LMFDB - Embedded newform 4003.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60205 q^{2} +1.48054 q^{3} +4.77066 q^{4} +1.31197 q^{5} -3.85243 q^{6} +3.44490 q^{7} -7.20939 q^{8} -0.808005 q^{9} +O(q^{10})$	\(q-2.60205 q^{2} +1.48054 q^{3} +4.77066 q^{4} +1.31197 q^{5} -3.85243 q^{6} +3.44490 q^{7} -7.20939 q^{8} -0.808005 q^{9} -3.41380 q^{10} -4.34159 q^{11} +7.06314 q^{12} +1.60278 q^{13} -8.96381 q^{14} +1.94242 q^{15} +9.21787 q^{16} -2.68007 q^{17} +2.10247 q^{18} +1.39273 q^{19} +6.25894 q^{20} +5.10031 q^{21} +11.2970 q^{22} -1.41743 q^{23} -10.6738 q^{24} -3.27874 q^{25} -4.17050 q^{26} -5.63790 q^{27} +16.4345 q^{28} -9.46568 q^{29} -5.05426 q^{30} -8.88883 q^{31} -9.56656 q^{32} -6.42789 q^{33} +6.97367 q^{34} +4.51960 q^{35} -3.85472 q^{36} +6.69542 q^{37} -3.62395 q^{38} +2.37297 q^{39} -9.45848 q^{40} -3.03509 q^{41} -13.2713 q^{42} +11.4209 q^{43} -20.7122 q^{44} -1.06008 q^{45} +3.68821 q^{46} +1.90734 q^{47} +13.6474 q^{48} +4.86737 q^{49} +8.53145 q^{50} -3.96794 q^{51} +7.64630 q^{52} +9.71534 q^{53} +14.6701 q^{54} -5.69602 q^{55} -24.8357 q^{56} +2.06199 q^{57} +24.6302 q^{58} +1.71390 q^{59} +9.26661 q^{60} -11.5122 q^{61} +23.1292 q^{62} -2.78350 q^{63} +6.45693 q^{64} +2.10279 q^{65} +16.7257 q^{66} +0.441675 q^{67} -12.7857 q^{68} -2.09856 q^{69} -11.7602 q^{70} -7.97411 q^{71} +5.82522 q^{72} -5.45206 q^{73} -17.4218 q^{74} -4.85431 q^{75} +6.64423 q^{76} -14.9564 q^{77} -6.17459 q^{78} +2.73268 q^{79} +12.0935 q^{80} -5.92311 q^{81} +7.89745 q^{82} -15.9563 q^{83} +24.3319 q^{84} -3.51616 q^{85} -29.7176 q^{86} -14.0143 q^{87} +31.3002 q^{88} -10.0380 q^{89} +2.75837 q^{90} +5.52141 q^{91} -6.76206 q^{92} -13.1603 q^{93} -4.96299 q^{94} +1.82721 q^{95} -14.1637 q^{96} -0.127111 q^{97} -12.6651 q^{98} +3.50803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * 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 $

$2$	−2.60205	−1.83993	−0.919963	−	0.392005i	$-0.871782\pi$
$2$	−2.60205	−1.83993	−0.919963	+	0.392005i	$0.871782\pi$
$3$	1.48054	0.854789	0.427395	−	0.904065i	$-0.359431\pi$
$3$	1.48054	0.854789	0.427395	+	0.904065i	$0.359431\pi$
$4$	4.77066	2.38533
$5$	1.31197	0.586729	0.293365	−	0.956001i	$-0.405225\pi$
$5$	1.31197	0.586729	0.293365	+	0.956001i	$0.405225\pi$
$6$	−3.85243	−1.57275
$7$	3.44490	1.30205	0.651026	−	0.759056i	$-0.274339\pi$
$7$	3.44490	1.30205	0.651026	+	0.759056i	$0.274339\pi$
$8$	−7.20939	−2.54890
$9$	−0.808005	−0.269335
$10$	−3.41380	−1.07954
$11$	−4.34159	−1.30904	−0.654519	−	0.756045i	$-0.727129\pi$
$11$	−4.34159	−1.30904	−0.654519	+	0.756045i	$0.727129\pi$
$12$	7.06314	2.03895
$13$	1.60278	0.444530	0.222265	−	0.974986i	$-0.428655\pi$
$13$	1.60278	0.444530	0.222265	+	0.974986i	$0.428655\pi$
$14$	−8.96381	−2.39568
$15$	1.94242	0.501530
$16$	9.21787	2.30447
$17$	−2.68007	−0.650012	−0.325006	−	0.945712i	$-0.605366\pi$
$17$	−2.68007	−0.650012	−0.325006	+	0.945712i	$0.605366\pi$
$18$	2.10247	0.495557
$19$	1.39273	0.319514	0.159757	−	0.987156i	$-0.448929\pi$
$19$	1.39273	0.319514	0.159757	+	0.987156i	$0.448929\pi$
$20$	6.25894	1.39954
$21$	5.10031	1.11298
$22$	11.2970	2.40853
$23$	−1.41743	−0.295554	−0.147777	−	0.989021i	$-0.547212\pi$
$23$	−1.41743	−0.295554	−0.147777	+	0.989021i	$0.547212\pi$
$24$	−10.6738	−2.17878
$25$	−3.27874	−0.655749
$26$	−4.17050	−0.817902
$27$	−5.63790	−1.08501
$28$	16.4345	3.10582
$29$	−9.46568	−1.75773	−0.878866	−	0.477069i	$-0.841699\pi$
$29$	−9.46568	−1.75773	−0.878866	+	0.477069i	$0.841699\pi$
$30$	−5.05426	−0.922778
$31$	−8.88883	−1.59648	−0.798241	−	0.602338i	$-0.794236\pi$
$31$	−8.88883	−1.59648	−0.798241	+	0.602338i	$0.794236\pi$
$32$	−9.56656	−1.69115
$33$	−6.42789	−1.11895
$34$	6.97367	1.19597
$35$	4.51960	0.763952
$36$	−3.85472	−0.642453
$37$	6.69542	1.10072	0.550360	−	0.834927i	$-0.314490\pi$
$37$	6.69542	1.10072	0.550360	+	0.834927i	$0.314490\pi$
$38$	−3.62395	−0.587882
$39$	2.37297	0.379980
$40$	−9.45848	−1.49552
$41$	−3.03509	−0.474001	−0.237001	−	0.971509i	$-0.576164\pi$
$41$	−3.03509	−0.474001	−0.237001	+	0.971509i	$0.576164\pi$
$42$	−13.2713	−2.04780
$43$	11.4209	1.74166	0.870832	−	0.491581i	$-0.163581\pi$
$43$	11.4209	1.74166	0.870832	+	0.491581i	$0.163581\pi$
$44$	−20.7122	−3.12249
$45$	−1.06008	−0.158027
$46$	3.68821	0.543797
$47$	1.90734	0.278214	0.139107	−	0.990277i	$-0.455577\pi$
$47$	1.90734	0.278214	0.139107	+	0.990277i	$0.455577\pi$
$48$	13.6474	1.96983
$49$	4.86737	0.695338
$50$	8.53145	1.20653
$51$	−3.96794	−0.555623
$52$	7.64630	1.06035
$53$	9.71534	1.33451	0.667253	−	0.744832i	$-0.267470\pi$
$53$	9.71534	1.33451	0.667253	+	0.744832i	$0.267470\pi$
$54$	14.6701	1.99635
$55$	−5.69602	−0.768051
$56$	−24.8357	−3.31880
$57$	2.06199	0.273117
$58$	24.6302	3.23410
$59$	1.71390	0.223131	0.111566	−	0.993757i	$-0.464414\pi$
$59$	1.71390	0.223131	0.111566	+	0.993757i	$0.464414\pi$
$60$	9.26661	1.19631
$61$	−11.5122	−1.47398	−0.736991	−	0.675902i	$-0.763754\pi$
$61$	−11.5122	−1.47398	−0.736991	+	0.675902i	$0.763754\pi$
$62$	23.1292	2.93741
$63$	−2.78350	−0.350688
$64$	6.45693	0.807117
$65$	2.10279	0.260819
$66$	16.7257	2.05879
$67$	0.441675	0.0539592	0.0269796	−	0.999636i	$-0.491411\pi$
$67$	0.441675	0.0539592	0.0269796	+	0.999636i	$0.491411\pi$
$68$	−12.7857	−1.55049
$69$	−2.09856	−0.252636
$70$	−11.7602	−1.40561
$71$	−7.97411	−0.946353	−0.473176	−	0.880968i	$-0.656893\pi$
$71$	−7.97411	−0.946353	−0.473176	+	0.880968i	$0.656893\pi$
$72$	5.82522	0.686509
$73$	−5.45206	−0.638115	−0.319057	−	0.947735i	$-0.603366\pi$
$73$	−5.45206	−0.638115	−0.319057	+	0.947735i	$0.603366\pi$
$74$	−17.4218	−2.02524
$75$	−4.85431	−0.560527
$76$	6.64423	0.762146
$77$	−14.9564	−1.70444
$78$	−6.17459	−0.699134
$79$	2.73268	0.307450	0.153725	−	0.988114i	$-0.450873\pi$
$79$	2.73268	0.307450	0.153725	+	0.988114i	$0.450873\pi$
$80$	12.0935	1.35210
$81$	−5.92311	−0.658124
$82$	7.89745	0.872128
$83$	−15.9563	−1.75143	−0.875714	−	0.482829i	$-0.839609\pi$
$83$	−15.9563	−1.75143	−0.875714	+	0.482829i	$0.839609\pi$
$84$	24.3319	2.65482
$85$	−3.51616	−0.381381
$86$	−29.7176	−3.20453
$87$	−14.0143	−1.50249
$88$	31.3002	3.33661
$89$	−10.0380	−1.06403	−0.532015	−	0.846735i	$-0.678565\pi$
$89$	−10.0380	−1.06403	−0.532015	+	0.846735i	$0.678565\pi$
$90$	2.75837	0.290758
$91$	5.52141	0.578801
$92$	−6.76206	−0.704993
$93$	−13.1603	−1.36466
$94$	−4.96299	−0.511893
$95$	1.82721	0.187468
$96$	−14.1637	−1.44557
$97$	−0.127111	−0.0129062	−0.00645309	−	0.999979i	$-0.502054\pi$
$97$	−0.127111	−0.0129062	−0.00645309	+	0.999979i	$0.502054\pi$
$98$	−12.6651	−1.27937
$99$	3.50803	0.352570
$100$	−15.6418	−1.56418
$101$	17.1694	1.70842	0.854212	−	0.519926i	$-0.174040\pi$
$101$	17.1694	1.70842	0.854212	+	0.519926i	$0.174040\pi$
$102$	10.3248	1.02231
$103$	−15.5235	−1.52958	−0.764789	−	0.644280i	$-0.777157\pi$
$103$	−15.5235	−1.52958	−0.764789	+	0.644280i	$0.777157\pi$
$104$	−11.5550	−1.13306
$105$	6.69144	0.653018
$106$	−25.2798	−2.45539
$107$	−12.5337	−1.21168	−0.605841	−	0.795586i	$-0.707163\pi$
$107$	−12.5337	−1.21168	−0.605841	+	0.795586i	$0.707163\pi$
$108$	−26.8965	−2.58812
$109$	−12.3496	−1.18287	−0.591437	−	0.806351i	$-0.701439\pi$
$109$	−12.3496	−1.18287	−0.591437	+	0.806351i	$0.701439\pi$
$110$	14.8213	1.41316
$111$	9.91283	0.940884
$112$	31.7547	3.00053
$113$	11.0784	1.04217	0.521086	−	0.853504i	$-0.325527\pi$
$113$	11.0784	1.04217	0.521086	+	0.853504i	$0.325527\pi$
$114$	−5.36539	−0.502515
$115$	−1.85962	−0.173410
$116$	−45.1575	−4.19277
$117$	−1.29505	−0.119728
$118$	−4.45966	−0.410545
$119$	−9.23258	−0.846349
$120$	−14.0036	−1.27835
$121$	7.84940	0.713582
$122$	29.9552	2.71202
$123$	−4.49357	−0.405171
$124$	−42.4056	−3.80814
$125$	−10.8614	−0.971476
$126$	7.24280	0.645240
$127$	−1.19854	−0.106354	−0.0531768	−	0.998585i	$-0.516935\pi$
$127$	−1.19854	−0.106354	−0.0531768	+	0.998585i	$0.516935\pi$
$128$	2.33187	0.206111
$129$	16.9090	1.48876
$130$	−5.47156	−0.479887
$131$	−9.66189	−0.844164	−0.422082	−	0.906558i	$-0.638700\pi$
$131$	−9.66189	−0.844164	−0.422082	+	0.906558i	$0.638700\pi$
$132$	−30.6653	−2.66907
$133$	4.79782	0.416023
$134$	−1.14926	−0.0992810
$135$	−7.39673	−0.636609
$136$	19.3217	1.65682
$137$	3.72997	0.318673	0.159336	−	0.987224i	$-0.449065\pi$
$137$	3.72997	0.318673	0.159336	+	0.987224i	$0.449065\pi$
$138$	5.46054	0.464832
$139$	−0.224646	−0.0190542	−0.00952711	−	0.999955i	$-0.503033\pi$
$139$	−0.224646	−0.0190542	−0.00952711	+	0.999955i	$0.503033\pi$
$140$	21.5615	1.82228
$141$	2.82389	0.237814
$142$	20.7490	1.74122
$143$	−6.95859	−0.581907
$144$	−7.44809	−0.620674
$145$	−12.4186	−1.03131
$146$	14.1865	1.17408
$147$	7.20632	0.594368
$148$	31.9416	2.62558
$149$	−9.42229	−0.771904	−0.385952	−	0.922519i	$-0.626127\pi$
$149$	−9.42229	−0.771904	−0.385952	+	0.922519i	$0.626127\pi$
$150$	12.6311	1.03133
$151$	0.999601	0.0813464	0.0406732	−	0.999173i	$-0.487050\pi$
$151$	0.999601	0.0813464	0.0406732	+	0.999173i	$0.487050\pi$
$152$	−10.0407	−0.814410
$153$	2.16551	0.175071
$154$	38.9172	3.13604
$155$	−11.6619	−0.936702
$156$	11.3206	0.906376
$157$	−14.4240	−1.15116	−0.575579	−	0.817746i	$-0.695223\pi$
$157$	−14.4240	−1.15116	−0.575579	+	0.817746i	$0.695223\pi$
$158$	−7.11056	−0.565686
$159$	14.3839	1.14072
$160$	−12.5510	−0.992244
$161$	−4.88290	−0.384826
$162$	15.4122	1.21090
$163$	21.5843	1.69061	0.845307	−	0.534281i	$-0.179418\pi$
$163$	21.5843	1.69061	0.845307	+	0.534281i	$0.179418\pi$
$164$	−14.4794	−1.13065
$165$	−8.43318	−0.656522
$166$	41.5190	3.22250
$167$	0.473361	0.0366298	0.0183149	−	0.999832i	$-0.494170\pi$
$167$	0.473361	0.0366298	0.0183149	+	0.999832i	$0.494170\pi$
$168$	−36.7702	−2.83688
$169$	−10.4311	−0.802393
$170$	9.14922	0.701713
$171$	−1.12533	−0.0860563
$172$	54.4850	4.15444
$173$	18.9142	1.43802	0.719008	−	0.695001i	$-0.244596\pi$
$173$	18.9142	1.43802	0.719008	+	0.695001i	$0.244596\pi$
$174$	36.4659	2.76447
$175$	−11.2950	−0.853819
$176$	−40.0202	−3.01664
$177$	2.53750	0.190730
$178$	26.1194	1.95774
$179$	5.48237	0.409772	0.204886	−	0.978786i	$-0.434318\pi$
$179$	5.48237	0.409772	0.204886	+	0.978786i	$0.434318\pi$
$180$	−5.05726	−0.376946
$181$	12.4653	0.926535	0.463268	−	0.886218i	$-0.346677\pi$
$181$	12.4653	0.926535	0.463268	+	0.886218i	$0.346677\pi$
$182$	−14.3670	−1.06495
$183$	−17.0442	−1.25994
$184$	10.2188	0.753339
$185$	8.78417	0.645825
$186$	34.2437	2.51087
$187$	11.6358	0.850891
$188$	9.09926	0.663632
$189$	−19.4220	−1.41274
$190$	−4.75450	−0.344927
$191$	−3.06566	−0.221823	−0.110912	−	0.993830i	$-0.535377\pi$
$191$	−3.06566	−0.221823	−0.110912	+	0.993830i	$0.535377\pi$
$192$	9.55974	0.689915
$193$	1.51384	0.108969	0.0544844	−	0.998515i	$-0.482648\pi$
$193$	1.51384	0.108969	0.0544844	+	0.998515i	$0.482648\pi$
$194$	0.330749	0.0237464
$195$	3.11326	0.222945
$196$	23.2205	1.65861
$197$	2.60094	0.185309	0.0926546	−	0.995698i	$-0.470465\pi$
$197$	2.60094	0.185309	0.0926546	+	0.995698i	$0.470465\pi$
$198$	−9.12806	−0.648703
$199$	10.1842	0.721937	0.360968	−	0.932578i	$-0.382446\pi$
$199$	10.1842	0.721937	0.360968	+	0.932578i	$0.382446\pi$
$200$	23.6377	1.67144
$201$	0.653917	0.0461238
$202$	−44.6757	−3.14337
$203$	−32.6083	−2.28866
$204$	−18.9297	−1.32534
$205$	−3.98193	−0.278110
$206$	40.3930	2.81431
$207$	1.14529	0.0796030
$208$	14.7742	1.02440
$209$	−6.04666	−0.418256
$210$	−17.4115	−1.20150
$211$	−23.7382	−1.63421	−0.817103	−	0.576491i	$-0.804421\pi$
$211$	−23.7382	−1.63421	−0.817103	+	0.576491i	$0.804421\pi$
$212$	46.3486	3.18323
$213$	−11.8060	−0.808932
$214$	32.6134	2.22941
$215$	14.9838	1.02189
$216$	40.6458	2.76560
$217$	−30.6212	−2.07870
$218$	32.1342	2.17640
$219$	−8.07198	−0.545454
$220$	−27.1738	−1.83205
$221$	−4.29555	−0.288950
$222$	−25.7937	−1.73116
$223$	−2.63196	−0.176249	−0.0881245	−	0.996109i	$-0.528087\pi$
$223$	−2.63196	−0.176249	−0.0881245	+	0.996109i	$0.528087\pi$
$224$	−32.9559	−2.20196
$225$	2.64924	0.176616
$226$	−28.8266	−1.91752
$227$	13.6806	0.908011	0.454006	−	0.890999i	$-0.349995\pi$
$227$	13.6806	0.908011	0.454006	+	0.890999i	$0.349995\pi$
$228$	9.83704	0.651474
$229$	−13.8201	−0.913259	−0.456629	−	0.889657i	$-0.650943\pi$
$229$	−13.8201	−0.913259	−0.456629	+	0.889657i	$0.650943\pi$
$230$	4.83881	0.319062
$231$	−22.1435	−1.45693
$232$	68.2417	4.48029
$233$	12.1247	0.794315	0.397157	−	0.917750i	$-0.369997\pi$
$233$	12.1247	0.794315	0.397157	+	0.917750i	$0.369997\pi$
$234$	3.36979	0.220290
$235$	2.50236	0.163236
$236$	8.17644	0.532241
$237$	4.04584	0.262805
$238$	24.0236	1.55722
$239$	1.62258	0.104956	0.0524780	−	0.998622i	$-0.483288\pi$
$239$	1.62258	0.104956	0.0524780	+	0.998622i	$0.483288\pi$
$240$	17.9049	1.15576
$241$	0.150756	0.00971105	0.00485552	−	0.999988i	$-0.498454\pi$
$241$	0.150756	0.00971105	0.00485552	+	0.999988i	$0.498454\pi$
$242$	−20.4245	−1.31294
$243$	8.14430	0.522457
$244$	−54.9207	−3.51593
$245$	6.38582	0.407975
$246$	11.6925	0.745485
$247$	2.23223	0.142033
$248$	64.0831	4.06928
$249$	−23.6239	−1.49710
$250$	28.2620	1.78744
$251$	4.44342	0.280466	0.140233	−	0.990119i	$-0.455215\pi$
$251$	4.44342	0.280466	0.140233	+	0.990119i	$0.455215\pi$
$252$	−13.2791	−0.836507
$253$	6.15389	0.386891
$254$	3.11867	0.195683
$255$	−5.20581	−0.326000
$256$	−18.9815	−1.18634
$257$	−21.8189	−1.36103	−0.680513	−	0.732736i	$-0.738243\pi$
$257$	−21.8189	−1.36103	−0.680513	+	0.732736i	$0.738243\pi$
$258$	−43.9981	−2.73920
$259$	23.0651	1.43319
$260$	10.0317	0.622139
$261$	7.64832	0.473419
$262$	25.1407	1.55320
$263$	−11.9036	−0.734010	−0.367005	−	0.930219i	$-0.619617\pi$
$263$	−11.9036	−0.734010	−0.367005	+	0.930219i	$0.619617\pi$
$264$	46.3412	2.85210
$265$	12.7462	0.782993
$266$	−12.4842	−0.765453
$267$	−14.8617	−0.909521
$268$	2.10708	0.128711
$269$	22.6301	1.37978	0.689889	−	0.723915i	$-0.257659\pi$
$269$	22.6301	1.37978	0.689889	+	0.723915i	$0.257659\pi$
$270$	19.2467	1.17131
$271$	19.0156	1.15511	0.577557	−	0.816350i	$-0.304006\pi$
$271$	19.0156	1.15511	0.577557	+	0.816350i	$0.304006\pi$
$272$	−24.7045	−1.49793
$273$	8.17466	0.494753
$274$	−9.70557	−0.586335
$275$	14.2350	0.858401
$276$	−10.0115	−0.602621
$277$	1.69360	0.101758	0.0508791	−	0.998705i	$-0.483798\pi$
$277$	1.69360	0.101758	0.0508791	+	0.998705i	$0.483798\pi$
$278$	0.584540	0.0350584
$279$	7.18222	0.429989
$280$	−32.5835	−1.94724
$281$	−11.7182	−0.699047	−0.349524	−	0.936928i	$-0.613657\pi$
$281$	−11.7182	−0.699047	−0.349524	+	0.936928i	$0.613657\pi$
$282$	−7.34789	−0.437561
$283$	−2.12721	−0.126450	−0.0632248	−	0.997999i	$-0.520139\pi$
$283$	−2.12721	−0.126450	−0.0632248	+	0.997999i	$0.520139\pi$
$284$	−38.0418	−2.25736
$285$	2.70526	0.160246
$286$	18.1066	1.07067
$287$	−10.4556	−0.617174
$288$	7.72983	0.455485
$289$	−9.81724	−0.577485
$290$	32.3139	1.89754
$291$	−0.188193	−0.0110321
$292$	−26.0099	−1.52211
$293$	26.7323	1.56172	0.780859	−	0.624708i	$-0.214782\pi$
$293$	26.7323	1.56172	0.780859	+	0.624708i	$0.214782\pi$
$294$	−18.7512	−1.09359
$295$	2.24858	0.130918
$296$	−48.2699	−2.80563
$297$	24.4774	1.42033
$298$	24.5173	1.42025
$299$	−2.27182	−0.131383
$300$	−23.1582	−1.33704
$301$	39.3438	2.26774
$302$	−2.60101	−0.149671
$303$	25.4200	1.46034
$304$	12.8380	0.736309
$305$	−15.1036	−0.864829
$306$	−5.63476	−0.322118
$307$	−11.0660	−0.631571	−0.315786	−	0.948831i	$-0.602268\pi$
$307$	−11.0660	−0.631571	−0.315786	+	0.948831i	$0.602268\pi$
$308$	−71.3517	−4.06564
$309$	−22.9832	−1.30747
$310$	30.3447	1.72346
$311$	0.166353	0.00943300	0.00471650	−	0.999989i	$-0.498499\pi$
$311$	0.166353	0.00943300	0.00471650	+	0.999989i	$0.498499\pi$
$312$	−17.1077	−0.968531
$313$	−34.0108	−1.92241	−0.961203	−	0.275842i	$-0.911043\pi$
$313$	−34.0108	−1.92241	−0.961203	+	0.275842i	$0.911043\pi$
$314$	37.5319	2.11805
$315$	−3.65186	−0.205759
$316$	13.0367	0.733370
$317$	−19.8900	−1.11713	−0.558567	−	0.829459i	$-0.688649\pi$
$317$	−19.8900	−1.11713	−0.558567	+	0.829459i	$0.688649\pi$
$318$	−37.4277	−2.09884
$319$	41.0961	2.30094
$320$	8.47128	0.473559
$321$	−18.5567	−1.03573
$322$	12.7055	0.708052
$323$	−3.73261	−0.207688
$324$	−28.2571	−1.56984
$325$	−5.25509	−0.291500
$326$	−56.1634	−3.11061
$327$	−18.2840	−1.01111
$328$	21.8811	1.20818
$329$	6.57060	0.362249
$330$	21.9435	1.20795
$331$	12.5197	0.688144	0.344072	−	0.938943i	$-0.388194\pi$
$331$	12.5197	0.688144	0.344072	+	0.938943i	$0.388194\pi$
$332$	−76.1220	−4.17773
$333$	−5.40994	−0.296463
$334$	−1.23171	−0.0673961
$335$	0.579463	0.0316595
$336$	47.0140	2.56483
$337$	35.0463	1.90910	0.954548	−	0.298058i	$-0.0963389\pi$
$337$	35.0463	1.90910	0.954548	+	0.298058i	$0.0963389\pi$
$338$	27.1423	1.47634
$339$	16.4021	0.890837
$340$	−16.7744	−0.909719
$341$	38.5917	2.08986
$342$	2.92817	0.158337
$343$	−7.34672	−0.396686
$344$	−82.3374	−4.43933
$345$	−2.75323	−0.148229
$346$	−49.2156	−2.64585
$347$	9.95569	0.534449	0.267225	−	0.963634i	$-0.413893\pi$
$347$	9.95569	0.534449	0.267225	+	0.963634i	$0.413893\pi$
$348$	−66.8574	−3.58394
$349$	−5.64792	−0.302326	−0.151163	−	0.988509i	$-0.548302\pi$
$349$	−5.64792	−0.302326	−0.151163	+	0.988509i	$0.548302\pi$
$350$	29.3900	1.57096
$351$	−9.03629	−0.482321
$352$	41.5341	2.21377
$353$	17.1652	0.913613	0.456806	−	0.889566i	$-0.348993\pi$
$353$	17.1652	0.913613	0.456806	+	0.889566i	$0.348993\pi$
$354$	−6.60270	−0.350929
$355$	−10.4618	−0.555253
$356$	−47.8880	−2.53806
$357$	−13.6692	−0.723450
$358$	−14.2654	−0.753950
$359$	−4.59637	−0.242587	−0.121294	−	0.992617i	$-0.538704\pi$
$359$	−4.59637	−0.242587	−0.121294	+	0.992617i	$0.538704\pi$
$360$	7.64250	0.402795
$361$	−17.0603	−0.897911
$362$	−32.4352	−1.70476
$363$	11.6213	0.609962
$364$	26.3408	1.38063
$365$	−7.15291	−0.374401
$366$	44.3499	2.31821
$367$	19.6206	1.02419	0.512093	−	0.858930i	$-0.328870\pi$
$367$	19.6206	1.02419	0.512093	+	0.858930i	$0.328870\pi$
$368$	−13.0657	−0.681094
$369$	2.45237	0.127665
$370$	−22.8568	−1.18827
$371$	33.4684	1.73759
$372$	−62.7831	−3.25515
$373$	18.1650	0.940547	0.470274	−	0.882521i	$-0.344155\pi$
$373$	18.1650	0.940547	0.470274	+	0.882521i	$0.344155\pi$
$374$	−30.2768	−1.56558
$375$	−16.0808	−0.830408
$376$	−13.7507	−0.709140
$377$	−15.1714	−0.781365
$378$	50.5371	2.59935
$379$	−29.2836	−1.50420	−0.752098	−	0.659051i	$-0.770958\pi$
$379$	−29.2836	−1.50420	−0.752098	+	0.659051i	$0.770958\pi$
$380$	8.71701	0.447173
$381$	−1.77449	−0.0909100
$382$	7.97700	0.408139
$383$	6.87287	0.351187	0.175594	−	0.984463i	$-0.443816\pi$
$383$	6.87287	0.351187	0.175594	+	0.984463i	$0.443816\pi$
$384$	3.45243	0.176181
$385$	−19.6222	−1.00004
$386$	−3.93910	−0.200495
$387$	−9.22811	−0.469091
$388$	−0.606404	−0.0307855
$389$	−2.96440	−0.150301	−0.0751506	−	0.997172i	$-0.523944\pi$
$389$	−2.96440	−0.150301	−0.0751506	+	0.997172i	$0.523944\pi$
$390$	−8.10085	−0.410203
$391$	3.79880	0.192114
$392$	−35.0907	−1.77235
$393$	−14.3048	−0.721582
$394$	−6.76777	−0.340955
$395$	3.58518	0.180390
$396$	16.7356	0.840996
$397$	11.0763	0.555905	0.277952	−	0.960595i	$-0.410344\pi$
$397$	11.0763	0.555905	0.277952	+	0.960595i	$0.410344\pi$
$398$	−26.4997	−1.32831
$399$	7.10335	0.355612
$400$	−30.2230	−1.51115
$401$	−13.5713	−0.677717	−0.338859	−	0.940837i	$-0.610041\pi$
$401$	−13.5713	−0.677717	−0.338859	+	0.940837i	$0.610041\pi$
$402$	−1.70153	−0.0848644
$403$	−14.2468	−0.709684
$404$	81.9095	4.07515
$405$	−7.77092	−0.386140
$406$	84.8485	4.21096
$407$	−29.0688	−1.44089
$408$	28.6065	1.41623
$409$	14.4605	0.715025	0.357512	−	0.933908i	$-0.383625\pi$
$409$	14.4605	0.715025	0.357512	+	0.933908i	$0.383625\pi$
$410$	10.3612	0.511703
$411$	5.52237	0.272398
$412$	−74.0575	−3.64855
$413$	5.90423	0.290528
$414$	−2.98010	−0.146464
$415$	−20.9341	−1.02761
$416$	−15.3331	−0.751765
$417$	−0.332597	−0.0162873
$418$	15.7337	0.769560
$419$	30.1880	1.47478	0.737389	−	0.675468i	$-0.236058\pi$
$419$	30.1880	1.47478	0.737389	+	0.675468i	$0.236058\pi$
$420$	31.9226	1.55766
$421$	34.0938	1.66163	0.830815	−	0.556549i	$-0.187875\pi$
$421$	34.0938	1.66163	0.830815	+	0.556549i	$0.187875\pi$
$422$	61.7680	3.00682
$423$	−1.54114	−0.0749327
$424$	−70.0417	−3.40153
$425$	8.78726	0.426245
$426$	30.7197	1.48838
$427$	−39.6583	−1.91920
$428$	−59.7942	−2.89026
$429$	−10.3025	−0.497408
$430$	−38.9885	−1.88019
$431$	−6.56659	−0.316302	−0.158151	−	0.987415i	$-0.550553\pi$
$431$	−6.56659	−0.316302	−0.158151	+	0.987415i	$0.550553\pi$
$432$	−51.9694	−2.50038
$433$	−9.39563	−0.451525	−0.225763	−	0.974182i	$-0.572487\pi$
$433$	−9.39563	−0.451525	−0.225763	+	0.974182i	$0.572487\pi$
$434$	79.6778	3.82466
$435$	−18.3863	−0.881555
$436$	−58.9156	−2.82155
$437$	−1.97409	−0.0944336
$438$	21.0037	1.00360
$439$	22.7287	1.08478	0.542390	−	0.840127i	$-0.317520\pi$
$439$	22.7287	1.08478	0.542390	+	0.840127i	$0.317520\pi$
$440$	41.0648	1.95769
$441$	−3.93286	−0.187279
$442$	11.1772	0.531646
$443$	17.7833	0.844910	0.422455	−	0.906384i	$-0.361168\pi$
$443$	17.7833	0.844910	0.422455	+	0.906384i	$0.361168\pi$
$444$	47.2907	2.24432
$445$	−13.1696	−0.624297
$446$	6.84848	0.324285
$447$	−13.9501	−0.659816
$448$	22.2435	1.05091
$449$	1.65386	0.0780505	0.0390253	−	0.999238i	$-0.487575\pi$
$449$	1.65386	0.0780505	0.0390253	+	0.999238i	$0.487575\pi$
$450$	−6.89346	−0.324961
$451$	13.1771	0.620486
$452$	52.8514	2.48592
$453$	1.47995	0.0695340
$454$	−35.5975	−1.67067
$455$	7.24390	0.339599
$456$	−14.8657	−0.696149
$457$	−39.0553	−1.82693	−0.913464	−	0.406919i	$-0.866603\pi$
$457$	−39.0553	−1.82693	−0.913464	+	0.406919i	$0.866603\pi$
$458$	35.9606	1.68033
$459$	15.1099	0.705272
$460$	−8.87159	−0.413640
$461$	22.6274	1.05386	0.526932	−	0.849908i	$-0.323342\pi$
$461$	22.6274	1.05386	0.526932	+	0.849908i	$0.323342\pi$
$462$	57.6184	2.68065
$463$	36.5371	1.69802	0.849012	−	0.528374i	$-0.177198\pi$
$463$	36.5371	1.69802	0.849012	+	0.528374i	$0.177198\pi$
$464$	−87.2534	−4.05064
$465$	−17.2658	−0.800683
$466$	−31.5490	−1.46148
$467$	−37.2025	−1.72152	−0.860762	−	0.509007i	$-0.830013\pi$
$467$	−37.2025	−1.72152	−0.860762	+	0.509007i	$0.830013\pi$
$468$	−6.17825	−0.285590
$469$	1.52153	0.0702577
$470$	−6.51127	−0.300343
$471$	−21.3552	−0.983997
$472$	−12.3562	−0.568740
$473$	−49.5847	−2.27991
$474$	−10.5275	−0.483542
$475$	−4.56640	−0.209521
$476$	−44.0455	−2.01882
$477$	−7.85005	−0.359429
$478$	−4.22203	−0.193111
$479$	−12.4048	−0.566788	−0.283394	−	0.959004i	$-0.591460\pi$
$479$	−12.4048	−0.566788	−0.283394	+	0.959004i	$0.591460\pi$
$480$	−18.5823	−0.848160
$481$	10.7313	0.489303
$482$	−0.392274	−0.0178676
$483$	−7.22932	−0.328946
$484$	37.4468	1.70213
$485$	−0.166765	−0.00757243
$486$	−21.1919	−0.961283
$487$	−28.1608	−1.27609	−0.638045	−	0.769999i	$-0.720256\pi$
$487$	−28.1608	−1.27609	−0.638045	+	0.769999i	$0.720256\pi$
$488$	82.9958	3.75704
$489$	31.9564	1.44512
$490$	−16.6162	−0.750644
$491$	−31.2776	−1.41154	−0.705769	−	0.708443i	$-0.749398\pi$
$491$	−31.2776	−1.41154	−0.705769	+	0.708443i	$0.749398\pi$
$492$	−21.4373	−0.966467
$493$	25.3686	1.14255
$494$	−5.80838	−0.261331
$495$	4.60241	0.206863
$496$	−81.9361	−3.67904
$497$	−27.4700	−1.23220
$498$	61.4705	2.75456
$499$	−30.5993	−1.36981	−0.684907	−	0.728631i	$-0.740157\pi$
$499$	−30.5993	−1.36981	−0.684907	+	0.728631i	$0.740157\pi$
$500$	−51.8162	−2.31729
$501$	0.700829	0.0313107
$502$	−11.5620	−0.516037
$503$	3.50860	0.156441	0.0782203	−	0.996936i	$-0.475076\pi$
$503$	3.50860	0.156441	0.0782203	+	0.996936i	$0.475076\pi$
$504$	20.0673	0.893870
$505$	22.5257	1.00238
$506$	−16.0127	−0.711852
$507$	−15.4437	−0.685877
$508$	−5.71785	−0.253688
$509$	−0.315424	−0.0139809	−0.00699047	−	0.999976i	$-0.502225\pi$
$509$	−0.315424	−0.0139809	−0.00699047	+	0.999976i	$0.502225\pi$
$510$	13.5458	0.599817
$511$	−18.7818	−0.830859
$512$	44.7271	1.97668
$513$	−7.85206	−0.346677
$514$	56.7738	2.50419
$515$	−20.3663	−0.897448
$516$	80.6672	3.55117
$517$	−8.28088	−0.364193
$518$	−60.0165	−2.63697
$519$	28.0031	1.22920
$520$	−15.1598	−0.664802
$521$	−37.9517	−1.66269	−0.831346	−	0.555755i	$-0.812429\pi$
$521$	−37.9517	−1.66269	−0.831346	+	0.555755i	$0.812429\pi$
$522$	−19.9013	−0.871056
$523$	−16.5865	−0.725279	−0.362639	−	0.931930i	$-0.618124\pi$
$523$	−16.5865	−0.725279	−0.362639	+	0.931930i	$0.618124\pi$
$524$	−46.0936	−2.01361
$525$	−16.7226	−0.729835
$526$	30.9738	1.35052
$527$	23.8227	1.03773
$528$	−59.2515	−2.57859
$529$	−20.9909	−0.912648
$530$	−33.1662	−1.44065
$531$	−1.38484	−0.0600970
$532$	22.8887	0.992353
$533$	−4.86457	−0.210708
$534$	38.6709	1.67345
$535$	−16.4438	−0.710929
$536$	−3.18421	−0.137537
$537$	8.11686	0.350268
$538$	−58.8845	−2.53869
$539$	−21.1321	−0.910224
$540$	−35.2873	−1.51852
$541$	18.7201	0.804838	0.402419	−	0.915456i	$-0.368169\pi$
$541$	18.7201	0.804838	0.402419	+	0.915456i	$0.368169\pi$
$542$	−49.4795	−2.12532
$543$	18.4553	0.791992
$544$	25.6390	1.09926
$545$	−16.2022	−0.694027
$546$	−21.2709	−0.910309
$547$	7.78139	0.332708	0.166354	−	0.986066i	$-0.446801\pi$
$547$	7.78139	0.332708	0.166354	+	0.986066i	$0.446801\pi$
$548$	17.7944	0.760140
$549$	9.30190	0.396995
$550$	−37.0401	−1.57939
$551$	−13.1831	−0.561620
$552$	15.1293	0.643946
$553$	9.41381	0.400316
$554$	−4.40682	−0.187228
$555$	13.0053	0.552044
$556$	−1.07171	−0.0454506
$557$	4.05324	0.171741	0.0858707	−	0.996306i	$-0.472633\pi$
$557$	4.05324	0.171741	0.0858707	+	0.996306i	$0.472633\pi$
$558$	−18.6885	−0.791147
$559$	18.3051	0.774222
$560$	41.6611	1.76050
$561$	17.2272	0.727332
$562$	30.4912	1.28620
$563$	26.2850	1.10778	0.553891	−	0.832589i	$-0.313142\pi$
$563$	26.2850	1.10778	0.553891	+	0.832589i	$0.313142\pi$
$564$	13.4718	0.567265
$565$	14.5345	0.611473
$566$	5.53511	0.232658
$567$	−20.4046	−0.856911
$568$	57.4885	2.41216
$569$	43.4456	1.82134	0.910668	−	0.413139i	$-0.135568\pi$
$569$	43.4456	1.82134	0.910668	+	0.413139i	$0.135568\pi$
$570$	−7.03922	−0.294840
$571$	−12.0931	−0.506079	−0.253040	−	0.967456i	$-0.581430\pi$
$571$	−12.0931	−0.506079	−0.253040	+	0.967456i	$0.581430\pi$
$572$	−33.1971	−1.38804
$573$	−4.53883	−0.189612
$574$	27.2060	1.13556
$575$	4.64738	0.193809
$576$	−5.21723	−0.217385
$577$	27.3145	1.13712	0.568559	−	0.822642i	$-0.307501\pi$
$577$	27.3145	1.13712	0.568559	+	0.822642i	$0.307501\pi$
$578$	25.5449	1.06253
$579$	2.24130	0.0931454
$580$	−59.2451	−2.46002
$581$	−54.9678	−2.28045
$582$	0.489687	0.0202982
$583$	−42.1800	−1.74692
$584$	39.3060	1.62649
$585$	−1.69906	−0.0702476
$586$	−69.5587	−2.87345
$587$	−23.6528	−0.976255	−0.488128	−	0.872772i	$-0.662320\pi$
$587$	−23.6528	−0.976255	−0.488128	+	0.872772i	$0.662320\pi$
$588$	34.3789	1.41776
$589$	−12.3797	−0.510098
$590$	−5.85092	−0.240879
$591$	3.85079	0.158400
$592$	61.7175	2.53657
$593$	5.32673	0.218743	0.109371	−	0.994001i	$-0.465116\pi$
$593$	5.32673	0.218743	0.109371	+	0.994001i	$0.465116\pi$
$594$	−63.6915	−2.61329
$595$	−12.1128	−0.496578
$596$	−44.9505	−1.84125
$597$	15.0781	0.617104
$598$	5.91138	0.241734
$599$	−10.6513	−0.435200	−0.217600	−	0.976038i	$-0.569823\pi$
$599$	−10.6513	−0.435200	−0.217600	+	0.976038i	$0.569823\pi$
$600$	34.9966	1.42873
$601$	−41.2415	−1.68228	−0.841139	−	0.540820i	$-0.818114\pi$
$601$	−41.2415	−1.68228	−0.841139	+	0.540820i	$0.818114\pi$
$602$	−102.374	−4.17247
$603$	−0.356876	−0.0145331
$604$	4.76876	0.194038
$605$	10.2982	0.418679
$606$	−66.1441	−2.68692
$607$	18.8857	0.766547	0.383273	−	0.923635i	$-0.374797\pi$
$607$	18.8857	0.766547	0.383273	+	0.923635i	$0.374797\pi$
$608$	−13.3236	−0.540344
$609$	−48.2779	−1.95632
$610$	39.3003	1.59122
$611$	3.05703	0.123674
$612$	10.3309	0.417602
$613$	−10.7188	−0.432928	−0.216464	−	0.976291i	$-0.569452\pi$
$613$	−10.7188	−0.432928	−0.216464	+	0.976291i	$0.569452\pi$
$614$	28.7943	1.16204
$615$	−5.89541	−0.237726
$616$	107.826	4.34444
$617$	−38.2334	−1.53922	−0.769609	−	0.638515i	$-0.779549\pi$
$617$	−38.2334	−1.53922	−0.769609	+	0.638515i	$0.779549\pi$
$618$	59.8034	2.40564
$619$	−12.0424	−0.484024	−0.242012	−	0.970273i	$-0.577807\pi$
$619$	−12.0424	−0.484024	−0.242012	+	0.970273i	$0.577807\pi$
$620$	−55.6347	−2.23434
$621$	7.99131	0.320680
$622$	−0.432858	−0.0173560
$623$	−34.5801	−1.38542
$624$	21.8737	0.875650
$625$	2.14389	0.0857555
$626$	88.4978	3.53709
$627$	−8.95231	−0.357521
$628$	−68.8118	−2.74589
$629$	−17.9442	−0.715481
$630$	9.50232	0.378581
$631$	−39.6422	−1.57813	−0.789065	−	0.614310i	$-0.789435\pi$
$631$	−39.6422	−1.57813	−0.789065	+	0.614310i	$0.789435\pi$
$632$	−19.7009	−0.783661
$633$	−35.1454	−1.39690
$634$	51.7548	2.05545
$635$	−1.57245	−0.0624008
$636$	68.6209	2.72099
$637$	7.80130	0.309099
$638$	−106.934	−4.23356
$639$	6.44312	0.254886
$640$	3.05934	0.120931
$641$	−35.5559	−1.40438	−0.702188	−	0.711992i	$-0.747793\pi$
$641$	−35.5559	−1.40438	−0.702188	+	0.711992i	$0.747793\pi$
$642$	48.2854	1.90567
$643$	10.1768	0.401335	0.200667	−	0.979659i	$-0.435689\pi$
$643$	10.1768	0.401335	0.200667	+	0.979659i	$0.435689\pi$
$644$	−23.2946	−0.917938
$645$	22.1841	0.873497
$646$	9.71242	0.382130
$647$	−32.6724	−1.28449	−0.642243	−	0.766501i	$-0.721996\pi$
$647$	−32.6724	−1.28449	−0.642243	+	0.766501i	$0.721996\pi$
$648$	42.7020	1.67749
$649$	−7.44106	−0.292087
$650$	13.6740	0.536339
$651$	−45.3359	−1.77685
$652$	102.971	4.03267
$653$	−45.5013	−1.78061	−0.890303	−	0.455369i	$-0.849507\pi$
$653$	−45.5013	−1.78061	−0.890303	+	0.455369i	$0.849507\pi$
$654$	47.5759	1.86037
$655$	−12.6761	−0.495295
$656$	−27.9771	−1.09232
$657$	4.40529	0.171867
$658$	−17.0970	−0.666511
$659$	22.6247	0.881335	0.440667	−	0.897670i	$-0.354742\pi$
$659$	22.6247	0.881335	0.440667	+	0.897670i	$0.354742\pi$
$660$	−40.2318	−1.56602
$661$	5.20283	0.202367	0.101183	−	0.994868i	$-0.467737\pi$
$661$	5.20283	0.202367	0.101183	+	0.994868i	$0.467737\pi$
$662$	−32.5768	−1.26613
$663$	−6.35972	−0.246991
$664$	115.035	4.46422
$665$	6.29457	0.244093
$666$	14.0769	0.545469
$667$	13.4169	0.519505
$668$	2.25824	0.0873741
$669$	−3.89672	−0.150656
$670$	−1.50779	−0.0582511
$671$	49.9811	1.92950
$672$	−48.7925	−1.88221
$673$	−11.2688	−0.434380	−0.217190	−	0.976129i	$-0.569689\pi$
$673$	−11.2688	−0.434380	−0.217190	+	0.976129i	$0.569689\pi$
$674$	−91.1923	−3.51260
$675$	18.4852	0.711497
$676$	−49.7633	−1.91397
$677$	30.4679	1.17098	0.585489	−	0.810681i	$-0.300903\pi$
$677$	30.4679	1.17098	0.585489	+	0.810681i	$0.300903\pi$
$678$	−42.6790	−1.63908
$679$	−0.437886	−0.0168045
$680$	25.3494	0.972103
$681$	20.2546	0.776158
$682$	−100.417	−3.84518
$683$	10.0579	0.384855	0.192428	−	0.981311i	$-0.438364\pi$
$683$	10.0579	0.384855	0.192428	+	0.981311i	$0.438364\pi$
$684$	−5.36857	−0.205273
$685$	4.89360	0.186975
$686$	19.1165	0.729872
$687$	−20.4612	−0.780644
$688$	105.276	4.01361
$689$	15.5715	0.593227
$690$	7.16405	0.272731
$691$	4.87401	0.185416	0.0927080	−	0.995693i	$-0.470448\pi$
$691$	4.87401	0.185416	0.0927080	+	0.995693i	$0.470448\pi$
$692$	90.2330	3.43014
$693$	12.0848	0.459064
$694$	−25.9052	−0.983348
$695$	−0.294728	−0.0111797
$696$	101.035	3.82970
$697$	8.13424	0.308106
$698$	14.6962	0.556258
$699$	17.9511	0.678972
$700$	−53.8844	−2.03664
$701$	31.7819	1.20039	0.600193	−	0.799855i	$-0.295090\pi$
$701$	31.7819	1.20039	0.600193	+	0.799855i	$0.295090\pi$
$702$	23.5129	0.887436
$703$	9.32490	0.351695
$704$	−28.0334	−1.05655
$705$	3.70485	0.139533
$706$	−44.6647	−1.68098
$707$	59.1471	2.22445
$708$	12.1055	0.454954
$709$	43.1464	1.62040	0.810199	−	0.586155i	$-0.199359\pi$
$709$	43.1464	1.62040	0.810199	+	0.586155i	$0.199359\pi$
$710$	27.2220	1.02162
$711$	−2.20802	−0.0828071
$712$	72.3681	2.71211
$713$	12.5993	0.471846
$714$	35.5679	1.33109
$715$	−9.12944	−0.341422
$716$	26.1545	0.977440
$717$	2.40229	0.0897153
$718$	11.9600	0.446343
$719$	−40.5854	−1.51358	−0.756790	−	0.653658i	$-0.773234\pi$
$719$	−40.5854	−1.51358	−0.756790	+	0.653658i	$0.773234\pi$
$720$	−9.77164	−0.364167
$721$	−53.4771	−1.99159
$722$	44.3918	1.65209
$723$	0.223200	0.00830090
$724$	59.4675	2.21009
$725$	31.0355	1.15263
$726$	−30.2393	−1.12229
$727$	41.3587	1.53391	0.766954	−	0.641702i	$-0.221771\pi$
$727$	41.3587	1.53391	0.766954	+	0.641702i	$0.221771\pi$
$728$	−39.8060	−1.47531
$729$	29.8273	1.10471
$730$	18.6122	0.688870
$731$	−30.6087	−1.13210
$732$	−81.3122	−3.00538
$733$	42.4747	1.56884	0.784419	−	0.620231i	$-0.212961\pi$
$733$	42.4747	1.56884	0.784419	+	0.620231i	$0.212961\pi$
$734$	−51.0537	−1.88443
$735$	9.45445	0.348733
$736$	13.5599	0.499825
$737$	−1.91757	−0.0706347
$738$	−6.38118	−0.234895
$739$	29.2367	1.07549	0.537744	−	0.843108i	$-0.319277\pi$
$739$	29.2367	1.07549	0.537744	+	0.843108i	$0.319277\pi$
$740$	41.9063	1.54050
$741$	3.30490	0.121409
$742$	−87.0865	−3.19705
$743$	21.3907	0.784750	0.392375	−	0.919805i	$-0.371653\pi$
$743$	21.3907	0.784750	0.392375	+	0.919805i	$0.371653\pi$
$744$	94.8775	3.47838
$745$	−12.3617	−0.452899
$746$	−47.2662	−1.73054
$747$	12.8928	0.471721
$748$	55.5102	2.02965
$749$	−43.1775	−1.57767
$750$	41.8430	1.52789
$751$	45.7959	1.67112	0.835558	−	0.549402i	$-0.185144\pi$
$751$	45.7959	1.67112	0.835558	+	0.549402i	$0.185144\pi$
$752$	17.5816	0.641135
$753$	6.57865	0.239739
$754$	39.4766	1.43765
$755$	1.31144	0.0477283
$756$	−92.6558	−3.36986
$757$	−42.7929	−1.55533	−0.777667	−	0.628677i	$-0.783597\pi$
$757$	−42.7929	−1.55533	−0.777667	+	0.628677i	$0.783597\pi$
$758$	76.1973	2.76761
$759$	9.11107	0.330711
$760$	−13.1731	−0.477838
$761$	6.55615	0.237660	0.118830	−	0.992915i	$-0.462086\pi$
$761$	6.55615	0.237660	0.118830	+	0.992915i	$0.462086\pi$
$762$	4.61731	0.167268
$763$	−42.5431	−1.54016
$764$	−14.6252	−0.529122
$765$	2.84107	0.102719
$766$	−17.8835	−0.646158
$767$	2.74700	0.0991885
$768$	−28.1029	−1.01407
$769$	25.8243	0.931246	0.465623	−	0.884983i	$-0.345830\pi$
$769$	25.8243	0.931246	0.465623	+	0.884983i	$0.345830\pi$
$770$	51.0580	1.84000
$771$	−32.3037	−1.16339
$772$	7.22203	0.259927
$773$	−41.8808	−1.50635	−0.753174	−	0.657822i	$-0.771478\pi$
$773$	−41.8808	−1.50635	−0.753174	+	0.657822i	$0.771478\pi$
$774$	24.0120	0.863093
$775$	29.1442	1.04689
$776$	0.916393	0.0328966
$777$	34.1488	1.22508
$778$	7.71353	0.276543
$779$	−4.22706	−0.151450
$780$	14.8523	0.531797
$781$	34.6203	1.23881
$782$	−9.88466	−0.353475
$783$	53.3665	1.90716
$784$	44.8667	1.60238
$785$	−18.9238	−0.675418
$786$	37.2218	1.32766
$787$	1.46512	0.0522259	0.0261129	−	0.999659i	$-0.491687\pi$
$787$	1.46512	0.0522259	0.0261129	+	0.999659i	$0.491687\pi$
$788$	12.4082	0.442023
$789$	−17.6238	−0.627424
$790$	−9.32882	−0.331904
$791$	38.1642	1.35696
$792$	−25.2907	−0.898667
$793$	−18.4514	−0.655230
$794$	−28.8211	−1.02282
$795$	18.8712	0.669294
$796$	48.5852	1.72206
$797$	−2.22341	−0.0787572	−0.0393786	−	0.999224i	$-0.512538\pi$
$797$	−2.22341	−0.0787572	−0.0393786	+	0.999224i	$0.512538\pi$
$798$	−18.4833	−0.654301
$799$	−5.11179	−0.180842
$800$	31.3663	1.10897
$801$	8.11078	0.286580
$802$	35.3131	1.24695
$803$	23.6706	0.835317
$804$	3.11962	0.110020
$805$	−6.40620	−0.225789
$806$	37.0709	1.30577
$807$	33.5047	1.17942
$808$	−123.781	−4.35461
$809$	−1.45886	−0.0512908	−0.0256454	−	0.999671i	$-0.508164\pi$
$809$	−1.45886	−0.0512908	−0.0256454	+	0.999671i	$0.508164\pi$
$810$	20.2203	0.710470
$811$	−8.64314	−0.303502	−0.151751	−	0.988419i	$-0.548491\pi$
$811$	−8.64314	−0.303502	−0.151751	+	0.988419i	$0.548491\pi$
$812$	−155.563	−5.45920
$813$	28.1533	0.987379
$814$	75.6384	2.65112
$815$	28.3179	0.991932
$816$	−36.5760	−1.28042
$817$	15.9061	0.556486
$818$	−37.6269	−1.31559
$819$	−4.46133	−0.155891
$820$	−18.9965	−0.663385
$821$	23.7587	0.829185	0.414592	−	0.910007i	$-0.363924\pi$
$821$	23.7587	0.829185	0.414592	+	0.910007i	$0.363924\pi$
$822$	−14.3695	−0.501193
$823$	−42.8423	−1.49339	−0.746694	−	0.665167i	$-0.768360\pi$
$823$	−42.8423	−1.49339	−0.746694	+	0.665167i	$0.768360\pi$
$824$	111.915	3.89875
$825$	21.0754	0.733752
$826$	−15.3631	−0.534550
$827$	−14.3999	−0.500733	−0.250367	−	0.968151i	$-0.580551\pi$
$827$	−14.3999	−0.500733	−0.250367	+	0.968151i	$0.580551\pi$
$828$	5.46378	0.189879
$829$	−46.3832	−1.61095	−0.805477	−	0.592627i	$-0.798091\pi$
$829$	−46.3832	−1.61095	−0.805477	+	0.592627i	$0.798091\pi$
$830$	54.4715	1.89073
$831$	2.50743	0.0869819
$832$	10.3490	0.358787
$833$	−13.0449	−0.451978
$834$	0.865434	0.0299675
$835$	0.621034	0.0214918
$836$	−28.8465	−0.997678
$837$	50.1144	1.73221
$838$	−78.5506	−2.71348
$839$	18.0317	0.622524	0.311262	−	0.950324i	$-0.399248\pi$
$839$	18.0317	0.622524	0.311262	+	0.950324i	$0.399248\pi$
$840$	−48.2412	−1.66448
$841$	60.5990	2.08962
$842$	−88.7137	−3.05728
$843$	−17.3492	−0.597538
$844$	−113.247	−3.89812
$845$	−13.6853	−0.470787
$846$	4.01012	0.137871
$847$	27.0404	0.929121
$848$	89.5548	3.07532
$849$	−3.14942	−0.108088
$850$	−22.8649	−0.784259
$851$	−9.49027	−0.325322
$852$	−56.3223	−1.92957
$853$	24.3943	0.835245	0.417623	−	0.908621i	$-0.362863\pi$
$853$	24.3943	0.835245	0.417623	+	0.908621i	$0.362863\pi$
$854$	103.193	3.53119
$855$	−1.47640	−0.0504917
$856$	90.3606	3.08846
$857$	−18.6142	−0.635848	−0.317924	−	0.948116i	$-0.602986\pi$
$857$	−18.6142	−0.635848	−0.317924	+	0.948116i	$0.602986\pi$
$858$	26.8075	0.915194
$859$	11.9363	0.407262	0.203631	−	0.979048i	$-0.434726\pi$
$859$	11.9363	0.407262	0.203631	+	0.979048i	$0.434726\pi$
$860$	71.4825	2.43753
$861$	−15.4799	−0.527554
$862$	17.0866	0.581972
$863$	−34.0880	−1.16037	−0.580184	−	0.814485i	$-0.697019\pi$
$863$	−34.0880	−1.16037	−0.580184	+	0.814485i	$0.697019\pi$
$864$	53.9353	1.83492
$865$	24.8147	0.843726
$866$	24.4479	0.830773
$867$	−14.5348	−0.493628
$868$	−146.083	−4.95839
$869$	−11.8642	−0.402464
$870$	47.8420	1.62200
$871$	0.707907	0.0239865
$872$	89.0329	3.01503
$873$	0.102706	0.00347609
$874$	5.13668	0.173751
$875$	−37.4166	−1.26491
$876$	−38.5087	−1.30109
$877$	12.6060	0.425676	0.212838	−	0.977088i	$-0.431729\pi$
$877$	12.6060	0.425676	0.212838	+	0.977088i	$0.431729\pi$
$878$	−59.1411	−1.99591
$879$	39.5782	1.33494
$880$	−52.5052	−1.76995
$881$	20.9995	0.707491	0.353745	−	0.935342i	$-0.384908\pi$
$881$	20.9995	0.707491	0.353745	+	0.935342i	$0.384908\pi$
$882$	10.2335	0.344579
$883$	−40.6386	−1.36760	−0.683799	−	0.729670i	$-0.739674\pi$
$883$	−40.6386	−1.36760	−0.683799	+	0.729670i	$0.739674\pi$
$884$	−20.4926	−0.689240
$885$	3.32911	0.111907
$886$	−46.2730	−1.55457
$887$	29.8058	1.00078	0.500390	−	0.865800i	$-0.333190\pi$
$887$	29.8058	1.00078	0.500390	+	0.865800i	$0.333190\pi$
$888$	−71.4655	−2.39822
$889$	−4.12887	−0.138478
$890$	34.2678	1.14866
$891$	25.7157	0.861509
$892$	−12.5562	−0.420412
$893$	2.65640	0.0888932
$894$	36.2988	1.21401
$895$	7.19268	0.240425
$896$	8.03308	0.268367
$897$	−3.36351	−0.112304
$898$	−4.30343	−0.143607
$899$	84.1388	2.80619
$900$	12.6386	0.421288
$901$	−26.0378	−0.867444
$902$	−34.2875	−1.14165
$903$	58.2499	1.93844
$904$	−79.8688	−2.65640
$905$	16.3540	0.543625
$906$	−3.85090	−0.127938
$907$	7.29489	0.242223	0.121111	−	0.992639i	$-0.461354\pi$
$907$	7.29489	0.242223	0.121111	+	0.992639i	$0.461354\pi$
$908$	65.2653	2.16591
$909$	−13.8730	−0.460138
$910$	−18.8490	−0.624838
$911$	−41.9506	−1.38989	−0.694943	−	0.719065i	$-0.744570\pi$
$911$	−41.9506	−1.38989	−0.694943	+	0.719065i	$0.744570\pi$
$912$	19.0071	0.629389
$913$	69.2756	2.29269
$914$	101.624	3.36141
$915$	−22.3614	−0.739246
$916$	−65.9310	−2.17842
$917$	−33.2843	−1.09914
$918$	−39.3168	−1.29765
$919$	16.6118	0.547971	0.273986	−	0.961734i	$-0.411658\pi$
$919$	16.6118	0.547971	0.273986	+	0.961734i	$0.411658\pi$
$920$	13.4067	0.442006
$921$	−16.3837	−0.539861
$922$	−58.8776	−1.93903
$923$	−12.7807	−0.420682
$924$	−105.639	−3.47527
$925$	−21.9526	−0.721796
$926$	−95.0714	−3.12424
$927$	12.5431	0.411969
$928$	90.5540	2.97258
$929$	−8.29258	−0.272071	−0.136035	−	0.990704i	$-0.543436\pi$
$929$	−8.29258	−0.272071	−0.136035	+	0.990704i	$0.543436\pi$
$930$	44.9265	1.47320
$931$	6.77892	0.222170
$932$	57.8428	1.89470
$933$	0.246292	0.00806323
$934$	96.8026	3.16748
$935$	15.2657	0.499242
$936$	9.33653	0.305174
$937$	−39.6407	−1.29500	−0.647502	−	0.762063i	$-0.724186\pi$
$937$	−39.6407	−1.29500	−0.647502	+	0.762063i	$0.724186\pi$
$938$	−3.95909	−0.129269
$939$	−50.3543	−1.64325
$940$	11.9379	0.389372
$941$	33.5679	1.09428	0.547141	−	0.837040i	$-0.315716\pi$
$941$	33.5679	1.09428	0.547141	+	0.837040i	$0.315716\pi$
$942$	55.5674	1.81048
$943$	4.30202	0.140093
$944$	15.7985	0.514198
$945$	−25.4810	−0.828898
$946$	129.022	4.19486
$947$	−6.22150	−0.202172	−0.101086	−	0.994878i	$-0.532232\pi$
$947$	−6.22150	−0.202172	−0.101086	+	0.994878i	$0.532232\pi$
$948$	19.3013	0.626877
$949$	−8.73842	−0.283661
$950$	11.8820	0.385503
$951$	−29.4479	−0.954915
$952$	66.5612	2.15726
$953$	29.0411	0.940732	0.470366	−	0.882471i	$-0.344122\pi$
$953$	29.0411	0.940732	0.470366	+	0.882471i	$0.344122\pi$
$954$	20.4262	0.661323
$955$	−4.02204	−0.130150
$956$	7.74078	0.250355
$957$	60.8443	1.96682
$958$	32.2778	1.04285
$959$	12.8494	0.414928
$960$	12.5421	0.404793
$961$	48.0114	1.54875
$962$	−27.9233	−0.900282
$963$	10.1273	0.326348
$964$	0.719205	0.0231640
$965$	1.98611	0.0639352
$966$	18.8110	0.605236
$967$	34.5250	1.11025	0.555125	−	0.831767i	$-0.312670\pi$
$967$	34.5250	1.11025	0.555125	+	0.831767i	$0.312670\pi$
$968$	−56.5894	−1.81885
$969$	−5.52627	−0.177529
$970$	0.433932	0.0139327
$971$	−14.1435	−0.453885	−0.226943	−	0.973908i	$-0.572873\pi$
$971$	−14.1435	−0.453885	−0.226943	+	0.973908i	$0.572873\pi$
$972$	38.8537	1.24623
$973$	−0.773884	−0.0248096
$974$	73.2759	2.34791
$975$	−7.78037	−0.249171
$976$	−106.118	−3.39674
$977$	25.1451	0.804463	0.402232	−	0.915538i	$-0.368235\pi$
$977$	25.1451	0.804463	0.402232	+	0.915538i	$0.368235\pi$
$978$	−83.1521	−2.65891
$979$	43.5810	1.39286
$980$	30.4646	0.973155
$981$	9.97852	0.318590
$982$	81.3858	2.59712
$983$	−10.0409	−0.320254	−0.160127	−	0.987096i	$-0.551190\pi$
$983$	−10.0409	−0.320254	−0.160127	+	0.987096i	$0.551190\pi$
$984$	32.3959	1.03274
$985$	3.41234	0.108726
$986$	−66.0105	−2.10220
$987$	9.72802	0.309646
$988$	10.6492	0.338797
$989$	−16.1882	−0.514756
$990$	−11.9757	−0.380613
$991$	−29.1337	−0.925461	−0.462731	−	0.886499i	$-0.653130\pi$
$991$	−29.1337	−0.925461	−0.462731	+	0.886499i	$0.653130\pi$
$992$	85.0356	2.69988
$993$	18.5359	0.588218
$994$	71.4784	2.26716
$995$	13.3613	0.423581
$996$	−112.701	−3.57108
$997$	4.72192	0.149545	0.0747724	−	0.997201i	$-0.476177\pi$
$997$	4.72192	0.149545	0.0747724	+	0.997201i	$0.476177\pi$
$998$	79.6209	2.52036
$999$	−37.7481	−1.19430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.9	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.9	✓	152	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60205 q^{2} +1.48054 q^{3} +4.77066 q^{4} +1.31197 q^{5} -3.85243 q^{6} +3.44490 q^{7} -7.20939 q^{8} -0.808005 q^{9} +O(q^{10})\)	\(q-2.60205 q^{2} +1.48054 q^{3} +4.77066 q^{4} +1.31197 q^{5} -3.85243 q^{6} +3.44490 q^{7} -7.20939 q^{8} -0.808005 q^{9} -3.41380 q^{10} -4.34159 q^{11} +7.06314 q^{12} +1.60278 q^{13} -8.96381 q^{14} +1.94242 q^{15} +9.21787 q^{16} -2.68007 q^{17} +2.10247 q^{18} +1.39273 q^{19} +6.25894 q^{20} +5.10031 q^{21} +11.2970 q^{22} -1.41743 q^{23} -10.6738 q^{24} -3.27874 q^{25} -4.17050 q^{26} -5.63790 q^{27} +16.4345 q^{28} -9.46568 q^{29} -5.05426 q^{30} -8.88883 q^{31} -9.56656 q^{32} -6.42789 q^{33} +6.97367 q^{34} +4.51960 q^{35} -3.85472 q^{36} +6.69542 q^{37} -3.62395 q^{38} +2.37297 q^{39} -9.45848 q^{40} -3.03509 q^{41} -13.2713 q^{42} +11.4209 q^{43} -20.7122 q^{44} -1.06008 q^{45} +3.68821 q^{46} +1.90734 q^{47} +13.6474 q^{48} +4.86737 q^{49} +8.53145 q^{50} -3.96794 q^{51} +7.64630 q^{52} +9.71534 q^{53} +14.6701 q^{54} -5.69602 q^{55} -24.8357 q^{56} +2.06199 q^{57} +24.6302 q^{58} +1.71390 q^{59} +9.26661 q^{60} -11.5122 q^{61} +23.1292 q^{62} -2.78350 q^{63} +6.45693 q^{64} +2.10279 q^{65} +16.7257 q^{66} +0.441675 q^{67} -12.7857 q^{68} -2.09856 q^{69} -11.7602 q^{70} -7.97411 q^{71} +5.82522 q^{72} -5.45206 q^{73} -17.4218 q^{74} -4.85431 q^{75} +6.64423 q^{76} -14.9564 q^{77} -6.17459 q^{78} +2.73268 q^{79} +12.0935 q^{80} -5.92311 q^{81} +7.89745 q^{82} -15.9563 q^{83} +24.3319 q^{84} -3.51616 q^{85} -29.7176 q^{86} -14.0143 q^{87} +31.3002 q^{88} -10.0380 q^{89} +2.75837 q^{90} +5.52141 q^{91} -6.76206 q^{92} -13.1603 q^{93} -4.96299 q^{94} +1.82721 q^{95} -14.1637 q^{96} -0.127111 q^{97} -12.6651 q^{98} +3.50803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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