LMFDB - Embedded newform 4031.2.a.c.1.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.431567 q^{2} +0.116041 q^{3} -1.81375 q^{4} -0.280770 q^{5} +0.0500795 q^{6} +1.12936 q^{7} -1.64589 q^{8} -2.98653 q^{9} +O(q^{10})$	\(q+0.431567 q^{2} +0.116041 q^{3} -1.81375 q^{4} -0.280770 q^{5} +0.0500795 q^{6} +1.12936 q^{7} -1.64589 q^{8} -2.98653 q^{9} -0.121171 q^{10} +2.54903 q^{11} -0.210470 q^{12} +0.311426 q^{13} +0.487394 q^{14} -0.0325809 q^{15} +2.91719 q^{16} -3.83202 q^{17} -1.28889 q^{18} +1.16861 q^{19} +0.509246 q^{20} +0.131052 q^{21} +1.10007 q^{22} +2.97492 q^{23} -0.190991 q^{24} -4.92117 q^{25} +0.134401 q^{26} -0.694684 q^{27} -2.04838 q^{28} -1.00000 q^{29} -0.0140608 q^{30} +9.18623 q^{31} +4.55074 q^{32} +0.295792 q^{33} -1.65377 q^{34} -0.317091 q^{35} +5.41683 q^{36} +9.69082 q^{37} +0.504332 q^{38} +0.0361382 q^{39} +0.462115 q^{40} +11.6305 q^{41} +0.0565578 q^{42} -8.94047 q^{43} -4.62330 q^{44} +0.838529 q^{45} +1.28388 q^{46} -12.7996 q^{47} +0.338514 q^{48} -5.72454 q^{49} -2.12381 q^{50} -0.444672 q^{51} -0.564848 q^{52} -4.10544 q^{53} -0.299803 q^{54} -0.715689 q^{55} -1.85880 q^{56} +0.135607 q^{57} -0.431567 q^{58} +2.96172 q^{59} +0.0590935 q^{60} -14.6369 q^{61} +3.96447 q^{62} -3.37288 q^{63} -3.87044 q^{64} -0.0874389 q^{65} +0.127654 q^{66} -7.57315 q^{67} +6.95032 q^{68} +0.345213 q^{69} -0.136846 q^{70} -13.0047 q^{71} +4.91550 q^{72} -1.93842 q^{73} +4.18223 q^{74} -0.571058 q^{75} -2.11956 q^{76} +2.87877 q^{77} +0.0155960 q^{78} -3.60852 q^{79} -0.819059 q^{80} +8.87899 q^{81} +5.01934 q^{82} -5.22878 q^{83} -0.237696 q^{84} +1.07591 q^{85} -3.85841 q^{86} -0.116041 q^{87} -4.19541 q^{88} -8.11999 q^{89} +0.361881 q^{90} +0.351712 q^{91} -5.39576 q^{92} +1.06598 q^{93} -5.52389 q^{94} -0.328110 q^{95} +0.528073 q^{96} +6.72429 q^{97} -2.47052 q^{98} -7.61275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	0.431567	0.305164	0.152582	−	0.988291i	$-0.451241\pi$
$2$	0.431567	0.305164	0.152582	+	0.988291i	$0.451241\pi$
$3$	0.116041	0.0669964	0.0334982	−	0.999439i	$-0.489335\pi$
$3$	0.116041	0.0669964	0.0334982	+	0.999439i	$0.489335\pi$
$4$	−1.81375	−0.906875
$5$	−0.280770	−0.125564	−0.0627820	−	0.998027i	$-0.519997\pi$
$5$	−0.280770	−0.125564	−0.0627820	+	0.998027i	$0.519997\pi$
$6$	0.0500795	0.0204449
$7$	1.12936	0.426858	0.213429	−	0.976959i	$-0.431537\pi$
$7$	1.12936	0.426858	0.213429	+	0.976959i	$0.431537\pi$
$8$	−1.64589	−0.581909
$9$	−2.98653	−0.995511
$10$	−0.121171	−0.0383176
$11$	2.54903	0.768560	0.384280	−	0.923217i	$-0.374450\pi$
$11$	2.54903	0.768560	0.384280	+	0.923217i	$0.374450\pi$
$12$	−0.210470	−0.0607574
$13$	0.311426	0.0863739	0.0431870	−	0.999067i	$-0.486249\pi$
$13$	0.311426	0.0863739	0.0431870	+	0.999067i	$0.486249\pi$
$14$	0.487394	0.130262
$15$	−0.0325809	−0.00841234
$16$	2.91719	0.729298
$17$	−3.83202	−0.929401	−0.464700	−	0.885468i	$-0.653838\pi$
$17$	−3.83202	−0.929401	−0.464700	+	0.885468i	$0.653838\pi$
$18$	−1.28889	−0.303794
$19$	1.16861	0.268097	0.134049	−	0.990975i	$-0.457202\pi$
$19$	1.16861	0.268097	0.134049	+	0.990975i	$0.457202\pi$
$20$	0.509246	0.113871
$21$	0.131052	0.0285980
$22$	1.10007	0.234537
$23$	2.97492	0.620313	0.310157	−	0.950685i	$-0.399618\pi$
$23$	2.97492	0.620313	0.310157	+	0.950685i	$0.399618\pi$
$24$	−0.190991	−0.0389858
$25$	−4.92117	−0.984234
$26$	0.134401	0.0263582
$27$	−0.694684	−0.133692
$28$	−2.04838	−0.387107
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.0140608	−0.00256714
$31$	9.18623	1.64990	0.824948	−	0.565209i	$-0.191204\pi$
$31$	9.18623	1.64990	0.824948	+	0.565209i	$0.191204\pi$
$32$	4.55074	0.804464
$33$	0.295792	0.0514908
$34$	−1.65377	−0.283619
$35$	−0.317091	−0.0535981
$36$	5.41683	0.902805
$37$	9.69082	1.59316	0.796581	−	0.604532i	$-0.206640\pi$
$37$	9.69082	1.59316	0.796581	+	0.604532i	$0.206640\pi$
$38$	0.504332	0.0818135
$39$	0.0361382	0.00578674
$40$	0.462115	0.0730668
$41$	11.6305	1.81638	0.908191	−	0.418555i	$-0.137463\pi$
$41$	11.6305	1.81638	0.908191	+	0.418555i	$0.137463\pi$
$42$	0.0565578	0.00872706
$43$	−8.94047	−1.36341	−0.681705	−	0.731628i	$-0.738761\pi$
$43$	−8.94047	−1.36341	−0.681705	+	0.731628i	$0.738761\pi$
$44$	−4.62330	−0.696988
$45$	0.838529	0.125000
$46$	1.28388	0.189297
$47$	−12.7996	−1.86702	−0.933508	−	0.358557i	$-0.883269\pi$
$47$	−12.7996	−1.86702	−0.933508	+	0.358557i	$0.883269\pi$
$48$	0.338514	0.0488603
$49$	−5.72454	−0.817792
$50$	−2.12381	−0.300352
$51$	−0.444672	−0.0622665
$52$	−0.564848	−0.0783304
$53$	−4.10544	−0.563926	−0.281963	−	0.959425i	$-0.590986\pi$
$53$	−4.10544	−0.563926	−0.281963	+	0.959425i	$0.590986\pi$
$54$	−0.299803	−0.0407980
$55$	−0.715689	−0.0965035
$56$	−1.85880	−0.248393
$57$	0.135607	0.0179615
$58$	−0.431567	−0.0566675
$59$	2.96172	0.385584	0.192792	−	0.981240i	$-0.438246\pi$
$59$	2.96172	0.385584	0.192792	+	0.981240i	$0.438246\pi$
$60$	0.0590935	0.00762894
$61$	−14.6369	−1.87406	−0.937031	−	0.349246i	$-0.886438\pi$
$61$	−14.6369	−1.87406	−0.937031	+	0.349246i	$0.886438\pi$
$62$	3.96447	0.503488
$63$	−3.37288	−0.424942
$64$	−3.87044	−0.483805
$65$	−0.0874389	−0.0108455
$66$	0.127654	0.0157131
$67$	−7.57315	−0.925207	−0.462603	−	0.886565i	$-0.653085\pi$
$67$	−7.57315	−0.925207	−0.462603	+	0.886565i	$0.653085\pi$
$68$	6.95032	0.842850
$69$	0.345213	0.0415588
$70$	−0.136846	−0.0163562
$71$	−13.0047	−1.54338	−0.771690	−	0.635999i	$-0.780588\pi$
$71$	−13.0047	−1.54338	−0.771690	+	0.635999i	$0.780588\pi$
$72$	4.91550	0.579297
$73$	−1.93842	−0.226875	−0.113437	−	0.993545i	$-0.536186\pi$
$73$	−1.93842	−0.226875	−0.113437	+	0.993545i	$0.536186\pi$
$74$	4.18223	0.486175
$75$	−0.571058	−0.0659401
$76$	−2.11956	−0.243131
$77$	2.87877	0.328066
$78$	0.0155960	0.00176590
$79$	−3.60852	−0.405990	−0.202995	−	0.979180i	$-0.565067\pi$
$79$	−3.60852	−0.405990	−0.202995	+	0.979180i	$0.565067\pi$
$80$	−0.819059	−0.0915736
$81$	8.87899	0.986555
$82$	5.01934	0.554294
$83$	−5.22878	−0.573933	−0.286966	−	0.957941i	$-0.592647\pi$
$83$	−5.22878	−0.573933	−0.286966	+	0.957941i	$0.592647\pi$
$84$	−0.237696	−0.0259348
$85$	1.07591	0.116699
$86$	−3.85841	−0.416063
$87$	−0.116041	−0.0124409
$88$	−4.19541	−0.447232
$89$	−8.11999	−0.860718	−0.430359	−	0.902658i	$-0.641613\pi$
$89$	−8.11999	−0.860718	−0.430359	+	0.902658i	$0.641613\pi$
$90$	0.361881	0.0381456
$91$	0.351712	0.0368694
$92$	−5.39576	−0.562547
$93$	1.06598	0.110537
$94$	−5.52389	−0.569745
$95$	−0.328110	−0.0336634
$96$	0.528073	0.0538962
$97$	6.72429	0.682749	0.341374	−	0.939927i	$-0.389108\pi$
$97$	6.72429	0.682749	0.341374	+	0.939927i	$0.389108\pi$
$98$	−2.47052	−0.249560
$99$	−7.61275	−0.765111
$100$	8.92577	0.892577
$101$	1.97020	0.196042	0.0980211	−	0.995184i	$-0.468749\pi$
$101$	1.97020	0.196042	0.0980211	+	0.995184i	$0.468749\pi$
$102$	−0.191905	−0.0190015
$103$	2.22516	0.219252	0.109626	−	0.993973i	$-0.465035\pi$
$103$	2.22516	0.219252	0.109626	+	0.993973i	$0.465035\pi$
$104$	−0.512571	−0.0502617
$105$	−0.0367956	−0.00359088
$106$	−1.77177	−0.172090
$107$	18.0345	1.74346	0.871728	−	0.489989i	$-0.162999\pi$
$107$	18.0345	1.74346	0.871728	+	0.489989i	$0.162999\pi$
$108$	1.25998	0.121242
$109$	9.79190	0.937894	0.468947	−	0.883226i	$-0.344634\pi$
$109$	9.79190	0.937894	0.468947	+	0.883226i	$0.344634\pi$
$110$	−0.308868	−0.0294494
$111$	1.12453	0.106736
$112$	3.29456	0.311307
$113$	−11.9240	−1.12171	−0.560857	−	0.827913i	$-0.689528\pi$
$113$	−11.9240	−1.12171	−0.560857	+	0.827913i	$0.689528\pi$
$114$	0.0585233	0.00548121
$115$	−0.835267	−0.0778891
$116$	1.81375	0.168402
$117$	−0.930083	−0.0859862
$118$	1.27818	0.117666
$119$	−4.32773	−0.396723
$120$	0.0536244	0.00489522
$121$	−4.50247	−0.409315
$122$	−6.31679	−0.571896
$123$	1.34962	0.121691
$124$	−16.6615	−1.49625
$125$	2.78556	0.249148
$126$	−1.45562	−0.129677
$127$	8.25496	0.732510	0.366255	−	0.930515i	$-0.380640\pi$
$127$	8.25496	0.732510	0.366255	+	0.930515i	$0.380640\pi$
$128$	−10.7718	−0.952104
$129$	−1.03746	−0.0913435
$130$	−0.0377357	−0.00330964
$131$	1.09618	0.0957737	0.0478869	−	0.998853i	$-0.484751\pi$
$131$	1.09618	0.0957737	0.0478869	+	0.998853i	$0.484751\pi$
$132$	−0.536493	−0.0466957
$133$	1.31978	0.114440
$134$	−3.26832	−0.282339
$135$	0.195046	0.0167869
$136$	6.30707	0.540827
$137$	2.81083	0.240146	0.120073	−	0.992765i	$-0.461687\pi$
$137$	2.81083	0.240146	0.120073	+	0.992765i	$0.461687\pi$
$138$	0.148982	0.0126822
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	0.575123	0.0486068
$141$	−1.48528	−0.125083
$142$	−5.61241	−0.470983
$143$	0.793832	0.0663835
$144$	−8.71229	−0.726024
$145$	0.280770	0.0233167
$146$	−0.836556	−0.0692339
$147$	−0.664283	−0.0547891
$148$	−17.5767	−1.44480
$149$	4.46322	0.365641	0.182821	−	0.983146i	$-0.441477\pi$
$149$	4.46322	0.365641	0.182821	+	0.983146i	$0.441477\pi$
$150$	−0.246450	−0.0201225
$151$	−11.0675	−0.900660	−0.450330	−	0.892862i	$-0.648694\pi$
$151$	−11.0675	−0.900660	−0.450330	+	0.892862i	$0.648694\pi$
$152$	−1.92340	−0.156008
$153$	11.4445	0.925229
$154$	1.24238	0.100114
$155$	−2.57922	−0.207168
$156$	−0.0655456	−0.00524785
$157$	−21.1341	−1.68668	−0.843342	−	0.537377i	$-0.819415\pi$
$157$	−21.1341	−1.68668	−0.843342	+	0.537377i	$0.819415\pi$
$158$	−1.55731	−0.123893
$159$	−0.476400	−0.0377810
$160$	−1.27771	−0.101012
$161$	3.35976	0.264786
$162$	3.83188	0.301061
$163$	−9.12904	−0.715042	−0.357521	−	0.933905i	$-0.616378\pi$
$163$	−9.12904	−0.715042	−0.357521	+	0.933905i	$0.616378\pi$
$164$	−21.0949	−1.64723
$165$	−0.0830494	−0.00646539
$166$	−2.25657	−0.175143
$167$	9.27906	0.718036	0.359018	−	0.933331i	$-0.383112\pi$
$167$	9.27906	0.718036	0.359018	+	0.933331i	$0.383112\pi$
$168$	−0.215697	−0.0166414
$169$	−12.9030	−0.992540
$170$	0.464329	0.0356124
$171$	−3.49009	−0.266894
$172$	16.2158	1.23644
$173$	−22.4225	−1.70475	−0.852374	−	0.522932i	$-0.824838\pi$
$173$	−22.4225	−1.70475	−0.852374	+	0.522932i	$0.824838\pi$
$174$	−0.0500795	−0.00379652
$175$	−5.55778	−0.420128
$176$	7.43600	0.560509
$177$	0.343682	0.0258327
$178$	−3.50432	−0.262660
$179$	−17.7203	−1.32447	−0.662237	−	0.749294i	$-0.730393\pi$
$179$	−17.7203	−1.32447	−0.662237	+	0.749294i	$0.730393\pi$
$180$	−1.52088	−0.113360
$181$	−15.8944	−1.18142	−0.590712	−	0.806882i	$-0.701153\pi$
$181$	−15.8944	−1.18142	−0.590712	+	0.806882i	$0.701153\pi$
$182$	0.151787	0.0112512
$183$	−1.69848	−0.125555
$184$	−4.89638	−0.360966
$185$	−2.72089	−0.200044
$186$	0.460042	0.0337319
$187$	−9.76791	−0.714300
$188$	23.2153	1.69315
$189$	−0.784550	−0.0570676
$190$	−0.141601	−0.0102728
$191$	−11.4817	−0.830783	−0.415392	−	0.909643i	$-0.636355\pi$
$191$	−11.4817	−0.830783	−0.415392	+	0.909643i	$0.636355\pi$
$192$	−0.449130	−0.0324132
$193$	−4.94728	−0.356113	−0.178056	−	0.984020i	$-0.556981\pi$
$193$	−4.94728	−0.356113	−0.178056	+	0.984020i	$0.556981\pi$
$194$	2.90198	0.208350
$195$	−0.0101465	−0.000726607 0
$196$	10.3829	0.741635
$197$	25.4620	1.81409	0.907045	−	0.421033i	$-0.138332\pi$
$197$	25.4620	1.81409	0.907045	+	0.421033i	$0.138332\pi$
$198$	−3.28541	−0.233484
$199$	−26.3113	−1.86516	−0.932579	−	0.360967i	$-0.882447\pi$
$199$	−26.3113	−1.86516	−0.932579	+	0.360967i	$0.882447\pi$
$200$	8.09969	0.572734
$201$	−0.878797	−0.0619855
$202$	0.850272	0.0598249
$203$	−1.12936	−0.0792656
$204$	0.806524	0.0564679
$205$	−3.26550	−0.228072
$206$	0.960304	0.0669076
$207$	−8.88470	−0.617529
$208$	0.908488	0.0629923
$209$	2.97881	0.206049
$210$	−0.0158797	−0.00109581
$211$	−16.9608	−1.16763	−0.583815	−	0.811887i	$-0.698441\pi$
$211$	−16.9608	−1.16763	−0.583815	+	0.811887i	$0.698441\pi$
$212$	7.44625	0.511410
$213$	−1.50909	−0.103401
$214$	7.78307	0.532040
$215$	2.51021	0.171195
$216$	1.14337	0.0777966
$217$	10.3746	0.704272
$218$	4.22585	0.286211
$219$	−0.224936	−0.0151998
$220$	1.29808	0.0875167
$221$	−1.19339	−0.0802760
$222$	0.485311	0.0325720
$223$	−7.78604	−0.521392	−0.260696	−	0.965421i	$-0.583952\pi$
$223$	−7.78604	−0.521392	−0.260696	+	0.965421i	$0.583952\pi$
$224$	5.13942	0.343392
$225$	14.6972	0.979816
$226$	−5.14599	−0.342306
$227$	−19.5733	−1.29913	−0.649564	−	0.760307i	$-0.725048\pi$
$227$	−19.5733	−1.29913	−0.649564	+	0.760307i	$0.725048\pi$
$228$	−0.245957	−0.0162889
$229$	−1.30739	−0.0863951	−0.0431975	−	0.999067i	$-0.513754\pi$
$229$	−1.30739	−0.0863951	−0.0431975	+	0.999067i	$0.513754\pi$
$230$	−0.360473	−0.0237689
$231$	0.334056	0.0219793
$232$	1.64589	0.108058
$233$	24.0625	1.57639	0.788193	−	0.615428i	$-0.211017\pi$
$233$	24.0625	1.57639	0.788193	+	0.615428i	$0.211017\pi$
$234$	−0.401393	−0.0262399
$235$	3.59375	0.234430
$236$	−5.37183	−0.349676
$237$	−0.418736	−0.0271999
$238$	−1.86770	−0.121065
$239$	6.86902	0.444320	0.222160	−	0.975010i	$-0.428689\pi$
$239$	6.86902	0.444320	0.222160	+	0.975010i	$0.428689\pi$
$240$	−0.0950446	−0.00613510
$241$	23.8266	1.53481	0.767404	−	0.641164i	$-0.221548\pi$
$241$	23.8266	1.53481	0.767404	+	0.641164i	$0.221548\pi$
$242$	−1.94311	−0.124908
$243$	3.11438	0.199788
$244$	26.5477	1.69954
$245$	1.60728	0.102685
$246$	0.582451	0.0371357
$247$	0.363935	0.0231566
$248$	−15.1195	−0.960089
$249$	−0.606754	−0.0384514
$250$	1.20216	0.0760310
$251$	−7.50291	−0.473580	−0.236790	−	0.971561i	$-0.576095\pi$
$251$	−7.50291	−0.473580	−0.236790	+	0.971561i	$0.576095\pi$
$252$	6.11756	0.385370
$253$	7.58314	0.476748
$254$	3.56257	0.223535
$255$	0.124850	0.00781844
$256$	3.09212	0.193257
$257$	0.825996	0.0515242	0.0257621	−	0.999668i	$-0.491799\pi$
$257$	0.825996	0.0515242	0.0257621	+	0.999668i	$0.491799\pi$
$258$	−0.447734	−0.0278747
$259$	10.9444	0.680054
$260$	0.158592	0.00983548
$261$	2.98653	0.184862
$262$	0.473075	0.0292267
$263$	−28.1850	−1.73796	−0.868979	−	0.494848i	$-0.835224\pi$
$263$	−28.1850	−1.73796	−0.868979	+	0.494848i	$0.835224\pi$
$264$	−0.486840	−0.0299629
$265$	1.15268	0.0708088
$266$	0.569573	0.0349228
$267$	−0.942253	−0.0576650
$268$	13.7358	0.839047
$269$	−2.59357	−0.158133	−0.0790664	−	0.996869i	$-0.525194\pi$
$269$	−2.59357	−0.158133	−0.0790664	+	0.996869i	$0.525194\pi$
$270$	0.0841755	0.00512276
$271$	−5.62276	−0.341558	−0.170779	−	0.985309i	$-0.554628\pi$
$271$	−5.62276	−0.341558	−0.170779	+	0.985309i	$0.554628\pi$
$272$	−11.1787	−0.677810
$273$	0.0408131	0.00247012
$274$	1.21306	0.0732838
$275$	−12.5442	−0.756443
$276$	−0.626130	−0.0376886
$277$	27.4068	1.64672	0.823358	−	0.567522i	$-0.192098\pi$
$277$	27.4068	1.64672	0.823358	+	0.567522i	$0.192098\pi$
$278$	−0.431567	−0.0258836
$279$	−27.4350	−1.64249
$280$	0.521895	0.0311892
$281$	−18.6189	−1.11071	−0.555355	−	0.831614i	$-0.687418\pi$
$281$	−18.6189	−1.11071	−0.555355	+	0.831614i	$0.687418\pi$
$282$	−0.640998	−0.0381709
$283$	−15.7528	−0.936405	−0.468202	−	0.883621i	$-0.655098\pi$
$283$	−15.7528	−0.936405	−0.468202	+	0.883621i	$0.655098\pi$
$284$	23.5874	1.39965
$285$	−0.0380743	−0.00225532
$286$	0.342591	0.0202578
$287$	13.1351	0.775338
$288$	−13.5909	−0.800853
$289$	−2.31564	−0.136214
$290$	0.121171	0.00711540
$291$	0.780295	0.0457417
$292$	3.51581	0.205747
$293$	3.48485	0.203587	0.101794	−	0.994806i	$-0.467542\pi$
$293$	3.48485	0.203587	0.101794	+	0.994806i	$0.467542\pi$
$294$	−0.286682	−0.0167196
$295$	−0.831563	−0.0484154
$296$	−15.9500	−0.927075
$297$	−1.77077	−0.102750
$298$	1.92618	0.111580
$299$	0.926466	0.0535789
$300$	1.03576	0.0597995
$301$	−10.0970	−0.581983
$302$	−4.77636	−0.274849
$303$	0.228624	0.0131341
$304$	3.40905	0.195523
$305$	4.10960	0.235315
$306$	4.93904	0.282346
$307$	−19.0494	−1.08721	−0.543603	−	0.839342i	$-0.682940\pi$
$307$	−19.0494	−1.08721	−0.543603	+	0.839342i	$0.682940\pi$
$308$	−5.22137	−0.297515
$309$	0.258210	0.0146891
$310$	−1.11310	−0.0632200
$311$	10.4189	0.590801	0.295400	−	0.955374i	$-0.404547\pi$
$311$	10.4189	0.590801	0.295400	+	0.955374i	$0.404547\pi$
$312$	−0.0594794	−0.00336736
$313$	24.4100	1.37974	0.689868	−	0.723935i	$-0.257669\pi$
$313$	24.4100	1.37974	0.689868	+	0.723935i	$0.257669\pi$
$314$	−9.12077	−0.514715
$315$	0.947002	0.0533575
$316$	6.54495	0.368182
$317$	−20.8736	−1.17238	−0.586190	−	0.810173i	$-0.699373\pi$
$317$	−20.8736	−1.17238	−0.586190	+	0.810173i	$0.699373\pi$
$318$	−0.205598	−0.0115294
$319$	−2.54903	−0.142718
$320$	1.08670	0.0607485
$321$	2.09274	0.116805
$322$	1.44996	0.0808030
$323$	−4.47813	−0.249170
$324$	−16.1043	−0.894682
$325$	−1.53258	−0.0850121
$326$	−3.93979	−0.218205
$327$	1.13626	0.0628355
$328$	−19.1425	−1.05697
$329$	−14.4554	−0.796951
$330$	−0.0358414	−0.00197300
$331$	30.3297	1.66707	0.833535	−	0.552466i	$-0.186313\pi$
$331$	30.3297	1.66707	0.833535	+	0.552466i	$0.186313\pi$
$332$	9.48370	0.520486
$333$	−28.9420	−1.58601
$334$	4.00453	0.219118
$335$	2.12631	0.116173
$336$	0.382305	0.0208564
$337$	25.8839	1.40999	0.704994	−	0.709214i	$-0.250950\pi$
$337$	25.8839	1.40999	0.704994	+	0.709214i	$0.250950\pi$
$338$	−5.56851	−0.302887
$339$	−1.38367	−0.0751508
$340$	−1.95144	−0.105832
$341$	23.4159	1.26804
$342$	−1.50621	−0.0814463
$343$	−14.3706	−0.775940
$344$	14.7150	0.793380
$345$	−0.0969254	−0.00521829
$346$	−9.67678	−0.520227
$347$	24.2007	1.29916	0.649580	−	0.760293i	$-0.274945\pi$
$347$	24.2007	1.29916	0.649580	+	0.760293i	$0.274945\pi$
$348$	0.210470	0.0112824
$349$	18.3078	0.979992	0.489996	−	0.871725i	$-0.336998\pi$
$349$	18.3078	0.979992	0.489996	+	0.871725i	$0.336998\pi$
$350$	−2.39855	−0.128208
$351$	−0.216342	−0.0115475
$352$	11.5999	0.618279
$353$	−9.11915	−0.485364	−0.242682	−	0.970106i	$-0.578027\pi$
$353$	−9.11915	−0.485364	−0.242682	+	0.970106i	$0.578027\pi$
$354$	0.148322	0.00788320
$355$	3.65134	0.193793
$356$	14.7276	0.780563
$357$	−0.502195	−0.0265790
$358$	−7.64747	−0.404182
$359$	−35.3388	−1.86511	−0.932555	−	0.361028i	$-0.882426\pi$
$359$	−35.3388	−1.86511	−0.932555	+	0.361028i	$0.882426\pi$
$360$	−1.38012	−0.0727389
$361$	−17.6344	−0.928124
$362$	−6.85951	−0.360528
$363$	−0.522472	−0.0274226
$364$	−0.637918	−0.0334360
$365$	0.544249	0.0284873
$366$	−0.733008	−0.0383149
$367$	1.25934	0.0657369	0.0328684	−	0.999460i	$-0.489536\pi$
$367$	1.25934	0.0657369	0.0328684	+	0.999460i	$0.489536\pi$
$368$	8.67840	0.452393
$369$	−34.7350	−1.80823
$370$	−1.17425	−0.0610461
$371$	−4.63653	−0.240717
$372$	−1.93342	−0.100243
$373$	−17.7386	−0.918469	−0.459234	−	0.888315i	$-0.651876\pi$
$373$	−17.7386	−0.918469	−0.459234	+	0.888315i	$0.651876\pi$
$374$	−4.21550	−0.217978
$375$	0.323240	0.0166920
$376$	21.0667	1.08643
$377$	−0.311426	−0.0160392
$378$	−0.338585	−0.0174150
$379$	−12.9268	−0.664004	−0.332002	−	0.943279i	$-0.607724\pi$
$379$	−12.9268	−0.664004	−0.332002	+	0.943279i	$0.607724\pi$
$380$	0.595110	0.0305285
$381$	0.957916	0.0490755
$382$	−4.95510	−0.253525
$383$	18.9617	0.968899	0.484449	−	0.874819i	$-0.339020\pi$
$383$	18.9617	0.968899	0.484449	+	0.874819i	$0.339020\pi$
$384$	−1.24997	−0.0637875
$385$	−0.808272	−0.0411934
$386$	−2.13508	−0.108673
$387$	26.7010	1.35729
$388$	−12.1962	−0.619168
$389$	−30.4863	−1.54572	−0.772858	−	0.634580i	$-0.781173\pi$
$389$	−30.4863	−1.54572	−0.772858	+	0.634580i	$0.781173\pi$
$390$	−0.00437889	−0.000221734 0
$391$	−11.3999	−0.576520
$392$	9.42195	0.475880
$393$	0.127202	0.00641650
$394$	10.9885	0.553594
$395$	1.01316	0.0509777
$396$	13.8076	0.693860
$397$	12.9002	0.647443	0.323722	−	0.946152i	$-0.395066\pi$
$397$	12.9002	0.647443	0.323722	+	0.946152i	$0.395066\pi$
$398$	−11.3551	−0.569178
$399$	0.153149	0.00766704
$400$	−14.3560	−0.717799
$401$	11.0575	0.552185	0.276093	−	0.961131i	$-0.410960\pi$
$401$	11.0575	0.552185	0.276093	+	0.961131i	$0.410960\pi$
$402$	−0.379259	−0.0189157
$403$	2.86083	0.142508
$404$	−3.57345	−0.177786
$405$	−2.49295	−0.123876
$406$	−0.487394	−0.0241890
$407$	24.7022	1.22444
$408$	0.731879	0.0362334
$409$	31.1882	1.54216	0.771079	−	0.636740i	$-0.219717\pi$
$409$	31.1882	1.54216	0.771079	+	0.636740i	$0.219717\pi$
$410$	−1.40928	−0.0695994
$411$	0.326173	0.0160889
$412$	−4.03588	−0.198834
$413$	3.34486	0.164590
$414$	−3.83434	−0.188447
$415$	1.46808	0.0720654
$416$	1.41722	0.0694847
$417$	−0.116041	−0.00568256
$418$	1.28556	0.0628786
$419$	−19.4368	−0.949549	−0.474774	−	0.880108i	$-0.657470\pi$
$419$	−19.4368	−0.949549	−0.474774	+	0.880108i	$0.657470\pi$
$420$	0.0667379	0.00325648
$421$	−7.74411	−0.377425	−0.188712	−	0.982032i	$-0.560431\pi$
$421$	−7.74411	−0.377425	−0.188712	+	0.982032i	$0.560431\pi$
$422$	−7.31971	−0.356318
$423$	38.2265	1.85864
$424$	6.75709	0.328154
$425$	18.8580	0.914747
$426$	−0.651271	−0.0315542
$427$	−16.5303	−0.799959
$428$	−32.7100	−1.58110
$429$	0.0921172	0.00444746
$430$	1.08332	0.0522425
$431$	40.5225	1.95190	0.975949	−	0.217999i	$-0.0699529\pi$
$431$	40.5225	1.95190	0.975949	+	0.217999i	$0.0699529\pi$
$432$	−2.02653	−0.0975013
$433$	15.4784	0.743846	0.371923	−	0.928264i	$-0.378698\pi$
$433$	15.4784	0.743846	0.371923	+	0.928264i	$0.378698\pi$
$434$	4.47732	0.214918
$435$	0.0325809	0.00156213
$436$	−17.7601	−0.850552
$437$	3.47651	0.166304
$438$	−0.0970750	−0.00463842
$439$	3.44487	0.164415	0.0822073	−	0.996615i	$-0.473803\pi$
$439$	3.44487	0.164415	0.0822073	+	0.996615i	$0.473803\pi$
$440$	1.17794	0.0561563
$441$	17.0965	0.814121
$442$	−0.515026	−0.0244973
$443$	26.2142	1.24547	0.622737	−	0.782431i	$-0.286021\pi$
$443$	26.2142	1.24547	0.622737	+	0.782431i	$0.286021\pi$
$444$	−2.03962	−0.0967963
$445$	2.27985	0.108075
$446$	−3.36019	−0.159110
$447$	0.517917	0.0244966
$448$	−4.37112	−0.206516
$449$	19.7732	0.933153	0.466576	−	0.884481i	$-0.345487\pi$
$449$	19.7732	0.933153	0.466576	+	0.884481i	$0.345487\pi$
$450$	6.34284	0.299004
$451$	29.6465	1.39600
$452$	21.6271	1.01725
$453$	−1.28429	−0.0603410
$454$	−8.44719	−0.396446
$455$	−0.0987501	−0.00462948
$456$	−0.223193	−0.0104520
$457$	−38.0468	−1.77976	−0.889878	−	0.456200i	$-0.849210\pi$
$457$	−38.0468	−1.77976	−0.889878	+	0.456200i	$0.849210\pi$
$458$	−0.564228	−0.0263646
$459$	2.66204	0.124254
$460$	1.51497	0.0706357
$461$	32.5625	1.51659	0.758293	−	0.651914i	$-0.226034\pi$
$461$	32.5625	1.51659	0.758293	+	0.651914i	$0.226034\pi$
$462$	0.144167	0.00670727
$463$	−24.7790	−1.15158	−0.575788	−	0.817599i	$-0.695305\pi$
$463$	−24.7790	−1.15158	−0.575788	+	0.817599i	$0.695305\pi$
$464$	−2.91719	−0.135427
$465$	−0.299295	−0.0138795
$466$	10.3846	0.481056
$467$	−1.37883	−0.0638045	−0.0319022	−	0.999491i	$-0.510157\pi$
$467$	−1.37883	−0.0638045	−0.0319022	+	0.999491i	$0.510157\pi$
$468$	1.68694	0.0779788
$469$	−8.55282	−0.394932
$470$	1.55094	0.0715395
$471$	−2.45243	−0.113002
$472$	−4.87466	−0.224375
$473$	−22.7895	−1.04786
$474$	−0.180713	−0.00830041
$475$	−5.75092	−0.263870
$476$	7.84942	0.359778
$477$	12.2610	0.561395
$478$	2.96444	0.135590
$479$	24.0021	1.09668	0.548341	−	0.836255i	$-0.315259\pi$
$479$	24.0021	1.09668	0.548341	+	0.836255i	$0.315259\pi$
$480$	−0.148267	−0.00676743
$481$	3.01797	0.137608
$482$	10.2828	0.468368
$483$	0.389870	0.0177397
$484$	8.16635	0.371198
$485$	−1.88798	−0.0857287
$486$	1.34406	0.0609679
$487$	12.7714	0.578727	0.289363	−	0.957219i	$-0.406556\pi$
$487$	12.7714	0.578727	0.289363	+	0.957219i	$0.406556\pi$
$488$	24.0907	1.09053
$489$	−1.05934	−0.0479052
$490$	0.693648	0.0313358
$491$	−34.8491	−1.57272	−0.786359	−	0.617770i	$-0.788036\pi$
$491$	−34.8491	−1.57272	−0.786359	+	0.617770i	$0.788036\pi$
$492$	−2.44787	−0.110359
$493$	3.83202	0.172585
$494$	0.157062	0.00706655
$495$	2.13743	0.0960704
$496$	26.7980	1.20327
$497$	−14.6871	−0.658804
$498$	−0.261854	−0.0117340
$499$	37.2423	1.66719	0.833596	−	0.552374i	$-0.186278\pi$
$499$	37.2423	1.66719	0.833596	+	0.552374i	$0.186278\pi$
$500$	−5.05232	−0.225947
$501$	1.07675	0.0481058
$502$	−3.23801	−0.144519
$503$	−14.5353	−0.648098	−0.324049	−	0.946040i	$-0.605044\pi$
$503$	−14.5353	−0.648098	−0.324049	+	0.946040i	$0.605044\pi$
$504$	5.55137	0.247278
$505$	−0.553172	−0.0246158
$506$	3.27263	0.145486
$507$	−1.49728	−0.0664966
$508$	−14.9724	−0.664295
$509$	−38.4949	−1.70626	−0.853128	−	0.521702i	$-0.825297\pi$
$509$	−38.4949	−1.70626	−0.853128	+	0.521702i	$0.825297\pi$
$510$	0.0538813	0.00238590
$511$	−2.18917	−0.0968434
$512$	22.8781	1.01108
$513$	−0.811814	−0.0358425
$514$	0.356472	0.0157233
$515$	−0.624758	−0.0275301
$516$	1.88170	0.0828372
$517$	−32.6265	−1.43491
$518$	4.72325	0.207528
$519$	−2.60193	−0.114212
$520$	0.143915	0.00631107
$521$	−32.3780	−1.41851	−0.709253	−	0.704954i	$-0.750968\pi$
$521$	−32.3780	−1.41851	−0.709253	+	0.704954i	$0.750968\pi$
$522$	1.28889	0.0564131
$523$	16.3398	0.714489	0.357245	−	0.934011i	$-0.383716\pi$
$523$	16.3398	0.714489	0.357245	+	0.934011i	$0.383716\pi$
$524$	−1.98820	−0.0868548
$525$	−0.644931	−0.0281471
$526$	−12.1637	−0.530362
$527$	−35.2018	−1.53341
$528$	0.862882	0.0375521
$529$	−14.1499	−0.615211
$530$	0.497460	0.0216083
$531$	−8.84529	−0.383853
$532$	−2.39375	−0.103782
$533$	3.62204	0.156888
$534$	−0.406645	−0.0175973
$535$	−5.06353	−0.218916
$536$	12.4645	0.538386
$537$	−2.05628	−0.0887351
$538$	−1.11930	−0.0482564
$539$	−14.5920	−0.628522
$540$	−0.353765	−0.0152236
$541$	−25.2154	−1.08410	−0.542048	−	0.840348i	$-0.682351\pi$
$541$	−25.2154	−1.08410	−0.542048	+	0.840348i	$0.682351\pi$
$542$	−2.42659	−0.104231
$543$	−1.84441	−0.0791512
$544$	−17.4385	−0.747669
$545$	−2.74927	−0.117766
$546$	0.0176136	0.000753790 0
$547$	−5.07760	−0.217103	−0.108551	−	0.994091i	$-0.534621\pi$
$547$	−5.07760	−0.217103	−0.108551	+	0.994091i	$0.534621\pi$
$548$	−5.09815	−0.217782
$549$	43.7136	1.86565
$550$	−5.41365	−0.230839
$551$	−1.16861	−0.0497844
$552$	−0.568182	−0.0241834
$553$	−4.07532	−0.173300
$554$	11.8279	0.502518
$555$	−0.315735	−0.0134022
$556$	1.81375	0.0769201
$557$	−20.4536	−0.866647	−0.433324	−	0.901238i	$-0.642659\pi$
$557$	−20.4536	−0.866647	−0.433324	+	0.901238i	$0.642659\pi$
$558$	−11.8400	−0.501228
$559$	−2.78429	−0.117763
$560$	−0.925014	−0.0390890
$561$	−1.13348	−0.0478556
$562$	−8.03529	−0.338948
$563$	21.7928	0.918459	0.459229	−	0.888318i	$-0.348126\pi$
$563$	21.7928	0.918459	0.459229	+	0.888318i	$0.348126\pi$
$564$	2.69393	0.113435
$565$	3.34789	0.140847
$566$	−6.79837	−0.285757
$567$	10.0276	0.421119
$568$	21.4043	0.898106
$569$	37.9762	1.59204	0.796022	−	0.605268i	$-0.206934\pi$
$569$	37.9762	1.59204	0.796022	+	0.605268i	$0.206934\pi$
$570$	−0.0164316	−0.000688243 0
$571$	−7.06087	−0.295488	−0.147744	−	0.989026i	$-0.547201\pi$
$571$	−7.06087	−0.295488	−0.147744	+	0.989026i	$0.547201\pi$
$572$	−1.43981	−0.0602016
$573$	−1.33234	−0.0556595
$574$	5.66865	0.236605
$575$	−14.6401	−0.610533
$576$	11.5592	0.481633
$577$	−4.96325	−0.206623	−0.103311	−	0.994649i	$-0.532944\pi$
$577$	−4.96325	−0.206623	−0.103311	+	0.994649i	$0.532944\pi$
$578$	−0.999354	−0.0415677
$579$	−0.574088	−0.0238583
$580$	−0.509246	−0.0211453
$581$	−5.90518	−0.244988
$582$	0.336749	0.0139587
$583$	−10.4649	−0.433411
$584$	3.19042	0.132020
$585$	0.261139	0.0107968
$586$	1.50395	0.0621275
$587$	35.1554	1.45102	0.725509	−	0.688213i	$-0.241605\pi$
$587$	35.1554	1.45102	0.725509	+	0.688213i	$0.241605\pi$
$588$	1.20484	0.0496869
$589$	10.7351	0.442332
$590$	−0.358875	−0.0147746
$591$	2.95464	0.121538
$592$	28.2700	1.16189
$593$	30.1770	1.23922	0.619611	−	0.784909i	$-0.287290\pi$
$593$	30.1770	1.23922	0.619611	+	0.784909i	$0.287290\pi$
$594$	−0.764204	−0.0313557
$595$	1.21510	0.0498141
$596$	−8.09516	−0.331591
$597$	−3.05319	−0.124959
$598$	0.399832	0.0163503
$599$	34.7234	1.41876	0.709379	−	0.704827i	$-0.248975\pi$
$599$	34.7234	1.41876	0.709379	+	0.704827i	$0.248975\pi$
$600$	0.939897	0.0383711
$601$	−11.8372	−0.482849	−0.241425	−	0.970420i	$-0.577615\pi$
$601$	−11.8372	−0.482849	−0.241425	+	0.970420i	$0.577615\pi$
$602$	−4.35754	−0.177600
$603$	22.6175	0.921054
$604$	20.0737	0.816786
$605$	1.26416	0.0513953
$606$	0.0986665	0.00400805
$607$	−14.9512	−0.606852	−0.303426	−	0.952855i	$-0.598131\pi$
$607$	−14.9512	−0.606852	−0.303426	+	0.952855i	$0.598131\pi$
$608$	5.31803	0.215675
$609$	−0.131052	−0.00531051
$610$	1.77356	0.0718095
$611$	−3.98613	−0.161261
$612$	−20.7574	−0.839067
$613$	45.0690	1.82032	0.910159	−	0.414259i	$-0.135959\pi$
$613$	45.0690	1.82032	0.910159	+	0.414259i	$0.135959\pi$
$614$	−8.22108	−0.331776
$615$	−0.378932	−0.0152800
$616$	−4.73813	−0.190905
$617$	−8.91275	−0.358814	−0.179407	−	0.983775i	$-0.557418\pi$
$617$	−8.91275	−0.358814	−0.179407	+	0.983775i	$0.557418\pi$
$618$	0.111435	0.00448257
$619$	5.91521	0.237752	0.118876	−	0.992909i	$-0.462071\pi$
$619$	5.91521	0.237752	0.118876	+	0.992909i	$0.462071\pi$
$620$	4.67805	0.187875
$621$	−2.06663	−0.0829310
$622$	4.49644	0.180291
$623$	−9.17040	−0.367405
$624$	0.105422	0.00422026
$625$	23.8237	0.952950
$626$	10.5345	0.421045
$627$	0.345665	0.0138045
$628$	38.3320	1.52961
$629$	−37.1354	−1.48069
$630$	0.408694	0.0162828
$631$	−25.2393	−1.00476	−0.502381	−	0.864646i	$-0.667543\pi$
$631$	−25.2393	−1.00476	−0.502381	+	0.864646i	$0.667543\pi$
$632$	5.93921	0.236249
$633$	−1.96815	−0.0782270
$634$	−9.00836	−0.357768
$635$	−2.31774	−0.0919769
$636$	0.864071	0.0342627
$637$	−1.78277	−0.0706359
$638$	−1.10007	−0.0435524
$639$	38.8391	1.53645
$640$	3.02440	0.119550
$641$	29.7548	1.17525	0.587623	−	0.809135i	$-0.300064\pi$
$641$	29.7548	1.17525	0.587623	+	0.809135i	$0.300064\pi$
$642$	0.903156	0.0356447
$643$	5.99954	0.236599	0.118299	−	0.992978i	$-0.462256\pi$
$643$	5.99954	0.236599	0.118299	+	0.992978i	$0.462256\pi$
$644$	−6.09376	−0.240128
$645$	0.291288	0.0114695
$646$	−1.93261	−0.0760375
$647$	31.0120	1.21921	0.609604	−	0.792706i	$-0.291328\pi$
$647$	31.0120	1.21921	0.609604	+	0.792706i	$0.291328\pi$
$648$	−14.6138	−0.574085
$649$	7.54951	0.296344
$650$	−0.661409	−0.0259426
$651$	1.20388	0.0471837
$652$	16.5578	0.648453
$653$	15.9197	0.622988	0.311494	−	0.950248i	$-0.399171\pi$
$653$	15.9197	0.622988	0.311494	+	0.950248i	$0.399171\pi$
$654$	0.490373	0.0191751
$655$	−0.307774	−0.0120257
$656$	33.9285	1.32468
$657$	5.78915	0.225856
$658$	−6.23846	−0.243201
$659$	−1.80806	−0.0704320	−0.0352160	−	0.999380i	$-0.511212\pi$
$659$	−1.80806	−0.0704320	−0.0352160	+	0.999380i	$0.511212\pi$
$660$	0.150631	0.00586330
$661$	35.8856	1.39579	0.697894	−	0.716201i	$-0.254121\pi$
$661$	35.8856	1.39579	0.697894	+	0.716201i	$0.254121\pi$
$662$	13.0893	0.508729
$663$	−0.138482	−0.00537820
$664$	8.60598	0.333977
$665$	−0.370555	−0.0143695
$666$	−12.4904	−0.483993
$667$	−2.97492	−0.115189
$668$	−16.8299	−0.651169
$669$	−0.903501	−0.0349314
$670$	0.917644	0.0354517
$671$	−37.3098	−1.44033
$672$	0.596385	0.0230060
$673$	−28.9362	−1.11541	−0.557704	−	0.830040i	$-0.688318\pi$
$673$	−28.9362	−1.11541	−0.557704	+	0.830040i	$0.688318\pi$
$674$	11.1706	0.430277
$675$	3.41866	0.131584
$676$	23.4028	0.900109
$677$	−26.7757	−1.02907	−0.514537	−	0.857468i	$-0.672036\pi$
$677$	−26.7757	−1.02907	−0.514537	+	0.857468i	$0.672036\pi$
$678$	−0.597147	−0.0229333
$679$	7.59416	0.291437
$680$	−1.77083	−0.0679084
$681$	−2.27131	−0.0870368
$682$	10.1055	0.386961
$683$	5.76437	0.220567	0.110284	−	0.993900i	$-0.464824\pi$
$683$	5.76437	0.220567	0.110284	+	0.993900i	$0.464824\pi$
$684$	6.33015	0.242039
$685$	−0.789198	−0.0301537
$686$	−6.20187	−0.236789
$687$	−0.151712	−0.00578816
$688$	−26.0811	−0.994331
$689$	−1.27854	−0.0487085
$690$	−0.0418297	−0.00159243
$691$	−8.22389	−0.312852	−0.156426	−	0.987690i	$-0.549997\pi$
$691$	−8.22389	−0.312852	−0.156426	+	0.987690i	$0.549997\pi$
$692$	40.6688	1.54599
$693$	−8.59755	−0.326594
$694$	10.4442	0.396456
$695$	0.280770	0.0106502
$696$	0.190991	0.00723948
$697$	−44.5684	−1.68815
$698$	7.90102	0.299058
$699$	2.79224	0.105612
$700$	10.0804	0.381004
$701$	8.97999	0.339169	0.169585	−	0.985516i	$-0.445757\pi$
$701$	8.97999	0.339169	0.169585	+	0.985516i	$0.445757\pi$
$702$	−0.0933662	−0.00352388
$703$	11.3248	0.427122
$704$	−9.86584	−0.371833
$705$	0.417022	0.0157060
$706$	−3.93552	−0.148115
$707$	2.22507	0.0836822
$708$	−0.623353	−0.0234270
$709$	−33.6896	−1.26524	−0.632619	−	0.774463i	$-0.718020\pi$
$709$	−33.6896	−1.26524	−0.632619	+	0.774463i	$0.718020\pi$
$710$	1.57580	0.0591386
$711$	10.7770	0.404168
$712$	13.3646	0.500859
$713$	27.3283	1.02345
$714$	−0.216731	−0.00811094
$715$	−0.222884	−0.00833539
$716$	32.1401	1.20113
$717$	0.797089	0.0297678
$718$	−15.2510	−0.569164
$719$	8.53294	0.318225	0.159112	−	0.987260i	$-0.449137\pi$
$719$	8.53294	0.318225	0.159112	+	0.987260i	$0.449137\pi$
$720$	2.44615	0.0911626
$721$	2.51301	0.0935894
$722$	−7.61040	−0.283230
$723$	2.76487	0.102827
$724$	28.8286	1.07140
$725$	4.92117	0.182768
$726$	−0.225481	−0.00836839
$727$	−10.6639	−0.395501	−0.197751	−	0.980252i	$-0.563364\pi$
$727$	−10.6639	−0.395501	−0.197751	+	0.980252i	$0.563364\pi$
$728$	−0.578878	−0.0214546
$729$	−26.2756	−0.973170
$730$	0.234880	0.00869329
$731$	34.2600	1.26715
$732$	3.08062	0.113863
$733$	−3.39646	−0.125451	−0.0627255	−	0.998031i	$-0.519979\pi$
$733$	−3.39646	−0.125451	−0.0627255	+	0.998031i	$0.519979\pi$
$734$	0.543488	0.0200605
$735$	0.186511	0.00687954
$736$	13.5381	0.499020
$737$	−19.3041	−0.711077
$738$	−14.9904	−0.551806
$739$	12.1503	0.446957	0.223478	−	0.974709i	$-0.428259\pi$
$739$	12.1503	0.446957	0.223478	+	0.974709i	$0.428259\pi$
$740$	4.93502	0.181415
$741$	0.0422314	0.00155141
$742$	−2.00097	−0.0734579
$743$	25.7901	0.946148	0.473074	−	0.881023i	$-0.343144\pi$
$743$	25.7901	0.946148	0.473074	+	0.881023i	$0.343144\pi$
$744$	−1.75448	−0.0643225
$745$	−1.25314	−0.0459114
$746$	−7.65538	−0.280283
$747$	15.6159	0.571357
$748$	17.7166	0.647781
$749$	20.3674	0.744209
$750$	0.139500	0.00509381
$751$	41.6825	1.52102	0.760508	−	0.649328i	$-0.224950\pi$
$751$	41.6825	1.52102	0.760508	+	0.649328i	$0.224950\pi$
$752$	−37.3389	−1.36161
$753$	−0.870647	−0.0317281
$754$	−0.134401	−0.00489459
$755$	3.10742	0.113091
$756$	1.42298	0.0517532
$757$	37.4819	1.36230	0.681151	−	0.732143i	$-0.261480\pi$
$757$	37.4819	1.36230	0.681151	+	0.732143i	$0.261480\pi$
$758$	−5.57876	−0.202630
$759$	0.879957	0.0319404
$760$	0.540032	0.0195890
$761$	24.6396	0.893184	0.446592	−	0.894738i	$-0.352638\pi$
$761$	24.6396	0.893184	0.446592	+	0.894738i	$0.352638\pi$
$762$	0.413404	0.0149761
$763$	11.0586	0.400348
$764$	20.8249	0.753417
$765$	−3.21326	−0.116176
$766$	8.18324	0.295673
$767$	0.922356	0.0333044
$768$	0.358813	0.0129475
$769$	−18.9866	−0.684673	−0.342337	−	0.939577i	$-0.611218\pi$
$769$	−18.9866	−0.684673	−0.342337	+	0.939577i	$0.611218\pi$
$770$	−0.348823	−0.0125707
$771$	0.0958495	0.00345194
$772$	8.97313	0.322950
$773$	−50.1426	−1.80351	−0.901753	−	0.432252i	$-0.857719\pi$
$773$	−50.1426	−1.80351	−0.901753	+	0.432252i	$0.857719\pi$
$774$	11.5233	0.414195
$775$	−45.2070	−1.62388
$776$	−11.0674	−0.397297
$777$	1.27001	0.0455612
$778$	−13.1569	−0.471696
$779$	13.5915	0.486967
$780$	0.0184032	0.000658942 0
$781$	−33.1494	−1.18618
$782$	−4.91983	−0.175933
$783$	0.694684	0.0248260
$784$	−16.6996	−0.596414
$785$	5.93382	0.211787
$786$	0.0548962	0.00195808
$787$	−3.90476	−0.139190	−0.0695949	−	0.997575i	$-0.522171\pi$
$787$	−3.90476	−0.139190	−0.0695949	+	0.997575i	$0.522171\pi$
$788$	−46.1817	−1.64515
$789$	−3.27061	−0.116437
$790$	0.437247	0.0155565
$791$	−13.4665	−0.478813
$792$	12.5297	0.445225
$793$	−4.55830	−0.161870
$794$	5.56730	0.197576
$795$	0.133759	0.00474394
$796$	47.7221	1.69147
$797$	−28.0672	−0.994192	−0.497096	−	0.867696i	$-0.665600\pi$
$797$	−28.0672	−0.994192	−0.497096	+	0.867696i	$0.665600\pi$
$798$	0.0660940	0.00233970
$799$	49.0483	1.73521
$800$	−22.3949	−0.791781
$801$	24.2506	0.856854
$802$	4.77205	0.168507
$803$	−4.94108	−0.174367
$804$	1.59392	0.0562131
$805$	−0.943318	−0.0332476
$806$	1.23464	0.0434882
$807$	−0.300961	−0.0105943
$808$	−3.24272	−0.114079
$809$	17.9039	0.629468	0.314734	−	0.949180i	$-0.398085\pi$
$809$	17.9039	0.629468	0.314734	+	0.949180i	$0.398085\pi$
$810$	−1.07587	−0.0378024
$811$	−14.0472	−0.493263	−0.246631	−	0.969109i	$-0.579324\pi$
$811$	−14.0472	−0.493263	−0.246631	+	0.969109i	$0.579324\pi$
$812$	2.04838	0.0718840
$813$	−0.652471	−0.0228832
$814$	10.6606	0.373655
$815$	2.56316	0.0897835
$816$	−1.29719	−0.0454108
$817$	−10.4479	−0.365526
$818$	13.4598	0.470610
$819$	−1.05040	−0.0367039
$820$	5.92280	0.206833
$821$	−19.6144	−0.684546	−0.342273	−	0.939600i	$-0.611197\pi$
$821$	−19.6144	−0.684546	−0.342273	+	0.939600i	$0.611197\pi$
$822$	0.140765	0.00490975
$823$	2.22528	0.0775684	0.0387842	−	0.999248i	$-0.487652\pi$
$823$	2.22528	0.0775684	0.0387842	+	0.999248i	$0.487652\pi$
$824$	−3.66236	−0.127584
$825$	−1.45564	−0.0506789
$826$	1.44353	0.0502268
$827$	−13.8918	−0.483067	−0.241533	−	0.970393i	$-0.577650\pi$
$827$	−13.8918	−0.483067	−0.241533	+	0.970393i	$0.577650\pi$
$828$	16.1146	0.560022
$829$	−10.9325	−0.379700	−0.189850	−	0.981813i	$-0.560800\pi$
$829$	−10.9325	−0.379700	−0.189850	+	0.981813i	$0.560800\pi$
$830$	0.633575	0.0219917
$831$	3.18032	0.110324
$832$	−1.20535	−0.0417881
$833$	21.9365	0.760056
$834$	−0.0500795	−0.00173411
$835$	−2.60528	−0.0901595
$836$	−5.40282	−0.186861
$837$	−6.38153	−0.220578
$838$	−8.38826	−0.289768
$839$	−21.4014	−0.738857	−0.369429	−	0.929259i	$-0.620447\pi$
$839$	−21.4014	−0.738857	−0.369429	+	0.929259i	$0.620447\pi$
$840$	0.0605613	0.00208956
$841$	1.00000	0.0344828
$842$	−3.34210	−0.115176
$843$	−2.16056	−0.0744135
$844$	30.7627	1.05889
$845$	3.62278	0.124627
$846$	16.4973	0.567188
$847$	−5.08491	−0.174720
$848$	−11.9764	−0.411270
$849$	−1.82797	−0.0627357
$850$	8.13848	0.279148
$851$	28.8294	0.988259
$852$	2.73710	0.0937717
$853$	−34.3358	−1.17564	−0.587818	−	0.808993i	$-0.700013\pi$
$853$	−34.3358	−1.17564	−0.587818	+	0.808993i	$0.700013\pi$
$854$	−7.13394	−0.244118
$855$	0.979912	0.0335123
$856$	−29.6827	−1.01453
$857$	−2.61691	−0.0893918	−0.0446959	−	0.999001i	$-0.514232\pi$
$857$	−2.61691	−0.0893918	−0.0446959	+	0.999001i	$0.514232\pi$
$858$	0.0397547	0.00135720
$859$	−14.3229	−0.488690	−0.244345	−	0.969688i	$-0.578573\pi$
$859$	−14.3229	−0.488690	−0.244345	+	0.969688i	$0.578573\pi$
$860$	−4.55290	−0.155253
$861$	1.52421	0.0519449
$862$	17.4881	0.595648
$863$	−30.8938	−1.05164	−0.525818	−	0.850597i	$-0.676241\pi$
$863$	−30.8938	−1.05164	−0.525818	+	0.850597i	$0.676241\pi$
$864$	−3.16133	−0.107550
$865$	6.29555	0.214055
$866$	6.67998	0.226995
$867$	−0.268710	−0.00912587
$868$	−18.8169	−0.638687
$869$	−9.19820	−0.312028
$870$	0.0140608	0.000476706 0
$871$	−2.35847	−0.0799137
$872$	−16.1164	−0.545769
$873$	−20.0823	−0.679684
$874$	1.50035	0.0507500
$875$	3.14591	0.106351
$876$	0.407978	0.0137843
$877$	1.99498	0.0673656	0.0336828	−	0.999433i	$-0.489276\pi$
$877$	1.99498	0.0673656	0.0336828	+	0.999433i	$0.489276\pi$
$878$	1.48669	0.0501733
$879$	0.404387	0.0136396
$880$	−2.08780	−0.0703798
$881$	−23.9401	−0.806562	−0.403281	−	0.915076i	$-0.632130\pi$
$881$	−23.9401	−0.806562	−0.403281	+	0.915076i	$0.632130\pi$
$882$	7.37830	0.248440
$883$	47.6172	1.60245	0.801223	−	0.598366i	$-0.204183\pi$
$883$	47.6172	1.60245	0.801223	+	0.598366i	$0.204183\pi$
$884$	2.16451	0.0728003
$885$	−0.0964955	−0.00324366
$886$	11.3132	0.380074
$887$	−13.7078	−0.460262	−0.230131	−	0.973160i	$-0.573915\pi$
$887$	−13.7078	−0.460262	−0.230131	+	0.973160i	$0.573915\pi$
$888$	−1.85086	−0.0621107
$889$	9.32284	0.312678
$890$	0.983906	0.0329806
$891$	22.6328	0.758227
$892$	14.1219	0.472837
$893$	−14.9577	−0.500542
$894$	0.223516	0.00747548
$895$	4.97532	0.166306
$896$	−12.1653	−0.406413
$897$	0.107508	0.00358959
$898$	8.53343	0.284764
$899$	−9.18623	−0.306378
$900$	−26.6571	−0.888571
$901$	15.7321	0.524113
$902$	12.7944	0.426008
$903$	−1.17167	−0.0389907
$904$	19.6255	0.652735
$905$	4.46268	0.148344
$906$	−0.554254	−0.0184139
$907$	1.58710	0.0526989	0.0263495	−	0.999653i	$-0.491612\pi$
$907$	1.58710	0.0526989	0.0263495	+	0.999653i	$0.491612\pi$
$908$	35.5011	1.17815
$909$	−5.88407	−0.195162
$910$	−0.0426172	−0.00141275
$911$	9.69455	0.321195	0.160597	−	0.987020i	$-0.448658\pi$
$911$	9.69455	0.321195	0.160597	+	0.987020i	$0.448658\pi$
$912$	0.395591	0.0130993
$913$	−13.3283	−0.441102
$914$	−16.4197	−0.543116
$915$	0.476883	0.0157653
$916$	2.37129	0.0783496
$917$	1.23798	0.0408818
$918$	1.14885	0.0379177
$919$	15.6836	0.517356	0.258678	−	0.965964i	$-0.416713\pi$
$919$	15.6836	0.517356	0.258678	+	0.965964i	$0.416713\pi$
$920$	1.37476	0.0453243
$921$	−2.21051	−0.0728389
$922$	14.0529	0.462807
$923$	−4.05001	−0.133308
$924$	−0.605894	−0.0199325
$925$	−47.6902	−1.56804
$926$	−10.6938	−0.351419
$927$	−6.64552	−0.218267
$928$	−4.55074	−0.149385
$929$	−47.5752	−1.56089	−0.780446	−	0.625223i	$-0.785008\pi$
$929$	−47.5752	−1.56089	−0.780446	+	0.625223i	$0.785008\pi$
$930$	−0.129166	−0.00423551
$931$	−6.68975	−0.219248
$932$	−43.6434	−1.42959
$933$	1.20902	0.0395815
$934$	−0.595055	−0.0194708
$935$	2.74253	0.0896905
$936$	1.53081	0.0500361
$937$	−37.9607	−1.24012	−0.620062	−	0.784553i	$-0.712892\pi$
$937$	−37.9607	−1.24012	−0.620062	+	0.784553i	$0.712892\pi$
$938$	−3.69111	−0.120519
$939$	2.83257	0.0924373
$940$	−6.51816	−0.212599
$941$	21.3061	0.694560	0.347280	−	0.937761i	$-0.387105\pi$
$941$	21.3061	0.694560	0.347280	+	0.937761i	$0.387105\pi$
$942$	−1.05838	−0.0344840
$943$	34.5999	1.12673
$944$	8.63991	0.281205
$945$	0.220278	0.00716564
$946$	−9.83518	−0.319769
$947$	27.9932	0.909656	0.454828	−	0.890579i	$-0.349701\pi$
$947$	27.9932	0.909656	0.454828	+	0.890579i	$0.349701\pi$
$948$	0.759483	0.0246669
$949$	−0.603673	−0.0195960
$950$	−2.48190	−0.0805236
$951$	−2.42220	−0.0785453
$952$	7.12296	0.230856
$953$	13.3842	0.433557	0.216778	−	0.976221i	$-0.430445\pi$
$953$	13.3842	0.433557	0.216778	+	0.976221i	$0.430445\pi$
$954$	5.29146	0.171317
$955$	3.22370	0.104317
$956$	−12.4587	−0.402943
$957$	−0.295792	−0.00956160
$958$	10.3585	0.334668
$959$	3.17445	0.102508
$960$	0.126102	0.00406993
$961$	53.3868	1.72216
$962$	1.30245	0.0419928
$963$	−53.8605	−1.73563
$964$	−43.2156	−1.39188
$965$	1.38905	0.0447150
$966$	0.168255	0.00541351
$967$	−0.229111	−0.00736773	−0.00368386	−	0.999993i	$-0.501173\pi$
$967$	−0.229111	−0.00736773	−0.00368386	+	0.999993i	$0.501173\pi$
$968$	7.41055	0.238184
$969$	−0.519647	−0.0166935
$970$	−0.814788	−0.0261613
$971$	22.3642	0.717703	0.358851	−	0.933395i	$-0.383168\pi$
$971$	22.3642	0.717703	0.358851	+	0.933395i	$0.383168\pi$
$972$	−5.64871	−0.181183
$973$	−1.12936	−0.0362057
$974$	5.51170	0.176606
$975$	−0.177842	−0.00569551
$976$	−42.6986	−1.36675
$977$	7.81157	0.249914	0.124957	−	0.992162i	$-0.460121\pi$
$977$	7.81157	0.249914	0.124957	+	0.992162i	$0.460121\pi$
$978$	−0.457178	−0.0146189
$979$	−20.6981	−0.661513
$980$	−2.91520	−0.0931227
$981$	−29.2438	−0.933684
$982$	−15.0397	−0.479936
$983$	−1.09592	−0.0349544	−0.0174772	−	0.999847i	$-0.505563\pi$
$983$	−1.09592	−0.0349544	−0.0174772	+	0.999847i	$0.505563\pi$
$984$	−2.22132	−0.0708131
$985$	−7.14895	−0.227785
$986$	1.65377	0.0526668
$987$	−1.67742	−0.0533929
$988$	−0.660086	−0.0210001
$989$	−26.5972	−0.845741
$990$	0.922444	0.0293172
$991$	−61.6269	−1.95764	−0.978821	−	0.204716i	$-0.934373\pi$
$991$	−61.6269	−1.95764	−0.978821	+	0.204716i	$0.934373\pi$
$992$	41.8041	1.32728
$993$	3.51949	0.111688
$994$	−6.33844	−0.201043
$995$	7.38741	0.234197
$996$	1.10050	0.0348707
$997$	1.41529	0.0448226	0.0224113	−	0.999749i	$-0.492866\pi$
$997$	1.41529	0.0448226	0.0224113	+	0.999749i	$0.492866\pi$
$998$	16.0725	0.508767
$999$	−6.73206	−0.212993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.35	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.35	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q+0.431567 q^{2} +0.116041 q^{3} -1.81375 q^{4} -0.280770 q^{5} +0.0500795 q^{6} +1.12936 q^{7} -1.64589 q^{8} -2.98653 q^{9} +O(q^{10})\)	\(q+0.431567 q^{2} +0.116041 q^{3} -1.81375 q^{4} -0.280770 q^{5} +0.0500795 q^{6} +1.12936 q^{7} -1.64589 q^{8} -2.98653 q^{9} -0.121171 q^{10} +2.54903 q^{11} -0.210470 q^{12} +0.311426 q^{13} +0.487394 q^{14} -0.0325809 q^{15} +2.91719 q^{16} -3.83202 q^{17} -1.28889 q^{18} +1.16861 q^{19} +0.509246 q^{20} +0.131052 q^{21} +1.10007 q^{22} +2.97492 q^{23} -0.190991 q^{24} -4.92117 q^{25} +0.134401 q^{26} -0.694684 q^{27} -2.04838 q^{28} -1.00000 q^{29} -0.0140608 q^{30} +9.18623 q^{31} +4.55074 q^{32} +0.295792 q^{33} -1.65377 q^{34} -0.317091 q^{35} +5.41683 q^{36} +9.69082 q^{37} +0.504332 q^{38} +0.0361382 q^{39} +0.462115 q^{40} +11.6305 q^{41} +0.0565578 q^{42} -8.94047 q^{43} -4.62330 q^{44} +0.838529 q^{45} +1.28388 q^{46} -12.7996 q^{47} +0.338514 q^{48} -5.72454 q^{49} -2.12381 q^{50} -0.444672 q^{51} -0.564848 q^{52} -4.10544 q^{53} -0.299803 q^{54} -0.715689 q^{55} -1.85880 q^{56} +0.135607 q^{57} -0.431567 q^{58} +2.96172 q^{59} +0.0590935 q^{60} -14.6369 q^{61} +3.96447 q^{62} -3.37288 q^{63} -3.87044 q^{64} -0.0874389 q^{65} +0.127654 q^{66} -7.57315 q^{67} +6.95032 q^{68} +0.345213 q^{69} -0.136846 q^{70} -13.0047 q^{71} +4.91550 q^{72} -1.93842 q^{73} +4.18223 q^{74} -0.571058 q^{75} -2.11956 q^{76} +2.87877 q^{77} +0.0155960 q^{78} -3.60852 q^{79} -0.819059 q^{80} +8.87899 q^{81} +5.01934 q^{82} -5.22878 q^{83} -0.237696 q^{84} +1.07591 q^{85} -3.85841 q^{86} -0.116041 q^{87} -4.19541 q^{88} -8.11999 q^{89} +0.361881 q^{90} +0.351712 q^{91} -5.39576 q^{92} +1.06598 q^{93} -5.52389 q^{94} -0.328110 q^{95} +0.528073 q^{96} +6.72429 q^{97} -2.47052 q^{98} -7.61275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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