LMFDB - Embedded newform 4029.2.a.g.1.11

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:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-0.0913921 q^{2} -1.00000 q^{3} -1.99165 q^{4} -1.96751 q^{5} +0.0913921 q^{6} -3.33061 q^{7} +0.364805 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0913921 q^{2} -1.00000 q^{3} -1.99165 q^{4} -1.96751 q^{5} +0.0913921 q^{6} -3.33061 q^{7} +0.364805 q^{8} +1.00000 q^{9} +0.179815 q^{10} -2.42472 q^{11} +1.99165 q^{12} +3.46533 q^{13} +0.304392 q^{14} +1.96751 q^{15} +3.94995 q^{16} -1.00000 q^{17} -0.0913921 q^{18} -3.16974 q^{19} +3.91858 q^{20} +3.33061 q^{21} +0.221600 q^{22} +1.46501 q^{23} -0.364805 q^{24} -1.12891 q^{25} -0.316704 q^{26} -1.00000 q^{27} +6.63341 q^{28} +6.25690 q^{29} -0.179815 q^{30} -4.93975 q^{31} -1.09060 q^{32} +2.42472 q^{33} +0.0913921 q^{34} +6.55301 q^{35} -1.99165 q^{36} +10.5341 q^{37} +0.289690 q^{38} -3.46533 q^{39} -0.717757 q^{40} +9.88092 q^{41} -0.304392 q^{42} +5.41854 q^{43} +4.82918 q^{44} -1.96751 q^{45} -0.133891 q^{46} -1.44767 q^{47} -3.94995 q^{48} +4.09298 q^{49} +0.103173 q^{50} +1.00000 q^{51} -6.90171 q^{52} -4.67511 q^{53} +0.0913921 q^{54} +4.77065 q^{55} -1.21502 q^{56} +3.16974 q^{57} -0.571831 q^{58} -7.65345 q^{59} -3.91858 q^{60} +5.29995 q^{61} +0.451454 q^{62} -3.33061 q^{63} -7.80024 q^{64} -6.81806 q^{65} -0.221600 q^{66} +7.83833 q^{67} +1.99165 q^{68} -1.46501 q^{69} -0.598893 q^{70} +7.70390 q^{71} +0.364805 q^{72} -3.41020 q^{73} -0.962730 q^{74} +1.12891 q^{75} +6.31301 q^{76} +8.07579 q^{77} +0.316704 q^{78} -1.00000 q^{79} -7.77157 q^{80} +1.00000 q^{81} -0.903038 q^{82} -0.840176 q^{83} -6.63341 q^{84} +1.96751 q^{85} -0.495211 q^{86} -6.25690 q^{87} -0.884548 q^{88} +8.74770 q^{89} +0.179815 q^{90} -11.5417 q^{91} -2.91779 q^{92} +4.93975 q^{93} +0.132305 q^{94} +6.23650 q^{95} +1.09060 q^{96} -3.22692 q^{97} -0.374066 q^{98} -2.42472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * 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 $

$2$	−0.0913921	−0.0646240	−0.0323120	−	0.999478i	$-0.510287\pi$
$2$	−0.0913921	−0.0646240	−0.0323120	+	0.999478i	$0.510287\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99165	−0.995824
$5$	−1.96751	−0.879897	−0.439948	−	0.898023i	$-0.645003\pi$
$5$	−1.96751	−0.879897	−0.439948	+	0.898023i	$0.645003\pi$
$6$	0.0913921	0.0373107
$7$	−3.33061	−1.25885	−0.629427	−	0.777060i	$-0.716710\pi$
$7$	−3.33061	−1.25885	−0.629427	+	0.777060i	$0.716710\pi$
$8$	0.364805	0.128978
$9$	1.00000	0.333333
$10$	0.179815	0.0568624
$11$	−2.42472	−0.731079	−0.365540	−	0.930796i	$-0.619116\pi$
$11$	−2.42472	−0.731079	−0.365540	+	0.930796i	$0.619116\pi$
$12$	1.99165	0.574939
$13$	3.46533	0.961109	0.480555	−	0.876965i	$-0.340435\pi$
$13$	3.46533	0.961109	0.480555	+	0.876965i	$0.340435\pi$
$14$	0.304392	0.0813521
$15$	1.96751	0.508008
$16$	3.94995	0.987489
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.0913921	−0.0215413
$19$	−3.16974	−0.727189	−0.363595	−	0.931557i	$-0.618451\pi$
$19$	−3.16974	−0.727189	−0.363595	+	0.931557i	$0.618451\pi$
$20$	3.91858	0.876222
$21$	3.33061	0.726799
$22$	0.221600	0.0472452
$23$	1.46501	0.305477	0.152738	−	0.988267i	$-0.451191\pi$
$23$	1.46501	0.305477	0.152738	+	0.988267i	$0.451191\pi$
$24$	−0.364805	−0.0744655
$25$	−1.12891	−0.225782
$26$	−0.316704	−0.0621107
$27$	−1.00000	−0.192450
$28$	6.63341	1.25360
$29$	6.25690	1.16188	0.580939	−	0.813947i	$-0.302686\pi$
$29$	6.25690	1.16188	0.580939	+	0.813947i	$0.302686\pi$
$30$	−0.179815	−0.0328295
$31$	−4.93975	−0.887205	−0.443603	−	0.896224i	$-0.646300\pi$
$31$	−4.93975	−0.887205	−0.443603	+	0.896224i	$0.646300\pi$
$32$	−1.09060	−0.192793
$33$	2.42472	0.422089
$34$	0.0913921	0.0156736
$35$	6.55301	1.10766
$36$	−1.99165	−0.331941
$37$	10.5341	1.73179	0.865894	−	0.500227i	$-0.166750\pi$
$37$	10.5341	1.73179	0.865894	+	0.500227i	$0.166750\pi$
$38$	0.289690	0.0469939
$39$	−3.46533	−0.554897
$40$	−0.717757	−0.113487
$41$	9.88092	1.54314	0.771570	−	0.636144i	$-0.219472\pi$
$41$	9.88092	1.54314	0.771570	+	0.636144i	$0.219472\pi$
$42$	−0.304392	−0.0469687
$43$	5.41854	0.826319	0.413160	−	0.910659i	$-0.364425\pi$
$43$	5.41854	0.826319	0.413160	+	0.910659i	$0.364425\pi$
$44$	4.82918	0.728026
$45$	−1.96751	−0.293299
$46$	−0.133891	−0.0197411
$47$	−1.44767	−0.211164	−0.105582	−	0.994411i	$-0.533671\pi$
$47$	−1.44767	−0.211164	−0.105582	+	0.994411i	$0.533671\pi$
$48$	−3.94995	−0.570127
$49$	4.09298	0.584711
$50$	0.103173	0.0145909
$51$	1.00000	0.140028
$52$	−6.90171	−0.957095
$53$	−4.67511	−0.642175	−0.321088	−	0.947049i	$-0.604048\pi$
$53$	−4.67511	−0.642175	−0.321088	+	0.947049i	$0.604048\pi$
$54$	0.0913921	0.0124369
$55$	4.77065	0.643274
$56$	−1.21502	−0.162364
$57$	3.16974	0.419843
$58$	−0.571831	−0.0750851
$59$	−7.65345	−0.996394	−0.498197	−	0.867064i	$-0.666004\pi$
$59$	−7.65345	−0.996394	−0.498197	+	0.867064i	$0.666004\pi$
$60$	−3.91858	−0.505887
$61$	5.29995	0.678590	0.339295	−	0.940680i	$-0.389812\pi$
$61$	5.29995	0.678590	0.339295	+	0.940680i	$0.389812\pi$
$62$	0.451454	0.0573347
$63$	−3.33061	−0.419618
$64$	−7.80024	−0.975030
$65$	−6.81806	−0.845677
$66$	−0.221600	−0.0272771
$67$	7.83833	0.957605	0.478802	−	0.877923i	$-0.341071\pi$
$67$	7.83833	0.957605	0.478802	+	0.877923i	$0.341071\pi$
$68$	1.99165	0.241523
$69$	−1.46501	−0.176367
$70$	−0.598893	−0.0715814
$71$	7.70390	0.914285	0.457143	−	0.889393i	$-0.348873\pi$
$71$	7.70390	0.914285	0.457143	+	0.889393i	$0.348873\pi$
$72$	0.364805	0.0429927
$73$	−3.41020	−0.399134	−0.199567	−	0.979884i	$-0.563954\pi$
$73$	−3.41020	−0.399134	−0.199567	+	0.979884i	$0.563954\pi$
$74$	−0.962730	−0.111915
$75$	1.12891	0.130355
$76$	6.31301	0.724152
$77$	8.07579	0.920321
$78$	0.316704	0.0358596
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−7.77157	−0.868888
$81$	1.00000	0.111111
$82$	−0.903038	−0.0997238
$83$	−0.840176	−0.0922213	−0.0461106	−	0.998936i	$-0.514683\pi$
$83$	−0.840176	−0.0922213	−0.0461106	+	0.998936i	$0.514683\pi$
$84$	−6.63341	−0.723764
$85$	1.96751	0.213406
$86$	−0.495211	−0.0534000
$87$	−6.25690	−0.670810
$88$	−0.884548	−0.0942932
$89$	8.74770	0.927254	0.463627	−	0.886030i	$-0.346548\pi$
$89$	8.74770	0.927254	0.463627	+	0.886030i	$0.346548\pi$
$90$	0.179815	0.0189541
$91$	−11.5417	−1.20990
$92$	−2.91779	−0.304201
$93$	4.93975	0.512228
$94$	0.132305	0.0136463
$95$	6.23650	0.639851
$96$	1.09060	0.111309
$97$	−3.22692	−0.327644	−0.163822	−	0.986490i	$-0.552382\pi$
$97$	−3.22692	−0.327644	−0.163822	+	0.986490i	$0.552382\pi$
$98$	−0.374066	−0.0377864
$99$	−2.42472	−0.243693
$100$	2.24839	0.224839
$101$	8.12321	0.808290	0.404145	−	0.914695i	$-0.367569\pi$
$101$	8.12321	0.808290	0.404145	+	0.914695i	$0.367569\pi$
$102$	−0.0913921	−0.00904917
$103$	−7.40981	−0.730110	−0.365055	−	0.930986i	$-0.618950\pi$
$103$	−7.40981	−0.730110	−0.365055	+	0.930986i	$0.618950\pi$
$104$	1.26417	0.123962
$105$	−6.55301	−0.639508
$106$	0.427268	0.0414999
$107$	−4.64987	−0.449520	−0.224760	−	0.974414i	$-0.572160\pi$
$107$	−4.64987	−0.449520	−0.224760	+	0.974414i	$0.572160\pi$
$108$	1.99165	0.191646
$109$	2.75371	0.263758	0.131879	−	0.991266i	$-0.457899\pi$
$109$	2.75371	0.263758	0.131879	+	0.991266i	$0.457899\pi$
$110$	−0.436000	−0.0415709
$111$	−10.5341	−0.999849
$112$	−13.1558	−1.24310
$113$	18.3091	1.72238	0.861189	−	0.508285i	$-0.169720\pi$
$113$	18.3091	1.72238	0.861189	+	0.508285i	$0.169720\pi$
$114$	−0.289690	−0.0271319
$115$	−2.88243	−0.268788
$116$	−12.4615	−1.15703
$117$	3.46533	0.320370
$118$	0.699465	0.0643909
$119$	3.33061	0.305317
$120$	0.717757	0.0655219
$121$	−5.12076	−0.465523
$122$	−0.484374	−0.0438532
$123$	−9.88092	−0.890932
$124$	9.83824	0.883500
$125$	12.0587	1.07856
$126$	0.304392	0.0271174
$127$	−20.7513	−1.84138	−0.920691	−	0.390292i	$-0.872374\pi$
$127$	−20.7513	−1.84138	−0.920691	+	0.390292i	$0.872374\pi$
$128$	2.89409	0.255804
$129$	−5.41854	−0.477076
$130$	0.623117	0.0546510
$131$	−18.0462	−1.57671	−0.788354	−	0.615223i	$-0.789066\pi$
$131$	−18.0462	−1.57671	−0.788354	+	0.615223i	$0.789066\pi$
$132$	−4.82918	−0.420326
$133$	10.5572	0.915425
$134$	−0.716362	−0.0618842
$135$	1.96751	0.169336
$136$	−0.364805	−0.0312818
$137$	−14.1565	−1.20947	−0.604736	−	0.796426i	$-0.706721\pi$
$137$	−14.1565	−1.20947	−0.604736	+	0.796426i	$0.706721\pi$
$138$	0.133891	0.0113975
$139$	5.51303	0.467609	0.233805	−	0.972284i	$-0.424882\pi$
$139$	5.51303	0.467609	0.233805	+	0.972284i	$0.424882\pi$
$140$	−13.0513	−1.10303
$141$	1.44767	0.121916
$142$	−0.704076	−0.0590847
$143$	−8.40244	−0.702647
$144$	3.94995	0.329163
$145$	−12.3105	−1.02233
$146$	0.311665	0.0257936
$147$	−4.09298	−0.337583
$148$	−20.9801	−1.72456
$149$	−16.7491	−1.37214	−0.686070	−	0.727535i	$-0.740666\pi$
$149$	−16.7491	−1.37214	−0.686070	+	0.727535i	$0.740666\pi$
$150$	−0.103173	−0.00842408
$151$	2.79196	0.227207	0.113603	−	0.993526i	$-0.463761\pi$
$151$	2.79196	0.227207	0.113603	+	0.993526i	$0.463761\pi$
$152$	−1.15634	−0.0937915
$153$	−1.00000	−0.0808452
$154$	−0.738063	−0.0594748
$155$	9.71900	0.780649
$156$	6.90171	0.552579
$157$	−21.0908	−1.68323	−0.841614	−	0.540080i	$-0.818394\pi$
$157$	−21.0908	−1.68323	−0.841614	+	0.540080i	$0.818394\pi$
$158$	0.0913921	0.00727076
$159$	4.67511	0.370760
$160$	2.14577	0.169638
$161$	−4.87940	−0.384550
$162$	−0.0913921	−0.00718044
$163$	19.3825	1.51816	0.759078	−	0.650999i	$-0.225650\pi$
$163$	19.3825	1.51816	0.759078	+	0.650999i	$0.225650\pi$
$164$	−19.6793	−1.53670
$165$	−4.77065	−0.371394
$166$	0.0767854	0.00595970
$167$	−24.0885	−1.86403	−0.932013	−	0.362426i	$-0.881949\pi$
$167$	−24.0885	−1.86403	−0.932013	+	0.362426i	$0.881949\pi$
$168$	1.21502	0.0937412
$169$	−0.991498	−0.0762691
$170$	−0.179815	−0.0137912
$171$	−3.16974	−0.242396
$172$	−10.7918	−0.822868
$173$	−6.35759	−0.483359	−0.241679	−	0.970356i	$-0.577698\pi$
$173$	−6.35759	−0.483359	−0.241679	+	0.970356i	$0.577698\pi$
$174$	0.571831	0.0433504
$175$	3.75996	0.284227
$176$	−9.57752	−0.721932
$177$	7.65345	0.575268
$178$	−0.799470	−0.0599228
$179$	6.75456	0.504860	0.252430	−	0.967615i	$-0.418770\pi$
$179$	6.75456	0.504860	0.252430	+	0.967615i	$0.418770\pi$
$180$	3.91858	0.292074
$181$	−21.7043	−1.61327	−0.806634	−	0.591051i	$-0.798713\pi$
$181$	−21.7043	−1.61327	−0.806634	+	0.591051i	$0.798713\pi$
$182$	1.05482	0.0781882
$183$	−5.29995	−0.391784
$184$	0.534445	0.0393998
$185$	−20.7259	−1.52380
$186$	−0.451454	−0.0331022
$187$	2.42472	0.177313
$188$	2.88325	0.210282
$189$	3.33061	0.242266
$190$	−0.569967	−0.0413497
$191$	1.44625	0.104647	0.0523236	−	0.998630i	$-0.483337\pi$
$191$	1.44625	0.104647	0.0523236	+	0.998630i	$0.483337\pi$
$192$	7.80024	0.562934
$193$	7.56273	0.544377	0.272188	−	0.962244i	$-0.412253\pi$
$193$	7.56273	0.544377	0.272188	+	0.962244i	$0.412253\pi$
$194$	0.294915	0.0211737
$195$	6.81806	0.488252
$196$	−8.15177	−0.582270
$197$	8.18777	0.583354	0.291677	−	0.956517i	$-0.405787\pi$
$197$	8.18777	0.583354	0.291677	+	0.956517i	$0.405787\pi$
$198$	0.221600	0.0157484
$199$	7.79653	0.552682	0.276341	−	0.961060i	$-0.410878\pi$
$199$	7.79653	0.552682	0.276341	+	0.961060i	$0.410878\pi$
$200$	−0.411832	−0.0291209
$201$	−7.83833	−0.552873
$202$	−0.742397	−0.0522349
$203$	−20.8393	−1.46263
$204$	−1.99165	−0.139443
$205$	−19.4408	−1.35780
$206$	0.677198	0.0471826
$207$	1.46501	0.101826
$208$	13.6879	0.949084
$209$	7.68573	0.531633
$210$	0.598893	0.0413276
$211$	9.80270	0.674846	0.337423	−	0.941353i	$-0.390445\pi$
$211$	9.80270	0.674846	0.337423	+	0.941353i	$0.390445\pi$
$212$	9.31117	0.639494
$213$	−7.70390	−0.527863
$214$	0.424961	0.0290498
$215$	−10.6610	−0.727075
$216$	−0.364805	−0.0248218
$217$	16.4524	1.11686
$218$	−0.251668	−0.0170451
$219$	3.41020	0.230440
$220$	−9.50145	−0.640588
$221$	−3.46533	−0.233103
$222$	0.962730	0.0646142
$223$	−2.53986	−0.170082	−0.0850409	−	0.996377i	$-0.527102\pi$
$223$	−2.53986	−0.170082	−0.0850409	+	0.996377i	$0.527102\pi$
$224$	3.63238	0.242699
$225$	−1.12891	−0.0752607
$226$	−1.67331	−0.111307
$227$	−0.0351116	−0.00233044	−0.00116522	−	0.999999i	$-0.500371\pi$
$227$	−0.0351116	−0.00233044	−0.00116522	+	0.999999i	$0.500371\pi$
$228$	−6.31301	−0.418090
$229$	22.1605	1.46441	0.732204	−	0.681085i	$-0.238492\pi$
$229$	22.1605	1.46441	0.732204	+	0.681085i	$0.238492\pi$
$230$	0.263431	0.0173701
$231$	−8.07579	−0.531348
$232$	2.28255	0.149857
$233$	8.61006	0.564064	0.282032	−	0.959405i	$-0.408992\pi$
$233$	8.61006	0.564064	0.282032	+	0.959405i	$0.408992\pi$
$234$	−0.316704	−0.0207036
$235$	2.84830	0.185803
$236$	15.2430	0.992233
$237$	1.00000	0.0649570
$238$	−0.304392	−0.0197308
$239$	−22.6256	−1.46353	−0.731765	−	0.681558i	$-0.761303\pi$
$239$	−22.6256	−1.46353	−0.731765	+	0.681558i	$0.761303\pi$
$240$	7.77157	0.501653
$241$	−19.0066	−1.22432	−0.612162	−	0.790732i	$-0.709700\pi$
$241$	−19.0066	−1.22432	−0.612162	+	0.790732i	$0.709700\pi$
$242$	0.467997	0.0300840
$243$	−1.00000	−0.0641500
$244$	−10.5556	−0.675756
$245$	−8.05297	−0.514486
$246$	0.903038	0.0575756
$247$	−10.9842	−0.698908
$248$	−1.80205	−0.114430
$249$	0.840176	0.0532440
$250$	−1.10207	−0.0697009
$251$	21.6490	1.36647	0.683237	−	0.730197i	$-0.260572\pi$
$251$	21.6490	1.36647	0.683237	+	0.730197i	$0.260572\pi$
$252$	6.63341	0.417865
$253$	−3.55224	−0.223328
$254$	1.89651	0.118997
$255$	−1.96751	−0.123210
$256$	15.3360	0.958499
$257$	0.532783	0.0332341	0.0166170	−	0.999862i	$-0.494710\pi$
$257$	0.532783	0.0332341	0.0166170	+	0.999862i	$0.494710\pi$
$258$	0.495211	0.0308305
$259$	−35.0849	−2.18007
$260$	13.5792	0.842145
$261$	6.25690	0.387293
$262$	1.64928	0.101893
$263$	−14.5211	−0.895407	−0.447703	−	0.894182i	$-0.647758\pi$
$263$	−14.5211	−0.895407	−0.447703	+	0.894182i	$0.647758\pi$
$264$	0.884548	0.0544402
$265$	9.19831	0.565048
$266$	−0.964844	−0.0591584
$267$	−8.74770	−0.535350
$268$	−15.6112	−0.953606
$269$	−2.56993	−0.156692	−0.0783458	−	0.996926i	$-0.524964\pi$
$269$	−2.56993	−0.156692	−0.0783458	+	0.996926i	$0.524964\pi$
$270$	−0.179815	−0.0109432
$271$	2.92504	0.177683	0.0888417	−	0.996046i	$-0.471683\pi$
$271$	2.92504	0.177683	0.0888417	+	0.996046i	$0.471683\pi$
$272$	−3.94995	−0.239501
$273$	11.5417	0.698533
$274$	1.29379	0.0781609
$275$	2.73729	0.165065
$276$	2.91779	0.175631
$277$	−16.2652	−0.977283	−0.488641	−	0.872485i	$-0.662507\pi$
$277$	−16.2652	−0.977283	−0.488641	+	0.872485i	$0.662507\pi$
$278$	−0.503848	−0.0302188
$279$	−4.93975	−0.295735
$280$	2.39057	0.142864
$281$	30.0346	1.79171	0.895857	−	0.444343i	$-0.146563\pi$
$281$	30.0346	1.79171	0.895857	+	0.444343i	$0.146563\pi$
$282$	−0.132305	−0.00787868
$283$	−18.1264	−1.07751	−0.538753	−	0.842464i	$-0.681104\pi$
$283$	−18.1264	−1.07751	−0.538753	+	0.842464i	$0.681104\pi$
$284$	−15.3435	−0.910467
$285$	−6.23650	−0.369418
$286$	0.767916	0.0454078
$287$	−32.9095	−1.94259
$288$	−1.09060	−0.0642645
$289$	1.00000	0.0588235
$290$	1.12508	0.0660672
$291$	3.22692	0.189166
$292$	6.79192	0.397467
$293$	29.5743	1.72775	0.863875	−	0.503707i	$-0.168031\pi$
$293$	29.5743	1.72775	0.863875	+	0.503707i	$0.168031\pi$
$294$	0.374066	0.0218160
$295$	15.0582	0.876724
$296$	3.84288	0.223363
$297$	2.42472	0.140696
$298$	1.53074	0.0886732
$299$	5.07676	0.293596
$300$	−2.24839	−0.129811
$301$	−18.0470	−1.04021
$302$	−0.255163	−0.0146830
$303$	−8.12321	−0.466666
$304$	−12.5203	−0.718091
$305$	−10.4277	−0.597089
$306$	0.0913921	0.00522454
$307$	6.05707	0.345695	0.172848	−	0.984949i	$-0.444703\pi$
$307$	6.05707	0.345695	0.172848	+	0.984949i	$0.444703\pi$
$308$	−16.0841	−0.916478
$309$	7.40981	0.421529
$310$	−0.888240	−0.0504486
$311$	12.9976	0.737025	0.368512	−	0.929623i	$-0.379867\pi$
$311$	12.9976	0.737025	0.368512	+	0.929623i	$0.379867\pi$
$312$	−1.26417	−0.0715695
$313$	8.76239	0.495280	0.247640	−	0.968852i	$-0.420345\pi$
$313$	8.76239	0.495280	0.247640	+	0.968852i	$0.420345\pi$
$314$	1.92753	0.108777
$315$	6.55301	0.369220
$316$	1.99165	0.112039
$317$	−2.55056	−0.143254	−0.0716269	−	0.997431i	$-0.522819\pi$
$317$	−2.55056	−0.143254	−0.0716269	+	0.997431i	$0.522819\pi$
$318$	−0.427268	−0.0239600
$319$	−15.1712	−0.849425
$320$	15.3470	0.857925
$321$	4.64987	0.259530
$322$	0.445938	0.0248512
$323$	3.16974	0.176369
$324$	−1.99165	−0.110647
$325$	−3.91205	−0.217001
$326$	−1.77141	−0.0981093
$327$	−2.75371	−0.152281
$328$	3.60461	0.199031
$329$	4.82162	0.265825
$330$	0.436000	0.0240010
$331$	−11.8373	−0.650638	−0.325319	−	0.945604i	$-0.605472\pi$
$331$	−11.8373	−0.650638	−0.325319	+	0.945604i	$0.605472\pi$
$332$	1.67333	0.0918361
$333$	10.5341	0.577263
$334$	2.20150	0.120461
$335$	−15.4220	−0.842593
$336$	13.1558	0.717706
$337$	22.6787	1.23539	0.617693	−	0.786420i	$-0.288068\pi$
$337$	22.6787	1.23539	0.617693	+	0.786420i	$0.288068\pi$
$338$	0.0906151	0.00492881
$339$	−18.3091	−0.994415
$340$	−3.91858	−0.212515
$341$	11.9775	0.648617
$342$	0.289690	0.0156646
$343$	9.68216	0.522787
$344$	1.97671	0.106577
$345$	2.88243	0.155185
$346$	0.581034	0.0312366
$347$	18.5997	0.998486	0.499243	−	0.866462i	$-0.333612\pi$
$347$	18.5997	0.998486	0.499243	+	0.866462i	$0.333612\pi$
$348$	12.4615	0.668009
$349$	−28.9722	−1.55085	−0.775423	−	0.631443i	$-0.782463\pi$
$349$	−28.9722	−1.55085	−0.775423	+	0.631443i	$0.782463\pi$
$350$	−0.343631	−0.0183678
$351$	−3.46533	−0.184966
$352$	2.64441	0.140947
$353$	−9.01359	−0.479745	−0.239873	−	0.970804i	$-0.577106\pi$
$353$	−9.01359	−0.479745	−0.239873	+	0.970804i	$0.577106\pi$
$354$	−0.699465	−0.0371761
$355$	−15.1575	−0.804476
$356$	−17.4223	−0.923382
$357$	−3.33061	−0.176275
$358$	−0.617314	−0.0326260
$359$	4.60130	0.242847	0.121424	−	0.992601i	$-0.461254\pi$
$359$	4.60130	0.242847	0.121424	+	0.992601i	$0.461254\pi$
$360$	−0.717757	−0.0378291
$361$	−8.95272	−0.471196
$362$	1.98360	0.104256
$363$	5.12076	0.268770
$364$	22.9869	1.20484
$365$	6.70960	0.351196
$366$	0.484374	0.0253186
$367$	8.33584	0.435127	0.217564	−	0.976046i	$-0.430189\pi$
$367$	8.33584	0.435127	0.217564	+	0.976046i	$0.430189\pi$
$368$	5.78674	0.301655
$369$	9.88092	0.514380
$370$	1.89418	0.0984737
$371$	15.5710	0.808405
$372$	−9.83824	−0.510089
$373$	−0.762887	−0.0395008	−0.0197504	−	0.999805i	$-0.506287\pi$
$373$	−0.762887	−0.0395008	−0.0197504	+	0.999805i	$0.506287\pi$
$374$	−0.221600	−0.0114587
$375$	−12.0587	−0.622708
$376$	−0.528117	−0.0272355
$377$	21.6822	1.11669
$378$	−0.304392	−0.0156562
$379$	−14.1245	−0.725525	−0.362763	−	0.931882i	$-0.618166\pi$
$379$	−14.1245	−0.725525	−0.362763	+	0.931882i	$0.618166\pi$
$380$	−12.4209	−0.637179
$381$	20.7513	1.06312
$382$	−0.132176	−0.00676271
$383$	4.78879	0.244696	0.122348	−	0.992487i	$-0.460958\pi$
$383$	4.78879	0.244696	0.122348	+	0.992487i	$0.460958\pi$
$384$	−2.89409	−0.147688
$385$	−15.8892	−0.809788
$386$	−0.691173	−0.0351798
$387$	5.41854	0.275440
$388$	6.42689	0.326276
$389$	3.52027	0.178485	0.0892424	−	0.996010i	$-0.471555\pi$
$389$	3.52027	0.178485	0.0892424	+	0.996010i	$0.471555\pi$
$390$	−0.623117	−0.0315528
$391$	−1.46501	−0.0740890
$392$	1.49314	0.0754149
$393$	18.0462	0.910312
$394$	−0.748297	−0.0376987
$395$	1.96751	0.0989961
$396$	4.82918	0.242675
$397$	18.3771	0.922321	0.461161	−	0.887317i	$-0.347433\pi$
$397$	18.3771	0.922321	0.461161	+	0.887317i	$0.347433\pi$
$398$	−0.712541	−0.0357165
$399$	−10.5572	−0.528521
$400$	−4.45915	−0.222957
$401$	24.6726	1.23209	0.616045	−	0.787711i	$-0.288734\pi$
$401$	24.6726	1.23209	0.616045	+	0.787711i	$0.288734\pi$
$402$	0.716362	0.0357289
$403$	−17.1179	−0.852701
$404$	−16.1786	−0.804914
$405$	−1.96751	−0.0977663
$406$	1.90455	0.0945212
$407$	−25.5421	−1.26607
$408$	0.364805	0.0180605
$409$	−33.7936	−1.67099	−0.835493	−	0.549501i	$-0.814818\pi$
$409$	−33.7936	−1.67099	−0.835493	+	0.549501i	$0.814818\pi$
$410$	1.77673	0.0877467
$411$	14.1565	0.698289
$412$	14.7577	0.727061
$413$	25.4907	1.25431
$414$	−0.133891	−0.00658037
$415$	1.65305	0.0811452
$416$	−3.77930	−0.185296
$417$	−5.51303	−0.269974
$418$	−0.702415	−0.0343562
$419$	−21.5965	−1.05506	−0.527530	−	0.849536i	$-0.676882\pi$
$419$	−21.5965	−1.05506	−0.527530	+	0.849536i	$0.676882\pi$
$420$	13.0513	0.636837
$421$	−22.8119	−1.11178	−0.555892	−	0.831254i	$-0.687623\pi$
$421$	−22.8119	−1.11178	−0.555892	+	0.831254i	$0.687623\pi$
$422$	−0.895889	−0.0436112
$423$	−1.44767	−0.0703881
$424$	−1.70550	−0.0828265
$425$	1.12891	0.0547602
$426$	0.704076	0.0341126
$427$	−17.6521	−0.854245
$428$	9.26090	0.447642
$429$	8.40244	0.405673
$430$	0.974333	0.0469865
$431$	30.4438	1.46642	0.733212	−	0.680000i	$-0.238020\pi$
$431$	30.4438	1.46642	0.733212	+	0.680000i	$0.238020\pi$
$432$	−3.94995	−0.190042
$433$	−28.2541	−1.35781	−0.678903	−	0.734228i	$-0.737544\pi$
$433$	−28.2541	−1.35781	−0.678903	+	0.734228i	$0.737544\pi$
$434$	−1.50362	−0.0721760
$435$	12.3105	0.590244
$436$	−5.48443	−0.262656
$437$	−4.64372	−0.222139
$438$	−0.311665	−0.0148919
$439$	17.4545	0.833056	0.416528	−	0.909123i	$-0.363247\pi$
$439$	17.4545	0.833056	0.416528	+	0.909123i	$0.363247\pi$
$440$	1.74036	0.0829682
$441$	4.09298	0.194904
$442$	0.316704	0.0150641
$443$	2.56690	0.121957	0.0609785	−	0.998139i	$-0.480578\pi$
$443$	2.56690	0.121957	0.0609785	+	0.998139i	$0.480578\pi$
$444$	20.9801	0.995673
$445$	−17.2112	−0.815888
$446$	0.232123	0.0109914
$447$	16.7491	0.792206
$448$	25.9796	1.22742
$449$	8.40811	0.396803	0.198402	−	0.980121i	$-0.436425\pi$
$449$	8.40811	0.396803	0.198402	+	0.980121i	$0.436425\pi$
$450$	0.103173	0.00486365
$451$	−23.9584	−1.12816
$452$	−36.4653	−1.71518
$453$	−2.79196	−0.131178
$454$	0.00320893	0.000150602 0
$455$	22.7083	1.06458
$456$	1.15634	0.0541505
$457$	−18.4994	−0.865365	−0.432683	−	0.901546i	$-0.642433\pi$
$457$	−18.4994	−0.865365	−0.432683	+	0.901546i	$0.642433\pi$
$458$	−2.02530	−0.0946359
$459$	1.00000	0.0466760
$460$	5.74078	0.267665
$461$	11.9392	0.556064	0.278032	−	0.960572i	$-0.410318\pi$
$461$	11.9392	0.556064	0.278032	+	0.960572i	$0.410318\pi$
$462$	0.738063	0.0343378
$463$	−31.0628	−1.44361	−0.721807	−	0.692095i	$-0.756688\pi$
$463$	−31.0628	−1.44361	−0.721807	+	0.692095i	$0.756688\pi$
$464$	24.7145	1.14734
$465$	−9.71900	−0.450708
$466$	−0.786891	−0.0364520
$467$	−15.7753	−0.729995	−0.364997	−	0.931009i	$-0.618930\pi$
$467$	−15.7753	−0.729995	−0.364997	+	0.931009i	$0.618930\pi$
$468$	−6.90171	−0.319032
$469$	−26.1065	−1.20548
$470$	−0.260312	−0.0120073
$471$	21.0908	0.971812
$472$	−2.79202	−0.128513
$473$	−13.1384	−0.604105
$474$	−0.0913921	−0.00419778
$475$	3.57836	0.164186
$476$	−6.63341	−0.304042
$477$	−4.67511	−0.214058
$478$	2.06780	0.0945791
$479$	3.45201	0.157726	0.0788632	−	0.996885i	$-0.474871\pi$
$479$	3.45201	0.157726	0.0788632	+	0.996885i	$0.474871\pi$
$480$	−2.14577	−0.0979407
$481$	36.5040	1.66444
$482$	1.73705	0.0791207
$483$	4.87940	0.222020
$484$	10.1987	0.463579
$485$	6.34900	0.288293
$486$	0.0913921	0.00414563
$487$	25.1417	1.13928	0.569640	−	0.821894i	$-0.307083\pi$
$487$	25.1417	1.13928	0.569640	+	0.821894i	$0.307083\pi$
$488$	1.93345	0.0875232
$489$	−19.3825	−0.876508
$490$	0.735978	0.0332481
$491$	22.8537	1.03138	0.515688	−	0.856777i	$-0.327537\pi$
$491$	22.8537	1.03138	0.515688	+	0.856777i	$0.327537\pi$
$492$	19.6793	0.887212
$493$	−6.25690	−0.281797
$494$	1.00387	0.0451662
$495$	4.77065	0.214425
$496$	−19.5118	−0.876105
$497$	−25.6587	−1.15095
$498$	−0.0767854	−0.00344084
$499$	−13.6165	−0.609558	−0.304779	−	0.952423i	$-0.598583\pi$
$499$	−13.6165	−0.609558	−0.304779	+	0.952423i	$0.598583\pi$
$500$	−24.0166	−1.07406
$501$	24.0885	1.07620
$502$	−1.97855	−0.0883069
$503$	20.4823	0.913263	0.456631	−	0.889656i	$-0.349056\pi$
$503$	20.4823	0.913263	0.456631	+	0.889656i	$0.349056\pi$
$504$	−1.21502	−0.0541215
$505$	−15.9825	−0.711211
$506$	0.324647	0.0144323
$507$	0.991498	0.0440340
$508$	41.3293	1.83369
$509$	10.7144	0.474905	0.237453	−	0.971399i	$-0.423688\pi$
$509$	10.7144	0.474905	0.237453	+	0.971399i	$0.423688\pi$
$510$	0.179815	0.00796233
$511$	11.3581	0.502451
$512$	−7.18977	−0.317746
$513$	3.16974	0.139948
$514$	−0.0486921	−0.00214772
$515$	14.5789	0.642422
$516$	10.7918	0.475083
$517$	3.51018	0.154378
$518$	3.20648	0.140885
$519$	6.35759	0.279067
$520$	−2.48726	−0.109074
$521$	−34.6072	−1.51617	−0.758086	−	0.652155i	$-0.773865\pi$
$521$	−34.6072	−1.51617	−0.758086	+	0.652155i	$0.773865\pi$
$522$	−0.571831	−0.0250284
$523$	−1.32334	−0.0578657	−0.0289329	−	0.999581i	$-0.509211\pi$
$523$	−1.32334	−0.0578657	−0.0289329	+	0.999581i	$0.509211\pi$
$524$	35.9417	1.57012
$525$	−3.75996	−0.164098
$526$	1.32711	0.0578647
$527$	4.93975	0.215179
$528$	9.57752	0.416808
$529$	−20.8537	−0.906684
$530$	−0.840653	−0.0365156
$531$	−7.65345	−0.332131
$532$	−21.0262	−0.911602
$533$	34.2406	1.48313
$534$	0.799470	0.0345965
$535$	9.14866	0.395531
$536$	2.85946	0.123510
$537$	−6.75456	−0.291481
$538$	0.234872	0.0101260
$539$	−9.92431	−0.427470
$540$	−3.91858	−0.168629
$541$	−32.4479	−1.39504	−0.697521	−	0.716564i	$-0.745714\pi$
$541$	−32.4479	−1.39504	−0.697521	+	0.716564i	$0.745714\pi$
$542$	−0.267325	−0.0114826
$543$	21.7043	0.931421
$544$	1.09060	0.0467593
$545$	−5.41796	−0.232080
$546$	−1.05482	−0.0451420
$547$	−6.57932	−0.281312	−0.140656	−	0.990059i	$-0.544921\pi$
$547$	−6.57932	−0.281312	−0.140656	+	0.990059i	$0.544921\pi$
$548$	28.1948	1.20442
$549$	5.29995	0.226197
$550$	−0.250166	−0.0106671
$551$	−19.8328	−0.844905
$552$	−0.534445	−0.0227475
$553$	3.33061	0.141632
$554$	1.48651	0.0631559
$555$	20.7259	0.879763
$556$	−10.9800	−0.465656
$557$	21.0338	0.891230	0.445615	−	0.895225i	$-0.352985\pi$
$557$	21.0338	0.891230	0.445615	+	0.895225i	$0.352985\pi$
$558$	0.451454	0.0191116
$559$	18.7770	0.794183
$560$	25.8841	1.09380
$561$	−2.42472	−0.102372
$562$	−2.74492	−0.115788
$563$	−36.4517	−1.53626	−0.768128	−	0.640297i	$-0.778811\pi$
$563$	−36.4517	−1.53626	−0.768128	+	0.640297i	$0.778811\pi$
$564$	−2.88325	−0.121407
$565$	−36.0234	−1.51551
$566$	1.65661	0.0696327
$567$	−3.33061	−0.139873
$568$	2.81042	0.117923
$569$	−4.46934	−0.187364	−0.0936822	−	0.995602i	$-0.529864\pi$
$569$	−4.46934	−0.187364	−0.0936822	+	0.995602i	$0.529864\pi$
$570$	0.569967	0.0238733
$571$	−32.2955	−1.35152	−0.675761	−	0.737120i	$-0.736185\pi$
$571$	−32.2955	−1.35152	−0.675761	+	0.737120i	$0.736185\pi$
$572$	16.7347	0.699713
$573$	−1.44625	−0.0604181
$574$	3.00767	0.125538
$575$	−1.65387	−0.0689712
$576$	−7.80024	−0.325010
$577$	−32.0051	−1.33239	−0.666194	−	0.745778i	$-0.732078\pi$
$577$	−32.0051	−1.33239	−0.666194	+	0.745778i	$0.732078\pi$
$578$	−0.0913921	−0.00380141
$579$	−7.56273	−0.314296
$580$	24.5182	1.01806
$581$	2.79830	0.116093
$582$	−0.294915	−0.0122246
$583$	11.3358	0.469481
$584$	−1.24406	−0.0514795
$585$	−6.81806	−0.281892
$586$	−2.70286	−0.111654
$587$	31.3769	1.29506	0.647531	−	0.762039i	$-0.275802\pi$
$587$	31.3769	1.29506	0.647531	+	0.762039i	$0.275802\pi$
$588$	8.15177	0.336173
$589$	15.6577	0.645166
$590$	−1.37620	−0.0566574
$591$	−8.18777	−0.336800
$592$	41.6091	1.71012
$593$	−30.3279	−1.24542	−0.622710	−	0.782453i	$-0.713968\pi$
$593$	−30.3279	−1.24542	−0.622710	+	0.782453i	$0.713968\pi$
$594$	−0.221600	−0.00909235
$595$	−6.55301	−0.268647
$596$	33.3583	1.36641
$597$	−7.79653	−0.319091
$598$	−0.463976	−0.0189734
$599$	−3.72055	−0.152017	−0.0760087	−	0.997107i	$-0.524218\pi$
$599$	−3.72055	−0.152017	−0.0760087	+	0.997107i	$0.524218\pi$
$600$	0.411832	0.0168130
$601$	−2.92474	−0.119303	−0.0596514	−	0.998219i	$-0.518999\pi$
$601$	−2.92474	−0.119303	−0.0596514	+	0.998219i	$0.518999\pi$
$602$	1.64936	0.0672228
$603$	7.83833	0.319202
$604$	−5.56060	−0.226258
$605$	10.0751	0.409612
$606$	0.742397	0.0301578
$607$	6.24014	0.253279	0.126640	−	0.991949i	$-0.459581\pi$
$607$	6.24014	0.253279	0.126640	+	0.991949i	$0.459581\pi$
$608$	3.45694	0.140197
$609$	20.8393	0.844452
$610$	0.953010	0.0385862
$611$	−5.01665	−0.202952
$612$	1.99165	0.0805076
$613$	20.3033	0.820043	0.410022	−	0.912076i	$-0.365521\pi$
$613$	20.3033	0.820043	0.410022	+	0.912076i	$0.365521\pi$
$614$	−0.553569	−0.0223402
$615$	19.4408	0.783928
$616$	2.94609	0.118701
$617$	26.2940	1.05856	0.529279	−	0.848448i	$-0.322463\pi$
$617$	26.2940	1.05856	0.529279	+	0.848448i	$0.322463\pi$
$618$	−0.677198	−0.0272409
$619$	−2.08470	−0.0837911	−0.0418956	−	0.999122i	$-0.513340\pi$
$619$	−2.08470	−0.0837911	−0.0418956	+	0.999122i	$0.513340\pi$
$620$	−19.3568	−0.777389
$621$	−1.46501	−0.0587890
$622$	−1.18788	−0.0476295
$623$	−29.1352	−1.16728
$624$	−13.6879	−0.547954
$625$	−18.0810	−0.723240
$626$	−0.800813	−0.0320069
$627$	−7.68573	−0.306938
$628$	42.0054	1.67620
$629$	−10.5341	−0.420021
$630$	−0.598893	−0.0238605
$631$	−9.49231	−0.377883	−0.188941	−	0.981988i	$-0.560506\pi$
$631$	−9.49231	−0.377883	−0.188941	+	0.981988i	$0.560506\pi$
$632$	−0.364805	−0.0145112
$633$	−9.80270	−0.389622
$634$	0.233101	0.00925763
$635$	40.8284	1.62023
$636$	−9.31117	−0.369212
$637$	14.1835	0.561972
$638$	1.38653	0.0548932
$639$	7.70390	0.304762
$640$	−5.69415	−0.225081
$641$	28.2985	1.11772	0.558861	−	0.829261i	$-0.311239\pi$
$641$	28.2985	1.11772	0.558861	+	0.829261i	$0.311239\pi$
$642$	−0.424961	−0.0167719
$643$	9.60129	0.378638	0.189319	−	0.981916i	$-0.439372\pi$
$643$	9.60129	0.378638	0.189319	+	0.981916i	$0.439372\pi$
$644$	9.71804	0.382944
$645$	10.6610	0.419777
$646$	−0.289690	−0.0113977
$647$	36.6741	1.44181	0.720904	−	0.693035i	$-0.243727\pi$
$647$	36.6741	1.44181	0.720904	+	0.693035i	$0.243727\pi$
$648$	0.364805	0.0143309
$649$	18.5574	0.728443
$650$	0.357530	0.0140235
$651$	−16.4524	−0.644820
$652$	−38.6032	−1.51182
$653$	−13.8159	−0.540659	−0.270329	−	0.962768i	$-0.587133\pi$
$653$	−13.8159	−0.540659	−0.270329	+	0.962768i	$0.587133\pi$
$654$	0.251668	0.00984098
$655$	35.5061	1.38734
$656$	39.0292	1.52383
$657$	−3.41020	−0.133045
$658$	−0.440658	−0.0171786
$659$	33.4925	1.30468	0.652341	−	0.757925i	$-0.273787\pi$
$659$	33.4925	1.30468	0.652341	+	0.757925i	$0.273787\pi$
$660$	9.50145	0.369843
$661$	−41.9520	−1.63175	−0.815873	−	0.578232i	$-0.803743\pi$
$661$	−41.9520	−1.63175	−0.815873	+	0.578232i	$0.803743\pi$
$662$	1.08184	0.0420468
$663$	3.46533	0.134582
$664$	−0.306500	−0.0118945
$665$	−20.7714	−0.805479
$666$	−0.962730	−0.0373050
$667$	9.16645	0.354927
$668$	47.9758	1.85624
$669$	2.53986	0.0981967
$670$	1.40945	0.0544517
$671$	−12.8509	−0.496103
$672$	−3.63238	−0.140122
$673$	32.5144	1.25334	0.626669	−	0.779286i	$-0.284418\pi$
$673$	32.5144	1.25334	0.626669	+	0.779286i	$0.284418\pi$
$674$	−2.07265	−0.0798355
$675$	1.12891	0.0434518
$676$	1.97471	0.0759506
$677$	−19.8493	−0.762869	−0.381435	−	0.924396i	$-0.624570\pi$
$677$	−19.8493	−0.762869	−0.381435	+	0.924396i	$0.624570\pi$
$678$	1.67331	0.0642631
$679$	10.7476	0.412456
$680$	0.717757	0.0275247
$681$	0.0351116	0.00134548
$682$	−1.09465	−0.0419162
$683$	6.09368	0.233168	0.116584	−	0.993181i	$-0.462806\pi$
$683$	6.09368	0.233168	0.116584	+	0.993181i	$0.462806\pi$
$684$	6.31301	0.241384
$685$	27.8530	1.06421
$686$	−0.884873	−0.0337846
$687$	−22.1605	−0.845477
$688$	21.4030	0.815981
$689$	−16.2008	−0.617201
$690$	−0.263431	−0.0100287
$691$	−39.1626	−1.48982	−0.744908	−	0.667167i	$-0.767507\pi$
$691$	−39.1626	−1.48982	−0.744908	+	0.667167i	$0.767507\pi$
$692$	12.6621	0.481340
$693$	8.07579	0.306774
$694$	−1.69987	−0.0645261
$695$	−10.8469	−0.411448
$696$	−2.28255	−0.0865198
$697$	−9.88092	−0.374266
$698$	2.64783	0.100222
$699$	−8.61006	−0.325662
$700$	−7.48852	−0.283040
$701$	−27.7437	−1.04786	−0.523932	−	0.851760i	$-0.675535\pi$
$701$	−27.7437	−1.04786	−0.523932	+	0.851760i	$0.675535\pi$
$702$	0.316704	0.0119532
$703$	−33.3903	−1.25934
$704$	18.9134	0.712824
$705$	−2.84830	−0.107273
$706$	0.823771	0.0310030
$707$	−27.0553	−1.01752
$708$	−15.2430	−0.572866
$709$	−28.1998	−1.05906	−0.529532	−	0.848290i	$-0.677632\pi$
$709$	−28.1998	−1.05906	−0.529532	+	0.848290i	$0.677632\pi$
$710$	1.38528	0.0519885
$711$	−1.00000	−0.0375029
$712$	3.19120	0.119595
$713$	−7.23681	−0.271021
$714$	0.304392	0.0113916
$715$	16.5319	0.618257
$716$	−13.4527	−0.502751
$717$	22.6256	0.844969
$718$	−0.420522	−0.0156938
$719$	5.12310	0.191060	0.0955298	−	0.995427i	$-0.469545\pi$
$719$	5.12310	0.191060	0.0955298	+	0.995427i	$0.469545\pi$
$720$	−7.77157	−0.289629
$721$	24.6792	0.919102
$722$	0.818208	0.0304505
$723$	19.0066	0.706864
$724$	43.2273	1.60653
$725$	−7.06348	−0.262331
$726$	−0.467997	−0.0173690
$727$	−32.9440	−1.22183	−0.610913	−	0.791698i	$-0.709197\pi$
$727$	−32.9440	−1.22183	−0.610913	+	0.791698i	$0.709197\pi$
$728$	−4.21046	−0.156050
$729$	1.00000	0.0370370
$730$	−0.613204	−0.0226957
$731$	−5.41854	−0.200412
$732$	10.5556	0.390148
$733$	−30.6086	−1.13056	−0.565278	−	0.824900i	$-0.691231\pi$
$733$	−30.6086	−1.13056	−0.565278	+	0.824900i	$0.691231\pi$
$734$	−0.761829	−0.0281196
$735$	8.05297	0.297038
$736$	−1.59775	−0.0588939
$737$	−19.0057	−0.700085
$738$	−0.903038	−0.0332413
$739$	29.6100	1.08922	0.544611	−	0.838689i	$-0.316677\pi$
$739$	29.6100	1.08922	0.544611	+	0.838689i	$0.316677\pi$
$740$	41.2786	1.51743
$741$	10.9842	0.403515
$742$	−1.42306	−0.0522423
$743$	−25.2942	−0.927956	−0.463978	−	0.885847i	$-0.653578\pi$
$743$	−25.2942	−0.927956	−0.463978	+	0.885847i	$0.653578\pi$
$744$	1.80205	0.0660662
$745$	32.9540	1.20734
$746$	0.0697218	0.00255270
$747$	−0.840176	−0.0307404
$748$	−4.82918	−0.176572
$749$	15.4869	0.565879
$750$	1.10207	0.0402418
$751$	−50.6254	−1.84735	−0.923673	−	0.383182i	$-0.874828\pi$
$751$	−50.6254	−1.84735	−0.923673	+	0.383182i	$0.874828\pi$
$752$	−5.71823	−0.208522
$753$	−21.6490	−0.788934
$754$	−1.98158	−0.0721650
$755$	−5.49321	−0.199918
$756$	−6.63341	−0.241255
$757$	27.4947	0.999312	0.499656	−	0.866224i	$-0.333460\pi$
$757$	27.4947	0.999312	0.499656	+	0.866224i	$0.333460\pi$
$758$	1.29087	0.0468863
$759$	3.55224	0.128938
$760$	2.27511	0.0825268
$761$	27.8385	1.00914	0.504572	−	0.863369i	$-0.331650\pi$
$761$	27.8385	1.00914	0.504572	+	0.863369i	$0.331650\pi$
$762$	−1.89651	−0.0687032
$763$	−9.17155	−0.332033
$764$	−2.88042	−0.104210
$765$	1.96751	0.0711354
$766$	−0.437658	−0.0158132
$767$	−26.5217	−0.957643
$768$	−15.3360	−0.553389
$769$	1.23772	0.0446332	0.0223166	−	0.999751i	$-0.492896\pi$
$769$	1.23772	0.0446332	0.0223166	+	0.999751i	$0.492896\pi$
$770$	1.45215	0.0523317
$771$	−0.532783	−0.0191877
$772$	−15.0623	−0.542103
$773$	38.5195	1.38545	0.692725	−	0.721202i	$-0.256410\pi$
$773$	38.5195	1.38545	0.692725	+	0.721202i	$0.256410\pi$
$774$	−0.495211	−0.0178000
$775$	5.57653	0.200315
$776$	−1.17720	−0.0422589
$777$	35.0849	1.25866
$778$	−0.321725	−0.0115344
$779$	−31.3200	−1.12216
$780$	−13.5792	−0.486213
$781$	−18.6798	−0.668415
$782$	0.133891	0.00478792
$783$	−6.25690	−0.223603
$784$	16.1671	0.577396
$785$	41.4963	1.48107
$786$	−1.64928	−0.0588280
$787$	12.2643	0.437173	0.218587	−	0.975818i	$-0.429855\pi$
$787$	12.2643	0.437173	0.218587	+	0.975818i	$0.429855\pi$
$788$	−16.3071	−0.580918
$789$	14.5211	0.516963
$790$	−0.179815	−0.00639752
$791$	−60.9806	−2.16822
$792$	−0.884548	−0.0314311
$793$	18.3661	0.652199
$794$	−1.67952	−0.0596041
$795$	−9.19831	−0.326231
$796$	−15.5279	−0.550373
$797$	−38.8611	−1.37653	−0.688266	−	0.725458i	$-0.741628\pi$
$797$	−38.8611	−1.37653	−0.688266	+	0.725458i	$0.741628\pi$
$798$	0.964844	0.0341551
$799$	1.44767	0.0512148
$800$	1.23120	0.0435293
$801$	8.74770	0.309085
$802$	−2.25488	−0.0796226
$803$	8.26876	0.291798
$804$	15.6112	0.550564
$805$	9.60025	0.338365
$806$	1.56444	0.0551049
$807$	2.56993	0.0904660
$808$	2.96339	0.104252
$809$	45.4229	1.59698	0.798491	−	0.602006i	$-0.205632\pi$
$809$	45.4229	1.59698	0.798491	+	0.602006i	$0.205632\pi$
$810$	0.179815	0.00631805
$811$	−17.0315	−0.598056	−0.299028	−	0.954244i	$-0.596662\pi$
$811$	−17.0315	−0.598056	−0.299028	+	0.954244i	$0.596662\pi$
$812$	41.5046	1.45652
$813$	−2.92504	−0.102586
$814$	2.33435	0.0818188
$815$	−38.1353	−1.33582
$816$	3.94995	0.138276
$817$	−17.1754	−0.600890
$818$	3.08847	0.107986
$819$	−11.5417	−0.403298
$820$	38.7192	1.35213
$821$	−19.3554	−0.675507	−0.337753	−	0.941235i	$-0.609667\pi$
$821$	−19.3554	−0.675507	−0.337753	+	0.941235i	$0.609667\pi$
$822$	−1.29379	−0.0451262
$823$	5.67590	0.197849	0.0989247	−	0.995095i	$-0.468460\pi$
$823$	5.67590	0.197849	0.0989247	+	0.995095i	$0.468460\pi$
$824$	−2.70314	−0.0941682
$825$	−2.73729	−0.0953001
$826$	−2.32965	−0.0810587
$827$	−15.5621	−0.541146	−0.270573	−	0.962700i	$-0.587213\pi$
$827$	−15.5621	−0.541146	−0.270573	+	0.962700i	$0.587213\pi$
$828$	−2.91779	−0.101400
$829$	3.37063	0.117067	0.0585335	−	0.998285i	$-0.481358\pi$
$829$	3.37063	0.117067	0.0585335	+	0.998285i	$0.481358\pi$
$830$	−0.151076	−0.00524392
$831$	16.2652	0.564234
$832$	−27.0304	−0.937110
$833$	−4.09298	−0.141813
$834$	0.503848	0.0174468
$835$	47.3944	1.64015
$836$	−15.3073	−0.529413
$837$	4.93975	0.170743
$838$	1.97375	0.0681822
$839$	−39.4235	−1.36105	−0.680526	−	0.732724i	$-0.738249\pi$
$839$	−39.4235	−1.36105	−0.680526	+	0.732724i	$0.738249\pi$
$840$	−2.39057	−0.0824825
$841$	10.1488	0.349959
$842$	2.08483	0.0718479
$843$	−30.0346	−1.03445
$844$	−19.5235	−0.672027
$845$	1.95078	0.0671089
$846$	0.132305	0.00454876
$847$	17.0553	0.586025
$848$	−18.4665	−0.634141
$849$	18.1264	0.622098
$850$	−0.103173	−0.00353882
$851$	15.4326	0.529021
$852$	15.3435	0.525658
$853$	24.7067	0.845941	0.422971	−	0.906143i	$-0.360987\pi$
$853$	24.7067	0.845941	0.422971	+	0.906143i	$0.360987\pi$
$854$	1.61326	0.0552047
$855$	6.23650	0.213284
$856$	−1.69630	−0.0579782
$857$	17.9610	0.613537	0.306768	−	0.951784i	$-0.400752\pi$
$857$	17.9610	0.613537	0.306768	+	0.951784i	$0.400752\pi$
$858$	−0.767916	−0.0262162
$859$	41.4843	1.41543	0.707714	−	0.706499i	$-0.249727\pi$
$859$	41.4843	1.41543	0.707714	+	0.706499i	$0.249727\pi$
$860$	21.2330	0.724039
$861$	32.9095	1.12155
$862$	−2.78232	−0.0947662
$863$	−3.16150	−0.107619	−0.0538094	−	0.998551i	$-0.517136\pi$
$863$	−3.16150	−0.107619	−0.0538094	+	0.998551i	$0.517136\pi$
$864$	1.09060	0.0371031
$865$	12.5086	0.425306
$866$	2.58220	0.0877469
$867$	−1.00000	−0.0339618
$868$	−32.7674	−1.11220
$869$	2.42472	0.0822528
$870$	−1.12508	−0.0381439
$871$	27.1624	0.920363
$872$	1.00457	0.0340190
$873$	−3.22692	−0.109215
$874$	0.424400	0.0143555
$875$	−40.1628	−1.35775
$876$	−6.79192	−0.229478
$877$	−33.7102	−1.13831	−0.569156	−	0.822229i	$-0.692730\pi$
$877$	−33.7102	−1.13831	−0.569156	+	0.822229i	$0.692730\pi$
$878$	−1.59520	−0.0538354
$879$	−29.5743	−0.997517
$880$	18.8438	0.635226
$881$	5.86351	0.197547	0.0987733	−	0.995110i	$-0.468508\pi$
$881$	5.86351	0.197547	0.0987733	+	0.995110i	$0.468508\pi$
$882$	−0.374066	−0.0125955
$883$	49.7795	1.67522	0.837608	−	0.546272i	$-0.183954\pi$
$883$	49.7795	1.67522	0.837608	+	0.546272i	$0.183954\pi$
$884$	6.90171	0.232130
$885$	−15.0582	−0.506177
$886$	−0.234594	−0.00788135
$887$	22.9942	0.772069	0.386034	−	0.922484i	$-0.373845\pi$
$887$	22.9942	0.772069	0.386034	+	0.922484i	$0.373845\pi$
$888$	−3.84288	−0.128959
$889$	69.1146	2.31803
$890$	1.57296	0.0527259
$891$	−2.42472	−0.0812310
$892$	5.05851	0.169371
$893$	4.58874	0.153556
$894$	−1.53074	−0.0511955
$895$	−13.2897	−0.444224
$896$	−9.63909	−0.322019
$897$	−5.07676	−0.169508
$898$	−0.768435	−0.0256430
$899$	−30.9075	−1.03082
$900$	2.24839	0.0749464
$901$	4.67511	0.155750
$902$	2.18961	0.0729060
$903$	18.0470	0.600568
$904$	6.67926	0.222149
$905$	42.7034	1.41951
$906$	0.255163	0.00847723
$907$	−41.7148	−1.38512	−0.692558	−	0.721362i	$-0.743516\pi$
$907$	−41.7148	−1.38512	−0.692558	+	0.721362i	$0.743516\pi$
$908$	0.0699300	0.00232071
$909$	8.12321	0.269430
$910$	−2.07536	−0.0687976
$911$	−34.9278	−1.15721	−0.578604	−	0.815608i	$-0.696402\pi$
$911$	−34.9278	−1.15721	−0.578604	+	0.815608i	$0.696402\pi$
$912$	12.5203	0.414590
$913$	2.03719	0.0674210
$914$	1.69070	0.0559234
$915$	10.4277	0.344729
$916$	−44.1359	−1.45829
$917$	60.1050	1.98484
$918$	−0.0913921	−0.00301639
$919$	1.46186	0.0482224	0.0241112	−	0.999709i	$-0.492324\pi$
$919$	1.46186	0.0482224	0.0241112	+	0.999709i	$0.492324\pi$
$920$	−1.05152	−0.0346677
$921$	−6.05707	−0.199587
$922$	−1.09115	−0.0359350
$923$	26.6966	0.878728
$924$	16.0841	0.529129
$925$	−11.8920	−0.391007
$926$	2.83890	0.0932920
$927$	−7.40981	−0.243370
$928$	−6.82381	−0.224002
$929$	−17.6663	−0.579614	−0.289807	−	0.957085i	$-0.593591\pi$
$929$	−17.6663	−0.579614	−0.289807	+	0.957085i	$0.593591\pi$
$930$	0.888240	0.0291265
$931$	−12.9737	−0.425196
$932$	−17.1482	−0.561708
$933$	−12.9976	−0.425521
$934$	1.44174	0.0471752
$935$	−4.77065	−0.156017
$936$	1.26417	0.0413207
$937$	−1.51705	−0.0495600	−0.0247800	−	0.999693i	$-0.507889\pi$
$937$	−1.51705	−0.0495600	−0.0247800	+	0.999693i	$0.507889\pi$
$938$	2.38592	0.0779032
$939$	−8.76239	−0.285950
$940$	−5.67281	−0.185027
$941$	−9.96909	−0.324983	−0.162492	−	0.986710i	$-0.551953\pi$
$941$	−9.96909	−0.324983	−0.162492	+	0.986710i	$0.551953\pi$
$942$	−1.92753	−0.0628023
$943$	14.4757	0.471393
$944$	−30.2308	−0.983928
$945$	−6.55301	−0.213169
$946$	1.20075	0.0390396
$947$	−43.5543	−1.41533	−0.707663	−	0.706550i	$-0.750250\pi$
$947$	−43.5543	−1.41533	−0.707663	+	0.706550i	$0.750250\pi$
$948$	−1.99165	−0.0646857
$949$	−11.8175	−0.383611
$950$	−0.327034	−0.0106104
$951$	2.55056	0.0827076
$952$	1.21502	0.0393792
$953$	−18.8611	−0.610970	−0.305485	−	0.952197i	$-0.598819\pi$
$953$	−18.8611	−0.610970	−0.305485	+	0.952197i	$0.598819\pi$
$954$	0.427268	0.0138333
$955$	−2.84551	−0.0920787
$956$	45.0622	1.45742
$957$	15.1712	0.490415
$958$	−0.315486	−0.0101929
$959$	47.1498	1.52255
$960$	−15.3470	−0.495323
$961$	−6.59888	−0.212867
$962$	−3.33618	−0.107563
$963$	−4.64987	−0.149840
$964$	37.8545	1.21921
$965$	−14.8797	−0.478995
$966$	−0.445938	−0.0143478
$967$	−37.4232	−1.20345	−0.601724	−	0.798704i	$-0.705519\pi$
$967$	−37.4232	−1.20345	−0.601724	+	0.798704i	$0.705519\pi$
$968$	−1.86808	−0.0600423
$969$	−3.16974	−0.101827
$970$	−0.580248	−0.0186306
$971$	4.77848	0.153349	0.0766744	−	0.997056i	$-0.475570\pi$
$971$	4.77848	0.153349	0.0766744	+	0.997056i	$0.475570\pi$
$972$	1.99165	0.0638821
$973$	−18.3618	−0.588651
$974$	−2.29776	−0.0736248
$975$	3.91205	0.125286
$976$	20.9346	0.670100
$977$	−48.2279	−1.54295	−0.771473	−	0.636262i	$-0.780480\pi$
$977$	−48.2279	−1.54295	−0.771473	+	0.636262i	$0.780480\pi$
$978$	1.77141	0.0566434
$979$	−21.2107	−0.677896
$980$	16.0387	0.512337
$981$	2.75371	0.0879193
$982$	−2.08865	−0.0666516
$983$	45.0669	1.43741	0.718706	−	0.695315i	$-0.244735\pi$
$983$	45.0669	1.43741	0.718706	+	0.695315i	$0.244735\pi$
$984$	−3.60461	−0.114911
$985$	−16.1095	−0.513291
$986$	0.571831	0.0182108
$987$	−4.82162	−0.153474
$988$	21.8767	0.695990
$989$	7.93824	0.252421
$990$	−0.436000	−0.0138570
$991$	−44.1527	−1.40256	−0.701278	−	0.712888i	$-0.747387\pi$
$991$	−44.1527	−1.40256	−0.701278	+	0.712888i	$0.747387\pi$
$992$	5.38731	0.171047
$993$	11.8373	0.375646
$994$	2.34500	0.0743790
$995$	−15.3397	−0.486303
$996$	−1.67333	−0.0530216
$997$	47.1514	1.49330	0.746650	−	0.665218i	$-0.231661\pi$
$997$	47.1514	1.49330	0.746650	+	0.665218i	$0.231661\pi$
$998$	1.24444	0.0393921
$999$	−10.5341	−0.333283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.11	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.11	✓	22	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)

\(f(q)\)	\(=\)	\(q-0.0913921 q^{2} -1.00000 q^{3} -1.99165 q^{4} -1.96751 q^{5} +0.0913921 q^{6} -3.33061 q^{7} +0.364805 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0913921 q^{2} -1.00000 q^{3} -1.99165 q^{4} -1.96751 q^{5} +0.0913921 q^{6} -3.33061 q^{7} +0.364805 q^{8} +1.00000 q^{9} +0.179815 q^{10} -2.42472 q^{11} +1.99165 q^{12} +3.46533 q^{13} +0.304392 q^{14} +1.96751 q^{15} +3.94995 q^{16} -1.00000 q^{17} -0.0913921 q^{18} -3.16974 q^{19} +3.91858 q^{20} +3.33061 q^{21} +0.221600 q^{22} +1.46501 q^{23} -0.364805 q^{24} -1.12891 q^{25} -0.316704 q^{26} -1.00000 q^{27} +6.63341 q^{28} +6.25690 q^{29} -0.179815 q^{30} -4.93975 q^{31} -1.09060 q^{32} +2.42472 q^{33} +0.0913921 q^{34} +6.55301 q^{35} -1.99165 q^{36} +10.5341 q^{37} +0.289690 q^{38} -3.46533 q^{39} -0.717757 q^{40} +9.88092 q^{41} -0.304392 q^{42} +5.41854 q^{43} +4.82918 q^{44} -1.96751 q^{45} -0.133891 q^{46} -1.44767 q^{47} -3.94995 q^{48} +4.09298 q^{49} +0.103173 q^{50} +1.00000 q^{51} -6.90171 q^{52} -4.67511 q^{53} +0.0913921 q^{54} +4.77065 q^{55} -1.21502 q^{56} +3.16974 q^{57} -0.571831 q^{58} -7.65345 q^{59} -3.91858 q^{60} +5.29995 q^{61} +0.451454 q^{62} -3.33061 q^{63} -7.80024 q^{64} -6.81806 q^{65} -0.221600 q^{66} +7.83833 q^{67} +1.99165 q^{68} -1.46501 q^{69} -0.598893 q^{70} +7.70390 q^{71} +0.364805 q^{72} -3.41020 q^{73} -0.962730 q^{74} +1.12891 q^{75} +6.31301 q^{76} +8.07579 q^{77} +0.316704 q^{78} -1.00000 q^{79} -7.77157 q^{80} +1.00000 q^{81} -0.903038 q^{82} -0.840176 q^{83} -6.63341 q^{84} +1.96751 q^{85} -0.495211 q^{86} -6.25690 q^{87} -0.884548 q^{88} +8.74770 q^{89} +0.179815 q^{90} -11.5417 q^{91} -2.91779 q^{92} +4.93975 q^{93} +0.132305 q^{94} +6.23650 q^{95} +1.09060 q^{96} -3.22692 q^{97} -0.374066 q^{98} -2.42472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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