LMFDB - Embedded newform 859.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [859,2,Mod(1,859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	859.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:	$6.85914953363$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12947 q^{2} +0.0307143 q^{3} +2.53465 q^{4} +3.38617 q^{5} -0.0654052 q^{6} -2.08550 q^{7} -1.13853 q^{8} -2.99906 q^{9} +O(q^{10})$	\(q-2.12947 q^{2} +0.0307143 q^{3} +2.53465 q^{4} +3.38617 q^{5} -0.0654052 q^{6} -2.08550 q^{7} -1.13853 q^{8} -2.99906 q^{9} -7.21075 q^{10} +4.40397 q^{11} +0.0778500 q^{12} -3.70230 q^{13} +4.44101 q^{14} +0.104004 q^{15} -2.64484 q^{16} -3.12177 q^{17} +6.38641 q^{18} -8.00732 q^{19} +8.58276 q^{20} -0.0640546 q^{21} -9.37812 q^{22} -3.81820 q^{23} -0.0349691 q^{24} +6.46612 q^{25} +7.88395 q^{26} -0.184257 q^{27} -5.28602 q^{28} -7.88060 q^{29} -0.221473 q^{30} -1.32112 q^{31} +7.90917 q^{32} +0.135265 q^{33} +6.64773 q^{34} -7.06185 q^{35} -7.60157 q^{36} +8.22925 q^{37} +17.0514 q^{38} -0.113713 q^{39} -3.85525 q^{40} -8.05240 q^{41} +0.136402 q^{42} +5.42542 q^{43} +11.1625 q^{44} -10.1553 q^{45} +8.13075 q^{46} +11.9935 q^{47} -0.0812343 q^{48} -2.65069 q^{49} -13.7694 q^{50} -0.0958829 q^{51} -9.38405 q^{52} +3.41236 q^{53} +0.392369 q^{54} +14.9126 q^{55} +2.37440 q^{56} -0.245939 q^{57} +16.7815 q^{58} -8.51744 q^{59} +0.263613 q^{60} -0.788903 q^{61} +2.81328 q^{62} +6.25453 q^{63} -11.5527 q^{64} -12.5366 q^{65} -0.288042 q^{66} -5.82044 q^{67} -7.91261 q^{68} -0.117273 q^{69} +15.0380 q^{70} -8.70690 q^{71} +3.41451 q^{72} -3.21035 q^{73} -17.5240 q^{74} +0.198602 q^{75} -20.2958 q^{76} -9.18447 q^{77} +0.242150 q^{78} +2.21787 q^{79} -8.95587 q^{80} +8.99151 q^{81} +17.1474 q^{82} -6.06095 q^{83} -0.162356 q^{84} -10.5708 q^{85} -11.5533 q^{86} -0.242047 q^{87} -5.01404 q^{88} +0.199717 q^{89} +21.6254 q^{90} +7.72115 q^{91} -9.67781 q^{92} -0.0405771 q^{93} -25.5398 q^{94} -27.1141 q^{95} +0.242924 q^{96} -9.41326 q^{97} +5.64458 q^{98} -13.2077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 10 q^{2} - 5 q^{3} + 20 q^{4} - 21 q^{5} - 7 q^{6} - 4 q^{7} - 27 q^{8} + 6 q^{9}+O(q^{10}) $ 29 * q - 10 * q^2 - 5 * q^3 + 20 * q^4 - 21 * q^5 - 7 * q^6 - 4 * q^7 - 27 * q^8 + 6 * q^9	\( 29 q - 10 q^{2} - 5 q^{3} + 20 q^{4} - 21 q^{5} - 7 q^{6} - 4 q^{7} - 27 q^{8} + 6 q^{9} - 5 q^{10} - 24 q^{11} - 10 q^{12} - 16 q^{13} - 24 q^{14} - 17 q^{15} + 6 q^{16} - 24 q^{17} - 11 q^{18} - 21 q^{19} - 25 q^{20} - 47 q^{21} + 6 q^{22} - 19 q^{23} - 3 q^{24} + 16 q^{25} - 12 q^{26} - 17 q^{27} + 14 q^{28} - 97 q^{29} - 3 q^{30} - 5 q^{31} - 34 q^{32} - 7 q^{33} + 12 q^{34} - 26 q^{35} - 19 q^{36} - 21 q^{37} - 2 q^{38} - 15 q^{39} + 2 q^{40} - 50 q^{41} + 19 q^{42} - 20 q^{43} - 51 q^{44} - 28 q^{45} - 5 q^{46} + 4 q^{47} + 3 q^{48} + 7 q^{49} - 16 q^{50} - 33 q^{51} - 15 q^{52} - 73 q^{53} + 16 q^{54} + q^{55} - 48 q^{56} - 15 q^{57} + 51 q^{58} - 37 q^{59} + 10 q^{60} - 32 q^{61} - 4 q^{62} + 16 q^{63} + q^{64} - 48 q^{65} - 14 q^{66} + 4 q^{67} - 5 q^{68} - 43 q^{69} + 50 q^{70} - 32 q^{71} - 6 q^{72} + 11 q^{73} - 10 q^{74} + 19 q^{75} - 18 q^{76} - 60 q^{77} + 49 q^{78} - 5 q^{79} - 9 q^{80} - 35 q^{81} + 57 q^{82} - 9 q^{83} - 23 q^{84} - 8 q^{85} - 22 q^{86} + 18 q^{87} + 64 q^{88} - 35 q^{89} + 15 q^{90} + 2 q^{91} - 9 q^{92} - 27 q^{93} + 27 q^{94} - 39 q^{95} + 11 q^{96} + 29 q^{97} - 29 q^{98} - 20 q^{99}+O(q^{100}) \) 29 * q - 10 * q^2 - 5 * q^3 + 20 * q^4 - 21 * q^5 - 7 * q^6 - 4 * q^7 - 27 * q^8 + 6 * q^9 - 5 * q^10 - 24 * q^11 - 10 * q^12 - 16 * q^13 - 24 * q^14 - 17 * q^15 + 6 * q^16 - 24 * q^17 - 11 * q^18 - 21 * q^19 - 25 * q^20 - 47 * q^21 + 6 * q^22 - 19 * q^23 - 3 * q^24 + 16 * q^25 - 12 * q^26 - 17 * q^27 + 14 * q^28 - 97 * q^29 - 3 * q^30 - 5 * q^31 - 34 * q^32 - 7 * q^33 + 12 * q^34 - 26 * q^35 - 19 * q^36 - 21 * q^37 - 2 * q^38 - 15 * q^39 + 2 * q^40 - 50 * q^41 + 19 * q^42 - 20 * q^43 - 51 * q^44 - 28 * q^45 - 5 * q^46 + 4 * q^47 + 3 * q^48 + 7 * q^49 - 16 * q^50 - 33 * q^51 - 15 * q^52 - 73 * q^53 + 16 * q^54 + q^55 - 48 * q^56 - 15 * q^57 + 51 * q^58 - 37 * q^59 + 10 * q^60 - 32 * q^61 - 4 * q^62 + 16 * q^63 + q^64 - 48 * q^65 - 14 * q^66 + 4 * q^67 - 5 * q^68 - 43 * q^69 + 50 * q^70 - 32 * q^71 - 6 * q^72 + 11 * q^73 - 10 * q^74 + 19 * q^75 - 18 * q^76 - 60 * q^77 + 49 * q^78 - 5 * q^79 - 9 * q^80 - 35 * q^81 + 57 * q^82 - 9 * q^83 - 23 * q^84 - 8 * q^85 - 22 * q^86 + 18 * q^87 + 64 * q^88 - 35 * q^89 + 15 * q^90 + 2 * q^91 - 9 * q^92 - 27 * q^93 + 27 * q^94 - 39 * q^95 + 11 * q^96 + 29 * q^97 - 29 * q^98 - 20 * 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 $

$2$	−2.12947	−1.50576	−0.752882	−	0.658155i	$-0.771337\pi$
$2$	−2.12947	−1.50576	−0.752882	+	0.658155i	$0.771337\pi$
$3$	0.0307143	0.0177329	0.00886645	−	0.999961i	$-0.497178\pi$
$3$	0.0307143	0.0177329	0.00886645	+	0.999961i	$0.497178\pi$
$4$	2.53465	1.26733
$5$	3.38617	1.51434	0.757170	−	0.653218i	$-0.226582\pi$
$5$	3.38617	1.51434	0.757170	+	0.653218i	$0.226582\pi$
$6$	−0.0654052	−0.0267016
$7$	−2.08550	−0.788245	−0.394122	−	0.919058i	$-0.628951\pi$
$7$	−2.08550	−0.788245	−0.394122	+	0.919058i	$0.628951\pi$
$8$	−1.13853	−0.402531
$9$	−2.99906	−0.999686
$10$	−7.21075	−2.28024
$11$	4.40397	1.32785	0.663923	−	0.747801i	$-0.268890\pi$
$11$	4.40397	1.32785	0.663923	+	0.747801i	$0.268890\pi$
$12$	0.0778500	0.0224734
$13$	−3.70230	−1.02683	−0.513417	−	0.858139i	$-0.671620\pi$
$13$	−3.70230	−1.02683	−0.513417	+	0.858139i	$0.671620\pi$
$14$	4.44101	1.18691
$15$	0.104004	0.0268536
$16$	−2.64484	−0.661210
$17$	−3.12177	−0.757141	−0.378570	−	0.925573i	$-0.623584\pi$
$17$	−3.12177	−0.757141	−0.378570	+	0.925573i	$0.623584\pi$
$18$	6.38641	1.50529
$19$	−8.00732	−1.83701	−0.918503	−	0.395414i	$-0.870601\pi$
$19$	−8.00732	−1.83701	−0.918503	+	0.395414i	$0.870601\pi$
$20$	8.58276	1.91916
$21$	−0.0640546	−0.0139779
$22$	−9.37812	−1.99942
$23$	−3.81820	−0.796150	−0.398075	−	0.917353i	$-0.630322\pi$
$23$	−3.81820	−0.796150	−0.398075	+	0.917353i	$0.630322\pi$
$24$	−0.0349691	−0.00713803
$25$	6.46612	1.29322
$26$	7.88395	1.54617
$27$	−0.184257	−0.0354602
$28$	−5.28602	−0.998963
$29$	−7.88060	−1.46339	−0.731696	−	0.681631i	$-0.761271\pi$
$29$	−7.88060	−1.46339	−0.731696	+	0.681631i	$0.761271\pi$
$30$	−0.221473	−0.0404352
$31$	−1.32112	−0.237280	−0.118640	−	0.992937i	$-0.537853\pi$
$31$	−1.32112	−0.237280	−0.118640	+	0.992937i	$0.537853\pi$
$32$	7.90917	1.39816
$33$	0.135265	0.0235465
$34$	6.64773	1.14008
$35$	−7.06185	−1.19367
$36$	−7.60157	−1.26693
$37$	8.22925	1.35288	0.676440	−	0.736498i	$-0.263522\pi$
$37$	8.22925	1.35288	0.676440	+	0.736498i	$0.263522\pi$
$38$	17.0514	2.76610
$39$	−0.113713	−0.0182087
$40$	−3.85525	−0.609568
$41$	−8.05240	−1.25757	−0.628787	−	0.777578i	$-0.716448\pi$
$41$	−8.05240	−1.25757	−0.628787	+	0.777578i	$0.716448\pi$
$42$	0.136402	0.0210474
$43$	5.42542	0.827369	0.413684	−	0.910420i	$-0.364242\pi$
$43$	5.42542	0.827369	0.413684	+	0.910420i	$0.364242\pi$
$44$	11.1625	1.68281
$45$	−10.1553	−1.51386
$46$	8.13075	1.19881
$47$	11.9935	1.74943	0.874714	−	0.484640i	$-0.161049\pi$
$47$	11.9935	1.74943	0.874714	+	0.484640i	$0.161049\pi$
$48$	−0.0812343	−0.0117252
$49$	−2.65069	−0.378671
$50$	−13.7694	−1.94729
$51$	−0.0958829	−0.0134263
$52$	−9.38405	−1.30133
$53$	3.41236	0.468724	0.234362	−	0.972149i	$-0.424700\pi$
$53$	3.41236	0.468724	0.234362	+	0.972149i	$0.424700\pi$
$54$	0.392369	0.0533947
$55$	14.9126	2.01081
$56$	2.37440	0.317293
$57$	−0.245939	−0.0325754
$58$	16.7815	2.20352
$59$	−8.51744	−1.10888	−0.554438	−	0.832225i	$-0.687067\pi$
$59$	−8.51744	−1.10888	−0.554438	+	0.832225i	$0.687067\pi$
$60$	0.263613	0.0340323
$61$	−0.788903	−0.101009	−0.0505043	−	0.998724i	$-0.516083\pi$
$61$	−0.788903	−0.101009	−0.0505043	+	0.998724i	$0.516083\pi$
$62$	2.81328	0.357287
$63$	6.25453	0.787997
$64$	−11.5527	−1.44409
$65$	−12.5366	−1.55497
$66$	−0.288042	−0.0354555
$67$	−5.82044	−0.711080	−0.355540	−	0.934661i	$-0.615703\pi$
$67$	−5.82044	−0.711080	−0.355540	+	0.934661i	$0.615703\pi$
$68$	−7.91261	−0.959545
$69$	−0.117273	−0.0141180
$70$	15.0380	1.79739
$71$	−8.70690	−1.03332	−0.516659	−	0.856191i	$-0.672825\pi$
$71$	−8.70690	−1.03332	−0.516659	+	0.856191i	$0.672825\pi$
$72$	3.41451	0.402404
$73$	−3.21035	−0.375743	−0.187872	−	0.982194i	$-0.560159\pi$
$73$	−3.21035	−0.375743	−0.187872	+	0.982194i	$0.560159\pi$
$74$	−17.5240	−2.03712
$75$	0.198602	0.0229326
$76$	−20.2958	−2.32809
$77$	−9.18447	−1.04667
$78$	0.242150	0.0274181
$79$	2.21787	0.249530	0.124765	−	0.992186i	$-0.460182\pi$
$79$	2.21787	0.249530	0.124765	+	0.992186i	$0.460182\pi$
$80$	−8.95587	−1.00130
$81$	8.99151	0.999057
$82$	17.1474	1.89361
$83$	−6.06095	−0.665275	−0.332638	−	0.943055i	$-0.607939\pi$
$83$	−6.06095	−0.665275	−0.332638	+	0.943055i	$0.607939\pi$
$84$	−0.162356	−0.0177145
$85$	−10.5708	−1.14657
$86$	−11.5533	−1.24582
$87$	−0.242047	−0.0259502
$88$	−5.01404	−0.534499
$89$	0.199717	0.0211699	0.0105850	−	0.999944i	$-0.496631\pi$
$89$	0.199717	0.0211699	0.0105850	+	0.999944i	$0.496631\pi$
$90$	21.6254	2.27952
$91$	7.72115	0.809396
$92$	−9.67781	−1.00898
$93$	−0.0405771	−0.00420765
$94$	−25.5398	−2.63423
$95$	−27.1141	−2.78185
$96$	0.242924	0.0247934
$97$	−9.41326	−0.955772	−0.477886	−	0.878422i	$-0.658597\pi$
$97$	−9.41326	−0.955772	−0.477886	+	0.878422i	$0.658597\pi$
$98$	5.64458	0.570189
$99$	−13.2077	−1.32743
$100$	16.3894	1.63894
$101$	−7.19820	−0.716248	−0.358124	−	0.933674i	$-0.616583\pi$
$101$	−7.19820	−0.716248	−0.358124	+	0.933674i	$0.616583\pi$
$102$	0.204180	0.0202168
$103$	2.23275	0.220000	0.110000	−	0.993932i	$-0.464915\pi$
$103$	2.23275	0.220000	0.110000	+	0.993932i	$0.464915\pi$
$104$	4.21518	0.413332
$105$	−0.216899	−0.0211672
$106$	−7.26653	−0.705788
$107$	1.56786	0.151570	0.0757852	−	0.997124i	$-0.475854\pi$
$107$	1.56786	0.151570	0.0757852	+	0.997124i	$0.475854\pi$
$108$	−0.467027	−0.0449397
$109$	−1.75238	−0.167847	−0.0839236	−	0.996472i	$-0.526745\pi$
$109$	−1.75238	−0.167847	−0.0839236	+	0.996472i	$0.526745\pi$
$110$	−31.7559	−3.02781
$111$	0.252755	0.0239905
$112$	5.51581	0.521195
$113$	1.60391	0.150883	0.0754417	−	0.997150i	$-0.475963\pi$
$113$	1.60391	0.150883	0.0754417	+	0.997150i	$0.475963\pi$
$114$	0.523720	0.0490509
$115$	−12.9291	−1.20564
$116$	−19.9746	−1.85459
$117$	11.1034	1.02651
$118$	18.1377	1.66971
$119$	6.51045	0.596812
$120$	−0.118411	−0.0108094
$121$	8.39492	0.763174
$122$	1.67995	0.152095
$123$	−0.247324	−0.0223004
$124$	−3.34857	−0.300711
$125$	4.96453	0.444041
$126$	−13.3188	−1.18654
$127$	−6.88083	−0.610575	−0.305287	−	0.952260i	$-0.598753\pi$
$127$	−6.88083	−0.610575	−0.305287	+	0.952260i	$0.598753\pi$
$128$	8.78278	0.776295
$129$	0.166638	0.0146716
$130$	26.6964	2.34143
$131$	20.4028	1.78260	0.891301	−	0.453413i	$-0.149794\pi$
$131$	20.4028	1.78260	0.891301	+	0.453413i	$0.149794\pi$
$132$	0.342849	0.0298412
$133$	16.6993	1.44801
$134$	12.3945	1.07072
$135$	−0.623924	−0.0536988
$136$	3.55423	0.304772
$137$	−6.35454	−0.542905	−0.271453	−	0.962452i	$-0.587504\pi$
$137$	−6.35454	−0.542905	−0.271453	+	0.962452i	$0.587504\pi$
$138$	0.249730	0.0212584
$139$	14.4231	1.22335	0.611677	−	0.791108i	$-0.290495\pi$
$139$	14.4231	1.22335	0.611677	+	0.791108i	$0.290495\pi$
$140$	−17.8993	−1.51277
$141$	0.368371	0.0310224
$142$	18.5411	1.55593
$143$	−16.3048	−1.36348
$144$	7.93203	0.661002
$145$	−26.6850	−2.21607
$146$	6.83636	0.565781
$147$	−0.0814141	−0.00671492
$148$	20.8583	1.71454
$149$	−18.3785	−1.50563	−0.752815	−	0.658233i	$-0.771304\pi$
$149$	−18.3785	−1.50563	−0.752815	+	0.658233i	$0.771304\pi$
$150$	−0.422918	−0.0345311
$151$	−4.26361	−0.346968	−0.173484	−	0.984837i	$-0.555502\pi$
$151$	−4.26361	−0.346968	−0.173484	+	0.984837i	$0.555502\pi$
$152$	9.11657	0.739451
$153$	9.36237	0.756903
$154$	19.5581	1.57603
$155$	−4.47352	−0.359322
$156$	−0.288224	−0.0230764
$157$	17.3036	1.38098	0.690490	−	0.723342i	$-0.257395\pi$
$157$	17.3036	1.38098	0.690490	+	0.723342i	$0.257395\pi$
$158$	−4.72290	−0.375733
$159$	0.104808	0.00831183
$160$	26.7818	2.11728
$161$	7.96285	0.627561
$162$	−19.1472	−1.50434
$163$	13.9703	1.09424	0.547118	−	0.837055i	$-0.315725\pi$
$163$	13.9703	1.09424	0.547118	+	0.837055i	$0.315725\pi$
$164$	−20.4100	−1.59376
$165$	0.458028	0.0356575
$166$	12.9066	1.00175
$167$	20.0956	1.55505	0.777524	−	0.628854i	$-0.216476\pi$
$167$	20.0956	1.55505	0.777524	+	0.628854i	$0.216476\pi$
$168$	0.0729280	0.00562652
$169$	0.707033	0.0543872
$170$	22.5103	1.72646
$171$	24.0144	1.83643
$172$	13.7516	1.04855
$173$	−11.9370	−0.907551	−0.453775	−	0.891116i	$-0.649923\pi$
$173$	−11.9370	−0.907551	−0.453775	+	0.891116i	$0.649923\pi$
$174$	0.515432	0.0390748
$175$	−13.4851	−1.01938
$176$	−11.6478	−0.877985
$177$	−0.261607	−0.0196636
$178$	−0.425291	−0.0318769
$179$	−0.825335	−0.0616884	−0.0308442	−	0.999524i	$-0.509820\pi$
$179$	−0.825335	−0.0616884	−0.0308442	+	0.999524i	$0.509820\pi$
$180$	−25.7402	−1.91856
$181$	7.08627	0.526718	0.263359	−	0.964698i	$-0.415170\pi$
$181$	7.08627	0.526718	0.263359	+	0.964698i	$0.415170\pi$
$182$	−16.4420	−1.21876
$183$	−0.0242306	−0.00179118
$184$	4.34713	0.320475
$185$	27.8656	2.04872
$186$	0.0864079	0.00633573
$187$	−13.7482	−1.00537
$188$	30.3993	2.21710
$189$	0.384267	0.0279513
$190$	57.7388	4.18881
$191$	−2.75700	−0.199490	−0.0997449	−	0.995013i	$-0.531803\pi$
$191$	−2.75700	−0.199490	−0.0997449	+	0.995013i	$0.531803\pi$
$192$	−0.354832	−0.0256078
$193$	−18.7021	−1.34621	−0.673103	−	0.739548i	$-0.735039\pi$
$193$	−18.7021	−1.34621	−0.673103	+	0.739548i	$0.735039\pi$
$194$	20.0453	1.43917
$195$	−0.385053	−0.0275742
$196$	−6.71859	−0.479899
$197$	−15.4702	−1.10221	−0.551104	−	0.834436i	$-0.685793\pi$
$197$	−15.4702	−1.10221	−0.551104	+	0.834436i	$0.685793\pi$
$198$	28.1255	1.99879
$199$	−16.9414	−1.20094	−0.600472	−	0.799646i	$-0.705021\pi$
$199$	−16.9414	−1.20094	−0.600472	+	0.799646i	$0.705021\pi$
$200$	−7.36187	−0.520562
$201$	−0.178771	−0.0126095
$202$	15.3284	1.07850
$203$	16.4350	1.15351
$204$	−0.243030	−0.0170155
$205$	−27.2668	−1.90439
$206$	−4.75458	−0.331268
$207$	11.4510	0.795899
$208$	9.79200	0.678953
$209$	−35.2640	−2.43926
$210$	0.461881	0.0318728
$211$	6.51074	0.448218	0.224109	−	0.974564i	$-0.428053\pi$
$211$	6.51074	0.448218	0.224109	+	0.974564i	$0.428053\pi$
$212$	8.64915	0.594026
$213$	−0.267426	−0.0183237
$214$	−3.33871	−0.228229
$215$	18.3714	1.25292
$216$	0.209781	0.0142738
$217$	2.75519	0.187034
$218$	3.73164	0.252738
$219$	−0.0986036	−0.00666302
$220$	37.7982	2.54835
$221$	11.5577	0.777458
$222$	−0.538235	−0.0361240
$223$	−24.1815	−1.61931	−0.809656	−	0.586904i	$-0.800346\pi$
$223$	−24.1815	−1.61931	−0.809656	+	0.586904i	$0.800346\pi$
$224$	−16.4946	−1.10209
$225$	−19.3923	−1.29282
$226$	−3.41549	−0.227195
$227$	15.4044	1.02242	0.511212	−	0.859455i	$-0.329197\pi$
$227$	15.4044	1.02242	0.511212	+	0.859455i	$0.329197\pi$
$228$	−0.623370	−0.0412837
$229$	−2.22838	−0.147256	−0.0736278	−	0.997286i	$-0.523458\pi$
$229$	−2.22838	−0.147256	−0.0736278	+	0.997286i	$0.523458\pi$
$230$	27.5321	1.81541
$231$	−0.282094	−0.0185604
$232$	8.97229	0.589060
$233$	−26.3377	−1.72544	−0.862721	−	0.505681i	$-0.831241\pi$
$233$	−26.3377	−1.72544	−0.862721	+	0.505681i	$0.831241\pi$
$234$	−23.6444	−1.54568
$235$	40.6119	2.64923
$236$	−21.5888	−1.40531
$237$	0.0681203	0.00442489
$238$	−13.8638	−0.898658
$239$	22.8306	1.47679	0.738393	−	0.674371i	$-0.235585\pi$
$239$	22.8306	1.47679	0.738393	+	0.674371i	$0.235585\pi$
$240$	−0.275073	−0.0177559
$241$	19.9304	1.28383	0.641916	−	0.766775i	$-0.278140\pi$
$241$	19.9304	1.28383	0.641916	+	0.766775i	$0.278140\pi$
$242$	−17.8767	−1.14916
$243$	0.828938	0.0531764
$244$	−1.99959	−0.128011
$245$	−8.97569	−0.573436
$246$	0.526669	0.0335792
$247$	29.6455	1.88630
$248$	1.50413	0.0955123
$249$	−0.186158	−0.0117973
$250$	−10.5718	−0.668622
$251$	21.1182	1.33297	0.666485	−	0.745518i	$-0.267798\pi$
$251$	21.1182	1.33297	0.666485	+	0.745518i	$0.267798\pi$
$252$	15.8531	0.998649
$253$	−16.8152	−1.05716
$254$	14.6525	0.919382
$255$	−0.324676	−0.0203320
$256$	4.40269	0.275168
$257$	2.45630	0.153220	0.0766099	−	0.997061i	$-0.475590\pi$
$257$	2.45630	0.153220	0.0766099	+	0.997061i	$0.475590\pi$
$258$	−0.354851	−0.0220920
$259$	−17.1621	−1.06640
$260$	−31.7759	−1.97066
$261$	23.6344	1.46293
$262$	−43.4472	−2.68418
$263$	3.66974	0.226286	0.113143	−	0.993579i	$-0.463908\pi$
$263$	3.66974	0.226286	0.113143	+	0.993579i	$0.463908\pi$
$264$	−0.154003	−0.00947821
$265$	11.5548	0.709807
$266$	−35.5606	−2.18036
$267$	0.00613415	0.000375404 0
$268$	−14.7528	−0.901171
$269$	−4.14754	−0.252880	−0.126440	−	0.991974i	$-0.540355\pi$
$269$	−4.14754	−0.252880	−0.126440	+	0.991974i	$0.540355\pi$
$270$	1.32863	0.0808577
$271$	−16.4480	−0.999145	−0.499573	−	0.866272i	$-0.666510\pi$
$271$	−16.4480	−0.999145	−0.499573	+	0.866272i	$0.666510\pi$
$272$	8.25659	0.500629
$273$	0.237149	0.0143529
$274$	13.5318	0.817487
$275$	28.4766	1.71720
$276$	−0.297247	−0.0178922
$277$	0.155800	0.00936109	0.00468055	−	0.999989i	$-0.498510\pi$
$277$	0.155800	0.00936109	0.00468055	+	0.999989i	$0.498510\pi$
$278$	−30.7137	−1.84208
$279$	3.96210	0.237205
$280$	8.04012	0.480489
$281$	−11.3428	−0.676657	−0.338329	−	0.941028i	$-0.609862\pi$
$281$	−11.3428	−0.676657	−0.338329	+	0.941028i	$0.609862\pi$
$282$	−0.784435	−0.0467124
$283$	9.89717	0.588325	0.294163	−	0.955755i	$-0.404959\pi$
$283$	9.89717	0.588325	0.294163	+	0.955755i	$0.404959\pi$
$284$	−22.0690	−1.30955
$285$	−0.832791	−0.0493303
$286$	34.7206	2.05307
$287$	16.7933	0.991276
$288$	−23.7201	−1.39772
$289$	−7.25454	−0.426738
$290$	56.8250	3.33688
$291$	−0.289121	−0.0169486
$292$	−8.13713	−0.476189
$293$	28.8620	1.68614	0.843069	−	0.537806i	$-0.180747\pi$
$293$	28.8620	1.68614	0.843069	+	0.537806i	$0.180747\pi$
$294$	0.173369	0.0101111
$295$	−28.8415	−1.67922
$296$	−9.36923	−0.544576
$297$	−0.811460	−0.0470857
$298$	39.1366	2.26712
$299$	14.1361	0.817513
$300$	0.503388	0.0290631
$301$	−11.3147	−0.652169
$302$	9.07925	0.522452
$303$	−0.221088	−0.0127011
$304$	21.1781	1.21465
$305$	−2.67136	−0.152961
$306$	−19.9369	−1.13972
$307$	15.3312	0.875000	0.437500	−	0.899218i	$-0.355864\pi$
$307$	15.3312	0.875000	0.437500	+	0.899218i	$0.355864\pi$
$308$	−23.2794	−1.32647
$309$	0.0685774	0.00390123
$310$	9.52624	0.541054
$311$	21.6592	1.22818	0.614090	−	0.789236i	$-0.289523\pi$
$311$	21.6592	1.22818	0.614090	+	0.789236i	$0.289523\pi$
$312$	0.129466	0.00732957
$313$	−0.765095	−0.0432457	−0.0216229	−	0.999766i	$-0.506883\pi$
$313$	−0.765095	−0.0432457	−0.0216229	+	0.999766i	$0.506883\pi$
$314$	−36.8476	−2.07943
$315$	21.1789	1.19329
$316$	5.62153	0.316236
$317$	26.3538	1.48018	0.740090	−	0.672508i	$-0.234783\pi$
$317$	26.3538	1.48018	0.740090	+	0.672508i	$0.234783\pi$
$318$	−0.223186	−0.0125157
$319$	−34.7059	−1.94316
$320$	−39.1193	−2.18684
$321$	0.0481556	0.00268778
$322$	−16.9567	−0.944958
$323$	24.9970	1.39087
$324$	22.7904	1.26613
$325$	−23.9395	−1.32793
$326$	−29.7493	−1.64766
$327$	−0.0538229	−0.00297642
$328$	9.16789	0.506212
$329$	−25.0124	−1.37898
$330$	−0.975359	−0.0536917
$331$	−7.93796	−0.436310	−0.218155	−	0.975914i	$-0.570004\pi$
$331$	−7.93796	−0.436310	−0.218155	+	0.975914i	$0.570004\pi$
$332$	−15.3624	−0.843121
$333$	−24.6800	−1.35245
$334$	−42.7931	−2.34153
$335$	−19.7090	−1.07682
$336$	0.169414	0.00924230
$337$	−22.7435	−1.23892	−0.619460	−	0.785028i	$-0.712648\pi$
$337$	−22.7435	−1.23892	−0.619460	+	0.785028i	$0.712648\pi$
$338$	−1.50561	−0.0818942
$339$	0.0492630	0.00267560
$340$	−26.7934	−1.45308
$341$	−5.81815	−0.315071
$342$	−51.1380	−2.76523
$343$	20.1265	1.08673
$344$	−6.17700	−0.333041
$345$	−0.397107	−0.0213795
$346$	25.4194	1.36656
$347$	−36.3511	−1.95143	−0.975714	−	0.219046i	$-0.929705\pi$
$347$	−36.3511	−1.95143	−0.975714	+	0.219046i	$0.929705\pi$
$348$	−0.613505	−0.0328873
$349$	13.1703	0.704989	0.352495	−	0.935814i	$-0.385334\pi$
$349$	13.1703	0.704989	0.352495	+	0.935814i	$0.385334\pi$
$350$	28.7161	1.53494
$351$	0.682174	0.0364117
$352$	34.8317	1.85654
$353$	−35.6273	−1.89625	−0.948125	−	0.317898i	$-0.897023\pi$
$353$	−35.6273	−1.89625	−0.948125	+	0.317898i	$0.897023\pi$
$354$	0.557085	0.0296087
$355$	−29.4830	−1.56480
$356$	0.506213	0.0268292
$357$	0.199964	0.0105832
$358$	1.75753	0.0928882
$359$	−1.50058	−0.0791976	−0.0395988	−	0.999216i	$-0.512608\pi$
$359$	−1.50058	−0.0791976	−0.0395988	+	0.999216i	$0.512608\pi$
$360$	11.5621	0.609376
$361$	45.1172	2.37459
$362$	−15.0900	−0.793114
$363$	0.257844	0.0135333
$364$	19.5704	1.02577
$365$	−10.8708	−0.569003
$366$	0.0515983	0.00269709
$367$	26.9967	1.40922	0.704608	−	0.709596i	$-0.251123\pi$
$367$	26.9967	1.40922	0.704608	+	0.709596i	$0.251123\pi$
$368$	10.0985	0.526422
$369$	24.1496	1.25718
$370$	−59.3390	−3.08489
$371$	−7.11648	−0.369469
$372$	−0.102849	−0.00533247
$373$	−15.6542	−0.810544	−0.405272	−	0.914196i	$-0.632823\pi$
$373$	−15.6542	−0.810544	−0.405272	+	0.914196i	$0.632823\pi$
$374$	29.2764	1.51384
$375$	0.152482	0.00787414
$376$	−13.6549	−0.704198
$377$	29.1764	1.50266
$378$	−0.818286	−0.0420881
$379$	25.9246	1.33166	0.665828	−	0.746105i	$-0.268079\pi$
$379$	25.9246	1.33166	0.665828	+	0.746105i	$0.268079\pi$
$380$	−68.7249	−3.52551
$381$	−0.211340	−0.0108273
$382$	5.87096	0.300385
$383$	14.5511	0.743525	0.371762	−	0.928328i	$-0.378754\pi$
$383$	14.5511	0.743525	0.371762	+	0.928328i	$0.378754\pi$
$384$	0.269757	0.0137660
$385$	−31.1001	−1.58501
$386$	39.8256	2.02707
$387$	−16.2711	−0.827109
$388$	−23.8593	−1.21127
$389$	−36.9586	−1.87388	−0.936939	−	0.349493i	$-0.886354\pi$
$389$	−36.9586	−1.87388	−0.936939	+	0.349493i	$0.886354\pi$
$390$	0.819959	0.0415202
$391$	11.9195	0.602797
$392$	3.01789	0.152427
$393$	0.626657	0.0316107
$394$	32.9434	1.65967
$395$	7.51008	0.377873
$396$	−33.4770	−1.68228
$397$	34.7045	1.74177	0.870884	−	0.491489i	$-0.163547\pi$
$397$	34.7045	1.74177	0.870884	+	0.491489i	$0.163547\pi$
$398$	36.0762	1.80834
$399$	0.512906	0.0256774
$400$	−17.1019	−0.855093
$401$	−33.7731	−1.68655	−0.843275	−	0.537483i	$-0.819375\pi$
$401$	−33.7731	−1.68655	−0.843275	+	0.537483i	$0.819375\pi$
$402$	0.380687	0.0189869
$403$	4.89117	0.243647
$404$	−18.2449	−0.907720
$405$	30.4467	1.51291
$406$	−34.9979	−1.73691
$407$	36.2413	1.79642
$408$	0.109165	0.00540450
$409$	14.0259	0.693534	0.346767	−	0.937951i	$-0.387279\pi$
$409$	14.0259	0.693534	0.346767	+	0.937951i	$0.387279\pi$
$410$	58.0638	2.86757
$411$	−0.195175	−0.00962728
$412$	5.65925	0.278811
$413$	17.7631	0.874066
$414$	−24.3846	−1.19844
$415$	−20.5234	−1.00745
$416$	−29.2821	−1.43567
$417$	0.442996	0.0216936
$418$	75.0937	3.67295
$419$	−19.7049	−0.962646	−0.481323	−	0.876543i	$-0.659844\pi$
$419$	−19.7049	−0.962646	−0.481323	+	0.876543i	$0.659844\pi$
$420$	−0.549765	−0.0268258
$421$	−23.3353	−1.13729	−0.568647	−	0.822582i	$-0.692533\pi$
$421$	−23.3353	−1.13729	−0.568647	+	0.822582i	$0.692533\pi$
$422$	−13.8644	−0.674910
$423$	−35.9691	−1.74888
$424$	−3.88507	−0.188676
$425$	−20.1858	−0.979153
$426$	0.569476	0.0275912
$427$	1.64526	0.0796195
$428$	3.97397	0.192089
$429$	−0.500790	−0.0241784
$430$	−39.1213	−1.88660
$431$	−38.9525	−1.87628	−0.938139	−	0.346259i	$-0.887452\pi$
$431$	−38.9525	−1.87628	−0.938139	+	0.346259i	$0.887452\pi$
$432$	0.487329	0.0234466
$433$	3.81874	0.183517	0.0917586	−	0.995781i	$-0.470751\pi$
$433$	3.81874	0.183517	0.0917586	+	0.995781i	$0.470751\pi$
$434$	−5.86709	−0.281630
$435$	−0.819611	−0.0392974
$436$	−4.44166	−0.212717
$437$	30.5736	1.46253
$438$	0.209974	0.0100329
$439$	−18.0219	−0.860139	−0.430070	−	0.902796i	$-0.641511\pi$
$439$	−18.0219	−0.860139	−0.430070	+	0.902796i	$0.641511\pi$
$440$	−16.9784	−0.809412
$441$	7.94958	0.378551
$442$	−24.6119	−1.17067
$443$	7.84473	0.372714	0.186357	−	0.982482i	$-0.440332\pi$
$443$	7.84473	0.372714	0.186357	+	0.982482i	$0.440332\pi$
$444$	0.640647	0.0304038
$445$	0.676274	0.0320585
$446$	51.4938	2.43830
$447$	−0.564484	−0.0266992
$448$	24.0931	1.13829
$449$	17.6090	0.831019	0.415510	−	0.909589i	$-0.363603\pi$
$449$	17.6090	0.831019	0.415510	+	0.909589i	$0.363603\pi$
$450$	41.2953	1.94668
$451$	−35.4625	−1.66986
$452$	4.06536	0.191219
$453$	−0.130954	−0.00615275
$454$	−32.8032	−1.53953
$455$	26.1451	1.22570
$456$	0.280009	0.0131126
$457$	12.1957	0.570491	0.285245	−	0.958455i	$-0.407925\pi$
$457$	12.1957	0.570491	0.285245	+	0.958455i	$0.407925\pi$
$458$	4.74528	0.221732
$459$	0.575207	0.0268484
$460$	−32.7707	−1.52794
$461$	−8.43259	−0.392745	−0.196372	−	0.980529i	$-0.562916\pi$
$461$	−8.43259	−0.392745	−0.196372	+	0.980529i	$0.562916\pi$
$462$	0.600712	0.0279476
$463$	−2.26773	−0.105390	−0.0526952	−	0.998611i	$-0.516781\pi$
$463$	−2.26773	−0.105390	−0.0526952	+	0.998611i	$0.516781\pi$
$464$	20.8429	0.967609
$465$	−0.137401	−0.00637181
$466$	56.0854	2.59811
$467$	−38.9656	−1.80311	−0.901557	−	0.432660i	$-0.857575\pi$
$467$	−38.9656	−1.80311	−0.901557	+	0.432660i	$0.857575\pi$
$468$	28.1433	1.30092
$469$	12.1385	0.560505
$470$	−86.4819	−3.98911
$471$	0.531469	0.0244888
$472$	9.69735	0.446357
$473$	23.8934	1.09862
$474$	−0.145060	−0.00666284
$475$	−51.7763	−2.37566
$476$	16.5017	0.756356
$477$	−10.2339	−0.468576
$478$	−48.6170	−2.22369
$479$	−16.5955	−0.758269	−0.379134	−	0.925342i	$-0.623778\pi$
$479$	−16.5955	−0.758269	−0.379134	+	0.925342i	$0.623778\pi$
$480$	0.822583	0.0375456
$481$	−30.4671	−1.38918
$482$	−42.4413	−1.93315
$483$	0.244573	0.0111285
$484$	21.2782	0.967191
$485$	−31.8749	−1.44736
$486$	−1.76520	−0.0800711
$487$	−6.39182	−0.289641	−0.144820	−	0.989458i	$-0.546260\pi$
$487$	−6.39182	−0.289641	−0.144820	+	0.989458i	$0.546260\pi$
$488$	0.898188	0.0406591
$489$	0.429087	0.0194040
$490$	19.1135	0.863459
$491$	15.9308	0.718946	0.359473	−	0.933155i	$-0.382956\pi$
$491$	15.9308	0.718946	0.359473	+	0.933155i	$0.382956\pi$
$492$	−0.626879	−0.0282619
$493$	24.6014	1.10799
$494$	−63.1293	−2.84032
$495$	−44.7236	−2.01018
$496$	3.49414	0.156892
$497$	18.1582	0.814508
$498$	0.396417	0.0177639
$499$	−0.00717785	−0.000321325 0	−0.000160662	−	1.00000i	$-0.500051\pi$
$499$	−0.00717785	−0.000321325 0	−0.000160662		1.00000i	$0.500051\pi$
$500$	12.5834	0.562745
$501$	0.617223	0.0275755
$502$	−44.9707	−2.00714
$503$	21.4599	0.956851	0.478425	−	0.878128i	$-0.341208\pi$
$503$	21.4599	0.956851	0.478425	+	0.878128i	$0.341208\pi$
$504$	−7.12096	−0.317193
$505$	−24.3743	−1.08464
$506$	35.8075	1.59184
$507$	0.0217160	0.000964442 0
$508$	−17.4405	−0.773798
$509$	14.1416	0.626816	0.313408	−	0.949619i	$-0.398529\pi$
$509$	14.1416	0.626816	0.313408	+	0.949619i	$0.398529\pi$
$510$	0.691388	0.0306152
$511$	6.69519	0.296178
$512$	−26.9410	−1.19063
$513$	1.47540	0.0651406
$514$	−5.23063	−0.230713
$515$	7.56047	0.333154
$516$	0.422369	0.0185938
$517$	52.8188	2.32297
$518$	36.5462	1.60575
$519$	−0.366635	−0.0160935
$520$	14.2733	0.625925
$521$	−14.6263	−0.640790	−0.320395	−	0.947284i	$-0.603816\pi$
$521$	−14.6263	−0.640790	−0.320395	+	0.947284i	$0.603816\pi$
$522$	−50.3288	−2.20283
$523$	39.4730	1.72604	0.863018	−	0.505174i	$-0.168572\pi$
$523$	39.4730	1.72604	0.863018	+	0.505174i	$0.168572\pi$
$524$	51.7140	2.25914
$525$	−0.414185	−0.0180765
$526$	−7.81460	−0.340733
$527$	4.12422	0.179654
$528$	−0.357753	−0.0155692
$529$	−8.42136	−0.366146
$530$	−24.6057	−1.06880
$531$	25.5443	1.10853
$532$	42.3268	1.83510
$533$	29.8124	1.29132
$534$	−0.0130625	−0.000565270 0
$535$	5.30903	0.229529
$536$	6.62674	0.286232
$537$	−0.0253496	−0.00109391
$538$	8.83208	0.380778
$539$	−11.6736	−0.502816
$540$	−1.58143	−0.0680539
$541$	9.41800	0.404911	0.202456	−	0.979291i	$-0.435108\pi$
$541$	9.41800	0.404911	0.202456	+	0.979291i	$0.435108\pi$
$542$	35.0256	1.50448
$543$	0.217650	0.00934024
$544$	−24.6906	−1.05860
$545$	−5.93384	−0.254178
$546$	−0.505003	−0.0216121
$547$	−8.98129	−0.384012	−0.192006	−	0.981394i	$-0.561499\pi$
$547$	−8.98129	−0.384012	−0.192006	+	0.981394i	$0.561499\pi$
$548$	−16.1066	−0.688038
$549$	2.36596	0.100977
$550$	−60.6401	−2.58570
$551$	63.1025	2.68826
$552$	0.133519	0.00568294
$553$	−4.62537	−0.196691
$554$	−0.331771	−0.0140956
$555$	0.855871	0.0363297
$556$	36.5576	1.55039
$557$	−8.66891	−0.367314	−0.183657	−	0.982990i	$-0.558793\pi$
$557$	−8.66891	−0.367314	−0.183657	+	0.982990i	$0.558793\pi$
$558$	−8.43719	−0.357175
$559$	−20.0865	−0.849570
$560$	18.6775	0.789267
$561$	−0.422265	−0.0178280
$562$	24.1543	1.01889
$563$	−5.62196	−0.236937	−0.118469	−	0.992958i	$-0.537799\pi$
$563$	−5.62196	−0.236937	−0.118469	+	0.992958i	$0.537799\pi$
$564$	0.933692	0.0393155
$565$	5.43112	0.228489
$566$	−21.0757	−0.885879
$567$	−18.7518	−0.787501
$568$	9.91305	0.415942
$569$	−16.3557	−0.685667	−0.342833	−	0.939396i	$-0.611387\pi$
$569$	−16.3557	−0.685667	−0.342833	+	0.939396i	$0.611387\pi$
$570$	1.77340	0.0742797
$571$	45.7264	1.91359	0.956795	−	0.290763i	$-0.0939090\pi$
$571$	45.7264	1.91359	0.956795	+	0.290763i	$0.0939090\pi$
$572$	−41.3270	−1.72797
$573$	−0.0846793	−0.00353753
$574$	−35.7608	−1.49263
$575$	−24.6889	−1.02960
$576$	34.6472	1.44363
$577$	−33.0322	−1.37515	−0.687575	−	0.726113i	$-0.741325\pi$
$577$	−33.0322	−1.37515	−0.687575	+	0.726113i	$0.741325\pi$
$578$	15.4484	0.642567
$579$	−0.574421	−0.0238721
$580$	−67.6373	−2.80849
$581$	12.6401	0.524400
$582$	0.615676	0.0255206
$583$	15.0279	0.622393
$584$	3.65508	0.151248
$585$	37.5980	1.55449
$586$	−61.4609	−2.53893
$587$	−16.6983	−0.689213	−0.344606	−	0.938747i	$-0.611988\pi$
$587$	−16.6983	−0.689213	−0.344606	+	0.938747i	$0.611988\pi$
$588$	−0.206357	−0.00851000
$589$	10.5786	0.435884
$590$	61.4171	2.52850
$591$	−0.475157	−0.0195453
$592$	−21.7650	−0.894538
$593$	34.0427	1.39797	0.698983	−	0.715138i	$-0.253636\pi$
$593$	34.0427	1.39797	0.698983	+	0.715138i	$0.253636\pi$
$594$	1.72798	0.0708999
$595$	22.0455	0.903776
$596$	−46.5832	−1.90812
$597$	−0.520343	−0.0212962
$598$	−30.1025	−1.23098
$599$	−33.7077	−1.37726	−0.688630	−	0.725113i	$-0.741787\pi$
$599$	−33.7077	−1.37726	−0.688630	+	0.725113i	$0.741787\pi$
$600$	−0.226114	−0.00923108
$601$	−9.81449	−0.400341	−0.200171	−	0.979761i	$-0.564150\pi$
$601$	−9.81449	−0.400341	−0.200171	+	0.979761i	$0.564150\pi$
$602$	24.0944	0.982013
$603$	17.4558	0.710857
$604$	−10.8068	−0.439722
$605$	28.4266	1.15570
$606$	0.470800	0.0191249
$607$	35.8299	1.45429	0.727145	−	0.686484i	$-0.240847\pi$
$607$	35.8299	1.45429	0.727145	+	0.686484i	$0.240847\pi$
$608$	−63.3313	−2.56842
$609$	0.504789	0.0204551
$610$	5.68858	0.230324
$611$	−44.4034	−1.79637
$612$	23.7304	0.959243
$613$	27.6625	1.11728	0.558639	−	0.829411i	$-0.311324\pi$
$613$	27.6625	1.11728	0.558639	+	0.829411i	$0.311324\pi$
$614$	−32.6474	−1.31754
$615$	−0.837479	−0.0337704
$616$	10.4568	0.421316
$617$	18.1284	0.729822	0.364911	−	0.931042i	$-0.381099\pi$
$617$	18.1284	0.729822	0.364911	+	0.931042i	$0.381099\pi$
$618$	−0.146034	−0.00587433
$619$	−12.8305	−0.515703	−0.257851	−	0.966185i	$-0.583014\pi$
$619$	−12.8305	−0.515703	−0.257851	+	0.966185i	$0.583014\pi$
$620$	−11.3388	−0.455378
$621$	0.703528	0.0282316
$622$	−46.1226	−1.84935
$623$	−0.416509	−0.0166871
$624$	0.300754	0.0120398
$625$	−15.5199	−0.620795
$626$	1.62925	0.0651179
$627$	−1.08311	−0.0432551
$628$	43.8587	1.75015
$629$	−25.6898	−1.02432
$630$	−45.0998	−1.79682
$631$	−9.46773	−0.376904	−0.188452	−	0.982082i	$-0.560347\pi$
$631$	−9.46773	−0.376904	−0.188452	+	0.982082i	$0.560347\pi$
$632$	−2.52511	−0.100443
$633$	0.199973	0.00794820
$634$	−56.1198	−2.22880
$635$	−23.2996	−0.924618
$636$	0.265652	0.0105338
$637$	9.81367	0.388832
$638$	73.9053	2.92594
$639$	26.1125	1.03299
$640$	29.7399	1.17557
$641$	−0.221103	−0.00873305	−0.00436652	−	0.999990i	$-0.501390\pi$
$641$	−0.221103	−0.00873305	−0.00436652	+	0.999990i	$0.501390\pi$
$642$	−0.102546	−0.00404717
$643$	11.1495	0.439694	0.219847	−	0.975534i	$-0.429444\pi$
$643$	11.1495	0.439694	0.219847	+	0.975534i	$0.429444\pi$
$644$	20.1831	0.795324
$645$	0.564263	0.0222179
$646$	−53.2305	−2.09433
$647$	−31.9675	−1.25677	−0.628387	−	0.777901i	$-0.716284\pi$
$647$	−31.9675	−1.25677	−0.628387	+	0.777901i	$0.716284\pi$
$648$	−10.2371	−0.402151
$649$	−37.5105	−1.47242
$650$	50.9786	1.99954
$651$	0.0846236	0.00331666
$652$	35.4098	1.38675
$653$	35.6875	1.39656	0.698279	−	0.715825i	$-0.253949\pi$
$653$	35.6875	1.39656	0.698279	+	0.715825i	$0.253949\pi$
$654$	0.114614	0.00448178
$655$	69.0873	2.69946
$656$	21.2973	0.831520
$657$	9.62803	0.375625
$658$	53.2632	2.07641
$659$	32.7162	1.27444	0.637222	−	0.770680i	$-0.280083\pi$
$659$	32.7162	1.27444	0.637222	+	0.770680i	$0.280083\pi$
$660$	1.16094	0.0451896
$661$	41.4013	1.61032	0.805162	−	0.593055i	$-0.202078\pi$
$661$	41.4013	1.61032	0.805162	+	0.593055i	$0.202078\pi$
$662$	16.9037	0.656980
$663$	0.354987	0.0137866
$664$	6.90056	0.267794
$665$	56.5465	2.19278
$666$	52.5553	2.03648
$667$	30.0897	1.16508
$668$	50.9355	1.97075
$669$	−0.742717	−0.0287151
$670$	41.9697	1.62143
$671$	−3.47430	−0.134124
$672$	−0.506619	−0.0195432
$673$	19.3573	0.746168	0.373084	−	0.927798i	$-0.378300\pi$
$673$	19.3573	0.746168	0.373084	+	0.927798i	$0.378300\pi$
$674$	48.4318	1.86552
$675$	−1.19143	−0.0458580
$676$	1.79208	0.0689263
$677$	−9.10146	−0.349798	−0.174899	−	0.984586i	$-0.555960\pi$
$677$	−9.10146	−0.349798	−0.174899	+	0.984586i	$0.555960\pi$
$678$	−0.104904	−0.00402882
$679$	19.6313	0.753382
$680$	12.0352	0.461529
$681$	0.473134	0.0181305
$682$	12.3896	0.474422
$683$	13.7579	0.526430	0.263215	−	0.964737i	$-0.415217\pi$
$683$	13.7579	0.526430	0.263215	+	0.964737i	$0.415217\pi$
$684$	60.8682	2.32735
$685$	−21.5175	−0.822143
$686$	−42.8589	−1.63636
$687$	−0.0684431	−0.00261127
$688$	−14.3494	−0.547065
$689$	−12.6336	−0.481301
$690$	0.845627	0.0321925
$691$	−17.3517	−0.660088	−0.330044	−	0.943966i	$-0.607064\pi$
$691$	−17.3517	−0.660088	−0.330044	+	0.943966i	$0.607064\pi$
$692$	−30.2561	−1.15016
$693$	27.5447	1.04634
$694$	77.4086	2.93839
$695$	48.8391	1.85257
$696$	0.275577	0.0104457
$697$	25.1378	0.952160
$698$	−28.0458	−1.06155
$699$	−0.808944	−0.0305971
$700$	−34.1800	−1.29188
$701$	−1.09457	−0.0413415	−0.0206707	−	0.999786i	$-0.506580\pi$
$701$	−1.09457	−0.0413415	−0.0206707	+	0.999786i	$0.506580\pi$
$702$	−1.45267	−0.0548275
$703$	−65.8942	−2.48525
$704$	−50.8776	−1.91752
$705$	1.24736	0.0469785
$706$	75.8674	2.85531
$707$	15.0118	0.564578
$708$	−0.663083	−0.0249202
$709$	31.8576	1.19644	0.598219	−	0.801332i	$-0.295875\pi$
$709$	31.8576	1.19644	0.598219	+	0.801332i	$0.295875\pi$
$710$	62.7832	2.35621
$711$	−6.65152	−0.249452
$712$	−0.227383	−0.00852155
$713$	5.04429	0.188910
$714$	−0.425817	−0.0159358
$715$	−55.2108	−2.06477
$716$	−2.09194	−0.0781794
$717$	0.701224	0.0261877
$718$	3.19545	0.119253
$719$	2.03088	0.0757392	0.0378696	−	0.999283i	$-0.487943\pi$
$719$	2.03088	0.0757392	0.0378696	+	0.999283i	$0.487943\pi$
$720$	26.8592	1.00098
$721$	−4.65640	−0.173414
$722$	−96.0759	−3.57557
$723$	0.612148	0.0227660
$724$	17.9612	0.667524
$725$	−50.9569	−1.89249
$726$	−0.549071	−0.0203779
$727$	7.88725	0.292522	0.146261	−	0.989246i	$-0.453276\pi$
$727$	7.88725	0.292522	0.146261	+	0.989246i	$0.453276\pi$
$728$	−8.79075	−0.325807
$729$	−26.9491	−0.998114
$730$	23.1490	0.856785
$731$	−16.9369	−0.626435
$732$	−0.0614161	−0.00227000
$733$	−25.8389	−0.954382	−0.477191	−	0.878800i	$-0.658345\pi$
$733$	−25.8389	−0.954382	−0.477191	+	0.878800i	$0.658345\pi$
$734$	−57.4888	−2.12195
$735$	−0.275682	−0.0101687
$736$	−30.1988	−1.11314
$737$	−25.6330	−0.944205
$738$	−51.4259	−1.89301
$739$	−13.4811	−0.495911	−0.247955	−	0.968771i	$-0.579759\pi$
$739$	−13.4811	−0.495911	−0.247955	+	0.968771i	$0.579759\pi$
$740$	70.6296	2.59640
$741$	0.910540	0.0334495
$742$	15.1543	0.556333
$743$	−43.6706	−1.60212	−0.801059	−	0.598585i	$-0.795730\pi$
$743$	−43.6706	−1.60212	−0.801059	+	0.598585i	$0.795730\pi$
$744$	0.0461982	0.00169371
$745$	−62.2328	−2.28003
$746$	33.3352	1.22049
$747$	18.1771	0.665066
$748$	−34.8468	−1.27413
$749$	−3.26977	−0.119475
$750$	−0.324706	−0.0118566
$751$	44.6238	1.62834	0.814172	−	0.580624i	$-0.197191\pi$
$751$	44.6238	1.62834	0.814172	+	0.580624i	$0.197191\pi$
$752$	−31.7208	−1.15674
$753$	0.648631	0.0236374
$754$	−62.1303	−2.26265
$755$	−14.4373	−0.525427
$756$	0.973984	0.0354234
$757$	51.4607	1.87037	0.935185	−	0.354160i	$-0.115233\pi$
$757$	51.4607	1.87037	0.935185	+	0.354160i	$0.115233\pi$
$758$	−55.2057	−2.00516
$759$	−0.516467	−0.0187466
$760$	30.8702	1.11978
$761$	40.6875	1.47492	0.737461	−	0.675390i	$-0.236025\pi$
$761$	40.6875	1.47492	0.737461	+	0.675390i	$0.236025\pi$
$762$	0.450042	0.0163033
$763$	3.65458	0.132305
$764$	−6.98805	−0.252819
$765$	31.7025	1.14621
$766$	−30.9861	−1.11957
$767$	31.5341	1.13863
$768$	0.135225	0.00487952
$769$	30.9876	1.11744	0.558720	−	0.829356i	$-0.311293\pi$
$769$	30.9876	1.11744	0.558720	+	0.829356i	$0.311293\pi$
$770$	66.2269	2.38665
$771$	0.0754435	0.00271703
$772$	−47.4033	−1.70608
$773$	−4.44582	−0.159905	−0.0799526	−	0.996799i	$-0.525477\pi$
$773$	−4.44582	−0.159905	−0.0799526	+	0.996799i	$0.525477\pi$
$774$	34.6490	1.24543
$775$	−8.54250	−0.306856
$776$	10.7173	0.384727
$777$	−0.527121	−0.0189104
$778$	78.7024	2.82162
$779$	64.4782	2.31017
$780$	−0.975975	−0.0349455
$781$	−38.3449	−1.37209
$782$	−25.3823	−0.907671
$783$	1.45205	0.0518922
$784$	7.01066	0.250381
$785$	58.5930	2.09127
$786$	−1.33445	−0.0475982
$787$	−7.64386	−0.272474	−0.136237	−	0.990676i	$-0.543501\pi$
$787$	−7.64386	−0.272474	−0.136237	+	0.990676i	$0.543501\pi$
$788$	−39.2117	−1.39686
$789$	0.112713	0.00401270
$790$	−15.9925	−0.568988
$791$	−3.34496	−0.118933
$792$	15.0374	0.534331
$793$	2.92076	0.103719
$794$	−73.9022	−2.62269
$795$	0.354898	0.0125869
$796$	−42.9406	−1.52199
$797$	−25.1397	−0.890494	−0.445247	−	0.895408i	$-0.646884\pi$
$797$	−25.1397	−0.890494	−0.445247	+	0.895408i	$0.646884\pi$
$798$	−1.09222	−0.0386641
$799$	−37.4409	−1.32456
$800$	51.1417	1.80813
$801$	−0.598962	−0.0211633
$802$	71.9190	2.53955
$803$	−14.1383	−0.498929
$804$	−0.453121	−0.0159804
$805$	26.9635	0.950340
$806$	−10.4156	−0.366874
$807$	−0.127389	−0.00448430
$808$	8.19536	0.288312
$809$	40.3922	1.42012	0.710058	−	0.704144i	$-0.248669\pi$
$809$	40.3922	1.42012	0.710058	+	0.704144i	$0.248669\pi$
$810$	−64.8355	−2.27809
$811$	−19.5777	−0.687465	−0.343732	−	0.939068i	$-0.611691\pi$
$811$	−19.5777	−0.687465	−0.343732	+	0.939068i	$0.611691\pi$
$812$	41.6570	1.46187
$813$	−0.505188	−0.0177177
$814$	−77.1749	−2.70498
$815$	47.3057	1.65704
$816$	0.253595	0.00887760
$817$	−43.4431	−1.51988
$818$	−29.8677	−1.04430
$819$	−23.1562	−0.809141
$820$	−69.1118	−2.41349
$821$	−6.11526	−0.213424	−0.106712	−	0.994290i	$-0.534032\pi$
$821$	−6.11526	−0.213424	−0.106712	+	0.994290i	$0.534032\pi$
$822$	0.415620	0.0144964
$823$	−44.5641	−1.55341	−0.776703	−	0.629867i	$-0.783109\pi$
$823$	−44.5641	−1.55341	−0.776703	+	0.629867i	$0.783109\pi$
$824$	−2.54205	−0.0885566
$825$	0.874637	0.0304510
$826$	−37.8261	−1.31614
$827$	−5.47102	−0.190246	−0.0951230	−	0.995466i	$-0.530324\pi$
$827$	−5.47102	−0.190246	−0.0951230	+	0.995466i	$0.530324\pi$
$828$	29.0243	1.00866
$829$	−13.2694	−0.460865	−0.230432	−	0.973088i	$-0.574014\pi$
$829$	−13.2694	−0.460865	−0.230432	+	0.973088i	$0.574014\pi$
$830$	43.7039	1.51699
$831$	0.00478527	0.000165999 0
$832$	42.7715	1.48284
$833$	8.27486	0.286707
$834$	−0.943347	−0.0326654
$835$	68.0472	2.35487
$836$	−89.3819	−3.09134
$837$	0.243424	0.00841398
$838$	41.9610	1.44952
$839$	−33.7644	−1.16567	−0.582837	−	0.812589i	$-0.698058\pi$
$839$	−33.7644	−1.16567	−0.582837	+	0.812589i	$0.698058\pi$
$840$	0.246946	0.00852046
$841$	33.1039	1.14151
$842$	49.6919	1.71250
$843$	−0.348387	−0.0119991
$844$	16.5025	0.568038
$845$	2.39413	0.0823606
$846$	76.5952	2.63340
$847$	−17.5076	−0.601568
$848$	−9.02515	−0.309925
$849$	0.303984	0.0104327
$850$	42.9850	1.47437
$851$	−31.4209	−1.07709
$852$	−0.677832	−0.0232221
$853$	−49.7831	−1.70454	−0.852270	−	0.523102i	$-0.824775\pi$
$853$	−49.7831	−1.70454	−0.852270	+	0.523102i	$0.824775\pi$
$854$	−3.50353	−0.119888
$855$	81.3168	2.78098
$856$	−1.78505	−0.0610118
$857$	−49.7937	−1.70092	−0.850461	−	0.526038i	$-0.823677\pi$
$857$	−49.7937	−1.70092	−0.850461	+	0.526038i	$0.823677\pi$
$858$	1.06642	0.0364069
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	46.5651	1.58786
$861$	0.515793	0.0175782
$862$	82.9484	2.82523
$863$	−27.9124	−0.950149	−0.475074	−	0.879946i	$-0.657579\pi$
$863$	−27.9124	−0.950149	−0.475074	+	0.879946i	$0.657579\pi$
$864$	−1.45732	−0.0495789
$865$	−40.4206	−1.37434
$866$	−8.13191	−0.276334
$867$	−0.222818	−0.00756730
$868$	6.98344	0.237033
$869$	9.76743	0.331337
$870$	1.74534	0.0591726
$871$	21.5490	0.730161
$872$	1.99513	0.0675636
$873$	28.2309	0.955471
$874$	−65.1055	−2.20223
$875$	−10.3535	−0.350013
$876$	−0.249926	−0.00844422
$877$	−42.5289	−1.43610	−0.718050	−	0.695992i	$-0.754965\pi$
$877$	−42.5289	−1.43610	−0.718050	+	0.695992i	$0.754965\pi$
$878$	38.3772	1.29517
$879$	0.886476	0.0299001
$880$	−39.4413	−1.32957
$881$	51.2854	1.72785	0.863924	−	0.503622i	$-0.168000\pi$
$881$	51.2854	1.72785	0.863924	+	0.503622i	$0.168000\pi$
$882$	−16.9284	−0.570009
$883$	21.5077	0.723791	0.361896	−	0.932219i	$-0.382130\pi$
$883$	21.5077	0.723791	0.361896	+	0.932219i	$0.382130\pi$
$884$	29.2949	0.985292
$885$	−0.885845	−0.0297773
$886$	−16.7051	−0.561220
$887$	−13.9412	−0.468101	−0.234050	−	0.972224i	$-0.575198\pi$
$887$	−13.9412	−0.468101	−0.234050	+	0.972224i	$0.575198\pi$
$888$	−0.287769	−0.00965690
$889$	14.3500	0.481282
$890$	−1.44011	−0.0482725
$891$	39.5983	1.32659
$892$	−61.2917	−2.05220
$893$	−96.0356	−3.21371
$894$	1.20205	0.0402026
$895$	−2.79472	−0.0934172
$896$	−18.3165	−0.611910
$897$	0.434181	0.0144969
$898$	−37.4979	−1.25132
$899$	10.4112	0.347233
$900$	−49.1527	−1.63842
$901$	−10.6526	−0.354890
$902$	75.5164	2.51442
$903$	−0.347523	−0.0115648
$904$	−1.82610	−0.0607352
$905$	23.9953	0.797630
$906$	0.278863	0.00926459
$907$	−40.6475	−1.34968	−0.674839	−	0.737965i	$-0.735787\pi$
$907$	−40.6475	−1.34968	−0.674839	+	0.737965i	$0.735787\pi$
$908$	39.0447	1.29574
$909$	21.5878	0.716023
$910$	−55.6752	−1.84562
$911$	−29.6850	−0.983509	−0.491754	−	0.870734i	$-0.663644\pi$
$911$	−29.6850	−0.983509	−0.491754	+	0.870734i	$0.663644\pi$
$912$	0.650470	0.0215392
$913$	−26.6922	−0.883383
$914$	−25.9704	−0.859024
$915$	−0.0820487	−0.00271245
$916$	−5.64817	−0.186621
$917$	−42.5500	−1.40513
$918$	−1.22489	−0.0404273
$919$	2.46330	0.0812567	0.0406283	−	0.999174i	$-0.487064\pi$
$919$	2.46330	0.0812567	0.0406283	+	0.999174i	$0.487064\pi$
$920$	14.7201	0.485307
$921$	0.470888	0.0155163
$922$	17.9570	0.591381
$923$	32.2356	1.06105
$924$	−0.715011	−0.0235221
$925$	53.2113	1.74958
$926$	4.82907	0.158693
$927$	−6.69615	−0.219930
$928$	−62.3291	−2.04605
$929$	55.5518	1.82260	0.911298	−	0.411747i	$-0.135081\pi$
$929$	55.5518	1.82260	0.911298	+	0.411747i	$0.135081\pi$
$930$	0.292591	0.00959445
$931$	21.2250	0.695620
$932$	−66.7570	−2.18670
$933$	0.665246	0.0217792
$934$	82.9762	2.71506
$935$	−46.5536	−1.52247
$936$	−12.6416	−0.413202
$937$	6.20667	0.202763	0.101382	−	0.994848i	$-0.467674\pi$
$937$	6.20667	0.202763	0.101382	+	0.994848i	$0.467674\pi$
$938$	−25.8487	−0.843989
$939$	−0.0234993	−0.000766872 0
$940$	102.937	3.35744
$941$	−7.58486	−0.247259	−0.123630	−	0.992328i	$-0.539453\pi$
$941$	−7.58486	−0.247259	−0.123630	+	0.992328i	$0.539453\pi$
$942$	−1.13175	−0.0368743
$943$	30.7457	1.00122
$944$	22.5273	0.733200
$945$	1.30119	0.0423278
$946$	−50.8803	−1.65426
$947$	34.3982	1.11779	0.558895	−	0.829238i	$-0.311225\pi$
$947$	34.3982	1.11779	0.558895	+	0.829238i	$0.311225\pi$
$948$	0.172661	0.00560778
$949$	11.8857	0.385826
$950$	110.256	3.57719
$951$	0.809439	0.0262479
$952$	−7.41234	−0.240235
$953$	−34.2124	−1.10825	−0.554124	−	0.832434i	$-0.686947\pi$
$953$	−34.2124	−1.10825	−0.554124	+	0.832434i	$0.686947\pi$
$954$	21.7927	0.705566
$955$	−9.33567	−0.302095
$956$	57.8675	1.87157
$957$	−1.06597	−0.0344578
$958$	35.3397	1.14177
$959$	13.2524	0.427942
$960$	−1.20152	−0.0387789
$961$	−29.2547	−0.943698
$962$	64.8789	2.09178
$963$	−4.70209	−0.151523
$964$	50.5167	1.62703
$965$	−63.3284	−2.03861
$966$	−0.520812	−0.0167568
$967$	−37.8853	−1.21831	−0.609155	−	0.793051i	$-0.708491\pi$
$967$	−37.8853	−1.21831	−0.609155	+	0.793051i	$0.708491\pi$
$968$	−9.55785	−0.307201
$969$	0.767766	0.0246642
$970$	67.8766	2.17939
$971$	−42.5203	−1.36454	−0.682270	−	0.731100i	$-0.739007\pi$
$971$	−42.5203	−1.36454	−0.682270	+	0.731100i	$0.739007\pi$
$972$	2.10107	0.0673918
$973$	−30.0794	−0.964302
$974$	13.6112	0.436131
$975$	−0.735285	−0.0235480
$976$	2.08652	0.0667879
$977$	27.9757	0.895021	0.447511	−	0.894279i	$-0.352311\pi$
$977$	27.9757	0.895021	0.447511	+	0.894279i	$0.352311\pi$
$978$	−0.913728	−0.0292178
$979$	0.879546	0.0281104
$980$	−22.7503	−0.726730
$981$	5.25547	0.167794
$982$	−33.9242	−1.08256
$983$	−25.7375	−0.820899	−0.410449	−	0.911883i	$-0.634628\pi$
$983$	−25.7375	−0.820899	−0.410449	+	0.911883i	$0.634628\pi$
$984$	0.281585	0.00897660
$985$	−52.3848	−1.66912
$986$	−52.3881	−1.66838
$987$	−0.768237	−0.0244532
$988$	75.1411	2.39056
$989$	−20.7153	−0.658709
$990$	95.2377	3.02685
$991$	−0.531212	−0.0168745	−0.00843724	−	0.999964i	$-0.502686\pi$
$991$	−0.531212	−0.0168745	−0.00843724	+	0.999964i	$0.502686\pi$
$992$	−10.4489	−0.331754
$993$	−0.243809	−0.00773704
$994$	−38.6674	−1.22646
$995$	−57.3664	−1.81864
$996$	−0.471845	−0.0149510
$997$	−58.1198	−1.84067	−0.920336	−	0.391129i	$-0.872085\pi$
$997$	−58.1198	−1.84067	−0.920336	+	0.391129i	$0.872085\pi$
$998$	0.0152850	0.000483839 0
$999$	−1.51629	−0.0479734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	859.2.a.a.1.6	✓	29
3.2	odd	2		7731.2.a.c.1.24		29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
859.2.a.a.1.6	✓	29	1.1	even	1	trivial
7731.2.a.c.1.24		29	3.2	odd	2

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:	\( N \)	\(=\)	\( 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	859.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12947 q^{2} +0.0307143 q^{3} +2.53465 q^{4} +3.38617 q^{5} -0.0654052 q^{6} -2.08550 q^{7} -1.13853 q^{8} -2.99906 q^{9} +O(q^{10})\)	\(q-2.12947 q^{2} +0.0307143 q^{3} +2.53465 q^{4} +3.38617 q^{5} -0.0654052 q^{6} -2.08550 q^{7} -1.13853 q^{8} -2.99906 q^{9} -7.21075 q^{10} +4.40397 q^{11} +0.0778500 q^{12} -3.70230 q^{13} +4.44101 q^{14} +0.104004 q^{15} -2.64484 q^{16} -3.12177 q^{17} +6.38641 q^{18} -8.00732 q^{19} +8.58276 q^{20} -0.0640546 q^{21} -9.37812 q^{22} -3.81820 q^{23} -0.0349691 q^{24} +6.46612 q^{25} +7.88395 q^{26} -0.184257 q^{27} -5.28602 q^{28} -7.88060 q^{29} -0.221473 q^{30} -1.32112 q^{31} +7.90917 q^{32} +0.135265 q^{33} +6.64773 q^{34} -7.06185 q^{35} -7.60157 q^{36} +8.22925 q^{37} +17.0514 q^{38} -0.113713 q^{39} -3.85525 q^{40} -8.05240 q^{41} +0.136402 q^{42} +5.42542 q^{43} +11.1625 q^{44} -10.1553 q^{45} +8.13075 q^{46} +11.9935 q^{47} -0.0812343 q^{48} -2.65069 q^{49} -13.7694 q^{50} -0.0958829 q^{51} -9.38405 q^{52} +3.41236 q^{53} +0.392369 q^{54} +14.9126 q^{55} +2.37440 q^{56} -0.245939 q^{57} +16.7815 q^{58} -8.51744 q^{59} +0.263613 q^{60} -0.788903 q^{61} +2.81328 q^{62} +6.25453 q^{63} -11.5527 q^{64} -12.5366 q^{65} -0.288042 q^{66} -5.82044 q^{67} -7.91261 q^{68} -0.117273 q^{69} +15.0380 q^{70} -8.70690 q^{71} +3.41451 q^{72} -3.21035 q^{73} -17.5240 q^{74} +0.198602 q^{75} -20.2958 q^{76} -9.18447 q^{77} +0.242150 q^{78} +2.21787 q^{79} -8.95587 q^{80} +8.99151 q^{81} +17.1474 q^{82} -6.06095 q^{83} -0.162356 q^{84} -10.5708 q^{85} -11.5533 q^{86} -0.242047 q^{87} -5.01404 q^{88} +0.199717 q^{89} +21.6254 q^{90} +7.72115 q^{91} -9.67781 q^{92} -0.0405771 q^{93} -25.5398 q^{94} -27.1141 q^{95} +0.242924 q^{96} -9.41326 q^{97} +5.64458 q^{98} -13.2077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 10 q^{2} - 5 q^{3} + 20 q^{4} - 21 q^{5} - 7 q^{6} - 4 q^{7} - 27 q^{8} + 6 q^{9}+O(q^{10}) \) 29 * q - 10 * q^2 - 5 * q^3 + 20 * q^4 - 21 * q^5 - 7 * q^6 - 4 * q^7 - 27 * q^8 + 6 * q^9	\( 29 q - 10 q^{2} - 5 q^{3} + 20 q^{4} - 21 q^{5} - 7 q^{6} - 4 q^{7} - 27 q^{8} + 6 q^{9} - 5 q^{10} - 24 q^{11} - 10 q^{12} - 16 q^{13} - 24 q^{14} - 17 q^{15} + 6 q^{16} - 24 q^{17} - 11 q^{18} - 21 q^{19} - 25 q^{20} - 47 q^{21} + 6 q^{22} - 19 q^{23} - 3 q^{24} + 16 q^{25} - 12 q^{26} - 17 q^{27} + 14 q^{28} - 97 q^{29} - 3 q^{30} - 5 q^{31} - 34 q^{32} - 7 q^{33} + 12 q^{34} - 26 q^{35} - 19 q^{36} - 21 q^{37} - 2 q^{38} - 15 q^{39} + 2 q^{40} - 50 q^{41} + 19 q^{42} - 20 q^{43} - 51 q^{44} - 28 q^{45} - 5 q^{46} + 4 q^{47} + 3 q^{48} + 7 q^{49} - 16 q^{50} - 33 q^{51} - 15 q^{52} - 73 q^{53} + 16 q^{54} + q^{55} - 48 q^{56} - 15 q^{57} + 51 q^{58} - 37 q^{59} + 10 q^{60} - 32 q^{61} - 4 q^{62} + 16 q^{63} + q^{64} - 48 q^{65} - 14 q^{66} + 4 q^{67} - 5 q^{68} - 43 q^{69} + 50 q^{70} - 32 q^{71} - 6 q^{72} + 11 q^{73} - 10 q^{74} + 19 q^{75} - 18 q^{76} - 60 q^{77} + 49 q^{78} - 5 q^{79} - 9 q^{80} - 35 q^{81} + 57 q^{82} - 9 q^{83} - 23 q^{84} - 8 q^{85} - 22 q^{86} + 18 q^{87} + 64 q^{88} - 35 q^{89} + 15 q^{90} + 2 q^{91} - 9 q^{92} - 27 q^{93} + 27 q^{94} - 39 q^{95} + 11 q^{96} + 29 q^{97} - 29 q^{98} - 20 q^{99}+O(q^{100}) \) 29 * q - 10 * q^2 - 5 * q^3 + 20 * q^4 - 21 * q^5 - 7 * q^6 - 4 * q^7 - 27 * q^8 + 6 * q^9 - 5 * q^10 - 24 * q^11 - 10 * q^12 - 16 * q^13 - 24 * q^14 - 17 * q^15 + 6 * q^16 - 24 * q^17 - 11 * q^18 - 21 * q^19 - 25 * q^20 - 47 * q^21 + 6 * q^22 - 19 * q^23 - 3 * q^24 + 16 * q^25 - 12 * q^26 - 17 * q^27 + 14 * q^28 - 97 * q^29 - 3 * q^30 - 5 * q^31 - 34 * q^32 - 7 * q^33 + 12 * q^34 - 26 * q^35 - 19 * q^36 - 21 * q^37 - 2 * q^38 - 15 * q^39 + 2 * q^40 - 50 * q^41 + 19 * q^42 - 20 * q^43 - 51 * q^44 - 28 * q^45 - 5 * q^46 + 4 * q^47 + 3 * q^48 + 7 * q^49 - 16 * q^50 - 33 * q^51 - 15 * q^52 - 73 * q^53 + 16 * q^54 + q^55 - 48 * q^56 - 15 * q^57 + 51 * q^58 - 37 * q^59 + 10 * q^60 - 32 * q^61 - 4 * q^62 + 16 * q^63 + q^64 - 48 * q^65 - 14 * q^66 + 4 * q^67 - 5 * q^68 - 43 * q^69 + 50 * q^70 - 32 * q^71 - 6 * q^72 + 11 * q^73 - 10 * q^74 + 19 * q^75 - 18 * q^76 - 60 * q^77 + 49 * q^78 - 5 * q^79 - 9 * q^80 - 35 * q^81 + 57 * q^82 - 9 * q^83 - 23 * q^84 - 8 * q^85 - 22 * q^86 + 18 * q^87 + 64 * q^88 - 35 * q^89 + 15 * q^90 + 2 * q^91 - 9 * q^92 - 27 * q^93 + 27 * q^94 - 39 * q^95 + 11 * q^96 + 29 * q^97 - 29 * q^98 - 20 * q^99

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