LMFDB - Embedded newform 4011.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42203 q^{2} +1.00000 q^{3} +3.86625 q^{4} +1.50568 q^{5} -2.42203 q^{6} +1.00000 q^{7} -4.52011 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.42203 q^{2} +1.00000 q^{3} +3.86625 q^{4} +1.50568 q^{5} -2.42203 q^{6} +1.00000 q^{7} -4.52011 q^{8} +1.00000 q^{9} -3.64681 q^{10} -2.29749 q^{11} +3.86625 q^{12} -3.95871 q^{13} -2.42203 q^{14} +1.50568 q^{15} +3.21537 q^{16} +6.76598 q^{17} -2.42203 q^{18} +6.60199 q^{19} +5.82134 q^{20} +1.00000 q^{21} +5.56460 q^{22} +8.27590 q^{23} -4.52011 q^{24} -2.73292 q^{25} +9.58814 q^{26} +1.00000 q^{27} +3.86625 q^{28} -0.934325 q^{29} -3.64681 q^{30} +4.90812 q^{31} +1.25248 q^{32} -2.29749 q^{33} -16.3874 q^{34} +1.50568 q^{35} +3.86625 q^{36} +0.901092 q^{37} -15.9902 q^{38} -3.95871 q^{39} -6.80585 q^{40} -7.22158 q^{41} -2.42203 q^{42} -11.5710 q^{43} -8.88267 q^{44} +1.50568 q^{45} -20.0445 q^{46} -4.21712 q^{47} +3.21537 q^{48} +1.00000 q^{49} +6.61923 q^{50} +6.76598 q^{51} -15.3054 q^{52} +10.0585 q^{53} -2.42203 q^{54} -3.45929 q^{55} -4.52011 q^{56} +6.60199 q^{57} +2.26297 q^{58} +7.86728 q^{59} +5.82134 q^{60} +0.887307 q^{61} -11.8876 q^{62} +1.00000 q^{63} -9.46431 q^{64} -5.96056 q^{65} +5.56460 q^{66} -7.42719 q^{67} +26.1590 q^{68} +8.27590 q^{69} -3.64681 q^{70} +2.31105 q^{71} -4.52011 q^{72} +4.70238 q^{73} -2.18247 q^{74} -2.73292 q^{75} +25.5249 q^{76} -2.29749 q^{77} +9.58814 q^{78} +11.8751 q^{79} +4.84133 q^{80} +1.00000 q^{81} +17.4909 q^{82} +12.8321 q^{83} +3.86625 q^{84} +10.1874 q^{85} +28.0253 q^{86} -0.934325 q^{87} +10.3849 q^{88} +2.55646 q^{89} -3.64681 q^{90} -3.95871 q^{91} +31.9967 q^{92} +4.90812 q^{93} +10.2140 q^{94} +9.94050 q^{95} +1.25248 q^{96} -9.78138 q^{97} -2.42203 q^{98} -2.29749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * 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 $

$2$	−2.42203	−1.71264	−0.856318	−	0.516449i	$-0.827254\pi$
$2$	−2.42203	−1.71264	−0.856318	+	0.516449i	$0.827254\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.86625	1.93312
$5$	1.50568	0.673361	0.336681	−	0.941619i	$-0.390696\pi$
$5$	1.50568	0.673361	0.336681	+	0.941619i	$0.390696\pi$
$6$	−2.42203	−0.988791
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.52011	−1.59810
$9$	1.00000	0.333333
$10$	−3.64681	−1.15322
$11$	−2.29749	−0.692720	−0.346360	−	0.938102i	$-0.612582\pi$
$11$	−2.29749	−0.692720	−0.346360	+	0.938102i	$0.612582\pi$
$12$	3.86625	1.11609
$13$	−3.95871	−1.09795	−0.548975	−	0.835839i	$-0.684982\pi$
$13$	−3.95871	−1.09795	−0.548975	+	0.835839i	$0.684982\pi$
$14$	−2.42203	−0.647316
$15$	1.50568	0.388765
$16$	3.21537	0.803844
$17$	6.76598	1.64099	0.820496	−	0.571652i	$-0.193697\pi$
$17$	6.76598	1.64099	0.820496	+	0.571652i	$0.193697\pi$
$18$	−2.42203	−0.570879
$19$	6.60199	1.51460	0.757300	−	0.653067i	$-0.226518\pi$
$19$	6.60199	1.51460	0.757300	+	0.653067i	$0.226518\pi$
$20$	5.82134	1.30169
$21$	1.00000	0.218218
$22$	5.56460	1.18638
$23$	8.27590	1.72565	0.862823	−	0.505507i	$-0.168694\pi$
$23$	8.27590	1.72565	0.862823	+	0.505507i	$0.168694\pi$
$24$	−4.52011	−0.922664
$25$	−2.73292	−0.546584
$26$	9.58814	1.88039
$27$	1.00000	0.192450
$28$	3.86625	0.730652
$29$	−0.934325	−0.173500	−0.0867499	−	0.996230i	$-0.527648\pi$
$29$	−0.934325	−0.173500	−0.0867499	+	0.996230i	$0.527648\pi$
$30$	−3.64681	−0.665814
$31$	4.90812	0.881525	0.440762	−	0.897624i	$-0.354708\pi$
$31$	4.90812	0.881525	0.440762	+	0.897624i	$0.354708\pi$
$32$	1.25248	0.221410
$33$	−2.29749	−0.399942
$34$	−16.3874	−2.81042
$35$	1.50568	0.254507
$36$	3.86625	0.644375
$37$	0.901092	0.148139	0.0740693	−	0.997253i	$-0.476401\pi$
$37$	0.901092	0.148139	0.0740693	+	0.997253i	$0.476401\pi$
$38$	−15.9902	−2.59396
$39$	−3.95871	−0.633901
$40$	−6.80585	−1.07610
$41$	−7.22158	−1.12782	−0.563910	−	0.825836i	$-0.690704\pi$
$41$	−7.22158	−1.12782	−0.563910	+	0.825836i	$0.690704\pi$
$42$	−2.42203	−0.373728
$43$	−11.5710	−1.76456	−0.882279	−	0.470728i	$-0.843991\pi$
$43$	−11.5710	−1.76456	−0.882279	+	0.470728i	$0.843991\pi$
$44$	−8.88267	−1.33911
$45$	1.50568	0.224454
$46$	−20.0445	−2.95540
$47$	−4.21712	−0.615131	−0.307565	−	0.951527i	$-0.599514\pi$
$47$	−4.21712	−0.615131	−0.307565	+	0.951527i	$0.599514\pi$
$48$	3.21537	0.464099
$49$	1.00000	0.142857
$50$	6.61923	0.936100
$51$	6.76598	0.947427
$52$	−15.3054	−2.12247
$53$	10.0585	1.38164	0.690818	−	0.723029i	$-0.257251\pi$
$53$	10.0585	1.38164	0.690818	+	0.723029i	$0.257251\pi$
$54$	−2.42203	−0.329597
$55$	−3.45929	−0.466451
$56$	−4.52011	−0.604026
$57$	6.60199	0.874455
$58$	2.26297	0.297142
$59$	7.86728	1.02423	0.512116	−	0.858916i	$-0.328862\pi$
$59$	7.86728	1.02423	0.512116	+	0.858916i	$0.328862\pi$
$60$	5.82134	0.751532
$61$	0.887307	0.113608	0.0568040	−	0.998385i	$-0.481909\pi$
$61$	0.887307	0.113608	0.0568040	+	0.998385i	$0.481909\pi$
$62$	−11.8876	−1.50973
$63$	1.00000	0.125988
$64$	−9.46431	−1.18304
$65$	−5.96056	−0.739317
$66$	5.56460	0.684955
$67$	−7.42719	−0.907375	−0.453688	−	0.891161i	$-0.649892\pi$
$67$	−7.42719	−0.907375	−0.453688	+	0.891161i	$0.649892\pi$
$68$	26.1590	3.17224
$69$	8.27590	0.996302
$70$	−3.64681	−0.435877
$71$	2.31105	0.274271	0.137136	−	0.990552i	$-0.456210\pi$
$71$	2.31105	0.274271	0.137136	+	0.990552i	$0.456210\pi$
$72$	−4.52011	−0.532701
$73$	4.70238	0.550372	0.275186	−	0.961391i	$-0.411261\pi$
$73$	4.70238	0.550372	0.275186	+	0.961391i	$0.411261\pi$
$74$	−2.18247	−0.253707
$75$	−2.73292	−0.315571
$76$	25.5249	2.92791
$77$	−2.29749	−0.261823
$78$	9.58814	1.08564
$79$	11.8751	1.33606	0.668028	−	0.744136i	$-0.267139\pi$
$79$	11.8751	1.33606	0.668028	+	0.744136i	$0.267139\pi$
$80$	4.84133	0.541277
$81$	1.00000	0.111111
$82$	17.4909	1.93155
$83$	12.8321	1.40851	0.704254	−	0.709948i	$-0.251282\pi$
$83$	12.8321	1.40851	0.704254	+	0.709948i	$0.251282\pi$
$84$	3.86625	0.421842
$85$	10.1874	1.10498
$86$	28.0253	3.02205
$87$	−0.934325	−0.100170
$88$	10.3849	1.10704
$89$	2.55646	0.270984	0.135492	−	0.990778i	$-0.456738\pi$
$89$	2.55646	0.270984	0.135492	+	0.990778i	$0.456738\pi$
$90$	−3.64681	−0.384408
$91$	−3.95871	−0.414986
$92$	31.9967	3.33589
$93$	4.90812	0.508948
$94$	10.2140	1.05350
$95$	9.94050	1.01987
$96$	1.25248	0.127831
$97$	−9.78138	−0.993149	−0.496575	−	0.867994i	$-0.665409\pi$
$97$	−9.78138	−0.993149	−0.496575	+	0.867994i	$0.665409\pi$
$98$	−2.42203	−0.244662
$99$	−2.29749	−0.230907
$100$	−10.5662	−1.05662
$101$	−5.55675	−0.552917	−0.276458	−	0.961026i	$-0.589161\pi$
$101$	−5.55675	−0.552917	−0.276458	+	0.961026i	$0.589161\pi$
$102$	−16.3874	−1.62260
$103$	−10.0408	−0.989347	−0.494674	−	0.869079i	$-0.664712\pi$
$103$	−10.0408	−0.989347	−0.494674	+	0.869079i	$0.664712\pi$
$104$	17.8938	1.75463
$105$	1.50568	0.146940
$106$	−24.3619	−2.36624
$107$	−7.81185	−0.755200	−0.377600	−	0.925969i	$-0.623251\pi$
$107$	−7.81185	−0.755200	−0.377600	+	0.925969i	$0.623251\pi$
$108$	3.86625	0.372030
$109$	−9.18047	−0.879329	−0.439665	−	0.898162i	$-0.644903\pi$
$109$	−9.18047	−0.879329	−0.439665	+	0.898162i	$0.644903\pi$
$110$	8.37852	0.798860
$111$	0.901092	0.0855278
$112$	3.21537	0.303824
$113$	15.2271	1.43245	0.716224	−	0.697870i	$-0.245869\pi$
$113$	15.2271	1.43245	0.716224	+	0.697870i	$0.245869\pi$
$114$	−15.9902	−1.49762
$115$	12.4609	1.16198
$116$	−3.61233	−0.335397
$117$	−3.95871	−0.365983
$118$	−19.0548	−1.75414
$119$	6.76598	0.620237
$120$	−6.80585	−0.621287
$121$	−5.72154	−0.520140
$122$	−2.14909	−0.194569
$123$	−7.22158	−0.651148
$124$	18.9760	1.70410
$125$	−11.6433	−1.04141
$126$	−2.42203	−0.215772
$127$	0.248562	0.0220563	0.0110281	−	0.999939i	$-0.496490\pi$
$127$	0.248562	0.0220563	0.0110281	+	0.999939i	$0.496490\pi$
$128$	20.4179	1.80470
$129$	−11.5710	−1.01877
$130$	14.4367	1.26618
$131$	−2.53084	−0.221121	−0.110560	−	0.993869i	$-0.535265\pi$
$131$	−2.53084	−0.221121	−0.110560	+	0.993869i	$0.535265\pi$
$132$	−8.88267	−0.773137
$133$	6.60199	0.572465
$134$	17.9889	1.55400
$135$	1.50568	0.129588
$136$	−30.5830	−2.62247
$137$	17.0146	1.45365	0.726826	−	0.686821i	$-0.240995\pi$
$137$	17.0146	1.45365	0.726826	+	0.686821i	$0.240995\pi$
$138$	−20.0445	−1.70630
$139$	18.6591	1.58264	0.791322	−	0.611399i	$-0.209393\pi$
$139$	18.6591	1.58264	0.791322	+	0.611399i	$0.209393\pi$
$140$	5.82134	0.491993
$141$	−4.21712	−0.355146
$142$	−5.59745	−0.469727
$143$	9.09511	0.760571
$144$	3.21537	0.267948
$145$	−1.40680	−0.116828
$146$	−11.3893	−0.942587
$147$	1.00000	0.0824786
$148$	3.48384	0.286370
$149$	17.9376	1.46951	0.734753	−	0.678335i	$-0.237298\pi$
$149$	17.9376	1.46951	0.734753	+	0.678335i	$0.237298\pi$
$150$	6.61923	0.540458
$151$	−6.02937	−0.490663	−0.245332	−	0.969439i	$-0.578897\pi$
$151$	−6.02937	−0.490663	−0.245332	+	0.969439i	$0.578897\pi$
$152$	−29.8418	−2.42049
$153$	6.76598	0.546997
$154$	5.56460	0.448408
$155$	7.39007	0.593585
$156$	−15.3054	−1.22541
$157$	6.84302	0.546133	0.273066	−	0.961995i	$-0.411962\pi$
$157$	6.84302	0.546133	0.273066	+	0.961995i	$0.411962\pi$
$158$	−28.7620	−2.28818
$159$	10.0585	0.797688
$160$	1.88584	0.149089
$161$	8.27590	0.652233
$162$	−2.42203	−0.190293
$163$	22.4360	1.75733	0.878663	−	0.477443i	$-0.158436\pi$
$163$	22.4360	1.75733	0.878663	+	0.477443i	$0.158436\pi$
$164$	−27.9204	−2.18022
$165$	−3.45929	−0.269305
$166$	−31.0798	−2.41226
$167$	−13.3217	−1.03086	−0.515431	−	0.856931i	$-0.672368\pi$
$167$	−13.3217	−1.03086	−0.515431	+	0.856931i	$0.672368\pi$
$168$	−4.52011	−0.348734
$169$	2.67141	0.205493
$170$	−24.6743	−1.89243
$171$	6.60199	0.504867
$172$	−44.7363	−3.41111
$173$	−21.8313	−1.65980	−0.829901	−	0.557911i	$-0.811603\pi$
$173$	−21.8313	−1.65980	−0.829901	+	0.557911i	$0.811603\pi$
$174$	2.26297	0.171555
$175$	−2.73292	−0.206589
$176$	−7.38729	−0.556838
$177$	7.86728	0.591341
$178$	−6.19183	−0.464097
$179$	−5.30716	−0.396676	−0.198338	−	0.980134i	$-0.563554\pi$
$179$	−5.30716	−0.396676	−0.198338	+	0.980134i	$0.563554\pi$
$180$	5.82134	0.433897
$181$	−11.0696	−0.822795	−0.411397	−	0.911456i	$-0.634959\pi$
$181$	−11.0696	−0.822795	−0.411397	+	0.911456i	$0.634959\pi$
$182$	9.58814	0.710720
$183$	0.887307	0.0655916
$184$	−37.4080	−2.75776
$185$	1.35676	0.0997508
$186$	−11.8876	−0.871644
$187$	−15.5448	−1.13675
$188$	−16.3044	−1.18912
$189$	1.00000	0.0727393
$190$	−24.0762	−1.74667
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−9.46431	−0.683027
$193$	−6.75705	−0.486383	−0.243192	−	0.969978i	$-0.578194\pi$
$193$	−6.75705	−0.486383	−0.243192	+	0.969978i	$0.578194\pi$
$194$	23.6908	1.70090
$195$	−5.96056	−0.426845
$196$	3.86625	0.276161
$197$	22.5867	1.60924	0.804620	−	0.593791i	$-0.202369\pi$
$197$	22.5867	1.60924	0.804620	+	0.593791i	$0.202369\pi$
$198$	5.56460	0.395459
$199$	8.40653	0.595923	0.297961	−	0.954578i	$-0.403693\pi$
$199$	8.40653	0.595923	0.297961	+	0.954578i	$0.403693\pi$
$200$	12.3531	0.873497
$201$	−7.42719	−0.523873
$202$	13.4586	0.946946
$203$	−0.934325	−0.0655768
$204$	26.1590	1.83149
$205$	−10.8734	−0.759431
$206$	24.3191	1.69439
$207$	8.27590	0.575215
$208$	−12.7287	−0.882579
$209$	−15.1680	−1.04919
$210$	−3.64681	−0.251654
$211$	17.4880	1.20393	0.601963	−	0.798524i	$-0.294386\pi$
$211$	17.4880	1.20393	0.601963	+	0.798524i	$0.294386\pi$
$212$	38.8885	2.67087
$213$	2.31105	0.158351
$214$	18.9206	1.29338
$215$	−17.4222	−1.18818
$216$	−4.52011	−0.307555
$217$	4.90812	0.333185
$218$	22.2354	1.50597
$219$	4.70238	0.317757
$220$	−13.3745	−0.901707
$221$	−26.7846	−1.80173
$222$	−2.18247	−0.146478
$223$	9.19635	0.615833	0.307917	−	0.951413i	$-0.400368\pi$
$223$	9.19635	0.615833	0.307917	+	0.951413i	$0.400368\pi$
$224$	1.25248	0.0836851
$225$	−2.73292	−0.182195
$226$	−36.8806	−2.45326
$227$	9.49722	0.630352	0.315176	−	0.949033i	$-0.397936\pi$
$227$	9.49722	0.630352	0.315176	+	0.949033i	$0.397936\pi$
$228$	25.5249	1.69043
$229$	−1.97384	−0.130435	−0.0652174	−	0.997871i	$-0.520774\pi$
$229$	−1.97384	−0.130435	−0.0652174	+	0.997871i	$0.520774\pi$
$230$	−30.1807	−1.99005
$231$	−2.29749	−0.151164
$232$	4.22326	0.277270
$233$	−8.23215	−0.539306	−0.269653	−	0.962958i	$-0.586909\pi$
$233$	−8.23215	−0.539306	−0.269653	+	0.962958i	$0.586909\pi$
$234$	9.58814	0.626796
$235$	−6.34965	−0.414205
$236$	30.4169	1.97997
$237$	11.8751	0.771372
$238$	−16.3874	−1.06224
$239$	1.35691	0.0877709	0.0438855	−	0.999037i	$-0.486026\pi$
$239$	1.35691	0.0877709	0.0438855	+	0.999037i	$0.486026\pi$
$240$	4.84133	0.312507
$241$	−11.2200	−0.722746	−0.361373	−	0.932421i	$-0.617692\pi$
$241$	−11.2200	−0.722746	−0.361373	+	0.932421i	$0.617692\pi$
$242$	13.8578	0.890810
$243$	1.00000	0.0641500
$244$	3.43055	0.219618
$245$	1.50568	0.0961945
$246$	17.4909	1.11518
$247$	−26.1354	−1.66295
$248$	−22.1853	−1.40877
$249$	12.8321	0.813203
$250$	28.2005	1.78356
$251$	29.7190	1.87585	0.937923	−	0.346844i	$-0.112747\pi$
$251$	29.7190	1.87585	0.937923	+	0.346844i	$0.112747\pi$
$252$	3.86625	0.243551
$253$	−19.0138	−1.19539
$254$	−0.602025	−0.0377744
$255$	10.1874	0.637961
$256$	−30.5242	−1.90776
$257$	−7.27439	−0.453764	−0.226882	−	0.973922i	$-0.572853\pi$
$257$	−7.27439	−0.453764	−0.226882	+	0.973922i	$0.572853\pi$
$258$	28.0253	1.74478
$259$	0.901092	0.0559911
$260$	−23.0450	−1.42919
$261$	−0.934325	−0.0578333
$262$	6.12978	0.378699
$263$	−1.90403	−0.117408	−0.0587039	−	0.998275i	$-0.518697\pi$
$263$	−1.90403	−0.117408	−0.0587039	+	0.998275i	$0.518697\pi$
$264$	10.3849	0.639148
$265$	15.1448	0.930340
$266$	−15.9902	−0.980425
$267$	2.55646	0.156453
$268$	−28.7153	−1.75407
$269$	8.88210	0.541551	0.270776	−	0.962642i	$-0.412720\pi$
$269$	8.88210	0.541551	0.270776	+	0.962642i	$0.412720\pi$
$270$	−3.64681	−0.221938
$271$	−21.8086	−1.32478	−0.662389	−	0.749160i	$-0.730457\pi$
$271$	−21.8086	−1.32478	−0.662389	+	0.749160i	$0.730457\pi$
$272$	21.7552	1.31910
$273$	−3.95871	−0.239592
$274$	−41.2098	−2.48958
$275$	6.27886	0.378630
$276$	31.9967	1.92597
$277$	6.28833	0.377829	0.188915	−	0.981994i	$-0.439503\pi$
$277$	6.28833	0.377829	0.188915	+	0.981994i	$0.439503\pi$
$278$	−45.1930	−2.71049
$279$	4.90812	0.293842
$280$	−6.80585	−0.406728
$281$	−0.227607	−0.0135779	−0.00678895	−	0.999977i	$-0.502161\pi$
$281$	−0.227607	−0.0135779	−0.00678895	+	0.999977i	$0.502161\pi$
$282$	10.2140	0.608236
$283$	−2.79415	−0.166095	−0.0830474	−	0.996546i	$-0.526465\pi$
$283$	−2.79415	−0.166095	−0.0830474	+	0.996546i	$0.526465\pi$
$284$	8.93510	0.530201
$285$	9.94050	0.588824
$286$	−22.0287	−1.30258
$287$	−7.22158	−0.426276
$288$	1.25248	0.0738033
$289$	28.7785	1.69285
$290$	3.40731	0.200084
$291$	−9.78138	−0.573395
$292$	18.1806	1.06394
$293$	17.6269	1.02978	0.514888	−	0.857258i	$-0.327834\pi$
$293$	17.6269	1.02978	0.514888	+	0.857258i	$0.327834\pi$
$294$	−2.42203	−0.141256
$295$	11.8456	0.689679
$296$	−4.07304	−0.236740
$297$	−2.29749	−0.133314
$298$	−43.4455	−2.51673
$299$	−32.7619	−1.89467
$300$	−10.5662	−0.610037
$301$	−11.5710	−0.666940
$302$	14.6033	0.840328
$303$	−5.55675	−0.319227
$304$	21.2279	1.21750
$305$	1.33600	0.0764993
$306$	−16.3874	−0.936807
$307$	15.4572	0.882191	0.441096	−	0.897460i	$-0.354590\pi$
$307$	15.4572	0.882191	0.441096	+	0.897460i	$0.354590\pi$
$308$	−8.88267	−0.506137
$309$	−10.0408	−0.571200
$310$	−17.8990	−1.01659
$311$	−6.88320	−0.390310	−0.195155	−	0.980772i	$-0.562521\pi$
$311$	−6.88320	−0.390310	−0.195155	+	0.980772i	$0.562521\pi$
$312$	17.8938	1.01304
$313$	2.10273	0.118853	0.0594265	−	0.998233i	$-0.481073\pi$
$313$	2.10273	0.118853	0.0594265	+	0.998233i	$0.481073\pi$
$314$	−16.5740	−0.935326
$315$	1.50568	0.0848356
$316$	45.9122	2.58276
$317$	−18.4185	−1.03449	−0.517243	−	0.855839i	$-0.673042\pi$
$317$	−18.4185	−1.03449	−0.517243	+	0.855839i	$0.673042\pi$
$318$	−24.3619	−1.36615
$319$	2.14660	0.120187
$320$	−14.2502	−0.796612
$321$	−7.81185	−0.436015
$322$	−20.0445	−1.11704
$323$	44.6690	2.48545
$324$	3.86625	0.214792
$325$	10.8189	0.600122
$326$	−54.3408	−3.00966
$327$	−9.18047	−0.507681
$328$	32.6423	1.80237
$329$	−4.21712	−0.232498
$330$	8.37852	0.461222
$331$	2.63914	0.145060	0.0725300	−	0.997366i	$-0.476893\pi$
$331$	2.63914	0.145060	0.0725300	+	0.997366i	$0.476893\pi$
$332$	49.6122	2.72282
$333$	0.901092	0.0493795
$334$	32.2655	1.76549
$335$	−11.1830	−0.610992
$336$	3.21537	0.175413
$337$	16.4792	0.897678	0.448839	−	0.893613i	$-0.351838\pi$
$337$	16.4792	0.897678	0.448839	+	0.893613i	$0.351838\pi$
$338$	−6.47024	−0.351934
$339$	15.2271	0.827025
$340$	39.3871	2.13606
$341$	−11.2764	−0.610649
$342$	−15.9902	−0.864653
$343$	1.00000	0.0539949
$344$	52.3021	2.81994
$345$	12.4609	0.670871
$346$	52.8761	2.84264
$347$	−30.0569	−1.61354	−0.806769	−	0.590867i	$-0.798786\pi$
$347$	−30.0569	−1.61354	−0.806769	+	0.590867i	$0.798786\pi$
$348$	−3.61233	−0.193641
$349$	26.5298	1.42011	0.710054	−	0.704148i	$-0.248671\pi$
$349$	26.5298	1.42011	0.710054	+	0.704148i	$0.248671\pi$
$350$	6.61923	0.353813
$351$	−3.95871	−0.211300
$352$	−2.87757	−0.153375
$353$	−2.00123	−0.106515	−0.0532574	−	0.998581i	$-0.516960\pi$
$353$	−2.00123	−0.106515	−0.0532574	+	0.998581i	$0.516960\pi$
$354$	−19.0548	−1.01275
$355$	3.47971	0.184684
$356$	9.88391	0.523846
$357$	6.76598	0.358094
$358$	12.8541	0.679361
$359$	24.2465	1.27968	0.639840	−	0.768508i	$-0.279000\pi$
$359$	24.2465	1.27968	0.639840	+	0.768508i	$0.279000\pi$
$360$	−6.80585	−0.358700
$361$	24.5863	1.29402
$362$	26.8109	1.40915
$363$	−5.72154	−0.300303
$364$	−15.3054	−0.802219
$365$	7.08029	0.370599
$366$	−2.14909	−0.112335
$367$	−14.0732	−0.734614	−0.367307	−	0.930100i	$-0.619720\pi$
$367$	−14.0732	−0.734614	−0.367307	+	0.930100i	$0.619720\pi$
$368$	26.6101	1.38715
$369$	−7.22158	−0.375940
$370$	−3.28611	−0.170837
$371$	10.0585	0.522209
$372$	18.9760	0.983860
$373$	−30.9525	−1.60266	−0.801329	−	0.598224i	$-0.795873\pi$
$373$	−30.9525	−1.60266	−0.801329	+	0.598224i	$0.795873\pi$
$374$	37.6500	1.94683
$375$	−11.6433	−0.601259
$376$	19.0619	0.983042
$377$	3.69873	0.190494
$378$	−2.42203	−0.124576
$379$	−20.6331	−1.05985	−0.529925	−	0.848044i	$-0.677780\pi$
$379$	−20.6331	−1.05985	−0.529925	+	0.848044i	$0.677780\pi$
$380$	38.4324	1.97154
$381$	0.248562	0.0127342
$382$	−2.42203	−0.123922
$383$	5.14345	0.262818	0.131409	−	0.991328i	$-0.458050\pi$
$383$	5.14345	0.262818	0.131409	+	0.991328i	$0.458050\pi$
$384$	20.4179	1.04195
$385$	−3.45929	−0.176302
$386$	16.3658	0.832998
$387$	−11.5710	−0.588186
$388$	−37.8172	−1.91988
$389$	20.9418	1.06179	0.530895	−	0.847438i	$-0.321856\pi$
$389$	20.9418	1.06179	0.530895	+	0.847438i	$0.321856\pi$
$390$	14.4367	0.731030
$391$	55.9946	2.83177
$392$	−4.52011	−0.228300
$393$	−2.53084	−0.127664
$394$	−54.7059	−2.75604
$395$	17.8802	0.899649
$396$	−8.88267	−0.446371
$397$	−1.66874	−0.0837518	−0.0418759	−	0.999123i	$-0.513333\pi$
$397$	−1.66874	−0.0837518	−0.0418759	+	0.999123i	$0.513333\pi$
$398$	−20.3609	−1.02060
$399$	6.60199	0.330513
$400$	−8.78737	−0.439368
$401$	1.95998	0.0978766	0.0489383	−	0.998802i	$-0.484416\pi$
$401$	1.95998	0.0978766	0.0489383	+	0.998802i	$0.484416\pi$
$402$	17.9889	0.897205
$403$	−19.4298	−0.967869
$404$	−21.4838	−1.06886
$405$	1.50568	0.0748179
$406$	2.26297	0.112309
$407$	−2.07025	−0.102618
$408$	−30.5830	−1.51408
$409$	−11.5137	−0.569316	−0.284658	−	0.958629i	$-0.591880\pi$
$409$	−11.5137	−0.569316	−0.284658	+	0.958629i	$0.591880\pi$
$410$	26.3357	1.30063
$411$	17.0146	0.839267
$412$	−38.8201	−1.91253
$413$	7.86728	0.387124
$414$	−20.0445	−0.985134
$415$	19.3211	0.948435
$416$	−4.95822	−0.243097
$417$	18.6591	0.913740
$418$	36.7374	1.79689
$419$	10.4582	0.510917	0.255458	−	0.966820i	$-0.417774\pi$
$419$	10.4582	0.510917	0.255458	+	0.966820i	$0.417774\pi$
$420$	5.82134	0.284052
$421$	37.3335	1.81952	0.909762	−	0.415131i	$-0.136264\pi$
$421$	37.3335	1.81952	0.909762	+	0.415131i	$0.136264\pi$
$422$	−42.3566	−2.06189
$423$	−4.21712	−0.205044
$424$	−45.4654	−2.20799
$425$	−18.4909	−0.896940
$426$	−5.59745	−0.271197
$427$	0.887307	0.0429398
$428$	−30.2025	−1.45989
$429$	9.09511	0.439116
$430$	42.1972	2.03493
$431$	−18.3822	−0.885440	−0.442720	−	0.896660i	$-0.645986\pi$
$431$	−18.3822	−0.885440	−0.442720	+	0.896660i	$0.645986\pi$
$432$	3.21537	0.154700
$433$	−9.21975	−0.443073	−0.221537	−	0.975152i	$-0.571107\pi$
$433$	−9.21975	−0.443073	−0.221537	+	0.975152i	$0.571107\pi$
$434$	−11.8876	−0.570625
$435$	−1.40680	−0.0674507
$436$	−35.4940	−1.69985
$437$	54.6374	2.61366
$438$	−11.3893	−0.544203
$439$	17.0972	0.816003	0.408002	−	0.912981i	$-0.366226\pi$
$439$	17.0972	0.816003	0.408002	+	0.912981i	$0.366226\pi$
$440$	15.6364	0.745436
$441$	1.00000	0.0476190
$442$	64.8732	3.08570
$443$	−25.3695	−1.20534	−0.602671	−	0.797990i	$-0.705897\pi$
$443$	−25.3695	−1.20534	−0.602671	+	0.797990i	$0.705897\pi$
$444$	3.48384	0.165336
$445$	3.84922	0.182470
$446$	−22.2739	−1.05470
$447$	17.9376	0.848420
$448$	−9.46431	−0.447146
$449$	34.7753	1.64115	0.820573	−	0.571542i	$-0.193654\pi$
$449$	34.7753	1.64115	0.820573	+	0.571542i	$0.193654\pi$
$450$	6.61923	0.312033
$451$	16.5915	0.781263
$452$	58.8719	2.76910
$453$	−6.02937	−0.283285
$454$	−23.0026	−1.07956
$455$	−5.96056	−0.279435
$456$	−29.8418	−1.39747
$457$	−23.6669	−1.10709	−0.553546	−	0.832819i	$-0.686726\pi$
$457$	−23.6669	−1.10709	−0.553546	+	0.832819i	$0.686726\pi$
$458$	4.78070	0.223387
$459$	6.76598	0.315809
$460$	48.1768	2.24626
$461$	−6.05063	−0.281806	−0.140903	−	0.990023i	$-0.545001\pi$
$461$	−6.05063	−0.281806	−0.140903	+	0.990023i	$0.545001\pi$
$462$	5.56460	0.258889
$463$	4.54394	0.211175	0.105587	−	0.994410i	$-0.466328\pi$
$463$	4.54394	0.211175	0.105587	+	0.994410i	$0.466328\pi$
$464$	−3.00421	−0.139467
$465$	7.39007	0.342706
$466$	19.9385	0.923635
$467$	−6.39115	−0.295747	−0.147874	−	0.989006i	$-0.547243\pi$
$467$	−6.39115	−0.295747	−0.147874	+	0.989006i	$0.547243\pi$
$468$	−15.3054	−0.707491
$469$	−7.42719	−0.342956
$470$	15.3791	0.709383
$471$	6.84302	0.315310
$472$	−35.5610	−1.63683
$473$	26.5842	1.22234
$474$	−28.7620	−1.32108
$475$	−18.0427	−0.827857
$476$	26.1590	1.19899
$477$	10.0585	0.460545
$478$	−3.28647	−0.150320
$479$	−24.8783	−1.13672	−0.568360	−	0.822780i	$-0.692422\pi$
$479$	−24.8783	−1.13672	−0.568360	+	0.822780i	$0.692422\pi$
$480$	1.88584	0.0860765
$481$	−3.56716	−0.162649
$482$	27.1753	1.23780
$483$	8.27590	0.376567
$484$	−22.1209	−1.00549
$485$	−14.7277	−0.668748
$486$	−2.42203	−0.109866
$487$	6.79824	0.308058	0.154029	−	0.988066i	$-0.450775\pi$
$487$	6.79824	0.308058	0.154029	+	0.988066i	$0.450775\pi$
$488$	−4.01073	−0.181557
$489$	22.4360	1.01459
$490$	−3.64681	−0.164746
$491$	13.1347	0.592759	0.296380	−	0.955070i	$-0.404221\pi$
$491$	13.1347	0.592759	0.296380	+	0.955070i	$0.404221\pi$
$492$	−27.9204	−1.25875
$493$	−6.32163	−0.284712
$494$	63.3008	2.84804
$495$	−3.45929	−0.155484
$496$	15.7814	0.708608
$497$	2.31105	0.103665
$498$	−31.0798	−1.39272
$499$	31.2157	1.39741	0.698704	−	0.715411i	$-0.253761\pi$
$499$	31.2157	1.39741	0.698704	+	0.715411i	$0.253761\pi$
$500$	−45.0160	−2.01317
$501$	−13.3217	−0.595168
$502$	−71.9804	−3.21264
$503$	−13.9842	−0.623523	−0.311761	−	0.950160i	$-0.600919\pi$
$503$	−13.9842	−0.623523	−0.311761	+	0.950160i	$0.600919\pi$
$504$	−4.52011	−0.201342
$505$	−8.36669	−0.372313
$506$	46.0521	2.04727
$507$	2.67141	0.118641
$508$	0.961001	0.0426375
$509$	43.9490	1.94801	0.974003	−	0.226537i	$-0.0727403\pi$
$509$	43.9490	1.94801	0.974003	+	0.226537i	$0.0727403\pi$
$510$	−24.6743	−1.09260
$511$	4.70238	0.208021
$512$	33.0949	1.46260
$513$	6.60199	0.291485
$514$	17.6188	0.777132
$515$	−15.1182	−0.666188
$516$	−44.7363	−1.96940
$517$	9.68880	0.426113
$518$	−2.18247	−0.0958924
$519$	−21.8313	−0.958287
$520$	26.9424	1.18150
$521$	26.3981	1.15652	0.578262	−	0.815851i	$-0.303731\pi$
$521$	26.3981	1.15652	0.578262	+	0.815851i	$0.303731\pi$
$522$	2.26297	0.0990474
$523$	23.8046	1.04090	0.520452	−	0.853891i	$-0.325764\pi$
$523$	23.8046	1.04090	0.520452	+	0.853891i	$0.325764\pi$
$524$	−9.78486	−0.427453
$525$	−2.73292	−0.119274
$526$	4.61163	0.201077
$527$	33.2083	1.44657
$528$	−7.38729	−0.321491
$529$	45.4906	1.97785
$530$	−36.6813	−1.59333
$531$	7.86728	0.341411
$532$	25.5249	1.10665
$533$	28.5881	1.23829
$534$	−6.19183	−0.267947
$535$	−11.7622	−0.508523
$536$	33.5717	1.45008
$537$	−5.30716	−0.229021
$538$	−21.5127	−0.927480
$539$	−2.29749	−0.0989599
$540$	5.82134	0.250511
$541$	−41.4961	−1.78406	−0.892028	−	0.451980i	$-0.850718\pi$
$541$	−41.4961	−1.78406	−0.892028	+	0.451980i	$0.850718\pi$
$542$	52.8211	2.26886
$543$	−11.0696	−0.475041
$544$	8.47428	0.363332
$545$	−13.8229	−0.592107
$546$	9.58814	0.410334
$547$	−9.68451	−0.414080	−0.207040	−	0.978333i	$-0.566383\pi$
$547$	−9.68451	−0.414080	−0.207040	+	0.978333i	$0.566383\pi$
$548$	65.7825	2.81009
$549$	0.887307	0.0378693
$550$	−15.2076	−0.648455
$551$	−6.16841	−0.262783
$552$	−37.4080	−1.59219
$553$	11.8751	0.504982
$554$	−15.2305	−0.647084
$555$	1.35676	0.0575911
$556$	72.1407	3.05945
$557$	0.0830489	0.00351890	0.00175945	−	0.999998i	$-0.499440\pi$
$557$	0.0830489	0.00351890	0.00175945	+	0.999998i	$0.499440\pi$
$558$	−11.8876	−0.503244
$559$	45.8062	1.93739
$560$	4.84133	0.204584
$561$	−15.5448	−0.656301
$562$	0.551272	0.0232540
$563$	−27.2775	−1.14961	−0.574804	−	0.818291i	$-0.694922\pi$
$563$	−27.2775	−1.14961	−0.574804	+	0.818291i	$0.694922\pi$
$564$	−16.3044	−0.686541
$565$	22.9272	0.964556
$566$	6.76752	0.284460
$567$	1.00000	0.0419961
$568$	−10.4462	−0.438314
$569$	−9.45734	−0.396472	−0.198236	−	0.980154i	$-0.563521\pi$
$569$	−9.45734	−0.396472	−0.198236	+	0.980154i	$0.563521\pi$
$570$	−24.0762	−1.00844
$571$	−7.32078	−0.306365	−0.153183	−	0.988198i	$-0.548952\pi$
$571$	−7.32078	−0.306365	−0.153183	+	0.988198i	$0.548952\pi$
$572$	35.1639	1.47028
$573$	1.00000	0.0417756
$574$	17.4909	0.730056
$575$	−22.6174	−0.943211
$576$	−9.46431	−0.394346
$577$	5.75849	0.239729	0.119864	−	0.992790i	$-0.461754\pi$
$577$	5.75849	0.239729	0.119864	+	0.992790i	$0.461754\pi$
$578$	−69.7025	−2.89924
$579$	−6.75705	−0.280813
$580$	−5.43902	−0.225843
$581$	12.8321	0.532366
$582$	23.6908	0.982017
$583$	−23.1092	−0.957086
$584$	−21.2553	−0.879550
$585$	−5.96056	−0.246439
$586$	−42.6930	−1.76363
$587$	−32.8516	−1.35593	−0.677965	−	0.735095i	$-0.737138\pi$
$587$	−32.8516	−1.35593	−0.677965	+	0.735095i	$0.737138\pi$
$588$	3.86625	0.159441
$589$	32.4034	1.33516
$590$	−28.6905	−1.18117
$591$	22.5867	0.929095
$592$	2.89735	0.119080
$593$	29.8685	1.22655	0.613277	−	0.789868i	$-0.289851\pi$
$593$	29.8685	1.22655	0.613277	+	0.789868i	$0.289851\pi$
$594$	5.56460	0.228318
$595$	10.1874	0.417643
$596$	69.3512	2.84074
$597$	8.40653	0.344056
$598$	79.3505	3.24488
$599$	−45.1692	−1.84556	−0.922781	−	0.385324i	$-0.874090\pi$
$599$	−45.1692	−1.84556	−0.922781	+	0.385324i	$0.874090\pi$
$600$	12.3531	0.504314
$601$	−31.1745	−1.27164	−0.635818	−	0.771839i	$-0.719337\pi$
$601$	−31.1745	−1.27164	−0.635818	+	0.771839i	$0.719337\pi$
$602$	28.0253	1.14223
$603$	−7.42719	−0.302458
$604$	−23.3110	−0.948513
$605$	−8.61481	−0.350242
$606$	13.4586	0.546719
$607$	−17.3429	−0.703926	−0.351963	−	0.936014i	$-0.614486\pi$
$607$	−17.3429	−0.703926	−0.351963	+	0.936014i	$0.614486\pi$
$608$	8.26889	0.335348
$609$	−0.934325	−0.0378608
$610$	−3.23584	−0.131015
$611$	16.6944	0.675382
$612$	26.1590	1.05741
$613$	18.3956	0.742990	0.371495	−	0.928435i	$-0.378845\pi$
$613$	18.3956	0.742990	0.371495	+	0.928435i	$0.378845\pi$
$614$	−37.4380	−1.51087
$615$	−10.8734	−0.438458
$616$	10.3849	0.418420
$617$	−21.0229	−0.846351	−0.423176	−	0.906048i	$-0.639085\pi$
$617$	−21.0229	−0.846351	−0.423176	+	0.906048i	$0.639085\pi$
$618$	24.3191	0.978258
$619$	−16.2023	−0.651224	−0.325612	−	0.945503i	$-0.605570\pi$
$619$	−16.2023	−0.651224	−0.325612	+	0.945503i	$0.605570\pi$
$620$	28.5718	1.14747
$621$	8.27590	0.332101
$622$	16.6713	0.668460
$623$	2.55646	0.102422
$624$	−12.7287	−0.509558
$625$	−3.86653	−0.154661
$626$	−5.09287	−0.203552
$627$	−15.1680	−0.605752
$628$	26.4568	1.05574
$629$	6.09677	0.243094
$630$	−3.64681	−0.145292
$631$	40.3438	1.60606	0.803030	−	0.595938i	$-0.203220\pi$
$631$	40.3438	1.60606	0.803030	+	0.595938i	$0.203220\pi$
$632$	−53.6769	−2.13515
$633$	17.4880	0.695087
$634$	44.6102	1.77170
$635$	0.374255	0.0148519
$636$	38.8885	1.54203
$637$	−3.95871	−0.156850
$638$	−5.19915	−0.205836
$639$	2.31105	0.0914238
$640$	30.7429	1.21522
$641$	46.3877	1.83221	0.916103	−	0.400943i	$-0.131317\pi$
$641$	46.3877	1.83221	0.916103	+	0.400943i	$0.131317\pi$
$642$	18.9206	0.746735
$643$	−15.5280	−0.612363	−0.306182	−	0.951973i	$-0.599051\pi$
$643$	−15.5280	−0.612363	−0.306182	+	0.951973i	$0.599051\pi$
$644$	31.9967	1.26085
$645$	−17.4222	−0.685999
$646$	−108.190	−4.25667
$647$	−29.4139	−1.15638	−0.578190	−	0.815902i	$-0.696241\pi$
$647$	−29.4139	−1.15638	−0.578190	+	0.815902i	$0.696241\pi$
$648$	−4.52011	−0.177567
$649$	−18.0750	−0.709506
$650$	−26.2036	−1.02779
$651$	4.90812	0.192364
$652$	86.7433	3.39713
$653$	16.5609	0.648077	0.324038	−	0.946044i	$-0.394959\pi$
$653$	16.5609	0.648077	0.324038	+	0.946044i	$0.394959\pi$
$654$	22.2354	0.869473
$655$	−3.81064	−0.148894
$656$	−23.2201	−0.906591
$657$	4.70238	0.183457
$658$	10.2140	0.398184
$659$	2.12582	0.0828102	0.0414051	−	0.999142i	$-0.486817\pi$
$659$	2.12582	0.0828102	0.0414051	+	0.999142i	$0.486817\pi$
$660$	−13.3745	−0.520601
$661$	−5.39501	−0.209842	−0.104921	−	0.994481i	$-0.533459\pi$
$661$	−5.39501	−0.209842	−0.104921	+	0.994481i	$0.533459\pi$
$662$	−6.39208	−0.248435
$663$	−26.7846	−1.04023
$664$	−58.0027	−2.25094
$665$	9.94050	0.385476
$666$	−2.18247	−0.0845692
$667$	−7.73239	−0.299399
$668$	−51.5049	−1.99278
$669$	9.19635	0.355552
$670$	27.0856	1.04641
$671$	−2.03858	−0.0786985
$672$	1.25248	0.0483156
$673$	−23.4623	−0.904404	−0.452202	−	0.891916i	$-0.649361\pi$
$673$	−23.4623	−0.904404	−0.452202	+	0.891916i	$0.649361\pi$
$674$	−39.9131	−1.53740
$675$	−2.73292	−0.105190
$676$	10.3283	0.397243
$677$	35.3478	1.35853	0.679263	−	0.733895i	$-0.262300\pi$
$677$	35.3478	1.35853	0.679263	+	0.733895i	$0.262300\pi$
$678$	−36.8806	−1.41639
$679$	−9.78138	−0.375375
$680$	−46.0483	−1.76587
$681$	9.49722	0.363934
$682$	27.3117	1.04582
$683$	23.4038	0.895520	0.447760	−	0.894154i	$-0.352222\pi$
$683$	23.4038	0.895520	0.447760	+	0.894154i	$0.352222\pi$
$684$	25.5249	0.975970
$685$	25.6185	0.978833
$686$	−2.42203	−0.0924737
$687$	−1.97384	−0.0753066
$688$	−37.2050	−1.41843
$689$	−39.8186	−1.51697
$690$	−30.1807	−1.14896
$691$	9.73574	0.370365	0.185182	−	0.982704i	$-0.440712\pi$
$691$	9.73574	0.370365	0.185182	+	0.982704i	$0.440712\pi$
$692$	−84.4051	−3.20860
$693$	−2.29749	−0.0872745
$694$	72.7988	2.76340
$695$	28.0947	1.06569
$696$	4.22326	0.160082
$697$	−48.8611	−1.85074
$698$	−64.2560	−2.43213
$699$	−8.23215	−0.311368
$700$	−10.5662	−0.399363
$701$	22.1987	0.838433	0.419216	−	0.907886i	$-0.362305\pi$
$701$	22.1987	0.838433	0.419216	+	0.907886i	$0.362305\pi$
$702$	9.58814	0.361881
$703$	5.94900	0.224371
$704$	21.7442	0.819514
$705$	−6.34965	−0.239142
$706$	4.84705	0.182421
$707$	−5.55675	−0.208983
$708$	30.4169	1.14314
$709$	24.3918	0.916053	0.458027	−	0.888938i	$-0.348556\pi$
$709$	24.3918	0.916053	0.458027	+	0.888938i	$0.348556\pi$
$710$	−8.42797	−0.316296
$711$	11.8751	0.445352
$712$	−11.5555	−0.433060
$713$	40.6191	1.52120
$714$	−16.3874	−0.613284
$715$	13.6943	0.512139
$716$	−20.5188	−0.766823
$717$	1.35691	0.0506746
$718$	−58.7258	−2.19163
$719$	41.0246	1.52996	0.764980	−	0.644054i	$-0.222749\pi$
$719$	41.0246	1.52996	0.764980	+	0.644054i	$0.222749\pi$
$720$	4.84133	0.180426
$721$	−10.0408	−0.373938
$722$	−59.5488	−2.21618
$723$	−11.2200	−0.417278
$724$	−42.7977	−1.59056
$725$	2.55344	0.0948323
$726$	13.8578	0.514310
$727$	−0.708608	−0.0262808	−0.0131404	−	0.999914i	$-0.504183\pi$
$727$	−0.708608	−0.0262808	−0.0131404	+	0.999914i	$0.504183\pi$
$728$	17.8938	0.663190
$729$	1.00000	0.0370370
$730$	−17.1487	−0.634702
$731$	−78.2890	−2.89562
$732$	3.43055	0.126797
$733$	−43.5004	−1.60672	−0.803361	−	0.595492i	$-0.796957\pi$
$733$	−43.5004	−1.60672	−0.803361	+	0.595492i	$0.796957\pi$
$734$	34.0857	1.25813
$735$	1.50568	0.0555379
$736$	10.3654	0.382075
$737$	17.0639	0.628557
$738$	17.4909	0.643849
$739$	26.2262	0.964746	0.482373	−	0.875966i	$-0.339775\pi$
$739$	26.2262	0.964746	0.482373	+	0.875966i	$0.339775\pi$
$740$	5.24556	0.192831
$741$	−26.1354	−0.960107
$742$	−24.3619	−0.894355
$743$	−34.4663	−1.26445	−0.632223	−	0.774787i	$-0.717857\pi$
$743$	−34.4663	−1.26445	−0.632223	+	0.774787i	$0.717857\pi$
$744$	−22.1853	−0.813351
$745$	27.0083	0.989509
$746$	74.9679	2.74477
$747$	12.8321	0.469503
$748$	−60.1000	−2.19747
$749$	−7.81185	−0.285439
$750$	28.2005	1.02974
$751$	25.8639	0.943786	0.471893	−	0.881656i	$-0.343571\pi$
$751$	25.8639	0.943786	0.471893	+	0.881656i	$0.343571\pi$
$752$	−13.5596	−0.494469
$753$	29.7190	1.08302
$754$	−8.95844	−0.326247
$755$	−9.07831	−0.330394
$756$	3.86625	0.140614
$757$	10.7395	0.390333	0.195167	−	0.980770i	$-0.437475\pi$
$757$	10.7395	0.390333	0.195167	+	0.980770i	$0.437475\pi$
$758$	49.9740	1.81514
$759$	−19.0138	−0.690158
$760$	−44.9322	−1.62986
$761$	1.56636	0.0567803	0.0283902	−	0.999597i	$-0.490962\pi$
$761$	1.56636	0.0567803	0.0283902	+	0.999597i	$0.490962\pi$
$762$	−0.602025	−0.0218091
$763$	−9.18047	−0.332355
$764$	3.86625	0.139876
$765$	10.1874	0.368327
$766$	−12.4576	−0.450112
$767$	−31.1443	−1.12456
$768$	−30.5242	−1.10145
$769$	−13.6790	−0.493278	−0.246639	−	0.969107i	$-0.579326\pi$
$769$	−13.6790	−0.493278	−0.246639	+	0.969107i	$0.579326\pi$
$770$	8.37852	0.301941
$771$	−7.27439	−0.261981
$772$	−26.1244	−0.940239
$773$	39.9255	1.43602	0.718010	−	0.696033i	$-0.245053\pi$
$773$	39.9255	1.43602	0.718010	+	0.696033i	$0.245053\pi$
$774$	28.0253	1.00735
$775$	−13.4135	−0.481828
$776$	44.2130	1.58715
$777$	0.901092	0.0323265
$778$	−50.7216	−1.81846
$779$	−47.6768	−1.70820
$780$	−23.0450	−0.825144
$781$	−5.30962	−0.189993
$782$	−135.621	−4.84979
$783$	−0.934325	−0.0333901
$784$	3.21537	0.114835
$785$	10.3034	0.367745
$786$	6.12978	0.218642
$787$	49.4286	1.76194	0.880970	−	0.473171i	$-0.156891\pi$
$787$	49.4286	1.76194	0.880970	+	0.473171i	$0.156891\pi$
$788$	87.3260	3.11086
$789$	−1.90403	−0.0677854
$790$	−43.3064	−1.54077
$791$	15.2271	0.541415
$792$	10.3849	0.369012
$793$	−3.51259	−0.124736
$794$	4.04175	0.143436
$795$	15.1448	0.537132
$796$	32.5017	1.15199
$797$	17.6121	0.623854	0.311927	−	0.950106i	$-0.399026\pi$
$797$	17.6121	0.623854	0.311927	+	0.950106i	$0.399026\pi$
$798$	−15.9902	−0.566049
$799$	−28.5330	−1.00942
$800$	−3.42294	−0.121019
$801$	2.55646	0.0903281
$802$	−4.74713	−0.167627
$803$	−10.8037	−0.381253
$804$	−28.7153	−1.01271
$805$	12.4609	0.439188
$806$	47.0597	1.65761
$807$	8.88210	0.312665
$808$	25.1171	0.883617
$809$	−46.3539	−1.62972	−0.814858	−	0.579661i	$-0.803185\pi$
$809$	−46.3539	−1.62972	−0.814858	+	0.579661i	$0.803185\pi$
$810$	−3.64681	−0.128136
$811$	−30.5558	−1.07296	−0.536480	−	0.843913i	$-0.680246\pi$
$811$	−30.5558	−1.07296	−0.536480	+	0.843913i	$0.680246\pi$
$812$	−3.61233	−0.126768
$813$	−21.8086	−0.764860
$814$	5.01421	0.175748
$815$	33.7815	1.18332
$816$	21.7552	0.761583
$817$	−76.3915	−2.67260
$818$	27.8866	0.975031
$819$	−3.95871	−0.138329
$820$	−42.0392	−1.46807
$821$	5.23138	0.182577	0.0912883	−	0.995825i	$-0.470902\pi$
$821$	5.23138	0.182577	0.0912883	+	0.995825i	$0.470902\pi$
$822$	−41.2098	−1.43736
$823$	42.5634	1.48367	0.741833	−	0.670585i	$-0.233957\pi$
$823$	42.5634	1.48367	0.741833	+	0.670585i	$0.233957\pi$
$824$	45.3855	1.58108
$825$	6.27886	0.218602
$826$	−19.0548	−0.663002
$827$	7.80292	0.271334	0.135667	−	0.990754i	$-0.456682\pi$
$827$	7.80292	0.271334	0.135667	+	0.990754i	$0.456682\pi$
$828$	31.9967	1.11196
$829$	−20.8746	−0.725006	−0.362503	−	0.931983i	$-0.618078\pi$
$829$	−20.8746	−0.725006	−0.362503	+	0.931983i	$0.618078\pi$
$830$	−46.7963	−1.62432
$831$	6.28833	0.218140
$832$	37.4665	1.29892
$833$	6.76598	0.234427
$834$	−45.1930	−1.56490
$835$	−20.0582	−0.694143
$836$	−58.6433	−2.02822
$837$	4.90812	0.169649
$838$	−25.3301	−0.875015
$839$	−40.7290	−1.40612	−0.703061	−	0.711130i	$-0.748184\pi$
$839$	−40.7290	−1.40612	−0.703061	+	0.711130i	$0.748184\pi$
$840$	−6.80585	−0.234824
$841$	−28.1270	−0.969898
$842$	−90.4230	−3.11618
$843$	−0.227607	−0.00783920
$844$	67.6130	2.32734
$845$	4.02229	0.138371
$846$	10.2140	0.351165
$847$	−5.72154	−0.196594
$848$	32.3417	1.11062
$849$	−2.79415	−0.0958949
$850$	44.7856	1.53613
$851$	7.45735	0.255635
$852$	8.93510	0.306111
$853$	11.8387	0.405350	0.202675	−	0.979246i	$-0.435037\pi$
$853$	11.8387	0.405350	0.202675	+	0.979246i	$0.435037\pi$
$854$	−2.14909	−0.0735403
$855$	9.94050	0.339958
$856$	35.3104	1.20689
$857$	−32.3341	−1.10451	−0.552256	−	0.833675i	$-0.686233\pi$
$857$	−32.3341	−1.10451	−0.552256	+	0.833675i	$0.686233\pi$
$858$	−22.0287	−0.752046
$859$	39.5374	1.34900	0.674499	−	0.738275i	$-0.264359\pi$
$859$	39.5374	1.34900	0.674499	+	0.738275i	$0.264359\pi$
$860$	−67.3586	−2.29691
$861$	−7.22158	−0.246111
$862$	44.5224	1.51644
$863$	−52.0310	−1.77115	−0.885577	−	0.464492i	$-0.846237\pi$
$863$	−52.0310	−1.77115	−0.885577	+	0.464492i	$0.846237\pi$
$864$	1.25248	0.0426104
$865$	−32.8710	−1.11765
$866$	22.3306	0.758823
$867$	28.7785	0.977370
$868$	18.9760	0.644088
$869$	−27.2830	−0.925512
$870$	3.40731	0.115519
$871$	29.4021	0.996252
$872$	41.4968	1.40526
$873$	−9.78138	−0.331050
$874$	−132.334	−4.47625
$875$	−11.6433	−0.393616
$876$	18.1806	0.614264
$877$	11.4947	0.388148	0.194074	−	0.980987i	$-0.437830\pi$
$877$	11.4947	0.388148	0.194074	+	0.980987i	$0.437830\pi$
$878$	−41.4099	−1.39752
$879$	17.6269	0.594541
$880$	−11.1229	−0.374953
$881$	−14.4514	−0.486880	−0.243440	−	0.969916i	$-0.578276\pi$
$881$	−14.4514	−0.486880	−0.243440	+	0.969916i	$0.578276\pi$
$882$	−2.42203	−0.0815541
$883$	−51.4627	−1.73186	−0.865930	−	0.500166i	$-0.833272\pi$
$883$	−51.4627	−1.73186	−0.865930	+	0.500166i	$0.833272\pi$
$884$	−103.556	−3.48296
$885$	11.8456	0.398186
$886$	61.4458	2.06431
$887$	−1.06718	−0.0358324	−0.0179162	−	0.999839i	$-0.505703\pi$
$887$	−1.06718	−0.0358324	−0.0179162	+	0.999839i	$0.505703\pi$
$888$	−4.07304	−0.136682
$889$	0.248562	0.00833649
$890$	−9.32293	−0.312505
$891$	−2.29749	−0.0769688
$892$	35.5554	1.19048
$893$	−27.8414	−0.931677
$894$	−43.4455	−1.45303
$895$	−7.99089	−0.267106
$896$	20.4179	0.682114
$897$	−32.7619	−1.09389
$898$	−84.2269	−2.81069
$899$	−4.58578	−0.152944
$900$	−10.5662	−0.352205
$901$	68.0554	2.26725
$902$	−40.1852	−1.33802
$903$	−11.5710	−0.385058
$904$	−68.8284	−2.28920
$905$	−16.6673	−0.554038
$906$	14.6033	0.485163
$907$	16.9844	0.563957	0.281979	−	0.959421i	$-0.409009\pi$
$907$	16.9844	0.563957	0.281979	+	0.959421i	$0.409009\pi$
$908$	36.7186	1.21855
$909$	−5.55675	−0.184306
$910$	14.4367	0.478571
$911$	16.9254	0.560763	0.280382	−	0.959889i	$-0.409539\pi$
$911$	16.9254	0.560763	0.280382	+	0.959889i	$0.409539\pi$
$912$	21.2279	0.702925
$913$	−29.4817	−0.975701
$914$	57.3221	1.89605
$915$	1.33600	0.0441669
$916$	−7.63134	−0.252147
$917$	−2.53084	−0.0835757
$918$	−16.3874	−0.540866
$919$	−35.4670	−1.16995	−0.584974	−	0.811052i	$-0.698895\pi$
$919$	−35.4670	−1.16995	−0.584974	+	0.811052i	$0.698895\pi$
$920$	−56.3246	−1.85697
$921$	15.4572	0.509333
$922$	14.6548	0.482631
$923$	−9.14879	−0.301136
$924$	−8.88267	−0.292218
$925$	−2.46261	−0.0809702
$926$	−11.0056	−0.361666
$927$	−10.0408	−0.329782
$928$	−1.17023	−0.0384146
$929$	−40.6823	−1.33474	−0.667372	−	0.744724i	$-0.732581\pi$
$929$	−40.6823	−1.33474	−0.667372	+	0.744724i	$0.732581\pi$
$930$	−17.8990	−0.586931
$931$	6.60199	0.216372
$932$	−31.8275	−1.04254
$933$	−6.88320	−0.225346
$934$	15.4796	0.506508
$935$	−23.4055	−0.765442
$936$	17.8938	0.584878
$937$	37.7286	1.23254	0.616271	−	0.787534i	$-0.288643\pi$
$937$	37.7286	1.23254	0.616271	+	0.787534i	$0.288643\pi$
$938$	17.9889	0.587358
$939$	2.10273	0.0686199
$940$	−24.5493	−0.800710
$941$	3.27413	0.106734	0.0533669	−	0.998575i	$-0.483005\pi$
$941$	3.27413	0.106734	0.0533669	+	0.998575i	$0.483005\pi$
$942$	−16.5740	−0.540011
$943$	−59.7651	−1.94622
$944$	25.2963	0.823323
$945$	1.50568	0.0489798
$946$	−64.3879	−2.09343
$947$	−53.4843	−1.73801	−0.869004	−	0.494806i	$-0.835239\pi$
$947$	−53.4843	−1.73801	−0.869004	+	0.494806i	$0.835239\pi$
$948$	45.9122	1.49116
$949$	−18.6154	−0.604280
$950$	43.7001	1.41782
$951$	−18.4185	−0.597260
$952$	−30.5830	−0.991201
$953$	−20.2477	−0.655886	−0.327943	−	0.944697i	$-0.606355\pi$
$953$	−20.2477	−0.655886	−0.327943	+	0.944697i	$0.606355\pi$
$954$	−24.3619	−0.788747
$955$	1.50568	0.0487227
$956$	5.24613	0.169672
$957$	2.14660	0.0693898
$958$	60.2562	1.94679
$959$	17.0146	0.549429
$960$	−14.2502	−0.459924
$961$	−6.91034	−0.222914
$962$	8.63979	0.278558
$963$	−7.81185	−0.251733
$964$	−43.3795	−1.39716
$965$	−10.1740	−0.327512
$966$	−20.0445	−0.644922
$967$	−29.4057	−0.945624	−0.472812	−	0.881163i	$-0.656761\pi$
$967$	−29.4057	−0.945624	−0.472812	+	0.881163i	$0.656761\pi$
$968$	25.8620	0.831236
$969$	44.6690	1.43497
$970$	35.6709	1.14532
$971$	29.6780	0.952413	0.476206	−	0.879334i	$-0.342012\pi$
$971$	29.6780	0.952413	0.476206	+	0.879334i	$0.342012\pi$
$972$	3.86625	0.124010
$973$	18.6591	0.598183
$974$	−16.4656	−0.527591
$975$	10.8189	0.346481
$976$	2.85302	0.0913231
$977$	−21.9357	−0.701785	−0.350893	−	0.936416i	$-0.614122\pi$
$977$	−21.9357	−0.701785	−0.350893	+	0.936416i	$0.614122\pi$
$978$	−54.3408	−1.73763
$979$	−5.87344	−0.187716
$980$	5.82134	0.185956
$981$	−9.18047	−0.293110
$982$	−31.8126	−1.01518
$983$	−14.5214	−0.463160	−0.231580	−	0.972816i	$-0.574390\pi$
$983$	−14.5214	−0.463160	−0.231580	+	0.972816i	$0.574390\pi$
$984$	32.6423	1.04060
$985$	34.0085	1.08360
$986$	15.3112	0.487608
$987$	−4.21712	−0.134233
$988$	−101.046	−3.21470
$989$	−95.7603	−3.04500
$990$	8.37852	0.266287
$991$	−23.3065	−0.740356	−0.370178	−	0.928961i	$-0.620703\pi$
$991$	−23.3065	−0.740356	−0.370178	+	0.928961i	$0.620703\pi$
$992$	6.14734	0.195178
$993$	2.63914	0.0837505
$994$	−5.59745	−0.177540
$995$	12.6576	0.401271
$996$	49.6122	1.57202
$997$	−19.7195	−0.624521	−0.312261	−	0.949996i	$-0.601086\pi$
$997$	−19.7195	−0.624521	−0.312261	+	0.949996i	$0.601086\pi$
$998$	−75.6055	−2.39325
$999$	0.901092	0.0285093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.3	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.3	✓	27	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42203 q^{2} +1.00000 q^{3} +3.86625 q^{4} +1.50568 q^{5} -2.42203 q^{6} +1.00000 q^{7} -4.52011 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.42203 q^{2} +1.00000 q^{3} +3.86625 q^{4} +1.50568 q^{5} -2.42203 q^{6} +1.00000 q^{7} -4.52011 q^{8} +1.00000 q^{9} -3.64681 q^{10} -2.29749 q^{11} +3.86625 q^{12} -3.95871 q^{13} -2.42203 q^{14} +1.50568 q^{15} +3.21537 q^{16} +6.76598 q^{17} -2.42203 q^{18} +6.60199 q^{19} +5.82134 q^{20} +1.00000 q^{21} +5.56460 q^{22} +8.27590 q^{23} -4.52011 q^{24} -2.73292 q^{25} +9.58814 q^{26} +1.00000 q^{27} +3.86625 q^{28} -0.934325 q^{29} -3.64681 q^{30} +4.90812 q^{31} +1.25248 q^{32} -2.29749 q^{33} -16.3874 q^{34} +1.50568 q^{35} +3.86625 q^{36} +0.901092 q^{37} -15.9902 q^{38} -3.95871 q^{39} -6.80585 q^{40} -7.22158 q^{41} -2.42203 q^{42} -11.5710 q^{43} -8.88267 q^{44} +1.50568 q^{45} -20.0445 q^{46} -4.21712 q^{47} +3.21537 q^{48} +1.00000 q^{49} +6.61923 q^{50} +6.76598 q^{51} -15.3054 q^{52} +10.0585 q^{53} -2.42203 q^{54} -3.45929 q^{55} -4.52011 q^{56} +6.60199 q^{57} +2.26297 q^{58} +7.86728 q^{59} +5.82134 q^{60} +0.887307 q^{61} -11.8876 q^{62} +1.00000 q^{63} -9.46431 q^{64} -5.96056 q^{65} +5.56460 q^{66} -7.42719 q^{67} +26.1590 q^{68} +8.27590 q^{69} -3.64681 q^{70} +2.31105 q^{71} -4.52011 q^{72} +4.70238 q^{73} -2.18247 q^{74} -2.73292 q^{75} +25.5249 q^{76} -2.29749 q^{77} +9.58814 q^{78} +11.8751 q^{79} +4.84133 q^{80} +1.00000 q^{81} +17.4909 q^{82} +12.8321 q^{83} +3.86625 q^{84} +10.1874 q^{85} +28.0253 q^{86} -0.934325 q^{87} +10.3849 q^{88} +2.55646 q^{89} -3.64681 q^{90} -3.95871 q^{91} +31.9967 q^{92} +4.90812 q^{93} +10.2140 q^{94} +9.94050 q^{95} +1.25248 q^{96} -9.78138 q^{97} -2.42203 q^{98} -2.29749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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