LMFDB - Embedded newform 1849.4.a.d.1.1

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 $ x^10 - x^9 - 59x^8 + 42x^7 + 1187x^6 - 541x^5 - 9389x^4 + 2180x^3 + 22676x^2 - 320x - 768
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.31336$ of defining polynomial
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)

$f(q)$	$=$	$q-5.31336 q^{2} +8.05642 q^{3} +20.2317 q^{4} +15.9193 q^{5} -42.8066 q^{6} +16.6323 q^{7} -64.9916 q^{8} +37.9059 q^{9} +O(q^{10})$	\(q-5.31336 q^{2} +8.05642 q^{3} +20.2317 q^{4} +15.9193 q^{5} -42.8066 q^{6} +16.6323 q^{7} -64.9916 q^{8} +37.9059 q^{9} -84.5852 q^{10} +31.4464 q^{11} +162.995 q^{12} +9.11045 q^{13} -88.3732 q^{14} +128.253 q^{15} +183.469 q^{16} +30.4259 q^{17} -201.407 q^{18} +7.43181 q^{19} +322.076 q^{20} +133.997 q^{21} -167.086 q^{22} +54.3032 q^{23} -523.599 q^{24} +128.426 q^{25} -48.4071 q^{26} +87.8621 q^{27} +336.500 q^{28} +264.757 q^{29} -681.453 q^{30} +314.176 q^{31} -454.906 q^{32} +253.345 q^{33} -161.664 q^{34} +264.775 q^{35} +766.901 q^{36} -206.172 q^{37} -39.4878 q^{38} +73.3976 q^{39} -1034.62 q^{40} -174.881 q^{41} -711.971 q^{42} +636.215 q^{44} +603.436 q^{45} -288.532 q^{46} -356.666 q^{47} +1478.11 q^{48} -66.3675 q^{49} -682.371 q^{50} +245.124 q^{51} +184.320 q^{52} -169.935 q^{53} -466.842 q^{54} +500.606 q^{55} -1080.96 q^{56} +59.8737 q^{57} -1406.75 q^{58} -673.320 q^{59} +2594.78 q^{60} +161.911 q^{61} -1669.33 q^{62} +630.460 q^{63} +949.319 q^{64} +145.032 q^{65} -1346.11 q^{66} +118.294 q^{67} +615.569 q^{68} +437.489 q^{69} -1406.84 q^{70} -90.1617 q^{71} -2463.56 q^{72} -98.0399 q^{73} +1095.47 q^{74} +1034.65 q^{75} +150.358 q^{76} +523.025 q^{77} -389.988 q^{78} +464.529 q^{79} +2920.71 q^{80} -315.604 q^{81} +929.203 q^{82} -149.834 q^{83} +2710.98 q^{84} +484.360 q^{85} +2132.99 q^{87} -2043.75 q^{88} +799.972 q^{89} -3206.27 q^{90} +151.528 q^{91} +1098.65 q^{92} +2531.13 q^{93} +1895.09 q^{94} +118.310 q^{95} -3664.91 q^{96} -862.058 q^{97} +352.634 q^{98} +1192.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + 5 q^{3} + 39 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} - 36 q^{8} + 117 q^{9}+O(q^{10}) $ 10 * q - q^2 + 5 * q^3 + 39 * q^4 + 19 * q^5 - 15 * q^6 + 51 * q^7 - 36 * q^8 + 117 * q^9	\( 10 q - q^{2} + 5 q^{3} + 39 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} - 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} + 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} - 247 q^{18} - 78 q^{19} + 495 q^{20} - 9 q^{21} + 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} + 21 q^{26} - 97 q^{27} + 794 q^{28} + 53 q^{29} - 627 q^{30} - 253 q^{31} - 399 q^{32} + 424 q^{33} + 231 q^{34} + 355 q^{35} + 1092 q^{36} + 129 q^{37} + 854 q^{38} + 691 q^{39} - 1345 q^{40} + 391 q^{41} + 31 q^{42} + 377 q^{44} + 944 q^{45} + 40 q^{46} - 334 q^{47} + 2401 q^{48} + 115 q^{49} - 424 q^{50} + 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} + 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} - 437 q^{61} - 1509 q^{62} + 2222 q^{63} - 738 q^{64} - 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} + 3503 q^{69} - 85 q^{70} + 1545 q^{71} - 3834 q^{72} - 1292 q^{73} + 2232 q^{74} + 82 q^{75} + 252 q^{76} - 1448 q^{77} + 2822 q^{78} + 1405 q^{79} + 3157 q^{80} - 974 q^{81} + 3304 q^{82} - 543 q^{83} + 3652 q^{84} + 973 q^{85} + 1409 q^{87} - 2686 q^{88} + 2196 q^{89} - 742 q^{90} + 3513 q^{91} - 2629 q^{92} + 983 q^{93} + 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} + 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q - q^2 + 5 * q^3 + 39 * q^4 + 19 * q^5 - 15 * q^6 + 51 * q^7 - 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 + 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 - 247 * q^18 - 78 * q^19 + 495 * q^20 - 9 * q^21 + 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 + 21 * q^26 - 97 * q^27 + 794 * q^28 + 53 * q^29 - 627 * q^30 - 253 * q^31 - 399 * q^32 + 424 * q^33 + 231 * q^34 + 355 * q^35 + 1092 * q^36 + 129 * q^37 + 854 * q^38 + 691 * q^39 - 1345 * q^40 + 391 * q^41 + 31 * q^42 + 377 * q^44 + 944 * q^45 + 40 * q^46 - 334 * q^47 + 2401 * q^48 + 115 * q^49 - 424 * q^50 + 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 + 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 - 437 * q^61 - 1509 * q^62 + 2222 * q^63 - 738 * q^64 - 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 + 3503 * q^69 - 85 * q^70 + 1545 * q^71 - 3834 * q^72 - 1292 * q^73 + 2232 * q^74 + 82 * q^75 + 252 * q^76 - 1448 * q^77 + 2822 * q^78 + 1405 * q^79 + 3157 * q^80 - 974 * q^81 + 3304 * q^82 - 543 * q^83 + 3652 * q^84 + 973 * q^85 + 1409 * q^87 - 2686 * q^88 + 2196 * q^89 - 742 * q^90 + 3513 * q^91 - 2629 * q^92 + 983 * q^93 + 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 + 213 * q^98 + 3181 * 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 $

$2$	−5.31336	−1.87855	−0.939277	−	0.343159i	$-0.888503\pi$
$2$	−5.31336	−1.87855	−0.939277	+	0.343159i	$0.888503\pi$
$3$	8.05642	1.55046	0.775229	−	0.631680i	$-0.217634\pi$
$3$	8.05642	1.55046	0.775229	+	0.631680i	$0.217634\pi$
$4$	20.2317	2.52897
$5$	15.9193	1.42387	0.711935	−	0.702245i	$-0.247819\pi$
$5$	15.9193	1.42387	0.711935	+	0.702245i	$0.247819\pi$
$6$	−42.8066	−2.91262
$7$	16.6323	0.898058	0.449029	−	0.893517i	$-0.351770\pi$
$7$	16.6323	0.898058	0.449029	+	0.893517i	$0.351770\pi$
$8$	−64.9916	−2.87225
$9$	37.9059	1.40392
$10$	−84.5852	−2.67482
$11$	31.4464	0.861949	0.430974	−	0.902364i	$-0.358170\pi$
$11$	31.4464	0.861949	0.430974	+	0.902364i	$0.358170\pi$
$12$	162.995	3.92106
$13$	9.11045	0.194368	0.0971840	−	0.995266i	$-0.469016\pi$
$13$	9.11045	0.194368	0.0971840	+	0.995266i	$0.469016\pi$
$14$	−88.3732	−1.68705
$15$	128.253	2.20765
$16$	183.469	2.86671
$17$	30.4259	0.434080	0.217040	−	0.976163i	$-0.430360\pi$
$17$	30.4259	0.434080	0.217040	+	0.976163i	$0.430360\pi$
$18$	−201.407	−2.63734
$19$	7.43181	0.0897354	0.0448677	−	0.998993i	$-0.485713\pi$
$19$	7.43181	0.0897354	0.0448677	+	0.998993i	$0.485713\pi$
$20$	322.076	3.60092
$21$	133.997	1.39240
$22$	−167.086	−1.61922
$23$	54.3032	0.492304	0.246152	−	0.969231i	$-0.420834\pi$
$23$	54.3032	0.492304	0.246152	+	0.969231i	$0.420834\pi$
$24$	−523.599	−4.45330
$25$	128.426	1.02741
$26$	−48.4071	−0.365131
$27$	87.8621	0.626262
$28$	336.500	2.27116
$29$	264.757	1.69531	0.847657	−	0.530545i	$-0.178013\pi$
$29$	264.757	1.69531	0.847657	+	0.530545i	$0.178013\pi$
$30$	−681.453	−4.14719
$31$	314.176	1.82025	0.910124	−	0.414336i	$-0.135986\pi$
$31$	314.176	1.82025	0.910124	+	0.414336i	$0.135986\pi$
$32$	−454.906	−2.51302
$33$	253.345	1.33642
$34$	−161.664	−0.815443
$35$	264.775	1.27872
$36$	766.901	3.55047
$37$	−206.172	−0.916067	−0.458033	−	0.888935i	$-0.651446\pi$
$37$	−206.172	−0.916067	−0.458033	+	0.888935i	$0.651446\pi$
$38$	−39.4878	−0.168573
$39$	73.3976	0.301360
$40$	−1034.62	−4.08971
$41$	−174.881	−0.666141	−0.333070	−	0.942902i	$-0.608085\pi$
$41$	−174.881	−0.666141	−0.333070	+	0.942902i	$0.608085\pi$
$42$	−711.971	−2.61570
$43$	0	0
$43$	0	0
$44$	636.215	2.17984
$45$	603.436	1.99900
$46$	−288.532	−0.924820
$47$	−356.666	−1.10692	−0.553458	−	0.832877i	$-0.686692\pi$
$47$	−356.666	−1.10692	−0.553458	+	0.832877i	$0.686692\pi$
$48$	1478.11	4.44471
$49$	−66.3675	−0.193491
$50$	−682.371	−1.93004
$51$	245.124	0.673023
$52$	184.320	0.491551
$53$	−169.935	−0.440421	−0.220211	−	0.975452i	$-0.570674\pi$
$53$	−169.935	−0.440421	−0.220211	+	0.975452i	$0.570674\pi$
$54$	−466.842	−1.17647
$55$	500.606	1.22730
$56$	−1080.96	−2.57945
$57$	59.8737	0.139131
$58$	−1406.75	−3.18474
$59$	−673.320	−1.48574	−0.742871	−	0.669435i	$-0.766536\pi$
$59$	−673.320	−1.48574	−0.742871	+	0.669435i	$0.766536\pi$
$60$	2594.78	5.58308
$61$	161.911	0.339846	0.169923	−	0.985457i	$-0.445648\pi$
$61$	161.911	0.339846	0.169923	+	0.985457i	$0.445648\pi$
$62$	−1669.33	−3.41944
$63$	630.460	1.26080
$64$	949.319	1.85414
$65$	145.032	0.276755
$66$	−1346.11	−2.51053
$67$	118.294	0.215700	0.107850	−	0.994167i	$-0.465603\pi$
$67$	118.294	0.215700	0.107850	+	0.994167i	$0.465603\pi$
$68$	615.569	1.09777
$69$	437.489	0.763297
$70$	−1406.84	−2.40214
$71$	−90.1617	−0.150707	−0.0753537	−	0.997157i	$-0.524009\pi$
$71$	−90.1617	−0.150707	−0.0753537	+	0.997157i	$0.524009\pi$
$72$	−2463.56	−4.03241
$73$	−98.0399	−0.157188	−0.0785939	−	0.996907i	$-0.525043\pi$
$73$	−98.0399	−0.157188	−0.0785939	+	0.996907i	$0.525043\pi$
$74$	1095.47	1.72088
$75$	1034.65	1.59295
$76$	150.358	0.226938
$77$	523.025	0.774080
$78$	−389.988	−0.566120
$79$	464.529	0.661564	0.330782	−	0.943707i	$-0.392688\pi$
$79$	464.529	0.661564	0.330782	+	0.943707i	$0.392688\pi$
$80$	2920.71	4.08182
$81$	−315.604	−0.432928
$82$	929.203	1.25138
$83$	−149.834	−0.198150	−0.0990749	−	0.995080i	$-0.531588\pi$
$83$	−149.834	−0.198150	−0.0990749	+	0.995080i	$0.531588\pi$
$84$	2710.98	3.52134
$85$	484.360	0.618074
$86$	0	0
$87$	2132.99	2.62851
$88$	−2043.75	−2.47573
$89$	799.972	0.952773	0.476387	−	0.879236i	$-0.341946\pi$
$89$	799.972	0.952773	0.476387	+	0.879236i	$0.341946\pi$
$90$	−3206.27	−3.75523
$91$	151.528	0.174554
$92$	1098.65	1.24502
$93$	2531.13	2.82222
$94$	1895.09	2.07940
$95$	118.310	0.127772
$96$	−3664.91	−3.89634
$97$	−862.058	−0.902358	−0.451179	−	0.892433i	$-0.648996\pi$
$97$	−862.058	−0.902358	−0.451179	+	0.892433i	$0.648996\pi$
$98$	352.634	0.363484
$99$	1192.00	1.21011
$100$	2598.28	2.59828
$101$	−1027.99	−1.01276	−0.506380	−	0.862310i	$-0.669017\pi$
$101$	−1027.99	−1.01276	−0.506380	+	0.862310i	$0.669017\pi$
$102$	−1302.43	−1.26431
$103$	−1454.63	−1.39155	−0.695773	−	0.718262i	$-0.744938\pi$
$103$	−1454.63	−1.39155	−0.695773	+	0.718262i	$0.744938\pi$
$104$	−592.103	−0.558274
$105$	2133.14	1.98260
$106$	902.923	0.827355
$107$	1686.41	1.52366	0.761830	−	0.647778i	$-0.224301\pi$
$107$	1686.41	1.52366	0.761830	+	0.647778i	$0.224301\pi$
$108$	1777.60	1.58380
$109$	1724.21	1.51513	0.757567	−	0.652758i	$-0.226388\pi$
$109$	1724.21	1.51513	0.757567	+	0.652758i	$0.226388\pi$
$110$	−2659.90	−2.30556
$111$	−1661.01	−1.42032
$112$	3051.51	2.57447
$113$	365.815	0.304539	0.152270	−	0.988339i	$-0.451342\pi$
$113$	365.815	0.304539	0.152270	+	0.988339i	$0.451342\pi$
$114$	−318.130	−0.261365
$115$	864.471	0.700977
$116$	5356.49	4.28739
$117$	345.339	0.272877
$118$	3577.59	2.79105
$119$	506.052	0.389829
$120$	−8335.36	−6.34092
$121$	−342.125	−0.257044
$122$	−860.292	−0.638420
$123$	−1408.91	−1.03282
$124$	6356.33	4.60335
$125$	54.5347	0.0390219
$126$	−3349.86	−2.36849
$127$	−2486.96	−1.73765	−0.868827	−	0.495115i	$-0.835126\pi$
$127$	−2486.96	−1.73765	−0.868827	+	0.495115i	$0.835126\pi$
$128$	−1404.83	−0.970080
$129$	0	0
$130$	−770.609	−0.519899
$131$	2385.96	1.59131	0.795657	−	0.605748i	$-0.207126\pi$
$131$	2385.96	1.59131	0.795657	+	0.605748i	$0.207126\pi$
$132$	5125.61	3.37975
$133$	123.608	0.0805877
$134$	−628.537	−0.405204
$135$	1398.71	0.891715
$136$	−1977.43	−1.24679
$137$	273.052	0.170280	0.0851400	−	0.996369i	$-0.472866\pi$
$137$	273.052	0.170280	0.0851400	+	0.996369i	$0.472866\pi$
$138$	−2324.53	−1.43389
$139$	−96.8821	−0.0591182	−0.0295591	−	0.999563i	$-0.509410\pi$
$139$	−96.8821	−0.0591182	−0.0295591	+	0.999563i	$0.509410\pi$
$140$	5356.86	3.23384
$141$	−2873.45	−1.71623
$142$	479.061	0.283112
$143$	286.491	0.167535
$144$	6954.57	4.02463
$145$	4214.76	2.41391
$146$	520.921	0.295286
$147$	−534.684	−0.300000
$148$	−4171.22	−2.31670
$149$	1045.49	0.574833	0.287416	−	0.957806i	$-0.407204\pi$
$149$	1045.49	0.574833	0.287416	+	0.957806i	$0.407204\pi$
$150$	−5497.47	−2.99244
$151$	−2794.03	−1.50580	−0.752898	−	0.658138i	$-0.771344\pi$
$151$	−2794.03	−1.50580	−0.752898	+	0.658138i	$0.771344\pi$
$152$	−483.005	−0.257743
$153$	1153.32	0.609414
$154$	−2779.02	−1.45415
$155$	5001.48	2.59180
$156$	1484.96	0.762129
$157$	−731.392	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$157$	−731.392	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$158$	−2468.21	−1.24278
$159$	−1369.06	−0.682854
$160$	−7241.80	−3.57822
$161$	903.185	0.442118
$162$	1676.92	0.813279
$163$	−833.064	−0.400311	−0.200155	−	0.979764i	$-0.564145\pi$
$163$	−833.064	−0.400311	−0.200155	+	0.979764i	$0.564145\pi$
$164$	−3538.14	−1.68465
$165$	4033.09	1.90288
$166$	796.122	0.372235
$167$	−2486.11	−1.15198	−0.575990	−	0.817457i	$-0.695383\pi$
$167$	−2486.11	−1.15198	−0.575990	+	0.817457i	$0.695383\pi$
$168$	−8708.65	−3.99933
$169$	−2114.00	−0.962221
$170$	−2573.58	−1.16109
$171$	281.709	0.125981
$172$	0	0
$173$	−3354.66	−1.47428	−0.737139	−	0.675741i	$-0.763824\pi$
$173$	−3354.66	−1.47428	−0.737139	+	0.675741i	$0.763824\pi$
$174$	−11333.3	−4.93781
$175$	2136.01	0.922670
$176$	5769.45	2.47096
$177$	−5424.54	−2.30358
$178$	−4250.53	−1.78984
$179$	−2570.05	−1.07315	−0.536576	−	0.843852i	$-0.680283\pi$
$179$	−2570.05	−1.07315	−0.536576	+	0.843852i	$0.680283\pi$
$180$	12208.6	5.05541
$181$	3433.14	1.40985	0.704927	−	0.709280i	$-0.250980\pi$
$181$	3433.14	1.40985	0.704927	+	0.709280i	$0.250980\pi$
$182$	−805.120	−0.327909
$183$	1304.43	0.526917
$184$	−3529.25	−1.41402
$185$	−3282.12	−1.30436
$186$	−13448.8	−5.30169
$187$	956.784	0.374155
$188$	−7215.97	−2.79936
$189$	1461.35	0.562420
$190$	−628.621	−0.240026
$191$	3252.00	1.23197	0.615986	−	0.787757i	$-0.288758\pi$
$191$	3252.00	1.23197	0.615986	+	0.787757i	$0.288758\pi$
$192$	7648.11	2.87477
$193$	−1575.55	−0.587620	−0.293810	−	0.955864i	$-0.594923\pi$
$193$	−1575.55	−0.587620	−0.293810	+	0.955864i	$0.594923\pi$
$194$	4580.42	1.69513
$195$	1168.44	0.429097
$196$	−1342.73	−0.489333
$197$	619.947	0.224210	0.112105	−	0.993696i	$-0.464241\pi$
$197$	619.947	0.224210	0.112105	+	0.993696i	$0.464241\pi$
$198$	−6333.53	−2.27325
$199$	−734.573	−0.261671	−0.130835	−	0.991404i	$-0.541766\pi$
$199$	−734.573	−0.261671	−0.130835	+	0.991404i	$0.541766\pi$
$200$	−8346.59	−2.95096
$201$	953.024	0.334434
$202$	5462.08	1.90253
$203$	4403.51	1.52249
$204$	4959.28	1.70205
$205$	−2783.99	−0.948498
$206$	7728.98	2.61409
$207$	2058.41	0.691156
$208$	1671.49	0.557197
$209$	233.703	0.0773474
$210$	−11334.1	−3.72442
$211$	1132.27	0.369425	0.184713	−	0.982793i	$-0.440865\pi$
$211$	1132.27	0.369425	0.184713	+	0.982793i	$0.440865\pi$
$212$	−3438.07	−1.11381
$213$	−726.380	−0.233666
$214$	−8960.50	−2.86228
$215$	0	0
$216$	−5710.30	−1.79878
$217$	5225.46	1.63469
$218$	−9161.35	−2.84626
$219$	−789.850	−0.243713
$220$	10128.1	3.10381
$221$	277.194	0.0843713
$222$	8825.52	2.66815
$223$	−1053.16	−0.316255	−0.158127	−	0.987419i	$-0.550546\pi$
$223$	−1053.16	−0.316255	−0.158127	+	0.987419i	$0.550546\pi$
$224$	−7566.11	−2.25684
$225$	4868.09	1.44240
$226$	−1943.70	−0.572094
$227$	3799.35	1.11089	0.555444	−	0.831554i	$-0.312548\pi$
$227$	3799.35	1.11089	0.555444	+	0.831554i	$0.312548\pi$
$228$	1211.35	0.351858
$229$	−6324.08	−1.82492	−0.912460	−	0.409165i	$-0.865820\pi$
$229$	−6324.08	−1.82492	−0.912460	+	0.409165i	$0.865820\pi$
$230$	−4593.24	−1.31682
$231$	4213.70	1.20018
$232$	−17207.0	−4.86936
$233$	1260.20	0.354329	0.177164	−	0.984181i	$-0.443308\pi$
$233$	1260.20	0.354329	0.177164	+	0.984181i	$0.443308\pi$
$234$	−1834.91	−0.512615
$235$	−5677.89	−1.57610
$236$	−13622.4	−3.75739
$237$	3742.44	1.02573
$238$	−2688.83	−0.732316
$239$	−1489.44	−0.403111	−0.201556	−	0.979477i	$-0.564600\pi$
$239$	−1489.44	−0.403111	−0.201556	+	0.979477i	$0.564600\pi$
$240$	23530.5	6.32869
$241$	−2610.20	−0.697667	−0.348833	−	0.937185i	$-0.613422\pi$
$241$	−2610.20	−0.697667	−0.348833	+	0.937185i	$0.613422\pi$
$242$	1817.83	0.482871
$243$	−4914.92	−1.29750
$244$	3275.75	0.859460
$245$	−1056.53	−0.275506
$246$	7486.05	1.94022
$247$	67.7071	0.0174417
$248$	−20418.8	−5.22821
$249$	−1207.13	−0.307223
$250$	−289.762	−0.0733047
$251$	1203.05	0.302534	0.151267	−	0.988493i	$-0.451665\pi$
$251$	1203.05	0.302534	0.151267	+	0.988493i	$0.451665\pi$
$252$	12755.3	3.18853
$253$	1707.64	0.424341
$254$	13214.1	3.26428
$255$	3902.21	0.958297
$256$	−130.215	−0.0317909
$257$	−2722.72	−0.660851	−0.330426	−	0.943832i	$-0.607192\pi$
$257$	−2722.72	−0.660851	−0.330426	+	0.943832i	$0.607192\pi$
$258$	0	0
$259$	−3429.11	−0.822681
$260$	2934.26	0.699904
$261$	10035.8	2.38009
$262$	−12677.4	−2.98937
$263$	2090.60	0.490159	0.245079	−	0.969503i	$-0.421186\pi$
$263$	2090.60	0.490159	0.245079	+	0.969503i	$0.421186\pi$
$264$	−16465.3	−3.83852
$265$	−2705.25	−0.627102
$266$	−656.772	−0.151388
$267$	6444.90	1.47723
$268$	2393.29	0.545498
$269$	6705.95	1.51996	0.759980	−	0.649947i	$-0.225209\pi$
$269$	6705.95	1.51996	0.759980	+	0.649947i	$0.225209\pi$
$270$	−7431.83	−1.67514
$271$	1691.98	0.379264	0.189632	−	0.981855i	$-0.439271\pi$
$271$	1691.98	0.379264	0.189632	+	0.981855i	$0.439271\pi$
$272$	5582.22	1.24438
$273$	1220.77	0.270638
$274$	−1450.82	−0.319880
$275$	4038.52	0.885571
$276$	8851.16	1.93035
$277$	−1523.64	−0.330494	−0.165247	−	0.986252i	$-0.552842\pi$
$277$	−1523.64	−0.330494	−0.165247	+	0.986252i	$0.552842\pi$
$278$	514.769	0.111057
$279$	11909.1	2.55548
$280$	−17208.1	−3.67280
$281$	5118.39	1.08661	0.543305	−	0.839535i	$-0.317173\pi$
$281$	5118.39	1.08661	0.543305	+	0.839535i	$0.317173\pi$
$282$	15267.7	3.22403
$283$	−2730.30	−0.573497	−0.286749	−	0.958006i	$-0.592574\pi$
$283$	−2730.30	−0.573497	−0.286749	+	0.958006i	$0.592574\pi$
$284$	−1824.13	−0.381134
$285$	953.151	0.198105
$286$	−1522.23	−0.314724
$287$	−2908.66	−0.598233
$288$	−17243.6	−3.52808
$289$	−3987.27	−0.811574
$290$	−22394.5	−4.53466
$291$	−6945.10	−1.39907
$292$	−1983.52	−0.397523
$293$	−1885.86	−0.376018	−0.188009	−	0.982167i	$-0.560203\pi$
$293$	−1885.86	−0.376018	−0.188009	+	0.982167i	$0.560203\pi$
$294$	2840.97	0.563567
$295$	−10718.8	−2.11550
$296$	13399.4	2.63117
$297$	2762.94	0.539806
$298$	−5555.07	−1.07986
$299$	494.726	0.0956882
$300$	20932.8	4.02852
$301$	0	0
$302$	14845.7	2.82872
$303$	−8281.92	−1.57024
$304$	1363.51	0.257245
$305$	2577.52	0.483897
$306$	−6128.00	−1.14482
$307$	4571.21	0.849813	0.424907	−	0.905237i	$-0.360307\pi$
$307$	4571.21	0.849813	0.424907	+	0.905237i	$0.360307\pi$
$308$	10581.7	1.95762
$309$	−11719.1	−2.15753
$310$	−26574.6	−4.86883
$311$	−7395.34	−1.34840	−0.674198	−	0.738550i	$-0.735511\pi$
$311$	−7395.34	−1.34840	−0.674198	+	0.738550i	$0.735511\pi$
$312$	−4770.23	−0.865580
$313$	−384.858	−0.0694998	−0.0347499	−	0.999396i	$-0.511063\pi$
$313$	−384.858	−0.0694998	−0.0347499	+	0.999396i	$0.511063\pi$
$314$	3886.14	0.698432
$315$	10036.5	1.79522
$316$	9398.22	1.67307
$317$	7188.20	1.27359	0.636797	−	0.771031i	$-0.280259\pi$
$317$	7188.20	1.27359	0.636797	+	0.771031i	$0.280259\pi$
$318$	7274.32	1.28278
$319$	8325.64	1.46127
$320$	15112.5	2.64005
$321$	13586.4	2.36237
$322$	−4798.94	−0.830542
$323$	226.119	0.0389524
$324$	−6385.23	−1.09486
$325$	1170.02	0.199695
$326$	4426.37	0.752006
$327$	13891.0	2.34915
$328$	11365.8	1.91332
$329$	−5932.16	−0.994075
$330$	−21429.2	−3.57467
$331$	−6318.35	−1.04921	−0.524604	−	0.851346i	$-0.675787\pi$
$331$	−6318.35	−1.04921	−0.524604	+	0.851346i	$0.675787\pi$
$332$	−3031.40	−0.501114
$333$	−7815.13	−1.28608
$334$	13209.6	2.16406
$335$	1883.16	0.307128
$336$	24584.3	3.99161
$337$	−297.364	−0.0480667	−0.0240333	−	0.999711i	$-0.507651\pi$
$337$	−297.364	−0.0480667	−0.0240333	+	0.999711i	$0.507651\pi$
$338$	11232.4	1.80758
$339$	2947.16	0.472176
$340$	9799.45	1.56309
$341$	9879.70	1.56896
$342$	−1496.82	−0.236663
$343$	−6808.71	−1.07182
$344$	0	0
$345$	6964.54	1.08684
$346$	17824.5	2.76951
$347$	1785.11	0.276166	0.138083	−	0.990421i	$-0.455906\pi$
$347$	1785.11	0.276166	0.138083	+	0.990421i	$0.455906\pi$
$348$	43154.1	6.64742
$349$	−1031.55	−0.158216	−0.0791081	−	0.996866i	$-0.525207\pi$
$349$	−1031.55	−0.158216	−0.0791081	+	0.996866i	$0.525207\pi$
$350$	−11349.4	−1.73329
$351$	800.463	0.121725
$352$	−14305.1	−2.16610
$353$	9938.77	1.49855	0.749274	−	0.662260i	$-0.230403\pi$
$353$	9938.77	1.49855	0.749274	+	0.662260i	$0.230403\pi$
$354$	28822.5	4.32740
$355$	−1435.32	−0.214588
$356$	16184.8	2.40953
$357$	4076.96	0.604414
$358$	13655.6	2.01598
$359$	−10918.0	−1.60510	−0.802549	−	0.596586i	$-0.796524\pi$
$359$	−10918.0	−1.60510	−0.802549	+	0.596586i	$0.796524\pi$
$360$	−39218.3	−5.74163
$361$	−6803.77	−0.991948
$362$	−18241.5	−2.64849
$363$	−2756.31	−0.398536
$364$	3065.67	0.441441
$365$	−1560.73	−0.223815
$366$	−6930.87	−0.989843
$367$	−7088.77	−1.00826	−0.504129	−	0.863628i	$-0.668186\pi$
$367$	−7088.77	−1.00826	−0.504129	+	0.863628i	$0.668186\pi$
$368$	9962.97	1.41129
$369$	−6629.00	−0.935209
$370$	17439.1	2.45031
$371$	−2826.40	−0.395524
$372$	51209.2	7.13730
$373$	14328.1	1.98896	0.994478	−	0.104942i	$-0.0334658\pi$
$373$	14328.1	1.98896	0.994478	+	0.104942i	$0.0334658\pi$
$374$	−5083.73	−0.702871
$375$	439.354	0.0605018
$376$	23180.3	3.17934
$377$	2412.05	0.329515
$378$	−7764.65	−1.05654
$379$	3776.04	0.511774	0.255887	−	0.966707i	$-0.417633\pi$
$379$	3776.04	0.511774	0.255887	+	0.966707i	$0.417633\pi$
$380$	2393.61	0.323130
$381$	−20036.0	−2.69416
$382$	−17279.0	−2.31433
$383$	−2959.22	−0.394802	−0.197401	−	0.980323i	$-0.563250\pi$
$383$	−2959.22	−0.394802	−0.197401	+	0.980323i	$0.563250\pi$
$384$	−11317.9	−1.50407
$385$	8326.21	1.10219
$386$	8371.46	1.10388
$387$	0	0
$388$	−17440.9	−2.28203
$389$	−11332.9	−1.47713	−0.738564	−	0.674184i	$-0.764496\pi$
$389$	−11332.9	−1.47713	−0.738564	+	0.674184i	$0.764496\pi$
$390$	−6208.35	−0.806082
$391$	1652.22	0.213699
$392$	4313.33	0.555755
$393$	19222.3	2.46726
$394$	−3294.00	−0.421191
$395$	7394.99	0.941981
$396$	24116.3	3.06032
$397$	−5811.71	−0.734714	−0.367357	−	0.930080i	$-0.619737\pi$
$397$	−5811.71	−0.734714	−0.367357	+	0.930080i	$0.619737\pi$
$398$	3903.05	0.491563
$399$	995.836	0.124948
$400$	23562.2	2.94527
$401$	5842.65	0.727601	0.363800	−	0.931477i	$-0.381479\pi$
$401$	5842.65	0.727601	0.363800	+	0.931477i	$0.381479\pi$
$402$	−5063.76	−0.628252
$403$	2862.29	0.353798
$404$	−20798.0	−2.56124
$405$	−5024.22	−0.616433
$406$	−23397.4	−2.86008
$407$	−6483.36	−0.789603
$408$	−15931.0	−1.93309
$409$	5605.42	0.677677	0.338839	−	0.940845i	$-0.389966\pi$
$409$	5605.42	0.677677	0.338839	+	0.940845i	$0.389966\pi$
$410$	14792.3	1.78180
$411$	2199.82	0.264012
$412$	−29429.8	−3.51917
$413$	−11198.8	−1.33428
$414$	−10937.0	−1.29837
$415$	−2385.26	−0.282139
$416$	−4144.40	−0.488451
$417$	−780.523	−0.0916603
$418$	−1241.75	−0.145301
$419$	1304.47	0.152094	0.0760471	−	0.997104i	$-0.475770\pi$
$419$	1304.47	0.152094	0.0760471	+	0.997104i	$0.475770\pi$
$420$	43157.1	5.01393
$421$	5302.77	0.613875	0.306937	−	0.951730i	$-0.400696\pi$
$421$	5302.77	0.613875	0.306937	+	0.951730i	$0.400696\pi$
$422$	−6016.15	−0.693985
$423$	−13519.7	−1.55402
$424$	11044.3	1.26500
$425$	3907.47	0.445976
$426$	3859.52	0.438954
$427$	2692.95	0.305202
$428$	34119.0	3.85328
$429$	2308.09	0.259757
$430$	0	0
$431$	−6201.04	−0.693025	−0.346512	−	0.938045i	$-0.612634\pi$
$431$	−6201.04	−0.693025	−0.346512	+	0.938045i	$0.612634\pi$
$432$	16120.0	1.79531
$433$	2725.05	0.302443	0.151221	−	0.988500i	$-0.451679\pi$
$433$	2725.05	0.302443	0.151221	+	0.988500i	$0.451679\pi$
$434$	−27764.7	−3.07085
$435$	33955.8	3.74266
$436$	34883.8	3.83172
$437$	403.571	0.0441771
$438$	4196.76	0.457828
$439$	4535.65	0.493109	0.246554	−	0.969129i	$-0.420702\pi$
$439$	4535.65	0.493109	0.246554	+	0.969129i	$0.420702\pi$
$440$	−32535.2	−3.52512
$441$	−2515.72	−0.271646
$442$	−1472.83	−0.158496
$443$	−4004.86	−0.429518	−0.214759	−	0.976667i	$-0.568897\pi$
$443$	−4004.86	−0.429518	−0.214759	+	0.976667i	$0.568897\pi$
$444$	−33605.1	−3.59195
$445$	12735.0	1.35663
$446$	5595.82	0.594102
$447$	8422.93	0.891254
$448$	15789.3	1.66513
$449$	1949.51	0.204906	0.102453	−	0.994738i	$-0.467331\pi$
$449$	1949.51	0.204906	0.102453	+	0.994738i	$0.467331\pi$
$450$	−25865.9	−2.70962
$451$	−5499.36	−0.574179
$452$	7401.07	0.770170
$453$	−22509.9	−2.33467
$454$	−20187.3	−2.08686
$455$	2412.22	0.248542
$456$	−3891.29	−0.399619
$457$	8398.51	0.859662	0.429831	−	0.902909i	$-0.358573\pi$
$457$	8398.51	0.859662	0.429831	+	0.902909i	$0.358573\pi$
$458$	33602.1	3.42821
$459$	2673.28	0.271848
$460$	17489.8	1.77275
$461$	−4279.12	−0.432318	−0.216159	−	0.976358i	$-0.569353\pi$
$461$	−4279.12	−0.432318	−0.216159	+	0.976358i	$0.569353\pi$
$462$	−22388.9	−2.25460
$463$	12361.8	1.24082	0.620412	−	0.784276i	$-0.286965\pi$
$463$	12361.8	1.24082	0.620412	+	0.784276i	$0.286965\pi$
$464$	48574.8	4.85997
$465$	40294.0	4.01847
$466$	−6695.91	−0.665626
$467$	14344.7	1.42140	0.710702	−	0.703493i	$-0.248377\pi$
$467$	14344.7	1.42140	0.710702	+	0.703493i	$0.248377\pi$
$468$	6986.82	0.690098
$469$	1967.49	0.193711
$470$	30168.6	2.96080
$471$	−5892.40	−0.576449
$472$	43760.1	4.26742
$473$	0	0
$474$	−19884.9	−1.92688
$475$	954.435	0.0921947
$476$	10238.3	0.985866
$477$	−6441.52	−0.618316
$478$	7913.90	0.757267
$479$	−7487.06	−0.714181	−0.357090	−	0.934070i	$-0.616231\pi$
$479$	−7487.06	−0.714181	−0.357090	+	0.934070i	$0.616231\pi$
$480$	−58343.0	−5.54787
$481$	−1878.32	−0.178054
$482$	13868.9	1.31060
$483$	7276.43	0.685485
$484$	−6921.79	−0.650056
$485$	−13723.4	−1.28484
$486$	26114.7	2.43742
$487$	−6910.13	−0.642973	−0.321487	−	0.946914i	$-0.604183\pi$
$487$	−6910.13	−0.642973	−0.321487	+	0.946914i	$0.604183\pi$
$488$	−10522.9	−0.976123
$489$	−6711.51	−0.620665
$490$	5613.71	0.517554
$491$	16290.5	1.49731	0.748656	−	0.662959i	$-0.230700\pi$
$491$	16290.5	1.49731	0.748656	+	0.662959i	$0.230700\pi$
$492$	−28504.7	−2.61198
$493$	8055.46	0.735902
$494$	−359.752	−0.0327652
$495$	18975.9	1.72304
$496$	57641.7	5.21812
$497$	−1499.59	−0.135344
$498$	6413.89	0.577135
$499$	12574.1	1.12804	0.564022	−	0.825760i	$-0.309253\pi$
$499$	12574.1	1.12804	0.564022	+	0.825760i	$0.309253\pi$
$500$	1103.33	0.0986850
$501$	−20029.1	−1.78610
$502$	−6392.24	−0.568326
$503$	6289.08	0.557488	0.278744	−	0.960366i	$-0.410082\pi$
$503$	6289.08	0.557488	0.278744	+	0.960366i	$0.410082\pi$
$504$	−40974.6	−3.62134
$505$	−16364.9	−1.44204
$506$	−9073.28	−0.797148
$507$	−17031.3	−1.49188
$508$	−50315.6	−4.39447
$509$	5528.64	0.481440	0.240720	−	0.970595i	$-0.422616\pi$
$509$	5528.64	0.481440	0.240720	+	0.970595i	$0.422616\pi$
$510$	−20733.8	−1.80021
$511$	−1630.63	−0.141164
$512$	11930.5	1.02980
$513$	652.974	0.0561979
$514$	14466.8	1.24145
$515$	−23156.8	−1.98138
$516$	0	0
$517$	−11215.8	−0.954105
$518$	18220.1	1.54545
$519$	−27026.5	−2.28581
$520$	−9425.89	−0.794909
$521$	−767.214	−0.0645149	−0.0322574	−	0.999480i	$-0.510270\pi$
$521$	−767.214	−0.0645149	−0.0322574	+	0.999480i	$0.510270\pi$
$522$	−53323.9	−4.47112
$523$	−12324.9	−1.03046	−0.515229	−	0.857052i	$-0.672293\pi$
$523$	−12324.9	−1.03046	−0.515229	+	0.857052i	$0.672293\pi$
$524$	48272.1	4.02438
$525$	17208.6	1.43056
$526$	−11108.1	−0.920790
$527$	9559.09	0.790134
$528$	46481.1	3.83112
$529$	−9218.17	−0.757637
$530$	14373.9	1.17805
$531$	−25522.8	−2.08586
$532$	2500.80	0.203804
$533$	−1593.24	−0.129476
$534$	−34244.1	−2.77507
$535$	26846.6	2.16949
$536$	−7688.10	−0.619544
$537$	−20705.4	−1.66388
$538$	−35631.1	−2.85533
$539$	−2087.02	−0.166780
$540$	28298.3	2.25512
$541$	12669.5	1.00684	0.503422	−	0.864041i	$-0.332074\pi$
$541$	12669.5	1.00684	0.503422	+	0.864041i	$0.332074\pi$
$542$	−8990.09	−0.712468
$543$	27658.8	2.18592
$544$	−13840.9	−1.09085
$545$	27448.3	2.15735
$546$	−6486.38	−0.508409
$547$	3010.76	0.235340	0.117670	−	0.993053i	$-0.462458\pi$
$547$	3010.76	0.235340	0.117670	+	0.993053i	$0.462458\pi$
$548$	5524.31	0.430633
$549$	6137.39	0.477117
$550$	−21458.1	−1.66359
$551$	1967.62	0.152130
$552$	−28433.1	−2.19238
$553$	7726.17	0.594123
$554$	8095.65	0.620851
$555$	−26442.2	−2.02236
$556$	−1960.09	−0.149508
$557$	11347.0	0.863177	0.431589	−	0.902071i	$-0.357953\pi$
$557$	11347.0	0.863177	0.431589	+	0.902071i	$0.357953\pi$
$558$	−63277.4	−4.80062
$559$	0	0
$560$	48578.1	3.66571
$561$	7708.25	0.580112
$562$	−27195.8	−2.04126
$563$	23560.2	1.76366	0.881832	−	0.471565i	$-0.156311\pi$
$563$	23560.2	1.76366	0.881832	+	0.471565i	$0.156311\pi$
$564$	−58134.9	−4.34028
$565$	5823.53	0.433624
$566$	14507.1	1.07735
$567$	−5249.22	−0.388794
$568$	5859.75	0.432869
$569$	13831.0	1.01903	0.509513	−	0.860463i	$-0.329826\pi$
$569$	13831.0	1.01903	0.509513	+	0.860463i	$0.329826\pi$
$570$	−5064.43	−0.372150
$571$	−8885.36	−0.651210	−0.325605	−	0.945506i	$-0.605568\pi$
$571$	−8885.36	−0.651210	−0.325605	+	0.945506i	$0.605568\pi$
$572$	5796.21	0.423691
$573$	26199.5	1.91012
$574$	15454.8	1.12381
$575$	6973.92	0.505796
$576$	35984.8	2.60306
$577$	−18749.7	−1.35279	−0.676396	−	0.736539i	$-0.736459\pi$
$577$	−18749.7	−1.35279	−0.676396	+	0.736539i	$0.736459\pi$
$578$	21185.8	1.52459
$579$	−12693.3	−0.911080
$580$	85271.9	6.10469
$581$	−2492.08	−0.177950
$582$	36901.8	2.62823
$583$	−5343.83	−0.379620
$584$	6371.77	0.451482
$585$	5497.58	0.388542
$586$	10020.3	0.706371
$587$	15424.9	1.08459	0.542296	−	0.840188i	$-0.317555\pi$
$587$	15424.9	1.08459	0.542296	+	0.840188i	$0.317555\pi$
$588$	−10817.6	−0.758690
$589$	2334.90	0.163341
$590$	56952.9	3.97409
$591$	4994.55	0.347628
$592$	−37826.3	−2.62610
$593$	−20825.7	−1.44218	−0.721088	−	0.692844i	$-0.756358\pi$
$593$	−20825.7	−1.44218	−0.721088	+	0.692844i	$0.756358\pi$
$594$	−14680.5	−1.01405
$595$	8056.01	0.555066
$596$	21152.1	1.45373
$597$	−5918.02	−0.405710
$598$	−2628.66	−0.179755
$599$	21242.2	1.44897	0.724484	−	0.689292i	$-0.242078\pi$
$599$	21242.2	1.44897	0.724484	+	0.689292i	$0.242078\pi$
$600$	−67243.6	−4.57535
$601$	1556.16	0.105619	0.0528095	−	0.998605i	$-0.483182\pi$
$601$	1556.16	0.105619	0.0528095	+	0.998605i	$0.483182\pi$
$602$	0	0
$603$	4484.03	0.302825
$604$	−56528.1	−3.80811
$605$	−5446.42	−0.365997
$606$	44004.8	2.94979
$607$	−11941.0	−0.798470	−0.399235	−	0.916849i	$-0.630724\pi$
$607$	−11941.0	−0.798470	−0.399235	+	0.916849i	$0.630724\pi$
$608$	−3380.77	−0.225507
$609$	35476.5	2.36056
$610$	−13695.3	−0.909027
$611$	−3249.39	−0.215149
$612$	23333.7	1.54119
$613$	−5125.04	−0.337681	−0.168840	−	0.985643i	$-0.554002\pi$
$613$	−5125.04	−0.337681	−0.168840	+	0.985643i	$0.554002\pi$
$614$	−24288.5	−1.59642
$615$	−22429.0	−1.47061
$616$	−33992.2	−2.22335
$617$	−21253.5	−1.38676	−0.693381	−	0.720571i	$-0.743880\pi$
$617$	−21253.5	−1.38676	−0.693381	+	0.720571i	$0.743880\pi$
$618$	62267.9	4.05304
$619$	−16229.9	−1.05385	−0.526926	−	0.849911i	$-0.676656\pi$
$619$	−16229.9	−1.05385	−0.526926	+	0.849911i	$0.676656\pi$
$620$	101189.	6.55457
$621$	4771.19	0.308311
$622$	39294.1	2.53304
$623$	13305.3	0.855646
$624$	13466.2	0.863910
$625$	−15185.1	−0.971843
$626$	2044.89	0.130559
$627$	1882.81	0.119924
$628$	−14797.3	−0.940251
$629$	−6272.97	−0.397646
$630$	−53327.6	−3.37242
$631$	11379.3	0.717910	0.358955	−	0.933355i	$-0.383133\pi$
$631$	11379.3	0.717910	0.358955	+	0.933355i	$0.383133\pi$
$632$	−30190.4	−1.90018
$633$	9122.04	0.572778
$634$	−38193.5	−2.39252
$635$	−39590.8	−2.47419
$636$	−27698.6	−1.72692
$637$	−604.638	−0.0376085
$638$	−44237.1	−2.74508
$639$	−3417.66	−0.211581
$640$	−22363.9	−1.38127
$641$	−6841.44	−0.421561	−0.210781	−	0.977533i	$-0.567601\pi$
$641$	−6841.44	−0.421561	−0.210781	+	0.977533i	$0.567601\pi$
$642$	−72189.5	−4.43784
$643$	4167.38	0.255592	0.127796	−	0.991800i	$-0.459210\pi$
$643$	4167.38	0.255592	0.127796	+	0.991800i	$0.459210\pi$
$644$	18273.0	1.11810
$645$	0	0
$646$	−1201.45	−0.0731742
$647$	−17803.0	−1.08178	−0.540888	−	0.841094i	$-0.681912\pi$
$647$	−17803.0	−1.08178	−0.540888	+	0.841094i	$0.681912\pi$
$648$	20511.6	1.24348
$649$	−21173.5	−1.28063
$650$	−6216.71	−0.375138
$651$	42098.5	2.53452
$652$	−16854.3	−1.01237
$653$	14735.0	0.883037	0.441519	−	0.897252i	$-0.354440\pi$
$653$	14735.0	0.883037	0.441519	+	0.897252i	$0.354440\pi$
$654$	−73807.7	−4.41301
$655$	37982.9	2.26582
$656$	−32085.3	−1.90963
$657$	−3716.29	−0.220679
$658$	31519.7	1.86742
$659$	−10846.8	−0.641169	−0.320585	−	0.947220i	$-0.603879\pi$
$659$	−10846.8	−0.641169	−0.320585	+	0.947220i	$0.603879\pi$
$660$	81596.4	4.81233
$661$	8365.45	0.492251	0.246126	−	0.969238i	$-0.420842\pi$
$661$	8365.45	0.492251	0.246126	+	0.969238i	$0.420842\pi$
$662$	33571.6	1.97099
$663$	2233.19	0.130814
$664$	9737.96	0.569136
$665$	1967.76	0.114746
$666$	41524.5	2.41598
$667$	14377.1	0.834610
$668$	−50298.3	−2.91332
$669$	−8484.70	−0.490340
$670$	−10005.9	−0.576958
$671$	5091.52	0.292930
$672$	−60955.8	−3.49914
$673$	−4305.90	−0.246627	−0.123314	−	0.992368i	$-0.539352\pi$
$673$	−4305.90	−0.246627	−0.123314	+	0.992368i	$0.539352\pi$
$674$	1580.00	0.0902959
$675$	11283.7	0.643425
$676$	−42769.9	−2.43343
$677$	6938.20	0.393880	0.196940	−	0.980416i	$-0.436900\pi$
$677$	6938.20	0.393880	0.196940	+	0.980416i	$0.436900\pi$
$678$	−15659.3	−0.887008
$679$	−14338.0	−0.810370
$680$	−31479.4	−1.77526
$681$	30609.1	1.72238
$682$	−52494.4	−2.94738
$683$	−23567.3	−1.32032	−0.660160	−	0.751125i	$-0.729511\pi$
$683$	−23567.3	−1.32032	−0.660160	+	0.751125i	$0.729511\pi$
$684$	5699.46	0.318603
$685$	4346.80	0.242457
$686$	36177.1	2.01348
$687$	−50949.4	−2.82946
$688$	0	0
$689$	−1548.18	−0.0856038
$690$	−37005.1	−2.04168
$691$	22295.2	1.22742	0.613710	−	0.789531i	$-0.289676\pi$
$691$	22295.2	1.22742	0.613710	+	0.789531i	$0.289676\pi$
$692$	−67870.6	−3.72840
$693$	19825.7	1.08675
$694$	−9484.91	−0.518793
$695$	−1542.30	−0.0841767
$696$	−138626.	−7.54975
$697$	−5320.90	−0.289158
$698$	5480.98	0.297218
$699$	10152.7	0.549372
$700$	43215.2	2.33340
$701$	−7387.69	−0.398044	−0.199022	−	0.979995i	$-0.563777\pi$
$701$	−7387.69	−0.398044	−0.199022	+	0.979995i	$0.563777\pi$
$702$	−4253.15	−0.228668
$703$	−1532.23	−0.0822037
$704$	29852.7	1.59817
$705$	−45743.4	−2.44368
$706$	−52808.2	−2.81510
$707$	−17097.8	−0.909518
$708$	−109748.	−5.82568
$709$	−20824.0	−1.10305	−0.551525	−	0.834159i	$-0.685954\pi$
$709$	−20824.0	−1.10305	−0.551525	+	0.834159i	$0.685954\pi$
$710$	7626.34	0.403115
$711$	17608.3	0.928783
$712$	−51991.4	−2.73660
$713$	17060.8	0.896115
$714$	−21662.4	−1.13542
$715$	4560.75	0.238549
$716$	−51996.5	−2.71397
$717$	−11999.5	−0.625007
$718$	58011.3	3.01527
$719$	−20442.9	−1.06035	−0.530175	−	0.847888i	$-0.677874\pi$
$719$	−20442.9	−1.06035	−0.530175	+	0.847888i	$0.677874\pi$
$720$	110712.	5.73055
$721$	−24193.8	−1.24969
$722$	36150.8	1.86343
$723$	−21028.8	−1.08170
$724$	69458.4	3.56547
$725$	34001.6	1.74177
$726$	14645.2	0.748671
$727$	−6810.77	−0.347452	−0.173726	−	0.984794i	$-0.555581\pi$
$727$	−6810.77	−0.347452	−0.173726	+	0.984794i	$0.555581\pi$
$728$	−9848.01	−0.501362
$729$	−31075.3	−1.57879
$730$	8292.72	0.420448
$731$	0	0
$732$	26390.8	1.33256
$733$	−18357.3	−0.925025	−0.462512	−	0.886613i	$-0.653052\pi$
$733$	−18357.3	−0.925025	−0.462512	+	0.886613i	$0.653052\pi$
$734$	37665.2	1.89407
$735$	−8511.82	−0.427161
$736$	−24702.8	−1.23717
$737$	3719.91	0.185922
$738$	35222.2	1.75684
$739$	18743.1	0.932985	0.466493	−	0.884525i	$-0.345517\pi$
$739$	18743.1	0.932985	0.466493	+	0.884525i	$0.345517\pi$
$740$	−66403.1	−3.29868
$741$	545.477	0.0270426
$742$	15017.7	0.743013
$743$	−4326.42	−0.213622	−0.106811	−	0.994279i	$-0.534064\pi$
$743$	−4326.42	−0.213622	−0.106811	+	0.994279i	$0.534064\pi$
$744$	−164502.	−8.10612
$745$	16643.6	0.818487
$746$	−76130.3	−3.73636
$747$	−5679.59	−0.278186
$748$	19357.4	0.946226
$749$	28048.8	1.36833
$750$	−2334.45	−0.113656
$751$	6667.40	0.323964	0.161982	−	0.986794i	$-0.448211\pi$
$751$	6667.40	0.323964	0.161982	+	0.986794i	$0.448211\pi$
$752$	−65437.3	−3.17321
$753$	9692.28	0.469066
$754$	−12816.1	−0.619012
$755$	−44479.2	−2.14406
$756$	29565.6	1.42234
$757$	−40354.2	−1.93751	−0.968757	−	0.248014i	$-0.920222\pi$
$757$	−40354.2	−1.93751	−0.968757	+	0.248014i	$0.920222\pi$
$758$	−20063.4	−0.961395
$759$	13757.4	0.657923
$760$	−7689.12	−0.366992
$761$	16939.6	0.806911	0.403455	−	0.914999i	$-0.367809\pi$
$761$	16939.6	0.806911	0.403455	+	0.914999i	$0.367809\pi$
$762$	106458.	5.06113
$763$	28677.6	1.36068
$764$	65793.6	3.11562
$765$	18360.1	0.867726
$766$	15723.4	0.741657
$767$	−6134.25	−0.288781
$768$	−1049.07	−0.0492904
$769$	−41567.3	−1.94923	−0.974613	−	0.223897i	$-0.928122\pi$
$769$	−41567.3	−1.94923	−0.974613	+	0.223897i	$0.928122\pi$
$770$	−44240.1	−2.07052
$771$	−21935.4	−1.02462
$772$	−31876.1	−1.48607
$773$	21859.3	1.01711	0.508555	−	0.861030i	$-0.330180\pi$
$773$	21859.3	1.01711	0.508555	+	0.861030i	$0.330180\pi$
$774$	0	0
$775$	40348.3	1.87013
$776$	56026.5	2.59180
$777$	−27626.3	−1.27553
$778$	60215.9	2.77486
$779$	−1299.68	−0.0597764
$780$	23639.6	1.08517
$781$	−2835.26	−0.129902
$782$	−8778.84	−0.401446
$783$	23262.1	1.06171
$784$	−12176.4	−0.554683
$785$	−11643.3	−0.529384
$786$	−102135.	−4.63489
$787$	33518.2	1.51816	0.759081	−	0.650996i	$-0.225649\pi$
$787$	33518.2	1.51816	0.759081	+	0.650996i	$0.225649\pi$
$788$	12542.6	0.567020
$789$	16842.7	0.759970
$790$	−39292.2	−1.76956
$791$	6084.33	0.273494
$792$	−77470.1	−3.47573
$793$	1475.09	0.0660553
$794$	30879.7	1.38020
$795$	−21794.6	−0.972296
$796$	−14861.7	−0.661757
$797$	4177.21	0.185652	0.0928259	−	0.995682i	$-0.470410\pi$
$797$	4177.21	0.185652	0.0928259	+	0.995682i	$0.470410\pi$
$798$	−5291.23	−0.234721
$799$	−10851.9	−0.480490
$800$	−58421.6	−2.58189
$801$	30323.6	1.33762
$802$	−31044.1	−1.36684
$803$	−3083.00	−0.135488
$804$	19281.3	0.845772
$805$	14378.1	0.629518
$806$	−15208.3	−0.664629
$807$	54026.0	2.35663
$808$	66810.7	2.90890
$809$	43230.5	1.87874	0.939372	−	0.342899i	$-0.111409\pi$
$809$	43230.5	1.87874	0.939372	+	0.342899i	$0.111409\pi$
$810$	26695.4	1.15800
$811$	2253.54	0.0975738	0.0487869	−	0.998809i	$-0.484464\pi$
$811$	2253.54	0.0975738	0.0487869	+	0.998809i	$0.484464\pi$
$812$	89090.6	3.85033
$813$	13631.3	0.588032
$814$	34448.4	1.48331
$815$	−13261.8	−0.569990
$816$	44972.7	1.92936
$817$	0	0
$818$	−29783.6	−1.27305
$819$	5743.78	0.245060
$820$	−56324.9	−2.39872
$821$	−31030.5	−1.31909	−0.659545	−	0.751665i	$-0.729251\pi$
$821$	−31030.5	−1.31909	−0.659545	+	0.751665i	$0.729251\pi$
$822$	−11688.4	−0.495961
$823$	21943.1	0.929389	0.464695	−	0.885471i	$-0.346164\pi$
$823$	21943.1	0.929389	0.464695	+	0.885471i	$0.346164\pi$
$824$	94538.9	3.99687
$825$	32536.0	1.37304
$826$	59503.4	2.50652
$827$	−4293.41	−0.180528	−0.0902639	−	0.995918i	$-0.528771\pi$
$827$	−4293.41	−0.180528	−0.0902639	+	0.995918i	$0.528771\pi$
$828$	41645.2	1.74791
$829$	27147.6	1.13736	0.568682	−	0.822558i	$-0.307454\pi$
$829$	27147.6	1.13736	0.568682	+	0.822558i	$0.307454\pi$
$830$	12673.7	0.530014
$831$	−12275.1	−0.512417
$832$	8648.73	0.360385
$833$	−2019.29	−0.0839907
$834$	4147.19	0.172189
$835$	−39577.2	−1.64027
$836$	4728.23	0.195609
$837$	27604.2	1.13995
$838$	−6931.11	−0.285717
$839$	37996.0	1.56349	0.781744	−	0.623599i	$-0.214330\pi$
$839$	37996.0	1.56349	0.781744	+	0.623599i	$0.214330\pi$
$840$	−138636.	−5.69452
$841$	45707.2	1.87409
$842$	−28175.5	−1.15320
$843$	41235.9	1.68474
$844$	22907.8	0.934264
$845$	−33653.5	−1.37008
$846$	71835.1	2.91932
$847$	−5690.32	−0.230840
$848$	−31177.8	−1.26256
$849$	−21996.5	−0.889183
$850$	−20761.8	−0.837791
$851$	−11195.8	−0.450983
$852$	−14695.9	−0.590933
$853$	5202.98	0.208847	0.104424	−	0.994533i	$-0.466700\pi$
$853$	5202.98	0.208847	0.104424	+	0.994533i	$0.466700\pi$
$854$	−14308.6	−0.573338
$855$	4484.62	0.179381
$856$	−109603.	−4.37633
$857$	42394.2	1.68980	0.844900	−	0.534925i	$-0.179660\pi$
$857$	42394.2	1.68980	0.844900	+	0.534925i	$0.179660\pi$
$858$	−12263.7	−0.487967
$859$	−39517.4	−1.56964	−0.784818	−	0.619727i	$-0.787243\pi$
$859$	−39517.4	−1.56964	−0.784818	+	0.619727i	$0.787243\pi$
$860$	0	0
$861$	−23433.4	−0.927536
$862$	32948.3	1.30189
$863$	13568.4	0.535195	0.267597	−	0.963531i	$-0.413770\pi$
$863$	13568.4	0.535195	0.267597	+	0.963531i	$0.413770\pi$
$864$	−39969.0	−1.57381
$865$	−53404.0	−2.09918
$866$	−14479.2	−0.568155
$867$	−32123.1	−1.25831
$868$	105720.	4.13408
$869$	14607.7	0.570234
$870$	−180419.	−7.03079
$871$	1077.71	0.0419252
$872$	−112059.	−4.35184
$873$	−32677.0	−1.26684
$874$	−2144.31	−0.0829891
$875$	907.036	0.0350439
$876$	−15980.0	−0.616342
$877$	38668.9	1.48889	0.744444	−	0.667685i	$-0.232715\pi$
$877$	38668.9	1.48889	0.744444	+	0.667685i	$0.232715\pi$
$878$	−24099.5	−0.926332
$879$	−15193.3	−0.583000
$880$	91845.9	3.51832
$881$	−3206.89	−0.122637	−0.0613183	−	0.998118i	$-0.519530\pi$
$881$	−3206.89	−0.122637	−0.0613183	+	0.998118i	$0.519530\pi$
$882$	13366.9	0.510302
$883$	21071.4	0.803067	0.401533	−	0.915844i	$-0.368477\pi$
$883$	21071.4	0.803067	0.401533	+	0.915844i	$0.368477\pi$
$884$	5608.11	0.213372
$885$	−86355.2	−3.28000
$886$	21279.2	0.806873
$887$	−34055.1	−1.28913	−0.644565	−	0.764550i	$-0.722961\pi$
$887$	−34055.1	−1.28913	−0.644565	+	0.764550i	$0.722961\pi$
$888$	107952.	4.07952
$889$	−41363.8	−1.56052
$890$	−67665.7	−2.54849
$891$	−9924.61	−0.373162
$892$	−21307.3	−0.799799
$893$	−2650.67	−0.0993296
$894$	−44754.0	−1.67427
$895$	−40913.5	−1.52803
$896$	−23365.4	−0.871188
$897$	3985.72	0.148360
$898$	−10358.4	−0.384927
$899$	83180.3	3.08589
$900$	98489.8	3.64777
$901$	−5170.41	−0.191178
$902$	29220.1	1.07863
$903$	0	0
$904$	−23774.9	−0.874713
$905$	54653.4	2.00745
$906$	119603.	4.38581
$907$	2553.70	0.0934887	0.0467443	−	0.998907i	$-0.485115\pi$
$907$	2553.70	0.0934887	0.0467443	+	0.998907i	$0.485115\pi$
$908$	76867.4	2.80940
$909$	−38966.8	−1.42184
$910$	−12817.0	−0.466900
$911$	−27220.5	−0.989960	−0.494980	−	0.868904i	$-0.664825\pi$
$911$	−27220.5	−0.989960	−0.494980	+	0.868904i	$0.664825\pi$
$912$	10985.0	0.398848
$913$	−4711.74	−0.170795
$914$	−44624.3	−1.61492
$915$	20765.6	0.750262
$916$	−127947.	−4.61516
$917$	39683.9	1.42909
$918$	−14204.1	−0.510681
$919$	23260.3	0.834914	0.417457	−	0.908697i	$-0.362921\pi$
$919$	23260.3	0.834914	0.417457	+	0.908697i	$0.362921\pi$
$920$	−56183.3	−2.01338
$921$	36827.6	1.31760
$922$	22736.5	0.812132
$923$	−821.414	−0.0292927
$924$	85250.6	3.03521
$925$	−26477.8	−0.941172
$926$	−65682.6	−2.33096
$927$	−55139.1	−1.95362
$928$	−120439.	−4.26036
$929$	24748.2	0.874016	0.437008	−	0.899458i	$-0.356038\pi$
$929$	24748.2	0.874016	0.437008	+	0.899458i	$0.356038\pi$
$930$	−214096.	−7.54892
$931$	−493.230	−0.0173630
$932$	25496.1	0.896087
$933$	−59580.0	−2.09063
$934$	−76218.7	−2.67018
$935$	15231.4	0.532748
$936$	−22444.2	−0.783772
$937$	−17033.4	−0.593870	−0.296935	−	0.954898i	$-0.595964\pi$
$937$	−17033.4	−0.593870	−0.296935	+	0.954898i	$0.595964\pi$
$938$	−10454.0	−0.363897
$939$	−3100.58	−0.107757
$940$	−114874.	−3.98592
$941$	41401.2	1.43426	0.717131	−	0.696939i	$-0.245455\pi$
$941$	41401.2	1.43426	0.717131	+	0.696939i	$0.245455\pi$
$942$	31308.4	1.08289
$943$	−9496.57	−0.327944
$944$	−123534.	−4.25919
$945$	23263.7	0.800812
$946$	0	0
$947$	−7077.16	−0.242848	−0.121424	−	0.992601i	$-0.538746\pi$
$947$	−7077.16	−0.242848	−0.121424	+	0.992601i	$0.538746\pi$
$948$	75716.0	2.59403
$949$	−893.188	−0.0305523
$950$	−5071.25	−0.173193
$951$	57911.1	1.97466
$952$	−32889.1	−1.11969
$953$	23196.5	0.788466	0.394233	−	0.919011i	$-0.371010\pi$
$953$	23196.5	0.788466	0.394233	+	0.919011i	$0.371010\pi$
$954$	34226.1	1.16154
$955$	51769.7	1.75417
$956$	−30133.9	−1.01946
$957$	67074.8	2.26564
$958$	39781.4	1.34163
$959$	4541.47	0.152921
$960$	121753.	4.09329
$961$	68915.6	2.31330
$962$	9980.18	0.334484
$963$	63924.8	2.13910
$964$	−52808.9	−1.76438
$965$	−25081.7	−0.836694
$966$	−38662.3	−1.28772
$967$	−19029.4	−0.632827	−0.316413	−	0.948621i	$-0.602479\pi$
$967$	−19029.4	−0.632827	−0.316413	+	0.948621i	$0.602479\pi$
$968$	22235.3	0.738294
$969$	1821.71	0.0603940
$970$	72917.3	2.41364
$971$	24534.4	0.810860	0.405430	−	0.914126i	$-0.367122\pi$
$971$	24534.4	0.810860	0.405430	+	0.914126i	$0.367122\pi$
$972$	−99437.3	−3.28133
$973$	−1611.37	−0.0530916
$974$	36716.0	1.20786
$975$	9426.14	0.309618
$976$	29705.8	0.974241
$977$	20716.3	0.678375	0.339187	−	0.940719i	$-0.389848\pi$
$977$	20716.3	0.678375	0.339187	+	0.940719i	$0.389848\pi$
$978$	35660.7	1.16595
$979$	25156.2	0.821242
$980$	−21375.4	−0.696747
$981$	65357.7	2.12713
$982$	−86557.2	−2.81278
$983$	8923.01	0.289522	0.144761	−	0.989467i	$-0.453759\pi$
$983$	8923.01	0.289522	0.144761	+	0.989467i	$0.453759\pi$
$984$	91567.4	2.96653
$985$	9869.15	0.319246
$986$	−42801.5	−1.38243
$987$	−47792.0	−1.54127
$988$	1369.83	0.0441095
$989$	0	0
$990$	−100826.	−3.23682
$991$	−15414.5	−0.494104	−0.247052	−	0.969002i	$-0.579462\pi$
$991$	−15414.5	−0.494104	−0.247052	+	0.969002i	$0.579462\pi$
$992$	−142920.	−4.57432
$993$	−50903.3	−1.62675
$994$	7967.88	0.254251
$995$	−11693.9	−0.372585
$996$	−24422.3	−0.776957
$997$	672.384	0.0213587	0.0106793	−	0.999943i	$-0.496601\pi$
$997$	672.384	0.0213587	0.0106793	+	0.999943i	$0.496601\pi$
$998$	−66810.7	−2.11909
$999$	−18114.7	−0.573698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.d.1.1		10
43.6	even	3		43.4.c.a.36.1	yes	20
43.36	even	3		43.4.c.a.6.1	✓	20
43.42	odd	2		1849.4.a.f.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.1	✓	20	43.36	even	3
43.4.c.a.36.1	yes	20	43.6	even	3
1849.4.a.d.1.1		10	1.1	even	1	trivial
1849.4.a.f.1.10		10	43.42	odd	2

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)

\(f(q)\)	\(=\)	\(q-5.31336 q^{2} +8.05642 q^{3} +20.2317 q^{4} +15.9193 q^{5} -42.8066 q^{6} +16.6323 q^{7} -64.9916 q^{8} +37.9059 q^{9} +O(q^{10})\)	\(q-5.31336 q^{2} +8.05642 q^{3} +20.2317 q^{4} +15.9193 q^{5} -42.8066 q^{6} +16.6323 q^{7} -64.9916 q^{8} +37.9059 q^{9} -84.5852 q^{10} +31.4464 q^{11} +162.995 q^{12} +9.11045 q^{13} -88.3732 q^{14} +128.253 q^{15} +183.469 q^{16} +30.4259 q^{17} -201.407 q^{18} +7.43181 q^{19} +322.076 q^{20} +133.997 q^{21} -167.086 q^{22} +54.3032 q^{23} -523.599 q^{24} +128.426 q^{25} -48.4071 q^{26} +87.8621 q^{27} +336.500 q^{28} +264.757 q^{29} -681.453 q^{30} +314.176 q^{31} -454.906 q^{32} +253.345 q^{33} -161.664 q^{34} +264.775 q^{35} +766.901 q^{36} -206.172 q^{37} -39.4878 q^{38} +73.3976 q^{39} -1034.62 q^{40} -174.881 q^{41} -711.971 q^{42} +636.215 q^{44} +603.436 q^{45} -288.532 q^{46} -356.666 q^{47} +1478.11 q^{48} -66.3675 q^{49} -682.371 q^{50} +245.124 q^{51} +184.320 q^{52} -169.935 q^{53} -466.842 q^{54} +500.606 q^{55} -1080.96 q^{56} +59.8737 q^{57} -1406.75 q^{58} -673.320 q^{59} +2594.78 q^{60} +161.911 q^{61} -1669.33 q^{62} +630.460 q^{63} +949.319 q^{64} +145.032 q^{65} -1346.11 q^{66} +118.294 q^{67} +615.569 q^{68} +437.489 q^{69} -1406.84 q^{70} -90.1617 q^{71} -2463.56 q^{72} -98.0399 q^{73} +1095.47 q^{74} +1034.65 q^{75} +150.358 q^{76} +523.025 q^{77} -389.988 q^{78} +464.529 q^{79} +2920.71 q^{80} -315.604 q^{81} +929.203 q^{82} -149.834 q^{83} +2710.98 q^{84} +484.360 q^{85} +2132.99 q^{87} -2043.75 q^{88} +799.972 q^{89} -3206.27 q^{90} +151.528 q^{91} +1098.65 q^{92} +2531.13 q^{93} +1895.09 q^{94} +118.310 q^{95} -3664.91 q^{96} -862.058 q^{97} +352.634 q^{98} +1192.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + 5 q^{3} + 39 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} - 36 q^{8} + 117 q^{9}+O(q^{10}) \) 10 * q - q^2 + 5 * q^3 + 39 * q^4 + 19 * q^5 - 15 * q^6 + 51 * q^7 - 36 * q^8 + 117 * q^9	\( 10 q - q^{2} + 5 q^{3} + 39 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} - 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} + 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} - 247 q^{18} - 78 q^{19} + 495 q^{20} - 9 q^{21} + 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} + 21 q^{26} - 97 q^{27} + 794 q^{28} + 53 q^{29} - 627 q^{30} - 253 q^{31} - 399 q^{32} + 424 q^{33} + 231 q^{34} + 355 q^{35} + 1092 q^{36} + 129 q^{37} + 854 q^{38} + 691 q^{39} - 1345 q^{40} + 391 q^{41} + 31 q^{42} + 377 q^{44} + 944 q^{45} + 40 q^{46} - 334 q^{47} + 2401 q^{48} + 115 q^{49} - 424 q^{50} + 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} + 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} - 437 q^{61} - 1509 q^{62} + 2222 q^{63} - 738 q^{64} - 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} + 3503 q^{69} - 85 q^{70} + 1545 q^{71} - 3834 q^{72} - 1292 q^{73} + 2232 q^{74} + 82 q^{75} + 252 q^{76} - 1448 q^{77} + 2822 q^{78} + 1405 q^{79} + 3157 q^{80} - 974 q^{81} + 3304 q^{82} - 543 q^{83} + 3652 q^{84} + 973 q^{85} + 1409 q^{87} - 2686 q^{88} + 2196 q^{89} - 742 q^{90} + 3513 q^{91} - 2629 q^{92} + 983 q^{93} + 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} + 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q - q^2 + 5 * q^3 + 39 * q^4 + 19 * q^5 - 15 * q^6 + 51 * q^7 - 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 + 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 - 247 * q^18 - 78 * q^19 + 495 * q^20 - 9 * q^21 + 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 + 21 * q^26 - 97 * q^27 + 794 * q^28 + 53 * q^29 - 627 * q^30 - 253 * q^31 - 399 * q^32 + 424 * q^33 + 231 * q^34 + 355 * q^35 + 1092 * q^36 + 129 * q^37 + 854 * q^38 + 691 * q^39 - 1345 * q^40 + 391 * q^41 + 31 * q^42 + 377 * q^44 + 944 * q^45 + 40 * q^46 - 334 * q^47 + 2401 * q^48 + 115 * q^49 - 424 * q^50 + 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 + 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 - 437 * q^61 - 1509 * q^62 + 2222 * q^63 - 738 * q^64 - 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 + 3503 * q^69 - 85 * q^70 + 1545 * q^71 - 3834 * q^72 - 1292 * q^73 + 2232 * q^74 + 82 * q^75 + 252 * q^76 - 1448 * q^77 + 2822 * q^78 + 1405 * q^79 + 3157 * q^80 - 974 * q^81 + 3304 * q^82 - 543 * q^83 + 3652 * q^84 + 973 * q^85 + 1409 * q^87 - 2686 * q^88 + 2196 * q^89 - 742 * q^90 + 3513 * q^91 - 2629 * q^92 + 983 * q^93 + 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 + 213 * q^98 + 3181 * q^99

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