LMFDB - Embedded newform 8007.2.a.e.1.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.42
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23259 q^{2} +1.00000 q^{3} +2.98445 q^{4} -0.174718 q^{5} +2.23259 q^{6} -0.387530 q^{7} +2.19786 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.23259 q^{2} +1.00000 q^{3} +2.98445 q^{4} -0.174718 q^{5} +2.23259 q^{6} -0.387530 q^{7} +2.19786 q^{8} +1.00000 q^{9} -0.390073 q^{10} +1.83040 q^{11} +2.98445 q^{12} -4.67279 q^{13} -0.865195 q^{14} -0.174718 q^{15} -1.06197 q^{16} -1.00000 q^{17} +2.23259 q^{18} -7.51260 q^{19} -0.521436 q^{20} -0.387530 q^{21} +4.08653 q^{22} -2.76489 q^{23} +2.19786 q^{24} -4.96947 q^{25} -10.4324 q^{26} +1.00000 q^{27} -1.15656 q^{28} -6.05264 q^{29} -0.390073 q^{30} -3.90678 q^{31} -6.76667 q^{32} +1.83040 q^{33} -2.23259 q^{34} +0.0677085 q^{35} +2.98445 q^{36} +1.19030 q^{37} -16.7725 q^{38} -4.67279 q^{39} -0.384006 q^{40} +11.2232 q^{41} -0.865195 q^{42} +1.65444 q^{43} +5.46274 q^{44} -0.174718 q^{45} -6.17287 q^{46} -3.93966 q^{47} -1.06197 q^{48} -6.84982 q^{49} -11.0948 q^{50} -1.00000 q^{51} -13.9457 q^{52} -2.61934 q^{53} +2.23259 q^{54} -0.319804 q^{55} -0.851737 q^{56} -7.51260 q^{57} -13.5130 q^{58} -3.30964 q^{59} -0.521436 q^{60} -12.5452 q^{61} -8.72222 q^{62} -0.387530 q^{63} -12.9832 q^{64} +0.816420 q^{65} +4.08653 q^{66} +2.07176 q^{67} -2.98445 q^{68} -2.76489 q^{69} +0.151165 q^{70} +13.5519 q^{71} +2.19786 q^{72} +3.09711 q^{73} +2.65745 q^{74} -4.96947 q^{75} -22.4210 q^{76} -0.709336 q^{77} -10.4324 q^{78} +15.7351 q^{79} +0.185546 q^{80} +1.00000 q^{81} +25.0567 q^{82} -3.50148 q^{83} -1.15656 q^{84} +0.174718 q^{85} +3.69367 q^{86} -6.05264 q^{87} +4.02297 q^{88} +2.66818 q^{89} -0.390073 q^{90} +1.81085 q^{91} -8.25167 q^{92} -3.90678 q^{93} -8.79563 q^{94} +1.31259 q^{95} -6.76667 q^{96} +12.6146 q^{97} -15.2928 q^{98} +1.83040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	2.23259	1.57868	0.789339	−	0.613958i	$-0.210424\pi$
$2$	2.23259	1.57868	0.789339	+	0.613958i	$0.210424\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.98445	1.49222
$5$	−0.174718	−0.0781363	−0.0390681	−	0.999237i	$-0.512439\pi$
$5$	−0.174718	−0.0781363	−0.0390681	+	0.999237i	$0.512439\pi$
$6$	2.23259	0.911450
$7$	−0.387530	−0.146473	−0.0732363	−	0.997315i	$-0.523333\pi$
$7$	−0.387530	−0.146473	−0.0732363	+	0.997315i	$0.523333\pi$
$8$	2.19786	0.777061
$9$	1.00000	0.333333
$10$	−0.390073	−0.123352
$11$	1.83040	0.551887	0.275944	−	0.961174i	$-0.411010\pi$
$11$	1.83040	0.551887	0.275944	+	0.961174i	$0.411010\pi$
$12$	2.98445	0.861535
$13$	−4.67279	−1.29600	−0.647999	−	0.761641i	$-0.724394\pi$
$13$	−4.67279	−1.29600	−0.647999	+	0.761641i	$0.724394\pi$
$14$	−0.865195	−0.231233
$15$	−0.174718	−0.0451120
$16$	−1.06197	−0.265494
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.23259	0.526226
$19$	−7.51260	−1.72351	−0.861755	−	0.507326i	$-0.830634\pi$
$19$	−7.51260	−1.72351	−0.861755	+	0.507326i	$0.830634\pi$
$20$	−0.521436	−0.116597
$21$	−0.387530	−0.0845660
$22$	4.08653	0.871252
$23$	−2.76489	−0.576520	−0.288260	−	0.957552i	$-0.593077\pi$
$23$	−2.76489	−0.576520	−0.288260	+	0.957552i	$0.593077\pi$
$24$	2.19786	0.448637
$25$	−4.96947	−0.993895
$26$	−10.4324	−2.04596
$27$	1.00000	0.192450
$28$	−1.15656	−0.218570
$29$	−6.05264	−1.12395	−0.561973	−	0.827155i	$-0.689958\pi$
$29$	−6.05264	−1.12395	−0.561973	+	0.827155i	$0.689958\pi$
$30$	−0.390073	−0.0712173
$31$	−3.90678	−0.701678	−0.350839	−	0.936436i	$-0.614103\pi$
$31$	−3.90678	−0.701678	−0.350839	+	0.936436i	$0.614103\pi$
$32$	−6.76667	−1.19619
$33$	1.83040	0.318632
$34$	−2.23259	−0.382886
$35$	0.0677085	0.0114448
$36$	2.98445	0.497408
$37$	1.19030	0.195685	0.0978423	−	0.995202i	$-0.468806\pi$
$37$	1.19030	0.195685	0.0978423	+	0.995202i	$0.468806\pi$
$38$	−16.7725	−2.72087
$39$	−4.67279	−0.748245
$40$	−0.384006	−0.0607167
$41$	11.2232	1.75277	0.876384	−	0.481613i	$-0.159949\pi$
$41$	11.2232	1.75277	0.876384	+	0.481613i	$0.159949\pi$
$42$	−0.865195	−0.133502
$43$	1.65444	0.252299	0.126150	−	0.992011i	$-0.459738\pi$
$43$	1.65444	0.252299	0.126150	+	0.992011i	$0.459738\pi$
$44$	5.46274	0.823538
$45$	−0.174718	−0.0260454
$46$	−6.17287	−0.910139
$47$	−3.93966	−0.574658	−0.287329	−	0.957832i	$-0.592767\pi$
$47$	−3.93966	−0.574658	−0.287329	+	0.957832i	$0.592767\pi$
$48$	−1.06197	−0.153283
$49$	−6.84982	−0.978546
$50$	−11.0948	−1.56904
$51$	−1.00000	−0.140028
$52$	−13.9457	−1.93392
$53$	−2.61934	−0.359794	−0.179897	−	0.983685i	$-0.557576\pi$
$53$	−2.61934	−0.359794	−0.179897	+	0.983685i	$0.557576\pi$
$54$	2.23259	0.303817
$55$	−0.319804	−0.0431224
$56$	−0.851737	−0.113818
$57$	−7.51260	−0.995068
$58$	−13.5130	−1.77435
$59$	−3.30964	−0.430878	−0.215439	−	0.976517i	$-0.569118\pi$
$59$	−3.30964	−0.430878	−0.215439	+	0.976517i	$0.569118\pi$
$60$	−0.521436	−0.0673171
$61$	−12.5452	−1.60624	−0.803122	−	0.595814i	$-0.796829\pi$
$61$	−12.5452	−1.60624	−0.803122	+	0.595814i	$0.796829\pi$
$62$	−8.72222	−1.10772
$63$	−0.387530	−0.0488242
$64$	−12.9832	−1.62290
$65$	0.816420	0.101264
$66$	4.08653	0.503017
$67$	2.07176	0.253105	0.126553	−	0.991960i	$-0.459609\pi$
$67$	2.07176	0.253105	0.126553	+	0.991960i	$0.459609\pi$
$68$	−2.98445	−0.361917
$69$	−2.76489	−0.332854
$70$	0.151165	0.0180677
$71$	13.5519	1.60832	0.804159	−	0.594414i	$-0.202616\pi$
$71$	13.5519	1.60832	0.804159	+	0.594414i	$0.202616\pi$
$72$	2.19786	0.259020
$73$	3.09711	0.362489	0.181244	−	0.983438i	$-0.441988\pi$
$73$	3.09711	0.362489	0.181244	+	0.983438i	$0.441988\pi$
$74$	2.65745	0.308923
$75$	−4.96947	−0.573825
$76$	−22.4210	−2.57186
$77$	−0.709336	−0.0808363
$78$	−10.4324	−1.18124
$79$	15.7351	1.77033	0.885167	−	0.465273i	$-0.154044\pi$
$79$	15.7351	1.77033	0.885167	+	0.465273i	$0.154044\pi$
$80$	0.185546	0.0207447
$81$	1.00000	0.111111
$82$	25.0567	2.76705
$83$	−3.50148	−0.384337	−0.192169	−	0.981362i	$-0.561552\pi$
$83$	−3.50148	−0.384337	−0.192169	+	0.981362i	$0.561552\pi$
$84$	−1.15656	−0.126191
$85$	0.174718	0.0189508
$86$	3.69367	0.398299
$87$	−6.05264	−0.648911
$88$	4.02297	0.428850
$89$	2.66818	0.282827	0.141413	−	0.989951i	$-0.454835\pi$
$89$	2.66818	0.282827	0.141413	+	0.989951i	$0.454835\pi$
$90$	−0.390073	−0.0411173
$91$	1.81085	0.189828
$92$	−8.25167	−0.860296
$93$	−3.90678	−0.405114
$94$	−8.79563	−0.907200
$95$	1.31259	0.134669
$96$	−6.76667	−0.690621
$97$	12.6146	1.28082	0.640410	−	0.768033i	$-0.278764\pi$
$97$	12.6146	1.28082	0.640410	+	0.768033i	$0.278764\pi$
$98$	−15.2928	−1.54481
$99$	1.83040	0.183962
$100$	−14.8311	−1.48311
$101$	18.1840	1.80937	0.904686	−	0.426080i	$-0.140106\pi$
$101$	18.1840	1.80937	0.904686	+	0.426080i	$0.140106\pi$
$102$	−2.23259	−0.221059
$103$	17.2970	1.70432	0.852161	−	0.523279i	$-0.175292\pi$
$103$	17.2970	1.70432	0.852161	+	0.523279i	$0.175292\pi$
$104$	−10.2701	−1.00707
$105$	0.0677085	0.00660767
$106$	−5.84791	−0.567999
$107$	−1.21689	−0.117641	−0.0588205	−	0.998269i	$-0.518734\pi$
$107$	−1.21689	−0.117641	−0.0588205	+	0.998269i	$0.518734\pi$
$108$	2.98445	0.287178
$109$	2.01833	0.193321	0.0966606	−	0.995317i	$-0.469184\pi$
$109$	2.01833	0.193321	0.0966606	+	0.995317i	$0.469184\pi$
$110$	−0.713991	−0.0680763
$111$	1.19030	0.112979
$112$	0.411547	0.0388875
$113$	5.36608	0.504798	0.252399	−	0.967623i	$-0.418780\pi$
$113$	5.36608	0.504798	0.252399	+	0.967623i	$0.418780\pi$
$114$	−16.7725	−1.57089
$115$	0.483077	0.0450471
$116$	−18.0638	−1.67718
$117$	−4.67279	−0.431999
$118$	−7.38906	−0.680218
$119$	0.387530	0.0355248
$120$	−0.384006	−0.0350548
$121$	−7.64963	−0.695421
$122$	−28.0082	−2.53574
$123$	11.2232	1.01196
$124$	−11.6596	−1.04706
$125$	1.74185	0.155795
$126$	−0.865195	−0.0770777
$127$	−21.1544	−1.87715	−0.938574	−	0.345077i	$-0.887853\pi$
$127$	−21.1544	−1.87715	−0.938574	+	0.345077i	$0.887853\pi$
$128$	−15.4529	−1.36585
$129$	1.65444	0.145665
$130$	1.82273	0.159864
$131$	2.57203	0.224719	0.112360	−	0.993668i	$-0.464159\pi$
$131$	2.57203	0.224719	0.112360	+	0.993668i	$0.464159\pi$
$132$	5.46274	0.475470
$133$	2.91136	0.252447
$134$	4.62537	0.399572
$135$	−0.174718	−0.0150373
$136$	−2.19786	−0.188465
$137$	−14.5653	−1.24440	−0.622201	−	0.782858i	$-0.713761\pi$
$137$	−14.5653	−1.24440	−0.622201	+	0.782858i	$0.713761\pi$
$138$	−6.17287	−0.525469
$139$	−11.4520	−0.971346	−0.485673	−	0.874141i	$-0.661425\pi$
$139$	−11.4520	−0.971346	−0.485673	+	0.874141i	$0.661425\pi$
$140$	0.202072	0.0170782
$141$	−3.93966	−0.331779
$142$	30.2559	2.53902
$143$	−8.55308	−0.715244
$144$	−1.06197	−0.0884979
$145$	1.05750	0.0878210
$146$	6.91456	0.572253
$147$	−6.84982	−0.564964
$148$	3.55239	0.292005
$149$	14.9386	1.22382	0.611910	−	0.790927i	$-0.290401\pi$
$149$	14.9386	1.22382	0.611910	+	0.790927i	$0.290401\pi$
$150$	−11.0948	−0.905885
$151$	−23.4818	−1.91092	−0.955462	−	0.295114i	$-0.904642\pi$
$151$	−23.4818	−1.91092	−0.955462	+	0.295114i	$0.904642\pi$
$152$	−16.5117	−1.33927
$153$	−1.00000	−0.0808452
$154$	−1.58365	−0.127614
$155$	0.682584	0.0548265
$156$	−13.9457	−1.11655
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	35.1299	2.79479
$159$	−2.61934	−0.207727
$160$	1.18226	0.0934658
$161$	1.07148	0.0844444
$162$	2.23259	0.175409
$163$	−22.8590	−1.79046	−0.895228	−	0.445607i	$-0.852988\pi$
$163$	−22.8590	−1.79046	−0.895228	+	0.445607i	$0.852988\pi$
$164$	33.4950	2.61552
$165$	−0.319804	−0.0248967
$166$	−7.81736	−0.606745
$167$	2.89366	0.223918	0.111959	−	0.993713i	$-0.464287\pi$
$167$	2.89366	0.223918	0.111959	+	0.993713i	$0.464287\pi$
$168$	−0.851737	−0.0657129
$169$	8.83494	0.679611
$170$	0.390073	0.0299172
$171$	−7.51260	−0.574503
$172$	4.93757	0.376487
$173$	0.291828	0.0221873	0.0110936	−	0.999938i	$-0.496469\pi$
$173$	0.291828	0.0221873	0.0110936	+	0.999938i	$0.496469\pi$
$174$	−13.5130	−1.02442
$175$	1.92582	0.145578
$176$	−1.94384	−0.146523
$177$	−3.30964	−0.248768
$178$	5.95695	0.446492
$179$	1.02169	0.0763648	0.0381824	−	0.999271i	$-0.487843\pi$
$179$	1.02169	0.0763648	0.0381824	+	0.999271i	$0.487843\pi$
$180$	−0.521436	−0.0388656
$181$	10.1013	0.750822	0.375411	−	0.926858i	$-0.377502\pi$
$181$	10.1013	0.750822	0.375411	+	0.926858i	$0.377502\pi$
$182$	4.04287	0.299677
$183$	−12.5452	−0.927366
$184$	−6.07685	−0.447991
$185$	−0.207967	−0.0152901
$186$	−8.72222	−0.639544
$187$	−1.83040	−0.133852
$188$	−11.7577	−0.857518
$189$	−0.387530	−0.0281887
$190$	2.93046	0.212598
$191$	21.2555	1.53799	0.768995	−	0.639254i	$-0.220757\pi$
$191$	21.2555	1.53799	0.768995	+	0.639254i	$0.220757\pi$
$192$	−12.9832	−0.936985
$193$	−9.59480	−0.690649	−0.345324	−	0.938483i	$-0.612231\pi$
$193$	−9.59480	−0.690649	−0.345324	+	0.938483i	$0.612231\pi$
$194$	28.1632	2.02200
$195$	0.816420	0.0584650
$196$	−20.4429	−1.46021
$197$	6.48101	0.461753	0.230877	−	0.972983i	$-0.425841\pi$
$197$	6.48101	0.461753	0.230877	+	0.972983i	$0.425841\pi$
$198$	4.08653	0.290417
$199$	14.6924	1.04151	0.520757	−	0.853705i	$-0.325650\pi$
$199$	14.6924	1.04151	0.520757	+	0.853705i	$0.325650\pi$
$200$	−10.9222	−0.772317
$201$	2.07176	0.146130
$202$	40.5973	2.85641
$203$	2.34558	0.164627
$204$	−2.98445	−0.208953
$205$	−1.96089	−0.136955
$206$	38.6170	2.69058
$207$	−2.76489	−0.192173
$208$	4.96238	0.344079
$209$	−13.7511	−0.951182
$210$	0.151165	0.0104314
$211$	1.47601	0.101613	0.0508064	−	0.998709i	$-0.483821\pi$
$211$	1.47601	0.101613	0.0508064	+	0.998709i	$0.483821\pi$
$212$	−7.81728	−0.536893
$213$	13.5519	0.928563
$214$	−2.71681	−0.185717
$215$	−0.289060	−0.0197137
$216$	2.19786	0.149546
$217$	1.51399	0.102777
$218$	4.50610	0.305192
$219$	3.09711	0.209283
$220$	−0.954438	−0.0643482
$221$	4.67279	0.314326
$222$	2.65745	0.178357
$223$	−25.2295	−1.68950	−0.844748	−	0.535165i	$-0.820250\pi$
$223$	−25.2295	−1.68950	−0.844748	+	0.535165i	$0.820250\pi$
$224$	2.62229	0.175209
$225$	−4.96947	−0.331298
$226$	11.9802	0.796914
$227$	25.8575	1.71622	0.858110	−	0.513466i	$-0.171639\pi$
$227$	25.8575	1.71622	0.858110	+	0.513466i	$0.171639\pi$
$228$	−22.4210	−1.48486
$229$	11.7716	0.777892	0.388946	−	0.921261i	$-0.372839\pi$
$229$	11.7716	0.777892	0.388946	+	0.921261i	$0.372839\pi$
$230$	1.07851	0.0711149
$231$	−0.709336	−0.0466709
$232$	−13.3029	−0.873375
$233$	−0.612270	−0.0401111	−0.0200556	−	0.999799i	$-0.506384\pi$
$233$	−0.612270	−0.0401111	−0.0200556	+	0.999799i	$0.506384\pi$
$234$	−10.4324	−0.681988
$235$	0.688329	0.0449016
$236$	−9.87744	−0.642966
$237$	15.7351	1.02210
$238$	0.865195	0.0560822
$239$	−0.540676	−0.0349734	−0.0174867	−	0.999847i	$-0.505566\pi$
$239$	−0.540676	−0.0349734	−0.0174867	+	0.999847i	$0.505566\pi$
$240$	0.185546	0.0119769
$241$	−16.9186	−1.08982	−0.544912	−	0.838493i	$-0.683437\pi$
$241$	−16.9186	−1.08982	−0.544912	+	0.838493i	$0.683437\pi$
$242$	−17.0785	−1.09785
$243$	1.00000	0.0641500
$244$	−37.4404	−2.39687
$245$	1.19679	0.0764599
$246$	25.0567	1.59756
$247$	35.1048	2.23366
$248$	−8.58655	−0.545247
$249$	−3.50148	−0.221897
$250$	3.88882	0.245951
$251$	29.6762	1.87315	0.936574	−	0.350471i	$-0.113979\pi$
$251$	29.6762	1.87315	0.936574	+	0.350471i	$0.113979\pi$
$252$	−1.15656	−0.0728566
$253$	−5.06087	−0.318174
$254$	−47.2290	−2.96341
$255$	0.174718	0.0109413
$256$	−8.53340	−0.533337
$257$	6.07501	0.378949	0.189475	−	0.981886i	$-0.439322\pi$
$257$	6.07501	0.378949	0.189475	+	0.981886i	$0.439322\pi$
$258$	3.69367	0.229958
$259$	−0.461278	−0.0286624
$260$	2.43656	0.151109
$261$	−6.05264	−0.374649
$262$	5.74228	0.354760
$263$	−14.4199	−0.889167	−0.444584	−	0.895737i	$-0.646648\pi$
$263$	−14.4199	−0.889167	−0.444584	+	0.895737i	$0.646648\pi$
$264$	4.02297	0.247597
$265$	0.457646	0.0281130
$266$	6.49986	0.398532
$267$	2.66818	0.163290
$268$	6.18304	0.377689
$269$	−13.4559	−0.820423	−0.410211	−	0.911990i	$-0.634545\pi$
$269$	−13.4559	−0.820423	−0.410211	+	0.911990i	$0.634545\pi$
$270$	−0.390073	−0.0237391
$271$	−16.9997	−1.03266	−0.516328	−	0.856391i	$-0.672701\pi$
$271$	−16.9997	−1.03266	−0.516328	+	0.856391i	$0.672701\pi$
$272$	1.06197	0.0643917
$273$	1.81085	0.109597
$274$	−32.5184	−1.96451
$275$	−9.09614	−0.548518
$276$	−8.25167	−0.496692
$277$	−22.7794	−1.36868	−0.684342	−	0.729161i	$-0.739910\pi$
$277$	−22.7794	−1.36868	−0.684342	+	0.729161i	$0.739910\pi$
$278$	−25.5676	−1.53344
$279$	−3.90678	−0.233893
$280$	0.148814	0.00889332
$281$	−2.12967	−0.127046	−0.0635228	−	0.997980i	$-0.520234\pi$
$281$	−2.12967	−0.127046	−0.0635228	+	0.997980i	$0.520234\pi$
$282$	−8.79563	−0.523772
$283$	−12.7090	−0.755469	−0.377735	−	0.925914i	$-0.623297\pi$
$283$	−12.7090	−0.755469	−0.377735	+	0.925914i	$0.623297\pi$
$284$	40.4450	2.39997
$285$	1.31259	0.0777509
$286$	−19.0955	−1.12914
$287$	−4.34932	−0.256732
$288$	−6.76667	−0.398730
$289$	1.00000	0.0588235
$290$	2.36097	0.138641
$291$	12.6146	0.739482
$292$	9.24314	0.540914
$293$	−22.6585	−1.32372	−0.661861	−	0.749627i	$-0.730233\pi$
$293$	−22.6585	−1.32372	−0.661861	+	0.749627i	$0.730233\pi$
$294$	−15.2928	−0.891895
$295$	0.578253	0.0336672
$296$	2.61612	0.152059
$297$	1.83040	0.106211
$298$	33.3518	1.93202
$299$	12.9198	0.747169
$300$	−14.8311	−0.856275
$301$	−0.641144	−0.0369549
$302$	−52.4252	−3.01673
$303$	18.1840	1.04464
$304$	7.97819	0.457581
$305$	2.19187	0.125506
$306$	−2.23259	−0.127629
$307$	4.49120	0.256327	0.128163	−	0.991753i	$-0.459092\pi$
$307$	4.49120	0.256327	0.128163	+	0.991753i	$0.459092\pi$
$308$	−2.11697	−0.120626
$309$	17.2970	0.983991
$310$	1.52393	0.0865533
$311$	−17.3582	−0.984292	−0.492146	−	0.870513i	$-0.663787\pi$
$311$	−17.3582	−0.984292	−0.492146	+	0.870513i	$0.663787\pi$
$312$	−10.2701	−0.581432
$313$	−10.4876	−0.592796	−0.296398	−	0.955065i	$-0.595785\pi$
$313$	−10.4876	−0.592796	−0.296398	+	0.955065i	$0.595785\pi$
$314$	2.23259	0.125992
$315$	0.0677085	0.00381494
$316$	46.9605	2.64173
$317$	2.15300	0.120925	0.0604623	−	0.998170i	$-0.480743\pi$
$317$	2.15300	0.120925	0.0604623	+	0.998170i	$0.480743\pi$
$318$	−5.84791	−0.327934
$319$	−11.0788	−0.620291
$320$	2.26841	0.126808
$321$	−1.21689	−0.0679201
$322$	2.39217	0.133310
$323$	7.51260	0.418012
$324$	2.98445	0.165803
$325$	23.2213	1.28809
$326$	−51.0348	−2.82655
$327$	2.01833	0.111614
$328$	24.6670	1.36201
$329$	1.52674	0.0841717
$330$	−0.713991	−0.0393039
$331$	−0.151911	−0.00834979	−0.00417489	−	0.999991i	$-0.501329\pi$
$331$	−0.151911	−0.00834979	−0.00417489	+	0.999991i	$0.501329\pi$
$332$	−10.4500	−0.573517
$333$	1.19030	0.0652282
$334$	6.46035	0.353494
$335$	−0.361973	−0.0197767
$336$	0.411547	0.0224517
$337$	0.963300	0.0524743	0.0262372	−	0.999656i	$-0.491647\pi$
$337$	0.963300	0.0524743	0.0262372	+	0.999656i	$0.491647\pi$
$338$	19.7248	1.07289
$339$	5.36608	0.291445
$340$	0.521436	0.0282789
$341$	−7.15097	−0.387247
$342$	−16.7725	−0.906955
$343$	5.36722	0.289803
$344$	3.63622	0.196052
$345$	0.483077	0.0260080
$346$	0.651531	0.0350265
$347$	−15.6105	−0.838015	−0.419008	−	0.907983i	$-0.637622\pi$
$347$	−15.6105	−0.838015	−0.419008	+	0.907983i	$0.637622\pi$
$348$	−18.0638	−0.968319
$349$	26.1209	1.39822	0.699109	−	0.715015i	$-0.253580\pi$
$349$	26.1209	1.39822	0.699109	+	0.715015i	$0.253580\pi$
$350$	4.29956	0.229821
$351$	−4.67279	−0.249415
$352$	−12.3857	−0.660162
$353$	−29.3466	−1.56196	−0.780982	−	0.624553i	$-0.785281\pi$
$353$	−29.3466	−1.56196	−0.780982	+	0.624553i	$0.785281\pi$
$354$	−7.38906	−0.392724
$355$	−2.36777	−0.125668
$356$	7.96304	0.422040
$357$	0.387530	0.0205103
$358$	2.28101	0.120555
$359$	14.4801	0.764228	0.382114	−	0.924115i	$-0.375196\pi$
$359$	14.4801	0.764228	0.382114	+	0.924115i	$0.375196\pi$
$360$	−0.384006	−0.0202389
$361$	37.4392	1.97048
$362$	22.5520	1.18531
$363$	−7.64963	−0.401501
$364$	5.40437	0.283266
$365$	−0.541120	−0.0283235
$366$	−28.0082	−1.46401
$367$	0.999443	0.0521705	0.0260852	−	0.999660i	$-0.491696\pi$
$367$	0.999443	0.0521705	0.0260852	+	0.999660i	$0.491696\pi$
$368$	2.93625	0.153062
$369$	11.2232	0.584256
$370$	−0.464305	−0.0241381
$371$	1.01507	0.0527000
$372$	−11.6596	−0.604520
$373$	0.196352	0.0101667	0.00508336	−	0.999987i	$-0.498382\pi$
$373$	0.196352	0.0101667	0.00508336	+	0.999987i	$0.498382\pi$
$374$	−4.08653	−0.211310
$375$	1.74185	0.0899486
$376$	−8.65882	−0.446545
$377$	28.2827	1.45663
$378$	−0.865195	−0.0445008
$379$	−35.4421	−1.82054	−0.910270	−	0.414014i	$-0.864126\pi$
$379$	−35.4421	−1.82054	−0.910270	+	0.414014i	$0.864126\pi$
$380$	3.91734	0.200955
$381$	−21.1544	−1.08377
$382$	47.4547	2.42799
$383$	−18.3284	−0.936535	−0.468268	−	0.883587i	$-0.655122\pi$
$383$	−18.3284	−0.936535	−0.468268	+	0.883587i	$0.655122\pi$
$384$	−15.4529	−0.788576
$385$	0.123934	0.00631625
$386$	−21.4212	−1.09031
$387$	1.65444	0.0840997
$388$	37.6476	1.91127
$389$	−35.5397	−1.80194	−0.900968	−	0.433886i	$-0.857142\pi$
$389$	−35.5397	−1.80194	−0.900968	+	0.433886i	$0.857142\pi$
$390$	1.82273	0.0922975
$391$	2.76489	0.139827
$392$	−15.0550	−0.760390
$393$	2.57203	0.129742
$394$	14.4694	0.728959
$395$	−2.74920	−0.138327
$396$	5.46274	0.274513
$397$	23.3736	1.17309	0.586545	−	0.809917i	$-0.300488\pi$
$397$	23.3736	1.17309	0.586545	+	0.809917i	$0.300488\pi$
$398$	32.8020	1.64422
$399$	2.91136	0.145750
$400$	5.27746	0.263873
$401$	−6.94467	−0.346800	−0.173400	−	0.984851i	$-0.555475\pi$
$401$	−6.94467	−0.346800	−0.173400	+	0.984851i	$0.555475\pi$
$402$	4.62537	0.230693
$403$	18.2555	0.909373
$404$	54.2690	2.69999
$405$	−0.174718	−0.00868181
$406$	5.23671	0.259893
$407$	2.17873	0.107996
$408$	−2.19786	−0.108810
$409$	−13.7519	−0.679986	−0.339993	−	0.940428i	$-0.610425\pi$
$409$	−13.7519	−0.679986	−0.339993	+	0.940428i	$0.610425\pi$
$410$	−4.37786	−0.216207
$411$	−14.5653	−0.718455
$412$	51.6219	2.54323
$413$	1.28258	0.0631118
$414$	−6.17287	−0.303380
$415$	0.611771	0.0300307
$416$	31.6192	1.55026
$417$	−11.4520	−0.560807
$418$	−30.7005	−1.50161
$419$	−33.2133	−1.62258	−0.811288	−	0.584647i	$-0.801233\pi$
$419$	−33.2133	−1.62258	−0.811288	+	0.584647i	$0.801233\pi$
$420$	0.202072	0.00986011
$421$	0.967755	0.0471655	0.0235828	−	0.999722i	$-0.492493\pi$
$421$	0.967755	0.0471655	0.0235828	+	0.999722i	$0.492493\pi$
$422$	3.29532	0.160414
$423$	−3.93966	−0.191553
$424$	−5.75695	−0.279582
$425$	4.96947	0.241055
$426$	30.2559	1.46590
$427$	4.86163	0.235271
$428$	−3.63174	−0.175547
$429$	−8.55308	−0.412947
$430$	−0.645351	−0.0311216
$431$	−20.7417	−0.999091	−0.499546	−	0.866288i	$-0.666500\pi$
$431$	−20.7417	−0.999091	−0.499546	+	0.866288i	$0.666500\pi$
$432$	−1.06197	−0.0510943
$433$	−30.7427	−1.47740	−0.738700	−	0.674034i	$-0.764560\pi$
$433$	−30.7427	−1.47740	−0.738700	+	0.674034i	$0.764560\pi$
$434$	3.38012	0.162251
$435$	1.05750	0.0507035
$436$	6.02360	0.288478
$437$	20.7715	0.993638
$438$	6.91456	0.330390
$439$	19.9329	0.951344	0.475672	−	0.879623i	$-0.342205\pi$
$439$	19.9329	0.951344	0.475672	+	0.879623i	$0.342205\pi$
$440$	−0.702885	−0.0335087
$441$	−6.84982	−0.326182
$442$	10.4324	0.496219
$443$	6.81777	0.323922	0.161961	−	0.986797i	$-0.448218\pi$
$443$	6.81777	0.323922	0.161961	+	0.986797i	$0.448218\pi$
$444$	3.55239	0.168589
$445$	−0.466179	−0.0220990
$446$	−56.3272	−2.66717
$447$	14.9386	0.706573
$448$	5.03139	0.237711
$449$	−8.17777	−0.385933	−0.192966	−	0.981205i	$-0.561811\pi$
$449$	−8.17777	−0.385933	−0.192966	+	0.981205i	$0.561811\pi$
$450$	−11.0948	−0.523013
$451$	20.5429	0.967330
$452$	16.0148	0.753271
$453$	−23.4818	−1.10327
$454$	57.7290	2.70936
$455$	−0.316387	−0.0148325
$456$	−16.5117	−0.773229
$457$	−29.0317	−1.35805	−0.679023	−	0.734117i	$-0.737596\pi$
$457$	−29.0317	−1.35805	−0.679023	+	0.734117i	$0.737596\pi$
$458$	26.2812	1.22804
$459$	−1.00000	−0.0466760
$460$	1.44172	0.0672203
$461$	11.6901	0.544464	0.272232	−	0.962232i	$-0.412238\pi$
$461$	11.6901	0.544464	0.272232	+	0.962232i	$0.412238\pi$
$462$	−1.58365	−0.0736782
$463$	−7.08113	−0.329088	−0.164544	−	0.986370i	$-0.552615\pi$
$463$	−7.08113	−0.329088	−0.164544	+	0.986370i	$0.552615\pi$
$464$	6.42775	0.298401
$465$	0.682584	0.0316541
$466$	−1.36695	−0.0633225
$467$	−16.1891	−0.749143	−0.374572	−	0.927198i	$-0.622210\pi$
$467$	−16.1891	−0.749143	−0.374572	+	0.927198i	$0.622210\pi$
$468$	−13.9457	−0.644639
$469$	−0.802867	−0.0370730
$470$	1.53675	0.0708852
$471$	1.00000	0.0460776
$472$	−7.27413	−0.334819
$473$	3.02828	0.139241
$474$	35.1299	1.61357
$475$	37.3337	1.71299
$476$	1.15656	0.0530109
$477$	−2.61934	−0.119931
$478$	−1.20711	−0.0552118
$479$	34.8410	1.59192	0.795962	−	0.605346i	$-0.206965\pi$
$479$	34.8410	1.59192	0.795962	+	0.605346i	$0.206965\pi$
$480$	1.18226	0.0539625
$481$	−5.56203	−0.253607
$482$	−37.7723	−1.72048
$483$	1.07148	0.0487540
$484$	−22.8299	−1.03772
$485$	−2.20400	−0.100079
$486$	2.23259	0.101272
$487$	−30.5331	−1.38359	−0.691793	−	0.722096i	$-0.743179\pi$
$487$	−30.5331	−1.38359	−0.691793	+	0.722096i	$0.743179\pi$
$488$	−27.5725	−1.24815
$489$	−22.8590	−1.03372
$490$	2.67193	0.120706
$491$	9.79294	0.441949	0.220975	−	0.975280i	$-0.429076\pi$
$491$	9.79294	0.441949	0.220975	+	0.975280i	$0.429076\pi$
$492$	33.4950	1.51007
$493$	6.05264	0.272597
$494$	78.3745	3.52624
$495$	−0.319804	−0.0143741
$496$	4.14890	0.186291
$497$	−5.25178	−0.235574
$498$	−7.81736	−0.350304
$499$	−0.923932	−0.0413609	−0.0206804	−	0.999786i	$-0.506583\pi$
$499$	−0.923932	−0.0413609	−0.0206804	+	0.999786i	$0.506583\pi$
$500$	5.19845	0.232482
$501$	2.89366	0.129279
$502$	66.2548	2.95710
$503$	9.16418	0.408610	0.204305	−	0.978907i	$-0.434506\pi$
$503$	9.16418	0.408610	0.204305	+	0.978907i	$0.434506\pi$
$504$	−0.851737	−0.0379394
$505$	−3.17706	−0.141377
$506$	−11.2988	−0.502294
$507$	8.83494	0.392374
$508$	−63.1341	−2.80112
$509$	−33.3464	−1.47805	−0.739026	−	0.673677i	$-0.764714\pi$
$509$	−33.3464	−1.47805	−0.739026	+	0.673677i	$0.764714\pi$
$510$	0.390073	0.0172727
$511$	−1.20022	−0.0530947
$512$	11.8542	0.523886
$513$	−7.51260	−0.331689
$514$	13.5630	0.598238
$515$	−3.02209	−0.133169
$516$	4.93757	0.217365
$517$	−7.21116	−0.317146
$518$	−1.02984	−0.0452487
$519$	0.291828	0.0128098
$520$	1.79438	0.0786887
$521$	−11.6455	−0.510200	−0.255100	−	0.966915i	$-0.582108\pi$
$521$	−11.6455	−0.510200	−0.255100	+	0.966915i	$0.582108\pi$
$522$	−13.5130	−0.591450
$523$	−9.28998	−0.406222	−0.203111	−	0.979156i	$-0.565105\pi$
$523$	−9.28998	−0.406222	−0.203111	+	0.979156i	$0.565105\pi$
$524$	7.67609	0.335331
$525$	1.92582	0.0840497
$526$	−32.1936	−1.40371
$527$	3.90678	0.170182
$528$	−1.94384	−0.0845948
$529$	−15.3554	−0.667625
$530$	1.02173	0.0443813
$531$	−3.30964	−0.143626
$532$	8.68879	0.376707
$533$	−52.4436	−2.27158
$534$	5.95695	0.257782
$535$	0.212612	0.00919203
$536$	4.55343	0.196678
$537$	1.02169	0.0440892
$538$	−30.0415	−1.29518
$539$	−12.5379	−0.540047
$540$	−0.521436	−0.0224390
$541$	23.0103	0.989290	0.494645	−	0.869095i	$-0.335298\pi$
$541$	23.0103	0.989290	0.494645	+	0.869095i	$0.335298\pi$
$542$	−37.9532	−1.63023
$543$	10.1013	0.433487
$544$	6.76667	0.290119
$545$	−0.352639	−0.0151054
$546$	4.04287	0.173019
$547$	20.1748	0.862613	0.431306	−	0.902206i	$-0.358053\pi$
$547$	20.1748	0.862613	0.431306	+	0.902206i	$0.358053\pi$
$548$	−43.4695	−1.85692
$549$	−12.5452	−0.535415
$550$	−20.3079	−0.865932
$551$	45.4710	1.93713
$552$	−6.07685	−0.258648
$553$	−6.09781	−0.259305
$554$	−50.8571	−2.16071
$555$	−0.207967	−0.00882772
$556$	−34.1779	−1.44947
$557$	4.80613	0.203642	0.101821	−	0.994803i	$-0.467533\pi$
$557$	4.80613	0.203642	0.101821	+	0.994803i	$0.467533\pi$
$558$	−8.72222	−0.369241
$559$	−7.73083	−0.326979
$560$	−0.0719047	−0.00303853
$561$	−1.83040	−0.0772796
$562$	−4.75468	−0.200564
$563$	37.0471	1.56135	0.780675	−	0.624937i	$-0.214875\pi$
$563$	37.0471	1.56135	0.780675	+	0.624937i	$0.214875\pi$
$564$	−11.7577	−0.495088
$565$	−0.937550	−0.0394430
$566$	−28.3739	−1.19264
$567$	−0.387530	−0.0162747
$568$	29.7853	1.24976
$569$	−4.18204	−0.175320	−0.0876602	−	0.996150i	$-0.527939\pi$
$569$	−4.18204	−0.175320	−0.0876602	+	0.996150i	$0.527939\pi$
$570$	2.93046	0.122744
$571$	25.4630	1.06560	0.532798	−	0.846243i	$-0.321141\pi$
$571$	25.4630	1.06560	0.532798	+	0.846243i	$0.321141\pi$
$572$	−25.5262	−1.06730
$573$	21.2555	0.887959
$574$	−9.71024	−0.405298
$575$	13.7401	0.573000
$576$	−12.9832	−0.540968
$577$	14.5270	0.604766	0.302383	−	0.953187i	$-0.402218\pi$
$577$	14.5270	0.604766	0.302383	+	0.953187i	$0.402218\pi$
$578$	2.23259	0.0928634
$579$	−9.59480	−0.398746
$580$	3.15606	0.131048
$581$	1.35693	0.0562949
$582$	28.1632	1.16740
$583$	−4.79445	−0.198566
$584$	6.80701	0.281676
$585$	0.816420	0.0337548
$586$	−50.5870	−2.08973
$587$	−7.02132	−0.289801	−0.144900	−	0.989446i	$-0.546286\pi$
$587$	−7.02132	−0.289801	−0.144900	+	0.989446i	$0.546286\pi$
$588$	−20.4429	−0.843052
$589$	29.3500	1.20935
$590$	1.29100	0.0531497
$591$	6.48101	0.266593
$592$	−1.26407	−0.0519530
$593$	−33.0984	−1.35919	−0.679594	−	0.733588i	$-0.737844\pi$
$593$	−33.0984	−1.35919	−0.679594	+	0.733588i	$0.737844\pi$
$594$	4.08653	0.167672
$595$	−0.0677085	−0.00277578
$596$	44.5835	1.82621
$597$	14.6924	0.601319
$598$	28.8445	1.17954
$599$	−44.6705	−1.82519	−0.912593	−	0.408870i	$-0.865923\pi$
$599$	−44.6705	−1.82519	−0.912593	+	0.408870i	$0.865923\pi$
$600$	−10.9222	−0.445897
$601$	−15.9796	−0.651821	−0.325911	−	0.945401i	$-0.605671\pi$
$601$	−15.9796	−0.651821	−0.325911	+	0.945401i	$0.605671\pi$
$602$	−1.43141	−0.0583399
$603$	2.07176	0.0843684
$604$	−70.0802	−2.85152
$605$	1.33653	0.0543376
$606$	40.5973	1.64915
$607$	17.3392	0.703776	0.351888	−	0.936042i	$-0.385540\pi$
$607$	17.3392	0.703776	0.351888	+	0.936042i	$0.385540\pi$
$608$	50.8353	2.06164
$609$	2.34558	0.0950476
$610$	4.89353	0.198133
$611$	18.4092	0.744756
$612$	−2.98445	−0.120639
$613$	24.6646	0.996194	0.498097	−	0.867121i	$-0.334032\pi$
$613$	24.6646	0.996194	0.498097	+	0.867121i	$0.334032\pi$
$614$	10.0270	0.404657
$615$	−1.96089	−0.0790708
$616$	−1.55902	−0.0628148
$617$	−30.3869	−1.22333	−0.611665	−	0.791117i	$-0.709500\pi$
$617$	−30.3869	−1.22333	−0.611665	+	0.791117i	$0.709500\pi$
$618$	38.6170	1.55340
$619$	−31.0288	−1.24715	−0.623577	−	0.781762i	$-0.714321\pi$
$619$	−31.0288	−1.24715	−0.623577	+	0.781762i	$0.714321\pi$
$620$	2.03713	0.0818133
$621$	−2.76489	−0.110951
$622$	−38.7537	−1.55388
$623$	−1.03400	−0.0414263
$624$	4.96238	0.198654
$625$	24.5430	0.981721
$626$	−23.4145	−0.935833
$627$	−13.7511	−0.549165
$628$	2.98445	0.119092
$629$	−1.19030	−0.0474605
$630$	0.151165	0.00602256
$631$	−16.5772	−0.659926	−0.329963	−	0.943994i	$-0.607036\pi$
$631$	−16.5772	−0.659926	−0.329963	+	0.943994i	$0.607036\pi$
$632$	34.5835	1.37566
$633$	1.47601	0.0586662
$634$	4.80676	0.190901
$635$	3.69605	0.146673
$636$	−7.81728	−0.309975
$637$	32.0078	1.26819
$638$	−24.7343	−0.979240
$639$	13.5519	0.536106
$640$	2.69989	0.106723
$641$	40.4325	1.59699	0.798494	−	0.602003i	$-0.205630\pi$
$641$	40.4325	1.59699	0.798494	+	0.602003i	$0.205630\pi$
$642$	−2.71681	−0.107224
$643$	1.82606	0.0720129	0.0360065	−	0.999352i	$-0.488536\pi$
$643$	1.82606	0.0720129	0.0360065	+	0.999352i	$0.488536\pi$
$644$	3.19777	0.126010
$645$	−0.289060	−0.0113817
$646$	16.7725	0.659907
$647$	14.3310	0.563410	0.281705	−	0.959501i	$-0.409100\pi$
$647$	14.3310	0.563410	0.281705	+	0.959501i	$0.409100\pi$
$648$	2.19786	0.0863401
$649$	−6.05797	−0.237796
$650$	51.8436	2.03347
$651$	1.51399	0.0593381
$652$	−68.2215	−2.67176
$653$	46.2219	1.80880	0.904402	−	0.426682i	$-0.140318\pi$
$653$	46.2219	1.80880	0.904402	+	0.426682i	$0.140318\pi$
$654$	4.50610	0.176203
$655$	−0.449380	−0.0175587
$656$	−11.9187	−0.465349
$657$	3.09711	0.120830
$658$	3.40857	0.132880
$659$	−20.8777	−0.813278	−0.406639	−	0.913589i	$-0.633299\pi$
$659$	−20.8777	−0.813278	−0.406639	+	0.913589i	$0.633299\pi$
$660$	−0.954438	−0.0371515
$661$	46.3352	1.80223	0.901115	−	0.433580i	$-0.142750\pi$
$661$	46.3352	1.80223	0.901115	+	0.433580i	$0.142750\pi$
$662$	−0.339155	−0.0131816
$663$	4.67279	0.181476
$664$	−7.69577	−0.298654
$665$	−0.508667	−0.0197252
$666$	2.65745	0.102974
$667$	16.7349	0.647978
$668$	8.63597	0.334136
$669$	−25.2295	−0.975431
$670$	−0.808136	−0.0312210
$671$	−22.9627	−0.886465
$672$	2.62229	0.101157
$673$	−34.1968	−1.31819	−0.659094	−	0.752060i	$-0.729060\pi$
$673$	−34.1968	−1.31819	−0.659094	+	0.752060i	$0.729060\pi$
$674$	2.15065	0.0828400
$675$	−4.96947	−0.191275
$676$	26.3674	1.01413
$677$	27.3503	1.05116	0.525579	−	0.850745i	$-0.323849\pi$
$677$	27.3503	1.05116	0.525579	+	0.850745i	$0.323849\pi$
$678$	11.9802	0.460098
$679$	−4.88854	−0.187605
$680$	0.384006	0.0147260
$681$	25.8575	0.990860
$682$	−15.9652	−0.611338
$683$	14.1156	0.540117	0.270059	−	0.962844i	$-0.412957\pi$
$683$	14.1156	0.540117	0.270059	+	0.962844i	$0.412957\pi$
$684$	−22.4210	−0.857287
$685$	2.54483	0.0972329
$686$	11.9828	0.457505
$687$	11.7716	0.449116
$688$	−1.75697	−0.0669838
$689$	12.2396	0.466293
$690$	1.07851	0.0410582
$691$	43.8475	1.66804	0.834019	−	0.551736i	$-0.186034\pi$
$691$	43.8475	1.66804	0.834019	+	0.551736i	$0.186034\pi$
$692$	0.870944	0.0331083
$693$	−0.709336	−0.0269454
$694$	−34.8518	−1.32296
$695$	2.00087	0.0758974
$696$	−13.3029	−0.504243
$697$	−11.2232	−0.425109
$698$	58.3171	2.20734
$699$	−0.612270	−0.0231582
$700$	5.74751	0.217235
$701$	24.0251	0.907414	0.453707	−	0.891151i	$-0.350101\pi$
$701$	24.0251	0.907414	0.453707	+	0.891151i	$0.350101\pi$
$702$	−10.4324	−0.393746
$703$	−8.94227	−0.337264
$704$	−23.7646	−0.895660
$705$	0.688329	0.0259240
$706$	−65.5189	−2.46584
$707$	−7.04683	−0.265023
$708$	−9.87744	−0.371217
$709$	11.7943	0.442946	0.221473	−	0.975167i	$-0.428914\pi$
$709$	11.7943	0.442946	0.221473	+	0.975167i	$0.428914\pi$
$710$	−5.28624	−0.198389
$711$	15.7351	0.590111
$712$	5.86429	0.219774
$713$	10.8018	0.404531
$714$	0.865195	0.0323791
$715$	1.49438	0.0558865
$716$	3.04918	0.113953
$717$	−0.540676	−0.0201919
$718$	32.3280	1.20647
$719$	−46.5992	−1.73786	−0.868929	−	0.494937i	$-0.835191\pi$
$719$	−46.5992	−1.73786	−0.868929	+	0.494937i	$0.835191\pi$
$720$	0.185546	0.00691489
$721$	−6.70310	−0.249636
$722$	83.5862	3.11076
$723$	−16.9186	−0.629210
$724$	30.1467	1.12039
$725$	30.0784	1.11708
$726$	−17.0785	−0.633841
$727$	−5.15676	−0.191254	−0.0956269	−	0.995417i	$-0.530486\pi$
$727$	−5.15676	−0.191254	−0.0956269	+	0.995417i	$0.530486\pi$
$728$	3.97999	0.147508
$729$	1.00000	0.0370370
$730$	−1.20810	−0.0447137
$731$	−1.65444	−0.0611915
$732$	−37.4404	−1.38384
$733$	47.2861	1.74655	0.873277	−	0.487225i	$-0.161991\pi$
$733$	47.2861	1.74655	0.873277	+	0.487225i	$0.161991\pi$
$734$	2.23134	0.0823604
$735$	1.19679	0.0441441
$736$	18.7091	0.689628
$737$	3.79215	0.139685
$738$	25.0567	0.922352
$739$	3.09597	0.113887	0.0569436	−	0.998377i	$-0.481864\pi$
$739$	3.09597	0.113887	0.0569436	+	0.998377i	$0.481864\pi$
$740$	−0.620667	−0.0228162
$741$	35.1048	1.28961
$742$	2.26624	0.0831963
$743$	−45.0503	−1.65273	−0.826367	−	0.563131i	$-0.809596\pi$
$743$	−45.0503	−1.65273	−0.826367	+	0.563131i	$0.809596\pi$
$744$	−8.58655	−0.314798
$745$	−2.61005	−0.0956247
$746$	0.438373	0.0160500
$747$	−3.50148	−0.128112
$748$	−5.46274	−0.199737
$749$	0.471581	0.0172312
$750$	3.88882	0.142000
$751$	−43.7094	−1.59498	−0.797489	−	0.603334i	$-0.793839\pi$
$751$	−43.7094	−1.59498	−0.797489	+	0.603334i	$0.793839\pi$
$752$	4.18382	0.152568
$753$	29.6762	1.08146
$754$	63.1436	2.29955
$755$	4.10270	0.149312
$756$	−1.15656	−0.0420638
$757$	−0.377313	−0.0137137	−0.00685684	−	0.999976i	$-0.502183\pi$
$757$	−0.377313	−0.0137137	−0.00685684	+	0.999976i	$0.502183\pi$
$758$	−79.1277	−2.87405
$759$	−5.06087	−0.183698
$760$	2.88488	0.104646
$761$	27.0822	0.981728	0.490864	−	0.871236i	$-0.336681\pi$
$761$	27.0822	0.981728	0.490864	+	0.871236i	$0.336681\pi$
$762$	−47.2290	−1.71093
$763$	−0.782164	−0.0283162
$764$	63.4357	2.29502
$765$	0.174718	0.00631694
$766$	−40.9197	−1.47849
$767$	15.4652	0.558417
$768$	−8.53340	−0.307922
$769$	26.1210	0.941947	0.470973	−	0.882147i	$-0.343903\pi$
$769$	26.1210	0.941947	0.470973	+	0.882147i	$0.343903\pi$
$770$	0.276693	0.00997132
$771$	6.07501	0.218786
$772$	−28.6352	−1.03060
$773$	31.9228	1.14818	0.574091	−	0.818791i	$-0.305355\pi$
$773$	31.9228	1.14818	0.574091	+	0.818791i	$0.305355\pi$
$774$	3.69367	0.132766
$775$	19.4146	0.697394
$776$	27.7252	0.995276
$777$	−0.461278	−0.0165483
$778$	−79.3455	−2.84468
$779$	−84.3153	−3.02091
$780$	2.43656	0.0872429
$781$	24.8055	0.887610
$782$	6.17287	0.220741
$783$	−6.05264	−0.216304
$784$	7.27434	0.259798
$785$	−0.174718	−0.00623595
$786$	5.74228	0.204821
$787$	40.8312	1.45548	0.727738	−	0.685855i	$-0.240572\pi$
$787$	40.8312	1.45548	0.727738	+	0.685855i	$0.240572\pi$
$788$	19.3422	0.689039
$789$	−14.4199	−0.513361
$790$	−6.13783	−0.218374
$791$	−2.07952	−0.0739391
$792$	4.02297	0.142950
$793$	58.6209	2.08169
$794$	52.1837	1.85193
$795$	0.457646	0.0162310
$796$	43.8486	1.55417
$797$	8.15193	0.288756	0.144378	−	0.989523i	$-0.453882\pi$
$797$	8.15193	0.288756	0.144378	+	0.989523i	$0.453882\pi$
$798$	6.49986	0.230093
$799$	3.93966	0.139375
$800$	33.6268	1.18889
$801$	2.66818	0.0942755
$802$	−15.5046	−0.547486
$803$	5.66895	0.200053
$804$	6.18304	0.218059
$805$	−0.187207	−0.00659817
$806$	40.7571	1.43561
$807$	−13.4559	−0.473671
$808$	39.9658	1.40599
$809$	−48.1366	−1.69239	−0.846197	−	0.532870i	$-0.821113\pi$
$809$	−48.1366	−1.69239	−0.846197	+	0.532870i	$0.821113\pi$
$810$	−0.390073	−0.0137058
$811$	−24.5368	−0.861602	−0.430801	−	0.902447i	$-0.641769\pi$
$811$	−24.5368	−0.861602	−0.430801	+	0.902447i	$0.641769\pi$
$812$	7.00025	0.245661
$813$	−16.9997	−0.596204
$814$	4.86421	0.170490
$815$	3.99388	0.139900
$816$	1.06197	0.0371766
$817$	−12.4291	−0.434840
$818$	−30.7023	−1.07348
$819$	1.81085	0.0632761
$820$	−5.85218	−0.204367
$821$	0.261557	0.00912840	0.00456420	−	0.999990i	$-0.498547\pi$
$821$	0.261557	0.00912840	0.00456420	+	0.999990i	$0.498547\pi$
$822$	−32.5184	−1.13421
$823$	54.6042	1.90338	0.951691	−	0.307059i	$-0.0993447\pi$
$823$	54.6042	1.90338	0.951691	+	0.307059i	$0.0993447\pi$
$824$	38.0164	1.32436
$825$	−9.09614	−0.316687
$826$	2.86348	0.0996332
$827$	−41.7009	−1.45008	−0.725042	−	0.688705i	$-0.758179\pi$
$827$	−41.7009	−1.45008	−0.725042	+	0.688705i	$0.758179\pi$
$828$	−8.25167	−0.286765
$829$	−37.3876	−1.29853	−0.649263	−	0.760564i	$-0.724922\pi$
$829$	−37.3876	−1.29853	−0.649263	+	0.760564i	$0.724922\pi$
$830$	1.36583	0.0474088
$831$	−22.7794	−0.790210
$832$	60.6679	2.10328
$833$	6.84982	0.237332
$834$	−25.5676	−0.885333
$835$	−0.505574	−0.0174961
$836$	−41.0394	−1.41938
$837$	−3.90678	−0.135038
$838$	−74.1516	−2.56152
$839$	25.7724	0.889760	0.444880	−	0.895590i	$-0.353246\pi$
$839$	25.7724	0.889760	0.444880	+	0.895590i	$0.353246\pi$
$840$	0.148814	0.00513456
$841$	7.63441	0.263255
$842$	2.16060	0.0744591
$843$	−2.12967	−0.0733498
$844$	4.40508	0.151629
$845$	−1.54362	−0.0531022
$846$	−8.79563	−0.302400
$847$	2.96446	0.101860
$848$	2.78167	0.0955231
$849$	−12.7090	−0.436170
$850$	11.0948	0.380548
$851$	−3.29106	−0.112816
$852$	40.4450	1.38562
$853$	17.9746	0.615439	0.307719	−	0.951477i	$-0.400434\pi$
$853$	17.9746	0.615439	0.307719	+	0.951477i	$0.400434\pi$
$854$	10.8540	0.371417
$855$	1.31259	0.0448895
$856$	−2.67455	−0.0914143
$857$	4.58808	0.156726	0.0783629	−	0.996925i	$-0.475031\pi$
$857$	4.58808	0.156726	0.0783629	+	0.996925i	$0.475031\pi$
$858$	−19.0955	−0.651910
$859$	−9.50836	−0.324421	−0.162211	−	0.986756i	$-0.551862\pi$
$859$	−9.50836	−0.324421	−0.162211	+	0.986756i	$0.551862\pi$
$860$	−0.862683	−0.0294172
$861$	−4.34932	−0.148225
$862$	−46.3076	−1.57724
$863$	3.30343	0.112450	0.0562250	−	0.998418i	$-0.482094\pi$
$863$	3.30343	0.112450	0.0562250	+	0.998418i	$0.482094\pi$
$864$	−6.76667	−0.230207
$865$	−0.0509876	−0.00173363
$866$	−68.6358	−2.33234
$867$	1.00000	0.0339618
$868$	4.51843	0.153365
$869$	28.8015	0.977024
$870$	2.36097	0.0800444
$871$	−9.68087	−0.328024
$872$	4.43601	0.150222
$873$	12.6146	0.426940
$874$	46.3743	1.56863
$875$	−0.675018	−0.0228198
$876$	9.24314	0.312297
$877$	−25.7839	−0.870661	−0.435330	−	0.900271i	$-0.643368\pi$
$877$	−25.7839	−0.870661	−0.435330	+	0.900271i	$0.643368\pi$
$878$	44.5019	1.50187
$879$	−22.6585	−0.764251
$880$	0.339624	0.0114487
$881$	−45.5330	−1.53404	−0.767022	−	0.641621i	$-0.778262\pi$
$881$	−45.5330	−1.53404	−0.767022	+	0.641621i	$0.778262\pi$
$882$	−15.2928	−0.514936
$883$	29.8554	1.00471	0.502357	−	0.864660i	$-0.332466\pi$
$883$	29.8554	1.00471	0.502357	+	0.864660i	$0.332466\pi$
$884$	13.9457	0.469044
$885$	0.578253	0.0194378
$886$	15.2213	0.511369
$887$	44.7770	1.50347	0.751733	−	0.659468i	$-0.229218\pi$
$887$	44.7770	1.50347	0.751733	+	0.659468i	$0.229218\pi$
$888$	2.61612	0.0877912
$889$	8.19796	0.274951
$890$	−1.04079	−0.0348872
$891$	1.83040	0.0613208
$892$	−75.2962	−2.52110
$893$	29.5971	0.990429
$894$	33.3518	1.11545
$895$	−0.178508	−0.00596686
$896$	5.98845	0.200060
$897$	12.9198	0.431378
$898$	−18.2576	−0.609263
$899$	23.6463	0.788648
$900$	−14.8311	−0.494371
$901$	2.61934	0.0872629
$902$	45.8639	1.52710
$903$	−0.641144	−0.0213359
$904$	11.7939	0.392259
$905$	−1.76487	−0.0586664
$906$	−52.4252	−1.74171
$907$	−39.8567	−1.32342	−0.661710	−	0.749760i	$-0.730169\pi$
$907$	−39.8567	−1.32342	−0.661710	+	0.749760i	$0.730169\pi$
$908$	77.1702	2.56098
$909$	18.1840	0.603124
$910$	−0.706362	−0.0234157
$911$	−31.6723	−1.04935	−0.524676	−	0.851302i	$-0.675813\pi$
$911$	−31.6723	−1.04935	−0.524676	+	0.851302i	$0.675813\pi$
$912$	7.97819	0.264184
$913$	−6.40912	−0.212111
$914$	−64.8158	−2.14392
$915$	2.19187	0.0724609
$916$	35.1318	1.16079
$917$	−0.996739	−0.0329152
$918$	−2.23259	−0.0736864
$919$	43.1865	1.42459	0.712296	−	0.701879i	$-0.247655\pi$
$919$	43.1865	1.42459	0.712296	+	0.701879i	$0.247655\pi$
$920$	1.06174	0.0350044
$921$	4.49120	0.147990
$922$	26.0992	0.859533
$923$	−63.3253	−2.08438
$924$	−2.11697	−0.0696433
$925$	−5.91518	−0.194490
$926$	−15.8092	−0.519524
$927$	17.2970	0.568107
$928$	40.9562	1.34445
$929$	8.21597	0.269557	0.134779	−	0.990876i	$-0.456968\pi$
$929$	8.21597	0.269557	0.134779	+	0.990876i	$0.456968\pi$
$930$	1.52393	0.0499716
$931$	51.4600	1.68653
$932$	−1.82729	−0.0598547
$933$	−17.3582	−0.568282
$934$	−36.1436	−1.18266
$935$	0.319804	0.0104587
$936$	−10.2701	−0.335690
$937$	−2.64836	−0.0865183	−0.0432591	−	0.999064i	$-0.513774\pi$
$937$	−2.64836	−0.0865183	−0.0432591	+	0.999064i	$0.513774\pi$
$938$	−1.79247	−0.0585263
$939$	−10.4876	−0.342251
$940$	2.05428	0.0670032
$941$	4.15181	0.135345	0.0676726	−	0.997708i	$-0.478443\pi$
$941$	4.15181	0.135345	0.0676726	+	0.997708i	$0.478443\pi$
$942$	2.23259	0.0727416
$943$	−31.0309	−1.01051
$944$	3.51475	0.114395
$945$	0.0677085	0.00220256
$946$	6.76091	0.219816
$947$	−6.50417	−0.211357	−0.105678	−	0.994400i	$-0.533701\pi$
$947$	−6.50417	−0.211357	−0.105678	+	0.994400i	$0.533701\pi$
$948$	46.9605	1.52521
$949$	−14.4721	−0.469785
$950$	83.3507	2.70425
$951$	2.15300	0.0698158
$952$	0.851737	0.0276050
$953$	12.7446	0.412839	0.206419	−	0.978464i	$-0.433819\pi$
$953$	12.7446	0.412839	0.206419	+	0.978464i	$0.433819\pi$
$954$	−5.84791	−0.189333
$955$	−3.71371	−0.120173
$956$	−1.61362	−0.0521881
$957$	−11.0788	−0.358125
$958$	77.7855	2.51314
$959$	5.64451	0.182271
$960$	2.26841	0.0732125
$961$	−15.7371	−0.507649
$962$	−12.4177	−0.400363
$963$	−1.21689	−0.0392137
$964$	−50.4927	−1.62626
$965$	1.67638	0.0539647
$966$	2.39217	0.0769668
$967$	−7.13449	−0.229430	−0.114715	−	0.993398i	$-0.536595\pi$
$967$	−7.13449	−0.229430	−0.114715	+	0.993398i	$0.536595\pi$
$968$	−16.8128	−0.540385
$969$	7.51260	0.241340
$970$	−4.92062	−0.157992
$971$	−28.7413	−0.922352	−0.461176	−	0.887309i	$-0.652572\pi$
$971$	−28.7413	−0.922352	−0.461176	+	0.887309i	$0.652572\pi$
$972$	2.98445	0.0957261
$973$	4.43799	0.142276
$974$	−68.1678	−2.18424
$975$	23.2213	0.743677
$976$	13.3227	0.426448
$977$	17.1874	0.549875	0.274938	−	0.961462i	$-0.411343\pi$
$977$	17.1874	0.549875	0.274938	+	0.961462i	$0.411343\pi$
$978$	−51.0348	−1.63191
$979$	4.88384	0.156088
$980$	3.57175	0.114095
$981$	2.01833	0.0644404
$982$	21.8636	0.697695
$983$	41.2426	1.31543	0.657717	−	0.753265i	$-0.271522\pi$
$983$	41.2426	1.31543	0.657717	+	0.753265i	$0.271522\pi$
$984$	24.6670	0.786356
$985$	−1.13235	−0.0360797
$986$	13.5130	0.430343
$987$	1.52674	0.0485965
$988$	104.768	3.33313
$989$	−4.57434	−0.145456
$990$	−0.713991	−0.0226921
$991$	−30.0281	−0.953874	−0.476937	−	0.878937i	$-0.658253\pi$
$991$	−30.0281	−0.953874	−0.476937	+	0.878937i	$0.658253\pi$
$992$	26.4359	0.839340
$993$	−0.151911	−0.00482075
$994$	−11.7251	−0.371896
$995$	−2.56702	−0.0813801
$996$	−10.4500	−0.331120
$997$	−19.8633	−0.629079	−0.314539	−	0.949244i	$-0.601850\pi$
$997$	−19.8633	−0.629079	−0.314539	+	0.949244i	$0.601850\pi$
$998$	−2.06276	−0.0652955
$999$	1.19030	0.0376595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.42	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.42	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.23259 q^{2} +1.00000 q^{3} +2.98445 q^{4} -0.174718 q^{5} +2.23259 q^{6} -0.387530 q^{7} +2.19786 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.23259 q^{2} +1.00000 q^{3} +2.98445 q^{4} -0.174718 q^{5} +2.23259 q^{6} -0.387530 q^{7} +2.19786 q^{8} +1.00000 q^{9} -0.390073 q^{10} +1.83040 q^{11} +2.98445 q^{12} -4.67279 q^{13} -0.865195 q^{14} -0.174718 q^{15} -1.06197 q^{16} -1.00000 q^{17} +2.23259 q^{18} -7.51260 q^{19} -0.521436 q^{20} -0.387530 q^{21} +4.08653 q^{22} -2.76489 q^{23} +2.19786 q^{24} -4.96947 q^{25} -10.4324 q^{26} +1.00000 q^{27} -1.15656 q^{28} -6.05264 q^{29} -0.390073 q^{30} -3.90678 q^{31} -6.76667 q^{32} +1.83040 q^{33} -2.23259 q^{34} +0.0677085 q^{35} +2.98445 q^{36} +1.19030 q^{37} -16.7725 q^{38} -4.67279 q^{39} -0.384006 q^{40} +11.2232 q^{41} -0.865195 q^{42} +1.65444 q^{43} +5.46274 q^{44} -0.174718 q^{45} -6.17287 q^{46} -3.93966 q^{47} -1.06197 q^{48} -6.84982 q^{49} -11.0948 q^{50} -1.00000 q^{51} -13.9457 q^{52} -2.61934 q^{53} +2.23259 q^{54} -0.319804 q^{55} -0.851737 q^{56} -7.51260 q^{57} -13.5130 q^{58} -3.30964 q^{59} -0.521436 q^{60} -12.5452 q^{61} -8.72222 q^{62} -0.387530 q^{63} -12.9832 q^{64} +0.816420 q^{65} +4.08653 q^{66} +2.07176 q^{67} -2.98445 q^{68} -2.76489 q^{69} +0.151165 q^{70} +13.5519 q^{71} +2.19786 q^{72} +3.09711 q^{73} +2.65745 q^{74} -4.96947 q^{75} -22.4210 q^{76} -0.709336 q^{77} -10.4324 q^{78} +15.7351 q^{79} +0.185546 q^{80} +1.00000 q^{81} +25.0567 q^{82} -3.50148 q^{83} -1.15656 q^{84} +0.174718 q^{85} +3.69367 q^{86} -6.05264 q^{87} +4.02297 q^{88} +2.66818 q^{89} -0.390073 q^{90} +1.81085 q^{91} -8.25167 q^{92} -3.90678 q^{93} -8.79563 q^{94} +1.31259 q^{95} -6.76667 q^{96} +12.6146 q^{97} -15.2928 q^{98} +1.83040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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