LMFDB - Embedded newform 4334.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.995042$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.995042 q^{3} +1.00000 q^{4} +2.56257 q^{5} -0.995042 q^{6} -3.12926 q^{7} -1.00000 q^{8} -2.00989 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.995042 q^{3} +1.00000 q^{4} +2.56257 q^{5} -0.995042 q^{6} -3.12926 q^{7} -1.00000 q^{8} -2.00989 q^{9} -2.56257 q^{10} +1.00000 q^{11} +0.995042 q^{12} +1.90374 q^{13} +3.12926 q^{14} +2.54987 q^{15} +1.00000 q^{16} +3.95449 q^{17} +2.00989 q^{18} -0.294531 q^{19} +2.56257 q^{20} -3.11374 q^{21} -1.00000 q^{22} -4.99330 q^{23} -0.995042 q^{24} +1.56678 q^{25} -1.90374 q^{26} -4.98505 q^{27} -3.12926 q^{28} -6.71448 q^{29} -2.54987 q^{30} -2.58674 q^{31} -1.00000 q^{32} +0.995042 q^{33} -3.95449 q^{34} -8.01895 q^{35} -2.00989 q^{36} -8.71417 q^{37} +0.294531 q^{38} +1.89431 q^{39} -2.56257 q^{40} -2.08498 q^{41} +3.11374 q^{42} +3.12603 q^{43} +1.00000 q^{44} -5.15049 q^{45} +4.99330 q^{46} +5.20872 q^{47} +0.995042 q^{48} +2.79225 q^{49} -1.56678 q^{50} +3.93489 q^{51} +1.90374 q^{52} -3.14683 q^{53} +4.98505 q^{54} +2.56257 q^{55} +3.12926 q^{56} -0.293071 q^{57} +6.71448 q^{58} -6.61212 q^{59} +2.54987 q^{60} +6.08266 q^{61} +2.58674 q^{62} +6.28947 q^{63} +1.00000 q^{64} +4.87848 q^{65} -0.995042 q^{66} +1.50401 q^{67} +3.95449 q^{68} -4.96854 q^{69} +8.01895 q^{70} -3.24584 q^{71} +2.00989 q^{72} -10.5747 q^{73} +8.71417 q^{74} +1.55901 q^{75} -0.294531 q^{76} -3.12926 q^{77} -1.89431 q^{78} +5.87951 q^{79} +2.56257 q^{80} +1.06934 q^{81} +2.08498 q^{82} +11.7347 q^{83} -3.11374 q^{84} +10.1337 q^{85} -3.12603 q^{86} -6.68119 q^{87} -1.00000 q^{88} -8.04190 q^{89} +5.15049 q^{90} -5.95731 q^{91} -4.99330 q^{92} -2.57392 q^{93} -5.20872 q^{94} -0.754757 q^{95} -0.995042 q^{96} -16.7515 q^{97} -2.79225 q^{98} -2.00989 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.995042	0.574488	0.287244	−	0.957857i	$-0.407261\pi$
$3$	0.995042	0.574488	0.287244	+	0.957857i	$0.407261\pi$
$4$	1.00000	0.500000
$5$	2.56257	1.14602	0.573009	−	0.819549i	$-0.305776\pi$
$5$	2.56257	1.14602	0.573009	+	0.819549i	$0.305776\pi$
$6$	−0.995042	−0.406224
$7$	−3.12926	−1.18275	−0.591374	−	0.806397i	$-0.701414\pi$
$7$	−3.12926	−1.18275	−0.591374	+	0.806397i	$0.701414\pi$
$8$	−1.00000	−0.353553
$9$	−2.00989	−0.669964
$10$	−2.56257	−0.810357
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.995042	0.287244
$13$	1.90374	0.528004	0.264002	−	0.964522i	$-0.414958\pi$
$13$	1.90374	0.528004	0.264002	+	0.964522i	$0.414958\pi$
$14$	3.12926	0.836329
$15$	2.54987	0.658373
$16$	1.00000	0.250000
$17$	3.95449	0.959105	0.479553	−	0.877513i	$-0.340799\pi$
$17$	3.95449	0.959105	0.479553	+	0.877513i	$0.340799\pi$
$18$	2.00989	0.473736
$19$	−0.294531	−0.0675701	−0.0337850	−	0.999429i	$-0.510756\pi$
$19$	−0.294531	−0.0675701	−0.0337850	+	0.999429i	$0.510756\pi$
$20$	2.56257	0.573009
$21$	−3.11374	−0.679474
$22$	−1.00000	−0.213201
$23$	−4.99330	−1.04117	−0.520587	−	0.853808i	$-0.674287\pi$
$23$	−4.99330	−1.04117	−0.520587	+	0.853808i	$0.674287\pi$
$24$	−0.995042	−0.203112
$25$	1.56678	0.313356
$26$	−1.90374	−0.373355
$27$	−4.98505	−0.959374
$28$	−3.12926	−0.591374
$29$	−6.71448	−1.24685	−0.623424	−	0.781884i	$-0.714259\pi$
$29$	−6.71448	−1.24685	−0.623424	+	0.781884i	$0.714259\pi$
$30$	−2.54987	−0.465540
$31$	−2.58674	−0.464593	−0.232296	−	0.972645i	$-0.574624\pi$
$31$	−2.58674	−0.464593	−0.232296	+	0.972645i	$0.574624\pi$
$32$	−1.00000	−0.176777
$33$	0.995042	0.173215
$34$	−3.95449	−0.678190
$35$	−8.01895	−1.35545
$36$	−2.00989	−0.334982
$37$	−8.71417	−1.43260	−0.716300	−	0.697792i	$-0.754166\pi$
$37$	−8.71417	−1.43260	−0.716300	+	0.697792i	$0.754166\pi$
$38$	0.294531	0.0477793
$39$	1.89431	0.303332
$40$	−2.56257	−0.405178
$41$	−2.08498	−0.325619	−0.162810	−	0.986658i	$-0.552056\pi$
$41$	−2.08498	−0.325619	−0.162810	+	0.986658i	$0.552056\pi$
$42$	3.11374	0.480461
$43$	3.12603	0.476715	0.238357	−	0.971178i	$-0.423391\pi$
$43$	3.12603	0.476715	0.238357	+	0.971178i	$0.423391\pi$
$44$	1.00000	0.150756
$45$	−5.15049	−0.767790
$46$	4.99330	0.736222
$47$	5.20872	0.759770	0.379885	−	0.925034i	$-0.375964\pi$
$47$	5.20872	0.759770	0.379885	+	0.925034i	$0.375964\pi$
$48$	0.995042	0.143622
$49$	2.79225	0.398894
$50$	−1.56678	−0.221576
$51$	3.93489	0.550994
$52$	1.90374	0.264002
$53$	−3.14683	−0.432251	−0.216125	−	0.976366i	$-0.569342\pi$
$53$	−3.14683	−0.432251	−0.216125	+	0.976366i	$0.569342\pi$
$54$	4.98505	0.678380
$55$	2.56257	0.345537
$56$	3.12926	0.418165
$57$	−0.293071	−0.0388182
$58$	6.71448	0.881654
$59$	−6.61212	−0.860825	−0.430412	−	0.902632i	$-0.641632\pi$
$59$	−6.61212	−0.860825	−0.430412	+	0.902632i	$0.641632\pi$
$60$	2.54987	0.329186
$61$	6.08266	0.778805	0.389403	−	0.921068i	$-0.372681\pi$
$61$	6.08266	0.778805	0.389403	+	0.921068i	$0.372681\pi$
$62$	2.58674	0.328517
$63$	6.28947	0.792399
$64$	1.00000	0.125000
$65$	4.87848	0.605101
$66$	−0.995042	−0.122481
$67$	1.50401	0.183743	0.0918717	−	0.995771i	$-0.470715\pi$
$67$	1.50401	0.183743	0.0918717	+	0.995771i	$0.470715\pi$
$68$	3.95449	0.479553
$69$	−4.96854	−0.598142
$70$	8.01895	0.958448
$71$	−3.24584	−0.385211	−0.192605	−	0.981276i	$-0.561694\pi$
$71$	−3.24584	−0.385211	−0.192605	+	0.981276i	$0.561694\pi$
$72$	2.00989	0.236868
$73$	−10.5747	−1.23767	−0.618835	−	0.785521i	$-0.712395\pi$
$73$	−10.5747	−1.23767	−0.618835	+	0.785521i	$0.712395\pi$
$74$	8.71417	1.01300
$75$	1.55901	0.180019
$76$	−0.294531	−0.0337850
$77$	−3.12926	−0.356612
$78$	−1.89431	−0.214488
$79$	5.87951	0.661496	0.330748	−	0.943719i	$-0.392699\pi$
$79$	5.87951	0.661496	0.330748	+	0.943719i	$0.392699\pi$
$80$	2.56257	0.286504
$81$	1.06934	0.118815
$82$	2.08498	0.230247
$83$	11.7347	1.28806	0.644028	−	0.765002i	$-0.277262\pi$
$83$	11.7347	1.28806	0.644028	+	0.765002i	$0.277262\pi$
$84$	−3.11374	−0.339737
$85$	10.1337	1.09915
$86$	−3.12603	−0.337088
$87$	−6.68119	−0.716299
$88$	−1.00000	−0.106600
$89$	−8.04190	−0.852440	−0.426220	−	0.904620i	$-0.640155\pi$
$89$	−8.04190	−0.852440	−0.426220	+	0.904620i	$0.640155\pi$
$90$	5.15049	0.542910
$91$	−5.95731	−0.624495
$92$	−4.99330	−0.520587
$93$	−2.57392	−0.266903
$94$	−5.20872	−0.537239
$95$	−0.754757	−0.0774365
$96$	−0.995042	−0.101556
$97$	−16.7515	−1.70086	−0.850429	−	0.526090i	$-0.823657\pi$
$97$	−16.7515	−1.70086	−0.850429	+	0.526090i	$0.823657\pi$
$98$	−2.79225	−0.282060
$99$	−2.00989	−0.202002
$100$	1.56678	0.156678
$101$	−8.54689	−0.850447	−0.425223	−	0.905088i	$-0.639804\pi$
$101$	−8.54689	−0.850447	−0.425223	+	0.905088i	$0.639804\pi$
$102$	−3.93489	−0.389612
$103$	0.178334	0.0175718	0.00878588	−	0.999961i	$-0.497203\pi$
$103$	0.178334	0.0175718	0.00878588	+	0.999961i	$0.497203\pi$
$104$	−1.90374	−0.186677
$105$	−7.97919	−0.778689
$106$	3.14683	0.305648
$107$	8.85153	0.855710	0.427855	−	0.903847i	$-0.359269\pi$
$107$	8.85153	0.855710	0.427855	+	0.903847i	$0.359269\pi$
$108$	−4.98505	−0.479687
$109$	12.3937	1.18710	0.593549	−	0.804798i	$-0.297726\pi$
$109$	12.3937	1.18710	0.593549	+	0.804798i	$0.297726\pi$
$110$	−2.56257	−0.244332
$111$	−8.67096	−0.823012
$112$	−3.12926	−0.295687
$113$	−17.8263	−1.67696	−0.838481	−	0.544931i	$-0.816556\pi$
$113$	−17.8263	−1.67696	−0.838481	+	0.544931i	$0.816556\pi$
$114$	0.293071	0.0274486
$115$	−12.7957	−1.19320
$116$	−6.71448	−0.623424
$117$	−3.82632	−0.353743
$118$	6.61212	0.608695
$119$	−12.3746	−1.13438
$120$	−2.54987	−0.232770
$121$	1.00000	0.0909091
$122$	−6.08266	−0.550699
$123$	−2.07464	−0.187064
$124$	−2.58674	−0.232296
$125$	−8.79788	−0.786906
$126$	−6.28947	−0.560310
$127$	3.69625	0.327989	0.163995	−	0.986461i	$-0.447562\pi$
$127$	3.69625	0.327989	0.163995	+	0.986461i	$0.447562\pi$
$128$	−1.00000	−0.0883883
$129$	3.11053	0.273867
$130$	−4.87848	−0.427871
$131$	22.7260	1.98558	0.992790	−	0.119870i	$-0.0382479\pi$
$131$	22.7260	1.98558	0.992790	+	0.119870i	$0.0382479\pi$
$132$	0.995042	0.0866073
$133$	0.921664	0.0799184
$134$	−1.50401	−0.129926
$135$	−12.7746	−1.09946
$136$	−3.95449	−0.339095
$137$	−9.12680	−0.779755	−0.389878	−	0.920867i	$-0.627483\pi$
$137$	−9.12680	−0.779755	−0.389878	+	0.920867i	$0.627483\pi$
$138$	4.96854	0.422950
$139$	−18.4287	−1.56311	−0.781553	−	0.623839i	$-0.785572\pi$
$139$	−18.4287	−1.56311	−0.781553	+	0.623839i	$0.785572\pi$
$140$	−8.01895	−0.677725
$141$	5.18290	0.436479
$142$	3.24584	0.272385
$143$	1.90374	0.159199
$144$	−2.00989	−0.167491
$145$	−17.2063	−1.42891
$146$	10.5747	0.875165
$147$	2.77841	0.229159
$148$	−8.71417	−0.716300
$149$	−13.5549	−1.11046	−0.555229	−	0.831698i	$-0.687369\pi$
$149$	−13.5549	−1.11046	−0.555229	+	0.831698i	$0.687369\pi$
$150$	−1.55901	−0.127293
$151$	−1.63328	−0.132914	−0.0664572	−	0.997789i	$-0.521170\pi$
$151$	−1.63328	−0.132914	−0.0664572	+	0.997789i	$0.521170\pi$
$152$	0.294531	0.0238896
$153$	−7.94810	−0.642566
$154$	3.12926	0.252163
$155$	−6.62872	−0.532431
$156$	1.89431	0.151666
$157$	5.93137	0.473375	0.236687	−	0.971586i	$-0.423938\pi$
$157$	5.93137	0.473375	0.236687	+	0.971586i	$0.423938\pi$
$158$	−5.87951	−0.467749
$159$	−3.13123	−0.248323
$160$	−2.56257	−0.202589
$161$	15.6253	1.23145
$162$	−1.06934	−0.0840151
$163$	10.1123	0.792053	0.396026	−	0.918239i	$-0.370389\pi$
$163$	10.1123	0.792053	0.396026	+	0.918239i	$0.370389\pi$
$164$	−2.08498	−0.162810
$165$	2.54987	0.198507
$166$	−11.7347	−0.910793
$167$	7.53363	0.582970	0.291485	−	0.956575i	$-0.405851\pi$
$167$	7.53363	0.582970	0.291485	+	0.956575i	$0.405851\pi$
$168$	3.11374	0.240230
$169$	−9.37576	−0.721212
$170$	−10.1337	−0.777217
$171$	0.591976	0.0452695
$172$	3.12603	0.238357
$173$	−20.0913	−1.52752	−0.763758	−	0.645503i	$-0.776648\pi$
$173$	−20.0913	−1.52752	−0.763758	+	0.645503i	$0.776648\pi$
$174$	6.68119	0.506500
$175$	−4.90285	−0.370621
$176$	1.00000	0.0753778
$177$	−6.57934	−0.494533
$178$	8.04190	0.602766
$179$	−19.4821	−1.45616	−0.728079	−	0.685493i	$-0.759587\pi$
$179$	−19.4821	−1.45616	−0.728079	+	0.685493i	$0.759587\pi$
$180$	−5.15049	−0.383895
$181$	18.7951	1.39703	0.698514	−	0.715597i	$-0.253845\pi$
$181$	18.7951	1.39703	0.698514	+	0.715597i	$0.253845\pi$
$182$	5.95731	0.441585
$183$	6.05251	0.447414
$184$	4.99330	0.368111
$185$	−22.3307	−1.64179
$186$	2.57392	0.188729
$187$	3.95449	0.289181
$188$	5.20872	0.379885
$189$	15.5995	1.13470
$190$	0.754757	0.0547559
$191$	2.99065	0.216396	0.108198	−	0.994129i	$-0.465492\pi$
$191$	2.99065	0.216396	0.108198	+	0.994129i	$0.465492\pi$
$192$	0.995042	0.0718110
$193$	9.06545	0.652545	0.326273	−	0.945276i	$-0.394207\pi$
$193$	9.06545	0.652545	0.326273	+	0.945276i	$0.394207\pi$
$194$	16.7515	1.20269
$195$	4.85430	0.347623
$196$	2.79225	0.199447
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.00989	0.142837
$199$	17.8130	1.26273	0.631366	−	0.775485i	$-0.282495\pi$
$199$	17.8130	1.26273	0.631366	+	0.775485i	$0.282495\pi$
$200$	−1.56678	−0.110788
$201$	1.49655	0.105558
$202$	8.54689	0.601357
$203$	21.0113	1.47471
$204$	3.93489	0.275497
$205$	−5.34291	−0.373165
$206$	−0.178334	−0.0124251
$207$	10.0360	0.697549
$208$	1.90374	0.132001
$209$	−0.294531	−0.0203731
$210$	7.97919	0.550617
$211$	−3.94688	−0.271714	−0.135857	−	0.990728i	$-0.543379\pi$
$211$	−3.94688	−0.271714	−0.135857	+	0.990728i	$0.543379\pi$
$212$	−3.14683	−0.216125
$213$	−3.22975	−0.221299
$214$	−8.85153	−0.605078
$215$	8.01067	0.546323
$216$	4.98505	0.339190
$217$	8.09459	0.549496
$218$	−12.3937	−0.839405
$219$	−10.5222	−0.711027
$220$	2.56257	0.172769
$221$	7.52834	0.506411
$222$	8.67096	0.581957
$223$	3.49131	0.233796	0.116898	−	0.993144i	$-0.462705\pi$
$223$	3.49131	0.233796	0.116898	+	0.993144i	$0.462705\pi$
$224$	3.12926	0.209082
$225$	−3.14905	−0.209937
$226$	17.8263	1.18579
$227$	−21.8667	−1.45135	−0.725673	−	0.688039i	$-0.758472\pi$
$227$	−21.8667	−1.45135	−0.725673	+	0.688039i	$0.758472\pi$
$228$	−0.293071	−0.0194091
$229$	−9.38410	−0.620119	−0.310059	−	0.950717i	$-0.600349\pi$
$229$	−9.38410	−0.620119	−0.310059	+	0.950717i	$0.600349\pi$
$230$	12.7957	0.843723
$231$	−3.11374	−0.204869
$232$	6.71448	0.440827
$233$	−13.8547	−0.907653	−0.453827	−	0.891090i	$-0.649941\pi$
$233$	−13.8547	−0.907653	−0.453827	+	0.891090i	$0.649941\pi$
$234$	3.82632	0.250134
$235$	13.3477	0.870710
$236$	−6.61212	−0.430412
$237$	5.85036	0.380022
$238$	12.3746	0.802128
$239$	1.63869	0.105998	0.0529991	−	0.998595i	$-0.483122\pi$
$239$	1.63869	0.105998	0.0529991	+	0.998595i	$0.483122\pi$
$240$	2.54987	0.164593
$241$	−25.5272	−1.64435	−0.822175	−	0.569235i	$-0.807240\pi$
$241$	−25.5272	−1.64435	−0.822175	+	0.569235i	$0.807240\pi$
$242$	−1.00000	−0.0642824
$243$	16.0192	1.02763
$244$	6.08266	0.389403
$245$	7.15536	0.457139
$246$	2.07464	0.132274
$247$	−0.560712	−0.0356772
$248$	2.58674	0.164258
$249$	11.6766	0.739972
$250$	8.79788	0.556427
$251$	−6.88946	−0.434859	−0.217429	−	0.976076i	$-0.569767\pi$
$251$	−6.88946	−0.434859	−0.217429	+	0.976076i	$0.569767\pi$
$252$	6.28947	0.396199
$253$	−4.99330	−0.313926
$254$	−3.69625	−0.231924
$255$	10.0834	0.631449
$256$	1.00000	0.0625000
$257$	18.4023	1.14790	0.573952	−	0.818889i	$-0.305410\pi$
$257$	18.4023	1.14790	0.573952	+	0.818889i	$0.305410\pi$
$258$	−3.11053	−0.193653
$259$	27.2689	1.69441
$260$	4.87848	0.302551
$261$	13.4954	0.835343
$262$	−22.7260	−1.40402
$263$	−16.6847	−1.02882	−0.514410	−	0.857544i	$-0.671989\pi$
$263$	−16.6847	−1.02882	−0.514410	+	0.857544i	$0.671989\pi$
$264$	−0.995042	−0.0612406
$265$	−8.06399	−0.495367
$266$	−0.921664	−0.0565108
$267$	−8.00203	−0.489716
$268$	1.50401	0.0918717
$269$	8.70770	0.530918	0.265459	−	0.964122i	$-0.414477\pi$
$269$	8.70770	0.530918	0.265459	+	0.964122i	$0.414477\pi$
$270$	12.7746	0.777435
$271$	−31.1650	−1.89314	−0.946571	−	0.322496i	$-0.895478\pi$
$271$	−31.1650	−1.89314	−0.946571	+	0.322496i	$0.895478\pi$
$272$	3.95449	0.239776
$273$	−5.92777	−0.358765
$274$	9.12680	0.551370
$275$	1.56678	0.0944803
$276$	−4.96854	−0.299071
$277$	13.6513	0.820225	0.410113	−	0.912035i	$-0.365489\pi$
$277$	13.6513	0.820225	0.410113	+	0.912035i	$0.365489\pi$
$278$	18.4287	1.10528
$279$	5.19907	0.311260
$280$	8.01895	0.479224
$281$	18.9769	1.13207	0.566034	−	0.824382i	$-0.308477\pi$
$281$	18.9769	1.13207	0.566034	+	0.824382i	$0.308477\pi$
$282$	−5.18290	−0.308637
$283$	−17.5818	−1.04513	−0.522565	−	0.852599i	$-0.675025\pi$
$283$	−17.5818	−1.04513	−0.522565	+	0.852599i	$0.675025\pi$
$284$	−3.24584	−0.192605
$285$	−0.751015	−0.0444863
$286$	−1.90374	−0.112571
$287$	6.52444	0.385125
$288$	2.00989	0.118434
$289$	−1.36199	−0.0801172
$290$	17.2063	1.01039
$291$	−16.6684	−0.977122
$292$	−10.5747	−0.618835
$293$	12.4294	0.726135	0.363068	−	0.931763i	$-0.381729\pi$
$293$	12.4294	0.726135	0.363068	+	0.931763i	$0.381729\pi$
$294$	−2.77841	−0.162040
$295$	−16.9440	−0.986520
$296$	8.71417	0.506501
$297$	−4.98505	−0.289262
$298$	13.5549	0.785212
$299$	−9.50596	−0.549744
$300$	1.55901	0.0900095
$301$	−9.78214	−0.563833
$302$	1.63328	0.0939847
$303$	−8.50451	−0.488571
$304$	−0.294531	−0.0168925
$305$	15.5873	0.892524
$306$	7.94810	0.454363
$307$	9.74562	0.556212	0.278106	−	0.960550i	$-0.410293\pi$
$307$	9.74562	0.556212	0.278106	+	0.960550i	$0.410293\pi$
$308$	−3.12926	−0.178306
$309$	0.177450	0.0100948
$310$	6.62872	0.376486
$311$	1.36689	0.0775090	0.0387545	−	0.999249i	$-0.487661\pi$
$311$	1.36689	0.0775090	0.0387545	+	0.999249i	$0.487661\pi$
$312$	−1.89431	−0.107244
$313$	−26.7863	−1.51405	−0.757026	−	0.653385i	$-0.773348\pi$
$313$	−26.7863	−1.51405	−0.757026	+	0.653385i	$0.773348\pi$
$314$	−5.93137	−0.334726
$315$	16.1172	0.908102
$316$	5.87951	0.330748
$317$	−19.7902	−1.11153	−0.555763	−	0.831341i	$-0.687574\pi$
$317$	−19.7902	−1.11153	−0.555763	+	0.831341i	$0.687574\pi$
$318$	3.13123	0.175591
$319$	−6.71448	−0.375939
$320$	2.56257	0.143252
$321$	8.80765	0.491595
$322$	−15.6253	−0.870765
$323$	−1.16472	−0.0648068
$324$	1.06934	0.0594077
$325$	2.98275	0.165453
$326$	−10.1123	−0.560066
$327$	12.3322	0.681973
$328$	2.08498	0.115124
$329$	−16.2994	−0.898617
$330$	−2.54987	−0.140366
$331$	18.6813	1.02681	0.513407	−	0.858145i	$-0.328383\pi$
$331$	18.6813	1.02681	0.513407	+	0.858145i	$0.328383\pi$
$332$	11.7347	0.644028
$333$	17.5145	0.959791
$334$	−7.53363	−0.412222
$335$	3.85412	0.210573
$336$	−3.11374	−0.169869
$337$	8.20542	0.446977	0.223489	−	0.974707i	$-0.428255\pi$
$337$	8.20542	0.446977	0.223489	+	0.974707i	$0.428255\pi$
$338$	9.37576	0.509974
$339$	−17.7380	−0.963394
$340$	10.1337	0.549576
$341$	−2.58674	−0.140080
$342$	−0.591976	−0.0320104
$343$	13.1671	0.710958
$344$	−3.12603	−0.168544
$345$	−12.7322	−0.685481
$346$	20.0913	1.08012
$347$	9.33023	0.500873	0.250436	−	0.968133i	$-0.419426\pi$
$347$	9.33023	0.500873	0.250436	+	0.968133i	$0.419426\pi$
$348$	−6.68119	−0.358149
$349$	−1.32129	−0.0707270	−0.0353635	−	0.999375i	$-0.511259\pi$
$349$	−1.32129	−0.0707270	−0.0353635	+	0.999375i	$0.511259\pi$
$350$	4.90285	0.262069
$351$	−9.49026	−0.506553
$352$	−1.00000	−0.0533002
$353$	2.28040	0.121373	0.0606866	−	0.998157i	$-0.480671\pi$
$353$	2.28040	0.121373	0.0606866	+	0.998157i	$0.480671\pi$
$354$	6.57934	0.349688
$355$	−8.31771	−0.441458
$356$	−8.04190	−0.426220
$357$	−12.3133	−0.651687
$358$	19.4821	1.02966
$359$	5.33610	0.281629	0.140814	−	0.990036i	$-0.455028\pi$
$359$	5.33610	0.281629	0.140814	+	0.990036i	$0.455028\pi$
$360$	5.15049	0.271455
$361$	−18.9133	−0.995434
$362$	−18.7951	−0.987848
$363$	0.995042	0.0522262
$364$	−5.95731	−0.312248
$365$	−27.0983	−1.41839
$366$	−6.05251	−0.316370
$367$	2.73239	0.142630	0.0713149	−	0.997454i	$-0.477280\pi$
$367$	2.73239	0.142630	0.0713149	+	0.997454i	$0.477280\pi$
$368$	−4.99330	−0.260294
$369$	4.19058	0.218153
$370$	22.3307	1.16092
$371$	9.84725	0.511244
$372$	−2.57392	−0.133451
$373$	−17.1447	−0.887721	−0.443860	−	0.896096i	$-0.646391\pi$
$373$	−17.1447	−0.887721	−0.443860	+	0.896096i	$0.646391\pi$
$374$	−3.95449	−0.204482
$375$	−8.75426	−0.452068
$376$	−5.20872	−0.268619
$377$	−12.7827	−0.658340
$378$	−15.5995	−0.802352
$379$	7.08218	0.363787	0.181894	−	0.983318i	$-0.441777\pi$
$379$	7.08218	0.363787	0.181894	+	0.983318i	$0.441777\pi$
$380$	−0.754757	−0.0387182
$381$	3.67793	0.188426
$382$	−2.99065	−0.153015
$383$	26.7343	1.36606	0.683030	−	0.730390i	$-0.260662\pi$
$383$	26.7343	1.36606	0.683030	+	0.730390i	$0.260662\pi$
$384$	−0.995042	−0.0507780
$385$	−8.01895	−0.408684
$386$	−9.06545	−0.461419
$387$	−6.28297	−0.319382
$388$	−16.7515	−0.850429
$389$	0.457062	0.0231740	0.0115870	−	0.999933i	$-0.496312\pi$
$389$	0.457062	0.0231740	0.0115870	+	0.999933i	$0.496312\pi$
$390$	−4.85430	−0.245807
$391$	−19.7460	−0.998596
$392$	−2.79225	−0.141030
$393$	22.6133	1.14069
$394$	−1.00000	−0.0503793
$395$	15.0667	0.758086
$396$	−2.00989	−0.101001
$397$	3.76562	0.188991	0.0944955	−	0.995525i	$-0.469876\pi$
$397$	3.76562	0.188991	0.0944955	+	0.995525i	$0.469876\pi$
$398$	−17.8130	−0.892886
$399$	0.917094	0.0459121
$400$	1.56678	0.0783389
$401$	−32.4273	−1.61934	−0.809672	−	0.586883i	$-0.800355\pi$
$401$	−32.4273	−1.61934	−0.809672	+	0.586883i	$0.800355\pi$
$402$	−1.49655	−0.0746410
$403$	−4.92450	−0.245307
$404$	−8.54689	−0.425223
$405$	2.74026	0.136164
$406$	−21.0113	−1.04278
$407$	−8.71417	−0.431945
$408$	−3.93489	−0.194806
$409$	−22.8999	−1.13233	−0.566164	−	0.824292i	$-0.691573\pi$
$409$	−22.8999	−1.13233	−0.566164	+	0.824292i	$0.691573\pi$
$410$	5.34291	0.263868
$411$	−9.08155	−0.447960
$412$	0.178334	0.00878588
$413$	20.6910	1.01814
$414$	−10.0360	−0.493242
$415$	30.0711	1.47613
$416$	−1.90374	−0.0933387
$417$	−18.3374	−0.897985
$418$	0.294531	0.0144060
$419$	−8.17923	−0.399582	−0.199791	−	0.979839i	$-0.564026\pi$
$419$	−8.17923	−0.399582	−0.199791	+	0.979839i	$0.564026\pi$
$420$	−7.97919	−0.389345
$421$	−13.4607	−0.656035	−0.328018	−	0.944672i	$-0.606381\pi$
$421$	−13.4607	−0.656035	−0.328018	+	0.944672i	$0.606381\pi$
$422$	3.94688	0.192131
$423$	−10.4690	−0.509019
$424$	3.14683	0.152824
$425$	6.19581	0.300541
$426$	3.22975	0.156482
$427$	−19.0342	−0.921131
$428$	8.85153	0.427855
$429$	1.89431	0.0914579
$430$	−8.01067	−0.386309
$431$	28.0492	1.35108	0.675541	−	0.737322i	$-0.263910\pi$
$431$	28.0492	1.35108	0.675541	+	0.737322i	$0.263910\pi$
$432$	−4.98505	−0.239843
$433$	27.0089	1.29797	0.648983	−	0.760803i	$-0.275195\pi$
$433$	27.0089	1.29797	0.648983	+	0.760803i	$0.275195\pi$
$434$	−8.09459	−0.388553
$435$	−17.1210	−0.820891
$436$	12.3937	0.593549
$437$	1.47068	0.0703522
$438$	10.5222	0.502772
$439$	−4.82076	−0.230082	−0.115041	−	0.993361i	$-0.536700\pi$
$439$	−4.82076	−0.230082	−0.115041	+	0.993361i	$0.536700\pi$
$440$	−2.56257	−0.122166
$441$	−5.61213	−0.267244
$442$	−7.52834	−0.358087
$443$	−22.2916	−1.05910	−0.529552	−	0.848277i	$-0.677640\pi$
$443$	−22.2916	−1.05910	−0.529552	+	0.848277i	$0.677640\pi$
$444$	−8.67096	−0.411506
$445$	−20.6079	−0.976910
$446$	−3.49131	−0.165318
$447$	−13.4877	−0.637944
$448$	−3.12926	−0.147844
$449$	20.7460	0.979063	0.489532	−	0.871986i	$-0.337168\pi$
$449$	20.7460	0.979063	0.489532	+	0.871986i	$0.337168\pi$
$450$	3.14905	0.148448
$451$	−2.08498	−0.0981778
$452$	−17.8263	−0.838481
$453$	−1.62518	−0.0763577
$454$	21.8667	1.02626
$455$	−15.2660	−0.715683
$456$	0.293071	0.0137243
$457$	6.90837	0.323160	0.161580	−	0.986860i	$-0.448341\pi$
$457$	6.90837	0.323160	0.161580	+	0.986860i	$0.448341\pi$
$458$	9.38410	0.438490
$459$	−19.7134	−0.920140
$460$	−12.7957	−0.596602
$461$	30.7360	1.43152	0.715759	−	0.698347i	$-0.246081\pi$
$461$	30.7360	1.43152	0.715759	+	0.698347i	$0.246081\pi$
$462$	3.11374	0.144864
$463$	−20.8646	−0.969659	−0.484829	−	0.874609i	$-0.661118\pi$
$463$	−20.8646	−0.969659	−0.484829	+	0.874609i	$0.661118\pi$
$464$	−6.71448	−0.311712
$465$	−6.59585	−0.305875
$466$	13.8547	0.641808
$467$	−11.0242	−0.510140	−0.255070	−	0.966923i	$-0.582098\pi$
$467$	−11.0242	−0.510140	−0.255070	+	0.966923i	$0.582098\pi$
$468$	−3.82632	−0.176872
$469$	−4.70642	−0.217322
$470$	−13.3477	−0.615685
$471$	5.90196	0.271948
$472$	6.61212	0.304347
$473$	3.12603	0.143735
$474$	−5.85036	−0.268716
$475$	−0.461465	−0.0211735
$476$	−12.3746	−0.567190
$477$	6.32479	0.289592
$478$	−1.63869	−0.0749521
$479$	−0.454795	−0.0207801	−0.0103901	−	0.999946i	$-0.503307\pi$
$479$	−0.454795	−0.0207801	−0.0103901	+	0.999946i	$0.503307\pi$
$480$	−2.54987	−0.116385
$481$	−16.5896	−0.756418
$482$	25.5272	1.16273
$483$	15.5478	0.707452
$484$	1.00000	0.0454545
$485$	−42.9269	−1.94921
$486$	−16.0192	−0.726645
$487$	−10.9083	−0.494304	−0.247152	−	0.968977i	$-0.579495\pi$
$487$	−10.9083	−0.494304	−0.247152	+	0.968977i	$0.579495\pi$
$488$	−6.08266	−0.275349
$489$	10.0621	0.455025
$490$	−7.15536	−0.323246
$491$	−4.13367	−0.186550	−0.0932751	−	0.995640i	$-0.529734\pi$
$491$	−4.13367	−0.186550	−0.0932751	+	0.995640i	$0.529734\pi$
$492$	−2.07464	−0.0935321
$493$	−26.5524	−1.19586
$494$	0.560712	0.0252276
$495$	−5.15049	−0.231497
$496$	−2.58674	−0.116148
$497$	10.1571	0.455607
$498$	−11.6766	−0.523239
$499$	−34.1697	−1.52965	−0.764824	−	0.644239i	$-0.777174\pi$
$499$	−34.1697	−1.52965	−0.764824	+	0.644239i	$0.777174\pi$
$500$	−8.79788	−0.393453
$501$	7.49628	0.334909
$502$	6.88946	0.307491
$503$	−7.35332	−0.327868	−0.163934	−	0.986471i	$-0.552418\pi$
$503$	−7.35332	−0.327868	−0.163934	+	0.986471i	$0.552418\pi$
$504$	−6.28947	−0.280155
$505$	−21.9020	−0.974627
$506$	4.99330	0.221979
$507$	−9.32927	−0.414328
$508$	3.69625	0.163995
$509$	12.2409	0.542569	0.271284	−	0.962499i	$-0.412552\pi$
$509$	12.2409	0.542569	0.271284	+	0.962499i	$0.412552\pi$
$510$	−10.0834	−0.446502
$511$	33.0908	1.46385
$512$	−1.00000	−0.0441942
$513$	1.46825	0.0648250
$514$	−18.4023	−0.811690
$515$	0.456993	0.0201375
$516$	3.11053	0.136933
$517$	5.20872	0.229079
$518$	−27.2689	−1.19813
$519$	−19.9917	−0.877539
$520$	−4.87848	−0.213936
$521$	44.5314	1.95096	0.975479	−	0.220095i	$-0.0706366\pi$
$521$	44.5314	1.95096	0.975479	+	0.220095i	$0.0706366\pi$
$522$	−13.4954	−0.590676
$523$	23.6154	1.03263	0.516314	−	0.856399i	$-0.327304\pi$
$523$	23.6154	1.03263	0.516314	+	0.856399i	$0.327304\pi$
$524$	22.7260	0.992790
$525$	−4.87855	−0.212917
$526$	16.6847	0.727486
$527$	−10.2293	−0.445593
$528$	0.995042	0.0433036
$529$	1.93303	0.0840446
$530$	8.06399	0.350277
$531$	13.2896	0.576721
$532$	0.921664	0.0399592
$533$	−3.96927	−0.171928
$534$	8.00203	0.346282
$535$	22.6827	0.980659
$536$	−1.50401	−0.0649631
$537$	−19.3855	−0.836545
$538$	−8.70770	−0.375416
$539$	2.79225	0.120271
$540$	−12.7746	−0.549729
$541$	−28.5526	−1.22757	−0.613786	−	0.789472i	$-0.710354\pi$
$541$	−28.5526	−1.22757	−0.613786	+	0.789472i	$0.710354\pi$
$542$	31.1650	1.33865
$543$	18.7019	0.802575
$544$	−3.95449	−0.169547
$545$	31.7597	1.36043
$546$	5.92777	0.253685
$547$	19.0536	0.814674	0.407337	−	0.913278i	$-0.366457\pi$
$547$	19.0536	0.814674	0.407337	+	0.913278i	$0.366457\pi$
$548$	−9.12680	−0.389878
$549$	−12.2255	−0.521771
$550$	−1.56678	−0.0668077
$551$	1.97762	0.0842496
$552$	4.96854	0.211475
$553$	−18.3985	−0.782384
$554$	−13.6513	−0.579987
$555$	−22.2200	−0.943185
$556$	−18.4287	−0.781553
$557$	2.63193	0.111518	0.0557592	−	0.998444i	$-0.482242\pi$
$557$	2.63193	0.111518	0.0557592	+	0.998444i	$0.482242\pi$
$558$	−5.19907	−0.220094
$559$	5.95116	0.251707
$560$	−8.01895	−0.338863
$561$	3.93489	0.166131
$562$	−18.9769	−0.800493
$563$	27.1339	1.14356	0.571779	−	0.820408i	$-0.306254\pi$
$563$	27.1339	1.14356	0.571779	+	0.820408i	$0.306254\pi$
$564$	5.18290	0.218239
$565$	−45.6813	−1.92183
$566$	17.5818	0.739019
$567$	−3.34624	−0.140529
$568$	3.24584	0.136193
$569$	−7.97804	−0.334457	−0.167228	−	0.985918i	$-0.553482\pi$
$569$	−7.97804	−0.334457	−0.167228	+	0.985918i	$0.553482\pi$
$570$	0.751015	0.0314566
$571$	−29.6305	−1.24000	−0.619998	−	0.784603i	$-0.712867\pi$
$571$	−29.6305	−1.24000	−0.619998	+	0.784603i	$0.712867\pi$
$572$	1.90374	0.0795995
$573$	2.97583	0.124317
$574$	−6.52444	−0.272325
$575$	−7.82339	−0.326258
$576$	−2.00989	−0.0837455
$577$	24.5831	1.02341	0.511705	−	0.859161i	$-0.329014\pi$
$577$	24.5831	1.02341	0.511705	+	0.859161i	$0.329014\pi$
$578$	1.36199	0.0566514
$579$	9.02050	0.374879
$580$	−17.2063	−0.714454
$581$	−36.7210	−1.52345
$582$	16.6684	0.690929
$583$	−3.14683	−0.130329
$584$	10.5747	0.437583
$585$	−9.80522	−0.405396
$586$	−12.4294	−0.513455
$587$	24.0361	0.992075	0.496038	−	0.868301i	$-0.334788\pi$
$587$	24.0361	0.992075	0.496038	+	0.868301i	$0.334788\pi$
$588$	2.77841	0.114580
$589$	0.761876	0.0313926
$590$	16.9440	0.697575
$591$	0.995042	0.0409306
$592$	−8.71417	−0.358150
$593$	11.5671	0.475004	0.237502	−	0.971387i	$-0.423671\pi$
$593$	11.5671	0.475004	0.237502	+	0.971387i	$0.423671\pi$
$594$	4.98505	0.204539
$595$	−31.7109	−1.30002
$596$	−13.5549	−0.555229
$597$	17.7247	0.725423
$598$	9.50596	0.388728
$599$	18.2758	0.746728	0.373364	−	0.927685i	$-0.378204\pi$
$599$	18.2758	0.746728	0.373364	+	0.927685i	$0.378204\pi$
$600$	−1.55901	−0.0636463
$601$	7.20217	0.293783	0.146891	−	0.989153i	$-0.453073\pi$
$601$	7.20217	0.293783	0.146891	+	0.989153i	$0.453073\pi$
$602$	9.78214	0.398690
$603$	−3.02289	−0.123101
$604$	−1.63328	−0.0664572
$605$	2.56257	0.104183
$606$	8.50451	0.345472
$607$	35.8257	1.45412	0.727060	−	0.686573i	$-0.240886\pi$
$607$	35.8257	1.45412	0.727060	+	0.686573i	$0.240886\pi$
$608$	0.294531	0.0119448
$609$	20.9072	0.847201
$610$	−15.5873	−0.631110
$611$	9.91608	0.401161
$612$	−7.94810	−0.321283
$613$	−36.6366	−1.47974	−0.739869	−	0.672751i	$-0.765112\pi$
$613$	−36.6366	−1.47974	−0.739869	+	0.672751i	$0.765112\pi$
$614$	−9.74562	−0.393301
$615$	−5.31642	−0.214379
$616$	3.12926	0.126081
$617$	10.9171	0.439506	0.219753	−	0.975556i	$-0.429475\pi$
$617$	10.9171	0.439506	0.219753	+	0.975556i	$0.429475\pi$
$618$	−0.177450	−0.00713807
$619$	−38.9758	−1.56657	−0.783284	−	0.621664i	$-0.786457\pi$
$619$	−38.9758	−1.56657	−0.783284	+	0.621664i	$0.786457\pi$
$620$	−6.62872	−0.266216
$621$	24.8919	0.998876
$622$	−1.36689	−0.0548072
$623$	25.1652	1.00822
$624$	1.89431	0.0758329
$625$	−30.3791	−1.21516
$626$	26.7863	1.07060
$627$	−0.293071	−0.0117041
$628$	5.93137	0.236687
$629$	−34.4601	−1.37401
$630$	−16.1172	−0.642125
$631$	3.68578	0.146729	0.0733644	−	0.997305i	$-0.476626\pi$
$631$	3.68578	0.146729	0.0733644	+	0.997305i	$0.476626\pi$
$632$	−5.87951	−0.233874
$633$	−3.92731	−0.156097
$634$	19.7902	0.785968
$635$	9.47192	0.375881
$636$	−3.13123	−0.124161
$637$	5.31574	0.210617
$638$	6.71448	0.265829
$639$	6.52379	0.258077
$640$	−2.56257	−0.101295
$641$	35.2533	1.39242	0.696210	−	0.717838i	$-0.254868\pi$
$641$	35.2533	1.39242	0.696210	+	0.717838i	$0.254868\pi$
$642$	−8.80765	−0.347610
$643$	26.7484	1.05485	0.527427	−	0.849600i	$-0.323157\pi$
$643$	26.7484	1.05485	0.527427	+	0.849600i	$0.323157\pi$
$644$	15.6253	0.615724
$645$	7.97095	0.313856
$646$	1.16472	0.0458253
$647$	40.5449	1.59399	0.796993	−	0.603989i	$-0.206423\pi$
$647$	40.5449	1.59399	0.796993	+	0.603989i	$0.206423\pi$
$648$	−1.06934	−0.0420076
$649$	−6.61212	−0.259548
$650$	−2.98275	−0.116993
$651$	8.05445	0.315679
$652$	10.1123	0.396026
$653$	21.5110	0.841792	0.420896	−	0.907109i	$-0.361716\pi$
$653$	21.5110	0.841792	0.420896	+	0.907109i	$0.361716\pi$
$654$	−12.3322	−0.482228
$655$	58.2370	2.27551
$656$	−2.08498	−0.0814048
$657$	21.2539	0.829194
$658$	16.2994	0.635418
$659$	−28.6952	−1.11781	−0.558903	−	0.829233i	$-0.688778\pi$
$659$	−28.6952	−1.11781	−0.558903	+	0.829233i	$0.688778\pi$
$660$	2.54987	0.0992534
$661$	43.7005	1.69975	0.849876	−	0.526983i	$-0.176677\pi$
$661$	43.7005	1.69975	0.849876	+	0.526983i	$0.176677\pi$
$662$	−18.6813	−0.726068
$663$	7.49102	0.290927
$664$	−11.7347	−0.455396
$665$	2.36183	0.0915879
$666$	−17.5145	−0.678674
$667$	33.5274	1.29819
$668$	7.53363	0.291485
$669$	3.47400	0.134313
$670$	−3.85412	−0.148898
$671$	6.08266	0.234819
$672$	3.11374	0.120115
$673$	9.03236	0.348172	0.174086	−	0.984730i	$-0.444303\pi$
$673$	9.03236	0.348172	0.174086	+	0.984730i	$0.444303\pi$
$674$	−8.20542	−0.316061
$675$	−7.81047	−0.300625
$676$	−9.37576	−0.360606
$677$	−36.3899	−1.39858	−0.699289	−	0.714839i	$-0.746500\pi$
$677$	−36.3899	−1.39858	−0.699289	+	0.714839i	$0.746500\pi$
$678$	17.7380	0.681222
$679$	52.4198	2.01169
$680$	−10.1337	−0.388609
$681$	−21.7583	−0.833781
$682$	2.58674	0.0990515
$683$	−16.2003	−0.619888	−0.309944	−	0.950755i	$-0.600310\pi$
$683$	−16.2003	−0.619888	−0.309944	+	0.950755i	$0.600310\pi$
$684$	0.591976	0.0226348
$685$	−23.3881	−0.893613
$686$	−13.1671	−0.502723
$687$	−9.33757	−0.356251
$688$	3.12603	0.119179
$689$	−5.99077	−0.228230
$690$	12.7322	0.484708
$691$	−21.3504	−0.812208	−0.406104	−	0.913827i	$-0.633113\pi$
$691$	−21.3504	−0.812208	−0.406104	+	0.913827i	$0.633113\pi$
$692$	−20.0913	−0.763758
$693$	6.28947	0.238917
$694$	−9.33023	−0.354171
$695$	−47.2250	−1.79135
$696$	6.68119	0.253250
$697$	−8.24503	−0.312303
$698$	1.32129	0.0500115
$699$	−13.7860	−0.521436
$700$	−4.90285	−0.185310
$701$	−1.42100	−0.0536705	−0.0268352	−	0.999640i	$-0.508543\pi$
$701$	−1.42100	−0.0536705	−0.0268352	+	0.999640i	$0.508543\pi$
$702$	9.49026	0.358187
$703$	2.56659	0.0968009
$704$	1.00000	0.0376889
$705$	13.2816	0.500212
$706$	−2.28040	−0.0858238
$707$	26.7454	1.00586
$708$	−6.57934	−0.247267
$709$	−3.84648	−0.144458	−0.0722288	−	0.997388i	$-0.523011\pi$
$709$	−3.84648	−0.144458	−0.0722288	+	0.997388i	$0.523011\pi$
$710$	8.31771	0.312158
$711$	−11.8172	−0.443179
$712$	8.04190	0.301383
$713$	12.9164	0.483722
$714$	12.3133	0.460813
$715$	4.87848	0.182445
$716$	−19.4821	−0.728079
$717$	1.63057	0.0608947
$718$	−5.33610	−0.199142
$719$	−6.28497	−0.234390	−0.117195	−	0.993109i	$-0.537390\pi$
$719$	−6.28497	−0.234390	−0.117195	+	0.993109i	$0.537390\pi$
$720$	−5.15049	−0.191948
$721$	−0.558053	−0.0207830
$722$	18.9133	0.703878
$723$	−25.4006	−0.944659
$724$	18.7951	0.698514
$725$	−10.5201	−0.390707
$726$	−0.995042	−0.0369295
$727$	−9.54742	−0.354094	−0.177047	−	0.984202i	$-0.556655\pi$
$727$	−9.54742	−0.354094	−0.177047	+	0.984202i	$0.556655\pi$
$728$	5.95731	0.220792
$729$	12.7318	0.471546
$730$	27.0983	1.00295
$731$	12.3618	0.457219
$732$	6.05251	0.223707
$733$	11.2994	0.417353	0.208677	−	0.977985i	$-0.433084\pi$
$733$	11.2994	0.417353	0.208677	+	0.977985i	$0.433084\pi$
$734$	−2.73239	−0.100854
$735$	7.11988	0.262621
$736$	4.99330	0.184055
$737$	1.50401	0.0554007
$738$	−4.19058	−0.154257
$739$	−44.7141	−1.64484	−0.822418	−	0.568884i	$-0.807375\pi$
$739$	−44.7141	−1.64484	−0.822418	+	0.568884i	$0.807375\pi$
$740$	−22.3307	−0.820893
$741$	−0.557932	−0.0204961
$742$	−9.84725	−0.361504
$743$	25.9003	0.950191	0.475096	−	0.879934i	$-0.342413\pi$
$743$	25.9003	0.950191	0.475096	+	0.879934i	$0.342413\pi$
$744$	2.57392	0.0943644
$745$	−34.7353	−1.27260
$746$	17.1447	0.627714
$747$	−23.5856	−0.862951
$748$	3.95449	0.144591
$749$	−27.6987	−1.01209
$750$	8.75426	0.319660
$751$	−2.08433	−0.0760583	−0.0380291	−	0.999277i	$-0.512108\pi$
$751$	−2.08433	−0.0760583	−0.0380291	+	0.999277i	$0.512108\pi$
$752$	5.20872	0.189943
$753$	−6.85530	−0.249821
$754$	12.7827	0.465517
$755$	−4.18540	−0.152322
$756$	15.5995	0.567349
$757$	−32.6203	−1.18560	−0.592802	−	0.805348i	$-0.701978\pi$
$757$	−32.6203	−1.18560	−0.592802	+	0.805348i	$0.701978\pi$
$758$	−7.08218	−0.257236
$759$	−4.96854	−0.180347
$760$	0.754757	0.0273779
$761$	31.2108	1.13139	0.565696	−	0.824614i	$-0.308608\pi$
$761$	31.2108	1.13139	0.565696	+	0.824614i	$0.308608\pi$
$762$	−3.67793	−0.133237
$763$	−38.7830	−1.40404
$764$	2.99065	0.108198
$765$	−20.3676	−0.736392
$766$	−26.7343	−0.965950
$767$	−12.5878	−0.454519
$768$	0.995042	0.0359055
$769$	3.67189	0.132412	0.0662058	−	0.997806i	$-0.478911\pi$
$769$	3.67189	0.132412	0.0662058	+	0.997806i	$0.478911\pi$
$770$	8.01895	0.288983
$771$	18.3111	0.659457
$772$	9.06545	0.326273
$773$	−10.1714	−0.365839	−0.182919	−	0.983128i	$-0.558555\pi$
$773$	−10.1714	−0.365839	−0.182919	+	0.983128i	$0.558555\pi$
$774$	6.28297	0.225837
$775$	−4.05285	−0.145583
$776$	16.7515	0.601344
$777$	27.1337	0.973415
$778$	−0.457062	−0.0163865
$779$	0.614091	0.0220021
$780$	4.85430	0.173812
$781$	−3.24584	−0.116145
$782$	19.7460	0.706114
$783$	33.4720	1.19619
$784$	2.79225	0.0997234
$785$	15.1996	0.542496
$786$	−22.6133	−0.806590
$787$	4.77793	0.170315	0.0851574	−	0.996368i	$-0.472861\pi$
$787$	4.77793	0.170315	0.0851574	+	0.996368i	$0.472861\pi$
$788$	1.00000	0.0356235
$789$	−16.6019	−0.591045
$790$	−15.0667	−0.536048
$791$	55.7832	1.98342
$792$	2.00989	0.0714184
$793$	11.5798	0.411212
$794$	−3.76562	−0.133637
$795$	−8.02401	−0.284582
$796$	17.8130	0.631366
$797$	35.4770	1.25666	0.628330	−	0.777947i	$-0.283739\pi$
$797$	35.4770	1.25666	0.628330	+	0.777947i	$0.283739\pi$
$798$	−0.917094	−0.0324648
$799$	20.5979	0.728700
$800$	−1.56678	−0.0553940
$801$	16.1633	0.571104
$802$	32.4273	1.14505
$803$	−10.5747	−0.373172
$804$	1.49655	0.0527792
$805$	40.0410	1.41126
$806$	4.92450	0.173458
$807$	8.66452	0.305006
$808$	8.54689	0.300678
$809$	−14.6835	−0.516243	−0.258121	−	0.966112i	$-0.583103\pi$
$809$	−14.6835	−0.516243	−0.258121	+	0.966112i	$0.583103\pi$
$810$	−2.74026	−0.0962828
$811$	39.0318	1.37059	0.685295	−	0.728265i	$-0.259673\pi$
$811$	39.0318	1.37059	0.685295	+	0.728265i	$0.259673\pi$
$812$	21.0113	0.737353
$813$	−31.0105	−1.08759
$814$	8.71417	0.305431
$815$	25.9134	0.907706
$816$	3.93489	0.137749
$817$	−0.920712	−0.0322116
$818$	22.8999	0.800677
$819$	11.9735	0.418389
$820$	−5.34291	−0.186583
$821$	55.0725	1.92204	0.961021	−	0.276474i	$-0.0891659\pi$
$821$	55.0725	1.92204	0.961021	+	0.276474i	$0.0891659\pi$
$822$	9.08155	0.316755
$823$	23.5681	0.821533	0.410767	−	0.911740i	$-0.365261\pi$
$823$	23.5681	0.821533	0.410767	+	0.911740i	$0.365261\pi$
$824$	−0.178334	−0.00621255
$825$	1.55901	0.0542778
$826$	−20.6910	−0.719933
$827$	−20.3938	−0.709161	−0.354580	−	0.935026i	$-0.615376\pi$
$827$	−20.3938	−0.709161	−0.354580	+	0.935026i	$0.615376\pi$
$828$	10.0360	0.348775
$829$	−50.0122	−1.73699	−0.868497	−	0.495694i	$-0.834914\pi$
$829$	−50.0122	−1.73699	−0.868497	+	0.495694i	$0.834914\pi$
$830$	−30.0711	−1.04378
$831$	13.5836	0.471209
$832$	1.90374	0.0660005
$833$	11.0419	0.382581
$834$	18.3374	0.634971
$835$	19.3055	0.668093
$836$	−0.294531	−0.0101866
$837$	12.8951	0.445718
$838$	8.17923	0.282547
$839$	27.8434	0.961259	0.480630	−	0.876924i	$-0.340408\pi$
$839$	27.8434	0.961259	0.480630	+	0.876924i	$0.340408\pi$
$840$	7.97919	0.275308
$841$	16.0842	0.554629
$842$	13.4607	0.463887
$843$	18.8828	0.650359
$844$	−3.94688	−0.135857
$845$	−24.0261	−0.826522
$846$	10.4690	0.359931
$847$	−3.12926	−0.107523
$848$	−3.14683	−0.108063
$849$	−17.4946	−0.600415
$850$	−6.19581	−0.212515
$851$	43.5124	1.49159
$852$	−3.22975	−0.110649
$853$	−21.0784	−0.721711	−0.360855	−	0.932622i	$-0.617515\pi$
$853$	−21.0784	−0.721711	−0.360855	+	0.932622i	$0.617515\pi$
$854$	19.0342	0.651338
$855$	1.51698	0.0518796
$856$	−8.85153	−0.302539
$857$	2.15342	0.0735593	0.0367796	−	0.999323i	$-0.488290\pi$
$857$	2.15342	0.0735593	0.0367796	+	0.999323i	$0.488290\pi$
$858$	−1.89431	−0.0646705
$859$	−9.58472	−0.327026	−0.163513	−	0.986541i	$-0.552283\pi$
$859$	−9.58472	−0.327026	−0.163513	+	0.986541i	$0.552283\pi$
$860$	8.01067	0.273162
$861$	6.49209	0.221250
$862$	−28.0492	−0.955359
$863$	25.9499	0.883346	0.441673	−	0.897176i	$-0.354385\pi$
$863$	25.9499	0.883346	0.441673	+	0.897176i	$0.354385\pi$
$864$	4.98505	0.169595
$865$	−51.4855	−1.75056
$866$	−27.0089	−0.917800
$867$	−1.35524	−0.0460263
$868$	8.09459	0.274748
$869$	5.87951	0.199449
$870$	17.1210	0.580457
$871$	2.86324	0.0970172
$872$	−12.3937	−0.419702
$873$	33.6687	1.13951
$874$	−1.47068	−0.0497465
$875$	27.5308	0.930712
$876$	−10.5222	−0.355513
$877$	24.1158	0.814334	0.407167	−	0.913354i	$-0.366517\pi$
$877$	24.1158	0.814334	0.407167	+	0.913354i	$0.366517\pi$
$878$	4.82076	0.162693
$879$	12.3678	0.417156
$880$	2.56257	0.0863843
$881$	−8.59796	−0.289673	−0.144836	−	0.989456i	$-0.546266\pi$
$881$	−8.59796	−0.289673	−0.144836	+	0.989456i	$0.546266\pi$
$882$	5.61213	0.188970
$883$	−11.3673	−0.382541	−0.191270	−	0.981537i	$-0.561261\pi$
$883$	−11.3673	−0.382541	−0.191270	+	0.981537i	$0.561261\pi$
$884$	7.52834	0.253206
$885$	−16.8600	−0.566744
$886$	22.2916	0.748900
$887$	−42.8502	−1.43877	−0.719385	−	0.694611i	$-0.755576\pi$
$887$	−42.8502	−1.43877	−0.719385	+	0.694611i	$0.755576\pi$
$888$	8.67096	0.290979
$889$	−11.5665	−0.387929
$890$	20.6079	0.690780
$891$	1.06934	0.0358242
$892$	3.49131	0.116898
$893$	−1.53413	−0.0513377
$894$	13.4877	0.451095
$895$	−49.9242	−1.66878
$896$	3.12926	0.104541
$897$	−9.45883	−0.315821
$898$	−20.7460	−0.692302
$899$	17.3686	0.579276
$900$	−3.14905	−0.104968
$901$	−12.4441	−0.414574
$902$	2.08498	0.0694222
$903$	−9.73364	−0.323915
$904$	17.8263	0.592895
$905$	48.1638	1.60102
$906$	1.62518	0.0539930
$907$	12.9470	0.429899	0.214949	−	0.976625i	$-0.431041\pi$
$907$	12.9470	0.429899	0.214949	+	0.976625i	$0.431041\pi$
$908$	−21.8667	−0.725673
$909$	17.1783	0.569769
$910$	15.2660	0.506064
$911$	−9.71771	−0.321962	−0.160981	−	0.986958i	$-0.551466\pi$
$911$	−9.71771	−0.321962	−0.160981	+	0.986958i	$0.551466\pi$
$912$	−0.293071	−0.00970454
$913$	11.7347	0.388363
$914$	−6.90837	−0.228509
$915$	15.5100	0.512744
$916$	−9.38410	−0.310059
$917$	−71.1155	−2.34844
$918$	19.7134	0.650638
$919$	−24.2958	−0.801445	−0.400722	−	0.916200i	$-0.631241\pi$
$919$	−24.2958	−0.801445	−0.400722	+	0.916200i	$0.631241\pi$
$920$	12.7957	0.421861
$921$	9.69730	0.319537
$922$	−30.7360	−1.01224
$923$	−6.17925	−0.203393
$924$	−3.11374	−0.102435
$925$	−13.6532	−0.448914
$926$	20.8646	0.685652
$927$	−0.358432	−0.0117724
$928$	6.71448	0.220414
$929$	28.4257	0.932618	0.466309	−	0.884622i	$-0.345584\pi$
$929$	28.4257	0.932618	0.466309	+	0.884622i	$0.345584\pi$
$930$	6.59585	0.216287
$931$	−0.822406	−0.0269533
$932$	−13.8547	−0.453827
$933$	1.36011	0.0445280
$934$	11.0242	0.360723
$935$	10.1337	0.331407
$936$	3.82632	0.125067
$937$	19.3229	0.631253	0.315626	−	0.948884i	$-0.397785\pi$
$937$	19.3229	0.631253	0.315626	+	0.948884i	$0.397785\pi$
$938$	4.70642	0.153670
$939$	−26.6535	−0.869804
$940$	13.3477	0.435355
$941$	−22.9015	−0.746567	−0.373283	−	0.927717i	$-0.621768\pi$
$941$	−22.9015	−0.746567	−0.373283	+	0.927717i	$0.621768\pi$
$942$	−5.90196	−0.192296
$943$	10.4109	0.339026
$944$	−6.61212	−0.215206
$945$	39.9749	1.30038
$946$	−3.12603	−0.101636
$947$	−2.13705	−0.0694448	−0.0347224	−	0.999397i	$-0.511055\pi$
$947$	−2.13705	−0.0694448	−0.0347224	+	0.999397i	$0.511055\pi$
$948$	5.85036	0.190011
$949$	−20.1315	−0.653495
$950$	0.461465	0.0149719
$951$	−19.6920	−0.638558
$952$	12.3746	0.401064
$953$	44.7005	1.44799	0.723995	−	0.689805i	$-0.242304\pi$
$953$	44.7005	1.44799	0.723995	+	0.689805i	$0.242304\pi$
$954$	−6.32479	−0.204773
$955$	7.66377	0.247994
$956$	1.63869	0.0529991
$957$	−6.68119	−0.215972
$958$	0.454795	0.0146938
$959$	28.5601	0.922254
$960$	2.54987	0.0822966
$961$	−24.3088	−0.784154
$962$	16.5896	0.534869
$963$	−17.7906	−0.573295
$964$	−25.5272	−0.822175
$965$	23.2309	0.747828
$966$	−15.5478	−0.500244
$967$	16.0521	0.516202	0.258101	−	0.966118i	$-0.416903\pi$
$967$	16.0521	0.516202	0.258101	+	0.966118i	$0.416903\pi$
$968$	−1.00000	−0.0321412
$969$	−1.15895	−0.0372307
$970$	42.9269	1.37830
$971$	−42.8898	−1.37640	−0.688200	−	0.725521i	$-0.741599\pi$
$971$	−42.8898	−1.37640	−0.688200	+	0.725521i	$0.741599\pi$
$972$	16.0192	0.513816
$973$	57.6683	1.84876
$974$	10.9083	0.349525
$975$	2.96796	0.0950507
$976$	6.08266	0.194701
$977$	−49.3586	−1.57912	−0.789561	−	0.613672i	$-0.789692\pi$
$977$	−49.3586	−1.57912	−0.789561	+	0.613672i	$0.789692\pi$
$978$	−10.0621	−0.321751
$979$	−8.04190	−0.257020
$980$	7.15536	0.228569
$981$	−24.9099	−0.795312
$982$	4.13367	0.131911
$983$	18.6318	0.594262	0.297131	−	0.954837i	$-0.403970\pi$
$983$	18.6318	0.594262	0.297131	+	0.954837i	$0.403970\pi$
$984$	2.07464	0.0661372
$985$	2.56257	0.0816504
$986$	26.5524	0.845599
$987$	−16.2186	−0.516244
$988$	−0.560712	−0.0178386
$989$	−15.6092	−0.496343
$990$	5.15049	0.163693
$991$	−46.2037	−1.46771	−0.733855	−	0.679306i	$-0.762281\pi$
$991$	−46.2037	−1.46771	−0.733855	+	0.679306i	$0.762281\pi$
$992$	2.58674	0.0821292
$993$	18.5886	0.589893
$994$	−10.1571	−0.322163
$995$	45.6471	1.44711
$996$	11.6766	0.369986
$997$	−2.35218	−0.0744944	−0.0372472	−	0.999306i	$-0.511859\pi$
$997$	−2.35218	−0.0744944	−0.0372472	+	0.999306i	$0.511859\pi$
$998$	34.1697	1.08162
$999$	43.4406	1.37440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.11	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.11	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.995042 q^{3} +1.00000 q^{4} +2.56257 q^{5} -0.995042 q^{6} -3.12926 q^{7} -1.00000 q^{8} -2.00989 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.995042 q^{3} +1.00000 q^{4} +2.56257 q^{5} -0.995042 q^{6} -3.12926 q^{7} -1.00000 q^{8} -2.00989 q^{9} -2.56257 q^{10} +1.00000 q^{11} +0.995042 q^{12} +1.90374 q^{13} +3.12926 q^{14} +2.54987 q^{15} +1.00000 q^{16} +3.95449 q^{17} +2.00989 q^{18} -0.294531 q^{19} +2.56257 q^{20} -3.11374 q^{21} -1.00000 q^{22} -4.99330 q^{23} -0.995042 q^{24} +1.56678 q^{25} -1.90374 q^{26} -4.98505 q^{27} -3.12926 q^{28} -6.71448 q^{29} -2.54987 q^{30} -2.58674 q^{31} -1.00000 q^{32} +0.995042 q^{33} -3.95449 q^{34} -8.01895 q^{35} -2.00989 q^{36} -8.71417 q^{37} +0.294531 q^{38} +1.89431 q^{39} -2.56257 q^{40} -2.08498 q^{41} +3.11374 q^{42} +3.12603 q^{43} +1.00000 q^{44} -5.15049 q^{45} +4.99330 q^{46} +5.20872 q^{47} +0.995042 q^{48} +2.79225 q^{49} -1.56678 q^{50} +3.93489 q^{51} +1.90374 q^{52} -3.14683 q^{53} +4.98505 q^{54} +2.56257 q^{55} +3.12926 q^{56} -0.293071 q^{57} +6.71448 q^{58} -6.61212 q^{59} +2.54987 q^{60} +6.08266 q^{61} +2.58674 q^{62} +6.28947 q^{63} +1.00000 q^{64} +4.87848 q^{65} -0.995042 q^{66} +1.50401 q^{67} +3.95449 q^{68} -4.96854 q^{69} +8.01895 q^{70} -3.24584 q^{71} +2.00989 q^{72} -10.5747 q^{73} +8.71417 q^{74} +1.55901 q^{75} -0.294531 q^{76} -3.12926 q^{77} -1.89431 q^{78} +5.87951 q^{79} +2.56257 q^{80} +1.06934 q^{81} +2.08498 q^{82} +11.7347 q^{83} -3.11374 q^{84} +10.1337 q^{85} -3.12603 q^{86} -6.68119 q^{87} -1.00000 q^{88} -8.04190 q^{89} +5.15049 q^{90} -5.95731 q^{91} -4.99330 q^{92} -2.57392 q^{93} -5.20872 q^{94} -0.754757 q^{95} -0.995042 q^{96} -16.7515 q^{97} -2.79225 q^{98} -2.00989 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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