pi$
$98$	−5.18251	−0.523513
$99$	36.3107	3.64936
$100$	−5.60274	−0.560274
$101$	−4.16134	−0.414069	−0.207034	−	0.978334i	$-0.566381\pi$
$101$	−4.16134	−0.414069	−0.207034	+	0.978334i	$0.566381\pi$
$102$	25.3926	2.51424
$103$	−16.9244	−1.66761	−0.833804	−	0.552061i	$-0.813842\pi$
$103$	−16.9244	−1.66761	−0.833804	+	0.552061i	$0.813842\pi$
$104$	1.70169	0.166864
$105$	6.94799	0.678055
$106$	−3.06021	−0.297234
$107$	−9.96975	−0.963812	−0.481906	−	0.876223i	$-0.660055\pi$
$107$	−9.96975	−0.963812	−0.481906	+	0.876223i	$0.660055\pi$
$108$	−25.2197	−2.42677
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−4.63635	−0.442058
$111$	3.46032	0.328439
$112$	15.5704	1.47127
$113$	10.4500	0.983056	0.491528	−	0.870862i	$-0.336438\pi$
$113$	10.4500	0.983056	0.491528	+	0.870862i	$0.336438\pi$
$114$	16.3594	1.53220
$115$	−3.32455	−0.310016
$116$	2.27454	0.211186
$117$	10.9107	1.00869
$118$	−0.427360	−0.0393417
$119$	−12.8593	−1.17881
$120$	−3.09248	−0.282304
$121$	5.37254	0.488413
$122$	16.6953	1.51152
$123$	11.1583	1.00611
$124$	−0.315366	−0.0283207
$125$	−6.12504	−0.547840
$126$	50.6364	4.51105
$127$	−14.6429	−1.29935	−0.649674	−	0.760213i	$-0.725095\pi$
$127$	−14.6429	−1.29935	−0.649674	+	0.760213i	$0.725095\pi$
$128$	−10.3454	−0.914410
$129$	12.8758	1.13365
$130$	−1.39313	−0.122186
$131$	10.1270	0.884800	0.442400	−	0.896818i	$-0.354127\pi$
$131$	10.1270	0.884800	0.442400	+	0.896818i	$0.354127\pi$
$132$	−17.0823	−1.48683
$133$	−8.28471	−0.718376
$134$	22.9302	1.98087
$135$	−13.1994	−1.13602
$136$	5.72354	0.490789
$137$	17.3717	1.48416	0.742080	−	0.670311i	$-0.233839\pi$
$137$	17.3717	1.48416	0.742080	+	0.670311i	$0.233839\pi$
$138$	−32.3290	−2.75203
$139$	2.53559	0.215066	0.107533	−	0.994202i	$-0.465705\pi$
$139$	2.53559	0.215066	0.107533	+	0.994202i	$0.465705\pi$
$140$	−2.44972	−0.207039
$141$	−26.7508	−2.25282
$142$	−1.79003	−0.150216
$143$	4.91964	0.411401
$144$	−44.4345	−3.70288
$145$	1.19044	0.0988607
$146$	4.01757	0.332497
$147$	−9.99369	−0.824265
$148$	−1.22004	−0.100286
$149$	−5.95065	−0.487496	−0.243748	−	0.969839i	$-0.578377\pi$
$149$	−5.95065	−0.487496	−0.243748	+	0.969839i	$0.578377\pi$
$150$	−28.5150	−2.32824
$151$	−20.4659	−1.66549	−0.832744	−	0.553658i	$-0.813232\pi$
$151$	−20.4659	−1.66549	−0.832744	+	0.553658i	$0.813232\pi$
$152$	3.68744	0.299091
$153$	36.6975	2.96682
$154$	22.8320	1.83986
$155$	−0.165055	−0.0132575
$156$	−5.13292	−0.410963
$157$	20.8483	1.66388	0.831939	−	0.554866i	$-0.187231\pi$
$157$	20.8483	1.66388	0.831939	+	0.554866i	$0.187231\pi$
$158$	−16.8378	−1.33955
$159$	−5.90115	−0.467991
$160$	3.88624	0.307235
$161$	16.3720	1.29030
$162$	−80.0462	−6.28902
$163$	8.39302	0.657392	0.328696	−	0.944436i	$-0.393391\pi$
$163$	8.39302	0.657392	0.328696	+	0.944436i	$0.393391\pi$
$164$	−3.93418	−0.307208
$165$	−8.94049	−0.696016
$166$	−16.2508	−1.26131
$167$	−4.79742	−0.371235	−0.185618	−	0.982622i	$-0.559429\pi$
$167$	−4.79742	−0.371235	−0.185618	+	0.982622i	$0.559429\pi$
$168$	15.2292	1.17496
$169$	−11.5217	−0.886288
$170$	−4.68574	−0.359380
$171$	23.6427	1.80801
$172$	−4.53975	−0.346153
$173$	−5.38797	−0.409640	−0.204820	−	0.978800i	$-0.565661\pi$
$173$	−5.38797	−0.409640	−0.204820	+	0.978800i	$0.565661\pi$
$174$	11.5762	0.877591
$175$	14.4405	1.09160
$176$	−20.0356	−1.51024
$177$	−0.824100	−0.0619431
$178$	−24.5343	−1.83893
$179$	−6.13478	−0.458535	−0.229268	−	0.973363i	$-0.573633\pi$
$179$	−6.13478	−0.458535	−0.229268	+	0.973363i	$0.573633\pi$
$180$	6.99097	0.521076
$181$	16.0702	1.19449	0.597245	−	0.802059i	$-0.296262\pi$
$181$	16.0702	1.19449	0.597245	+	0.802059i	$0.296262\pi$
$182$	6.86060	0.508541
$183$	32.1943	2.37987
$184$	−7.28702	−0.537206
$185$	−0.638539	−0.0469463
$186$	−1.60505	−0.117688
$187$	16.5470	1.21003
$188$	9.43178	0.687884
$189$	65.0014	4.72816
$190$	−3.01883	−0.219009
$191$	11.3267	0.819568	0.409784	−	0.912183i	$-0.365604\pi$
$191$	11.3267	0.819568	0.409784	+	0.912183i	$0.365604\pi$
$192$	3.52296	0.254248
$193$	20.6211	1.48434	0.742171	−	0.670210i	$-0.233796\pi$
$193$	20.6211	1.48434	0.742171	+	0.670210i	$0.233796\pi$
$194$	10.1120	0.726000
$195$	−2.68645	−0.192381
$196$	3.52357	0.251684
$197$	1.06227	0.0756837	0.0378418	−	0.999284i	$-0.487952\pi$
$197$	1.06227	0.0756837	0.0378418	+	0.999284i	$0.487952\pi$
$198$	−65.1576	−4.63055
$199$	−4.74288	−0.336214	−0.168107	−	0.985769i	$-0.553765\pi$
$199$	−4.74288	−0.336214	−0.168107	+	0.985769i	$0.553765\pi$
$200$	−6.42734	−0.454482
$201$	44.2174	3.11886
$202$	7.46730	0.525397
$203$	−5.86241	−0.411461
$204$	−17.2643	−1.20874
$205$	−2.05906	−0.143811
$206$	30.3699	2.11597
$207$	−46.7221	−3.24741
$208$	−6.02032	−0.417434
$209$	10.6605	0.737405
$210$	−12.4678	−0.860360
$211$	7.61495	0.524235	0.262117	−	0.965036i	$-0.415579\pi$
$211$	7.61495	0.524235	0.262117	+	0.965036i	$0.415579\pi$
$212$	2.08062	0.142898
$213$	−3.45181	−0.236514
$214$	17.8902	1.22295
$215$	−2.37600	−0.162042
$216$	−28.9315	−1.96854
$217$	0.812825	0.0551782
$218$	1.79445	0.121535
$219$	7.74728	0.523513
$220$	3.15224	0.212524
$221$	4.97205	0.334456
$222$	−6.20936	−0.416745
$223$	−24.7998	−1.66072	−0.830358	−	0.557230i	$-0.811864\pi$
$223$	−24.7998	−1.66072	−0.830358	+	0.557230i	$0.811864\pi$
$224$	−19.1381	−1.27872
$225$	−41.2101	−2.74734
$226$	−18.7520	−1.24737
$227$	−4.61132	−0.306064	−0.153032	−	0.988221i	$-0.548904\pi$
$227$	−4.61132	−0.306064	−0.153032	+	0.988221i	$0.548904\pi$
$228$	−11.1227	−0.736619
$229$	−1.26362	−0.0835025	−0.0417512	−	0.999128i	$-0.513294\pi$
$229$	−1.26362	−0.0835025	−0.0417512	+	0.999128i	$0.513294\pi$
$230$	5.96573	0.393369
$231$	44.0281	2.89684
$232$	2.60930	0.171309
$233$	8.15044	0.533953	0.266976	−	0.963703i	$-0.413975\pi$
$233$	8.15044	0.533953	0.266976	+	0.963703i	$0.413975\pi$
$234$	−19.5786	−1.27990
$235$	4.93637	0.322013
$236$	0.290561	0.0189139
$237$	−32.4692	−2.10910
$238$	23.0753	1.49575
$239$	−9.97624	−0.645309	−0.322655	−	0.946517i	$-0.604575\pi$
$239$	−9.97624	−0.645309	−0.322655	+	0.946517i	$0.604575\pi$
$240$	10.9408	0.706223
$241$	0.698791	0.0450131	0.0225065	−	0.999747i	$-0.492835\pi$
$241$	0.698791	0.0450131	0.0225065	+	0.999747i	$0.492835\pi$
$242$	−9.64074	−0.619730
$243$	−92.3431	−5.92381
$244$	−11.3511	−0.726678
$245$	1.84415	0.117819
$246$	−20.0229	−1.27662
$247$	3.20329	0.203821
$248$	−0.361781	−0.0229731
$249$	−31.3373	−1.98592
$250$	10.9910	0.695135
$251$	−31.2240	−1.97084	−0.985419	−	0.170143i	$-0.945577\pi$
$251$	−31.2240	−1.97084	−0.985419	+	0.170143i	$0.945577\pi$
$252$	−34.4275	−2.16873
$253$	−21.0671	−1.32448
$254$	26.2759	1.64870
$255$	−9.03574	−0.565840
$256$	20.6004	1.28753
$257$	−10.3381	−0.644871	−0.322436	−	0.946591i	$-0.604502\pi$
$257$	−10.3381	−0.644871	−0.322436	+	0.946591i	$0.604502\pi$
$258$	−23.1050	−1.43845
$259$	3.14453	0.195392
$260$	0.947188	0.0587421
$261$	16.7300	1.03556
$262$	−18.1724	−1.12269
$263$	−16.1000	−0.992769	−0.496385	−	0.868103i	$-0.665339\pi$
$263$	−16.1000	−0.992769	−0.496385	+	0.868103i	$0.665339\pi$
$264$	−19.5965	−1.20608
$265$	1.08895	0.0668936
$266$	14.8665	0.911522
$267$	−47.3107	−2.89537
$268$	−15.5902	−0.952321
$269$	−3.64020	−0.221947	−0.110973	−	0.993823i	$-0.535397\pi$
$269$	−3.64020	−0.221947	−0.110973	+	0.993823i	$0.535397\pi$
$270$	23.6856	1.44146
$271$	21.9557	1.33371	0.666857	−	0.745186i	$-0.267639\pi$
$271$	21.9557	1.33371	0.666857	+	0.745186i	$0.267639\pi$
$272$	−20.2490	−1.22778
$273$	13.2296	0.800693
$274$	−31.1725	−1.88320
$275$	−18.5817	−1.12052
$276$	21.9804	1.32306
$277$	29.5407	1.77493	0.887465	−	0.460875i	$-0.152464\pi$
$277$	29.5407	1.77493	0.887465	+	0.460875i	$0.152464\pi$
$278$	−4.54997	−0.272889
$279$	−2.31962	−0.138872
$280$	−2.81027	−0.167946
$281$	5.14782	0.307093	0.153546	−	0.988141i	$-0.450931\pi$
$281$	5.14782	0.307093	0.153546	+	0.988141i	$0.450931\pi$
$282$	48.0029	2.85853
$283$	10.7408	0.638474	0.319237	−	0.947675i	$-0.396573\pi$
$283$	10.7408	0.638474	0.319237	+	0.947675i	$0.396573\pi$
$284$	1.21704	0.0722179
$285$	−5.82136	−0.344828
$286$	−8.82803	−0.522012
$287$	10.1400	0.598544
$288$	54.6159	3.21827
$289$	−0.276746	−0.0162792
$290$	−2.13618	−0.125441
$291$	19.4995	1.14308
$292$	−2.73153	−0.159851
$293$	−22.9768	−1.34232	−0.671161	−	0.741312i	$-0.734204\pi$
$293$	−22.9768	−1.34232	−0.671161	+	0.741312i	$0.734204\pi$
$294$	17.9331	1.04588
$295$	0.152073	0.00885401
$296$	−1.39960	−0.0813501
$297$	−83.6421	−4.85341
$298$	10.6781	0.618567
$299$	−6.33026	−0.366088
$300$	19.3873	1.11932
$301$	11.7008	0.674422
$302$	36.7249	2.11328
$303$	14.3996	0.827233
$304$	−13.0456	−0.748219
$305$	−5.94088	−0.340174
$306$	−65.8518	−3.76449
$307$	−13.1918	−0.752894	−0.376447	−	0.926438i	$-0.622854\pi$
$307$	−13.1918	−0.752894	−0.376447	+	0.926438i	$0.622854\pi$
$308$	−15.5234	−0.884529
$309$	58.5637	3.33157
$310$	0.296182	0.0168220
$311$	−2.56839	−0.145640	−0.0728201	−	0.997345i	$-0.523200\pi$
$311$	−2.56839	−0.145640	−0.0728201	+	0.997345i	$0.523200\pi$
$312$	−5.88837	−0.333364
$313$	2.98639	0.168801	0.0844004	−	0.996432i	$-0.473103\pi$
$313$	2.98639	0.168801	0.0844004	+	0.996432i	$0.473103\pi$
$314$	−37.4112	−2.11124
$315$	−18.0186	−1.01523
$316$	11.4480	0.643999
$317$	18.4006	1.03348	0.516742	−	0.856141i	$-0.327145\pi$
$317$	18.4006	1.03348	0.516742	+	0.856141i	$0.327145\pi$
$318$	10.5893	0.593818
$319$	7.54360	0.422360
$320$	−0.650099	−0.0363416
$321$	34.4985	1.92552
$322$	−29.3787	−1.63721
$323$	10.7741	0.599488
$324$	54.4231	3.02351
$325$	−5.58345	−0.309714
$326$	−15.0608	−0.834142
$327$	3.46032	0.191356
$328$	−4.51321	−0.249200
$329$	−24.3095	−1.34023
$330$	16.0432	0.883151
$331$	24.3773	1.33990	0.669948	−	0.742408i	$-0.266317\pi$
$331$	24.3773	1.33990	0.669948	+	0.742408i	$0.266317\pi$
$332$	11.0489	0.606387
$333$	−8.97380	−0.491761
$334$	8.60871	0.471048
$335$	−8.15952	−0.445802
$336$	−53.8786	−2.93932
$337$	27.1638	1.47970	0.739852	−	0.672769i	$-0.234895\pi$
$337$	27.1638	1.47970	0.739852	+	0.672769i	$0.234895\pi$
$338$	20.6751	1.12458
$339$	−36.1604	−1.96397
$340$	3.18582	0.172775
$341$	−1.04592	−0.0566399
$342$	−42.4256	−2.29412
$343$	12.9301	0.698157
$344$	−5.20790	−0.280791
$345$	11.5040	0.619355
$346$	9.66843	0.519778
$347$	−11.4545	−0.614911	−0.307455	−	0.951563i	$-0.599477\pi$
$347$	−11.4545	−0.614911	−0.307455	+	0.951563i	$0.599477\pi$
$348$	−7.87063	−0.421910
$349$	−5.85508	−0.313416	−0.156708	−	0.987645i	$-0.550088\pi$
$349$	−5.85508	−0.313416	−0.156708	+	0.987645i	$0.550088\pi$
$350$	−25.9128	−1.38510
$351$	−25.1329	−1.34149
$352$	24.6264	1.31259
$353$	−22.2710	−1.18537	−0.592684	−	0.805435i	$-0.701932\pi$
$353$	−22.2710	−1.18537	−0.592684	+	0.805435i	$0.701932\pi$
$354$	1.47880	0.0785975
$355$	0.636968	0.0338068
$356$	16.6808	0.884081
$357$	44.4972	2.35504
$358$	11.0085	0.581819
$359$	8.46028	0.446517	0.223258	−	0.974759i	$-0.428331\pi$
$359$	8.46028	0.446517	0.223258	+	0.974759i	$0.428331\pi$
$360$	8.01988	0.422685
$361$	−12.0587	−0.634667
$362$	−28.8371	−1.51565
$363$	−18.5907	−0.975759
$364$	−4.66450	−0.244486
$365$	−1.42962	−0.0748297
$366$	−57.7710	−3.01974
$367$	−18.1325	−0.946507	−0.473253	−	0.880926i	$-0.656920\pi$
$367$	−18.1325	−0.946507	−0.473253	+	0.880926i	$0.656920\pi$
$368$	25.7804	1.34390
$369$	−28.9373	−1.50641
$370$	1.14582	0.0595685
$371$	−5.36261	−0.278413
$372$	1.09127	0.0565795
$373$	−1.31804	−0.0682455	−0.0341227	−	0.999418i	$-0.510864\pi$
$373$	−1.31804	−0.0682455	−0.0341227	+	0.999418i	$0.510864\pi$
$374$	−29.6926	−1.53537
$375$	21.1946	1.09448
$376$	10.8199	0.557995
$377$	2.26671	0.116741
$378$	−116.642	−5.99940
$379$	−5.70463	−0.293027	−0.146514	−	0.989209i	$-0.546805\pi$
$379$	−5.70463	−0.293027	−0.146514	+	0.989209i	$0.546805\pi$
$380$	2.05249	0.105291
$381$	50.6691	2.59586
$382$	−20.3251	−1.03992
$383$	0.473295	0.0241842	0.0120921	−	0.999927i	$-0.496151\pi$
$383$	0.473295	0.0241842	0.0120921	+	0.999927i	$0.496151\pi$
$384$	35.7983	1.82682
$385$	−8.12459	−0.414067
$386$	−37.0035	−1.88343
$387$	−33.3915	−1.69738
$388$	−6.87512	−0.349031
$389$	−7.37125	−0.373737	−0.186869	−	0.982385i	$-0.559834\pi$
$389$	−7.37125	−0.373737	−0.186869	+	0.982385i	$0.559834\pi$
$390$	4.82069	0.244105
$391$	−21.2915	−1.07676
$392$	4.04216	0.204160
$393$	−35.0427	−1.76767
$394$	−1.90619	−0.0960324
$395$	5.99160	0.301470
$396$	44.3004	2.22618
$397$	−12.2213	−0.613369	−0.306685	−	0.951811i	$-0.599220\pi$
$397$	−12.2213	−0.613369	−0.306685	+	0.951811i	$0.599220\pi$
$398$	8.51085	0.426610
$399$	28.6677	1.43518
$400$	22.7390	1.13695
$401$	−18.5159	−0.924641	−0.462321	−	0.886713i	$-0.652983\pi$
$401$	−18.5159	−0.924641	−0.462321	+	0.886713i	$0.652983\pi$
$402$	−79.3458	−3.95741
$403$	−0.314280	−0.0156554
$404$	−5.07699	−0.252590
$405$	28.4838	1.41537
$406$	10.5198	0.522088
$407$	−4.04630	−0.200568
$408$	−19.8053	−0.980506
$409$	9.97198	0.493083	0.246541	−	0.969132i	$-0.420706\pi$
$409$	9.97198	0.493083	0.246541	+	0.969132i	$0.420706\pi$
$410$	3.69487	0.182477
$411$	−60.1114	−2.96508
$412$	−20.6484	−1.01727
$413$	−0.748893	−0.0368506
$414$	83.8403	4.12053
$415$	5.78273	0.283863
$416$	7.39977	0.362803
$417$	−8.77393	−0.429661
$418$	−19.1298	−0.935668
$419$	−31.9986	−1.56323	−0.781617	−	0.623759i	$-0.785605\pi$
$419$	−31.9986	−1.56323	−0.781617	+	0.623759i	$0.785605\pi$
$420$	8.47682	0.413626
$421$	−21.2305	−1.03471	−0.517356	−	0.855770i	$-0.673084\pi$
$421$	−21.2305	−1.03471	−0.517356	+	0.855770i	$0.673084\pi$
$422$	−13.6646	−0.665183
$423$	69.3740	3.37308
$424$	2.38685	0.115915
$425$	−18.7797	−0.910947
$426$	6.19408	0.300104
$427$	29.2563	1.41581
$428$	−12.1635	−0.587944
$429$	−17.0235	−0.821903
$430$	4.26360	0.205609
$431$	4.76264	0.229408	0.114704	−	0.993400i	$-0.463408\pi$
$431$	4.76264	0.229408	0.114704	+	0.993400i	$0.463408\pi$
$432$	102.355	4.92458
$433$	9.61784	0.462204	0.231102	−	0.972930i	$-0.425767\pi$
$433$	9.61784	0.462204	0.231102	+	0.972930i	$0.425767\pi$
$434$	−1.45857	−0.0700137
$435$	−4.11930	−0.197505
$436$	−1.22004	−0.0584292
$437$	−13.7173	−0.656185
$438$	−13.9021	−0.664267
$439$	−19.9729	−0.953253	−0.476627	−	0.879106i	$-0.658141\pi$
$439$	−19.9729	−0.953253	−0.476627	+	0.879106i	$0.658141\pi$
$440$	3.61618	0.172394
$441$	25.9171	1.23415
$442$	−8.92208	−0.424380
$443$	−19.6285	−0.932578	−0.466289	−	0.884632i	$-0.654409\pi$
$443$	−19.6285	−0.932578	−0.466289	+	0.884632i	$0.654409\pi$
$444$	4.22172	0.200354
$445$	8.73034	0.413858
$446$	44.5019	2.10723
$447$	20.5912	0.973928
$448$	3.20146	0.151255
$449$	27.6325	1.30406	0.652030	−	0.758193i	$-0.273918\pi$
$449$	27.6325	1.30406	0.652030	+	0.758193i	$0.273918\pi$
$450$	73.9493	3.48600
$451$	−13.0479	−0.614400
$452$	12.7494	0.599683
$453$	70.8184	3.32734
$454$	8.27476	0.388354
$455$	−2.44129	−0.114449
$456$	−12.7597	−0.597529
$457$	−24.3961	−1.14120	−0.570601	−	0.821227i	$-0.693290\pi$
$457$	−24.3961	−1.14120	−0.570601	+	0.821227i	$0.693290\pi$
$458$	2.26750	0.105953
$459$	−84.5332	−3.94567
$460$	−4.05608	−0.189116
$461$	−16.4237	−0.764926	−0.382463	−	0.923971i	$-0.624924\pi$
$461$	−16.4237	−0.764926	−0.382463	+	0.923971i	$0.624924\pi$
$462$	−79.0061	−3.67570
$463$	0.372151	0.0172953	0.00864767	−	0.999963i	$-0.497247\pi$
$463$	0.372151	0.0172953	0.00864767	+	0.999963i	$0.497247\pi$
$464$	−9.23133	−0.428554
$465$	0.571143	0.0264861
$466$	−14.6255	−0.677514
$467$	5.77830	0.267388	0.133694	−	0.991023i	$-0.457316\pi$
$467$	5.77830	0.267388	0.133694	+	0.991023i	$0.457316\pi$
$468$	13.3114	0.615322
$469$	40.1822	1.85544
$470$	−8.85805	−0.408592
$471$	−72.1419	−3.32412
$472$	0.333325	0.0153425
$473$	−15.0563	−0.692287
$474$	58.2642	2.67617
$475$	−12.0990	−0.555139
$476$	−15.6888	−0.719095
$477$	15.3037	0.700709
$478$	17.9018	0.818811
$479$	38.6767	1.76719	0.883593	−	0.468256i	$-0.155118\pi$
$479$	38.6767	1.76719	0.883593	+	0.468256i	$0.155118\pi$
$480$	−13.4476	−0.613798
$481$	−1.21584	−0.0554374
$482$	−1.25394	−0.0571156
$483$	−56.6524	−2.57777
$484$	6.55471	0.297941
$485$	−3.59827	−0.163389
$486$	165.705	7.51652
$487$	−15.4186	−0.698686	−0.349343	−	0.936995i	$-0.613595\pi$
$487$	−15.4186	−0.698686	−0.349343	+	0.936995i	$0.613595\pi$
$488$	−13.0217	−0.589464
$489$	−29.0425	−1.31335
$490$	−3.30923	−0.149496
$491$	−18.0859	−0.816206	−0.408103	−	0.912936i	$-0.633810\pi$
$491$	−18.0859	−0.816206	−0.408103	+	0.912936i	$0.633810\pi$
$492$	13.6135	0.613745
$493$	7.62396	0.343366
$494$	−5.74814	−0.258621
$495$	23.1858	1.04212
$496$	1.27993	0.0574704
$497$	−3.13680	−0.140705
$498$	56.2331	2.51987
$499$	−7.97978	−0.357224	−0.178612	−	0.983920i	$-0.557161\pi$
$499$	−7.97978	−0.357224	−0.178612	+	0.983920i	$0.557161\pi$
$500$	−7.47278	−0.334193
$501$	16.6006	0.741660
$502$	56.0297	2.50073
$503$	−32.6930	−1.45771	−0.728854	−	0.684669i	$-0.759947\pi$
$503$	−32.6930	−1.45771	−0.728854	+	0.684669i	$0.759947\pi$
$504$	−39.4945	−1.75922
$505$	−2.65718	−0.118243
$506$	37.8037	1.68058
$507$	39.8689	1.77064
$508$	−17.8649	−0.792627
$509$	−12.6978	−0.562819	−0.281409	−	0.959588i	$-0.590802\pi$
$509$	−12.6978	−0.562819	−0.281409	+	0.959588i	$0.590802\pi$
$510$	16.2142	0.717975
$511$	7.04027	0.311443
$512$	−16.2756	−0.719287
$513$	−54.4613	−2.40453
$514$	18.5511	0.818255
$515$	−10.8069	−0.476208
$516$	15.7090	0.691550
$517$	31.2809	1.37573
$518$	−5.64269	−0.247926
$519$	18.6441	0.818385
$520$	1.08659	0.0476502
$521$	18.8413	0.825451	0.412725	−	0.910855i	$-0.364577\pi$
$521$	18.8413	0.825451	0.412725	+	0.910855i	$0.364577\pi$
$522$	−30.0211	−1.31399
$523$	22.8883	1.00084	0.500418	−	0.865784i	$-0.333180\pi$
$523$	22.8883	1.00084	0.500418	+	0.865784i	$0.333180\pi$
$524$	12.3553	0.539745
$525$	−49.9688	−2.18082
$526$	28.8906	1.25969
$527$	−1.05706	−0.0460465
$528$	69.3295	3.01718
$529$	4.10766	0.178594
$530$	−1.95406	−0.0848790
$531$	2.13718	0.0927455
$532$	−10.1077	−0.438223
$533$	−3.92064	−0.169822
$534$	84.8966	3.67383
$535$	−6.36607	−0.275229
$536$	−17.8847	−0.772501
$537$	21.2283	0.916068
$538$	6.53214	0.281620
$539$	11.6861	0.503354
$540$	−16.1038	−0.692996
$541$	−12.9222	−0.555567	−0.277783	−	0.960644i	$-0.589600\pi$
$541$	−12.9222	−0.555567	−0.277783	+	0.960644i	$0.589600\pi$
$542$	−39.3983	−1.69230
$543$	−55.6080	−2.38637
$544$	24.8887	1.06710
$545$	−0.638539	−0.0273520
$546$	−23.7398	−1.01597
$547$	29.9884	1.28221	0.641106	−	0.767452i	$-0.278476\pi$
$547$	29.9884	1.28221	0.641106	+	0.767452i	$0.278476\pi$
$548$	21.1941	0.905366
$549$	−83.4910	−3.56331
$550$	33.3439	1.42179
$551$	4.91181	0.209250
$552$	25.2154	1.07324
$553$	−29.5061	−1.25473
$554$	−53.0093	−2.25215
$555$	2.20955	0.0937901
$556$	3.09351	0.131194
$557$	−23.4347	−0.992958	−0.496479	−	0.868049i	$-0.665374\pi$
$557$	−23.4347	−0.992958	−0.496479	+	0.868049i	$0.665374\pi$
$558$	4.16244	0.176210
$559$	−4.52412	−0.191350
$560$	9.94231	0.420139
$561$	−57.2578	−2.41743
$562$	−9.23748	−0.389660
$563$	37.8916	1.59694	0.798470	−	0.602035i	$-0.205643\pi$
$563$	37.8916	1.59694	0.798470	+	0.602035i	$0.205643\pi$
$564$	−32.6370	−1.37426
$565$	6.67275	0.280725
$566$	−19.2738	−0.810137
$567$	−140.270	−5.89080
$568$	1.39616	0.0585815
$569$	40.6091	1.70242	0.851211	−	0.524824i	$-0.175869\pi$
$569$	40.6091	1.70242	0.851211	+	0.524824i	$0.175869\pi$
$570$	10.4461	0.437540
$571$	35.2834	1.47657	0.738283	−	0.674491i	$-0.235637\pi$
$571$	35.2834	1.47657	0.738283	+	0.674491i	$0.235637\pi$
$572$	6.00215	0.250962
$573$	−39.1938	−1.63735
$574$	−18.1957	−0.759472
$575$	23.9096	0.997101
$576$	−9.13626	−0.380678
$577$	−18.1892	−0.757226	−0.378613	−	0.925555i	$-0.623599\pi$
$577$	−18.1892	−0.757226	−0.378613	+	0.925555i	$0.623599\pi$
$578$	0.496607	0.0206561
$579$	−71.3557	−2.96544
$580$	1.45238	0.0603069
$581$	−28.4775	−1.18144
$582$	−34.9908	−1.45041
$583$	6.90047	0.285788
$584$	−3.13355	−0.129667
$585$	6.96689	0.288046
$586$	41.2307	1.70323
$587$	−34.7253	−1.43326	−0.716632	−	0.697451i	$-0.754317\pi$
$587$	−34.7253	−1.43326	−0.716632	+	0.697451i	$0.754317\pi$
$588$	−12.1927	−0.502817
$589$	−0.681024	−0.0280611
$590$	−0.272886	−0.0112345
$591$	−3.67580	−0.151202
$592$	4.95158	0.203509
$593$	−6.41866	−0.263583	−0.131791	−	0.991277i	$-0.542073\pi$
$593$	−6.41866	−0.263583	−0.131791	+	0.991277i	$0.542073\pi$
$594$	150.091	6.15832
$595$	−8.21115	−0.336624
$596$	−7.26002	−0.297382
$597$	16.4119	0.671694
$598$	11.3593	0.464517
$599$	14.9263	0.609871	0.304936	−	0.952373i	$-0.401365\pi$
$599$	14.9263	0.609871	0.304936	+	0.952373i	$0.401365\pi$
$600$	22.2406	0.907970
$601$	−17.6623	−0.720460	−0.360230	−	0.932864i	$-0.617302\pi$
$601$	−17.6623	−0.720460	−0.360230	+	0.932864i	$0.617302\pi$
$602$	−20.9964	−0.855750
$603$	−114.671	−4.66977
$604$	−24.9691	−1.01598
$605$	3.43058	0.139473
$606$	−25.8392	−1.04965
$607$	−21.7644	−0.883390	−0.441695	−	0.897165i	$-0.645623\pi$
$607$	−21.7644	−0.883390	−0.441695	+	0.897165i	$0.645623\pi$
$608$	16.0348	0.650298
$609$	20.2858	0.822023
$610$	10.6606	0.431635
$611$	9.39931	0.380255
$612$	44.7724	1.80982
$613$	25.3984	1.02583	0.512916	−	0.858439i	$-0.328565\pi$
$613$	25.3984	1.02583	0.512916	+	0.858439i	$0.328565\pi$
$614$	23.6719	0.955321
$615$	7.12500	0.287308
$616$	−17.8081	−0.717510
$617$	−17.5000	−0.704522	−0.352261	−	0.935902i	$-0.614587\pi$
$617$	−17.5000	−0.704522	−0.352261	+	0.935902i	$0.614587\pi$
$618$	−105.089	−4.22732
$619$	10.5974	0.425944	0.212972	−	0.977058i	$-0.431686\pi$
$619$	10.5974	0.425944	0.212972	+	0.977058i	$0.431686\pi$
$620$	−0.201373	−0.00808735
$621$	107.625	4.31884
$622$	4.60884	0.184798
$623$	−42.9932	−1.72249
$624$	20.8322	0.833956
$625$	19.0503	0.762011
$626$	−5.35892	−0.214186
$627$	−36.8889	−1.47320
$628$	25.4358	1.01500
$629$	−4.08941	−0.163055
$630$	32.3333	1.28819
$631$	44.0126	1.75211	0.876057	−	0.482207i	$-0.160165\pi$
$631$	44.0126	1.75211	0.876057	+	0.482207i	$0.160165\pi$
$632$	13.1329	0.522397
$633$	−26.3502	−1.04732
$634$	−33.0190	−1.31135
$635$	−9.35007	−0.371046
$636$	−7.19962	−0.285484
$637$	3.51144	0.139128
$638$	−13.5366	−0.535918
$639$	8.95173	0.354125
$640$	−6.60592	−0.261122
$641$	20.4319	0.807010	0.403505	−	0.914977i	$-0.367792\pi$
$641$	20.4319	0.807010	0.403505	+	0.914977i	$0.367792\pi$
$642$	−61.9057	−2.44322
$643$	44.2650	1.74564	0.872821	−	0.488040i	$-0.162288\pi$
$643$	44.2650	1.74564	0.872821	+	0.488040i	$0.162288\pi$
$644$	19.9745	0.787105
$645$	8.22171	0.323730
$646$	−19.3336	−0.760669
$647$	44.3296	1.74278	0.871388	−	0.490595i	$-0.163221\pi$
$647$	44.3296	1.74278	0.871388	+	0.490595i	$0.163221\pi$
$648$	62.4330	2.45260
$649$	0.963655	0.0378268
$650$	10.0192	0.392985
$651$	−2.81263	−0.110236
$652$	10.2398	0.401022
$653$	29.5455	1.15620	0.578102	−	0.815964i	$-0.303794\pi$
$653$	29.5455	1.15620	0.578102	+	0.815964i	$0.303794\pi$
$654$	−6.20936	−0.242805
$655$	6.46649	0.252666
$656$	15.9671	0.623409
$657$	−20.0914	−0.783839
$658$	43.6222	1.70057
$659$	−12.3747	−0.482049	−0.241024	−	0.970519i	$-0.577483\pi$
$659$	−12.3747	−0.482049	−0.241024	+	0.970519i	$0.577483\pi$
$660$	−10.9077	−0.424583
$661$	−5.78116	−0.224861	−0.112431	−	0.993660i	$-0.535864\pi$
$661$	−5.78116	−0.224861	−0.112431	+	0.993660i	$0.535864\pi$
$662$	−43.7437	−1.70015
$663$	−17.2049	−0.668182
$664$	12.6750	0.491887
$665$	−5.29011	−0.205142
$666$	16.1030	0.623979
$667$	−9.70658	−0.375840
$668$	−5.85303	−0.226461
$669$	85.8152	3.31781
$670$	14.6418	0.565663
$671$	−37.6462	−1.45332
$672$	66.2239	2.55464
$673$	−37.4386	−1.44315	−0.721575	−	0.692336i	$-0.756582\pi$
$673$	−37.4386	−1.44315	−0.721575	+	0.692336i	$0.756582\pi$
$674$	−48.7439	−1.87755
$675$	94.9280	3.65378
$676$	−14.0570	−0.540652
$677$	−37.8014	−1.45283	−0.726413	−	0.687258i	$-0.758814\pi$
$677$	−37.8014	−1.45283	−0.726413	+	0.687258i	$0.758814\pi$
$678$	64.8880	2.49201
$679$	17.7200	0.680030
$680$	3.65470	0.140151
$681$	15.9566	0.611459
$682$	1.87685	0.0718683
$683$	34.7982	1.33152	0.665758	−	0.746167i	$-0.268108\pi$
$683$	34.7982	1.33152	0.665758	+	0.746167i	$0.268108\pi$
$684$	28.8450	1.10292
$685$	11.0925	0.423822
$686$	−23.2023	−0.885868
$687$	4.37253	0.166823
$688$	18.4248	0.702439
$689$	2.07346	0.0789925
$690$	−20.6433	−0.785878
$691$	29.5475	1.12404	0.562021	−	0.827123i	$-0.310024\pi$
$691$	29.5475	1.12404	0.562021	+	0.827123i	$0.310024\pi$
$692$	−6.57353	−0.249888
$693$	−114.180	−4.33735
$694$	20.5545	0.780239
$695$	1.61907	0.0614148
$696$	−9.02901	−0.342244
$697$	−13.1869	−0.499488
$698$	10.5066	0.397682
$699$	−28.2031	−1.06674
$700$	17.6180	0.665898
$701$	−7.77757	−0.293755	−0.146877	−	0.989155i	$-0.546922\pi$
$701$	−7.77757	−0.293755	−0.146877	+	0.989155i	$0.546922\pi$
$702$	45.0996	1.70217
$703$	−2.63464	−0.0993673
$704$	−4.11955	−0.155262
$705$	−17.0814	−0.643323
$706$	39.9642	1.50407
$707$	13.0855	0.492130
$708$	−1.00543	−0.0377865
$709$	−38.1007	−1.43090	−0.715451	−	0.698663i	$-0.753779\pi$
$709$	−38.1007	−1.43090	−0.715451	+	0.698663i	$0.753779\pi$
$710$	−1.14301	−0.0428962
$711$	84.2039	3.15789
$712$	19.1358	0.717146
$713$	1.34582	0.0504014
$714$	−79.8478	−2.98823
$715$	3.14138	0.117481
$716$	−7.48466	−0.279715
$717$	34.5210	1.28921
$718$	−15.1815	−0.566569
$719$	7.52410	0.280602	0.140301	−	0.990109i	$-0.455193\pi$
$719$	7.52410	0.280602	0.140301	+	0.990109i	$0.455193\pi$
$720$	−28.3732	−1.05741
$721$	53.2192	1.98199
$722$	21.6386	0.805307
$723$	−2.41804	−0.0899279
$724$	19.6063	0.728661
$725$	−8.56145	−0.317964
$726$	33.3600	1.23811
$727$	−13.5189	−0.501387	−0.250693	−	0.968067i	$-0.580659\pi$
$727$	−13.5189	−0.501387	−0.250693	+	0.968067i	$0.580659\pi$
$728$	−5.35101	−0.198321
$729$	185.713	6.87828
$730$	2.56538	0.0949488
$731$	−15.2167	−0.562808
$732$	39.2783	1.45177
$733$	−49.5274	−1.82933	−0.914667	−	0.404208i	$-0.867547\pi$
$733$	−49.5274	−1.82933	−0.914667	+	0.404208i	$0.867547\pi$
$734$	32.5377	1.20099
$735$	−6.38136	−0.235380
$736$	−31.6875	−1.16802
$737$	−51.7054	−1.90459
$738$	51.9264	1.91144
$739$	−2.41508	−0.0888402	−0.0444201	−	0.999013i	$-0.514144\pi$
$739$	−2.41508	−0.0888402	−0.0444201	+	0.999013i	$0.514144\pi$
$740$	−0.779042	−0.0286381
$741$	−11.0844	−0.407196
$742$	9.62292	0.353269
$743$	−31.0505	−1.13913	−0.569565	−	0.821946i	$-0.692888\pi$
$743$	−31.0505	−1.13913	−0.569565	+	0.821946i	$0.692888\pi$
$744$	1.25188	0.0458960
$745$	−3.79972	−0.139211
$746$	2.36515	0.0865943
$747$	81.2685	2.97346
$748$	20.1879	0.738144
$749$	31.3502	1.14551
$750$	−38.0325	−1.38875
$751$	13.4610	0.491198	0.245599	−	0.969371i	$-0.421015\pi$
$751$	13.4610	0.491198	0.245599	+	0.969371i	$0.421015\pi$
$752$	−38.2794	−1.39590
$753$	108.045	3.93737
$754$	−4.06749	−0.148129
$755$	−13.0683	−0.475602
$756$	79.3042	2.88427
$757$	49.0633	1.78324	0.891618	−	0.452787i	$-0.149570\pi$
$757$	49.0633	1.78324	0.891618	+	0.452787i	$0.149570\pi$
$758$	10.2367	0.371812
$759$	72.8988	2.64606
$760$	2.35458	0.0854094
$761$	−28.6130	−1.03722	−0.518610	−	0.855011i	$-0.673550\pi$
$761$	−28.6130	−1.03722	−0.518610	+	0.855011i	$0.673550\pi$
$762$	−90.9230	−3.29379
$763$	3.14453	0.113840
$764$	13.8189	0.499952
$765$	23.4328	0.847215
$766$	−0.849302	−0.0306865
$767$	0.289560	0.0104554
$768$	−71.2840	−2.57224
$769$	−39.8840	−1.43825	−0.719127	−	0.694878i	$-0.755458\pi$
$769$	−39.8840	−1.43825	−0.719127	+	0.694878i	$0.755458\pi$
$770$	14.5791	0.525396
$771$	35.7730	1.28833
$772$	25.1586	0.905477
$773$	25.1545	0.904744	0.452372	−	0.891829i	$-0.350578\pi$
$773$	25.1545	0.904744	0.452372	+	0.891829i	$0.350578\pi$
$774$	59.9192	2.15375
$775$	1.18705	0.0426400
$776$	−7.88698	−0.283126
$777$	−10.8811	−0.390357
$778$	13.2273	0.474222
$779$	−8.49577	−0.304392
$780$	−3.27757	−0.117356
$781$	4.03635	0.144432
$782$	38.2065	1.36626
$783$	−38.5378	−1.37723
$784$	−14.3006	−0.510735
$785$	13.3125	0.475143
$786$	62.8822	2.24293
$787$	−11.4491	−0.408116	−0.204058	−	0.978959i	$-0.565413\pi$
$787$	−11.4491	−0.408116	−0.204058	+	0.978959i	$0.565413\pi$
$788$	1.29601	0.0461685
$789$	55.7112	1.98337
$790$	−10.7516	−0.382525
$791$	−32.8605	−1.16838
$792$	50.8205	1.80583
$793$	−11.3120	−0.401700
$794$	21.9305	0.778283
$795$	−3.76811	−0.133641
$796$	−5.78650	−0.205097
$797$	18.9437	0.671019	0.335509	−	0.942037i	$-0.391092\pi$
$797$	18.9437	0.671019	0.335509	+	0.942037i	$0.391092\pi$
$798$	−51.4427	−1.82105
$799$	31.6141	1.11843
$800$	−27.9492	−0.988155
$801$	122.693	4.33515
$802$	33.2258	1.17325
$803$	−9.05923	−0.319693
$804$	53.9469	1.90256
$805$	10.4542	0.368461
$806$	0.563958	0.0198646
$807$	12.5962	0.443408
$808$	−5.82421	−0.204895
$809$	−27.7381	−0.975220	−0.487610	−	0.873062i	$-0.662131\pi$
$809$	−27.7381	−0.975220	−0.487610	+	0.873062i	$0.662131\pi$
$810$	−51.1126	−1.79591
$811$	−28.0963	−0.986595	−0.493297	−	0.869861i	$-0.664209\pi$
$811$	−28.0963	−0.986595	−0.493297	+	0.869861i	$0.664209\pi$
$812$	−7.15236	−0.250999
$813$	−75.9737	−2.66451
$814$	7.26087	0.254493
$815$	5.35927	0.187727
$816$	70.0681	2.45288
$817$	−9.80348	−0.342980
$818$	−17.8942	−0.625655
$819$	−34.3090	−1.19885
$820$	−2.51213	−0.0877273
$821$	−15.6437	−0.545968	−0.272984	−	0.962019i	$-0.588011\pi$
$821$	−15.6437	−0.545968	−0.272984	+	0.962019i	$0.588011\pi$
$822$	107.867	3.76229
$823$	1.17763	0.0410496	0.0205248	−	0.999789i	$-0.493466\pi$
$823$	1.17763	0.0410496	0.0205248	+	0.999789i	$0.493466\pi$
$824$	−23.6874	−0.825188
$825$	64.2986	2.23859
$826$	1.34385	0.0467585
$827$	47.8161	1.66273	0.831365	−	0.555727i	$-0.187560\pi$
$827$	47.8161	1.66273	0.831365	+	0.555727i	$0.187560\pi$
$828$	−57.0027	−1.98098
$829$	−14.5616	−0.505747	−0.252873	−	0.967499i	$-0.581376\pi$
$829$	−14.5616	−0.505747	−0.252873	+	0.967499i	$0.581376\pi$
$830$	−10.3768	−0.360184
$831$	−102.220	−3.54598
$832$	−1.23785	−0.0429147
$833$	11.8105	0.409211
$834$	15.7444	0.545182
$835$	−3.06334	−0.106011
$836$	13.0063	0.449831
$837$	5.34328	0.184691
$838$	57.4198	1.98353
$839$	12.1008	0.417768	0.208884	−	0.977940i	$-0.433017\pi$
$839$	12.1008	0.417768	0.208884	+	0.977940i	$0.433017\pi$
$840$	9.72441	0.335524
$841$	−25.5243	−0.880149
$842$	38.0970	1.31291
$843$	−17.8131	−0.613515
$844$	9.29053	0.319793
$845$	−7.35708	−0.253091
$846$	−124.488	−4.27999
$847$	−16.8941	−0.580489
$848$	−8.44432	−0.289979
$849$	−37.1665	−1.27555
$850$	33.6991	1.15587
$851$	5.20650	0.178477
$852$	−4.21134	−0.144278
$853$	−24.1041	−0.825307	−0.412654	−	0.910888i	$-0.635398\pi$
$853$	−24.1041	−0.825307	−0.412654	+	0.910888i	$0.635398\pi$
$854$	−52.4989	−1.79647
$855$	15.0968	0.516300
$856$	−13.9537	−0.476926
$857$	−21.2418	−0.725605	−0.362803	−	0.931866i	$-0.618180\pi$
$857$	−21.2418	−0.725605	−0.362803	+	0.931866i	$0.618180\pi$
$858$	30.5478	1.04288
$859$	−51.5073	−1.75741	−0.878703	−	0.477370i	$-0.841590\pi$
$859$	−51.5073	−1.75741	−0.878703	+	0.477370i	$0.841590\pi$
$860$	−2.89881	−0.0988485
$861$	−35.0876	−1.19578
$862$	−8.54630	−0.291088
$863$	−56.3974	−1.91979	−0.959896	−	0.280358i	$-0.909547\pi$
$863$	−56.3974	−1.91979	−0.959896	+	0.280358i	$0.909547\pi$
$864$	−125.808	−4.28009
$865$	−3.44043	−0.116978
$866$	−17.2587	−0.586474
$867$	0.957631	0.0325228
$868$	0.991678	0.0336597
$869$	37.9676	1.28796
$870$	7.39187	0.250608
$871$	−15.5365	−0.526434
$872$	−1.39960	−0.0473964
$873$	−50.5689	−1.71150
$874$	24.6149	0.832611
$875$	19.2604	0.651119
$876$	9.45197	0.319353
$877$	−58.5883	−1.97839	−0.989193	−	0.146618i	$-0.953161\pi$
$877$	−58.5883	−1.97839	−0.989193	+	0.146618i	$0.953161\pi$
$878$	35.8403	1.20955
$879$	79.5072	2.68171
$880$	−12.7935	−0.431269
$881$	−18.7277	−0.630951	−0.315475	−	0.948934i	$-0.602164\pi$
$881$	−18.7277	−0.630951	−0.315475	+	0.948934i	$0.602164\pi$
$882$	−46.5068	−1.56597
$883$	41.8871	1.40961	0.704806	−	0.709400i	$-0.251034\pi$
$883$	41.8871	1.40961	0.704806	+	0.709400i	$0.251034\pi$
$884$	6.06609	0.204025
$885$	−0.526220	−0.0176887
$886$	35.2223	1.18332
$887$	47.4909	1.59459	0.797294	−	0.603591i	$-0.206264\pi$
$887$	47.4909	1.59459	0.797294	+	0.603591i	$0.206264\pi$
$888$	4.84306	0.162523
$889$	46.0451	1.54430
$890$	−15.6661	−0.525130
$891$	180.496	6.04685
$892$	−30.2567	−1.01307
$893$	20.3677	0.681579
$894$	−36.9497	−1.23578
$895$	−3.91730	−0.130941
$896$	32.5313	1.08680
$897$	21.9047	0.731377
$898$	−49.5851	−1.65468
$899$	−0.481905	−0.0160724
$900$	−50.2779	−1.67593
$901$	6.97398	0.232337
$902$	23.4137	0.779590
$903$	−40.4884	−1.34737
$904$	14.6259	0.486449
$905$	10.2615	0.341102
$906$	−127.080	−4.22194
$907$	15.9132	0.528390	0.264195	−	0.964469i	$-0.414894\pi$
$907$	15.9132	0.528390	0.264195	+	0.964469i	$0.414894\pi$
$908$	−5.62598	−0.186705
$909$	−37.3430	−1.23859
$910$	4.38076	0.145221
$911$	−34.0106	−1.12682	−0.563410	−	0.826177i	$-0.690511\pi$
$911$	−34.0106	−1.12682	−0.563410	+	0.826177i	$0.690511\pi$
$912$	45.1421	1.49480
$913$	36.6441	1.21274
$914$	43.7775	1.44803
$915$	20.5573	0.679605
$916$	−1.54167	−0.0509381
$917$	−31.8447	−1.05160
$918$	151.690	5.00653
$919$	30.1639	0.995016	0.497508	−	0.867459i	$-0.334248\pi$
$919$	30.1639	0.995016	0.497508	+	0.867459i	$0.334248\pi$
$920$	−4.65305	−0.153406
$921$	45.6477	1.50414
$922$	29.4714	0.970588
$923$	1.21285	0.0399213
$924$	53.7160	1.76713
$925$	4.59227	0.150993
$926$	−0.667805	−0.0219454
$927$	−151.876	−4.98826
$928$	11.3465	0.372468
$929$	42.8317	1.40526	0.702631	−	0.711555i	$-0.252009\pi$
$929$	42.8317	1.40526	0.702631	+	0.711555i	$0.252009\pi$
$930$	−1.02488	−0.0336073
$931$	7.60906	0.249377
$932$	9.94384	0.325721
$933$	8.88746	0.290962
$934$	−10.3689	−0.339279
$935$	10.5659	0.345541
$936$	15.2706	0.499135
$937$	35.1057	1.14685	0.573427	−	0.819256i	$-0.305614\pi$
$937$	35.1057	1.14685	0.573427	+	0.819256i	$0.305614\pi$
$938$	−72.1048	−2.35430
$939$	−10.3339	−0.337233
$940$	6.02256	0.196434
$941$	−30.9999	−1.01057	−0.505285	−	0.862953i	$-0.668613\pi$
$941$	−30.9999	−1.01057	−0.505285	+	0.862953i	$0.668613\pi$
$942$	129.455	4.21786
$943$	16.7891	0.546728
$944$	−1.17926	−0.0383815
$945$	41.5059	1.35019
$946$	27.0176	0.878419
$947$	16.8063	0.546131	0.273065	−	0.961995i	$-0.411962\pi$
$947$	16.8063	0.546131	0.273065	+	0.961995i	$0.411962\pi$
$948$	−39.6137	−1.28659
$949$	−2.72213	−0.0883640
$950$	21.7110	0.704397
$951$	−63.6721	−2.06471
$952$	−17.9978	−0.583313
$953$	−47.6716	−1.54423	−0.772117	−	0.635481i	$-0.780802\pi$
$953$	−47.6716	−1.54423	−0.772117	+	0.635481i	$0.780802\pi$
$954$	−27.4617	−0.889105
$955$	7.23251	0.234038
$956$	−12.1714	−0.393651
$957$	−26.1032	−0.843798
$958$	−69.4033	−2.24232
$959$	−54.6257	−1.76396
$960$	2.24955	0.0726039
$961$	−30.9332	−0.997845
$962$	2.18175	0.0703426
$963$	−89.4666	−2.88302
$964$	0.852552	0.0274588
$965$	13.1674	0.423874
$966$	101.660	3.27085
$967$	−4.55347	−0.146430	−0.0732149	−	0.997316i	$-0.523326\pi$
$967$	−4.55347	−0.146430	−0.0732149	+	0.997316i	$0.523326\pi$
$968$	7.51941	0.241683
$969$	−37.2819	−1.19767
$970$	6.45691	0.207319
$971$	48.8389	1.56732	0.783658	−	0.621193i	$-0.213352\pi$
$971$	48.8389	1.56732	0.783658	+	0.621193i	$0.213352\pi$
$972$	−112.662	−3.61364
$973$	−7.97323	−0.255610
$974$	27.6679	0.886538
$975$	19.3205	0.618752
$976$	46.0689	1.47463
$977$	17.1969	0.550179	0.275090	−	0.961419i	$-0.411292\pi$
$977$	17.1969	0.550179	0.275090	+	0.961419i	$0.411292\pi$
$978$	52.1153	1.66646
$979$	55.3225	1.76811
$980$	2.24994	0.0718716
$981$	−8.97380	−0.286511
$982$	32.4542	1.03566
$983$	45.9245	1.46476	0.732382	−	0.680894i	$-0.238409\pi$
$983$	45.9245	1.46476	0.732382	+	0.680894i	$0.238409\pi$
$984$	15.6171	0.497856
$985$	0.678301	0.0216125
$986$	−13.6808	−0.435685
$987$	84.1187	2.67753
$988$	3.90814	0.124334
$989$	19.3734	0.616037
$990$	−41.6057	−1.32231
$991$	38.3542	1.21836	0.609180	−	0.793032i	$-0.291499\pi$
$991$	38.3542	1.21836	0.609180	+	0.793032i	$0.291499\pi$
$992$	−1.57320	−0.0499491
$993$	−84.3531	−2.67686
$994$	5.62882	0.178535
$995$	−3.02852	−0.0960104
$996$	−38.2327	−1.21145
$997$	53.5169	1.69490	0.847449	−	0.530878i	$-0.178138\pi$
$997$	53.5169	1.69490	0.847449	+	0.530878i	$0.178138\pi$
$998$	14.3193	0.453269
$999$	20.6713	0.654010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.19	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.19	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79445 q^{2} -3.46032 q^{3} +1.22004 q^{4} +0.638539 q^{5} +6.20936 q^{6} -3.14453 q^{7} +1.39960 q^{8} +8.97380 q^{9} +O(q^{10})\)	\(q-1.79445 q^{2} -3.46032 q^{3} +1.22004 q^{4} +0.638539 q^{5} +6.20936 q^{6} -3.14453 q^{7} +1.39960 q^{8} +8.97380 q^{9} -1.14582 q^{10} +4.04630 q^{11} -4.22172 q^{12} +1.21584 q^{13} +5.64269 q^{14} -2.20955 q^{15} -4.95158 q^{16} +4.08941 q^{17} -16.1030 q^{18} +2.63464 q^{19} +0.779042 q^{20} +10.8811 q^{21} -7.26087 q^{22} -5.20650 q^{23} -4.84306 q^{24} -4.59227 q^{25} -2.18175 q^{26} -20.6713 q^{27} -3.83645 q^{28} +1.86432 q^{29} +3.96491 q^{30} -0.258488 q^{31} +6.08615 q^{32} -14.0015 q^{33} -7.33822 q^{34} -2.00791 q^{35} +10.9484 q^{36} -1.00000 q^{37} -4.72772 q^{38} -4.20718 q^{39} +0.893699 q^{40} -3.22464 q^{41} -19.5255 q^{42} -3.72099 q^{43} +4.93664 q^{44} +5.73012 q^{45} +9.34279 q^{46} +7.73073 q^{47} +17.1341 q^{48} +2.88808 q^{49} +8.24058 q^{50} -14.1507 q^{51} +1.48337 q^{52} +1.70538 q^{53} +37.0935 q^{54} +2.58372 q^{55} -4.40109 q^{56} -9.11669 q^{57} -3.34542 q^{58} +0.238157 q^{59} -2.69573 q^{60} -9.30387 q^{61} +0.463844 q^{62} -28.2184 q^{63} -1.01810 q^{64} +0.776359 q^{65} +25.1249 q^{66} -12.7784 q^{67} +4.98923 q^{68} +18.0162 q^{69} +3.60308 q^{70} +0.997540 q^{71} +12.5597 q^{72} -2.23889 q^{73} +1.79445 q^{74} +15.8907 q^{75} +3.21436 q^{76} -12.7237 q^{77} +7.54956 q^{78} +9.38330 q^{79} -3.16178 q^{80} +44.6077 q^{81} +5.78644 q^{82} +9.05619 q^{83} +13.2753 q^{84} +2.61125 q^{85} +6.67712 q^{86} -6.45114 q^{87} +5.66320 q^{88} +13.6724 q^{89} -10.2824 q^{90} -3.82324 q^{91} -6.35213 q^{92} +0.894452 q^{93} -13.8724 q^{94} +1.68232 q^{95} -21.0600 q^{96} -5.63517 q^{97} -5.18251 q^{98} +36.3107 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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