LMFDB - Embedded newform 1849.4.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.55366 q^{2} -4.29077 q^{3} +12.7358 q^{4} -2.70051 q^{5} +19.5387 q^{6} +9.48123 q^{7} -21.5655 q^{8} -8.58929 q^{9} +O(q^{10})$	\(q-4.55366 q^{2} -4.29077 q^{3} +12.7358 q^{4} -2.70051 q^{5} +19.5387 q^{6} +9.48123 q^{7} -21.5655 q^{8} -8.58929 q^{9} +12.2972 q^{10} -16.2615 q^{11} -54.6466 q^{12} -58.6297 q^{13} -43.1743 q^{14} +11.5873 q^{15} -3.68497 q^{16} +67.1818 q^{17} +39.1127 q^{18} +41.5179 q^{19} -34.3933 q^{20} -40.6818 q^{21} +74.0492 q^{22} -85.8598 q^{23} +92.5324 q^{24} -117.707 q^{25} +266.980 q^{26} +152.705 q^{27} +120.752 q^{28} +162.947 q^{29} -52.7645 q^{30} +270.662 q^{31} +189.304 q^{32} +69.7742 q^{33} -305.923 q^{34} -25.6041 q^{35} -109.392 q^{36} -226.823 q^{37} -189.058 q^{38} +251.566 q^{39} +58.2377 q^{40} -360.349 q^{41} +185.251 q^{42} -207.103 q^{44} +23.1954 q^{45} +390.977 q^{46} +437.762 q^{47} +15.8114 q^{48} -253.106 q^{49} +535.999 q^{50} -288.262 q^{51} -746.698 q^{52} -377.821 q^{53} -695.369 q^{54} +43.9142 q^{55} -204.467 q^{56} -178.144 q^{57} -742.008 q^{58} -279.572 q^{59} +147.574 q^{60} +30.6533 q^{61} -1232.50 q^{62} -81.4370 q^{63} -832.546 q^{64} +158.330 q^{65} -317.728 q^{66} +904.150 q^{67} +855.617 q^{68} +368.405 q^{69} +116.593 q^{70} -121.791 q^{71} +185.232 q^{72} -372.695 q^{73} +1032.87 q^{74} +505.055 q^{75} +528.765 q^{76} -154.179 q^{77} -1145.55 q^{78} +730.616 q^{79} +9.95129 q^{80} -423.313 q^{81} +1640.91 q^{82} -73.2890 q^{83} -518.117 q^{84} -181.425 q^{85} -699.170 q^{87} +350.686 q^{88} +1156.75 q^{89} -105.624 q^{90} -555.881 q^{91} -1093.50 q^{92} -1161.35 q^{93} -1993.42 q^{94} -112.119 q^{95} -812.259 q^{96} -446.639 q^{97} +1152.56 q^{98} +139.674 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} + 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} + 386 q^{18} - 12 q^{19} - 108 q^{20} - 408 q^{21} - 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} - 1493 q^{26} - 10 q^{27} + 242 q^{28} - 208 q^{29} + 48 q^{30} - 932 q^{31} + 1124 q^{32} - 254 q^{33} - 765 q^{34} - 1452 q^{35} + 747 q^{36} + 90 q^{37} - 1213 q^{38} + 1610 q^{39} - 1693 q^{40} - 1354 q^{41} + 16 q^{42} - 2704 q^{44} - 4508 q^{45} - 233 q^{46} - 3484 q^{47} + 376 q^{48} + 1324 q^{49} + 408 q^{50} - 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} + 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} - 1172 q^{61} + 1546 q^{62} + 3686 q^{63} + 606 q^{64} - 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} - 136 q^{69} + 1310 q^{70} - 162 q^{71} + 5814 q^{72} - 746 q^{73} - 4332 q^{74} - 236 q^{75} - 1338 q^{76} - 2024 q^{77} - 2782 q^{78} - 2656 q^{79} + 5713 q^{80} - 86 q^{81} + 4168 q^{82} - 3514 q^{83} - 4269 q^{84} + 7558 q^{85} - 10278 q^{87} - 11692 q^{88} - 2640 q^{89} - 8286 q^{90} + 5946 q^{91} - 4271 q^{92} + 2 q^{93} - 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} + 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 + 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 + 386 * q^18 - 12 * q^19 - 108 * q^20 - 408 * q^21 - 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 - 1493 * q^26 - 10 * q^27 + 242 * q^28 - 208 * q^29 + 48 * q^30 - 932 * q^31 + 1124 * q^32 - 254 * q^33 - 765 * q^34 - 1452 * q^35 + 747 * q^36 + 90 * q^37 - 1213 * q^38 + 1610 * q^39 - 1693 * q^40 - 1354 * q^41 + 16 * q^42 - 2704 * q^44 - 4508 * q^45 - 233 * q^46 - 3484 * q^47 + 376 * q^48 + 1324 * q^49 + 408 * q^50 - 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 + 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 - 1172 * q^61 + 1546 * q^62 + 3686 * q^63 + 606 * q^64 - 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 - 136 * q^69 + 1310 * q^70 - 162 * q^71 + 5814 * q^72 - 746 * q^73 - 4332 * q^74 - 236 * q^75 - 1338 * q^76 - 2024 * q^77 - 2782 * q^78 - 2656 * q^79 + 5713 * q^80 - 86 * q^81 + 4168 * q^82 - 3514 * q^83 - 4269 * q^84 + 7558 * q^85 - 10278 * q^87 - 11692 * q^88 - 2640 * q^89 - 8286 * q^90 + 5946 * q^91 - 4271 * q^92 + 2 * q^93 - 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 + 2826 * q^98 - 8174 * 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 $

$2$	−4.55366	−1.60996	−0.804982	−	0.593300i	$-0.797825\pi$
$2$	−4.55366	−1.60996	−0.804982	+	0.593300i	$0.797825\pi$
$3$	−4.29077	−0.825759	−0.412880	−	0.910786i	$-0.635477\pi$
$3$	−4.29077	−0.825759	−0.412880	+	0.910786i	$0.635477\pi$
$4$	12.7358	1.59198
$5$	−2.70051	−0.241541	−0.120770	−	0.992680i	$-0.538536\pi$
$5$	−2.70051	−0.241541	−0.120770	+	0.992680i	$0.538536\pi$
$6$	19.5387	1.32944
$7$	9.48123	0.511938	0.255969	−	0.966685i	$-0.417605\pi$
$7$	9.48123	0.511938	0.255969	+	0.966685i	$0.417605\pi$
$8$	−21.5655	−0.953067
$9$	−8.58929	−0.318122
$10$	12.2972	0.388872
$11$	−16.2615	−0.445729	−0.222864	−	0.974849i	$-0.571541\pi$
$11$	−16.2615	−0.445729	−0.222864	+	0.974849i	$0.571541\pi$
$12$	−54.6466	−1.31459
$13$	−58.6297	−1.25084	−0.625421	−	0.780288i	$-0.715073\pi$
$13$	−58.6297	−1.25084	−0.625421	+	0.780288i	$0.715073\pi$
$14$	−43.1743	−0.824202
$15$	11.5873	0.199455
$16$	−3.68497	−0.0575776
$17$	67.1818	0.958469	0.479235	−	0.877687i	$-0.340914\pi$
$17$	67.1818	0.958469	0.479235	+	0.877687i	$0.340914\pi$
$18$	39.1127	0.512164
$19$	41.5179	0.501308	0.250654	−	0.968077i	$-0.419354\pi$
$19$	41.5179	0.501308	0.250654	+	0.968077i	$0.419354\pi$
$20$	−34.3933	−0.384528
$21$	−40.6818	−0.422738
$22$	74.0492	0.717607
$23$	−85.8598	−0.778392	−0.389196	−	0.921155i	$-0.627247\pi$
$23$	−85.8598	−0.778392	−0.389196	+	0.921155i	$0.627247\pi$
$24$	92.5324	0.787004
$25$	−117.707	−0.941658
$26$	266.980	2.01381
$27$	152.705	1.08845
$28$	120.752	0.814996
$29$	162.947	1.04340	0.521700	−	0.853129i	$-0.325298\pi$
$29$	162.947	1.04340	0.521700	+	0.853129i	$0.325298\pi$
$30$	−52.7645	−0.321114
$31$	270.662	1.56814	0.784069	−	0.620673i	$-0.213141\pi$
$31$	270.662	1.56814	0.784069	+	0.620673i	$0.213141\pi$
$32$	189.304	1.04577
$33$	69.7742	0.368065
$34$	−305.923	−1.54310
$35$	−25.6041	−0.123654
$36$	−109.392	−0.506444
$37$	−226.823	−1.00782	−0.503911	−	0.863755i	$-0.668106\pi$
$37$	−226.823	−1.00782	−0.503911	+	0.863755i	$0.668106\pi$
$38$	−189.058	−0.807088
$39$	251.566	1.03289
$40$	58.2377	0.230205
$41$	−360.349	−1.37261	−0.686305	−	0.727314i	$-0.740768\pi$
$41$	−360.349	−1.37261	−0.686305	+	0.727314i	$0.740768\pi$
$42$	185.251	0.680592
$43$	0	0
$43$	0	0
$44$	−207.103	−0.709592
$45$	23.1954	0.0768394
$46$	390.977	1.25318
$47$	437.762	1.35860	0.679299	−	0.733862i	$-0.262284\pi$
$47$	437.762	1.35860	0.679299	+	0.733862i	$0.262284\pi$
$48$	15.8114	0.0475453
$49$	−253.106	−0.737919
$50$	535.999	1.51603
$51$	−288.262	−0.791465
$52$	−746.698	−1.99132
$53$	−377.821	−0.979203	−0.489601	−	0.871946i	$-0.662858\pi$
$53$	−377.821	−0.979203	−0.489601	+	0.871946i	$0.662858\pi$
$54$	−695.369	−1.75237
$55$	43.9142	0.107662
$56$	−204.467	−0.487912
$57$	−178.144	−0.413960
$58$	−742.008	−1.67983
$59$	−279.572	−0.616901	−0.308450	−	0.951240i	$-0.599810\pi$
$59$	−279.572	−0.616901	−0.308450	+	0.951240i	$0.599810\pi$
$60$	147.574	0.317528
$61$	30.6533	0.0643403	0.0321701	−	0.999482i	$-0.489758\pi$
$61$	30.6533	0.0643403	0.0321701	+	0.999482i	$0.489758\pi$
$62$	−1232.50	−2.52465
$63$	−81.4370	−0.162859
$64$	−832.546	−1.62607
$65$	158.330	0.302129
$66$	−317.728	−0.592570
$67$	904.150	1.64865	0.824325	−	0.566117i	$-0.191555\pi$
$67$	904.150	1.64865	0.824325	+	0.566117i	$0.191555\pi$
$68$	855.617	1.52587
$69$	368.405	0.642764
$70$	116.593	0.199078
$71$	−121.791	−0.203577	−0.101788	−	0.994806i	$-0.532456\pi$
$71$	−121.791	−0.203577	−0.101788	+	0.994806i	$0.532456\pi$
$72$	185.232	0.303191
$73$	−372.695	−0.597543	−0.298771	−	0.954325i	$-0.596577\pi$
$73$	−372.695	−0.597543	−0.298771	+	0.954325i	$0.596577\pi$
$74$	1032.87	1.62256
$75$	505.055	0.777583
$76$	528.765	0.798073
$77$	−154.179	−0.228186
$78$	−1145.55	−1.66292
$79$	730.616	1.04052	0.520258	−	0.854009i	$-0.325836\pi$
$79$	730.616	1.04052	0.520258	+	0.854009i	$0.325836\pi$
$80$	9.95129	0.0139073
$81$	−423.313	−0.580677
$82$	1640.91	2.20985
$83$	−73.2890	−0.0969218	−0.0484609	−	0.998825i	$-0.515432\pi$
$83$	−73.2890	−0.0969218	−0.0484609	+	0.998825i	$0.515432\pi$
$84$	−518.117	−0.672991
$85$	−181.425	−0.231509
$86$	0	0
$87$	−699.170	−0.861596
$88$	350.686	0.424809
$89$	1156.75	1.37769	0.688847	−	0.724906i	$-0.258117\pi$
$89$	1156.75	1.37769	0.688847	+	0.724906i	$0.258117\pi$
$90$	−105.624	−0.123709
$91$	−555.881	−0.640354
$92$	−1093.50	−1.23919
$93$	−1161.35	−1.29490
$94$	−1993.42	−2.18729
$95$	−112.119	−0.121086
$96$	−812.259	−0.863550
$97$	−446.639	−0.467519	−0.233760	−	0.972294i	$-0.575103\pi$
$97$	−446.639	−0.467519	−0.233760	+	0.972294i	$0.575103\pi$
$98$	1152.56	1.18802
$99$	139.674	0.141796
$100$	−1499.10	−1.49910
$101$	−1256.53	−1.23791	−0.618955	−	0.785426i	$-0.712444\pi$
$101$	−1256.53	−1.23791	−0.618955	+	0.785426i	$0.712444\pi$
$102$	1312.65	1.27423
$103$	1196.91	1.14500	0.572499	−	0.819905i	$-0.305974\pi$
$103$	1196.91	1.14500	0.572499	+	0.819905i	$0.305974\pi$
$104$	1264.38	1.19214
$105$	109.862	0.102108
$106$	1720.47	1.57648
$107$	−1724.07	−1.55768	−0.778842	−	0.627220i	$-0.784193\pi$
$107$	−1724.07	−1.55768	−0.778842	+	0.627220i	$0.784193\pi$
$108$	1944.83	1.73279
$109$	1367.97	1.20209	0.601044	−	0.799216i	$-0.294752\pi$
$109$	1367.97	1.20209	0.601044	+	0.799216i	$0.294752\pi$
$110$	−199.971	−0.173331
$111$	973.244	0.832219
$112$	−34.9380	−0.0294762
$113$	1850.28	1.54035	0.770175	−	0.637833i	$-0.220169\pi$
$113$	1850.28	1.54035	0.770175	+	0.637833i	$0.220169\pi$
$114$	811.206	0.666460
$115$	231.865	0.188013
$116$	2075.27	1.66107
$117$	503.587	0.397920
$118$	1273.08	0.993188
$119$	636.966	0.490677
$120$	−249.885	−0.190094
$121$	−1066.56	−0.801326
$122$	−139.585	−0.103585
$123$	1546.17	1.13344
$124$	3447.11	2.49645
$125$	655.433	0.468990
$126$	370.837	0.262197
$127$	1723.13	1.20396	0.601981	−	0.798510i	$-0.294378\pi$
$127$	1723.13	1.20396	0.601981	+	0.798510i	$0.294378\pi$
$128$	2276.70	1.57214
$129$	0	0
$130$	−720.981	−0.486417
$131$	−333.186	−0.222219	−0.111109	−	0.993808i	$-0.535440\pi$
$131$	−333.186	−0.222219	−0.111109	+	0.993808i	$0.535440\pi$
$132$	888.634	0.585952
$133$	393.641	0.256639
$134$	−4117.20	−2.65427
$135$	−412.382	−0.262905
$136$	−1448.81	−0.913486
$137$	−2522.39	−1.57301	−0.786505	−	0.617584i	$-0.788112\pi$
$137$	−2522.39	−1.57301	−0.786505	+	0.617584i	$0.788112\pi$
$138$	−1677.59	−1.03483
$139$	2241.41	1.36772	0.683862	−	0.729612i	$-0.260299\pi$
$139$	2241.41	1.36772	0.683862	+	0.729612i	$0.260299\pi$
$140$	−326.091	−0.196855
$141$	−1878.33	−1.12187
$142$	554.596	0.327751
$143$	953.404	0.557536
$144$	31.6512	0.0183167
$145$	−440.041	−0.252023
$146$	1697.13	0.962022
$147$	1086.02	0.609343
$148$	−2888.78	−1.60443
$149$	816.248	0.448789	0.224395	−	0.974498i	$-0.427960\pi$
$149$	816.248	0.448789	0.224395	+	0.974498i	$0.427960\pi$
$150$	−2299.85	−1.25188
$151$	33.6537	0.0181371	0.00906853	−	0.999959i	$-0.497113\pi$
$151$	33.6537	0.0181371	0.00906853	+	0.999959i	$0.497113\pi$
$152$	−895.352	−0.477781
$153$	−577.044	−0.304910
$154$	702.078	0.367370
$155$	−730.924	−0.378769
$156$	3203.91	1.64435
$157$	1660.28	0.843979	0.421990	−	0.906601i	$-0.361332\pi$
$157$	1660.28	0.843979	0.421990	+	0.906601i	$0.361332\pi$
$158$	−3326.98	−1.67519
$159$	1621.14	0.808586
$160$	−511.216	−0.252595
$161$	−814.057	−0.398489
$162$	1927.63	0.934868
$163$	3488.21	1.67618	0.838091	−	0.545531i	$-0.183672\pi$
$163$	3488.21	1.67618	0.838091	+	0.545531i	$0.183672\pi$
$164$	−4589.34	−2.18517
$165$	−188.426	−0.0889026
$166$	333.733	0.156041
$167$	1841.55	0.853314	0.426657	−	0.904414i	$-0.359691\pi$
$167$	1841.55	0.853314	0.426657	+	0.904414i	$0.359691\pi$
$168$	877.321	0.402898
$169$	1240.44	0.564605
$170$	826.148	0.372722
$171$	−356.609	−0.159477
$172$	0	0
$173$	2820.94	1.23972	0.619862	−	0.784711i	$-0.287189\pi$
$173$	2820.94	1.23972	0.619862	+	0.784711i	$0.287189\pi$
$174$	3183.78	1.38714
$175$	−1116.01	−0.482071
$176$	59.9230	0.0256640
$177$	1199.58	0.509412
$178$	−5267.43	−2.21804
$179$	1287.81	0.537738	0.268869	−	0.963177i	$-0.413350\pi$
$179$	1287.81	0.537738	0.268869	+	0.963177i	$0.413350\pi$
$180$	295.414	0.122327
$181$	2583.98	1.06114	0.530569	−	0.847642i	$-0.321978\pi$
$181$	2583.98	1.06114	0.530569	+	0.847642i	$0.321978\pi$
$182$	2531.30	1.03095
$183$	−131.526	−0.0531296
$184$	1851.61	0.741860
$185$	612.537	0.243430
$186$	5288.39	2.08475
$187$	−1092.47	−0.427217
$188$	5575.26	2.16286
$189$	1447.84	0.557220
$190$	510.554	0.194945
$191$	−1810.98	−0.686064	−0.343032	−	0.939324i	$-0.611454\pi$
$191$	−1810.98	−0.686064	−0.343032	+	0.939324i	$0.611454\pi$
$192$	3572.26	1.34274
$193$	−3979.51	−1.48420	−0.742101	−	0.670288i	$-0.766171\pi$
$193$	−3979.51	−1.48420	−0.742101	+	0.670288i	$0.766171\pi$
$194$	2033.85	0.752688
$195$	−679.357	−0.249486
$196$	−3223.52	−1.17475
$197$	−2135.93	−0.772480	−0.386240	−	0.922398i	$-0.626226\pi$
$197$	−2135.93	−0.772480	−0.386240	+	0.922398i	$0.626226\pi$
$198$	−636.030	−0.228286
$199$	−2804.85	−0.999149	−0.499575	−	0.866271i	$-0.666510\pi$
$199$	−2804.85	−0.999149	−0.499575	+	0.866271i	$0.666510\pi$
$200$	2538.41	0.897464
$201$	−3879.50	−1.36139
$202$	5721.79	1.99299
$203$	1544.94	0.534156
$204$	−3671.26	−1.26000
$205$	973.124	0.331541
$206$	−5450.31	−1.84340
$207$	737.475	0.247623
$208$	216.048	0.0720205
$209$	−675.141	−0.223447
$210$	−500.272	−0.164391
$211$	2756.80	0.899459	0.449730	−	0.893165i	$-0.351520\pi$
$211$	2756.80	0.899459	0.449730	+	0.893165i	$0.351520\pi$
$212$	−4811.88	−1.55887
$213$	522.578	0.168105
$214$	7850.84	2.50781
$215$	0	0
$216$	−3293.16	−1.03737
$217$	2566.21	0.802790
$218$	−6229.27	−1.93532
$219$	1599.15	0.493427
$220$	559.285	0.171395
$221$	−3938.85	−1.19889
$222$	−4431.83	−1.33984
$223$	3779.12	1.13484	0.567418	−	0.823430i	$-0.307942\pi$
$223$	3779.12	1.13484	0.567418	+	0.823430i	$0.307942\pi$
$224$	1794.83	0.535367
$225$	1011.02	0.299562
$226$	−8425.54	−2.47991
$227$	−3727.76	−1.08996	−0.544979	−	0.838450i	$-0.683462\pi$
$227$	−3727.76	−1.08996	−0.544979	+	0.838450i	$0.683462\pi$
$228$	−2268.81	−0.659016
$229$	3616.46	1.04359	0.521796	−	0.853070i	$-0.325262\pi$
$229$	3616.46	1.04359	0.521796	+	0.853070i	$0.325262\pi$
$230$	−1055.84	−0.302695
$231$	661.545	0.188426
$232$	−3514.03	−0.994430
$233$	−52.8357	−0.0148557	−0.00742786	−	0.999972i	$-0.502364\pi$
$233$	−52.8357	−0.0148557	−0.00742786	+	0.999972i	$0.502364\pi$
$234$	−2293.17	−0.640636
$235$	−1182.18	−0.328157
$236$	−3560.58	−0.982095
$237$	−3134.91	−0.859215
$238$	−2900.53	−0.789972
$239$	−1707.71	−0.462187	−0.231094	−	0.972932i	$-0.574230\pi$
$239$	−1707.71	−0.462187	−0.231094	+	0.972932i	$0.574230\pi$
$240$	−42.6987	−0.0114841
$241$	−604.111	−0.161470	−0.0807348	−	0.996736i	$-0.525727\pi$
$241$	−604.111	−0.161470	−0.0807348	+	0.996736i	$0.525727\pi$
$242$	4856.78	1.29011
$243$	−2306.71	−0.608952
$244$	390.396	0.102429
$245$	683.516	0.178238
$246$	−7040.75	−1.82480
$247$	−2434.18	−0.627057
$248$	−5836.94	−1.49454
$249$	314.466	0.0800341
$250$	−2984.62	−0.755056
$251$	−1637.24	−0.411720	−0.205860	−	0.978581i	$-0.565999\pi$
$251$	−1637.24	−0.411720	−0.205860	+	0.978581i	$0.565999\pi$
$252$	−1037.17	−0.259268
$253$	1396.21	0.346952
$254$	−7846.56	−1.93833
$255$	778.453	0.191171
$256$	−3706.97	−0.905022
$257$	−7248.10	−1.75924	−0.879619	−	0.475679i	$-0.842202\pi$
$257$	−7248.10	−1.75924	−0.879619	+	0.475679i	$0.842202\pi$
$258$	0	0
$259$	−2150.56	−0.515943
$260$	2016.47	0.480984
$261$	−1399.60	−0.331928
$262$	1517.22	0.357764
$263$	4668.09	1.09447	0.547237	−	0.836977i	$-0.315679\pi$
$263$	4668.09	1.09447	0.547237	+	0.836977i	$0.315679\pi$
$264$	−1504.71	−0.350790
$265$	1020.31	0.236517
$266$	−1792.51	−0.413179
$267$	−4963.33	−1.13764
$268$	11515.1	2.62462
$269$	2919.35	0.661696	0.330848	−	0.943684i	$-0.392665\pi$
$269$	2919.35	0.661696	0.330848	+	0.943684i	$0.392665\pi$
$270$	1877.85	0.423268
$271$	−4747.60	−1.06419	−0.532096	−	0.846684i	$-0.678595\pi$
$271$	−4747.60	−1.06419	−0.532096	+	0.846684i	$0.678595\pi$
$272$	−247.563	−0.0551864
$273$	2385.16	0.528778
$274$	11486.1	2.53249
$275$	1914.09	0.419724
$276$	4691.95	1.02327
$277$	429.145	0.0930861	0.0465431	−	0.998916i	$-0.485180\pi$
$277$	429.145	0.0930861	0.0465431	+	0.998916i	$0.485180\pi$
$278$	−10206.6	−2.20198
$279$	−2324.79	−0.498859
$280$	552.165	0.117851
$281$	59.2317	0.0125746	0.00628731	−	0.999980i	$-0.497999\pi$
$281$	59.2317	0.0125746	0.00628731	+	0.999980i	$0.497999\pi$
$282$	8553.30	1.80618
$283$	−5470.70	−1.14911	−0.574557	−	0.818464i	$-0.694826\pi$
$283$	−5470.70	−1.14911	−0.574557	+	0.818464i	$0.694826\pi$
$284$	−1551.11	−0.324090
$285$	481.079	0.0999882
$286$	−4341.48	−0.897612
$287$	−3416.55	−0.702691
$288$	−1625.98	−0.332681
$289$	−399.606	−0.0813364
$290$	2003.80	0.405748
$291$	1916.43	0.386058
$292$	−4746.58	−0.951277
$293$	2179.76	0.434617	0.217308	−	0.976103i	$-0.430272\pi$
$293$	2179.76	0.434617	0.217308	+	0.976103i	$0.430272\pi$
$294$	−4945.37	−0.981020
$295$	754.986	0.149007
$296$	4891.54	0.960523
$297$	−2483.21	−0.485154
$298$	−3716.92	−0.722534
$299$	5033.93	0.973645
$300$	6432.30	1.23790
$301$	0	0
$302$	−153.247	−0.0292000
$303$	5391.46	1.02222
$304$	−152.992	−0.0288641
$305$	−82.7796	−0.0155408
$306$	2627.66	0.490894
$307$	7118.86	1.32344	0.661718	−	0.749753i	$-0.269827\pi$
$307$	7118.86	1.32344	0.661718	+	0.749753i	$0.269827\pi$
$308$	−1963.60	−0.363267
$309$	−5135.66	−0.945493
$310$	3328.38	0.609805
$311$	3986.21	0.726808	0.363404	−	0.931632i	$-0.381614\pi$
$311$	3986.21	0.726808	0.363404	+	0.931632i	$0.381614\pi$
$312$	−5425.14	−0.984418
$313$	9318.69	1.68282	0.841411	−	0.540395i	$-0.181725\pi$
$313$	9318.69	1.68282	0.841411	+	0.540395i	$0.181725\pi$
$314$	−7560.35	−1.35878
$315$	219.921	0.0393370
$316$	9305.01	1.65648
$317$	−8476.89	−1.50192	−0.750961	−	0.660346i	$-0.770409\pi$
$317$	−8476.89	−1.50192	−0.750961	+	0.660346i	$0.770409\pi$
$318$	−7382.15	−1.30179
$319$	−2649.76	−0.465073
$320$	2248.30	0.392761
$321$	7397.59	1.28627
$322$	3706.94	0.641552
$323$	2789.25	0.480489
$324$	−5391.25	−0.924426
$325$	6901.14	1.17787
$326$	−15884.1	−2.69859
$327$	−5869.64	−0.992635
$328$	7771.08	1.30819
$329$	4150.52	0.695518
$330$	858.028	0.143130
$331$	−1225.47	−0.203499	−0.101749	−	0.994810i	$-0.532444\pi$
$331$	−1225.47	−0.203499	−0.101749	+	0.994810i	$0.532444\pi$
$332$	−933.398	−0.154298
$333$	1948.25	0.320610
$334$	−8385.80	−1.37380
$335$	−2441.67	−0.398216
$336$	149.911	0.0243402
$337$	1486.27	0.240244	0.120122	−	0.992759i	$-0.461671\pi$
$337$	1486.27	0.240244	0.120122	+	0.992759i	$0.461671\pi$
$338$	−5648.53	−0.908993
$339$	−7939.12	−1.27196
$340$	−2310.60	−0.368559
$341$	−4401.36	−0.698964
$342$	1623.88	0.256752
$343$	−5651.82	−0.889708
$344$	0	0
$345$	−994.881	−0.155254
$346$	−12845.6	−1.99591
$347$	8460.85	1.30894	0.654470	−	0.756088i	$-0.272892\pi$
$347$	8460.85	1.30894	0.654470	+	0.756088i	$0.272892\pi$
$348$	−8904.52	−1.37165
$349$	11788.1	1.80803	0.904015	−	0.427501i	$-0.140606\pi$
$349$	11788.1	1.80803	0.904015	+	0.427501i	$0.140606\pi$
$350$	5081.93	0.776116
$351$	−8953.07	−1.36148
$352$	−3078.36	−0.466128
$353$	−4732.50	−0.713557	−0.356778	−	0.934189i	$-0.616125\pi$
$353$	−4732.50	−0.713557	−0.356778	+	0.934189i	$0.616125\pi$
$354$	−5462.48	−0.820134
$355$	328.898	0.0491721
$356$	14732.1	2.19326
$357$	−2733.08	−0.405181
$358$	−5864.23	−0.865739
$359$	−6028.18	−0.886226	−0.443113	−	0.896466i	$-0.646126\pi$
$359$	−6028.18	−0.886226	−0.443113	+	0.896466i	$0.646126\pi$
$360$	−500.220	−0.0732331
$361$	−5135.27	−0.748690
$362$	−11766.6	−1.70839
$363$	4576.39	0.661702
$364$	−7079.62	−1.01943
$365$	1006.47	0.144331
$366$	598.927	0.0855367
$367$	−2429.27	−0.345523	−0.172761	−	0.984964i	$-0.555269\pi$
$367$	−2429.27	−0.345523	−0.172761	+	0.984964i	$0.555269\pi$
$368$	316.391	0.0448180
$369$	3095.14	0.436657
$370$	−2789.29	−0.391914
$371$	−3582.21	−0.501292
$372$	−14790.7	−2.06146
$373$	8992.11	1.24824	0.624120	−	0.781328i	$-0.285458\pi$
$373$	8992.11	1.24824	0.624120	+	0.781328i	$0.285458\pi$
$374$	4974.76	0.687804
$375$	−2812.31	−0.387273
$376$	−9440.53	−1.29484
$377$	−9553.55	−1.30513
$378$	−6592.96	−0.897104
$379$	−5750.17	−0.779331	−0.389666	−	0.920956i	$-0.627409\pi$
$379$	−5750.17	−0.779331	−0.389666	+	0.920956i	$0.627409\pi$
$380$	−1427.94	−0.192767
$381$	−7393.56	−0.994183
$382$	8246.61	1.10454
$383$	282.965	0.0377516	0.0188758	−	0.999822i	$-0.493991\pi$
$383$	282.965	0.0377516	0.0188758	+	0.999822i	$0.493991\pi$
$384$	−9768.81	−1.29821
$385$	416.361	0.0551161
$386$	18121.3	2.38951
$387$	0	0
$388$	−5688.33	−0.744282
$389$	−11295.8	−1.47229	−0.736145	−	0.676824i	$-0.763356\pi$
$389$	−11295.8	−1.47229	−0.736145	+	0.676824i	$0.763356\pi$
$390$	3093.56	0.401663
$391$	−5768.22	−0.746065
$392$	5458.35	0.703287
$393$	1429.63	0.183499
$394$	9726.30	1.24366
$395$	−1973.03	−0.251327
$396$	1778.87	0.225737
$397$	3635.34	0.459579	0.229789	−	0.973240i	$-0.426196\pi$
$397$	3635.34	0.459579	0.229789	+	0.973240i	$0.426196\pi$
$398$	12772.3	1.60859
$399$	−1689.02	−0.211922
$400$	433.747	0.0542184
$401$	−11126.5	−1.38562	−0.692809	−	0.721121i	$-0.743627\pi$
$401$	−11126.5	−1.38562	−0.692809	+	0.721121i	$0.743627\pi$
$402$	17665.9	2.19178
$403$	−15868.8	−1.96149
$404$	−16002.9	−1.97073
$405$	1143.16	0.140257
$406$	−7035.15	−0.859972
$407$	3688.47	0.449215
$408$	6216.49	0.754319
$409$	−9047.71	−1.09384	−0.546920	−	0.837185i	$-0.684200\pi$
$409$	−9047.71	−1.09384	−0.546920	+	0.837185i	$0.684200\pi$
$410$	−4431.28	−0.533769
$411$	10823.0	1.29893
$412$	15243.6	1.82282
$413$	−2650.69	−0.315815
$414$	−3358.21	−0.398665
$415$	197.918	0.0234106
$416$	−11098.8	−1.30809
$417$	−9617.36	−1.12941
$418$	3074.37	0.359742
$419$	−12094.5	−1.41015	−0.705077	−	0.709130i	$-0.749088\pi$
$419$	−12094.5	−1.41015	−0.705077	+	0.709130i	$0.749088\pi$
$420$	1399.18	0.162555
$421$	−4362.59	−0.505035	−0.252517	−	0.967592i	$-0.581258\pi$
$421$	−4362.59	−0.505035	−0.252517	+	0.967592i	$0.581258\pi$
$422$	−12553.5	−1.44810
$423$	−3760.06	−0.432199
$424$	8147.89	0.933246
$425$	−7907.79	−0.902550
$426$	−2379.64	−0.270643
$427$	290.631	0.0329383
$428$	−21957.5	−2.47980
$429$	−4090.84	−0.460390
$430$	0	0
$431$	12667.9	1.41576	0.707880	−	0.706333i	$-0.249652\pi$
$431$	12667.9	1.41576	0.707880	+	0.706333i	$0.249652\pi$
$432$	−562.715	−0.0626704
$433$	−15698.9	−1.74236	−0.871180	−	0.490963i	$-0.836645\pi$
$433$	−15698.9	−1.74236	−0.871180	+	0.490963i	$0.836645\pi$
$434$	−11685.6	−1.29246
$435$	1888.11	0.208111
$436$	17422.2	1.91370
$437$	−3564.72	−0.390214
$438$	−7281.98	−0.794398
$439$	−2524.91	−0.274505	−0.137252	−	0.990536i	$-0.543827\pi$
$439$	−2524.91	−0.274505	−0.137252	+	0.990536i	$0.543827\pi$
$440$	−947.030	−0.102609
$441$	2174.00	0.234748
$442$	17936.2	1.93017
$443$	−8347.92	−0.895308	−0.447654	−	0.894207i	$-0.647740\pi$
$443$	−8347.92	−0.895308	−0.447654	+	0.894207i	$0.647740\pi$
$444$	12395.1	1.32488
$445$	−3123.80	−0.332770
$446$	−17208.8	−1.82705
$447$	−3502.33	−0.370592
$448$	−7893.56	−0.832446
$449$	−3832.87	−0.402861	−0.201430	−	0.979503i	$-0.564559\pi$
$449$	−3832.87	−0.402861	−0.201430	+	0.979503i	$0.564559\pi$
$450$	−4603.85	−0.482284
$451$	5859.79	0.611811
$452$	23564.9	2.45221
$453$	−144.400	−0.0149768
$454$	16975.0	1.75479
$455$	1501.16	0.154672
$456$	3841.75	0.394532
$457$	−7651.81	−0.783231	−0.391616	−	0.920129i	$-0.628084\pi$
$457$	−7651.81	−0.783231	−0.391616	+	0.920129i	$0.628084\pi$
$458$	−16468.2	−1.68014
$459$	10259.0	1.04325
$460$	2953.00	0.299314
$461$	−11080.0	−1.11941	−0.559704	−	0.828692i	$-0.689085\pi$
$461$	−11080.0	−1.11941	−0.559704	+	0.828692i	$0.689085\pi$
$462$	−3012.45	−0.303359
$463$	12167.8	1.22135	0.610674	−	0.791882i	$-0.290899\pi$
$463$	12167.8	1.22135	0.610674	+	0.791882i	$0.290899\pi$
$464$	−600.456	−0.0600764
$465$	3136.23	0.312772
$466$	240.596	0.0239172
$467$	−9164.29	−0.908079	−0.454039	−	0.890982i	$-0.650017\pi$
$467$	−9164.29	−0.908079	−0.454039	+	0.890982i	$0.650017\pi$
$468$	6413.61	0.633481
$469$	8572.46	0.844007
$470$	5383.24	0.528320
$471$	−7123.88	−0.696924
$472$	6029.09	0.587948
$473$	0	0
$474$	14275.3	1.38330
$475$	−4886.96	−0.472061
$476$	8112.30	0.781149
$477$	3245.22	0.311506
$478$	7776.34	0.744104
$479$	−2661.40	−0.253867	−0.126934	−	0.991911i	$-0.540514\pi$
$479$	−2661.40	−0.253867	−0.126934	+	0.991911i	$0.540514\pi$
$480$	2193.51	0.208583
$481$	13298.5	1.26063
$482$	2750.92	0.259960
$483$	3492.93	0.329056
$484$	−13583.6	−1.27570
$485$	1206.15	0.112925
$486$	10504.0	0.980390
$487$	−15963.7	−1.48539	−0.742696	−	0.669629i	$-0.766453\pi$
$487$	−15963.7	−1.48539	−0.742696	+	0.669629i	$0.766453\pi$
$488$	−661.053	−0.0613206
$489$	−14967.1	−1.38412
$490$	−3112.50	−0.286956
$491$	−13980.6	−1.28500	−0.642501	−	0.766285i	$-0.722103\pi$
$491$	−13980.6	−1.28500	−0.642501	+	0.766285i	$0.722103\pi$
$492$	19691.8	1.80442
$493$	10947.1	1.00007
$494$	11084.4	1.00954
$495$	−377.192	−0.0342495
$496$	−997.380	−0.0902897
$497$	−1154.73	−0.104219
$498$	−1431.97	−0.128852
$499$	−11789.0	−1.05761	−0.528804	−	0.848744i	$-0.677359\pi$
$499$	−11789.0	−1.05761	−0.528804	+	0.848744i	$0.677359\pi$
$500$	8347.49	0.746623
$501$	−7901.67	−0.704632
$502$	7455.45	0.662855
$503$	10616.1	0.941050	0.470525	−	0.882387i	$-0.344065\pi$
$503$	10616.1	0.941050	0.470525	+	0.882387i	$0.344065\pi$
$504$	1756.23	0.155215
$505$	3393.26	0.299006
$506$	−6357.85	−0.558579
$507$	−5322.43	−0.466228
$508$	21945.5	1.91668
$509$	−16222.9	−1.41270	−0.706352	−	0.707861i	$-0.749660\pi$
$509$	−16222.9	−1.41270	−0.706352	+	0.707861i	$0.749660\pi$
$510$	−3544.81	−0.307778
$511$	−3533.61	−0.305905
$512$	−1333.32	−0.115088
$513$	6340.01	0.545649
$514$	33005.4	2.83231
$515$	−3232.26	−0.276564
$516$	0	0
$517$	−7118.64	−0.605566
$518$	9792.92	0.830649
$519$	−12104.0	−1.02371
$520$	−3414.46	−0.287950
$521$	2799.09	0.235375	0.117688	−	0.993051i	$-0.462452\pi$
$521$	2799.09	0.235375	0.117688	+	0.993051i	$0.462452\pi$
$522$	6373.32	0.534392
$523$	−11873.6	−0.992726	−0.496363	−	0.868115i	$-0.665331\pi$
$523$	−11873.6	−0.992726	−0.496363	+	0.868115i	$0.665331\pi$
$524$	−4243.41	−0.353768
$525$	4788.54	0.398074
$526$	−21256.9	−1.76206
$527$	18183.5	1.50301
$528$	−257.116	−0.0211923
$529$	−4795.09	−0.394106
$530$	−4646.15	−0.380784
$531$	2401.32	0.196250
$532$	5013.35	0.408564
$533$	21127.1	1.71692
$534$	22601.3	1.83157
$535$	4655.87	0.376244
$536$	−19498.4	−1.57127
$537$	−5525.68	−0.444042
$538$	−13293.8	−1.06531
$539$	4115.88	0.328912
$540$	−5252.04	−0.418540
$541$	−15732.1	−1.25023	−0.625116	−	0.780532i	$-0.714948\pi$
$541$	−15732.1	−1.25023	−0.625116	+	0.780532i	$0.714948\pi$
$542$	21619.0	1.71331
$543$	−11087.3	−0.876244
$544$	12717.8	1.00233
$545$	−3694.21	−0.290353
$546$	−10861.2	−0.851313
$547$	11050.4	0.863764	0.431882	−	0.901930i	$-0.357850\pi$
$547$	11050.4	0.863764	0.431882	+	0.901930i	$0.357850\pi$
$548$	−32124.8	−2.50420
$549$	−263.290	−0.0204680
$550$	−8716.13	−0.675740
$551$	6765.23	0.523065
$552$	−7944.82	−0.612598
$553$	6927.14	0.532680
$554$	−1954.18	−0.149865
$555$	−2628.25	−0.201015
$556$	28546.2	2.17739
$557$	−9079.45	−0.690680	−0.345340	−	0.938478i	$-0.612236\pi$
$557$	−9079.45	−0.690680	−0.345340	+	0.938478i	$0.612236\pi$
$558$	10586.3	0.803145
$559$	0	0
$560$	94.3505	0.00711970
$561$	4687.56	0.352779
$562$	−269.721	−0.0202447
$563$	3751.33	0.280817	0.140408	−	0.990094i	$-0.455158\pi$
$563$	3751.33	0.280817	0.140408	+	0.990094i	$0.455158\pi$
$564$	−23922.2	−1.78600
$565$	−4996.69	−0.372057
$566$	24911.7	1.85003
$567$	−4013.53	−0.297271
$568$	2626.48	0.194022
$569$	19349.0	1.42557	0.712787	−	0.701380i	$-0.247432\pi$
$569$	19349.0	1.42557	0.712787	+	0.701380i	$0.247432\pi$
$570$	−2190.67	−0.160977
$571$	−4876.77	−0.357419	−0.178710	−	0.983902i	$-0.557192\pi$
$571$	−4876.77	−0.357419	−0.178710	+	0.983902i	$0.557192\pi$
$572$	12142.4	0.887587
$573$	7770.51	0.566523
$574$	15557.8	1.13131
$575$	10106.3	0.732979
$576$	7150.97	0.517287
$577$	11927.2	0.860546	0.430273	−	0.902699i	$-0.358417\pi$
$577$	11927.2	0.860546	0.430273	+	0.902699i	$0.358417\pi$
$578$	1819.67	0.130949
$579$	17075.1	1.22559
$580$	−5604.29	−0.401217
$581$	−694.870	−0.0496180
$582$	−8726.76	−0.621539
$583$	6143.93	0.436459
$584$	8037.33	0.569499
$585$	−1359.94	−0.0961139
$586$	−9925.87	−0.699717
$587$	20820.2	1.46395	0.731977	−	0.681330i	$-0.238598\pi$
$587$	20820.2	1.46395	0.731977	+	0.681330i	$0.238598\pi$
$588$	13831.4	0.970063
$589$	11237.3	0.786121
$590$	−3437.95	−0.239895
$591$	9164.78	0.637883
$592$	835.835	0.0580280
$593$	15515.4	1.07444	0.537218	−	0.843443i	$-0.319475\pi$
$593$	15515.4	1.07444	0.537218	+	0.843443i	$0.319475\pi$
$594$	11307.7	0.781080
$595$	−1720.13	−0.118519
$596$	10395.6	0.714464
$597$	12035.0	0.825056
$598$	−22922.8	−1.56753
$599$	−1698.64	−0.115868	−0.0579338	−	0.998320i	$-0.518451\pi$
$599$	−1698.64	−0.115868	−0.0579338	+	0.998320i	$0.518451\pi$
$600$	−10891.7	−0.741089
$601$	−17559.3	−1.19178	−0.595888	−	0.803068i	$-0.703200\pi$
$601$	−17559.3	−1.19178	−0.595888	+	0.803068i	$0.703200\pi$
$602$	0	0
$603$	−7766.01	−0.524472
$604$	428.608	0.0288738
$605$	2880.27	0.193553
$606$	−24550.9	−1.64573
$607$	25020.3	1.67305	0.836525	−	0.547929i	$-0.184584\pi$
$607$	25020.3	1.67305	0.836525	+	0.547929i	$0.184584\pi$
$608$	7859.49	0.524251
$609$	−6628.99	−0.441084
$610$	376.950	0.0250201
$611$	−25665.8	−1.69939
$612$	−7349.14	−0.485411
$613$	−2905.86	−0.191462	−0.0957312	−	0.995407i	$-0.530519\pi$
$613$	−2905.86	−0.191462	−0.0957312	+	0.995407i	$0.530519\pi$
$614$	−32416.9	−2.13068
$615$	−4175.45	−0.273773
$616$	3324.93	0.217476
$617$	−24437.2	−1.59450	−0.797249	−	0.603651i	$-0.793712\pi$
$617$	−24437.2	−1.59450	−0.797249	+	0.603651i	$0.793712\pi$
$618$	23386.0	1.52221
$619$	13786.3	0.895182	0.447591	−	0.894238i	$-0.352282\pi$
$619$	13786.3	0.895182	0.447591	+	0.894238i	$0.352282\pi$
$620$	−9308.94	−0.602994
$621$	−13111.3	−0.847242
$622$	−18151.9	−1.17013
$623$	10967.4	0.705295
$624$	−927.014	−0.0594716
$625$	12943.4	0.828378
$626$	−42434.2	−2.70928
$627$	2896.88	0.184514
$628$	21145.1	1.34360
$629$	−15238.4	−0.965967
$630$	−1001.45	−0.0633312
$631$	−29405.5	−1.85517	−0.927586	−	0.373610i	$-0.878120\pi$
$631$	−29405.5	−1.85517	−0.927586	+	0.373610i	$0.878120\pi$
$632$	−15756.1	−0.991681
$633$	−11828.8	−0.742737
$634$	38600.9	2.41804
$635$	−4653.33	−0.290806
$636$	20646.7	1.28725
$637$	14839.5	0.923020
$638$	12066.1	0.748750
$639$	1046.10	0.0647622
$640$	−6148.25	−0.379736
$641$	−2989.09	−0.184184	−0.0920921	−	0.995750i	$-0.529355\pi$
$641$	−2989.09	−0.184184	−0.0920921	+	0.995750i	$0.529355\pi$
$642$	−33686.2	−2.07085
$643$	15849.7	0.972083	0.486041	−	0.873936i	$-0.338440\pi$
$643$	15849.7	0.972083	0.486041	+	0.873936i	$0.338440\pi$
$644$	−10367.7	−0.634386
$645$	0	0
$646$	−12701.3	−0.773569
$647$	30447.1	1.85007	0.925037	−	0.379876i	$-0.124033\pi$
$647$	30447.1	1.85007	0.925037	+	0.379876i	$0.124033\pi$
$648$	9128.94	0.553424
$649$	4546.25	0.274970
$650$	−31425.5	−1.89632
$651$	−11011.0	−0.662911
$652$	44425.3	2.66845
$653$	9838.49	0.589601	0.294801	−	0.955559i	$-0.404747\pi$
$653$	9838.49	0.589601	0.294801	+	0.955559i	$0.404747\pi$
$654$	26728.4	1.59811
$655$	899.773	0.0536749
$656$	1327.87	0.0790316
$657$	3201.18	0.190091
$658$	−18900.1	−1.11976
$659$	−8170.61	−0.482977	−0.241488	−	0.970404i	$-0.577636\pi$
$659$	−8170.61	−0.482977	−0.241488	+	0.970404i	$0.577636\pi$
$660$	−2399.76	−0.141531
$661$	22065.7	1.29842	0.649212	−	0.760608i	$-0.275099\pi$
$661$	22065.7	1.29842	0.649212	+	0.760608i	$0.275099\pi$
$662$	5580.39	0.327626
$663$	16900.7	0.989997
$664$	1580.51	0.0923731
$665$	−1063.03	−0.0619888
$666$	−8871.66	−0.516171
$667$	−13990.6	−0.812173
$668$	23453.7	1.35846
$669$	−16215.3	−0.937102
$670$	11118.5	0.641114
$671$	−498.468	−0.0286783
$672$	−7701.22	−0.442085
$673$	1828.23	0.104715	0.0523573	−	0.998628i	$-0.483327\pi$
$673$	1828.23	0.104715	0.0523573	+	0.998628i	$0.483327\pi$
$674$	−6767.97	−0.386784
$675$	−17974.5	−1.02495
$676$	15798.0	0.898840
$677$	−21093.1	−1.19745	−0.598724	−	0.800955i	$-0.704325\pi$
$677$	−21093.1	−1.19745	−0.598724	+	0.800955i	$0.704325\pi$
$678$	36152.1	2.04780
$679$	−4234.69	−0.239341
$680$	3912.51	0.220644
$681$	15995.0	0.900042
$682$	20042.3	1.12531
$683$	−11074.6	−0.620438	−0.310219	−	0.950665i	$-0.600402\pi$
$683$	−11074.6	−0.620438	−0.310219	+	0.950665i	$0.600402\pi$
$684$	−4541.72	−0.253884
$685$	6811.74	0.379946
$686$	25736.5	1.43240
$687$	−15517.4	−0.861756
$688$	0	0
$689$	22151.5	1.22483
$690$	4530.35	0.249953
$691$	−10854.2	−0.597557	−0.298778	−	0.954323i	$-0.596579\pi$
$691$	−10854.2	−0.597557	−0.298778	+	0.954323i	$0.596579\pi$
$692$	35927.1	1.97362
$693$	1324.29	0.0725908
$694$	−38527.9	−2.10735
$695$	−6052.94	−0.330361
$696$	15077.9	0.821159
$697$	−24208.9	−1.31560
$698$	−53679.0	−2.91086
$699$	226.706	0.0122672
$700$	−14213.3	−0.767448
$701$	32035.1	1.72603	0.863015	−	0.505177i	$-0.168573\pi$
$701$	32035.1	1.72603	0.863015	+	0.505177i	$0.168573\pi$
$702$	40769.3	2.19193
$703$	−9417.20	−0.505230
$704$	13538.4	0.724784
$705$	5072.46	0.270978
$706$	21550.2	1.14880
$707$	−11913.4	−0.633734
$708$	15277.7	0.810974
$709$	−14009.1	−0.742064	−0.371032	−	0.928620i	$-0.620996\pi$
$709$	−14009.1	−0.742064	−0.371032	+	0.928620i	$0.620996\pi$
$710$	−1497.69	−0.0791653
$711$	−6275.47	−0.331011
$712$	−24945.8	−1.31304
$713$	−23239.0	−1.22063
$714$	12445.5	0.652327
$715$	−2574.68	−0.134668
$716$	16401.3	0.856069
$717$	7327.40	0.381655
$718$	27450.3	1.42679
$719$	−12270.7	−0.636467	−0.318234	−	0.948012i	$-0.603090\pi$
$719$	−12270.7	−0.636467	−0.318234	+	0.948012i	$0.603090\pi$
$720$	−85.4745	−0.00442423
$721$	11348.2	0.586168
$722$	23384.3	1.20536
$723$	2592.10	0.133335
$724$	32909.2	1.68931
$725$	−19180.1	−0.982525
$726$	−20839.3	−1.06532
$727$	23264.9	1.18686	0.593431	−	0.804885i	$-0.297773\pi$
$727$	23264.9	1.18686	0.593431	+	0.804885i	$0.297773\pi$
$728$	11987.8	0.610300
$729$	21327.0	1.08352
$730$	−4583.11	−0.232368
$731$	0	0
$732$	−1675.10	−0.0845813
$733$	−10120.4	−0.509965	−0.254982	−	0.966946i	$-0.582070\pi$
$733$	−10120.4	−0.509965	−0.254982	+	0.966946i	$0.582070\pi$
$734$	11062.1	0.556278
$735$	−2932.81	−0.147181
$736$	−16253.6	−0.814015
$737$	−14702.8	−0.734851
$738$	−14094.2	−0.703002
$739$	16955.4	0.843998	0.421999	−	0.906596i	$-0.361329\pi$
$739$	16955.4	0.843998	0.421999	+	0.906596i	$0.361329\pi$
$740$	7801.18	0.387536
$741$	10444.5	0.517798
$742$	16312.2	0.807061
$743$	−30362.0	−1.49916	−0.749579	−	0.661915i	$-0.769744\pi$
$743$	−30362.0	−1.49916	−0.749579	+	0.661915i	$0.769744\pi$
$744$	25045.0	1.23413
$745$	−2204.28	−0.108401
$746$	−40947.0	−2.00962
$747$	629.500	0.0308330
$748$	−13913.6	−0.680122
$749$	−16346.3	−0.797439
$750$	12806.3	0.623494
$751$	10733.4	0.521529	0.260765	−	0.965402i	$-0.416025\pi$
$751$	10733.4	0.521529	0.260765	+	0.965402i	$0.416025\pi$
$752$	−1613.14	−0.0782248
$753$	7025.03	0.339982
$754$	43503.7	2.10121
$755$	−90.8820	−0.00438084
$756$	18439.4	0.887084
$757$	−21386.9	−1.02684	−0.513422	−	0.858136i	$-0.671623\pi$
$757$	−21386.9	−1.02684	−0.513422	+	0.858136i	$0.671623\pi$
$758$	26184.4	1.25469
$759$	−5990.80	−0.286498
$760$	2417.91	0.115403
$761$	12272.6	0.584601	0.292300	−	0.956327i	$-0.405579\pi$
$761$	12272.6	0.584601	0.292300	+	0.956327i	$0.405579\pi$
$762$	33667.8	1.60060
$763$	12970.0	0.615395
$764$	−23064.4	−1.09220
$765$	1558.31	0.0736482
$766$	−1288.53	−0.0607787
$767$	16391.2	0.771645
$768$	15905.8	0.747331
$769$	−6111.07	−0.286568	−0.143284	−	0.989682i	$-0.545766\pi$
$769$	−6111.07	−0.286568	−0.143284	+	0.989682i	$0.545766\pi$
$770$	−1895.97	−0.0887349
$771$	31099.9	1.45271
$772$	−50682.4	−2.36282
$773$	−19226.4	−0.894600	−0.447300	−	0.894384i	$-0.647614\pi$
$773$	−19226.4	−0.894600	−0.447300	+	0.894384i	$0.647614\pi$
$774$	0	0
$775$	−31858.9	−1.47665
$776$	9631.98	0.445577
$777$	9227.56	0.426045
$778$	51437.4	2.37033
$779$	−14960.9	−0.688100
$780$	−8652.19	−0.397177
$781$	1980.50	0.0907400
$782$	26266.5	1.20114
$783$	24883.0	1.13569
$784$	932.688	0.0424876
$785$	−4483.60	−0.203855
$786$	−6510.04	−0.295427
$787$	17479.0	0.791690	0.395845	−	0.918317i	$-0.370452\pi$
$787$	17479.0	0.791690	0.395845	+	0.918317i	$0.370452\pi$
$788$	−27202.9	−1.22977
$789$	−20029.7	−0.903773
$790$	8984.53	0.404627
$791$	17542.9	0.788564
$792$	−3012.14	−0.135141
$793$	−1797.19	−0.0804795
$794$	−16554.1	−0.739905
$795$	−4377.92	−0.195306
$796$	−35722.2	−1.59063
$797$	−4386.69	−0.194962	−0.0974809	−	0.995237i	$-0.531078\pi$
$797$	−4386.69	−0.194962	−0.0974809	+	0.995237i	$0.531078\pi$
$798$	7691.24	0.341186
$799$	29409.6	1.30217
$800$	−22282.4	−0.984753
$801$	−9935.63	−0.438275
$802$	50666.5	2.23079
$803$	6060.56	0.266342
$804$	−49408.7	−2.16730
$805$	2198.37	0.0962513
$806$	72261.2	3.15793
$807$	−12526.3	−0.546401
$808$	27097.5	1.17981
$809$	−42338.7	−1.83999	−0.919994	−	0.391932i	$-0.871807\pi$
$809$	−42338.7	−1.83999	−0.919994	+	0.391932i	$0.871807\pi$
$810$	−5205.57	−0.225809
$811$	27748.6	1.20146	0.600730	−	0.799452i	$-0.294877\pi$
$811$	27748.6	1.20146	0.600730	+	0.799452i	$0.294877\pi$
$812$	19676.1	0.850366
$813$	20370.9	0.878766
$814$	−16796.0	−0.723220
$815$	−9419.94	−0.404866
$816$	1062.24	0.0455707
$817$	0	0
$818$	41200.2	1.76104
$819$	4774.63	0.203711
$820$	12393.6	0.527807
$821$	−490.567	−0.0208537	−0.0104269	−	0.999946i	$-0.503319\pi$
$821$	−490.567	−0.0208537	−0.0104269	+	0.999946i	$0.503319\pi$
$822$	−49284.3	−2.09123
$823$	−26286.3	−1.11334	−0.556672	−	0.830732i	$-0.687922\pi$
$823$	−26286.3	−1.11334	−0.556672	+	0.830732i	$0.687922\pi$
$824$	−25811.9	−1.09126
$825$	−8212.93	−0.346591
$826$	12070.3	0.508451
$827$	545.162	0.0229228	0.0114614	−	0.999934i	$-0.496352\pi$
$827$	545.162	0.0229228	0.0114614	+	0.999934i	$0.496352\pi$
$828$	9392.37	0.394212
$829$	−45337.7	−1.89945	−0.949724	−	0.313090i	$-0.898636\pi$
$829$	−45337.7	−1.89945	−0.949724	+	0.313090i	$0.898636\pi$
$830$	−901.250	−0.0376902
$831$	−1841.36	−0.0768667
$832$	48811.9	2.03395
$833$	−17004.1	−0.707273
$834$	43794.2	1.81831
$835$	−4973.12	−0.206110
$836$	−8598.50	−0.355724
$837$	41331.5	1.70684
$838$	55074.3	2.27030
$839$	16487.5	0.678439	0.339219	−	0.940707i	$-0.389837\pi$
$839$	16487.5	0.678439	0.339219	+	0.940707i	$0.389837\pi$
$840$	−2369.21	−0.0973162
$841$	2162.86	0.0886818
$842$	19865.8	0.813087
$843$	−254.150	−0.0103836
$844$	35110.2	1.43192
$845$	−3349.81	−0.136375
$846$	17122.0	0.695825
$847$	−10112.3	−0.410230
$848$	1392.26	0.0563802
$849$	23473.5	0.948892
$850$	36009.4	1.45307
$851$	19475.0	0.784481
$852$	6655.47	0.267621
$853$	10283.7	0.412786	0.206393	−	0.978469i	$-0.433827\pi$
$853$	10283.7	0.412786	0.206393	+	0.978469i	$0.433827\pi$
$854$	−1323.44	−0.0530294
$855$	963.026	0.0385202
$856$	37180.4	1.48458
$857$	7061.07	0.281449	0.140724	−	0.990049i	$-0.455057\pi$
$857$	7061.07	0.281449	0.140724	+	0.990049i	$0.455057\pi$
$858$	18628.3	0.741212
$859$	−7401.74	−0.293998	−0.146999	−	0.989137i	$-0.546961\pi$
$859$	−7401.74	−0.293998	−0.146999	+	0.989137i	$0.546961\pi$
$860$	0	0
$861$	14659.6	0.580254
$862$	−57685.4	−2.27932
$863$	−5356.38	−0.211278	−0.105639	−	0.994405i	$-0.533689\pi$
$863$	−5356.38	−0.211278	−0.105639	+	0.994405i	$0.533689\pi$
$864$	28907.7	1.13826
$865$	−7617.98	−0.299444
$866$	71487.6	2.80514
$867$	1714.62	0.0671643
$868$	32682.8	1.27803
$869$	−11880.9	−0.463787
$870$	−8597.84	−0.335051
$871$	−53010.0	−2.06220
$872$	−29500.9	−1.14567
$873$	3836.31	0.148728
$874$	16232.5	0.628231
$875$	6214.31	0.240094
$876$	20366.5	0.785526
$877$	−24690.2	−0.950660	−0.475330	−	0.879808i	$-0.657671\pi$
$877$	−24690.2	−0.950660	−0.475330	+	0.879808i	$0.657671\pi$
$878$	11497.6	0.441942
$879$	−9352.83	−0.358889
$880$	−161.822	−0.00619890
$881$	−14555.9	−0.556640	−0.278320	−	0.960488i	$-0.589778\pi$
$881$	−14555.9	−0.556640	−0.278320	+	0.960488i	$0.589778\pi$
$882$	−9899.67	−0.377936
$883$	25326.8	0.965251	0.482625	−	0.875827i	$-0.339683\pi$
$883$	25326.8	0.965251	0.482625	+	0.875827i	$0.339683\pi$
$884$	−50164.5	−1.90862
$885$	−3239.47	−0.123044
$886$	38013.6	1.44141
$887$	15323.2	0.580049	0.290025	−	0.957019i	$-0.406337\pi$
$887$	15323.2	0.580049	0.290025	+	0.957019i	$0.406337\pi$
$888$	−20988.5	−0.793161
$889$	16337.4	0.616354
$890$	14224.7	0.535747
$891$	6883.69	0.258824
$892$	48130.3	1.80664
$893$	18174.9	0.681076
$894$	15948.4	0.596639
$895$	−3477.73	−0.129886
$896$	21585.9	0.804839
$897$	−21599.5	−0.803996
$898$	17453.6	0.648591
$899$	44103.6	1.63619
$900$	12876.2	0.476897
$901$	−25382.7	−0.938536
$902$	−26683.5	−0.984994
$903$	0	0
$904$	−39902.1	−1.46806
$905$	−6978.06	−0.256308
$906$	657.549	0.0241122
$907$	8536.27	0.312505	0.156253	−	0.987717i	$-0.450059\pi$
$907$	8536.27	0.312505	0.156253	+	0.987717i	$0.450059\pi$
$908$	−47476.2	−1.73519
$909$	10792.7	0.393806
$910$	−6835.79	−0.249016
$911$	−50638.5	−1.84163	−0.920817	−	0.389995i	$-0.872477\pi$
$911$	−50638.5	−1.84163	−0.920817	+	0.389995i	$0.872477\pi$
$912$	656.454	0.0238348
$913$	1191.79	0.0432008
$914$	34843.8	1.26097
$915$	355.188	0.0128330
$916$	46058.7	1.66138
$917$	−3159.02	−0.113762
$918$	−46716.2	−1.67959
$919$	−47429.0	−1.70244	−0.851218	−	0.524812i	$-0.824136\pi$
$919$	−47429.0	−1.70244	−0.851218	+	0.524812i	$0.824136\pi$
$920$	−5000.28	−0.179189
$921$	−30545.4	−1.09284
$922$	50454.6	1.80221
$923$	7140.57	0.254642
$924$	8425.34	0.299971
$925$	26698.7	0.949024
$926$	−55407.9	−1.96633
$927$	−10280.6	−0.364249
$928$	30846.6	1.09115
$929$	24002.2	0.847671	0.423836	−	0.905739i	$-0.360683\pi$
$929$	24002.2	0.847671	0.423836	+	0.905739i	$0.360683\pi$
$930$	−14281.3	−0.503552
$931$	−10508.4	−0.369925
$932$	−672.907	−0.0236500
$933$	−17103.9	−0.600169
$934$	41731.1	1.46197
$935$	2950.24	0.103190
$936$	−10860.1	−0.379245
$937$	10994.5	0.383325	0.191662	−	0.981461i	$-0.438612\pi$
$937$	10994.5	0.383325	0.191662	+	0.981461i	$0.438612\pi$
$938$	−39036.1	−1.35882
$939$	−39984.4	−1.38961
$940$	−15056.0	−0.522419
$941$	−17775.3	−0.615790	−0.307895	−	0.951420i	$-0.599625\pi$
$941$	−17775.3	−0.615790	−0.307895	+	0.951420i	$0.599625\pi$
$942$	32439.7	1.12202
$943$	30939.5	1.06843
$944$	1030.21	0.0355197
$945$	−3909.89	−0.134591
$946$	0	0
$947$	−19576.9	−0.671767	−0.335884	−	0.941904i	$-0.609035\pi$
$947$	−19576.9	−0.671767	−0.335884	+	0.941904i	$0.609035\pi$
$948$	−39925.7	−1.36785
$949$	21851.0	0.747432
$950$	22253.6	0.760001
$951$	36372.4	1.24023
$952$	−13736.5	−0.467649
$953$	−32542.6	−1.10615	−0.553074	−	0.833132i	$-0.686545\pi$
$953$	−32542.6	−1.10615	−0.553074	+	0.833132i	$0.686545\pi$
$954$	−14777.6	−0.501513
$955$	4890.58	0.165712
$956$	−21749.2	−0.735793
$957$	11369.5	0.384038
$958$	12119.1	0.408717
$959$	−23915.4	−0.805284
$960$	−9646.93	−0.324326
$961$	43466.8	1.45906
$962$	−60557.1	−2.02956
$963$	14808.5	0.495533
$964$	−7693.86	−0.257057
$965$	10746.7	0.358496
$966$	−15905.6	−0.529768
$967$	−31808.6	−1.05780	−0.528901	−	0.848683i	$-0.677396\pi$
$967$	−31808.6	−1.05780	−0.528901	+	0.848683i	$0.677396\pi$
$968$	23001.0	0.763718
$969$	−11968.0	−0.396768
$970$	−5492.42	−0.181805
$971$	−34826.2	−1.15100	−0.575502	−	0.817800i	$-0.695193\pi$
$971$	−34826.2	−1.15100	−0.575502	+	0.817800i	$0.695193\pi$
$972$	−29377.9	−0.969440
$973$	21251.3	0.700190
$974$	72693.5	2.39143
$975$	−29611.2	−0.972633
$976$	−112.957	−0.00370456
$977$	−3393.59	−0.111126	−0.0555632	−	0.998455i	$-0.517695\pi$
$977$	−3393.59	−0.111126	−0.0555632	+	0.998455i	$0.517695\pi$
$978$	68155.1	2.22839
$979$	−18810.4	−0.614078
$980$	8705.15	0.283751
$981$	−11749.9	−0.382410
$982$	63663.0	2.06881
$983$	−10880.2	−0.353025	−0.176513	−	0.984298i	$-0.556482\pi$
$983$	−10880.2	−0.353025	−0.176513	+	0.984298i	$0.556482\pi$
$984$	−33343.9	−1.08025
$985$	5768.09	0.186585
$986$	−49849.4	−1.61007
$987$	−17808.9	−0.574331
$988$	−31001.3	−0.998263
$989$	0	0
$990$	1717.60	0.0551405
$991$	−47618.4	−1.52639	−0.763194	−	0.646170i	$-0.776370\pi$
$991$	−47618.4	−1.52639	−0.763194	+	0.646170i	$0.776370\pi$
$992$	51237.3	1.63990
$993$	5258.23	0.168041
$994$	5258.25	0.167788
$995$	7574.53	0.241335
$996$	4004.99	0.127413
$997$	−4548.20	−0.144476	−0.0722381	−	0.997387i	$-0.523014\pi$
$997$	−4548.20	−0.144476	−0.0722381	+	0.997387i	$0.523014\pi$
$998$	53682.9	1.70271
$999$	−34637.1	−1.09697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.5	yes	50
43.42	odd	2		1849.4.a.i.1.46	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.46	✓	50	43.42	odd	2
1849.4.a.j.1.5	yes	50	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-4.55366 q^{2} -4.29077 q^{3} +12.7358 q^{4} -2.70051 q^{5} +19.5387 q^{6} +9.48123 q^{7} -21.5655 q^{8} -8.58929 q^{9} +O(q^{10})\)	\(q-4.55366 q^{2} -4.29077 q^{3} +12.7358 q^{4} -2.70051 q^{5} +19.5387 q^{6} +9.48123 q^{7} -21.5655 q^{8} -8.58929 q^{9} +12.2972 q^{10} -16.2615 q^{11} -54.6466 q^{12} -58.6297 q^{13} -43.1743 q^{14} +11.5873 q^{15} -3.68497 q^{16} +67.1818 q^{17} +39.1127 q^{18} +41.5179 q^{19} -34.3933 q^{20} -40.6818 q^{21} +74.0492 q^{22} -85.8598 q^{23} +92.5324 q^{24} -117.707 q^{25} +266.980 q^{26} +152.705 q^{27} +120.752 q^{28} +162.947 q^{29} -52.7645 q^{30} +270.662 q^{31} +189.304 q^{32} +69.7742 q^{33} -305.923 q^{34} -25.6041 q^{35} -109.392 q^{36} -226.823 q^{37} -189.058 q^{38} +251.566 q^{39} +58.2377 q^{40} -360.349 q^{41} +185.251 q^{42} -207.103 q^{44} +23.1954 q^{45} +390.977 q^{46} +437.762 q^{47} +15.8114 q^{48} -253.106 q^{49} +535.999 q^{50} -288.262 q^{51} -746.698 q^{52} -377.821 q^{53} -695.369 q^{54} +43.9142 q^{55} -204.467 q^{56} -178.144 q^{57} -742.008 q^{58} -279.572 q^{59} +147.574 q^{60} +30.6533 q^{61} -1232.50 q^{62} -81.4370 q^{63} -832.546 q^{64} +158.330 q^{65} -317.728 q^{66} +904.150 q^{67} +855.617 q^{68} +368.405 q^{69} +116.593 q^{70} -121.791 q^{71} +185.232 q^{72} -372.695 q^{73} +1032.87 q^{74} +505.055 q^{75} +528.765 q^{76} -154.179 q^{77} -1145.55 q^{78} +730.616 q^{79} +9.95129 q^{80} -423.313 q^{81} +1640.91 q^{82} -73.2890 q^{83} -518.117 q^{84} -181.425 q^{85} -699.170 q^{87} +350.686 q^{88} +1156.75 q^{89} -105.624 q^{90} -555.881 q^{91} -1093.50 q^{92} -1161.35 q^{93} -1993.42 q^{94} -112.119 q^{95} -812.259 q^{96} -446.639 q^{97} +1152.56 q^{98} +139.674 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} + 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} + 386 q^{18} - 12 q^{19} - 108 q^{20} - 408 q^{21} - 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} - 1493 q^{26} - 10 q^{27} + 242 q^{28} - 208 q^{29} + 48 q^{30} - 932 q^{31} + 1124 q^{32} - 254 q^{33} - 765 q^{34} - 1452 q^{35} + 747 q^{36} + 90 q^{37} - 1213 q^{38} + 1610 q^{39} - 1693 q^{40} - 1354 q^{41} + 16 q^{42} - 2704 q^{44} - 4508 q^{45} - 233 q^{46} - 3484 q^{47} + 376 q^{48} + 1324 q^{49} + 408 q^{50} - 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} + 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} - 1172 q^{61} + 1546 q^{62} + 3686 q^{63} + 606 q^{64} - 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} - 136 q^{69} + 1310 q^{70} - 162 q^{71} + 5814 q^{72} - 746 q^{73} - 4332 q^{74} - 236 q^{75} - 1338 q^{76} - 2024 q^{77} - 2782 q^{78} - 2656 q^{79} + 5713 q^{80} - 86 q^{81} + 4168 q^{82} - 3514 q^{83} - 4269 q^{84} + 7558 q^{85} - 10278 q^{87} - 11692 q^{88} - 2640 q^{89} - 8286 q^{90} + 5946 q^{91} - 4271 q^{92} + 2 q^{93} - 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} + 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q + 10 * q^2 + 2 * q^3 + 186 * q^4 - 8 * q^5 - 51 * q^6 + 6 * q^7 + 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 + 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 + 386 * q^18 - 12 * q^19 - 108 * q^20 - 408 * q^21 - 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 - 1493 * q^26 - 10 * q^27 + 242 * q^28 - 208 * q^29 + 48 * q^30 - 932 * q^31 + 1124 * q^32 - 254 * q^33 - 765 * q^34 - 1452 * q^35 + 747 * q^36 + 90 * q^37 - 1213 * q^38 + 1610 * q^39 - 1693 * q^40 - 1354 * q^41 + 16 * q^42 - 2704 * q^44 - 4508 * q^45 - 233 * q^46 - 3484 * q^47 + 376 * q^48 + 1324 * q^49 + 408 * q^50 - 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 + 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 - 1172 * q^61 + 1546 * q^62 + 3686 * q^63 + 606 * q^64 - 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 - 136 * q^69 + 1310 * q^70 - 162 * q^71 + 5814 * q^72 - 746 * q^73 - 4332 * q^74 - 236 * q^75 - 1338 * q^76 - 2024 * q^77 - 2782 * q^78 - 2656 * q^79 + 5713 * q^80 - 86 * q^81 + 4168 * q^82 - 3514 * q^83 - 4269 * q^84 + 7558 * q^85 - 10278 * q^87 - 11692 * q^88 - 2640 * q^89 - 8286 * q^90 + 5946 * q^91 - 4271 * q^92 + 2 * q^93 - 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 + 2826 * q^98 - 8174 * q^99

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