LMFDB - Embedded newform 4026.2.a.t.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.825785$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14386 q^{5} +1.00000 q^{6} -1.54771 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14386 q^{5} +1.00000 q^{6} -1.54771 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.14386 q^{10} -1.00000 q^{11} +1.00000 q^{12} -6.01809 q^{13} -1.54771 q^{14} +1.14386 q^{15} +1.00000 q^{16} -5.63616 q^{17} +1.00000 q^{18} -2.94459 q^{19} +1.14386 q^{20} -1.54771 q^{21} -1.00000 q^{22} -3.47735 q^{23} +1.00000 q^{24} -3.69157 q^{25} -6.01809 q^{26} +1.00000 q^{27} -1.54771 q^{28} -2.10386 q^{29} +1.14386 q^{30} -4.77881 q^{31} +1.00000 q^{32} -1.00000 q^{33} -5.63616 q^{34} -1.77037 q^{35} +1.00000 q^{36} +6.21040 q^{37} -2.94459 q^{38} -6.01809 q^{39} +1.14386 q^{40} -1.67348 q^{41} -1.54771 q^{42} +5.01112 q^{43} -1.00000 q^{44} +1.14386 q^{45} -3.47735 q^{46} -4.26267 q^{47} +1.00000 q^{48} -4.60459 q^{49} -3.69157 q^{50} -5.63616 q^{51} -6.01809 q^{52} +2.04697 q^{53} +1.00000 q^{54} -1.14386 q^{55} -1.54771 q^{56} -2.94459 q^{57} -2.10386 q^{58} -6.35280 q^{59} +1.14386 q^{60} -1.00000 q^{61} -4.77881 q^{62} -1.54771 q^{63} +1.00000 q^{64} -6.88388 q^{65} -1.00000 q^{66} +1.66651 q^{67} -5.63616 q^{68} -3.47735 q^{69} -1.77037 q^{70} +8.23547 q^{71} +1.00000 q^{72} +3.82894 q^{73} +6.21040 q^{74} -3.69157 q^{75} -2.94459 q^{76} +1.54771 q^{77} -6.01809 q^{78} +2.20893 q^{79} +1.14386 q^{80} +1.00000 q^{81} -1.67348 q^{82} -4.41497 q^{83} -1.54771 q^{84} -6.44700 q^{85} +5.01112 q^{86} -2.10386 q^{87} -1.00000 q^{88} +1.84073 q^{89} +1.14386 q^{90} +9.31426 q^{91} -3.47735 q^{92} -4.77881 q^{93} -4.26267 q^{94} -3.36821 q^{95} +1.00000 q^{96} +8.66391 q^{97} -4.60459 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{14} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 8 q^{19} - 4 q^{20} - 6 q^{21} - 4 q^{22} - 7 q^{23} + 4 q^{24} - 6 q^{25} - 5 q^{26} + 4 q^{27} - 6 q^{28} - 4 q^{29} - 4 q^{30} - 9 q^{31} + 4 q^{32} - 4 q^{33} - 10 q^{34} - q^{35} + 4 q^{36} - 11 q^{37} - 8 q^{38} - 5 q^{39} - 4 q^{40} - 17 q^{41} - 6 q^{42} - 11 q^{43} - 4 q^{44} - 4 q^{45} - 7 q^{46} - 7 q^{47} + 4 q^{48} - 6 q^{49} - 6 q^{50} - 10 q^{51} - 5 q^{52} + 16 q^{53} + 4 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{57} - 4 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} - 9 q^{62} - 6 q^{63} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 10 q^{68} - 7 q^{69} - q^{70} - 10 q^{71} + 4 q^{72} - 9 q^{73} - 11 q^{74} - 6 q^{75} - 8 q^{76} + 6 q^{77} - 5 q^{78} - 11 q^{79} - 4 q^{80} + 4 q^{81} - 17 q^{82} + 5 q^{83} - 6 q^{84} - 8 q^{85} - 11 q^{86} - 4 q^{87} - 4 q^{88} + 8 q^{89} - 4 q^{90} - 3 q^{91} - 7 q^{92} - 9 q^{93} - 7 q^{94} + 7 q^{95} + 4 q^{96} - 12 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^14 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 - 4 * q^22 - 7 * q^23 + 4 * q^24 - 6 * q^25 - 5 * q^26 + 4 * q^27 - 6 * q^28 - 4 * q^29 - 4 * q^30 - 9 * q^31 + 4 * q^32 - 4 * q^33 - 10 * q^34 - q^35 + 4 * q^36 - 11 * q^37 - 8 * q^38 - 5 * q^39 - 4 * q^40 - 17 * q^41 - 6 * q^42 - 11 * q^43 - 4 * q^44 - 4 * q^45 - 7 * q^46 - 7 * q^47 + 4 * q^48 - 6 * q^49 - 6 * q^50 - 10 * q^51 - 5 * q^52 + 16 * q^53 + 4 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^57 - 4 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 - 9 * q^62 - 6 * q^63 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 10 * q^68 - 7 * q^69 - q^70 - 10 * q^71 + 4 * q^72 - 9 * q^73 - 11 * q^74 - 6 * q^75 - 8 * q^76 + 6 * q^77 - 5 * q^78 - 11 * q^79 - 4 * q^80 + 4 * q^81 - 17 * q^82 + 5 * q^83 - 6 * q^84 - 8 * q^85 - 11 * q^86 - 4 * q^87 - 4 * q^88 + 8 * q^89 - 4 * q^90 - 3 * q^91 - 7 * q^92 - 9 * q^93 - 7 * q^94 + 7 * q^95 + 4 * q^96 - 12 * q^97 - 6 * q^98 - 4 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.14386	0.511552	0.255776	−	0.966736i	$-0.417669\pi$
$5$	1.14386	0.511552	0.255776	+	0.966736i	$0.417669\pi$
$6$	1.00000	0.408248
$7$	−1.54771	−0.584979	−0.292490	−	0.956269i	$-0.594484\pi$
$7$	−1.54771	−0.584979	−0.292490	+	0.956269i	$0.594484\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.14386	0.361722
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−6.01809	−1.66912	−0.834559	−	0.550918i	$-0.814278\pi$
$13$	−6.01809	−1.66912	−0.834559	+	0.550918i	$0.814278\pi$
$14$	−1.54771	−0.413643
$15$	1.14386	0.295345
$16$	1.00000	0.250000
$17$	−5.63616	−1.36697	−0.683485	−	0.729965i	$-0.739536\pi$
$17$	−5.63616	−1.36697	−0.683485	+	0.729965i	$0.739536\pi$
$18$	1.00000	0.235702
$19$	−2.94459	−0.675534	−0.337767	−	0.941230i	$-0.609672\pi$
$19$	−2.94459	−0.675534	−0.337767	+	0.941230i	$0.609672\pi$
$20$	1.14386	0.255776
$21$	−1.54771	−0.337738
$22$	−1.00000	−0.213201
$23$	−3.47735	−0.725078	−0.362539	−	0.931969i	$-0.618090\pi$
$23$	−3.47735	−0.725078	−0.362539	+	0.931969i	$0.618090\pi$
$24$	1.00000	0.204124
$25$	−3.69157	−0.738315
$26$	−6.01809	−1.18025
$27$	1.00000	0.192450
$28$	−1.54771	−0.292490
$29$	−2.10386	−0.390677	−0.195338	−	0.980736i	$-0.562581\pi$
$29$	−2.10386	−0.390677	−0.195338	+	0.980736i	$0.562581\pi$
$30$	1.14386	0.208840
$31$	−4.77881	−0.858300	−0.429150	−	0.903233i	$-0.641187\pi$
$31$	−4.77881	−0.858300	−0.429150	+	0.903233i	$0.641187\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−5.63616	−0.966593
$35$	−1.77037	−0.299247
$36$	1.00000	0.166667
$37$	6.21040	1.02098	0.510492	−	0.859883i	$-0.329463\pi$
$37$	6.21040	1.02098	0.510492	+	0.859883i	$0.329463\pi$
$38$	−2.94459	−0.477675
$39$	−6.01809	−0.963666
$40$	1.14386	0.180861
$41$	−1.67348	−0.261354	−0.130677	−	0.991425i	$-0.541715\pi$
$41$	−1.67348	−0.261354	−0.130677	+	0.991425i	$0.541715\pi$
$42$	−1.54771	−0.238817
$43$	5.01112	0.764189	0.382095	−	0.924123i	$-0.375203\pi$
$43$	5.01112	0.764189	0.382095	+	0.924123i	$0.375203\pi$
$44$	−1.00000	−0.150756
$45$	1.14386	0.170517
$46$	−3.47735	−0.512708
$47$	−4.26267	−0.621774	−0.310887	−	0.950447i	$-0.600626\pi$
$47$	−4.26267	−0.621774	−0.310887	+	0.950447i	$0.600626\pi$
$48$	1.00000	0.144338
$49$	−4.60459	−0.657799
$50$	−3.69157	−0.522067
$51$	−5.63616	−0.789220
$52$	−6.01809	−0.834559
$53$	2.04697	0.281174	0.140587	−	0.990068i	$-0.455101\pi$
$53$	2.04697	0.281174	0.140587	+	0.990068i	$0.455101\pi$
$54$	1.00000	0.136083
$55$	−1.14386	−0.154239
$56$	−1.54771	−0.206821
$57$	−2.94459	−0.390020
$58$	−2.10386	−0.276250
$59$	−6.35280	−0.827064	−0.413532	−	0.910490i	$-0.635705\pi$
$59$	−6.35280	−0.827064	−0.413532	+	0.910490i	$0.635705\pi$
$60$	1.14386	0.147672
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−4.77881	−0.606909
$63$	−1.54771	−0.194993
$64$	1.00000	0.125000
$65$	−6.88388	−0.853841
$66$	−1.00000	−0.123091
$67$	1.66651	0.203597	0.101798	−	0.994805i	$-0.467540\pi$
$67$	1.66651	0.203597	0.101798	+	0.994805i	$0.467540\pi$
$68$	−5.63616	−0.683485
$69$	−3.47735	−0.418624
$70$	−1.77037	−0.211600
$71$	8.23547	0.977370	0.488685	−	0.872460i	$-0.337477\pi$
$71$	8.23547	0.977370	0.488685	+	0.872460i	$0.337477\pi$
$72$	1.00000	0.117851
$73$	3.82894	0.448143	0.224072	−	0.974573i	$-0.428065\pi$
$73$	3.82894	0.448143	0.224072	+	0.974573i	$0.428065\pi$
$74$	6.21040	0.721945
$75$	−3.69157	−0.426266
$76$	−2.94459	−0.337767
$77$	1.54771	0.176378
$78$	−6.01809	−0.681415
$79$	2.20893	0.248524	0.124262	−	0.992249i	$-0.460344\pi$
$79$	2.20893	0.248524	0.124262	+	0.992249i	$0.460344\pi$
$80$	1.14386	0.127888
$81$	1.00000	0.111111
$82$	−1.67348	−0.184805
$83$	−4.41497	−0.484606	−0.242303	−	0.970201i	$-0.577903\pi$
$83$	−4.41497	−0.484606	−0.242303	+	0.970201i	$0.577903\pi$
$84$	−1.54771	−0.168869
$85$	−6.44700	−0.699276
$86$	5.01112	0.540363
$87$	−2.10386	−0.225557
$88$	−1.00000	−0.106600
$89$	1.84073	0.195117	0.0975583	−	0.995230i	$-0.468897\pi$
$89$	1.84073	0.195117	0.0975583	+	0.995230i	$0.468897\pi$
$90$	1.14386	0.120574
$91$	9.31426	0.976400
$92$	−3.47735	−0.362539
$93$	−4.77881	−0.495540
$94$	−4.26267	−0.439660
$95$	−3.36821	−0.345571
$96$	1.00000	0.102062
$97$	8.66391	0.879687	0.439843	−	0.898075i	$-0.355034\pi$
$97$	8.66391	0.879687	0.439843	+	0.898075i	$0.355034\pi$
$98$	−4.60459	−0.465134
$99$	−1.00000	−0.100504
$100$	−3.69157	−0.369157
$101$	−3.46891	−0.345170	−0.172585	−	0.984995i	$-0.555212\pi$
$101$	−3.46891	−0.345170	−0.172585	+	0.984995i	$0.555212\pi$
$102$	−5.63616	−0.558063
$103$	6.43306	0.633869	0.316934	−	0.948447i	$-0.397347\pi$
$103$	6.43306	0.633869	0.316934	+	0.948447i	$0.397347\pi$
$104$	−6.01809	−0.590123
$105$	−1.77037	−0.172770
$106$	2.04697	0.198820
$107$	12.6671	1.22457	0.612285	−	0.790637i	$-0.290250\pi$
$107$	12.6671	1.22457	0.612285	+	0.790637i	$0.290250\pi$
$108$	1.00000	0.0962250
$109$	15.4374	1.47864	0.739319	−	0.673356i	$-0.235148\pi$
$109$	15.4374	1.47864	0.739319	+	0.673356i	$0.235148\pi$
$110$	−1.14386	−0.109063
$111$	6.21040	0.589465
$112$	−1.54771	−0.146245
$113$	13.8316	1.30117	0.650585	−	0.759434i	$-0.274524\pi$
$113$	13.8316	1.30117	0.650585	+	0.759434i	$0.274524\pi$
$114$	−2.94459	−0.275786
$115$	−3.97762	−0.370915
$116$	−2.10386	−0.195338
$117$	−6.01809	−0.556373
$118$	−6.35280	−0.584822
$119$	8.72314	0.799649
$120$	1.14386	0.104420
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−1.67348	−0.150893
$124$	−4.77881	−0.429150
$125$	−9.94198	−0.889238
$126$	−1.54771	−0.137881
$127$	−12.0709	−1.07112	−0.535560	−	0.844497i	$-0.679899\pi$
$127$	−12.0709	−1.07112	−0.535560	+	0.844497i	$0.679899\pi$
$128$	1.00000	0.0883883
$129$	5.01112	0.441205
$130$	−6.88388	−0.603757
$131$	−8.83422	−0.771850	−0.385925	−	0.922530i	$-0.626118\pi$
$131$	−8.83422	−0.771850	−0.385925	+	0.922530i	$0.626118\pi$
$132$	−1.00000	−0.0870388
$133$	4.55736	0.395174
$134$	1.66651	0.143965
$135$	1.14386	0.0984482
$136$	−5.63616	−0.483297
$137$	2.60794	0.222812	0.111406	−	0.993775i	$-0.464465\pi$
$137$	2.60794	0.222812	0.111406	+	0.993775i	$0.464465\pi$
$138$	−3.47735	−0.296012
$139$	−4.32920	−0.367198	−0.183599	−	0.983001i	$-0.558775\pi$
$139$	−4.32920	−0.367198	−0.183599	+	0.983001i	$0.558775\pi$
$140$	−1.77037	−0.149624
$141$	−4.26267	−0.358981
$142$	8.23547	0.691105
$143$	6.01809	0.503258
$144$	1.00000	0.0833333
$145$	−2.40653	−0.199851
$146$	3.82894	0.316885
$147$	−4.60459	−0.379781
$148$	6.21040	0.510492
$149$	11.5049	0.942517	0.471259	−	0.881995i	$-0.343800\pi$
$149$	11.5049	0.942517	0.471259	+	0.881995i	$0.343800\pi$
$150$	−3.69157	−0.301416
$151$	11.2723	0.917328	0.458664	−	0.888610i	$-0.348328\pi$
$151$	11.2723	0.917328	0.458664	+	0.888610i	$0.348328\pi$
$152$	−2.94459	−0.238837
$153$	−5.63616	−0.455657
$154$	1.54771	0.124718
$155$	−5.46631	−0.439065
$156$	−6.01809	−0.481833
$157$	−3.83301	−0.305908	−0.152954	−	0.988233i	$-0.548879\pi$
$157$	−3.83301	−0.305908	−0.152954	+	0.988233i	$0.548879\pi$
$158$	2.20893	0.175733
$159$	2.04697	0.162336
$160$	1.14386	0.0904304
$161$	5.38193	0.424156
$162$	1.00000	0.0785674
$163$	−13.1555	−1.03041	−0.515207	−	0.857066i	$-0.672285\pi$
$163$	−13.1555	−1.03041	−0.515207	+	0.857066i	$0.672285\pi$
$164$	−1.67348	−0.130677
$165$	−1.14386	−0.0890497
$166$	−4.41497	−0.342668
$167$	−4.19399	−0.324541	−0.162270	−	0.986746i	$-0.551882\pi$
$167$	−4.19399	−0.324541	−0.162270	+	0.986746i	$0.551882\pi$
$168$	−1.54771	−0.119408
$169$	23.2175	1.78596
$170$	−6.44700	−0.494463
$171$	−2.94459	−0.225178
$172$	5.01112	0.382095
$173$	−21.3762	−1.62520	−0.812600	−	0.582821i	$-0.801949\pi$
$173$	−21.3762	−1.62520	−0.812600	+	0.582821i	$0.801949\pi$
$174$	−2.10386	−0.159493
$175$	5.71349	0.431899
$176$	−1.00000	−0.0753778
$177$	−6.35280	−0.477505
$178$	1.84073	0.137968
$179$	−0.955454	−0.0714140	−0.0357070	−	0.999362i	$-0.511368\pi$
$179$	−0.955454	−0.0714140	−0.0357070	+	0.999362i	$0.511368\pi$
$180$	1.14386	0.0852586
$181$	2.51086	0.186631	0.0933153	−	0.995637i	$-0.470254\pi$
$181$	2.51086	0.186631	0.0933153	+	0.995637i	$0.470254\pi$
$182$	9.31426	0.690419
$183$	−1.00000	−0.0739221
$184$	−3.47735	−0.256354
$185$	7.10386	0.522286
$186$	−4.77881	−0.350399
$187$	5.63616	0.412157
$188$	−4.26267	−0.310887
$189$	−1.54771	−0.112579
$190$	−3.36821	−0.244355
$191$	7.60896	0.550565	0.275283	−	0.961363i	$-0.411229\pi$
$191$	7.60896	0.550565	0.275283	+	0.961363i	$0.411229\pi$
$192$	1.00000	0.0721688
$193$	−16.7374	−1.20479	−0.602393	−	0.798200i	$-0.705786\pi$
$193$	−16.7374	−1.20479	−0.602393	+	0.798200i	$0.705786\pi$
$194$	8.66391	0.622032
$195$	−6.88388	−0.492965
$196$	−4.60459	−0.328900
$197$	−5.10533	−0.363740	−0.181870	−	0.983323i	$-0.558215\pi$
$197$	−5.10533	−0.363740	−0.181870	+	0.983323i	$0.558215\pi$
$198$	−1.00000	−0.0710669
$199$	−4.96121	−0.351691	−0.175845	−	0.984418i	$-0.556266\pi$
$199$	−4.96121	−0.351691	−0.175845	+	0.984418i	$0.556266\pi$
$200$	−3.69157	−0.261034
$201$	1.66651	0.117547
$202$	−3.46891	−0.244072
$203$	3.25616	0.228538
$204$	−5.63616	−0.394610
$205$	−1.91423	−0.133696
$206$	6.43306	0.448213
$207$	−3.47735	−0.241693
$208$	−6.01809	−0.417280
$209$	2.94459	0.203681
$210$	−1.77037	−0.122167
$211$	−6.87376	−0.473209	−0.236605	−	0.971606i	$-0.576035\pi$
$211$	−6.87376	−0.473209	−0.236605	+	0.971606i	$0.576035\pi$
$212$	2.04697	0.140587
$213$	8.23547	0.564285
$214$	12.6671	0.865902
$215$	5.73205	0.390922
$216$	1.00000	0.0680414
$217$	7.39621	0.502088
$218$	15.4374	1.04555
$219$	3.82894	0.258736
$220$	−1.14386	−0.0771193
$221$	33.9189	2.28163
$222$	6.21040	0.416815
$223$	9.82868	0.658177	0.329089	−	0.944299i	$-0.393259\pi$
$223$	9.82868	0.658177	0.329089	+	0.944299i	$0.393259\pi$
$224$	−1.54771	−0.103411
$225$	−3.69157	−0.246105
$226$	13.8316	0.920066
$227$	15.0610	0.999633	0.499817	−	0.866131i	$-0.333401\pi$
$227$	15.0610	0.999633	0.499817	+	0.866131i	$0.333401\pi$
$228$	−2.94459	−0.195010
$229$	−19.7109	−1.30253	−0.651266	−	0.758850i	$-0.725762\pi$
$229$	−19.7109	−1.30253	−0.651266	+	0.758850i	$0.725762\pi$
$230$	−3.97762	−0.262277
$231$	1.54771	0.101832
$232$	−2.10386	−0.138125
$233$	6.12771	0.401440	0.200720	−	0.979649i	$-0.435672\pi$
$233$	6.12771	0.401440	0.200720	+	0.979649i	$0.435672\pi$
$234$	−6.01809	−0.393415
$235$	−4.87591	−0.318069
$236$	−6.35280	−0.413532
$237$	2.20893	0.143486
$238$	8.72314	0.565437
$239$	−25.9673	−1.67969	−0.839843	−	0.542830i	$-0.817353\pi$
$239$	−25.9673	−1.67969	−0.839843	+	0.542830i	$0.817353\pi$
$240$	1.14386	0.0738361
$241$	−8.41518	−0.542069	−0.271035	−	0.962570i	$-0.587366\pi$
$241$	−8.41518	−0.542069	−0.271035	+	0.962570i	$0.587366\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−5.26703	−0.336498
$246$	−1.67348	−0.106697
$247$	17.7208	1.12755
$248$	−4.77881	−0.303455
$249$	−4.41497	−0.279787
$250$	−9.94198	−0.628786
$251$	13.5839	0.857408	0.428704	−	0.903445i	$-0.358970\pi$
$251$	13.5839	0.857408	0.428704	+	0.903445i	$0.358970\pi$
$252$	−1.54771	−0.0974965
$253$	3.47735	0.218619
$254$	−12.0709	−0.757396
$255$	−6.44700	−0.403727
$256$	1.00000	0.0625000
$257$	13.9075	0.867525	0.433762	−	0.901027i	$-0.357186\pi$
$257$	13.9075	0.867525	0.433762	+	0.901027i	$0.357186\pi$
$258$	5.01112	0.311979
$259$	−9.61190	−0.597255
$260$	−6.88388	−0.426920
$261$	−2.10386	−0.130226
$262$	−8.83422	−0.545780
$263$	−16.1892	−0.998271	−0.499136	−	0.866524i	$-0.666349\pi$
$263$	−16.1892	−0.998271	−0.499136	+	0.866524i	$0.666349\pi$
$264$	−1.00000	−0.0615457
$265$	2.34146	0.143835
$266$	4.55736	0.279430
$267$	1.84073	0.112651
$268$	1.66651	0.101798
$269$	−17.2230	−1.05010	−0.525051	−	0.851071i	$-0.675954\pi$
$269$	−17.2230	−1.05010	−0.525051	+	0.851071i	$0.675954\pi$
$270$	1.14386	0.0696134
$271$	12.5280	0.761023	0.380511	−	0.924776i	$-0.375748\pi$
$271$	12.5280	0.761023	0.380511	+	0.924776i	$0.375748\pi$
$272$	−5.63616	−0.341742
$273$	9.31426	0.563725
$274$	2.60794	0.157552
$275$	3.69157	0.222610
$276$	−3.47735	−0.209312
$277$	−18.6572	−1.12100	−0.560501	−	0.828154i	$-0.689391\pi$
$277$	−18.6572	−1.12100	−0.560501	+	0.828154i	$0.689391\pi$
$278$	−4.32920	−0.259648
$279$	−4.77881	−0.286100
$280$	−1.77037	−0.105800
$281$	−25.9633	−1.54884	−0.774421	−	0.632671i	$-0.781959\pi$
$281$	−25.9633	−1.54884	−0.774421	+	0.632671i	$0.781959\pi$
$282$	−4.26267	−0.253838
$283$	3.92557	0.233351	0.116675	−	0.993170i	$-0.462776\pi$
$283$	3.92557	0.233351	0.116675	+	0.993170i	$0.462776\pi$
$284$	8.23547	0.488685
$285$	−3.36821	−0.199515
$286$	6.01809	0.355857
$287$	2.59006	0.152887
$288$	1.00000	0.0589256
$289$	14.7663	0.868606
$290$	−2.40653	−0.141316
$291$	8.66391	0.507887
$292$	3.82894	0.224072
$293$	−20.0651	−1.17222	−0.586109	−	0.810232i	$-0.699341\pi$
$293$	−20.0651	−1.17222	−0.586109	+	0.810232i	$0.699341\pi$
$294$	−4.60459	−0.268545
$295$	−7.26674	−0.423086
$296$	6.21040	0.360972
$297$	−1.00000	−0.0580259
$298$	11.5049	0.666460
$299$	20.9270	1.21024
$300$	−3.69157	−0.213133
$301$	−7.75577	−0.447035
$302$	11.2723	0.648649
$303$	−3.46891	−0.199284
$304$	−2.94459	−0.168884
$305$	−1.14386	−0.0654975
$306$	−5.63616	−0.322198
$307$	−32.6505	−1.86346	−0.931732	−	0.363147i	$-0.881702\pi$
$307$	−32.6505	−1.86346	−0.931732	+	0.363147i	$0.881702\pi$
$308$	1.54771	0.0881889
$309$	6.43306	0.365964
$310$	−5.46631	−0.310466
$311$	11.7716	0.667505	0.333753	−	0.942661i	$-0.391685\pi$
$311$	11.7716	0.667505	0.333753	+	0.942661i	$0.391685\pi$
$312$	−6.01809	−0.340707
$313$	−8.45250	−0.477764	−0.238882	−	0.971049i	$-0.576781\pi$
$313$	−8.45250	−0.477764	−0.238882	+	0.971049i	$0.576781\pi$
$314$	−3.83301	−0.216309
$315$	−1.77037	−0.0997491
$316$	2.20893	0.124262
$317$	−5.00055	−0.280859	−0.140429	−	0.990091i	$-0.544848\pi$
$317$	−5.00055	−0.280859	−0.140429	+	0.990091i	$0.544848\pi$
$318$	2.04697	0.114789
$319$	2.10386	0.117794
$320$	1.14386	0.0639440
$321$	12.6671	0.707006
$322$	5.38193	0.299923
$323$	16.5962	0.923435
$324$	1.00000	0.0555556
$325$	22.2162	1.23234
$326$	−13.1555	−0.728613
$327$	15.4374	0.853692
$328$	−1.67348	−0.0924025
$329$	6.59737	0.363725
$330$	−1.14386	−0.0629677
$331$	−6.39549	−0.351528	−0.175764	−	0.984432i	$-0.556240\pi$
$331$	−6.39549	−0.351528	−0.175764	+	0.984432i	$0.556240\pi$
$332$	−4.41497	−0.242303
$333$	6.21040	0.340328
$334$	−4.19399	−0.229485
$335$	1.90626	0.104150
$336$	−1.54771	−0.0844345
$337$	−14.0854	−0.767279	−0.383640	−	0.923483i	$-0.625330\pi$
$337$	−14.0854	−0.767279	−0.383640	+	0.923483i	$0.625330\pi$
$338$	23.2175	1.26286
$339$	13.8316	0.751231
$340$	−6.44700	−0.349638
$341$	4.77881	0.258787
$342$	−2.94459	−0.159225
$343$	17.9605	0.969778
$344$	5.01112	0.270182
$345$	−3.97762	−0.214148
$346$	−21.3762	−1.14919
$347$	1.12362	0.0603191	0.0301596	−	0.999545i	$-0.490398\pi$
$347$	1.12362	0.0603191	0.0301596	+	0.999545i	$0.490398\pi$
$348$	−2.10386	−0.112779
$349$	−37.3020	−1.99673	−0.998365	−	0.0571555i	$-0.981797\pi$
$349$	−37.3020	−1.99673	−0.998365	+	0.0571555i	$0.981797\pi$
$350$	5.71349	0.305399
$351$	−6.01809	−0.321222
$352$	−1.00000	−0.0533002
$353$	8.22287	0.437659	0.218830	−	0.975763i	$-0.429776\pi$
$353$	8.22287	0.437659	0.218830	+	0.975763i	$0.429776\pi$
$354$	−6.35280	−0.337647
$355$	9.42026	0.499975
$356$	1.84073	0.0975583
$357$	8.72314	0.461677
$358$	−0.955454	−0.0504973
$359$	26.1370	1.37946	0.689728	−	0.724068i	$-0.257730\pi$
$359$	26.1370	1.37946	0.689728	+	0.724068i	$0.257730\pi$
$360$	1.14386	0.0602869
$361$	−10.3294	−0.543653
$362$	2.51086	0.131968
$363$	1.00000	0.0524864
$364$	9.31426	0.488200
$365$	4.37978	0.229248
$366$	−1.00000	−0.0522708
$367$	−1.89808	−0.0990789	−0.0495395	−	0.998772i	$-0.515775\pi$
$367$	−1.89808	−0.0990789	−0.0495395	+	0.998772i	$0.515775\pi$
$368$	−3.47735	−0.181270
$369$	−1.67348	−0.0871179
$370$	7.10386	0.369312
$371$	−3.16812	−0.164481
$372$	−4.77881	−0.247770
$373$	6.34293	0.328425	0.164212	−	0.986425i	$-0.447492\pi$
$373$	6.34293	0.328425	0.164212	+	0.986425i	$0.447492\pi$
$374$	5.63616	0.291439
$375$	−9.94198	−0.513402
$376$	−4.26267	−0.219830
$377$	12.6612	0.652086
$378$	−1.54771	−0.0796056
$379$	−3.41136	−0.175230	−0.0876150	−	0.996154i	$-0.527925\pi$
$379$	−3.41136	−0.175230	−0.0876150	+	0.996154i	$0.527925\pi$
$380$	−3.36821	−0.172785
$381$	−12.0709	−0.618411
$382$	7.60896	0.389308
$383$	21.7791	1.11286	0.556430	−	0.830894i	$-0.312171\pi$
$383$	21.7791	1.11286	0.556430	+	0.830894i	$0.312171\pi$
$384$	1.00000	0.0510310
$385$	1.77037	0.0902264
$386$	−16.7374	−0.851912
$387$	5.01112	0.254730
$388$	8.66391	0.439843
$389$	6.13374	0.310993	0.155497	−	0.987836i	$-0.450302\pi$
$389$	6.13374	0.310993	0.155497	+	0.987836i	$0.450302\pi$
$390$	−6.88388	−0.348579
$391$	19.5989	0.991160
$392$	−4.60459	−0.232567
$393$	−8.83422	−0.445628
$394$	−5.10533	−0.257203
$395$	2.52672	0.127133
$396$	−1.00000	−0.0502519
$397$	−26.8601	−1.34807	−0.674035	−	0.738699i	$-0.735440\pi$
$397$	−26.8601	−1.34807	−0.674035	+	0.738699i	$0.735440\pi$
$398$	−4.96121	−0.248683
$399$	4.55736	0.228154
$400$	−3.69157	−0.184579
$401$	−19.5396	−0.975761	−0.487881	−	0.872910i	$-0.662230\pi$
$401$	−19.5396	−0.975761	−0.487881	+	0.872910i	$0.662230\pi$
$402$	1.66651	0.0831180
$403$	28.7593	1.43260
$404$	−3.46891	−0.172585
$405$	1.14386	0.0568391
$406$	3.25616	0.161601
$407$	−6.21040	−0.307838
$408$	−5.63616	−0.279031
$409$	−35.7307	−1.76677	−0.883386	−	0.468647i	$-0.844742\pi$
$409$	−35.7307	−1.76677	−0.883386	+	0.468647i	$0.844742\pi$
$410$	−1.91423	−0.0945373
$411$	2.60794	0.128640
$412$	6.43306	0.316934
$413$	9.83229	0.483815
$414$	−3.47735	−0.170903
$415$	−5.05013	−0.247901
$416$	−6.01809	−0.295061
$417$	−4.32920	−0.212002
$418$	2.94459	0.144024
$419$	15.2745	0.746207	0.373103	−	0.927790i	$-0.378294\pi$
$419$	15.2745	0.746207	0.373103	+	0.927790i	$0.378294\pi$
$420$	−1.77037	−0.0863852
$421$	3.07637	0.149933	0.0749665	−	0.997186i	$-0.476115\pi$
$421$	3.07637	0.149933	0.0749665	+	0.997186i	$0.476115\pi$
$422$	−6.87376	−0.334609
$423$	−4.26267	−0.207258
$424$	2.04697	0.0994099
$425$	20.8063	1.00925
$426$	8.23547	0.399010
$427$	1.54771	0.0748989
$428$	12.6671	0.612285
$429$	6.01809	0.290556
$430$	5.73205	0.276424
$431$	−24.3343	−1.17214	−0.586071	−	0.810259i	$-0.699326\pi$
$431$	−24.3343	−1.17214	−0.586071	+	0.810259i	$0.699326\pi$
$432$	1.00000	0.0481125
$433$	9.42530	0.452951	0.226476	−	0.974017i	$-0.427280\pi$
$433$	9.42530	0.452951	0.226476	+	0.974017i	$0.427280\pi$
$434$	7.39621	0.355029
$435$	−2.40653	−0.115384
$436$	15.4374	0.739319
$437$	10.2394	0.489815
$438$	3.82894	0.182954
$439$	−9.34704	−0.446110	−0.223055	−	0.974806i	$-0.571603\pi$
$439$	−9.34704	−0.446110	−0.223055	+	0.974806i	$0.571603\pi$
$440$	−1.14386	−0.0545316
$441$	−4.60459	−0.219266
$442$	33.9189	1.61336
$443$	13.3608	0.634789	0.317395	−	0.948294i	$-0.397192\pi$
$443$	13.3608	0.634789	0.317395	+	0.948294i	$0.397192\pi$
$444$	6.21040	0.294733
$445$	2.10554	0.0998122
$446$	9.82868	0.465402
$447$	11.5049	0.544163
$448$	−1.54771	−0.0731224
$449$	32.0943	1.51462	0.757312	−	0.653054i	$-0.226512\pi$
$449$	32.0943	1.51462	0.757312	+	0.653054i	$0.226512\pi$
$450$	−3.69157	−0.174022
$451$	1.67348	0.0788011
$452$	13.8316	0.650585
$453$	11.2723	0.529620
$454$	15.0610	0.706848
$455$	10.6543	0.499479
$456$	−2.94459	−0.137893
$457$	3.25201	0.152123	0.0760613	−	0.997103i	$-0.475766\pi$
$457$	3.25201	0.152123	0.0760613	+	0.997103i	$0.475766\pi$
$458$	−19.7109	−0.921029
$459$	−5.63616	−0.263073
$460$	−3.97762	−0.185458
$461$	−27.8572	−1.29744	−0.648720	−	0.761027i	$-0.724695\pi$
$461$	−27.8572	−1.29744	−0.648720	+	0.761027i	$0.724695\pi$
$462$	1.54771	0.0720060
$463$	14.2854	0.663898	0.331949	−	0.943297i	$-0.392294\pi$
$463$	14.2854	0.663898	0.331949	+	0.943297i	$0.392294\pi$
$464$	−2.10386	−0.0976692
$465$	−5.46631	−0.253494
$466$	6.12771	0.283861
$467$	3.68621	0.170577	0.0852886	−	0.996356i	$-0.472819\pi$
$467$	3.68621	0.170577	0.0852886	+	0.996356i	$0.472819\pi$
$468$	−6.01809	−0.278186
$469$	−2.57927	−0.119100
$470$	−4.87591	−0.224909
$471$	−3.83301	−0.176616
$472$	−6.35280	−0.292411
$473$	−5.01112	−0.230412
$474$	2.20893	0.101460
$475$	10.8702	0.498757
$476$	8.72314	0.399824
$477$	2.04697	0.0937245
$478$	−25.9673	−1.18772
$479$	−2.84073	−0.129796	−0.0648980	−	0.997892i	$-0.520672\pi$
$479$	−2.84073	−0.129796	−0.0648980	+	0.997892i	$0.520672\pi$
$480$	1.14386	0.0522100
$481$	−37.3748	−1.70414
$482$	−8.41518	−0.383301
$483$	5.38193	0.244886
$484$	1.00000	0.0454545
$485$	9.91034	0.450005
$486$	1.00000	0.0453609
$487$	−0.355400	−0.0161047	−0.00805236	−	0.999968i	$-0.502563\pi$
$487$	−0.355400	−0.0161047	−0.00805236	+	0.999968i	$0.502563\pi$
$488$	−1.00000	−0.0452679
$489$	−13.1555	−0.594910
$490$	−5.26703	−0.237940
$491$	0.325971	0.0147108	0.00735542	−	0.999973i	$-0.497659\pi$
$491$	0.325971	0.0147108	0.00735542	+	0.999973i	$0.497659\pi$
$492$	−1.67348	−0.0754463
$493$	11.8577	0.534043
$494$	17.7208	0.797296
$495$	−1.14386	−0.0514129
$496$	−4.77881	−0.214575
$497$	−12.7461	−0.571741
$498$	−4.41497	−0.197840
$499$	5.48869	0.245707	0.122854	−	0.992425i	$-0.460795\pi$
$499$	5.48869	0.245707	0.122854	+	0.992425i	$0.460795\pi$
$500$	−9.94198	−0.444619
$501$	−4.19399	−0.187374
$502$	13.5839	0.606279
$503$	−22.6743	−1.01100	−0.505498	−	0.862828i	$-0.668691\pi$
$503$	−22.6743	−1.01100	−0.505498	+	0.862828i	$0.668691\pi$
$504$	−1.54771	−0.0689405
$505$	−3.96797	−0.176572
$506$	3.47735	0.154587
$507$	23.2175	1.03112
$508$	−12.0709	−0.535560
$509$	−15.6169	−0.692208	−0.346104	−	0.938196i	$-0.612496\pi$
$509$	−15.6169	−0.692208	−0.346104	+	0.938196i	$0.612496\pi$
$510$	−6.44700	−0.285478
$511$	−5.92608	−0.262154
$512$	1.00000	0.0441942
$513$	−2.94459	−0.130007
$514$	13.9075	0.613432
$515$	7.35855	0.324257
$516$	5.01112	0.220602
$517$	4.26267	0.187472
$518$	−9.61190	−0.422323
$519$	−21.3762	−0.938310
$520$	−6.88388	−0.301878
$521$	15.6639	0.686248	0.343124	−	0.939290i	$-0.388515\pi$
$521$	15.6639	0.686248	0.343124	+	0.939290i	$0.388515\pi$
$522$	−2.10386	−0.0920834
$523$	−5.37349	−0.234967	−0.117483	−	0.993075i	$-0.537483\pi$
$523$	−5.37349	−0.234967	−0.117483	+	0.993075i	$0.537483\pi$
$524$	−8.83422	−0.385925
$525$	5.71349	0.249357
$526$	−16.1892	−0.705884
$527$	26.9341	1.17327
$528$	−1.00000	−0.0435194
$529$	−10.9080	−0.474261
$530$	2.34146	0.101707
$531$	−6.35280	−0.275688
$532$	4.55736	0.197587
$533$	10.0712	0.436230
$534$	1.84073	0.0796560
$535$	14.4894	0.626431
$536$	1.66651	0.0719823
$537$	−0.955454	−0.0412309
$538$	−17.2230	−0.742534
$539$	4.60459	0.198334
$540$	1.14386	0.0492241
$541$	12.2164	0.525226	0.262613	−	0.964901i	$-0.415416\pi$
$541$	12.2164	0.525226	0.262613	+	0.964901i	$0.415416\pi$
$542$	12.5280	0.538124
$543$	2.51086	0.107751
$544$	−5.63616	−0.241648
$545$	17.6583	0.756400
$546$	9.31426	0.398614
$547$	22.5464	0.964013	0.482006	−	0.876168i	$-0.339908\pi$
$547$	22.5464	0.964013	0.482006	+	0.876168i	$0.339908\pi$
$548$	2.60794	0.111406
$549$	−1.00000	−0.0426790
$550$	3.69157	0.157409
$551$	6.19499	0.263916
$552$	−3.47735	−0.148006
$553$	−3.41879	−0.145382
$554$	−18.6572	−0.792668
$555$	7.10386	0.301542
$556$	−4.32920	−0.183599
$557$	3.57593	0.151517	0.0757584	−	0.997126i	$-0.475862\pi$
$557$	3.57593	0.151517	0.0757584	+	0.997126i	$0.475862\pi$
$558$	−4.77881	−0.202303
$559$	−30.1574	−1.27552
$560$	−1.77037	−0.0748118
$561$	5.63616	0.237959
$562$	−25.9633	−1.09520
$563$	24.2914	1.02376	0.511881	−	0.859056i	$-0.328949\pi$
$563$	24.2914	1.02376	0.511881	+	0.859056i	$0.328949\pi$
$564$	−4.26267	−0.179491
$565$	15.8215	0.665615
$566$	3.92557	0.165004
$567$	−1.54771	−0.0649977
$568$	8.23547	0.345553
$569$	7.65836	0.321055	0.160528	−	0.987031i	$-0.448680\pi$
$569$	7.65836	0.321055	0.160528	+	0.987031i	$0.448680\pi$
$570$	−3.36821	−0.141079
$571$	18.8773	0.789988	0.394994	−	0.918684i	$-0.370747\pi$
$571$	18.8773	0.789988	0.394994	+	0.918684i	$0.370747\pi$
$572$	6.01809	0.251629
$573$	7.60896	0.317869
$574$	2.59006	0.108107
$575$	12.8369	0.535336
$576$	1.00000	0.0416667
$577$	−15.0116	−0.624941	−0.312470	−	0.949928i	$-0.601157\pi$
$577$	−15.0116	−0.624941	−0.312470	+	0.949928i	$0.601157\pi$
$578$	14.7663	0.614197
$579$	−16.7374	−0.695583
$580$	−2.40653	−0.0999257
$581$	6.83309	0.283484
$582$	8.66391	0.359131
$583$	−2.04697	−0.0847770
$584$	3.82894	0.158443
$585$	−6.88388	−0.284614
$586$	−20.0651	−0.828884
$587$	0.397132	0.0163914	0.00819570	−	0.999966i	$-0.497391\pi$
$587$	0.397132	0.0163914	0.00819570	+	0.999966i	$0.497391\pi$
$588$	−4.60459	−0.189890
$589$	14.0716	0.579811
$590$	−7.26674	−0.299167
$591$	−5.10533	−0.210005
$592$	6.21040	0.255246
$593$	−31.4054	−1.28967	−0.644833	−	0.764324i	$-0.723073\pi$
$593$	−31.4054	−1.28967	−0.644833	+	0.764324i	$0.723073\pi$
$594$	−1.00000	−0.0410305
$595$	9.97809	0.409062
$596$	11.5049	0.471259
$597$	−4.96121	−0.203049
$598$	20.9270	0.855770
$599$	−45.0103	−1.83907	−0.919535	−	0.393008i	$-0.871435\pi$
$599$	−45.0103	−1.83907	−0.919535	+	0.393008i	$0.871435\pi$
$600$	−3.69157	−0.150708
$601$	26.4778	1.08005	0.540025	−	0.841649i	$-0.318415\pi$
$601$	26.4778	1.08005	0.540025	+	0.841649i	$0.318415\pi$
$602$	−7.75577	−0.316101
$603$	1.66651	0.0678656
$604$	11.2723	0.458664
$605$	1.14386	0.0465047
$606$	−3.46891	−0.140915
$607$	−16.0547	−0.651642	−0.325821	−	0.945431i	$-0.605641\pi$
$607$	−16.0547	−0.651642	−0.325821	+	0.945431i	$0.605641\pi$
$608$	−2.94459	−0.119419
$609$	3.25616	0.131946
$610$	−1.14386	−0.0463137
$611$	25.6531	1.03781
$612$	−5.63616	−0.227828
$613$	−41.5765	−1.67926	−0.839629	−	0.543160i	$-0.817228\pi$
$613$	−41.5765	−1.67926	−0.839629	+	0.543160i	$0.817228\pi$
$614$	−32.6505	−1.31767
$615$	−1.91423	−0.0771894
$616$	1.54771	0.0623590
$617$	19.6019	0.789143	0.394572	−	0.918865i	$-0.370893\pi$
$617$	19.6019	0.789143	0.394572	+	0.918865i	$0.370893\pi$
$618$	6.43306	0.258776
$619$	−7.25062	−0.291427	−0.145714	−	0.989327i	$-0.546548\pi$
$619$	−7.25062	−0.291427	−0.145714	+	0.989327i	$0.546548\pi$
$620$	−5.46631	−0.219532
$621$	−3.47735	−0.139541
$622$	11.7716	0.471998
$623$	−2.84891	−0.114139
$624$	−6.01809	−0.240917
$625$	7.08559	0.283424
$626$	−8.45250	−0.337830
$627$	2.94459	0.117595
$628$	−3.83301	−0.152954
$629$	−35.0028	−1.39565
$630$	−1.77037	−0.0705332
$631$	−34.3973	−1.36933	−0.684667	−	0.728856i	$-0.740053\pi$
$631$	−34.3973	−1.36933	−0.684667	+	0.728856i	$0.740053\pi$
$632$	2.20893	0.0878666
$633$	−6.87376	−0.273208
$634$	−5.00055	−0.198597
$635$	−13.8075	−0.547933
$636$	2.04697	0.0811678
$637$	27.7109	1.09795
$638$	2.10386	0.0832926
$639$	8.23547	0.325790
$640$	1.14386	0.0452152
$641$	−24.2311	−0.957071	−0.478535	−	0.878068i	$-0.658832\pi$
$641$	−24.2311	−0.957071	−0.478535	+	0.878068i	$0.658832\pi$
$642$	12.6671	0.499929
$643$	−22.1010	−0.871578	−0.435789	−	0.900049i	$-0.643531\pi$
$643$	−22.1010	−0.871578	−0.435789	+	0.900049i	$0.643531\pi$
$644$	5.38193	0.212078
$645$	5.73205	0.225699
$646$	16.5962	0.652967
$647$	38.2758	1.50478	0.752389	−	0.658719i	$-0.228902\pi$
$647$	38.2758	1.50478	0.752389	+	0.658719i	$0.228902\pi$
$648$	1.00000	0.0392837
$649$	6.35280	0.249369
$650$	22.2162	0.871393
$651$	7.39621	0.289880
$652$	−13.1555	−0.515207
$653$	−7.53814	−0.294990	−0.147495	−	0.989063i	$-0.547121\pi$
$653$	−7.53814	−0.294990	−0.147495	+	0.989063i	$0.547121\pi$
$654$	15.4374	0.603651
$655$	−10.1052	−0.394841
$656$	−1.67348	−0.0653384
$657$	3.82894	0.149381
$658$	6.59737	0.257192
$659$	6.18971	0.241117	0.120558	−	0.992706i	$-0.461532\pi$
$659$	6.18971	0.241117	0.120558	+	0.992706i	$0.461532\pi$
$660$	−1.14386	−0.0445249
$661$	−25.4189	−0.988680	−0.494340	−	0.869269i	$-0.664590\pi$
$661$	−25.4189	−0.988680	−0.494340	+	0.869269i	$0.664590\pi$
$662$	−6.39549	−0.248568
$663$	33.9189	1.31730
$664$	−4.41497	−0.171334
$665$	5.21301	0.202152
$666$	6.21040	0.240648
$667$	7.31586	0.283271
$668$	−4.19399	−0.162270
$669$	9.82868	0.379999
$670$	1.90626	0.0736453
$671$	1.00000	0.0386046
$672$	−1.54771	−0.0597042
$673$	−13.4520	−0.518538	−0.259269	−	0.965805i	$-0.583482\pi$
$673$	−13.4520	−0.518538	−0.259269	+	0.965805i	$0.583482\pi$
$674$	−14.0854	−0.542549
$675$	−3.69157	−0.142089
$676$	23.2175	0.892979
$677$	37.7852	1.45220	0.726102	−	0.687588i	$-0.241330\pi$
$677$	37.7852	1.45220	0.726102	+	0.687588i	$0.241330\pi$
$678$	13.8316	0.531200
$679$	−13.4092	−0.514598
$680$	−6.44700	−0.247231
$681$	15.0610	0.577139
$682$	4.77881	0.182990
$683$	34.2172	1.30928	0.654642	−	0.755939i	$-0.272820\pi$
$683$	34.2172	1.30928	0.654642	+	0.755939i	$0.272820\pi$
$684$	−2.94459	−0.112589
$685$	2.98313	0.113980
$686$	17.9605	0.685737
$687$	−19.7109	−0.752017
$688$	5.01112	0.191047
$689$	−12.3189	−0.469312
$690$	−3.97762	−0.151425
$691$	−11.5119	−0.437932	−0.218966	−	0.975733i	$-0.570268\pi$
$691$	−11.5119	−0.437932	−0.218966	+	0.975733i	$0.570268\pi$
$692$	−21.3762	−0.812600
$693$	1.54771	0.0587926
$694$	1.12362	0.0426521
$695$	−4.95202	−0.187841
$696$	−2.10386	−0.0797466
$697$	9.43200	0.357263
$698$	−37.3020	−1.41190
$699$	6.12771	0.231771
$700$	5.71349	0.215949
$701$	−41.5119	−1.56788	−0.783941	−	0.620835i	$-0.786794\pi$
$701$	−41.5119	−1.56788	−0.783941	+	0.620835i	$0.786794\pi$
$702$	−6.01809	−0.227138
$703$	−18.2871	−0.689710
$704$	−1.00000	−0.0376889
$705$	−4.87591	−0.183637
$706$	8.22287	0.309472
$707$	5.36887	0.201917
$708$	−6.35280	−0.238753
$709$	29.8660	1.12164	0.560820	−	0.827938i	$-0.310486\pi$
$709$	29.8660	1.12164	0.560820	+	0.827938i	$0.310486\pi$
$710$	9.42026	0.353536
$711$	2.20893	0.0828415
$712$	1.84073	0.0689841
$713$	16.6176	0.622334
$714$	8.72314	0.326455
$715$	6.88388	0.257443
$716$	−0.955454	−0.0357070
$717$	−25.9673	−0.969767
$718$	26.1370	0.975423
$719$	−19.0971	−0.712203	−0.356102	−	0.934447i	$-0.615894\pi$
$719$	−19.0971	−0.712203	−0.356102	+	0.934447i	$0.615894\pi$
$720$	1.14386	0.0426293
$721$	−9.95652	−0.370800
$722$	−10.3294	−0.384421
$723$	−8.41518	−0.312964
$724$	2.51086	0.0933153
$725$	7.76655	0.288443
$726$	1.00000	0.0371135
$727$	5.83041	0.216238	0.108119	−	0.994138i	$-0.465517\pi$
$727$	5.83041	0.216238	0.108119	+	0.994138i	$0.465517\pi$
$728$	9.31426	0.345210
$729$	1.00000	0.0370370
$730$	4.37978	0.162103
$731$	−28.2435	−1.04462
$732$	−1.00000	−0.0369611
$733$	−25.5046	−0.942036	−0.471018	−	0.882124i	$-0.656113\pi$
$733$	−25.5046	−0.942036	−0.471018	+	0.882124i	$0.656113\pi$
$734$	−1.89808	−0.0700594
$735$	−5.26703	−0.194277
$736$	−3.47735	−0.128177
$737$	−1.66651	−0.0613867
$738$	−1.67348	−0.0616017
$739$	24.5394	0.902695	0.451347	−	0.892348i	$-0.350944\pi$
$739$	24.5394	0.902695	0.451347	+	0.892348i	$0.350944\pi$
$740$	7.10386	0.261143
$741$	17.7208	0.650990
$742$	−3.16812	−0.116305
$743$	24.8283	0.910862	0.455431	−	0.890271i	$-0.349485\pi$
$743$	24.8283	0.910862	0.455431	+	0.890271i	$0.349485\pi$
$744$	−4.77881	−0.175200
$745$	13.1600	0.482146
$746$	6.34293	0.232231
$747$	−4.41497	−0.161535
$748$	5.63616	0.206078
$749$	−19.6049	−0.716349
$750$	−9.94198	−0.363030
$751$	−41.1854	−1.50288	−0.751439	−	0.659803i	$-0.770640\pi$
$751$	−41.1854	−1.50288	−0.751439	+	0.659803i	$0.770640\pi$
$752$	−4.26267	−0.155443
$753$	13.5839	0.495025
$754$	12.6612	0.461095
$755$	12.8940	0.469261
$756$	−1.54771	−0.0562897
$757$	11.2611	0.409291	0.204645	−	0.978836i	$-0.434396\pi$
$757$	11.2611	0.409291	0.204645	+	0.978836i	$0.434396\pi$
$758$	−3.41136	−0.123906
$759$	3.47735	0.126220
$760$	−3.36821	−0.122178
$761$	26.0515	0.944366	0.472183	−	0.881500i	$-0.343466\pi$
$761$	26.0515	0.944366	0.472183	+	0.881500i	$0.343466\pi$
$762$	−12.0709	−0.437283
$763$	−23.8927	−0.864972
$764$	7.60896	0.275283
$765$	−6.44700	−0.233092
$766$	21.7791	0.786911
$767$	38.2317	1.38047
$768$	1.00000	0.0360844
$769$	3.61399	0.130324	0.0651619	−	0.997875i	$-0.479244\pi$
$769$	3.61399	0.130324	0.0651619	+	0.997875i	$0.479244\pi$
$770$	1.77037	0.0637997
$771$	13.9075	0.500866
$772$	−16.7374	−0.602393
$773$	2.82559	0.101629	0.0508147	−	0.998708i	$-0.483818\pi$
$773$	2.82559	0.101629	0.0508147	+	0.998708i	$0.483818\pi$
$774$	5.01112	0.180121
$775$	17.6413	0.633695
$776$	8.66391	0.311016
$777$	−9.61190	−0.344825
$778$	6.13374	0.219905
$779$	4.92771	0.176553
$780$	−6.88388	−0.246483
$781$	−8.23547	−0.294688
$782$	19.5989	0.700856
$783$	−2.10386	−0.0751858
$784$	−4.60459	−0.164450
$785$	−4.38444	−0.156488
$786$	−8.83422	−0.315106
$787$	45.5008	1.62193	0.810965	−	0.585095i	$-0.198943\pi$
$787$	45.5008	1.62193	0.810965	+	0.585095i	$0.198943\pi$
$788$	−5.10533	−0.181870
$789$	−16.1892	−0.576352
$790$	2.52672	0.0898967
$791$	−21.4073	−0.761157
$792$	−1.00000	−0.0355335
$793$	6.01809	0.213709
$794$	−26.8601	−0.953230
$795$	2.34146	0.0830431
$796$	−4.96121	−0.175845
$797$	−0.623272	−0.0220774	−0.0110387	−	0.999939i	$-0.503514\pi$
$797$	−0.623272	−0.0220774	−0.0110387	+	0.999939i	$0.503514\pi$
$798$	4.55736	0.161329
$799$	24.0251	0.849946
$800$	−3.69157	−0.130517
$801$	1.84073	0.0650389
$802$	−19.5396	−0.689968
$803$	−3.82894	−0.135120
$804$	1.66651	0.0587733
$805$	6.15620	0.216978
$806$	28.7593	1.01300
$807$	−17.2230	−0.606277
$808$	−3.46891	−0.122036
$809$	26.9794	0.948545	0.474272	−	0.880378i	$-0.342711\pi$
$809$	26.9794	0.948545	0.474272	+	0.880378i	$0.342711\pi$
$810$	1.14386	0.0401913
$811$	19.2449	0.675780	0.337890	−	0.941186i	$-0.390287\pi$
$811$	19.2449	0.675780	0.337890	+	0.941186i	$0.390287\pi$
$812$	3.25616	0.114269
$813$	12.5280	0.439377
$814$	−6.21040	−0.217675
$815$	−15.0481	−0.527111
$816$	−5.63616	−0.197305
$817$	−14.7557	−0.516236
$818$	−35.7307	−1.24930
$819$	9.31426	0.325467
$820$	−1.91423	−0.0668480
$821$	5.78725	0.201976	0.100988	−	0.994888i	$-0.467800\pi$
$821$	5.78725	0.201976	0.100988	+	0.994888i	$0.467800\pi$
$822$	2.60794	0.0909625
$823$	0.746602	0.0260249	0.0130125	−	0.999915i	$-0.495858\pi$
$823$	0.746602	0.0260249	0.0130125	+	0.999915i	$0.495858\pi$
$824$	6.43306	0.224106
$825$	3.69157	0.128524
$826$	9.83229	0.342109
$827$	22.9269	0.797247	0.398623	−	0.917115i	$-0.369488\pi$
$827$	22.9269	0.797247	0.398623	+	0.917115i	$0.369488\pi$
$828$	−3.47735	−0.120846
$829$	4.67965	0.162531	0.0812656	−	0.996692i	$-0.474104\pi$
$829$	4.67965	0.162531	0.0812656	+	0.996692i	$0.474104\pi$
$830$	−5.05013	−0.175292
$831$	−18.6572	−0.647211
$832$	−6.01809	−0.208640
$833$	25.9522	0.899191
$834$	−4.32920	−0.149908
$835$	−4.79736	−0.166019
$836$	2.94459	0.101841
$837$	−4.77881	−0.165180
$838$	15.2745	0.527648
$839$	−12.5600	−0.433620	−0.216810	−	0.976214i	$-0.569565\pi$
$839$	−12.5600	−0.433620	−0.216810	+	0.976214i	$0.569565\pi$
$840$	−1.77037	−0.0610836
$841$	−24.5738	−0.847372
$842$	3.07637	0.106019
$843$	−25.9633	−0.894224
$844$	−6.87376	−0.236605
$845$	26.5576	0.913610
$846$	−4.26267	−0.146553
$847$	−1.54771	−0.0531799
$848$	2.04697	0.0702934
$849$	3.92557	0.134725
$850$	20.8063	0.713650
$851$	−21.5958	−0.740293
$852$	8.23547	0.282142
$853$	24.2648	0.830810	0.415405	−	0.909637i	$-0.363640\pi$
$853$	24.2648	0.830810	0.415405	+	0.909637i	$0.363640\pi$
$854$	1.54771	0.0529615
$855$	−3.36821	−0.115190
$856$	12.6671	0.432951
$857$	19.8569	0.678299	0.339149	−	0.940733i	$-0.389861\pi$
$857$	19.8569	0.678299	0.339149	+	0.940733i	$0.389861\pi$
$858$	6.01809	0.205454
$859$	−18.0597	−0.616187	−0.308094	−	0.951356i	$-0.599691\pi$
$859$	−18.0597	−0.616187	−0.308094	+	0.951356i	$0.599691\pi$
$860$	5.73205	0.195461
$861$	2.59006	0.0882691
$862$	−24.3343	−0.828830
$863$	21.2506	0.723380	0.361690	−	0.932299i	$-0.382200\pi$
$863$	21.2506	0.723380	0.361690	+	0.932299i	$0.382200\pi$
$864$	1.00000	0.0340207
$865$	−24.4515	−0.831374
$866$	9.42530	0.320285
$867$	14.7663	0.501490
$868$	7.39621	0.251044
$869$	−2.20893	−0.0749329
$870$	−2.40653	−0.0815890
$871$	−10.0292	−0.339827
$872$	15.4374	0.522777
$873$	8.66391	0.293229
$874$	10.2394	0.346352
$875$	15.3873	0.520186
$876$	3.82894	0.129368
$877$	55.8771	1.88683	0.943417	−	0.331608i	$-0.107591\pi$
$877$	55.8771	1.88683	0.943417	+	0.331608i	$0.107591\pi$
$878$	−9.34704	−0.315447
$879$	−20.0651	−0.676781
$880$	−1.14386	−0.0385597
$881$	41.7173	1.40549	0.702745	−	0.711442i	$-0.251957\pi$
$881$	41.7173	1.40549	0.702745	+	0.711442i	$0.251957\pi$
$882$	−4.60459	−0.155045
$883$	−9.54973	−0.321374	−0.160687	−	0.987005i	$-0.551371\pi$
$883$	−9.54973	−0.321374	−0.160687	+	0.987005i	$0.551371\pi$
$884$	33.9189	1.14082
$885$	−7.26674	−0.244269
$886$	13.3608	0.448864
$887$	49.7771	1.67135	0.835676	−	0.549223i	$-0.185076\pi$
$887$	49.7771	1.67135	0.835676	+	0.549223i	$0.185076\pi$
$888$	6.21040	0.208407
$889$	18.6823	0.626583
$890$	2.10554	0.0705779
$891$	−1.00000	−0.0335013
$892$	9.82868	0.329089
$893$	12.5518	0.420029
$894$	11.5049	0.384781
$895$	−1.09291	−0.0365319
$896$	−1.54771	−0.0517054
$897$	20.9270	0.698734
$898$	32.0943	1.07100
$899$	10.0539	0.335318
$900$	−3.69157	−0.123052
$901$	−11.5371	−0.384356
$902$	1.67348	0.0557208
$903$	−7.75577	−0.258096
$904$	13.8316	0.460033
$905$	2.87208	0.0954712
$906$	11.2723	0.374498
$907$	−15.2560	−0.506568	−0.253284	−	0.967392i	$-0.581511\pi$
$907$	−15.2560	−0.506568	−0.253284	+	0.967392i	$0.581511\pi$
$908$	15.0610	0.499817
$909$	−3.46891	−0.115057
$910$	10.6543	0.353185
$911$	29.6740	0.983144	0.491572	−	0.870837i	$-0.336422\pi$
$911$	29.6740	0.983144	0.491572	+	0.870837i	$0.336422\pi$
$912$	−2.94459	−0.0975050
$913$	4.41497	0.146114
$914$	3.25201	0.107567
$915$	−1.14386	−0.0378150
$916$	−19.7109	−0.651266
$917$	13.6728	0.451516
$918$	−5.63616	−0.186021
$919$	−27.8478	−0.918615	−0.459307	−	0.888277i	$-0.651902\pi$
$919$	−27.8478	−0.918615	−0.459307	+	0.888277i	$0.651902\pi$
$920$	−3.97762	−0.131138
$921$	−32.6505	−1.07587
$922$	−27.8572	−0.917429
$923$	−49.5618	−1.63135
$924$	1.54771	0.0509159
$925$	−22.9262	−0.753808
$926$	14.2854	0.469447
$927$	6.43306	0.211290
$928$	−2.10386	−0.0690626
$929$	32.5994	1.06955	0.534775	−	0.844994i	$-0.320396\pi$
$929$	32.5994	1.06955	0.534775	+	0.844994i	$0.320396\pi$
$930$	−5.46631	−0.179247
$931$	13.5586	0.444366
$932$	6.12771	0.200720
$933$	11.7716	0.385384
$934$	3.68621	0.120616
$935$	6.44700	0.210840
$936$	−6.01809	−0.196708
$937$	−24.4733	−0.799507	−0.399754	−	0.916623i	$-0.630904\pi$
$937$	−24.4733	−0.799507	−0.399754	+	0.916623i	$0.630904\pi$
$938$	−2.57927	−0.0842163
$939$	−8.45250	−0.275837
$940$	−4.87591	−0.159035
$941$	−24.4258	−0.796260	−0.398130	−	0.917329i	$-0.630341\pi$
$941$	−24.4258	−0.796260	−0.398130	+	0.917329i	$0.630341\pi$
$942$	−3.83301	−0.124886
$943$	5.81928	0.189502
$944$	−6.35280	−0.206766
$945$	−1.77037	−0.0575901
$946$	−5.01112	−0.162926
$947$	43.8490	1.42490	0.712450	−	0.701722i	$-0.247585\pi$
$947$	43.8490	1.42490	0.712450	+	0.701722i	$0.247585\pi$
$948$	2.20893	0.0717428
$949$	−23.0429	−0.748004
$950$	10.8702	0.352674
$951$	−5.00055	−0.162154
$952$	8.72314	0.282719
$953$	41.9758	1.35973	0.679864	−	0.733338i	$-0.262039\pi$
$953$	41.9758	1.35973	0.679864	+	0.733338i	$0.262039\pi$
$954$	2.04697	0.0662732
$955$	8.70362	0.281643
$956$	−25.9673	−0.839843
$957$	2.10386	0.0680081
$958$	−2.84073	−0.0917797
$959$	−4.03634	−0.130340
$960$	1.14386	0.0369181
$961$	−8.16298	−0.263322
$962$	−37.3748	−1.20501
$963$	12.6671	0.408190
$964$	−8.41518	−0.271035
$965$	−19.1453	−0.616310
$966$	5.38193	0.173161
$967$	−56.1526	−1.80575	−0.902873	−	0.429908i	$-0.858546\pi$
$967$	−56.1526	−1.80575	−0.902873	+	0.429908i	$0.858546\pi$
$968$	1.00000	0.0321412
$969$	16.5962	0.533145
$970$	9.91034	0.318202
$971$	−53.5720	−1.71921	−0.859604	−	0.510961i	$-0.829290\pi$
$971$	−53.5720	−1.71921	−0.859604	+	0.510961i	$0.829290\pi$
$972$	1.00000	0.0320750
$973$	6.70035	0.214803
$974$	−0.355400	−0.0113878
$975$	22.2162	0.711489
$976$	−1.00000	−0.0320092
$977$	−9.78762	−0.313134	−0.156567	−	0.987667i	$-0.550043\pi$
$977$	−9.78762	−0.313134	−0.156567	+	0.987667i	$0.550043\pi$
$978$	−13.1555	−0.420665
$979$	−1.84073	−0.0588299
$980$	−5.26703	−0.168249
$981$	15.4374	0.492879
$982$	0.325971	0.0104021
$983$	8.23545	0.262670	0.131335	−	0.991338i	$-0.458074\pi$
$983$	8.23545	0.262670	0.131335	+	0.991338i	$0.458074\pi$
$984$	−1.67348	−0.0533486
$985$	−5.83981	−0.186072
$986$	11.8577	0.377626
$987$	6.59737	0.209997
$988$	17.7208	0.563774
$989$	−17.4255	−0.554097
$990$	−1.14386	−0.0363544
$991$	17.9021	0.568678	0.284339	−	0.958724i	$-0.408226\pi$
$991$	17.9021	0.568678	0.284339	+	0.958724i	$0.408226\pi$
$992$	−4.77881	−0.151727
$993$	−6.39549	−0.202955
$994$	−12.7461	−0.404282
$995$	−5.67495	−0.179908
$996$	−4.41497	−0.139894
$997$	5.35246	0.169514	0.0847570	−	0.996402i	$-0.472989\pi$
$997$	5.35246	0.169514	0.0847570	+	0.996402i	$0.472989\pi$
$998$	5.48869	0.173741
$999$	6.21040	0.196488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.t.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.t.1.4	✓	4	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14386 q^{5} +1.00000 q^{6} -1.54771 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14386 q^{5} +1.00000 q^{6} -1.54771 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.14386 q^{10} -1.00000 q^{11} +1.00000 q^{12} -6.01809 q^{13} -1.54771 q^{14} +1.14386 q^{15} +1.00000 q^{16} -5.63616 q^{17} +1.00000 q^{18} -2.94459 q^{19} +1.14386 q^{20} -1.54771 q^{21} -1.00000 q^{22} -3.47735 q^{23} +1.00000 q^{24} -3.69157 q^{25} -6.01809 q^{26} +1.00000 q^{27} -1.54771 q^{28} -2.10386 q^{29} +1.14386 q^{30} -4.77881 q^{31} +1.00000 q^{32} -1.00000 q^{33} -5.63616 q^{34} -1.77037 q^{35} +1.00000 q^{36} +6.21040 q^{37} -2.94459 q^{38} -6.01809 q^{39} +1.14386 q^{40} -1.67348 q^{41} -1.54771 q^{42} +5.01112 q^{43} -1.00000 q^{44} +1.14386 q^{45} -3.47735 q^{46} -4.26267 q^{47} +1.00000 q^{48} -4.60459 q^{49} -3.69157 q^{50} -5.63616 q^{51} -6.01809 q^{52} +2.04697 q^{53} +1.00000 q^{54} -1.14386 q^{55} -1.54771 q^{56} -2.94459 q^{57} -2.10386 q^{58} -6.35280 q^{59} +1.14386 q^{60} -1.00000 q^{61} -4.77881 q^{62} -1.54771 q^{63} +1.00000 q^{64} -6.88388 q^{65} -1.00000 q^{66} +1.66651 q^{67} -5.63616 q^{68} -3.47735 q^{69} -1.77037 q^{70} +8.23547 q^{71} +1.00000 q^{72} +3.82894 q^{73} +6.21040 q^{74} -3.69157 q^{75} -2.94459 q^{76} +1.54771 q^{77} -6.01809 q^{78} +2.20893 q^{79} +1.14386 q^{80} +1.00000 q^{81} -1.67348 q^{82} -4.41497 q^{83} -1.54771 q^{84} -6.44700 q^{85} +5.01112 q^{86} -2.10386 q^{87} -1.00000 q^{88} +1.84073 q^{89} +1.14386 q^{90} +9.31426 q^{91} -3.47735 q^{92} -4.77881 q^{93} -4.26267 q^{94} -3.36821 q^{95} +1.00000 q^{96} +8.66391 q^{97} -4.60459 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{14} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 8 q^{19} - 4 q^{20} - 6 q^{21} - 4 q^{22} - 7 q^{23} + 4 q^{24} - 6 q^{25} - 5 q^{26} + 4 q^{27} - 6 q^{28} - 4 q^{29} - 4 q^{30} - 9 q^{31} + 4 q^{32} - 4 q^{33} - 10 q^{34} - q^{35} + 4 q^{36} - 11 q^{37} - 8 q^{38} - 5 q^{39} - 4 q^{40} - 17 q^{41} - 6 q^{42} - 11 q^{43} - 4 q^{44} - 4 q^{45} - 7 q^{46} - 7 q^{47} + 4 q^{48} - 6 q^{49} - 6 q^{50} - 10 q^{51} - 5 q^{52} + 16 q^{53} + 4 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{57} - 4 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} - 9 q^{62} - 6 q^{63} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 10 q^{68} - 7 q^{69} - q^{70} - 10 q^{71} + 4 q^{72} - 9 q^{73} - 11 q^{74} - 6 q^{75} - 8 q^{76} + 6 q^{77} - 5 q^{78} - 11 q^{79} - 4 q^{80} + 4 q^{81} - 17 q^{82} + 5 q^{83} - 6 q^{84} - 8 q^{85} - 11 q^{86} - 4 q^{87} - 4 q^{88} + 8 q^{89} - 4 q^{90} - 3 q^{91} - 7 q^{92} - 9 q^{93} - 7 q^{94} + 7 q^{95} + 4 q^{96} - 12 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^14 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 - 4 * q^22 - 7 * q^23 + 4 * q^24 - 6 * q^25 - 5 * q^26 + 4 * q^27 - 6 * q^28 - 4 * q^29 - 4 * q^30 - 9 * q^31 + 4 * q^32 - 4 * q^33 - 10 * q^34 - q^35 + 4 * q^36 - 11 * q^37 - 8 * q^38 - 5 * q^39 - 4 * q^40 - 17 * q^41 - 6 * q^42 - 11 * q^43 - 4 * q^44 - 4 * q^45 - 7 * q^46 - 7 * q^47 + 4 * q^48 - 6 * q^49 - 6 * q^50 - 10 * q^51 - 5 * q^52 + 16 * q^53 + 4 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^57 - 4 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 - 9 * q^62 - 6 * q^63 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 10 * q^68 - 7 * q^69 - q^70 - 10 * q^71 + 4 * q^72 - 9 * q^73 - 11 * q^74 - 6 * q^75 - 8 * q^76 + 6 * q^77 - 5 * q^78 - 11 * q^79 - 4 * q^80 + 4 * q^81 - 17 * q^82 + 5 * q^83 - 6 * q^84 - 8 * q^85 - 11 * q^86 - 4 * q^87 - 4 * q^88 + 8 * q^89 - 4 * q^90 - 3 * q^91 - 7 * q^92 - 9 * q^93 - 7 * q^94 + 7 * q^95 + 4 * q^96 - 12 * q^97 - 6 * q^98 - 4 * q^99

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