LMFDB - Embedded newform 9251.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 $ x^18 - 24x^16 - x^15 + 233x^14 + 24x^13 - 1184x^12 - 207x^11 + 3413x^10 + 820x^9 - 5661x^8 - 1595x^7 + 5262x^6 + 1498x^5 - 2567x^4 - 605x^3 + 583x^2 + 80*x - 41
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.28498$ of defining polynomial
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28498 q^{2} +2.11040 q^{3} +3.22114 q^{4} -2.11975 q^{5} -4.82223 q^{6} +0.447429 q^{7} -2.79028 q^{8} +1.45380 q^{9} +O(q^{10})$	\(q-2.28498 q^{2} +2.11040 q^{3} +3.22114 q^{4} -2.11975 q^{5} -4.82223 q^{6} +0.447429 q^{7} -2.79028 q^{8} +1.45380 q^{9} +4.84359 q^{10} -1.00000 q^{11} +6.79790 q^{12} +4.49312 q^{13} -1.02237 q^{14} -4.47353 q^{15} -0.0665397 q^{16} +4.92551 q^{17} -3.32190 q^{18} +0.499000 q^{19} -6.82801 q^{20} +0.944256 q^{21} +2.28498 q^{22} +1.74985 q^{23} -5.88861 q^{24} -0.506656 q^{25} -10.2667 q^{26} -3.26311 q^{27} +1.44123 q^{28} +10.2219 q^{30} -5.04756 q^{31} +5.73260 q^{32} -2.11040 q^{33} -11.2547 q^{34} -0.948439 q^{35} +4.68288 q^{36} +4.39381 q^{37} -1.14021 q^{38} +9.48229 q^{39} +5.91470 q^{40} -3.48281 q^{41} -2.15761 q^{42} -11.5876 q^{43} -3.22114 q^{44} -3.08169 q^{45} -3.99838 q^{46} +1.63500 q^{47} -0.140426 q^{48} -6.79981 q^{49} +1.15770 q^{50} +10.3948 q^{51} +14.4730 q^{52} +5.91748 q^{53} +7.45614 q^{54} +2.11975 q^{55} -1.24845 q^{56} +1.05309 q^{57} -10.2945 q^{59} -14.4099 q^{60} -1.52341 q^{61} +11.5336 q^{62} +0.650471 q^{63} -12.9658 q^{64} -9.52429 q^{65} +4.82223 q^{66} -8.52341 q^{67} +15.8657 q^{68} +3.69290 q^{69} +2.16716 q^{70} +6.84762 q^{71} -4.05650 q^{72} -10.6475 q^{73} -10.0398 q^{74} -1.06925 q^{75} +1.60735 q^{76} -0.447429 q^{77} -21.6668 q^{78} +4.62648 q^{79} +0.141048 q^{80} -11.2479 q^{81} +7.95814 q^{82} -2.97550 q^{83} +3.04158 q^{84} -10.4408 q^{85} +26.4774 q^{86} +2.79028 q^{88} +11.9589 q^{89} +7.04160 q^{90} +2.01035 q^{91} +5.63652 q^{92} -10.6524 q^{93} -3.73595 q^{94} -1.05776 q^{95} +12.0981 q^{96} +4.88053 q^{97} +15.5374 q^{98} -1.45380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * 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 $

$2$	−2.28498	−1.61573	−0.807863	−	0.589370i	$-0.799376\pi$
$2$	−2.28498	−1.61573	−0.807863	+	0.589370i	$0.799376\pi$
$3$	2.11040	1.21844	0.609221	−	0.793001i	$-0.291482\pi$
$3$	2.11040	1.21844	0.609221	+	0.793001i	$0.291482\pi$
$4$	3.22114	1.61057
$5$	−2.11975	−0.947981	−0.473991	−	0.880530i	$-0.657187\pi$
$5$	−2.11975	−0.947981	−0.473991	+	0.880530i	$0.657187\pi$
$6$	−4.82223	−1.96867
$7$	0.447429	0.169112	0.0845562	−	0.996419i	$-0.473053\pi$
$7$	0.447429	0.169112	0.0845562	+	0.996419i	$0.473053\pi$
$8$	−2.79028	−0.986513
$9$	1.45380	0.484599
$10$	4.84359	1.53168
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	6.79790	1.96238
$13$	4.49312	1.24617	0.623083	−	0.782155i	$-0.285880\pi$
$13$	4.49312	1.24617	0.623083	+	0.782155i	$0.285880\pi$
$14$	−1.02237	−0.273239
$15$	−4.47353	−1.15506
$16$	−0.0665397	−0.0166349
$17$	4.92551	1.19461	0.597305	−	0.802014i	$-0.296238\pi$
$17$	4.92551	1.19461	0.597305	+	0.802014i	$0.296238\pi$
$18$	−3.32190	−0.782979
$19$	0.499000	0.114478	0.0572392	−	0.998360i	$-0.481770\pi$
$19$	0.499000	0.114478	0.0572392	+	0.998360i	$0.481770\pi$
$20$	−6.82801	−1.52679
$21$	0.944256	0.206053
$22$	2.28498	0.487160
$23$	1.74985	0.364870	0.182435	−	0.983218i	$-0.441602\pi$
$23$	1.74985	0.364870	0.182435	+	0.983218i	$0.441602\pi$
$24$	−5.88861	−1.20201
$25$	−0.506656	−0.101331
$26$	−10.2667	−2.01346
$27$	−3.26311	−0.627986
$28$	1.44123	0.272367
$29$	0	0
$29$	0	0
$30$	10.2219	1.86626
$31$	−5.04756	−0.906569	−0.453285	−	0.891366i	$-0.649748\pi$
$31$	−5.04756	−0.906569	−0.453285	+	0.891366i	$0.649748\pi$
$32$	5.73260	1.01339
$33$	−2.11040	−0.367374
$34$	−11.2547	−1.93016
$35$	−0.948439	−0.160315
$36$	4.68288	0.780481
$37$	4.39381	0.722337	0.361169	−	0.932501i	$-0.382378\pi$
$37$	4.39381	0.722337	0.361169	+	0.932501i	$0.382378\pi$
$38$	−1.14021	−0.184966
$39$	9.48229	1.51838
$40$	5.91470	0.935196
$41$	−3.48281	−0.543923	−0.271961	−	0.962308i	$-0.587672\pi$
$41$	−3.48281	−0.543923	−0.271961	+	0.962308i	$0.587672\pi$
$42$	−2.15761	−0.332926
$43$	−11.5876	−1.76709	−0.883544	−	0.468348i	$-0.844849\pi$
$43$	−11.5876	−1.76709	−0.883544	+	0.468348i	$0.844849\pi$
$44$	−3.22114	−0.485605
$45$	−3.08169	−0.459391
$46$	−3.99838	−0.589529
$47$	1.63500	0.238490	0.119245	−	0.992865i	$-0.461953\pi$
$47$	1.63500	0.238490	0.119245	+	0.992865i	$0.461953\pi$
$48$	−0.140426	−0.0202687
$49$	−6.79981	−0.971401
$50$	1.15770	0.163723
$51$	10.3948	1.45556
$52$	14.4730	2.00704
$53$	5.91748	0.812829	0.406414	−	0.913689i	$-0.366779\pi$
$53$	5.91748	0.812829	0.406414	+	0.913689i	$0.366779\pi$
$54$	7.45614	1.01465
$55$	2.11975	0.285827
$56$	−1.24845	−0.166832
$57$	1.05309	0.139485
$58$	0	0
$59$	−10.2945	−1.34023	−0.670113	−	0.742259i	$-0.733754\pi$
$59$	−10.2945	−1.34023	−0.670113	+	0.742259i	$0.733754\pi$
$60$	−14.4099	−1.86030
$61$	−1.52341	−0.195053	−0.0975265	−	0.995233i	$-0.531093\pi$
$61$	−1.52341	−0.195053	−0.0975265	+	0.995233i	$0.531093\pi$
$62$	11.5336	1.46477
$63$	0.650471	0.0819517
$64$	−12.9658	−1.62073
$65$	−9.52429	−1.18134
$66$	4.82223	0.593575
$67$	−8.52341	−1.04130	−0.520650	−	0.853770i	$-0.674310\pi$
$67$	−8.52341	−1.04130	−0.520650	+	0.853770i	$0.674310\pi$
$68$	15.8657	1.92400
$69$	3.69290	0.444572
$70$	2.16716	0.259026
$71$	6.84762	0.812663	0.406331	−	0.913726i	$-0.366808\pi$
$71$	6.84762	0.812663	0.406331	+	0.913726i	$0.366808\pi$
$72$	−4.05650	−0.478063
$73$	−10.6475	−1.24619	−0.623096	−	0.782145i	$-0.714126\pi$
$73$	−10.6475	−1.24619	−0.623096	+	0.782145i	$0.714126\pi$
$74$	−10.0398	−1.16710
$75$	−1.06925	−0.123466
$76$	1.60735	0.184376
$77$	−0.447429	−0.0509893
$78$	−21.6668	−2.45329
$79$	4.62648	0.520519	0.260260	−	0.965539i	$-0.416192\pi$
$79$	4.62648	0.520519	0.260260	+	0.965539i	$0.416192\pi$
$80$	0.141048	0.0157696
$81$	−11.2479	−1.24976
$82$	7.95814	0.878830
$83$	−2.97550	−0.326604	−0.163302	−	0.986576i	$-0.552214\pi$
$83$	−2.97550	−0.326604	−0.163302	+	0.986576i	$0.552214\pi$
$84$	3.04158	0.331864
$85$	−10.4408	−1.13247
$86$	26.4774	2.85513
$87$	0	0
$88$	2.79028	0.297445
$89$	11.9589	1.26764	0.633820	−	0.773481i	$-0.281486\pi$
$89$	11.9589	1.26764	0.633820	+	0.773481i	$0.281486\pi$
$90$	7.04160	0.742250
$91$	2.01035	0.210742
$92$	5.63652	0.587648
$93$	−10.6524	−1.10460
$94$	−3.73595	−0.385334
$95$	−1.05776	−0.108523
$96$	12.0981	1.23476
$97$	4.88053	0.495542	0.247771	−	0.968819i	$-0.420302\pi$
$97$	4.88053	0.495542	0.247771	+	0.968819i	$0.420302\pi$
$98$	15.5374	1.56952
$99$	−1.45380	−0.146112
$100$	−1.63201	−0.163201
$101$	−4.48969	−0.446740	−0.223370	−	0.974734i	$-0.571706\pi$
$101$	−4.48969	−0.446740	−0.223370	+	0.974734i	$0.571706\pi$
$102$	−23.7519	−2.35179
$103$	−16.0435	−1.58081	−0.790404	−	0.612586i	$-0.790129\pi$
$103$	−16.0435	−1.58081	−0.790404	+	0.612586i	$0.790129\pi$
$104$	−12.5371	−1.22936
$105$	−2.00159	−0.195335
$106$	−13.5213	−1.31331
$107$	−11.7215	−1.13316	−0.566579	−	0.824008i	$-0.691733\pi$
$107$	−11.7215	−1.13316	−0.566579	+	0.824008i	$0.691733\pi$
$108$	−10.5109	−1.01141
$109$	−3.13845	−0.300609	−0.150305	−	0.988640i	$-0.548025\pi$
$109$	−3.13845	−0.300609	−0.150305	+	0.988640i	$0.548025\pi$
$110$	−4.84359	−0.461818
$111$	9.27270	0.880125
$112$	−0.0297718	−0.00281317
$113$	−10.5804	−0.995320	−0.497660	−	0.867372i	$-0.665807\pi$
$113$	−10.5804	−0.995320	−0.497660	+	0.867372i	$0.665807\pi$
$114$	−2.40629	−0.225370
$115$	−3.70925	−0.345890
$116$	0	0
$117$	6.53208	0.603891
$118$	23.5227	2.16544
$119$	2.20382	0.202023
$120$	12.4824	1.13948
$121$	1.00000	0.0909091
$122$	3.48097	0.315152
$123$	−7.35012	−0.662738
$124$	−16.2589	−1.46009
$125$	11.6727	1.04404
$126$	−1.48632	−0.132411
$127$	18.8230	1.67027	0.835136	−	0.550043i	$-0.185389\pi$
$127$	18.8230	1.67027	0.835136	+	0.550043i	$0.185389\pi$
$128$	18.1614	1.60526
$129$	−24.4544	−2.15309
$130$	21.7628	1.90873
$131$	14.6802	1.28262	0.641308	−	0.767283i	$-0.278392\pi$
$131$	14.6802	1.28262	0.641308	+	0.767283i	$0.278392\pi$
$132$	−6.79790	−0.591681
$133$	0.223267	0.0193597
$134$	19.4758	1.68246
$135$	6.91698	0.595319
$136$	−13.7435	−1.17850
$137$	−6.55568	−0.560090	−0.280045	−	0.959987i	$-0.590349\pi$
$137$	−6.55568	−0.560090	−0.280045	+	0.959987i	$0.590349\pi$
$138$	−8.43820	−0.718307
$139$	−10.9574	−0.929395	−0.464698	−	0.885469i	$-0.653837\pi$
$139$	−10.9574	−0.929395	−0.464698	+	0.885469i	$0.653837\pi$
$140$	−3.05505	−0.258199
$141$	3.45052	0.290586
$142$	−15.6467	−1.31304
$143$	−4.49312	−0.375733
$144$	−0.0967352	−0.00806127
$145$	0	0
$146$	24.3293	2.01351
$147$	−14.3503	−1.18360
$148$	14.1531	1.16337
$149$	13.7229	1.12422	0.562111	−	0.827062i	$-0.309990\pi$
$149$	13.7229	1.12422	0.562111	+	0.827062i	$0.309990\pi$
$150$	2.44321	0.199487
$151$	−1.56775	−0.127582	−0.0637908	−	0.997963i	$-0.520319\pi$
$151$	−1.56775	−0.127582	−0.0637908	+	0.997963i	$0.520319\pi$
$152$	−1.39235	−0.112935
$153$	7.16069	0.578907
$154$	1.02237	0.0823847
$155$	10.6996	0.859411
$156$	30.5438	2.44546
$157$	18.1641	1.44965	0.724826	−	0.688932i	$-0.241920\pi$
$157$	18.1641	1.44965	0.724826	+	0.688932i	$0.241920\pi$
$158$	−10.5714	−0.841017
$159$	12.4883	0.990384
$160$	−12.1517	−0.960676
$161$	0.782936	0.0617040
$162$	25.7012	2.01927
$163$	2.75446	0.215746	0.107873	−	0.994165i	$-0.465596\pi$
$163$	2.75446	0.215746	0.107873	+	0.994165i	$0.465596\pi$
$164$	−11.2186	−0.876026
$165$	4.47353	0.348264
$166$	6.79896	0.527702
$167$	−11.3994	−0.882113	−0.441056	−	0.897479i	$-0.645396\pi$
$167$	−11.3994	−0.882113	−0.441056	+	0.897479i	$0.645396\pi$
$168$	−2.63474	−0.203274
$169$	7.18811	0.552932
$170$	23.8571	1.82976
$171$	0.725445	0.0554762
$172$	−37.3252	−2.84602
$173$	6.08882	0.462924	0.231462	−	0.972844i	$-0.425649\pi$
$173$	6.08882	0.462924	0.231462	+	0.972844i	$0.425649\pi$
$174$	0	0
$175$	−0.226693	−0.0171364
$176$	0.0665397	0.00501562
$177$	−21.7255	−1.63299
$178$	−27.3258	−2.04816
$179$	23.1931	1.73354	0.866768	−	0.498712i	$-0.166193\pi$
$179$	23.1931	1.73354	0.866768	+	0.498712i	$0.166193\pi$
$180$	−9.92655	−0.739881
$181$	18.3727	1.36563	0.682815	−	0.730592i	$-0.260756\pi$
$181$	18.3727	1.36563	0.682815	+	0.730592i	$0.260756\pi$
$182$	−4.59362	−0.340502
$183$	−3.21501	−0.237661
$184$	−4.88258	−0.359949
$185$	−9.31377	−0.684762
$186$	24.3405	1.78473
$187$	−4.92551	−0.360189
$188$	5.26658	0.384104
$189$	−1.46001	−0.106200
$190$	2.41695	0.175344
$191$	−21.3750	−1.54664	−0.773321	−	0.634015i	$-0.781406\pi$
$191$	−21.3750	−1.54664	−0.773321	+	0.634015i	$0.781406\pi$
$192$	−27.3631	−1.97476
$193$	−14.8011	−1.06540	−0.532702	−	0.846303i	$-0.678823\pi$
$193$	−14.8011	−1.06540	−0.532702	+	0.846303i	$0.678823\pi$
$194$	−11.1519	−0.800660
$195$	−20.1001	−1.43940
$196$	−21.9031	−1.56451
$197$	−21.7618	−1.55046	−0.775232	−	0.631676i	$-0.782367\pi$
$197$	−21.7618	−1.55046	−0.775232	+	0.631676i	$0.782367\pi$
$198$	3.32190	0.236077
$199$	−23.6932	−1.67957	−0.839785	−	0.542919i	$-0.817319\pi$
$199$	−23.6932	−1.67957	−0.839785	+	0.542919i	$0.817319\pi$
$200$	1.41371	0.0999645
$201$	−17.9878	−1.26876
$202$	10.2588	0.721810
$203$	0	0
$204$	33.4831	2.34429
$205$	7.38268	0.515629
$206$	36.6590	2.55415
$207$	2.54393	0.176816
$208$	−0.298971	−0.0207299
$209$	−0.499000	−0.0345166
$210$	4.57359	0.315608
$211$	24.0471	1.65547	0.827737	−	0.561116i	$-0.189628\pi$
$211$	24.0471	1.65547	0.827737	+	0.561116i	$0.189628\pi$
$212$	19.0610	1.30912
$213$	14.4512	0.990182
$214$	26.7833	1.83087
$215$	24.5628	1.67517
$216$	9.10499	0.619516
$217$	−2.25843	−0.153312
$218$	7.17130	0.485702
$219$	−22.4705	−1.51841
$220$	6.82801	0.460345
$221$	22.1309	1.48868
$222$	−21.1879	−1.42204
$223$	−10.6190	−0.711101	−0.355551	−	0.934657i	$-0.615707\pi$
$223$	−10.6190	−0.711101	−0.355551	+	0.934657i	$0.615707\pi$
$224$	2.56493	0.171377
$225$	−0.736575	−0.0491050
$226$	24.1760	1.60816
$227$	14.9899	0.994914	0.497457	−	0.867489i	$-0.334267\pi$
$227$	14.9899	0.994914	0.497457	+	0.867489i	$0.334267\pi$
$228$	3.39215	0.224651
$229$	3.02691	0.200024	0.100012	−	0.994986i	$-0.468112\pi$
$229$	3.02691	0.200024	0.100012	+	0.994986i	$0.468112\pi$
$230$	8.47558	0.558863
$231$	−0.944256	−0.0621275
$232$	0	0
$233$	−2.88986	−0.189321	−0.0946604	−	0.995510i	$-0.530177\pi$
$233$	−2.88986	−0.189321	−0.0946604	+	0.995510i	$0.530177\pi$
$234$	−14.9257	−0.975723
$235$	−3.46580	−0.226084
$236$	−33.1599	−2.15853
$237$	9.76373	0.634222
$238$	−5.03568	−0.326414
$239$	10.8133	0.699454	0.349727	−	0.936852i	$-0.386274\pi$
$239$	10.8133	0.699454	0.349727	+	0.936852i	$0.386274\pi$
$240$	0.297667	0.0192143
$241$	−24.9385	−1.60643	−0.803214	−	0.595690i	$-0.796879\pi$
$241$	−24.9385	−1.60643	−0.803214	+	0.595690i	$0.796879\pi$
$242$	−2.28498	−0.146884
$243$	−13.9482	−0.894777
$244$	−4.90713	−0.314147
$245$	14.4139	0.920870
$246$	16.7949	1.07080
$247$	2.24207	0.142659
$248$	14.0841	0.894343
$249$	−6.27950	−0.397947
$250$	−26.6720	−1.68688
$251$	26.4574	1.66998	0.834988	−	0.550269i	$-0.185475\pi$
$251$	26.4574	1.66998	0.834988	+	0.550269i	$0.185475\pi$
$252$	2.09526	0.131989
$253$	−1.74985	−0.110012
$254$	−43.0102	−2.69870
$255$	−22.0344	−1.37985
$256$	−15.5669	−0.972932
$257$	−11.4892	−0.716677	−0.358339	−	0.933592i	$-0.616657\pi$
$257$	−11.4892	−0.716677	−0.358339	+	0.933592i	$0.616657\pi$
$258$	55.8779	3.47881
$259$	1.96592	0.122156
$260$	−30.6791	−1.90264
$261$	0	0
$262$	−33.5440	−2.07236
$263$	30.5457	1.88353	0.941766	−	0.336270i	$-0.109165\pi$
$263$	30.5457	1.88353	0.941766	+	0.336270i	$0.109165\pi$
$264$	5.88861	0.362419
$265$	−12.5436	−0.770547
$266$	−0.510161	−0.0312800
$267$	25.2381	1.54454
$268$	−27.4551	−1.67709
$269$	24.7001	1.50599	0.752997	−	0.658024i	$-0.228607\pi$
$269$	24.7001	1.50599	0.752997	+	0.658024i	$0.228607\pi$
$270$	−15.8052	−0.961872
$271$	−12.4580	−0.756768	−0.378384	−	0.925649i	$-0.623520\pi$
$271$	−12.4580	−0.756768	−0.378384	+	0.925649i	$0.623520\pi$
$272$	−0.327742	−0.0198723
$273$	4.24265	0.256777
$274$	14.9796	0.904951
$275$	0.506656	0.0305525
$276$	11.8953	0.716015
$277$	−2.54814	−0.153103	−0.0765514	−	0.997066i	$-0.524391\pi$
$277$	−2.54814	−0.153103	−0.0765514	+	0.997066i	$0.524391\pi$
$278$	25.0375	1.50165
$279$	−7.33814	−0.439323
$280$	2.64641	0.158153
$281$	5.30893	0.316704	0.158352	−	0.987383i	$-0.449382\pi$
$281$	5.30893	0.316704	0.158352	+	0.987383i	$0.449382\pi$
$282$	−7.88436	−0.469507
$283$	−21.2668	−1.26418	−0.632090	−	0.774895i	$-0.717803\pi$
$283$	−21.2668	−1.26418	−0.632090	+	0.774895i	$0.717803\pi$
$284$	22.0571	1.30885
$285$	−2.23229	−0.132229
$286$	10.2667	0.607082
$287$	−1.55831	−0.0919841
$288$	8.33404	0.491088
$289$	7.26061	0.427095
$290$	0	0
$291$	10.2999	0.603789
$292$	−34.2970	−2.00708
$293$	−7.97614	−0.465971	−0.232986	−	0.972480i	$-0.574849\pi$
$293$	−7.97614	−0.465971	−0.232986	+	0.972480i	$0.574849\pi$
$294$	32.7902	1.91236
$295$	21.8217	1.27051
$296$	−12.2600	−0.712595
$297$	3.26311	0.189345
$298$	−31.3565	−1.81643
$299$	7.86230	0.454689
$300$	−3.44420	−0.198851
$301$	−5.18462	−0.298837
$302$	3.58228	0.206137
$303$	−9.47504	−0.544327
$304$	−0.0332033	−0.00190434
$305$	3.22926	0.184907
$306$	−16.3620	−0.935355
$307$	−0.260691	−0.0148784	−0.00743922	−	0.999972i	$-0.502368\pi$
$307$	−0.260691	−0.0148784	−0.00743922	+	0.999972i	$0.502368\pi$
$308$	−1.44123	−0.0821218
$309$	−33.8581	−1.92612
$310$	−24.4483	−1.38857
$311$	1.54707	0.0877264	0.0438632	−	0.999038i	$-0.486033\pi$
$311$	1.54707	0.0877264	0.0438632	+	0.999038i	$0.486033\pi$
$312$	−26.4582	−1.49790
$313$	−25.1098	−1.41929	−0.709646	−	0.704559i	$-0.751145\pi$
$313$	−25.1098	−1.41929	−0.709646	+	0.704559i	$0.751145\pi$
$314$	−41.5046	−2.34224
$315$	−1.37884	−0.0776887
$316$	14.9025	0.838333
$317$	−23.9085	−1.34284	−0.671419	−	0.741078i	$-0.734315\pi$
$317$	−23.9085	−1.34284	−0.671419	+	0.741078i	$0.734315\pi$
$318$	−28.5355	−1.60019
$319$	0	0
$320$	27.4843	1.53642
$321$	−24.7370	−1.38069
$322$	−1.78899	−0.0996967
$323$	2.45783	0.136757
$324$	−36.2309	−2.01283
$325$	−2.27646	−0.126276
$326$	−6.29389	−0.348586
$327$	−6.62339	−0.366274
$328$	9.71800	0.536587
$329$	0.731549	0.0403316
$330$	−10.2219	−0.562698
$331$	5.05703	0.277959	0.138980	−	0.990295i	$-0.455618\pi$
$331$	5.05703	0.277959	0.138980	+	0.990295i	$0.455618\pi$
$332$	−9.58450	−0.526018
$333$	6.38770	0.350044
$334$	26.0474	1.42525
$335$	18.0675	0.987134
$336$	−0.0628305	−0.00342768
$337$	−13.2372	−0.721078	−0.360539	−	0.932744i	$-0.617407\pi$
$337$	−13.2372	−0.721078	−0.360539	+	0.932744i	$0.617407\pi$
$338$	−16.4247	−0.893386
$339$	−22.3289	−1.21274
$340$	−33.6314	−1.82392
$341$	5.04756	0.273341
$342$	−1.65763	−0.0896342
$343$	−6.17444	−0.333388
$344$	32.3326	1.74326
$345$	−7.82802	−0.421446
$346$	−13.9128	−0.747958
$347$	−22.3483	−1.19972	−0.599859	−	0.800106i	$-0.704777\pi$
$347$	−22.3483	−1.19972	−0.599859	+	0.800106i	$0.704777\pi$
$348$	0	0
$349$	−23.1402	−1.23866	−0.619332	−	0.785129i	$-0.712597\pi$
$349$	−23.1402	−1.23866	−0.619332	+	0.785129i	$0.712597\pi$
$350$	0.517988	0.0276876
$351$	−14.6615	−0.782575
$352$	−5.73260	−0.305549
$353$	4.19254	0.223146	0.111573	−	0.993756i	$-0.464411\pi$
$353$	4.19254	0.223146	0.111573	+	0.993756i	$0.464411\pi$
$354$	49.6423	2.63846
$355$	−14.5152	−0.770389
$356$	38.5212	2.04162
$357$	4.65094	0.246154
$358$	−52.9959	−2.80092
$359$	−20.0286	−1.05707	−0.528535	−	0.848911i	$-0.677259\pi$
$359$	−20.0286	−1.05707	−0.528535	+	0.848911i	$0.677259\pi$
$360$	8.59877	0.453195
$361$	−18.7510	−0.986895
$362$	−41.9812	−2.20648
$363$	2.11040	0.110767
$364$	6.47563	0.339415
$365$	22.5700	1.18137
$366$	7.34625	0.383995
$367$	21.6167	1.12838	0.564191	−	0.825644i	$-0.309188\pi$
$367$	21.6167	1.12838	0.564191	+	0.825644i	$0.309188\pi$
$368$	−0.116435	−0.00606958
$369$	−5.06329	−0.263584
$370$	21.2818	1.10639
$371$	2.64766	0.137459
$372$	−34.3128	−1.77904
$373$	−33.2905	−1.72372	−0.861858	−	0.507150i	$-0.830699\pi$
$373$	−33.2905	−1.72372	−0.861858	+	0.507150i	$0.830699\pi$
$374$	11.2547	0.581966
$375$	24.6342	1.27210
$376$	−4.56212	−0.235273
$377$	0	0
$378$	3.33610	0.171590
$379$	4.18571	0.215005	0.107503	−	0.994205i	$-0.465715\pi$
$379$	4.18571	0.215005	0.107503	+	0.994205i	$0.465715\pi$
$380$	−3.40718	−0.174785
$381$	39.7241	2.03513
$382$	48.8415	2.49895
$383$	17.6818	0.903499	0.451750	−	0.892145i	$-0.350800\pi$
$383$	17.6818	0.903499	0.451750	+	0.892145i	$0.350800\pi$
$384$	38.3279	1.95591
$385$	0.948439	0.0483369
$386$	33.8202	1.72140
$387$	−16.8460	−0.856329
$388$	15.7209	0.798105
$389$	−25.5595	−1.29592	−0.647958	−	0.761676i	$-0.724377\pi$
$389$	−25.5595	−1.29592	−0.647958	+	0.761676i	$0.724377\pi$
$390$	45.9283	2.32567
$391$	8.61892	0.435877
$392$	18.9734	0.958300
$393$	30.9812	1.56279
$394$	49.7253	2.50513
$395$	−9.80698	−0.493443
$396$	−4.68288	−0.235324
$397$	−33.1155	−1.66202	−0.831011	−	0.556256i	$-0.812237\pi$
$397$	−33.1155	−1.66202	−0.831011	+	0.556256i	$0.812237\pi$
$398$	54.1386	2.71372
$399$	0.471184	0.0235887
$400$	0.0337127	0.00168564
$401$	−28.7846	−1.43744	−0.718718	−	0.695301i	$-0.755271\pi$
$401$	−28.7846	−1.43744	−0.718718	+	0.695301i	$0.755271\pi$
$402$	41.1019	2.04997
$403$	−22.6793	−1.12974
$404$	−14.4619	−0.719507
$405$	23.8427	1.18475
$406$	0	0
$407$	−4.39381	−0.217793
$408$	−29.0044	−1.43593
$409$	−19.3545	−0.957016	−0.478508	−	0.878083i	$-0.658822\pi$
$409$	−19.3545	−0.957016	−0.478508	+	0.878083i	$0.658822\pi$
$410$	−16.8693	−0.833115
$411$	−13.8351	−0.682436
$412$	−51.6782	−2.54600
$413$	−4.60605	−0.226649
$414$	−5.81284	−0.285685
$415$	6.30732	0.309614
$416$	25.7573	1.26285
$417$	−23.1245	−1.13241
$418$	1.14021	0.0557693
$419$	−6.90447	−0.337305	−0.168653	−	0.985676i	$-0.553942\pi$
$419$	−6.90447	−0.337305	−0.168653	+	0.985676i	$0.553942\pi$
$420$	−6.44739	−0.314600
$421$	−10.4732	−0.510433	−0.255217	−	0.966884i	$-0.582147\pi$
$421$	−10.4732	−0.510433	−0.255217	+	0.966884i	$0.582147\pi$
$422$	−54.9473	−2.67479
$423$	2.37696	0.115572
$424$	−16.5114	−0.801866
$425$	−2.49554	−0.121051
$426$	−33.0208	−1.59986
$427$	−0.681620	−0.0329859
$428$	−37.7565	−1.82503
$429$	−9.48229	−0.457809
$430$	−56.1255	−2.70661
$431$	−23.0819	−1.11182	−0.555909	−	0.831243i	$-0.687630\pi$
$431$	−23.0819	−1.11182	−0.555909	+	0.831243i	$0.687630\pi$
$432$	0.217126	0.0104465
$433$	22.3072	1.07202	0.536008	−	0.844213i	$-0.319932\pi$
$433$	22.3072	1.07202	0.536008	+	0.844213i	$0.319932\pi$
$434$	5.16047	0.247710
$435$	0	0
$436$	−10.1094	−0.484152
$437$	0.873177	0.0417697
$438$	51.3446	2.45334
$439$	1.78437	0.0851633	0.0425816	−	0.999093i	$-0.486442\pi$
$439$	1.78437	0.0851633	0.0425816	+	0.999093i	$0.486442\pi$
$440$	−5.91470	−0.281972
$441$	−9.88554	−0.470740
$442$	−50.5686	−2.40531
$443$	26.9077	1.27842	0.639212	−	0.769030i	$-0.279261\pi$
$443$	26.9077	1.27842	0.639212	+	0.769030i	$0.279261\pi$
$444$	29.8687	1.41750
$445$	−25.3499	−1.20170
$446$	24.2642	1.14894
$447$	28.9608	1.36980
$448$	−5.80128	−0.274085
$449$	22.3293	1.05379	0.526893	−	0.849932i	$-0.323357\pi$
$449$	22.3293	1.05379	0.526893	+	0.849932i	$0.323357\pi$
$450$	1.68306	0.0793402
$451$	3.48281	0.163999
$452$	−34.0809	−1.60303
$453$	−3.30858	−0.155451
$454$	−34.2516	−1.60751
$455$	−4.26145	−0.199780
$456$	−2.93842	−0.137604
$457$	−29.6524	−1.38708	−0.693541	−	0.720417i	$-0.743950\pi$
$457$	−29.6524	−1.38708	−0.693541	+	0.720417i	$0.743950\pi$
$458$	−6.91643	−0.323184
$459$	−16.0725	−0.750198
$460$	−11.9480	−0.557080
$461$	−35.0736	−1.63354	−0.816770	−	0.576963i	$-0.804238\pi$
$461$	−35.0736	−1.63354	−0.816770	+	0.576963i	$0.804238\pi$
$462$	2.15761	0.100381
$463$	14.8544	0.690340	0.345170	−	0.938540i	$-0.387821\pi$
$463$	14.8544	0.690340	0.345170	+	0.938540i	$0.387821\pi$
$464$	0	0
$465$	22.5804	1.04714
$466$	6.60327	0.305891
$467$	−35.1444	−1.62629	−0.813145	−	0.582062i	$-0.802246\pi$
$467$	−35.1444	−1.62629	−0.813145	+	0.582062i	$0.802246\pi$
$468$	21.0407	0.972609
$469$	−3.81363	−0.176097
$470$	7.91929	0.365290
$471$	38.3335	1.76632
$472$	28.7245	1.32215
$473$	11.5876	0.532797
$474$	−22.3099	−1.02473
$475$	−0.252821	−0.0116002
$476$	7.09880	0.325373
$477$	8.60282	0.393896
$478$	−24.7082	−1.13013
$479$	−13.7759	−0.629437	−0.314719	−	0.949185i	$-0.601910\pi$
$479$	−13.7759	−0.629437	−0.314719	+	0.949185i	$0.601910\pi$
$480$	−25.6450	−1.17053
$481$	19.7419	0.900153
$482$	56.9839	2.59555
$483$	1.65231	0.0751827
$484$	3.22114	0.146415
$485$	−10.3455	−0.469765
$486$	31.8714	1.44571
$487$	35.4237	1.60520	0.802601	−	0.596517i	$-0.203449\pi$
$487$	35.4237	1.60520	0.802601	+	0.596517i	$0.203449\pi$
$488$	4.25075	0.192422
$489$	5.81301	0.262874
$490$	−32.9355	−1.48787
$491$	−35.0041	−1.57971	−0.789857	−	0.613291i	$-0.789845\pi$
$491$	−35.0041	−1.57971	−0.789857	+	0.613291i	$0.789845\pi$
$492$	−23.6758	−1.06739
$493$	0	0
$494$	−5.12308	−0.230498
$495$	3.08169	0.138512
$496$	0.335863	0.0150807
$497$	3.06383	0.137431
$498$	14.3485	0.642974
$499$	21.7648	0.974325	0.487162	−	0.873311i	$-0.338032\pi$
$499$	21.7648	0.974325	0.487162	+	0.873311i	$0.338032\pi$
$500$	37.5995	1.68150
$501$	−24.0573	−1.07480
$502$	−60.4546	−2.69822
$503$	−34.7084	−1.54757	−0.773787	−	0.633446i	$-0.781640\pi$
$503$	−34.7084	−1.54757	−0.773787	+	0.633446i	$0.781640\pi$
$504$	−1.81500	−0.0808464
$505$	9.51702	0.423502
$506$	3.99838	0.177750
$507$	15.1698	0.673715
$508$	60.6316	2.69009
$509$	−19.7850	−0.876953	−0.438477	−	0.898743i	$-0.644482\pi$
$509$	−19.7850	−0.876953	−0.438477	+	0.898743i	$0.644482\pi$
$510$	50.3482	2.22945
$511$	−4.76399	−0.210747
$512$	−0.752775	−0.0332682
$513$	−1.62829	−0.0718908
$514$	26.2526	1.15795
$515$	34.0081	1.49858
$516$	−78.7712	−3.46771
$517$	−1.63500	−0.0719074
$518$	−4.49208	−0.197371
$519$	12.8499	0.564046
$520$	26.5754	1.16541
$521$	5.60256	0.245453	0.122726	−	0.992441i	$-0.460836\pi$
$521$	5.60256	0.245453	0.122726	+	0.992441i	$0.460836\pi$
$522$	0	0
$523$	21.9899	0.961552	0.480776	−	0.876843i	$-0.340355\pi$
$523$	21.9899	0.961552	0.480776	+	0.876843i	$0.340355\pi$
$524$	47.2870	2.06574
$525$	−0.478413	−0.0208796
$526$	−69.7965	−3.04327
$527$	−24.8618	−1.08300
$528$	0.140426	0.00611124
$529$	−19.9380	−0.866870
$530$	28.6619	1.24499
$531$	−14.9661	−0.649473
$532$	0.719175	0.0311802
$533$	−15.6487	−0.677818
$534$	−57.6685	−2.49556
$535$	24.8466	1.07421
$536$	23.7827	1.02726
$537$	48.9468	2.11221
$538$	−56.4393	−2.43327
$539$	6.79981	0.292888
$540$	22.2806	0.958803
$541$	−28.3163	−1.21741	−0.608707	−	0.793395i	$-0.708312\pi$
$541$	−28.3163	−1.21741	−0.608707	+	0.793395i	$0.708312\pi$
$542$	28.4662	1.22273
$543$	38.7737	1.66394
$544$	28.2360	1.21061
$545$	6.65273	0.284972
$546$	−9.69438	−0.414881
$547$	3.11264	0.133087	0.0665434	−	0.997784i	$-0.478803\pi$
$547$	3.11264	0.133087	0.0665434	+	0.997784i	$0.478803\pi$
$548$	−21.1168	−0.902064
$549$	−2.21473	−0.0945225
$550$	−1.15770	−0.0493645
$551$	0	0
$552$	−10.3042	−0.438577
$553$	2.07002	0.0880263
$554$	5.82244	0.247372
$555$	−19.6558	−0.834343
$556$	−35.2953	−1.49686
$557$	−14.1231	−0.598417	−0.299208	−	0.954188i	$-0.596723\pi$
$557$	−14.1231	−0.598417	−0.299208	+	0.954188i	$0.596723\pi$
$558$	16.7675	0.709825
$559$	−52.0643	−2.20209
$560$	0.0631088	0.00266683
$561$	−10.3948	−0.438869
$562$	−12.1308	−0.511708
$563$	−7.81976	−0.329564	−0.164782	−	0.986330i	$-0.552692\pi$
$563$	−7.81976	−0.329564	−0.164782	+	0.986330i	$0.552692\pi$
$564$	11.1146	0.468009
$565$	22.4278	0.943545
$566$	48.5942	2.04257
$567$	−5.03262	−0.211350
$568$	−19.1068	−0.801703
$569$	30.9155	1.29604	0.648022	−	0.761622i	$-0.275597\pi$
$569$	30.9155	1.29604	0.648022	+	0.761622i	$0.275597\pi$
$570$	5.10074	0.213647
$571$	45.5837	1.90762	0.953810	−	0.300410i	$-0.0971234\pi$
$571$	45.5837	1.90762	0.953810	+	0.300410i	$0.0971234\pi$
$572$	−14.4730	−0.605145
$573$	−45.1099	−1.88449
$574$	3.56071	0.148621
$575$	−0.886574	−0.0369727
$576$	−18.8497	−0.785403
$577$	31.6357	1.31701	0.658506	−	0.752575i	$-0.271189\pi$
$577$	31.6357	1.31701	0.658506	+	0.752575i	$0.271189\pi$
$578$	−16.5904	−0.690068
$579$	−31.2362	−1.29813
$580$	0	0
$581$	−1.33133	−0.0552327
$582$	−23.5350	−0.975558
$583$	−5.91748	−0.245077
$584$	29.7094	1.22939
$585$	−13.8464	−0.572478
$586$	18.2253	0.752882
$587$	24.8583	1.02601	0.513005	−	0.858385i	$-0.328532\pi$
$587$	24.8583	1.02601	0.513005	+	0.858385i	$0.328532\pi$
$588$	−46.2244	−1.90626
$589$	−2.51873	−0.103783
$590$	−49.8622	−2.05280
$591$	−45.9262	−1.88915
$592$	−0.292363	−0.0120160
$593$	9.15335	0.375883	0.187941	−	0.982180i	$-0.439818\pi$
$593$	9.15335	0.375883	0.187941	+	0.982180i	$0.439818\pi$
$594$	−7.45614	−0.305929
$595$	−4.67154	−0.191514
$596$	44.2033	1.81064
$597$	−50.0023	−2.04646
$598$	−17.9652	−0.734652
$599$	3.28745	0.134322	0.0671608	−	0.997742i	$-0.478606\pi$
$599$	3.28745	0.134322	0.0671608	+	0.997742i	$0.478606\pi$
$600$	2.98350	0.121801
$601$	27.1507	1.10750	0.553751	−	0.832683i	$-0.313196\pi$
$601$	27.1507	1.10750	0.553751	+	0.832683i	$0.313196\pi$
$602$	11.8468	0.482838
$603$	−12.3913	−0.504613
$604$	−5.04994	−0.205479
$605$	−2.11975	−0.0861801
$606$	21.6503	0.879483
$607$	45.1098	1.83095	0.915474	−	0.402376i	$-0.131816\pi$
$607$	45.1098	1.83095	0.915474	+	0.402376i	$0.131816\pi$
$608$	2.86057	0.116011
$609$	0	0
$610$	−7.37879	−0.298759
$611$	7.34626	0.297198
$612$	23.0656	0.932370
$613$	−18.9676	−0.766095	−0.383047	−	0.923729i	$-0.625125\pi$
$613$	−18.9676	−0.766095	−0.383047	+	0.923729i	$0.625125\pi$
$614$	0.595675	0.0240395
$615$	15.5804	0.628263
$616$	1.24845	0.0503016
$617$	−5.92762	−0.238637	−0.119319	−	0.992856i	$-0.538071\pi$
$617$	−5.92762	−0.238637	−0.119319	+	0.992856i	$0.538071\pi$
$618$	77.3652	3.11209
$619$	17.1153	0.687921	0.343960	−	0.938984i	$-0.388231\pi$
$619$	17.1153	0.687921	0.343960	+	0.938984i	$0.388231\pi$
$620$	34.4648	1.38414
$621$	−5.70997	−0.229133
$622$	−3.53503	−0.141742
$623$	5.35076	0.214374
$624$	−0.630948	−0.0252582
$625$	−22.2100	−0.888401
$626$	57.3755	2.29319
$627$	−1.05309	−0.0420564
$628$	58.5091	2.33477
$629$	21.6417	0.862912
$630$	3.15062	0.125524
$631$	29.4331	1.17171	0.585857	−	0.810414i	$-0.300758\pi$
$631$	29.4331	1.17171	0.585857	+	0.810414i	$0.300758\pi$
$632$	−12.9092	−0.513499
$633$	50.7492	2.01710
$634$	54.6306	2.16966
$635$	−39.9001	−1.58339
$636$	40.2265	1.59508
$637$	−30.5523	−1.21053
$638$	0	0
$639$	9.95505	0.393816
$640$	−38.4977	−1.52176
$641$	6.71157	0.265091	0.132545	−	0.991177i	$-0.457685\pi$
$641$	6.71157	0.265091	0.132545	+	0.991177i	$0.457685\pi$
$642$	56.5236	2.23081
$643$	−8.26040	−0.325758	−0.162879	−	0.986646i	$-0.552078\pi$
$643$	−8.26040	−0.325758	−0.162879	+	0.986646i	$0.552078\pi$
$644$	2.52195	0.0993786
$645$	51.8373	2.04109
$646$	−5.61609	−0.220962
$647$	22.0711	0.867703	0.433852	−	0.900984i	$-0.357154\pi$
$647$	22.0711	0.867703	0.433852	+	0.900984i	$0.357154\pi$
$648$	31.3847	1.23291
$649$	10.2945	0.404094
$650$	5.20168	0.204027
$651$	−4.76619	−0.186802
$652$	8.87249	0.347474
$653$	−4.73521	−0.185303	−0.0926516	−	0.995699i	$-0.529534\pi$
$653$	−4.73521	−0.185303	−0.0926516	+	0.995699i	$0.529534\pi$
$654$	15.1343	0.591799
$655$	−31.1184	−1.21590
$656$	0.231745	0.00904811
$657$	−15.4793	−0.603904
$658$	−1.67157	−0.0651648
$659$	−12.8135	−0.499142	−0.249571	−	0.968357i	$-0.580290\pi$
$659$	−12.8135	−0.499142	−0.249571	+	0.968357i	$0.580290\pi$
$660$	14.4099	0.560903
$661$	−18.4495	−0.717603	−0.358802	−	0.933414i	$-0.616815\pi$
$661$	−18.4495	−0.717603	−0.358802	+	0.933414i	$0.616815\pi$
$662$	−11.5552	−0.449106
$663$	46.7051	1.81387
$664$	8.30248	0.322199
$665$	−0.473271	−0.0183527
$666$	−14.5958	−0.565575
$667$	0	0
$668$	−36.7191	−1.42070
$669$	−22.4104	−0.866435
$670$	−41.2839	−1.59494
$671$	1.52341	0.0588107
$672$	5.41304	0.208813
$673$	15.8405	0.610605	0.305302	−	0.952255i	$-0.401242\pi$
$673$	15.8405	0.610605	0.305302	+	0.952255i	$0.401242\pi$
$674$	30.2468	1.16506
$675$	1.65327	0.0636345
$676$	23.1539	0.890535
$677$	4.52085	0.173751	0.0868753	−	0.996219i	$-0.472312\pi$
$677$	4.52085	0.173751	0.0868753	+	0.996219i	$0.472312\pi$
$678$	51.0211	1.95945
$679$	2.18369	0.0838023
$680$	29.1329	1.11720
$681$	31.6347	1.21224
$682$	−11.5336	−0.441644
$683$	−9.63141	−0.368535	−0.184268	−	0.982876i	$-0.558991\pi$
$683$	−9.63141	−0.368535	−0.184268	+	0.982876i	$0.558991\pi$
$684$	2.33676	0.0893482
$685$	13.8964	0.530955
$686$	14.1085	0.538664
$687$	6.38800	0.243717
$688$	0.771034	0.0293954
$689$	26.5880	1.01292
$690$	17.8869	0.680942
$691$	21.5623	0.820267	0.410134	−	0.912025i	$-0.365482\pi$
$691$	21.5623	0.820267	0.410134	+	0.912025i	$0.365482\pi$
$692$	19.6129	0.745572
$693$	−0.650471	−0.0247094
$694$	51.0654	1.93841
$695$	23.2270	0.881050
$696$	0	0
$697$	−17.1546	−0.649776
$698$	52.8748	2.00134
$699$	−6.09876	−0.230676
$700$	−0.730209	−0.0275993
$701$	26.9097	1.01637	0.508183	−	0.861249i	$-0.330318\pi$
$701$	26.9097	1.01637	0.508183	+	0.861249i	$0.330318\pi$
$702$	33.5013	1.26443
$703$	2.19251	0.0826921
$704$	12.9658	0.488667
$705$	−7.31423	−0.275470
$706$	−9.57987	−0.360543
$707$	−2.00882	−0.0755493
$708$	−69.9808	−2.63004
$709$	45.6869	1.71581	0.857904	−	0.513810i	$-0.171766\pi$
$709$	45.6869	1.71581	0.857904	+	0.513810i	$0.171766\pi$
$710$	33.1671	1.24474
$711$	6.72596	0.252243
$712$	−33.3687	−1.25054
$713$	−8.83250	−0.330780
$714$	−10.6273	−0.397717
$715$	9.52429	0.356188
$716$	74.7083	2.79198
$717$	22.8204	0.852244
$718$	45.7650	1.70794
$719$	−16.3898	−0.611236	−0.305618	−	0.952154i	$-0.598863\pi$
$719$	−16.3898	−0.611236	−0.305618	+	0.952154i	$0.598863\pi$
$720$	0.205055	0.00764193
$721$	−7.17831	−0.267334
$722$	42.8457	1.59455
$723$	−52.6302	−1.95734
$724$	59.1809	2.19944
$725$	0	0
$726$	−4.82223	−0.178970
$727$	−15.9338	−0.590951	−0.295476	−	0.955350i	$-0.595478\pi$
$727$	−15.9338	−0.590951	−0.295476	+	0.955350i	$0.595478\pi$
$728$	−5.60945	−0.207900
$729$	4.30731	0.159530
$730$	−51.5720	−1.90877
$731$	−57.0747	−2.11098
$732$	−10.3560	−0.382769
$733$	−32.2321	−1.19052	−0.595261	−	0.803533i	$-0.702951\pi$
$733$	−32.2321	−1.19052	−0.595261	+	0.803533i	$0.702951\pi$
$734$	−49.3937	−1.82316
$735$	30.4191	1.12203
$736$	10.0312	0.369756
$737$	8.52341	0.313964
$738$	11.5695	0.425880
$739$	−4.23289	−0.155709	−0.0778547	−	0.996965i	$-0.524807\pi$
$739$	−4.23289	−0.155709	−0.0778547	+	0.996965i	$0.524807\pi$
$740$	−30.0010	−1.10286
$741$	4.73166	0.173822
$742$	−6.04984	−0.222097
$743$	−0.342820	−0.0125768	−0.00628842	−	0.999980i	$-0.502002\pi$
$743$	−0.342820	−0.0125768	−0.00628842	+	0.999980i	$0.502002\pi$
$744$	29.7232	1.08970
$745$	−29.0891	−1.06574
$746$	76.0681	2.78505
$747$	−4.32577	−0.158272
$748$	−15.8657	−0.580109
$749$	−5.24453	−0.191631
$750$	−56.2886	−2.05537
$751$	−16.1697	−0.590040	−0.295020	−	0.955491i	$-0.595326\pi$
$751$	−16.1697	−0.590040	−0.295020	+	0.955491i	$0.595326\pi$
$752$	−0.108793	−0.00396726
$753$	55.8357	2.03477
$754$	0	0
$755$	3.32324	0.120945
$756$	−4.70290	−0.171043
$757$	−48.5100	−1.76312	−0.881562	−	0.472068i	$-0.843508\pi$
$757$	−48.5100	−1.76312	−0.881562	+	0.472068i	$0.843508\pi$
$758$	−9.56427	−0.347390
$759$	−3.69290	−0.134044
$760$	2.95144	0.107060
$761$	−31.6392	−1.14692	−0.573460	−	0.819233i	$-0.694399\pi$
$761$	−31.6392	−1.14692	−0.573460	+	0.819233i	$0.694399\pi$
$762$	−90.7689	−3.28821
$763$	−1.40423	−0.0508367
$764$	−68.8519	−2.49098
$765$	−15.1789	−0.548793
$766$	−40.4027	−1.45981
$767$	−46.2543	−1.67015
$768$	−32.8524	−1.18546
$769$	−50.3321	−1.81502	−0.907512	−	0.420026i	$-0.862021\pi$
$769$	−50.3321	−1.81502	−0.907512	+	0.420026i	$0.862021\pi$
$770$	−2.16716	−0.0780992
$771$	−24.2469	−0.873229
$772$	−47.6763	−1.71591
$773$	0.450068	0.0161878	0.00809390	−	0.999967i	$-0.497424\pi$
$773$	0.450068	0.0161878	0.00809390	+	0.999967i	$0.497424\pi$
$774$	38.4928	1.38359
$775$	2.55738	0.0918637
$776$	−13.6180	−0.488859
$777$	4.14888	0.148840
$778$	58.4029	2.09384
$779$	−1.73792	−0.0622674
$780$	−64.7452	−2.31825
$781$	−6.84762	−0.245027
$782$	−19.6941	−0.704258
$783$	0	0
$784$	0.452457	0.0161592
$785$	−38.5033	−1.37424
$786$	−70.7914	−2.52504
$787$	−16.0743	−0.572987	−0.286494	−	0.958082i	$-0.592490\pi$
$787$	−16.0743	−0.572987	−0.286494	+	0.958082i	$0.592490\pi$
$788$	−70.0978	−2.49713
$789$	64.4638	2.29497
$790$	22.4088	0.797268
$791$	−4.73398	−0.168321
$792$	4.05650	0.144142
$793$	−6.84488	−0.243069
$794$	75.6684	2.68537
$795$	−26.4720	−0.938866
$796$	−76.3193	−2.70506
$797$	−10.4596	−0.370497	−0.185249	−	0.982692i	$-0.559309\pi$
$797$	−10.4596	−0.370497	−0.185249	+	0.982692i	$0.559309\pi$
$798$	−1.07665	−0.0381128
$799$	8.05322	0.284902
$800$	−2.90446	−0.102688
$801$	17.3858	0.614297
$802$	65.7724	2.32250
$803$	10.6475	0.375741
$804$	−57.9413	−2.04343
$805$	−1.65963	−0.0584942
$806$	51.8218	1.82534
$807$	52.1272	1.83496
$808$	12.5275	0.440715
$809$	1.97170	0.0693214	0.0346607	−	0.999399i	$-0.488965\pi$
$809$	1.97170	0.0693214	0.0346607	+	0.999399i	$0.488965\pi$
$810$	−54.4801	−1.91423
$811$	−35.6631	−1.25230	−0.626151	−	0.779702i	$-0.715370\pi$
$811$	−35.6631	−1.25230	−0.626151	+	0.779702i	$0.715370\pi$
$812$	0	0
$813$	−26.2913	−0.922077
$814$	10.0398	0.351894
$815$	−5.83877	−0.204523
$816$	−0.691667	−0.0242132
$817$	−5.78220	−0.202294
$818$	44.2246	1.54628
$819$	2.92264	0.102125
$820$	23.7806	0.830456
$821$	−17.8325	−0.622359	−0.311180	−	0.950351i	$-0.600724\pi$
$821$	−17.8325	−0.622359	−0.311180	+	0.950351i	$0.600724\pi$
$822$	31.6130	1.10263
$823$	23.3265	0.813111	0.406555	−	0.913626i	$-0.366730\pi$
$823$	23.3265	0.813111	0.406555	+	0.913626i	$0.366730\pi$
$824$	44.7657	1.55949
$825$	1.06925	0.0372264
$826$	10.5247	0.366202
$827$	13.3167	0.463066	0.231533	−	0.972827i	$-0.425626\pi$
$827$	13.3167	0.463066	0.231533	+	0.972827i	$0.425626\pi$
$828$	8.19436	0.284774
$829$	31.7271	1.10193	0.550963	−	0.834529i	$-0.314260\pi$
$829$	31.7271	1.10193	0.550963	+	0.834529i	$0.314260\pi$
$830$	−14.4121	−0.500252
$831$	−5.37759	−0.186547
$832$	−58.2569	−2.01970
$833$	−33.4925	−1.16045
$834$	52.8391	1.82967
$835$	24.1639	0.836226
$836$	−1.60735	−0.0555913
$837$	16.4708	0.569313
$838$	15.7766	0.544993
$839$	−29.9492	−1.03396	−0.516981	−	0.855997i	$-0.672944\pi$
$839$	−29.9492	−1.03396	−0.516981	+	0.855997i	$0.672944\pi$
$840$	5.58499	0.192700
$841$	0	0
$842$	23.9311	0.824720
$843$	11.2040	0.385886
$844$	77.4592	2.66626
$845$	−15.2370	−0.524169
$846$	−5.43132	−0.186733
$847$	0.447429	0.0153739
$848$	−0.393748	−0.0135213
$849$	−44.8815	−1.54033
$850$	5.70225	0.195586
$851$	7.68852	0.263559
$852$	46.5494	1.59476
$853$	26.6894	0.913828	0.456914	−	0.889511i	$-0.348955\pi$
$853$	26.6894	0.913828	0.456914	+	0.889511i	$0.348955\pi$
$854$	1.55749	0.0532962
$855$	−1.53776	−0.0525904
$856$	32.7062	1.11787
$857$	26.1734	0.894066	0.447033	−	0.894517i	$-0.352481\pi$
$857$	26.1734	0.894066	0.447033	+	0.894517i	$0.352481\pi$
$858$	21.6668	0.739694
$859$	−18.8152	−0.641968	−0.320984	−	0.947085i	$-0.604013\pi$
$859$	−18.8152	−0.641968	−0.320984	+	0.947085i	$0.604013\pi$
$860$	79.1201	2.69797
$861$	−3.28866	−0.112077
$862$	52.7418	1.79639
$863$	44.5807	1.51754	0.758772	−	0.651357i	$-0.225800\pi$
$863$	44.5807	1.51754	0.758772	+	0.651357i	$0.225800\pi$
$864$	−18.7061	−0.636395
$865$	−12.9068	−0.438844
$866$	−50.9716	−1.73208
$867$	15.3228	0.520390
$868$	−7.27471	−0.246920
$869$	−4.62648	−0.156942
$870$	0	0
$871$	−38.2967	−1.29763
$872$	8.75716	0.296555
$873$	7.09529	0.240139
$874$	−1.99519	−0.0674884
$875$	5.22273	0.176560
$876$	−72.3805	−2.44551
$877$	−37.3930	−1.26267	−0.631336	−	0.775509i	$-0.717493\pi$
$877$	−37.3930	−1.26267	−0.631336	+	0.775509i	$0.717493\pi$
$878$	−4.07725	−0.137601
$879$	−16.8329	−0.567758
$880$	−0.141048	−0.00475471
$881$	24.7255	0.833025	0.416512	−	0.909130i	$-0.363252\pi$
$881$	24.7255	0.833025	0.416512	+	0.909130i	$0.363252\pi$
$882$	22.5883	0.760587
$883$	25.5481	0.859762	0.429881	−	0.902886i	$-0.358555\pi$
$883$	25.5481	0.859762	0.429881	+	0.902886i	$0.358555\pi$
$884$	71.2867	2.39763
$885$	46.0526	1.54804
$886$	−61.4836	−2.06558
$887$	−47.6180	−1.59885	−0.799427	−	0.600763i	$-0.794864\pi$
$887$	−47.6180	−1.59885	−0.799427	+	0.600763i	$0.794864\pi$
$888$	−25.8734	−0.868255
$889$	8.42197	0.282464
$890$	57.9240	1.94162
$891$	11.2479	0.376818
$892$	−34.2053	−1.14528
$893$	0.815867	0.0273019
$894$	−66.1748	−2.21322
$895$	−49.1636	−1.64336
$896$	8.12596	0.271469
$897$	16.5926	0.554011
$898$	−51.0221	−1.70263
$899$	0	0
$900$	−2.37261	−0.0790870
$901$	29.1466	0.971014
$902$	−7.95814	−0.264977
$903$	−10.9416	−0.364115
$904$	29.5223	0.981897
$905$	−38.9455	−1.29459
$906$	7.56005	0.251166
$907$	−26.2662	−0.872154	−0.436077	−	0.899909i	$-0.643632\pi$
$907$	−26.2662	−0.872154	−0.436077	+	0.899909i	$0.643632\pi$
$908$	48.2845	1.60238
$909$	−6.52709	−0.216490
$910$	9.73733	0.322789
$911$	12.1947	0.404028	0.202014	−	0.979383i	$-0.435251\pi$
$911$	12.1947	0.404028	0.202014	+	0.979383i	$0.435251\pi$
$912$	−0.0700723	−0.00232033
$913$	2.97550	0.0984747
$914$	67.7552	2.24114
$915$	6.81503	0.225298
$916$	9.75010	0.322152
$917$	6.56836	0.216906
$918$	36.7253	1.21212
$919$	−5.61477	−0.185214	−0.0926070	−	0.995703i	$-0.529520\pi$
$919$	−5.61477	−0.185214	−0.0926070	+	0.995703i	$0.529520\pi$
$920$	10.3499	0.341225
$921$	−0.550163	−0.0181285
$922$	80.1425	2.63935
$923$	30.7672	1.01271
$924$	−3.04158	−0.100061
$925$	−2.22615	−0.0731953
$926$	−33.9419	−1.11540
$927$	−23.3239	−0.766058
$928$	0	0
$929$	16.2678	0.533730	0.266865	−	0.963734i	$-0.414012\pi$
$929$	16.2678	0.533730	0.266865	+	0.963734i	$0.414012\pi$
$930$	−51.5958	−1.69189
$931$	−3.39310	−0.111204
$932$	−9.30864	−0.304915
$933$	3.26494	0.106889
$934$	80.3043	2.62764
$935$	10.4408	0.341452
$936$	−18.2263	−0.595747
$937$	36.4680	1.19136	0.595679	−	0.803222i	$-0.296883\pi$
$937$	36.4680	1.19136	0.595679	+	0.803222i	$0.296883\pi$
$938$	8.71406	0.284524
$939$	−52.9918	−1.72932
$940$	−11.1638	−0.364124
$941$	−13.2041	−0.430442	−0.215221	−	0.976565i	$-0.569047\pi$
$941$	−13.2041	−0.430442	−0.215221	+	0.976565i	$0.569047\pi$
$942$	−87.5914	−2.85388
$943$	−6.09440	−0.198461
$944$	0.684991	0.0222946
$945$	3.09486	0.100676
$946$	−26.4774	−0.860854
$947$	53.9852	1.75428	0.877141	−	0.480232i	$-0.159448\pi$
$947$	53.9852	1.75428	0.877141	+	0.480232i	$0.159448\pi$
$948$	31.4503	1.02146
$949$	−47.8404	−1.55296
$950$	0.577692	0.0187428
$951$	−50.4566	−1.63617
$952$	−6.14926	−0.199299
$953$	51.5101	1.66858	0.834288	−	0.551329i	$-0.185879\pi$
$953$	51.5101	1.66858	0.834288	+	0.551329i	$0.185879\pi$
$954$	−19.6573	−0.636428
$955$	45.3097	1.46619
$956$	34.8311	1.12652
$957$	0	0
$958$	31.4777	1.01700
$959$	−2.93320	−0.0947181
$960$	58.0029	1.87204
$961$	−5.52209	−0.178132
$962$	−45.1098	−1.45440
$963$	−17.0406	−0.549127
$964$	−80.3303	−2.58726
$965$	31.3746	1.00998
$966$	−3.77550	−0.121475
$967$	−46.3577	−1.49076	−0.745382	−	0.666638i	$-0.767733\pi$
$967$	−46.3577	−1.49076	−0.745382	+	0.666638i	$0.767733\pi$
$968$	−2.79028	−0.0896830
$969$	5.18700	0.166631
$970$	23.6393	0.759011
$971$	−7.90267	−0.253609	−0.126804	−	0.991928i	$-0.540472\pi$
$971$	−7.90267	−0.253609	−0.126804	+	0.991928i	$0.540472\pi$
$972$	−44.9291	−1.44110
$973$	−4.90267	−0.157172
$974$	−80.9425	−2.59357
$975$	−4.80426	−0.153859
$976$	0.101367	0.00324469
$977$	−10.5388	−0.337165	−0.168582	−	0.985688i	$-0.553919\pi$
$977$	−10.5388	−0.337165	−0.168582	+	0.985688i	$0.553919\pi$
$978$	−13.2826	−0.424732
$979$	−11.9589	−0.382208
$980$	46.4292	1.48313
$981$	−4.56267	−0.145675
$982$	79.9838	2.55238
$983$	−34.1585	−1.08949	−0.544743	−	0.838603i	$-0.683373\pi$
$983$	−34.1585	−1.08949	−0.544743	+	0.838603i	$0.683373\pi$
$984$	20.5089	0.653800
$985$	46.1296	1.46981
$986$	0	0
$987$	1.54386	0.0491417
$988$	7.22201	0.229763
$989$	−20.2766	−0.644757
$990$	−7.04160	−0.223797
$991$	−4.67656	−0.148556	−0.0742779	−	0.997238i	$-0.523665\pi$
$991$	−4.67656	−0.148556	−0.0742779	+	0.997238i	$0.523665\pi$
$992$	−28.9357	−0.918709
$993$	10.6724	0.338677
$994$	−7.00078	−0.222051
$995$	50.2238	1.59220
$996$	−20.2272	−0.640922
$997$	9.61103	0.304384	0.152192	−	0.988351i	$-0.451367\pi$
$997$	9.61103	0.304384	0.152192	+	0.988351i	$0.451367\pi$
$998$	−49.7321	−1.57424
$999$	−14.3375	−0.453618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.2	yes	18
29.28	even	2		9251.2.a.s.1.17	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.17	✓	18	29.28	even	2
9251.2.a.t.1.2	yes	18	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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28498 q^{2} +2.11040 q^{3} +3.22114 q^{4} -2.11975 q^{5} -4.82223 q^{6} +0.447429 q^{7} -2.79028 q^{8} +1.45380 q^{9} +O(q^{10})\)	\(q-2.28498 q^{2} +2.11040 q^{3} +3.22114 q^{4} -2.11975 q^{5} -4.82223 q^{6} +0.447429 q^{7} -2.79028 q^{8} +1.45380 q^{9} +4.84359 q^{10} -1.00000 q^{11} +6.79790 q^{12} +4.49312 q^{13} -1.02237 q^{14} -4.47353 q^{15} -0.0665397 q^{16} +4.92551 q^{17} -3.32190 q^{18} +0.499000 q^{19} -6.82801 q^{20} +0.944256 q^{21} +2.28498 q^{22} +1.74985 q^{23} -5.88861 q^{24} -0.506656 q^{25} -10.2667 q^{26} -3.26311 q^{27} +1.44123 q^{28} +10.2219 q^{30} -5.04756 q^{31} +5.73260 q^{32} -2.11040 q^{33} -11.2547 q^{34} -0.948439 q^{35} +4.68288 q^{36} +4.39381 q^{37} -1.14021 q^{38} +9.48229 q^{39} +5.91470 q^{40} -3.48281 q^{41} -2.15761 q^{42} -11.5876 q^{43} -3.22114 q^{44} -3.08169 q^{45} -3.99838 q^{46} +1.63500 q^{47} -0.140426 q^{48} -6.79981 q^{49} +1.15770 q^{50} +10.3948 q^{51} +14.4730 q^{52} +5.91748 q^{53} +7.45614 q^{54} +2.11975 q^{55} -1.24845 q^{56} +1.05309 q^{57} -10.2945 q^{59} -14.4099 q^{60} -1.52341 q^{61} +11.5336 q^{62} +0.650471 q^{63} -12.9658 q^{64} -9.52429 q^{65} +4.82223 q^{66} -8.52341 q^{67} +15.8657 q^{68} +3.69290 q^{69} +2.16716 q^{70} +6.84762 q^{71} -4.05650 q^{72} -10.6475 q^{73} -10.0398 q^{74} -1.06925 q^{75} +1.60735 q^{76} -0.447429 q^{77} -21.6668 q^{78} +4.62648 q^{79} +0.141048 q^{80} -11.2479 q^{81} +7.95814 q^{82} -2.97550 q^{83} +3.04158 q^{84} -10.4408 q^{85} +26.4774 q^{86} +2.79028 q^{88} +11.9589 q^{89} +7.04160 q^{90} +2.01035 q^{91} +5.63652 q^{92} -10.6524 q^{93} -3.73595 q^{94} -1.05776 q^{95} +12.0981 q^{96} +4.88053 q^{97} +15.5374 q^{98} -1.45380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

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