LMFDB - Embedded newform 966.4.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
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} - 560x^{3} + 2247x^{2} + 58113x - 197784 $ x^5 - x^4 - 560x^3 + 2247x^2 + 58113*x - 197784
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-22.4726$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.4726 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.4726 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +42.9452 q^{10} +1.00022 q^{11} +12.0000 q^{12} +23.0343 q^{13} -14.0000 q^{14} -64.4178 q^{15} +16.0000 q^{16} -117.452 q^{17} -18.0000 q^{18} +56.5069 q^{19} -85.8904 q^{20} +21.0000 q^{21} -2.00045 q^{22} -23.0000 q^{23} -24.0000 q^{24} +336.072 q^{25} -46.0687 q^{26} +27.0000 q^{27} +28.0000 q^{28} -141.480 q^{29} +128.836 q^{30} -148.161 q^{31} -32.0000 q^{32} +3.00067 q^{33} +234.904 q^{34} -150.308 q^{35} +36.0000 q^{36} -80.0226 q^{37} -113.014 q^{38} +69.1030 q^{39} +171.781 q^{40} -177.972 q^{41} -42.0000 q^{42} -562.105 q^{43} +4.00090 q^{44} -193.253 q^{45} +46.0000 q^{46} +270.500 q^{47} +48.0000 q^{48} +49.0000 q^{49} -672.144 q^{50} -352.356 q^{51} +92.1374 q^{52} -38.8329 q^{53} -54.0000 q^{54} -21.4774 q^{55} -56.0000 q^{56} +169.521 q^{57} +282.961 q^{58} +764.446 q^{59} -257.671 q^{60} +384.046 q^{61} +296.323 q^{62} +63.0000 q^{63} +64.0000 q^{64} -494.607 q^{65} -6.00135 q^{66} -107.284 q^{67} -469.808 q^{68} -69.0000 q^{69} +300.616 q^{70} +1053.84 q^{71} -72.0000 q^{72} +797.395 q^{73} +160.045 q^{74} +1008.22 q^{75} +226.028 q^{76} +7.00157 q^{77} -138.206 q^{78} +186.543 q^{79} -343.561 q^{80} +81.0000 q^{81} +355.944 q^{82} -219.967 q^{83} +84.0000 q^{84} +2522.00 q^{85} +1124.21 q^{86} -424.441 q^{87} -8.00180 q^{88} -86.8434 q^{89} +386.507 q^{90} +161.240 q^{91} -92.0000 q^{92} -444.484 q^{93} -541.000 q^{94} -1213.35 q^{95} -96.0000 q^{96} -408.883 q^{97} -98.0000 q^{98} +9.00202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} - 12 q^{10} - 50 q^{11} + 60 q^{12} + 66 q^{13} - 70 q^{14} + 18 q^{15} + 80 q^{16} - 198 q^{17} - 90 q^{18} + 120 q^{19} + 24 q^{20} + 105 q^{21} + 100 q^{22} - 115 q^{23} - 120 q^{24} + 503 q^{25} - 132 q^{26} + 135 q^{27} + 140 q^{28} + 301 q^{29} - 36 q^{30} + 314 q^{31} - 160 q^{32} - 150 q^{33} + 396 q^{34} + 42 q^{35} + 180 q^{36} + 269 q^{37} - 240 q^{38} + 198 q^{39} - 48 q^{40} + 479 q^{41} - 210 q^{42} - 290 q^{43} - 200 q^{44} + 54 q^{45} + 230 q^{46} + 69 q^{47} + 240 q^{48} + 245 q^{49} - 1006 q^{50} - 594 q^{51} + 264 q^{52} + 339 q^{53} - 270 q^{54} + 957 q^{55} - 280 q^{56} + 360 q^{57} - 602 q^{58} + 2065 q^{59} + 72 q^{60} + 531 q^{61} - 628 q^{62} + 315 q^{63} + 320 q^{64} + 1227 q^{65} + 300 q^{66} + 855 q^{67} - 792 q^{68} - 345 q^{69} - 84 q^{70} - 863 q^{71} - 360 q^{72} + 618 q^{73} - 538 q^{74} + 1509 q^{75} + 480 q^{76} - 350 q^{77} - 396 q^{78} + 254 q^{79} + 96 q^{80} + 405 q^{81} - 958 q^{82} - 1700 q^{83} + 420 q^{84} + 1977 q^{85} + 580 q^{86} + 903 q^{87} + 400 q^{88} - 275 q^{89} - 108 q^{90} + 462 q^{91} - 460 q^{92} + 942 q^{93} - 138 q^{94} + 171 q^{95} - 480 q^{96} - 979 q^{97} - 490 q^{98} - 450 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 - 12 * q^10 - 50 * q^11 + 60 * q^12 + 66 * q^13 - 70 * q^14 + 18 * q^15 + 80 * q^16 - 198 * q^17 - 90 * q^18 + 120 * q^19 + 24 * q^20 + 105 * q^21 + 100 * q^22 - 115 * q^23 - 120 * q^24 + 503 * q^25 - 132 * q^26 + 135 * q^27 + 140 * q^28 + 301 * q^29 - 36 * q^30 + 314 * q^31 - 160 * q^32 - 150 * q^33 + 396 * q^34 + 42 * q^35 + 180 * q^36 + 269 * q^37 - 240 * q^38 + 198 * q^39 - 48 * q^40 + 479 * q^41 - 210 * q^42 - 290 * q^43 - 200 * q^44 + 54 * q^45 + 230 * q^46 + 69 * q^47 + 240 * q^48 + 245 * q^49 - 1006 * q^50 - 594 * q^51 + 264 * q^52 + 339 * q^53 - 270 * q^54 + 957 * q^55 - 280 * q^56 + 360 * q^57 - 602 * q^58 + 2065 * q^59 + 72 * q^60 + 531 * q^61 - 628 * q^62 + 315 * q^63 + 320 * q^64 + 1227 * q^65 + 300 * q^66 + 855 * q^67 - 792 * q^68 - 345 * q^69 - 84 * q^70 - 863 * q^71 - 360 * q^72 + 618 * q^73 - 538 * q^74 + 1509 * q^75 + 480 * q^76 - 350 * q^77 - 396 * q^78 + 254 * q^79 + 96 * q^80 + 405 * q^81 - 958 * q^82 - 1700 * q^83 + 420 * q^84 + 1977 * q^85 + 580 * q^86 + 903 * q^87 + 400 * q^88 - 275 * q^89 - 108 * q^90 + 462 * q^91 - 460 * q^92 + 942 * q^93 - 138 * q^94 + 171 * q^95 - 480 * q^96 - 979 * q^97 - 490 * q^98 - 450 * 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
$5$	−21.4726	−1.92057	−0.960283	−	0.279027i	$-0.909988\pi$
$5$	−21.4726	−1.92057	−0.960283	+	0.279027i	$0.909988\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	42.9452	1.35805
$11$	1.00022	0.0274163	0.0137081	−	0.999906i	$-0.495636\pi$
$11$	1.00022	0.0274163	0.0137081	+	0.999906i	$0.495636\pi$
$12$	12.0000	0.288675
$13$	23.0343	0.491429	0.245714	−	0.969342i	$-0.420977\pi$
$13$	23.0343	0.491429	0.245714	+	0.969342i	$0.420977\pi$
$14$	−14.0000	−0.267261
$15$	−64.4178	−1.10884
$16$	16.0000	0.250000
$17$	−117.452	−1.67567	−0.837833	−	0.545927i	$-0.816178\pi$
$17$	−117.452	−1.67567	−0.837833	+	0.545927i	$0.816178\pi$
$18$	−18.0000	−0.235702
$19$	56.5069	0.682294	0.341147	−	0.940010i	$-0.389185\pi$
$19$	56.5069	0.682294	0.341147	+	0.940010i	$0.389185\pi$
$20$	−85.8904	−0.960283
$21$	21.0000	0.218218
$22$	−2.00045	−0.0193862
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	336.072	2.68858
$26$	−46.0687	−0.347493
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−141.480	−0.905940	−0.452970	−	0.891526i	$-0.649635\pi$
$29$	−141.480	−0.905940	−0.452970	+	0.891526i	$0.649635\pi$
$30$	128.836	0.784068
$31$	−148.161	−0.858406	−0.429203	−	0.903208i	$-0.641205\pi$
$31$	−148.161	−0.858406	−0.429203	+	0.903208i	$0.641205\pi$
$32$	−32.0000	−0.176777
$33$	3.00067	0.0158288
$34$	234.904	1.18487
$35$	−150.308	−0.725906
$36$	36.0000	0.166667
$37$	−80.0226	−0.355558	−0.177779	−	0.984070i	$-0.556891\pi$
$37$	−80.0226	−0.355558	−0.177779	+	0.984070i	$0.556891\pi$
$38$	−113.014	−0.482454
$39$	69.1030	0.283727
$40$	171.781	0.679023
$41$	−177.972	−0.677915	−0.338958	−	0.940802i	$-0.610074\pi$
$41$	−177.972	−0.677915	−0.338958	+	0.940802i	$0.610074\pi$
$42$	−42.0000	−0.154303
$43$	−562.105	−1.99349	−0.996746	−	0.0806057i	$-0.974315\pi$
$43$	−562.105	−1.99349	−0.996746	+	0.0806057i	$0.974315\pi$
$44$	4.00090	0.0137081
$45$	−193.253	−0.640189
$46$	46.0000	0.147442
$47$	270.500	0.839499	0.419750	−	0.907640i	$-0.362118\pi$
$47$	270.500	0.839499	0.419750	+	0.907640i	$0.362118\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−672.144	−1.90111
$51$	−352.356	−0.967446
$52$	92.1374	0.245714
$53$	−38.8329	−0.100644	−0.0503218	−	0.998733i	$-0.516025\pi$
$53$	−38.8329	−0.100644	−0.0503218	+	0.998733i	$0.516025\pi$
$54$	−54.0000	−0.136083
$55$	−21.4774	−0.0526548
$56$	−56.0000	−0.133631
$57$	169.521	0.393922
$58$	282.961	0.640596
$59$	764.446	1.68682	0.843410	−	0.537271i	$-0.180545\pi$
$59$	764.446	1.68682	0.843410	+	0.537271i	$0.180545\pi$
$60$	−257.671	−0.554420
$61$	384.046	0.806098	0.403049	−	0.915178i	$-0.367950\pi$
$61$	384.046	0.806098	0.403049	+	0.915178i	$0.367950\pi$
$62$	296.323	0.606984
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−494.607	−0.943822
$66$	−6.00135	−0.0111926
$67$	−107.284	−0.195625	−0.0978124	−	0.995205i	$-0.531185\pi$
$67$	−107.284	−0.195625	−0.0978124	+	0.995205i	$0.531185\pi$
$68$	−469.808	−0.837833
$69$	−69.0000	−0.120386
$70$	300.616	0.513293
$71$	1053.84	1.76151	0.880756	−	0.473571i	$-0.157035\pi$
$71$	1053.84	1.76151	0.880756	+	0.473571i	$0.157035\pi$
$72$	−72.0000	−0.117851
$73$	797.395	1.27847	0.639233	−	0.769013i	$-0.279252\pi$
$73$	797.395	1.27847	0.639233	+	0.769013i	$0.279252\pi$
$74$	160.045	0.251417
$75$	1008.22	1.55225
$76$	226.028	0.341147
$77$	7.00157	0.0103624
$78$	−138.206	−0.200625
$79$	186.543	0.265668	0.132834	−	0.991138i	$-0.457592\pi$
$79$	186.543	0.265668	0.132834	+	0.991138i	$0.457592\pi$
$80$	−343.561	−0.480142
$81$	81.0000	0.111111
$82$	355.944	0.479359
$83$	−219.967	−0.290897	−0.145449	−	0.989366i	$-0.546463\pi$
$83$	−219.967	−0.290897	−0.145449	+	0.989366i	$0.546463\pi$
$84$	84.0000	0.109109
$85$	2522.00	3.21823
$86$	1124.21	1.40961
$87$	−424.441	−0.523044
$88$	−8.00180	−0.00969312
$89$	−86.8434	−0.103431	−0.0517156	−	0.998662i	$-0.516469\pi$
$89$	−86.8434	−0.103431	−0.0517156	+	0.998662i	$0.516469\pi$
$90$	386.507	0.452682
$91$	161.240	0.185743
$92$	−92.0000	−0.104257
$93$	−444.484	−0.495601
$94$	−541.000	−0.593616
$95$	−1213.35	−1.31039
$96$	−96.0000	−0.102062
$97$	−408.883	−0.427998	−0.213999	−	0.976834i	$-0.568649\pi$
$97$	−408.883	−0.427998	−0.213999	+	0.976834i	$0.568649\pi$
$98$	−98.0000	−0.101015
$99$	9.00202	0.00913876
$100$	1344.29	1.34429
$101$	169.160	0.166654	0.0833268	−	0.996522i	$-0.473445\pi$
$101$	169.160	0.166654	0.0833268	+	0.996522i	$0.473445\pi$
$102$	704.713	0.684088
$103$	1261.72	1.20700	0.603499	−	0.797364i	$-0.293773\pi$
$103$	1261.72	1.20700	0.603499	+	0.797364i	$0.293773\pi$
$104$	−184.275	−0.173746
$105$	−450.924	−0.419102
$106$	77.6658	0.0711658
$107$	1988.01	1.79615	0.898076	−	0.439839i	$-0.144965\pi$
$107$	1988.01	1.79615	0.898076	+	0.439839i	$0.144965\pi$
$108$	108.000	0.0962250
$109$	−113.637	−0.0998573	−0.0499286	−	0.998753i	$-0.515899\pi$
$109$	−113.637	−0.0998573	−0.0499286	+	0.998753i	$0.515899\pi$
$110$	42.9548	0.0372326
$111$	−240.068	−0.205281
$112$	112.000	0.0944911
$113$	−1127.48	−0.938619	−0.469310	−	0.883034i	$-0.655497\pi$
$113$	−1127.48	−0.938619	−0.469310	+	0.883034i	$0.655497\pi$
$114$	−339.042	−0.278545
$115$	493.870	0.400466
$116$	−565.922	−0.452970
$117$	207.309	0.163810
$118$	−1528.89	−1.19276
$119$	−822.165	−0.633342
$120$	515.342	0.392034
$121$	−1330.00	−0.999248
$122$	−768.091	−0.569997
$123$	−533.915	−0.391395
$124$	−592.646	−0.429203
$125$	−4532.26	−3.24302
$126$	−126.000	−0.0890871
$127$	549.888	0.384210	0.192105	−	0.981374i	$-0.438469\pi$
$127$	549.888	0.384210	0.192105	+	0.981374i	$0.438469\pi$
$128$	−128.000	−0.0883883
$129$	−1686.31	−1.15094
$130$	989.214	0.667383
$131$	1383.02	0.922406	0.461203	−	0.887295i	$-0.347418\pi$
$131$	1383.02	0.922406	0.461203	+	0.887295i	$0.347418\pi$
$132$	12.0027	0.00791440
$133$	395.548	0.257883
$134$	214.569	0.138328
$135$	−579.760	−0.369613
$136$	939.617	0.592437
$137$	559.346	0.348819	0.174409	−	0.984673i	$-0.444198\pi$
$137$	559.346	0.348819	0.174409	+	0.984673i	$0.444198\pi$
$138$	138.000	0.0851257
$139$	2940.26	1.79417	0.897084	−	0.441860i	$-0.145681\pi$
$139$	2940.26	1.79417	0.897084	+	0.441860i	$0.145681\pi$
$140$	−601.232	−0.362953
$141$	811.500	0.484685
$142$	−2107.67	−1.24558
$143$	23.0395	0.0134732
$144$	144.000	0.0833333
$145$	3037.95	1.73992
$146$	−1594.79	−0.904013
$147$	147.000	0.0824786
$148$	−320.090	−0.177779
$149$	2825.81	1.55369	0.776843	−	0.629694i	$-0.216820\pi$
$149$	2825.81	1.55369	0.776843	+	0.629694i	$0.216820\pi$
$150$	−2016.43	−1.09761
$151$	−825.978	−0.445147	−0.222573	−	0.974916i	$-0.571446\pi$
$151$	−825.978	−0.445147	−0.222573	+	0.974916i	$0.571446\pi$
$152$	−452.055	−0.241227
$153$	−1057.07	−0.558555
$154$	−14.0031	−0.00732731
$155$	3181.41	1.64863
$156$	276.412	0.141863
$157$	−670.645	−0.340913	−0.170456	−	0.985365i	$-0.554524\pi$
$157$	−670.645	−0.340913	−0.170456	+	0.985365i	$0.554524\pi$
$158$	−373.087	−0.187856
$159$	−116.499	−0.0581066
$160$	687.123	0.339511
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	−833.278	−0.400413	−0.200207	−	0.979754i	$-0.564161\pi$
$163$	−833.278	−0.400413	−0.200207	+	0.979754i	$0.564161\pi$
$164$	−711.887	−0.338958
$165$	−64.4322	−0.0304003
$166$	439.933	0.205695
$167$	3749.17	1.73724	0.868621	−	0.495477i	$-0.165007\pi$
$167$	3749.17	1.73724	0.868621	+	0.495477i	$0.165007\pi$
$168$	−168.000	−0.0771517
$169$	−1666.42	−0.758498
$170$	−5044.00	−2.27563
$171$	508.562	0.227431
$172$	−2248.42	−0.996746
$173$	2527.97	1.11097	0.555485	−	0.831526i	$-0.312532\pi$
$173$	2527.97	1.11097	0.555485	+	0.831526i	$0.312532\pi$
$174$	848.882	0.369848
$175$	2352.50	1.01619
$176$	16.0036	0.00685407
$177$	2293.34	0.973886
$178$	173.687	0.0731370
$179$	−3005.65	−1.25504	−0.627521	−	0.778599i	$-0.715931\pi$
$179$	−3005.65	−1.25504	−0.627521	+	0.778599i	$0.715931\pi$
$180$	−773.013	−0.320094
$181$	3847.72	1.58010	0.790051	−	0.613041i	$-0.210054\pi$
$181$	3847.72	1.58010	0.790051	+	0.613041i	$0.210054\pi$
$182$	−322.481	−0.131340
$183$	1152.14	0.465401
$184$	184.000	0.0737210
$185$	1718.29	0.682872
$186$	888.968	0.350443
$187$	−117.478	−0.0459405
$188$	1082.00	0.419750
$189$	189.000	0.0727393
$190$	2426.70	0.926586
$191$	156.191	0.0591707	0.0295853	−	0.999562i	$-0.490581\pi$
$191$	156.191	0.0591707	0.0295853	+	0.999562i	$0.490581\pi$
$192$	192.000	0.0721688
$193$	−3007.56	−1.12170	−0.560852	−	0.827916i	$-0.689527\pi$
$193$	−3007.56	−1.12170	−0.560852	+	0.827916i	$0.689527\pi$
$194$	817.766	0.302640
$195$	−1483.82	−0.544916
$196$	196.000	0.0714286
$197$	−354.748	−0.128298	−0.0641491	−	0.997940i	$-0.520433\pi$
$197$	−354.748	−0.128298	−0.0641491	+	0.997940i	$0.520433\pi$
$198$	−18.0040	−0.00646208
$199$	722.445	0.257351	0.128675	−	0.991687i	$-0.458928\pi$
$199$	722.445	0.257351	0.128675	+	0.991687i	$0.458928\pi$
$200$	−2688.58	−0.950555
$201$	−321.853	−0.112944
$202$	−338.319	−0.117842
$203$	−990.363	−0.342413
$204$	−1409.43	−0.483723
$205$	3821.52	1.30198
$206$	−2523.44	−0.853477
$207$	−207.000	−0.0695048
$208$	368.549	0.122857
$209$	56.5196	0.0187060
$210$	901.849	0.296350
$211$	2577.75	0.841041	0.420520	−	0.907283i	$-0.361848\pi$
$211$	2577.75	0.841041	0.420520	+	0.907283i	$0.361848\pi$
$212$	−155.332	−0.0503218
$213$	3161.51	1.01701
$214$	−3976.02	−1.27007
$215$	12069.8	3.82863
$216$	−216.000	−0.0680414
$217$	−1037.13	−0.324447
$218$	227.274	0.0706098
$219$	2392.19	0.738123
$220$	−85.9096	−0.0263274
$221$	−2705.43	−0.823471
$222$	480.136	0.145156
$223$	3306.15	0.992809	0.496404	−	0.868091i	$-0.334653\pi$
$223$	3306.15	0.992809	0.496404	+	0.868091i	$0.334653\pi$
$224$	−224.000	−0.0668153
$225$	3024.65	0.896192
$226$	2254.95	0.663704
$227$	−4630.17	−1.35381	−0.676906	−	0.736069i	$-0.736680\pi$
$227$	−4630.17	−1.35381	−0.676906	+	0.736069i	$0.736680\pi$
$228$	678.083	0.196961
$229$	−10.9728	−0.00316638	−0.00158319	−	0.999999i	$-0.500504\pi$
$229$	−10.9728	−0.00316638	−0.00158319	+	0.999999i	$0.500504\pi$
$230$	−987.739	−0.283172
$231$	21.0047	0.00598272
$232$	1131.84	0.320298
$233$	1252.68	0.352213	0.176107	−	0.984371i	$-0.443650\pi$
$233$	1252.68	0.352213	0.176107	+	0.984371i	$0.443650\pi$
$234$	−414.618	−0.115831
$235$	−5808.33	−1.61231
$236$	3057.78	0.843410
$237$	559.630	0.153384
$238$	1644.33	0.447841
$239$	−374.274	−0.101296	−0.0506480	−	0.998717i	$-0.516129\pi$
$239$	−374.274	−0.101296	−0.0506480	+	0.998717i	$0.516129\pi$
$240$	−1030.68	−0.277210
$241$	−4899.76	−1.30963	−0.654817	−	0.755788i	$-0.727254\pi$
$241$	−4899.76	−1.30963	−0.654817	+	0.755788i	$0.727254\pi$
$242$	2660.00	0.706575
$243$	243.000	0.0641500
$244$	1536.18	0.403049
$245$	−1052.16	−0.274367
$246$	1067.83	0.276758
$247$	1301.60	0.335299
$248$	1185.29	0.303492
$249$	−659.900	−0.167950
$250$	9064.52	2.29316
$251$	3508.15	0.882201	0.441101	−	0.897458i	$-0.354588\pi$
$251$	3508.15	0.882201	0.441101	+	0.897458i	$0.354588\pi$
$252$	252.000	0.0629941
$253$	−23.0052	−0.00571669
$254$	−1099.78	−0.271677
$255$	7566.00	1.85804
$256$	256.000	0.0625000
$257$	−6134.57	−1.48897	−0.744483	−	0.667642i	$-0.767304\pi$
$257$	−6134.57	−1.48897	−0.744483	+	0.667642i	$0.767304\pi$
$258$	3372.63	0.813840
$259$	−560.158	−0.134388
$260$	−1978.43	−0.471911
$261$	−1273.32	−0.301980
$262$	−2766.04	−0.652240
$263$	7243.69	1.69835	0.849173	−	0.528115i	$-0.177101\pi$
$263$	7243.69	1.69835	0.849173	+	0.528115i	$0.177101\pi$
$264$	−24.0054	−0.00559632
$265$	833.843	0.193293
$266$	−791.097	−0.182351
$267$	−260.530	−0.0597161
$268$	−429.137	−0.0978124
$269$	3257.65	0.738372	0.369186	−	0.929355i	$-0.379636\pi$
$269$	3257.65	0.738372	0.369186	+	0.929355i	$0.379636\pi$
$270$	1159.52	0.261356
$271$	4586.57	1.02810	0.514048	−	0.857761i	$-0.328145\pi$
$271$	4586.57	1.02810	0.514048	+	0.857761i	$0.328145\pi$
$272$	−1879.23	−0.418916
$273$	483.721	0.107239
$274$	−1118.69	−0.246652
$275$	336.147	0.0737108
$276$	−276.000	−0.0601929
$277$	−5858.76	−1.27083	−0.635413	−	0.772172i	$-0.719170\pi$
$277$	−5858.76	−1.27083	−0.635413	+	0.772172i	$0.719170\pi$
$278$	−5880.51	−1.26867
$279$	−1333.45	−0.286135
$280$	1202.46	0.256647
$281$	4277.79	0.908154	0.454077	−	0.890962i	$-0.349969\pi$
$281$	4277.79	0.908154	0.454077	+	0.890962i	$0.349969\pi$
$282$	−1623.00	−0.342724
$283$	5363.01	1.12649	0.563247	−	0.826289i	$-0.309552\pi$
$283$	5363.01	1.12649	0.563247	+	0.826289i	$0.309552\pi$
$284$	4215.34	0.880756
$285$	−3640.05	−0.756554
$286$	−46.0790	−0.00952696
$287$	−1245.80	−0.256228
$288$	−288.000	−0.0589256
$289$	8882.00	1.80786
$290$	−6075.90	−1.23031
$291$	−1226.65	−0.247105
$292$	3189.58	0.639233
$293$	−1832.46	−0.365370	−0.182685	−	0.983172i	$-0.558479\pi$
$293$	−1832.46	−0.365370	−0.182685	+	0.983172i	$0.558479\pi$
$294$	−294.000	−0.0583212
$295$	−16414.6	−3.23965
$296$	640.181	0.125709
$297$	27.0061	0.00527627
$298$	−5651.62	−1.09862
$299$	−529.790	−0.102470
$300$	4032.86	0.776125
$301$	−3934.73	−0.753469
$302$	1651.96	0.314766
$303$	507.479	0.0962175
$304$	904.111	0.170573
$305$	−8246.45	−1.54817
$306$	2114.14	0.394958
$307$	9299.72	1.72887	0.864435	−	0.502744i	$-0.167676\pi$
$307$	9299.72	1.72887	0.864435	+	0.502744i	$0.167676\pi$
$308$	28.0063	0.00518119
$309$	3785.16	0.696861
$310$	−6362.82	−1.16575
$311$	2316.60	0.422387	0.211194	−	0.977444i	$-0.432265\pi$
$311$	2316.60	0.422387	0.211194	+	0.977444i	$0.432265\pi$
$312$	−552.824	−0.100313
$313$	5013.98	0.905453	0.452727	−	0.891649i	$-0.350451\pi$
$313$	5013.98	0.905453	0.452727	+	0.891649i	$0.350451\pi$
$314$	1341.29	0.241062
$315$	−1352.77	−0.241969
$316$	746.174	0.132834
$317$	−285.016	−0.0504987	−0.0252493	−	0.999681i	$-0.508038\pi$
$317$	−285.016	−0.0504987	−0.0252493	+	0.999681i	$0.508038\pi$
$318$	232.998	0.0410876
$319$	−141.512	−0.0248375
$320$	−1374.25	−0.240071
$321$	5964.04	1.03701
$322$	322.000	0.0557278
$323$	−6636.86	−1.14330
$324$	324.000	0.0555556
$325$	7741.20	1.32124
$326$	1666.56	0.283135
$327$	−340.911	−0.0576526
$328$	1423.77	0.239679
$329$	1893.50	0.317301
$330$	128.864	0.0214962
$331$	11764.2	1.95353	0.976764	−	0.214319i	$-0.0687533\pi$
$331$	11764.2	1.95353	0.976764	+	0.214319i	$0.0687533\pi$
$332$	−879.866	−0.145449
$333$	−720.203	−0.118519
$334$	−7498.34	−1.22842
$335$	2303.67	0.375711
$336$	336.000	0.0545545
$337$	3339.03	0.539729	0.269864	−	0.962898i	$-0.413021\pi$
$337$	3339.03	0.539729	0.269864	+	0.962898i	$0.413021\pi$
$338$	3332.84	0.536339
$339$	−3382.43	−0.541912
$340$	10088.0	1.60911
$341$	−148.195	−0.0235343
$342$	−1017.12	−0.160818
$343$	343.000	0.0539949
$344$	4496.84	0.704806
$345$	1481.61	0.231209
$346$	−5055.94	−0.785575
$347$	2355.12	0.364350	0.182175	−	0.983266i	$-0.441686\pi$
$347$	2355.12	0.364350	0.182175	+	0.983266i	$0.441686\pi$
$348$	−1697.76	−0.261522
$349$	−5474.65	−0.839688	−0.419844	−	0.907596i	$-0.637915\pi$
$349$	−5474.65	−0.839688	−0.419844	+	0.907596i	$0.637915\pi$
$350$	−4705.01	−0.718552
$351$	621.927	0.0945755
$352$	−32.0072	−0.00484656
$353$	−11409.3	−1.72027	−0.860134	−	0.510069i	$-0.829620\pi$
$353$	−11409.3	−1.72027	−0.860134	+	0.510069i	$0.829620\pi$
$354$	−4586.67	−0.688641
$355$	−22628.6	−3.38310
$356$	−347.374	−0.0517156
$357$	−2466.49	−0.365660
$358$	6011.30	0.887449
$359$	−1693.18	−0.248921	−0.124460	−	0.992225i	$-0.539720\pi$
$359$	−1693.18	−0.248921	−0.124460	+	0.992225i	$0.539720\pi$
$360$	1546.03	0.226341
$361$	−3665.97	−0.534475
$362$	−7695.43	−1.11730
$363$	−3990.00	−0.576916
$364$	644.962	0.0928713
$365$	−17122.1	−2.45538
$366$	−2304.27	−0.329088
$367$	9744.73	1.38602	0.693012	−	0.720926i	$-0.256283\pi$
$367$	9744.73	1.38602	0.693012	+	0.720926i	$0.256283\pi$
$368$	−368.000	−0.0521286
$369$	−1601.75	−0.225972
$370$	−3436.58	−0.482864
$371$	−271.830	−0.0380397
$372$	−1777.94	−0.247800
$373$	−13283.5	−1.84396	−0.921978	−	0.387243i	$-0.873428\pi$
$373$	−13283.5	−1.84396	−0.921978	+	0.387243i	$0.873428\pi$
$374$	234.957	0.0324849
$375$	−13596.8	−1.87236
$376$	−2164.00	−0.296808
$377$	−3258.91	−0.445205
$378$	−378.000	−0.0514344
$379$	−4397.03	−0.595937	−0.297969	−	0.954576i	$-0.596309\pi$
$379$	−4397.03	−0.595937	−0.297969	+	0.954576i	$0.596309\pi$
$380$	−4853.40	−0.655195
$381$	1649.66	0.221824
$382$	−312.382	−0.0418400
$383$	5120.43	0.683138	0.341569	−	0.939857i	$-0.389042\pi$
$383$	5120.43	0.683138	0.341569	+	0.939857i	$0.389042\pi$
$384$	−384.000	−0.0510310
$385$	−150.342	−0.0199016
$386$	6015.12	0.793165
$387$	−5058.94	−0.664497
$388$	−1635.53	−0.213999
$389$	3450.81	0.449776	0.224888	−	0.974385i	$-0.427798\pi$
$389$	3450.81	0.449776	0.224888	+	0.974385i	$0.427798\pi$
$390$	2967.64	0.385314
$391$	2701.40	0.349400
$392$	−392.000	−0.0505076
$393$	4149.07	0.532552
$394$	709.495	0.0907205
$395$	−4005.57	−0.510233
$396$	36.0081	0.00456938
$397$	−436.050	−0.0551252	−0.0275626	−	0.999620i	$-0.508775\pi$
$397$	−436.050	−0.0551252	−0.0275626	+	0.999620i	$0.508775\pi$
$398$	−1444.89	−0.181974
$399$	1186.65	0.148889
$400$	5377.15	0.672144
$401$	−5228.68	−0.651142	−0.325571	−	0.945518i	$-0.605557\pi$
$401$	−5228.68	−0.651142	−0.325571	+	0.945518i	$0.605557\pi$
$402$	643.706	0.0798635
$403$	−3412.80	−0.421845
$404$	676.639	0.0833268
$405$	−1739.28	−0.213396
$406$	1980.73	0.242123
$407$	−80.0406	−0.00974807
$408$	2818.85	0.342044
$409$	−9784.10	−1.18287	−0.591433	−	0.806354i	$-0.701438\pi$
$409$	−9784.10	−1.18287	−0.591433	+	0.806354i	$0.701438\pi$
$410$	−7643.03	−0.920640
$411$	1678.04	0.201391
$412$	5046.87	0.603499
$413$	5351.12	0.637558
$414$	414.000	0.0491473
$415$	4723.25	0.558688
$416$	−737.099	−0.0868732
$417$	8820.77	1.03586
$418$	−113.039	−0.0132271
$419$	−1624.30	−0.189385	−0.0946925	−	0.995507i	$-0.530187\pi$
$419$	−1624.30	−0.189385	−0.0946925	+	0.995507i	$0.530187\pi$
$420$	−1803.70	−0.209551
$421$	−10539.1	−1.22006	−0.610030	−	0.792378i	$-0.708843\pi$
$421$	−10539.1	−1.22006	−0.610030	+	0.792378i	$0.708843\pi$
$422$	−5155.50	−0.594706
$423$	2434.50	0.279833
$424$	310.663	0.0355829
$425$	−39472.4	−4.50516
$426$	−6323.02	−0.719134
$427$	2688.32	0.304676
$428$	7952.05	0.898076
$429$	69.1185	0.00777873
$430$	−24139.7	−2.70725
$431$	−3589.11	−0.401117	−0.200559	−	0.979682i	$-0.564276\pi$
$431$	−3589.11	−0.401117	−0.200559	+	0.979682i	$0.564276\pi$
$432$	432.000	0.0481125
$433$	−13199.3	−1.46494	−0.732469	−	0.680800i	$-0.761632\pi$
$433$	−13199.3	−1.46494	−0.732469	+	0.680800i	$0.761632\pi$
$434$	2074.26	0.229419
$435$	9113.85	1.00454
$436$	−454.548	−0.0499286
$437$	−1299.66	−0.142268
$438$	−4784.37	−0.521932
$439$	−3351.47	−0.364367	−0.182183	−	0.983265i	$-0.558316\pi$
$439$	−3351.47	−0.364367	−0.182183	+	0.983265i	$0.558316\pi$
$440$	171.819	0.0186163
$441$	441.000	0.0476190
$442$	5410.86	0.582282
$443$	−15170.4	−1.62701	−0.813506	−	0.581556i	$-0.802444\pi$
$443$	−15170.4	−1.62701	−0.813506	+	0.581556i	$0.802444\pi$
$444$	−960.271	−0.102641
$445$	1864.75	0.198647
$446$	−6612.30	−0.702022
$447$	8477.43	0.897021
$448$	448.000	0.0472456
$449$	11447.6	1.20322	0.601608	−	0.798791i	$-0.294527\pi$
$449$	11447.6	1.20322	0.601608	+	0.798791i	$0.294527\pi$
$450$	−6049.30	−0.633703
$451$	−178.012	−0.0185859
$452$	−4509.90	−0.469310
$453$	−2477.93	−0.257006
$454$	9260.35	0.957290
$455$	−3462.25	−0.356731
$456$	−1356.17	−0.139273
$457$	14813.8	1.51632	0.758160	−	0.652069i	$-0.226099\pi$
$457$	14813.8	1.51632	0.758160	+	0.652069i	$0.226099\pi$
$458$	21.9456	0.00223897
$459$	−3171.21	−0.322482
$460$	1975.48	0.200233
$461$	−15117.2	−1.52728	−0.763642	−	0.645640i	$-0.776591\pi$
$461$	−15117.2	−1.52728	−0.763642	+	0.645640i	$0.776591\pi$
$462$	−42.0094	−0.00423042
$463$	−2065.39	−0.207315	−0.103657	−	0.994613i	$-0.533055\pi$
$463$	−2065.39	−0.207315	−0.103657	+	0.994613i	$0.533055\pi$
$464$	−2263.69	−0.226485
$465$	9544.23	0.951834
$466$	−2505.36	−0.249052
$467$	12233.1	1.21216	0.606080	−	0.795404i	$-0.292741\pi$
$467$	12233.1	1.21216	0.606080	+	0.795404i	$0.292741\pi$
$468$	829.236	0.0819048
$469$	−750.990	−0.0739392
$470$	11616.7	1.14008
$471$	−2011.94	−0.196826
$472$	−6115.56	−0.596381
$473$	−562.231	−0.0546541
$474$	−1119.26	−0.108459
$475$	18990.4	1.83440
$476$	−3288.66	−0.316671
$477$	−349.496	−0.0335479
$478$	748.548	0.0716271
$479$	−8162.14	−0.778575	−0.389288	−	0.921116i	$-0.627279\pi$
$479$	−8162.14	−0.778575	−0.389288	+	0.921116i	$0.627279\pi$
$480$	2061.37	0.196017
$481$	−1843.27	−0.174731
$482$	9799.53	0.926050
$483$	−483.000	−0.0455016
$484$	−5320.00	−0.499624
$485$	8779.78	0.821998
$486$	−486.000	−0.0453609
$487$	−6246.91	−0.581262	−0.290631	−	0.956835i	$-0.593865\pi$
$487$	−6246.91	−0.581262	−0.290631	+	0.956835i	$0.593865\pi$
$488$	−3072.36	−0.284999
$489$	−2499.83	−0.231179
$490$	2104.31	0.194007
$491$	−14298.7	−1.31424	−0.657119	−	0.753786i	$-0.728225\pi$
$491$	−14298.7	−1.31424	−0.657119	+	0.753786i	$0.728225\pi$
$492$	−2135.66	−0.195697
$493$	16617.2	1.51805
$494$	−2603.20	−0.237092
$495$	−193.297	−0.0175516
$496$	−2370.58	−0.214601
$497$	7376.85	0.665789
$498$	1319.80	0.118758
$499$	1903.31	0.170749	0.0853747	−	0.996349i	$-0.472791\pi$
$499$	1903.31	0.170749	0.0853747	+	0.996349i	$0.472791\pi$
$500$	−18129.0	−1.62151
$501$	11247.5	1.00300
$502$	−7016.30	−0.623811
$503$	−20195.7	−1.79022	−0.895112	−	0.445842i	$-0.852904\pi$
$503$	−20195.7	−1.79022	−0.895112	+	0.445842i	$0.852904\pi$
$504$	−504.000	−0.0445435
$505$	−3632.30	−0.320069
$506$	46.0103	0.00404231
$507$	−4999.26	−0.437919
$508$	2199.55	0.192105
$509$	1165.45	0.101488	0.0507441	−	0.998712i	$-0.483841\pi$
$509$	1165.45	0.101488	0.0507441	+	0.998712i	$0.483841\pi$
$510$	−15132.0	−1.31384
$511$	5581.77	0.483215
$512$	−512.000	−0.0441942
$513$	1525.69	0.131307
$514$	12269.1	1.05286
$515$	−27092.4	−2.31812
$516$	−6745.26	−0.575472
$517$	270.561	0.0230159
$518$	1120.32	0.0950268
$519$	7583.91	0.641419
$520$	3956.86	0.333691
$521$	15751.2	1.32452	0.662259	−	0.749275i	$-0.269598\pi$
$521$	15751.2	1.32452	0.662259	+	0.749275i	$0.269598\pi$
$522$	2546.65	0.213532
$523$	7129.29	0.596065	0.298033	−	0.954556i	$-0.403670\pi$
$523$	7129.29	0.596065	0.298033	+	0.954556i	$0.403670\pi$
$524$	5532.09	0.461203
$525$	7057.51	0.586695
$526$	−14487.4	−1.20091
$527$	17401.9	1.43840
$528$	48.0108	0.00395720
$529$	529.000	0.0434783
$530$	−1667.69	−0.136679
$531$	6880.01	0.562273
$532$	1582.19	0.128941
$533$	−4099.46	−0.333147
$534$	521.061	0.0422256
$535$	−42687.8	−3.44963
$536$	858.274	0.0691638
$537$	−9016.94	−0.724599
$538$	−6515.29	−0.522108
$539$	49.0110	0.00391661
$540$	−2319.04	−0.184807
$541$	20839.6	1.65613	0.828063	−	0.560635i	$-0.189443\pi$
$541$	20839.6	1.65613	0.828063	+	0.560635i	$0.189443\pi$
$542$	−9173.13	−0.726974
$543$	11543.2	0.912273
$544$	3758.47	0.296219
$545$	2440.08	0.191783
$546$	−967.442	−0.0758291
$547$	9652.53	0.754502	0.377251	−	0.926111i	$-0.376869\pi$
$547$	9652.53	0.754502	0.377251	+	0.926111i	$0.376869\pi$
$548$	2237.39	0.174409
$549$	3456.41	0.268699
$550$	−672.295	−0.0521214
$551$	−7994.62	−0.618117
$552$	552.000	0.0425628
$553$	1305.80	0.100413
$554$	11717.5	0.898610
$555$	5154.88	0.394256
$556$	11761.0	0.897084
$557$	6537.97	0.497348	0.248674	−	0.968587i	$-0.420005\pi$
$557$	6537.97	0.497348	0.248674	+	0.968587i	$0.420005\pi$
$558$	2666.91	0.202328
$559$	−12947.7	−0.979660
$560$	−2404.93	−0.181476
$561$	−352.435	−0.0265238
$562$	−8555.57	−0.642162
$563$	7744.22	0.579715	0.289858	−	0.957070i	$-0.406392\pi$
$563$	7744.22	0.579715	0.289858	+	0.957070i	$0.406392\pi$
$564$	3246.00	0.242343
$565$	24209.8	1.80268
$566$	−10726.0	−0.796552
$567$	567.000	0.0419961
$568$	−8430.69	−0.622788
$569$	5424.37	0.399651	0.199826	−	0.979831i	$-0.435962\pi$
$569$	5424.37	0.399651	0.199826	+	0.979831i	$0.435962\pi$
$570$	7280.10	0.534965
$571$	7408.79	0.542992	0.271496	−	0.962440i	$-0.412482\pi$
$571$	7408.79	0.542992	0.271496	+	0.962440i	$0.412482\pi$
$572$	92.1581	0.00673658
$573$	468.573	0.0341622
$574$	2491.61	0.181180
$575$	−7729.66	−0.560607
$576$	576.000	0.0416667
$577$	2828.61	0.204084	0.102042	−	0.994780i	$-0.467462\pi$
$577$	2828.61	0.204084	0.102042	+	0.994780i	$0.467462\pi$
$578$	−17764.0	−1.27835
$579$	−9022.69	−0.647617
$580$	12151.8	0.869959
$581$	−1539.77	−0.109949
$582$	2453.30	0.174729
$583$	−38.8416	−0.00275927
$584$	−6379.16	−0.452006
$585$	−4451.46	−0.314607
$586$	3664.91	0.258355
$587$	6002.07	0.422031	0.211015	−	0.977483i	$-0.432323\pi$
$587$	6002.07	0.422031	0.211015	+	0.977483i	$0.432323\pi$
$588$	588.000	0.0412393
$589$	−8372.15	−0.585685
$590$	32829.2	2.29078
$591$	−1064.24	−0.0740729
$592$	−1280.36	−0.0888894
$593$	17373.8	1.20313	0.601565	−	0.798824i	$-0.294544\pi$
$593$	17373.8	1.20313	0.601565	+	0.798824i	$0.294544\pi$
$594$	−54.0121	−0.00373088
$595$	17654.0	1.21638
$596$	11303.2	0.776843
$597$	2167.33	0.148581
$598$	1059.58	0.0724572
$599$	6781.38	0.462570	0.231285	−	0.972886i	$-0.425707\pi$
$599$	6781.38	0.462570	0.231285	+	0.972886i	$0.425707\pi$
$600$	−8065.73	−0.548803
$601$	19405.8	1.31711	0.658553	−	0.752535i	$-0.271169\pi$
$601$	19405.8	1.31711	0.658553	+	0.752535i	$0.271169\pi$
$602$	7869.47	0.532783
$603$	−965.559	−0.0652083
$604$	−3303.91	−0.222573
$605$	28558.5	1.91912
$606$	−1014.96	−0.0680361
$607$	−8809.97	−0.589103	−0.294552	−	0.955636i	$-0.595170\pi$
$607$	−8809.97	−0.589103	−0.294552	+	0.955636i	$0.595170\pi$
$608$	−1808.22	−0.120614
$609$	−2971.09	−0.197692
$610$	16492.9	1.09472
$611$	6230.79	0.412554
$612$	−4228.28	−0.279278
$613$	−270.090	−0.0177958	−0.00889791	−	0.999960i	$-0.502832\pi$
$613$	−270.090	−0.0177958	−0.00889791	+	0.999960i	$0.502832\pi$
$614$	−18599.4	−1.22250
$615$	11464.5	0.751699
$616$	−56.0126	−0.00366365
$617$	−4438.19	−0.289587	−0.144793	−	0.989462i	$-0.546252\pi$
$617$	−4438.19	−0.289587	−0.144793	+	0.989462i	$0.546252\pi$
$618$	−7570.31	−0.492755
$619$	−14666.7	−0.952352	−0.476176	−	0.879350i	$-0.657977\pi$
$619$	−14666.7	−0.952352	−0.476176	+	0.879350i	$0.657977\pi$
$620$	12725.6	0.824313
$621$	−621.000	−0.0401286
$622$	−4633.21	−0.298673
$623$	−607.904	−0.0390933
$624$	1105.65	0.0709317
$625$	55310.4	3.53987
$626$	−10028.0	−0.640252
$627$	169.559	0.0107999
$628$	−2682.58	−0.170456
$629$	9398.82	0.595796
$630$	2705.55	0.171098
$631$	−1989.64	−0.125525	−0.0627626	−	0.998028i	$-0.519991\pi$
$631$	−1989.64	−0.125525	−0.0627626	+	0.998028i	$0.519991\pi$
$632$	−1492.35	−0.0939279
$633$	7733.25	0.485575
$634$	570.031	0.0357079
$635$	−11807.5	−0.737901
$636$	−465.995	−0.0290533
$637$	1128.68	0.0702041
$638$	283.024	0.0175628
$639$	9484.52	0.587171
$640$	2748.49	0.169756
$641$	−28767.6	−1.77262	−0.886310	−	0.463092i	$-0.846740\pi$
$641$	−28767.6	−1.77262	−0.886310	+	0.463092i	$0.846740\pi$
$642$	−11928.1	−0.733276
$643$	−14071.7	−0.863036	−0.431518	−	0.902104i	$-0.642022\pi$
$643$	−14071.7	−0.863036	−0.431518	+	0.902104i	$0.642022\pi$
$644$	−644.000	−0.0394055
$645$	36209.5	2.21046
$646$	13273.7	0.808432
$647$	16564.9	1.00655	0.503273	−	0.864128i	$-0.332129\pi$
$647$	16564.9	1.00655	0.503273	+	0.864128i	$0.332129\pi$
$648$	−648.000	−0.0392837
$649$	764.617	0.0462463
$650$	−15482.4	−0.934261
$651$	−3111.39	−0.187319
$652$	−3333.11	−0.200207
$653$	8086.46	0.484606	0.242303	−	0.970201i	$-0.422097\pi$
$653$	8086.46	0.484606	0.242303	+	0.970201i	$0.422097\pi$
$654$	681.822	0.0407666
$655$	−29697.1	−1.77154
$656$	−2847.55	−0.169479
$657$	7176.56	0.426156
$658$	−3787.00	−0.224366
$659$	7026.37	0.415339	0.207669	−	0.978199i	$-0.433412\pi$
$659$	7026.37	0.415339	0.207669	+	0.978199i	$0.433412\pi$
$660$	−257.729	−0.0152001
$661$	13827.4	0.813652	0.406826	−	0.913506i	$-0.366635\pi$
$661$	13827.4	0.813652	0.406826	+	0.913506i	$0.366635\pi$
$662$	−23528.3	−1.38135
$663$	−8116.29	−0.475431
$664$	1759.73	0.102848
$665$	−8493.45	−0.495281
$666$	1440.41	0.0838057
$667$	3254.05	0.188901
$668$	14996.7	0.868621
$669$	9918.46	0.573198
$670$	−4607.34	−0.265667
$671$	384.132	0.0221002
$672$	−672.000	−0.0385758
$673$	−7344.88	−0.420690	−0.210345	−	0.977627i	$-0.567459\pi$
$673$	−7344.88	−0.420690	−0.210345	+	0.977627i	$0.567459\pi$
$674$	−6678.06	−0.381646
$675$	9073.94	0.517417
$676$	−6665.68	−0.379249
$677$	−19591.1	−1.11218	−0.556090	−	0.831122i	$-0.687699\pi$
$677$	−19591.1	−1.11218	−0.556090	+	0.831122i	$0.687699\pi$
$678$	6764.85	0.383190
$679$	−2862.18	−0.161768
$680$	−20176.0	−1.13782
$681$	−13890.5	−0.781624
$682$	296.389	0.0166413
$683$	−30107.7	−1.68673	−0.843367	−	0.537337i	$-0.819430\pi$
$683$	−30107.7	−1.68673	−0.843367	+	0.537337i	$0.819430\pi$
$684$	2034.25	0.113716
$685$	−12010.6	−0.669930
$686$	−686.000	−0.0381802
$687$	−32.9184	−0.00182811
$688$	−8993.68	−0.498373
$689$	−894.491	−0.0494592
$690$	−2963.22	−0.163489
$691$	−2466.36	−0.135781	−0.0678905	−	0.997693i	$-0.521627\pi$
$691$	−2466.36	−0.135781	−0.0678905	+	0.997693i	$0.521627\pi$
$692$	10111.9	0.555485
$693$	63.0141	0.00345413
$694$	−4710.24	−0.257634
$695$	−63134.9	−3.44582
$696$	3395.53	0.184924
$697$	20903.2	1.13596
$698$	10949.3	0.593749
$699$	3758.04	0.203350
$700$	9410.02	0.508093
$701$	186.760	0.0100625	0.00503126	−	0.999987i	$-0.498398\pi$
$701$	186.760	0.0100625	0.00503126	+	0.999987i	$0.498398\pi$
$702$	−1243.85	−0.0668750
$703$	−4521.83	−0.242595
$704$	64.0144	0.00342703
$705$	−17425.0	−0.930870
$706$	22818.5	1.21641
$707$	1184.12	0.0629891
$708$	9173.35	0.486943
$709$	24386.9	1.29178	0.645889	−	0.763431i	$-0.276487\pi$
$709$	24386.9	1.29178	0.645889	+	0.763431i	$0.276487\pi$
$710$	45257.2	2.39221
$711$	1678.89	0.0885560
$712$	694.747	0.0365685
$713$	3407.71	0.178990
$714$	4932.99	0.258561
$715$	−494.718	−0.0258761
$716$	−12022.6	−0.627521
$717$	−1122.82	−0.0584833
$718$	3386.36	0.176014
$719$	−35577.7	−1.84537	−0.922687	−	0.385549i	$-0.874012\pi$
$719$	−35577.7	−1.84537	−0.922687	+	0.385549i	$0.874012\pi$
$720$	−3092.05	−0.160047
$721$	8832.03	0.456203
$722$	7331.93	0.377931
$723$	−14699.3	−0.756117
$724$	15390.9	0.790051
$725$	−47547.6	−2.43569
$726$	7980.00	0.407941
$727$	−10260.1	−0.523418	−0.261709	−	0.965147i	$-0.584286\pi$
$727$	−10260.1	−0.523418	−0.261709	+	0.965147i	$0.584286\pi$
$728$	−1289.92	−0.0656700
$729$	729.000	0.0370370
$730$	34244.3	1.73622
$731$	66020.4	3.34043
$732$	4608.55	0.232701
$733$	−24871.6	−1.25328	−0.626641	−	0.779308i	$-0.715571\pi$
$733$	−24871.6	−1.25328	−0.626641	+	0.779308i	$0.715571\pi$
$734$	−19489.5	−0.980067
$735$	−3156.47	−0.158406
$736$	736.000	0.0368605
$737$	−107.308	−0.00536331
$738$	3203.49	0.159786
$739$	−14802.4	−0.736827	−0.368414	−	0.929662i	$-0.620099\pi$
$739$	−14802.4	−0.736827	−0.368414	+	0.929662i	$0.620099\pi$
$740$	6873.17	0.341436
$741$	3904.80	0.193585
$742$	543.661	0.0268981
$743$	28279.1	1.39631	0.698155	−	0.715947i	$-0.254005\pi$
$743$	28279.1	1.39631	0.698155	+	0.715947i	$0.254005\pi$
$744$	3555.87	0.175221
$745$	−60677.4	−2.98396
$746$	26567.1	1.30387
$747$	−1979.70	−0.0969657
$748$	−469.914	−0.0229703
$749$	13916.1	0.678882
$750$	27193.6	1.32396
$751$	−14706.0	−0.714556	−0.357278	−	0.933998i	$-0.616295\pi$
$751$	−14706.0	−0.714556	−0.357278	+	0.933998i	$0.616295\pi$
$752$	4328.00	0.209875
$753$	10524.5	0.509339
$754$	6517.81	0.314807
$755$	17735.9	0.854934
$756$	756.000	0.0363696
$757$	6926.84	0.332577	0.166288	−	0.986077i	$-0.446822\pi$
$757$	6926.84	0.332577	0.166288	+	0.986077i	$0.446822\pi$
$758$	8794.06	0.421391
$759$	−69.0155	−0.00330053
$760$	9706.80	0.463293
$761$	−22958.2	−1.09361	−0.546804	−	0.837261i	$-0.684156\pi$
$761$	−22958.2	−1.09361	−0.546804	+	0.837261i	$0.684156\pi$
$762$	−3299.33	−0.156853
$763$	−795.458	−0.0377425
$764$	624.765	0.0295853
$765$	22698.0	1.07274
$766$	−10240.9	−0.483051
$767$	17608.5	0.828952
$768$	768.000	0.0360844
$769$	−29494.5	−1.38309	−0.691547	−	0.722332i	$-0.743070\pi$
$769$	−29494.5	−1.38309	−0.691547	+	0.722332i	$0.743070\pi$
$770$	300.684	0.0140726
$771$	−18403.7	−0.859655
$772$	−12030.2	−0.560852
$773$	26464.7	1.23140	0.615698	−	0.787982i	$-0.288874\pi$
$773$	26464.7	1.23140	0.615698	+	0.787982i	$0.288874\pi$
$774$	10117.9	0.469871
$775$	−49792.9	−2.30789
$776$	3271.07	0.151320
$777$	−1680.47	−0.0775890
$778$	−6901.62	−0.318040
$779$	−10056.6	−0.462537
$780$	−5935.28	−0.272458
$781$	1054.07	0.0482941
$782$	−5402.80	−0.247063
$783$	−3819.97	−0.174348
$784$	784.000	0.0357143
$785$	14400.5	0.654746
$786$	−8298.13	−0.376571
$787$	−39142.3	−1.77290	−0.886449	−	0.462826i	$-0.846835\pi$
$787$	−39142.3	−1.77290	−0.886449	+	0.462826i	$0.846835\pi$
$788$	−1418.99	−0.0641491
$789$	21731.1	0.980540
$790$	8011.14	0.360789
$791$	−7892.33	−0.354765
$792$	−72.0162	−0.00323104
$793$	8846.23	0.396140
$794$	872.100	0.0389794
$795$	2501.53	0.111598
$796$	2889.78	0.128675
$797$	33372.2	1.48319	0.741595	−	0.670848i	$-0.234070\pi$
$797$	33372.2	1.48319	0.741595	+	0.670848i	$0.234070\pi$
$798$	−2373.29	−0.105280
$799$	−31770.8	−1.40672
$800$	−10754.3	−0.475278
$801$	−781.591	−0.0344771
$802$	10457.4	0.460427
$803$	797.575	0.0350508
$804$	−1287.41	−0.0564720
$805$	3457.09	0.151362
$806$	6825.60	0.298290
$807$	9772.94	0.426300
$808$	−1353.28	−0.0589209
$809$	37123.8	1.61335	0.806676	−	0.590994i	$-0.201264\pi$
$809$	37123.8	1.61335	0.806676	+	0.590994i	$0.201264\pi$
$810$	3478.56	0.150894
$811$	8834.76	0.382528	0.191264	−	0.981539i	$-0.438741\pi$
$811$	8834.76	0.382528	0.191264	+	0.981539i	$0.438741\pi$
$812$	−3961.45	−0.171206
$813$	13759.7	0.593572
$814$	160.081	0.00689292
$815$	17892.6	0.769021
$816$	−5637.70	−0.241862
$817$	−31762.8	−1.36015
$818$	19568.2	0.836413
$819$	1451.16	0.0619142
$820$	15286.1	0.650991
$821$	1152.17	0.0489780	0.0244890	−	0.999700i	$-0.492204\pi$
$821$	1152.17	0.0489780	0.0244890	+	0.999700i	$0.492204\pi$
$822$	−3356.08	−0.142405
$823$	25477.0	1.07907	0.539534	−	0.841964i	$-0.318600\pi$
$823$	25477.0	1.07907	0.539534	+	0.841964i	$0.318600\pi$
$824$	−10093.7	−0.426738
$825$	1008.44	0.0425569
$826$	−10702.2	−0.450821
$827$	13902.4	0.584564	0.292282	−	0.956332i	$-0.405585\pi$
$827$	13902.4	0.584564	0.292282	+	0.956332i	$0.405585\pi$
$828$	−828.000	−0.0347524
$829$	29236.3	1.22487	0.612437	−	0.790520i	$-0.290189\pi$
$829$	29236.3	1.22487	0.612437	+	0.790520i	$0.290189\pi$
$830$	−9446.50	−0.395052
$831$	−17576.3	−0.733712
$832$	1474.20	0.0614286
$833$	−5755.15	−0.239381
$834$	−17641.5	−0.732466
$835$	−80504.4	−3.33649
$836$	226.078	0.00935298
$837$	−4000.36	−0.165200
$838$	3248.60	0.133915
$839$	−9455.26	−0.389073	−0.194536	−	0.980895i	$-0.562320\pi$
$839$	−9455.26	−0.389073	−0.194536	+	0.980895i	$0.562320\pi$
$840$	3607.39	0.148175
$841$	−4372.30	−0.179274
$842$	21078.3	0.862713
$843$	12833.4	0.524323
$844$	10311.0	0.420520
$845$	35782.3	1.45675
$846$	−4869.00	−0.197872
$847$	−9310.00	−0.377680
$848$	−621.327	−0.0251609
$849$	16089.0	0.650382
$850$	78944.7	3.18563
$851$	1840.52	0.0741389
$852$	12646.0	0.508505
$853$	22447.2	0.901029	0.450515	−	0.892769i	$-0.351241\pi$
$853$	22447.2	0.901029	0.450515	+	0.892769i	$0.351241\pi$
$854$	−5376.64	−0.215439
$855$	−10920.1	−0.436797
$856$	−15904.1	−0.635036
$857$	17253.7	0.687719	0.343860	−	0.939021i	$-0.388266\pi$
$857$	17253.7	0.687719	0.343860	+	0.939021i	$0.388266\pi$
$858$	−138.237	−0.00550039
$859$	6607.28	0.262442	0.131221	−	0.991353i	$-0.458110\pi$
$859$	6607.28	0.262442	0.131221	+	0.991353i	$0.458110\pi$
$860$	48279.4	1.91432
$861$	−3737.41	−0.147933
$862$	7178.23	0.283633
$863$	44529.5	1.75643	0.878216	−	0.478264i	$-0.158734\pi$
$863$	44529.5	1.75643	0.878216	+	0.478264i	$0.158734\pi$
$864$	−864.000	−0.0340207
$865$	−54282.0	−2.13369
$866$	26398.6	1.03587
$867$	26646.0	1.04377
$868$	−4148.52	−0.162223
$869$	186.585	0.00728363
$870$	−18227.7	−0.710318
$871$	−2471.22	−0.0961357
$872$	909.095	0.0353049
$873$	−3679.95	−0.142666
$874$	2599.32	0.100599
$875$	−31725.8	−1.22575
$876$	9568.75	0.369062
$877$	32457.1	1.24971	0.624857	−	0.780740i	$-0.285157\pi$
$877$	32457.1	1.24971	0.624857	+	0.780740i	$0.285157\pi$
$878$	6702.94	0.257646
$879$	−5497.37	−0.210946
$880$	−343.639	−0.0131637
$881$	−9116.01	−0.348611	−0.174305	−	0.984692i	$-0.555768\pi$
$881$	−9116.01	−0.348611	−0.174305	+	0.984692i	$0.555768\pi$
$882$	−882.000	−0.0336718
$883$	4290.80	0.163530	0.0817649	−	0.996652i	$-0.473944\pi$
$883$	4290.80	0.163530	0.0817649	+	0.996652i	$0.473944\pi$
$884$	−10821.7	−0.411735
$885$	−49243.9	−1.87041
$886$	30340.8	1.15047
$887$	44007.4	1.66587	0.832933	−	0.553374i	$-0.186660\pi$
$887$	44007.4	1.66587	0.832933	+	0.553374i	$0.186660\pi$
$888$	1920.54	0.0725779
$889$	3849.22	0.145218
$890$	−3729.51	−0.140464
$891$	81.0182	0.00304625
$892$	13224.6	0.496404
$893$	15285.1	0.572785
$894$	−16954.9	−0.634290
$895$	64539.0	2.41039
$896$	−896.000	−0.0334077
$897$	−1589.37	−0.0591611
$898$	−22895.1	−0.850802
$899$	20961.9	0.777664
$900$	12098.6	0.448096
$901$	4561.01	0.168645
$902$	356.024	0.0131422
$903$	−11804.2	−0.435016
$904$	9019.81	0.331852
$905$	−82620.5	−3.03469
$906$	4955.87	0.181730
$907$	−6884.01	−0.252018	−0.126009	−	0.992029i	$-0.540217\pi$
$907$	−6884.01	−0.252018	−0.126009	+	0.992029i	$0.540217\pi$
$908$	−18520.7	−0.676906
$909$	1522.44	0.0555512
$910$	6924.50	0.252247
$911$	37123.7	1.35012	0.675062	−	0.737761i	$-0.264117\pi$
$911$	37123.7	1.35012	0.675062	+	0.737761i	$0.264117\pi$
$912$	2712.33	0.0984806
$913$	−220.016	−0.00797532
$914$	−29627.5	−1.07220
$915$	−24739.4	−0.893834
$916$	−43.8911	−0.00158319
$917$	9681.16	0.348637
$918$	6342.41	0.228029
$919$	16363.9	0.587372	0.293686	−	0.955902i	$-0.405118\pi$
$919$	16363.9	0.587372	0.293686	+	0.955902i	$0.405118\pi$
$920$	−3950.96	−0.141586
$921$	27899.2	0.998164
$922$	30234.4	1.07995
$923$	24274.4	0.865658
$924$	84.0189	0.00299136
$925$	−26893.4	−0.955944
$926$	4130.78	0.146594
$927$	11355.5	0.402333
$928$	4527.37	0.160149
$929$	−1335.52	−0.0471657	−0.0235829	−	0.999722i	$-0.507507\pi$
$929$	−1335.52	−0.0471657	−0.0235829	+	0.999722i	$0.507507\pi$
$930$	−19088.5	−0.673048
$931$	2768.84	0.0974705
$932$	5010.71	0.176107
$933$	6949.81	0.243865
$934$	−24466.1	−0.857126
$935$	2522.57	0.0882318
$936$	−1658.47	−0.0579155
$937$	−51457.7	−1.79408	−0.897038	−	0.441953i	$-0.854286\pi$
$937$	−51457.7	−1.79408	−0.897038	+	0.441953i	$0.854286\pi$
$938$	1501.98	0.0522829
$939$	15041.9	0.522764
$940$	−23233.3	−0.806157
$941$	14545.4	0.503898	0.251949	−	0.967741i	$-0.418928\pi$
$941$	14545.4	0.503898	0.251949	+	0.967741i	$0.418928\pi$
$942$	4023.87	0.139177
$943$	4093.35	0.141355
$944$	12231.1	0.421705
$945$	−4058.32	−0.139701
$946$	1124.46	0.0386463
$947$	−22825.9	−0.783253	−0.391627	−	0.920124i	$-0.628088\pi$
$947$	−22825.9	−0.783253	−0.391627	+	0.920124i	$0.628088\pi$
$948$	2238.52	0.0766918
$949$	18367.5	0.628276
$950$	−37980.8	−1.29712
$951$	−855.047	−0.0291554
$952$	6577.32	0.223920
$953$	−21158.9	−0.719207	−0.359603	−	0.933105i	$-0.617088\pi$
$953$	−21158.9	−0.719207	−0.359603	+	0.933105i	$0.617088\pi$
$954$	698.993	0.0237219
$955$	−3353.83	−0.113641
$956$	−1497.10	−0.0506480
$957$	−424.536	−0.0143399
$958$	16324.3	0.550536
$959$	3915.42	0.131841
$960$	−4122.74	−0.138605
$961$	−7839.20	−0.263140
$962$	3686.53	0.123554
$963$	17892.1	0.598718
$964$	−19599.1	−0.654817
$965$	64580.1	2.15431
$966$	966.000	0.0321745
$967$	−44015.1	−1.46373	−0.731866	−	0.681448i	$-0.761351\pi$
$967$	−44015.1	−1.46373	−0.731866	+	0.681448i	$0.761351\pi$
$968$	10640.0	0.353288
$969$	−19910.6	−0.660082
$970$	−17559.6	−0.581241
$971$	59657.6	1.97168	0.985841	−	0.167683i	$-0.0536286\pi$
$971$	59657.6	1.97168	0.985841	+	0.167683i	$0.0536286\pi$
$972$	972.000	0.0320750
$973$	20581.8	0.678132
$974$	12493.8	0.411014
$975$	23223.6	0.762821
$976$	6144.73	0.201525
$977$	9939.12	0.325466	0.162733	−	0.986670i	$-0.447969\pi$
$977$	9939.12	0.325466	0.162733	+	0.986670i	$0.447969\pi$
$978$	4999.67	0.163468
$979$	−86.8629	−0.00283570
$980$	−4208.63	−0.137183
$981$	−1022.73	−0.0332858
$982$	28597.4	0.929307
$983$	−52416.0	−1.70072	−0.850361	−	0.526199i	$-0.823617\pi$
$983$	−52416.0	−1.70072	−0.850361	+	0.526199i	$0.823617\pi$
$984$	4271.32	0.138379
$985$	7617.35	0.246405
$986$	−33234.3	−1.07342
$987$	5680.50	0.183194
$988$	5206.40	0.167649
$989$	12928.4	0.415672
$990$	386.593	0.0124109
$991$	−26699.8	−0.855849	−0.427924	−	0.903815i	$-0.640755\pi$
$991$	−26699.8	−0.855849	−0.427924	+	0.903815i	$0.640755\pi$
$992$	4741.17	0.151746
$993$	35292.5	1.12787
$994$	−14753.7	−0.470784
$995$	−15512.8	−0.494259
$996$	−2639.60	−0.0839748
$997$	21237.9	0.674635	0.337317	−	0.941391i	$-0.390480\pi$
$997$	21237.9	0.674635	0.337317	+	0.941391i	$0.390480\pi$
$998$	−3806.63	−0.120738
$999$	−2160.61	−0.0684271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.o.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.o.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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.4726 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -21.4726 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +42.9452 q^{10} +1.00022 q^{11} +12.0000 q^{12} +23.0343 q^{13} -14.0000 q^{14} -64.4178 q^{15} +16.0000 q^{16} -117.452 q^{17} -18.0000 q^{18} +56.5069 q^{19} -85.8904 q^{20} +21.0000 q^{21} -2.00045 q^{22} -23.0000 q^{23} -24.0000 q^{24} +336.072 q^{25} -46.0687 q^{26} +27.0000 q^{27} +28.0000 q^{28} -141.480 q^{29} +128.836 q^{30} -148.161 q^{31} -32.0000 q^{32} +3.00067 q^{33} +234.904 q^{34} -150.308 q^{35} +36.0000 q^{36} -80.0226 q^{37} -113.014 q^{38} +69.1030 q^{39} +171.781 q^{40} -177.972 q^{41} -42.0000 q^{42} -562.105 q^{43} +4.00090 q^{44} -193.253 q^{45} +46.0000 q^{46} +270.500 q^{47} +48.0000 q^{48} +49.0000 q^{49} -672.144 q^{50} -352.356 q^{51} +92.1374 q^{52} -38.8329 q^{53} -54.0000 q^{54} -21.4774 q^{55} -56.0000 q^{56} +169.521 q^{57} +282.961 q^{58} +764.446 q^{59} -257.671 q^{60} +384.046 q^{61} +296.323 q^{62} +63.0000 q^{63} +64.0000 q^{64} -494.607 q^{65} -6.00135 q^{66} -107.284 q^{67} -469.808 q^{68} -69.0000 q^{69} +300.616 q^{70} +1053.84 q^{71} -72.0000 q^{72} +797.395 q^{73} +160.045 q^{74} +1008.22 q^{75} +226.028 q^{76} +7.00157 q^{77} -138.206 q^{78} +186.543 q^{79} -343.561 q^{80} +81.0000 q^{81} +355.944 q^{82} -219.967 q^{83} +84.0000 q^{84} +2522.00 q^{85} +1124.21 q^{86} -424.441 q^{87} -8.00180 q^{88} -86.8434 q^{89} +386.507 q^{90} +161.240 q^{91} -92.0000 q^{92} -444.484 q^{93} -541.000 q^{94} -1213.35 q^{95} -96.0000 q^{96} -408.883 q^{97} -98.0000 q^{98} +9.00202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} - 12 q^{10} - 50 q^{11} + 60 q^{12} + 66 q^{13} - 70 q^{14} + 18 q^{15} + 80 q^{16} - 198 q^{17} - 90 q^{18} + 120 q^{19} + 24 q^{20} + 105 q^{21} + 100 q^{22} - 115 q^{23} - 120 q^{24} + 503 q^{25} - 132 q^{26} + 135 q^{27} + 140 q^{28} + 301 q^{29} - 36 q^{30} + 314 q^{31} - 160 q^{32} - 150 q^{33} + 396 q^{34} + 42 q^{35} + 180 q^{36} + 269 q^{37} - 240 q^{38} + 198 q^{39} - 48 q^{40} + 479 q^{41} - 210 q^{42} - 290 q^{43} - 200 q^{44} + 54 q^{45} + 230 q^{46} + 69 q^{47} + 240 q^{48} + 245 q^{49} - 1006 q^{50} - 594 q^{51} + 264 q^{52} + 339 q^{53} - 270 q^{54} + 957 q^{55} - 280 q^{56} + 360 q^{57} - 602 q^{58} + 2065 q^{59} + 72 q^{60} + 531 q^{61} - 628 q^{62} + 315 q^{63} + 320 q^{64} + 1227 q^{65} + 300 q^{66} + 855 q^{67} - 792 q^{68} - 345 q^{69} - 84 q^{70} - 863 q^{71} - 360 q^{72} + 618 q^{73} - 538 q^{74} + 1509 q^{75} + 480 q^{76} - 350 q^{77} - 396 q^{78} + 254 q^{79} + 96 q^{80} + 405 q^{81} - 958 q^{82} - 1700 q^{83} + 420 q^{84} + 1977 q^{85} + 580 q^{86} + 903 q^{87} + 400 q^{88} - 275 q^{89} - 108 q^{90} + 462 q^{91} - 460 q^{92} + 942 q^{93} - 138 q^{94} + 171 q^{95} - 480 q^{96} - 979 q^{97} - 490 q^{98} - 450 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 - 12 * q^10 - 50 * q^11 + 60 * q^12 + 66 * q^13 - 70 * q^14 + 18 * q^15 + 80 * q^16 - 198 * q^17 - 90 * q^18 + 120 * q^19 + 24 * q^20 + 105 * q^21 + 100 * q^22 - 115 * q^23 - 120 * q^24 + 503 * q^25 - 132 * q^26 + 135 * q^27 + 140 * q^28 + 301 * q^29 - 36 * q^30 + 314 * q^31 - 160 * q^32 - 150 * q^33 + 396 * q^34 + 42 * q^35 + 180 * q^36 + 269 * q^37 - 240 * q^38 + 198 * q^39 - 48 * q^40 + 479 * q^41 - 210 * q^42 - 290 * q^43 - 200 * q^44 + 54 * q^45 + 230 * q^46 + 69 * q^47 + 240 * q^48 + 245 * q^49 - 1006 * q^50 - 594 * q^51 + 264 * q^52 + 339 * q^53 - 270 * q^54 + 957 * q^55 - 280 * q^56 + 360 * q^57 - 602 * q^58 + 2065 * q^59 + 72 * q^60 + 531 * q^61 - 628 * q^62 + 315 * q^63 + 320 * q^64 + 1227 * q^65 + 300 * q^66 + 855 * q^67 - 792 * q^68 - 345 * q^69 - 84 * q^70 - 863 * q^71 - 360 * q^72 + 618 * q^73 - 538 * q^74 + 1509 * q^75 + 480 * q^76 - 350 * q^77 - 396 * q^78 + 254 * q^79 + 96 * q^80 + 405 * q^81 - 958 * q^82 - 1700 * q^83 + 420 * q^84 + 1977 * q^85 + 580 * q^86 + 903 * q^87 + 400 * q^88 - 275 * q^89 - 108 * q^90 + 462 * q^91 - 460 * q^92 + 942 * q^93 - 138 * q^94 + 171 * q^95 - 480 * q^96 - 979 * q^97 - 490 * q^98 - 450 * q^99

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