LMFDB - Embedded newform 9251.2.a.t.1.4

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			1.4
Root			$1.89582$ 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)

$f(q)$	$=$	$q-1.89582 q^{2} +2.92716 q^{3} +1.59413 q^{4} +3.33397 q^{5} -5.54937 q^{6} -1.77166 q^{7} +0.769459 q^{8} +5.56828 q^{9} +O(q^{10})$	\(q-1.89582 q^{2} +2.92716 q^{3} +1.59413 q^{4} +3.33397 q^{5} -5.54937 q^{6} -1.77166 q^{7} +0.769459 q^{8} +5.56828 q^{9} -6.32060 q^{10} -1.00000 q^{11} +4.66627 q^{12} -6.76156 q^{13} +3.35874 q^{14} +9.75906 q^{15} -4.64701 q^{16} -2.82072 q^{17} -10.5565 q^{18} +0.483136 q^{19} +5.31477 q^{20} -5.18593 q^{21} +1.89582 q^{22} +4.88441 q^{23} +2.25233 q^{24} +6.11534 q^{25} +12.8187 q^{26} +7.51778 q^{27} -2.82425 q^{28} -18.5014 q^{30} +3.10561 q^{31} +7.27097 q^{32} -2.92716 q^{33} +5.34757 q^{34} -5.90665 q^{35} +8.87655 q^{36} -7.47476 q^{37} -0.915938 q^{38} -19.7922 q^{39} +2.56535 q^{40} -4.01448 q^{41} +9.83158 q^{42} -11.2195 q^{43} -1.59413 q^{44} +18.5645 q^{45} -9.25995 q^{46} -8.66824 q^{47} -13.6026 q^{48} -3.86123 q^{49} -11.5936 q^{50} -8.25670 q^{51} -10.7788 q^{52} -9.89373 q^{53} -14.2523 q^{54} -3.33397 q^{55} -1.36322 q^{56} +1.41422 q^{57} -7.39943 q^{59} +15.5572 q^{60} +6.20176 q^{61} -5.88768 q^{62} -9.86509 q^{63} -4.49042 q^{64} -22.5428 q^{65} +5.54937 q^{66} -4.52890 q^{67} -4.49659 q^{68} +14.2974 q^{69} +11.1979 q^{70} +3.22615 q^{71} +4.28457 q^{72} +16.0650 q^{73} +14.1708 q^{74} +17.9006 q^{75} +0.770181 q^{76} +1.77166 q^{77} +37.5224 q^{78} -4.41957 q^{79} -15.4930 q^{80} +5.30092 q^{81} +7.61073 q^{82} -7.64237 q^{83} -8.26704 q^{84} -9.40418 q^{85} +21.2701 q^{86} -0.769459 q^{88} +10.0683 q^{89} -35.1949 q^{90} +11.9792 q^{91} +7.78637 q^{92} +9.09063 q^{93} +16.4334 q^{94} +1.61076 q^{95} +21.2833 q^{96} +13.9404 q^{97} +7.32019 q^{98} -5.56828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.89582	−1.34055	−0.670273	−	0.742115i	$-0.733823\pi$
$2$	−1.89582	−1.34055	−0.670273	+	0.742115i	$0.733823\pi$
$3$	2.92716	1.69000	0.844999	−	0.534768i	$-0.179601\pi$
$3$	2.92716	1.69000	0.844999	+	0.534768i	$0.179601\pi$
$4$	1.59413	0.797064
$5$	3.33397	1.49100	0.745498	−	0.666508i	$-0.232212\pi$
$5$	3.33397	1.49100	0.745498	+	0.666508i	$0.232212\pi$
$6$	−5.54937	−2.26552
$7$	−1.77166	−0.669624	−0.334812	−	0.942285i	$-0.608673\pi$
$7$	−1.77166	−0.669624	−0.334812	+	0.942285i	$0.608673\pi$
$8$	0.769459	0.272045
$9$	5.56828	1.85609
$10$	−6.32060	−1.99875
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.66627	1.34704
$13$	−6.76156	−1.87532	−0.937660	−	0.347553i	$-0.887013\pi$
$13$	−6.76156	−1.87532	−0.937660	+	0.347553i	$0.887013\pi$
$14$	3.35874	0.897662
$15$	9.75906	2.51978
$16$	−4.64701	−1.16175
$17$	−2.82072	−0.684125	−0.342062	−	0.939677i	$-0.611125\pi$
$17$	−2.82072	−0.684125	−0.342062	+	0.939677i	$0.611125\pi$
$18$	−10.5565	−2.48818
$19$	0.483136	0.110839	0.0554195	−	0.998463i	$-0.482350\pi$
$19$	0.483136	0.110839	0.0554195	+	0.998463i	$0.482350\pi$
$20$	5.31477	1.18842
$21$	−5.18593	−1.13166
$22$	1.89582	0.404190
$23$	4.88441	1.01847	0.509234	−	0.860628i	$-0.329929\pi$
$23$	4.88441	1.01847	0.509234	+	0.860628i	$0.329929\pi$
$24$	2.25233	0.459756
$25$	6.11534	1.22307
$26$	12.8187	2.51395
$27$	7.51778	1.44680
$28$	−2.82425	−0.533733
$29$	0	0
$29$	0	0
$30$	−18.5014	−3.37788
$31$	3.10561	0.557784	0.278892	−	0.960322i	$-0.410033\pi$
$31$	3.10561	0.557784	0.278892	+	0.960322i	$0.410033\pi$
$32$	7.27097	1.28534
$33$	−2.92716	−0.509554
$34$	5.34757	0.917101
$35$	−5.90665	−0.998406
$36$	8.87655	1.47943
$37$	−7.47476	−1.22884	−0.614422	−	0.788978i	$-0.710611\pi$
$37$	−7.47476	−1.22884	−0.614422	+	0.788978i	$0.710611\pi$
$38$	−0.915938	−0.148585
$39$	−19.7922	−3.16929
$40$	2.56535	0.405618
$41$	−4.01448	−0.626957	−0.313478	−	0.949595i	$-0.601494\pi$
$41$	−4.01448	−0.626957	−0.313478	+	0.949595i	$0.601494\pi$
$42$	9.83158	1.51705
$43$	−11.2195	−1.71096	−0.855479	−	0.517837i	$-0.826737\pi$
$43$	−11.2195	−1.71096	−0.855479	+	0.517837i	$0.826737\pi$
$44$	−1.59413	−0.240324
$45$	18.5645	2.76743
$46$	−9.25995	−1.36530
$47$	−8.66824	−1.26439	−0.632196	−	0.774808i	$-0.717846\pi$
$47$	−8.66824	−1.26439	−0.632196	+	0.774808i	$0.717846\pi$
$48$	−13.6026	−1.96336
$49$	−3.86123	−0.551604
$50$	−11.5936	−1.63958
$51$	−8.25670	−1.15617
$52$	−10.7788	−1.49475
$53$	−9.89373	−1.35901	−0.679504	−	0.733672i	$-0.737805\pi$
$53$	−9.89373	−1.35901	−0.679504	+	0.733672i	$0.737805\pi$
$54$	−14.2523	−1.93950
$55$	−3.33397	−0.449552
$56$	−1.36322	−0.182168
$57$	1.41422	0.187318
$58$	0	0
$59$	−7.39943	−0.963324	−0.481662	−	0.876357i	$-0.659967\pi$
$59$	−7.39943	−0.963324	−0.481662	+	0.876357i	$0.659967\pi$
$60$	15.5572	2.00843
$61$	6.20176	0.794054	0.397027	−	0.917807i	$-0.370042\pi$
$61$	6.20176	0.794054	0.397027	+	0.917807i	$0.370042\pi$
$62$	−5.88768	−0.747736
$63$	−9.86509	−1.24288
$64$	−4.49042	−0.561303
$65$	−22.5428	−2.79609
$66$	5.54937	0.683080
$67$	−4.52890	−0.553293	−0.276647	−	0.960972i	$-0.589223\pi$
$67$	−4.52890	−0.553293	−0.276647	+	0.960972i	$0.589223\pi$
$68$	−4.49659	−0.545291
$69$	14.2974	1.72121
$70$	11.1979	1.33841
$71$	3.22615	0.382874	0.191437	−	0.981505i	$-0.438685\pi$
$71$	3.22615	0.382874	0.191437	+	0.981505i	$0.438685\pi$
$72$	4.28457	0.504941
$73$	16.0650	1.88027	0.940133	−	0.340807i	$-0.110700\pi$
$73$	16.0650	1.88027	0.940133	+	0.340807i	$0.110700\pi$
$74$	14.1708	1.64732
$75$	17.9006	2.06698
$76$	0.770181	0.0883458
$77$	1.77166	0.201899
$78$	37.5224	4.24858
$79$	−4.41957	−0.497240	−0.248620	−	0.968601i	$-0.579977\pi$
$79$	−4.41957	−0.497240	−0.248620	+	0.968601i	$0.579977\pi$
$80$	−15.4930	−1.73217
$81$	5.30092	0.588991
$82$	7.61073	0.840464
$83$	−7.64237	−0.838859	−0.419430	−	0.907788i	$-0.637770\pi$
$83$	−7.64237	−0.838859	−0.419430	+	0.907788i	$0.637770\pi$
$84$	−8.26704	−0.902008
$85$	−9.40418	−1.02003
$86$	21.2701	2.29362
$87$	0	0
$88$	−0.769459	−0.0820247
$89$	10.0683	1.06723	0.533617	−	0.845726i	$-0.320832\pi$
$89$	10.0683	1.06723	0.533617	+	0.845726i	$0.320832\pi$
$90$	−35.1949	−3.70986
$91$	11.9792	1.25576
$92$	7.78637	0.811785
$93$	9.09063	0.942655
$94$	16.4334	1.69498
$95$	1.61076	0.165260
$96$	21.2833	2.17222
$97$	13.9404	1.41543	0.707715	−	0.706498i	$-0.249726\pi$
$97$	13.9404	1.41543	0.707715	+	0.706498i	$0.249726\pi$
$98$	7.32019	0.739451
$99$	−5.56828	−0.559633
$100$	9.74863	0.974863
$101$	0.396276	0.0394309	0.0197155	−	0.999806i	$-0.493724\pi$
$101$	0.396276	0.0394309	0.0197155	+	0.999806i	$0.493724\pi$
$102$	15.6532	1.54990
$103$	−7.52497	−0.741457	−0.370728	−	0.928741i	$-0.620892\pi$
$103$	−7.52497	−0.741457	−0.370728	+	0.928741i	$0.620892\pi$
$104$	−5.20275	−0.510172
$105$	−17.2897	−1.68730
$106$	18.7567	1.82181
$107$	15.0869	1.45850	0.729252	−	0.684246i	$-0.239868\pi$
$107$	15.0869	1.45850	0.729252	+	0.684246i	$0.239868\pi$
$108$	11.9843	1.15319
$109$	−16.8472	−1.61367	−0.806833	−	0.590780i	$-0.798820\pi$
$109$	−16.8472	−1.61367	−0.806833	+	0.590780i	$0.798820\pi$
$110$	6.32060	0.602645
$111$	−21.8799	−2.07674
$112$	8.23291	0.777937
$113$	−10.2770	−0.966781	−0.483391	−	0.875405i	$-0.660595\pi$
$113$	−10.2770	−0.966781	−0.483391	+	0.875405i	$0.660595\pi$
$114$	−2.68110	−0.251108
$115$	16.2844	1.51853
$116$	0	0
$117$	−37.6503	−3.48077
$118$	14.0280	1.29138
$119$	4.99735	0.458106
$120$	7.50920	0.685493
$121$	1.00000	0.0909091
$122$	−11.7574	−1.06447
$123$	−11.7510	−1.05956
$124$	4.95074	0.444590
$125$	3.71849	0.332592
$126$	18.7024	1.66614
$127$	−2.84010	−0.252018	−0.126009	−	0.992029i	$-0.540217\pi$
$127$	−2.84010	−0.252018	−0.126009	+	0.992029i	$0.540217\pi$
$128$	−6.02892	−0.532886
$129$	−32.8413	−2.89152
$130$	42.7371	3.74829
$131$	−22.4489	−1.96137	−0.980685	−	0.195594i	$-0.937337\pi$
$131$	−22.4489	−1.96137	−0.980685	+	0.195594i	$0.937337\pi$
$132$	−4.66627	−0.406147
$133$	−0.855952	−0.0742204
$134$	8.58597	0.741715
$135$	25.0640	2.15717
$136$	−2.17043	−0.186113
$137$	0.424773	0.0362908	0.0181454	−	0.999835i	$-0.494224\pi$
$137$	0.424773	0.0362908	0.0181454	+	0.999835i	$0.494224\pi$
$138$	−27.1054	−2.30736
$139$	7.26632	0.616321	0.308161	−	0.951334i	$-0.400287\pi$
$139$	7.26632	0.616321	0.308161	+	0.951334i	$0.400287\pi$
$140$	−9.41595	−0.795793
$141$	−25.3733	−2.13682
$142$	−6.11620	−0.513260
$143$	6.76156	0.565430
$144$	−25.8759	−2.15632
$145$	0	0
$146$	−30.4563	−2.52058
$147$	−11.3024	−0.932210
$148$	−11.9157	−0.979467
$149$	−9.21091	−0.754587	−0.377293	−	0.926094i	$-0.623145\pi$
$149$	−9.21091	−0.754587	−0.377293	+	0.926094i	$0.623145\pi$
$150$	−33.9363	−2.77088
$151$	−8.56166	−0.696738	−0.348369	−	0.937358i	$-0.613264\pi$
$151$	−8.56166	−0.696738	−0.348369	+	0.937358i	$0.613264\pi$
$152$	0.371754	0.0301532
$153$	−15.7066	−1.26980
$154$	−3.35874	−0.270655
$155$	10.3540	0.831654
$156$	−31.5513	−2.52613
$157$	23.3066	1.86007	0.930033	−	0.367476i	$-0.119778\pi$
$157$	23.3066	1.86007	0.930033	+	0.367476i	$0.119778\pi$
$158$	8.37870	0.666574
$159$	−28.9606	−2.29672
$160$	24.2412	1.91643
$161$	−8.65349	−0.681991
$162$	−10.0496	−0.789570
$163$	21.7160	1.70093	0.850463	−	0.526036i	$-0.176322\pi$
$163$	21.7160	1.70093	0.850463	+	0.526036i	$0.176322\pi$
$164$	−6.39960	−0.499724
$165$	−9.75906	−0.759742
$166$	14.4885	1.12453
$167$	3.51679	0.272138	0.136069	−	0.990699i	$-0.456553\pi$
$167$	3.51679	0.272138	0.136069	+	0.990699i	$0.456553\pi$
$168$	−3.99036	−0.307863
$169$	32.7187	2.51683
$170$	17.8286	1.36739
$171$	2.69024	0.205728
$172$	−17.8853	−1.36374
$173$	3.18060	0.241816	0.120908	−	0.992664i	$-0.461419\pi$
$173$	3.18060	0.241816	0.120908	+	0.992664i	$0.461419\pi$
$174$	0	0
$175$	−10.8343	−0.818995
$176$	4.64701	0.350282
$177$	−21.6593	−1.62802
$178$	−19.0876	−1.43068
$179$	−4.19182	−0.313311	−0.156656	−	0.987653i	$-0.550071\pi$
$179$	−4.19182	−0.313311	−0.156656	+	0.987653i	$0.550071\pi$
$180$	29.5941	2.20582
$181$	−18.3239	−1.36201	−0.681003	−	0.732280i	$-0.738456\pi$
$181$	−18.3239	−1.36201	−0.681003	+	0.732280i	$0.738456\pi$
$182$	−22.7103	−1.68340
$183$	18.1536	1.34195
$184$	3.75835	0.277069
$185$	−24.9206	−1.83220
$186$	−17.2342	−1.26367
$187$	2.82072	0.206271
$188$	−13.8183	−1.00780
$189$	−13.3189	−0.968810
$190$	−3.05371	−0.221539
$191$	4.76220	0.344581	0.172290	−	0.985046i	$-0.444883\pi$
$191$	4.76220	0.344581	0.172290	+	0.985046i	$0.444883\pi$
$192$	−13.1442	−0.948600
$193$	−11.0603	−0.796140	−0.398070	−	0.917355i	$-0.630320\pi$
$193$	−11.0603	−0.796140	−0.398070	+	0.917355i	$0.630320\pi$
$194$	−26.4284	−1.89745
$195$	−65.9865	−4.72539
$196$	−6.15529	−0.439664
$197$	−3.32925	−0.237199	−0.118600	−	0.992942i	$-0.537840\pi$
$197$	−3.32925	−0.237199	−0.118600	+	0.992942i	$0.537840\pi$
$198$	10.5565	0.750214
$199$	−15.9299	−1.12924	−0.564620	−	0.825351i	$-0.690977\pi$
$199$	−15.9299	−1.12924	−0.564620	+	0.825351i	$0.690977\pi$
$200$	4.70550	0.332729
$201$	−13.2568	−0.935064
$202$	−0.751268	−0.0528590
$203$	0	0
$204$	−13.1622	−0.921541
$205$	−13.3841	−0.934789
$206$	14.2660	0.993957
$207$	27.1977	1.89037
$208$	31.4211	2.17866
$209$	−0.483136	−0.0334192
$210$	32.7782	2.26191
$211$	22.8622	1.57390	0.786949	−	0.617018i	$-0.211660\pi$
$211$	22.8622	1.57390	0.786949	+	0.617018i	$0.211660\pi$
$212$	−15.7719	−1.08322
$213$	9.44348	0.647057
$214$	−28.6020	−1.95519
$215$	−37.4055	−2.55103
$216$	5.78463	0.393594
$217$	−5.50208	−0.373506
$218$	31.9392	2.16319
$219$	47.0249	3.17765
$220$	−5.31477	−0.358322
$221$	19.0725	1.28295
$222$	41.4802	2.78397
$223$	−2.46621	−0.165150	−0.0825748	−	0.996585i	$-0.526314\pi$
$223$	−2.46621	−0.165150	−0.0825748	+	0.996585i	$0.526314\pi$
$224$	−12.8817	−0.860693
$225$	34.0519	2.27013
$226$	19.4834	1.29602
$227$	−1.04932	−0.0696460	−0.0348230	−	0.999393i	$-0.511087\pi$
$227$	−1.04932	−0.0696460	−0.0348230	+	0.999393i	$0.511087\pi$
$228$	2.25444	0.149304
$229$	−14.6063	−0.965215	−0.482607	−	0.875837i	$-0.660310\pi$
$229$	−14.6063	−0.965215	−0.482607	+	0.875837i	$0.660310\pi$
$230$	−30.8724	−2.03566
$231$	5.18593	0.341209
$232$	0	0
$233$	15.9175	1.04279	0.521396	−	0.853315i	$-0.325412\pi$
$233$	15.9175	1.04279	0.521396	+	0.853315i	$0.325412\pi$
$234$	71.3781	4.66613
$235$	−28.8996	−1.88520
$236$	−11.7956	−0.767831
$237$	−12.9368	−0.840336
$238$	−9.47407	−0.614113
$239$	−0.682160	−0.0441253	−0.0220626	−	0.999757i	$-0.507023\pi$
$239$	−0.682160	−0.0441253	−0.0220626	+	0.999757i	$0.507023\pi$
$240$	−45.3505	−2.92736
$241$	−0.372946	−0.0240236	−0.0120118	−	0.999928i	$-0.503824\pi$
$241$	−0.372946	−0.0240236	−0.0120118	+	0.999928i	$0.503824\pi$
$242$	−1.89582	−0.121868
$243$	−7.03669	−0.451404
$244$	9.88640	0.632912
$245$	−12.8732	−0.822439
$246$	22.2778	1.42038
$247$	−3.26676	−0.207859
$248$	2.38964	0.151742
$249$	−22.3705	−1.41767
$250$	−7.04959	−0.445855
$251$	−2.83987	−0.179251	−0.0896256	−	0.995976i	$-0.528567\pi$
$251$	−2.83987	−0.179251	−0.0896256	+	0.995976i	$0.528567\pi$
$252$	−15.7262	−0.990659
$253$	−4.88441	−0.307080
$254$	5.38431	0.337841
$255$	−27.5276	−1.72384
$256$	20.4106	1.27566
$257$	−28.2905	−1.76471	−0.882357	−	0.470581i	$-0.844044\pi$
$257$	−28.2905	−1.76471	−0.882357	+	0.470581i	$0.844044\pi$
$258$	62.2612	3.87621
$259$	13.2427	0.822863
$260$	−35.9362	−2.22867
$261$	0	0
$262$	42.5591	2.62931
$263$	18.2857	1.12754	0.563771	−	0.825931i	$-0.309350\pi$
$263$	18.2857	1.12754	0.563771	+	0.825931i	$0.309350\pi$
$264$	−2.25233	−0.138622
$265$	−32.9854	−2.02627
$266$	1.62273	0.0994959
$267$	29.4715	1.80362
$268$	−7.21965	−0.441010
$269$	−14.3782	−0.876657	−0.438329	−	0.898815i	$-0.644429\pi$
$269$	−14.3782	−0.876657	−0.438329	+	0.898815i	$0.644429\pi$
$270$	−47.5169	−2.89178
$271$	17.9557	1.09073	0.545364	−	0.838199i	$-0.316391\pi$
$271$	17.9557	1.09073	0.545364	+	0.838199i	$0.316391\pi$
$272$	13.1079	0.794784
$273$	35.0650	2.12223
$274$	−0.805292	−0.0486495
$275$	−6.11534	−0.368769
$276$	22.7920	1.37192
$277$	−0.998421	−0.0599893	−0.0299947	−	0.999550i	$-0.509549\pi$
$277$	−0.998421	−0.0599893	−0.0299947	+	0.999550i	$0.509549\pi$
$278$	−13.7756	−0.826207
$279$	17.2929	1.03530
$280$	−4.54493	−0.271611
$281$	−21.4137	−1.27743	−0.638717	−	0.769442i	$-0.720535\pi$
$281$	−21.4137	−1.27743	−0.638717	+	0.769442i	$0.720535\pi$
$282$	48.1032	2.86451
$283$	5.86124	0.348414	0.174207	−	0.984709i	$-0.444264\pi$
$283$	5.86124	0.348414	0.174207	+	0.984709i	$0.444264\pi$
$284$	5.14290	0.305175
$285$	4.71496	0.279290
$286$	−12.8187	−0.757986
$287$	7.11229	0.419825
$288$	40.4868	2.38571
$289$	−9.04354	−0.531973
$290$	0	0
$291$	40.8058	2.39208
$292$	25.6097	1.49869
$293$	−2.01336	−0.117622	−0.0588109	−	0.998269i	$-0.518731\pi$
$293$	−2.01336	−0.117622	−0.0588109	+	0.998269i	$0.518731\pi$
$294$	21.4274	1.24967
$295$	−24.6695	−1.43631
$296$	−5.75153	−0.334301
$297$	−7.51778	−0.436226
$298$	17.4622	1.01156
$299$	−33.0262	−1.90996
$300$	28.5358	1.64752
$301$	19.8771	1.14570
$302$	16.2313	0.934009
$303$	1.15996	0.0666382
$304$	−2.24514	−0.128768
$305$	20.6765	1.18393
$306$	29.7768	1.70223
$307$	−13.8047	−0.787876	−0.393938	−	0.919137i	$-0.628888\pi$
$307$	−13.8047	−0.787876	−0.393938	+	0.919137i	$0.628888\pi$
$308$	2.82425	0.160927
$309$	−22.0268	−1.25306
$310$	−19.6293	−1.11487
$311$	3.90227	0.221278	0.110639	−	0.993861i	$-0.464710\pi$
$311$	3.90227	0.221278	0.110639	+	0.993861i	$0.464710\pi$
$312$	−15.2293	−0.862189
$313$	8.24943	0.466285	0.233143	−	0.972443i	$-0.425099\pi$
$313$	8.24943	0.466285	0.233143	+	0.972443i	$0.425099\pi$
$314$	−44.1850	−2.49350
$315$	−32.8899	−1.85314
$316$	−7.04536	−0.396333
$317$	20.3600	1.14353	0.571766	−	0.820417i	$-0.306258\pi$
$317$	20.3600	1.14353	0.571766	+	0.820417i	$0.306258\pi$
$318$	54.9040	3.07886
$319$	0	0
$320$	−14.9709	−0.836900
$321$	44.1617	2.46487
$322$	16.4055	0.914240
$323$	−1.36279	−0.0758277
$324$	8.45034	0.469464
$325$	−41.3492	−2.29364
$326$	−41.1695	−2.28017
$327$	−49.3144	−2.72709
$328$	−3.08898	−0.170560
$329$	15.3571	0.846667
$330$	18.5014	1.01847
$331$	20.2352	1.11223	0.556113	−	0.831106i	$-0.312292\pi$
$331$	20.2352	1.11223	0.556113	+	0.831106i	$0.312292\pi$
$332$	−12.1829	−0.668624
$333$	−41.6216	−2.28085
$334$	−6.66720	−0.364813
$335$	−15.0992	−0.824957
$336$	24.0991	1.31471
$337$	0.412081	0.0224475	0.0112237	−	0.999937i	$-0.496427\pi$
$337$	0.412081	0.0224475	0.0112237	+	0.999937i	$0.496427\pi$
$338$	−62.0288	−3.37392
$339$	−30.0825	−1.63386
$340$	−14.9915	−0.813027
$341$	−3.10561	−0.168178
$342$	−5.10020	−0.275787
$343$	19.2424	1.03899
$344$	−8.63295	−0.465458
$345$	47.6672	2.56632
$346$	−6.02984	−0.324166
$347$	−10.3036	−0.553124	−0.276562	−	0.960996i	$-0.589195\pi$
$347$	−10.3036	−0.553124	−0.276562	+	0.960996i	$0.589195\pi$
$348$	0	0
$349$	−15.8250	−0.847094	−0.423547	−	0.905874i	$-0.639215\pi$
$349$	−15.8250	−0.847094	−0.423547	+	0.905874i	$0.639215\pi$
$350$	20.5398	1.09790
$351$	−50.8319	−2.71321
$352$	−7.27097	−0.387544
$353$	25.3563	1.34958	0.674790	−	0.738010i	$-0.264234\pi$
$353$	25.3563	1.34958	0.674790	+	0.738010i	$0.264234\pi$
$354$	41.0622	2.18243
$355$	10.7559	0.570864
$356$	16.0501	0.850654
$357$	14.6281	0.774199
$358$	7.94693	0.420008
$359$	−17.1864	−0.907063	−0.453531	−	0.891240i	$-0.649836\pi$
$359$	−17.1864	−0.907063	−0.453531	+	0.891240i	$0.649836\pi$
$360$	14.2846	0.752865
$361$	−18.7666	−0.987715
$362$	34.7388	1.82583
$363$	2.92716	0.153636
$364$	19.0963	1.00092
$365$	53.5602	2.80347
$366$	−34.4159	−1.79895
$367$	−7.63734	−0.398666	−0.199333	−	0.979932i	$-0.563877\pi$
$367$	−7.63734	−0.398666	−0.199333	+	0.979932i	$0.563877\pi$
$368$	−22.6979	−1.18321
$369$	−22.3538	−1.16369
$370$	47.2450	2.45615
$371$	17.5283	0.910024
$372$	14.4916	0.751356
$373$	−4.31097	−0.223214	−0.111607	−	0.993752i	$-0.535600\pi$
$373$	−4.31097	−0.223214	−0.111607	+	0.993752i	$0.535600\pi$
$374$	−5.34757	−0.276516
$375$	10.8846	0.562080
$376$	−6.66986	−0.343972
$377$	0	0
$378$	25.2503	1.29873
$379$	−30.5605	−1.56979	−0.784894	−	0.619630i	$-0.787283\pi$
$379$	−30.5605	−1.56979	−0.784894	+	0.619630i	$0.787283\pi$
$380$	2.56776	0.131723
$381$	−8.31342	−0.425910
$382$	−9.02826	−0.461926
$383$	−22.0838	−1.12843	−0.564214	−	0.825628i	$-0.690821\pi$
$383$	−22.0838	−1.12843	−0.564214	+	0.825628i	$0.690821\pi$
$384$	−17.6476	−0.900577
$385$	5.90665	0.301031
$386$	20.9684	1.06726
$387$	−62.4734	−3.17570
$388$	22.2227	1.12819
$389$	8.96387	0.454486	0.227243	−	0.973838i	$-0.427029\pi$
$389$	8.96387	0.454486	0.227243	+	0.973838i	$0.427029\pi$
$390$	125.099	6.33461
$391$	−13.7775	−0.696760
$392$	−2.97106	−0.150061
$393$	−65.7116	−3.31471
$394$	6.31165	0.317977
$395$	−14.7347	−0.741383
$396$	−8.87655	−0.446064
$397$	29.4066	1.47587	0.737937	−	0.674869i	$-0.235800\pi$
$397$	29.4066	1.47587	0.737937	+	0.674869i	$0.235800\pi$
$398$	30.2002	1.51380
$399$	−2.50551	−0.125432
$400$	−28.4180	−1.42090
$401$	−2.47411	−0.123551	−0.0617756	−	0.998090i	$-0.519676\pi$
$401$	−2.47411	−0.123551	−0.0617756	+	0.998090i	$0.519676\pi$
$402$	25.1325	1.25350
$403$	−20.9988	−1.04602
$404$	0.631715	0.0314290
$405$	17.6731	0.878183
$406$	0	0
$407$	7.47476	0.370510
$408$	−6.35320	−0.314530
$409$	9.09456	0.449697	0.224849	−	0.974394i	$-0.427811\pi$
$409$	9.09456	0.449697	0.224849	+	0.974394i	$0.427811\pi$
$410$	25.3739	1.25313
$411$	1.24338	0.0613313
$412$	−11.9958	−0.590989
$413$	13.1093	0.645065
$414$	−51.5620	−2.53413
$415$	−25.4794	−1.25074
$416$	−49.1631	−2.41042
$417$	21.2697	1.04158
$418$	0.915938	0.0448000
$419$	−25.6402	−1.25260	−0.626302	−	0.779581i	$-0.715432\pi$
$419$	−25.6402	−1.25260	−0.626302	+	0.779581i	$0.715432\pi$
$420$	−27.5620	−1.34489
$421$	1.07542	0.0524126	0.0262063	−	0.999657i	$-0.491657\pi$
$421$	1.07542	0.0524126	0.0262063	+	0.999657i	$0.491657\pi$
$422$	−43.3426	−2.10988
$423$	−48.2672	−2.34683
$424$	−7.61282	−0.369711
$425$	−17.2496	−0.836731
$426$	−17.9031	−0.867409
$427$	−10.9874	−0.531717
$428$	24.0504	1.16252
$429$	19.7922	0.955576
$430$	70.9140	3.41977
$431$	9.18545	0.442447	0.221224	−	0.975223i	$-0.428995\pi$
$431$	9.18545	0.442447	0.221224	+	0.975223i	$0.428995\pi$
$432$	−34.9352	−1.68082
$433$	27.1708	1.30574	0.652872	−	0.757468i	$-0.273564\pi$
$433$	27.1708	1.30574	0.652872	+	0.757468i	$0.273564\pi$
$434$	10.4310	0.500702
$435$	0	0
$436$	−26.8565	−1.28620
$437$	2.35983	0.112886
$438$	−89.1506	−4.25978
$439$	1.19752	0.0571547	0.0285773	−	0.999592i	$-0.490902\pi$
$439$	1.19752	0.0571547	0.0285773	+	0.999592i	$0.490902\pi$
$440$	−2.56535	−0.122298
$441$	−21.5004	−1.02383
$442$	−36.1579	−1.71986
$443$	33.2018	1.57747	0.788733	−	0.614735i	$-0.210737\pi$
$443$	33.2018	1.57747	0.788733	+	0.614735i	$0.210737\pi$
$444$	−34.8793	−1.65530
$445$	33.5673	1.59124
$446$	4.67549	0.221391
$447$	−26.9618	−1.27525
$448$	7.95549	0.375862
$449$	−25.5332	−1.20498	−0.602492	−	0.798125i	$-0.705826\pi$
$449$	−25.5332	−1.20498	−0.602492	+	0.798125i	$0.705826\pi$
$450$	−64.5563	−3.04321
$451$	4.01448	0.189034
$452$	−16.3829	−0.770587
$453$	−25.0614	−1.17749
$454$	1.98933	0.0933637
$455$	39.9382	1.87233
$456$	1.08818	0.0509589
$457$	4.86308	0.227485	0.113743	−	0.993510i	$-0.463716\pi$
$457$	4.86308	0.227485	0.113743	+	0.993510i	$0.463716\pi$
$458$	27.6910	1.29391
$459$	−21.2055	−0.989790
$460$	25.9595	1.21037
$461$	37.2029	1.73271	0.866356	−	0.499427i	$-0.166456\pi$
$461$	37.2029	1.73271	0.866356	+	0.499427i	$0.166456\pi$
$462$	−9.83158	−0.457407
$463$	5.04975	0.234682	0.117341	−	0.993092i	$-0.462563\pi$
$463$	5.04975	0.234682	0.117341	+	0.993092i	$0.462563\pi$
$464$	0	0
$465$	30.3079	1.40549
$466$	−30.1767	−1.39791
$467$	24.1695	1.11843	0.559216	−	0.829022i	$-0.311102\pi$
$467$	24.1695	1.11843	0.559216	+	0.829022i	$0.311102\pi$
$468$	−60.0194	−2.77440
$469$	8.02366	0.370498
$470$	54.7884	2.52720
$471$	68.2221	3.14351
$472$	−5.69356	−0.262068
$473$	11.2195	0.515873
$474$	24.5258	1.12651
$475$	2.95454	0.135564
$476$	7.96641	0.365140
$477$	−55.0911	−2.52245
$478$	1.29325	0.0591519
$479$	1.21910	0.0557019	0.0278510	−	0.999612i	$-0.491134\pi$
$479$	1.21910	0.0557019	0.0278510	+	0.999612i	$0.491134\pi$
$480$	70.9579	3.23877
$481$	50.5411	2.30448
$482$	0.707039	0.0322047
$483$	−25.3302	−1.15256
$484$	1.59413	0.0724604
$485$	46.4768	2.11040
$486$	13.3403	0.605128
$487$	−1.99007	−0.0901786	−0.0450893	−	0.998983i	$-0.514357\pi$
$487$	−1.99007	−0.0901786	−0.0450893	+	0.998983i	$0.514357\pi$
$488$	4.77200	0.216018
$489$	63.5661	2.87456
$490$	24.4053	1.10252
$491$	10.1323	0.457262	0.228631	−	0.973513i	$-0.426575\pi$
$491$	10.1323	0.457262	0.228631	+	0.973513i	$0.426575\pi$
$492$	−18.7327	−0.844534
$493$	0	0
$494$	6.19318	0.278644
$495$	−18.5645	−0.834411
$496$	−14.4318	−0.648008
$497$	−5.71564	−0.256382
$498$	42.4103	1.90045
$499$	21.8845	0.979686	0.489843	−	0.871811i	$-0.337054\pi$
$499$	21.8845	0.979686	0.489843	+	0.871811i	$0.337054\pi$
$500$	5.92776	0.265097
$501$	10.2942	0.459912
$502$	5.38388	0.240294
$503$	7.91740	0.353019	0.176510	−	0.984299i	$-0.443519\pi$
$503$	7.91740	0.353019	0.176510	+	0.984299i	$0.443519\pi$
$504$	−7.59079	−0.338121
$505$	1.32117	0.0587914
$506$	9.25995	0.411655
$507$	95.7731	4.25343
$508$	−4.52748	−0.200874
$509$	10.3687	0.459585	0.229793	−	0.973240i	$-0.426195\pi$
$509$	10.3687	0.459585	0.229793	+	0.973240i	$0.426195\pi$
$510$	52.1873	2.31089
$511$	−28.4617	−1.25907
$512$	−26.6369	−1.17720
$513$	3.63211	0.160362
$514$	53.6337	2.36568
$515$	−25.0880	−1.10551
$516$	−52.3533	−2.30472
$517$	8.66824	0.381229
$518$	−25.1058	−1.10309
$519$	9.31013	0.408669
$520$	−17.3458	−0.760663
$521$	2.02296	0.0886276	0.0443138	−	0.999018i	$-0.485890\pi$
$521$	2.02296	0.0886276	0.0443138	+	0.999018i	$0.485890\pi$
$522$	0	0
$523$	5.09328	0.222714	0.111357	−	0.993780i	$-0.464480\pi$
$523$	5.09328	0.222714	0.111357	+	0.993780i	$0.464480\pi$
$524$	−35.7864	−1.56334
$525$	−31.7137	−1.38410
$526$	−34.6663	−1.51152
$527$	−8.76006	−0.381594
$528$	13.6026	0.591975
$529$	0.857415	0.0372789
$530$	62.5343	2.71631
$531$	−41.2021	−1.78802
$532$	−1.36450	−0.0591584
$533$	27.1442	1.17574
$534$	−55.8725	−2.41784
$535$	50.2992	2.17462
$536$	−3.48480	−0.150521
$537$	−12.2701	−0.529495
$538$	27.2585	1.17520
$539$	3.86123	0.166315
$540$	39.9553	1.71940
$541$	18.4164	0.791785	0.395892	−	0.918297i	$-0.370435\pi$
$541$	18.4164	0.791785	0.395892	+	0.918297i	$0.370435\pi$
$542$	−34.0407	−1.46217
$543$	−53.6371	−2.30179
$544$	−20.5094	−0.879332
$545$	−56.1679	−2.40597
$546$	−66.4769	−2.84495
$547$	2.29409	0.0980883	0.0490441	−	0.998797i	$-0.484383\pi$
$547$	2.29409	0.0980883	0.0490441	+	0.998797i	$0.484383\pi$
$548$	0.677142	0.0289261
$549$	34.5331	1.47384
$550$	11.5936	0.494351
$551$	0	0
$552$	11.0013	0.468247
$553$	7.82997	0.332964
$554$	1.89283	0.0804185
$555$	−72.9467	−3.09642
$556$	11.5834	0.491248
$557$	−36.1526	−1.53184	−0.765918	−	0.642938i	$-0.777715\pi$
$557$	−36.1526	−1.53184	−0.765918	+	0.642938i	$0.777715\pi$
$558$	−32.7842	−1.38787
$559$	75.8614	3.20860
$560$	27.4483	1.15990
$561$	8.25670	0.348598
$562$	40.5965	1.71246
$563$	14.6470	0.617295	0.308648	−	0.951176i	$-0.400124\pi$
$563$	14.6470	0.617295	0.308648	+	0.951176i	$0.400124\pi$
$564$	−40.4484	−1.70318
$565$	−34.2633	−1.44147
$566$	−11.1118	−0.467066
$567$	−9.39141	−0.394402
$568$	2.48240	0.104159
$569$	21.8652	0.916637	0.458318	−	0.888788i	$-0.348452\pi$
$569$	21.8652	0.916637	0.458318	+	0.888788i	$0.348452\pi$
$570$	−8.93870	−0.374401
$571$	−8.66646	−0.362680	−0.181340	−	0.983420i	$-0.558043\pi$
$571$	−8.66646	−0.362680	−0.181340	+	0.983420i	$0.558043\pi$
$572$	10.7788	0.450684
$573$	13.9397	0.582340
$574$	−13.4836	−0.562795
$575$	29.8698	1.24566
$576$	−25.0039	−1.04183
$577$	−30.9699	−1.28929	−0.644646	−	0.764481i	$-0.722995\pi$
$577$	−30.9699	−1.28929	−0.644646	+	0.764481i	$0.722995\pi$
$578$	17.1449	0.713135
$579$	−32.3754	−1.34548
$580$	0	0
$581$	13.5397	0.561720
$582$	−77.3603	−3.20669
$583$	9.89373	0.409756
$584$	12.3614	0.511517
$585$	−125.525	−5.18981
$586$	3.81697	0.157677
$587$	−34.3556	−1.41801	−0.709005	−	0.705204i	$-0.750855\pi$
$587$	−34.3556	−1.41801	−0.709005	+	0.705204i	$0.750855\pi$
$588$	−18.0175	−0.743031
$589$	1.50043	0.0618243
$590$	46.7688	1.92544
$591$	−9.74526	−0.400866
$592$	34.7353	1.42761
$593$	−9.33274	−0.383250	−0.191625	−	0.981468i	$-0.561376\pi$
$593$	−9.33274	−0.383250	−0.191625	+	0.981468i	$0.561376\pi$
$594$	14.2523	0.584781
$595$	16.6610	0.683034
$596$	−14.6834	−0.601454
$597$	−46.6294	−1.90841
$598$	62.6117	2.56038
$599$	−21.8944	−0.894580	−0.447290	−	0.894389i	$-0.647611\pi$
$599$	−21.8944	−0.894580	−0.447290	+	0.894389i	$0.647611\pi$
$600$	13.7738	0.562312
$601$	−45.9764	−1.87542	−0.937708	−	0.347425i	$-0.887056\pi$
$601$	−45.9764	−1.87542	−0.937708	+	0.347425i	$0.887056\pi$
$602$	−37.6834	−1.53586
$603$	−25.2182	−1.02696
$604$	−13.6484	−0.555345
$605$	3.33397	0.135545
$606$	−2.19908	−0.0893316
$607$	17.2896	0.701764	0.350882	−	0.936420i	$-0.385882\pi$
$607$	17.2896	0.701764	0.350882	+	0.936420i	$0.385882\pi$
$608$	3.51287	0.142466
$609$	0	0
$610$	−39.1988	−1.58711
$611$	58.6108	2.37114
$612$	−25.0383	−1.01211
$613$	25.3154	1.02248	0.511240	−	0.859438i	$-0.329186\pi$
$613$	25.3154	1.02248	0.511240	+	0.859438i	$0.329186\pi$
$614$	26.1712	1.05618
$615$	−39.1776	−1.57979
$616$	1.36322	0.0549257
$617$	17.5416	0.706200	0.353100	−	0.935586i	$-0.385128\pi$
$617$	17.5416	0.706200	0.353100	+	0.935586i	$0.385128\pi$
$618$	41.7588	1.67979
$619$	−39.6637	−1.59422	−0.797110	−	0.603835i	$-0.793639\pi$
$619$	−39.6637	−1.59422	−0.797110	+	0.603835i	$0.793639\pi$
$620$	16.5056	0.662882
$621$	36.7199	1.47352
$622$	−7.39800	−0.296633
$623$	−17.8375	−0.714645
$624$	91.9746	3.68193
$625$	−18.1793	−0.727174
$626$	−15.6394	−0.625077
$627$	−1.41422	−0.0564784
$628$	37.1536	1.48259
$629$	21.0842	0.840683
$630$	62.3533	2.48421
$631$	−7.66344	−0.305077	−0.152538	−	0.988298i	$-0.548745\pi$
$631$	−7.66344	−0.305077	−0.152538	+	0.988298i	$0.548745\pi$
$632$	−3.40068	−0.135272
$633$	66.9213	2.65988
$634$	−38.5989	−1.53296
$635$	−9.46879	−0.375757
$636$	−46.1668	−1.83063
$637$	26.1079	1.03443
$638$	0	0
$639$	17.9641	0.710650
$640$	−20.1002	−0.794531
$641$	−16.5149	−0.652299	−0.326149	−	0.945318i	$-0.605751\pi$
$641$	−16.5149	−0.652299	−0.326149	+	0.945318i	$0.605751\pi$
$642$	−83.7227	−3.30427
$643$	42.6288	1.68112	0.840558	−	0.541722i	$-0.182228\pi$
$643$	42.6288	1.68112	0.840558	+	0.541722i	$0.182228\pi$
$644$	−13.7948	−0.543590
$645$	−109.492	−4.31124
$646$	2.58361	0.101651
$647$	13.7956	0.542360	0.271180	−	0.962529i	$-0.412586\pi$
$647$	13.7956	0.542360	0.271180	+	0.962529i	$0.412586\pi$
$648$	4.07884	0.160232
$649$	7.39943	0.290453
$650$	78.3907	3.07473
$651$	−16.1055	−0.631224
$652$	34.6180	1.35575
$653$	−4.02999	−0.157706	−0.0788528	−	0.996886i	$-0.525126\pi$
$653$	−4.02999	−0.157706	−0.0788528	+	0.996886i	$0.525126\pi$
$654$	93.4912	3.65579
$655$	−74.8439	−2.92439
$656$	18.6553	0.728369
$657$	89.4545	3.48995
$658$	−29.1144	−1.13500
$659$	−10.8658	−0.423271	−0.211636	−	0.977349i	$-0.567879\pi$
$659$	−10.8658	−0.423271	−0.211636	+	0.977349i	$0.567879\pi$
$660$	−15.5572	−0.605563
$661$	−15.2020	−0.591288	−0.295644	−	0.955298i	$-0.595534\pi$
$661$	−15.2020	−0.591288	−0.295644	+	0.955298i	$0.595534\pi$
$662$	−38.3623	−1.49099
$663$	55.8282	2.16819
$664$	−5.88049	−0.228207
$665$	−2.85372	−0.110662
$666$	78.9070	3.05758
$667$	0	0
$668$	5.60622	0.216911
$669$	−7.21900	−0.279103
$670$	28.6253	1.10589
$671$	−6.20176	−0.239416
$672$	−37.7068	−1.45457
$673$	23.3850	0.901424	0.450712	−	0.892669i	$-0.351170\pi$
$673$	23.3850	0.901424	0.450712	+	0.892669i	$0.351170\pi$
$674$	−0.781231	−0.0300919
$675$	45.9737	1.76953
$676$	52.1579	2.00607
$677$	10.5818	0.406692	0.203346	−	0.979107i	$-0.434818\pi$
$677$	10.5818	0.406692	0.203346	+	0.979107i	$0.434818\pi$
$678$	57.0310	2.19026
$679$	−24.6976	−0.947806
$680$	−7.23614	−0.277493
$681$	−3.07154	−0.117702
$682$	5.88768	0.225451
$683$	−10.2925	−0.393831	−0.196916	−	0.980420i	$-0.563093\pi$
$683$	−10.2925	−0.393831	−0.196916	+	0.980420i	$0.563093\pi$
$684$	4.28858	0.163978
$685$	1.41618	0.0541094
$686$	−36.4801	−1.39282
$687$	−42.7552	−1.63121
$688$	52.1372	1.98771
$689$	66.8971	2.54858
$690$	−90.3684	−3.44027
$691$	−27.0163	−1.02775	−0.513874	−	0.857865i	$-0.671790\pi$
$691$	−27.0163	−1.02775	−0.513874	+	0.857865i	$0.671790\pi$
$692$	5.07028	0.192743
$693$	9.86509	0.374744
$694$	19.5337	0.741488
$695$	24.2257	0.918932
$696$	0	0
$697$	11.3237	0.428917
$698$	30.0014	1.13557
$699$	46.5932	1.76232
$700$	−17.2712	−0.652791
$701$	8.92019	0.336911	0.168456	−	0.985709i	$-0.446122\pi$
$701$	8.92019	0.336911	0.168456	+	0.985709i	$0.446122\pi$
$702$	96.3682	3.63718
$703$	−3.61133	−0.136204
$704$	4.49042	0.169239
$705$	−84.5939	−3.18599
$706$	−48.0709	−1.80917
$707$	−0.702066	−0.0264039
$708$	−34.5278	−1.29763
$709$	23.2987	0.875000	0.437500	−	0.899218i	$-0.355864\pi$
$709$	23.2987	0.875000	0.437500	+	0.899218i	$0.355864\pi$
$710$	−20.3912	−0.765269
$711$	−24.6094	−0.922925
$712$	7.74712	0.290336
$713$	15.1691	0.568086
$714$	−27.7321	−1.03785
$715$	22.5428	0.843054
$716$	−6.68230	−0.249729
$717$	−1.99679	−0.0745716
$718$	32.5823	1.21596
$719$	−22.0084	−0.820776	−0.410388	−	0.911911i	$-0.634607\pi$
$719$	−22.0084	−0.820776	−0.410388	+	0.911911i	$0.634607\pi$
$720$	−86.2693	−3.21507
$721$	13.3317	0.496497
$722$	35.5780	1.32408
$723$	−1.09167	−0.0405998
$724$	−29.2107	−1.08561
$725$	0	0
$726$	−5.54937	−0.205956
$727$	−10.9534	−0.406237	−0.203119	−	0.979154i	$-0.565108\pi$
$727$	−10.9534	−0.406237	−0.203119	+	0.979154i	$0.565108\pi$
$728$	9.21749	0.341623
$729$	−36.5003	−1.35186
$730$	−101.540	−3.75818
$731$	31.6471	1.17051
$732$	28.9391	1.06962
$733$	17.4927	0.646108	0.323054	−	0.946381i	$-0.395290\pi$
$733$	17.4927	0.646108	0.323054	+	0.946381i	$0.395290\pi$
$734$	14.4790	0.534430
$735$	−37.6820	−1.38992
$736$	35.5144	1.30908
$737$	4.52890	0.166824
$738$	42.3787	1.55998
$739$	−20.6642	−0.760147	−0.380073	−	0.924956i	$-0.624101\pi$
$739$	−20.6642	−0.760147	−0.380073	+	0.924956i	$0.624101\pi$
$740$	−39.7267	−1.46038
$741$	−9.56233	−0.351281
$742$	−33.2305	−1.21993
$743$	−33.6591	−1.23483	−0.617417	−	0.786636i	$-0.711821\pi$
$743$	−33.6591	−1.23483	−0.617417	+	0.786636i	$0.711821\pi$
$744$	6.99487	0.256445
$745$	−30.7089	−1.12509
$746$	8.17283	0.299228
$747$	−42.5549	−1.55700
$748$	4.49659	0.164412
$749$	−26.7288	−0.976648
$750$	−20.6353	−0.753495
$751$	−38.0932	−1.39004	−0.695021	−	0.718990i	$-0.744605\pi$
$751$	−38.0932	−1.39004	−0.695021	+	0.718990i	$0.744605\pi$
$752$	40.2814	1.46891
$753$	−8.31277	−0.302934
$754$	0	0
$755$	−28.5443	−1.03883
$756$	−21.2321	−0.772203
$757$	21.5821	0.784413	0.392207	−	0.919877i	$-0.371712\pi$
$757$	21.5821	0.784413	0.392207	+	0.919877i	$0.371712\pi$
$758$	57.9372	2.10437
$759$	−14.2974	−0.518965
$760$	1.23941	0.0449583
$761$	−3.07633	−0.111517	−0.0557585	−	0.998444i	$-0.517758\pi$
$761$	−3.07633	−0.111517	−0.0557585	+	0.998444i	$0.517758\pi$
$762$	15.7607	0.570952
$763$	29.8474	1.08055
$764$	7.59155	0.274653
$765$	−52.3652	−1.89327
$766$	41.8668	1.51271
$767$	50.0317	1.80654
$768$	59.7451	2.15587
$769$	−14.9593	−0.539446	−0.269723	−	0.962938i	$-0.586932\pi$
$769$	−14.9593	−0.539446	−0.269723	+	0.962938i	$0.586932\pi$
$770$	−11.1979	−0.403546
$771$	−82.8109	−2.98236
$772$	−17.6316	−0.634575
$773$	−22.1486	−0.796630	−0.398315	−	0.917249i	$-0.630405\pi$
$773$	−22.1486	−0.796630	−0.398315	+	0.917249i	$0.630405\pi$
$774$	118.438	4.25717
$775$	18.9919	0.682208
$776$	10.7266	0.385061
$777$	38.7636	1.39064
$778$	−16.9939	−0.609260
$779$	−1.93954	−0.0694912
$780$	−105.191	−3.76644
$781$	−3.22615	−0.115441
$782$	26.1197	0.934039
$783$	0	0
$784$	17.9432	0.640828
$785$	77.7033	2.77335
$786$	124.577	4.44352
$787$	−34.5685	−1.23223	−0.616117	−	0.787654i	$-0.711295\pi$
$787$	−34.5685	−1.23223	−0.616117	+	0.787654i	$0.711295\pi$
$788$	−5.30725	−0.189063
$789$	53.5251	1.90555
$790$	27.9343	0.993859
$791$	18.2074	0.647380
$792$	−4.28457	−0.152245
$793$	−41.9336	−1.48911
$794$	−55.7496	−1.97848
$795$	−96.5535	−3.42440
$796$	−25.3943	−0.900076
$797$	12.2330	0.433316	0.216658	−	0.976248i	$-0.430484\pi$
$797$	12.2330	0.433316	0.216658	+	0.976248i	$0.430484\pi$
$798$	4.74999	0.168148
$799$	24.4507	0.865002
$800$	44.4644	1.57206
$801$	56.0629	1.98089
$802$	4.69046	0.165626
$803$	−16.0650	−0.566922
$804$	−21.1331	−0.745306
$805$	−28.8505	−1.01685
$806$	39.8099	1.40224
$807$	−42.0875	−1.48155
$808$	0.304918	0.0107270
$809$	47.8557	1.68252	0.841258	−	0.540634i	$-0.181815\pi$
$809$	47.8557	1.68252	0.841258	+	0.540634i	$0.181815\pi$
$810$	−33.5050	−1.17724
$811$	9.72419	0.341463	0.170731	−	0.985318i	$-0.445387\pi$
$811$	9.72419	0.341463	0.170731	+	0.985318i	$0.445387\pi$
$812$	0	0
$813$	52.5592	1.84333
$814$	−14.1708	−0.496686
$815$	72.4003	2.53607
$816$	38.3690	1.34318
$817$	−5.42055	−0.189641
$818$	−17.2416	−0.602840
$819$	66.7034	2.33081
$820$	−21.3360	−0.745087
$821$	−25.6162	−0.894011	−0.447005	−	0.894531i	$-0.647510\pi$
$821$	−25.6162	−0.894011	−0.447005	+	0.894531i	$0.647510\pi$
$822$	−2.35722	−0.0822175
$823$	−20.3470	−0.709254	−0.354627	−	0.935008i	$-0.615392\pi$
$823$	−20.3470	−0.709254	−0.354627	+	0.935008i	$0.615392\pi$
$824$	−5.79016	−0.201710
$825$	−17.9006	−0.623218
$826$	−24.8528	−0.864739
$827$	30.4012	1.05715	0.528577	−	0.848885i	$-0.322726\pi$
$827$	30.4012	1.05715	0.528577	+	0.848885i	$0.322726\pi$
$828$	43.3567	1.50675
$829$	−19.4731	−0.676330	−0.338165	−	0.941087i	$-0.609806\pi$
$829$	−19.4731	−0.676330	−0.338165	+	0.941087i	$0.609806\pi$
$830$	48.3043	1.67667
$831$	−2.92254	−0.101382
$832$	30.3623	1.05262
$833$	10.8914	0.377366
$834$	−40.3235	−1.39629
$835$	11.7249	0.405756
$836$	−0.770181	−0.0266373
$837$	23.3473	0.807001
$838$	48.6091	1.67917
$839$	25.9476	0.895811	0.447906	−	0.894081i	$-0.352170\pi$
$839$	25.9476	0.895811	0.447906	+	0.894081i	$0.352170\pi$
$840$	−13.3037	−0.459023
$841$	0	0
$842$	−2.03880	−0.0702616
$843$	−62.6814	−2.15886
$844$	36.4453	1.25450
$845$	109.083	3.75258
$846$	91.5058	3.14603
$847$	−1.77166	−0.0608749
$848$	45.9763	1.57883
$849$	17.1568	0.588820
$850$	32.7022	1.12168
$851$	−36.5098	−1.25154
$852$	15.0541	0.515746
$853$	1.46244	0.0500730	0.0250365	−	0.999687i	$-0.492030\pi$
$853$	1.46244	0.0500730	0.0250365	+	0.999687i	$0.492030\pi$
$854$	20.8301	0.712792
$855$	8.96917	0.306739
$856$	11.6087	0.396779
$857$	19.5136	0.666573	0.333286	−	0.942826i	$-0.391842\pi$
$857$	19.5136	0.666573	0.333286	+	0.942826i	$0.391842\pi$
$858$	−37.5224	−1.28099
$859$	−4.18048	−0.142636	−0.0713180	−	0.997454i	$-0.522721\pi$
$859$	−4.18048	−0.142636	−0.0713180	+	0.997454i	$0.522721\pi$
$860$	−59.6291	−2.03334
$861$	20.8188	0.709503
$862$	−17.4139	−0.593121
$863$	35.7755	1.21781	0.608906	−	0.793243i	$-0.291609\pi$
$863$	35.7755	1.21781	0.608906	+	0.793243i	$0.291609\pi$
$864$	54.6616	1.85962
$865$	10.6040	0.360547
$866$	−51.5109	−1.75041
$867$	−26.4719	−0.899034
$868$	−8.77102	−0.297708
$869$	4.41957	0.149924
$870$	0	0
$871$	30.6224	1.03760
$872$	−12.9632	−0.438990
$873$	77.6240	2.62717
$874$	−4.47381	−0.151329
$875$	−6.58790	−0.222712
$876$	74.9637	2.53279
$877$	−16.6625	−0.562654	−0.281327	−	0.959612i	$-0.590775\pi$
$877$	−16.6625	−0.562654	−0.281327	+	0.959612i	$0.590775\pi$
$878$	−2.27029	−0.0766185
$879$	−5.89343	−0.198781
$880$	15.4930	0.522268
$881$	−15.7426	−0.530380	−0.265190	−	0.964196i	$-0.585435\pi$
$881$	−15.7426	−0.530380	−0.265190	+	0.964196i	$0.585435\pi$
$882$	40.7609	1.37249
$883$	28.0650	0.944464	0.472232	−	0.881474i	$-0.343448\pi$
$883$	28.0650	0.944464	0.472232	+	0.881474i	$0.343448\pi$
$884$	30.4040	1.02260
$885$	−72.2115	−2.42736
$886$	−62.9447	−2.11467
$887$	−54.8874	−1.84294	−0.921469	−	0.388453i	$-0.873010\pi$
$887$	−54.8874	−1.84294	−0.921469	+	0.388453i	$0.873010\pi$
$888$	−16.8357	−0.564968
$889$	5.03168	0.168757
$890$	−63.6374	−2.13313
$891$	−5.30092	−0.177587
$892$	−3.93145	−0.131635
$893$	−4.18794	−0.140144
$894$	51.1147	1.70953
$895$	−13.9754	−0.467146
$896$	10.6812	0.356833
$897$	−96.6731	−3.22782
$898$	48.4062	1.61534
$899$	0	0
$900$	54.2831	1.80944
$901$	27.9074	0.929731
$902$	−7.61073	−0.253409
$903$	58.1836	1.93623
$904$	−7.90776	−0.263008
$905$	−61.0914	−2.03075
$906$	47.5118	1.57847
$907$	−27.0405	−0.897865	−0.448932	−	0.893566i	$-0.648196\pi$
$907$	−27.0405	−0.897865	−0.448932	+	0.893566i	$0.648196\pi$
$908$	−1.67275	−0.0555123
$909$	2.20658	0.0731875
$910$	−75.7156	−2.50995
$911$	12.8486	0.425692	0.212846	−	0.977086i	$-0.431727\pi$
$911$	12.8486	0.425692	0.212846	+	0.977086i	$0.431727\pi$
$912$	−6.57189	−0.217617
$913$	7.64237	0.252926
$914$	−9.21952	−0.304955
$915$	60.5234	2.00084
$916$	−23.2844	−0.769338
$917$	39.7718	1.31338
$918$	40.2019	1.32686
$919$	34.0323	1.12262	0.561312	−	0.827605i	$-0.310297\pi$
$919$	34.0323	1.12262	0.561312	+	0.827605i	$0.310297\pi$
$920$	12.5302	0.413109
$921$	−40.4086	−1.33151
$922$	−70.5300	−2.32278
$923$	−21.8139	−0.718012
$924$	8.26704	0.271966
$925$	−45.7107	−1.50296
$926$	−9.57342	−0.314602
$927$	−41.9011	−1.37621
$928$	0	0
$929$	−25.5610	−0.838629	−0.419315	−	0.907841i	$-0.637730\pi$
$929$	−25.5610	−0.838629	−0.419315	+	0.907841i	$0.637730\pi$
$930$	−57.4582	−1.88413
$931$	−1.86550	−0.0611393
$932$	25.3746	0.831172
$933$	11.4226	0.373959
$934$	−45.8210	−1.49931
$935$	9.40418	0.307550
$936$	−28.9704	−0.946926
$937$	55.0372	1.79799	0.898994	−	0.437962i	$-0.144299\pi$
$937$	55.0372	1.79799	0.898994	+	0.437962i	$0.144299\pi$
$938$	−15.2114	−0.496670
$939$	24.1474	0.788021
$940$	−46.0697	−1.50263
$941$	21.4617	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$941$	21.4617	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$942$	−129.337	−4.21402
$943$	−19.6083	−0.638536
$944$	34.3853	1.11914
$945$	−44.4049	−1.44449
$946$	−21.2701	−0.691552
$947$	−7.19710	−0.233874	−0.116937	−	0.993139i	$-0.537308\pi$
$947$	−7.19710	−0.233874	−0.116937	+	0.993139i	$0.537308\pi$
$948$	−20.6229	−0.669801
$949$	−108.625	−3.52610
$950$	−5.60127	−0.181729
$951$	59.5971	1.93257
$952$	3.84526	0.124626
$953$	29.3344	0.950235	0.475118	−	0.879922i	$-0.342406\pi$
$953$	29.3344	0.950235	0.475118	+	0.879922i	$0.342406\pi$
$954$	104.443	3.38146
$955$	15.8770	0.513768
$956$	−1.08745	−0.0351707
$957$	0	0
$958$	−2.31118	−0.0746710
$959$	−0.752552	−0.0243012
$960$	−43.8223	−1.41436
$961$	−21.3552	−0.688877
$962$	−95.8168	−3.08926
$963$	84.0080	2.70712
$964$	−0.594524	−0.0191483
$965$	−36.8748	−1.18704
$966$	48.0214	1.54506
$967$	45.8661	1.47495	0.737477	−	0.675372i	$-0.236017\pi$
$967$	45.8661	1.47495	0.737477	+	0.675372i	$0.236017\pi$
$968$	0.769459	0.0247314
$969$	−3.98911	−0.128149
$970$	−88.1115	−2.82909
$971$	30.3720	0.974683	0.487341	−	0.873211i	$-0.337967\pi$
$971$	30.3720	0.974683	0.487341	+	0.873211i	$0.337967\pi$
$972$	−11.2174	−0.359798
$973$	−12.8734	−0.412703
$974$	3.77281	0.120889
$975$	−121.036	−3.87625
$976$	−28.8197	−0.922495
$977$	32.3546	1.03511	0.517557	−	0.855649i	$-0.326842\pi$
$977$	32.3546	1.03511	0.517557	+	0.855649i	$0.326842\pi$
$978$	−120.510	−3.85348
$979$	−10.0683	−0.321783
$980$	−20.5215	−0.655537
$981$	−93.8098	−2.99512
$982$	−19.2089	−0.612981
$983$	−9.04418	−0.288464	−0.144232	−	0.989544i	$-0.546071\pi$
$983$	−9.04418	−0.288464	−0.144232	+	0.989544i	$0.546071\pi$
$984$	−9.04195	−0.288247
$985$	−11.0996	−0.353663
$986$	0	0
$987$	44.9529	1.43087
$988$	−5.20763	−0.165677
$989$	−54.8006	−1.74256
$990$	35.1949	1.11857
$991$	−27.3034	−0.867321	−0.433661	−	0.901076i	$-0.642778\pi$
$991$	−27.3034	−0.867321	−0.433661	+	0.901076i	$0.642778\pi$
$992$	22.5808	0.716942
$993$	59.2317	1.87966
$994$	10.8358	0.343691
$995$	−53.1097	−1.68369
$996$	−35.6614	−1.12997
$997$	−47.7649	−1.51273	−0.756364	−	0.654151i	$-0.773026\pi$
$997$	−47.7649	−1.51273	−0.756364	+	0.654151i	$0.773026\pi$
$998$	−41.4891	−1.31331
$999$	−56.1936	−1.77789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.4	yes	18
29.28	even	2		9251.2.a.s.1.15	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.15	✓	18	29.28	even	2
9251.2.a.t.1.4	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)

\(f(q)\)	\(=\)	\(q-1.89582 q^{2} +2.92716 q^{3} +1.59413 q^{4} +3.33397 q^{5} -5.54937 q^{6} -1.77166 q^{7} +0.769459 q^{8} +5.56828 q^{9} +O(q^{10})\)	\(q-1.89582 q^{2} +2.92716 q^{3} +1.59413 q^{4} +3.33397 q^{5} -5.54937 q^{6} -1.77166 q^{7} +0.769459 q^{8} +5.56828 q^{9} -6.32060 q^{10} -1.00000 q^{11} +4.66627 q^{12} -6.76156 q^{13} +3.35874 q^{14} +9.75906 q^{15} -4.64701 q^{16} -2.82072 q^{17} -10.5565 q^{18} +0.483136 q^{19} +5.31477 q^{20} -5.18593 q^{21} +1.89582 q^{22} +4.88441 q^{23} +2.25233 q^{24} +6.11534 q^{25} +12.8187 q^{26} +7.51778 q^{27} -2.82425 q^{28} -18.5014 q^{30} +3.10561 q^{31} +7.27097 q^{32} -2.92716 q^{33} +5.34757 q^{34} -5.90665 q^{35} +8.87655 q^{36} -7.47476 q^{37} -0.915938 q^{38} -19.7922 q^{39} +2.56535 q^{40} -4.01448 q^{41} +9.83158 q^{42} -11.2195 q^{43} -1.59413 q^{44} +18.5645 q^{45} -9.25995 q^{46} -8.66824 q^{47} -13.6026 q^{48} -3.86123 q^{49} -11.5936 q^{50} -8.25670 q^{51} -10.7788 q^{52} -9.89373 q^{53} -14.2523 q^{54} -3.33397 q^{55} -1.36322 q^{56} +1.41422 q^{57} -7.39943 q^{59} +15.5572 q^{60} +6.20176 q^{61} -5.88768 q^{62} -9.86509 q^{63} -4.49042 q^{64} -22.5428 q^{65} +5.54937 q^{66} -4.52890 q^{67} -4.49659 q^{68} +14.2974 q^{69} +11.1979 q^{70} +3.22615 q^{71} +4.28457 q^{72} +16.0650 q^{73} +14.1708 q^{74} +17.9006 q^{75} +0.770181 q^{76} +1.77166 q^{77} +37.5224 q^{78} -4.41957 q^{79} -15.4930 q^{80} +5.30092 q^{81} +7.61073 q^{82} -7.64237 q^{83} -8.26704 q^{84} -9.40418 q^{85} +21.2701 q^{86} -0.769459 q^{88} +10.0683 q^{89} -35.1949 q^{90} +11.9792 q^{91} +7.78637 q^{92} +9.09063 q^{93} +16.4334 q^{94} +1.61076 q^{95} +21.2833 q^{96} +13.9404 q^{97} +7.32019 q^{98} -5.56828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 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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