LMFDB - Embedded newform 8029.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70672 q^{2} +2.12991 q^{3} +5.32631 q^{4} -2.23028 q^{5} -5.76507 q^{6} +1.00000 q^{7} -9.00339 q^{8} +1.53652 q^{9} +O(q^{10})$	\(q-2.70672 q^{2} +2.12991 q^{3} +5.32631 q^{4} -2.23028 q^{5} -5.76507 q^{6} +1.00000 q^{7} -9.00339 q^{8} +1.53652 q^{9} +6.03675 q^{10} +4.95603 q^{11} +11.3446 q^{12} -5.36363 q^{13} -2.70672 q^{14} -4.75031 q^{15} +13.7170 q^{16} +6.72943 q^{17} -4.15894 q^{18} -0.773178 q^{19} -11.8792 q^{20} +2.12991 q^{21} -13.4146 q^{22} -6.47732 q^{23} -19.1764 q^{24} -0.0258357 q^{25} +14.5178 q^{26} -3.11707 q^{27} +5.32631 q^{28} +5.18642 q^{29} +12.8577 q^{30} +1.00000 q^{31} -19.1212 q^{32} +10.5559 q^{33} -18.2147 q^{34} -2.23028 q^{35} +8.18402 q^{36} +1.00000 q^{37} +2.09277 q^{38} -11.4241 q^{39} +20.0801 q^{40} -9.63660 q^{41} -5.76507 q^{42} -1.75577 q^{43} +26.3974 q^{44} -3.42689 q^{45} +17.5323 q^{46} -5.65376 q^{47} +29.2160 q^{48} +1.00000 q^{49} +0.0699299 q^{50} +14.3331 q^{51} -28.5684 q^{52} +1.55771 q^{53} +8.43703 q^{54} -11.0534 q^{55} -9.00339 q^{56} -1.64680 q^{57} -14.0382 q^{58} -1.15151 q^{59} -25.3016 q^{60} -5.88076 q^{61} -2.70672 q^{62} +1.53652 q^{63} +24.3218 q^{64} +11.9624 q^{65} -28.5719 q^{66} +6.84298 q^{67} +35.8431 q^{68} -13.7961 q^{69} +6.03675 q^{70} +14.3450 q^{71} -13.8339 q^{72} +11.7703 q^{73} -2.70672 q^{74} -0.0550277 q^{75} -4.11819 q^{76} +4.95603 q^{77} +30.9217 q^{78} +12.1352 q^{79} -30.5928 q^{80} -11.2487 q^{81} +26.0835 q^{82} +15.9764 q^{83} +11.3446 q^{84} -15.0085 q^{85} +4.75236 q^{86} +11.0466 q^{87} -44.6211 q^{88} +17.2589 q^{89} +9.27561 q^{90} -5.36363 q^{91} -34.5002 q^{92} +2.12991 q^{93} +15.3031 q^{94} +1.72441 q^{95} -40.7266 q^{96} -5.29694 q^{97} -2.70672 q^{98} +7.61507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) $ 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * 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 $

$2$	−2.70672	−1.91394	−0.956969	−	0.290191i	$-0.906281\pi$
$2$	−2.70672	−1.91394	−0.956969	+	0.290191i	$0.906281\pi$
$3$	2.12991	1.22971	0.614853	−	0.788642i	$-0.289215\pi$
$3$	2.12991	1.22971	0.614853	+	0.788642i	$0.289215\pi$
$4$	5.32631	2.66316
$5$	−2.23028	−0.997413	−0.498707	−	0.866771i	$-0.666191\pi$
$5$	−2.23028	−0.997413	−0.498707	+	0.866771i	$0.666191\pi$
$6$	−5.76507	−2.35358
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.00339	−3.18318
$9$	1.53652	0.512175
$10$	6.03675	1.90899
$11$	4.95603	1.49430	0.747150	−	0.664655i	$-0.231421\pi$
$11$	4.95603	1.49430	0.747150	+	0.664655i	$0.231421\pi$
$12$	11.3446	3.27490
$13$	−5.36363	−1.48760	−0.743802	−	0.668400i	$-0.766980\pi$
$13$	−5.36363	−1.48760	−0.743802	+	0.668400i	$0.766980\pi$
$14$	−2.70672	−0.723400
$15$	−4.75031	−1.22652
$16$	13.7170	3.42925
$17$	6.72943	1.63213	0.816063	−	0.577962i	$-0.196152\pi$
$17$	6.72943	1.63213	0.816063	+	0.577962i	$0.196152\pi$
$18$	−4.15894	−0.980271
$19$	−0.773178	−0.177379	−0.0886896	−	0.996059i	$-0.528268\pi$
$19$	−0.773178	−0.177379	−0.0886896	+	0.996059i	$0.528268\pi$
$20$	−11.8792	−2.65627
$21$	2.12991	0.464785
$22$	−13.4146	−2.86000
$23$	−6.47732	−1.35061	−0.675307	−	0.737537i	$-0.735989\pi$
$23$	−6.47732	−1.35061	−0.675307	+	0.737537i	$0.735989\pi$
$24$	−19.1764	−3.91437
$25$	−0.0258357	−0.00516714
$26$	14.5178	2.84718
$27$	−3.11707	−0.599881
$28$	5.32631	1.00658
$29$	5.18642	0.963094	0.481547	−	0.876420i	$-0.340075\pi$
$29$	5.18642	0.963094	0.481547	+	0.876420i	$0.340075\pi$
$30$	12.8577	2.34749
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−19.1212	−3.38019
$33$	10.5559	1.83755
$34$	−18.2147	−3.12379
$35$	−2.23028	−0.376987
$36$	8.18402	1.36400
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	2.09277	0.339493
$39$	−11.4241	−1.82931
$40$	20.0801	3.17494
$41$	−9.63660	−1.50498	−0.752492	−	0.658602i	$-0.771148\pi$
$41$	−9.63660	−1.50498	−0.752492	+	0.658602i	$0.771148\pi$
$42$	−5.76507	−0.889569
$43$	−1.75577	−0.267752	−0.133876	−	0.990998i	$-0.542742\pi$
$43$	−1.75577	−0.267752	−0.133876	+	0.990998i	$0.542742\pi$
$44$	26.3974	3.97956
$45$	−3.42689	−0.510850
$46$	17.5323	2.58499
$47$	−5.65376	−0.824686	−0.412343	−	0.911029i	$-0.635289\pi$
$47$	−5.65376	−0.824686	−0.412343	+	0.911029i	$0.635289\pi$
$48$	29.2160	4.21697
$49$	1.00000	0.142857
$50$	0.0699299	0.00988958
$51$	14.3331	2.00704
$52$	−28.5684	−3.96172
$53$	1.55771	0.213968	0.106984	−	0.994261i	$-0.465881\pi$
$53$	1.55771	0.213968	0.106984	+	0.994261i	$0.465881\pi$
$54$	8.43703	1.14813
$55$	−11.0534	−1.49044
$56$	−9.00339	−1.20313
$57$	−1.64680	−0.218124
$58$	−14.0382	−1.84330
$59$	−1.15151	−0.149914	−0.0749572	−	0.997187i	$-0.523882\pi$
$59$	−1.15151	−0.149914	−0.0749572	+	0.997187i	$0.523882\pi$
$60$	−25.3016	−3.26643
$61$	−5.88076	−0.752954	−0.376477	−	0.926426i	$-0.622865\pi$
$61$	−5.88076	−0.752954	−0.376477	+	0.926426i	$0.622865\pi$
$62$	−2.70672	−0.343753
$63$	1.53652	0.193584
$64$	24.3218	3.04022
$65$	11.9624	1.48376
$66$	−28.5719	−3.51696
$67$	6.84298	0.836003	0.418002	−	0.908446i	$-0.362731\pi$
$67$	6.84298	0.836003	0.418002	+	0.908446i	$0.362731\pi$
$68$	35.8431	4.34661
$69$	−13.7961	−1.66086
$70$	6.03675	0.721529
$71$	14.3450	1.70244	0.851219	−	0.524811i	$-0.175864\pi$
$71$	14.3450	1.70244	0.851219	+	0.524811i	$0.175864\pi$
$72$	−13.8339	−1.63034
$73$	11.7703	1.37761	0.688804	−	0.724948i	$-0.258136\pi$
$73$	11.7703	1.37761	0.688804	+	0.724948i	$0.258136\pi$
$74$	−2.70672	−0.314649
$75$	−0.0550277	−0.00635406
$76$	−4.11819	−0.472389
$77$	4.95603	0.564793
$78$	30.9217	3.50119
$79$	12.1352	1.36532	0.682661	−	0.730735i	$-0.260823\pi$
$79$	12.1352	1.36532	0.682661	+	0.730735i	$0.260823\pi$
$80$	−30.5928	−3.42038
$81$	−11.2487	−1.24985
$82$	26.0835	2.88044
$83$	15.9764	1.75364	0.876821	−	0.480818i	$-0.159660\pi$
$83$	15.9764	1.75364	0.876821	+	0.480818i	$0.159660\pi$
$84$	11.3446	1.23780
$85$	−15.0085	−1.62790
$86$	4.75236	0.512460
$87$	11.0466	1.18432
$88$	−44.6211	−4.75663
$89$	17.2589	1.82944	0.914721	−	0.404087i	$-0.132411\pi$
$89$	17.2589	1.82944	0.914721	+	0.404087i	$0.132411\pi$
$90$	9.27561	0.977735
$91$	−5.36363	−0.562262
$92$	−34.5002	−3.59690
$93$	2.12991	0.220862
$94$	15.3031	1.57840
$95$	1.72441	0.176920
$96$	−40.7266	−4.15664
$97$	−5.29694	−0.537822	−0.268911	−	0.963165i	$-0.586664\pi$
$97$	−5.29694	−0.537822	−0.268911	+	0.963165i	$0.586664\pi$
$98$	−2.70672	−0.273420
$99$	7.61507	0.765343
$100$	−0.137609	−0.0137609
$101$	15.0260	1.49514	0.747571	−	0.664182i	$-0.231220\pi$
$101$	15.0260	1.49514	0.747571	+	0.664182i	$0.231220\pi$
$102$	−38.7956	−3.84134
$103$	−5.50726	−0.542646	−0.271323	−	0.962488i	$-0.587461\pi$
$103$	−5.50726	−0.542646	−0.271323	+	0.962488i	$0.587461\pi$
$104$	48.2909	4.73531
$105$	−4.75031	−0.463583
$106$	−4.21628	−0.409521
$107$	−0.513430	−0.0496352	−0.0248176	−	0.999692i	$-0.507900\pi$
$107$	−0.513430	−0.0496352	−0.0248176	+	0.999692i	$0.507900\pi$
$108$	−16.6025	−1.59758
$109$	−15.1299	−1.44918	−0.724589	−	0.689181i	$-0.757971\pi$
$109$	−15.1299	−1.44918	−0.724589	+	0.689181i	$0.757971\pi$
$110$	29.9183	2.85260
$111$	2.12991	0.202162
$112$	13.7170	1.29613
$113$	−5.68137	−0.534458	−0.267229	−	0.963633i	$-0.586108\pi$
$113$	−5.68137	−0.534458	−0.267229	+	0.963633i	$0.586108\pi$
$114$	4.45743	0.417476
$115$	14.4463	1.34712
$116$	27.6245	2.56487
$117$	−8.24136	−0.761914
$118$	3.11682	0.286927
$119$	6.72943	0.616886
$120$	42.7689	3.90425
$121$	13.5623	1.23293
$122$	15.9175	1.44111
$123$	−20.5251	−1.85069
$124$	5.32631	0.478317
$125$	11.2090	1.00257
$126$	−4.15894	−0.370508
$127$	−6.27201	−0.556551	−0.278276	−	0.960501i	$-0.589763\pi$
$127$	−6.27201	−0.556551	−0.278276	+	0.960501i	$0.589763\pi$
$128$	−27.5897	−2.43861
$129$	−3.73963	−0.329256
$130$	−32.3789	−2.83982
$131$	3.63621	0.317697	0.158848	−	0.987303i	$-0.449222\pi$
$131$	3.63621	0.317697	0.158848	+	0.987303i	$0.449222\pi$
$132$	56.2241	4.89368
$133$	−0.773178	−0.0670431
$134$	−18.5220	−1.60006
$135$	6.95196	0.598329
$136$	−60.5877	−5.19535
$137$	12.4841	1.06659	0.533296	−	0.845929i	$-0.320953\pi$
$137$	12.4841	1.06659	0.533296	+	0.845929i	$0.320953\pi$
$138$	37.3422	3.17878
$139$	9.06042	0.768495	0.384248	−	0.923230i	$-0.374461\pi$
$139$	9.06042	0.768495	0.384248	+	0.923230i	$0.374461\pi$
$140$	−11.8792	−1.00397
$141$	−12.0420	−1.01412
$142$	−38.8278	−3.25836
$143$	−26.5824	−2.22293
$144$	21.0765	1.75638
$145$	−11.5672	−0.960602
$146$	−31.8588	−2.63665
$147$	2.12991	0.175672
$148$	5.32631	0.437820
$149$	7.36512	0.603374	0.301687	−	0.953407i	$-0.402450\pi$
$149$	7.36512	0.603374	0.301687	+	0.953407i	$0.402450\pi$
$150$	0.148945	0.0121613
$151$	−4.98815	−0.405930	−0.202965	−	0.979186i	$-0.565058\pi$
$151$	−4.98815	−0.405930	−0.202965	+	0.979186i	$0.565058\pi$
$152$	6.96123	0.564630
$153$	10.3399	0.835935
$154$	−13.4146	−1.08098
$155$	−2.23028	−0.179141
$156$	−60.8482	−4.87175
$157$	−2.80030	−0.223488	−0.111744	−	0.993737i	$-0.535644\pi$
$157$	−2.80030	−0.223488	−0.111744	+	0.993737i	$0.535644\pi$
$158$	−32.8467	−2.61314
$159$	3.31778	0.263117
$160$	42.6458	3.37145
$161$	−6.47732	−0.510484
$162$	30.4470	2.39214
$163$	−22.3849	−1.75332	−0.876661	−	0.481108i	$-0.840235\pi$
$163$	−22.3849	−1.75332	−0.876661	+	0.481108i	$0.840235\pi$
$164$	−51.3275	−4.00801
$165$	−23.5427	−1.83280
$166$	−43.2437	−3.35636
$167$	6.99214	0.541068	0.270534	−	0.962710i	$-0.412800\pi$
$167$	6.99214	0.541068	0.270534	+	0.962710i	$0.412800\pi$
$168$	−19.1764	−1.47949
$169$	15.7686	1.21297
$170$	40.6239	3.11571
$171$	−1.18801	−0.0908492
$172$	−9.35177	−0.713065
$173$	0.859556	0.0653509	0.0326754	−	0.999466i	$-0.489597\pi$
$173$	0.859556	0.0653509	0.0326754	+	0.999466i	$0.489597\pi$
$174$	−29.9001	−2.26672
$175$	−0.0258357	−0.00195299
$176$	67.9819	5.12433
$177$	−2.45262	−0.184351
$178$	−46.7150	−3.50144
$179$	7.00339	0.523458	0.261729	−	0.965141i	$-0.415707\pi$
$179$	7.00339	0.523458	0.261729	+	0.965141i	$0.415707\pi$
$180$	−18.2527	−1.36047
$181$	−18.0941	−1.34493	−0.672463	−	0.740131i	$-0.734764\pi$
$181$	−18.0941	−1.34493	−0.672463	+	0.740131i	$0.734764\pi$
$182$	14.5178	1.07613
$183$	−12.5255	−0.925911
$184$	58.3178	4.29925
$185$	−2.23028	−0.163974
$186$	−5.76507	−0.422715
$187$	33.3513	2.43889
$188$	−30.1137	−2.19627
$189$	−3.11707	−0.226734
$190$	−4.66748	−0.338615
$191$	0.494943	0.0358129	0.0179064	−	0.999840i	$-0.494300\pi$
$191$	0.494943	0.0358129	0.0179064	+	0.999840i	$0.494300\pi$
$192$	51.8033	3.73858
$193$	17.7276	1.27606	0.638030	−	0.770012i	$-0.279750\pi$
$193$	17.7276	1.27606	0.638030	+	0.770012i	$0.279750\pi$
$194$	14.3373	1.02936
$195$	25.4789	1.82458
$196$	5.32631	0.380451
$197$	−11.4738	−0.817477	−0.408739	−	0.912651i	$-0.634031\pi$
$197$	−11.4738	−0.817477	−0.408739	+	0.912651i	$0.634031\pi$
$198$	−20.6118	−1.46482
$199$	−0.363320	−0.0257551	−0.0128775	−	0.999917i	$-0.504099\pi$
$199$	−0.363320	−0.0257551	−0.0128775	+	0.999917i	$0.504099\pi$
$200$	0.232609	0.0164479
$201$	14.5749	1.02804
$202$	−40.6711	−2.86161
$203$	5.18642	0.364015
$204$	76.3426	5.34505
$205$	21.4923	1.50109
$206$	14.9066	1.03859
$207$	−9.95256	−0.691751
$208$	−73.5730	−5.10137
$209$	−3.83190	−0.265058
$210$	12.8577	0.887268
$211$	−13.6345	−0.938639	−0.469320	−	0.883028i	$-0.655501\pi$
$211$	−13.6345	−0.938639	−0.469320	+	0.883028i	$0.655501\pi$
$212$	8.29685	0.569830
$213$	30.5536	2.09350
$214$	1.38971	0.0949986
$215$	3.91586	0.267059
$216$	28.0642	1.90953
$217$	1.00000	0.0678844
$218$	40.9523	2.77364
$219$	25.0697	1.69405
$220$	−58.8737	−3.96926
$221$	−36.0942	−2.42796
$222$	−5.76507	−0.386926
$223$	17.0743	1.14338	0.571689	−	0.820471i	$-0.306288\pi$
$223$	17.0743	1.14338	0.571689	+	0.820471i	$0.306288\pi$
$224$	−19.1212	−1.27759
$225$	−0.0396972	−0.00264648
$226$	15.3778	1.02292
$227$	18.4559	1.22496	0.612482	−	0.790485i	$-0.290171\pi$
$227$	18.4559	1.22496	0.612482	+	0.790485i	$0.290171\pi$
$228$	−8.77138	−0.580899
$229$	9.95185	0.657637	0.328818	−	0.944393i	$-0.393350\pi$
$229$	9.95185	0.657637	0.328818	+	0.944393i	$0.393350\pi$
$230$	−39.1019	−2.57830
$231$	10.5559	0.694528
$232$	−46.6954	−3.06570
$233$	−25.6279	−1.67894	−0.839471	−	0.543404i	$-0.817135\pi$
$233$	−25.6279	−1.67894	−0.839471	+	0.543404i	$0.817135\pi$
$234$	22.3070	1.45826
$235$	12.6095	0.822552
$236$	−6.13333	−0.399246
$237$	25.8470	1.67894
$238$	−18.2147	−1.18068
$239$	−4.12222	−0.266644	−0.133322	−	0.991073i	$-0.542564\pi$
$239$	−4.12222	−0.266644	−0.133322	+	0.991073i	$0.542564\pi$
$240$	−65.1600	−4.20606
$241$	9.40872	0.606069	0.303034	−	0.952980i	$-0.402000\pi$
$241$	9.40872	0.606069	0.303034	+	0.952980i	$0.402000\pi$
$242$	−36.7093	−2.35976
$243$	−14.6074	−0.937068
$244$	−31.3228	−2.00523
$245$	−2.23028	−0.142488
$246$	55.5556	3.54210
$247$	4.14704	0.263870
$248$	−9.00339	−0.571716
$249$	34.0284	2.15646
$250$	−30.3397	−1.91885
$251$	22.5330	1.42227	0.711136	−	0.703055i	$-0.248181\pi$
$251$	22.5330	1.42227	0.711136	+	0.703055i	$0.248181\pi$
$252$	8.18402	0.515545
$253$	−32.1018	−2.01822
$254$	16.9766	1.06520
$255$	−31.9669	−2.00184
$256$	26.0340	1.62712
$257$	−6.85995	−0.427912	−0.213956	−	0.976843i	$-0.568635\pi$
$257$	−6.85995	−0.427912	−0.213956	+	0.976843i	$0.568635\pi$
$258$	10.1221	0.630175
$259$	1.00000	0.0621370
$260$	63.7156	3.95148
$261$	7.96906	0.493273
$262$	−9.84218	−0.608052
$263$	0.0615964	0.00379820	0.00189910	−	0.999998i	$-0.499395\pi$
$263$	0.0615964	0.00379820	0.00189910	+	0.999998i	$0.499395\pi$
$264$	−95.0391	−5.84925
$265$	−3.47413	−0.213414
$266$	2.09277	0.128316
$267$	36.7600	2.24967
$268$	36.4479	2.22641
$269$	11.1217	0.678104	0.339052	−	0.940768i	$-0.389894\pi$
$269$	11.1217	0.678104	0.339052	+	0.940768i	$0.389894\pi$
$270$	−18.8170	−1.14516
$271$	−26.3793	−1.60243	−0.801216	−	0.598376i	$-0.795813\pi$
$271$	−26.3793	−1.60243	−0.801216	+	0.598376i	$0.795813\pi$
$272$	92.3076	5.59697
$273$	−11.4241	−0.691416
$274$	−33.7910	−2.04139
$275$	−0.128043	−0.00772126
$276$	−73.4825	−4.42313
$277$	−5.30262	−0.318603	−0.159302	−	0.987230i	$-0.550924\pi$
$277$	−5.30262	−0.318603	−0.159302	+	0.987230i	$0.550924\pi$
$278$	−24.5240	−1.47085
$279$	1.53652	0.0919893
$280$	20.0801	1.20002
$281$	30.9459	1.84607	0.923037	−	0.384710i	$-0.125699\pi$
$281$	30.9459	1.84607	0.923037	+	0.384710i	$0.125699\pi$
$282$	32.5943	1.94096
$283$	13.2330	0.786622	0.393311	−	0.919405i	$-0.371330\pi$
$283$	13.2330	0.786622	0.393311	+	0.919405i	$0.371330\pi$
$284$	76.4059	4.53386
$285$	3.67283	0.217560
$286$	71.9509	4.25455
$287$	−9.63660	−0.568830
$288$	−29.3803	−1.73125
$289$	28.2853	1.66384
$290$	31.3091	1.83853
$291$	−11.2820	−0.661363
$292$	62.6922	3.66879
$293$	−4.32958	−0.252937	−0.126468	−	0.991971i	$-0.540364\pi$
$293$	−4.32958	−0.252937	−0.126468	+	0.991971i	$0.540364\pi$
$294$	−5.76507	−0.336226
$295$	2.56820	0.149527
$296$	−9.00339	−0.523311
$297$	−15.4483	−0.896403
$298$	−19.9353	−1.15482
$299$	34.7420	2.00918
$300$	−0.293095	−0.0169219
$301$	−1.75577	−0.101201
$302$	13.5015	0.776925
$303$	32.0040	1.83858
$304$	−10.6057	−0.608278
$305$	13.1158	0.751006
$306$	−27.9873	−1.59993
$307$	13.1072	0.748066	0.374033	−	0.927415i	$-0.377975\pi$
$307$	13.1072	0.748066	0.374033	+	0.927415i	$0.377975\pi$
$308$	26.3974	1.50413
$309$	−11.7300	−0.667295
$310$	6.03675	0.342864
$311$	10.7239	0.608095	0.304048	−	0.952657i	$-0.401662\pi$
$311$	10.7239	0.608095	0.304048	+	0.952657i	$0.401662\pi$
$312$	102.855	5.82304
$313$	−18.7665	−1.06074	−0.530372	−	0.847765i	$-0.677948\pi$
$313$	−18.7665	−1.06074	−0.530372	+	0.847765i	$0.677948\pi$
$314$	7.57961	0.427742
$315$	−3.42689	−0.193083
$316$	64.6361	3.63607
$317$	16.0499	0.901453	0.450726	−	0.892662i	$-0.351165\pi$
$317$	16.0499	0.901453	0.450726	+	0.892662i	$0.351165\pi$
$318$	−8.98030	−0.503590
$319$	25.7041	1.43915
$320$	−54.2445	−3.03236
$321$	−1.09356	−0.0610366
$322$	17.5323	0.977035
$323$	−5.20305	−0.289505
$324$	−59.9139	−3.32855
$325$	0.138573	0.00768666
$326$	60.5897	3.35575
$327$	−32.2253	−1.78206
$328$	86.7621	4.79063
$329$	−5.65376	−0.311702
$330$	63.7234	3.50786
$331$	15.6915	0.862481	0.431240	−	0.902237i	$-0.358076\pi$
$331$	15.6915	0.862481	0.431240	+	0.902237i	$0.358076\pi$
$332$	85.0955	4.67022
$333$	1.53652	0.0842011
$334$	−18.9257	−1.03557
$335$	−15.2618	−0.833840
$336$	29.2160	1.59386
$337$	−9.17039	−0.499543	−0.249771	−	0.968305i	$-0.580355\pi$
$337$	−9.17039	−0.499543	−0.249771	+	0.968305i	$0.580355\pi$
$338$	−42.6810	−2.32154
$339$	−12.1008	−0.657226
$340$	−79.9402	−4.33537
$341$	4.95603	0.268384
$342$	3.21560	0.173880
$343$	1.00000	0.0539949
$344$	15.8079	0.852302
$345$	30.7693	1.65656
$346$	−2.32658	−0.125077
$347$	0.489439	0.0262745	0.0131372	−	0.999914i	$-0.495818\pi$
$347$	0.489439	0.0262745	0.0131372	+	0.999914i	$0.495818\pi$
$348$	58.8378	3.15403
$349$	6.72850	0.360169	0.180084	−	0.983651i	$-0.442363\pi$
$349$	6.72850	0.360169	0.180084	+	0.983651i	$0.442363\pi$
$350$	0.0699299	0.00373791
$351$	16.7188	0.892385
$352$	−94.7656	−5.05102
$353$	−20.8092	−1.10756	−0.553780	−	0.832663i	$-0.686815\pi$
$353$	−20.8092	−1.10756	−0.553780	+	0.832663i	$0.686815\pi$
$354$	6.63856	0.352835
$355$	−31.9934	−1.69803
$356$	91.9264	4.87209
$357$	14.3331	0.758588
$358$	−18.9562	−1.00187
$359$	−18.8235	−0.993466	−0.496733	−	0.867903i	$-0.665467\pi$
$359$	−18.8235	−0.993466	−0.496733	+	0.867903i	$0.665467\pi$
$360$	30.8536	1.62613
$361$	−18.4022	−0.968537
$362$	48.9757	2.57410
$363$	28.8865	1.51615
$364$	−28.5684	−1.49739
$365$	−26.2511	−1.37404
$366$	33.9030	1.77214
$367$	36.3530	1.89761	0.948806	−	0.315860i	$-0.102293\pi$
$367$	36.3530	1.89761	0.948806	+	0.315860i	$0.102293\pi$
$368$	−88.8494	−4.63159
$369$	−14.8069	−0.770815
$370$	6.03675	0.313835
$371$	1.55771	0.0808722
$372$	11.3446	0.588189
$373$	−32.0232	−1.65810	−0.829049	−	0.559176i	$-0.811118\pi$
$373$	−32.0232	−1.65810	−0.829049	+	0.559176i	$0.811118\pi$
$374$	−90.2725	−4.66788
$375$	23.8743	1.23286
$376$	50.9030	2.62512
$377$	−27.8181	−1.43270
$378$	8.43703	0.433954
$379$	33.0848	1.69945	0.849727	−	0.527223i	$-0.176767\pi$
$379$	33.0848	1.69945	0.849727	+	0.527223i	$0.176767\pi$
$380$	9.18473	0.471167
$381$	−13.3588	−0.684394
$382$	−1.33967	−0.0685436
$383$	30.8149	1.57457	0.787284	−	0.616591i	$-0.211487\pi$
$383$	30.8149	1.57457	0.787284	+	0.616591i	$0.211487\pi$
$384$	−58.7637	−2.99877
$385$	−11.0534	−0.563332
$386$	−47.9835	−2.44230
$387$	−2.69778	−0.137136
$388$	−28.2132	−1.43231
$389$	−8.22603	−0.417076	−0.208538	−	0.978014i	$-0.566871\pi$
$389$	−8.22603	−0.417076	−0.208538	+	0.978014i	$0.566871\pi$
$390$	−68.9642	−3.49214
$391$	−43.5887	−2.20437
$392$	−9.00339	−0.454740
$393$	7.74480	0.390674
$394$	31.0564	1.56460
$395$	−27.0650	−1.36179
$396$	40.5603	2.03823
$397$	10.5592	0.529952	0.264976	−	0.964255i	$-0.414636\pi$
$397$	10.5592	0.529952	0.264976	+	0.964255i	$0.414636\pi$
$398$	0.983405	0.0492936
$399$	−1.64680	−0.0824432
$400$	−0.354388	−0.0177194
$401$	26.9031	1.34348	0.671739	−	0.740788i	$-0.265548\pi$
$401$	26.9031	1.34348	0.671739	+	0.740788i	$0.265548\pi$
$402$	−39.4502	−1.96760
$403$	−5.36363	−0.267182
$404$	80.0331	3.98180
$405$	25.0877	1.24662
$406$	−14.0382	−0.696703
$407$	4.95603	0.245662
$408$	−129.046	−6.38875
$409$	16.9620	0.838716	0.419358	−	0.907821i	$-0.362255\pi$
$409$	16.9620	0.838716	0.419358	+	0.907821i	$0.362255\pi$
$410$	−58.1737	−2.87299
$411$	26.5901	1.31159
$412$	−29.3334	−1.44515
$413$	−1.15151	−0.0566623
$414$	26.9388	1.32397
$415$	−35.6320	−1.74910
$416$	102.559	5.02839
$417$	19.2979	0.945022
$418$	10.3719	0.507304
$419$	32.4084	1.58326	0.791628	−	0.611003i	$-0.209234\pi$
$419$	32.4084	1.58326	0.791628	+	0.611003i	$0.209234\pi$
$420$	−25.3016	−1.23459
$421$	27.1769	1.32452	0.662260	−	0.749274i	$-0.269597\pi$
$421$	27.1769	1.32452	0.662260	+	0.749274i	$0.269597\pi$
$422$	36.9048	1.79650
$423$	−8.68714	−0.422383
$424$	−14.0247	−0.681098
$425$	−0.173860	−0.00843343
$426$	−82.6998	−4.00682
$427$	−5.88076	−0.284590
$428$	−2.73469	−0.132186
$429$	−56.6181	−2.73355
$430$	−10.5991	−0.511135
$431$	−16.4070	−0.790295	−0.395148	−	0.918618i	$-0.629307\pi$
$431$	−16.4070	−0.790295	−0.395148	+	0.918618i	$0.629307\pi$
$432$	−42.7569	−2.05714
$433$	−6.13627	−0.294890	−0.147445	−	0.989070i	$-0.547105\pi$
$433$	−6.13627	−0.294890	−0.147445	+	0.989070i	$0.547105\pi$
$434$	−2.70672	−0.129927
$435$	−24.6371	−1.18126
$436$	−80.5865	−3.85939
$437$	5.00812	0.239571
$438$	−67.8565	−3.24231
$439$	34.6611	1.65429	0.827143	−	0.561992i	$-0.189965\pi$
$439$	34.6611	1.65429	0.827143	+	0.561992i	$0.189965\pi$
$440$	99.5177	4.74432
$441$	1.53652	0.0731679
$442$	97.6968	4.64696
$443$	−3.48138	−0.165406	−0.0827028	−	0.996574i	$-0.526355\pi$
$443$	−3.48138	−0.165406	−0.0827028	+	0.996574i	$0.526355\pi$
$444$	11.3446	0.538390
$445$	−38.4923	−1.82471
$446$	−46.2152	−2.18835
$447$	15.6871	0.741972
$448$	24.3218	1.14910
$449$	−15.9861	−0.754429	−0.377214	−	0.926126i	$-0.623118\pi$
$449$	−15.9861	−0.754429	−0.377214	+	0.926126i	$0.623118\pi$
$450$	0.107449	0.00506520
$451$	−47.7593	−2.24890
$452$	−30.2607	−1.42335
$453$	−10.6243	−0.499175
$454$	−49.9550	−2.34450
$455$	11.9624	0.560807
$456$	14.8268	0.694328
$457$	13.8833	0.649433	0.324716	−	0.945811i	$-0.394731\pi$
$457$	13.8833	0.649433	0.324716	+	0.945811i	$0.394731\pi$
$458$	−26.9368	−1.25868
$459$	−20.9761	−0.979082
$460$	76.9453	3.58759
$461$	−10.7269	−0.499599	−0.249800	−	0.968298i	$-0.580365\pi$
$461$	−10.7269	−0.499599	−0.249800	+	0.968298i	$0.580365\pi$
$462$	−28.5719	−1.32928
$463$	−0.581977	−0.0270467	−0.0135234	−	0.999909i	$-0.504305\pi$
$463$	−0.581977	−0.0270467	−0.0135234	+	0.999909i	$0.504305\pi$
$464$	71.1421	3.30269
$465$	−4.75031	−0.220290
$466$	69.3676	3.21339
$467$	−15.8538	−0.733625	−0.366812	−	0.930295i	$-0.619551\pi$
$467$	−15.8538	−0.733625	−0.366812	+	0.930295i	$0.619551\pi$
$468$	−43.8961	−2.02910
$469$	6.84298	0.315979
$470$	−34.1303	−1.57431
$471$	−5.96439	−0.274824
$472$	10.3675	0.477205
$473$	−8.70164	−0.400102
$474$	−69.9605	−3.21339
$475$	0.0199756	0.000916543 0
$476$	35.8431	1.64286
$477$	2.39346	0.109589
$478$	11.1577	0.510340
$479$	−19.7766	−0.903616	−0.451808	−	0.892115i	$-0.649221\pi$
$479$	−19.7766	−0.903616	−0.451808	+	0.892115i	$0.649221\pi$
$480$	90.8318	4.14589
$481$	−5.36363	−0.244561
$482$	−25.4667	−1.15998
$483$	−13.7961	−0.627745
$484$	72.2370	3.28350
$485$	11.8137	0.536431
$486$	39.5382	1.79349
$487$	21.3885	0.969207	0.484604	−	0.874734i	$-0.338964\pi$
$487$	21.3885	0.969207	0.484604	+	0.874734i	$0.338964\pi$
$488$	52.9467	2.39679
$489$	−47.6779	−2.15607
$490$	6.03675	0.272712
$491$	−41.6324	−1.87884	−0.939422	−	0.342762i	$-0.888638\pi$
$491$	−41.6324	−1.87884	−0.939422	+	0.342762i	$0.888638\pi$
$492$	−109.323	−4.92867
$493$	34.9017	1.57189
$494$	−11.2249	−0.505031
$495$	−16.9838	−0.763364
$496$	13.7170	0.615911
$497$	14.3450	0.643461
$498$	−92.1052	−4.12733
$499$	2.75083	0.123144	0.0615721	−	0.998103i	$-0.480389\pi$
$499$	2.75083	0.123144	0.0615721	+	0.998103i	$0.480389\pi$
$500$	59.7029	2.66999
$501$	14.8926	0.665354
$502$	−60.9905	−2.72214
$503$	−14.3451	−0.639618	−0.319809	−	0.947482i	$-0.603619\pi$
$503$	−14.3451	−0.639618	−0.319809	+	0.947482i	$0.603619\pi$
$504$	−13.8339	−0.616212
$505$	−33.5122	−1.49127
$506$	86.8905	3.86276
$507$	33.5856	1.49159
$508$	−33.4067	−1.48218
$509$	25.9304	1.14935	0.574673	−	0.818383i	$-0.305129\pi$
$509$	25.9304	1.14935	0.574673	+	0.818383i	$0.305129\pi$
$510$	86.5253	3.83140
$511$	11.7703	0.520687
$512$	−15.2871	−0.675601
$513$	2.41005	0.106406
$514$	18.5679	0.818997
$515$	12.2827	0.541243
$516$	−19.9184	−0.876860
$517$	−28.0202	−1.23233
$518$	−2.70672	−0.118926
$519$	1.83078	0.0803623
$520$	−107.702	−4.72306
$521$	20.6937	0.906608	0.453304	−	0.891356i	$-0.350245\pi$
$521$	20.6937	0.906608	0.453304	+	0.891356i	$0.350245\pi$
$522$	−21.5700	−0.944093
$523$	−28.8744	−1.26259	−0.631295	−	0.775543i	$-0.717476\pi$
$523$	−28.8744	−1.26259	−0.631295	+	0.775543i	$0.717476\pi$
$524$	19.3676	0.846077
$525$	−0.0550277	−0.00240161
$526$	−0.166724	−0.00726951
$527$	6.72943	0.293139
$528$	144.796	6.30142
$529$	18.9557	0.824159
$530$	9.40349	0.408462
$531$	−1.76933	−0.0767824
$532$	−4.11819	−0.178546
$533$	51.6872	2.23882
$534$	−99.4988	−4.30573
$535$	1.14509	0.0495068
$536$	−61.6100	−2.66115
$537$	14.9166	0.643699
$538$	−30.1034	−1.29785
$539$	4.95603	0.213472
$540$	37.0283	1.59344
$541$	−35.1306	−1.51038	−0.755190	−	0.655506i	$-0.772456\pi$
$541$	−35.1306	−1.51038	−0.755190	+	0.655506i	$0.772456\pi$
$542$	71.4014	3.06695
$543$	−38.5389	−1.65386
$544$	−128.675	−5.51690
$545$	33.7439	1.44543
$546$	30.9217	1.32333
$547$	32.6671	1.39674	0.698371	−	0.715736i	$-0.253909\pi$
$547$	32.6671	1.39674	0.698371	+	0.715736i	$0.253909\pi$
$548$	66.4945	2.84050
$549$	−9.03593	−0.385644
$550$	0.346575	0.0147780
$551$	−4.01003	−0.170833
$552$	124.212	5.28681
$553$	12.1352	0.516043
$554$	14.3527	0.609787
$555$	−4.75031	−0.201639
$556$	48.2587	2.04662
$557$	−21.3207	−0.903386	−0.451693	−	0.892173i	$-0.649180\pi$
$557$	−21.3207	−0.903386	−0.451693	+	0.892173i	$0.649180\pi$
$558$	−4.15894	−0.176062
$559$	9.41729	0.398309
$560$	−30.5928	−1.29278
$561$	71.0353	2.99911
$562$	−83.7617	−3.53327
$563$	42.6582	1.79783	0.898914	−	0.438125i	$-0.144357\pi$
$563$	42.6582	1.79783	0.898914	+	0.438125i	$0.144357\pi$
$564$	−64.1395	−2.70076
$565$	12.6711	0.533075
$566$	−35.8181	−1.50555
$567$	−11.2487	−0.472400
$568$	−129.154	−5.41916
$569$	7.60001	0.318609	0.159305	−	0.987229i	$-0.449075\pi$
$569$	7.60001	0.318609	0.159305	+	0.987229i	$0.449075\pi$
$570$	−9.94132	−0.416396
$571$	24.2485	1.01477	0.507385	−	0.861719i	$-0.330612\pi$
$571$	24.2485	1.01477	0.507385	+	0.861719i	$0.330612\pi$
$572$	−141.586	−5.92001
$573$	1.05419	0.0440393
$574$	26.0835	1.08871
$575$	0.167346	0.00697881
$576$	37.3711	1.55713
$577$	3.62156	0.150768	0.0753838	−	0.997155i	$-0.475982\pi$
$577$	3.62156	0.150768	0.0753838	+	0.997155i	$0.475982\pi$
$578$	−76.5602	−3.18448
$579$	37.7582	1.56918
$580$	−61.6105	−2.55824
$581$	15.9764	0.662814
$582$	30.5372	1.26581
$583$	7.72006	0.319732
$584$	−105.972	−4.38517
$585$	18.3806	0.759943
$586$	11.7189	0.484105
$587$	−33.2563	−1.37263	−0.686317	−	0.727303i	$-0.740774\pi$
$587$	−33.2563	−1.37263	−0.686317	+	0.727303i	$0.740774\pi$
$588$	11.3446	0.467843
$589$	−0.773178	−0.0318583
$590$	−6.95140	−0.286185
$591$	−24.4383	−1.00526
$592$	13.7170	0.563765
$593$	23.2605	0.955193	0.477597	−	0.878579i	$-0.341508\pi$
$593$	23.2605	0.955193	0.477597	+	0.878579i	$0.341508\pi$
$594$	41.8142	1.71566
$595$	−15.0085	−0.615290
$596$	39.2290	1.60688
$597$	−0.773840	−0.0316712
$598$	−94.0367	−3.84544
$599$	−38.2467	−1.56272	−0.781359	−	0.624082i	$-0.785473\pi$
$599$	−38.2467	−1.56272	−0.781359	+	0.624082i	$0.785473\pi$
$600$	0.495436	0.0202261
$601$	−20.1839	−0.823319	−0.411659	−	0.911338i	$-0.635051\pi$
$601$	−20.1839	−0.823319	−0.411659	+	0.911338i	$0.635051\pi$
$602$	4.75236	0.193692
$603$	10.5144	0.428180
$604$	−26.5685	−1.08106
$605$	−30.2477	−1.22975
$606$	−86.6258	−3.51893
$607$	−26.5553	−1.07785	−0.538924	−	0.842355i	$-0.681169\pi$
$607$	−26.5553	−1.07785	−0.538924	+	0.842355i	$0.681169\pi$
$608$	14.7841	0.599576
$609$	11.0466	0.447631
$610$	−35.5006	−1.43738
$611$	30.3247	1.22681
$612$	55.0738	2.22623
$613$	−3.45638	−0.139602	−0.0698010	−	0.997561i	$-0.522236\pi$
$613$	−3.45638	−0.139602	−0.0698010	+	0.997561i	$0.522236\pi$
$614$	−35.4774	−1.43175
$615$	45.7768	1.84590
$616$	−44.6211	−1.79784
$617$	−24.5763	−0.989407	−0.494703	−	0.869062i	$-0.664723\pi$
$617$	−24.5763	−0.989407	−0.494703	+	0.869062i	$0.664723\pi$
$618$	31.7497	1.27716
$619$	−18.4586	−0.741914	−0.370957	−	0.928650i	$-0.620970\pi$
$619$	−18.4586	−0.741914	−0.370957	+	0.928650i	$0.620970\pi$
$620$	−11.8792	−0.477080
$621$	20.1903	0.810208
$622$	−29.0265	−1.16386
$623$	17.2589	0.691464
$624$	−156.704	−6.27318
$625$	−24.8702	−0.994806
$626$	50.7956	2.03020
$627$	−8.16161	−0.325943
$628$	−14.9153	−0.595184
$629$	6.72943	0.268320
$630$	9.27561	0.369549
$631$	31.9814	1.27316	0.636580	−	0.771211i	$-0.280349\pi$
$631$	31.9814	1.27316	0.636580	+	0.771211i	$0.280349\pi$
$632$	−109.258	−4.34606
$633$	−29.0403	−1.15425
$634$	−43.4425	−1.72532
$635$	13.9884	0.555112
$636$	17.6716	0.700723
$637$	−5.36363	−0.212515
$638$	−69.5736	−2.75445
$639$	22.0414	0.871946
$640$	61.5329	2.43230
$641$	10.2768	0.405911	0.202955	−	0.979188i	$-0.434945\pi$
$641$	10.2768	0.405911	0.202955	+	0.979188i	$0.434945\pi$
$642$	2.95996	0.116820
$643$	−34.7751	−1.37140	−0.685699	−	0.727885i	$-0.740503\pi$
$643$	−34.7751	−1.37140	−0.685699	+	0.727885i	$0.740503\pi$
$644$	−34.5002	−1.35950
$645$	8.34043	0.328404
$646$	14.0832	0.554095
$647$	1.13797	0.0447384	0.0223692	−	0.999750i	$-0.492879\pi$
$647$	1.13797	0.0447384	0.0223692	+	0.999750i	$0.492879\pi$
$648$	101.276	3.97850
$649$	−5.70695	−0.224017
$650$	−0.375078	−0.0147118
$651$	2.12991	0.0834778
$652$	−119.229	−4.66937
$653$	30.1586	1.18020	0.590099	−	0.807331i	$-0.299089\pi$
$653$	30.1586	1.18020	0.590099	+	0.807331i	$0.299089\pi$
$654$	87.2247	3.41076
$655$	−8.10977	−0.316875
$656$	−132.185	−5.16096
$657$	18.0853	0.705576
$658$	15.3031	0.596578
$659$	−25.8396	−1.00657	−0.503284	−	0.864121i	$-0.667875\pi$
$659$	−25.8396	−1.00657	−0.503284	+	0.864121i	$0.667875\pi$
$660$	−125.396	−4.88102
$661$	41.3589	1.60868	0.804338	−	0.594173i	$-0.202520\pi$
$661$	41.3589	1.60868	0.804338	+	0.594173i	$0.202520\pi$
$662$	−42.4723	−1.65073
$663$	−76.8775	−2.98567
$664$	−143.842	−5.58215
$665$	1.72441	0.0668696
$666$	−4.15894	−0.161156
$667$	−33.5941	−1.30077
$668$	37.2423	1.44095
$669$	36.3667	1.40602
$670$	41.3093	1.59592
$671$	−29.1452	−1.12514
$672$	−40.7266	−1.57106
$673$	21.0157	0.810095	0.405047	−	0.914296i	$-0.367255\pi$
$673$	21.0157	0.810095	0.405047	+	0.914296i	$0.367255\pi$
$674$	24.8216	0.956094
$675$	0.0805317	0.00309967
$676$	83.9883	3.23032
$677$	−10.7118	−0.411689	−0.205845	−	0.978585i	$-0.565994\pi$
$677$	−10.7118	−0.411689	−0.205845	+	0.978585i	$0.565994\pi$
$678$	32.7535	1.25789
$679$	−5.29694	−0.203278
$680$	135.128	5.18191
$681$	39.3095	1.50634
$682$	−13.4146	−0.513671
$683$	18.8890	0.722768	0.361384	−	0.932417i	$-0.382304\pi$
$683$	18.8890	0.722768	0.361384	+	0.932417i	$0.382304\pi$
$684$	−6.32770	−0.241946
$685$	−27.8432	−1.06383
$686$	−2.70672	−0.103343
$687$	21.1966	0.808700
$688$	−24.0838	−0.918188
$689$	−8.35498	−0.318299
$690$	−83.2837	−3.17055
$691$	30.7547	1.16997	0.584983	−	0.811046i	$-0.301101\pi$
$691$	30.7547	1.16997	0.584983	+	0.811046i	$0.301101\pi$
$692$	4.57827	0.174040
$693$	7.61507	0.289273
$694$	−1.32477	−0.0502877
$695$	−20.2073	−0.766507
$696$	−99.4570	−3.76991
$697$	−64.8488	−2.45632
$698$	−18.2122	−0.689340
$699$	−54.5853	−2.06460
$700$	−0.137609	−0.00520113
$701$	37.4913	1.41603	0.708014	−	0.706198i	$-0.249591\pi$
$701$	37.4913	1.41603	0.708014	+	0.706198i	$0.249591\pi$
$702$	−45.2532	−1.70797
$703$	−0.773178	−0.0291610
$704$	120.540	4.54301
$705$	26.8571	1.01150
$706$	56.3245	2.11980
$707$	15.0260	0.565110
$708$	−13.0635	−0.490955
$709$	11.2896	0.423988	0.211994	−	0.977271i	$-0.432004\pi$
$709$	11.2896	0.423988	0.211994	+	0.977271i	$0.432004\pi$
$710$	86.5970	3.24993
$711$	18.6461	0.699284
$712$	−155.389	−5.82344
$713$	−6.47732	−0.242578
$714$	−38.7956	−1.45189
$715$	59.2862	2.21718
$716$	37.3023	1.39405
$717$	−8.77996	−0.327894
$718$	50.9499	1.90143
$719$	31.7421	1.18378	0.591890	−	0.806019i	$-0.298382\pi$
$719$	31.7421	1.18378	0.591890	+	0.806019i	$0.298382\pi$
$720$	−47.0066	−1.75183
$721$	−5.50726	−0.205101
$722$	49.8095	1.85372
$723$	20.0397	0.745286
$724$	−96.3750	−3.58175
$725$	−0.133995	−0.00497644
$726$	−78.1875	−2.90181
$727$	−43.7135	−1.62124	−0.810622	−	0.585570i	$-0.800871\pi$
$727$	−43.7135	−1.62124	−0.810622	+	0.585570i	$0.800871\pi$
$728$	48.2909	1.78978
$729$	2.63342	0.0975339
$730$	71.0542	2.62983
$731$	−11.8153	−0.437005
$732$	−66.7147	−2.46585
$733$	19.3095	0.713212	0.356606	−	0.934255i	$-0.383934\pi$
$733$	19.3095	0.713212	0.356606	+	0.934255i	$0.383934\pi$
$734$	−98.3973	−3.63191
$735$	−4.75031	−0.175218
$736$	123.854	4.56533
$737$	33.9141	1.24924
$738$	40.0780	1.47529
$739$	−1.02619	−0.0377490	−0.0188745	−	0.999822i	$-0.506008\pi$
$739$	−1.02619	−0.0377490	−0.0188745	+	0.999822i	$0.506008\pi$
$740$	−11.8792	−0.436688
$741$	8.83284	0.324482
$742$	−4.21628	−0.154784
$743$	11.9787	0.439455	0.219728	−	0.975561i	$-0.429483\pi$
$743$	11.9787	0.439455	0.219728	+	0.975561i	$0.429483\pi$
$744$	−19.1764	−0.703042
$745$	−16.4263	−0.601813
$746$	86.6777	3.17350
$747$	24.5482	0.898171
$748$	177.640	6.49514
$749$	−0.513430	−0.0187603
$750$	−64.6209	−2.35962
$751$	−0.0981807	−0.00358266	−0.00179133	−	0.999998i	$-0.500570\pi$
$751$	−0.0981807	−0.00358266	−0.00179133	+	0.999998i	$0.500570\pi$
$752$	−77.5526	−2.82805
$753$	47.9933	1.74897
$754$	75.2956	2.74210
$755$	11.1250	0.404880
$756$	−16.6025	−0.603828
$757$	−12.1189	−0.440470	−0.220235	−	0.975447i	$-0.570682\pi$
$757$	−12.1189	−0.440470	−0.220235	+	0.975447i	$0.570682\pi$
$758$	−89.5513	−3.25265
$759$	−68.3740	−2.48182
$760$	−15.5255	−0.563169
$761$	−5.89734	−0.213778	−0.106889	−	0.994271i	$-0.534089\pi$
$761$	−5.89734	−0.213778	−0.106889	+	0.994271i	$0.534089\pi$
$762$	36.1586	1.30989
$763$	−15.1299	−0.547738
$764$	2.63622	0.0953753
$765$	−23.0610	−0.833772
$766$	−83.4072	−3.01362
$767$	6.17630	0.223013
$768$	55.4500	2.00088
$769$	48.9344	1.76462	0.882309	−	0.470671i	$-0.155988\pi$
$769$	48.9344	1.76462	0.882309	+	0.470671i	$0.155988\pi$
$770$	29.9183	1.07818
$771$	−14.6111	−0.526205
$772$	94.4227	3.39835
$773$	44.0262	1.58351	0.791756	−	0.610837i	$-0.209167\pi$
$773$	44.0262	1.58351	0.791756	+	0.610837i	$0.209167\pi$
$774$	7.30212	0.262469
$775$	−0.0258357	−0.000928045 0
$776$	47.6904	1.71199
$777$	2.12991	0.0764102
$778$	22.2655	0.798258
$779$	7.45081	0.266953
$780$	135.709	4.85915
$781$	71.0943	2.54395
$782$	117.982	4.21903
$783$	−16.1664	−0.577742
$784$	13.7170	0.489893
$785$	6.24546	0.222910
$786$	−20.9630	−0.747725
$787$	4.78562	0.170589	0.0852945	−	0.996356i	$-0.472817\pi$
$787$	4.78562	0.170589	0.0852945	+	0.996356i	$0.472817\pi$
$788$	−61.1133	−2.17707
$789$	0.131195	0.00467066
$790$	73.2574	2.60638
$791$	−5.68137	−0.202006
$792$	−68.5615	−2.43623
$793$	31.5422	1.12010
$794$	−28.5808	−1.01430
$795$	−7.39960	−0.262437
$796$	−1.93516	−0.0685898
$797$	52.2526	1.85088	0.925440	−	0.378893i	$-0.123695\pi$
$797$	52.2526	1.85088	0.925440	+	0.378893i	$0.123695\pi$
$798$	4.45743	0.157791
$799$	−38.0466	−1.34599
$800$	0.494011	0.0174659
$801$	26.5188	0.936994
$802$	−72.8192	−2.57133
$803$	58.3339	2.05856
$804$	77.6308	2.73783
$805$	14.4463	0.509164
$806$	14.5178	0.511369
$807$	23.6883	0.833868
$808$	−135.285	−4.75930
$809$	26.1186	0.918281	0.459140	−	0.888364i	$-0.348157\pi$
$809$	26.1186	0.918281	0.459140	+	0.888364i	$0.348157\pi$
$810$	−67.9053	−2.38595
$811$	−43.4580	−1.52602	−0.763009	−	0.646388i	$-0.776279\pi$
$811$	−43.4580	−1.52602	−0.763009	+	0.646388i	$0.776279\pi$
$812$	27.6245	0.969430
$813$	−56.1857	−1.97052
$814$	−13.4146	−0.470181
$815$	49.9247	1.74879
$816$	196.607	6.88262
$817$	1.35752	0.0474936
$818$	−45.9113	−1.60525
$819$	−8.24136	−0.287976
$820$	114.475	3.99764
$821$	−2.54141	−0.0886958	−0.0443479	−	0.999016i	$-0.514121\pi$
$821$	−2.54141	−0.0886958	−0.0443479	+	0.999016i	$0.514121\pi$
$822$	−71.9719	−2.51031
$823$	47.5239	1.65658	0.828290	−	0.560299i	$-0.189314\pi$
$823$	47.5239	1.65658	0.828290	+	0.560299i	$0.189314\pi$
$824$	49.5840	1.72734
$825$	−0.272719	−0.00949487
$826$	3.11682	0.108448
$827$	−35.2877	−1.22707	−0.613537	−	0.789666i	$-0.710254\pi$
$827$	−35.2877	−1.22707	−0.613537	+	0.789666i	$0.710254\pi$
$828$	−53.0105	−1.84224
$829$	0.510918	0.0177449	0.00887246	−	0.999961i	$-0.497176\pi$
$829$	0.510918	0.0177449	0.00887246	+	0.999961i	$0.497176\pi$
$830$	96.4456	3.34768
$831$	−11.2941	−0.391788
$832$	−130.453	−4.52265
$833$	6.72943	0.233161
$834$	−52.2340	−1.80871
$835$	−15.5945	−0.539668
$836$	−20.4099	−0.705891
$837$	−3.11707	−0.107742
$838$	−87.7205	−3.03025
$839$	48.0248	1.65800	0.829001	−	0.559247i	$-0.188910\pi$
$839$	48.0248	1.65800	0.829001	+	0.559247i	$0.188910\pi$
$840$	42.7689	1.47567
$841$	−2.10105	−0.0724501
$842$	−73.5602	−2.53505
$843$	65.9119	2.27013
$844$	−72.6218	−2.49974
$845$	−35.1684	−1.20983
$846$	23.5136	0.808415
$847$	13.5623	0.466005
$848$	21.3671	0.733749
$849$	28.1852	0.967313
$850$	0.470588	0.0161411
$851$	−6.47732	−0.222040
$852$	162.738	5.57531
$853$	−20.8181	−0.712797	−0.356398	−	0.934334i	$-0.615995\pi$
$853$	−20.8181	−0.712797	−0.356398	+	0.934334i	$0.615995\pi$
$854$	15.9175	0.544687
$855$	2.64959	0.0906142
$856$	4.62261	0.157998
$857$	37.0033	1.26401	0.632005	−	0.774964i	$-0.282232\pi$
$857$	37.0033	1.26401	0.632005	+	0.774964i	$0.282232\pi$
$858$	153.249	5.23184
$859$	10.4623	0.356967	0.178484	−	0.983943i	$-0.442881\pi$
$859$	10.4623	0.356967	0.178484	+	0.983943i	$0.442881\pi$
$860$	20.8571	0.711221
$861$	−20.5251	−0.699494
$862$	44.4090	1.51258
$863$	2.43568	0.0829115	0.0414557	−	0.999140i	$-0.486800\pi$
$863$	2.43568	0.0829115	0.0414557	+	0.999140i	$0.486800\pi$
$864$	59.6023	2.02771
$865$	−1.91705	−0.0651818
$866$	16.6091	0.564402
$867$	60.2451	2.04603
$868$	5.32631	0.180787
$869$	60.1427	2.04020
$870$	66.6856	2.26085
$871$	−36.7032	−1.24364
$872$	136.220	4.61300
$873$	−8.13888	−0.275459
$874$	−13.5556	−0.458524
$875$	11.2090	0.378935
$876$	133.529	4.51152
$877$	−32.9610	−1.11301	−0.556507	−	0.830843i	$-0.687859\pi$
$877$	−32.9610	−1.11301	−0.556507	+	0.830843i	$0.687859\pi$
$878$	−93.8179	−3.16620
$879$	−9.22162	−0.311037
$880$	−151.619	−5.11107
$881$	33.2002	1.11854	0.559272	−	0.828984i	$-0.311081\pi$
$881$	33.2002	1.11854	0.559272	+	0.828984i	$0.311081\pi$
$882$	−4.15894	−0.140039
$883$	34.8091	1.17142	0.585709	−	0.810521i	$-0.300816\pi$
$883$	34.8091	1.17142	0.585709	+	0.810521i	$0.300816\pi$
$884$	−192.249	−6.46604
$885$	5.47005	0.183874
$886$	9.42312	0.316576
$887$	−3.57310	−0.119973	−0.0599864	−	0.998199i	$-0.519106\pi$
$887$	−3.57310	−0.119973	−0.0599864	+	0.998199i	$0.519106\pi$
$888$	−19.1764	−0.643519
$889$	−6.27201	−0.210357
$890$	104.188	3.49238
$891$	−55.7488	−1.86765
$892$	90.9429	3.04499
$893$	4.37136	0.146282
$894$	−42.4604	−1.42009
$895$	−15.6195	−0.522104
$896$	−27.5897	−0.921708
$897$	73.9973	2.47070
$898$	43.2697	1.44393
$899$	5.18642	0.172977
$900$	−0.211440	−0.00704799
$901$	10.4825	0.349223
$902$	129.271	4.30425
$903$	−3.73963	−0.124447
$904$	51.1516	1.70128
$905$	40.3550	1.34145
$906$	28.7571	0.955389
$907$	−49.4292	−1.64127	−0.820635	−	0.571453i	$-0.806380\pi$
$907$	−49.4292	−1.64127	−0.820635	+	0.571453i	$0.806380\pi$
$908$	98.3021	3.26227
$909$	23.0878	0.765774
$910$	−32.3789	−1.07335
$911$	−44.5730	−1.47677	−0.738385	−	0.674379i	$-0.764411\pi$
$911$	−44.5730	−1.47677	−0.738385	+	0.674379i	$0.764411\pi$
$912$	−22.5892	−0.748002
$913$	79.1797	2.62047
$914$	−37.5781	−1.24297
$915$	27.9354	0.923516
$916$	53.0067	1.75139
$917$	3.63621	0.120078
$918$	56.7764	1.87390
$919$	−13.7219	−0.452645	−0.226322	−	0.974052i	$-0.572670\pi$
$919$	−13.7219	−0.452645	−0.226322	+	0.974052i	$0.572670\pi$
$920$	−130.065	−4.28813
$921$	27.9171	0.919900
$922$	29.0345	0.956202
$923$	−76.9413	−2.53255
$924$	56.2241	1.84964
$925$	−0.0258357	−0.000849472 0
$926$	1.57525	0.0517658
$927$	−8.46204	−0.277930
$928$	−99.1708	−3.25544
$929$	−37.9634	−1.24554	−0.622770	−	0.782405i	$-0.713993\pi$
$929$	−37.9634	−1.24554	−0.622770	+	0.782405i	$0.713993\pi$
$930$	12.8577	0.421622
$931$	−0.773178	−0.0253399
$932$	−136.502	−4.47129
$933$	22.8409	0.747778
$934$	42.9116	1.40411
$935$	−74.3828	−2.43258
$936$	74.2002	2.42531
$937$	55.6687	1.81862	0.909309	−	0.416123i	$-0.136611\pi$
$937$	55.6687	1.81862	0.909309	+	0.416123i	$0.136611\pi$
$938$	−18.5220	−0.604765
$939$	−39.9710	−1.30440
$940$	67.1621	2.19059
$941$	9.46269	0.308475	0.154237	−	0.988034i	$-0.450708\pi$
$941$	9.46269	0.308475	0.154237	+	0.988034i	$0.450708\pi$
$942$	16.1439	0.525997
$943$	62.4193	2.03265
$944$	−15.7953	−0.514094
$945$	6.95196	0.226147
$946$	23.5529	0.765770
$947$	−55.1487	−1.79209	−0.896047	−	0.443960i	$-0.853573\pi$
$947$	−55.1487	−1.79209	−0.896047	+	0.443960i	$0.853573\pi$
$948$	137.669	4.47129
$949$	−63.1315	−2.04933
$950$	−0.0540683	−0.00175421
$951$	34.1849	1.10852
$952$	−60.5877	−1.96366
$953$	1.73841	0.0563125	0.0281562	−	0.999604i	$-0.491036\pi$
$953$	1.73841	0.0563125	0.0281562	+	0.999604i	$0.491036\pi$
$954$	−6.47841	−0.209746
$955$	−1.10386	−0.0357202
$956$	−21.9562	−0.710115
$957$	54.7474	1.76973
$958$	53.5297	1.72946
$959$	12.4841	0.403134
$960$	−115.536	−3.72891
$961$	1.00000	0.0322581
$962$	14.5178	0.468074
$963$	−0.788898	−0.0254219
$964$	50.1138	1.61406
$965$	−39.5375	−1.27276
$966$	37.3422	1.20147
$967$	−0.657920	−0.0211573	−0.0105786	−	0.999944i	$-0.503367\pi$
$967$	−0.657920	−0.0211573	−0.0105786	+	0.999944i	$0.503367\pi$
$968$	−122.107	−3.92465
$969$	−11.0820	−0.356006
$970$	−31.9763	−1.02670
$971$	29.0373	0.931850	0.465925	−	0.884824i	$-0.345722\pi$
$971$	29.0373	0.931850	0.465925	+	0.884824i	$0.345722\pi$
$972$	−77.8039	−2.49556
$973$	9.06042	0.290464
$974$	−57.8927	−1.85500
$975$	0.295149	0.00945232
$976$	−80.6663	−2.58207
$977$	58.3705	1.86744	0.933718	−	0.358009i	$-0.116544\pi$
$977$	58.3705	1.86744	0.933718	+	0.358009i	$0.116544\pi$
$978$	129.051	4.12658
$979$	85.5358	2.73374
$980$	−11.8792	−0.379467
$981$	−23.2474	−0.742233
$982$	112.687	3.59599
$983$	−21.3073	−0.679598	−0.339799	−	0.940498i	$-0.610359\pi$
$983$	−21.3073	−0.679598	−0.339799	+	0.940498i	$0.610359\pi$
$984$	184.796	5.89107
$985$	25.5899	0.815363
$986$	−94.4689	−3.00850
$987$	−12.0420	−0.383301
$988$	22.0885	0.702728
$989$	11.3727	0.361630
$990$	45.9702	1.46103
$991$	−2.95350	−0.0938209	−0.0469104	−	0.998899i	$-0.514938\pi$
$991$	−2.95350	−0.0938209	−0.0469104	+	0.998899i	$0.514938\pi$
$992$	−19.1212	−0.607100
$993$	33.4214	1.06060
$994$	−38.8278	−1.23154
$995$	0.810307	0.0256885
$996$	181.246	5.74300
$997$	37.0037	1.17192	0.585960	−	0.810340i	$-0.300718\pi$
$997$	37.0037	1.17192	0.585960	+	0.810340i	$0.300718\pi$
$998$	−7.44573	−0.235690
$999$	−3.11707	−0.0986198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.g.1.2	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.g.1.2	✓	70	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70672 q^{2} +2.12991 q^{3} +5.32631 q^{4} -2.23028 q^{5} -5.76507 q^{6} +1.00000 q^{7} -9.00339 q^{8} +1.53652 q^{9} +O(q^{10})\)	\(q-2.70672 q^{2} +2.12991 q^{3} +5.32631 q^{4} -2.23028 q^{5} -5.76507 q^{6} +1.00000 q^{7} -9.00339 q^{8} +1.53652 q^{9} +6.03675 q^{10} +4.95603 q^{11} +11.3446 q^{12} -5.36363 q^{13} -2.70672 q^{14} -4.75031 q^{15} +13.7170 q^{16} +6.72943 q^{17} -4.15894 q^{18} -0.773178 q^{19} -11.8792 q^{20} +2.12991 q^{21} -13.4146 q^{22} -6.47732 q^{23} -19.1764 q^{24} -0.0258357 q^{25} +14.5178 q^{26} -3.11707 q^{27} +5.32631 q^{28} +5.18642 q^{29} +12.8577 q^{30} +1.00000 q^{31} -19.1212 q^{32} +10.5559 q^{33} -18.2147 q^{34} -2.23028 q^{35} +8.18402 q^{36} +1.00000 q^{37} +2.09277 q^{38} -11.4241 q^{39} +20.0801 q^{40} -9.63660 q^{41} -5.76507 q^{42} -1.75577 q^{43} +26.3974 q^{44} -3.42689 q^{45} +17.5323 q^{46} -5.65376 q^{47} +29.2160 q^{48} +1.00000 q^{49} +0.0699299 q^{50} +14.3331 q^{51} -28.5684 q^{52} +1.55771 q^{53} +8.43703 q^{54} -11.0534 q^{55} -9.00339 q^{56} -1.64680 q^{57} -14.0382 q^{58} -1.15151 q^{59} -25.3016 q^{60} -5.88076 q^{61} -2.70672 q^{62} +1.53652 q^{63} +24.3218 q^{64} +11.9624 q^{65} -28.5719 q^{66} +6.84298 q^{67} +35.8431 q^{68} -13.7961 q^{69} +6.03675 q^{70} +14.3450 q^{71} -13.8339 q^{72} +11.7703 q^{73} -2.70672 q^{74} -0.0550277 q^{75} -4.11819 q^{76} +4.95603 q^{77} +30.9217 q^{78} +12.1352 q^{79} -30.5928 q^{80} -11.2487 q^{81} +26.0835 q^{82} +15.9764 q^{83} +11.3446 q^{84} -15.0085 q^{85} +4.75236 q^{86} +11.0466 q^{87} -44.6211 q^{88} +17.2589 q^{89} +9.27561 q^{90} -5.36363 q^{91} -34.5002 q^{92} +2.12991 q^{93} +15.3031 q^{94} +1.72441 q^{95} -40.7266 q^{96} -5.29694 q^{97} -2.70672 q^{98} +7.61507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

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