LMFDB - Embedded newform 4029.2.a.k.1.31

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:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
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)

$f(q)$	$=$	$q+2.79075 q^{2} +1.00000 q^{3} +5.78827 q^{4} +1.94242 q^{5} +2.79075 q^{6} -1.90835 q^{7} +10.5721 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.79075 q^{2} +1.00000 q^{3} +5.78827 q^{4} +1.94242 q^{5} +2.79075 q^{6} -1.90835 q^{7} +10.5721 q^{8} +1.00000 q^{9} +5.42080 q^{10} +0.728977 q^{11} +5.78827 q^{12} -5.07463 q^{13} -5.32573 q^{14} +1.94242 q^{15} +17.9275 q^{16} +1.00000 q^{17} +2.79075 q^{18} +2.91151 q^{19} +11.2432 q^{20} -1.90835 q^{21} +2.03439 q^{22} -1.70578 q^{23} +10.5721 q^{24} -1.22701 q^{25} -14.1620 q^{26} +1.00000 q^{27} -11.0461 q^{28} +1.56991 q^{29} +5.42080 q^{30} +3.84094 q^{31} +28.8870 q^{32} +0.728977 q^{33} +2.79075 q^{34} -3.70682 q^{35} +5.78827 q^{36} +5.97065 q^{37} +8.12530 q^{38} -5.07463 q^{39} +20.5355 q^{40} -6.77167 q^{41} -5.32573 q^{42} -8.00902 q^{43} +4.21952 q^{44} +1.94242 q^{45} -4.76040 q^{46} -3.49039 q^{47} +17.9275 q^{48} -3.35818 q^{49} -3.42427 q^{50} +1.00000 q^{51} -29.3733 q^{52} -0.650338 q^{53} +2.79075 q^{54} +1.41598 q^{55} -20.1753 q^{56} +2.91151 q^{57} +4.38121 q^{58} +4.88899 q^{59} +11.2432 q^{60} -4.59372 q^{61} +10.7191 q^{62} -1.90835 q^{63} +44.7613 q^{64} -9.85706 q^{65} +2.03439 q^{66} -7.38015 q^{67} +5.78827 q^{68} -1.70578 q^{69} -10.3448 q^{70} -2.04673 q^{71} +10.5721 q^{72} +6.82975 q^{73} +16.6626 q^{74} -1.22701 q^{75} +16.8526 q^{76} -1.39115 q^{77} -14.1620 q^{78} +1.00000 q^{79} +34.8228 q^{80} +1.00000 q^{81} -18.8980 q^{82} +0.725114 q^{83} -11.0461 q^{84} +1.94242 q^{85} -22.3511 q^{86} +1.56991 q^{87} +7.70682 q^{88} +14.2468 q^{89} +5.42080 q^{90} +9.68419 q^{91} -9.87352 q^{92} +3.84094 q^{93} -9.74080 q^{94} +5.65538 q^{95} +28.8870 q^{96} +1.34728 q^{97} -9.37184 q^{98} +0.728977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	2.79075	1.97336	0.986678	−	0.162684i	$-0.0520152\pi$
$2$	2.79075	1.97336	0.986678	+	0.162684i	$0.0520152\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.78827	2.89414
$5$	1.94242	0.868676	0.434338	−	0.900750i	$-0.356982\pi$
$5$	1.94242	0.868676	0.434338	+	0.900750i	$0.356982\pi$
$6$	2.79075	1.13932
$7$	−1.90835	−0.721290	−0.360645	−	0.932703i	$-0.617443\pi$
$7$	−1.90835	−0.721290	−0.360645	+	0.932703i	$0.617443\pi$
$8$	10.5721	3.73780
$9$	1.00000	0.333333
$10$	5.42080	1.71421
$11$	0.728977	0.219795	0.109897	−	0.993943i	$-0.464948\pi$
$11$	0.728977	0.219795	0.109897	+	0.993943i	$0.464948\pi$
$12$	5.78827	1.67093
$13$	−5.07463	−1.40745	−0.703725	−	0.710473i	$-0.748481\pi$
$13$	−5.07463	−1.40745	−0.703725	+	0.710473i	$0.748481\pi$
$14$	−5.32573	−1.42336
$15$	1.94242	0.501530
$16$	17.9275	4.48188
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.79075	0.657785
$19$	2.91151	0.667947	0.333974	−	0.942582i	$-0.391610\pi$
$19$	2.91151	0.667947	0.333974	+	0.942582i	$0.391610\pi$
$20$	11.2432	2.51407
$21$	−1.90835	−0.416437
$22$	2.03439	0.433734
$23$	−1.70578	−0.355680	−0.177840	−	0.984059i	$-0.556911\pi$
$23$	−1.70578	−0.355680	−0.177840	+	0.984059i	$0.556911\pi$
$24$	10.5721	2.15802
$25$	−1.22701	−0.245402
$26$	−14.1620	−2.77740
$27$	1.00000	0.192450
$28$	−11.0461	−2.08751
$29$	1.56991	0.291524	0.145762	−	0.989320i	$-0.453437\pi$
$29$	1.56991	0.291524	0.145762	+	0.989320i	$0.453437\pi$
$30$	5.42080	0.989698
$31$	3.84094	0.689853	0.344926	−	0.938630i	$-0.387904\pi$
$31$	3.84094	0.689853	0.344926	+	0.938630i	$0.387904\pi$
$32$	28.8870	5.10655
$33$	0.728977	0.126899
$34$	2.79075	0.478609
$35$	−3.70682	−0.626568
$36$	5.78827	0.964712
$37$	5.97065	0.981568	0.490784	−	0.871281i	$-0.336710\pi$
$37$	5.97065	0.981568	0.490784	+	0.871281i	$0.336710\pi$
$38$	8.12530	1.31810
$39$	−5.07463	−0.812591
$40$	20.5355	3.24694
$41$	−6.77167	−1.05756	−0.528778	−	0.848760i	$-0.677350\pi$
$41$	−6.77167	−1.05756	−0.528778	+	0.848760i	$0.677350\pi$
$42$	−5.32573	−0.821779
$43$	−8.00902	−1.22136	−0.610682	−	0.791876i	$-0.709105\pi$
$43$	−8.00902	−1.22136	−0.610682	+	0.791876i	$0.709105\pi$
$44$	4.21952	0.636116
$45$	1.94242	0.289559
$46$	−4.76040	−0.701883
$47$	−3.49039	−0.509126	−0.254563	−	0.967056i	$-0.581932\pi$
$47$	−3.49039	−0.509126	−0.254563	+	0.967056i	$0.581932\pi$
$48$	17.9275	2.58762
$49$	−3.35818	−0.479741
$50$	−3.42427	−0.484265
$51$	1.00000	0.140028
$52$	−29.3733	−4.07335
$53$	−0.650338	−0.0893308	−0.0446654	−	0.999002i	$-0.514222\pi$
$53$	−0.650338	−0.0893308	−0.0446654	+	0.999002i	$0.514222\pi$
$54$	2.79075	0.379773
$55$	1.41598	0.190931
$56$	−20.1753	−2.69604
$57$	2.91151	0.385639
$58$	4.38121	0.575281
$59$	4.88899	0.636492	0.318246	−	0.948008i	$-0.396906\pi$
$59$	4.88899	0.636492	0.318246	+	0.948008i	$0.396906\pi$
$60$	11.2432	1.45150
$61$	−4.59372	−0.588165	−0.294083	−	0.955780i	$-0.595014\pi$
$61$	−4.59372	−0.588165	−0.294083	+	0.955780i	$0.595014\pi$
$62$	10.7191	1.36133
$63$	−1.90835	−0.240430
$64$	44.7613	5.59516
$65$	−9.85706	−1.22262
$66$	2.03439	0.250416
$67$	−7.38015	−0.901628	−0.450814	−	0.892618i	$-0.648866\pi$
$67$	−7.38015	−0.901628	−0.450814	+	0.892618i	$0.648866\pi$
$68$	5.78827	0.701931
$69$	−1.70578	−0.205352
$70$	−10.3448	−1.23644
$71$	−2.04673	−0.242902	−0.121451	−	0.992597i	$-0.538755\pi$
$71$	−2.04673	−0.242902	−0.121451	+	0.992597i	$0.538755\pi$
$72$	10.5721	1.24593
$73$	6.82975	0.799361	0.399681	−	0.916654i	$-0.369121\pi$
$73$	6.82975	0.799361	0.399681	+	0.916654i	$0.369121\pi$
$74$	16.6626	1.93698
$75$	−1.22701	−0.141683
$76$	16.8526	1.93313
$77$	−1.39115	−0.158536
$78$	−14.1620	−1.60353
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	34.8228	3.89331
$81$	1.00000	0.111111
$82$	−18.8980	−2.08694
$83$	0.725114	0.0795916	0.0397958	−	0.999208i	$-0.487329\pi$
$83$	0.725114	0.0795916	0.0397958	+	0.999208i	$0.487329\pi$
$84$	−11.0461	−1.20523
$85$	1.94242	0.210685
$86$	−22.3511	−2.41019
$87$	1.56991	0.168312
$88$	7.70682	0.821550
$89$	14.2468	1.51016	0.755081	−	0.655631i	$-0.227597\pi$
$89$	14.2468	1.51016	0.755081	+	0.655631i	$0.227597\pi$
$90$	5.42080	0.571403
$91$	9.68419	1.01518
$92$	−9.87352	−1.02939
$93$	3.84094	0.398287
$94$	−9.74080	−1.00469
$95$	5.65538	0.580230
$96$	28.8870	2.94827
$97$	1.34728	0.136796	0.0683980	−	0.997658i	$-0.478211\pi$
$97$	1.34728	0.136796	0.0683980	+	0.997658i	$0.478211\pi$
$98$	−9.37184	−0.946699
$99$	0.728977	0.0732649
$100$	−7.10225	−0.710225
$101$	3.14860	0.313297	0.156649	−	0.987654i	$-0.449931\pi$
$101$	3.14860	0.313297	0.156649	+	0.987654i	$0.449931\pi$
$102$	2.79075	0.276325
$103$	0.254452	0.0250719	0.0125359	−	0.999921i	$-0.496010\pi$
$103$	0.254452	0.0250719	0.0125359	+	0.999921i	$0.496010\pi$
$104$	−53.6495	−5.26077
$105$	−3.70682	−0.361749
$106$	−1.81493	−0.176282
$107$	−9.82984	−0.950286	−0.475143	−	0.879909i	$-0.657604\pi$
$107$	−9.82984	−0.950286	−0.475143	+	0.879909i	$0.657604\pi$
$108$	5.78827	0.556977
$109$	5.67320	0.543394	0.271697	−	0.962383i	$-0.412415\pi$
$109$	5.67320	0.543394	0.271697	+	0.962383i	$0.412415\pi$
$110$	3.95164	0.376774
$111$	5.97065	0.566709
$112$	−34.2121	−3.23274
$113$	−15.4508	−1.45349	−0.726743	−	0.686909i	$-0.758967\pi$
$113$	−15.4508	−1.45349	−0.726743	+	0.686909i	$0.758967\pi$
$114$	8.12530	0.761004
$115$	−3.31334	−0.308971
$116$	9.08704	0.843710
$117$	−5.07463	−0.469150
$118$	13.6439	1.25602
$119$	−1.90835	−0.174939
$120$	20.5355	1.87462
$121$	−10.4686	−0.951690
$122$	−12.8199	−1.16066
$123$	−6.77167	−0.610581
$124$	22.2324	1.99653
$125$	−12.0955	−1.08185
$126$	−5.32573	−0.474454
$127$	−12.3414	−1.09512	−0.547559	−	0.836767i	$-0.684443\pi$
$127$	−12.3414	−1.09512	−0.547559	+	0.836767i	$0.684443\pi$
$128$	67.1434	5.93469
$129$	−8.00902	−0.705154
$130$	−27.5086	−2.41266
$131$	−0.723440	−0.0632073	−0.0316036	−	0.999500i	$-0.510061\pi$
$131$	−0.723440	−0.0632073	−0.0316036	+	0.999500i	$0.510061\pi$
$132$	4.21952	0.367262
$133$	−5.55620	−0.481784
$134$	−20.5961	−1.77923
$135$	1.94242	0.167177
$136$	10.5721	0.906551
$137$	−19.2652	−1.64594	−0.822968	−	0.568088i	$-0.807683\pi$
$137$	−19.2652	−1.64594	−0.822968	+	0.568088i	$0.807683\pi$
$138$	−4.76040	−0.405232
$139$	11.7922	1.00020	0.500099	−	0.865968i	$-0.333297\pi$
$139$	11.7922	1.00020	0.500099	+	0.865968i	$0.333297\pi$
$140$	−21.4561	−1.81337
$141$	−3.49039	−0.293944
$142$	−5.71190	−0.479332
$143$	−3.69929	−0.309350
$144$	17.9275	1.49396
$145$	3.04941	0.253240
$146$	19.0601	1.57742
$147$	−3.35818	−0.276978
$148$	34.5597	2.84079
$149$	6.16909	0.505391	0.252696	−	0.967546i	$-0.418683\pi$
$149$	6.16909	0.505391	0.252696	+	0.967546i	$0.418683\pi$
$150$	−3.42427	−0.279590
$151$	−0.0262637	−0.00213731	−0.00106865	−	0.999999i	$-0.500340\pi$
$151$	−0.0262637	−0.00213731	−0.00106865	+	0.999999i	$0.500340\pi$
$152$	30.7808	2.49666
$153$	1.00000	0.0808452
$154$	−3.88234	−0.312848
$155$	7.46071	0.599259
$156$	−29.3733	−2.35175
$157$	−5.23085	−0.417468	−0.208734	−	0.977972i	$-0.566934\pi$
$157$	−5.23085	−0.417468	−0.208734	+	0.977972i	$0.566934\pi$
$158$	2.79075	0.222020
$159$	−0.650338	−0.0515752
$160$	56.1107	4.43594
$161$	3.25523	0.256548
$162$	2.79075	0.219262
$163$	5.12894	0.401729	0.200865	−	0.979619i	$-0.435625\pi$
$163$	5.12894	0.401729	0.200865	+	0.979619i	$0.435625\pi$
$164$	−39.1962	−3.06071
$165$	1.41598	0.110234
$166$	2.02361	0.157063
$167$	11.7624	0.910202	0.455101	−	0.890440i	$-0.349603\pi$
$167$	11.7624	0.910202	0.455101	+	0.890440i	$0.349603\pi$
$168$	−20.1753	−1.55656
$169$	12.7519	0.980914
$170$	5.42080	0.415756
$171$	2.91151	0.222649
$172$	−46.3583	−3.53479
$173$	−20.1161	−1.52940	−0.764698	−	0.644388i	$-0.777112\pi$
$173$	−20.1161	−1.52940	−0.764698	+	0.644388i	$0.777112\pi$
$174$	4.38121	0.332139
$175$	2.34157	0.177006
$176$	13.0688	0.985095
$177$	4.88899	0.367479
$178$	39.7593	2.98009
$179$	−25.3240	−1.89280	−0.946401	−	0.322995i	$-0.895310\pi$
$179$	−25.3240	−1.89280	−0.946401	+	0.322995i	$0.895310\pi$
$180$	11.2432	0.838022
$181$	13.6444	1.01418	0.507089	−	0.861894i	$-0.330722\pi$
$181$	13.6444	1.01418	0.507089	+	0.861894i	$0.330722\pi$
$182$	27.0261	2.00331
$183$	−4.59372	−0.339577
$184$	−18.0337	−1.32946
$185$	11.5975	0.852665
$186$	10.7191	0.785961
$187$	0.728977	0.0533081
$188$	−20.2033	−1.47348
$189$	−1.90835	−0.138812
$190$	15.7827	1.14500
$191$	−20.5686	−1.48829	−0.744147	−	0.668016i	$-0.767144\pi$
$191$	−20.5686	−1.48829	−0.744147	+	0.668016i	$0.767144\pi$
$192$	44.7613	3.23037
$193$	−1.84454	−0.132773	−0.0663864	−	0.997794i	$-0.521147\pi$
$193$	−1.84454	−0.132773	−0.0663864	+	0.997794i	$0.521147\pi$
$194$	3.75993	0.269947
$195$	−9.85706	−0.705879
$196$	−19.4381	−1.38843
$197$	−0.829338	−0.0590879	−0.0295439	−	0.999563i	$-0.509405\pi$
$197$	−0.829338	−0.0590879	−0.0295439	+	0.999563i	$0.509405\pi$
$198$	2.03439	0.144578
$199$	13.5266	0.958872	0.479436	−	0.877577i	$-0.340841\pi$
$199$	13.5266	0.958872	0.479436	+	0.877577i	$0.340841\pi$
$200$	−12.9721	−0.917263
$201$	−7.38015	−0.520555
$202$	8.78694	0.618247
$203$	−2.99594	−0.210273
$204$	5.78827	0.405260
$205$	−13.1534	−0.918674
$206$	0.710110	0.0494757
$207$	−1.70578	−0.118560
$208$	−90.9756	−6.30802
$209$	2.12243	0.146811
$210$	−10.3448	−0.713860
$211$	8.65973	0.596160	0.298080	−	0.954541i	$-0.403654\pi$
$211$	8.65973	0.596160	0.298080	+	0.954541i	$0.403654\pi$
$212$	−3.76433	−0.258536
$213$	−2.04673	−0.140239
$214$	−27.4326	−1.87525
$215$	−15.5569	−1.06097
$216$	10.5721	0.719341
$217$	−7.32987	−0.497584
$218$	15.8325	1.07231
$219$	6.82975	0.461512
$220$	8.19607	0.552579
$221$	−5.07463	−0.341357
$222$	16.6626	1.11832
$223$	−2.39813	−0.160591	−0.0802953	−	0.996771i	$-0.525586\pi$
$223$	−2.39813	−0.160591	−0.0802953	+	0.996771i	$0.525586\pi$
$224$	−55.1266	−3.68330
$225$	−1.22701	−0.0818005
$226$	−43.1192	−2.86825
$227$	2.69707	0.179010	0.0895052	−	0.995986i	$-0.471471\pi$
$227$	2.69707	0.179010	0.0895052	+	0.995986i	$0.471471\pi$
$228$	16.8526	1.11609
$229$	12.7293	0.841178	0.420589	−	0.907251i	$-0.361824\pi$
$229$	12.7293	0.841178	0.420589	+	0.907251i	$0.361824\pi$
$230$	−9.24670	−0.609709
$231$	−1.39115	−0.0915307
$232$	16.5972	1.08966
$233$	22.2306	1.45637	0.728187	−	0.685378i	$-0.240363\pi$
$233$	22.2306	1.45637	0.728187	+	0.685378i	$0.240363\pi$
$234$	−14.1620	−0.925800
$235$	−6.77980	−0.442265
$236$	28.2988	1.84209
$237$	1.00000	0.0649570
$238$	−5.32573	−0.345216
$239$	−12.7117	−0.822253	−0.411126	−	0.911578i	$-0.634864\pi$
$239$	−12.7117	−0.822253	−0.411126	+	0.911578i	$0.634864\pi$
$240$	34.8228	2.24780
$241$	14.1253	0.909892	0.454946	−	0.890519i	$-0.349659\pi$
$241$	14.1253	0.909892	0.454946	+	0.890519i	$0.349659\pi$
$242$	−29.2152	−1.87802
$243$	1.00000	0.0641500
$244$	−26.5897	−1.70223
$245$	−6.52300	−0.416739
$246$	−18.8980	−1.20489
$247$	−14.7749	−0.940102
$248$	40.6068	2.57853
$249$	0.725114	0.0459523
$250$	−33.7554	−2.13488
$251$	−25.0146	−1.57891	−0.789454	−	0.613810i	$-0.789636\pi$
$251$	−25.0146	−1.57891	−0.789454	+	0.613810i	$0.789636\pi$
$252$	−11.0461	−0.695837
$253$	−1.24347	−0.0781766
$254$	−34.4416	−2.16106
$255$	1.94242	0.121639
$256$	97.8576	6.11610
$257$	13.1770	0.821957	0.410979	−	0.911645i	$-0.365187\pi$
$257$	13.1770	0.821957	0.410979	+	0.911645i	$0.365187\pi$
$258$	−22.3511	−1.39152
$259$	−11.3941	−0.707996
$260$	−57.0553	−3.53842
$261$	1.56991	0.0971747
$262$	−2.01894	−0.124730
$263$	−0.489041	−0.0301556	−0.0150778	−	0.999886i	$-0.504800\pi$
$263$	−0.489041	−0.0301556	−0.0150778	+	0.999886i	$0.504800\pi$
$264$	7.70682	0.474322
$265$	−1.26323	−0.0775996
$266$	−15.5060	−0.950731
$267$	14.2468	0.871893
$268$	−42.7183	−2.60943
$269$	−19.3444	−1.17945	−0.589724	−	0.807605i	$-0.700764\pi$
$269$	−19.3444	−1.17945	−0.589724	+	0.807605i	$0.700764\pi$
$270$	5.42080	0.329899
$271$	21.1471	1.28459	0.642297	−	0.766456i	$-0.277981\pi$
$271$	21.1471	1.28459	0.642297	+	0.766456i	$0.277981\pi$
$272$	17.9275	1.08702
$273$	9.68419	0.586114
$274$	−53.7642	−3.24802
$275$	−0.894461	−0.0539380
$276$	−9.87352	−0.594316
$277$	1.87627	0.112734	0.0563671	−	0.998410i	$-0.482048\pi$
$277$	1.87627	0.112734	0.0563671	+	0.998410i	$0.482048\pi$
$278$	32.9089	1.97375
$279$	3.84094	0.229951
$280$	−39.1889	−2.34199
$281$	15.0541	0.898052	0.449026	−	0.893519i	$-0.351771\pi$
$281$	15.0541	0.898052	0.449026	+	0.893519i	$0.351771\pi$
$282$	−9.74080	−0.580056
$283$	13.1946	0.784339	0.392170	−	0.919893i	$-0.371725\pi$
$283$	13.1946	0.784339	0.392170	+	0.919893i	$0.371725\pi$
$284$	−11.8470	−0.702991
$285$	5.65538	0.334996
$286$	−10.3238	−0.610458
$287$	12.9227	0.762805
$288$	28.8870	1.70218
$289$	1.00000	0.0588235
$290$	8.51015	0.499733
$291$	1.34728	0.0789792
$292$	39.5324	2.31346
$293$	19.7871	1.15597	0.577986	−	0.816046i	$-0.303839\pi$
$293$	19.7871	1.15597	0.577986	+	0.816046i	$0.303839\pi$
$294$	−9.37184	−0.546577
$295$	9.49646	0.552905
$296$	63.1223	3.66891
$297$	0.728977	0.0422995
$298$	17.2164	0.997317
$299$	8.65621	0.500601
$300$	−7.10225	−0.410049
$301$	15.2840	0.880957
$302$	−0.0732953	−0.00421767
$303$	3.14860	0.180882
$304$	52.1963	2.99366
$305$	−8.92293	−0.510925
$306$	2.79075	0.159536
$307$	−19.5428	−1.11537	−0.557684	−	0.830053i	$-0.688310\pi$
$307$	−19.5428	−1.11537	−0.557684	+	0.830053i	$0.688310\pi$
$308$	−8.05233	−0.458824
$309$	0.254452	0.0144753
$310$	20.8210	1.18255
$311$	32.8697	1.86387	0.931934	−	0.362629i	$-0.118121\pi$
$311$	32.8697	1.86387	0.931934	+	0.362629i	$0.118121\pi$
$312$	−53.6495	−3.03731
$313$	−5.31108	−0.300200	−0.150100	−	0.988671i	$-0.547960\pi$
$313$	−5.31108	−0.300200	−0.150100	+	0.988671i	$0.547960\pi$
$314$	−14.5980	−0.823812
$315$	−3.70682	−0.208856
$316$	5.78827	0.325616
$317$	19.1926	1.07797	0.538983	−	0.842317i	$-0.318809\pi$
$317$	19.1926	1.07797	0.538983	+	0.842317i	$0.318809\pi$
$318$	−1.81493	−0.101776
$319$	1.14443	0.0640755
$320$	86.9451	4.86038
$321$	−9.82984	−0.548648
$322$	9.08453	0.506261
$323$	2.91151	0.162001
$324$	5.78827	0.321571
$325$	6.22661	0.345390
$326$	14.3136	0.792755
$327$	5.67320	0.313728
$328$	−71.5908	−3.95294
$329$	6.66090	0.367227
$330$	3.95164	0.217531
$331$	−17.8557	−0.981438	−0.490719	−	0.871318i	$-0.663266\pi$
$331$	−17.8557	−0.981438	−0.490719	+	0.871318i	$0.663266\pi$
$332$	4.19716	0.230349
$333$	5.97065	0.327189
$334$	32.8259	1.79615
$335$	−14.3353	−0.783223
$336$	−34.2121	−1.86642
$337$	21.0436	1.14632	0.573159	−	0.819444i	$-0.305718\pi$
$337$	21.0436	1.14632	0.573159	+	0.819444i	$0.305718\pi$
$338$	35.5873	1.93569
$339$	−15.4508	−0.839171
$340$	11.2432	0.609751
$341$	2.79995	0.151626
$342$	8.12530	0.439366
$343$	19.7671	1.06732
$344$	−84.6722	−4.56522
$345$	−3.31334	−0.178384
$346$	−56.1389	−3.01804
$347$	23.9004	1.28304	0.641520	−	0.767107i	$-0.278304\pi$
$347$	23.9004	1.28304	0.641520	+	0.767107i	$0.278304\pi$
$348$	9.08704	0.487116
$349$	10.1944	0.545692	0.272846	−	0.962058i	$-0.412035\pi$
$349$	10.1944	0.545692	0.272846	+	0.962058i	$0.412035\pi$
$350$	6.53472	0.349295
$351$	−5.07463	−0.270864
$352$	21.0580	1.12239
$353$	−10.3401	−0.550348	−0.275174	−	0.961394i	$-0.588735\pi$
$353$	−10.3401	−0.550348	−0.275174	+	0.961394i	$0.588735\pi$
$354$	13.6439	0.725166
$355$	−3.97560	−0.211003
$356$	82.4646	4.37061
$357$	−1.90835	−0.101001
$358$	−70.6728	−3.73517
$359$	29.7536	1.57034	0.785168	−	0.619283i	$-0.212577\pi$
$359$	29.7536	1.57034	0.785168	+	0.619283i	$0.212577\pi$
$360$	20.5355	1.08231
$361$	−10.5231	−0.553847
$362$	38.0780	2.00133
$363$	−10.4686	−0.549459
$364$	56.0547	2.93807
$365$	13.2662	0.694386
$366$	−12.8199	−0.670107
$367$	−30.4262	−1.58823	−0.794117	−	0.607765i	$-0.792066\pi$
$367$	−30.4262	−1.58823	−0.794117	+	0.607765i	$0.792066\pi$
$368$	−30.5804	−1.59412
$369$	−6.77167	−0.352519
$370$	32.3657	1.68261
$371$	1.24108	0.0644335
$372$	22.2324	1.15270
$373$	−33.5287	−1.73605	−0.868024	−	0.496522i	$-0.834610\pi$
$373$	−33.5287	−1.73605	−0.868024	+	0.496522i	$0.834610\pi$
$374$	2.03439	0.105196
$375$	−12.0955	−0.624607
$376$	−36.9008	−1.90301
$377$	−7.96669	−0.410306
$378$	−5.32573	−0.273926
$379$	27.1423	1.39421	0.697103	−	0.716971i	$-0.254472\pi$
$379$	27.1423	1.39421	0.697103	+	0.716971i	$0.254472\pi$
$380$	32.7349	1.67926
$381$	−12.3414	−0.632267
$382$	−57.4018	−2.93693
$383$	15.7419	0.804376	0.402188	−	0.915557i	$-0.368250\pi$
$383$	15.7419	0.804376	0.402188	+	0.915557i	$0.368250\pi$
$384$	67.1434	3.42640
$385$	−2.70219	−0.137716
$386$	−5.14764	−0.262008
$387$	−8.00902	−0.407121
$388$	7.79844	0.395906
$389$	−21.5896	−1.09464	−0.547319	−	0.836924i	$-0.684352\pi$
$389$	−21.5896	−1.09464	−0.547319	+	0.836924i	$0.684352\pi$
$390$	−27.5086	−1.39295
$391$	−1.70578	−0.0862650
$392$	−35.5031	−1.79318
$393$	−0.723440	−0.0364927
$394$	−2.31447	−0.116601
$395$	1.94242	0.0977337
$396$	4.21952	0.212039
$397$	−34.9449	−1.75383	−0.876916	−	0.480643i	$-0.840403\pi$
$397$	−34.9449	−1.75383	−0.876916	+	0.480643i	$0.840403\pi$
$398$	37.7492	1.89220
$399$	−5.55620	−0.278158
$400$	−21.9972	−1.09986
$401$	−31.7284	−1.58444	−0.792220	−	0.610235i	$-0.791075\pi$
$401$	−31.7284	−1.58444	−0.792220	+	0.610235i	$0.791075\pi$
$402$	−20.5961	−1.02724
$403$	−19.4913	−0.970933
$404$	18.2249	0.906725
$405$	1.94242	0.0965196
$406$	−8.36090	−0.414945
$407$	4.35246	0.215744
$408$	10.5721	0.523397
$409$	−2.48412	−0.122832	−0.0614159	−	0.998112i	$-0.519562\pi$
$409$	−2.48412	−0.122832	−0.0614159	+	0.998112i	$0.519562\pi$
$410$	−36.7079	−1.81287
$411$	−19.2652	−0.950281
$412$	1.47284	0.0725614
$413$	−9.32992	−0.459095
$414$	−4.76040	−0.233961
$415$	1.40848	0.0691394
$416$	−146.591	−7.18721
$417$	11.7922	0.577465
$418$	5.92316	0.289711
$419$	31.5735	1.54246	0.771232	−	0.636554i	$-0.219641\pi$
$419$	31.5735	1.54246	0.771232	+	0.636554i	$0.219641\pi$
$420$	−21.4561	−1.04695
$421$	24.2739	1.18304	0.591518	−	0.806292i	$-0.298529\pi$
$421$	24.2739	1.18304	0.591518	+	0.806292i	$0.298529\pi$
$422$	24.1671	1.17644
$423$	−3.49039	−0.169709
$424$	−6.87545	−0.333901
$425$	−1.22701	−0.0595186
$426$	−5.71190	−0.276742
$427$	8.76644	0.424238
$428$	−56.8978	−2.75026
$429$	−3.69929	−0.178603
$430$	−43.4153	−2.09367
$431$	2.30327	0.110945	0.0554723	−	0.998460i	$-0.482334\pi$
$431$	2.30327	0.110945	0.0554723	+	0.998460i	$0.482334\pi$
$432$	17.9275	0.862539
$433$	−8.19767	−0.393955	−0.196977	−	0.980408i	$-0.563113\pi$
$433$	−8.19767	−0.393955	−0.196977	+	0.980408i	$0.563113\pi$
$434$	−20.4558	−0.981910
$435$	3.04941	0.146208
$436$	32.8380	1.57265
$437$	−4.96640	−0.237575
$438$	19.0601	0.910727
$439$	−26.0343	−1.24255	−0.621276	−	0.783592i	$-0.713385\pi$
$439$	−26.0343	−1.24255	−0.621276	+	0.783592i	$0.713385\pi$
$440$	14.9699	0.713661
$441$	−3.35818	−0.159914
$442$	−14.1620	−0.673618
$443$	7.75205	0.368311	0.184155	−	0.982897i	$-0.441045\pi$
$443$	7.75205	0.368311	0.184155	+	0.982897i	$0.441045\pi$
$444$	34.5597	1.64013
$445$	27.6733	1.31184
$446$	−6.69258	−0.316903
$447$	6.16909	0.291788
$448$	−85.4204	−4.03573
$449$	−8.05555	−0.380165	−0.190082	−	0.981768i	$-0.560876\pi$
$449$	−8.05555	−0.380165	−0.190082	+	0.981768i	$0.560876\pi$
$450$	−3.42427	−0.161422
$451$	−4.93639	−0.232446
$452$	−89.4332	−4.20659
$453$	−0.0262637	−0.00123398
$454$	7.52683	0.353252
$455$	18.8108	0.881862
$456$	30.7808	1.44144
$457$	24.6901	1.15496	0.577478	−	0.816406i	$-0.304037\pi$
$457$	24.6901	1.15496	0.577478	+	0.816406i	$0.304037\pi$
$458$	35.5243	1.65994
$459$	1.00000	0.0466760
$460$	−19.1785	−0.894203
$461$	−14.4539	−0.673187	−0.336593	−	0.941650i	$-0.609275\pi$
$461$	−14.4539	−0.673187	−0.336593	+	0.941650i	$0.609275\pi$
$462$	−3.88234	−0.180623
$463$	6.44871	0.299697	0.149849	−	0.988709i	$-0.452121\pi$
$463$	6.44871	0.299697	0.149849	+	0.988709i	$0.452121\pi$
$464$	28.1445	1.30658
$465$	7.46071	0.345982
$466$	62.0400	2.87395
$467$	24.9074	1.15258	0.576288	−	0.817246i	$-0.304501\pi$
$467$	24.9074	1.15258	0.576288	+	0.817246i	$0.304501\pi$
$468$	−29.3733	−1.35778
$469$	14.0839	0.650336
$470$	−18.9207	−0.872747
$471$	−5.23085	−0.241025
$472$	51.6869	2.37908
$473$	−5.83839	−0.268449
$474$	2.79075	0.128183
$475$	−3.57245	−0.163915
$476$	−11.0461	−0.506296
$477$	−0.650338	−0.0297769
$478$	−35.4752	−1.62260
$479$	−25.2049	−1.15164	−0.575820	−	0.817576i	$-0.695317\pi$
$479$	−25.2049	−1.15164	−0.575820	+	0.817576i	$0.695317\pi$
$480$	56.1107	2.56109
$481$	−30.2988	−1.38151
$482$	39.4202	1.79554
$483$	3.25523	0.148118
$484$	−60.5950	−2.75432
$485$	2.61699	0.118831
$486$	2.79075	0.126591
$487$	3.57093	0.161814	0.0809072	−	0.996722i	$-0.474218\pi$
$487$	3.57093	0.161814	0.0809072	+	0.996722i	$0.474218\pi$
$488$	−48.5653	−2.19845
$489$	5.12894	0.231939
$490$	−18.2040	−0.822375
$491$	20.7968	0.938547	0.469274	−	0.883053i	$-0.344516\pi$
$491$	20.7968	0.938547	0.469274	+	0.883053i	$0.344516\pi$
$492$	−39.1962	−1.76710
$493$	1.56991	0.0707050
$494$	−41.2329	−1.85516
$495$	1.41598	0.0636435
$496$	68.8585	3.09184
$497$	3.90588	0.175203
$498$	2.02361	0.0906802
$499$	21.0047	0.940297	0.470149	−	0.882587i	$-0.344200\pi$
$499$	21.0047	0.940297	0.470149	+	0.882587i	$0.344200\pi$
$500$	−70.0118	−3.13102
$501$	11.7624	0.525506
$502$	−69.8094	−3.11575
$503$	10.4222	0.464703	0.232351	−	0.972632i	$-0.425358\pi$
$503$	10.4222	0.464703	0.232351	+	0.972632i	$0.425358\pi$
$504$	−20.1753	−0.898680
$505$	6.11590	0.272154
$506$	−3.47022	−0.154270
$507$	12.7519	0.566331
$508$	−71.4351	−3.16942
$509$	−8.69354	−0.385334	−0.192667	−	0.981264i	$-0.561714\pi$
$509$	−8.69354	−0.385334	−0.192667	+	0.981264i	$0.561714\pi$
$510$	5.42080	0.240037
$511$	−13.0336	−0.576571
$512$	138.809	6.13456
$513$	2.91151	0.128546
$514$	36.7736	1.62201
$515$	0.494252	0.0217793
$516$	−46.3583	−2.04081
$517$	−2.54441	−0.111903
$518$	−31.7981	−1.39713
$519$	−20.1161	−0.882998
$520$	−104.210	−4.56991
$521$	−6.64820	−0.291263	−0.145632	−	0.989339i	$-0.546521\pi$
$521$	−6.64820	−0.291263	−0.145632	+	0.989339i	$0.546521\pi$
$522$	4.38121	0.191760
$523$	21.2684	0.930000	0.465000	−	0.885311i	$-0.346054\pi$
$523$	21.2684	0.930000	0.465000	+	0.885311i	$0.346054\pi$
$524$	−4.18747	−0.182930
$525$	2.34157	0.102194
$526$	−1.36479	−0.0595077
$527$	3.84094	0.167314
$528$	13.0688	0.568745
$529$	−20.0903	−0.873492
$530$	−3.52535	−0.153132
$531$	4.88899	0.212164
$532$	−32.1608	−1.39435
$533$	34.3637	1.48846
$534$	39.7593	1.72056
$535$	−19.0937	−0.825491
$536$	−78.0237	−3.37011
$537$	−25.3240	−1.09281
$538$	−53.9853	−2.32747
$539$	−2.44804	−0.105445
$540$	11.2432	0.483832
$541$	34.1809	1.46955	0.734775	−	0.678310i	$-0.237288\pi$
$541$	34.1809	1.46955	0.734775	+	0.678310i	$0.237288\pi$
$542$	59.0162	2.53496
$543$	13.6444	0.585536
$544$	28.8870	1.23852
$545$	11.0197	0.472033
$546$	27.0261	1.15661
$547$	4.09131	0.174932	0.0874658	−	0.996168i	$-0.472123\pi$
$547$	4.09131	0.174932	0.0874658	+	0.996168i	$0.472123\pi$
$548$	−111.512	−4.76356
$549$	−4.59372	−0.196055
$550$	−2.49621	−0.106439
$551$	4.57080	0.194723
$552$	−18.0337	−0.767565
$553$	−1.90835	−0.0811515
$554$	5.23620	0.222465
$555$	11.5975	0.492286
$556$	68.2562	2.89471
$557$	−36.3705	−1.54107	−0.770534	−	0.637398i	$-0.780011\pi$
$557$	−36.3705	−1.54107	−0.770534	+	0.637398i	$0.780011\pi$
$558$	10.7191	0.453775
$559$	40.6428	1.71901
$560$	−66.4542	−2.80820
$561$	0.728977	0.0307774
$562$	42.0122	1.77218
$563$	31.8179	1.34096	0.670482	−	0.741926i	$-0.266087\pi$
$563$	31.8179	1.34096	0.670482	+	0.741926i	$0.266087\pi$
$564$	−20.2033	−0.850713
$565$	−30.0119	−1.26261
$566$	36.8229	1.54778
$567$	−1.90835	−0.0801433
$568$	−21.6382	−0.907919
$569$	24.8618	1.04226	0.521131	−	0.853477i	$-0.325510\pi$
$569$	24.8618	1.04226	0.521131	+	0.853477i	$0.325510\pi$
$570$	15.7827	0.661066
$571$	−31.9857	−1.33856	−0.669279	−	0.743011i	$-0.733397\pi$
$571$	−31.9857	−1.33856	−0.669279	+	0.743011i	$0.733397\pi$
$572$	−21.4125	−0.895301
$573$	−20.5686	−0.859267
$574$	36.0641	1.50529
$575$	2.09301	0.0872844
$576$	44.7613	1.86505
$577$	38.5829	1.60623	0.803114	−	0.595825i	$-0.203175\pi$
$577$	38.5829	1.60623	0.803114	+	0.595825i	$0.203175\pi$
$578$	2.79075	0.116080
$579$	−1.84454	−0.0766564
$580$	17.6508	0.732911
$581$	−1.38377	−0.0574087
$582$	3.75993	0.155854
$583$	−0.474082	−0.0196345
$584$	72.2048	2.98786
$585$	−9.85706	−0.407539
$586$	55.2207	2.28115
$587$	19.9414	0.823069	0.411534	−	0.911394i	$-0.364993\pi$
$587$	19.9414	0.823069	0.411534	+	0.911394i	$0.364993\pi$
$588$	−19.4381	−0.801613
$589$	11.1829	0.460785
$590$	26.5022	1.09108
$591$	−0.829338	−0.0341144
$592$	107.039	4.39928
$593$	15.8316	0.650127	0.325064	−	0.945692i	$-0.394614\pi$
$593$	15.8316	0.650127	0.325064	+	0.945692i	$0.394614\pi$
$594$	2.03439	0.0834721
$595$	−3.70682	−0.151965
$596$	35.7084	1.46267
$597$	13.5266	0.553605
$598$	24.1573	0.987865
$599$	18.9035	0.772375	0.386187	−	0.922420i	$-0.373792\pi$
$599$	18.9035	0.772375	0.386187	+	0.922420i	$0.373792\pi$
$600$	−12.9721	−0.529582
$601$	−9.86749	−0.402503	−0.201252	−	0.979540i	$-0.564501\pi$
$601$	−9.86749	−0.402503	−0.201252	+	0.979540i	$0.564501\pi$
$602$	42.6539	1.73844
$603$	−7.38015	−0.300543
$604$	−0.152021	−0.00618566
$605$	−20.3344	−0.826711
$606$	8.78694	0.356945
$607$	−4.76537	−0.193420	−0.0967102	−	0.995313i	$-0.530832\pi$
$607$	−4.76537	−0.193420	−0.0967102	+	0.995313i	$0.530832\pi$
$608$	84.1049	3.41091
$609$	−2.99594	−0.121401
$610$	−24.9016	−1.00824
$611$	17.7124	0.716569
$612$	5.78827	0.233977
$613$	−35.6753	−1.44091	−0.720457	−	0.693500i	$-0.756068\pi$
$613$	−35.6753	−1.44091	−0.720457	+	0.693500i	$0.756068\pi$
$614$	−54.5391	−2.20102
$615$	−13.1534	−0.530397
$616$	−14.7073	−0.592576
$617$	−0.769026	−0.0309598	−0.0154799	−	0.999880i	$-0.504928\pi$
$617$	−0.769026	−0.0309598	−0.0154799	+	0.999880i	$0.504928\pi$
$618$	0.710110	0.0285648
$619$	−18.6570	−0.749886	−0.374943	−	0.927048i	$-0.622338\pi$
$619$	−18.6570	−0.749886	−0.374943	+	0.927048i	$0.622338\pi$
$620$	43.1846	1.73434
$621$	−1.70578	−0.0684506
$622$	91.7309	3.67807
$623$	−27.1880	−1.08927
$624$	−90.9756	−3.64194
$625$	−17.3594	−0.694376
$626$	−14.8219	−0.592402
$627$	2.12243	0.0847616
$628$	−30.2776	−1.20821
$629$	5.97065	0.238065
$630$	−10.3448	−0.412147
$631$	−11.5196	−0.458587	−0.229294	−	0.973357i	$-0.573642\pi$
$631$	−11.5196	−0.458587	−0.229294	+	0.973357i	$0.573642\pi$
$632$	10.5721	0.420536
$633$	8.65973	0.344193
$634$	53.5618	2.12721
$635$	−23.9721	−0.951303
$636$	−3.76433	−0.149266
$637$	17.0415	0.675211
$638$	3.19380	0.126444
$639$	−2.04673	−0.0809673
$640$	130.421	5.15533
$641$	48.1715	1.90266	0.951331	−	0.308172i	$-0.0997174\pi$
$641$	48.1715	1.90266	0.951331	+	0.308172i	$0.0997174\pi$
$642$	−27.4326	−1.08268
$643$	46.8129	1.84612	0.923061	−	0.384653i	$-0.125679\pi$
$643$	46.8129	1.84612	0.923061	+	0.384653i	$0.125679\pi$
$644$	18.8422	0.742486
$645$	−15.5569	−0.612551
$646$	8.12530	0.319686
$647$	−29.4022	−1.15592	−0.577960	−	0.816065i	$-0.696151\pi$
$647$	−29.4022	−1.15592	−0.577960	+	0.816065i	$0.696151\pi$
$648$	10.5721	0.415312
$649$	3.56396	0.139898
$650$	17.3769	0.681578
$651$	−7.32987	−0.287280
$652$	29.6877	1.16266
$653$	−42.8825	−1.67812	−0.839061	−	0.544038i	$-0.816895\pi$
$653$	−42.8825	−1.67812	−0.839061	+	0.544038i	$0.816895\pi$
$654$	15.8325	0.619098
$655$	−1.40522	−0.0549066
$656$	−121.399	−4.73985
$657$	6.82975	0.266454
$658$	18.5889	0.724670
$659$	−21.8026	−0.849309	−0.424654	−	0.905356i	$-0.639604\pi$
$659$	−21.8026	−0.849309	−0.424654	+	0.905356i	$0.639604\pi$
$660$	8.19607	0.319032
$661$	13.6636	0.531452	0.265726	−	0.964049i	$-0.414388\pi$
$661$	13.6636	0.531452	0.265726	+	0.964049i	$0.414388\pi$
$662$	−49.8307	−1.93673
$663$	−5.07463	−0.197082
$664$	7.66598	0.297498
$665$	−10.7925	−0.418514
$666$	16.6626	0.645661
$667$	−2.67791	−0.103689
$668$	68.0840	2.63425
$669$	−2.39813	−0.0927171
$670$	−40.0063	−1.54558
$671$	−3.34871	−0.129276
$672$	−55.1266	−2.12656
$673$	−31.3719	−1.20930	−0.604650	−	0.796491i	$-0.706687\pi$
$673$	−31.3719	−1.20930	−0.604650	+	0.796491i	$0.706687\pi$
$674$	58.7274	2.26210
$675$	−1.22701	−0.0472276
$676$	73.8113	2.83890
$677$	6.90208	0.265269	0.132634	−	0.991165i	$-0.457656\pi$
$677$	6.90208	0.265269	0.132634	+	0.991165i	$0.457656\pi$
$678$	−43.1192	−1.65598
$679$	−2.57109	−0.0986695
$680$	20.5355	0.787499
$681$	2.69707	0.103352
$682$	7.81397	0.299212
$683$	8.42252	0.322279	0.161139	−	0.986932i	$-0.448483\pi$
$683$	8.42252	0.322279	0.161139	+	0.986932i	$0.448483\pi$
$684$	16.8526	0.644376
$685$	−37.4210	−1.42978
$686$	55.1649	2.10621
$687$	12.7293	0.485654
$688$	−143.582	−5.47401
$689$	3.30023	0.125729
$690$	−9.24670	−0.352016
$691$	2.56869	0.0977176	0.0488588	−	0.998806i	$-0.484442\pi$
$691$	2.56869	0.0977176	0.0488588	+	0.998806i	$0.484442\pi$
$692$	−116.437	−4.42628
$693$	−1.39115	−0.0528453
$694$	66.6999	2.53189
$695$	22.9053	0.868848
$696$	16.5972	0.629116
$697$	−6.77167	−0.256495
$698$	28.4499	1.07684
$699$	22.2306	0.840838
$700$	13.5536	0.512279
$701$	−12.0198	−0.453980	−0.226990	−	0.973897i	$-0.572889\pi$
$701$	−12.0198	−0.453980	−0.226990	+	0.973897i	$0.572889\pi$
$702$	−14.1620	−0.534511
$703$	17.3836	0.655636
$704$	32.6299	1.22979
$705$	−6.77980	−0.255342
$706$	−28.8566	−1.08603
$707$	−6.00864	−0.225978
$708$	28.2988	1.06353
$709$	24.0030	0.901453	0.450726	−	0.892662i	$-0.351165\pi$
$709$	24.0030	0.901453	0.450726	+	0.892662i	$0.351165\pi$
$710$	−11.0949	−0.416384
$711$	1.00000	0.0375029
$712$	150.619	5.64469
$713$	−6.55180	−0.245367
$714$	−5.32573	−0.199311
$715$	−7.18557	−0.268725
$716$	−146.582	−5.47802
$717$	−12.7117	−0.474728
$718$	83.0348	3.09883
$719$	24.9395	0.930088	0.465044	−	0.885288i	$-0.346039\pi$
$719$	24.9395	0.930088	0.465044	+	0.885288i	$0.346039\pi$
$720$	34.8228	1.29777
$721$	−0.485584	−0.0180841
$722$	−29.3673	−1.09294
$723$	14.1253	0.525326
$724$	78.9773	2.93517
$725$	−1.92629	−0.0715405
$726$	−29.2152	−1.08428
$727$	−37.3887	−1.38667	−0.693334	−	0.720616i	$-0.743859\pi$
$727$	−37.3887	−1.38667	−0.693334	+	0.720616i	$0.743859\pi$
$728$	102.382	3.79454
$729$	1.00000	0.0370370
$730$	37.0227	1.37027
$731$	−8.00902	−0.296224
$732$	−26.5897	−0.982783
$733$	−5.35179	−0.197673	−0.0988365	−	0.995104i	$-0.531512\pi$
$733$	−5.35179	−0.197673	−0.0988365	+	0.995104i	$0.531512\pi$
$734$	−84.9118	−3.13415
$735$	−6.52300	−0.240605
$736$	−49.2749	−1.81630
$737$	−5.37996	−0.198173
$738$	−18.8980	−0.695645
$739$	32.8310	1.20771	0.603853	−	0.797095i	$-0.293631\pi$
$739$	32.8310	1.20771	0.603853	+	0.797095i	$0.293631\pi$
$740$	67.1295	2.46773
$741$	−14.7749	−0.542768
$742$	3.46353	0.127150
$743$	−7.07270	−0.259472	−0.129736	−	0.991549i	$-0.541413\pi$
$743$	−7.07270	−0.259472	−0.129736	+	0.991549i	$0.541413\pi$
$744$	40.6068	1.48872
$745$	11.9830	0.439022
$746$	−93.5700	−3.42584
$747$	0.725114	0.0265305
$748$	4.21952	0.154281
$749$	18.7588	0.685432
$750$	−33.7554	−1.23257
$751$	−28.4344	−1.03759	−0.518793	−	0.854900i	$-0.673618\pi$
$751$	−28.4344	−1.03759	−0.518793	+	0.854900i	$0.673618\pi$
$752$	−62.5741	−2.28184
$753$	−25.0146	−0.911583
$754$	−22.2330	−0.809679
$755$	−0.0510151	−0.00185663
$756$	−11.0461	−0.401742
$757$	−48.6512	−1.76826	−0.884128	−	0.467244i	$-0.845247\pi$
$757$	−48.6512	−1.76826	−0.884128	+	0.467244i	$0.845247\pi$
$758$	75.7473	2.75126
$759$	−1.24347	−0.0451353
$760$	59.7893	2.16879
$761$	26.9493	0.976912	0.488456	−	0.872588i	$-0.337560\pi$
$761$	26.9493	0.976912	0.488456	+	0.872588i	$0.337560\pi$
$762$	−34.4416	−1.24769
$763$	−10.8265	−0.391944
$764$	−119.057	−4.30732
$765$	1.94242	0.0702283
$766$	43.9318	1.58732
$767$	−24.8098	−0.895830
$768$	97.8576	3.53113
$769$	47.7573	1.72217	0.861087	−	0.508458i	$-0.169784\pi$
$769$	47.7573	1.72217	0.861087	+	0.508458i	$0.169784\pi$
$770$	−7.54113	−0.271763
$771$	13.1770	0.474557
$772$	−10.6767	−0.384262
$773$	−46.4959	−1.67234	−0.836170	−	0.548470i	$-0.815210\pi$
$773$	−46.4959	−1.67234	−0.836170	+	0.548470i	$0.815210\pi$
$774$	−22.3511	−0.803395
$775$	−4.71286	−0.169291
$776$	14.2436	0.511316
$777$	−11.3941	−0.408761
$778$	−60.2512	−2.16011
$779$	−19.7158	−0.706392
$780$	−57.0553	−2.04291
$781$	−1.49202	−0.0533886
$782$	−4.76040	−0.170232
$783$	1.56991	0.0561038
$784$	−60.2040	−2.15014
$785$	−10.1605	−0.362644
$786$	−2.01894	−0.0720132
$787$	54.1885	1.93161	0.965806	−	0.259264i	$-0.0834800\pi$
$787$	54.1885	1.93161	0.965806	+	0.259264i	$0.0834800\pi$
$788$	−4.80043	−0.171008
$789$	−0.489041	−0.0174103
$790$	5.42080	0.192863
$791$	29.4855	1.04839
$792$	7.70682	0.273850
$793$	23.3114	0.827813
$794$	−97.5223	−3.46094
$795$	−1.26323	−0.0448021
$796$	78.2954	2.77511
$797$	−27.0675	−0.958779	−0.479389	−	0.877602i	$-0.659142\pi$
$797$	−27.0675	−0.958779	−0.479389	+	0.877602i	$0.659142\pi$
$798$	−15.5060	−0.548905
$799$	−3.49039	−0.123481
$800$	−35.4446	−1.25316
$801$	14.2468	0.503388
$802$	−88.5459	−3.12667
$803$	4.97873	0.175696
$804$	−42.7183	−1.50656
$805$	6.32303	0.222857
$806$	−54.3954	−1.91600
$807$	−19.3444	−0.680955
$808$	33.2873	1.17104
$809$	29.7385	1.04555	0.522774	−	0.852471i	$-0.324897\pi$
$809$	29.7385	1.04555	0.522774	+	0.852471i	$0.324897\pi$
$810$	5.42080	0.190468
$811$	3.67896	0.129186	0.0645928	−	0.997912i	$-0.479425\pi$
$811$	3.67896	0.129186	0.0645928	+	0.997912i	$0.479425\pi$
$812$	−17.3413	−0.608560
$813$	21.1471	0.741661
$814$	12.1466	0.425739
$815$	9.96255	0.348973
$816$	17.9275	0.627589
$817$	−23.3184	−0.815806
$818$	−6.93255	−0.242391
$819$	9.68419	0.338393
$820$	−76.1355	−2.65877
$821$	33.6043	1.17280	0.586399	−	0.810022i	$-0.300545\pi$
$821$	33.6043	1.17280	0.586399	+	0.810022i	$0.300545\pi$
$822$	−53.7642	−1.87524
$823$	−20.5777	−0.717292	−0.358646	−	0.933474i	$-0.616761\pi$
$823$	−20.5777	−0.717292	−0.358646	+	0.933474i	$0.616761\pi$
$824$	2.69009	0.0937137
$825$	−0.894461	−0.0311411
$826$	−26.0374	−0.905958
$827$	9.68490	0.336777	0.168388	−	0.985721i	$-0.446144\pi$
$827$	9.68490	0.336777	0.168388	+	0.985721i	$0.446144\pi$
$828$	−9.87352	−0.343129
$829$	−16.8882	−0.586550	−0.293275	−	0.956028i	$-0.594745\pi$
$829$	−16.8882	−0.586550	−0.293275	+	0.956028i	$0.594745\pi$
$830$	3.93070	0.136437
$831$	1.87627	0.0650871
$832$	−227.147	−7.87490
$833$	−3.35818	−0.116354
$834$	32.9089	1.13954
$835$	22.8475	0.790671
$836$	12.2852	0.424892
$837$	3.84094	0.132762
$838$	88.1135	3.04383
$839$	51.2385	1.76895	0.884474	−	0.466589i	$-0.154517\pi$
$839$	51.2385	1.76895	0.884474	+	0.466589i	$0.154517\pi$
$840$	−39.1889	−1.35215
$841$	−26.5354	−0.915014
$842$	67.7422	2.33455
$843$	15.0541	0.518491
$844$	50.1248	1.72537
$845$	24.7695	0.852097
$846$	−9.74080	−0.334895
$847$	19.9778	0.686445
$848$	−11.6590	−0.400370
$849$	13.1946	0.452839
$850$	−3.42427	−0.117451
$851$	−10.1846	−0.349124
$852$	−11.8470	−0.405872
$853$	1.19199	0.0408129	0.0204065	−	0.999792i	$-0.493504\pi$
$853$	1.19199	0.0408129	0.0204065	+	0.999792i	$0.493504\pi$
$854$	24.4649	0.837172
$855$	5.65538	0.193410
$856$	−103.922	−3.55198
$857$	−12.5262	−0.427887	−0.213943	−	0.976846i	$-0.568631\pi$
$857$	−12.5262	−0.427887	−0.213943	+	0.976846i	$0.568631\pi$
$858$	−10.3238	−0.352448
$859$	−37.1477	−1.26746	−0.633731	−	0.773553i	$-0.718478\pi$
$859$	−37.1477	−1.26746	−0.633731	+	0.773553i	$0.718478\pi$
$860$	−90.0473	−3.07059
$861$	12.9227	0.440406
$862$	6.42784	0.218933
$863$	10.3387	0.351933	0.175967	−	0.984396i	$-0.443695\pi$
$863$	10.3387	0.351933	0.175967	+	0.984396i	$0.443695\pi$
$864$	28.8870	0.982756
$865$	−39.0738	−1.32855
$866$	−22.8776	−0.777413
$867$	1.00000	0.0339618
$868$	−42.4273	−1.44008
$869$	0.728977	0.0247289
$870$	8.51015	0.288521
$871$	37.4515	1.26900
$872$	59.9776	2.03110
$873$	1.34728	0.0455986
$874$	−13.8600	−0.468821
$875$	23.0824	0.780328
$876$	39.5324	1.33568
$877$	4.67364	0.157818	0.0789089	−	0.996882i	$-0.474856\pi$
$877$	4.67364	0.157818	0.0789089	+	0.996882i	$0.474856\pi$
$878$	−72.6553	−2.45200
$879$	19.7871	0.667401
$880$	25.3850	0.855728
$881$	45.0632	1.51822	0.759109	−	0.650964i	$-0.225635\pi$
$881$	45.0632	1.51822	0.759109	+	0.650964i	$0.225635\pi$
$882$	−9.37184	−0.315566
$883$	49.0403	1.65034	0.825169	−	0.564887i	$-0.191080\pi$
$883$	49.0403	1.65034	0.825169	+	0.564887i	$0.191080\pi$
$884$	−29.3733	−0.987932
$885$	9.49646	0.319220
$886$	21.6340	0.726808
$887$	−8.77250	−0.294552	−0.147276	−	0.989095i	$-0.547051\pi$
$887$	−8.77250	−0.294552	−0.147276	+	0.989095i	$0.547051\pi$
$888$	63.1223	2.11825
$889$	23.5517	0.789898
$890$	77.2293	2.58873
$891$	0.728977	0.0244216
$892$	−13.8810	−0.464771
$893$	−10.1623	−0.340069
$894$	17.2164	0.575802
$895$	−49.1897	−1.64423
$896$	−128.133	−4.28063
$897$	8.65621	0.289022
$898$	−22.4810	−0.750201
$899$	6.02991	0.201109
$900$	−7.10225	−0.236742
$901$	−0.650338	−0.0216659
$902$	−13.7762	−0.458698
$903$	15.2840	0.508621
$904$	−163.347	−5.43285
$905$	26.5031	0.880992
$906$	−0.0732953	−0.00243507
$907$	−25.5684	−0.848986	−0.424493	−	0.905431i	$-0.639548\pi$
$907$	−25.5684	−0.848986	−0.424493	+	0.905431i	$0.639548\pi$
$908$	15.6113	0.518081
$909$	3.14860	0.104432
$910$	52.4961	1.74023
$911$	8.12334	0.269138	0.134569	−	0.990904i	$-0.457035\pi$
$911$	8.12334	0.269138	0.134569	+	0.990904i	$0.457035\pi$
$912$	52.1963	1.72839
$913$	0.528592	0.0174938
$914$	68.9040	2.27914
$915$	−8.92293	−0.294983
$916$	73.6808	2.43448
$917$	1.38058	0.0455908
$918$	2.79075	0.0921084
$919$	49.0491	1.61798	0.808991	−	0.587822i	$-0.200014\pi$
$919$	49.0491	1.61798	0.808991	+	0.587822i	$0.200014\pi$
$920$	−35.0290	−1.15487
$921$	−19.5428	−0.643958
$922$	−40.3373	−1.32844
$923$	10.3864	0.341872
$924$	−8.05233	−0.264902
$925$	−7.32603	−0.240878
$926$	17.9967	0.591409
$927$	0.254452	0.00835729
$928$	45.3499	1.48868
$929$	−39.8287	−1.30674	−0.653368	−	0.757040i	$-0.726645\pi$
$929$	−39.8287	−1.30674	−0.653368	+	0.757040i	$0.726645\pi$
$930$	20.8210	0.682746
$931$	−9.77740	−0.320441
$932$	128.677	4.21495
$933$	32.8697	1.07610
$934$	69.5102	2.27444
$935$	1.41598	0.0463075
$936$	−53.6495	−1.75359
$937$	13.0541	0.426460	0.213230	−	0.977002i	$-0.431602\pi$
$937$	13.0541	0.426460	0.213230	+	0.977002i	$0.431602\pi$
$938$	39.3047	1.28334
$939$	−5.31108	−0.173321
$940$	−39.2433	−1.27998
$941$	−17.5580	−0.572373	−0.286187	−	0.958174i	$-0.592388\pi$
$941$	−17.5580	−0.572373	−0.286187	+	0.958174i	$0.592388\pi$
$942$	−14.5980	−0.475628
$943$	11.5510	0.376152
$944$	87.6475	2.85268
$945$	−3.70682	−0.120583
$946$	−16.2935	−0.529746
$947$	27.1065	0.880842	0.440421	−	0.897791i	$-0.354829\pi$
$947$	27.1065	0.880842	0.440421	+	0.897791i	$0.354829\pi$
$948$	5.78827	0.187994
$949$	−34.6584	−1.12506
$950$	−9.96981	−0.323463
$951$	19.1926	0.622364
$952$	−20.1753	−0.653886
$953$	−46.5260	−1.50713	−0.753563	−	0.657376i	$-0.771666\pi$
$953$	−46.5260	−1.50713	−0.753563	+	0.657376i	$0.771666\pi$
$954$	−1.81493	−0.0587605
$955$	−39.9529	−1.29285
$956$	−73.5788	−2.37971
$957$	1.14443	0.0369940
$958$	−70.3405	−2.27260
$959$	36.7648	1.18720
$960$	86.9451	2.80614
$961$	−16.2472	−0.524103
$962$	−84.5564	−2.72621
$963$	−9.82984	−0.316762
$964$	81.7611	2.63335
$965$	−3.58287	−0.115337
$966$	9.08453	0.292290
$967$	−6.43165	−0.206828	−0.103414	−	0.994638i	$-0.532977\pi$
$967$	−6.43165	−0.206828	−0.103414	+	0.994638i	$0.532977\pi$
$968$	−110.675	−3.55723
$969$	2.91151	0.0935313
$970$	7.30336	0.234497
$971$	33.7215	1.08218	0.541088	−	0.840966i	$-0.318013\pi$
$971$	33.7215	1.08218	0.541088	+	0.840966i	$0.318013\pi$
$972$	5.78827	0.185659
$973$	−22.5036	−0.721433
$974$	9.96557	0.319318
$975$	6.22661	0.199411
$976$	−82.3540	−2.63609
$977$	21.6218	0.691742	0.345871	−	0.938282i	$-0.387583\pi$
$977$	21.6218	0.691742	0.345871	+	0.938282i	$0.387583\pi$
$978$	14.3136	0.457697
$979$	10.3856	0.331926
$980$	−37.7569	−1.20610
$981$	5.67320	0.181131
$982$	58.0387	1.85209
$983$	37.2007	1.18652	0.593259	−	0.805011i	$-0.297841\pi$
$983$	37.2007	1.18652	0.593259	+	0.805011i	$0.297841\pi$
$984$	−71.5908	−2.28223
$985$	−1.61092	−0.0513282
$986$	4.38121	0.139526
$987$	6.66090	0.212019
$988$	−85.5209	−2.72078
$989$	13.6616	0.434414
$990$	3.95164	0.125591
$991$	−55.3440	−1.75806	−0.879030	−	0.476766i	$-0.841809\pi$
$991$	−55.3440	−1.75806	−0.879030	+	0.476766i	$0.841809\pi$
$992$	110.953	3.52277
$993$	−17.8557	−0.566633
$994$	10.9003	0.345737
$995$	26.2742	0.832950
$996$	4.19716	0.132992
$997$	−10.6302	−0.336660	−0.168330	−	0.985731i	$-0.553837\pi$
$997$	−10.6302	−0.336660	−0.168330	+	0.985731i	$0.553837\pi$
$998$	58.6187	1.85554
$999$	5.97065	0.188903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.31	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.31	✓	31	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)

\(f(q)\)	\(=\)	\(q+2.79075 q^{2} +1.00000 q^{3} +5.78827 q^{4} +1.94242 q^{5} +2.79075 q^{6} -1.90835 q^{7} +10.5721 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.79075 q^{2} +1.00000 q^{3} +5.78827 q^{4} +1.94242 q^{5} +2.79075 q^{6} -1.90835 q^{7} +10.5721 q^{8} +1.00000 q^{9} +5.42080 q^{10} +0.728977 q^{11} +5.78827 q^{12} -5.07463 q^{13} -5.32573 q^{14} +1.94242 q^{15} +17.9275 q^{16} +1.00000 q^{17} +2.79075 q^{18} +2.91151 q^{19} +11.2432 q^{20} -1.90835 q^{21} +2.03439 q^{22} -1.70578 q^{23} +10.5721 q^{24} -1.22701 q^{25} -14.1620 q^{26} +1.00000 q^{27} -11.0461 q^{28} +1.56991 q^{29} +5.42080 q^{30} +3.84094 q^{31} +28.8870 q^{32} +0.728977 q^{33} +2.79075 q^{34} -3.70682 q^{35} +5.78827 q^{36} +5.97065 q^{37} +8.12530 q^{38} -5.07463 q^{39} +20.5355 q^{40} -6.77167 q^{41} -5.32573 q^{42} -8.00902 q^{43} +4.21952 q^{44} +1.94242 q^{45} -4.76040 q^{46} -3.49039 q^{47} +17.9275 q^{48} -3.35818 q^{49} -3.42427 q^{50} +1.00000 q^{51} -29.3733 q^{52} -0.650338 q^{53} +2.79075 q^{54} +1.41598 q^{55} -20.1753 q^{56} +2.91151 q^{57} +4.38121 q^{58} +4.88899 q^{59} +11.2432 q^{60} -4.59372 q^{61} +10.7191 q^{62} -1.90835 q^{63} +44.7613 q^{64} -9.85706 q^{65} +2.03439 q^{66} -7.38015 q^{67} +5.78827 q^{68} -1.70578 q^{69} -10.3448 q^{70} -2.04673 q^{71} +10.5721 q^{72} +6.82975 q^{73} +16.6626 q^{74} -1.22701 q^{75} +16.8526 q^{76} -1.39115 q^{77} -14.1620 q^{78} +1.00000 q^{79} +34.8228 q^{80} +1.00000 q^{81} -18.8980 q^{82} +0.725114 q^{83} -11.0461 q^{84} +1.94242 q^{85} -22.3511 q^{86} +1.56991 q^{87} +7.70682 q^{88} +14.2468 q^{89} +5.42080 q^{90} +9.68419 q^{91} -9.87352 q^{92} +3.84094 q^{93} -9.74080 q^{94} +5.65538 q^{95} +28.8870 q^{96} +1.34728 q^{97} -9.37184 q^{98} +0.728977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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