LMFDB - Embedded newform 4029.2.a.k.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.56879 q^{2} +1.00000 q^{3} +4.59868 q^{4} +3.14567 q^{5} -2.56879 q^{6} -0.137684 q^{7} -6.67546 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.56879 q^{2} +1.00000 q^{3} +4.59868 q^{4} +3.14567 q^{5} -2.56879 q^{6} -0.137684 q^{7} -6.67546 q^{8} +1.00000 q^{9} -8.08058 q^{10} +0.886329 q^{11} +4.59868 q^{12} +0.153446 q^{13} +0.353681 q^{14} +3.14567 q^{15} +7.95050 q^{16} +1.00000 q^{17} -2.56879 q^{18} +6.70747 q^{19} +14.4660 q^{20} -0.137684 q^{21} -2.27679 q^{22} +7.75524 q^{23} -6.67546 q^{24} +4.89527 q^{25} -0.394171 q^{26} +1.00000 q^{27} -0.633165 q^{28} +4.03660 q^{29} -8.08058 q^{30} -6.23265 q^{31} -7.07224 q^{32} +0.886329 q^{33} -2.56879 q^{34} -0.433109 q^{35} +4.59868 q^{36} +8.71769 q^{37} -17.2301 q^{38} +0.153446 q^{39} -20.9988 q^{40} +4.00646 q^{41} +0.353681 q^{42} +1.85994 q^{43} +4.07594 q^{44} +3.14567 q^{45} -19.9216 q^{46} -8.83188 q^{47} +7.95050 q^{48} -6.98104 q^{49} -12.5749 q^{50} +1.00000 q^{51} +0.705650 q^{52} -1.81352 q^{53} -2.56879 q^{54} +2.78810 q^{55} +0.919105 q^{56} +6.70747 q^{57} -10.3692 q^{58} +1.89769 q^{59} +14.4660 q^{60} -6.28907 q^{61} +16.0104 q^{62} -0.137684 q^{63} +2.26609 q^{64} +0.482691 q^{65} -2.27679 q^{66} -12.1576 q^{67} +4.59868 q^{68} +7.75524 q^{69} +1.11257 q^{70} +7.83419 q^{71} -6.67546 q^{72} +0.0892372 q^{73} -22.3939 q^{74} +4.89527 q^{75} +30.8455 q^{76} -0.122033 q^{77} -0.394171 q^{78} +1.00000 q^{79} +25.0097 q^{80} +1.00000 q^{81} -10.2918 q^{82} +6.29504 q^{83} -0.633165 q^{84} +3.14567 q^{85} -4.77778 q^{86} +4.03660 q^{87} -5.91665 q^{88} -9.08666 q^{89} -8.08058 q^{90} -0.0211271 q^{91} +35.6639 q^{92} -6.23265 q^{93} +22.6872 q^{94} +21.0995 q^{95} -7.07224 q^{96} -16.3940 q^{97} +17.9328 q^{98} +0.886329 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.56879	−1.81641	−0.908204	−	0.418527i	$-0.862546\pi$
$2$	−2.56879	−1.81641	−0.908204	+	0.418527i	$0.862546\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.59868	2.29934
$5$	3.14567	1.40679	0.703394	−	0.710800i	$-0.251667\pi$
$5$	3.14567	1.40679	0.703394	+	0.710800i	$0.251667\pi$
$6$	−2.56879	−1.04870
$7$	−0.137684	−0.0520397	−0.0260198	−	0.999661i	$-0.508283\pi$
$7$	−0.137684	−0.0520397	−0.0260198	+	0.999661i	$0.508283\pi$
$8$	−6.67546	−2.36013
$9$	1.00000	0.333333
$10$	−8.08058	−2.55530
$11$	0.886329	0.267238	0.133619	−	0.991033i	$-0.457340\pi$
$11$	0.886329	0.267238	0.133619	+	0.991033i	$0.457340\pi$
$12$	4.59868	1.32752
$13$	0.153446	0.0425583	0.0212791	−	0.999774i	$-0.493226\pi$
$13$	0.153446	0.0425583	0.0212791	+	0.999774i	$0.493226\pi$
$14$	0.353681	0.0945254
$15$	3.14567	0.812210
$16$	7.95050	1.98763
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.56879	−0.605470
$19$	6.70747	1.53880	0.769400	−	0.638768i	$-0.220555\pi$
$19$	6.70747	1.53880	0.769400	+	0.638768i	$0.220555\pi$
$20$	14.4660	3.23468
$21$	−0.137684	−0.0300451
$22$	−2.27679	−0.485414
$23$	7.75524	1.61708	0.808540	−	0.588442i	$-0.200258\pi$
$23$	7.75524	1.61708	0.808540	+	0.588442i	$0.200258\pi$
$24$	−6.67546	−1.36262
$25$	4.89527	0.979053
$26$	−0.394171	−0.0773033
$27$	1.00000	0.192450
$28$	−0.633165	−0.119657
$29$	4.03660	0.749577	0.374789	−	0.927110i	$-0.377715\pi$
$29$	4.03660	0.749577	0.374789	+	0.927110i	$0.377715\pi$
$30$	−8.08058	−1.47530
$31$	−6.23265	−1.11942	−0.559709	−	0.828690i	$-0.689087\pi$
$31$	−6.23265	−1.11942	−0.559709	+	0.828690i	$0.689087\pi$
$32$	−7.07224	−1.25021
$33$	0.886329	0.154290
$34$	−2.56879	−0.440544
$35$	−0.433109	−0.0732088
$36$	4.59868	0.766447
$37$	8.71769	1.43318	0.716589	−	0.697495i	$-0.245702\pi$
$37$	8.71769	1.43318	0.716589	+	0.697495i	$0.245702\pi$
$38$	−17.2301	−2.79509
$39$	0.153446	0.0245710
$40$	−20.9988	−3.32021
$41$	4.00646	0.625705	0.312852	−	0.949802i	$-0.398716\pi$
$41$	4.00646	0.625705	0.312852	+	0.949802i	$0.398716\pi$
$42$	0.353681	0.0545742
$43$	1.85994	0.283638	0.141819	−	0.989893i	$-0.454705\pi$
$43$	1.85994	0.283638	0.141819	+	0.989893i	$0.454705\pi$
$44$	4.07594	0.614471
$45$	3.14567	0.468929
$46$	−19.9216	−2.93728
$47$	−8.83188	−1.28826	−0.644131	−	0.764915i	$-0.722781\pi$
$47$	−8.83188	−1.28826	−0.644131	+	0.764915i	$0.722781\pi$
$48$	7.95050	1.14756
$49$	−6.98104	−0.997292
$50$	−12.5749	−1.77836
$51$	1.00000	0.140028
$52$	0.705650	0.0978560
$53$	−1.81352	−0.249107	−0.124553	−	0.992213i	$-0.539750\pi$
$53$	−1.81352	−0.249107	−0.124553	+	0.992213i	$0.539750\pi$
$54$	−2.56879	−0.349568
$55$	2.78810	0.375947
$56$	0.919105	0.122821
$57$	6.70747	0.888426
$58$	−10.3692	−1.36154
$59$	1.89769	0.247058	0.123529	−	0.992341i	$-0.460579\pi$
$59$	1.89769	0.247058	0.123529	+	0.992341i	$0.460579\pi$
$60$	14.4660	1.86755
$61$	−6.28907	−0.805233	−0.402617	−	0.915369i	$-0.631899\pi$
$61$	−6.28907	−0.805233	−0.402617	+	0.915369i	$0.631899\pi$
$62$	16.0104	2.03332
$63$	−0.137684	−0.0173466
$64$	2.26609	0.283261
$65$	0.482691	0.0598705
$66$	−2.27679	−0.280254
$67$	−12.1576	−1.48529	−0.742643	−	0.669688i	$-0.766428\pi$
$67$	−12.1576	−1.48529	−0.742643	+	0.669688i	$0.766428\pi$
$68$	4.59868	0.557672
$69$	7.75524	0.933621
$70$	1.11257	0.132977
$71$	7.83419	0.929747	0.464873	−	0.885377i	$-0.346100\pi$
$71$	7.83419	0.929747	0.464873	+	0.885377i	$0.346100\pi$
$72$	−6.67546	−0.786711
$73$	0.0892372	0.0104444	0.00522221	−	0.999986i	$-0.498338\pi$
$73$	0.0892372	0.0104444	0.00522221	+	0.999986i	$0.498338\pi$
$74$	−22.3939	−2.60324
$75$	4.89527	0.565257
$76$	30.8455	3.53822
$77$	−0.122033	−0.0139070
$78$	−0.394171	−0.0446311
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	25.0097	2.79617
$81$	1.00000	0.111111
$82$	−10.2918	−1.13654
$83$	6.29504	0.690970	0.345485	−	0.938424i	$-0.387714\pi$
$83$	6.29504	0.690970	0.345485	+	0.938424i	$0.387714\pi$
$84$	−0.633165	−0.0690840
$85$	3.14567	0.341196
$86$	−4.77778	−0.515202
$87$	4.03660	0.432769
$88$	−5.91665	−0.630717
$89$	−9.08666	−0.963184	−0.481592	−	0.876396i	$-0.659941\pi$
$89$	−9.08666	−0.963184	−0.481592	+	0.876396i	$0.659941\pi$
$90$	−8.08058	−0.851767
$91$	−0.0211271	−0.00221472
$92$	35.6639	3.71822
$93$	−6.23265	−0.646296
$94$	22.6872	2.34001
$95$	21.0995	2.16477
$96$	−7.07224	−0.721807
$97$	−16.3940	−1.66456	−0.832280	−	0.554355i	$-0.812965\pi$
$97$	−16.3940	−1.66456	−0.832280	+	0.554355i	$0.812965\pi$
$98$	17.9328	1.81149
$99$	0.886329	0.0890794
$100$	22.5118	2.25118
$101$	13.6640	1.35962	0.679809	−	0.733389i	$-0.262063\pi$
$101$	13.6640	1.35962	0.679809	+	0.733389i	$0.262063\pi$
$102$	−2.56879	−0.254348
$103$	6.32754	0.623471	0.311736	−	0.950169i	$-0.399090\pi$
$103$	6.32754	0.623471	0.311736	+	0.950169i	$0.399090\pi$
$104$	−1.02432	−0.100443
$105$	−0.433109	−0.0422671
$106$	4.65856	0.452479
$107$	−10.5763	−1.02245	−0.511226	−	0.859446i	$-0.670809\pi$
$107$	−10.5763	−1.02245	−0.511226	+	0.859446i	$0.670809\pi$
$108$	4.59868	0.442508
$109$	4.47043	0.428190	0.214095	−	0.976813i	$-0.431320\pi$
$109$	4.47043	0.428190	0.214095	+	0.976813i	$0.431320\pi$
$110$	−7.16204	−0.682874
$111$	8.71769	0.827446
$112$	−1.09466	−0.103435
$113$	11.7239	1.10289	0.551447	−	0.834210i	$-0.314076\pi$
$113$	11.7239	1.10289	0.551447	+	0.834210i	$0.314076\pi$
$114$	−17.2301	−1.61375
$115$	24.3955	2.27489
$116$	18.5630	1.72353
$117$	0.153446	0.0141861
$118$	−4.87477	−0.448759
$119$	−0.137684	−0.0126215
$120$	−20.9988	−1.91692
$121$	−10.2144	−0.928584
$122$	16.1553	1.46263
$123$	4.00646	0.361251
$124$	−28.6620	−2.57392
$125$	−0.329457	−0.0294675
$126$	0.353681	0.0315085
$127$	9.39492	0.833665	0.416832	−	0.908983i	$-0.363140\pi$
$127$	9.39492	0.833665	0.416832	+	0.908983i	$0.363140\pi$
$128$	8.32337	0.735689
$129$	1.85994	0.163758
$130$	−1.23993	−0.108749
$131$	17.4924	1.52832	0.764158	−	0.645029i	$-0.223155\pi$
$131$	17.4924	1.52832	0.764158	+	0.645029i	$0.223155\pi$
$132$	4.07594	0.354765
$133$	−0.923512	−0.0800787
$134$	31.2303	2.69789
$135$	3.14567	0.270737
$136$	−6.67546	−0.572416
$137$	−6.18726	−0.528614	−0.264307	−	0.964439i	$-0.585143\pi$
$137$	−6.18726	−0.528614	−0.264307	+	0.964439i	$0.585143\pi$
$138$	−19.9216	−1.69584
$139$	−13.4519	−1.14098	−0.570488	−	0.821306i	$-0.693246\pi$
$139$	−13.4519	−1.14098	−0.570488	+	0.821306i	$0.693246\pi$
$140$	−1.99173	−0.168332
$141$	−8.83188	−0.743778
$142$	−20.1244	−1.68880
$143$	0.136004	0.0113732
$144$	7.95050	0.662542
$145$	12.6978	1.05450
$146$	−0.229232	−0.0189713
$147$	−6.98104	−0.575787
$148$	40.0899	3.29537
$149$	7.97695	0.653497	0.326749	−	0.945111i	$-0.394047\pi$
$149$	7.97695	0.653497	0.326749	+	0.945111i	$0.394047\pi$
$150$	−12.5749	−1.02674
$151$	6.34255	0.516150	0.258075	−	0.966125i	$-0.416912\pi$
$151$	6.34255	0.516150	0.258075	+	0.966125i	$0.416912\pi$
$152$	−44.7755	−3.63177
$153$	1.00000	0.0808452
$154$	0.313478	0.0252608
$155$	−19.6059	−1.57478
$156$	0.705650	0.0564972
$157$	−4.96083	−0.395918	−0.197959	−	0.980210i	$-0.563431\pi$
$157$	−4.96083	−0.395918	−0.197959	+	0.980210i	$0.563431\pi$
$158$	−2.56879	−0.204362
$159$	−1.81352	−0.143822
$160$	−22.2470	−1.75878
$161$	−1.06777	−0.0841523
$162$	−2.56879	−0.201823
$163$	−17.8809	−1.40054	−0.700272	−	0.713877i	$-0.746938\pi$
$163$	−17.8809	−1.40054	−0.700272	+	0.713877i	$0.746938\pi$
$164$	18.4244	1.43871
$165$	2.78810	0.217053
$166$	−16.1706	−1.25508
$167$	−0.248750	−0.0192489	−0.00962443	−	0.999954i	$-0.503064\pi$
$167$	−0.248750	−0.0192489	−0.00962443	+	0.999954i	$0.503064\pi$
$168$	0.919105	0.0709105
$169$	−12.9765	−0.998189
$170$	−8.08058	−0.619752
$171$	6.70747	0.512933
$172$	8.55325	0.652179
$173$	−20.4864	−1.55755	−0.778774	−	0.627304i	$-0.784158\pi$
$173$	−20.4864	−1.55755	−0.778774	+	0.627304i	$0.784158\pi$
$174$	−10.3692	−0.786085
$175$	−0.674000	−0.0509496
$176$	7.04676	0.531169
$177$	1.89769	0.142639
$178$	23.3417	1.74954
$179$	20.3027	1.51750	0.758748	−	0.651384i	$-0.225811\pi$
$179$	20.3027	1.51750	0.758748	+	0.651384i	$0.225811\pi$
$180$	14.4660	1.07823
$181$	6.39501	0.475337	0.237669	−	0.971346i	$-0.423617\pi$
$181$	6.39501	0.475337	0.237669	+	0.971346i	$0.423617\pi$
$182$	0.0542711	0.00402284
$183$	−6.28907	−0.464902
$184$	−51.7698	−3.81652
$185$	27.4230	2.01618
$186$	16.0104	1.17394
$187$	0.886329	0.0648148
$188$	−40.6150	−2.96215
$189$	−0.137684	−0.0100150
$190$	−54.2002	−3.93210
$191$	6.78820	0.491177	0.245588	−	0.969374i	$-0.421019\pi$
$191$	6.78820	0.491177	0.245588	+	0.969374i	$0.421019\pi$
$192$	2.26609	0.163541
$193$	0.0206068	0.00148331	0.000741653	−	1.00000i	$-0.499764\pi$
$193$	0.0206068	0.00148331	0.000741653		1.00000i	$0.499764\pi$
$194$	42.1128	3.02352
$195$	0.482691	0.0345663
$196$	−32.1036	−2.29311
$197$	5.35940	0.381841	0.190921	−	0.981605i	$-0.438853\pi$
$197$	5.35940	0.381841	0.190921	+	0.981605i	$0.438853\pi$
$198$	−2.27679	−0.161805
$199$	−18.6041	−1.31881	−0.659405	−	0.751788i	$-0.729192\pi$
$199$	−18.6041	−1.31881	−0.659405	+	0.751788i	$0.729192\pi$
$200$	−32.6782	−2.31070
$201$	−12.1576	−0.857530
$202$	−35.0999	−2.46962
$203$	−0.555775	−0.0390078
$204$	4.59868	0.321972
$205$	12.6030	0.880234
$206$	−16.2541	−1.13248
$207$	7.75524	0.539026
$208$	1.21997	0.0845899
$209$	5.94502	0.411226
$210$	1.11257	0.0767744
$211$	12.3382	0.849400	0.424700	−	0.905334i	$-0.360380\pi$
$211$	12.3382	0.849400	0.424700	+	0.905334i	$0.360380\pi$
$212$	−8.33981	−0.572781
$213$	7.83419	0.536790
$214$	27.1684	1.85719
$215$	5.85075	0.399018
$216$	−6.67546	−0.454208
$217$	0.858137	0.0582541
$218$	−11.4836	−0.777767
$219$	0.0892372	0.00603009
$220$	12.8216	0.864431
$221$	0.153446	0.0103219
$222$	−22.3939	−1.50298
$223$	2.52511	0.169094	0.0845469	−	0.996419i	$-0.473056\pi$
$223$	2.52511	0.169094	0.0845469	+	0.996419i	$0.473056\pi$
$224$	0.973735	0.0650604
$225$	4.89527	0.326351
$226$	−30.1163	−2.00331
$227$	−11.0846	−0.735711	−0.367855	−	0.929883i	$-0.619908\pi$
$227$	−11.0846	−0.735711	−0.367855	+	0.929883i	$0.619908\pi$
$228$	30.8455	2.04279
$229$	−9.95351	−0.657746	−0.328873	−	0.944374i	$-0.606669\pi$
$229$	−9.95351	−0.657746	−0.328873	+	0.944374i	$0.606669\pi$
$230$	−62.6668	−4.13213
$231$	−0.122033	−0.00802920
$232$	−26.9462	−1.76910
$233$	−19.2676	−1.26226	−0.631131	−	0.775676i	$-0.717409\pi$
$233$	−19.2676	−1.26226	−0.631131	+	0.775676i	$0.717409\pi$
$234$	−0.394171	−0.0257678
$235$	−27.7822	−1.81231
$236$	8.72687	0.568071
$237$	1.00000	0.0649570
$238$	0.353681	0.0229258
$239$	16.5390	1.06982	0.534911	−	0.844909i	$-0.320345\pi$
$239$	16.5390	1.06982	0.534911	+	0.844909i	$0.320345\pi$
$240$	25.0097	1.61437
$241$	26.3974	1.70041	0.850203	−	0.526454i	$-0.176479\pi$
$241$	26.3974	1.70041	0.850203	+	0.526454i	$0.176479\pi$
$242$	26.2387	1.68669
$243$	1.00000	0.0641500
$244$	−28.9214	−1.85150
$245$	−21.9601	−1.40298
$246$	−10.2918	−0.656179
$247$	1.02924	0.0654887
$248$	41.6058	2.64197
$249$	6.29504	0.398932
$250$	0.846305	0.0535250
$251$	1.40438	0.0886437	0.0443219	−	0.999017i	$-0.485887\pi$
$251$	1.40438	0.0886437	0.0443219	+	0.999017i	$0.485887\pi$
$252$	−0.633165	−0.0398857
$253$	6.87369	0.432145
$254$	−24.1336	−1.51428
$255$	3.14567	0.196990
$256$	−25.9132	−1.61957
$257$	−11.3803	−0.709881	−0.354941	−	0.934889i	$-0.615499\pi$
$257$	−11.3803	−0.709881	−0.354941	+	0.934889i	$0.615499\pi$
$258$	−4.77778	−0.297452
$259$	−1.20029	−0.0745822
$260$	2.21974	0.137663
$261$	4.03660	0.249859
$262$	−44.9342	−2.77605
$263$	−18.9971	−1.17141	−0.585705	−	0.810525i	$-0.699182\pi$
$263$	−18.9971	−1.17141	−0.585705	+	0.810525i	$0.699182\pi$
$264$	−5.91665	−0.364145
$265$	−5.70475	−0.350440
$266$	2.37231	0.145456
$267$	−9.08666	−0.556095
$268$	−55.9089	−3.41518
$269$	−8.23267	−0.501955	−0.250977	−	0.967993i	$-0.580752\pi$
$269$	−8.23267	−0.501955	−0.250977	+	0.967993i	$0.580752\pi$
$270$	−8.08058	−0.491768
$271$	−0.135088	−0.00820603	−0.00410301	−	0.999992i	$-0.501306\pi$
$271$	−0.135088	−0.00820603	−0.00410301	+	0.999992i	$0.501306\pi$
$272$	7.95050	0.482070
$273$	−0.0211271	−0.00127867
$274$	15.8938	0.960178
$275$	4.33881	0.261640
$276$	35.6639	2.14671
$277$	−23.2923	−1.39950	−0.699749	−	0.714388i	$-0.746705\pi$
$277$	−23.2923	−1.39950	−0.699749	+	0.714388i	$0.746705\pi$
$278$	34.5551	2.07248
$279$	−6.23265	−0.373139
$280$	2.89121	0.172783
$281$	25.7854	1.53823	0.769113	−	0.639113i	$-0.220698\pi$
$281$	25.7854	1.53823	0.769113	+	0.639113i	$0.220698\pi$
$282$	22.6872	1.35101
$283$	18.9333	1.12547	0.562735	−	0.826637i	$-0.309749\pi$
$283$	18.9333	1.12547	0.562735	+	0.826637i	$0.309749\pi$
$284$	36.0269	2.13780
$285$	21.0995	1.24983
$286$	−0.349365	−0.0206584
$287$	−0.551626	−0.0325615
$288$	−7.07224	−0.416736
$289$	1.00000	0.0588235
$290$	−32.6180	−1.91540
$291$	−16.3940	−0.961035
$292$	0.410374	0.0240153
$293$	7.36864	0.430481	0.215240	−	0.976561i	$-0.430946\pi$
$293$	7.36864	0.430481	0.215240	+	0.976561i	$0.430946\pi$
$294$	17.9328	1.04586
$295$	5.96952	0.347559
$296$	−58.1946	−3.38249
$297$	0.886329	0.0514300
$298$	−20.4911	−1.18702
$299$	1.19001	0.0688201
$300$	22.5118	1.29972
$301$	−0.256084	−0.0147604
$302$	−16.2927	−0.937539
$303$	13.6640	0.784976
$304$	53.3278	3.05856
$305$	−19.7834	−1.13279
$306$	−2.56879	−0.146848
$307$	−24.2984	−1.38678	−0.693391	−	0.720561i	$-0.743884\pi$
$307$	−24.2984	−1.38678	−0.693391	+	0.720561i	$0.743884\pi$
$308$	−0.561192	−0.0319769
$309$	6.32754	0.359961
$310$	50.3634	2.86045
$311$	−6.81598	−0.386499	−0.193249	−	0.981150i	$-0.561903\pi$
$311$	−6.81598	−0.386499	−0.193249	+	0.981150i	$0.561903\pi$
$312$	−1.02432	−0.0579909
$313$	22.8625	1.29226	0.646131	−	0.763226i	$-0.276386\pi$
$313$	22.8625	1.29226	0.646131	+	0.763226i	$0.276386\pi$
$314$	12.7433	0.719148
$315$	−0.433109	−0.0244029
$316$	4.59868	0.258696
$317$	10.9591	0.615525	0.307762	−	0.951463i	$-0.400420\pi$
$317$	10.9591	0.615525	0.307762	+	0.951463i	$0.400420\pi$
$318$	4.65856	0.261239
$319$	3.57775	0.200316
$320$	7.12838	0.398489
$321$	−10.5763	−0.590313
$322$	2.74288	0.152855
$323$	6.70747	0.373214
$324$	4.59868	0.255482
$325$	0.751160	0.0416668
$326$	45.9324	2.54396
$327$	4.47043	0.247215
$328$	−26.7450	−1.47675
$329$	1.21601	0.0670408
$330$	−7.16204	−0.394258
$331$	24.6789	1.35647	0.678236	−	0.734844i	$-0.262745\pi$
$331$	24.6789	1.35647	0.678236	+	0.734844i	$0.262745\pi$
$332$	28.9489	1.58878
$333$	8.71769	0.477726
$334$	0.638987	0.0349638
$335$	−38.2438	−2.08948
$336$	−1.09466	−0.0597185
$337$	18.1589	0.989181	0.494590	−	0.869126i	$-0.335318\pi$
$337$	18.1589	0.989181	0.494590	+	0.869126i	$0.335318\pi$
$338$	33.3338	1.81312
$339$	11.7239	0.636756
$340$	14.4660	0.784526
$341$	−5.52418	−0.299151
$342$	−17.2301	−0.931696
$343$	1.92497	0.103938
$344$	−12.4159	−0.669422
$345$	24.3955	1.31341
$346$	52.6251	2.82914
$347$	4.94297	0.265353	0.132676	−	0.991159i	$-0.457643\pi$
$347$	4.94297	0.265353	0.132676	+	0.991159i	$0.457643\pi$
$348$	18.5630	0.995082
$349$	−10.9480	−0.586032	−0.293016	−	0.956108i	$-0.594659\pi$
$349$	−10.9480	−0.586032	−0.293016	+	0.956108i	$0.594659\pi$
$350$	1.73137	0.0925454
$351$	0.153446	0.00819035
$352$	−6.26833	−0.334103
$353$	−6.40755	−0.341039	−0.170520	−	0.985354i	$-0.554545\pi$
$353$	−6.40755	−0.341039	−0.170520	+	0.985354i	$0.554545\pi$
$354$	−4.87477	−0.259091
$355$	24.6438	1.30796
$356$	−41.7866	−2.21469
$357$	−0.137684	−0.00728702
$358$	−52.1534	−2.75639
$359$	−26.0161	−1.37308	−0.686538	−	0.727094i	$-0.740870\pi$
$359$	−26.0161	−1.37308	−0.686538	+	0.727094i	$0.740870\pi$
$360$	−20.9988	−1.10674
$361$	25.9902	1.36790
$362$	−16.4274	−0.863407
$363$	−10.2144	−0.536118
$364$	−0.0971567	−0.00509240
$365$	0.280711	0.0146931
$366$	16.1553	0.844451
$367$	7.02332	0.366614	0.183307	−	0.983056i	$-0.441320\pi$
$367$	7.02332	0.366614	0.183307	+	0.983056i	$0.441320\pi$
$368$	61.6580	3.21415
$369$	4.00646	0.208568
$370$	−70.4439	−3.66221
$371$	0.249693	0.0129634
$372$	−28.6620	−1.48605
$373$	−20.5593	−1.06452	−0.532260	−	0.846581i	$-0.678657\pi$
$373$	−20.5593	−1.06452	−0.532260	+	0.846581i	$0.678657\pi$
$374$	−2.27679	−0.117730
$375$	−0.329457	−0.0170131
$376$	58.9569	3.04047
$377$	0.619400	0.0319007
$378$	0.353681	0.0181914
$379$	−28.3640	−1.45696	−0.728480	−	0.685067i	$-0.759773\pi$
$379$	−28.3640	−1.45696	−0.728480	+	0.685067i	$0.759773\pi$
$380$	97.0300	4.97753
$381$	9.39492	0.481317
$382$	−17.4375	−0.892178
$383$	−0.877959	−0.0448616	−0.0224308	−	0.999748i	$-0.507141\pi$
$383$	−0.877959	−0.0448616	−0.0224308	+	0.999748i	$0.507141\pi$
$384$	8.32337	0.424750
$385$	−0.383877	−0.0195642
$386$	−0.0529344	−0.00269429
$387$	1.85994	0.0945458
$388$	−75.3909	−3.82739
$389$	18.5261	0.939313	0.469657	−	0.882849i	$-0.344378\pi$
$389$	18.5261	0.939313	0.469657	+	0.882849i	$0.344378\pi$
$390$	−1.23993	−0.0627864
$391$	7.75524	0.392199
$392$	46.6017	2.35374
$393$	17.4924	0.882374
$394$	−13.7672	−0.693580
$395$	3.14567	0.158276
$396$	4.07594	0.204824
$397$	7.78973	0.390955	0.195478	−	0.980708i	$-0.437374\pi$
$397$	7.78973	0.390955	0.195478	+	0.980708i	$0.437374\pi$
$398$	47.7900	2.39550
$399$	−0.923512	−0.0462334
$400$	38.9198	1.94599
$401$	30.5551	1.52585	0.762923	−	0.646489i	$-0.223763\pi$
$401$	30.5551	1.52585	0.762923	+	0.646489i	$0.223763\pi$
$402$	31.2303	1.55762
$403$	−0.956376	−0.0476405
$404$	62.8363	3.12622
$405$	3.14567	0.156310
$406$	1.42767	0.0708541
$407$	7.72673	0.383000
$408$	−6.67546	−0.330485
$409$	39.4597	1.95116	0.975579	−	0.219651i	$-0.0704918\pi$
$409$	39.4597	1.95116	0.975579	+	0.219651i	$0.0704918\pi$
$410$	−32.3745	−1.59886
$411$	−6.18726	−0.305195
$412$	29.0983	1.43357
$413$	−0.261282	−0.0128568
$414$	−19.9216	−0.979092
$415$	19.8021	0.972049
$416$	−1.08521	−0.0532067
$417$	−13.4519	−0.658742
$418$	−15.2715	−0.746954
$419$	−3.10743	−0.151808	−0.0759039	−	0.997115i	$-0.524184\pi$
$419$	−3.10743	−0.151808	−0.0759039	+	0.997115i	$0.524184\pi$
$420$	−1.99173	−0.0971865
$421$	−11.1773	−0.544748	−0.272374	−	0.962192i	$-0.587809\pi$
$421$	−11.1773	−0.544748	−0.272374	+	0.962192i	$0.587809\pi$
$422$	−31.6943	−1.54286
$423$	−8.83188	−0.429421
$424$	12.1061	0.587925
$425$	4.89527	0.237455
$426$	−20.1244	−0.975029
$427$	0.865905	0.0419041
$428$	−48.6372	−2.35097
$429$	0.136004	0.00656632
$430$	−15.0294	−0.724780
$431$	7.74831	0.373223	0.186611	−	0.982434i	$-0.440249\pi$
$431$	7.74831	0.373223	0.186611	+	0.982434i	$0.440249\pi$
$432$	7.95050	0.382519
$433$	−12.6430	−0.607584	−0.303792	−	0.952738i	$-0.598253\pi$
$433$	−12.6430	−0.607584	−0.303792	+	0.952738i	$0.598253\pi$
$434$	−2.20437	−0.105813
$435$	12.6978	0.608814
$436$	20.5581	0.984554
$437$	52.0180	2.48836
$438$	−0.229232	−0.0109531
$439$	24.0391	1.14733	0.573663	−	0.819092i	$-0.305522\pi$
$439$	24.0391	1.14733	0.573663	+	0.819092i	$0.305522\pi$
$440$	−18.6119	−0.887286
$441$	−6.98104	−0.332431
$442$	−0.394171	−0.0187488
$443$	−8.61339	−0.409235	−0.204617	−	0.978842i	$-0.565595\pi$
$443$	−8.61339	−0.409235	−0.204617	+	0.978842i	$0.565595\pi$
$444$	40.0899	1.90258
$445$	−28.5837	−1.35500
$446$	−6.48648	−0.307144
$447$	7.97695	0.377297
$448$	−0.312005	−0.0147408
$449$	−41.1657	−1.94273	−0.971365	−	0.237592i	$-0.923642\pi$
$449$	−41.1657	−1.94273	−0.971365	+	0.237592i	$0.923642\pi$
$450$	−12.5749	−0.592787
$451$	3.55104	0.167212
$452$	53.9146	2.53593
$453$	6.34255	0.297999
$454$	28.4740	1.33635
$455$	−0.0664589	−0.00311564
$456$	−44.7755	−2.09680
$457$	−39.5093	−1.84817	−0.924084	−	0.382190i	$-0.875170\pi$
$457$	−39.5093	−1.84817	−0.924084	+	0.382190i	$0.875170\pi$
$458$	25.5685	1.19474
$459$	1.00000	0.0466760
$460$	112.187	5.23074
$461$	28.8203	1.34229	0.671147	−	0.741324i	$-0.265802\pi$
$461$	28.8203	1.34229	0.671147	+	0.741324i	$0.265802\pi$
$462$	0.313478	0.0145843
$463$	21.6787	1.00749	0.503747	−	0.863851i	$-0.331954\pi$
$463$	21.6787	1.00749	0.503747	+	0.863851i	$0.331954\pi$
$464$	32.0930	1.48988
$465$	−19.6059	−0.909201
$466$	49.4944	2.29278
$467$	−7.24370	−0.335198	−0.167599	−	0.985855i	$-0.553601\pi$
$467$	−7.24370	−0.335198	−0.167599	+	0.985855i	$0.553601\pi$
$468$	0.705650	0.0326187
$469$	1.67391	0.0772938
$470$	71.3667	3.29190
$471$	−4.96083	−0.228583
$472$	−12.6680	−0.583090
$473$	1.64851	0.0757988
$474$	−2.56879	−0.117988
$475$	32.8349	1.50657
$476$	−0.633165	−0.0290211
$477$	−1.81352	−0.0830355
$478$	−42.4853	−1.94323
$479$	−13.3885	−0.611737	−0.305869	−	0.952074i	$-0.598947\pi$
$479$	−13.3885	−0.611737	−0.305869	+	0.952074i	$0.598947\pi$
$480$	−22.2470	−1.01543
$481$	1.33770	0.0609936
$482$	−67.8094	−3.08863
$483$	−1.06777	−0.0485854
$484$	−46.9729	−2.13513
$485$	−51.5702	−2.34168
$486$	−2.56879	−0.116523
$487$	8.61232	0.390261	0.195131	−	0.980777i	$-0.437487\pi$
$487$	8.61232	0.390261	0.195131	+	0.980777i	$0.437487\pi$
$488$	41.9825	1.90046
$489$	−17.8809	−0.808604
$490$	56.4108	2.54838
$491$	26.6586	1.20308	0.601542	−	0.798841i	$-0.294553\pi$
$491$	26.6586	1.20308	0.601542	+	0.798841i	$0.294553\pi$
$492$	18.4244	0.830638
$493$	4.03660	0.181799
$494$	−2.64389	−0.118954
$495$	2.78810	0.125316
$496$	−49.5527	−2.22498
$497$	−1.07864	−0.0483837
$498$	−16.1706	−0.724623
$499$	−6.29777	−0.281927	−0.140963	−	0.990015i	$-0.545020\pi$
$499$	−6.29777	−0.281927	−0.140963	+	0.990015i	$0.545020\pi$
$500$	−1.51507	−0.0677558
$501$	−0.248750	−0.0111133
$502$	−3.60756	−0.161013
$503$	17.6609	0.787460	0.393730	−	0.919226i	$-0.371185\pi$
$503$	17.6609	0.787460	0.393730	+	0.919226i	$0.371185\pi$
$504$	0.919105	0.0409402
$505$	42.9825	1.91269
$506$	−17.6571	−0.784952
$507$	−12.9765	−0.576305
$508$	43.2043	1.91688
$509$	−5.36610	−0.237848	−0.118924	−	0.992903i	$-0.537944\pi$
$509$	−5.36610	−0.237848	−0.118924	+	0.992903i	$0.537944\pi$
$510$	−8.08058	−0.357814
$511$	−0.0122865	−0.000543525 0
$512$	49.9187	2.20612
$513$	6.70747	0.296142
$514$	29.2335	1.28943
$515$	19.9044	0.877092
$516$	8.55325	0.376536
$517$	−7.82795	−0.344273
$518$	3.08328	0.135472
$519$	−20.4864	−0.899251
$520$	−3.22219	−0.141302
$521$	−6.54100	−0.286566	−0.143283	−	0.989682i	$-0.545766\pi$
$521$	−6.54100	−0.286566	−0.143283	+	0.989682i	$0.545766\pi$
$522$	−10.3692	−0.453846
$523$	24.4974	1.07120	0.535599	−	0.844473i	$-0.320086\pi$
$523$	24.4974	1.07120	0.535599	+	0.844473i	$0.320086\pi$
$524$	80.4418	3.51412
$525$	−0.674000	−0.0294158
$526$	48.7995	2.12776
$527$	−6.23265	−0.271499
$528$	7.04676	0.306671
$529$	37.1437	1.61494
$530$	14.6543	0.636543
$531$	1.89769	0.0823528
$532$	−4.24694	−0.184128
$533$	0.614776	0.0266289
$534$	23.3417	1.01009
$535$	−33.2697	−1.43837
$536$	81.1575	3.50547
$537$	20.3027	0.876127
$538$	21.1480	0.911755
$539$	−6.18750	−0.266514
$540$	14.4660	0.622515
$541$	−42.9711	−1.84747	−0.923737	−	0.383028i	$-0.874881\pi$
$541$	−42.9711	−1.84747	−0.923737	+	0.383028i	$0.874881\pi$
$542$	0.347013	0.0149055
$543$	6.39501	0.274436
$544$	−7.07224	−0.303220
$545$	14.0625	0.602372
$546$	0.0542711	0.00232259
$547$	9.48682	0.405627	0.202814	−	0.979217i	$-0.434991\pi$
$547$	9.48682	0.405627	0.202814	+	0.979217i	$0.434991\pi$
$548$	−28.4532	−1.21546
$549$	−6.28907	−0.268411
$550$	−11.1455	−0.475246
$551$	27.0754	1.15345
$552$	−51.7698	−2.20347
$553$	−0.137684	−0.00585492
$554$	59.8330	2.54206
$555$	27.4230	1.16404
$556$	−61.8610	−2.62349
$557$	−16.5982	−0.703290	−0.351645	−	0.936133i	$-0.614378\pi$
$557$	−16.5982	−0.703290	−0.351645	+	0.936133i	$0.614378\pi$
$558$	16.0104	0.677773
$559$	0.285400	0.0120711
$560$	−3.44344	−0.145512
$561$	0.886329	0.0374208
$562$	−66.2372	−2.79405
$563$	12.6343	0.532471	0.266236	−	0.963908i	$-0.414220\pi$
$563$	12.6343	0.532471	0.266236	+	0.963908i	$0.414220\pi$
$564$	−40.6150	−1.71020
$565$	36.8796	1.55154
$566$	−48.6357	−2.04431
$567$	−0.137684	−0.00578219
$568$	−52.2968	−2.19433
$569$	24.9192	1.04467	0.522334	−	0.852741i	$-0.325062\pi$
$569$	24.9192	1.04467	0.522334	+	0.852741i	$0.325062\pi$
$570$	−54.2002	−2.27020
$571$	6.28106	0.262854	0.131427	−	0.991326i	$-0.458044\pi$
$571$	6.28106	0.262854	0.131427	+	0.991326i	$0.458044\pi$
$572$	0.625437	0.0261509
$573$	6.78820	0.283581
$574$	1.41701	0.0591449
$575$	37.9640	1.58321
$576$	2.26609	0.0944204
$577$	−33.9537	−1.41351	−0.706756	−	0.707457i	$-0.749842\pi$
$577$	−33.9537	−1.41351	−0.706756	+	0.707457i	$0.749842\pi$
$578$	−2.56879	−0.106848
$579$	0.0206068	0.000856388 0
$580$	58.3932	2.42465
$581$	−0.866727	−0.0359579
$582$	42.1128	1.74563
$583$	−1.60738	−0.0665708
$584$	−0.595700	−0.0246502
$585$	0.482691	0.0199568
$586$	−18.9285	−0.781929
$587$	33.7214	1.39183	0.695916	−	0.718124i	$-0.254999\pi$
$587$	33.7214	1.39183	0.695916	+	0.718124i	$0.254999\pi$
$588$	−32.1036	−1.32393
$589$	−41.8053	−1.72256
$590$	−15.3344	−0.631309
$591$	5.35940	0.220456
$592$	69.3100	2.84862
$593$	−31.6351	−1.29910	−0.649549	−	0.760320i	$-0.725042\pi$
$593$	−31.6351	−1.29910	−0.649549	+	0.760320i	$0.725042\pi$
$594$	−2.27679	−0.0934179
$595$	−0.433109	−0.0177558
$596$	36.6834	1.50261
$597$	−18.6041	−0.761415
$598$	−3.05689	−0.125005
$599$	−10.0084	−0.408931	−0.204465	−	0.978874i	$-0.565546\pi$
$599$	−10.0084	−0.408931	−0.204465	+	0.978874i	$0.565546\pi$
$600$	−32.6782	−1.33408
$601$	39.2087	1.59936	0.799679	−	0.600428i	$-0.205003\pi$
$601$	39.2087	1.59936	0.799679	+	0.600428i	$0.205003\pi$
$602$	0.657825	0.0268109
$603$	−12.1576	−0.495095
$604$	29.1674	1.18680
$605$	−32.1312	−1.30632
$606$	−35.0999	−1.42584
$607$	−1.91002	−0.0775251	−0.0387626	−	0.999248i	$-0.512342\pi$
$607$	−1.91002	−0.0775251	−0.0387626	+	0.999248i	$0.512342\pi$
$608$	−47.4368	−1.92382
$609$	−0.555775	−0.0225211
$610$	50.8193	2.05761
$611$	−1.35522	−0.0548262
$612$	4.59868	0.185891
$613$	−10.1587	−0.410305	−0.205152	−	0.978730i	$-0.565769\pi$
$613$	−10.1587	−0.410305	−0.205152	+	0.978730i	$0.565769\pi$
$614$	62.4175	2.51896
$615$	12.6030	0.508203
$616$	0.814629	0.0328223
$617$	6.58019	0.264909	0.132454	−	0.991189i	$-0.457714\pi$
$617$	6.58019	0.264909	0.132454	+	0.991189i	$0.457714\pi$
$618$	−16.2541	−0.653837
$619$	−20.5201	−0.824771	−0.412386	−	0.911009i	$-0.635304\pi$
$619$	−20.5201	−0.824771	−0.412386	+	0.911009i	$0.635304\pi$
$620$	−90.1612	−3.62096
$621$	7.75524	0.311207
$622$	17.5088	0.702040
$623$	1.25109	0.0501238
$624$	1.21997	0.0488380
$625$	−25.5127	−1.02051
$626$	−58.7289	−2.34728
$627$	5.94502	0.237421
$628$	−22.8133	−0.910349
$629$	8.71769	0.347597
$630$	1.11257	0.0443257
$631$	22.7532	0.905792	0.452896	−	0.891563i	$-0.350391\pi$
$631$	22.7532	0.905792	0.452896	+	0.891563i	$0.350391\pi$
$632$	−6.67546	−0.265536
$633$	12.3382	0.490401
$634$	−28.1516	−1.11804
$635$	29.5534	1.17279
$636$	−8.33981	−0.330695
$637$	−1.07121	−0.0424430
$638$	−9.19049	−0.363855
$639$	7.83419	0.309916
$640$	26.1826	1.03496
$641$	34.8738	1.37743	0.688715	−	0.725032i	$-0.258175\pi$
$641$	34.8738	1.37743	0.688715	+	0.725032i	$0.258175\pi$
$642$	27.1684	1.07225
$643$	36.3233	1.43245	0.716225	−	0.697870i	$-0.245868\pi$
$643$	36.3233	1.43245	0.716225	+	0.697870i	$0.245868\pi$
$644$	−4.91035	−0.193495
$645$	5.85075	0.230373
$646$	−17.2301	−0.677909
$647$	13.9056	0.546687	0.273343	−	0.961917i	$-0.411870\pi$
$647$	13.9056	0.546687	0.273343	+	0.961917i	$0.411870\pi$
$648$	−6.67546	−0.262237
$649$	1.68198	0.0660234
$650$	−1.92957	−0.0756840
$651$	0.858137	0.0336330
$652$	−82.2287	−3.22032
$653$	−37.4461	−1.46538	−0.732690	−	0.680562i	$-0.761736\pi$
$653$	−37.4461	−1.46538	−0.732690	+	0.680562i	$0.761736\pi$
$654$	−11.4836	−0.449044
$655$	55.0253	2.15002
$656$	31.8534	1.24367
$657$	0.0892372	0.00348148
$658$	−3.12367	−0.121773
$659$	−28.9304	−1.12697	−0.563485	−	0.826126i	$-0.690540\pi$
$659$	−28.9304	−1.12697	−0.563485	+	0.826126i	$0.690540\pi$
$660$	12.8216	0.499080
$661$	21.5071	0.836529	0.418264	−	0.908325i	$-0.362639\pi$
$661$	21.5071	0.836529	0.418264	+	0.908325i	$0.362639\pi$
$662$	−63.3948	−2.46391
$663$	0.153446	0.00595935
$664$	−42.0223	−1.63078
$665$	−2.90507	−0.112654
$666$	−22.3939	−0.867746
$667$	31.3048	1.21213
$668$	−1.14392	−0.0442597
$669$	2.52511	0.0976264
$670$	98.2403	3.79535
$671$	−5.57418	−0.215189
$672$	0.973735	0.0375626
$673$	−28.6479	−1.10430	−0.552148	−	0.833746i	$-0.686192\pi$
$673$	−28.6479	−1.10430	−0.552148	+	0.833746i	$0.686192\pi$
$674$	−46.6465	−1.79676
$675$	4.89527	0.188419
$676$	−59.6746	−2.29518
$677$	−5.18671	−0.199341	−0.0996707	−	0.995020i	$-0.531779\pi$
$677$	−5.18671	−0.199341	−0.0996707	+	0.995020i	$0.531779\pi$
$678$	−30.1163	−1.15661
$679$	2.25720	0.0866232
$680$	−20.9988	−0.805269
$681$	−11.0846	−0.424763
$682$	14.1904	0.543380
$683$	3.48378	0.133303	0.0666516	−	0.997776i	$-0.478768\pi$
$683$	3.48378	0.133303	0.0666516	+	0.997776i	$0.478768\pi$
$684$	30.8455	1.17941
$685$	−19.4631	−0.743647
$686$	−4.94484	−0.188795
$687$	−9.95351	−0.379750
$688$	14.7874	0.563765
$689$	−0.278278	−0.0106016
$690$	−62.6668	−2.38568
$691$	−13.1216	−0.499169	−0.249584	−	0.968353i	$-0.580294\pi$
$691$	−13.1216	−0.499169	−0.249584	+	0.968353i	$0.580294\pi$
$692$	−94.2102	−3.58133
$693$	−0.122033	−0.00463566
$694$	−12.6975	−0.481989
$695$	−42.3153	−1.60511
$696$	−26.9462	−1.02139
$697$	4.00646	0.151756
$698$	28.1231	1.06447
$699$	−19.2676	−0.728767
$700$	−3.09951	−0.117151
$701$	−33.0949	−1.24998	−0.624988	−	0.780634i	$-0.714896\pi$
$701$	−33.0949	−1.24998	−0.624988	+	0.780634i	$0.714896\pi$
$702$	−0.394171	−0.0148770
$703$	58.4736	2.20537
$704$	2.00850	0.0756982
$705$	−27.7822	−1.04634
$706$	16.4596	0.619467
$707$	−1.88131	−0.0707541
$708$	8.72687	0.327976
$709$	6.41526	0.240930	0.120465	−	0.992718i	$-0.461561\pi$
$709$	6.41526	0.240930	0.120465	+	0.992718i	$0.461561\pi$
$710$	−63.3047	−2.37578
$711$	1.00000	0.0375029
$712$	60.6577	2.27324
$713$	−48.3357	−1.81019
$714$	0.353681	0.0132362
$715$	0.427823	0.0159997
$716$	93.3657	3.48924
$717$	16.5390	0.617662
$718$	66.8298	2.49407
$719$	13.4629	0.502081	0.251040	−	0.967977i	$-0.419227\pi$
$719$	13.4629	0.502081	0.251040	+	0.967977i	$0.419227\pi$
$720$	25.0097	0.932056
$721$	−0.871202	−0.0324452
$722$	−66.7633	−2.48467
$723$	26.3974	0.981730
$724$	29.4086	1.09296
$725$	19.7602	0.733876
$726$	26.2387	0.973810
$727$	−24.5117	−0.909090	−0.454545	−	0.890724i	$-0.650198\pi$
$727$	−24.5117	−0.909090	−0.454545	+	0.890724i	$0.650198\pi$
$728$	0.141033	0.00522704
$729$	1.00000	0.0370370
$730$	−0.721088	−0.0266887
$731$	1.85994	0.0687922
$732$	−28.9214	−1.06897
$733$	46.4494	1.71565	0.857824	−	0.513944i	$-0.171816\pi$
$733$	46.4494	1.71565	0.857824	+	0.513944i	$0.171816\pi$
$734$	−18.0414	−0.665921
$735$	−21.9601	−0.810010
$736$	−54.8469	−2.02168
$737$	−10.7756	−0.396925
$738$	−10.2918	−0.378845
$739$	−25.7210	−0.946163	−0.473081	−	0.881019i	$-0.656858\pi$
$739$	−25.7210	−0.946163	−0.473081	+	0.881019i	$0.656858\pi$
$740$	126.110	4.63588
$741$	1.02924	0.0378099
$742$	−0.641410	−0.0235469
$743$	−40.1614	−1.47338	−0.736689	−	0.676232i	$-0.763612\pi$
$743$	−40.1614	−1.47338	−0.736689	+	0.676232i	$0.763612\pi$
$744$	41.6058	1.52534
$745$	25.0929	0.919332
$746$	52.8125	1.93360
$747$	6.29504	0.230323
$748$	4.07594	0.149031
$749$	1.45619	0.0532081
$750$	0.846305	0.0309027
$751$	−34.8498	−1.27169	−0.635844	−	0.771818i	$-0.719348\pi$
$751$	−34.8498	−1.27169	−0.635844	+	0.771818i	$0.719348\pi$
$752$	−70.2179	−2.56058
$753$	1.40438	0.0511785
$754$	−1.59111	−0.0579448
$755$	19.9516	0.726113
$756$	−0.633165	−0.0230280
$757$	23.6413	0.859259	0.429629	−	0.903005i	$-0.358644\pi$
$757$	23.6413	0.859259	0.429629	+	0.903005i	$0.358644\pi$
$758$	72.8611	2.64643
$759$	6.87369	0.249499
$760$	−140.849	−5.10913
$761$	−23.9851	−0.869458	−0.434729	−	0.900561i	$-0.643156\pi$
$761$	−23.9851	−0.869458	−0.434729	+	0.900561i	$0.643156\pi$
$762$	−24.1336	−0.874267
$763$	−0.615507	−0.0222829
$764$	31.2168	1.12938
$765$	3.14567	0.113732
$766$	2.25529	0.0814870
$767$	0.291193	0.0105144
$768$	−25.9132	−0.935061
$769$	5.09074	0.183577	0.0917884	−	0.995779i	$-0.470742\pi$
$769$	5.09074	0.183577	0.0917884	+	0.995779i	$0.470742\pi$
$770$	0.986100	0.0355366
$771$	−11.3803	−0.409850
$772$	0.0947639	0.00341063
$773$	−39.5891	−1.42392	−0.711960	−	0.702220i	$-0.752192\pi$
$773$	−39.5891	−1.42392	−0.711960	+	0.702220i	$0.752192\pi$
$774$	−4.77778	−0.171734
$775$	−30.5105	−1.09597
$776$	109.438	3.92858
$777$	−1.20029	−0.0430600
$778$	−47.5898	−1.70618
$779$	26.8732	0.962834
$780$	2.21974	0.0794796
$781$	6.94366	0.248464
$782$	−19.9216	−0.712394
$783$	4.03660	0.144256
$784$	−55.5028	−1.98224
$785$	−15.6052	−0.556972
$786$	−44.9342	−1.60275
$787$	13.0925	0.466697	0.233348	−	0.972393i	$-0.425032\pi$
$787$	13.0925	0.466697	0.233348	+	0.972393i	$0.425032\pi$
$788$	24.6461	0.877983
$789$	−18.9971	−0.676313
$790$	−8.08058	−0.287494
$791$	−1.61420	−0.0573943
$792$	−5.91665	−0.210239
$793$	−0.965034	−0.0342693
$794$	−20.0102	−0.710134
$795$	−5.70475	−0.202327
$796$	−85.5543	−3.03239
$797$	−18.4655	−0.654082	−0.327041	−	0.945010i	$-0.606052\pi$
$797$	−18.4655	−0.654082	−0.327041	+	0.945010i	$0.606052\pi$
$798$	2.37231	0.0839788
$799$	−8.83188	−0.312449
$800$	−34.6205	−1.22402
$801$	−9.08666	−0.321061
$802$	−78.4895	−2.77156
$803$	0.0790935	0.00279115
$804$	−55.9089	−1.97175
$805$	−3.35887	−0.118384
$806$	2.45673	0.0865346
$807$	−8.23267	−0.289804
$808$	−91.2135	−3.20888
$809$	−49.5903	−1.74350	−0.871751	−	0.489949i	$-0.837015\pi$
$809$	−49.5903	−1.74350	−0.871751	+	0.489949i	$0.837015\pi$
$810$	−8.08058	−0.283922
$811$	17.5640	0.616756	0.308378	−	0.951264i	$-0.400214\pi$
$811$	17.5640	0.616756	0.308378	+	0.951264i	$0.400214\pi$
$812$	−2.55583	−0.0896921
$813$	−0.135088	−0.00473775
$814$	−19.8484	−0.695684
$815$	−56.2476	−1.97027
$816$	7.95050	0.278323
$817$	12.4755	0.436461
$818$	−101.364	−3.54410
$819$	−0.0211271	−0.000738240 0
$820$	57.9573	2.02396
$821$	−37.4516	−1.30707	−0.653535	−	0.756896i	$-0.726715\pi$
$821$	−37.4516	−1.30707	−0.653535	+	0.756896i	$0.726715\pi$
$822$	15.8938	0.554359
$823$	−0.551602	−0.0192276	−0.00961382	−	0.999954i	$-0.503060\pi$
$823$	−0.551602	−0.0192276	−0.00961382	+	0.999954i	$0.503060\pi$
$824$	−42.2393	−1.47147
$825$	4.33881	0.151058
$826$	0.671178	0.0233533
$827$	−23.1491	−0.804971	−0.402486	−	0.915426i	$-0.631854\pi$
$827$	−23.1491	−0.804971	−0.402486	+	0.915426i	$0.631854\pi$
$828$	35.6639	1.23941
$829$	25.0048	0.868454	0.434227	−	0.900803i	$-0.357022\pi$
$829$	25.0048	0.868454	0.434227	+	0.900803i	$0.357022\pi$
$830$	−50.8675	−1.76564
$831$	−23.2923	−0.808001
$832$	0.347723	0.0120551
$833$	−6.98104	−0.241879
$834$	34.5551	1.19655
$835$	−0.782487	−0.0270791
$836$	27.3393	0.945548
$837$	−6.23265	−0.215432
$838$	7.98232	0.275745
$839$	11.0268	0.380687	0.190343	−	0.981718i	$-0.439040\pi$
$839$	11.0268	0.380687	0.190343	+	0.981718i	$0.439040\pi$
$840$	2.89121	0.0997561
$841$	−12.7059	−0.438134
$842$	28.7121	0.989484
$843$	25.7854	0.888095
$844$	56.7396	1.95306
$845$	−40.8197	−1.40424
$846$	22.6872	0.780003
$847$	1.40636	0.0483232
$848$	−14.4184	−0.495131
$849$	18.9333	0.649790
$850$	−12.5749	−0.431316
$851$	67.6077	2.31756
$852$	36.0269	1.23426
$853$	39.0814	1.33812	0.669061	−	0.743207i	$-0.266696\pi$
$853$	39.0814	1.33812	0.669061	+	0.743207i	$0.266696\pi$
$854$	−2.22433	−0.0761149
$855$	21.0995	0.721588
$856$	70.6019	2.41312
$857$	−42.7467	−1.46020	−0.730099	−	0.683341i	$-0.760526\pi$
$857$	−42.7467	−1.46020	−0.730099	+	0.683341i	$0.760526\pi$
$858$	−0.349365	−0.0119271
$859$	42.2640	1.44203	0.721014	−	0.692920i	$-0.243676\pi$
$859$	42.2640	1.44203	0.721014	+	0.692920i	$0.243676\pi$
$860$	26.9057	0.917478
$861$	−0.551626	−0.0187994
$862$	−19.9038	−0.677925
$863$	−10.1925	−0.346958	−0.173479	−	0.984838i	$-0.555501\pi$
$863$	−10.1925	−0.346958	−0.173479	+	0.984838i	$0.555501\pi$
$864$	−7.07224	−0.240602
$865$	−64.4434	−2.19114
$866$	32.4772	1.10362
$867$	1.00000	0.0339618
$868$	3.94630	0.133946
$869$	0.886329	0.0300666
$870$	−32.6180	−1.10585
$871$	−1.86553	−0.0632112
$872$	−29.8422	−1.01058
$873$	−16.3940	−0.554854
$874$	−133.623	−4.51988
$875$	0.0453610	0.00153348
$876$	0.410374	0.0138652
$877$	−29.6015	−0.999571	−0.499786	−	0.866149i	$-0.666588\pi$
$877$	−29.6015	−0.999571	−0.499786	+	0.866149i	$0.666588\pi$
$878$	−61.7515	−2.08401
$879$	7.36864	0.248538
$880$	22.1668	0.747243
$881$	18.6139	0.627117	0.313559	−	0.949569i	$-0.398479\pi$
$881$	18.6139	0.627117	0.313559	+	0.949569i	$0.398479\pi$
$882$	17.9328	0.603830
$883$	−20.1737	−0.678899	−0.339449	−	0.940624i	$-0.610241\pi$
$883$	−20.1737	−0.678899	−0.339449	+	0.940624i	$0.610241\pi$
$884$	0.705650	0.0237336
$885$	5.96952	0.200663
$886$	22.1260	0.743337
$887$	32.5535	1.09304	0.546521	−	0.837446i	$-0.315952\pi$
$887$	32.5535	1.09304	0.546521	+	0.837446i	$0.315952\pi$
$888$	−58.1946	−1.95288
$889$	−1.29353	−0.0433837
$890$	73.4254	2.46123
$891$	0.886329	0.0296931
$892$	11.6122	0.388804
$893$	−59.2396	−1.98238
$894$	−20.4911	−0.685325
$895$	63.8657	2.13480
$896$	−1.14600	−0.0382850
$897$	1.19001	0.0397333
$898$	105.746	3.52879
$899$	−25.1587	−0.839090
$900$	22.5118	0.750392
$901$	−1.81352	−0.0604172
$902$	−9.12188	−0.303725
$903$	−0.256084	−0.00852193
$904$	−78.2626	−2.60298
$905$	20.1166	0.668699
$906$	−16.2927	−0.541288
$907$	−48.4169	−1.60766	−0.803829	−	0.594860i	$-0.797207\pi$
$907$	−48.4169	−1.60766	−0.803829	+	0.594860i	$0.797207\pi$
$908$	−50.9745	−1.69165
$909$	13.6640	0.453206
$910$	0.170719	0.00565928
$911$	25.5200	0.845517	0.422758	−	0.906242i	$-0.361062\pi$
$911$	25.5200	0.845517	0.422758	+	0.906242i	$0.361062\pi$
$912$	53.3278	1.76586
$913$	5.57947	0.184654
$914$	101.491	3.35703
$915$	−19.7834	−0.654018
$916$	−45.7730	−1.51238
$917$	−2.40842	−0.0795331
$918$	−2.56879	−0.0847827
$919$	45.6377	1.50545	0.752724	−	0.658337i	$-0.228740\pi$
$919$	45.6377	1.50545	0.752724	+	0.658337i	$0.228740\pi$
$920$	−162.851	−5.36904
$921$	−24.2984	−0.800659
$922$	−74.0332	−2.43815
$923$	1.20213	0.0395684
$924$	−0.561192	−0.0184619
$925$	42.6754	1.40316
$926$	−55.6880	−1.83002
$927$	6.32754	0.207824
$928$	−28.5478	−0.937127
$929$	28.5673	0.937262	0.468631	−	0.883394i	$-0.344747\pi$
$929$	28.5673	0.937262	0.468631	+	0.883394i	$0.344747\pi$
$930$	50.3634	1.65148
$931$	−46.8252	−1.53463
$932$	−88.6055	−2.90237
$933$	−6.81598	−0.223145
$934$	18.6075	0.608857
$935$	2.78810	0.0911806
$936$	−1.02432	−0.0334811
$937$	−28.4968	−0.930951	−0.465476	−	0.885061i	$-0.654117\pi$
$937$	−28.4968	−0.930951	−0.465476	+	0.885061i	$0.654117\pi$
$938$	−4.29991	−0.140397
$939$	22.8625	0.746088
$940$	−127.762	−4.16712
$941$	−17.4581	−0.569119	−0.284559	−	0.958658i	$-0.591847\pi$
$941$	−17.4581	−0.569119	−0.284559	+	0.958658i	$0.591847\pi$
$942$	12.7433	0.415200
$943$	31.0711	1.01181
$944$	15.0876	0.491059
$945$	−0.433109	−0.0140890
$946$	−4.23469	−0.137682
$947$	−45.4816	−1.47795	−0.738976	−	0.673731i	$-0.764690\pi$
$947$	−45.4816	−1.47795	−0.738976	+	0.673731i	$0.764690\pi$
$948$	4.59868	0.149358
$949$	0.0136931	0.000444497 0
$950$	−84.3459	−2.73654
$951$	10.9591	0.355373
$952$	0.919105	0.0297884
$953$	40.1735	1.30135	0.650674	−	0.759357i	$-0.274486\pi$
$953$	40.1735	1.30135	0.650674	+	0.759357i	$0.274486\pi$
$954$	4.65856	0.150826
$955$	21.3535	0.690982
$956$	76.0577	2.45988
$957$	3.57775	0.115652
$958$	34.3923	1.11116
$959$	0.851888	0.0275089
$960$	7.12838	0.230067
$961$	7.84593	0.253094
$962$	−3.43626	−0.110789
$963$	−10.5763	−0.340817
$964$	121.393	3.90981
$965$	0.0648221	0.00208670
$966$	2.74288	0.0882509
$967$	31.9226	1.02656	0.513281	−	0.858221i	$-0.328430\pi$
$967$	31.9226	1.02656	0.513281	+	0.858221i	$0.328430\pi$
$968$	68.1860	2.19158
$969$	6.70747	0.215475
$970$	132.473	4.25346
$971$	−14.9843	−0.480869	−0.240434	−	0.970665i	$-0.577290\pi$
$971$	−14.9843	−0.480869	−0.240434	+	0.970665i	$0.577290\pi$
$972$	4.59868	0.147503
$973$	1.85211	0.0593760
$974$	−22.1232	−0.708874
$975$	0.751160	0.0240564
$976$	−50.0013	−1.60050
$977$	−8.88467	−0.284246	−0.142123	−	0.989849i	$-0.545393\pi$
$977$	−8.88467	−0.284246	−0.142123	+	0.989849i	$0.545393\pi$
$978$	45.9324	1.46876
$979$	−8.05377	−0.257399
$980$	−100.987	−3.22592
$981$	4.47043	0.142730
$982$	−68.4803	−2.18529
$983$	33.4795	1.06783	0.533915	−	0.845538i	$-0.320720\pi$
$983$	33.4795	1.06783	0.533915	+	0.845538i	$0.320720\pi$
$984$	−26.7450	−0.852600
$985$	16.8589	0.537170
$986$	−10.3692	−0.330222
$987$	1.21601	0.0387060
$988$	4.73313	0.150581
$989$	14.4242	0.458664
$990$	−7.16204	−0.227625
$991$	−52.5256	−1.66853	−0.834265	−	0.551364i	$-0.814108\pi$
$991$	−52.5256	−1.66853	−0.834265	+	0.551364i	$0.814108\pi$
$992$	44.0788	1.39950
$993$	24.6789	0.783160
$994$	2.77081	0.0878847
$995$	−58.5224	−1.85529
$996$	28.9489	0.917280
$997$	10.5707	0.334776	0.167388	−	0.985891i	$-0.446467\pi$
$997$	10.5707	0.334776	0.167388	+	0.985891i	$0.446467\pi$
$998$	16.1776	0.512094
$999$	8.71769	0.275815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.2	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.56879 q^{2} +1.00000 q^{3} +4.59868 q^{4} +3.14567 q^{5} -2.56879 q^{6} -0.137684 q^{7} -6.67546 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.56879 q^{2} +1.00000 q^{3} +4.59868 q^{4} +3.14567 q^{5} -2.56879 q^{6} -0.137684 q^{7} -6.67546 q^{8} +1.00000 q^{9} -8.08058 q^{10} +0.886329 q^{11} +4.59868 q^{12} +0.153446 q^{13} +0.353681 q^{14} +3.14567 q^{15} +7.95050 q^{16} +1.00000 q^{17} -2.56879 q^{18} +6.70747 q^{19} +14.4660 q^{20} -0.137684 q^{21} -2.27679 q^{22} +7.75524 q^{23} -6.67546 q^{24} +4.89527 q^{25} -0.394171 q^{26} +1.00000 q^{27} -0.633165 q^{28} +4.03660 q^{29} -8.08058 q^{30} -6.23265 q^{31} -7.07224 q^{32} +0.886329 q^{33} -2.56879 q^{34} -0.433109 q^{35} +4.59868 q^{36} +8.71769 q^{37} -17.2301 q^{38} +0.153446 q^{39} -20.9988 q^{40} +4.00646 q^{41} +0.353681 q^{42} +1.85994 q^{43} +4.07594 q^{44} +3.14567 q^{45} -19.9216 q^{46} -8.83188 q^{47} +7.95050 q^{48} -6.98104 q^{49} -12.5749 q^{50} +1.00000 q^{51} +0.705650 q^{52} -1.81352 q^{53} -2.56879 q^{54} +2.78810 q^{55} +0.919105 q^{56} +6.70747 q^{57} -10.3692 q^{58} +1.89769 q^{59} +14.4660 q^{60} -6.28907 q^{61} +16.0104 q^{62} -0.137684 q^{63} +2.26609 q^{64} +0.482691 q^{65} -2.27679 q^{66} -12.1576 q^{67} +4.59868 q^{68} +7.75524 q^{69} +1.11257 q^{70} +7.83419 q^{71} -6.67546 q^{72} +0.0892372 q^{73} -22.3939 q^{74} +4.89527 q^{75} +30.8455 q^{76} -0.122033 q^{77} -0.394171 q^{78} +1.00000 q^{79} +25.0097 q^{80} +1.00000 q^{81} -10.2918 q^{82} +6.29504 q^{83} -0.633165 q^{84} +3.14567 q^{85} -4.77778 q^{86} +4.03660 q^{87} -5.91665 q^{88} -9.08666 q^{89} -8.08058 q^{90} -0.0211271 q^{91} +35.6639 q^{92} -6.23265 q^{93} +22.6872 q^{94} +21.0995 q^{95} -7.07224 q^{96} -16.3940 q^{97} +17.9328 q^{98} +0.886329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 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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