LMFDB - Embedded newform 4031.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77566 q^{2} +2.36943 q^{3} +5.70431 q^{4} +1.60665 q^{5} -6.57673 q^{6} +0.747628 q^{7} -10.2819 q^{8} +2.61418 q^{9} +O(q^{10})$	\(q-2.77566 q^{2} +2.36943 q^{3} +5.70431 q^{4} +1.60665 q^{5} -6.57673 q^{6} +0.747628 q^{7} -10.2819 q^{8} +2.61418 q^{9} -4.45952 q^{10} +0.0925242 q^{11} +13.5159 q^{12} -2.86675 q^{13} -2.07516 q^{14} +3.80683 q^{15} +17.1305 q^{16} -5.55509 q^{17} -7.25607 q^{18} -4.01849 q^{19} +9.16482 q^{20} +1.77145 q^{21} -0.256816 q^{22} +2.10825 q^{23} -24.3622 q^{24} -2.41868 q^{25} +7.95713 q^{26} -0.914181 q^{27} +4.26470 q^{28} +1.00000 q^{29} -10.5665 q^{30} -6.82037 q^{31} -26.9847 q^{32} +0.219229 q^{33} +15.4191 q^{34} +1.20118 q^{35} +14.9121 q^{36} -2.38476 q^{37} +11.1540 q^{38} -6.79255 q^{39} -16.5194 q^{40} +2.84099 q^{41} -4.91695 q^{42} -10.8137 q^{43} +0.527786 q^{44} +4.20006 q^{45} -5.85180 q^{46} +0.944693 q^{47} +40.5894 q^{48} -6.44105 q^{49} +6.71344 q^{50} -13.1624 q^{51} -16.3528 q^{52} +10.5301 q^{53} +2.53746 q^{54} +0.148654 q^{55} -7.68704 q^{56} -9.52152 q^{57} -2.77566 q^{58} +10.2532 q^{59} +21.7153 q^{60} -2.43094 q^{61} +18.9310 q^{62} +1.95443 q^{63} +40.6394 q^{64} -4.60586 q^{65} -0.608506 q^{66} +6.94880 q^{67} -31.6879 q^{68} +4.99535 q^{69} -3.33406 q^{70} -11.4026 q^{71} -26.8787 q^{72} +8.47338 q^{73} +6.61930 q^{74} -5.73088 q^{75} -22.9227 q^{76} +0.0691737 q^{77} +18.8538 q^{78} -13.0931 q^{79} +27.5227 q^{80} -10.0086 q^{81} -7.88564 q^{82} +11.1840 q^{83} +10.1049 q^{84} -8.92508 q^{85} +30.0151 q^{86} +2.36943 q^{87} -0.951325 q^{88} -9.66106 q^{89} -11.6580 q^{90} -2.14326 q^{91} +12.0261 q^{92} -16.1604 q^{93} -2.62215 q^{94} -6.45631 q^{95} -63.9381 q^{96} -6.21484 q^{97} +17.8782 q^{98} +0.241875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * 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 $

$2$	−2.77566	−1.96269	−0.981345	−	0.192255i	$-0.938420\pi$
$2$	−2.77566	−1.96269	−0.981345	+	0.192255i	$0.938420\pi$
$3$	2.36943	1.36799	0.683994	−	0.729487i	$-0.260241\pi$
$3$	2.36943	1.36799	0.683994	+	0.729487i	$0.260241\pi$
$4$	5.70431	2.85215
$5$	1.60665	0.718515	0.359258	−	0.933238i	$-0.383030\pi$
$5$	1.60665	0.718515	0.359258	+	0.933238i	$0.383030\pi$
$6$	−6.57673	−2.68494
$7$	0.747628	0.282577	0.141288	−	0.989968i	$-0.454875\pi$
$7$	0.747628	0.282577	0.141288	+	0.989968i	$0.454875\pi$
$8$	−10.2819	−3.63520
$9$	2.61418	0.871392
$10$	−4.45952	−1.41022
$11$	0.0925242	0.0278971	0.0139485	−	0.999903i	$-0.495560\pi$
$11$	0.0925242	0.0278971	0.0139485	+	0.999903i	$0.495560\pi$
$12$	13.5159	3.90171
$13$	−2.86675	−0.795093	−0.397547	−	0.917582i	$-0.630138\pi$
$13$	−2.86675	−0.795093	−0.397547	+	0.917582i	$0.630138\pi$
$14$	−2.07516	−0.554611
$15$	3.80683	0.982920
$16$	17.1305	4.28262
$17$	−5.55509	−1.34731	−0.673654	−	0.739047i	$-0.735276\pi$
$17$	−5.55509	−1.34731	−0.673654	+	0.739047i	$0.735276\pi$
$18$	−7.25607	−1.71027
$19$	−4.01849	−0.921906	−0.460953	−	0.887425i	$-0.652492\pi$
$19$	−4.01849	−0.921906	−0.460953	+	0.887425i	$0.652492\pi$
$20$	9.16482	2.04932
$21$	1.77145	0.386562
$22$	−0.256816	−0.0547534
$23$	2.10825	0.439601	0.219801	−	0.975545i	$-0.429459\pi$
$23$	2.10825	0.439601	0.219801	+	0.975545i	$0.429459\pi$
$24$	−24.3622	−4.97291
$25$	−2.41868	−0.483736
$26$	7.95713	1.56052
$27$	−0.914181	−0.175934
$28$	4.26470	0.805953
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−10.5665	−1.92917
$31$	−6.82037	−1.22497	−0.612487	−	0.790481i	$-0.709831\pi$
$31$	−6.82037	−1.22497	−0.612487	+	0.790481i	$0.709831\pi$
$32$	−26.9847	−4.77026
$33$	0.219229	0.0381629
$34$	15.4191	2.64435
$35$	1.20118	0.203036
$36$	14.9121	2.48534
$37$	−2.38476	−0.392052	−0.196026	−	0.980599i	$-0.562804\pi$
$37$	−2.38476	−0.392052	−0.196026	+	0.980599i	$0.562804\pi$
$38$	11.1540	1.80942
$39$	−6.79255	−1.08768
$40$	−16.5194	−2.61195
$41$	2.84099	0.443689	0.221844	−	0.975082i	$-0.428792\pi$
$41$	2.84099	0.443689	0.221844	+	0.975082i	$0.428792\pi$
$42$	−4.91695	−0.758701
$43$	−10.8137	−1.64907	−0.824534	−	0.565812i	$-0.808563\pi$
$43$	−10.8137	−1.64907	−0.824534	+	0.565812i	$0.808563\pi$
$44$	0.527786	0.0795668
$45$	4.20006	0.626108
$46$	−5.85180	−0.862801
$47$	0.944693	0.137798	0.0688988	−	0.997624i	$-0.478051\pi$
$47$	0.944693	0.137798	0.0688988	+	0.997624i	$0.478051\pi$
$48$	40.5894	5.85858
$49$	−6.44105	−0.920150
$50$	6.71344	0.949424
$51$	−13.1624	−1.84310
$52$	−16.3528	−2.26773
$53$	10.5301	1.44642	0.723209	−	0.690629i	$-0.242666\pi$
$53$	10.5301	1.44642	0.723209	+	0.690629i	$0.242666\pi$
$54$	2.53746	0.345304
$55$	0.148654	0.0200445
$56$	−7.68704	−1.02722
$57$	−9.52152	−1.26116
$58$	−2.77566	−0.364462
$59$	10.2532	1.33486	0.667428	−	0.744674i	$-0.267395\pi$
$59$	10.2532	1.33486	0.667428	+	0.744674i	$0.267395\pi$
$60$	21.7153	2.80344
$61$	−2.43094	−0.311251	−0.155625	−	0.987816i	$-0.549739\pi$
$61$	−2.43094	−0.311251	−0.155625	+	0.987816i	$0.549739\pi$
$62$	18.9310	2.40425
$63$	1.95443	0.246235
$64$	40.6394	5.07992
$65$	−4.60586	−0.571287
$66$	−0.608506	−0.0749020
$67$	6.94880	0.848931	0.424465	−	0.905444i	$-0.360462\pi$
$67$	6.94880	0.848931	0.424465	+	0.905444i	$0.360462\pi$
$68$	−31.6879	−3.84273
$69$	4.99535	0.601370
$70$	−3.33406	−0.398497
$71$	−11.4026	−1.35323	−0.676617	−	0.736335i	$-0.736555\pi$
$71$	−11.4026	−1.35323	−0.676617	+	0.736335i	$0.736555\pi$
$72$	−26.8787	−3.16769
$73$	8.47338	0.991734	0.495867	−	0.868399i	$-0.334850\pi$
$73$	8.47338	0.991734	0.495867	+	0.868399i	$0.334850\pi$
$74$	6.61930	0.769478
$75$	−5.73088	−0.661745
$76$	−22.9227	−2.62942
$77$	0.0691737	0.00788308
$78$	18.8538	2.13478
$79$	−13.0931	−1.47309	−0.736547	−	0.676387i	$-0.763545\pi$
$79$	−13.0931	−1.47309	−0.736547	+	0.676387i	$0.763545\pi$
$80$	27.5227	3.07713
$81$	−10.0086	−1.11207
$82$	−7.88564	−0.870823
$83$	11.1840	1.22760	0.613799	−	0.789462i	$-0.289640\pi$
$83$	11.1840	1.22760	0.613799	+	0.789462i	$0.289640\pi$
$84$	10.1049	1.10253
$85$	−8.92508	−0.968061
$86$	30.0151	3.23661
$87$	2.36943	0.254029
$88$	−0.951325	−0.101412
$89$	−9.66106	−1.02407	−0.512035	−	0.858964i	$-0.671108\pi$
$89$	−9.66106	−1.02407	−0.512035	+	0.858964i	$0.671108\pi$
$90$	−11.6580	−1.22886
$91$	−2.14326	−0.224675
$92$	12.0261	1.25381
$93$	−16.1604	−1.67575
$94$	−2.62215	−0.270454
$95$	−6.45631	−0.662403
$96$	−63.9381	−6.52566
$97$	−6.21484	−0.631021	−0.315511	−	0.948922i	$-0.602176\pi$
$97$	−6.21484	−0.631021	−0.315511	+	0.948922i	$0.602176\pi$
$98$	17.8782	1.80597
$99$	0.241875	0.0243093
$100$	−13.7969	−1.37969
$101$	−2.43456	−0.242248	−0.121124	−	0.992637i	$-0.538650\pi$
$101$	−2.43456	−0.242248	−0.121124	+	0.992637i	$0.538650\pi$
$102$	36.5343	3.61744
$103$	8.19689	0.807663	0.403832	−	0.914833i	$-0.367678\pi$
$103$	8.19689	0.807663	0.403832	+	0.914833i	$0.367678\pi$
$104$	29.4756	2.89033
$105$	2.84610	0.277751
$106$	−29.2280	−2.83887
$107$	6.52527	0.630822	0.315411	−	0.948955i	$-0.397858\pi$
$107$	6.52527	0.630822	0.315411	+	0.948955i	$0.397858\pi$
$108$	−5.21477	−0.501791
$109$	−17.5643	−1.68236	−0.841179	−	0.540757i	$-0.818138\pi$
$109$	−17.5643	−1.68236	−0.841179	+	0.540757i	$0.818138\pi$
$110$	−0.412613	−0.0393411
$111$	−5.65052	−0.536323
$112$	12.8072	1.21017
$113$	2.47640	0.232960	0.116480	−	0.993193i	$-0.462839\pi$
$113$	2.47640	0.232960	0.116480	+	0.993193i	$0.462839\pi$
$114$	26.4285	2.47526
$115$	3.38722	0.315860
$116$	5.70431	0.529631
$117$	−7.49419	−0.692838
$118$	−28.4595	−2.61991
$119$	−4.15314	−0.380718
$120$	−39.1415	−3.57311
$121$	−10.9914	−0.999222
$122$	6.74748	0.610888
$123$	6.73152	0.606961
$124$	−38.9055	−3.49381
$125$	−11.9192	−1.06609
$126$	−5.42485	−0.483284
$127$	−7.31395	−0.649008	−0.324504	−	0.945884i	$-0.605197\pi$
$127$	−7.31395	−0.649008	−0.324504	+	0.945884i	$0.605197\pi$
$128$	−58.8318	−5.20005
$129$	−25.6222	−2.25591
$130$	12.7843	1.12126
$131$	−9.19093	−0.803015	−0.401508	−	0.915856i	$-0.631514\pi$
$131$	−9.19093	−0.803015	−0.401508	+	0.915856i	$0.631514\pi$
$132$	1.25055	0.108846
$133$	−3.00434	−0.260509
$134$	−19.2875	−1.66619
$135$	−1.46877	−0.126411
$136$	57.1169	4.89774
$137$	13.7841	1.17765	0.588826	−	0.808260i	$-0.299590\pi$
$137$	13.7841	1.17765	0.588826	+	0.808260i	$0.299590\pi$
$138$	−13.8654	−1.18030
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	6.85188	0.579089
$141$	2.23838	0.188506
$142$	31.6496	2.65598
$143$	−0.265244	−0.0221808
$144$	44.7821	3.73184
$145$	1.60665	0.133425
$146$	−23.5192	−1.94647
$147$	−15.2616	−1.25875
$148$	−13.6034	−1.11819
$149$	−9.67696	−0.792768	−0.396384	−	0.918085i	$-0.629735\pi$
$149$	−9.67696	−0.792768	−0.396384	+	0.918085i	$0.629735\pi$
$150$	15.9070	1.29880
$151$	2.27725	0.185320	0.0926599	−	0.995698i	$-0.470463\pi$
$151$	2.27725	0.185320	0.0926599	+	0.995698i	$0.470463\pi$
$152$	41.3178	3.35131
$153$	−14.5220	−1.17403
$154$	−0.192003	−0.0154720
$155$	−10.9579	−0.880163
$156$	−38.7468	−3.10223
$157$	12.9208	1.03119	0.515595	−	0.856832i	$-0.327571\pi$
$157$	12.9208	1.03119	0.515595	+	0.856832i	$0.327571\pi$
$158$	36.3421	2.89123
$159$	24.9502	1.97868
$160$	−43.3549	−3.42750
$161$	1.57619	0.124221
$162$	27.7805	2.18264
$163$	−14.9061	−1.16754	−0.583768	−	0.811920i	$-0.698422\pi$
$163$	−14.9061	−1.16754	−0.583768	+	0.811920i	$0.698422\pi$
$164$	16.2059	1.26547
$165$	0.352224	0.0274206
$166$	−31.0429	−2.40940
$167$	−1.82946	−0.141568	−0.0707839	−	0.997492i	$-0.522550\pi$
$167$	−1.82946	−0.141568	−0.0707839	+	0.997492i	$0.522550\pi$
$168$	−18.2139	−1.40523
$169$	−4.78174	−0.367827
$170$	24.7730	1.90000
$171$	−10.5051	−0.803341
$172$	−61.6845	−4.70340
$173$	−16.2037	−1.23194	−0.615972	−	0.787768i	$-0.711237\pi$
$173$	−16.2037	−1.23194	−0.615972	+	0.787768i	$0.711237\pi$
$174$	−6.57673	−0.498580
$175$	−1.80827	−0.136693
$176$	1.58499	0.119473
$177$	24.2942	1.82607
$178$	26.8159	2.00993
$179$	−22.2686	−1.66443	−0.832215	−	0.554453i	$-0.812928\pi$
$179$	−22.2686	−1.66443	−0.832215	+	0.554453i	$0.812928\pi$
$180$	23.9584	1.78576
$181$	2.72614	0.202632	0.101316	−	0.994854i	$-0.467695\pi$
$181$	2.72614	0.202632	0.101316	+	0.994854i	$0.467695\pi$
$182$	5.94898	0.440968
$183$	−5.75994	−0.425787
$184$	−21.6769	−1.59804
$185$	−3.83148	−0.281696
$186$	44.8557	3.28898
$187$	−0.513981	−0.0375860
$188$	5.38882	0.393020
$189$	−0.683468	−0.0497150
$190$	17.9205	1.30009
$191$	10.7473	0.777649	0.388825	−	0.921312i	$-0.372881\pi$
$191$	10.7473	0.777649	0.388825	+	0.921312i	$0.372881\pi$
$192$	96.2919	6.94927
$193$	17.3390	1.24809	0.624043	−	0.781390i	$-0.285489\pi$
$193$	17.3390	1.24809	0.624043	+	0.781390i	$0.285489\pi$
$194$	17.2503	1.23850
$195$	−10.9132	−0.781514
$196$	−36.7417	−2.62441
$197$	−19.5444	−1.39248	−0.696242	−	0.717807i	$-0.745146\pi$
$197$	−19.5444	−1.39248	−0.696242	+	0.717807i	$0.745146\pi$
$198$	−0.671362	−0.0477116
$199$	−14.5866	−1.03401	−0.517007	−	0.855981i	$-0.672954\pi$
$199$	−14.5866	−1.03401	−0.517007	+	0.855981i	$0.672954\pi$
$200$	24.8686	1.75848
$201$	16.4647	1.16133
$202$	6.75751	0.475457
$203$	0.747628	0.0524732
$204$	−75.0822	−5.25681
$205$	4.56448	0.318797
$206$	−22.7518	−1.58519
$207$	5.51135	0.383065
$208$	−49.1088	−3.40508
$209$	−0.371808	−0.0257185
$210$	−7.89981	−0.545139
$211$	21.5467	1.48334	0.741670	−	0.670765i	$-0.234034\pi$
$211$	21.5467	1.48334	0.741670	+	0.670765i	$0.234034\pi$
$212$	60.0668	4.12541
$213$	−27.0175	−1.85121
$214$	−18.1120	−1.23811
$215$	−17.3738	−1.18488
$216$	9.39952	0.639556
$217$	−5.09910	−0.346150
$218$	48.7527	3.30195
$219$	20.0770	1.35668
$220$	0.847967	0.0571700
$221$	15.9251	1.07124
$222$	15.6839	1.05264
$223$	10.8981	0.729793	0.364897	−	0.931048i	$-0.381104\pi$
$223$	10.8981	0.729793	0.364897	+	0.931048i	$0.381104\pi$
$224$	−20.1745	−1.34797
$225$	−6.32285	−0.421524
$226$	−6.87365	−0.457229
$227$	7.73219	0.513204	0.256602	−	0.966517i	$-0.417397\pi$
$227$	7.73219	0.513204	0.256602	+	0.966517i	$0.417397\pi$
$228$	−54.3137	−3.59701
$229$	17.1388	1.13257	0.566283	−	0.824211i	$-0.308381\pi$
$229$	17.1388	1.13257	0.566283	+	0.824211i	$0.308381\pi$
$230$	−9.40179	−0.619936
$231$	0.163902	0.0107840
$232$	−10.2819	−0.675040
$233$	17.2865	1.13248	0.566239	−	0.824241i	$-0.308398\pi$
$233$	17.2865	1.13248	0.566239	+	0.824241i	$0.308398\pi$
$234$	20.8013	1.35983
$235$	1.51779	0.0990097
$236$	58.4875	3.80721
$237$	−31.0232	−2.01517
$238$	11.5277	0.747232
$239$	15.8610	1.02596	0.512982	−	0.858399i	$-0.328541\pi$
$239$	15.8610	1.02596	0.512982	+	0.858399i	$0.328541\pi$
$240$	65.2129	4.20948
$241$	17.0576	1.09878	0.549390	−	0.835566i	$-0.314860\pi$
$241$	17.0576	1.09878	0.549390	+	0.835566i	$0.314860\pi$
$242$	30.5085	1.96116
$243$	−20.9721	−1.34536
$244$	−13.8669	−0.887734
$245$	−10.3485	−0.661142
$246$	−18.6844	−1.19128
$247$	11.5200	0.733001
$248$	70.1264	4.45303
$249$	26.4995	1.67934
$250$	33.0837	2.09240
$251$	−14.8299	−0.936055	−0.468027	−	0.883714i	$-0.655035\pi$
$251$	−14.8299	−0.936055	−0.468027	+	0.883714i	$0.655035\pi$
$252$	11.1487	0.702301
$253$	0.195065	0.0122636
$254$	20.3011	1.27380
$255$	−21.1473	−1.32430
$256$	82.0186	5.12616
$257$	22.1852	1.38387	0.691937	−	0.721958i	$-0.256758\pi$
$257$	22.1852	1.38387	0.691937	+	0.721958i	$0.256758\pi$
$258$	71.1185	4.42765
$259$	−1.78292	−0.110785
$260$	−26.2732	−1.62940
$261$	2.61418	0.161813
$262$	25.5109	1.57607
$263$	−17.4605	−1.07666	−0.538331	−	0.842733i	$-0.680945\pi$
$263$	−17.4605	−1.07666	−0.538331	+	0.842733i	$0.680945\pi$
$264$	−2.25409	−0.138730
$265$	16.9182	1.03927
$266$	8.33904	0.511299
$267$	−22.8912	−1.40092
$268$	39.6381	2.42128
$269$	−7.21395	−0.439843	−0.219921	−	0.975518i	$-0.570580\pi$
$269$	−7.21395	−0.439843	−0.219921	+	0.975518i	$0.570580\pi$
$270$	4.07680	0.248106
$271$	18.2301	1.10740	0.553700	−	0.832716i	$-0.313215\pi$
$271$	18.2301	1.10740	0.553700	+	0.832716i	$0.313215\pi$
$272$	−95.1615	−5.77001
$273$	−5.07830	−0.307353
$274$	−38.2599	−2.31137
$275$	−0.223786	−0.0134948
$276$	28.4950	1.71520
$277$	7.40761	0.445080	0.222540	−	0.974924i	$-0.428565\pi$
$277$	7.40761	0.445080	0.222540	+	0.974924i	$0.428565\pi$
$278$	−2.77566	−0.166473
$279$	−17.8296	−1.06743
$280$	−12.3504	−0.738076
$281$	−3.90604	−0.233015	−0.116507	−	0.993190i	$-0.537170\pi$
$281$	−3.90604	−0.233015	−0.116507	+	0.993190i	$0.537170\pi$
$282$	−6.21299	−0.369978
$283$	7.92854	0.471303	0.235651	−	0.971838i	$-0.424278\pi$
$283$	7.92854	0.471303	0.235651	+	0.971838i	$0.424278\pi$
$284$	−65.0436	−3.85963
$285$	−15.2977	−0.906160
$286$	0.736227	0.0435340
$287$	2.12401	0.125376
$288$	−70.5427	−4.15677
$289$	13.8590	0.815238
$290$	−4.45952	−0.261872
$291$	−14.7256	−0.863230
$292$	48.3347	2.82858
$293$	27.7439	1.62082	0.810409	−	0.585865i	$-0.199245\pi$
$293$	27.7439	1.62082	0.810409	+	0.585865i	$0.199245\pi$
$294$	42.3610	2.47055
$295$	16.4733	0.959114
$296$	24.5199	1.42519
$297$	−0.0845839	−0.00490805
$298$	26.8600	1.55596
$299$	−6.04384	−0.349524
$300$	−32.6907	−1.88740
$301$	−8.08461	−0.465989
$302$	−6.32088	−0.363726
$303$	−5.76850	−0.331392
$304$	−68.8388	−3.94818
$305$	−3.90567	−0.223638
$306$	40.3081	2.30426
$307$	−11.8565	−0.676688	−0.338344	−	0.941022i	$-0.609867\pi$
$307$	−11.8565	−0.676688	−0.338344	+	0.941022i	$0.609867\pi$
$308$	0.394588	0.0224837
$309$	19.4219	1.10487
$310$	30.4155	1.72749
$311$	26.0104	1.47492	0.737458	−	0.675393i	$-0.236026\pi$
$311$	26.0104	1.47492	0.737458	+	0.675393i	$0.236026\pi$
$312$	69.8403	3.95393
$313$	0.437104	0.0247066	0.0123533	−	0.999924i	$-0.496068\pi$
$313$	0.437104	0.0247066	0.0123533	+	0.999924i	$0.496068\pi$
$314$	−35.8637	−2.02391
$315$	3.14009	0.176924
$316$	−74.6873	−4.20149
$317$	19.3099	1.08455	0.542277	−	0.840200i	$-0.317562\pi$
$317$	19.3099	1.08455	0.542277	+	0.840200i	$0.317562\pi$
$318$	−69.2535	−3.88354
$319$	0.0925242	0.00518036
$320$	65.2932	3.65000
$321$	15.4611	0.862957
$322$	−4.37497	−0.243808
$323$	22.3231	1.24209
$324$	−57.0922	−3.17179
$325$	6.93375	0.384615
$326$	41.3743	2.29151
$327$	−41.6174	−2.30145
$328$	−29.2108	−1.61290
$329$	0.706279	0.0389384
$330$	−0.977656	−0.0538182
$331$	12.1698	0.668913	0.334457	−	0.942411i	$-0.391447\pi$
$331$	12.1698	0.668913	0.334457	+	0.942411i	$0.391447\pi$
$332$	63.7967	3.50130
$333$	−6.23419	−0.341631
$334$	5.07796	0.277854
$335$	11.1643	0.609970
$336$	30.3458	1.65550
$337$	−22.7266	−1.23800	−0.618998	−	0.785393i	$-0.712461\pi$
$337$	−22.7266	−1.23800	−0.618998	+	0.785393i	$0.712461\pi$
$338$	13.2725	0.721930
$339$	5.86765	0.318687
$340$	−50.9114	−2.76106
$341$	−0.631049	−0.0341732
$342$	29.1585	1.57671
$343$	−10.0489	−0.542590
$344$	111.185	5.99470
$345$	8.02578	0.432093
$346$	44.9760	2.41793
$347$	−12.8714	−0.690972	−0.345486	−	0.938424i	$-0.612286\pi$
$347$	−12.8714	−0.690972	−0.345486	+	0.938424i	$0.612286\pi$
$348$	13.5159	0.724530
$349$	−30.7313	−1.64501	−0.822504	−	0.568760i	$-0.807423\pi$
$349$	−30.7313	−1.64501	−0.822504	+	0.568760i	$0.807423\pi$
$350$	5.01916	0.268285
$351$	2.62073	0.139884
$352$	−2.49673	−0.133076
$353$	−12.4132	−0.660689	−0.330345	−	0.943860i	$-0.607165\pi$
$353$	−12.4132	−0.660689	−0.330345	+	0.943860i	$0.607165\pi$
$354$	−67.4326	−3.58400
$355$	−18.3199	−0.972319
$356$	−55.1096	−2.92081
$357$	−9.84057	−0.520818
$358$	61.8100	3.26676
$359$	9.36458	0.494244	0.247122	−	0.968984i	$-0.420515\pi$
$359$	9.36458	0.494244	0.247122	+	0.968984i	$0.420515\pi$
$360$	−43.1846	−2.27603
$361$	−2.85170	−0.150089
$362$	−7.56684	−0.397704
$363$	−26.0434	−1.36692
$364$	−12.2258	−0.640808
$365$	13.6137	0.712576
$366$	15.9877	0.835688
$367$	−35.5630	−1.85638	−0.928188	−	0.372112i	$-0.878634\pi$
$367$	−35.5630	−1.85638	−0.928188	+	0.372112i	$0.878634\pi$
$368$	36.1154	1.88265
$369$	7.42686	0.386627
$370$	10.6349	0.552881
$371$	7.87259	0.408725
$372$	−92.1836	−4.77950
$373$	−3.76740	−0.195068	−0.0975342	−	0.995232i	$-0.531096\pi$
$373$	−3.76740	−0.195068	−0.0975342	+	0.995232i	$0.531096\pi$
$374$	1.42664	0.0737696
$375$	−28.2417	−1.45839
$376$	−9.71324	−0.500922
$377$	−2.86675	−0.147645
$378$	1.89708	0.0975750
$379$	−12.8082	−0.657911	−0.328956	−	0.944345i	$-0.606697\pi$
$379$	−12.8082	−0.657911	−0.328956	+	0.944345i	$0.606697\pi$
$380$	−36.8288	−1.88928
$381$	−17.3299	−0.887836
$382$	−29.8310	−1.52628
$383$	−33.1230	−1.69251	−0.846253	−	0.532782i	$-0.821147\pi$
$383$	−33.1230	−1.69251	−0.846253	+	0.532782i	$0.821147\pi$
$384$	−139.398	−7.11360
$385$	0.111138	0.00566411
$386$	−48.1271	−2.44961
$387$	−28.2688	−1.43699
$388$	−35.4513	−1.79977
$389$	5.48144	0.277920	0.138960	−	0.990298i	$-0.455624\pi$
$389$	5.48144	0.277920	0.138960	+	0.990298i	$0.455624\pi$
$390$	30.2915	1.53387
$391$	−11.7115	−0.592278
$392$	66.2263	3.34493
$393$	−21.7772	−1.09852
$394$	54.2488	2.73301
$395$	−21.0361	−1.05844
$396$	1.37973	0.0693339
$397$	−4.86442	−0.244138	−0.122069	−	0.992522i	$-0.538953\pi$
$397$	−4.86442	−0.244138	−0.122069	+	0.992522i	$0.538953\pi$
$398$	40.4874	2.02945
$399$	−7.11856	−0.356374
$400$	−41.4332	−2.07166
$401$	33.4309	1.66946	0.834729	−	0.550660i	$-0.185624\pi$
$401$	33.4309	1.66946	0.834729	+	0.550660i	$0.185624\pi$
$402$	−45.7003	−2.27933
$403$	19.5523	0.973969
$404$	−13.8875	−0.690927
$405$	−16.0803	−0.799038
$406$	−2.07516	−0.102989
$407$	−0.220648	−0.0109371
$408$	135.334	6.70005
$409$	3.73824	0.184844	0.0924221	−	0.995720i	$-0.470539\pi$
$409$	3.73824	0.184844	0.0924221	+	0.995720i	$0.470539\pi$
$410$	−12.6695	−0.625700
$411$	32.6603	1.61101
$412$	46.7575	2.30358
$413$	7.66560	0.377200
$414$	−15.2976	−0.751838
$415$	17.9687	0.882048
$416$	77.3583	3.79280
$417$	2.36943	0.116031
$418$	1.03201	0.0504774
$419$	−21.1745	−1.03444	−0.517220	−	0.855852i	$-0.673033\pi$
$419$	−21.1745	−1.03444	−0.517220	+	0.855852i	$0.673033\pi$
$420$	16.2350	0.792187
$421$	23.5578	1.14814	0.574068	−	0.818808i	$-0.305364\pi$
$421$	23.5578	1.14814	0.574068	+	0.818808i	$0.305364\pi$
$422$	−59.8065	−2.91134
$423$	2.46959	0.120076
$424$	−108.269	−5.25802
$425$	13.4360	0.651741
$426$	74.9915	3.63335
$427$	−1.81744	−0.0879522
$428$	37.2221	1.79920
$429$	−0.628475	−0.0303431
$430$	48.2237	2.32555
$431$	10.9763	0.528709	0.264355	−	0.964426i	$-0.414841\pi$
$431$	10.9763	0.528709	0.264355	+	0.964426i	$0.414841\pi$
$432$	−15.6604	−0.753460
$433$	14.1551	0.680250	0.340125	−	0.940380i	$-0.389531\pi$
$433$	14.1551	0.680250	0.340125	+	0.940380i	$0.389531\pi$
$434$	14.1534	0.679384
$435$	3.80683	0.182524
$436$	−100.192	−4.79834
$437$	−8.47201	−0.405271
$438$	−55.7271	−2.66274
$439$	−27.0935	−1.29310	−0.646551	−	0.762870i	$-0.723789\pi$
$439$	−27.0935	−1.29310	−0.646551	+	0.762870i	$0.723789\pi$
$440$	−1.52845	−0.0728658
$441$	−16.8380	−0.801812
$442$	−44.2026	−2.10250
$443$	1.97241	0.0937120	0.0468560	−	0.998902i	$-0.485080\pi$
$443$	1.97241	0.0937120	0.0468560	+	0.998902i	$0.485080\pi$
$444$	−32.2323	−1.52968
$445$	−15.5219	−0.735810
$446$	−30.2496	−1.43236
$447$	−22.9288	−1.08450
$448$	30.3831	1.43547
$449$	−16.0124	−0.755670	−0.377835	−	0.925873i	$-0.623331\pi$
$449$	−16.0124	−0.755670	−0.377835	+	0.925873i	$0.623331\pi$
$450$	17.5501	0.827320
$451$	0.262861	0.0123776
$452$	14.1261	0.664438
$453$	5.39577	0.253515
$454$	−21.4620	−1.00726
$455$	−3.44347	−0.161432
$456$	97.8994	4.58456
$457$	24.9586	1.16751	0.583756	−	0.811929i	$-0.301582\pi$
$457$	24.9586	1.16751	0.583756	+	0.811929i	$0.301582\pi$
$458$	−47.5716	−2.22288
$459$	5.07836	0.237037
$460$	19.3218	0.900882
$461$	−0.577494	−0.0268966	−0.0134483	−	0.999910i	$-0.504281\pi$
$461$	−0.577494	−0.0268966	−0.0134483	+	0.999910i	$0.504281\pi$
$462$	−0.454937	−0.0211656
$463$	29.4353	1.36798	0.683988	−	0.729493i	$-0.260244\pi$
$463$	29.4353	1.36798	0.683988	+	0.729493i	$0.260244\pi$
$464$	17.1305	0.795263
$465$	−25.9640	−1.20405
$466$	−47.9816	−2.22270
$467$	10.6955	0.494931	0.247465	−	0.968897i	$-0.420402\pi$
$467$	10.6955	0.494931	0.247465	+	0.968897i	$0.420402\pi$
$468$	−42.7491	−1.97608
$469$	5.19512	0.239888
$470$	−4.21287	−0.194325
$471$	30.6148	1.41066
$472$	−105.423	−4.85247
$473$	−1.00053	−0.0460042
$474$	86.1100	3.95516
$475$	9.71945	0.445959
$476$	−23.6908	−1.08587
$477$	27.5275	1.26040
$478$	−44.0249	−2.01365
$479$	5.03562	0.230083	0.115042	−	0.993361i	$-0.463300\pi$
$479$	5.03562	0.230083	0.115042	+	0.993361i	$0.463300\pi$
$480$	−102.726	−4.68879
$481$	6.83652	0.311718
$482$	−47.3463	−2.15656
$483$	3.73467	0.169933
$484$	−62.6985	−2.84993
$485$	−9.98506	−0.453398
$486$	58.2115	2.64053
$487$	0.415383	0.0188228	0.00941140	−	0.999956i	$-0.497004\pi$
$487$	0.415383	0.0188228	0.00941140	+	0.999956i	$0.497004\pi$
$488$	24.9947	1.13146
$489$	−35.3189	−1.59718
$490$	28.7240	1.29762
$491$	−6.34691	−0.286432	−0.143216	−	0.989691i	$-0.545744\pi$
$491$	−6.34691	−0.286432	−0.143216	+	0.989691i	$0.545744\pi$
$492$	38.3986	1.73114
$493$	−5.55509	−0.250189
$494$	−31.9757	−1.43865
$495$	0.388608	0.0174666
$496$	−116.836	−5.24610
$497$	−8.52487	−0.382393
$498$	−73.5538	−3.29603
$499$	−3.69224	−0.165287	−0.0826436	−	0.996579i	$-0.526336\pi$
$499$	−3.69224	−0.165287	−0.0826436	+	0.996579i	$0.526336\pi$
$500$	−67.9908	−3.04064
$501$	−4.33477	−0.193663
$502$	41.1628	1.83719
$503$	−33.1485	−1.47802	−0.739009	−	0.673695i	$-0.764706\pi$
$503$	−33.1485	−1.47802	−0.739009	+	0.673695i	$0.764706\pi$
$504$	−20.0953	−0.895115
$505$	−3.91148	−0.174059
$506$	−0.541434	−0.0240697
$507$	−11.3300	−0.503182
$508$	−41.7210	−1.85107
$509$	−22.8008	−1.01063	−0.505313	−	0.862936i	$-0.668623\pi$
$509$	−22.8008	−1.01063	−0.505313	+	0.862936i	$0.668623\pi$
$510$	58.6978	2.59918
$511$	6.33494	0.280241
$512$	−109.992	−4.86102
$513$	3.67363	0.162195
$514$	−61.5786	−2.71612
$515$	13.1695	0.580318
$516$	−146.157	−6.43419
$517$	0.0874070	0.00384415
$518$	4.94877	0.217437
$519$	−38.3935	−1.68529
$520$	47.3570	2.07674
$521$	11.0941	0.486042	0.243021	−	0.970021i	$-0.421862\pi$
$521$	11.0941	0.486042	0.243021	+	0.970021i	$0.421862\pi$
$522$	−7.25607	−0.317590
$523$	15.4695	0.676433	0.338216	−	0.941068i	$-0.390176\pi$
$523$	15.4695	0.676433	0.338216	+	0.941068i	$0.390176\pi$
$524$	−52.4279	−2.29032
$525$	−4.28457	−0.186994
$526$	48.4645	2.11315
$527$	37.8878	1.65042
$528$	3.75550	0.163437
$529$	−18.5553	−0.806751
$530$	−46.9591	−2.03977
$531$	26.8037	1.16318
$532$	−17.1377	−0.743013
$533$	−8.14442	−0.352774
$534$	63.5382	2.74956
$535$	10.4838	0.453255
$536$	−71.4469	−3.08603
$537$	−52.7637	−2.27692
$538$	20.0235	0.863275
$539$	−0.595953	−0.0256695
$540$	−8.37830	−0.360545
$541$	−12.9905	−0.558506	−0.279253	−	0.960218i	$-0.590087\pi$
$541$	−12.9905	−0.558506	−0.279253	+	0.960218i	$0.590087\pi$
$542$	−50.6007	−2.17348
$543$	6.45938	0.277199
$544$	149.902	6.42701
$545$	−28.2197	−1.20880
$546$	14.0957	0.603239
$547$	25.8782	1.10647	0.553236	−	0.833025i	$-0.313393\pi$
$547$	25.8782	1.10647	0.553236	+	0.833025i	$0.313393\pi$
$548$	78.6285	3.35884
$549$	−6.35492	−0.271221
$550$	0.621156	0.0264862
$551$	−4.01849	−0.171194
$552$	−51.3617	−2.18610
$553$	−9.78880	−0.416262
$554$	−20.5610	−0.873554
$555$	−9.07839	−0.385356
$556$	5.70431	0.241916
$557$	39.2529	1.66320	0.831600	−	0.555375i	$-0.187425\pi$
$557$	39.2529	1.66320	0.831600	+	0.555375i	$0.187425\pi$
$558$	49.4891	2.09504
$559$	31.0001	1.31116
$560$	20.5767	0.869526
$561$	−1.21784	−0.0514172
$562$	10.8419	0.457336
$563$	7.53609	0.317608	0.158804	−	0.987310i	$-0.449236\pi$
$563$	7.53609	0.317608	0.158804	+	0.987310i	$0.449236\pi$
$564$	12.7684	0.537647
$565$	3.97871	0.167385
$566$	−22.0070	−0.925021
$567$	−7.48272	−0.314245
$568$	117.240	4.91928
$569$	0.967099	0.0405429	0.0202715	−	0.999795i	$-0.493547\pi$
$569$	0.967099	0.0405429	0.0202715	+	0.999795i	$0.493547\pi$
$570$	42.4614	1.77851
$571$	6.79106	0.284197	0.142098	−	0.989853i	$-0.454615\pi$
$571$	6.79106	0.284197	0.142098	+	0.989853i	$0.454615\pi$
$572$	−1.51303	−0.0632630
$573$	25.4650	1.06382
$574$	−5.89553	−0.246075
$575$	−5.09919	−0.212651
$576$	106.238	4.42660
$577$	3.99590	0.166351	0.0831757	−	0.996535i	$-0.473494\pi$
$577$	3.99590	0.166351	0.0831757	+	0.996535i	$0.473494\pi$
$578$	−38.4681	−1.60006
$579$	41.0834	1.70737
$580$	9.16482	0.380548
$581$	8.36144	0.346891
$582$	40.8733	1.69425
$583$	0.974288	0.0403509
$584$	−87.1225	−3.60515
$585$	−12.0405	−0.497815
$586$	−77.0078	−3.18116
$587$	−37.9215	−1.56519	−0.782594	−	0.622532i	$-0.786104\pi$
$587$	−37.9215	−1.56519	−0.782594	+	0.622532i	$0.786104\pi$
$588$	−87.0568	−3.59016
$589$	27.4076	1.12931
$590$	−45.7244	−1.88244
$591$	−46.3091	−1.90490
$592$	−40.8521	−1.67901
$593$	44.1295	1.81218	0.906090	−	0.423085i	$-0.139053\pi$
$593$	44.1295	1.81218	0.906090	+	0.423085i	$0.139053\pi$
$594$	0.234776	0.00963299
$595$	−6.67265	−0.273552
$596$	−55.2003	−2.26109
$597$	−34.5618	−1.41452
$598$	16.7757	0.686008
$599$	23.8077	0.972757	0.486379	−	0.873748i	$-0.338318\pi$
$599$	23.8077	0.972757	0.486379	+	0.873748i	$0.338318\pi$
$600$	58.9244	2.40558
$601$	−2.06120	−0.0840781	−0.0420391	−	0.999116i	$-0.513385\pi$
$601$	−2.06120	−0.0840781	−0.0420391	+	0.999116i	$0.513385\pi$
$602$	22.4401	0.914592
$603$	18.1654	0.739752
$604$	12.9901	0.528561
$605$	−17.6594	−0.717956
$606$	16.0114	0.650420
$607$	12.0138	0.487624	0.243812	−	0.969822i	$-0.421602\pi$
$607$	12.0138	0.487624	0.243812	+	0.969822i	$0.421602\pi$
$608$	108.438	4.39773
$609$	1.77145	0.0717828
$610$	10.8408	0.438933
$611$	−2.70820	−0.109562
$612$	−82.8379	−3.34852
$613$	2.55995	0.103395	0.0516977	−	0.998663i	$-0.483537\pi$
$613$	2.55995	0.103395	0.0516977	+	0.998663i	$0.483537\pi$
$614$	32.9097	1.32813
$615$	10.8152	0.436111
$616$	−0.711238	−0.0286566
$617$	−18.7683	−0.755583	−0.377791	−	0.925891i	$-0.623316\pi$
$617$	−18.7683	−0.755583	−0.377791	+	0.925891i	$0.623316\pi$
$618$	−53.9087	−2.16853
$619$	36.4190	1.46380	0.731902	−	0.681409i	$-0.238633\pi$
$619$	36.4190	1.46380	0.731902	+	0.681409i	$0.238633\pi$
$620$	−62.5074	−2.51036
$621$	−1.92733	−0.0773409
$622$	−72.1962	−2.89480
$623$	−7.22288	−0.289379
$624$	−116.360	−4.65812
$625$	−7.05660	−0.282264
$626$	−1.21325	−0.0484913
$627$	−0.880971	−0.0351826
$628$	73.7040	2.94111
$629$	13.2476	0.528215
$630$	−8.71582	−0.347247
$631$	14.9740	0.596105	0.298053	−	0.954549i	$-0.403663\pi$
$631$	14.9740	0.596105	0.298053	+	0.954549i	$0.403663\pi$
$632$	134.622	5.35499
$633$	51.0534	2.02919
$634$	−53.5979	−2.12864
$635$	−11.7510	−0.466322
$636$	142.324	5.64351
$637$	18.4649	0.731605
$638$	−0.256816	−0.0101674
$639$	−29.8083	−1.17920
$640$	−94.5221	−3.73631
$641$	4.40277	0.173899	0.0869496	−	0.996213i	$-0.472288\pi$
$641$	4.40277	0.173899	0.0869496	+	0.996213i	$0.472288\pi$
$642$	−42.9149	−1.69372
$643$	−24.0010	−0.946507	−0.473253	−	0.880926i	$-0.656920\pi$
$643$	−24.0010	−0.946507	−0.473253	+	0.880926i	$0.656920\pi$
$644$	8.99107	0.354298
$645$	−41.1658	−1.62090
$646$	−61.9614	−2.43784
$647$	−32.7735	−1.28846	−0.644230	−	0.764831i	$-0.722822\pi$
$647$	−32.7735	−1.28846	−0.644230	+	0.764831i	$0.722822\pi$
$648$	102.908	4.04259
$649$	0.948671	0.0372386
$650$	−19.2457	−0.754880
$651$	−12.0819	−0.473529
$652$	−85.0290	−3.32999
$653$	−41.6807	−1.63109	−0.815547	−	0.578691i	$-0.803564\pi$
$653$	−41.6807	−1.63109	−0.815547	+	0.578691i	$0.803564\pi$
$654$	115.516	4.51702
$655$	−14.7666	−0.576979
$656$	48.6676	1.90015
$657$	22.1509	0.864189
$658$	−1.96039	−0.0764241
$659$	25.9432	1.01060	0.505301	−	0.862943i	$-0.331381\pi$
$659$	25.9432	1.01060	0.505301	+	0.862943i	$0.331381\pi$
$660$	2.00920	0.0782078
$661$	−19.5529	−0.760519	−0.380259	−	0.924880i	$-0.624165\pi$
$661$	−19.5529	−0.760519	−0.380259	+	0.924880i	$0.624165\pi$
$662$	−33.7793	−1.31287
$663$	37.7332	1.46544
$664$	−114.992	−4.46257
$665$	−4.82692	−0.187180
$666$	17.3040	0.670517
$667$	2.10825	0.0816319
$668$	−10.4358	−0.403773
$669$	25.8223	0.998348
$670$	−30.9883	−1.19718
$671$	−0.224921	−0.00868299
$672$	−47.8020	−1.84400
$673$	−47.1509	−1.81753	−0.908767	−	0.417303i	$-0.862975\pi$
$673$	−47.1509	−1.81753	−0.908767	+	0.417303i	$0.862975\pi$
$674$	63.0813	2.42980
$675$	2.21111	0.0851057
$676$	−27.2765	−1.04910
$677$	12.8438	0.493628	0.246814	−	0.969063i	$-0.420616\pi$
$677$	12.8438	0.493628	0.246814	+	0.969063i	$0.420616\pi$
$678$	−16.2866	−0.625483
$679$	−4.64639	−0.178312
$680$	91.7668	3.51910
$681$	18.3209	0.702057
$682$	1.75158	0.0670715
$683$	24.8016	0.949007	0.474503	−	0.880254i	$-0.342628\pi$
$683$	24.8016	0.949007	0.474503	+	0.880254i	$0.342628\pi$
$684$	−59.9240	−2.29125
$685$	22.1462	0.846161
$686$	27.8924	1.06494
$687$	40.6092	1.54934
$688$	−185.243	−7.06234
$689$	−30.1871	−1.15004
$690$	−22.2768	−0.848065
$691$	−28.3376	−1.07801	−0.539007	−	0.842302i	$-0.681200\pi$
$691$	−28.3376	−1.07801	−0.539007	+	0.842302i	$0.681200\pi$
$692$	−92.4309	−3.51370
$693$	0.180832	0.00686925
$694$	35.7266	1.35616
$695$	1.60665	0.0609437
$696$	−24.3622	−0.923447
$697$	−15.7820	−0.597785
$698$	85.2997	3.22864
$699$	40.9591	1.54922
$700$	−10.3149	−0.389868
$701$	−27.1089	−1.02389	−0.511945	−	0.859018i	$-0.671075\pi$
$701$	−27.1089	−1.02389	−0.511945	+	0.859018i	$0.671075\pi$
$702$	−7.27426	−0.274549
$703$	9.58315	0.361435
$704$	3.76012	0.141715
$705$	3.59629	0.135444
$706$	34.4549	1.29673
$707$	−1.82014	−0.0684536
$708$	138.582	5.20822
$709$	−15.1906	−0.570496	−0.285248	−	0.958454i	$-0.592076\pi$
$709$	−15.1906	−0.570496	−0.285248	+	0.958454i	$0.592076\pi$
$710$	50.8499	1.90836
$711$	−34.2278	−1.28364
$712$	99.3341	3.72270
$713$	−14.3791	−0.538500
$714$	27.3141	1.02220
$715$	−0.426154	−0.0159372
$716$	−127.027	−4.74721
$717$	37.5815	1.40351
$718$	−25.9929	−0.970047
$719$	−8.45304	−0.315245	−0.157623	−	0.987499i	$-0.550383\pi$
$719$	−8.45304	−0.315245	−0.157623	+	0.987499i	$0.550383\pi$
$720$	71.9491	2.68139
$721$	6.12823	0.228227
$722$	7.91536	0.294579
$723$	40.4168	1.50312
$724$	15.5507	0.577938
$725$	−2.41868	−0.0898275
$726$	72.2877	2.68285
$727$	−7.85112	−0.291182	−0.145591	−	0.989345i	$-0.546508\pi$
$727$	−7.85112	−0.291182	−0.145591	+	0.989345i	$0.546508\pi$
$728$	22.0368	0.816739
$729$	−19.6660	−0.728371
$730$	−37.7872	−1.39857
$731$	60.0709	2.22180
$732$	−32.8565	−1.21441
$733$	−12.4867	−0.461208	−0.230604	−	0.973048i	$-0.574070\pi$
$733$	−12.4867	−0.461208	−0.230604	+	0.973048i	$0.574070\pi$
$734$	98.7110	3.64349
$735$	−24.5200	−0.904435
$736$	−56.8905	−2.09701
$737$	0.642932	0.0236827
$738$	−20.6144	−0.758828
$739$	−23.7965	−0.875368	−0.437684	−	0.899129i	$-0.644201\pi$
$739$	−23.7965	−0.875368	−0.437684	+	0.899129i	$0.644201\pi$
$740$	−21.8559	−0.803439
$741$	27.2958	1.00274
$742$	−21.8517	−0.802200
$743$	37.0279	1.35842	0.679211	−	0.733943i	$-0.262322\pi$
$743$	37.0279	1.35842	0.679211	+	0.733943i	$0.262322\pi$
$744$	166.159	6.09169
$745$	−15.5475	−0.569616
$746$	10.4570	0.382859
$747$	29.2368	1.06972
$748$	−2.93190	−0.107201
$749$	4.87848	0.178256
$750$	78.3894	2.86238
$751$	−26.1080	−0.952696	−0.476348	−	0.879257i	$-0.658040\pi$
$751$	−26.1080	−0.952696	−0.476348	+	0.879257i	$0.658040\pi$
$752$	16.1831	0.590135
$753$	−35.1383	−1.28051
$754$	7.95713	0.289782
$755$	3.65874	0.133155
$756$	−3.89871	−0.141795
$757$	33.7444	1.22646	0.613231	−	0.789903i	$-0.289869\pi$
$757$	33.7444	1.22646	0.613231	+	0.789903i	$0.289869\pi$
$758$	35.5512	1.29128
$759$	0.462191	0.0167765
$760$	66.3832	2.40797
$761$	−35.5875	−1.29005	−0.645023	−	0.764163i	$-0.723152\pi$
$761$	−35.5875	−1.29005	−0.645023	+	0.764163i	$0.723152\pi$
$762$	48.1019	1.74255
$763$	−13.1316	−0.475396
$764$	61.3060	2.21797
$765$	−23.3317	−0.843561
$766$	91.9383	3.32186
$767$	−29.3934	−1.06134
$768$	194.337	7.01253
$769$	−21.8103	−0.786500	−0.393250	−	0.919432i	$-0.628649\pi$
$769$	−21.8103	−0.786500	−0.393250	+	0.919432i	$0.628649\pi$
$770$	−0.308481	−0.0111169
$771$	52.5661	1.89312
$772$	98.9067	3.55973
$773$	−24.6784	−0.887621	−0.443811	−	0.896121i	$-0.646374\pi$
$773$	−24.6784	−0.887621	−0.443811	+	0.896121i	$0.646374\pi$
$774$	78.4648	2.82036
$775$	16.4963	0.592564
$776$	63.9004	2.29389
$777$	−4.22449	−0.151553
$778$	−15.2146	−0.545471
$779$	−11.4165	−0.409039
$780$	−62.2525	−2.22900
$781$	−1.05501	−0.0377513
$782$	32.5073	1.16246
$783$	−0.914181	−0.0326702
$784$	−110.338	−3.94066
$785$	20.7591	0.740926
$786$	60.4462	2.15605
$787$	35.1547	1.25313	0.626564	−	0.779370i	$-0.284461\pi$
$787$	35.1547	1.25313	0.626564	+	0.779370i	$0.284461\pi$
$788$	−111.487	−3.97158
$789$	−41.3714	−1.47286
$790$	58.3891	2.07739
$791$	1.85143	0.0658292
$792$	−2.48693	−0.0883693
$793$	6.96891	0.247473
$794$	13.5020	0.479168
$795$	40.0863	1.42171
$796$	−83.2062	−2.94917
$797$	5.85110	0.207257	0.103628	−	0.994616i	$-0.466955\pi$
$797$	5.85110	0.207257	0.103628	+	0.994616i	$0.466955\pi$
$798$	19.7587	0.699451
$799$	−5.24786	−0.185656
$800$	65.2672	2.30755
$801$	−25.2557	−0.892367
$802$	−92.7929	−3.27663
$803$	0.783993	0.0276665
$804$	93.9194	3.31228
$805$	2.53239	0.0892549
$806$	−54.2706	−1.91160
$807$	−17.0929	−0.601699
$808$	25.0319	0.880619
$809$	−6.27428	−0.220592	−0.110296	−	0.993899i	$-0.535180\pi$
$809$	−6.27428	−0.220592	−0.110296	+	0.993899i	$0.535180\pi$
$810$	44.6336	1.56826
$811$	−26.0156	−0.913530	−0.456765	−	0.889587i	$-0.650992\pi$
$811$	−26.0156	−0.913530	−0.456765	+	0.889587i	$0.650992\pi$
$812$	4.26470	0.149662
$813$	43.1949	1.51491
$814$	0.612445	0.0214662
$815$	−23.9489	−0.838893
$816$	−225.478	−7.89331
$817$	43.4547	1.52029
$818$	−10.3761	−0.362792
$819$	−5.60287	−0.195780
$820$	26.0372	0.909258
$821$	21.6121	0.754266	0.377133	−	0.926159i	$-0.376910\pi$
$821$	21.6121	0.754266	0.377133	+	0.926159i	$0.376910\pi$
$822$	−90.6540	−3.16192
$823$	0.701704	0.0244598	0.0122299	−	0.999925i	$-0.496107\pi$
$823$	0.701704	0.0244598	0.0122299	+	0.999925i	$0.496107\pi$
$824$	−84.2796	−2.93602
$825$	−0.530245	−0.0184608
$826$	−21.2771	−0.740326
$827$	−17.1488	−0.596322	−0.298161	−	0.954516i	$-0.596373\pi$
$827$	−17.1488	−0.596322	−0.298161	+	0.954516i	$0.596373\pi$
$828$	31.4384	1.09256
$829$	44.0191	1.52885	0.764424	−	0.644714i	$-0.223023\pi$
$829$	44.0191	1.52885	0.764424	+	0.644714i	$0.223023\pi$
$830$	−49.8750	−1.73119
$831$	17.5518	0.608864
$832$	−116.503	−4.03901
$833$	35.7806	1.23973
$834$	−6.57673	−0.227733
$835$	−2.93930	−0.101719
$836$	−2.12091	−0.0733531
$837$	6.23505	0.215515
$838$	58.7732	2.03029
$839$	7.15662	0.247074	0.123537	−	0.992340i	$-0.460576\pi$
$839$	7.15662	0.247074	0.123537	+	0.992340i	$0.460576\pi$
$840$	−29.2633	−1.00968
$841$	1.00000	0.0344828
$842$	−65.3885	−2.25344
$843$	−9.25508	−0.318762
$844$	122.909	4.23071
$845$	−7.68259	−0.264289
$846$	−6.85476	−0.235672
$847$	−8.21751	−0.282357
$848$	180.386	6.19446
$849$	18.7861	0.644737
$850$	−37.2938	−1.27917
$851$	−5.02769	−0.172347
$852$	−154.116	−5.27993
$853$	−56.3181	−1.92830	−0.964148	−	0.265364i	$-0.914508\pi$
$853$	−56.3181	−1.92830	−0.964148	+	0.265364i	$0.914508\pi$
$854$	5.04461	0.172623
$855$	−16.8779	−0.577213
$856$	−67.0922	−2.29316
$857$	−19.5708	−0.668527	−0.334264	−	0.942480i	$-0.608488\pi$
$857$	−19.5708	−0.668527	−0.334264	+	0.942480i	$0.608488\pi$
$858$	1.74444	0.0595541
$859$	−30.4932	−1.04042	−0.520208	−	0.854040i	$-0.674146\pi$
$859$	−30.4932	−1.04042	−0.520208	+	0.854040i	$0.674146\pi$
$860$	−99.1053	−3.37946
$861$	5.03268	0.171513
$862$	−30.4665	−1.03769
$863$	40.2306	1.36947	0.684733	−	0.728794i	$-0.259919\pi$
$863$	40.2306	1.36947	0.684733	+	0.728794i	$0.259919\pi$
$864$	24.6689	0.839252
$865$	−26.0337	−0.885171
$866$	−39.2897	−1.33512
$867$	32.8380	1.11524
$868$	−29.0868	−0.987271
$869$	−1.21143	−0.0410950
$870$	−10.5665	−0.358238
$871$	−19.9205	−0.674979
$872$	180.595	6.11571
$873$	−16.2467	−0.549867
$874$	23.5154	0.795422
$875$	−8.91114	−0.301252
$876$	114.526	3.86946
$877$	18.4955	0.624550	0.312275	−	0.949992i	$-0.398909\pi$
$877$	18.4955	0.624550	0.312275	+	0.949992i	$0.398909\pi$
$878$	75.2025	2.53796
$879$	65.7372	2.21726
$880$	2.54651	0.0858430
$881$	14.5618	0.490601	0.245301	−	0.969447i	$-0.421113\pi$
$881$	14.5618	0.490601	0.245301	+	0.969447i	$0.421113\pi$
$882$	46.7367	1.57371
$883$	18.8430	0.634116	0.317058	−	0.948406i	$-0.397305\pi$
$883$	18.8430	0.634116	0.317058	+	0.948406i	$0.397305\pi$
$884$	90.8414	3.05533
$885$	39.0323	1.31206
$886$	−5.47474	−0.183928
$887$	−27.1544	−0.911756	−0.455878	−	0.890042i	$-0.650675\pi$
$887$	−27.1544	−0.911756	−0.455878	+	0.890042i	$0.650675\pi$
$888$	58.0981	1.94964
$889$	−5.46812	−0.183395
$890$	43.0837	1.44417
$891$	−0.926039	−0.0310235
$892$	62.1663	2.08148
$893$	−3.79624	−0.127036
$894$	63.6427	2.12853
$895$	−35.7778	−1.19592
$896$	−43.9843	−1.46941
$897$	−14.3204	−0.478145
$898$	44.4449	1.48315
$899$	−6.82037	−0.227472
$900$	−36.0675	−1.20225
$901$	−58.4956	−1.94877
$902$	−0.729612	−0.0242934
$903$	−19.1559	−0.637467
$904$	−25.4621	−0.846857
$905$	4.37995	0.145594
$906$	−14.9768	−0.497572
$907$	−44.6488	−1.48254	−0.741270	−	0.671207i	$-0.765776\pi$
$907$	−44.6488	−1.48254	−0.741270	+	0.671207i	$0.765776\pi$
$908$	44.1068	1.46374
$909$	−6.36436	−0.211093
$910$	9.55792	0.316842
$911$	−19.4798	−0.645394	−0.322697	−	0.946502i	$-0.604589\pi$
$911$	−19.4798	−0.645394	−0.322697	+	0.946502i	$0.604589\pi$
$912$	−163.108	−5.40106
$913$	1.03479	0.0342464
$914$	−69.2766	−2.29146
$915$	−9.25420	−0.305935
$916$	97.7651	3.23025
$917$	−6.87140	−0.226914
$918$	−14.0958	−0.465231
$919$	0.780819	0.0257568	0.0128784	−	0.999917i	$-0.495901\pi$
$919$	0.780819	0.0257568	0.0128784	+	0.999917i	$0.495901\pi$
$920$	−34.8271	−1.14822
$921$	−28.0932	−0.925701
$922$	1.60293	0.0527897
$923$	32.6883	1.07595
$924$	0.934947	0.0307575
$925$	5.76797	0.189650
$926$	−81.7026	−2.68491
$927$	21.4281	0.703791
$928$	−26.9847	−0.885815
$929$	41.0665	1.34735	0.673675	−	0.739028i	$-0.264715\pi$
$929$	41.0665	1.34735	0.673675	+	0.739028i	$0.264715\pi$
$930$	72.0674	2.36318
$931$	25.8833	0.848292
$932$	98.6077	3.23000
$933$	61.6297	2.01767
$934$	−29.6872	−0.971396
$935$	−0.825786	−0.0270061
$936$	77.0545	2.51861
$937$	−9.75336	−0.318628	−0.159314	−	0.987228i	$-0.550928\pi$
$937$	−9.75336	−0.318628	−0.159314	+	0.987228i	$0.550928\pi$
$938$	−14.4199	−0.470826
$939$	1.03568	0.0337983
$940$	8.65794	0.282391
$941$	6.41169	0.209015	0.104508	−	0.994524i	$-0.466673\pi$
$941$	6.41169	0.209015	0.104508	+	0.994524i	$0.466673\pi$
$942$	−84.9764	−2.76868
$943$	5.98953	0.195046
$944$	175.643	5.71668
$945$	−1.09809	−0.0357210
$946$	2.77712	0.0902921
$947$	−5.08835	−0.165349	−0.0826745	−	0.996577i	$-0.526346\pi$
$947$	−5.08835	−0.165349	−0.0826745	+	0.996577i	$0.526346\pi$
$948$	−176.966	−5.74759
$949$	−24.2911	−0.788521
$950$	−26.9779	−0.875279
$951$	45.7535	1.48366
$952$	42.7022	1.38399
$953$	58.5887	1.89787	0.948937	−	0.315465i	$-0.102161\pi$
$953$	58.5887	1.89787	0.948937	+	0.315465i	$0.102161\pi$
$954$	−76.4071	−2.47377
$955$	17.2672	0.558753
$956$	90.4762	2.92621
$957$	0.219229	0.00708667
$958$	−13.9772	−0.451582
$959$	10.3054	0.332777
$960$	154.707	4.99316
$961$	15.5174	0.500562
$962$	−18.9759	−0.611806
$963$	17.0582	0.549693
$964$	97.3020	3.13389
$965$	27.8576	0.896769
$966$	−10.3662	−0.333526
$967$	−51.6693	−1.66157	−0.830787	−	0.556591i	$-0.812109\pi$
$967$	−51.6693	−1.66157	−0.830787	+	0.556591i	$0.812109\pi$
$968$	113.013	3.63237
$969$	52.8929	1.69917
$970$	27.7152	0.889881
$971$	−58.0162	−1.86183	−0.930913	−	0.365240i	$-0.880987\pi$
$971$	−58.0162	−1.86183	−0.930913	+	0.365240i	$0.880987\pi$
$972$	−119.631	−3.83718
$973$	0.747628	0.0239679
$974$	−1.15296	−0.0369433
$975$	16.4290	0.526149
$976$	−41.6433	−1.33297
$977$	−13.3239	−0.426268	−0.213134	−	0.977023i	$-0.568367\pi$
$977$	−13.3239	−0.426268	−0.213134	+	0.977023i	$0.568367\pi$
$978$	98.0334	3.13476
$979$	−0.893882	−0.0285686
$980$	−59.0311	−1.88568
$981$	−45.9163	−1.46599
$982$	17.6169	0.562177
$983$	40.2800	1.28473	0.642367	−	0.766397i	$-0.277953\pi$
$983$	40.2800	1.28473	0.642367	+	0.766397i	$0.277953\pi$
$984$	−69.2128	−2.20642
$985$	−31.4011	−1.00052
$986$	15.4191	0.491043
$987$	1.67348	0.0532673
$988$	65.7137	2.09063
$989$	−22.7980	−0.724933
$990$	−1.07864	−0.0342815
$991$	−39.6290	−1.25886	−0.629428	−	0.777059i	$-0.716711\pi$
$991$	−39.6290	−1.25886	−0.629428	+	0.777059i	$0.716711\pi$
$992$	184.045	5.84345
$993$	28.8355	0.915065
$994$	23.6622	0.750519
$995$	−23.4355	−0.742955
$996$	151.162	4.78974
$997$	23.1379	0.732783	0.366392	−	0.930461i	$-0.380593\pi$
$997$	23.1379	0.732783	0.366392	+	0.930461i	$0.380593\pi$
$998$	10.2484	0.324408
$999$	2.18010	0.0689754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.b.1.1	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.b.1.1	✓	59	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77566 q^{2} +2.36943 q^{3} +5.70431 q^{4} +1.60665 q^{5} -6.57673 q^{6} +0.747628 q^{7} -10.2819 q^{8} +2.61418 q^{9} +O(q^{10})\)	\(q-2.77566 q^{2} +2.36943 q^{3} +5.70431 q^{4} +1.60665 q^{5} -6.57673 q^{6} +0.747628 q^{7} -10.2819 q^{8} +2.61418 q^{9} -4.45952 q^{10} +0.0925242 q^{11} +13.5159 q^{12} -2.86675 q^{13} -2.07516 q^{14} +3.80683 q^{15} +17.1305 q^{16} -5.55509 q^{17} -7.25607 q^{18} -4.01849 q^{19} +9.16482 q^{20} +1.77145 q^{21} -0.256816 q^{22} +2.10825 q^{23} -24.3622 q^{24} -2.41868 q^{25} +7.95713 q^{26} -0.914181 q^{27} +4.26470 q^{28} +1.00000 q^{29} -10.5665 q^{30} -6.82037 q^{31} -26.9847 q^{32} +0.219229 q^{33} +15.4191 q^{34} +1.20118 q^{35} +14.9121 q^{36} -2.38476 q^{37} +11.1540 q^{38} -6.79255 q^{39} -16.5194 q^{40} +2.84099 q^{41} -4.91695 q^{42} -10.8137 q^{43} +0.527786 q^{44} +4.20006 q^{45} -5.85180 q^{46} +0.944693 q^{47} +40.5894 q^{48} -6.44105 q^{49} +6.71344 q^{50} -13.1624 q^{51} -16.3528 q^{52} +10.5301 q^{53} +2.53746 q^{54} +0.148654 q^{55} -7.68704 q^{56} -9.52152 q^{57} -2.77566 q^{58} +10.2532 q^{59} +21.7153 q^{60} -2.43094 q^{61} +18.9310 q^{62} +1.95443 q^{63} +40.6394 q^{64} -4.60586 q^{65} -0.608506 q^{66} +6.94880 q^{67} -31.6879 q^{68} +4.99535 q^{69} -3.33406 q^{70} -11.4026 q^{71} -26.8787 q^{72} +8.47338 q^{73} +6.61930 q^{74} -5.73088 q^{75} -22.9227 q^{76} +0.0691737 q^{77} +18.8538 q^{78} -13.0931 q^{79} +27.5227 q^{80} -10.0086 q^{81} -7.88564 q^{82} +11.1840 q^{83} +10.1049 q^{84} -8.92508 q^{85} +30.0151 q^{86} +2.36943 q^{87} -0.951325 q^{88} -9.66106 q^{89} -11.6580 q^{90} -2.14326 q^{91} +12.0261 q^{92} -16.1604 q^{93} -2.62215 q^{94} -6.45631 q^{95} -63.9381 q^{96} -6.21484 q^{97} +17.8782 q^{98} +0.241875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * q^99

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