LMFDB - Embedded newform 6023.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76348 q^{2} -3.02907 q^{3} +5.63680 q^{4} +4.42510 q^{5} +8.37075 q^{6} -1.32943 q^{7} -10.0502 q^{8} +6.17524 q^{9} +O(q^{10})$	\(q-2.76348 q^{2} -3.02907 q^{3} +5.63680 q^{4} +4.42510 q^{5} +8.37075 q^{6} -1.32943 q^{7} -10.0502 q^{8} +6.17524 q^{9} -12.2287 q^{10} -5.11933 q^{11} -17.0742 q^{12} +4.12658 q^{13} +3.67385 q^{14} -13.4039 q^{15} +16.4999 q^{16} +3.00667 q^{17} -17.0651 q^{18} -1.00000 q^{19} +24.9434 q^{20} +4.02693 q^{21} +14.1471 q^{22} +8.54639 q^{23} +30.4428 q^{24} +14.5815 q^{25} -11.4037 q^{26} -9.61802 q^{27} -7.49374 q^{28} -8.75748 q^{29} +37.0414 q^{30} +4.21776 q^{31} -25.4967 q^{32} +15.5068 q^{33} -8.30887 q^{34} -5.88286 q^{35} +34.8086 q^{36} +6.40696 q^{37} +2.76348 q^{38} -12.4997 q^{39} -44.4732 q^{40} +0.393183 q^{41} -11.1283 q^{42} +0.902428 q^{43} -28.8567 q^{44} +27.3261 q^{45} -23.6177 q^{46} -2.22943 q^{47} -49.9794 q^{48} -5.23261 q^{49} -40.2956 q^{50} -9.10741 q^{51} +23.2607 q^{52} +9.35675 q^{53} +26.5792 q^{54} -22.6535 q^{55} +13.3611 q^{56} +3.02907 q^{57} +24.2011 q^{58} +5.46563 q^{59} -75.5552 q^{60} -0.305570 q^{61} -11.6557 q^{62} -8.20956 q^{63} +37.4598 q^{64} +18.2605 q^{65} -42.8527 q^{66} -0.386770 q^{67} +16.9480 q^{68} -25.8876 q^{69} +16.2572 q^{70} -9.38195 q^{71} -62.0625 q^{72} +6.76004 q^{73} -17.7055 q^{74} -44.1683 q^{75} -5.63680 q^{76} +6.80580 q^{77} +34.5426 q^{78} +11.9149 q^{79} +73.0138 q^{80} +10.6079 q^{81} -1.08655 q^{82} +2.10628 q^{83} +22.6990 q^{84} +13.3048 q^{85} -2.49384 q^{86} +26.5270 q^{87} +51.4504 q^{88} -8.39951 q^{89} -75.5149 q^{90} -5.48600 q^{91} +48.1743 q^{92} -12.7759 q^{93} +6.16099 q^{94} -4.42510 q^{95} +77.2313 q^{96} -7.86853 q^{97} +14.4602 q^{98} -31.6131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.76348	−1.95407	−0.977036	−	0.213072i	$-0.931653\pi$
$2$	−2.76348	−1.95407	−0.977036	+	0.213072i	$0.931653\pi$
$3$	−3.02907	−1.74883	−0.874416	−	0.485177i	$-0.838755\pi$
$3$	−3.02907	−1.74883	−0.874416	+	0.485177i	$0.838755\pi$
$4$	5.63680	2.81840
$5$	4.42510	1.97896	0.989482	−	0.144657i	$-0.0462078\pi$
$5$	4.42510	1.97896	0.989482	+	0.144657i	$0.0462078\pi$
$6$	8.37075	3.41735
$7$	−1.32943	−0.502478	−0.251239	−	0.967925i	$-0.580838\pi$
$7$	−1.32943	−0.502478	−0.251239	+	0.967925i	$0.580838\pi$
$8$	−10.0502	−3.55329
$9$	6.17524	2.05841
$10$	−12.2287	−3.86704
$11$	−5.11933	−1.54354	−0.771768	−	0.635904i	$-0.780627\pi$
$11$	−5.11933	−1.54354	−0.771768	+	0.635904i	$0.780627\pi$
$12$	−17.0742	−4.92891
$13$	4.12658	1.14451	0.572253	−	0.820077i	$-0.306069\pi$
$13$	4.12658	1.14451	0.572253	+	0.820077i	$0.306069\pi$
$14$	3.67385	0.981878
$15$	−13.4039	−3.46088
$16$	16.4999	4.12498
$17$	3.00667	0.729225	0.364613	−	0.931159i	$-0.381201\pi$
$17$	3.00667	0.729225	0.364613	+	0.931159i	$0.381201\pi$
$18$	−17.0651	−4.02229
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	24.9434	5.57751
$21$	4.02693	0.878749
$22$	14.1471	3.01618
$23$	8.54639	1.78205	0.891023	−	0.453958i	$-0.149989\pi$
$23$	8.54639	1.78205	0.891023	+	0.453958i	$0.149989\pi$
$24$	30.4428	6.21411
$25$	14.5815	2.91630
$26$	−11.4037	−2.23645
$27$	−9.61802	−1.85099
$28$	−7.49374	−1.41618
$29$	−8.75748	−1.62622	−0.813112	−	0.582108i	$-0.802228\pi$
$29$	−8.75748	−1.62622	−0.813112	+	0.582108i	$0.802228\pi$
$30$	37.0414	6.76280
$31$	4.21776	0.757532	0.378766	−	0.925493i	$-0.376349\pi$
$31$	4.21776	0.757532	0.378766	+	0.925493i	$0.376349\pi$
$32$	−25.4967	−4.50723
$33$	15.5068	2.69939
$34$	−8.30887	−1.42496
$35$	−5.88286	−0.994385
$36$	34.8086	5.80144
$37$	6.40696	1.05330	0.526649	−	0.850083i	$-0.323448\pi$
$37$	6.40696	1.05330	0.526649	+	0.850083i	$0.323448\pi$
$38$	2.76348	0.448295
$39$	−12.4997	−2.00155
$40$	−44.4732	−7.03183
$41$	0.393183	0.0614048	0.0307024	−	0.999529i	$-0.490226\pi$
$41$	0.393183	0.0614048	0.0307024	+	0.999529i	$0.490226\pi$
$42$	−11.1283	−1.71714
$43$	0.902428	0.137619	0.0688095	−	0.997630i	$-0.478080\pi$
$43$	0.902428	0.137619	0.0688095	+	0.997630i	$0.478080\pi$
$44$	−28.8567	−4.35030
$45$	27.3261	4.07353
$46$	−23.6177	−3.48225
$47$	−2.22943	−0.325196	−0.162598	−	0.986692i	$-0.551987\pi$
$47$	−2.22943	−0.325196	−0.162598	+	0.986692i	$0.551987\pi$
$48$	−49.9794	−7.21390
$49$	−5.23261	−0.747516
$50$	−40.2956	−5.69866
$51$	−9.10741	−1.27529
$52$	23.2607	3.22568
$53$	9.35675	1.28525	0.642624	−	0.766181i	$-0.277846\pi$
$53$	9.35675	1.28525	0.642624	+	0.766181i	$0.277846\pi$
$54$	26.5792	3.61697
$55$	−22.6535	−3.05460
$56$	13.3611	1.78545
$57$	3.02907	0.401210
$58$	24.2011	3.17776
$59$	5.46563	0.711564	0.355782	−	0.934569i	$-0.384215\pi$
$59$	5.46563	0.711564	0.355782	+	0.934569i	$0.384215\pi$
$60$	−75.5552	−9.75414
$61$	−0.305570	−0.0391242	−0.0195621	−	0.999809i	$-0.506227\pi$
$61$	−0.305570	−0.0391242	−0.0195621	+	0.999809i	$0.506227\pi$
$62$	−11.6557	−1.48027
$63$	−8.20956	−1.03431
$64$	37.4598	4.68247
$65$	18.2605	2.26494
$66$	−42.8527	−5.27480
$67$	−0.386770	−0.0472515	−0.0236257	−	0.999721i	$-0.507521\pi$
$67$	−0.386770	−0.0472515	−0.0236257	+	0.999721i	$0.507521\pi$
$68$	16.9480	2.05525
$69$	−25.8876	−3.11650
$70$	16.2572	1.94310
$71$	−9.38195	−1.11343	−0.556717	−	0.830703i	$-0.687939\pi$
$71$	−9.38195	−1.11343	−0.556717	+	0.830703i	$0.687939\pi$
$72$	−62.0625	−7.31414
$73$	6.76004	0.791203	0.395601	−	0.918422i	$-0.370536\pi$
$73$	6.76004	0.791203	0.395601	+	0.918422i	$0.370536\pi$
$74$	−17.7055	−2.05822
$75$	−44.1683	−5.10012
$76$	−5.63680	−0.646586
$77$	6.80580	0.775592
$78$	34.5426	3.91118
$79$	11.9149	1.34053	0.670264	−	0.742123i	$-0.266181\pi$
$79$	11.9149	1.34053	0.670264	+	0.742123i	$0.266181\pi$
$80$	73.0138	8.16319
$81$	10.6079	1.17866
$82$	−1.08655	−0.119989
$83$	2.10628	0.231195	0.115597	−	0.993296i	$-0.463122\pi$
$83$	2.10628	0.231195	0.115597	+	0.993296i	$0.463122\pi$
$84$	22.6990	2.47667
$85$	13.3048	1.44311
$86$	−2.49384	−0.268917
$87$	26.5270	2.84399
$88$	51.4504	5.48463
$89$	−8.39951	−0.890347	−0.445173	−	0.895444i	$-0.646858\pi$
$89$	−8.39951	−0.890347	−0.445173	+	0.895444i	$0.646858\pi$
$90$	−75.5149	−7.95997
$91$	−5.48600	−0.575089
$92$	48.1743	5.02252
$93$	−12.7759	−1.32480
$94$	6.16099	0.635458
$95$	−4.42510	−0.454005
$96$	77.2313	7.88239
$97$	−7.86853	−0.798928	−0.399464	−	0.916749i	$-0.630804\pi$
$97$	−7.86853	−0.798928	−0.399464	+	0.916749i	$0.630804\pi$
$98$	14.4602	1.46070
$99$	−31.6131	−3.17724
$100$	82.1930	8.21930
$101$	4.79916	0.477535	0.238767	−	0.971077i	$-0.423257\pi$
$101$	4.79916	0.477535	0.238767	+	0.971077i	$0.423257\pi$
$102$	25.1681	2.49201
$103$	12.8922	1.27031	0.635153	−	0.772386i	$-0.280937\pi$
$103$	12.8922	1.27031	0.635153	+	0.772386i	$0.280937\pi$
$104$	−41.4730	−4.06676
$105$	17.8196	1.73901
$106$	−25.8572	−2.51147
$107$	−5.28550	−0.510969	−0.255484	−	0.966813i	$-0.582235\pi$
$107$	−5.28550	−0.510969	−0.255484	+	0.966813i	$0.582235\pi$
$108$	−54.2149	−5.21683
$109$	−5.18008	−0.496162	−0.248081	−	0.968739i	$-0.579800\pi$
$109$	−5.18008	−0.496162	−0.248081	+	0.968739i	$0.579800\pi$
$110$	62.6025	5.96892
$111$	−19.4071	−1.84204
$112$	−21.9355	−2.07271
$113$	13.6156	1.28085	0.640425	−	0.768021i	$-0.278758\pi$
$113$	13.6156	1.28085	0.640425	+	0.768021i	$0.278758\pi$
$114$	−8.37075	−0.783993
$115$	37.8186	3.52660
$116$	−49.3642	−4.58335
$117$	25.4826	2.35587
$118$	−15.1041	−1.39045
$119$	−3.99716	−0.366419
$120$	134.712	12.2975
$121$	15.2075	1.38250
$122$	0.844435	0.0764516
$123$	−1.19098	−0.107387
$124$	23.7747	2.13503
$125$	42.3990	3.79228
$126$	22.6869	2.02111
$127$	−2.34241	−0.207855	−0.103928	−	0.994585i	$-0.533141\pi$
$127$	−2.34241	−0.207855	−0.103928	+	0.994585i	$0.533141\pi$
$128$	−52.5258	−4.64266
$129$	−2.73351	−0.240672
$130$	−50.4625	−4.42585
$131$	2.53971	0.221895	0.110948	−	0.993826i	$-0.464611\pi$
$131$	2.53971	0.221895	0.110948	+	0.993826i	$0.464611\pi$
$132$	87.4087	7.60795
$133$	1.32943	0.115276
$134$	1.06883	0.0923329
$135$	−42.5607	−3.66304
$136$	−30.2177	−2.59115
$137$	−10.3938	−0.888001	−0.444001	−	0.896026i	$-0.646441\pi$
$137$	−10.3938	−0.888001	−0.444001	+	0.896026i	$0.646441\pi$
$138$	71.5397	6.08987
$139$	−3.19029	−0.270597	−0.135298	−	0.990805i	$-0.543199\pi$
$139$	−3.19029	−0.270597	−0.135298	+	0.990805i	$0.543199\pi$
$140$	−33.1605	−2.80258
$141$	6.75311	0.568714
$142$	25.9268	2.17573
$143$	−21.1253	−1.76659
$144$	101.891	8.49093
$145$	−38.7527	−3.21824
$146$	−18.6812	−1.54607
$147$	15.8499	1.30728
$148$	36.1148	2.96862
$149$	7.33498	0.600905	0.300453	−	0.953797i	$-0.402862\pi$
$149$	7.33498	0.600905	0.300453	+	0.953797i	$0.402862\pi$
$150$	122.058	9.96600
$151$	6.33180	0.515274	0.257637	−	0.966242i	$-0.417056\pi$
$151$	6.33180	0.515274	0.257637	+	0.966242i	$0.417056\pi$
$152$	10.0502	0.815180
$153$	18.5669	1.50105
$154$	−18.8077	−1.51556
$155$	18.6640	1.49913
$156$	−70.4582	−5.64117
$157$	−18.6844	−1.49118	−0.745590	−	0.666405i	$-0.767832\pi$
$157$	−18.6844	−1.49118	−0.745590	+	0.666405i	$0.767832\pi$
$158$	−32.9265	−2.61949
$159$	−28.3422	−2.24768
$160$	−112.826	−8.91965
$161$	−11.3618	−0.895438
$162$	−29.3147	−2.30318
$163$	19.6481	1.53896	0.769478	−	0.638674i	$-0.220517\pi$
$163$	19.6481	1.53896	0.769478	+	0.638674i	$0.220517\pi$
$164$	2.21629	0.173063
$165$	68.6191	5.34199
$166$	−5.82066	−0.451771
$167$	6.73191	0.520931	0.260466	−	0.965483i	$-0.416124\pi$
$167$	6.73191	0.520931	0.260466	+	0.965483i	$0.416124\pi$
$168$	−40.4716	−3.12245
$169$	4.02865	0.309896
$170$	−36.7675	−2.81994
$171$	−6.17524	−0.472233
$172$	5.08681	0.387865
$173$	17.0841	1.29888	0.649439	−	0.760414i	$-0.275004\pi$
$173$	17.0841	1.29888	0.649439	+	0.760414i	$0.275004\pi$
$174$	−73.3067	−5.55737
$175$	−19.3851	−1.46537
$176$	−84.4686	−6.36706
$177$	−16.5558	−1.24441
$178$	23.2119	1.73980
$179$	0.679399	0.0507806	0.0253903	−	0.999678i	$-0.491917\pi$
$179$	0.679399	0.0507806	0.0253903	+	0.999678i	$0.491917\pi$
$180$	154.032	11.4808
$181$	−7.45479	−0.554110	−0.277055	−	0.960854i	$-0.589358\pi$
$181$	−7.45479	−0.554110	−0.277055	+	0.960854i	$0.589358\pi$
$182$	15.1604	1.12377
$183$	0.925592	0.0684217
$184$	−85.8931	−6.33212
$185$	28.3514	2.08444
$186$	35.3058	2.58875
$187$	−15.3921	−1.12559
$188$	−12.5669	−0.916534
$189$	12.7865	0.930081
$190$	12.2287	0.887160
$191$	17.3433	1.25492	0.627460	−	0.778649i	$-0.284094\pi$
$191$	17.3433	1.25492	0.627460	+	0.778649i	$0.284094\pi$
$192$	−113.468	−8.18886
$193$	18.2564	1.31412	0.657061	−	0.753837i	$-0.271799\pi$
$193$	18.2564	1.31412	0.657061	+	0.753837i	$0.271799\pi$
$194$	21.7445	1.56116
$195$	−55.3123	−3.96100
$196$	−29.4952	−2.10680
$197$	−26.2036	−1.86693	−0.933463	−	0.358673i	$-0.883229\pi$
$197$	−26.2036	−1.86693	−0.933463	+	0.358673i	$0.883229\pi$
$198$	87.3621	6.20855
$199$	8.34079	0.591263	0.295632	−	0.955302i	$-0.404470\pi$
$199$	8.34079	0.591263	0.295632	+	0.955302i	$0.404470\pi$
$200$	−146.547	−10.3624
$201$	1.17155	0.0826349
$202$	−13.2624	−0.933137
$203$	11.6425	0.817141
$204$	−51.3367	−3.59429
$205$	1.73987	0.121518
$206$	−35.6273	−2.48227
$207$	52.7760	3.66819
$208$	68.0883	4.72107
$209$	5.11933	0.354111
$210$	−49.2440	−3.39816
$211$	−14.8073	−1.01938	−0.509689	−	0.860358i	$-0.670240\pi$
$211$	−14.8073	−1.01938	−0.509689	+	0.860358i	$0.670240\pi$
$212$	52.7422	3.62235
$213$	28.4186	1.94721
$214$	14.6064	0.998470
$215$	3.99333	0.272343
$216$	96.6632	6.57710
$217$	−5.60722	−0.380643
$218$	14.3150	0.969536
$219$	−20.4766	−1.38368
$220$	−127.693	−8.60909
$221$	12.4073	0.834603
$222$	53.6311	3.59948
$223$	0.793611	0.0531441	0.0265721	−	0.999647i	$-0.491541\pi$
$223$	0.793611	0.0531441	0.0265721	+	0.999647i	$0.491541\pi$
$224$	33.8962	2.26478
$225$	90.0442	6.00295
$226$	−37.6264	−2.50287
$227$	−19.5771	−1.29938	−0.649689	−	0.760200i	$-0.725101\pi$
$227$	−19.5771	−1.29938	−0.649689	+	0.760200i	$0.725101\pi$
$228$	17.0742	1.13077
$229$	−10.9363	−0.722692	−0.361346	−	0.932432i	$-0.617683\pi$
$229$	−10.9363	−0.722692	−0.361346	+	0.932432i	$0.617683\pi$
$230$	−104.511	−6.89124
$231$	−20.6152	−1.35638
$232$	88.0146	5.77844
$233$	−9.96323	−0.652713	−0.326356	−	0.945247i	$-0.605821\pi$
$233$	−9.96323	−0.652713	−0.326356	+	0.945247i	$0.605821\pi$
$234$	−70.4206	−4.60354
$235$	−9.86547	−0.643552
$236$	30.8087	2.00547
$237$	−36.0910	−2.34436
$238$	11.0461	0.716010
$239$	−16.6634	−1.07787	−0.538934	−	0.842348i	$-0.681173\pi$
$239$	−16.6634	−1.07787	−0.538934	+	0.842348i	$0.681173\pi$
$240$	−221.164	−14.2761
$241$	−6.21521	−0.400357	−0.200179	−	0.979759i	$-0.564152\pi$
$241$	−6.21521	−0.400357	−0.200179	+	0.979759i	$0.564152\pi$
$242$	−42.0257	−2.70151
$243$	−3.27796	−0.210281
$244$	−1.72244	−0.110268
$245$	−23.1548	−1.47931
$246$	3.29123	0.209841
$247$	−4.12658	−0.262568
$248$	−42.3894	−2.69173
$249$	−6.38007	−0.404320
$250$	−117.169	−7.41040
$251$	−19.5227	−1.23227	−0.616133	−	0.787643i	$-0.711301\pi$
$251$	−19.5227	−1.23227	−0.616133	+	0.787643i	$0.711301\pi$
$252$	−46.2757	−2.91509
$253$	−43.7518	−2.75065
$254$	6.47319	0.406164
$255$	−40.3012	−2.52376
$256$	70.2341	4.38963
$257$	−3.39934	−0.212045	−0.106022	−	0.994364i	$-0.533812\pi$
$257$	−3.39934	−0.212045	−0.106022	+	0.994364i	$0.533812\pi$
$258$	7.55400	0.470292
$259$	−8.51761	−0.529259
$260$	102.931	6.38350
$261$	−54.0796	−3.34744
$262$	−7.01842	−0.433599
$263$	−20.2525	−1.24882	−0.624411	−	0.781096i	$-0.714661\pi$
$263$	−20.2525	−1.24882	−0.624411	+	0.781096i	$0.714661\pi$
$264$	−155.847	−9.59170
$265$	41.4045	2.54346
$266$	−3.67385	−0.225258
$267$	25.4427	1.55707
$268$	−2.18015	−0.133174
$269$	14.6147	0.891074	0.445537	−	0.895263i	$-0.353013\pi$
$269$	14.6147	0.891074	0.445537	+	0.895263i	$0.353013\pi$
$270$	117.615	7.15785
$271$	19.5447	1.18726	0.593628	−	0.804740i	$-0.297695\pi$
$271$	19.5447	1.18726	0.593628	+	0.804740i	$0.297695\pi$
$272$	49.6099	3.00804
$273$	16.6175	1.00573
$274$	28.7230	1.73522
$275$	−74.6475	−4.50141
$276$	−145.923	−8.78354
$277$	9.98443	0.599907	0.299953	−	0.953954i	$-0.403029\pi$
$277$	9.98443	0.599907	0.299953	+	0.953954i	$0.403029\pi$
$278$	8.81629	0.528766
$279$	26.0457	1.55931
$280$	59.1240	3.53334
$281$	19.0528	1.13660	0.568299	−	0.822822i	$-0.307602\pi$
$281$	19.0528	1.13660	0.568299	+	0.822822i	$0.307602\pi$
$282$	−18.6620	−1.11131
$283$	−7.37655	−0.438490	−0.219245	−	0.975670i	$-0.570359\pi$
$283$	−7.37655	−0.438490	−0.219245	+	0.975670i	$0.570359\pi$
$284$	−52.8842	−3.13810
$285$	13.4039	0.793979
$286$	58.3793	3.45204
$287$	−0.522709	−0.0308545
$288$	−157.449	−9.27775
$289$	−7.95992	−0.468231
$290$	107.092	6.28867
$291$	23.8343	1.39719
$292$	38.1050	2.22993
$293$	−4.90699	−0.286669	−0.143335	−	0.989674i	$-0.545782\pi$
$293$	−4.90699	−0.286669	−0.143335	+	0.989674i	$0.545782\pi$
$294$	−43.8009	−2.55452
$295$	24.1859	1.40816
$296$	−64.3914	−3.74267
$297$	49.2378	2.85707
$298$	−20.2700	−1.17421
$299$	35.2673	2.03956
$300$	−248.968	−14.3742
$301$	−1.19972	−0.0691505
$302$	−17.4978	−1.00688
$303$	−14.5370	−0.835128
$304$	−16.4999	−0.946336
$305$	−1.35218	−0.0774254
$306$	−51.3093	−2.93316
$307$	11.6948	0.667459	0.333730	−	0.942669i	$-0.391693\pi$
$307$	11.6948	0.667459	0.333730	+	0.942669i	$0.391693\pi$
$308$	38.3629	2.18593
$309$	−39.0513	−2.22155
$310$	−51.5775	−2.92940
$311$	6.49310	0.368190	0.184095	−	0.982908i	$-0.441065\pi$
$311$	6.49310	0.368190	0.184095	+	0.982908i	$0.441065\pi$
$312$	125.624	7.11209
$313$	8.11202	0.458519	0.229259	−	0.973365i	$-0.426370\pi$
$313$	8.11202	0.458519	0.229259	+	0.973365i	$0.426370\pi$
$314$	51.6340	2.91387
$315$	−36.3281	−2.04686
$316$	67.1618	3.77815
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	78.3231	4.39214
$319$	44.8324	2.51013
$320$	165.763	9.26645
$321$	16.0101	0.893598
$322$	31.3982	1.74975
$323$	−3.00667	−0.167296
$324$	59.7946	3.32192
$325$	60.1717	3.33772
$326$	−54.2970	−3.00723
$327$	15.6908	0.867704
$328$	−3.95157	−0.218189
$329$	2.96388	0.163404
$330$	−189.627	−10.4386
$331$	27.2124	1.49573	0.747865	−	0.663851i	$-0.231079\pi$
$331$	27.2124	1.49573	0.747865	+	0.663851i	$0.231079\pi$
$332$	11.8727	0.651599
$333$	39.5646	2.16812
$334$	−18.6035	−1.01794
$335$	−1.71150	−0.0935090
$336$	66.4442	3.62483
$337$	−3.33084	−0.181443	−0.0907213	−	0.995876i	$-0.528917\pi$
$337$	−3.33084	−0.181443	−0.0907213	+	0.995876i	$0.528917\pi$
$338$	−11.1331	−0.605559
$339$	−41.2426	−2.23999
$340$	74.9966	4.06726
$341$	−21.5921	−1.16928
$342$	17.0651	0.922777
$343$	16.2624	0.878088
$344$	−9.06960	−0.489000
$345$	−114.555	−6.16744
$346$	−47.2114	−2.53810
$347$	−19.0649	−1.02346	−0.511730	−	0.859146i	$-0.670995\pi$
$347$	−19.0649	−1.02346	−0.511730	+	0.859146i	$0.670995\pi$
$348$	149.527	8.01551
$349$	1.99724	0.106910	0.0534549	−	0.998570i	$-0.482977\pi$
$349$	1.99724	0.106910	0.0534549	+	0.998570i	$0.482977\pi$
$350$	53.5702	2.86345
$351$	−39.6895	−2.11847
$352$	130.526	6.95707
$353$	−1.25918	−0.0670192	−0.0335096	−	0.999438i	$-0.510668\pi$
$353$	−1.25918	−0.0670192	−0.0335096	+	0.999438i	$0.510668\pi$
$354$	45.7514	2.43166
$355$	−41.5161	−2.20344
$356$	−47.3464	−2.50935
$357$	12.1077	0.640806
$358$	−1.87750	−0.0992291
$359$	23.2094	1.22495	0.612473	−	0.790492i	$-0.290175\pi$
$359$	23.2094	1.22495	0.612473	+	0.790492i	$0.290175\pi$
$360$	−274.633	−14.4744
$361$	1.00000	0.0526316
$362$	20.6011	1.08277
$363$	−46.0646	−2.41777
$364$	−30.9235	−1.62083
$365$	29.9138	1.56576
$366$	−2.55785	−0.133701
$367$	24.8213	1.29566	0.647831	−	0.761784i	$-0.275676\pi$
$367$	24.8213	1.29566	0.647831	+	0.761784i	$0.275676\pi$
$368$	141.015	7.35091
$369$	2.42800	0.126397
$370$	−78.3485	−4.07315
$371$	−12.4392	−0.645809
$372$	−72.0150	−3.73381
$373$	−4.43608	−0.229692	−0.114846	−	0.993383i	$-0.536637\pi$
$373$	−4.43608	−0.229692	−0.114846	+	0.993383i	$0.536637\pi$
$374$	42.5358	2.19948
$375$	−128.429	−6.63207
$376$	22.4063	1.15552
$377$	−36.1384	−1.86122
$378$	−35.3352	−1.81745
$379$	4.20943	0.216224	0.108112	−	0.994139i	$-0.465519\pi$
$379$	4.20943	0.216224	0.108112	+	0.994139i	$0.465519\pi$
$380$	−24.9434	−1.27957
$381$	7.09531	0.363504
$382$	−47.9279	−2.45221
$383$	−25.2281	−1.28909	−0.644547	−	0.764565i	$-0.722954\pi$
$383$	−25.2281	−1.28909	−0.644547	+	0.764565i	$0.722954\pi$
$384$	159.104	8.11924
$385$	30.1163	1.53487
$386$	−50.4510	−2.56789
$387$	5.57271	0.283277
$388$	−44.3534	−2.25170
$389$	20.3504	1.03181	0.515903	−	0.856647i	$-0.327456\pi$
$389$	20.3504	1.03181	0.515903	+	0.856647i	$0.327456\pi$
$390$	152.854	7.74008
$391$	25.6962	1.29951
$392$	52.5889	2.65614
$393$	−7.69294	−0.388057
$394$	72.4129	3.64811
$395$	52.7245	2.65286
$396$	−178.197	−8.95473
$397$	−9.14590	−0.459020	−0.229510	−	0.973306i	$-0.573712\pi$
$397$	−9.14590	−0.459020	−0.229510	+	0.973306i	$0.573712\pi$
$398$	−23.0496	−1.15537
$399$	−4.02693	−0.201599
$400$	240.594	12.0297
$401$	16.3925	0.818601	0.409301	−	0.912400i	$-0.365773\pi$
$401$	16.3925	0.818601	0.409301	+	0.912400i	$0.365773\pi$
$402$	−3.23756	−0.161475
$403$	17.4049	0.867000
$404$	27.0519	1.34588
$405$	46.9410	2.33252
$406$	−32.1737	−1.59675
$407$	−32.7994	−1.62580
$408$	91.5314	4.53148
$409$	−9.26861	−0.458303	−0.229152	−	0.973391i	$-0.573595\pi$
$409$	−9.26861	−0.458303	−0.229152	+	0.973391i	$0.573595\pi$
$410$	−4.80809	−0.237455
$411$	31.4835	1.55297
$412$	72.6708	3.58023
$413$	−7.26618	−0.357545
$414$	−145.845	−7.16791
$415$	9.32050	0.457526
$416$	−105.214	−5.15856
$417$	9.66360	0.473228
$418$	−14.1471	−0.691960
$419$	−30.4540	−1.48777	−0.743887	−	0.668305i	$-0.767020\pi$
$419$	−30.4540	−1.48777	−0.743887	+	0.668305i	$0.767020\pi$
$420$	100.445	4.90124
$421$	−26.0446	−1.26934	−0.634669	−	0.772784i	$-0.718864\pi$
$421$	−26.0446	−1.26934	−0.634669	+	0.772784i	$0.718864\pi$
$422$	40.9197	1.99194
$423$	−13.7673	−0.669389
$424$	−94.0374	−4.56686
$425$	43.8417	2.12664
$426$	−78.5340	−3.80499
$427$	0.406234	0.0196591
$428$	−29.7933	−1.44011
$429$	63.9900	3.08947
$430$	−11.0355	−0.532178
$431$	−10.3250	−0.497339	−0.248669	−	0.968588i	$-0.579993\pi$
$431$	−10.3250	−0.497339	−0.248669	+	0.968588i	$0.579993\pi$
$432$	−158.697	−7.63530
$433$	−10.1315	−0.486888	−0.243444	−	0.969915i	$-0.578277\pi$
$433$	−10.1315	−0.486888	−0.243444	+	0.969915i	$0.578277\pi$
$434$	15.4954	0.743804
$435$	117.385	5.62816
$436$	−29.1991	−1.39838
$437$	−8.54639	−0.408829
$438$	56.5866	2.70381
$439$	−12.3846	−0.591085	−0.295542	−	0.955330i	$-0.595500\pi$
$439$	−12.3846	−0.591085	−0.295542	+	0.955330i	$0.595500\pi$
$440$	227.673	10.8539
$441$	−32.3127	−1.53870
$442$	−34.2872	−1.63088
$443$	1.19982	0.0570050	0.0285025	−	0.999594i	$-0.490926\pi$
$443$	1.19982	0.0570050	0.0285025	+	0.999594i	$0.490926\pi$
$444$	−109.394	−5.19161
$445$	−37.1687	−1.76196
$446$	−2.19313	−0.103848
$447$	−22.2181	−1.05088
$448$	−49.8002	−2.35284
$449$	−15.5381	−0.733287	−0.366644	−	0.930361i	$-0.619493\pi$
$449$	−15.5381	−0.733287	−0.366644	+	0.930361i	$0.619493\pi$
$450$	−248.835	−11.7302
$451$	−2.01283	−0.0947805
$452$	76.7485	3.60995
$453$	−19.1794	−0.901128
$454$	54.1008	2.53908
$455$	−24.2761	−1.13808
$456$	−30.4428	−1.42561
$457$	−11.6553	−0.545210	−0.272605	−	0.962126i	$-0.587885\pi$
$457$	−11.6553	−0.545210	−0.272605	+	0.962126i	$0.587885\pi$
$458$	30.2222	1.41219
$459$	−28.9182	−1.34979
$460$	213.176	9.93938
$461$	10.0029	0.465881	0.232941	−	0.972491i	$-0.425165\pi$
$461$	10.0029	0.465881	0.232941	+	0.972491i	$0.425165\pi$
$462$	56.9696	2.65047
$463$	19.9799	0.928544	0.464272	−	0.885693i	$-0.346316\pi$
$463$	19.9799	0.928544	0.464272	+	0.885693i	$0.346316\pi$
$464$	−144.498	−6.70814
$465$	−56.5345	−2.62172
$466$	27.5332	1.27545
$467$	−35.9677	−1.66439	−0.832194	−	0.554484i	$-0.812916\pi$
$467$	−35.9677	−1.66439	−0.832194	+	0.554484i	$0.812916\pi$
$468$	143.641	6.63978
$469$	0.514184	0.0237428
$470$	27.2630	1.25755
$471$	56.5964	2.60782
$472$	−54.9308	−2.52839
$473$	−4.61983	−0.212420
$474$	99.7365	4.58105
$475$	−14.5815	−0.669045
$476$	−22.5312	−1.03272
$477$	57.7802	2.64557
$478$	46.0490	2.10623
$479$	−20.3275	−0.928789	−0.464394	−	0.885629i	$-0.653728\pi$
$479$	−20.3275	−0.928789	−0.464394	+	0.885629i	$0.653728\pi$
$480$	341.756	15.5990
$481$	26.4388	1.20551
$482$	17.1756	0.782327
$483$	34.4158	1.56597
$484$	85.7219	3.89645
$485$	−34.8190	−1.58105
$486$	9.05856	0.410904
$487$	−13.3563	−0.605230	−0.302615	−	0.953113i	$-0.597860\pi$
$487$	−13.3563	−0.605230	−0.302615	+	0.953113i	$0.597860\pi$
$488$	3.07104	0.139020
$489$	−59.5153	−2.69138
$490$	63.9878	2.89067
$491$	27.5999	1.24557	0.622784	−	0.782394i	$-0.286002\pi$
$491$	27.5999	1.24557	0.622784	+	0.782394i	$0.286002\pi$
$492$	−6.71330	−0.302659
$493$	−26.3309	−1.18588
$494$	11.4037	0.513077
$495$	−139.891	−6.28764
$496$	69.5927	3.12481
$497$	12.4727	0.559475
$498$	17.6312	0.790072
$499$	−11.8544	−0.530674	−0.265337	−	0.964156i	$-0.585483\pi$
$499$	−11.8544	−0.530674	−0.265337	+	0.964156i	$0.585483\pi$
$500$	238.995	10.6882
$501$	−20.3914	−0.911021
$502$	53.9507	2.40794
$503$	5.84055	0.260417	0.130209	−	0.991487i	$-0.458435\pi$
$503$	5.84055	0.260417	0.130209	+	0.991487i	$0.458435\pi$
$504$	82.5079	3.67519
$505$	21.2368	0.945024
$506$	120.907	5.37497
$507$	−12.2030	−0.541956
$508$	−13.2037	−0.585819
$509$	−29.5449	−1.30955	−0.654777	−	0.755822i	$-0.727238\pi$
$509$	−29.5449	−1.30955	−0.654777	+	0.755822i	$0.727238\pi$
$510$	111.371	4.93161
$511$	−8.98701	−0.397562
$512$	−89.0388	−3.93500
$513$	9.61802	0.424646
$514$	9.39399	0.414351
$515$	57.0492	2.51389
$516$	−15.4083	−0.678312
$517$	11.4132	0.501952
$518$	23.5382	1.03421
$519$	−51.7488	−2.27152
$520$	−183.522	−8.04798
$521$	42.5685	1.86496	0.932479	−	0.361223i	$-0.117641\pi$
$521$	42.5685	1.86496	0.932479	+	0.361223i	$0.117641\pi$
$522$	149.448	6.54114
$523$	−28.0309	−1.22571	−0.612853	−	0.790197i	$-0.709978\pi$
$523$	−28.0309	−1.22571	−0.612853	+	0.790197i	$0.709978\pi$
$524$	14.3158	0.625390
$525$	58.7187	2.56269
$526$	55.9673	2.44029
$527$	12.6814	0.552411
$528$	255.861	11.1349
$529$	50.0408	2.17569
$530$	−114.420	−4.97011
$531$	33.7516	1.46469
$532$	7.49374	0.324895
$533$	1.62250	0.0702782
$534$	−70.3103	−3.04262
$535$	−23.3889	−1.01119
$536$	3.88712	0.167898
$537$	−2.05794	−0.0888068
$538$	−40.3874	−1.74122
$539$	26.7875	1.15382
$540$	−239.906	−10.3239
$541$	−20.8903	−0.898143	−0.449072	−	0.893496i	$-0.648245\pi$
$541$	−20.8903	−0.898143	−0.449072	+	0.893496i	$0.648245\pi$
$542$	−54.0113	−2.31998
$543$	22.5811	0.969046
$544$	−76.6603	−3.28679
$545$	−22.9224	−0.981886
$546$	−45.9220	−1.96528
$547$	35.7425	1.52824	0.764119	−	0.645075i	$-0.223174\pi$
$547$	35.7425	1.52824	0.764119	+	0.645075i	$0.223174\pi$
$548$	−58.5877	−2.50274
$549$	−1.88697	−0.0805339
$550$	206.286	8.79608
$551$	8.75748	0.373081
$552$	260.176	11.0738
$553$	−15.8400	−0.673586
$554$	−27.5918	−1.17226
$555$	−85.8784	−3.64533
$556$	−17.9830	−0.762650
$557$	−7.10224	−0.300931	−0.150466	−	0.988615i	$-0.548077\pi$
$557$	−7.10224	−0.300931	−0.150466	+	0.988615i	$0.548077\pi$
$558$	−71.9766	−3.04701
$559$	3.72394	0.157506
$560$	−97.0668	−4.10182
$561$	46.6238	1.96846
$562$	−52.6521	−2.22099
$563$	6.85382	0.288854	0.144427	−	0.989515i	$-0.453866\pi$
$563$	6.85382	0.288854	0.144427	+	0.989515i	$0.453866\pi$
$564$	38.0659	1.60286
$565$	60.2504	2.53475
$566$	20.3849	0.856842
$567$	−14.1025	−0.592248
$568$	94.2907	3.95635
$569$	−40.6133	−1.70260	−0.851299	−	0.524680i	$-0.824185\pi$
$569$	−40.6133	−1.70260	−0.851299	+	0.524680i	$0.824185\pi$
$570$	−37.0414	−1.55149
$571$	7.94906	0.332658	0.166329	−	0.986070i	$-0.446809\pi$
$571$	7.94906	0.332658	0.166329	+	0.986070i	$0.446809\pi$
$572$	−119.079	−4.97895
$573$	−52.5342	−2.19465
$574$	1.44449	0.0602920
$575$	124.619	5.19698
$576$	231.323	9.63847
$577$	−7.69302	−0.320265	−0.160132	−	0.987096i	$-0.551192\pi$
$577$	−7.69302	−0.320265	−0.160132	+	0.987096i	$0.551192\pi$
$578$	21.9971	0.914957
$579$	−55.2997	−2.29818
$580$	−218.441	−9.07028
$581$	−2.80016	−0.116170
$582$	−65.8655	−2.73021
$583$	−47.9003	−1.98383
$584$	−67.9399	−2.81137
$585$	112.763	4.66218
$586$	13.5603	0.560172
$587$	44.6016	1.84091	0.920453	−	0.390854i	$-0.127820\pi$
$587$	44.6016	1.84091	0.920453	+	0.390854i	$0.127820\pi$
$588$	89.3429	3.68444
$589$	−4.21776	−0.173790
$590$	−66.8373	−2.75165
$591$	79.3723	3.26494
$592$	105.714	4.34484
$593$	−9.19463	−0.377578	−0.188789	−	0.982018i	$-0.560456\pi$
$593$	−9.19463	−0.377578	−0.188789	+	0.982018i	$0.560456\pi$
$594$	−136.068	−5.58292
$595$	−17.6878	−0.725131
$596$	41.3458	1.69359
$597$	−25.2648	−1.03402
$598$	−97.4605	−3.98546
$599$	14.9139	0.609365	0.304682	−	0.952454i	$-0.401450\pi$
$599$	14.9139	0.609365	0.304682	+	0.952454i	$0.401450\pi$
$600$	443.901	18.1222
$601$	20.2247	0.824985	0.412492	−	0.910961i	$-0.364658\pi$
$601$	20.2247	0.824985	0.412492	+	0.910961i	$0.364658\pi$
$602$	3.31539	0.135125
$603$	−2.38840	−0.0972631
$604$	35.6911	1.45225
$605$	67.2949	2.73592
$606$	40.1726	1.63190
$607$	41.6198	1.68929	0.844647	−	0.535324i	$-0.179810\pi$
$607$	41.6198	1.68929	0.844647	+	0.535324i	$0.179810\pi$
$608$	25.4967	1.03403
$609$	−35.2658	−1.42904
$610$	3.73671	0.151295
$611$	−9.19994	−0.372190
$612$	104.658	4.23055
$613$	−38.7529	−1.56521	−0.782607	−	0.622517i	$-0.786110\pi$
$613$	−38.7529	−1.56521	−0.782607	+	0.622517i	$0.786110\pi$
$614$	−32.3184	−1.30426
$615$	−5.27019	−0.212514
$616$	−68.3997	−2.75590
$617$	−37.0839	−1.49294	−0.746471	−	0.665418i	$-0.768253\pi$
$617$	−37.0839	−1.49294	−0.746471	+	0.665418i	$0.768253\pi$
$618$	107.917	4.34107
$619$	34.0742	1.36956	0.684779	−	0.728751i	$-0.259899\pi$
$619$	34.0742	1.36956	0.684779	+	0.728751i	$0.259899\pi$
$620$	105.205	4.22514
$621$	−82.1994	−3.29855
$622$	−17.9435	−0.719470
$623$	11.1666	0.447379
$624$	−206.244	−8.25636
$625$	114.712	4.58849
$626$	−22.4174	−0.895979
$627$	−15.5068	−0.619282
$628$	−105.320	−4.20274
$629$	19.2636	0.768091
$630$	100.392	3.99971
$631$	16.6941	0.664582	0.332291	−	0.943177i	$-0.392178\pi$
$631$	16.6941	0.664582	0.332291	+	0.943177i	$0.392178\pi$
$632$	−119.747	−4.76328
$633$	44.8524	1.78272
$634$	−2.76348	−0.109752
$635$	−10.3654	−0.411338
$636$	−159.760	−6.33488
$637$	−21.5928	−0.855537
$638$	−123.893	−4.90499
$639$	−57.9358	−2.29191
$640$	−232.432	−9.18767
$641$	−4.36085	−0.172243	−0.0861217	−	0.996285i	$-0.527447\pi$
$641$	−4.36085	−0.172243	−0.0861217	+	0.996285i	$0.527447\pi$
$642$	−44.2436	−1.74616
$643$	9.19828	0.362745	0.181372	−	0.983414i	$-0.441946\pi$
$643$	9.19828	0.362745	0.181372	+	0.983414i	$0.441946\pi$
$644$	−64.0444	−2.52370
$645$	−12.0961	−0.476282
$646$	8.30887	0.326908
$647$	−20.5620	−0.808376	−0.404188	−	0.914676i	$-0.632446\pi$
$647$	−20.5620	−0.808376	−0.404188	+	0.914676i	$0.632446\pi$
$648$	−106.612	−4.18810
$649$	−27.9804	−1.09833
$650$	−166.283	−6.52215
$651$	16.9846	0.665680
$652$	110.752	4.33739
$653$	−9.59390	−0.375438	−0.187719	−	0.982223i	$-0.560109\pi$
$653$	−9.59390	−0.375438	−0.187719	+	0.982223i	$0.560109\pi$
$654$	−43.3612	−1.69556
$655$	11.2384	0.439122
$656$	6.48749	0.253294
$657$	41.7449	1.62862
$658$	−8.19061	−0.319303
$659$	−33.8772	−1.31967	−0.659834	−	0.751411i	$-0.729373\pi$
$659$	−33.8772	−1.31967	−0.659834	+	0.751411i	$0.729373\pi$
$660$	386.792	15.0559
$661$	9.71896	0.378024	0.189012	−	0.981975i	$-0.439472\pi$
$661$	9.71896	0.378024	0.189012	+	0.981975i	$0.439472\pi$
$662$	−75.2008	−2.92276
$663$	−37.5824	−1.45958
$664$	−21.1686	−0.821501
$665$	5.88286	0.228128
$666$	−109.336	−4.23667
$667$	−74.8448	−2.89800
$668$	37.9465	1.46819
$669$	−2.40390	−0.0929402
$670$	4.72968	0.182723
$671$	1.56431	0.0603897
$672$	−102.674	−3.96073
$673$	2.70036	0.104091	0.0520456	−	0.998645i	$-0.483426\pi$
$673$	2.70036	0.104091	0.0520456	+	0.998645i	$0.483426\pi$
$674$	9.20471	0.354552
$675$	−140.245	−5.39804
$676$	22.7087	0.873411
$677$	−23.0678	−0.886566	−0.443283	−	0.896382i	$-0.646186\pi$
$677$	−23.0678	−0.886566	−0.443283	+	0.896382i	$0.646186\pi$
$678$	113.973	4.37710
$679$	10.4607	0.401444
$680$	−133.716	−5.12779
$681$	59.3003	2.27239
$682$	59.6692	2.28485
$683$	11.8766	0.454447	0.227223	−	0.973843i	$-0.427035\pi$
$683$	11.8766	0.454447	0.227223	+	0.973843i	$0.427035\pi$
$684$	−34.8086	−1.33094
$685$	−45.9935	−1.75732
$686$	−44.9408	−1.71585
$687$	33.1268	1.26387
$688$	14.8900	0.567676
$689$	38.6114	1.47098
$690$	316.570	12.0516
$691$	9.28925	0.353380	0.176690	−	0.984267i	$-0.443461\pi$
$691$	9.28925	0.353380	0.176690	+	0.984267i	$0.443461\pi$
$692$	96.2996	3.66076
$693$	42.0274	1.59649
$694$	52.6855	1.99991
$695$	−14.1173	−0.535501
$696$	−266.602	−10.1055
$697$	1.18217	0.0447779
$698$	−5.51932	−0.208910
$699$	30.1793	1.14149
$700$	−109.270	−4.13001
$701$	0.802850	0.0303232	0.0151616	−	0.999885i	$-0.495174\pi$
$701$	0.802850	0.0303232	0.0151616	+	0.999885i	$0.495174\pi$
$702$	109.681	4.13964
$703$	−6.40696	−0.241643
$704$	−191.769	−7.22757
$705$	29.8831	1.12546
$706$	3.47971	0.130960
$707$	−6.38016	−0.239950
$708$	−93.3215	−3.50724
$709$	24.2269	0.909861	0.454930	−	0.890527i	$-0.349664\pi$
$709$	24.2269	0.909861	0.454930	+	0.890527i	$0.349664\pi$
$710$	114.729	4.30569
$711$	73.5773	2.75936
$712$	84.4169	3.16366
$713$	36.0466	1.34996
$714$	−33.4593	−1.25218
$715$	−93.4816	−3.49601
$716$	3.82964	0.143120
$717$	50.4746	1.88501
$718$	−64.1386	−2.39363
$719$	−42.9541	−1.60192	−0.800959	−	0.598719i	$-0.795676\pi$
$719$	−42.9541	−1.60192	−0.800959	+	0.598719i	$0.795676\pi$
$720$	450.878	16.8032
$721$	−17.1393	−0.638300
$722$	−2.76348	−0.102846
$723$	18.8263	0.700158
$724$	−42.0212	−1.56170
$725$	−127.697	−4.74255
$726$	127.299	4.72449
$727$	13.9812	0.518535	0.259268	−	0.965806i	$-0.416519\pi$
$727$	13.9812	0.518535	0.259268	+	0.965806i	$0.416519\pi$
$728$	55.1355	2.04346
$729$	−21.8945	−0.810909
$730$	−82.6662	−3.05961
$731$	2.71330	0.100355
$732$	5.21738	0.192840
$733$	40.0769	1.48027	0.740137	−	0.672457i	$-0.234761\pi$
$733$	40.0769	1.48027	0.740137	+	0.672457i	$0.234761\pi$
$734$	−68.5932	−2.53182
$735$	70.1375	2.58706
$736$	−217.905	−8.03209
$737$	1.98000	0.0729344
$738$	−6.70971	−0.246988
$739$	8.21731	0.302279	0.151139	−	0.988512i	$-0.451706\pi$
$739$	8.21731	0.302279	0.151139	+	0.988512i	$0.451706\pi$
$740$	159.811	5.87479
$741$	12.4997	0.459187
$742$	34.3753	1.26196
$743$	13.8027	0.506374	0.253187	−	0.967417i	$-0.418521\pi$
$743$	13.8027	0.506374	0.253187	+	0.967417i	$0.418521\pi$
$744$	128.400	4.70738
$745$	32.4580	1.18917
$746$	12.2590	0.448834
$747$	13.0068	0.475894
$748$	−86.7625	−3.17235
$749$	7.02671	0.256750
$750$	354.912	12.9595
$751$	16.4630	0.600745	0.300372	−	0.953822i	$-0.402889\pi$
$751$	16.4630	0.600745	0.300372	+	0.953822i	$0.402889\pi$
$752$	−36.7855	−1.34143
$753$	59.1357	2.15502
$754$	99.8677	3.63697
$755$	28.0188	1.01971
$756$	72.0749	2.62134
$757$	19.0945	0.694000	0.347000	−	0.937865i	$-0.387200\pi$
$757$	19.0945	0.694000	0.347000	+	0.937865i	$0.387200\pi$
$758$	−11.6327	−0.422518
$759$	132.527	4.81043
$760$	44.4732	1.61321
$761$	−48.0630	−1.74228	−0.871141	−	0.491033i	$-0.836620\pi$
$761$	−48.0630	−1.74228	−0.871141	+	0.491033i	$0.836620\pi$
$762$	−19.6077	−0.710313
$763$	6.88656	0.249310
$764$	97.7610	3.53687
$765$	82.1605	2.97052
$766$	69.7171	2.51898
$767$	22.5543	0.814390
$768$	−212.744	−7.67673
$769$	26.0140	0.938087	0.469044	−	0.883175i	$-0.344599\pi$
$769$	26.0140	0.938087	0.469044	+	0.883175i	$0.344599\pi$
$770$	−83.2257	−2.99925
$771$	10.2968	0.370831
$772$	102.908	3.70372
$773$	48.3381	1.73860	0.869300	−	0.494286i	$-0.164570\pi$
$773$	48.3381	1.73860	0.869300	+	0.494286i	$0.164570\pi$
$774$	−15.4001	−0.553544
$775$	61.5012	2.20919
$776$	79.0805	2.83882
$777$	25.8004	0.925585
$778$	−56.2379	−2.01623
$779$	−0.393183	−0.0140872
$780$	−311.784	−11.1637
$781$	48.0293	1.71862
$782$	−71.0108	−2.53934
$783$	84.2296	3.01012
$784$	−86.3378	−3.08349
$785$	−82.6804	−2.95099
$786$	21.2593	0.758292
$787$	0.526146	0.0187551	0.00937753	−	0.999956i	$-0.497015\pi$
$787$	0.526146	0.0187551	0.00937753	+	0.999956i	$0.497015\pi$
$788$	−147.704	−5.26175
$789$	61.3462	2.18398
$790$	−145.703	−5.18388
$791$	−18.1010	−0.643598
$792$	317.719	11.2896
$793$	−1.26096	−0.0447779
$794$	25.2745	0.896958
$795$	−125.417	−4.44809
$796$	47.0154	1.66642
$797$	30.1340	1.06740	0.533701	−	0.845673i	$-0.320801\pi$
$797$	30.1340	1.06740	0.533701	+	0.845673i	$0.320801\pi$
$798$	11.1283	0.393939
$799$	−6.70318	−0.237141
$800$	−371.781	−13.1444
$801$	−51.8690	−1.83270
$802$	−45.3002	−1.59961
$803$	−34.6069	−1.22125
$804$	6.60381	0.232898
$805$	−50.2772	−1.77204
$806$	−48.0980	−1.69418
$807$	−44.2689	−1.55834
$808$	−48.2326	−1.69682
$809$	49.7362	1.74863	0.874315	−	0.485358i	$-0.161311\pi$
$809$	49.7362	1.74863	0.874315	+	0.485358i	$0.161311\pi$
$810$	−129.720	−4.55791
$811$	−5.12674	−0.180024	−0.0900120	−	0.995941i	$-0.528691\pi$
$811$	−5.12674	−0.180024	−0.0900120	+	0.995941i	$0.528691\pi$
$812$	65.6263	2.30303
$813$	−59.2022	−2.07631
$814$	90.6403	3.17694
$815$	86.9446	3.04554
$816$	−150.272	−5.26056
$817$	−0.902428	−0.0315720
$818$	25.6136	0.895558
$819$	−33.8774	−1.18377
$820$	9.80731	0.342486
$821$	−47.7370	−1.66603	−0.833017	−	0.553248i	$-0.813388\pi$
$821$	−47.7370	−1.66603	−0.833017	+	0.553248i	$0.813388\pi$
$822$	−87.0038	−3.03461
$823$	−1.22046	−0.0425426	−0.0212713	−	0.999774i	$-0.506771\pi$
$823$	−1.22046	−0.0425426	−0.0212713	+	0.999774i	$0.506771\pi$
$824$	−129.569	−4.51376
$825$	226.112	7.87221
$826$	20.0799	0.698669
$827$	−15.9570	−0.554878	−0.277439	−	0.960743i	$-0.589486\pi$
$827$	−15.9570	−0.554878	−0.277439	+	0.960743i	$0.589486\pi$
$828$	297.488	10.3384
$829$	19.6627	0.682914	0.341457	−	0.939897i	$-0.389080\pi$
$829$	19.6627	0.682914	0.341457	+	0.939897i	$0.389080\pi$
$830$	−25.7570	−0.894038
$831$	−30.2435	−1.04914
$832$	154.581	5.35912
$833$	−15.7328	−0.545108
$834$	−26.7051	−0.924723
$835$	29.7894	1.03090
$836$	28.8567	0.998028
$837$	−40.5665	−1.40218
$838$	84.1589	2.90722
$839$	−12.8057	−0.442103	−0.221051	−	0.975262i	$-0.570949\pi$
$839$	−12.8057	−0.442103	−0.221051	+	0.975262i	$0.570949\pi$
$840$	−179.091	−6.17921
$841$	47.6935	1.64460
$842$	71.9738	2.48038
$843$	−57.7123	−1.98772
$844$	−83.4660	−2.87302
$845$	17.8272	0.613273
$846$	38.0456	1.30803
$847$	−20.2174	−0.694677
$848$	154.386	5.30163
$849$	22.3440	0.766846
$850$	−121.156	−4.15560
$851$	54.7564	1.87703
$852$	160.190	5.48801
$853$	17.4491	0.597445	0.298722	−	0.954340i	$-0.403440\pi$
$853$	17.4491	0.597445	0.298722	+	0.954340i	$0.403440\pi$
$854$	−1.12262	−0.0384152
$855$	−27.3261	−0.934531
$856$	53.1204	1.81562
$857$	19.3546	0.661141	0.330570	−	0.943781i	$-0.392759\pi$
$857$	19.3546	0.661141	0.330570	+	0.943781i	$0.392759\pi$
$858$	−176.835	−6.03704
$859$	−41.9274	−1.43055	−0.715273	−	0.698845i	$-0.753698\pi$
$859$	−41.9274	−1.43055	−0.715273	+	0.698845i	$0.753698\pi$
$860$	22.5096	0.767572
$861$	1.58332	0.0539594
$862$	28.5329	0.971836
$863$	30.3474	1.03304	0.516519	−	0.856276i	$-0.327228\pi$
$863$	30.3474	1.03304	0.516519	+	0.856276i	$0.327228\pi$
$864$	245.228	8.34283
$865$	75.5987	2.57043
$866$	27.9981	0.951415
$867$	24.1111	0.818857
$868$	−31.6068	−1.07280
$869$	−60.9962	−2.06915
$870$	−324.389	−10.9978
$871$	−1.59604	−0.0540797
$872$	52.0609	1.76301
$873$	−48.5901	−1.64453
$874$	23.6177	0.798882
$875$	−56.3666	−1.90554
$876$	−115.423	−3.89977
$877$	0.599847	0.0202554	0.0101277	−	0.999949i	$-0.496776\pi$
$877$	0.599847	0.0202554	0.0101277	+	0.999949i	$0.496776\pi$
$878$	34.2245	1.15502
$879$	14.8636	0.501336
$880$	−373.782	−12.6002
$881$	26.5058	0.893004	0.446502	−	0.894783i	$-0.352670\pi$
$881$	26.5058	0.893004	0.446502	+	0.894783i	$0.352670\pi$
$882$	89.2953	3.00673
$883$	−7.88059	−0.265203	−0.132601	−	0.991169i	$-0.542333\pi$
$883$	−7.88059	−0.265203	−0.132601	+	0.991169i	$0.542333\pi$
$884$	69.9373	2.35225
$885$	−73.2608	−2.46264
$886$	−3.31567	−0.111392
$887$	22.8843	0.768378	0.384189	−	0.923254i	$-0.374481\pi$
$887$	22.8843	0.768378	0.384189	+	0.923254i	$0.374481\pi$
$888$	195.046	6.54531
$889$	3.11407	0.104443
$890$	102.715	3.44301
$891$	−54.3053	−1.81930
$892$	4.47343	0.149782
$893$	2.22943	0.0746052
$894$	61.3993	2.05350
$895$	3.00641	0.100493
$896$	69.8294	2.33284
$897$	−106.827	−3.56685
$898$	42.9391	1.43290
$899$	−36.9369	−1.23192
$900$	507.562	16.9187
$901$	28.1327	0.937236
$902$	5.56241	0.185208
$903$	3.63402	0.120933
$904$	−136.840	−4.55123
$905$	−32.9882	−1.09656
$906$	53.0019	1.76087
$907$	−27.3436	−0.907929	−0.453965	−	0.891020i	$-0.649991\pi$
$907$	−27.3436	−0.907929	−0.453965	+	0.891020i	$0.649991\pi$
$908$	−110.352	−3.66217
$909$	29.6360	0.982964
$910$	67.0864	2.22389
$911$	1.41887	0.0470093	0.0235046	−	0.999724i	$-0.492518\pi$
$911$	1.41887	0.0470093	0.0235046	+	0.999724i	$0.492518\pi$
$912$	49.9794	1.65498
$913$	−10.7828	−0.356857
$914$	32.2091	1.06538
$915$	4.09583	0.135404
$916$	−61.6458	−2.03683
$917$	−3.37636	−0.111497
$918$	79.9149	2.63758
$919$	−5.82571	−0.192172	−0.0960862	−	0.995373i	$-0.530632\pi$
$919$	−5.82571	−0.192172	−0.0960862	+	0.995373i	$0.530632\pi$
$920$	−380.085	−12.5310
$921$	−35.4244	−1.16727
$922$	−27.6428	−0.910366
$923$	−38.7154	−1.27433
$924$	−116.204	−3.82283
$925$	93.4231	3.07173
$926$	−55.2140	−1.81444
$927$	79.6124	2.61482
$928$	223.287	7.32976
$929$	26.8553	0.881095	0.440548	−	0.897729i	$-0.354784\pi$
$929$	26.8553	0.881095	0.440548	+	0.897729i	$0.354784\pi$
$930$	156.232	5.12304
$931$	5.23261	0.171492
$932$	−56.1608	−1.83961
$933$	−19.6680	−0.643903
$934$	99.3960	3.25234
$935$	−68.1117	−2.22749
$936$	−256.106	−8.37108
$937$	22.7359	0.742749	0.371374	−	0.928483i	$-0.378887\pi$
$937$	22.7359	0.742749	0.371374	+	0.928483i	$0.378887\pi$
$938$	−1.42094	−0.0463952
$939$	−24.5718	−0.801872
$940$	−55.6097	−1.81379
$941$	−50.6264	−1.65037	−0.825186	−	0.564861i	$-0.808930\pi$
$941$	−50.6264	−1.65037	−0.825186	+	0.564861i	$0.808930\pi$
$942$	−156.403	−5.09587
$943$	3.36029	0.109426
$944$	90.1825	2.93519
$945$	56.5815	1.84060
$946$	12.7668	0.415084
$947$	17.9569	0.583520	0.291760	−	0.956492i	$-0.405759\pi$
$947$	17.9569	0.583520	0.291760	+	0.956492i	$0.405759\pi$
$948$	−203.438	−6.60735
$949$	27.8958	0.905537
$950$	40.2956	1.30736
$951$	−3.02907	−0.0982242
$952$	40.1724	1.30199
$953$	36.4671	1.18129	0.590643	−	0.806933i	$-0.298874\pi$
$953$	36.4671	1.18129	0.590643	+	0.806933i	$0.298874\pi$
$954$	−159.674	−5.16965
$955$	76.7460	2.48344
$956$	−93.9284	−3.03786
$957$	−135.800	−4.38980
$958$	56.1747	1.81492
$959$	13.8178	0.446201
$960$	−502.108	−16.2055
$961$	−13.2105	−0.426146
$962$	−73.0631	−2.35565
$963$	−32.6393	−1.05179
$964$	−35.0339	−1.12837
$965$	80.7862	2.60060
$966$	−95.1071	−3.06002
$967$	32.8198	1.05541	0.527707	−	0.849427i	$-0.323052\pi$
$967$	32.8198	1.05541	0.527707	+	0.849427i	$0.323052\pi$
$968$	−152.839	−4.91243
$969$	9.10741	0.292572
$970$	96.2215	3.08949
$971$	38.9640	1.25041	0.625207	−	0.780459i	$-0.285015\pi$
$971$	38.9640	1.25041	0.625207	+	0.780459i	$0.285015\pi$
$972$	−18.4772	−0.592656
$973$	4.24127	0.135969
$974$	36.9097	1.18266
$975$	−182.264	−5.83712
$976$	−5.04188	−0.161387
$977$	9.33926	0.298789	0.149395	−	0.988778i	$-0.452268\pi$
$977$	9.33926	0.298789	0.149395	+	0.988778i	$0.452268\pi$
$978$	164.469	5.25914
$979$	42.9999	1.37428
$980$	−130.519	−4.16928
$981$	−31.9883	−1.02131
$982$	−76.2718	−2.43393
$983$	−30.1153	−0.960528	−0.480264	−	0.877124i	$-0.659459\pi$
$983$	−30.1153	−0.960528	−0.480264	+	0.877124i	$0.659459\pi$
$984$	11.9696	0.381576
$985$	−115.953	−3.69458
$986$	72.7647	2.31730
$987$	−8.97779	−0.285766
$988$	−23.2607	−0.740022
$989$	7.71250	0.245243
$990$	386.586	12.2865
$991$	−11.2117	−0.356151	−0.178075	−	0.984017i	$-0.556987\pi$
$991$	−11.2117	−0.356151	−0.178075	+	0.984017i	$0.556987\pi$
$992$	−107.539	−3.41437
$993$	−82.4282	−2.61578
$994$	−34.4679	−1.09326
$995$	36.9088	1.17009
$996$	−35.9632	−1.13954
$997$	0.718541	0.0227564	0.0113782	−	0.999935i	$-0.496378\pi$
$997$	0.718541	0.0227564	0.0113782	+	0.999935i	$0.496378\pi$
$998$	32.7593	1.03698
$999$	−61.6223	−1.94964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.3	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.3	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76348 q^{2} -3.02907 q^{3} +5.63680 q^{4} +4.42510 q^{5} +8.37075 q^{6} -1.32943 q^{7} -10.0502 q^{8} +6.17524 q^{9} +O(q^{10})\)	\(q-2.76348 q^{2} -3.02907 q^{3} +5.63680 q^{4} +4.42510 q^{5} +8.37075 q^{6} -1.32943 q^{7} -10.0502 q^{8} +6.17524 q^{9} -12.2287 q^{10} -5.11933 q^{11} -17.0742 q^{12} +4.12658 q^{13} +3.67385 q^{14} -13.4039 q^{15} +16.4999 q^{16} +3.00667 q^{17} -17.0651 q^{18} -1.00000 q^{19} +24.9434 q^{20} +4.02693 q^{21} +14.1471 q^{22} +8.54639 q^{23} +30.4428 q^{24} +14.5815 q^{25} -11.4037 q^{26} -9.61802 q^{27} -7.49374 q^{28} -8.75748 q^{29} +37.0414 q^{30} +4.21776 q^{31} -25.4967 q^{32} +15.5068 q^{33} -8.30887 q^{34} -5.88286 q^{35} +34.8086 q^{36} +6.40696 q^{37} +2.76348 q^{38} -12.4997 q^{39} -44.4732 q^{40} +0.393183 q^{41} -11.1283 q^{42} +0.902428 q^{43} -28.8567 q^{44} +27.3261 q^{45} -23.6177 q^{46} -2.22943 q^{47} -49.9794 q^{48} -5.23261 q^{49} -40.2956 q^{50} -9.10741 q^{51} +23.2607 q^{52} +9.35675 q^{53} +26.5792 q^{54} -22.6535 q^{55} +13.3611 q^{56} +3.02907 q^{57} +24.2011 q^{58} +5.46563 q^{59} -75.5552 q^{60} -0.305570 q^{61} -11.6557 q^{62} -8.20956 q^{63} +37.4598 q^{64} +18.2605 q^{65} -42.8527 q^{66} -0.386770 q^{67} +16.9480 q^{68} -25.8876 q^{69} +16.2572 q^{70} -9.38195 q^{71} -62.0625 q^{72} +6.76004 q^{73} -17.7055 q^{74} -44.1683 q^{75} -5.63680 q^{76} +6.80580 q^{77} +34.5426 q^{78} +11.9149 q^{79} +73.0138 q^{80} +10.6079 q^{81} -1.08655 q^{82} +2.10628 q^{83} +22.6990 q^{84} +13.3048 q^{85} -2.49384 q^{86} +26.5270 q^{87} +51.4504 q^{88} -8.39951 q^{89} -75.5149 q^{90} -5.48600 q^{91} +48.1743 q^{92} -12.7759 q^{93} +6.16099 q^{94} -4.42510 q^{95} +77.2313 q^{96} -7.86853 q^{97} +14.4602 q^{98} -31.6131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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