LMFDB - Embedded newform 1849.4.a.i.1.38

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			1.38
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	$-0.357746\pi$
$2$	2.44476	0.864351	0.432176	+	0.901789i	$0.357746\pi$
$3$	8.05562	1.55031	0.775153	−	0.631774i	$-0.217673\pi$
$3$	8.05562	1.55031	0.775153	+	0.631774i	$0.217673\pi$
$4$	−2.02317	−0.252897
$5$	13.2954	1.18918	0.594589	−	0.804030i	$-0.297315\pi$
$5$	13.2954	1.18918	0.594589	+	0.804030i	$0.297315\pi$
$6$	19.6940	1.34001
$7$	−1.50720	−0.0813809	−0.0406904	−	0.999172i	$-0.512956\pi$
$7$	−1.50720	−0.0813809	−0.0406904	+	0.999172i	$0.512956\pi$
$8$	−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	$-0.718932\pi$
$19$	−105.153	−1.26967	−0.634836	+	0.772647i	$0.718932\pi$
$20$	−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	$-0.253197\pi$
$29$	218.628	1.39994	0.699970	+	0.714172i	$0.253197\pi$
$30$	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	$-0.574653\pi$
$37$	−104.603	−0.464773	−0.232387	+	0.972623i	$0.574653\pi$
$38$	−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	$-0.387350\pi$
$61$	330.219	0.693119	0.346559	+	0.938028i	$0.387350\pi$
$62$	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	$-0.486938\pi$
$71$	49.0861	0.0820486	0.0410243	+	0.999158i	$0.486938\pi$
$72$	−928.539	−1.51985
$73$	−919.255	−1.47384	−0.736922	−	0.675978i	$-0.763722\pi$
$73$	−919.255	−1.47384	−0.736922	+	0.675978i	$0.763722\pi$
$74$	−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	$-0.349562\pi$
$89$	764.419	0.910430	0.455215	+	0.890382i	$0.349562\pi$
$90$	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	$-0.597052\pi$
$113$	−721.193	−0.600391	−0.300195	+	0.953878i	$0.597052\pi$
$114$	−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	$-0.478971\pi$
$131$	197.970	0.132036	0.0660180	+	0.997818i	$0.478971\pi$
$132$	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	$-0.743143\pi$
$137$	−2218.38	−1.38342	−0.691712	+	0.722174i	$0.743143\pi$
$138$	−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	$-0.471529\pi$
$149$	324.928	0.178652	0.0893259	+	0.996002i	$0.471529\pi$
$150$	1019.52	0.554955
$151$	−1010.13	−0.544391	−0.272196	−	0.962242i	$-0.587750\pi$
$151$	−1010.13	−0.544391	−0.272196	+	0.962242i	$0.587750\pi$
$152$	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	$-0.250143\pi$
$157$	2780.79	1.41358	0.706788	+	0.707425i	$0.250143\pi$
$158$	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	$-0.479992\pi$
$163$	261.449	0.125634	0.0628168	+	0.998025i	$0.479992\pi$
$164$	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	$-0.410373\pi$
$179$	1330.90	0.555731	0.277866	+	0.960620i	$0.410373\pi$
$180$	−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	$-0.385119\pi$
$191$	1864.27	0.706249	0.353125	+	0.935576i	$0.385119\pi$
$192$	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	$-0.425957\pi$
$199$	1294.26	0.461045	0.230522	+	0.973067i	$0.425957\pi$
$200$	−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	$-0.688734\pi$
$211$	−3425.33	−1.11758	−0.558790	+	0.829309i	$0.688734\pi$
$212$	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	$-0.315273\pi$
$223$	3651.82	1.09661	0.548305	+	0.836278i	$0.315273\pi$
$224$	−134.360	−0.0400772
$225$	1961.64	0.581228
$226$	−1763.14	−0.518949
$227$	−4830.81	−1.41248	−0.706239	−	0.707974i	$-0.749609\pi$
$227$	−4830.81	−1.41248	−0.706239	+	0.707974i	$0.749609\pi$
$228$	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	$-0.598802\pi$
$233$	−2172.62	−0.610872	−0.305436	+	0.952213i	$0.598802\pi$
$234$	−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	$-0.520886\pi$
$241$	−490.620	−0.131135	−0.0655677	+	0.997848i	$0.520886\pi$
$242$	−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	$-0.673611\pi$
$257$	−4274.70	−1.03754	−0.518772	+	0.854913i	$0.673611\pi$
$258$	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	$-0.838845\pi$
$263$	−7460.19	−1.74911	−0.874553	+	0.484931i	$0.838845\pi$
$264$	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	$-0.872094\pi$
$277$	−8485.97	−1.84070	−0.920348	+	0.391101i	$0.872094\pi$
$278$	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	$-0.429385\pi$
$313$	2436.83	0.440057	0.220029	+	0.975493i	$0.429385\pi$
$314$	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	$-0.874825\pi$
$331$	−11124.7	−1.84734	−0.923669	+	0.383190i	$0.874825\pi$
$332$	−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	$-0.597659\pi$
$347$	−3904.37	−0.604028	−0.302014	+	0.953303i	$0.597659\pi$
$348$	−3563.18	−0.548870
$349$	−6023.61	−0.923887	−0.461943	−	0.886909i	$-0.652848\pi$
$349$	−6023.61	−0.923887	−0.461943	+	0.886909i	$0.652848\pi$
$350$	−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	$-0.508260\pi$
$373$	−373.809	−0.0518903	−0.0259452	+	0.999663i	$0.508260\pi$
$374$	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	$-0.409891\pi$
$383$	4187.25	0.558638	0.279319	+	0.960198i	$0.409891\pi$
$384$	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	$-0.431461\pi$
$389$	3278.56	0.427326	0.213663	+	0.976907i	$0.431461\pi$
$390$	−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	$-0.658668\pi$
$409$	−7908.92	−0.956163	−0.478082	+	0.878315i	$0.658668\pi$
$410$	−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	$-0.676852\pi$
$419$	−9047.57	−1.05490	−0.527449	+	0.849587i	$0.676852\pi$
$420$	326.590	0.0379428
$421$	4816.23	0.557551	0.278775	−	0.960356i	$-0.410072\pi$
$421$	4816.23	0.557551	0.278775	+	0.960356i	$0.410072\pi$
$422$	−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	$-0.296886\pi$
$433$	10734.2	1.19134	0.595672	+	0.803228i	$0.296886\pi$
$434$	−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	$-0.437992\pi$
$449$	3683.37	0.387147	0.193573	+	0.981086i	$0.437992\pi$
$450$	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	$-0.562291\pi$
$457$	−3799.32	−0.388894	−0.194447	+	0.980913i	$0.562291\pi$
$458$	−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	$-0.427521\pi$
$463$	4497.86	0.451476	0.225738	+	0.974188i	$0.427521\pi$
$464$	−9558.73	−0.956364
$465$	9845.55	0.981885
$466$	−5311.52	−0.528008
$467$	−6088.74	−0.603326	−0.301663	−	0.953415i	$-0.597542\pi$
$467$	−6088.74	−0.603326	−0.301663	+	0.953415i	$0.597542\pi$
$468$	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	$-0.486697\pi$
$491$	909.154	0.0835632	0.0417816	+	0.999127i	$0.486697\pi$
$492$	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	$-0.806260\pi$
$499$	−18290.1	−1.64084	−0.820420	+	0.571762i	$0.806260\pi$
$500$	1969.86	0.176190
$501$	−8395.85	−0.748700
$502$	−10280.3	−0.914008
$503$	3307.69	0.293206	0.146603	−	0.989195i	$-0.453166\pi$
$503$	3307.69	0.293206	0.146603	+	0.989195i	$0.453166\pi$
$504$	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	$-0.319619\pi$
$521$	12768.2	1.07367	0.536837	+	0.843686i	$0.319619\pi$
$522$	20253.6	1.69823
$523$	5646.14	0.472062	0.236031	−	0.971746i	$-0.424153\pi$
$523$	5646.14	0.472062	0.236031	+	0.971746i	$0.424153\pi$
$524$	−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	$-0.709885\pi$
$571$	−16717.7	−1.22524	−0.612621	+	0.790377i	$0.709885\pi$
$572$	−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	$-0.451688\pi$
$577$	4191.15	0.302391	0.151196	+	0.988504i	$0.451688\pi$
$578$	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	$-0.654960\pi$
$587$	−13306.5	−0.935636	−0.467818	+	0.883825i	$0.654960\pi$
$588$	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	$-0.532731\pi$
$593$	−2964.50	−0.205290	−0.102645	+	0.994718i	$0.532731\pi$
$594$	−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	$-0.612967\pi$
$601$	−10239.7	−0.694984	−0.347492	+	0.937683i	$0.612967\pi$
$602$	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	$-0.579225\pi$
$607$	−7367.72	−0.492663	−0.246331	+	0.969186i	$0.579225\pi$
$608$	−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	$-0.483832\pi$
$631$	1609.55	0.101545	0.0507726	+	0.998710i	$0.483832\pi$
$632$	−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	$-0.417803\pi$
$641$	8288.64	0.510736	0.255368	+	0.966844i	$0.417803\pi$
$642$	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	$-0.262205\pi$
$647$	22364.7	1.35896	0.679481	+	0.733693i	$0.262205\pi$
$648$	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	$-0.412820\pi$
$653$	9026.60	0.540946	0.270473	+	0.962728i	$0.412820\pi$
$654$	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	$-0.236319\pi$
$673$	25729.1	1.47367	0.736837	+	0.676071i	$0.236319\pi$
$674$	1756.84	0.100402
$675$	4542.65	0.259032
$676$	−496.613	−0.0282552
$677$	18088.6	1.02688	0.513442	−	0.858124i	$-0.328370\pi$
$677$	18088.6	1.02688	0.513442	+	0.858124i	$0.328370\pi$
$678$	−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	$-0.685911\pi$
$691$	−20032.0	−1.10283	−0.551413	+	0.834232i	$0.685911\pi$
$692$	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	$-0.758004\pi$
$727$	−28409.8	−1.44933	−0.724663	+	0.689104i	$0.758004\pi$
$728$	−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	$-0.560225\pi$
$733$	−7464.74	−0.376148	−0.188074	+	0.982155i	$0.560225\pi$
$734$	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	$-0.633103\pi$
$739$	−16315.6	−0.812150	−0.406075	+	0.913840i	$0.633103\pi$
$740$	2813.70	0.139775
$741$	41863.4	2.07543
$742$	2572.15	0.127260
$743$	−5142.26	−0.253905	−0.126952	−	0.991909i	$-0.540520\pi$
$743$	−5142.26	−0.253905	−0.126952	+	0.991909i	$0.540520\pi$
$744$	−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	$-0.464385\pi$
$751$	4595.89	0.223311	0.111656	+	0.993747i	$0.464385\pi$
$752$	−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	$-0.277025\pi$
$757$	26851.1	1.28919	0.644597	+	0.764523i	$0.277025\pi$
$758$	−6619.47	−0.317190
$759$	27656.0	1.32259
$760$	34258.2	1.63510
$761$	19351.7	0.921813	0.460906	−	0.887449i	$-0.347524\pi$
$761$	19351.7	0.921813	0.460906	+	0.887449i	$0.347524\pi$
$762$	−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	$-0.305902\pi$
$773$	24615.9	1.14537	0.572685	+	0.819775i	$0.305902\pi$
$774$	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	$-0.228102\pi$
$811$	34830.2	1.50808	0.754041	+	0.656828i	$0.228102\pi$
$812$	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	$-0.806306\pi$
$829$	−39168.9	−1.64100	−0.820501	+	0.571644i	$0.806306\pi$
$830$	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	$-0.553705\pi$
$839$	−8161.55	−0.335838	−0.167919	+	0.985801i	$0.553705\pi$
$840$	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	$-0.344730\pi$
$859$	23599.2	0.937361	0.468681	+	0.883368i	$0.344730\pi$
$860$	0	0
$861$	4946.79	0.195803
$862$	−9333.94	−0.368811
$863$	37727.6	1.48814	0.744068	−	0.668104i	$-0.232894\pi$
$863$	37727.6	1.48814	0.744068	+	0.668104i	$0.232894\pi$
$864$	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	$-0.297038\pi$
$887$	31451.6	1.19058	0.595288	+	0.803512i	$0.297038\pi$
$888$	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	$-0.330588\pi$
$911$	27906.3	1.01490	0.507452	+	0.861680i	$0.330588\pi$
$912$	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	$-0.141569\pi$
$929$	51121.7	1.80544	0.902718	+	0.430234i	$0.141569\pi$
$930$	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	$-0.582611\pi$
$937$	−14721.1	−0.513252	−0.256626	+	0.966511i	$0.582611\pi$
$938$	−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	$-0.728127\pi$
$953$	−38650.9	−1.31377	−0.656887	+	0.753989i	$0.728127\pi$
$954$	−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	$-0.610539\pi$
$983$	−20977.9	−0.680663	−0.340332	+	0.940305i	$0.610539\pi$
$984$	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	$-0.780416\pi$
$991$	−48127.0	−1.54269	−0.771345	+	0.636417i	$0.780416\pi$
$992$	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	$-0.477707\pi$
$997$	4405.84	0.139954	0.0699771	+	0.997549i	$0.477707\pi$
$998$	−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.i.1.38	✓	50
43.42	odd	2		1849.4.a.j.1.13	yes	50

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

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