LMFDB - Embedded newform 230.6.a.e.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,6,Mod(1,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,12,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$36.8882785570$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 403x - 1230 $ x^3 - 403*x - 1230
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.12806$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} +5.12806 q^{3} +16.0000 q^{4} -25.0000 q^{5} +20.5122 q^{6} +104.519 q^{7} +64.0000 q^{8} -216.703 q^{9} -100.000 q^{10} -489.208 q^{11} +82.0489 q^{12} -424.080 q^{13} +418.077 q^{14} -128.201 q^{15} +256.000 q^{16} -320.259 q^{17} -866.812 q^{18} -1684.51 q^{19} -400.000 q^{20} +535.980 q^{21} -1956.83 q^{22} +529.000 q^{23} +328.196 q^{24} +625.000 q^{25} -1696.32 q^{26} -2357.38 q^{27} +1672.31 q^{28} +126.359 q^{29} -512.806 q^{30} +6436.31 q^{31} +1024.00 q^{32} -2508.69 q^{33} -1281.03 q^{34} -2612.98 q^{35} -3467.25 q^{36} -10974.5 q^{37} -6738.05 q^{38} -2174.71 q^{39} -1600.00 q^{40} -2394.04 q^{41} +2143.92 q^{42} -8655.60 q^{43} -7827.33 q^{44} +5417.58 q^{45} +2116.00 q^{46} -25099.9 q^{47} +1312.78 q^{48} -5882.75 q^{49} +2500.00 q^{50} -1642.31 q^{51} -6785.28 q^{52} -4255.25 q^{53} -9429.53 q^{54} +12230.2 q^{55} +6689.22 q^{56} -8638.28 q^{57} +505.438 q^{58} +42758.6 q^{59} -2051.22 q^{60} -13450.6 q^{61} +25745.2 q^{62} -22649.6 q^{63} +4096.00 q^{64} +10602.0 q^{65} -10034.8 q^{66} +46832.2 q^{67} -5124.14 q^{68} +2712.74 q^{69} -10451.9 q^{70} +4120.28 q^{71} -13869.0 q^{72} -66925.5 q^{73} -43897.8 q^{74} +3205.04 q^{75} -26952.2 q^{76} -51131.6 q^{77} -8698.83 q^{78} -57340.7 q^{79} -6400.00 q^{80} +40570.0 q^{81} -9576.15 q^{82} +119870. q^{83} +8575.68 q^{84} +8006.47 q^{85} -34622.4 q^{86} +647.978 q^{87} -31309.3 q^{88} -85802.5 q^{89} +21670.3 q^{90} -44324.5 q^{91} +8464.00 q^{92} +33005.8 q^{93} -100400. q^{94} +42112.8 q^{95} +5251.13 q^{96} -23217.4 q^{97} -23531.0 q^{98} +106013. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12 q^{2} + 6 q^{3} + 48 q^{4} - 75 q^{5} + 24 q^{6} + 5 q^{7} + 192 q^{8} + 89 q^{9} - 300 q^{10} - 962 q^{11} + 96 q^{12} - 776 q^{13} + 20 q^{14} - 150 q^{15} + 768 q^{16} - 2317 q^{17} + 356 q^{18}+ \cdots + 24042 q^{99}+O(q^{100}) $ 3 * q + 12 * q^2 + 6 * q^3 + 48 * q^4 - 75 * q^5 + 24 * q^6 + 5 * q^7 + 192 * q^8 + 89 * q^9 - 300 * q^10 - 962 * q^11 + 96 * q^12 - 776 * q^13 + 20 * q^14 - 150 * q^15 + 768 * q^16 - 2317 * q^17 + 356 * q^18 + 654 * q^19 - 1200 * q^20 - 4996 * q^21 - 3848 * q^22 + 1587 * q^23 + 384 * q^24 + 1875 * q^25 - 3104 * q^26 - 1746 * q^27 + 80 * q^28 - 2223 * q^29 - 600 * q^30 - 6927 * q^31 + 3072 * q^32 - 13844 * q^33 - 9268 * q^34 - 125 * q^35 + 1424 * q^36 - 18801 * q^37 + 2616 * q^38 - 12666 * q^39 - 4800 * q^40 - 8369 * q^41 - 19984 * q^42 - 26064 * q^43 - 15392 * q^44 - 2225 * q^45 + 6348 * q^46 - 8974 * q^47 + 1536 * q^48 + 3524 * q^49 + 7500 * q^50 - 14180 * q^51 - 12416 * q^52 + 26079 * q^53 - 6984 * q^54 + 24050 * q^55 + 320 * q^56 - 16292 * q^57 - 8892 * q^58 + 21311 * q^59 - 2400 * q^60 - 19408 * q^61 - 27708 * q^62 - 42647 * q^63 + 12288 * q^64 + 19400 * q^65 - 55376 * q^66 - 40315 * q^67 - 37072 * q^68 + 3174 * q^69 - 500 * q^70 - 49333 * q^71 + 5696 * q^72 - 308 * q^73 - 75204 * q^74 + 3750 * q^75 + 10464 * q^76 + 49586 * q^77 - 50664 * q^78 - 51216 * q^79 - 19200 * q^80 - 104485 * q^81 - 33476 * q^82 + 38693 * q^83 - 79936 * q^84 + 57925 * q^85 - 104256 * q^86 + 29998 * q^87 - 61568 * q^88 - 109600 * q^89 - 8900 * q^90 + 44890 * q^91 + 25392 * q^92 + 65494 * q^93 - 35896 * q^94 - 16350 * q^95 + 6144 * q^96 - 26806 * q^97 + 14096 * q^98 + 24042 * q^99

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	5.12806	0.328965	0.164483	−	0.986380i	$-0.447405\pi$
$3$	5.12806	0.328965	0.164483	+	0.986380i	$0.447405\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	20.5122	0.232613
$7$	104.519	0.806215	0.403107	−	0.915153i	$-0.367930\pi$
$7$	104.519	0.806215	0.403107	+	0.915153i	$0.367930\pi$
$8$	64.0000	0.353553
$9$	−216.703	−0.891782
$10$	−100.000	−0.316228
$11$	−489.208	−1.21902	−0.609512	−	0.792777i	$-0.708635\pi$
$11$	−489.208	−1.21902	−0.609512	+	0.792777i	$0.708635\pi$
$12$	82.0489	0.164483
$13$	−424.080	−0.695969	−0.347984	−	0.937500i	$-0.613134\pi$
$13$	−424.080	−0.695969	−0.347984	+	0.937500i	$0.613134\pi$
$14$	418.077	0.570080
$15$	−128.201	−0.147118
$16$	256.000	0.250000
$17$	−320.259	−0.268769	−0.134384	−	0.990929i	$-0.542906\pi$
$17$	−320.259	−0.268769	−0.134384	+	0.990929i	$0.542906\pi$
$18$	−866.812	−0.630585
$19$	−1684.51	−1.07051	−0.535255	−	0.844691i	$-0.679784\pi$
$19$	−1684.51	−1.07051	−0.535255	+	0.844691i	$0.679784\pi$
$20$	−400.000	−0.223607
$21$	535.980	0.265216
$22$	−1956.83	−0.861980
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	328.196	0.116307
$25$	625.000	0.200000
$26$	−1696.32	−0.492124
$27$	−2357.38	−0.622330
$28$	1672.31	0.403107
$29$	126.359	0.0279005	0.0139503	−	0.999903i	$-0.495559\pi$
$29$	126.359	0.0279005	0.0139503	+	0.999903i	$0.495559\pi$
$30$	−512.806	−0.104028
$31$	6436.31	1.20291	0.601454	−	0.798907i	$-0.294588\pi$
$31$	6436.31	1.20291	0.601454	+	0.798907i	$0.294588\pi$
$32$	1024.00	0.176777
$33$	−2508.69	−0.401016
$34$	−1281.03	−0.190048
$35$	−2612.98	−0.360550
$36$	−3467.25	−0.445891
$37$	−10974.5	−1.31789	−0.658944	−	0.752192i	$-0.728997\pi$
$37$	−10974.5	−1.31789	−0.658944	+	0.752192i	$0.728997\pi$
$38$	−6738.05	−0.756965
$39$	−2174.71	−0.228949
$40$	−1600.00	−0.158114
$41$	−2394.04	−0.222419	−0.111209	−	0.993797i	$-0.535472\pi$
$41$	−2394.04	−0.222419	−0.111209	+	0.993797i	$0.535472\pi$
$42$	2143.92	0.187536
$43$	−8655.60	−0.713881	−0.356941	−	0.934127i	$-0.616180\pi$
$43$	−8655.60	−0.713881	−0.356941	+	0.934127i	$0.616180\pi$
$44$	−7827.33	−0.609512
$45$	5417.58	0.398817
$46$	2116.00	0.147442
$47$	−25099.9	−1.65740	−0.828701	−	0.559691i	$-0.810920\pi$
$47$	−25099.9	−1.65740	−0.828701	+	0.559691i	$0.810920\pi$
$48$	1312.78	0.0822413
$49$	−5882.75	−0.350018
$50$	2500.00	0.141421
$51$	−1642.31	−0.0884155
$52$	−6785.28	−0.347984
$53$	−4255.25	−0.208083	−0.104041	−	0.994573i	$-0.533177\pi$
$53$	−4255.25	−0.208083	−0.104041	+	0.994573i	$0.533177\pi$
$54$	−9429.53	−0.440054
$55$	12230.2	0.545164
$56$	6689.22	0.285040
$57$	−8638.28	−0.352160
$58$	505.438	0.0197287
$59$	42758.6	1.59917	0.799584	−	0.600555i	$-0.205054\pi$
$59$	42758.6	1.59917	0.799584	+	0.600555i	$0.205054\pi$
$60$	−2051.22	−0.0735588
$61$	−13450.6	−0.462825	−0.231413	−	0.972856i	$-0.574335\pi$
$61$	−13450.6	−0.462825	−0.231413	+	0.972856i	$0.574335\pi$
$62$	25745.2	0.850585
$63$	−22649.6	−0.718968
$64$	4096.00	0.125000
$65$	10602.0	0.311247
$66$	−10034.8	−0.283561
$67$	46832.2	1.27455	0.637276	−	0.770635i	$-0.280061\pi$
$67$	46832.2	1.27455	0.637276	+	0.770635i	$0.280061\pi$
$68$	−5124.14	−0.134384
$69$	2712.74	0.0685940
$70$	−10451.9	−0.254947
$71$	4120.28	0.0970020	0.0485010	−	0.998823i	$-0.484556\pi$
$71$	4120.28	0.0970020	0.0485010	+	0.998823i	$0.484556\pi$
$72$	−13869.0	−0.315293
$73$	−66925.5	−1.46989	−0.734945	−	0.678127i	$-0.762792\pi$
$73$	−66925.5	−1.46989	−0.734945	+	0.678127i	$0.762792\pi$
$74$	−43897.8	−0.931887
$75$	3205.04	0.0657930
$76$	−26952.2	−0.535255
$77$	−51131.6	−0.982795
$78$	−8698.83	−0.161892
$79$	−57340.7	−1.03370	−0.516851	−	0.856076i	$-0.672896\pi$
$79$	−57340.7	−1.03370	−0.516851	+	0.856076i	$0.672896\pi$
$80$	−6400.00	−0.111803
$81$	40570.0	0.687057
$82$	−9576.15	−0.157274
$83$	119870.	1.90992	0.954959	−	0.296737i	$-0.0958985\pi$
$83$	119870.	1.90992	0.954959	+	0.296737i	$0.0958985\pi$
$84$	8575.68	0.132608
$85$	8006.47	0.120197
$86$	−34622.4	−0.504790
$87$	647.978	0.00917830
$88$	−31309.3	−0.430990
$89$	−85802.5	−1.14822	−0.574110	−	0.818778i	$-0.694652\pi$
$89$	−85802.5	−1.14822	−0.574110	+	0.818778i	$0.694652\pi$
$90$	21670.3	0.282006
$91$	−44324.5	−0.561100
$92$	8464.00	0.104257
$93$	33005.8	0.395715
$94$	−100400.	−1.17196
$95$	42112.8	0.478746
$96$	5251.13	0.0581534
$97$	−23217.4	−0.250544	−0.125272	−	0.992122i	$-0.539980\pi$
$97$	−23217.4	−0.250544	−0.125272	+	0.992122i	$0.539980\pi$
$98$	−23531.0	−0.247500
$99$	106013.	1.08710
$100$	10000.0	0.100000
$101$	−53571.5	−0.522553	−0.261276	−	0.965264i	$-0.584143\pi$
$101$	−53571.5	−0.522553	−0.261276	+	0.965264i	$0.584143\pi$
$102$	−6569.22	−0.0625192
$103$	−74243.3	−0.689547	−0.344774	−	0.938686i	$-0.612044\pi$
$103$	−74243.3	−0.689547	−0.344774	+	0.938686i	$0.612044\pi$
$104$	−27141.1	−0.246062
$105$	−13399.5	−0.118608
$106$	−17021.0	−0.147137
$107$	−8236.50	−0.0695478	−0.0347739	−	0.999395i	$-0.511071\pi$
$107$	−8236.50	−0.0695478	−0.0347739	+	0.999395i	$0.511071\pi$
$108$	−37718.1	−0.311165
$109$	34585.4	0.278822	0.139411	−	0.990235i	$-0.455479\pi$
$109$	34585.4	0.278822	0.139411	+	0.990235i	$0.455479\pi$
$110$	48920.8	0.385489
$111$	−56277.6	−0.433539
$112$	26756.9	0.201554
$113$	234561.	1.72806	0.864031	−	0.503438i	$-0.167932\pi$
$113$	234561.	1.72806	0.864031	+	0.503438i	$0.167932\pi$
$114$	−34553.1	−0.249015
$115$	−13225.0	−0.0932505
$116$	2021.75	0.0139503
$117$	91899.5	0.620652
$118$	171035.	1.13078
$119$	−33473.2	−0.216685
$120$	−8204.89	−0.0520139
$121$	78273.8	0.486019
$122$	−53802.4	−0.327267
$123$	−12276.8	−0.0731680
$124$	102981.	0.601454
$125$	−15625.0	−0.0894427
$126$	−90598.5	−0.508387
$127$	−212332.	−1.16817	−0.584084	−	0.811693i	$-0.698546\pi$
$127$	−212332.	−1.16817	−0.584084	+	0.811693i	$0.698546\pi$
$128$	16384.0	0.0883883
$129$	−44386.4	−0.234842
$130$	42408.0	0.220085
$131$	311950.	1.58820	0.794102	−	0.607784i	$-0.207941\pi$
$131$	311950.	1.58820	0.794102	+	0.607784i	$0.207941\pi$
$132$	−40139.0	−0.200508
$133$	−176064.	−0.863061
$134$	187329.	0.901245
$135$	58934.6	0.278315
$136$	−20496.6	−0.0950241
$137$	−110712.	−0.503957	−0.251978	−	0.967733i	$-0.581081\pi$
$137$	−110712.	−0.503957	−0.251978	+	0.967733i	$0.581081\pi$
$138$	10851.0	0.0485033
$139$	264616.	1.16166	0.580830	−	0.814025i	$-0.302728\pi$
$139$	264616.	1.16166	0.580830	+	0.814025i	$0.302728\pi$
$140$	−41807.7	−0.180275
$141$	−128714.	−0.545228
$142$	16481.1	0.0685908
$143$	207464.	0.848402
$144$	−55476.0	−0.222945
$145$	−3158.99	−0.0124775
$146$	−267702.	−1.03937
$147$	−30167.1	−0.115144
$148$	−175591.	−0.658944
$149$	−20423.4	−0.0753639	−0.0376820	−	0.999290i	$-0.511997\pi$
$149$	−20423.4	−0.0753639	−0.0376820	+	0.999290i	$0.511997\pi$
$150$	12820.1	0.0465227
$151$	336425.	1.20073	0.600366	−	0.799726i	$-0.295022\pi$
$151$	336425.	1.20073	0.600366	+	0.799726i	$0.295022\pi$
$152$	−107809.	−0.378482
$153$	69401.0	0.239683
$154$	−204527.	−0.694941
$155$	−160908.	−0.537957
$156$	−34795.3	−0.114475
$157$	460283.	1.49031	0.745153	−	0.666893i	$-0.232376\pi$
$157$	460283.	1.49031	0.745153	+	0.666893i	$0.232376\pi$
$158$	−229363.	−0.730937
$159$	−21821.2	−0.0684519
$160$	−25600.0	−0.0790569
$161$	55290.6	0.168107
$162$	162280.	0.485823
$163$	−541579.	−1.59659	−0.798294	−	0.602267i	$-0.794264\pi$
$163$	−541579.	−1.59659	−0.798294	+	0.602267i	$0.794264\pi$
$164$	−38304.6	−0.111209
$165$	62717.2	0.179340
$166$	479480.	1.35052
$167$	94938.7	0.263422	0.131711	−	0.991288i	$-0.457953\pi$
$167$	94938.7	0.263422	0.131711	+	0.991288i	$0.457953\pi$
$168$	34302.7	0.0937682
$169$	−191449.	−0.515628
$170$	32025.9	0.0849921
$171$	365039.	0.954661
$172$	−138490.	−0.356941
$173$	−145374.	−0.369294	−0.184647	−	0.982805i	$-0.559114\pi$
$173$	−145374.	−0.369294	−0.184647	+	0.982805i	$0.559114\pi$
$174$	2591.91	0.00649004
$175$	65324.5	0.161243
$176$	−125237.	−0.304756
$177$	219269.	0.526070
$178$	−343210.	−0.811914
$179$	398105.	0.928678	0.464339	−	0.885658i	$-0.346292\pi$
$179$	398105.	0.928678	0.464339	+	0.885658i	$0.346292\pi$
$180$	86681.2	0.199409
$181$	435143.	0.987269	0.493635	−	0.869669i	$-0.335668\pi$
$181$	435143.	0.987269	0.493635	+	0.869669i	$0.335668\pi$
$182$	−177298.	−0.396758
$183$	−68975.5	−0.152253
$184$	33856.0	0.0737210
$185$	274361.	0.589377
$186$	132023.	0.279813
$187$	156673.	0.327635
$188$	−401599.	−0.828701
$189$	−246392.	−0.501732
$190$	168451.	0.338525
$191$	488032.	0.967976	0.483988	−	0.875075i	$-0.339188\pi$
$191$	488032.	0.967976	0.483988	+	0.875075i	$0.339188\pi$
$192$	21004.5	0.0411206
$193$	316888.	0.612367	0.306184	−	0.951972i	$-0.400948\pi$
$193$	316888.	0.612367	0.306184	+	0.951972i	$0.400948\pi$
$194$	−92869.6	−0.177161
$195$	54367.7	0.102389
$196$	−94124.0	−0.175009
$197$	904711.	1.66090	0.830451	−	0.557091i	$-0.188083\pi$
$197$	904711.	1.66090	0.830451	+	0.557091i	$0.188083\pi$
$198$	424052.	0.768698
$199$	−952131.	−1.70437	−0.852185	−	0.523240i	$-0.824723\pi$
$199$	−952131.	−1.70437	−0.852185	+	0.523240i	$0.824723\pi$
$200$	40000.0	0.0707107
$201$	240158.	0.419283
$202$	−214286.	−0.369500
$203$	13207.0	0.0224938
$204$	−26276.9	−0.0442077
$205$	59850.9	0.0994687
$206$	−296973.	−0.487584
$207$	−114636.	−0.185949
$208$	−108565.	−0.173992
$209$	824078.	1.30498
$210$	−53598.0	−0.0838688
$211$	281552.	0.435365	0.217682	−	0.976020i	$-0.430150\pi$
$211$	281552.	0.435365	0.217682	+	0.976020i	$0.430150\pi$
$212$	−68084.0	−0.104041
$213$	21129.0	0.0319103
$214$	−32946.0	−0.0491777
$215$	216390.	0.319257
$216$	−150873.	−0.220027
$217$	672717.	0.969802
$218$	138342.	0.197157
$219$	−343198.	−0.483542
$220$	195683.	0.272582
$221$	135815.	0.187055
$222$	−225110.	−0.306558
$223$	232188.	0.312663	0.156332	−	0.987705i	$-0.450033\pi$
$223$	232188.	0.312663	0.156332	+	0.987705i	$0.450033\pi$
$224$	107028.	0.142520
$225$	−135439.	−0.178356
$226$	938243.	1.22192
$227$	197153.	0.253945	0.126972	−	0.991906i	$-0.459474\pi$
$227$	197153.	0.253945	0.126972	+	0.991906i	$0.459474\pi$
$228$	−138213.	−0.176080
$229$	−455428.	−0.573893	−0.286946	−	0.957947i	$-0.592640\pi$
$229$	−455428.	−0.573893	−0.286946	+	0.957947i	$0.592640\pi$
$230$	−52900.0	−0.0659380
$231$	−262206.	−0.323305
$232$	8087.00	0.00986433
$233$	−126870.	−0.153098	−0.0765492	−	0.997066i	$-0.524390\pi$
$233$	−126870.	−0.153098	−0.0765492	+	0.997066i	$0.524390\pi$
$234$	367598.	0.438867
$235$	627499.	0.741213
$236$	684138.	0.799584
$237$	−294046.	−0.340052
$238$	−133893.	−0.153220
$239$	−1.65192e6	−1.87066	−0.935330	−	0.353777i	$-0.884897\pi$
$239$	−1.65192e6	−1.87066	−0.935330	+	0.353777i	$0.884897\pi$
$240$	−32819.6	−0.0367794
$241$	−1.32764e6	−1.47244	−0.736220	−	0.676743i	$-0.763391\pi$
$241$	−1.32764e6	−1.47244	−0.736220	+	0.676743i	$0.763391\pi$
$242$	313095.	0.343667
$243$	780890.	0.848348
$244$	−215210.	−0.231413
$245$	147069.	0.156533
$246$	−49107.1	−0.0517376
$247$	714369.	0.745041
$248$	411924.	0.425292
$249$	614700.	0.628296
$250$	−62500.0	−0.0632456
$251$	−350486.	−0.351145	−0.175572	−	0.984467i	$-0.556178\pi$
$251$	−350486.	−0.351145	−0.175572	+	0.984467i	$0.556178\pi$
$252$	−362394.	−0.359484
$253$	−258791.	−0.254184
$254$	−849327.	−0.826020
$255$	41057.6	0.0395406
$256$	65536.0	0.0625000
$257$	−668229.	−0.631092	−0.315546	−	0.948910i	$-0.602188\pi$
$257$	−668229.	−0.631092	−0.315546	+	0.948910i	$0.602188\pi$
$258$	−177546.	−0.166058
$259$	−1.14704e6	−1.06250
$260$	169632.	0.155623
$261$	−27382.5	−0.0248812
$262$	1.24780e6	1.12303
$263$	−1.84958e6	−1.64886	−0.824431	−	0.565962i	$-0.808505\pi$
$263$	−1.84958e6	−1.64886	−0.824431	+	0.565962i	$0.808505\pi$
$264$	−160556.	−0.141781
$265$	106381.	0.0930573
$266$	−704256.	−0.610276
$267$	−440000.	−0.377724
$268$	749316.	0.637276
$269$	−276109.	−0.232649	−0.116324	−	0.993211i	$-0.537111\pi$
$269$	−276109.	−0.232649	−0.116324	+	0.993211i	$0.537111\pi$
$270$	235738.	0.196798
$271$	1.74330e6	1.44194	0.720972	−	0.692964i	$-0.243695\pi$
$271$	1.74330e6	1.44194	0.720972	+	0.692964i	$0.243695\pi$
$272$	−81986.2	−0.0671922
$273$	−227299.	−0.184582
$274$	−442848.	−0.356351
$275$	−305755.	−0.243805
$276$	43403.9	0.0342970
$277$	1.57020e6	1.22958	0.614790	−	0.788691i	$-0.289241\pi$
$277$	1.57020e6	1.22958	0.614790	+	0.788691i	$0.289241\pi$
$278$	1.05846e6	0.821418
$279$	−1.39477e6	−1.07273
$280$	−167231.	−0.127474
$281$	−426078.	−0.321902	−0.160951	−	0.986962i	$-0.551456\pi$
$281$	−426078.	−0.321902	−0.160951	+	0.986962i	$0.551456\pi$
$282$	−514856.	−0.385534
$283$	−683597.	−0.507381	−0.253691	−	0.967285i	$-0.581644\pi$
$283$	−683597.	−0.507381	−0.253691	+	0.967285i	$0.581644\pi$
$284$	65924.4	0.0485010
$285$	215957.	0.157491
$286$	829854.	0.599911
$287$	−250223.	−0.179317
$288$	−221904.	−0.157646
$289$	−1.31729e6	−0.927763
$290$	−12635.9	−0.00882293
$291$	−119060.	−0.0824203
$292$	−1.07081e6	−0.734945
$293$	−1.08021e6	−0.735088	−0.367544	−	0.930006i	$-0.619801\pi$
$293$	−1.08021e6	−0.735088	−0.367544	+	0.930006i	$0.619801\pi$
$294$	−120668.	−0.0814188
$295$	−1.06897e6	−0.715169
$296$	−702365.	−0.465944
$297$	1.15325e6	0.758635
$298$	−81693.8	−0.0532903
$299$	−224338.	−0.145120
$300$	51280.6	0.0328965
$301$	−904676.	−0.575542
$302$	1.34570e6	0.849045
$303$	−274718.	−0.171902
$304$	−431236.	−0.267627
$305$	336265.	0.206982
$306$	277604.	0.169482
$307$	−1.91426e6	−1.15919	−0.579596	−	0.814904i	$-0.696789\pi$
$307$	−1.91426e6	−1.15919	−0.579596	+	0.814904i	$0.696789\pi$
$308$	−818106.	−0.491397
$309$	−380724.	−0.226837
$310$	−643631.	−0.380393
$311$	−1.21503e6	−0.712337	−0.356168	−	0.934422i	$-0.615917\pi$
$311$	−1.21503e6	−0.712337	−0.356168	+	0.934422i	$0.615917\pi$
$312$	−139181.	−0.0809458
$313$	−1.36860e6	−0.789616	−0.394808	−	0.918764i	$-0.629189\pi$
$313$	−1.36860e6	−0.789616	−0.394808	+	0.918764i	$0.629189\pi$
$314$	1.84113e6	1.05381
$315$	566240.	0.321532
$316$	−917451.	−0.516851
$317$	−56127.9	−0.0313712	−0.0156856	−	0.999877i	$-0.504993\pi$
$317$	−56127.9	−0.0313712	−0.0156856	+	0.999877i	$0.504993\pi$
$318$	−87284.7	−0.0484028
$319$	−61816.1	−0.0340114
$320$	−102400.	−0.0559017
$321$	−42237.3	−0.0228788
$322$	221162.	0.118870
$323$	539480.	0.287719
$324$	649121.	0.343529
$325$	−265050.	−0.139194
$326$	−2.16632e6	−1.12896
$327$	177356.	0.0917227
$328$	−153218.	−0.0786369
$329$	−2.62342e6	−1.33622
$330$	250869.	0.126812
$331$	675416.	0.338845	0.169423	−	0.985543i	$-0.445810\pi$
$331$	675416.	0.338845	0.169423	+	0.985543i	$0.445810\pi$
$332$	1.91792e6	0.954959
$333$	2.37820e6	1.17527
$334$	379755.	0.186268
$335$	−1.17081e6	−0.569997
$336$	137211.	0.0663041
$337$	1.07147e6	0.513933	0.256967	−	0.966420i	$-0.417277\pi$
$337$	1.07147e6	0.513933	0.256967	+	0.966420i	$0.417277\pi$
$338$	−765796.	−0.364604
$339$	1.20284e6	0.568472
$340$	128103.	0.0600985
$341$	−3.14870e6	−1.46637
$342$	1.46016e6	0.675047
$343$	−2.37151e6	−1.08840
$344$	−553958.	−0.252395
$345$	−67818.6	−0.0306761
$346$	−581498.	−0.261131
$347$	1.99569e6	0.889754	0.444877	−	0.895592i	$-0.353247\pi$
$347$	1.99569e6	0.889754	0.444877	+	0.895592i	$0.353247\pi$
$348$	10367.7	0.00458915
$349$	−1.97861e6	−0.869555	−0.434778	−	0.900538i	$-0.643173\pi$
$349$	−1.97861e6	−0.869555	−0.434778	+	0.900538i	$0.643173\pi$
$350$	261298.	0.114016
$351$	999720.	0.433122
$352$	−500949.	−0.215495
$353$	−792209.	−0.338378	−0.169189	−	0.985584i	$-0.554115\pi$
$353$	−792209.	−0.338378	−0.169189	+	0.985584i	$0.554115\pi$
$354$	877075.	0.371988
$355$	−103007.	−0.0433806
$356$	−1.37284e6	−0.574110
$357$	−171652.	−0.0712819
$358$	1.59242e6	0.656675
$359$	−2.31691e6	−0.948796	−0.474398	−	0.880310i	$-0.657334\pi$
$359$	−2.31691e6	−0.948796	−0.474398	+	0.880310i	$0.657334\pi$
$360$	346725.	0.141003
$361$	361487.	0.145991
$362$	1.74057e6	0.698105
$363$	401393.	0.159883
$364$	−709192.	−0.280550
$365$	1.67314e6	0.657355
$366$	−275902.	−0.107659
$367$	1.10314e6	0.427530	0.213765	−	0.976885i	$-0.431427\pi$
$367$	1.10314e6	0.427530	0.213765	+	0.976885i	$0.431427\pi$
$368$	135424.	0.0521286
$369$	518795.	0.198349
$370$	1.09745e6	0.416753
$371$	−444755.	−0.167759
$372$	528092.	0.197857
$373$	−216080.	−0.0804161	−0.0402081	−	0.999191i	$-0.512802\pi$
$373$	−216080.	−0.0804161	−0.0402081	+	0.999191i	$0.512802\pi$
$374$	626693.	0.231673
$375$	−80125.9	−0.0294235
$376$	−1.60640e6	−0.585980
$377$	−53586.5	−0.0194179
$378$	−985567.	−0.354778
$379$	−5.01720e6	−1.79417	−0.897084	−	0.441860i	$-0.854319\pi$
$379$	−5.01720e6	−1.79417	−0.897084	+	0.441860i	$0.854319\pi$
$380$	673805.	0.239373
$381$	−1.08885e6	−0.384287
$382$	1.95213e6	0.684463
$383$	−1.66886e6	−0.581329	−0.290664	−	0.956825i	$-0.593876\pi$
$383$	−1.66886e6	−0.581329	−0.290664	+	0.956825i	$0.593876\pi$
$384$	84018.1	0.0290767
$385$	1.27829e6	0.439519
$386$	1.26755e6	0.433009
$387$	1.87569e6	0.636626
$388$	−371478.	−0.125272
$389$	−1.22486e6	−0.410403	−0.205202	−	0.978720i	$-0.565785\pi$
$389$	−1.22486e6	−0.410403	−0.205202	+	0.978720i	$0.565785\pi$
$390$	217471.	0.0724002
$391$	−169417.	−0.0560421
$392$	−376496.	−0.123750
$393$	1.59970e6	0.522464
$394$	3.61884e6	1.17444
$395$	1.43352e6	0.462285
$396$	1.69621e6	0.543552
$397$	2.61435e6	0.832507	0.416254	−	0.909249i	$-0.363343\pi$
$397$	2.61435e6	0.832507	0.416254	+	0.909249i	$0.363343\pi$
$398$	−3.80852e6	−1.20517
$399$	−902866.	−0.283917
$400$	160000.	0.0500000
$401$	−417138.	−0.129545	−0.0647723	−	0.997900i	$-0.520632\pi$
$401$	−417138.	−0.129545	−0.0647723	+	0.997900i	$0.520632\pi$
$402$	960633.	0.296478
$403$	−2.72951e6	−0.837186
$404$	−857143.	−0.261276
$405$	−1.01425e6	−0.307261
$406$	52827.9	0.0159055
$407$	5.36879e6	1.60654
$408$	−105108.	−0.0312596
$409$	3.54344e6	1.04741	0.523704	−	0.851900i	$-0.324550\pi$
$409$	3.54344e6	1.04741	0.523704	+	0.851900i	$0.324550\pi$
$410$	239404.	0.0703350
$411$	−567737.	−0.165784
$412$	−1.18789e6	−0.344774
$413$	4.46910e6	1.28927
$414$	−458544.	−0.131486
$415$	−2.99675e6	−0.854142
$416$	−434258.	−0.123031
$417$	1.35697e6	0.382146
$418$	3.29631e6	0.922758
$419$	−4.74678e6	−1.32088	−0.660442	−	0.750877i	$-0.729631\pi$
$419$	−4.74678e6	−1.32088	−0.660442	+	0.750877i	$0.729631\pi$
$420$	−214392.	−0.0593042
$421$	−1.46862e6	−0.403836	−0.201918	−	0.979402i	$-0.564717\pi$
$421$	−1.46862e6	−0.403836	−0.201918	+	0.979402i	$0.564717\pi$
$422$	1.12621e6	0.307849
$423$	5.43923e6	1.47804
$424$	−272336.	−0.0735683
$425$	−200162.	−0.0537537
$426$	84516.1	0.0225640
$427$	−1.40585e6	−0.373137
$428$	−131784.	−0.0347739
$429$	1.06389e6	0.279095
$430$	865560.	0.225749
$431$	−5.31826e6	−1.37904	−0.689520	−	0.724267i	$-0.742178\pi$
$431$	−5.31826e6	−1.37904	−0.689520	+	0.724267i	$0.742178\pi$
$432$	−603490.	−0.155583
$433$	−2.69027e6	−0.689565	−0.344783	−	0.938683i	$-0.612047\pi$
$433$	−2.69027e6	−0.689565	−0.344783	+	0.938683i	$0.612047\pi$
$434$	2.69087e6	0.685754
$435$	−16199.5	−0.00410466
$436$	553367.	0.139411
$437$	−891108.	−0.223217
$438$	−1.37279e6	−0.341916
$439$	−505170.	−0.125105	−0.0625527	−	0.998042i	$-0.519924\pi$
$439$	−505170.	−0.125105	−0.0625527	+	0.998042i	$0.519924\pi$
$440$	782733.	0.192745
$441$	1.27481e6	0.312140
$442$	543262.	0.132268
$443$	−86611.2	−0.0209684	−0.0104842	−	0.999945i	$-0.503337\pi$
$443$	−86611.2	−0.0209684	−0.0104842	+	0.999945i	$0.503337\pi$
$444$	−900442.	−0.216770
$445$	2.14506e6	0.513499
$446$	928751.	0.221086
$447$	−104733.	−0.0247921
$448$	428110.	0.100777
$449$	4.57903e6	1.07191	0.535954	−	0.844247i	$-0.319952\pi$
$449$	4.57903e6	1.07191	0.535954	+	0.844247i	$0.319952\pi$
$450$	−541758.	−0.126117
$451$	1.17118e6	0.271134
$452$	3.75297e6	0.864031
$453$	1.72521e6	0.394999
$454$	788614.	0.179566
$455$	1.10811e6	0.250932
$456$	−552850.	−0.124507
$457$	4.75445e6	1.06490	0.532452	−	0.846460i	$-0.321271\pi$
$457$	4.75445e6	1.06490	0.532452	+	0.846460i	$0.321271\pi$
$458$	−1.82171e6	−0.405804
$459$	754973.	0.167263
$460$	−211600.	−0.0466252
$461$	8.68028e6	1.90231	0.951155	−	0.308714i	$-0.0998987\pi$
$461$	8.68028e6	1.90231	0.951155	+	0.308714i	$0.0998987\pi$
$462$	−1.04882e6	−0.228611
$463$	5.09262e6	1.10405	0.552025	−	0.833827i	$-0.313855\pi$
$463$	5.09262e6	1.10405	0.552025	+	0.833827i	$0.313855\pi$
$464$	32348.0	0.00697514
$465$	−825144.	−0.176969
$466$	−507481.	−0.108257
$467$	4.02408e6	0.853836	0.426918	−	0.904290i	$-0.359599\pi$
$467$	4.02408e6	0.853836	0.426918	+	0.904290i	$0.359599\pi$
$468$	1.47039e6	0.310326
$469$	4.89486e6	1.02756
$470$	2.50999e6	0.524117
$471$	2.36036e6	0.490259
$472$	2.73655e6	0.565391
$473$	4.23439e6	0.870238
$474$	−1.17619e6	−0.240453
$475$	−1.05282e6	−0.214102
$476$	−535571.	−0.108343
$477$	922126.	0.185564
$478$	−6.60769e6	−1.32276
$479$	−1.74790e6	−0.348080	−0.174040	−	0.984739i	$-0.555682\pi$
$479$	−1.74790e6	−0.348080	−0.174040	+	0.984739i	$0.555682\pi$
$480$	−131278.	−0.0260070
$481$	4.65405e6	0.917209
$482$	−5.31056e6	−1.04117
$483$	283534.	0.0553015
$484$	1.25238e6	0.243009
$485$	580435.	0.112047
$486$	3.12356e6	0.599873
$487$	−4.42380e6	−0.845226	−0.422613	−	0.906310i	$-0.638887\pi$
$487$	−4.42380e6	−0.845226	−0.422613	+	0.906310i	$0.638887\pi$
$488$	−860838.	−0.163633
$489$	−2.77725e6	−0.525222
$490$	588275.	0.110685
$491$	1.47947e6	0.276951	0.138476	−	0.990366i	$-0.455780\pi$
$491$	1.47947e6	0.276951	0.138476	+	0.990366i	$0.455780\pi$
$492$	−196428.	−0.0365840
$493$	−40467.7	−0.00749879
$494$	2.85748e6	0.526824
$495$	−2.65032e6	−0.486167
$496$	1.64769e6	0.300727
$497$	430648.	0.0782044
$498$	2.45880e6	0.444273
$499$	−5.17679e6	−0.930698	−0.465349	−	0.885127i	$-0.654071\pi$
$499$	−5.17679e6	−0.930698	−0.465349	+	0.885127i	$0.654071\pi$
$500$	−250000.	−0.0447214
$501$	486851.	0.0866567
$502$	−1.40194e6	−0.248297
$503$	4.58821e6	0.808581	0.404291	−	0.914631i	$-0.367518\pi$
$503$	4.58821e6	0.808581	0.404291	+	0.914631i	$0.367518\pi$
$504$	−1.44958e6	−0.254193
$505$	1.33929e6	0.233693
$506$	−1.03516e6	−0.179735
$507$	−981761.	−0.169623
$508$	−3.39731e6	−0.584084
$509$	−268539.	−0.0459423	−0.0229711	−	0.999736i	$-0.507313\pi$
$509$	−268539.	−0.0459423	−0.0229711	+	0.999736i	$0.507313\pi$
$510$	164231.	0.0279594
$511$	−6.99500e6	−1.18505
$512$	262144.	0.0441942
$513$	3.97104e6	0.666210
$514$	−2.67292e6	−0.446249
$515$	1.85608e6	0.308375
$516$	−710183.	−0.117421
$517$	1.22791e7	2.02041
$518$	−4.58816e6	−0.751301
$519$	−745488.	−0.121485
$520$	678528.	0.110042
$521$	−4.43206e6	−0.715337	−0.357669	−	0.933849i	$-0.616428\pi$
$521$	−4.43206e6	−0.715337	−0.357669	+	0.933849i	$0.616428\pi$
$522$	−109530.	−0.0175937
$523$	−5.86604e6	−0.937758	−0.468879	−	0.883263i	$-0.655342\pi$
$523$	−5.86604e6	−0.937758	−0.468879	+	0.883263i	$0.655342\pi$
$524$	4.99120e6	0.794102
$525$	334988.	0.0530433
$526$	−7.39833e6	−1.16592
$527$	−2.06128e6	−0.323304
$528$	−642224.	−0.100254
$529$	279841.	0.0434783
$530$	425525.	0.0658015
$531$	−9.26593e6	−1.42611
$532$	−2.81702e6	−0.431530
$533$	1.01526e6	0.154796
$534$	−1.76000e6	−0.267091
$535$	205913.	0.0311027
$536$	2.99726e6	0.450622
$537$	2.04151e6	0.305503
$538$	−1.10444e6	−0.164507
$539$	2.87789e6	0.426680
$540$	942953.	0.139157
$541$	−1.11245e7	−1.63413	−0.817066	−	0.576544i	$-0.804401\pi$
$541$	−1.11245e7	−1.63413	−0.817066	+	0.576544i	$0.804401\pi$
$542$	6.97320e6	1.01961
$543$	2.23144e6	0.324777
$544$	−327945.	−0.0475120
$545$	−864636.	−0.124693
$546$	−909194.	−0.130519
$547$	−8.58501e6	−1.22680	−0.613398	−	0.789774i	$-0.710198\pi$
$547$	−8.58501e6	−1.22680	−0.613398	+	0.789774i	$0.710198\pi$
$548$	−1.77139e6	−0.251978
$549$	2.91479e6	0.412739
$550$	−1.22302e6	−0.172396
$551$	−212854.	−0.0298678
$552$	173616.	0.0242516
$553$	−5.99320e6	−0.833385
$554$	6.28082e6	0.869444
$555$	1.40694e6	0.193885
$556$	4.23386e6	0.580830
$557$	6.88488e6	0.940283	0.470142	−	0.882591i	$-0.344203\pi$
$557$	6.88488e6	0.940283	0.470142	+	0.882591i	$0.344203\pi$
$558$	−5.57907e6	−0.758536
$559$	3.67067e6	0.496839
$560$	−668922.	−0.0901375
$561$	803429.	0.107781
$562$	−1.70431e6	−0.227619
$563$	−7.98545e6	−1.06177	−0.530883	−	0.847445i	$-0.678139\pi$
$563$	−7.98545e6	−1.06177	−0.530883	+	0.847445i	$0.678139\pi$
$564$	−2.05942e6	−0.272614
$565$	−5.86402e6	−0.772813
$566$	−2.73439e6	−0.358773
$567$	4.24035e6	0.553916
$568$	263698.	0.0342954
$569$	−8.70908e6	−1.12769	−0.563847	−	0.825879i	$-0.690679\pi$
$569$	−8.70908e6	−1.12769	−0.563847	+	0.825879i	$0.690679\pi$
$570$	863828.	0.111363
$571$	−3.30076e6	−0.423665	−0.211833	−	0.977306i	$-0.567943\pi$
$571$	−3.30076e6	−0.423665	−0.211833	+	0.977306i	$0.567943\pi$
$572$	3.31942e6	0.424201
$573$	2.50266e6	0.318430
$574$	−1.00089e6	−0.126796
$575$	330625.	0.0417029
$576$	−887616.	−0.111473
$577$	−7.08072e6	−0.885397	−0.442699	−	0.896671i	$-0.645979\pi$
$577$	−7.08072e6	−0.885397	−0.442699	+	0.896671i	$0.645979\pi$
$578$	−5.26917e6	−0.656028
$579$	1.62502e6	0.201447
$580$	−50543.8	−0.00623875
$581$	1.25287e7	1.53980
$582$	−476241.	−0.0582799
$583$	2.08170e6	0.253658
$584$	−4.28323e6	−0.519684
$585$	−2.29749e6	−0.277564
$586$	−4.32084e6	−0.519786
$587$	1.03908e7	1.24467	0.622337	−	0.782749i	$-0.286183\pi$
$587$	1.03908e7	1.24467	0.622337	+	0.782749i	$0.286183\pi$
$588$	−482673.	−0.0575718
$589$	−1.08420e7	−1.28772
$590$	−4.27586e6	−0.505701
$591$	4.63941e6	0.546379
$592$	−2.80946e6	−0.329472
$593$	2.83849e6	0.331474	0.165737	−	0.986170i	$-0.447000\pi$
$593$	2.83849e6	0.331474	0.165737	+	0.986170i	$0.447000\pi$
$594$	4.61301e6	0.536436
$595$	836829.	0.0969046
$596$	−326775.	−0.0376820
$597$	−4.88258e6	−0.560678
$598$	−897354.	−0.102615
$599$	2.47797e6	0.282182	0.141091	−	0.989997i	$-0.454939\pi$
$599$	2.47797e6	0.282182	0.141091	+	0.989997i	$0.454939\pi$
$600$	205122.	0.0232613
$601$	8.09718e6	0.914423	0.457212	−	0.889358i	$-0.348848\pi$
$601$	8.09718e6	0.914423	0.457212	+	0.889358i	$0.348848\pi$
$602$	−3.61870e6	−0.406969
$603$	−1.01487e7	−1.13662
$604$	5.38280e6	0.600366
$605$	−1.95685e6	−0.217354
$606$	−1.09887e6	−0.121553
$607$	−8.85118e6	−0.975056	−0.487528	−	0.873107i	$-0.662101\pi$
$607$	−8.85118e6	−0.975056	−0.487528	+	0.873107i	$0.662101\pi$
$608$	−1.72494e6	−0.189241
$609$	67726.2	0.00739968
$610$	1.34506e6	0.146358
$611$	1.06444e7	1.15350
$612$	1.11042e6	0.119842
$613$	5.10106e6	0.548289	0.274144	−	0.961689i	$-0.411605\pi$
$613$	5.10106e6	0.548289	0.274144	+	0.961689i	$0.411605\pi$
$614$	−7.65704e6	−0.819672
$615$	306919.	0.0327217
$616$	−3.27242e6	−0.347470
$617$	−1.14098e7	−1.20660	−0.603301	−	0.797514i	$-0.706148\pi$
$617$	−1.14098e7	−1.20660	−0.603301	+	0.797514i	$0.706148\pi$
$618$	−1.52290e6	−0.160398
$619$	−1.16321e7	−1.22020	−0.610099	−	0.792325i	$-0.708870\pi$
$619$	−1.16321e7	−1.22020	−0.610099	+	0.792325i	$0.708870\pi$
$620$	−2.57452e6	−0.268978
$621$	−1.24706e6	−0.129765
$622$	−4.86011e6	−0.503698
$623$	−8.96800e6	−0.925712
$624$	−556725.	−0.0572373
$625$	390625.	0.0400000
$626$	−5.47440e6	−0.558343
$627$	4.22592e6	0.429292
$628$	7.36452e6	0.745153
$629$	3.51466e6	0.354207
$630$	2.26496e6	0.227358
$631$	−5.32018e6	−0.531928	−0.265964	−	0.963983i	$-0.585690\pi$
$631$	−5.32018e6	−0.531928	−0.265964	+	0.963983i	$0.585690\pi$
$632$	−3.66980e6	−0.365469
$633$	1.44382e6	0.143220
$634$	−224512.	−0.0221828
$635$	5.30829e6	0.522421
$636$	−349139.	−0.0342259
$637$	2.49476e6	0.243601
$638$	−247264.	−0.0240497
$639$	−892877.	−0.0865046
$640$	−409600.	−0.0395285
$641$	−4.97864e6	−0.478592	−0.239296	−	0.970947i	$-0.576917\pi$
$641$	−4.97864e6	−0.478592	−0.239296	+	0.970947i	$0.576917\pi$
$642$	−168949.	−0.0161777
$643$	−1.29254e7	−1.23287	−0.616435	−	0.787405i	$-0.711424\pi$
$643$	−1.29254e7	−1.23287	−0.616435	+	0.787405i	$0.711424\pi$
$644$	884650.	0.0840537
$645$	1.10966e6	0.105025
$646$	2.15792e6	0.203448
$647$	1.69341e7	1.59038	0.795190	−	0.606360i	$-0.207371\pi$
$647$	1.69341e7	1.59038	0.795190	+	0.606360i	$0.207371\pi$
$648$	2.59648e6	0.242911
$649$	−2.09179e7	−1.94942
$650$	−1.06020e6	−0.0984248
$651$	3.44973e6	0.319031
$652$	−8.66527e6	−0.798294
$653$	8.08392e6	0.741889	0.370945	−	0.928655i	$-0.379034\pi$
$653$	8.08392e6	0.741889	0.370945	+	0.928655i	$0.379034\pi$
$654$	709425.	0.0648577
$655$	−7.79874e6	−0.710267
$656$	−612874.	−0.0556047
$657$	1.45030e7	1.31082
$658$	−1.04937e7	−0.944852
$659$	8.35712e6	0.749624	0.374812	−	0.927101i	$-0.377707\pi$
$659$	8.35712e6	0.749624	0.374812	+	0.927101i	$0.377707\pi$
$660$	1.00348e6	0.0896699
$661$	1.61532e7	1.43799	0.718995	−	0.695016i	$-0.244603\pi$
$661$	1.61532e7	1.43799	0.718995	+	0.695016i	$0.244603\pi$
$662$	2.70167e6	0.239600
$663$	696469.	0.0615344
$664$	7.67167e6	0.675258
$665$	4.40160e6	0.385972
$666$	9.51279e6	0.831040
$667$	66844.1	0.00581767
$668$	1.51902e6	0.131711
$669$	1.19067e6	0.102855
$670$	−4.68322e6	−0.403049
$671$	6.58015e6	0.564195
$672$	548844.	0.0468841
$673$	1.10004e7	0.936201	0.468100	−	0.883675i	$-0.344939\pi$
$673$	1.10004e7	0.936201	0.468100	+	0.883675i	$0.344939\pi$
$674$	4.28589e6	0.363406
$675$	−1.47336e6	−0.124466
$676$	−3.06318e6	−0.257814
$677$	−4.52303e6	−0.379279	−0.189639	−	0.981854i	$-0.560732\pi$
$677$	−4.52303e6	−0.379279	−0.189639	+	0.981854i	$0.560732\pi$
$678$	4.81137e6	0.401970
$679$	−2.42666e6	−0.201992
$680$	512414.	0.0424961
$681$	1.01101e6	0.0835390
$682$	−1.25948e7	−1.03688
$683$	3.46082e6	0.283875	0.141937	−	0.989876i	$-0.454667\pi$
$683$	3.46082e6	0.283875	0.141937	+	0.989876i	$0.454667\pi$
$684$	5.84063e6	0.477331
$685$	2.76780e6	0.225376
$686$	−9.48605e6	−0.769618
$687$	−2.33546e6	−0.188791
$688$	−2.21583e6	−0.178470
$689$	1.80457e6	0.144819
$690$	−271274.	−0.0216913
$691$	−4.28867e6	−0.341687	−0.170843	−	0.985298i	$-0.554649\pi$
$691$	−4.28867e6	−0.341687	−0.170843	+	0.985298i	$0.554649\pi$
$692$	−2.32599e6	−0.184647
$693$	1.10804e7	0.876439
$694$	7.98277e6	0.629151
$695$	−6.61540e6	−0.519510
$696$	41470.6	0.00324502
$697$	766711.	0.0597792
$698$	−7.91445e6	−0.614869
$699$	−650599.	−0.0503640
$700$	1.04519e6	0.0806215
$701$	−4.42265e6	−0.339929	−0.169964	−	0.985450i	$-0.554365\pi$
$701$	−4.42265e6	−0.339929	−0.169964	+	0.985450i	$0.554365\pi$
$702$	3.99888e6	0.306264
$703$	1.84866e7	1.41081
$704$	−2.00380e6	−0.152378
$705$	3.21785e6	0.243833
$706$	−3.16883e6	−0.239270
$707$	−5.59924e6	−0.421290
$708$	3.50830e6	0.263035
$709$	1.59675e7	1.19295	0.596473	−	0.802633i	$-0.296568\pi$
$709$	1.59675e7	1.19295	0.596473	+	0.802633i	$0.296568\pi$
$710$	−412028.	−0.0306747
$711$	1.24259e7	0.921836
$712$	−5.49136e6	−0.405957
$713$	3.40481e6	0.250824
$714$	−686609.	−0.0504039
$715$	−5.18659e6	−0.379417
$716$	6.36968e6	0.464339
$717$	−8.47115e6	−0.615382
$718$	−9.26764e6	−0.670900
$719$	−2.55631e6	−0.184413	−0.0922064	−	0.995740i	$-0.529392\pi$
$719$	−2.55631e6	−0.184413	−0.0922064	+	0.995740i	$0.529392\pi$
$720$	1.38690e6	0.0997043
$721$	−7.75984e6	−0.555923
$722$	1.44595e6	0.103231
$723$	−6.80821e6	−0.484381
$724$	6.96229e6	0.493635
$725$	78974.6	0.00558011
$726$	1.60557e6	0.113054
$727$	−1.18418e7	−0.830961	−0.415481	−	0.909602i	$-0.636387\pi$
$727$	−1.18418e7	−0.830961	−0.415481	+	0.909602i	$0.636387\pi$
$728$	−2.83677e6	−0.198379
$729$	−5.85407e6	−0.407980
$730$	6.69255e6	0.464820
$731$	2.77203e6	0.191869
$732$	−1.10361e6	−0.0761267
$733$	1.04357e7	0.717398	0.358699	−	0.933453i	$-0.383220\pi$
$733$	1.04357e7	0.717398	0.358699	+	0.933453i	$0.383220\pi$
$734$	4.41257e6	0.302309
$735$	754177.	0.0514938
$736$	541696.	0.0368605
$737$	−2.29107e7	−1.55371
$738$	2.07518e6	0.140254
$739$	−9.37320e6	−0.631360	−0.315680	−	0.948866i	$-0.602233\pi$
$739$	−9.37320e6	−0.631360	−0.315680	+	0.948866i	$0.602233\pi$
$740$	4.38978e6	0.294689
$741$	3.66333e6	0.245092
$742$	−1.77902e6	−0.118624
$743$	4.26137e6	0.283190	0.141595	−	0.989925i	$-0.454777\pi$
$743$	4.26137e6	0.283190	0.141595	+	0.989925i	$0.454777\pi$
$744$	2.11237e6	0.139906
$745$	510586.	0.0337038
$746$	−864321.	−0.0568628
$747$	−2.59762e7	−1.70323
$748$	2.50677e6	0.163818
$749$	−860872.	−0.0560704
$750$	−320504.	−0.0208056
$751$	−2.69554e7	−1.74400	−0.872000	−	0.489506i	$-0.837177\pi$
$751$	−2.69554e7	−1.74400	−0.872000	+	0.489506i	$0.837177\pi$
$752$	−6.42559e6	−0.414351
$753$	−1.79731e6	−0.115514
$754$	−214346.	−0.0137305
$755$	−8.41063e6	−0.536983
$756$	−3.94227e6	−0.250866
$757$	−2.60895e7	−1.65472	−0.827362	−	0.561670i	$-0.810159\pi$
$757$	−2.60895e7	−1.65472	−0.827362	+	0.561670i	$0.810159\pi$
$758$	−2.00688e7	−1.26867
$759$	−1.32710e6	−0.0836177
$760$	2.69522e6	0.169262
$761$	3.15196e7	1.97296	0.986482	−	0.163870i	$-0.0523978\pi$
$761$	3.15196e7	1.97296	0.986482	+	0.163870i	$0.0523978\pi$
$762$	−4.35540e6	−0.271732
$763$	3.61484e6	0.224790
$764$	7.80851e6	0.483988
$765$	−1.73503e6	−0.107190
$766$	−6.67542e6	−0.411061
$767$	−1.81331e7	−1.11297
$768$	336072.	0.0205603
$769$	1.94937e7	1.18872	0.594358	−	0.804201i	$-0.297406\pi$
$769$	1.94937e7	1.18872	0.594358	+	0.804201i	$0.297406\pi$
$770$	5.11316e6	0.310787
$771$	−3.42672e6	−0.207607
$772$	5.07020e6	0.306184
$773$	2.32947e7	1.40220	0.701098	−	0.713065i	$-0.252694\pi$
$773$	2.32947e7	1.40220	0.701098	+	0.713065i	$0.252694\pi$
$774$	7.50278e6	0.450163
$775$	4.02269e6	0.240582
$776$	−1.48591e6	−0.0885807
$777$	−5.88209e6	−0.349526
$778$	−4.89942e6	−0.290199
$779$	4.03279e6	0.238101
$780$	869883.	0.0511946
$781$	−2.01567e6	−0.118248
$782$	−677667.	−0.0396278
$783$	−297878.	−0.0173634
$784$	−1.50598e6	−0.0875045
$785$	−1.15071e7	−0.666485
$786$	6.39879e6	0.369438
$787$	−1.92761e7	−1.10939	−0.554694	−	0.832055i	$-0.687165\pi$
$787$	−1.92761e7	−1.10939	−0.554694	+	0.832055i	$0.687165\pi$
$788$	1.44754e7	0.830451
$789$	−9.48477e6	−0.542418
$790$	5.73407e6	0.326885
$791$	2.45161e7	1.39319
$792$	6.78483e6	0.384349
$793$	5.70413e6	0.322112
$794$	1.04574e7	0.588671
$795$	545529.	0.0306126
$796$	−1.52341e7	−0.852185
$797$	2.42767e7	1.35377	0.676883	−	0.736091i	$-0.263330\pi$
$797$	2.42767e7	1.35377	0.676883	+	0.736091i	$0.263330\pi$
$798$	−3.61146e6	−0.200759
$799$	8.03848e6	0.445458
$800$	640000.	0.0353553
$801$	1.85937e7	1.02396
$802$	−1.66855e6	−0.0916019
$803$	3.27405e7	1.79183
$804$	3.84253e6	0.209642
$805$	−1.38227e6	−0.0751799
$806$	−1.09180e7	−0.591980
$807$	−1.41591e6	−0.0765333
$808$	−3.42857e6	−0.184750
$809$	−3.64087e7	−1.95585	−0.977923	−	0.208968i	$-0.932990\pi$
$809$	−3.64087e7	−1.95585	−0.977923	+	0.208968i	$0.932990\pi$
$810$	−4.05700e6	−0.217267
$811$	1.38242e7	0.738055	0.369027	−	0.929419i	$-0.379691\pi$
$811$	1.38242e7	0.738055	0.369027	+	0.929419i	$0.379691\pi$
$812$	211312.	0.0112469
$813$	8.93974e6	0.474349
$814$	2.14752e7	1.13599
$815$	1.35395e7	0.714016
$816$	−420430.	−0.0221039
$817$	1.45805e7	0.764217
$818$	1.41737e7	0.740630
$819$	9.60525e6	0.500379
$820$	957615.	0.0497343
$821$	1.60767e7	0.832412	0.416206	−	0.909270i	$-0.363360\pi$
$821$	1.60767e7	0.832412	0.416206	+	0.909270i	$0.363360\pi$
$822$	−2.27095e6	−0.117227
$823$	−2.28923e6	−0.117812	−0.0589059	−	0.998264i	$-0.518761\pi$
$823$	−2.28923e6	−0.117812	−0.0589059	+	0.998264i	$0.518761\pi$
$824$	−4.75157e6	−0.243792
$825$	−1.56793e6	−0.0802032
$826$	1.78764e7	0.911653
$827$	−2.07011e7	−1.05252	−0.526258	−	0.850325i	$-0.676405\pi$
$827$	−2.07011e7	−1.05252	−0.526258	+	0.850325i	$0.676405\pi$
$828$	−1.83417e6	−0.0929747
$829$	−2.59324e7	−1.31056	−0.655280	−	0.755386i	$-0.727449\pi$
$829$	−2.59324e7	−1.31056	−0.655280	+	0.755386i	$0.727449\pi$
$830$	−1.19870e7	−0.603969
$831$	8.05210e6	0.404489
$832$	−1.73703e6	−0.0869961
$833$	1.88400e6	0.0940738
$834$	5.42786e6	0.270218
$835$	−2.37347e6	−0.117806
$836$	1.31853e7	0.652488
$837$	−1.51728e7	−0.748606
$838$	−1.89871e7	−0.934006
$839$	1.05840e7	0.519093	0.259547	−	0.965731i	$-0.416427\pi$
$839$	1.05840e7	0.519093	0.259547	+	0.965731i	$0.416427\pi$
$840$	−857568.	−0.0419344
$841$	−2.04952e7	−0.999222
$842$	−5.87449e6	−0.285555
$843$	−2.18495e6	−0.105894
$844$	4.50484e6	0.217682
$845$	4.78622e6	0.230596
$846$	2.17569e7	1.04513
$847$	8.18111e6	0.391835
$848$	−1.08934e6	−0.0520206
$849$	−3.50553e6	−0.166911
$850$	−800647.	−0.0380096
$851$	−5.80548e6	−0.274799
$852$	338064.	0.0159551
$853$	−2.48365e7	−1.16874	−0.584371	−	0.811487i	$-0.698659\pi$
$853$	−2.48365e7	−1.16874	−0.584371	+	0.811487i	$0.698659\pi$
$854$	−5.62338e6	−0.263847
$855$	−9.12598e6	−0.426937
$856$	−527136.	−0.0245889
$857$	1.65560e7	0.770021	0.385010	−	0.922912i	$-0.374198\pi$
$857$	1.65560e7	0.770021	0.385010	+	0.922912i	$0.374198\pi$
$858$	4.25554e6	0.197350
$859$	−7.85305e6	−0.363124	−0.181562	−	0.983379i	$-0.558115\pi$
$859$	−7.85305e6	−0.363124	−0.181562	+	0.983379i	$0.558115\pi$
$860$	3.46224e6	0.159629
$861$	−1.28316e6	−0.0589891
$862$	−2.12731e7	−0.975128
$863$	1.86431e7	0.852103	0.426051	−	0.904699i	$-0.359904\pi$
$863$	1.86431e7	0.852103	0.426051	+	0.904699i	$0.359904\pi$
$864$	−2.41396e6	−0.110013
$865$	3.63436e6	0.165153
$866$	−1.07611e7	−0.487596
$867$	−6.75515e6	−0.305202
$868$	1.07635e7	0.484901
$869$	2.80515e7	1.26011
$870$	−64797.8	−0.00290243
$871$	−1.98606e7	−0.887049
$872$	2.21347e6	0.0985785
$873$	5.03128e6	0.223431
$874$	−3.56443e6	−0.157838
$875$	−1.63311e6	−0.0721100
$876$	−5.49117e6	−0.241771
$877$	−7.24381e6	−0.318030	−0.159015	−	0.987276i	$-0.550832\pi$
$877$	−7.24381e6	−0.318030	−0.159015	+	0.987276i	$0.550832\pi$
$878$	−2.02068e6	−0.0884629
$879$	−5.53938e6	−0.241818
$880$	3.13093e6	0.136291
$881$	3.66509e7	1.59091	0.795453	−	0.606016i	$-0.207233\pi$
$881$	3.66509e7	1.59091	0.795453	+	0.606016i	$0.207233\pi$
$882$	5.09924e6	0.220716
$883$	2.61573e7	1.12899	0.564496	−	0.825436i	$-0.309070\pi$
$883$	2.61573e7	1.12899	0.564496	+	0.825436i	$0.309070\pi$
$884$	2.17305e6	0.0935273
$885$	−5.48172e6	−0.235266
$886$	−346445.	−0.0148269
$887$	−3.23015e7	−1.37852	−0.689262	−	0.724513i	$-0.742065\pi$
$887$	−3.23015e7	−1.37852	−0.689262	+	0.724513i	$0.742065\pi$
$888$	−3.60177e6	−0.153279
$889$	−2.21927e7	−0.941795
$890$	8.58025e6	0.363099
$891$	−1.98472e7	−0.837539
$892$	3.71500e6	0.156332
$893$	4.22812e7	1.77427
$894$	−418930.	−0.0175307
$895$	−9.95263e6	−0.415317
$896$	1.71244e6	0.0712600
$897$	−1.15042e6	−0.0477392
$898$	1.83161e7	0.757954
$899$	813288.	0.0335618
$900$	−2.16703e6	−0.0891782
$901$	1.36278e6	0.0559261
$902$	4.68473e6	0.191720
$903$	−4.63923e6	−0.189333
$904$	1.50119e7	0.610962
$905$	−1.08786e7	−0.441520
$906$	6.90083e6	0.279306
$907$	−1.89257e6	−0.0763894	−0.0381947	−	0.999270i	$-0.512161\pi$
$907$	−1.89257e6	−0.0763894	−0.0381947	+	0.999270i	$0.512161\pi$
$908$	3.15445e6	0.126972
$909$	1.16091e7	0.466003
$910$	4.43245e6	0.177435
$911$	9.13162e6	0.364546	0.182273	−	0.983248i	$-0.441655\pi$
$911$	9.13162e6	0.364546	0.182273	+	0.983248i	$0.441655\pi$
$912$	−2.21140e6	−0.0880401
$913$	−5.86413e7	−2.32824
$914$	1.90178e7	0.753000
$915$	1.72439e6	0.0680898
$916$	−7.28685e6	−0.286946
$917$	3.26047e7	1.28043
$918$	3.01989e6	0.118273
$919$	7.75728e6	0.302985	0.151492	−	0.988458i	$-0.451592\pi$
$919$	7.75728e6	0.302985	0.151492	+	0.988458i	$0.451592\pi$
$920$	−846400.	−0.0329690
$921$	−9.81644e6	−0.381333
$922$	3.47211e7	1.34514
$923$	−1.74733e6	−0.0675104
$924$	−4.19530e6	−0.161653
$925$	−6.85903e6	−0.263578
$926$	2.03705e7	0.780681
$927$	1.60887e7	0.614926
$928$	129392.	0.00493217
$929$	1.20964e7	0.459852	0.229926	−	0.973208i	$-0.426152\pi$
$929$	1.20964e7	0.459852	0.229926	+	0.973208i	$0.426152\pi$
$930$	−3.30058e6	−0.125136
$931$	9.90957e6	0.374697
$932$	−2.02993e6	−0.0765492
$933$	−6.23074e6	−0.234334
$934$	1.60963e7	0.603753
$935$	−3.91683e6	−0.146523
$936$	5.88157e6	0.219434
$937$	−5.86967e6	−0.218406	−0.109203	−	0.994019i	$-0.534830\pi$
$937$	−5.86967e6	−0.218406	−0.109203	+	0.994019i	$0.534830\pi$
$938$	1.95795e7	0.726597
$939$	−7.01826e6	−0.259756
$940$	1.00400e7	0.370607
$941$	−2.75640e7	−1.01477	−0.507385	−	0.861719i	$-0.669388\pi$
$941$	−2.75640e7	−1.01477	−0.507385	+	0.861719i	$0.669388\pi$
$942$	9.44142e6	0.346665
$943$	−1.26645e6	−0.0463775
$944$	1.09462e7	0.399792
$945$	6.15979e6	0.224381
$946$	1.69376e7	0.615351
$947$	−1.37554e7	−0.498423	−0.249212	−	0.968449i	$-0.580171\pi$
$947$	−1.37554e7	−0.498423	−0.249212	+	0.968449i	$0.580171\pi$
$948$	−4.70474e6	−0.170026
$949$	2.83818e7	1.02300
$950$	−4.21128e6	−0.151393
$951$	−287827.	−0.0103200
$952$	−2.14228e6	−0.0766098
$953$	−4.32445e7	−1.54241	−0.771203	−	0.636589i	$-0.780345\pi$
$953$	−4.32445e7	−1.54241	−0.771203	+	0.636589i	$0.780345\pi$
$954$	3.68850e6	0.131214
$955$	−1.22008e7	−0.432892
$956$	−2.64308e7	−0.935330
$957$	−316996.	−0.0111886
$958$	−6.99161e6	−0.246129
$959$	−1.15715e7	−0.406297
$960$	−525113.	−0.0183897
$961$	1.27969e7	0.446988
$962$	1.86162e7	0.648564
$963$	1.78487e6	0.0620215
$964$	−2.12422e7	−0.736220
$965$	−7.92219e6	−0.273859
$966$	1.13413e6	0.0391040
$967$	−1.65583e7	−0.569442	−0.284721	−	0.958610i	$-0.591901\pi$
$967$	−1.65583e7	−0.569442	−0.284721	+	0.958610i	$0.591901\pi$
$968$	5.00952e6	0.171834
$969$	2.76649e6	0.0946496
$970$	2.32174e6	0.0792290
$971$	−3.44060e7	−1.17108	−0.585539	−	0.810644i	$-0.699117\pi$
$971$	−3.44060e7	−1.17108	−0.585539	+	0.810644i	$0.699117\pi$
$972$	1.24942e7	0.424174
$973$	2.76574e7	0.936547
$974$	−1.76952e7	−0.597665
$975$	−1.35919e6	−0.0457899
$976$	−3.44335e6	−0.115706
$977$	5.40972e7	1.81317	0.906584	−	0.422024i	$-0.138680\pi$
$977$	5.40972e7	1.81317	0.906584	+	0.422024i	$0.138680\pi$
$978$	−1.11090e7	−0.371388
$979$	4.19753e7	1.39971
$980$	2.35310e6	0.0782664
$981$	−7.49477e6	−0.248648
$982$	5.91789e6	0.195834
$983$	5.86268e7	1.93514	0.967571	−	0.252601i	$-0.0812860\pi$
$983$	5.86268e7	1.93514	0.967571	+	0.252601i	$0.0812860\pi$
$984$	−785713.	−0.0258688
$985$	−2.26178e7	−0.742778
$986$	−161871.	−0.00530245
$987$	−1.34531e7	−0.439571
$988$	1.14299e7	0.372521
$989$	−4.57881e6	−0.148855
$990$	−1.06013e7	−0.343772
$991$	1.84799e7	0.597745	0.298873	−	0.954293i	$-0.403389\pi$
$991$	1.84799e7	0.597745	0.298873	+	0.954293i	$0.403389\pi$
$992$	6.59078e6	0.212646
$993$	3.46357e6	0.111468
$994$	1.72259e6	0.0552989
$995$	2.38033e7	0.762218
$996$	9.83519e6	0.314148
$997$	−4.04351e7	−1.28831	−0.644155	−	0.764895i	$-0.722791\pi$
$997$	−4.04351e7	−1.28831	−0.644155	+	0.764895i	$0.722791\pi$
$998$	−2.07071e7	−0.658103
$999$	2.58710e7	0.820161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.e.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.e.1.2	✓	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +5.12806 q^{3} +16.0000 q^{4} -25.0000 q^{5} +20.5122 q^{6} +104.519 q^{7} +64.0000 q^{8} -216.703 q^{9} -100.000 q^{10} -489.208 q^{11} +82.0489 q^{12} -424.080 q^{13} +418.077 q^{14} -128.201 q^{15} +256.000 q^{16} -320.259 q^{17} -866.812 q^{18} -1684.51 q^{19} -400.000 q^{20} +535.980 q^{21} -1956.83 q^{22} +529.000 q^{23} +328.196 q^{24} +625.000 q^{25} -1696.32 q^{26} -2357.38 q^{27} +1672.31 q^{28} +126.359 q^{29} -512.806 q^{30} +6436.31 q^{31} +1024.00 q^{32} -2508.69 q^{33} -1281.03 q^{34} -2612.98 q^{35} -3467.25 q^{36} -10974.5 q^{37} -6738.05 q^{38} -2174.71 q^{39} -1600.00 q^{40} -2394.04 q^{41} +2143.92 q^{42} -8655.60 q^{43} -7827.33 q^{44} +5417.58 q^{45} +2116.00 q^{46} -25099.9 q^{47} +1312.78 q^{48} -5882.75 q^{49} +2500.00 q^{50} -1642.31 q^{51} -6785.28 q^{52} -4255.25 q^{53} -9429.53 q^{54} +12230.2 q^{55} +6689.22 q^{56} -8638.28 q^{57} +505.438 q^{58} +42758.6 q^{59} -2051.22 q^{60} -13450.6 q^{61} +25745.2 q^{62} -22649.6 q^{63} +4096.00 q^{64} +10602.0 q^{65} -10034.8 q^{66} +46832.2 q^{67} -5124.14 q^{68} +2712.74 q^{69} -10451.9 q^{70} +4120.28 q^{71} -13869.0 q^{72} -66925.5 q^{73} -43897.8 q^{74} +3205.04 q^{75} -26952.2 q^{76} -51131.6 q^{77} -8698.83 q^{78} -57340.7 q^{79} -6400.00 q^{80} +40570.0 q^{81} -9576.15 q^{82} +119870. q^{83} +8575.68 q^{84} +8006.47 q^{85} -34622.4 q^{86} +647.978 q^{87} -31309.3 q^{88} -85802.5 q^{89} +21670.3 q^{90} -44324.5 q^{91} +8464.00 q^{92} +33005.8 q^{93} -100400. q^{94} +42112.8 q^{95} +5251.13 q^{96} -23217.4 q^{97} -23531.0 q^{98} +106013. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12 q^{2} + 6 q^{3} + 48 q^{4} - 75 q^{5} + 24 q^{6} + 5 q^{7} + 192 q^{8} + 89 q^{9} - 300 q^{10} - 962 q^{11} + 96 q^{12} - 776 q^{13} + 20 q^{14} - 150 q^{15} + 768 q^{16} - 2317 q^{17} + 356 q^{18}+ \cdots + 24042 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 + 6 * q^3 + 48 * q^4 - 75 * q^5 + 24 * q^6 + 5 * q^7 + 192 * q^8 + 89 * q^9 - 300 * q^10 - 962 * q^11 + 96 * q^12 - 776 * q^13 + 20 * q^14 - 150 * q^15 + 768 * q^16 - 2317 * q^17 + 356 * q^18 + 654 * q^19 - 1200 * q^20 - 4996 * q^21 - 3848 * q^22 + 1587 * q^23 + 384 * q^24 + 1875 * q^25 - 3104 * q^26 - 1746 * q^27 + 80 * q^28 - 2223 * q^29 - 600 * q^30 - 6927 * q^31 + 3072 * q^32 - 13844 * q^33 - 9268 * q^34 - 125 * q^35 + 1424 * q^36 - 18801 * q^37 + 2616 * q^38 - 12666 * q^39 - 4800 * q^40 - 8369 * q^41 - 19984 * q^42 - 26064 * q^43 - 15392 * q^44 - 2225 * q^45 + 6348 * q^46 - 8974 * q^47 + 1536 * q^48 + 3524 * q^49 + 7500 * q^50 - 14180 * q^51 - 12416 * q^52 + 26079 * q^53 - 6984 * q^54 + 24050 * q^55 + 320 * q^56 - 16292 * q^57 - 8892 * q^58 + 21311 * q^59 - 2400 * q^60 - 19408 * q^61 - 27708 * q^62 - 42647 * q^63 + 12288 * q^64 + 19400 * q^65 - 55376 * q^66 - 40315 * q^67 - 37072 * q^68 + 3174 * q^69 - 500 * q^70 - 49333 * q^71 + 5696 * q^72 - 308 * q^73 - 75204 * q^74 + 3750 * q^75 + 10464 * q^76 + 49586 * q^77 - 50664 * q^78 - 51216 * q^79 - 19200 * q^80 - 104485 * q^81 - 33476 * q^82 + 38693 * q^83 - 79936 * q^84 + 57925 * q^85 - 104256 * q^86 + 29998 * q^87 - 61568 * q^88 - 109600 * q^89 - 8900 * q^90 + 44890 * q^91 + 25392 * q^92 + 65494 * q^93 - 35896 * q^94 - 16350 * q^95 + 6144 * q^96 - 26806 * q^97 + 14096 * q^98 + 24042 * q^99

Introduction

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