LMFDB - Embedded newform 115.6.a.c.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,6,Mod(1,115)] 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("115.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	115.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$18.4441392785$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 196x^{5} + 464x^{4} + 11003x^{3} - 21041x^{2} - 142416x + 243340 $ x^7 - 3x^6 - 196x^5 + 464x^4 + 11003x^3 - 21041x^2 - 142416x + 243340
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			1.5
Root			$-4.26829$ of defining polynomial
Character	$\chi$	$=$	115.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.26829 q^{2} -11.8410 q^{3} -4.24511 q^{4} -25.0000 q^{5} -62.3818 q^{6} +72.8708 q^{7} -190.950 q^{8} -102.791 q^{9} -131.707 q^{10} +732.810 q^{11} +50.2663 q^{12} +676.311 q^{13} +383.904 q^{14} +296.025 q^{15} -870.135 q^{16} +381.818 q^{17} -541.533 q^{18} +853.077 q^{19} +106.128 q^{20} -862.862 q^{21} +3860.66 q^{22} +529.000 q^{23} +2261.03 q^{24} +625.000 q^{25} +3563.00 q^{26} +4094.51 q^{27} -309.345 q^{28} -3162.45 q^{29} +1559.54 q^{30} +6803.69 q^{31} +1526.27 q^{32} -8677.20 q^{33} +2011.53 q^{34} -1821.77 q^{35} +436.359 q^{36} -2630.93 q^{37} +4494.26 q^{38} -8008.19 q^{39} +4773.74 q^{40} +15206.0 q^{41} -4545.81 q^{42} -6961.13 q^{43} -3110.86 q^{44} +2569.78 q^{45} +2786.93 q^{46} +8075.94 q^{47} +10303.3 q^{48} -11496.8 q^{49} +3292.68 q^{50} -4521.10 q^{51} -2871.01 q^{52} -1322.64 q^{53} +21571.1 q^{54} -18320.3 q^{55} -13914.7 q^{56} -10101.3 q^{57} -16660.7 q^{58} -2011.03 q^{59} -1256.66 q^{60} -19642.0 q^{61} +35843.8 q^{62} -7490.46 q^{63} +35885.2 q^{64} -16907.8 q^{65} -45714.0 q^{66} +23755.1 q^{67} -1620.86 q^{68} -6263.88 q^{69} -9597.61 q^{70} +44466.6 q^{71} +19627.9 q^{72} +9203.35 q^{73} -13860.5 q^{74} -7400.62 q^{75} -3621.41 q^{76} +53400.5 q^{77} -42189.5 q^{78} +27674.3 q^{79} +21753.4 q^{80} -23504.8 q^{81} +80109.8 q^{82} +32584.3 q^{83} +3662.94 q^{84} -9545.45 q^{85} -36673.3 q^{86} +37446.5 q^{87} -139930. q^{88} -117078. q^{89} +13538.3 q^{90} +49283.3 q^{91} -2245.66 q^{92} -80562.4 q^{93} +42546.4 q^{94} -21326.9 q^{95} -18072.5 q^{96} -28382.3 q^{97} -60568.7 q^{98} -75326.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} - 3 q^{3} + 178 q^{4} - 175 q^{5} - 381 q^{6} + 33 q^{7} + 546 q^{8} + 440 q^{9} - 100 q^{10} + 1373 q^{11} - 285 q^{12} + 605 q^{13} + 1317 q^{14} + 75 q^{15} + 3770 q^{16} + 2505 q^{17}+ \cdots + 237333 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 - 3 * q^3 + 178 * q^4 - 175 * q^5 - 381 * q^6 + 33 * q^7 + 546 * q^8 + 440 * q^9 - 100 * q^10 + 1373 * q^11 - 285 * q^12 + 605 * q^13 + 1317 * q^14 + 75 * q^15 + 3770 * q^16 + 2505 * q^17 + 7971 * q^18 - 115 * q^19 - 4450 * q^20 + 608 * q^21 + 2977 * q^22 + 3703 * q^23 - 12447 * q^24 + 4375 * q^25 + 9379 * q^26 - 12276 * q^27 + 5777 * q^28 + 2440 * q^29 + 9525 * q^30 + 13565 * q^31 + 14086 * q^32 + 10519 * q^33 + 26997 * q^34 - 825 * q^35 + 79889 * q^36 + 9414 * q^37 + 28717 * q^38 - 21738 * q^39 - 13650 * q^40 + 13725 * q^41 + 12426 * q^42 + 76694 * q^43 + 55203 * q^44 - 11000 * q^45 + 2116 * q^46 + 59692 * q^47 - 32985 * q^48 - 53608 * q^49 + 2500 * q^50 - 24725 * q^51 + 61195 * q^52 + 49536 * q^53 - 156168 * q^54 - 34325 * q^55 - 54461 * q^56 - 7580 * q^57 - 95562 * q^58 + 44536 * q^59 + 7125 * q^60 - 49097 * q^61 - 25763 * q^62 - 3578 * q^63 - 18654 * q^64 - 15125 * q^65 - 201873 * q^66 + 788 * q^67 + 163845 * q^68 - 1587 * q^69 - 32925 * q^70 + 49521 * q^71 + 328503 * q^72 - 3760 * q^73 + 88170 * q^74 - 1875 * q^75 - 411465 * q^76 + 77728 * q^77 - 389832 * q^78 + 918 * q^79 - 94250 * q^80 + 121235 * q^81 - 227459 * q^82 + 99202 * q^83 + 336602 * q^84 - 62625 * q^85 + 24584 * q^86 - 38666 * q^87 - 201275 * q^88 - 141676 * q^89 - 199275 * q^90 - 223605 * q^91 + 94162 * q^92 + 51412 * q^93 - 354292 * q^94 + 2875 * q^95 - 592095 * q^96 + 28731 * q^97 - 149557 * q^98 + 237333 * 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 $

$2$	5.26829	0.931311	0.465656	−	0.884966i	$-0.345819\pi$
$2$	5.26829	0.931311	0.465656	+	0.884966i	$0.345819\pi$
$3$	−11.8410	−0.759600	−0.379800	−	0.925069i	$-0.624007\pi$
$3$	−11.8410	−0.759600	−0.379800	+	0.925069i	$0.624007\pi$
$4$	−4.24511	−0.132660
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−62.3818	−0.707424
$7$	72.8708	0.562093	0.281047	−	0.959694i	$-0.409318\pi$
$7$	72.8708	0.562093	0.281047	+	0.959694i	$0.409318\pi$
$8$	−190.950	−1.05486
$9$	−102.791	−0.423008
$10$	−131.707	−0.416495
$11$	732.810	1.82604	0.913019	−	0.407917i	$-0.133745\pi$
$11$	732.810	1.82604	0.913019	+	0.407917i	$0.133745\pi$
$12$	50.2663	0.100768
$13$	676.311	1.10991	0.554955	−	0.831880i	$-0.312735\pi$
$13$	676.311	1.10991	0.554955	+	0.831880i	$0.312735\pi$
$14$	383.904	0.523484
$15$	296.025	0.339703
$16$	−870.135	−0.849742
$17$	381.818	0.320431	0.160215	−	0.987082i	$-0.448781\pi$
$17$	381.818	0.320431	0.160215	+	0.987082i	$0.448781\pi$
$18$	−541.533	−0.393952
$19$	853.077	0.542131	0.271066	−	0.962561i	$-0.412624\pi$
$19$	853.077	0.542131	0.271066	+	0.962561i	$0.412624\pi$
$20$	106.128	0.0593272
$21$	−862.862	−0.426966
$22$	3860.66	1.70061
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	2261.03	0.801270
$25$	625.000	0.200000
$26$	3563.00	1.03367
$27$	4094.51	1.08092
$28$	−309.345	−0.0745671
$29$	−3162.45	−0.698278	−0.349139	−	0.937071i	$-0.613526\pi$
$29$	−3162.45	−0.698278	−0.349139	+	0.937071i	$0.613526\pi$
$30$	1559.54	0.316369
$31$	6803.69	1.27157	0.635785	−	0.771866i	$-0.280677\pi$
$31$	6803.69	1.27157	0.635785	+	0.771866i	$0.280677\pi$
$32$	1526.27	0.263485
$33$	−8677.20	−1.38706
$34$	2011.53	0.298421
$35$	−1821.77	−0.251376
$36$	436.359	0.0561162
$37$	−2630.93	−0.315940	−0.157970	−	0.987444i	$-0.550495\pi$
$37$	−2630.93	−0.315940	−0.157970	+	0.987444i	$0.550495\pi$
$38$	4494.26	0.504893
$39$	−8008.19	−0.843087
$40$	4773.74	0.471747
$41$	15206.0	1.41272	0.706360	−	0.707852i	$-0.250336\pi$
$41$	15206.0	1.41272	0.706360	+	0.707852i	$0.250336\pi$
$42$	−4545.81	−0.397638
$43$	−6961.13	−0.574128	−0.287064	−	0.957911i	$-0.592679\pi$
$43$	−6961.13	−0.574128	−0.287064	+	0.957911i	$0.592679\pi$
$44$	−3110.86	−0.242242
$45$	2569.78	0.189175
$46$	2786.93	0.194192
$47$	8075.94	0.533271	0.266636	−	0.963797i	$-0.414088\pi$
$47$	8075.94	0.533271	0.266636	+	0.963797i	$0.414088\pi$
$48$	10303.3	0.645464
$49$	−11496.8	−0.684051
$50$	3292.68	0.186262
$51$	−4521.10	−0.243399
$52$	−2871.01	−0.147240
$53$	−1322.64	−0.0646774	−0.0323387	−	0.999477i	$-0.510296\pi$
$53$	−1322.64	−0.0646774	−0.0323387	+	0.999477i	$0.510296\pi$
$54$	21571.1	1.00667
$55$	−18320.3	−0.816629
$56$	−13914.7	−0.592929
$57$	−10101.3	−0.411803
$58$	−16660.7	−0.650314
$59$	−2011.03	−0.0752122	−0.0376061	−	0.999293i	$-0.511973\pi$
$59$	−2011.03	−0.0752122	−0.0376061	+	0.999293i	$0.511973\pi$
$60$	−1256.66	−0.0450649
$61$	−19642.0	−0.675866	−0.337933	−	0.941170i	$-0.609728\pi$
$61$	−19642.0	−0.675866	−0.337933	+	0.941170i	$0.609728\pi$
$62$	35843.8	1.18423
$63$	−7490.46	−0.237770
$64$	35885.2	1.09513
$65$	−16907.8	−0.496367
$66$	−45714.0	−1.29178
$67$	23755.1	0.646502	0.323251	−	0.946313i	$-0.395224\pi$
$67$	23755.1	0.646502	0.323251	+	0.946313i	$0.395224\pi$
$68$	−1620.86	−0.0425083
$69$	−6263.88	−0.158387
$70$	−9597.61	−0.234109
$71$	44466.6	1.04686	0.523429	−	0.852069i	$-0.324653\pi$
$71$	44466.6	1.04686	0.523429	+	0.852069i	$0.324653\pi$
$72$	19627.9	0.446214
$73$	9203.35	0.202134	0.101067	−	0.994880i	$-0.467774\pi$
$73$	9203.35	0.202134	0.101067	+	0.994880i	$0.467774\pi$
$74$	−13860.5	−0.294238
$75$	−7400.62	−0.151920
$76$	−3621.41	−0.0719190
$77$	53400.5	1.02640
$78$	−42189.5	−0.785177
$79$	27674.3	0.498895	0.249447	−	0.968388i	$-0.419751\pi$
$79$	27674.3	0.498895	0.249447	+	0.968388i	$0.419751\pi$
$80$	21753.4	0.380016
$81$	−23504.8	−0.398056
$82$	80109.8	1.31568
$83$	32584.3	0.519175	0.259587	−	0.965720i	$-0.416413\pi$
$83$	32584.3	0.519175	0.259587	+	0.965720i	$0.416413\pi$
$84$	3662.94	0.0566412
$85$	−9545.45	−0.143301
$86$	−36673.3	−0.534692
$87$	37446.5	0.530412
$88$	−139930.	−1.92621
$89$	−117078.	−1.56675	−0.783377	−	0.621547i	$-0.786505\pi$
$89$	−117078.	−1.56675	−0.783377	+	0.621547i	$0.786505\pi$
$90$	13538.3	0.176181
$91$	49283.3	0.623873
$92$	−2245.66	−0.0276615
$93$	−80562.4	−0.965884
$94$	42546.4	0.496642
$95$	−21326.9	−0.242448
$96$	−18072.5	−0.200143
$97$	−28382.3	−0.306280	−0.153140	−	0.988204i	$-0.548939\pi$
$97$	−28382.3	−0.306280	−0.153140	+	0.988204i	$0.548939\pi$
$98$	−60568.7	−0.637064
$99$	−75326.3	−0.772429
$100$	−2653.19	−0.0265319
$101$	−55582.3	−0.542167	−0.271083	−	0.962556i	$-0.587382\pi$
$101$	−55582.3	−0.542167	−0.271083	+	0.962556i	$0.587382\pi$
$102$	−23818.5	−0.226680
$103$	−52035.7	−0.483290	−0.241645	−	0.970365i	$-0.577687\pi$
$103$	−52035.7	−0.483290	−0.241645	+	0.970365i	$0.577687\pi$
$104$	−129141.	−1.17080
$105$	21571.6	0.190945
$106$	−6968.06	−0.0602348
$107$	−5725.28	−0.0483434	−0.0241717	−	0.999708i	$-0.507695\pi$
$107$	−5725.28	−0.0483434	−0.0241717	+	0.999708i	$0.507695\pi$
$108$	−17381.6	−0.143394
$109$	188458.	1.51932	0.759660	−	0.650321i	$-0.225366\pi$
$109$	188458.	1.51932	0.759660	+	0.650321i	$0.225366\pi$
$110$	−96516.4	−0.760536
$111$	31152.8	0.239988
$112$	−63407.5	−0.477634
$113$	117240.	0.863735	0.431868	−	0.901937i	$-0.357855\pi$
$113$	117240.	0.863735	0.431868	+	0.901937i	$0.357855\pi$
$114$	−53216.5	−0.383516
$115$	−13225.0	−0.0932505
$116$	13424.9	0.0926334
$117$	−69518.6	−0.469501
$118$	−10594.7	−0.0700459
$119$	27823.4	0.180112
$120$	−56525.9	−0.358339
$121$	375960.	2.33442
$122$	−103480.	−0.629441
$123$	−180054.	−1.07310
$124$	−28882.4	−0.168686
$125$	−15625.0	−0.0894427
$126$	−39461.9	−0.221438
$127$	130123.	0.715887	0.357944	−	0.933743i	$-0.383478\pi$
$127$	130123.	0.715887	0.357944	+	0.933743i	$0.383478\pi$
$128$	140213.	0.756420
$129$	82426.7	0.436107
$130$	−89075.0	−0.462272
$131$	−336278.	−1.71206	−0.856032	−	0.516923i	$-0.827077\pi$
$131$	−336278.	−1.71206	−0.856032	+	0.516923i	$0.827077\pi$
$132$	36835.7	0.184007
$133$	62164.4	0.304728
$134$	125149.	0.602095
$135$	−102363.	−0.483401
$136$	−72908.1	−0.338009
$137$	158649.	0.722166	0.361083	−	0.932534i	$-0.382407\pi$
$137$	158649.	0.722166	0.361083	+	0.932534i	$0.382407\pi$
$138$	−33000.0	−0.147508
$139$	343153.	1.50644	0.753218	−	0.657771i	$-0.228501\pi$
$139$	343153.	1.50644	0.753218	+	0.657771i	$0.228501\pi$
$140$	7733.61	0.0333474
$141$	−95627.1	−0.405073
$142$	234263.	0.974950
$143$	495607.	2.02674
$144$	89442.1	0.359448
$145$	79061.2	0.312280
$146$	48485.9	0.188249
$147$	136134.	0.519605
$148$	11168.6	0.0419125
$149$	343414.	1.26722	0.633611	−	0.773652i	$-0.281572\pi$
$149$	343414.	1.26722	0.633611	+	0.773652i	$0.281572\pi$
$150$	−38988.6	−0.141485
$151$	−518178.	−1.84943	−0.924713	−	0.380666i	$-0.875695\pi$
$151$	−518178.	−1.84943	−0.924713	+	0.380666i	$0.875695\pi$
$152$	−162895.	−0.571872
$153$	−39247.5	−0.135545
$154$	281329.	0.955901
$155$	−170092.	−0.568663
$156$	33995.6	0.111844
$157$	96581.7	0.312713	0.156356	−	0.987701i	$-0.450025\pi$
$157$	96581.7	0.312713	0.156356	+	0.987701i	$0.450025\pi$
$158$	145796.	0.464626
$159$	15661.4	0.0491290
$160$	−38156.7	−0.117834
$161$	38548.6	0.117205
$162$	−123830.	−0.370714
$163$	218234.	0.643360	0.321680	−	0.946848i	$-0.395752\pi$
$163$	218234.	0.643360	0.321680	+	0.946848i	$0.395752\pi$
$164$	−64551.3	−0.187411
$165$	216930.	0.620311
$166$	171664.	0.483513
$167$	633975.	1.75906	0.879530	−	0.475843i	$-0.157857\pi$
$167$	633975.	1.75906	0.879530	+	0.475843i	$0.157857\pi$
$168$	164763.	0.450389
$169$	86103.1	0.231901
$170$	−50288.2	−0.133458
$171$	−87688.7	−0.229326
$172$	29550.8	0.0761637
$173$	423316.	1.07535	0.537674	−	0.843153i	$-0.319303\pi$
$173$	423316.	1.07535	0.537674	+	0.843153i	$0.319303\pi$
$174$	197279.	0.493979
$175$	45544.2	0.112419
$176$	−637644.	−1.55166
$177$	23812.6	0.0571312
$178$	−616802.	−1.45914
$179$	−411280.	−0.959411	−0.479705	−	0.877430i	$-0.659256\pi$
$179$	−411280.	−0.959411	−0.479705	+	0.877430i	$0.659256\pi$
$180$	−10909.0	−0.0250959
$181$	−3600.89	−0.00816984	−0.00408492	−	0.999992i	$-0.501300\pi$
$181$	−3600.89	−0.00816984	−0.00408492	+	0.999992i	$0.501300\pi$
$182$	259639.	0.581020
$183$	232580.	0.513387
$184$	−101012.	−0.219953
$185$	65773.2	0.141293
$186$	−424426.	−0.899539
$187$	279800.	0.585119
$188$	−34283.2	−0.0707436
$189$	298370.	0.607576
$190$	−112356.	−0.225795
$191$	−111906.	−0.221957	−0.110979	−	0.993823i	$-0.535399\pi$
$191$	−111906.	−0.221957	−0.110979	+	0.993823i	$0.535399\pi$
$192$	−424916.	−0.831859
$193$	498666.	0.963643	0.481822	−	0.876269i	$-0.339975\pi$
$193$	498666.	0.963643	0.481822	+	0.876269i	$0.339975\pi$
$194$	−149526.	−0.285242
$195$	200205.	0.377040
$196$	48805.4	0.0907460
$197$	−352505.	−0.647142	−0.323571	−	0.946204i	$-0.604883\pi$
$197$	−352505.	−0.647142	−0.323571	+	0.946204i	$0.604883\pi$
$198$	−396841.	−0.719372
$199$	−619579.	−1.10908	−0.554542	−	0.832156i	$-0.687106\pi$
$199$	−619579.	−1.10908	−0.554542	+	0.832156i	$0.687106\pi$
$200$	−119344.	−0.210972
$201$	−281284.	−0.491083
$202$	−292824.	−0.504926
$203$	−230450.	−0.392497
$204$	19192.6	0.0322893
$205$	−380151.	−0.631788
$206$	−274139.	−0.450094
$207$	−54376.4	−0.0882033
$208$	−588482.	−0.943137
$209$	625144.	0.989952
$210$	113645.	0.177829
$211$	−1.28079e6	−1.98048	−0.990241	−	0.139366i	$-0.955494\pi$
$211$	−1.28079e6	−1.98048	−0.990241	+	0.139366i	$0.955494\pi$
$212$	5614.76	0.00858009
$213$	−526528.	−0.795193
$214$	−30162.4	−0.0450227
$215$	174028.	0.256758
$216$	−781845.	−1.14021
$217$	495790.	0.714741
$218$	992853.	1.41496
$219$	−108977.	−0.153541
$220$	77771.5	0.108334
$221$	258228.	0.355649
$222$	164122.	0.223503
$223$	156448.	0.210673	0.105336	−	0.994437i	$-0.466408\pi$
$223$	156448.	0.210673	0.105336	+	0.994437i	$0.466408\pi$
$224$	111220.	0.148103
$225$	−64244.4	−0.0846017
$226$	617656.	0.804406
$227$	212664.	0.273924	0.136962	−	0.990576i	$-0.456266\pi$
$227$	212664.	0.273924	0.136962	+	0.990576i	$0.456266\pi$
$228$	42881.0	0.0546296
$229$	−719349.	−0.906465	−0.453232	−	0.891392i	$-0.649729\pi$
$229$	−719349.	−0.906465	−0.453232	+	0.891392i	$0.649729\pi$
$230$	−69673.1	−0.0868452
$231$	−632314.	−0.779656
$232$	603869.	0.736585
$233$	1.61407e6	1.94774	0.973871	−	0.227103i	$-0.0729256\pi$
$233$	1.61407e6	1.94774	0.973871	+	0.227103i	$0.0729256\pi$
$234$	−366244.	−0.437252
$235$	−201898.	−0.238486
$236$	8537.04	0.00997763
$237$	−327691.	−0.378960
$238$	146582.	0.167740
$239$	−1.00977e6	−1.14347	−0.571737	−	0.820437i	$-0.693730\pi$
$239$	−1.00977e6	−1.14347	−0.571737	+	0.820437i	$0.693730\pi$
$240$	−257582.	−0.288660
$241$	−995482.	−1.10406	−0.552028	−	0.833826i	$-0.686146\pi$
$241$	−995482.	−1.10406	−0.552028	+	0.833826i	$0.686146\pi$
$242$	1.98067e6	2.17407
$243$	−716645.	−0.778554
$244$	83382.3	0.0896601
$245$	287421.	0.305917
$246$	−948579.	−0.999392
$247$	576945.	0.601717
$248$	−1.29916e6	−1.34133
$249$	−385831.	−0.394365
$250$	−82317.0	−0.0832990
$251$	−599825.	−0.600953	−0.300476	−	0.953789i	$-0.597146\pi$
$251$	−599825.	−0.600953	−0.300476	+	0.953789i	$0.597146\pi$
$252$	31797.8	0.0315425
$253$	387657.	0.380755
$254$	685525.	0.666713
$255$	113028.	0.108851
$256$	−409643.	−0.390666
$257$	−1.57463e6	−1.48712	−0.743559	−	0.668670i	$-0.766864\pi$
$257$	−1.57463e6	−1.48712	−0.743559	+	0.668670i	$0.766864\pi$
$258$	434248.	0.406152
$259$	−191718.	−0.177588
$260$	71775.3	0.0658479
$261$	325071.	0.295377
$262$	−1.77161e6	−1.59446
$263$	−1.47167e6	−1.31196	−0.655982	−	0.754777i	$-0.727745\pi$
$263$	−1.47167e6	−1.31196	−0.655982	+	0.754777i	$0.727745\pi$
$264$	1.65691e6	1.46315
$265$	33066.1	0.0289246
$266$	327500.	0.283797
$267$	1.38632e6	1.19011
$268$	−100843.	−0.0857648
$269$	−135287.	−0.113992	−0.0569959	−	0.998374i	$-0.518152\pi$
$269$	−135287.	−0.113992	−0.0569959	+	0.998374i	$0.518152\pi$
$270$	−539276.	−0.450196
$271$	876933.	0.725342	0.362671	−	0.931917i	$-0.381865\pi$
$271$	876933.	0.725342	0.362671	+	0.931917i	$0.381865\pi$
$272$	−332234.	−0.272283
$273$	−583563.	−0.473894
$274$	835811.	0.672561
$275$	458006.	0.365208
$276$	26590.9	0.0210116
$277$	−329285.	−0.257853	−0.128927	−	0.991654i	$-0.541153\pi$
$277$	−329285.	−0.257853	−0.128927	+	0.991654i	$0.541153\pi$
$278$	1.80783e6	1.40296
$279$	−699358.	−0.537885
$280$	347867.	0.265166
$281$	413432.	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$281$	413432.	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$282$	−503791.	−0.377249
$283$	1.93000e6	1.43249	0.716246	−	0.697848i	$-0.245859\pi$
$283$	1.93000e6	1.43249	0.716246	+	0.697848i	$0.245859\pi$
$284$	−188766.	−0.138876
$285$	252532.	0.184164
$286$	2.61100e6	1.88752
$287$	1.10808e6	0.794081
$288$	−156886.	−0.111456
$289$	−1.27407e6	−0.897324
$290$	416518.	0.290829
$291$	336075.	0.232650
$292$	−39069.2	−0.0268150
$293$	−2.02419e6	−1.37747	−0.688736	−	0.725013i	$-0.741834\pi$
$293$	−2.02419e6	−1.37747	−0.688736	+	0.725013i	$0.741834\pi$
$294$	717194.	0.483914
$295$	50275.7	0.0336359
$296$	502375.	0.333272
$297$	3.00050e6	1.97380
$298$	1.80921e6	1.18018
$299$	357768.	0.231432
$300$	31416.4	0.0201537
$301$	−507263.	−0.322713
$302$	−2.72991e6	−1.72239
$303$	658149.	0.411830
$304$	−742293.	−0.460672
$305$	491049.	0.302256
$306$	−206767.	−0.126234
$307$	−2.44745e6	−1.48207	−0.741034	−	0.671467i	$-0.765664\pi$
$307$	−2.44745e6	−1.48207	−0.741034	+	0.671467i	$0.765664\pi$
$308$	−226691.	−0.136162
$309$	616154.	0.367107
$310$	−896095.	−0.529602
$311$	−962776.	−0.564448	−0.282224	−	0.959348i	$-0.591072\pi$
$311$	−962776.	−0.564448	−0.282224	+	0.959348i	$0.591072\pi$
$312$	1.52916e6	0.889338
$313$	1.33248e6	0.768774	0.384387	−	0.923172i	$-0.374413\pi$
$313$	1.33248e6	0.768774	0.384387	+	0.923172i	$0.374413\pi$
$314$	508821.	0.291233
$315$	187262.	0.106334
$316$	−117480.	−0.0661832
$317$	2.64829e6	1.48019	0.740096	−	0.672501i	$-0.234780\pi$
$317$	2.64829e6	1.48019	0.740096	+	0.672501i	$0.234780\pi$
$318$	82508.8	0.0457543
$319$	−2.31748e6	−1.27508
$320$	−897129.	−0.489756
$321$	67793.0	0.0367216
$322$	203085.	0.109154
$323$	325720.	0.173716
$324$	99780.5	0.0528060
$325$	422694.	0.221982
$326$	1.14972e6	0.599168
$327$	−2.23153e6	−1.15407
$328$	−2.90359e6	−1.49022
$329$	588500.	0.299748
$330$	1.14285e6	0.577703
$331$	−3.03269e6	−1.52145	−0.760725	−	0.649075i	$-0.775156\pi$
$331$	−3.03269e6	−1.52145	−0.760725	+	0.649075i	$0.775156\pi$
$332$	−138324.	−0.0688735
$333$	270436.	0.133645
$334$	3.33996e6	1.63823
$335$	−593878.	−0.289125
$336$	750807.	0.362811
$337$	−3.06223e6	−1.46880	−0.734402	−	0.678715i	$-0.762537\pi$
$337$	−3.06223e6	−1.46880	−0.734402	+	0.678715i	$0.762537\pi$
$338$	453616.	0.215972
$339$	−1.38824e6	−0.656093
$340$	40521.5	0.0190103
$341$	4.98581e6	2.32194
$342$	−461969.	−0.213574
$343$	−2.06252e6	−0.946594
$344$	1.32923e6	0.605624
$345$	156597.	0.0708330
$346$	2.23015e6	1.00148
$347$	3.47125e6	1.54761	0.773806	−	0.633423i	$-0.218351\pi$
$347$	3.47125e6	1.54761	0.773806	+	0.633423i	$0.218351\pi$
$348$	−158965.	−0.0703643
$349$	−607747.	−0.267091	−0.133546	−	0.991043i	$-0.542636\pi$
$349$	−607747.	−0.267091	−0.133546	+	0.991043i	$0.542636\pi$
$350$	239940.	0.104697
$351$	2.76916e6	1.19972
$352$	1.11846e6	0.481133
$353$	4.43515e6	1.89440	0.947201	−	0.320641i	$-0.103898\pi$
$353$	4.43515e6	1.89440	0.947201	+	0.320641i	$0.103898\pi$
$354$	125452.	0.0532069
$355$	−1.11166e6	−0.468169
$356$	497010.	0.207845
$357$	−329456.	−0.136813
$358$	−2.16674e6	−0.893510
$359$	979250.	0.401012	0.200506	−	0.979692i	$-0.435741\pi$
$359$	979250.	0.401012	0.200506	+	0.979692i	$0.435741\pi$
$360$	−490698.	−0.199553
$361$	−1.74836e6	−0.706094
$362$	−18970.5	−0.00760866
$363$	−4.45174e6	−1.77322
$364$	−209213.	−0.0827628
$365$	−230084.	−0.0903969
$366$	1.22530e6	0.478123
$367$	578609.	0.224244	0.112122	−	0.993694i	$-0.464235\pi$
$367$	578609.	0.224244	0.112122	+	0.993694i	$0.464235\pi$
$368$	−460302.	−0.177183
$369$	−1.56304e6	−0.597592
$370$	346512.	0.131587
$371$	−96382.0	−0.0363547
$372$	341996.	0.128134
$373$	−5.24299e6	−1.95122	−0.975612	−	0.219504i	$-0.929556\pi$
$373$	−5.24299e6	−1.95122	−0.975612	+	0.219504i	$0.929556\pi$
$374$	1.47407e6	0.544928
$375$	185015.	0.0679407
$376$	−1.54210e6	−0.562526
$377$	−2.13880e6	−0.775026
$378$	1.57190e6	0.565842
$379$	−1.60569e6	−0.574202	−0.287101	−	0.957900i	$-0.592692\pi$
$379$	−1.60569e6	−0.574202	−0.287101	+	0.957900i	$0.592692\pi$
$380$	90535.2	0.0321631
$381$	−1.54078e6	−0.543788
$382$	−589553.	−0.206711
$383$	−4.63165e6	−1.61339	−0.806694	−	0.590969i	$-0.798745\pi$
$383$	−4.63165e6	−1.61339	−0.806694	+	0.590969i	$0.798745\pi$
$384$	−1.66026e6	−0.574576
$385$	−1.33501e6	−0.459022
$386$	2.62712e6	0.897452
$387$	715542.	0.242861
$388$	120486.	0.0406310
$389$	4.24906e6	1.42370	0.711850	−	0.702331i	$-0.247857\pi$
$389$	4.24906e6	1.42370	0.711850	+	0.702331i	$0.247857\pi$
$390$	1.05474e6	0.351142
$391$	201982.	0.0668144
$392$	2.19532e6	0.721577
$393$	3.98186e6	1.30048
$394$	−1.85710e6	−0.602690
$395$	−691857.	−0.223112
$396$	319769.	0.102470
$397$	−735094.	−0.234081	−0.117041	−	0.993127i	$-0.537341\pi$
$397$	−735094.	−0.234081	−0.117041	+	0.993127i	$0.537341\pi$
$398$	−3.26413e6	−1.03290
$399$	−736088.	−0.231472
$400$	−543835.	−0.169948
$401$	3.02966e6	0.940879	0.470439	−	0.882432i	$-0.344095\pi$
$401$	3.02966e6	0.940879	0.470439	+	0.882432i	$0.344095\pi$
$402$	−1.48189e6	−0.457351
$403$	4.60141e6	1.41133
$404$	235953.	0.0719237
$405$	587620.	0.178016
$406$	−1.21408e6	−0.365537
$407$	−1.92797e6	−0.576919
$408$	863304.	0.256752
$409$	−4.45759e6	−1.31762	−0.658812	−	0.752307i	$-0.728941\pi$
$409$	−4.45759e6	−1.31762	−0.658812	+	0.752307i	$0.728941\pi$
$410$	−2.00275e6	−0.588391
$411$	−1.87856e6	−0.548557
$412$	220897.	0.0641132
$413$	−146545.	−0.0422763
$414$	−286471.	−0.0821447
$415$	−814608.	−0.232182
$416$	1.03223e6	0.292444
$417$	−4.06327e6	−1.14429
$418$	3.29344e6	0.921954
$419$	6.56774e6	1.82760	0.913799	−	0.406166i	$-0.133135\pi$
$419$	6.56774e6	1.82760	0.913799	+	0.406166i	$0.133135\pi$
$420$	−91573.6	−0.0253307
$421$	5.39612e6	1.48380	0.741902	−	0.670508i	$-0.233924\pi$
$421$	5.39612e6	1.48380	0.741902	+	0.670508i	$0.233924\pi$
$422$	−6.74756e6	−1.84444
$423$	−830134.	−0.225578
$424$	252558.	0.0682255
$425$	238636.	0.0640862
$426$	−2.77390e6	−0.740572
$427$	−1.43133e6	−0.379899
$428$	24304.4	0.00641322
$429$	−5.86848e6	−1.53951
$430$	916832.	0.239121
$431$	2.83429e6	0.734938	0.367469	−	0.930036i	$-0.380224\pi$
$431$	2.83429e6	0.734938	0.367469	+	0.930036i	$0.380224\pi$
$432$	−3.56278e6	−0.918500
$433$	−6.24204e6	−1.59995	−0.799975	−	0.600033i	$-0.795154\pi$
$433$	−6.24204e6	−1.59995	−0.799975	+	0.600033i	$0.795154\pi$
$434$	2.61197e6	0.665646
$435$	−936163.	−0.237207
$436$	−800026.	−0.201552
$437$	451278.	0.113042
$438$	−574121.	−0.142994
$439$	−3.28139e6	−0.812637	−0.406319	−	0.913731i	$-0.633188\pi$
$439$	−3.28139e6	−0.812637	−0.406319	+	0.913731i	$0.633188\pi$
$440$	3.49825e6	0.861428
$441$	1.18177e6	0.289359
$442$	1.36042e6	0.331220
$443$	−1.20220e6	−0.291050	−0.145525	−	0.989355i	$-0.546487\pi$
$443$	−1.20220e6	−0.291050	−0.145525	+	0.989355i	$0.546487\pi$
$444$	−132247.	−0.0318367
$445$	2.92695e6	0.700674
$446$	824215.	0.196202
$447$	−4.06637e6	−0.962582
$448$	2.61498e6	0.615564
$449$	889806.	0.208295	0.104148	−	0.994562i	$-0.466789\pi$
$449$	889806.	0.208295	0.104148	+	0.994562i	$0.466789\pi$
$450$	−338458.	−0.0787905
$451$	1.11431e7	2.57968
$452$	−497698.	−0.114583
$453$	6.13574e6	1.40482
$454$	1.12038e6	0.255108
$455$	−1.23208e6	−0.279004
$456$	1.92884e6	0.434394
$457$	−1.58331e6	−0.354631	−0.177315	−	0.984154i	$-0.556741\pi$
$457$	−1.58331e6	−0.354631	−0.177315	+	0.984154i	$0.556741\pi$
$458$	−3.78974e6	−0.844200
$459$	1.56336e6	0.346359
$460$	56141.6	0.0123706
$461$	2.11854e6	0.464284	0.232142	−	0.972682i	$-0.425427\pi$
$461$	2.11854e6	0.464284	0.232142	+	0.972682i	$0.425427\pi$
$462$	−3.33122e6	−0.726102
$463$	−3.20820e6	−0.695520	−0.347760	−	0.937584i	$-0.613058\pi$
$463$	−3.20820e6	−0.695520	−0.347760	+	0.937584i	$0.613058\pi$
$464$	2.75176e6	0.593356
$465$	2.01406e6	0.431957
$466$	8.50337e6	1.81395
$467$	−2.09653e6	−0.444844	−0.222422	−	0.974950i	$-0.571396\pi$
$467$	−2.09653e6	−0.444844	−0.222422	+	0.974950i	$0.571396\pi$
$468$	295114.	0.0622839
$469$	1.73105e6	0.363395
$470$	−1.06366e6	−0.222105
$471$	−1.14362e6	−0.237537
$472$	384005.	0.0793382
$473$	−5.10119e6	−1.04838
$474$	−1.72637e6	−0.352930
$475$	533173.	0.108426
$476$	−118113.	−0.0238936
$477$	135956.	0.0273591
$478$	−5.31975e6	−1.06493
$479$	−6.14042e6	−1.22281	−0.611406	−	0.791317i	$-0.709396\pi$
$479$	−6.14042e6	−1.22281	−0.611406	+	0.791317i	$0.709396\pi$
$480$	451813.	0.0895066
$481$	−1.77932e6	−0.350665
$482$	−5.24449e6	−1.02822
$483$	−456454.	−0.0890285
$484$	−1.59599e6	−0.309683
$485$	709558.	0.136973
$486$	−3.77550e6	−0.725076
$487$	6.29369e6	1.20249	0.601247	−	0.799064i	$-0.294671\pi$
$487$	6.29369e6	1.20249	0.601247	+	0.799064i	$0.294671\pi$
$488$	3.75063e6	0.712943
$489$	−2.58411e6	−0.488696
$490$	1.51422e6	0.284904
$491$	3.02860e6	0.566941	0.283470	−	0.958981i	$-0.408514\pi$
$491$	3.02860e6	0.566941	0.283470	+	0.958981i	$0.408514\pi$
$492$	764351.	0.142357
$493$	−1.20748e6	−0.223750
$494$	3.03952e6	0.560386
$495$	1.88316e6	0.345441
$496$	−5.92013e6	−1.08051
$497$	3.24031e6	0.588432
$498$	−2.03267e6	−0.367276
$499$	−5.56440e6	−1.00038	−0.500192	−	0.865914i	$-0.666737\pi$
$499$	−5.56440e6	−1.00038	−0.500192	+	0.865914i	$0.666737\pi$
$500$	66329.9	0.0118654
$501$	−7.50689e6	−1.33618
$502$	−3.16005e6	−0.559674
$503$	4.17981e6	0.736608	0.368304	−	0.929705i	$-0.379938\pi$
$503$	4.17981e6	0.736608	0.368304	+	0.929705i	$0.379938\pi$
$504$	1.43030e6	0.250814
$505$	1.38956e6	0.242464
$506$	2.04229e6	0.354602
$507$	−1.01955e6	−0.176152
$508$	−552386.	−0.0949694
$509$	−2.36278e6	−0.404230	−0.202115	−	0.979362i	$-0.564782\pi$
$509$	−2.36278e6	−0.404230	−0.202115	+	0.979362i	$0.564782\pi$
$510$	595462.	0.101375
$511$	670655.	0.113618
$512$	−6.64493e6	−1.12025
$513$	3.49293e6	0.585999
$514$	−8.29560e6	−1.38497
$515$	1.30089e6	0.216134
$516$	−349910.	−0.0578539
$517$	5.91813e6	0.973774
$518$	−1.01003e6	−0.165389
$519$	−5.01247e6	−0.816834
$520$	3.22853e6	0.523597
$521$	−7.34682e6	−1.18578	−0.592891	−	0.805282i	$-0.702014\pi$
$521$	−7.34682e6	−1.18578	−0.592891	+	0.805282i	$0.702014\pi$
$522$	1.71257e6	0.275088
$523$	4.81938e6	0.770436	0.385218	−	0.922826i	$-0.374126\pi$
$523$	4.81938e6	0.770436	0.385218	+	0.922826i	$0.374126\pi$
$524$	1.42754e6	0.227122
$525$	−539289.	−0.0853932
$526$	−7.75320e6	−1.22185
$527$	2.59777e6	0.407450
$528$	7.55034e6	1.17864
$529$	279841.	0.0434783
$530$	174202.	0.0269378
$531$	206716.	0.0318154
$532$	−263895.	−0.0404252
$533$	1.02840e7	1.56799
$534$	7.30354e6	1.10836
$535$	143132.	0.0216198
$536$	−4.53603e6	−0.681968
$537$	4.86996e6	0.728768
$538$	−712729.	−0.106162
$539$	−8.42501e6	−1.24910
$540$	434541.	0.0641278
$541$	8.00206e6	1.17546	0.587731	−	0.809056i	$-0.300021\pi$
$541$	8.00206e6	1.17546	0.587731	+	0.809056i	$0.300021\pi$
$542$	4.61994e6	0.675519
$543$	42638.1	0.00620580
$544$	582756.	0.0844286
$545$	−4.71146e6	−0.679460
$546$	−3.07438e6	−0.441342
$547$	1.18832e7	1.69811	0.849057	−	0.528302i	$-0.177171\pi$
$547$	1.18832e7	1.69811	0.849057	+	0.528302i	$0.177171\pi$
$548$	−673484.	−0.0958023
$549$	2.01902e6	0.285897
$550$	2.41291e6	0.340122
$551$	−2.69781e6	−0.378558
$552$	1.19609e6	0.167076
$553$	2.01665e6	0.280425
$554$	−1.73477e6	−0.240142
$555$	−778820.	−0.107326
$556$	−1.45672e6	−0.199843
$557$	1.13254e7	1.54673	0.773367	−	0.633959i	$-0.218571\pi$
$557$	1.13254e7	1.54673	0.773367	+	0.633959i	$0.218571\pi$
$558$	−3.68442e6	−0.500938
$559$	−4.70789e6	−0.637230
$560$	1.58519e6	0.213604
$561$	−3.31311e6	−0.444456
$562$	2.17808e6	0.290893
$563$	1.13454e7	1.50852	0.754259	−	0.656578i	$-0.227997\pi$
$563$	1.13454e7	1.50852	0.754259	+	0.656578i	$0.227997\pi$
$564$	405948.	0.0537368
$565$	−2.93101e6	−0.386274
$566$	1.01678e7	1.33409
$567$	−1.71281e6	−0.223744
$568$	−8.49088e6	−1.10429
$569$	5.30510e6	0.686930	0.343465	−	0.939165i	$-0.388399\pi$
$569$	5.30510e6	0.686930	0.343465	+	0.939165i	$0.388399\pi$
$570$	1.33041e6	0.171514
$571$	1.42416e7	1.82796	0.913981	−	0.405756i	$-0.132992\pi$
$571$	1.42416e7	1.82796	0.913981	+	0.405756i	$0.132992\pi$
$572$	−2.10391e6	−0.268867
$573$	1.32508e6	0.168599
$574$	5.83766e6	0.739536
$575$	330625.	0.0417029
$576$	−3.68867e6	−0.463248
$577$	−567010.	−0.0709008	−0.0354504	−	0.999371i	$-0.511287\pi$
$577$	−567010.	−0.0709008	−0.0354504	+	0.999371i	$0.511287\pi$
$578$	−6.71218e6	−0.835688
$579$	−5.90470e6	−0.731983
$580$	−335624.	−0.0414269
$581$	2.37444e6	0.291824
$582$	1.77054e6	0.216670
$583$	−969246.	−0.118103
$584$	−1.75738e6	−0.213222
$585$	1.73797e6	0.209967
$586$	−1.06640e7	−1.28285
$587$	−2.37878e6	−0.284944	−0.142472	−	0.989799i	$-0.545505\pi$
$587$	−2.37878e6	−0.284944	−0.142472	+	0.989799i	$0.545505\pi$
$588$	−577904.	−0.0689307
$589$	5.80407e6	0.689358
$590$	264867.	0.0313255
$591$	4.17400e6	0.491569
$592$	2.28926e6	0.268467
$593$	1.40968e7	1.64621	0.823103	−	0.567892i	$-0.192241\pi$
$593$	1.40968e7	1.64621	0.823103	+	0.567892i	$0.192241\pi$
$594$	1.58075e7	1.83822
$595$	−695585.	−0.0805485
$596$	−1.45783e6	−0.168109
$597$	7.33643e6	0.842460
$598$	1.88483e6	0.215535
$599$	1.02416e7	1.16628	0.583139	−	0.812372i	$-0.301824\pi$
$599$	1.02416e7	1.16628	0.583139	+	0.812372i	$0.301824\pi$
$600$	1.41315e6	0.160254
$601$	−312364.	−0.0352756	−0.0176378	−	0.999844i	$-0.505615\pi$
$601$	−312364.	−0.0352756	−0.0176378	+	0.999844i	$0.505615\pi$
$602$	−2.67241e6	−0.300547
$603$	−2.44181e6	−0.273476
$604$	2.19972e6	0.245344
$605$	−9.39900e6	−1.04398
$606$	3.46732e6	0.383541
$607$	−1.50992e7	−1.66335	−0.831673	−	0.555266i	$-0.812616\pi$
$607$	−1.50992e7	−1.66335	−0.831673	+	0.555266i	$0.812616\pi$
$608$	1.30202e6	0.142843
$609$	2.72876e6	0.298141
$610$	2.58699e6	0.281495
$611$	5.46184e6	0.591883
$612$	166610.	0.0179813
$613$	1.01867e7	1.09492	0.547460	−	0.836832i	$-0.315595\pi$
$613$	1.01867e7	1.09492	0.547460	+	0.836832i	$0.315595\pi$
$614$	−1.28939e7	−1.38027
$615$	4.50136e6	0.479906
$616$	−1.01968e7	−1.08271
$617$	3.28554e6	0.347452	0.173726	−	0.984794i	$-0.444419\pi$
$617$	3.28554e6	0.347452	0.173726	+	0.984794i	$0.444419\pi$
$618$	3.24608e6	0.341891
$619$	−3.05545e6	−0.320515	−0.160257	−	0.987075i	$-0.551232\pi$
$619$	−3.05545e6	−0.320515	−0.160257	+	0.987075i	$0.551232\pi$
$620$	722060.	0.0754387
$621$	2.16599e6	0.225387
$622$	−5.07218e6	−0.525677
$623$	−8.53158e6	−0.880662
$624$	6.96821e6	0.716407
$625$	390625.	0.0400000
$626$	7.01987e6	0.715967
$627$	−7.40232e6	−0.751968
$628$	−410000.	−0.0414844
$629$	−1.00454e6	−0.101237
$630$	986548.	0.0990300
$631$	−1.67806e7	−1.67777	−0.838887	−	0.544305i	$-0.816793\pi$
$631$	−1.67806e7	−1.67777	−0.838887	+	0.544305i	$0.816793\pi$
$632$	−5.28440e6	−0.526263
$633$	1.51658e7	1.50437
$634$	1.39520e7	1.37852
$635$	−3.25307e6	−0.320154
$636$	−66484.3	−0.00651743
$637$	−7.77544e6	−0.759235
$638$	−1.22091e7	−1.18750
$639$	−4.57076e6	−0.442830
$640$	−3.50532e6	−0.338281
$641$	2.00724e6	0.192954	0.0964772	−	0.995335i	$-0.469243\pi$
$641$	2.00724e6	0.192954	0.0964772	+	0.995335i	$0.469243\pi$
$642$	357153.	0.0341993
$643$	188198.	0.0179509	0.00897547	−	0.999960i	$-0.497143\pi$
$643$	188198.	0.0179509	0.00897547	+	0.999960i	$0.497143\pi$
$644$	−163643.	−0.0155483
$645$	−2.06067e6	−0.195033
$646$	1.71599e6	0.161783
$647$	−1.32071e7	−1.24035	−0.620177	−	0.784462i	$-0.712939\pi$
$647$	−1.32071e7	−1.24035	−0.620177	+	0.784462i	$0.712939\pi$
$648$	4.48824e6	0.419893
$649$	−1.47370e6	−0.137340
$650$	2.22688e6	0.206734
$651$	−5.87065e6	−0.542917
$652$	−926429.	−0.0853479
$653$	−5.31660e6	−0.487922	−0.243961	−	0.969785i	$-0.578447\pi$
$653$	−5.31660e6	−0.487922	−0.243961	+	0.969785i	$0.578447\pi$
$654$	−1.17564e7	−1.07480
$655$	8.40694e6	0.765658
$656$	−1.32313e7	−1.20045
$657$	−946021.	−0.0855042
$658$	3.10039e6	0.279159
$659$	5.38018e6	0.482596	0.241298	−	0.970451i	$-0.422427\pi$
$659$	5.38018e6	0.482596	0.241298	+	0.970451i	$0.422427\pi$
$660$	−920892.	−0.0822903
$661$	8.76312e6	0.780108	0.390054	−	0.920792i	$-0.372456\pi$
$661$	8.76312e6	0.780108	0.390054	+	0.920792i	$0.372456\pi$
$662$	−1.59771e7	−1.41694
$663$	−3.05767e6	−0.270151
$664$	−6.22197e6	−0.547656
$665$	−1.55411e6	−0.136279
$666$	1.42473e6	0.124465
$667$	−1.67294e6	−0.145601
$668$	−2.69129e6	−0.233356
$669$	−1.85250e6	−0.160027
$670$	−3.12872e6	−0.269265
$671$	−1.43938e7	−1.23416
$672$	−1.31696e6	−0.112499
$673$	−1.18629e7	−1.00961	−0.504804	−	0.863234i	$-0.668435\pi$
$673$	−1.18629e7	−1.00961	−0.504804	+	0.863234i	$0.668435\pi$
$674$	−1.61327e7	−1.36791
$675$	2.55907e6	0.216183
$676$	−365517.	−0.0307639
$677$	−8.08201e6	−0.677716	−0.338858	−	0.940838i	$-0.610041\pi$
$677$	−8.08201e6	−0.677716	−0.338858	+	0.940838i	$0.610041\pi$
$678$	−7.31365e6	−0.611027
$679$	−2.06824e6	−0.172158
$680$	1.82270e6	0.151162
$681$	−2.51815e6	−0.208072
$682$	2.62667e7	2.16244
$683$	−7.94744e6	−0.651892	−0.325946	−	0.945388i	$-0.605683\pi$
$683$	−7.94744e6	−0.651892	−0.325946	+	0.945388i	$0.605683\pi$
$684$	372248.	0.0304223
$685$	−3.96623e6	−0.322962
$686$	−1.08660e7	−0.881573
$687$	8.51780e6	0.688550
$688$	6.05713e6	0.487860
$689$	−894517.	−0.0717861
$690$	824999.	0.0659676
$691$	−7.05380e6	−0.561989	−0.280995	−	0.959709i	$-0.590664\pi$
$691$	−7.05380e6	−0.561989	−0.280995	+	0.959709i	$0.590664\pi$
$692$	−1.79702e6	−0.142655
$693$	−5.48909e6	−0.434177
$694$	1.82875e7	1.44131
$695$	−8.57882e6	−0.673699
$696$	−7.15040e6	−0.559510
$697$	5.80594e6	0.452679
$698$	−3.20179e6	−0.248745
$699$	−1.91121e7	−1.47950
$700$	−193340.	−0.0149134
$701$	−1.85070e7	−1.42246	−0.711231	−	0.702958i	$-0.751862\pi$
$701$	−1.85070e7	−1.42246	−0.711231	+	0.702958i	$0.751862\pi$
$702$	1.45887e7	1.11731
$703$	−2.24439e6	−0.171281
$704$	2.62970e7	1.99975
$705$	2.39068e6	0.181154
$706$	2.33657e7	1.76428
$707$	−4.05032e6	−0.304748
$708$	−101087.	−0.00757900
$709$	−2.58780e6	−0.193337	−0.0966686	−	0.995317i	$-0.530819\pi$
$709$	−2.58780e6	−0.193337	−0.0966686	+	0.995317i	$0.530819\pi$
$710$	−5.85657e6	−0.436011
$711$	−2.84467e6	−0.211037
$712$	2.23561e7	1.65270
$713$	3.59915e6	0.265141
$714$	−1.73567e6	−0.127415
$715$	−1.23902e7	−0.906385
$716$	1.74593e6	0.127275
$717$	1.19566e7	0.868583
$718$	5.15897e6	0.373467
$719$	−4.54097e6	−0.327587	−0.163793	−	0.986495i	$-0.552373\pi$
$719$	−4.54097e6	−0.327587	−0.163793	+	0.986495i	$0.552373\pi$
$720$	−2.23605e6	−0.160750
$721$	−3.79188e6	−0.271654
$722$	−9.21086e6	−0.657593
$723$	1.17875e7	0.838640
$724$	15286.2	0.00108381
$725$	−1.97653e6	−0.139656
$726$	−2.34530e7	−1.65142
$727$	−3.73890e6	−0.262366	−0.131183	−	0.991358i	$-0.541878\pi$
$727$	−3.73890e6	−0.262366	−0.131183	+	0.991358i	$0.541878\pi$
$728$	−9.41063e6	−0.658098
$729$	1.41975e7	0.989445
$730$	−1.21215e6	−0.0841877
$731$	−2.65789e6	−0.183968
$732$	−987329.	−0.0681058
$733$	2.81782e6	0.193710	0.0968552	−	0.995298i	$-0.469122\pi$
$733$	2.81782e6	0.193710	0.0968552	+	0.995298i	$0.469122\pi$
$734$	3.04828e6	0.208841
$735$	−3.40335e6	−0.232374
$736$	807395.	0.0549404
$737$	1.74080e7	1.18054
$738$	−8.23457e6	−0.556544
$739$	−7.31760e6	−0.492899	−0.246449	−	0.969156i	$-0.579264\pi$
$739$	−7.31760e6	−0.492899	−0.246449	+	0.969156i	$0.579264\pi$
$740$	−279215.	−0.0187438
$741$	−6.83160e6	−0.457064
$742$	−507768.	−0.0338576
$743$	−1.99679e7	−1.32697	−0.663484	−	0.748190i	$-0.730923\pi$
$743$	−1.99679e7	−1.32697	−0.663484	+	0.748190i	$0.730923\pi$
$744$	1.53834e7	1.01887
$745$	−8.58536e6	−0.566719
$746$	−2.76216e7	−1.81720
$747$	−3.34937e6	−0.219615
$748$	−1.18778e6	−0.0776217
$749$	−417205.	−0.0271735
$750$	974715.	0.0632739
$751$	2.20695e7	1.42788	0.713942	−	0.700205i	$-0.246908\pi$
$751$	2.20695e7	1.42788	0.713942	+	0.700205i	$0.246908\pi$
$752$	−7.02716e6	−0.453143
$753$	7.10252e6	0.456484
$754$	−1.12678e7	−0.721790
$755$	1.29545e7	0.827088
$756$	−1.26661e6	−0.0806008
$757$	1.41851e7	0.899688	0.449844	−	0.893107i	$-0.351480\pi$
$757$	1.41851e7	0.899688	0.449844	+	0.893107i	$0.351480\pi$
$758$	−8.45926e6	−0.534761
$759$	−4.59024e6	−0.289222
$760$	4.07237e6	0.255749
$761$	1.21787e6	0.0762320	0.0381160	−	0.999273i	$-0.487864\pi$
$761$	1.21787e6	0.0762320	0.0381160	+	0.999273i	$0.487864\pi$
$762$	−8.11730e6	−0.506435
$763$	1.37331e7	0.853999
$764$	475053.	0.0294448
$765$	981187.	0.0606175
$766$	−2.44009e7	−1.50257
$767$	−1.36008e6	−0.0834788
$768$	4.85057e6	0.296749
$769$	−5.12952e6	−0.312796	−0.156398	−	0.987694i	$-0.549988\pi$
$769$	−5.12952e6	−0.312796	−0.156398	+	0.987694i	$0.549988\pi$
$770$	−7.03323e6	−0.427492
$771$	1.86452e7	1.12961
$772$	−2.11689e6	−0.127837
$773$	2.48406e7	1.49525	0.747624	−	0.664122i	$-0.231194\pi$
$773$	2.48406e7	1.49525	0.747624	+	0.664122i	$0.231194\pi$
$774$	3.76968e6	0.226179
$775$	4.25231e6	0.254314
$776$	5.41960e6	0.323082
$777$	2.27013e6	0.134896
$778$	2.23853e7	1.32591
$779$	1.29719e7	0.765880
$780$	−849891.	−0.0500180
$781$	3.25856e7	1.91160
$782$	1.06410e6	0.0622250
$783$	−1.29487e7	−0.754781
$784$	1.00038e7	0.581267
$785$	−2.41454e6	−0.139849
$786$	2.09776e7	1.21115
$787$	1.56230e7	0.899140	0.449570	−	0.893245i	$-0.351577\pi$
$787$	1.56230e7	0.899140	0.449570	+	0.893245i	$0.351577\pi$
$788$	1.49642e6	0.0858496
$789$	1.74261e7	0.996567
$790$	−3.64491e6	−0.207787
$791$	8.54339e6	0.485500
$792$	1.43835e7	0.814804
$793$	−1.32841e7	−0.750150
$794$	−3.87269e6	−0.218002
$795$	−391535.	−0.0219711
$796$	2.63018e6	0.147131
$797$	−2.24931e7	−1.25431	−0.627153	−	0.778896i	$-0.715780\pi$
$797$	−2.24931e7	−1.25431	−0.627153	+	0.778896i	$0.715780\pi$
$798$	−3.87793e6	−0.215572
$799$	3.08354e6	0.170877
$800$	953916.	0.0526969
$801$	1.20346e7	0.662750
$802$	1.59612e7	0.876251
$803$	6.74431e6	0.369104
$804$	1.19408e6	0.0651469
$805$	−963716.	−0.0524155
$806$	2.42416e7	1.31439
$807$	1.60193e6	0.0865882
$808$	1.06134e7	0.571909
$809$	3.22031e7	1.72992	0.864961	−	0.501838i	$-0.167343\pi$
$809$	3.22031e7	1.72992	0.864961	+	0.501838i	$0.167343\pi$
$810$	3.09575e6	0.165788
$811$	−3.63596e7	−1.94119	−0.970593	−	0.240728i	$-0.922614\pi$
$811$	−3.63596e7	−1.94119	−0.970593	+	0.240728i	$0.922614\pi$
$812$	978286.	0.0520686
$813$	−1.03837e7	−0.550970
$814$	−1.01571e7	−0.537291
$815$	−5.45586e6	−0.287719
$816$	3.93397e6	0.206826
$817$	−5.93838e6	−0.311253
$818$	−2.34839e7	−1.22712
$819$	−5.06588e6	−0.263903
$820$	1.61378e6	0.0838128
$821$	1.58072e7	0.818457	0.409229	−	0.912432i	$-0.365798\pi$
$821$	1.58072e7	0.818457	0.409229	+	0.912432i	$0.365798\pi$
$822$	−9.89683e6	−0.510877
$823$	5.26367e6	0.270888	0.135444	−	0.990785i	$-0.456754\pi$
$823$	5.26367e6	0.270888	0.135444	+	0.990785i	$0.456754\pi$
$824$	9.93620e6	0.509803
$825$	−5.42325e6	−0.277412
$826$	−772043.	−0.0393723
$827$	−7.34520e6	−0.373457	−0.186728	−	0.982412i	$-0.559788\pi$
$827$	−7.34520e6	−0.373457	−0.186728	+	0.982412i	$0.559788\pi$
$828$	230834.	0.0117010
$829$	5.06008e6	0.255724	0.127862	−	0.991792i	$-0.459189\pi$
$829$	5.06008e6	0.255724	0.127862	+	0.991792i	$0.459189\pi$
$830$	−4.29159e6	−0.216234
$831$	3.89906e6	0.195865
$832$	2.42695e7	1.21549
$833$	−4.38971e6	−0.219191
$834$	−2.14065e7	−1.06569
$835$	−1.58494e7	−0.786676
$836$	−2.65381e6	−0.131327
$837$	2.78578e7	1.37446
$838$	3.46008e7	1.70206
$839$	3.39646e7	1.66580	0.832898	−	0.553426i	$-0.186680\pi$
$839$	3.39646e7	1.66580	0.832898	+	0.553426i	$0.186680\pi$
$840$	−4.11908e6	−0.201420
$841$	−1.05101e7	−0.512407
$842$	2.84283e7	1.38188
$843$	−4.89544e6	−0.237259
$844$	5.43708e6	0.262730
$845$	−2.15258e6	−0.103709
$846$	−4.37339e6	−0.210083
$847$	2.73965e7	1.31216
$848$	1.15088e6	0.0549591
$849$	−2.28531e7	−1.08812
$850$	1.25721e6	0.0596842
$851$	−1.39176e6	−0.0658780
$852$	2.23517e6	0.105490
$853$	−3.72237e7	−1.75165	−0.875824	−	0.482631i	$-0.839681\pi$
$853$	−3.72237e7	−1.75165	−0.875824	+	0.482631i	$0.839681\pi$
$854$	−7.54064e6	−0.353805
$855$	2.19222e6	0.102558
$856$	1.09324e6	0.0509954
$857$	−3.24074e7	−1.50728	−0.753638	−	0.657290i	$-0.771703\pi$
$857$	−3.24074e7	−1.50728	−0.753638	+	0.657290i	$0.771703\pi$
$858$	−3.09169e7	−1.43376
$859$	−2.08628e7	−0.964694	−0.482347	−	0.875980i	$-0.660216\pi$
$859$	−2.08628e7	−0.964694	−0.482347	+	0.875980i	$0.660216\pi$
$860$	−738769.	−0.0340614
$861$	−1.31207e7	−0.603183
$862$	1.49319e7	0.684456
$863$	292318.	0.0133607	0.00668034	−	0.999978i	$-0.497874\pi$
$863$	292318.	0.0133607	0.00668034	+	0.999978i	$0.497874\pi$
$864$	6.24931e6	0.284805
$865$	−1.05829e7	−0.480910
$866$	−3.28849e7	−1.49005
$867$	1.50863e7	0.681607
$868$	−2.10468e6	−0.0948173
$869$	2.02800e7	0.911000
$870$	−4.93198e6	−0.220914
$871$	1.60658e7	0.717559
$872$	−3.59861e7	−1.60267
$873$	2.91745e6	0.129559
$874$	2.37746e6	0.105277
$875$	−1.13861e6	−0.0502751
$876$	462618.	0.0203687
$877$	−2.37558e6	−0.104297	−0.0521484	−	0.998639i	$-0.516607\pi$
$877$	−2.37558e6	−0.104297	−0.0521484	+	0.998639i	$0.516607\pi$
$878$	−1.72873e7	−0.756818
$879$	2.39684e7	1.04633
$880$	1.59411e7	0.693924
$881$	−371982.	−0.0161466	−0.00807331	−	0.999967i	$-0.502570\pi$
$881$	−371982.	−0.0161466	−0.00807331	+	0.999967i	$0.502570\pi$
$882$	6.22592e6	0.269484
$883$	−2.97561e7	−1.28432	−0.642162	−	0.766569i	$-0.721963\pi$
$883$	−2.97561e7	−1.28432	−0.642162	+	0.766569i	$0.721963\pi$
$884$	−1.09621e6	−0.0471804
$885$	−595314.	−0.0255498
$886$	−6.33354e6	−0.271058
$887$	−6.56407e6	−0.280133	−0.140066	−	0.990142i	$-0.544732\pi$
$887$	−6.56407e6	−0.280133	−0.140066	+	0.990142i	$0.544732\pi$
$888$	−5.94862e6	−0.253153
$889$	9.48216e6	0.402395
$890$	1.54200e7	0.652545
$891$	−1.72246e7	−0.726865
$892$	−664140.	−0.0279478
$893$	6.88940e6	0.289103
$894$	−2.14228e7	−0.896463
$895$	1.02820e7	0.429061
$896$	1.02174e7	0.425179
$897$	−4.23633e6	−0.175796
$898$	4.68776e6	0.193988
$899$	−2.15163e7	−0.887910
$900$	272724.	0.0112232
$901$	−505009.	−0.0207246
$902$	5.87053e7	2.40249
$903$	6.00650e6	0.245133
$904$	−2.23870e7	−0.911118
$905$	90022.2	0.00365366
$906$	3.23249e7	1.30833
$907$	2.06805e6	0.0834726	0.0417363	−	0.999129i	$-0.486711\pi$
$907$	2.06805e6	0.0834726	0.0417363	+	0.999129i	$0.486711\pi$
$908$	−902782.	−0.0363386
$909$	5.71336e6	0.229341
$910$	−6.49097e6	−0.259840
$911$	−4.17228e7	−1.66563	−0.832813	−	0.553555i	$-0.813271\pi$
$911$	−4.17228e7	−1.66563	−0.832813	+	0.553555i	$0.813271\pi$
$912$	8.78948e6	0.349926
$913$	2.38781e7	0.948033
$914$	−8.34136e6	−0.330272
$915$	−5.81451e6	−0.229594
$916$	3.05372e6	0.120251
$917$	−2.45048e7	−0.962339
$918$	8.23622e6	0.322568
$919$	−8.00374e6	−0.312611	−0.156305	−	0.987709i	$-0.549958\pi$
$919$	−8.00374e6	−0.312611	−0.156305	+	0.987709i	$0.549958\pi$
$920$	2.52531e6	0.0983661
$921$	2.89802e7	1.12578
$922$	1.11611e7	0.432393
$923$	3.00732e7	1.16192
$924$	2.68424e6	0.103429
$925$	−1.64433e6	−0.0631880
$926$	−1.69017e7	−0.647745
$927$	5.34880e6	0.204436
$928$	−4.82674e6	−0.183986
$929$	−1.54596e7	−0.587704	−0.293852	−	0.955851i	$-0.594937\pi$
$929$	−1.54596e7	−0.587704	−0.293852	+	0.955851i	$0.594937\pi$
$930$	1.06107e7	0.402286
$931$	−9.80770e6	−0.370846
$932$	−6.85189e6	−0.258387
$933$	1.14002e7	0.428755
$934$	−1.10451e7	−0.414289
$935$	−6.99501e6	−0.261673
$936$	1.32746e7	0.495257
$937$	−1.21380e7	−0.451645	−0.225822	−	0.974169i	$-0.572507\pi$
$937$	−1.21380e7	−0.451645	−0.225822	+	0.974169i	$0.572507\pi$
$938$	9.11969e6	0.338433
$939$	−1.57778e7	−0.583960
$940$	857081.	0.0316375
$941$	−3.01783e7	−1.11102	−0.555509	−	0.831510i	$-0.687477\pi$
$941$	−3.01783e7	−1.11102	−0.555509	+	0.831510i	$0.687477\pi$
$942$	−6.02494e6	−0.221221
$943$	8.04399e6	0.294573
$944$	1.74987e6	0.0639109
$945$	−7.45925e6	−0.271716
$946$	−2.68745e7	−0.976368
$947$	2.58524e7	0.936753	0.468377	−	0.883529i	$-0.344839\pi$
$947$	2.58524e7	0.936753	0.468377	+	0.883529i	$0.344839\pi$
$948$	1.39108e6	0.0502727
$949$	6.22432e6	0.224350
$950$	2.80891e6	0.100979
$951$	−3.13584e7	−1.12435
$952$	−5.31287e6	−0.189993
$953$	2.11978e7	0.756063	0.378031	−	0.925793i	$-0.376601\pi$
$953$	2.11978e7	0.756063	0.378031	+	0.925793i	$0.376601\pi$
$954$	716254.	0.0254798
$955$	2.79765e6	0.0992623
$956$	4.28657e6	0.151693
$957$	2.74412e7	0.968553
$958$	−3.23495e7	−1.13882
$959$	1.15609e7	0.405924
$960$	1.06229e7	0.372019
$961$	1.76610e7	0.616890
$962$	−9.37400e6	−0.326578
$963$	588507.	0.0204497
$964$	4.22593e6	0.146464
$965$	−1.24666e7	−0.430954
$966$	−2.40473e6	−0.0829133
$967$	−3.49861e7	−1.20318	−0.601588	−	0.798806i	$-0.705465\pi$
$967$	−3.49861e7	−1.20318	−0.601588	+	0.798806i	$0.705465\pi$
$968$	−7.17895e7	−2.46248
$969$	−3.85685e6	−0.131954
$970$	3.73816e6	0.127564
$971$	3.23066e7	1.09962	0.549810	−	0.835289i	$-0.314700\pi$
$971$	3.23066e7	1.09962	0.549810	+	0.835289i	$0.314700\pi$
$972$	3.04224e6	0.103283
$973$	2.50058e7	0.846757
$974$	3.31570e7	1.11990
$975$	−5.00512e6	−0.168617
$976$	1.70912e7	0.574311
$977$	−5.73644e7	−1.92268	−0.961338	−	0.275371i	$-0.911199\pi$
$977$	−5.73644e7	−1.92268	−0.961338	+	0.275371i	$0.911199\pi$
$978$	−1.36138e7	−0.455128
$979$	−8.57961e7	−2.86095
$980$	−1.22013e6	−0.0405829
$981$	−1.93718e7	−0.642684
$982$	1.59555e7	0.527998
$983$	3.81083e7	1.25787	0.628935	−	0.777458i	$-0.283491\pi$
$983$	3.81083e7	1.25787	0.628935	+	0.777458i	$0.283491\pi$
$984$	3.43814e7	1.13197
$985$	8.81262e6	0.289411
$986$	−6.36136e6	−0.208381
$987$	−6.96842e6	−0.227689
$988$	−2.44920e6	−0.0798236
$989$	−3.68244e6	−0.119714
$990$	9.92102e6	0.321713
$991$	1.93897e7	0.627171	0.313586	−	0.949560i	$-0.398470\pi$
$991$	1.93897e7	0.627171	0.313586	+	0.949560i	$0.398470\pi$
$992$	1.03842e7	0.335039
$993$	3.59100e7	1.15569
$994$	1.70709e7	0.548013
$995$	1.54895e7	0.495997
$996$	1.63789e6	0.0523163
$997$	−3.27681e7	−1.04403	−0.522015	−	0.852936i	$-0.674820\pi$
$997$	−3.27681e7	−1.04403	−0.522015	+	0.852936i	$0.674820\pi$
$998$	−2.93149e7	−0.931669
$999$	−1.07724e7	−0.341505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.6.a.c.1.5	✓	7
3.2	odd	2		1035.6.a.b.1.3		7
5.4	even	2		575.6.a.d.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.6.a.c.1.5	✓	7	1.1	even	1	trivial
575.6.a.d.1.3		7	5.4	even	2
1035.6.a.b.1.3		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	115.a (trivial)

\(f(q)\)	\(=\)	\(q+5.26829 q^{2} -11.8410 q^{3} -4.24511 q^{4} -25.0000 q^{5} -62.3818 q^{6} +72.8708 q^{7} -190.950 q^{8} -102.791 q^{9} -131.707 q^{10} +732.810 q^{11} +50.2663 q^{12} +676.311 q^{13} +383.904 q^{14} +296.025 q^{15} -870.135 q^{16} +381.818 q^{17} -541.533 q^{18} +853.077 q^{19} +106.128 q^{20} -862.862 q^{21} +3860.66 q^{22} +529.000 q^{23} +2261.03 q^{24} +625.000 q^{25} +3563.00 q^{26} +4094.51 q^{27} -309.345 q^{28} -3162.45 q^{29} +1559.54 q^{30} +6803.69 q^{31} +1526.27 q^{32} -8677.20 q^{33} +2011.53 q^{34} -1821.77 q^{35} +436.359 q^{36} -2630.93 q^{37} +4494.26 q^{38} -8008.19 q^{39} +4773.74 q^{40} +15206.0 q^{41} -4545.81 q^{42} -6961.13 q^{43} -3110.86 q^{44} +2569.78 q^{45} +2786.93 q^{46} +8075.94 q^{47} +10303.3 q^{48} -11496.8 q^{49} +3292.68 q^{50} -4521.10 q^{51} -2871.01 q^{52} -1322.64 q^{53} +21571.1 q^{54} -18320.3 q^{55} -13914.7 q^{56} -10101.3 q^{57} -16660.7 q^{58} -2011.03 q^{59} -1256.66 q^{60} -19642.0 q^{61} +35843.8 q^{62} -7490.46 q^{63} +35885.2 q^{64} -16907.8 q^{65} -45714.0 q^{66} +23755.1 q^{67} -1620.86 q^{68} -6263.88 q^{69} -9597.61 q^{70} +44466.6 q^{71} +19627.9 q^{72} +9203.35 q^{73} -13860.5 q^{74} -7400.62 q^{75} -3621.41 q^{76} +53400.5 q^{77} -42189.5 q^{78} +27674.3 q^{79} +21753.4 q^{80} -23504.8 q^{81} +80109.8 q^{82} +32584.3 q^{83} +3662.94 q^{84} -9545.45 q^{85} -36673.3 q^{86} +37446.5 q^{87} -139930. q^{88} -117078. q^{89} +13538.3 q^{90} +49283.3 q^{91} -2245.66 q^{92} -80562.4 q^{93} +42546.4 q^{94} -21326.9 q^{95} -18072.5 q^{96} -28382.3 q^{97} -60568.7 q^{98} -75326.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 3 q^{3} + 178 q^{4} - 175 q^{5} - 381 q^{6} + 33 q^{7} + 546 q^{8} + 440 q^{9} - 100 q^{10} + 1373 q^{11} - 285 q^{12} + 605 q^{13} + 1317 q^{14} + 75 q^{15} + 3770 q^{16} + 2505 q^{17}+ \cdots + 237333 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 - 3 * q^3 + 178 * q^4 - 175 * q^5 - 381 * q^6 + 33 * q^7 + 546 * q^8 + 440 * q^9 - 100 * q^10 + 1373 * q^11 - 285 * q^12 + 605 * q^13 + 1317 * q^14 + 75 * q^15 + 3770 * q^16 + 2505 * q^17 + 7971 * q^18 - 115 * q^19 - 4450 * q^20 + 608 * q^21 + 2977 * q^22 + 3703 * q^23 - 12447 * q^24 + 4375 * q^25 + 9379 * q^26 - 12276 * q^27 + 5777 * q^28 + 2440 * q^29 + 9525 * q^30 + 13565 * q^31 + 14086 * q^32 + 10519 * q^33 + 26997 * q^34 - 825 * q^35 + 79889 * q^36 + 9414 * q^37 + 28717 * q^38 - 21738 * q^39 - 13650 * q^40 + 13725 * q^41 + 12426 * q^42 + 76694 * q^43 + 55203 * q^44 - 11000 * q^45 + 2116 * q^46 + 59692 * q^47 - 32985 * q^48 - 53608 * q^49 + 2500 * q^50 - 24725 * q^51 + 61195 * q^52 + 49536 * q^53 - 156168 * q^54 - 34325 * q^55 - 54461 * q^56 - 7580 * q^57 - 95562 * q^58 + 44536 * q^59 + 7125 * q^60 - 49097 * q^61 - 25763 * q^62 - 3578 * q^63 - 18654 * q^64 - 15125 * q^65 - 201873 * q^66 + 788 * q^67 + 163845 * q^68 - 1587 * q^69 - 32925 * q^70 + 49521 * q^71 + 328503 * q^72 - 3760 * q^73 + 88170 * q^74 - 1875 * q^75 - 411465 * q^76 + 77728 * q^77 - 389832 * q^78 + 918 * q^79 - 94250 * q^80 + 121235 * q^81 - 227459 * q^82 + 99202 * q^83 + 336602 * q^84 - 62625 * q^85 + 24584 * q^86 - 38666 * q^87 - 201275 * q^88 - 141676 * q^89 - 199275 * q^90 - 223605 * q^91 + 94162 * q^92 + 51412 * q^93 - 354292 * q^94 + 2875 * q^95 - 592095 * q^96 + 28731 * q^97 - 149557 * q^98 + 237333 * q^99

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