LMFDB - Embedded newform 1849.4.a.j.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.44476 q^{2} -8.05562 q^{3} -2.02317 q^{4} -13.2954 q^{5} +19.6940 q^{6} +1.50720 q^{7} +24.5042 q^{8} +37.8930 q^{9} +O(q^{10})$	\(q-2.44476 q^{2} -8.05562 q^{3} -2.02317 q^{4} -13.2954 q^{5} +19.6940 q^{6} +1.50720 q^{7} +24.5042 q^{8} +37.8930 q^{9} +32.5040 q^{10} -19.9849 q^{11} +16.2979 q^{12} -49.4213 q^{13} -3.68472 q^{14} +107.103 q^{15} -43.7214 q^{16} -96.4429 q^{17} -92.6392 q^{18} +105.153 q^{19} +26.8989 q^{20} -12.1414 q^{21} +48.8582 q^{22} -171.786 q^{23} -197.397 q^{24} +51.7679 q^{25} +120.823 q^{26} -87.7502 q^{27} -3.04932 q^{28} -218.628 q^{29} -261.840 q^{30} +91.9262 q^{31} -89.1455 q^{32} +160.991 q^{33} +235.779 q^{34} -20.0388 q^{35} -76.6642 q^{36} +104.603 q^{37} -257.073 q^{38} +398.119 q^{39} -325.793 q^{40} -407.432 q^{41} +29.6827 q^{42} +40.4329 q^{44} -503.804 q^{45} +419.975 q^{46} +482.077 q^{47} +352.203 q^{48} -340.728 q^{49} -126.560 q^{50} +776.908 q^{51} +99.9878 q^{52} -698.058 q^{53} +214.528 q^{54} +265.708 q^{55} +36.9326 q^{56} -847.073 q^{57} +534.493 q^{58} +338.239 q^{59} -216.687 q^{60} -330.219 q^{61} -224.737 q^{62} +57.1122 q^{63} +567.710 q^{64} +657.076 q^{65} -393.583 q^{66} +307.046 q^{67} +195.121 q^{68} +1383.84 q^{69} +48.9899 q^{70} -49.0861 q^{71} +928.539 q^{72} +919.255 q^{73} -255.728 q^{74} -417.023 q^{75} -212.743 q^{76} -30.1212 q^{77} -973.304 q^{78} +682.335 q^{79} +581.294 q^{80} -316.229 q^{81} +996.070 q^{82} +411.921 q^{83} +24.5641 q^{84} +1282.25 q^{85} +1761.19 q^{87} -489.714 q^{88} -764.419 q^{89} +1231.68 q^{90} -74.4875 q^{91} +347.553 q^{92} -740.523 q^{93} -1178.56 q^{94} -1398.05 q^{95} +718.123 q^{96} +1512.74 q^{97} +832.997 q^{98} -757.289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.44476	−0.864351	−0.432176	−	0.901789i	$-0.642254\pi$
$2$	−2.44476	−0.864351	−0.432176	+	0.901789i	$0.642254\pi$
$3$	−8.05562	−1.55031	−0.775153	−	0.631774i	$-0.782327\pi$
$3$	−8.05562	−1.55031	−0.775153	+	0.631774i	$0.782327\pi$
$4$	−2.02317	−0.252897
$5$	−13.2954	−1.18918	−0.594589	−	0.804030i	$-0.702685\pi$
$5$	−13.2954	−1.18918	−0.594589	+	0.804030i	$0.702685\pi$
$6$	19.6940	1.34001
$7$	1.50720	0.0813809	0.0406904	−	0.999172i	$-0.487044\pi$
$7$	1.50720	0.0813809	0.0406904	+	0.999172i	$0.487044\pi$
$8$	24.5042	1.08294
$9$	37.8930	1.40345
$10$	32.5040	1.02787
$11$	−19.9849	−0.547789	−0.273894	−	0.961760i	$-0.588312\pi$
$11$	−19.9849	−0.547789	−0.273894	+	0.961760i	$0.588312\pi$
$12$	16.2979	0.392067
$13$	−49.4213	−1.05438	−0.527192	−	0.849746i	$-0.676755\pi$
$13$	−49.4213	−1.05438	−0.527192	+	0.849746i	$0.676755\pi$
$14$	−3.68472	−0.0703417
$15$	107.103	1.84359
$16$	−43.7214	−0.683147
$17$	−96.4429	−1.37593	−0.687966	−	0.725743i	$-0.741496\pi$
$17$	−96.4429	−1.37593	−0.687966	+	0.725743i	$0.741496\pi$
$18$	−92.6392	−1.21307
$19$	105.153	1.26967	0.634836	−	0.772647i	$-0.281068\pi$
$19$	105.153	1.26967	0.634836	+	0.772647i	$0.281068\pi$
$20$	26.8989	0.300739
$21$	−12.1414	−0.126165
$22$	48.8582	0.473482
$23$	−171.786	−1.55739	−0.778693	−	0.627405i	$-0.784117\pi$
$23$	−171.786	−1.55739	−0.778693	+	0.627405i	$0.784117\pi$
$24$	−197.397	−1.67889
$25$	51.7679	0.414143
$26$	120.823	0.911359
$27$	−87.7502	−0.625465
$28$	−3.04932	−0.0205809
$29$	−218.628	−1.39994	−0.699970	−	0.714172i	$-0.746803\pi$
$29$	−218.628	−1.39994	−0.699970	+	0.714172i	$0.746803\pi$
$30$	−261.840	−1.59351
$31$	91.9262	0.532595	0.266297	−	0.963891i	$-0.414200\pi$
$31$	91.9262	0.532595	0.266297	+	0.963891i	$0.414200\pi$
$32$	−89.1455	−0.492464
$33$	160.991	0.849240
$34$	235.779	1.18929
$35$	−20.0388	−0.0967763
$36$	−76.6642	−0.354927
$37$	104.603	0.464773	0.232387	−	0.972623i	$-0.425347\pi$
$37$	104.603	0.464773	0.232387	+	0.972623i	$0.425347\pi$
$38$	−257.073	−1.09744
$39$	398.119	1.63462
$40$	−325.793	−1.28781
$41$	−407.432	−1.55195	−0.775977	−	0.630761i	$-0.782743\pi$
$41$	−407.432	−1.55195	−0.775977	+	0.630761i	$0.782743\pi$
$42$	29.6827	0.109051
$43$	0	0
$43$	0	0
$44$	40.4329	0.138534
$45$	−503.804	−1.66895
$46$	419.975	1.34613
$47$	482.077	1.49613	0.748066	−	0.663624i	$-0.230983\pi$
$47$	482.077	1.49613	0.748066	+	0.663624i	$0.230983\pi$
$48$	352.203	1.05909
$49$	−340.728	−0.993377
$50$	−126.560	−0.357965
$51$	776.908	2.13311
$52$	99.9878	0.266650
$53$	−698.058	−1.80916	−0.904581	−	0.426302i	$-0.859816\pi$
$53$	−698.058	−1.80916	−0.904581	+	0.426302i	$0.859816\pi$
$54$	214.528	0.540621
$55$	265.708	0.651418
$56$	36.9326	0.0881309
$57$	−847.073	−1.96838
$58$	534.493	1.21004
$59$	338.239	0.746355	0.373177	−	0.927760i	$-0.378268\pi$
$59$	338.239	0.746355	0.373177	+	0.927760i	$0.378268\pi$
$60$	−216.687	−0.466237
$61$	−330.219	−0.693119	−0.346559	−	0.938028i	$-0.612650\pi$
$61$	−330.219	−0.693119	−0.346559	+	0.938028i	$0.612650\pi$
$62$	−224.737	−0.460349
$63$	57.1122	0.114214
$64$	567.710	1.10881
$65$	657.076	1.25385
$66$	−393.583	−0.734042
$67$	307.046	0.559875	0.279937	−	0.960018i	$-0.409686\pi$
$67$	307.046	0.559875	0.279937	+	0.960018i	$0.409686\pi$
$68$	195.121	0.347968
$69$	1383.84	2.41442
$70$	48.9899	0.0836488
$71$	−49.0861	−0.0820486	−0.0410243	−	0.999158i	$-0.513062\pi$
$71$	−49.0861	−0.0820486	−0.0410243	+	0.999158i	$0.513062\pi$
$72$	928.539	1.51985
$73$	919.255	1.47384	0.736922	−	0.675978i	$-0.236278\pi$
$73$	919.255	1.47384	0.736922	+	0.675978i	$0.236278\pi$
$74$	−255.728	−0.401727
$75$	−417.023	−0.642048
$76$	−212.743	−0.321096
$77$	−30.1212	−0.0445796
$78$	−973.304	−1.41288
$79$	682.335	0.971755	0.485878	−	0.874027i	$-0.338500\pi$
$79$	682.335	0.971755	0.485878	+	0.874027i	$0.338500\pi$
$80$	581.294	0.812383
$81$	−316.229	−0.433785
$82$	996.070	1.34143
$83$	411.921	0.544750	0.272375	−	0.962191i	$-0.412191\pi$
$83$	411.921	0.544750	0.272375	+	0.962191i	$0.412191\pi$
$84$	24.5641	0.0319067
$85$	1282.25	1.63623
$86$	0	0
$87$	1761.19	2.17033
$88$	−489.714	−0.593224
$89$	−764.419	−0.910430	−0.455215	−	0.890382i	$-0.650438\pi$
$89$	−764.419	−0.910430	−0.455215	+	0.890382i	$0.650438\pi$
$90$	1231.68	1.44256
$91$	−74.4875	−0.0858067
$92$	347.553	0.393858
$93$	−740.523	−0.825684
$94$	−1178.56	−1.29318
$95$	−1398.05	−1.50987
$96$	718.123	0.763470
$97$	1512.74	1.58346	0.791729	−	0.610873i	$-0.209181\pi$
$97$	1512.74	1.58346	0.791729	+	0.610873i	$0.209181\pi$
$98$	832.997	0.858627
$99$	−757.289	−0.768792
$100$	−104.735	−0.104735
$101$	833.158	0.820815	0.410408	−	0.911902i	$-0.365386\pi$
$101$	833.158	0.820815	0.410408	+	0.911902i	$0.365386\pi$
$102$	−1899.35	−1.84376
$103$	609.451	0.583019	0.291510	−	0.956568i	$-0.405842\pi$
$103$	609.451	0.583019	0.291510	+	0.956568i	$0.405842\pi$
$104$	−1211.03	−1.14184
$105$	161.425	0.150033
$106$	1706.58	1.56375
$107$	1522.90	1.37593	0.687964	−	0.725745i	$-0.258505\pi$
$107$	1522.90	1.37593	0.687964	+	0.725745i	$0.258505\pi$
$108$	177.534	0.158178
$109$	593.526	0.521555	0.260778	−	0.965399i	$-0.416021\pi$
$109$	593.526	0.521555	0.260778	+	0.965399i	$0.416021\pi$
$110$	−649.590	−0.563054
$111$	−842.641	−0.720540
$112$	−65.8967	−0.0555951
$113$	721.193	0.600391	0.300195	−	0.953878i	$-0.402948\pi$
$113$	721.193	0.600391	0.300195	+	0.953878i	$0.402948\pi$
$114$	2070.89	1.70137
$115$	2283.97	1.85201
$116$	442.323	0.354040
$117$	−1872.72	−1.47977
$118$	−826.911	−0.645113
$119$	−145.358	−0.111975
$120$	2624.47	1.99650
$121$	−931.603	−0.699927
$122$	807.305	0.599098
$123$	3282.11	2.40600
$124$	−185.983	−0.134691
$125$	973.651	0.696688
$126$	−139.625	−0.0987208
$127$	−488.453	−0.341285	−0.170643	−	0.985333i	$-0.554584\pi$
$127$	−488.453	−0.341285	−0.170643	+	0.985333i	$0.554584\pi$
$128$	−674.748	−0.465936
$129$	0	0
$130$	−1606.39	−1.08377
$131$	−197.970	−0.132036	−0.0660180	−	0.997818i	$-0.521029\pi$
$131$	−197.970	−0.132036	−0.0660180	+	0.997818i	$0.521029\pi$
$132$	−325.712	−0.214770
$133$	158.486	0.103327
$134$	−750.651	−0.483928
$135$	1166.68	0.743788
$136$	−2363.26	−1.49006
$137$	2218.38	1.38342	0.691712	−	0.722174i	$-0.256857\pi$
$137$	2218.38	1.38342	0.691712	+	0.722174i	$0.256857\pi$
$138$	−3383.16	−2.08691
$139$	1426.45	0.870428	0.435214	−	0.900327i	$-0.356673\pi$
$139$	1426.45	0.870428	0.435214	+	0.900327i	$0.356673\pi$
$140$	40.5419	0.0244744
$141$	−3883.43	−2.31946
$142$	120.004	0.0709189
$143$	987.680	0.577580
$144$	−1656.74	−0.958760
$145$	2906.75	1.66478
$146$	−2247.35	−1.27392
$147$	2744.78	1.54004
$148$	−211.630	−0.117540
$149$	−324.928	−0.178652	−0.0893259	−	0.996002i	$-0.528471\pi$
$149$	−324.928	−0.178652	−0.0893259	+	0.996002i	$0.528471\pi$
$150$	1019.52	0.554955
$151$	1010.13	0.544391	0.272196	−	0.962242i	$-0.412250\pi$
$151$	1010.13	0.544391	0.272196	+	0.962242i	$0.412250\pi$
$152$	2576.69	1.37498
$153$	−3654.52	−1.93105
$154$	73.6389	0.0385324
$155$	−1222.20	−0.633350
$156$	−805.464	−0.413389
$157$	−2780.79	−1.41358	−0.706788	−	0.707425i	$-0.749857\pi$
$157$	−2780.79	−1.41358	−0.706788	+	0.707425i	$0.749857\pi$
$158$	−1668.14	−0.839938
$159$	5623.29	2.80475
$160$	1185.23	0.585627
$161$	−258.915	−0.126741
$162$	773.103	0.374943
$163$	−261.449	−0.125634	−0.0628168	−	0.998025i	$-0.520008\pi$
$163$	−261.449	−0.125634	−0.0628168	+	0.998025i	$0.520008\pi$
$164$	824.304	0.392484
$165$	−2140.44	−1.00990
$166$	−1007.05	−0.470855
$167$	−1042.23	−0.482937	−0.241469	−	0.970409i	$-0.577629\pi$
$167$	−1042.23	−0.482937	−0.241469	+	0.970409i	$0.577629\pi$
$168$	−297.515	−0.136630
$169$	245.462	0.111726
$170$	−3134.78	−1.41428
$171$	3984.57	1.78192
$172$	0	0
$173$	−676.020	−0.297092	−0.148546	−	0.988906i	$-0.547459\pi$
$173$	−676.020	−0.297092	−0.148546	+	0.988906i	$0.547459\pi$
$174$	−4305.67	−1.87593
$175$	78.0243	0.0337033
$176$	873.768	0.374220
$177$	−2724.72	−1.15708
$178$	1868.82	0.786931
$179$	−1330.90	−0.555731	−0.277866	−	0.960620i	$-0.589627\pi$
$179$	−1330.90	−0.555731	−0.277866	+	0.960620i	$0.589627\pi$
$180$	1019.28	0.422071
$181$	−1960.59	−0.805137	−0.402568	−	0.915390i	$-0.631882\pi$
$181$	−1960.59	−0.805137	−0.402568	+	0.915390i	$0.631882\pi$
$182$	182.104	0.0741672
$183$	2660.12	1.07455
$184$	−4209.48	−1.68656
$185$	−1390.74	−0.552698
$186$	1810.40	0.713681
$187$	1927.40	0.753720
$188$	−975.326	−0.378367
$189$	−132.257	−0.0509009
$190$	3417.90	1.30505
$191$	−1864.27	−0.706249	−0.353125	−	0.935576i	$-0.614881\pi$
$191$	−1864.27	−0.706249	−0.353125	+	0.935576i	$0.614881\pi$
$192$	−4573.26	−1.71899
$193$	−1508.73	−0.562697	−0.281348	−	0.959606i	$-0.590782\pi$
$193$	−1508.73	−0.562697	−0.281348	+	0.959606i	$0.590782\pi$
$194$	−3698.28	−1.36866
$195$	−5293.16	−1.94385
$196$	689.352	0.251222
$197$	−1352.69	−0.489216	−0.244608	−	0.969622i	$-0.578659\pi$
$197$	−1352.69	−0.489216	−0.244608	+	0.969622i	$0.578659\pi$
$198$	1851.39	0.664507
$199$	−1294.26	−0.461045	−0.230522	−	0.973067i	$-0.574043\pi$
$199$	−1294.26	−0.461045	−0.230522	+	0.973067i	$0.574043\pi$
$200$	1268.53	0.448493
$201$	−2473.44	−0.867976
$202$	−2036.87	−0.709473
$203$	−329.516	−0.113928
$204$	−1571.82	−0.539457
$205$	5416.97	1.84555
$206$	−1489.96	−0.503933
$207$	−6509.50	−2.18571
$208$	2160.77	0.720299
$209$	−2101.47	−0.695512
$210$	−394.644	−0.129681
$211$	3425.33	1.11758	0.558790	−	0.829309i	$-0.311266\pi$
$211$	3425.33	1.11758	0.558790	+	0.829309i	$0.311266\pi$
$212$	1412.29	0.457531
$213$	395.419	0.127200
$214$	−3723.12	−1.18929
$215$	0	0
$216$	−2150.25	−0.677342
$217$	138.551	0.0433430
$218$	−1451.03	−0.450807
$219$	−7405.17	−2.28491
$220$	−537.572	−0.164741
$221$	4766.33	1.45076
$222$	2060.05	0.622800
$223$	−3651.82	−1.09661	−0.548305	−	0.836278i	$-0.684727\pi$
$223$	−3651.82	−1.09661	−0.548305	+	0.836278i	$0.684727\pi$
$224$	−134.360	−0.0400772
$225$	1961.64	0.581228
$226$	−1763.14	−0.518949
$227$	4830.81	1.41248	0.706239	−	0.707974i	$-0.250391\pi$
$227$	4830.81	1.41248	0.706239	+	0.707974i	$0.250391\pi$
$228$	1713.78	0.497796
$229$	−833.344	−0.240476	−0.120238	−	0.992745i	$-0.538366\pi$
$229$	−833.344	−0.240476	−0.120238	+	0.992745i	$0.538366\pi$
$230$	−5583.74	−1.60079
$231$	242.645	0.0691119
$232$	−5357.31	−1.51605
$233$	2172.62	0.610872	0.305436	−	0.952213i	$-0.401198\pi$
$233$	2172.62	0.610872	0.305436	+	0.952213i	$0.401198\pi$
$234$	4578.35	1.27904
$235$	−6409.42	−1.77917
$236$	−684.315	−0.188751
$237$	−5496.63	−1.50652
$238$	355.365	0.0967854
$239$	−1933.97	−0.523423	−0.261712	−	0.965146i	$-0.584287\pi$
$239$	−1933.97	−0.523423	−0.261712	+	0.965146i	$0.584287\pi$
$240$	−4682.68	−1.25944
$241$	490.620	0.131135	0.0655677	−	0.997848i	$-0.479114\pi$
$241$	490.620	0.131135	0.0655677	+	0.997848i	$0.479114\pi$
$242$	2277.54	0.604983
$243$	4916.68	1.29796
$244$	668.091	0.175287
$245$	4530.12	1.18130
$246$	−8023.97	−2.07963
$247$	−5196.80	−1.33872
$248$	2252.58	0.576770
$249$	−3318.28	−0.844528
$250$	−2380.34	−0.602183
$251$	−4205.04	−1.05745	−0.528725	−	0.848793i	$-0.677330\pi$
$251$	−4205.04	−1.05745	−0.528725	+	0.848793i	$0.677330\pi$
$252$	−115.548	−0.0288843
$253$	3433.13	0.853119
$254$	1194.15	0.294990
$255$	−10329.3	−2.53665
$256$	−2892.09	−0.706076
$257$	4274.70	1.03754	0.518772	−	0.854913i	$-0.326389\pi$
$257$	4274.70	1.03754	0.518772	+	0.854913i	$0.326389\pi$
$258$	0	0
$259$	157.657	0.0378237
$260$	−1329.38	−0.317094
$261$	−8284.49	−1.96474
$262$	483.988	0.114125
$263$	7460.19	1.74911	0.874553	−	0.484931i	$-0.161155\pi$
$263$	7460.19	1.74911	0.874553	+	0.484931i	$0.161155\pi$
$264$	3944.95	0.919679
$265$	9280.96	2.15141
$266$	−387.460	−0.0893109
$267$	6157.87	1.41144
$268$	−621.206	−0.141590
$269$	2275.62	0.515789	0.257894	−	0.966173i	$-0.416971\pi$
$269$	2275.62	0.515789	0.257894	+	0.966173i	$0.416971\pi$
$270$	−2852.24	−0.642895
$271$	6143.57	1.37710	0.688552	−	0.725187i	$-0.258247\pi$
$271$	6143.57	1.37710	0.688552	+	0.725187i	$0.258247\pi$
$272$	4216.62	0.939963
$273$	600.043	0.133027
$274$	−5423.40	−1.19576
$275$	−1034.58	−0.226863
$276$	−2799.75	−0.610599
$277$	8485.97	1.84070	0.920348	−	0.391101i	$-0.127906\pi$
$277$	8485.97	1.84070	0.920348	+	0.391101i	$0.127906\pi$
$278$	−3487.31	−0.752356
$279$	3483.36	0.747468
$280$	−491.034	−0.104803
$281$	−5614.23	−1.19187	−0.595937	−	0.803031i	$-0.703219\pi$
$281$	−5614.23	−1.19187	−0.595937	+	0.803031i	$0.703219\pi$
$282$	9494.04	2.00483
$283$	−3413.12	−0.716921	−0.358461	−	0.933545i	$-0.616698\pi$
$283$	−3413.12	−0.716921	−0.358461	+	0.933545i	$0.616698\pi$
$284$	99.3097	0.0207498
$285$	11262.2	2.34075
$286$	−2414.64	−0.499232
$287$	−614.079	−0.126299
$288$	−3378.00	−0.691147
$289$	4388.23	0.893188
$290$	−7106.30	−1.43895
$291$	−12186.1	−2.45484
$292$	−1859.81	−0.372730
$293$	9178.45	1.83007	0.915036	−	0.403373i	$-0.132162\pi$
$293$	9178.45	1.83007	0.915036	+	0.403373i	$0.132162\pi$
$294$	−6710.31	−1.33113
$295$	−4497.02	−0.887548
$296$	2563.21	0.503323
$297$	1753.68	0.342623
$298$	794.369	0.154418
$299$	8489.89	1.64208
$300$	843.709	0.162372
$301$	0	0
$302$	−2469.52	−0.470545
$303$	−6711.61	−1.27251
$304$	−4597.44	−0.867372
$305$	4390.40	0.824241
$306$	8934.40	1.66910
$307$	−7166.19	−1.33223	−0.666117	−	0.745847i	$-0.732045\pi$
$307$	−7166.19	−1.33223	−0.666117	+	0.745847i	$0.732045\pi$
$308$	60.9403	0.0112740
$309$	−4909.50	−0.903857
$310$	2987.97	0.547437
$311$	−6648.99	−1.21231	−0.606157	−	0.795345i	$-0.707290\pi$
$311$	−6648.99	−1.21231	−0.606157	+	0.795345i	$0.707290\pi$
$312$	9755.59	1.77020
$313$	−2436.83	−0.440057	−0.220029	−	0.975493i	$-0.570615\pi$
$313$	−2436.83	−0.440057	−0.220029	+	0.975493i	$0.570615\pi$
$314$	6798.36	1.22183
$315$	−759.330	−0.135820
$316$	−1380.48	−0.245754
$317$	2411.80	0.427318	0.213659	−	0.976908i	$-0.431462\pi$
$317$	2411.80	0.427318	0.213659	+	0.976908i	$0.431462\pi$
$318$	−13747.6	−2.42429
$319$	4369.27	0.766872
$320$	−7547.94	−1.31857
$321$	−12267.9	−2.13311
$322$	632.984	0.109549
$323$	−10141.3	−1.74698
$324$	639.787	0.109703
$325$	−2558.44	−0.436666
$326$	639.179	0.108592
$327$	−4781.22	−0.808570
$328$	−9983.78	−1.68068
$329$	726.585	0.121757
$330$	5232.85	0.872906
$331$	11124.7	1.84734	0.923669	−	0.383190i	$-0.125175\pi$
$331$	11124.7	1.84734	0.923669	+	0.383190i	$0.125175\pi$
$332$	−833.387	−0.137765
$333$	3963.72	0.652284
$334$	2548.01	0.417428
$335$	−4082.30	−0.665790
$336$	530.839	0.0861894
$337$	718.615	0.116159	0.0580793	−	0.998312i	$-0.481502\pi$
$337$	718.615	0.116159	0.0580793	+	0.998312i	$0.481502\pi$
$338$	−600.095	−0.0965706
$339$	−5809.66	−0.930789
$340$	−2594.21	−0.413796
$341$	−1837.14	−0.291749
$342$	−9741.30	−1.54020
$343$	−1030.51	−0.162223
$344$	0	0
$345$	−18398.8	−2.87118
$346$	1652.70	0.256792
$347$	3904.37	0.604028	0.302014	−	0.953303i	$-0.402341\pi$
$347$	3904.37	0.604028	0.302014	+	0.953303i	$0.402341\pi$
$348$	−3563.18	−0.548870
$349$	6023.61	0.923887	0.461943	−	0.886909i	$-0.347152\pi$
$349$	6023.61	0.923887	0.461943	+	0.886909i	$0.347152\pi$
$350$	−190.750	−0.0291315
$351$	4336.73	0.659480
$352$	1781.57	0.269766
$353$	−3398.18	−0.512371	−0.256186	−	0.966628i	$-0.582466\pi$
$353$	−3398.18	−0.512371	−0.256186	+	0.966628i	$0.582466\pi$
$354$	6661.28	1.00012
$355$	652.620	0.0975704
$356$	1546.55	0.230245
$357$	1170.95	0.173595
$358$	3253.72	0.480347
$359$	10550.4	1.55106	0.775531	−	0.631310i	$-0.217482\pi$
$359$	10550.4	1.55106	0.775531	+	0.631310i	$0.217482\pi$
$360$	−12345.3	−1.80737
$361$	4198.17	0.612067
$362$	4793.17	0.695921
$363$	7504.64	1.08510
$364$	150.701	0.0217002
$365$	−12221.9	−1.75266
$366$	−6503.35	−0.928785
$367$	7171.06	1.01996	0.509981	−	0.860186i	$-0.329652\pi$
$367$	7171.06	1.01996	0.509981	+	0.860186i	$0.329652\pi$
$368$	7510.73	1.06392
$369$	−15438.8	−2.17808
$370$	3400.01	0.477725
$371$	−1052.11	−0.147231
$372$	1498.21	0.208813
$373$	373.809	0.0518903	0.0259452	−	0.999663i	$-0.491740\pi$
$373$	373.809	0.0518903	0.0259452	+	0.999663i	$0.491740\pi$
$374$	−4712.03	−0.651479
$375$	−7843.36	−1.08008
$376$	11812.9	1.62023
$377$	10804.9	1.47607
$378$	323.335	0.0439962
$379$	−2707.62	−0.366969	−0.183484	−	0.983023i	$-0.558738\pi$
$379$	−2707.62	−0.366969	−0.183484	+	0.983023i	$0.558738\pi$
$380$	2828.50	0.381840
$381$	3934.80	0.529096
$382$	4557.68	0.610448
$383$	−4187.25	−0.558638	−0.279319	−	0.960198i	$-0.590109\pi$
$383$	−4187.25	−0.558638	−0.279319	+	0.960198i	$0.590109\pi$
$384$	5435.52	0.722344
$385$	400.473	0.0530130
$386$	3688.47	0.486368
$387$	0	0
$388$	−3060.53	−0.400451
$389$	−3278.56	−0.427326	−0.213663	−	0.976907i	$-0.568539\pi$
$389$	−3278.56	−0.427326	−0.213663	+	0.976907i	$0.568539\pi$
$390$	12940.5	1.68017
$391$	16567.6	2.14286
$392$	−8349.28	−1.07577
$393$	1594.77	0.204696
$394$	3307.01	0.422854
$395$	−9071.92	−1.15559
$396$	1532.13	0.194425
$397$	−10583.0	−1.33790	−0.668951	−	0.743306i	$-0.733257\pi$
$397$	−10583.0	−1.33790	−0.668951	+	0.743306i	$0.733257\pi$
$398$	3164.16	0.398505
$399$	−1276.70	−0.160188
$400$	−2263.36	−0.282921
$401$	6969.95	0.867986	0.433993	−	0.900916i	$-0.357104\pi$
$401$	6969.95	0.867986	0.433993	+	0.900916i	$0.357104\pi$
$402$	6046.96	0.750237
$403$	−4543.11	−0.561559
$404$	−1685.62	−0.207581
$405$	4204.40	0.515848
$406$	805.585	0.0984741
$407$	−2090.48	−0.254598
$408$	19037.5	2.31004
$409$	7908.92	0.956163	0.478082	−	0.878315i	$-0.341332\pi$
$409$	7908.92	0.956163	0.478082	+	0.878315i	$0.341332\pi$
$410$	−13243.2	−1.59520
$411$	−17870.4	−2.14473
$412$	−1233.02	−0.147444
$413$	509.792	0.0607390
$414$	15914.1	1.88922
$415$	−5476.66	−0.647804
$416$	4405.69	0.519246
$417$	−11490.9	−1.34943
$418$	5137.59	0.601167
$419$	9047.57	1.05490	0.527449	−	0.849587i	$-0.323148\pi$
$419$	9047.57	1.05490	0.527449	+	0.849587i	$0.323148\pi$
$420$	−326.590	−0.0379428
$421$	−4816.23	−0.557551	−0.278775	−	0.960356i	$-0.589928\pi$
$421$	−4816.23	−0.557551	−0.278775	+	0.960356i	$0.589928\pi$
$422$	−8374.09	−0.965982
$423$	18267.4	2.09974
$424$	−17105.3	−1.95922
$425$	−4992.65	−0.569833
$426$	−966.704	−0.109946
$427$	−497.705	−0.0564066
$428$	−3081.09	−0.347968
$429$	−7956.38	−0.895425
$430$	0	0
$431$	−3817.94	−0.426691	−0.213346	−	0.976977i	$-0.568436\pi$
$431$	−3817.94	−0.426691	−0.213346	+	0.976977i	$0.568436\pi$
$432$	3836.56	0.427284
$433$	−10734.2	−1.19134	−0.595672	−	0.803228i	$-0.703114\pi$
$433$	−10734.2	−1.19134	−0.595672	+	0.803228i	$0.703114\pi$
$434$	−338.723	−0.0374636
$435$	−23415.7	−2.58091
$436$	−1200.81	−0.131900
$437$	−18063.8	−1.97737
$438$	18103.8	1.97496
$439$	−10079.6	−1.09584	−0.547920	−	0.836531i	$-0.684580\pi$
$439$	−10079.6	−1.09584	−0.547920	+	0.836531i	$0.684580\pi$
$440$	6510.95	0.705449
$441$	−12911.2	−1.39415
$442$	−11652.5	−1.25397
$443$	−3418.64	−0.366646	−0.183323	−	0.983053i	$-0.558685\pi$
$443$	−3418.64	−0.366646	−0.183323	+	0.983053i	$0.558685\pi$
$444$	1704.81	0.182222
$445$	10163.3	1.08266
$446$	8927.81	0.947856
$447$	2617.50	0.276965
$448$	855.650	0.0902358
$449$	−3683.37	−0.387147	−0.193573	−	0.981086i	$-0.562008\pi$
$449$	−3683.37	−0.387147	−0.193573	+	0.981086i	$0.562008\pi$
$450$	−4795.74	−0.502385
$451$	8142.48	0.850143
$452$	−1459.10	−0.151837
$453$	−8137.21	−0.843972
$454$	−11810.2	−1.22088
$455$	990.342	0.102039
$456$	−20756.9	−2.13164
$457$	3799.32	0.388894	0.194447	−	0.980913i	$-0.437709\pi$
$457$	3799.32	0.388894	0.194447	+	0.980913i	$0.437709\pi$
$458$	2037.32	0.207855
$459$	8462.89	0.860597
$460$	−4620.86	−0.468367
$461$	−4025.57	−0.406701	−0.203351	−	0.979106i	$-0.565183\pi$
$461$	−4025.57	−0.406701	−0.203351	+	0.979106i	$0.565183\pi$
$462$	−593.207	−0.0597370
$463$	−4497.86	−0.451476	−0.225738	−	0.974188i	$-0.572479\pi$
$463$	−4497.86	−0.451476	−0.225738	+	0.974188i	$0.572479\pi$
$464$	9558.73	0.956364
$465$	9845.55	0.981885
$466$	−5311.52	−0.528008
$467$	6088.74	0.603326	0.301663	−	0.953415i	$-0.402458\pi$
$467$	6088.74	0.603326	0.301663	+	0.953415i	$0.402458\pi$
$468$	3788.84	0.374229
$469$	462.778	0.0455631
$470$	15669.5	1.53783
$471$	22401.0	2.19148
$472$	8288.27	0.808260
$473$	0	0
$474$	13437.9	1.30216
$475$	5443.55	0.525826
$476$	294.085	0.0283180
$477$	−26451.5	−2.53906
$478$	4728.09	0.452422
$479$	−18228.9	−1.73883	−0.869414	−	0.494084i	$-0.835503\pi$
$479$	−18228.9	−1.73883	−0.869414	+	0.494084i	$0.835503\pi$
$480$	−9547.73	−0.907901
$481$	−5169.61	−0.490050
$482$	−1199.45	−0.113347
$483$	2085.72	0.196488
$484$	1884.79	0.177009
$485$	−20112.5	−1.88301
$486$	−12020.1	−1.12190
$487$	−507.709	−0.0472412	−0.0236206	−	0.999721i	$-0.507519\pi$
$487$	−507.709	−0.0472412	−0.0236206	+	0.999721i	$0.507519\pi$
$488$	−8091.76	−0.750608
$489$	2106.13	0.194770
$490$	−11075.0	−1.02106
$491$	−909.154	−0.0835632	−0.0417816	−	0.999127i	$-0.513303\pi$
$491$	−909.154	−0.0835632	−0.0417816	+	0.999127i	$0.513303\pi$
$492$	−6640.28	−0.608470
$493$	21085.1	1.92622
$494$	12704.9	1.15713
$495$	10068.5	0.914231
$496$	−4019.14	−0.363840
$497$	−73.9824	−0.00667719
$498$	8112.38	0.729969
$499$	18290.1	1.64084	0.820420	−	0.571762i	$-0.193740\pi$
$499$	18290.1	1.64084	0.820420	+	0.571762i	$0.193740\pi$
$500$	−1969.86	−0.176190
$501$	8395.85	0.748700
$502$	10280.3	0.914008
$503$	−3307.69	−0.293206	−0.146603	−	0.989195i	$-0.546834\pi$
$503$	−3307.69	−0.293206	−0.146603	+	0.989195i	$0.546834\pi$
$504$	1399.49	0.123687
$505$	−11077.2	−0.976095
$506$	−8393.16	−0.737395
$507$	−1977.35	−0.173210
$508$	988.225	0.0863099
$509$	−3239.45	−0.282094	−0.141047	−	0.990003i	$-0.545047\pi$
$509$	−3239.45	−0.282094	−0.141047	+	0.990003i	$0.545047\pi$
$510$	25252.6	2.19256
$511$	1385.50	0.119943
$512$	12468.4	1.07623
$513$	−9227.21	−0.794135
$514$	−10450.6	−0.896802
$515$	−8102.90	−0.693313
$516$	0	0
$517$	−9634.28	−0.819565
$518$	−385.433	−0.0326929
$519$	5445.76	0.460583
$520$	16101.1	1.35785
$521$	−12768.2	−1.07367	−0.536837	−	0.843686i	$-0.680381\pi$
$521$	−12768.2	−1.07367	−0.536837	+	0.843686i	$0.680381\pi$
$522$	20253.6	1.69823
$523$	−5646.14	−0.472062	−0.236031	−	0.971746i	$-0.575847\pi$
$523$	−5646.14	−0.472062	−0.236031	+	0.971746i	$0.575847\pi$
$524$	400.527	0.0333914
$525$	−628.535	−0.0522505
$526$	−18238.3	−1.51184
$527$	−8865.63	−0.732814
$528$	−7038.75	−0.580156
$529$	17343.5	1.42545
$530$	−22689.7	−1.85958
$531$	12816.9	1.04747
$532$	−320.645	−0.0261311
$533$	20135.8	1.63636
$534$	−15054.5	−1.21998
$535$	−20247.6	−1.63622
$536$	7523.91	0.606312
$537$	10721.2	0.861553
$538$	−5563.34	−0.445823
$539$	6809.43	0.544161
$540$	−2360.39	−0.188102
$541$	8682.75	0.690020	0.345010	−	0.938599i	$-0.387876\pi$
$541$	8682.75	0.690020	0.345010	+	0.938599i	$0.387876\pi$
$542$	−15019.5	−1.19030
$543$	15793.8	1.24821
$544$	8597.45	0.677597
$545$	−7891.18	−0.620222
$546$	−1466.96	−0.114982
$547$	18179.6	1.42103	0.710516	−	0.703681i	$-0.248461\pi$
$547$	18179.6	1.42103	0.710516	+	0.703681i	$0.248461\pi$
$548$	−4488.17	−0.349863
$549$	−12513.0	−0.972755
$550$	2529.29	0.196089
$551$	−22989.4	−1.77746
$552$	33910.0	2.61468
$553$	1028.41	0.0790823
$554$	−20746.1	−1.59101
$555$	11203.3	0.856850
$556$	−2885.95	−0.220128
$557$	21995.2	1.67319	0.836596	−	0.547821i	$-0.184542\pi$
$557$	21995.2	1.67319	0.836596	+	0.547821i	$0.184542\pi$
$558$	−8515.97	−0.646075
$559$	0	0
$560$	876.123	0.0661124
$561$	−15526.4	−1.16850
$562$	13725.4	1.03020
$563$	5894.15	0.441224	0.220612	−	0.975362i	$-0.429195\pi$
$563$	5894.15	0.441224	0.220612	+	0.975362i	$0.429195\pi$
$564$	7856.86	0.586584
$565$	−9588.56	−0.713971
$566$	8344.24	0.619672
$567$	−476.619	−0.0353018
$568$	−1202.82	−0.0888540
$569$	−23140.1	−1.70489	−0.852446	−	0.522815i	$-0.824882\pi$
$569$	−23140.1	−1.70489	−0.852446	+	0.522815i	$0.824882\pi$
$570$	−27533.3	−2.02323
$571$	16717.7	1.22524	0.612621	−	0.790377i	$-0.290115\pi$
$571$	16717.7	1.22524	0.612621	+	0.790377i	$0.290115\pi$
$572$	−1998.25	−0.146068
$573$	15017.8	1.09490
$574$	1501.27	0.109167
$575$	−8893.01	−0.644981
$576$	21512.3	1.55615
$577$	−4191.15	−0.302391	−0.151196	−	0.988504i	$-0.548312\pi$
$577$	−4191.15	−0.302391	−0.151196	+	0.988504i	$0.548312\pi$
$578$	−10728.2	−0.772029
$579$	12153.7	0.872352
$580$	−5880.86	−0.421016
$581$	620.846	0.0443322
$582$	29791.9	2.12185
$583$	13950.6	0.991039
$584$	22525.6	1.59609
$585$	24898.6	1.75971
$586$	−22439.1	−1.58182
$587$	13306.5	0.935636	0.467818	−	0.883825i	$-0.345040\pi$
$587$	13306.5	0.935636	0.467818	+	0.883825i	$0.345040\pi$
$588$	−5553.16	−0.389470
$589$	9666.32	0.676220
$590$	10994.1	0.767154
$591$	10896.8	0.758434
$592$	−4573.38	−0.317508
$593$	2964.50	0.205290	0.102645	−	0.994718i	$-0.467269\pi$
$593$	2964.50	0.205290	0.102645	+	0.994718i	$0.467269\pi$
$594$	−4287.32	−0.296146
$595$	1932.60	0.133158
$596$	657.385	0.0451804
$597$	10426.1	0.714760
$598$	−20755.7	−1.41934
$599$	−93.2120	−0.00635816	−0.00317908	−	0.999995i	$-0.501012\pi$
$599$	−93.2120	−0.00635816	−0.00317908	+	0.999995i	$0.501012\pi$
$600$	−10218.8	−0.695302
$601$	10239.7	0.694984	0.347492	−	0.937683i	$-0.387033\pi$
$601$	10239.7	0.694984	0.347492	+	0.937683i	$0.387033\pi$
$602$	0	0
$603$	11634.9	0.785754
$604$	−2043.66	−0.137675
$605$	12386.0	0.832338
$606$	16408.2	1.09990
$607$	7367.72	0.492663	0.246331	−	0.969186i	$-0.420775\pi$
$607$	7367.72	0.492663	0.246331	+	0.969186i	$0.420775\pi$
$608$	−9373.92	−0.625268
$609$	2654.45	0.176624
$610$	−10733.5	−0.712434
$611$	−23824.9	−1.57750
$612$	7393.72	0.488355
$613$	4128.99	0.272053	0.136026	−	0.990705i	$-0.456567\pi$
$613$	4128.99	0.272053	0.136026	+	0.990705i	$0.456567\pi$
$614$	17519.6	1.15152
$615$	−43637.1	−2.86116
$616$	−738.095	−0.0482771
$617$	−16159.7	−1.05440	−0.527199	−	0.849742i	$-0.676758\pi$
$617$	−16159.7	−1.05440	−0.527199	+	0.849742i	$0.676758\pi$
$618$	12002.5	0.781251
$619$	−15805.2	−1.02628	−0.513138	−	0.858306i	$-0.671517\pi$
$619$	−15805.2	−1.02628	−0.513138	+	0.858306i	$0.671517\pi$
$620$	2472.71	0.160172
$621$	15074.3	0.974090
$622$	16255.2	1.04787
$623$	−1152.13	−0.0740916
$624$	−17406.3	−1.11668
$625$	−19416.1	−1.24263
$626$	5957.46	0.380364
$627$	16928.7	1.07826
$628$	5626.03	0.357489
$629$	−10088.2	−0.639496
$630$	1856.38	0.117397
$631$	−1609.55	−0.101545	−0.0507726	−	0.998710i	$-0.516168\pi$
$631$	−1609.55	−0.101545	−0.0507726	+	0.998710i	$0.516168\pi$
$632$	16720.1	1.05236
$633$	−27593.2	−1.73259
$634$	−5896.25	−0.369353
$635$	6494.19	0.405849
$636$	−11376.9	−0.709312
$637$	16839.2	1.04740
$638$	−10681.8	−0.662847
$639$	−1860.02	−0.115151
$640$	8971.05	0.554081
$641$	−8288.64	−0.510736	−0.255368	−	0.966844i	$-0.582197\pi$
$641$	−8288.64	−0.510736	−0.255368	+	0.966844i	$0.582197\pi$
$642$	29992.0	1.84376
$643$	−18375.4	−1.12699	−0.563496	−	0.826119i	$-0.690544\pi$
$643$	−18375.4	−1.12699	−0.563496	+	0.826119i	$0.690544\pi$
$644$	523.830	0.0320525
$645$	0	0
$646$	24792.9	1.51001
$647$	−22364.7	−1.35896	−0.679481	−	0.733693i	$-0.737795\pi$
$647$	−22364.7	−1.35896	−0.679481	+	0.733693i	$0.737795\pi$
$648$	−7748.95	−0.469765
$649$	−6759.67	−0.408845
$650$	6254.75	0.377433
$651$	−1116.11	−0.0671949
$652$	528.957	0.0317723
$653$	−9026.60	−0.540946	−0.270473	−	0.962728i	$-0.587180\pi$
$653$	−9026.60	−0.540946	−0.270473	+	0.962728i	$0.587180\pi$
$654$	11688.9	0.698888
$655$	2632.09	0.157014
$656$	17813.5	1.06021
$657$	34833.4	2.06846
$658$	−1776.32	−0.105240
$659$	−14302.0	−0.845413	−0.422707	−	0.906267i	$-0.638920\pi$
$659$	−14302.0	−0.845413	−0.422707	+	0.906267i	$0.638920\pi$
$660$	4330.48	0.255400
$661$	1869.11	0.109985	0.0549925	−	0.998487i	$-0.482487\pi$
$661$	1869.11	0.109985	0.0549925	+	0.998487i	$0.482487\pi$
$662$	−27197.2	−1.59675
$663$	−38395.8	−2.24912
$664$	10093.8	0.589933
$665$	−2107.14	−0.122874
$666$	−9690.33	−0.563803
$667$	37557.3	2.18025
$668$	2108.62	0.122133
$669$	29417.7	1.70008
$670$	9980.22	0.575477
$671$	6599.40	0.379683
$672$	1082.35	0.0621318
$673$	−25729.1	−1.47367	−0.736837	−	0.676071i	$-0.763681\pi$
$673$	−25729.1	−1.47367	−0.736837	+	0.676071i	$0.763681\pi$
$674$	−1756.84	−0.100402
$675$	−4542.65	−0.259032
$676$	−496.613	−0.0282552
$677$	−18088.6	−1.02688	−0.513442	−	0.858124i	$-0.671630\pi$
$677$	−18088.6	−1.02688	−0.513442	+	0.858124i	$0.671630\pi$
$678$	14203.2	0.804529
$679$	2279.99	0.128863
$680$	31420.5	1.77194
$681$	−38915.2	−2.18977
$682$	4491.35	0.252174
$683$	15040.0	0.842588	0.421294	−	0.906924i	$-0.361576\pi$
$683$	15040.0	0.842588	0.421294	+	0.906924i	$0.361576\pi$
$684$	−8061.47	−0.450640
$685$	−29494.3	−1.64514
$686$	2519.35	0.140218
$687$	6713.10	0.372811
$688$	0	0
$689$	34498.9	1.90755
$690$	44980.5	2.48171
$691$	20032.0	1.10283	0.551413	−	0.834232i	$-0.314089\pi$
$691$	20032.0	1.10283	0.551413	+	0.834232i	$0.314089\pi$
$692$	1367.71	0.0751335
$693$	−1141.38	−0.0625650
$694$	−9545.24	−0.522092
$695$	−18965.2	−1.03509
$696$	43156.5	2.35035
$697$	39293.9	2.13538
$698$	−14726.3	−0.798563
$699$	−17501.8	−0.947037
$700$	−157.857	−0.00852346
$701$	9706.13	0.522961	0.261480	−	0.965209i	$-0.415789\pi$
$701$	9706.13	0.522961	0.261480	+	0.965209i	$0.415789\pi$
$702$	−10602.2	−0.570022
$703$	10999.3	0.590109
$704$	−11345.6	−0.607393
$705$	51631.8	2.75825
$706$	8307.72	0.442869
$707$	1255.73	0.0667987
$708$	5512.59	0.292621
$709$	−13899.8	−0.736275	−0.368138	−	0.929771i	$-0.620004\pi$
$709$	−13899.8	−0.736275	−0.368138	+	0.929771i	$0.620004\pi$
$710$	−1595.50	−0.0843351
$711$	25855.7	1.36381
$712$	−18731.5	−0.985944
$713$	−15791.6	−0.829455
$714$	−2862.69	−0.150047
$715$	−13131.6	−0.686845
$716$	2692.63	0.140543
$717$	15579.3	0.811466
$718$	−25793.2	−1.34066
$719$	23427.1	1.21514	0.607568	−	0.794268i	$-0.292145\pi$
$719$	23427.1	1.21514	0.607568	+	0.794268i	$0.292145\pi$
$720$	22027.0	1.14014
$721$	918.561	0.0474466
$722$	−10263.5	−0.529041
$723$	−3952.25	−0.203300
$724$	3966.62	0.203616
$725$	−11317.9	−0.579776
$726$	−18347.0	−0.937908
$727$	28409.8	1.44933	0.724663	−	0.689104i	$-0.241996\pi$
$727$	28409.8	1.44933	0.724663	+	0.689104i	$0.241996\pi$
$728$	−1825.26	−0.0929238
$729$	−31068.7	−1.57846
$730$	29879.5	1.51492
$731$	0	0
$732$	−5381.89	−0.271749
$733$	7464.74	0.376148	0.188074	−	0.982155i	$-0.439775\pi$
$733$	7464.74	0.376148	0.188074	+	0.982155i	$0.439775\pi$
$734$	−17531.5	−0.881606
$735$	−36493.0	−1.83138
$736$	15314.0	0.766957
$737$	−6136.28	−0.306693
$738$	37744.1	1.88263
$739$	16315.6	0.812150	0.406075	−	0.913840i	$-0.366897\pi$
$739$	16315.6	0.812150	0.406075	+	0.913840i	$0.366897\pi$
$740$	2813.70	0.139775
$741$	41863.4	2.07543
$742$	2572.15	0.127260
$743$	5142.26	0.253905	0.126952	−	0.991909i	$-0.459480\pi$
$743$	5142.26	0.253905	0.126952	+	0.991909i	$0.459480\pi$
$744$	−18145.9	−0.894169
$745$	4320.05	0.212449
$746$	−913.871	−0.0448515
$747$	15608.9	0.764527
$748$	−3899.47	−0.190613
$749$	2295.31	0.111974
$750$	19175.1	0.933568
$751$	−4595.89	−0.223311	−0.111656	−	0.993747i	$-0.535615\pi$
$751$	−4595.89	−0.223311	−0.111656	+	0.993747i	$0.535615\pi$
$752$	−21077.1	−1.02208
$753$	33874.2	1.63937
$754$	−26415.3	−1.27585
$755$	−13430.1	−0.647378
$756$	267.578	0.0128727
$757$	−26851.1	−1.28919	−0.644597	−	0.764523i	$-0.722975\pi$
$757$	−26851.1	−1.28919	−0.644597	+	0.764523i	$0.722975\pi$
$758$	6619.47	0.317190
$759$	−27656.0	−1.32259
$760$	−34258.2	−1.63510
$761$	−19351.7	−0.921813	−0.460906	−	0.887449i	$-0.652476\pi$
$761$	−19351.7	−0.921813	−0.460906	+	0.887449i	$0.652476\pi$
$762$	−9619.61	−0.457325
$763$	894.560	0.0424446
$764$	3771.73	0.178608
$765$	48588.3	2.29636
$766$	10236.8	0.482860
$767$	−16716.2	−0.786945
$768$	23297.6	1.09463
$769$	9736.85	0.456593	0.228296	−	0.973592i	$-0.426684\pi$
$769$	9736.85	0.456593	0.228296	+	0.973592i	$0.426684\pi$
$770$	−979.059	−0.0458219
$771$	−34435.4	−1.60851
$772$	3052.41	0.142304
$773$	−24615.9	−1.14537	−0.572685	−	0.819775i	$-0.694098\pi$
$773$	−24615.9	−1.14537	−0.572685	+	0.819775i	$0.694098\pi$
$774$	0	0
$775$	4758.83	0.220570
$776$	37068.5	1.71479
$777$	−1270.02	−0.0586382
$778$	8015.28	0.369359
$779$	−42842.7	−1.97047
$780$	10709.0	0.491593
$781$	980.982	0.0449453
$782$	−40503.6	−1.85218
$783$	19184.7	0.875613
$784$	14897.1	0.678622
$785$	36971.8	1.68099
$786$	−3898.82	−0.176929
$787$	16844.6	0.762955	0.381477	−	0.924378i	$-0.375415\pi$
$787$	16844.6	0.762955	0.381477	+	0.924378i	$0.375415\pi$
$788$	2736.73	0.123721
$789$	−60096.4	−2.71165
$790$	22178.6	0.998836
$791$	1086.98	0.0488603
$792$	−18556.8	−0.832558
$793$	16319.9	0.730814
$794$	25872.9	1.15642
$795$	−74763.9	−3.33535
$796$	2618.52	0.116597
$797$	31705.8	1.40913	0.704566	−	0.709638i	$-0.251142\pi$
$797$	31705.8	1.40913	0.704566	+	0.709638i	$0.251142\pi$
$798$	3121.23	0.138459
$799$	−46492.9	−2.05858
$800$	−4614.88	−0.203951
$801$	−28966.2	−1.27774
$802$	−17039.8	−0.750245
$803$	−18371.2	−0.807356
$804$	5004.20	0.219508
$805$	3442.38	0.150718
$806$	11106.8	0.485385
$807$	−18331.6	−0.799630
$808$	20415.9	0.888896
$809$	−9917.38	−0.430997	−0.215498	−	0.976504i	$-0.569138\pi$
$809$	−9917.38	−0.430997	−0.215498	+	0.976504i	$0.569138\pi$
$810$	−10278.7	−0.445874
$811$	−34830.2	−1.50808	−0.754041	−	0.656828i	$-0.771898\pi$
$811$	−34830.2	−1.50808	−0.754041	+	0.656828i	$0.771898\pi$
$812$	666.667	0.0288121
$813$	−49490.2	−2.13493
$814$	5110.71	0.220062
$815$	3476.07	0.149401
$816$	−33967.5	−1.45723
$817$	0	0
$818$	−19335.4	−0.826461
$819$	−2822.56	−0.120425
$820$	−10959.5	−0.466733
$821$	−11834.0	−0.503056	−0.251528	−	0.967850i	$-0.580933\pi$
$821$	−11834.0	−0.503056	−0.251528	+	0.967850i	$0.580933\pi$
$822$	43688.8	1.85380
$823$	1274.38	0.0539757	0.0269879	−	0.999636i	$-0.491408\pi$
$823$	1274.38	0.0539757	0.0269879	+	0.999636i	$0.491408\pi$
$824$	14934.1	0.631376
$825$	8334.16	0.351707
$826$	−1246.32	−0.0524999
$827$	28342.9	1.19175	0.595876	−	0.803076i	$-0.296805\pi$
$827$	28342.9	1.19175	0.595876	+	0.803076i	$0.296805\pi$
$828$	13169.8	0.552758
$829$	39168.9	1.64100	0.820501	−	0.571644i	$-0.193694\pi$
$829$	39168.9	1.64100	0.820501	+	0.571644i	$0.193694\pi$
$830$	13389.1	0.559930
$831$	−68359.8	−2.85364
$832$	−28057.0	−1.16911
$833$	32860.8	1.36682
$834$	28092.5	1.16638
$835$	13856.9	0.574298
$836$	4251.65	0.175893
$837$	−8066.55	−0.333119
$838$	−22119.1	−0.911803
$839$	8161.55	0.335838	0.167919	−	0.985801i	$-0.446295\pi$
$839$	8161.55	0.335838	0.167919	+	0.985801i	$0.446295\pi$
$840$	3955.59	0.162477
$841$	23409.3	0.959831
$842$	11774.5	0.481920
$843$	45226.1	1.84777
$844$	−6930.03	−0.282632
$845$	−3263.52	−0.132862
$846$	−44659.3	−1.81491
$847$	−1404.11	−0.0569607
$848$	30520.1	1.23592
$849$	27494.8	1.11145
$850$	12205.8	0.492536
$851$	−17969.3	−0.723831
$852$	−800.002	−0.0321685
$853$	−1042.20	−0.0418337	−0.0209169	−	0.999781i	$-0.506659\pi$
$853$	−1042.20	−0.0418337	−0.0209169	+	0.999781i	$0.506659\pi$
$854$	1216.77	0.0487551
$855$	−52976.5	−2.11901
$856$	37317.5	1.49005
$857$	42411.7	1.69050	0.845249	−	0.534373i	$-0.179452\pi$
$857$	42411.7	1.69050	0.845249	+	0.534373i	$0.179452\pi$
$858$	19451.4	0.773962
$859$	−23599.2	−0.937361	−0.468681	−	0.883368i	$-0.655270\pi$
$859$	−23599.2	−0.937361	−0.468681	+	0.883368i	$0.655270\pi$
$860$	0	0
$861$	4946.79	0.195803
$862$	9333.94	0.368811
$863$	−37727.6	−1.48814	−0.744068	−	0.668104i	$-0.767106\pi$
$863$	−37727.6	−1.48814	−0.744068	+	0.668104i	$0.767106\pi$
$864$	7822.54	0.308019
$865$	8987.96	0.353295
$866$	26242.4	1.02974
$867$	−35350.0	−1.38471
$868$	−280.312	−0.0109613
$869$	−13636.4	−0.532317
$870$	57245.7	2.23082
$871$	−15174.6	−0.590323
$872$	14543.9	0.564815
$873$	57322.3	2.22230
$874$	44161.6	1.70914
$875$	1467.48	0.0566971
$876$	14981.9	0.577845
$877$	−42264.0	−1.62731	−0.813656	−	0.581346i	$-0.802526\pi$
$877$	−42264.0	−1.62731	−0.813656	+	0.581346i	$0.802526\pi$
$878$	24642.2	0.947191
$879$	−73938.1	−2.83717
$880$	−11617.1	−0.445014
$881$	11404.2	0.436114	0.218057	−	0.975936i	$-0.430028\pi$
$881$	11404.2	0.436114	0.218057	+	0.975936i	$0.430028\pi$
$882$	31564.8	1.20504
$883$	−11567.7	−0.440864	−0.220432	−	0.975402i	$-0.570747\pi$
$883$	−11567.7	−0.440864	−0.220432	+	0.975402i	$0.570747\pi$
$884$	−9643.11	−0.366892
$885$	36226.3	1.37597
$886$	8357.73	0.316911
$887$	−31451.6	−1.19058	−0.595288	−	0.803512i	$-0.702962\pi$
$887$	−31451.6	−1.19058	−0.595288	+	0.803512i	$0.702962\pi$
$888$	−20648.3	−0.780304
$889$	−736.194	−0.0277741
$890$	−24846.7	−0.935801
$891$	6319.82	0.237623
$892$	7388.26	0.277329
$893$	50691.9	1.89960
$894$	−6399.14	−0.239395
$895$	17694.8	0.660863
$896$	−1016.98	−0.0379183
$897$	−68391.3	−2.54573
$898$	9004.93	0.334631
$899$	−20097.7	−0.745600
$900$	−3968.74	−0.146990
$901$	67322.7	2.48928
$902$	−19906.4	−0.734823
$903$	0	0
$904$	17672.3	0.650189
$905$	26066.9	0.957451
$906$	19893.5	0.729489
$907$	39084.0	1.43083	0.715414	−	0.698701i	$-0.246238\pi$
$907$	39084.0	1.43083	0.715414	+	0.698701i	$0.246238\pi$
$908$	−9773.57	−0.357211
$909$	31570.9	1.15197
$910$	−2421.14	−0.0881979
$911$	−27906.3	−1.01490	−0.507452	−	0.861680i	$-0.669412\pi$
$911$	−27906.3	−1.01490	−0.507452	+	0.861680i	$0.669412\pi$
$912$	37035.2	1.34469
$913$	−8232.21	−0.298408
$914$	−9288.40	−0.336141
$915$	−35367.4	−1.27783
$916$	1686.00	0.0608154
$917$	−298.379	−0.0107452
$918$	−20689.7	−0.743858
$919$	−28865.1	−1.03609	−0.518047	−	0.855352i	$-0.673341\pi$
$919$	−28865.1	−1.03609	−0.518047	+	0.855352i	$0.673341\pi$
$920$	55966.8	2.00562
$921$	57728.1	2.06537
$922$	9841.52	0.351533
$923$	2425.90	0.0865108
$924$	−490.912	−0.0174782
$925$	5415.07	0.192483
$926$	10996.2	0.390234
$927$	23093.9	0.818236
$928$	19489.7	0.689420
$929$	−51121.7	−1.80544	−0.902718	−	0.430234i	$-0.858431\pi$
$929$	−51121.7	−1.80544	−0.902718	+	0.430234i	$0.858431\pi$
$930$	−24070.0	−0.848694
$931$	−35828.6	−1.26126
$932$	−4395.58	−0.154487
$933$	53561.7	1.87946
$934$	−14885.5	−0.521486
$935$	−25625.6	−0.896307
$936$	−45889.6	−1.60251
$937$	14721.1	0.513252	0.256626	−	0.966511i	$-0.417389\pi$
$937$	14721.1	0.513252	0.256626	+	0.966511i	$0.417389\pi$
$938$	−1131.38	−0.0393825
$939$	19630.2	0.682223
$940$	12967.4	0.449945
$941$	9191.00	0.318404	0.159202	−	0.987246i	$-0.449108\pi$
$941$	9191.00	0.318404	0.159202	+	0.987246i	$0.449108\pi$
$942$	−54765.0	−1.89420
$943$	69991.1	2.41699
$944$	−14788.3	−0.509870
$945$	1758.41	0.0605302
$946$	0	0
$947$	29365.9	1.00767	0.503835	−	0.863800i	$-0.331922\pi$
$947$	29365.9	1.00767	0.503835	+	0.863800i	$0.331922\pi$
$948$	11120.6	0.380993
$949$	−45430.7	−1.55400
$950$	−13308.2	−0.454498
$951$	−19428.5	−0.662474
$952$	−3561.89	−0.121262
$953$	38650.9	1.31377	0.656887	−	0.753989i	$-0.271873\pi$
$953$	38650.9	1.31377	0.656887	+	0.753989i	$0.271873\pi$
$954$	64667.5	2.19464
$955$	24786.2	0.839856
$956$	3912.76	0.132372
$957$	−35197.2	−1.18888
$958$	44565.1	1.50296
$959$	3343.53	0.112584
$960$	60803.3	2.04419
$961$	−21340.6	−0.716343
$962$	12638.4	0.423575
$963$	57707.3	1.93104
$964$	−992.610	−0.0331637
$965$	20059.1	0.669146
$966$	−5099.08	−0.169835
$967$	−37964.3	−1.26251	−0.631256	−	0.775574i	$-0.717460\pi$
$967$	−37964.3	−1.26251	−0.631256	+	0.775574i	$0.717460\pi$
$968$	−22828.2	−0.757981
$969$	81694.2	2.70836
$970$	49170.1	1.62758
$971$	−1349.75	−0.0446091	−0.0223045	−	0.999751i	$-0.507100\pi$
$971$	−1349.75	−0.0446091	−0.0223045	+	0.999751i	$0.507100\pi$
$972$	−9947.29	−0.328251
$973$	2149.93	0.0708362
$974$	1241.22	0.0408330
$975$	20609.8	0.676966
$976$	14437.6	0.473502
$977$	−15711.0	−0.514471	−0.257236	−	0.966349i	$-0.582812\pi$
$977$	−15711.0	−0.514471	−0.257236	+	0.966349i	$0.582812\pi$
$978$	−5148.98	−0.168350
$979$	15276.8	0.498723
$980$	−9165.22	−0.298747
$981$	22490.5	0.731975
$982$	2222.66	0.0722280
$983$	20977.9	0.680663	0.340332	−	0.940305i	$-0.389461\pi$
$983$	20977.9	0.680663	0.340332	+	0.940305i	$0.389461\pi$
$984$	80425.6	2.60556
$985$	17984.6	0.581764
$986$	−51548.0	−1.66493
$987$	−5853.09	−0.188760
$988$	10514.0	0.338558
$989$	0	0
$990$	−24614.9	−0.790216
$991$	48127.0	1.54269	0.771345	−	0.636417i	$-0.219584\pi$
$991$	48127.0	1.54269	0.771345	+	0.636417i	$0.219584\pi$
$992$	−8194.81	−0.262284
$993$	−89616.4	−2.86394
$994$	180.869	0.00577144
$995$	17207.8	0.548264
$996$	6713.45	0.213578
$997$	−4405.84	−0.139954	−0.0699771	−	0.997549i	$-0.522293\pi$
$997$	−4405.84	−0.139954	−0.0699771	+	0.997549i	$0.522293\pi$
$998$	−44714.9	−1.41826
$999$	−9178.93	−0.290699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.j.1.13	yes	50
43.42	odd	2		1849.4.a.i.1.38	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.38	✓	50	43.42	odd	2
1849.4.a.j.1.13	yes	50	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.44476 q^{2} -8.05562 q^{3} -2.02317 q^{4} -13.2954 q^{5} +19.6940 q^{6} +1.50720 q^{7} +24.5042 q^{8} +37.8930 q^{9} +O(q^{10})\)	\(q-2.44476 q^{2} -8.05562 q^{3} -2.02317 q^{4} -13.2954 q^{5} +19.6940 q^{6} +1.50720 q^{7} +24.5042 q^{8} +37.8930 q^{9} +32.5040 q^{10} -19.9849 q^{11} +16.2979 q^{12} -49.4213 q^{13} -3.68472 q^{14} +107.103 q^{15} -43.7214 q^{16} -96.4429 q^{17} -92.6392 q^{18} +105.153 q^{19} +26.8989 q^{20} -12.1414 q^{21} +48.8582 q^{22} -171.786 q^{23} -197.397 q^{24} +51.7679 q^{25} +120.823 q^{26} -87.7502 q^{27} -3.04932 q^{28} -218.628 q^{29} -261.840 q^{30} +91.9262 q^{31} -89.1455 q^{32} +160.991 q^{33} +235.779 q^{34} -20.0388 q^{35} -76.6642 q^{36} +104.603 q^{37} -257.073 q^{38} +398.119 q^{39} -325.793 q^{40} -407.432 q^{41} +29.6827 q^{42} +40.4329 q^{44} -503.804 q^{45} +419.975 q^{46} +482.077 q^{47} +352.203 q^{48} -340.728 q^{49} -126.560 q^{50} +776.908 q^{51} +99.9878 q^{52} -698.058 q^{53} +214.528 q^{54} +265.708 q^{55} +36.9326 q^{56} -847.073 q^{57} +534.493 q^{58} +338.239 q^{59} -216.687 q^{60} -330.219 q^{61} -224.737 q^{62} +57.1122 q^{63} +567.710 q^{64} +657.076 q^{65} -393.583 q^{66} +307.046 q^{67} +195.121 q^{68} +1383.84 q^{69} +48.9899 q^{70} -49.0861 q^{71} +928.539 q^{72} +919.255 q^{73} -255.728 q^{74} -417.023 q^{75} -212.743 q^{76} -30.1212 q^{77} -973.304 q^{78} +682.335 q^{79} +581.294 q^{80} -316.229 q^{81} +996.070 q^{82} +411.921 q^{83} +24.5641 q^{84} +1282.25 q^{85} +1761.19 q^{87} -489.714 q^{88} -764.419 q^{89} +1231.68 q^{90} -74.4875 q^{91} +347.553 q^{92} -740.523 q^{93} -1178.56 q^{94} -1398.05 q^{95} +718.123 q^{96} +1512.74 q^{97} +832.997 q^{98} -757.289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 10 q^{2} + 2 q^{3} + 186 q^{4} - 8 q^{5} - 51 q^{6} + 6 q^{7} + 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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