LMFDB - Embedded newform 930.4.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,4,Mod(1,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	930.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$54.8717763053$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 494x^{3} - 3718x^{2} + 517x + 32927 $ x^5 - x^4 - 494x^3 - 3718x^2 + 517*x + 32927
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.61833$ of defining polynomial
Character	$\chi$	$=$	930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -28.8371 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -28.8371 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +52.6056 q^{11} +12.0000 q^{12} -66.6794 q^{13} -57.6742 q^{14} -15.0000 q^{15} +16.0000 q^{16} +109.766 q^{17} +18.0000 q^{18} +105.945 q^{19} -20.0000 q^{20} -86.5112 q^{21} +105.211 q^{22} -106.047 q^{23} +24.0000 q^{24} +25.0000 q^{25} -133.359 q^{26} +27.0000 q^{27} -115.348 q^{28} +121.013 q^{29} -30.0000 q^{30} -31.0000 q^{31} +32.0000 q^{32} +157.817 q^{33} +219.532 q^{34} +144.185 q^{35} +36.0000 q^{36} -102.294 q^{37} +211.890 q^{38} -200.038 q^{39} -40.0000 q^{40} +344.756 q^{41} -173.022 q^{42} -146.631 q^{43} +210.423 q^{44} -45.0000 q^{45} -212.094 q^{46} +430.162 q^{47} +48.0000 q^{48} +488.577 q^{49} +50.0000 q^{50} +329.297 q^{51} -266.717 q^{52} +404.874 q^{53} +54.0000 q^{54} -263.028 q^{55} -230.697 q^{56} +317.835 q^{57} +242.027 q^{58} +793.282 q^{59} -60.0000 q^{60} -224.692 q^{61} -62.0000 q^{62} -259.534 q^{63} +64.0000 q^{64} +333.397 q^{65} +315.634 q^{66} -340.100 q^{67} +439.063 q^{68} -318.141 q^{69} +288.371 q^{70} +573.325 q^{71} +72.0000 q^{72} -0.779768 q^{73} -204.588 q^{74} +75.0000 q^{75} +423.780 q^{76} -1516.99 q^{77} -400.076 q^{78} +587.734 q^{79} -80.0000 q^{80} +81.0000 q^{81} +689.513 q^{82} +1093.09 q^{83} -346.045 q^{84} -548.829 q^{85} -293.263 q^{86} +363.040 q^{87} +420.845 q^{88} -379.500 q^{89} -90.0000 q^{90} +1922.84 q^{91} -424.188 q^{92} -93.0000 q^{93} +860.324 q^{94} -529.725 q^{95} +96.0000 q^{96} -1372.01 q^{97} +977.154 q^{98} +473.451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 25 q^{5} + 30 q^{6} + 15 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 25 * q^5 + 30 * q^6 + 15 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 25 q^{5} + 30 q^{6} + 15 q^{7} + 40 q^{8} + 45 q^{9} - 50 q^{10} + 69 q^{11} + 60 q^{12} + 44 q^{13} + 30 q^{14} - 75 q^{15} + 80 q^{16} + 170 q^{17} + 90 q^{18} + 139 q^{19} - 100 q^{20} + 45 q^{21} + 138 q^{22} + 39 q^{23} + 120 q^{24} + 125 q^{25} + 88 q^{26} + 135 q^{27} + 60 q^{28} + 100 q^{29} - 150 q^{30} - 155 q^{31} + 160 q^{32} + 207 q^{33} + 340 q^{34} - 75 q^{35} + 180 q^{36} + 472 q^{37} + 278 q^{38} + 132 q^{39} - 200 q^{40} + 794 q^{41} + 90 q^{42} + 503 q^{43} + 276 q^{44} - 225 q^{45} + 78 q^{46} + 544 q^{47} + 240 q^{48} + 850 q^{49} + 250 q^{50} + 510 q^{51} + 176 q^{52} + 639 q^{53} + 270 q^{54} - 345 q^{55} + 120 q^{56} + 417 q^{57} + 200 q^{58} + 470 q^{59} - 300 q^{60} + 694 q^{61} - 310 q^{62} + 135 q^{63} + 320 q^{64} - 220 q^{65} + 414 q^{66} + 816 q^{67} + 680 q^{68} + 117 q^{69} - 150 q^{70} + 963 q^{71} + 360 q^{72} + 1547 q^{73} + 944 q^{74} + 375 q^{75} + 556 q^{76} - 347 q^{77} + 264 q^{78} + 1743 q^{79} - 400 q^{80} + 405 q^{81} + 1588 q^{82} + 1310 q^{83} + 180 q^{84} - 850 q^{85} + 1006 q^{86} + 300 q^{87} + 552 q^{88} - 547 q^{89} - 450 q^{90} + 2630 q^{91} + 156 q^{92} - 465 q^{93} + 1088 q^{94} - 695 q^{95} + 480 q^{96} + 936 q^{97} + 1700 q^{98} + 621 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 25 * q^5 + 30 * q^6 + 15 * q^7 + 40 * q^8 + 45 * q^9 - 50 * q^10 + 69 * q^11 + 60 * q^12 + 44 * q^13 + 30 * q^14 - 75 * q^15 + 80 * q^16 + 170 * q^17 + 90 * q^18 + 139 * q^19 - 100 * q^20 + 45 * q^21 + 138 * q^22 + 39 * q^23 + 120 * q^24 + 125 * q^25 + 88 * q^26 + 135 * q^27 + 60 * q^28 + 100 * q^29 - 150 * q^30 - 155 * q^31 + 160 * q^32 + 207 * q^33 + 340 * q^34 - 75 * q^35 + 180 * q^36 + 472 * q^37 + 278 * q^38 + 132 * q^39 - 200 * q^40 + 794 * q^41 + 90 * q^42 + 503 * q^43 + 276 * q^44 - 225 * q^45 + 78 * q^46 + 544 * q^47 + 240 * q^48 + 850 * q^49 + 250 * q^50 + 510 * q^51 + 176 * q^52 + 639 * q^53 + 270 * q^54 - 345 * q^55 + 120 * q^56 + 417 * q^57 + 200 * q^58 + 470 * q^59 - 300 * q^60 + 694 * q^61 - 310 * q^62 + 135 * q^63 + 320 * q^64 - 220 * q^65 + 414 * q^66 + 816 * q^67 + 680 * q^68 + 117 * q^69 - 150 * q^70 + 963 * q^71 + 360 * q^72 + 1547 * q^73 + 944 * q^74 + 375 * q^75 + 556 * q^76 - 347 * q^77 + 264 * q^78 + 1743 * q^79 - 400 * q^80 + 405 * q^81 + 1588 * q^82 + 1310 * q^83 + 180 * q^84 - 850 * q^85 + 1006 * q^86 + 300 * q^87 + 552 * q^88 - 547 * q^89 - 450 * q^90 + 2630 * q^91 + 156 * q^92 - 465 * q^93 + 1088 * q^94 - 695 * q^95 + 480 * q^96 + 936 * q^97 + 1700 * q^98 + 621 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	6.00000	0.408248
$7$	−28.8371	−1.55706	−0.778528	−	0.627610i	$-0.784033\pi$
$7$	−28.8371	−1.55706	−0.778528	+	0.627610i	$0.784033\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	52.6056	1.44193	0.720963	−	0.692973i	$-0.243700\pi$
$11$	52.6056	1.44193	0.720963	+	0.692973i	$0.243700\pi$
$12$	12.0000	0.288675
$13$	−66.6794	−1.42258	−0.711290	−	0.702899i	$-0.751889\pi$
$13$	−66.6794	−1.42258	−0.711290	+	0.702899i	$0.751889\pi$
$14$	−57.6742	−1.10100
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	109.766	1.56601	0.783003	−	0.622017i	$-0.213687\pi$
$17$	109.766	1.56601	0.783003	+	0.622017i	$0.213687\pi$
$18$	18.0000	0.235702
$19$	105.945	1.27924	0.639618	−	0.768693i	$-0.279093\pi$
$19$	105.945	1.27924	0.639618	+	0.768693i	$0.279093\pi$
$20$	−20.0000	−0.223607
$21$	−86.5112	−0.898967
$22$	105.211	1.01960
$23$	−106.047	−0.961407	−0.480703	−	0.876883i	$-0.659619\pi$
$23$	−106.047	−0.961407	−0.480703	+	0.876883i	$0.659619\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−133.359	−1.00592
$27$	27.0000	0.192450
$28$	−115.348	−0.778528
$29$	121.013	0.774883	0.387442	−	0.921894i	$-0.373359\pi$
$29$	121.013	0.774883	0.387442	+	0.921894i	$0.373359\pi$
$30$	−30.0000	−0.182574
$31$	−31.0000	−0.179605
$31$	−31.0000	−0.179605
$32$	32.0000	0.176777
$33$	157.817	0.832497
$34$	219.532	1.10733
$35$	144.185	0.696337
$36$	36.0000	0.166667
$37$	−102.294	−0.454514	−0.227257	−	0.973835i	$-0.572976\pi$
$37$	−102.294	−0.454514	−0.227257	+	0.973835i	$0.572976\pi$
$38$	211.890	0.904556
$39$	−200.038	−0.821326
$40$	−40.0000	−0.158114
$41$	344.756	1.31322	0.656608	−	0.754232i	$-0.271990\pi$
$41$	344.756	1.31322	0.656608	+	0.754232i	$0.271990\pi$
$42$	−173.022	−0.635665
$43$	−146.631	−0.520025	−0.260012	−	0.965605i	$-0.583727\pi$
$43$	−146.631	−0.520025	−0.260012	+	0.965605i	$0.583727\pi$
$44$	210.423	0.720963
$45$	−45.0000	−0.149071
$46$	−212.094	−0.679817
$47$	430.162	1.33501	0.667506	−	0.744604i	$-0.267362\pi$
$47$	430.162	1.33501	0.667506	+	0.744604i	$0.267362\pi$
$48$	48.0000	0.144338
$49$	488.577	1.42442
$50$	50.0000	0.141421
$51$	329.297	0.904134
$52$	−266.717	−0.711290
$53$	404.874	1.04931	0.524657	−	0.851314i	$-0.324194\pi$
$53$	404.874	1.04931	0.524657	+	0.851314i	$0.324194\pi$
$54$	54.0000	0.136083
$55$	−263.028	−0.644849
$56$	−230.697	−0.550502
$57$	317.835	0.738567
$58$	242.027	0.547925
$59$	793.282	1.75045	0.875225	−	0.483716i	$-0.160713\pi$
$59$	793.282	1.75045	0.875225	+	0.483716i	$0.160713\pi$
$60$	−60.0000	−0.129099
$61$	−224.692	−0.471621	−0.235810	−	0.971799i	$-0.575774\pi$
$61$	−224.692	−0.471621	−0.235810	+	0.971799i	$0.575774\pi$
$62$	−62.0000	−0.127000
$63$	−259.534	−0.519019
$64$	64.0000	0.125000
$65$	333.397	0.636197
$66$	315.634	0.588664
$67$	−340.100	−0.620148	−0.310074	−	0.950713i	$-0.600354\pi$
$67$	−340.100	−0.620148	−0.310074	+	0.950713i	$0.600354\pi$
$68$	439.063	0.783003
$69$	−318.141	−0.555068
$70$	288.371	0.492384
$71$	573.325	0.958326	0.479163	−	0.877726i	$-0.340940\pi$
$71$	573.325	0.958326	0.479163	+	0.877726i	$0.340940\pi$
$72$	72.0000	0.117851
$73$	−0.779768	−0.00125020	−0.000625102	−	1.00000i	$-0.500199\pi$
$73$	−0.779768	−0.00125020	−0.000625102		1.00000i	$0.500199\pi$
$74$	−204.588	−0.321390
$75$	75.0000	0.115470
$76$	423.780	0.639618
$77$	−1516.99	−2.24516
$78$	−400.076	−0.580765
$79$	587.734	0.837028	0.418514	−	0.908210i	$-0.362551\pi$
$79$	587.734	0.837028	0.418514	+	0.908210i	$0.362551\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	689.513	0.928584
$83$	1093.09	1.44557	0.722787	−	0.691071i	$-0.242861\pi$
$83$	1093.09	1.44557	0.722787	+	0.691071i	$0.242861\pi$
$84$	−346.045	−0.449483
$85$	−548.829	−0.700340
$86$	−293.263	−0.367713
$87$	363.040	0.447379
$88$	420.845	0.509798
$89$	−379.500	−0.451988	−0.225994	−	0.974129i	$-0.572563\pi$
$89$	−379.500	−0.451988	−0.225994	+	0.974129i	$0.572563\pi$
$90$	−90.0000	−0.105409
$91$	1922.84	2.21504
$92$	−424.188	−0.480703
$93$	−93.0000	−0.103695
$94$	860.324	0.943996
$95$	−529.725	−0.572091
$96$	96.0000	0.102062
$97$	−1372.01	−1.43615	−0.718073	−	0.695968i	$-0.754975\pi$
$97$	−1372.01	−1.43615	−0.718073	+	0.695968i	$0.754975\pi$
$98$	977.154	1.00722
$99$	473.451	0.480642
$100$	100.000	0.100000
$101$	1788.40	1.76190	0.880952	−	0.473206i	$-0.156903\pi$
$101$	1788.40	1.76190	0.880952	+	0.473206i	$0.156903\pi$
$102$	658.595	0.639320
$103$	−100.925	−0.0965480	−0.0482740	−	0.998834i	$-0.515372\pi$
$103$	−100.925	−0.0965480	−0.0482740	+	0.998834i	$0.515372\pi$
$104$	−533.435	−0.502958
$105$	432.556	0.402030
$106$	809.747	0.741977
$107$	−463.856	−0.419090	−0.209545	−	0.977799i	$-0.567198\pi$
$107$	−463.856	−0.419090	−0.209545	+	0.977799i	$0.567198\pi$
$108$	108.000	0.0962250
$109$	1528.74	1.34337	0.671683	−	0.740838i	$-0.265572\pi$
$109$	1528.74	1.34337	0.671683	+	0.740838i	$0.265572\pi$
$110$	−526.056	−0.455977
$111$	−306.882	−0.262414
$112$	−461.393	−0.389264
$113$	299.959	0.249714	0.124857	−	0.992175i	$-0.460153\pi$
$113$	299.959	0.249714	0.124857	+	0.992175i	$0.460153\pi$
$114$	635.670	0.522246
$115$	530.236	0.429954
$116$	484.053	0.387442
$117$	−600.114	−0.474193
$118$	1586.56	1.23776
$119$	−3165.33	−2.43836
$120$	−120.000	−0.0912871
$121$	1436.35	1.07915
$122$	−449.384	−0.333486
$123$	1034.27	0.758186
$124$	−124.000	−0.0898027
$125$	−125.000	−0.0894427
$126$	−519.067	−0.367002
$127$	−1819.32	−1.27117	−0.635584	−	0.772032i	$-0.719240\pi$
$127$	−1819.32	−1.27117	−0.635584	+	0.772032i	$0.719240\pi$
$128$	128.000	0.0883883
$129$	−439.894	−0.300237
$130$	666.794	0.449859
$131$	−1888.91	−1.25981	−0.629904	−	0.776673i	$-0.716906\pi$
$131$	−1888.91	−1.25981	−0.629904	+	0.776673i	$0.716906\pi$
$132$	631.268	0.416248
$133$	−3055.15	−1.99184
$134$	−680.201	−0.438511
$135$	−135.000	−0.0860663
$136$	878.126	0.553667
$137$	−1412.96	−0.881146	−0.440573	−	0.897717i	$-0.645225\pi$
$137$	−1412.96	−0.881146	−0.440573	+	0.897717i	$0.645225\pi$
$138$	−636.283	−0.392493
$139$	−452.838	−0.276325	−0.138163	−	0.990410i	$-0.544120\pi$
$139$	−452.838	−0.276325	−0.138163	+	0.990410i	$0.544120\pi$
$140$	576.742	0.348168
$141$	1290.49	0.770770
$142$	1146.65	0.677639
$143$	−3507.71	−2.05125
$144$	144.000	0.0833333
$145$	−605.067	−0.346538
$146$	−1.55954	−0.000884028 0
$147$	1465.73	0.822391
$148$	−409.175	−0.227257
$149$	−2738.84	−1.50587	−0.752935	−	0.658095i	$-0.771362\pi$
$149$	−2738.84	−1.50587	−0.752935	+	0.658095i	$0.771362\pi$
$150$	150.000	0.0816497
$151$	−1916.02	−1.03260	−0.516302	−	0.856407i	$-0.672692\pi$
$151$	−1916.02	−1.03260	−0.516302	+	0.856407i	$0.672692\pi$
$152$	847.561	0.452278
$153$	987.892	0.522002
$154$	−3033.99	−1.58757
$155$	155.000	0.0803219
$156$	−800.152	−0.410663
$157$	225.534	0.114647	0.0573235	−	0.998356i	$-0.481743\pi$
$157$	225.534	0.114647	0.0573235	+	0.998356i	$0.481743\pi$
$158$	1175.47	0.591868
$159$	1214.62	0.605822
$160$	−160.000	−0.0790569
$161$	3058.09	1.49696
$162$	162.000	0.0785674
$163$	766.233	0.368196	0.184098	−	0.982908i	$-0.441064\pi$
$163$	766.233	0.368196	0.184098	+	0.982908i	$0.441064\pi$
$164$	1379.03	0.656608
$165$	−789.084	−0.372304
$166$	2186.19	1.02218
$167$	1192.93	0.552764	0.276382	−	0.961048i	$-0.410864\pi$
$167$	1192.93	0.552764	0.276382	+	0.961048i	$0.410864\pi$
$168$	−692.090	−0.317833
$169$	2249.14	1.02373
$170$	−1097.66	−0.495215
$171$	953.506	0.426412
$172$	−586.525	−0.260012
$173$	661.196	0.290577	0.145288	−	0.989389i	$-0.453589\pi$
$173$	661.196	0.290577	0.145288	+	0.989389i	$0.453589\pi$
$174$	726.080	0.316345
$175$	−720.927	−0.311411
$176$	841.690	0.360482
$177$	2379.85	1.01062
$178$	−759.000	−0.319604
$179$	−216.314	−0.0903242	−0.0451621	−	0.998980i	$-0.514380\pi$
$179$	−216.314	−0.0903242	−0.0451621	+	0.998980i	$0.514380\pi$
$180$	−180.000	−0.0745356
$181$	−2109.82	−0.866417	−0.433208	−	0.901294i	$-0.642619\pi$
$181$	−2109.82	−0.866417	−0.433208	+	0.901294i	$0.642619\pi$
$182$	3845.68	1.56627
$183$	−674.076	−0.272290
$184$	−848.377	−0.339909
$185$	511.469	0.203265
$186$	−186.000	−0.0733236
$187$	5774.30	2.25807
$188$	1720.65	0.667506
$189$	−778.601	−0.299656
$190$	−1059.45	−0.404530
$191$	488.879	0.185204	0.0926022	−	0.995703i	$-0.470482\pi$
$191$	488.879	0.185204	0.0926022	+	0.995703i	$0.470482\pi$
$192$	192.000	0.0721688
$193$	−1956.26	−0.729609	−0.364805	−	0.931084i	$-0.618864\pi$
$193$	−1956.26	−0.729609	−0.364805	+	0.931084i	$0.618864\pi$
$194$	−2744.01	−1.01551
$195$	1000.19	0.367308
$196$	1954.31	0.712212
$197$	13.4628	0.00486895	0.00243448	−	0.999997i	$-0.499225\pi$
$197$	13.4628	0.00486895	0.00243448	+	0.999997i	$0.499225\pi$
$198$	946.901	0.339865
$199$	3994.18	1.42281	0.711406	−	0.702781i	$-0.248059\pi$
$199$	3994.18	1.42281	0.711406	+	0.702781i	$0.248059\pi$
$200$	200.000	0.0707107
$201$	−1020.30	−0.358042
$202$	3576.80	1.24585
$203$	−3489.67	−1.20654
$204$	1317.19	0.452067
$205$	−1723.78	−0.587288
$206$	−201.850	−0.0682697
$207$	−954.424	−0.320469
$208$	−1066.87	−0.355645
$209$	5573.31	1.84456
$210$	865.112	0.284278
$211$	−1979.17	−0.645743	−0.322871	−	0.946443i	$-0.604648\pi$
$211$	−1979.17	−0.645743	−0.322871	+	0.946443i	$0.604648\pi$
$212$	1619.49	0.524657
$213$	1719.98	0.553290
$214$	−927.712	−0.296341
$215$	733.157	0.232562
$216$	216.000	0.0680414
$217$	893.949	0.279655
$218$	3057.49	0.949904
$219$	−2.33930	−0.000721806 0
$220$	−1052.11	−0.322425
$221$	−7319.11	−2.22777
$222$	−613.763	−0.185554
$223$	6067.35	1.82197	0.910986	−	0.412437i	$-0.135322\pi$
$223$	6067.35	1.82197	0.910986	+	0.412437i	$0.135322\pi$
$224$	−922.787	−0.275251
$225$	225.000	0.0666667
$226$	599.917	0.176575
$227$	−3565.09	−1.04239	−0.521197	−	0.853436i	$-0.674514\pi$
$227$	−3565.09	−1.04239	−0.521197	+	0.853436i	$0.674514\pi$
$228$	1271.34	0.369283
$229$	1551.73	0.447780	0.223890	−	0.974614i	$-0.428124\pi$
$229$	1551.73	0.447780	0.223890	+	0.974614i	$0.428124\pi$
$230$	1060.47	0.304023
$231$	−4550.98	−1.29624
$232$	968.107	0.273963
$233$	6659.54	1.87245	0.936225	−	0.351401i	$-0.114295\pi$
$233$	6659.54	1.87245	0.936225	+	0.351401i	$0.114295\pi$
$234$	−1200.23	−0.335305
$235$	−2150.81	−0.597036
$236$	3173.13	0.875225
$237$	1763.20	0.483258
$238$	−6330.65	−1.72418
$239$	−3449.74	−0.933662	−0.466831	−	0.884347i	$-0.654604\pi$
$239$	−3449.74	−0.933662	−0.466831	+	0.884347i	$0.654604\pi$
$240$	−240.000	−0.0645497
$241$	1637.99	0.437809	0.218905	−	0.975746i	$-0.429752\pi$
$241$	1637.99	0.437809	0.218905	+	0.975746i	$0.429752\pi$
$242$	2872.70	0.763076
$243$	243.000	0.0641500
$244$	−898.768	−0.235810
$245$	−2442.89	−0.637021
$246$	2068.54	0.536118
$247$	−7064.35	−1.81981
$248$	−248.000	−0.0635001
$249$	3279.28	0.834602
$250$	−250.000	−0.0632456
$251$	−2598.48	−0.653445	−0.326722	−	0.945120i	$-0.605944\pi$
$251$	−2598.48	−0.653445	−0.326722	+	0.945120i	$0.605944\pi$
$252$	−1038.13	−0.259509
$253$	−5578.68	−1.38628
$254$	−3638.63	−0.898851
$255$	−1646.49	−0.404341
$256$	256.000	0.0625000
$257$	−5062.46	−1.22874	−0.614372	−	0.789016i	$-0.710591\pi$
$257$	−5062.46	−1.22874	−0.614372	+	0.789016i	$0.710591\pi$
$258$	−879.788	−0.212299
$259$	2949.86	0.707703
$260$	1333.59	0.318098
$261$	1089.12	0.258294
$262$	−3777.82	−0.890819
$263$	6814.95	1.59782	0.798912	−	0.601448i	$-0.205409\pi$
$263$	6814.95	1.59782	0.798912	+	0.601448i	$0.205409\pi$
$264$	1262.54	0.294332
$265$	−2024.37	−0.469268
$266$	−6110.29	−1.40844
$267$	−1138.50	−0.260955
$268$	−1360.40	−0.310074
$269$	−4628.08	−1.04899	−0.524497	−	0.851413i	$-0.675746\pi$
$269$	−4628.08	−1.04899	−0.524497	+	0.851413i	$0.675746\pi$
$270$	−270.000	−0.0608581
$271$	−6747.98	−1.51258	−0.756292	−	0.654234i	$-0.772991\pi$
$271$	−6747.98	−1.51258	−0.756292	+	0.654234i	$0.772991\pi$
$272$	1756.25	0.391502
$273$	5768.51	1.27885
$274$	−2825.91	−0.623064
$275$	1315.14	0.288385
$276$	−1272.57	−0.277534
$277$	7858.71	1.70464	0.852318	−	0.523023i	$-0.175196\pi$
$277$	7858.71	1.70464	0.852318	+	0.523023i	$0.175196\pi$
$278$	−905.675	−0.195391
$279$	−279.000	−0.0598684
$280$	1153.48	0.246192
$281$	−1082.75	−0.229862	−0.114931	−	0.993373i	$-0.536665\pi$
$281$	−1082.75	−0.229862	−0.114931	+	0.993373i	$0.536665\pi$
$282$	2580.97	0.545016
$283$	1749.65	0.367512	0.183756	−	0.982972i	$-0.441174\pi$
$283$	1749.65	0.367512	0.183756	+	0.982972i	$0.441174\pi$
$284$	2293.30	0.479163
$285$	−1589.18	−0.330297
$286$	−7015.42	−1.45046
$287$	−9941.76	−2.04475
$288$	288.000	0.0589256
$289$	7135.53	1.45238
$290$	−1210.13	−0.245040
$291$	−4116.02	−0.829159
$292$	−3.11907	−0.000625102 0
$293$	−6009.41	−1.19820	−0.599102	−	0.800673i	$-0.704475\pi$
$293$	−6009.41	−1.19820	−0.599102	+	0.800673i	$0.704475\pi$
$294$	2931.46	0.581518
$295$	−3966.41	−0.782825
$296$	−818.351	−0.160695
$297$	1420.35	0.277499
$298$	−5477.68	−1.06481
$299$	7071.15	1.36768
$300$	300.000	0.0577350
$301$	4228.42	0.809708
$302$	−3832.03	−0.730161
$303$	5365.20	1.01724
$304$	1695.12	0.319809
$305$	1123.46	0.210915
$306$	1975.78	0.369111
$307$	−1810.15	−0.336516	−0.168258	−	0.985743i	$-0.553814\pi$
$307$	−1810.15	−0.336516	−0.168258	+	0.985743i	$0.553814\pi$
$308$	−6067.97	−1.12258
$309$	−302.775	−0.0557420
$310$	310.000	0.0567962
$311$	1069.87	0.195069	0.0975347	−	0.995232i	$-0.468904\pi$
$311$	1069.87	0.195069	0.0975347	+	0.995232i	$0.468904\pi$
$312$	−1600.30	−0.290383
$313$	4753.46	0.858407	0.429204	−	0.903208i	$-0.358794\pi$
$313$	4753.46	0.858407	0.429204	+	0.903208i	$0.358794\pi$
$314$	451.069	0.0810677
$315$	1297.67	0.232112
$316$	2350.93	0.418514
$317$	7295.42	1.29259	0.646296	−	0.763087i	$-0.276317\pi$
$317$	7295.42	1.29259	0.646296	+	0.763087i	$0.276317\pi$
$318$	2429.24	0.428381
$319$	6365.98	1.11732
$320$	−320.000	−0.0559017
$321$	−1391.57	−0.241962
$322$	6116.18	1.05851
$323$	11629.1	2.00329
$324$	324.000	0.0555556
$325$	−1666.98	−0.284516
$326$	1532.47	0.260354
$327$	4586.23	0.775593
$328$	2758.05	0.464292
$329$	−12404.6	−2.07869
$330$	−1578.17	−0.263259
$331$	−2717.33	−0.451233	−0.225617	−	0.974216i	$-0.572440\pi$
$331$	−2717.33	−0.451233	−0.225617	+	0.974216i	$0.572440\pi$
$332$	4372.38	0.722787
$333$	−920.645	−0.151505
$334$	2385.86	0.390863
$335$	1700.50	0.277338
$336$	−1384.18	−0.224742
$337$	−4725.34	−0.763815	−0.381908	−	0.924200i	$-0.624733\pi$
$337$	−4725.34	−0.763815	−0.381908	+	0.924200i	$0.624733\pi$
$338$	4498.28	0.723887
$339$	899.876	0.144173
$340$	−2195.32	−0.350170
$341$	−1630.77	−0.258978
$342$	1907.01	0.301519
$343$	−4198.02	−0.660851
$344$	−1173.05	−0.183857
$345$	1590.71	0.248234
$346$	1322.39	0.205469
$347$	9314.28	1.44097	0.720485	−	0.693470i	$-0.243919\pi$
$347$	9314.28	1.44097	0.720485	+	0.693470i	$0.243919\pi$
$348$	1452.16	0.223690
$349$	−10650.6	−1.63356	−0.816780	−	0.576949i	$-0.804243\pi$
$349$	−10650.6	−1.63356	−0.816780	+	0.576949i	$0.804243\pi$
$350$	−1441.85	−0.220201
$351$	−1800.34	−0.273775
$352$	1683.38	0.254899
$353$	−6606.81	−0.996161	−0.498081	−	0.867131i	$-0.665962\pi$
$353$	−6606.81	−0.996161	−0.498081	+	0.867131i	$0.665962\pi$
$354$	4759.69	0.714618
$355$	−2866.63	−0.428577
$356$	−1518.00	−0.225994
$357$	−9495.98	−1.40779
$358$	−432.627	−0.0638689
$359$	8063.60	1.18546	0.592730	−	0.805401i	$-0.298050\pi$
$359$	8063.60	1.18546	0.592730	+	0.805401i	$0.298050\pi$
$360$	−360.000	−0.0527046
$361$	4365.36	0.636442
$362$	−4219.63	−0.612649
$363$	4309.06	0.623049
$364$	7691.35	1.10752
$365$	3.89884	0.000559108 0
$366$	−1348.15	−0.192538
$367$	−9858.96	−1.40227	−0.701135	−	0.713028i	$-0.747323\pi$
$367$	−9858.96	−1.40227	−0.701135	+	0.713028i	$0.747323\pi$
$368$	−1696.75	−0.240352
$369$	3102.81	0.437739
$370$	1022.94	0.143730
$371$	−11675.4	−1.63384
$372$	−372.000	−0.0518476
$373$	2429.85	0.337299	0.168650	−	0.985676i	$-0.446059\pi$
$373$	2429.85	0.337299	0.168650	+	0.985676i	$0.446059\pi$
$374$	11548.6	1.59669
$375$	−375.000	−0.0516398
$376$	3441.30	0.471998
$377$	−8069.09	−1.10233
$378$	−1557.20	−0.211888
$379$	−3863.37	−0.523610	−0.261805	−	0.965121i	$-0.584318\pi$
$379$	−3863.37	−0.523610	−0.261805	+	0.965121i	$0.584318\pi$
$380$	−2118.90	−0.286046
$381$	−5457.95	−0.733909
$382$	977.758	0.130959
$383$	−10702.3	−1.42784	−0.713919	−	0.700229i	$-0.753081\pi$
$383$	−10702.3	−1.42784	−0.713919	+	0.700229i	$0.753081\pi$
$384$	384.000	0.0510310
$385$	7584.96	1.00407
$386$	−3912.52	−0.515912
$387$	−1319.68	−0.173342
$388$	−5488.02	−0.718073
$389$	8102.07	1.05602	0.528009	−	0.849239i	$-0.322939\pi$
$389$	8102.07	1.05602	0.528009	+	0.849239i	$0.322939\pi$
$390$	2000.38	0.259726
$391$	−11640.3	−1.50557
$392$	3908.62	0.503610
$393$	−5666.73	−0.727350
$394$	26.9256	0.00344287
$395$	−2938.67	−0.374330
$396$	1893.80	0.240321
$397$	−5098.37	−0.644534	−0.322267	−	0.946649i	$-0.604445\pi$
$397$	−5098.37	−0.644534	−0.322267	+	0.946649i	$0.604445\pi$
$398$	7988.35	1.00608
$399$	−9165.44	−1.14999
$400$	400.000	0.0500000
$401$	6459.22	0.804385	0.402192	−	0.915555i	$-0.368248\pi$
$401$	6459.22	0.804385	0.402192	+	0.915555i	$0.368248\pi$
$402$	−2040.60	−0.253174
$403$	2067.06	0.255503
$404$	7153.59	0.880952
$405$	−405.000	−0.0496904
$406$	−6979.34	−0.853150
$407$	−5381.23	−0.655375
$408$	2634.38	0.319660
$409$	6864.48	0.829894	0.414947	−	0.909846i	$-0.363800\pi$
$409$	6864.48	0.829894	0.414947	+	0.909846i	$0.363800\pi$
$410$	−3447.56	−0.415276
$411$	−4238.87	−0.508730
$412$	−403.700	−0.0482740
$413$	−22876.0	−2.72555
$414$	−1908.85	−0.226606
$415$	−5465.47	−0.646480
$416$	−2133.74	−0.251479
$417$	−1358.51	−0.159536
$418$	11146.6	1.30430
$419$	−236.875	−0.0276184	−0.0138092	−	0.999905i	$-0.504396\pi$
$419$	−236.875	−0.0276184	−0.0138092	+	0.999905i	$0.504396\pi$
$420$	1730.22	0.201015
$421$	−4872.94	−0.564115	−0.282057	−	0.959398i	$-0.591017\pi$
$421$	−4872.94	−0.564115	−0.282057	+	0.959398i	$0.591017\pi$
$422$	−3958.34	−0.456609
$423$	3871.46	0.445004
$424$	3238.99	0.370989
$425$	2744.14	0.313201
$426$	3439.95	0.391235
$427$	6479.46	0.734340
$428$	−1855.42	−0.209545
$429$	−10523.1	−1.18429
$430$	1466.31	0.164446
$431$	−12827.1	−1.43355	−0.716775	−	0.697304i	$-0.754383\pi$
$431$	−12827.1	−1.43355	−0.716775	+	0.697304i	$0.754383\pi$
$432$	432.000	0.0481125
$433$	−6024.80	−0.668668	−0.334334	−	0.942455i	$-0.608511\pi$
$433$	−6024.80	−0.668668	−0.334334	+	0.942455i	$0.608511\pi$
$434$	1787.90	0.197746
$435$	−1815.20	−0.200074
$436$	6114.97	0.671683
$437$	−11235.2	−1.22987
$438$	−4.67861	−0.000510394 0
$439$	−8440.05	−0.917589	−0.458795	−	0.888542i	$-0.651719\pi$
$439$	−8440.05	−0.917589	−0.458795	+	0.888542i	$0.651719\pi$
$440$	−2104.23	−0.227989
$441$	4397.19	0.474808
$442$	−14638.2	−1.57527
$443$	14852.0	1.59287	0.796435	−	0.604724i	$-0.206716\pi$
$443$	14852.0	1.59287	0.796435	+	0.604724i	$0.206716\pi$
$444$	−1227.53	−0.131207
$445$	1897.50	0.202135
$446$	12134.7	1.28833
$447$	−8216.52	−0.869414
$448$	−1845.57	−0.194632
$449$	1219.56	0.128184	0.0640922	−	0.997944i	$-0.479585\pi$
$449$	1219.56	0.128184	0.0640922	+	0.997944i	$0.479585\pi$
$450$	450.000	0.0471405
$451$	18136.1	1.89356
$452$	1199.83	0.124857
$453$	−5748.05	−0.596174
$454$	−7130.19	−0.737084
$455$	−9614.19	−0.990594
$456$	2542.68	0.261123
$457$	9640.80	0.986822	0.493411	−	0.869796i	$-0.335750\pi$
$457$	9640.80	0.986822	0.493411	+	0.869796i	$0.335750\pi$
$458$	3103.47	0.316628
$459$	2963.68	0.301378
$460$	2120.94	0.214977
$461$	−8106.97	−0.819044	−0.409522	−	0.912300i	$-0.634304\pi$
$461$	−8106.97	−0.819044	−0.409522	+	0.912300i	$0.634304\pi$
$462$	−9101.96	−0.916583
$463$	16852.3	1.69156	0.845781	−	0.533530i	$-0.179135\pi$
$463$	16852.3	1.69156	0.845781	+	0.533530i	$0.179135\pi$
$464$	1936.21	0.193721
$465$	465.000	0.0463739
$466$	13319.1	1.32402
$467$	3038.59	0.301091	0.150545	−	0.988603i	$-0.451897\pi$
$467$	3038.59	0.301091	0.150545	+	0.988603i	$0.451897\pi$
$468$	−2400.46	−0.237097
$469$	9807.50	0.965604
$470$	−4301.62	−0.422168
$471$	676.603	0.0661915
$472$	6346.26	0.618878
$473$	−7713.63	−0.749838
$474$	3526.40	0.341715
$475$	2648.63	0.255847
$476$	−12661.3	−1.21918
$477$	3643.86	0.349771
$478$	−6899.48	−0.660199
$479$	−1898.49	−0.181095	−0.0905473	−	0.995892i	$-0.528862\pi$
$479$	−1898.49	−0.181095	−0.0905473	+	0.995892i	$0.528862\pi$
$480$	−480.000	−0.0456435
$481$	6820.89	0.646582
$482$	3275.97	0.309578
$483$	9174.27	0.864273
$484$	5745.41	0.539576
$485$	6860.03	0.642264
$486$	486.000	0.0453609
$487$	12875.8	1.19807	0.599033	−	0.800724i	$-0.295552\pi$
$487$	12875.8	1.19807	0.599033	+	0.800724i	$0.295552\pi$
$488$	−1797.54	−0.166743
$489$	2298.70	0.212578
$490$	−4885.77	−0.450442
$491$	−17687.0	−1.62567	−0.812836	−	0.582492i	$-0.802078\pi$
$491$	−17687.0	−1.62567	−0.812836	+	0.582492i	$0.802078\pi$
$492$	4137.08	0.379093
$493$	13283.1	1.21347
$494$	−14128.7	−1.28680
$495$	−2367.25	−0.214950
$496$	−496.000	−0.0449013
$497$	−16533.0	−1.49217
$498$	6558.56	0.590153
$499$	−8895.46	−0.798027	−0.399014	−	0.916945i	$-0.630647\pi$
$499$	−8895.46	−0.798027	−0.399014	+	0.916945i	$0.630647\pi$
$500$	−500.000	−0.0447214
$501$	3578.79	0.319139
$502$	−5196.96	−0.462055
$503$	21609.8	1.91557	0.957785	−	0.287486i	$-0.0928196\pi$
$503$	21609.8	1.91557	0.957785	+	0.287486i	$0.0928196\pi$
$504$	−2076.27	−0.183501
$505$	−8941.99	−0.787947
$506$	−11157.4	−0.980247
$507$	6747.41	0.591052
$508$	−7277.27	−0.635584
$509$	−21774.0	−1.89610	−0.948049	−	0.318124i	$-0.896947\pi$
$509$	−21774.0	−1.89610	−0.948049	+	0.318124i	$0.896947\pi$
$510$	−3292.97	−0.285912
$511$	22.4862	0.00194664
$512$	512.000	0.0441942
$513$	2860.52	0.246189
$514$	−10124.9	−0.868853
$515$	504.625	0.0431776
$516$	−1759.58	−0.150118
$517$	22628.9	1.92499
$518$	5899.71	0.500422
$519$	1983.59	0.167765
$520$	2667.17	0.224930
$521$	10551.4	0.887268	0.443634	−	0.896208i	$-0.353689\pi$
$521$	10551.4	0.887268	0.443634	+	0.896208i	$0.353689\pi$
$522$	2178.24	0.182642
$523$	−14726.6	−1.23126	−0.615632	−	0.788034i	$-0.711099\pi$
$523$	−14726.6	−1.23126	−0.615632	+	0.788034i	$0.711099\pi$
$524$	−7555.64	−0.629904
$525$	−2162.78	−0.179793
$526$	13629.9	1.12983
$527$	−3402.74	−0.281263
$528$	2525.07	0.208124
$529$	−921.008	−0.0756972
$530$	−4048.74	−0.331822
$531$	7139.54	0.583484
$532$	−12220.6	−0.995920
$533$	−22988.1	−1.86815
$534$	−2277.00	−0.184523
$535$	2319.28	0.187423
$536$	−2720.80	−0.219255
$537$	−648.941	−0.0521487
$538$	−9256.16	−0.741750
$539$	25701.9	2.05391
$540$	−540.000	−0.0430331
$541$	11546.6	0.917608	0.458804	−	0.888537i	$-0.348278\pi$
$541$	11546.6	0.917608	0.458804	+	0.888537i	$0.348278\pi$
$542$	−13496.0	−1.06956
$543$	−6329.45	−0.500226
$544$	3512.51	0.276834
$545$	−7643.71	−0.600772
$546$	11537.0	0.904284
$547$	−19494.9	−1.52384	−0.761921	−	0.647670i	$-0.775744\pi$
$547$	−19494.9	−1.52384	−0.761921	+	0.647670i	$0.775744\pi$
$548$	−5651.82	−0.440573
$549$	−2022.23	−0.157207
$550$	2630.28	0.203919
$551$	12820.8	0.991258
$552$	−2545.13	−0.196246
$553$	−16948.5	−1.30330
$554$	15717.4	1.20536
$555$	1534.41	0.117355
$556$	−1811.35	−0.138163
$557$	443.939	0.0337708	0.0168854	−	0.999857i	$-0.494625\pi$
$557$	443.939	0.0337708	0.0168854	+	0.999857i	$0.494625\pi$
$558$	−558.000	−0.0423334
$559$	9777.29	0.739777
$560$	2306.97	0.174084
$561$	17322.9	1.30370
$562$	−2165.50	−0.162537
$563$	3079.57	0.230530	0.115265	−	0.993335i	$-0.463228\pi$
$563$	3079.57	0.230530	0.115265	+	0.993335i	$0.463228\pi$
$564$	5161.94	0.385385
$565$	−1499.79	−0.111676
$566$	3499.30	0.259870
$567$	−2335.80	−0.173006
$568$	4586.60	0.338820
$569$	13901.3	1.02421	0.512104	−	0.858923i	$-0.328866\pi$
$569$	13901.3	1.02421	0.512104	+	0.858923i	$0.328866\pi$
$570$	−3178.35	−0.233555
$571$	8518.74	0.624340	0.312170	−	0.950026i	$-0.398944\pi$
$571$	8518.74	0.624340	0.312170	+	0.950026i	$0.398944\pi$
$572$	−14030.8	−1.02563
$573$	1466.64	0.106928
$574$	−19883.5	−1.44586
$575$	−2651.18	−0.192281
$576$	576.000	0.0416667
$577$	9622.69	0.694277	0.347138	−	0.937814i	$-0.387153\pi$
$577$	9622.69	0.694277	0.347138	+	0.937814i	$0.387153\pi$
$578$	14271.1	1.02699
$579$	−5868.77	−0.421240
$580$	−2420.27	−0.173269
$581$	−31521.6	−2.25084
$582$	−8232.03	−0.586304
$583$	21298.6	1.51303
$584$	−6.23814	−0.000442014 0
$585$	3000.57	0.212066
$586$	−12018.8	−0.847258
$587$	−25865.3	−1.81870	−0.909349	−	0.416034i	$-0.863420\pi$
$587$	−25865.3	−1.81870	−0.909349	+	0.416034i	$0.863420\pi$
$588$	5862.93	0.411196
$589$	−3284.30	−0.229757
$590$	−7932.82	−0.553541
$591$	40.3884	0.00281109
$592$	−1636.70	−0.113628
$593$	−14460.2	−1.00136	−0.500682	−	0.865632i	$-0.666917\pi$
$593$	−14460.2	−1.00136	−0.500682	+	0.865632i	$0.666917\pi$
$594$	2840.70	0.196221
$595$	15826.6	1.09047
$596$	−10955.4	−0.752935
$597$	11982.5	0.821461
$598$	14142.3	0.967094
$599$	−8395.04	−0.572641	−0.286320	−	0.958134i	$-0.592432\pi$
$599$	−8395.04	−0.572641	−0.286320	+	0.958134i	$0.592432\pi$
$600$	600.000	0.0408248
$601$	13250.7	0.899343	0.449672	−	0.893194i	$-0.351541\pi$
$601$	13250.7	0.899343	0.449672	+	0.893194i	$0.351541\pi$
$602$	8456.84	0.572550
$603$	−3060.90	−0.206716
$604$	−7664.06	−0.516302
$605$	−7181.76	−0.482612
$606$	10730.4	0.719294
$607$	−21942.3	−1.46724	−0.733618	−	0.679563i	$-0.762170\pi$
$607$	−21942.3	−1.46724	−0.733618	+	0.679563i	$0.762170\pi$
$608$	3390.24	0.226139
$609$	−10469.0	−0.696594
$610$	2246.92	0.149140
$611$	−28682.9	−1.89916
$612$	3951.57	0.261001
$613$	13134.1	0.865386	0.432693	−	0.901541i	$-0.357563\pi$
$613$	13134.1	0.865386	0.432693	+	0.901541i	$0.357563\pi$
$614$	−3620.29	−0.237953
$615$	−5171.34	−0.339071
$616$	−12135.9	−0.793784
$617$	−1008.68	−0.0658150	−0.0329075	−	0.999458i	$-0.510477\pi$
$617$	−1008.68	−0.0658150	−0.0329075	+	0.999458i	$0.510477\pi$
$618$	−605.550	−0.0394155
$619$	−340.692	−0.0221221	−0.0110610	−	0.999939i	$-0.503521\pi$
$619$	−340.692	−0.0221221	−0.0110610	+	0.999939i	$0.503521\pi$
$620$	620.000	0.0401610
$621$	−2863.27	−0.185023
$622$	2139.73	0.137935
$623$	10943.7	0.703771
$624$	−3200.61	−0.205332
$625$	625.000	0.0400000
$626$	9506.92	0.606986
$627$	16719.9	1.06496
$628$	902.137	0.0573235
$629$	−11228.4	−0.711771
$630$	2595.34	0.164128
$631$	−28409.9	−1.79236	−0.896182	−	0.443687i	$-0.853670\pi$
$631$	−28409.9	−1.79236	−0.896182	+	0.443687i	$0.853670\pi$
$632$	4701.87	0.295934
$633$	−5937.51	−0.372820
$634$	14590.8	0.914001
$635$	9096.58	0.568483
$636$	4858.48	0.302911
$637$	−32578.0	−2.02635
$638$	12732.0	0.790068
$639$	5159.93	0.319442
$640$	−640.000	−0.0395285
$641$	1243.95	0.0766506	0.0383253	−	0.999265i	$-0.487798\pi$
$641$	1243.95	0.0766506	0.0383253	+	0.999265i	$0.487798\pi$
$642$	−2783.13	−0.171093
$643$	−20706.3	−1.26995	−0.634973	−	0.772534i	$-0.718989\pi$
$643$	−20706.3	−1.26995	−0.634973	+	0.772534i	$0.718989\pi$
$644$	12232.4	0.748482
$645$	2199.47	0.134270
$646$	23258.3	1.41654
$647$	27665.2	1.68104	0.840519	−	0.541782i	$-0.182250\pi$
$647$	27665.2	1.68104	0.840519	+	0.541782i	$0.182250\pi$
$648$	648.000	0.0392837
$649$	41731.1	2.52402
$650$	−3333.97	−0.201183
$651$	2681.85	0.161459
$652$	3064.93	0.184098
$653$	25685.5	1.53928	0.769641	−	0.638477i	$-0.220435\pi$
$653$	25685.5	1.53928	0.769641	+	0.638477i	$0.220435\pi$
$654$	9172.46	0.548427
$655$	9444.55	0.563403
$656$	5516.10	0.328304
$657$	−7.01791	−0.000416735 0
$658$	−24809.2	−1.46985
$659$	11995.7	0.709083	0.354541	−	0.935040i	$-0.384637\pi$
$659$	11995.7	0.709083	0.354541	+	0.935040i	$0.384637\pi$
$660$	−3156.34	−0.186152
$661$	4481.64	0.263715	0.131857	−	0.991269i	$-0.457906\pi$
$661$	4481.64	0.263715	0.131857	+	0.991269i	$0.457906\pi$
$662$	−5434.67	−0.319070
$663$	−21957.3	−1.28620
$664$	8744.75	0.511088
$665$	15275.7	0.890778
$666$	−1841.29	−0.107130
$667$	−12833.1	−0.744978
$668$	4771.72	0.276382
$669$	18202.1	1.05192
$670$	3401.00	0.196108
$671$	−11820.1	−0.680043
$672$	−2768.36	−0.158916
$673$	11569.2	0.662643	0.331322	−	0.943518i	$-0.392505\pi$
$673$	11569.2	0.662643	0.331322	+	0.943518i	$0.392505\pi$
$674$	−9450.68	−0.540099
$675$	675.000	0.0384900
$676$	8996.55	0.511866
$677$	−14475.2	−0.821754	−0.410877	−	0.911691i	$-0.634777\pi$
$677$	−14475.2	−0.821754	−0.410877	+	0.911691i	$0.634777\pi$
$678$	1799.75	0.101945
$679$	39564.6	2.23616
$680$	−4390.63	−0.247607
$681$	−10695.3	−0.601827
$682$	−3261.55	−0.183125
$683$	783.751	0.0439083	0.0219542	−	0.999759i	$-0.493011\pi$
$683$	783.751	0.0439083	0.0219542	+	0.999759i	$0.493011\pi$
$684$	3814.02	0.213206
$685$	7064.78	0.394060
$686$	−8396.04	−0.467292
$687$	4655.20	0.258526
$688$	−2346.10	−0.130006
$689$	−26996.7	−1.49273
$690$	3181.41	0.175528
$691$	8243.91	0.453854	0.226927	−	0.973912i	$-0.427132\pi$
$691$	8243.91	0.453854	0.226927	+	0.973912i	$0.427132\pi$
$692$	2644.78	0.145288
$693$	−13652.9	−0.748387
$694$	18628.6	1.01892
$695$	2264.19	0.123576
$696$	2904.32	0.158172
$697$	37842.4	2.05651
$698$	−21301.2	−1.15510
$699$	19978.6	1.08106
$700$	−2883.71	−0.155706
$701$	18361.6	0.989312	0.494656	−	0.869089i	$-0.335294\pi$
$701$	18361.6	0.989312	0.494656	+	0.869089i	$0.335294\pi$
$702$	−3600.69	−0.193588
$703$	−10837.5	−0.581430
$704$	3366.76	0.180241
$705$	−6452.43	−0.344699
$706$	−13213.6	−0.704392
$707$	−51572.2	−2.74338
$708$	9519.39	0.505312
$709$	7416.10	0.392832	0.196416	−	0.980521i	$-0.437070\pi$
$709$	7416.10	0.392832	0.196416	+	0.980521i	$0.437070\pi$
$710$	−5733.25	−0.303049
$711$	5289.60	0.279009
$712$	−3036.00	−0.159802
$713$	3287.46	0.172674
$714$	−18992.0	−0.995456
$715$	17538.5	0.917349
$716$	−865.255	−0.0451621
$717$	−10349.2	−0.539050
$718$	16127.2	0.838247
$719$	6362.17	0.329998	0.164999	−	0.986294i	$-0.447238\pi$
$719$	6362.17	0.329998	0.164999	+	0.986294i	$0.447238\pi$
$720$	−720.000	−0.0372678
$721$	2910.38	0.150331
$722$	8730.72	0.450033
$723$	4913.96	0.252769
$724$	−8439.27	−0.433208
$725$	3025.33	0.154977
$726$	8618.11	0.440562
$727$	−28300.2	−1.44374	−0.721868	−	0.692031i	$-0.756716\pi$
$727$	−28300.2	−1.44374	−0.721868	+	0.692031i	$0.756716\pi$
$728$	15382.7	0.783133
$729$	729.000	0.0370370
$730$	7.79768	0.000395349 0
$731$	−16095.1	−0.814363
$732$	−2696.30	−0.136145
$733$	34312.8	1.72902	0.864510	−	0.502615i	$-0.167629\pi$
$733$	34312.8	1.72902	0.864510	+	0.502615i	$0.167629\pi$
$734$	−19717.9	−0.991555
$735$	−7328.66	−0.367784
$736$	−3393.51	−0.169954
$737$	−17891.2	−0.894207
$738$	6205.61	0.309528
$739$	15245.5	0.758883	0.379442	−	0.925216i	$-0.376116\pi$
$739$	15245.5	0.758883	0.379442	+	0.925216i	$0.376116\pi$
$740$	2045.88	0.101632
$741$	−21193.0	−1.05067
$742$	−23350.7	−1.15530
$743$	35079.1	1.73207	0.866035	−	0.499983i	$-0.166660\pi$
$743$	35079.1	1.73207	0.866035	+	0.499983i	$0.166660\pi$
$744$	−744.000	−0.0366618
$745$	13694.2	0.673445
$746$	4859.69	0.238507
$747$	9837.84	0.481858
$748$	23097.2	1.12903
$749$	13376.2	0.652547
$750$	−750.000	−0.0365148
$751$	18759.2	0.911497	0.455748	−	0.890109i	$-0.349372\pi$
$751$	18759.2	0.911497	0.455748	+	0.890109i	$0.349372\pi$
$752$	6882.59	0.333753
$753$	−7795.44	−0.377267
$754$	−16138.2	−0.779467
$755$	9580.08	0.461794
$756$	−3114.40	−0.149828
$757$	−3716.01	−0.178416	−0.0892078	−	0.996013i	$-0.528434\pi$
$757$	−3716.01	−0.178416	−0.0892078	+	0.996013i	$0.528434\pi$
$758$	−7726.74	−0.370248
$759$	−16736.0	−0.800368
$760$	−4237.80	−0.202265
$761$	21491.4	1.02374	0.511868	−	0.859064i	$-0.328954\pi$
$761$	21491.4	1.02374	0.511868	+	0.859064i	$0.328954\pi$
$762$	−10915.9	−0.518952
$763$	−44084.5	−2.09170
$764$	1955.52	0.0926022
$765$	−4939.46	−0.233447
$766$	−21404.6	−1.00963
$767$	−52895.6	−2.49015
$768$	768.000	0.0360844
$769$	−6751.56	−0.316603	−0.158301	−	0.987391i	$-0.550602\pi$
$769$	−6751.56	−0.316603	−0.158301	+	0.987391i	$0.550602\pi$
$770$	15169.9	0.709982
$771$	−15187.4	−0.709416
$772$	−7825.03	−0.364805
$773$	−4588.82	−0.213517	−0.106758	−	0.994285i	$-0.534047\pi$
$773$	−4588.82	−0.213517	−0.106758	+	0.994285i	$0.534047\pi$
$774$	−2639.36	−0.122571
$775$	−775.000	−0.0359211
$776$	−10976.0	−0.507754
$777$	8849.57	0.408593
$778$	16204.1	0.746718
$779$	36525.2	1.67991
$780$	4000.76	0.183654
$781$	30160.1	1.38184
$782$	−23280.7	−1.06460
$783$	3267.36	0.149126
$784$	7817.23	0.356106
$785$	−1127.67	−0.0512717
$786$	−11333.5	−0.514314
$787$	8086.82	0.366282	0.183141	−	0.983087i	$-0.441373\pi$
$787$	8086.82	0.366282	0.183141	+	0.983087i	$0.441373\pi$
$788$	53.8511	0.00243448
$789$	20444.8	0.922504
$790$	−5877.34	−0.264691
$791$	−8649.93	−0.388819
$792$	3787.61	0.169933
$793$	14982.3	0.670918
$794$	−10196.7	−0.455754
$795$	−6073.10	−0.270932
$796$	15976.7	0.711406
$797$	24318.5	1.08081	0.540406	−	0.841405i	$-0.318271\pi$
$797$	24318.5	1.08081	0.540406	+	0.841405i	$0.318271\pi$
$798$	−18330.9	−0.813165
$799$	47217.1	2.09064
$800$	800.000	0.0353553
$801$	−3415.50	−0.150663
$802$	12918.4	0.568786
$803$	−41.0202	−0.00180270
$804$	−4081.21	−0.179021
$805$	−15290.4	−0.669463
$806$	4134.12	0.180668
$807$	−13884.2	−0.605636
$808$	14307.2	0.622927
$809$	12033.0	0.522939	0.261469	−	0.965212i	$-0.415793\pi$
$809$	12033.0	0.522939	0.261469	+	0.965212i	$0.415793\pi$
$810$	−810.000	−0.0351364
$811$	−35383.9	−1.53205	−0.766027	−	0.642808i	$-0.777769\pi$
$811$	−35383.9	−1.53205	−0.766027	+	0.642808i	$0.777769\pi$
$812$	−13958.7	−0.603268
$813$	−20243.9	−0.873291
$814$	−10762.5	−0.463420
$815$	−3831.16	−0.164662
$816$	5268.76	0.226034
$817$	−15534.9	−0.665234
$818$	13729.0	0.586823
$819$	17305.5	0.738345
$820$	−6895.13	−0.293644
$821$	43881.1	1.86536	0.932681	−	0.360702i	$-0.117463\pi$
$821$	43881.1	1.86536	0.932681	+	0.360702i	$0.117463\pi$
$822$	−8477.74	−0.359726
$823$	−33183.2	−1.40546	−0.702729	−	0.711457i	$-0.748036\pi$
$823$	−33183.2	−1.40546	−0.702729	+	0.711457i	$0.748036\pi$
$824$	−807.400	−0.0341349
$825$	3945.42	0.166499
$826$	−45751.9	−1.92725
$827$	25748.4	1.08266	0.541329	−	0.840811i	$-0.317921\pi$
$827$	25748.4	1.08266	0.541329	+	0.840811i	$0.317921\pi$
$828$	−3817.70	−0.160234
$829$	27884.3	1.16823	0.584114	−	0.811672i	$-0.301442\pi$
$829$	27884.3	1.16823	0.584114	+	0.811672i	$0.301442\pi$
$830$	−10930.9	−0.457131
$831$	23576.1	0.984173
$832$	−4267.48	−0.177822
$833$	53629.1	2.23066
$834$	−2717.03	−0.112809
$835$	−5964.65	−0.247204
$836$	22293.2	0.922282
$837$	−837.000	−0.0345651
$838$	−473.750	−0.0195291
$839$	7740.35	0.318506	0.159253	−	0.987238i	$-0.449091\pi$
$839$	7740.35	0.318506	0.159253	+	0.987238i	$0.449091\pi$
$840$	3460.45	0.142139
$841$	−9744.77	−0.399556
$842$	−9745.87	−0.398889
$843$	−3248.24	−0.132711
$844$	−7916.68	−0.322871
$845$	−11245.7	−0.457827
$846$	7742.92	0.314665
$847$	−41420.2	−1.68030
$848$	6477.98	0.262329
$849$	5248.95	0.212183
$850$	5488.29	0.221467
$851$	10848.0	0.436972
$852$	6879.90	0.276645
$853$	−38375.2	−1.54038	−0.770189	−	0.637816i	$-0.779838\pi$
$853$	−38375.2	−1.54038	−0.770189	+	0.637816i	$0.779838\pi$
$854$	12958.9	0.519257
$855$	−4767.53	−0.190697
$856$	−3710.85	−0.148171
$857$	20601.3	0.821152	0.410576	−	0.911826i	$-0.365328\pi$
$857$	20601.3	0.821152	0.410576	+	0.911826i	$0.365328\pi$
$858$	−21046.3	−0.837421
$859$	−13398.8	−0.532200	−0.266100	−	0.963945i	$-0.585735\pi$
$859$	−13398.8	−0.532200	−0.266100	+	0.963945i	$0.585735\pi$
$860$	2932.63	0.116281
$861$	−29825.3	−1.18054
$862$	−25654.2	−1.01367
$863$	−36238.4	−1.42940	−0.714699	−	0.699432i	$-0.753436\pi$
$863$	−36238.4	−1.42940	−0.714699	+	0.699432i	$0.753436\pi$
$864$	864.000	0.0340207
$865$	−3305.98	−0.129950
$866$	−12049.6	−0.472820
$867$	21406.6	0.838531
$868$	3575.80	0.139828
$869$	30918.1	1.20693
$870$	−3630.40	−0.141474
$871$	22677.7	0.882209
$872$	12229.9	0.474952
$873$	−12348.1	−0.478715
$874$	−22470.3	−0.869646
$875$	3604.63	0.139267
$876$	−9.35721	−0.000360903 0
$877$	14544.6	0.560020	0.280010	−	0.959997i	$-0.409662\pi$
$877$	14544.6	0.560020	0.280010	+	0.959997i	$0.409662\pi$
$878$	−16880.1	−0.648834
$879$	−18028.2	−0.691783
$880$	−4208.45	−0.161212
$881$	−40281.3	−1.54042	−0.770210	−	0.637791i	$-0.779849\pi$
$881$	−40281.3	−1.54042	−0.770210	+	0.637791i	$0.779849\pi$
$882$	8794.39	0.335740
$883$	−44120.7	−1.68152	−0.840759	−	0.541409i	$-0.817891\pi$
$883$	−44120.7	−1.68152	−0.840759	+	0.541409i	$0.817891\pi$
$884$	−29276.5	−1.11388
$885$	−11899.2	−0.451964
$886$	29704.1	1.12633
$887$	11486.4	0.434810	0.217405	−	0.976082i	$-0.430241\pi$
$887$	11486.4	0.434810	0.217405	+	0.976082i	$0.430241\pi$
$888$	−2455.05	−0.0927772
$889$	52463.8	1.97928
$890$	3795.00	0.142931
$891$	4261.06	0.160214
$892$	24269.4	0.910986
$893$	45573.5	1.70779
$894$	−16433.0	−0.614769
$895$	1081.57	0.0403942
$896$	−3691.15	−0.137626
$897$	21213.5	0.789629
$898$	2439.13	0.0906400
$899$	−3751.41	−0.139173
$900$	900.000	0.0333333
$901$	44441.3	1.64323
$902$	36272.2	1.33895
$903$	12685.3	0.467485
$904$	2399.67	0.0882874
$905$	10549.1	0.387473
$906$	−11496.1	−0.421559
$907$	−3280.55	−0.120098	−0.0600490	−	0.998195i	$-0.519126\pi$
$907$	−3280.55	−0.120098	−0.0600490	+	0.998195i	$0.519126\pi$
$908$	−14260.4	−0.521197
$909$	16095.6	0.587301
$910$	−19228.4	−0.700456
$911$	−2604.46	−0.0947198	−0.0473599	−	0.998878i	$-0.515081\pi$
$911$	−2604.46	−0.0947198	−0.0473599	+	0.998878i	$0.515081\pi$
$912$	5085.36	0.184642
$913$	57502.9	2.08441
$914$	19281.6	0.697788
$915$	3370.38	0.121772
$916$	6206.94	0.223890
$917$	54470.6	1.96159
$918$	5927.35	0.213107
$919$	6364.72	0.228458	0.114229	−	0.993454i	$-0.463560\pi$
$919$	6364.72	0.228458	0.114229	+	0.993454i	$0.463560\pi$
$920$	4241.88	0.152012
$921$	−5430.44	−0.194288
$922$	−16213.9	−0.579152
$923$	−38229.0	−1.36330
$924$	−18203.9	−0.648122
$925$	−2557.35	−0.0909027
$926$	33704.6	1.19611
$927$	−908.326	−0.0321827
$928$	3872.43	0.136981
$929$	31455.8	1.11090	0.555452	−	0.831549i	$-0.312545\pi$
$929$	31455.8	1.11090	0.555452	+	0.831549i	$0.312545\pi$
$930$	930.000	0.0327913
$931$	51762.3	1.82217
$932$	26638.1	0.936225
$933$	3209.60	0.112623
$934$	6077.19	0.212903
$935$	−28871.5	−1.00984
$936$	−4800.91	−0.167653
$937$	−26539.5	−0.925302	−0.462651	−	0.886540i	$-0.653102\pi$
$937$	−26539.5	−0.925302	−0.462651	+	0.886540i	$0.653102\pi$
$938$	19615.0	0.682785
$939$	14260.4	0.495602
$940$	−8603.24	−0.298518
$941$	−451.141	−0.0156289	−0.00781445	−	0.999969i	$-0.502487\pi$
$941$	−451.141	−0.0156289	−0.00781445	+	0.999969i	$0.502487\pi$
$942$	1353.21	0.0468045
$943$	−36560.4	−1.26254
$944$	12692.5	0.437613
$945$	3893.01	0.134010
$946$	−15427.3	−0.530215
$947$	−50568.0	−1.73520	−0.867602	−	0.497259i	$-0.834340\pi$
$947$	−50568.0	−1.73520	−0.867602	+	0.497259i	$0.834340\pi$
$948$	7052.80	0.241629
$949$	51.9944	0.00177851
$950$	5297.25	0.180911
$951$	21886.3	0.746279
$952$	−25322.6	−0.862091
$953$	4935.57	0.167764	0.0838818	−	0.996476i	$-0.473268\pi$
$953$	4935.57	0.167764	0.0838818	+	0.996476i	$0.473268\pi$
$954$	7287.72	0.247326
$955$	−2444.39	−0.0828259
$956$	−13799.0	−0.466831
$957$	19097.9	0.645088
$958$	−3796.98	−0.128053
$959$	40745.5	1.37199
$960$	−960.000	−0.0322749
$961$	961.000	0.0322581
$962$	13641.8	0.457202
$963$	−4174.70	−0.139697
$964$	6551.95	0.218905
$965$	9781.29	0.326291
$966$	18348.5	0.611133
$967$	39403.6	1.31038	0.655188	−	0.755466i	$-0.272590\pi$
$967$	39403.6	1.31038	0.655188	+	0.755466i	$0.272590\pi$
$968$	11490.8	0.381538
$969$	34887.4	1.15660
$970$	13720.1	0.454149
$971$	−8662.94	−0.286310	−0.143155	−	0.989700i	$-0.545725\pi$
$971$	−8662.94	−0.286310	−0.143155	+	0.989700i	$0.545725\pi$
$972$	972.000	0.0320750
$973$	13058.5	0.430254
$974$	25751.6	0.847160
$975$	−5000.95	−0.164265
$976$	−3595.07	−0.117905
$977$	45404.9	1.48683	0.743414	−	0.668831i	$-0.233205\pi$
$977$	45404.9	1.48683	0.743414	+	0.668831i	$0.233205\pi$
$978$	4597.40	0.150315
$979$	−19963.8	−0.651734
$980$	−9771.54	−0.318511
$981$	13758.7	0.447789
$982$	−35374.1	−1.14952
$983$	28403.0	0.921582	0.460791	−	0.887509i	$-0.347566\pi$
$983$	28403.0	0.921582	0.460791	+	0.887509i	$0.347566\pi$
$984$	8274.15	0.268059
$985$	−67.3139	−0.00217746
$986$	26566.3	0.858055
$987$	−37213.8	−1.20013
$988$	−28257.4	−0.909907
$989$	15549.8	0.499955
$990$	−4734.51	−0.151992
$991$	8343.09	0.267434	0.133717	−	0.991020i	$-0.457309\pi$
$991$	8343.09	0.267434	0.133717	+	0.991020i	$0.457309\pi$
$992$	−992.000	−0.0317500
$993$	−8152.00	−0.260520
$994$	−33066.0	−1.05512
$995$	−19970.9	−0.636301
$996$	13117.1	0.417301
$997$	−42089.5	−1.33700	−0.668500	−	0.743712i	$-0.733063\pi$
$997$	−42089.5	−1.33700	−0.668500	+	0.743712i	$0.733063\pi$
$998$	−17790.9	−0.564291
$999$	−2761.93	−0.0874712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.a.q.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.a.q.1.1	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	930.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -28.8371 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -28.8371 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +52.6056 q^{11} +12.0000 q^{12} -66.6794 q^{13} -57.6742 q^{14} -15.0000 q^{15} +16.0000 q^{16} +109.766 q^{17} +18.0000 q^{18} +105.945 q^{19} -20.0000 q^{20} -86.5112 q^{21} +105.211 q^{22} -106.047 q^{23} +24.0000 q^{24} +25.0000 q^{25} -133.359 q^{26} +27.0000 q^{27} -115.348 q^{28} +121.013 q^{29} -30.0000 q^{30} -31.0000 q^{31} +32.0000 q^{32} +157.817 q^{33} +219.532 q^{34} +144.185 q^{35} +36.0000 q^{36} -102.294 q^{37} +211.890 q^{38} -200.038 q^{39} -40.0000 q^{40} +344.756 q^{41} -173.022 q^{42} -146.631 q^{43} +210.423 q^{44} -45.0000 q^{45} -212.094 q^{46} +430.162 q^{47} +48.0000 q^{48} +488.577 q^{49} +50.0000 q^{50} +329.297 q^{51} -266.717 q^{52} +404.874 q^{53} +54.0000 q^{54} -263.028 q^{55} -230.697 q^{56} +317.835 q^{57} +242.027 q^{58} +793.282 q^{59} -60.0000 q^{60} -224.692 q^{61} -62.0000 q^{62} -259.534 q^{63} +64.0000 q^{64} +333.397 q^{65} +315.634 q^{66} -340.100 q^{67} +439.063 q^{68} -318.141 q^{69} +288.371 q^{70} +573.325 q^{71} +72.0000 q^{72} -0.779768 q^{73} -204.588 q^{74} +75.0000 q^{75} +423.780 q^{76} -1516.99 q^{77} -400.076 q^{78} +587.734 q^{79} -80.0000 q^{80} +81.0000 q^{81} +689.513 q^{82} +1093.09 q^{83} -346.045 q^{84} -548.829 q^{85} -293.263 q^{86} +363.040 q^{87} +420.845 q^{88} -379.500 q^{89} -90.0000 q^{90} +1922.84 q^{91} -424.188 q^{92} -93.0000 q^{93} +860.324 q^{94} -529.725 q^{95} +96.0000 q^{96} -1372.01 q^{97} +977.154 q^{98} +473.451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 25 q^{5} + 30 q^{6} + 15 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 25 * q^5 + 30 * q^6 + 15 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 25 q^{5} + 30 q^{6} + 15 q^{7} + 40 q^{8} + 45 q^{9} - 50 q^{10} + 69 q^{11} + 60 q^{12} + 44 q^{13} + 30 q^{14} - 75 q^{15} + 80 q^{16} + 170 q^{17} + 90 q^{18} + 139 q^{19} - 100 q^{20} + 45 q^{21} + 138 q^{22} + 39 q^{23} + 120 q^{24} + 125 q^{25} + 88 q^{26} + 135 q^{27} + 60 q^{28} + 100 q^{29} - 150 q^{30} - 155 q^{31} + 160 q^{32} + 207 q^{33} + 340 q^{34} - 75 q^{35} + 180 q^{36} + 472 q^{37} + 278 q^{38} + 132 q^{39} - 200 q^{40} + 794 q^{41} + 90 q^{42} + 503 q^{43} + 276 q^{44} - 225 q^{45} + 78 q^{46} + 544 q^{47} + 240 q^{48} + 850 q^{49} + 250 q^{50} + 510 q^{51} + 176 q^{52} + 639 q^{53} + 270 q^{54} - 345 q^{55} + 120 q^{56} + 417 q^{57} + 200 q^{58} + 470 q^{59} - 300 q^{60} + 694 q^{61} - 310 q^{62} + 135 q^{63} + 320 q^{64} - 220 q^{65} + 414 q^{66} + 816 q^{67} + 680 q^{68} + 117 q^{69} - 150 q^{70} + 963 q^{71} + 360 q^{72} + 1547 q^{73} + 944 q^{74} + 375 q^{75} + 556 q^{76} - 347 q^{77} + 264 q^{78} + 1743 q^{79} - 400 q^{80} + 405 q^{81} + 1588 q^{82} + 1310 q^{83} + 180 q^{84} - 850 q^{85} + 1006 q^{86} + 300 q^{87} + 552 q^{88} - 547 q^{89} - 450 q^{90} + 2630 q^{91} + 156 q^{92} - 465 q^{93} + 1088 q^{94} - 695 q^{95} + 480 q^{96} + 936 q^{97} + 1700 q^{98} + 621 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 - 25 * q^5 + 30 * q^6 + 15 * q^7 + 40 * q^8 + 45 * q^9 - 50 * q^10 + 69 * q^11 + 60 * q^12 + 44 * q^13 + 30 * q^14 - 75 * q^15 + 80 * q^16 + 170 * q^17 + 90 * q^18 + 139 * q^19 - 100 * q^20 + 45 * q^21 + 138 * q^22 + 39 * q^23 + 120 * q^24 + 125 * q^25 + 88 * q^26 + 135 * q^27 + 60 * q^28 + 100 * q^29 - 150 * q^30 - 155 * q^31 + 160 * q^32 + 207 * q^33 + 340 * q^34 - 75 * q^35 + 180 * q^36 + 472 * q^37 + 278 * q^38 + 132 * q^39 - 200 * q^40 + 794 * q^41 + 90 * q^42 + 503 * q^43 + 276 * q^44 - 225 * q^45 + 78 * q^46 + 544 * q^47 + 240 * q^48 + 850 * q^49 + 250 * q^50 + 510 * q^51 + 176 * q^52 + 639 * q^53 + 270 * q^54 - 345 * q^55 + 120 * q^56 + 417 * q^57 + 200 * q^58 + 470 * q^59 - 300 * q^60 + 694 * q^61 - 310 * q^62 + 135 * q^63 + 320 * q^64 - 220 * q^65 + 414 * q^66 + 816 * q^67 + 680 * q^68 + 117 * q^69 - 150 * q^70 + 963 * q^71 + 360 * q^72 + 1547 * q^73 + 944 * q^74 + 375 * q^75 + 556 * q^76 - 347 * q^77 + 264 * q^78 + 1743 * q^79 - 400 * q^80 + 405 * q^81 + 1588 * q^82 + 1310 * q^83 + 180 * q^84 - 850 * q^85 + 1006 * q^86 + 300 * q^87 + 552 * q^88 - 547 * q^89 - 450 * q^90 + 2630 * q^91 + 156 * q^92 - 465 * q^93 + 1088 * q^94 - 695 * q^95 + 480 * q^96 + 936 * q^97 + 1700 * q^98 + 621 * q^99

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