LMFDB - Embedded newform 1849.4.a.j.1.40

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			1.40
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)

$f(q)$	$=$	$q+3.53489 q^{2} -7.81725 q^{3} +4.49548 q^{4} -1.07981 q^{5} -27.6332 q^{6} +33.3014 q^{7} -12.3881 q^{8} +34.1094 q^{9} +O(q^{10})$	\(q+3.53489 q^{2} -7.81725 q^{3} +4.49548 q^{4} -1.07981 q^{5} -27.6332 q^{6} +33.3014 q^{7} -12.3881 q^{8} +34.1094 q^{9} -3.81700 q^{10} -6.35516 q^{11} -35.1423 q^{12} +16.4672 q^{13} +117.717 q^{14} +8.44112 q^{15} -79.7545 q^{16} +8.35561 q^{17} +120.573 q^{18} -141.509 q^{19} -4.85424 q^{20} -260.325 q^{21} -22.4648 q^{22} +123.588 q^{23} +96.8411 q^{24} -123.834 q^{25} +58.2100 q^{26} -55.5761 q^{27} +149.706 q^{28} +54.4135 q^{29} +29.8385 q^{30} -253.413 q^{31} -182.819 q^{32} +49.6799 q^{33} +29.5362 q^{34} -35.9591 q^{35} +153.338 q^{36} +246.339 q^{37} -500.219 q^{38} -128.729 q^{39} +13.3768 q^{40} +492.491 q^{41} -920.222 q^{42} -28.5695 q^{44} -36.8316 q^{45} +436.871 q^{46} -335.420 q^{47} +623.461 q^{48} +765.982 q^{49} -437.740 q^{50} -65.3179 q^{51} +74.0281 q^{52} +386.753 q^{53} -196.456 q^{54} +6.86235 q^{55} -412.542 q^{56} +1106.21 q^{57} +192.346 q^{58} -480.563 q^{59} +37.9468 q^{60} +264.683 q^{61} -895.789 q^{62} +1135.89 q^{63} -8.20876 q^{64} -17.7814 q^{65} +175.613 q^{66} -308.944 q^{67} +37.5624 q^{68} -966.120 q^{69} -127.111 q^{70} +67.5365 q^{71} -422.552 q^{72} -835.918 q^{73} +870.782 q^{74} +968.042 q^{75} -636.150 q^{76} -211.636 q^{77} -455.042 q^{78} -17.9914 q^{79} +86.1195 q^{80} -486.502 q^{81} +1740.90 q^{82} +1011.82 q^{83} -1170.29 q^{84} -9.02244 q^{85} -425.364 q^{87} +78.7286 q^{88} -1240.09 q^{89} -130.196 q^{90} +548.382 q^{91} +555.588 q^{92} +1980.99 q^{93} -1185.67 q^{94} +152.802 q^{95} +1429.14 q^{96} -287.048 q^{97} +2707.67 q^{98} -216.771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.53489	1.24977	0.624887	−	0.780715i	$-0.285145\pi$
$2$	3.53489	1.24977	0.624887	+	0.780715i	$0.285145\pi$
$3$	−7.81725	−1.50443	−0.752215	−	0.658917i	$-0.771015\pi$
$3$	−7.81725	−1.50443	−0.752215	+	0.658917i	$0.771015\pi$
$4$	4.49548	0.561934
$5$	−1.07981	−0.0965809	−0.0482904	−	0.998833i	$-0.515377\pi$
$5$	−1.07981	−0.0965809	−0.0482904	+	0.998833i	$0.515377\pi$
$6$	−27.6332	−1.88020
$7$	33.3014	1.79811	0.899053	−	0.437840i	$-0.144256\pi$
$7$	33.3014	1.79811	0.899053	+	0.437840i	$0.144256\pi$
$8$	−12.3881	−0.547483
$9$	34.1094	1.26331
$10$	−3.81700	−0.120704
$11$	−6.35516	−0.174196	−0.0870979	−	0.996200i	$-0.527759\pi$
$11$	−6.35516	−0.174196	−0.0870979	+	0.996200i	$0.527759\pi$
$12$	−35.1423	−0.845391
$13$	16.4672	0.351323	0.175661	−	0.984451i	$-0.443794\pi$
$13$	16.4672	0.351323	0.175661	+	0.984451i	$0.443794\pi$
$14$	117.717	2.24723
$15$	8.44112	0.145299
$16$	−79.7545	−1.24616
$17$	8.35561	0.119208	0.0596039	−	0.998222i	$-0.481016\pi$
$17$	8.35561	0.119208	0.0596039	+	0.998222i	$0.481016\pi$
$18$	120.573	1.57885
$19$	−141.509	−1.70865	−0.854326	−	0.519738i	$-0.826030\pi$
$19$	−141.509	−1.70865	−0.854326	+	0.519738i	$0.826030\pi$
$20$	−4.85424	−0.0542721
$21$	−260.325	−2.70513
$22$	−22.4648	−0.217705
$23$	123.588	1.12043	0.560216	−	0.828347i	$-0.310718\pi$
$23$	123.588	1.12043	0.560216	+	0.828347i	$0.310718\pi$
$24$	96.8411	0.823650
$25$	−123.834	−0.990672
$26$	58.2100	0.439074
$27$	−55.5761	−0.396134
$28$	149.706	1.01042
$29$	54.4135	0.348425	0.174213	−	0.984708i	$-0.444262\pi$
$29$	54.4135	0.348425	0.174213	+	0.984708i	$0.444262\pi$
$30$	29.8385	0.181591
$31$	−253.413	−1.46820	−0.734102	−	0.679039i	$-0.762397\pi$
$31$	−253.413	−1.46820	−0.734102	+	0.679039i	$0.762397\pi$
$32$	−182.819	−1.00994
$33$	49.6799	0.262066
$34$	29.5362	0.148983
$35$	−35.9591	−0.173663
$36$	153.338	0.709898
$37$	246.339	1.09454	0.547269	−	0.836957i	$-0.315668\pi$
$37$	246.339	1.09454	0.547269	+	0.836957i	$0.315668\pi$
$38$	−500.219	−2.13543
$39$	−128.729	−0.528540
$40$	13.3768	0.0528764
$41$	492.491	1.87596	0.937978	−	0.346695i	$-0.112696\pi$
$41$	492.491	1.87596	0.937978	+	0.346695i	$0.112696\pi$
$42$	−920.222	−3.38079
$43$	0	0
$43$	0	0
$44$	−28.5695	−0.0978866
$45$	−36.8316	−0.122012
$46$	436.871	1.40029
$47$	−335.420	−1.04098	−0.520489	−	0.853868i	$-0.674250\pi$
$47$	−335.420	−1.04098	−0.520489	+	0.853868i	$0.674250\pi$
$48$	623.461	1.87477
$49$	765.982	2.23318
$50$	−437.740	−1.23812
$51$	−65.3179	−0.179340
$52$	74.0281	0.197420
$53$	386.753	1.00235	0.501176	−	0.865345i	$-0.332901\pi$
$53$	386.753	1.00235	0.501176	+	0.865345i	$0.332901\pi$
$54$	−196.456	−0.495078
$55$	6.86235	0.0168240
$56$	−412.542	−0.984432
$57$	1106.21	2.57055
$58$	192.346	0.435452
$59$	−480.563	−1.06041	−0.530203	−	0.847871i	$-0.677884\pi$
$59$	−480.563	−1.06041	−0.530203	+	0.847871i	$0.677884\pi$
$60$	37.9468	0.0816486
$61$	264.683	0.555560	0.277780	−	0.960645i	$-0.410401\pi$
$61$	264.683	0.555560	0.277780	+	0.960645i	$0.410401\pi$
$62$	−895.789	−1.83492
$63$	1135.89	2.27157
$64$	−8.20876	−0.0160327
$65$	−17.7814	−0.0339310
$66$	175.613	0.327523
$67$	−308.944	−0.563337	−0.281668	−	0.959512i	$-0.590888\pi$
$67$	−308.944	−0.563337	−0.281668	+	0.959512i	$0.590888\pi$
$68$	37.5624	0.0669869
$69$	−966.120	−1.68561
$70$	−127.111	−0.217039
$71$	67.5365	0.112889	0.0564444	−	0.998406i	$-0.482024\pi$
$71$	67.5365	0.112889	0.0564444	+	0.998406i	$0.482024\pi$
$72$	−422.552	−0.691642
$73$	−835.918	−1.34023	−0.670115	−	0.742257i	$-0.733755\pi$
$73$	−835.918	−1.34023	−0.670115	+	0.742257i	$0.733755\pi$
$74$	870.782	1.36792
$75$	968.042	1.49040
$76$	−636.150	−0.960150
$77$	−211.636	−0.313223
$78$	−455.042	−0.660556
$79$	−17.9914	−0.0256226	−0.0128113	−	0.999918i	$-0.504078\pi$
$79$	−17.9914	−0.0256226	−0.0128113	+	0.999918i	$0.504078\pi$
$80$	86.1195	0.120356
$81$	−486.502	−0.667355
$82$	1740.90	2.34452
$83$	1011.82	1.33809	0.669046	−	0.743221i	$-0.266703\pi$
$83$	1011.82	1.33809	0.669046	+	0.743221i	$0.266703\pi$
$84$	−1170.29	−1.52010
$85$	−9.02244	−0.0115132
$86$	0	0
$87$	−425.364	−0.524181
$88$	78.7286	0.0953692
$89$	−1240.09	−1.47696	−0.738480	−	0.674276i	$-0.764456\pi$
$89$	−1240.09	−1.47696	−0.738480	+	0.674276i	$0.764456\pi$
$90$	−130.196	−0.152487
$91$	548.382	0.631715
$92$	555.588	0.629609
$93$	1980.99	2.20881
$94$	−1185.67	−1.30099
$95$	152.802	0.165023
$96$	1429.14	1.51939
$97$	−287.048	−0.300467	−0.150233	−	0.988651i	$-0.548002\pi$
$97$	−287.048	−0.300467	−0.150233	+	0.988651i	$0.548002\pi$
$98$	2707.67	2.79098
$99$	−216.771	−0.220064
$100$	−556.693	−0.556693
$101$	182.090	0.179392	0.0896960	−	0.995969i	$-0.471410\pi$
$101$	182.090	0.179392	0.0896960	+	0.995969i	$0.471410\pi$
$102$	−230.892	−0.224134
$103$	−1002.89	−0.959398	−0.479699	−	0.877433i	$-0.659254\pi$
$103$	−1002.89	−0.959398	−0.479699	+	0.877433i	$0.659254\pi$
$104$	−203.998	−0.192343
$105$	281.101	0.261263
$106$	1367.13	1.25271
$107$	−574.209	−0.518793	−0.259397	−	0.965771i	$-0.583524\pi$
$107$	−574.209	−0.518793	−0.259397	+	0.965771i	$0.583524\pi$
$108$	−249.841	−0.222601
$109$	−817.925	−0.718743	−0.359372	−	0.933195i	$-0.617009\pi$
$109$	−817.925	−0.718743	−0.359372	+	0.933195i	$0.617009\pi$
$110$	24.2577	0.0210262
$111$	−1925.69	−1.64666
$112$	−2655.94	−2.24073
$113$	−1835.80	−1.52830	−0.764148	−	0.645040i	$-0.776841\pi$
$113$	−1835.80	−1.52830	−0.764148	+	0.645040i	$0.776841\pi$
$114$	3910.34	3.21260
$115$	−133.451	−0.108212
$116$	244.614	0.195792
$117$	561.688	0.443830
$118$	−1698.74	−1.32527
$119$	278.253	0.214348
$120$	−104.570	−0.0795488
$121$	−1290.61	−0.969656
$122$	935.626	0.694324
$123$	−3849.93	−2.82225
$124$	−1139.21	−0.825035
$125$	268.693	0.192261
$126$	4015.25	2.83895
$127$	−2487.57	−1.73808	−0.869040	−	0.494742i	$-0.835263\pi$
$127$	−2487.57	−1.73808	−0.869040	+	0.494742i	$0.835263\pi$
$128$	1433.53	0.989903
$129$	0	0
$130$	−62.8555	−0.0424061
$131$	1043.93	0.696250	0.348125	−	0.937448i	$-0.386818\pi$
$131$	1043.93	0.696250	0.348125	+	0.937448i	$0.386818\pi$
$132$	223.335	0.147264
$133$	−4712.44	−3.07234
$134$	−1092.09	−0.704044
$135$	60.0114	0.0382590
$136$	−103.510	−0.0652642
$137$	1036.27	0.646238	0.323119	−	0.946358i	$-0.395269\pi$
$137$	1036.27	0.646238	0.323119	+	0.946358i	$0.395269\pi$
$138$	−3415.13	−2.10663
$139$	−2253.15	−1.37489	−0.687444	−	0.726237i	$-0.741267\pi$
$139$	−2253.15	−1.37489	−0.687444	+	0.726237i	$0.741267\pi$
$140$	−161.653	−0.0975870
$141$	2622.06	1.56608
$142$	238.734	0.141085
$143$	−104.652	−0.0611989
$144$	−2720.38	−1.57429
$145$	−58.7560	−0.0336512
$146$	−2954.88	−1.67498
$147$	−5987.88	−3.35967
$148$	1107.41	0.615058
$149$	326.948	0.179763	0.0898813	−	0.995952i	$-0.471351\pi$
$149$	326.948	0.179763	0.0898813	+	0.995952i	$0.471351\pi$
$150$	3421.92	1.86266
$151$	1201.25	0.647393	0.323696	−	0.946161i	$-0.395074\pi$
$151$	1201.25	0.647393	0.323696	+	0.946161i	$0.395074\pi$
$152$	1753.03	0.935457
$153$	285.005	0.150597
$154$	−748.110	−0.391457
$155$	273.637	0.141800
$156$	−578.696	−0.297005
$157$	−446.815	−0.227132	−0.113566	−	0.993530i	$-0.536227\pi$
$157$	−446.815	−0.227132	−0.113566	+	0.993530i	$0.536227\pi$
$158$	−63.5976	−0.0320225
$159$	−3023.35	−1.50797
$160$	197.409	0.0975409
$161$	4115.66	2.01465
$162$	−1719.73	−0.834043
$163$	2436.57	1.17084	0.585420	−	0.810730i	$-0.300930\pi$
$163$	2436.57	1.17084	0.585420	+	0.810730i	$0.300930\pi$
$164$	2213.98	1.05416
$165$	−53.6447	−0.0253105
$166$	3576.68	1.67231
$167$	−941.174	−0.436109	−0.218055	−	0.975937i	$-0.569971\pi$
$167$	−941.174	−0.436109	−0.218055	+	0.975937i	$0.569971\pi$
$168$	3224.94	1.48101
$169$	−1925.83	−0.876572
$170$	−31.8934	−0.0143889
$171$	−4826.79	−2.15856
$172$	0	0
$173$	−3622.60	−1.59203	−0.796015	−	0.605276i	$-0.793063\pi$
$173$	−3622.60	−1.59203	−0.796015	+	0.605276i	$0.793063\pi$
$174$	−1503.62	−0.655108
$175$	−4123.84	−1.78133
$176$	506.853	0.217077
$177$	3756.68	1.59531
$178$	−4383.59	−1.84587
$179$	−1272.84	−0.531490	−0.265745	−	0.964043i	$-0.585618\pi$
$179$	−1272.84	−0.531490	−0.265745	+	0.964043i	$0.585618\pi$
$180$	−165.575	−0.0685626
$181$	388.903	0.159707	0.0798535	−	0.996807i	$-0.474555\pi$
$181$	388.903	0.159707	0.0798535	+	0.996807i	$0.474555\pi$
$182$	1938.47	0.789501
$183$	−2069.09	−0.835802
$184$	−1531.03	−0.613417
$185$	−265.998	−0.105711
$186$	7002.61	2.76052
$187$	−53.1013	−0.0207655
$188$	−1507.87	−0.584961
$189$	−1850.76	−0.712291
$190$	540.140	0.206241
$191$	−1090.91	−0.413273	−0.206637	−	0.978418i	$-0.566252\pi$
$191$	−1090.91	−0.413273	−0.206637	+	0.978418i	$0.566252\pi$
$192$	64.1699	0.0241201
$193$	−1563.18	−0.583006	−0.291503	−	0.956570i	$-0.594155\pi$
$193$	−1563.18	−0.583006	−0.291503	+	0.956570i	$0.594155\pi$
$194$	−1014.68	−0.375515
$195$	139.002	0.0510469
$196$	3443.45	1.25490
$197$	1743.94	0.630714	0.315357	−	0.948973i	$-0.397876\pi$
$197$	1743.94	0.630714	0.315357	+	0.948973i	$0.397876\pi$
$198$	−766.262	−0.275030
$199$	−2681.34	−0.955153	−0.477576	−	0.878590i	$-0.658485\pi$
$199$	−2681.34	−0.955153	−0.477576	+	0.878590i	$0.658485\pi$
$200$	1534.07	0.542376
$201$	2415.10	0.847501
$202$	643.668	0.224199
$203$	1812.04	0.626505
$204$	−293.635	−0.100777
$205$	−531.795	−0.181181
$206$	−3545.12	−1.19903
$207$	4215.52	1.41545
$208$	−1313.34	−0.437806
$209$	899.313	0.297640
$210$	993.662	0.326520
$211$	1214.47	0.396246	0.198123	−	0.980177i	$-0.436515\pi$
$211$	1214.47	0.396246	0.198123	+	0.980177i	$0.436515\pi$
$212$	1738.64	0.563256
$213$	−527.949	−0.169833
$214$	−2029.77	−0.648374
$215$	0	0
$216$	688.484	0.216877
$217$	−8439.01	−2.63999
$218$	−2891.28	−0.898267
$219$	6534.58	2.01628
$220$	30.8495	0.00945397
$221$	137.594	0.0418804
$222$	−6807.12	−2.05795
$223$	1371.11	0.411733	0.205866	−	0.978580i	$-0.433999\pi$
$223$	1371.11	0.411733	0.205866	+	0.978580i	$0.433999\pi$
$224$	−6088.12	−1.81598
$225$	−4223.91	−1.25153
$226$	−6489.36	−1.91003
$227$	−6269.63	−1.83317	−0.916586	−	0.399837i	$-0.869067\pi$
$227$	−6269.63	−1.83317	−0.916586	+	0.399837i	$0.869067\pi$
$228$	4972.94	1.44448
$229$	2566.13	0.740502	0.370251	−	0.928932i	$-0.379272\pi$
$229$	2566.13	0.740502	0.370251	+	0.928932i	$0.379272\pi$
$230$	−471.736	−0.135241
$231$	1654.41	0.471222
$232$	−674.081	−0.190757
$233$	−2868.19	−0.806443	−0.403222	−	0.915102i	$-0.632110\pi$
$233$	−2868.19	−0.806443	−0.403222	+	0.915102i	$0.632110\pi$
$234$	1985.51	0.554687
$235$	362.188	0.100539
$236$	−2160.36	−0.595879
$237$	140.643	0.0385475
$238$	983.596	0.267887
$239$	−2256.13	−0.610614	−0.305307	−	0.952254i	$-0.598759\pi$
$239$	−2256.13	−0.610614	−0.305307	+	0.952254i	$0.598759\pi$
$240$	−673.217	−0.181067
$241$	3471.87	0.927978	0.463989	−	0.885841i	$-0.346418\pi$
$241$	3471.87	0.927978	0.463989	+	0.885841i	$0.346418\pi$
$242$	−4562.18	−1.21185
$243$	5303.66	1.40012
$244$	1189.88	0.312188
$245$	−827.113	−0.215683
$246$	−13609.1	−3.52717
$247$	−2330.26	−0.600288
$248$	3139.31	0.803817
$249$	−7909.65	−2.01307
$250$	949.800	0.240283
$251$	1420.71	0.357268	0.178634	−	0.983916i	$-0.442832\pi$
$251$	1420.71	0.357268	0.178634	+	0.983916i	$0.442832\pi$
$252$	5106.37	1.27647
$253$	−785.423	−0.195174
$254$	−8793.30	−2.17221
$255$	70.5307	0.0173208
$256$	5133.06	1.25319
$257$	2942.79	0.714265	0.357132	−	0.934054i	$-0.383754\pi$
$257$	2942.79	0.714265	0.357132	+	0.934054i	$0.383754\pi$
$258$	0	0
$259$	8203.43	1.96809
$260$	−79.9361	−0.0190670
$261$	1856.01	0.440169
$262$	3690.19	0.870155
$263$	6616.80	1.55137	0.775684	−	0.631122i	$-0.217405\pi$
$263$	6616.80	1.55137	0.775684	+	0.631122i	$0.217405\pi$
$264$	−615.441	−0.143476
$265$	−417.619	−0.0968080
$266$	−16658.0	−3.83972
$267$	9694.10	2.22198
$268$	−1388.85	−0.316558
$269$	−4982.02	−1.12922	−0.564608	−	0.825359i	$-0.690973\pi$
$269$	−4982.02	−1.12922	−0.564608	+	0.825359i	$0.690973\pi$
$270$	212.134	0.0478151
$271$	677.961	0.151967	0.0759837	−	0.997109i	$-0.475790\pi$
$271$	677.961	0.151967	0.0759837	+	0.997109i	$0.475790\pi$
$272$	−666.397	−0.148552
$273$	−4286.84	−0.950372
$274$	3663.11	0.807651
$275$	786.986	0.172571
$276$	−4343.17	−0.947203
$277$	−1893.18	−0.410651	−0.205326	−	0.978694i	$-0.565825\pi$
$277$	−1893.18	−0.410651	−0.205326	+	0.978694i	$0.565825\pi$
$278$	−7964.64	−1.71830
$279$	−8643.78	−1.85480
$280$	445.465	0.0950773
$281$	−2436.21	−0.517196	−0.258598	−	0.965985i	$-0.583261\pi$
$281$	−2436.21	−0.517196	−0.258598	+	0.965985i	$0.583261\pi$
$282$	9268.70	1.95724
$283$	−3181.08	−0.668181	−0.334091	−	0.942541i	$-0.608429\pi$
$283$	−3181.08	−0.668181	−0.334091	+	0.942541i	$0.608429\pi$
$284$	303.608	0.0634361
$285$	−1194.49	−0.248266
$286$	−369.934	−0.0764848
$287$	16400.6	3.37317
$288$	−6235.84	−1.27587
$289$	−4843.18	−0.985790
$290$	−207.696	−0.0420564
$291$	2243.92	0.452031
$292$	−3757.85	−0.753121
$293$	−3835.76	−0.764804	−0.382402	−	0.923996i	$-0.624903\pi$
$293$	−3835.76	−0.764804	−0.382402	+	0.923996i	$0.624903\pi$
$294$	−21166.5	−4.19883
$295$	518.915	0.102415
$296$	−3051.68	−0.599240
$297$	353.195	0.0690049
$298$	1155.73	0.224662
$299$	2035.16	0.393633
$300$	4351.81	0.837506
$301$	0	0
$302$	4246.29	0.809095
$303$	−1423.44	−0.269883
$304$	11286.0	2.12926
$305$	−285.806	−0.0536565
$306$	1007.46	0.188212
$307$	−1959.51	−0.364284	−0.182142	−	0.983272i	$-0.558303\pi$
$307$	−1959.51	−0.364284	−0.182142	+	0.983272i	$0.558303\pi$
$308$	−951.403	−0.176011
$309$	7839.87	1.44335
$310$	967.279	0.177219
$311$	−499.497	−0.0910735	−0.0455368	−	0.998963i	$-0.514500\pi$
$311$	−499.497	−0.0910735	−0.0455368	+	0.998963i	$0.514500\pi$
$312$	1594.71	0.289367
$313$	2114.30	0.381812	0.190906	−	0.981608i	$-0.438857\pi$
$313$	2114.30	0.381812	0.190906	+	0.981608i	$0.438857\pi$
$314$	−1579.44	−0.283863
$315$	−1226.54	−0.219390
$316$	−80.8798	−0.0143982
$317$	−5233.27	−0.927223	−0.463611	−	0.886039i	$-0.653447\pi$
$317$	−5233.27	−0.927223	−0.463611	+	0.886039i	$0.653447\pi$
$318$	−10687.2	−1.88462
$319$	−345.806	−0.0606942
$320$	8.86387	0.00154845
$321$	4488.74	0.780489
$322$	14548.4	2.51786
$323$	−1182.39	−0.203685
$324$	−2187.06	−0.375010
$325$	−2039.21	−0.348045
$326$	8613.01	1.46328
$327$	6393.93	1.08130
$328$	−6101.04	−1.02705
$329$	−11169.9	−1.87179
$330$	−189.628	−0.0316324
$331$	1835.50	0.304798	0.152399	−	0.988319i	$-0.451300\pi$
$331$	1835.50	0.304798	0.152399	+	0.988319i	$0.451300\pi$
$332$	4548.61	0.751920
$333$	8402.48	1.38274
$334$	−3326.95	−0.545038
$335$	333.600	0.0544076
$336$	20762.1	3.37103
$337$	−579.996	−0.0937519	−0.0468759	−	0.998901i	$-0.514927\pi$
$337$	−579.996	−0.0937519	−0.0468759	+	0.998901i	$0.514927\pi$
$338$	−6807.60	−1.09552
$339$	14350.9	2.29922
$340$	−40.5602	−0.00646966
$341$	1610.48	0.255755
$342$	−17062.2	−2.69771
$343$	14085.9	2.21740
$344$	0	0
$345$	1043.22	0.162798
$346$	−12805.5	−1.98968
$347$	21.1393	0.00327037	0.00163518	−	0.999999i	$-0.499480\pi$
$347$	21.1393	0.00327037	0.00163518	+	0.999999i	$0.499480\pi$
$348$	−1912.21	−0.294555
$349$	6876.17	1.05465	0.527325	−	0.849664i	$-0.323195\pi$
$349$	6876.17	1.05465	0.527325	+	0.849664i	$0.323195\pi$
$350$	−14577.4	−2.22626
$351$	−915.185	−0.139171
$352$	1161.84	0.175927
$353$	−7977.84	−1.20288	−0.601442	−	0.798917i	$-0.705407\pi$
$353$	−7977.84	−1.20288	−0.601442	+	0.798917i	$0.705407\pi$
$354$	13279.5	1.99377
$355$	−72.9263	−0.0109029
$356$	−5574.80	−0.829954
$357$	−2175.18	−0.322472
$358$	−4499.36	−0.664242
$359$	−8138.55	−1.19648	−0.598240	−	0.801317i	$-0.704133\pi$
$359$	−8138.55	−1.19648	−0.598240	+	0.801317i	$0.704133\pi$
$360$	456.274	0.0667993
$361$	13165.8	1.91949
$362$	1374.73	0.199598
$363$	10089.0	1.45878
$364$	2465.24	0.354982
$365$	902.630	0.129441
$366$	−7314.02	−1.04456
$367$	−318.114	−0.0452464	−0.0226232	−	0.999744i	$-0.507202\pi$
$367$	−318.114	−0.0452464	−0.0226232	+	0.999744i	$0.507202\pi$
$368$	−9856.71	−1.39624
$369$	16798.6	2.36992
$370$	−940.276	−0.132115
$371$	12879.4	1.80234
$372$	8905.51	1.24121
$373$	337.098	0.0467943	0.0233972	−	0.999726i	$-0.492552\pi$
$373$	337.098	0.0467943	0.0233972	+	0.999726i	$0.492552\pi$
$374$	−187.707	−0.0259522
$375$	−2100.44	−0.289243
$376$	4155.22	0.569918
$377$	896.040	0.122410
$378$	−6542.24	−0.890203
$379$	−1600.93	−0.216976	−0.108488	−	0.994098i	$-0.534601\pi$
$379$	−1600.93	−0.216976	−0.108488	+	0.994098i	$0.534601\pi$
$380$	686.919	0.0927321
$381$	19446.0	2.61482
$382$	−3856.24	−0.516498
$383$	−3960.47	−0.528383	−0.264191	−	0.964470i	$-0.585105\pi$
$383$	−3960.47	−0.528383	−0.264191	+	0.964470i	$0.585105\pi$
$384$	−11206.3	−1.48924
$385$	228.526	0.0302513
$386$	−5525.68	−0.728626
$387$	0	0
$388$	−1290.42	−0.168843
$389$	−2377.10	−0.309830	−0.154915	−	0.987928i	$-0.549510\pi$
$389$	−2377.10	−0.309830	−0.154915	+	0.987928i	$0.549510\pi$
$390$	491.357	0.0637971
$391$	1032.65	0.133564
$392$	−9489.08	−1.22263
$393$	−8160.68	−1.04746
$394$	6164.65	0.788250
$395$	19.4272	0.00247466
$396$	−974.488	−0.123661
$397$	−5522.04	−0.698094	−0.349047	−	0.937105i	$-0.613495\pi$
$397$	−5522.04	−0.698094	−0.349047	+	0.937105i	$0.613495\pi$
$398$	−9478.26	−1.19372
$399$	36838.4	4.62212
$400$	9876.32	1.23454
$401$	−5659.01	−0.704732	−0.352366	−	0.935862i	$-0.614623\pi$
$401$	−5659.01	−0.704732	−0.352366	+	0.935862i	$0.614623\pi$
$402$	8537.11	1.05918
$403$	−4173.02	−0.515814
$404$	818.580	0.100807
$405$	525.328	0.0644537
$406$	6405.38	0.782990
$407$	−1565.52	−0.190664
$408$	809.166	0.0981855
$409$	−51.5079	−0.00622715	−0.00311357	−	0.999995i	$-0.500991\pi$
$409$	−51.5079	−0.00622715	−0.00311357	+	0.999995i	$0.500991\pi$
$410$	−1879.84	−0.226436
$411$	−8100.79	−0.972220
$412$	−4508.48	−0.539119
$413$	−16003.4	−1.90672
$414$	14901.4	1.76900
$415$	−1092.57	−0.129234
$416$	−3010.52	−0.354815
$417$	17613.4	2.06842
$418$	3178.97	0.371983
$419$	−9152.59	−1.06714	−0.533572	−	0.845755i	$-0.679151\pi$
$419$	−9152.59	−1.06714	−0.533572	+	0.845755i	$0.679151\pi$
$420$	1263.68	0.146813
$421$	6750.56	0.781478	0.390739	−	0.920502i	$-0.372220\pi$
$421$	6750.56	0.781478	0.390739	+	0.920502i	$0.372220\pi$
$422$	4293.04	0.495218
$423$	−11441.0	−1.31508
$424$	−4791.15	−0.548771
$425$	−1034.71	−0.118096
$426$	−1866.25	−0.212253
$427$	8814.30	0.998956
$428$	−2581.34	−0.291528
$429$	818.092	0.0920695
$430$	0	0
$431$	2652.89	0.296485	0.148243	−	0.988951i	$-0.452638\pi$
$431$	2652.89	0.296485	0.148243	+	0.988951i	$0.452638\pi$
$432$	4432.44	0.493648
$433$	−5593.70	−0.620822	−0.310411	−	0.950602i	$-0.600467\pi$
$433$	−5593.70	−0.620822	−0.310411	+	0.950602i	$0.600467\pi$
$434$	−29831.0	−3.29939
$435$	459.311	0.0506259
$436$	−3676.96	−0.403887
$437$	−17488.8	−1.91443
$438$	23099.0	2.51990
$439$	−17064.4	−1.85521	−0.927605	−	0.373563i	$-0.878136\pi$
$439$	−17064.4	−1.85521	−0.927605	+	0.373563i	$0.878136\pi$
$440$	−85.0116	−0.00921084
$441$	26127.2	2.82121
$442$	486.380	0.0523410
$443$	−5178.57	−0.555398	−0.277699	−	0.960668i	$-0.589572\pi$
$443$	−5178.57	−0.555398	−0.277699	+	0.960668i	$0.589572\pi$
$444$	−8656.91	−0.925312
$445$	1339.06	0.142646
$446$	4846.73	0.514573
$447$	−2555.83	−0.270440
$448$	−273.363	−0.0288285
$449$	10238.7	1.07616	0.538079	−	0.842894i	$-0.319150\pi$
$449$	10238.7	1.07616	0.538079	+	0.842894i	$0.319150\pi$
$450$	−14931.1	−1.56413
$451$	−3129.86	−0.326784
$452$	−8252.79	−0.858803
$453$	−9390.47	−0.973958
$454$	−22162.5	−2.29105
$455$	−592.147	−0.0610116
$456$	−13703.9	−1.40733
$457$	−6009.74	−0.615150	−0.307575	−	0.951524i	$-0.599518\pi$
$457$	−6009.74	−0.615150	−0.307575	+	0.951524i	$0.599518\pi$
$458$	9071.01	0.925460
$459$	−464.372	−0.0472223
$460$	−599.927	−0.0608082
$461$	13361.1	1.34987	0.674933	−	0.737879i	$-0.264173\pi$
$461$	13361.1	1.34987	0.674933	+	0.737879i	$0.264173\pi$
$462$	5848.16	0.588920
$463$	−14853.4	−1.49092	−0.745461	−	0.666550i	$-0.767771\pi$
$463$	−14853.4	−1.49092	−0.745461	+	0.666550i	$0.767771\pi$
$464$	−4339.72	−0.434195
$465$	−2139.09	−0.213329
$466$	−10138.7	−1.00787
$467$	−4779.44	−0.473589	−0.236794	−	0.971560i	$-0.576097\pi$
$467$	−4779.44	−0.473589	−0.236794	+	0.971560i	$0.576097\pi$
$468$	2525.06	0.249403
$469$	−10288.3	−1.01294
$470$	1280.30	0.125650
$471$	3492.86	0.341704
$472$	5953.27	0.580554
$473$	0	0
$474$	497.158	0.0481756
$475$	17523.6	1.69271
$476$	1250.88	0.120450
$477$	13191.9	1.26628
$478$	−7975.17	−0.763129
$479$	−12824.8	−1.22334	−0.611670	−	0.791113i	$-0.709502\pi$
$479$	−12824.8	−1.22334	−0.611670	+	0.791113i	$0.709502\pi$
$480$	−1543.19	−0.146744
$481$	4056.52	0.384536
$482$	12272.7	1.15976
$483$	−32173.1	−3.03091
$484$	−5801.91	−0.544883
$485$	309.956	0.0290193
$486$	18747.9	1.74984
$487$	2927.00	0.272351	0.136175	−	0.990685i	$-0.456519\pi$
$487$	2927.00	0.272351	0.136175	+	0.990685i	$0.456519\pi$
$488$	−3278.92	−0.304160
$489$	−19047.3	−1.76145
$490$	−2923.76	−0.269555
$491$	20421.5	1.87700	0.938501	−	0.345275i	$-0.112214\pi$
$491$	20421.5	1.87700	0.938501	+	0.345275i	$0.112214\pi$
$492$	−17307.2	−1.58592
$493$	454.657	0.0415350
$494$	−8237.23	−0.750224
$495$	234.071	0.0212539
$496$	20210.8	1.82962
$497$	2249.06	0.202986
$498$	−27959.8	−2.51588
$499$	14855.3	1.33270	0.666348	−	0.745641i	$-0.267856\pi$
$499$	14855.3	1.33270	0.666348	+	0.745641i	$0.267856\pi$
$500$	1207.90	0.108038
$501$	7357.39	0.656096
$502$	5022.06	0.446505
$503$	−11694.4	−1.03663	−0.518317	−	0.855188i	$-0.673441\pi$
$503$	−11694.4	−1.03663	−0.518317	+	0.855188i	$0.673441\pi$
$504$	−14071.6	−1.24364
$505$	−196.622	−0.0173258
$506$	−2776.39	−0.243924
$507$	15054.7	1.31874
$508$	−11182.8	−0.976687
$509$	13214.1	1.15070	0.575348	−	0.817909i	$-0.304867\pi$
$509$	13214.1	1.15070	0.575348	+	0.817909i	$0.304867\pi$
$510$	249.318	0.0216471
$511$	−27837.2	−2.40988
$512$	6676.55	0.576298
$513$	7864.51	0.676855
$514$	10402.4	0.892670
$515$	1082.93	0.0926595
$516$	0	0
$517$	2131.65	0.181334
$518$	28998.2	2.45967
$519$	28318.8	2.39510
$520$	220.279	0.0185767
$521$	14682.6	1.23465	0.617327	−	0.786707i	$-0.288216\pi$
$521$	14682.6	1.23465	0.617327	+	0.786707i	$0.288216\pi$
$522$	6560.80	0.550112
$523$	13237.8	1.10679	0.553394	−	0.832920i	$-0.313332\pi$
$523$	13237.8	1.10679	0.553394	+	0.832920i	$0.313332\pi$
$524$	4692.97	0.391247
$525$	32237.1	2.67989
$526$	23389.7	1.93886
$527$	−2117.42	−0.175021
$528$	−3962.20	−0.326577
$529$	3107.04	0.255366
$530$	−1476.24	−0.120988
$531$	−16391.7	−1.33962
$532$	−21184.7	−1.72645
$533$	8109.97	0.659066
$534$	34267.6	2.77698
$535$	620.035	0.0501055
$536$	3827.24	0.308417
$537$	9950.13	0.799590
$538$	−17610.9	−1.41126
$539$	−4867.94	−0.389011
$540$	269.780	0.0214990
$541$	16167.1	1.28480	0.642400	−	0.766370i	$-0.277939\pi$
$541$	16167.1	1.28480	0.642400	+	0.766370i	$0.277939\pi$
$542$	2396.52	0.189925
$543$	−3040.15	−0.240268
$544$	−1527.56	−0.120393
$545$	883.201	0.0694169
$546$	−15153.5	−1.18775
$547$	10235.6	0.800077	0.400038	−	0.916498i	$-0.368997\pi$
$547$	10235.6	0.800077	0.400038	+	0.916498i	$0.368997\pi$
$548$	4658.53	0.363143
$549$	9028.18	0.701846
$550$	2781.91	0.215675
$551$	−7699.99	−0.595337
$552$	11968.4	0.922843
$553$	−599.138	−0.0460722
$554$	−6692.21	−0.513221
$555$	2079.38	0.159035
$556$	−10129.0	−0.772597
$557$	−16151.9	−1.22868	−0.614342	−	0.789040i	$-0.710578\pi$
$557$	−16151.9	−1.22868	−0.614342	+	0.789040i	$0.710578\pi$
$558$	−30554.8	−2.31808
$559$	0	0
$560$	2867.90	0.216412
$561$	415.106	0.0312403
$562$	−8611.74	−0.646378
$563$	18574.5	1.39045	0.695224	−	0.718793i	$-0.255305\pi$
$563$	18574.5	1.39045	0.695224	+	0.718793i	$0.255305\pi$
$564$	11787.4	0.880034
$565$	1982.31	0.147604
$566$	−11244.8	−0.835076
$567$	−16201.2	−1.19998
$568$	−836.650	−0.0618047
$569$	9426.53	0.694518	0.347259	−	0.937769i	$-0.387113\pi$
$569$	9426.53	0.694518	0.347259	+	0.937769i	$0.387113\pi$
$570$	−4222.41	−0.310276
$571$	4825.73	0.353679	0.176839	−	0.984240i	$-0.443413\pi$
$571$	4825.73	0.353679	0.176839	+	0.984240i	$0.443413\pi$
$572$	−470.461	−0.0343898
$573$	8527.89	0.621741
$574$	57974.5	4.21570
$575$	−15304.4	−1.10998
$576$	−279.996	−0.0202543
$577$	−9870.62	−0.712165	−0.356083	−	0.934455i	$-0.615888\pi$
$577$	−9870.62	−0.712165	−0.356083	+	0.934455i	$0.615888\pi$
$578$	−17120.1	−1.23201
$579$	12219.8	0.877093
$580$	−264.136	−0.0189098
$581$	33695.0	2.40603
$582$	7932.03	0.564937
$583$	−2457.88	−0.174606
$584$	10355.5	0.733753
$585$	−606.515	−0.0428655
$586$	−13559.0	−0.955833
$587$	−22261.7	−1.56531	−0.782657	−	0.622453i	$-0.786136\pi$
$587$	−22261.7	−1.56531	−0.782657	+	0.622453i	$0.786136\pi$
$588$	−26918.3	−1.88791
$589$	35860.2	2.50865
$590$	1834.31	0.127995
$591$	−13632.8	−0.948866
$592$	−19646.6	−1.36397
$593$	6241.50	0.432222	0.216111	−	0.976369i	$-0.430663\pi$
$593$	6241.50	0.432222	0.216111	+	0.976369i	$0.430663\pi$
$594$	1248.51	0.0862406
$595$	−300.460	−0.0207019
$596$	1469.79	0.101015
$597$	20960.7	1.43696
$598$	7194.07	0.491952
$599$	735.572	0.0501747	0.0250873	−	0.999685i	$-0.492014\pi$
$599$	735.572	0.0501747	0.0250873	+	0.999685i	$0.492014\pi$
$600$	−11992.2	−0.815967
$601$	−15890.1	−1.07848	−0.539242	−	0.842151i	$-0.681289\pi$
$601$	−15890.1	−1.07848	−0.539242	+	0.842151i	$0.681289\pi$
$602$	0	0
$603$	−10537.9	−0.711670
$604$	5400.19	0.363792
$605$	1393.61	0.0936502
$606$	−5031.71	−0.337293
$607$	12391.3	0.828580	0.414290	−	0.910145i	$-0.364030\pi$
$607$	12391.3	0.828580	0.414290	+	0.910145i	$0.364030\pi$
$608$	25870.5	1.72564
$609$	−14165.2	−0.942533
$610$	−1010.30	−0.0670584
$611$	−5523.44	−0.365719
$612$	1281.23	0.0846254
$613$	15142.2	0.997699	0.498850	−	0.866689i	$-0.333756\pi$
$613$	15142.2	0.997699	0.498850	+	0.866689i	$0.333756\pi$
$614$	−6926.66	−0.455273
$615$	4157.18	0.272575
$616$	2621.77	0.171484
$617$	19712.7	1.28623	0.643113	−	0.765771i	$-0.277643\pi$
$617$	19712.7	1.28623	0.643113	+	0.765771i	$0.277643\pi$
$618$	27713.1	1.80386
$619$	18495.4	1.20096	0.600478	−	0.799641i	$-0.294977\pi$
$619$	18495.4	1.20096	0.600478	+	0.799641i	$0.294977\pi$
$620$	1230.13	0.0796826
$621$	−6868.55	−0.443841
$622$	−1765.67	−0.113821
$623$	−41296.7	−2.65573
$624$	10266.7	0.658648
$625$	15189.1	0.972103
$626$	7473.83	0.477179
$627$	−7030.15	−0.447779
$628$	−2008.64	−0.127633
$629$	2058.31	0.130477
$630$	−4335.70	−0.274188
$631$	−5867.54	−0.370179	−0.185090	−	0.982722i	$-0.559258\pi$
$631$	−5867.54	−0.370179	−0.185090	+	0.982722i	$0.559258\pi$
$632$	222.879	0.0140280
$633$	−9493.85	−0.596124
$634$	−18499.0	−1.15882
$635$	2686.10	0.167865
$636$	−13591.4	−0.847380
$637$	12613.6	0.784568
$638$	−1222.39	−0.0758540
$639$	2303.63	0.142614
$640$	−1547.94	−0.0956057
$641$	16245.6	1.00103	0.500517	−	0.865727i	$-0.333143\pi$
$641$	16245.6	1.00103	0.500517	+	0.865727i	$0.333143\pi$
$642$	15867.2	0.975434
$643$	18563.9	1.13855	0.569276	−	0.822147i	$-0.307224\pi$
$643$	18563.9	1.13855	0.569276	+	0.822147i	$0.307224\pi$
$644$	18501.8	1.13210
$645$	0	0
$646$	−4179.63	−0.254560
$647$	−25883.5	−1.57277	−0.786386	−	0.617735i	$-0.788050\pi$
$647$	−25883.5	−1.57277	−0.786386	+	0.617735i	$0.788050\pi$
$648$	6026.85	0.365366
$649$	3054.06	0.184718
$650$	−7208.38	−0.434978
$651$	65969.9	3.97168
$652$	10953.5	0.657935
$653$	−26760.2	−1.60369	−0.801843	−	0.597535i	$-0.796147\pi$
$653$	−26760.2	−1.60369	−0.801843	+	0.597535i	$0.796147\pi$
$654$	22601.9	1.35138
$655$	−1127.25	−0.0672444
$656$	−39278.4	−2.33775
$657$	−28512.7	−1.69313
$658$	−39484.5	−2.33931
$659$	−1429.13	−0.0844781	−0.0422390	−	0.999108i	$-0.513449\pi$
$659$	−1429.13	−0.0844781	−0.0422390	+	0.999108i	$0.513449\pi$
$660$	−241.158	−0.0142228
$661$	20836.3	1.22608	0.613040	−	0.790052i	$-0.289946\pi$
$661$	20836.3	1.22608	0.613040	+	0.790052i	$0.289946\pi$
$662$	6488.30	0.380929
$663$	−1075.61	−0.0630061
$664$	−12534.5	−0.732583
$665$	5088.53	0.296729
$666$	29701.9	1.72811
$667$	6724.86	0.390386
$668$	−4231.02	−0.245065
$669$	−10718.3	−0.619423
$670$	1179.24	0.0679971
$671$	−1682.10	−0.0967763
$672$	47592.3	2.73202
$673$	8550.02	0.489716	0.244858	−	0.969559i	$-0.421259\pi$
$673$	8550.02	0.489716	0.244858	+	0.969559i	$0.421259\pi$
$674$	−2050.22	−0.117169
$675$	6882.21	0.392439
$676$	−8657.52	−0.492576
$677$	22443.6	1.27412	0.637059	−	0.770815i	$-0.280151\pi$
$677$	22443.6	1.27412	0.637059	+	0.770815i	$0.280151\pi$
$678$	50728.9	2.87350
$679$	−9559.08	−0.540271
$680$	111.771	0.00630327
$681$	49011.3	2.75788
$682$	5692.89	0.319636
$683$	−28556.4	−1.59982	−0.799912	−	0.600118i	$-0.795120\pi$
$683$	−28556.4	−1.59982	−0.799912	+	0.600118i	$0.795120\pi$
$684$	−21698.7	−1.21297
$685$	−1118.97	−0.0624142
$686$	49792.1	2.77124
$687$	−20060.1	−1.11403
$688$	0	0
$689$	6368.76	0.352149
$690$	3687.68	0.203460
$691$	−13020.8	−0.716837	−0.358418	−	0.933561i	$-0.616684\pi$
$691$	−13020.8	−0.716837	−0.358418	+	0.933561i	$0.616684\pi$
$692$	−16285.3	−0.894617
$693$	−7218.77	−0.395698
$694$	74.7252	0.00408722
$695$	2432.96	0.132788
$696$	5269.46	0.286980
$697$	4115.06	0.223629
$698$	24306.5	1.31807
$699$	22421.3	1.21324
$700$	−18538.6	−1.00099
$701$	−13786.5	−0.742811	−0.371405	−	0.928471i	$-0.621124\pi$
$701$	−13786.5	−0.742811	−0.371405	+	0.928471i	$0.621124\pi$
$702$	−3235.08	−0.173932
$703$	−34859.2	−1.87018
$704$	52.1680	0.00279283
$705$	−2831.32	−0.151253
$706$	−28200.8	−1.50333
$707$	6063.84	0.322566
$708$	16888.1	0.896458
$709$	−1202.37	−0.0636895	−0.0318448	−	0.999493i	$-0.510138\pi$
$709$	−1202.37	−0.0636895	−0.0318448	+	0.999493i	$0.510138\pi$
$710$	−257.787	−0.0136262
$711$	−613.675	−0.0323694
$712$	15362.4	0.808610
$713$	−31318.9	−1.64502
$714$	−7689.02	−0.403017
$715$	113.004	0.00591064
$716$	−5722.03	−0.298663
$717$	17636.7	0.918626
$718$	−28768.9	−1.49533
$719$	10079.5	0.522814	0.261407	−	0.965229i	$-0.415814\pi$
$719$	10079.5	0.522814	0.261407	+	0.965229i	$0.415814\pi$
$720$	2937.48	0.152047
$721$	−33397.7	−1.72510
$722$	46539.6	2.39893
$723$	−27140.5	−1.39608
$724$	1748.31	0.0897448
$725$	−6738.24	−0.345175
$726$	35663.7	1.82314
$727$	28825.4	1.47053	0.735265	−	0.677779i	$-0.237058\pi$
$727$	28825.4	1.47053	0.735265	+	0.677779i	$0.237058\pi$
$728$	−6793.43	−0.345853
$729$	−28324.5	−1.43903
$730$	3190.70	0.161771
$731$	0	0
$732$	−9301.55	−0.469666
$733$	−19783.5	−0.996892	−0.498446	−	0.866921i	$-0.666096\pi$
$733$	−19783.5	−0.996892	−0.498446	+	0.866921i	$0.666096\pi$
$734$	−1124.50	−0.0565478
$735$	6465.75	0.324480
$736$	−22594.2	−1.13157
$737$	1963.39	0.0981309
$738$	59381.2	2.96186
$739$	946.083	0.0470937	0.0235468	−	0.999723i	$-0.492504\pi$
$739$	946.083	0.0470937	0.0235468	+	0.999723i	$0.492504\pi$
$740$	−1195.79	−0.0594028
$741$	18216.3	0.903091
$742$	45527.4	2.25251
$743$	2376.31	0.117333	0.0586664	−	0.998278i	$-0.481315\pi$
$743$	2376.31	0.117333	0.0586664	+	0.998278i	$0.481315\pi$
$744$	−24540.8	−1.20929
$745$	−353.041	−0.0173616
$746$	1191.61	0.0584823
$747$	34512.6	1.69043
$748$	−238.715	−0.0116688
$749$	−19122.0	−0.932845
$750$	−7424.83	−0.361488
$751$	6844.89	0.332588	0.166294	−	0.986076i	$-0.446820\pi$
$751$	6844.89	0.332588	0.166294	+	0.986076i	$0.446820\pi$
$752$	26751.2	1.29723
$753$	−11106.0	−0.537485
$754$	3167.41	0.152984
$755$	−1297.12	−0.0625258
$756$	−8320.05	−0.400261
$757$	30909.6	1.48406	0.742028	−	0.670369i	$-0.233864\pi$
$757$	30909.6	1.48406	0.742028	+	0.670369i	$0.233864\pi$
$758$	−5659.10	−0.271171
$759$	6139.85	0.293626
$760$	−1892.93	−0.0903473
$761$	22285.2	1.06155	0.530774	−	0.847513i	$-0.321901\pi$
$761$	22285.2	1.06155	0.530774	+	0.847513i	$0.321901\pi$
$762$	68739.4	3.26793
$763$	−27238.0	−1.29238
$764$	−4904.14	−0.232232
$765$	−307.750	−0.0145447
$766$	−13999.8	−0.660359
$767$	−7913.55	−0.372545
$768$	−40126.4	−1.88533
$769$	−2946.09	−0.138152	−0.0690758	−	0.997611i	$-0.522005\pi$
$769$	−2946.09	−0.138152	−0.0690758	+	0.997611i	$0.522005\pi$
$770$	807.814	0.0378073
$771$	−23004.5	−1.07456
$772$	−7027.24	−0.327611
$773$	36175.2	1.68322	0.841612	−	0.540082i	$-0.181607\pi$
$773$	36175.2	1.68322	0.841612	+	0.540082i	$0.181607\pi$
$774$	0	0
$775$	31381.2	1.45451
$776$	3555.98	0.164500
$777$	−64128.3	−2.96086
$778$	−8402.81	−0.387218
$779$	−69691.9	−3.20535
$780$	624.880	0.0286850
$781$	−429.205	−0.0196648
$782$	3650.32	0.166925
$783$	−3024.09	−0.138023
$784$	−61090.5	−2.78291
$785$	482.473	0.0219366
$786$	−28847.1	−1.30909
$787$	−2197.30	−0.0995237	−0.0497619	−	0.998761i	$-0.515846\pi$
$787$	−2197.30	−0.0995237	−0.0497619	+	0.998761i	$0.515846\pi$
$788$	7839.85	0.354420
$789$	−51725.2	−2.33392
$790$	68.6731	0.00309276
$791$	−61134.7	−2.74804
$792$	2685.39	0.120481
$793$	4358.60	0.195181
$794$	−19519.8	−0.872460
$795$	3264.63	0.145641
$796$	−12053.9	−0.536733
$797$	−26747.2	−1.18875	−0.594375	−	0.804188i	$-0.702600\pi$
$797$	−26747.2	−1.18875	−0.594375	+	0.804188i	$0.702600\pi$
$798$	130220.	5.77660
$799$	−2802.63	−0.124093
$800$	22639.2	1.00052
$801$	−42298.8	−1.86586
$802$	−20004.0	−0.880756
$803$	5312.40	0.233462
$804$	10857.0	0.476240
$805$	−4444.12	−0.194577
$806$	−14751.2	−0.644650
$807$	38945.7	1.69883
$808$	−2255.75	−0.0982141
$809$	−24269.0	−1.05470	−0.527351	−	0.849648i	$-0.676815\pi$
$809$	−24269.0	−1.05470	−0.527351	+	0.849648i	$0.676815\pi$
$810$	1856.98	0.0805526
$811$	−39266.0	−1.70014	−0.850071	−	0.526668i	$-0.823441\pi$
$811$	−39266.0	−1.70014	−0.850071	+	0.526668i	$0.823441\pi$
$812$	8146.00	0.352055
$813$	−5299.79	−0.228625
$814$	−5533.96	−0.238287
$815$	−2631.02	−0.113081
$816$	5209.39	0.223487
$817$	0	0
$818$	−182.075	−0.00778253
$819$	18705.0	0.798053
$820$	−2390.67	−0.101812
$821$	15760.0	0.669950	0.334975	−	0.942227i	$-0.391272\pi$
$821$	15760.0	0.669950	0.334975	+	0.942227i	$0.391272\pi$
$822$	−28635.4	−1.21505
$823$	−11856.7	−0.502185	−0.251092	−	0.967963i	$-0.580790\pi$
$823$	−11856.7	−0.502185	−0.251092	+	0.967963i	$0.580790\pi$
$824$	12424.0	0.525254
$825$	−6152.06	−0.259621
$826$	−56570.4	−2.38297
$827$	5549.47	0.233342	0.116671	−	0.993171i	$-0.462778\pi$
$827$	5549.47	0.233342	0.116671	+	0.993171i	$0.462778\pi$
$828$	18950.8	0.795392
$829$	−11901.0	−0.498600	−0.249300	−	0.968426i	$-0.580201\pi$
$829$	−11901.0	−0.498600	−0.249300	+	0.968426i	$0.580201\pi$
$830$	−3862.12	−0.161513
$831$	14799.5	0.617796
$832$	−135.176	−0.00563266
$833$	6400.25	0.266213
$834$	62261.6	2.58506
$835$	1016.29	0.0421198
$836$	4042.84	0.167254
$837$	14083.7	0.581606
$838$	−32353.4	−1.33369
$839$	−13419.6	−0.552200	−0.276100	−	0.961129i	$-0.589042\pi$
$839$	−13419.6	−0.552200	−0.276100	+	0.961129i	$0.589042\pi$
$840$	−3482.31	−0.143037
$841$	−21428.2	−0.878600
$842$	23862.5	0.976670
$843$	19044.5	0.778086
$844$	5459.64	0.222664
$845$	2079.52	0.0846601
$846$	−40442.6	−1.64355
$847$	−42979.2	−1.74354
$848$	−30845.3	−1.24910
$849$	24867.3	1.00523
$850$	−3657.58	−0.147593
$851$	30444.6	1.22635
$852$	−2373.38	−0.0954352
$853$	36696.4	1.47299	0.736496	−	0.676442i	$-0.236479\pi$
$853$	36696.4	1.47299	0.736496	+	0.676442i	$0.236479\pi$
$854$	31157.6	1.24847
$855$	5212.00	0.208476
$856$	7113.37	0.284030
$857$	−39381.5	−1.56971	−0.784857	−	0.619677i	$-0.787264\pi$
$857$	−39381.5	−1.56971	−0.784857	+	0.619677i	$0.787264\pi$
$858$	2891.87	0.115066
$859$	6521.17	0.259022	0.129511	−	0.991578i	$-0.458659\pi$
$859$	6521.17	0.259022	0.129511	+	0.991578i	$0.458659\pi$
$860$	0	0
$861$	−128208.	−5.07470
$862$	9377.68	0.370540
$863$	11989.4	0.472912	0.236456	−	0.971642i	$-0.424014\pi$
$863$	11989.4	0.472912	0.236456	+	0.971642i	$0.424014\pi$
$864$	10160.4	0.400072
$865$	3911.71	0.153760
$866$	−19773.1	−0.775887
$867$	37860.4	1.48305
$868$	−37937.4	−1.48350
$869$	114.338	0.00446336
$870$	1623.61	0.0632709
$871$	−5087.46	−0.197913
$872$	10132.6	0.393500
$873$	−9791.02	−0.379583
$874$	−61821.2	−2.39260
$875$	8947.84	0.345705
$876$	29376.0	1.13302
$877$	−11656.2	−0.448807	−0.224403	−	0.974496i	$-0.572043\pi$
$877$	−11656.2	−0.448807	−0.224403	+	0.974496i	$0.572043\pi$
$878$	−60320.7	−2.31859
$879$	29985.1	1.15060
$880$	−547.303	−0.0209654
$881$	2593.62	0.0991843	0.0495922	−	0.998770i	$-0.484208\pi$
$881$	2593.62	0.0991843	0.0495922	+	0.998770i	$0.484208\pi$
$882$	92356.9	3.52587
$883$	−6995.75	−0.266620	−0.133310	−	0.991074i	$-0.542561\pi$
$883$	−6995.75	−0.266620	−0.133310	+	0.991074i	$0.542561\pi$
$884$	618.550	0.0235340
$885$	−4056.49	−0.154076
$886$	−18305.7	−0.694122
$887$	6259.93	0.236965	0.118482	−	0.992956i	$-0.462197\pi$
$887$	6259.93	0.236965	0.118482	+	0.992956i	$0.462197\pi$
$888$	23855.7	0.901516
$889$	−82839.5	−3.12525
$890$	4733.43	0.178275
$891$	3091.80	0.116251
$892$	6163.79	0.231367
$893$	47464.9	1.77867
$894$	−9034.60	−0.337989
$895$	1374.42	0.0513318
$896$	47738.6	1.77995
$897$	−15909.3	−0.592193
$898$	36192.8	1.34496
$899$	−13789.1	−0.511559
$900$	−18988.5	−0.703276
$901$	3231.56	0.119488
$902$	−11063.7	−0.408406
$903$	0	0
$904$	22742.1	0.836716
$905$	−419.940	−0.0154246
$906$	−33194.3	−1.21723
$907$	−29084.2	−1.06475	−0.532373	−	0.846510i	$-0.678700\pi$
$907$	−29084.2	−1.06475	−0.532373	+	0.846510i	$0.678700\pi$
$908$	−28185.0	−1.03012
$909$	6210.97	0.226628
$910$	−2093.18	−0.0762507
$911$	50509.9	1.83696	0.918478	−	0.395472i	$-0.129419\pi$
$911$	50509.9	1.83696	0.918478	+	0.395472i	$0.129419\pi$
$912$	−88225.3	−3.20332
$913$	−6430.28	−0.233090
$914$	−21243.8	−0.768799
$915$	2234.22	0.0807224
$916$	11536.0	0.416113
$917$	34764.4	1.25193
$918$	−1641.51	−0.0590172
$919$	43794.2	1.57197	0.785984	−	0.618247i	$-0.212157\pi$
$919$	43794.2	1.57197	0.785984	+	0.618247i	$0.212157\pi$
$920$	1653.21	0.0592443
$921$	15318.0	0.548040
$922$	47230.0	1.68703
$923$	1112.14	0.0396604
$924$	7437.36	0.264796
$925$	−30505.1	−1.08433
$926$	−52505.2	−1.86331
$927$	−34208.1	−1.21202
$928$	−9947.80	−0.351888
$929$	−20727.8	−0.732030	−0.366015	−	0.930609i	$-0.619278\pi$
$929$	−20727.8	−0.732030	−0.366015	+	0.930609i	$0.619278\pi$
$930$	−7561.46	−0.266613
$931$	−108393.	−3.81573
$932$	−12893.9	−0.453168
$933$	3904.69	0.137014
$934$	−16894.8	−0.591879
$935$	57.3391	0.00200555
$936$	−6958.26	−0.242989
$937$	−21684.7	−0.756037	−0.378018	−	0.925798i	$-0.623394\pi$
$937$	−21684.7	−0.756037	−0.378018	+	0.925798i	$0.623394\pi$
$938$	−36368.0	−1.26594
$939$	−16528.0	−0.574410
$940$	1628.21	0.0564961
$941$	20387.6	0.706287	0.353144	−	0.935569i	$-0.385113\pi$
$941$	20387.6	0.706287	0.353144	+	0.935569i	$0.385113\pi$
$942$	12346.9	0.427053
$943$	60866.1	2.10188
$944$	38327.1	1.32144
$945$	1998.46	0.0687937
$946$	0	0
$947$	−51110.0	−1.75380	−0.876902	−	0.480669i	$-0.840394\pi$
$947$	−51110.0	−1.75380	−0.876902	+	0.480669i	$0.840394\pi$
$948$	632.258	0.0216612
$949$	−13765.3	−0.470853
$950$	61944.1	2.11551
$951$	40909.8	1.39494
$952$	−3447.04	−0.117352
$953$	2618.42	0.0890019	0.0445009	−	0.999009i	$-0.485830\pi$
$953$	2618.42	0.0890019	0.0445009	+	0.999009i	$0.485830\pi$
$954$	46632.1	1.58257
$955$	1177.97	0.0399143
$956$	−10142.4	−0.343125
$957$	2703.26	0.0913102
$958$	−45334.3	−1.52890
$959$	34509.2	1.16200
$960$	−69.2911	−0.00232954
$961$	34427.3	1.15563
$962$	14339.4	0.480582
$963$	−19585.9	−0.655398
$964$	15607.7	0.521463
$965$	1687.93	0.0563073
$966$	−113729.	−3.78795
$967$	34263.7	1.13945	0.569724	−	0.821836i	$-0.307050\pi$
$967$	34263.7	1.13945	0.569724	+	0.821836i	$0.307050\pi$
$968$	15988.3	0.530870
$969$	9243.06	0.306429
$970$	1095.66	0.0362676
$971$	−30032.7	−0.992581	−0.496290	−	0.868157i	$-0.665305\pi$
$971$	−30032.7	−0.992581	−0.496290	+	0.868157i	$0.665305\pi$
$972$	23842.5	0.786778
$973$	−75032.9	−2.47220
$974$	10346.6	0.340377
$975$	15941.0	0.523610
$976$	−21109.6	−0.692319
$977$	10403.9	0.340686	0.170343	−	0.985385i	$-0.445512\pi$
$977$	10403.9	0.340686	0.170343	+	0.985385i	$0.445512\pi$
$978$	−67330.1	−2.20141
$979$	7880.98	0.257280
$980$	−3718.26	−0.121200
$981$	−27899.0	−0.907997
$982$	72187.8	2.34583
$983$	−53412.2	−1.73305	−0.866523	−	0.499138i	$-0.833650\pi$
$983$	−53412.2	−1.73305	−0.866523	+	0.499138i	$0.833650\pi$
$984$	47693.4	1.54513
$985$	−1883.12	−0.0609149
$986$	1607.17	0.0519093
$987$	87318.2	2.81598
$988$	−10475.6	−0.337322
$989$	0	0
$990$	827.415	0.0265626
$991$	−23203.1	−0.743765	−0.371882	−	0.928280i	$-0.621288\pi$
$991$	−23203.1	−0.743765	−0.371882	+	0.928280i	$0.621288\pi$
$992$	46328.7	1.48280
$993$	−14348.6	−0.458548
$994$	7950.18	0.253687
$995$	2895.33	0.0922495
$996$	−35557.6	−1.13121
$997$	10323.0	0.327916	0.163958	−	0.986467i	$-0.447574\pi$
$997$	10323.0	0.327916	0.163958	+	0.986467i	$0.447574\pi$
$998$	52512.0	1.66557
$999$	−13690.6	−0.433584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.40	yes	50
43.42	odd	2		1849.4.a.i.1.11	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.11	✓	50	43.42	odd	2
1849.4.a.j.1.40	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)

\(f(q)\)	\(=\)	\(q+3.53489 q^{2} -7.81725 q^{3} +4.49548 q^{4} -1.07981 q^{5} -27.6332 q^{6} +33.3014 q^{7} -12.3881 q^{8} +34.1094 q^{9} +O(q^{10})\)	\(q+3.53489 q^{2} -7.81725 q^{3} +4.49548 q^{4} -1.07981 q^{5} -27.6332 q^{6} +33.3014 q^{7} -12.3881 q^{8} +34.1094 q^{9} -3.81700 q^{10} -6.35516 q^{11} -35.1423 q^{12} +16.4672 q^{13} +117.717 q^{14} +8.44112 q^{15} -79.7545 q^{16} +8.35561 q^{17} +120.573 q^{18} -141.509 q^{19} -4.85424 q^{20} -260.325 q^{21} -22.4648 q^{22} +123.588 q^{23} +96.8411 q^{24} -123.834 q^{25} +58.2100 q^{26} -55.5761 q^{27} +149.706 q^{28} +54.4135 q^{29} +29.8385 q^{30} -253.413 q^{31} -182.819 q^{32} +49.6799 q^{33} +29.5362 q^{34} -35.9591 q^{35} +153.338 q^{36} +246.339 q^{37} -500.219 q^{38} -128.729 q^{39} +13.3768 q^{40} +492.491 q^{41} -920.222 q^{42} -28.5695 q^{44} -36.8316 q^{45} +436.871 q^{46} -335.420 q^{47} +623.461 q^{48} +765.982 q^{49} -437.740 q^{50} -65.3179 q^{51} +74.0281 q^{52} +386.753 q^{53} -196.456 q^{54} +6.86235 q^{55} -412.542 q^{56} +1106.21 q^{57} +192.346 q^{58} -480.563 q^{59} +37.9468 q^{60} +264.683 q^{61} -895.789 q^{62} +1135.89 q^{63} -8.20876 q^{64} -17.7814 q^{65} +175.613 q^{66} -308.944 q^{67} +37.5624 q^{68} -966.120 q^{69} -127.111 q^{70} +67.5365 q^{71} -422.552 q^{72} -835.918 q^{73} +870.782 q^{74} +968.042 q^{75} -636.150 q^{76} -211.636 q^{77} -455.042 q^{78} -17.9914 q^{79} +86.1195 q^{80} -486.502 q^{81} +1740.90 q^{82} +1011.82 q^{83} -1170.29 q^{84} -9.02244 q^{85} -425.364 q^{87} +78.7286 q^{88} -1240.09 q^{89} -130.196 q^{90} +548.382 q^{91} +555.588 q^{92} +1980.99 q^{93} -1185.67 q^{94} +152.802 q^{95} +1429.14 q^{96} -287.048 q^{97} +2707.67 q^{98} -216.771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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