LMFDB - Embedded newform 4017.2.a.j.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.506527 q^{2} -1.00000 q^{3} -1.74343 q^{4} +4.00697 q^{5} -0.506527 q^{6} +4.25155 q^{7} -1.89615 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.506527 q^{2} -1.00000 q^{3} -1.74343 q^{4} +4.00697 q^{5} -0.506527 q^{6} +4.25155 q^{7} -1.89615 q^{8} +1.00000 q^{9} +2.02964 q^{10} -0.00859157 q^{11} +1.74343 q^{12} +1.00000 q^{13} +2.15352 q^{14} -4.00697 q^{15} +2.52641 q^{16} -2.55474 q^{17} +0.506527 q^{18} +5.31133 q^{19} -6.98588 q^{20} -4.25155 q^{21} -0.00435186 q^{22} +7.33175 q^{23} +1.89615 q^{24} +11.0558 q^{25} +0.506527 q^{26} -1.00000 q^{27} -7.41228 q^{28} -3.63092 q^{29} -2.02964 q^{30} -4.47636 q^{31} +5.07199 q^{32} +0.00859157 q^{33} -1.29404 q^{34} +17.0358 q^{35} -1.74343 q^{36} -4.40497 q^{37} +2.69033 q^{38} -1.00000 q^{39} -7.59781 q^{40} +10.3946 q^{41} -2.15352 q^{42} -8.16666 q^{43} +0.0149788 q^{44} +4.00697 q^{45} +3.71373 q^{46} +10.6650 q^{47} -2.52641 q^{48} +11.0757 q^{49} +5.60007 q^{50} +2.55474 q^{51} -1.74343 q^{52} -8.47563 q^{53} -0.506527 q^{54} -0.0344262 q^{55} -8.06157 q^{56} -5.31133 q^{57} -1.83916 q^{58} -9.30787 q^{59} +6.98588 q^{60} +9.90044 q^{61} -2.26740 q^{62} +4.25155 q^{63} -2.48372 q^{64} +4.00697 q^{65} +0.00435186 q^{66} -4.26929 q^{67} +4.45401 q^{68} -7.33175 q^{69} +8.62911 q^{70} -5.41974 q^{71} -1.89615 q^{72} +11.7345 q^{73} -2.23124 q^{74} -11.0558 q^{75} -9.25993 q^{76} -0.0365275 q^{77} -0.506527 q^{78} -10.8270 q^{79} +10.1233 q^{80} +1.00000 q^{81} +5.26515 q^{82} +4.73251 q^{83} +7.41228 q^{84} -10.2368 q^{85} -4.13663 q^{86} +3.63092 q^{87} +0.0162909 q^{88} +14.1868 q^{89} +2.02964 q^{90} +4.25155 q^{91} -12.7824 q^{92} +4.47636 q^{93} +5.40212 q^{94} +21.2823 q^{95} -5.07199 q^{96} -16.4976 q^{97} +5.61013 q^{98} -0.00859157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	0.506527	0.358169	0.179084	−	0.983834i	$-0.442687\pi$
$2$	0.506527	0.358169	0.179084	+	0.983834i	$0.442687\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.74343	−0.871715
$5$	4.00697	1.79197	0.895986	−	0.444082i	$-0.146470\pi$
$5$	4.00697	1.79197	0.895986	+	0.444082i	$0.146470\pi$
$6$	−0.506527	−0.206789
$7$	4.25155	1.60694	0.803468	−	0.595348i	$-0.202986\pi$
$7$	4.25155	1.60694	0.803468	+	0.595348i	$0.202986\pi$
$8$	−1.89615	−0.670390
$9$	1.00000	0.333333
$10$	2.02964	0.641828
$11$	−0.00859157	−0.00259045	−0.00129523	−	0.999999i	$-0.500412\pi$
$11$	−0.00859157	−0.00259045	−0.00129523	+	0.999999i	$0.500412\pi$
$12$	1.74343	0.503285
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.15352	0.575554
$15$	−4.00697	−1.03460
$16$	2.52641	0.631603
$17$	−2.55474	−0.619615	−0.309807	−	0.950799i	$-0.600265\pi$
$17$	−2.55474	−0.619615	−0.309807	+	0.950799i	$0.600265\pi$
$18$	0.506527	0.119390
$19$	5.31133	1.21850	0.609251	−	0.792977i	$-0.291470\pi$
$19$	5.31133	1.21850	0.609251	+	0.792977i	$0.291470\pi$
$20$	−6.98588	−1.56209
$21$	−4.25155	−0.927764
$22$	−0.00435186	−0.000927819 0
$23$	7.33175	1.52878	0.764388	−	0.644756i	$-0.223041\pi$
$23$	7.33175	1.52878	0.764388	+	0.644756i	$0.223041\pi$
$24$	1.89615	0.387050
$25$	11.0558	2.21116
$26$	0.506527	0.0993381
$27$	−1.00000	−0.192450
$28$	−7.41228	−1.40079
$29$	−3.63092	−0.674245	−0.337122	−	0.941461i	$-0.609454\pi$
$29$	−3.63092	−0.674245	−0.337122	+	0.941461i	$0.609454\pi$
$30$	−2.02964	−0.370560
$31$	−4.47636	−0.803978	−0.401989	−	0.915644i	$-0.631681\pi$
$31$	−4.47636	−0.803978	−0.401989	+	0.915644i	$0.631681\pi$
$32$	5.07199	0.896610
$33$	0.00859157	0.00149560
$34$	−1.29404	−0.221927
$35$	17.0358	2.87958
$36$	−1.74343	−0.290572
$37$	−4.40497	−0.724173	−0.362086	−	0.932145i	$-0.617935\pi$
$37$	−4.40497	−0.724173	−0.362086	+	0.932145i	$0.617935\pi$
$38$	2.69033	0.436429
$39$	−1.00000	−0.160128
$40$	−7.59781	−1.20132
$41$	10.3946	1.62337	0.811683	−	0.584099i	$-0.198552\pi$
$41$	10.3946	1.62337	0.811683	+	0.584099i	$0.198552\pi$
$42$	−2.15352	−0.332296
$43$	−8.16666	−1.24540	−0.622702	−	0.782459i	$-0.713965\pi$
$43$	−8.16666	−1.24540	−0.622702	+	0.782459i	$0.713965\pi$
$44$	0.0149788	0.00225814
$45$	4.00697	0.597324
$46$	3.71373	0.547560
$47$	10.6650	1.55565	0.777827	−	0.628478i	$-0.216322\pi$
$47$	10.6650	1.55565	0.777827	+	0.628478i	$0.216322\pi$
$48$	−2.52641	−0.364656
$49$	11.0757	1.58224
$50$	5.60007	0.791970
$51$	2.55474	0.357735
$52$	−1.74343	−0.241770
$53$	−8.47563	−1.16422	−0.582109	−	0.813111i	$-0.697772\pi$
$53$	−8.47563	−1.16422	−0.582109	+	0.813111i	$0.697772\pi$
$54$	−0.506527	−0.0689296
$55$	−0.0344262	−0.00464202
$56$	−8.06157	−1.07727
$57$	−5.31133	−0.703502
$58$	−1.83916	−0.241493
$59$	−9.30787	−1.21178	−0.605891	−	0.795548i	$-0.707183\pi$
$59$	−9.30787	−1.21178	−0.605891	+	0.795548i	$0.707183\pi$
$60$	6.98588	0.901873
$61$	9.90044	1.26762	0.633810	−	0.773488i	$-0.281490\pi$
$61$	9.90044	1.26762	0.633810	+	0.773488i	$0.281490\pi$
$62$	−2.26740	−0.287960
$63$	4.25155	0.535645
$64$	−2.48372	−0.310465
$65$	4.00697	0.497004
$66$	0.00435186	0.000535677 0
$67$	−4.26929	−0.521577	−0.260789	−	0.965396i	$-0.583983\pi$
$67$	−4.26929	−0.521577	−0.260789	+	0.965396i	$0.583983\pi$
$68$	4.45401	0.540128
$69$	−7.33175	−0.882639
$70$	8.62911	1.03138
$71$	−5.41974	−0.643204	−0.321602	−	0.946875i	$-0.604221\pi$
$71$	−5.41974	−0.643204	−0.321602	+	0.946875i	$0.604221\pi$
$72$	−1.89615	−0.223463
$73$	11.7345	1.37342	0.686708	−	0.726934i	$-0.259055\pi$
$73$	11.7345	1.37342	0.686708	+	0.726934i	$0.259055\pi$
$74$	−2.23124	−0.259376
$75$	−11.0558	−1.27662
$76$	−9.25993	−1.06219
$77$	−0.0365275	−0.00416269
$78$	−0.506527	−0.0573529
$79$	−10.8270	−1.21813	−0.609064	−	0.793121i	$-0.708455\pi$
$79$	−10.8270	−1.21813	−0.609064	+	0.793121i	$0.708455\pi$
$80$	10.1233	1.13181
$81$	1.00000	0.111111
$82$	5.26515	0.581438
$83$	4.73251	0.519461	0.259730	−	0.965681i	$-0.416366\pi$
$83$	4.73251	0.519461	0.259730	+	0.965681i	$0.416366\pi$
$84$	7.41228	0.808746
$85$	−10.2368	−1.11033
$86$	−4.13663	−0.446064
$87$	3.63092	0.389276
$88$	0.0162909	0.00173661
$89$	14.1868	1.50380	0.751901	−	0.659276i	$-0.229137\pi$
$89$	14.1868	1.50380	0.751901	+	0.659276i	$0.229137\pi$
$90$	2.02964	0.213943
$91$	4.25155	0.445684
$92$	−12.7824	−1.33266
$93$	4.47636	0.464177
$94$	5.40212	0.557187
$95$	21.2823	2.18352
$96$	−5.07199	−0.517658
$97$	−16.4976	−1.67508	−0.837538	−	0.546379i	$-0.816006\pi$
$97$	−16.4976	−1.67508	−0.837538	+	0.546379i	$0.816006\pi$
$98$	5.61013	0.566709
$99$	−0.00859157	−0.000863485 0
$100$	−19.2751	−1.92751
$101$	−13.0311	−1.29664	−0.648321	−	0.761367i	$-0.724529\pi$
$101$	−13.0311	−1.29664	−0.648321	+	0.761367i	$0.724529\pi$
$102$	1.29404	0.128129
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.89615	−0.185933
$105$	−17.0358	−1.66253
$106$	−4.29313	−0.416986
$107$	−10.2303	−0.989005	−0.494503	−	0.869176i	$-0.664650\pi$
$107$	−10.2303	−0.989005	−0.494503	+	0.869176i	$0.664650\pi$
$108$	1.74343	0.167762
$109$	−11.0315	−1.05662	−0.528312	−	0.849050i	$-0.677175\pi$
$109$	−11.0315	−1.05662	−0.528312	+	0.849050i	$0.677175\pi$
$110$	−0.0174378	−0.00166263
$111$	4.40497	0.418101
$112$	10.7412	1.01494
$113$	0.592472	0.0557350	0.0278675	−	0.999612i	$-0.491128\pi$
$113$	0.592472	0.0557350	0.0278675	+	0.999612i	$0.491128\pi$
$114$	−2.69033	−0.251972
$115$	29.3781	2.73952
$116$	6.33026	0.587750
$117$	1.00000	0.0924500
$118$	−4.71469	−0.434022
$119$	−10.8616	−0.995681
$120$	7.59781	0.693582
$121$	−10.9999	−0.999993
$122$	5.01484	0.454022
$123$	−10.3946	−0.937250
$124$	7.80423	0.700840
$125$	24.2655	2.17037
$126$	2.15352	0.191851
$127$	17.4613	1.54944	0.774722	−	0.632303i	$-0.217890\pi$
$127$	17.4613	1.54944	0.774722	+	0.632303i	$0.217890\pi$
$128$	−11.4021	−1.00781
$129$	8.16666	0.719034
$130$	2.02964	0.178011
$131$	−12.1714	−1.06342	−0.531712	−	0.846925i	$-0.678451\pi$
$131$	−12.1714	−1.06342	−0.531712	+	0.846925i	$0.678451\pi$
$132$	−0.0149788	−0.00130374
$133$	22.5814	1.95805
$134$	−2.16251	−0.186813
$135$	−4.00697	−0.344865
$136$	4.84416	0.415383
$137$	−1.60038	−0.136730	−0.0683649	−	0.997660i	$-0.521778\pi$
$137$	−1.60038	−0.136730	−0.0683649	+	0.997660i	$0.521778\pi$
$138$	−3.71373	−0.316134
$139$	12.6546	1.07335	0.536675	−	0.843789i	$-0.319680\pi$
$139$	12.6546	1.07335	0.536675	+	0.843789i	$0.319680\pi$
$140$	−29.7008	−2.51018
$141$	−10.6650	−0.898158
$142$	−2.74524	−0.230376
$143$	−0.00859157	−0.000718463 0
$144$	2.52641	0.210534
$145$	−14.5490	−1.20823
$146$	5.94382	0.491914
$147$	−11.0757	−0.913507
$148$	7.67976	0.631272
$149$	10.1161	0.828745	0.414372	−	0.910107i	$-0.364001\pi$
$149$	10.1161	0.828745	0.414372	+	0.910107i	$0.364001\pi$
$150$	−5.60007	−0.457244
$151$	4.99137	0.406192	0.203096	−	0.979159i	$-0.434900\pi$
$151$	4.99137	0.406192	0.203096	+	0.979159i	$0.434900\pi$
$152$	−10.0711	−0.816871
$153$	−2.55474	−0.206538
$154$	−0.0185022	−0.00149095
$155$	−17.9367	−1.44071
$156$	1.74343	0.139586
$157$	−5.97346	−0.476734	−0.238367	−	0.971175i	$-0.576612\pi$
$157$	−5.97346	−0.476734	−0.238367	+	0.971175i	$0.576612\pi$
$158$	−5.48414	−0.436295
$159$	8.47563	0.672161
$160$	20.3233	1.60670
$161$	31.1713	2.45664
$162$	0.506527	0.0397965
$163$	−3.22756	−0.252802	−0.126401	−	0.991979i	$-0.540343\pi$
$163$	−3.22756	−0.252802	−0.126401	+	0.991979i	$0.540343\pi$
$164$	−18.1223	−1.41511
$165$	0.0344262	0.00268007
$166$	2.39714	0.186055
$167$	9.12586	0.706180	0.353090	−	0.935589i	$-0.385131\pi$
$167$	9.12586	0.706180	0.353090	+	0.935589i	$0.385131\pi$
$168$	8.06157	0.621964
$169$	1.00000	0.0769231
$170$	−5.18519	−0.397686
$171$	5.31133	0.406167
$172$	14.2380	1.08564
$173$	3.89271	0.295957	0.147979	−	0.988991i	$-0.452723\pi$
$173$	3.89271	0.295957	0.147979	+	0.988991i	$0.452723\pi$
$174$	1.83916	0.139426
$175$	47.0044	3.55320
$176$	−0.0217058	−0.00163614
$177$	9.30787	0.699623
$178$	7.18601	0.538614
$179$	15.1591	1.13305	0.566524	−	0.824045i	$-0.308288\pi$
$179$	15.1591	1.13305	0.566524	+	0.824045i	$0.308288\pi$
$180$	−6.98588	−0.520697
$181$	−17.0656	−1.26848	−0.634239	−	0.773137i	$-0.718687\pi$
$181$	−17.0656	−1.26848	−0.634239	+	0.773137i	$0.718687\pi$
$182$	2.15352	0.159630
$183$	−9.90044	−0.731861
$184$	−13.9021	−1.02488
$185$	−17.6506	−1.29770
$186$	2.26740	0.166254
$187$	0.0219492	0.00160508
$188$	−18.5937	−1.35609
$189$	−4.25155	−0.309255
$190$	10.7801	0.782069
$191$	−19.9820	−1.44585	−0.722925	−	0.690926i	$-0.757203\pi$
$191$	−19.9820	−1.44585	−0.722925	+	0.690926i	$0.757203\pi$
$192$	2.48372	0.179247
$193$	20.8721	1.50241	0.751203	−	0.660071i	$-0.229474\pi$
$193$	20.8721	1.50241	0.751203	+	0.660071i	$0.229474\pi$
$194$	−8.35647	−0.599960
$195$	−4.00697	−0.286945
$196$	−19.3097	−1.37926
$197$	−6.55617	−0.467108	−0.233554	−	0.972344i	$-0.575036\pi$
$197$	−6.55617	−0.467108	−0.233554	+	0.972344i	$0.575036\pi$
$198$	−0.00435186	−0.000309273 0
$199$	6.22649	0.441384	0.220692	−	0.975344i	$-0.429168\pi$
$199$	6.22649	0.441384	0.220692	+	0.975344i	$0.429168\pi$
$200$	−20.9635	−1.48234
$201$	4.26929	0.301133
$202$	−6.60060	−0.464416
$203$	−15.4370	−1.08347
$204$	−4.45401	−0.311843
$205$	41.6509	2.90903
$206$	−0.506527	−0.0352914
$207$	7.33175	0.509592
$208$	2.52641	0.175175
$209$	−0.0456326	−0.00315647
$210$	−8.62911	−0.595465
$211$	−8.28439	−0.570321	−0.285160	−	0.958480i	$-0.592047\pi$
$211$	−8.28439	−0.570321	−0.285160	+	0.958480i	$0.592047\pi$
$212$	14.7767	1.01487
$213$	5.41974	0.371354
$214$	−5.18195	−0.354231
$215$	−32.7236	−2.23173
$216$	1.89615	0.129017
$217$	−19.0315	−1.29194
$218$	−5.58774	−0.378450
$219$	−11.7345	−0.792942
$220$	0.0600196	0.00404652
$221$	−2.55474	−0.171850
$222$	2.23124	0.149751
$223$	26.0408	1.74382	0.871910	−	0.489666i	$-0.162881\pi$
$223$	26.0408	1.74382	0.871910	+	0.489666i	$0.162881\pi$
$224$	21.5638	1.44079
$225$	11.0558	0.737055
$226$	0.300103	0.0199625
$227$	−5.19680	−0.344924	−0.172462	−	0.985016i	$-0.555172\pi$
$227$	−5.19680	−0.344924	−0.172462	+	0.985016i	$0.555172\pi$
$228$	9.25993	0.613254
$229$	17.8295	1.17821	0.589104	−	0.808057i	$-0.299481\pi$
$229$	17.8295	1.17821	0.589104	+	0.808057i	$0.299481\pi$
$230$	14.8808	0.981212
$231$	0.0365275	0.00240333
$232$	6.88476	0.452007
$233$	16.5553	1.08457	0.542285	−	0.840194i	$-0.317559\pi$
$233$	16.5553	1.08457	0.542285	+	0.840194i	$0.317559\pi$
$234$	0.506527	0.0331127
$235$	42.7345	2.78769
$236$	16.2276	1.05633
$237$	10.8270	0.703286
$238$	−5.50169	−0.356622
$239$	18.2439	1.18010	0.590050	−	0.807367i	$-0.299108\pi$
$239$	18.2439	1.18010	0.590050	+	0.807367i	$0.299108\pi$
$240$	−10.1233	−0.653454
$241$	17.4518	1.12417	0.562083	−	0.827081i	$-0.310000\pi$
$241$	17.4518	1.12417	0.562083	+	0.827081i	$0.310000\pi$
$242$	−5.57176	−0.358166
$243$	−1.00000	−0.0641500
$244$	−17.2607	−1.10500
$245$	44.3800	2.83533
$246$	−5.26515	−0.335694
$247$	5.31133	0.337952
$248$	8.48785	0.538979
$249$	−4.73251	−0.299911
$250$	12.2911	0.777359
$251$	24.8925	1.57120	0.785600	−	0.618735i	$-0.212355\pi$
$251$	24.8925	1.57120	0.785600	+	0.618735i	$0.212355\pi$
$252$	−7.41228	−0.466930
$253$	−0.0629912	−0.00396023
$254$	8.84464	0.554962
$255$	10.2368	0.641051
$256$	−0.808001	−0.0505000
$257$	−17.5455	−1.09446	−0.547229	−	0.836983i	$-0.684317\pi$
$257$	−17.5455	−1.09446	−0.547229	+	0.836983i	$0.684317\pi$
$258$	4.13663	0.257535
$259$	−18.7280	−1.16370
$260$	−6.98588	−0.433246
$261$	−3.63092	−0.224748
$262$	−6.16516	−0.380885
$263$	22.6846	1.39879	0.699397	−	0.714733i	$-0.253452\pi$
$263$	22.6846	1.39879	0.699397	+	0.714733i	$0.253452\pi$
$264$	−0.0162909	−0.00100263
$265$	−33.9616	−2.08624
$266$	11.4381	0.701313
$267$	−14.1868	−0.868220
$268$	7.44322	0.454667
$269$	6.79797	0.414480	0.207240	−	0.978290i	$-0.433552\pi$
$269$	6.79797	0.414480	0.207240	+	0.978290i	$0.433552\pi$
$270$	−2.02964	−0.123520
$271$	13.1078	0.796240	0.398120	−	0.917333i	$-0.369663\pi$
$271$	13.1078	0.796240	0.398120	+	0.917333i	$0.369663\pi$
$272$	−6.45432	−0.391350
$273$	−4.25155	−0.257316
$274$	−0.810636	−0.0489723
$275$	−0.0949868	−0.00572792
$276$	12.7824	0.769410
$277$	−20.3224	−1.22105	−0.610526	−	0.791996i	$-0.709042\pi$
$277$	−20.3224	−1.22105	−0.610526	+	0.791996i	$0.709042\pi$
$278$	6.40990	0.384440
$279$	−4.47636	−0.267993
$280$	−32.3025	−1.93044
$281$	−11.1509	−0.665210	−0.332605	−	0.943066i	$-0.607928\pi$
$281$	−11.1509	−0.665210	−0.332605	+	0.943066i	$0.607928\pi$
$282$	−5.40212	−0.321692
$283$	−15.4541	−0.918652	−0.459326	−	0.888268i	$-0.651909\pi$
$283$	−15.4541	−0.918652	−0.459326	+	0.888268i	$0.651909\pi$
$284$	9.44893	0.560691
$285$	−21.2823	−1.26066
$286$	−0.00435186	−0.000257331 0
$287$	44.1932	2.60864
$288$	5.07199	0.298870
$289$	−10.4733	−0.616078
$290$	−7.36946	−0.432749
$291$	16.4976	0.967106
$292$	−20.4582	−1.19723
$293$	13.0203	0.760655	0.380327	−	0.924852i	$-0.375811\pi$
$293$	13.0203	0.760655	0.380327	+	0.924852i	$0.375811\pi$
$294$	−5.61013	−0.327190
$295$	−37.2964	−2.17148
$296$	8.35248	0.485478
$297$	0.00859157	0.000498533 0
$298$	5.12409	0.296830
$299$	7.33175	0.424006
$300$	19.2751	1.11285
$301$	−34.7210	−2.00128
$302$	2.52826	0.145485
$303$	13.0311	0.748617
$304$	13.4186	0.769609
$305$	39.6708	2.27154
$306$	−1.29404	−0.0739755
$307$	1.46207	0.0834446	0.0417223	−	0.999129i	$-0.486716\pi$
$307$	1.46207	0.0834446	0.0417223	+	0.999129i	$0.486716\pi$
$308$	0.0636831	0.00362868
$309$	1.00000	0.0568880
$310$	−9.08540	−0.516016
$311$	0.0221015	0.00125326	0.000626630	−	1.00000i	$-0.499801\pi$
$311$	0.0221015	0.00125326	0.000626630		1.00000i	$0.499801\pi$
$312$	1.89615	0.107348
$313$	14.6248	0.826641	0.413320	−	0.910586i	$-0.364369\pi$
$313$	14.6248	0.826641	0.413320	+	0.910586i	$0.364369\pi$
$314$	−3.02572	−0.170751
$315$	17.0358	0.959861
$316$	18.8760	1.06186
$317$	−7.50750	−0.421663	−0.210832	−	0.977522i	$-0.567617\pi$
$317$	−7.50750	−0.421663	−0.210832	+	0.977522i	$0.567617\pi$
$318$	4.29313	0.240747
$319$	0.0311953	0.00174660
$320$	−9.95221	−0.556345
$321$	10.2303	0.571002
$322$	15.7891	0.879893
$323$	−13.5690	−0.755002
$324$	−1.74343	−0.0968573
$325$	11.0558	0.613267
$326$	−1.63485	−0.0905458
$327$	11.0315	0.610042
$328$	−19.7097	−1.08829
$329$	45.3429	2.49984
$330$	0.0174378	0.000959918 0
$331$	−25.3692	−1.39442	−0.697209	−	0.716868i	$-0.745575\pi$
$331$	−25.3692	−1.39442	−0.697209	+	0.716868i	$0.745575\pi$
$332$	−8.25081	−0.452822
$333$	−4.40497	−0.241391
$334$	4.62249	0.252932
$335$	−17.1069	−0.934652
$336$	−10.7412	−0.585979
$337$	3.07697	0.167613	0.0838065	−	0.996482i	$-0.473292\pi$
$337$	3.07697	0.167613	0.0838065	+	0.996482i	$0.473292\pi$
$338$	0.506527	0.0275514
$339$	−0.592472	−0.0321786
$340$	17.8471	0.967894
$341$	0.0384590	0.00208267
$342$	2.69033	0.145476
$343$	17.3280	0.935623
$344$	15.4852	0.834905
$345$	−29.3781	−1.58167
$346$	1.97176	0.106003
$347$	−12.1451	−0.651982	−0.325991	−	0.945373i	$-0.605698\pi$
$347$	−12.1451	−0.651982	−0.325991	+	0.945373i	$0.605698\pi$
$348$	−6.33026	−0.339337
$349$	−18.1385	−0.970930	−0.485465	−	0.874256i	$-0.661350\pi$
$349$	−18.1385	−0.970930	−0.485465	+	0.874256i	$0.661350\pi$
$350$	23.8090	1.27264
$351$	−1.00000	−0.0533761
$352$	−0.0435763	−0.00232263
$353$	13.6578	0.726931	0.363465	−	0.931608i	$-0.381594\pi$
$353$	13.6578	0.726931	0.363465	+	0.931608i	$0.381594\pi$
$354$	4.71469	0.250583
$355$	−21.7167	−1.15260
$356$	−24.7338	−1.31089
$357$	10.8616	0.574857
$358$	7.67852	0.405822
$359$	18.9649	1.00093	0.500466	−	0.865756i	$-0.333162\pi$
$359$	18.9649	1.00093	0.500466	+	0.865756i	$0.333162\pi$
$360$	−7.59781	−0.400440
$361$	9.21020	0.484747
$362$	−8.64420	−0.454329
$363$	10.9999	0.577346
$364$	−7.41228	−0.388509
$365$	47.0197	2.46112
$366$	−5.01484	−0.262130
$367$	20.2870	1.05897	0.529486	−	0.848319i	$-0.322385\pi$
$367$	20.2870	1.05897	0.529486	+	0.848319i	$0.322385\pi$
$368$	18.5230	0.965579
$369$	10.3946	0.541122
$370$	−8.94050	−0.464794
$371$	−36.0346	−1.87082
$372$	−7.80423	−0.404630
$373$	−1.32244	−0.0684732	−0.0342366	−	0.999414i	$-0.510900\pi$
$373$	−1.32244	−0.0684732	−0.0342366	+	0.999414i	$0.510900\pi$
$374$	0.0111179	0.000574891 0
$375$	−24.2655	−1.25307
$376$	−20.2225	−1.04289
$377$	−3.63092	−0.187002
$378$	−2.15352	−0.110765
$379$	9.02528	0.463598	0.231799	−	0.972764i	$-0.425539\pi$
$379$	9.02528	0.463598	0.231799	+	0.972764i	$0.425539\pi$
$380$	−37.1043	−1.90341
$381$	−17.4613	−0.894571
$382$	−10.1214	−0.517858
$383$	−22.3456	−1.14181	−0.570903	−	0.821018i	$-0.693407\pi$
$383$	−22.3456	−1.14181	−0.570903	+	0.821018i	$0.693407\pi$
$384$	11.4021	0.581859
$385$	−0.146365	−0.00745943
$386$	10.5723	0.538115
$387$	−8.16666	−0.415134
$388$	28.7624	1.46019
$389$	18.9373	0.960159	0.480080	−	0.877225i	$-0.340608\pi$
$389$	18.9373	0.960159	0.480080	+	0.877225i	$0.340608\pi$
$390$	−2.02964	−0.102775
$391$	−18.7307	−0.947252
$392$	−21.0011	−1.06072
$393$	12.1714	0.613968
$394$	−3.32088	−0.167303
$395$	−43.3833	−2.18285
$396$	0.0149788	0.000752713 0
$397$	−27.9231	−1.40142	−0.700711	−	0.713445i	$-0.747134\pi$
$397$	−27.9231	−1.40142	−0.700711	+	0.713445i	$0.747134\pi$
$398$	3.15388	0.158090
$399$	−22.5814	−1.13048
$400$	27.9316	1.39658
$401$	−29.3659	−1.46646	−0.733232	−	0.679978i	$-0.761989\pi$
$401$	−29.3659	−1.46646	−0.733232	+	0.679978i	$0.761989\pi$
$402$	2.16251	0.107856
$403$	−4.47636	−0.222983
$404$	22.7188	1.13030
$405$	4.00697	0.199108
$406$	−7.81928	−0.388064
$407$	0.0378456	0.00187594
$408$	−4.84416	−0.239822
$409$	−16.0837	−0.795288	−0.397644	−	0.917540i	$-0.630172\pi$
$409$	−16.0837	−0.795288	−0.397644	+	0.917540i	$0.630172\pi$
$410$	21.0973	1.04192
$411$	1.60038	0.0789410
$412$	1.74343	0.0858927
$413$	−39.5729	−1.94726
$414$	3.71373	0.182520
$415$	18.9630	0.930859
$416$	5.07199	0.248675
$417$	−12.6546	−0.619699
$418$	−0.0231141	−0.00113055
$419$	31.8611	1.55652	0.778259	−	0.627943i	$-0.216103\pi$
$419$	31.8611	1.55652	0.778259	+	0.627943i	$0.216103\pi$
$420$	29.7008	1.44925
$421$	−8.15980	−0.397684	−0.198842	−	0.980032i	$-0.563718\pi$
$421$	−8.15980	−0.397684	−0.198842	+	0.980032i	$0.563718\pi$
$422$	−4.19626	−0.204271
$423$	10.6650	0.518552
$424$	16.0710	0.780479
$425$	−28.2447	−1.37007
$426$	2.74524	0.133007
$427$	42.0922	2.03698
$428$	17.8359	0.862131
$429$	0.00859157	0.000414805 0
$430$	−16.5754	−0.799335
$431$	10.3519	0.498632	0.249316	−	0.968422i	$-0.419794\pi$
$431$	10.3519	0.498632	0.249316	+	0.968422i	$0.419794\pi$
$432$	−2.52641	−0.121552
$433$	−30.4781	−1.46469	−0.732343	−	0.680936i	$-0.761573\pi$
$433$	−30.4781	−1.46469	−0.732343	+	0.680936i	$0.761573\pi$
$434$	−9.63996	−0.462733
$435$	14.5490	0.697571
$436$	19.2326	0.921075
$437$	38.9413	1.86282
$438$	−5.94382	−0.284007
$439$	23.1848	1.10655	0.553274	−	0.832999i	$-0.313378\pi$
$439$	23.1848	1.10655	0.553274	+	0.832999i	$0.313378\pi$
$440$	0.0652771	0.00311196
$441$	11.0757	0.527414
$442$	−1.29404	−0.0615513
$443$	−1.18205	−0.0561607	−0.0280804	−	0.999606i	$-0.508939\pi$
$443$	−1.18205	−0.0561607	−0.0280804	+	0.999606i	$0.508939\pi$
$444$	−7.67976	−0.364465
$445$	56.8462	2.69477
$446$	13.1904	0.624581
$447$	−10.1161	−0.478476
$448$	−10.5597	−0.498898
$449$	−19.6807	−0.928789	−0.464395	−	0.885628i	$-0.653728\pi$
$449$	−19.6807	−0.928789	−0.464395	+	0.885628i	$0.653728\pi$
$450$	5.60007	0.263990
$451$	−0.0893060	−0.00420525
$452$	−1.03293	−0.0485851
$453$	−4.99137	−0.234515
$454$	−2.63232	−0.123541
$455$	17.0358	0.798653
$456$	10.0711	0.471621
$457$	−33.0186	−1.54454	−0.772272	−	0.635292i	$-0.780880\pi$
$457$	−33.0186	−1.54454	−0.772272	+	0.635292i	$0.780880\pi$
$458$	9.03113	0.421997
$459$	2.55474	0.119245
$460$	−51.2187	−2.38809
$461$	−13.0434	−0.607493	−0.303747	−	0.952753i	$-0.598238\pi$
$461$	−13.0434	−0.607493	−0.303747	+	0.952753i	$0.598238\pi$
$462$	0.0185022	0.000860798 0
$463$	−20.3792	−0.947102	−0.473551	−	0.880766i	$-0.657028\pi$
$463$	−20.3792	−0.947102	−0.473551	+	0.880766i	$0.657028\pi$
$464$	−9.17320	−0.425855
$465$	17.9367	0.831793
$466$	8.38568	0.388459
$467$	5.87118	0.271686	0.135843	−	0.990730i	$-0.456626\pi$
$467$	5.87118	0.271686	0.135843	+	0.990730i	$0.456626\pi$
$468$	−1.74343	−0.0805901
$469$	−18.1511	−0.838141
$470$	21.6462	0.998463
$471$	5.97346	0.275243
$472$	17.6491	0.812366
$473$	0.0701644	0.00322616
$474$	5.48414	0.251895
$475$	58.7211	2.69431
$476$	18.9364	0.867950
$477$	−8.47563	−0.388072
$478$	9.24103	0.422675
$479$	21.3276	0.974484	0.487242	−	0.873267i	$-0.338003\pi$
$479$	21.3276	0.974484	0.487242	+	0.873267i	$0.338003\pi$
$480$	−20.3233	−0.927629
$481$	−4.40497	−0.200849
$482$	8.83979	0.402641
$483$	−31.1713	−1.41834
$484$	19.1776	0.871709
$485$	−66.1054	−3.00169
$486$	−0.506527	−0.0229765
$487$	30.8957	1.40002	0.700008	−	0.714135i	$-0.253180\pi$
$487$	30.8957	1.40002	0.700008	+	0.714135i	$0.253180\pi$
$488$	−18.7727	−0.849800
$489$	3.22756	0.145955
$490$	22.4796	1.01553
$491$	27.6350	1.24715	0.623576	−	0.781763i	$-0.285679\pi$
$491$	27.6350	1.24715	0.623576	+	0.781763i	$0.285679\pi$
$492$	18.1223	0.817015
$493$	9.27605	0.417772
$494$	2.69033	0.121044
$495$	−0.0344262	−0.00154734
$496$	−11.3091	−0.507795
$497$	−23.0423	−1.03359
$498$	−2.39714	−0.107419
$499$	−40.3219	−1.80506	−0.902528	−	0.430630i	$-0.858291\pi$
$499$	−40.3219	−1.80506	−0.902528	+	0.430630i	$0.858291\pi$
$500$	−42.3052	−1.89195
$501$	−9.12586	−0.407713
$502$	12.6087	0.562754
$503$	−6.57249	−0.293053	−0.146526	−	0.989207i	$-0.546809\pi$
$503$	−6.57249	−0.293053	−0.146526	+	0.989207i	$0.546809\pi$
$504$	−8.06157	−0.359091
$505$	−52.2152	−2.32355
$506$	−0.0319068	−0.00141843
$507$	−1.00000	−0.0444116
$508$	−30.4426	−1.35067
$509$	6.69358	0.296688	0.148344	−	0.988936i	$-0.452606\pi$
$509$	6.69358	0.296688	0.148344	+	0.988936i	$0.452606\pi$
$510$	5.18519	0.229604
$511$	49.8897	2.20699
$512$	22.3948	0.989721
$513$	−5.31133	−0.234501
$514$	−8.88727	−0.392001
$515$	−4.00697	−0.176568
$516$	−14.2380	−0.626793
$517$	−0.0916293	−0.00402985
$518$	−9.48621	−0.416800
$519$	−3.89271	−0.170871
$520$	−7.59781	−0.333186
$521$	39.7298	1.74060	0.870298	−	0.492526i	$-0.163926\pi$
$521$	39.7298	1.74060	0.870298	+	0.492526i	$0.163926\pi$
$522$	−1.83916	−0.0804978
$523$	30.0567	1.31429	0.657144	−	0.753765i	$-0.271765\pi$
$523$	30.0567	1.31429	0.657144	+	0.753765i	$0.271765\pi$
$524$	21.2201	0.927003
$525$	−47.0044	−2.05144
$526$	11.4904	0.501004
$527$	11.4359	0.498157
$528$	0.0217058	0.000944625 0
$529$	30.7546	1.33716
$530$	−17.2025	−0.747227
$531$	−9.30787	−0.403927
$532$	−39.3691	−1.70687
$533$	10.3946	0.450240
$534$	−7.18601	−0.310969
$535$	−40.9927	−1.77227
$536$	8.09521	0.349660
$537$	−15.1591	−0.654166
$538$	3.44335	0.148454
$539$	−0.0951575	−0.00409872
$540$	6.98588	0.300624
$541$	−2.54647	−0.109481	−0.0547406	−	0.998501i	$-0.517433\pi$
$541$	−2.54647	−0.109481	−0.0547406	+	0.998501i	$0.517433\pi$
$542$	6.63943	0.285188
$543$	17.0656	0.732357
$544$	−12.9576	−0.555553
$545$	−44.2028	−1.89344
$546$	−2.15352	−0.0921623
$547$	−31.6332	−1.35254	−0.676269	−	0.736655i	$-0.736404\pi$
$547$	−31.6332	−1.35254	−0.676269	+	0.736655i	$0.736404\pi$
$548$	2.79015	0.119189
$549$	9.90044	0.422540
$550$	−0.0481134	−0.00205156
$551$	−19.2850	−0.821569
$552$	13.9021	0.591712
$553$	−46.0314	−1.95745
$554$	−10.2938	−0.437343
$555$	17.6506	0.749226
$556$	−22.0624	−0.935656
$557$	−32.1107	−1.36058	−0.680288	−	0.732945i	$-0.738145\pi$
$557$	−32.1107	−1.36058	−0.680288	+	0.732945i	$0.738145\pi$
$558$	−2.26740	−0.0959866
$559$	−8.16666	−0.345413
$560$	43.0396	1.81875
$561$	−0.0219492	−0.000926696 0
$562$	−5.64825	−0.238257
$563$	−11.1913	−0.471656	−0.235828	−	0.971795i	$-0.575780\pi$
$563$	−11.1913	−0.471656	−0.235828	+	0.971795i	$0.575780\pi$
$564$	18.5937	0.782938
$565$	2.37402	0.0998756
$566$	−7.82792	−0.329032
$567$	4.25155	0.178548
$568$	10.2766	0.431197
$569$	−33.0632	−1.38608	−0.693041	−	0.720898i	$-0.743729\pi$
$569$	−33.0632	−1.38608	−0.693041	+	0.720898i	$0.743729\pi$
$570$	−10.7801	−0.451528
$571$	22.4153	0.938053	0.469026	−	0.883184i	$-0.344605\pi$
$571$	22.4153	0.938053	0.469026	+	0.883184i	$0.344605\pi$
$572$	0.0149788	0.000626295 0
$573$	19.9820	0.834762
$574$	22.3850	0.934334
$575$	81.0586	3.38038
$576$	−2.48372	−0.103488
$577$	−11.8411	−0.492952	−0.246476	−	0.969149i	$-0.579273\pi$
$577$	−11.8411	−0.492952	−0.246476	+	0.969149i	$0.579273\pi$
$578$	−5.30502	−0.220660
$579$	−20.8721	−0.867415
$580$	25.3652	1.05323
$581$	20.1205	0.834740
$582$	8.35647	0.346387
$583$	0.0728189	0.00301585
$584$	−22.2503	−0.920723
$585$	4.00697	0.165668
$586$	6.59514	0.272443
$587$	−8.59238	−0.354646	−0.177323	−	0.984153i	$-0.556744\pi$
$587$	−8.59238	−0.354646	−0.177323	+	0.984153i	$0.556744\pi$
$588$	19.3097	0.796318
$589$	−23.7754	−0.979649
$590$	−18.8916	−0.777756
$591$	6.55617	0.269685
$592$	−11.1288	−0.457390
$593$	−30.4558	−1.25067	−0.625335	−	0.780356i	$-0.715038\pi$
$593$	−30.4558	−1.25067	−0.625335	+	0.780356i	$0.715038\pi$
$594$	0.00435186	0.000178559 0
$595$	−43.5221	−1.78423
$596$	−17.6368	−0.722430
$597$	−6.22649	−0.254833
$598$	3.71373	0.151866
$599$	−2.70297	−0.110440	−0.0552202	−	0.998474i	$-0.517586\pi$
$599$	−2.70297	−0.110440	−0.0552202	+	0.998474i	$0.517586\pi$
$600$	20.9635	0.855830
$601$	−18.4778	−0.753726	−0.376863	−	0.926269i	$-0.622997\pi$
$601$	−18.4778	−0.753726	−0.376863	+	0.926269i	$0.622997\pi$
$602$	−17.5871	−0.716796
$603$	−4.26929	−0.173859
$604$	−8.70211	−0.354084
$605$	−44.0764	−1.79196
$606$	6.60060	0.268131
$607$	10.2233	0.414950	0.207475	−	0.978240i	$-0.433476\pi$
$607$	10.2233	0.414950	0.207475	+	0.978240i	$0.433476\pi$
$608$	26.9390	1.09252
$609$	15.4370	0.625541
$610$	20.0943	0.813595
$611$	10.6650	0.431461
$612$	4.45401	0.180043
$613$	−34.8904	−1.40921	−0.704604	−	0.709601i	$-0.748875\pi$
$613$	−34.8904	−1.40921	−0.704604	+	0.709601i	$0.748875\pi$
$614$	0.740577	0.0298872
$615$	−41.6509	−1.67953
$616$	0.0692615	0.00279063
$617$	−46.4525	−1.87011	−0.935053	−	0.354508i	$-0.884648\pi$
$617$	−46.4525	−1.87011	−0.935053	+	0.354508i	$0.884648\pi$
$618$	0.506527	0.0203755
$619$	−23.3126	−0.937012	−0.468506	−	0.883460i	$-0.655208\pi$
$619$	−23.3126	−0.937012	−0.468506	+	0.883460i	$0.655208\pi$
$620$	31.2713	1.25589
$621$	−7.33175	−0.294213
$622$	0.0111950	0.000448878 0
$623$	60.3160	2.41651
$624$	−2.52641	−0.101137
$625$	41.9521	1.67808
$626$	7.40784	0.296077
$627$	0.0456326	0.00182239
$628$	10.4143	0.415576
$629$	11.2535	0.448708
$630$	8.62911	0.343792
$631$	−41.3825	−1.64741	−0.823706	−	0.567017i	$-0.808097\pi$
$631$	−41.3825	−1.64741	−0.823706	+	0.567017i	$0.808097\pi$
$632$	20.5295	0.816620
$633$	8.28439	0.329275
$634$	−3.80275	−0.151027
$635$	69.9671	2.77656
$636$	−14.7767	−0.585933
$637$	11.0757	0.438835
$638$	0.0158013	0.000625578 0
$639$	−5.41974	−0.214401
$640$	−45.6877	−1.80597
$641$	−35.4437	−1.39994	−0.699971	−	0.714172i	$-0.746804\pi$
$641$	−35.4437	−1.39994	−0.699971	+	0.714172i	$0.746804\pi$
$642$	5.18195	0.204515
$643$	−26.7711	−1.05575	−0.527874	−	0.849323i	$-0.677011\pi$
$643$	−26.7711	−1.05575	−0.527874	+	0.849323i	$0.677011\pi$
$644$	−54.3450	−2.14149
$645$	32.7236	1.28849
$646$	−6.87309	−0.270418
$647$	13.2253	0.519939	0.259970	−	0.965617i	$-0.416287\pi$
$647$	13.2253	0.519939	0.259970	+	0.965617i	$0.416287\pi$
$648$	−1.89615	−0.0744877
$649$	0.0799692	0.00313907
$650$	5.60007	0.219653
$651$	19.0315	0.745903
$652$	5.62703	0.220372
$653$	−6.90906	−0.270372	−0.135186	−	0.990820i	$-0.543163\pi$
$653$	−6.90906	−0.270372	−0.135186	+	0.990820i	$0.543163\pi$
$654$	5.58774	0.218498
$655$	−48.7706	−1.90563
$656$	26.2611	1.02532
$657$	11.7345	0.457805
$658$	22.9674	0.895363
$659$	6.31810	0.246118	0.123059	−	0.992399i	$-0.460730\pi$
$659$	6.31810	0.246118	0.123059	+	0.992399i	$0.460730\pi$
$660$	−0.0600196	−0.00233626
$661$	−41.4314	−1.61149	−0.805747	−	0.592260i	$-0.798236\pi$
$661$	−41.4314	−1.61149	−0.805747	+	0.592260i	$0.798236\pi$
$662$	−12.8502	−0.499436
$663$	2.55474	0.0992178
$664$	−8.97355	−0.348241
$665$	90.4829	3.50878
$666$	−2.23124	−0.0864586
$667$	−26.6210	−1.03077
$668$	−15.9103	−0.615588
$669$	−26.0408	−1.00679
$670$	−8.66512	−0.334763
$671$	−0.0850603	−0.00328371
$672$	−21.5638	−0.831843
$673$	12.1167	0.467064	0.233532	−	0.972349i	$-0.424972\pi$
$673$	12.1167	0.467064	0.233532	+	0.972349i	$0.424972\pi$
$674$	1.55857	0.0600337
$675$	−11.0558	−0.425539
$676$	−1.74343	−0.0670550
$677$	−7.07689	−0.271987	−0.135994	−	0.990710i	$-0.543423\pi$
$677$	−7.07689	−0.271987	−0.135994	+	0.990710i	$0.543423\pi$
$678$	−0.300103	−0.0115254
$679$	−70.1403	−2.69174
$680$	19.4104	0.744355
$681$	5.19680	0.199142
$682$	0.0194805	0.000745947 0
$683$	−4.37044	−0.167230	−0.0836151	−	0.996498i	$-0.526647\pi$
$683$	−4.37044	−0.167230	−0.0836151	+	0.996498i	$0.526647\pi$
$684$	−9.25993	−0.354062
$685$	−6.41268	−0.245016
$686$	8.77709	0.335111
$687$	−17.8295	−0.680239
$688$	−20.6323	−0.786600
$689$	−8.47563	−0.322896
$690$	−14.8808	−0.566503
$691$	5.57841	0.212213	0.106106	−	0.994355i	$-0.466162\pi$
$691$	5.57841	0.212213	0.106106	+	0.994355i	$0.466162\pi$
$692$	−6.78667	−0.257991
$693$	−0.0365275	−0.00138756
$694$	−6.15181	−0.233519
$695$	50.7067	1.92341
$696$	−6.88476	−0.260966
$697$	−26.5555	−1.00586
$698$	−9.18762	−0.347757
$699$	−16.5553	−0.626177
$700$	−81.9489	−3.09738
$701$	−39.9798	−1.51001	−0.755007	−	0.655716i	$-0.772367\pi$
$701$	−39.9798	−1.51001	−0.755007	+	0.655716i	$0.772367\pi$
$702$	−0.506527	−0.0191176
$703$	−23.3962	−0.882406
$704$	0.0213391	0.000804247 0
$705$	−42.7345	−1.60947
$706$	6.91804	0.260364
$707$	−55.4023	−2.08362
$708$	−16.2276	−0.609872
$709$	−1.08728	−0.0408335	−0.0204168	−	0.999792i	$-0.506499\pi$
$709$	−1.08728	−0.0408335	−0.0204168	+	0.999792i	$0.506499\pi$
$710$	−11.0001	−0.412827
$711$	−10.8270	−0.406043
$712$	−26.9003	−1.00813
$713$	−32.8196	−1.22910
$714$	5.50169	0.205896
$715$	−0.0344262	−0.00128747
$716$	−26.4289	−0.987695
$717$	−18.2439	−0.681331
$718$	9.60625	0.358502
$719$	13.0425	0.486403	0.243201	−	0.969976i	$-0.421802\pi$
$719$	13.0425	0.486403	0.243201	+	0.969976i	$0.421802\pi$
$720$	10.1233	0.377272
$721$	−4.25155	−0.158336
$722$	4.66521	0.173621
$723$	−17.4518	−0.649038
$724$	29.7528	1.10575
$725$	−40.1428	−1.49087
$726$	5.57176	0.206787
$727$	−29.6388	−1.09924	−0.549621	−	0.835414i	$-0.685228\pi$
$727$	−29.6388	−1.09924	−0.549621	+	0.835414i	$0.685228\pi$
$728$	−8.06157	−0.298782
$729$	1.00000	0.0370370
$730$	23.8167	0.881497
$731$	20.8637	0.771670
$732$	17.2607	0.637975
$733$	−8.36554	−0.308988	−0.154494	−	0.987994i	$-0.549375\pi$
$733$	−8.36554	−0.308988	−0.154494	+	0.987994i	$0.549375\pi$
$734$	10.2759	0.379290
$735$	−44.3800	−1.63698
$736$	37.1866	1.37072
$737$	0.0366799	0.00135112
$738$	5.26515	0.193813
$739$	29.3976	1.08141	0.540704	−	0.841213i	$-0.318158\pi$
$739$	29.3976	1.08141	0.540704	+	0.841213i	$0.318158\pi$
$740$	30.7726	1.13122
$741$	−5.31133	−0.195116
$742$	−18.2525	−0.670069
$743$	−40.6657	−1.49188	−0.745940	−	0.666013i	$-0.768000\pi$
$743$	−40.6657	−1.49188	−0.745940	+	0.666013i	$0.768000\pi$
$744$	−8.48785	−0.311180
$745$	40.5350	1.48509
$746$	−0.669850	−0.0245249
$747$	4.73251	0.173154
$748$	−0.0382669	−0.00139918
$749$	−43.4948	−1.58927
$750$	−12.2911	−0.448809
$751$	−5.13585	−0.187410	−0.0937049	−	0.995600i	$-0.529871\pi$
$751$	−5.13585	−0.187410	−0.0937049	+	0.995600i	$0.529871\pi$
$752$	26.9443	0.982556
$753$	−24.8925	−0.907132
$754$	−1.83916	−0.0669782
$755$	20.0003	0.727885
$756$	7.41228	0.269582
$757$	−18.1990	−0.661453	−0.330727	−	0.943727i	$-0.607294\pi$
$757$	−18.1990	−0.661453	−0.330727	+	0.943727i	$0.607294\pi$
$758$	4.57155	0.166046
$759$	0.0629912	0.00228644
$760$	−40.3545	−1.46381
$761$	3.50791	0.127162	0.0635808	−	0.997977i	$-0.479748\pi$
$761$	3.50791	0.127162	0.0635808	+	0.997977i	$0.479748\pi$
$762$	−8.84464	−0.320407
$763$	−46.9009	−1.69793
$764$	34.8373	1.26037
$765$	−10.2368	−0.370111
$766$	−11.3186	−0.408959
$767$	−9.30787	−0.336088
$768$	0.808001	0.0291562
$769$	45.7620	1.65022	0.825111	−	0.564971i	$-0.191113\pi$
$769$	45.7620	1.65022	0.825111	+	0.564971i	$0.191113\pi$
$770$	−0.0741376	−0.00267173
$771$	17.5455	0.631886
$772$	−36.3890	−1.30967
$773$	48.5204	1.74516	0.872578	−	0.488474i	$-0.162446\pi$
$773$	48.5204	1.74516	0.872578	+	0.488474i	$0.162446\pi$
$774$	−4.13663	−0.148688
$775$	−49.4899	−1.77773
$776$	31.2819	1.12295
$777$	18.7280	0.671862
$778$	9.59225	0.343899
$779$	55.2092	1.97807
$780$	6.98588	0.250135
$781$	0.0465640	0.00166619
$782$	−9.48760	−0.339276
$783$	3.63092	0.129759
$784$	27.9817	0.999348
$785$	−23.9355	−0.854294
$786$	6.16516	0.219904
$787$	36.3138	1.29445	0.647223	−	0.762300i	$-0.275930\pi$
$787$	36.3138	1.29445	0.647223	+	0.762300i	$0.275930\pi$
$788$	11.4302	0.407185
$789$	−22.6846	−0.807594
$790$	−21.9748	−0.781829
$791$	2.51892	0.0895626
$792$	0.0162909	0.000578871 0
$793$	9.90044	0.351575
$794$	−14.1438	−0.501946
$795$	33.9616	1.20449
$796$	−10.8555	−0.384761
$797$	2.10868	0.0746933	0.0373467	−	0.999302i	$-0.488109\pi$
$797$	2.10868	0.0746933	0.0373467	+	0.999302i	$0.488109\pi$
$798$	−11.4381	−0.404903
$799$	−27.2464	−0.963907
$800$	56.0750	1.98255
$801$	14.1868	0.501267
$802$	−14.8746	−0.525242
$803$	−0.100817	−0.00355777
$804$	−7.44322	−0.262502
$805$	124.903	4.40224
$806$	−2.26740	−0.0798657
$807$	−6.79797	−0.239300
$808$	24.7089	0.869255
$809$	11.4830	0.403719	0.201860	−	0.979414i	$-0.435301\pi$
$809$	11.4830	0.403719	0.201860	+	0.979414i	$0.435301\pi$
$810$	2.02964	0.0713142
$811$	22.9272	0.805083	0.402542	−	0.915402i	$-0.368127\pi$
$811$	22.9272	0.805083	0.402542	+	0.915402i	$0.368127\pi$
$812$	26.9134	0.944476
$813$	−13.1078	−0.459709
$814$	0.0191698	0.000671901 0
$815$	−12.9328	−0.453015
$816$	6.45432	0.225946
$817$	−43.3758	−1.51753
$818$	−8.14682	−0.284847
$819$	4.25155	0.148561
$820$	−72.6155	−2.53584
$821$	4.37509	0.152692	0.0763459	−	0.997081i	$-0.475675\pi$
$821$	4.37509	0.152692	0.0763459	+	0.997081i	$0.475675\pi$
$822$	0.810636	0.0282742
$823$	16.2346	0.565903	0.282952	−	0.959134i	$-0.408686\pi$
$823$	16.2346	0.565903	0.282952	+	0.959134i	$0.408686\pi$
$824$	1.89615	0.0660554
$825$	0.0949868	0.00330702
$826$	−20.0447	−0.697446
$827$	43.5291	1.51366	0.756828	−	0.653614i	$-0.226748\pi$
$827$	43.5291	1.51366	0.756828	+	0.653614i	$0.226748\pi$
$828$	−12.7824	−0.444219
$829$	−25.1296	−0.872786	−0.436393	−	0.899756i	$-0.643744\pi$
$829$	−25.1296	−0.872786	−0.436393	+	0.899756i	$0.643744\pi$
$830$	9.60529	0.333405
$831$	20.3224	0.704975
$832$	−2.48372	−0.0861076
$833$	−28.2955	−0.980380
$834$	−6.40990	−0.221957
$835$	36.5671	1.26546
$836$	0.0795573	0.00275155
$837$	4.47636	0.154726
$838$	16.1385	0.557496
$839$	−16.4830	−0.569055	−0.284527	−	0.958668i	$-0.591837\pi$
$839$	−16.4830	−0.569055	−0.284527	+	0.958668i	$0.591837\pi$
$840$	32.3025	1.11454
$841$	−15.8164	−0.545394
$842$	−4.13316	−0.142438
$843$	11.1509	0.384059
$844$	14.4433	0.497157
$845$	4.00697	0.137844
$846$	5.40212	0.185729
$847$	−46.7667	−1.60692
$848$	−21.4129	−0.735323
$849$	15.4541	0.530384
$850$	−14.3067	−0.490716
$851$	−32.2962	−1.10710
$852$	−9.44893	−0.323715
$853$	9.71729	0.332714	0.166357	−	0.986066i	$-0.446800\pi$
$853$	9.71729	0.332714	0.166357	+	0.986066i	$0.446800\pi$
$854$	21.3208	0.729584
$855$	21.2823	0.727841
$856$	19.3983	0.663019
$857$	−9.02043	−0.308132	−0.154066	−	0.988061i	$-0.549237\pi$
$857$	−9.02043	−0.308132	−0.154066	+	0.988061i	$0.549237\pi$
$858$	0.00435186	0.000148570 0
$859$	−28.5445	−0.973927	−0.486964	−	0.873422i	$-0.661896\pi$
$859$	−28.5445	−0.973927	−0.486964	+	0.873422i	$0.661896\pi$
$860$	57.0513	1.94543
$861$	−44.1932	−1.50610
$862$	5.24350	0.178594
$863$	14.5119	0.493991	0.246995	−	0.969017i	$-0.420557\pi$
$863$	14.5119	0.493991	0.246995	+	0.969017i	$0.420557\pi$
$864$	−5.07199	−0.172553
$865$	15.5980	0.530348
$866$	−15.4380	−0.524604
$867$	10.4733	0.355693
$868$	33.1801	1.12620
$869$	0.0930205	0.00315551
$870$	7.36946	0.249848
$871$	−4.26929	−0.144659
$872$	20.9173	0.708350
$873$	−16.4976	−0.558359
$874$	19.7248	0.667202
$875$	103.166	3.48765
$876$	20.4582	0.691219
$877$	−20.7347	−0.700161	−0.350081	−	0.936720i	$-0.613846\pi$
$877$	−20.7347	−0.700161	−0.350081	+	0.936720i	$0.613846\pi$
$878$	11.7437	0.396331
$879$	−13.0203	−0.439164
$880$	−0.0869746	−0.00293191
$881$	12.5990	0.424471	0.212235	−	0.977219i	$-0.431926\pi$
$881$	12.5990	0.424471	0.212235	+	0.977219i	$0.431926\pi$
$882$	5.61013	0.188903
$883$	19.1594	0.644766	0.322383	−	0.946609i	$-0.395516\pi$
$883$	19.1594	0.644766	0.322383	+	0.946609i	$0.395516\pi$
$884$	4.45401	0.149804
$885$	37.2964	1.25370
$886$	−0.598738	−0.0201150
$887$	19.5244	0.655567	0.327783	−	0.944753i	$-0.393698\pi$
$887$	19.5244	0.655567	0.327783	+	0.944753i	$0.393698\pi$
$888$	−8.35248	−0.280291
$889$	74.2378	2.48985
$890$	28.7941	0.965182
$891$	−0.00859157	−0.000287828 0
$892$	−45.4003	−1.52011
$893$	56.6455	1.89557
$894$	−5.12409	−0.171375
$895$	60.7423	2.03039
$896$	−48.4764	−1.61948
$897$	−7.33175	−0.244800
$898$	−9.96880	−0.332663
$899$	16.2533	0.542078
$900$	−19.2751	−0.642502
$901$	21.6530	0.721366
$902$	−0.0452359	−0.00150619
$903$	34.7210	1.15544
$904$	−1.12341	−0.0373642
$905$	−68.3815	−2.27308
$906$	−2.52826	−0.0839959
$907$	24.8627	0.825552	0.412776	−	0.910833i	$-0.364559\pi$
$907$	24.8627	0.825552	0.412776	+	0.910833i	$0.364559\pi$
$908$	9.06026	0.300675
$909$	−13.0311	−0.432214
$910$	8.62911	0.286052
$911$	22.6448	0.750256	0.375128	−	0.926973i	$-0.377599\pi$
$911$	22.6448	0.750256	0.375128	+	0.926973i	$0.377599\pi$
$912$	−13.4186	−0.444334
$913$	−0.0406597	−0.00134564
$914$	−16.7248	−0.553207
$915$	−39.6708	−1.31148
$916$	−31.0845	−1.02706
$917$	−51.7475	−1.70885
$918$	1.29404	0.0427098
$919$	6.95440	0.229405	0.114702	−	0.993400i	$-0.463409\pi$
$919$	6.95440	0.229405	0.114702	+	0.993400i	$0.463409\pi$
$920$	−55.7053	−1.83655
$921$	−1.46207	−0.0481768
$922$	−6.60685	−0.217585
$923$	−5.41974	−0.178393
$924$	−0.0636831	−0.00209502
$925$	−48.7006	−1.60126
$926$	−10.3226	−0.339222
$927$	−1.00000	−0.0328443
$928$	−18.4160	−0.604535
$929$	−26.1620	−0.858348	−0.429174	−	0.903222i	$-0.641195\pi$
$929$	−26.1620	−0.858348	−0.429174	+	0.903222i	$0.641195\pi$
$930$	9.08540	0.297922
$931$	58.8266	1.92796
$932$	−28.8629	−0.945437
$933$	−0.0221015	−0.000723570 0
$934$	2.97391	0.0973093
$935$	0.0879498	0.00287627
$936$	−1.89615	−0.0619775
$937$	22.7288	0.742516	0.371258	−	0.928530i	$-0.378926\pi$
$937$	22.7288	0.742516	0.371258	+	0.928530i	$0.378926\pi$
$938$	−9.19403	−0.300196
$939$	−14.6248	−0.477261
$940$	−74.5046	−2.43007
$941$	52.5328	1.71252	0.856260	−	0.516545i	$-0.172782\pi$
$941$	52.5328	1.71252	0.856260	+	0.516545i	$0.172782\pi$
$942$	3.02572	0.0985832
$943$	76.2107	2.48176
$944$	−23.5155	−0.765365
$945$	−17.0358	−0.554176
$946$	0.0355401	0.00115551
$947$	41.9432	1.36297	0.681485	−	0.731832i	$-0.261334\pi$
$947$	41.9432	1.36297	0.681485	+	0.731832i	$0.261334\pi$
$948$	−18.8760	−0.613066
$949$	11.7345	0.380917
$950$	29.7438	0.965017
$951$	7.50750	0.243447
$952$	20.5952	0.667494
$953$	5.12231	0.165928	0.0829639	−	0.996553i	$-0.473561\pi$
$953$	5.12231	0.165928	0.0829639	+	0.996553i	$0.473561\pi$
$954$	−4.29313	−0.138995
$955$	−80.0675	−2.59092
$956$	−31.8070	−1.02871
$957$	−0.0311953	−0.00100840
$958$	10.8030	0.349030
$959$	−6.80410	−0.219716
$960$	9.95221	0.321206
$961$	−10.9622	−0.353619
$962$	−2.23124	−0.0719379
$963$	−10.2303	−0.329668
$964$	−30.4259	−0.979953
$965$	83.6339	2.69227
$966$	−15.7891	−0.508006
$967$	−36.6550	−1.17874	−0.589372	−	0.807861i	$-0.700625\pi$
$967$	−36.6550	−1.17874	−0.589372	+	0.807861i	$0.700625\pi$
$968$	20.8575	0.670385
$969$	13.5690	0.435901
$970$	−33.4841	−1.07511
$971$	−19.1260	−0.613784	−0.306892	−	0.951744i	$-0.599289\pi$
$971$	−19.1260	−0.613784	−0.306892	+	0.951744i	$0.599289\pi$
$972$	1.74343	0.0559206
$973$	53.8017	1.72480
$974$	15.6495	0.501442
$975$	−11.0558	−0.354070
$976$	25.0126	0.800633
$977$	−27.2464	−0.871690	−0.435845	−	0.900022i	$-0.643550\pi$
$977$	−27.2464	−0.871690	−0.435845	+	0.900022i	$0.643550\pi$
$978$	1.63485	0.0522767
$979$	−0.121887	−0.00389553
$980$	−77.3734	−2.47160
$981$	−11.0315	−0.352208
$982$	13.9979	0.446691
$983$	52.7288	1.68179	0.840893	−	0.541201i	$-0.182030\pi$
$983$	52.7288	1.68179	0.840893	+	0.541201i	$0.182030\pi$
$984$	19.7097	0.628323
$985$	−26.2704	−0.837045
$986$	4.69857	0.149633
$987$	−45.3429	−1.44328
$988$	−9.25993	−0.294598
$989$	−59.8759	−1.90394
$990$	−0.0174378	−0.000554209 0
$991$	−34.3420	−1.09091	−0.545455	−	0.838140i	$-0.683643\pi$
$991$	−34.3420	−1.09091	−0.545455	+	0.838140i	$0.683643\pi$
$992$	−22.7041	−0.720855
$993$	25.3692	0.805067
$994$	−11.6715	−0.370199
$995$	24.9494	0.790948
$996$	8.25081	0.261437
$997$	17.7242	0.561330	0.280665	−	0.959806i	$-0.409445\pi$
$997$	17.7242	0.561330	0.280665	+	0.959806i	$0.409445\pi$
$998$	−20.4241	−0.646515
$999$	4.40497	0.139367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.14	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.506527 q^{2} -1.00000 q^{3} -1.74343 q^{4} +4.00697 q^{5} -0.506527 q^{6} +4.25155 q^{7} -1.89615 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.506527 q^{2} -1.00000 q^{3} -1.74343 q^{4} +4.00697 q^{5} -0.506527 q^{6} +4.25155 q^{7} -1.89615 q^{8} +1.00000 q^{9} +2.02964 q^{10} -0.00859157 q^{11} +1.74343 q^{12} +1.00000 q^{13} +2.15352 q^{14} -4.00697 q^{15} +2.52641 q^{16} -2.55474 q^{17} +0.506527 q^{18} +5.31133 q^{19} -6.98588 q^{20} -4.25155 q^{21} -0.00435186 q^{22} +7.33175 q^{23} +1.89615 q^{24} +11.0558 q^{25} +0.506527 q^{26} -1.00000 q^{27} -7.41228 q^{28} -3.63092 q^{29} -2.02964 q^{30} -4.47636 q^{31} +5.07199 q^{32} +0.00859157 q^{33} -1.29404 q^{34} +17.0358 q^{35} -1.74343 q^{36} -4.40497 q^{37} +2.69033 q^{38} -1.00000 q^{39} -7.59781 q^{40} +10.3946 q^{41} -2.15352 q^{42} -8.16666 q^{43} +0.0149788 q^{44} +4.00697 q^{45} +3.71373 q^{46} +10.6650 q^{47} -2.52641 q^{48} +11.0757 q^{49} +5.60007 q^{50} +2.55474 q^{51} -1.74343 q^{52} -8.47563 q^{53} -0.506527 q^{54} -0.0344262 q^{55} -8.06157 q^{56} -5.31133 q^{57} -1.83916 q^{58} -9.30787 q^{59} +6.98588 q^{60} +9.90044 q^{61} -2.26740 q^{62} +4.25155 q^{63} -2.48372 q^{64} +4.00697 q^{65} +0.00435186 q^{66} -4.26929 q^{67} +4.45401 q^{68} -7.33175 q^{69} +8.62911 q^{70} -5.41974 q^{71} -1.89615 q^{72} +11.7345 q^{73} -2.23124 q^{74} -11.0558 q^{75} -9.25993 q^{76} -0.0365275 q^{77} -0.506527 q^{78} -10.8270 q^{79} +10.1233 q^{80} +1.00000 q^{81} +5.26515 q^{82} +4.73251 q^{83} +7.41228 q^{84} -10.2368 q^{85} -4.13663 q^{86} +3.63092 q^{87} +0.0162909 q^{88} +14.1868 q^{89} +2.02964 q^{90} +4.25155 q^{91} -12.7824 q^{92} +4.47636 q^{93} +5.40212 q^{94} +21.2823 q^{95} -5.07199 q^{96} -16.4976 q^{97} +5.61013 q^{98} -0.00859157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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