LMFDB - Embedded newform 8015.2.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26027 q^{2} +2.68549 q^{3} +3.10882 q^{4} +1.00000 q^{5} -6.06994 q^{6} -1.00000 q^{7} -2.50623 q^{8} +4.21188 q^{9} +O(q^{10})$	\(q-2.26027 q^{2} +2.68549 q^{3} +3.10882 q^{4} +1.00000 q^{5} -6.06994 q^{6} -1.00000 q^{7} -2.50623 q^{8} +4.21188 q^{9} -2.26027 q^{10} -4.01701 q^{11} +8.34871 q^{12} -3.92654 q^{13} +2.26027 q^{14} +2.68549 q^{15} -0.552885 q^{16} +0.783575 q^{17} -9.51998 q^{18} +4.35807 q^{19} +3.10882 q^{20} -2.68549 q^{21} +9.07952 q^{22} +5.35968 q^{23} -6.73046 q^{24} +1.00000 q^{25} +8.87504 q^{26} +3.25449 q^{27} -3.10882 q^{28} +0.420322 q^{29} -6.06994 q^{30} -3.30251 q^{31} +6.26213 q^{32} -10.7876 q^{33} -1.77109 q^{34} -1.00000 q^{35} +13.0940 q^{36} +3.98055 q^{37} -9.85041 q^{38} -10.5447 q^{39} -2.50623 q^{40} -5.55746 q^{41} +6.06994 q^{42} -9.62469 q^{43} -12.4881 q^{44} +4.21188 q^{45} -12.1143 q^{46} -3.60160 q^{47} -1.48477 q^{48} +1.00000 q^{49} -2.26027 q^{50} +2.10428 q^{51} -12.2069 q^{52} -6.21293 q^{53} -7.35603 q^{54} -4.01701 q^{55} +2.50623 q^{56} +11.7036 q^{57} -0.950041 q^{58} +1.38397 q^{59} +8.34871 q^{60} +5.60897 q^{61} +7.46455 q^{62} -4.21188 q^{63} -13.0483 q^{64} -3.92654 q^{65} +24.3830 q^{66} -11.6655 q^{67} +2.43599 q^{68} +14.3934 q^{69} +2.26027 q^{70} -7.98094 q^{71} -10.5559 q^{72} +8.23419 q^{73} -8.99711 q^{74} +2.68549 q^{75} +13.5484 q^{76} +4.01701 q^{77} +23.8339 q^{78} +9.36876 q^{79} -0.552885 q^{80} -3.89572 q^{81} +12.5614 q^{82} -6.12838 q^{83} -8.34871 q^{84} +0.783575 q^{85} +21.7544 q^{86} +1.12877 q^{87} +10.0675 q^{88} -14.0744 q^{89} -9.51998 q^{90} +3.92654 q^{91} +16.6623 q^{92} -8.86886 q^{93} +8.14058 q^{94} +4.35807 q^{95} +16.8169 q^{96} +4.45892 q^{97} -2.26027 q^{98} -16.9191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * 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 $

$2$	−2.26027	−1.59825	−0.799126	−	0.601164i	$-0.794704\pi$
$2$	−2.26027	−1.59825	−0.799126	+	0.601164i	$0.794704\pi$
$3$	2.68549	1.55047	0.775235	−	0.631673i	$-0.217631\pi$
$3$	2.68549	1.55047	0.775235	+	0.631673i	$0.217631\pi$
$4$	3.10882	1.55441
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.06994	−2.47804
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.50623	−0.886086
$9$	4.21188	1.40396
$10$	−2.26027	−0.714760
$11$	−4.01701	−1.21117	−0.605587	−	0.795779i	$-0.707061\pi$
$11$	−4.01701	−1.21117	−0.605587	+	0.795779i	$0.707061\pi$
$12$	8.34871	2.41007
$13$	−3.92654	−1.08903	−0.544513	−	0.838752i	$-0.683286\pi$
$13$	−3.92654	−1.08903	−0.544513	+	0.838752i	$0.683286\pi$
$14$	2.26027	0.604082
$15$	2.68549	0.693392
$16$	−0.552885	−0.138221
$17$	0.783575	0.190045	0.0950224	−	0.995475i	$-0.469708\pi$
$17$	0.783575	0.190045	0.0950224	+	0.995475i	$0.469708\pi$
$18$	−9.51998	−2.24388
$19$	4.35807	0.999809	0.499905	−	0.866080i	$-0.333368\pi$
$19$	4.35807	0.999809	0.499905	+	0.866080i	$0.333368\pi$
$20$	3.10882	0.695153
$21$	−2.68549	−0.586023
$22$	9.07952	1.93576
$23$	5.35968	1.11757	0.558786	−	0.829312i	$-0.311267\pi$
$23$	5.35968	1.11757	0.558786	+	0.829312i	$0.311267\pi$
$24$	−6.73046	−1.37385
$25$	1.00000	0.200000
$26$	8.87504	1.74054
$27$	3.25449	0.626327
$28$	−3.10882	−0.587511
$29$	0.420322	0.0780518	0.0390259	−	0.999238i	$-0.487575\pi$
$29$	0.420322	0.0780518	0.0390259	+	0.999238i	$0.487575\pi$
$30$	−6.06994	−1.10821
$31$	−3.30251	−0.593148	−0.296574	−	0.955010i	$-0.595844\pi$
$31$	−3.30251	−0.593148	−0.296574	+	0.955010i	$0.595844\pi$
$32$	6.26213	1.10700
$33$	−10.7876	−1.87789
$34$	−1.77109	−0.303739
$35$	−1.00000	−0.169031
$36$	13.0940	2.18233
$37$	3.98055	0.654398	0.327199	−	0.944955i	$-0.393895\pi$
$37$	3.98055	0.654398	0.327199	+	0.944955i	$0.393895\pi$
$38$	−9.85041	−1.59795
$39$	−10.5447	−1.68850
$40$	−2.50623	−0.396270
$41$	−5.55746	−0.867930	−0.433965	−	0.900930i	$-0.642886\pi$
$41$	−5.55746	−0.867930	−0.433965	+	0.900930i	$0.642886\pi$
$42$	6.06994	0.936612
$43$	−9.62469	−1.46775	−0.733876	−	0.679284i	$-0.762290\pi$
$43$	−9.62469	−1.46775	−0.733876	+	0.679284i	$0.762290\pi$
$44$	−12.4881	−1.88266
$45$	4.21188	0.627870
$46$	−12.1143	−1.78616
$47$	−3.60160	−0.525347	−0.262673	−	0.964885i	$-0.584604\pi$
$47$	−3.60160	−0.525347	−0.262673	+	0.964885i	$0.584604\pi$
$48$	−1.48477	−0.214308
$49$	1.00000	0.142857
$50$	−2.26027	−0.319650
$51$	2.10428	0.294659
$52$	−12.2069	−1.69279
$53$	−6.21293	−0.853411	−0.426706	−	0.904391i	$-0.640326\pi$
$53$	−6.21293	−0.853411	−0.426706	+	0.904391i	$0.640326\pi$
$54$	−7.35603	−1.00103
$55$	−4.01701	−0.541653
$56$	2.50623	0.334909
$57$	11.7036	1.55018
$58$	−0.950041	−0.124746
$59$	1.38397	0.180178	0.0900889	−	0.995934i	$-0.471285\pi$
$59$	1.38397	0.180178	0.0900889	+	0.995934i	$0.471285\pi$
$60$	8.34871	1.07781
$61$	5.60897	0.718154	0.359077	−	0.933308i	$-0.383091\pi$
$61$	5.60897	0.718154	0.359077	+	0.933308i	$0.383091\pi$
$62$	7.46455	0.947999
$63$	−4.21188	−0.530647
$64$	−13.0483	−1.63104
$65$	−3.92654	−0.487027
$66$	24.3830	3.00134
$67$	−11.6655	−1.42516	−0.712582	−	0.701589i	$-0.752474\pi$
$67$	−11.6655	−1.42516	−0.712582	+	0.701589i	$0.752474\pi$
$68$	2.43599	0.295407
$69$	14.3934	1.73276
$70$	2.26027	0.270154
$71$	−7.98094	−0.947163	−0.473582	−	0.880750i	$-0.657039\pi$
$71$	−7.98094	−0.947163	−0.473582	+	0.880750i	$0.657039\pi$
$72$	−10.5559	−1.24403
$73$	8.23419	0.963739	0.481869	−	0.876243i	$-0.339958\pi$
$73$	8.23419	0.963739	0.481869	+	0.876243i	$0.339958\pi$
$74$	−8.99711	−1.04589
$75$	2.68549	0.310094
$76$	13.5484	1.55411
$77$	4.01701	0.457780
$78$	23.8339	2.69865
$79$	9.36876	1.05407	0.527034	−	0.849844i	$-0.323304\pi$
$79$	9.36876	1.05407	0.527034	+	0.849844i	$0.323304\pi$
$80$	−0.552885	−0.0618144
$81$	−3.89572	−0.432858
$82$	12.5614	1.38717
$83$	−6.12838	−0.672677	−0.336339	−	0.941741i	$-0.609189\pi$
$83$	−6.12838	−0.672677	−0.336339	+	0.941741i	$0.609189\pi$
$84$	−8.34871	−0.910919
$85$	0.783575	0.0849906
$86$	21.7544	2.34584
$87$	1.12877	0.121017
$88$	10.0675	1.07320
$89$	−14.0744	−1.49188	−0.745940	−	0.666013i	$-0.767999\pi$
$89$	−14.0744	−1.49188	−0.745940	+	0.666013i	$0.767999\pi$
$90$	−9.51998	−1.00349
$91$	3.92654	0.411613
$92$	16.6623	1.73716
$93$	−8.86886	−0.919658
$94$	8.14058	0.839637
$95$	4.35807	0.447128
$96$	16.8169	1.71637
$97$	4.45892	0.452735	0.226368	−	0.974042i	$-0.427315\pi$
$97$	4.45892	0.452735	0.226368	+	0.974042i	$0.427315\pi$
$98$	−2.26027	−0.228322
$99$	−16.9191	−1.70044
$100$	3.10882	0.310882
$101$	5.22163	0.519572	0.259786	−	0.965666i	$-0.416348\pi$
$101$	5.22163	0.519572	0.259786	+	0.965666i	$0.416348\pi$
$102$	−4.75625	−0.470939
$103$	−8.15389	−0.803426	−0.401713	−	0.915766i	$-0.631585\pi$
$103$	−8.15389	−0.803426	−0.401713	+	0.915766i	$0.631585\pi$
$104$	9.84081	0.964970
$105$	−2.68549	−0.262077
$106$	14.0429	1.36397
$107$	7.51255	0.726266	0.363133	−	0.931737i	$-0.381707\pi$
$107$	7.51255	0.726266	0.363133	+	0.931737i	$0.381707\pi$
$108$	10.1176	0.973568
$109$	−8.18571	−0.784049	−0.392025	−	0.919955i	$-0.628225\pi$
$109$	−8.18571	−0.784049	−0.392025	+	0.919955i	$0.628225\pi$
$110$	9.07952	0.865698
$111$	10.6897	1.01462
$112$	0.552885	0.0522427
$113$	4.35144	0.409349	0.204675	−	0.978830i	$-0.434386\pi$
$113$	4.35144	0.409349	0.204675	+	0.978830i	$0.434386\pi$
$114$	−26.4532	−2.47757
$115$	5.35968	0.499793
$116$	1.30670	0.121324
$117$	−16.5381	−1.52895
$118$	−3.12815	−0.287970
$119$	−0.783575	−0.0718302
$120$	−6.73046	−0.614404
$121$	5.13635	0.466940
$122$	−12.6778	−1.14779
$123$	−14.9245	−1.34570
$124$	−10.2669	−0.921994
$125$	1.00000	0.0894427
$126$	9.51998	0.848107
$127$	11.9367	1.05921	0.529607	−	0.848243i	$-0.322339\pi$
$127$	11.9367	1.05921	0.529607	+	0.848243i	$0.322339\pi$
$128$	16.9685	1.49982
$129$	−25.8470	−2.27571
$130$	8.87504	0.778392
$131$	2.16050	0.188764	0.0943818	−	0.995536i	$-0.469913\pi$
$131$	2.16050	0.188764	0.0943818	+	0.995536i	$0.469913\pi$
$132$	−33.5368	−2.91901
$133$	−4.35807	−0.377892
$134$	26.3671	2.27777
$135$	3.25449	0.280102
$136$	−1.96382	−0.168396
$137$	−16.3714	−1.39871	−0.699353	−	0.714776i	$-0.746528\pi$
$137$	−16.3714	−1.39871	−0.699353	+	0.714776i	$0.746528\pi$
$138$	−32.5330	−2.76939
$139$	−0.0524197	−0.00444618	−0.00222309	−	0.999998i	$-0.500708\pi$
$139$	−0.0524197	−0.00444618	−0.00222309	+	0.999998i	$0.500708\pi$
$140$	−3.10882	−0.262743
$141$	−9.67207	−0.814535
$142$	18.0391	1.51381
$143$	15.7729	1.31900
$144$	−2.32868	−0.194057
$145$	0.420322	0.0349058
$146$	−18.6115	−1.54030
$147$	2.68549	0.221496
$148$	12.3748	1.01720
$149$	−12.0693	−0.988757	−0.494379	−	0.869247i	$-0.664604\pi$
$149$	−12.0693	−0.988757	−0.494379	+	0.869247i	$0.664604\pi$
$150$	−6.06994	−0.495609
$151$	5.20223	0.423351	0.211676	−	0.977340i	$-0.432108\pi$
$151$	5.20223	0.423351	0.211676	+	0.977340i	$0.432108\pi$
$152$	−10.9223	−0.885917
$153$	3.30032	0.266815
$154$	−9.07952	−0.731648
$155$	−3.30251	−0.265264
$156$	−32.7816	−2.62462
$157$	−17.8568	−1.42513	−0.712563	−	0.701608i	$-0.752466\pi$
$157$	−17.8568	−1.42513	−0.712563	+	0.701608i	$0.752466\pi$
$158$	−21.1759	−1.68467
$159$	−16.6848	−1.32319
$160$	6.26213	0.495065
$161$	−5.35968	−0.422402
$162$	8.80537	0.691816
$163$	−2.26610	−0.177494	−0.0887472	−	0.996054i	$-0.528286\pi$
$163$	−2.26610	−0.177494	−0.0887472	+	0.996054i	$0.528286\pi$
$164$	−17.2771	−1.34912
$165$	−10.7876	−0.839817
$166$	13.8518	1.07511
$167$	14.5885	1.12889	0.564445	−	0.825471i	$-0.309090\pi$
$167$	14.5885	1.12889	0.564445	+	0.825471i	$0.309090\pi$
$168$	6.73046	0.519266
$169$	2.41771	0.185978
$170$	−1.77109	−0.135836
$171$	18.3557	1.40369
$172$	−29.9214	−2.28149
$173$	−7.71858	−0.586833	−0.293416	−	0.955985i	$-0.594792\pi$
$173$	−7.71858	−0.586833	−0.293416	+	0.955985i	$0.594792\pi$
$174$	−2.55133	−0.193416
$175$	−1.00000	−0.0755929
$176$	2.22094	0.167410
$177$	3.71665	0.279360
$178$	31.8119	2.38440
$179$	21.2291	1.58674	0.793369	−	0.608741i	$-0.208325\pi$
$179$	21.2291	1.58674	0.793369	+	0.608741i	$0.208325\pi$
$180$	13.0940	0.975966
$181$	−6.16803	−0.458466	−0.229233	−	0.973372i	$-0.573622\pi$
$181$	−6.16803	−0.458466	−0.229233	+	0.973372i	$0.573622\pi$
$182$	−8.87504	−0.657862
$183$	15.0628	1.11348
$184$	−13.4326	−0.990264
$185$	3.98055	0.292656
$186$	20.0460	1.46985
$187$	−3.14762	−0.230177
$188$	−11.1967	−0.816604
$189$	−3.25449	−0.236729
$190$	−9.85041	−0.714624
$191$	−13.9291	−1.00788	−0.503938	−	0.863740i	$-0.668116\pi$
$191$	−13.9291	−1.00788	−0.503938	+	0.863740i	$0.668116\pi$
$192$	−35.0412	−2.52888
$193$	−16.4152	−1.18159	−0.590797	−	0.806820i	$-0.701187\pi$
$193$	−16.4152	−1.18159	−0.590797	+	0.806820i	$0.701187\pi$
$194$	−10.0784	−0.723585
$195$	−10.5447	−0.755122
$196$	3.10882	0.222058
$197$	10.6128	0.756134	0.378067	−	0.925778i	$-0.376589\pi$
$197$	10.6128	0.756134	0.378067	+	0.925778i	$0.376589\pi$
$198$	38.2418	2.71773
$199$	−23.0594	−1.63464	−0.817320	−	0.576185i	$-0.804541\pi$
$199$	−23.0594	−1.63464	−0.817320	+	0.576185i	$0.804541\pi$
$200$	−2.50623	−0.177217
$201$	−31.3275	−2.20967
$202$	−11.8023	−0.830406
$203$	−0.420322	−0.0295008
$204$	6.54184	0.458020
$205$	−5.55746	−0.388150
$206$	18.4300	1.28408
$207$	22.5743	1.56902
$208$	2.17092	0.150527
$209$	−17.5064	−1.21094
$210$	6.06994	0.418866
$211$	6.54981	0.450908	0.225454	−	0.974254i	$-0.427614\pi$
$211$	6.54981	0.450908	0.225454	+	0.974254i	$0.427614\pi$
$212$	−19.3149	−1.32655
$213$	−21.4328	−1.46855
$214$	−16.9804	−1.16076
$215$	−9.62469	−0.656398
$216$	−8.15650	−0.554979
$217$	3.30251	0.224189
$218$	18.5019	1.25311
$219$	22.1129	1.49425
$220$	−12.4881	−0.841951
$221$	−3.07674	−0.206964
$222$	−24.1617	−1.62163
$223$	−10.1359	−0.678749	−0.339374	−	0.940651i	$-0.610215\pi$
$223$	−10.1359	−0.678749	−0.339374	+	0.940651i	$0.610215\pi$
$224$	−6.26213	−0.418406
$225$	4.21188	0.280792
$226$	−9.83543	−0.654243
$227$	15.5838	1.03433	0.517165	−	0.855886i	$-0.326987\pi$
$227$	15.5838	1.03433	0.517165	+	0.855886i	$0.326987\pi$
$228$	36.3843	2.40961
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−12.1143	−0.798795
$231$	10.7876	0.709775
$232$	−1.05342	−0.0691606
$233$	15.4652	1.01316	0.506581	−	0.862192i	$-0.330909\pi$
$233$	15.4652	1.01316	0.506581	+	0.862192i	$0.330909\pi$
$234$	37.3806	2.44364
$235$	−3.60160	−0.234942
$236$	4.30252	0.280070
$237$	25.1597	1.63430
$238$	1.77109	0.114803
$239$	−17.8054	−1.15174	−0.575869	−	0.817542i	$-0.695336\pi$
$239$	−17.8054	−1.15174	−0.575869	+	0.817542i	$0.695336\pi$
$240$	−1.48477	−0.0958414
$241$	−4.03384	−0.259842	−0.129921	−	0.991524i	$-0.541472\pi$
$241$	−4.03384	−0.259842	−0.129921	+	0.991524i	$0.541472\pi$
$242$	−11.6095	−0.746289
$243$	−20.2254	−1.29746
$244$	17.4373	1.11631
$245$	1.00000	0.0638877
$246$	33.7335	2.15077
$247$	−17.1121	−1.08882
$248$	8.27684	0.525580
$249$	−16.4577	−1.04297
$250$	−2.26027	−0.142952
$251$	−5.86197	−0.370004	−0.185002	−	0.982738i	$-0.559229\pi$
$251$	−5.86197	−0.370004	−0.185002	+	0.982738i	$0.559229\pi$
$252$	−13.0940	−0.824842
$253$	−21.5299	−1.35357
$254$	−26.9803	−1.69289
$255$	2.10428	0.131775
$256$	−12.2567	−0.766043
$257$	27.2256	1.69829	0.849144	−	0.528161i	$-0.177118\pi$
$257$	27.2256	1.69829	0.849144	+	0.528161i	$0.177118\pi$
$258$	58.4213	3.63715
$259$	−3.98055	−0.247339
$260$	−12.2069	−0.757040
$261$	1.77034	0.109582
$262$	−4.88331	−0.301692
$263$	−5.20255	−0.320803	−0.160402	−	0.987052i	$-0.551279\pi$
$263$	−5.20255	−0.320803	−0.160402	+	0.987052i	$0.551279\pi$
$264$	27.0363	1.66397
$265$	−6.21293	−0.381657
$266$	9.85041	0.603967
$267$	−37.7966	−2.31312
$268$	−36.2658	−2.21529
$269$	27.8485	1.69795	0.848976	−	0.528431i	$-0.177219\pi$
$269$	27.8485	1.69795	0.848976	+	0.528431i	$0.177219\pi$
$270$	−7.35603	−0.447673
$271$	−26.0266	−1.58100	−0.790501	−	0.612460i	$-0.790180\pi$
$271$	−26.0266	−1.58100	−0.790501	+	0.612460i	$0.790180\pi$
$272$	−0.433227	−0.0262682
$273$	10.5447	0.638194
$274$	37.0039	2.23548
$275$	−4.01701	−0.242235
$276$	44.7465	2.69342
$277$	−23.5463	−1.41476	−0.707379	−	0.706834i	$-0.750123\pi$
$277$	−23.5463	−1.41476	−0.707379	+	0.706834i	$0.750123\pi$
$278$	0.118483	0.00710611
$279$	−13.9098	−0.832755
$280$	2.50623	0.149776
$281$	8.18227	0.488113	0.244057	−	0.969761i	$-0.421522\pi$
$281$	8.18227	0.488113	0.244057	+	0.969761i	$0.421522\pi$
$282$	21.8615	1.30183
$283$	19.5497	1.16211	0.581055	−	0.813865i	$-0.302640\pi$
$283$	19.5497	1.16211	0.581055	+	0.813865i	$0.302640\pi$
$284$	−24.8113	−1.47228
$285$	11.7036	0.693259
$286$	−35.6511	−2.10809
$287$	5.55746	0.328047
$288$	26.3753	1.55418
$289$	−16.3860	−0.963883
$290$	−0.950041	−0.0557883
$291$	11.9744	0.701952
$292$	25.5986	1.49804
$293$	3.49094	0.203943	0.101971	−	0.994787i	$-0.467485\pi$
$293$	3.49094	0.203943	0.101971	+	0.994787i	$0.467485\pi$
$294$	−6.06994	−0.354006
$295$	1.38397	0.0805780
$296$	−9.97616	−0.579853
$297$	−13.0733	−0.758590
$298$	27.2799	1.58028
$299$	−21.0450	−1.21706
$300$	8.34871	0.482013
$301$	9.62469	0.554758
$302$	−11.7584	−0.676622
$303$	14.0227	0.805581
$304$	−2.40951	−0.138195
$305$	5.60897	0.321168
$306$	−7.45961	−0.426438
$307$	−25.6441	−1.46359	−0.731793	−	0.681527i	$-0.761316\pi$
$307$	−25.6441	−1.46359	−0.731793	+	0.681527i	$0.761316\pi$
$308$	12.4881	0.711578
$309$	−21.8972	−1.24569
$310$	7.46455	0.423958
$311$	−31.5865	−1.79111	−0.895553	−	0.444956i	$-0.853219\pi$
$311$	−31.5865	−1.79111	−0.895553	+	0.444956i	$0.853219\pi$
$312$	26.4274	1.49616
$313$	3.12003	0.176354	0.0881771	−	0.996105i	$-0.471896\pi$
$313$	3.12003	0.176354	0.0881771	+	0.996105i	$0.471896\pi$
$314$	40.3611	2.27771
$315$	−4.21188	−0.237312
$316$	29.1258	1.63845
$317$	−35.3159	−1.98354	−0.991770	−	0.128031i	$-0.959134\pi$
$317$	−35.3159	−1.98354	−0.991770	+	0.128031i	$0.959134\pi$
$318$	37.7121	2.11479
$319$	−1.68844	−0.0945343
$320$	−13.0483	−0.729423
$321$	20.1749	1.12605
$322$	12.1143	0.675105
$323$	3.41487	0.190009
$324$	−12.1111	−0.672838
$325$	−3.92654	−0.217805
$326$	5.12199	0.283681
$327$	−21.9827	−1.21564
$328$	13.9283	0.769060
$329$	3.60160	0.198562
$330$	24.3830	1.34224
$331$	−13.4697	−0.740364	−0.370182	−	0.928959i	$-0.620705\pi$
$331$	−13.4697	−0.740364	−0.370182	+	0.928959i	$0.620705\pi$
$332$	−19.0520	−1.04562
$333$	16.7656	0.918748
$334$	−32.9739	−1.80425
$335$	−11.6655	−0.637353
$336$	1.48477	0.0810008
$337$	−19.0841	−1.03958	−0.519788	−	0.854295i	$-0.673989\pi$
$337$	−19.0841	−1.03958	−0.519788	+	0.854295i	$0.673989\pi$
$338$	−5.46468	−0.297240
$339$	11.6858	0.634684
$340$	2.43599	0.132110
$341$	13.2662	0.718405
$342$	−41.4887	−2.24345
$343$	−1.00000	−0.0539949
$344$	24.1217	1.30055
$345$	14.3934	0.774915
$346$	17.4461	0.937906
$347$	4.70667	0.252667	0.126334	−	0.991988i	$-0.459679\pi$
$347$	4.70667	0.252667	0.126334	+	0.991988i	$0.459679\pi$
$348$	3.50915	0.188110
$349$	−23.2971	−1.24707	−0.623533	−	0.781797i	$-0.714303\pi$
$349$	−23.2971	−1.24707	−0.623533	+	0.781797i	$0.714303\pi$
$350$	2.26027	0.120816
$351$	−12.7789	−0.682086
$352$	−25.1550	−1.34077
$353$	11.2597	0.599292	0.299646	−	0.954050i	$-0.403131\pi$
$353$	11.2597	0.599292	0.299646	+	0.954050i	$0.403131\pi$
$354$	−8.40063	−0.446488
$355$	−7.98094	−0.423584
$356$	−43.7547	−2.31899
$357$	−2.10428	−0.111371
$358$	−47.9835	−2.53601
$359$	16.8795	0.890865	0.445433	−	0.895316i	$-0.353050\pi$
$359$	16.8795	0.890865	0.445433	+	0.895316i	$0.353050\pi$
$360$	−10.5559	−0.556346
$361$	−0.00724108	−0.000381110 0
$362$	13.9414	0.732744
$363$	13.7936	0.723978
$364$	12.2069	0.639815
$365$	8.23419	0.430997
$366$	−34.0461	−1.77962
$367$	−13.0510	−0.681259	−0.340629	−	0.940198i	$-0.610640\pi$
$367$	−13.0510	−0.681259	−0.340629	+	0.940198i	$0.610640\pi$
$368$	−2.96329	−0.154472
$369$	−23.4074	−1.21854
$370$	−8.99711	−0.467737
$371$	6.21293	0.322559
$372$	−27.5717	−1.42952
$373$	−8.22658	−0.425956	−0.212978	−	0.977057i	$-0.568316\pi$
$373$	−8.22658	−0.425956	−0.212978	+	0.977057i	$0.568316\pi$
$374$	7.11448	0.367881
$375$	2.68549	0.138678
$376$	9.02642	0.465502
$377$	−1.65041	−0.0850005
$378$	7.35603	0.378353
$379$	−14.9967	−0.770329	−0.385164	−	0.922848i	$-0.625855\pi$
$379$	−14.9967	−0.770329	−0.385164	+	0.922848i	$0.625855\pi$
$380$	13.5484	0.695020
$381$	32.0561	1.64228
$382$	31.4836	1.61084
$383$	5.95662	0.304369	0.152185	−	0.988352i	$-0.451369\pi$
$383$	5.95662	0.304369	0.152185	+	0.988352i	$0.451369\pi$
$384$	45.5687	2.32542
$385$	4.01701	0.204726
$386$	37.1029	1.88849
$387$	−40.5380	−2.06066
$388$	13.8620	0.703736
$389$	9.33318	0.473211	0.236606	−	0.971606i	$-0.423965\pi$
$389$	9.33318	0.473211	0.236606	+	0.971606i	$0.423965\pi$
$390$	23.8339	1.20687
$391$	4.19971	0.212389
$392$	−2.50623	−0.126584
$393$	5.80200	0.292672
$394$	−23.9879	−1.20849
$395$	9.36876	0.471393
$396$	−52.5985	−2.64318
$397$	−23.0054	−1.15461	−0.577305	−	0.816529i	$-0.695896\pi$
$397$	−23.0054	−1.15461	−0.577305	+	0.816529i	$0.695896\pi$
$398$	52.1205	2.61257
$399$	−11.7036	−0.585911
$400$	−0.552885	−0.0276442
$401$	2.59903	0.129789	0.0648947	−	0.997892i	$-0.479329\pi$
$401$	2.59903	0.129789	0.0648947	+	0.997892i	$0.479329\pi$
$402$	70.8087	3.53162
$403$	12.9674	0.645953
$404$	16.2331	0.807627
$405$	−3.89572	−0.193580
$406$	0.950041	0.0471497
$407$	−15.9899	−0.792589
$408$	−5.27382	−0.261093
$409$	−6.26569	−0.309819	−0.154909	−	0.987929i	$-0.549509\pi$
$409$	−6.26569	−0.309819	−0.154909	+	0.987929i	$0.549509\pi$
$410$	12.5614	0.620362
$411$	−43.9654	−2.16865
$412$	−25.3490	−1.24885
$413$	−1.38397	−0.0681008
$414$	−51.0241	−2.50770
$415$	−6.12838	−0.300830
$416$	−24.5885	−1.20555
$417$	−0.140773	−0.00689367
$418$	39.5692	1.93539
$419$	−10.7933	−0.527288	−0.263644	−	0.964620i	$-0.584924\pi$
$419$	−10.7933	−0.527288	−0.263644	+	0.964620i	$0.584924\pi$
$420$	−8.34871	−0.407375
$421$	20.4635	0.997330	0.498665	−	0.866795i	$-0.333824\pi$
$421$	20.4635	0.997330	0.498665	+	0.866795i	$0.333824\pi$
$422$	−14.8043	−0.720664
$423$	−15.1695	−0.737566
$424$	15.5710	0.756195
$425$	0.783575	0.0380090
$426$	48.4438	2.34711
$427$	−5.60897	−0.271437
$428$	23.3552	1.12891
$429$	42.3581	2.04507
$430$	21.7544	1.04909
$431$	2.95172	0.142179	0.0710897	−	0.997470i	$-0.477352\pi$
$431$	2.95172	0.142179	0.0710897	+	0.997470i	$0.477352\pi$
$432$	−1.79936	−0.0865717
$433$	14.1747	0.681193	0.340596	−	0.940210i	$-0.389371\pi$
$433$	14.1747	0.681193	0.340596	+	0.940210i	$0.389371\pi$
$434$	−7.46455	−0.358310
$435$	1.12877	0.0541205
$436$	−25.4479	−1.21873
$437$	23.3579	1.11736
$438$	−49.9810	−2.38819
$439$	−5.18949	−0.247681	−0.123841	−	0.992302i	$-0.539521\pi$
$439$	−5.18949	−0.247681	−0.123841	+	0.992302i	$0.539521\pi$
$440$	10.0675	0.479951
$441$	4.21188	0.200566
$442$	6.95425	0.330780
$443$	−34.8938	−1.65786	−0.828928	−	0.559356i	$-0.811049\pi$
$443$	−34.8938	−1.65786	−0.828928	+	0.559356i	$0.811049\pi$
$444$	33.2324	1.57714
$445$	−14.0744	−0.667189
$446$	22.9098	1.08481
$447$	−32.4121	−1.53304
$448$	13.0483	0.616475
$449$	−23.6110	−1.11427	−0.557135	−	0.830422i	$-0.688100\pi$
$449$	−23.6110	−1.11427	−0.557135	+	0.830422i	$0.688100\pi$
$450$	−9.51998	−0.448776
$451$	22.3244	1.05121
$452$	13.5278	0.636296
$453$	13.9706	0.656394
$454$	−35.2235	−1.65312
$455$	3.92654	0.184079
$456$	−29.3318	−1.37359
$457$	25.9758	1.21510	0.607549	−	0.794282i	$-0.292153\pi$
$457$	25.9758	1.21510	0.607549	+	0.794282i	$0.292153\pi$
$458$	−2.26027	−0.105615
$459$	2.55014	0.119030
$460$	16.6623	0.776883
$461$	1.46273	0.0681262	0.0340631	−	0.999420i	$-0.489155\pi$
$461$	1.46273	0.0681262	0.0340631	+	0.999420i	$0.489155\pi$
$462$	−24.3830	−1.13440
$463$	15.2207	0.707365	0.353683	−	0.935366i	$-0.384929\pi$
$463$	15.2207	0.707365	0.353683	+	0.935366i	$0.384929\pi$
$464$	−0.232390	−0.0107884
$465$	−8.86886	−0.411284
$466$	−34.9556	−1.61929
$467$	18.7707	0.868605	0.434302	−	0.900767i	$-0.356995\pi$
$467$	18.7707	0.868605	0.434302	+	0.900767i	$0.356995\pi$
$468$	−51.4140	−2.37661
$469$	11.6655	0.538661
$470$	8.14058	0.375497
$471$	−47.9543	−2.20962
$472$	−3.46855	−0.159653
$473$	38.6624	1.77770
$474$	−56.8678	−2.61202
$475$	4.35807	0.199962
$476$	−2.43599	−0.111653
$477$	−26.1681	−1.19815
$478$	40.2451	1.84077
$479$	18.4807	0.844407	0.422203	−	0.906501i	$-0.361257\pi$
$479$	18.4807	0.844407	0.422203	+	0.906501i	$0.361257\pi$
$480$	16.8169	0.767583
$481$	−15.6298	−0.712656
$482$	9.11756	0.415294
$483$	−14.3934	−0.654922
$484$	15.9680	0.725817
$485$	4.45892	0.202469
$486$	45.7149	2.07367
$487$	12.5008	0.566466	0.283233	−	0.959051i	$-0.408593\pi$
$487$	12.5008	0.566466	0.283233	+	0.959051i	$0.408593\pi$
$488$	−14.0573	−0.636346
$489$	−6.08559	−0.275200
$490$	−2.26027	−0.102109
$491$	−25.5151	−1.15148	−0.575740	−	0.817633i	$-0.695286\pi$
$491$	−25.5151	−1.15148	−0.575740	+	0.817633i	$0.695286\pi$
$492$	−46.3977	−2.09177
$493$	0.329354	0.0148333
$494$	38.6780	1.74021
$495$	−16.9191	−0.760459
$496$	1.82591	0.0819856
$497$	7.98094	0.357994
$498$	37.1989	1.66692
$499$	35.7307	1.59953	0.799763	−	0.600316i	$-0.204959\pi$
$499$	35.7307	1.59953	0.799763	+	0.600316i	$0.204959\pi$
$500$	3.10882	0.139031
$501$	39.1773	1.75031
$502$	13.2496	0.591360
$503$	1.34647	0.0600359	0.0300180	−	0.999549i	$-0.490444\pi$
$503$	1.34647	0.0600359	0.0300180	+	0.999549i	$0.490444\pi$
$504$	10.5559	0.470198
$505$	5.22163	0.232360
$506$	48.6634	2.16335
$507$	6.49275	0.288353
$508$	37.1092	1.64645
$509$	−24.3580	−1.07965	−0.539825	−	0.841777i	$-0.681510\pi$
$509$	−24.3580	−1.07965	−0.539825	+	0.841777i	$0.681510\pi$
$510$	−4.75625	−0.210610
$511$	−8.23419	−0.364259
$512$	−6.23355	−0.275486
$513$	14.1833	0.626208
$514$	−61.5373	−2.71429
$515$	−8.15389	−0.359303
$516$	−80.3538	−3.53738
$517$	14.4676	0.636286
$518$	8.99711	0.395310
$519$	−20.7282	−0.909867
$520$	9.84081	0.431548
$521$	0.602173	0.0263817	0.0131908	−	0.999913i	$-0.495801\pi$
$521$	0.602173	0.0263817	0.0131908	+	0.999913i	$0.495801\pi$
$522$	−4.00146	−0.175139
$523$	2.19000	0.0957619	0.0478809	−	0.998853i	$-0.484753\pi$
$523$	2.19000	0.0957619	0.0478809	+	0.998853i	$0.484753\pi$
$524$	6.71659	0.293416
$525$	−2.68549	−0.117205
$526$	11.7592	0.512724
$527$	−2.58776	−0.112725
$528$	5.96433	0.259564
$529$	5.72622	0.248966
$530$	14.0429	0.609984
$531$	5.82912	0.252962
$532$	−13.5484	−0.587399
$533$	21.8216	0.945198
$534$	85.4306	3.69694
$535$	7.51255	0.324796
$536$	29.2363	1.26282
$537$	57.0106	2.46019
$538$	−62.9451	−2.71376
$539$	−4.01701	−0.173025
$540$	10.1176	0.435393
$541$	19.4721	0.837171	0.418586	−	0.908177i	$-0.362526\pi$
$541$	19.4721	0.837171	0.418586	+	0.908177i	$0.362526\pi$
$542$	58.8271	2.52684
$543$	−16.5642	−0.710838
$544$	4.90684	0.210379
$545$	−8.18571	−0.350637
$546$	−23.8339	−1.02000
$547$	13.2108	0.564852	0.282426	−	0.959289i	$-0.408861\pi$
$547$	13.2108	0.564852	0.282426	+	0.959289i	$0.408861\pi$
$548$	−50.8958	−2.17416
$549$	23.6243	1.00826
$550$	9.07952	0.387152
$551$	1.83179	0.0780369
$552$	−36.0731	−1.53538
$553$	−9.36876	−0.398400
$554$	53.2209	2.26114
$555$	10.6897	0.453754
$556$	−0.162963	−0.00691118
$557$	25.2330	1.06916	0.534578	−	0.845119i	$-0.320471\pi$
$557$	25.2330	1.06916	0.534578	+	0.845119i	$0.320471\pi$
$558$	31.4398	1.33095
$559$	37.7917	1.59842
$560$	0.552885	0.0233637
$561$	−8.45293	−0.356883
$562$	−18.4941	−0.780128
$563$	14.3244	0.603702	0.301851	−	0.953355i	$-0.402395\pi$
$563$	14.3244	0.603702	0.301851	+	0.953355i	$0.402395\pi$
$564$	−30.0687	−1.26612
$565$	4.35144	0.183067
$566$	−44.1876	−1.85734
$567$	3.89572	0.163605
$568$	20.0021	0.839268
$569$	17.4857	0.733040	0.366520	−	0.930410i	$-0.380549\pi$
$569$	17.4857	0.733040	0.366520	+	0.930410i	$0.380549\pi$
$570$	−26.4532	−1.10800
$571$	31.6774	1.32566	0.662829	−	0.748771i	$-0.269356\pi$
$571$	31.6774	1.32566	0.662829	+	0.748771i	$0.269356\pi$
$572$	49.0352	2.05026
$573$	−37.4066	−1.56268
$574$	−12.5614	−0.524301
$575$	5.35968	0.223514
$576$	−54.9579	−2.28991
$577$	−17.1514	−0.714023	−0.357012	−	0.934100i	$-0.616204\pi$
$577$	−17.1514	−0.714023	−0.357012	+	0.934100i	$0.616204\pi$
$578$	37.0368	1.54053
$579$	−44.0830	−1.83203
$580$	1.30670	0.0542580
$581$	6.12838	0.254248
$582$	−27.0654	−1.12190
$583$	24.9574	1.03363
$584$	−20.6367	−0.853955
$585$	−16.5381	−0.683766
$586$	−7.89046	−0.325952
$587$	22.4334	0.925924	0.462962	−	0.886378i	$-0.346787\pi$
$587$	22.4334	0.925924	0.462962	+	0.886378i	$0.346787\pi$
$588$	8.34871	0.344295
$589$	−14.3925	−0.593035
$590$	−3.12815	−0.128784
$591$	28.5007	1.17236
$592$	−2.20078	−0.0904517
$593$	15.9240	0.653921	0.326960	−	0.945038i	$-0.393976\pi$
$593$	15.9240	0.653921	0.326960	+	0.945038i	$0.393976\pi$
$594$	29.5492	1.21242
$595$	−0.783575	−0.0321234
$596$	−37.5213	−1.53693
$597$	−61.9259	−2.53446
$598$	47.5674	1.94518
$599$	32.6641	1.33462	0.667309	−	0.744781i	$-0.267446\pi$
$599$	32.6641	1.33462	0.667309	+	0.744781i	$0.267446\pi$
$600$	−6.73046	−0.274770
$601$	−45.9652	−1.87496	−0.937480	−	0.348038i	$-0.886848\pi$
$601$	−45.9652	−1.87496	−0.937480	+	0.348038i	$0.886848\pi$
$602$	−21.7544	−0.886643
$603$	−49.1335	−2.00087
$604$	16.1728	0.658061
$605$	5.13635	0.208822
$606$	−31.6950	−1.28752
$607$	11.2228	0.455518	0.227759	−	0.973717i	$-0.426860\pi$
$607$	11.2228	0.455518	0.227759	+	0.973717i	$0.426860\pi$
$608$	27.2908	1.10679
$609$	−1.12877	−0.0457402
$610$	−12.6778	−0.513308
$611$	14.1418	0.572117
$612$	10.2601	0.414740
$613$	−25.3027	−1.02197	−0.510984	−	0.859590i	$-0.670719\pi$
$613$	−25.3027	−1.02197	−0.510984	+	0.859590i	$0.670719\pi$
$614$	57.9626	2.33918
$615$	−14.9245	−0.601815
$616$	−10.0675	−0.405633
$617$	35.1899	1.41669	0.708347	−	0.705864i	$-0.249441\pi$
$617$	35.1899	1.41669	0.708347	+	0.705864i	$0.249441\pi$
$618$	49.4936	1.99093
$619$	−25.7696	−1.03577	−0.517884	−	0.855451i	$-0.673280\pi$
$619$	−25.7696	−1.03577	−0.517884	+	0.855451i	$0.673280\pi$
$620$	−10.2669	−0.412328
$621$	17.4430	0.699965
$622$	71.3940	2.86264
$623$	14.0744	0.563878
$624$	5.83001	0.233387
$625$	1.00000	0.0400000
$626$	−7.05210	−0.281859
$627$	−47.0133	−1.87753
$628$	−55.5135	−2.21523
$629$	3.11906	0.124365
$630$	9.51998	0.379285
$631$	11.7435	0.467501	0.233751	−	0.972297i	$-0.424900\pi$
$631$	11.7435	0.467501	0.233751	+	0.972297i	$0.424900\pi$
$632$	−23.4803	−0.933994
$633$	17.5895	0.699119
$634$	79.8235	3.17020
$635$	11.9367	0.473695
$636$	−51.8699	−2.05678
$637$	−3.92654	−0.155575
$638$	3.81632	0.151090
$639$	−33.6147	−1.32978
$640$	16.9685	0.670738
$641$	−18.0951	−0.714715	−0.357358	−	0.933968i	$-0.616322\pi$
$641$	−18.0951	−0.714715	−0.357358	+	0.933968i	$0.616322\pi$
$642$	−45.6007	−1.79972
$643$	−15.3032	−0.603499	−0.301749	−	0.953387i	$-0.597571\pi$
$643$	−15.3032	−0.603499	−0.301749	+	0.953387i	$0.597571\pi$
$644$	−16.6623	−0.656586
$645$	−25.8470	−1.01773
$646$	−7.71853	−0.303682
$647$	−21.5323	−0.846522	−0.423261	−	0.906008i	$-0.639115\pi$
$647$	−21.5323	−0.846522	−0.423261	+	0.906008i	$0.639115\pi$
$648$	9.76356	0.383549
$649$	−5.55943	−0.218227
$650$	8.87504	0.348108
$651$	8.86886	0.347598
$652$	−7.04488	−0.275899
$653$	−21.8937	−0.856768	−0.428384	−	0.903597i	$-0.640917\pi$
$653$	−21.8937	−0.856768	−0.428384	+	0.903597i	$0.640917\pi$
$654$	49.6868	1.94291
$655$	2.16050	0.0844176
$656$	3.07264	0.119966
$657$	34.6814	1.35305
$658$	−8.14058	−0.317353
$659$	−5.20675	−0.202826	−0.101413	−	0.994844i	$-0.532336\pi$
$659$	−5.20675	−0.202826	−0.101413	+	0.994844i	$0.532336\pi$
$660$	−33.5368	−1.30542
$661$	28.8509	1.12217	0.561084	−	0.827759i	$-0.310384\pi$
$661$	28.8509	1.12217	0.561084	+	0.827759i	$0.310384\pi$
$662$	30.4452	1.18329
$663$	−8.26256	−0.320891
$664$	15.3591	0.596050
$665$	−4.35807	−0.168999
$666$	−37.8947	−1.46839
$667$	2.25279	0.0872285
$668$	45.3529	1.75476
$669$	−27.2198	−1.05238
$670$	26.3671	1.01865
$671$	−22.5313	−0.869809
$672$	−16.8169	−0.648726
$673$	−23.1594	−0.892730	−0.446365	−	0.894851i	$-0.647282\pi$
$673$	−23.1594	−0.892730	−0.446365	+	0.894851i	$0.647282\pi$
$674$	43.1351	1.66150
$675$	3.25449	0.125265
$676$	7.51623	0.289086
$677$	11.1497	0.428516	0.214258	−	0.976777i	$-0.431267\pi$
$677$	11.1497	0.428516	0.214258	+	0.976777i	$0.431267\pi$
$678$	−26.4130	−1.01439
$679$	−4.45892	−0.171118
$680$	−1.96382	−0.0753089
$681$	41.8501	1.60370
$682$	−29.9852	−1.14819
$683$	2.69239	0.103021	0.0515106	−	0.998672i	$-0.483596\pi$
$683$	2.69239	0.103021	0.0515106	+	0.998672i	$0.483596\pi$
$684$	57.0644	2.18191
$685$	−16.3714	−0.625520
$686$	2.26027	0.0862975
$687$	2.68549	0.102458
$688$	5.32135	0.202874
$689$	24.3953	0.929387
$690$	−32.5330	−1.23851
$691$	−20.0300	−0.761977	−0.380989	−	0.924580i	$-0.624416\pi$
$691$	−20.0300	−0.761977	−0.380989	+	0.924580i	$0.624416\pi$
$692$	−23.9957	−0.912178
$693$	16.9191	0.642705
$694$	−10.6383	−0.403826
$695$	−0.0524197	−0.00198839
$696$	−2.82896	−0.107231
$697$	−4.35469	−0.164946
$698$	52.6578	1.99313
$699$	41.5318	1.57088
$700$	−3.10882	−0.117502
$701$	−30.0091	−1.13343	−0.566714	−	0.823915i	$-0.691785\pi$
$701$	−30.0091	−1.13343	−0.566714	+	0.823915i	$0.691785\pi$
$702$	28.8837	1.09015
$703$	17.3475	0.654273
$704$	52.4152	1.97547
$705$	−9.67207	−0.364271
$706$	−25.4499	−0.957820
$707$	−5.22163	−0.196380
$708$	11.5544	0.434240
$709$	−14.0856	−0.528995	−0.264497	−	0.964386i	$-0.585206\pi$
$709$	−14.0856	−0.528995	−0.264497	+	0.964386i	$0.585206\pi$
$710$	18.0391	0.676994
$711$	39.4601	1.47987
$712$	35.2736	1.32193
$713$	−17.7004	−0.662885
$714$	4.75625	0.177998
$715$	15.7729	0.589874
$716$	65.9974	2.46644
$717$	−47.8164	−1.78573
$718$	−38.1522	−1.42383
$719$	−14.6438	−0.546122	−0.273061	−	0.961997i	$-0.588036\pi$
$719$	−14.6438	−0.546122	−0.273061	+	0.961997i	$0.588036\pi$
$720$	−2.32868	−0.0867849
$721$	8.15389	0.303667
$722$	0.0163668	0.000609109 0
$723$	−10.8328	−0.402878
$724$	−19.1753	−0.712643
$725$	0.420322	0.0156104
$726$	−31.1773	−1.15710
$727$	−3.86159	−0.143218	−0.0716092	−	0.997433i	$-0.522813\pi$
$727$	−3.86159	−0.143218	−0.0716092	+	0.997433i	$0.522813\pi$
$728$	−9.84081	−0.364725
$729$	−42.6280	−1.57882
$730$	−18.6115	−0.688842
$731$	−7.54166	−0.278938
$732$	46.8276	1.73080
$733$	−0.843881	−0.0311695	−0.0155847	−	0.999879i	$-0.504961\pi$
$733$	−0.843881	−0.0311695	−0.0155847	+	0.999879i	$0.504961\pi$
$734$	29.4989	1.08882
$735$	2.68549	0.0990559
$736$	33.5630	1.23715
$737$	46.8603	1.72612
$738$	52.9069	1.94753
$739$	16.7430	0.615902	0.307951	−	0.951402i	$-0.400357\pi$
$739$	16.7430	0.615902	0.307951	+	0.951402i	$0.400357\pi$
$740$	12.3748	0.454907
$741$	−45.9545	−1.68818
$742$	−14.0429	−0.515531
$743$	43.2671	1.58732	0.793658	−	0.608364i	$-0.208174\pi$
$743$	43.2671	1.58732	0.793658	+	0.608364i	$0.208174\pi$
$744$	22.2274	0.814896
$745$	−12.0693	−0.442186
$746$	18.5943	0.680785
$747$	−25.8120	−0.944411
$748$	−9.78539	−0.357789
$749$	−7.51255	−0.274503
$750$	−6.06994	−0.221643
$751$	23.0952	0.842756	0.421378	−	0.906885i	$-0.361547\pi$
$751$	23.0952	0.842756	0.421378	+	0.906885i	$0.361547\pi$
$752$	1.99127	0.0726141
$753$	−15.7423	−0.573681
$754$	3.73037	0.135852
$755$	5.20223	0.189329
$756$	−10.1176	−0.367974
$757$	46.0148	1.67244	0.836218	−	0.548397i	$-0.184762\pi$
$757$	46.0148	1.67244	0.836218	+	0.548397i	$0.184762\pi$
$758$	33.8966	1.23118
$759$	−57.8184	−2.09867
$760$	−10.9223	−0.396194
$761$	−36.5677	−1.32558	−0.662789	−	0.748806i	$-0.730627\pi$
$761$	−36.5677	−1.32558	−0.662789	+	0.748806i	$0.730627\pi$
$762$	−72.4553	−2.62478
$763$	8.18571	0.296343
$764$	−43.3031	−1.56665
$765$	3.30032	0.119323
$766$	−13.4636	−0.486459
$767$	−5.43422	−0.196218
$768$	−32.9152	−1.18773
$769$	−18.2031	−0.656421	−0.328210	−	0.944605i	$-0.606445\pi$
$769$	−18.2031	−0.656421	−0.328210	+	0.944605i	$0.606445\pi$
$770$	−9.07952	−0.327203
$771$	73.1143	2.63315
$772$	−51.0320	−1.83668
$773$	53.3680	1.91951	0.959756	−	0.280835i	$-0.0906114\pi$
$773$	53.3680	1.91951	0.959756	+	0.280835i	$0.0906114\pi$
$774$	91.6268	3.29346
$775$	−3.30251	−0.118630
$776$	−11.1751	−0.401162
$777$	−10.6897	−0.383492
$778$	−21.0955	−0.756311
$779$	−24.2198	−0.867764
$780$	−32.7816	−1.17377
$781$	32.0595	1.14718
$782$	−9.49248	−0.339450
$783$	1.36793	0.0488860
$784$	−0.552885	−0.0197459
$785$	−17.8568	−0.637336
$786$	−13.1141	−0.467764
$787$	−6.28335	−0.223977	−0.111989	−	0.993709i	$-0.535722\pi$
$787$	−6.28335	−0.223977	−0.111989	+	0.993709i	$0.535722\pi$
$788$	32.9934	1.17534
$789$	−13.9714	−0.497396
$790$	−21.1759	−0.753405
$791$	−4.35144	−0.154720
$792$	42.4032	1.50673
$793$	−22.0238	−0.782089
$794$	51.9985	1.84536
$795$	−16.6848	−0.591748
$796$	−71.6876	−2.54090
$797$	−25.7280	−0.911333	−0.455667	−	0.890150i	$-0.650599\pi$
$797$	−25.7280	−0.911333	−0.455667	+	0.890150i	$0.650599\pi$
$798$	26.4532	0.936434
$799$	−2.82212	−0.0998394
$800$	6.26213	0.221400
$801$	−59.2795	−2.09454
$802$	−5.87451	−0.207436
$803$	−33.0768	−1.16725
$804$	−97.3916	−3.43474
$805$	−5.35968	−0.188904
$806$	−29.3099	−1.03240
$807$	74.7870	2.63263
$808$	−13.0866	−0.460385
$809$	10.1336	0.356279	0.178139	−	0.984005i	$-0.442992\pi$
$809$	10.1336	0.356279	0.178139	+	0.984005i	$0.442992\pi$
$810$	8.80537	0.309389
$811$	−45.5649	−1.60000	−0.800000	−	0.600000i	$-0.795167\pi$
$811$	−45.5649	−1.60000	−0.800000	+	0.600000i	$0.795167\pi$
$812$	−1.30670	−0.0458563
$813$	−69.8942	−2.45130
$814$	36.1415	1.26676
$815$	−2.26610	−0.0793779
$816$	−1.16343	−0.0407281
$817$	−41.9450	−1.46747
$818$	14.1622	0.495168
$819$	16.5381	0.577888
$820$	−17.2771	−0.603344
$821$	−25.6724	−0.895974	−0.447987	−	0.894040i	$-0.647859\pi$
$821$	−25.6724	−0.895974	−0.447987	+	0.894040i	$0.647859\pi$
$822$	99.3736	3.46605
$823$	42.4999	1.48145	0.740727	−	0.671806i	$-0.234481\pi$
$823$	42.4999	1.48145	0.740727	+	0.671806i	$0.234481\pi$
$824$	20.4355	0.711905
$825$	−10.7876	−0.375578
$826$	3.12815	0.108842
$827$	−18.3140	−0.636841	−0.318421	−	0.947950i	$-0.603152\pi$
$827$	−18.3140	−0.636841	−0.318421	+	0.947950i	$0.603152\pi$
$828$	70.1795	2.43891
$829$	−41.0348	−1.42520	−0.712599	−	0.701572i	$-0.752482\pi$
$829$	−41.0348	−1.42520	−0.712599	+	0.701572i	$0.752482\pi$
$830$	13.8518	0.480803
$831$	−63.2334	−2.19354
$832$	51.2348	1.77625
$833$	0.783575	0.0271493
$834$	0.318184	0.0110178
$835$	14.5885	0.504855
$836$	−54.4242	−1.88230
$837$	−10.7480	−0.371504
$838$	24.3958	0.842739
$839$	11.1918	0.386385	0.193192	−	0.981161i	$-0.438116\pi$
$839$	11.1918	0.386385	0.193192	+	0.981161i	$0.438116\pi$
$840$	6.73046	0.232223
$841$	−28.8233	−0.993908
$842$	−46.2530	−1.59398
$843$	21.9734	0.756806
$844$	20.3622	0.700895
$845$	2.41771	0.0831719
$846$	34.2871	1.17882
$847$	−5.13635	−0.176487
$848$	3.43503	0.117960
$849$	52.5006	1.80182
$850$	−1.77109	−0.0607479
$851$	21.3345	0.731336
$852$	−66.6306	−2.28273
$853$	46.0029	1.57511	0.787555	−	0.616245i	$-0.211347\pi$
$853$	46.0029	1.57511	0.787555	+	0.616245i	$0.211347\pi$
$854$	12.6778	0.433825
$855$	18.3557	0.627750
$856$	−18.8282	−0.643534
$857$	30.1368	1.02945	0.514726	−	0.857355i	$-0.327894\pi$
$857$	30.1368	1.02945	0.514726	+	0.857355i	$0.327894\pi$
$858$	−95.7408	−3.26854
$859$	−39.4804	−1.34705	−0.673526	−	0.739163i	$-0.735221\pi$
$859$	−39.4804	−1.34705	−0.673526	+	0.739163i	$0.735221\pi$
$860$	−29.9214	−1.02031
$861$	14.9245	0.508627
$862$	−6.67168	−0.227238
$863$	47.6629	1.62246	0.811231	−	0.584725i	$-0.198798\pi$
$863$	47.6629	1.62246	0.811231	+	0.584725i	$0.198798\pi$
$864$	20.3800	0.693343
$865$	−7.71858	−0.262440
$866$	−32.0387	−1.08872
$867$	−44.0045	−1.49447
$868$	10.2669	0.348481
$869$	−37.6344	−1.27666
$870$	−2.55133	−0.0864982
$871$	45.8049	1.55204
$872$	20.5153	0.694734
$873$	18.7804	0.635622
$874$	−52.7951	−1.78582
$875$	−1.00000	−0.0338062
$876$	68.7449	2.32267
$877$	28.8843	0.975353	0.487676	−	0.873024i	$-0.337845\pi$
$877$	28.8843	0.975353	0.487676	+	0.873024i	$0.337845\pi$
$878$	11.7297	0.395857
$879$	9.37489	0.316207
$880$	2.22094	0.0748680
$881$	−16.4014	−0.552576	−0.276288	−	0.961075i	$-0.589104\pi$
$881$	−16.4014	−0.552576	−0.276288	+	0.961075i	$0.589104\pi$
$882$	−9.51998	−0.320554
$883$	37.0625	1.24725	0.623626	−	0.781723i	$-0.285659\pi$
$883$	37.0625	1.24725	0.623626	+	0.781723i	$0.285659\pi$
$884$	−9.56502	−0.321706
$885$	3.71665	0.124934
$886$	78.8695	2.64967
$887$	9.97662	0.334982	0.167491	−	0.985874i	$-0.446433\pi$
$887$	9.97662	0.334982	0.167491	+	0.985874i	$0.446433\pi$
$888$	−26.7909	−0.899044
$889$	−11.9367	−0.400346
$890$	31.8119	1.06634
$891$	15.6491	0.524266
$892$	−31.5106	−1.05505
$893$	−15.6960	−0.525247
$894$	73.2600	2.45018
$895$	21.2291	0.709611
$896$	−16.9685	−0.566877
$897$	−56.5163	−1.88702
$898$	53.3672	1.78088
$899$	−1.38812	−0.0462963
$900$	13.0940	0.436465
$901$	−4.86829	−0.162186
$902$	−50.4591	−1.68010
$903$	25.8470	0.860136
$904$	−10.9057	−0.362719
$905$	−6.16803	−0.205032
$906$	−31.5772	−1.04908
$907$	−58.9938	−1.95886	−0.979428	−	0.201794i	$-0.935323\pi$
$907$	−58.9938	−1.95886	−0.979428	+	0.201794i	$0.935323\pi$
$908$	48.4471	1.60777
$909$	21.9929	0.729458
$910$	−8.87504	−0.294205
$911$	14.0114	0.464219	0.232109	−	0.972690i	$-0.425437\pi$
$911$	14.0114	0.464219	0.232109	+	0.972690i	$0.425437\pi$
$912$	−6.47073	−0.214267
$913$	24.6177	0.814729
$914$	−58.7124	−1.94203
$915$	15.0628	0.497962
$916$	3.10882	0.102718
$917$	−2.16050	−0.0713459
$918$	−5.76399	−0.190240
$919$	15.1377	0.499347	0.249674	−	0.968330i	$-0.419677\pi$
$919$	15.1377	0.499347	0.249674	+	0.968330i	$0.419677\pi$
$920$	−13.4326	−0.442859
$921$	−68.8671	−2.26925
$922$	−3.30617	−0.108883
$923$	31.3375	1.03149
$924$	33.5368	1.10328
$925$	3.98055	0.130880
$926$	−34.4028	−1.13055
$927$	−34.3432	−1.12798
$928$	2.63211	0.0864032
$929$	36.5377	1.19876	0.599382	−	0.800463i	$-0.295413\pi$
$929$	36.5377	1.19876	0.599382	+	0.800463i	$0.295413\pi$
$930$	20.0460	0.657335
$931$	4.35807	0.142830
$932$	48.0786	1.57487
$933$	−84.8253	−2.77706
$934$	−42.4269	−1.38825
$935$	−3.14762	−0.102938
$936$	41.4483	1.35478
$937$	−32.0419	−1.04676	−0.523382	−	0.852098i	$-0.675330\pi$
$937$	−32.0419	−1.04676	−0.523382	+	0.852098i	$0.675330\pi$
$938$	−26.3671	−0.860916
$939$	8.37881	0.273432
$940$	−11.1967	−0.365196
$941$	5.64517	0.184027	0.0920136	−	0.995758i	$-0.470670\pi$
$941$	5.64517	0.184027	0.0920136	+	0.995758i	$0.470670\pi$
$942$	108.390	3.53152
$943$	−29.7862	−0.969974
$944$	−0.765177	−0.0249044
$945$	−3.25449	−0.105869
$946$	−87.3875	−2.84121
$947$	−40.8786	−1.32838	−0.664188	−	0.747565i	$-0.731223\pi$
$947$	−40.8786	−1.32838	−0.664188	+	0.747565i	$0.731223\pi$
$948$	78.2171	2.54037
$949$	−32.3319	−1.04954
$950$	−9.85041	−0.319589
$951$	−94.8407	−3.07542
$952$	1.96382	0.0636477
$953$	−51.3729	−1.66413	−0.832066	−	0.554676i	$-0.812842\pi$
$953$	−51.3729	−1.66413	−0.832066	+	0.554676i	$0.812842\pi$
$954$	59.1469	1.91495
$955$	−13.9291	−0.450736
$956$	−55.3538	−1.79027
$957$	−4.53429	−0.146573
$958$	−41.7715	−1.34957
$959$	16.3714	0.528661
$960$	−35.0412	−1.13095
$961$	−20.0935	−0.648176
$962$	35.3275	1.13900
$963$	31.6419	1.01965
$964$	−12.5405	−0.403901
$965$	−16.4152	−0.528425
$966$	32.5330	1.04673
$967$	−21.6790	−0.697149	−0.348574	−	0.937281i	$-0.613334\pi$
$967$	−21.6790	−0.697149	−0.348574	+	0.937281i	$0.613334\pi$
$968$	−12.8729	−0.413749
$969$	9.17062	0.294603
$970$	−10.0784	−0.323597
$971$	−30.3135	−0.972807	−0.486403	−	0.873734i	$-0.661691\pi$
$971$	−30.3135	−0.972807	−0.486403	+	0.873734i	$0.661691\pi$
$972$	−62.8771	−2.01678
$973$	0.0524197	0.00168050
$974$	−28.2552	−0.905355
$975$	−10.5447	−0.337701
$976$	−3.10111	−0.0992642
$977$	−10.5947	−0.338953	−0.169477	−	0.985534i	$-0.554208\pi$
$977$	−10.5947	−0.338953	−0.169477	+	0.985534i	$0.554208\pi$
$978$	13.7551	0.439838
$979$	56.5368	1.80693
$980$	3.10882	0.0993076
$981$	−34.4772	−1.10077
$982$	57.6710	1.84036
$983$	−47.4815	−1.51442	−0.757212	−	0.653170i	$-0.773439\pi$
$983$	−47.4815	−1.51442	−0.757212	+	0.653170i	$0.773439\pi$
$984$	37.4043	1.19241
$985$	10.6128	0.338153
$986$	−0.744428	−0.0237074
$987$	9.67207	0.307865
$988$	−53.1985	−1.69247
$989$	−51.5853	−1.64032
$990$	38.2418	1.21540
$991$	−18.9067	−0.600590	−0.300295	−	0.953846i	$-0.597085\pi$
$991$	−18.9067	−0.600590	−0.300295	+	0.953846i	$0.597085\pi$
$992$	−20.6807	−0.656613
$993$	−36.1729	−1.14791
$994$	−18.0391	−0.572165
$995$	−23.0594	−0.731033
$996$	−51.1641	−1.62120
$997$	42.9818	1.36125	0.680623	−	0.732634i	$-0.261709\pi$
$997$	42.9818	1.36125	0.680623	+	0.732634i	$0.261709\pi$
$998$	−80.7610	−2.55644
$999$	12.9547	0.409867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.5	✓	44	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26027 q^{2} +2.68549 q^{3} +3.10882 q^{4} +1.00000 q^{5} -6.06994 q^{6} -1.00000 q^{7} -2.50623 q^{8} +4.21188 q^{9} +O(q^{10})\)	\(q-2.26027 q^{2} +2.68549 q^{3} +3.10882 q^{4} +1.00000 q^{5} -6.06994 q^{6} -1.00000 q^{7} -2.50623 q^{8} +4.21188 q^{9} -2.26027 q^{10} -4.01701 q^{11} +8.34871 q^{12} -3.92654 q^{13} +2.26027 q^{14} +2.68549 q^{15} -0.552885 q^{16} +0.783575 q^{17} -9.51998 q^{18} +4.35807 q^{19} +3.10882 q^{20} -2.68549 q^{21} +9.07952 q^{22} +5.35968 q^{23} -6.73046 q^{24} +1.00000 q^{25} +8.87504 q^{26} +3.25449 q^{27} -3.10882 q^{28} +0.420322 q^{29} -6.06994 q^{30} -3.30251 q^{31} +6.26213 q^{32} -10.7876 q^{33} -1.77109 q^{34} -1.00000 q^{35} +13.0940 q^{36} +3.98055 q^{37} -9.85041 q^{38} -10.5447 q^{39} -2.50623 q^{40} -5.55746 q^{41} +6.06994 q^{42} -9.62469 q^{43} -12.4881 q^{44} +4.21188 q^{45} -12.1143 q^{46} -3.60160 q^{47} -1.48477 q^{48} +1.00000 q^{49} -2.26027 q^{50} +2.10428 q^{51} -12.2069 q^{52} -6.21293 q^{53} -7.35603 q^{54} -4.01701 q^{55} +2.50623 q^{56} +11.7036 q^{57} -0.950041 q^{58} +1.38397 q^{59} +8.34871 q^{60} +5.60897 q^{61} +7.46455 q^{62} -4.21188 q^{63} -13.0483 q^{64} -3.92654 q^{65} +24.3830 q^{66} -11.6655 q^{67} +2.43599 q^{68} +14.3934 q^{69} +2.26027 q^{70} -7.98094 q^{71} -10.5559 q^{72} +8.23419 q^{73} -8.99711 q^{74} +2.68549 q^{75} +13.5484 q^{76} +4.01701 q^{77} +23.8339 q^{78} +9.36876 q^{79} -0.552885 q^{80} -3.89572 q^{81} +12.5614 q^{82} -6.12838 q^{83} -8.34871 q^{84} +0.783575 q^{85} +21.7544 q^{86} +1.12877 q^{87} +10.0675 q^{88} -14.0744 q^{89} -9.51998 q^{90} +3.92654 q^{91} +16.6623 q^{92} -8.86886 q^{93} +8.14058 q^{94} +4.35807 q^{95} +16.8169 q^{96} +4.45892 q^{97} -2.26027 q^{98} -16.9191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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