LMFDB - Embedded newform 6035.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$58$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56061 q^{2} -2.33055 q^{3} +0.435498 q^{4} +1.00000 q^{5} +3.63707 q^{6} +3.61265 q^{7} +2.44157 q^{8} +2.43146 q^{9} +O(q^{10})$	\(q-1.56061 q^{2} -2.33055 q^{3} +0.435498 q^{4} +1.00000 q^{5} +3.63707 q^{6} +3.61265 q^{7} +2.44157 q^{8} +2.43146 q^{9} -1.56061 q^{10} +5.29786 q^{11} -1.01495 q^{12} -1.60244 q^{13} -5.63793 q^{14} -2.33055 q^{15} -4.68134 q^{16} +1.00000 q^{17} -3.79455 q^{18} -7.78553 q^{19} +0.435498 q^{20} -8.41946 q^{21} -8.26788 q^{22} +1.22123 q^{23} -5.69021 q^{24} +1.00000 q^{25} +2.50078 q^{26} +1.32502 q^{27} +1.57330 q^{28} +9.07829 q^{29} +3.63707 q^{30} -10.3849 q^{31} +2.42259 q^{32} -12.3469 q^{33} -1.56061 q^{34} +3.61265 q^{35} +1.05889 q^{36} -2.05905 q^{37} +12.1502 q^{38} +3.73456 q^{39} +2.44157 q^{40} +6.06933 q^{41} +13.1395 q^{42} -2.53993 q^{43} +2.30721 q^{44} +2.43146 q^{45} -1.90586 q^{46} +13.5167 q^{47} +10.9101 q^{48} +6.05125 q^{49} -1.56061 q^{50} -2.33055 q^{51} -0.697859 q^{52} -7.86292 q^{53} -2.06784 q^{54} +5.29786 q^{55} +8.82056 q^{56} +18.1445 q^{57} -14.1677 q^{58} +10.8726 q^{59} -1.01495 q^{60} +2.72600 q^{61} +16.2068 q^{62} +8.78400 q^{63} +5.58197 q^{64} -1.60244 q^{65} +19.2687 q^{66} -11.7154 q^{67} +0.435498 q^{68} -2.84614 q^{69} -5.63793 q^{70} +1.00000 q^{71} +5.93658 q^{72} -1.04299 q^{73} +3.21336 q^{74} -2.33055 q^{75} -3.39058 q^{76} +19.1393 q^{77} -5.82818 q^{78} +6.21431 q^{79} -4.68134 q^{80} -10.3824 q^{81} -9.47185 q^{82} +12.4646 q^{83} -3.66666 q^{84} +1.00000 q^{85} +3.96384 q^{86} -21.1574 q^{87} +12.9351 q^{88} +12.6092 q^{89} -3.79455 q^{90} -5.78905 q^{91} +0.531844 q^{92} +24.2025 q^{93} -21.0943 q^{94} -7.78553 q^{95} -5.64595 q^{96} +0.361129 q^{97} -9.44363 q^{98} +12.8815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) $ 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * 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 $

$2$	−1.56061	−1.10352	−0.551758	−	0.834004i	$-0.686043\pi$
$2$	−1.56061	−1.10352	−0.551758	+	0.834004i	$0.686043\pi$
$3$	−2.33055	−1.34554	−0.672771	−	0.739850i	$-0.734896\pi$
$3$	−2.33055	−1.34554	−0.672771	+	0.739850i	$0.734896\pi$
$4$	0.435498	0.217749
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.63707	1.48483
$7$	3.61265	1.36545	0.682727	−	0.730674i	$-0.260794\pi$
$7$	3.61265	1.36545	0.682727	+	0.730674i	$0.260794\pi$
$8$	2.44157	0.863227
$9$	2.43146	0.810485
$10$	−1.56061	−0.493508
$11$	5.29786	1.59736	0.798682	−	0.601753i	$-0.205531\pi$
$11$	5.29786	1.59736	0.798682	+	0.601753i	$0.205531\pi$
$12$	−1.01495	−0.292991
$13$	−1.60244	−0.444436	−0.222218	−	0.974997i	$-0.571330\pi$
$13$	−1.60244	−0.444436	−0.222218	+	0.974997i	$0.571330\pi$
$14$	−5.63793	−1.50680
$15$	−2.33055	−0.601745
$16$	−4.68134	−1.17033
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.79455	−0.894384
$19$	−7.78553	−1.78612	−0.893061	−	0.449935i	$-0.851447\pi$
$19$	−7.78553	−1.78612	−0.893061	+	0.449935i	$0.851447\pi$
$20$	0.435498	0.0973804
$21$	−8.41946	−1.83728
$22$	−8.26788	−1.76272
$23$	1.22123	0.254644	0.127322	−	0.991861i	$-0.459362\pi$
$23$	1.22123	0.254644	0.127322	+	0.991861i	$0.459362\pi$
$24$	−5.69021	−1.16151
$25$	1.00000	0.200000
$26$	2.50078	0.490443
$27$	1.32502	0.255000
$28$	1.57330	0.297326
$29$	9.07829	1.68580	0.842899	−	0.538073i	$-0.180847\pi$
$29$	9.07829	1.68580	0.842899	+	0.538073i	$0.180847\pi$
$30$	3.63707	0.664036
$31$	−10.3849	−1.86518	−0.932592	−	0.360934i	$-0.882458\pi$
$31$	−10.3849	−1.86518	−0.932592	+	0.360934i	$0.882458\pi$
$32$	2.42259	0.428257
$33$	−12.3469	−2.14932
$34$	−1.56061	−0.267642
$35$	3.61265	0.610649
$36$	1.05889	0.176482
$37$	−2.05905	−0.338505	−0.169253	−	0.985573i	$-0.554135\pi$
$37$	−2.05905	−0.338505	−0.169253	+	0.985573i	$0.554135\pi$
$38$	12.1502	1.97102
$39$	3.73456	0.598008
$40$	2.44157	0.386047
$41$	6.06933	0.947870	0.473935	−	0.880560i	$-0.342833\pi$
$41$	6.06933	0.947870	0.473935	+	0.880560i	$0.342833\pi$
$42$	13.1395	2.02747
$43$	−2.53993	−0.387336	−0.193668	−	0.981067i	$-0.562038\pi$
$43$	−2.53993	−0.387336	−0.193668	+	0.981067i	$0.562038\pi$
$44$	2.30721	0.347825
$45$	2.43146	0.362460
$46$	−1.90586	−0.281004
$47$	13.5167	1.97162	0.985809	−	0.167869i	$-0.0536887\pi$
$47$	13.5167	1.97162	0.985809	+	0.167869i	$0.0536887\pi$
$48$	10.9101	1.57474
$49$	6.05125	0.864464
$50$	−1.56061	−0.220703
$51$	−2.33055	−0.326342
$52$	−0.697859	−0.0967756
$53$	−7.86292	−1.08005	−0.540027	−	0.841648i	$-0.681586\pi$
$53$	−7.86292	−1.08005	−0.540027	+	0.841648i	$0.681586\pi$
$54$	−2.06784	−0.281397
$55$	5.29786	0.714363
$56$	8.82056	1.17870
$57$	18.1445	2.40330
$58$	−14.1677	−1.86031
$59$	10.8726	1.41549	0.707747	−	0.706466i	$-0.249712\pi$
$59$	10.8726	1.41549	0.707747	+	0.706466i	$0.249712\pi$
$60$	−1.01495	−0.131029
$61$	2.72600	0.349028	0.174514	−	0.984655i	$-0.444164\pi$
$61$	2.72600	0.349028	0.174514	+	0.984655i	$0.444164\pi$
$62$	16.2068	2.05826
$63$	8.78400	1.10668
$64$	5.58197	0.697746
$65$	−1.60244	−0.198758
$66$	19.2687	2.37181
$67$	−11.7154	−1.43126	−0.715630	−	0.698479i	$-0.753861\pi$
$67$	−11.7154	−1.43126	−0.715630	+	0.698479i	$0.753861\pi$
$68$	0.435498	0.0528119
$69$	−2.84614	−0.342635
$70$	−5.63793	−0.673862
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	5.93658	0.699633
$73$	−1.04299	−0.122072	−0.0610361	−	0.998136i	$-0.519440\pi$
$73$	−1.04299	−0.122072	−0.0610361	+	0.998136i	$0.519440\pi$
$74$	3.21336	0.373546
$75$	−2.33055	−0.269109
$76$	−3.39058	−0.388927
$77$	19.1393	2.18113
$78$	−5.82818	−0.659912
$79$	6.21431	0.699165	0.349582	−	0.936906i	$-0.386324\pi$
$79$	6.21431	0.699165	0.349582	+	0.936906i	$0.386324\pi$
$80$	−4.68134	−0.523389
$81$	−10.3824	−1.15360
$82$	−9.47185	−1.04599
$83$	12.4646	1.36816	0.684081	−	0.729406i	$-0.260203\pi$
$83$	12.4646	1.36816	0.684081	+	0.729406i	$0.260203\pi$
$84$	−3.66666	−0.400065
$85$	1.00000	0.108465
$86$	3.96384	0.427432
$87$	−21.1574	−2.26831
$88$	12.9351	1.37889
$89$	12.6092	1.33658	0.668288	−	0.743902i	$-0.267027\pi$
$89$	12.6092	1.33658	0.668288	+	0.743902i	$0.267027\pi$
$90$	−3.79455	−0.399981
$91$	−5.78905	−0.606857
$92$	0.531844	0.0554485
$93$	24.2025	2.50968
$94$	−21.0943	−2.17571
$95$	−7.78553	−0.798778
$96$	−5.64595	−0.576238
$97$	0.361129	0.0366671	0.0183336	−	0.999832i	$-0.494164\pi$
$97$	0.361129	0.0366671	0.0183336	+	0.999832i	$0.494164\pi$
$98$	−9.44363	−0.953950
$99$	12.8815	1.29464
$100$	0.435498	0.0435498
$101$	−7.92643	−0.788710	−0.394355	−	0.918958i	$-0.629032\pi$
$101$	−7.92643	−0.788710	−0.394355	+	0.918958i	$0.629032\pi$
$102$	3.63707	0.360124
$103$	2.97563	0.293197	0.146599	−	0.989196i	$-0.453167\pi$
$103$	2.97563	0.293197	0.146599	+	0.989196i	$0.453167\pi$
$104$	−3.91247	−0.383649
$105$	−8.41946	−0.821655
$106$	12.2709	1.19186
$107$	−15.6540	−1.51333	−0.756663	−	0.653805i	$-0.773172\pi$
$107$	−15.6540	−1.51333	−0.756663	+	0.653805i	$0.773172\pi$
$108$	0.577044	0.0555261
$109$	18.4149	1.76383	0.881915	−	0.471409i	$-0.156254\pi$
$109$	18.4149	1.76383	0.881915	+	0.471409i	$0.156254\pi$
$110$	−8.26788	−0.788311
$111$	4.79871	0.455473
$112$	−16.9120	−1.59804
$113$	−5.42878	−0.510697	−0.255348	−	0.966849i	$-0.582190\pi$
$113$	−5.42878	−0.510697	−0.255348	+	0.966849i	$0.582190\pi$
$114$	−28.3165	−2.65209
$115$	1.22123	0.113880
$116$	3.95358	0.367081
$117$	−3.89626	−0.360209
$118$	−16.9679	−1.56202
$119$	3.61265	0.331171
$120$	−5.69021	−0.519442
$121$	17.0673	1.55157
$122$	−4.25422	−0.385159
$123$	−14.1449	−1.27540
$124$	−4.52261	−0.406142
$125$	1.00000	0.0894427
$126$	−13.7084	−1.22124
$127$	−5.20561	−0.461923	−0.230962	−	0.972963i	$-0.574187\pi$
$127$	−5.20561	−0.461923	−0.230962	+	0.972963i	$0.574187\pi$
$128$	−13.5564	−1.19823
$129$	5.91944	0.521177
$130$	2.50078	0.219333
$131$	0.183868	0.0160646	0.00803231	−	0.999968i	$-0.497443\pi$
$131$	0.183868	0.0160646	0.00803231	+	0.999968i	$0.497443\pi$
$132$	−5.37706	−0.468013
$133$	−28.1264	−2.43887
$134$	18.2831	1.57942
$135$	1.32502	0.114040
$136$	2.44157	0.209363
$137$	−14.3305	−1.22434	−0.612170	−	0.790726i	$-0.709703\pi$
$137$	−14.3305	−1.22434	−0.612170	+	0.790726i	$0.709703\pi$
$138$	4.44170	0.378103
$139$	14.3114	1.21387	0.606937	−	0.794750i	$-0.292398\pi$
$139$	14.3114	1.21387	0.606937	+	0.794750i	$0.292398\pi$
$140$	1.57330	0.132968
$141$	−31.5014	−2.65290
$142$	−1.56061	−0.130963
$143$	−8.48949	−0.709927
$144$	−11.3825	−0.948539
$145$	9.07829	0.753911
$146$	1.62769	0.134709
$147$	−14.1027	−1.16317
$148$	−0.896711	−0.0737092
$149$	22.5125	1.84429	0.922147	−	0.386840i	$-0.126433\pi$
$149$	22.5125	1.84429	0.922147	+	0.386840i	$0.126433\pi$
$150$	3.63707	0.296966
$151$	−14.9115	−1.21348	−0.606741	−	0.794899i	$-0.707524\pi$
$151$	−14.9115	−1.21348	−0.606741	+	0.794899i	$0.707524\pi$
$152$	−19.0089	−1.54183
$153$	2.43146	0.196572
$154$	−29.8690	−2.40691
$155$	−10.3849	−0.834135
$156$	1.62639	0.130216
$157$	10.8687	0.867416	0.433708	−	0.901053i	$-0.357205\pi$
$157$	10.8687	0.867416	0.433708	+	0.901053i	$0.357205\pi$
$158$	−9.69810	−0.771540
$159$	18.3249	1.45326
$160$	2.42259	0.191522
$161$	4.41188	0.347705
$162$	16.2028	1.27302
$163$	15.7391	1.23278	0.616391	−	0.787441i	$-0.288594\pi$
$163$	15.7391	1.23278	0.616391	+	0.787441i	$0.288594\pi$
$164$	2.64318	0.206398
$165$	−12.3469	−0.961206
$166$	−19.4523	−1.50979
$167$	−1.23516	−0.0955795	−0.0477898	−	0.998857i	$-0.515218\pi$
$167$	−1.23516	−0.0955795	−0.0477898	+	0.998857i	$0.515218\pi$
$168$	−20.5567	−1.58599
$169$	−10.4322	−0.802476
$170$	−1.56061	−0.119693
$171$	−18.9302	−1.44763
$172$	−1.10614	−0.0843421
$173$	−12.2207	−0.929120	−0.464560	−	0.885542i	$-0.653787\pi$
$173$	−12.2207	−0.929120	−0.464560	+	0.885542i	$0.653787\pi$
$174$	33.0184	2.50312
$175$	3.61265	0.273091
$176$	−24.8011	−1.86945
$177$	−25.3391	−1.90461
$178$	−19.6781	−1.47493
$179$	8.33447	0.622947	0.311474	−	0.950255i	$-0.399177\pi$
$179$	8.33447	0.622947	0.311474	+	0.950255i	$0.399177\pi$
$180$	1.05889	0.0789254
$181$	−19.2614	−1.43169	−0.715844	−	0.698260i	$-0.753958\pi$
$181$	−19.2614	−1.43169	−0.715844	+	0.698260i	$0.753958\pi$
$182$	9.03444	0.669677
$183$	−6.35307	−0.469633
$184$	2.98172	0.219816
$185$	−2.05905	−0.151384
$186$	−37.7706	−2.76948
$187$	5.29786	0.387418
$188$	5.88652	0.429318
$189$	4.78683	0.348191
$190$	12.1502	0.881465
$191$	1.91376	0.138475	0.0692376	−	0.997600i	$-0.477943\pi$
$191$	1.91376	0.138475	0.0692376	+	0.997600i	$0.477943\pi$
$192$	−13.0090	−0.938847
$193$	−4.73382	−0.340748	−0.170374	−	0.985380i	$-0.554498\pi$
$193$	−4.73382	−0.340748	−0.170374	+	0.985380i	$0.554498\pi$
$194$	−0.563581	−0.0404628
$195$	3.73456	0.267437
$196$	2.63531	0.188236
$197$	13.2406	0.943352	0.471676	−	0.881772i	$-0.343649\pi$
$197$	13.2406	0.943352	0.471676	+	0.881772i	$0.343649\pi$
$198$	−20.1030	−1.42866
$199$	−4.53255	−0.321304	−0.160652	−	0.987011i	$-0.551360\pi$
$199$	−4.53255	−0.321304	−0.160652	+	0.987011i	$0.551360\pi$
$200$	2.44157	0.172645
$201$	27.3033	1.92582
$202$	12.3701	0.870354
$203$	32.7967	2.30188
$204$	−1.01495	−0.0710607
$205$	6.06933	0.423900
$206$	−4.64379	−0.323548
$207$	2.96937	0.206385
$208$	7.50155	0.520139
$209$	−41.2466	−2.85309
$210$	13.1395	0.906710
$211$	2.91610	0.200753	0.100376	−	0.994950i	$-0.467995\pi$
$211$	2.91610	0.200753	0.100376	+	0.994950i	$0.467995\pi$
$212$	−3.42429	−0.235181
$213$	−2.33055	−0.159687
$214$	24.4297	1.66998
$215$	−2.53993	−0.173222
$216$	3.23513	0.220123
$217$	−37.5170	−2.54682
$218$	−28.7385	−1.94642
$219$	2.43073	0.164253
$220$	2.30721	0.155552
$221$	−1.60244	−0.107792
$222$	−7.48890	−0.502622
$223$	−6.77017	−0.453364	−0.226682	−	0.973969i	$-0.572788\pi$
$223$	−6.77017	−0.453364	−0.226682	+	0.973969i	$0.572788\pi$
$224$	8.75196	0.584765
$225$	2.43146	0.162097
$226$	8.47220	0.563563
$227$	1.25641	0.0833909	0.0416955	−	0.999130i	$-0.486724\pi$
$227$	1.25641	0.0833909	0.0416955	+	0.999130i	$0.486724\pi$
$228$	7.90192	0.523317
$229$	16.8143	1.11112	0.555559	−	0.831477i	$-0.312504\pi$
$229$	16.8143	1.11112	0.555559	+	0.831477i	$0.312504\pi$
$230$	−1.90586	−0.125669
$231$	−44.6051	−2.93480
$232$	22.1653	1.45523
$233$	−8.08704	−0.529800	−0.264900	−	0.964276i	$-0.585339\pi$
$233$	−8.08704	−0.529800	−0.264900	+	0.964276i	$0.585339\pi$
$234$	6.08053	0.397497
$235$	13.5167	0.881735
$236$	4.73500	0.308222
$237$	−14.4828	−0.940756
$238$	−5.63793	−0.365453
$239$	−4.35370	−0.281617	−0.140809	−	0.990037i	$-0.544970\pi$
$239$	−4.35370	−0.281617	−0.140809	+	0.990037i	$0.544970\pi$
$240$	10.9101	0.704243
$241$	9.37904	0.604157	0.302079	−	0.953283i	$-0.402320\pi$
$241$	9.37904	0.604157	0.302079	+	0.953283i	$0.402320\pi$
$242$	−26.6353	−1.71218
$243$	20.2216	1.29722
$244$	1.18717	0.0760007
$245$	6.05125	0.386600
$246$	22.0746	1.40742
$247$	12.4758	0.793818
$248$	−25.3555	−1.61008
$249$	−29.0492	−1.84092
$250$	−1.56061	−0.0987015
$251$	8.50456	0.536803	0.268401	−	0.963307i	$-0.413505\pi$
$251$	8.50456	0.536803	0.268401	+	0.963307i	$0.413505\pi$
$252$	3.82542	0.240979
$253$	6.46990	0.406759
$254$	8.12392	0.509740
$255$	−2.33055	−0.145945
$256$	9.99235	0.624522
$257$	15.2549	0.951577	0.475788	−	0.879560i	$-0.342163\pi$
$257$	15.2549	0.951577	0.475788	+	0.879560i	$0.342163\pi$
$258$	−9.23792	−0.575128
$259$	−7.43862	−0.462213
$260$	−0.697859	−0.0432794
$261$	22.0735	1.36631
$262$	−0.286946	−0.0177276
$263$	−17.7151	−1.09236	−0.546179	−	0.837668i	$-0.683918\pi$
$263$	−17.7151	−1.09236	−0.546179	+	0.837668i	$0.683918\pi$
$264$	−30.1459	−1.85535
$265$	−7.86292	−0.483015
$266$	43.8943	2.69133
$267$	−29.3864	−1.79842
$268$	−5.10203	−0.311656
$269$	−31.2908	−1.90784	−0.953918	−	0.300068i	$-0.902991\pi$
$269$	−31.2908	−1.90784	−0.953918	+	0.300068i	$0.902991\pi$
$270$	−2.06784	−0.125845
$271$	12.0457	0.731725	0.365863	−	0.930669i	$-0.380774\pi$
$271$	12.0457	0.731725	0.365863	+	0.930669i	$0.380774\pi$
$272$	−4.68134	−0.283848
$273$	13.4917	0.816552
$274$	22.3644	1.35108
$275$	5.29786	0.319473
$276$	−1.23949	−0.0746084
$277$	19.4473	1.16848	0.584239	−	0.811582i	$-0.301393\pi$
$277$	19.4473	1.16848	0.584239	+	0.811582i	$0.301393\pi$
$278$	−22.3344	−1.33953
$279$	−25.2504	−1.51170
$280$	8.82056	0.527129
$281$	28.1187	1.67742	0.838712	−	0.544576i	$-0.183309\pi$
$281$	28.1187	1.67742	0.838712	+	0.544576i	$0.183309\pi$
$282$	49.1614	2.92752
$283$	12.6147	0.749868	0.374934	−	0.927052i	$-0.377665\pi$
$283$	12.6147	0.749868	0.374934	+	0.927052i	$0.377665\pi$
$284$	0.435498	0.0258421
$285$	18.1445	1.07479
$286$	13.2488	0.783416
$287$	21.9264	1.29427
$288$	5.89041	0.347096
$289$	1.00000	0.0588235
$290$	−14.1677	−0.831954
$291$	−0.841629	−0.0493372
$292$	−0.454219	−0.0265811
$293$	−18.0231	−1.05292	−0.526461	−	0.850200i	$-0.676481\pi$
$293$	−18.0231	−1.05292	−0.526461	+	0.850200i	$0.676481\pi$
$294$	22.0088	1.28358
$295$	10.8726	0.633028
$296$	−5.02731	−0.292207
$297$	7.01977	0.407328
$298$	−35.1332	−2.03521
$299$	−1.95695	−0.113173
$300$	−1.01495	−0.0585982
$301$	−9.17589	−0.528890
$302$	23.2710	1.33910
$303$	18.4729	1.06124
$304$	36.4467	2.09036
$305$	2.72600	0.156090
$306$	−3.79455	−0.216920
$307$	24.4360	1.39464	0.697318	−	0.716762i	$-0.254377\pi$
$307$	24.4360	1.39464	0.697318	+	0.716762i	$0.254377\pi$
$308$	8.33514	0.474938
$309$	−6.93485	−0.394510
$310$	16.2068	0.920482
$311$	22.0685	1.25139	0.625694	−	0.780068i	$-0.284816\pi$
$311$	22.0685	1.25139	0.625694	+	0.780068i	$0.284816\pi$
$312$	9.11820	0.516217
$313$	−26.1078	−1.47570	−0.737850	−	0.674965i	$-0.764159\pi$
$313$	−26.1078	−1.47570	−0.737850	+	0.674965i	$0.764159\pi$
$314$	−16.9618	−0.957208
$315$	8.78400	0.494922
$316$	2.70632	0.152242
$317$	14.8071	0.831651	0.415826	−	0.909444i	$-0.363493\pi$
$317$	14.8071	0.831651	0.415826	+	0.909444i	$0.363493\pi$
$318$	−28.5980	−1.60370
$319$	48.0955	2.69283
$320$	5.58197	0.312041
$321$	36.4823	2.03625
$322$	−6.88521	−0.383698
$323$	−7.78553	−0.433198
$324$	−4.52151	−0.251195
$325$	−1.60244	−0.0888873
$326$	−24.5626	−1.36039
$327$	−42.9169	−2.37331
$328$	14.8187	0.818227
$329$	48.8312	2.69215
$330$	19.2687	1.06071
$331$	−16.3946	−0.901131	−0.450566	−	0.892743i	$-0.648778\pi$
$331$	−16.3946	−0.901131	−0.450566	+	0.892743i	$0.648778\pi$
$332$	5.42829	0.297916
$333$	−5.00648	−0.274353
$334$	1.92760	0.105474
$335$	−11.7154	−0.640079
$336$	39.4143	2.15023
$337$	−27.8569	−1.51746	−0.758731	−	0.651404i	$-0.774181\pi$
$337$	−27.8569	−1.51746	−0.758731	+	0.651404i	$0.774181\pi$
$338$	16.2806	0.885546
$339$	12.6520	0.687165
$340$	0.435498	0.0236182
$341$	−55.0177	−2.97938
$342$	29.5426	1.59748
$343$	−3.42751	−0.185068
$344$	−6.20143	−0.334359
$345$	−2.84614	−0.153231
$346$	19.0717	1.02530
$347$	−8.19891	−0.440141	−0.220070	−	0.975484i	$-0.570629\pi$
$347$	−8.19891	−0.440141	−0.220070	+	0.975484i	$0.570629\pi$
$348$	−9.21402	−0.493923
$349$	10.5186	0.563047	0.281523	−	0.959554i	$-0.409160\pi$
$349$	10.5186	0.563047	0.281523	+	0.959554i	$0.409160\pi$
$350$	−5.63793	−0.301360
$351$	−2.12326	−0.113331
$352$	12.8345	0.684082
$353$	−23.5156	−1.25161	−0.625804	−	0.779980i	$-0.715229\pi$
$353$	−23.5156	−1.25161	−0.625804	+	0.779980i	$0.715229\pi$
$354$	39.5445	2.10177
$355$	1.00000	0.0530745
$356$	5.49130	0.291038
$357$	−8.41946	−0.445605
$358$	−13.0068	−0.687433
$359$	17.0018	0.897319	0.448659	−	0.893703i	$-0.351902\pi$
$359$	17.0018	0.897319	0.448659	+	0.893703i	$0.351902\pi$
$360$	5.93658	0.312885
$361$	41.6144	2.19023
$362$	30.0595	1.57989
$363$	−39.7761	−2.08771
$364$	−2.52112	−0.132143
$365$	−1.04299	−0.0545924
$366$	9.91466	0.518248
$367$	1.46695	0.0765742	0.0382871	−	0.999267i	$-0.487810\pi$
$367$	1.46695	0.0765742	0.0382871	+	0.999267i	$0.487810\pi$
$368$	−5.71699	−0.298019
$369$	14.7573	0.768235
$370$	3.21336	0.167055
$371$	−28.4060	−1.47476
$372$	10.5402	0.546482
$373$	30.4911	1.57877	0.789384	−	0.613900i	$-0.210400\pi$
$373$	30.4911	1.57877	0.789384	+	0.613900i	$0.210400\pi$
$374$	−8.26788	−0.427522
$375$	−2.33055	−0.120349
$376$	33.0021	1.70195
$377$	−14.5474	−0.749229
$378$	−7.47037	−0.384235
$379$	−15.0998	−0.775623	−0.387812	−	0.921739i	$-0.626769\pi$
$379$	−15.0998	−0.775623	−0.387812	+	0.921739i	$0.626769\pi$
$380$	−3.39058	−0.173933
$381$	12.1319	0.621538
$382$	−2.98664	−0.152810
$383$	6.34418	0.324172	0.162086	−	0.986777i	$-0.448178\pi$
$383$	6.34418	0.324172	0.162086	+	0.986777i	$0.448178\pi$
$384$	31.5939	1.61227
$385$	19.1393	0.975429
$386$	7.38763	0.376021
$387$	−6.17573	−0.313930
$388$	0.157271	0.00798424
$389$	−9.32307	−0.472698	−0.236349	−	0.971668i	$-0.575951\pi$
$389$	−9.32307	−0.472698	−0.236349	+	0.971668i	$0.575951\pi$
$390$	−5.82818	−0.295122
$391$	1.22123	0.0617603
$392$	14.7746	0.746228
$393$	−0.428513	−0.0216156
$394$	−20.6634	−1.04100
$395$	6.21431	0.312676
$396$	5.60987	0.281907
$397$	9.89810	0.496771	0.248386	−	0.968661i	$-0.420100\pi$
$397$	9.89810	0.496771	0.248386	+	0.968661i	$0.420100\pi$
$398$	7.07353	0.354564
$399$	65.5499	3.28160
$400$	−4.68134	−0.234067
$401$	25.4229	1.26956	0.634780	−	0.772693i	$-0.281091\pi$
$401$	25.4229	1.26956	0.634780	+	0.772693i	$0.281091\pi$
$402$	−42.6097	−2.12518
$403$	16.6412	0.828955
$404$	−3.45195	−0.171741
$405$	−10.3824	−0.515905
$406$	−51.1828	−2.54016
$407$	−10.9085	−0.540716
$408$	−5.69021	−0.281707
$409$	6.89872	0.341120	0.170560	−	0.985347i	$-0.445442\pi$
$409$	6.89872	0.341120	0.170560	+	0.985347i	$0.445442\pi$
$410$	−9.47185	−0.467781
$411$	33.3980	1.64740
$412$	1.29588	0.0638435
$413$	39.2789	1.93279
$414$	−4.63402	−0.227750
$415$	12.4646	0.611861
$416$	−3.88204	−0.190333
$417$	−33.3533	−1.63332
$418$	64.3698	3.14843
$419$	29.4830	1.44034	0.720170	−	0.693798i	$-0.244064\pi$
$419$	29.4830	1.44034	0.720170	+	0.693798i	$0.244064\pi$
$420$	−3.66666	−0.178915
$421$	−30.0465	−1.46438	−0.732190	−	0.681101i	$-0.761501\pi$
$421$	−30.0465	−1.46438	−0.732190	+	0.681101i	$0.761501\pi$
$422$	−4.55089	−0.221534
$423$	32.8653	1.59797
$424$	−19.1979	−0.932332
$425$	1.00000	0.0485071
$426$	3.63707	0.176217
$427$	9.84808	0.476582
$428$	−6.81728	−0.329526
$429$	19.7852	0.955237
$430$	3.96384	0.191153
$431$	13.7438	0.662014	0.331007	−	0.943628i	$-0.392612\pi$
$431$	13.7438	0.662014	0.331007	+	0.943628i	$0.392612\pi$
$432$	−6.20287	−0.298436
$433$	7.15579	0.343885	0.171943	−	0.985107i	$-0.444996\pi$
$433$	7.15579	0.343885	0.171943	+	0.985107i	$0.444996\pi$
$434$	58.5494	2.81046
$435$	−21.1574	−1.01442
$436$	8.01967	0.384072
$437$	−9.50792	−0.454826
$438$	−3.79342	−0.181256
$439$	−40.5860	−1.93706	−0.968532	−	0.248890i	$-0.919934\pi$
$439$	−40.5860	−1.93706	−0.968532	+	0.248890i	$0.919934\pi$
$440$	12.9351	0.616657
$441$	14.7133	0.700635
$442$	2.50078	0.118950
$443$	−9.48058	−0.450436	−0.225218	−	0.974308i	$-0.572309\pi$
$443$	−9.48058	−0.450436	−0.225218	+	0.974308i	$0.572309\pi$
$444$	2.08983	0.0991789
$445$	12.6092	0.597735
$446$	10.5656	0.500295
$447$	−52.4664	−2.48158
$448$	20.1657	0.952740
$449$	23.4759	1.10790	0.553948	−	0.832551i	$-0.313121\pi$
$449$	23.4759	1.10790	0.553948	+	0.832551i	$0.313121\pi$
$450$	−3.79455	−0.178877
$451$	32.1544	1.51409
$452$	−2.36423	−0.111204
$453$	34.7520	1.63279
$454$	−1.96077	−0.0920233
$455$	−5.78905	−0.271395
$456$	44.3013	2.07460
$457$	10.1394	0.474303	0.237152	−	0.971473i	$-0.423786\pi$
$457$	10.1394	0.474303	0.237152	+	0.971473i	$0.423786\pi$
$458$	−26.2405	−1.22614
$459$	1.32502	0.0618466
$460$	0.531844	0.0247973
$461$	25.3377	1.18009	0.590046	−	0.807370i	$-0.299110\pi$
$461$	25.3377	1.18009	0.590046	+	0.807370i	$0.299110\pi$
$462$	69.6111	3.23860
$463$	−28.9225	−1.34414	−0.672072	−	0.740485i	$-0.734596\pi$
$463$	−28.9225	−1.34414	−0.672072	+	0.740485i	$0.734596\pi$
$464$	−42.4986	−1.97295
$465$	24.2025	1.12236
$466$	12.6207	0.584643
$467$	37.8812	1.75293	0.876466	−	0.481464i	$-0.159895\pi$
$467$	37.8812	1.75293	0.876466	+	0.481464i	$0.159895\pi$
$468$	−1.69681	−0.0784352
$469$	−42.3236	−1.95432
$470$	−21.0943	−0.973009
$471$	−25.3300	−1.16715
$472$	26.5463	1.22189
$473$	−13.4562	−0.618717
$474$	22.6019	1.03814
$475$	−7.78553	−0.357224
$476$	1.57330	0.0721122
$477$	−19.1183	−0.875368
$478$	6.79441	0.310769
$479$	−0.679996	−0.0310698	−0.0155349	−	0.999879i	$-0.504945\pi$
$479$	−0.679996	−0.0310698	−0.0155349	+	0.999879i	$0.504945\pi$
$480$	−5.64595	−0.257701
$481$	3.29949	0.150444
$482$	−14.6370	−0.666697
$483$	−10.2821	−0.467852
$484$	7.43277	0.337853
$485$	0.361129	0.0163980
$486$	−31.5580	−1.43150
$487$	−39.3921	−1.78503	−0.892513	−	0.451021i	$-0.851060\pi$
$487$	−39.3921	−1.78503	−0.892513	+	0.451021i	$0.851060\pi$
$488$	6.65573	0.301291
$489$	−36.6807	−1.65876
$490$	−9.44363	−0.426620
$491$	−30.6421	−1.38286	−0.691430	−	0.722444i	$-0.743019\pi$
$491$	−30.6421	−1.38286	−0.691430	+	0.722444i	$0.743019\pi$
$492$	−6.16007	−0.277717
$493$	9.07829	0.408866
$494$	−19.4699	−0.875991
$495$	12.8815	0.578981
$496$	48.6152	2.18289
$497$	3.61265	0.162050
$498$	45.3345	2.03149
$499$	−32.7161	−1.46457	−0.732286	−	0.680997i	$-0.761547\pi$
$499$	−32.7161	−1.46457	−0.732286	+	0.680997i	$0.761547\pi$
$500$	0.435498	0.0194761
$501$	2.87860	0.128606
$502$	−13.2723	−0.592371
$503$	−17.5621	−0.783057	−0.391528	−	0.920166i	$-0.628054\pi$
$503$	−17.5621	−0.783057	−0.391528	+	0.920166i	$0.628054\pi$
$504$	21.4468	0.955316
$505$	−7.92643	−0.352722
$506$	−10.0970	−0.448866
$507$	24.3127	1.07977
$508$	−2.26704	−0.100583
$509$	22.9817	1.01865	0.509323	−	0.860575i	$-0.329896\pi$
$509$	22.9817	1.01865	0.509323	+	0.860575i	$0.329896\pi$
$510$	3.63707	0.161052
$511$	−3.76794	−0.166684
$512$	11.5187	0.509060
$513$	−10.3160	−0.455462
$514$	−23.8070	−1.05008
$515$	2.97563	0.131122
$516$	2.57790	0.113486
$517$	71.6097	3.14939
$518$	11.6088	0.510060
$519$	28.4808	1.25017
$520$	−3.91247	−0.171573
$521$	−31.9798	−1.40106	−0.700531	−	0.713622i	$-0.747053\pi$
$521$	−31.9798	−1.40106	−0.700531	+	0.713622i	$0.747053\pi$
$522$	−34.4480	−1.50775
$523$	−35.0686	−1.53344	−0.766721	−	0.641980i	$-0.778113\pi$
$523$	−35.0686	−1.53344	−0.766721	+	0.641980i	$0.778113\pi$
$524$	0.0800742	0.00349806
$525$	−8.41946	−0.367455
$526$	27.6463	1.20544
$527$	−10.3849	−0.452373
$528$	57.8001	2.51542
$529$	−21.5086	−0.935156
$530$	12.2709	0.533015
$531$	26.4363	1.14724
$532$	−12.2490	−0.531061
$533$	−9.72572	−0.421268
$534$	45.8607	1.98459
$535$	−15.6540	−0.676780
$536$	−28.6040	−1.23550
$537$	−19.4239	−0.838202
$538$	48.8327	2.10533
$539$	32.0586	1.38086
$540$	0.577044	0.0248320
$541$	17.6690	0.759648	0.379824	−	0.925059i	$-0.375984\pi$
$541$	17.6690	0.759648	0.379824	+	0.925059i	$0.375984\pi$
$542$	−18.7986	−0.807471
$543$	44.8896	1.92640
$544$	2.42259	0.103868
$545$	18.4149	0.788809
$546$	−21.0552	−0.901079
$547$	−17.3677	−0.742589	−0.371294	−	0.928515i	$-0.621086\pi$
$547$	−17.3677	−0.742589	−0.371294	+	0.928515i	$0.621086\pi$
$548$	−6.24093	−0.266599
$549$	6.62815	0.282882
$550$	−8.26788	−0.352544
$551$	−70.6793	−3.01104
$552$	−6.94905	−0.295771
$553$	22.4501	0.954677
$554$	−30.3497	−1.28943
$555$	4.79871	0.203694
$556$	6.23258	0.264320
$557$	−8.13972	−0.344891	−0.172445	−	0.985019i	$-0.555167\pi$
$557$	−8.13972	−0.344891	−0.172445	+	0.985019i	$0.555167\pi$
$558$	39.4060	1.66819
$559$	4.07009	0.172146
$560$	−16.9120	−0.714664
$561$	−12.3469	−0.521287
$562$	−43.8823	−1.85106
$563$	10.4510	0.440457	0.220229	−	0.975448i	$-0.429320\pi$
$563$	10.4510	0.440457	0.220229	+	0.975448i	$0.429320\pi$
$564$	−13.7188	−0.577666
$565$	−5.42878	−0.228391
$566$	−19.6866	−0.827491
$567$	−37.5080	−1.57519
$568$	2.44157	0.102446
$569$	25.7111	1.07787	0.538933	−	0.842349i	$-0.318828\pi$
$569$	25.7111	1.07787	0.538933	+	0.842349i	$0.318828\pi$
$570$	−28.3165	−1.18605
$571$	1.84162	0.0770696	0.0385348	−	0.999257i	$-0.487731\pi$
$571$	1.84162	0.0770696	0.0385348	+	0.999257i	$0.487731\pi$
$572$	−3.69716	−0.154586
$573$	−4.46012	−0.186324
$574$	−34.2185	−1.42825
$575$	1.22123	0.0509288
$576$	13.5723	0.565513
$577$	10.5290	0.438330	0.219165	−	0.975688i	$-0.429667\pi$
$577$	10.5290	0.438330	0.219165	+	0.975688i	$0.429667\pi$
$578$	−1.56061	−0.0649127
$579$	11.0324	0.458490
$580$	3.95358	0.164164
$581$	45.0301	1.86816
$582$	1.31345	0.0544444
$583$	−41.6566	−1.72524
$584$	−2.54653	−0.105376
$585$	−3.89626	−0.161090
$586$	28.1270	1.16192
$587$	−19.0971	−0.788220	−0.394110	−	0.919063i	$-0.628947\pi$
$587$	−19.0971	−0.788220	−0.394110	+	0.919063i	$0.628947\pi$
$588$	−6.14171	−0.253280
$589$	80.8519	3.33145
$590$	−16.9679	−0.698557
$591$	−30.8578	−1.26932
$592$	9.63909	0.396164
$593$	16.4603	0.675942	0.337971	−	0.941157i	$-0.390259\pi$
$593$	16.4603	0.675942	0.337971	+	0.941157i	$0.390259\pi$
$594$	−10.9551	−0.449493
$595$	3.61265	0.148104
$596$	9.80415	0.401593
$597$	10.5633	0.432328
$598$	3.05403	0.124888
$599$	44.8801	1.83375	0.916875	−	0.399174i	$-0.130703\pi$
$599$	44.8801	1.83375	0.916875	+	0.399174i	$0.130703\pi$
$600$	−5.69021	−0.232302
$601$	37.8537	1.54409	0.772043	−	0.635570i	$-0.219235\pi$
$601$	37.8537	1.54409	0.772043	+	0.635570i	$0.219235\pi$
$602$	14.3200	0.583638
$603$	−28.4854	−1.16002
$604$	−6.49394	−0.264235
$605$	17.0673	0.693884
$606$	−28.8290	−1.17110
$607$	−21.8292	−0.886018	−0.443009	−	0.896517i	$-0.646089\pi$
$607$	−21.8292	−0.886018	−0.443009	+	0.896517i	$0.646089\pi$
$608$	−18.8611	−0.764919
$609$	−76.4343	−3.09727
$610$	−4.25422	−0.172248
$611$	−21.6597	−0.876259
$612$	1.05889	0.0428033
$613$	10.1573	0.410251	0.205125	−	0.978736i	$-0.434240\pi$
$613$	10.1573	0.410251	0.205125	+	0.978736i	$0.434240\pi$
$614$	−38.1350	−1.53900
$615$	−14.1449	−0.570376
$616$	46.7300	1.88281
$617$	−17.8598	−0.719010	−0.359505	−	0.933143i	$-0.617054\pi$
$617$	−17.8598	−0.719010	−0.359505	+	0.933143i	$0.617054\pi$
$618$	10.8226	0.435348
$619$	7.57218	0.304351	0.152176	−	0.988353i	$-0.451372\pi$
$619$	7.57218	0.304351	0.152176	+	0.988353i	$0.451372\pi$
$620$	−4.52261	−0.181632
$621$	1.61815	0.0649343
$622$	−34.4402	−1.38093
$623$	45.5528	1.82503
$624$	−17.4827	−0.699870
$625$	1.00000	0.0400000
$626$	40.7440	1.62846
$627$	96.1272	3.83895
$628$	4.73330	0.188879
$629$	−2.05905	−0.0820995
$630$	−13.7084	−0.546155
$631$	16.1998	0.644905	0.322452	−	0.946586i	$-0.395493\pi$
$631$	16.1998	0.644905	0.322452	+	0.946586i	$0.395493\pi$
$632$	15.1727	0.603538
$633$	−6.79611	−0.270121
$634$	−23.1081	−0.917741
$635$	−5.20561	−0.206578
$636$	7.98047	0.316446
$637$	−9.69675	−0.384199
$638$	−75.0582	−2.97158
$639$	2.43146	0.0961869
$640$	−13.5564	−0.535865
$641$	−32.8510	−1.29754	−0.648768	−	0.760986i	$-0.724716\pi$
$641$	−32.8510	−1.29754	−0.648768	+	0.760986i	$0.724716\pi$
$642$	−56.9347	−2.24703
$643$	−1.74022	−0.0686275	−0.0343137	−	0.999411i	$-0.510925\pi$
$643$	−1.74022	−0.0686275	−0.0343137	+	0.999411i	$0.510925\pi$
$644$	1.92137	0.0757124
$645$	5.91944	0.233078
$646$	12.1502	0.478042
$647$	29.9988	1.17938	0.589688	−	0.807631i	$-0.299251\pi$
$647$	29.9988	1.17938	0.589688	+	0.807631i	$0.299251\pi$
$648$	−25.3494	−0.995818
$649$	57.6015	2.26106
$650$	2.50078	0.0980886
$651$	87.4352	3.42686
$652$	6.85435	0.268437
$653$	14.1406	0.553365	0.276682	−	0.960961i	$-0.410765\pi$
$653$	14.1406	0.553365	0.276682	+	0.960961i	$0.410765\pi$
$654$	66.9764	2.61899
$655$	0.183868	0.00718432
$656$	−28.4126	−1.10932
$657$	−2.53597	−0.0989378
$658$	−76.2064	−2.97084
$659$	10.0362	0.390957	0.195478	−	0.980708i	$-0.437374\pi$
$659$	10.0362	0.390957	0.195478	+	0.980708i	$0.437374\pi$
$660$	−5.37706	−0.209302
$661$	11.7904	0.458592	0.229296	−	0.973357i	$-0.426358\pi$
$661$	11.7904	0.458592	0.229296	+	0.973357i	$0.426358\pi$
$662$	25.5856	0.994413
$663$	3.73456	0.145038
$664$	30.4331	1.18103
$665$	−28.1264	−1.09069
$666$	7.81315	0.302754
$667$	11.0867	0.429278
$668$	−0.537910	−0.0208124
$669$	15.7782	0.610021
$670$	18.2831	0.706338
$671$	14.4420	0.557525
$672$	−20.3969	−0.786826
$673$	7.73039	0.297985	0.148992	−	0.988838i	$-0.452397\pi$
$673$	7.73039	0.297985	0.148992	+	0.988838i	$0.452397\pi$
$674$	43.4737	1.67455
$675$	1.32502	0.0510000
$676$	−4.54320	−0.174739
$677$	18.1037	0.695783	0.347892	−	0.937535i	$-0.386898\pi$
$677$	18.1037	0.695783	0.347892	+	0.937535i	$0.386898\pi$
$678$	−19.7449	−0.758298
$679$	1.30463	0.0500673
$680$	2.44157	0.0936301
$681$	−2.92813	−0.112206
$682$	85.8611	3.28779
$683$	37.4710	1.43379	0.716894	−	0.697182i	$-0.245563\pi$
$683$	37.4710	1.43379	0.716894	+	0.697182i	$0.245563\pi$
$684$	−8.24406	−0.315219
$685$	−14.3305	−0.547542
$686$	5.34901	0.204226
$687$	−39.1864	−1.49506
$688$	11.8903	0.453313
$689$	12.5998	0.480016
$690$	4.44170	0.169093
$691$	−11.7788	−0.448085	−0.224043	−	0.974579i	$-0.571925\pi$
$691$	−11.7788	−0.448085	−0.224043	+	0.974579i	$0.571925\pi$
$692$	−5.32208	−0.202315
$693$	46.5364	1.76777
$694$	12.7953	0.485702
$695$	14.3114	0.542861
$696$	−51.6574	−1.95807
$697$	6.06933	0.229892
$698$	−16.4154	−0.621331
$699$	18.8472	0.712868
$700$	1.57330	0.0594653
$701$	24.6046	0.929303	0.464651	−	0.885494i	$-0.346180\pi$
$701$	24.6046	0.929303	0.464651	+	0.885494i	$0.346180\pi$
$702$	3.31358	0.125063
$703$	16.0308	0.604612
$704$	29.5725	1.11455
$705$	−31.5014	−1.18641
$706$	36.6986	1.38117
$707$	−28.6354	−1.07695
$708$	−11.0352	−0.414727
$709$	27.2314	1.02270	0.511349	−	0.859373i	$-0.329146\pi$
$709$	27.2314	1.02270	0.511349	+	0.859373i	$0.329146\pi$
$710$	−1.56061	−0.0585686
$711$	15.1098	0.566663
$712$	30.7864	1.15377
$713$	−12.6824	−0.474958
$714$	13.1395	0.491733
$715$	−8.48949	−0.317489
$716$	3.62965	0.135646
$717$	10.1465	0.378928
$718$	−26.5331	−0.990207
$719$	−35.8940	−1.33862	−0.669311	−	0.742983i	$-0.733411\pi$
$719$	−35.8940	−1.33862	−0.669311	+	0.742983i	$0.733411\pi$
$720$	−11.3825	−0.424199
$721$	10.7499	0.400348
$722$	−64.9438	−2.41696
$723$	−21.8583	−0.812919
$724$	−8.38831	−0.311749
$725$	9.07829	0.337159
$726$	62.0750	2.30382
$727$	41.4488	1.53725	0.768626	−	0.639699i	$-0.220941\pi$
$727$	41.4488	1.53725	0.768626	+	0.639699i	$0.220941\pi$
$728$	−14.1344	−0.523856
$729$	−15.9803	−0.591861
$730$	1.62769	0.0602436
$731$	−2.53993	−0.0939428
$732$	−2.76675	−0.102262
$733$	−18.8721	−0.697057	−0.348529	−	0.937298i	$-0.613319\pi$
$733$	−18.8721	−0.697057	−0.348529	+	0.937298i	$0.613319\pi$
$734$	−2.28934	−0.0845009
$735$	−14.1027	−0.520187
$736$	2.95854	0.109053
$737$	−62.0664	−2.28624
$738$	−23.0304	−0.847760
$739$	0.257114	0.00945810	0.00472905	−	0.999989i	$-0.498495\pi$
$739$	0.257114	0.00945810	0.00472905	+	0.999989i	$0.498495\pi$
$740$	−0.896711	−0.0329638
$741$	−29.0755	−1.06812
$742$	44.3306	1.62743
$743$	9.12869	0.334899	0.167450	−	0.985881i	$-0.446447\pi$
$743$	9.12869	0.334899	0.167450	+	0.985881i	$0.446447\pi$
$744$	59.0922	2.16643
$745$	22.5125	0.824793
$746$	−47.5846	−1.74220
$747$	30.3070	1.10888
$748$	2.30721	0.0843599
$749$	−56.5523	−2.06638
$750$	3.63707	0.132807
$751$	−6.41936	−0.234246	−0.117123	−	0.993117i	$-0.537367\pi$
$751$	−6.41936	−0.234246	−0.117123	+	0.993117i	$0.537367\pi$
$752$	−63.2764	−2.30745
$753$	−19.8203	−0.722291
$754$	22.7028	0.826787
$755$	−14.9115	−0.542686
$756$	2.08466	0.0758183
$757$	−27.2565	−0.990654	−0.495327	−	0.868707i	$-0.664952\pi$
$757$	−27.2565	−0.990654	−0.495327	+	0.868707i	$0.664952\pi$
$758$	23.5648	0.855913
$759$	−15.0784	−0.547312
$760$	−19.0089	−0.689527
$761$	14.5717	0.528225	0.264112	−	0.964492i	$-0.414921\pi$
$761$	14.5717	0.528225	0.264112	+	0.964492i	$0.414921\pi$
$762$	−18.9332	−0.685877
$763$	66.5267	2.40843
$764$	0.833441	0.0301529
$765$	2.43146	0.0879095
$766$	−9.90078	−0.357730
$767$	−17.4227	−0.629097
$768$	−23.2877	−0.840321
$769$	6.71208	0.242044	0.121022	−	0.992650i	$-0.461383\pi$
$769$	6.71208	0.242044	0.121022	+	0.992650i	$0.461383\pi$
$770$	−29.8690	−1.07640
$771$	−35.5524	−1.28039
$772$	−2.06157	−0.0741975
$773$	39.5055	1.42091	0.710457	−	0.703740i	$-0.248488\pi$
$773$	39.5055	1.42091	0.710457	+	0.703740i	$0.248488\pi$
$774$	9.63790	0.346427
$775$	−10.3849	−0.373037
$776$	0.881724	0.0316521
$777$	17.3361	0.621927
$778$	14.5497	0.521631
$779$	−47.2529	−1.69301
$780$	1.62639	0.0582343
$781$	5.29786	0.189572
$782$	−1.90586	−0.0681535
$783$	12.0289	0.429879
$784$	−28.3279	−1.01171
$785$	10.8687	0.387920
$786$	0.668741	0.0238532
$787$	20.1519	0.718338	0.359169	−	0.933273i	$-0.383060\pi$
$787$	20.1519	0.718338	0.359169	+	0.933273i	$0.383060\pi$
$788$	5.76625	0.205414
$789$	41.2858	1.46981
$790$	−9.69810	−0.345043
$791$	−19.6123	−0.697333
$792$	31.4511	1.11757
$793$	−4.36825	−0.155121
$794$	−15.4471	−0.548195
$795$	18.3249	0.649917
$796$	−1.97392	−0.0699636
$797$	13.2264	0.468503	0.234252	−	0.972176i	$-0.424736\pi$
$797$	13.2264	0.468503	0.234252	+	0.972176i	$0.424736\pi$
$798$	−102.298	−3.62130
$799$	13.5167	0.478188
$800$	2.42259	0.0856514
$801$	30.6588	1.08328
$802$	−39.6752	−1.40098
$803$	−5.52559	−0.194994
$804$	11.8905	0.419346
$805$	4.41188	0.155498
$806$	−25.9703	−0.914766
$807$	72.9248	2.56707
$808$	−19.3530	−0.680835
$809$	−15.8824	−0.558395	−0.279197	−	0.960234i	$-0.590068\pi$
$809$	−15.8824	−0.558395	−0.279197	+	0.960234i	$0.590068\pi$
$810$	16.2028	0.569310
$811$	36.8968	1.29562	0.647811	−	0.761801i	$-0.275685\pi$
$811$	36.8968	1.29562	0.647811	+	0.761801i	$0.275685\pi$
$812$	14.2829	0.501232
$813$	−28.0731	−0.984567
$814$	17.0239	0.596689
$815$	15.7391	0.551317
$816$	10.9101	0.381929
$817$	19.7747	0.691830
$818$	−10.7662	−0.376431
$819$	−14.0758	−0.491849
$820$	2.64318	0.0923039
$821$	−6.63048	−0.231405	−0.115703	−	0.993284i	$-0.536912\pi$
$821$	−6.63048	−0.231405	−0.115703	+	0.993284i	$0.536912\pi$
$822$	−52.1212	−1.81794
$823$	−22.9170	−0.798837	−0.399419	−	0.916769i	$-0.630788\pi$
$823$	−22.9170	−0.798837	−0.399419	+	0.916769i	$0.630788\pi$
$824$	7.26522	0.253096
$825$	−12.3469	−0.429864
$826$	−61.2990	−2.13287
$827$	31.9512	1.11105	0.555526	−	0.831499i	$-0.312517\pi$
$827$	31.9512	1.11105	0.555526	+	0.831499i	$0.312517\pi$
$828$	1.29315	0.0449402
$829$	2.88019	0.100033	0.0500165	−	0.998748i	$-0.484073\pi$
$829$	2.88019	0.100033	0.0500165	+	0.998748i	$0.484073\pi$
$830$	−19.4523	−0.675199
$831$	−45.3230	−1.57224
$832$	−8.94476	−0.310104
$833$	6.05125	0.209663
$834$	52.0515	1.80240
$835$	−1.23516	−0.0427445
$836$	−17.9628	−0.621257
$837$	−13.7602	−0.475622
$838$	−46.0115	−1.58944
$839$	−47.4443	−1.63796	−0.818979	−	0.573824i	$-0.805459\pi$
$839$	−47.4443	−1.63796	−0.818979	+	0.573824i	$0.805459\pi$
$840$	−20.5567	−0.709275
$841$	53.4154	1.84191
$842$	46.8909	1.61597
$843$	−65.5321	−2.25704
$844$	1.26996	0.0437137
$845$	−10.4322	−0.358878
$846$	−51.2899	−1.76338
$847$	61.6581	2.11860
$848$	36.8090	1.26403
$849$	−29.3992	−1.00898
$850$	−1.56061	−0.0535284
$851$	−2.51457	−0.0861983
$852$	−1.01495	−0.0347716
$853$	−19.3514	−0.662579	−0.331289	−	0.943529i	$-0.607484\pi$
$853$	−19.3514	−0.662579	−0.331289	+	0.943529i	$0.607484\pi$
$854$	−15.3690	−0.525916
$855$	−18.9302	−0.647398
$856$	−38.2203	−1.30634
$857$	2.91005	0.0994055	0.0497027	−	0.998764i	$-0.484173\pi$
$857$	2.91005	0.0994055	0.0497027	+	0.998764i	$0.484173\pi$
$858$	−30.8769	−1.05412
$859$	−27.8815	−0.951304	−0.475652	−	0.879634i	$-0.657788\pi$
$859$	−27.8815	−0.951304	−0.475652	+	0.879634i	$0.657788\pi$
$860$	−1.10614	−0.0377189
$861$	−51.1005	−1.74150
$862$	−21.4486	−0.730544
$863$	55.9281	1.90381	0.951907	−	0.306387i	$-0.0991203\pi$
$863$	55.9281	1.90381	0.951907	+	0.306387i	$0.0991203\pi$
$864$	3.20998	0.109206
$865$	−12.2207	−0.415515
$866$	−11.1674	−0.379483
$867$	−2.33055	−0.0791496
$868$	−16.3386	−0.554568
$869$	32.9225	1.11682
$870$	33.0184	1.11943
$871$	18.7732	0.636104
$872$	44.9614	1.52259
$873$	0.878070	0.0297182
$874$	14.8381	0.501908
$875$	3.61265	0.122130
$876$	1.05858	0.0357661
$877$	−41.3227	−1.39537	−0.697684	−	0.716406i	$-0.745786\pi$
$877$	−41.3227	−1.39537	−0.697684	+	0.716406i	$0.745786\pi$
$878$	63.3388	2.13758
$879$	42.0037	1.41675
$880$	−24.8011	−0.836043
$881$	24.4881	0.825024	0.412512	−	0.910952i	$-0.364652\pi$
$881$	24.4881	0.825024	0.412512	+	0.910952i	$0.364652\pi$
$882$	−22.9618	−0.773163
$883$	−45.2344	−1.52226	−0.761129	−	0.648600i	$-0.775355\pi$
$883$	−45.2344	−1.52226	−0.761129	+	0.648600i	$0.775355\pi$
$884$	−0.697859	−0.0234715
$885$	−25.3391	−0.851766
$886$	14.7955	0.497063
$887$	23.6984	0.795713	0.397856	−	0.917448i	$-0.369754\pi$
$887$	23.6984	0.795713	0.397856	+	0.917448i	$0.369754\pi$
$888$	11.7164	0.393177
$889$	−18.8061	−0.630735
$890$	−19.6781	−0.659611
$891$	−55.0044	−1.84272
$892$	−2.94840	−0.0987197
$893$	−105.235	−3.52155
$894$	81.8795	2.73846
$895$	8.33447	0.278590
$896$	−48.9747	−1.63613
$897$	4.56076	0.152279
$898$	−36.6367	−1.22258
$899$	−94.2772	−3.14432
$900$	1.05889	0.0352965
$901$	−7.86292	−0.261952
$902$	−50.1805	−1.67083
$903$	21.3849	0.711643
$904$	−13.2548	−0.440847
$905$	−19.2614	−0.640271
$906$	−54.2343	−1.80181
$907$	−33.3510	−1.10740	−0.553701	−	0.832716i	$-0.686785\pi$
$907$	−33.3510	−1.10740	−0.553701	+	0.832716i	$0.686785\pi$
$908$	0.547165	0.0181583
$909$	−19.2728	−0.639238
$910$	9.03444	0.299489
$911$	18.7661	0.621749	0.310875	−	0.950451i	$-0.399378\pi$
$911$	18.7661	0.621749	0.310875	+	0.950451i	$0.399378\pi$
$912$	−84.9408	−2.81267
$913$	66.0354	2.18545
$914$	−15.8237	−0.523402
$915$	−6.35307	−0.210026
$916$	7.32258	0.241945
$917$	0.664251	0.0219355
$918$	−2.06784	−0.0682488
$919$	−47.5212	−1.56758	−0.783790	−	0.621025i	$-0.786716\pi$
$919$	−47.5212	−1.56758	−0.783790	+	0.621025i	$0.786716\pi$
$920$	2.98172	0.0983045
$921$	−56.9493	−1.87654
$922$	−39.5422	−1.30225
$923$	−1.60244	−0.0527449
$924$	−19.4254	−0.639050
$925$	−2.05905	−0.0677010
$926$	45.1368	1.48329
$927$	7.23511	0.237632
$928$	21.9930	0.721954
$929$	32.2598	1.05841	0.529205	−	0.848494i	$-0.322490\pi$
$929$	32.2598	1.05841	0.529205	+	0.848494i	$0.322490\pi$
$930$	−37.7706	−1.23855
$931$	−47.1121	−1.54404
$932$	−3.52189	−0.115363
$933$	−51.4317	−1.68380
$934$	−59.1177	−1.93439
$935$	5.29786	0.173258
$936$	−9.51300	−0.310942
$937$	6.93588	0.226585	0.113293	−	0.993562i	$-0.463860\pi$
$937$	6.93588	0.226585	0.113293	+	0.993562i	$0.463860\pi$
$938$	66.0505	2.15663
$939$	60.8455	1.98562
$940$	5.88652	0.191997
$941$	23.6751	0.771787	0.385893	−	0.922543i	$-0.373893\pi$
$941$	23.6751	0.771787	0.385893	+	0.922543i	$0.373893\pi$
$942$	39.5302	1.28796
$943$	7.41205	0.241370
$944$	−50.8984	−1.65660
$945$	4.78683	0.155716
$946$	20.9999	0.682764
$947$	40.2014	1.30637	0.653185	−	0.757198i	$-0.273432\pi$
$947$	40.2014	1.30637	0.653185	+	0.757198i	$0.273432\pi$
$948$	−6.30721	−0.204849
$949$	1.67132	0.0542534
$950$	12.1502	0.394203
$951$	−34.5087	−1.11902
$952$	8.82056	0.285876
$953$	20.4128	0.661234	0.330617	−	0.943765i	$-0.392743\pi$
$953$	20.4128	0.661234	0.330617	+	0.943765i	$0.392743\pi$
$954$	29.8362	0.965984
$955$	1.91376	0.0619280
$956$	−1.89603	−0.0613219
$957$	−112.089	−3.62332
$958$	1.06121	0.0342861
$959$	−51.7712	−1.67178
$960$	−13.0090	−0.419865
$961$	76.8461	2.47891
$962$	−5.14922	−0.166017
$963$	−38.0619	−1.22653
$964$	4.08456	0.131555
$965$	−4.73382	−0.152387
$966$	16.0463	0.516282
$967$	−45.9269	−1.47691	−0.738454	−	0.674303i	$-0.764444\pi$
$967$	−45.9269	−1.47691	−0.738454	+	0.674303i	$0.764444\pi$
$968$	41.6710	1.33936
$969$	18.1445	0.582887
$970$	−0.563581	−0.0180955
$971$	−41.3456	−1.32684	−0.663422	−	0.748246i	$-0.730897\pi$
$971$	−41.3456	−1.32684	−0.663422	+	0.748246i	$0.730897\pi$
$972$	8.80647	0.282468
$973$	51.7020	1.65749
$974$	61.4756	1.96981
$975$	3.73456	0.119602
$976$	−12.7613	−0.408480
$977$	−14.1193	−0.451717	−0.225858	−	0.974160i	$-0.572519\pi$
$977$	−14.1193	−0.451717	−0.225858	+	0.974160i	$0.572519\pi$
$978$	57.2442	1.83047
$979$	66.8019	2.13500
$980$	2.63531	0.0841818
$981$	44.7751	1.42956
$982$	47.8203	1.52601
$983$	36.0844	1.15091	0.575457	−	0.817832i	$-0.304824\pi$
$983$	36.0844	1.15091	0.575457	+	0.817832i	$0.304824\pi$
$984$	−34.5357	−1.10096
$985$	13.2406	0.421880
$986$	−14.1677	−0.451190
$987$	−113.804	−3.62241
$988$	5.43320	0.172853
$989$	−3.10184	−0.0986329
$990$	−20.1030	−0.638915
$991$	−29.2146	−0.928031	−0.464015	−	0.885827i	$-0.653592\pi$
$991$	−29.2146	−0.928031	−0.464015	+	0.885827i	$0.653592\pi$
$992$	−25.1583	−0.798777
$993$	38.2085	1.21251
$994$	−5.63793	−0.178824
$995$	−4.53255	−0.143691
$996$	−12.6509	−0.400859
$997$	27.7046	0.877413	0.438706	−	0.898631i	$-0.355437\pi$
$997$	27.7046	0.877413	0.438706	+	0.898631i	$0.355437\pi$
$998$	51.0570	1.61618
$999$	−2.72828	−0.0863189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.g.1.15	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.g.1.15	✓	58	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.56061 q^{2} -2.33055 q^{3} +0.435498 q^{4} +1.00000 q^{5} +3.63707 q^{6} +3.61265 q^{7} +2.44157 q^{8} +2.43146 q^{9} +O(q^{10})\)	\(q-1.56061 q^{2} -2.33055 q^{3} +0.435498 q^{4} +1.00000 q^{5} +3.63707 q^{6} +3.61265 q^{7} +2.44157 q^{8} +2.43146 q^{9} -1.56061 q^{10} +5.29786 q^{11} -1.01495 q^{12} -1.60244 q^{13} -5.63793 q^{14} -2.33055 q^{15} -4.68134 q^{16} +1.00000 q^{17} -3.79455 q^{18} -7.78553 q^{19} +0.435498 q^{20} -8.41946 q^{21} -8.26788 q^{22} +1.22123 q^{23} -5.69021 q^{24} +1.00000 q^{25} +2.50078 q^{26} +1.32502 q^{27} +1.57330 q^{28} +9.07829 q^{29} +3.63707 q^{30} -10.3849 q^{31} +2.42259 q^{32} -12.3469 q^{33} -1.56061 q^{34} +3.61265 q^{35} +1.05889 q^{36} -2.05905 q^{37} +12.1502 q^{38} +3.73456 q^{39} +2.44157 q^{40} +6.06933 q^{41} +13.1395 q^{42} -2.53993 q^{43} +2.30721 q^{44} +2.43146 q^{45} -1.90586 q^{46} +13.5167 q^{47} +10.9101 q^{48} +6.05125 q^{49} -1.56061 q^{50} -2.33055 q^{51} -0.697859 q^{52} -7.86292 q^{53} -2.06784 q^{54} +5.29786 q^{55} +8.82056 q^{56} +18.1445 q^{57} -14.1677 q^{58} +10.8726 q^{59} -1.01495 q^{60} +2.72600 q^{61} +16.2068 q^{62} +8.78400 q^{63} +5.58197 q^{64} -1.60244 q^{65} +19.2687 q^{66} -11.7154 q^{67} +0.435498 q^{68} -2.84614 q^{69} -5.63793 q^{70} +1.00000 q^{71} +5.93658 q^{72} -1.04299 q^{73} +3.21336 q^{74} -2.33055 q^{75} -3.39058 q^{76} +19.1393 q^{77} -5.82818 q^{78} +6.21431 q^{79} -4.68134 q^{80} -10.3824 q^{81} -9.47185 q^{82} +12.4646 q^{83} -3.66666 q^{84} +1.00000 q^{85} +3.96384 q^{86} -21.1574 q^{87} +12.9351 q^{88} +12.6092 q^{89} -3.79455 q^{90} -5.78905 q^{91} +0.531844 q^{92} +24.2025 q^{93} -21.0943 q^{94} -7.78553 q^{95} -5.64595 q^{96} +0.361129 q^{97} -9.44363 q^{98} +12.8815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * q^99

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