LMFDB - Embedded newform 1849.4.a.i.1.10

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			1.10
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)

$f(q)$	$=$	$q-3.81936 q^{2} +8.34786 q^{3} +6.58755 q^{4} +2.56409 q^{5} -31.8835 q^{6} -3.42361 q^{7} +5.39467 q^{8} +42.6867 q^{9} +O(q^{10})$	\(q-3.81936 q^{2} +8.34786 q^{3} +6.58755 q^{4} +2.56409 q^{5} -31.8835 q^{6} -3.42361 q^{7} +5.39467 q^{8} +42.6867 q^{9} -9.79321 q^{10} -24.5225 q^{11} +54.9919 q^{12} -46.2969 q^{13} +13.0760 q^{14} +21.4047 q^{15} -73.3046 q^{16} +97.5824 q^{17} -163.036 q^{18} -131.921 q^{19} +16.8911 q^{20} -28.5798 q^{21} +93.6603 q^{22} +175.382 q^{23} +45.0339 q^{24} -118.425 q^{25} +176.825 q^{26} +130.950 q^{27} -22.5532 q^{28} -83.1501 q^{29} -81.7523 q^{30} +128.550 q^{31} +236.820 q^{32} -204.710 q^{33} -372.703 q^{34} -8.77845 q^{35} +281.201 q^{36} +301.363 q^{37} +503.853 q^{38} -386.480 q^{39} +13.8324 q^{40} -201.066 q^{41} +109.157 q^{42} -161.543 q^{44} +109.453 q^{45} -669.846 q^{46} -335.227 q^{47} -611.936 q^{48} -331.279 q^{49} +452.310 q^{50} +814.604 q^{51} -304.983 q^{52} +373.842 q^{53} -500.147 q^{54} -62.8779 q^{55} -18.4692 q^{56} -1101.25 q^{57} +317.581 q^{58} +578.431 q^{59} +141.004 q^{60} -892.641 q^{61} -490.980 q^{62} -146.143 q^{63} -318.064 q^{64} -118.710 q^{65} +781.862 q^{66} +2.66116 q^{67} +642.829 q^{68} +1464.06 q^{69} +33.5281 q^{70} +467.961 q^{71} +230.281 q^{72} -481.550 q^{73} -1151.01 q^{74} -988.598 q^{75} -869.034 q^{76} +83.9554 q^{77} +1476.11 q^{78} -296.213 q^{79} -187.960 q^{80} -59.3866 q^{81} +767.945 q^{82} +122.365 q^{83} -188.271 q^{84} +250.210 q^{85} -694.125 q^{87} -132.291 q^{88} +746.209 q^{89} -418.040 q^{90} +158.503 q^{91} +1155.33 q^{92} +1073.12 q^{93} +1280.36 q^{94} -338.257 q^{95} +1976.94 q^{96} -1723.34 q^{97} +1265.27 q^{98} -1046.78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) $ 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9} - 137 q^{10} - 252 q^{11} - 48 q^{12} - 192 q^{13} - 272 q^{14} - 314 q^{15} + 542 q^{16} - 236 q^{17} - 386 q^{18} + 12 q^{19} + 108 q^{20} - 408 q^{21} + 1235 q^{22} - 630 q^{23} - 613 q^{24} + 1098 q^{25} + 1493 q^{26} + 10 q^{27} - 242 q^{28} + 208 q^{29} - 48 q^{30} - 932 q^{31} - 1124 q^{32} + 254 q^{33} + 765 q^{34} - 1452 q^{35} + 747 q^{36} - 90 q^{37} - 1213 q^{38} - 1610 q^{39} - 1693 q^{40} - 1354 q^{41} - 16 q^{42} - 2704 q^{44} + 4508 q^{45} + 233 q^{46} - 3484 q^{47} - 376 q^{48} + 1324 q^{49} - 408 q^{50} + 4054 q^{51} - 2176 q^{52} - 726 q^{53} - 6497 q^{54} - 3288 q^{55} - 7097 q^{56} - 870 q^{57} + 275 q^{58} - 4370 q^{59} - 3891 q^{60} + 1172 q^{61} - 1546 q^{62} - 3686 q^{63} + 606 q^{64} + 2610 q^{65} - 4697 q^{66} - 344 q^{67} - 3221 q^{68} + 136 q^{69} - 1310 q^{70} + 162 q^{71} - 5814 q^{72} + 746 q^{73} - 4332 q^{74} + 236 q^{75} + 1338 q^{76} + 2024 q^{77} - 2782 q^{78} - 2656 q^{79} - 5713 q^{80} - 86 q^{81} - 4168 q^{82} - 3514 q^{83} - 4269 q^{84} - 7558 q^{85} - 10278 q^{87} + 11692 q^{88} + 2640 q^{89} - 8286 q^{90} - 5946 q^{91} - 4271 q^{92} - 2 q^{93} + 9062 q^{94} - 12140 q^{95} - 700 q^{96} - 3864 q^{97} - 2826 q^{98} - 8174 q^{99}+O(q^{100}) \) 50 * q - 10 * q^2 - 2 * q^3 + 186 * q^4 + 8 * q^5 - 51 * q^6 - 6 * q^7 - 138 * q^8 + 360 * q^9 - 137 * q^10 - 252 * q^11 - 48 * q^12 - 192 * q^13 - 272 * q^14 - 314 * q^15 + 542 * q^16 - 236 * q^17 - 386 * q^18 + 12 * q^19 + 108 * q^20 - 408 * q^21 + 1235 * q^22 - 630 * q^23 - 613 * q^24 + 1098 * q^25 + 1493 * q^26 + 10 * q^27 - 242 * q^28 + 208 * q^29 - 48 * q^30 - 932 * q^31 - 1124 * q^32 + 254 * q^33 + 765 * q^34 - 1452 * q^35 + 747 * q^36 - 90 * q^37 - 1213 * q^38 - 1610 * q^39 - 1693 * q^40 - 1354 * q^41 - 16 * q^42 - 2704 * q^44 + 4508 * q^45 + 233 * q^46 - 3484 * q^47 - 376 * q^48 + 1324 * q^49 - 408 * q^50 + 4054 * q^51 - 2176 * q^52 - 726 * q^53 - 6497 * q^54 - 3288 * q^55 - 7097 * q^56 - 870 * q^57 + 275 * q^58 - 4370 * q^59 - 3891 * q^60 + 1172 * q^61 - 1546 * q^62 - 3686 * q^63 + 606 * q^64 + 2610 * q^65 - 4697 * q^66 - 344 * q^67 - 3221 * q^68 + 136 * q^69 - 1310 * q^70 + 162 * q^71 - 5814 * q^72 + 746 * q^73 - 4332 * q^74 + 236 * q^75 + 1338 * q^76 + 2024 * q^77 - 2782 * q^78 - 2656 * q^79 - 5713 * q^80 - 86 * q^81 - 4168 * q^82 - 3514 * q^83 - 4269 * q^84 - 7558 * q^85 - 10278 * q^87 + 11692 * q^88 + 2640 * q^89 - 8286 * q^90 - 5946 * q^91 - 4271 * q^92 - 2 * q^93 + 9062 * q^94 - 12140 * q^95 - 700 * q^96 - 3864 * q^97 - 2826 * q^98 - 8174 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.81936	−1.35035	−0.675175	−	0.737658i	$-0.735932\pi$
$2$	−3.81936	−1.35035	−0.675175	+	0.737658i	$0.735932\pi$
$3$	8.34786	1.60655	0.803273	−	0.595611i	$-0.203090\pi$
$3$	8.34786	1.60655	0.803273	+	0.595611i	$0.203090\pi$
$4$	6.58755	0.823443
$5$	2.56409	0.229339	0.114670	−	0.993404i	$-0.463419\pi$
$5$	2.56409	0.229339	0.114670	+	0.993404i	$0.463419\pi$
$6$	−31.8835	−2.16940
$7$	−3.42361	−0.184858	−0.0924288	−	0.995719i	$-0.529463\pi$
$7$	−3.42361	−0.184858	−0.0924288	+	0.995719i	$0.529463\pi$
$8$	5.39467	0.238413
$9$	42.6867	1.58099
$10$	−9.79321	−0.309688
$11$	−24.5225	−0.672164	−0.336082	−	0.941833i	$-0.609102\pi$
$11$	−24.5225	−0.672164	−0.336082	+	0.941833i	$0.609102\pi$
$12$	54.9919	1.32290
$13$	−46.2969	−0.987727	−0.493864	−	0.869539i	$-0.664416\pi$
$13$	−46.2969	−0.987727	−0.493864	+	0.869539i	$0.664416\pi$
$14$	13.0760	0.249622
$15$	21.4047	0.368444
$16$	−73.3046	−1.14538
$17$	97.5824	1.39219	0.696095	−	0.717950i	$-0.254919\pi$
$17$	97.5824	1.39219	0.696095	+	0.717950i	$0.254919\pi$
$18$	−163.036	−2.13489
$19$	−131.921	−1.59288	−0.796439	−	0.604719i	$-0.793285\pi$
$19$	−131.921	−1.59288	−0.796439	+	0.604719i	$0.793285\pi$
$20$	16.8911	0.188848
$21$	−28.5798	−0.296982
$22$	93.6603	0.907656
$23$	175.382	1.58998	0.794991	−	0.606621i	$-0.207475\pi$
$23$	175.382	1.58998	0.794991	+	0.606621i	$0.207475\pi$
$24$	45.0339	0.383021
$25$	−118.425	−0.947403
$26$	176.825	1.33378
$27$	130.950	0.933385
$28$	−22.5532	−0.152220
$29$	−83.1501	−0.532434	−0.266217	−	0.963913i	$-0.585774\pi$
$29$	−83.1501	−0.532434	−0.266217	+	0.963913i	$0.585774\pi$
$30$	−81.7523	−0.497529
$31$	128.550	0.744783	0.372392	−	0.928076i	$-0.378538\pi$
$31$	128.550	0.744783	0.372392	+	0.928076i	$0.378538\pi$
$32$	236.820	1.30826
$33$	−204.710	−1.07986
$34$	−372.703	−1.87994
$35$	−8.77845	−0.0423951
$36$	281.201	1.30186
$37$	301.363	1.33902	0.669510	−	0.742803i	$-0.266504\pi$
$37$	301.363	1.33902	0.669510	+	0.742803i	$0.266504\pi$
$38$	503.853	2.15094
$39$	−386.480	−1.58683
$40$	13.8324	0.0546775
$41$	−201.066	−0.765884	−0.382942	−	0.923772i	$-0.625089\pi$
$41$	−201.066	−0.765884	−0.382942	+	0.923772i	$0.625089\pi$
$42$	109.157	0.401030
$43$	0	0
$43$	0	0
$44$	−161.543	−0.553489
$45$	109.453	0.362583
$46$	−669.846	−2.14703
$47$	−335.227	−1.04038	−0.520191	−	0.854050i	$-0.674139\pi$
$47$	−335.227	−1.04038	−0.520191	+	0.854050i	$0.674139\pi$
$48$	−611.936	−1.84011
$49$	−331.279	−0.965828
$50$	452.310	1.27933
$51$	814.604	2.23662
$52$	−304.983	−0.813338
$53$	373.842	0.968891	0.484445	−	0.874822i	$-0.339021\pi$
$53$	373.842	0.968891	0.484445	+	0.874822i	$0.339021\pi$
$54$	−500.147	−1.26040
$55$	−62.8779	−0.154154
$56$	−18.4692	−0.0440724
$57$	−1101.25	−2.55903
$58$	317.581	0.718972
$59$	578.431	1.27636	0.638180	−	0.769887i	$-0.279688\pi$
$59$	578.431	1.27636	0.638180	+	0.769887i	$0.279688\pi$
$60$	141.004	0.303393
$61$	−892.641	−1.87362	−0.936811	−	0.349835i	$-0.886238\pi$
$61$	−892.641	−1.87362	−0.936811	+	0.349835i	$0.886238\pi$
$62$	−490.980	−1.00572
$63$	−146.143	−0.292258
$64$	−318.064	−0.621218
$65$	−118.710	−0.226525
$66$	781.862	1.45819
$67$	2.66116	0.00485242	0.00242621	−	0.999997i	$-0.499228\pi$
$67$	2.66116	0.00485242	0.00242621	+	0.999997i	$0.499228\pi$
$68$	642.829	1.14639
$69$	1464.06	2.55438
$70$	33.5281	0.0572482
$71$	467.961	0.782208	0.391104	−	0.920346i	$-0.372093\pi$
$71$	467.961	0.782208	0.391104	+	0.920346i	$0.372093\pi$
$72$	230.281	0.376928
$73$	−481.550	−0.772070	−0.386035	−	0.922484i	$-0.626156\pi$
$73$	−481.550	−0.772070	−0.386035	+	0.922484i	$0.626156\pi$
$74$	−1151.01	−1.80814
$75$	−988.598	−1.52205
$76$	−869.034	−1.31164
$77$	83.9554	0.124255
$78$	1476.11	2.14277
$79$	−296.213	−0.421856	−0.210928	−	0.977502i	$-0.567649\pi$
$79$	−296.213	−0.421856	−0.210928	+	0.977502i	$0.567649\pi$
$80$	−187.960	−0.262682
$81$	−59.3866	−0.0814631
$82$	767.945	1.03421
$83$	122.365	0.161823	0.0809116	−	0.996721i	$-0.474217\pi$
$83$	122.365	0.161823	0.0809116	+	0.996721i	$0.474217\pi$
$84$	−188.271	−0.244548
$85$	250.210	0.319284
$86$	0	0
$87$	−694.125	−0.855379
$88$	−132.291	−0.160253
$89$	746.209	0.888742	0.444371	−	0.895843i	$-0.353427\pi$
$89$	746.209	0.888742	0.444371	+	0.895843i	$0.353427\pi$
$90$	−418.040	−0.489614
$91$	158.503	0.182589
$92$	1155.33	1.30926
$93$	1073.12	1.19653
$94$	1280.36	1.40488
$95$	−338.257	−0.365310
$96$	1976.94	2.10177
$97$	−1723.34	−1.80390	−0.901949	−	0.431842i	$-0.857864\pi$
$97$	−1723.34	−1.80390	−0.901949	+	0.431842i	$0.857864\pi$
$98$	1265.27	1.30420
$99$	−1046.78	−1.06268
$100$	−780.133	−0.780133
$101$	−384.032	−0.378343	−0.189171	−	0.981944i	$-0.560580\pi$
$101$	−384.032	−0.378343	−0.189171	+	0.981944i	$0.560580\pi$
$102$	−3111.27	−3.02021
$103$	187.491	0.179360	0.0896798	−	0.995971i	$-0.471416\pi$
$103$	187.491	0.179360	0.0896798	+	0.995971i	$0.471416\pi$
$104$	−249.757	−0.235487
$105$	−73.2813	−0.0681097
$106$	−1427.84	−1.30834
$107$	−1145.03	−1.03453	−0.517263	−	0.855827i	$-0.673049\pi$
$107$	−1145.03	−1.03453	−0.517263	+	0.855827i	$0.673049\pi$
$108$	862.641	0.768590
$109$	−1108.95	−0.974482	−0.487241	−	0.873268i	$-0.661997\pi$
$109$	−1108.95	−0.974482	−0.487241	+	0.873268i	$0.661997\pi$
$110$	240.154	0.208161
$111$	2515.73	2.15120
$112$	250.966	0.211733
$113$	−1450.93	−1.20789	−0.603947	−	0.797025i	$-0.706406\pi$
$113$	−1450.93	−1.20789	−0.603947	+	0.797025i	$0.706406\pi$
$114$	4206.09	3.45558
$115$	449.695	0.364646
$116$	−547.755	−0.438429
$117$	−1976.26	−1.56159
$118$	−2209.24	−1.72353
$119$	−334.084	−0.257357
$120$	115.471	0.0878419
$121$	−729.648	−0.548196
$122$	3409.32	2.53004
$123$	−1678.47	−1.23043
$124$	846.830	0.613287
$125$	−624.165	−0.446616
$126$	558.172	0.394650
$127$	−2025.38	−1.41515	−0.707574	−	0.706640i	$-0.750210\pi$
$127$	−2025.38	−1.41515	−0.707574	+	0.706640i	$0.750210\pi$
$128$	−679.755	−0.469394
$129$	0	0
$130$	453.395	0.305888
$131$	2553.08	1.70278	0.851390	−	0.524534i	$-0.175760\pi$
$131$	2553.08	1.70278	0.851390	+	0.524534i	$0.175760\pi$
$132$	−1348.54	−0.889205
$133$	451.645	0.294455
$134$	−10.1639	−0.00655246
$135$	335.769	0.214062
$136$	526.425	0.331916
$137$	−1338.26	−0.834564	−0.417282	−	0.908777i	$-0.637017\pi$
$137$	−1338.26	−0.834564	−0.417282	+	0.908777i	$0.637017\pi$
$138$	−5591.78	−3.44930
$139$	687.366	0.419436	0.209718	−	0.977762i	$-0.432745\pi$
$139$	687.366	0.419436	0.209718	+	0.977762i	$0.432745\pi$
$140$	−57.8285	−0.0349100
$141$	−2798.43	−1.67142
$142$	−1787.31	−1.05625
$143$	1135.31	0.663915
$144$	−3129.13	−1.81084
$145$	−213.205	−0.122108
$146$	1839.21	1.04256
$147$	−2765.47	−1.55165
$148$	1985.24	1.10261
$149$	−467.843	−0.257230	−0.128615	−	0.991695i	$-0.541053\pi$
$149$	−467.843	−0.257230	−0.128615	+	0.991695i	$0.541053\pi$
$150$	3775.82	2.05530
$151$	−1726.18	−0.930293	−0.465147	−	0.885234i	$-0.653998\pi$
$151$	−1726.18	−0.930293	−0.465147	+	0.885234i	$0.653998\pi$
$152$	−711.668	−0.379763
$153$	4165.47	2.20104
$154$	−320.656	−0.167787
$155$	329.614	0.170808
$156$	−2545.96	−1.30666
$157$	488.504	0.248324	0.124162	−	0.992262i	$-0.460376\pi$
$157$	488.504	0.248324	0.124162	+	0.992262i	$0.460376\pi$
$158$	1131.35	0.569653
$159$	3120.78	1.55657
$160$	607.228	0.300035
$161$	−600.438	−0.293920
$162$	226.819	0.110004
$163$	1013.08	0.486814	0.243407	−	0.969924i	$-0.421735\pi$
$163$	1013.08	0.486814	0.243407	+	0.969924i	$0.421735\pi$
$164$	−1324.53	−0.630662
$165$	−524.896	−0.247655
$166$	−467.357	−0.218518
$167$	−916.697	−0.424767	−0.212384	−	0.977186i	$-0.568123\pi$
$167$	−916.697	−0.424767	−0.212384	+	0.977186i	$0.568123\pi$
$168$	−154.179	−0.0708044
$169$	−53.5953	−0.0243948
$170$	−955.645	−0.431145
$171$	−5631.26	−2.51832
$172$	0	0
$173$	−4040.24	−1.77557	−0.887786	−	0.460257i	$-0.847757\pi$
$173$	−4040.24	−1.77557	−0.887786	+	0.460257i	$0.847757\pi$
$174$	2651.12	1.15506
$175$	405.442	0.175135
$176$	1797.61	0.769886
$177$	4828.65	2.05053
$178$	−2850.04	−1.20011
$179$	−818.629	−0.341828	−0.170914	−	0.985286i	$-0.554672\pi$
$179$	−818.629	−0.341828	−0.170914	+	0.985286i	$0.554672\pi$
$180$	721.025	0.298567
$181$	−1761.43	−0.723350	−0.361675	−	0.932304i	$-0.617795\pi$
$181$	−1761.43	−0.723350	−0.361675	+	0.932304i	$0.617795\pi$
$182$	−605.379	−0.246559
$183$	−7451.64	−3.01006
$184$	946.126	0.379072
$185$	772.722	0.307090
$186$	−4098.63	−1.61573
$187$	−2392.96	−0.935779
$188$	−2208.33	−0.856696
$189$	−448.323	−0.172543
$190$	1291.93	0.493296
$191$	1206.69	0.457137	0.228568	−	0.973528i	$-0.426596\pi$
$191$	1206.69	0.457137	0.228568	+	0.973528i	$0.426596\pi$
$192$	−2655.15	−0.998016
$193$	−1227.19	−0.457694	−0.228847	−	0.973462i	$-0.573496\pi$
$193$	−1227.19	−0.457694	−0.228847	+	0.973462i	$0.573496\pi$
$194$	6582.05	2.43589
$195$	−990.971	−0.363922
$196$	−2182.32	−0.795305
$197$	2906.38	1.05112	0.525560	−	0.850756i	$-0.323856\pi$
$197$	2906.38	1.05112	0.525560	+	0.850756i	$0.323856\pi$
$198$	3998.05	1.43499
$199$	1960.29	0.698299	0.349149	−	0.937067i	$-0.386471\pi$
$199$	1960.29	0.698299	0.349149	+	0.937067i	$0.386471\pi$
$200$	−638.866	−0.225873
$201$	22.2149	0.00779563
$202$	1466.76	0.510895
$203$	284.673	0.0984244
$204$	5366.24	1.84173
$205$	−515.552	−0.175647
$206$	−716.097	−0.242198
$207$	7486.46	2.51374
$208$	3393.78	1.13133
$209$	3235.02	1.07067
$210$	279.888	0.0919719
$211$	5227.84	1.70568	0.852841	−	0.522170i	$-0.174877\pi$
$211$	5227.84	1.70568	0.852841	+	0.522170i	$0.174877\pi$
$212$	2462.70	0.797827
$213$	3906.47	1.25665
$214$	4373.29	1.39697
$215$	0	0
$216$	706.434	0.222531
$217$	−440.105	−0.137679
$218$	4235.50	1.31589
$219$	−4019.91	−1.24037
$220$	−414.211	−0.126937
$221$	−4517.77	−1.37510
$222$	−9608.50	−2.90487
$223$	1121.01	0.336631	0.168315	−	0.985733i	$-0.446167\pi$
$223$	1121.01	0.336631	0.168315	+	0.985733i	$0.446167\pi$
$224$	−810.778	−0.241841
$225$	−5055.19	−1.49783
$226$	5541.63	1.63108
$227$	499.397	0.146018	0.0730092	−	0.997331i	$-0.476740\pi$
$227$	499.397	0.146018	0.0730092	+	0.997331i	$0.476740\pi$
$228$	−7254.57	−2.10722
$229$	1384.89	0.399633	0.199817	−	0.979833i	$-0.435965\pi$
$229$	1384.89	0.399633	0.199817	+	0.979833i	$0.435965\pi$
$230$	−1717.55	−0.492399
$231$	700.847	0.199621
$232$	−448.567	−0.126939
$233$	−259.379	−0.0729291	−0.0364646	−	0.999335i	$-0.511610\pi$
$233$	−259.379	−0.0729291	−0.0364646	+	0.999335i	$0.511610\pi$
$234$	7548.07	2.10869
$235$	−859.554	−0.238601
$236$	3810.44	1.05101
$237$	−2472.75	−0.677730
$238$	1275.99	0.347521
$239$	4228.11	1.14432	0.572162	−	0.820140i	$-0.306105\pi$
$239$	4228.11	1.14432	0.572162	+	0.820140i	$0.306105\pi$
$240$	−1569.06	−0.422010
$241$	7388.11	1.97473	0.987365	−	0.158463i	$-0.0506539\pi$
$241$	7388.11	1.97473	0.987365	+	0.158463i	$0.0506539\pi$
$242$	2786.79	0.740256
$243$	−4031.41	−1.06426
$244$	−5880.32	−1.54282
$245$	−849.430	−0.221502
$246$	6410.69	1.66151
$247$	6107.52	1.57333
$248$	693.485	0.177566
$249$	1021.49	0.259976
$250$	2383.92	0.603088
$251$	−2006.43	−0.504561	−0.252280	−	0.967654i	$-0.581180\pi$
$251$	−2006.43	−0.504561	−0.252280	+	0.967654i	$0.581180\pi$
$252$	−962.721	−0.240658
$253$	−4300.79	−1.06873
$254$	7735.68	1.91094
$255$	2088.72	0.512944
$256$	5140.74	1.25506
$257$	−356.050	−0.0864195	−0.0432098	−	0.999066i	$-0.513758\pi$
$257$	−356.050	−0.0864195	−0.0432098	+	0.999066i	$0.513758\pi$
$258$	0	0
$259$	−1031.75	−0.247528
$260$	−782.005	−0.186530
$261$	−3549.40	−0.841772
$262$	−9751.16	−2.29935
$263$	−2558.23	−0.599800	−0.299900	−	0.953971i	$-0.596953\pi$
$263$	−2558.23	−0.599800	−0.299900	+	0.953971i	$0.596953\pi$
$264$	−1104.34	−0.257453
$265$	958.567	0.222205
$266$	−1725.00	−0.397618
$267$	6229.25	1.42780
$268$	17.5305	0.00399569
$269$	7645.48	1.73291	0.866455	−	0.499255i	$-0.166393\pi$
$269$	7645.48	1.73291	0.866455	+	0.499255i	$0.166393\pi$
$270$	−1282.42	−0.289059
$271$	−2563.79	−0.574683	−0.287342	−	0.957828i	$-0.592772\pi$
$271$	−2563.79	−0.574683	−0.287342	+	0.957828i	$0.592772\pi$
$272$	−7153.24	−1.59459
$273$	1323.16	0.293337
$274$	5111.31	1.12695
$275$	2904.08	0.636810
$276$	9644.57	2.10339
$277$	−5655.56	−1.22675	−0.613375	−	0.789792i	$-0.710189\pi$
$277$	−5655.56	−1.22675	−0.613375	+	0.789792i	$0.710189\pi$
$278$	−2625.30	−0.566386
$279$	5487.38	1.17749
$280$	−47.3568	−0.0101075
$281$	−6410.59	−1.36094	−0.680469	−	0.732777i	$-0.738224\pi$
$281$	−6410.59	−1.36094	−0.680469	+	0.732777i	$0.738224\pi$
$282$	10688.2	2.25700
$283$	−8030.69	−1.68684	−0.843419	−	0.537256i	$-0.819461\pi$
$283$	−8030.69	−1.68684	−0.843419	+	0.537256i	$0.819461\pi$
$284$	3082.72	0.644104
$285$	−2823.72	−0.586887
$286$	−4336.18	−0.896517
$287$	688.372	0.141579
$288$	10109.0	2.06834
$289$	4609.33	0.938191
$290$	814.306	0.164889
$291$	−14386.2	−2.89805
$292$	−3172.23	−0.635756
$293$	−3612.22	−0.720232	−0.360116	−	0.932908i	$-0.617263\pi$
$293$	−3612.22	−0.720232	−0.360116	+	0.932908i	$0.617263\pi$
$294$	10562.3	2.09526
$295$	1483.15	0.292720
$296$	1625.75	0.319240
$297$	−3211.23	−0.627388
$298$	1786.86	0.347350
$299$	−8119.63	−1.57047
$300$	−6512.44	−1.25332
$301$	0	0
$302$	6592.90	1.25622
$303$	−3205.84	−0.607825
$304$	9670.39	1.82446
$305$	−2288.81	−0.429696
$306$	−15909.5	−2.97217
$307$	−1282.10	−0.238349	−0.119174	−	0.992873i	$-0.538025\pi$
$307$	−1282.10	−0.238349	−0.119174	+	0.992873i	$0.538025\pi$
$308$	553.060	0.102317
$309$	1565.15	0.288149
$310$	−1258.92	−0.230651
$311$	−9145.70	−1.66754	−0.833770	−	0.552111i	$-0.813822\pi$
$311$	−9145.70	−1.66754	−0.833770	+	0.552111i	$0.813822\pi$
$312$	−2084.93	−0.378321
$313$	−3256.64	−0.588103	−0.294051	−	0.955790i	$-0.595004\pi$
$313$	−3256.64	−0.588103	−0.294051	+	0.955790i	$0.595004\pi$
$314$	−1865.78	−0.335324
$315$	−374.723	−0.0670262
$316$	−1951.32	−0.347374
$317$	6460.36	1.14464	0.572319	−	0.820031i	$-0.306044\pi$
$317$	6460.36	1.14464	0.572319	+	0.820031i	$0.306044\pi$
$318$	−11919.4	−2.10191
$319$	2039.05	0.357883
$320$	−815.545	−0.142470
$321$	−9558.54	−1.66201
$322$	2293.29	0.396895
$323$	−12873.1	−2.21759
$324$	−391.212	−0.0670802
$325$	5482.73	0.935776
$326$	−3869.33	−0.657369
$327$	−9257.39	−1.56555
$328$	−1084.69	−0.182597
$329$	1147.69	0.192322
$330$	2004.77	0.334421
$331$	−6472.81	−1.07486	−0.537429	−	0.843309i	$-0.680604\pi$
$331$	−6472.81	−1.07486	−0.537429	+	0.843309i	$0.680604\pi$
$332$	806.086	0.133252
$333$	12864.2	2.11697
$334$	3501.20	0.573584
$335$	6.82345	0.00111285
$336$	2095.03	0.340159
$337$	1072.36	0.173339	0.0866695	−	0.996237i	$-0.472378\pi$
$337$	1072.36	0.173339	0.0866695	+	0.996237i	$0.472378\pi$
$338$	204.700	0.0329415
$339$	−12112.2	−1.94054
$340$	1648.27	0.262912
$341$	−3152.37	−0.500616
$342$	21507.8	3.40061
$343$	2308.47	0.363398
$344$	0	0
$345$	3753.99	0.585820
$346$	15431.2	2.39764
$347$	1353.35	0.209371	0.104686	−	0.994505i	$-0.466616\pi$
$347$	1353.35	0.209371	0.104686	+	0.994505i	$0.466616\pi$
$348$	−4572.58	−0.704357
$349$	8713.86	1.33651	0.668256	−	0.743932i	$-0.267041\pi$
$349$	8713.86	1.33651	0.668256	+	0.743932i	$0.267041\pi$
$350$	−1548.53	−0.236493
$351$	−6062.60	−0.921930
$352$	−5807.40	−0.879363
$353$	6064.05	0.914325	0.457163	−	0.889383i	$-0.348866\pi$
$353$	6064.05	0.914325	0.457163	+	0.889383i	$0.348866\pi$
$354$	−18442.4	−2.76893
$355$	1199.90	0.179391
$356$	4915.69	0.731829
$357$	−2788.89	−0.413455
$358$	3126.64	0.461587
$359$	2672.80	0.392939	0.196469	−	0.980510i	$-0.437052\pi$
$359$	2672.80	0.392939	0.196469	+	0.980510i	$0.437052\pi$
$360$	590.461	0.0864445
$361$	10544.1	1.53726
$362$	6727.56	0.976775
$363$	−6091.00	−0.880701
$364$	1044.14	0.150352
$365$	−1234.74	−0.177066
$366$	28460.5	4.06463
$367$	3206.83	0.456117	0.228059	−	0.973647i	$-0.426762\pi$
$367$	3206.83	0.456117	0.228059	+	0.973647i	$0.426762\pi$
$368$	−12856.3	−1.82114
$369$	−8582.85	−1.21085
$370$	−2951.31	−0.414679
$371$	−1279.89	−0.179107
$372$	7069.22	0.985273
$373$	−2341.81	−0.325079	−0.162539	−	0.986702i	$-0.551968\pi$
$373$	−2341.81	−0.325079	−0.162539	+	0.986702i	$0.551968\pi$
$374$	9139.60	1.26363
$375$	−5210.44	−0.717510
$376$	−1808.44	−0.248041
$377$	3849.59	0.525900
$378$	1712.31	0.232994
$379$	−12165.1	−1.64876	−0.824382	−	0.566034i	$-0.808477\pi$
$379$	−12165.1	−1.64876	−0.824382	+	0.566034i	$0.808477\pi$
$380$	−2228.28	−0.300812
$381$	−16907.6	−2.27350
$382$	−4608.80	−0.617295
$383$	10219.7	1.36345	0.681727	−	0.731606i	$-0.261229\pi$
$383$	10219.7	1.36345	0.681727	+	0.731606i	$0.261229\pi$
$384$	−5674.50	−0.754103
$385$	215.269	0.0284965
$386$	4687.08	0.618047
$387$	0	0
$388$	−11352.6	−1.48541
$389$	−9610.28	−1.25260	−0.626299	−	0.779583i	$-0.715431\pi$
$389$	−9610.28	−1.25260	−0.626299	+	0.779583i	$0.715431\pi$
$390$	3784.88	0.491422
$391$	17114.2	2.21356
$392$	−1787.14	−0.230266
$393$	21312.8	2.73559
$394$	−11100.5	−1.41938
$395$	−759.518	−0.0967481
$396$	−6895.74	−0.875060
$397$	8283.95	1.04725	0.523627	−	0.851948i	$-0.324579\pi$
$397$	8283.95	1.04725	0.523627	+	0.851948i	$0.324579\pi$
$398$	−7487.07	−0.942947
$399$	3770.26	0.473056
$400$	8681.13	1.08514
$401$	−12685.4	−1.57975	−0.789874	−	0.613269i	$-0.789854\pi$
$401$	−12685.4	−1.57975	−0.789874	+	0.613269i	$0.789854\pi$
$402$	−84.8470	−0.0105268
$403$	−5951.47	−0.735643
$404$	−2529.83	−0.311544
$405$	−152.273	−0.0186827
$406$	−1087.27	−0.132907
$407$	−7390.16	−0.900040
$408$	4394.52	0.533238
$409$	981.857	0.118703	0.0593517	−	0.998237i	$-0.481097\pi$
$409$	981.857	0.118703	0.0593517	+	0.998237i	$0.481097\pi$
$410$	1969.08	0.237185
$411$	−11171.6	−1.34077
$412$	1235.11	0.147693
$413$	−1980.32	−0.235945
$414$	−28593.5	−3.39443
$415$	313.756	0.0371124
$416$	−10964.0	−1.29220
$417$	5738.03	0.673844
$418$	−12355.7	−1.44578
$419$	−10930.0	−1.27439	−0.637193	−	0.770704i	$-0.719905\pi$
$419$	−10930.0	−1.27439	−0.637193	+	0.770704i	$0.719905\pi$
$420$	−482.744	−0.0560845
$421$	−12352.3	−1.42996	−0.714980	−	0.699145i	$-0.753564\pi$
$421$	−12352.3	−1.42996	−0.714980	+	0.699145i	$0.753564\pi$
$422$	−19967.0	−2.30327
$423$	−14309.8	−1.64483
$424$	2016.76	0.230996
$425$	−11556.2	−1.31896
$426$	−14920.2	−1.69692
$427$	3056.05	0.346353
$428$	−7542.94	−0.851873
$429$	9477.44	1.06661
$430$	0	0
$431$	−6534.96	−0.730343	−0.365172	−	0.930940i	$-0.618990\pi$
$431$	−6534.96	−0.730343	−0.365172	+	0.930940i	$0.618990\pi$
$432$	−9599.26	−1.06908
$433$	−12272.7	−1.36210	−0.681048	−	0.732239i	$-0.738476\pi$
$433$	−12272.7	−1.36210	−0.681048	+	0.732239i	$0.738476\pi$
$434$	1680.92	0.185914
$435$	−1779.80	−0.196172
$436$	−7305.29	−0.802431
$437$	−23136.5	−2.53265
$438$	15353.5	1.67493
$439$	−2806.41	−0.305108	−0.152554	−	0.988295i	$-0.548750\pi$
$439$	−2806.41	−0.305108	−0.152554	+	0.988295i	$0.548750\pi$
$440$	−339.205	−0.0367522
$441$	−14141.2	−1.52696
$442$	17255.0	1.85687
$443$	−9336.79	−1.00136	−0.500682	−	0.865631i	$-0.666917\pi$
$443$	−9336.79	−1.00136	−0.500682	+	0.865631i	$0.666917\pi$
$444$	16572.5	1.77139
$445$	1913.35	0.203824
$446$	−4281.56	−0.454569
$447$	−3905.49	−0.413251
$448$	1088.93	0.114837
$449$	−7212.30	−0.758062	−0.379031	−	0.925384i	$-0.623743\pi$
$449$	−7212.30	−0.758062	−0.379031	+	0.925384i	$0.623743\pi$
$450$	19307.6	2.02260
$451$	4930.64	0.514800
$452$	−9558.07	−0.994632
$453$	−14409.9	−1.49456
$454$	−1907.38	−0.197176
$455$	406.415	0.0418748
$456$	−5940.90	−0.610106
$457$	1378.40	0.141091	0.0705455	−	0.997509i	$-0.477526\pi$
$457$	1378.40	0.141091	0.0705455	+	0.997509i	$0.477526\pi$
$458$	−5289.40	−0.539645
$459$	12778.4	1.29945
$460$	2962.39	0.300265
$461$	−11245.2	−1.13610	−0.568048	−	0.822996i	$-0.692301\pi$
$461$	−11245.2	−1.13610	−0.568048	+	0.822996i	$0.692301\pi$
$462$	−2676.79	−0.269558
$463$	−2077.54	−0.208535	−0.104267	−	0.994549i	$-0.533250\pi$
$463$	−2077.54	−0.208535	−0.104267	+	0.994549i	$0.533250\pi$
$464$	6095.28	0.609842
$465$	2751.57	0.274411
$466$	990.663	0.0984798
$467$	2016.77	0.199839	0.0999197	−	0.994996i	$-0.468141\pi$
$467$	2016.77	0.199839	0.0999197	+	0.994996i	$0.468141\pi$
$468$	−13018.7	−1.28588
$469$	−9.11076	−0.000897006 0
$470$	3282.95	0.322194
$471$	4077.96	0.398944
$472$	3120.44	0.304301
$473$	0	0
$474$	9444.32	0.915173
$475$	15622.8	1.50910
$476$	−2200.80	−0.211919
$477$	15958.1	1.53181
$478$	−16148.7	−1.54524
$479$	10427.0	0.994620	0.497310	−	0.867573i	$-0.334321\pi$
$479$	10427.0	0.994620	0.497310	+	0.867573i	$0.334321\pi$
$480$	5069.05	0.482019
$481$	−13952.2	−1.32259
$482$	−28217.9	−2.66658
$483$	−5012.37	−0.472196
$484$	−4806.59	−0.451408
$485$	−4418.79	−0.413705
$486$	15397.4	1.43712
$487$	−4165.93	−0.387631	−0.193815	−	0.981038i	$-0.562086\pi$
$487$	−4165.93	−0.387631	−0.193815	+	0.981038i	$0.562086\pi$
$488$	−4815.50	−0.446696
$489$	8457.06	0.782089
$490$	3244.28	0.299106
$491$	11303.6	1.03895	0.519475	−	0.854486i	$-0.326127\pi$
$491$	11303.6	1.03895	0.519475	+	0.854486i	$0.326127\pi$
$492$	−11057.0	−1.01319
$493$	−8113.99	−0.741249
$494$	−23326.8	−2.12454
$495$	−2684.05	−0.243715
$496$	−9423.31	−0.853063
$497$	−1602.12	−0.144597
$498$	−3901.43	−0.351059
$499$	−13070.3	−1.17256	−0.586281	−	0.810108i	$-0.699408\pi$
$499$	−13070.3	−1.17256	−0.586281	+	0.810108i	$0.699408\pi$
$500$	−4111.72	−0.367763
$501$	−7652.45	−0.682408
$502$	7663.29	0.681333
$503$	−9968.27	−0.883625	−0.441812	−	0.897107i	$-0.645664\pi$
$503$	−9968.27	−0.883625	−0.441812	+	0.897107i	$0.645664\pi$
$504$	−788.391	−0.0696780
$505$	−984.694	−0.0867689
$506$	16426.3	1.44316
$507$	−447.406	−0.0391913
$508$	−13342.3	−1.16529
$509$	11910.6	1.03719	0.518594	−	0.855021i	$-0.326456\pi$
$509$	11910.6	1.03719	0.518594	+	0.855021i	$0.326456\pi$
$510$	−7977.59	−0.692654
$511$	1648.64	0.142723
$512$	−14196.3	−1.22538
$513$	−17275.0	−1.48677
$514$	1359.89	0.116697
$515$	480.744	0.0411342
$516$	0	0
$517$	8220.61	0.699307
$518$	3940.62	0.334249
$519$	−33727.4	−2.85254
$520$	−640.399	−0.0540065
$521$	7264.31	0.610854	0.305427	−	0.952215i	$-0.401201\pi$
$521$	7264.31	0.610854	0.305427	+	0.952215i	$0.401201\pi$
$522$	13556.5	1.13669
$523$	11647.5	0.973823	0.486912	−	0.873451i	$-0.338123\pi$
$523$	11647.5	0.973823	0.486912	+	0.873451i	$0.338123\pi$
$524$	16818.6	1.40214
$525$	3384.57	0.281362
$526$	9770.83	0.809940
$527$	12544.2	1.03688
$528$	15006.2	1.23686
$529$	18591.7	1.52804
$530$	−3661.12	−0.300054
$531$	24691.3	2.01791
$532$	2975.23	0.242467
$533$	9308.74	0.756485
$534$	−23791.8	−1.92803
$535$	−2935.96	−0.237257
$536$	14.3561	0.00115688
$537$	−6833.80	−0.549162
$538$	−29200.9	−2.34003
$539$	8123.78	0.649195
$540$	2211.89	0.176268
$541$	3578.45	0.284380	0.142190	−	0.989839i	$-0.454586\pi$
$541$	3578.45	0.284380	0.142190	+	0.989839i	$0.454586\pi$
$542$	9792.05	0.776023
$543$	−14704.2	−1.16209
$544$	23109.4	1.82134
$545$	−2843.46	−0.223487
$546$	−5053.62	−0.396108
$547$	−15440.8	−1.20695	−0.603475	−	0.797382i	$-0.706218\pi$
$547$	−15440.8	−1.20695	−0.603475	+	0.797382i	$0.706218\pi$
$548$	−8815.86	−0.687217
$549$	−38103.9	−2.96218
$550$	−11091.8	−0.859917
$551$	10969.2	0.848102
$552$	7898.12	0.608997
$553$	1014.12	0.0779832
$554$	21600.7	1.65654
$555$	6450.57	0.493354
$556$	4528.06	0.345382
$557$	−2684.18	−0.204187	−0.102094	−	0.994775i	$-0.532554\pi$
$557$	−2684.18	−0.204187	−0.102094	+	0.994775i	$0.532554\pi$
$558$	−20958.3	−1.59003
$559$	0	0
$560$	643.501	0.0485587
$561$	−19976.1	−1.50337
$562$	24484.4	1.83774
$563$	−10345.1	−0.774412	−0.387206	−	0.921993i	$-0.626560\pi$
$563$	−10345.1	−0.774412	−0.387206	+	0.921993i	$0.626560\pi$
$564$	−18434.8	−1.37632
$565$	−3720.32	−0.277018
$566$	30672.1	2.27782
$567$	203.316	0.0150591
$568$	2524.50	0.186489
$569$	60.6533	0.00446875	0.00223438	−	0.999998i	$-0.499289\pi$
$569$	60.6533	0.00446875	0.00223438	+	0.999998i	$0.499289\pi$
$570$	10784.8	0.792502
$571$	2225.56	0.163111	0.0815557	−	0.996669i	$-0.474011\pi$
$571$	2225.56	0.163111	0.0815557	+	0.996669i	$0.474011\pi$
$572$	7478.94	0.546696
$573$	10073.3	0.734411
$574$	−2629.14	−0.191182
$575$	−20769.6	−1.50635
$576$	−13577.1	−0.982139
$577$	16249.2	1.17238	0.586190	−	0.810173i	$-0.300627\pi$
$577$	16249.2	1.17238	0.586190	+	0.810173i	$0.300627\pi$
$578$	−17604.7	−1.26689
$579$	−10244.4	−0.735306
$580$	−1404.50	−0.100549
$581$	−418.930	−0.0299142
$582$	54946.0	3.91337
$583$	−9167.54	−0.651253
$584$	−2597.80	−0.184072
$585$	−5067.32	−0.358133
$586$	13796.4	0.972564
$587$	−10104.6	−0.710496	−0.355248	−	0.934772i	$-0.615604\pi$
$587$	−10104.6	−0.710496	−0.355248	+	0.934772i	$0.615604\pi$
$588$	−18217.7	−1.27769
$589$	−16958.4	−1.18635
$590$	−5664.69	−0.395274
$591$	24262.0	1.68867
$592$	−22091.3	−1.53369
$593$	10930.9	0.756962	0.378481	−	0.925609i	$-0.376447\pi$
$593$	10930.9	0.756962	0.378481	+	0.925609i	$0.376447\pi$
$594$	12264.8	0.847193
$595$	−856.623	−0.0590220
$596$	−3081.94	−0.211814
$597$	16364.2	1.12185
$598$	31011.8	2.12068
$599$	−21584.2	−1.47230	−0.736149	−	0.676819i	$-0.763358\pi$
$599$	−21584.2	−1.47230	−0.736149	+	0.676819i	$0.763358\pi$
$600$	−5333.16	−0.362876
$601$	18226.1	1.23704	0.618519	−	0.785770i	$-0.287733\pi$
$601$	18226.1	1.23704	0.618519	+	0.785770i	$0.287733\pi$
$602$	0	0
$603$	113.596	0.00767162
$604$	−11371.3	−0.766044
$605$	−1870.89	−0.125723
$606$	12244.3	0.820776
$607$	24757.1	1.65546	0.827728	−	0.561130i	$-0.189633\pi$
$607$	24757.1	1.65546	0.827728	+	0.561130i	$0.189633\pi$
$608$	−31241.4	−2.08389
$609$	2376.41	0.158123
$610$	8741.82	0.580239
$611$	15520.0	1.02761
$612$	27440.2	1.81243
$613$	−19983.4	−1.31668	−0.658339	−	0.752722i	$-0.728741\pi$
$613$	−19983.4	−1.31668	−0.658339	+	0.752722i	$0.728741\pi$
$614$	4896.79	0.321854
$615$	−4303.76	−0.282186
$616$	452.911	0.0296239
$617$	26758.7	1.74597	0.872985	−	0.487746i	$-0.162181\pi$
$617$	26758.7	1.74597	0.872985	+	0.487746i	$0.162181\pi$
$618$	−5977.87	−0.389102
$619$	3557.65	0.231008	0.115504	−	0.993307i	$-0.463152\pi$
$619$	3557.65	0.231008	0.115504	+	0.993307i	$0.463152\pi$
$620$	2171.35	0.140651
$621$	22966.3	1.48407
$622$	34930.8	2.25176
$623$	−2554.73	−0.164291
$624$	28330.8	1.81753
$625$	13202.8	0.844977
$626$	12438.3	0.794144
$627$	27005.5	1.72009
$628$	3218.05	0.204481
$629$	29407.7	1.86417
$630$	1431.20	0.0905088
$631$	−22683.1	−1.43106	−0.715532	−	0.698580i	$-0.753816\pi$
$631$	−22683.1	−1.43106	−0.715532	+	0.698580i	$0.753816\pi$
$632$	−1597.97	−0.100576
$633$	43641.2	2.74026
$634$	−24674.5	−1.54566
$635$	−5193.27	−0.324549
$636$	20558.3	1.28174
$637$	15337.2	0.953974
$638$	−7787.86	−0.483267
$639$	19975.7	1.23666
$640$	−1742.96	−0.107651
$641$	−3214.41	−0.198068	−0.0990341	−	0.995084i	$-0.531575\pi$
$641$	−3214.41	−0.198068	−0.0990341	+	0.995084i	$0.531575\pi$
$642$	36507.6	2.24430
$643$	5096.07	0.312550	0.156275	−	0.987714i	$-0.450051\pi$
$643$	5096.07	0.312550	0.156275	+	0.987714i	$0.450051\pi$
$644$	−3955.42	−0.242027
$645$	0	0
$646$	49167.2	2.99452
$647$	−2031.59	−0.123447	−0.0617234	−	0.998093i	$-0.519660\pi$
$647$	−2031.59	−0.123447	−0.0617234	+	0.998093i	$0.519660\pi$
$648$	−320.371	−0.0194218
$649$	−14184.5	−0.857923
$650$	−20940.6	−1.26362
$651$	−3673.94	−0.221187
$652$	6673.72	0.400864
$653$	−6868.13	−0.411594	−0.205797	−	0.978595i	$-0.565979\pi$
$653$	−6868.13	−0.411594	−0.205797	+	0.978595i	$0.565979\pi$
$654$	35357.3	2.11404
$655$	6546.35	0.390514
$656$	14739.1	0.877232
$657$	−20555.8	−1.22063
$658$	−4383.44	−0.259702
$659$	−11046.0	−0.652947	−0.326474	−	0.945206i	$-0.605860\pi$
$659$	−11046.0	−0.652947	−0.326474	+	0.945206i	$0.605860\pi$
$660$	−3457.78	−0.203930
$661$	19990.5	1.17631	0.588156	−	0.808748i	$-0.299854\pi$
$661$	19990.5	1.17631	0.588156	+	0.808748i	$0.299854\pi$
$662$	24722.0	1.45143
$663$	−37713.7	−2.20917
$664$	660.120	0.0385807
$665$	1158.06	0.0675302
$666$	−49133.0	−2.85865
$667$	−14583.0	−0.846561
$668$	−6038.78	−0.349772
$669$	9358.06	0.540812
$670$	−26.0612	−0.00150274
$671$	21889.8	1.25938
$672$	−6768.26	−0.388529
$673$	−17975.7	−1.02958	−0.514792	−	0.857315i	$-0.672131\pi$
$673$	−17975.7	−1.02958	−0.514792	+	0.857315i	$0.672131\pi$
$674$	−4095.74	−0.234068
$675$	−15507.8	−0.884292
$676$	−353.062	−0.0200877
$677$	−742.490	−0.0421510	−0.0210755	−	0.999778i	$-0.506709\pi$
$677$	−742.490	−0.0421510	−0.0210755	+	0.999778i	$0.506709\pi$
$678$	46260.7	2.62040
$679$	5900.03	0.333464
$680$	1349.80	0.0761214
$681$	4168.90	0.234585
$682$	12040.0	0.676007
$683$	29791.7	1.66903	0.834514	−	0.550987i	$-0.185748\pi$
$683$	29791.7	1.66903	0.834514	+	0.550987i	$0.185748\pi$
$684$	−37096.2	−2.07370
$685$	−3431.42	−0.191399
$686$	−8816.88	−0.490714
$687$	11560.9	0.642029
$688$	0	0
$689$	−17307.7	−0.957000
$690$	−14337.8	−0.791062
$691$	−3361.09	−0.185039	−0.0925196	−	0.995711i	$-0.529492\pi$
$691$	−3361.09	−0.185039	−0.0925196	+	0.995711i	$0.529492\pi$
$692$	−26615.3	−1.46208
$693$	3583.78	0.196445
$694$	−5168.95	−0.282724
$695$	1762.47	0.0961933
$696$	−3744.58	−0.203934
$697$	−19620.5	−1.06626
$698$	−33281.4	−1.80476
$699$	−2165.26	−0.117164
$700$	2670.87	0.144213
$701$	23288.1	1.25475	0.627373	−	0.778719i	$-0.284130\pi$
$701$	23288.1	1.25475	0.627373	+	0.778719i	$0.284130\pi$
$702$	23155.3	1.24493
$703$	−39755.9	−2.13289
$704$	7799.71	0.417561
$705$	−7175.44	−0.383323
$706$	−23160.8	−1.23466
$707$	1314.78	0.0699395
$708$	31809.0	1.68850
$709$	17503.7	0.927171	0.463585	−	0.886052i	$-0.346563\pi$
$709$	17503.7	0.927171	0.463585	+	0.886052i	$0.346563\pi$
$710$	−4582.84	−0.242241
$711$	−12644.4	−0.666949
$712$	4025.55	0.211888
$713$	22545.3	1.18419
$714$	10651.8	0.558309
$715$	2911.05	0.152262
$716$	−5392.76	−0.281476
$717$	35295.6	1.83841
$718$	−10208.4	−0.530605
$719$	−10970.4	−0.569024	−0.284512	−	0.958673i	$-0.591832\pi$
$719$	−10970.4	−0.569024	−0.284512	+	0.958673i	$0.591832\pi$
$720$	−8023.38	−0.415297
$721$	−641.896	−0.0331560
$722$	−40271.6	−2.07584
$723$	61674.9	3.17249
$724$	−11603.5	−0.595638
$725$	9847.09	0.504430
$726$	23263.8	1.18925
$727$	747.962	0.0381573	0.0190787	−	0.999818i	$-0.493927\pi$
$727$	747.962	0.0381573	0.0190787	+	0.999818i	$0.493927\pi$
$728$	855.069	0.0435315
$729$	−32050.2	−1.62832
$730$	4715.91	0.239101
$731$	0	0
$732$	−49088.0	−2.47861
$733$	21811.3	1.09907	0.549534	−	0.835471i	$-0.314805\pi$
$733$	21811.3	1.09907	0.549534	+	0.835471i	$0.314805\pi$
$734$	−12248.0	−0.615918
$735$	−7090.92	−0.355854
$736$	41533.8	2.08010
$737$	−65.2581	−0.00326162
$738$	32781.0	1.63508
$739$	13215.5	0.657834	0.328917	−	0.944359i	$-0.393316\pi$
$739$	13215.5	0.657834	0.328917	+	0.944359i	$0.393316\pi$
$740$	5090.34	0.252871
$741$	50984.7	2.52762
$742$	4888.37	0.241857
$743$	25963.2	1.28196	0.640980	−	0.767558i	$-0.278528\pi$
$743$	25963.2	1.28196	0.640980	+	0.767558i	$0.278528\pi$
$744$	5789.12	0.285268
$745$	−1199.59	−0.0589929
$746$	8944.24	0.438970
$747$	5223.36	0.255841
$748$	−15763.8	−0.770561
$749$	3920.13	0.191240
$750$	19900.6	0.968889
$751$	−3717.93	−0.180651	−0.0903256	−	0.995912i	$-0.528791\pi$
$751$	−3717.93	−0.180651	−0.0903256	+	0.995912i	$0.528791\pi$
$752$	24573.7	1.19164
$753$	−16749.4	−0.810600
$754$	−14703.0	−0.710148
$755$	−4426.08	−0.213353
$756$	−2953.35	−0.142080
$757$	120.818	0.00580079	0.00290039	−	0.999996i	$-0.499077\pi$
$757$	120.818	0.00580079	0.00290039	+	0.999996i	$0.499077\pi$
$758$	46463.1	2.22641
$759$	−35902.4	−1.71696
$760$	−1824.78	−0.0870945
$761$	23248.7	1.10744	0.553722	−	0.832702i	$-0.313207\pi$
$761$	23248.7	1.10744	0.553722	+	0.832702i	$0.313207\pi$
$762$	64576.3	3.07002
$763$	3796.62	0.180140
$764$	7949.14	0.376426
$765$	10680.7	0.504784
$766$	−39032.8	−1.84114
$767$	−26779.6	−1.26070
$768$	42914.2	2.01632
$769$	12713.4	0.596174	0.298087	−	0.954539i	$-0.403651\pi$
$769$	12713.4	0.596174	0.298087	+	0.954539i	$0.403651\pi$
$770$	−822.192	−0.0384802
$771$	−2972.26	−0.138837
$772$	−8084.16	−0.376885
$773$	−6472.11	−0.301146	−0.150573	−	0.988599i	$-0.548112\pi$
$773$	−6472.11	−0.301146	−0.150573	+	0.988599i	$0.548112\pi$
$774$	0	0
$775$	−15223.6	−0.705610
$776$	−9296.82	−0.430073
$777$	−8612.88	−0.397665
$778$	36705.2	1.69144
$779$	26524.8	1.21996
$780$	−6528.07	−0.299670
$781$	−11475.6	−0.525772
$782$	−65365.2	−2.98907
$783$	−10888.5	−0.496966
$784$	24284.3	1.10624
$785$	1252.57	0.0569505
$786$	−81401.3	−3.69401
$787$	−25596.9	−1.15938	−0.579689	−	0.814838i	$-0.696826\pi$
$787$	−25596.9	−1.15938	−0.579689	+	0.814838i	$0.696826\pi$
$788$	19145.9	0.865538
$789$	−21355.8	−0.963606
$790$	2900.88	0.130644
$791$	4967.42	0.223288
$792$	−5647.05	−0.253358
$793$	41326.5	1.85063
$794$	−31639.4	−1.41416
$795$	8001.98	0.356982
$796$	12913.5	0.575010
$797$	−26835.0	−1.19265	−0.596327	−	0.802742i	$-0.703374\pi$
$797$	−26835.0	−1.19265	−0.596327	+	0.802742i	$0.703374\pi$
$798$	−14400.0	−0.638791
$799$	−32712.3	−1.44841
$800$	−28045.5	−1.23945
$801$	31853.2	1.40509
$802$	48450.2	2.13321
$803$	11808.8	0.518958
$804$	146.342	0.00641926
$805$	−1539.58	−0.0674075
$806$	22730.9	0.993375
$807$	63823.3	2.78400
$808$	−2071.73	−0.0902018
$809$	−22386.4	−0.972887	−0.486443	−	0.873712i	$-0.661706\pi$
$809$	−22386.4	−0.972887	−0.486443	+	0.873712i	$0.661706\pi$
$810$	581.585	0.0252282
$811$	−12050.9	−0.521781	−0.260891	−	0.965368i	$-0.584016\pi$
$811$	−12050.9	−0.521781	−0.260891	+	0.965368i	$0.584016\pi$
$812$	1875.30	0.0810470
$813$	−21402.2	−0.923255
$814$	28225.7	1.21537
$815$	2597.64	0.111646
$816$	−59714.2	−2.56178
$817$	0	0
$818$	−3750.07	−0.160291
$819$	6765.95	0.288671
$820$	−3396.23	−0.144636
$821$	2118.86	0.0900717	0.0450358	−	0.998985i	$-0.485660\pi$
$821$	2118.86	0.0900717	0.0450358	+	0.998985i	$0.485660\pi$
$822$	42668.4	1.81050
$823$	−15733.7	−0.666396	−0.333198	−	0.942857i	$-0.608128\pi$
$823$	−15733.7	−0.666396	−0.333198	+	0.942857i	$0.608128\pi$
$824$	1011.45	0.0427617
$825$	24242.9	1.02306
$826$	7563.57	0.318608
$827$	−19983.4	−0.840256	−0.420128	−	0.907465i	$-0.638015\pi$
$827$	−19983.4	−0.840256	−0.420128	+	0.907465i	$0.638015\pi$
$828$	49317.4	2.06993
$829$	−34475.6	−1.44437	−0.722187	−	0.691698i	$-0.756863\pi$
$829$	−34475.6	−1.44437	−0.722187	+	0.691698i	$0.756863\pi$
$830$	−1198.35	−0.0501147
$831$	−47211.8	−1.97083
$832$	14725.4	0.613594
$833$	−32327.0	−1.34461
$834$	−21915.6	−0.909924
$835$	−2350.50	−0.0974159
$836$	21310.8	0.881640
$837$	16833.7	0.695170
$838$	41745.8	1.72087
$839$	9582.61	0.394313	0.197156	−	0.980372i	$-0.436829\pi$
$839$	9582.61	0.394313	0.197156	+	0.980372i	$0.436829\pi$
$840$	−395.328	−0.0162382
$841$	−17475.1	−0.716514
$842$	47177.9	1.93095
$843$	−53514.7	−2.18641
$844$	34438.6	1.40453
$845$	−137.423	−0.00559468
$846$	54654.2	2.22110
$847$	2498.03	0.101338
$848$	−27404.4	−1.10975
$849$	−67039.1	−2.70998
$850$	44137.5	1.78106
$851$	52853.5	2.12902
$852$	25734.1	1.03478
$853$	−31343.1	−1.25811	−0.629055	−	0.777361i	$-0.716558\pi$
$853$	−31343.1	−1.25811	−0.629055	+	0.777361i	$0.716558\pi$
$854$	−11672.2	−0.467698
$855$	−14439.1	−0.577550
$856$	−6177.06	−0.246644
$857$	−3018.06	−0.120298	−0.0601488	−	0.998189i	$-0.519158\pi$
$857$	−3018.06	−0.120298	−0.0601488	+	0.998189i	$0.519158\pi$
$858$	−36197.8	−1.44030
$859$	20259.2	0.804697	0.402349	−	0.915487i	$-0.368194\pi$
$859$	20259.2	0.804697	0.402349	+	0.915487i	$0.368194\pi$
$860$	0	0
$861$	5746.43	0.227454
$862$	24959.4	0.986219
$863$	40225.7	1.58667	0.793336	−	0.608785i	$-0.208343\pi$
$863$	40225.7	1.58667	0.793336	+	0.608785i	$0.208343\pi$
$864$	31011.6	1.22111
$865$	−10359.6	−0.407209
$866$	46873.9	1.83931
$867$	38478.0	1.50725
$868$	−2899.22	−0.113371
$869$	7263.88	0.283556
$870$	6797.71	0.264901
$871$	−123.203	−0.00479286
$872$	−5982.44	−0.232329
$873$	−73563.5	−2.85194
$874$	88366.6	3.41996
$875$	2136.90	0.0825604
$876$	−26481.3	−1.02137
$877$	9078.63	0.349559	0.174780	−	0.984608i	$-0.444079\pi$
$877$	9078.63	0.349559	0.174780	+	0.984608i	$0.444079\pi$
$878$	10718.7	0.412003
$879$	−30154.3	−1.15708
$880$	4609.24	0.176565
$881$	−1661.65	−0.0635440	−0.0317720	−	0.999495i	$-0.510115\pi$
$881$	−1661.65	−0.0635440	−0.0317720	+	0.999495i	$0.510115\pi$
$882$	54010.4	2.06193
$883$	10862.1	0.413974	0.206987	−	0.978344i	$-0.433634\pi$
$883$	10862.1	0.413974	0.206987	+	0.978344i	$0.433634\pi$
$884$	−29761.0	−1.13232
$885$	12381.1	0.470268
$886$	35660.6	1.35219
$887$	12633.9	0.478248	0.239124	−	0.970989i	$-0.423140\pi$
$887$	12633.9	0.478248	0.239124	+	0.970989i	$0.423140\pi$
$888$	13571.5	0.512873
$889$	6934.12	0.261601
$890$	−7307.78	−0.275233
$891$	1456.31	0.0547565
$892$	7384.73	0.277196
$893$	44223.4	1.65720
$894$	14916.5	0.558034
$895$	−2099.04	−0.0783946
$896$	2327.22	0.0867710
$897$	−67781.5	−2.52303
$898$	27546.4	1.02365
$899$	−10689.0	−0.396548
$900$	−33301.3	−1.23338
$901$	36480.4	1.34888
$902$	−18831.9	−0.695160
$903$	0	0
$904$	−7827.29	−0.287977
$905$	−4516.48	−0.165893
$906$	55036.6	2.01818
$907$	43157.9	1.57997	0.789987	−	0.613124i	$-0.210087\pi$
$907$	43157.9	1.57997	0.789987	+	0.613124i	$0.210087\pi$
$908$	3289.80	0.120238
$909$	−16393.1	−0.598156
$910$	−1552.25	−0.0565456
$911$	−8726.36	−0.317363	−0.158681	−	0.987330i	$-0.550724\pi$
$911$	−8726.36	−0.317363	−0.158681	+	0.987330i	$0.550724\pi$
$912$	80727.0	2.93107
$913$	−3000.70	−0.108772
$914$	−5264.59	−0.190522
$915$	−19106.7	−0.690325
$916$	9123.02	0.329076
$917$	−8740.76	−0.314772
$918$	−48805.6	−1.75471
$919$	−25907.4	−0.929932	−0.464966	−	0.885328i	$-0.653934\pi$
$919$	−25907.4	−0.929932	−0.464966	+	0.885328i	$0.653934\pi$
$920$	2425.95	0.0869363
$921$	−10702.8	−0.382918
$922$	42949.4	1.53413
$923$	−21665.2	−0.772609
$924$	4616.86	0.164376
$925$	−35689.0	−1.26859
$926$	7934.89	0.281595
$927$	8003.37	0.283566
$928$	−19691.6	−0.696560
$929$	32728.1	1.15584	0.577919	−	0.816094i	$-0.303865\pi$
$929$	32728.1	1.15584	0.577919	+	0.816094i	$0.303865\pi$
$930$	−10509.3	−0.370551
$931$	43702.5	1.53845
$932$	−1708.67	−0.0600530
$933$	−76347.0	−2.67898
$934$	−7702.78	−0.269853
$935$	−6135.78	−0.214611
$936$	−10661.3	−0.372302
$937$	5170.31	0.180263	0.0901316	−	0.995930i	$-0.471271\pi$
$937$	5170.31	0.180263	0.0901316	+	0.995930i	$0.471271\pi$
$938$	34.7973	0.00121127
$939$	−27186.0	−0.944814
$940$	−5662.36	−0.196474
$941$	−23338.4	−0.808511	−0.404255	−	0.914646i	$-0.632469\pi$
$941$	−23338.4	−0.808511	−0.404255	+	0.914646i	$0.632469\pi$
$942$	−15575.2	−0.538714
$943$	−35263.3	−1.21774
$944$	−42401.6	−1.46192
$945$	−1149.54	−0.0395710
$946$	0	0
$947$	6979.11	0.239483	0.119742	−	0.992805i	$-0.461793\pi$
$947$	6979.11	0.239483	0.119742	+	0.992805i	$0.461793\pi$
$948$	−16289.3	−0.558073
$949$	22294.3	0.762595
$950$	−59669.0	−2.03781
$951$	53930.2	1.83891
$952$	−1802.27	−0.0613572
$953$	15961.8	0.542552	0.271276	−	0.962502i	$-0.412554\pi$
$953$	15961.8	0.542552	0.271276	+	0.962502i	$0.412554\pi$
$954$	−60949.8	−2.06847
$955$	3094.07	0.104840
$956$	27852.9	0.942287
$957$	17021.7	0.574955
$958$	−39824.6	−1.34308
$959$	4581.68	0.154276
$960$	−6808.05	−0.228884
$961$	−13265.9	−0.445298
$962$	53288.4	1.78595
$963$	−48877.5	−1.63557
$964$	48669.5	1.62608
$965$	−3146.62	−0.104967
$966$	19144.1	0.637630
$967$	−15404.6	−0.512283	−0.256142	−	0.966639i	$-0.582451\pi$
$967$	−15404.6	−0.512283	−0.256142	+	0.966639i	$0.582451\pi$
$968$	−3936.21	−0.130697
$969$	−107463.	−3.56265
$970$	16877.0	0.558646
$971$	−814.407	−0.0269161	−0.0134581	−	0.999909i	$-0.504284\pi$
$971$	−814.407	−0.0269161	−0.0134581	+	0.999909i	$0.504284\pi$
$972$	−26557.1	−0.876357
$973$	−2353.27	−0.0775360
$974$	15911.2	0.523437
$975$	45769.1	1.50337
$976$	65434.7	2.14602
$977$	3952.69	0.129435	0.0647174	−	0.997904i	$-0.479385\pi$
$977$	3952.69	0.129435	0.0647174	+	0.997904i	$0.479385\pi$
$978$	−32300.6	−1.05609
$979$	−18298.9	−0.597380
$980$	−5595.66	−0.182395
$981$	−47337.6	−1.54064
$982$	−43172.6	−1.40295
$983$	2736.55	0.0887918	0.0443959	−	0.999014i	$-0.485864\pi$
$983$	2736.55	0.0887918	0.0443959	+	0.999014i	$0.485864\pi$
$984$	−9054.80	−0.293350
$985$	7452.22	0.241063
$986$	30990.3	1.00094
$987$	9580.73	0.308975
$988$	40233.6	1.29555
$989$	0	0
$990$	10251.4	0.329101
$991$	24139.6	0.773783	0.386892	−	0.922125i	$-0.373549\pi$
$991$	24139.6	0.773783	0.386892	+	0.922125i	$0.373549\pi$
$992$	30443.2	0.974367
$993$	−54034.1	−1.72681
$994$	6119.07	0.195257
$995$	5026.37	0.160147
$996$	6729.09	0.214076
$997$	−27188.4	−0.863656	−0.431828	−	0.901956i	$-0.642131\pi$
$997$	−27188.4	−0.863656	−0.431828	+	0.901956i	$0.642131\pi$
$998$	49920.3	1.58337
$999$	39463.5	1.24982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.10	✓	50
43.42	odd	2		1849.4.a.j.1.41	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.10	✓	50	1.1	even	1	trivial
1849.4.a.j.1.41	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)

\(f(q)\)	\(=\)	\(q-3.81936 q^{2} +8.34786 q^{3} +6.58755 q^{4} +2.56409 q^{5} -31.8835 q^{6} -3.42361 q^{7} +5.39467 q^{8} +42.6867 q^{9} +O(q^{10})\)	\(q-3.81936 q^{2} +8.34786 q^{3} +6.58755 q^{4} +2.56409 q^{5} -31.8835 q^{6} -3.42361 q^{7} +5.39467 q^{8} +42.6867 q^{9} -9.79321 q^{10} -24.5225 q^{11} +54.9919 q^{12} -46.2969 q^{13} +13.0760 q^{14} +21.4047 q^{15} -73.3046 q^{16} +97.5824 q^{17} -163.036 q^{18} -131.921 q^{19} +16.8911 q^{20} -28.5798 q^{21} +93.6603 q^{22} +175.382 q^{23} +45.0339 q^{24} -118.425 q^{25} +176.825 q^{26} +130.950 q^{27} -22.5532 q^{28} -83.1501 q^{29} -81.7523 q^{30} +128.550 q^{31} +236.820 q^{32} -204.710 q^{33} -372.703 q^{34} -8.77845 q^{35} +281.201 q^{36} +301.363 q^{37} +503.853 q^{38} -386.480 q^{39} +13.8324 q^{40} -201.066 q^{41} +109.157 q^{42} -161.543 q^{44} +109.453 q^{45} -669.846 q^{46} -335.227 q^{47} -611.936 q^{48} -331.279 q^{49} +452.310 q^{50} +814.604 q^{51} -304.983 q^{52} +373.842 q^{53} -500.147 q^{54} -62.8779 q^{55} -18.4692 q^{56} -1101.25 q^{57} +317.581 q^{58} +578.431 q^{59} +141.004 q^{60} -892.641 q^{61} -490.980 q^{62} -146.143 q^{63} -318.064 q^{64} -118.710 q^{65} +781.862 q^{66} +2.66116 q^{67} +642.829 q^{68} +1464.06 q^{69} +33.5281 q^{70} +467.961 q^{71} +230.281 q^{72} -481.550 q^{73} -1151.01 q^{74} -988.598 q^{75} -869.034 q^{76} +83.9554 q^{77} +1476.11 q^{78} -296.213 q^{79} -187.960 q^{80} -59.3866 q^{81} +767.945 q^{82} +122.365 q^{83} -188.271 q^{84} +250.210 q^{85} -694.125 q^{87} -132.291 q^{88} +746.209 q^{89} -418.040 q^{90} +158.503 q^{91} +1155.33 q^{92} +1073.12 q^{93} +1280.36 q^{94} -338.257 q^{95} +1976.94 q^{96} -1723.34 q^{97} +1265.27 q^{98} -1046.78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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