LMFDB - Embedded newform 1849.4.a.f.1.2

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:	$10$
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			1.2
Root			$-3.82341$ 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)

$f(q)$	$=$	$q-3.82341 q^{2} +7.76517 q^{3} +6.61843 q^{4} -18.1323 q^{5} -29.6894 q^{6} -5.19796 q^{7} +5.28231 q^{8} +33.2979 q^{9} +O(q^{10})$	\(q-3.82341 q^{2} +7.76517 q^{3} +6.61843 q^{4} -18.1323 q^{5} -29.6894 q^{6} -5.19796 q^{7} +5.28231 q^{8} +33.2979 q^{9} +69.3271 q^{10} +31.5438 q^{11} +51.3932 q^{12} -71.3248 q^{13} +19.8739 q^{14} -140.800 q^{15} -73.1438 q^{16} +136.180 q^{17} -127.311 q^{18} +1.39966 q^{19} -120.007 q^{20} -40.3630 q^{21} -120.605 q^{22} -60.7163 q^{23} +41.0180 q^{24} +203.780 q^{25} +272.704 q^{26} +48.9039 q^{27} -34.4023 q^{28} -29.6008 q^{29} +538.337 q^{30} +87.2661 q^{31} +237.400 q^{32} +244.943 q^{33} -520.672 q^{34} +94.2509 q^{35} +220.379 q^{36} -255.642 q^{37} -5.35146 q^{38} -553.849 q^{39} -95.7804 q^{40} +23.1367 q^{41} +154.324 q^{42} +208.771 q^{44} -603.766 q^{45} +232.143 q^{46} -1.08229 q^{47} -567.974 q^{48} -315.981 q^{49} -779.133 q^{50} +1057.46 q^{51} -472.058 q^{52} -66.8923 q^{53} -186.979 q^{54} -571.962 q^{55} -27.4572 q^{56} +10.8686 q^{57} +113.176 q^{58} +465.968 q^{59} -931.877 q^{60} +580.345 q^{61} -333.654 q^{62} -173.081 q^{63} -322.526 q^{64} +1293.28 q^{65} -936.517 q^{66} +328.856 q^{67} +901.299 q^{68} -471.472 q^{69} -360.359 q^{70} -832.806 q^{71} +175.890 q^{72} +1049.14 q^{73} +977.423 q^{74} +1582.39 q^{75} +9.26354 q^{76} -163.963 q^{77} +2117.59 q^{78} +808.341 q^{79} +1326.27 q^{80} -519.295 q^{81} -88.4608 q^{82} +1038.31 q^{83} -267.140 q^{84} -2469.26 q^{85} -229.855 q^{87} +166.624 q^{88} -875.226 q^{89} +2308.44 q^{90} +370.744 q^{91} -401.846 q^{92} +677.636 q^{93} +4.13803 q^{94} -25.3790 q^{95} +1843.45 q^{96} +88.7982 q^{97} +1208.12 q^{98} +1050.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.82341	−1.35178	−0.675889	−	0.737003i	$-0.736240\pi$
$2$	−3.82341	−1.35178	−0.675889	+	0.737003i	$0.736240\pi$
$3$	7.76517	1.49441	0.747204	−	0.664595i	$-0.231396\pi$
$3$	7.76517	1.49441	0.747204	+	0.664595i	$0.231396\pi$
$4$	6.61843	0.827303
$5$	−18.1323	−1.62180	−0.810901	−	0.585184i	$-0.801022\pi$
$5$	−18.1323	−1.62180	−0.810901	+	0.585184i	$0.801022\pi$
$6$	−29.6894	−2.02011
$7$	−5.19796	−0.280663	−0.140332	−	0.990105i	$-0.544817\pi$
$7$	−5.19796	−0.280663	−0.140332	+	0.990105i	$0.544817\pi$
$8$	5.28231	0.233447
$9$	33.2979	1.23325
$10$	69.3271	2.19232
$11$	31.5438	0.864620	0.432310	−	0.901725i	$-0.357699\pi$
$11$	31.5438	0.864620	0.432310	+	0.901725i	$0.357699\pi$
$12$	51.3932	1.23633
$13$	−71.3248	−1.52169	−0.760844	−	0.648935i	$-0.775215\pi$
$13$	−71.3248	−1.52169	−0.760844	+	0.648935i	$0.775215\pi$
$14$	19.8739	0.379395
$15$	−140.800	−2.42363
$16$	−73.1438	−1.14287
$17$	136.180	1.94286	0.971428	−	0.237334i	$-0.0762736\pi$
$17$	136.180	1.94286	0.971428	+	0.237334i	$0.0762736\pi$
$18$	−127.311	−1.66709
$19$	1.39966	0.0169002	0.00845010	−	0.999964i	$-0.497310\pi$
$19$	1.39966	0.0169002	0.00845010	+	0.999964i	$0.497310\pi$
$20$	−120.007	−1.34172
$21$	−40.3630	−0.419425
$22$	−120.605	−1.16877
$23$	−60.7163	−0.550444	−0.275222	−	0.961381i	$-0.588751\pi$
$23$	−60.7163	−0.550444	−0.275222	+	0.961381i	$0.588751\pi$
$24$	41.0180	0.348865
$25$	203.780	1.63024
$26$	272.704	2.05698
$27$	48.9039	0.348576
$28$	−34.4023	−0.232194
$29$	−29.6008	−0.189542	−0.0947712	−	0.995499i	$-0.530212\pi$
$29$	−29.6008	−0.189542	−0.0947712	+	0.995499i	$0.530212\pi$
$30$	538.337	3.27621
$31$	87.2661	0.505595	0.252798	−	0.967519i	$-0.418649\pi$
$31$	87.2661	0.505595	0.252798	+	0.967519i	$0.418649\pi$
$32$	237.400	1.31146
$33$	244.943	1.29209
$34$	−520.672	−2.62631
$35$	94.2509	0.455180
$36$	220.379	1.02028
$37$	−255.642	−1.13587	−0.567936	−	0.823073i	$-0.692258\pi$
$37$	−255.642	−1.13587	−0.567936	+	0.823073i	$0.692258\pi$
$38$	−5.35146	−0.0228453
$39$	−553.849	−2.27402
$40$	−95.7804	−0.378605
$41$	23.1367	0.0881302	0.0440651	−	0.999029i	$-0.485969\pi$
$41$	23.1367	0.0881302	0.0440651	+	0.999029i	$0.485969\pi$
$42$	154.324	0.566970
$43$	0	0
$43$	0	0
$44$	208.771	0.715303
$45$	−603.766	−2.00009
$46$	232.143	0.744079
$47$	−1.08229	−0.00335890	−0.00167945	−	0.999999i	$-0.500535\pi$
$47$	−1.08229	−0.00335890	−0.00167945	+	0.999999i	$0.500535\pi$
$48$	−567.974	−1.70792
$49$	−315.981	−0.921228
$50$	−779.133	−2.20372
$51$	1057.46	2.90342
$52$	−472.058	−1.25890
$53$	−66.8923	−0.173365	−0.0866827	−	0.996236i	$-0.527627\pi$
$53$	−66.8923	−0.173365	−0.0866827	+	0.996236i	$0.527627\pi$
$54$	−186.979	−0.471198
$55$	−571.962	−1.40224
$56$	−27.4572	−0.0655201
$57$	10.8686	0.0252558
$58$	113.176	0.256219
$59$	465.968	1.02820	0.514101	−	0.857730i	$-0.328126\pi$
$59$	465.968	1.02820	0.514101	+	0.857730i	$0.328126\pi$
$60$	−931.877	−2.00508
$61$	580.345	1.21812	0.609062	−	0.793123i	$-0.291546\pi$
$61$	580.345	1.21812	0.609062	+	0.793123i	$0.291546\pi$
$62$	−333.654	−0.683452
$63$	−173.081	−0.346129
$64$	−322.526	−0.629933
$65$	1293.28	2.46788
$66$	−936.517	−1.74663
$67$	328.856	0.599644	0.299822	−	0.953995i	$-0.403073\pi$
$67$	328.856	0.599644	0.299822	+	0.953995i	$0.403073\pi$
$68$	901.299	1.60733
$69$	−471.472	−0.822588
$70$	−360.359	−0.615303
$71$	−832.806	−1.39205	−0.696027	−	0.718016i	$-0.745051\pi$
$71$	−832.806	−1.39205	−0.696027	+	0.718016i	$0.745051\pi$
$72$	175.890	0.287900
$73$	1049.14	1.68210	0.841048	−	0.540961i	$-0.181939\pi$
$73$	1049.14	1.68210	0.841048	+	0.540961i	$0.181939\pi$
$74$	977.423	1.53545
$75$	1582.39	2.43624
$76$	9.26354	0.0139816
$77$	−163.963	−0.242667
$78$	2117.59	3.07397
$79$	808.341	1.15121	0.575605	−	0.817728i	$-0.304767\pi$
$79$	808.341	1.15121	0.575605	+	0.817728i	$0.304767\pi$
$80$	1326.27	1.85351
$81$	−519.295	−0.712339
$82$	−88.4608	−0.119132
$83$	1038.31	1.37312	0.686560	−	0.727074i	$-0.259120\pi$
$83$	1038.31	1.37312	0.686560	+	0.727074i	$0.259120\pi$
$84$	−267.140	−0.346992
$85$	−2469.26	−3.15093
$86$	0	0
$87$	−229.855	−0.283254
$88$	166.624	0.201843
$89$	−875.226	−1.04240	−0.521201	−	0.853434i	$-0.674516\pi$
$89$	−875.226	−1.04240	−0.521201	+	0.853434i	$0.674516\pi$
$90$	2308.44	2.70368
$91$	370.744	0.427082
$92$	−401.846	−0.455385
$93$	677.636	0.755565
$94$	4.13803	0.00454048
$95$	−25.3790	−0.0274088
$96$	1843.45	1.95986
$97$	88.7982	0.0929494	0.0464747	−	0.998919i	$-0.485201\pi$
$97$	88.7982	0.0929494	0.0464747	+	0.998919i	$0.485201\pi$
$98$	1208.12	1.24530
$99$	1050.34	1.06630
$100$	1348.70	1.34870
$101$	1277.36	1.25843	0.629216	−	0.777230i	$-0.283376\pi$
$101$	1277.36	1.25843	0.629216	+	0.777230i	$0.283376\pi$
$102$	−4043.11	−3.92478
$103$	−928.067	−0.887817	−0.443909	−	0.896072i	$-0.646409\pi$
$103$	−928.067	−0.887817	−0.443909	+	0.896072i	$0.646409\pi$
$104$	−376.760	−0.355234
$105$	731.874	0.680225
$106$	255.757	0.234352
$107$	−1194.14	−1.07890	−0.539448	−	0.842019i	$-0.681367\pi$
$107$	−1194.14	−1.07890	−0.539448	+	0.842019i	$0.681367\pi$
$108$	323.667	0.288378
$109$	671.431	0.590013	0.295007	−	0.955495i	$-0.404678\pi$
$109$	671.431	0.590013	0.295007	+	0.955495i	$0.404678\pi$
$110$	2186.84	1.89552
$111$	−1985.10	−1.69746
$112$	380.199	0.320762
$113$	263.783	0.219598	0.109799	−	0.993954i	$-0.464979\pi$
$113$	263.783	0.219598	0.109799	+	0.993954i	$0.464979\pi$
$114$	−41.5550	−0.0341402
$115$	1100.93	0.892712
$116$	−195.911	−0.156809
$117$	−2374.96	−1.87663
$118$	−1781.59	−1.38990
$119$	−707.859	−0.545289
$120$	−743.751	−0.565791
$121$	−335.987	−0.252432
$122$	−2218.89	−1.64663
$123$	179.660	0.131702
$124$	577.564	0.418281
$125$	−1428.46	−1.02212
$126$	661.758	0.467890
$127$	−1082.71	−0.756499	−0.378249	−	0.925704i	$-0.623474\pi$
$127$	−1082.71	−0.756499	−0.378249	+	0.925704i	$0.623474\pi$
$128$	−666.053	−0.459932
$129$	0	0
$130$	−4944.74	−3.33602
$131$	−1370.38	−0.913972	−0.456986	−	0.889474i	$-0.651071\pi$
$131$	−1370.38	−0.913972	−0.456986	+	0.889474i	$0.651071\pi$
$132$	1621.14	1.06895
$133$	−7.27537	−0.00474327
$134$	−1257.35	−0.810586
$135$	−886.739	−0.565321
$136$	719.346	0.453555
$137$	−1001.07	−0.624283	−0.312142	−	0.950036i	$-0.601046\pi$
$137$	−1001.07	−0.624283	−0.312142	+	0.950036i	$0.601046\pi$
$138$	1802.63	1.11196
$139$	−598.525	−0.365225	−0.182612	−	0.983185i	$-0.558455\pi$
$139$	−598.525	−0.365225	−0.182612	+	0.983185i	$0.558455\pi$
$140$	623.793	0.376572
$141$	−8.40416	−0.00501956
$142$	3184.15	1.88175
$143$	−2249.86	−1.31568
$144$	−2435.53	−1.40945
$145$	536.730	0.307400
$146$	−4011.30	−2.27382
$147$	−2453.65	−1.37669
$148$	−1691.95	−0.939711
$149$	710.011	0.390378	0.195189	−	0.980766i	$-0.437468\pi$
$149$	710.011	0.390378	0.195189	+	0.980766i	$0.437468\pi$
$150$	−6050.10	−3.29326
$151$	−1699.83	−0.916093	−0.458047	−	0.888928i	$-0.651451\pi$
$151$	−1699.83	−0.916093	−0.458047	+	0.888928i	$0.651451\pi$
$152$	7.39343	0.00394531
$153$	4534.51	2.39603
$154$	626.899	0.328032
$155$	−1582.33	−0.819975
$156$	−3665.61	−1.88131
$157$	−1361.92	−0.692311	−0.346155	−	0.938177i	$-0.612513\pi$
$157$	−1361.92	−0.692311	−0.346155	+	0.938177i	$0.612513\pi$
$158$	−3090.62	−1.55618
$159$	−519.430	−0.259079
$160$	−4304.61	−2.12693
$161$	315.601	0.154490
$162$	1985.48	0.962924
$163$	−2881.57	−1.38467	−0.692336	−	0.721575i	$-0.743418\pi$
$163$	−2881.57	−1.38467	−0.692336	+	0.721575i	$0.743418\pi$
$164$	153.128	0.0729104
$165$	−4441.38	−2.09552
$166$	−3969.86	−1.85615
$167$	986.781	0.457242	0.228621	−	0.973515i	$-0.426578\pi$
$167$	986.781	0.457242	0.228621	+	0.973515i	$0.426578\pi$
$168$	−213.210	−0.0979138
$169$	2890.23	1.31554
$170$	9440.98	4.25935
$171$	46.6056	0.0208422
$172$	0	0
$173$	595.012	0.261491	0.130746	−	0.991416i	$-0.458263\pi$
$173$	595.012	0.261491	0.130746	+	0.991416i	$0.458263\pi$
$174$	878.830	0.382896
$175$	−1059.24	−0.457549
$176$	−2307.24	−0.988150
$177$	3618.32	1.53655
$178$	3346.34	1.40910
$179$	−2320.31	−0.968872	−0.484436	−	0.874827i	$-0.660975\pi$
$179$	−2320.31	−0.968872	−0.484436	+	0.874827i	$0.660975\pi$
$180$	−3995.98	−1.65468
$181$	1531.17	0.628792	0.314396	−	0.949292i	$-0.398198\pi$
$181$	1531.17	0.628792	0.314396	+	0.949292i	$0.398198\pi$
$182$	−1417.50	−0.577320
$183$	4506.48	1.82037
$184$	−320.722	−0.128500
$185$	4635.37	1.84216
$186$	−2590.88	−1.02136
$187$	4295.65	1.67983
$188$	−7.16306	−0.00277883
$189$	−254.200	−0.0978326
$190$	97.0343	0.0370506
$191$	−1733.51	−0.656714	−0.328357	−	0.944554i	$-0.606495\pi$
$191$	−1733.51	−0.656714	−0.328357	+	0.944554i	$0.606495\pi$
$192$	−2504.47	−0.941377
$193$	1109.49	0.413798	0.206899	−	0.978362i	$-0.433663\pi$
$193$	1109.49	0.413798	0.206899	+	0.978362i	$0.433663\pi$
$194$	−339.512	−0.125647
$195$	10042.6	3.68801
$196$	−2091.30	−0.762135
$197$	1579.78	0.571343	0.285672	−	0.958328i	$-0.407783\pi$
$197$	1579.78	0.571343	0.285672	+	0.958328i	$0.407783\pi$
$198$	−4015.88	−1.44140
$199$	−3596.57	−1.28118	−0.640588	−	0.767885i	$-0.721309\pi$
$199$	−3596.57	−1.28118	−0.640588	+	0.767885i	$0.721309\pi$
$200$	1076.43	0.380575
$201$	2553.62	0.896112
$202$	−4883.85	−1.70112
$203$	153.864	0.0531976
$204$	6998.74	2.40201
$205$	−419.521	−0.142930
$206$	3548.38	1.20013
$207$	−2021.72	−0.678838
$208$	5216.97	1.73910
$209$	44.1506	0.0146123
$210$	−2798.25	−0.919513
$211$	−3927.29	−1.28135	−0.640676	−	0.767811i	$-0.721346\pi$
$211$	−3927.29	−1.28135	−0.640676	+	0.767811i	$0.721346\pi$
$212$	−442.722	−0.143426
$213$	−6466.88	−2.08030
$214$	4565.68	1.45843
$215$	0	0
$216$	258.326	0.0813742
$217$	−453.606	−0.141902
$218$	−2567.15	−0.797567
$219$	8146.78	2.51374
$220$	−3785.49	−1.16008
$221$	−9713.03	−2.95642
$222$	7589.85	2.29458
$223$	249.842	0.0750255	0.0375127	−	0.999296i	$-0.488057\pi$
$223$	249.842	0.0750255	0.0375127	+	0.999296i	$0.488057\pi$
$224$	−1234.00	−0.368079
$225$	6785.44	2.01050
$226$	−1008.55	−0.296848
$227$	−5231.99	−1.52978	−0.764889	−	0.644163i	$-0.777206\pi$
$227$	−5231.99	−1.52978	−0.764889	+	0.644163i	$0.777206\pi$
$228$	71.9330	0.0208942
$229$	−948.401	−0.273677	−0.136839	−	0.990593i	$-0.543694\pi$
$229$	−948.401	−0.273677	−0.136839	+	0.990593i	$0.543694\pi$
$230$	−4209.28	−1.20675
$231$	−1273.20	−0.362644
$232$	−156.361	−0.0442482
$233$	−3452.38	−0.970699	−0.485350	−	0.874320i	$-0.661308\pi$
$233$	−3452.38	−0.970699	−0.485350	+	0.874320i	$0.661308\pi$
$234$	9080.45	2.53678
$235$	19.6244	0.00544747
$236$	3083.98	0.850635
$237$	6276.91	1.72038
$238$	2706.43	0.737109
$239$	−1033.96	−0.279838	−0.139919	−	0.990163i	$-0.544684\pi$
$239$	−1033.96	−0.279838	−0.139919	+	0.990163i	$0.544684\pi$
$240$	10298.7	2.76990
$241$	−925.893	−0.247477	−0.123739	−	0.992315i	$-0.539488\pi$
$241$	−925.893	−0.247477	−0.123739	+	0.992315i	$0.539488\pi$
$242$	1284.62	0.341232
$243$	−5352.82	−1.41310
$244$	3840.97	1.00776
$245$	5729.46	1.49405
$246$	−686.913	−0.178032
$247$	−99.8304	−0.0257168
$248$	460.967	0.118030
$249$	8062.62	2.05200
$250$	5461.59	1.38168
$251$	−1376.38	−0.346120	−0.173060	−	0.984911i	$-0.555365\pi$
$251$	−1376.38	−0.346120	−0.173060	+	0.984911i	$0.555365\pi$
$252$	−1145.52	−0.286354
$253$	−1915.22	−0.475925
$254$	4139.65	1.02262
$255$	−19174.2	−4.70877
$256$	5126.80	1.25166
$257$	582.311	0.141337	0.0706685	−	0.997500i	$-0.477487\pi$
$257$	582.311	0.141337	0.0706685	+	0.997500i	$0.477487\pi$
$258$	0	0
$259$	1328.82	0.318798
$260$	8559.50	2.04168
$261$	−985.643	−0.233754
$262$	5239.50	1.23549
$263$	130.662	0.0306348	0.0153174	−	0.999883i	$-0.495124\pi$
$263$	130.662	0.0306348	0.0153174	+	0.999883i	$0.495124\pi$
$264$	1293.87	0.301636
$265$	1212.91	0.281164
$266$	27.8167	0.00641184
$267$	−6796.28	−1.55777
$268$	2176.51	0.496088
$269$	−7250.60	−1.64341	−0.821704	−	0.569914i	$-0.806976\pi$
$269$	−7250.60	−1.64341	−0.821704	+	0.569914i	$0.806976\pi$
$270$	3390.36	0.764189
$271$	4219.91	0.945909	0.472955	−	0.881087i	$-0.343187\pi$
$271$	4219.91	0.945909	0.472955	+	0.881087i	$0.343187\pi$
$272$	−9960.74	−2.22044
$273$	2878.89	0.638235
$274$	3827.48	0.843892
$275$	6428.00	1.40954
$276$	−3120.40	−0.680530
$277$	−397.916	−0.0863121	−0.0431560	−	0.999068i	$-0.513741\pi$
$277$	−397.916	−0.0863121	−0.0431560	+	0.999068i	$0.513741\pi$
$278$	2288.40	0.493703
$279$	2905.77	0.623527
$280$	497.863	0.106261
$281$	−5264.19	−1.11756	−0.558781	−	0.829315i	$-0.688731\pi$
$281$	−5264.19	−1.11756	−0.558781	+	0.829315i	$0.688731\pi$
$282$	32.1325	0.00678533
$283$	−4632.62	−0.973076	−0.486538	−	0.873659i	$-0.661740\pi$
$283$	−4632.62	−0.973076	−0.486538	+	0.873659i	$0.661740\pi$
$284$	−5511.86	−1.15165
$285$	−197.072	−0.0409599
$286$	8602.12	1.77851
$287$	−120.263	−0.0247349
$288$	7904.91	1.61737
$289$	13632.1	2.77469
$290$	−2052.14	−0.415537
$291$	689.533	0.138904
$292$	6943.68	1.39160
$293$	−519.305	−0.103543	−0.0517716	−	0.998659i	$-0.516487\pi$
$293$	−519.305	−0.103543	−0.0517716	+	0.998659i	$0.516487\pi$
$294$	9381.29	1.86098
$295$	−8449.08	−1.66754
$296$	−1350.38	−0.265166
$297$	1542.62	0.301386
$298$	−2714.66	−0.527704
$299$	4330.58	0.837605
$300$	10472.9	2.01551
$301$	0	0
$302$	6499.13	1.23835
$303$	9918.88	1.88061
$304$	−102.376	−0.0193148
$305$	−10523.0	−1.97555
$306$	−17337.3	−3.23891
$307$	1193.72	0.221920	0.110960	−	0.993825i	$-0.464607\pi$
$307$	1193.72	0.221920	0.110960	+	0.993825i	$0.464607\pi$
$308$	−1085.18	−0.200759
$309$	−7206.60	−1.32676
$310$	6049.90	1.10842
$311$	−2588.37	−0.471938	−0.235969	−	0.971761i	$-0.575826\pi$
$311$	−2588.37	−0.471938	−0.235969	+	0.971761i	$0.575826\pi$
$312$	−2925.60	−0.530865
$313$	−423.736	−0.0765208	−0.0382604	−	0.999268i	$-0.512182\pi$
$313$	−423.736	−0.0765208	−0.0382604	+	0.999268i	$0.512182\pi$
$314$	5207.16	0.935851
$315$	3138.35	0.561353
$316$	5349.95	0.952399
$317$	1368.80	0.242522	0.121261	−	0.992621i	$-0.461306\pi$
$317$	1368.80	0.242522	0.121261	+	0.992621i	$0.461306\pi$
$318$	1985.99	0.350217
$319$	−933.723	−0.163882
$320$	5848.13	1.02163
$321$	−9272.71	−1.61231
$322$	−1206.67	−0.208836
$323$	190.606	0.0328347
$324$	−3436.92	−0.589320
$325$	−14534.6	−2.48072
$326$	11017.4	1.87177
$327$	5213.78	0.881720
$328$	122.215	0.0205738
$329$	5.62570	0.000942720 0
$330$	16981.2	2.83268
$331$	2454.58	0.407601	0.203801	−	0.979012i	$-0.434671\pi$
$331$	2454.58	0.407601	0.203801	+	0.979012i	$0.434671\pi$
$332$	6871.95	1.13599
$333$	−8512.33	−1.40082
$334$	−3772.87	−0.618090
$335$	−5962.91	−0.972504
$336$	2952.31	0.479350
$337$	7409.08	1.19762	0.598810	−	0.800891i	$-0.295640\pi$
$337$	7409.08	1.19762	0.598810	+	0.800891i	$0.295640\pi$
$338$	−11050.5	−1.77831
$339$	2048.32	0.328169
$340$	−16342.6	−2.60677
$341$	2752.71	0.437148
$342$	−178.192	−0.0281741
$343$	3425.36	0.539218
$344$	0	0
$345$	8548.87	1.33407
$346$	−2274.97	−0.353478
$347$	10125.5	1.56647	0.783237	−	0.621723i	$-0.213567\pi$
$347$	10125.5	1.56647	0.783237	+	0.621723i	$0.213567\pi$
$348$	−1521.28	−0.234337
$349$	−67.8059	−0.0103999	−0.00519995	−	0.999986i	$-0.501655\pi$
$349$	−67.8059	−0.0103999	−0.00519995	+	0.999986i	$0.501655\pi$
$350$	4049.90	0.618504
$351$	−3488.06	−0.530424
$352$	7488.51	1.13392
$353$	−6725.07	−1.01399	−0.506996	−	0.861948i	$-0.669244\pi$
$353$	−6725.07	−1.01399	−0.506996	+	0.861948i	$0.669244\pi$
$354$	−13834.3	−2.07708
$355$	15100.7	2.25764
$356$	−5792.62	−0.862383
$357$	−5496.65	−0.814883
$358$	8871.49	1.30970
$359$	−9260.90	−1.36148	−0.680740	−	0.732525i	$-0.738342\pi$
$359$	−9260.90	−1.36148	−0.680740	+	0.732525i	$0.738342\pi$
$360$	−3189.28	−0.466916
$361$	−6857.04	−0.999714
$362$	−5854.30	−0.849987
$363$	−2609.00	−0.377236
$364$	2453.74	0.353327
$365$	−19023.4	−2.72802
$366$	−17230.1	−2.46074
$367$	1180.46	0.167901	0.0839504	−	0.996470i	$-0.473246\pi$
$367$	1180.46	0.167901	0.0839504	+	0.996470i	$0.473246\pi$
$368$	4441.02	0.629088
$369$	770.401	0.108687
$370$	−17722.9	−2.49019
$371$	347.704	0.0486573
$372$	4484.88	0.625082
$373$	6144.38	0.852933	0.426466	−	0.904503i	$-0.359758\pi$
$373$	6144.38	0.852933	0.426466	+	0.904503i	$0.359758\pi$
$374$	−16424.0	−2.27076
$375$	−11092.2	−1.52747
$376$	−5.71699	−0.000784126 0
$377$	2111.27	0.288425
$378$	971.911	0.132248
$379$	−8452.78	−1.14562	−0.572810	−	0.819688i	$-0.694147\pi$
$379$	−8452.78	−1.14562	−0.572810	+	0.819688i	$0.694147\pi$
$380$	−167.969	−0.0226754
$381$	−8407.46	−1.13052
$382$	6627.91	0.887731
$383$	−3796.02	−0.506443	−0.253221	−	0.967408i	$-0.581490\pi$
$383$	−3796.02	−0.506443	−0.253221	+	0.967408i	$0.581490\pi$
$384$	−5172.02	−0.687326
$385$	2973.03	0.393558
$386$	−4242.04	−0.559363
$387$	0	0
$388$	587.705	0.0768974
$389$	−12372.4	−1.61261	−0.806303	−	0.591502i	$-0.798535\pi$
$389$	−12372.4	−1.61261	−0.806303	+	0.591502i	$0.798535\pi$
$390$	−38396.8	−4.98537
$391$	−8268.36	−1.06943
$392$	−1669.11	−0.215058
$393$	−10641.2	−1.36585
$394$	−6040.14	−0.772329
$395$	−14657.1	−1.86703
$396$	6951.61	0.882150
$397$	−12525.5	−1.58346	−0.791731	−	0.610869i	$-0.790820\pi$
$397$	−12525.5	−1.58346	−0.791731	+	0.610869i	$0.790820\pi$
$398$	13751.1	1.73186
$399$	−56.4945	−0.00708837
$400$	−14905.2	−1.86316
$401$	8542.42	1.06381	0.531905	−	0.846804i	$-0.321476\pi$
$401$	8542.42	1.06381	0.531905	+	0.846804i	$0.321476\pi$
$402$	−9763.53	−1.21135
$403$	−6224.24	−0.769358
$404$	8454.09	1.04111
$405$	9416.01	1.15527
$406$	−588.284	−0.0719114
$407$	−8063.92	−0.982098
$408$	5585.85	0.677796
$409$	9148.33	1.10601	0.553003	−	0.833180i	$-0.313482\pi$
$409$	9148.33	1.10601	0.553003	+	0.833180i	$0.313482\pi$
$410$	1604.00	0.193209
$411$	−7773.45	−0.932934
$412$	−6142.34	−0.734494
$413$	−2422.08	−0.288579
$414$	7729.86	0.917638
$415$	−18826.9	−2.22693
$416$	−16932.5	−1.99564
$417$	−4647.65	−0.545794
$418$	−168.806	−0.0197525
$419$	−8781.89	−1.02392	−0.511961	−	0.859009i	$-0.671081\pi$
$419$	−8781.89	−1.02392	−0.511961	+	0.859009i	$0.671081\pi$
$420$	4843.86	0.562752
$421$	7723.93	0.894160	0.447080	−	0.894494i	$-0.352464\pi$
$421$	7723.93	0.894160	0.447080	+	0.894494i	$0.352464\pi$
$422$	15015.6	1.73210
$423$	−36.0379	−0.00414237
$424$	−353.346	−0.0404717
$425$	27750.8	3.16732
$426$	24725.5	2.81210
$427$	−3016.61	−0.341883
$428$	−7903.33	−0.892575
$429$	−17470.5	−1.96617
$430$	0	0
$431$	−5925.41	−0.662221	−0.331110	−	0.943592i	$-0.607423\pi$
$431$	−5925.41	−0.662221	−0.331110	+	0.943592i	$0.607423\pi$
$432$	−3577.02	−0.398378
$433$	3909.25	0.433871	0.216936	−	0.976186i	$-0.430394\pi$
$433$	3909.25	0.433871	0.216936	+	0.976186i	$0.430394\pi$
$434$	1734.32	0.191820
$435$	4167.80	0.459381
$436$	4443.82	0.488120
$437$	−84.9821	−0.00930262
$438$	−31148.4	−3.39801
$439$	−4441.26	−0.482846	−0.241423	−	0.970420i	$-0.577614\pi$
$439$	−4441.26	−0.482846	−0.241423	+	0.970420i	$0.577614\pi$
$440$	−3021.28	−0.327350
$441$	−10521.5	−1.13611
$442$	37136.9	3.99643
$443$	−7712.27	−0.827136	−0.413568	−	0.910473i	$-0.635718\pi$
$443$	−7712.27	−0.827136	−0.413568	+	0.910473i	$0.635718\pi$
$444$	−13138.3	−1.40431
$445$	15869.9	1.69057
$446$	−955.248	−0.101418
$447$	5513.35	0.583384
$448$	1676.48	0.176799
$449$	−1293.48	−0.135954	−0.0679769	−	0.997687i	$-0.521654\pi$
$449$	−1293.48	−0.135954	−0.0679769	+	0.997687i	$0.521654\pi$
$450$	−25943.5	−2.71775
$451$	729.818	0.0761991
$452$	1745.83	0.181674
$453$	−13199.5	−1.36902
$454$	20004.0	2.06792
$455$	−6722.43	−0.692643
$456$	57.4113	0.00589590
$457$	5561.70	0.569290	0.284645	−	0.958633i	$-0.408124\pi$
$457$	5561.70	0.569290	0.284645	+	0.958633i	$0.408124\pi$
$458$	3626.12	0.369951
$459$	6659.74	0.677233
$460$	7286.40	0.738543
$461$	−15913.7	−1.60776	−0.803878	−	0.594795i	$-0.797233\pi$
$461$	−15913.7	−1.60776	−0.803878	+	0.594795i	$0.797233\pi$
$462$	4867.98	0.490214
$463$	−15646.3	−1.57051	−0.785256	−	0.619172i	$-0.787468\pi$
$463$	−15646.3	−1.57051	−0.785256	+	0.619172i	$0.787468\pi$
$464$	2165.12	0.216623
$465$	−12287.1	−1.22538
$466$	13199.8	1.31217
$467$	−9463.86	−0.937762	−0.468881	−	0.883261i	$-0.655343\pi$
$467$	−9463.86	−0.937762	−0.468881	+	0.883261i	$0.655343\pi$
$468$	−15718.5	−1.55254
$469$	−1709.38	−0.168298
$470$	−75.0320	−0.00736376
$471$	−10575.5	−1.03459
$472$	2461.39	0.240031
$473$	0	0
$474$	−23999.2	−2.32557
$475$	285.223	0.0275514
$476$	−4684.91	−0.451119
$477$	−2227.37	−0.213804
$478$	3953.24	0.378278
$479$	3861.05	0.368301	0.184150	−	0.982898i	$-0.441047\pi$
$479$	3861.05	0.368301	0.184150	+	0.982898i	$0.441047\pi$
$480$	−33426.0	−3.17850
$481$	18233.6	1.72844
$482$	3540.06	0.334534
$483$	2450.69	0.230870
$484$	−2223.71	−0.208838
$485$	−1610.12	−0.150746
$486$	20466.0	1.91020
$487$	3513.12	0.326888	0.163444	−	0.986553i	$-0.447740\pi$
$487$	3513.12	0.326888	0.163444	+	0.986553i	$0.447740\pi$
$488$	3065.56	0.284368
$489$	−22375.8	−2.06926
$490$	−21906.1	−2.01962
$491$	19277.8	1.77188	0.885940	−	0.463799i	$-0.153514\pi$
$491$	19277.8	1.77188	0.885940	+	0.463799i	$0.153514\pi$
$492$	1189.07	0.108958
$493$	−4031.04	−0.368254
$494$	381.692	0.0347635
$495$	−19045.1	−1.72932
$496$	−6382.98	−0.577831
$497$	4328.89	0.390699
$498$	−30826.7	−2.77385
$499$	7626.32	0.684170	0.342085	−	0.939669i	$-0.388867\pi$
$499$	7626.32	0.684170	0.342085	+	0.939669i	$0.388867\pi$
$500$	−9454.17	−0.845607
$501$	7662.53	0.683306
$502$	5262.45	0.467878
$503$	−9139.85	−0.810190	−0.405095	−	0.914275i	$-0.632762\pi$
$503$	−9139.85	−0.810190	−0.405095	+	0.914275i	$0.632762\pi$
$504$	−914.267	−0.0808029
$505$	−23161.4	−2.04093
$506$	7322.68	0.643345
$507$	22443.1	1.96595
$508$	−7165.86	−0.625854
$509$	−13821.6	−1.20360	−0.601799	−	0.798647i	$-0.705549\pi$
$509$	−13821.6	−1.20360	−0.601799	+	0.798647i	$0.705549\pi$
$510$	73310.8	6.36521
$511$	−5453.40	−0.472103
$512$	−14273.4	−1.23203
$513$	68.4488	0.00589101
$514$	−2226.41	−0.191056
$515$	16828.0	1.43986
$516$	0	0
$517$	−34.1396	−0.00290417
$518$	−5080.60	−0.430944
$519$	4620.37	0.390774
$520$	6831.52	0.576119
$521$	10933.9	0.919427	0.459714	−	0.888067i	$-0.347952\pi$
$521$	10933.9	0.919427	0.459714	+	0.888067i	$0.347952\pi$
$522$	3768.51	0.315983
$523$	15350.3	1.28340	0.641701	−	0.766955i	$-0.278229\pi$
$523$	15350.3	1.28340	0.641701	+	0.766955i	$0.278229\pi$
$524$	−9069.74	−0.756132
$525$	−8225.18	−0.683764
$526$	−499.573	−0.0414115
$527$	11883.9	0.982299
$528$	−17916.1	−1.47670
$529$	−8480.53	−0.697011
$530$	−4637.45	−0.380072
$531$	15515.7	1.26803
$532$	−48.1515	−0.00392412
$533$	−1650.22	−0.134107
$534$	25984.9	2.10576
$535$	21652.5	1.74976
$536$	1737.12	0.139985
$537$	−18017.6	−1.44789
$538$	27722.0	2.22152
$539$	−9967.26	−0.796512
$540$	−5868.82	−0.467692
$541$	21902.0	1.74055	0.870277	−	0.492562i	$-0.163940\pi$
$541$	21902.0	1.74055	0.870277	+	0.492562i	$0.163940\pi$
$542$	−16134.4	−1.27866
$543$	11889.8	0.939671
$544$	32329.2	2.54798
$545$	−12174.6	−0.956884
$546$	−11007.1	−0.862752
$547$	3326.60	0.260028	0.130014	−	0.991512i	$-0.458498\pi$
$547$	3326.60	0.260028	0.130014	+	0.991512i	$0.458498\pi$
$548$	−6625.48	−0.516472
$549$	19324.2	1.50226
$550$	−24576.8	−1.90538
$551$	−41.4310	−0.00320331
$552$	−2490.46	−0.192031
$553$	−4201.73	−0.323102
$554$	1521.39	0.116675
$555$	35994.5	2.75294
$556$	−3961.29	−0.302152
$557$	−16723.9	−1.27220	−0.636098	−	0.771608i	$-0.719453\pi$
$557$	−16723.9	−1.27220	−0.636098	+	0.771608i	$0.719453\pi$
$558$	−11109.9	−0.842870
$559$	0	0
$560$	−6893.87	−0.520213
$561$	33356.4	2.51035
$562$	20127.1	1.51070
$563$	−8139.07	−0.609273	−0.304637	−	0.952469i	$-0.598535\pi$
$563$	−8139.07	−0.609273	−0.304637	+	0.952469i	$0.598535\pi$
$564$	−55.6223	−0.00415270
$565$	−4782.98	−0.356145
$566$	17712.4	1.31538
$567$	2699.27	0.199927
$568$	−4399.14	−0.324971
$569$	−10529.4	−0.775771	−0.387885	−	0.921708i	$-0.626794\pi$
$569$	−10529.4	−0.775771	−0.387885	+	0.921708i	$0.626794\pi$
$570$	753.488	0.0553686
$571$	−21060.5	−1.54353	−0.771765	−	0.635908i	$-0.780626\pi$
$571$	−21060.5	−1.54353	−0.771765	+	0.635908i	$0.780626\pi$
$572$	−14890.5	−1.08847
$573$	−13461.0	−0.981398
$574$	459.816	0.0334361
$575$	−12372.8	−0.897356
$576$	−10739.4	−0.776868
$577$	832.149	0.0600395	0.0300198	−	0.999549i	$-0.490443\pi$
$577$	832.149	0.0600395	0.0300198	+	0.999549i	$0.490443\pi$
$578$	−52120.9	−3.75077
$579$	8615.40	0.618383
$580$	3552.31	0.254313
$581$	−5397.07	−0.385384
$582$	−2636.37	−0.187768
$583$	−2110.04	−0.149895
$584$	5541.90	0.392681
$585$	43063.5	3.04352
$586$	1985.51	0.139967
$587$	21831.1	1.53504	0.767519	−	0.641027i	$-0.221491\pi$
$587$	21831.1	1.53504	0.767519	+	0.641027i	$0.221491\pi$
$588$	−16239.3	−1.13894
$589$	122.143	0.00854466
$590$	32304.2	2.25414
$591$	12267.3	0.853820
$592$	18698.6	1.29816
$593$	−22576.3	−1.56340	−0.781702	−	0.623653i	$-0.785648\pi$
$593$	−22576.3	−1.56340	−0.781702	+	0.623653i	$0.785648\pi$
$594$	−5898.04	−0.407407
$595$	12835.1	0.884350
$596$	4699.15	0.322961
$597$	−27928.0	−1.91460
$598$	−16557.6	−1.13226
$599$	−2926.37	−0.199613	−0.0998065	−	0.995007i	$-0.531822\pi$
$599$	−2926.37	−0.199613	−0.0998065	+	0.995007i	$0.531822\pi$
$600$	8358.66	0.568734
$601$	−26815.7	−1.82003	−0.910013	−	0.414579i	$-0.863929\pi$
$601$	−26815.7	−1.82003	−0.910013	+	0.414579i	$0.863929\pi$
$602$	0	0
$603$	10950.2	0.739513
$604$	−11250.2	−0.757887
$605$	6092.22	0.409395
$606$	−37923.9	−2.54217
$607$	−19629.5	−1.31258	−0.656290	−	0.754508i	$-0.727875\pi$
$607$	−19629.5	−1.31258	−0.656290	+	0.754508i	$0.727875\pi$
$608$	332.279	0.0221640
$609$	1194.78	0.0794989
$610$	40233.6	2.67051
$611$	77.1941	0.00511120
$612$	30011.3	1.98225
$613$	−14870.5	−0.979793	−0.489896	−	0.871781i	$-0.662965\pi$
$613$	−14870.5	−0.979793	−0.489896	+	0.871781i	$0.662965\pi$
$614$	−4564.09	−0.299986
$615$	−3257.65	−0.213595
$616$	−866.106	−0.0566500
$617$	3238.39	0.211301	0.105650	−	0.994403i	$-0.466308\pi$
$617$	3238.39	0.211301	0.105650	+	0.994403i	$0.466308\pi$
$618$	27553.7	1.79349
$619$	20133.6	1.30733	0.653666	−	0.756783i	$-0.273230\pi$
$619$	20133.6	1.30733	0.653666	+	0.756783i	$0.273230\pi$
$620$	−10472.6	−0.678368
$621$	−2969.26	−0.191872
$622$	9896.37	0.637955
$623$	4549.39	0.292564
$624$	40510.7	2.59892
$625$	428.784	0.0274422
$626$	1620.12	0.103439
$627$	342.837	0.0218367
$628$	−9013.75	−0.572751
$629$	−34813.4	−2.20684
$630$	−11999.2	−0.758824
$631$	6227.34	0.392879	0.196439	−	0.980516i	$-0.437062\pi$
$631$	6227.34	0.392879	0.196439	+	0.980516i	$0.437062\pi$
$632$	4269.91	0.268747
$633$	−30496.0	−1.91486
$634$	−5233.47	−0.327835
$635$	19632.1	1.22689
$636$	−3437.81	−0.214337
$637$	22537.3	1.40182
$638$	3570.00	0.221532
$639$	−27730.6	−1.71676
$640$	12077.1	0.745919
$641$	−12495.3	−0.769945	−0.384973	−	0.922928i	$-0.625789\pi$
$641$	−12495.3	−0.769945	−0.384973	+	0.922928i	$0.625789\pi$
$642$	35453.3	2.17949
$643$	4940.90	0.303033	0.151516	−	0.988455i	$-0.451584\pi$
$643$	4940.90	0.303033	0.151516	+	0.988455i	$0.451584\pi$
$644$	2088.78	0.127810
$645$	0	0
$646$	−728.764	−0.0443852
$647$	−6624.13	−0.402506	−0.201253	−	0.979539i	$-0.564501\pi$
$647$	−6624.13	−0.402506	−0.201253	+	0.979539i	$0.564501\pi$
$648$	−2743.08	−0.166294
$649$	14698.4	0.889004
$650$	55571.6	3.35338
$651$	−3522.32	−0.212060
$652$	−19071.4	−1.14554
$653$	4497.38	0.269519	0.134760	−	0.990878i	$-0.456974\pi$
$653$	4497.38	0.269519	0.134760	+	0.990878i	$0.456974\pi$
$654$	−19934.4	−1.19189
$655$	24848.1	1.48228
$656$	−1692.30	−0.100722
$657$	34934.2	2.07445
$658$	−21.5093	−0.00127435
$659$	26308.3	1.55512	0.777562	−	0.628806i	$-0.216456\pi$
$659$	26308.3	1.55512	0.777562	+	0.628806i	$0.216456\pi$
$660$	−29395.0	−1.73363
$661$	15971.0	0.939788	0.469894	−	0.882723i	$-0.344292\pi$
$661$	15971.0	0.939788	0.469894	+	0.882723i	$0.344292\pi$
$662$	−9384.86	−0.550986
$663$	−75423.3	−4.41810
$664$	5484.66	0.320551
$665$	131.919	0.00769264
$666$	32546.1	1.89360
$667$	1797.25	0.104333
$668$	6530.94	0.378278
$669$	1940.07	0.112119
$670$	22798.6	1.31461
$671$	18306.3	1.05321
$672$	−9582.18	−0.550061
$673$	−3279.61	−0.187845	−0.0939226	−	0.995580i	$-0.529941\pi$
$673$	−3279.61	−0.187845	−0.0939226	+	0.995580i	$0.529941\pi$
$674$	−28327.9	−1.61892
$675$	9965.63	0.568263
$676$	19128.8	1.08835
$677$	33062.8	1.87697	0.938483	−	0.345325i	$-0.112231\pi$
$677$	33062.8	1.87697	0.938483	+	0.345325i	$0.112231\pi$
$678$	−7831.55	−0.443612
$679$	−461.570	−0.0260875
$680$	−13043.4	−0.735576
$681$	−40627.3	−2.28611
$682$	−10524.7	−0.590927
$683$	−28185.8	−1.57906	−0.789531	−	0.613711i	$-0.789676\pi$
$683$	−28185.8	−1.57906	−0.789531	+	0.613711i	$0.789676\pi$
$684$	308.456	0.0172429
$685$	18151.6	1.01246
$686$	−13096.5	−0.728903
$687$	−7364.49	−0.408985
$688$	0	0
$689$	4771.08	0.263808
$690$	−32685.8	−1.80337
$691$	20756.6	1.14272	0.571359	−	0.820700i	$-0.306416\pi$
$691$	20756.6	1.14272	0.571359	+	0.820700i	$0.306416\pi$
$692$	3938.05	0.216332
$693$	−5459.63	−0.299270
$694$	−38714.0	−2.11753
$695$	10852.6	0.592322
$696$	−1214.17	−0.0661248
$697$	3150.75	0.171224
$698$	259.249	0.0140584
$699$	−26808.3	−1.45062
$700$	−7010.50	−0.378532
$701$	−32953.3	−1.77550	−0.887751	−	0.460324i	$-0.847733\pi$
$701$	−32953.3	−1.77550	−0.887751	+	0.460324i	$0.847733\pi$
$702$	13336.3	0.717016
$703$	−357.812	−0.0191965
$704$	−10173.7	−0.544653
$705$	152.387	0.00814073
$706$	25712.7	1.37069
$707$	−6639.64	−0.353196
$708$	23947.6	1.27120
$709$	10596.1	0.561276	0.280638	−	0.959814i	$-0.409454\pi$
$709$	10596.1	0.561276	0.280638	+	0.959814i	$0.409454\pi$
$710$	−57736.0	−3.05182
$711$	26916.0	1.41973
$712$	−4623.22	−0.243346
$713$	−5298.47	−0.278302
$714$	21015.9	1.10154
$715$	40795.1	2.13378
$716$	−15356.8	−0.801551
$717$	−8028.86	−0.418191
$718$	35408.2	1.84042
$719$	−27081.5	−1.40469	−0.702344	−	0.711838i	$-0.747863\pi$
$719$	−27081.5	−1.40469	−0.702344	+	0.711838i	$0.747863\pi$
$720$	44161.8	2.28585
$721$	4824.05	0.249178
$722$	26217.2	1.35139
$723$	−7189.72	−0.369832
$724$	10134.0	0.520201
$725$	−6032.05	−0.309000
$726$	9975.25	0.509940
$727$	2011.78	0.102631	0.0513155	−	0.998682i	$-0.483659\pi$
$727$	2011.78	0.102631	0.0513155	+	0.998682i	$0.483659\pi$
$728$	1958.38	0.0997012
$729$	−27544.6	−1.39941
$730$	72734.1	3.68768
$731$	0	0
$732$	29825.8	1.50600
$733$	−9401.81	−0.473757	−0.236878	−	0.971539i	$-0.576124\pi$
$733$	−9401.81	−0.473757	−0.236878	+	0.971539i	$0.576124\pi$
$734$	−4513.38	−0.226965
$735$	44490.3	2.23272
$736$	−14414.0	−0.721887
$737$	10373.4	0.518464
$738$	−2945.55	−0.146921
$739$	18781.6	0.934900	0.467450	−	0.884019i	$-0.345173\pi$
$739$	18781.6	0.934900	0.467450	+	0.884019i	$0.345173\pi$
$740$	30678.9	1.52402
$741$	−775.200	−0.0384314
$742$	−1329.41	−0.0657739
$743$	−32099.5	−1.58495	−0.792474	−	0.609906i	$-0.791207\pi$
$743$	−32099.5	−1.58495	−0.792474	+	0.609906i	$0.791207\pi$
$744$	3579.48	0.176385
$745$	−12874.1	−0.633116
$746$	−23492.4	−1.15298
$747$	34573.4	1.69340
$748$	28430.4	1.38973
$749$	6207.09	0.302807
$750$	42410.2	2.06480
$751$	22982.6	1.11671	0.558353	−	0.829603i	$-0.311433\pi$
$751$	22982.6	1.11671	0.558353	+	0.829603i	$0.311433\pi$
$752$	79.1628	0.00383879
$753$	−10687.8	−0.517245
$754$	−8072.25	−0.389886
$755$	30821.8	1.48572
$756$	−1682.41	−0.0809372
$757$	−4670.82	−0.224259	−0.112129	−	0.993694i	$-0.535767\pi$
$757$	−4670.82	−0.224259	−0.112129	+	0.993694i	$0.535767\pi$
$758$	32318.4	1.54862
$759$	−14872.0	−0.711226
$760$	−134.060	−0.00639851
$761$	14771.7	0.703643	0.351821	−	0.936067i	$-0.385562\pi$
$761$	14771.7	0.703643	0.351821	+	0.936067i	$0.385562\pi$
$762$	32145.1	1.52821
$763$	−3490.07	−0.165595
$764$	−11473.1	−0.543301
$765$	−82221.0	−3.88589
$766$	14513.7	0.684598
$767$	−33235.1	−1.56460
$768$	39810.5	1.87049
$769$	15650.6	0.733910	0.366955	−	0.930239i	$-0.380400\pi$
$769$	15650.6	0.733910	0.366955	+	0.930239i	$0.380400\pi$
$770$	−11367.1	−0.532003
$771$	4521.75	0.211215
$772$	7343.10	0.342337
$773$	31462.6	1.46395	0.731975	−	0.681332i	$-0.238599\pi$
$773$	31462.6	1.46395	0.731975	+	0.681332i	$0.238599\pi$
$774$	0	0
$775$	17783.1	0.824242
$776$	469.060	0.0216988
$777$	10318.5	0.476414
$778$	47304.6	2.17989
$779$	32.3834	0.00148942
$780$	66465.9	3.05111
$781$	−26269.9	−1.20360
$782$	31613.3	1.44564
$783$	−1447.59	−0.0660700
$784$	23112.1	1.05285
$785$	24694.7	1.12279
$786$	40685.6	1.84632
$787$	14116.6	0.639391	0.319696	−	0.947520i	$-0.396419\pi$
$787$	14116.6	0.639391	0.319696	+	0.947520i	$0.396419\pi$
$788$	10455.7	0.472674
$789$	1014.61	0.0457809
$790$	56040.0	2.52381
$791$	−1371.13	−0.0616331
$792$	5548.23	0.248924
$793$	−41393.0	−1.85360
$794$	47889.9	2.14049
$795$	9418.46	0.420174
$796$	−23803.6	−1.05992
$797$	21531.5	0.956946	0.478473	−	0.878102i	$-0.341191\pi$
$797$	21531.5	0.956946	0.478473	+	0.878102i	$0.341191\pi$
$798$	216.001	0.00958191
$799$	−147.386	−0.00652586
$800$	48377.4	2.13800
$801$	−29143.1	−1.28555
$802$	−32661.1	−1.43804
$803$	33094.0	1.45437
$804$	16901.0	0.741357
$805$	−5722.56	−0.250551
$806$	23797.8	1.04000
$807$	−56302.1	−2.45592
$808$	6747.39	0.293778
$809$	−9241.88	−0.401641	−0.200820	−	0.979628i	$-0.564361\pi$
$809$	−9241.88	−0.401641	−0.200820	+	0.979628i	$0.564361\pi$
$810$	−36001.2	−1.56167
$811$	−25173.8	−1.08998	−0.544989	−	0.838443i	$-0.683466\pi$
$811$	−25173.8	−1.08998	−0.544989	+	0.838443i	$0.683466\pi$
$812$	1018.34	0.0440106
$813$	32768.3	1.41357
$814$	30831.6	1.32758
$815$	52249.4	2.24566
$816$	−77346.9	−3.31824
$817$	0	0
$818$	−34977.8	−1.49507
$819$	12345.0	0.526701
$820$	−2776.57	−0.118246
$821$	−10451.1	−0.444272	−0.222136	−	0.975016i	$-0.571303\pi$
$821$	−10451.1	−0.444272	−0.222136	+	0.975016i	$0.571303\pi$
$822$	29721.0	1.26112
$823$	4757.91	0.201519	0.100760	−	0.994911i	$-0.467873\pi$
$823$	4757.91	0.201519	0.100760	+	0.994911i	$0.467873\pi$
$824$	−4902.34	−0.207259
$825$	49914.5	2.10642
$826$	9260.61	0.390094
$827$	−15905.4	−0.668785	−0.334393	−	0.942434i	$-0.608531\pi$
$827$	−15905.4	−0.668785	−0.334393	+	0.942434i	$0.608531\pi$
$828$	−13380.6	−0.561605
$829$	3943.21	0.165203	0.0826016	−	0.996583i	$-0.473677\pi$
$829$	3943.21	0.165203	0.0826016	+	0.996583i	$0.473677\pi$
$830$	71982.7	3.01031
$831$	−3089.88	−0.128985
$832$	23004.1	0.958562
$833$	−43030.4	−1.78981
$834$	17769.8	0.737793
$835$	−17892.6	−0.741556
$836$	292.208	0.0120888
$837$	4267.65	0.176238
$838$	33576.7	1.38411
$839$	19902.5	0.818962	0.409481	−	0.912319i	$-0.365710\pi$
$839$	19902.5	0.818962	0.409481	+	0.912319i	$0.365710\pi$
$840$	3865.99	0.158797
$841$	−23512.8	−0.964074
$842$	−29531.7	−1.20871
$843$	−40877.3	−1.67009
$844$	−25992.5	−1.06007
$845$	−52406.5	−2.13354
$846$	137.788	0.00559957
$847$	1746.45	0.0708485
$848$	4892.76	0.198135
$849$	−35973.1	−1.45417
$850$	−106103.	−4.28152
$851$	15521.6	0.625234
$852$	−42800.6	−1.72104
$853$	44071.9	1.76904	0.884521	−	0.466500i	$-0.154485\pi$
$853$	44071.9	1.76904	0.884521	+	0.466500i	$0.154485\pi$
$854$	11533.7	0.462150
$855$	−845.067	−0.0338020
$856$	−6307.82	−0.251866
$857$	−17150.5	−0.683606	−0.341803	−	0.939772i	$-0.611038\pi$
$857$	−17150.5	−0.683606	−0.341803	+	0.939772i	$0.611038\pi$
$858$	66796.9	2.65782
$859$	−48887.4	−1.94181	−0.970907	−	0.239457i	$-0.923030\pi$
$859$	−48887.4	−1.94181	−0.970907	+	0.239457i	$0.923030\pi$
$860$	0	0
$861$	−933.865	−0.0369640
$862$	22655.3	0.895175
$863$	38864.3	1.53297	0.766486	−	0.642260i	$-0.222003\pi$
$863$	38864.3	1.53297	0.766486	+	0.642260i	$0.222003\pi$
$864$	11609.8	0.457145
$865$	−10788.9	−0.424087
$866$	−14946.6	−0.586498
$867$	105855.	4.14652
$868$	−3002.16	−0.117396
$869$	25498.2	0.995358
$870$	−15935.2	−0.620981
$871$	−23455.6	−0.912471
$872$	3546.71	0.137737
$873$	2956.79	0.114630
$874$	324.921	0.0125751
$875$	7425.08	0.286873
$876$	53918.9	2.07962
$877$	−12583.6	−0.484515	−0.242258	−	0.970212i	$-0.577888\pi$
$877$	−12583.6	−0.484515	−0.242258	+	0.970212i	$0.577888\pi$
$878$	16980.7	0.652701
$879$	−4032.49	−0.154736
$880$	41835.5	1.60258
$881$	−27901.3	−1.06699	−0.533495	−	0.845803i	$-0.679122\pi$
$881$	−27901.3	−1.06699	−0.533495	+	0.845803i	$0.679122\pi$
$882$	40227.9	1.53577
$883$	−50179.5	−1.91243	−0.956215	−	0.292666i	$-0.905458\pi$
$883$	−50179.5	−1.91243	−0.956215	+	0.292666i	$0.905458\pi$
$884$	−64285.0	−2.44586
$885$	−65608.5	−2.49198
$886$	29487.1	1.11810
$887$	9359.99	0.354315	0.177158	−	0.984182i	$-0.443310\pi$
$887$	9359.99	0.354315	0.177158	+	0.984182i	$0.443310\pi$
$888$	−10485.9	−0.396267
$889$	5627.90	0.212321
$890$	−60676.9	−2.28527
$891$	−16380.6	−0.615903
$892$	1653.56	0.0620688
$893$	−1.51484	−5.67660e−5 0
$894$	−21079.8	−0.788605
$895$	42072.5	1.57132
$896$	3462.12	0.129086
$897$	33627.7	1.25172
$898$	4945.51	0.183779
$899$	−2583.15	−0.0958318
$900$	44908.9	1.66329
$901$	−9109.41	−0.336824
$902$	−2790.39	−0.103004
$903$	0	0
$904$	1393.38	0.0512646
$905$	−27763.7	−1.01978
$906$	50466.9	1.85061
$907$	−41146.5	−1.50633	−0.753167	−	0.657829i	$-0.771475\pi$
$907$	−41146.5	−1.50633	−0.753167	+	0.657829i	$0.771475\pi$
$908$	−34627.6	−1.26559
$909$	42533.2	1.55197
$910$	25702.6	0.936299
$911$	−16872.6	−0.613626	−0.306813	−	0.951770i	$-0.599263\pi$
$911$	−16872.6	−0.613626	−0.306813	+	0.951770i	$0.599263\pi$
$912$	−794.970	−0.0288641
$913$	32752.1	1.18723
$914$	−21264.6	−0.769554
$915$	−81712.7	−2.95228
$916$	−6276.92	−0.226414
$917$	7123.16	0.256519
$918$	−25462.9	−0.915469
$919$	47698.3	1.71210	0.856052	−	0.516890i	$-0.172910\pi$
$919$	47698.3	1.71210	0.856052	+	0.516890i	$0.172910\pi$
$920$	5815.43	0.208401
$921$	9269.46	0.331639
$922$	60844.5	2.17333
$923$	59399.7	2.11827
$924$	−8426.61	−0.300016
$925$	−52094.7	−1.85174
$926$	59822.3	2.12298
$927$	−30902.6	−1.09490
$928$	−7027.23	−0.248578
$929$	−17674.8	−0.624210	−0.312105	−	0.950048i	$-0.601034\pi$
$929$	−17674.8	−0.624210	−0.312105	+	0.950048i	$0.601034\pi$
$930$	46978.5	1.65644
$931$	−442.266	−0.0155689
$932$	−22849.3	−0.803063
$933$	−20099.1	−0.705268
$934$	36184.2	1.26765
$935$	−77889.9	−2.72435
$936$	−12545.3	−0.438094
$937$	−17557.9	−0.612158	−0.306079	−	0.952006i	$-0.599017\pi$
$937$	−17557.9	−0.612158	−0.306079	+	0.952006i	$0.599017\pi$
$938$	6535.65	0.227502
$939$	−3290.39	−0.114353
$940$	129.883	0.00450671
$941$	42936.2	1.48744	0.743719	−	0.668492i	$-0.233060\pi$
$941$	42936.2	1.48744	0.743719	+	0.668492i	$0.233060\pi$
$942$	40434.5	1.39854
$943$	−1404.77	−0.0485108
$944$	−34082.7	−1.17510
$945$	4609.24	0.158665
$946$	0	0
$947$	−4691.32	−0.160979	−0.0804897	−	0.996755i	$-0.525648\pi$
$947$	−4691.32	−0.160979	−0.0804897	+	0.996755i	$0.525648\pi$
$948$	41543.3	1.42327
$949$	−74830.0	−2.55962
$950$	−1090.52	−0.0372433
$951$	10629.0	0.362426
$952$	−3739.13	−0.127296
$953$	24602.9	0.836271	0.418135	−	0.908385i	$-0.362684\pi$
$953$	24602.9	0.836271	0.418135	+	0.908385i	$0.362684\pi$
$954$	8516.14	0.289015
$955$	31432.5	1.06506
$956$	−6843.18	−0.231511
$957$	−7250.51	−0.244907
$958$	−14762.4	−0.497861
$959$	5203.50	0.175213
$960$	45411.7	1.52673
$961$	−22175.6	−0.744373
$962$	−69714.5	−2.33647
$963$	−39762.3	−1.33055
$964$	−6127.96	−0.204739
$965$	−20117.7	−0.671099
$966$	−9369.99	−0.312086
$967$	1371.38	0.0456056	0.0228028	−	0.999740i	$-0.492741\pi$
$967$	1371.38	0.0456056	0.0228028	+	0.999740i	$0.492741\pi$
$968$	−1774.79	−0.0589296
$969$	1480.09	0.0490684
$970$	6156.12	0.203774
$971$	33787.3	1.11667	0.558335	−	0.829616i	$-0.311440\pi$
$971$	33787.3	1.11667	0.558335	+	0.829616i	$0.311440\pi$
$972$	−35427.2	−1.16906
$973$	3111.11	0.102505
$974$	−13432.1	−0.441880
$975$	−112863.	−3.70720
$976$	−42448.6	−1.39216
$977$	9124.24	0.298782	0.149391	−	0.988778i	$-0.452269\pi$
$977$	9124.24	0.298782	0.149391	+	0.988778i	$0.452269\pi$
$978$	85551.9	2.79719
$979$	−27608.0	−0.901282
$980$	37920.0	1.23603
$981$	22357.2	0.727636
$982$	−73706.7	−2.39519
$983$	9300.65	0.301775	0.150887	−	0.988551i	$-0.451787\pi$
$983$	9300.65	0.301775	0.150887	+	0.988551i	$0.451787\pi$
$984$	949.020	0.0307456
$985$	−28645.0	−0.926605
$986$	15412.3	0.497797
$987$	43.6845	0.00140881
$988$	−660.721	−0.0212756
$989$	0	0
$990$	72817.1	2.33766
$991$	−17367.8	−0.556717	−0.278358	−	0.960477i	$-0.589790\pi$
$991$	−17367.8	−0.556717	−0.278358	+	0.960477i	$0.589790\pi$
$992$	20717.0	0.663069
$993$	19060.2	0.609122
$994$	−16551.1	−0.528138
$995$	65214.0	2.07781
$996$	53361.9	1.69763
$997$	36720.9	1.16646	0.583230	−	0.812307i	$-0.301789\pi$
$997$	36720.9	1.16646	0.583230	+	0.812307i	$0.301789\pi$
$998$	−29158.5	−0.924846
$999$	−12501.9	−0.395938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.f.1.2		10
43.7	odd	6		43.4.c.a.6.9	✓	20
43.37	odd	6		43.4.c.a.36.9	yes	20
43.42	odd	2		1849.4.a.d.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.9	✓	20	43.7	odd	6
43.4.c.a.36.9	yes	20	43.37	odd	6
1849.4.a.d.1.9		10	43.42	odd	2
1849.4.a.f.1.2		10	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)

\(f(q)\)	\(=\)	\(q-3.82341 q^{2} +7.76517 q^{3} +6.61843 q^{4} -18.1323 q^{5} -29.6894 q^{6} -5.19796 q^{7} +5.28231 q^{8} +33.2979 q^{9} +O(q^{10})\)	\(q-3.82341 q^{2} +7.76517 q^{3} +6.61843 q^{4} -18.1323 q^{5} -29.6894 q^{6} -5.19796 q^{7} +5.28231 q^{8} +33.2979 q^{9} +69.3271 q^{10} +31.5438 q^{11} +51.3932 q^{12} -71.3248 q^{13} +19.8739 q^{14} -140.800 q^{15} -73.1438 q^{16} +136.180 q^{17} -127.311 q^{18} +1.39966 q^{19} -120.007 q^{20} -40.3630 q^{21} -120.605 q^{22} -60.7163 q^{23} +41.0180 q^{24} +203.780 q^{25} +272.704 q^{26} +48.9039 q^{27} -34.4023 q^{28} -29.6008 q^{29} +538.337 q^{30} +87.2661 q^{31} +237.400 q^{32} +244.943 q^{33} -520.672 q^{34} +94.2509 q^{35} +220.379 q^{36} -255.642 q^{37} -5.35146 q^{38} -553.849 q^{39} -95.7804 q^{40} +23.1367 q^{41} +154.324 q^{42} +208.771 q^{44} -603.766 q^{45} +232.143 q^{46} -1.08229 q^{47} -567.974 q^{48} -315.981 q^{49} -779.133 q^{50} +1057.46 q^{51} -472.058 q^{52} -66.8923 q^{53} -186.979 q^{54} -571.962 q^{55} -27.4572 q^{56} +10.8686 q^{57} +113.176 q^{58} +465.968 q^{59} -931.877 q^{60} +580.345 q^{61} -333.654 q^{62} -173.081 q^{63} -322.526 q^{64} +1293.28 q^{65} -936.517 q^{66} +328.856 q^{67} +901.299 q^{68} -471.472 q^{69} -360.359 q^{70} -832.806 q^{71} +175.890 q^{72} +1049.14 q^{73} +977.423 q^{74} +1582.39 q^{75} +9.26354 q^{76} -163.963 q^{77} +2117.59 q^{78} +808.341 q^{79} +1326.27 q^{80} -519.295 q^{81} -88.4608 q^{82} +1038.31 q^{83} -267.140 q^{84} -2469.26 q^{85} -229.855 q^{87} +166.624 q^{88} -875.226 q^{89} +2308.44 q^{90} +370.744 q^{91} -401.846 q^{92} +677.636 q^{93} +4.13803 q^{94} -25.3790 q^{95} +1843.45 q^{96} +88.7982 q^{97} +1208.12 q^{98} +1050.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) \) 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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