LMFDB - Embedded newform 1849.4.a.i.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.25115 q^{2} +4.02813 q^{3} -2.93234 q^{4} +4.98765 q^{5} -9.06790 q^{6} +5.25109 q^{7} +24.6103 q^{8} -10.7742 q^{9} +O(q^{10})$	\(q-2.25115 q^{2} +4.02813 q^{3} -2.93234 q^{4} +4.98765 q^{5} -9.06790 q^{6} +5.25109 q^{7} +24.6103 q^{8} -10.7742 q^{9} -11.2279 q^{10} +25.9553 q^{11} -11.8118 q^{12} +14.2068 q^{13} -11.8210 q^{14} +20.0909 q^{15} -31.9427 q^{16} +20.3859 q^{17} +24.2543 q^{18} -2.21919 q^{19} -14.6255 q^{20} +21.1520 q^{21} -58.4292 q^{22} +39.1220 q^{23} +99.1334 q^{24} -100.123 q^{25} -31.9817 q^{26} -152.159 q^{27} -15.3980 q^{28} -277.025 q^{29} -45.2275 q^{30} -47.2599 q^{31} -124.975 q^{32} +104.551 q^{33} -45.8917 q^{34} +26.1906 q^{35} +31.5936 q^{36} -43.9224 q^{37} +4.99572 q^{38} +57.2270 q^{39} +122.748 q^{40} +98.7920 q^{41} -47.6164 q^{42} -76.1098 q^{44} -53.7380 q^{45} -88.0694 q^{46} +488.535 q^{47} -128.669 q^{48} -315.426 q^{49} +225.392 q^{50} +82.1171 q^{51} -41.6593 q^{52} -230.167 q^{53} +342.533 q^{54} +129.456 q^{55} +129.231 q^{56} -8.93917 q^{57} +623.623 q^{58} -400.770 q^{59} -58.9133 q^{60} -13.3239 q^{61} +106.389 q^{62} -56.5763 q^{63} +536.878 q^{64} +70.8588 q^{65} -235.360 q^{66} -640.592 q^{67} -59.7785 q^{68} +157.588 q^{69} -58.9589 q^{70} -251.714 q^{71} -265.156 q^{72} +526.799 q^{73} +98.8758 q^{74} -403.309 q^{75} +6.50741 q^{76} +136.294 q^{77} -128.826 q^{78} +978.288 q^{79} -159.319 q^{80} -322.013 q^{81} -222.395 q^{82} -37.2953 q^{83} -62.0250 q^{84} +101.678 q^{85} -1115.89 q^{87} +638.768 q^{88} -437.612 q^{89} +120.972 q^{90} +74.6014 q^{91} -114.719 q^{92} -190.369 q^{93} -1099.76 q^{94} -11.0685 q^{95} -503.414 q^{96} -1121.71 q^{97} +710.070 q^{98} -279.648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.25115	−0.795900	−0.397950	−	0.917407i	$-0.630278\pi$
$2$	−2.25115	−0.795900	−0.397950	+	0.917407i	$0.630278\pi$
$3$	4.02813	0.775213	0.387607	−	0.921825i	$-0.373302\pi$
$3$	4.02813	0.775213	0.387607	+	0.921825i	$0.373302\pi$
$4$	−2.93234	−0.366543
$5$	4.98765	0.446109	0.223054	−	0.974806i	$-0.428397\pi$
$5$	4.98765	0.446109	0.223054	+	0.974806i	$0.428397\pi$
$6$	−9.06790	−0.616992
$7$	5.25109	0.283532	0.141766	−	0.989900i	$-0.454722\pi$
$7$	5.25109	0.283532	0.141766	+	0.989900i	$0.454722\pi$
$8$	24.6103	1.08763
$9$	−10.7742	−0.399045
$10$	−11.2279	−0.355058
$11$	25.9553	0.711438	0.355719	−	0.934593i	$-0.384236\pi$
$11$	25.9553	0.711438	0.355719	+	0.934593i	$0.384236\pi$
$12$	−11.8118	−0.284149
$13$	14.2068	0.303098	0.151549	−	0.988450i	$-0.451574\pi$
$13$	14.2068	0.303098	0.151549	+	0.988450i	$0.451574\pi$
$14$	−11.8210	−0.225663
$15$	20.0909	0.345830
$16$	−31.9427	−0.499104
$17$	20.3859	0.290842	0.145421	−	0.989370i	$-0.453546\pi$
$17$	20.3859	0.290842	0.145421	+	0.989370i	$0.453546\pi$
$18$	24.2543	0.317600
$19$	−2.21919	−0.0267956	−0.0133978	−	0.999910i	$-0.504265\pi$
$19$	−2.21919	−0.0267956	−0.0133978	+	0.999910i	$0.504265\pi$
$20$	−14.6255	−0.163518
$21$	21.1520	0.219798
$22$	−58.4292	−0.566234
$23$	39.1220	0.354674	0.177337	−	0.984150i	$-0.443252\pi$
$23$	39.1220	0.354674	0.177337	+	0.984150i	$0.443252\pi$
$24$	99.1334	0.843146
$25$	−100.123	−0.800987
$26$	−31.9817	−0.241236
$27$	−152.159	−1.08456
$28$	−15.3980	−0.103927
$29$	−277.025	−1.77387	−0.886934	−	0.461896i	$-0.847169\pi$
$29$	−277.025	−1.77387	−0.886934	+	0.461896i	$0.847169\pi$
$30$	−45.2275	−0.275246
$31$	−47.2599	−0.273810	−0.136905	−	0.990584i	$-0.543716\pi$
$31$	−47.2599	−0.273810	−0.136905	+	0.990584i	$0.543716\pi$
$32$	−124.975	−0.690395
$33$	104.551	0.551516
$34$	−45.8917	−0.231481
$35$	26.1906	0.126486
$36$	31.5936	0.146267
$37$	−43.9224	−0.195157	−0.0975784	−	0.995228i	$-0.531110\pi$
$37$	−43.9224	−0.195157	−0.0975784	+	0.995228i	$0.531110\pi$
$38$	4.99572	0.0213266
$39$	57.2270	0.234965
$40$	122.748	0.485202
$41$	98.7920	0.376310	0.188155	−	0.982139i	$-0.439749\pi$
$41$	98.7920	0.376310	0.188155	+	0.982139i	$0.439749\pi$
$42$	−47.6164	−0.174937
$43$	0	0
$43$	0	0
$44$	−76.1098	−0.260772
$45$	−53.7380	−0.178017
$46$	−88.0694	−0.282285
$47$	488.535	1.51617	0.758086	−	0.652154i	$-0.226134\pi$
$47$	488.535	1.51617	0.758086	+	0.652154i	$0.226134\pi$
$48$	−128.669	−0.386912
$49$	−315.426	−0.919609
$50$	225.392	0.637506
$51$	82.1171	0.225465
$52$	−41.6593	−0.111098
$53$	−230.167	−0.596525	−0.298263	−	0.954484i	$-0.596407\pi$
$53$	−230.167	−0.596525	−0.298263	+	0.954484i	$0.596407\pi$
$54$	342.533	0.863200
$55$	129.456	0.317379
$56$	129.231	0.308379
$57$	−8.93917	−0.0207723
$58$	623.623	1.41182
$59$	−400.770	−0.884335	−0.442167	−	0.896933i	$-0.645790\pi$
$59$	−400.770	−0.884335	−0.442167	+	0.896933i	$0.645790\pi$
$60$	−58.9133	−0.126761
$61$	−13.3239	−0.0279665	−0.0139832	−	0.999902i	$-0.504451\pi$
$61$	−13.3239	−0.0279665	−0.0139832	+	0.999902i	$0.504451\pi$
$62$	106.389	0.217926
$63$	−56.5763	−0.113142
$64$	536.878	1.04859
$65$	70.8588	0.135215
$66$	−235.360	−0.438952
$67$	−640.592	−1.16807	−0.584036	−	0.811728i	$-0.698527\pi$
$67$	−640.592	−1.16807	−0.584036	+	0.811728i	$0.698527\pi$
$68$	−59.7785	−0.106606
$69$	157.588	0.274948
$70$	−58.9589	−0.100670
$71$	−251.714	−0.420746	−0.210373	−	0.977621i	$-0.567468\pi$
$71$	−251.714	−0.420746	−0.210373	+	0.977621i	$0.567468\pi$
$72$	−265.156	−0.434014
$73$	526.799	0.844618	0.422309	−	0.906452i	$-0.361220\pi$
$73$	526.799	0.844618	0.422309	+	0.906452i	$0.361220\pi$
$74$	98.8758	0.155325
$75$	−403.309	−0.620935
$76$	6.50741	0.00982173
$77$	136.294	0.201716
$78$	−128.826	−0.187009
$79$	978.288	1.39324	0.696620	−	0.717440i	$-0.254686\pi$
$79$	978.288	1.39324	0.696620	+	0.717440i	$0.254686\pi$
$80$	−159.319	−0.222655
$81$	−322.013	−0.441719
$82$	−222.395	−0.299505
$83$	−37.2953	−0.0493215	−0.0246608	−	0.999696i	$-0.507851\pi$
$83$	−37.2953	−0.0493215	−0.0246608	+	0.999696i	$0.507851\pi$
$84$	−62.0250	−0.0805653
$85$	101.678	0.129747
$86$	0	0
$87$	−1115.89	−1.37513
$88$	638.768	0.773783
$89$	−437.612	−0.521200	−0.260600	−	0.965447i	$-0.583920\pi$
$89$	−437.612	−0.521200	−0.260600	+	0.965447i	$0.583920\pi$
$90$	120.972	0.141684
$91$	74.6014	0.0859380
$92$	−114.719	−0.130003
$93$	−190.369	−0.212261
$94$	−1099.76	−1.20672
$95$	−11.0685	−0.0119538
$96$	−503.414	−0.535203
$97$	−1121.71	−1.17415	−0.587075	−	0.809533i	$-0.699721\pi$
$97$	−1121.71	−1.17415	−0.587075	+	0.809533i	$0.699721\pi$
$98$	710.070	0.731918
$99$	−279.648	−0.283896
$100$	293.596	0.293596
$101$	1581.80	1.55837	0.779183	−	0.626796i	$-0.215634\pi$
$101$	1581.80	1.55837	0.779183	+	0.626796i	$0.215634\pi$
$102$	−184.858	−0.179447
$103$	−972.456	−0.930281	−0.465141	−	0.885237i	$-0.653996\pi$
$103$	−972.456	−0.930281	−0.465141	+	0.885237i	$0.653996\pi$
$104$	349.635	0.329659
$105$	105.499	0.0980538
$106$	518.139	0.474775
$107$	1961.57	1.77226	0.886132	−	0.463433i	$-0.153383\pi$
$107$	1961.57	1.77226	0.886132	+	0.463433i	$0.153383\pi$
$108$	446.183	0.397537
$109$	−2028.69	−1.78269	−0.891347	−	0.453322i	$-0.850239\pi$
$109$	−2028.69	−1.78269	−0.891347	+	0.453322i	$0.850239\pi$
$110$	−291.424	−0.252602
$111$	−176.925	−0.151288
$112$	−167.734	−0.141512
$113$	−1359.59	−1.13185	−0.565925	−	0.824457i	$-0.691481\pi$
$113$	−1359.59	−1.13185	−0.565925	+	0.824457i	$0.691481\pi$
$114$	20.1234	0.0165327
$115$	195.127	0.158223
$116$	812.330	0.650198
$117$	−153.067	−0.120950
$118$	902.191	0.703842
$119$	107.048	0.0824631
$120$	494.443	0.376135
$121$	−657.322	−0.493856
$122$	29.9941	0.0222585
$123$	397.946	0.291720
$124$	138.582	0.100363
$125$	−1122.84	−0.803436
$126$	127.362	0.0900498
$127$	641.350	0.448115	0.224057	−	0.974576i	$-0.428070\pi$
$127$	641.350	0.448115	0.224057	+	0.974576i	$0.428070\pi$
$128$	−208.792	−0.144178
$129$	0	0
$130$	−159.513	−0.107617
$131$	1243.19	0.829146	0.414573	−	0.910016i	$-0.363931\pi$
$131$	1243.19	0.829146	0.414573	+	0.910016i	$0.363931\pi$
$132$	−306.580	−0.202154
$133$	−11.6532	−0.00759742
$134$	1442.07	0.929669
$135$	−758.917	−0.483831
$136$	501.704	0.316329
$137$	2114.51	1.31865	0.659323	−	0.751860i	$-0.270843\pi$
$137$	2114.51	1.31865	0.659323	+	0.751860i	$0.270843\pi$
$138$	−354.755	−0.218831
$139$	−3137.34	−1.91443	−0.957216	−	0.289374i	$-0.906553\pi$
$139$	−3137.34	−1.91443	−0.957216	+	0.289374i	$0.906553\pi$
$140$	−76.7997	−0.0463626
$141$	1967.88	1.17536
$142$	566.645	0.334872
$143$	368.743	0.215635
$144$	344.157	0.199165
$145$	−1381.70	−0.791338
$146$	−1185.90	−0.672232
$147$	−1270.58	−0.712893
$148$	128.795	0.0715332
$149$	1460.78	0.803167	0.401584	−	0.915822i	$-0.368460\pi$
$149$	1460.78	0.803167	0.401584	+	0.915822i	$0.368460\pi$
$150$	907.908	0.494203
$151$	3084.79	1.66249	0.831246	−	0.555905i	$-0.187628\pi$
$151$	3084.79	1.66249	0.831246	+	0.555905i	$0.187628\pi$
$152$	−54.6149	−0.0291438
$153$	−219.642	−0.116059
$154$	−306.817	−0.160546
$155$	−235.716	−0.122149
$156$	−167.809	−0.0861248
$157$	−2713.54	−1.37939	−0.689695	−	0.724100i	$-0.742255\pi$
$157$	−2713.54	−1.37939	−0.689695	+	0.724100i	$0.742255\pi$
$158$	−2202.27	−1.10888
$159$	−927.141	−0.462434
$160$	−623.331	−0.307991
$161$	205.433	0.100562
$162$	724.898	0.351564
$163$	1564.36	0.751721	0.375860	−	0.926676i	$-0.377347\pi$
$163$	1564.36	0.751721	0.375860	+	0.926676i	$0.377347\pi$
$164$	−289.692	−0.137934
$165$	521.465	0.246036
$166$	83.9571	0.0392550
$167$	508.284	0.235522	0.117761	−	0.993042i	$-0.462428\pi$
$167$	508.284	0.235522	0.117761	+	0.993042i	$0.462428\pi$
$168$	520.558	0.239059
$169$	−1995.17	−0.908132
$170$	−228.892	−0.103266
$171$	23.9100	0.0106926
$172$	0	0
$173$	−2615.65	−1.14950	−0.574751	−	0.818328i	$-0.694901\pi$
$173$	−2615.65	−1.14950	−0.574751	+	0.818328i	$0.694901\pi$
$174$	2512.03	1.09446
$175$	−525.757	−0.227106
$176$	−829.082	−0.355082
$177$	−1614.35	−0.685548
$178$	985.129	0.414823
$179$	−1299.11	−0.542458	−0.271229	−	0.962515i	$-0.587430\pi$
$179$	−1299.11	−0.542458	−0.271229	+	0.962515i	$0.587430\pi$
$180$	157.578	0.0652509
$181$	−1263.14	−0.518721	−0.259360	−	0.965781i	$-0.583512\pi$
$181$	−1263.14	−0.518721	−0.259360	+	0.965781i	$0.583512\pi$
$182$	−167.939	−0.0683981
$183$	−53.6705	−0.0216800
$184$	962.805	0.385755
$185$	−219.070	−0.0870612
$186$	428.548	0.168939
$187$	529.123	0.206916
$188$	−1432.55	−0.555742
$189$	−799.002	−0.307507
$190$	24.9169	0.00951400
$191$	−1507.21	−0.570985	−0.285493	−	0.958381i	$-0.592157\pi$
$191$	−1507.21	−0.570985	−0.285493	+	0.958381i	$0.592157\pi$
$192$	2162.61	0.812880
$193$	643.966	0.240175	0.120087	−	0.992763i	$-0.461683\pi$
$193$	643.966	0.240175	0.120087	+	0.992763i	$0.461683\pi$
$194$	2525.14	0.934506
$195$	285.428	0.104820
$196$	924.937	0.337076
$197$	−3128.98	−1.13163	−0.565813	−	0.824534i	$-0.691438\pi$
$197$	−3128.98	−1.13163	−0.565813	+	0.824534i	$0.691438\pi$
$198$	629.528	0.225953
$199$	−4879.50	−1.73818	−0.869092	−	0.494650i	$-0.835296\pi$
$199$	−4879.50	−1.73818	−0.869092	+	0.494650i	$0.835296\pi$
$200$	−2464.07	−0.871179
$201$	−2580.39	−0.905505
$202$	−3560.86	−1.24030
$203$	−1454.68	−0.502949
$204$	−240.795	−0.0826424
$205$	492.740	0.167875
$206$	2189.14	0.740411
$207$	−421.509	−0.141531
$208$	−453.804	−0.151277
$209$	−57.5997	−0.0190634
$210$	−237.494	−0.0780411
$211$	−79.4254	−0.0259141	−0.0129570	−	0.999916i	$-0.504124\pi$
$211$	−79.4254	−0.0259141	−0.0129570	+	0.999916i	$0.504124\pi$
$212$	674.927	0.218652
$213$	−1013.94	−0.326168
$214$	−4415.78	−1.41055
$215$	0	0
$216$	−3744.68	−1.17960
$217$	−248.166	−0.0776341
$218$	4566.89	1.41885
$219$	2122.01	0.654759
$220$	−379.609	−0.116333
$221$	289.620	0.0881536
$222$	398.284	0.120410
$223$	2831.34	0.850226	0.425113	−	0.905140i	$-0.360234\pi$
$223$	2831.34	0.850226	0.425113	+	0.905140i	$0.360234\pi$
$224$	−656.254	−0.195749
$225$	1078.75	0.319629
$226$	3060.63	0.900840
$227$	3030.54	0.886097	0.443049	−	0.896498i	$-0.353897\pi$
$227$	3030.54	0.886097	0.443049	+	0.896498i	$0.353897\pi$
$228$	26.2127	0.00761393
$229$	6084.93	1.75591	0.877956	−	0.478742i	$-0.158907\pi$
$229$	6084.93	1.75591	0.877956	+	0.478742i	$0.158907\pi$
$230$	−439.260	−0.125930
$231$	549.008	0.156373
$232$	−6817.66	−1.92932
$233$	−5872.34	−1.65111	−0.825557	−	0.564319i	$-0.809139\pi$
$233$	−5872.34	−1.65111	−0.825557	+	0.564319i	$0.809139\pi$
$234$	344.577	0.0962638
$235$	2436.64	0.676378
$236$	1175.19	0.324146
$237$	3940.66	1.08006
$238$	−240.982	−0.0656324
$239$	−1168.26	−0.316187	−0.158093	−	0.987424i	$-0.550535\pi$
$239$	−1168.26	−0.316187	−0.158093	+	0.987424i	$0.550535\pi$
$240$	−641.756	−0.172605
$241$	2150.85	0.574890	0.287445	−	0.957797i	$-0.407194\pi$
$241$	2150.85	0.574890	0.287445	+	0.957797i	$0.407194\pi$
$242$	1479.73	0.393060
$243$	2811.19	0.742132
$244$	39.0703	0.0102509
$245$	−1573.23	−0.410246
$246$	−895.836	−0.232180
$247$	−31.5277	−0.00812169
$248$	−1163.08	−0.297805
$249$	−150.230	−0.0382347
$250$	2527.67	0.639455
$251$	−982.679	−0.247116	−0.123558	−	0.992337i	$-0.539431\pi$
$251$	−982.679	−0.247116	−0.123558	+	0.992337i	$0.539431\pi$
$252$	165.901	0.0414714
$253$	1015.42	0.252329
$254$	−1443.77	−0.356655
$255$	409.572	0.100582
$256$	−3825.00	−0.933838
$257$	585.060	0.142004	0.0710020	−	0.997476i	$-0.477380\pi$
$257$	585.060	0.142004	0.0710020	+	0.997476i	$0.477380\pi$
$258$	0	0
$259$	−230.640	−0.0553332
$260$	−207.782	−0.0495619
$261$	2984.72	0.707852
$262$	−2798.60	−0.659917
$263$	−104.375	−0.0244715	−0.0122358	−	0.999925i	$-0.503895\pi$
$263$	−104.375	−0.0244715	−0.0122358	+	0.999925i	$0.503895\pi$
$264$	2573.04	0.599847
$265$	−1147.99	−0.266115
$266$	26.2329	0.00604679
$267$	−1762.76	−0.404041
$268$	1878.44	0.428148
$269$	5940.70	1.34651	0.673254	−	0.739411i	$-0.264896\pi$
$269$	5940.70	1.34651	0.673254	+	0.739411i	$0.264896\pi$
$270$	1708.43	0.385081
$271$	3256.54	0.729965	0.364982	−	0.931014i	$-0.381075\pi$
$271$	3256.54	0.729965	0.364982	+	0.931014i	$0.381075\pi$
$272$	−651.181	−0.145160
$273$	300.504	0.0666202
$274$	−4760.06	−1.04951
$275$	−2598.73	−0.569853
$276$	−462.103	−0.100780
$277$	−5348.68	−1.16018	−0.580092	−	0.814551i	$-0.696983\pi$
$277$	−5348.68	−1.16018	−0.580092	+	0.814551i	$0.696983\pi$
$278$	7062.62	1.52370
$279$	509.187	0.109263
$280$	644.558	0.137570
$281$	−3582.54	−0.760557	−0.380279	−	0.924872i	$-0.624172\pi$
$281$	−3582.54	−0.760557	−0.380279	+	0.924872i	$0.624172\pi$
$282$	−4429.98	−0.935467
$283$	−7997.08	−1.67978	−0.839889	−	0.542759i	$-0.817380\pi$
$283$	−7997.08	−1.67978	−0.839889	+	0.542759i	$0.817380\pi$
$284$	738.111	0.154221
$285$	−44.5854	−0.00926671
$286$	−830.095	−0.171624
$287$	518.765	0.106696
$288$	1346.50	0.275498
$289$	−4497.41	−0.915411
$290$	3110.41	0.629827
$291$	−4518.39	−0.910216
$292$	−1544.75	−0.309589
$293$	−8020.77	−1.59924	−0.799621	−	0.600504i	$-0.794966\pi$
$293$	−8020.77	−1.59924	−0.799621	+	0.600504i	$0.794966\pi$
$294$	2860.25	0.567392
$295$	−1998.90	−0.394510
$296$	−1080.94	−0.212259
$297$	−3949.34	−0.771596
$298$	−3288.43	−0.639241
$299$	555.801	0.107501
$300$	1182.64	0.227599
$301$	0	0
$302$	−6944.30	−1.32318
$303$	6371.69	1.20807
$304$	70.8867	0.0133738
$305$	−66.4552	−0.0124761
$306$	494.447	0.0923714
$307$	4940.98	0.918556	0.459278	−	0.888292i	$-0.348108\pi$
$307$	4940.98	0.918556	0.459278	+	0.888292i	$0.348108\pi$
$308$	−399.659	−0.0739374
$309$	−3917.18	−0.721166
$310$	530.630	0.0972186
$311$	3934.00	0.717288	0.358644	−	0.933474i	$-0.383239\pi$
$311$	3934.00	0.717288	0.358644	+	0.933474i	$0.383239\pi$
$312$	1408.37	0.255556
$313$	2101.15	0.379437	0.189719	−	0.981839i	$-0.439242\pi$
$313$	2101.15	0.379437	0.189719	+	0.981839i	$0.439242\pi$
$314$	6108.58	1.09786
$315$	−282.183	−0.0504737
$316$	−2868.67	−0.510682
$317$	5062.65	0.896993	0.448497	−	0.893785i	$-0.351960\pi$
$317$	5062.65	0.896993	0.448497	+	0.893785i	$0.351960\pi$
$318$	2087.13	0.368051
$319$	−7190.26	−1.26200
$320$	2677.76	0.467785
$321$	7901.45	1.37388
$322$	−462.460	−0.0800370
$323$	−45.2402	−0.00779329
$324$	944.252	0.161909
$325$	−1422.44	−0.242777
$326$	−3521.61	−0.598295
$327$	−8171.83	−1.38197
$328$	2431.30	0.409287
$329$	2565.34	0.429884
$330$	−1173.89	−0.195820
$331$	−7137.29	−1.18520	−0.592599	−	0.805497i	$-0.701898\pi$
$331$	−7137.29	−1.18520	−0.592599	+	0.805497i	$0.701898\pi$
$332$	109.362	0.0180784
$333$	473.229	0.0778762
$334$	−1144.22	−0.187452
$335$	−3195.05	−0.521087
$336$	−675.653	−0.109702
$337$	−6668.67	−1.07794	−0.538970	−	0.842325i	$-0.681186\pi$
$337$	−6668.67	−1.07794	−0.538970	+	0.842325i	$0.681186\pi$
$338$	4491.41	0.722782
$339$	−5476.58	−0.877425
$340$	−298.154	−0.0475579
$341$	−1226.64	−0.194799
$342$	−53.8249	−0.00851028
$343$	−3457.45	−0.544271
$344$	0	0
$345$	785.996	0.122657
$346$	5888.20	0.914889
$347$	7743.07	1.19790	0.598948	−	0.800788i	$-0.295586\pi$
$347$	7743.07	1.19790	0.598948	+	0.800788i	$0.295586\pi$
$348$	3272.17	0.504042
$349$	928.356	0.142389	0.0711945	−	0.997462i	$-0.477319\pi$
$349$	928.356	0.142389	0.0711945	+	0.997462i	$0.477319\pi$
$350$	1183.56	0.180753
$351$	−2161.70	−0.328727
$352$	−3243.76	−0.491173
$353$	−4940.92	−0.744982	−0.372491	−	0.928036i	$-0.621496\pi$
$353$	−4940.92	−0.744982	−0.372491	+	0.928036i	$0.621496\pi$
$354$	3634.14	0.545628
$355$	−1255.46	−0.187699
$356$	1283.23	0.191042
$357$	431.204	0.0639265
$358$	2924.49	0.431743
$359$	−308.245	−0.0453163	−0.0226581	−	0.999743i	$-0.507213\pi$
$359$	−308.245	−0.0453163	−0.0226581	+	0.999743i	$0.507213\pi$
$360$	−1322.51	−0.193617
$361$	−6854.08	−0.999282
$362$	2843.51	0.412850
$363$	−2647.78	−0.382843
$364$	−218.757	−0.0314999
$365$	2627.49	0.376792
$366$	120.820	0.0172551
$367$	−8207.98	−1.16745	−0.583724	−	0.811952i	$-0.698405\pi$
$367$	−8207.98	−1.16745	−0.583724	+	0.811952i	$0.698405\pi$
$368$	−1249.66	−0.177019
$369$	−1064.40	−0.150164
$370$	493.158	0.0692920
$371$	−1208.63	−0.169134
$372$	558.226	0.0778028
$373$	6480.94	0.899653	0.449826	−	0.893116i	$-0.351486\pi$
$373$	6480.94	0.899653	0.449826	+	0.893116i	$0.351486\pi$
$374$	−1191.13	−0.164685
$375$	−4522.93	−0.622834
$376$	12023.0	1.64904
$377$	−3935.65	−0.537655
$378$	1798.67	0.244745
$379$	−7927.62	−1.07444	−0.537222	−	0.843441i	$-0.680526\pi$
$379$	−7927.62	−1.07444	−0.537222	+	0.843441i	$0.680526\pi$
$380$	32.4567	0.00438156
$381$	2583.44	0.347384
$382$	3392.96	0.454447
$383$	−13330.3	−1.77845	−0.889227	−	0.457467i	$-0.848757\pi$
$383$	−13330.3	−1.77845	−0.889227	+	0.457467i	$0.848757\pi$
$384$	−841.041	−0.111769
$385$	679.785	0.0899872
$386$	−1449.66	−0.191155
$387$	0	0
$388$	3289.24	0.430376
$389$	−83.9976	−0.0109482	−0.00547410	−	0.999985i	$-0.501742\pi$
$389$	−83.9976	−0.0109482	−0.00547410	+	0.999985i	$0.501742\pi$
$390$	−642.540	−0.0834264
$391$	797.540	0.103154
$392$	−7762.73	−1.00020
$393$	5007.73	0.642765
$394$	7043.78	0.900661
$395$	4879.36	0.621537
$396$	820.023	0.104060
$397$	−3720.21	−0.470307	−0.235154	−	0.971958i	$-0.575559\pi$
$397$	−3720.21	−0.470307	−0.235154	+	0.971958i	$0.575559\pi$
$398$	10984.5	1.38342
$399$	−46.9404	−0.00588962
$400$	3198.21	0.399776
$401$	−10601.0	−1.32018	−0.660088	−	0.751188i	$-0.729481\pi$
$401$	−10601.0	−1.32018	−0.660088	+	0.751188i	$0.729481\pi$
$402$	5808.83	0.720692
$403$	−671.414	−0.0829913
$404$	−4638.38	−0.571208
$405$	−1606.09	−0.197055
$406$	3274.70	0.400297
$407$	−1140.02	−0.138842
$408$	2020.93	0.245223
$409$	−3919.36	−0.473839	−0.236919	−	0.971529i	$-0.576138\pi$
$409$	−3919.36	−0.473839	−0.236919	+	0.971529i	$0.576138\pi$
$410$	−1109.23	−0.133612
$411$	8517.50	1.02223
$412$	2851.57	0.340988
$413$	−2104.48	−0.250737
$414$	948.878	0.112644
$415$	−186.016	−0.0220028
$416$	−1775.50	−0.209257
$417$	−12637.6	−1.48409
$418$	129.665	0.0151726
$419$	4415.24	0.514793	0.257397	−	0.966306i	$-0.417135\pi$
$419$	4415.24	0.514793	0.257397	+	0.966306i	$0.417135\pi$
$420$	−309.359	−0.0359409
$421$	−7715.34	−0.893165	−0.446583	−	0.894742i	$-0.647359\pi$
$421$	−7715.34	−0.893165	−0.446583	+	0.894742i	$0.647359\pi$
$422$	178.798	0.0206250
$423$	−5263.57	−0.605021
$424$	−5664.47	−0.648800
$425$	−2041.11	−0.232961
$426$	2282.52	0.259597
$427$	−69.9652	−0.00792940
$428$	−5751.99	−0.649610
$429$	1485.34	0.167163
$430$	0	0
$431$	10963.5	1.22527	0.612636	−	0.790365i	$-0.290109\pi$
$431$	10963.5	1.22527	0.612636	+	0.790365i	$0.290109\pi$
$432$	4860.37	0.541307
$433$	−3896.75	−0.432485	−0.216242	−	0.976340i	$-0.569380\pi$
$433$	−3896.75	−0.432485	−0.216242	+	0.976340i	$0.569380\pi$
$434$	558.657	0.0617890
$435$	−5565.67	−0.613456
$436$	5948.82	0.653433
$437$	−86.8191	−0.00950371
$438$	−4776.96	−0.521123
$439$	−7414.58	−0.806102	−0.403051	−	0.915178i	$-0.632050\pi$
$439$	−7414.58	−0.806102	−0.403051	+	0.915178i	$0.632050\pi$
$440$	3185.95	0.345191
$441$	3398.46	0.366965
$442$	−651.977	−0.0701615
$443$	−8192.89	−0.878681	−0.439341	−	0.898321i	$-0.644788\pi$
$443$	−8192.89	−0.878681	−0.439341	+	0.898321i	$0.644788\pi$
$444$	518.804	0.0554535
$445$	−2182.66	−0.232512
$446$	−6373.76	−0.676695
$447$	5884.21	0.622626
$448$	2819.19	0.297309
$449$	−8163.71	−0.858061	−0.429031	−	0.903290i	$-0.641145\pi$
$449$	−8163.71	−0.858061	−0.429031	+	0.903290i	$0.641145\pi$
$450$	−2428.42	−0.254393
$451$	2564.18	0.267721
$452$	3986.77	0.414871
$453$	12425.9	1.28879
$454$	−6822.19	−0.705245
$455$	372.086	0.0383377
$456$	−219.996	−0.0225926
$457$	−7695.45	−0.787698	−0.393849	−	0.919175i	$-0.628857\pi$
$457$	−7695.45	−0.787698	−0.393849	+	0.919175i	$0.628857\pi$
$458$	−13698.1	−1.39753
$459$	−3101.91	−0.315435
$460$	−572.179	−0.0579956
$461$	−2082.47	−0.210392	−0.105196	−	0.994452i	$-0.533547\pi$
$461$	−2082.47	−0.210392	−0.105196	+	0.994452i	$0.533547\pi$
$462$	−1235.90	−0.124457
$463$	2804.81	0.281535	0.140767	−	0.990043i	$-0.455043\pi$
$463$	2804.81	0.281535	0.140767	+	0.990043i	$0.455043\pi$
$464$	8848.90	0.885345
$465$	−949.492	−0.0946917
$466$	13219.5	1.31412
$467$	−17860.1	−1.76974	−0.884869	−	0.465839i	$-0.845752\pi$
$467$	−17860.1	−1.76974	−0.884869	+	0.465839i	$0.845752\pi$
$468$	448.846	0.0443331
$469$	−3363.81	−0.331186
$470$	−5485.23	−0.538330
$471$	−10930.5	−1.06932
$472$	−9863.06	−0.961831
$473$	0	0
$474$	−8871.01	−0.859618
$475$	222.192	0.0214629
$476$	−313.902	−0.0302262
$477$	2479.86	0.238040
$478$	2629.93	0.251653
$479$	920.735	0.0878277	0.0439138	−	0.999035i	$-0.486017\pi$
$479$	920.735	0.0878277	0.0439138	+	0.999035i	$0.486017\pi$
$480$	−2510.85	−0.238759
$481$	−623.999	−0.0591516
$482$	−4841.88	−0.457555
$483$	827.511	0.0779567
$484$	1927.49	0.181019
$485$	−5594.70	−0.523799
$486$	−6328.40	−0.590663
$487$	1931.99	0.179768	0.0898839	−	0.995952i	$-0.471350\pi$
$487$	1931.99	0.179768	0.0898839	+	0.995952i	$0.471350\pi$
$488$	−327.906	−0.0304172
$489$	6301.46	0.582744
$490$	3541.58	0.326515
$491$	14234.0	1.30830	0.654148	−	0.756367i	$-0.273027\pi$
$491$	14234.0	1.30830	0.654148	+	0.756367i	$0.273027\pi$
$492$	−1166.91	−0.106928
$493$	−5647.41	−0.515916
$494$	70.9734	0.00646405
$495$	−1394.79	−0.126648
$496$	1509.61	0.136660
$497$	−1321.77	−0.119295
$498$	338.190	0.0304310
$499$	−477.809	−0.0428651	−0.0214325	−	0.999770i	$-0.506823\pi$
$499$	−477.809	−0.0428651	−0.0214325	+	0.999770i	$0.506823\pi$
$500$	3292.54	0.294494
$501$	2047.43	0.182580
$502$	2212.15	0.196680
$503$	−2881.02	−0.255384	−0.127692	−	0.991814i	$-0.540757\pi$
$503$	−2881.02	−0.255384	−0.127692	+	0.991814i	$0.540757\pi$
$504$	−1392.36	−0.123057
$505$	7889.47	0.695201
$506$	−2285.87	−0.200829
$507$	−8036.78	−0.703996
$508$	−1880.66	−0.164253
$509$	−15177.9	−1.32171	−0.660854	−	0.750514i	$-0.729806\pi$
$509$	−15177.9	−1.32171	−0.660854	+	0.750514i	$0.729806\pi$
$510$	−922.005	−0.0800531
$511$	2766.27	0.239476
$512$	10281.0	0.887420
$513$	337.670	0.0290614
$514$	−1317.05	−0.113021
$515$	−4850.27	−0.415007
$516$	0	0
$517$	12680.1	1.07866
$518$	519.205	0.0440397
$519$	−10536.1	−0.891109
$520$	1743.86	0.147064
$521$	5817.50	0.489192	0.244596	−	0.969625i	$-0.421345\pi$
$521$	5817.50	0.489192	0.244596	+	0.969625i	$0.421345\pi$
$522$	−6719.04	−0.563380
$523$	7595.81	0.635070	0.317535	−	0.948247i	$-0.397145\pi$
$523$	7595.81	0.635070	0.317535	+	0.948247i	$0.397145\pi$
$524$	−3645.46	−0.303917
$525$	−2117.81	−0.176055
$526$	234.962	0.0194769
$527$	−963.437	−0.0796356
$528$	−3339.64	−0.275264
$529$	−10636.5	−0.874206
$530$	2584.30	0.211801
$531$	4317.97	0.352889
$532$	34.1710	0.00278478
$533$	1403.52	0.114059
$534$	3968.22	0.321576
$535$	9783.63	0.790623
$536$	−15765.2	−1.27043
$537$	−5232.98	−0.420521
$538$	−13373.4	−1.07169
$539$	−8186.98	−0.654245
$540$	2225.40	0.177345
$541$	5132.13	0.407851	0.203925	−	0.978986i	$-0.434630\pi$
$541$	5132.13	0.407851	0.203925	+	0.978986i	$0.434630\pi$
$542$	−7330.94	−0.580979
$543$	−5088.09	−0.402119
$544$	−2547.73	−0.200796
$545$	−10118.4	−0.795276
$546$	−676.478	−0.0530231
$547$	6569.33	0.513500	0.256750	−	0.966478i	$-0.417348\pi$
$547$	6569.33	0.513500	0.256750	+	0.966478i	$0.417348\pi$
$548$	−6200.45	−0.483340
$549$	143.555	0.0111599
$550$	5850.13	0.453546
$551$	614.769	0.0475319
$552$	3878.30	0.299042
$553$	5137.08	0.395028
$554$	12040.7	0.923390
$555$	−882.440	−0.0674910
$556$	9199.76	0.701721
$557$	7594.11	0.577689	0.288845	−	0.957376i	$-0.406729\pi$
$557$	7594.11	0.577689	0.288845	+	0.957376i	$0.406729\pi$
$558$	−1146.26	−0.0869621
$559$	0	0
$560$	−836.597	−0.0631298
$561$	2131.38	0.160404
$562$	8064.83	0.605328
$563$	12214.0	0.914318	0.457159	−	0.889385i	$-0.348867\pi$
$563$	12214.0	0.914318	0.457159	+	0.889385i	$0.348867\pi$
$564$	−5770.49	−0.430818
$565$	−6781.14	−0.504929
$566$	18002.6	1.33694
$567$	−1690.92	−0.125241
$568$	−6194.76	−0.457617
$569$	−11696.6	−0.861772	−0.430886	−	0.902406i	$-0.641799\pi$
$569$	−11696.6	−0.861772	−0.430886	+	0.902406i	$0.641799\pi$
$570$	100.368	0.00737538
$571$	17353.9	1.27187	0.635936	−	0.771742i	$-0.280614\pi$
$571$	17353.9	1.27187	0.635936	+	0.771742i	$0.280614\pi$
$572$	−1081.28	−0.0790395
$573$	−6071.25	−0.442635
$574$	−1167.82	−0.0849194
$575$	−3917.03	−0.284089
$576$	−5784.43	−0.418434
$577$	−14209.3	−1.02520	−0.512602	−	0.858626i	$-0.671318\pi$
$577$	−14209.3	−1.02520	−0.512602	+	0.858626i	$0.671318\pi$
$578$	10124.3	0.728576
$579$	2593.98	0.186186
$580$	4051.62	0.290059
$581$	−195.841	−0.0139842
$582$	10171.6	0.724441
$583$	−5974.05	−0.424391
$584$	12964.7	0.918634
$585$	−763.447	−0.0539567
$586$	18055.9	1.27284
$587$	12326.7	0.866740	0.433370	−	0.901216i	$-0.357324\pi$
$587$	12326.7	0.866740	0.433370	+	0.901216i	$0.357324\pi$
$588$	3725.76	0.261306
$589$	104.878	0.00733691
$590$	4499.81	0.313990
$591$	−12603.9	−0.877251
$592$	1403.00	0.0974035
$593$	−18961.8	−1.31310	−0.656548	−	0.754284i	$-0.727984\pi$
$593$	−18961.8	−1.31310	−0.656548	+	0.754284i	$0.727984\pi$
$594$	8890.54	0.614113
$595$	533.920	0.0367875
$596$	−4283.51	−0.294395
$597$	−19655.3	−1.34746
$598$	−1251.19	−0.0855601
$599$	14749.8	1.00611	0.503054	−	0.864255i	$-0.332210\pi$
$599$	14749.8	1.00611	0.503054	+	0.864255i	$0.332210\pi$
$600$	−9925.56	−0.675349
$601$	14740.4	1.00045	0.500227	−	0.865894i	$-0.333250\pi$
$601$	14740.4	1.00045	0.500227	+	0.865894i	$0.333250\pi$
$602$	0	0
$603$	6901.87	0.466113
$604$	−9045.64	−0.609374
$605$	−3278.49	−0.220313
$606$	−14343.6	−0.961501
$607$	28252.6	1.88919	0.944595	−	0.328239i	$-0.106455\pi$
$607$	28252.6	1.88919	0.944595	+	0.328239i	$0.106455\pi$
$608$	277.342	0.0184995
$609$	−5859.64	−0.389892
$610$	149.600	0.00992973
$611$	6940.54	0.459549
$612$	644.066	0.0425406
$613$	−24635.3	−1.62318	−0.811591	−	0.584226i	$-0.801398\pi$
$613$	−24635.3	−1.62318	−0.811591	+	0.584226i	$0.801398\pi$
$614$	−11122.9	−0.731079
$615$	1984.82	0.130139
$616$	3354.23	0.219392
$617$	−2636.49	−0.172028	−0.0860140	−	0.996294i	$-0.527413\pi$
$617$	−2636.49	−0.172028	−0.0860140	+	0.996294i	$0.527413\pi$
$618$	8818.14	0.573977
$619$	9682.05	0.628683	0.314341	−	0.949310i	$-0.398216\pi$
$619$	9682.05	0.628683	0.314341	+	0.949310i	$0.398216\pi$
$620$	691.198	0.0447729
$621$	−5952.78	−0.384665
$622$	−8856.01	−0.570890
$623$	−2297.94	−0.147777
$624$	−1827.98	−0.117272
$625$	6915.10	0.442567
$626$	−4729.99	−0.301994
$627$	−232.019	−0.0147782
$628$	7957.03	0.505605
$629$	−895.400	−0.0567598
$630$	635.235	0.0401720
$631$	−6750.28	−0.425871	−0.212935	−	0.977066i	$-0.568302\pi$
$631$	−6750.28	−0.425871	−0.212935	+	0.977066i	$0.568302\pi$
$632$	24075.9	1.51533
$633$	−319.936	−0.0200889
$634$	−11396.8	−0.713917
$635$	3198.83	0.199908
$636$	2718.69	0.169502
$637$	−4481.21	−0.278732
$638$	16186.3	1.00442
$639$	2712.02	0.167896
$640$	−1041.38	−0.0643191
$641$	−4005.28	−0.246801	−0.123400	−	0.992357i	$-0.539380\pi$
$641$	−4005.28	−0.246801	−0.123400	+	0.992357i	$0.539380\pi$
$642$	−17787.3	−1.09347
$643$	21183.8	1.29923	0.649617	−	0.760262i	$-0.274929\pi$
$643$	21183.8	1.29923	0.649617	+	0.760262i	$0.274929\pi$
$644$	−602.401	−0.0368601
$645$	0	0
$646$	101.842	0.00620268
$647$	−8425.30	−0.511952	−0.255976	−	0.966683i	$-0.582397\pi$
$647$	−8425.30	−0.511952	−0.255976	+	0.966683i	$0.582397\pi$
$648$	−7924.84	−0.480427
$649$	−10402.1	−0.629150
$650$	3202.11	0.193227
$651$	−999.643	−0.0601829
$652$	−4587.25	−0.275538
$653$	15075.9	0.903467	0.451733	−	0.892153i	$-0.350806\pi$
$653$	15075.9	0.903467	0.451733	+	0.892153i	$0.350806\pi$
$654$	18396.0	1.09991
$655$	6200.60	0.369889
$656$	−3155.68	−0.187818
$657$	−5675.84	−0.337040
$658$	−5774.96	−0.342145
$659$	−15177.4	−0.897159	−0.448580	−	0.893743i	$-0.648070\pi$
$659$	−15177.4	−0.897159	−0.448580	+	0.893743i	$0.648070\pi$
$660$	−1529.11	−0.0901828
$661$	8032.86	0.472681	0.236340	−	0.971670i	$-0.424052\pi$
$661$	8032.86	0.472681	0.236340	+	0.971670i	$0.424052\pi$
$662$	16067.1	0.943300
$663$	1166.63	0.0683378
$664$	−917.848	−0.0536437
$665$	−58.1218	−0.00338928
$666$	−1065.31	−0.0619817
$667$	−10837.8	−0.629145
$668$	−1490.46	−0.0863288
$669$	11405.0	0.659107
$670$	7192.53	0.414734
$671$	−345.827	−0.0198964
$672$	−2643.47	−0.151747
$673$	2275.45	0.130330	0.0651651	−	0.997874i	$-0.479243\pi$
$673$	2275.45	0.130330	0.0651651	+	0.997874i	$0.479243\pi$
$674$	15012.1	0.857932
$675$	15234.7	0.868716
$676$	5850.50	0.332869
$677$	−10618.2	−0.602793	−0.301397	−	0.953499i	$-0.597453\pi$
$677$	−10618.2	−0.602793	−0.301397	+	0.953499i	$0.597453\pi$
$678$	12328.6	0.698343
$679$	−5890.21	−0.332909
$680$	2502.32	0.141117
$681$	12207.4	0.686914
$682$	2761.36	0.155041
$683$	−19742.9	−1.10606	−0.553031	−	0.833161i	$-0.686529\pi$
$683$	−19742.9	−1.10606	−0.553031	+	0.833161i	$0.686529\pi$
$684$	−70.1122	−0.00391931
$685$	10546.4	0.588260
$686$	7783.24	0.433186
$687$	24510.9	1.36121
$688$	0	0
$689$	−3269.94	−0.180805
$690$	−1769.39	−0.0976226
$691$	−8138.94	−0.448075	−0.224037	−	0.974581i	$-0.571924\pi$
$691$	−8138.94	−0.448075	−0.224037	+	0.974581i	$0.571924\pi$
$692$	7669.96	0.421341
$693$	−1468.46	−0.0804935
$694$	−17430.8	−0.953406
$695$	−15648.0	−0.854045
$696$	−27462.4	−1.49563
$697$	2013.97	0.109447
$698$	−2089.86	−0.113327
$699$	−23654.5	−1.27997
$700$	1541.70	0.0832438
$701$	30481.7	1.64234	0.821169	−	0.570685i	$-0.193322\pi$
$701$	30481.7	1.64234	0.821169	+	0.570685i	$0.193322\pi$
$702$	4866.31	0.261634
$703$	97.4720	0.00522934
$704$	13934.8	0.746007
$705$	9815.09	0.524337
$706$	11122.7	0.592931
$707$	8306.18	0.441847
$708$	4733.82	0.251283
$709$	−84.5679	−0.00447957	−0.00223978	−	0.999997i	$-0.500713\pi$
$709$	−84.5679	−0.00447957	−0.00223978	+	0.999997i	$0.500713\pi$
$710$	2826.23	0.149389
$711$	−10540.3	−0.555965
$712$	−10769.8	−0.566873
$713$	−1848.90	−0.0971135
$714$	−970.704	−0.0508791
$715$	1839.16	0.0961968
$716$	3809.43	0.198834
$717$	−4705.91	−0.245112
$718$	693.905	0.0360673
$719$	19339.8	1.00314	0.501568	−	0.865118i	$-0.332757\pi$
$719$	19339.8	1.00314	0.501568	+	0.865118i	$0.332757\pi$
$720$	1716.53	0.0888492
$721$	−5106.46	−0.263765
$722$	15429.5	0.795329
$723$	8663.90	0.445662
$724$	3703.96	0.190133
$725$	27736.6	1.42084
$726$	5960.53	0.304705
$727$	25267.6	1.28903	0.644514	−	0.764592i	$-0.277060\pi$
$727$	25267.6	1.28903	0.644514	+	0.764592i	$0.277060\pi$
$728$	1835.96	0.0934688
$729$	20018.2	1.01703
$730$	−5914.86	−0.299889
$731$	0	0
$732$	157.380	0.00794664
$733$	−22425.0	−1.13000	−0.564998	−	0.825092i	$-0.691123\pi$
$733$	−22425.0	−1.13000	−0.564998	+	0.825092i	$0.691123\pi$
$734$	18477.4	0.929172
$735$	−6337.19	−0.318028
$736$	−4889.27	−0.244865
$737$	−16626.8	−0.831011
$738$	2396.13	0.119516
$739$	31297.4	1.55791	0.778953	−	0.627083i	$-0.215751\pi$
$739$	31297.4	1.55791	0.778953	+	0.627083i	$0.215751\pi$
$740$	642.387	0.0319116
$741$	−126.997	−0.00629604
$742$	2720.79	0.134614
$743$	−26708.5	−1.31876	−0.659380	−	0.751810i	$-0.729181\pi$
$743$	−26708.5	−1.31876	−0.659380	+	0.751810i	$0.729181\pi$
$744$	−4685.03	−0.230862
$745$	7285.87	0.358300
$746$	−14589.6	−0.716034
$747$	401.827	0.0196815
$748$	−1551.57	−0.0758436
$749$	10300.4	0.502494
$750$	10181.8	0.495714
$751$	−36421.1	−1.76967	−0.884837	−	0.465901i	$-0.845730\pi$
$751$	−36421.1	−1.76967	−0.884837	+	0.465901i	$0.845730\pi$
$752$	−15605.1	−0.756728
$753$	−3958.35	−0.191568
$754$	8859.71	0.427920
$755$	15385.8	0.741653
$756$	2342.95	0.112714
$757$	16912.5	0.812016	0.406008	−	0.913870i	$-0.366921\pi$
$757$	16912.5	0.812016	0.406008	+	0.913870i	$0.366921\pi$
$758$	17846.2	0.855151
$759$	4090.26	0.195609
$760$	−272.400	−0.0130013
$761$	39596.2	1.88615	0.943075	−	0.332581i	$-0.107919\pi$
$761$	39596.2	1.88615	0.943075	+	0.332581i	$0.107919\pi$
$762$	−5815.69	−0.276483
$763$	−10652.9	−0.505451
$764$	4419.66	0.209290
$765$	−1095.50	−0.0517750
$766$	30008.5	1.41547
$767$	−5693.67	−0.268040
$768$	−15407.6	−0.723924
$769$	35365.1	1.65839	0.829193	−	0.558962i	$-0.188800\pi$
$769$	35365.1	1.65839	0.829193	+	0.558962i	$0.188800\pi$
$770$	−1530.30	−0.0716208
$771$	2356.69	0.110083
$772$	−1888.33	−0.0880342
$773$	3602.72	0.167634	0.0838169	−	0.996481i	$-0.473289\pi$
$773$	3602.72	0.167634	0.0838169	+	0.996481i	$0.473289\pi$
$774$	0	0
$775$	4731.82	0.219318
$776$	−27605.6	−1.27704
$777$	−929.049	−0.0428950
$778$	189.091	0.00871367
$779$	−219.238	−0.0100835
$780$	−836.972	−0.0384210
$781$	−6533.32	−0.299335
$782$	−1795.38	−0.0821005
$783$	42151.8	1.92386
$784$	10075.5	0.458981
$785$	−13534.2	−0.615358
$786$	−11273.1	−0.511577
$787$	−18197.3	−0.824224	−0.412112	−	0.911133i	$-0.635209\pi$
$787$	−18197.3	−0.824224	−0.412112	+	0.911133i	$0.635209\pi$
$788$	9175.22	0.414789
$789$	−420.434	−0.0189706
$790$	−10984.1	−0.494681
$791$	−7139.31	−0.320916
$792$	−6882.22	−0.308774
$793$	−189.291	−0.00847658
$794$	8374.74	0.374318
$795$	−4624.25	−0.206296
$796$	14308.4	0.637119
$797$	−5337.43	−0.237216	−0.118608	−	0.992941i	$-0.537843\pi$
$797$	−5337.43	−0.237216	−0.118608	+	0.992941i	$0.537843\pi$
$798$	105.670	0.00468755
$799$	9959.24	0.440967
$800$	12512.9	0.552997
$801$	4714.92	0.207982
$802$	23864.5	1.05073
$803$	13673.2	0.600894
$804$	7566.57	0.331906
$805$	1024.63	0.0448614
$806$	1511.45	0.0660528
$807$	23929.9	1.04383
$808$	38928.6	1.69493
$809$	29582.7	1.28563	0.642813	−	0.766023i	$-0.277767\pi$
$809$	29582.7	1.28563	0.642813	+	0.766023i	$0.277767\pi$
$810$	3615.54	0.156836
$811$	28394.0	1.22941	0.614703	−	0.788759i	$-0.289276\pi$
$811$	28394.0	1.22941	0.614703	+	0.788759i	$0.289276\pi$
$812$	4265.62	0.184352
$813$	13117.7	0.565878
$814$	2566.35	0.110504
$815$	7802.50	0.335349
$816$	−2623.04	−0.112530
$817$	0	0
$818$	8823.06	0.377129
$819$	−803.771	−0.0342931
$820$	−1444.88	−0.0615334
$821$	−11641.0	−0.494852	−0.247426	−	0.968907i	$-0.579585\pi$
$821$	−11641.0	−0.494852	−0.247426	+	0.968907i	$0.579585\pi$
$822$	−19174.1	−0.813594
$823$	−12556.6	−0.531827	−0.265914	−	0.963997i	$-0.585674\pi$
$823$	−12556.6	−0.531827	−0.265914	+	0.963997i	$0.585674\pi$
$824$	−23932.4	−1.01180
$825$	−10468.0	−0.441757
$826$	4737.49	0.199562
$827$	−38940.8	−1.63737	−0.818684	−	0.574245i	$-0.805296\pi$
$827$	−38940.8	−1.63737	−0.818684	+	0.574245i	$0.805296\pi$
$828$	1236.01	0.0518771
$829$	23760.5	0.995461	0.497731	−	0.867332i	$-0.334167\pi$
$829$	23760.5	0.995461	0.497731	+	0.867332i	$0.334167\pi$
$830$	418.749	0.0175120
$831$	−21545.1	−0.899389
$832$	7627.34	0.317825
$833$	−6430.26	−0.267461
$834$	28449.1	1.18119
$835$	2535.14	0.105068
$836$	168.902	0.00698755
$837$	7191.02	0.296963
$838$	−9939.34	−0.409724
$839$	1611.44	0.0663087	0.0331544	−	0.999450i	$-0.489445\pi$
$839$	1611.44	0.0663087	0.0331544	+	0.999450i	$0.489445\pi$
$840$	2596.36	0.106646
$841$	52353.6	2.14661
$842$	17368.4	0.710871
$843$	−14430.9	−0.589594
$844$	232.902	0.00949862
$845$	−9951.19	−0.405126
$846$	11849.1	0.481536
$847$	−3451.66	−0.140024
$848$	7352.14	0.297728
$849$	−32213.2	−1.30219
$850$	4594.83	0.185414
$851$	−1718.33	−0.0692171
$852$	2973.21	0.119554
$853$	−38499.2	−1.54536	−0.772678	−	0.634799i	$-0.781083\pi$
$853$	−38499.2	−1.54536	−0.772678	+	0.634799i	$0.781083\pi$
$854$	157.502	0.00631101
$855$	119.255	0.00477008
$856$	48274.8	1.92757
$857$	−1365.17	−0.0544146	−0.0272073	−	0.999630i	$-0.508661\pi$
$857$	−1365.17	−0.0544146	−0.0272073	+	0.999630i	$0.508661\pi$
$858$	−3343.73	−0.133045
$859$	35044.7	1.39198	0.695989	−	0.718052i	$-0.254966\pi$
$859$	35044.7	1.39198	0.695989	+	0.718052i	$0.254966\pi$
$860$	0	0
$861$	2089.65	0.0827121
$862$	−24680.4	−0.975195
$863$	−41315.3	−1.62965	−0.814826	−	0.579706i	$-0.803167\pi$
$863$	−41315.3	−1.62965	−0.814826	+	0.579706i	$0.803167\pi$
$864$	19016.1	0.748773
$865$	−13045.9	−0.512803
$866$	8772.16	0.344215
$867$	−18116.1	−0.709638
$868$	727.707	0.0284562
$869$	25391.8	0.991204
$870$	12529.1	0.488250
$871$	−9100.80	−0.354040
$872$	−49926.8	−1.93891
$873$	12085.5	0.468538
$874$	195.443	0.00756401
$875$	−5896.11	−0.227800
$876$	−6222.46	−0.239997
$877$	27801.4	1.07045	0.535227	−	0.844708i	$-0.320226\pi$
$877$	27801.4	1.07045	0.535227	+	0.844708i	$0.320226\pi$
$878$	16691.3	0.641577
$879$	−32308.7	−1.23975
$880$	−4135.17	−0.158405
$881$	−34464.0	−1.31796	−0.658980	−	0.752161i	$-0.729012\pi$
$881$	−34464.0	−1.31796	−0.658980	+	0.752161i	$0.729012\pi$
$882$	−7650.44	−0.292068
$883$	37024.3	1.41106	0.705531	−	0.708679i	$-0.250709\pi$
$883$	37024.3	1.41106	0.705531	+	0.708679i	$0.250709\pi$
$884$	−849.264	−0.0323120
$885$	−8051.81	−0.305829
$886$	18443.4	0.699343
$887$	−13945.5	−0.527898	−0.263949	−	0.964537i	$-0.585025\pi$
$887$	−13945.5	−0.527898	−0.263949	+	0.964537i	$0.585025\pi$
$888$	−4354.18	−0.164546
$889$	3367.78	0.127055
$890$	4913.48	0.185056
$891$	−8357.95	−0.314256
$892$	−8302.45	−0.311644
$893$	−1084.15	−0.0406268
$894$	−13246.2	−0.495548
$895$	−6479.50	−0.241995
$896$	−1096.39	−0.0408791
$897$	2238.84	0.0833362
$898$	18377.7	0.682931
$899$	13092.1	0.485703
$900$	−3163.26	−0.117158
$901$	−4692.17	−0.173495
$902$	−5772.34	−0.213080
$903$	0	0
$904$	−33459.8	−1.23104
$905$	−6300.10	−0.231406
$906$	−27972.5	−1.02574
$907$	−24719.4	−0.904955	−0.452478	−	0.891776i	$-0.649460\pi$
$907$	−24719.4	−0.904955	−0.452478	+	0.891776i	$0.649460\pi$
$908$	−8886.58	−0.324792
$909$	−17042.6	−0.621858
$910$	−837.619	−0.0305130
$911$	29271.0	1.06454	0.532268	−	0.846576i	$-0.321340\pi$
$911$	29271.0	1.06454	0.532268	+	0.846576i	$0.321340\pi$
$912$	285.541	0.0103675
$913$	−968.011	−0.0350892
$914$	17323.6	0.626929
$915$	−267.690	−0.00967164
$916$	−17843.1	−0.643616
$917$	6528.11	0.235090
$918$	6982.85	0.251055
$919$	8933.98	0.320680	0.160340	−	0.987062i	$-0.448741\pi$
$919$	8933.98	0.320680	0.160340	+	0.987062i	$0.448741\pi$
$920$	4802.13	0.172089
$921$	19902.9	0.712077
$922$	4687.95	0.167451
$923$	−3576.06	−0.127527
$924$	−1609.88	−0.0573172
$925$	4397.66	0.156318
$926$	−6314.04	−0.224074
$927$	10477.4	0.371224
$928$	34621.1	1.22467
$929$	34274.1	1.21044	0.605218	−	0.796060i	$-0.293086\pi$
$929$	34274.1	1.21044	0.605218	+	0.796060i	$0.293086\pi$
$930$	2137.45	0.0753652
$931$	699.989	0.0246415
$932$	17219.7	0.605204
$933$	15846.6	0.556051
$934$	40205.7	1.40854
$935$	2639.08	0.0923072
$936$	−3767.04	−0.131549
$937$	15930.4	0.555414	0.277707	−	0.960666i	$-0.410425\pi$
$937$	15930.4	0.555414	0.277707	+	0.960666i	$0.410425\pi$
$938$	7572.42	0.263591
$939$	8463.68	0.294145
$940$	−7145.06	−0.247921
$941$	−10078.6	−0.349154	−0.174577	−	0.984644i	$-0.555856\pi$
$941$	−10078.6	−0.349154	−0.174577	+	0.984644i	$0.555856\pi$
$942$	24606.1	0.851073
$943$	3864.94	0.133468
$944$	12801.6	0.441375
$945$	−3985.14	−0.137182
$946$	0	0
$947$	17097.1	0.586675	0.293338	−	0.956009i	$-0.405234\pi$
$947$	17097.1	0.586675	0.293338	+	0.956009i	$0.405234\pi$
$948$	−11555.4	−0.395887
$949$	7484.15	0.256002
$950$	−500.188	−0.0170824
$951$	20393.0	0.695361
$952$	2634.49	0.0896895
$953$	3511.84	0.119370	0.0596850	−	0.998217i	$-0.480990\pi$
$953$	3511.84	0.119370	0.0596850	+	0.998217i	$0.480990\pi$
$954$	−5582.54	−0.189456
$955$	−7517.46	−0.254722
$956$	3425.74	0.115896
$957$	−28963.3	−0.978317
$958$	−2072.71	−0.0699021
$959$	11103.5	0.373878
$960$	10786.3	0.362633
$961$	−27557.5	−0.925028
$962$	1404.71	0.0470787
$963$	−21134.4	−0.707212
$964$	−6307.03	−0.210722
$965$	3211.88	0.107144
$966$	−1862.85	−0.0620457
$967$	−24101.7	−0.801509	−0.400755	−	0.916185i	$-0.631252\pi$
$967$	−24101.7	−0.801509	−0.400755	+	0.916185i	$0.631252\pi$
$968$	−16176.9	−0.537133
$969$	−182.233	−0.00604146
$970$	12594.5	0.416892
$971$	−43736.1	−1.44548	−0.722739	−	0.691121i	$-0.757117\pi$
$971$	−43736.1	−1.44548	−0.722739	+	0.691121i	$0.757117\pi$
$972$	−8243.37	−0.272023
$973$	−16474.5	−0.542803
$974$	−4349.20	−0.143077
$975$	−5729.75	−0.188204
$976$	425.602	0.0139582
$977$	10718.7	0.350995	0.175497	−	0.984480i	$-0.443847\pi$
$977$	10718.7	0.350995	0.175497	+	0.984480i	$0.443847\pi$
$978$	−14185.5	−0.463806
$979$	−11358.4	−0.370801
$980$	4613.26	0.150373
$981$	21857.6	0.711374
$982$	−32042.9	−1.04127
$983$	47327.5	1.53562	0.767809	−	0.640679i	$-0.221347\pi$
$983$	47327.5	1.53562	0.767809	+	0.640679i	$0.221347\pi$
$984$	9793.58	0.317284
$985$	−15606.2	−0.504828
$986$	12713.1	0.410617
$987$	10333.5	0.333252
$988$	92.4498	0.00297694
$989$	0	0
$990$	3139.87	0.100799
$991$	20633.6	0.661402	0.330701	−	0.943736i	$-0.392715\pi$
$991$	20633.6	0.661402	0.330701	+	0.943736i	$0.392715\pi$
$992$	5906.29	0.189037
$993$	−28749.9	−0.918781
$994$	2975.50	0.0949470
$995$	−24337.3	−0.775420
$996$	440.526	0.0140146
$997$	18221.2	0.578806	0.289403	−	0.957207i	$-0.406543\pi$
$997$	18221.2	0.578806	0.289403	+	0.957207i	$0.406543\pi$
$998$	1075.62	0.0341163
$999$	6683.20	0.211659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.i.1.18	✓	50
43.42	odd	2		1849.4.a.j.1.33	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.i.1.18	✓	50	1.1	even	1	trivial
1849.4.a.j.1.33	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)

\(f(q)\)	\(=\)	\(q-2.25115 q^{2} +4.02813 q^{3} -2.93234 q^{4} +4.98765 q^{5} -9.06790 q^{6} +5.25109 q^{7} +24.6103 q^{8} -10.7742 q^{9} +O(q^{10})\)	\(q-2.25115 q^{2} +4.02813 q^{3} -2.93234 q^{4} +4.98765 q^{5} -9.06790 q^{6} +5.25109 q^{7} +24.6103 q^{8} -10.7742 q^{9} -11.2279 q^{10} +25.9553 q^{11} -11.8118 q^{12} +14.2068 q^{13} -11.8210 q^{14} +20.0909 q^{15} -31.9427 q^{16} +20.3859 q^{17} +24.2543 q^{18} -2.21919 q^{19} -14.6255 q^{20} +21.1520 q^{21} -58.4292 q^{22} +39.1220 q^{23} +99.1334 q^{24} -100.123 q^{25} -31.9817 q^{26} -152.159 q^{27} -15.3980 q^{28} -277.025 q^{29} -45.2275 q^{30} -47.2599 q^{31} -124.975 q^{32} +104.551 q^{33} -45.8917 q^{34} +26.1906 q^{35} +31.5936 q^{36} -43.9224 q^{37} +4.99572 q^{38} +57.2270 q^{39} +122.748 q^{40} +98.7920 q^{41} -47.6164 q^{42} -76.1098 q^{44} -53.7380 q^{45} -88.0694 q^{46} +488.535 q^{47} -128.669 q^{48} -315.426 q^{49} +225.392 q^{50} +82.1171 q^{51} -41.6593 q^{52} -230.167 q^{53} +342.533 q^{54} +129.456 q^{55} +129.231 q^{56} -8.93917 q^{57} +623.623 q^{58} -400.770 q^{59} -58.9133 q^{60} -13.3239 q^{61} +106.389 q^{62} -56.5763 q^{63} +536.878 q^{64} +70.8588 q^{65} -235.360 q^{66} -640.592 q^{67} -59.7785 q^{68} +157.588 q^{69} -58.9589 q^{70} -251.714 q^{71} -265.156 q^{72} +526.799 q^{73} +98.8758 q^{74} -403.309 q^{75} +6.50741 q^{76} +136.294 q^{77} -128.826 q^{78} +978.288 q^{79} -159.319 q^{80} -322.013 q^{81} -222.395 q^{82} -37.2953 q^{83} -62.0250 q^{84} +101.678 q^{85} -1115.89 q^{87} +638.768 q^{88} -437.612 q^{89} +120.972 q^{90} +74.6014 q^{91} -114.719 q^{92} -190.369 q^{93} -1099.76 q^{94} -11.0685 q^{95} -503.414 q^{96} -1121.71 q^{97} +710.070 q^{98} -279.648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 10 q^{2} - 2 q^{3} + 186 q^{4} + 8 q^{5} - 51 q^{6} - 6 q^{7} - 138 q^{8} + 360 q^{9}+O(q^{10}) \) 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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