LMFDB - Embedded newform 4006.2.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, 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("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.84484 q^{3} +1.00000 q^{4} -3.34479 q^{5} +1.84484 q^{6} +2.16076 q^{7} -1.00000 q^{8} +0.403448 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.84484 q^{3} +1.00000 q^{4} -3.34479 q^{5} +1.84484 q^{6} +2.16076 q^{7} -1.00000 q^{8} +0.403448 q^{9} +3.34479 q^{10} +3.73765 q^{11} -1.84484 q^{12} +4.02604 q^{13} -2.16076 q^{14} +6.17062 q^{15} +1.00000 q^{16} +4.29909 q^{17} -0.403448 q^{18} -2.98092 q^{19} -3.34479 q^{20} -3.98627 q^{21} -3.73765 q^{22} +6.16576 q^{23} +1.84484 q^{24} +6.18765 q^{25} -4.02604 q^{26} +4.79023 q^{27} +2.16076 q^{28} +7.30530 q^{29} -6.17062 q^{30} +3.71705 q^{31} -1.00000 q^{32} -6.89538 q^{33} -4.29909 q^{34} -7.22731 q^{35} +0.403448 q^{36} -10.1033 q^{37} +2.98092 q^{38} -7.42742 q^{39} +3.34479 q^{40} +3.69304 q^{41} +3.98627 q^{42} -2.64166 q^{43} +3.73765 q^{44} -1.34945 q^{45} -6.16576 q^{46} -4.03904 q^{47} -1.84484 q^{48} -2.33110 q^{49} -6.18765 q^{50} -7.93115 q^{51} +4.02604 q^{52} +4.27288 q^{53} -4.79023 q^{54} -12.5017 q^{55} -2.16076 q^{56} +5.49934 q^{57} -7.30530 q^{58} +11.2765 q^{59} +6.17062 q^{60} -4.32811 q^{61} -3.71705 q^{62} +0.871756 q^{63} +1.00000 q^{64} -13.4663 q^{65} +6.89538 q^{66} +11.9286 q^{67} +4.29909 q^{68} -11.3749 q^{69} +7.22731 q^{70} -9.20425 q^{71} -0.403448 q^{72} +1.57852 q^{73} +10.1033 q^{74} -11.4152 q^{75} -2.98092 q^{76} +8.07618 q^{77} +7.42742 q^{78} -6.40229 q^{79} -3.34479 q^{80} -10.0476 q^{81} -3.69304 q^{82} +12.2289 q^{83} -3.98627 q^{84} -14.3796 q^{85} +2.64166 q^{86} -13.4771 q^{87} -3.73765 q^{88} -12.0552 q^{89} +1.34945 q^{90} +8.69932 q^{91} +6.16576 q^{92} -6.85737 q^{93} +4.03904 q^{94} +9.97058 q^{95} +1.84484 q^{96} -7.79901 q^{97} +2.33110 q^{98} +1.50795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.84484	−1.06512	−0.532560	−	0.846392i	$-0.678770\pi$
$3$	−1.84484	−1.06512	−0.532560	+	0.846392i	$0.678770\pi$
$4$	1.00000	0.500000
$5$	−3.34479	−1.49584	−0.747919	−	0.663790i	$-0.768947\pi$
$5$	−3.34479	−1.49584	−0.747919	+	0.663790i	$0.768947\pi$
$6$	1.84484	0.753154
$7$	2.16076	0.816692	0.408346	−	0.912827i	$-0.366106\pi$
$7$	2.16076	0.816692	0.408346	+	0.912827i	$0.366106\pi$
$8$	−1.00000	−0.353553
$9$	0.403448	0.134483
$10$	3.34479	1.05772
$11$	3.73765	1.12694	0.563472	−	0.826135i	$-0.309465\pi$
$11$	3.73765	1.12694	0.563472	+	0.826135i	$0.309465\pi$
$12$	−1.84484	−0.532560
$13$	4.02604	1.11662	0.558312	−	0.829631i	$-0.311449\pi$
$13$	4.02604	1.11662	0.558312	+	0.829631i	$0.311449\pi$
$14$	−2.16076	−0.577488
$15$	6.17062	1.59325
$16$	1.00000	0.250000
$17$	4.29909	1.04268	0.521342	−	0.853348i	$-0.325432\pi$
$17$	4.29909	1.04268	0.521342	+	0.853348i	$0.325432\pi$
$18$	−0.403448	−0.0950936
$19$	−2.98092	−0.683871	−0.341935	−	0.939723i	$-0.611082\pi$
$19$	−2.98092	−0.683871	−0.341935	+	0.939723i	$0.611082\pi$
$20$	−3.34479	−0.747919
$21$	−3.98627	−0.869876
$22$	−3.73765	−0.796870
$23$	6.16576	1.28565	0.642825	−	0.766013i	$-0.277762\pi$
$23$	6.16576	1.28565	0.642825	+	0.766013i	$0.277762\pi$
$24$	1.84484	0.376577
$25$	6.18765	1.23753
$26$	−4.02604	−0.789572
$27$	4.79023	0.921881
$28$	2.16076	0.408346
$29$	7.30530	1.35656	0.678280	−	0.734803i	$-0.262726\pi$
$29$	7.30530	1.35656	0.678280	+	0.734803i	$0.262726\pi$
$30$	−6.17062	−1.12660
$31$	3.71705	0.667601	0.333801	−	0.942644i	$-0.391669\pi$
$31$	3.71705	0.667601	0.333801	+	0.942644i	$0.391669\pi$
$32$	−1.00000	−0.176777
$33$	−6.89538	−1.20033
$34$	−4.29909	−0.737288
$35$	−7.22731	−1.22164
$36$	0.403448	0.0672413
$37$	−10.1033	−1.66097	−0.830483	−	0.557043i	$-0.811936\pi$
$37$	−10.1033	−1.66097	−0.830483	+	0.557043i	$0.811936\pi$
$38$	2.98092	0.483570
$39$	−7.42742	−1.18934
$40$	3.34479	0.528858
$41$	3.69304	0.576756	0.288378	−	0.957517i	$-0.406884\pi$
$41$	3.69304	0.576756	0.288378	+	0.957517i	$0.406884\pi$
$42$	3.98627	0.615095
$43$	−2.64166	−0.402849	−0.201425	−	0.979504i	$-0.564557\pi$
$43$	−2.64166	−0.402849	−0.201425	+	0.979504i	$0.564557\pi$
$44$	3.73765	0.563472
$45$	−1.34945	−0.201164
$46$	−6.16576	−0.909092
$47$	−4.03904	−0.589154	−0.294577	−	0.955628i	$-0.595179\pi$
$47$	−4.03904	−0.589154	−0.294577	+	0.955628i	$0.595179\pi$
$48$	−1.84484	−0.266280
$49$	−2.33110	−0.333015
$50$	−6.18765	−0.875066
$51$	−7.93115	−1.11058
$52$	4.02604	0.558312
$53$	4.27288	0.586925	0.293463	−	0.955971i	$-0.405192\pi$
$53$	4.27288	0.586925	0.293463	+	0.955971i	$0.405192\pi$
$54$	−4.79023	−0.651868
$55$	−12.5017	−1.68573
$56$	−2.16076	−0.288744
$57$	5.49934	0.728405
$58$	−7.30530	−0.959233
$59$	11.2765	1.46808	0.734038	−	0.679109i	$-0.237634\pi$
$59$	11.2765	1.46808	0.734038	+	0.679109i	$0.237634\pi$
$60$	6.17062	0.796624
$61$	−4.32811	−0.554158	−0.277079	−	0.960847i	$-0.589366\pi$
$61$	−4.32811	−0.554158	−0.277079	+	0.960847i	$0.589366\pi$
$62$	−3.71705	−0.472065
$63$	0.871756	0.109831
$64$	1.00000	0.125000
$65$	−13.4663	−1.67029
$66$	6.89538	0.848763
$67$	11.9286	1.45731	0.728654	−	0.684882i	$-0.240146\pi$
$67$	11.9286	1.45731	0.728654	+	0.684882i	$0.240146\pi$
$68$	4.29909	0.521342
$69$	−11.3749	−1.36937
$70$	7.22731	0.863829
$71$	−9.20425	−1.09234	−0.546172	−	0.837673i	$-0.683915\pi$
$71$	−9.20425	−1.09234	−0.546172	+	0.837673i	$0.683915\pi$
$72$	−0.403448	−0.0475468
$73$	1.57852	0.184751	0.0923756	−	0.995724i	$-0.470554\pi$
$73$	1.57852	0.184751	0.0923756	+	0.995724i	$0.470554\pi$
$74$	10.1033	1.17448
$75$	−11.4152	−1.31812
$76$	−2.98092	−0.341935
$77$	8.07618	0.920366
$78$	7.42742	0.840989
$79$	−6.40229	−0.720314	−0.360157	−	0.932892i	$-0.617277\pi$
$79$	−6.40229	−0.720314	−0.360157	+	0.932892i	$0.617277\pi$
$80$	−3.34479	−0.373959
$81$	−10.0476	−1.11640
$82$	−3.69304	−0.407828
$83$	12.2289	1.34230	0.671148	−	0.741323i	$-0.265801\pi$
$83$	12.2289	1.34230	0.671148	+	0.741323i	$0.265801\pi$
$84$	−3.98627	−0.434938
$85$	−14.3796	−1.55968
$86$	2.64166	0.284857
$87$	−13.4771	−1.44490
$88$	−3.73765	−0.398435
$89$	−12.0552	−1.27785	−0.638926	−	0.769268i	$-0.720621\pi$
$89$	−12.0552	−1.27785	−0.638926	+	0.769268i	$0.720621\pi$
$90$	1.34945	0.142245
$91$	8.69932	0.911937
$92$	6.16576	0.642825
$93$	−6.85737	−0.711076
$94$	4.03904	0.416595
$95$	9.97058	1.02296
$96$	1.84484	0.188289
$97$	−7.79901	−0.791870	−0.395935	−	0.918279i	$-0.629579\pi$
$97$	−7.79901	−0.791870	−0.395935	+	0.918279i	$0.629579\pi$
$98$	2.33110	0.235477
$99$	1.50795	0.151554
$100$	6.18765	0.618765
$101$	2.20182	0.219089	0.109544	−	0.993982i	$-0.465061\pi$
$101$	2.20182	0.219089	0.109544	+	0.993982i	$0.465061\pi$
$102$	7.93115	0.785301
$103$	−8.12246	−0.800330	−0.400165	−	0.916443i	$-0.631047\pi$
$103$	−8.12246	−0.800330	−0.400165	+	0.916443i	$0.631047\pi$
$104$	−4.02604	−0.394786
$105$	13.3333	1.30119
$106$	−4.27288	−0.415019
$107$	−5.80465	−0.561157	−0.280579	−	0.959831i	$-0.590526\pi$
$107$	−5.80465	−0.561157	−0.280579	+	0.959831i	$0.590526\pi$
$108$	4.79023	0.460940
$109$	17.6446	1.69004	0.845021	−	0.534733i	$-0.179588\pi$
$109$	17.6446	1.69004	0.845021	+	0.534733i	$0.179588\pi$
$110$	12.5017	1.19199
$111$	18.6389	1.76913
$112$	2.16076	0.204173
$113$	1.47504	0.138760	0.0693800	−	0.997590i	$-0.477898\pi$
$113$	1.47504	0.138760	0.0693800	+	0.997590i	$0.477898\pi$
$114$	−5.49934	−0.515060
$115$	−20.6232	−1.92312
$116$	7.30530	0.678280
$117$	1.62430	0.150166
$118$	−11.2765	−1.03809
$119$	9.28932	0.851551
$120$	−6.17062	−0.563298
$121$	2.97004	0.270004
$122$	4.32811	0.391849
$123$	−6.81309	−0.614315
$124$	3.71705	0.333801
$125$	−3.97245	−0.355307
$126$	−0.871756	−0.0776622
$127$	3.89371	0.345511	0.172755	−	0.984965i	$-0.444733\pi$
$127$	3.89371	0.345511	0.172755	+	0.984965i	$0.444733\pi$
$128$	−1.00000	−0.0883883
$129$	4.87345	0.429083
$130$	13.4663	1.18107
$131$	4.49818	0.393008	0.196504	−	0.980503i	$-0.437041\pi$
$131$	4.49818	0.393008	0.196504	+	0.980503i	$0.437041\pi$
$132$	−6.89538	−0.600166
$133$	−6.44107	−0.558512
$134$	−11.9286	−1.03047
$135$	−16.0223	−1.37898
$136$	−4.29909	−0.368644
$137$	−19.0101	−1.62414	−0.812069	−	0.583561i	$-0.801659\pi$
$137$	−19.0101	−1.62414	−0.812069	+	0.583561i	$0.801659\pi$
$138$	11.3749	0.968293
$139$	−6.21298	−0.526978	−0.263489	−	0.964662i	$-0.584873\pi$
$139$	−6.21298	−0.526978	−0.263489	+	0.964662i	$0.584873\pi$
$140$	−7.22731	−0.610819
$141$	7.45139	0.627520
$142$	9.20425	0.772404
$143$	15.0479	1.25837
$144$	0.403448	0.0336207
$145$	−24.4347	−2.02919
$146$	−1.57852	−0.130639
$147$	4.30052	0.354701
$148$	−10.1033	−0.830483
$149$	1.45564	0.119250	0.0596252	−	0.998221i	$-0.481009\pi$
$149$	1.45564	0.119250	0.0596252	+	0.998221i	$0.481009\pi$
$150$	11.4152	0.932051
$151$	−8.66529	−0.705171	−0.352586	−	0.935780i	$-0.614697\pi$
$151$	−8.66529	−0.705171	−0.352586	+	0.935780i	$0.614697\pi$
$152$	2.98092	0.241785
$153$	1.73446	0.140223
$154$	−8.07618	−0.650797
$155$	−12.4328	−0.998623
$156$	−7.42742	−0.594669
$157$	8.85098	0.706385	0.353193	−	0.935551i	$-0.385096\pi$
$157$	8.85098	0.706385	0.353193	+	0.935551i	$0.385096\pi$
$158$	6.40229	0.509339
$159$	−7.88279	−0.625146
$160$	3.34479	0.264429
$161$	13.3228	1.04998
$162$	10.0476	0.789412
$163$	4.99582	0.391303	0.195651	−	0.980674i	$-0.437318\pi$
$163$	4.99582	0.391303	0.195651	+	0.980674i	$0.437318\pi$
$164$	3.69304	0.288378
$165$	23.0636	1.79550
$166$	−12.2289	−0.949147
$167$	15.5509	1.20336	0.601681	−	0.798737i	$-0.294498\pi$
$167$	15.5509	1.20336	0.601681	+	0.798737i	$0.294498\pi$
$168$	3.98627	0.307547
$169$	3.20901	0.246847
$170$	14.3796	1.10286
$171$	−1.20265	−0.0919688
$172$	−2.64166	−0.201425
$173$	15.0843	1.14684	0.573420	−	0.819262i	$-0.305616\pi$
$173$	15.0843	1.14684	0.573420	+	0.819262i	$0.305616\pi$
$174$	13.4771	1.02170
$175$	13.3700	1.01068
$176$	3.73765	0.281736
$177$	−20.8034	−1.56368
$178$	12.0552	0.903577
$179$	13.0992	0.979081	0.489541	−	0.871981i	$-0.337165\pi$
$179$	13.0992	0.979081	0.489541	+	0.871981i	$0.337165\pi$
$180$	−1.34945	−0.100582
$181$	−3.82038	−0.283966	−0.141983	−	0.989869i	$-0.545348\pi$
$181$	−3.82038	−0.283966	−0.141983	+	0.989869i	$0.545348\pi$
$182$	−8.69932	−0.644837
$183$	7.98469	0.590245
$184$	−6.16576	−0.454546
$185$	33.7934	2.48454
$186$	6.85737	0.502807
$187$	16.0685	1.17505
$188$	−4.03904	−0.294577
$189$	10.3506	0.752892
$190$	−9.97058	−0.723342
$191$	6.61086	0.478345	0.239173	−	0.970977i	$-0.423124\pi$
$191$	6.61086	0.478345	0.239173	+	0.970977i	$0.423124\pi$
$192$	−1.84484	−0.133140
$193$	−23.9726	−1.72558	−0.862792	−	0.505559i	$-0.831286\pi$
$193$	−23.9726	−1.72558	−0.862792	+	0.505559i	$0.831286\pi$
$194$	7.79901	0.559936
$195$	24.8432	1.77906
$196$	−2.33110	−0.166507
$197$	1.83205	0.130528	0.0652641	−	0.997868i	$-0.479211\pi$
$197$	1.83205	0.130528	0.0652641	+	0.997868i	$0.479211\pi$
$198$	−1.50795	−0.107165
$199$	21.3313	1.51213	0.756067	−	0.654494i	$-0.227118\pi$
$199$	21.3313	1.51213	0.756067	+	0.654494i	$0.227118\pi$
$200$	−6.18765	−0.437533
$201$	−22.0064	−1.55221
$202$	−2.20182	−0.154919
$203$	15.7850	1.10789
$204$	−7.93115	−0.555292
$205$	−12.3525	−0.862734
$206$	8.12246	0.565919
$207$	2.48756	0.172898
$208$	4.02604	0.279156
$209$	−11.1417	−0.770684
$210$	−13.3333	−0.920082
$211$	1.77484	0.122185	0.0610925	−	0.998132i	$-0.480542\pi$
$211$	1.77484	0.122185	0.0610925	+	0.998132i	$0.480542\pi$
$212$	4.27288	0.293463
$213$	16.9804	1.16348
$214$	5.80465	0.396798
$215$	8.83581	0.602597
$216$	−4.79023	−0.325934
$217$	8.03166	0.545225
$218$	−17.6446	−1.19504
$219$	−2.91211	−0.196782
$220$	−12.5017	−0.842863
$221$	17.3083	1.16428
$222$	−18.6389	−1.25096
$223$	0.457579	0.0306418	0.0153209	−	0.999883i	$-0.495123\pi$
$223$	0.457579	0.0306418	0.0153209	+	0.999883i	$0.495123\pi$
$224$	−2.16076	−0.144372
$225$	2.49640	0.166426
$226$	−1.47504	−0.0981182
$227$	−4.20188	−0.278889	−0.139444	−	0.990230i	$-0.544532\pi$
$227$	−4.20188	−0.278889	−0.139444	+	0.990230i	$0.544532\pi$
$228$	5.49934	0.364203
$229$	16.0636	1.06151	0.530757	−	0.847524i	$-0.321908\pi$
$229$	16.0636	1.06151	0.530757	+	0.847524i	$0.321908\pi$
$230$	20.6232	1.35985
$231$	−14.8993	−0.980301
$232$	−7.30530	−0.479617
$233$	4.51703	0.295921	0.147960	−	0.988993i	$-0.452729\pi$
$233$	4.51703	0.295921	0.147960	+	0.988993i	$0.452729\pi$
$234$	−1.62430	−0.106184
$235$	13.5097	0.881279
$236$	11.2765	0.734038
$237$	11.8112	0.767222
$238$	−9.28932	−0.602137
$239$	12.0238	0.777752	0.388876	−	0.921290i	$-0.372863\pi$
$239$	12.0238	0.777752	0.388876	+	0.921290i	$0.372863\pi$
$240$	6.17062	0.398312
$241$	15.2875	0.984753	0.492376	−	0.870382i	$-0.336128\pi$
$241$	15.2875	0.984753	0.492376	+	0.870382i	$0.336128\pi$
$242$	−2.97004	−0.190921
$243$	4.16551	0.267217
$244$	−4.32811	−0.277079
$245$	7.79706	0.498136
$246$	6.81309	0.434387
$247$	−12.0013	−0.763626
$248$	−3.71705	−0.236033
$249$	−22.5604	−1.42971
$250$	3.97245	0.251240
$251$	10.9232	0.689465	0.344732	−	0.938701i	$-0.387970\pi$
$251$	10.9232	0.689465	0.344732	+	0.938701i	$0.387970\pi$
$252$	0.871756	0.0549154
$253$	23.0455	1.44886
$254$	−3.89371	−0.244313
$255$	26.5281	1.66125
$256$	1.00000	0.0625000
$257$	−6.85348	−0.427508	−0.213754	−	0.976888i	$-0.568569\pi$
$257$	−6.85348	−0.427508	−0.213754	+	0.976888i	$0.568569\pi$
$258$	−4.87345	−0.303408
$259$	−21.8308	−1.35650
$260$	−13.4663	−0.835143
$261$	2.94731	0.182434
$262$	−4.49818	−0.277898
$263$	−15.9844	−0.985641	−0.492820	−	0.870131i	$-0.664034\pi$
$263$	−15.9844	−0.985641	−0.492820	+	0.870131i	$0.664034\pi$
$264$	6.89538	0.424381
$265$	−14.2919	−0.877945
$266$	6.44107	0.394927
$267$	22.2400	1.36107
$268$	11.9286	0.728654
$269$	2.88174	0.175703	0.0878514	−	0.996134i	$-0.472000\pi$
$269$	2.88174	0.175703	0.0878514	+	0.996134i	$0.472000\pi$
$270$	16.0223	0.975089
$271$	−2.82486	−0.171598	−0.0857989	−	0.996312i	$-0.527344\pi$
$271$	−2.82486	−0.171598	−0.0857989	+	0.996312i	$0.527344\pi$
$272$	4.29909	0.260671
$273$	−16.0489	−0.971323
$274$	19.0101	1.14844
$275$	23.1273	1.39463
$276$	−11.3749	−0.684686
$277$	−15.4362	−0.927469	−0.463734	−	0.885974i	$-0.653491\pi$
$277$	−15.4362	−0.927469	−0.463734	+	0.885974i	$0.653491\pi$
$278$	6.21298	0.372630
$279$	1.49964	0.0897808
$280$	7.22731	0.431914
$281$	15.9094	0.949074	0.474537	−	0.880236i	$-0.342616\pi$
$281$	15.9094	0.949074	0.474537	+	0.880236i	$0.342616\pi$
$282$	−7.45139	−0.443724
$283$	−12.6508	−0.752010	−0.376005	−	0.926618i	$-0.622703\pi$
$283$	−12.6508	−0.752010	−0.376005	+	0.926618i	$0.622703\pi$
$284$	−9.20425	−0.546172
$285$	−18.3942	−1.08958
$286$	−15.0479	−0.889803
$287$	7.97979	0.471032
$288$	−0.403448	−0.0237734
$289$	1.48220	0.0871882
$290$	24.4347	1.43486
$291$	14.3880	0.843437
$292$	1.57852	0.0923756
$293$	−1.79612	−0.104931	−0.0524653	−	0.998623i	$-0.516708\pi$
$293$	−1.79612	−0.104931	−0.0524653	+	0.998623i	$0.516708\pi$
$294$	−4.30052	−0.250811
$295$	−37.7176	−2.19600
$296$	10.1033	0.587241
$297$	17.9042	1.03891
$298$	−1.45564	−0.0843227
$299$	24.8236	1.43559
$300$	−11.4152	−0.659060
$301$	−5.70800	−0.329004
$302$	8.66529	0.498631
$303$	−4.06201	−0.233356
$304$	−2.98092	−0.170968
$305$	14.4766	0.828930
$306$	−1.73446	−0.0991525
$307$	−7.47704	−0.426737	−0.213369	−	0.976972i	$-0.568444\pi$
$307$	−7.47704	−0.426737	−0.213369	+	0.976972i	$0.568444\pi$
$308$	8.07618	0.460183
$309$	14.9847	0.852448
$310$	12.4328	0.706133
$311$	−18.1497	−1.02917	−0.514587	−	0.857438i	$-0.672055\pi$
$311$	−18.1497	−1.02917	−0.514587	+	0.857438i	$0.672055\pi$
$312$	7.42742	0.420495
$313$	19.7049	1.11379	0.556894	−	0.830583i	$-0.311993\pi$
$313$	19.7049	1.11379	0.556894	+	0.830583i	$0.311993\pi$
$314$	−8.85098	−0.499490
$315$	−2.91584	−0.164289
$316$	−6.40229	−0.360157
$317$	−35.0317	−1.96758	−0.983789	−	0.179327i	$-0.942608\pi$
$317$	−35.0317	−1.96758	−0.983789	+	0.179327i	$0.942608\pi$
$318$	7.88279	0.442045
$319$	27.3047	1.52877
$320$	−3.34479	−0.186980
$321$	10.7087	0.597700
$322$	−13.3228	−0.742448
$323$	−12.8153	−0.713060
$324$	−10.0476	−0.558199
$325$	24.9117	1.38185
$326$	−4.99582	−0.276693
$327$	−32.5515	−1.80010
$328$	−3.69304	−0.203914
$329$	−8.72740	−0.481157
$330$	−23.0636	−1.26961
$331$	−2.41141	−0.132543	−0.0662716	−	0.997802i	$-0.521110\pi$
$331$	−2.41141	−0.132543	−0.0662716	+	0.997802i	$0.521110\pi$
$332$	12.2289	0.671148
$333$	−4.07614	−0.223371
$334$	−15.5509	−0.850905
$335$	−39.8986	−2.17990
$336$	−3.98627	−0.217469
$337$	26.3120	1.43331	0.716653	−	0.697430i	$-0.245673\pi$
$337$	26.3120	1.43331	0.716653	+	0.697430i	$0.245673\pi$
$338$	−3.20901	−0.174547
$339$	−2.72122	−0.147796
$340$	−14.3796	−0.779842
$341$	13.8930	0.752350
$342$	1.20265	0.0650317
$343$	−20.1623	−1.08866
$344$	2.64166	0.142429
$345$	38.0466	2.04836
$346$	−15.0843	−0.810938
$347$	−10.2412	−0.549776	−0.274888	−	0.961476i	$-0.588641\pi$
$347$	−10.2412	−0.549776	−0.274888	+	0.961476i	$0.588641\pi$
$348$	−13.4771	−0.722450
$349$	−2.25201	−0.120547	−0.0602736	−	0.998182i	$-0.519197\pi$
$349$	−2.25201	−0.120547	−0.0602736	+	0.998182i	$0.519197\pi$
$350$	−13.3700	−0.714659
$351$	19.2857	1.02939
$352$	−3.73765	−0.199218
$353$	36.8762	1.96272	0.981362	−	0.192170i	$-0.0615527\pi$
$353$	36.8762	1.96272	0.981362	+	0.192170i	$0.0615527\pi$
$354$	20.8034	1.10569
$355$	30.7863	1.63397
$356$	−12.0552	−0.638926
$357$	−17.1373	−0.907005
$358$	−13.0992	−0.692315
$359$	−10.6032	−0.559618	−0.279809	−	0.960056i	$-0.590271\pi$
$359$	−10.6032	−0.559618	−0.279809	+	0.960056i	$0.590271\pi$
$360$	1.34945	0.0711223
$361$	−10.1141	−0.532321
$362$	3.82038	0.200795
$363$	−5.47926	−0.287587
$364$	8.69932	0.455968
$365$	−5.27981	−0.276358
$366$	−7.98469	−0.417366
$367$	−26.8860	−1.40344	−0.701720	−	0.712453i	$-0.747584\pi$
$367$	−26.8860	−1.40344	−0.701720	+	0.712453i	$0.747584\pi$
$368$	6.16576	0.321413
$369$	1.48995	0.0775637
$370$	−33.7934	−1.75683
$371$	9.23268	0.479337
$372$	−6.85737	−0.355538
$373$	−0.705113	−0.0365094	−0.0182547	−	0.999833i	$-0.505811\pi$
$373$	−0.705113	−0.0365094	−0.0182547	+	0.999833i	$0.505811\pi$
$374$	−16.0685	−0.830883
$375$	7.32855	0.378444
$376$	4.03904	0.208297
$377$	29.4114	1.51477
$378$	−10.3506	−0.532375
$379$	−7.53244	−0.386916	−0.193458	−	0.981109i	$-0.561970\pi$
$379$	−7.53244	−0.386916	−0.193458	+	0.981109i	$0.561970\pi$
$380$	9.97058	0.511480
$381$	−7.18329	−0.368011
$382$	−6.61086	−0.338241
$383$	36.9743	1.88930	0.944648	−	0.328085i	$-0.106403\pi$
$383$	36.9743	1.88930	0.944648	+	0.328085i	$0.106403\pi$
$384$	1.84484	0.0941443
$385$	−27.0132	−1.37672
$386$	23.9726	1.22017
$387$	−1.06577	−0.0541762
$388$	−7.79901	−0.395935
$389$	8.25718	0.418656	0.209328	−	0.977846i	$-0.432872\pi$
$389$	8.25718	0.418656	0.209328	+	0.977846i	$0.432872\pi$
$390$	−24.8432	−1.25798
$391$	26.5072	1.34053
$392$	2.33110	0.117738
$393$	−8.29843	−0.418601
$394$	−1.83205	−0.0922973
$395$	21.4143	1.07747
$396$	1.50795	0.0757772
$397$	18.9853	0.952847	0.476424	−	0.879216i	$-0.341933\pi$
$397$	18.9853	0.952847	0.476424	+	0.879216i	$0.341933\pi$
$398$	−21.3313	−1.06924
$399$	11.8828	0.594882
$400$	6.18765	0.309383
$401$	−3.52138	−0.175850	−0.0879248	−	0.996127i	$-0.528024\pi$
$401$	−3.52138	−0.175850	−0.0879248	+	0.996127i	$0.528024\pi$
$402$	22.0064	1.09758
$403$	14.9650	0.745459
$404$	2.20182	0.109544
$405$	33.6071	1.66995
$406$	−15.7850	−0.783398
$407$	−37.7625	−1.87182
$408$	7.93115	0.392651
$409$	17.6403	0.872259	0.436130	−	0.899884i	$-0.356349\pi$
$409$	17.6403	0.872259	0.436130	+	0.899884i	$0.356349\pi$
$410$	12.3525	0.610045
$411$	35.0706	1.72990
$412$	−8.12246	−0.400165
$413$	24.3658	1.19896
$414$	−2.48756	−0.122257
$415$	−40.9032	−2.00786
$416$	−4.02604	−0.197393
$417$	11.4620	0.561295
$418$	11.1417	0.544956
$419$	16.8503	0.823191	0.411595	−	0.911367i	$-0.364972\pi$
$419$	16.8503	0.823191	0.411595	+	0.911367i	$0.364972\pi$
$420$	13.3333	0.650596
$421$	−8.30535	−0.404778	−0.202389	−	0.979305i	$-0.564871\pi$
$421$	−8.30535	−0.404778	−0.202389	+	0.979305i	$0.564871\pi$
$422$	−1.77484	−0.0863978
$423$	−1.62954	−0.0792310
$424$	−4.27288	−0.207509
$425$	26.6013	1.29035
$426$	−16.9804	−0.822703
$427$	−9.35202	−0.452576
$428$	−5.80465	−0.280579
$429$	−27.7611	−1.34032
$430$	−8.83581	−0.426100
$431$	−14.6726	−0.706755	−0.353377	−	0.935481i	$-0.614967\pi$
$431$	−14.6726	−0.706755	−0.353377	+	0.935481i	$0.614967\pi$
$432$	4.79023	0.230470
$433$	−5.98990	−0.287856	−0.143928	−	0.989588i	$-0.545973\pi$
$433$	−5.98990	−0.287856	−0.143928	+	0.989588i	$0.545973\pi$
$434$	−8.03166	−0.385532
$435$	45.0783	2.16134
$436$	17.6446	0.845021
$437$	−18.3797	−0.879218
$438$	2.91211	0.139146
$439$	12.0067	0.573048	0.286524	−	0.958073i	$-0.407500\pi$
$439$	12.0067	0.573048	0.286524	+	0.958073i	$0.407500\pi$
$440$	12.5017	0.595994
$441$	−0.940478	−0.0447847
$442$	−17.3083	−0.823273
$443$	15.2651	0.725268	0.362634	−	0.931932i	$-0.381878\pi$
$443$	15.2651	0.725268	0.362634	+	0.931932i	$0.381878\pi$
$444$	18.6389	0.884565
$445$	40.3223	1.91146
$446$	−0.457579	−0.0216670
$447$	−2.68542	−0.127016
$448$	2.16076	0.102086
$449$	29.6411	1.39885	0.699424	−	0.714707i	$-0.253440\pi$
$449$	29.6411	1.39885	0.699424	+	0.714707i	$0.253440\pi$
$450$	−2.49640	−0.117681
$451$	13.8033	0.649972
$452$	1.47504	0.0693800
$453$	15.9861	0.751093
$454$	4.20188	0.197204
$455$	−29.0974	−1.36411
$456$	−5.49934	−0.257530
$457$	26.6595	1.24708	0.623539	−	0.781792i	$-0.285694\pi$
$457$	26.6595	1.24708	0.623539	+	0.781792i	$0.285694\pi$
$458$	−16.0636	−0.750604
$459$	20.5937	0.961229
$460$	−20.6232	−0.961562
$461$	14.3833	0.669896	0.334948	−	0.942237i	$-0.391281\pi$
$461$	14.3833	0.669896	0.334948	+	0.942237i	$0.391281\pi$
$462$	14.8993	0.693178
$463$	14.9597	0.695237	0.347619	−	0.937636i	$-0.386990\pi$
$463$	14.9597	0.695237	0.347619	+	0.937636i	$0.386990\pi$
$464$	7.30530	0.339140
$465$	22.9365	1.06365
$466$	−4.51703	−0.209247
$467$	−8.01190	−0.370747	−0.185373	−	0.982668i	$-0.559349\pi$
$467$	−8.01190	−0.370747	−0.185373	+	0.982668i	$0.559349\pi$
$468$	1.62430	0.0750832
$469$	25.7748	1.19017
$470$	−13.5097	−0.623158
$471$	−16.3287	−0.752386
$472$	−11.2765	−0.519043
$473$	−9.87360	−0.453989
$474$	−11.8112	−0.542508
$475$	−18.4449	−0.846311
$476$	9.28932	0.425775
$477$	1.72388	0.0789313
$478$	−12.0238	−0.549954
$479$	24.8257	1.13432	0.567158	−	0.823609i	$-0.308043\pi$
$479$	24.8257	1.13432	0.567158	+	0.823609i	$0.308043\pi$
$480$	−6.17062	−0.281649
$481$	−40.6762	−1.85467
$482$	−15.2875	−0.696325
$483$	−24.5784	−1.11836
$484$	2.97004	0.135002
$485$	26.0861	1.18451
$486$	−4.16551	−0.188951
$487$	−23.1937	−1.05101	−0.525503	−	0.850792i	$-0.676123\pi$
$487$	−23.1937	−1.05101	−0.525503	+	0.850792i	$0.676123\pi$
$488$	4.32811	0.195924
$489$	−9.21651	−0.416785
$490$	−7.79706	−0.352235
$491$	13.3963	0.604565	0.302283	−	0.953218i	$-0.402251\pi$
$491$	13.3963	0.604565	0.302283	+	0.953218i	$0.402251\pi$
$492$	−6.81309	−0.307158
$493$	31.4062	1.41446
$494$	12.0013	0.539965
$495$	−5.04378	−0.226701
$496$	3.71705	0.166900
$497$	−19.8882	−0.892108
$498$	22.5604	1.01096
$499$	42.1878	1.88859	0.944293	−	0.329106i	$-0.106747\pi$
$499$	42.1878	1.88859	0.944293	+	0.329106i	$0.106747\pi$
$500$	−3.97245	−0.177653
$501$	−28.6889	−1.28173
$502$	−10.9232	−0.487525
$503$	−15.7253	−0.701157	−0.350578	−	0.936533i	$-0.614015\pi$
$503$	−15.7253	−0.701157	−0.350578	+	0.936533i	$0.614015\pi$
$504$	−0.871756	−0.0388311
$505$	−7.36462	−0.327721
$506$	−23.0455	−1.02450
$507$	−5.92012	−0.262922
$508$	3.89371	0.172755
$509$	24.4530	1.08386	0.541931	−	0.840423i	$-0.317693\pi$
$509$	24.4530	1.08386	0.541931	+	0.840423i	$0.317693\pi$
$510$	−26.5281	−1.17468
$511$	3.41080	0.150885
$512$	−1.00000	−0.0441942
$513$	−14.2793	−0.630447
$514$	6.85348	0.302294
$515$	27.1680	1.19716
$516$	4.87345	0.214542
$517$	−15.0965	−0.663944
$518$	21.8308	0.959189
$519$	−27.8282	−1.22152
$520$	13.4663	0.590536
$521$	11.9195	0.522204	0.261102	−	0.965311i	$-0.415914\pi$
$521$	11.9195	0.522204	0.261102	+	0.965311i	$0.415914\pi$
$522$	−2.94731	−0.129000
$523$	−21.6505	−0.946712	−0.473356	−	0.880871i	$-0.656957\pi$
$523$	−21.6505	−0.946712	−0.473356	+	0.880871i	$0.656957\pi$
$524$	4.49818	0.196504
$525$	−24.6657	−1.07650
$526$	15.9844	0.696953
$527$	15.9799	0.696097
$528$	−6.89538	−0.300083
$529$	15.0166	0.652896
$530$	14.2919	0.620801
$531$	4.54948	0.197431
$532$	−6.44107	−0.279256
$533$	14.8683	0.644020
$534$	−22.2400	−0.962419
$535$	19.4154	0.839400
$536$	−11.9286	−0.515236
$537$	−24.1660	−1.04284
$538$	−2.88174	−0.124241
$539$	−8.71285	−0.375289
$540$	−16.0223	−0.689492
$541$	30.6570	1.31805	0.659024	−	0.752122i	$-0.270969\pi$
$541$	30.6570	1.31805	0.659024	+	0.752122i	$0.270969\pi$
$542$	2.82486	0.121338
$543$	7.04800	0.302459
$544$	−4.29909	−0.184322
$545$	−59.0174	−2.52803
$546$	16.0489	0.686829
$547$	14.1313	0.604209	0.302105	−	0.953275i	$-0.402311\pi$
$547$	14.1313	0.604209	0.302105	+	0.953275i	$0.402311\pi$
$548$	−19.0101	−0.812069
$549$	−1.74617	−0.0745246
$550$	−23.1273	−0.986151
$551$	−21.7765	−0.927712
$552$	11.3749	0.484146
$553$	−13.8338	−0.588275
$554$	15.4362	0.655819
$555$	−62.3435	−2.64633
$556$	−6.21298	−0.263489
$557$	13.0406	0.552546	0.276273	−	0.961079i	$-0.410901\pi$
$557$	13.0406	0.552546	0.276273	+	0.961079i	$0.410901\pi$
$558$	−1.49964	−0.0634846
$559$	−10.6354	−0.449831
$560$	−7.22731	−0.305410
$561$	−29.6439	−1.25157
$562$	−15.9094	−0.671096
$563$	−39.3976	−1.66041	−0.830205	−	0.557458i	$-0.811777\pi$
$563$	−39.3976	−1.66041	−0.830205	+	0.557458i	$0.811777\pi$
$564$	7.45139	0.313760
$565$	−4.93370	−0.207563
$566$	12.6508	0.531752
$567$	−21.7104	−0.911752
$568$	9.20425	0.386202
$569$	−33.1812	−1.39103	−0.695514	−	0.718512i	$-0.744823\pi$
$569$	−33.1812	−1.39103	−0.695514	+	0.718512i	$0.744823\pi$
$570$	18.3942	0.770446
$571$	−23.0335	−0.963920	−0.481960	−	0.876193i	$-0.660075\pi$
$571$	−23.0335	−0.963920	−0.481960	+	0.876193i	$0.660075\pi$
$572$	15.0479	0.629186
$573$	−12.1960	−0.509496
$574$	−7.97979	−0.333070
$575$	38.1516	1.59103
$576$	0.403448	0.0168103
$577$	−33.4154	−1.39110	−0.695552	−	0.718476i	$-0.744840\pi$
$577$	−33.4154	−1.39110	−0.695552	+	0.718476i	$0.744840\pi$
$578$	−1.48220	−0.0616513
$579$	44.2257	1.83796
$580$	−24.4347	−1.01460
$581$	26.4238	1.09624
$582$	−14.3880	−0.596400
$583$	15.9705	0.661432
$584$	−1.57852	−0.0653194
$585$	−5.43294	−0.224625
$586$	1.79612	0.0741972
$587$	7.25131	0.299294	0.149647	−	0.988740i	$-0.452186\pi$
$587$	7.25131	0.299294	0.149647	+	0.988740i	$0.452186\pi$
$588$	4.30052	0.177350
$589$	−11.0802	−0.456553
$590$	37.7176	1.55281
$591$	−3.37985	−0.139028
$592$	−10.1033	−0.415242
$593$	8.08453	0.331992	0.165996	−	0.986126i	$-0.446916\pi$
$593$	8.08453	0.331992	0.165996	+	0.986126i	$0.446916\pi$
$594$	−17.9042	−0.734619
$595$	−31.0709	−1.27378
$596$	1.45564	0.0596252
$597$	−39.3529	−1.61061
$598$	−24.8236	−1.01511
$599$	−14.0259	−0.573084	−0.286542	−	0.958068i	$-0.592506\pi$
$599$	−14.0259	−0.573084	−0.286542	+	0.958068i	$0.592506\pi$
$600$	11.4152	0.466026
$601$	−28.1391	−1.14782	−0.573909	−	0.818919i	$-0.694574\pi$
$601$	−28.1391	−1.14782	−0.573909	+	0.818919i	$0.694574\pi$
$602$	5.70800	0.232641
$603$	4.81256	0.195983
$604$	−8.66529	−0.352586
$605$	−9.93417	−0.403882
$606$	4.06201	0.165008
$607$	−16.3586	−0.663975	−0.331988	−	0.943284i	$-0.607719\pi$
$607$	−16.3586	−0.663975	−0.331988	+	0.943284i	$0.607719\pi$
$608$	2.98092	0.120892
$609$	−29.1209	−1.18004
$610$	−14.4766	−0.586142
$611$	−16.2613	−0.657863
$612$	1.73446	0.0701114
$613$	24.8962	1.00555	0.502773	−	0.864418i	$-0.332313\pi$
$613$	24.8962	1.00555	0.502773	+	0.864418i	$0.332313\pi$
$614$	7.47704	0.301749
$615$	22.7884	0.918916
$616$	−8.07618	−0.325399
$617$	−23.1063	−0.930226	−0.465113	−	0.885251i	$-0.653986\pi$
$617$	−23.1063	−0.930226	−0.465113	+	0.885251i	$0.653986\pi$
$618$	−14.9847	−0.602772
$619$	3.04879	0.122541	0.0612706	−	0.998121i	$-0.480485\pi$
$619$	3.04879	0.122541	0.0612706	+	0.998121i	$0.480485\pi$
$620$	−12.4328	−0.499312
$621$	29.5354	1.18522
$622$	18.1497	0.727736
$623$	−26.0485	−1.04361
$624$	−7.42742	−0.297335
$625$	−17.6512	−0.706049
$626$	−19.7049	−0.787568
$627$	20.5546	0.820872
$628$	8.85098	0.353193
$629$	−43.4349	−1.73186
$630$	2.91584	0.116170
$631$	−28.4659	−1.13321	−0.566604	−	0.823990i	$-0.691743\pi$
$631$	−28.4659	−1.13321	−0.566604	+	0.823990i	$0.691743\pi$
$632$	6.40229	0.254669
$633$	−3.27430	−0.130142
$634$	35.0317	1.39129
$635$	−13.0237	−0.516828
$636$	−7.88279	−0.312573
$637$	−9.38511	−0.371852
$638$	−27.3047	−1.08100
$639$	−3.71344	−0.146901
$640$	3.34479	0.132215
$641$	16.6672	0.658314	0.329157	−	0.944275i	$-0.393235\pi$
$641$	16.6672	0.658314	0.329157	+	0.944275i	$0.393235\pi$
$642$	−10.7087	−0.422638
$643$	−12.2241	−0.482073	−0.241036	−	0.970516i	$-0.577487\pi$
$643$	−12.2241	−0.482073	−0.241036	+	0.970516i	$0.577487\pi$
$644$	13.3228	0.524990
$645$	−16.3007	−0.641839
$646$	12.8153	0.504210
$647$	−28.0938	−1.10448	−0.552241	−	0.833684i	$-0.686227\pi$
$647$	−28.0938	−1.10448	−0.552241	+	0.833684i	$0.686227\pi$
$648$	10.0476	0.394706
$649$	42.1476	1.65444
$650$	−24.9117	−0.977119
$651$	−14.8172	−0.580730
$652$	4.99582	0.195651
$653$	−35.2343	−1.37883	−0.689413	−	0.724369i	$-0.742131\pi$
$653$	−35.2343	−1.37883	−0.689413	+	0.724369i	$0.742131\pi$
$654$	32.5515	1.27286
$655$	−15.0455	−0.587876
$656$	3.69304	0.144189
$657$	0.636849	0.0248458
$658$	8.72740	0.340230
$659$	0.987860	0.0384815	0.0192408	−	0.999815i	$-0.493875\pi$
$659$	0.987860	0.0384815	0.0192408	+	0.999815i	$0.493875\pi$
$660$	23.0636	0.897751
$661$	37.7539	1.46846	0.734228	−	0.678903i	$-0.237544\pi$
$661$	37.7539	1.46846	0.734228	+	0.678903i	$0.237544\pi$
$662$	2.41141	0.0937222
$663$	−31.9312	−1.24010
$664$	−12.2289	−0.474573
$665$	21.5441	0.835443
$666$	4.07614	0.157947
$667$	45.0427	1.74406
$668$	15.5509	0.601681
$669$	−0.844162	−0.0326372
$670$	39.8986	1.54142
$671$	−16.1770	−0.624505
$672$	3.98627	0.153774
$673$	24.1985	0.932785	0.466392	−	0.884578i	$-0.345553\pi$
$673$	24.1985	0.932785	0.466392	+	0.884578i	$0.345553\pi$
$674$	−26.3120	−1.01350
$675$	29.6403	1.14086
$676$	3.20901	0.123424
$677$	−13.6233	−0.523586	−0.261793	−	0.965124i	$-0.584314\pi$
$677$	−13.6233	−0.523586	−0.261793	+	0.965124i	$0.584314\pi$
$678$	2.72122	0.104508
$679$	−16.8518	−0.646714
$680$	14.3796	0.551432
$681$	7.75181	0.297050
$682$	−13.8930	−0.531992
$683$	11.4647	0.438684	0.219342	−	0.975648i	$-0.429609\pi$
$683$	11.4647	0.438684	0.219342	+	0.975648i	$0.429609\pi$
$684$	−1.20265	−0.0459844
$685$	63.5847	2.42945
$686$	20.1623	0.769800
$687$	−29.6349	−1.13064
$688$	−2.64166	−0.100712
$689$	17.2028	0.655374
$690$	−38.0466	−1.44841
$691$	−3.42446	−0.130272	−0.0651362	−	0.997876i	$-0.520748\pi$
$691$	−3.42446	−0.130272	−0.0651362	+	0.997876i	$0.520748\pi$
$692$	15.0843	0.573420
$693$	3.25832	0.123773
$694$	10.2412	0.388750
$695$	20.7811	0.788274
$696$	13.4771	0.510850
$697$	15.8767	0.601374
$698$	2.25201	0.0852398
$699$	−8.33322	−0.315191
$700$	13.3700	0.505340
$701$	1.06995	0.0404113	0.0202056	−	0.999796i	$-0.493568\pi$
$701$	1.06995	0.0404113	0.0202056	+	0.999796i	$0.493568\pi$
$702$	−19.2857	−0.727891
$703$	30.1171	1.13589
$704$	3.73765	0.140868
$705$	−24.9234	−0.938668
$706$	−36.8762	−1.38785
$707$	4.75760	0.178928
$708$	−20.8034	−0.781839
$709$	−1.58168	−0.0594012	−0.0297006	−	0.999559i	$-0.509455\pi$
$709$	−1.58168	−0.0594012	−0.0297006	+	0.999559i	$0.509455\pi$
$710$	−30.7863	−1.15539
$711$	−2.58299	−0.0968698
$712$	12.0552	0.451789
$713$	22.9184	0.858302
$714$	17.1373	0.641349
$715$	−50.3323	−1.88232
$716$	13.0992	0.489541
$717$	−22.1820	−0.828400
$718$	10.6032	0.395709
$719$	16.9788	0.633203	0.316601	−	0.948559i	$-0.397458\pi$
$719$	16.9788	0.633203	0.316601	+	0.948559i	$0.397458\pi$
$720$	−1.34945	−0.0502911
$721$	−17.5507	−0.653623
$722$	10.1141	0.376408
$723$	−28.2030	−1.04888
$724$	−3.82038	−0.141983
$725$	45.2027	1.67878
$726$	5.47926	0.203354
$727$	−3.38417	−0.125512	−0.0627560	−	0.998029i	$-0.519989\pi$
$727$	−3.38417	−0.125512	−0.0627560	+	0.998029i	$0.519989\pi$
$728$	−8.69932	−0.322418
$729$	22.4580	0.831778
$730$	5.27981	0.195415
$731$	−11.3567	−0.420044
$732$	7.98469	0.295123
$733$	−33.2338	−1.22752	−0.613759	−	0.789493i	$-0.710343\pi$
$733$	−33.2338	−1.22752	−0.613759	+	0.789493i	$0.710343\pi$
$734$	26.8860	0.992381
$735$	−14.3844	−0.530575
$736$	−6.16576	−0.227273
$737$	44.5849	1.64230
$738$	−1.48995	−0.0548459
$739$	9.70002	0.356821	0.178411	−	0.983956i	$-0.442904\pi$
$739$	9.70002	0.356821	0.178411	+	0.983956i	$0.442904\pi$
$740$	33.7934	1.24227
$741$	22.1406	0.813354
$742$	−9.23268	−0.338942
$743$	7.65583	0.280865	0.140433	−	0.990090i	$-0.455151\pi$
$743$	7.65583	0.280865	0.140433	+	0.990090i	$0.455151\pi$
$744$	6.85737	0.251403
$745$	−4.86880	−0.178379
$746$	0.705113	0.0258160
$747$	4.93373	0.180516
$748$	16.0685	0.587523
$749$	−12.5425	−0.458292
$750$	−7.32855	−0.267601
$751$	−36.4908	−1.33157	−0.665785	−	0.746144i	$-0.731903\pi$
$751$	−36.4908	−1.33157	−0.665785	+	0.746144i	$0.731903\pi$
$752$	−4.03904	−0.147288
$753$	−20.1515	−0.734363
$754$	−29.4114	−1.07110
$755$	28.9836	1.05482
$756$	10.3506	0.376446
$757$	33.5592	1.21973	0.609864	−	0.792506i	$-0.291224\pi$
$757$	33.5592	1.21973	0.609864	+	0.792506i	$0.291224\pi$
$758$	7.53244	0.273591
$759$	−42.5153	−1.54321
$760$	−9.97058	−0.361671
$761$	31.8877	1.15593	0.577964	−	0.816062i	$-0.303847\pi$
$761$	31.8877	1.15593	0.577964	+	0.816062i	$0.303847\pi$
$762$	7.18329	0.260223
$763$	38.1257	1.38024
$764$	6.61086	0.239173
$765$	−5.80141	−0.209751
$766$	−36.9743	−1.33593
$767$	45.3997	1.63929
$768$	−1.84484	−0.0665701
$769$	6.05985	0.218524	0.109262	−	0.994013i	$-0.465151\pi$
$769$	6.05985	0.218524	0.109262	+	0.994013i	$0.465151\pi$
$770$	27.0132	0.973487
$771$	12.6436	0.455348
$772$	−23.9726	−0.862792
$773$	4.95519	0.178226	0.0891128	−	0.996022i	$-0.471597\pi$
$773$	4.95519	0.178226	0.0891128	+	0.996022i	$0.471597\pi$
$774$	1.06577	0.0383084
$775$	22.9998	0.826177
$776$	7.79901	0.279968
$777$	40.2744	1.44483
$778$	−8.25718	−0.296034
$779$	−11.0087	−0.394427
$780$	24.8432	0.889529
$781$	−34.4023	−1.23101
$782$	−26.5072	−0.947895
$783$	34.9941	1.25059
$784$	−2.33110	−0.0832536
$785$	−29.6047	−1.05664
$786$	8.29843	0.295995
$787$	−45.8329	−1.63377	−0.816883	−	0.576804i	$-0.804300\pi$
$787$	−45.8329	−1.63377	−0.816883	+	0.576804i	$0.804300\pi$
$788$	1.83205	0.0652641
$789$	29.4887	1.04983
$790$	−21.4143	−0.761888
$791$	3.18721	0.113324
$792$	−1.50795	−0.0535826
$793$	−17.4252	−0.618785
$794$	−18.9853	−0.673765
$795$	26.3663	0.935117
$796$	21.3313	0.756067
$797$	12.5277	0.443755	0.221877	−	0.975075i	$-0.428782\pi$
$797$	12.5277	0.443755	0.221877	+	0.975075i	$0.428782\pi$
$798$	−11.8828	−0.420645
$799$	−17.3642	−0.614301
$800$	−6.18765	−0.218766
$801$	−4.86366	−0.171849
$802$	3.52138	0.124344
$803$	5.89994	0.208204
$804$	−22.0064	−0.776104
$805$	−44.5619	−1.57060
$806$	−14.9650	−0.527119
$807$	−5.31636	−0.187145
$808$	−2.20182	−0.0774596
$809$	2.49640	0.0877687	0.0438844	−	0.999037i	$-0.486027\pi$
$809$	2.49640	0.0877687	0.0438844	+	0.999037i	$0.486027\pi$
$810$	−33.6071	−1.18083
$811$	18.0070	0.632311	0.316155	−	0.948707i	$-0.397608\pi$
$811$	18.0070	0.632311	0.316155	+	0.948707i	$0.397608\pi$
$812$	15.7850	0.553946
$813$	5.21142	0.182772
$814$	37.7625	1.32357
$815$	−16.7100	−0.585326
$816$	−7.93115	−0.277646
$817$	7.87458	0.275497
$818$	−17.6403	−0.616780
$819$	3.50972	0.122640
$820$	−12.3525	−0.431367
$821$	−29.0093	−1.01243	−0.506216	−	0.862407i	$-0.668956\pi$
$821$	−29.0093	−1.01243	−0.506216	+	0.862407i	$0.668956\pi$
$822$	−35.0706	−1.22323
$823$	−15.4379	−0.538131	−0.269066	−	0.963122i	$-0.586715\pi$
$823$	−15.4379	−0.538131	−0.269066	+	0.963122i	$0.586715\pi$
$824$	8.12246	0.282959
$825$	−42.6662	−1.48545
$826$	−24.3658	−0.847796
$827$	−46.9468	−1.63250	−0.816251	−	0.577698i	$-0.803951\pi$
$827$	−46.9468	−1.63250	−0.816251	+	0.577698i	$0.803951\pi$
$828$	2.48756	0.0864488
$829$	−23.9522	−0.831895	−0.415948	−	0.909389i	$-0.636550\pi$
$829$	−23.9522	−0.831895	−0.415948	+	0.909389i	$0.636550\pi$
$830$	40.9032	1.41977
$831$	28.4773	0.987866
$832$	4.02604	0.139578
$833$	−10.0216	−0.347229
$834$	−11.4620	−0.396896
$835$	−52.0144	−1.80003
$836$	−11.1417	−0.385342
$837$	17.8055	0.615449
$838$	−16.8503	−0.582084
$839$	18.1471	0.626506	0.313253	−	0.949670i	$-0.398581\pi$
$839$	18.1471	0.626506	0.313253	+	0.949670i	$0.398581\pi$
$840$	−13.3333	−0.460041
$841$	24.3674	0.840256
$842$	8.30535	0.286221
$843$	−29.3503	−1.01088
$844$	1.77484	0.0610925
$845$	−10.7335	−0.369243
$846$	1.62954	0.0560248
$847$	6.41755	0.220510
$848$	4.27288	0.146731
$849$	23.3387	0.800982
$850$	−26.6013	−0.912417
$851$	−62.2943	−2.13542
$852$	16.9804	0.581739
$853$	41.6232	1.42515	0.712576	−	0.701595i	$-0.247529\pi$
$853$	41.6232	1.42515	0.712576	+	0.701595i	$0.247529\pi$
$854$	9.35202	0.320020
$855$	4.02261	0.137570
$856$	5.80465	0.198399
$857$	−19.1409	−0.653840	−0.326920	−	0.945052i	$-0.606011\pi$
$857$	−19.1409	−0.653840	−0.326920	+	0.945052i	$0.606011\pi$
$858$	27.7611	0.947748
$859$	−12.6941	−0.433118	−0.216559	−	0.976270i	$-0.569483\pi$
$859$	−12.6941	−0.433118	−0.216559	+	0.976270i	$0.569483\pi$
$860$	8.83581	0.301298
$861$	−14.7215	−0.501706
$862$	14.6726	0.499751
$863$	−0.497137	−0.0169227	−0.00846137	−	0.999964i	$-0.502693\pi$
$863$	−0.497137	−0.0169227	−0.00846137	+	0.999964i	$0.502693\pi$
$864$	−4.79023	−0.162967
$865$	−50.4539	−1.71549
$866$	5.98990	0.203545
$867$	−2.73442	−0.0928659
$868$	8.03166	0.272612
$869$	−23.9295	−0.811754
$870$	−45.0783	−1.52830
$871$	48.0249	1.62726
$872$	−17.6446	−0.597520
$873$	−3.14650	−0.106493
$874$	18.3797	0.621701
$875$	−8.58352	−0.290176
$876$	−2.91211	−0.0983912
$877$	−3.54908	−0.119844	−0.0599219	−	0.998203i	$-0.519085\pi$
$877$	−3.54908	−0.119844	−0.0599219	+	0.998203i	$0.519085\pi$
$878$	−12.0067	−0.405206
$879$	3.31357	0.111764
$880$	−12.5017	−0.421431
$881$	32.1024	1.08156	0.540778	−	0.841165i	$-0.318130\pi$
$881$	32.1024	1.08156	0.540778	+	0.841165i	$0.318130\pi$
$882$	0.940478	0.0316676
$883$	−36.6780	−1.23431	−0.617157	−	0.786840i	$-0.711716\pi$
$883$	−36.6780	−1.23431	−0.617157	+	0.786840i	$0.711716\pi$
$884$	17.3083	0.582142
$885$	69.5830	2.33901
$886$	−15.2651	−0.512842
$887$	17.8692	0.599989	0.299994	−	0.953941i	$-0.403015\pi$
$887$	17.8692	0.599989	0.299994	+	0.953941i	$0.403015\pi$
$888$	−18.6389	−0.625482
$889$	8.41339	0.282176
$890$	−40.3223	−1.35161
$891$	−37.5543	−1.25812
$892$	0.457579	0.0153209
$893$	12.0401	0.402905
$894$	2.68542	0.0898139
$895$	−43.8142	−1.46455
$896$	−2.16076	−0.0721860
$897$	−45.7957	−1.52907
$898$	−29.6411	−0.989135
$899$	27.1542	0.905642
$900$	2.49640	0.0832132
$901$	18.3695	0.611977
$902$	−13.8033	−0.459600
$903$	10.5304	0.350429
$904$	−1.47504	−0.0490591
$905$	12.7784	0.424768
$906$	−15.9861	−0.531103
$907$	−16.8167	−0.558390	−0.279195	−	0.960234i	$-0.590068\pi$
$907$	−16.8167	−0.558390	−0.279195	+	0.960234i	$0.590068\pi$
$908$	−4.20188	−0.139444
$909$	0.888318	0.0294637
$910$	29.0974	0.964571
$911$	−16.1268	−0.534305	−0.267153	−	0.963654i	$-0.586083\pi$
$911$	−16.1268	−0.534305	−0.267153	+	0.963654i	$0.586083\pi$
$912$	5.49934	0.182101
$913$	45.7074	1.51269
$914$	−26.6595	−0.881817
$915$	−26.7071	−0.882911
$916$	16.0636	0.530757
$917$	9.71950	0.320966
$918$	−20.5937	−0.679692
$919$	34.4697	1.13705	0.568525	−	0.822666i	$-0.307514\pi$
$919$	34.4697	1.13705	0.568525	+	0.822666i	$0.307514\pi$
$920$	20.6232	0.679927
$921$	13.7940	0.454527
$922$	−14.3833	−0.473688
$923$	−37.0567	−1.21974
$924$	−14.8993	−0.490151
$925$	−62.5155	−2.05550
$926$	−14.9597	−0.491607
$927$	−3.27699	−0.107631
$928$	−7.30530	−0.239808
$929$	−32.6522	−1.07129	−0.535643	−	0.844445i	$-0.679931\pi$
$929$	−32.6522	−1.07129	−0.535643	+	0.844445i	$0.679931\pi$
$930$	−22.9365	−0.752117
$931$	6.94884	0.227739
$932$	4.51703	0.147960
$933$	33.4833	1.09620
$934$	8.01190	0.262157
$935$	−53.7459	−1.75768
$936$	−1.62430	−0.0530919
$937$	22.1997	0.725233	0.362617	−	0.931938i	$-0.381883\pi$
$937$	22.1997	0.725233	0.362617	+	0.931938i	$0.381883\pi$
$938$	−25.7748	−0.841578
$939$	−36.3525	−1.18632
$940$	13.5097	0.440639
$941$	−30.5215	−0.994973	−0.497487	−	0.867472i	$-0.665744\pi$
$941$	−30.5215	−0.994973	−0.497487	+	0.867472i	$0.665744\pi$
$942$	16.3287	0.532017
$943$	22.7704	0.741507
$944$	11.2765	0.367019
$945$	−34.6205	−1.12620
$946$	9.87360	0.321018
$947$	24.8387	0.807148	0.403574	−	0.914947i	$-0.367768\pi$
$947$	24.8387	0.807148	0.403574	+	0.914947i	$0.367768\pi$
$948$	11.8112	0.383611
$949$	6.35517	0.206297
$950$	18.4449	0.598432
$951$	64.6281	2.09571
$952$	−9.28932	−0.301069
$953$	32.2595	1.04499	0.522493	−	0.852643i	$-0.325002\pi$
$953$	32.2595	1.04499	0.522493	+	0.852643i	$0.325002\pi$
$954$	−1.72388	−0.0558128
$955$	−22.1120	−0.715527
$956$	12.0238	0.388876
$957$	−50.3728	−1.62832
$958$	−24.8257	−0.802083
$959$	−41.0762	−1.32642
$960$	6.17062	0.199156
$961$	−17.1836	−0.554308
$962$	40.6762	1.31145
$963$	−2.34188	−0.0754659
$964$	15.2875	0.492376
$965$	80.1834	2.58119
$966$	24.5784	0.790797
$967$	58.4615	1.88000	0.939998	−	0.341181i	$-0.110827\pi$
$967$	58.4615	1.88000	0.939998	+	0.341181i	$0.110827\pi$
$968$	−2.97004	−0.0954607
$969$	23.6422	0.759496
$970$	−26.0861	−0.837574
$971$	7.93671	0.254701	0.127351	−	0.991858i	$-0.459353\pi$
$971$	7.93671	0.254701	0.127351	+	0.991858i	$0.459353\pi$
$972$	4.16551	0.133609
$973$	−13.4248	−0.430379
$974$	23.1937	0.743174
$975$	−45.9583	−1.47184
$976$	−4.32811	−0.138539
$977$	−14.1711	−0.453374	−0.226687	−	0.973968i	$-0.572789\pi$
$977$	−14.1711	−0.453374	−0.226687	+	0.973968i	$0.572789\pi$
$978$	9.21651	0.294711
$979$	−45.0582	−1.44007
$980$	7.79706	0.249068
$981$	7.11866	0.227281
$982$	−13.3963	−0.427492
$983$	−40.0098	−1.27611	−0.638057	−	0.769989i	$-0.720262\pi$
$983$	−40.0098	−1.27611	−0.638057	+	0.769989i	$0.720262\pi$
$984$	6.81309	0.217193
$985$	−6.12783	−0.195249
$986$	−31.4062	−1.00018
$987$	16.1007	0.512491
$988$	−12.0013	−0.381813
$989$	−16.2878	−0.517923
$990$	5.04378	0.160302
$991$	−42.4937	−1.34986	−0.674928	−	0.737883i	$-0.735826\pi$
$991$	−42.4937	−1.34986	−0.674928	+	0.737883i	$0.735826\pi$
$992$	−3.71705	−0.118016
$993$	4.44868	0.141174
$994$	19.8882	0.630816
$995$	−71.3488	−2.26191
$996$	−22.5604	−0.714854
$997$	60.8884	1.92836	0.964178	−	0.265256i	$-0.0854564\pi$
$997$	60.8884	1.92836	0.964178	+	0.265256i	$0.0854564\pi$
$998$	−42.1878	−1.33543
$999$	−48.3970	−1.53121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.10	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.10	✓	42	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.84484 q^{3} +1.00000 q^{4} -3.34479 q^{5} +1.84484 q^{6} +2.16076 q^{7} -1.00000 q^{8} +0.403448 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.84484 q^{3} +1.00000 q^{4} -3.34479 q^{5} +1.84484 q^{6} +2.16076 q^{7} -1.00000 q^{8} +0.403448 q^{9} +3.34479 q^{10} +3.73765 q^{11} -1.84484 q^{12} +4.02604 q^{13} -2.16076 q^{14} +6.17062 q^{15} +1.00000 q^{16} +4.29909 q^{17} -0.403448 q^{18} -2.98092 q^{19} -3.34479 q^{20} -3.98627 q^{21} -3.73765 q^{22} +6.16576 q^{23} +1.84484 q^{24} +6.18765 q^{25} -4.02604 q^{26} +4.79023 q^{27} +2.16076 q^{28} +7.30530 q^{29} -6.17062 q^{30} +3.71705 q^{31} -1.00000 q^{32} -6.89538 q^{33} -4.29909 q^{34} -7.22731 q^{35} +0.403448 q^{36} -10.1033 q^{37} +2.98092 q^{38} -7.42742 q^{39} +3.34479 q^{40} +3.69304 q^{41} +3.98627 q^{42} -2.64166 q^{43} +3.73765 q^{44} -1.34945 q^{45} -6.16576 q^{46} -4.03904 q^{47} -1.84484 q^{48} -2.33110 q^{49} -6.18765 q^{50} -7.93115 q^{51} +4.02604 q^{52} +4.27288 q^{53} -4.79023 q^{54} -12.5017 q^{55} -2.16076 q^{56} +5.49934 q^{57} -7.30530 q^{58} +11.2765 q^{59} +6.17062 q^{60} -4.32811 q^{61} -3.71705 q^{62} +0.871756 q^{63} +1.00000 q^{64} -13.4663 q^{65} +6.89538 q^{66} +11.9286 q^{67} +4.29909 q^{68} -11.3749 q^{69} +7.22731 q^{70} -9.20425 q^{71} -0.403448 q^{72} +1.57852 q^{73} +10.1033 q^{74} -11.4152 q^{75} -2.98092 q^{76} +8.07618 q^{77} +7.42742 q^{78} -6.40229 q^{79} -3.34479 q^{80} -10.0476 q^{81} -3.69304 q^{82} +12.2289 q^{83} -3.98627 q^{84} -14.3796 q^{85} +2.64166 q^{86} -13.4771 q^{87} -3.73765 q^{88} -12.0552 q^{89} +1.34945 q^{90} +8.69932 q^{91} +6.16576 q^{92} -6.85737 q^{93} +4.03904 q^{94} +9.97058 q^{95} +1.84484 q^{96} -7.79901 q^{97} +2.33110 q^{98} +1.50795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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