LMFDB - Embedded newform 4015.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58131 q^{2} +3.02998 q^{3} +4.66316 q^{4} -1.00000 q^{5} -7.82131 q^{6} +4.31568 q^{7} -6.87443 q^{8} +6.18077 q^{9} +O(q^{10})$	\(q-2.58131 q^{2} +3.02998 q^{3} +4.66316 q^{4} -1.00000 q^{5} -7.82131 q^{6} +4.31568 q^{7} -6.87443 q^{8} +6.18077 q^{9} +2.58131 q^{10} +1.00000 q^{11} +14.1293 q^{12} -7.03654 q^{13} -11.1401 q^{14} -3.02998 q^{15} +8.41873 q^{16} -6.76970 q^{17} -15.9545 q^{18} -8.08232 q^{19} -4.66316 q^{20} +13.0764 q^{21} -2.58131 q^{22} -6.49721 q^{23} -20.8294 q^{24} +1.00000 q^{25} +18.1635 q^{26} +9.63767 q^{27} +20.1247 q^{28} +2.93421 q^{29} +7.82131 q^{30} +5.12495 q^{31} -7.98247 q^{32} +3.02998 q^{33} +17.4747 q^{34} -4.31568 q^{35} +28.8219 q^{36} -3.00332 q^{37} +20.8630 q^{38} -21.3206 q^{39} +6.87443 q^{40} -8.12663 q^{41} -33.7543 q^{42} -1.69685 q^{43} +4.66316 q^{44} -6.18077 q^{45} +16.7713 q^{46} +1.27652 q^{47} +25.5086 q^{48} +11.6251 q^{49} -2.58131 q^{50} -20.5120 q^{51} -32.8125 q^{52} -12.3536 q^{53} -24.8778 q^{54} -1.00000 q^{55} -29.6679 q^{56} -24.4893 q^{57} -7.57410 q^{58} -2.35312 q^{59} -14.1293 q^{60} +1.59948 q^{61} -13.2291 q^{62} +26.6742 q^{63} +3.76777 q^{64} +7.03654 q^{65} -7.82131 q^{66} -0.966957 q^{67} -31.5682 q^{68} -19.6864 q^{69} +11.1401 q^{70} -9.01607 q^{71} -42.4893 q^{72} +1.00000 q^{73} +7.75250 q^{74} +3.02998 q^{75} -37.6891 q^{76} +4.31568 q^{77} +55.0350 q^{78} +8.32169 q^{79} -8.41873 q^{80} +10.6596 q^{81} +20.9773 q^{82} -2.20321 q^{83} +60.9774 q^{84} +6.76970 q^{85} +4.38010 q^{86} +8.89059 q^{87} -6.87443 q^{88} -10.3647 q^{89} +15.9545 q^{90} -30.3675 q^{91} -30.2975 q^{92} +15.5285 q^{93} -3.29509 q^{94} +8.08232 q^{95} -24.1867 q^{96} -5.64861 q^{97} -30.0080 q^{98} +6.18077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−2.58131	−1.82526	−0.912631	−	0.408785i	$-0.865953\pi$
$2$	−2.58131	−1.82526	−0.912631	+	0.408785i	$0.865953\pi$
$3$	3.02998	1.74936	0.874680	−	0.484702i	$-0.161072\pi$
$3$	3.02998	1.74936	0.874680	+	0.484702i	$0.161072\pi$
$4$	4.66316	2.33158
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−7.82131	−3.19304
$7$	4.31568	1.63117	0.815587	−	0.578634i	$-0.196414\pi$
$7$	4.31568	1.63117	0.815587	+	0.578634i	$0.196414\pi$
$8$	−6.87443	−2.43048
$9$	6.18077	2.06026
$10$	2.58131	0.816282
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	14.1293	4.07877
$13$	−7.03654	−1.95159	−0.975793	−	0.218698i	$-0.929819\pi$
$13$	−7.03654	−1.95159	−0.975793	+	0.218698i	$0.929819\pi$
$14$	−11.1401	−2.97732
$15$	−3.02998	−0.782337
$16$	8.41873	2.10468
$17$	−6.76970	−1.64189	−0.820946	−	0.571005i	$-0.806554\pi$
$17$	−6.76970	−1.64189	−0.820946	+	0.571005i	$0.806554\pi$
$18$	−15.9545	−3.76051
$19$	−8.08232	−1.85421	−0.927106	−	0.374800i	$-0.877711\pi$
$19$	−8.08232	−1.85421	−0.927106	+	0.374800i	$0.877711\pi$
$20$	−4.66316	−1.04271
$21$	13.0764	2.85351
$22$	−2.58131	−0.550337
$23$	−6.49721	−1.35476	−0.677381	−	0.735632i	$-0.736885\pi$
$23$	−6.49721	−1.35476	−0.677381	+	0.735632i	$0.736885\pi$
$24$	−20.8294	−4.25178
$25$	1.00000	0.200000
$26$	18.1635	3.56215
$27$	9.63767	1.85477
$28$	20.1247	3.80321
$29$	2.93421	0.544869	0.272435	−	0.962174i	$-0.412171\pi$
$29$	2.93421	0.544869	0.272435	+	0.962174i	$0.412171\pi$
$30$	7.82131	1.42797
$31$	5.12495	0.920469	0.460234	−	0.887797i	$-0.347765\pi$
$31$	5.12495	0.920469	0.460234	+	0.887797i	$0.347765\pi$
$32$	−7.98247	−1.41111
$33$	3.02998	0.527452
$34$	17.4747	2.99688
$35$	−4.31568	−0.729483
$36$	28.8219	4.80365
$37$	−3.00332	−0.493743	−0.246871	−	0.969048i	$-0.579403\pi$
$37$	−3.00332	−0.493743	−0.246871	+	0.969048i	$0.579403\pi$
$38$	20.8630	3.38442
$39$	−21.3206	−3.41402
$40$	6.87443	1.08694
$41$	−8.12663	−1.26917	−0.634583	−	0.772855i	$-0.718828\pi$
$41$	−8.12663	−1.26917	−0.634583	+	0.772855i	$0.718828\pi$
$42$	−33.7543	−5.20840
$43$	−1.69685	−0.258767	−0.129384	−	0.991595i	$-0.541300\pi$
$43$	−1.69685	−0.258767	−0.129384	+	0.991595i	$0.541300\pi$
$44$	4.66316	0.702998
$45$	−6.18077	−0.921375
$46$	16.7713	2.47279
$47$	1.27652	0.186200	0.0930998	−	0.995657i	$-0.470322\pi$
$47$	1.27652	0.186200	0.0930998	+	0.995657i	$0.470322\pi$
$48$	25.5086	3.68184
$49$	11.6251	1.66073
$50$	−2.58131	−0.365052
$51$	−20.5120	−2.87226
$52$	−32.8125	−4.55028
$53$	−12.3536	−1.69690	−0.848451	−	0.529274i	$-0.822464\pi$
$53$	−12.3536	−1.69690	−0.848451	+	0.529274i	$0.822464\pi$
$54$	−24.8778	−3.38544
$55$	−1.00000	−0.134840
$56$	−29.6679	−3.96454
$57$	−24.4893	−3.24368
$58$	−7.57410	−0.994528
$59$	−2.35312	−0.306350	−0.153175	−	0.988199i	$-0.548950\pi$
$59$	−2.35312	−0.306350	−0.153175	+	0.988199i	$0.548950\pi$
$60$	−14.1293	−1.82408
$61$	1.59948	0.204792	0.102396	−	0.994744i	$-0.467349\pi$
$61$	1.59948	0.204792	0.102396	+	0.994744i	$0.467349\pi$
$62$	−13.2291	−1.68010
$63$	26.6742	3.36064
$64$	3.76777	0.470971
$65$	7.03654	0.872775
$66$	−7.82131	−0.962737
$67$	−0.966957	−0.118133	−0.0590663	−	0.998254i	$-0.518812\pi$
$67$	−0.966957	−0.118133	−0.0590663	+	0.998254i	$0.518812\pi$
$68$	−31.5682	−3.82820
$69$	−19.6864	−2.36996
$70$	11.1401	1.33150
$71$	−9.01607	−1.07001	−0.535005	−	0.844849i	$-0.679690\pi$
$71$	−9.01607	−1.07001	−0.535005	+	0.844849i	$0.679690\pi$
$72$	−42.4893	−5.00741
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	7.75250	0.901210
$75$	3.02998	0.349872
$76$	−37.6891	−4.32324
$77$	4.31568	0.491818
$78$	55.0350	6.23148
$79$	8.32169	0.936263	0.468131	−	0.883659i	$-0.344927\pi$
$79$	8.32169	0.936263	0.468131	+	0.883659i	$0.344927\pi$
$80$	−8.41873	−0.941242
$81$	10.6596	1.18440
$82$	20.9773	2.31656
$83$	−2.20321	−0.241834	−0.120917	−	0.992663i	$-0.538584\pi$
$83$	−2.20321	−0.241834	−0.120917	+	0.992663i	$0.538584\pi$
$84$	60.9774	6.65318
$85$	6.76970	0.734277
$86$	4.38010	0.472318
$87$	8.89059	0.953172
$88$	−6.87443	−0.732817
$89$	−10.3647	−1.09866	−0.549331	−	0.835605i	$-0.685117\pi$
$89$	−10.3647	−1.09866	−0.549331	+	0.835605i	$0.685117\pi$
$90$	15.9545	1.68175
$91$	−30.3675	−3.18338
$92$	−30.2975	−3.15873
$93$	15.5285	1.61023
$94$	−3.29509	−0.339863
$95$	8.08232	0.829228
$96$	−24.1867	−2.46855
$97$	−5.64861	−0.573529	−0.286765	−	0.958001i	$-0.592580\pi$
$97$	−5.64861	−0.573529	−0.286765	+	0.958001i	$0.592580\pi$
$98$	−30.0080	−3.03127
$99$	6.18077	0.621191
$100$	4.66316	0.466316
$101$	−9.78595	−0.973738	−0.486869	−	0.873475i	$-0.661861\pi$
$101$	−9.78595	−0.973738	−0.486869	+	0.873475i	$0.661861\pi$
$102$	52.9479	5.24263
$103$	12.1215	1.19437	0.597185	−	0.802104i	$-0.296286\pi$
$103$	12.1215	1.19437	0.597185	+	0.802104i	$0.296286\pi$
$104$	48.3722	4.74329
$105$	−13.0764	−1.27613
$106$	31.8885	3.09729
$107$	10.8169	1.04571	0.522856	−	0.852421i	$-0.324867\pi$
$107$	10.8169	1.04571	0.522856	+	0.852421i	$0.324867\pi$
$108$	44.9420	4.32454
$109$	−5.34556	−0.512012	−0.256006	−	0.966675i	$-0.582407\pi$
$109$	−5.34556	−0.512012	−0.256006	+	0.966675i	$0.582407\pi$
$110$	2.58131	0.246118
$111$	−9.10000	−0.863733
$112$	36.3325	3.43310
$113$	5.45731	0.513381	0.256690	−	0.966494i	$-0.417368\pi$
$113$	5.45731	0.513381	0.256690	+	0.966494i	$0.417368\pi$
$114$	63.2143	5.92057
$115$	6.49721	0.605868
$116$	13.6827	1.27041
$117$	−43.4913	−4.02077
$118$	6.07413	0.559169
$119$	−29.2159	−2.67821
$120$	20.8294	1.90145
$121$	1.00000	0.0909091
$122$	−4.12875	−0.373799
$123$	−24.6235	−2.22023
$124$	23.8985	2.14615
$125$	−1.00000	−0.0894427
$126$	−68.8545	−6.13404
$127$	−11.7972	−1.04683	−0.523415	−	0.852078i	$-0.675342\pi$
$127$	−11.7972	−1.04683	−0.523415	+	0.852078i	$0.675342\pi$
$128$	6.23917	0.551470
$129$	−5.14142	−0.452677
$130$	−18.1635	−1.59304
$131$	0.715565	0.0625192	0.0312596	−	0.999511i	$-0.490048\pi$
$131$	0.715565	0.0625192	0.0312596	+	0.999511i	$0.490048\pi$
$132$	14.1293	1.22980
$133$	−34.8807	−3.02454
$134$	2.49601	0.215623
$135$	−9.63767	−0.829479
$136$	46.5378	3.99059
$137$	−5.07980	−0.433996	−0.216998	−	0.976172i	$-0.569627\pi$
$137$	−5.07980	−0.433996	−0.216998	+	0.976172i	$0.569627\pi$
$138$	50.8167	4.32581
$139$	7.70185	0.653262	0.326631	−	0.945152i	$-0.394086\pi$
$139$	7.70185	0.653262	0.326631	+	0.945152i	$0.394086\pi$
$140$	−20.1247	−1.70085
$141$	3.86783	0.325730
$142$	23.2733	1.95305
$143$	−7.03654	−0.588425
$144$	52.0342	4.33619
$145$	−2.93421	−0.243673
$146$	−2.58131	−0.213631
$147$	35.2238	2.90521
$148$	−14.0050	−1.15120
$149$	14.0123	1.14793	0.573966	−	0.818879i	$-0.305404\pi$
$149$	14.0123	1.14793	0.573966	+	0.818879i	$0.305404\pi$
$150$	−7.82131	−0.638608
$151$	2.15350	0.175250	0.0876248	−	0.996154i	$-0.472072\pi$
$151$	2.15350	0.175250	0.0876248	+	0.996154i	$0.472072\pi$
$152$	55.5614	4.50662
$153$	−41.8420	−3.38272
$154$	−11.1401	−0.897696
$155$	−5.12495	−0.411646
$156$	−99.4212	−7.96007
$157$	−3.05569	−0.243871	−0.121935	−	0.992538i	$-0.538910\pi$
$157$	−3.05569	−0.243871	−0.121935	+	0.992538i	$0.538910\pi$
$158$	−21.4808	−1.70892
$159$	−37.4312	−2.96849
$160$	7.98247	0.631069
$161$	−28.0399	−2.20985
$162$	−27.5158	−2.16184
$163$	20.5349	1.60842	0.804209	−	0.594346i	$-0.202589\pi$
$163$	20.5349	1.60842	0.804209	+	0.594346i	$0.202589\pi$
$164$	−37.8958	−2.95916
$165$	−3.02998	−0.235884
$166$	5.68718	0.441410
$167$	−3.25405	−0.251806	−0.125903	−	0.992043i	$-0.540183\pi$
$167$	−3.25405	−0.251806	−0.125903	+	0.992043i	$0.540183\pi$
$168$	−89.8930	−6.93540
$169$	36.5129	2.80868
$170$	−17.4747	−1.34025
$171$	−49.9550	−3.82015
$172$	−7.91268	−0.603336
$173$	−20.4127	−1.55195	−0.775973	−	0.630766i	$-0.782741\pi$
$173$	−20.4127	−1.55195	−0.775973	+	0.630766i	$0.782741\pi$
$174$	−22.9494	−1.73979
$175$	4.31568	0.326235
$176$	8.41873	0.634585
$177$	−7.12991	−0.535917
$178$	26.7546	2.00534
$179$	17.6672	1.32051	0.660255	−	0.751042i	$-0.270448\pi$
$179$	17.6672	1.32051	0.660255	+	0.751042i	$0.270448\pi$
$180$	−28.8219	−2.14826
$181$	5.33022	0.396192	0.198096	−	0.980183i	$-0.436524\pi$
$181$	5.33022	0.396192	0.198096	+	0.980183i	$0.436524\pi$
$182$	78.3878	5.81049
$183$	4.84639	0.358255
$184$	44.6646	3.29272
$185$	3.00332	0.220809
$186$	−40.0839	−2.93909
$187$	−6.76970	−0.495049
$188$	5.95261	0.434139
$189$	41.5931	3.02545
$190$	−20.8630	−1.51356
$191$	18.2325	1.31926	0.659629	−	0.751592i	$-0.270714\pi$
$191$	18.2325	1.31926	0.659629	+	0.751592i	$0.270714\pi$
$192$	11.4162	0.823897
$193$	−3.81329	−0.274487	−0.137243	−	0.990537i	$-0.543824\pi$
$193$	−3.81329	−0.274487	−0.137243	+	0.990537i	$0.543824\pi$
$194$	14.5808	1.04684
$195$	21.3206	1.52680
$196$	54.2097	3.87212
$197$	24.0187	1.71126	0.855631	−	0.517586i	$-0.173169\pi$
$197$	24.0187	1.71126	0.855631	+	0.517586i	$0.173169\pi$
$198$	−15.9545	−1.13384
$199$	0.0778796	0.00552074	0.00276037	−	0.999996i	$-0.499121\pi$
$199$	0.0778796	0.00552074	0.00276037	+	0.999996i	$0.499121\pi$
$200$	−6.87443	−0.486096
$201$	−2.92986	−0.206656
$202$	25.2606	1.77733
$203$	12.6631	0.888776
$204$	−95.6509	−6.69690
$205$	8.12663	0.567588
$206$	−31.2894	−2.18004
$207$	−40.1578	−2.79116
$208$	−59.2387	−4.10747
$209$	−8.08232	−0.559066
$210$	33.7543	2.32927
$211$	19.6711	1.35421	0.677107	−	0.735884i	$-0.263233\pi$
$211$	19.6711	1.35421	0.677107	+	0.735884i	$0.263233\pi$
$212$	−57.6069	−3.95646
$213$	−27.3185	−1.87183
$214$	−27.9218	−1.90870
$215$	1.69685	0.115724
$216$	−66.2535	−4.50798
$217$	22.1177	1.50145
$218$	13.7985	0.934555
$219$	3.02998	0.204747
$220$	−4.66316	−0.314390
$221$	47.6353	3.20429
$222$	23.4899	1.57654
$223$	−16.4546	−1.10188	−0.550941	−	0.834544i	$-0.685731\pi$
$223$	−16.4546	−1.10188	−0.550941	+	0.834544i	$0.685731\pi$
$224$	−34.4498	−2.30177
$225$	6.18077	0.412051
$226$	−14.0870	−0.937054
$227$	1.96390	0.130349	0.0651743	−	0.997874i	$-0.479240\pi$
$227$	1.96390	0.130349	0.0651743	+	0.997874i	$0.479240\pi$
$228$	−114.197	−7.56290
$229$	3.87439	0.256027	0.128013	−	0.991772i	$-0.459140\pi$
$229$	3.87439	0.256027	0.128013	+	0.991772i	$0.459140\pi$
$230$	−16.7713	−1.10587
$231$	13.0764	0.860366
$232$	−20.1710	−1.32429
$233$	−23.3987	−1.53290	−0.766449	−	0.642306i	$-0.777978\pi$
$233$	−23.3987	−1.53290	−0.766449	+	0.642306i	$0.777978\pi$
$234$	112.264	7.33895
$235$	−1.27652	−0.0832710
$236$	−10.9730	−0.714280
$237$	25.2145	1.63786
$238$	75.4152	4.88844
$239$	−18.2354	−1.17955	−0.589776	−	0.807567i	$-0.700784\pi$
$239$	−18.2354	−1.17955	−0.589776	+	0.807567i	$0.700784\pi$
$240$	−25.5086	−1.64657
$241$	−4.70558	−0.303113	−0.151556	−	0.988449i	$-0.548429\pi$
$241$	−4.70558	−0.303113	−0.151556	+	0.988449i	$0.548429\pi$
$242$	−2.58131	−0.165933
$243$	3.38542	0.217175
$244$	7.45862	0.477489
$245$	−11.6251	−0.742701
$246$	63.5609	4.05250
$247$	56.8716	3.61865
$248$	−35.2312	−2.23718
$249$	−6.67569	−0.423055
$250$	2.58131	0.163256
$251$	−1.87213	−0.118168	−0.0590838	−	0.998253i	$-0.518818\pi$
$251$	−1.87213	−0.118168	−0.0590838	+	0.998253i	$0.518818\pi$
$252$	124.386	7.83560
$253$	−6.49721	−0.408476
$254$	30.4521	1.91074
$255$	20.5120	1.28451
$256$	−23.6408	−1.47755
$257$	13.2457	0.826244	0.413122	−	0.910676i	$-0.364438\pi$
$257$	13.2457	0.826244	0.413122	+	0.910676i	$0.364438\pi$
$258$	13.2716	0.826253
$259$	−12.9614	−0.805381
$260$	32.8125	2.03494
$261$	18.1357	1.12257
$262$	−1.84710	−0.114114
$263$	−11.8768	−0.732354	−0.366177	−	0.930545i	$-0.619334\pi$
$263$	−11.8768	−0.732354	−0.366177	+	0.930545i	$0.619334\pi$
$264$	−20.8294	−1.28196
$265$	12.3536	0.758878
$266$	90.0379	5.52058
$267$	−31.4050	−1.92195
$268$	−4.50907	−0.275435
$269$	−20.1730	−1.22997	−0.614984	−	0.788539i	$-0.710838\pi$
$269$	−20.1730	−1.22997	−0.614984	+	0.788539i	$0.710838\pi$
$270$	24.8778	1.51402
$271$	−24.7834	−1.50548	−0.752742	−	0.658316i	$-0.771269\pi$
$271$	−24.7834	−1.50548	−0.752742	+	0.658316i	$0.771269\pi$
$272$	−56.9922	−3.45566
$273$	−92.0128	−5.56887
$274$	13.1125	0.792157
$275$	1.00000	0.0603023
$276$	−91.8008	−5.52576
$277$	26.8303	1.61207	0.806037	−	0.591865i	$-0.201608\pi$
$277$	26.8303	1.61207	0.806037	+	0.591865i	$0.201608\pi$
$278$	−19.8809	−1.19237
$279$	31.6762	1.89640
$280$	29.6679	1.77299
$281$	10.6423	0.634866	0.317433	−	0.948281i	$-0.397179\pi$
$281$	10.6423	0.634866	0.317433	+	0.948281i	$0.397179\pi$
$282$	−9.98406	−0.594542
$283$	21.4627	1.27583	0.637913	−	0.770108i	$-0.279798\pi$
$283$	21.4627	1.27583	0.637913	+	0.770108i	$0.279798\pi$
$284$	−42.0433	−2.49481
$285$	24.4893	1.45062
$286$	18.1635	1.07403
$287$	−35.0720	−2.07023
$288$	−49.3378	−2.90726
$289$	28.8288	1.69581
$290$	7.57410	0.444767
$291$	−17.1152	−1.00331
$292$	4.66316	0.272891
$293$	16.9878	0.992440	0.496220	−	0.868197i	$-0.334721\pi$
$293$	16.9878	0.992440	0.496220	+	0.868197i	$0.334721\pi$
$294$	−90.9236	−5.30277
$295$	2.35312	0.137004
$296$	20.6461	1.20003
$297$	9.63767	0.559234
$298$	−36.1701	−2.09528
$299$	45.7179	2.64393
$300$	14.1293	0.815754
$301$	−7.32307	−0.422094
$302$	−5.55886	−0.319876
$303$	−29.6512	−1.70342
$304$	−68.0428	−3.90252
$305$	−1.59948	−0.0915859
$306$	108.007	6.17435
$307$	−34.4073	−1.96373	−0.981863	−	0.189591i	$-0.939284\pi$
$307$	−34.4073	−1.96373	−0.981863	+	0.189591i	$0.939284\pi$
$308$	20.1247	1.14671
$309$	36.7280	2.08938
$310$	13.2291	0.751362
$311$	−1.04169	−0.0590689	−0.0295344	−	0.999564i	$-0.509402\pi$
$311$	−1.04169	−0.0590689	−0.0295344	+	0.999564i	$0.509402\pi$
$312$	146.567	8.29771
$313$	−11.8375	−0.669093	−0.334547	−	0.942379i	$-0.608583\pi$
$313$	−11.8375	−0.669093	−0.334547	+	0.942379i	$0.608583\pi$
$314$	7.88768	0.445127
$315$	−26.6742	−1.50292
$316$	38.8053	2.18297
$317$	18.4045	1.03370	0.516850	−	0.856076i	$-0.327105\pi$
$317$	18.4045	1.03370	0.516850	+	0.856076i	$0.327105\pi$
$318$	96.6216	5.41827
$319$	2.93421	0.164284
$320$	−3.76777	−0.210624
$321$	32.7750	1.82932
$322$	72.3796	4.03356
$323$	54.7149	3.04442
$324$	49.7075	2.76153
$325$	−7.03654	−0.390317
$326$	−53.0070	−2.93578
$327$	−16.1969	−0.895692
$328$	55.8660	3.08468
$329$	5.50905	0.303724
$330$	7.82131	0.430549
$331$	−10.2608	−0.563985	−0.281993	−	0.959417i	$-0.590995\pi$
$331$	−10.2608	−0.563985	−0.281993	+	0.959417i	$0.590995\pi$
$332$	−10.2739	−0.563855
$333$	−18.5628	−1.01724
$334$	8.39971	0.459612
$335$	0.966957	0.0528305
$336$	110.087	6.00573
$337$	16.0388	0.873690	0.436845	−	0.899537i	$-0.356096\pi$
$337$	16.0388	0.873690	0.436845	+	0.899537i	$0.356096\pi$
$338$	−94.2511	−5.12658
$339$	16.5355	0.898088
$340$	31.5682	1.71202
$341$	5.12495	0.277532
$342$	128.949	6.97278
$343$	19.9605	1.07777
$344$	11.6649	0.628928
$345$	19.6864	1.05988
$346$	52.6914	2.83271
$347$	−13.4262	−0.720758	−0.360379	−	0.932806i	$-0.617353\pi$
$347$	−13.4262	−0.720758	−0.360379	+	0.932806i	$0.617353\pi$
$348$	41.4582	2.22239
$349$	23.4978	1.25781	0.628904	−	0.777483i	$-0.283504\pi$
$349$	23.4978	1.25781	0.628904	+	0.777483i	$0.283504\pi$
$350$	−11.1401	−0.595464
$351$	−67.8159	−3.61974
$352$	−7.98247	−0.425467
$353$	−6.84068	−0.364093	−0.182046	−	0.983290i	$-0.558272\pi$
$353$	−6.84068	−0.364093	−0.182046	+	0.983290i	$0.558272\pi$
$354$	18.4045	0.978188
$355$	9.01607	0.478523
$356$	−48.3325	−2.56162
$357$	−88.5234	−4.68516
$358$	−45.6046	−2.41028
$359$	19.1780	1.01218	0.506089	−	0.862481i	$-0.331091\pi$
$359$	19.1780	1.01218	0.506089	+	0.862481i	$0.331091\pi$
$360$	42.4893	2.23938
$361$	46.3239	2.43810
$362$	−13.7589	−0.723154
$363$	3.02998	0.159033
$364$	−141.608	−7.42229
$365$	−1.00000	−0.0523424
$366$	−12.5100	−0.653910
$367$	−21.8300	−1.13952	−0.569759	−	0.821812i	$-0.692964\pi$
$367$	−21.8300	−1.13952	−0.569759	+	0.821812i	$0.692964\pi$
$368$	−54.6982	−2.85134
$369$	−50.2288	−2.61481
$370$	−7.75250	−0.403033
$371$	−53.3143	−2.76794
$372$	72.4119	3.75438
$373$	−1.51966	−0.0786852	−0.0393426	−	0.999226i	$-0.512526\pi$
$373$	−1.51966	−0.0786852	−0.0393426	+	0.999226i	$0.512526\pi$
$374$	17.4747	0.903594
$375$	−3.02998	−0.156467
$376$	−8.77535	−0.452554
$377$	−20.6467	−1.06336
$378$	−107.365	−5.52225
$379$	25.6599	1.31806	0.659031	−	0.752116i	$-0.270967\pi$
$379$	25.6599	1.31806	0.659031	+	0.752116i	$0.270967\pi$
$380$	37.6891	1.93341
$381$	−35.7452	−1.83128
$382$	−47.0637	−2.40799
$383$	8.95741	0.457702	0.228851	−	0.973461i	$-0.426503\pi$
$383$	8.95741	0.457702	0.228851	+	0.973461i	$0.426503\pi$
$384$	18.9045	0.964719
$385$	−4.31568	−0.219948
$386$	9.84329	0.501010
$387$	−10.4878	−0.533127
$388$	−26.3404	−1.33723
$389$	22.8989	1.16102	0.580511	−	0.814252i	$-0.302853\pi$
$389$	22.8989	1.16102	0.580511	+	0.814252i	$0.302853\pi$
$390$	−55.0350	−2.78680
$391$	43.9841	2.22437
$392$	−79.9161	−4.03637
$393$	2.16815	0.109369
$394$	−61.9997	−3.12350
$395$	−8.32169	−0.418709
$396$	28.8219	1.44836
$397$	−14.7241	−0.738982	−0.369491	−	0.929234i	$-0.620468\pi$
$397$	−14.7241	−0.738982	−0.369491	+	0.929234i	$0.620468\pi$
$398$	−0.201031	−0.0100768
$399$	−105.688	−5.29101
$400$	8.41873	0.420936
$401$	−36.3701	−1.81623	−0.908117	−	0.418716i	$-0.862480\pi$
$401$	−36.3701	−1.81623	−0.908117	+	0.418716i	$0.862480\pi$
$402$	7.56287	0.377202
$403$	−36.0619	−1.79637
$404$	−45.6334	−2.27035
$405$	−10.6596	−0.529681
$406$	−32.6874	−1.62225
$407$	−3.00332	−0.148869
$408$	141.009	6.98097
$409$	−5.51911	−0.272902	−0.136451	−	0.990647i	$-0.543570\pi$
$409$	−5.51911	−0.272902	−0.136451	+	0.990647i	$0.543570\pi$
$410$	−20.9773	−1.03600
$411$	−15.3917	−0.759215
$412$	56.5246	2.78477
$413$	−10.1553	−0.499711
$414$	103.660	5.09459
$415$	2.20321	0.108151
$416$	56.1690	2.75391
$417$	23.3364	1.14279
$418$	20.8630	1.02044
$419$	15.9322	0.778340	0.389170	−	0.921166i	$-0.372762\pi$
$419$	15.9322	0.778340	0.389170	+	0.921166i	$0.372762\pi$
$420$	−60.9774	−2.97539
$421$	−4.61742	−0.225039	−0.112520	−	0.993650i	$-0.535892\pi$
$421$	−4.61742	−0.225039	−0.112520	+	0.993650i	$0.535892\pi$
$422$	−50.7772	−2.47180
$423$	7.88988	0.383619
$424$	84.9242	4.12429
$425$	−6.76970	−0.328379
$426$	70.5175	3.41658
$427$	6.90284	0.334052
$428$	50.4410	2.43816
$429$	−21.3206	−1.02937
$430$	−4.38010	−0.211227
$431$	−18.7578	−0.903533	−0.451767	−	0.892136i	$-0.649206\pi$
$431$	−18.7578	−0.903533	−0.451767	+	0.892136i	$0.649206\pi$
$432$	81.1369	3.90370
$433$	0.616828	0.0296429	0.0148214	−	0.999890i	$-0.495282\pi$
$433$	0.616828	0.0296429	0.0148214	+	0.999890i	$0.495282\pi$
$434$	−57.0925	−2.74053
$435$	−8.89059	−0.426271
$436$	−24.9272	−1.19380
$437$	52.5125	2.51201
$438$	−7.82131	−0.373717
$439$	−1.26829	−0.0605320	−0.0302660	−	0.999542i	$-0.509635\pi$
$439$	−1.26829	−0.0605320	−0.0302660	+	0.999542i	$0.509635\pi$
$440$	6.87443	0.327726
$441$	71.8522	3.42153
$442$	−122.961	−5.84867
$443$	−8.00354	−0.380260	−0.190130	−	0.981759i	$-0.560891\pi$
$443$	−8.00354	−0.380260	−0.190130	+	0.981759i	$0.560891\pi$
$444$	−42.4347	−2.01386
$445$	10.3647	0.491336
$446$	42.4744	2.01122
$447$	42.4570	2.00815
$448$	16.2605	0.768235
$449$	−4.69953	−0.221784	−0.110892	−	0.993832i	$-0.535371\pi$
$449$	−4.69953	−0.221784	−0.110892	+	0.993832i	$0.535371\pi$
$450$	−15.9545	−0.752102
$451$	−8.12663	−0.382668
$452$	25.4483	1.19699
$453$	6.52507	0.306575
$454$	−5.06943	−0.237920
$455$	30.3675	1.42365
$456$	168.350	7.88370
$457$	−32.5171	−1.52109	−0.760543	−	0.649287i	$-0.775067\pi$
$457$	−32.5171	−1.52109	−0.760543	+	0.649287i	$0.775067\pi$
$458$	−10.0010	−0.467316
$459$	−65.2441	−3.04533
$460$	30.2975	1.41263
$461$	14.8617	0.692176	0.346088	−	0.938202i	$-0.387510\pi$
$461$	14.8617	0.692176	0.346088	+	0.938202i	$0.387510\pi$
$462$	−33.7543	−1.57039
$463$	11.4121	0.530367	0.265183	−	0.964198i	$-0.414568\pi$
$463$	11.4121	0.530367	0.265183	+	0.964198i	$0.414568\pi$
$464$	24.7023	1.14678
$465$	−15.5285	−0.720117
$466$	60.3992	2.79794
$467$	−7.32004	−0.338731	−0.169366	−	0.985553i	$-0.554172\pi$
$467$	−7.32004	−0.338731	−0.169366	+	0.985553i	$0.554172\pi$
$468$	−202.807	−9.37474
$469$	−4.17308	−0.192695
$470$	3.29509	0.151991
$471$	−9.25867	−0.426617
$472$	16.1764	0.744578
$473$	−1.69685	−0.0780213
$474$	−65.0865	−2.98952
$475$	−8.08232	−0.370842
$476$	−136.238	−6.24447
$477$	−76.3550	−3.49605
$478$	47.0713	2.15299
$479$	12.8248	0.585981	0.292990	−	0.956115i	$-0.405350\pi$
$479$	12.8248	0.585981	0.292990	+	0.956115i	$0.405350\pi$
$480$	24.1867	1.10397
$481$	21.1330	0.963581
$482$	12.1465	0.553260
$483$	−84.9603	−3.86583
$484$	4.66316	0.211962
$485$	5.64861	0.256490
$486$	−8.73883	−0.396401
$487$	−30.8605	−1.39842	−0.699211	−	0.714915i	$-0.746465\pi$
$487$	−30.8605	−1.39842	−0.699211	+	0.714915i	$0.746465\pi$
$488$	−10.9955	−0.497744
$489$	62.2204	2.81370
$490$	30.0080	1.35562
$491$	16.5835	0.748404	0.374202	−	0.927347i	$-0.377917\pi$
$491$	16.5835	0.748404	0.374202	+	0.927347i	$0.377917\pi$
$492$	−114.823	−5.17664
$493$	−19.8637	−0.894617
$494$	−146.803	−6.60498
$495$	−6.18077	−0.277805
$496$	43.1456	1.93729
$497$	−38.9105	−1.74537
$498$	17.2320	0.772185
$499$	−24.6051	−1.10148	−0.550739	−	0.834678i	$-0.685654\pi$
$499$	−24.6051	−1.10148	−0.550739	+	0.834678i	$0.685654\pi$
$500$	−4.66316	−0.208543
$501$	−9.85970	−0.440499
$502$	4.83254	0.215687
$503$	−1.00105	−0.0446348	−0.0223174	−	0.999751i	$-0.507104\pi$
$503$	−1.00105	−0.0446348	−0.0223174	+	0.999751i	$0.507104\pi$
$504$	−183.370	−8.16796
$505$	9.78595	0.435469
$506$	16.7713	0.745576
$507$	110.633	4.91340
$508$	−55.0121	−2.44077
$509$	24.1388	1.06994	0.534968	−	0.844872i	$-0.320324\pi$
$509$	24.1388	1.06994	0.534968	+	0.844872i	$0.320324\pi$
$510$	−52.9479	−2.34457
$511$	4.31568	0.190915
$512$	48.5458	2.14544
$513$	−77.8947	−3.43914
$514$	−34.1913	−1.50811
$515$	−12.1215	−0.534138
$516$	−23.9753	−1.05545
$517$	1.27652	0.0561413
$518$	33.4573	1.47003
$519$	−61.8499	−2.71491
$520$	−48.3722	−2.12126
$521$	−27.1383	−1.18895	−0.594476	−	0.804113i	$-0.702640\pi$
$521$	−27.1383	−1.18895	−0.594476	+	0.804113i	$0.702640\pi$
$522$	−46.8138	−2.04898
$523$	2.06781	0.0904189	0.0452095	−	0.998978i	$-0.485604\pi$
$523$	2.06781	0.0904189	0.0452095	+	0.998978i	$0.485604\pi$
$524$	3.33679	0.145769
$525$	13.0764	0.570702
$526$	30.6577	1.33674
$527$	−34.6944	−1.51131
$528$	25.5086	1.11012
$529$	19.2137	0.835380
$530$	−31.8885	−1.38515
$531$	−14.5441	−0.631160
$532$	−162.654	−7.05196
$533$	57.1834	2.47689
$534$	81.0659	3.50807
$535$	−10.8169	−0.467656
$536$	6.64728	0.287119
$537$	53.5313	2.31005
$538$	52.0727	2.24501
$539$	11.6251	0.500729
$540$	−44.9420	−1.93400
$541$	4.96271	0.213364	0.106682	−	0.994293i	$-0.465977\pi$
$541$	4.96271	0.213364	0.106682	+	0.994293i	$0.465977\pi$
$542$	63.9736	2.74790
$543$	16.1504	0.693082
$544$	54.0389	2.31690
$545$	5.34556	0.228979
$546$	237.513	10.1646
$547$	−1.22546	−0.0523967	−0.0261983	−	0.999657i	$-0.508340\pi$
$547$	−1.22546	−0.0523967	−0.0261983	+	0.999657i	$0.508340\pi$
$548$	−23.6879	−1.01190
$549$	9.88602	0.421925
$550$	−2.58131	−0.110067
$551$	−23.7152	−1.01030
$552$	135.333	5.76015
$553$	35.9137	1.52721
$554$	−69.2572	−2.94246
$555$	9.10000	0.386273
$556$	35.9149	1.52313
$557$	2.68716	0.113858	0.0569292	−	0.998378i	$-0.481869\pi$
$557$	2.68716	0.113858	0.0569292	+	0.998378i	$0.481869\pi$
$558$	−81.7660	−3.46143
$559$	11.9400	0.505006
$560$	−36.3325	−1.53533
$561$	−20.5120	−0.866019
$562$	−27.4710	−1.15880
$563$	−24.3797	−1.02748	−0.513741	−	0.857945i	$-0.671741\pi$
$563$	−24.3797	−1.02748	−0.513741	+	0.857945i	$0.671741\pi$
$564$	18.0363	0.759465
$565$	−5.45731	−0.229591
$566$	−55.4019	−2.32872
$567$	46.0036	1.93197
$568$	61.9804	2.60064
$569$	20.2100	0.847248	0.423624	−	0.905838i	$-0.360758\pi$
$569$	20.2100	0.847248	0.423624	+	0.905838i	$0.360758\pi$
$570$	−63.2143	−2.64776
$571$	−32.1123	−1.34386	−0.671930	−	0.740615i	$-0.734534\pi$
$571$	−32.1123	−1.34386	−0.671930	+	0.740615i	$0.734534\pi$
$572$	−32.8125	−1.37196
$573$	55.2441	2.30785
$574$	90.5316	3.77871
$575$	−6.49721	−0.270952
$576$	23.2877	0.970321
$577$	−30.5877	−1.27338	−0.636691	−	0.771119i	$-0.719697\pi$
$577$	−30.5877	−1.27338	−0.636691	+	0.771119i	$0.719697\pi$
$578$	−74.4161	−3.09530
$579$	−11.5542	−0.480176
$580$	−13.6827	−0.568142
$581$	−9.50837	−0.394474
$582$	44.1795	1.83130
$583$	−12.3536	−0.511635
$584$	−6.87443	−0.284466
$585$	43.4913	1.79814
$586$	−43.8509	−1.81146
$587$	−42.2148	−1.74239	−0.871195	−	0.490937i	$-0.836654\pi$
$587$	−42.2148	−1.74239	−0.871195	+	0.490937i	$0.836654\pi$
$588$	164.254	6.77373
$589$	−41.4215	−1.70674
$590$	−6.07413	−0.250068
$591$	72.7762	2.99361
$592$	−25.2841	−1.03917
$593$	0.00784197	0.000322031 0	0.000161016	−	1.00000i	$-0.499949\pi$
$593$	0.00784197	0.000322031 0	0.000161016		1.00000i	$0.499949\pi$
$594$	−24.8778	−1.02075
$595$	29.2159	1.19773
$596$	65.3416	2.67650
$597$	0.235973	0.00965775
$598$	−118.012	−4.82587
$599$	18.2765	0.746759	0.373379	−	0.927679i	$-0.378199\pi$
$599$	18.2765	0.746759	0.373379	+	0.927679i	$0.378199\pi$
$600$	−20.8294	−0.850356
$601$	−13.2814	−0.541760	−0.270880	−	0.962613i	$-0.587315\pi$
$601$	−13.2814	−0.541760	−0.270880	+	0.962613i	$0.587315\pi$
$602$	18.9031	0.770433
$603$	−5.97654	−0.243383
$604$	10.0421	0.408608
$605$	−1.00000	−0.0406558
$606$	76.5389	3.10918
$607$	−15.6752	−0.636236	−0.318118	−	0.948051i	$-0.603051\pi$
$607$	−15.6752	−0.636236	−0.318118	+	0.948051i	$0.603051\pi$
$608$	64.5168	2.61650
$609$	38.3690	1.55479
$610$	4.12875	0.167168
$611$	−8.98229	−0.363384
$612$	−195.116	−7.88708
$613$	−14.5970	−0.589566	−0.294783	−	0.955564i	$-0.595247\pi$
$613$	−14.5970	−0.589566	−0.294783	+	0.955564i	$0.595247\pi$
$614$	88.8158	3.58431
$615$	24.6235	0.992916
$616$	−29.6679	−1.19535
$617$	12.7810	0.514543	0.257271	−	0.966339i	$-0.417177\pi$
$617$	12.7810	0.514543	0.257271	+	0.966339i	$0.417177\pi$
$618$	−94.8063	−3.81367
$619$	20.0929	0.807602	0.403801	−	0.914847i	$-0.367689\pi$
$619$	20.0929	0.807602	0.403801	+	0.914847i	$0.367689\pi$
$620$	−23.8985	−0.959786
$621$	−62.6180	−2.51277
$622$	2.68893	0.107816
$623$	−44.7310	−1.79211
$624$	−179.492	−7.18543
$625$	1.00000	0.0400000
$626$	30.5562	1.22127
$627$	−24.4893	−0.978007
$628$	−14.2492	−0.568603
$629$	20.3316	0.810673
$630$	68.8545	2.74323
$631$	−1.67449	−0.0666605	−0.0333303	−	0.999444i	$-0.510611\pi$
$631$	−1.67449	−0.0666605	−0.0333303	+	0.999444i	$0.510611\pi$
$632$	−57.2069	−2.27557
$633$	59.6030	2.36901
$634$	−47.5077	−1.88677
$635$	11.7972	0.468156
$636$	−174.548	−6.92127
$637$	−81.8006	−3.24106
$638$	−7.57410	−0.299862
$639$	−55.7263	−2.20450
$640$	−6.23917	−0.246625
$641$	−16.2440	−0.641598	−0.320799	−	0.947147i	$-0.603951\pi$
$641$	−16.2440	−0.641598	−0.320799	+	0.947147i	$0.603951\pi$
$642$	−84.6025	−3.33900
$643$	−22.2536	−0.877595	−0.438797	−	0.898586i	$-0.644595\pi$
$643$	−22.2536	−0.877595	−0.438797	+	0.898586i	$0.644595\pi$
$644$	−130.754	−5.15245
$645$	5.14142	0.202443
$646$	−141.236	−5.55685
$647$	29.7903	1.17118	0.585589	−	0.810608i	$-0.300863\pi$
$647$	29.7903	1.17118	0.585589	+	0.810608i	$0.300863\pi$
$648$	−73.2789	−2.87867
$649$	−2.35312	−0.0923681
$650$	18.1635	0.712431
$651$	67.0161	2.62657
$652$	95.7576	3.75016
$653$	34.9894	1.36924	0.684621	−	0.728900i	$-0.259968\pi$
$653$	34.9894	1.36924	0.684621	+	0.728900i	$0.259968\pi$
$654$	41.8093	1.63487
$655$	−0.715565	−0.0279595
$656$	−68.4159	−2.67119
$657$	6.18077	0.241135
$658$	−14.2206	−0.554376
$659$	41.4641	1.61521	0.807606	−	0.589722i	$-0.200763\pi$
$659$	41.4641	1.61521	0.807606	+	0.589722i	$0.200763\pi$
$660$	−14.1293	−0.549981
$661$	4.79723	0.186590	0.0932952	−	0.995638i	$-0.470260\pi$
$661$	4.79723	0.186590	0.0932952	+	0.995638i	$0.470260\pi$
$662$	26.4863	1.02942
$663$	144.334	5.60546
$664$	15.1458	0.587773
$665$	34.8807	1.35262
$666$	47.9164	1.85672
$667$	−19.0642	−0.738168
$668$	−15.1741	−0.587105
$669$	−49.8571	−1.92759
$670$	−2.49601	−0.0964294
$671$	1.59948	0.0617472
$672$	−104.382	−4.02663
$673$	−40.4540	−1.55939	−0.779694	−	0.626160i	$-0.784626\pi$
$673$	−40.4540	−1.55939	−0.779694	+	0.626160i	$0.784626\pi$
$674$	−41.4012	−1.59471
$675$	9.63767	0.370954
$676$	170.265	6.54867
$677$	10.7032	0.411358	0.205679	−	0.978619i	$-0.434060\pi$
$677$	10.7032	0.411358	0.205679	+	0.978619i	$0.434060\pi$
$678$	−42.6834	−1.63924
$679$	−24.3776	−0.935527
$680$	−46.5378	−1.78464
$681$	5.95058	0.228027
$682$	−13.2291	−0.506568
$683$	−32.1343	−1.22958	−0.614792	−	0.788689i	$-0.710760\pi$
$683$	−32.1343	−1.22958	−0.614792	+	0.788689i	$0.710760\pi$
$684$	−232.948	−8.90699
$685$	5.07980	0.194089
$686$	−51.5242	−1.96720
$687$	11.7393	0.447883
$688$	−14.2853	−0.544623
$689$	86.9268	3.31165
$690$	−50.8167	−1.93456
$691$	−26.3617	−1.00285	−0.501423	−	0.865203i	$-0.667190\pi$
$691$	−26.3617	−1.00285	−0.501423	+	0.865203i	$0.667190\pi$
$692$	−95.1874	−3.61848
$693$	26.6742	1.01327
$694$	34.6573	1.31557
$695$	−7.70185	−0.292148
$696$	−61.1178	−2.31666
$697$	55.0148	2.08384
$698$	−60.6551	−2.29583
$699$	−70.8974	−2.68159
$700$	20.1247	0.760642
$701$	36.9647	1.39614	0.698068	−	0.716032i	$-0.254043\pi$
$701$	36.9647	1.39614	0.698068	+	0.716032i	$0.254043\pi$
$702$	175.054	6.60698
$703$	24.2738	0.915503
$704$	3.76777	0.142003
$705$	−3.86783	−0.145671
$706$	17.6579	0.664564
$707$	−42.2330	−1.58834
$708$	−33.2479	−1.24953
$709$	−6.56235	−0.246454	−0.123227	−	0.992378i	$-0.539324\pi$
$709$	−6.56235	−0.246454	−0.123227	+	0.992378i	$0.539324\pi$
$710$	−23.2733	−0.873430
$711$	51.4344	1.92894
$712$	71.2518	2.67027
$713$	−33.2979	−1.24702
$714$	228.506	8.55164
$715$	7.03654	0.263152
$716$	82.3850	3.07887
$717$	−55.2529	−2.06346
$718$	−49.5044	−1.84749
$719$	−16.0798	−0.599675	−0.299837	−	0.953990i	$-0.596932\pi$
$719$	−16.0798	−0.599675	−0.299837	+	0.953990i	$0.596932\pi$
$720$	−52.0342	−1.93920
$721$	52.3127	1.94823
$722$	−119.576	−4.45017
$723$	−14.2578	−0.530253
$724$	24.8556	0.923753
$725$	2.93421	0.108974
$726$	−7.82131	−0.290276
$727$	23.7196	0.879710	0.439855	−	0.898069i	$-0.355030\pi$
$727$	23.7196	0.879710	0.439855	+	0.898069i	$0.355030\pi$
$728$	208.759	7.73713
$729$	−21.7211	−0.804486
$730$	2.58131	0.0955385
$731$	11.4872	0.424868
$732$	22.5995	0.835301
$733$	36.4745	1.34722	0.673608	−	0.739089i	$-0.264744\pi$
$733$	36.4745	1.34722	0.673608	+	0.739089i	$0.264744\pi$
$734$	56.3501	2.07992
$735$	−35.2238	−1.29925
$736$	51.8638	1.91172
$737$	−0.966957	−0.0356183
$738$	129.656	4.77271
$739$	−6.87268	−0.252816	−0.126408	−	0.991978i	$-0.540345\pi$
$739$	−6.87268	−0.252816	−0.126408	+	0.991978i	$0.540345\pi$
$740$	14.0050	0.514832
$741$	172.320	6.33032
$742$	137.621	5.05222
$743$	−35.9416	−1.31857	−0.659284	−	0.751894i	$-0.729140\pi$
$743$	−35.9416	−1.31857	−0.659284	+	0.751894i	$0.729140\pi$
$744$	−106.750	−3.91363
$745$	−14.0123	−0.513371
$746$	3.92272	0.143621
$747$	−13.6176	−0.498240
$748$	−31.5682	−1.15425
$749$	46.6824	1.70574
$750$	7.82131	0.285594
$751$	−3.29189	−0.120123	−0.0600615	−	0.998195i	$-0.519130\pi$
$751$	−3.29189	−0.120123	−0.0600615	+	0.998195i	$0.519130\pi$
$752$	10.7467	0.391891
$753$	−5.67250	−0.206717
$754$	53.2955	1.94091
$755$	−2.15350	−0.0783740
$756$	193.955	7.05409
$757$	16.2294	0.589867	0.294934	−	0.955518i	$-0.404702\pi$
$757$	16.2294	0.589867	0.294934	+	0.955518i	$0.404702\pi$
$758$	−66.2362	−2.40581
$759$	−19.6864	−0.714571
$760$	−55.5614	−2.01542
$761$	7.11891	0.258060	0.129030	−	0.991641i	$-0.458814\pi$
$761$	7.11891	0.258060	0.129030	+	0.991641i	$0.458814\pi$
$762$	92.2693	3.34257
$763$	−23.0697	−0.835180
$764$	85.0210	3.07595
$765$	41.8420	1.51280
$766$	−23.1218	−0.835426
$767$	16.5578	0.597869
$768$	−71.6310	−2.58476
$769$	−22.8549	−0.824168	−0.412084	−	0.911146i	$-0.635199\pi$
$769$	−22.8549	−0.824168	−0.412084	+	0.911146i	$0.635199\pi$
$770$	11.1401	0.401462
$771$	40.1342	1.44540
$772$	−17.7820	−0.639988
$773$	−24.7888	−0.891591	−0.445796	−	0.895135i	$-0.647079\pi$
$773$	−24.7888	−0.891591	−0.445796	+	0.895135i	$0.647079\pi$
$774$	27.0724	0.973096
$775$	5.12495	0.184094
$776$	38.8310	1.39395
$777$	−39.2727	−1.40890
$778$	−59.1092	−2.11917
$779$	65.6820	2.35330
$780$	99.4212	3.55985
$781$	−9.01607	−0.322620
$782$	−113.537	−4.06006
$783$	28.2789	1.01061
$784$	97.8686	3.49531
$785$	3.05569	0.109062
$786$	−5.59666	−0.199626
$787$	−22.0483	−0.785935	−0.392968	−	0.919552i	$-0.628552\pi$
$787$	−22.0483	−0.785935	−0.392968	+	0.919552i	$0.628552\pi$
$788$	112.003	3.98994
$789$	−35.9864	−1.28115
$790$	21.4808	0.764254
$791$	23.5520	0.837414
$792$	−42.4893	−1.50979
$793$	−11.2548	−0.399670
$794$	38.0075	1.34884
$795$	37.4312	1.32755
$796$	0.363165	0.0128720
$797$	−22.4686	−0.795879	−0.397939	−	0.917412i	$-0.630275\pi$
$797$	−22.4686	−0.795879	−0.397939	+	0.917412i	$0.630275\pi$
$798$	272.813	9.65748
$799$	−8.64166	−0.305720
$800$	−7.98247	−0.282223
$801$	−64.0622	−2.26352
$802$	93.8824	3.31510
$803$	1.00000	0.0352892
$804$	−13.6624	−0.481835
$805$	28.0399	0.988276
$806$	93.0870	3.27885
$807$	−61.1237	−2.15166
$808$	67.2728	2.36665
$809$	27.1344	0.953995	0.476998	−	0.878905i	$-0.341725\pi$
$809$	27.1344	0.953995	0.476998	+	0.878905i	$0.341725\pi$
$810$	27.5158	0.966806
$811$	−47.3975	−1.66435	−0.832176	−	0.554512i	$-0.812905\pi$
$811$	−47.3975	−1.66435	−0.832176	+	0.554512i	$0.812905\pi$
$812$	59.0501	2.07225
$813$	−75.0931	−2.63363
$814$	7.75250	0.271725
$815$	−20.5349	−0.719307
$816$	−172.685	−6.04519
$817$	13.7145	0.479809
$818$	14.2465	0.498118
$819$	−187.694	−6.55857
$820$	37.8958	1.32338
$821$	33.7671	1.17848	0.589239	−	0.807959i	$-0.299428\pi$
$821$	33.7671	1.17848	0.589239	+	0.807959i	$0.299428\pi$
$822$	39.7307	1.38577
$823$	−32.7476	−1.14151	−0.570755	−	0.821120i	$-0.693350\pi$
$823$	−32.7476	−1.14151	−0.570755	+	0.821120i	$0.693350\pi$
$824$	−83.3287	−2.90289
$825$	3.02998	0.105490
$826$	26.2140	0.912103
$827$	−28.2792	−0.983364	−0.491682	−	0.870775i	$-0.663618\pi$
$827$	−28.2792	−0.983364	−0.491682	+	0.870775i	$0.663618\pi$
$828$	−187.262	−6.50780
$829$	30.9368	1.07448	0.537239	−	0.843430i	$-0.319467\pi$
$829$	30.9368	1.07448	0.537239	+	0.843430i	$0.319467\pi$
$830$	−5.68718	−0.197405
$831$	81.2951	2.82010
$832$	−26.5120	−0.919139
$833$	−78.6985	−2.72674
$834$	−60.2386	−2.08589
$835$	3.25405	0.112611
$836$	−37.6891	−1.30351
$837$	49.3926	1.70726
$838$	−41.1260	−1.42067
$839$	−1.00720	−0.0347724	−0.0173862	−	0.999849i	$-0.505534\pi$
$839$	−1.00720	−0.0347724	−0.0173862	+	0.999849i	$0.505534\pi$
$840$	89.8930	3.10160
$841$	−20.3904	−0.703118
$842$	11.9190	0.410755
$843$	32.2459	1.11061
$844$	91.7295	3.15746
$845$	−36.5129	−1.25608
$846$	−20.3662	−0.700205
$847$	4.31568	0.148289
$848$	−104.002	−3.57144
$849$	65.0316	2.23188
$850$	17.4747	0.599377
$851$	19.5132	0.668904
$852$	−127.390	−4.36432
$853$	22.5519	0.772162	0.386081	−	0.922465i	$-0.373829\pi$
$853$	22.5519	0.772162	0.386081	+	0.922465i	$0.373829\pi$
$854$	−17.8184	−0.609732
$855$	49.9550	1.70842
$856$	−74.3602	−2.54158
$857$	11.0856	0.378677	0.189339	−	0.981912i	$-0.439366\pi$
$857$	11.0856	0.378677	0.189339	+	0.981912i	$0.439366\pi$
$858$	55.0350	1.87886
$859$	−42.2168	−1.44042	−0.720209	−	0.693757i	$-0.755954\pi$
$859$	−42.2168	−1.44042	−0.720209	+	0.693757i	$0.755954\pi$
$860$	7.91268	0.269820
$861$	−106.267	−3.62158
$862$	48.4198	1.64918
$863$	−28.3467	−0.964935	−0.482467	−	0.875914i	$-0.660259\pi$
$863$	−28.3467	−0.964935	−0.482467	+	0.875914i	$0.660259\pi$
$864$	−76.9324	−2.61729
$865$	20.4127	0.694051
$866$	−1.59222	−0.0541060
$867$	87.3507	2.96658
$868$	103.138	3.50074
$869$	8.32169	0.282294
$870$	22.9494	0.778057
$871$	6.80403	0.230546
$872$	36.7477	1.24443
$873$	−34.9128	−1.18162
$874$	−135.551	−4.58508
$875$	−4.31568	−0.145897
$876$	14.1293	0.477384
$877$	19.9638	0.674131	0.337066	−	0.941481i	$-0.390566\pi$
$877$	19.9638	0.674131	0.337066	+	0.941481i	$0.390566\pi$
$878$	3.27384	0.110487
$879$	51.4728	1.73613
$880$	−8.41873	−0.283795
$881$	−32.5387	−1.09626	−0.548128	−	0.836395i	$-0.684659\pi$
$881$	−32.5387	−1.09626	−0.548128	+	0.836395i	$0.684659\pi$
$882$	−185.473	−6.24519
$883$	−16.3669	−0.550792	−0.275396	−	0.961331i	$-0.588809\pi$
$883$	−16.3669	−0.550792	−0.275396	+	0.961331i	$0.588809\pi$
$884$	222.131	7.47106
$885$	7.12991	0.239669
$886$	20.6596	0.694073
$887$	43.4720	1.45965	0.729824	−	0.683635i	$-0.239602\pi$
$887$	43.4720	1.45965	0.729824	+	0.683635i	$0.239602\pi$
$888$	62.5573	2.09929
$889$	−50.9128	−1.70756
$890$	−26.7546	−0.896817
$891$	10.6596	0.357111
$892$	−76.7305	−2.56913
$893$	−10.3172	−0.345253
$894$	−109.595	−3.66539
$895$	−17.6672	−0.590550
$896$	26.9263	0.899543
$897$	138.524	4.62519
$898$	12.1309	0.404815
$899$	15.0377	0.501535
$900$	28.8219	0.960731
$901$	83.6304	2.78613
$902$	20.9773	0.698469
$903$	−22.1887	−0.738395
$904$	−37.5160	−1.24776
$905$	−5.33022	−0.177182
$906$	−16.8432	−0.559579
$907$	14.9221	0.495479	0.247740	−	0.968827i	$-0.420312\pi$
$907$	14.9221	0.495479	0.247740	+	0.968827i	$0.420312\pi$
$908$	9.15798	0.303918
$909$	−60.4847	−2.00615
$910$	−78.3878	−2.59853
$911$	8.50714	0.281854	0.140927	−	0.990020i	$-0.454992\pi$
$911$	8.50714	0.281854	0.140927	+	0.990020i	$0.454992\pi$
$912$	−206.168	−6.82692
$913$	−2.20321	−0.0729157
$914$	83.9368	2.77638
$915$	−4.84639	−0.160217
$916$	18.0669	0.596947
$917$	3.08815	0.101980
$918$	168.415	5.55853
$919$	−45.8008	−1.51083	−0.755415	−	0.655247i	$-0.772565\pi$
$919$	−45.8008	−1.51083	−0.755415	+	0.655247i	$0.772565\pi$
$920$	−44.6646	−1.47255
$921$	−104.253	−3.43526
$922$	−38.3625	−1.26340
$923$	63.4419	2.08822
$924$	60.9774	2.00601
$925$	−3.00332	−0.0987486
$926$	−29.4582	−0.968058
$927$	74.9204	2.46071
$928$	−23.4222	−0.768872
$929$	7.02224	0.230392	0.115196	−	0.993343i	$-0.463250\pi$
$929$	7.02224	0.230392	0.115196	+	0.993343i	$0.463250\pi$
$930$	40.0839	1.31440
$931$	−93.9578	−3.07934
$932$	−109.112	−3.57407
$933$	−3.15630	−0.103333
$934$	18.8953	0.618273
$935$	6.76970	0.221393
$936$	298.978	9.77239
$937$	−13.5878	−0.443895	−0.221947	−	0.975059i	$-0.571241\pi$
$937$	−13.5878	−0.443895	−0.221947	+	0.975059i	$0.571241\pi$
$938$	10.7720	0.351718
$939$	−35.8673	−1.17048
$940$	−5.95261	−0.194153
$941$	−45.9851	−1.49907	−0.749536	−	0.661963i	$-0.769723\pi$
$941$	−45.9851	−1.49907	−0.749536	+	0.661963i	$0.769723\pi$
$942$	23.8995	0.778688
$943$	52.8004	1.71942
$944$	−19.8103	−0.644770
$945$	−41.5931	−1.35302
$946$	4.38010	0.142409
$947$	27.6062	0.897083	0.448541	−	0.893762i	$-0.351944\pi$
$947$	27.6062	0.897083	0.448541	+	0.893762i	$0.351944\pi$
$948$	117.579	3.81880
$949$	−7.03654	−0.228416
$950$	20.8630	0.676884
$951$	55.7652	1.80831
$952$	200.843	6.50934
$953$	5.63983	0.182692	0.0913461	−	0.995819i	$-0.470883\pi$
$953$	5.63983	0.182692	0.0913461	+	0.995819i	$0.470883\pi$
$954$	197.096	6.38121
$955$	−18.2325	−0.589990
$956$	−85.0346	−2.75022
$957$	8.89059	0.287392
$958$	−33.1048	−1.06957
$959$	−21.9228	−0.707924
$960$	−11.4162	−0.368458
$961$	−4.73485	−0.152737
$962$	−54.5508	−1.75879
$963$	66.8569	2.15443
$964$	−21.9428	−0.706731
$965$	3.81329	0.122754
$966$	219.309	7.05614
$967$	−5.31606	−0.170953	−0.0854765	−	0.996340i	$-0.527241\pi$
$967$	−5.31606	−0.170953	−0.0854765	+	0.996340i	$0.527241\pi$
$968$	−6.87443	−0.220953
$969$	165.785	5.32578
$970$	−14.5808	−0.468162
$971$	−58.9057	−1.89038	−0.945188	−	0.326527i	$-0.894121\pi$
$971$	−58.9057	−1.89038	−0.945188	+	0.326527i	$0.894121\pi$
$972$	15.7868	0.506361
$973$	33.2387	1.06558
$974$	79.6604	2.55249
$975$	−21.3206	−0.682805
$976$	13.4656	0.431023
$977$	6.64233	0.212507	0.106253	−	0.994339i	$-0.466114\pi$
$977$	6.64233	0.212507	0.106253	+	0.994339i	$0.466114\pi$
$978$	−160.610	−5.13574
$979$	−10.3647	−0.331259
$980$	−54.2097	−1.73167
$981$	−33.0397	−1.05488
$982$	−42.8072	−1.36603
$983$	8.00951	0.255464	0.127732	−	0.991809i	$-0.459230\pi$
$983$	8.00951	0.255464	0.127732	+	0.991809i	$0.459230\pi$
$984$	169.273	5.39622
$985$	−24.0187	−0.765300
$986$	51.2744	1.63291
$987$	16.6923	0.531322
$988$	265.201	8.43717
$989$	11.0248	0.350568
$990$	15.9545	0.507067
$991$	7.23250	0.229748	0.114874	−	0.993380i	$-0.463354\pi$
$991$	7.23250	0.229748	0.114874	+	0.993380i	$0.463354\pi$
$992$	−40.9098	−1.29889
$993$	−31.0900	−0.986613
$994$	100.440	3.18576
$995$	−0.0778796	−0.00246895
$996$	−31.1298	−0.986385
$997$	20.6096	0.652714	0.326357	−	0.945247i	$-0.394179\pi$
$997$	20.6096	0.652714	0.326357	+	0.945247i	$0.394179\pi$
$998$	63.5135	2.01048
$999$	−28.9450	−0.915780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.4	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.4	✓	31	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58131 q^{2} +3.02998 q^{3} +4.66316 q^{4} -1.00000 q^{5} -7.82131 q^{6} +4.31568 q^{7} -6.87443 q^{8} +6.18077 q^{9} +O(q^{10})\)	\(q-2.58131 q^{2} +3.02998 q^{3} +4.66316 q^{4} -1.00000 q^{5} -7.82131 q^{6} +4.31568 q^{7} -6.87443 q^{8} +6.18077 q^{9} +2.58131 q^{10} +1.00000 q^{11} +14.1293 q^{12} -7.03654 q^{13} -11.1401 q^{14} -3.02998 q^{15} +8.41873 q^{16} -6.76970 q^{17} -15.9545 q^{18} -8.08232 q^{19} -4.66316 q^{20} +13.0764 q^{21} -2.58131 q^{22} -6.49721 q^{23} -20.8294 q^{24} +1.00000 q^{25} +18.1635 q^{26} +9.63767 q^{27} +20.1247 q^{28} +2.93421 q^{29} +7.82131 q^{30} +5.12495 q^{31} -7.98247 q^{32} +3.02998 q^{33} +17.4747 q^{34} -4.31568 q^{35} +28.8219 q^{36} -3.00332 q^{37} +20.8630 q^{38} -21.3206 q^{39} +6.87443 q^{40} -8.12663 q^{41} -33.7543 q^{42} -1.69685 q^{43} +4.66316 q^{44} -6.18077 q^{45} +16.7713 q^{46} +1.27652 q^{47} +25.5086 q^{48} +11.6251 q^{49} -2.58131 q^{50} -20.5120 q^{51} -32.8125 q^{52} -12.3536 q^{53} -24.8778 q^{54} -1.00000 q^{55} -29.6679 q^{56} -24.4893 q^{57} -7.57410 q^{58} -2.35312 q^{59} -14.1293 q^{60} +1.59948 q^{61} -13.2291 q^{62} +26.6742 q^{63} +3.76777 q^{64} +7.03654 q^{65} -7.82131 q^{66} -0.966957 q^{67} -31.5682 q^{68} -19.6864 q^{69} +11.1401 q^{70} -9.01607 q^{71} -42.4893 q^{72} +1.00000 q^{73} +7.75250 q^{74} +3.02998 q^{75} -37.6891 q^{76} +4.31568 q^{77} +55.0350 q^{78} +8.32169 q^{79} -8.41873 q^{80} +10.6596 q^{81} +20.9773 q^{82} -2.20321 q^{83} +60.9774 q^{84} +6.76970 q^{85} +4.38010 q^{86} +8.89059 q^{87} -6.87443 q^{88} -10.3647 q^{89} +15.9545 q^{90} -30.3675 q^{91} -30.2975 q^{92} +15.5285 q^{93} -3.29509 q^{94} +8.08232 q^{95} -24.1867 q^{96} -5.64861 q^{97} -30.0080 q^{98} +6.18077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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