LMFDB - Embedded newform 1849.4.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$1$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.78088 q^{2} +1.15757 q^{3} +14.8568 q^{4} -21.3015 q^{5} -5.53419 q^{6} +24.0536 q^{7} -32.7814 q^{8} -25.6600 q^{9} +O(q^{10})$	\(q-4.78088 q^{2} +1.15757 q^{3} +14.8568 q^{4} -21.3015 q^{5} -5.53419 q^{6} +24.0536 q^{7} -32.7814 q^{8} -25.6600 q^{9} +101.840 q^{10} +17.5943 q^{11} +17.1977 q^{12} -56.9423 q^{13} -114.997 q^{14} -24.6580 q^{15} +37.8697 q^{16} -74.3144 q^{17} +122.677 q^{18} +100.891 q^{19} -316.472 q^{20} +27.8436 q^{21} -84.1161 q^{22} -13.9922 q^{23} -37.9467 q^{24} +328.755 q^{25} +272.234 q^{26} -60.9576 q^{27} +357.359 q^{28} +87.1198 q^{29} +117.887 q^{30} -127.229 q^{31} +81.2011 q^{32} +20.3666 q^{33} +355.288 q^{34} -512.378 q^{35} -381.226 q^{36} +125.930 q^{37} -482.347 q^{38} -65.9146 q^{39} +698.294 q^{40} -82.7414 q^{41} -133.117 q^{42} +261.394 q^{44} +546.598 q^{45} +66.8948 q^{46} -71.5573 q^{47} +43.8367 q^{48} +235.575 q^{49} -1571.74 q^{50} -86.0239 q^{51} -845.980 q^{52} +152.062 q^{53} +291.431 q^{54} -374.785 q^{55} -788.511 q^{56} +116.788 q^{57} -416.509 q^{58} +319.919 q^{59} -366.338 q^{60} -353.020 q^{61} +608.268 q^{62} -617.216 q^{63} -691.170 q^{64} +1212.96 q^{65} -97.3701 q^{66} +37.2004 q^{67} -1104.07 q^{68} -16.1969 q^{69} +2449.62 q^{70} -781.921 q^{71} +841.173 q^{72} +1171.74 q^{73} -602.056 q^{74} +380.556 q^{75} +1498.91 q^{76} +423.206 q^{77} +315.130 q^{78} +841.963 q^{79} -806.682 q^{80} +622.259 q^{81} +395.577 q^{82} -1113.00 q^{83} +413.667 q^{84} +1583.01 q^{85} +100.847 q^{87} -576.766 q^{88} +308.616 q^{89} -2613.22 q^{90} -1369.67 q^{91} -207.879 q^{92} -147.277 q^{93} +342.106 q^{94} -2149.13 q^{95} +93.9957 q^{96} +1108.36 q^{97} -1126.25 q^{98} -451.470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.78088	−1.69030	−0.845148	−	0.534533i	$-0.820487\pi$
$2$	−4.78088	−1.69030	−0.845148	+	0.534533i	$0.820487\pi$
$3$	1.15757	0.222774	0.111387	−	0.993777i	$-0.464471\pi$
$3$	1.15757	0.222774	0.111387	+	0.993777i	$0.464471\pi$
$4$	14.8568	1.85710
$5$	−21.3015	−1.90527	−0.952633	−	0.304122i	$-0.901637\pi$
$5$	−21.3015	−1.90527	−0.952633	+	0.304122i	$0.901637\pi$
$6$	−5.53419	−0.376554
$7$	24.0536	1.29877	0.649386	−	0.760459i	$-0.275026\pi$
$7$	24.0536	1.29877	0.649386	+	0.760459i	$0.275026\pi$
$8$	−32.7814	−1.44875
$9$	−25.6600	−0.950372
$10$	101.840	3.22046
$11$	17.5943	0.482262	0.241131	−	0.970493i	$-0.422482\pi$
$11$	17.5943	0.482262	0.241131	+	0.970493i	$0.422482\pi$
$12$	17.1977	0.413713
$13$	−56.9423	−1.21484	−0.607422	−	0.794380i	$-0.707796\pi$
$13$	−56.9423	−1.21484	−0.607422	+	0.794380i	$0.707796\pi$
$14$	−114.997	−2.19531
$15$	−24.6580	−0.424444
$16$	37.8697	0.591714
$17$	−74.3144	−1.06023	−0.530114	−	0.847926i	$-0.677851\pi$
$17$	−74.3144	−1.06023	−0.530114	+	0.847926i	$0.677851\pi$
$18$	122.677	1.60641
$19$	100.891	1.21821	0.609104	−	0.793090i	$-0.291529\pi$
$19$	100.891	1.21821	0.609104	+	0.793090i	$0.291529\pi$
$20$	−316.472	−3.53827
$21$	27.8436	0.289332
$22$	−84.1161	−0.815164
$23$	−13.9922	−0.126851	−0.0634254	−	0.997987i	$-0.520202\pi$
$23$	−13.9922	−0.126851	−0.0634254	+	0.997987i	$0.520202\pi$
$24$	−37.9467	−0.322743
$25$	328.755	2.63004
$26$	272.234	2.05344
$27$	−60.9576	−0.434492
$28$	357.359	2.41195
$29$	87.1198	0.557853	0.278927	−	0.960312i	$-0.410021\pi$
$29$	87.1198	0.557853	0.278927	+	0.960312i	$0.410021\pi$
$30$	117.887	0.717435
$31$	−127.229	−0.737131	−0.368566	−	0.929602i	$-0.620151\pi$
$31$	−127.229	−0.737131	−0.368566	+	0.929602i	$0.620151\pi$
$32$	81.2011	0.448577
$33$	20.3666	0.107435
$34$	355.288	1.79210
$35$	−512.378	−2.47451
$36$	−381.226	−1.76493
$37$	125.930	0.559535	0.279767	−	0.960068i	$-0.409743\pi$
$37$	125.930	0.559535	0.279767	+	0.960068i	$0.409743\pi$
$38$	−482.347	−2.05913
$39$	−65.9146	−0.270635
$40$	698.294	2.76025
$41$	−82.7414	−0.315172	−0.157586	−	0.987505i	$-0.550371\pi$
$41$	−82.7414	−0.315172	−0.157586	+	0.987505i	$0.550371\pi$
$42$	−133.117	−0.489057
$43$	0	0
$43$	0	0
$44$	261.394	0.895607
$45$	546.598	1.81071
$46$	66.8948	0.214415
$47$	−71.5573	−0.222079	−0.111039	−	0.993816i	$-0.535418\pi$
$47$	−71.5573	−0.222079	−0.111039	+	0.993816i	$0.535418\pi$
$48$	43.8367	0.131818
$49$	235.575	0.686807
$50$	−1571.74	−4.44554
$51$	−86.0239	−0.236191
$52$	−845.980	−2.25608
$53$	152.062	0.394101	0.197050	−	0.980393i	$-0.436864\pi$
$53$	152.062	0.394101	0.197050	+	0.980393i	$0.436864\pi$
$54$	291.431	0.734420
$55$	−374.785	−0.918837
$56$	−788.511	−1.88159
$57$	116.788	0.271385
$58$	−416.509	−0.942936
$59$	319.919	0.705931	0.352965	−	0.935636i	$-0.385173\pi$
$59$	319.919	0.705931	0.352965	+	0.935636i	$0.385173\pi$
$60$	−366.338	−0.788234
$61$	−353.020	−0.740977	−0.370488	−	0.928837i	$-0.620810\pi$
$61$	−353.020	−0.740977	−0.370488	+	0.928837i	$0.620810\pi$
$62$	608.268	1.24597
$63$	−617.216	−1.23432
$64$	−691.170	−1.34994
$65$	1212.96	2.31460
$66$	−97.3701	−0.181597
$67$	37.2004	0.0678320	0.0339160	−	0.999425i	$-0.489202\pi$
$67$	37.2004	0.0678320	0.0339160	+	0.999425i	$0.489202\pi$
$68$	−1104.07	−1.96895
$69$	−16.1969	−0.0282591
$70$	2449.62	4.18264
$71$	−781.921	−1.30700	−0.653500	−	0.756927i	$-0.726700\pi$
$71$	−781.921	−1.30700	−0.653500	+	0.756927i	$0.726700\pi$
$72$	841.173	1.37685
$73$	1171.74	1.87866	0.939331	−	0.343013i	$-0.111448\pi$
$73$	1171.74	1.87866	0.939331	+	0.343013i	$0.111448\pi$
$74$	−602.056	−0.945779
$75$	380.556	0.585905
$76$	1498.91	2.26233
$77$	423.206	0.626347
$78$	315.130	0.457454
$79$	841.963	1.19909	0.599546	−	0.800340i	$-0.295348\pi$
$79$	841.963	1.19909	0.599546	+	0.800340i	$0.295348\pi$
$80$	−806.682	−1.12737
$81$	622.259	0.853578
$82$	395.577	0.532733
$83$	−1113.00	−1.47190	−0.735950	−	0.677036i	$-0.763264\pi$
$83$	−1113.00	−1.47190	−0.735950	+	0.677036i	$0.763264\pi$
$84$	413.667	0.537319
$85$	1583.01	2.02002
$86$	0	0
$87$	100.847	0.124275
$88$	−576.766	−0.698675
$89$	308.616	0.367564	0.183782	−	0.982967i	$-0.441166\pi$
$89$	308.616	0.367564	0.183782	+	0.982967i	$0.441166\pi$
$90$	−2613.22	−3.06064
$91$	−1369.67	−1.57780
$92$	−207.879	−0.235574
$93$	−147.277	−0.164214
$94$	342.106	0.375379
$95$	−2149.13	−2.32101
$96$	93.9957	0.0999312
$97$	1108.36	1.16017	0.580085	−	0.814556i	$-0.303019\pi$
$97$	1108.36	1.16017	0.580085	+	0.814556i	$0.303019\pi$
$98$	−1126.25	−1.16091
$99$	−451.470	−0.458328
$100$	4884.24	4.88424
$101$	−774.120	−0.762652	−0.381326	−	0.924441i	$-0.624532\pi$
$101$	−774.120	−0.762652	−0.381326	+	0.924441i	$0.624532\pi$
$102$	411.270	0.399233
$103$	317.377	0.303612	0.151806	−	0.988410i	$-0.451491\pi$
$103$	317.377	0.303612	0.151806	+	0.988410i	$0.451491\pi$
$104$	1866.65	1.76000
$105$	−593.112	−0.551255
$106$	−726.990	−0.666146
$107$	648.591	0.585997	0.292998	−	0.956113i	$-0.405347\pi$
$107$	648.591	0.585997	0.292998	+	0.956113i	$0.405347\pi$
$108$	−905.633	−0.806894
$109$	575.465	0.505684	0.252842	−	0.967508i	$-0.418635\pi$
$109$	575.465	0.505684	0.252842	+	0.967508i	$0.418635\pi$
$110$	1791.80	1.55311
$111$	145.773	0.124650
$112$	910.902	0.768501
$113$	509.868	0.424463	0.212232	−	0.977219i	$-0.431927\pi$
$113$	509.868	0.424463	0.212232	+	0.977219i	$0.431927\pi$
$114$	−558.349	−0.458721
$115$	298.055	0.241685
$116$	1294.32	1.03599
$117$	1461.14	1.15455
$118$	−1529.49	−1.19323
$119$	−1787.53	−1.37699
$120$	808.323	0.614912
$121$	−1021.44	−0.767424
$122$	1687.75	1.25247
$123$	−95.7788	−0.0702121
$124$	−1890.22	−1.36892
$125$	−4340.29	−3.10566
$126$	2950.83	2.08636
$127$	2623.19	1.83284	0.916421	−	0.400217i	$-0.131065\pi$
$127$	2623.19	1.83284	0.916421	+	0.400217i	$0.131065\pi$
$128$	2654.79	1.83322
$129$	0	0
$130$	−5799.01	−3.91236
$131$	2604.53	1.73709	0.868544	−	0.495611i	$-0.165056\pi$
$131$	2604.53	1.73709	0.868544	+	0.495611i	$0.165056\pi$
$132$	302.582	0.199518
$133$	2426.79	1.58217
$134$	−177.850	−0.114656
$135$	1298.49	0.827823
$136$	2436.13	1.53600
$137$	−665.268	−0.414873	−0.207437	−	0.978248i	$-0.566512\pi$
$137$	−665.268	−0.414873	−0.207437	+	0.978248i	$0.566512\pi$
$138$	77.4353	0.0477662
$139$	−876.154	−0.534636	−0.267318	−	0.963608i	$-0.586137\pi$
$139$	−876.154	−0.534636	−0.267318	+	0.963608i	$0.586137\pi$
$140$	−7612.29	−4.59540
$141$	−82.8324	−0.0494734
$142$	3738.27	2.20921
$143$	−1001.86	−0.585872
$144$	−971.738	−0.562348
$145$	−1855.78	−1.06286
$146$	−5601.96	−3.17549
$147$	272.694	0.153003
$148$	1870.92	1.03911
$149$	−1157.27	−0.636289	−0.318144	−	0.948042i	$-0.603060\pi$
$149$	−1157.27	−0.636289	−0.318144	+	0.948042i	$0.603060\pi$
$150$	−1819.39	−0.990352
$151$	−1380.36	−0.743922	−0.371961	−	0.928248i	$-0.621314\pi$
$151$	−1380.36	−0.743922	−0.371961	+	0.928248i	$0.621314\pi$
$152$	−3307.35	−1.76488
$153$	1906.91	1.00761
$154$	−2023.29	−1.05871
$155$	2710.18	1.40443
$156$	−979.279	−0.502596
$157$	−2859.38	−1.45352	−0.726762	−	0.686890i	$-0.758976\pi$
$157$	−2859.38	−1.45352	−0.726762	+	0.686890i	$0.758976\pi$
$158$	−4025.32	−2.02682
$159$	176.022	0.0877954
$160$	−1729.71	−0.854658
$161$	−336.562	−0.164750
$162$	−2974.94	−1.44280
$163$	−1990.78	−0.956627	−0.478314	−	0.878189i	$-0.658752\pi$
$163$	−1990.78	−0.956627	−0.478314	+	0.878189i	$0.658752\pi$
$164$	−1229.27	−0.585305
$165$	−433.839	−0.204693
$166$	5321.12	2.48794
$167$	−1753.53	−0.812527	−0.406263	−	0.913756i	$-0.633168\pi$
$167$	−1753.53	−0.812527	−0.406263	+	0.913756i	$0.633168\pi$
$168$	−912.754	−0.419170
$169$	1045.43	0.475844
$170$	−7568.17	−3.41443
$171$	−2588.86	−1.15775
$172$	0	0
$173$	1857.37	0.816263	0.408131	−	0.912923i	$-0.366180\pi$
$173$	1857.37	0.816263	0.408131	+	0.912923i	$0.366180\pi$
$174$	−482.137	−0.210062
$175$	7907.73	3.41582
$176$	666.290	0.285361
$177$	370.328	0.157263
$178$	−1475.45	−0.621291
$179$	3915.43	1.63493	0.817467	−	0.575975i	$-0.195377\pi$
$179$	3915.43	1.63493	0.817467	+	0.575975i	$0.195377\pi$
$180$	8120.69	3.36267
$181$	3009.44	1.23586	0.617928	−	0.786234i	$-0.287972\pi$
$181$	3009.44	1.23586	0.617928	+	0.786234i	$0.287972\pi$
$182$	6548.21	2.66695
$183$	−408.645	−0.165070
$184$	458.683	0.183775
$185$	−2682.50	−1.06606
$186$	704.111	0.277570
$187$	−1307.51	−0.511308
$188$	−1063.11	−0.412422
$189$	−1466.25	−0.564306
$190$	10274.7	3.92319
$191$	393.305	0.148998	0.0744989	−	0.997221i	$-0.476264\pi$
$191$	393.305	0.148998	0.0744989	+	0.997221i	$0.476264\pi$
$192$	−800.076	−0.300732
$193$	1329.16	0.495725	0.247862	−	0.968795i	$-0.420272\pi$
$193$	1329.16	0.495725	0.247862	+	0.968795i	$0.420272\pi$
$194$	−5298.91	−1.96103
$195$	1404.08	0.515633
$196$	3499.88	1.27547
$197$	−533.591	−0.192978	−0.0964892	−	0.995334i	$-0.530761\pi$
$197$	−533.591	−0.192978	−0.0964892	+	0.995334i	$0.530761\pi$
$198$	2158.42	0.774709
$199$	2186.74	0.778964	0.389482	−	0.921034i	$-0.372654\pi$
$199$	2186.74	0.778964	0.389482	+	0.921034i	$0.372654\pi$
$200$	−10777.1	−3.81026
$201$	43.0619	0.0151112
$202$	3700.97	1.28911
$203$	2095.54	0.724524
$204$	−1278.04	−0.438630
$205$	1762.52	0.600486
$206$	−1517.34	−0.513195
$207$	359.040	0.120555
$208$	−2156.39	−0.718840
$209$	1775.10	0.587495
$210$	2835.60	0.931784
$211$	5062.24	1.65165	0.825827	−	0.563923i	$-0.190709\pi$
$211$	5062.24	1.65165	0.825827	+	0.563923i	$0.190709\pi$
$212$	2259.15	0.731883
$213$	−905.127	−0.291165
$214$	−3100.83	−0.990508
$215$	0	0
$216$	1998.28	0.629470
$217$	−3060.32	−0.957365
$218$	−2751.23	−0.854755
$219$	1356.37	0.418517
$220$	−5568.10	−1.70637
$221$	4231.63	1.28801
$222$	−696.921	−0.210695
$223$	5423.05	1.62850	0.814248	−	0.580518i	$-0.197150\pi$
$223$	5423.05	1.62850	0.814248	+	0.580518i	$0.197150\pi$
$224$	1953.18	0.582599
$225$	−8435.87	−2.49952
$226$	−2437.62	−0.717468
$227$	1368.39	0.400103	0.200052	−	0.979785i	$-0.435889\pi$
$227$	1368.39	0.400103	0.200052	+	0.979785i	$0.435889\pi$
$228$	1735.09	0.503988
$229$	3079.65	0.888685	0.444342	−	0.895857i	$-0.353437\pi$
$229$	3079.65	0.888685	0.444342	+	0.895857i	$0.353437\pi$
$230$	−1424.96	−0.408518
$231$	489.889	0.139534
$232$	−2855.91	−0.808189
$233$	1874.11	0.526939	0.263469	−	0.964668i	$-0.415133\pi$
$233$	1874.11	0.526939	0.263469	+	0.964668i	$0.415133\pi$
$234$	−6985.54	−1.95153
$235$	1524.28	0.423119
$236$	4752.97	1.31098
$237$	974.629	0.267126
$238$	8545.95	2.32753
$239$	−2112.85	−0.571837	−0.285919	−	0.958254i	$-0.592299\pi$
$239$	−2112.85	−0.571837	−0.285919	+	0.958254i	$0.592299\pi$
$240$	−933.789	−0.251149
$241$	−242.170	−0.0647285	−0.0323642	−	0.999476i	$-0.510304\pi$
$241$	−242.170	−0.0647285	−0.0323642	+	0.999476i	$0.510304\pi$
$242$	4883.38	1.29717
$243$	2366.16	0.624647
$244$	−5244.74	−1.37607
$245$	−5018.10	−1.30855
$246$	457.907	0.118679
$247$	−5744.96	−1.47993
$248$	4170.76	1.06792
$249$	−1288.37	−0.327901
$250$	20750.4	5.24948
$251$	−2026.35	−0.509569	−0.254784	−	0.966998i	$-0.582005\pi$
$251$	−2026.35	−0.509569	−0.254784	+	0.966998i	$0.582005\pi$
$252$	−9169.84	−2.29224
$253$	−246.182	−0.0611753
$254$	−12541.2	−3.09804
$255$	1832.44	0.450007
$256$	−7162.86	−1.74875
$257$	2709.06	0.657534	0.328767	−	0.944411i	$-0.393367\pi$
$257$	2709.06	0.657534	0.328767	+	0.944411i	$0.393367\pi$
$258$	0	0
$259$	3029.07	0.726707
$260$	18020.7	4.29844
$261$	−2235.50	−0.530168
$262$	−12451.9	−2.93619
$263$	1614.38	0.378507	0.189253	−	0.981928i	$-0.439393\pi$
$263$	1614.38	0.378507	0.189253	+	0.981928i	$0.439393\pi$
$264$	−667.645	−0.155647
$265$	−3239.15	−0.750867
$266$	−11602.2	−2.67434
$267$	357.243	0.0818837
$268$	552.678	0.125971
$269$	−3571.10	−0.809420	−0.404710	−	0.914445i	$-0.632627\pi$
$269$	−3571.10	−0.809420	−0.404710	+	0.914445i	$0.632627\pi$
$270$	−6207.92	−1.39927
$271$	−7251.79	−1.62552	−0.812758	−	0.582602i	$-0.802035\pi$
$271$	−7251.79	−1.62552	−0.812758	+	0.582602i	$0.802035\pi$
$272$	−2814.26	−0.627352
$273$	−1585.48	−0.351494
$274$	3180.56	0.701258
$275$	5784.21	1.26837
$276$	−240.634	−0.0524799
$277$	−4897.85	−1.06239	−0.531197	−	0.847248i	$-0.678258\pi$
$277$	−4897.85	−1.06239	−0.531197	+	0.847248i	$0.678258\pi$
$278$	4188.78	0.903693
$279$	3264.71	0.700549
$280$	16796.5	3.58493
$281$	−3332.97	−0.707573	−0.353787	−	0.935326i	$-0.615106\pi$
$281$	−3332.97	−0.707573	−0.353787	+	0.935326i	$0.615106\pi$
$282$	396.011	0.0836246
$283$	−3141.03	−0.659770	−0.329885	−	0.944021i	$-0.607010\pi$
$283$	−3141.03	−0.659770	−0.329885	+	0.944021i	$0.607010\pi$
$284$	−11616.8	−2.42723
$285$	−2487.76	−0.517061
$286$	4789.77	0.990297
$287$	−1990.23	−0.409336
$288$	−2083.62	−0.426315
$289$	609.628	0.124085
$290$	8872.28	1.79654
$291$	1283.00	0.258456
$292$	17408.3	3.48886
$293$	−4342.75	−0.865891	−0.432945	−	0.901420i	$-0.642526\pi$
$293$	−4342.75	−0.865891	−0.432945	+	0.901420i	$0.642526\pi$
$294$	−1303.71	−0.258620
$295$	−6814.76	−1.34499
$296$	−4128.17	−0.810625
$297$	−1072.50	−0.209539
$298$	5532.75	1.07552
$299$	796.747	0.154104
$300$	5653.84	1.08808
$301$	0	0
$302$	6599.34	1.25745
$303$	−896.096	−0.169899
$304$	3820.70	0.720830
$305$	7519.87	1.41176
$306$	−9116.70	−1.70316
$307$	−8180.43	−1.52079	−0.760394	−	0.649462i	$-0.774994\pi$
$307$	−8180.43	−1.52079	−0.760394	+	0.649462i	$0.774994\pi$
$308$	6287.47	1.16319
$309$	367.385	0.0676370
$310$	−12957.0	−2.37390
$311$	−4932.66	−0.899375	−0.449687	−	0.893186i	$-0.648465\pi$
$311$	−4932.66	−0.899375	−0.449687	+	0.893186i	$0.648465\pi$
$312$	2160.77	0.392083
$313$	−4008.91	−0.723952	−0.361976	−	0.932187i	$-0.617898\pi$
$313$	−4008.91	−0.723952	−0.361976	+	0.932187i	$0.617898\pi$
$314$	13670.3	2.45688
$315$	13147.6	2.35170
$316$	12508.9	2.22683
$317$	1568.08	0.277831	0.138915	−	0.990304i	$-0.455638\pi$
$317$	1568.08	0.277831	0.138915	+	0.990304i	$0.455638\pi$
$318$	−841.540	−0.148400
$319$	1532.81	0.269031
$320$	14723.0	2.57200
$321$	750.788	0.130545
$322$	1609.06	0.278477
$323$	−7497.64	−1.29158
$324$	9244.76	1.58518
$325$	−18720.1	−3.19509
$326$	9517.69	1.61698
$327$	666.140	0.112653
$328$	2712.38	0.456604
$329$	−1721.21	−0.288429
$330$	2074.13	0.345991
$331$	2987.88	0.496160	0.248080	−	0.968740i	$-0.420200\pi$
$331$	2987.88	0.496160	0.248080	+	0.968740i	$0.420200\pi$
$332$	−16535.6	−2.73346
$333$	−3231.37	−0.531766
$334$	8383.39	1.37341
$335$	−792.424	−0.129238
$336$	1054.43	0.171202
$337$	−5177.88	−0.836965	−0.418483	−	0.908225i	$-0.637438\pi$
$337$	−5177.88	−0.836965	−0.418483	+	0.908225i	$0.637438\pi$
$338$	−4998.07	−0.804317
$339$	590.207	0.0945594
$340$	23518.4	3.75137
$341$	−2238.51	−0.355490
$342$	12377.0	1.95694
$343$	−2583.96	−0.406766
$344$	0	0
$345$	345.018	0.0538411
$346$	−8879.87	−1.37973
$347$	−8237.38	−1.27437	−0.637184	−	0.770712i	$-0.719901\pi$
$347$	−8237.38	−1.27437	−0.637184	+	0.770712i	$0.719901\pi$
$348$	1498.26	0.230791
$349$	2750.91	0.421928	0.210964	−	0.977494i	$-0.432340\pi$
$349$	2750.91	0.421928	0.210964	+	0.977494i	$0.432340\pi$
$350$	−37805.9	−5.77374
$351$	3471.07	0.527840
$352$	1428.67	0.216331
$353$	−109.272	−0.0164758	−0.00823789	−	0.999966i	$-0.502622\pi$
$353$	−109.272	−0.0164758	−0.00823789	+	0.999966i	$0.502622\pi$
$354$	−1770.49	−0.265821
$355$	16656.1	2.49018
$356$	4585.03	0.682602
$357$	−2069.18	−0.306759
$358$	−18719.2	−2.76352
$359$	−11539.3	−1.69643	−0.848216	−	0.529650i	$-0.822323\pi$
$359$	−11539.3	−1.69643	−0.848216	+	0.529650i	$0.822323\pi$
$360$	−17918.3	−2.62326
$361$	3319.96	0.484030
$362$	−14387.8	−2.08896
$363$	−1182.39	−0.170962
$364$	−20348.8	−2.93013
$365$	−24959.9	−3.57935
$366$	1953.68	0.279018
$367$	−13092.1	−1.86213	−0.931064	−	0.364857i	$-0.881118\pi$
$367$	−13092.1	−1.86213	−0.931064	+	0.364857i	$0.881118\pi$
$368$	−529.879	−0.0750594
$369$	2123.15	0.299530
$370$	12824.7	1.80196
$371$	3657.64	0.511847
$372$	−2188.06	−0.304961
$373$	−9972.25	−1.38430	−0.692150	−	0.721754i	$-0.743336\pi$
$373$	−9972.25	−1.38430	−0.692150	+	0.721754i	$0.743336\pi$
$374$	6251.04	0.864261
$375$	−5024.18	−0.691860
$376$	2345.75	0.321736
$377$	−4960.80	−0.677704
$378$	7009.95	0.953843
$379$	1702.20	0.230702	0.115351	−	0.993325i	$-0.463201\pi$
$379$	1702.20	0.230702	0.115351	+	0.993325i	$0.463201\pi$
$380$	−31929.1	−4.31034
$381$	3036.52	0.408309
$382$	−1880.34	−0.251850
$383$	3035.45	0.404972	0.202486	−	0.979285i	$-0.435098\pi$
$383$	3035.45	0.404972	0.202486	+	0.979285i	$0.435098\pi$
$384$	3073.10	0.408394
$385$	−9014.92	−1.19336
$386$	−6354.54	−0.837921
$387$	0	0
$388$	16466.6	2.15455
$389$	−9435.36	−1.22980	−0.614900	−	0.788605i	$-0.710804\pi$
$389$	−9435.36	−1.22980	−0.614900	+	0.788605i	$0.710804\pi$
$390$	−6712.74	−0.871571
$391$	1039.82	0.134491
$392$	−7722.47	−0.995010
$393$	3014.92	0.386978
$394$	2551.03	0.326191
$395$	−17935.1	−2.28459
$396$	−6707.39	−0.851159
$397$	4943.82	0.624995	0.312498	−	0.949919i	$-0.398834\pi$
$397$	4943.82	0.624995	0.312498	+	0.949919i	$0.398834\pi$
$398$	−10454.5	−1.31668
$399$	2809.17	0.352467
$400$	12449.8	1.55623
$401$	−10139.0	−1.26264	−0.631318	−	0.775524i	$-0.717486\pi$
$401$	−10139.0	−1.26264	−0.631318	+	0.775524i	$0.717486\pi$
$402$	−205.874	−0.0255424
$403$	7244.74	0.895499
$404$	−11500.9	−1.41632
$405$	−13255.1	−1.62629
$406$	−10018.5	−1.22466
$407$	2215.65	0.269842
$408$	2819.99	0.342182
$409$	740.411	0.0895134	0.0447567	−	0.998998i	$-0.485749\pi$
$409$	740.411	0.0895134	0.0447567	+	0.998998i	$0.485749\pi$
$410$	−8426.39	−1.01500
$411$	−770.092	−0.0924230
$412$	4715.20	0.563838
$413$	7695.20	0.916843
$414$	−1716.52	−0.203774
$415$	23708.6	2.80436
$416$	−4623.78	−0.544950
$417$	−1014.21	−0.119103
$418$	−8486.55	−0.993040
$419$	−12031.8	−1.40284	−0.701421	−	0.712747i	$-0.747451\pi$
$419$	−12031.8	−1.40284	−0.701421	+	0.712747i	$0.747451\pi$
$420$	−8811.74	−1.02374
$421$	1281.44	0.148346	0.0741731	−	0.997245i	$-0.476368\pi$
$421$	1281.44	0.148346	0.0741731	+	0.997245i	$0.476368\pi$
$422$	−24202.0	−2.79178
$423$	1836.16	0.211057
$424$	−4984.81	−0.570952
$425$	−24431.2	−2.78844
$426$	4327.30	0.492156
$427$	−8491.40	−0.962360
$428$	9635.98	1.08825
$429$	−1159.72	−0.130517
$430$	0	0
$431$	−5537.45	−0.618862	−0.309431	−	0.950922i	$-0.600139\pi$
$431$	−5537.45	−0.618862	−0.309431	+	0.950922i	$0.600139\pi$
$432$	−2308.44	−0.257095
$433$	−10109.8	−1.12205	−0.561023	−	0.827800i	$-0.689592\pi$
$433$	−10109.8	−1.12205	−0.561023	+	0.827800i	$0.689592\pi$
$434$	14631.0	1.61823
$435$	−2148.20	−0.236777
$436$	8549.56	0.939104
$437$	−1411.68	−0.154531
$438$	−6484.65	−0.707417
$439$	13005.7	1.41396	0.706981	−	0.707233i	$-0.250057\pi$
$439$	13005.7	1.41396	0.706981	+	0.707233i	$0.250057\pi$
$440$	12286.0	1.33116
$441$	−6044.86	−0.652722
$442$	−20230.9	−2.17712
$443$	12636.5	1.35526	0.677630	−	0.735403i	$-0.263007\pi$
$443$	12636.5	1.35526	0.677630	+	0.735403i	$0.263007\pi$
$444$	2165.71	0.231487
$445$	−6573.98	−0.700307
$446$	−25926.9	−2.75264
$447$	−1339.61	−0.141749
$448$	−16625.1	−1.75326
$449$	−1602.63	−0.168447	−0.0842237	−	0.996447i	$-0.526841\pi$
$449$	−1602.63	−0.168447	−0.0842237	+	0.996447i	$0.526841\pi$
$450$	40330.8	4.22492
$451$	−1455.78	−0.151995
$452$	7575.00	0.788269
$453$	−1597.86	−0.165726
$454$	−6542.12	−0.676292
$455$	29176.0	3.00614
$456$	−3828.48	−0.393168
$457$	12386.5	1.26786	0.633932	−	0.773389i	$-0.281440\pi$
$457$	12386.5	1.26786	0.633932	+	0.773389i	$0.281440\pi$
$458$	−14723.4	−1.50214
$459$	4530.02	0.460661
$460$	4428.13	0.448832
$461$	7814.88	0.789534	0.394767	−	0.918781i	$-0.370825\pi$
$461$	7814.88	0.789534	0.394767	+	0.918781i	$0.370825\pi$
$462$	−2342.10	−0.235854
$463$	7828.20	0.785761	0.392881	−	0.919589i	$-0.371479\pi$
$463$	7828.20	0.785761	0.392881	+	0.919589i	$0.371479\pi$
$464$	3299.20	0.330089
$465$	3137.22	0.312871
$466$	−8959.87	−0.890682
$467$	372.814	0.0369417	0.0184709	−	0.999829i	$-0.494120\pi$
$467$	372.814	0.0369417	0.0184709	+	0.999829i	$0.494120\pi$
$468$	21707.9	2.14412
$469$	894.802	0.0880983
$470$	−7287.39	−0.715196
$471$	−3309.92	−0.323807
$472$	−10487.4	−1.02272
$473$	0	0
$474$	−4659.58	−0.451522
$475$	33168.4	3.20393
$476$	−26556.9	−2.55721
$477$	−3901.92	−0.374542
$478$	10101.3	0.966574
$479$	6085.36	0.580474	0.290237	−	0.956955i	$-0.406266\pi$
$479$	6085.36	0.580474	0.290237	+	0.956955i	$0.406266\pi$
$480$	−2002.25	−0.190396
$481$	−7170.75	−0.679747
$482$	1157.79	0.109410
$483$	−389.593	−0.0367021
$484$	−15175.3	−1.42518
$485$	−23609.7	−2.21043
$486$	−11312.3	−1.05584
$487$	−1655.22	−0.154015	−0.0770075	−	0.997031i	$-0.524537\pi$
$487$	−1655.22	−0.154015	−0.0770075	+	0.997031i	$0.524537\pi$
$488$	11572.5	1.07349
$489$	−2304.47	−0.213112
$490$	23990.9	2.21184
$491$	14763.9	1.35700	0.678498	−	0.734602i	$-0.262631\pi$
$491$	14763.9	1.35700	0.678498	+	0.734602i	$0.262631\pi$
$492$	−1422.97	−0.130391
$493$	−6474.25	−0.591452
$494$	27465.9	2.50152
$495$	9617.00	0.873236
$496$	−4818.14	−0.436171
$497$	−18808.0	−1.69749
$498$	6159.55	0.554249
$499$	−5889.43	−0.528350	−0.264175	−	0.964475i	$-0.585100\pi$
$499$	−5889.43	−0.528350	−0.264175	+	0.964475i	$0.585100\pi$
$500$	−64482.8	−5.76751
$501$	−2029.83	−0.181010
$502$	9687.71	0.861322
$503$	−18376.1	−1.62893	−0.814463	−	0.580215i	$-0.802968\pi$
$503$	−18376.1	−1.62893	−0.814463	+	0.580215i	$0.802968\pi$
$504$	20233.2	1.78821
$505$	16489.9	1.45305
$506$	1176.97	0.103404
$507$	1210.16	0.106006
$508$	38972.2	3.40376
$509$	8355.89	0.727639	0.363820	−	0.931469i	$-0.381472\pi$
$509$	8355.89	0.727639	0.363820	+	0.931469i	$0.381472\pi$
$510$	−8760.67	−0.760645
$511$	28184.6	2.43995
$512$	13006.4	1.12267
$513$	−6150.06	−0.529302
$514$	−12951.7	−1.11143
$515$	−6760.61	−0.578463
$516$	0	0
$517$	−1259.00	−0.107100
$518$	−14481.6	−1.22835
$519$	2150.04	0.181842
$520$	−39762.5	−3.35327
$521$	−19044.7	−1.60146	−0.800732	−	0.599022i	$-0.795556\pi$
$521$	−19044.7	−1.60146	−0.800732	+	0.599022i	$0.795556\pi$
$522$	10687.6	0.896140
$523$	5907.61	0.493923	0.246961	−	0.969025i	$-0.420568\pi$
$523$	5907.61	0.493923	0.246961	+	0.969025i	$0.420568\pi$
$524$	38694.9	3.22594
$525$	9153.74	0.760956
$526$	−7718.18	−0.639788
$527$	9454.97	0.781528
$528$	771.276	0.0635710
$529$	−11971.2	−0.983909
$530$	15486.0	1.26919
$531$	−8209.14	−0.670897
$532$	36054.2	2.93825
$533$	4711.49	0.382884
$534$	−1707.94	−0.138408
$535$	−13816.0	−1.11648
$536$	−1219.48	−0.0982715
$537$	4532.38	0.364221
$538$	17073.0	1.36816
$539$	4144.77	0.331221
$540$	19291.4	1.53735
$541$	−22011.7	−1.74927	−0.874636	−	0.484780i	$-0.838900\pi$
$541$	−22011.7	−1.74927	−0.874636	+	0.484780i	$0.838900\pi$
$542$	34669.9	2.74760
$543$	3483.63	0.275317
$544$	−6034.41	−0.475594
$545$	−12258.3	−0.963463
$546$	7579.99	0.594128
$547$	−19182.2	−1.49940	−0.749700	−	0.661777i	$-0.769802\pi$
$547$	−19182.2	−1.49940	−0.749700	+	0.661777i	$0.769802\pi$
$548$	−9883.74	−0.770460
$549$	9058.51	0.704204
$550$	−27653.6	−2.14391
$551$	8789.59	0.679581
$552$	530.957	0.0409403
$553$	20252.2	1.55735
$554$	23416.0	1.79576
$555$	−3105.18	−0.237491
$556$	−13016.8	−0.992872
$557$	12163.8	0.925306	0.462653	−	0.886539i	$-0.346898\pi$
$557$	12163.8	0.925306	0.462653	+	0.886539i	$0.346898\pi$
$558$	−15608.2	−1.18413
$559$	0	0
$560$	−19403.6	−1.46420
$561$	−1513.53	−0.113906
$562$	15934.5	1.19601
$563$	9583.99	0.717437	0.358718	−	0.933446i	$-0.383214\pi$
$563$	9583.99	0.717437	0.358718	+	0.933446i	$0.383214\pi$
$564$	−1230.62	−0.0918769
$565$	−10861.0	−0.808715
$566$	15016.9	1.11521
$567$	14967.5	1.10860
$568$	25632.5	1.89351
$569$	7956.37	0.586201	0.293100	−	0.956082i	$-0.405313\pi$
$569$	7956.37	0.586201	0.293100	+	0.956082i	$0.405313\pi$
$570$	11893.7	0.873985
$571$	−4971.46	−0.364360	−0.182180	−	0.983265i	$-0.558315\pi$
$571$	−4971.46	−0.364360	−0.182180	+	0.983265i	$0.558315\pi$
$572$	−14884.4	−1.08802
$573$	455.277	0.0331928
$574$	9515.03	0.691899
$575$	−4600.00	−0.333623
$576$	17735.4	1.28295
$577$	−23376.7	−1.68663	−0.843315	−	0.537420i	$-0.819399\pi$
$577$	−23376.7	−1.68663	−0.843315	+	0.537420i	$0.819399\pi$
$578$	−2914.56	−0.209740
$579$	1538.59	0.110435
$580$	−27571.0	−1.97383
$581$	−26771.6	−1.91166
$582$	−6133.85	−0.436866
$583$	2675.42	0.190060
$584$	−38411.4	−2.72171
$585$	−31124.6	−2.19973
$586$	20762.1	1.46361
$587$	13790.5	0.969670	0.484835	−	0.874606i	$-0.338880\pi$
$587$	13790.5	0.969670	0.484835	+	0.874606i	$0.338880\pi$
$588$	4051.35	0.284141
$589$	−12836.3	−0.897979
$590$	32580.5	2.27342
$591$	−617.667	−0.0429906
$592$	4768.93	0.331084
$593$	−22432.3	−1.55343	−0.776716	−	0.629851i	$-0.783116\pi$
$593$	−22432.3	−1.55343	−0.776716	+	0.629851i	$0.783116\pi$
$594$	5127.51	0.354182
$595$	38077.1	2.62354
$596$	−17193.3	−1.18165
$597$	2531.30	0.173533
$598$	−3809.15	−0.260481
$599$	2181.92	0.148833	0.0744165	−	0.997227i	$-0.476291\pi$
$599$	2181.92	0.148833	0.0744165	+	0.997227i	$0.476291\pi$
$600$	−12475.2	−0.848828
$601$	10415.4	0.706907	0.353453	−	0.935452i	$-0.385007\pi$
$601$	10415.4	0.706907	0.353453	+	0.935452i	$0.385007\pi$
$602$	0	0
$603$	−954.562	−0.0644657
$604$	−20507.7	−1.38154
$605$	21758.3	1.46215
$606$	4284.12	0.287179
$607$	−6163.42	−0.412134	−0.206067	−	0.978538i	$-0.566067\pi$
$607$	−6163.42	−0.412134	−0.206067	+	0.978538i	$0.566067\pi$
$608$	8192.44	0.546460
$609$	2425.73	0.161405
$610$	−35951.6	−2.38629
$611$	4074.64	0.269791
$612$	28330.5	1.87123
$613$	6705.56	0.441819	0.220910	−	0.975294i	$-0.429097\pi$
$613$	6705.56	0.441819	0.220910	+	0.975294i	$0.429097\pi$
$614$	39109.6	2.57058
$615$	2040.24	0.133773
$616$	−13873.3	−0.907420
$617$	−1560.14	−0.101797	−0.0508985	−	0.998704i	$-0.516209\pi$
$617$	−1560.14	−0.101797	−0.0508985	+	0.998704i	$0.516209\pi$
$618$	−1756.42	−0.114326
$619$	−17652.2	−1.14621	−0.573104	−	0.819483i	$-0.694261\pi$
$619$	−17652.2	−1.14621	−0.573104	+	0.819483i	$0.694261\pi$
$620$	40264.5	2.60817
$621$	852.929	0.0551157
$622$	23582.4	1.52021
$623$	7423.31	0.477381
$624$	−2496.17	−0.160139
$625$	51360.5	3.28707
$626$	19166.1	1.22369
$627$	2054.80	0.130879
$628$	−42481.1	−2.69933
$629$	−9358.42	−0.593235
$630$	−62857.2	−3.97507
$631$	−31138.2	−1.96449	−0.982245	−	0.187601i	$-0.939929\pi$
$631$	−31138.2	−1.96449	−0.982245	+	0.187601i	$0.939929\pi$
$632$	−27600.7	−1.73718
$633$	5859.89	0.367946
$634$	−7496.81	−0.469616
$635$	−55878.0	−3.49205
$636$	2615.12	0.163045
$637$	−13414.2	−0.834363
$638$	−7328.18	−0.454742
$639$	20064.1	1.24214
$640$	−56551.1	−3.49278
$641$	−17820.0	−1.09805	−0.549023	−	0.835807i	$-0.685000\pi$
$641$	−17820.0	−1.09805	−0.549023	+	0.835807i	$0.685000\pi$
$642$	−3589.43	−0.220659
$643$	−3961.12	−0.242941	−0.121471	−	0.992595i	$-0.538761\pi$
$643$	−3961.12	−0.242941	−0.121471	+	0.992595i	$0.538761\pi$
$644$	−5000.23	−0.305957
$645$	0	0
$646$	35845.3	2.18315
$647$	−1807.07	−0.109804	−0.0549019	−	0.998492i	$-0.517485\pi$
$647$	−1807.07	−0.109804	−0.0549019	+	0.998492i	$0.517485\pi$
$648$	−20398.5	−1.23662
$649$	5628.75	0.340443
$650$	89498.4	5.40064
$651$	−3542.53	−0.213276
$652$	−29576.6	−1.77655
$653$	20608.3	1.23502	0.617509	−	0.786564i	$-0.288142\pi$
$653$	20608.3	1.23502	0.617509	+	0.786564i	$0.288142\pi$
$654$	−3184.73	−0.190417
$655$	−55480.4	−3.30962
$656$	−3133.39	−0.186492
$657$	−30067.0	−1.78543
$658$	8228.89	0.487531
$659$	−5125.22	−0.302959	−0.151480	−	0.988460i	$-0.548404\pi$
$659$	−5125.22	−0.302959	−0.151480	+	0.988460i	$0.548404\pi$
$660$	−6445.45	−0.380135
$661$	−19830.2	−1.16688	−0.583439	−	0.812157i	$-0.698293\pi$
$661$	−19830.2	−1.16688	−0.583439	+	0.812157i	$0.698293\pi$
$662$	−14284.7	−0.838656
$663$	4898.40	0.286935
$664$	36485.7	2.13241
$665$	−51694.2	−3.01446
$666$	15448.8	0.898841
$667$	−1219.00	−0.0707641
$668$	−26051.8	−1.50894
$669$	6277.55	0.362786
$670$	3788.48	0.218451
$671$	−6211.14	−0.357345
$672$	2260.93	0.129788
$673$	20904.7	1.19735	0.598675	−	0.800992i	$-0.295694\pi$
$673$	20904.7	1.19735	0.598675	+	0.800992i	$0.295694\pi$
$674$	24754.8	1.41472
$675$	−20040.1	−1.14273
$676$	15531.7	0.883689
$677$	8266.41	0.469282	0.234641	−	0.972082i	$-0.424608\pi$
$677$	8266.41	0.469282	0.234641	+	0.972082i	$0.424608\pi$
$678$	−2821.70	−0.159833
$679$	26659.9	1.50680
$680$	−51893.3	−2.92650
$681$	1584.01	0.0891326
$682$	10702.0	0.600883
$683$	−27099.4	−1.51820	−0.759098	−	0.650976i	$-0.774360\pi$
$683$	−27099.4	−1.51820	−0.759098	+	0.650976i	$0.774360\pi$
$684$	−38462.2	−2.15006
$685$	14171.2	0.790444
$686$	12353.6	0.687555
$687$	3564.90	0.197976
$688$	0	0
$689$	−8658.77	−0.478770
$690$	−1649.49	−0.0910073
$691$	18247.5	1.00458	0.502292	−	0.864698i	$-0.332490\pi$
$691$	18247.5	1.00458	0.502292	+	0.864698i	$0.332490\pi$
$692$	27594.6	1.51588
$693$	−10859.5	−0.595263
$694$	39381.9	2.15406
$695$	18663.4	1.01862
$696$	−3305.91	−0.180043
$697$	6148.88	0.334154
$698$	−13151.8	−0.713183
$699$	2169.40	0.117388
$700$	117483.	6.34351
$701$	27373.3	1.47486	0.737430	−	0.675424i	$-0.236039\pi$
$701$	27373.3	1.47486	0.737430	+	0.675424i	$0.236039\pi$
$702$	−16594.7	−0.892205
$703$	12705.2	0.681629
$704$	−12160.6	−0.651025
$705$	1764.46	0.0942599
$706$	522.415	0.0278489
$707$	−18620.4	−0.990510
$708$	5501.88	0.292053
$709$	−12752.9	−0.675524	−0.337762	−	0.941232i	$-0.609670\pi$
$709$	−12752.9	−0.675524	−0.337762	+	0.941232i	$0.609670\pi$
$710$	−79630.8	−4.20914
$711$	−21604.8	−1.13958
$712$	−10116.9	−0.532507
$713$	1780.21	0.0935057
$714$	9892.51	0.518513
$715$	21341.1	1.11624
$716$	58170.7	3.03623
$717$	−2445.77	−0.127391
$718$	55167.8	2.86747
$719$	−26662.5	−1.38295	−0.691477	−	0.722398i	$-0.743040\pi$
$719$	−26662.5	−1.38295	−0.691477	+	0.722398i	$0.743040\pi$
$720$	20699.5	1.07142
$721$	7634.05	0.394323
$722$	−15872.3	−0.818154
$723$	−280.328	−0.0144198
$724$	44710.6	2.29511
$725$	28641.1	1.46718
$726$	5652.85	0.288976
$727$	−27767.2	−1.41655	−0.708273	−	0.705939i	$-0.750525\pi$
$727$	−27767.2	−1.41655	−0.708273	+	0.705939i	$0.750525\pi$
$728$	44899.6	2.28584
$729$	−14062.0	−0.714423
$730$	119330.	6.05016
$731$	0	0
$732$	−6071.14	−0.306552
$733$	−5819.92	−0.293265	−0.146633	−	0.989191i	$-0.546844\pi$
$733$	−5819.92	−0.293265	−0.146633	+	0.989191i	$0.546844\pi$
$734$	62591.6	3.14754
$735$	−5808.79	−0.291511
$736$	−1136.18	−0.0569023
$737$	654.514	0.0327128
$738$	−10150.5	−0.506295
$739$	4469.69	0.222490	0.111245	−	0.993793i	$-0.464516\pi$
$739$	4469.69	0.222490	0.111245	+	0.993793i	$0.464516\pi$
$740$	−39853.4	−1.97978
$741$	−6650.18	−0.329690
$742$	−17486.7	−0.865172
$743$	31260.1	1.54350	0.771752	−	0.635924i	$-0.219381\pi$
$743$	31260.1	1.54350	0.771752	+	0.635924i	$0.219381\pi$
$744$	4827.94	0.237904
$745$	24651.6	1.21230
$746$	47676.1	2.33987
$747$	28559.6	1.39885
$748$	−19425.4	−0.949548
$749$	15600.9	0.761076
$750$	24020.0	1.16945
$751$	−9943.65	−0.483154	−0.241577	−	0.970382i	$-0.577665\pi$
$751$	−9943.65	−0.483154	−0.241577	+	0.970382i	$0.577665\pi$
$752$	−2709.85	−0.131407
$753$	−2345.63	−0.113519
$754$	23717.0	1.14552
$755$	29403.8	1.41737
$756$	−21783.7	−1.04797
$757$	11664.7	0.560056	0.280028	−	0.959992i	$-0.409656\pi$
$757$	11664.7	0.560056	0.280028	+	0.959992i	$0.409656\pi$
$758$	−8138.02	−0.389955
$759$	−284.973	−0.0136283
$760$	70451.5	3.36256
$761$	23261.8	1.10807	0.554033	−	0.832495i	$-0.313088\pi$
$761$	23261.8	1.10807	0.554033	+	0.832495i	$0.313088\pi$
$762$	−14517.2	−0.690163
$763$	13842.0	0.656768
$764$	5843.25	0.276703
$765$	−40620.1	−1.91977
$766$	−14512.1	−0.684522
$767$	−18216.9	−0.857595
$768$	−8291.50	−0.389575
$769$	−12725.0	−0.596717	−0.298358	−	0.954454i	$-0.596439\pi$
$769$	−12725.0	−0.596717	−0.298358	+	0.954454i	$0.596439\pi$
$770$	43099.2	2.01713
$771$	3135.92	0.146482
$772$	19747.0	0.920609
$773$	−31896.0	−1.48411	−0.742056	−	0.670337i	$-0.766149\pi$
$773$	−31896.0	−1.48411	−0.742056	+	0.670337i	$0.766149\pi$
$774$	0	0
$775$	−41827.3	−1.93868
$776$	−36333.5	−1.68079
$777$	3506.35	0.161892
$778$	45109.3	2.07872
$779$	−8347.85	−0.383945
$780$	20860.1	0.957580
$781$	−13757.3	−0.630316
$782$	−4971.25	−0.227329
$783$	−5310.61	−0.242383
$784$	8921.14	0.406393
$785$	60909.1	2.76935
$786$	−14413.9	−0.654107
$787$	−3554.63	−0.161003	−0.0805013	−	0.996755i	$-0.525652\pi$
$787$	−3554.63	−0.161003	−0.0805013	+	0.996755i	$0.525652\pi$
$788$	−7927.44	−0.358380
$789$	1868.76	0.0843214
$790$	85745.5	3.86163
$791$	12264.1	0.551281
$792$	14799.8	0.664001
$793$	20101.8	0.900171
$794$	−23635.8	−1.05643
$795$	−3749.54	−0.167274
$796$	32487.9	1.44661
$797$	15944.6	0.708640	0.354320	−	0.935124i	$-0.384712\pi$
$797$	15944.6	0.708640	0.354320	+	0.935124i	$0.384712\pi$
$798$	−13430.3	−0.595773
$799$	5317.73	0.235454
$800$	26695.3	1.17977
$801$	−7919.09	−0.349322
$802$	48473.2	2.13423
$803$	20616.0	0.906006
$804$	639.762	0.0280630
$805$	7169.28	0.313893
$806$	−34636.2	−1.51366
$807$	−4133.79	−0.180318
$808$	25376.7	1.10489
$809$	12758.5	0.554467	0.277234	−	0.960803i	$-0.410582\pi$
$809$	12758.5	0.554467	0.277234	+	0.960803i	$0.410582\pi$
$810$	63370.8	2.74892
$811$	−33232.7	−1.43891	−0.719457	−	0.694537i	$-0.755609\pi$
$811$	−33232.7	−1.43891	−0.719457	+	0.694537i	$0.755609\pi$
$812$	31133.0	1.34551
$813$	−8394.44	−0.362123
$814$	−10592.8	−0.456113
$815$	42406.7	1.82263
$816$	−3257.70	−0.139758
$817$	0	0
$818$	−3539.81	−0.151304
$819$	35145.7	1.49950
$820$	26185.4	1.11516
$821$	1216.94	0.0517314	0.0258657	−	0.999665i	$-0.491766\pi$
$821$	1216.94	0.0517314	0.0258657	+	0.999665i	$0.491766\pi$
$822$	3681.72	0.156222
$823$	4475.87	0.189574	0.0947869	−	0.995498i	$-0.469783\pi$
$823$	4475.87	0.189574	0.0947869	+	0.995498i	$0.469783\pi$
$824$	−10404.1	−0.439858
$825$	6695.61	0.282559
$826$	−36789.8	−1.54973
$827$	38299.6	1.61041	0.805205	−	0.592997i	$-0.202055\pi$
$827$	38299.6	1.61041	0.805205	+	0.592997i	$0.202055\pi$
$828$	5334.17	0.223883
$829$	−14373.6	−0.602192	−0.301096	−	0.953594i	$-0.597352\pi$
$829$	−14373.6	−0.602192	−0.301096	+	0.953594i	$0.597352\pi$
$830$	−113348.	−4.74020
$831$	−5669.59	−0.236674
$832$	39356.8	1.63997
$833$	−17506.6	−0.728172
$834$	4848.80	0.201319
$835$	37352.8	1.54808
$836$	26372.3	1.09104
$837$	7755.59	0.320278
$838$	57522.5	2.37122
$839$	−20770.8	−0.854691	−0.427346	−	0.904088i	$-0.640551\pi$
$839$	−20770.8	−0.854691	−0.427346	+	0.904088i	$0.640551\pi$
$840$	19443.1	0.798630
$841$	−16799.1	−0.688800
$842$	−6126.43	−0.250749
$843$	−3858.13	−0.157629
$844$	75208.6	3.06728
$845$	−22269.2	−0.906609
$846$	−8778.47	−0.356749
$847$	−24569.3	−0.996708
$848$	5758.54	0.233195
$849$	−3635.96	−0.146980
$850$	116803.	4.71329
$851$	−1762.04	−0.0709774
$852$	−13447.3	−0.540723
$853$	21536.0	0.864455	0.432228	−	0.901765i	$-0.357728\pi$
$853$	21536.0	0.864455	0.432228	+	0.901765i	$0.357728\pi$
$854$	40596.3	1.62667
$855$	55146.7	2.20582
$856$	−21261.7	−0.848962
$857$	34255.5	1.36540	0.682699	−	0.730700i	$-0.260806\pi$
$857$	34255.5	1.36540	0.682699	+	0.730700i	$0.260806\pi$
$858$	5544.48	0.220612
$859$	−39691.7	−1.57656	−0.788279	−	0.615317i	$-0.789028\pi$
$859$	−39691.7	−1.57656	−0.788279	+	0.615317i	$0.789028\pi$
$860$	0	0
$861$	−2303.82	−0.0911894
$862$	26473.9	1.04606
$863$	−10554.4	−0.416310	−0.208155	−	0.978096i	$-0.566746\pi$
$863$	−10554.4	−0.416310	−0.208155	+	0.978096i	$0.566746\pi$
$864$	−4949.82	−0.194903
$865$	−39564.9	−1.55520
$866$	48333.7	1.89659
$867$	705.686	0.0276429
$868$	−45466.5	−1.77792
$869$	14813.7	0.578276
$870$	10270.3	0.400224
$871$	−2118.27	−0.0824053
$872$	−18864.6	−0.732608
$873$	−28440.5	−1.10259
$874$	6749.08	0.261202
$875$	−104400.	−4.03354
$876$	20151.3	0.777227
$877$	−2628.97	−0.101224	−0.0506122	−	0.998718i	$-0.516117\pi$
$877$	−2628.97	−0.101224	−0.0506122	+	0.998718i	$0.516117\pi$
$878$	−62178.7	−2.39001
$879$	−5027.02	−0.192898
$880$	−14193.0	−0.543688
$881$	−44531.4	−1.70295	−0.851476	−	0.524394i	$-0.824292\pi$
$881$	−44531.4	−1.70295	−0.851476	+	0.524394i	$0.824292\pi$
$882$	28899.7	1.10329
$883$	12638.0	0.481657	0.240828	−	0.970568i	$-0.422581\pi$
$883$	12638.0	0.481657	0.240828	+	0.970568i	$0.422581\pi$
$884$	62868.5	2.39196
$885$	−7888.55	−0.299628
$886$	−60413.8	−2.29079
$887$	47366.5	1.79302	0.896511	−	0.443022i	$-0.146094\pi$
$887$	47366.5	1.79302	0.896511	+	0.443022i	$0.146094\pi$
$888$	−4778.63	−0.180586
$889$	63097.2	2.38044
$890$	31429.4	1.18373
$891$	10948.2	0.411648
$892$	80569.1	3.02427
$893$	−7219.47	−0.270538
$894$	6404.53	0.239597
$895$	−83404.7	−3.11499
$896$	63857.2	2.38094
$897$	922.288	0.0343303
$898$	7661.99	0.284726
$899$	−11084.2	−0.411211
$900$	−125330.	−4.64184
$901$	−11300.4	−0.417837
$902$	6959.89	0.256917
$903$	0	0
$904$	−16714.2	−0.614940
$905$	−64105.7	−2.35464
$906$	7639.18	0.280127
$907$	3162.85	0.115789	0.0578946	−	0.998323i	$-0.481561\pi$
$907$	3162.85	0.115789	0.0578946	+	0.998323i	$0.481561\pi$
$908$	20329.9	0.743031
$909$	19863.9	0.724802
$910$	−139487.	−5.08126
$911$	13963.5	0.507829	0.253914	−	0.967227i	$-0.418282\pi$
$911$	13963.5	0.507829	0.253914	+	0.967227i	$0.418282\pi$
$912$	4422.72	0.160582
$913$	−19582.4	−0.709840
$914$	−59218.1	−2.14306
$915$	8704.75	0.314503
$916$	45753.7	1.65037
$917$	62648.2	2.25608
$918$	−21657.5	−0.778653
$919$	5006.75	0.179714	0.0898572	−	0.995955i	$-0.471359\pi$
$919$	5006.75	0.179714	0.0898572	+	0.995955i	$0.471359\pi$
$920$	−9770.65	−0.350140
$921$	−9469.40	−0.338792
$922$	−37362.0	−1.33455
$923$	44524.4	1.58780
$924$	7278.18	0.259128
$925$	41400.1	1.47160
$926$	−37425.7	−1.32817
$927$	−8143.91	−0.288545
$928$	7074.22	0.250240
$929$	35356.7	1.24867	0.624336	−	0.781156i	$-0.285370\pi$
$929$	35356.7	1.24867	0.624336	+	0.781156i	$0.285370\pi$
$930$	−14998.6	−0.528844
$931$	23767.3	0.836673
$932$	27843.2	0.978577
$933$	−5709.89	−0.200357
$934$	−1782.38	−0.0624425
$935$	27851.9	0.974177
$936$	−47898.3	−1.67266
$937$	42579.5	1.48454	0.742269	−	0.670103i	$-0.233750\pi$
$937$	42579.5	1.48454	0.742269	+	0.670103i	$0.233750\pi$
$938$	−4277.94	−0.148912
$939$	−4640.58	−0.161278
$940$	22645.9	0.785774
$941$	−24475.5	−0.847905	−0.423952	−	0.905685i	$-0.639358\pi$
$941$	−24475.5	−0.847905	−0.423952	+	0.905685i	$0.639358\pi$
$942$	15824.3	0.547330
$943$	1157.73	0.0399798
$944$	12115.2	0.417709
$945$	31233.3	1.07515
$946$	0	0
$947$	5042.58	0.173032	0.0865162	−	0.996250i	$-0.472427\pi$
$947$	5042.58	0.173032	0.0865162	+	0.996250i	$0.472427\pi$
$948$	14479.9	0.496080
$949$	−66721.8	−2.28228
$950$	−158574.	−5.41560
$951$	1815.16	0.0618934
$952$	58597.7	1.99492
$953$	−22662.7	−0.770323	−0.385161	−	0.922849i	$-0.625854\pi$
$953$	−22662.7	−0.770323	−0.385161	+	0.922849i	$0.625854\pi$
$954$	18654.6	0.633087
$955$	−8378.00	−0.283880
$956$	−31390.2	−1.06196
$957$	1774.33	0.0599331
$958$	−29093.4	−0.981173
$959$	−16002.1	−0.538826
$960$	17042.8	0.572974
$961$	−13603.7	−0.456638
$962$	34282.5	1.14897
$963$	−16642.9	−0.556915
$964$	−3597.87	−0.120207
$965$	−28313.1	−0.944488
$966$	1862.60	0.0620373
$967$	20319.2	0.675720	0.337860	−	0.941196i	$-0.390297\pi$
$967$	20319.2	0.675720	0.337860	+	0.941196i	$0.390297\pi$
$968$	33484.3	1.11180
$969$	−8679.03	−0.287730
$970$	112875.	3.73628
$971$	2458.32	0.0812474	0.0406237	−	0.999175i	$-0.487066\pi$
$971$	2458.32	0.0812474	0.0406237	+	0.999175i	$0.487066\pi$
$972$	35153.5	1.16003
$973$	−21074.6	−0.694370
$974$	7913.41	0.260331
$975$	−21669.8	−0.711782
$976$	−13368.8	−0.438446
$977$	56845.4	1.86146	0.930729	−	0.365709i	$-0.119174\pi$
$977$	56845.4	1.86146	0.930729	+	0.365709i	$0.119174\pi$
$978$	11017.4	0.360222
$979$	5429.87	0.177262
$980$	−74552.8	−2.43010
$981$	−14766.5	−0.480588
$982$	−70584.4	−2.29372
$983$	−9749.84	−0.316350	−0.158175	−	0.987411i	$-0.550561\pi$
$983$	−9749.84	−0.316350	−0.158175	+	0.987411i	$0.550561\pi$
$984$	3139.77	0.101720
$985$	11366.3	0.367675
$986$	30952.6	0.999728
$987$	−1992.42	−0.0642546
$988$	−85351.6	−2.74838
$989$	0	0
$990$	−45977.7	−1.47603
$991$	44926.5	1.44010	0.720050	−	0.693922i	$-0.244119\pi$
$991$	44926.5	1.44010	0.720050	+	0.693922i	$0.244119\pi$
$992$	−10331.2	−0.330660
$993$	3458.68	0.110531
$994$	89918.7	2.86926
$995$	−46580.9	−1.48413
$996$	−19141.1	−0.608944
$997$	1536.04	0.0487934	0.0243967	−	0.999702i	$-0.492234\pi$
$997$	1536.04	0.0487934	0.0243967	+	0.999702i	$0.492234\pi$
$998$	28156.6	0.893068
$999$	−7676.39	−0.243113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.7	✓	50
43.42	odd	2		1849.4.a.j.1.44	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.7	✓	50	1.1	even	1	trivial
1849.4.a.j.1.44	yes	50	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)

\(f(q)\)	\(=\)	\(q-4.78088 q^{2} +1.15757 q^{3} +14.8568 q^{4} -21.3015 q^{5} -5.53419 q^{6} +24.0536 q^{7} -32.7814 q^{8} -25.6600 q^{9} +O(q^{10})\)	\(q-4.78088 q^{2} +1.15757 q^{3} +14.8568 q^{4} -21.3015 q^{5} -5.53419 q^{6} +24.0536 q^{7} -32.7814 q^{8} -25.6600 q^{9} +101.840 q^{10} +17.5943 q^{11} +17.1977 q^{12} -56.9423 q^{13} -114.997 q^{14} -24.6580 q^{15} +37.8697 q^{16} -74.3144 q^{17} +122.677 q^{18} +100.891 q^{19} -316.472 q^{20} +27.8436 q^{21} -84.1161 q^{22} -13.9922 q^{23} -37.9467 q^{24} +328.755 q^{25} +272.234 q^{26} -60.9576 q^{27} +357.359 q^{28} +87.1198 q^{29} +117.887 q^{30} -127.229 q^{31} +81.2011 q^{32} +20.3666 q^{33} +355.288 q^{34} -512.378 q^{35} -381.226 q^{36} +125.930 q^{37} -482.347 q^{38} -65.9146 q^{39} +698.294 q^{40} -82.7414 q^{41} -133.117 q^{42} +261.394 q^{44} +546.598 q^{45} +66.8948 q^{46} -71.5573 q^{47} +43.8367 q^{48} +235.575 q^{49} -1571.74 q^{50} -86.0239 q^{51} -845.980 q^{52} +152.062 q^{53} +291.431 q^{54} -374.785 q^{55} -788.511 q^{56} +116.788 q^{57} -416.509 q^{58} +319.919 q^{59} -366.338 q^{60} -353.020 q^{61} +608.268 q^{62} -617.216 q^{63} -691.170 q^{64} +1212.96 q^{65} -97.3701 q^{66} +37.2004 q^{67} -1104.07 q^{68} -16.1969 q^{69} +2449.62 q^{70} -781.921 q^{71} +841.173 q^{72} +1171.74 q^{73} -602.056 q^{74} +380.556 q^{75} +1498.91 q^{76} +423.206 q^{77} +315.130 q^{78} +841.963 q^{79} -806.682 q^{80} +622.259 q^{81} +395.577 q^{82} -1113.00 q^{83} +413.667 q^{84} +1583.01 q^{85} +100.847 q^{87} -576.766 q^{88} +308.616 q^{89} -2613.22 q^{90} -1369.67 q^{91} -207.879 q^{92} -147.277 q^{93} +342.106 q^{94} -2149.13 q^{95} +93.9957 q^{96} +1108.36 q^{97} -1126.25 q^{98} -451.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

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