LMFDB - Embedded newform 935.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(1,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.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:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.381812160.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 14x^{3} + 15x^{2} - 22x + 3 $ x^6 - 2x^5 - 8x^4 + 14x^3 + 15x^2 - 22*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.62765$ of defining polynomial
Character	$\chi$	$=$	935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62765 q^{2} -0.0998927 q^{3} +4.90452 q^{4} -1.00000 q^{5} +0.262483 q^{6} +3.66691 q^{7} -7.63206 q^{8} -2.99002 q^{9} +O(q^{10})$	\(q-2.62765 q^{2} -0.0998927 q^{3} +4.90452 q^{4} -1.00000 q^{5} +0.262483 q^{6} +3.66691 q^{7} -7.63206 q^{8} -2.99002 q^{9} +2.62765 q^{10} -1.00000 q^{11} -0.489926 q^{12} +2.17699 q^{13} -9.63535 q^{14} +0.0998927 q^{15} +10.2453 q^{16} +1.00000 q^{17} +7.85672 q^{18} +0.404429 q^{19} -4.90452 q^{20} -0.366298 q^{21} +2.62765 q^{22} +7.06504 q^{23} +0.762387 q^{24} +1.00000 q^{25} -5.72035 q^{26} +0.598359 q^{27} +17.9845 q^{28} -3.97841 q^{29} -0.262483 q^{30} -1.26248 q^{31} -11.6569 q^{32} +0.0998927 q^{33} -2.62765 q^{34} -3.66691 q^{35} -14.6646 q^{36} +6.03208 q^{37} -1.06270 q^{38} -0.217465 q^{39} +7.63206 q^{40} -6.95517 q^{41} +0.962500 q^{42} -4.47553 q^{43} -4.90452 q^{44} +2.99002 q^{45} -18.5644 q^{46} +6.76360 q^{47} -1.02343 q^{48} +6.44624 q^{49} -2.62765 q^{50} -0.0998927 q^{51} +10.6771 q^{52} -3.65972 q^{53} -1.57228 q^{54} +1.00000 q^{55} -27.9861 q^{56} -0.0403995 q^{57} +10.4539 q^{58} +13.9501 q^{59} +0.489926 q^{60} +2.51449 q^{61} +3.31736 q^{62} -10.9641 q^{63} +10.1397 q^{64} -2.17699 q^{65} -0.262483 q^{66} -4.53287 q^{67} +4.90452 q^{68} -0.705746 q^{69} +9.63535 q^{70} +10.2396 q^{71} +22.8200 q^{72} -12.1386 q^{73} -15.8502 q^{74} -0.0998927 q^{75} +1.98353 q^{76} -3.66691 q^{77} +0.571421 q^{78} +0.825084 q^{79} -10.2453 q^{80} +8.91029 q^{81} +18.2757 q^{82} +1.63206 q^{83} -1.79652 q^{84} -1.00000 q^{85} +11.7601 q^{86} +0.397414 q^{87} +7.63206 q^{88} -2.44945 q^{89} -7.85672 q^{90} +7.98282 q^{91} +34.6507 q^{92} +0.126113 q^{93} -17.7723 q^{94} -0.404429 q^{95} +1.16444 q^{96} +9.80975 q^{97} -16.9384 q^{98} +2.99002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{9} + 2 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{13} + 8 q^{14} - 4 q^{15} + 4 q^{16} + 6 q^{17} - 8 q^{18} - 2 q^{19} - 8 q^{20} + 2 q^{22} + 14 q^{23} + 10 q^{24} + 6 q^{25} + 22 q^{27} + 22 q^{28} - 4 q^{29} + 10 q^{30} + 4 q^{31} - 24 q^{32} - 4 q^{33} - 2 q^{34} - 6 q^{35} + 10 q^{36} + 18 q^{37} - 4 q^{38} + 30 q^{39} + 6 q^{40} + 12 q^{41} + 14 q^{42} - 10 q^{43} - 8 q^{44} - 12 q^{45} - 24 q^{46} + 20 q^{47} - 6 q^{48} + 54 q^{49} - 2 q^{50} + 4 q^{51} + 44 q^{52} + 10 q^{53} - 60 q^{54} + 6 q^{55} - 14 q^{56} + 2 q^{57} + 52 q^{58} + 14 q^{59} - 10 q^{60} + 2 q^{61} - 16 q^{62} - 6 q^{63} - 14 q^{64} - 10 q^{65} + 10 q^{66} - 34 q^{67} + 8 q^{68} - 28 q^{69} - 8 q^{70} - 18 q^{71} + 16 q^{72} + 10 q^{73} - 30 q^{74} + 4 q^{75} + 8 q^{76} - 6 q^{77} - 6 q^{78} + 8 q^{79} - 4 q^{80} + 26 q^{81} + 20 q^{82} - 30 q^{83} - 60 q^{84} - 6 q^{85} - 6 q^{86} - 24 q^{87} + 6 q^{88} - 30 q^{89} + 8 q^{90} + 30 q^{91} + 36 q^{92} + 10 q^{93} - 26 q^{94} + 2 q^{95} + 14 q^{96} + 58 q^{97} - 42 q^{98} - 12 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^9 + 2 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^13 + 8 * q^14 - 4 * q^15 + 4 * q^16 + 6 * q^17 - 8 * q^18 - 2 * q^19 - 8 * q^20 + 2 * q^22 + 14 * q^23 + 10 * q^24 + 6 * q^25 + 22 * q^27 + 22 * q^28 - 4 * q^29 + 10 * q^30 + 4 * q^31 - 24 * q^32 - 4 * q^33 - 2 * q^34 - 6 * q^35 + 10 * q^36 + 18 * q^37 - 4 * q^38 + 30 * q^39 + 6 * q^40 + 12 * q^41 + 14 * q^42 - 10 * q^43 - 8 * q^44 - 12 * q^45 - 24 * q^46 + 20 * q^47 - 6 * q^48 + 54 * q^49 - 2 * q^50 + 4 * q^51 + 44 * q^52 + 10 * q^53 - 60 * q^54 + 6 * q^55 - 14 * q^56 + 2 * q^57 + 52 * q^58 + 14 * q^59 - 10 * q^60 + 2 * q^61 - 16 * q^62 - 6 * q^63 - 14 * q^64 - 10 * q^65 + 10 * q^66 - 34 * q^67 + 8 * q^68 - 28 * q^69 - 8 * q^70 - 18 * q^71 + 16 * q^72 + 10 * q^73 - 30 * q^74 + 4 * q^75 + 8 * q^76 - 6 * q^77 - 6 * q^78 + 8 * q^79 - 4 * q^80 + 26 * q^81 + 20 * q^82 - 30 * q^83 - 60 * q^84 - 6 * q^85 - 6 * q^86 - 24 * q^87 + 6 * q^88 - 30 * q^89 + 8 * q^90 + 30 * q^91 + 36 * q^92 + 10 * q^93 - 26 * q^94 + 2 * q^95 + 14 * q^96 + 58 * q^97 - 42 * q^98 - 12 * 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 $

$2$	−2.62765	−1.85803	−0.929013	−	0.370046i	$-0.879342\pi$
$2$	−2.62765	−1.85803	−0.929013	+	0.370046i	$0.879342\pi$
$3$	−0.0998927	−0.0576731	−0.0288365	−	0.999584i	$-0.509180\pi$
$3$	−0.0998927	−0.0576731	−0.0288365	+	0.999584i	$0.509180\pi$
$4$	4.90452	2.45226
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.262483	0.107158
$7$	3.66691	1.38596	0.692981	−	0.720956i	$-0.256297\pi$
$7$	3.66691	1.38596	0.692981	+	0.720956i	$0.256297\pi$
$8$	−7.63206	−2.69834
$9$	−2.99002	−0.996674
$10$	2.62765	0.830935
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.489926	−0.141429
$13$	2.17699	0.603787	0.301894	−	0.953342i	$-0.402381\pi$
$13$	2.17699	0.603787	0.301894	+	0.953342i	$0.402381\pi$
$14$	−9.63535	−2.57515
$15$	0.0998927	0.0257922
$16$	10.2453	2.56133
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	7.85672	1.85185
$19$	0.404429	0.0927825	0.0463912	−	0.998923i	$-0.485228\pi$
$19$	0.404429	0.0927825	0.0463912	+	0.998923i	$0.485228\pi$
$20$	−4.90452	−1.09669
$21$	−0.366298	−0.0799327
$22$	2.62765	0.560216
$23$	7.06504	1.47316	0.736582	−	0.676348i	$-0.236439\pi$
$23$	7.06504	1.47316	0.736582	+	0.676348i	$0.236439\pi$
$24$	0.762387	0.155622
$25$	1.00000	0.200000
$26$	−5.72035	−1.12185
$27$	0.598359	0.115154
$28$	17.9845	3.39874
$29$	−3.97841	−0.738773	−0.369386	−	0.929276i	$-0.620432\pi$
$29$	−3.97841	−0.738773	−0.369386	+	0.929276i	$0.620432\pi$
$30$	−0.262483	−0.0479225
$31$	−1.26248	−0.226749	−0.113374	−	0.993552i	$-0.536166\pi$
$31$	−1.26248	−0.226749	−0.113374	+	0.993552i	$0.536166\pi$
$32$	−11.6569	−2.06067
$33$	0.0998927	0.0173891
$34$	−2.62765	−0.450638
$35$	−3.66691	−0.619821
$36$	−14.6646	−2.44411
$37$	6.03208	0.991667	0.495834	−	0.868418i	$-0.334863\pi$
$37$	6.03208	0.991667	0.495834	+	0.868418i	$0.334863\pi$
$38$	−1.06270	−0.172392
$39$	−0.217465	−0.0348223
$40$	7.63206	1.20674
$41$	−6.95517	−1.08622	−0.543108	−	0.839663i	$-0.682753\pi$
$41$	−6.95517	−1.08622	−0.543108	+	0.839663i	$0.682753\pi$
$42$	0.962500	0.148517
$43$	−4.47553	−0.682512	−0.341256	−	0.939970i	$-0.610852\pi$
$43$	−4.47553	−0.682512	−0.341256	+	0.939970i	$0.610852\pi$
$44$	−4.90452	−0.739385
$45$	2.99002	0.445726
$46$	−18.5644	−2.73718
$47$	6.76360	0.986573	0.493286	−	0.869867i	$-0.335796\pi$
$47$	6.76360	0.986573	0.493286	+	0.869867i	$0.335796\pi$
$48$	−1.02343	−0.147720
$49$	6.44624	0.920892
$50$	−2.62765	−0.371605
$51$	−0.0998927	−0.0139878
$52$	10.6771	1.48064
$53$	−3.65972	−0.502701	−0.251351	−	0.967896i	$-0.580875\pi$
$53$	−3.65972	−0.502701	−0.251351	+	0.967896i	$0.580875\pi$
$54$	−1.57228	−0.213960
$55$	1.00000	0.134840
$56$	−27.9861	−3.73980
$57$	−0.0403995	−0.00535105
$58$	10.4539	1.37266
$59$	13.9501	1.81614	0.908071	−	0.418816i	$-0.137555\pi$
$59$	13.9501	1.81614	0.908071	+	0.418816i	$0.137555\pi$
$60$	0.489926	0.0632492
$61$	2.51449	0.321948	0.160974	−	0.986959i	$-0.448537\pi$
$61$	2.51449	0.321948	0.160974	+	0.986959i	$0.448537\pi$
$62$	3.31736	0.421305
$63$	−10.9641	−1.38135
$64$	10.1397	1.26746
$65$	−2.17699	−0.270022
$66$	−0.262483	−0.0323094
$67$	−4.53287	−0.553779	−0.276889	−	0.960902i	$-0.589304\pi$
$67$	−4.53287	−0.553779	−0.276889	+	0.960902i	$0.589304\pi$
$68$	4.90452	0.594761
$69$	−0.705746	−0.0849618
$70$	9.63535	1.15164
$71$	10.2396	1.21521	0.607606	−	0.794238i	$-0.292130\pi$
$71$	10.2396	1.21521	0.607606	+	0.794238i	$0.292130\pi$
$72$	22.8200	2.68937
$73$	−12.1386	−1.42072	−0.710361	−	0.703838i	$-0.751468\pi$
$73$	−12.1386	−1.42072	−0.710361	+	0.703838i	$0.751468\pi$
$74$	−15.8502	−1.84254
$75$	−0.0998927	−0.0115346
$76$	1.98353	0.227527
$77$	−3.66691	−0.417883
$78$	0.571421	0.0647007
$79$	0.825084	0.0928292	0.0464146	−	0.998922i	$-0.485220\pi$
$79$	0.825084	0.0928292	0.0464146	+	0.998922i	$0.485220\pi$
$80$	−10.2453	−1.14546
$81$	8.91029	0.990033
$82$	18.2757	2.01822
$83$	1.63206	0.179142	0.0895711	−	0.995980i	$-0.471450\pi$
$83$	1.63206	0.179142	0.0895711	+	0.995980i	$0.471450\pi$
$84$	−1.79652	−0.196016
$85$	−1.00000	−0.108465
$86$	11.7601	1.26813
$87$	0.397414	0.0426073
$88$	7.63206	0.813581
$89$	−2.44945	−0.259641	−0.129820	−	0.991538i	$-0.541440\pi$
$89$	−2.44945	−0.259641	−0.129820	+	0.991538i	$0.541440\pi$
$90$	−7.85672	−0.828171
$91$	7.98282	0.836826
$92$	34.6507	3.61258
$93$	0.126113	0.0130773
$94$	−17.7723	−1.83308
$95$	−0.404429	−0.0414936
$96$	1.16444	0.118845
$97$	9.80975	0.996029	0.498015	−	0.867169i	$-0.334063\pi$
$97$	9.80975	0.996029	0.498015	+	0.867169i	$0.334063\pi$
$98$	−16.9384	−1.71104
$99$	2.99002	0.300508
$100$	4.90452	0.490452
$101$	7.57120	0.753362	0.376681	−	0.926343i	$-0.377065\pi$
$101$	7.57120	0.753362	0.376681	+	0.926343i	$0.377065\pi$
$102$	0.262483	0.0259896
$103$	17.1047	1.68538	0.842690	−	0.538399i	$-0.180971\pi$
$103$	17.1047	1.68538	0.842690	+	0.538399i	$0.180971\pi$
$104$	−16.6149	−1.62922
$105$	0.366298	0.0357470
$106$	9.61645	0.934033
$107$	17.7703	1.71792	0.858960	−	0.512043i	$-0.171111\pi$
$107$	17.7703	1.71792	0.858960	+	0.512043i	$0.171111\pi$
$108$	2.93467	0.282388
$109$	17.1182	1.63963	0.819813	−	0.572632i	$-0.194077\pi$
$109$	17.1182	1.63963	0.819813	+	0.572632i	$0.194077\pi$
$110$	−2.62765	−0.250536
$111$	−0.602560	−0.0571925
$112$	37.5687	3.54991
$113$	10.8037	1.01633	0.508163	−	0.861261i	$-0.330325\pi$
$113$	10.8037	1.01633	0.508163	+	0.861261i	$0.330325\pi$
$114$	0.106156	0.00994239
$115$	−7.06504	−0.658819
$116$	−19.5122	−1.81167
$117$	−6.50923	−0.601779
$118$	−36.6558	−3.37444
$119$	3.66691	0.336145
$120$	−0.762387	−0.0695961
$121$	1.00000	0.0909091
$122$	−6.60719	−0.598187
$123$	0.694771	0.0626454
$124$	−6.19188	−0.556047
$125$	−1.00000	−0.0894427
$126$	28.8099	2.56659
$127$	15.4660	1.37238	0.686192	−	0.727420i	$-0.259281\pi$
$127$	15.4660	1.37238	0.686192	+	0.727420i	$0.259281\pi$
$128$	−3.32960	−0.294298
$129$	0.447073	0.0393625
$130$	5.72035	0.501708
$131$	−5.13154	−0.448344	−0.224172	−	0.974550i	$-0.571968\pi$
$131$	−5.13154	−0.448344	−0.224172	+	0.974550i	$0.571968\pi$
$132$	0.489926	0.0426426
$133$	1.48301	0.128593
$134$	11.9108	1.02894
$135$	−0.598359	−0.0514986
$136$	−7.63206	−0.654444
$137$	−5.74490	−0.490820	−0.245410	−	0.969419i	$-0.578923\pi$
$137$	−5.74490	−0.490820	−0.245410	+	0.969419i	$0.578923\pi$
$138$	1.85445	0.157861
$139$	−12.8253	−1.08783	−0.543913	−	0.839141i	$-0.683058\pi$
$139$	−12.8253	−1.08783	−0.543913	+	0.839141i	$0.683058\pi$
$140$	−17.9845	−1.51996
$141$	−0.675634	−0.0568986
$142$	−26.9059	−2.25790
$143$	−2.17699	−0.182049
$144$	−30.6337	−2.55281
$145$	3.97841	0.330389
$146$	31.8961	2.63974
$147$	−0.643932	−0.0531106
$148$	29.5845	2.43183
$149$	−11.7138	−0.959630	−0.479815	−	0.877370i	$-0.659296\pi$
$149$	−11.7138	−0.959630	−0.479815	+	0.877370i	$0.659296\pi$
$150$	0.262483	0.0214316
$151$	7.98048	0.649443	0.324721	−	0.945810i	$-0.394729\pi$
$151$	7.98048	0.649443	0.324721	+	0.945810i	$0.394729\pi$
$152$	−3.08663	−0.250359
$153$	−2.99002	−0.241729
$154$	9.63535	0.776438
$155$	1.26248	0.101405
$156$	−1.06656	−0.0853933
$157$	19.8844	1.58695	0.793473	−	0.608606i	$-0.208271\pi$
$157$	19.8844	1.58695	0.793473	+	0.608606i	$0.208271\pi$
$158$	−2.16803	−0.172479
$159$	0.365579	0.0289923
$160$	11.6569	0.921561
$161$	25.9069	2.04175
$162$	−23.4131	−1.83951
$163$	−18.6544	−1.46112	−0.730561	−	0.682848i	$-0.760741\pi$
$163$	−18.6544	−1.46112	−0.730561	+	0.682848i	$0.760741\pi$
$164$	−34.1118	−2.66369
$165$	−0.0998927	−0.00777663
$166$	−4.28849	−0.332851
$167$	20.5030	1.58657	0.793283	−	0.608853i	$-0.208370\pi$
$167$	20.5030	1.58657	0.793283	+	0.608853i	$0.208370\pi$
$168$	2.79561	0.215686
$169$	−8.26073	−0.635441
$170$	2.62765	0.201531
$171$	−1.20925	−0.0924738
$172$	−21.9503	−1.67370
$173$	−9.86607	−0.750104	−0.375052	−	0.927004i	$-0.622375\pi$
$173$	−9.86607	−0.750104	−0.375052	+	0.927004i	$0.622375\pi$
$174$	−1.04426	−0.0791655
$175$	3.66691	0.277192
$176$	−10.2453	−0.772270
$177$	−1.39351	−0.104742
$178$	6.43628	0.482420
$179$	−1.69363	−0.126588	−0.0632941	−	0.997995i	$-0.520161\pi$
$179$	−1.69363	−0.126588	−0.0632941	+	0.997995i	$0.520161\pi$
$180$	14.6646	1.09304
$181$	6.94664	0.516340	0.258170	−	0.966100i	$-0.416881\pi$
$181$	6.94664	0.516340	0.258170	+	0.966100i	$0.416881\pi$
$182$	−20.9760	−1.55485
$183$	−0.251179	−0.0185677
$184$	−53.9209	−3.97510
$185$	−6.03208	−0.443487
$186$	−0.331380	−0.0242979
$187$	−1.00000	−0.0731272
$188$	33.1722	2.41933
$189$	2.19413	0.159599
$190$	1.06270	0.0770962
$191$	−3.87901	−0.280675	−0.140338	−	0.990104i	$-0.544819\pi$
$191$	−3.87901	−0.280675	−0.140338	+	0.990104i	$0.544819\pi$
$192$	−1.01288	−0.0730982
$193$	−20.3975	−1.46825	−0.734124	−	0.679016i	$-0.762407\pi$
$193$	−20.3975	−1.46825	−0.734124	+	0.679016i	$0.762407\pi$
$194$	−25.7766	−1.85065
$195$	0.217465	0.0155730
$196$	31.6158	2.25827
$197$	8.37564	0.596739	0.298370	−	0.954450i	$-0.403557\pi$
$197$	8.37564	0.596739	0.298370	+	0.954450i	$0.403557\pi$
$198$	−7.85672	−0.558353
$199$	8.99670	0.637759	0.318880	−	0.947795i	$-0.396693\pi$
$199$	8.99670	0.637759	0.318880	+	0.947795i	$0.396693\pi$
$200$	−7.63206	−0.539668
$201$	0.452801	0.0319381
$202$	−19.8944	−1.39977
$203$	−14.5885	−1.02391
$204$	−0.489926	−0.0343017
$205$	6.95517	0.485770
$206$	−44.9452	−3.13148
$207$	−21.1246	−1.46826
$208$	22.3039	1.54650
$209$	−0.404429	−0.0279750
$210$	−0.962500	−0.0664188
$211$	−11.0925	−0.763639	−0.381819	−	0.924237i	$-0.624702\pi$
$211$	−11.0925	−0.763639	−0.381819	+	0.924237i	$0.624702\pi$
$212$	−17.9492	−1.23276
$213$	−1.02286	−0.0700850
$214$	−46.6940	−3.19194
$215$	4.47553	0.305229
$216$	−4.56672	−0.310726
$217$	−4.62941	−0.314265
$218$	−44.9806	−3.04647
$219$	1.21256	0.0819373
$220$	4.90452	0.330663
$221$	2.17699	0.146440
$222$	1.58331	0.106265
$223$	−23.6521	−1.58386	−0.791931	−	0.610611i	$-0.790924\pi$
$223$	−23.6521	−1.58386	−0.791931	+	0.610611i	$0.790924\pi$
$224$	−42.7449	−2.85602
$225$	−2.99002	−0.199335
$226$	−28.3883	−1.88836
$227$	−16.9243	−1.12330	−0.561652	−	0.827373i	$-0.689834\pi$
$227$	−16.9243	−1.12330	−0.561652	+	0.827373i	$0.689834\pi$
$228$	−0.198140	−0.0131222
$229$	14.9977	0.991073	0.495537	−	0.868587i	$-0.334971\pi$
$229$	14.9977	0.991073	0.495537	+	0.868587i	$0.334971\pi$
$230$	18.5644	1.22410
$231$	0.366298	0.0241006
$232$	30.3635	1.99346
$233$	17.2929	1.13290	0.566448	−	0.824097i	$-0.308317\pi$
$233$	17.2929	1.13290	0.566448	+	0.824097i	$0.308317\pi$
$234$	17.1040	1.11812
$235$	−6.76360	−0.441209
$236$	68.4184	4.45366
$237$	−0.0824199	−0.00535375
$238$	−9.63535	−0.624567
$239$	22.3738	1.44724	0.723620	−	0.690198i	$-0.242477\pi$
$239$	22.3738	1.44724	0.723620	+	0.690198i	$0.242477\pi$
$240$	1.02343	0.0660622
$241$	0.929315	0.0598624	0.0299312	−	0.999552i	$-0.490471\pi$
$241$	0.929315	0.0598624	0.0299312	+	0.999552i	$0.490471\pi$
$242$	−2.62765	−0.168911
$243$	−2.68515	−0.172252
$244$	12.3324	0.789500
$245$	−6.44624	−0.411835
$246$	−1.82561	−0.116397
$247$	0.880437	0.0560209
$248$	9.63535	0.611845
$249$	−0.163031	−0.0103317
$250$	2.62765	0.166187
$251$	11.1022	0.700767	0.350383	−	0.936606i	$-0.386051\pi$
$251$	11.1022	0.700767	0.350383	+	0.936606i	$0.386051\pi$
$252$	−53.7739	−3.38744
$253$	−7.06504	−0.444176
$254$	−40.6391	−2.54993
$255$	0.0998927	0.00625552
$256$	−11.5303	−0.720646
$257$	14.6103	0.911364	0.455682	−	0.890143i	$-0.349395\pi$
$257$	14.6103	0.911364	0.455682	+	0.890143i	$0.349395\pi$
$258$	−1.17475	−0.0731367
$259$	22.1191	1.37441
$260$	−10.6771	−0.662164
$261$	11.8955	0.736316
$262$	13.4839	0.833036
$263$	24.8184	1.53037	0.765183	−	0.643812i	$-0.222648\pi$
$263$	24.8184	1.53037	0.765183	+	0.643812i	$0.222648\pi$
$264$	−0.762387	−0.0469217
$265$	3.65972	0.224815
$266$	−3.89682	−0.238929
$267$	0.244682	0.0149743
$268$	−22.2316	−1.35801
$269$	−22.9036	−1.39646	−0.698229	−	0.715874i	$-0.746028\pi$
$269$	−22.9036	−1.39646	−0.698229	+	0.715874i	$0.746028\pi$
$270$	1.57228	0.0956857
$271$	2.73051	0.165867	0.0829333	−	0.996555i	$-0.473571\pi$
$271$	2.73051	0.165867	0.0829333	+	0.996555i	$0.473571\pi$
$272$	10.2453	0.621213
$273$	−0.797425	−0.0482623
$274$	15.0956	0.911956
$275$	−1.00000	−0.0603023
$276$	−3.46135	−0.208349
$277$	−13.8604	−0.832793	−0.416396	−	0.909183i	$-0.636707\pi$
$277$	−13.8604	−0.832793	−0.416396	+	0.909183i	$0.636707\pi$
$278$	33.7003	2.02121
$279$	3.77485	0.225994
$280$	27.9861	1.67249
$281$	−5.93352	−0.353964	−0.176982	−	0.984214i	$-0.556633\pi$
$281$	−5.93352	−0.353964	−0.176982	+	0.984214i	$0.556633\pi$
$282$	1.77533	0.105719
$283$	−27.1187	−1.61204	−0.806020	−	0.591888i	$-0.798383\pi$
$283$	−27.1187	−1.61204	−0.806020	+	0.591888i	$0.798383\pi$
$284$	50.2202	2.98002
$285$	0.0403995	0.00239306
$286$	5.72035	0.338251
$287$	−25.5040	−1.50545
$288$	34.8545	2.05382
$289$	1.00000	0.0588235
$290$	−10.4539	−0.613872
$291$	−0.979922	−0.0574441
$292$	−59.5343	−3.48398
$293$	−14.1051	−0.824031	−0.412015	−	0.911177i	$-0.635175\pi$
$293$	−14.1051	−0.824031	−0.412015	+	0.911177i	$0.635175\pi$
$294$	1.69203	0.0986810
$295$	−13.9501	−0.812204
$296$	−46.0372	−2.67586
$297$	−0.598359	−0.0347203
$298$	30.7797	1.78302
$299$	15.3805	0.889477
$300$	−0.489926	−0.0282859
$301$	−16.4114	−0.945936
$302$	−20.9699	−1.20668
$303$	−0.756307	−0.0434487
$304$	4.14351	0.237646
$305$	−2.51449	−0.143979
$306$	7.85672	0.449139
$307$	−7.81112	−0.445804	−0.222902	−	0.974841i	$-0.571553\pi$
$307$	−7.81112	−0.445804	−0.222902	+	0.974841i	$0.571553\pi$
$308$	−17.9845	−1.02476
$309$	−1.70864	−0.0972010
$310$	−3.31736	−0.188413
$311$	−19.9757	−1.13272	−0.566360	−	0.824158i	$-0.691649\pi$
$311$	−19.9757	−1.13272	−0.566360	+	0.824158i	$0.691649\pi$
$312$	1.65971	0.0939623
$313$	30.8581	1.74420	0.872102	−	0.489324i	$-0.162757\pi$
$313$	30.8581	1.74420	0.872102	+	0.489324i	$0.162757\pi$
$314$	−52.2491	−2.94859
$315$	10.9641	0.617760
$316$	4.04665	0.227642
$317$	17.4828	0.981935	0.490967	−	0.871178i	$-0.336643\pi$
$317$	17.4828	0.981935	0.490967	+	0.871178i	$0.336643\pi$
$318$	−0.960613	−0.0538685
$319$	3.97841	0.222748
$320$	−10.1397	−0.566825
$321$	−1.77512	−0.0990776
$322$	−68.0742	−3.79362
$323$	0.404429	0.0225031
$324$	43.7008	2.42782
$325$	2.17699	0.120757
$326$	49.0170	2.71480
$327$	−1.70998	−0.0945622
$328$	53.0823	2.93098
$329$	24.8015	1.36735
$330$	0.262483	0.0144492
$331$	−9.28748	−0.510486	−0.255243	−	0.966877i	$-0.582155\pi$
$331$	−9.28748	−0.510486	−0.255243	+	0.966877i	$0.582155\pi$
$332$	8.00450	0.439304
$333$	−18.0360	−0.988369
$334$	−53.8745	−2.94788
$335$	4.53287	0.247657
$336$	−3.75283	−0.204734
$337$	20.8360	1.13501	0.567506	−	0.823369i	$-0.307908\pi$
$337$	20.8360	1.13501	0.567506	+	0.823369i	$0.307908\pi$
$338$	21.7063	1.18067
$339$	−1.07921	−0.0586146
$340$	−4.90452	−0.265985
$341$	1.26248	0.0683673
$342$	3.17749	0.171819
$343$	−2.03058	−0.109641
$344$	34.1575	1.84165
$345$	0.705746	0.0379961
$346$	25.9246	1.39371
$347$	−20.5554	−1.10347	−0.551736	−	0.834019i	$-0.686034\pi$
$347$	−20.5554	−1.10347	−0.551736	+	0.834019i	$0.686034\pi$
$348$	1.94913	0.104484
$349$	−10.7769	−0.576872	−0.288436	−	0.957499i	$-0.593135\pi$
$349$	−10.7769	−0.576872	−0.288436	+	0.957499i	$0.593135\pi$
$350$	−9.63535	−0.515031
$351$	1.30262	0.0695287
$352$	11.6569	0.621317
$353$	−30.2261	−1.60877	−0.804387	−	0.594106i	$-0.797506\pi$
$353$	−30.2261	−1.60877	−0.804387	+	0.594106i	$0.797506\pi$
$354$	3.66165	0.194614
$355$	−10.2396	−0.543460
$356$	−12.0134	−0.636708
$357$	−0.366298	−0.0193865
$358$	4.45027	0.235204
$359$	−37.3475	−1.97112	−0.985562	−	0.169317i	$-0.945844\pi$
$359$	−37.3475	−1.97112	−0.985562	+	0.169317i	$0.945844\pi$
$360$	−22.8200	−1.20272
$361$	−18.8364	−0.991391
$362$	−18.2533	−0.959373
$363$	−0.0998927	−0.00524300
$364$	39.1519	2.05212
$365$	12.1386	0.635366
$366$	0.660010	0.0344993
$367$	21.3780	1.11592	0.557962	−	0.829867i	$-0.311584\pi$
$367$	21.3780	1.11592	0.557962	+	0.829867i	$0.311584\pi$
$368$	72.3836	3.77326
$369$	20.7961	1.08260
$370$	15.8502	0.824011
$371$	−13.4199	−0.696725
$372$	0.618523	0.0320689
$373$	21.6623	1.12163	0.560816	−	0.827941i	$-0.310488\pi$
$373$	21.6623	1.12163	0.560816	+	0.827941i	$0.310488\pi$
$374$	2.62765	0.135872
$375$	0.0998927	0.00515843
$376$	−51.6202	−2.66211
$377$	−8.66095	−0.446062
$378$	−5.76540	−0.296540
$379$	29.1722	1.49848	0.749239	−	0.662300i	$-0.230420\pi$
$379$	29.1722	1.49848	0.749239	+	0.662300i	$0.230420\pi$
$380$	−1.98353	−0.101753
$381$	−1.54494	−0.0791496
$382$	10.1927	0.521502
$383$	7.42866	0.379587	0.189793	−	0.981824i	$-0.439218\pi$
$383$	7.42866	0.379587	0.189793	+	0.981824i	$0.439218\pi$
$384$	0.332602	0.0169730
$385$	3.66691	0.186883
$386$	53.5975	2.72804
$387$	13.3819	0.680242
$388$	48.1122	2.44253
$389$	−21.4125	−1.08566	−0.542828	−	0.839844i	$-0.682647\pi$
$389$	−21.4125	−1.08566	−0.542828	+	0.839844i	$0.682647\pi$
$390$	−0.571421	−0.0289350
$391$	7.06504	0.357295
$392$	−49.1981	−2.48488
$393$	0.512603	0.0258574
$394$	−22.0082	−1.10876
$395$	−0.825084	−0.0415145
$396$	14.6646	0.736926
$397$	19.0898	0.958092	0.479046	−	0.877790i	$-0.340983\pi$
$397$	19.0898	0.958092	0.479046	+	0.877790i	$0.340983\pi$
$398$	−23.6401	−1.18497
$399$	−0.148141	−0.00741635
$400$	10.2453	0.512266
$401$	5.67051	0.283172	0.141586	−	0.989926i	$-0.454780\pi$
$401$	5.67051	0.283172	0.141586	+	0.989926i	$0.454780\pi$
$402$	−1.18980	−0.0593418
$403$	−2.74841	−0.136908
$404$	37.1331	1.84744
$405$	−8.91029	−0.442756
$406$	38.3334	1.90245
$407$	−6.03208	−0.298999
$408$	0.762387	0.0377438
$409$	6.93080	0.342706	0.171353	−	0.985210i	$-0.445186\pi$
$409$	6.93080	0.342706	0.171353	+	0.985210i	$0.445186\pi$
$410$	−18.2757	−0.902574
$411$	0.573873	0.0283071
$412$	83.8906	4.13299
$413$	51.1536	2.51710
$414$	55.5081	2.72807
$415$	−1.63206	−0.0801149
$416$	−25.3770	−1.24421
$417$	1.28115	0.0627383
$418$	1.06270	0.0519782
$419$	20.6839	1.01048	0.505238	−	0.862980i	$-0.331405\pi$
$419$	20.6839	1.01048	0.505238	+	0.862980i	$0.331405\pi$
$420$	1.79652	0.0876610
$421$	26.9647	1.31418	0.657090	−	0.753812i	$-0.271787\pi$
$421$	26.9647	1.31418	0.657090	+	0.753812i	$0.271787\pi$
$422$	29.1472	1.41886
$423$	−20.2233	−0.983291
$424$	27.9312	1.35646
$425$	1.00000	0.0485071
$426$	2.68771	0.130220
$427$	9.22042	0.446207
$428$	87.1549	4.21279
$429$	0.217465	0.0104993
$430$	−11.7601	−0.567123
$431$	−11.4428	−0.551180	−0.275590	−	0.961275i	$-0.588873\pi$
$431$	−11.4428	−0.551180	−0.275590	+	0.961275i	$0.588873\pi$
$432$	6.13038	0.294948
$433$	−10.3824	−0.498948	−0.249474	−	0.968382i	$-0.580258\pi$
$433$	−10.3824	−0.498948	−0.249474	+	0.968382i	$0.580258\pi$
$434$	12.1645	0.583913
$435$	−0.397414	−0.0190546
$436$	83.9566	4.02079
$437$	2.85731	0.136684
$438$	−3.18618	−0.152242
$439$	−13.4740	−0.643080	−0.321540	−	0.946896i	$-0.604200\pi$
$439$	−13.4740	−0.643080	−0.321540	+	0.946896i	$0.604200\pi$
$440$	−7.63206	−0.363844
$441$	−19.2744	−0.917829
$442$	−5.72035	−0.272089
$443$	−23.9557	−1.13817	−0.569085	−	0.822279i	$-0.692702\pi$
$443$	−23.9557	−1.13817	−0.569085	+	0.822279i	$0.692702\pi$
$444$	−2.95527	−0.140251
$445$	2.44945	0.116115
$446$	62.1493	2.94286
$447$	1.17012	0.0553448
$448$	37.1813	1.75665
$449$	−34.8825	−1.64621	−0.823104	−	0.567891i	$-0.807759\pi$
$449$	−34.8825	−1.64621	−0.823104	+	0.567891i	$0.807759\pi$
$450$	7.85672	0.370369
$451$	6.95517	0.327506
$452$	52.9870	2.49230
$453$	−0.797192	−0.0374553
$454$	44.4710	2.08713
$455$	−7.98282	−0.374240
$456$	0.308332	0.0144390
$457$	1.58445	0.0741174	0.0370587	−	0.999313i	$-0.488201\pi$
$457$	1.58445	0.0741174	0.0370587	+	0.999313i	$0.488201\pi$
$458$	−39.4085	−1.84144
$459$	0.598359	0.0279290
$460$	−34.6507	−1.61560
$461$	33.6528	1.56737	0.783684	−	0.621159i	$-0.213338\pi$
$461$	33.6528	1.56737	0.783684	+	0.621159i	$0.213338\pi$
$462$	−0.962500	−0.0447796
$463$	26.1641	1.21595	0.607975	−	0.793956i	$-0.291982\pi$
$463$	26.1641	1.21595	0.607975	+	0.793956i	$0.291982\pi$
$464$	−40.7601	−1.89224
$465$	−0.126113	−0.00584834
$466$	−45.4397	−2.10495
$467$	−28.2955	−1.30936	−0.654681	−	0.755905i	$-0.727197\pi$
$467$	−28.2955	−1.30936	−0.654681	+	0.755905i	$0.727197\pi$
$468$	−31.9247	−1.47572
$469$	−16.6216	−0.767516
$470$	17.7723	0.819777
$471$	−1.98630	−0.0915240
$472$	−106.468	−4.90057
$473$	4.47553	0.205785
$474$	0.216570	0.00994740
$475$	0.404429	0.0185565
$476$	17.9845	0.824316
$477$	10.9426	0.501029
$478$	−58.7904	−2.68901
$479$	−20.3094	−0.927959	−0.463980	−	0.885846i	$-0.653579\pi$
$479$	−20.3094	−0.927959	−0.463980	+	0.885846i	$0.653579\pi$
$480$	−1.16444	−0.0531493
$481$	13.1317	0.598756
$482$	−2.44191	−0.111226
$483$	−2.58791	−0.117754
$484$	4.90452	0.222933
$485$	−9.80975	−0.445438
$486$	7.05562	0.320050
$487$	−17.0397	−0.772142	−0.386071	−	0.922469i	$-0.626168\pi$
$487$	−17.0397	−0.772142	−0.386071	+	0.922469i	$0.626168\pi$
$488$	−19.1908	−0.868725
$489$	1.86343	0.0842673
$490$	16.9384	0.765201
$491$	−19.4470	−0.877631	−0.438816	−	0.898577i	$-0.644602\pi$
$491$	−19.4470	−0.877631	−0.438816	+	0.898577i	$0.644602\pi$
$492$	3.40752	0.153623
$493$	−3.97841	−0.179179
$494$	−2.31348	−0.104088
$495$	−2.99002	−0.134391
$496$	−12.9345	−0.580778
$497$	37.5476	1.68424
$498$	0.428388	0.0191965
$499$	−32.1449	−1.43900	−0.719501	−	0.694491i	$-0.755629\pi$
$499$	−32.1449	−1.43900	−0.719501	+	0.694491i	$0.755629\pi$
$500$	−4.90452	−0.219337
$501$	−2.04809	−0.0915021
$502$	−29.1727	−1.30204
$503$	−21.7228	−0.968570	−0.484285	−	0.874910i	$-0.660920\pi$
$503$	−21.7228	−0.968570	−0.484285	+	0.874910i	$0.660920\pi$
$504$	83.6791	3.72736
$505$	−7.57120	−0.336914
$506$	18.5644	0.825290
$507$	0.825186	0.0366478
$508$	75.8533	3.36545
$509$	2.06855	0.0916870	0.0458435	−	0.998949i	$-0.485402\pi$
$509$	2.06855	0.0916870	0.0458435	+	0.998949i	$0.485402\pi$
$510$	−0.262483	−0.0116229
$511$	−44.5113	−1.96907
$512$	36.9568	1.63328
$513$	0.241994	0.0106843
$514$	−38.3906	−1.69334
$515$	−17.1047	−0.753725
$516$	2.19268	0.0965273
$517$	−6.76360	−0.297463
$518$	−58.1211	−2.55370
$519$	0.985548	0.0432608
$520$	16.6149	0.728611
$521$	35.2254	1.54325	0.771627	−	0.636075i	$-0.219443\pi$
$521$	35.2254	1.54325	0.771627	+	0.636075i	$0.219443\pi$
$522$	−31.2573	−1.36809
$523$	−10.5982	−0.463426	−0.231713	−	0.972784i	$-0.574433\pi$
$523$	−10.5982	−0.463426	−0.231713	+	0.972784i	$0.574433\pi$
$524$	−25.1677	−1.09946
$525$	−0.366298	−0.0159865
$526$	−65.2139	−2.84346
$527$	−1.26248	−0.0549946
$528$	1.02343	0.0445391
$529$	26.9149	1.17021
$530$	−9.61645	−0.417712
$531$	−41.7110	−1.81010
$532$	7.27344	0.315344
$533$	−15.1413	−0.655843
$534$	−0.642937	−0.0278226
$535$	−17.7703	−0.768277
$536$	34.5952	1.49428
$537$	0.169182	0.00730072
$538$	60.1826	2.59466
$539$	−6.44624	−0.277659
$540$	−2.93467	−0.126288
$541$	−9.75210	−0.419276	−0.209638	−	0.977779i	$-0.567229\pi$
$541$	−9.75210	−0.419276	−0.209638	+	0.977779i	$0.567229\pi$
$542$	−7.17481	−0.308185
$543$	−0.693919	−0.0297789
$544$	−11.6569	−0.499787
$545$	−17.1182	−0.733263
$546$	2.09535	0.0896727
$547$	11.4061	0.487688	0.243844	−	0.969815i	$-0.421592\pi$
$547$	11.4061	0.487688	0.243844	+	0.969815i	$0.421592\pi$
$548$	−28.1760	−1.20362
$549$	−7.51838	−0.320877
$550$	2.62765	0.112043
$551$	−1.60899	−0.0685452
$552$	5.38630	0.229256
$553$	3.02551	0.128658
$554$	36.4203	1.54735
$555$	0.602560	0.0255772
$556$	−62.9020	−2.66764
$557$	−16.7175	−0.708342	−0.354171	−	0.935181i	$-0.615237\pi$
$557$	−16.7175	−0.708342	−0.354171	+	0.935181i	$0.615237\pi$
$558$	−9.91897	−0.419903
$559$	−9.74317	−0.412092
$560$	−37.5687	−1.58757
$561$	0.0998927	0.00421747
$562$	15.5912	0.657674
$563$	−27.7024	−1.16752	−0.583758	−	0.811928i	$-0.698418\pi$
$563$	−27.7024	−1.16752	−0.583758	+	0.811928i	$0.698418\pi$
$564$	−3.31366	−0.139530
$565$	−10.8037	−0.454515
$566$	71.2584	2.99521
$567$	32.6733	1.37215
$568$	−78.1490	−3.27906
$569$	−3.25198	−0.136330	−0.0681651	−	0.997674i	$-0.521714\pi$
$569$	−3.25198	−0.136330	−0.0681651	+	0.997674i	$0.521714\pi$
$570$	−0.106156	−0.00444637
$571$	−5.87690	−0.245941	−0.122970	−	0.992410i	$-0.539242\pi$
$571$	−5.87690	−0.245941	−0.122970	+	0.992410i	$0.539242\pi$
$572$	−10.6771	−0.446431
$573$	0.387484	0.0161874
$574$	67.0155	2.79717
$575$	7.06504	0.294633
$576$	−30.3178	−1.26324
$577$	−27.9489	−1.16353	−0.581764	−	0.813358i	$-0.697637\pi$
$577$	−27.9489	−1.16353	−0.581764	+	0.813358i	$0.697637\pi$
$578$	−2.62765	−0.109296
$579$	2.03756	0.0846783
$580$	19.5122	0.810201
$581$	5.98463	0.248284
$582$	2.57489	0.106733
$583$	3.65972	0.151570
$584$	92.6429	3.83359
$585$	6.50923	0.269124
$586$	37.0633	1.53107
$587$	−27.7295	−1.14452	−0.572259	−	0.820073i	$-0.693933\pi$
$587$	−27.7295	−1.14452	−0.572259	+	0.820073i	$0.693933\pi$
$588$	−3.15818	−0.130241
$589$	−0.510585	−0.0210383
$590$	36.6558	1.50910
$591$	−0.836665	−0.0344158
$592$	61.8005	2.53999
$593$	−7.78211	−0.319573	−0.159786	−	0.987152i	$-0.551081\pi$
$593$	−7.78211	−0.319573	−0.159786	+	0.987152i	$0.551081\pi$
$594$	1.57228	0.0645113
$595$	−3.66691	−0.150329
$596$	−57.4505	−2.35326
$597$	−0.898704	−0.0367815
$598$	−40.4145	−1.65267
$599$	25.7926	1.05386	0.526928	−	0.849910i	$-0.323344\pi$
$599$	25.7926	1.05386	0.526928	+	0.849910i	$0.323344\pi$
$600$	0.762387	0.0311243
$601$	−31.1093	−1.26897	−0.634487	−	0.772933i	$-0.718789\pi$
$601$	−31.1093	−1.26897	−0.634487	+	0.772933i	$0.718789\pi$
$602$	43.1233	1.75757
$603$	13.5534	0.551937
$604$	39.1405	1.59260
$605$	−1.00000	−0.0406558
$606$	1.98731	0.0807288
$607$	−8.48532	−0.344409	−0.172204	−	0.985061i	$-0.555089\pi$
$607$	−8.48532	−0.344409	−0.172204	+	0.985061i	$0.555089\pi$
$608$	−4.71441	−0.191194
$609$	1.45728	0.0590521
$610$	6.60719	0.267517
$611$	14.7243	0.595680
$612$	−14.6646	−0.592783
$613$	−46.1500	−1.86398	−0.931990	−	0.362483i	$-0.881929\pi$
$613$	−46.1500	−1.86398	−0.931990	+	0.362483i	$0.881929\pi$
$614$	20.5249	0.828316
$615$	−0.694771	−0.0280159
$616$	27.9861	1.12759
$617$	36.8768	1.48461	0.742303	−	0.670065i	$-0.233734\pi$
$617$	36.8768	1.48461	0.742303	+	0.670065i	$0.233734\pi$
$618$	4.48970	0.180602
$619$	−22.4148	−0.900927	−0.450464	−	0.892795i	$-0.648741\pi$
$619$	−22.4148	−0.900927	−0.450464	+	0.892795i	$0.648741\pi$
$620$	6.19188	0.248672
$621$	4.22743	0.169641
$622$	52.4891	2.10462
$623$	−8.98191	−0.359852
$624$	−2.22800	−0.0891912
$625$	1.00000	0.0400000
$626$	−81.0842	−3.24078
$627$	0.0403995	0.00161340
$628$	97.5234	3.89161
$629$	6.03208	0.240515
$630$	−28.8099	−1.14781
$631$	−42.7482	−1.70178	−0.850889	−	0.525346i	$-0.823936\pi$
$631$	−42.7482	−1.70178	−0.850889	+	0.525346i	$0.823936\pi$
$632$	−6.29710	−0.250485
$633$	1.10806	0.0440414
$634$	−45.9387	−1.82446
$635$	−15.4660	−0.613749
$636$	1.79299	0.0710968
$637$	14.0334	0.556023
$638$	−10.4539	−0.413872
$639$	−30.6165	−1.21117
$640$	3.32960	0.131614
$641$	21.2893	0.840876	0.420438	−	0.907321i	$-0.361876\pi$
$641$	21.2893	0.840876	0.420438	+	0.907321i	$0.361876\pi$
$642$	4.66439	0.184089
$643$	−21.8193	−0.860468	−0.430234	−	0.902717i	$-0.641569\pi$
$643$	−21.8193	−0.860468	−0.430234	+	0.902717i	$0.641569\pi$
$644$	127.061	5.00691
$645$	−0.447073	−0.0176035
$646$	−1.06270	−0.0418113
$647$	−49.1663	−1.93293	−0.966463	−	0.256805i	$-0.917330\pi$
$647$	−49.1663	−1.93293	−0.966463	+	0.256805i	$0.917330\pi$
$648$	−68.0039	−2.67145
$649$	−13.9501	−0.547587
$650$	−5.72035	−0.224371
$651$	0.462444	0.0181246
$652$	−91.4907	−3.58305
$653$	36.2175	1.41730	0.708649	−	0.705561i	$-0.249305\pi$
$653$	36.2175	1.41730	0.708649	+	0.705561i	$0.249305\pi$
$654$	4.49323	0.175699
$655$	5.13154	0.200506
$656$	−71.2579	−2.78215
$657$	36.2948	1.41600
$658$	−65.1696	−2.54058
$659$	6.51109	0.253636	0.126818	−	0.991926i	$-0.459524\pi$
$659$	6.51109	0.253636	0.126818	+	0.991926i	$0.459524\pi$
$660$	−0.489926	−0.0190703
$661$	−42.9746	−1.67152	−0.835758	−	0.549098i	$-0.814972\pi$
$661$	−42.9746	−1.67152	−0.835758	+	0.549098i	$0.814972\pi$
$662$	24.4042	0.948497
$663$	−0.217465	−0.00844564
$664$	−12.4560	−0.483387
$665$	−1.48301	−0.0575085
$666$	47.3923	1.83642
$667$	−28.1077	−1.08833
$668$	100.557	3.89068
$669$	2.36267	0.0913461
$670$	−11.9108	−0.460154
$671$	−2.51449	−0.0970709
$672$	4.26991	0.164715
$673$	38.8144	1.49619	0.748093	−	0.663594i	$-0.230970\pi$
$673$	38.8144	1.49619	0.748093	+	0.663594i	$0.230970\pi$
$674$	−54.7497	−2.10888
$675$	0.598359	0.0230309
$676$	−40.5150	−1.55827
$677$	10.0716	0.387084	0.193542	−	0.981092i	$-0.438002\pi$
$677$	10.0716	0.387084	0.193542	+	0.981092i	$0.438002\pi$
$678$	2.83578	0.108907
$679$	35.9715	1.38046
$680$	7.63206	0.292676
$681$	1.69061	0.0647844
$682$	−3.31736	−0.127028
$683$	0.885925	0.0338990	0.0169495	−	0.999856i	$-0.494605\pi$
$683$	0.885925	0.0338990	0.0169495	+	0.999856i	$0.494605\pi$
$684$	−5.93081	−0.226770
$685$	5.74490	0.219501
$686$	5.33564	0.203716
$687$	−1.49816	−0.0571582
$688$	−45.8532	−1.74814
$689$	−7.96716	−0.303525
$690$	−1.85445	−0.0705977
$691$	3.82441	0.145487	0.0727437	−	0.997351i	$-0.476825\pi$
$691$	3.82441	0.145487	0.0727437	+	0.997351i	$0.476825\pi$
$692$	−48.3884	−1.83945
$693$	10.9641	0.416493
$694$	54.0123	2.05028
$695$	12.8253	0.486491
$696$	−3.03309	−0.114969
$697$	−6.95517	−0.263446
$698$	28.3178	1.07184
$699$	−1.72744	−0.0653376
$700$	17.9845	0.679749
$701$	−26.1043	−0.985946	−0.492973	−	0.870045i	$-0.664090\pi$
$701$	−26.1043	−0.985946	−0.492973	+	0.870045i	$0.664090\pi$
$702$	−3.42282	−0.129186
$703$	2.43955	0.0920093
$704$	−10.1397	−0.382153
$705$	0.675634	0.0254458
$706$	79.4235	2.98914
$707$	27.7629	1.04413
$708$	−6.83449	−0.256856
$709$	−0.902007	−0.0338756	−0.0169378	−	0.999857i	$-0.505392\pi$
$709$	−0.902007	−0.0338756	−0.0169378	+	0.999857i	$0.505392\pi$
$710$	26.9059	1.00976
$711$	−2.46702	−0.0925205
$712$	18.6943	0.700600
$713$	−8.91950	−0.334038
$714$	0.962500	0.0360207
$715$	2.17699	0.0814147
$716$	−8.30647	−0.310427
$717$	−2.23498	−0.0834668
$718$	98.1359	3.66240
$719$	16.9937	0.633757	0.316878	−	0.948466i	$-0.397365\pi$
$719$	16.9937	0.633757	0.316878	+	0.948466i	$0.397365\pi$
$720$	30.6337	1.14165
$721$	62.7216	2.33587
$722$	49.4955	1.84203
$723$	−0.0928317	−0.00345245
$724$	34.0700	1.26620
$725$	−3.97841	−0.147755
$726$	0.262483	0.00974164
$727$	30.2242	1.12095	0.560477	−	0.828170i	$-0.310618\pi$
$727$	30.2242	1.12095	0.560477	+	0.828170i	$0.310618\pi$
$728$	−60.9254	−2.25804
$729$	−26.4627	−0.980098
$730$	−31.8961	−1.18053
$731$	−4.47553	−0.165533
$732$	−1.23191	−0.0455329
$733$	15.3689	0.567662	0.283831	−	0.958874i	$-0.408394\pi$
$733$	15.3689	0.567662	0.283831	+	0.958874i	$0.408394\pi$
$734$	−56.1739	−2.07342
$735$	0.643932	0.0237518
$736$	−82.3568	−3.03571
$737$	4.53287	0.166971
$738$	−54.6448	−2.01150
$739$	2.76649	0.101767	0.0508835	−	0.998705i	$-0.483796\pi$
$739$	2.76649	0.101767	0.0508835	+	0.998705i	$0.483796\pi$
$740$	−29.5845	−1.08755
$741$	−0.0879492	−0.00323089
$742$	35.2627	1.29453
$743$	−13.2824	−0.487283	−0.243642	−	0.969865i	$-0.578342\pi$
$743$	−13.2824	−0.487283	−0.243642	+	0.969865i	$0.578342\pi$
$744$	−0.962500	−0.0352870
$745$	11.7138	0.429160
$746$	−56.9208	−2.08402
$747$	−4.87991	−0.178546
$748$	−4.90452	−0.179327
$749$	65.1621	2.38097
$750$	−0.262483	−0.00958451
$751$	−25.1336	−0.917138	−0.458569	−	0.888659i	$-0.651638\pi$
$751$	−25.1336	−0.917138	−0.458569	+	0.888659i	$0.651638\pi$
$752$	69.2952	2.52694
$753$	−1.10903	−0.0404154
$754$	22.7579	0.828794
$755$	−7.98048	−0.290440
$756$	10.7612	0.391380
$757$	54.8867	1.99489	0.997446	−	0.0714192i	$-0.0227528\pi$
$757$	54.8867	1.99489	0.997446	+	0.0714192i	$0.0227528\pi$
$758$	−76.6543	−2.78421
$759$	0.705746	0.0256170
$760$	3.08663	0.111964
$761$	44.3257	1.60681	0.803403	−	0.595436i	$-0.203021\pi$
$761$	44.3257	1.60681	0.803403	+	0.595436i	$0.203021\pi$
$762$	4.05955	0.147062
$763$	62.7709	2.27246
$764$	−19.0247	−0.688289
$765$	2.99002	0.108104
$766$	−19.5199	−0.705282
$767$	30.3691	1.09656
$768$	1.15180	0.0415618
$769$	−34.7980	−1.25485	−0.627424	−	0.778678i	$-0.715891\pi$
$769$	−34.7980	−1.25485	−0.627424	+	0.778678i	$0.715891\pi$
$770$	−9.63535	−0.347234
$771$	−1.45946	−0.0525611
$772$	−100.040	−3.60053
$773$	1.06628	0.0383515	0.0191758	−	0.999816i	$-0.493896\pi$
$773$	1.06628	0.0383515	0.0191758	+	0.999816i	$0.493896\pi$
$774$	−35.1630	−1.26391
$775$	−1.26248	−0.0453497
$776$	−74.8687	−2.68763
$777$	−2.20953	−0.0792666
$778$	56.2645	2.01718
$779$	−2.81288	−0.100782
$780$	1.06656	0.0381890
$781$	−10.2396	−0.366400
$782$	−18.5644	−0.663863
$783$	−2.38052	−0.0850729
$784$	66.0438	2.35871
$785$	−19.8844	−0.709703
$786$	−1.34694	−0.0480437
$787$	11.9283	0.425199	0.212599	−	0.977139i	$-0.431807\pi$
$787$	11.9283	0.425199	0.212599	+	0.977139i	$0.431807\pi$
$788$	41.0785	1.46336
$789$	−2.47917	−0.0882609
$790$	2.16803	0.0771350
$791$	39.6162	1.40859
$792$	−22.8200	−0.810875
$793$	5.47401	0.194388
$794$	−50.1614	−1.78016
$795$	−0.365579	−0.0129658
$796$	44.1245	1.56395
$797$	1.48855	0.0527270	0.0263635	−	0.999652i	$-0.491607\pi$
$797$	1.48855	0.0527270	0.0263635	+	0.999652i	$0.491607\pi$
$798$	0.389263	0.0137798
$799$	6.76360	0.239279
$800$	−11.6569	−0.412135
$801$	7.32390	0.258777
$802$	−14.9001	−0.526140
$803$	12.1386	0.428364
$804$	2.22077	0.0783206
$805$	−25.9069	−0.913098
$806$	7.22184	0.254378
$807$	2.28790	0.0805380
$808$	−57.7839	−2.03283
$809$	−2.19226	−0.0770759	−0.0385379	−	0.999257i	$-0.512270\pi$
$809$	−2.19226	−0.0770759	−0.0385379	+	0.999257i	$0.512270\pi$
$810$	23.4131	0.822652
$811$	−6.60478	−0.231925	−0.115963	−	0.993254i	$-0.536995\pi$
$811$	−6.60478	−0.231925	−0.115963	+	0.993254i	$0.536995\pi$
$812$	−71.5496	−2.51090
$813$	−0.272758	−0.00956603
$814$	15.8502	0.555548
$815$	18.6544	0.653433
$816$	−1.02343	−0.0358273
$817$	−1.81004	−0.0633251
$818$	−18.2117	−0.636757
$819$	−23.8688	−0.834043
$820$	34.1118	1.19124
$821$	37.6957	1.31559	0.657795	−	0.753197i	$-0.271489\pi$
$821$	37.6957	1.31559	0.657795	+	0.753197i	$0.271489\pi$
$822$	−1.50794	−0.0525953
$823$	44.9216	1.56587	0.782934	−	0.622105i	$-0.213722\pi$
$823$	44.9216	1.56587	0.782934	+	0.622105i	$0.213722\pi$
$824$	−130.544	−4.54773
$825$	0.0998927	0.00347782
$826$	−134.414	−4.67685
$827$	−25.6234	−0.891013	−0.445506	−	0.895279i	$-0.646976\pi$
$827$	−25.6234	−0.891013	−0.445506	+	0.895279i	$0.646976\pi$
$828$	−103.606	−3.60057
$829$	−34.2176	−1.18843	−0.594213	−	0.804308i	$-0.702536\pi$
$829$	−34.2176	−1.18843	−0.594213	+	0.804308i	$0.702536\pi$
$830$	4.28849	0.148856
$831$	1.38456	0.0480297
$832$	22.0739	0.765275
$833$	6.44624	0.223349
$834$	−3.36642	−0.116569
$835$	−20.5030	−0.709534
$836$	−1.98353	−0.0686019
$837$	−0.755418	−0.0261111
$838$	−54.3500	−1.87749
$839$	8.40371	0.290128	0.145064	−	0.989422i	$-0.453661\pi$
$839$	8.40371	0.290128	0.145064	+	0.989422i	$0.453661\pi$
$840$	−2.79561	−0.0964576
$841$	−13.1722	−0.454215
$842$	−70.8537	−2.44178
$843$	0.592715	0.0204142
$844$	−54.4034	−1.87264
$845$	8.26073	0.284178
$846$	53.1397	1.82698
$847$	3.66691	0.125997
$848$	−37.4950	−1.28758
$849$	2.70896	0.0929713
$850$	−2.62765	−0.0901275
$851$	42.6169	1.46089
$852$	−5.01663	−0.171867
$853$	−36.3142	−1.24337	−0.621687	−	0.783266i	$-0.713552\pi$
$853$	−36.3142	−1.24337	−0.621687	+	0.783266i	$0.713552\pi$
$854$	−24.2280	−0.829065
$855$	1.20925	0.0413556
$856$	−135.624	−4.63553
$857$	29.6128	1.01155	0.505777	−	0.862664i	$-0.331206\pi$
$857$	29.6128	1.01155	0.505777	+	0.862664i	$0.331206\pi$
$858$	−0.571421	−0.0195080
$859$	57.1084	1.94851	0.974256	−	0.225444i	$-0.0723834\pi$
$859$	57.1084	1.94851	0.974256	+	0.225444i	$0.0723834\pi$
$860$	21.9503	0.748501
$861$	2.54766	0.0868241
$862$	30.0676	1.02411
$863$	13.0521	0.444299	0.222150	−	0.975013i	$-0.428693\pi$
$863$	13.0521	0.444299	0.222150	+	0.975013i	$0.428693\pi$
$864$	−6.97503	−0.237295
$865$	9.86607	0.335457
$866$	27.2813	0.927058
$867$	−0.0998927	−0.00339253
$868$	−22.7051	−0.770660
$869$	−0.825084	−0.0279891
$870$	1.04426	0.0354039
$871$	−9.86800	−0.334364
$872$	−130.647	−4.42427
$873$	−29.3314	−0.992716
$874$	−7.50800	−0.253962
$875$	−3.66691	−0.123964
$876$	5.94704	0.200932
$877$	−34.2321	−1.15593	−0.577967	−	0.816060i	$-0.696154\pi$
$877$	−34.2321	−1.15593	−0.577967	+	0.816060i	$0.696154\pi$
$878$	35.4049	1.19486
$879$	1.40900	0.0475244
$880$	10.2453	0.345369
$881$	−13.5861	−0.457727	−0.228864	−	0.973459i	$-0.573501\pi$
$881$	−13.5861	−0.457727	−0.228864	+	0.973459i	$0.573501\pi$
$882$	50.6463	1.70535
$883$	50.3001	1.69273	0.846367	−	0.532600i	$-0.178785\pi$
$883$	50.3001	1.69273	0.846367	+	0.532600i	$0.178785\pi$
$884$	10.6771	0.359109
$885$	1.39351	0.0468423
$886$	62.9471	2.11475
$887$	38.1009	1.27930	0.639651	−	0.768666i	$-0.279079\pi$
$887$	38.1009	1.27930	0.639651	+	0.768666i	$0.279079\pi$
$888$	4.59878	0.154325
$889$	56.7124	1.90207
$890$	−6.43628	−0.215745
$891$	−8.91029	−0.298506
$892$	−116.002	−3.88404
$893$	2.73540	0.0915366
$894$	−3.07466	−0.102832
$895$	1.69363	0.0566119
$896$	−12.2093	−0.407885
$897$	−1.53640	−0.0512989
$898$	91.6589	3.05870
$899$	5.02268	0.167516
$900$	−14.6646	−0.488821
$901$	−3.65972	−0.121923
$902$	−18.2757	−0.608515
$903$	1.63938	0.0545550
$904$	−82.4544	−2.74239
$905$	−6.94664	−0.230914
$906$	2.09474	0.0695930
$907$	−48.7768	−1.61961	−0.809803	−	0.586701i	$-0.800426\pi$
$907$	−48.7768	−1.61961	−0.809803	+	0.586701i	$0.800426\pi$
$908$	−83.0056	−2.75464
$909$	−22.6380	−0.750856
$910$	20.9760	0.695348
$911$	−32.8674	−1.08894	−0.544472	−	0.838779i	$-0.683270\pi$
$911$	−32.8674	−1.08894	−0.544472	+	0.838779i	$0.683270\pi$
$912$	−0.413906	−0.0137058
$913$	−1.63206	−0.0540134
$914$	−4.16337	−0.137712
$915$	0.251179	0.00830373
$916$	73.5564	2.43037
$917$	−18.8169	−0.621389
$918$	−1.57228	−0.0518928
$919$	9.97071	0.328903	0.164452	−	0.986385i	$-0.447415\pi$
$919$	9.97071	0.328903	0.164452	+	0.986385i	$0.447415\pi$
$920$	53.9209	1.77772
$921$	0.780273	0.0257109
$922$	−88.4277	−2.91221
$923$	22.2914	0.733730
$924$	1.79652	0.0591010
$925$	6.03208	0.198333
$926$	−68.7500	−2.25927
$927$	−51.1435	−1.67977
$928$	46.3761	1.52237
$929$	3.85393	0.126443	0.0632217	−	0.998000i	$-0.479862\pi$
$929$	3.85393	0.126443	0.0632217	+	0.998000i	$0.479862\pi$
$930$	0.331380	0.0108664
$931$	2.60705	0.0854426
$932$	84.8136	2.77816
$933$	1.99543	0.0653274
$934$	74.3507	2.43283
$935$	1.00000	0.0327035
$936$	49.6789	1.62381
$937$	−13.7383	−0.448810	−0.224405	−	0.974496i	$-0.572044\pi$
$937$	−13.7383	−0.448810	−0.224405	+	0.974496i	$0.572044\pi$
$938$	43.6758	1.42607
$939$	−3.08250	−0.100594
$940$	−33.1722	−1.08196
$941$	−9.41542	−0.306934	−0.153467	−	0.988154i	$-0.549044\pi$
$941$	−9.41542	−0.306934	−0.153467	+	0.988154i	$0.549044\pi$
$942$	5.21930	0.170054
$943$	−49.1386	−1.60017
$944$	142.923	4.65174
$945$	−2.19413	−0.0713751
$946$	−11.7601	−0.382354
$947$	44.7856	1.45534	0.727669	−	0.685929i	$-0.240604\pi$
$947$	44.7856	1.45534	0.727669	+	0.685929i	$0.240604\pi$
$948$	−0.404230	−0.0131288
$949$	−26.4257	−0.857813
$950$	−1.06270	−0.0344785
$951$	−1.74641	−0.0566312
$952$	−27.9861	−0.907035
$953$	28.0553	0.908801	0.454400	−	0.890798i	$-0.349854\pi$
$953$	28.0553	0.908801	0.454400	+	0.890798i	$0.349854\pi$
$954$	−28.7534	−0.930926
$955$	3.87901	0.125522
$956$	109.733	3.54901
$957$	−0.397414	−0.0128466
$958$	53.3659	1.72417
$959$	−21.0660	−0.680258
$960$	1.01288	0.0326905
$961$	−29.4061	−0.948585
$962$	−34.5056	−1.11250
$963$	−53.1336	−1.71221
$964$	4.55785	0.146798
$965$	20.3975	0.656620
$966$	6.80011	0.218790
$967$	−46.4617	−1.49411	−0.747054	−	0.664763i	$-0.768533\pi$
$967$	−46.4617	−1.49411	−0.747054	+	0.664763i	$0.768533\pi$
$968$	−7.63206	−0.245304
$969$	−0.0403995	−0.00129782
$970$	25.7766	0.827635
$971$	−2.57361	−0.0825912	−0.0412956	−	0.999147i	$-0.513149\pi$
$971$	−2.57361	−0.0825912	−0.0412956	+	0.999147i	$0.513149\pi$
$972$	−13.1694	−0.422408
$973$	−47.0292	−1.50769
$974$	44.7743	1.43466
$975$	−0.217465	−0.00696445
$976$	25.7618	0.824614
$977$	28.4191	0.909208	0.454604	−	0.890694i	$-0.349781\pi$
$977$	28.4191	0.909208	0.454604	+	0.890694i	$0.349781\pi$
$978$	−4.89644	−0.156571
$979$	2.44945	0.0782847
$980$	−31.6158	−1.00993
$981$	−51.1838	−1.63417
$982$	51.0999	1.63066
$983$	35.0502	1.11793	0.558963	−	0.829192i	$-0.311199\pi$
$983$	35.0502	1.11793	0.558963	+	0.829192i	$0.311199\pi$
$984$	−5.30253	−0.169039
$985$	−8.37564	−0.266870
$986$	10.4539	0.332919
$987$	−2.47749	−0.0788594
$988$	4.31813	0.137378
$989$	−31.6198	−1.00545
$990$	7.85672	0.249703
$991$	18.4415	0.585815	0.292907	−	0.956141i	$-0.405377\pi$
$991$	18.4415	0.585815	0.292907	+	0.956141i	$0.405377\pi$
$992$	14.7167	0.467255
$993$	0.927751	0.0294413
$994$	−98.6617	−3.12936
$995$	−8.99670	−0.285215
$996$	−0.799590	−0.0253360
$997$	49.2668	1.56029	0.780147	−	0.625596i	$-0.215144\pi$
$997$	49.2668	1.56029	0.780147	+	0.625596i	$0.215144\pi$
$998$	84.4653	2.67370
$999$	3.60935	0.114195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.a.h.1.1	✓	6
3.2	odd	2		8415.2.a.bj.1.6		6
5.4	even	2		4675.2.a.bh.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.a.h.1.1	✓	6	1.1	even	1	trivial
4675.2.a.bh.1.6		6	5.4	even	2
8415.2.a.bj.1.6		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62765 q^{2} -0.0998927 q^{3} +4.90452 q^{4} -1.00000 q^{5} +0.262483 q^{6} +3.66691 q^{7} -7.63206 q^{8} -2.99002 q^{9} +O(q^{10})\)	\(q-2.62765 q^{2} -0.0998927 q^{3} +4.90452 q^{4} -1.00000 q^{5} +0.262483 q^{6} +3.66691 q^{7} -7.63206 q^{8} -2.99002 q^{9} +2.62765 q^{10} -1.00000 q^{11} -0.489926 q^{12} +2.17699 q^{13} -9.63535 q^{14} +0.0998927 q^{15} +10.2453 q^{16} +1.00000 q^{17} +7.85672 q^{18} +0.404429 q^{19} -4.90452 q^{20} -0.366298 q^{21} +2.62765 q^{22} +7.06504 q^{23} +0.762387 q^{24} +1.00000 q^{25} -5.72035 q^{26} +0.598359 q^{27} +17.9845 q^{28} -3.97841 q^{29} -0.262483 q^{30} -1.26248 q^{31} -11.6569 q^{32} +0.0998927 q^{33} -2.62765 q^{34} -3.66691 q^{35} -14.6646 q^{36} +6.03208 q^{37} -1.06270 q^{38} -0.217465 q^{39} +7.63206 q^{40} -6.95517 q^{41} +0.962500 q^{42} -4.47553 q^{43} -4.90452 q^{44} +2.99002 q^{45} -18.5644 q^{46} +6.76360 q^{47} -1.02343 q^{48} +6.44624 q^{49} -2.62765 q^{50} -0.0998927 q^{51} +10.6771 q^{52} -3.65972 q^{53} -1.57228 q^{54} +1.00000 q^{55} -27.9861 q^{56} -0.0403995 q^{57} +10.4539 q^{58} +13.9501 q^{59} +0.489926 q^{60} +2.51449 q^{61} +3.31736 q^{62} -10.9641 q^{63} +10.1397 q^{64} -2.17699 q^{65} -0.262483 q^{66} -4.53287 q^{67} +4.90452 q^{68} -0.705746 q^{69} +9.63535 q^{70} +10.2396 q^{71} +22.8200 q^{72} -12.1386 q^{73} -15.8502 q^{74} -0.0998927 q^{75} +1.98353 q^{76} -3.66691 q^{77} +0.571421 q^{78} +0.825084 q^{79} -10.2453 q^{80} +8.91029 q^{81} +18.2757 q^{82} +1.63206 q^{83} -1.79652 q^{84} -1.00000 q^{85} +11.7601 q^{86} +0.397414 q^{87} +7.63206 q^{88} -2.44945 q^{89} -7.85672 q^{90} +7.98282 q^{91} +34.6507 q^{92} +0.126113 q^{93} -17.7723 q^{94} -0.404429 q^{95} +1.16444 q^{96} +9.80975 q^{97} -16.9384 q^{98} +2.99002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{9} + 2 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{13} + 8 q^{14} - 4 q^{15} + 4 q^{16} + 6 q^{17} - 8 q^{18} - 2 q^{19} - 8 q^{20} + 2 q^{22} + 14 q^{23} + 10 q^{24} + 6 q^{25} + 22 q^{27} + 22 q^{28} - 4 q^{29} + 10 q^{30} + 4 q^{31} - 24 q^{32} - 4 q^{33} - 2 q^{34} - 6 q^{35} + 10 q^{36} + 18 q^{37} - 4 q^{38} + 30 q^{39} + 6 q^{40} + 12 q^{41} + 14 q^{42} - 10 q^{43} - 8 q^{44} - 12 q^{45} - 24 q^{46} + 20 q^{47} - 6 q^{48} + 54 q^{49} - 2 q^{50} + 4 q^{51} + 44 q^{52} + 10 q^{53} - 60 q^{54} + 6 q^{55} - 14 q^{56} + 2 q^{57} + 52 q^{58} + 14 q^{59} - 10 q^{60} + 2 q^{61} - 16 q^{62} - 6 q^{63} - 14 q^{64} - 10 q^{65} + 10 q^{66} - 34 q^{67} + 8 q^{68} - 28 q^{69} - 8 q^{70} - 18 q^{71} + 16 q^{72} + 10 q^{73} - 30 q^{74} + 4 q^{75} + 8 q^{76} - 6 q^{77} - 6 q^{78} + 8 q^{79} - 4 q^{80} + 26 q^{81} + 20 q^{82} - 30 q^{83} - 60 q^{84} - 6 q^{85} - 6 q^{86} - 24 q^{87} + 6 q^{88} - 30 q^{89} + 8 q^{90} + 30 q^{91} + 36 q^{92} + 10 q^{93} - 26 q^{94} + 2 q^{95} + 14 q^{96} + 58 q^{97} - 42 q^{98} - 12 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^9 + 2 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^13 + 8 * q^14 - 4 * q^15 + 4 * q^16 + 6 * q^17 - 8 * q^18 - 2 * q^19 - 8 * q^20 + 2 * q^22 + 14 * q^23 + 10 * q^24 + 6 * q^25 + 22 * q^27 + 22 * q^28 - 4 * q^29 + 10 * q^30 + 4 * q^31 - 24 * q^32 - 4 * q^33 - 2 * q^34 - 6 * q^35 + 10 * q^36 + 18 * q^37 - 4 * q^38 + 30 * q^39 + 6 * q^40 + 12 * q^41 + 14 * q^42 - 10 * q^43 - 8 * q^44 - 12 * q^45 - 24 * q^46 + 20 * q^47 - 6 * q^48 + 54 * q^49 - 2 * q^50 + 4 * q^51 + 44 * q^52 + 10 * q^53 - 60 * q^54 + 6 * q^55 - 14 * q^56 + 2 * q^57 + 52 * q^58 + 14 * q^59 - 10 * q^60 + 2 * q^61 - 16 * q^62 - 6 * q^63 - 14 * q^64 - 10 * q^65 + 10 * q^66 - 34 * q^67 + 8 * q^68 - 28 * q^69 - 8 * q^70 - 18 * q^71 + 16 * q^72 + 10 * q^73 - 30 * q^74 + 4 * q^75 + 8 * q^76 - 6 * q^77 - 6 * q^78 + 8 * q^79 - 4 * q^80 + 26 * q^81 + 20 * q^82 - 30 * q^83 - 60 * q^84 - 6 * q^85 - 6 * q^86 - 24 * q^87 + 6 * q^88 - 30 * q^89 + 8 * q^90 + 30 * q^91 + 36 * q^92 + 10 * q^93 - 26 * q^94 + 2 * q^95 + 14 * q^96 + 58 * q^97 - 42 * q^98 - 12 * q^99

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