LMFDB - Embedded newform 1849.4.a.i.1.32

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			1.32
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)

$f(q)$	$=$	$q+1.67189 q^{2} +3.03153 q^{3} -5.20480 q^{4} -19.6184 q^{5} +5.06836 q^{6} +28.4637 q^{7} -22.0769 q^{8} -17.8099 q^{9} +O(q^{10})$	\(q+1.67189 q^{2} +3.03153 q^{3} -5.20480 q^{4} -19.6184 q^{5} +5.06836 q^{6} +28.4637 q^{7} -22.0769 q^{8} -17.8099 q^{9} -32.7997 q^{10} -28.1590 q^{11} -15.7785 q^{12} +20.8592 q^{13} +47.5880 q^{14} -59.4736 q^{15} +4.72834 q^{16} +24.2325 q^{17} -29.7760 q^{18} +118.903 q^{19} +102.110 q^{20} +86.2883 q^{21} -47.0785 q^{22} +61.3604 q^{23} -66.9267 q^{24} +259.881 q^{25} +34.8741 q^{26} -135.842 q^{27} -148.148 q^{28} +70.4167 q^{29} -99.4331 q^{30} +263.721 q^{31} +184.521 q^{32} -85.3646 q^{33} +40.5139 q^{34} -558.411 q^{35} +92.6967 q^{36} -360.375 q^{37} +198.791 q^{38} +63.2350 q^{39} +433.113 q^{40} +67.4488 q^{41} +144.264 q^{42} +146.562 q^{44} +349.401 q^{45} +102.588 q^{46} -457.632 q^{47} +14.3341 q^{48} +467.180 q^{49} +434.491 q^{50} +73.4614 q^{51} -108.568 q^{52} -148.507 q^{53} -227.113 q^{54} +552.433 q^{55} -628.390 q^{56} +360.456 q^{57} +117.729 q^{58} -182.072 q^{59} +309.548 q^{60} +215.513 q^{61} +440.912 q^{62} -506.934 q^{63} +270.670 q^{64} -409.223 q^{65} -142.720 q^{66} -631.508 q^{67} -126.125 q^{68} +186.016 q^{69} -933.599 q^{70} -575.441 q^{71} +393.187 q^{72} -1111.81 q^{73} -602.505 q^{74} +787.836 q^{75} -618.864 q^{76} -801.507 q^{77} +105.722 q^{78} -622.227 q^{79} -92.7624 q^{80} +69.0570 q^{81} +112.767 q^{82} -475.871 q^{83} -449.113 q^{84} -475.402 q^{85} +213.470 q^{87} +621.663 q^{88} -1393.87 q^{89} +584.158 q^{90} +593.728 q^{91} -319.369 q^{92} +799.478 q^{93} -765.109 q^{94} -2332.68 q^{95} +559.379 q^{96} +1066.32 q^{97} +781.071 q^{98} +501.507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.67189	0.591101	0.295550	−	0.955327i	$-0.404497\pi$
$2$	1.67189	0.591101	0.295550	+	0.955327i	$0.404497\pi$
$3$	3.03153	0.583417	0.291709	−	0.956507i	$-0.405776\pi$
$3$	3.03153	0.583417	0.291709	+	0.956507i	$0.405776\pi$
$4$	−5.20480	−0.650600
$5$	−19.6184	−1.75472	−0.877361	−	0.479831i	$-0.840698\pi$
$5$	−19.6184	−1.75472	−0.877361	+	0.479831i	$0.840698\pi$
$6$	5.06836	0.344858
$7$	28.4637	1.53689	0.768447	−	0.639914i	$-0.221030\pi$
$7$	28.4637	1.53689	0.768447	+	0.639914i	$0.221030\pi$
$8$	−22.0769	−0.975671
$9$	−17.8099	−0.659624
$10$	−32.7997	−1.03722
$11$	−28.1590	−0.771840	−0.385920	−	0.922532i	$-0.626116\pi$
$11$	−28.1590	−0.771840	−0.385920	+	0.922532i	$0.626116\pi$
$12$	−15.7785	−0.379571
$13$	20.8592	0.445022	0.222511	−	0.974930i	$-0.428575\pi$
$13$	20.8592	0.445022	0.222511	+	0.974930i	$0.428575\pi$
$14$	47.5880	0.908459
$15$	−59.4736	−1.02374
$16$	4.72834	0.0738803
$17$	24.2325	0.345720	0.172860	−	0.984946i	$-0.444699\pi$
$17$	24.2325	0.345720	0.172860	+	0.984946i	$0.444699\pi$
$18$	−29.7760	−0.389904
$19$	118.903	1.43569	0.717845	−	0.696203i	$-0.245128\pi$
$19$	118.903	1.43569	0.717845	+	0.696203i	$0.245128\pi$
$20$	102.110	1.14162
$21$	86.2883	0.896650
$22$	−47.0785	−0.456235
$23$	61.3604	0.556284	0.278142	−	0.960540i	$-0.410281\pi$
$23$	61.3604	0.556284	0.278142	+	0.960540i	$0.410281\pi$
$24$	−66.9267	−0.569223
$25$	259.881	2.07905
$26$	34.8741	0.263053
$27$	−135.842	−0.968254
$28$	−148.148	−0.999903
$29$	70.4167	0.450898	0.225449	−	0.974255i	$-0.427615\pi$
$29$	70.4167	0.450898	0.225449	+	0.974255i	$0.427615\pi$
$30$	−99.4331	−0.605131
$31$	263.721	1.52793	0.763964	−	0.645259i	$-0.223251\pi$
$31$	263.721	1.52793	0.763964	+	0.645259i	$0.223251\pi$
$32$	184.521	1.01934
$33$	−85.3646	−0.450305
$34$	40.5139	0.204355
$35$	−558.411	−2.69682
$36$	92.6967	0.429152
$37$	−360.375	−1.60122	−0.800611	−	0.599185i	$-0.795492\pi$
$37$	−360.375	−1.60122	−0.800611	+	0.599185i	$0.795492\pi$
$38$	198.791	0.848638
$39$	63.2350	0.259634
$40$	433.113	1.71203
$41$	67.4488	0.256920	0.128460	−	0.991715i	$-0.458997\pi$
$41$	67.4488	0.256920	0.128460	+	0.991715i	$0.458997\pi$
$42$	144.264	0.530011
$43$	0	0
$43$	0	0
$44$	146.562	0.502159
$45$	349.401	1.15746
$46$	102.588	0.328820
$47$	−457.632	−1.42027	−0.710134	−	0.704067i	$-0.751365\pi$
$47$	−457.632	−1.42027	−0.710134	+	0.704067i	$0.751365\pi$
$48$	14.3341	0.0431030
$49$	467.180	1.36204
$50$	434.491	1.22893
$51$	73.4614	0.201699
$52$	−108.568	−0.289531
$53$	−148.507	−0.384887	−0.192443	−	0.981308i	$-0.561641\pi$
$53$	−148.507	−0.384887	−0.192443	+	0.981308i	$0.561641\pi$
$54$	−227.113	−0.572335
$55$	552.433	1.35437
$56$	−628.390	−1.49950
$57$	360.456	0.837607
$58$	117.729	0.266526
$59$	−182.072	−0.401758	−0.200879	−	0.979616i	$-0.564380\pi$
$59$	−182.072	−0.401758	−0.200879	+	0.979616i	$0.564380\pi$
$60$	309.548	0.666042
$61$	215.513	0.452354	0.226177	−	0.974086i	$-0.427377\pi$
$61$	215.513	0.452354	0.226177	+	0.974086i	$0.427377\pi$
$62$	440.912	0.903159
$63$	−506.934	−1.01377
$64$	270.670	0.528653
$65$	−409.223	−0.780890
$66$	−142.720	−0.266176
$67$	−631.508	−1.15151	−0.575754	−	0.817623i	$-0.695291\pi$
$67$	−631.508	−1.15151	−0.575754	+	0.817623i	$0.695291\pi$
$68$	−126.125	−0.224925
$69$	186.016	0.324546
$70$	−933.599	−1.59409
$71$	−575.441	−0.961863	−0.480931	−	0.876758i	$-0.659701\pi$
$71$	−575.441	−0.961863	−0.480931	+	0.876758i	$0.659701\pi$
$72$	393.187	0.643576
$73$	−1111.81	−1.78256	−0.891281	−	0.453452i	$-0.850192\pi$
$73$	−1111.81	−1.78256	−0.891281	+	0.453452i	$0.850192\pi$
$74$	−602.505	−0.946483
$75$	787.836	1.21295
$76$	−618.864	−0.934060
$77$	−801.507	−1.18624
$78$	105.722	0.153470
$79$	−622.227	−0.886152	−0.443076	−	0.896484i	$-0.646113\pi$
$79$	−622.227	−0.886152	−0.443076	+	0.896484i	$0.646113\pi$
$80$	−92.7624	−0.129639
$81$	69.0570	0.0947284
$82$	112.767	0.151866
$83$	−475.871	−0.629320	−0.314660	−	0.949204i	$-0.601891\pi$
$83$	−475.871	−0.629320	−0.314660	+	0.949204i	$0.601891\pi$
$84$	−449.113	−0.583361
$85$	−475.402	−0.606642
$86$	0	0
$87$	213.470	0.263062
$88$	621.663	0.753062
$89$	−1393.87	−1.66011	−0.830053	−	0.557684i	$-0.811690\pi$
$89$	−1393.87	−1.66011	−0.830053	+	0.557684i	$0.811690\pi$
$90$	584.158	0.684174
$91$	593.728	0.683951
$92$	−319.369	−0.361918
$93$	799.478	0.891419
$94$	−765.109	−0.839521
$95$	−2332.68	−2.51924
$96$	559.379	0.594701
$97$	1066.32	1.11617	0.558084	−	0.829785i	$-0.311537\pi$
$97$	1066.32	1.11617	0.558084	+	0.829785i	$0.311537\pi$
$98$	781.071	0.805103
$99$	501.507	0.509125
$100$	−1352.63	−1.35263
$101$	1127.76	1.11105	0.555527	−	0.831498i	$-0.312516\pi$
$101$	1127.76	1.11105	0.555527	+	0.831498i	$0.312516\pi$
$102$	122.819	0.119224
$103$	−450.354	−0.430822	−0.215411	−	0.976523i	$-0.569109\pi$
$103$	−450.354	−0.430822	−0.215411	+	0.976523i	$0.569109\pi$
$104$	−460.506	−0.434195
$105$	−1692.84	−1.57337
$106$	−248.286	−0.227507
$107$	512.081	0.462661	0.231331	−	0.972875i	$-0.425692\pi$
$107$	512.081	0.462661	0.231331	+	0.972875i	$0.425692\pi$
$108$	707.031	0.629946
$109$	535.897	0.470914	0.235457	−	0.971885i	$-0.424341\pi$
$109$	535.897	0.470914	0.235457	+	0.971885i	$0.424341\pi$
$110$	923.605	0.800566
$111$	−1092.48	−0.934180
$112$	134.586	0.113546
$113$	2126.44	1.77025	0.885125	−	0.465353i	$-0.154073\pi$
$113$	2126.44	1.77025	0.885125	+	0.465353i	$0.154073\pi$
$114$	602.641	0.495110
$115$	−1203.79	−0.976124
$116$	−366.505	−0.293354
$117$	−371.498	−0.293547
$118$	−304.403	−0.237479
$119$	689.745	0.531335
$120$	1312.99	0.998828
$121$	−538.074	−0.404263
$122$	360.313	0.267387
$123$	204.473	0.149892
$124$	−1372.62	−0.994070
$125$	−2646.15	−1.89343
$126$	−847.535	−0.599241
$127$	−778.542	−0.543972	−0.271986	−	0.962301i	$-0.587680\pi$
$127$	−778.542	−0.543972	−0.271986	+	0.962301i	$0.587680\pi$
$128$	−1023.63	−0.706854
$129$	0	0
$130$	−684.174	−0.461585
$131$	−39.6709	−0.0264585	−0.0132292	−	0.999912i	$-0.504211\pi$
$131$	−39.6709	−0.0264585	−0.0132292	+	0.999912i	$0.504211\pi$
$132$	444.305	0.292968
$133$	3384.40	2.20650
$134$	−1055.81	−0.680657
$135$	2665.01	1.69902
$136$	−534.978	−0.337309
$137$	137.298	0.0856219	0.0428109	−	0.999083i	$-0.486369\pi$
$137$	137.298	0.0856219	0.0428109	+	0.999083i	$0.486369\pi$
$138$	310.997	0.191839
$139$	975.906	0.595505	0.297753	−	0.954643i	$-0.403763\pi$
$139$	975.906	0.595505	0.297753	+	0.954643i	$0.403763\pi$
$140$	2906.42	1.75455
$141$	−1387.32	−0.828608
$142$	−962.071	−0.568558
$143$	−587.372	−0.343486
$144$	−84.2110	−0.0487332
$145$	−1381.46	−0.791201
$146$	−1858.81	−1.05367
$147$	1416.27	0.794638
$148$	1875.68	1.04175
$149$	2381.63	1.30947	0.654734	−	0.755860i	$-0.272781\pi$
$149$	2381.63	1.30947	0.654734	+	0.755860i	$0.272781\pi$
$150$	1317.17	0.716978
$151$	−62.4879	−0.0336768	−0.0168384	−	0.999858i	$-0.505360\pi$
$151$	−62.4879	−0.0336768	−0.0168384	+	0.999858i	$0.505360\pi$
$152$	−2625.00	−1.40076
$153$	−431.577	−0.228045
$154$	−1340.03	−0.701185
$155$	−5173.79	−2.68109
$156$	−329.126	−0.168918
$157$	2186.50	1.11148	0.555738	−	0.831358i	$-0.312436\pi$
$157$	2186.50	1.11148	0.555738	+	0.831358i	$0.312436\pi$
$158$	−1040.29	−0.523805
$159$	−450.202	−0.224549
$160$	−3620.00	−1.78866
$161$	1746.54	0.854949
$162$	115.455	0.0559940
$163$	−2358.30	−1.13323	−0.566614	−	0.823984i	$-0.691747\pi$
$163$	−2358.30	−1.13323	−0.566614	+	0.823984i	$0.691747\pi$
$164$	−351.057	−0.167152
$165$	1674.72	0.790160
$166$	−795.601	−0.371992
$167$	−25.7856	−0.0119482	−0.00597410	−	0.999982i	$-0.501902\pi$
$167$	−25.7856	−0.0119482	−0.00597410	+	0.999982i	$0.501902\pi$
$168$	−1904.98	−0.874835
$169$	−1761.90	−0.801955
$170$	−794.818	−0.358587
$171$	−2117.64	−0.947016
$172$	0	0
$173$	−1222.65	−0.537318	−0.268659	−	0.963235i	$-0.586581\pi$
$173$	−1222.65	−0.537318	−0.268659	+	0.963235i	$0.586581\pi$
$174$	356.897	0.155496
$175$	7397.17	3.19528
$176$	−133.145	−0.0570238
$177$	−551.955	−0.234393
$178$	−2330.38	−0.981290
$179$	−1466.11	−0.612190	−0.306095	−	0.952001i	$-0.599023\pi$
$179$	−1466.11	−0.612190	−0.306095	+	0.952001i	$0.599023\pi$
$180$	−1818.56	−0.753042
$181$	−288.210	−0.118356	−0.0591782	−	0.998247i	$-0.518848\pi$
$181$	−288.210	−0.118356	−0.0591782	+	0.998247i	$0.518848\pi$
$182$	992.645	0.404284
$183$	653.333	0.263911
$184$	−1354.65	−0.542750
$185$	7069.97	2.80970
$186$	1336.64	0.526919
$187$	−682.361	−0.266841
$188$	2381.89	0.924026
$189$	−3866.57	−1.48810
$190$	−3899.97	−1.48912
$191$	−4516.92	−1.71117	−0.855584	−	0.517664i	$-0.826802\pi$
$191$	−4516.92	−1.71117	−0.855584	+	0.517664i	$0.826802\pi$
$192$	820.544	0.308425
$193$	333.088	0.124229	0.0621145	−	0.998069i	$-0.480216\pi$
$193$	333.088	0.124229	0.0621145	+	0.998069i	$0.480216\pi$
$194$	1782.76	0.659767
$195$	−1240.57	−0.455585
$196$	−2431.58	−0.886144
$197$	−2433.98	−0.880273	−0.440136	−	0.897931i	$-0.645070\pi$
$197$	−2433.98	−0.880273	−0.440136	+	0.897931i	$0.645070\pi$
$198$	838.462	0.300944
$199$	−450.298	−0.160406	−0.0802030	−	0.996779i	$-0.525557\pi$
$199$	−450.298	−0.160406	−0.0802030	+	0.996779i	$0.525557\pi$
$200$	−5737.37	−2.02847
$201$	−1914.43	−0.671809
$202$	1885.49	0.656745
$203$	2004.32	0.692982
$204$	−382.352	−0.131225
$205$	−1323.24	−0.450824
$206$	−752.940	−0.254659
$207$	−1092.82	−0.366938
$208$	98.6291	0.0328784
$209$	−3348.17	−1.10812
$210$	−2830.23	−0.930021
$211$	−2584.53	−0.843253	−0.421626	−	0.906770i	$-0.638541\pi$
$211$	−2584.53	−0.843253	−0.421626	+	0.906770i	$0.638541\pi$
$212$	772.949	0.250407
$213$	−1744.46	−0.561167
$214$	856.141	0.273479
$215$	0	0
$216$	2998.98	0.944697
$217$	7506.48	2.34826
$218$	895.958	0.278357
$219$	−3370.47	−1.03998
$220$	−2875.30	−0.881150
$221$	505.469	0.153853
$222$	−1826.51	−0.552195
$223$	1716.32	0.515395	0.257698	−	0.966226i	$-0.417036\pi$
$223$	1716.32	0.515395	0.257698	+	0.966226i	$0.417036\pi$
$224$	5252.13	1.56662
$225$	−4628.45	−1.37139
$226$	3555.16	1.04640
$227$	4106.23	1.20062	0.600308	−	0.799769i	$-0.295045\pi$
$227$	4106.23	1.20062	0.600308	+	0.799769i	$0.295045\pi$
$228$	−1876.10	−0.544947
$229$	3533.42	1.01963	0.509815	−	0.860284i	$-0.329714\pi$
$229$	3533.42	1.01963	0.509815	+	0.860284i	$0.329714\pi$
$230$	−2012.60	−0.576987
$231$	−2429.79	−0.692071
$232$	−1554.58	−0.439928
$233$	−4199.28	−1.18070	−0.590351	−	0.807146i	$-0.701011\pi$
$233$	−4199.28	−1.18070	−0.590351	+	0.807146i	$0.701011\pi$
$234$	−621.103	−0.173516
$235$	8978.01	2.49217
$236$	947.647	0.261384
$237$	−1886.30	−0.516996
$238$	1153.17	0.314072
$239$	−2813.11	−0.761358	−0.380679	−	0.924707i	$-0.624310\pi$
$239$	−2813.11	−0.761358	−0.380679	+	0.924707i	$0.624310\pi$
$240$	−281.212	−0.0756339
$241$	62.8282	0.0167930	0.00839652	−	0.999965i	$-0.497327\pi$
$241$	62.8282	0.0167930	0.00839652	+	0.999965i	$0.497327\pi$
$242$	−899.597	−0.238960
$243$	3877.09	1.02352
$244$	−1121.70	−0.294302
$245$	−9165.32	−2.39000
$246$	341.855	0.0886011
$247$	2480.21	0.638914
$248$	−5822.15	−1.49075
$249$	−1442.61	−0.367156
$250$	−4424.06	−1.11921
$251$	−4502.21	−1.13218	−0.566090	−	0.824344i	$-0.691544\pi$
$251$	−4502.21	−1.13218	−0.566090	+	0.824344i	$0.691544\pi$
$252$	2638.49	0.659560
$253$	−1727.84	−0.429362
$254$	−1301.63	−0.321542
$255$	−1441.19	−0.353926
$256$	−3876.76	−0.946475
$257$	−2165.60	−0.525629	−0.262815	−	0.964846i	$-0.584651\pi$
$257$	−2165.60	−0.525629	−0.262815	+	0.964846i	$0.584651\pi$
$258$	0	0
$259$	−10257.6	−2.46091
$260$	2129.92	0.508047
$261$	−1254.11	−0.297423
$262$	−66.3251	−0.0156396
$263$	3071.42	0.720122	0.360061	−	0.932929i	$-0.382756\pi$
$263$	3071.42	0.720122	0.360061	+	0.932929i	$0.382756\pi$
$264$	1884.59	0.439349
$265$	2913.47	0.675369
$266$	5658.33	1.30427
$267$	−4225.54	−0.968535
$268$	3286.87	0.749171
$269$	−4903.70	−1.11146	−0.555732	−	0.831362i	$-0.687562\pi$
$269$	−4903.70	−1.11146	−0.555732	+	0.831362i	$0.687562\pi$
$270$	4455.58	1.00429
$271$	−7712.31	−1.72874	−0.864371	−	0.502854i	$-0.832283\pi$
$271$	−7712.31	−1.72874	−0.864371	+	0.502854i	$0.832283\pi$
$272$	114.579	0.0255419
$273$	1799.90	0.399029
$274$	229.547	0.0506112
$275$	−7317.98	−1.60469
$276$	−968.174	−0.211149
$277$	4685.10	1.01625	0.508124	−	0.861284i	$-0.330339\pi$
$277$	4685.10	1.01625	0.508124	+	0.861284i	$0.330339\pi$
$278$	1631.60	0.352004
$279$	−4696.84	−1.00786
$280$	12328.0	2.63121
$281$	1467.16	0.311471	0.155736	−	0.987799i	$-0.450225\pi$
$281$	1467.16	0.311471	0.155736	+	0.987799i	$0.450225\pi$
$282$	−2319.45	−0.489791
$283$	−2041.78	−0.428873	−0.214437	−	0.976738i	$-0.568792\pi$
$283$	−2041.78	−0.428873	−0.214437	+	0.976738i	$0.568792\pi$
$284$	2995.05	0.625788
$285$	−7071.57	−1.46977
$286$	−982.018	−0.203035
$287$	1919.84	0.394859
$288$	−3286.28	−0.672382
$289$	−4325.79	−0.880478
$290$	−2309.65	−0.467680
$291$	3232.57	0.651191
$292$	5786.72	1.15973
$293$	−2842.26	−0.566712	−0.283356	−	0.959015i	$-0.591448\pi$
$293$	−2842.26	−0.566712	−0.283356	+	0.959015i	$0.591448\pi$
$294$	2367.84	0.469711
$295$	3571.95	0.704974
$296$	7955.96	1.56227
$297$	3825.17	0.747337
$298$	3981.81	0.774027
$299$	1279.93	0.247559
$300$	−4100.53	−0.789147
$301$	0	0
$302$	−104.473	−0.0199064
$303$	3418.84	0.648209
$304$	562.212	0.106069
$305$	−4228.02	−0.793756
$306$	−721.547	−0.134798
$307$	3037.25	0.564641	0.282321	−	0.959320i	$-0.408896\pi$
$307$	3037.25	0.564641	0.282321	+	0.959320i	$0.408896\pi$
$308$	4171.68	0.771765
$309$	−1365.26	−0.251349
$310$	−8649.98	−1.58479
$311$	−1850.61	−0.337423	−0.168712	−	0.985665i	$-0.553961\pi$
$311$	−1850.61	−0.337423	−0.168712	+	0.985665i	$0.553961\pi$
$312$	−1396.03	−0.253317
$313$	5020.17	0.906570	0.453285	−	0.891366i	$-0.350252\pi$
$313$	5020.17	0.906570	0.453285	+	0.891366i	$0.350252\pi$
$314$	3655.58	0.656994
$315$	9945.22	1.77889
$316$	3238.57	0.576530
$317$	−5164.62	−0.915060	−0.457530	−	0.889194i	$-0.651266\pi$
$317$	−5164.62	−0.915060	−0.457530	+	0.889194i	$0.651266\pi$
$318$	−752.687	−0.132731
$319$	−1982.86	−0.348021
$320$	−5310.12	−0.927639
$321$	1552.39	0.269925
$322$	2920.02	0.505361
$323$	2881.30	0.496347
$324$	−359.428	−0.0616303
$325$	5420.90	0.925223
$326$	−3942.80	−0.669851
$327$	1624.58	0.274739
$328$	−1489.06	−0.250670
$329$	−13025.9	−2.18280
$330$	2799.93	0.467064
$331$	−848.187	−0.140848	−0.0704238	−	0.997517i	$-0.522435\pi$
$331$	−848.187	−0.140848	−0.0704238	+	0.997517i	$0.522435\pi$
$332$	2476.81	0.409436
$333$	6418.22	1.05620
$334$	−43.1105	−0.00706259
$335$	12389.2	2.02058
$336$	408.000	0.0662448
$337$	−10239.4	−1.65512	−0.827560	−	0.561377i	$-0.810272\pi$
$337$	−10239.4	−1.65512	−0.827560	+	0.561377i	$0.810272\pi$
$338$	−2945.69	−0.474036
$339$	6446.35	1.03279
$340$	2474.37	0.394682
$341$	−7426.12	−1.17932
$342$	−3540.45	−0.559782
$343$	3534.62	0.556418
$344$	0	0
$345$	−3649.33	−0.569487
$346$	−2044.12	−0.317609
$347$	−5710.49	−0.883445	−0.441722	−	0.897152i	$-0.645632\pi$
$347$	−5710.49	−0.883445	−0.441722	+	0.897152i	$0.645632\pi$
$348$	−1111.07	−0.171148
$349$	11866.8	1.82009	0.910047	−	0.414504i	$-0.136045\pi$
$349$	11866.8	1.82009	0.910047	+	0.414504i	$0.136045\pi$
$350$	12367.2	1.88873
$351$	−2833.55	−0.430894
$352$	−5195.90	−0.786769
$353$	−9689.28	−1.46093	−0.730465	−	0.682950i	$-0.760697\pi$
$353$	−9689.28	−1.46093	−0.730465	+	0.682950i	$0.760697\pi$
$354$	−922.805	−0.138550
$355$	11289.2	1.68780
$356$	7254.79	1.08007
$357$	2090.98	0.309990
$358$	−2451.16	−0.361866
$359$	−1852.48	−0.272340	−0.136170	−	0.990685i	$-0.543479\pi$
$359$	−1852.48	−0.272340	−0.136170	+	0.990685i	$0.543479\pi$
$360$	−7713.69	−1.12930
$361$	7278.82	1.06121
$362$	−481.855	−0.0699606
$363$	−1631.18	−0.235854
$364$	−3090.23	−0.444979
$365$	21811.8	3.12790
$366$	1092.30	0.155998
$367$	−10639.3	−1.51326	−0.756631	−	0.653842i	$-0.773156\pi$
$367$	−10639.3	−1.51326	−0.756631	+	0.653842i	$0.773156\pi$
$368$	290.133	0.0410984
$369$	−1201.25	−0.169471
$370$	11820.2	1.66081
$371$	−4227.05	−0.591530
$372$	−4161.12	−0.579957
$373$	−6298.76	−0.874363	−0.437182	−	0.899373i	$-0.644023\pi$
$373$	−6298.76	−0.874363	−0.437182	+	0.899373i	$0.644023\pi$
$374$	−1140.83	−0.157730
$375$	−8021.87	−1.10466
$376$	10103.1	1.38571
$377$	1468.83	0.200660
$378$	−6464.46	−0.879618
$379$	9123.57	1.23653	0.618267	−	0.785968i	$-0.287835\pi$
$379$	9123.57	1.23653	0.618267	+	0.785968i	$0.287835\pi$
$380$	12141.1	1.63902
$381$	−2360.17	−0.317363
$382$	−7551.78	−1.01147
$383$	1733.50	0.231274	0.115637	−	0.993292i	$-0.463109\pi$
$383$	1733.50	0.231274	0.115637	+	0.993292i	$0.463109\pi$
$384$	−3103.17	−0.412391
$385$	15724.3	2.08151
$386$	556.885	0.0734318
$387$	0	0
$388$	−5549.97	−0.726179
$389$	−7013.26	−0.914104	−0.457052	−	0.889440i	$-0.651095\pi$
$389$	−7013.26	−0.914104	−0.457052	+	0.889440i	$0.651095\pi$
$390$	−2074.09	−0.269296
$391$	1486.91	0.192318
$392$	−10313.9	−1.32890
$393$	−120.263	−0.0154363
$394$	−4069.33	−0.520330
$395$	12207.1	1.55495
$396$	−2610.24	−0.331236
$397$	2694.24	0.340605	0.170303	−	0.985392i	$-0.445525\pi$
$397$	2694.24	0.340605	0.170303	+	0.985392i	$0.445525\pi$
$398$	−752.847	−0.0948161
$399$	10259.9	1.28731
$400$	1228.81	0.153601
$401$	−8286.12	−1.03189	−0.515946	−	0.856621i	$-0.672560\pi$
$401$	−8286.12	−1.03189	−0.515946	+	0.856621i	$0.672560\pi$
$402$	−3200.71	−0.397107
$403$	5501.00	0.679962
$404$	−5869.78	−0.722852
$405$	−1354.79	−0.166222
$406$	3350.99	0.409622
$407$	10147.8	1.23589
$408$	−1621.80	−0.196792
$409$	15422.0	1.86447	0.932233	−	0.361858i	$-0.117858\pi$
$409$	15422.0	1.86447	0.932233	+	0.361858i	$0.117858\pi$
$410$	−2212.30	−0.266482
$411$	416.224	0.0499533
$412$	2344.00	0.280293
$413$	−5182.43	−0.617459
$414$	−1827.07	−0.216898
$415$	9335.81	1.10428
$416$	3848.94	0.453629
$417$	2958.48	0.347428
$418$	−5597.76	−0.655013
$419$	−1966.87	−0.229327	−0.114663	−	0.993404i	$-0.536579\pi$
$419$	−1966.87	−0.229327	−0.114663	+	0.993404i	$0.536579\pi$
$420$	8810.88	1.02364
$421$	4738.17	0.548514	0.274257	−	0.961656i	$-0.411568\pi$
$421$	4738.17	0.548514	0.274257	+	0.961656i	$0.411568\pi$
$422$	−4321.04	−0.498447
$423$	8150.37	0.936843
$424$	3278.57	0.375523
$425$	6297.56	0.718769
$426$	−2916.54	−0.331706
$427$	6134.29	0.695220
$428$	−2665.28	−0.301007
$429$	−1780.63	−0.200396
$430$	0	0
$431$	−6730.57	−0.752205	−0.376102	−	0.926578i	$-0.622736\pi$
$431$	−6730.57	−0.752205	−0.376102	+	0.926578i	$0.622736\pi$
$432$	−642.308	−0.0715349
$433$	7458.24	0.827760	0.413880	−	0.910331i	$-0.364173\pi$
$433$	7458.24	0.827760	0.413880	+	0.910331i	$0.364173\pi$
$434$	12550.0	1.38806
$435$	−4187.94	−0.461600
$436$	−2789.23	−0.306376
$437$	7295.91	0.798652
$438$	−5635.03	−0.614731
$439$	11055.7	1.20196	0.600979	−	0.799265i	$-0.294778\pi$
$439$	11055.7	1.20196	0.600979	+	0.799265i	$0.294778\pi$
$440$	−12196.0	−1.32141
$441$	−8320.41	−0.898435
$442$	845.086	0.0909426
$443$	9314.23	0.998944	0.499472	−	0.866330i	$-0.333527\pi$
$443$	9314.23	0.998944	0.499472	+	0.866330i	$0.333527\pi$
$444$	5686.16	0.607778
$445$	27345.4	2.91303
$446$	2869.49	0.304650
$447$	7219.97	0.763966
$448$	7704.27	0.812483
$449$	8831.64	0.928265	0.464132	−	0.885766i	$-0.346366\pi$
$449$	8831.64	0.928265	0.464132	+	0.885766i	$0.346366\pi$
$450$	−7738.23	−0.810630
$451$	−1899.29	−0.198301
$452$	−11067.7	−1.15172
$453$	−189.434	−0.0196476
$454$	6865.14	0.709685
$455$	−11648.0	−1.20014
$456$	−7957.76	−0.817228
$457$	−4617.15	−0.472607	−0.236303	−	0.971679i	$-0.575936\pi$
$457$	−4617.15	−0.472607	−0.236303	+	0.971679i	$0.575936\pi$
$458$	5907.48	0.602704
$459$	−3291.79	−0.334745
$460$	6265.50	0.635066
$461$	3614.97	0.365219	0.182610	−	0.983186i	$-0.441546\pi$
$461$	3614.97	0.365219	0.182610	+	0.983186i	$0.441546\pi$
$462$	−4062.33	−0.409083
$463$	−7007.76	−0.703409	−0.351704	−	0.936111i	$-0.614398\pi$
$463$	−7007.76	−0.703409	−0.351704	+	0.936111i	$0.614398\pi$
$464$	332.954	0.0333125
$465$	−15684.5	−1.56419
$466$	−7020.71	−0.697914
$467$	15127.4	1.49896	0.749479	−	0.662028i	$-0.230304\pi$
$467$	15127.4	1.49896	0.749479	+	0.662028i	$0.230304\pi$
$468$	1933.57	0.190982
$469$	−17975.0	−1.76974
$470$	15010.2	1.47313
$471$	6628.43	0.648454
$472$	4019.58	0.391984
$473$	0	0
$474$	−3153.67	−0.305597
$475$	30900.5	2.98487
$476$	−3589.98	−0.345686
$477$	2644.89	0.253881
$478$	−4703.19	−0.450039
$479$	−18354.2	−1.75078	−0.875392	−	0.483415i	$-0.839396\pi$
$479$	−18354.2	−1.75078	−0.875392	+	0.483415i	$0.839396\pi$
$480$	−10974.1	−1.04354
$481$	−7517.11	−0.712579
$482$	105.042	0.00992638
$483$	5294.69	0.498792
$484$	2800.56	0.263013
$485$	−20919.5	−1.95856
$486$	6482.05	0.605003
$487$	−4112.61	−0.382669	−0.191335	−	0.981525i	$-0.561282\pi$
$487$	−4112.61	−0.382669	−0.191335	+	0.981525i	$0.561282\pi$
$488$	−4757.86	−0.441349
$489$	−7149.23	−0.661144
$490$	−15323.4	−1.41273
$491$	−7080.85	−0.650824	−0.325412	−	0.945572i	$-0.605503\pi$
$491$	−7080.85	−0.650824	−0.325412	+	0.945572i	$0.605503\pi$
$492$	−1064.24	−0.0975195
$493$	1706.37	0.155885
$494$	4146.62	0.377663
$495$	−9838.76	−0.893372
$496$	1246.96	0.112884
$497$	−16379.2	−1.47828
$498$	−2411.88	−0.217026
$499$	2894.70	0.259688	0.129844	−	0.991534i	$-0.458552\pi$
$499$	2894.70	0.259688	0.129844	+	0.991534i	$0.458552\pi$
$500$	13772.7	1.23187
$501$	−78.1696	−0.00697078
$502$	−7527.18	−0.669232
$503$	−933.370	−0.0827374	−0.0413687	−	0.999144i	$-0.513172\pi$
$503$	−933.370	−0.0827374	−0.0413687	+	0.999144i	$0.513172\pi$
$504$	11191.5	0.989108
$505$	−22124.9	−1.94959
$506$	−2888.76	−0.253796
$507$	−5341.23	−0.467875
$508$	4052.16	0.353908
$509$	14759.5	1.28527	0.642636	−	0.766171i	$-0.277841\pi$
$509$	14759.5	1.28527	0.642636	+	0.766171i	$0.277841\pi$
$510$	−2409.51	−0.209206
$511$	−31646.1	−2.73961
$512$	1707.57	0.147392
$513$	−16152.0	−1.39011
$514$	−3620.64	−0.310700
$515$	8835.22	0.755973
$516$	0	0
$517$	12886.4	1.09622
$518$	−17149.5	−1.45464
$519$	−3706.48	−0.313481
$520$	9034.38	0.761892
$521$	532.873	0.0448092	0.0224046	−	0.999749i	$-0.492868\pi$
$521$	532.873	0.0448092	0.0224046	+	0.999749i	$0.492868\pi$
$522$	−2096.73	−0.175807
$523$	4181.75	0.349627	0.174814	−	0.984602i	$-0.444068\pi$
$523$	4181.75	0.349627	0.174814	+	0.984602i	$0.444068\pi$
$524$	206.479	0.0172139
$525$	22424.7	1.86418
$526$	5135.07	0.425665
$527$	6390.62	0.528235
$528$	−403.633	−0.0332687
$529$	−8401.90	−0.690548
$530$	4870.98	0.399211
$531$	3242.67	0.265009
$532$	−17615.1	−1.43555
$533$	1406.92	0.114335
$534$	−7064.62	−0.572502
$535$	−10046.2	−0.811842
$536$	13941.7	1.12349
$537$	−4444.54	−0.357162
$538$	−8198.42	−0.656987
$539$	−13155.3	−1.05128
$540$	−13870.8	−1.10538
$541$	−2004.57	−0.159304	−0.0796518	−	0.996823i	$-0.525381\pi$
$541$	−2004.57	−0.159304	−0.0796518	+	0.996823i	$0.525381\pi$
$542$	−12894.1	−1.02186
$543$	−873.717	−0.0690512
$544$	4471.39	0.352407
$545$	−10513.4	−0.826323
$546$	3009.23	0.235866
$547$	540.046	0.0422134	0.0211067	−	0.999777i	$-0.493281\pi$
$547$	540.046	0.0422134	0.0211067	+	0.999777i	$0.493281\pi$
$548$	−714.611	−0.0557056
$549$	−3838.26	−0.298384
$550$	−12234.8	−0.948536
$551$	8372.73	0.647350
$552$	−4106.65	−0.316650
$553$	−17710.8	−1.36192
$554$	7832.95	0.600704
$555$	21432.8	1.63923
$556$	−5079.39	−0.387436
$557$	−10875.1	−0.827280	−0.413640	−	0.910441i	$-0.635743\pi$
$557$	−10875.1	−0.827280	−0.413640	+	0.910441i	$0.635743\pi$
$558$	−7852.58	−0.595746
$559$	0	0
$560$	−2640.36	−0.199242
$561$	−2068.60	−0.155679
$562$	2452.92	0.184111
$563$	−15197.2	−1.13763	−0.568814	−	0.822466i	$-0.692597\pi$
$563$	−15197.2	−1.13763	−0.568814	+	0.822466i	$0.692597\pi$
$564$	7220.74	0.539093
$565$	−41717.3	−3.10630
$566$	−3413.62	−0.253507
$567$	1965.62	0.145587
$568$	12704.0	0.938462
$569$	−24697.5	−1.81963	−0.909817	−	0.415010i	$-0.863778\pi$
$569$	−24697.5	−1.81963	−0.909817	+	0.415010i	$0.863778\pi$
$570$	−11822.9	−0.868780
$571$	−22999.3	−1.68562	−0.842810	−	0.538210i	$-0.819101\pi$
$571$	−22999.3	−1.68562	−0.842810	+	0.538210i	$0.819101\pi$
$572$	3057.15	0.223472
$573$	−13693.2	−0.998325
$574$	3209.75	0.233401
$575$	15946.4	1.15654
$576$	−4820.60	−0.348712
$577$	9086.76	0.655610	0.327805	−	0.944745i	$-0.393691\pi$
$577$	9086.76	0.655610	0.327805	+	0.944745i	$0.393691\pi$
$578$	−7232.22	−0.520451
$579$	1009.76	0.0724773
$580$	7190.23	0.514755
$581$	−13545.0	−0.967198
$582$	5404.49	0.384920
$583$	4181.80	0.297071
$584$	24545.2	1.73919
$585$	7288.20	0.515094
$586$	−4751.93	−0.334984
$587$	−9602.21	−0.675171	−0.337586	−	0.941295i	$-0.609610\pi$
$587$	−9602.21	−0.675171	−0.337586	+	0.941295i	$0.609610\pi$
$588$	−7371.39	−0.516992
$589$	31357.1	2.19363
$590$	5971.90	0.416710
$591$	−7378.67	−0.513566
$592$	−1703.97	−0.118299
$593$	−20476.0	−1.41796	−0.708980	−	0.705229i	$-0.750844\pi$
$593$	−20476.0	−1.41796	−0.708980	+	0.705229i	$0.750844\pi$
$594$	6395.25	0.441751
$595$	−13531.7	−0.932345
$596$	−12395.9	−0.851940
$597$	−1365.09	−0.0935837
$598$	2139.89	0.146332
$599$	11861.1	0.809070	0.404535	−	0.914523i	$-0.367433\pi$
$599$	11861.1	0.809070	0.404535	+	0.914523i	$0.367433\pi$
$600$	−17393.0	−1.18344
$601$	−11364.0	−0.771296	−0.385648	−	0.922646i	$-0.626022\pi$
$601$	−11364.0	−0.771296	−0.385648	+	0.922646i	$0.626022\pi$
$602$	0	0
$603$	11247.1	0.759562
$604$	325.237	0.0219101
$605$	10556.1	0.709368
$606$	5715.91	0.383157
$607$	−15781.3	−1.05526	−0.527631	−	0.849474i	$-0.676920\pi$
$607$	−15781.3	−1.05526	−0.527631	+	0.849474i	$0.676920\pi$
$608$	21940.0	1.46346
$609$	6076.14	0.404298
$610$	−7068.76	−0.469190
$611$	−9545.82	−0.632050
$612$	2246.27	0.148366
$613$	9869.44	0.650282	0.325141	−	0.945666i	$-0.394588\pi$
$613$	9869.44	0.650282	0.325141	+	0.945666i	$0.394588\pi$
$614$	5077.93	0.333760
$615$	−4011.42	−0.263018
$616$	17694.8	1.15738
$617$	−1089.90	−0.0711148	−0.0355574	−	0.999368i	$-0.511321\pi$
$617$	−1089.90	−0.0711148	−0.0355574	+	0.999368i	$0.511321\pi$
$618$	−2282.56	−0.148573
$619$	5880.92	0.381865	0.190932	−	0.981603i	$-0.438849\pi$
$619$	5880.92	0.381865	0.190932	+	0.981603i	$0.438849\pi$
$620$	26928.5	1.74432
$621$	−8335.33	−0.538624
$622$	−3094.01	−0.199451
$623$	−39674.5	−2.55141
$624$	298.997	0.0191818
$625$	19428.1	1.24340
$626$	8393.14	0.535874
$627$	−10150.1	−0.646499
$628$	−11380.3	−0.723126
$629$	−8732.77	−0.553574
$630$	16627.3	1.05150
$631$	26475.3	1.67031	0.835155	−	0.550014i	$-0.185378\pi$
$631$	26475.3	1.67031	0.835155	+	0.550014i	$0.185378\pi$
$632$	13736.8	0.864592
$633$	−7835.07	−0.491968
$634$	−8634.66	−0.540893
$635$	15273.7	0.954520
$636$	2343.21	0.146092
$637$	9744.98	0.606138
$638$	−3315.11	−0.205716
$639$	10248.5	0.634468
$640$	20082.1	1.24033
$641$	−31481.3	−1.93984	−0.969918	−	0.243431i	$-0.921727\pi$
$641$	−31481.3	−1.93984	−0.969918	+	0.243431i	$0.921727\pi$
$642$	2595.41	0.159553
$643$	3775.28	0.231543	0.115772	−	0.993276i	$-0.463066\pi$
$643$	3775.28	0.231543	0.115772	+	0.993276i	$0.463066\pi$
$644$	−9090.40	−0.556230
$645$	0	0
$646$	4817.21	0.293391
$647$	−20064.1	−1.21917	−0.609583	−	0.792722i	$-0.708663\pi$
$647$	−20064.1	−1.21917	−0.609583	+	0.792722i	$0.708663\pi$
$648$	−1524.57	−0.0924237
$649$	5126.95	0.310093
$650$	9063.12	0.546900
$651$	22756.1	1.37002
$652$	12274.5	0.737277
$653$	4142.49	0.248252	0.124126	−	0.992266i	$-0.460387\pi$
$653$	4142.49	0.248252	0.124126	+	0.992266i	$0.460387\pi$
$654$	2716.12	0.162399
$655$	778.278	0.0464272
$656$	318.921	0.0189813
$657$	19801.1	1.17582
$658$	−21777.8	−1.29025
$659$	−5352.37	−0.316386	−0.158193	−	0.987408i	$-0.550567\pi$
$659$	−5352.37	−0.316386	−0.158193	+	0.987408i	$0.550567\pi$
$660$	−8716.56	−0.514078
$661$	32014.0	1.88381	0.941906	−	0.335876i	$-0.109032\pi$
$661$	32014.0	1.88381	0.941906	+	0.335876i	$0.109032\pi$
$662$	−1418.07	−0.0832552
$663$	1532.34	0.0897605
$664$	10505.8	0.614009
$665$	−66396.5	−3.87180
$666$	10730.5	0.624323
$667$	4320.80	0.250827
$668$	134.209	0.00777349
$669$	5203.06	0.300690
$670$	20713.3	1.19436
$671$	−6068.62	−0.349145
$672$	15922.0	0.913993
$673$	−19539.2	−1.11914	−0.559568	−	0.828784i	$-0.689033\pi$
$673$	−19539.2	−1.11914	−0.559568	+	0.828784i	$0.689033\pi$
$674$	−17119.1	−0.978343
$675$	−35302.8	−2.01305
$676$	9170.32	0.521752
$677$	17239.8	0.978701	0.489350	−	0.872087i	$-0.337234\pi$
$677$	17239.8	0.978701	0.489350	+	0.872087i	$0.337234\pi$
$678$	10777.5	0.610486
$679$	30351.3	1.71543
$680$	10495.4	0.591883
$681$	12448.1	0.700460
$682$	−12415.6	−0.697094
$683$	−1098.55	−0.0615447	−0.0307723	−	0.999526i	$-0.509797\pi$
$683$	−1098.55	−0.0615447	−0.0307723	+	0.999526i	$0.509797\pi$
$684$	11021.9	0.616129
$685$	−2693.57	−0.150243
$686$	5909.48	0.328899
$687$	10711.7	0.594870
$688$	0	0
$689$	−3097.73	−0.171283
$690$	−6101.26	−0.336624
$691$	329.691	0.0181506	0.00907528	−	0.999959i	$-0.497111\pi$
$691$	329.691	0.0181506	0.00907528	+	0.999959i	$0.497111\pi$
$692$	6363.63	0.349579
$693$	14274.7	0.782470
$694$	−9547.29	−0.522205
$695$	−19145.7	−1.04495
$696$	−4712.76	−0.256662
$697$	1634.45	0.0888224
$698$	19839.9	1.07586
$699$	−12730.2	−0.688843
$700$	−38500.8	−2.07885
$701$	−14077.1	−0.758467	−0.379233	−	0.925301i	$-0.623812\pi$
$701$	−14077.1	−0.758467	−0.379233	+	0.925301i	$0.623812\pi$
$702$	−4737.38	−0.254702
$703$	−42849.5	−2.29886
$704$	−7621.79	−0.408036
$705$	27217.1	1.45398
$706$	−16199.4	−0.863557
$707$	32100.2	1.70757
$708$	2872.82	0.152496
$709$	−18090.1	−0.958235	−0.479118	−	0.877751i	$-0.659043\pi$
$709$	−18090.1	−0.958235	−0.479118	+	0.877751i	$0.659043\pi$
$710$	18874.3	0.997661
$711$	11081.8	0.584527
$712$	30772.3	1.61972
$713$	16182.1	0.849962
$714$	3495.88	0.183235
$715$	11523.3	0.602722
$716$	7630.79	0.398291
$717$	−8528.00	−0.444190
$718$	−3097.13	−0.160980
$719$	23754.1	1.23210	0.616050	−	0.787707i	$-0.288732\pi$
$719$	23754.1	1.23210	0.616050	+	0.787707i	$0.288732\pi$
$720$	1652.08	0.0855133
$721$	−12818.7	−0.662128
$722$	12169.4	0.627281
$723$	190.465	0.00979735
$724$	1500.08	0.0770027
$725$	18300.0	0.937440
$726$	−2727.15	−0.139413
$727$	31123.3	1.58776	0.793879	−	0.608076i	$-0.208058\pi$
$727$	31123.3	1.58776	0.793879	+	0.608076i	$0.208058\pi$
$728$	−13107.7	−0.667311
$729$	9888.95	0.502411
$730$	36466.9	1.84890
$731$	0	0
$732$	−3400.47	−0.171701
$733$	−1512.41	−0.0762101	−0.0381051	−	0.999274i	$-0.512132\pi$
$733$	−1512.41	−0.0762101	−0.0381051	+	0.999274i	$0.512132\pi$
$734$	−17787.7	−0.894490
$735$	−27784.9	−1.39437
$736$	11322.3	0.567043
$737$	17782.6	0.888780
$738$	−2008.36	−0.100174
$739$	30174.5	1.50201	0.751007	−	0.660295i	$-0.229569\pi$
$739$	30174.5	1.50201	0.751007	+	0.660295i	$0.229569\pi$
$740$	−36797.8	−1.82799
$741$	7518.81	0.372754
$742$	−7067.14	−0.349654
$743$	14115.4	0.696964	0.348482	−	0.937315i	$-0.386697\pi$
$743$	14115.4	0.696964	0.348482	+	0.937315i	$0.386697\pi$
$744$	−17650.0	−0.869732
$745$	−46723.7	−2.29775
$746$	−10530.8	−0.516837
$747$	8475.19	0.415115
$748$	3551.55	0.173606
$749$	14575.7	0.711061
$750$	−13411.7	−0.652966
$751$	−2268.61	−0.110230	−0.0551151	−	0.998480i	$-0.517553\pi$
$751$	−2268.61	−0.110230	−0.0551151	+	0.998480i	$0.517553\pi$
$752$	−2163.84	−0.104930
$753$	−13648.6	−0.660533
$754$	2455.72	0.118610
$755$	1225.91	0.0590934
$756$	20124.7	0.968159
$757$	−6032.16	−0.289620	−0.144810	−	0.989459i	$-0.546257\pi$
$757$	−6032.16	−0.289620	−0.144810	+	0.989459i	$0.546257\pi$
$758$	15253.6	0.730916
$759$	−5238.01	−0.250497
$760$	51498.3	2.45795
$761$	−23570.9	−1.12279	−0.561396	−	0.827547i	$-0.689735\pi$
$761$	−23570.9	−1.12279	−0.561396	+	0.827547i	$0.689735\pi$
$762$	−3945.93	−0.187593
$763$	15253.6	0.723744
$764$	23509.7	1.11329
$765$	8466.84	0.400156
$766$	2898.22	0.136706
$767$	−3797.86	−0.178791
$768$	−11752.5	−0.552190
$769$	−5217.26	−0.244654	−0.122327	−	0.992490i	$-0.539036\pi$
$769$	−5217.26	−0.244654	−0.122327	+	0.992490i	$0.539036\pi$
$770$	26289.2	1.23038
$771$	−6565.08	−0.306661
$772$	−1733.66	−0.0808234
$773$	−21883.6	−1.01824	−0.509119	−	0.860696i	$-0.670029\pi$
$773$	−21883.6	−1.01824	−0.509119	+	0.860696i	$0.670029\pi$
$774$	0	0
$775$	68536.2	3.17664
$776$	−23541.0	−1.08901
$777$	−31096.1	−1.43574
$778$	−11725.4	−0.540327
$779$	8019.83	0.368858
$780$	6456.92	0.296403
$781$	16203.8	0.742405
$782$	2485.95	0.113680
$783$	−9565.56	−0.436584
$784$	2208.99	0.100628
$785$	−42895.6	−1.95033
$786$	−201.066	−0.00912442
$787$	26159.7	1.18487	0.592435	−	0.805619i	$-0.298167\pi$
$787$	26159.7	1.18487	0.592435	+	0.805619i	$0.298167\pi$
$788$	12668.4	0.572706
$789$	9311.10	0.420132
$790$	20408.8	0.919132
$791$	60526.2	2.72069
$792$	−11071.7	−0.496738
$793$	4495.42	0.201308
$794$	4504.47	0.201332
$795$	8832.24	0.394022
$796$	2343.71	0.104360
$797$	29914.6	1.32952	0.664761	−	0.747056i	$-0.268533\pi$
$797$	29914.6	1.32952	0.664761	+	0.747056i	$0.268533\pi$
$798$	17153.4	0.760931
$799$	−11089.6	−0.491015
$800$	47953.4	2.11926
$801$	24824.5	1.09505
$802$	−13853.4	−0.609952
$803$	31307.3	1.37585
$804$	9964.24	0.437079
$805$	−34264.3	−1.50020
$806$	9197.05	0.401926
$807$	−14865.7	−0.648447
$808$	−24897.5	−1.08402
$809$	−18721.9	−0.813630	−0.406815	−	0.913511i	$-0.633361\pi$
$809$	−18721.9	−0.813630	−0.406815	+	0.913511i	$0.633361\pi$
$810$	−2265.05	−0.0982539
$811$	31993.9	1.38527	0.692637	−	0.721287i	$-0.256449\pi$
$811$	31993.9	1.38527	0.692637	+	0.721287i	$0.256449\pi$
$812$	−10432.1	−0.450854
$813$	−23380.1	−1.00858
$814$	16965.9	0.730534
$815$	46266.0	1.98850
$816$	347.350	0.0149016
$817$	0	0
$818$	25783.7	1.10209
$819$	−10574.2	−0.451151
$820$	6887.18	0.293306
$821$	−10202.7	−0.433710	−0.216855	−	0.976204i	$-0.569580\pi$
$821$	−10202.7	−0.433710	−0.216855	+	0.976204i	$0.569580\pi$
$822$	695.878	0.0295274
$823$	1991.87	0.0843647	0.0421824	−	0.999110i	$-0.486569\pi$
$823$	1991.87	0.0843647	0.0421824	+	0.999110i	$0.486569\pi$
$824$	9942.42	0.420341
$825$	−22184.6	−0.936206
$826$	−8664.42	−0.364981
$827$	28028.9	1.17855	0.589274	−	0.807933i	$-0.299414\pi$
$827$	28028.9	1.17855	0.589274	+	0.807933i	$0.299414\pi$
$828$	5687.91	0.238730
$829$	7115.74	0.298118	0.149059	−	0.988828i	$-0.452376\pi$
$829$	7115.74	0.298118	0.149059	+	0.988828i	$0.452376\pi$
$830$	15608.4	0.652742
$831$	14203.0	0.592896
$832$	5645.95	0.235262
$833$	11320.9	0.470885
$834$	4946.24	0.205365
$835$	505.872	0.0209658
$836$	17426.6	0.720945
$837$	−35824.5	−1.47942
$838$	−3288.38	−0.135555
$839$	−2743.35	−0.112886	−0.0564429	−	0.998406i	$-0.517976\pi$
$839$	−2743.35	−0.112886	−0.0564429	+	0.998406i	$0.517976\pi$
$840$	37372.6	1.53509
$841$	−19430.5	−0.796691
$842$	7921.67	0.324227
$843$	4447.73	0.181718
$844$	13452.0	0.548620
$845$	34565.6	1.40721
$846$	13626.5	0.553768
$847$	−15315.5	−0.621308
$848$	−702.191	−0.0284355
$849$	−6189.71	−0.250212
$850$	10528.8	0.424865
$851$	−22112.7	−0.890734
$852$	9079.58	0.365096
$853$	−20954.5	−0.841111	−0.420555	−	0.907267i	$-0.638165\pi$
$853$	−20954.5	−0.841111	−0.420555	+	0.907267i	$0.638165\pi$
$854$	10255.8	0.410945
$855$	41544.6	1.66175
$856$	−11305.2	−0.451405
$857$	11280.8	0.449644	0.224822	−	0.974400i	$-0.427820\pi$
$857$	11280.8	0.449644	0.224822	+	0.974400i	$0.427820\pi$
$858$	−2977.01	−0.118454
$859$	5173.87	0.205507	0.102753	−	0.994707i	$-0.467235\pi$
$859$	5173.87	0.205507	0.102753	+	0.994707i	$0.467235\pi$
$860$	0	0
$861$	5820.04	0.230368
$862$	−11252.7	−0.444629
$863$	8783.07	0.346442	0.173221	−	0.984883i	$-0.444583\pi$
$863$	8783.07	0.346442	0.173221	+	0.984883i	$0.444583\pi$
$864$	−25065.7	−0.986981
$865$	23986.3	0.942844
$866$	12469.3	0.489289
$867$	−13113.7	−0.513686
$868$	−39069.7	−1.52778
$869$	17521.2	0.683967
$870$	−7001.75	−0.272852
$871$	−13172.7	−0.512446
$872$	−11830.9	−0.459457
$873$	−18991.0	−0.736251
$874$	12197.9	0.472084
$875$	−75319.1	−2.91000
$876$	17542.6	0.676609
$877$	−8379.48	−0.322640	−0.161320	−	0.986902i	$-0.551575\pi$
$877$	−8379.48	−0.322640	−0.161320	+	0.986902i	$0.551575\pi$
$878$	18483.9	0.710478
$879$	−8616.38	−0.330629
$880$	2612.09	0.100061
$881$	−37719.4	−1.44245	−0.721225	−	0.692701i	$-0.756421\pi$
$881$	−37719.4	−1.44245	−0.721225	+	0.692701i	$0.756421\pi$
$882$	−13910.8	−0.531066
$883$	−41618.6	−1.58616	−0.793079	−	0.609119i	$-0.791523\pi$
$883$	−41618.6	−1.58616	−0.793079	+	0.609119i	$0.791523\pi$
$884$	−2630.86	−0.100097
$885$	10828.5	0.411294
$886$	15572.3	0.590477
$887$	−6659.01	−0.252072	−0.126036	−	0.992026i	$-0.540225\pi$
$887$	−6659.01	−0.252072	−0.126036	+	0.992026i	$0.540225\pi$
$888$	24118.7	0.911453
$889$	−22160.2	−0.836027
$890$	45718.4	1.72189
$891$	−1944.57	−0.0731152
$892$	−8933.09	−0.335316
$893$	−54413.7	−2.03906
$894$	12071.0	0.451581
$895$	28762.7	1.07422
$896$	−29136.4	−1.08636
$897$	3880.13	0.144430
$898$	14765.5	0.548698
$899$	18570.4	0.688940
$900$	24090.1	0.892227
$901$	−3598.69	−0.133063
$902$	−3175.39	−0.117216
$903$	0	0
$904$	−46945.1	−1.72718
$905$	5654.22	0.207683
$906$	−316.711	−0.0116137
$907$	−39091.2	−1.43109	−0.715547	−	0.698565i	$-0.753822\pi$
$907$	−39091.2	−1.43109	−0.715547	+	0.698565i	$0.753822\pi$
$908$	−21372.1	−0.781121
$909$	−20085.3	−0.732879
$910$	−19474.1	−0.709406
$911$	27839.3	1.01247	0.506233	−	0.862397i	$-0.331038\pi$
$911$	27839.3	1.01247	0.506233	+	0.862397i	$0.331038\pi$
$912$	1704.36	0.0618826
$913$	13400.0	0.485735
$914$	−7719.35	−0.279358
$915$	−12817.3	−0.463091
$916$	−18390.8	−0.663371
$917$	−1129.18	−0.0406638
$918$	−5503.50	−0.197868
$919$	−33937.5	−1.21816	−0.609082	−	0.793107i	$-0.708462\pi$
$919$	−33937.5	−1.21816	−0.609082	+	0.793107i	$0.708462\pi$
$920$	26576.0	0.952375
$921$	9207.49	0.329421
$922$	6043.82	0.215881
$923$	−12003.2	−0.428050
$924$	12646.6	0.450261
$925$	−93654.5	−3.32902
$926$	−11716.2	−0.415785
$927$	8020.74	0.284181
$928$	12993.3	0.459619
$929$	13108.9	0.462958	0.231479	−	0.972840i	$-0.425644\pi$
$929$	13108.9	0.462958	0.231479	+	0.972840i	$0.425644\pi$
$930$	−26222.6	−0.924596
$931$	55548.9	1.95547
$932$	21856.4	0.768165
$933$	−5610.18	−0.196859
$934$	25291.3	0.886036
$935$	13386.8	0.468231
$936$	8201.54	0.286406
$937$	−55740.1	−1.94338	−0.971691	−	0.236254i	$-0.924080\pi$
$937$	−55740.1	−1.94338	−0.971691	+	0.236254i	$0.924080\pi$
$938$	−30052.2	−1.04610
$939$	15218.8	0.528909
$940$	−46728.7	−1.62141
$941$	−12532.4	−0.434159	−0.217080	−	0.976154i	$-0.569653\pi$
$941$	−12532.4	−0.434159	−0.217080	+	0.976154i	$0.569653\pi$
$942$	11082.0	0.383302
$943$	4138.68	0.142921
$944$	−860.897	−0.0296820
$945$	75855.8	2.61121
$946$	0	0
$947$	3084.68	0.105849	0.0529243	−	0.998599i	$-0.483146\pi$
$947$	3084.68	0.105849	0.0529243	+	0.998599i	$0.483146\pi$
$948$	9817.79	0.336358
$949$	−23191.3	−0.793279
$950$	51662.2	1.76436
$951$	−15656.7	−0.533862
$952$	−15227.4	−0.518408
$953$	13984.3	0.475337	0.237669	−	0.971346i	$-0.423617\pi$
$953$	13984.3	0.475337	0.237669	+	0.971346i	$0.423617\pi$
$954$	4421.95	0.150069
$955$	88614.7	3.00262
$956$	14641.6	0.495340
$957$	−6011.09	−0.203042
$958$	−30686.1	−1.03489
$959$	3908.02	0.131592
$960$	−16097.8	−0.541201
$961$	39757.9	1.33456
$962$	−12567.7	−0.421206
$963$	−9120.09	−0.305183
$964$	−327.008	−0.0109255
$965$	−6534.65	−0.217987
$966$	8852.11	0.294836
$967$	−36409.1	−1.21079	−0.605396	−	0.795924i	$-0.706985\pi$
$967$	−36409.1	−1.21079	−0.605396	+	0.795924i	$0.706985\pi$
$968$	11879.0	0.394427
$969$	8734.75	0.289577
$970$	−34974.9	−1.15771
$971$	−22165.7	−0.732577	−0.366289	−	0.930501i	$-0.619372\pi$
$971$	−22165.7	−0.732577	−0.366289	+	0.930501i	$0.619372\pi$
$972$	−20179.5	−0.665902
$973$	27777.9	0.915228
$974$	−6875.80	−0.226196
$975$	16433.6	0.539791
$976$	1019.02	0.0334201
$977$	50362.6	1.64917	0.824587	−	0.565735i	$-0.191408\pi$
$977$	50362.6	1.64917	0.824587	+	0.565735i	$0.191408\pi$
$978$	−11952.7	−0.390803
$979$	39249.8	1.28134
$980$	47703.6	1.55494
$981$	−9544.24	−0.310626
$982$	−11838.4	−0.384702
$983$	5278.97	0.171285	0.0856424	−	0.996326i	$-0.472706\pi$
$983$	5278.97	0.171285	0.0856424	+	0.996326i	$0.472706\pi$
$984$	−4514.12	−0.146245
$985$	47750.7	1.54463
$986$	2852.86	0.0921434
$987$	−39488.3	−1.27348
$988$	−12909.0	−0.415677
$989$	0	0
$990$	−16449.3	−0.528073
$991$	−44303.9	−1.42014	−0.710070	−	0.704131i	$-0.751337\pi$
$991$	−44303.9	−1.42014	−0.710070	+	0.704131i	$0.751337\pi$
$992$	48662.0	1.55748
$993$	−2571.30	−0.0821730
$994$	−27384.1	−0.873813
$995$	8834.13	0.281468
$996$	7508.52	0.238872
$997$	−21056.6	−0.668874	−0.334437	−	0.942418i	$-0.608546\pi$
$997$	−21056.6	−0.668874	−0.334437	+	0.942418i	$0.608546\pi$
$998$	4839.60	0.153502
$999$	48954.1	1.55039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.32	✓	50
43.42	odd	2		1849.4.a.j.1.19	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.32	✓	50	1.1	even	1	trivial
1849.4.a.j.1.19	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)

\(f(q)\)	\(=\)	\(q+1.67189 q^{2} +3.03153 q^{3} -5.20480 q^{4} -19.6184 q^{5} +5.06836 q^{6} +28.4637 q^{7} -22.0769 q^{8} -17.8099 q^{9} +O(q^{10})\)	\(q+1.67189 q^{2} +3.03153 q^{3} -5.20480 q^{4} -19.6184 q^{5} +5.06836 q^{6} +28.4637 q^{7} -22.0769 q^{8} -17.8099 q^{9} -32.7997 q^{10} -28.1590 q^{11} -15.7785 q^{12} +20.8592 q^{13} +47.5880 q^{14} -59.4736 q^{15} +4.72834 q^{16} +24.2325 q^{17} -29.7760 q^{18} +118.903 q^{19} +102.110 q^{20} +86.2883 q^{21} -47.0785 q^{22} +61.3604 q^{23} -66.9267 q^{24} +259.881 q^{25} +34.8741 q^{26} -135.842 q^{27} -148.148 q^{28} +70.4167 q^{29} -99.4331 q^{30} +263.721 q^{31} +184.521 q^{32} -85.3646 q^{33} +40.5139 q^{34} -558.411 q^{35} +92.6967 q^{36} -360.375 q^{37} +198.791 q^{38} +63.2350 q^{39} +433.113 q^{40} +67.4488 q^{41} +144.264 q^{42} +146.562 q^{44} +349.401 q^{45} +102.588 q^{46} -457.632 q^{47} +14.3341 q^{48} +467.180 q^{49} +434.491 q^{50} +73.4614 q^{51} -108.568 q^{52} -148.507 q^{53} -227.113 q^{54} +552.433 q^{55} -628.390 q^{56} +360.456 q^{57} +117.729 q^{58} -182.072 q^{59} +309.548 q^{60} +215.513 q^{61} +440.912 q^{62} -506.934 q^{63} +270.670 q^{64} -409.223 q^{65} -142.720 q^{66} -631.508 q^{67} -126.125 q^{68} +186.016 q^{69} -933.599 q^{70} -575.441 q^{71} +393.187 q^{72} -1111.81 q^{73} -602.505 q^{74} +787.836 q^{75} -618.864 q^{76} -801.507 q^{77} +105.722 q^{78} -622.227 q^{79} -92.7624 q^{80} +69.0570 q^{81} +112.767 q^{82} -475.871 q^{83} -449.113 q^{84} -475.402 q^{85} +213.470 q^{87} +621.663 q^{88} -1393.87 q^{89} +584.158 q^{90} +593.728 q^{91} -319.369 q^{92} +799.478 q^{93} -765.109 q^{94} -2332.68 q^{95} +559.379 q^{96} +1066.32 q^{97} +781.071 q^{98} +501.507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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