LMFDB - Embedded newform 930.4.a.q.1.3

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			1.3
Root			$-15.7747$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +8.86118 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +8.86118 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +52.4444 q^{11} +12.0000 q^{12} +7.96624 q^{13} +17.7224 q^{14} -15.0000 q^{15} +16.0000 q^{16} -57.5961 q^{17} +18.0000 q^{18} -87.7086 q^{19} -20.0000 q^{20} +26.5835 q^{21} +104.889 q^{22} +178.070 q^{23} +24.0000 q^{24} +25.0000 q^{25} +15.9325 q^{26} +27.0000 q^{27} +35.4447 q^{28} +230.706 q^{29} -30.0000 q^{30} -31.0000 q^{31} +32.0000 q^{32} +157.333 q^{33} -115.192 q^{34} -44.3059 q^{35} +36.0000 q^{36} +17.5202 q^{37} -175.417 q^{38} +23.8987 q^{39} -40.0000 q^{40} -162.471 q^{41} +53.1671 q^{42} +258.822 q^{43} +209.778 q^{44} -45.0000 q^{45} +356.140 q^{46} -150.646 q^{47} +48.0000 q^{48} -264.480 q^{49} +50.0000 q^{50} -172.788 q^{51} +31.8650 q^{52} -239.784 q^{53} +54.0000 q^{54} -262.222 q^{55} +70.8894 q^{56} -263.126 q^{57} +461.413 q^{58} +496.435 q^{59} -60.0000 q^{60} +212.840 q^{61} -62.0000 q^{62} +79.7506 q^{63} +64.0000 q^{64} -39.8312 q^{65} +314.667 q^{66} -118.012 q^{67} -230.384 q^{68} +534.210 q^{69} -88.6118 q^{70} +878.655 q^{71} +72.0000 q^{72} +1173.88 q^{73} +35.0404 q^{74} +75.0000 q^{75} -350.834 q^{76} +464.719 q^{77} +47.7975 q^{78} +1212.38 q^{79} -80.0000 q^{80} +81.0000 q^{81} -324.942 q^{82} -323.711 q^{83} +106.334 q^{84} +287.980 q^{85} +517.645 q^{86} +692.119 q^{87} +419.555 q^{88} +32.2626 q^{89} -90.0000 q^{90} +70.5903 q^{91} +712.280 q^{92} -93.0000 q^{93} -301.292 q^{94} +438.543 q^{95} +96.0000 q^{96} -820.135 q^{97} -528.959 q^{98} +472.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	8.86118	0.478459	0.239229	−	0.970963i	$-0.423105\pi$
$7$	8.86118	0.478459	0.239229	+	0.970963i	$0.423105\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.0000	−0.316228
$11$	52.4444	1.43751	0.718754	−	0.695264i	$-0.244713\pi$
$11$	52.4444	1.43751	0.718754	+	0.695264i	$0.244713\pi$
$12$	12.0000	0.288675
$13$	7.96624	0.169957	0.0849784	−	0.996383i	$-0.472918\pi$
$13$	7.96624	0.169957	0.0849784	+	0.996383i	$0.472918\pi$
$14$	17.7224	0.338321
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	−57.5961	−0.821712	−0.410856	−	0.911700i	$-0.634770\pi$
$17$	−57.5961	−0.821712	−0.410856	+	0.911700i	$0.634770\pi$
$18$	18.0000	0.235702
$19$	−87.7086	−1.05904	−0.529519	−	0.848298i	$-0.677628\pi$
$19$	−87.7086	−1.05904	−0.529519	+	0.848298i	$0.677628\pi$
$20$	−20.0000	−0.223607
$21$	26.5835	0.276238
$22$	104.889	1.01647
$23$	178.070	1.61436	0.807178	−	0.590308i	$-0.200994\pi$
$23$	178.070	1.61436	0.807178	+	0.590308i	$0.200994\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	15.9325	0.120178
$27$	27.0000	0.192450
$28$	35.4447	0.239229
$29$	230.706	1.47728	0.738640	−	0.674100i	$-0.235469\pi$
$29$	230.706	1.47728	0.738640	+	0.674100i	$0.235469\pi$
$30$	−30.0000	−0.182574
$31$	−31.0000	−0.179605
$31$	−31.0000	−0.179605
$32$	32.0000	0.176777
$33$	157.333	0.829946
$34$	−115.192	−0.581038
$35$	−44.3059	−0.213973
$36$	36.0000	0.166667
$37$	17.5202	0.0778461	0.0389231	−	0.999242i	$-0.487607\pi$
$37$	17.5202	0.0778461	0.0389231	+	0.999242i	$0.487607\pi$
$38$	−175.417	−0.748853
$39$	23.8987	0.0981246
$40$	−40.0000	−0.158114
$41$	−162.471	−0.618872	−0.309436	−	0.950920i	$-0.600140\pi$
$41$	−162.471	−0.618872	−0.309436	+	0.950920i	$0.600140\pi$
$42$	53.1671	0.195330
$43$	258.822	0.917908	0.458954	−	0.888460i	$-0.348224\pi$
$43$	258.822	0.917908	0.458954	+	0.888460i	$0.348224\pi$
$44$	209.778	0.718754
$45$	−45.0000	−0.149071
$46$	356.140	1.14152
$47$	−150.646	−0.467532	−0.233766	−	0.972293i	$-0.575105\pi$
$47$	−150.646	−0.467532	−0.233766	+	0.972293i	$0.575105\pi$
$48$	48.0000	0.144338
$49$	−264.480	−0.771077
$50$	50.0000	0.141421
$51$	−172.788	−0.474416
$52$	31.8650	0.0849784
$53$	−239.784	−0.621450	−0.310725	−	0.950500i	$-0.600572\pi$
$53$	−239.784	−0.621450	−0.310725	+	0.950500i	$0.600572\pi$
$54$	54.0000	0.136083
$55$	−262.222	−0.642873
$56$	70.8894	0.169161
$57$	−263.126	−0.611436
$58$	461.413	1.04459
$59$	496.435	1.09543	0.547714	−	0.836665i	$-0.315498\pi$
$59$	496.435	1.09543	0.547714	+	0.836665i	$0.315498\pi$
$60$	−60.0000	−0.129099
$61$	212.840	0.446744	0.223372	−	0.974733i	$-0.428294\pi$
$61$	212.840	0.446744	0.223372	+	0.974733i	$0.428294\pi$
$62$	−62.0000	−0.127000
$63$	79.7506	0.159486
$64$	64.0000	0.125000
$65$	−39.8312	−0.0760070
$66$	314.667	0.586860
$67$	−118.012	−0.215186	−0.107593	−	0.994195i	$-0.534314\pi$
$67$	−118.012	−0.215186	−0.107593	+	0.994195i	$0.534314\pi$
$68$	−230.384	−0.410856
$69$	534.210	0.932049
$70$	−88.6118	−0.151302
$71$	878.655	1.46869	0.734347	−	0.678775i	$-0.237489\pi$
$71$	878.655	1.46869	0.734347	+	0.678775i	$0.237489\pi$
$72$	72.0000	0.117851
$73$	1173.88	1.88209	0.941043	−	0.338286i	$-0.109847\pi$
$73$	1173.88	1.88209	0.941043	+	0.338286i	$0.109847\pi$
$74$	35.0404	0.0550455
$75$	75.0000	0.115470
$76$	−350.834	−0.529519
$77$	464.719	0.687788
$78$	47.7975	0.0693846
$79$	1212.38	1.72662	0.863311	−	0.504672i	$-0.168387\pi$
$79$	1212.38	1.72662	0.863311	+	0.504672i	$0.168387\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	−324.942	−0.437608
$83$	−323.711	−0.428095	−0.214048	−	0.976823i	$-0.568665\pi$
$83$	−323.711	−0.428095	−0.214048	+	0.976823i	$0.568665\pi$
$84$	106.334	0.138119
$85$	287.980	0.367481
$86$	517.645	0.649059
$87$	692.119	0.852908
$88$	419.555	0.508236
$89$	32.2626	0.0384250	0.0192125	−	0.999815i	$-0.493884\pi$
$89$	32.2626	0.0384250	0.0192125	+	0.999815i	$0.493884\pi$
$90$	−90.0000	−0.105409
$91$	70.5903	0.0813173
$92$	712.280	0.807178
$93$	−93.0000	−0.103695
$94$	−301.292	−0.330595
$95$	438.543	0.473616
$96$	96.0000	0.102062
$97$	−820.135	−0.858476	−0.429238	−	0.903191i	$-0.641218\pi$
$97$	−820.135	−0.858476	−0.429238	+	0.903191i	$0.641218\pi$
$98$	−528.959	−0.545234
$99$	472.000	0.479169
$100$	100.000	0.100000
$101$	−1417.93	−1.39693	−0.698463	−	0.715646i	$-0.746132\pi$
$101$	−1417.93	−1.39693	−0.698463	+	0.715646i	$0.746132\pi$
$102$	−345.576	−0.335462
$103$	−19.6105	−0.0187600	−0.00938001	−	0.999956i	$-0.502986\pi$
$103$	−19.6105	−0.0187600	−0.00938001	+	0.999956i	$0.502986\pi$
$104$	63.7300	0.0600888
$105$	−132.918	−0.123537
$106$	−479.568	−0.439432
$107$	545.484	0.492840	0.246420	−	0.969163i	$-0.420746\pi$
$107$	545.484	0.492840	0.246420	+	0.969163i	$0.420746\pi$
$108$	108.000	0.0962250
$109$	339.706	0.298513	0.149257	−	0.988798i	$-0.452312\pi$
$109$	339.706	0.298513	0.149257	+	0.988798i	$0.452312\pi$
$110$	−524.444	−0.454580
$111$	52.5607	0.0449445
$112$	141.779	0.119615
$113$	−1199.02	−0.998180	−0.499090	−	0.866550i	$-0.666332\pi$
$113$	−1199.02	−0.998180	−0.499090	+	0.866550i	$0.666332\pi$
$114$	−526.251	−0.432351
$115$	−890.350	−0.721962
$116$	922.826	0.738640
$117$	71.6962	0.0566523
$118$	992.869	0.774585
$119$	−510.369	−0.393155
$120$	−120.000	−0.0912871
$121$	1419.42	1.06643
$122$	425.680	0.315896
$123$	−487.414	−0.357306
$124$	−124.000	−0.0898027
$125$	−125.000	−0.0894427
$126$	159.501	0.112774
$127$	1970.05	1.37648	0.688242	−	0.725481i	$-0.258383\pi$
$127$	1970.05	1.37648	0.688242	+	0.725481i	$0.258383\pi$
$128$	128.000	0.0883883
$129$	776.467	0.529954
$130$	−79.6624	−0.0537451
$131$	−1295.78	−0.864220	−0.432110	−	0.901821i	$-0.642231\pi$
$131$	−1295.78	−0.864220	−0.432110	+	0.901821i	$0.642231\pi$
$132$	629.333	0.414973
$133$	−777.201	−0.506706
$134$	−236.024	−0.152160
$135$	−135.000	−0.0860663
$136$	−460.769	−0.290519
$137$	−1109.55	−0.691933	−0.345967	−	0.938247i	$-0.612449\pi$
$137$	−1109.55	−0.691933	−0.345967	+	0.938247i	$0.612449\pi$
$138$	1068.42	0.659058
$139$	2424.88	1.47968	0.739839	−	0.672784i	$-0.234902\pi$
$139$	2424.88	1.47968	0.739839	+	0.672784i	$0.234902\pi$
$140$	−177.224	−0.106987
$141$	−451.939	−0.269930
$142$	1757.31	1.03852
$143$	417.785	0.244314
$144$	144.000	0.0833333
$145$	−1153.53	−0.660659
$146$	2347.76	1.33084
$147$	−793.439	−0.445182
$148$	70.0809	0.0389231
$149$	−2986.12	−1.64183	−0.820915	−	0.571051i	$-0.806536\pi$
$149$	−2986.12	−1.64183	−0.820915	+	0.571051i	$0.806536\pi$
$150$	150.000	0.0816497
$151$	−94.7065	−0.0510404	−0.0255202	−	0.999674i	$-0.508124\pi$
$151$	−94.7065	−0.0510404	−0.0255202	+	0.999674i	$0.508124\pi$
$152$	−701.669	−0.374427
$153$	−518.365	−0.273904
$154$	929.439	0.486340
$155$	155.000	0.0803219
$156$	95.5949	0.0490623
$157$	1779.03	0.904344	0.452172	−	0.891931i	$-0.350649\pi$
$157$	1779.03	0.904344	0.452172	+	0.891931i	$0.350649\pi$
$158$	2424.75	1.22091
$159$	−719.352	−0.358795
$160$	−160.000	−0.0790569
$161$	1577.91	0.772402
$162$	162.000	0.0785674
$163$	148.449	0.0713341	0.0356671	−	0.999364i	$-0.488644\pi$
$163$	148.449	0.0713341	0.0356671	+	0.999364i	$0.488644\pi$
$164$	−649.885	−0.309436
$165$	−786.666	−0.371163
$166$	−647.422	−0.302709
$167$	−38.9097	−0.0180295	−0.00901475	−	0.999959i	$-0.502870\pi$
$167$	−38.9097	−0.0180295	−0.00901475	+	0.999959i	$0.502870\pi$
$168$	212.668	0.0976649
$169$	−2133.54	−0.971115
$170$	575.961	0.259848
$171$	−789.377	−0.353013
$172$	1035.29	0.458954
$173$	−2219.25	−0.975297	−0.487648	−	0.873040i	$-0.662145\pi$
$173$	−2219.25	−0.975297	−0.487648	+	0.873040i	$0.662145\pi$
$174$	1384.24	0.603097
$175$	221.529	0.0956917
$176$	839.111	0.359377
$177$	1489.30	0.632446
$178$	64.5251	0.0271706
$179$	2344.67	0.979043	0.489522	−	0.871991i	$-0.337171\pi$
$179$	2344.67	0.979043	0.489522	+	0.871991i	$0.337171\pi$
$180$	−180.000	−0.0745356
$181$	−2359.75	−0.969055	−0.484528	−	0.874776i	$-0.661009\pi$
$181$	−2359.75	−0.969055	−0.484528	+	0.874776i	$0.661009\pi$
$182$	141.181	0.0575000
$183$	638.520	0.257928
$184$	1424.56	0.570761
$185$	−87.6011	−0.0348139
$186$	−186.000	−0.0733236
$187$	−3020.59	−1.18122
$188$	−602.585	−0.233766
$189$	239.252	0.0920794
$190$	877.086	0.334897
$191$	1056.70	0.400316	0.200158	−	0.979764i	$-0.435855\pi$
$191$	1056.70	0.400316	0.200158	+	0.979764i	$0.435855\pi$
$192$	192.000	0.0721688
$193$	1963.95	0.732480	0.366240	−	0.930521i	$-0.380645\pi$
$193$	1963.95	0.732480	0.366240	+	0.930521i	$0.380645\pi$
$194$	−1640.27	−0.607034
$195$	−119.494	−0.0438827
$196$	−1057.92	−0.385539
$197$	2603.50	0.941584	0.470792	−	0.882244i	$-0.343968\pi$
$197$	2603.50	0.941584	0.470792	+	0.882244i	$0.343968\pi$
$198$	944.000	0.338824
$199$	−5158.44	−1.83755	−0.918774	−	0.394783i	$-0.870820\pi$
$199$	−5158.44	−1.83755	−0.918774	+	0.394783i	$0.870820\pi$
$200$	200.000	0.0707107
$201$	−354.036	−0.124238
$202$	−2835.86	−0.987776
$203$	2044.33	0.706817
$204$	−691.153	−0.237208
$205$	812.356	0.276768
$206$	−39.2210	−0.0132653
$207$	1602.63	0.538119
$208$	127.460	0.0424892
$209$	−4599.83	−1.52238
$210$	−265.835	−0.0873542
$211$	−2580.92	−0.842074	−0.421037	−	0.907044i	$-0.638334\pi$
$211$	−2580.92	−0.842074	−0.421037	+	0.907044i	$0.638334\pi$
$212$	−959.136	−0.310725
$213$	2635.97	0.847950
$214$	1090.97	0.348491
$215$	−1294.11	−0.410501
$216$	216.000	0.0680414
$217$	−274.696	−0.0859337
$218$	679.412	0.211081
$219$	3521.64	1.08662
$220$	−1048.89	−0.321437
$221$	−458.824	−0.139656
$222$	105.121	0.0317806
$223$	−5707.24	−1.71383	−0.856917	−	0.515454i	$-0.827623\pi$
$223$	−5707.24	−1.71383	−0.856917	+	0.515454i	$0.827623\pi$
$224$	283.558	0.0845803
$225$	225.000	0.0666667
$226$	−2398.04	−0.705820
$227$	−4791.23	−1.40090	−0.700451	−	0.713700i	$-0.747018\pi$
$227$	−4791.23	−1.40090	−0.700451	+	0.713700i	$0.747018\pi$
$228$	−1052.50	−0.305718
$229$	140.885	0.0406548	0.0203274	−	0.999793i	$-0.493529\pi$
$229$	140.885	0.0406548	0.0203274	+	0.999793i	$0.493529\pi$
$230$	−1780.70	−0.510504
$231$	1394.16	0.397095
$232$	1845.65	0.522297
$233$	1169.82	0.328916	0.164458	−	0.986384i	$-0.447412\pi$
$233$	1169.82	0.328916	0.164458	+	0.986384i	$0.447412\pi$
$234$	143.392	0.0400592
$235$	753.231	0.209087
$236$	1985.74	0.547714
$237$	3637.13	0.996866
$238$	−1020.74	−0.278003
$239$	5399.28	1.46130	0.730650	−	0.682752i	$-0.239217\pi$
$239$	5399.28	1.46130	0.730650	+	0.682752i	$0.239217\pi$
$240$	−240.000	−0.0645497
$241$	−86.0576	−0.0230019	−0.0115009	−	0.999934i	$-0.503661\pi$
$241$	−86.0576	−0.0230019	−0.0115009	+	0.999934i	$0.503661\pi$
$242$	2838.83	0.754079
$243$	243.000	0.0641500
$244$	851.360	0.223372
$245$	1322.40	0.344836
$246$	−974.827	−0.252653
$247$	−698.708	−0.179991
$248$	−248.000	−0.0635001
$249$	−971.134	−0.247161
$250$	−250.000	−0.0632456
$251$	−46.7265	−0.0117504	−0.00587520	−	0.999983i	$-0.501870\pi$
$251$	−46.7265	−0.0117504	−0.00587520	+	0.999983i	$0.501870\pi$
$252$	319.002	0.0797431
$253$	9338.78	2.32065
$254$	3940.09	0.973321
$255$	863.941	0.212165
$256$	256.000	0.0625000
$257$	−737.034	−0.178891	−0.0894453	−	0.995992i	$-0.528509\pi$
$257$	−737.034	−0.178891	−0.0894453	+	0.995992i	$0.528509\pi$
$258$	1552.93	0.374734
$259$	155.250	0.0372462
$260$	−159.325	−0.0380035
$261$	2076.36	0.492426
$262$	−2591.56	−0.611096
$263$	607.583	0.142453	0.0712265	−	0.997460i	$-0.477309\pi$
$263$	607.583	0.142453	0.0712265	+	0.997460i	$0.477309\pi$
$264$	1258.67	0.293430
$265$	1198.92	0.277921
$266$	−1554.40	−0.358295
$267$	96.7877	0.0221847
$268$	−472.048	−0.107593
$269$	−5168.25	−1.17143	−0.585713	−	0.810518i	$-0.699185\pi$
$269$	−5168.25	−1.17143	−0.585713	+	0.810518i	$0.699185\pi$
$270$	−270.000	−0.0608581
$271$	7264.92	1.62846	0.814229	−	0.580543i	$-0.197160\pi$
$271$	7264.92	1.62846	0.814229	+	0.580543i	$0.197160\pi$
$272$	−921.537	−0.205428
$273$	211.771	0.0469486
$274$	−2219.09	−0.489271
$275$	1311.11	0.287502
$276$	2136.84	0.466024
$277$	−7303.23	−1.58415	−0.792074	−	0.610425i	$-0.790998\pi$
$277$	−7303.23	−1.58415	−0.792074	+	0.610425i	$0.790998\pi$
$278$	4849.75	1.04629
$279$	−279.000	−0.0598684
$280$	−354.447	−0.0756509
$281$	−6194.83	−1.31513	−0.657566	−	0.753397i	$-0.728414\pi$
$281$	−6194.83	−1.31513	−0.657566	+	0.753397i	$0.728414\pi$
$282$	−903.877	−0.190869
$283$	−5852.96	−1.22941	−0.614704	−	0.788758i	$-0.710725\pi$
$283$	−5852.96	−1.22941	−0.614704	+	0.788758i	$0.710725\pi$
$284$	3514.62	0.734347
$285$	1315.63	0.273443
$286$	835.570	0.172756
$287$	−1439.69	−0.296104
$288$	288.000	0.0589256
$289$	−1595.69	−0.324790
$290$	−2307.06	−0.467157
$291$	−2460.41	−0.495641
$292$	4695.52	0.941043
$293$	−4012.22	−0.799988	−0.399994	−	0.916518i	$-0.630988\pi$
$293$	−4012.22	−0.799988	−0.399994	+	0.916518i	$0.630988\pi$
$294$	−1586.88	−0.314791
$295$	−2482.17	−0.489890
$296$	140.162	0.0275228
$297$	1416.00	0.276649
$298$	−5972.24	−1.16095
$299$	1418.55	0.274371
$300$	300.000	0.0577350
$301$	2293.47	0.439181
$302$	−189.413	−0.0360910
$303$	−4253.80	−0.806516
$304$	−1403.34	−0.264760
$305$	−1064.20	−0.199790
$306$	−1036.73	−0.193679
$307$	6389.77	1.18789	0.593947	−	0.804504i	$-0.297569\pi$
$307$	6389.77	1.18789	0.593947	+	0.804504i	$0.297569\pi$
$308$	1858.88	0.343894
$309$	−58.8316	−0.0108311
$310$	310.000	0.0567962
$311$	−2173.98	−0.396383	−0.198192	−	0.980163i	$-0.563507\pi$
$311$	−2173.98	−0.396383	−0.198192	+	0.980163i	$0.563507\pi$
$312$	191.190	0.0346923
$313$	−816.879	−0.147517	−0.0737584	−	0.997276i	$-0.523499\pi$
$313$	−816.879	−0.147517	−0.0737584	+	0.997276i	$0.523499\pi$
$314$	3558.06	0.639468
$315$	−398.753	−0.0713244
$316$	4849.51	0.863311
$317$	−7365.65	−1.30503	−0.652517	−	0.757774i	$-0.726287\pi$
$317$	−7365.65	−1.30503	−0.652517	+	0.757774i	$0.726287\pi$
$318$	−1438.70	−0.253706
$319$	12099.3	2.12360
$320$	−320.000	−0.0559017
$321$	1636.45	0.284542
$322$	3155.82	0.546171
$323$	5051.67	0.870224
$324$	324.000	0.0555556
$325$	199.156	0.0339914
$326$	296.899	0.0504408
$327$	1019.12	0.172347
$328$	−1299.77	−0.218804
$329$	−1334.90	−0.223695
$330$	−1573.33	−0.262452
$331$	−6018.57	−0.999428	−0.499714	−	0.866190i	$-0.666562\pi$
$331$	−6018.57	−0.999428	−0.499714	+	0.866190i	$0.666562\pi$
$332$	−1294.84	−0.214048
$333$	157.682	0.0259487
$334$	−77.8195	−0.0127488
$335$	590.060	0.0962342
$336$	425.336	0.0690595
$337$	−5113.17	−0.826505	−0.413253	−	0.910616i	$-0.635607\pi$
$337$	−5113.17	−0.826505	−0.413253	+	0.910616i	$0.635607\pi$
$338$	−4267.08	−0.686682
$339$	−3597.06	−0.576299
$340$	1151.92	0.183740
$341$	−1625.78	−0.258184
$342$	−1578.75	−0.249618
$343$	−5382.98	−0.847387
$344$	2070.58	0.324529
$345$	−2671.05	−0.416825
$346$	−4438.50	−0.689639
$347$	−388.995	−0.0601796	−0.0300898	−	0.999547i	$-0.509579\pi$
$347$	−388.995	−0.0601796	−0.0300898	+	0.999547i	$0.509579\pi$
$348$	2768.48	0.426454
$349$	3570.97	0.547707	0.273854	−	0.961771i	$-0.411702\pi$
$349$	3570.97	0.547707	0.273854	+	0.961771i	$0.411702\pi$
$350$	443.059	0.0676643
$351$	215.089	0.0327082
$352$	1678.22	0.254118
$353$	5167.67	0.779172	0.389586	−	0.920990i	$-0.372618\pi$
$353$	5167.67	0.779172	0.389586	+	0.920990i	$0.372618\pi$
$354$	2978.61	0.447207
$355$	−4393.28	−0.656820
$356$	129.050	0.0192125
$357$	−1531.11	−0.226988
$358$	4689.34	0.692288
$359$	−8501.26	−1.24980	−0.624902	−	0.780703i	$-0.714861\pi$
$359$	−8501.26	−1.24980	−0.624902	+	0.780703i	$0.714861\pi$
$360$	−360.000	−0.0527046
$361$	833.794	0.121562
$362$	−4719.50	−0.685226
$363$	4258.25	0.615703
$364$	282.361	0.0406587
$365$	−5869.40	−0.841695
$366$	1277.04	0.182382
$367$	−3065.30	−0.435988	−0.217994	−	0.975950i	$-0.569951\pi$
$367$	−3065.30	−0.435988	−0.217994	+	0.975950i	$0.569951\pi$
$368$	2849.12	0.403589
$369$	−1462.24	−0.206291
$370$	−175.202	−0.0246171
$371$	−2124.77	−0.297338
$372$	−372.000	−0.0518476
$373$	8518.87	1.18255	0.591274	−	0.806471i	$-0.298625\pi$
$373$	8518.87	1.18255	0.591274	+	0.806471i	$0.298625\pi$
$374$	−6041.19	−0.835247
$375$	−375.000	−0.0516398
$376$	−1205.17	−0.165298
$377$	1837.86	0.251074
$378$	478.504	0.0651100
$379$	11312.7	1.53323	0.766615	−	0.642107i	$-0.221939\pi$
$379$	11312.7	1.53323	0.766615	+	0.642107i	$0.221939\pi$
$380$	1754.17	0.236808
$381$	5910.14	0.794713
$382$	2113.40	0.283066
$383$	−7676.63	−1.02417	−0.512086	−	0.858934i	$-0.671127\pi$
$383$	−7676.63	−1.02417	−0.512086	+	0.858934i	$0.671127\pi$
$384$	384.000	0.0510310
$385$	−2323.60	−0.307588
$386$	3927.91	0.517941
$387$	2329.40	0.305969
$388$	−3280.54	−0.429238
$389$	−3109.92	−0.405344	−0.202672	−	0.979247i	$-0.564963\pi$
$389$	−3109.92	−0.405344	−0.202672	+	0.979247i	$0.564963\pi$
$390$	−238.987	−0.0310297
$391$	−10256.1	−1.32654
$392$	−2115.84	−0.272617
$393$	−3887.34	−0.498958
$394$	5207.01	0.665800
$395$	−6061.89	−0.772169
$396$	1888.00	0.239585
$397$	−6919.00	−0.874697	−0.437348	−	0.899292i	$-0.644082\pi$
$397$	−6919.00	−0.874697	−0.437348	+	0.899292i	$0.644082\pi$
$398$	−10316.9	−1.29934
$399$	−2331.60	−0.292547
$400$	400.000	0.0500000
$401$	−9875.57	−1.22983	−0.614915	−	0.788593i	$-0.710810\pi$
$401$	−9875.57	−1.22983	−0.614915	+	0.788593i	$0.710810\pi$
$402$	−708.073	−0.0878494
$403$	−246.954	−0.0305251
$404$	−5671.73	−0.698463
$405$	−405.000	−0.0496904
$406$	4088.66	0.499795
$407$	918.838	0.111904
$408$	−1382.31	−0.167731
$409$	5290.90	0.639653	0.319827	−	0.947476i	$-0.396375\pi$
$409$	5290.90	0.639653	0.319827	+	0.947476i	$0.396375\pi$
$410$	1624.71	0.195704
$411$	−3328.64	−0.399488
$412$	−78.4421	−0.00938001
$413$	4398.99	0.524117
$414$	3205.26	0.380507
$415$	1618.56	0.191450
$416$	254.920	0.0300444
$417$	7274.63	0.854293
$418$	−9199.65	−1.07648
$419$	−6381.55	−0.744055	−0.372028	−	0.928222i	$-0.621337\pi$
$419$	−6381.55	−0.744055	−0.372028	+	0.928222i	$0.621337\pi$
$420$	−531.671	−0.0617687
$421$	1582.70	0.183221	0.0916105	−	0.995795i	$-0.470799\pi$
$421$	1582.70	0.183221	0.0916105	+	0.995795i	$0.470799\pi$
$422$	−5161.83	−0.595436
$423$	−1355.82	−0.155844
$424$	−1918.27	−0.219716
$425$	−1439.90	−0.164342
$426$	5271.93	0.599591
$427$	1886.01	0.213748
$428$	2181.94	0.246420
$429$	1253.36	0.141055
$430$	−2588.22	−0.290268
$431$	−12329.4	−1.37793	−0.688965	−	0.724795i	$-0.741935\pi$
$431$	−12329.4	−1.37793	−0.688965	+	0.724795i	$0.741935\pi$
$432$	432.000	0.0481125
$433$	3508.60	0.389405	0.194703	−	0.980862i	$-0.437626\pi$
$433$	3508.60	0.389405	0.194703	+	0.980862i	$0.437626\pi$
$434$	−549.393	−0.0607643
$435$	−3460.60	−0.381432
$436$	1358.82	0.149257
$437$	−15618.3	−1.70966
$438$	7043.28	0.768359
$439$	4838.53	0.526037	0.263019	−	0.964791i	$-0.415282\pi$
$439$	4838.53	0.526037	0.263019	+	0.964791i	$0.415282\pi$
$440$	−2097.78	−0.227290
$441$	−2380.32	−0.257026
$442$	−917.649	−0.0987514
$443$	8056.54	0.864058	0.432029	−	0.901860i	$-0.357798\pi$
$443$	8056.54	0.864058	0.432029	+	0.901860i	$0.357798\pi$
$444$	210.243	0.0224722
$445$	−161.313	−0.0171842
$446$	−11414.5	−1.21186
$447$	−8958.36	−0.947911
$448$	567.115	0.0598073
$449$	3468.53	0.364566	0.182283	−	0.983246i	$-0.441651\pi$
$449$	3468.53	0.364566	0.182283	+	0.983246i	$0.441651\pi$
$450$	450.000	0.0471405
$451$	−8520.71	−0.889633
$452$	−4796.08	−0.499090
$453$	−284.119	−0.0294682
$454$	−9582.45	−0.990588
$455$	−352.952	−0.0363662
$456$	−2105.01	−0.216175
$457$	622.692	0.0637381	0.0318690	−	0.999492i	$-0.489854\pi$
$457$	622.692	0.0637381	0.0318690	+	0.999492i	$0.489854\pi$
$458$	281.770	0.0287473
$459$	−1555.09	−0.158139
$460$	−3561.40	−0.360981
$461$	−12025.9	−1.21497	−0.607487	−	0.794330i	$-0.707822\pi$
$461$	−12025.9	−1.21497	−0.607487	+	0.794330i	$0.707822\pi$
$462$	2788.32	0.280788
$463$	14556.8	1.46115	0.730577	−	0.682831i	$-0.239251\pi$
$463$	14556.8	1.46115	0.730577	+	0.682831i	$0.239251\pi$
$464$	3691.30	0.369320
$465$	465.000	0.0463739
$466$	2339.64	0.232579
$467$	4134.33	0.409666	0.204833	−	0.978797i	$-0.434335\pi$
$467$	4134.33	0.409666	0.204833	+	0.978797i	$0.434335\pi$
$468$	286.785	0.0283261
$469$	−1045.73	−0.102958
$470$	1506.46	0.147847
$471$	5337.09	0.522123
$472$	3971.48	0.387292
$473$	13573.8	1.31950
$474$	7274.26	0.704890
$475$	−2192.71	−0.211808
$476$	−2041.48	−0.196578
$477$	−2158.06	−0.207150
$478$	10798.6	1.03330
$479$	16459.4	1.57004	0.785021	−	0.619469i	$-0.212652\pi$
$479$	16459.4	1.57004	0.785021	+	0.619469i	$0.212652\pi$
$480$	−480.000	−0.0456435
$481$	139.570	0.0132305
$482$	−172.115	−0.0162648
$483$	4733.73	0.445947
$484$	5677.67	0.533215
$485$	4100.68	0.383922
$486$	486.000	0.0453609
$487$	−7837.65	−0.729277	−0.364639	−	0.931149i	$-0.618807\pi$
$487$	−7837.65	−0.729277	−0.364639	+	0.931149i	$0.618807\pi$
$488$	1702.72	0.157948
$489$	445.348	0.0411848
$490$	2644.80	0.243836
$491$	−21126.3	−1.94178	−0.970891	−	0.239522i	$-0.923009\pi$
$491$	−21126.3	−1.94178	−0.970891	+	0.239522i	$0.923009\pi$
$492$	−1949.65	−0.178653
$493$	−13287.8	−1.21390
$494$	−1397.42	−0.127273
$495$	−2360.00	−0.214291
$496$	−496.000	−0.0449013
$497$	7785.92	0.702709
$498$	−1942.27	−0.174769
$499$	−1173.02	−0.105233	−0.0526167	−	0.998615i	$-0.516756\pi$
$499$	−1173.02	−0.105233	−0.0526167	+	0.998615i	$0.516756\pi$
$500$	−500.000	−0.0447214
$501$	−116.729	−0.0104093
$502$	−93.4530	−0.00830879
$503$	−17411.5	−1.54342	−0.771712	−	0.635973i	$-0.780599\pi$
$503$	−17411.5	−1.54342	−0.771712	+	0.635973i	$0.780599\pi$
$504$	638.005	0.0563869
$505$	7089.66	0.624724
$506$	18677.6	1.64095
$507$	−6400.62	−0.560673
$508$	7880.19	0.688242
$509$	10680.9	0.930104	0.465052	−	0.885283i	$-0.346036\pi$
$509$	10680.9	0.930104	0.465052	+	0.885283i	$0.346036\pi$
$510$	1727.88	0.150023
$511$	10402.0	0.900501
$512$	512.000	0.0441942
$513$	−2368.13	−0.203812
$514$	−1474.07	−0.126495
$515$	98.0526	0.00838973
$516$	3105.87	0.264977
$517$	−7900.55	−0.672081
$518$	310.500	0.0263370
$519$	−6657.74	−0.563088
$520$	−318.650	−0.0268725
$521$	7440.21	0.625646	0.312823	−	0.949811i	$-0.398725\pi$
$521$	7440.21	0.625646	0.312823	+	0.949811i	$0.398725\pi$
$522$	4152.72	0.348198
$523$	19915.3	1.66507	0.832537	−	0.553969i	$-0.186887\pi$
$523$	19915.3	1.66507	0.832537	+	0.553969i	$0.186887\pi$
$524$	−5183.12	−0.432110
$525$	664.588	0.0552476
$526$	1215.17	0.100730
$527$	1785.48	0.147584
$528$	2517.33	0.207486
$529$	19542.0	1.60614
$530$	2397.84	0.196520
$531$	4467.91	0.365143
$532$	−3108.80	−0.253353
$533$	−1294.29	−0.105181
$534$	193.575	0.0156869
$535$	−2727.42	−0.220405
$536$	−944.097	−0.0760798
$537$	7034.01	0.565251
$538$	−10336.5	−0.828323
$539$	−13870.5	−1.10843
$540$	−540.000	−0.0430331
$541$	−16437.2	−1.30626	−0.653132	−	0.757244i	$-0.726545\pi$
$541$	−16437.2	−1.30626	−0.653132	+	0.757244i	$0.726545\pi$
$542$	14529.8	1.15149
$543$	−7079.26	−0.559484
$544$	−1843.07	−0.145259
$545$	−1698.53	−0.133499
$546$	423.542	0.0331976
$547$	−337.629	−0.0263912	−0.0131956	−	0.999913i	$-0.504200\pi$
$547$	−337.629	−0.0263912	−0.0131956	+	0.999913i	$0.504200\pi$
$548$	−4438.18	−0.345967
$549$	1915.56	0.148915
$550$	2622.22	0.203294
$551$	−20234.9	−1.56450
$552$	4273.68	0.329529
$553$	10743.1	0.826117
$554$	−14606.5	−1.12016
$555$	−262.803	−0.0200998
$556$	9699.50	0.739839
$557$	−1792.53	−0.136359	−0.0681793	−	0.997673i	$-0.521719\pi$
$557$	−1792.53	−0.136359	−0.0681793	+	0.997673i	$0.521719\pi$
$558$	−558.000	−0.0423334
$559$	2061.84	0.156005
$560$	−708.894	−0.0534933
$561$	−9061.78	−0.681976
$562$	−12389.7	−0.929939
$563$	1817.02	0.136018	0.0680090	−	0.997685i	$-0.478335\pi$
$563$	1817.02	0.136018	0.0680090	+	0.997685i	$0.478335\pi$
$564$	−1807.75	−0.134965
$565$	5995.10	0.446399
$566$	−11705.9	−0.869323
$567$	717.755	0.0531621
$568$	7029.24	0.519261
$569$	4741.18	0.349315	0.174658	−	0.984629i	$-0.444118\pi$
$569$	4741.18	0.349315	0.174658	+	0.984629i	$0.444118\pi$
$570$	2631.26	0.193353
$571$	2499.66	0.183200	0.0916002	−	0.995796i	$-0.470802\pi$
$571$	2499.66	0.183200	0.0916002	+	0.995796i	$0.470802\pi$
$572$	1671.14	0.122157
$573$	3170.11	0.231122
$574$	−2879.37	−0.209377
$575$	4451.75	0.322871
$576$	576.000	0.0416667
$577$	−24313.6	−1.75423	−0.877114	−	0.480283i	$-0.840534\pi$
$577$	−24313.6	−1.75423	−0.877114	+	0.480283i	$0.840534\pi$
$578$	−3191.38	−0.229661
$579$	5891.86	0.422897
$580$	−4614.13	−0.330330
$581$	−2868.46	−0.204826
$582$	−4920.81	−0.350471
$583$	−12575.3	−0.893340
$584$	9391.05	0.665418
$585$	−358.481	−0.0253357
$586$	−8024.44	−0.565677
$587$	−10730.3	−0.754494	−0.377247	−	0.926113i	$-0.623129\pi$
$587$	−10730.3	−0.754494	−0.377247	+	0.926113i	$0.623129\pi$
$588$	−3173.75	−0.222591
$589$	2718.97	0.190209
$590$	−4964.35	−0.346405
$591$	7810.51	0.543624
$592$	280.324	0.0194615
$593$	13597.8	0.941645	0.470822	−	0.882228i	$-0.343957\pi$
$593$	13597.8	0.941645	0.470822	+	0.882228i	$0.343957\pi$
$594$	2832.00	0.195620
$595$	2551.85	0.175824
$596$	−11944.5	−0.820915
$597$	−15475.3	−1.06091
$598$	2837.10	0.194009
$599$	−16836.0	−1.14842	−0.574209	−	0.818709i	$-0.694690\pi$
$599$	−16836.0	−1.14842	−0.574209	+	0.818709i	$0.694690\pi$
$600$	600.000	0.0408248
$601$	20572.3	1.39628	0.698139	−	0.715962i	$-0.254012\pi$
$601$	20572.3	1.39628	0.698139	+	0.715962i	$0.254012\pi$
$602$	4586.94	0.310548
$603$	−1062.11	−0.0717287
$604$	−378.826	−0.0255202
$605$	−7097.09	−0.476922
$606$	−8507.59	−0.570293
$607$	−17411.4	−1.16426	−0.582132	−	0.813095i	$-0.697781\pi$
$607$	−17411.4	−1.16426	−0.582132	+	0.813095i	$0.697781\pi$
$608$	−2806.67	−0.187213
$609$	6132.99	0.408081
$610$	−2128.40	−0.141273
$611$	−1200.08	−0.0794603
$612$	−2073.46	−0.136952
$613$	−6433.94	−0.423922	−0.211961	−	0.977278i	$-0.567985\pi$
$613$	−6433.94	−0.423922	−0.211961	+	0.977278i	$0.567985\pi$
$614$	12779.5	0.839968
$615$	2437.07	0.159792
$616$	3717.75	0.243170
$617$	−5966.97	−0.389337	−0.194669	−	0.980869i	$-0.562363\pi$
$617$	−5966.97	−0.389337	−0.194669	+	0.980869i	$0.562363\pi$
$618$	−117.663	−0.00765874
$619$	27644.3	1.79502	0.897511	−	0.440992i	$-0.145373\pi$
$619$	27644.3	1.79502	0.897511	+	0.440992i	$0.145373\pi$
$620$	620.000	0.0401610
$621$	4807.89	0.310683
$622$	−4347.96	−0.280285
$623$	285.884	0.0183848
$624$	382.380	0.0245312
$625$	625.000	0.0400000
$626$	−1633.76	−0.104310
$627$	−13799.5	−0.878944
$628$	7116.12	0.452172
$629$	−1009.10	−0.0639671
$630$	−797.506	−0.0504340
$631$	20412.6	1.28782	0.643908	−	0.765103i	$-0.277312\pi$
$631$	20412.6	1.28782	0.643908	+	0.765103i	$0.277312\pi$
$632$	9699.02	0.610453
$633$	−7742.75	−0.486171
$634$	−14731.3	−0.922799
$635$	−9850.24	−0.615582
$636$	−2877.41	−0.179397
$637$	−2106.91	−0.131050
$638$	24198.5	1.50161
$639$	7907.90	0.489564
$640$	−640.000	−0.0395285
$641$	9587.10	0.590745	0.295373	−	0.955382i	$-0.404556\pi$
$641$	9587.10	0.590745	0.295373	+	0.955382i	$0.404556\pi$
$642$	3272.90	0.201201
$643$	−3105.53	−0.190467	−0.0952333	−	0.995455i	$-0.530360\pi$
$643$	−3105.53	−0.190467	−0.0952333	+	0.995455i	$0.530360\pi$
$644$	6311.64	0.386201
$645$	−3882.33	−0.237003
$646$	10103.3	0.615341
$647$	−8253.71	−0.501525	−0.250763	−	0.968049i	$-0.580681\pi$
$647$	−8253.71	−0.501525	−0.250763	+	0.968049i	$0.580681\pi$
$648$	648.000	0.0392837
$649$	26035.2	1.57469
$650$	398.312	0.0240355
$651$	−824.089	−0.0496138
$652$	593.798	0.0356671
$653$	−31100.8	−1.86381	−0.931905	−	0.362702i	$-0.881854\pi$
$653$	−31100.8	−1.86381	−0.931905	+	0.362702i	$0.881854\pi$
$654$	2038.24	0.121868
$655$	6478.90	0.386491
$656$	−2599.54	−0.154718
$657$	10564.9	0.627362
$658$	−2669.80	−0.158176
$659$	26434.0	1.56255	0.781275	−	0.624187i	$-0.214570\pi$
$659$	26434.0	1.56255	0.781275	+	0.624187i	$0.214570\pi$
$660$	−3146.67	−0.185581
$661$	13636.3	0.802407	0.401203	−	0.915989i	$-0.368592\pi$
$661$	13636.3	0.802407	0.401203	+	0.915989i	$0.368592\pi$
$662$	−12037.1	−0.706702
$663$	−1376.47	−0.0806302
$664$	−2589.69	−0.151355
$665$	3886.01	0.226606
$666$	315.364	0.0183485
$667$	41081.9	2.38485
$668$	−155.639	−0.00901475
$669$	−17121.7	−0.989483
$670$	1180.12	0.0680478
$671$	11162.3	0.642198
$672$	850.673	0.0488325
$673$	−23913.7	−1.36969	−0.684847	−	0.728687i	$-0.740131\pi$
$673$	−23913.7	−1.36969	−0.684847	+	0.728687i	$0.740131\pi$
$674$	−10226.3	−0.584428
$675$	675.000	0.0384900
$676$	−8534.16	−0.485557
$677$	3106.47	0.176354	0.0881769	−	0.996105i	$-0.471896\pi$
$677$	3106.47	0.176354	0.0881769	+	0.996105i	$0.471896\pi$
$678$	−7194.12	−0.407505
$679$	−7267.37	−0.410745
$680$	2303.84	0.129924
$681$	−14373.7	−0.808811
$682$	−3251.55	−0.182564
$683$	−4685.40	−0.262492	−0.131246	−	0.991350i	$-0.541898\pi$
$683$	−4685.40	−0.262492	−0.131246	+	0.991350i	$0.541898\pi$
$684$	−3157.51	−0.176506
$685$	5547.73	0.309442
$686$	−10766.0	−0.599193
$687$	422.655	0.0234720
$688$	4141.16	0.229477
$689$	−1910.18	−0.105620
$690$	−5342.10	−0.294740
$691$	11606.0	0.638949	0.319474	−	0.947595i	$-0.396494\pi$
$691$	11606.0	0.638949	0.319474	+	0.947595i	$0.396494\pi$
$692$	−8876.99	−0.487648
$693$	4182.47	0.229263
$694$	−777.989	−0.0425534
$695$	−12124.4	−0.661732
$696$	5536.95	0.301548
$697$	9357.70	0.508534
$698$	7141.95	0.387288
$699$	3509.46	0.189900
$700$	886.118	0.0478459
$701$	−17361.4	−0.935424	−0.467712	−	0.883881i	$-0.654922\pi$
$701$	−17361.4	−0.935424	−0.467712	+	0.883881i	$0.654922\pi$
$702$	430.177	0.0231282
$703$	−1536.67	−0.0824420
$704$	3356.44	0.179689
$705$	2259.69	0.120716
$706$	10335.3	0.550957
$707$	−12564.5	−0.668371
$708$	5957.21	0.316223
$709$	9556.65	0.506216	0.253108	−	0.967438i	$-0.418547\pi$
$709$	9556.65	0.506216	0.253108	+	0.967438i	$0.418547\pi$
$710$	−8786.55	−0.464442
$711$	10911.4	0.575541
$712$	258.100	0.0135853
$713$	−5520.17	−0.289947
$714$	−3062.21	−0.160505
$715$	−2088.93	−0.109261
$716$	9378.67	0.489522
$717$	16197.9	0.843682
$718$	−17002.5	−0.883744
$719$	16106.7	0.835434	0.417717	−	0.908577i	$-0.362830\pi$
$719$	16106.7	0.835434	0.417717	+	0.908577i	$0.362830\pi$
$720$	−720.000	−0.0372678
$721$	−173.772	−0.00897589
$722$	1667.59	0.0859574
$723$	−258.173	−0.0132801
$724$	−9439.01	−0.484528
$725$	5767.66	0.295456
$726$	8516.50	0.435368
$727$	−24805.9	−1.26548	−0.632738	−	0.774366i	$-0.718069\pi$
$727$	−24805.9	−1.26548	−0.632738	+	0.774366i	$0.718069\pi$
$728$	564.722	0.0287500
$729$	729.000	0.0370370
$730$	−11738.8	−0.595168
$731$	−14907.1	−0.754256
$732$	2554.08	0.128964
$733$	38795.8	1.95492	0.977459	−	0.211124i	$-0.0677124\pi$
$733$	38795.8	1.95492	0.977459	+	0.211124i	$0.0677124\pi$
$734$	−6130.61	−0.308290
$735$	3967.19	0.199091
$736$	5698.24	0.285380
$737$	−6189.08	−0.309332
$738$	−2924.48	−0.145869
$739$	−10199.0	−0.507683	−0.253842	−	0.967246i	$-0.581694\pi$
$739$	−10199.0	−0.507683	−0.253842	+	0.967246i	$0.581694\pi$
$740$	−350.404	−0.0174069
$741$	−2096.12	−0.103918
$742$	−4249.54	−0.210250
$743$	−32759.4	−1.61753	−0.808766	−	0.588130i	$-0.799864\pi$
$743$	−32759.4	−1.61753	−0.808766	+	0.588130i	$0.799864\pi$
$744$	−744.000	−0.0366618
$745$	14930.6	0.734248
$746$	17037.7	0.836187
$747$	−2913.40	−0.142698
$748$	−12082.4	−0.590609
$749$	4833.63	0.235804
$750$	−750.000	−0.0365148
$751$	−26850.4	−1.30464	−0.652321	−	0.757943i	$-0.726204\pi$
$751$	−26850.4	−1.30464	−0.652321	+	0.757943i	$0.726204\pi$
$752$	−2410.34	−0.116883
$753$	−140.180	−0.00678410
$754$	3675.73	0.177536
$755$	473.532	0.0228260
$756$	957.007	0.0460397
$757$	−5400.95	−0.259314	−0.129657	−	0.991559i	$-0.541388\pi$
$757$	−5400.95	−0.259314	−0.129657	+	0.991559i	$0.541388\pi$
$758$	22625.4	1.08416
$759$	28016.3	1.33983
$760$	3508.34	0.167449
$761$	−1971.64	−0.0939184	−0.0469592	−	0.998897i	$-0.514953\pi$
$761$	−1971.64	−0.0939184	−0.0469592	+	0.998897i	$0.514953\pi$
$762$	11820.3	0.561947
$763$	3010.20	0.142826
$764$	4226.81	0.200158
$765$	2591.82	0.122494
$766$	−15353.3	−0.724199
$767$	3954.72	0.186176
$768$	768.000	0.0360844
$769$	33193.0	1.55653	0.778265	−	0.627936i	$-0.216100\pi$
$769$	33193.0	1.55653	0.778265	+	0.627936i	$0.216100\pi$
$770$	−4647.19	−0.217498
$771$	−2211.10	−0.103283
$772$	7855.82	0.366240
$773$	19640.0	0.913845	0.456922	−	0.889507i	$-0.348952\pi$
$773$	19640.0	0.913845	0.456922	+	0.889507i	$0.348952\pi$
$774$	4658.80	0.216353
$775$	−775.000	−0.0359211
$776$	−6561.08	−0.303517
$777$	465.749	0.0215041
$778$	−6219.83	−0.286622
$779$	14250.1	0.655409
$780$	−477.975	−0.0219413
$781$	46080.6	2.11126
$782$	−20512.3	−0.938002
$783$	6229.07	0.284303
$784$	−4231.67	−0.192769
$785$	−8895.14	−0.404435
$786$	−7774.68	−0.352816
$787$	3229.13	0.146259	0.0731296	−	0.997322i	$-0.476701\pi$
$787$	3229.13	0.146259	0.0731296	+	0.997322i	$0.476701\pi$
$788$	10414.0	0.470792
$789$	1822.75	0.0822453
$790$	−12123.8	−0.546006
$791$	−10624.7	−0.477588
$792$	3776.00	0.169412
$793$	1695.54	0.0759272
$794$	−13838.0	−0.618504
$795$	3596.76	0.160458
$796$	−20633.8	−0.918774
$797$	−19677.0	−0.874524	−0.437262	−	0.899334i	$-0.644052\pi$
$797$	−19677.0	−0.874524	−0.437262	+	0.899334i	$0.644052\pi$
$798$	−4663.21	−0.206862
$799$	8676.63	0.384177
$800$	800.000	0.0353553
$801$	290.363	0.0128083
$802$	−19751.1	−0.869622
$803$	61563.5	2.70552
$804$	−1416.15	−0.0621189
$805$	−7889.55	−0.345429
$806$	−493.907	−0.0215845
$807$	−15504.7	−0.676323
$808$	−11343.5	−0.493888
$809$	24674.3	1.07232	0.536158	−	0.844118i	$-0.319875\pi$
$809$	24674.3	1.07232	0.536158	+	0.844118i	$0.319875\pi$
$810$	−810.000	−0.0351364
$811$	1555.10	0.0673327	0.0336664	−	0.999433i	$-0.489282\pi$
$811$	1555.10	0.0673327	0.0336664	+	0.999433i	$0.489282\pi$
$812$	8177.32	0.353409
$813$	21794.8	0.940191
$814$	1837.68	0.0791284
$815$	−742.247	−0.0319016
$816$	−2764.61	−0.118604
$817$	−22700.9	−0.972099
$818$	10581.8	0.452303
$819$	635.313	0.0271058
$820$	3249.42	0.138384
$821$	−14939.2	−0.635058	−0.317529	−	0.948248i	$-0.602853\pi$
$821$	−14939.2	−0.635058	−0.317529	+	0.948248i	$0.602853\pi$
$822$	−6657.27	−0.282481
$823$	22261.3	0.942869	0.471434	−	0.881901i	$-0.343736\pi$
$823$	22261.3	0.942869	0.471434	+	0.881901i	$0.343736\pi$
$824$	−156.884	−0.00663267
$825$	3933.33	0.165989
$826$	8797.99	0.370607
$827$	−21999.4	−0.925024	−0.462512	−	0.886613i	$-0.653052\pi$
$827$	−21999.4	−0.925024	−0.462512	+	0.886613i	$0.653052\pi$
$828$	6410.52	0.269059
$829$	28988.8	1.21450	0.607251	−	0.794510i	$-0.292272\pi$
$829$	28988.8	1.21450	0.607251	+	0.794510i	$0.292272\pi$
$830$	3237.11	0.135376
$831$	−21909.7	−0.914608
$832$	509.840	0.0212446
$833$	15233.0	0.633603
$834$	14549.3	0.604076
$835$	194.549	0.00806304
$836$	−18399.3	−0.761188
$837$	−837.000	−0.0345651
$838$	−12763.1	−0.526126
$839$	22517.0	0.926547	0.463274	−	0.886215i	$-0.346675\pi$
$839$	22517.0	0.926547	0.463274	+	0.886215i	$0.346675\pi$
$840$	−1063.34	−0.0436771
$841$	28836.4	1.18235
$842$	3165.40	0.129557
$843$	−18584.5	−0.759292
$844$	−10323.7	−0.421037
$845$	10667.7	0.434296
$846$	−2711.63	−0.110198
$847$	12577.7	0.510242
$848$	−3836.54	−0.155363
$849$	−17558.9	−0.709799
$850$	−2879.80	−0.116208
$851$	3119.83	0.125671
$852$	10543.9	0.423975
$853$	9534.49	0.382714	0.191357	−	0.981521i	$-0.438711\pi$
$853$	9534.49	0.382714	0.191357	+	0.981521i	$0.438711\pi$
$854$	3772.03	0.151143
$855$	3946.89	0.157872
$856$	4363.87	0.174245
$857$	−19405.6	−0.773492	−0.386746	−	0.922186i	$-0.626401\pi$
$857$	−19405.6	−0.773492	−0.386746	+	0.922186i	$0.626401\pi$
$858$	2506.71	0.0997409
$859$	33035.2	1.31216	0.656080	−	0.754691i	$-0.272213\pi$
$859$	33035.2	1.31216	0.656080	+	0.754691i	$0.272213\pi$
$860$	−5176.45	−0.205250
$861$	−4319.06	−0.170956
$862$	−24658.9	−0.974343
$863$	17068.8	0.673266	0.336633	−	0.941636i	$-0.390712\pi$
$863$	17068.8	0.673266	0.336633	+	0.941636i	$0.390712\pi$
$864$	864.000	0.0340207
$865$	11096.2	0.436166
$866$	7017.20	0.275351
$867$	−4787.08	−0.187517
$868$	−1098.79	−0.0429668
$869$	63582.4	2.48203
$870$	−6921.19	−0.269713
$871$	−940.113	−0.0365724
$872$	2717.65	0.105540
$873$	−7381.22	−0.286159
$874$	−31236.5	−1.20892
$875$	−1107.65	−0.0427946
$876$	14086.6	0.543312
$877$	40491.5	1.55907	0.779533	−	0.626361i	$-0.215457\pi$
$877$	40491.5	1.55907	0.779533	+	0.626361i	$0.215457\pi$
$878$	9677.06	0.371965
$879$	−12036.7	−0.461873
$880$	−4195.55	−0.160718
$881$	36932.7	1.41237	0.706183	−	0.708030i	$-0.250416\pi$
$881$	36932.7	1.41237	0.706183	+	0.708030i	$0.250416\pi$
$882$	−4760.63	−0.181745
$883$	−37192.3	−1.41747	−0.708733	−	0.705477i	$-0.750733\pi$
$883$	−37192.3	−1.41747	−0.708733	+	0.705477i	$0.750733\pi$
$884$	−1835.30	−0.0698278
$885$	−7446.52	−0.282838
$886$	16113.1	0.610981
$887$	−4500.06	−0.170346	−0.0851732	−	0.996366i	$-0.527144\pi$
$887$	−4500.06	−0.170346	−0.0851732	+	0.996366i	$0.527144\pi$
$888$	420.485	0.0158903
$889$	17456.9	0.658590
$890$	−322.626	−0.0121510
$891$	4248.00	0.159723
$892$	−22829.0	−0.856917
$893$	13213.0	0.495134
$894$	−17916.7	−0.670274
$895$	−11723.3	−0.437841
$896$	1134.23	0.0422902
$897$	4255.65	0.158408
$898$	6937.06	0.257787
$899$	−7151.90	−0.265327
$900$	900.000	0.0333333
$901$	13810.6	0.510653
$902$	−17041.4	−0.629065
$903$	6880.41	0.253561
$904$	−9592.16	−0.352910
$905$	11798.8	0.433375
$906$	−568.239	−0.0208372
$907$	11757.6	0.430435	0.215218	−	0.976566i	$-0.430954\pi$
$907$	11757.6	0.430435	0.215218	+	0.976566i	$0.430954\pi$
$908$	−19164.9	−0.700451
$909$	−12761.4	−0.465642
$910$	−705.903	−0.0257148
$911$	−31078.2	−1.13026	−0.565130	−	0.825002i	$-0.691174\pi$
$911$	−31078.2	−1.13026	−0.565130	+	0.825002i	$0.691174\pi$
$912$	−4210.01	−0.152859
$913$	−16976.8	−0.615391
$914$	1245.38	0.0450696
$915$	−3192.60	−0.115349
$916$	563.540	0.0203274
$917$	−11482.1	−0.413494
$918$	−3110.19	−0.111821
$919$	−44563.2	−1.59957	−0.799784	−	0.600287i	$-0.795053\pi$
$919$	−44563.2	−1.59957	−0.799784	+	0.600287i	$0.795053\pi$
$920$	−7122.80	−0.255252
$921$	19169.3	0.685831
$922$	−24051.8	−0.859116
$923$	6999.58	0.249614
$924$	5576.63	0.198547
$925$	438.006	0.0155692
$926$	29113.7	1.03319
$927$	−176.495	−0.00625334
$928$	7382.60	0.261149
$929$	56052.1	1.97956	0.989779	−	0.142612i	$-0.0455502\pi$
$929$	56052.1	1.97956	0.989779	+	0.142612i	$0.0455502\pi$
$930$	930.000	0.0327913
$931$	23197.1	0.816600
$932$	4679.28	0.164458
$933$	−6521.94	−0.228852
$934$	8268.66	0.289677
$935$	15103.0	0.528256
$936$	573.570	0.0200296
$937$	15224.8	0.530815	0.265408	−	0.964136i	$-0.414493\pi$
$937$	15224.8	0.530815	0.265408	+	0.964136i	$0.414493\pi$
$938$	−2091.45	−0.0728021
$939$	−2450.64	−0.0851689
$940$	3012.92	0.104543
$941$	26236.9	0.908927	0.454463	−	0.890765i	$-0.349831\pi$
$941$	26236.9	0.908927	0.454463	+	0.890765i	$0.349831\pi$
$942$	10674.2	0.369197
$943$	−28931.3	−0.999079
$944$	7942.95	0.273857
$945$	−1196.26	−0.0411792
$946$	27147.6	0.933027
$947$	−21246.6	−0.729061	−0.364531	−	0.931191i	$-0.618771\pi$
$947$	−21246.6	−0.729061	−0.364531	+	0.931191i	$0.618771\pi$
$948$	14548.5	0.498433
$949$	9351.42	0.319874
$950$	−4385.43	−0.149771
$951$	−22096.9	−0.753462
$952$	−4082.95	−0.139001
$953$	−18707.5	−0.635883	−0.317941	−	0.948110i	$-0.602991\pi$
$953$	−18707.5	−0.635883	−0.317941	+	0.948110i	$0.602991\pi$
$954$	−4316.11	−0.146477
$955$	−5283.51	−0.179027
$956$	21597.1	0.730650
$957$	36297.8	1.22606
$958$	32918.8	1.11019
$959$	−9831.88	−0.331061
$960$	−960.000	−0.0322749
$961$	961.000	0.0322581
$962$	279.141	0.00935536
$963$	4909.36	0.164280
$964$	−344.230	−0.0115009
$965$	−9819.77	−0.327575
$966$	9467.46	0.315332
$967$	−44326.4	−1.47408	−0.737042	−	0.675847i	$-0.763778\pi$
$967$	−44326.4	−1.47408	−0.737042	+	0.675847i	$0.763778\pi$
$968$	11355.3	0.377040
$969$	15155.0	0.502424
$970$	8201.35	0.271474
$971$	19021.9	0.628673	0.314336	−	0.949312i	$-0.398218\pi$
$971$	19021.9	0.628673	0.314336	+	0.949312i	$0.398218\pi$
$972$	972.000	0.0320750
$973$	21487.3	0.707965
$974$	−15675.3	−0.515677
$975$	597.468	0.0196249
$976$	3405.44	0.111686
$977$	2169.60	0.0710459	0.0355229	−	0.999369i	$-0.488690\pi$
$977$	2169.60	0.0710459	0.0355229	+	0.999369i	$0.488690\pi$
$978$	890.697	0.0291220
$979$	1691.99	0.0552362
$980$	5289.59	0.172418
$981$	3057.35	0.0995044
$982$	−42252.5	−1.37305
$983$	3165.43	0.102708	0.0513538	−	0.998681i	$-0.483646\pi$
$983$	3165.43	0.102708	0.0513538	+	0.998681i	$0.483646\pi$
$984$	−3899.31	−0.126327
$985$	−13017.5	−0.421089
$986$	−26575.6	−0.858355
$987$	−4004.71	−0.129150
$988$	−2794.83	−0.0899954
$989$	46088.5	1.48183
$990$	−4720.00	−0.151527
$991$	55632.0	1.78326	0.891629	−	0.452767i	$-0.149563\pi$
$991$	55632.0	1.78326	0.891629	+	0.452767i	$0.149563\pi$
$992$	−992.000	−0.0317500
$993$	−18055.7	−0.577020
$994$	15571.8	0.496890
$995$	25792.2	0.821777
$996$	−3884.53	−0.123581
$997$	−32230.3	−1.02382	−0.511908	−	0.859040i	$-0.671061\pi$
$997$	−32230.3	−1.02382	−0.511908	+	0.859040i	$0.671061\pi$
$998$	−2346.03	−0.0744113
$999$	473.046	0.0149815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.4.a.q.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.4.a.q.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +8.86118 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} +8.86118 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.0000 q^{10} +52.4444 q^{11} +12.0000 q^{12} +7.96624 q^{13} +17.7224 q^{14} -15.0000 q^{15} +16.0000 q^{16} -57.5961 q^{17} +18.0000 q^{18} -87.7086 q^{19} -20.0000 q^{20} +26.5835 q^{21} +104.889 q^{22} +178.070 q^{23} +24.0000 q^{24} +25.0000 q^{25} +15.9325 q^{26} +27.0000 q^{27} +35.4447 q^{28} +230.706 q^{29} -30.0000 q^{30} -31.0000 q^{31} +32.0000 q^{32} +157.333 q^{33} -115.192 q^{34} -44.3059 q^{35} +36.0000 q^{36} +17.5202 q^{37} -175.417 q^{38} +23.8987 q^{39} -40.0000 q^{40} -162.471 q^{41} +53.1671 q^{42} +258.822 q^{43} +209.778 q^{44} -45.0000 q^{45} +356.140 q^{46} -150.646 q^{47} +48.0000 q^{48} -264.480 q^{49} +50.0000 q^{50} -172.788 q^{51} +31.8650 q^{52} -239.784 q^{53} +54.0000 q^{54} -262.222 q^{55} +70.8894 q^{56} -263.126 q^{57} +461.413 q^{58} +496.435 q^{59} -60.0000 q^{60} +212.840 q^{61} -62.0000 q^{62} +79.7506 q^{63} +64.0000 q^{64} -39.8312 q^{65} +314.667 q^{66} -118.012 q^{67} -230.384 q^{68} +534.210 q^{69} -88.6118 q^{70} +878.655 q^{71} +72.0000 q^{72} +1173.88 q^{73} +35.0404 q^{74} +75.0000 q^{75} -350.834 q^{76} +464.719 q^{77} +47.7975 q^{78} +1212.38 q^{79} -80.0000 q^{80} +81.0000 q^{81} -324.942 q^{82} -323.711 q^{83} +106.334 q^{84} +287.980 q^{85} +517.645 q^{86} +692.119 q^{87} +419.555 q^{88} +32.2626 q^{89} -90.0000 q^{90} +70.5903 q^{91} +712.280 q^{92} -93.0000 q^{93} -301.292 q^{94} +438.543 q^{95} +96.0000 q^{96} -820.135 q^{97} -528.959 q^{98} +472.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 25 q^{5} + 30 q^{6} + 15 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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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