LMFDB - Embedded newform 6023.2.a.b.1.1

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:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.79086 q^{2} -1.66708 q^{3} +5.78891 q^{4} +1.47477 q^{5} +4.65258 q^{6} -1.60538 q^{7} -10.5743 q^{8} -0.220852 q^{9} +O(q^{10})$	\(q-2.79086 q^{2} -1.66708 q^{3} +5.78891 q^{4} +1.47477 q^{5} +4.65258 q^{6} -1.60538 q^{7} -10.5743 q^{8} -0.220852 q^{9} -4.11587 q^{10} +1.76231 q^{11} -9.65056 q^{12} +3.00110 q^{13} +4.48040 q^{14} -2.45855 q^{15} +17.9336 q^{16} -0.637489 q^{17} +0.616367 q^{18} -1.00000 q^{19} +8.53728 q^{20} +2.67630 q^{21} -4.91836 q^{22} -6.91710 q^{23} +17.6282 q^{24} -2.82507 q^{25} -8.37564 q^{26} +5.36941 q^{27} -9.29341 q^{28} +7.56995 q^{29} +6.86147 q^{30} +4.71855 q^{31} -28.9017 q^{32} -2.93791 q^{33} +1.77914 q^{34} -2.36756 q^{35} -1.27849 q^{36} -7.76535 q^{37} +2.79086 q^{38} -5.00306 q^{39} -15.5946 q^{40} +2.91992 q^{41} -7.46918 q^{42} -11.8373 q^{43} +10.2018 q^{44} -0.325705 q^{45} +19.3047 q^{46} +10.5942 q^{47} -29.8968 q^{48} -4.42275 q^{49} +7.88437 q^{50} +1.06274 q^{51} +17.3731 q^{52} +8.67812 q^{53} -14.9853 q^{54} +2.59899 q^{55} +16.9758 q^{56} +1.66708 q^{57} -21.1267 q^{58} -9.03653 q^{59} -14.2323 q^{60} -0.869732 q^{61} -13.1688 q^{62} +0.354552 q^{63} +44.7932 q^{64} +4.42591 q^{65} +8.19929 q^{66} +5.37380 q^{67} -3.69037 q^{68} +11.5313 q^{69} +6.60754 q^{70} +11.9269 q^{71} +2.33536 q^{72} -8.83344 q^{73} +21.6720 q^{74} +4.70960 q^{75} -5.78891 q^{76} -2.82918 q^{77} +13.9628 q^{78} +8.24783 q^{79} +26.4479 q^{80} -8.28867 q^{81} -8.14910 q^{82} +13.0316 q^{83} +15.4928 q^{84} -0.940147 q^{85} +33.0362 q^{86} -12.6197 q^{87} -18.6352 q^{88} -4.35438 q^{89} +0.908997 q^{90} -4.81791 q^{91} -40.0424 q^{92} -7.86619 q^{93} -29.5669 q^{94} -1.47477 q^{95} +48.1813 q^{96} -7.99494 q^{97} +12.3433 q^{98} -0.389209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * 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 $

$2$	−2.79086	−1.97344	−0.986719	−	0.162439i	$-0.948064\pi$
$2$	−2.79086	−1.97344	−0.986719	+	0.162439i	$0.948064\pi$
$3$	−1.66708	−0.962488	−0.481244	−	0.876587i	$-0.659815\pi$
$3$	−1.66708	−0.962488	−0.481244	+	0.876587i	$0.659815\pi$
$4$	5.78891	2.89445
$5$	1.47477	0.659535	0.329768	−	0.944062i	$-0.393030\pi$
$5$	1.47477	0.659535	0.329768	+	0.944062i	$0.393030\pi$
$6$	4.65258	1.89941
$7$	−1.60538	−0.606778	−0.303389	−	0.952867i	$-0.598118\pi$
$7$	−1.60538	−0.606778	−0.303389	+	0.952867i	$0.598118\pi$
$8$	−10.5743	−3.73859
$9$	−0.220852	−0.0736173
$10$	−4.11587	−1.30155
$11$	1.76231	0.531356	0.265678	−	0.964062i	$-0.414404\pi$
$11$	1.76231	0.531356	0.265678	+	0.964062i	$0.414404\pi$
$12$	−9.65056	−2.78588
$13$	3.00110	0.832354	0.416177	−	0.909284i	$-0.363370\pi$
$13$	3.00110	0.832354	0.416177	+	0.909284i	$0.363370\pi$
$14$	4.48040	1.19744
$15$	−2.45855	−0.634795
$16$	17.9336	4.48341
$17$	−0.637489	−0.154614	−0.0773069	−	0.997007i	$-0.524632\pi$
$17$	−0.637489	−0.154614	−0.0773069	+	0.997007i	$0.524632\pi$
$18$	0.616367	0.145279
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	8.53728	1.90899
$21$	2.67630	0.584016
$22$	−4.91836	−1.04860
$23$	−6.91710	−1.44231	−0.721157	−	0.692771i	$-0.756390\pi$
$23$	−6.91710	−1.44231	−0.721157	+	0.692771i	$0.756390\pi$
$24$	17.6282	3.59834
$25$	−2.82507	−0.565013
$26$	−8.37564	−1.64260
$27$	5.36941	1.03334
$28$	−9.29341	−1.75629
$29$	7.56995	1.40570	0.702852	−	0.711336i	$-0.251910\pi$
$29$	7.56995	1.40570	0.702852	+	0.711336i	$0.251910\pi$
$30$	6.86147	1.25273
$31$	4.71855	0.847477	0.423738	−	0.905785i	$-0.360718\pi$
$31$	4.71855	0.847477	0.423738	+	0.905785i	$0.360718\pi$
$32$	−28.9017	−5.10914
$33$	−2.93791	−0.511424
$34$	1.77914	0.305121
$35$	−2.36756	−0.400191
$36$	−1.27849	−0.213082
$37$	−7.76535	−1.27662	−0.638308	−	0.769781i	$-0.720365\pi$
$37$	−7.76535	−1.27662	−0.638308	+	0.769781i	$0.720365\pi$
$38$	2.79086	0.452738
$39$	−5.00306	−0.801131
$40$	−15.5946	−2.46573
$41$	2.91992	0.456015	0.228008	−	0.973659i	$-0.426779\pi$
$41$	2.91992	0.456015	0.228008	+	0.973659i	$0.426779\pi$
$42$	−7.46918	−1.15252
$43$	−11.8373	−1.80517	−0.902585	−	0.430511i	$-0.858333\pi$
$43$	−11.8373	−1.80517	−0.902585	+	0.430511i	$0.858333\pi$
$44$	10.2018	1.53799
$45$	−0.325705	−0.0485532
$46$	19.3047	2.84632
$47$	10.5942	1.54532	0.772659	−	0.634821i	$-0.218926\pi$
$47$	10.5942	1.54532	0.772659	+	0.634821i	$0.218926\pi$
$48$	−29.8968	−4.31523
$49$	−4.42275	−0.631821
$50$	7.88437	1.11502
$51$	1.06274	0.148814
$52$	17.3731	2.40921
$53$	8.67812	1.19203	0.596016	−	0.802973i	$-0.296750\pi$
$53$	8.67812	1.19203	0.596016	+	0.802973i	$0.296750\pi$
$54$	−14.9853	−2.03924
$55$	2.59899	0.350448
$56$	16.9758	2.26849
$57$	1.66708	0.220810
$58$	−21.1267	−2.77407
$59$	−9.03653	−1.17646	−0.588228	−	0.808695i	$-0.700174\pi$
$59$	−9.03653	−1.17646	−0.588228	+	0.808695i	$0.700174\pi$
$60$	−14.2323	−1.83738
$61$	−0.869732	−0.111358	−0.0556789	−	0.998449i	$-0.517732\pi$
$61$	−0.869732	−0.111358	−0.0556789	+	0.998449i	$0.517732\pi$
$62$	−13.1688	−1.67244
$63$	0.354552	0.0446693
$64$	44.7932	5.59916
$65$	4.42591	0.548967
$66$	8.19929	1.00926
$67$	5.37380	0.656515	0.328257	−	0.944588i	$-0.393539\pi$
$67$	5.37380	0.656515	0.328257	+	0.944588i	$0.393539\pi$
$68$	−3.69037	−0.447523
$69$	11.5313	1.38821
$70$	6.60754	0.789752
$71$	11.9269	1.41546	0.707732	−	0.706481i	$-0.249719\pi$
$71$	11.9269	1.41546	0.707732	+	0.706481i	$0.249719\pi$
$72$	2.33536	0.275224
$73$	−8.83344	−1.03388	−0.516938	−	0.856023i	$-0.672928\pi$
$73$	−8.83344	−1.03388	−0.516938	+	0.856023i	$0.672928\pi$
$74$	21.6720	2.51932
$75$	4.70960	0.543818
$76$	−5.78891	−0.664033
$77$	−2.82918	−0.322415
$78$	13.9628	1.58098
$79$	8.24783	0.927954	0.463977	−	0.885847i	$-0.346422\pi$
$79$	8.24783	0.927954	0.463977	+	0.885847i	$0.346422\pi$
$80$	26.4479	2.95697
$81$	−8.28867	−0.920963
$82$	−8.14910	−0.899918
$83$	13.0316	1.43041	0.715204	−	0.698916i	$-0.246334\pi$
$83$	13.0316	1.43041	0.715204	+	0.698916i	$0.246334\pi$
$84$	15.4928	1.69041
$85$	−0.940147	−0.101973
$86$	33.0362	3.56239
$87$	−12.6197	−1.35297
$88$	−18.6352	−1.98652
$89$	−4.35438	−0.461563	−0.230782	−	0.973006i	$-0.574128\pi$
$89$	−4.35438	−0.461563	−0.230782	+	0.973006i	$0.574128\pi$
$90$	0.908997	0.0958167
$91$	−4.81791	−0.505054
$92$	−40.0424	−4.17471
$93$	−7.86619	−0.815686
$94$	−29.5669	−3.04959
$95$	−1.47477	−0.151308
$96$	48.1813	4.91748
$97$	−7.99494	−0.811763	−0.405882	−	0.913926i	$-0.633036\pi$
$97$	−7.99494	−0.811763	−0.405882	+	0.913926i	$0.633036\pi$
$98$	12.3433	1.24686
$99$	−0.389209	−0.0391170
$100$	−16.3540	−1.63540
$101$	−11.1419	−1.10866	−0.554331	−	0.832296i	$-0.687026\pi$
$101$	−11.1419	−1.10866	−0.554331	+	0.832296i	$0.687026\pi$
$102$	−2.96597	−0.293675
$103$	−3.87795	−0.382105	−0.191053	−	0.981580i	$-0.561190\pi$
$103$	−3.87795	−0.382105	−0.191053	+	0.981580i	$0.561190\pi$
$104$	−31.7345	−3.11183
$105$	3.94691	0.385179
$106$	−24.2194	−2.35240
$107$	6.81402	0.658736	0.329368	−	0.944202i	$-0.393164\pi$
$107$	6.81402	0.658736	0.329368	+	0.944202i	$0.393164\pi$
$108$	31.0830	2.99096
$109$	12.3137	1.17944	0.589718	−	0.807609i	$-0.299239\pi$
$109$	12.3137	1.17944	0.589718	+	0.807609i	$0.299239\pi$
$110$	−7.25343	−0.691587
$111$	12.9454	1.22873
$112$	−28.7903	−2.72043
$113$	−15.4757	−1.45583	−0.727914	−	0.685669i	$-0.759510\pi$
$113$	−15.4757	−1.45583	−0.727914	+	0.685669i	$0.759510\pi$
$114$	−4.65258	−0.435754
$115$	−10.2011	−0.951258
$116$	43.8217	4.06874
$117$	−0.662797	−0.0612756
$118$	25.2197	2.32166
$119$	1.02341	0.0938162
$120$	25.9975	2.37323
$121$	−7.89427	−0.717661
$122$	2.42730	0.219758
$123$	−4.86774	−0.438909
$124$	27.3153	2.45298
$125$	−11.5401	−1.03218
$126$	−0.989504	−0.0881521
$127$	−5.13538	−0.455691	−0.227846	−	0.973697i	$-0.573168\pi$
$127$	−5.13538	−0.455691	−0.227846	+	0.973697i	$0.573168\pi$
$128$	−67.2084	−5.94044
$129$	19.7337	1.73745
$130$	−12.3521	−1.08335
$131$	13.8666	1.21153	0.605765	−	0.795644i	$-0.292867\pi$
$131$	13.8666	1.21153	0.605765	+	0.795644i	$0.292867\pi$
$132$	−17.0073	−1.48029
$133$	1.60538	0.139204
$134$	−14.9975	−1.29559
$135$	7.91862	0.681527
$136$	6.74101	0.578037
$137$	−2.61873	−0.223733	−0.111866	−	0.993723i	$-0.535683\pi$
$137$	−2.61873	−0.223733	−0.111866	+	0.993723i	$0.535683\pi$
$138$	−32.1824	−2.73955
$139$	−13.9434	−1.18267	−0.591333	−	0.806427i	$-0.701398\pi$
$139$	−13.9434	−1.18267	−0.591333	+	0.806427i	$0.701398\pi$
$140$	−13.7056	−1.15833
$141$	−17.6613	−1.48735
$142$	−33.2863	−2.79333
$143$	5.28886	0.442276
$144$	−3.96068	−0.330056
$145$	11.1639	0.927111
$146$	24.6529	2.04029
$147$	7.37306	0.608120
$148$	−44.9529	−3.69511
$149$	−16.2748	−1.33329	−0.666643	−	0.745377i	$-0.732270\pi$
$149$	−16.2748	−1.33329	−0.666643	+	0.745377i	$0.732270\pi$
$150$	−13.1439	−1.07319
$151$	−12.6627	−1.03047	−0.515237	−	0.857048i	$-0.672296\pi$
$151$	−12.6627	−1.03047	−0.515237	+	0.857048i	$0.672296\pi$
$152$	10.5743	0.857690
$153$	0.140791	0.0113822
$154$	7.89585	0.636266
$155$	6.95876	0.558941
$156$	−28.9623	−2.31884
$157$	17.1966	1.37244	0.686218	−	0.727396i	$-0.259270\pi$
$157$	17.1966	1.37244	0.686218	+	0.727396i	$0.259270\pi$
$158$	−23.0186	−1.83126
$159$	−14.4671	−1.14732
$160$	−42.6232	−3.36966
$161$	11.1046	0.875164
$162$	23.1325	1.81746
$163$	10.6954	0.837729	0.418865	−	0.908049i	$-0.362428\pi$
$163$	10.6954	0.837729	0.418865	+	0.908049i	$0.362428\pi$
$164$	16.9032	1.31992
$165$	−4.33272	−0.337302
$166$	−36.3695	−2.82282
$167$	0.00574492	0.000444555 0	0.000222278	−	1.00000i	$-0.499929\pi$
$167$	0.00574492	0.000444555 0	0.000222278		1.00000i	$0.499929\pi$
$168$	−28.3000	−2.18339
$169$	−3.99342	−0.307186
$170$	2.62382	0.201238
$171$	0.220852	0.0168890
$172$	−68.5250	−5.22498
$173$	3.55506	0.270286	0.135143	−	0.990826i	$-0.456851\pi$
$173$	3.55506	0.270286	0.135143	+	0.990826i	$0.456851\pi$
$174$	35.2198	2.67001
$175$	4.53531	0.342837
$176$	31.6046	2.38229
$177$	15.0646	1.13232
$178$	12.1525	0.910866
$179$	−4.25306	−0.317889	−0.158944	−	0.987288i	$-0.550809\pi$
$179$	−4.25306	−0.317889	−0.158944	+	0.987288i	$0.550809\pi$
$180$	−1.88547	−0.140535
$181$	−25.8527	−1.92162	−0.960808	−	0.277216i	$-0.910588\pi$
$181$	−25.8527	−1.92162	−0.960808	+	0.277216i	$0.910588\pi$
$182$	13.4461	0.996692
$183$	1.44991	0.107181
$184$	73.1436	5.39222
$185$	−11.4521	−0.841973
$186$	21.9534	1.60970
$187$	−1.12345	−0.0821550
$188$	61.3287	4.47285
$189$	−8.61996	−0.627010
$190$	4.11587	0.298596
$191$	22.8318	1.65205	0.826025	−	0.563633i	$-0.190597\pi$
$191$	22.8318	1.65205	0.826025	+	0.563633i	$0.190597\pi$
$192$	−74.6738	−5.38912
$193$	9.98216	0.718532	0.359266	−	0.933235i	$-0.383027\pi$
$193$	9.98216	0.718532	0.359266	+	0.933235i	$0.383027\pi$
$194$	22.3128	1.60196
$195$	−7.37834	−0.528374
$196$	−25.6029	−1.82878
$197$	−12.1823	−0.867951	−0.433976	−	0.900925i	$-0.642890\pi$
$197$	−12.1823	−0.867951	−0.433976	+	0.900925i	$0.642890\pi$
$198$	1.08623	0.0771949
$199$	19.7516	1.40015	0.700077	−	0.714068i	$-0.253149\pi$
$199$	19.7516	1.40015	0.700077	+	0.714068i	$0.253149\pi$
$200$	29.8731	2.11235
$201$	−8.95855	−0.631887
$202$	31.0955	2.18787
$203$	−12.1527	−0.852949
$204$	6.15213	0.430735
$205$	4.30620	0.300758
$206$	10.8228	0.754061
$207$	1.52765	0.106179
$208$	53.8206	3.73178
$209$	−1.76231	−0.121901
$210$	−11.0153	−0.760127
$211$	21.0500	1.44914	0.724571	−	0.689200i	$-0.242038\pi$
$211$	21.0500	1.44914	0.724571	+	0.689200i	$0.242038\pi$
$212$	50.2368	3.45028
$213$	−19.8831	−1.36237
$214$	−19.0170	−1.29997
$215$	−17.4572	−1.19057
$216$	−56.7778	−3.86324
$217$	−7.57508	−0.514230
$218$	−34.3657	−2.32754
$219$	14.7260	0.995093
$220$	15.0453	1.01436
$221$	−1.91317	−0.128693
$222$	−36.1289	−2.42482
$223$	−8.20113	−0.549188	−0.274594	−	0.961560i	$-0.588543\pi$
$223$	−8.20113	−0.549188	−0.274594	+	0.961560i	$0.588543\pi$
$224$	46.3982	3.10011
$225$	0.623921	0.0415947
$226$	43.1904	2.87298
$227$	−12.8116	−0.850336	−0.425168	−	0.905114i	$-0.639785\pi$
$227$	−12.8116	−0.850336	−0.425168	+	0.905114i	$0.639785\pi$
$228$	9.65056	0.639124
$229$	−19.9771	−1.32013	−0.660063	−	0.751210i	$-0.729471\pi$
$229$	−19.9771	−1.32013	−0.660063	+	0.751210i	$0.729471\pi$
$230$	28.4699	1.87725
$231$	4.71646	0.310320
$232$	−80.0470	−5.25534
$233$	11.6928	0.766021	0.383010	−	0.923744i	$-0.374887\pi$
$233$	11.6928	0.766021	0.383010	+	0.923744i	$0.374887\pi$
$234$	1.84978	0.120924
$235$	15.6239	1.01919
$236$	−52.3116	−3.40520
$237$	−13.7498	−0.893144
$238$	−2.85621	−0.185140
$239$	−7.63505	−0.493870	−0.246935	−	0.969032i	$-0.579423\pi$
$239$	−7.63505	−0.493870	−0.246935	+	0.969032i	$0.579423\pi$
$240$	−44.0907	−2.84604
$241$	17.7372	1.14256	0.571278	−	0.820757i	$-0.306448\pi$
$241$	17.7372	1.14256	0.571278	+	0.820757i	$0.306448\pi$
$242$	22.0318	1.41626
$243$	−2.29038	−0.146928
$244$	−5.03480	−0.322320
$245$	−6.52252	−0.416708
$246$	13.5852	0.866160
$247$	−3.00110	−0.190955
$248$	−49.8954	−3.16836
$249$	−21.7247	−1.37675
$250$	32.2069	2.03695
$251$	14.1950	0.895982	0.447991	−	0.894038i	$-0.352140\pi$
$251$	14.1950	0.895982	0.447991	+	0.894038i	$0.352140\pi$
$252$	2.05247	0.129293
$253$	−12.1901	−0.766383
$254$	14.3321	0.899277
$255$	1.56730	0.0981480
$256$	97.9829	6.12393
$257$	18.8713	1.17716	0.588580	−	0.808439i	$-0.299687\pi$
$257$	18.8713	1.17716	0.588580	+	0.808439i	$0.299687\pi$
$258$	−55.0740	−3.42876
$259$	12.4664	0.774622
$260$	25.6212	1.58896
$261$	−1.67184	−0.103484
$262$	−38.6997	−2.39088
$263$	−8.04943	−0.496349	−0.248175	−	0.968715i	$-0.579831\pi$
$263$	−8.04943	−0.496349	−0.248175	+	0.968715i	$0.579831\pi$
$264$	31.0663	1.91200
$265$	12.7982	0.786187
$266$	−4.48040	−0.274711
$267$	7.25909	0.444249
$268$	31.1084	1.90025
$269$	26.1179	1.59243	0.796217	−	0.605011i	$-0.206831\pi$
$269$	26.1179	1.59243	0.796217	+	0.605011i	$0.206831\pi$
$270$	−22.0998	−1.34495
$271$	−13.6713	−0.830471	−0.415235	−	0.909714i	$-0.636301\pi$
$271$	−13.6713	−0.830471	−0.415235	+	0.909714i	$0.636301\pi$
$272$	−11.4325	−0.693197
$273$	8.03182	0.486108
$274$	7.30850	0.441523
$275$	−4.97864	−0.300223
$276$	66.7539	4.01811
$277$	−11.4839	−0.689998	−0.344999	−	0.938603i	$-0.612121\pi$
$277$	−11.4839	−0.689998	−0.344999	+	0.938603i	$0.612121\pi$
$278$	38.9142	2.33392
$279$	−1.04210	−0.0623889
$280$	25.0354	1.49615
$281$	−0.834965	−0.0498099	−0.0249049	−	0.999690i	$-0.507928\pi$
$281$	−0.834965	−0.0498099	−0.0249049	+	0.999690i	$0.507928\pi$
$282$	49.2902	2.93519
$283$	28.2891	1.68161	0.840807	−	0.541336i	$-0.182081\pi$
$283$	28.2891	1.68161	0.840807	+	0.541336i	$0.182081\pi$
$284$	69.0438	4.09699
$285$	2.45855	0.145632
$286$	−14.7605	−0.872805
$287$	−4.68759	−0.276700
$288$	6.38298	0.376121
$289$	−16.5936	−0.976095
$290$	−31.1569	−1.82960
$291$	13.3282	0.781312
$292$	−51.1360	−2.99251
$293$	3.94594	0.230524	0.115262	−	0.993335i	$-0.463229\pi$
$293$	3.94594	0.230524	0.115262	+	0.993335i	$0.463229\pi$
$294$	−20.5772	−1.20009
$295$	−13.3268	−0.775915
$296$	82.1133	4.77274
$297$	9.46256	0.549073
$298$	45.4208	2.63116
$299$	−20.7589	−1.20052
$300$	27.2635	1.57406
$301$	19.0034	1.09534
$302$	35.3398	2.03357
$303$	18.5744	1.06707
$304$	−17.9336	−1.02856
$305$	−1.28265	−0.0734444
$306$	−0.392927	−0.0224622
$307$	−7.77529	−0.443759	−0.221880	−	0.975074i	$-0.571219\pi$
$307$	−7.77529	−0.443759	−0.221880	+	0.975074i	$0.571219\pi$
$308$	−16.3779	−0.933215
$309$	6.46484	0.367772
$310$	−19.4209	−1.10303
$311$	13.1183	0.743872	0.371936	−	0.928258i	$-0.378694\pi$
$311$	13.1183	0.743872	0.371936	+	0.928258i	$0.378694\pi$
$312$	52.9039	2.99510
$313$	−16.6411	−0.940613	−0.470306	−	0.882503i	$-0.655857\pi$
$313$	−16.6411	−0.940613	−0.470306	+	0.882503i	$0.655857\pi$
$314$	−47.9933	−2.70842
$315$	0.522881	0.0294610
$316$	47.7459	2.68592
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	40.3757	2.26416
$319$	13.3406	0.746929
$320$	66.0596	3.69284
$321$	−11.3595	−0.634026
$322$	−30.9914	−1.72708
$323$	0.637489	0.0354708
$324$	−47.9823	−2.66569
$325$	−8.47829	−0.470291
$326$	−29.8494	−1.65321
$327$	−20.5278	−1.13519
$328$	−30.8762	−1.70485
$329$	−17.0077	−0.937664
$330$	12.0920	0.665644
$331$	−14.3389	−0.788135	−0.394067	−	0.919082i	$-0.628932\pi$
$331$	−14.3389	−0.788135	−0.394067	+	0.919082i	$0.628932\pi$
$332$	75.4389	4.14025
$333$	1.71499	0.0939810
$334$	−0.0160333	−0.000877302 0
$335$	7.92510	0.432995
$336$	47.9957	2.61838
$337$	4.76806	0.259733	0.129866	−	0.991532i	$-0.458545\pi$
$337$	4.76806	0.259733	0.129866	+	0.991532i	$0.458545\pi$
$338$	11.1451	0.606213
$339$	25.7991	1.40122
$340$	−5.44243	−0.295157
$341$	8.31554	0.450312
$342$	−0.616367	−0.0333293
$343$	18.3379	0.990152
$344$	125.171	6.74878
$345$	17.0060	0.915574
$346$	−9.92167	−0.533392
$347$	32.1588	1.72638	0.863189	−	0.504882i	$-0.168464\pi$
$347$	32.1588	1.72638	0.863189	+	0.504882i	$0.168464\pi$
$348$	−73.0542	−3.91612
$349$	8.42544	0.451003	0.225502	−	0.974243i	$-0.427598\pi$
$349$	8.42544	0.451003	0.225502	+	0.974243i	$0.427598\pi$
$350$	−12.6574	−0.676568
$351$	16.1141	0.860108
$352$	−50.9336	−2.71477
$353$	−29.6599	−1.57864	−0.789320	−	0.613982i	$-0.789567\pi$
$353$	−29.6599	−1.57864	−0.789320	+	0.613982i	$0.789567\pi$
$354$	−42.0432	−2.23457
$355$	17.5894	0.933548
$356$	−25.2071	−1.33597
$357$	−1.70611	−0.0902970
$358$	11.8697	0.627333
$359$	17.1516	0.905229	0.452614	−	0.891706i	$-0.350491\pi$
$359$	17.1516	0.905229	0.452614	+	0.891706i	$0.350491\pi$
$360$	3.44410	0.181520
$361$	1.00000	0.0526316
$362$	72.1513	3.79219
$363$	13.1604	0.690740
$364$	−27.8904	−1.46185
$365$	−13.0273	−0.681878
$366$	−4.04650	−0.211514
$367$	8.06530	0.421005	0.210503	−	0.977593i	$-0.432490\pi$
$367$	8.06530	0.421005	0.210503	+	0.977593i	$0.432490\pi$
$368$	−124.049	−6.46649
$369$	−0.644870	−0.0335706
$370$	31.9612	1.66158
$371$	−13.9317	−0.723298
$372$	−45.5367	−2.36097
$373$	3.27675	0.169663	0.0848317	−	0.996395i	$-0.472965\pi$
$373$	3.27675	0.169663	0.0848317	+	0.996395i	$0.472965\pi$
$374$	3.13540	0.162128
$375$	19.2383	0.993462
$376$	−112.026	−5.77730
$377$	22.7181	1.17004
$378$	24.0571	1.23736
$379$	10.5128	0.540009	0.270004	−	0.962859i	$-0.412975\pi$
$379$	10.5128	0.540009	0.270004	+	0.962859i	$0.412975\pi$
$380$	−8.53728	−0.437953
$381$	8.56107	0.438597
$382$	−63.7204	−3.26022
$383$	−18.9950	−0.970600	−0.485300	−	0.874348i	$-0.661290\pi$
$383$	−18.9950	−0.970600	−0.485300	+	0.874348i	$0.661290\pi$
$384$	112.042	5.71760
$385$	−4.17238	−0.212644
$386$	−27.8588	−1.41798
$387$	2.61429	0.132892
$388$	−46.2820	−2.34961
$389$	−9.47760	−0.480534	−0.240267	−	0.970707i	$-0.577235\pi$
$389$	−9.47760	−0.480534	−0.240267	+	0.970707i	$0.577235\pi$
$390$	20.5919	1.04271
$391$	4.40958	0.223002
$392$	46.7675	2.36212
$393$	−23.1167	−1.16608
$394$	33.9990	1.71285
$395$	12.1636	0.612018
$396$	−2.25310	−0.113222
$397$	−34.5485	−1.73394	−0.866971	−	0.498359i	$-0.833936\pi$
$397$	−34.5485	−1.73394	−0.866971	+	0.498359i	$0.833936\pi$
$398$	−55.1240	−2.76311
$399$	−2.67630	−0.133982
$400$	−50.6637	−2.53318
$401$	25.8235	1.28956	0.644782	−	0.764367i	$-0.276948\pi$
$401$	25.8235	1.28956	0.644782	+	0.764367i	$0.276948\pi$
$402$	25.0021	1.24699
$403$	14.1608	0.705401
$404$	−64.4995	−3.20897
$405$	−12.2238	−0.607408
$406$	33.9164	1.68324
$407$	−13.6849	−0.678338
$408$	−11.2378	−0.556354
$409$	35.7879	1.76960	0.884798	−	0.465974i	$-0.154296\pi$
$409$	35.7879	1.76960	0.884798	+	0.465974i	$0.154296\pi$
$410$	−12.0180	−0.593528
$411$	4.36562	0.215340
$412$	−22.4491	−1.10599
$413$	14.5071	0.713847
$414$	−4.26347	−0.209538
$415$	19.2186	0.943404
$416$	−86.7366	−4.25261
$417$	23.2448	1.13830
$418$	4.91836	0.240565
$419$	−37.6689	−1.84025	−0.920124	−	0.391627i	$-0.871912\pi$
$419$	−37.6689	−1.84025	−0.920124	+	0.391627i	$0.871912\pi$
$420$	22.8483	1.11488
$421$	−4.57550	−0.222996	−0.111498	−	0.993765i	$-0.535565\pi$
$421$	−4.57550	−0.222996	−0.111498	+	0.993765i	$0.535565\pi$
$422$	−58.7476	−2.85979
$423$	−2.33974	−0.113762
$424$	−91.7652	−4.45651
$425$	1.80095	0.0873589
$426$	55.4909	2.68854
$427$	1.39625	0.0675694
$428$	39.4457	1.90668
$429$	−8.81694	−0.425686
$430$	48.7207	2.34952
$431$	−26.3981	−1.27155	−0.635775	−	0.771874i	$-0.719319\pi$
$431$	−26.3981	−1.27155	−0.635775	+	0.771874i	$0.719319\pi$
$432$	96.2930	4.63290
$433$	−20.7339	−0.996410	−0.498205	−	0.867059i	$-0.666007\pi$
$433$	−20.7339	−0.996410	−0.498205	+	0.867059i	$0.666007\pi$
$434$	21.1410	1.01480
$435$	−18.6111	−0.892333
$436$	71.2827	3.41382
$437$	6.91710	0.330890
$438$	−41.0983	−1.96375
$439$	−7.01026	−0.334581	−0.167291	−	0.985908i	$-0.553502\pi$
$439$	−7.01026	−0.334581	−0.167291	+	0.985908i	$0.553502\pi$
$440$	−27.4826	−1.31018
$441$	0.976772	0.0465129
$442$	5.33938	0.253968
$443$	−8.86017	−0.420959	−0.210480	−	0.977598i	$-0.567503\pi$
$443$	−8.86017	−0.420959	−0.210480	+	0.977598i	$0.567503\pi$
$444$	74.9400	3.55649
$445$	−6.42169	−0.304417
$446$	22.8882	1.08379
$447$	27.1314	1.28327
$448$	−71.9103	−3.39744
$449$	18.0063	0.849769	0.424885	−	0.905248i	$-0.360315\pi$
$449$	18.0063	0.849769	0.424885	+	0.905248i	$0.360315\pi$
$450$	−1.74128	−0.0820846
$451$	5.14581	0.242307
$452$	−89.5871	−4.21382
$453$	21.1097	0.991818
$454$	35.7554	1.67809
$455$	−7.10528	−0.333101
$456$	−17.6282	−0.825516
$457$	25.4252	1.18934	0.594671	−	0.803969i	$-0.297282\pi$
$457$	25.4252	1.18934	0.594671	+	0.803969i	$0.297282\pi$
$458$	55.7534	2.60519
$459$	−3.42294	−0.159769
$460$	−59.0532	−2.75337
$461$	−31.7667	−1.47952	−0.739762	−	0.672869i	$-0.765062\pi$
$461$	−31.7667	−1.47952	−0.739762	+	0.672869i	$0.765062\pi$
$462$	−13.1630	−0.612398
$463$	−33.6176	−1.56234	−0.781172	−	0.624316i	$-0.785378\pi$
$463$	−33.6176	−1.56234	−0.781172	+	0.624316i	$0.785378\pi$
$464$	135.757	6.30234
$465$	−11.6008	−0.537974
$466$	−32.6330	−1.51169
$467$	16.8467	0.779574	0.389787	−	0.920905i	$-0.372549\pi$
$467$	16.8467	0.779574	0.389787	+	0.920905i	$0.372549\pi$
$468$	−3.83687	−0.177360
$469$	−8.62701	−0.398358
$470$	−43.6042	−2.01131
$471$	−28.6680	−1.32095
$472$	95.5551	4.39828
$473$	−20.8610	−0.959188
$474$	38.3737	1.76256
$475$	2.82507	0.129623
$476$	5.92445	0.271547
$477$	−1.91658	−0.0877541
$478$	21.3084	0.974622
$479$	21.6908	0.991079	0.495539	−	0.868585i	$-0.334970\pi$
$479$	21.6908	0.991079	0.495539	+	0.868585i	$0.334970\pi$
$480$	71.0561	3.24325
$481$	−23.3046	−1.06260
$482$	−49.5022	−2.25476
$483$	−18.5122	−0.842335
$484$	−45.6992	−2.07724
$485$	−11.7907	−0.535387
$486$	6.39212	0.289952
$487$	−35.9859	−1.63068	−0.815338	−	0.578986i	$-0.803449\pi$
$487$	−35.9859	−1.63068	−0.815338	+	0.578986i	$0.803449\pi$
$488$	9.19682	0.416321
$489$	−17.8301	−0.806304
$490$	18.2034	0.822348
$491$	−24.6591	−1.11285	−0.556426	−	0.830897i	$-0.687828\pi$
$491$	−24.6591	−1.11285	−0.556426	+	0.830897i	$0.687828\pi$
$492$	−28.1789	−1.27040
$493$	−4.82576	−0.217341
$494$	8.37564	0.376838
$495$	−0.573992	−0.0257990
$496$	84.6208	3.79958
$497$	−19.1472	−0.858871
$498$	60.6307	2.71693
$499$	−22.2571	−0.996363	−0.498181	−	0.867073i	$-0.665999\pi$
$499$	−22.2571	−0.996363	−0.498181	+	0.867073i	$0.665999\pi$
$500$	−66.8048	−2.98760
$501$	−0.00957723	−0.000427879 0
$502$	−39.6163	−1.76816
$503$	−4.03338	−0.179840	−0.0899199	−	0.995949i	$-0.528661\pi$
$503$	−4.03338	−0.179840	−0.0899199	+	0.995949i	$0.528661\pi$
$504$	−3.74914	−0.167000
$505$	−16.4317	−0.731201
$506$	34.0208	1.51241
$507$	6.65735	0.295663
$508$	−29.7282	−1.31898
$509$	−38.4965	−1.70633	−0.853163	−	0.521644i	$-0.825319\pi$
$509$	−38.4965	−1.70633	−0.853163	+	0.521644i	$0.825319\pi$
$510$	−4.37411	−0.193689
$511$	14.1811	0.627333
$512$	−139.040	−6.14475
$513$	−5.36941	−0.237065
$514$	−52.6672	−2.32305
$515$	−5.71906	−0.252012
$516$	114.237	5.02898
$517$	18.6702	0.821114
$518$	−34.7919	−1.52867
$519$	−5.92656	−0.260147
$520$	−46.8010	−2.05236
$521$	44.2293	1.93772	0.968860	−	0.247608i	$-0.0796444\pi$
$521$	44.2293	1.93772	0.968860	+	0.247608i	$0.0796444\pi$
$522$	4.66586	0.204219
$523$	−26.5160	−1.15947	−0.579733	−	0.814807i	$-0.696843\pi$
$523$	−26.5160	−1.15947	−0.579733	+	0.814807i	$0.696843\pi$
$524$	80.2724	3.50671
$525$	−7.56072	−0.329977
$526$	22.4648	0.979514
$527$	−3.00803	−0.131032
$528$	−52.6873	−2.29292
$529$	24.8463	1.08027
$530$	−35.7180	−1.55149
$531$	1.99573	0.0866075
$532$	9.29341	0.402920
$533$	8.76297	0.379566
$534$	−20.2591	−0.876698
$535$	10.0491	0.434460
$536$	−56.8243	−2.45444
$537$	7.09018	0.305964
$538$	−72.8913	−3.14257
$539$	−7.79425	−0.335722
$540$	45.8402	1.97265
$541$	−33.1555	−1.42547	−0.712734	−	0.701435i	$-0.752543\pi$
$541$	−33.1555	−1.42547	−0.712734	+	0.701435i	$0.752543\pi$
$542$	38.1546	1.63888
$543$	43.0984	1.84953
$544$	18.4245	0.789944
$545$	18.1598	0.777879
$546$	−22.4157	−0.959304
$547$	13.5577	0.579687	0.289843	−	0.957074i	$-0.406397\pi$
$547$	13.5577	0.579687	0.289843	+	0.957074i	$0.406397\pi$
$548$	−15.1596	−0.647585
$549$	0.192082	0.00819786
$550$	13.8947	0.592472
$551$	−7.56995	−0.322491
$552$	−121.936	−5.18994
$553$	−13.2409	−0.563061
$554$	32.0499	1.36167
$555$	19.0915	0.810389
$556$	−80.7172	−3.42317
$557$	−19.2303	−0.814814	−0.407407	−	0.913247i	$-0.633567\pi$
$557$	−19.2303	−0.814814	−0.407407	+	0.913247i	$0.633567\pi$
$558$	2.90836	0.123121
$559$	−35.5249	−1.50254
$560$	−42.4590	−1.79422
$561$	1.87288	0.0790732
$562$	2.33027	0.0982966
$563$	−29.7936	−1.25565	−0.627825	−	0.778354i	$-0.716055\pi$
$563$	−29.7936	−1.25565	−0.627825	+	0.778354i	$0.716055\pi$
$564$	−102.240	−4.30507
$565$	−22.8230	−0.960169
$566$	−78.9510	−3.31856
$567$	13.3065	0.558820
$568$	−126.119	−5.29183
$569$	−0.302431	−0.0126786	−0.00633928	−	0.999980i	$-0.502018\pi$
$569$	−0.302431	−0.0126786	−0.00633928	+	0.999980i	$0.502018\pi$
$570$	−6.86147	−0.287395
$571$	8.20964	0.343563	0.171781	−	0.985135i	$-0.445048\pi$
$571$	8.20964	0.343563	0.171781	+	0.985135i	$0.445048\pi$
$572$	30.6167	1.28015
$573$	−38.0624	−1.59008
$574$	13.0824	0.546050
$575$	19.5413	0.814927
$576$	−9.89267	−0.412195
$577$	32.4061	1.34908	0.674542	−	0.738236i	$-0.264341\pi$
$577$	32.4061	1.34908	0.674542	+	0.738236i	$0.264341\pi$
$578$	46.3105	1.92626
$579$	−16.6410	−0.691578
$580$	64.6268	2.68348
$581$	−20.9207	−0.867939
$582$	−37.1971	−1.54187
$583$	15.2935	0.633393
$584$	93.4076	3.86523
$585$	−0.977471	−0.0404135
$586$	−11.0126	−0.454925
$587$	34.9183	1.44123	0.720617	−	0.693333i	$-0.243859\pi$
$587$	34.9183	1.44123	0.720617	+	0.693333i	$0.243859\pi$
$588$	42.6820	1.76018
$589$	−4.71855	−0.194425
$590$	37.1932	1.53122
$591$	20.3088	0.835392
$592$	−139.261	−5.72359
$593$	33.1001	1.35926	0.679630	−	0.733555i	$-0.262140\pi$
$593$	33.1001	1.35926	0.679630	+	0.733555i	$0.262140\pi$
$594$	−26.4087	−1.08356
$595$	1.50930	0.0618751
$596$	−94.2135	−3.85914
$597$	−32.9274	−1.34763
$598$	57.9351	2.36914
$599$	−48.0981	−1.96523	−0.982617	−	0.185642i	$-0.940563\pi$
$599$	−48.0981	−1.96523	−0.982617	+	0.185642i	$0.940563\pi$
$600$	−49.8008	−2.03311
$601$	−28.7990	−1.17473	−0.587367	−	0.809320i	$-0.699836\pi$
$601$	−28.7990	−1.17473	−0.587367	+	0.809320i	$0.699836\pi$
$602$	−53.0358	−2.16158
$603$	−1.18681	−0.0483308
$604$	−73.3030	−2.98266
$605$	−11.6422	−0.473323
$606$	−51.8387	−2.10580
$607$	−30.0228	−1.21859	−0.609294	−	0.792945i	$-0.708547\pi$
$607$	−30.0228	−1.21859	−0.609294	+	0.792945i	$0.708547\pi$
$608$	28.9017	1.17212
$609$	20.2594	0.820953
$610$	3.57970	0.144938
$611$	31.7941	1.28625
$612$	0.815024	0.0329454
$613$	−39.5554	−1.59763	−0.798814	−	0.601579i	$-0.794539\pi$
$613$	−39.5554	−1.59763	−0.798814	+	0.601579i	$0.794539\pi$
$614$	21.6998	0.875731
$615$	−7.17878	−0.289476
$616$	29.9166	1.20538
$617$	8.56120	0.344661	0.172331	−	0.985039i	$-0.444870\pi$
$617$	8.56120	0.344661	0.172331	+	0.985039i	$0.444870\pi$
$618$	−18.0425	−0.725774
$619$	−11.0026	−0.442231	−0.221116	−	0.975248i	$-0.570970\pi$
$619$	−11.0026	−0.442231	−0.221116	+	0.975248i	$0.570970\pi$
$620$	40.2836	1.61783
$621$	−37.1407	−1.49041
$622$	−36.6114	−1.46799
$623$	6.99045	0.280066
$624$	−89.7230	−3.59180
$625$	−2.89368	−0.115747
$626$	46.4431	1.85624
$627$	2.93791	0.117329
$628$	99.5494	3.97245
$629$	4.95033	0.197383
$630$	−1.45929	−0.0581394
$631$	11.3136	0.450387	0.225194	−	0.974314i	$-0.427698\pi$
$631$	11.3136	0.450387	0.225194	+	0.974314i	$0.427698\pi$
$632$	−87.2152	−3.46923
$633$	−35.0920	−1.39478
$634$	2.79086	0.110839
$635$	−7.57348	−0.300544
$636$	−83.7487	−3.32085
$637$	−13.2731	−0.525899
$638$	−37.2317	−1.47402
$639$	−2.63408	−0.104203
$640$	−99.1167	−3.91793
$641$	−3.43862	−0.135817	−0.0679087	−	0.997692i	$-0.521633\pi$
$641$	−3.43862	−0.135817	−0.0679087	+	0.997692i	$0.521633\pi$
$642$	31.7028	1.25121
$643$	−3.44233	−0.135752	−0.0678762	−	0.997694i	$-0.521622\pi$
$643$	−3.44233	−0.135752	−0.0678762	+	0.997694i	$0.521622\pi$
$644$	64.2834	2.53312
$645$	29.1026	1.14591
$646$	−1.77914	−0.0699995
$647$	−14.6929	−0.577639	−0.288820	−	0.957384i	$-0.593263\pi$
$647$	−14.6929	−0.577639	−0.288820	+	0.957384i	$0.593263\pi$
$648$	87.6470	3.44310
$649$	−15.9252	−0.625117
$650$	23.6617	0.928090
$651$	12.6282	0.494940
$652$	61.9148	2.42477
$653$	15.6734	0.613346	0.306673	−	0.951815i	$-0.400784\pi$
$653$	15.6734	0.613346	0.306673	+	0.951815i	$0.400784\pi$
$654$	57.2904	2.24023
$655$	20.4500	0.799046
$656$	52.3648	2.04450
$657$	1.95088	0.0761111
$658$	47.4661	1.85042
$659$	−33.1709	−1.29215	−0.646077	−	0.763272i	$-0.723591\pi$
$659$	−33.1709	−1.29215	−0.646077	+	0.763272i	$0.723591\pi$
$660$	−25.0817	−0.976305
$661$	−6.98589	−0.271719	−0.135860	−	0.990728i	$-0.543380\pi$
$661$	−6.98589	−0.271719	−0.135860	+	0.990728i	$0.543380\pi$
$662$	40.0177	1.55533
$663$	3.18940	0.123866
$664$	−137.801	−5.34770
$665$	2.36756	0.0918102
$666$	−4.78631	−0.185466
$667$	−52.3621	−2.02747
$668$	0.0332568	0.00128674
$669$	13.6719	0.528587
$670$	−22.1179	−0.854487
$671$	−1.53274	−0.0591707
$672$	−77.3494	−2.98382
$673$	27.2023	1.04857	0.524285	−	0.851543i	$-0.324333\pi$
$673$	27.2023	1.04857	0.524285	+	0.851543i	$0.324333\pi$
$674$	−13.3070	−0.512566
$675$	−15.1689	−0.583853
$676$	−23.1176	−0.889137
$677$	5.00982	0.192543	0.0962716	−	0.995355i	$-0.469308\pi$
$677$	5.00982	0.192543	0.0962716	+	0.995355i	$0.469308\pi$
$678$	−72.0018	−2.76521
$679$	12.8349	0.492560
$680$	9.94141	0.381236
$681$	21.3580	0.818438
$682$	−23.2075	−0.888662
$683$	−0.454863	−0.0174048	−0.00870242	−	0.999962i	$-0.502770\pi$
$683$	−0.454863	−0.0174048	−0.00870242	+	0.999962i	$0.502770\pi$
$684$	1.27849	0.0488843
$685$	−3.86201	−0.147560
$686$	−51.1785	−1.95400
$687$	33.3034	1.27061
$688$	−212.286	−8.09332
$689$	26.0439	0.992193
$690$	−47.4615	−1.80683
$691$	16.3220	0.620916	0.310458	−	0.950587i	$-0.399518\pi$
$691$	16.3220	0.620916	0.310458	+	0.950587i	$0.399518\pi$
$692$	20.5799	0.782330
$693$	0.624829	0.0237353
$694$	−89.7509	−3.40690
$695$	−20.5633	−0.780010
$696$	133.445	5.05820
$697$	−1.86142	−0.0705063
$698$	−23.5142	−0.890027
$699$	−19.4928	−0.737286
$700$	26.2545	0.992327
$701$	4.38283	0.165537	0.0827687	−	0.996569i	$-0.473624\pi$
$701$	4.38283	0.165537	0.0827687	+	0.996569i	$0.473624\pi$
$702$	−44.9723	−1.69737
$703$	7.76535	0.292876
$704$	78.9395	2.97515
$705$	−26.0463	−0.980960
$706$	82.7768	3.11535
$707$	17.8870	0.672711
$708$	87.2076	3.27746
$709$	−26.2711	−0.986632	−0.493316	−	0.869850i	$-0.664215\pi$
$709$	−26.2711	−0.986632	−0.493316	+	0.869850i	$0.664215\pi$
$710$	−49.0896	−1.84230
$711$	−1.82155	−0.0683134
$712$	46.0446	1.72559
$713$	−32.6387	−1.22233
$714$	4.76152	0.178195
$715$	7.79983	0.291697
$716$	−24.6206	−0.920114
$717$	12.7282	0.475344
$718$	−47.8678	−1.78641
$719$	−39.4160	−1.46997	−0.734985	−	0.678083i	$-0.762811\pi$
$719$	−39.4160	−1.46997	−0.734985	+	0.678083i	$0.762811\pi$
$720$	−5.84107	−0.217684
$721$	6.22559	0.231853
$722$	−2.79086	−0.103865
$723$	−29.5693	−1.09970
$724$	−149.659	−5.56203
$725$	−21.3856	−0.794241
$726$	−36.7287	−1.36313
$727$	−9.70602	−0.359976	−0.179988	−	0.983669i	$-0.557606\pi$
$727$	−9.70602	−0.359976	−0.179988	+	0.983669i	$0.557606\pi$
$728$	50.9461	1.88819
$729$	28.6842	1.06238
$730$	36.3573	1.34564
$731$	7.54615	0.279104
$732$	8.39340	0.310229
$733$	−25.1275	−0.928106	−0.464053	−	0.885808i	$-0.653605\pi$
$733$	−25.1275	−0.928106	−0.464053	+	0.885808i	$0.653605\pi$
$734$	−22.5091	−0.830827
$735$	10.8735	0.401077
$736$	199.916	7.36899
$737$	9.47030	0.348843
$738$	1.79974	0.0662495
$739$	−4.66784	−0.171709	−0.0858546	−	0.996308i	$-0.527362\pi$
$739$	−4.66784	−0.171709	−0.0858546	+	0.996308i	$0.527362\pi$
$740$	−66.2950	−2.43705
$741$	5.00306	0.183792
$742$	38.8815	1.42738
$743$	4.75426	0.174417	0.0872085	−	0.996190i	$-0.472205\pi$
$743$	4.75426	0.174417	0.0872085	+	0.996190i	$0.472205\pi$
$744$	83.1796	3.04951
$745$	−24.0016	−0.879350
$746$	−9.14494	−0.334820
$747$	−2.87806	−0.105303
$748$	−6.50356	−0.237794
$749$	−10.9391	−0.399706
$750$	−53.6915	−1.96053
$751$	4.10506	0.149796	0.0748979	−	0.997191i	$-0.476137\pi$
$751$	4.10506	0.149796	0.0748979	+	0.997191i	$0.476137\pi$
$752$	189.992	6.92829
$753$	−23.6642	−0.862371
$754$	−63.4032	−2.30901
$755$	−18.6745	−0.679634
$756$	−49.9001	−1.81485
$757$	16.6814	0.606296	0.303148	−	0.952943i	$-0.401962\pi$
$757$	16.6814	0.606296	0.303148	+	0.952943i	$0.401962\pi$
$758$	−29.3399	−1.06567
$759$	20.3218	0.737634
$760$	15.5946	0.565677
$761$	−40.2784	−1.46009	−0.730046	−	0.683398i	$-0.760501\pi$
$761$	−40.2784	−1.46009	−0.730046	+	0.683398i	$0.760501\pi$
$762$	−23.8928	−0.865544
$763$	−19.7681	−0.715655
$764$	132.171	4.78178
$765$	0.207633	0.00750699
$766$	53.0125	1.91542
$767$	−27.1195	−0.979228
$768$	−163.345	−5.89421
$769$	12.8078	0.461862	0.230931	−	0.972970i	$-0.425823\pi$
$769$	12.8078	0.461862	0.230931	+	0.972970i	$0.425823\pi$
$770$	11.6445	0.419640
$771$	−31.4600	−1.13300
$772$	57.7858	2.07976
$773$	−2.57445	−0.0925966	−0.0462983	−	0.998928i	$-0.514742\pi$
$773$	−2.57445	−0.0925966	−0.0462983	+	0.998928i	$0.514742\pi$
$774$	−7.29612	−0.262253
$775$	−13.3302	−0.478836
$776$	84.5410	3.03485
$777$	−20.7824	−0.745564
$778$	26.4507	0.948303
$779$	−2.91992	−0.104617
$780$	−42.7125	−1.52935
$781$	21.0189	0.752115
$782$	−12.3065	−0.440080
$783$	40.6461	1.45257
$784$	−79.3159	−2.83271
$785$	25.3609	0.905170
$786$	64.5154	2.30119
$787$	−41.2312	−1.46973	−0.734866	−	0.678212i	$-0.762755\pi$
$787$	−41.2312	−1.46973	−0.734866	+	0.678212i	$0.762755\pi$
$788$	−70.5220	−2.51224
$789$	13.4190	0.477730
$790$	−33.9470	−1.20778
$791$	24.8443	0.883363
$792$	4.11562	0.146242
$793$	−2.61015	−0.0926891
$794$	96.4202	3.42182
$795$	−21.3356	−0.756695
$796$	114.340	4.05268
$797$	−20.5250	−0.727034	−0.363517	−	0.931588i	$-0.618424\pi$
$797$	−20.5250	−0.727034	−0.363517	+	0.931588i	$0.618424\pi$
$798$	7.46918	0.264406
$799$	−6.75367	−0.238928
$800$	81.6491	2.88673
$801$	0.961673	0.0339790
$802$	−72.0698	−2.54487
$803$	−15.5673	−0.549356
$804$	−51.8602	−1.82897
$805$	16.3767	0.577202
$806$	−39.5209	−1.39206
$807$	−43.5405	−1.53270
$808$	117.818	4.14483
$809$	−22.1283	−0.777990	−0.388995	−	0.921240i	$-0.627178\pi$
$809$	−22.1283	−0.777990	−0.388995	+	0.921240i	$0.627178\pi$
$810$	34.1151	1.19868
$811$	33.8533	1.18875	0.594375	−	0.804188i	$-0.297399\pi$
$811$	33.8533	1.18875	0.594375	+	0.804188i	$0.297399\pi$
$812$	−70.3506	−2.46882
$813$	22.7911	0.799318
$814$	38.1928	1.33866
$815$	15.7732	0.552512
$816$	19.0589	0.667194
$817$	11.8373	0.414135
$818$	−99.8790	−3.49219
$819$	1.06404	0.0371807
$820$	24.9282	0.870531
$821$	19.7718	0.690042	0.345021	−	0.938595i	$-0.387872\pi$
$821$	19.7718	0.690042	0.345021	+	0.938595i	$0.387872\pi$
$822$	−12.1838	−0.424960
$823$	22.2353	0.775075	0.387537	−	0.921854i	$-0.373326\pi$
$823$	22.2353	0.775075	0.387537	+	0.921854i	$0.373326\pi$
$824$	41.0066	1.42853
$825$	8.29978	0.288961
$826$	−40.4873	−1.40873
$827$	49.9926	1.73841	0.869206	−	0.494450i	$-0.164631\pi$
$827$	49.9926	1.73841	0.869206	+	0.494450i	$0.164631\pi$
$828$	8.84345	0.307331
$829$	−33.0179	−1.14676	−0.573379	−	0.819290i	$-0.694368\pi$
$829$	−33.0179	−1.14676	−0.573379	+	0.819290i	$0.694368\pi$
$830$	−53.6365	−1.86175
$831$	19.1445	0.664115
$832$	134.429	4.66048
$833$	2.81945	0.0976883
$834$	−64.8730	−2.24637
$835$	0.00847241	0.000293200 0
$836$	−10.2018	−0.352838
$837$	25.3358	0.875735
$838$	105.129	3.63161
$839$	22.3431	0.771369	0.385684	−	0.922631i	$-0.373965\pi$
$839$	22.3431	0.771369	0.385684	+	0.922631i	$0.373965\pi$
$840$	−41.7359	−1.44003
$841$	28.3041	0.976002
$842$	12.7696	0.440069
$843$	1.39195	0.0479414
$844$	121.856	4.19447
$845$	−5.88937	−0.202600
$846$	6.52989	0.224502
$847$	12.6733	0.435460
$848$	155.630	5.34437
$849$	−47.1602	−1.61853
$850$	−5.02620	−0.172397
$851$	53.7137	1.84128
$852$	−115.101	−3.94331
$853$	16.1099	0.551592	0.275796	−	0.961216i	$-0.411059\pi$
$853$	16.1099	0.551592	0.275796	+	0.961216i	$0.411059\pi$
$854$	−3.89675	−0.133344
$855$	0.325705	0.0111389
$856$	−72.0536	−2.46274
$857$	−49.2768	−1.68326	−0.841631	−	0.540053i	$-0.818404\pi$
$857$	−49.2768	−1.68326	−0.841631	+	0.540053i	$0.818404\pi$
$858$	24.6068	0.840064
$859$	−38.3647	−1.30899	−0.654494	−	0.756067i	$-0.727118\pi$
$859$	−38.3647	−1.30899	−0.654494	+	0.756067i	$0.727118\pi$
$860$	−101.058	−3.44606
$861$	7.81458	0.266320
$862$	73.6734	2.50932
$863$	4.61485	0.157091	0.0785456	−	0.996911i	$-0.474972\pi$
$863$	4.61485	0.157091	0.0785456	+	0.996911i	$0.474972\pi$
$864$	−155.185	−5.27950
$865$	5.24288	0.178263
$866$	57.8656	1.96635
$867$	27.6628	0.939479
$868$	−43.8514	−1.48841
$869$	14.5352	0.493074
$870$	51.9410	1.76096
$871$	16.1273	0.546453
$872$	−130.209	−4.40942
$873$	1.76570	0.0597598
$874$	−19.3047	−0.652990
$875$	18.5263	0.626305
$876$	85.2476	2.88025
$877$	−3.22479	−0.108894	−0.0544468	−	0.998517i	$-0.517340\pi$
$877$	−3.22479	−0.108894	−0.0544468	+	0.998517i	$0.517340\pi$
$878$	19.5647	0.660275
$879$	−6.57819	−0.221877
$880$	46.6094	1.57120
$881$	−0.585620	−0.0197300	−0.00986502	−	0.999951i	$-0.503140\pi$
$881$	−0.585620	−0.0197300	−0.00986502	+	0.999951i	$0.503140\pi$
$882$	−2.72603	−0.0917904
$883$	−41.6107	−1.40031	−0.700155	−	0.713991i	$-0.746886\pi$
$883$	−41.6107	−1.40031	−0.700155	+	0.713991i	$0.746886\pi$
$884$	−11.0751	−0.372497
$885$	22.2168	0.746808
$886$	24.7275	0.830737
$887$	17.3700	0.583228	0.291614	−	0.956536i	$-0.405808\pi$
$887$	17.3700	0.583228	0.291614	+	0.956536i	$0.405808\pi$
$888$	−136.889	−4.59370
$889$	8.24424	0.276503
$890$	17.9221	0.600749
$891$	−14.6072	−0.489359
$892$	−47.4756	−1.58960
$893$	−10.5942	−0.354520
$894$	−75.7200	−2.53246
$895$	−6.27227	−0.209659
$896$	107.895	3.60453
$897$	34.6067	1.15548
$898$	−50.2530	−1.67697
$899$	35.7192	1.19130
$900$	3.61182	0.120394
$901$	−5.53221	−0.184305
$902$	−14.3612	−0.478177
$903$	−31.6801	−1.05425
$904$	163.644	5.44273
$905$	−38.1267	−1.26737
$906$	−58.9141	−1.95729
$907$	−32.5385	−1.08042	−0.540211	−	0.841530i	$-0.681656\pi$
$907$	−32.5385	−1.08042	−0.540211	+	0.841530i	$0.681656\pi$
$908$	−74.1652	−2.46126
$909$	2.46071	0.0816166
$910$	19.8299	0.657354
$911$	−32.8722	−1.08910	−0.544552	−	0.838727i	$-0.683300\pi$
$911$	−32.8722	−1.08910	−0.544552	+	0.838727i	$0.683300\pi$
$912$	29.8968	0.989981
$913$	22.9658	0.760056
$914$	−70.9583	−2.34709
$915$	2.13828	0.0706893
$916$	−115.646	−3.82104
$917$	−22.2612	−0.735129
$918$	9.55295	0.315294
$919$	58.0395	1.91455	0.957274	−	0.289182i	$-0.0933834\pi$
$919$	58.0395	1.91455	0.957274	+	0.289182i	$0.0933834\pi$
$920$	107.870	3.55636
$921$	12.9620	0.427113
$922$	88.6565	2.91975
$923$	35.7938	1.17817
$924$	27.3032	0.898208
$925$	21.9376	0.721305
$926$	93.8222	3.08319
$927$	0.856451	0.0281295
$928$	−218.784	−7.18193
$929$	−32.0482	−1.05147	−0.525734	−	0.850649i	$-0.676209\pi$
$929$	−32.0482	−1.05147	−0.525734	+	0.850649i	$0.676209\pi$
$930$	32.3762	1.06166
$931$	4.42275	0.144950
$932$	67.6885	2.21721
$933$	−21.8693	−0.715968
$934$	−47.0169	−1.53844
$935$	−1.65683	−0.0541841
$936$	7.00863	0.229084
$937$	4.59366	0.150068	0.0750342	−	0.997181i	$-0.476093\pi$
$937$	4.59366	0.150068	0.0750342	+	0.997181i	$0.476093\pi$
$938$	24.0768	0.786135
$939$	27.7421	0.905328
$940$	90.4454	2.95000
$941$	−7.13058	−0.232450	−0.116225	−	0.993223i	$-0.537079\pi$
$941$	−7.13058	−0.232450	−0.116225	+	0.993223i	$0.537079\pi$
$942$	80.0085	2.60682
$943$	−20.1974	−0.657718
$944$	−162.058	−5.27453
$945$	−12.7124	−0.413535
$946$	58.2201	1.89290
$947$	−11.0836	−0.360169	−0.180084	−	0.983651i	$-0.557637\pi$
$947$	−11.0836	−0.360169	−0.180084	+	0.983651i	$0.557637\pi$
$948$	−79.5962	−2.58516
$949$	−26.5100	−0.860551
$950$	−7.88437	−0.255803
$951$	1.66708	0.0540587
$952$	−10.8219	−0.350740
$953$	−17.2942	−0.560214	−0.280107	−	0.959969i	$-0.590370\pi$
$953$	−17.2942	−0.560214	−0.280107	+	0.959969i	$0.590370\pi$
$954$	5.34891	0.173177
$955$	33.6715	1.08959
$956$	−44.1986	−1.42949
$957$	−22.2398	−0.718910
$958$	−60.5361	−1.95583
$959$	4.20406	0.135756
$960$	−110.126	−3.55431
$961$	−8.73528	−0.281783
$962$	65.0398	2.09697
$963$	−1.50489	−0.0484944
$964$	102.679	3.30707
$965$	14.7213	0.473897
$966$	51.6650	1.66229
$967$	−30.6001	−0.984031	−0.492016	−	0.870586i	$-0.663740\pi$
$967$	−30.6001	−0.984031	−0.492016	+	0.870586i	$0.663740\pi$
$968$	83.4765	2.68304
$969$	−1.06274	−0.0341403
$970$	32.9061	1.05655
$971$	−54.1496	−1.73774	−0.868872	−	0.495036i	$-0.835155\pi$
$971$	−54.1496	−1.73774	−0.868872	+	0.495036i	$0.835155\pi$
$972$	−13.2588	−0.425275
$973$	22.3845	0.717616
$974$	100.432	3.21803
$975$	14.1340	0.452649
$976$	−15.5975	−0.499263
$977$	9.65440	0.308872	0.154436	−	0.988003i	$-0.450644\pi$
$977$	9.65440	0.308872	0.154436	+	0.988003i	$0.450644\pi$
$978$	49.7613	1.59119
$979$	−7.67376	−0.245255
$980$	−37.7582	−1.20614
$981$	−2.71950	−0.0868268
$982$	68.8202	2.19614
$983$	33.3082	1.06237	0.531183	−	0.847257i	$-0.321748\pi$
$983$	33.3082	1.06237	0.531183	+	0.847257i	$0.321748\pi$
$984$	51.4730	1.64090
$985$	−17.9660	−0.572444
$986$	13.4680	0.428909
$987$	28.3531	0.902491
$988$	−17.3731	−0.552711
$989$	81.8797	2.60362
$990$	1.60193	0.0509128
$991$	25.0874	0.796929	0.398464	−	0.917184i	$-0.369543\pi$
$991$	25.0874	0.796929	0.398464	+	0.917184i	$0.369543\pi$
$992$	−136.374	−4.32988
$993$	23.9040	0.758570
$994$	53.4373	1.69493
$995$	29.1290	0.923451
$996$	−125.763	−3.98494
$997$	−26.4911	−0.838982	−0.419491	−	0.907760i	$-0.637791\pi$
$997$	−26.4911	−0.838982	−0.419491	+	0.907760i	$0.637791\pi$
$998$	62.1164	1.96626
$999$	−41.6954	−1.31918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.1	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.1	✓	99	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)

\(f(q)\)	\(=\)	\(q-2.79086 q^{2} -1.66708 q^{3} +5.78891 q^{4} +1.47477 q^{5} +4.65258 q^{6} -1.60538 q^{7} -10.5743 q^{8} -0.220852 q^{9} +O(q^{10})\)	\(q-2.79086 q^{2} -1.66708 q^{3} +5.78891 q^{4} +1.47477 q^{5} +4.65258 q^{6} -1.60538 q^{7} -10.5743 q^{8} -0.220852 q^{9} -4.11587 q^{10} +1.76231 q^{11} -9.65056 q^{12} +3.00110 q^{13} +4.48040 q^{14} -2.45855 q^{15} +17.9336 q^{16} -0.637489 q^{17} +0.616367 q^{18} -1.00000 q^{19} +8.53728 q^{20} +2.67630 q^{21} -4.91836 q^{22} -6.91710 q^{23} +17.6282 q^{24} -2.82507 q^{25} -8.37564 q^{26} +5.36941 q^{27} -9.29341 q^{28} +7.56995 q^{29} +6.86147 q^{30} +4.71855 q^{31} -28.9017 q^{32} -2.93791 q^{33} +1.77914 q^{34} -2.36756 q^{35} -1.27849 q^{36} -7.76535 q^{37} +2.79086 q^{38} -5.00306 q^{39} -15.5946 q^{40} +2.91992 q^{41} -7.46918 q^{42} -11.8373 q^{43} +10.2018 q^{44} -0.325705 q^{45} +19.3047 q^{46} +10.5942 q^{47} -29.8968 q^{48} -4.42275 q^{49} +7.88437 q^{50} +1.06274 q^{51} +17.3731 q^{52} +8.67812 q^{53} -14.9853 q^{54} +2.59899 q^{55} +16.9758 q^{56} +1.66708 q^{57} -21.1267 q^{58} -9.03653 q^{59} -14.2323 q^{60} -0.869732 q^{61} -13.1688 q^{62} +0.354552 q^{63} +44.7932 q^{64} +4.42591 q^{65} +8.19929 q^{66} +5.37380 q^{67} -3.69037 q^{68} +11.5313 q^{69} +6.60754 q^{70} +11.9269 q^{71} +2.33536 q^{72} -8.83344 q^{73} +21.6720 q^{74} +4.70960 q^{75} -5.78891 q^{76} -2.82918 q^{77} +13.9628 q^{78} +8.24783 q^{79} +26.4479 q^{80} -8.28867 q^{81} -8.14910 q^{82} +13.0316 q^{83} +15.4928 q^{84} -0.940147 q^{85} +33.0362 q^{86} -12.6197 q^{87} -18.6352 q^{88} -4.35438 q^{89} +0.908997 q^{90} -4.81791 q^{91} -40.0424 q^{92} -7.86619 q^{93} -29.5669 q^{94} -1.47477 q^{95} +48.1813 q^{96} -7.99494 q^{97} +12.3433 q^{98} -0.389209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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