LMFDB - Embedded newform 8041.2.a.g.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47238 q^{2} -0.879695 q^{3} +4.11267 q^{4} -2.32585 q^{5} +2.17494 q^{6} +1.92542 q^{7} -5.22332 q^{8} -2.22614 q^{9} +O(q^{10})$	\(q-2.47238 q^{2} -0.879695 q^{3} +4.11267 q^{4} -2.32585 q^{5} +2.17494 q^{6} +1.92542 q^{7} -5.22332 q^{8} -2.22614 q^{9} +5.75038 q^{10} -1.00000 q^{11} -3.61789 q^{12} -4.82240 q^{13} -4.76038 q^{14} +2.04604 q^{15} +4.68871 q^{16} +1.00000 q^{17} +5.50386 q^{18} -4.21529 q^{19} -9.56544 q^{20} -1.69378 q^{21} +2.47238 q^{22} -6.36962 q^{23} +4.59493 q^{24} +0.409567 q^{25} +11.9228 q^{26} +4.59741 q^{27} +7.91862 q^{28} -3.79631 q^{29} -5.05858 q^{30} +7.93702 q^{31} -1.14563 q^{32} +0.879695 q^{33} -2.47238 q^{34} -4.47824 q^{35} -9.15536 q^{36} +2.21625 q^{37} +10.4218 q^{38} +4.24224 q^{39} +12.1487 q^{40} +3.28743 q^{41} +4.18768 q^{42} +1.00000 q^{43} -4.11267 q^{44} +5.17765 q^{45} +15.7481 q^{46} +2.42265 q^{47} -4.12463 q^{48} -3.29275 q^{49} -1.01261 q^{50} -0.879695 q^{51} -19.8329 q^{52} -2.66086 q^{53} -11.3665 q^{54} +2.32585 q^{55} -10.0571 q^{56} +3.70817 q^{57} +9.38592 q^{58} +15.1369 q^{59} +8.41467 q^{60} +9.46522 q^{61} -19.6233 q^{62} -4.28625 q^{63} -6.54499 q^{64} +11.2162 q^{65} -2.17494 q^{66} +14.5555 q^{67} +4.11267 q^{68} +5.60332 q^{69} +11.0719 q^{70} -5.67883 q^{71} +11.6278 q^{72} +7.91191 q^{73} -5.47941 q^{74} -0.360294 q^{75} -17.3361 q^{76} -1.92542 q^{77} -10.4884 q^{78} +3.11018 q^{79} -10.9052 q^{80} +2.63409 q^{81} -8.12778 q^{82} -0.124396 q^{83} -6.96597 q^{84} -2.32585 q^{85} -2.47238 q^{86} +3.33959 q^{87} +5.22332 q^{88} -3.66791 q^{89} -12.8011 q^{90} -9.28515 q^{91} -26.1961 q^{92} -6.98216 q^{93} -5.98972 q^{94} +9.80412 q^{95} +1.00780 q^{96} -13.6924 q^{97} +8.14093 q^{98} +2.22614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−2.47238	−1.74824	−0.874119	−	0.485712i	$-0.838560\pi$
$2$	−2.47238	−1.74824	−0.874119	+	0.485712i	$0.838560\pi$
$3$	−0.879695	−0.507892	−0.253946	−	0.967218i	$-0.581729\pi$
$3$	−0.879695	−0.507892	−0.253946	+	0.967218i	$0.581729\pi$
$4$	4.11267	2.05633
$5$	−2.32585	−1.04015	−0.520075	−	0.854120i	$-0.674096\pi$
$5$	−2.32585	−1.04015	−0.520075	+	0.854120i	$0.674096\pi$
$6$	2.17494	0.887916
$7$	1.92542	0.727741	0.363871	−	0.931450i	$-0.381455\pi$
$7$	1.92542	0.727741	0.363871	+	0.931450i	$0.381455\pi$
$8$	−5.22332	−1.84672
$9$	−2.22614	−0.742046
$10$	5.75038	1.81843
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.61789	−1.04440
$13$	−4.82240	−1.33749	−0.668746	−	0.743491i	$-0.733169\pi$
$13$	−4.82240	−1.33749	−0.668746	+	0.743491i	$0.733169\pi$
$14$	−4.76038	−1.27226
$15$	2.04604	0.528284
$16$	4.68871	1.17218
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.50386	1.29727
$19$	−4.21529	−0.967053	−0.483527	−	0.875330i	$-0.660644\pi$
$19$	−4.21529	−0.967053	−0.483527	+	0.875330i	$0.660644\pi$
$20$	−9.56544	−2.13890
$21$	−1.69378	−0.369614
$22$	2.47238	0.527113
$23$	−6.36962	−1.32816	−0.664078	−	0.747663i	$-0.731176\pi$
$23$	−6.36962	−1.32816	−0.664078	+	0.747663i	$0.731176\pi$
$24$	4.59493	0.937937
$25$	0.409567	0.0819134
$26$	11.9228	2.33825
$27$	4.59741	0.884771
$28$	7.91862	1.49648
$29$	−3.79631	−0.704957	−0.352478	−	0.935820i	$-0.614661\pi$
$29$	−3.79631	−0.704957	−0.352478	+	0.935820i	$0.614661\pi$
$30$	−5.05858	−0.923567
$31$	7.93702	1.42553	0.712765	−	0.701402i	$-0.247442\pi$
$31$	7.93702	1.42553	0.712765	+	0.701402i	$0.247442\pi$
$32$	−1.14563	−0.202521
$33$	0.879695	0.153135
$34$	−2.47238	−0.424010
$35$	−4.47824	−0.756960
$36$	−9.15536	−1.52589
$37$	2.21625	0.364349	0.182174	−	0.983266i	$-0.441686\pi$
$37$	2.21625	0.364349	0.182174	+	0.983266i	$0.441686\pi$
$38$	10.4218	1.69064
$39$	4.24224	0.679302
$40$	12.1487	1.92087
$41$	3.28743	0.513411	0.256705	−	0.966490i	$-0.417363\pi$
$41$	3.28743	0.513411	0.256705	+	0.966490i	$0.417363\pi$
$42$	4.18768	0.646173
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−4.11267	−0.620008
$45$	5.17765	0.771839
$46$	15.7481	2.32193
$47$	2.42265	0.353380	0.176690	−	0.984267i	$-0.443461\pi$
$47$	2.42265	0.353380	0.176690	+	0.984267i	$0.443461\pi$
$48$	−4.12463	−0.595340
$49$	−3.29275	−0.470393
$50$	−1.01261	−0.143204
$51$	−0.879695	−0.123182
$52$	−19.8329	−2.75033
$53$	−2.66086	−0.365497	−0.182749	−	0.983160i	$-0.558499\pi$
$53$	−2.66086	−0.365497	−0.182749	+	0.983160i	$0.558499\pi$
$54$	−11.3665	−1.54679
$55$	2.32585	0.313617
$56$	−10.0571	−1.34394
$57$	3.70817	0.491159
$58$	9.38592	1.23243
$59$	15.1369	1.97066	0.985328	−	0.170673i	$-0.0545942\pi$
$59$	15.1369	1.97066	0.985328	+	0.170673i	$0.0545942\pi$
$60$	8.41467	1.08633
$61$	9.46522	1.21190	0.605949	−	0.795504i	$-0.292794\pi$
$61$	9.46522	1.21190	0.605949	+	0.795504i	$0.292794\pi$
$62$	−19.6233	−2.49217
$63$	−4.28625	−0.540017
$64$	−6.54499	−0.818123
$65$	11.2162	1.39119
$66$	−2.17494	−0.267717
$67$	14.5555	1.77824	0.889121	−	0.457672i	$-0.151317\pi$
$67$	14.5555	1.77824	0.889121	+	0.457672i	$0.151317\pi$
$68$	4.11267	0.498734
$69$	5.60332	0.674560
$70$	11.0719	1.32335
$71$	−5.67883	−0.673954	−0.336977	−	0.941513i	$-0.609404\pi$
$71$	−5.67883	−0.673954	−0.336977	+	0.941513i	$0.609404\pi$
$72$	11.6278	1.37035
$73$	7.91191	0.926019	0.463009	−	0.886353i	$-0.346770\pi$
$73$	7.91191	0.926019	0.463009	+	0.886353i	$0.346770\pi$
$74$	−5.47941	−0.636968
$75$	−0.360294	−0.0416032
$76$	−17.3361	−1.98859
$77$	−1.92542	−0.219422
$78$	−10.4884	−1.18758
$79$	3.11018	0.349923	0.174962	−	0.984575i	$-0.444020\pi$
$79$	3.11018	0.349923	0.174962	+	0.984575i	$0.444020\pi$
$80$	−10.9052	−1.21924
$81$	2.63409	0.292677
$82$	−8.12778	−0.897564
$83$	−0.124396	−0.0136543	−0.00682713	−	0.999977i	$-0.502173\pi$
$83$	−0.124396	−0.0136543	−0.00682713	+	0.999977i	$0.502173\pi$
$84$	−6.96597	−0.760050
$85$	−2.32585	−0.252274
$86$	−2.47238	−0.266604
$87$	3.33959	0.358042
$88$	5.22332	0.556808
$89$	−3.66791	−0.388798	−0.194399	−	0.980923i	$-0.562276\pi$
$89$	−3.66791	−0.388798	−0.194399	+	0.980923i	$0.562276\pi$
$90$	−12.8011	−1.34936
$91$	−9.28515	−0.973348
$92$	−26.1961	−2.73113
$93$	−6.98216	−0.724016
$94$	−5.98972	−0.617792
$95$	9.80412	1.00588
$96$	1.00780	0.102859
$97$	−13.6924	−1.39026	−0.695129	−	0.718885i	$-0.744653\pi$
$97$	−13.6924	−1.39026	−0.695129	+	0.718885i	$0.744653\pi$
$98$	8.14093	0.822359
$99$	2.22614	0.223735
$100$	1.68441	0.168441
$101$	−12.0405	−1.19808	−0.599039	−	0.800720i	$-0.704450\pi$
$101$	−12.0405	−1.19808	−0.599039	+	0.800720i	$0.704450\pi$
$102$	2.17494	0.215351
$103$	10.7199	1.05627	0.528134	−	0.849161i	$-0.322892\pi$
$103$	10.7199	1.05627	0.528134	+	0.849161i	$0.322892\pi$
$104$	25.1889	2.46998
$105$	3.93948	0.384454
$106$	6.57866	0.638976
$107$	10.0113	0.967833	0.483917	−	0.875114i	$-0.339214\pi$
$107$	10.0113	0.967833	0.483917	+	0.875114i	$0.339214\pi$
$108$	18.9076	1.81939
$109$	16.8931	1.61806	0.809032	−	0.587764i	$-0.199992\pi$
$109$	16.8931	1.61806	0.809032	+	0.587764i	$0.199992\pi$
$110$	−5.75038	−0.548277
$111$	−1.94962	−0.185050
$112$	9.02774	0.853042
$113$	−14.5747	−1.37107	−0.685536	−	0.728039i	$-0.740432\pi$
$113$	−14.5747	−1.37107	−0.685536	+	0.728039i	$0.740432\pi$
$114$	−9.16801	−0.858662
$115$	14.8148	1.38148
$116$	−15.6130	−1.44963
$117$	10.7353	0.992480
$118$	−37.4242	−3.44517
$119$	1.92542	0.176503
$120$	−10.6871	−0.975595
$121$	1.00000	0.0909091
$122$	−23.4016	−2.11868
$123$	−2.89194	−0.260757
$124$	32.6423	2.93137
$125$	10.6766	0.954948
$126$	10.5972	0.944078
$127$	−2.79346	−0.247880	−0.123940	−	0.992290i	$-0.539553\pi$
$127$	−2.79346	−0.247880	−0.123940	+	0.992290i	$0.539553\pi$
$128$	18.4730	1.63279
$129$	−0.879695	−0.0774528
$130$	−27.7306	−2.43214
$131$	−14.6459	−1.27961	−0.639807	−	0.768535i	$-0.720986\pi$
$131$	−14.6459	−1.27961	−0.639807	+	0.768535i	$0.720986\pi$
$132$	3.61789	0.314897
$133$	−8.11621	−0.703765
$134$	−35.9868	−3.10879
$135$	−10.6929	−0.920295
$136$	−5.22332	−0.447896
$137$	7.29802	0.623512	0.311756	−	0.950162i	$-0.399083\pi$
$137$	7.29802	0.623512	0.311756	+	0.950162i	$0.399083\pi$
$138$	−13.8535	−1.17929
$139$	−8.44780	−0.716533	−0.358266	−	0.933619i	$-0.616632\pi$
$139$	−8.44780	−0.716533	−0.358266	+	0.933619i	$0.616632\pi$
$140$	−18.4175	−1.55656
$141$	−2.13119	−0.179479
$142$	14.0402	1.17823
$143$	4.82240	0.403269
$144$	−10.4377	−0.869809
$145$	8.82964	0.733261
$146$	−19.5613	−1.61890
$147$	2.89662	0.238909
$148$	9.11469	0.749223
$149$	−2.58036	−0.211391	−0.105696	−	0.994399i	$-0.533707\pi$
$149$	−2.58036	−0.211391	−0.105696	+	0.994399i	$0.533707\pi$
$150$	0.890785	0.0727323
$151$	17.5091	1.42487	0.712436	−	0.701737i	$-0.247592\pi$
$151$	17.5091	1.42487	0.712436	+	0.701737i	$0.247592\pi$
$152$	22.0178	1.78588
$153$	−2.22614	−0.179972
$154$	4.76038	0.383602
$155$	−18.4603	−1.48277
$156$	17.4469	1.39687
$157$	0.587939	0.0469227	0.0234613	−	0.999725i	$-0.492531\pi$
$157$	0.587939	0.0469227	0.0234613	+	0.999725i	$0.492531\pi$
$158$	−7.68956	−0.611749
$159$	2.34075	0.185633
$160$	2.66456	0.210652
$161$	−12.2642	−0.966554
$162$	−6.51248	−0.511669
$163$	15.9060	1.24585	0.622925	−	0.782281i	$-0.285944\pi$
$163$	15.9060	1.24585	0.622925	+	0.782281i	$0.285944\pi$
$164$	13.5201	1.05574
$165$	−2.04604	−0.159284
$166$	0.307555	0.0238709
$167$	−0.386377	−0.0298988	−0.0149494	−	0.999888i	$-0.504759\pi$
$167$	−0.386377	−0.0298988	−0.0149494	+	0.999888i	$0.504759\pi$
$168$	8.84718	0.682575
$169$	10.2555	0.788885
$170$	5.75038	0.441034
$171$	9.38381	0.717598
$172$	4.11267	0.313588
$173$	−22.5833	−1.71697	−0.858486	−	0.512836i	$-0.828595\pi$
$173$	−22.5833	−1.71697	−0.858486	+	0.512836i	$0.828595\pi$
$174$	−8.25675	−0.625943
$175$	0.788590	0.0596118
$176$	−4.68871	−0.353425
$177$	−13.3158	−1.00088
$178$	9.06847	0.679711
$179$	−8.95790	−0.669545	−0.334772	−	0.942299i	$-0.608659\pi$
$179$	−8.95790	−0.669545	−0.334772	+	0.942299i	$0.608659\pi$
$180$	21.2940	1.58716
$181$	−4.85208	−0.360652	−0.180326	−	0.983607i	$-0.557715\pi$
$181$	−4.85208	−0.360652	−0.180326	+	0.983607i	$0.557715\pi$
$182$	22.9564	1.70164
$183$	−8.32651	−0.615513
$184$	33.2706	2.45274
$185$	−5.15465	−0.378978
$186$	17.2626	1.26575
$187$	−1.00000	−0.0731272
$188$	9.96356	0.726668
$189$	8.85195	0.643884
$190$	−24.2395	−1.75852
$191$	−21.2646	−1.53865	−0.769325	−	0.638858i	$-0.779407\pi$
$191$	−21.2646	−1.53865	−0.769325	+	0.638858i	$0.779407\pi$
$192$	5.75759	0.415518
$193$	0.104969	0.00755585	0.00377793	−	0.999993i	$-0.498797\pi$
$193$	0.104969	0.00755585	0.00377793	+	0.999993i	$0.498797\pi$
$194$	33.8529	2.43050
$195$	−9.86680	−0.706576
$196$	−13.5420	−0.967285
$197$	21.2183	1.51174	0.755870	−	0.654722i	$-0.227214\pi$
$197$	21.2183	1.51174	0.755870	+	0.654722i	$0.227214\pi$
$198$	−5.50386	−0.391142
$199$	−1.00995	−0.0715932	−0.0357966	−	0.999359i	$-0.511397\pi$
$199$	−1.00995	−0.0715932	−0.0357966	+	0.999359i	$0.511397\pi$
$200$	−2.13930	−0.151271
$201$	−12.8044	−0.903155
$202$	29.7688	2.09452
$203$	−7.30950	−0.513026
$204$	−3.61789	−0.253303
$205$	−7.64607	−0.534024
$206$	−26.5038	−1.84661
$207$	14.1796	0.985553
$208$	−22.6108	−1.56778
$209$	4.21529	0.291578
$210$	−9.73991	−0.672117
$211$	8.38416	0.577189	0.288595	−	0.957451i	$-0.406812\pi$
$211$	8.38416	0.577189	0.288595	+	0.957451i	$0.406812\pi$
$212$	−10.9432	−0.751585
$213$	4.99564	0.342296
$214$	−24.7519	−1.69200
$215$	−2.32585	−0.158621
$216$	−24.0137	−1.63393
$217$	15.2821	1.03742
$218$	−41.7662	−2.82876
$219$	−6.96007	−0.470318
$220$	9.56544	0.644902
$221$	−4.82240	−0.324389
$222$	4.82021	0.323511
$223$	12.0564	0.807354	0.403677	−	0.914902i	$-0.367732\pi$
$223$	12.0564	0.807354	0.403677	+	0.914902i	$0.367732\pi$
$224$	−2.20582	−0.147382
$225$	−0.911752	−0.0607835
$226$	36.0342	2.39696
$227$	2.76081	0.183241	0.0916206	−	0.995794i	$-0.470795\pi$
$227$	2.76081	0.183241	0.0916206	+	0.995794i	$0.470795\pi$
$228$	15.2505	1.00999
$229$	3.87880	0.256318	0.128159	−	0.991754i	$-0.459093\pi$
$229$	3.87880	0.256318	0.128159	+	0.991754i	$0.459093\pi$
$230$	−36.6277	−2.41516
$231$	1.69378	0.111443
$232$	19.8294	1.30186
$233$	−18.3748	−1.20377	−0.601886	−	0.798582i	$-0.705584\pi$
$233$	−18.3748	−1.20377	−0.601886	+	0.798582i	$0.705584\pi$
$234$	−26.5418	−1.73509
$235$	−5.63472	−0.367568
$236$	62.2530	4.05233
$237$	−2.73601	−0.177723
$238$	−4.76038	−0.308569
$239$	−18.5901	−1.20249	−0.601245	−	0.799064i	$-0.705329\pi$
$239$	−18.5901	−1.20249	−0.601245	+	0.799064i	$0.705329\pi$
$240$	9.59327	0.619243
$241$	−26.5930	−1.71300	−0.856501	−	0.516145i	$-0.827367\pi$
$241$	−26.5930	−1.71300	−0.856501	+	0.516145i	$0.827367\pi$
$242$	−2.47238	−0.158931
$243$	−16.1094	−1.03342
$244$	38.9273	2.49207
$245$	7.65844	0.489279
$246$	7.14997	0.455866
$247$	20.3278	1.29343
$248$	−41.4576	−2.63256
$249$	0.109431	0.00693489
$250$	−26.3967	−1.66948
$251$	−1.52484	−0.0962469	−0.0481234	−	0.998841i	$-0.515324\pi$
$251$	−1.52484	−0.0962469	−0.0481234	+	0.998841i	$0.515324\pi$
$252$	−17.6279	−1.11046
$253$	6.36962	0.400454
$254$	6.90650	0.433352
$255$	2.04604	0.128128
$256$	−32.5822	−2.03639
$257$	−4.63335	−0.289020	−0.144510	−	0.989503i	$-0.546161\pi$
$257$	−4.63335	−0.289020	−0.144510	+	0.989503i	$0.546161\pi$
$258$	2.17494	0.135406
$259$	4.26721	0.265152
$260$	46.1283	2.86076
$261$	8.45110	0.523110
$262$	36.2101	2.23707
$263$	15.6670	0.966066	0.483033	−	0.875602i	$-0.339535\pi$
$263$	15.6670	0.966066	0.483033	+	0.875602i	$0.339535\pi$
$264$	−4.59493	−0.282799
$265$	6.18876	0.380172
$266$	20.0664	1.23035
$267$	3.22664	0.197467
$268$	59.8621	3.65666
$269$	−2.11295	−0.128829	−0.0644145	−	0.997923i	$-0.520518\pi$
$269$	−2.11295	−0.128829	−0.0644145	+	0.997923i	$0.520518\pi$
$270$	26.4368	1.60890
$271$	20.2685	1.23122	0.615611	−	0.788050i	$-0.288909\pi$
$271$	20.2685	1.23122	0.615611	+	0.788050i	$0.288909\pi$
$272$	4.68871	0.284295
$273$	8.16810	0.494356
$274$	−18.0435	−1.09005
$275$	−0.409567	−0.0246978
$276$	23.0446	1.38712
$277$	19.6328	1.17962	0.589810	−	0.807542i	$-0.299203\pi$
$277$	19.6328	1.17962	0.589810	+	0.807542i	$0.299203\pi$
$278$	20.8862	1.25267
$279$	−17.6689	−1.05781
$280$	23.3913	1.39790
$281$	30.9921	1.84884	0.924418	−	0.381380i	$-0.124551\pi$
$281$	30.9921	1.84884	0.924418	+	0.381380i	$0.124551\pi$
$282$	5.26913	0.313772
$283$	−10.2422	−0.608834	−0.304417	−	0.952539i	$-0.598462\pi$
$283$	−10.2422	−0.608834	−0.304417	+	0.952539i	$0.598462\pi$
$284$	−23.3552	−1.38587
$285$	−8.62463	−0.510879
$286$	−11.9228	−0.705010
$287$	6.32969	0.373630
$288$	2.55033	0.150279
$289$	1.00000	0.0588235
$290$	−21.8302	−1.28192
$291$	12.0452	0.706101
$292$	32.5391	1.90420
$293$	−8.75262	−0.511333	−0.255667	−	0.966765i	$-0.582295\pi$
$293$	−8.75262	−0.511333	−0.255667	+	0.966765i	$0.582295\pi$
$294$	−7.16154	−0.417669
$295$	−35.2061	−2.04978
$296$	−11.5762	−0.672852
$297$	−4.59741	−0.266769
$298$	6.37963	0.369562
$299$	30.7168	1.77640
$300$	−1.48177	−0.0855501
$301$	1.92542	0.110979
$302$	−43.2892	−2.49101
$303$	10.5920	0.608494
$304$	−19.7643	−1.13356
$305$	−22.0147	−1.26056
$306$	5.50386	0.314635
$307$	11.7814	0.672399	0.336200	−	0.941791i	$-0.390858\pi$
$307$	11.7814	0.672399	0.336200	+	0.941791i	$0.390858\pi$
$308$	−7.91862	−0.451205
$309$	−9.43028	−0.536470
$310$	45.6409	2.59223
$311$	21.0055	1.19111	0.595556	−	0.803314i	$-0.296932\pi$
$311$	21.0055	1.19111	0.595556	+	0.803314i	$0.296932\pi$
$312$	−22.1586	−1.25448
$313$	−15.0488	−0.850611	−0.425305	−	0.905050i	$-0.639833\pi$
$313$	−15.0488	−0.850611	−0.425305	+	0.905050i	$0.639833\pi$
$314$	−1.45361	−0.0820319
$315$	9.96917	0.561699
$316$	12.7912	0.719559
$317$	12.5377	0.704189	0.352095	−	0.935964i	$-0.385470\pi$
$317$	12.5377	0.704189	0.352095	+	0.935964i	$0.385470\pi$
$318$	−5.78722	−0.324531
$319$	3.79631	0.212553
$320$	15.2226	0.850971
$321$	−8.80693	−0.491555
$322$	30.3218	1.68977
$323$	−4.21529	−0.234545
$324$	10.8332	0.601842
$325$	−1.97509	−0.109559
$326$	−39.3256	−2.17804
$327$	−14.8608	−0.821802
$328$	−17.1713	−0.948127
$329$	4.66463	0.257169
$330$	5.05858	0.278466
$331$	6.38221	0.350798	0.175399	−	0.984497i	$-0.443878\pi$
$331$	6.38221	0.350798	0.175399	+	0.984497i	$0.443878\pi$
$332$	−0.511601	−0.0280777
$333$	−4.93367	−0.270363
$334$	0.955271	0.0522701
$335$	−33.8540	−1.84964
$336$	−7.94166	−0.433253
$337$	−18.6515	−1.01601	−0.508006	−	0.861353i	$-0.669617\pi$
$337$	−18.6515	−1.01601	−0.508006	+	0.861353i	$0.669617\pi$
$338$	−25.3555	−1.37916
$339$	12.8213	0.696357
$340$	−9.56544	−0.518759
$341$	−7.93702	−0.429814
$342$	−23.2003	−1.25453
$343$	−19.8179	−1.07007
$344$	−5.22332	−0.281623
$345$	−13.0325	−0.701645
$346$	55.8344	3.00168
$347$	23.4081	1.25661	0.628306	−	0.777966i	$-0.283748\pi$
$347$	23.4081	1.25661	0.628306	+	0.777966i	$0.283748\pi$
$348$	13.7346	0.736254
$349$	−13.5389	−0.724722	−0.362361	−	0.932038i	$-0.618029\pi$
$349$	−13.5389	−0.724722	−0.362361	+	0.932038i	$0.618029\pi$
$350$	−1.94969	−0.104216
$351$	−22.1705	−1.18337
$352$	1.14563	0.0610622
$353$	−15.2733	−0.812916	−0.406458	−	0.913669i	$-0.633236\pi$
$353$	−15.2733	−0.812916	−0.406458	+	0.913669i	$0.633236\pi$
$354$	32.9219	1.74978
$355$	13.2081	0.701013
$356$	−15.0849	−0.799498
$357$	−1.69378	−0.0896446
$358$	22.1473	1.17052
$359$	−22.7515	−1.20078	−0.600390	−	0.799708i	$-0.704988\pi$
$359$	−22.7515	−1.20078	−0.600390	+	0.799708i	$0.704988\pi$
$360$	−27.0446	−1.42537
$361$	−1.23135	−0.0648077
$362$	11.9962	0.630505
$363$	−0.879695	−0.0461720
$364$	−38.1867	−2.00153
$365$	−18.4019	−0.963199
$366$	20.5863	1.07606
$367$	−0.881547	−0.0460164	−0.0230082	−	0.999735i	$-0.507324\pi$
$367$	−0.881547	−0.0460164	−0.0230082	+	0.999735i	$0.507324\pi$
$368$	−29.8653	−1.55684
$369$	−7.31827	−0.380974
$370$	12.7443	0.662543
$371$	−5.12328	−0.265987
$372$	−28.7153	−1.48882
$373$	−1.33566	−0.0691579	−0.0345789	−	0.999402i	$-0.511009\pi$
$373$	−1.33566	−0.0691579	−0.0345789	+	0.999402i	$0.511009\pi$
$374$	2.47238	0.127844
$375$	−9.39219	−0.485011
$376$	−12.6543	−0.652595
$377$	18.3073	0.942874
$378$	−21.8854	−1.12566
$379$	−7.51912	−0.386231	−0.193116	−	0.981176i	$-0.561859\pi$
$379$	−7.51912	−0.386231	−0.193116	+	0.981176i	$0.561859\pi$
$380$	40.3211	2.06843
$381$	2.45739	0.125896
$382$	52.5741	2.68993
$383$	26.2712	1.34240	0.671198	−	0.741278i	$-0.265780\pi$
$383$	26.2712	1.34240	0.671198	+	0.741278i	$0.265780\pi$
$384$	−16.2506	−0.829284
$385$	4.47824	0.228232
$386$	−0.259524	−0.0132094
$387$	−2.22614	−0.113161
$388$	−56.3125	−2.85883
$389$	−9.85098	−0.499465	−0.249732	−	0.968315i	$-0.580343\pi$
$389$	−9.85098	−0.499465	−0.249732	+	0.968315i	$0.580343\pi$
$390$	24.3945	1.23526
$391$	−6.36962	−0.322125
$392$	17.1991	0.868686
$393$	12.8839	0.649906
$394$	−52.4597	−2.64288
$395$	−7.23381	−0.363973
$396$	9.15536	0.460074
$397$	−27.3557	−1.37294	−0.686471	−	0.727157i	$-0.740841\pi$
$397$	−27.3557	−1.37294	−0.686471	+	0.727157i	$0.740841\pi$
$398$	2.49697	0.125162
$399$	7.13979	0.357437
$400$	1.92034	0.0960171
$401$	−24.1483	−1.20591	−0.602954	−	0.797776i	$-0.706010\pi$
$401$	−24.1483	−1.20591	−0.602954	+	0.797776i	$0.706010\pi$
$402$	31.6574	1.57893
$403$	−38.2754	−1.90664
$404$	−49.5187	−2.46365
$405$	−6.12650	−0.304428
$406$	18.0719	0.896892
$407$	−2.21625	−0.109855
$408$	4.59493	0.227483
$409$	33.6102	1.66192	0.830959	−	0.556334i	$-0.187793\pi$
$409$	33.6102	1.66192	0.830959	+	0.556334i	$0.187793\pi$
$410$	18.9040	0.933601
$411$	−6.42003	−0.316677
$412$	44.0876	2.17204
$413$	29.1449	1.43413
$414$	−35.0575	−1.72298
$415$	0.289327	0.0142025
$416$	5.52468	0.270870
$417$	7.43149	0.363921
$418$	−10.4218	−0.509747
$419$	33.5302	1.63806	0.819028	−	0.573754i	$-0.194514\pi$
$419$	33.5302	1.63806	0.819028	+	0.573754i	$0.194514\pi$
$420$	16.2018	0.790567
$421$	38.5745	1.88001	0.940003	−	0.341166i	$-0.110822\pi$
$421$	38.5745	1.88001	0.940003	+	0.341166i	$0.110822\pi$
$422$	−20.7288	−1.00906
$423$	−5.39315	−0.262224
$424$	13.8985	0.674972
$425$	0.409567	0.0198669
$426$	−12.3511	−0.598414
$427$	18.2245	0.881948
$428$	41.1734	1.99019
$429$	−4.24224	−0.204817
$430$	5.75038	0.277308
$431$	−3.38003	−0.162811	−0.0814053	−	0.996681i	$-0.525941\pi$
$431$	−3.38003	−0.162811	−0.0814053	+	0.996681i	$0.525941\pi$
$432$	21.5559	1.03711
$433$	8.55798	0.411270	0.205635	−	0.978629i	$-0.434074\pi$
$433$	8.55798	0.411270	0.205635	+	0.978629i	$0.434074\pi$
$434$	−37.7832	−1.81365
$435$	−7.76739	−0.372418
$436$	69.4757	3.32728
$437$	26.8498	1.28440
$438$	17.2079	0.822227
$439$	−26.9160	−1.28463	−0.642316	−	0.766440i	$-0.722026\pi$
$439$	−26.9160	−1.28463	−0.642316	+	0.766440i	$0.722026\pi$
$440$	−12.1487	−0.579164
$441$	7.33011	0.349053
$442$	11.9228	0.567110
$443$	2.84538	0.135188	0.0675941	−	0.997713i	$-0.478468\pi$
$443$	2.84538	0.135188	0.0675941	+	0.997713i	$0.478468\pi$
$444$	−8.01815	−0.380525
$445$	8.53100	0.404408
$446$	−29.8079	−1.41145
$447$	2.26993	0.107364
$448$	−12.6019	−0.595382
$449$	4.83131	0.228004	0.114002	−	0.993481i	$-0.463633\pi$
$449$	4.83131	0.228004	0.114002	+	0.993481i	$0.463633\pi$
$450$	2.25420	0.106264
$451$	−3.28743	−0.154799
$452$	−59.9409	−2.81938
$453$	−15.4027	−0.723681
$454$	−6.82577	−0.320349
$455$	21.5958	1.01243
$456$	−19.3690	−0.907035
$457$	7.41184	0.346711	0.173356	−	0.984859i	$-0.444539\pi$
$457$	7.41184	0.346711	0.173356	+	0.984859i	$0.444539\pi$
$458$	−9.58987	−0.448105
$459$	4.59741	0.214589
$460$	60.9282	2.84079
$461$	−34.8948	−1.62521	−0.812607	−	0.582812i	$-0.801952\pi$
$461$	−34.8948	−1.62521	−0.812607	+	0.582812i	$0.801952\pi$
$462$	−4.18768	−0.194829
$463$	1.63086	0.0757924	0.0378962	−	0.999282i	$-0.487934\pi$
$463$	1.63086	0.0757924	0.0378962	+	0.999282i	$0.487934\pi$
$464$	−17.7998	−0.826334
$465$	16.2394	0.753086
$466$	45.4295	2.10448
$467$	40.5057	1.87438	0.937191	−	0.348818i	$-0.113417\pi$
$467$	40.5057	1.87438	0.937191	+	0.348818i	$0.113417\pi$
$468$	44.1508	2.04087
$469$	28.0256	1.29410
$470$	13.9312	0.642597
$471$	−0.517207	−0.0238317
$472$	−79.0649	−3.63926
$473$	−1.00000	−0.0459800
$474$	6.76447	0.310702
$475$	−1.72644	−0.0792147
$476$	7.91862	0.362950
$477$	5.92344	0.271216
$478$	45.9617	2.10224
$479$	−23.1740	−1.05885	−0.529424	−	0.848358i	$-0.677592\pi$
$479$	−23.1740	−1.05885	−0.529424	+	0.848358i	$0.677592\pi$
$480$	−2.34400	−0.106988
$481$	−10.6876	−0.487314
$482$	65.7479	2.99474
$483$	10.7888	0.490905
$484$	4.11267	0.186940
$485$	31.8465	1.44608
$486$	39.8286	1.80666
$487$	−13.4942	−0.611483	−0.305741	−	0.952115i	$-0.598904\pi$
$487$	−13.4942	−0.611483	−0.305741	+	0.952115i	$0.598904\pi$
$488$	−49.4399	−2.23804
$489$	−13.9924	−0.632758
$490$	−18.9346	−0.855377
$491$	28.9031	1.30438	0.652190	−	0.758056i	$-0.273851\pi$
$491$	28.9031	1.30438	0.652190	+	0.758056i	$0.273851\pi$
$492$	−11.8936	−0.536204
$493$	−3.79631	−0.170977
$494$	−50.2580	−2.26122
$495$	−5.17765	−0.232718
$496$	37.2144	1.67097
$497$	−10.9342	−0.490464
$498$	−0.270555	−0.0121238
$499$	25.5567	1.14407	0.572037	−	0.820228i	$-0.306153\pi$
$499$	25.5567	1.14407	0.572037	+	0.820228i	$0.306153\pi$
$500$	43.9095	1.96369
$501$	0.339894	0.0151853
$502$	3.76998	0.168262
$503$	19.6078	0.874268	0.437134	−	0.899396i	$-0.355994\pi$
$503$	19.6078	0.874268	0.437134	+	0.899396i	$0.355994\pi$
$504$	22.3885	0.997262
$505$	28.0044	1.24618
$506$	−15.7481	−0.700089
$507$	−9.02171	−0.400668
$508$	−11.4886	−0.509723
$509$	−16.5529	−0.733694	−0.366847	−	0.930281i	$-0.619563\pi$
$509$	−16.5529	−0.733694	−0.366847	+	0.930281i	$0.619563\pi$
$510$	−5.05858	−0.223998
$511$	15.2338	0.673902
$512$	43.6098	1.92730
$513$	−19.3794	−0.855621
$514$	11.4554	0.505276
$515$	−24.9330	−1.09868
$516$	−3.61789	−0.159269
$517$	−2.42265	−0.106548
$518$	−10.5502	−0.463548
$519$	19.8664	0.872037
$520$	−58.5856	−2.56915
$521$	−18.9400	−0.829775	−0.414888	−	0.909873i	$-0.636179\pi$
$521$	−18.9400	−0.829775	−0.414888	+	0.909873i	$0.636179\pi$
$522$	−20.8943	−0.914521
$523$	−19.6565	−0.859517	−0.429759	−	0.902944i	$-0.641401\pi$
$523$	−19.6565	−0.859517	−0.429759	+	0.902944i	$0.641401\pi$
$524$	−60.2336	−2.63132
$525$	−0.693718	−0.0302764
$526$	−38.7347	−1.68891
$527$	7.93702	0.345742
$528$	4.12463	0.179502
$529$	17.5720	0.764000
$530$	−15.3010	−0.664631
$531$	−33.6968	−1.46232
$532$	−33.3793	−1.44718
$533$	−15.8533	−0.686682
$534$	−7.97749	−0.345220
$535$	−23.2849	−1.00669
$536$	−76.0283	−3.28392
$537$	7.88022	0.340057
$538$	5.22402	0.225224
$539$	3.29275	0.141829
$540$	−43.9762	−1.89244
$541$	16.4944	0.709149	0.354575	−	0.935028i	$-0.384626\pi$
$541$	16.4944	0.709149	0.354575	+	0.935028i	$0.384626\pi$
$542$	−50.1114	−2.15247
$543$	4.26835	0.183172
$544$	−1.14563	−0.0491184
$545$	−39.2908	−1.68303
$546$	−20.1947	−0.864251
$547$	−5.64959	−0.241559	−0.120780	−	0.992679i	$-0.538539\pi$
$547$	−5.64959	−0.241559	−0.120780	+	0.992679i	$0.538539\pi$
$548$	30.0143	1.28215
$549$	−21.0709	−0.899283
$550$	1.01261	0.0431777
$551$	16.0025	0.681731
$552$	−29.2680	−1.24573
$553$	5.98842	0.254653
$554$	−48.5397	−2.06225
$555$	4.53452	0.192480
$556$	−34.7430	−1.47343
$557$	−14.8480	−0.629129	−0.314564	−	0.949236i	$-0.601858\pi$
$557$	−14.8480	−0.629129	−0.314564	+	0.949236i	$0.601858\pi$
$558$	43.6842	1.84930
$559$	−4.82240	−0.203966
$560$	−20.9972	−0.887292
$561$	0.879695	0.0371408
$562$	−76.6244	−3.23221
$563$	45.5967	1.92167	0.960836	−	0.277118i	$-0.0893795\pi$
$563$	45.5967	1.92167	0.960836	+	0.277118i	$0.0893795\pi$
$564$	−8.76490	−0.369069
$565$	33.8985	1.42612
$566$	25.3226	1.06439
$567$	5.07174	0.212993
$568$	29.6624	1.24461
$569$	−2.81528	−0.118023	−0.0590113	−	0.998257i	$-0.518795\pi$
$569$	−2.81528	−0.118023	−0.0590113	+	0.998257i	$0.518795\pi$
$570$	21.3234	0.893138
$571$	−27.2558	−1.14062	−0.570310	−	0.821430i	$-0.693177\pi$
$571$	−27.2558	−1.14062	−0.570310	+	0.821430i	$0.693177\pi$
$572$	19.8329	0.829256
$573$	18.7063	0.781468
$574$	−15.6494	−0.653194
$575$	−2.60879	−0.108794
$576$	14.5700	0.607085
$577$	−9.83680	−0.409511	−0.204756	−	0.978813i	$-0.565640\pi$
$577$	−9.83680	−0.409511	−0.204756	+	0.978813i	$0.565640\pi$
$578$	−2.47238	−0.102838
$579$	−0.0923410	−0.00383756
$580$	36.3134	1.50783
$581$	−0.239515	−0.00993677
$582$	−29.7803	−1.23443
$583$	2.66086	0.110202
$584$	−41.3264	−1.71010
$585$	−24.9687	−1.03233
$586$	21.6398	0.893932
$587$	14.7163	0.607406	0.303703	−	0.952767i	$-0.401777\pi$
$587$	14.7163	0.607406	0.303703	+	0.952767i	$0.401777\pi$
$588$	11.9128	0.491277
$589$	−33.4568	−1.37856
$590$	87.0429	3.58350
$591$	−18.6656	−0.767801
$592$	10.3913	0.427081
$593$	−37.3870	−1.53530	−0.767650	−	0.640870i	$-0.778574\pi$
$593$	−37.3870	−1.53530	−0.767650	+	0.640870i	$0.778574\pi$
$594$	11.3665	0.466375
$595$	−4.47824	−0.183590
$596$	−10.6122	−0.434691
$597$	0.888445	0.0363616
$598$	−75.9437	−3.10557
$599$	−1.18108	−0.0482575	−0.0241287	−	0.999709i	$-0.507681\pi$
$599$	−1.18108	−0.0482575	−0.0241287	+	0.999709i	$0.507681\pi$
$600$	1.88193	0.0768296
$601$	15.5749	0.635311	0.317656	−	0.948206i	$-0.397104\pi$
$601$	15.5749	0.635311	0.317656	+	0.948206i	$0.397104\pi$
$602$	−4.76038	−0.194018
$603$	−32.4026	−1.31954
$604$	72.0092	2.93001
$605$	−2.32585	−0.0945592
$606$	−26.1874	−1.06379
$607$	24.6929	1.00225	0.501127	−	0.865374i	$-0.332919\pi$
$607$	24.6929	1.00225	0.501127	+	0.865374i	$0.332919\pi$
$608$	4.82916	0.195848
$609$	6.43013	0.260562
$610$	54.4287	2.20375
$611$	−11.6830	−0.472643
$612$	−9.15536	−0.370084
$613$	−47.9599	−1.93708	−0.968541	−	0.248855i	$-0.919946\pi$
$613$	−47.9599	−1.93708	−0.968541	+	0.248855i	$0.919946\pi$
$614$	−29.1281	−1.17551
$615$	6.72621	0.271227
$616$	10.0571	0.405212
$617$	−13.2916	−0.535099	−0.267549	−	0.963544i	$-0.586214\pi$
$617$	−13.2916	−0.535099	−0.267549	+	0.963544i	$0.586214\pi$
$618$	23.3153	0.937877
$619$	17.3840	0.698722	0.349361	−	0.936988i	$-0.386399\pi$
$619$	17.3840	0.698722	0.349361	+	0.936988i	$0.386399\pi$
$620$	−75.9211	−3.04906
$621$	−29.2837	−1.17511
$622$	−51.9336	−2.08235
$623$	−7.06228	−0.282944
$624$	19.8906	0.796262
$625$	−26.8801	−1.07520
$626$	37.2065	1.48707
$627$	−3.70817	−0.148090
$628$	2.41800	0.0964887
$629$	2.21625	0.0883676
$630$	−24.6476	−0.981983
$631$	−17.1739	−0.683683	−0.341841	−	0.939758i	$-0.611051\pi$
$631$	−17.1739	−0.683683	−0.341841	+	0.939758i	$0.611051\pi$
$632$	−16.2455	−0.646211
$633$	−7.37550	−0.293150
$634$	−30.9981	−1.23109
$635$	6.49716	0.257832
$636$	9.62671	0.381724
$637$	15.8789	0.629147
$638$	−9.38592	−0.371592
$639$	12.6419	0.500104
$640$	−42.9653	−1.69835
$641$	20.4290	0.806898	0.403449	−	0.915002i	$-0.367811\pi$
$641$	20.4290	0.806898	0.403449	+	0.915002i	$0.367811\pi$
$642$	21.7741	0.859355
$643$	41.3083	1.62904	0.814520	−	0.580135i	$-0.197000\pi$
$643$	41.3083	1.62904	0.814520	+	0.580135i	$0.197000\pi$
$644$	−50.4386	−1.98756
$645$	2.04604	0.0805626
$646$	10.4218	0.410040
$647$	30.7706	1.20972	0.604859	−	0.796333i	$-0.293230\pi$
$647$	30.7706	1.20972	0.604859	+	0.796333i	$0.293230\pi$
$648$	−13.7587	−0.540494
$649$	−15.1369	−0.594175
$650$	4.88319	0.191534
$651$	−13.4436	−0.526896
$652$	65.4159	2.56189
$653$	−29.6311	−1.15955	−0.579777	−	0.814775i	$-0.696860\pi$
$653$	−29.6311	−1.15955	−0.579777	+	0.814775i	$0.696860\pi$
$654$	36.7415	1.43671
$655$	34.0640	1.33099
$656$	15.4138	0.601808
$657$	−17.6130	−0.687148
$658$	−11.5327	−0.449593
$659$	−9.52150	−0.370905	−0.185452	−	0.982653i	$-0.559375\pi$
$659$	−9.52150	−0.370905	−0.185452	+	0.982653i	$0.559375\pi$
$660$	−8.41467	−0.327541
$661$	−32.8213	−1.27660	−0.638300	−	0.769787i	$-0.720362\pi$
$661$	−32.8213	−1.27660	−0.638300	+	0.769787i	$0.720362\pi$
$662$	−15.7793	−0.613278
$663$	4.24224	0.164755
$664$	0.649762	0.0252156
$665$	18.8771	0.732021
$666$	12.1979	0.472659
$667$	24.1810	0.936293
$668$	−1.58904	−0.0614818
$669$	−10.6059	−0.410049
$670$	83.6999	3.23361
$671$	−9.46522	−0.365401
$672$	1.94045	0.0748544
$673$	34.9681	1.34792	0.673960	−	0.738768i	$-0.264592\pi$
$673$	34.9681	1.34792	0.673960	+	0.738768i	$0.264592\pi$
$674$	46.1137	1.77623
$675$	1.88295	0.0724747
$676$	42.1775	1.62221
$677$	16.3441	0.628153	0.314077	−	0.949398i	$-0.398305\pi$
$677$	16.3441	0.628153	0.314077	+	0.949398i	$0.398305\pi$
$678$	−31.6991	−1.21740
$679$	−26.3637	−1.01175
$680$	12.1487	0.465880
$681$	−2.42867	−0.0930668
$682$	19.6233	0.751416
$683$	−5.48141	−0.209740	−0.104870	−	0.994486i	$-0.533443\pi$
$683$	−5.48141	−0.209740	−0.104870	+	0.994486i	$0.533443\pi$
$684$	38.5925	1.47562
$685$	−16.9741	−0.648546
$686$	48.9974	1.87073
$687$	−3.41216	−0.130182
$688$	4.68871	0.178755
$689$	12.8317	0.488850
$690$	32.2212	1.22664
$691$	18.5963	0.707436	0.353718	−	0.935352i	$-0.384917\pi$
$691$	18.5963	0.707436	0.353718	+	0.935352i	$0.384917\pi$
$692$	−92.8774	−3.53067
$693$	4.28625	0.162821
$694$	−57.8738	−2.19686
$695$	19.6483	0.745302
$696$	−17.4438	−0.661205
$697$	3.28743	0.124520
$698$	33.4734	1.26699
$699$	16.1642	0.611386
$700$	3.24321	0.122582
$701$	−20.1014	−0.759218	−0.379609	−	0.925147i	$-0.623941\pi$
$701$	−20.1014	−0.759218	−0.379609	+	0.925147i	$0.623941\pi$
$702$	54.8140	2.06882
$703$	−9.34212	−0.352345
$704$	6.54499	0.246673
$705$	4.95683	0.186685
$706$	37.7614	1.42117
$707$	−23.1831	−0.871890
$708$	−54.7637	−2.05815
$709$	−45.3423	−1.70287	−0.851433	−	0.524464i	$-0.824266\pi$
$709$	−45.3423	−1.70287	−0.851433	+	0.524464i	$0.824266\pi$
$710$	−32.6555	−1.22554
$711$	−6.92369	−0.259659
$712$	19.1587	0.718002
$713$	−50.5558	−1.89333
$714$	4.18768	0.156720
$715$	−11.2162	−0.419461
$716$	−36.8409	−1.37681
$717$	16.3536	0.610736
$718$	56.2504	2.09925
$719$	−51.1045	−1.90588	−0.952938	−	0.303165i	$-0.901957\pi$
$719$	−51.1045	−1.90588	−0.952938	+	0.303165i	$0.901957\pi$
$720$	24.2765	0.904732
$721$	20.6404	0.768689
$722$	3.04436	0.113299
$723$	23.3937	0.870021
$724$	−19.9550	−0.741621
$725$	−1.55484	−0.0577454
$726$	2.17494	0.0807197
$727$	35.7737	1.32677	0.663386	−	0.748277i	$-0.269119\pi$
$727$	35.7737	1.32677	0.663386	+	0.748277i	$0.269119\pi$
$728$	48.4993	1.79750
$729$	6.26910	0.232189
$730$	45.4965	1.68390
$731$	1.00000	0.0369863
$732$	−34.2442	−1.26570
$733$	−22.4995	−0.831040	−0.415520	−	0.909584i	$-0.636400\pi$
$733$	−22.4995	−0.831040	−0.415520	+	0.909584i	$0.636400\pi$
$734$	2.17952	0.0804476
$735$	−6.73709	−0.248501
$736$	7.29722	0.268979
$737$	−14.5555	−0.536160
$738$	18.0936	0.666033
$739$	−3.80382	−0.139926	−0.0699628	−	0.997550i	$-0.522288\pi$
$739$	−3.80382	−0.139926	−0.0699628	+	0.997550i	$0.522288\pi$
$740$	−21.1994	−0.779305
$741$	−17.8823	−0.656921
$742$	12.6667	0.465009
$743$	−19.4553	−0.713746	−0.356873	−	0.934153i	$-0.616157\pi$
$743$	−19.4553	−0.713746	−0.356873	+	0.934153i	$0.616157\pi$
$744$	36.4701	1.33706
$745$	6.00152	0.219879
$746$	3.30226	0.120904
$747$	0.276923	0.0101321
$748$	−4.11267	−0.150374
$749$	19.2761	0.704332
$750$	23.2211	0.847914
$751$	14.6071	0.533021	0.266511	−	0.963832i	$-0.414129\pi$
$751$	14.6071	0.533021	0.266511	+	0.963832i	$0.414129\pi$
$752$	11.3591	0.414224
$753$	1.34139	0.0488830
$754$	−45.2626	−1.64837
$755$	−40.7235	−1.48208
$756$	36.4051	1.32404
$757$	15.1460	0.550492	0.275246	−	0.961374i	$-0.411241\pi$
$757$	15.1460	0.550492	0.275246	+	0.961374i	$0.411241\pi$
$758$	18.5901	0.675224
$759$	−5.60332	−0.203388
$760$	−51.2101	−1.85758
$761$	−46.6292	−1.69031	−0.845154	−	0.534523i	$-0.820491\pi$
$761$	−46.6292	−1.69031	−0.845154	+	0.534523i	$0.820491\pi$
$762$	−6.07561	−0.220096
$763$	32.5263	1.17753
$764$	−87.4541	−3.16398
$765$	5.17765	0.187198
$766$	−64.9525	−2.34683
$767$	−72.9961	−2.63574
$768$	28.6624	1.03427
$769$	29.0299	1.04685	0.523423	−	0.852073i	$-0.324655\pi$
$769$	29.0299	1.04685	0.523423	+	0.852073i	$0.324655\pi$
$770$	−11.0719	−0.399004
$771$	4.07593	0.146791
$772$	0.431704	0.0155374
$773$	−16.8310	−0.605369	−0.302685	−	0.953091i	$-0.597883\pi$
$773$	−16.8310	−0.605369	−0.302685	+	0.953091i	$0.597883\pi$
$774$	5.50386	0.197832
$775$	3.25074	0.116770
$776$	71.5201	2.56742
$777$	−3.75385	−0.134668
$778$	24.3554	0.873183
$779$	−13.8575	−0.496495
$780$	−40.5789	−1.45296
$781$	5.67883	0.203205
$782$	15.7481	0.563152
$783$	−17.4532	−0.623726
$784$	−15.4387	−0.551384
$785$	−1.36746	−0.0488066
$786$	−31.8539	−1.13619
$787$	−19.2321	−0.685551	−0.342775	−	0.939417i	$-0.611367\pi$
$787$	−19.2321	−0.685551	−0.342775	+	0.939417i	$0.611367\pi$
$788$	87.2637	3.10864
$789$	−13.7821	−0.490657
$790$	17.8847	0.636311
$791$	−28.0624	−0.997786
$792$	−11.6278	−0.413177
$793$	−45.6451	−1.62090
$794$	67.6337	2.40023
$795$	−5.44422	−0.193087
$796$	−4.15357	−0.147220
$797$	6.19905	0.219582	0.109791	−	0.993955i	$-0.464982\pi$
$797$	6.19905	0.219582	0.109791	+	0.993955i	$0.464982\pi$
$798$	−17.6523	−0.624884
$799$	2.42265	0.0857072
$800$	−0.469212	−0.0165891
$801$	8.16527	0.288506
$802$	59.7038	2.10822
$803$	−7.91191	−0.279205
$804$	−52.6604	−1.85719
$805$	28.5247	1.00536
$806$	94.6315	3.33325
$807$	1.85875	0.0654312
$808$	62.8916	2.21252
$809$	−33.9485	−1.19357	−0.596783	−	0.802403i	$-0.703555\pi$
$809$	−33.9485	−1.19357	−0.596783	+	0.802403i	$0.703555\pi$
$810$	15.1470	0.532213
$811$	−45.7766	−1.60743	−0.803717	−	0.595012i	$-0.797147\pi$
$811$	−45.7766	−1.60743	−0.803717	+	0.595012i	$0.797147\pi$
$812$	−30.0615	−1.05495
$813$	−17.8301	−0.625328
$814$	5.47941	0.192053
$815$	−36.9948	−1.29587
$816$	−4.12463	−0.144391
$817$	−4.21529	−0.147474
$818$	−83.0972	−2.90543
$819$	20.6700	0.722268
$820$	−31.4457	−1.09813
$821$	9.55209	0.333370	0.166685	−	0.986010i	$-0.446694\pi$
$821$	9.55209	0.333370	0.166685	+	0.986010i	$0.446694\pi$
$822$	15.8728	0.553626
$823$	−42.3357	−1.47573	−0.737865	−	0.674949i	$-0.764166\pi$
$823$	−42.3357	−1.47573	−0.737865	+	0.674949i	$0.764166\pi$
$824$	−55.9937	−1.95063
$825$	0.360294	0.0125438
$826$	−72.0573	−2.50719
$827$	−30.6193	−1.06474	−0.532369	−	0.846513i	$-0.678698\pi$
$827$	−30.6193	−1.06474	−0.532369	+	0.846513i	$0.678698\pi$
$828$	58.3161	2.02663
$829$	−22.9937	−0.798605	−0.399303	−	0.916819i	$-0.630748\pi$
$829$	−22.9937	−0.798605	−0.399303	+	0.916819i	$0.630748\pi$
$830$	−0.715326	−0.0248293
$831$	−17.2709	−0.599119
$832$	31.5625	1.09423
$833$	−3.29275	−0.114087
$834$	−18.3735	−0.636221
$835$	0.898654	0.0310992
$836$	17.3361	0.599581
$837$	36.4897	1.26127
$838$	−82.8993	−2.86371
$839$	32.3553	1.11703	0.558515	−	0.829495i	$-0.311371\pi$
$839$	32.3553	1.11703	0.558515	+	0.829495i	$0.311371\pi$
$840$	−20.5772	−0.709981
$841$	−14.5880	−0.503036
$842$	−95.3709	−3.28670
$843$	−27.2636	−0.939010
$844$	34.4813	1.18689
$845$	−23.8527	−0.820559
$846$	13.3339	0.458430
$847$	1.92542	0.0661583
$848$	−12.4760	−0.428428
$849$	9.00999	0.309222
$850$	−1.01261	−0.0347321
$851$	−14.1166	−0.483912
$852$	20.5454	0.703875
$853$	−19.6699	−0.673485	−0.336743	−	0.941597i	$-0.609325\pi$
$853$	−19.6699	−0.673485	−0.336743	+	0.941597i	$0.609325\pi$
$854$	−45.0580	−1.54185
$855$	−21.8253	−0.746410
$856$	−52.2925	−1.78732
$857$	8.60350	0.293890	0.146945	−	0.989145i	$-0.453056\pi$
$857$	8.60350	0.293890	0.146945	+	0.989145i	$0.453056\pi$
$858$	10.4884	0.358069
$859$	−9.56397	−0.326318	−0.163159	−	0.986600i	$-0.552168\pi$
$859$	−9.56397	−0.326318	−0.163159	+	0.986600i	$0.552168\pi$
$860$	−9.56544	−0.326179
$861$	−5.56820	−0.189764
$862$	8.35673	0.284632
$863$	5.33449	0.181588	0.0907940	−	0.995870i	$-0.471060\pi$
$863$	5.33449	0.181588	0.0907940	+	0.995870i	$0.471060\pi$
$864$	−5.26692	−0.179184
$865$	52.5252	1.78591
$866$	−21.1586	−0.718998
$867$	−0.879695	−0.0298760
$868$	62.8503	2.13328
$869$	−3.11018	−0.105506
$870$	19.2039	0.651075
$871$	−70.1926	−2.37838
$872$	−88.2381	−2.98812
$873$	30.4813	1.03163
$874$	−66.3829	−2.24543
$875$	20.5571	0.694955
$876$	−28.6244	−0.967130
$877$	15.4148	0.520521	0.260260	−	0.965538i	$-0.416192\pi$
$877$	15.4148	0.520521	0.260260	+	0.965538i	$0.416192\pi$
$878$	66.5467	2.24584
$879$	7.69964	0.259702
$880$	10.9052	0.367615
$881$	32.0065	1.07833	0.539164	−	0.842201i	$-0.318740\pi$
$881$	32.0065	1.07833	0.539164	+	0.842201i	$0.318740\pi$
$882$	−18.1228	−0.610227
$883$	42.0395	1.41474	0.707372	−	0.706842i	$-0.249881\pi$
$883$	42.0395	1.41474	0.707372	+	0.706842i	$0.249881\pi$
$884$	−19.8329	−0.667053
$885$	30.9706	1.04107
$886$	−7.03487	−0.236341
$887$	13.6350	0.457817	0.228909	−	0.973448i	$-0.426484\pi$
$887$	13.6350	0.457817	0.228909	+	0.973448i	$0.426484\pi$
$888$	10.1835	0.341736
$889$	−5.37859	−0.180392
$890$	−21.0919	−0.707002
$891$	−2.63409	−0.0882455
$892$	49.5839	1.66019
$893$	−10.2122	−0.341737
$894$	−5.61213	−0.187698
$895$	20.8347	0.696428
$896$	35.5682	1.18825
$897$	−27.0214	−0.902219
$898$	−11.9448	−0.398605
$899$	−30.1314	−1.00494
$900$	−3.74974	−0.124991
$901$	−2.66086	−0.0886461
$902$	8.12778	0.270626
$903$	−1.69378	−0.0563656
$904$	76.1284	2.53199
$905$	11.2852	0.375132
$906$	38.0813	1.26517
$907$	11.6591	0.387135	0.193568	−	0.981087i	$-0.437994\pi$
$907$	11.6591	0.387135	0.193568	+	0.981087i	$0.437994\pi$
$908$	11.3543	0.376805
$909$	26.8039	0.889028
$910$	−53.3931	−1.76997
$911$	13.4950	0.447109	0.223555	−	0.974691i	$-0.428234\pi$
$911$	13.4950	0.447109	0.223555	+	0.974691i	$0.428234\pi$
$912$	17.3865	0.575725
$913$	0.124396	0.00411691
$914$	−18.3249	−0.606134
$915$	19.3662	0.640227
$916$	15.9522	0.527076
$917$	−28.1995	−0.931228
$918$	−11.3665	−0.375152
$919$	−56.1596	−1.85253	−0.926267	−	0.376868i	$-0.877001\pi$
$919$	−56.1596	−1.85253	−0.926267	+	0.376868i	$0.877001\pi$
$920$	−77.3823	−2.55122
$921$	−10.3640	−0.341506
$922$	86.2733	2.84126
$923$	27.3856	0.901407
$924$	6.96597	0.229164
$925$	0.907702	0.0298451
$926$	−4.03210	−0.132503
$927$	−23.8641	−0.783799
$928$	4.34916	0.142768
$929$	−29.9165	−0.981529	−0.490764	−	0.871292i	$-0.663282\pi$
$929$	−29.9165	−0.981529	−0.490764	+	0.871292i	$0.663282\pi$
$930$	−40.1501	−1.31657
$931$	13.8799	0.454895
$932$	−75.5694	−2.47536
$933$	−18.4784	−0.604957
$934$	−100.146	−3.27686
$935$	2.32585	0.0760634
$936$	−56.0740	−1.83284
$937$	−57.7875	−1.88784	−0.943918	−	0.330181i	$-0.892890\pi$
$937$	−57.7875	−1.88784	−0.943918	+	0.330181i	$0.892890\pi$
$938$	−69.2899	−2.26239
$939$	13.2384	0.432019
$940$	−23.1737	−0.755844
$941$	−24.5572	−0.800542	−0.400271	−	0.916397i	$-0.631084\pi$
$941$	−24.5572	−0.800542	−0.400271	+	0.916397i	$0.631084\pi$
$942$	1.27873	0.0416634
$943$	−20.9397	−0.681890
$944$	70.9725	2.30996
$945$	−20.5883	−0.669737
$946$	2.47238	0.0803840
$947$	16.2524	0.528132	0.264066	−	0.964505i	$-0.414936\pi$
$947$	16.2524	0.528132	0.264066	+	0.964505i	$0.414936\pi$
$948$	−11.2523	−0.365458
$949$	−38.1543	−1.23854
$950$	4.26843	0.138486
$951$	−11.0294	−0.357652
$952$	−10.0571	−0.325953
$953$	54.5931	1.76844	0.884222	−	0.467066i	$-0.154689\pi$
$953$	54.5931	1.76844	0.884222	+	0.467066i	$0.154689\pi$
$954$	−14.6450	−0.474149
$955$	49.4581	1.60043
$956$	−76.4548	−2.47272
$957$	−3.33959	−0.107954
$958$	57.2950	1.85112
$959$	14.0518	0.453755
$960$	−13.3913	−0.432202
$961$	31.9963	1.03214
$962$	26.4239	0.851940
$963$	−22.2866	−0.718176
$964$	−109.368	−3.52251
$965$	−0.244143	−0.00785923
$966$	−26.6739	−0.858219
$967$	−49.1662	−1.58108	−0.790539	−	0.612412i	$-0.790200\pi$
$967$	−49.1662	−1.58108	−0.790539	+	0.612412i	$0.790200\pi$
$968$	−5.22332	−0.167884
$969$	3.70817	0.119124
$970$	−78.7368	−2.52809
$971$	−22.3824	−0.718286	−0.359143	−	0.933282i	$-0.616931\pi$
$971$	−22.3824	−0.718286	−0.359143	+	0.933282i	$0.616931\pi$
$972$	−66.2527	−2.12506
$973$	−16.2656	−0.521450
$974$	33.3629	1.06902
$975$	1.73748	0.0556439
$976$	44.3797	1.42056
$977$	17.3735	0.555827	0.277914	−	0.960606i	$-0.410357\pi$
$977$	17.3735	0.555827	0.277914	+	0.960606i	$0.410357\pi$
$978$	34.5945	1.10621
$979$	3.66791	0.117227
$980$	31.4966	1.00612
$981$	−37.6063	−1.20068
$982$	−71.4595	−2.28036
$983$	44.3865	1.41571	0.707855	−	0.706357i	$-0.249663\pi$
$983$	44.3865	1.41571	0.707855	+	0.706357i	$0.249663\pi$
$984$	15.1055	0.481547
$985$	−49.3505	−1.57244
$986$	9.38592	0.298909
$987$	−4.10345	−0.130614
$988$	83.6015	2.65972
$989$	−6.36962	−0.202542
$990$	12.8011	0.406847
$991$	36.0813	1.14616	0.573080	−	0.819500i	$-0.305749\pi$
$991$	36.0813	1.14616	0.573080	+	0.819500i	$0.305749\pi$
$992$	−9.09288	−0.288699
$993$	−5.61440	−0.178168
$994$	27.0334	0.857447
$995$	2.34898	0.0744677
$996$	0.450053	0.0142605
$997$	5.97118	0.189109	0.0945546	−	0.995520i	$-0.469857\pi$
$997$	5.97118	0.189109	0.0945546	+	0.995520i	$0.469857\pi$
$998$	−63.1858	−2.00011
$999$	10.1890	0.322365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.7	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.7	✓	69	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47238 q^{2} -0.879695 q^{3} +4.11267 q^{4} -2.32585 q^{5} +2.17494 q^{6} +1.92542 q^{7} -5.22332 q^{8} -2.22614 q^{9} +O(q^{10})\)	\(q-2.47238 q^{2} -0.879695 q^{3} +4.11267 q^{4} -2.32585 q^{5} +2.17494 q^{6} +1.92542 q^{7} -5.22332 q^{8} -2.22614 q^{9} +5.75038 q^{10} -1.00000 q^{11} -3.61789 q^{12} -4.82240 q^{13} -4.76038 q^{14} +2.04604 q^{15} +4.68871 q^{16} +1.00000 q^{17} +5.50386 q^{18} -4.21529 q^{19} -9.56544 q^{20} -1.69378 q^{21} +2.47238 q^{22} -6.36962 q^{23} +4.59493 q^{24} +0.409567 q^{25} +11.9228 q^{26} +4.59741 q^{27} +7.91862 q^{28} -3.79631 q^{29} -5.05858 q^{30} +7.93702 q^{31} -1.14563 q^{32} +0.879695 q^{33} -2.47238 q^{34} -4.47824 q^{35} -9.15536 q^{36} +2.21625 q^{37} +10.4218 q^{38} +4.24224 q^{39} +12.1487 q^{40} +3.28743 q^{41} +4.18768 q^{42} +1.00000 q^{43} -4.11267 q^{44} +5.17765 q^{45} +15.7481 q^{46} +2.42265 q^{47} -4.12463 q^{48} -3.29275 q^{49} -1.01261 q^{50} -0.879695 q^{51} -19.8329 q^{52} -2.66086 q^{53} -11.3665 q^{54} +2.32585 q^{55} -10.0571 q^{56} +3.70817 q^{57} +9.38592 q^{58} +15.1369 q^{59} +8.41467 q^{60} +9.46522 q^{61} -19.6233 q^{62} -4.28625 q^{63} -6.54499 q^{64} +11.2162 q^{65} -2.17494 q^{66} +14.5555 q^{67} +4.11267 q^{68} +5.60332 q^{69} +11.0719 q^{70} -5.67883 q^{71} +11.6278 q^{72} +7.91191 q^{73} -5.47941 q^{74} -0.360294 q^{75} -17.3361 q^{76} -1.92542 q^{77} -10.4884 q^{78} +3.11018 q^{79} -10.9052 q^{80} +2.63409 q^{81} -8.12778 q^{82} -0.124396 q^{83} -6.96597 q^{84} -2.32585 q^{85} -2.47238 q^{86} +3.33959 q^{87} +5.22332 q^{88} -3.66791 q^{89} -12.8011 q^{90} -9.28515 q^{91} -26.1961 q^{92} -6.98216 q^{93} -5.98972 q^{94} +9.80412 q^{95} +1.00780 q^{96} -13.6924 q^{97} +8.14093 q^{98} +2.22614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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