LMFDB - Embedded newform 4029.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32685 q^{2} +1.00000 q^{3} +3.41424 q^{4} -3.48051 q^{5} -2.32685 q^{6} +3.88205 q^{7} -3.29073 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.32685 q^{2} +1.00000 q^{3} +3.41424 q^{4} -3.48051 q^{5} -2.32685 q^{6} +3.88205 q^{7} -3.29073 q^{8} +1.00000 q^{9} +8.09862 q^{10} -3.96525 q^{11} +3.41424 q^{12} +0.505146 q^{13} -9.03295 q^{14} -3.48051 q^{15} +0.828553 q^{16} -1.00000 q^{17} -2.32685 q^{18} -2.84517 q^{19} -11.8833 q^{20} +3.88205 q^{21} +9.22655 q^{22} -1.37993 q^{23} -3.29073 q^{24} +7.11392 q^{25} -1.17540 q^{26} +1.00000 q^{27} +13.2542 q^{28} +6.89450 q^{29} +8.09862 q^{30} +4.97067 q^{31} +4.65353 q^{32} -3.96525 q^{33} +2.32685 q^{34} -13.5115 q^{35} +3.41424 q^{36} -6.19131 q^{37} +6.62030 q^{38} +0.505146 q^{39} +11.4534 q^{40} +4.01141 q^{41} -9.03295 q^{42} +3.11886 q^{43} -13.5383 q^{44} -3.48051 q^{45} +3.21089 q^{46} +13.3127 q^{47} +0.828553 q^{48} +8.07030 q^{49} -16.5530 q^{50} -1.00000 q^{51} +1.72469 q^{52} -14.1840 q^{53} -2.32685 q^{54} +13.8011 q^{55} -12.7748 q^{56} -2.84517 q^{57} -16.0425 q^{58} -8.83581 q^{59} -11.8833 q^{60} -13.1400 q^{61} -11.5660 q^{62} +3.88205 q^{63} -12.4852 q^{64} -1.75816 q^{65} +9.22655 q^{66} -10.5593 q^{67} -3.41424 q^{68} -1.37993 q^{69} +31.4392 q^{70} -13.0431 q^{71} -3.29073 q^{72} +12.4899 q^{73} +14.4063 q^{74} +7.11392 q^{75} -9.71410 q^{76} -15.3933 q^{77} -1.17540 q^{78} +1.00000 q^{79} -2.88378 q^{80} +1.00000 q^{81} -9.33395 q^{82} -3.56892 q^{83} +13.2542 q^{84} +3.48051 q^{85} -7.25713 q^{86} +6.89450 q^{87} +13.0486 q^{88} +14.4987 q^{89} +8.09862 q^{90} +1.96100 q^{91} -4.71141 q^{92} +4.97067 q^{93} -30.9766 q^{94} +9.90264 q^{95} +4.65353 q^{96} -13.1817 q^{97} -18.7784 q^{98} -3.96525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.32685	−1.64533	−0.822666	−	0.568524i	$-0.807514\pi$
$2$	−2.32685	−1.64533	−0.822666	+	0.568524i	$0.807514\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.41424	1.70712
$5$	−3.48051	−1.55653	−0.778265	−	0.627936i	$-0.783900\pi$
$5$	−3.48051	−1.55653	−0.778265	+	0.627936i	$0.783900\pi$
$6$	−2.32685	−0.949933
$7$	3.88205	1.46728	0.733638	−	0.679540i	$-0.237821\pi$
$7$	3.88205	1.46728	0.733638	+	0.679540i	$0.237821\pi$
$8$	−3.29073	−1.16345
$9$	1.00000	0.333333
$10$	8.09862	2.56101
$11$	−3.96525	−1.19557	−0.597784	−	0.801657i	$-0.703952\pi$
$11$	−3.96525	−1.19557	−0.597784	+	0.801657i	$0.703952\pi$
$12$	3.41424	0.985606
$13$	0.505146	0.140102	0.0700511	−	0.997543i	$-0.477684\pi$
$13$	0.505146	0.140102	0.0700511	+	0.997543i	$0.477684\pi$
$14$	−9.03295	−2.41416
$15$	−3.48051	−0.898663
$16$	0.828553	0.207138
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.32685	−0.548444
$19$	−2.84517	−0.652727	−0.326364	−	0.945244i	$-0.605823\pi$
$19$	−2.84517	−0.652727	−0.326364	+	0.945244i	$0.605823\pi$
$20$	−11.8833	−2.65718
$21$	3.88205	0.847132
$22$	9.22655	1.96711
$23$	−1.37993	−0.287735	−0.143868	−	0.989597i	$-0.545954\pi$
$23$	−1.37993	−0.287735	−0.143868	+	0.989597i	$0.545954\pi$
$24$	−3.29073	−0.671717
$25$	7.11392	1.42278
$26$	−1.17540	−0.230515
$27$	1.00000	0.192450
$28$	13.2542	2.50482
$29$	6.89450	1.28028	0.640138	−	0.768260i	$-0.278877\pi$
$29$	6.89450	1.28028	0.640138	+	0.768260i	$0.278877\pi$
$30$	8.09862	1.47860
$31$	4.97067	0.892759	0.446380	−	0.894844i	$-0.352713\pi$
$31$	4.97067	0.892759	0.446380	+	0.894844i	$0.352713\pi$
$32$	4.65353	0.822636
$33$	−3.96525	−0.690262
$34$	2.32685	0.399052
$35$	−13.5115	−2.28386
$36$	3.41424	0.569040
$37$	−6.19131	−1.01785	−0.508923	−	0.860812i	$-0.669956\pi$
$37$	−6.19131	−1.01785	−0.508923	+	0.860812i	$0.669956\pi$
$38$	6.62030	1.07395
$39$	0.505146	0.0808881
$40$	11.4534	1.81094
$41$	4.01141	0.626477	0.313238	−	0.949675i	$-0.398586\pi$
$41$	4.01141	0.626477	0.313238	+	0.949675i	$0.398586\pi$
$42$	−9.03295	−1.39381
$43$	3.11886	0.475622	0.237811	−	0.971311i	$-0.423570\pi$
$43$	3.11886	0.475622	0.237811	+	0.971311i	$0.423570\pi$
$44$	−13.5383	−2.04098
$45$	−3.48051	−0.518843
$46$	3.21089	0.473421
$47$	13.3127	1.94185	0.970927	−	0.239376i	$-0.0769430\pi$
$47$	13.3127	1.94185	0.970927	+	0.239376i	$0.0769430\pi$
$48$	0.828553	0.119591
$49$	8.07030	1.15290
$50$	−16.5530	−2.34095
$51$	−1.00000	−0.140028
$52$	1.72469	0.239171
$53$	−14.1840	−1.94832	−0.974160	−	0.225858i	$-0.927482\pi$
$53$	−14.1840	−1.94832	−0.974160	+	0.225858i	$0.927482\pi$
$54$	−2.32685	−0.316644
$55$	13.8011	1.86094
$56$	−12.7748	−1.70710
$57$	−2.84517	−0.376852
$58$	−16.0425	−2.10648
$59$	−8.83581	−1.15033	−0.575163	−	0.818039i	$-0.695061\pi$
$59$	−8.83581	−1.15033	−0.575163	+	0.818039i	$0.695061\pi$
$60$	−11.8833	−1.53412
$61$	−13.1400	−1.68240	−0.841202	−	0.540721i	$-0.818152\pi$
$61$	−13.1400	−1.68240	−0.841202	+	0.540721i	$0.818152\pi$
$62$	−11.5660	−1.46889
$63$	3.88205	0.489092
$64$	−12.4852	−1.56065
$65$	−1.75816	−0.218073
$66$	9.22655	1.13571
$67$	−10.5593	−1.29002	−0.645012	−	0.764172i	$-0.723148\pi$
$67$	−10.5593	−1.29002	−0.645012	+	0.764172i	$0.723148\pi$
$68$	−3.41424	−0.414037
$69$	−1.37993	−0.166124
$70$	31.4392	3.75771
$71$	−13.0431	−1.54793	−0.773963	−	0.633231i	$-0.781728\pi$
$71$	−13.0431	−1.54793	−0.773963	+	0.633231i	$0.781728\pi$
$72$	−3.29073	−0.387816
$73$	12.4899	1.46183	0.730915	−	0.682468i	$-0.239093\pi$
$73$	12.4899	1.46183	0.730915	+	0.682468i	$0.239093\pi$
$74$	14.4063	1.67469
$75$	7.11392	0.821444
$76$	−9.71410	−1.11428
$77$	−15.3933	−1.75423
$78$	−1.17540	−0.133088
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−2.88378	−0.322417
$81$	1.00000	0.111111
$82$	−9.33395	−1.03076
$83$	−3.56892	−0.391740	−0.195870	−	0.980630i	$-0.562753\pi$
$83$	−3.56892	−0.391740	−0.195870	+	0.980630i	$0.562753\pi$
$84$	13.2542	1.44616
$85$	3.48051	0.377514
$86$	−7.25713	−0.782556
$87$	6.89450	0.739168
$88$	13.0486	1.39098
$89$	14.4987	1.53686	0.768429	−	0.639935i	$-0.221039\pi$
$89$	14.4987	1.53686	0.768429	+	0.639935i	$0.221039\pi$
$90$	8.09862	0.853670
$91$	1.96100	0.205569
$92$	−4.71141	−0.491199
$93$	4.97067	0.515435
$94$	−30.9766	−3.19500
$95$	9.90264	1.01599
$96$	4.65353	0.474949
$97$	−13.1817	−1.33840	−0.669199	−	0.743083i	$-0.733363\pi$
$97$	−13.1817	−1.33840	−0.669199	+	0.743083i	$0.733363\pi$
$98$	−18.7784	−1.89690
$99$	−3.96525	−0.398523
$100$	24.2886	2.42886
$101$	18.2724	1.81817	0.909086	−	0.416607i	$-0.136781\pi$
$101$	18.2724	1.81817	0.909086	+	0.416607i	$0.136781\pi$
$102$	2.32685	0.230393
$103$	−13.4189	−1.32221	−0.661103	−	0.750295i	$-0.729912\pi$
$103$	−13.4189	−1.32221	−0.661103	+	0.750295i	$0.729912\pi$
$104$	−1.66230	−0.163002
$105$	−13.5115	−1.31859
$106$	33.0040	3.20564
$107$	−13.7236	−1.32671	−0.663353	−	0.748307i	$-0.730867\pi$
$107$	−13.7236	−1.32671	−0.663353	+	0.748307i	$0.730867\pi$
$108$	3.41424	0.328535
$109$	18.6843	1.78964	0.894818	−	0.446432i	$-0.147305\pi$
$109$	18.6843	1.78964	0.894818	+	0.446432i	$0.147305\pi$
$110$	−32.1131	−3.06186
$111$	−6.19131	−0.587653
$112$	3.21648	0.303929
$113$	14.2602	1.34148	0.670741	−	0.741691i	$-0.265976\pi$
$113$	14.2602	1.34148	0.670741	+	0.741691i	$0.265976\pi$
$114$	6.62030	0.620048
$115$	4.80286	0.447869
$116$	23.5395	2.18558
$117$	0.505146	0.0467007
$118$	20.5596	1.89267
$119$	−3.88205	−0.355867
$120$	11.4534	1.04555
$121$	4.72321	0.429383
$122$	30.5748	2.76812
$123$	4.01141	0.361696
$124$	16.9711	1.52405
$125$	−7.35750	−0.658074
$126$	−9.03295	−0.804719
$127$	4.35851	0.386755	0.193378	−	0.981124i	$-0.438056\pi$
$127$	4.35851	0.386755	0.193378	+	0.981124i	$0.438056\pi$
$128$	19.7441	1.74515
$129$	3.11886	0.274600
$130$	4.09098	0.358803
$131$	−11.8054	−1.03144	−0.515721	−	0.856757i	$-0.672476\pi$
$131$	−11.8054	−1.03144	−0.515721	+	0.856757i	$0.672476\pi$
$132$	−13.5383	−1.17836
$133$	−11.0451	−0.957732
$134$	24.5699	2.12252
$135$	−3.48051	−0.299554
$136$	3.29073	0.282177
$137$	7.90307	0.675205	0.337603	−	0.941289i	$-0.390384\pi$
$137$	7.90307	0.675205	0.337603	+	0.941289i	$0.390384\pi$
$138$	3.21089	0.273330
$139$	6.03479	0.511864	0.255932	−	0.966695i	$-0.417618\pi$
$139$	6.03479	0.511864	0.255932	+	0.966695i	$0.417618\pi$
$140$	−46.1315	−3.89882
$141$	13.3127	1.12113
$142$	30.3493	2.54685
$143$	−2.00303	−0.167502
$144$	0.828553	0.0690461
$145$	−23.9963	−1.99279
$146$	−29.0621	−2.40520
$147$	8.07030	0.665627
$148$	−21.1386	−1.73758
$149$	−7.64454	−0.626266	−0.313133	−	0.949709i	$-0.601378\pi$
$149$	−7.64454	−0.626266	−0.313133	+	0.949709i	$0.601378\pi$
$150$	−16.5530	−1.35155
$151$	−7.91745	−0.644313	−0.322157	−	0.946686i	$-0.604408\pi$
$151$	−7.91745	−0.644313	−0.322157	+	0.946686i	$0.604408\pi$
$152$	9.36269	0.759414
$153$	−1.00000	−0.0808452
$154$	35.8179	2.88629
$155$	−17.3005	−1.38961
$156$	1.72469	0.138086
$157$	−11.8847	−0.948499	−0.474249	−	0.880391i	$-0.657281\pi$
$157$	−11.8847	−0.948499	−0.474249	+	0.880391i	$0.657281\pi$
$158$	−2.32685	−0.185114
$159$	−14.1840	−1.12486
$160$	−16.1966	−1.28046
$161$	−5.35696	−0.422188
$162$	−2.32685	−0.182815
$163$	19.0056	1.48863	0.744316	−	0.667828i	$-0.232776\pi$
$163$	19.0056	1.48863	0.744316	+	0.667828i	$0.232776\pi$
$164$	13.6959	1.06947
$165$	13.8011	1.07441
$166$	8.30436	0.644543
$167$	6.76600	0.523568	0.261784	−	0.965126i	$-0.415689\pi$
$167$	6.76600	0.523568	0.261784	+	0.965126i	$0.415689\pi$
$168$	−12.7748	−0.985594
$169$	−12.7448	−0.980371
$170$	−8.09862	−0.621136
$171$	−2.84517	−0.217576
$172$	10.6485	0.811943
$173$	−5.75330	−0.437416	−0.218708	−	0.975790i	$-0.570184\pi$
$173$	−5.75330	−0.437416	−0.218708	+	0.975790i	$0.570184\pi$
$174$	−16.0425	−1.21618
$175$	27.6166	2.08762
$176$	−3.28542	−0.247648
$177$	−8.83581	−0.664140
$178$	−33.7363	−2.52864
$179$	−1.00337	−0.0749951	−0.0374975	−	0.999297i	$-0.511939\pi$
$179$	−1.00337	−0.0749951	−0.0374975	+	0.999297i	$0.511939\pi$
$180$	−11.8833	−0.885727
$181$	−12.4881	−0.928237	−0.464118	−	0.885773i	$-0.653629\pi$
$181$	−12.4881	−0.928237	−0.464118	+	0.885773i	$0.653629\pi$
$182$	−4.56296	−0.338229
$183$	−13.1400	−0.971337
$184$	4.54097	0.334765
$185$	21.5489	1.58431
$186$	−11.5660	−0.848062
$187$	3.96525	0.289968
$188$	45.4527	3.31498
$189$	3.88205	0.282377
$190$	−23.0420	−1.67164
$191$	−1.50390	−0.108818	−0.0544091	−	0.998519i	$-0.517328\pi$
$191$	−1.50390	−0.108818	−0.0544091	+	0.998519i	$0.517328\pi$
$192$	−12.4852	−0.901041
$193$	−10.0551	−0.723782	−0.361891	−	0.932220i	$-0.617869\pi$
$193$	−10.0551	−0.723782	−0.361891	+	0.932220i	$0.617869\pi$
$194$	30.6719	2.20211
$195$	−1.75816	−0.125905
$196$	27.5539	1.96814
$197$	−9.52184	−0.678403	−0.339202	−	0.940714i	$-0.610157\pi$
$197$	−9.52184	−0.678403	−0.339202	+	0.940714i	$0.610157\pi$
$198$	9.22655	0.655702
$199$	−15.2005	−1.07753	−0.538767	−	0.842455i	$-0.681110\pi$
$199$	−15.2005	−1.07753	−0.538767	+	0.842455i	$0.681110\pi$
$200$	−23.4100	−1.65533
$201$	−10.5593	−0.744796
$202$	−42.5172	−2.99150
$203$	26.7648	1.87852
$204$	−3.41424	−0.239045
$205$	−13.9617	−0.975129
$206$	31.2239	2.17547
$207$	−1.37993	−0.0959118
$208$	0.418540	0.0290205
$209$	11.2818	0.780380
$210$	31.4392	2.16951
$211$	12.4089	0.854262	0.427131	−	0.904190i	$-0.359524\pi$
$211$	12.4089	0.854262	0.427131	+	0.904190i	$0.359524\pi$
$212$	−48.4275	−3.32602
$213$	−13.0431	−0.893695
$214$	31.9327	2.18287
$215$	−10.8552	−0.740319
$216$	−3.29073	−0.223906
$217$	19.2964	1.30992
$218$	−43.4757	−2.94455
$219$	12.4899	0.843988
$220$	47.1202	3.17684
$221$	−0.505146	−0.0339798
$222$	14.4063	0.966885
$223$	−21.7208	−1.45453	−0.727265	−	0.686357i	$-0.759209\pi$
$223$	−21.7208	−1.45453	−0.727265	+	0.686357i	$0.759209\pi$
$224$	18.0652	1.20703
$225$	7.11392	0.474261
$226$	−33.1813	−2.20719
$227$	−22.7045	−1.50695	−0.753475	−	0.657476i	$-0.771624\pi$
$227$	−22.7045	−1.50695	−0.753475	+	0.657476i	$0.771624\pi$
$228$	−9.71410	−0.643332
$229$	5.20677	0.344073	0.172037	−	0.985091i	$-0.444965\pi$
$229$	5.20677	0.344073	0.172037	+	0.985091i	$0.444965\pi$
$230$	−11.1755	−0.736893
$231$	−15.3933	−1.01280
$232$	−22.6879	−1.48953
$233$	−5.64286	−0.369676	−0.184838	−	0.982769i	$-0.559176\pi$
$233$	−5.64286	−0.369676	−0.184838	+	0.982769i	$0.559176\pi$
$234$	−1.17540	−0.0768383
$235$	−46.3348	−3.02255
$236$	−30.1676	−1.96374
$237$	1.00000	0.0649570
$238$	9.03295	0.585519
$239$	27.8609	1.80217	0.901087	−	0.433638i	$-0.142770\pi$
$239$	27.8609	1.80217	0.901087	+	0.433638i	$0.142770\pi$
$240$	−2.88378	−0.186147
$241$	15.0146	0.967177	0.483588	−	0.875296i	$-0.339333\pi$
$241$	15.0146	0.967177	0.483588	+	0.875296i	$0.339333\pi$
$242$	−10.9902	−0.706478
$243$	1.00000	0.0641500
$244$	−44.8631	−2.87207
$245$	−28.0887	−1.79452
$246$	−9.33395	−0.595111
$247$	−1.43723	−0.0914486
$248$	−16.3571	−1.03868
$249$	−3.56892	−0.226171
$250$	17.1198	1.08275
$251$	2.70502	0.170739	0.0853697	−	0.996349i	$-0.472793\pi$
$251$	2.70502	0.170739	0.0853697	+	0.996349i	$0.472793\pi$
$252$	13.2542	0.834939
$253$	5.47177	0.344007
$254$	−10.1416	−0.636341
$255$	3.48051	0.217958
$256$	−20.9713	−1.31070
$257$	−11.6438	−0.726320	−0.363160	−	0.931727i	$-0.618302\pi$
$257$	−11.6438	−0.726320	−0.363160	+	0.931727i	$0.618302\pi$
$258$	−7.25713	−0.451809
$259$	−24.0350	−1.49346
$260$	−6.00279	−0.372277
$261$	6.89450	0.426759
$262$	27.4694	1.69707
$263$	−1.34413	−0.0828827	−0.0414414	−	0.999141i	$-0.513195\pi$
$263$	−1.34413	−0.0828827	−0.0414414	+	0.999141i	$0.513195\pi$
$264$	13.0486	0.803083
$265$	49.3674	3.03262
$266$	25.7003	1.57579
$267$	14.4987	0.887305
$268$	−36.0520	−2.20223
$269$	−25.7223	−1.56832	−0.784158	−	0.620561i	$-0.786905\pi$
$269$	−25.7223	−1.56832	−0.784158	+	0.620561i	$0.786905\pi$
$270$	8.09862	0.492866
$271$	−28.9195	−1.75674	−0.878368	−	0.477985i	$-0.841367\pi$
$271$	−28.9195	−1.75674	−0.878368	+	0.477985i	$0.841367\pi$
$272$	−0.828553	−0.0502384
$273$	1.96100	0.118685
$274$	−18.3893	−1.11094
$275$	−28.2085	−1.70103
$276$	−4.71141	−0.283594
$277$	−32.2511	−1.93778	−0.968891	−	0.247486i	$-0.920395\pi$
$277$	−32.2511	−1.93778	−0.968891	+	0.247486i	$0.920395\pi$
$278$	−14.0421	−0.842187
$279$	4.97067	0.297586
$280$	44.4626	2.65715
$281$	16.4890	0.983649	0.491824	−	0.870694i	$-0.336330\pi$
$281$	16.4890	0.983649	0.491824	+	0.870694i	$0.336330\pi$
$282$	−30.9766	−1.84463
$283$	−3.81575	−0.226823	−0.113412	−	0.993548i	$-0.536178\pi$
$283$	−3.81575	−0.226823	−0.113412	+	0.993548i	$0.536178\pi$
$284$	−44.5321	−2.64249
$285$	9.90264	0.586582
$286$	4.66075	0.275596
$287$	15.5725	0.919215
$288$	4.65353	0.274212
$289$	1.00000	0.0588235
$290$	55.8359	3.27880
$291$	−13.1817	−0.772725
$292$	42.6435	2.49552
$293$	5.56009	0.324824	0.162412	−	0.986723i	$-0.448073\pi$
$293$	5.56009	0.324824	0.162412	+	0.986723i	$0.448073\pi$
$294$	−18.7784	−1.09518
$295$	30.7531	1.79051
$296$	20.3739	1.18421
$297$	−3.96525	−0.230087
$298$	17.7877	1.03042
$299$	−0.697066	−0.0403124
$300$	24.2886	1.40230
$301$	12.1076	0.697869
$302$	18.4227	1.06011
$303$	18.2724	1.04972
$304$	−2.35738	−0.135205
$305$	45.7338	2.61871
$306$	2.32685	0.133017
$307$	4.16436	0.237672	0.118836	−	0.992914i	$-0.462084\pi$
$307$	4.16436	0.237672	0.118836	+	0.992914i	$0.462084\pi$
$308$	−52.5564	−2.99468
$309$	−13.4189	−0.763377
$310$	40.2556	2.28636
$311$	−1.89120	−0.107240	−0.0536201	−	0.998561i	$-0.517076\pi$
$311$	−1.89120	−0.107240	−0.0536201	+	0.998561i	$0.517076\pi$
$312$	−1.66230	−0.0941090
$313$	−0.540956	−0.0305767	−0.0152883	−	0.999883i	$-0.504867\pi$
$313$	−0.540956	−0.0305767	−0.0152883	+	0.999883i	$0.504867\pi$
$314$	27.6538	1.56060
$315$	−13.5115	−0.761286
$316$	3.41424	0.192066
$317$	−13.3712	−0.751002	−0.375501	−	0.926822i	$-0.622529\pi$
$317$	−13.3712	−0.751002	−0.375501	+	0.926822i	$0.622529\pi$
$318$	33.0040	1.85077
$319$	−27.3384	−1.53066
$320$	43.4548	2.42919
$321$	−13.7236	−0.765974
$322$	12.4648	0.694639
$323$	2.84517	0.158310
$324$	3.41424	0.189680
$325$	3.59357	0.199335
$326$	−44.2232	−2.44929
$327$	18.6843	1.03325
$328$	−13.2004	−0.728873
$329$	51.6805	2.84924
$330$	−32.1131	−1.76777
$331$	−30.8588	−1.69615	−0.848076	−	0.529875i	$-0.822239\pi$
$331$	−30.8588	−1.69615	−0.848076	+	0.529875i	$0.822239\pi$
$332$	−12.1852	−0.668748
$333$	−6.19131	−0.339282
$334$	−15.7435	−0.861444
$335$	36.7517	2.00796
$336$	3.21648	0.175474
$337$	3.01526	0.164252	0.0821258	−	0.996622i	$-0.473829\pi$
$337$	3.01526	0.164252	0.0821258	+	0.996622i	$0.473829\pi$
$338$	29.6553	1.61304
$339$	14.2602	0.774506
$340$	11.8833	0.644461
$341$	−19.7100	−1.06735
$342$	6.62030	0.357985
$343$	4.15497	0.224347
$344$	−10.2633	−0.553361
$345$	4.80286	0.258577
$346$	13.3871	0.719694
$347$	−9.75780	−0.523826	−0.261913	−	0.965091i	$-0.584353\pi$
$347$	−9.75780	−0.523826	−0.261913	+	0.965091i	$0.584353\pi$
$348$	23.5395	1.26185
$349$	31.0404	1.66156	0.830778	−	0.556605i	$-0.187896\pi$
$349$	31.0404	1.66156	0.830778	+	0.556605i	$0.187896\pi$
$350$	−64.2597	−3.43482
$351$	0.505146	0.0269627
$352$	−18.4524	−0.983517
$353$	−11.8060	−0.628368	−0.314184	−	0.949362i	$-0.601731\pi$
$353$	−11.8060	−0.628368	−0.314184	+	0.949362i	$0.601731\pi$
$354$	20.5596	1.09273
$355$	45.3964	2.40939
$356$	49.5020	2.62360
$357$	−3.88205	−0.205460
$358$	2.33468	0.123392
$359$	−27.1804	−1.43453	−0.717265	−	0.696801i	$-0.754606\pi$
$359$	−27.1804	−1.43453	−0.717265	+	0.696801i	$0.754606\pi$
$360$	11.4534	0.603647
$361$	−10.9050	−0.573947
$362$	29.0581	1.52726
$363$	4.72321	0.247904
$364$	6.69533	0.350930
$365$	−43.4711	−2.27538
$366$	30.5748	1.59817
$367$	22.1320	1.15528	0.577641	−	0.816291i	$-0.303973\pi$
$367$	22.1320	1.15528	0.577641	+	0.816291i	$0.303973\pi$
$368$	−1.14335	−0.0596010
$369$	4.01141	0.208826
$370$	−50.1411	−2.60671
$371$	−55.0629	−2.85872
$372$	16.9711	0.879909
$373$	0.384176	0.0198919	0.00994595	−	0.999951i	$-0.496834\pi$
$373$	0.384176	0.0198919	0.00994595	+	0.999951i	$0.496834\pi$
$374$	−9.22655	−0.477094
$375$	−7.35750	−0.379939
$376$	−43.8084	−2.25924
$377$	3.48273	0.179370
$378$	−9.03295	−0.464605
$379$	15.8630	0.814830	0.407415	−	0.913243i	$-0.366430\pi$
$379$	15.8630	0.814830	0.407415	+	0.913243i	$0.366430\pi$
$380$	33.8100	1.73442
$381$	4.35851	0.223293
$382$	3.49935	0.179042
$383$	−2.16327	−0.110538	−0.0552690	−	0.998471i	$-0.517602\pi$
$383$	−2.16327	−0.110538	−0.0552690	+	0.998471i	$0.517602\pi$
$384$	19.7441	1.00756
$385$	53.5764	2.73051
$386$	23.3967	1.19086
$387$	3.11886	0.158541
$388$	−45.0055	−2.28481
$389$	−16.9998	−0.861924	−0.430962	−	0.902370i	$-0.641826\pi$
$389$	−16.9998	−0.861924	−0.430962	+	0.902370i	$0.641826\pi$
$390$	4.09098	0.207155
$391$	1.37993	0.0697861
$392$	−26.5572	−1.34134
$393$	−11.8054	−0.595503
$394$	22.1559	1.11620
$395$	−3.48051	−0.175123
$396$	−13.5383	−0.680326
$397$	34.4274	1.72786	0.863931	−	0.503610i	$-0.167995\pi$
$397$	34.4274	1.72786	0.863931	+	0.503610i	$0.167995\pi$
$398$	35.3693	1.77290
$399$	−11.0451	−0.552947
$400$	5.89426	0.294713
$401$	−37.7957	−1.88743	−0.943714	−	0.330764i	$-0.892694\pi$
$401$	−37.7957	−1.88743	−0.943714	+	0.330764i	$0.892694\pi$
$402$	24.5699	1.22544
$403$	2.51091	0.125078
$404$	62.3864	3.10384
$405$	−3.48051	−0.172948
$406$	−62.2777	−3.09079
$407$	24.5501	1.21690
$408$	3.29073	0.162915
$409$	15.7139	0.777001	0.388501	−	0.921448i	$-0.372993\pi$
$409$	15.7139	0.777001	0.388501	+	0.921448i	$0.372993\pi$
$410$	32.4869	1.60441
$411$	7.90307	0.389830
$412$	−45.8155	−2.25717
$413$	−34.3011	−1.68784
$414$	3.21089	0.157807
$415$	12.4217	0.609755
$416$	2.35071	0.115253
$417$	6.03479	0.295525
$418$	−26.2511	−1.28398
$419$	−22.4392	−1.09622	−0.548112	−	0.836405i	$-0.684653\pi$
$419$	−22.4392	−1.09622	−0.548112	+	0.836405i	$0.684653\pi$
$420$	−46.1315	−2.25099
$421$	−27.6975	−1.34989	−0.674946	−	0.737867i	$-0.735833\pi$
$421$	−27.6975	−1.34989	−0.674946	+	0.737867i	$0.735833\pi$
$422$	−28.8736	−1.40555
$423$	13.3127	0.647285
$424$	46.6756	2.26677
$425$	−7.11392	−0.345076
$426$	30.3493	1.47043
$427$	−51.0101	−2.46855
$428$	−46.8555	−2.26485
$429$	−2.00303	−0.0967072
$430$	25.2585	1.21807
$431$	−1.92627	−0.0927854	−0.0463927	−	0.998923i	$-0.514773\pi$
$431$	−1.92627	−0.0927854	−0.0463927	+	0.998923i	$0.514773\pi$
$432$	0.828553	0.0398638
$433$	−32.5453	−1.56403	−0.782014	−	0.623260i	$-0.785808\pi$
$433$	−32.5453	−1.56403	−0.782014	+	0.623260i	$0.785808\pi$
$434$	−44.8998	−2.15526
$435$	−23.9963	−1.15054
$436$	63.7928	3.05512
$437$	3.92614	0.187813
$438$	−29.0621	−1.38864
$439$	−35.3913	−1.68914	−0.844568	−	0.535448i	$-0.820143\pi$
$439$	−35.3913	−1.68914	−0.844568	+	0.535448i	$0.820143\pi$
$440$	−45.4156	−2.16510
$441$	8.07030	0.384300
$442$	1.17540	0.0559081
$443$	−13.3933	−0.636334	−0.318167	−	0.948035i	$-0.603067\pi$
$443$	−13.3933	−0.636334	−0.318167	+	0.948035i	$0.603067\pi$
$444$	−21.1386	−1.00319
$445$	−50.4628	−2.39216
$446$	50.5410	2.39319
$447$	−7.64454	−0.361575
$448$	−48.4681	−2.28990
$449$	−0.118879	−0.00561026	−0.00280513	−	0.999996i	$-0.500893\pi$
$449$	−0.118879	−0.00561026	−0.00280513	+	0.999996i	$0.500893\pi$
$450$	−16.5530	−0.780317
$451$	−15.9062	−0.748996
$452$	48.6876	2.29007
$453$	−7.91745	−0.371994
$454$	52.8300	2.47943
$455$	−6.82527	−0.319974
$456$	9.36269	0.438448
$457$	−12.3788	−0.579054	−0.289527	−	0.957170i	$-0.593498\pi$
$457$	−12.3788	−0.579054	−0.289527	+	0.957170i	$0.593498\pi$
$458$	−12.1154	−0.566115
$459$	−1.00000	−0.0466760
$460$	16.3981	0.764565
$461$	−28.1926	−1.31306	−0.656531	−	0.754299i	$-0.727977\pi$
$461$	−28.1926	−1.31306	−0.656531	+	0.754299i	$0.727977\pi$
$462$	35.8179	1.66640
$463$	−13.2487	−0.615718	−0.307859	−	0.951432i	$-0.599612\pi$
$463$	−13.2487	−0.615718	−0.307859	+	0.951432i	$0.599612\pi$
$464$	5.71246	0.265194
$465$	−17.3005	−0.802289
$466$	13.1301	0.608240
$467$	−18.0122	−0.833503	−0.416752	−	0.909020i	$-0.636832\pi$
$467$	−18.0122	−0.833503	−0.416752	+	0.909020i	$0.636832\pi$
$468$	1.72469	0.0797238
$469$	−40.9917	−1.89282
$470$	107.814	4.97310
$471$	−11.8847	−0.547616
$472$	29.0762	1.33834
$473$	−12.3671	−0.568638
$474$	−2.32685	−0.106876
$475$	−20.2403	−0.928690
$476$	−13.2542	−0.607507
$477$	−14.1840	−0.649440
$478$	−64.8283	−2.96518
$479$	10.8075	0.493806	0.246903	−	0.969040i	$-0.420587\pi$
$479$	10.8075	0.493806	0.246903	+	0.969040i	$0.420587\pi$
$480$	−16.1966	−0.739272
$481$	−3.12751	−0.142602
$482$	−34.9368	−1.59133
$483$	−5.35696	−0.243750
$484$	16.1262	0.733008
$485$	45.8790	2.08326
$486$	−2.32685	−0.105548
$487$	4.71875	0.213827	0.106913	−	0.994268i	$-0.465903\pi$
$487$	4.71875	0.213827	0.106913	+	0.994268i	$0.465903\pi$
$488$	43.2401	1.95739
$489$	19.0056	0.859462
$490$	65.3583	2.95259
$491$	34.3534	1.55035	0.775174	−	0.631748i	$-0.217662\pi$
$491$	34.3534	1.55035	0.775174	+	0.631748i	$0.217662\pi$
$492$	13.6959	0.617459
$493$	−6.89450	−0.310513
$494$	3.34421	0.150463
$495$	13.8011	0.620312
$496$	4.11847	0.184925
$497$	−50.6338	−2.27123
$498$	8.30436	0.372127
$499$	−14.6001	−0.653588	−0.326794	−	0.945096i	$-0.605968\pi$
$499$	−14.6001	−0.653588	−0.326794	+	0.945096i	$0.605968\pi$
$500$	−25.1203	−1.12341
$501$	6.76600	0.302282
$502$	−6.29418	−0.280923
$503$	19.4829	0.868699	0.434349	−	0.900745i	$-0.356978\pi$
$503$	19.4829	0.868699	0.434349	+	0.900745i	$0.356978\pi$
$504$	−12.7748	−0.569033
$505$	−63.5972	−2.83004
$506$	−12.7320	−0.566007
$507$	−12.7448	−0.566018
$508$	14.8810	0.660238
$509$	8.03124	0.355979	0.177989	−	0.984032i	$-0.443041\pi$
$509$	8.03124	0.355979	0.177989	+	0.984032i	$0.443041\pi$
$510$	−8.09862	−0.358613
$511$	48.4863	2.14491
$512$	9.30878	0.411394
$513$	−2.84517	−0.125617
$514$	27.0934	1.19504
$515$	46.7047	2.05805
$516$	10.6485	0.468776
$517$	−52.7881	−2.32162
$518$	55.9258	2.45724
$519$	−5.75330	−0.252542
$520$	5.78563	0.253717
$521$	−18.6357	−0.816444	−0.408222	−	0.912883i	$-0.633851\pi$
$521$	−18.6357	−0.816444	−0.408222	+	0.912883i	$0.633851\pi$
$522$	−16.0425	−0.702160
$523$	14.0947	0.616318	0.308159	−	0.951335i	$-0.400287\pi$
$523$	14.0947	0.616318	0.308159	+	0.951335i	$0.400287\pi$
$524$	−40.3064	−1.76080
$525$	27.6166	1.20529
$526$	3.12760	0.136370
$527$	−4.97067	−0.216526
$528$	−3.28542	−0.142980
$529$	−21.0958	−0.917208
$530$	−114.871	−4.98967
$531$	−8.83581	−0.383442
$532$	−37.7106	−1.63496
$533$	2.02635	0.0877708
$534$	−33.7363	−1.45991
$535$	47.7649	2.06506
$536$	34.7478	1.50088
$537$	−1.00337	−0.0432984
$538$	59.8520	2.58040
$539$	−32.0008	−1.37837
$540$	−11.8833	−0.511375
$541$	−15.6199	−0.671552	−0.335776	−	0.941942i	$-0.608999\pi$
$541$	−15.6199	−0.671552	−0.335776	+	0.941942i	$0.608999\pi$
$542$	67.2914	2.89041
$543$	−12.4881	−0.535918
$544$	−4.65353	−0.199519
$545$	−65.0310	−2.78562
$546$	−4.56296	−0.195277
$547$	−18.0391	−0.771297	−0.385648	−	0.922646i	$-0.626022\pi$
$547$	−18.0391	−0.771297	−0.385648	+	0.922646i	$0.626022\pi$
$548$	26.9830	1.15266
$549$	−13.1400	−0.560801
$550$	65.6369	2.79877
$551$	−19.6160	−0.835671
$552$	4.54097	0.193277
$553$	3.88205	0.165082
$554$	75.0436	3.18830
$555$	21.5489	0.914699
$556$	20.6042	0.873813
$557$	0.404613	0.0171440	0.00857200	−	0.999963i	$-0.497271\pi$
$557$	0.404613	0.0171440	0.00857200	+	0.999963i	$0.497271\pi$
$558$	−11.5660	−0.489629
$559$	1.57548	0.0666357
$560$	−11.1950	−0.473075
$561$	3.96525	0.167413
$562$	−38.3674	−1.61843
$563$	24.9595	1.05192	0.525960	−	0.850509i	$-0.323706\pi$
$563$	24.9595	1.05192	0.525960	+	0.850509i	$0.323706\pi$
$564$	45.4527	1.91390
$565$	−49.6326	−2.08806
$566$	8.87870	0.373199
$567$	3.88205	0.163031
$568$	42.9211	1.80093
$569$	−23.7592	−0.996038	−0.498019	−	0.867166i	$-0.665939\pi$
$569$	−23.7592	−0.996038	−0.498019	+	0.867166i	$0.665939\pi$
$570$	−23.0420	−0.965122
$571$	39.2134	1.64103	0.820516	−	0.571624i	$-0.193686\pi$
$571$	39.2134	1.64103	0.820516	+	0.571624i	$0.193686\pi$
$572$	−6.83882	−0.285946
$573$	−1.50390	−0.0628263
$574$	−36.2349	−1.51241
$575$	−9.81671	−0.409385
$576$	−12.4852	−0.520216
$577$	45.2263	1.88280	0.941398	−	0.337298i	$-0.109513\pi$
$577$	45.2263	1.88280	0.941398	+	0.337298i	$0.109513\pi$
$578$	−2.32685	−0.0967843
$579$	−10.0551	−0.417876
$580$	−81.9292	−3.40193
$581$	−13.8547	−0.574791
$582$	30.6719	1.27139
$583$	56.2431	2.32935
$584$	−41.1008	−1.70076
$585$	−1.75816	−0.0726911
$586$	−12.9375	−0.534443
$587$	−2.08774	−0.0861702	−0.0430851	−	0.999071i	$-0.513719\pi$
$587$	−2.08774	−0.0861702	−0.0430851	+	0.999071i	$0.513719\pi$
$588$	27.5539	1.13631
$589$	−14.1424	−0.582728
$590$	−71.5579	−2.94599
$591$	−9.52184	−0.391676
$592$	−5.12983	−0.210835
$593$	−2.26874	−0.0931660	−0.0465830	−	0.998914i	$-0.514833\pi$
$593$	−2.26874	−0.0931660	−0.0465830	+	0.998914i	$0.514833\pi$
$594$	9.22655	0.378570
$595$	13.5115	0.553917
$596$	−26.1003	−1.06911
$597$	−15.2005	−0.622114
$598$	1.62197	0.0663273
$599$	−15.7651	−0.644145	−0.322073	−	0.946715i	$-0.604379\pi$
$599$	−15.7651	−0.644145	−0.322073	+	0.946715i	$0.604379\pi$
$600$	−23.4100	−0.955707
$601$	−35.6727	−1.45512	−0.727560	−	0.686044i	$-0.759346\pi$
$601$	−35.6727	−1.45512	−0.727560	+	0.686044i	$0.759346\pi$
$602$	−28.1725	−1.14823
$603$	−10.5593	−0.430008
$604$	−27.0321	−1.09992
$605$	−16.4392	−0.668347
$606$	−42.5172	−1.72714
$607$	22.3068	0.905404	0.452702	−	0.891662i	$-0.350460\pi$
$607$	22.3068	0.905404	0.452702	+	0.891662i	$0.350460\pi$
$608$	−13.2401	−0.536957
$609$	26.7648	1.08456
$610$	−106.416	−4.30865
$611$	6.72484	0.272058
$612$	−3.41424	−0.138012
$613$	−25.2814	−1.02111	−0.510553	−	0.859846i	$-0.670559\pi$
$613$	−25.2814	−1.02111	−0.510553	+	0.859846i	$0.670559\pi$
$614$	−9.68985	−0.391050
$615$	−13.9617	−0.562991
$616$	50.6551	2.04095
$617$	−31.4159	−1.26476	−0.632378	−	0.774660i	$-0.717921\pi$
$617$	−31.4159	−1.26476	−0.632378	+	0.774660i	$0.717921\pi$
$618$	31.2239	1.25601
$619$	11.7927	0.473989	0.236994	−	0.971511i	$-0.423838\pi$
$619$	11.7927	0.473989	0.236994	+	0.971511i	$0.423838\pi$
$620$	−59.0679	−2.37222
$621$	−1.37993	−0.0553747
$622$	4.40054	0.176446
$623$	56.2846	2.25500
$624$	0.418540	0.0167550
$625$	−9.96178	−0.398471
$626$	1.25872	0.0503088
$627$	11.2818	0.450553
$628$	−40.5771	−1.61920
$629$	6.19131	0.246864
$630$	31.4392	1.25257
$631$	33.8592	1.34791	0.673956	−	0.738772i	$-0.264594\pi$
$631$	33.8592	1.34791	0.673956	+	0.738772i	$0.264594\pi$
$632$	−3.29073	−0.130898
$633$	12.4089	0.493208
$634$	31.1128	1.23565
$635$	−15.1698	−0.601996
$636$	−48.4275	−1.92028
$637$	4.07668	0.161524
$638$	63.6124	2.51844
$639$	−13.0431	−0.515975
$640$	−68.7195	−2.71638
$641$	−8.60322	−0.339807	−0.169903	−	0.985461i	$-0.554346\pi$
$641$	−8.60322	−0.339807	−0.169903	+	0.985461i	$0.554346\pi$
$642$	31.9327	1.26028
$643$	32.8474	1.29538	0.647688	−	0.761906i	$-0.275736\pi$
$643$	32.8474	1.29538	0.647688	+	0.761906i	$0.275736\pi$
$644$	−18.2899	−0.720725
$645$	−10.8552	−0.427424
$646$	−6.62030	−0.260472
$647$	−25.2383	−0.992218	−0.496109	−	0.868260i	$-0.665238\pi$
$647$	−25.2383	−0.992218	−0.496109	+	0.868260i	$0.665238\pi$
$648$	−3.29073	−0.129272
$649$	35.0362	1.37529
$650$	−8.36169	−0.327973
$651$	19.2964	0.756285
$652$	64.8896	2.54127
$653$	−3.17628	−0.124297	−0.0621487	−	0.998067i	$-0.519795\pi$
$653$	−3.17628	−0.124297	−0.0621487	+	0.998067i	$0.519795\pi$
$654$	−43.4757	−1.70003
$655$	41.0887	1.60547
$656$	3.32367	0.129767
$657$	12.4899	0.487277
$658$	−120.253	−4.68794
$659$	−5.83948	−0.227474	−0.113737	−	0.993511i	$-0.536282\pi$
$659$	−5.83948	−0.227474	−0.113737	+	0.993511i	$0.536282\pi$
$660$	47.1202	1.83415
$661$	21.9252	0.852793	0.426396	−	0.904536i	$-0.359783\pi$
$661$	21.9252	0.852793	0.426396	+	0.904536i	$0.359783\pi$
$662$	71.8038	2.79073
$663$	−0.505146	−0.0196182
$664$	11.7444	0.455769
$665$	38.4425	1.49074
$666$	14.4063	0.558231
$667$	−9.51393	−0.368381
$668$	23.1007	0.893794
$669$	−21.7208	−0.839773
$670$	−85.5158	−3.30376
$671$	52.1034	2.01143
$672$	18.0652	0.696882
$673$	−11.5580	−0.445529	−0.222765	−	0.974872i	$-0.571508\pi$
$673$	−11.5580	−0.445529	−0.222765	+	0.974872i	$0.571508\pi$
$674$	−7.01606	−0.270249
$675$	7.11392	0.273815
$676$	−43.5139	−1.67361
$677$	51.7338	1.98829	0.994147	−	0.108039i	$-0.0344573\pi$
$677$	51.7338	1.98829	0.994147	+	0.108039i	$0.0344573\pi$
$678$	−33.1813	−1.27432
$679$	−51.1720	−1.96380
$680$	−11.4534	−0.439217
$681$	−22.7045	−0.870038
$682$	45.8622	1.75615
$683$	13.6515	0.522360	0.261180	−	0.965290i	$-0.415888\pi$
$683$	13.6515	0.522360	0.261180	+	0.965290i	$0.415888\pi$
$684$	−9.71410	−0.371428
$685$	−27.5067	−1.05098
$686$	−9.66800	−0.369126
$687$	5.20677	0.198651
$688$	2.58414	0.0985195
$689$	−7.16498	−0.272964
$690$	−11.1755	−0.425445
$691$	−16.8711	−0.641806	−0.320903	−	0.947112i	$-0.603986\pi$
$691$	−16.8711	−0.641806	−0.320903	+	0.947112i	$0.603986\pi$
$692$	−19.6432	−0.746721
$693$	−15.3933	−0.584743
$694$	22.7050	0.861868
$695$	−21.0041	−0.796731
$696$	−22.6879	−0.859983
$697$	−4.01141	−0.151943
$698$	−72.2264	−2.73381
$699$	−5.64286	−0.213432
$700$	94.2896	3.56381
$701$	43.9605	1.66037	0.830183	−	0.557491i	$-0.188236\pi$
$701$	43.9605	1.66037	0.830183	+	0.557491i	$0.188236\pi$
$702$	−1.17540	−0.0443626
$703$	17.6153	0.664375
$704$	49.5069	1.86586
$705$	−46.3348	−1.74507
$706$	27.4707	1.03387
$707$	70.9344	2.66776
$708$	−30.1676	−1.13377
$709$	17.0818	0.641521	0.320761	−	0.947160i	$-0.396061\pi$
$709$	17.0818	0.641521	0.320761	+	0.947160i	$0.396061\pi$
$710$	−105.631	−3.96425
$711$	1.00000	0.0375029
$712$	−47.7112	−1.78805
$713$	−6.85918	−0.256878
$714$	9.03295	0.338050
$715$	6.97156	0.260721
$716$	−3.42573	−0.128026
$717$	27.8609	1.04049
$718$	63.2449	2.36028
$719$	−3.53148	−0.131702	−0.0658510	−	0.997829i	$-0.520976\pi$
$719$	−3.53148	−0.131702	−0.0658510	+	0.997829i	$0.520976\pi$
$720$	−2.88378	−0.107472
$721$	−52.0930	−1.94004
$722$	25.3743	0.944334
$723$	15.0146	0.558400
$724$	−42.6375	−1.58461
$725$	49.0469	1.82156
$726$	−10.9902	−0.407885
$727$	−28.8576	−1.07027	−0.535134	−	0.844767i	$-0.679739\pi$
$727$	−28.8576	−1.07027	−0.535134	+	0.844767i	$0.679739\pi$
$728$	−6.45312	−0.239168
$729$	1.00000	0.0370370
$730$	101.151	3.74376
$731$	−3.11886	−0.115355
$732$	−44.8631	−1.65819
$733$	36.2678	1.33958	0.669790	−	0.742551i	$-0.266384\pi$
$733$	36.2678	1.33958	0.669790	+	0.742551i	$0.266384\pi$
$734$	−51.4979	−1.90082
$735$	−28.0887	−1.03607
$736$	−6.42155	−0.236702
$737$	41.8703	1.54231
$738$	−9.33395	−0.343588
$739$	33.2584	1.22343	0.611715	−	0.791078i	$-0.290480\pi$
$739$	33.2584	1.22343	0.611715	+	0.791078i	$0.290480\pi$
$740$	73.5731	2.70460
$741$	−1.43723	−0.0527979
$742$	128.123	4.70355
$743$	−32.5017	−1.19237	−0.596185	−	0.802847i	$-0.703318\pi$
$743$	−32.5017	−1.19237	−0.596185	+	0.802847i	$0.703318\pi$
$744$	−16.3571	−0.599681
$745$	26.6069	0.974801
$746$	−0.893921	−0.0327288
$747$	−3.56892	−0.130580
$748$	13.5383	0.495010
$749$	−53.2755	−1.94664
$750$	17.1198	0.625127
$751$	−22.7869	−0.831504	−0.415752	−	0.909478i	$-0.636482\pi$
$751$	−22.7869	−0.831504	−0.415752	+	0.909478i	$0.636482\pi$
$752$	11.0303	0.402232
$753$	2.70502	0.0985764
$754$	−8.10379	−0.295123
$755$	27.5567	1.00289
$756$	13.2542	0.482052
$757$	0.478238	0.0173819	0.00869093	−	0.999962i	$-0.497234\pi$
$757$	0.478238	0.0173819	0.00869093	+	0.999962i	$0.497234\pi$
$758$	−36.9110	−1.34067
$759$	5.47177	0.198613
$760$	−32.5869	−1.18205
$761$	−40.7339	−1.47660	−0.738302	−	0.674470i	$-0.764372\pi$
$761$	−40.7339	−1.47660	−0.738302	+	0.674470i	$0.764372\pi$
$762$	−10.1416	−0.367392
$763$	72.5335	2.62589
$764$	−5.13467	−0.185766
$765$	3.48051	0.125838
$766$	5.03362	0.181872
$767$	−4.46337	−0.161163
$768$	−20.9713	−0.756735
$769$	36.7235	1.32428	0.662142	−	0.749378i	$-0.269647\pi$
$769$	36.7235	1.32428	0.662142	+	0.749378i	$0.269647\pi$
$770$	−124.664	−4.49260
$771$	−11.6438	−0.419341
$772$	−34.3305	−1.23558
$773$	−21.1976	−0.762424	−0.381212	−	0.924488i	$-0.624493\pi$
$773$	−21.1976	−0.762424	−0.381212	+	0.924488i	$0.624493\pi$
$774$	−7.25713	−0.260852
$775$	35.3609	1.27020
$776$	43.3774	1.55716
$777$	−24.0350	−0.862250
$778$	39.5560	1.41815
$779$	−11.4131	−0.408919
$780$	−6.00279	−0.214934
$781$	51.7190	1.85065
$782$	−3.21089	−0.114821
$783$	6.89450	0.246389
$784$	6.68668	0.238810
$785$	41.3646	1.47637
$786$	27.4694	0.979801
$787$	8.15432	0.290670	0.145335	−	0.989383i	$-0.453574\pi$
$787$	8.15432	0.290670	0.145335	+	0.989383i	$0.453574\pi$
$788$	−32.5099	−1.15812
$789$	−1.34413	−0.0478524
$790$	8.09862	0.288136
$791$	55.3586	1.96833
$792$	13.0486	0.463660
$793$	−6.63762	−0.235709
$794$	−80.1075	−2.84291
$795$	49.3674	1.75088
$796$	−51.8981	−1.83948
$797$	31.6594	1.12143	0.560717	−	0.828007i	$-0.310525\pi$
$797$	31.6594	1.12143	0.560717	+	0.828007i	$0.310525\pi$
$798$	25.7003	0.909781
$799$	−13.3127	−0.470969
$800$	33.1048	1.17043
$801$	14.4987	0.512286
$802$	87.9450	3.10545
$803$	−49.5255	−1.74772
$804$	−36.0520	−1.27146
$805$	18.6449	0.657147
$806$	−5.84253	−0.205794
$807$	−25.7223	−0.905468
$808$	−60.1295	−2.11535
$809$	−11.3939	−0.400590	−0.200295	−	0.979736i	$-0.564190\pi$
$809$	−11.3939	−0.400590	−0.200295	+	0.979736i	$0.564190\pi$
$810$	8.09862	0.284557
$811$	−37.3853	−1.31278	−0.656388	−	0.754423i	$-0.727917\pi$
$811$	−37.3853	−1.31278	−0.656388	+	0.754423i	$0.727917\pi$
$812$	91.3813	3.20686
$813$	−28.9195	−1.01425
$814$	−57.1244	−2.00221
$815$	−66.1490	−2.31710
$816$	−0.828553	−0.0290052
$817$	−8.87370	−0.310451
$818$	−36.5639	−1.27843
$819$	1.96100	0.0685229
$820$	−47.6687	−1.66466
$821$	5.46022	0.190563	0.0952816	−	0.995450i	$-0.469625\pi$
$821$	5.46022	0.190563	0.0952816	+	0.995450i	$0.469625\pi$
$822$	−18.3893	−0.641400
$823$	19.0767	0.664971	0.332486	−	0.943108i	$-0.392113\pi$
$823$	19.0767	0.664971	0.332486	+	0.943108i	$0.392113\pi$
$824$	44.1580	1.53832
$825$	−28.2085	−0.982093
$826$	79.8135	2.77707
$827$	20.6770	0.719010	0.359505	−	0.933143i	$-0.382945\pi$
$827$	20.6770	0.719010	0.359505	+	0.933143i	$0.382945\pi$
$828$	−4.71141	−0.163733
$829$	−41.3023	−1.43449	−0.717244	−	0.696822i	$-0.754597\pi$
$829$	−41.3023	−1.43449	−0.717244	+	0.696822i	$0.754597\pi$
$830$	−28.9034	−1.00325
$831$	−32.2511	−1.11878
$832$	−6.30684	−0.218650
$833$	−8.07030	−0.279619
$834$	−14.0421	−0.486237
$835$	−23.5491	−0.814950
$836$	38.5189	1.33220
$837$	4.97067	0.171812
$838$	52.2126	1.80365
$839$	−9.30251	−0.321158	−0.160579	−	0.987023i	$-0.551336\pi$
$839$	−9.30251	−0.321158	−0.160579	+	0.987023i	$0.551336\pi$
$840$	44.4626	1.53411
$841$	18.5341	0.639106
$842$	64.4479	2.22102
$843$	16.4890	0.567910
$844$	42.3669	1.45833
$845$	44.3584	1.52598
$846$	−30.9766	−1.06500
$847$	18.3357	0.630024
$848$	−11.7522	−0.403572
$849$	−3.81575	−0.130956
$850$	16.5530	0.567764
$851$	8.54358	0.292870
$852$	−44.5321	−1.52564
$853$	−26.5579	−0.909324	−0.454662	−	0.890664i	$-0.650240\pi$
$853$	−26.5579	−0.909324	−0.454662	+	0.890664i	$0.650240\pi$
$854$	118.693	4.06159
$855$	9.90264	0.338663
$856$	45.1605	1.54355
$857$	−6.58969	−0.225100	−0.112550	−	0.993646i	$-0.535902\pi$
$857$	−6.58969	−0.225100	−0.112550	+	0.993646i	$0.535902\pi$
$858$	4.66075	0.159116
$859$	−22.2130	−0.757898	−0.378949	−	0.925418i	$-0.623714\pi$
$859$	−22.2130	−0.757898	−0.378949	+	0.925418i	$0.623714\pi$
$860$	−37.0623	−1.26381
$861$	15.5725	0.530709
$862$	4.48215	0.152663
$863$	−14.8257	−0.504674	−0.252337	−	0.967639i	$-0.581199\pi$
$863$	−14.8257	−0.504674	−0.252337	+	0.967639i	$0.581199\pi$
$864$	4.65353	0.158316
$865$	20.0244	0.680850
$866$	75.7282	2.57335
$867$	1.00000	0.0339618
$868$	65.8825	2.23620
$869$	−3.96525	−0.134512
$870$	55.8359	1.89301
$871$	−5.33399	−0.180735
$872$	−61.4851	−2.08215
$873$	−13.1817	−0.446133
$874$	−9.13555	−0.309015
$875$	−28.5622	−0.965577
$876$	42.6435	1.44079
$877$	10.7506	0.363021	0.181511	−	0.983389i	$-0.441901\pi$
$877$	10.7506	0.363021	0.181511	+	0.983389i	$0.441901\pi$
$878$	82.3504	2.77919
$879$	5.56009	0.187537
$880$	11.4349	0.385471
$881$	−36.0451	−1.21439	−0.607196	−	0.794552i	$-0.707706\pi$
$881$	−36.0451	−1.21439	−0.607196	+	0.794552i	$0.707706\pi$
$882$	−18.7784	−0.632302
$883$	15.4713	0.520650	0.260325	−	0.965521i	$-0.416170\pi$
$883$	15.4713	0.520650	0.260325	+	0.965521i	$0.416170\pi$
$884$	−1.72469	−0.0580076
$885$	30.7531	1.03375
$886$	31.1642	1.04698
$887$	40.7726	1.36901	0.684506	−	0.729008i	$-0.260018\pi$
$887$	40.7726	1.36901	0.684506	+	0.729008i	$0.260018\pi$
$888$	20.3739	0.683703
$889$	16.9200	0.567477
$890$	117.419	3.93591
$891$	−3.96525	−0.132841
$892$	−74.1599	−2.48306
$893$	−37.8769	−1.26750
$894$	17.7877	0.594910
$895$	3.49222	0.116732
$896$	76.6476	2.56062
$897$	−0.697066	−0.0232744
$898$	0.276614	0.00923075
$899$	34.2703	1.14298
$900$	24.2886	0.809621
$901$	14.1840	0.472537
$902$	37.0115	1.23235
$903$	12.1076	0.402915
$904$	−46.9263	−1.56074
$905$	43.4651	1.44483
$906$	18.4227	0.612055
$907$	51.7094	1.71698	0.858491	−	0.512829i	$-0.171402\pi$
$907$	51.7094	1.71698	0.858491	+	0.512829i	$0.171402\pi$
$908$	−77.5186	−2.57254
$909$	18.2724	0.606058
$910$	15.8814	0.526463
$911$	−25.5599	−0.846837	−0.423418	−	0.905934i	$-0.639170\pi$
$911$	−25.5599	−0.846837	−0.423418	+	0.905934i	$0.639170\pi$
$912$	−2.35738	−0.0780606
$913$	14.1517	0.468352
$914$	28.8036	0.952737
$915$	45.7338	1.51191
$916$	17.7772	0.587374
$917$	−45.8291	−1.51341
$918$	2.32685	0.0767976
$919$	−23.5497	−0.776833	−0.388417	−	0.921484i	$-0.626978\pi$
$919$	−23.5497	−0.776833	−0.388417	+	0.921484i	$0.626978\pi$
$920$	−15.8049	−0.521072
$921$	4.16436	0.137220
$922$	65.6001	2.16042
$923$	−6.58864	−0.216868
$924$	−52.5564	−1.72898
$925$	−44.0445	−1.44817
$926$	30.8277	1.01306
$927$	−13.4189	−0.440736
$928$	32.0838	1.05320
$929$	−30.3949	−0.997223	−0.498611	−	0.866826i	$-0.666157\pi$
$929$	−30.3949	−0.997223	−0.498611	+	0.866826i	$0.666157\pi$
$930$	40.2556	1.32003
$931$	−22.9614	−0.752530
$932$	−19.2661	−0.631081
$933$	−1.89120	−0.0619151
$934$	41.9116	1.37139
$935$	−13.8011	−0.451343
$936$	−1.66230	−0.0543339
$937$	−7.72470	−0.252355	−0.126177	−	0.992008i	$-0.540271\pi$
$937$	−7.72470	−0.252355	−0.126177	+	0.992008i	$0.540271\pi$
$938$	95.3817	3.11432
$939$	−0.540956	−0.0176534
$940$	−158.198	−5.15986
$941$	42.2485	1.37726	0.688631	−	0.725112i	$-0.258212\pi$
$941$	42.2485	1.37726	0.688631	+	0.725112i	$0.258212\pi$
$942$	27.6538	0.901011
$943$	−5.53547	−0.180260
$944$	−7.32094	−0.238276
$945$	−13.5115	−0.439529
$946$	28.7763	0.935599
$947$	8.70990	0.283034	0.141517	−	0.989936i	$-0.454802\pi$
$947$	8.70990	0.283034	0.141517	+	0.989936i	$0.454802\pi$
$948$	3.41424	0.110889
$949$	6.30921	0.204806
$950$	47.0962	1.52800
$951$	−13.3712	−0.433591
$952$	12.7748	0.414032
$953$	−27.3036	−0.884450	−0.442225	−	0.896904i	$-0.645811\pi$
$953$	−27.3036	−0.884450	−0.442225	+	0.896904i	$0.645811\pi$
$954$	33.0040	1.06855
$955$	5.23433	0.169379
$956$	95.1239	3.07653
$957$	−27.3384	−0.883725
$958$	−25.1474	−0.812475
$959$	30.6801	0.990713
$960$	43.4548	1.40250
$961$	−6.29242	−0.202981
$962$	7.27726	0.234628
$963$	−13.7236	−0.442235
$964$	51.2635	1.65109
$965$	34.9968	1.12659
$966$	12.4648	0.401050
$967$	34.2793	1.10235	0.551175	−	0.834390i	$-0.314180\pi$
$967$	34.2793	1.10235	0.551175	+	0.834390i	$0.314180\pi$
$968$	−15.5428	−0.499565
$969$	2.84517	0.0914001
$970$	−106.754	−3.42765
$971$	−38.5065	−1.23573	−0.617867	−	0.786283i	$-0.712003\pi$
$971$	−38.5065	−1.23573	−0.617867	+	0.786283i	$0.712003\pi$
$972$	3.41424	0.109512
$973$	23.4273	0.751046
$974$	−10.9798	−0.351817
$975$	3.59357	0.115086
$976$	−10.8872	−0.348490
$977$	8.01124	0.256302	0.128151	−	0.991755i	$-0.459096\pi$
$977$	8.01124	0.256302	0.128151	+	0.991755i	$0.459096\pi$
$978$	−44.2232	−1.41410
$979$	−57.4909	−1.83742
$980$	−95.9017	−3.06347
$981$	18.6843	0.596545
$982$	−79.9353	−2.55084
$983$	−38.6968	−1.23424	−0.617118	−	0.786870i	$-0.711700\pi$
$983$	−38.6968	−1.23424	−0.617118	+	0.786870i	$0.711700\pi$
$984$	−13.2004	−0.420815
$985$	33.1408	1.05595
$986$	16.0425	0.510896
$987$	51.6805	1.64501
$988$	−4.90704	−0.156114
$989$	−4.30381	−0.136853
$990$	−32.1131	−1.02062
$991$	27.9298	0.887221	0.443610	−	0.896220i	$-0.353697\pi$
$991$	27.9298	0.887221	0.443610	+	0.896220i	$0.353697\pi$
$992$	23.1312	0.734416
$993$	−30.8588	−0.979274
$994$	117.817	3.73694
$995$	52.9054	1.67721
$996$	−12.1852	−0.386102
$997$	−0.666435	−0.0211062	−0.0105531	−	0.999944i	$-0.503359\pi$
$997$	−0.666435	−0.0211062	−0.0105531	+	0.999944i	$0.503359\pi$
$998$	33.9722	1.07537
$999$	−6.19131	−0.195884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.4	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.4	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32685 q^{2} +1.00000 q^{3} +3.41424 q^{4} -3.48051 q^{5} -2.32685 q^{6} +3.88205 q^{7} -3.29073 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.32685 q^{2} +1.00000 q^{3} +3.41424 q^{4} -3.48051 q^{5} -2.32685 q^{6} +3.88205 q^{7} -3.29073 q^{8} +1.00000 q^{9} +8.09862 q^{10} -3.96525 q^{11} +3.41424 q^{12} +0.505146 q^{13} -9.03295 q^{14} -3.48051 q^{15} +0.828553 q^{16} -1.00000 q^{17} -2.32685 q^{18} -2.84517 q^{19} -11.8833 q^{20} +3.88205 q^{21} +9.22655 q^{22} -1.37993 q^{23} -3.29073 q^{24} +7.11392 q^{25} -1.17540 q^{26} +1.00000 q^{27} +13.2542 q^{28} +6.89450 q^{29} +8.09862 q^{30} +4.97067 q^{31} +4.65353 q^{32} -3.96525 q^{33} +2.32685 q^{34} -13.5115 q^{35} +3.41424 q^{36} -6.19131 q^{37} +6.62030 q^{38} +0.505146 q^{39} +11.4534 q^{40} +4.01141 q^{41} -9.03295 q^{42} +3.11886 q^{43} -13.5383 q^{44} -3.48051 q^{45} +3.21089 q^{46} +13.3127 q^{47} +0.828553 q^{48} +8.07030 q^{49} -16.5530 q^{50} -1.00000 q^{51} +1.72469 q^{52} -14.1840 q^{53} -2.32685 q^{54} +13.8011 q^{55} -12.7748 q^{56} -2.84517 q^{57} -16.0425 q^{58} -8.83581 q^{59} -11.8833 q^{60} -13.1400 q^{61} -11.5660 q^{62} +3.88205 q^{63} -12.4852 q^{64} -1.75816 q^{65} +9.22655 q^{66} -10.5593 q^{67} -3.41424 q^{68} -1.37993 q^{69} +31.4392 q^{70} -13.0431 q^{71} -3.29073 q^{72} +12.4899 q^{73} +14.4063 q^{74} +7.11392 q^{75} -9.71410 q^{76} -15.3933 q^{77} -1.17540 q^{78} +1.00000 q^{79} -2.88378 q^{80} +1.00000 q^{81} -9.33395 q^{82} -3.56892 q^{83} +13.2542 q^{84} +3.48051 q^{85} -7.25713 q^{86} +6.89450 q^{87} +13.0486 q^{88} +14.4987 q^{89} +8.09862 q^{90} +1.96100 q^{91} -4.71141 q^{92} +4.97067 q^{93} -30.9766 q^{94} +9.90264 q^{95} +4.65353 q^{96} -13.1817 q^{97} -18.7784 q^{98} -3.96525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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