LMFDB - Embedded newform 1849.4.a.h.1.24

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:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.60614 q^{2} -0.812227 q^{3} +5.00427 q^{4} +5.99647 q^{5} -2.92901 q^{6} -26.3629 q^{7} -10.8030 q^{8} -26.3403 q^{9} +O(q^{10})$	\(q+3.60614 q^{2} -0.812227 q^{3} +5.00427 q^{4} +5.99647 q^{5} -2.92901 q^{6} -26.3629 q^{7} -10.8030 q^{8} -26.3403 q^{9} +21.6241 q^{10} -27.0936 q^{11} -4.06461 q^{12} +83.2869 q^{13} -95.0685 q^{14} -4.87050 q^{15} -78.9914 q^{16} +19.3669 q^{17} -94.9869 q^{18} -1.45555 q^{19} +30.0080 q^{20} +21.4127 q^{21} -97.7034 q^{22} +56.8171 q^{23} +8.77451 q^{24} -89.0423 q^{25} +300.344 q^{26} +43.3244 q^{27} -131.927 q^{28} +187.383 q^{29} -17.5637 q^{30} +65.8760 q^{31} -198.430 q^{32} +22.0062 q^{33} +69.8398 q^{34} -158.085 q^{35} -131.814 q^{36} -164.226 q^{37} -5.24893 q^{38} -67.6479 q^{39} -64.7800 q^{40} -273.507 q^{41} +77.2172 q^{42} -135.584 q^{44} -157.949 q^{45} +204.891 q^{46} +111.518 q^{47} +64.1590 q^{48} +352.003 q^{49} -321.099 q^{50} -15.7303 q^{51} +416.790 q^{52} -637.668 q^{53} +156.234 q^{54} -162.466 q^{55} +284.799 q^{56} +1.18224 q^{57} +675.729 q^{58} +810.839 q^{59} -24.3733 q^{60} +789.470 q^{61} +237.558 q^{62} +694.407 q^{63} -83.6366 q^{64} +499.427 q^{65} +79.3573 q^{66} +125.028 q^{67} +96.9172 q^{68} -46.1484 q^{69} -570.075 q^{70} +731.846 q^{71} +284.555 q^{72} +432.763 q^{73} -592.222 q^{74} +72.3226 q^{75} -7.28398 q^{76} +714.266 q^{77} -243.948 q^{78} +119.998 q^{79} -473.670 q^{80} +675.998 q^{81} -986.305 q^{82} -45.8667 q^{83} +107.155 q^{84} +116.133 q^{85} -152.197 q^{87} +292.693 q^{88} +942.217 q^{89} -569.586 q^{90} -2195.68 q^{91} +284.328 q^{92} -53.5063 q^{93} +402.148 q^{94} -8.72818 q^{95} +161.170 q^{96} +355.167 q^{97} +1269.37 q^{98} +713.653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	3.60614	1.27496	0.637482	−	0.770465i	$-0.279976\pi$
$2$	3.60614	1.27496	0.637482	+	0.770465i	$0.279976\pi$
$3$	−0.812227	−0.156313	−0.0781566	−	0.996941i	$-0.524903\pi$
$3$	−0.812227	−0.156313	−0.0781566	+	0.996941i	$0.524903\pi$
$4$	5.00427	0.625534
$5$	5.99647	0.536341	0.268170	−	0.963371i	$-0.413581\pi$
$5$	5.99647	0.536341	0.268170	+	0.963371i	$0.413581\pi$
$6$	−2.92901	−0.199294
$7$	−26.3629	−1.42346	−0.711732	−	0.702451i	$-0.752089\pi$
$7$	−26.3629	−1.42346	−0.711732	+	0.702451i	$0.752089\pi$
$8$	−10.8030	−0.477431
$9$	−26.3403	−0.975566
$10$	21.6241	0.683815
$11$	−27.0936	−0.742639	−0.371319	−	0.928505i	$-0.621095\pi$
$11$	−27.0936	−0.742639	−0.371319	+	0.928505i	$0.621095\pi$
$12$	−4.06461	−0.0977792
$13$	83.2869	1.77689	0.888447	−	0.458979i	$-0.151785\pi$
$13$	83.2869	1.77689	0.888447	+	0.458979i	$0.151785\pi$
$14$	−95.0685	−1.81487
$15$	−4.87050	−0.0838371
$16$	−78.9914	−1.23424
$17$	19.3669	0.276304	0.138152	−	0.990411i	$-0.455884\pi$
$17$	19.3669	0.276304	0.138152	+	0.990411i	$0.455884\pi$
$18$	−94.9869	−1.24381
$19$	−1.45555	−0.0175751	−0.00878754	−	0.999961i	$-0.502797\pi$
$19$	−1.45555	−0.0175751	−0.00878754	+	0.999961i	$0.502797\pi$
$20$	30.0080	0.335499
$21$	21.4127	0.222506
$22$	−97.7034	−0.946838
$23$	56.8171	0.515095	0.257548	−	0.966266i	$-0.417086\pi$
$23$	56.8171	0.515095	0.257548	+	0.966266i	$0.417086\pi$
$24$	8.77451	0.0746287
$25$	−89.0423	−0.712339
$26$	300.344	2.26548
$27$	43.3244	0.308807
$28$	−131.927	−0.890425
$29$	187.383	1.19987	0.599933	−	0.800050i	$-0.295194\pi$
$29$	187.383	1.19987	0.599933	+	0.800050i	$0.295194\pi$
$30$	−17.5637	−0.106889
$31$	65.8760	0.381667	0.190834	−	0.981622i	$-0.438881\pi$
$31$	65.8760	0.381667	0.190834	+	0.981622i	$0.438881\pi$
$32$	−198.430	−1.09618
$33$	22.0062	0.116084
$34$	69.8398	0.352277
$35$	−158.085	−0.763462
$36$	−131.814	−0.610250
$37$	−164.226	−0.729691	−0.364845	−	0.931068i	$-0.618878\pi$
$37$	−164.226	−0.729691	−0.364845	+	0.931068i	$0.618878\pi$
$38$	−5.24893	−0.0224076
$39$	−67.6479	−0.277752
$40$	−64.7800	−0.256066
$41$	−273.507	−1.04182	−0.520910	−	0.853612i	$-0.674407\pi$
$41$	−273.507	−1.04182	−0.520910	+	0.853612i	$0.674407\pi$
$42$	77.2172	0.283687
$43$	0	0
$43$	0	0
$44$	−135.584	−0.464546
$45$	−157.949	−0.523236
$46$	204.891	0.656728
$47$	111.518	0.346096	0.173048	−	0.984913i	$-0.444638\pi$
$47$	111.518	0.346096	0.173048	+	0.984913i	$0.444638\pi$
$48$	64.1590	0.192928
$49$	352.003	1.02625
$50$	−321.099	−0.908206
$51$	−15.7303	−0.0431899
$52$	416.790	1.11151
$53$	−637.668	−1.65265	−0.826324	−	0.563194i	$-0.809572\pi$
$53$	−637.668	−1.65265	−0.826324	+	0.563194i	$0.809572\pi$
$54$	156.234	0.393718
$55$	−162.466	−0.398308
$56$	284.799	0.679605
$57$	1.18224	0.00274722
$58$	675.729	1.52979
$59$	810.839	1.78919	0.894596	−	0.446876i	$-0.147464\pi$
$59$	810.839	1.78919	0.894596	+	0.446876i	$0.147464\pi$
$60$	−24.3733	−0.0524430
$61$	789.470	1.65707	0.828535	−	0.559938i	$-0.189175\pi$
$61$	789.470	1.65707	0.828535	+	0.559938i	$0.189175\pi$
$62$	237.558	0.486612
$63$	694.407	1.38868
$64$	−83.6366	−0.163353
$65$	499.427	0.953021
$66$	79.3573	0.148003
$67$	125.028	0.227979	0.113990	−	0.993482i	$-0.463637\pi$
$67$	125.028	0.227979	0.113990	+	0.993482i	$0.463637\pi$
$68$	96.9172	0.172837
$69$	−46.1484	−0.0805162
$70$	−570.075	−0.973386
$71$	731.846	1.22330	0.611649	−	0.791130i	$-0.290507\pi$
$71$	731.846	1.22330	0.611649	+	0.791130i	$0.290507\pi$
$72$	284.555	0.465765
$73$	432.763	0.693850	0.346925	−	0.937893i	$-0.387226\pi$
$73$	432.763	0.693850	0.346925	+	0.937893i	$0.387226\pi$
$74$	−592.222	−0.930330
$75$	72.3226	0.111348
$76$	−7.28398	−0.0109938
$77$	714.266	1.05712
$78$	−243.948	−0.354124
$79$	119.998	0.170896	0.0854482	−	0.996343i	$-0.472768\pi$
$79$	119.998	0.170896	0.0854482	+	0.996343i	$0.472768\pi$
$80$	−473.670	−0.661974
$81$	675.998	0.927296
$82$	−986.305	−1.32828
$83$	−45.8667	−0.0606570	−0.0303285	−	0.999540i	$-0.509655\pi$
$83$	−45.8667	−0.0606570	−0.0303285	+	0.999540i	$0.509655\pi$
$84$	107.155	0.139185
$85$	116.133	0.148193
$86$	0	0
$87$	−152.197	−0.187555
$88$	292.693	0.354559
$89$	942.217	1.12219	0.561094	−	0.827752i	$-0.310381\pi$
$89$	942.217	1.12219	0.561094	+	0.827752i	$0.310381\pi$
$90$	−569.586	−0.667107
$91$	−2195.68	−2.52934
$92$	284.328	0.322210
$93$	−53.5063	−0.0596596
$94$	402.148	0.441260
$95$	−8.72818	−0.00942624
$96$	161.170	0.171348
$97$	355.167	0.371770	0.185885	−	0.982571i	$-0.440485\pi$
$97$	355.167	0.371770	0.185885	+	0.982571i	$0.440485\pi$
$98$	1269.37	1.30843
$99$	713.653	0.724493
$100$	−445.592	−0.445592
$101$	−217.765	−0.214539	−0.107270	−	0.994230i	$-0.534211\pi$
$101$	−217.765	−0.214539	−0.107270	+	0.994230i	$0.534211\pi$
$102$	−56.7258	−0.0550656
$103$	1538.74	1.47201	0.736005	−	0.676976i	$-0.236710\pi$
$103$	1538.74	1.47201	0.736005	+	0.676976i	$0.236710\pi$
$104$	−899.750	−0.848344
$105$	128.401	0.119339
$106$	−2299.52	−2.10707
$107$	932.741	0.842724	0.421362	−	0.906893i	$-0.361552\pi$
$107$	932.741	0.842724	0.421362	+	0.906893i	$0.361552\pi$
$108$	216.807	0.193169
$109$	1859.77	1.63426	0.817129	−	0.576455i	$-0.195564\pi$
$109$	1859.77	1.63426	0.817129	+	0.576455i	$0.195564\pi$
$110$	−585.876	−0.507828
$111$	133.389	0.114060
$112$	2082.44	1.75690
$113$	−1298.13	−1.08069	−0.540344	−	0.841444i	$-0.681706\pi$
$113$	−1298.13	−1.08069	−0.540344	+	0.841444i	$0.681706\pi$
$114$	4.26332	0.00350260
$115$	340.702	0.276267
$116$	937.714	0.750557
$117$	−2193.80	−1.73348
$118$	2924.00	2.28116
$119$	−510.568	−0.393308
$120$	52.6161	0.0400264
$121$	−596.937	−0.448488
$122$	2846.94	2.11270
$123$	222.150	0.162850
$124$	329.661	0.238746
$125$	−1283.50	−0.918397
$126$	2504.13	1.77052
$127$	−444.380	−0.310491	−0.155245	−	0.987876i	$-0.549617\pi$
$127$	−444.380	−0.310491	−0.155245	+	0.987876i	$0.549617\pi$
$128$	1285.84	0.887914
$129$	0	0
$130$	1801.01	1.21507
$131$	800.630	0.533980	0.266990	−	0.963699i	$-0.413971\pi$
$131$	800.630	0.533980	0.266990	+	0.963699i	$0.413971\pi$
$132$	110.125	0.0726146
$133$	38.3726	0.0250175
$134$	450.869	0.290665
$135$	259.794	0.165626
$136$	−209.221	−0.131916
$137$	1117.24	0.696735	0.348367	−	0.937358i	$-0.386736\pi$
$137$	1117.24	0.696735	0.348367	+	0.937358i	$0.386736\pi$
$138$	−166.418	−0.102655
$139$	−2130.76	−1.30021	−0.650105	−	0.759845i	$-0.725275\pi$
$139$	−2130.76	−1.30021	−0.650105	+	0.759845i	$0.725275\pi$
$140$	−791.098	−0.477571
$141$	−90.5776	−0.0540994
$142$	2639.14	1.55966
$143$	−2256.54	−1.31959
$144$	2080.66	1.20408
$145$	1123.64	0.643537
$146$	1560.60	0.884634
$147$	−285.907	−0.160416
$148$	−821.831	−0.456446
$149$	−307.578	−0.169113	−0.0845563	−	0.996419i	$-0.526947\pi$
$149$	−307.578	−0.169113	−0.0845563	+	0.996419i	$0.526947\pi$
$150$	260.806	0.141965
$151$	2633.15	1.41909	0.709545	−	0.704661i	$-0.248901\pi$
$151$	2633.15	1.41909	0.709545	+	0.704661i	$0.248901\pi$
$152$	15.7244	0.00839089
$153$	−510.130	−0.269553
$154$	2575.75	1.34779
$155$	395.024	0.204704
$156$	−338.528	−0.173743
$157$	−918.529	−0.466921	−0.233461	−	0.972366i	$-0.575005\pi$
$157$	−918.529	−0.466921	−0.233461	+	0.972366i	$0.575005\pi$
$158$	432.729	0.217887
$159$	517.931	0.258331
$160$	−1189.88	−0.587928
$161$	−1497.87	−0.733219
$162$	2437.75	1.18227
$163$	−823.215	−0.395578	−0.197789	−	0.980245i	$-0.563376\pi$
$163$	−823.215	−0.395578	−0.197789	+	0.980245i	$0.563376\pi$
$164$	−1368.70	−0.651694
$165$	131.959	0.0622607
$166$	−165.402	−0.0773355
$167$	1814.13	0.840607	0.420304	−	0.907384i	$-0.361924\pi$
$167$	1814.13	0.840607	0.420304	+	0.907384i	$0.361924\pi$
$168$	−231.322	−0.106231
$169$	4739.70	2.15735
$170$	418.793	0.188941
$171$	38.3397	0.0171457
$172$	0	0
$173$	−4328.67	−1.90233	−0.951163	−	0.308690i	$-0.900110\pi$
$173$	−4328.67	−1.90233	−0.951163	+	0.308690i	$0.900110\pi$
$174$	−548.845	−0.239126
$175$	2347.41	1.01399
$176$	2140.16	0.916595
$177$	−658.586	−0.279674
$178$	3397.77	1.43075
$179$	2571.96	1.07395	0.536976	−	0.843598i	$-0.319567\pi$
$179$	2571.96	1.07395	0.536976	+	0.843598i	$0.319567\pi$
$180$	−790.419	−0.327302
$181$	4230.81	1.73742	0.868712	−	0.495317i	$-0.164948\pi$
$181$	4230.81	1.73742	0.868712	+	0.495317i	$0.164948\pi$
$182$	−7917.95	−3.22482
$183$	−641.229	−0.259022
$184$	−613.797	−0.245922
$185$	−984.776	−0.391363
$186$	−192.951	−0.0760639
$187$	−524.719	−0.205194
$188$	558.064	0.216495
$189$	−1142.16	−0.439576
$190$	−31.4751	−0.0120181
$191$	−1341.08	−0.508048	−0.254024	−	0.967198i	$-0.581754\pi$
$191$	−1341.08	−0.508048	−0.254024	+	0.967198i	$0.581754\pi$
$192$	67.9319	0.0255342
$193$	−2927.70	−1.09192	−0.545959	−	0.837812i	$-0.683835\pi$
$193$	−2927.70	−1.09192	−0.545959	+	0.837812i	$0.683835\pi$
$194$	1280.78	0.473994
$195$	−405.648	−0.148970
$196$	1761.52	0.641953
$197$	429.316	0.155266	0.0776332	−	0.996982i	$-0.475264\pi$
$197$	429.316	0.155266	0.0776332	+	0.996982i	$0.475264\pi$
$198$	2573.54	0.923703
$199$	−2549.43	−0.908164	−0.454082	−	0.890960i	$-0.650033\pi$
$199$	−2549.43	−0.908164	−0.454082	+	0.890960i	$0.650033\pi$
$200$	961.926	0.340092
$201$	−101.551	−0.0356361
$202$	−785.293	−0.273530
$203$	−4939.96	−1.70796
$204$	−78.7188	−0.0270168
$205$	−1640.08	−0.558770
$206$	5548.93	1.87676
$207$	−1496.58	−0.502510
$208$	−6578.95	−2.19312
$209$	39.4362	0.0130519
$210$	463.031	0.152153
$211$	−3496.49	−1.14080	−0.570398	−	0.821368i	$-0.693211\pi$
$211$	−3496.49	−1.14080	−0.570398	+	0.821368i	$0.693211\pi$
$212$	−3191.06	−1.03379
$213$	−594.425	−0.191217
$214$	3363.60	1.07444
$215$	0	0
$216$	−468.035	−0.147434
$217$	−1736.68	−0.543289
$218$	6706.62	2.08362
$219$	−351.502	−0.108458
$220$	−813.024	−0.249155
$221$	1613.01	0.490962
$222$	481.019	0.145423
$223$	−5415.25	−1.62615	−0.813076	−	0.582158i	$-0.802208\pi$
$223$	−5415.25	−1.62615	−0.813076	+	0.582158i	$0.802208\pi$
$224$	5231.20	1.56038
$225$	2345.40	0.694933
$226$	−4681.24	−1.37784
$227$	3228.62	0.944014	0.472007	−	0.881595i	$-0.343530\pi$
$227$	3228.62	0.944014	0.472007	+	0.881595i	$0.343530\pi$
$228$	5.91625	0.00171848
$229$	−4595.18	−1.32602	−0.663010	−	0.748611i	$-0.730721\pi$
$229$	−4595.18	−1.32602	−0.663010	+	0.748611i	$0.730721\pi$
$230$	1228.62	0.352230
$231$	−580.146	−0.165242
$232$	−2024.30	−0.572853
$233$	248.763	0.0699442	0.0349721	−	0.999388i	$-0.488866\pi$
$233$	248.763	0.0699442	0.0349721	+	0.999388i	$0.488866\pi$
$234$	−7911.16	−2.21012
$235$	668.712	0.185625
$236$	4057.66	1.11920
$237$	−97.4655	−0.0267133
$238$	−1841.18	−0.501454
$239$	4503.78	1.21893	0.609467	−	0.792811i	$-0.291383\pi$
$239$	4503.78	1.21893	0.609467	+	0.792811i	$0.291383\pi$
$240$	384.728	0.103475
$241$	508.539	0.135925	0.0679625	−	0.997688i	$-0.478350\pi$
$241$	508.539	0.135925	0.0679625	+	0.997688i	$0.478350\pi$
$242$	−2152.64	−0.571806
$243$	−1718.82	−0.453756
$244$	3950.72	1.03655
$245$	2110.78	0.550419
$246$	801.104	0.207628
$247$	−121.228	−0.0312291
$248$	−711.660	−0.182220
$249$	37.2542	0.00948148
$250$	−4628.48	−1.17092
$251$	4760.66	1.19717	0.598586	−	0.801059i	$-0.295730\pi$
$251$	4760.66	1.19717	0.598586	+	0.801059i	$0.295730\pi$
$252$	3475.00	0.868669
$253$	−1539.38	−0.382530
$254$	−1602.50	−0.395865
$255$	−94.3264	−0.0231645
$256$	5306.00	1.29541
$257$	−2086.48	−0.506423	−0.253212	−	0.967411i	$-0.581487\pi$
$257$	−2086.48	−0.506423	−0.253212	+	0.967411i	$0.581487\pi$
$258$	0	0
$259$	4329.47	1.03869
$260$	2499.27	0.596147
$261$	−4935.72	−1.17055
$262$	2887.19	0.680806
$263$	7112.50	1.66759	0.833793	−	0.552077i	$-0.186165\pi$
$263$	7112.50	1.66759	0.833793	+	0.552077i	$0.186165\pi$
$264$	−237.733	−0.0554222
$265$	−3823.76	−0.886383
$266$	138.377	0.0318964
$267$	−765.294	−0.175413
$268$	625.674	0.142609
$269$	−5421.57	−1.22884	−0.614422	−	0.788977i	$-0.710611\pi$
$269$	−5421.57	−1.22884	−0.614422	+	0.788977i	$0.710611\pi$
$270$	936.854	0.211167
$271$	6809.33	1.52634	0.763169	−	0.646199i	$-0.223643\pi$
$271$	6809.33	1.52634	0.763169	+	0.646199i	$0.223643\pi$
$272$	−1529.82	−0.341025
$273$	1783.39	0.395370
$274$	4028.95	0.888312
$275$	2412.48	0.529010
$276$	−230.939	−0.0503656
$277$	6687.15	1.45051	0.725256	−	0.688480i	$-0.241722\pi$
$277$	6687.15	1.45051	0.725256	+	0.688480i	$0.241722\pi$
$278$	−7683.84	−1.65772
$279$	−1735.19	−0.372342
$280$	1707.79	0.364500
$281$	−6052.56	−1.28493	−0.642465	−	0.766315i	$-0.722088\pi$
$281$	−6052.56	−1.28493	−0.642465	+	0.766315i	$0.722088\pi$
$282$	−326.636	−0.0689747
$283$	−3810.80	−0.800453	−0.400227	−	0.916416i	$-0.631069\pi$
$283$	−3810.80	−0.800453	−0.400227	+	0.916416i	$0.631069\pi$
$284$	3662.35	0.765214
$285$	7.08926	0.00147344
$286$	−8137.41	−1.68243
$287$	7210.44	1.48299
$288$	5226.71	1.06940
$289$	−4537.92	−0.923656
$290$	4051.99	0.820487
$291$	−288.476	−0.0581126
$292$	2165.66	0.434027
$293$	−1344.32	−0.268041	−0.134020	−	0.990979i	$-0.542789\pi$
$293$	−1344.32	−0.268041	−0.134020	+	0.990979i	$0.542789\pi$
$294$	−1031.02	−0.204525
$295$	4862.18	0.959616
$296$	1774.14	0.348377
$297$	−1173.81	−0.229332
$298$	−1109.17	−0.215613
$299$	4732.12	0.915270
$300$	361.922	0.0696519
$301$	0	0
$302$	9495.51	1.80929
$303$	176.875	0.0335353
$304$	114.976	0.0216919
$305$	4734.03	0.888754
$306$	−1839.60	−0.343670
$307$	−8180.21	−1.52075	−0.760374	−	0.649486i	$-0.774984\pi$
$307$	−8180.21	−1.52075	−0.760374	+	0.649486i	$0.774984\pi$
$308$	3574.38	0.661264
$309$	−1249.81	−0.230095
$310$	1424.51	0.260990
$311$	198.784	0.0362445	0.0181222	−	0.999836i	$-0.494231\pi$
$311$	198.784	0.0362445	0.0181222	+	0.999836i	$0.494231\pi$
$312$	730.801	0.132607
$313$	−326.674	−0.0589926	−0.0294963	−	0.999565i	$-0.509390\pi$
$313$	−326.674	−0.0589926	−0.0294963	+	0.999565i	$0.509390\pi$
$314$	−3312.35	−0.595308
$315$	4163.99	0.744807
$316$	600.502	0.106901
$317$	−2068.44	−0.366484	−0.183242	−	0.983068i	$-0.558659\pi$
$317$	−2068.44	−0.366484	−0.183242	+	0.983068i	$0.558659\pi$
$318$	1867.73	0.329363
$319$	−5076.87	−0.891067
$320$	−501.525	−0.0876128
$321$	−757.597	−0.131729
$322$	−5401.52	−0.934829
$323$	−28.1895	−0.00485606
$324$	3382.88	0.580055
$325$	−7416.06	−1.26575
$326$	−2968.63	−0.504348
$327$	−1510.56	−0.255456
$328$	2954.70	0.497397
$329$	−2939.93	−0.492655
$330$	475.864	0.0793802
$331$	3764.18	0.625069	0.312535	−	0.949906i	$-0.398822\pi$
$331$	3764.18	0.625069	0.312535	+	0.949906i	$0.398822\pi$
$332$	−229.530	−0.0379430
$333$	4325.76	0.711862
$334$	6542.01	1.07174
$335$	749.727	0.122274
$336$	−1691.42	−0.274626
$337$	−5712.02	−0.923305	−0.461653	−	0.887061i	$-0.652743\pi$
$337$	−5712.02	−0.923305	−0.461653	+	0.887061i	$0.652743\pi$
$338$	17092.1	2.75055
$339$	1054.38	0.168926
$340$	581.162	0.0926997
$341$	−1784.82	−0.283441
$342$	138.258	0.0218601
$343$	−237.353	−0.0373640
$344$	0	0
$345$	−276.728	−0.0431841
$346$	−15609.8	−2.42540
$347$	12550.3	1.94160	0.970802	−	0.239881i	$-0.0771084\pi$
$347$	12550.3	1.94160	0.970802	+	0.239881i	$0.0771084\pi$
$348$	−761.637	−0.117322
$349$	5215.06	0.799874	0.399937	−	0.916543i	$-0.369032\pi$
$349$	5215.06	0.799874	0.399937	+	0.916543i	$0.369032\pi$
$350$	8465.12	1.29280
$351$	3608.36	0.548717
$352$	5376.19	0.814068
$353$	−2092.54	−0.315509	−0.157754	−	0.987478i	$-0.550425\pi$
$353$	−2092.54	−0.315509	−0.157754	+	0.987478i	$0.550425\pi$
$354$	−2374.95	−0.356575
$355$	4388.49	0.656104
$356$	4715.11	0.701967
$357$	414.697	0.0614792
$358$	9274.86	1.36925
$359$	−10088.2	−1.48310	−0.741549	−	0.670898i	$-0.765909\pi$
$359$	−10088.2	−1.48310	−0.741549	+	0.670898i	$0.765909\pi$
$360$	1706.32	0.249809
$361$	−6856.88	−0.999691
$362$	15256.9	2.21515
$363$	484.848	0.0701045
$364$	−10987.8	−1.58219
$365$	2595.05	0.372140
$366$	−2312.36	−0.330244
$367$	−2565.33	−0.364876	−0.182438	−	0.983217i	$-0.558399\pi$
$367$	−2565.33	−0.364876	−0.182438	+	0.983217i	$0.558399\pi$
$368$	−4488.07	−0.635752
$369$	7204.25	1.01636
$370$	−3551.24	−0.498974
$371$	16810.8	2.35249
$372$	−267.760	−0.0373191
$373$	−907.539	−0.125980	−0.0629900	−	0.998014i	$-0.520064\pi$
$373$	−907.539	−0.125980	−0.0629900	+	0.998014i	$0.520064\pi$
$374$	−1892.21	−0.261615
$375$	1042.49	0.143558
$376$	−1204.73	−0.165237
$377$	15606.5	2.13203
$378$	−4118.79	−0.560443
$379$	9411.80	1.27560	0.637799	−	0.770203i	$-0.279845\pi$
$379$	9411.80	1.27560	0.637799	+	0.770203i	$0.279845\pi$
$380$	−43.6782	−0.00589643
$381$	360.937	0.0485338
$382$	−4836.12	−0.647743
$383$	10469.6	1.39680	0.698398	−	0.715710i	$-0.253897\pi$
$383$	10469.6	1.39680	0.698398	+	0.715710i	$0.253897\pi$
$384$	−1044.39	−0.138793
$385$	4283.08	0.566976
$386$	−10557.7	−1.39216
$387$	0	0
$388$	1777.35	0.232555
$389$	−6173.88	−0.804700	−0.402350	−	0.915486i	$-0.631806\pi$
$389$	−6173.88	−0.804700	−0.402350	+	0.915486i	$0.631806\pi$
$390$	−1462.83	−0.189931
$391$	1100.37	0.142323
$392$	−3802.70	−0.489963
$393$	−650.294	−0.0834681
$394$	1548.17	0.197959
$395$	719.564	0.0916587
$396$	3571.31	0.453195
$397$	−3847.68	−0.486422	−0.243211	−	0.969973i	$-0.578201\pi$
$397$	−3847.68	−0.486422	−0.243211	+	0.969973i	$0.578201\pi$
$398$	−9193.63	−1.15788
$399$	−31.1673	−0.00391056
$400$	7033.58	0.879198
$401$	−2160.31	−0.269029	−0.134515	−	0.990912i	$-0.542948\pi$
$401$	−2160.31	−0.269029	−0.134515	+	0.990912i	$0.542948\pi$
$402$	−366.208	−0.0454348
$403$	5486.61	0.678182
$404$	−1089.76	−0.134202
$405$	4053.61	0.497346
$406$	−17814.2	−2.17759
$407$	4449.47	0.541897
$408$	169.935	0.0206202
$409$	4818.22	0.582508	0.291254	−	0.956646i	$-0.405927\pi$
$409$	4818.22	0.582508	0.291254	+	0.956646i	$0.405927\pi$
$410$	−5914.35	−0.712412
$411$	−907.457	−0.108909
$412$	7700.30	0.920792
$413$	−21376.1	−2.54685
$414$	−5396.88	−0.640682
$415$	−275.039	−0.0325328
$416$	−16526.6	−1.94780
$417$	1730.66	0.203240
$418$	142.212	0.0166408
$419$	924.481	0.107790	0.0538948	−	0.998547i	$-0.482836\pi$
$419$	924.481	0.107790	0.0538948	+	0.998547i	$0.482836\pi$
$420$	642.551	0.0746507
$421$	14389.0	1.66574	0.832870	−	0.553468i	$-0.186696\pi$
$421$	14389.0	1.66574	0.832870	+	0.553468i	$0.186696\pi$
$422$	−12608.8	−1.45448
$423$	−2937.40	−0.337640
$424$	6888.74	0.789025
$425$	−1724.47	−0.196822
$426$	−2143.58	−0.243795
$427$	−20812.7	−2.35878
$428$	4667.69	0.527153
$429$	1832.82	0.206269
$430$	0	0
$431$	2076.77	0.232098	0.116049	−	0.993243i	$-0.462977\pi$
$431$	2076.77	0.232098	0.116049	+	0.993243i	$0.462977\pi$
$432$	−3422.26	−0.381142
$433$	−1585.85	−0.176007	−0.0880033	−	0.996120i	$-0.528049\pi$
$433$	−1585.85	−0.176007	−0.0880033	+	0.996120i	$0.528049\pi$
$434$	−6262.73	−0.692674
$435$	−912.647	−0.100593
$436$	9306.82	1.02228
$437$	−82.7003	−0.00905284
$438$	−1267.57	−0.138280
$439$	−278.813	−0.0303121	−0.0151561	−	0.999885i	$-0.504825\pi$
$439$	−278.813	−0.0303121	−0.0151561	+	0.999885i	$0.504825\pi$
$440$	1755.12	0.190164
$441$	−9271.87	−1.00117
$442$	5816.74	0.625959
$443$	4961.81	0.532151	0.266075	−	0.963952i	$-0.414273\pi$
$443$	4961.81	0.532151	0.266075	+	0.963952i	$0.414273\pi$
$444$	667.513	0.0713486
$445$	5649.98	0.601875
$446$	−19528.2	−2.07328
$447$	249.823	0.0264345
$448$	2204.91	0.232527
$449$	12048.2	1.26634	0.633171	−	0.774012i	$-0.281753\pi$
$449$	12048.2	1.26634	0.633171	+	0.774012i	$0.281753\pi$
$450$	8457.85	0.886015
$451$	7410.29	0.773696
$452$	−6496.19	−0.676007
$453$	−2138.71	−0.221822
$454$	11642.9	1.20358
$455$	−13166.4	−1.35659
$456$	−12.7718	−0.00131161
$457$	12738.5	1.30390	0.651948	−	0.758263i	$-0.273952\pi$
$457$	12738.5	1.30390	0.651948	+	0.758263i	$0.273952\pi$
$458$	−16570.9	−1.69063
$459$	839.060	0.0853245
$460$	1704.97	0.172814
$461$	4651.57	0.469947	0.234973	−	0.972002i	$-0.424500\pi$
$461$	4651.57	0.469947	0.234973	+	0.972002i	$0.424500\pi$
$462$	−2092.09	−0.210677
$463$	217.350	0.0218166	0.0109083	−	0.999941i	$-0.496528\pi$
$463$	217.350	0.0218166	0.0109083	+	0.999941i	$0.496528\pi$
$464$	−14801.6	−1.48092
$465$	−320.849	−0.0319979
$466$	897.075	0.0891764
$467$	−1915.22	−0.189777	−0.0948887	−	0.995488i	$-0.530250\pi$
$467$	−1915.22	−0.189777	−0.0948887	+	0.995488i	$0.530250\pi$
$468$	−10978.4	−1.08435
$469$	−3296.10	−0.324520
$470$	2411.47	0.236666
$471$	746.054	0.0729859
$472$	−8759.52	−0.854215
$473$	0	0
$474$	−351.474	−0.0340586
$475$	129.606	0.0125194
$476$	−2555.02	−0.246028
$477$	16796.3	1.61227
$478$	16241.3	1.55410
$479$	−11167.6	−1.06526	−0.532630	−	0.846348i	$-0.678796\pi$
$479$	−11167.6	−1.06526	−0.532630	+	0.846348i	$0.678796\pi$
$480$	966.454	0.0919008
$481$	−13677.9	−1.29658
$482$	1833.87	0.173299
$483$	1216.61	0.114612
$484$	−2987.24	−0.280544
$485$	2129.75	0.199396
$486$	−6198.33	−0.578522
$487$	18058.4	1.68030	0.840150	−	0.542354i	$-0.182467\pi$
$487$	18058.4	1.68030	0.840150	+	0.542354i	$0.182467\pi$
$488$	−8528.66	−0.791136
$489$	668.638	0.0618340
$490$	7611.77	0.701765
$491$	−19234.3	−1.76789	−0.883945	−	0.467592i	$-0.845122\pi$
$491$	−19234.3	−1.76789	−0.883945	+	0.467592i	$0.845122\pi$
$492$	1111.70	0.101868
$493$	3629.02	0.331527
$494$	−437.167	−0.0398160
$495$	4279.40	0.388575
$496$	−5203.64	−0.471069
$497$	−19293.6	−1.74132
$498$	134.344	0.0120886
$499$	9828.54	0.881735	0.440868	−	0.897572i	$-0.354671\pi$
$499$	9828.54	0.881735	0.440868	+	0.897572i	$0.354671\pi$
$500$	−6422.98	−0.574489
$501$	−1473.48	−0.131398
$502$	17167.6	1.52635
$503$	−11481.5	−1.01776	−0.508880	−	0.860838i	$-0.669940\pi$
$503$	−11481.5	−1.01776	−0.508880	+	0.860838i	$0.669940\pi$
$504$	−7501.69	−0.663000
$505$	−1305.82	−0.115066
$506$	−5551.23	−0.487712
$507$	−3849.72	−0.337223
$508$	−2223.80	−0.194223
$509$	−3994.60	−0.347854	−0.173927	−	0.984759i	$-0.555646\pi$
$509$	−3994.60	−0.347854	−0.173927	+	0.984759i	$0.555646\pi$
$510$	−340.155	−0.0295339
$511$	−11408.9	−0.987670
$512$	8847.52	0.763689
$513$	−63.0610	−0.00542731
$514$	−7524.13	−0.645672
$515$	9227.04	0.789499
$516$	0	0
$517$	−3021.41	−0.257024
$518$	15612.7	1.32429
$519$	3515.86	0.297359
$520$	−5395.33	−0.455001
$521$	6982.25	0.587136	0.293568	−	0.955938i	$-0.405157\pi$
$521$	6982.25	0.587136	0.293568	+	0.955938i	$0.405157\pi$
$522$	−17798.9	−1.49241
$523$	8757.64	0.732208	0.366104	−	0.930574i	$-0.380691\pi$
$523$	8757.64	0.732208	0.366104	+	0.930574i	$0.380691\pi$
$524$	4006.57	0.334023
$525$	−1906.63	−0.158500
$526$	25648.7	2.12611
$527$	1275.81	0.105456
$528$	−1738.30	−0.143276
$529$	−8938.81	−0.734677
$530$	−13789.0	−1.13011
$531$	−21357.7	−1.74547
$532$	192.027	0.0156493
$533$	−22779.5	−1.85120
$534$	−2759.76	−0.223645
$535$	5593.16	0.451987
$536$	−1350.68	−0.108844
$537$	−2089.02	−0.167873
$538$	−19551.0	−1.56673
$539$	−9537.04	−0.762132
$540$	1300.08	0.103605
$541$	−3230.72	−0.256746	−0.128373	−	0.991726i	$-0.540976\pi$
$541$	−3230.72	−0.256746	−0.128373	+	0.991726i	$0.540976\pi$
$542$	24555.4	1.94603
$543$	−3436.38	−0.271582
$544$	−3842.98	−0.302879
$545$	11152.1	0.876519
$546$	6431.18	0.504082
$547$	−441.868	−0.0345391	−0.0172696	−	0.999851i	$-0.505497\pi$
$547$	−441.868	−0.0345391	−0.0172696	+	0.999851i	$0.505497\pi$
$548$	5591.00	0.435831
$549$	−20794.9	−1.61658
$550$	8699.74	0.674469
$551$	−272.745	−0.0210877
$552$	498.542	0.0384409
$553$	−3163.49	−0.243265
$554$	24114.8	1.84935
$555$	799.861	0.0611752
$556$	−10662.9	−0.813325
$557$	−12443.5	−0.946586	−0.473293	−	0.880905i	$-0.656935\pi$
$557$	−12443.5	−0.946586	−0.473293	+	0.880905i	$0.656935\pi$
$558$	−6257.36	−0.474722
$559$	0	0
$560$	12487.3	0.942296
$561$	426.191	0.0320745
$562$	−21826.4	−1.63824
$563$	12004.7	0.898647	0.449324	−	0.893369i	$-0.351665\pi$
$563$	12004.7	0.898647	0.449324	+	0.893369i	$0.351665\pi$
$564$	−453.275	−0.0338410
$565$	−7784.20	−0.579617
$566$	−13742.3	−1.02055
$567$	−17821.3	−1.31997
$568$	−7906.14	−0.584040
$569$	−17399.4	−1.28194	−0.640969	−	0.767567i	$-0.721467\pi$
$569$	−17399.4	−1.28194	−0.640969	+	0.767567i	$0.721467\pi$
$570$	25.5649	0.00187859
$571$	−187.663	−0.0137539	−0.00687694	−	0.999976i	$-0.502189\pi$
$571$	−187.663	−0.0137539	−0.00687694	+	0.999976i	$0.502189\pi$
$572$	−11292.3	−0.825449
$573$	1089.26	0.0794145
$574$	26001.9	1.89076
$575$	−5059.13	−0.366922
$576$	2203.01	0.159361
$577$	15258.1	1.10087	0.550437	−	0.834877i	$-0.314461\pi$
$577$	15258.1	1.10087	0.550437	+	0.834877i	$0.314461\pi$
$578$	−16364.4	−1.17763
$579$	2377.96	0.170681
$580$	5622.98	0.402554
$581$	1209.18	0.0863430
$582$	−1040.29	−0.0740915
$583$	17276.7	1.22732
$584$	−4675.15	−0.331265
$585$	−13155.1	−0.929735
$586$	−4847.81	−0.341743
$587$	20653.7	1.45225	0.726124	−	0.687563i	$-0.241320\pi$
$587$	20653.7	1.45225	0.726124	+	0.687563i	$0.241320\pi$
$588$	−1430.75	−0.100346
$589$	−95.8860	−0.00670783
$590$	17533.7	1.22348
$591$	−348.702	−0.0242702
$592$	12972.4	0.900614
$593$	−2747.81	−0.190285	−0.0951426	−	0.995464i	$-0.530331\pi$
$593$	−2747.81	−0.190285	−0.0951426	+	0.995464i	$0.530331\pi$
$594$	−4232.94	−0.292390
$595$	−3061.61	−0.210947
$596$	−1539.20	−0.105786
$597$	2070.72	0.141958
$598$	17064.7	1.16694
$599$	23896.4	1.63002	0.815008	−	0.579450i	$-0.196733\pi$
$599$	23896.4	1.63002	0.815008	+	0.579450i	$0.196733\pi$
$600$	−781.302	−0.0531609
$601$	15868.2	1.07700	0.538501	−	0.842625i	$-0.318991\pi$
$601$	15868.2	1.07700	0.538501	+	0.842625i	$0.318991\pi$
$602$	0	0
$603$	−3293.27	−0.222409
$604$	13177.0	0.887689
$605$	−3579.52	−0.240542
$606$	637.837	0.0427563
$607$	8394.74	0.561338	0.280669	−	0.959805i	$-0.409444\pi$
$607$	8394.74	0.561338	0.280669	+	0.959805i	$0.409444\pi$
$608$	288.826	0.0192655
$609$	4012.37	0.266977
$610$	17071.6	1.13313
$611$	9287.95	0.614976
$612$	−2552.83	−0.168614
$613$	−1487.66	−0.0980197	−0.0490099	−	0.998798i	$-0.515607\pi$
$613$	−1487.66	−0.0980197	−0.0490099	+	0.998798i	$0.515607\pi$
$614$	−29499.0	−1.93890
$615$	1332.11	0.0873432
$616$	−7716.23	−0.504701
$617$	7581.38	0.494676	0.247338	−	0.968929i	$-0.420444\pi$
$617$	7581.38	0.494676	0.247338	+	0.968929i	$0.420444\pi$
$618$	−4506.99	−0.293362
$619$	−328.731	−0.0213454	−0.0106727	−	0.999943i	$-0.503397\pi$
$619$	−328.731	−0.0213454	−0.0106727	+	0.999943i	$0.503397\pi$
$620$	1976.81	0.128049
$621$	2461.57	0.159065
$622$	716.845	0.0462104
$623$	−24839.6	−1.59739
$624$	5343.60	0.342813
$625$	3433.82	0.219765
$626$	−1178.03	−0.0752135
$627$	−32.0311	−0.00204019
$628$	−4596.57	−0.292075
$629$	−3180.54	−0.201616
$630$	15016.0	0.949603
$631$	−20258.2	−1.27807	−0.639037	−	0.769176i	$-0.720667\pi$
$631$	−20258.2	−1.27807	−0.639037	+	0.769176i	$0.720667\pi$
$632$	−1296.34	−0.0815911
$633$	2839.94	0.178322
$634$	−7459.10	−0.467253
$635$	−2664.71	−0.166529
$636$	2591.87	0.161595
$637$	29317.3	1.82354
$638$	−18307.9	−1.13608
$639$	−19277.0	−1.19341
$640$	7710.48	0.476224
$641$	−7317.96	−0.450924	−0.225462	−	0.974252i	$-0.572389\pi$
$641$	−7317.96	−0.450924	−0.225462	+	0.974252i	$0.572389\pi$
$642$	−2732.00	−0.167950
$643$	14629.6	0.897253	0.448627	−	0.893719i	$-0.351913\pi$
$643$	14629.6	0.897253	0.448627	+	0.893719i	$0.351913\pi$
$644$	−7495.73	−0.458654
$645$	0	0
$646$	−101.656	−0.00619130
$647$	−6446.09	−0.391688	−0.195844	−	0.980635i	$-0.562745\pi$
$647$	−6446.09	−0.391688	−0.195844	+	0.980635i	$0.562745\pi$
$648$	−7302.83	−0.442719
$649$	−21968.6	−1.32872
$650$	−26743.4	−1.61379
$651$	1410.58	0.0849233
$652$	−4119.59	−0.247447
$653$	15267.7	0.914961	0.457480	−	0.889220i	$-0.348752\pi$
$653$	15267.7	0.914961	0.457480	+	0.889220i	$0.348752\pi$
$654$	−5447.29	−0.325697
$655$	4800.96	0.286395
$656$	21604.7	1.28586
$657$	−11399.1	−0.676897
$658$	−10601.8	−0.628118
$659$	−13991.4	−0.827055	−0.413527	−	0.910492i	$-0.635703\pi$
$659$	−13991.4	−0.827055	−0.413527	+	0.910492i	$0.635703\pi$
$660$	660.360	0.0389462
$661$	17096.8	1.00603	0.503016	−	0.864277i	$-0.332224\pi$
$661$	17096.8	1.00603	0.503016	+	0.864277i	$0.332224\pi$
$662$	13574.2	0.796941
$663$	−1310.13	−0.0767439
$664$	495.499	0.0289595
$665$	230.100	0.0134179
$666$	15599.3	0.907598
$667$	10646.6	0.618045
$668$	9078.39	0.525829
$669$	4398.41	0.254189
$670$	2703.62	0.155896
$671$	−21389.6	−1.23060
$672$	−4248.92	−0.243907
$673$	9239.00	0.529179	0.264589	−	0.964361i	$-0.414764\pi$
$673$	9239.00	0.529179	0.264589	+	0.964361i	$0.414764\pi$
$674$	−20598.4	−1.17718
$675$	−3857.71	−0.219975
$676$	23718.8	1.34950
$677$	−4341.97	−0.246493	−0.123246	−	0.992376i	$-0.539331\pi$
$677$	−4341.97	−0.246493	−0.123246	+	0.992376i	$0.539331\pi$
$678$	3802.23	0.215374
$679$	−9363.23	−0.529202
$680$	−1254.59	−0.0707519
$681$	−2622.37	−0.147562
$682$	−6436.31	−0.361377
$683$	935.126	0.0523889	0.0261944	−	0.999657i	$-0.491661\pi$
$683$	935.126	0.0523889	0.0261944	+	0.999657i	$0.491661\pi$
$684$	191.862	0.0107252
$685$	6699.53	0.373687
$686$	−855.928	−0.0476377
$687$	3732.33	0.207274
$688$	0	0
$689$	−53109.3	−2.93658
$690$	−997.920	−0.0550582
$691$	14883.7	0.819398	0.409699	−	0.912221i	$-0.365634\pi$
$691$	14883.7	0.819398	0.409699	+	0.912221i	$0.365634\pi$
$692$	−21661.8	−1.18997
$693$	−18814.0	−1.03129
$694$	45258.3	2.47548
$695$	−12777.1	−0.697355
$696$	1644.19	0.0895444
$697$	−5296.98	−0.287859
$698$	18806.3	1.01981
$699$	−202.052	−0.0109332
$700$	11747.1	0.634284
$701$	−6934.09	−0.373605	−0.186802	−	0.982398i	$-0.559812\pi$
$701$	−6934.09	−0.373605	−0.186802	+	0.982398i	$0.559812\pi$
$702$	13012.2	0.699595
$703$	239.039	0.0128244
$704$	2266.02	0.121312
$705$	−543.146	−0.0290157
$706$	−7545.99	−0.402262
$707$	5740.93	0.305389
$708$	−3295.74	−0.174946
$709$	904.231	0.0478972	0.0239486	−	0.999713i	$-0.492376\pi$
$709$	904.231	0.0478972	0.0239486	+	0.999713i	$0.492376\pi$
$710$	15825.5	0.836509
$711$	−3160.78	−0.166721
$712$	−10178.8	−0.535767
$713$	3742.89	0.196595
$714$	1495.46	0.0783838
$715$	−13531.3	−0.707750
$716$	12870.8	0.671793
$717$	−3658.09	−0.190535
$718$	−36379.3	−1.89090
$719$	−23525.7	−1.22025	−0.610125	−	0.792306i	$-0.708881\pi$
$719$	−23525.7	−1.22025	−0.610125	+	0.792306i	$0.708881\pi$
$720$	12476.6	0.645799
$721$	−40565.8	−2.09535
$722$	−24726.9	−1.27457
$723$	−413.049	−0.0212469
$724$	21172.1	1.08682
$725$	−16685.0	−0.854710
$726$	1748.43	0.0893808
$727$	−33029.9	−1.68502	−0.842512	−	0.538678i	$-0.818924\pi$
$727$	−33029.9	−1.68502	−0.842512	+	0.538678i	$0.818924\pi$
$728$	23720.0	1.20759
$729$	−16855.9	−0.856368
$730$	9358.12	0.474465
$731$	0	0
$732$	−3208.88	−0.162027
$733$	−4063.29	−0.204749	−0.102375	−	0.994746i	$-0.532644\pi$
$733$	−4063.29	−0.204749	−0.102375	+	0.994746i	$0.532644\pi$
$734$	−9250.96	−0.465203
$735$	−1714.43	−0.0860377
$736$	−11274.2	−0.564639
$737$	−3387.46	−0.169306
$738$	25979.6	1.29583
$739$	9373.56	0.466593	0.233296	−	0.972406i	$-0.425049\pi$
$739$	9373.56	0.466593	0.233296	+	0.972406i	$0.425049\pi$
$740$	−4928.09	−0.244811
$741$	98.4650	0.00488151
$742$	60622.1	2.99934
$743$	21092.5	1.04147	0.520734	−	0.853719i	$-0.325659\pi$
$743$	21092.5	1.04147	0.520734	+	0.853719i	$0.325659\pi$
$744$	578.030	0.0284833
$745$	−1844.38	−0.0907020
$746$	−3272.71	−0.160620
$747$	1208.14	0.0591749
$748$	−2625.84	−0.128356
$749$	−24589.8	−1.19959
$750$	3759.38	0.183031
$751$	15261.7	0.741555	0.370777	−	0.928722i	$-0.379091\pi$
$751$	15261.7	0.741555	0.370777	+	0.928722i	$0.379091\pi$
$752$	−8808.93	−0.427166
$753$	−3866.73	−0.187134
$754$	56279.4	2.71827
$755$	15789.6	0.761115
$756$	−5715.67	−0.274969
$757$	6955.07	0.333932	0.166966	−	0.985963i	$-0.446603\pi$
$757$	6955.07	0.333932	0.166966	+	0.985963i	$0.446603\pi$
$758$	33940.3	1.62634
$759$	1250.33	0.0597944
$760$	94.2908	0.00450038
$761$	−3295.92	−0.157000	−0.0785000	−	0.996914i	$-0.525013\pi$
$761$	−3295.92	−0.157000	−0.0785000	+	0.996914i	$0.525013\pi$
$762$	1301.59	0.0618789
$763$	−49029.1	−2.32631
$764$	−6711.13	−0.317801
$765$	−3058.98	−0.144572
$766$	37755.0	1.78086
$767$	67532.3	3.17920
$768$	−4309.68	−0.202490
$769$	−5722.67	−0.268355	−0.134177	−	0.990957i	$-0.542839\pi$
$769$	−5722.67	−0.268355	−0.134177	+	0.990957i	$0.542839\pi$
$770$	15445.4	0.722875
$771$	1694.69	0.0791606
$772$	−14651.0	−0.683032
$773$	−17526.3	−0.815494	−0.407747	−	0.913095i	$-0.633685\pi$
$773$	−17526.3	−0.815494	−0.407747	+	0.913095i	$0.633685\pi$
$774$	0	0
$775$	−5865.75	−0.271876
$776$	−3836.88	−0.177495
$777$	−3516.51	−0.162361
$778$	−22263.9	−1.02596
$779$	398.104	0.0183101
$780$	−2029.98	−0.0931856
$781$	−19828.3	−0.908468
$782$	3968.10	0.181456
$783$	8118.25	0.370527
$784$	−27805.2	−1.26664
$785$	−5507.94	−0.250429
$786$	−2345.05	−0.106419
$787$	35884.3	1.62533	0.812667	−	0.582729i	$-0.198015\pi$
$787$	35884.3	1.62533	0.812667	+	0.582729i	$0.198015\pi$
$788$	2148.41	0.0971244
$789$	−5776.96	−0.260666
$790$	2594.85	0.116862
$791$	34222.5	1.53832
$792$	−7709.61	−0.345895
$793$	65752.5	2.94444
$794$	−13875.3	−0.620171
$795$	3105.76	0.138553
$796$	−12758.1	−0.568088
$797$	26874.0	1.19439	0.597194	−	0.802097i	$-0.296282\pi$
$797$	26874.0	1.19439	0.597194	+	0.802097i	$0.296282\pi$
$798$	−112.394	−0.00498583
$799$	2159.75	0.0956276
$800$	17668.7	0.780853
$801$	−24818.3	−1.09477
$802$	−7790.38	−0.343003
$803$	−11725.1	−0.515280
$804$	−508.189	−0.0222916
$805$	−8981.91	−0.393255
$806$	19785.5	0.864658
$807$	4403.55	0.192085
$808$	2352.53	0.102428
$809$	16365.2	0.711212	0.355606	−	0.934636i	$-0.384274\pi$
$809$	16365.2	0.711212	0.355606	+	0.934636i	$0.384274\pi$
$810$	14617.9	0.634099
$811$	−9500.55	−0.411356	−0.205678	−	0.978620i	$-0.565940\pi$
$811$	−9500.55	−0.411356	−0.205678	+	0.978620i	$0.565940\pi$
$812$	−24720.9	−1.06839
$813$	−5530.72	−0.238587
$814$	16045.4	0.690899
$815$	−4936.39	−0.212165
$816$	1242.56	0.0533068
$817$	0	0
$818$	17375.2	0.742677
$819$	57835.0	2.46754
$820$	−8207.39	−0.349530
$821$	−10038.9	−0.426748	−0.213374	−	0.976971i	$-0.568445\pi$
$821$	−10038.9	−0.426748	−0.213374	+	0.976971i	$0.568445\pi$
$822$	−3272.42	−0.138855
$823$	−23596.1	−0.999403	−0.499702	−	0.866198i	$-0.666557\pi$
$823$	−23596.1	−0.999403	−0.499702	+	0.866198i	$0.666557\pi$
$824$	−16623.1	−0.702783
$825$	−1959.48	−0.0826913
$826$	−77085.3	−3.24714
$827$	29302.6	1.23211	0.616053	−	0.787705i	$-0.288731\pi$
$827$	29302.6	1.23211	0.616053	+	0.787705i	$0.288731\pi$
$828$	−7489.29	−0.314337
$829$	−16593.4	−0.695190	−0.347595	−	0.937645i	$-0.613002\pi$
$829$	−16593.4	−0.695190	−0.347595	+	0.937645i	$0.613002\pi$
$830$	−991.829	−0.0414782
$831$	−5431.48	−0.226734
$832$	−6965.83	−0.290261
$833$	6817.21	0.283556
$834$	6241.02	0.259123
$835$	10878.4	0.450852
$836$	197.349	0.00816443
$837$	2854.04	0.117861
$838$	3333.81	0.137428
$839$	−16106.7	−0.662772	−0.331386	−	0.943495i	$-0.607516\pi$
$839$	−16106.7	−0.662772	−0.331386	+	0.943495i	$0.607516\pi$
$840$	−1387.11	−0.0569762
$841$	10723.3	0.439677
$842$	51888.8	2.12376
$843$	4916.05	0.200852
$844$	−17497.4	−0.713607
$845$	28421.5	1.15708
$846$	−10592.7	−0.430478
$847$	15737.0	0.638406
$848$	50370.3	2.03977
$849$	3095.23	0.125121
$850$	−6218.70	−0.250941
$851$	−9330.84	−0.375860
$852$	−2974.66	−0.119613
$853$	16973.0	0.681293	0.340647	−	0.940191i	$-0.389354\pi$
$853$	16973.0	0.681293	0.340647	+	0.940191i	$0.389354\pi$
$854$	−75053.7	−3.00736
$855$	229.903	0.00919592
$856$	−10076.4	−0.402342
$857$	−10313.8	−0.411101	−0.205551	−	0.978647i	$-0.565898\pi$
$857$	−10313.8	−0.411101	−0.205551	+	0.978647i	$0.565898\pi$
$858$	6609.43	0.262986
$859$	22942.2	0.911267	0.455634	−	0.890167i	$-0.349413\pi$
$859$	22942.2	0.911267	0.455634	+	0.890167i	$0.349413\pi$
$860$	0	0
$861$	−5856.51	−0.231811
$862$	7489.11	0.295917
$863$	−19747.4	−0.778920	−0.389460	−	0.921043i	$-0.627338\pi$
$863$	−19747.4	−0.778920	−0.389460	+	0.921043i	$0.627338\pi$
$864$	−8596.88	−0.338509
$865$	−25956.7	−1.02029
$866$	−5718.79	−0.224402
$867$	3685.82	0.144380
$868$	−8690.84	−0.339846
$869$	−3251.17	−0.126914
$870$	−3291.14	−0.128253
$871$	10413.2	0.405095
$872$	−20091.2	−0.780245
$873$	−9355.20	−0.362687
$874$	−298.229	−0.0115421
$875$	33836.8	1.30730
$876$	−1759.01	−0.0678441
$877$	9726.70	0.374512	0.187256	−	0.982311i	$-0.440041\pi$
$877$	9726.70	0.374512	0.187256	+	0.982311i	$0.440041\pi$
$878$	−1005.44	−0.0386469
$879$	1091.89	0.0418983
$880$	12833.4	0.491608
$881$	16960.9	0.648613	0.324306	−	0.945952i	$-0.394869\pi$
$881$	16960.9	0.648613	0.324306	+	0.945952i	$0.394869\pi$
$882$	−33435.7	−1.27646
$883$	23172.9	0.883159	0.441579	−	0.897222i	$-0.354418\pi$
$883$	23172.9	0.883159	0.441579	+	0.897222i	$0.354418\pi$
$884$	8071.93	0.307114
$885$	−3949.19	−0.150001
$886$	17893.0	0.678473
$887$	−38740.7	−1.46650	−0.733250	−	0.679959i	$-0.761998\pi$
$887$	−38740.7	−1.46650	−0.733250	+	0.679959i	$0.761998\pi$
$888$	−1441.00	−0.0544559
$889$	11715.2	0.441972
$890$	20374.6	0.767370
$891$	−18315.2	−0.688646
$892$	−27099.4	−1.01721
$893$	−162.320	−0.00608267
$894$	900.898	0.0337031
$895$	15422.7	0.576004
$896$	−33898.4	−1.26391
$897$	−3843.56	−0.143069
$898$	43447.4	1.61454
$899$	12344.0	0.457949
$900$	11737.0	0.434705
$901$	−12349.6	−0.456633
$902$	26722.6	0.986434
$903$	0	0
$904$	14023.7	0.515954
$905$	25370.0	0.931852
$906$	−7712.51	−0.282816
$907$	11304.7	0.413855	0.206928	−	0.978356i	$-0.433654\pi$
$907$	11304.7	0.413855	0.206928	+	0.978356i	$0.433654\pi$
$908$	16156.9	0.590513
$909$	5736.00	0.209297
$910$	−47479.8	−1.72960
$911$	15797.8	0.574537	0.287269	−	0.957850i	$-0.407253\pi$
$911$	15797.8	0.574537	0.287269	+	0.957850i	$0.407253\pi$
$912$	−93.3868	−0.00339073
$913$	1242.69	0.0450462
$914$	45936.8	1.66242
$915$	−3845.11	−0.138924
$916$	−22995.6	−0.829470
$917$	−21107.0	−0.760101
$918$	3025.77	0.108786
$919$	38867.9	1.39514	0.697570	−	0.716517i	$-0.254265\pi$
$919$	38867.9	1.39514	0.697570	+	0.716517i	$0.254265\pi$
$920$	−3680.62	−0.131898
$921$	6644.19	0.237713
$922$	16774.2	0.599165
$923$	60953.1	2.17367
$924$	−2903.21	−0.103364
$925$	14623.0	0.519787
$926$	783.795	0.0278154
$927$	−40531.0	−1.43604
$928$	−37182.4	−1.31527
$929$	13829.3	0.488400	0.244200	−	0.969725i	$-0.421475\pi$
$929$	13829.3	0.488400	0.244200	+	0.969725i	$0.421475\pi$
$930$	−1157.03	−0.0407961
$931$	−512.359	−0.0180364
$932$	1244.88	0.0437525
$933$	−161.458	−0.00566549
$934$	−6906.58	−0.241959
$935$	−3146.46	−0.110054
$936$	23699.7	0.827616
$937$	40293.0	1.40482	0.702410	−	0.711773i	$-0.252107\pi$
$937$	40293.0	1.40482	0.702410	+	0.711773i	$0.252107\pi$
$938$	−11886.2	−0.413751
$939$	265.333	0.00922132
$940$	3346.42	0.116115
$941$	−18141.7	−0.628482	−0.314241	−	0.949343i	$-0.601750\pi$
$941$	−18141.7	−0.628482	−0.314241	+	0.949343i	$0.601750\pi$
$942$	2690.38	0.0930544
$943$	−15539.9	−0.536636
$944$	−64049.4	−2.20829
$945$	−6848.92	−0.235762
$946$	0	0
$947$	−42305.7	−1.45169	−0.725845	−	0.687858i	$-0.758551\pi$
$947$	−42305.7	−1.45169	−0.725845	+	0.687858i	$0.758551\pi$
$948$	−487.744	−0.0167101
$949$	36043.5	1.23290
$950$	467.377	0.0159618
$951$	1680.04	0.0572862
$952$	5515.68	0.187777
$953$	34528.2	1.17364	0.586819	−	0.809718i	$-0.300380\pi$
$953$	34528.2	1.17364	0.586819	+	0.809718i	$0.300380\pi$
$954$	60570.0	2.05558
$955$	−8041.75	−0.272487
$956$	22538.1	0.762485
$957$	4123.57	0.139285
$958$	−40271.9	−1.35817
$959$	−29453.8	−0.991777
$960$	407.352	0.0136950
$961$	−25451.4	−0.854330
$962$	−49324.3	−1.65310
$963$	−24568.7	−0.822133
$964$	2544.87	0.0850257
$965$	−17555.9	−0.585641
$966$	4387.26	0.146126
$967$	−29151.9	−0.969454	−0.484727	−	0.874666i	$-0.661081\pi$
$967$	−29151.9	−0.969454	−0.484727	+	0.874666i	$0.661081\pi$
$968$	6448.72	0.214122
$969$	22.8963	0.000759066 0
$970$	7680.18	0.254222
$971$	4560.27	0.150717	0.0753584	−	0.997157i	$-0.475990\pi$
$971$	4560.27	0.150717	0.0753584	+	0.997157i	$0.475990\pi$
$972$	−8601.46	−0.283840
$973$	56173.2	1.85080
$974$	65121.3	2.14232
$975$	6023.52	0.197853
$976$	−62361.3	−2.04522
$977$	23774.7	0.778526	0.389263	−	0.921127i	$-0.372730\pi$
$977$	23774.7	0.778526	0.389263	+	0.921127i	$0.372730\pi$
$978$	2411.20	0.0788362
$979$	−25528.0	−0.833381
$980$	10562.9	0.344306
$981$	−48987.0	−1.59433
$982$	−69361.8	−2.25400
$983$	−53606.1	−1.73934	−0.869669	−	0.493636i	$-0.835667\pi$
$983$	−53606.1	−1.73934	−0.869669	+	0.493636i	$0.835667\pi$
$984$	−2399.89	−0.0777496
$985$	2574.38	0.0832757
$986$	13086.8	0.422685
$987$	2387.89	0.0770085
$988$	−606.660	−0.0195348
$989$	0	0
$990$	15432.1	0.495420
$991$	−33076.1	−1.06024	−0.530119	−	0.847923i	$-0.677853\pi$
$991$	−33076.1	−1.06024	−0.530119	+	0.847923i	$0.677853\pi$
$992$	−13071.8	−0.418377
$993$	−3057.37	−0.0977065
$994$	−69575.4	−2.22012
$995$	−15287.6	−0.487085
$996$	186.430	0.00593099
$997$	−31969.9	−1.01554	−0.507772	−	0.861491i	$-0.669531\pi$
$997$	−31969.9	−1.01554	−0.507772	+	0.861491i	$0.669531\pi$
$998$	35443.1	1.12418
$999$	−7114.99	−0.225334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.h.1.24		30
43.16	even	7		43.4.e.a.41.3	yes	60
43.35	even	7		43.4.e.a.21.3	✓	60
43.42	odd	2		1849.4.a.g.1.7		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.21.3	✓	60	43.35	even	7
43.4.e.a.41.3	yes	60	43.16	even	7
1849.4.a.g.1.7		30	43.42	odd	2
1849.4.a.h.1.24		30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.60614 q^{2} -0.812227 q^{3} +5.00427 q^{4} +5.99647 q^{5} -2.92901 q^{6} -26.3629 q^{7} -10.8030 q^{8} -26.3403 q^{9} +O(q^{10})\)	\(q+3.60614 q^{2} -0.812227 q^{3} +5.00427 q^{4} +5.99647 q^{5} -2.92901 q^{6} -26.3629 q^{7} -10.8030 q^{8} -26.3403 q^{9} +21.6241 q^{10} -27.0936 q^{11} -4.06461 q^{12} +83.2869 q^{13} -95.0685 q^{14} -4.87050 q^{15} -78.9914 q^{16} +19.3669 q^{17} -94.9869 q^{18} -1.45555 q^{19} +30.0080 q^{20} +21.4127 q^{21} -97.7034 q^{22} +56.8171 q^{23} +8.77451 q^{24} -89.0423 q^{25} +300.344 q^{26} +43.3244 q^{27} -131.927 q^{28} +187.383 q^{29} -17.5637 q^{30} +65.8760 q^{31} -198.430 q^{32} +22.0062 q^{33} +69.8398 q^{34} -158.085 q^{35} -131.814 q^{36} -164.226 q^{37} -5.24893 q^{38} -67.6479 q^{39} -64.7800 q^{40} -273.507 q^{41} +77.2172 q^{42} -135.584 q^{44} -157.949 q^{45} +204.891 q^{46} +111.518 q^{47} +64.1590 q^{48} +352.003 q^{49} -321.099 q^{50} -15.7303 q^{51} +416.790 q^{52} -637.668 q^{53} +156.234 q^{54} -162.466 q^{55} +284.799 q^{56} +1.18224 q^{57} +675.729 q^{58} +810.839 q^{59} -24.3733 q^{60} +789.470 q^{61} +237.558 q^{62} +694.407 q^{63} -83.6366 q^{64} +499.427 q^{65} +79.3573 q^{66} +125.028 q^{67} +96.9172 q^{68} -46.1484 q^{69} -570.075 q^{70} +731.846 q^{71} +284.555 q^{72} +432.763 q^{73} -592.222 q^{74} +72.3226 q^{75} -7.28398 q^{76} +714.266 q^{77} -243.948 q^{78} +119.998 q^{79} -473.670 q^{80} +675.998 q^{81} -986.305 q^{82} -45.8667 q^{83} +107.155 q^{84} +116.133 q^{85} -152.197 q^{87} +292.693 q^{88} +942.217 q^{89} -569.586 q^{90} -2195.68 q^{91} +284.328 q^{92} -53.5063 q^{93} +402.148 q^{94} -8.72818 q^{95} +161.170 q^{96} +355.167 q^{97} +1269.37 q^{98} +713.653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * q^99

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