LMFDB - Embedded newform 8015.2.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84251 q^{2} -2.60277 q^{3} +1.39485 q^{4} +1.00000 q^{5} +4.79563 q^{6} -1.00000 q^{7} +1.11499 q^{8} +3.77440 q^{9} +O(q^{10})$	\(q-1.84251 q^{2} -2.60277 q^{3} +1.39485 q^{4} +1.00000 q^{5} +4.79563 q^{6} -1.00000 q^{7} +1.11499 q^{8} +3.77440 q^{9} -1.84251 q^{10} +0.844378 q^{11} -3.63048 q^{12} -1.42325 q^{13} +1.84251 q^{14} -2.60277 q^{15} -4.84409 q^{16} +7.61174 q^{17} -6.95438 q^{18} +1.63633 q^{19} +1.39485 q^{20} +2.60277 q^{21} -1.55578 q^{22} -1.16483 q^{23} -2.90207 q^{24} +1.00000 q^{25} +2.62235 q^{26} -2.01559 q^{27} -1.39485 q^{28} -6.76868 q^{29} +4.79563 q^{30} -2.35985 q^{31} +6.69531 q^{32} -2.19772 q^{33} -14.0247 q^{34} -1.00000 q^{35} +5.26473 q^{36} +4.45677 q^{37} -3.01496 q^{38} +3.70438 q^{39} +1.11499 q^{40} +6.01358 q^{41} -4.79563 q^{42} +3.51931 q^{43} +1.17778 q^{44} +3.77440 q^{45} +2.14622 q^{46} +1.85467 q^{47} +12.6080 q^{48} +1.00000 q^{49} -1.84251 q^{50} -19.8116 q^{51} -1.98522 q^{52} -7.96189 q^{53} +3.71374 q^{54} +0.844378 q^{55} -1.11499 q^{56} -4.25899 q^{57} +12.4714 q^{58} -6.05599 q^{59} -3.63048 q^{60} -9.90884 q^{61} +4.34805 q^{62} -3.77440 q^{63} -2.64802 q^{64} -1.42325 q^{65} +4.04933 q^{66} +7.22455 q^{67} +10.6172 q^{68} +3.03179 q^{69} +1.84251 q^{70} -9.54885 q^{71} +4.20843 q^{72} -9.31639 q^{73} -8.21165 q^{74} -2.60277 q^{75} +2.28244 q^{76} -0.844378 q^{77} -6.82538 q^{78} +13.4099 q^{79} -4.84409 q^{80} -6.07710 q^{81} -11.0801 q^{82} -0.441751 q^{83} +3.63048 q^{84} +7.61174 q^{85} -6.48438 q^{86} +17.6173 q^{87} +0.941475 q^{88} -10.3738 q^{89} -6.95438 q^{90} +1.42325 q^{91} -1.62477 q^{92} +6.14213 q^{93} -3.41725 q^{94} +1.63633 q^{95} -17.4263 q^{96} -18.0160 q^{97} -1.84251 q^{98} +3.18702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.84251	−1.30285	−0.651427	−	0.758712i	$-0.725829\pi$
$2$	−1.84251	−1.30285	−0.651427	+	0.758712i	$0.725829\pi$
$3$	−2.60277	−1.50271	−0.751354	−	0.659899i	$-0.770599\pi$
$3$	−2.60277	−1.50271	−0.751354	+	0.659899i	$0.770599\pi$
$4$	1.39485	0.697426
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.79563	1.95781
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.11499	0.394209
$9$	3.77440	1.25813
$10$	−1.84251	−0.582654
$11$	0.844378	0.254590	0.127295	−	0.991865i	$-0.459371\pi$
$11$	0.844378	0.254590	0.127295	+	0.991865i	$0.459371\pi$
$12$	−3.63048	−1.04803
$13$	−1.42325	−0.394738	−0.197369	−	0.980329i	$-0.563240\pi$
$13$	−1.42325	−0.394738	−0.197369	+	0.980329i	$0.563240\pi$
$14$	1.84251	0.492432
$15$	−2.60277	−0.672032
$16$	−4.84409	−1.21102
$17$	7.61174	1.84612	0.923058	−	0.384660i	$-0.125681\pi$
$17$	7.61174	1.84612	0.923058	+	0.384660i	$0.125681\pi$
$18$	−6.95438	−1.63916
$19$	1.63633	0.375400	0.187700	−	0.982226i	$-0.439897\pi$
$19$	1.63633	0.375400	0.187700	+	0.982226i	$0.439897\pi$
$20$	1.39485	0.311898
$21$	2.60277	0.567971
$22$	−1.55578	−0.331693
$23$	−1.16483	−0.242885	−0.121442	−	0.992598i	$-0.538752\pi$
$23$	−1.16483	−0.242885	−0.121442	+	0.992598i	$0.538752\pi$
$24$	−2.90207	−0.592382
$25$	1.00000	0.200000
$26$	2.62235	0.514286
$27$	−2.01559	−0.387900
$28$	−1.39485	−0.263602
$29$	−6.76868	−1.25691	−0.628457	−	0.777845i	$-0.716313\pi$
$29$	−6.76868	−1.25691	−0.628457	+	0.777845i	$0.716313\pi$
$30$	4.79563	0.875559
$31$	−2.35985	−0.423841	−0.211920	−	0.977287i	$-0.567972\pi$
$31$	−2.35985	−0.423841	−0.211920	+	0.977287i	$0.567972\pi$
$32$	6.69531	1.18358
$33$	−2.19772	−0.382574
$34$	−14.0247	−2.40522
$35$	−1.00000	−0.169031
$36$	5.26473	0.877455
$37$	4.45677	0.732688	0.366344	−	0.930479i	$-0.380609\pi$
$37$	4.45677	0.732688	0.366344	+	0.930479i	$0.380609\pi$
$38$	−3.01496	−0.489092
$39$	3.70438	0.593176
$40$	1.11499	0.176296
$41$	6.01358	0.939163	0.469581	−	0.882889i	$-0.344405\pi$
$41$	6.01358	0.939163	0.469581	+	0.882889i	$0.344405\pi$
$42$	−4.79563	−0.739982
$43$	3.51931	0.536690	0.268345	−	0.963323i	$-0.413523\pi$
$43$	3.51931	0.536690	0.268345	+	0.963323i	$0.413523\pi$
$44$	1.17778	0.177557
$45$	3.77440	0.562654
$46$	2.14622	0.316443
$47$	1.85467	0.270531	0.135266	−	0.990809i	$-0.456811\pi$
$47$	1.85467	0.270531	0.135266	+	0.990809i	$0.456811\pi$
$48$	12.6080	1.81981
$49$	1.00000	0.142857
$50$	−1.84251	−0.260571
$51$	−19.8116	−2.77418
$52$	−1.98522	−0.275301
$53$	−7.96189	−1.09365	−0.546825	−	0.837247i	$-0.684164\pi$
$53$	−7.96189	−1.09365	−0.546825	+	0.837247i	$0.684164\pi$
$54$	3.71374	0.505376
$55$	0.844378	0.113856
$56$	−1.11499	−0.148997
$57$	−4.25899	−0.564118
$58$	12.4714	1.63757
$59$	−6.05599	−0.788423	−0.394211	−	0.919020i	$-0.628982\pi$
$59$	−6.05599	−0.788423	−0.394211	+	0.919020i	$0.628982\pi$
$60$	−3.63048	−0.468692
$61$	−9.90884	−1.26870	−0.634348	−	0.773047i	$-0.718732\pi$
$61$	−9.90884	−1.26870	−0.634348	+	0.773047i	$0.718732\pi$
$62$	4.34805	0.552202
$63$	−3.77440	−0.475530
$64$	−2.64802	−0.331002
$65$	−1.42325	−0.176532
$66$	4.04933	0.498438
$67$	7.22455	0.882620	0.441310	−	0.897355i	$-0.354514\pi$
$67$	7.22455	0.882620	0.441310	+	0.897355i	$0.354514\pi$
$68$	10.6172	1.28753
$69$	3.03179	0.364985
$70$	1.84251	0.220222
$71$	−9.54885	−1.13324	−0.566620	−	0.823979i	$-0.691749\pi$
$71$	−9.54885	−1.13324	−0.566620	+	0.823979i	$0.691749\pi$
$72$	4.20843	0.495968
$73$	−9.31639	−1.09040	−0.545201	−	0.838306i	$-0.683547\pi$
$73$	−9.31639	−1.09040	−0.545201	+	0.838306i	$0.683547\pi$
$74$	−8.21165	−0.954585
$75$	−2.60277	−0.300542
$76$	2.28244	0.261814
$77$	−0.844378	−0.0962258
$78$	−6.82538	−0.772822
$79$	13.4099	1.50873	0.754363	−	0.656457i	$-0.227946\pi$
$79$	13.4099	1.50873	0.754363	+	0.656457i	$0.227946\pi$
$80$	−4.84409	−0.541586
$81$	−6.07710	−0.675234
$82$	−11.0801	−1.22359
$83$	−0.441751	−0.0484885	−0.0242442	−	0.999706i	$-0.507718\pi$
$83$	−0.441751	−0.0484885	−0.0242442	+	0.999706i	$0.507718\pi$
$84$	3.63048	0.396117
$85$	7.61174	0.825609
$86$	−6.48438	−0.699228
$87$	17.6173	1.88877
$88$	0.941475	0.100362
$89$	−10.3738	−1.09962	−0.549812	−	0.835288i	$-0.685301\pi$
$89$	−10.3738	−1.09962	−0.549812	+	0.835288i	$0.685301\pi$
$90$	−6.95438	−0.733056
$91$	1.42325	0.149197
$92$	−1.62477	−0.169394
$93$	6.14213	0.636909
$94$	−3.41725	−0.352462
$95$	1.63633	0.167884
$96$	−17.4263	−1.77857
$97$	−18.0160	−1.82925	−0.914626	−	0.404301i	$-0.867515\pi$
$97$	−18.0160	−1.82925	−0.914626	+	0.404301i	$0.867515\pi$
$98$	−1.84251	−0.186122
$99$	3.18702	0.320308
$100$	1.39485	0.139485
$101$	−11.8297	−1.17710	−0.588548	−	0.808462i	$-0.700300\pi$
$101$	−11.8297	−1.17710	−0.588548	+	0.808462i	$0.700300\pi$
$102$	36.5031	3.61434
$103$	16.6091	1.63655	0.818273	−	0.574830i	$-0.194932\pi$
$103$	16.6091	1.63655	0.818273	+	0.574830i	$0.194932\pi$
$104$	−1.58691	−0.155609
$105$	2.60277	0.254004
$106$	14.6699	1.42487
$107$	−7.14422	−0.690657	−0.345329	−	0.938482i	$-0.612233\pi$
$107$	−7.14422	−0.690657	−0.345329	+	0.938482i	$0.612233\pi$
$108$	−2.81144	−0.270531
$109$	5.41789	0.518940	0.259470	−	0.965751i	$-0.416452\pi$
$109$	5.41789	0.518940	0.259470	+	0.965751i	$0.416452\pi$
$110$	−1.55578	−0.148338
$111$	−11.5999	−1.10102
$112$	4.84409	0.457724
$113$	−9.26945	−0.871997	−0.435998	−	0.899947i	$-0.643605\pi$
$113$	−9.26945	−0.871997	−0.435998	+	0.899947i	$0.643605\pi$
$114$	7.84725	0.734962
$115$	−1.16483	−0.108621
$116$	−9.44131	−0.876604
$117$	−5.37191	−0.496633
$118$	11.1582	1.02720
$119$	−7.61174	−0.697767
$120$	−2.90207	−0.264921
$121$	−10.2870	−0.935184
$122$	18.2572	1.65293
$123$	−15.6519	−1.41129
$124$	−3.29164	−0.295598
$125$	1.00000	0.0894427
$126$	6.95438	0.619545
$127$	13.9570	1.23849	0.619243	−	0.785199i	$-0.287440\pi$
$127$	13.9570	1.23849	0.619243	+	0.785199i	$0.287440\pi$
$128$	−8.51163	−0.752328
$129$	−9.15995	−0.806489
$130$	2.62235	0.229996
$131$	8.48609	0.741433	0.370717	−	0.928746i	$-0.379112\pi$
$131$	8.48609	0.741433	0.370717	+	0.928746i	$0.379112\pi$
$132$	−3.06550	−0.266817
$133$	−1.63633	−0.141888
$134$	−13.3113	−1.14992
$135$	−2.01559	−0.173474
$136$	8.48703	0.727757
$137$	0.151443	0.0129386	0.00646932	−	0.999979i	$-0.497941\pi$
$137$	0.151443	0.0129386	0.00646932	+	0.999979i	$0.497941\pi$
$138$	−5.58611	−0.475522
$139$	6.84428	0.580524	0.290262	−	0.956947i	$-0.406257\pi$
$139$	6.84428	0.580524	0.290262	+	0.956947i	$0.406257\pi$
$140$	−1.39485	−0.117887
$141$	−4.82727	−0.406529
$142$	17.5939	1.47645
$143$	−1.20176	−0.100496
$144$	−18.2835	−1.52363
$145$	−6.76868	−0.562109
$146$	17.1656	1.42063
$147$	−2.60277	−0.214673
$148$	6.21654	0.510996
$149$	−6.03930	−0.494759	−0.247379	−	0.968919i	$-0.579569\pi$
$149$	−6.03930	−0.494759	−0.247379	+	0.968919i	$0.579569\pi$
$150$	4.79563	0.391562
$151$	−14.9604	−1.21746	−0.608731	−	0.793377i	$-0.708321\pi$
$151$	−14.9604	−1.21746	−0.608731	+	0.793377i	$0.708321\pi$
$152$	1.82450	0.147986
$153$	28.7297	2.32266
$154$	1.55578	0.125368
$155$	−2.35985	−0.189547
$156$	5.16707	0.413697
$157$	1.33097	0.106223	0.0531115	−	0.998589i	$-0.483086\pi$
$157$	1.33097	0.106223	0.0531115	+	0.998589i	$0.483086\pi$
$158$	−24.7078	−1.96565
$159$	20.7230	1.64344
$160$	6.69531	0.529311
$161$	1.16483	0.0918017
$162$	11.1971	0.879730
$163$	4.05886	0.317915	0.158957	−	0.987285i	$-0.449187\pi$
$163$	4.05886	0.317915	0.158957	+	0.987285i	$0.449187\pi$
$164$	8.38805	0.654997
$165$	−2.19772	−0.171092
$166$	0.813932	0.0631734
$167$	11.0544	0.855414	0.427707	−	0.903917i	$-0.359321\pi$
$167$	11.0544	0.855414	0.427707	+	0.903917i	$0.359321\pi$
$168$	2.90207	0.223899
$169$	−10.9744	−0.844182
$170$	−14.0247	−1.07565
$171$	6.17617	0.472304
$172$	4.90892	0.374302
$173$	10.7860	0.820041	0.410020	−	0.912076i	$-0.365522\pi$
$173$	10.7860	0.820041	0.410020	+	0.912076i	$0.365522\pi$
$174$	−32.4601	−2.46080
$175$	−1.00000	−0.0755929
$176$	−4.09025	−0.308314
$177$	15.7623	1.18477
$178$	19.1139	1.43265
$179$	4.28899	0.320574	0.160287	−	0.987070i	$-0.448758\pi$
$179$	4.28899	0.320574	0.160287	+	0.987070i	$0.448758\pi$
$180$	5.26473	0.392410
$181$	13.1150	0.974829	0.487414	−	0.873171i	$-0.337940\pi$
$181$	13.1150	0.974829	0.487414	+	0.873171i	$0.337940\pi$
$182$	−2.62235	−0.194382
$183$	25.7904	1.90648
$184$	−1.29878	−0.0957474
$185$	4.45677	0.327668
$186$	−11.3170	−0.829799
$187$	6.42718	0.470002
$188$	2.58699	0.188675
$189$	2.01559	0.146612
$190$	−3.01496	−0.218728
$191$	3.05561	0.221096	0.110548	−	0.993871i	$-0.464739\pi$
$191$	3.05561	0.221096	0.110548	+	0.993871i	$0.464739\pi$
$192$	6.89217	0.497400
$193$	8.51412	0.612860	0.306430	−	0.951893i	$-0.400865\pi$
$193$	8.51412	0.612860	0.306430	+	0.951893i	$0.400865\pi$
$194$	33.1948	2.38325
$195$	3.70438	0.265277
$196$	1.39485	0.0996323
$197$	−3.12132	−0.222385	−0.111192	−	0.993799i	$-0.535467\pi$
$197$	−3.12132	−0.222385	−0.111192	+	0.993799i	$0.535467\pi$
$198$	−5.87213	−0.417314
$199$	−27.5501	−1.95297	−0.976487	−	0.215576i	$-0.930837\pi$
$199$	−27.5501	−1.95297	−0.976487	+	0.215576i	$0.930837\pi$
$200$	1.11499	0.0788419
$201$	−18.8038	−1.32632
$202$	21.7963	1.53358
$203$	6.76868	0.475068
$204$	−27.6342	−1.93478
$205$	6.01358	0.420006
$206$	−30.6025	−2.13218
$207$	−4.39655	−0.305581
$208$	6.89435	0.478037
$209$	1.38168	0.0955731
$210$	−4.79563	−0.330930
$211$	2.08919	0.143826	0.0719130	−	0.997411i	$-0.477090\pi$
$211$	2.08919	0.143826	0.0719130	+	0.997411i	$0.477090\pi$
$212$	−11.1057	−0.762740
$213$	24.8534	1.70293
$214$	13.1633	0.899825
$215$	3.51931	0.240015
$216$	−2.24736	−0.152914
$217$	2.35985	0.160197
$218$	−9.98254	−0.676103
$219$	24.2484	1.63856
$220$	1.17778	0.0794061
$221$	−10.8334	−0.728733
$222$	21.3730	1.43446
$223$	−17.2927	−1.15800	−0.579001	−	0.815327i	$-0.696557\pi$
$223$	−17.2927	−1.15800	−0.579001	+	0.815327i	$0.696557\pi$
$224$	−6.69531	−0.447350
$225$	3.77440	0.251627
$226$	17.0791	1.13608
$227$	9.05965	0.601310	0.300655	−	0.953733i	$-0.402795\pi$
$227$	9.05965	0.601310	0.300655	+	0.953733i	$0.402795\pi$
$228$	−5.94067	−0.393430
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	2.14622	0.141518
$231$	2.19772	0.144599
$232$	−7.54703	−0.495487
$233$	1.93453	0.126735	0.0633676	−	0.997990i	$-0.479816\pi$
$233$	1.93453	0.126735	0.0633676	+	0.997990i	$0.479816\pi$
$234$	9.89781	0.647040
$235$	1.85467	0.120985
$236$	−8.44721	−0.549867
$237$	−34.9027	−2.26718
$238$	14.0247	0.909087
$239$	−22.0161	−1.42411	−0.712053	−	0.702126i	$-0.752234\pi$
$239$	−22.0161	−1.42411	−0.712053	+	0.702126i	$0.752234\pi$
$240$	12.6080	0.813846
$241$	−24.6202	−1.58593	−0.792963	−	0.609270i	$-0.791463\pi$
$241$	−24.6202	−1.58593	−0.792963	+	0.609270i	$0.791463\pi$
$242$	18.9540	1.21841
$243$	21.8640	1.40258
$244$	−13.8214	−0.884822
$245$	1.00000	0.0638877
$246$	28.8389	1.83870
$247$	−2.32891	−0.148185
$248$	−2.63121	−0.167082
$249$	1.14978	0.0728641
$250$	−1.84251	−0.116531
$251$	24.2543	1.53092	0.765459	−	0.643485i	$-0.222512\pi$
$251$	24.2543	1.53092	0.765459	+	0.643485i	$0.222512\pi$
$252$	−5.26473	−0.331647
$253$	−0.983560	−0.0618359
$254$	−25.7160	−1.61357
$255$	−19.8116	−1.24065
$256$	20.9788	1.31118
$257$	25.2225	1.57334	0.786668	−	0.617376i	$-0.211804\pi$
$257$	25.2225	1.57334	0.786668	+	0.617376i	$0.211804\pi$
$258$	16.8773	1.05074
$259$	−4.45677	−0.276930
$260$	−1.98522	−0.123118
$261$	−25.5477	−1.58136
$262$	−15.6357	−0.965978
$263$	16.0746	0.991201	0.495601	−	0.868551i	$-0.334948\pi$
$263$	16.0746	0.991201	0.495601	+	0.868551i	$0.334948\pi$
$264$	−2.45044	−0.150814
$265$	−7.96189	−0.489095
$266$	3.01496	0.184859
$267$	27.0007	1.65241
$268$	10.0772	0.615562
$269$	−2.20476	−0.134427	−0.0672133	−	0.997739i	$-0.521411\pi$
$269$	−2.20476	−0.134427	−0.0672133	+	0.997739i	$0.521411\pi$
$270$	3.71374	0.226011
$271$	−2.43509	−0.147921	−0.0739606	−	0.997261i	$-0.523564\pi$
$271$	−2.43509	−0.147921	−0.0739606	+	0.997261i	$0.523564\pi$
$272$	−36.8719	−2.23569
$273$	−3.70438	−0.224200
$274$	−0.279036	−0.0168572
$275$	0.844378	0.0509179
$276$	4.22890	0.254550
$277$	−2.36031	−0.141817	−0.0709087	−	0.997483i	$-0.522590\pi$
$277$	−2.36031	−0.141817	−0.0709087	+	0.997483i	$0.522590\pi$
$278$	−12.6107	−0.756338
$279$	−8.90700	−0.533248
$280$	−1.11499	−0.0666335
$281$	−20.0409	−1.19554	−0.597771	−	0.801667i	$-0.703947\pi$
$281$	−20.0409	−1.19554	−0.597771	+	0.801667i	$0.703947\pi$
$282$	8.89430	0.529648
$283$	29.1298	1.73159	0.865793	−	0.500403i	$-0.166815\pi$
$283$	29.1298	1.73159	0.865793	+	0.500403i	$0.166815\pi$
$284$	−13.3192	−0.790351
$285$	−4.25899	−0.252281
$286$	2.21426	0.130932
$287$	−6.01358	−0.354970
$288$	25.2708	1.48910
$289$	40.9385	2.40815
$290$	12.4714	0.732345
$291$	46.8916	2.74883
$292$	−12.9950	−0.760474
$293$	−8.32827	−0.486543	−0.243271	−	0.969958i	$-0.578221\pi$
$293$	−8.32827	−0.486543	−0.243271	+	0.969958i	$0.578221\pi$
$294$	4.79563	0.279687
$295$	−6.05599	−0.352593
$296$	4.96927	0.288833
$297$	−1.70192	−0.0987552
$298$	11.1275	0.644598
$299$	1.65785	0.0958758
$300$	−3.63048	−0.209606
$301$	−3.51931	−0.202850
$302$	27.5648	1.58617
$303$	30.7899	1.76883
$304$	−7.92655	−0.454619
$305$	−9.90884	−0.567378
$306$	−52.9349	−3.02609
$307$	−26.7979	−1.52944	−0.764718	−	0.644365i	$-0.777122\pi$
$307$	−26.7979	−1.52944	−0.764718	+	0.644365i	$0.777122\pi$
$308$	−1.17778	−0.0671104
$309$	−43.2297	−2.45925
$310$	4.34805	0.246952
$311$	32.0606	1.81799	0.908995	−	0.416806i	$-0.136851\pi$
$311$	32.0606	1.81799	0.908995	+	0.416806i	$0.136851\pi$
$312$	4.13036	0.233836
$313$	5.66479	0.320193	0.160096	−	0.987101i	$-0.448819\pi$
$313$	5.66479	0.320193	0.160096	+	0.987101i	$0.448819\pi$
$314$	−2.45233	−0.138393
$315$	−3.77440	−0.212663
$316$	18.7048	1.05223
$317$	18.1209	1.01777	0.508885	−	0.860834i	$-0.330058\pi$
$317$	18.1209	1.01777	0.508885	+	0.860834i	$0.330058\pi$
$318$	−38.1823	−2.14116
$319$	−5.71533	−0.319997
$320$	−2.64802	−0.148029
$321$	18.5947	1.03786
$322$	−2.14622	−0.119604
$323$	12.4553	0.693033
$324$	−8.47666	−0.470925
$325$	−1.42325	−0.0789476
$326$	−7.47850	−0.414196
$327$	−14.1015	−0.779816
$328$	6.70509	0.370227
$329$	−1.85467	−0.102251
$330$	4.04933	0.222908
$331$	22.2715	1.22415	0.612075	−	0.790800i	$-0.290335\pi$
$331$	22.2715	1.22415	0.612075	+	0.790800i	$0.290335\pi$
$332$	−0.616178	−0.0338171
$333$	16.8216	0.921820
$334$	−20.3678	−1.11448
$335$	7.22455	0.394720
$336$	−12.6080	−0.687825
$337$	−17.5492	−0.955965	−0.477983	−	0.878369i	$-0.658632\pi$
$337$	−17.5492	−0.955965	−0.477983	+	0.878369i	$0.658632\pi$
$338$	20.2204	1.09984
$339$	24.1262	1.31036
$340$	10.6172	0.575801
$341$	−1.99260	−0.107905
$342$	−11.3797	−0.615343
$343$	−1.00000	−0.0539949
$344$	3.92401	0.211568
$345$	3.03179	0.163226
$346$	−19.8733	−1.06839
$347$	−10.2751	−0.551598	−0.275799	−	0.961215i	$-0.588942\pi$
$347$	−10.2751	−0.551598	−0.275799	+	0.961215i	$0.588942\pi$
$348$	24.5735	1.31728
$349$	14.0762	0.753481	0.376740	−	0.926319i	$-0.377045\pi$
$349$	14.0762	0.753481	0.376740	+	0.926319i	$0.377045\pi$
$350$	1.84251	0.0984864
$351$	2.86868	0.153119
$352$	5.65338	0.301326
$353$	−18.4338	−0.981135	−0.490567	−	0.871403i	$-0.663210\pi$
$353$	−18.4338	−0.981135	−0.490567	+	0.871403i	$0.663210\pi$
$354$	−29.0423	−1.54358
$355$	−9.54885	−0.506801
$356$	−14.4700	−0.766906
$357$	19.8116	1.04854
$358$	−7.90252	−0.417661
$359$	27.4659	1.44960	0.724798	−	0.688962i	$-0.241933\pi$
$359$	27.4659	1.44960	0.724798	+	0.688962i	$0.241933\pi$
$360$	4.20843	0.221804
$361$	−16.3224	−0.859075
$362$	−24.1645	−1.27006
$363$	26.7747	1.40531
$364$	1.98522	0.104054
$365$	−9.31639	−0.487642
$366$	−47.5191	−2.48387
$367$	6.82606	0.356318	0.178159	−	0.984002i	$-0.442986\pi$
$367$	6.82606	0.356318	0.178159	+	0.984002i	$0.442986\pi$
$368$	5.64256	0.294139
$369$	22.6976	1.18159
$370$	−8.21165	−0.426904
$371$	7.96189	0.413361
$372$	8.56737	0.444197
$373$	−12.9957	−0.672890	−0.336445	−	0.941703i	$-0.609225\pi$
$373$	−12.9957	−0.672890	−0.336445	+	0.941703i	$0.609225\pi$
$374$	−11.8422	−0.612344
$375$	−2.60277	−0.134406
$376$	2.06794	0.106646
$377$	9.63352	0.496151
$378$	−3.71374	−0.191014
$379$	−7.72947	−0.397036	−0.198518	−	0.980097i	$-0.563613\pi$
$379$	−7.72947	−0.397036	−0.198518	+	0.980097i	$0.563613\pi$
$380$	2.28244	0.117087
$381$	−36.3269	−1.86108
$382$	−5.63000	−0.288056
$383$	23.8283	1.21757	0.608785	−	0.793335i	$-0.291657\pi$
$383$	23.8283	1.21757	0.608785	+	0.793335i	$0.291657\pi$
$384$	22.1538	1.13053
$385$	−0.844378	−0.0430335
$386$	−15.6874	−0.798466
$387$	13.2833	0.675228
$388$	−25.1297	−1.27577
$389$	23.6698	1.20011	0.600053	−	0.799960i	$-0.295146\pi$
$389$	23.6698	1.20011	0.600053	+	0.799960i	$0.295146\pi$
$390$	−6.82538	−0.345616
$391$	−8.86640	−0.448393
$392$	1.11499	0.0563156
$393$	−22.0873	−1.11416
$394$	5.75107	0.289735
$395$	13.4099	0.674723
$396$	4.44542	0.223391
$397$	0.849497	0.0426351	0.0213175	−	0.999773i	$-0.493214\pi$
$397$	0.849497	0.0426351	0.0213175	+	0.999773i	$0.493214\pi$
$398$	50.7614	2.54444
$399$	4.25899	0.213216
$400$	−4.84409	−0.242205
$401$	18.5097	0.924328	0.462164	−	0.886794i	$-0.347073\pi$
$401$	18.5097	0.924328	0.462164	+	0.886794i	$0.347073\pi$
$402$	34.6463	1.72800
$403$	3.35865	0.167306
$404$	−16.5007	−0.820938
$405$	−6.07710	−0.301974
$406$	−12.4714	−0.618944
$407$	3.76320	0.186535
$408$	−22.0898	−1.09361
$409$	27.4600	1.35781	0.678904	−	0.734227i	$-0.262455\pi$
$409$	27.4600	1.35781	0.678904	+	0.734227i	$0.262455\pi$
$410$	−11.0801	−0.547207
$411$	−0.394171	−0.0194430
$412$	23.1673	1.14137
$413$	6.05599	0.297996
$414$	8.10069	0.398127
$415$	−0.441751	−0.0216847
$416$	−9.52909	−0.467202
$417$	−17.8141	−0.872359
$418$	−2.54577	−0.124518
$419$	0.645646	0.0315419	0.0157709	−	0.999876i	$-0.494980\pi$
$419$	0.645646	0.0315419	0.0157709	+	0.999876i	$0.494980\pi$
$420$	3.63048	0.177149
$421$	−29.4031	−1.43302	−0.716509	−	0.697578i	$-0.754261\pi$
$421$	−29.4031	−1.43302	−0.716509	+	0.697578i	$0.754261\pi$
$422$	−3.84936	−0.187384
$423$	7.00026	0.340364
$424$	−8.87745	−0.431127
$425$	7.61174	0.369223
$426$	−45.7928	−2.21867
$427$	9.90884	0.479522
$428$	−9.96513	−0.481683
$429$	3.12790	0.151017
$430$	−6.48438	−0.312704
$431$	−10.2176	−0.492162	−0.246081	−	0.969249i	$-0.579143\pi$
$431$	−10.2176	−0.492162	−0.246081	+	0.969249i	$0.579143\pi$
$432$	9.76368	0.469755
$433$	26.2784	1.26286	0.631429	−	0.775434i	$-0.282469\pi$
$433$	26.2784	1.26286	0.631429	+	0.775434i	$0.282469\pi$
$434$	−4.34805	−0.208713
$435$	17.6173	0.844686
$436$	7.55716	0.361922
$437$	−1.90606	−0.0911790
$438$	−44.6780	−2.13480
$439$	−11.2825	−0.538484	−0.269242	−	0.963073i	$-0.586773\pi$
$439$	−11.2825	−0.538484	−0.269242	+	0.963073i	$0.586773\pi$
$440$	0.941475	0.0448831
$441$	3.77440	0.179733
$442$	19.9607	0.949432
$443$	22.2175	1.05558	0.527792	−	0.849374i	$-0.323020\pi$
$443$	22.2175	1.05558	0.527792	+	0.849374i	$0.323020\pi$
$444$	−16.1802	−0.767878
$445$	−10.3738	−0.491767
$446$	31.8619	1.50871
$447$	15.7189	0.743478
$448$	2.64802	0.125107
$449$	−6.04915	−0.285477	−0.142738	−	0.989760i	$-0.545591\pi$
$449$	−6.04915	−0.285477	−0.142738	+	0.989760i	$0.545591\pi$
$450$	−6.95438	−0.327833
$451$	5.07773	0.239101
$452$	−12.9295	−0.608153
$453$	38.9385	1.82949
$454$	−16.6925	−0.783419
$455$	1.42325	0.0667229
$456$	−4.74875	−0.222380
$457$	−2.96807	−0.138841	−0.0694203	−	0.997588i	$-0.522115\pi$
$457$	−2.96807	−0.138841	−0.0694203	+	0.997588i	$0.522115\pi$
$458$	−1.84251	−0.0860950
$459$	−15.3421	−0.716108
$460$	−1.62477	−0.0757553
$461$	−25.3716	−1.18167	−0.590837	−	0.806791i	$-0.701202\pi$
$461$	−25.3716	−1.18167	−0.590837	+	0.806791i	$0.701202\pi$
$462$	−4.04933	−0.188392
$463$	−5.34981	−0.248627	−0.124313	−	0.992243i	$-0.539673\pi$
$463$	−5.34981	−0.248627	−0.124313	+	0.992243i	$0.539673\pi$
$464$	32.7881	1.52215
$465$	6.14213	0.284835
$466$	−3.56439	−0.165117
$467$	−4.34259	−0.200951	−0.100476	−	0.994940i	$-0.532036\pi$
$467$	−4.34259	−0.200951	−0.100476	+	0.994940i	$0.532036\pi$
$468$	−7.49302	−0.346365
$469$	−7.22455	−0.333599
$470$	−3.41725	−0.157626
$471$	−3.46421	−0.159622
$472$	−6.75238	−0.310804
$473$	2.97163	0.136636
$474$	64.3087	2.95380
$475$	1.63633	0.0750801
$476$	−10.6172	−0.486641
$477$	−30.0514	−1.37596
$478$	40.5650	1.85540
$479$	−15.9571	−0.729097	−0.364549	−	0.931184i	$-0.618777\pi$
$479$	−15.9571	−0.729097	−0.364549	+	0.931184i	$0.618777\pi$
$480$	−17.4263	−0.795400
$481$	−6.34309	−0.289220
$482$	45.3630	2.06623
$483$	−3.03179	−0.137951
$484$	−14.3489	−0.652222
$485$	−18.0160	−0.818066
$486$	−40.2848	−1.82735
$487$	−37.3342	−1.69178	−0.845888	−	0.533360i	$-0.820929\pi$
$487$	−37.3342	−1.69178	−0.845888	+	0.533360i	$0.820929\pi$
$488$	−11.0483	−0.500132
$489$	−10.5643	−0.477733
$490$	−1.84251	−0.0832362
$491$	−0.308509	−0.0139228	−0.00696141	−	0.999976i	$-0.502216\pi$
$491$	−0.308509	−0.0139228	−0.00696141	+	0.999976i	$0.502216\pi$
$492$	−21.8321	−0.984269
$493$	−51.5214	−2.32041
$494$	4.29104	0.193063
$495$	3.18702	0.143246
$496$	11.4313	0.513281
$497$	9.54885	0.428325
$498$	−2.11848	−0.0949312
$499$	33.0698	1.48041	0.740204	−	0.672382i	$-0.234729\pi$
$499$	33.0698	1.48041	0.740204	+	0.672382i	$0.234729\pi$
$500$	1.39485	0.0623797
$501$	−28.7720	−1.28544
$502$	−44.6888	−1.99456
$503$	−13.6722	−0.609614	−0.304807	−	0.952414i	$-0.598592\pi$
$503$	−13.6722	−0.609614	−0.304807	+	0.952414i	$0.598592\pi$
$504$	−4.20843	−0.187458
$505$	−11.8297	−0.526414
$506$	1.81222	0.0805631
$507$	28.5637	1.26856
$508$	19.4680	0.863752
$509$	1.75293	0.0776971	0.0388485	−	0.999245i	$-0.487631\pi$
$509$	1.75293	0.0776971	0.0388485	+	0.999245i	$0.487631\pi$
$510$	36.5031	1.61638
$511$	9.31639	0.412133
$512$	−21.6305	−0.955941
$513$	−3.29817	−0.145618
$514$	−46.4728	−2.04983
$515$	16.6091	0.731886
$516$	−12.7768	−0.562466
$517$	1.56604	0.0688744
$518$	8.21165	0.360799
$519$	−28.0733	−1.23228
$520$	−1.58691	−0.0695907
$521$	−28.6205	−1.25389	−0.626943	−	0.779065i	$-0.715694\pi$
$521$	−28.6205	−1.25389	−0.626943	+	0.779065i	$0.715694\pi$
$522$	47.0720	2.06029
$523$	−40.2317	−1.75921	−0.879604	−	0.475707i	$-0.842192\pi$
$523$	−40.2317	−1.75921	−0.879604	+	0.475707i	$0.842192\pi$
$524$	11.8368	0.517095
$525$	2.60277	0.113594
$526$	−29.6176	−1.29139
$527$	−17.9625	−0.782460
$528$	10.6460	0.463306
$529$	−21.6432	−0.941007
$530$	14.6699	0.637219
$531$	−22.8577	−0.991941
$532$	−2.28244	−0.0989564
$533$	−8.55881	−0.370723
$534$	−49.7491	−2.15285
$535$	−7.14422	−0.308871
$536$	8.05532	0.347937
$537$	−11.1633	−0.481730
$538$	4.06230	0.175138
$539$	0.844378	0.0363699
$540$	−2.81144	−0.120985
$541$	39.7173	1.70758	0.853790	−	0.520618i	$-0.174299\pi$
$541$	39.7173	1.70758	0.853790	+	0.520618i	$0.174299\pi$
$542$	4.48669	0.192720
$543$	−34.1353	−1.46488
$544$	50.9630	2.18502
$545$	5.41789	0.232077
$546$	6.82538	0.292099
$547$	9.71110	0.415217	0.207608	−	0.978212i	$-0.433432\pi$
$547$	9.71110	0.415217	0.207608	+	0.978212i	$0.433432\pi$
$548$	0.211241	0.00902375
$549$	−37.3999	−1.59619
$550$	−1.55578	−0.0663386
$551$	−11.0758	−0.471846
$552$	3.38042	0.143880
$553$	−13.4099	−0.570245
$554$	4.34891	0.184767
$555$	−11.5999	−0.492390
$556$	9.54676	0.404873
$557$	19.9540	0.845478	0.422739	−	0.906251i	$-0.361069\pi$
$557$	19.9540	0.845478	0.422739	+	0.906251i	$0.361069\pi$
$558$	16.4113	0.694744
$559$	−5.00886	−0.211852
$560$	4.84409	0.204700
$561$	−16.7285	−0.706276
$562$	36.9257	1.55762
$563$	−33.3179	−1.40418	−0.702091	−	0.712087i	$-0.747750\pi$
$563$	−33.3179	−1.40418	−0.702091	+	0.712087i	$0.747750\pi$
$564$	−6.73333	−0.283524
$565$	−9.26945	−0.389969
$566$	−53.6720	−2.25600
$567$	6.07710	0.255214
$568$	−10.6469	−0.446734
$569$	−36.6440	−1.53620	−0.768098	−	0.640332i	$-0.778797\pi$
$569$	−36.6440	−1.53620	−0.768098	+	0.640332i	$0.778797\pi$
$570$	7.84725	0.328685
$571$	−22.0203	−0.921519	−0.460759	−	0.887525i	$-0.652423\pi$
$571$	−22.0203	−0.921519	−0.460759	+	0.887525i	$0.652423\pi$
$572$	−1.67628	−0.0700887
$573$	−7.95304	−0.332243
$574$	11.0801	0.462474
$575$	−1.16483	−0.0485769
$576$	−9.99468	−0.416445
$577$	−18.1958	−0.757500	−0.378750	−	0.925499i	$-0.623646\pi$
$577$	−18.1958	−0.757500	−0.378750	+	0.925499i	$0.623646\pi$
$578$	−75.4297	−3.13746
$579$	−22.1603	−0.920950
$580$	−9.44131	−0.392029
$581$	0.441751	0.0183269
$582$	−86.3983	−3.58132
$583$	−6.72285	−0.278432
$584$	−10.3877	−0.429846
$585$	−5.37191	−0.222101
$586$	15.3449	0.633894
$587$	−25.1375	−1.03754	−0.518769	−	0.854915i	$-0.673609\pi$
$587$	−25.1375	−1.03754	−0.518769	+	0.854915i	$0.673609\pi$
$588$	−3.63048	−0.149718
$589$	−3.86149	−0.159110
$590$	11.1582	0.459377
$591$	8.12407	0.334180
$592$	−21.5890	−0.887303
$593$	−36.0224	−1.47926	−0.739631	−	0.673013i	$-0.765000\pi$
$593$	−36.0224	−1.47926	−0.739631	+	0.673013i	$0.765000\pi$
$594$	3.13580	0.128663
$595$	−7.61174	−0.312051
$596$	−8.42393	−0.345058
$597$	71.7065	2.93475
$598$	−3.05460	−0.124912
$599$	15.2351	0.622491	0.311246	−	0.950330i	$-0.399254\pi$
$599$	15.2351	0.622491	0.311246	+	0.950330i	$0.399254\pi$
$600$	−2.90207	−0.118476
$601$	−16.9819	−0.692705	−0.346352	−	0.938104i	$-0.612580\pi$
$601$	−16.9819	−0.692705	−0.346352	+	0.938104i	$0.612580\pi$
$602$	6.48438	0.264283
$603$	27.2684	1.11045
$604$	−20.8676	−0.849090
$605$	−10.2870	−0.418227
$606$	−56.7308	−2.30453
$607$	−27.5271	−1.11729	−0.558645	−	0.829407i	$-0.688678\pi$
$607$	−27.5271	−1.11729	−0.558645	+	0.829407i	$0.688678\pi$
$608$	10.9558	0.444315
$609$	−17.6173	−0.713890
$610$	18.2572	0.739211
$611$	−2.63965	−0.106789
$612$	40.0737	1.61988
$613$	−4.83262	−0.195188	−0.0975938	−	0.995226i	$-0.531115\pi$
$613$	−4.83262	−0.195188	−0.0975938	+	0.995226i	$0.531115\pi$
$614$	49.3754	1.99263
$615$	−15.6519	−0.631147
$616$	−0.941475	−0.0379331
$617$	−9.30158	−0.374468	−0.187234	−	0.982315i	$-0.559952\pi$
$617$	−9.30158	−0.374468	−0.187234	+	0.982315i	$0.559952\pi$
$618$	79.6513	3.20404
$619$	−16.5314	−0.664455	−0.332227	−	0.943199i	$-0.607800\pi$
$619$	−16.5314	−0.664455	−0.332227	+	0.943199i	$0.607800\pi$
$620$	−3.29164	−0.132195
$621$	2.34782	0.0942148
$622$	−59.0721	−2.36857
$623$	10.3738	0.415619
$624$	−17.9444	−0.718350
$625$	1.00000	0.0400000
$626$	−10.4374	−0.417164
$627$	−3.59620	−0.143618
$628$	1.85651	0.0740827
$629$	33.9238	1.35263
$630$	6.95438	0.277069
$631$	−7.11263	−0.283149	−0.141575	−	0.989928i	$-0.545217\pi$
$631$	−7.11263	−0.283149	−0.141575	+	0.989928i	$0.545217\pi$
$632$	14.9519	0.594754
$633$	−5.43768	−0.216128
$634$	−33.3880	−1.32601
$635$	13.9570	0.553868
$636$	28.9055	1.14618
$637$	−1.42325	−0.0563911
$638$	10.5306	0.416909
$639$	−36.0412	−1.42577
$640$	−8.51163	−0.336452
$641$	−26.9544	−1.06463	−0.532317	−	0.846545i	$-0.678678\pi$
$641$	−26.9544	−1.06463	−0.532317	+	0.846545i	$0.678678\pi$
$642$	−34.2610	−1.35218
$643$	−38.3532	−1.51250	−0.756251	−	0.654282i	$-0.772971\pi$
$643$	−38.3532	−1.51250	−0.756251	+	0.654282i	$0.772971\pi$
$644$	1.62477	0.0640249
$645$	−9.15995	−0.360673
$646$	−22.9491	−0.902920
$647$	−3.95033	−0.155303	−0.0776517	−	0.996981i	$-0.524742\pi$
$647$	−3.95033	−0.155303	−0.0776517	+	0.996981i	$0.524742\pi$
$648$	−6.77592	−0.266183
$649$	−5.11355	−0.200724
$650$	2.62235	0.102857
$651$	−6.14213	−0.240729
$652$	5.66151	0.221722
$653$	16.8843	0.660736	0.330368	−	0.943852i	$-0.392827\pi$
$653$	16.8843	0.660736	0.330368	+	0.943852i	$0.392827\pi$
$654$	25.9822	1.01599
$655$	8.48609	0.331579
$656$	−29.1303	−1.13735
$657$	−35.1638	−1.37187
$658$	3.41725	0.133218
$659$	39.2635	1.52949	0.764743	−	0.644335i	$-0.222866\pi$
$659$	39.2635	1.52949	0.764743	+	0.644335i	$0.222866\pi$
$660$	−3.06550	−0.119324
$661$	−18.1571	−0.706230	−0.353115	−	0.935580i	$-0.614878\pi$
$661$	−18.1571	−0.706230	−0.353115	+	0.935580i	$0.614878\pi$
$662$	−41.0355	−1.59489
$663$	28.1968	1.09507
$664$	−0.492549	−0.0191146
$665$	−1.63633	−0.0634543
$666$	−30.9941	−1.20100
$667$	7.88439	0.305285
$668$	15.4192	0.596588
$669$	45.0088	1.74014
$670$	−13.3113	−0.514262
$671$	−8.36681	−0.322997
$672$	17.4263	0.672236
$673$	17.7548	0.684398	0.342199	−	0.939628i	$-0.388828\pi$
$673$	17.7548	0.684398	0.342199	+	0.939628i	$0.388828\pi$
$674$	32.3346	1.24548
$675$	−2.01559	−0.0775799
$676$	−15.3076	−0.588754
$677$	5.92520	0.227724	0.113862	−	0.993497i	$-0.463678\pi$
$677$	5.92520	0.227724	0.113862	+	0.993497i	$0.463678\pi$
$678$	−44.4529	−1.70720
$679$	18.0160	0.691392
$680$	8.48703	0.325463
$681$	−23.5802	−0.903594
$682$	3.67140	0.140585
$683$	−44.3194	−1.69584	−0.847918	−	0.530127i	$-0.822144\pi$
$683$	−44.3194	−1.69584	−0.847918	+	0.530127i	$0.822144\pi$
$684$	8.61485	0.329397
$685$	0.151443	0.00578634
$686$	1.84251	0.0703475
$687$	−2.60277	−0.0993018
$688$	−17.0479	−0.649944
$689$	11.3317	0.431705
$690$	−5.58611	−0.212660
$691$	−33.0312	−1.25657	−0.628283	−	0.777985i	$-0.716242\pi$
$691$	−33.0312	−1.25657	−0.628283	+	0.777985i	$0.716242\pi$
$692$	15.0448	0.571918
$693$	−3.18702	−0.121065
$694$	18.9320	0.718651
$695$	6.84428	0.259618
$696$	19.6432	0.744572
$697$	45.7737	1.73380
$698$	−25.9355	−0.981674
$699$	−5.03513	−0.190446
$700$	−1.39485	−0.0527205
$701$	5.77482	0.218112	0.109056	−	0.994036i	$-0.465217\pi$
$701$	5.77482	0.218112	0.109056	+	0.994036i	$0.465217\pi$
$702$	−5.28557	−0.199491
$703$	7.29276	0.275052
$704$	−2.23593	−0.0842697
$705$	−4.82727	−0.181805
$706$	33.9646	1.27827
$707$	11.8297	0.444901
$708$	21.9861	0.826289
$709$	28.5813	1.07339	0.536696	−	0.843776i	$-0.319672\pi$
$709$	28.5813	1.07339	0.536696	+	0.843776i	$0.319672\pi$
$710$	17.5939	0.660287
$711$	50.6142	1.89818
$712$	−11.5667	−0.433482
$713$	2.74883	0.102944
$714$	−36.5031	−1.36609
$715$	−1.20176	−0.0449433
$716$	5.98251	0.223577
$717$	57.3029	2.14002
$718$	−50.6063	−1.88861
$719$	−31.6780	−1.18139	−0.590694	−	0.806896i	$-0.701146\pi$
$719$	−31.6780	−1.18139	−0.590694	+	0.806896i	$0.701146\pi$
$720$	−18.2835	−0.681387
$721$	−16.6091	−0.618556
$722$	30.0743	1.11925
$723$	64.0806	2.38318
$724$	18.2935	0.679871
$725$	−6.76868	−0.251383
$726$	−49.3328	−1.83091
$727$	2.99926	0.111236	0.0556182	−	0.998452i	$-0.482287\pi$
$727$	2.99926	0.111236	0.0556182	+	0.998452i	$0.482287\pi$
$728$	1.58691	0.0588148
$729$	−38.6757	−1.43243
$730$	17.1656	0.635326
$731$	26.7881	0.990793
$732$	35.9738	1.32963
$733$	6.02929	0.222697	0.111348	−	0.993781i	$-0.464483\pi$
$733$	6.02929	0.222697	0.111348	+	0.993781i	$0.464483\pi$
$734$	−12.5771	−0.464229
$735$	−2.60277	−0.0960045
$736$	−7.79893	−0.287472
$737$	6.10026	0.224706
$738$	−41.8207	−1.53944
$739$	−19.4615	−0.715901	−0.357951	−	0.933741i	$-0.616524\pi$
$739$	−19.4615	−0.715901	−0.357951	+	0.933741i	$0.616524\pi$
$740$	6.21654	0.228524
$741$	6.06161	0.222679
$742$	−14.6699	−0.538548
$743$	−19.9711	−0.732670	−0.366335	−	0.930483i	$-0.619388\pi$
$743$	−19.9711	−0.732670	−0.366335	+	0.930483i	$0.619388\pi$
$744$	6.84843	0.251076
$745$	−6.03930	−0.221263
$746$	23.9447	0.876676
$747$	−1.66735	−0.0610050
$748$	8.96497	0.327792
$749$	7.14422	0.261044
$750$	4.79563	0.175112
$751$	13.0677	0.476848	0.238424	−	0.971161i	$-0.423369\pi$
$751$	13.0677	0.476848	0.238424	+	0.971161i	$0.423369\pi$
$752$	−8.98418	−0.327619
$753$	−63.1283	−2.30052
$754$	−17.7499	−0.646412
$755$	−14.9604	−0.544466
$756$	2.81144	0.102251
$757$	−8.52555	−0.309866	−0.154933	−	0.987925i	$-0.549516\pi$
$757$	−8.52555	−0.309866	−0.154933	+	0.987925i	$0.549516\pi$
$758$	14.2416	0.517280
$759$	2.55998	0.0929213
$760$	1.82450	0.0661815
$761$	−44.6391	−1.61817	−0.809083	−	0.587695i	$-0.800036\pi$
$761$	−44.6391	−1.61817	−0.809083	+	0.587695i	$0.800036\pi$
$762$	66.9328	2.42472
$763$	−5.41789	−0.196141
$764$	4.26212	0.154198
$765$	28.7297	1.03873
$766$	−43.9040	−1.58632
$767$	8.61918	0.311221
$768$	−54.6030	−1.97031
$769$	42.8761	1.54615	0.773075	−	0.634315i	$-0.218718\pi$
$769$	42.8761	1.54615	0.773075	+	0.634315i	$0.218718\pi$
$770$	1.55578	0.0560663
$771$	−65.6483	−2.36427
$772$	11.8759	0.427424
$773$	15.8788	0.571120	0.285560	−	0.958361i	$-0.407820\pi$
$773$	15.8788	0.571120	0.285560	+	0.958361i	$0.407820\pi$
$774$	−24.4746	−0.879723
$775$	−2.35985	−0.0847682
$776$	−20.0877	−0.721108
$777$	11.5999	0.416145
$778$	−43.6119	−1.56356
$779$	9.84021	0.352562
$780$	5.16707	0.185011
$781$	−8.06284	−0.288511
$782$	16.3365	0.584191
$783$	13.6429	0.487556
$784$	−4.84409	−0.173003
$785$	1.33097	0.0475044
$786$	40.6962	1.45158
$787$	−33.3357	−1.18829	−0.594144	−	0.804359i	$-0.702509\pi$
$787$	−33.3357	−1.18829	−0.594144	+	0.804359i	$0.702509\pi$
$788$	−4.35378	−0.155097
$789$	−41.8384	−1.48949
$790$	−24.7078	−0.879065
$791$	9.26945	0.329584
$792$	3.55351	0.126268
$793$	14.1027	0.500803
$794$	−1.56521	−0.0555472
$795$	20.7230	0.734967
$796$	−38.4283	−1.36205
$797$	5.46416	0.193550	0.0967752	−	0.995306i	$-0.469147\pi$
$797$	5.46416	0.193550	0.0967752	+	0.995306i	$0.469147\pi$
$798$	−7.84725	−0.277790
$799$	14.1172	0.499432
$800$	6.69531	0.236715
$801$	−39.1550	−1.38347
$802$	−34.1043	−1.20426
$803$	−7.86656	−0.277605
$804$	−26.2286	−0.925010
$805$	1.16483	0.0410550
$806$	−6.18835	−0.217975
$807$	5.73848	0.202004
$808$	−13.1900	−0.464023
$809$	2.42887	0.0853944	0.0426972	−	0.999088i	$-0.486405\pi$
$809$	2.42887	0.0853944	0.0426972	+	0.999088i	$0.486405\pi$
$810$	11.1971	0.393427
$811$	−51.7350	−1.81666	−0.908331	−	0.418253i	$-0.862643\pi$
$811$	−51.7350	−1.81666	−0.908331	+	0.418253i	$0.862643\pi$
$812$	9.44131	0.331325
$813$	6.33798	0.222283
$814$	−6.93374	−0.243028
$815$	4.05886	0.142176
$816$	95.9691	3.35959
$817$	5.75877	0.201474
$818$	−50.5954	−1.76903
$819$	5.37191	0.187710
$820$	8.38805	0.292923
$821$	20.2971	0.708373	0.354186	−	0.935175i	$-0.384758\pi$
$821$	20.2971	0.708373	0.354186	+	0.935175i	$0.384758\pi$
$822$	0.726265	0.0253314
$823$	5.84778	0.203841	0.101920	−	0.994793i	$-0.467501\pi$
$823$	5.84778	0.203841	0.101920	+	0.994793i	$0.467501\pi$
$824$	18.5190	0.645142
$825$	−2.19772	−0.0765148
$826$	−11.1582	−0.388245
$827$	−13.8813	−0.482700	−0.241350	−	0.970438i	$-0.577590\pi$
$827$	−13.8813	−0.482700	−0.241350	+	0.970438i	$0.577590\pi$
$828$	−6.13253	−0.213120
$829$	37.4236	1.29978	0.649888	−	0.760030i	$-0.274816\pi$
$829$	37.4236	1.29978	0.649888	+	0.760030i	$0.274816\pi$
$830$	0.813932	0.0282520
$831$	6.14335	0.213110
$832$	3.76879	0.130659
$833$	7.61174	0.263731
$834$	32.8227	1.13656
$835$	11.0544	0.382553
$836$	1.92724	0.0666551
$837$	4.75647	0.164408
$838$	−1.18961	−0.0410945
$839$	−15.2340	−0.525936	−0.262968	−	0.964805i	$-0.584701\pi$
$839$	−15.2340	−0.525936	−0.262968	+	0.964805i	$0.584701\pi$
$840$	2.90207	0.100131
$841$	16.8151	0.579830
$842$	54.1755	1.86701
$843$	52.1619	1.79655
$844$	2.91411	0.100308
$845$	−10.9744	−0.377530
$846$	−12.8981	−0.443445
$847$	10.2870	0.353466
$848$	38.5681	1.32444
$849$	−75.8181	−2.60207
$850$	−14.0247	−0.481044
$851$	−5.19140	−0.177959
$852$	34.6669	1.18767
$853$	29.9901	1.02684	0.513421	−	0.858137i	$-0.328378\pi$
$853$	29.9901	1.02684	0.513421	+	0.858137i	$0.328378\pi$
$854$	−18.2572	−0.624747
$855$	6.17617	0.211221
$856$	−7.96575	−0.272264
$857$	−4.66032	−0.159194	−0.0795968	−	0.996827i	$-0.525363\pi$
$857$	−4.66032	−0.159194	−0.0795968	+	0.996827i	$0.525363\pi$
$858$	−5.76320	−0.196752
$859$	5.97994	0.204033	0.102017	−	0.994783i	$-0.467471\pi$
$859$	5.97994	0.204033	0.102017	+	0.994783i	$0.467471\pi$
$860$	4.90892	0.167393
$861$	15.6519	0.533417
$862$	18.8260	0.641215
$863$	42.3455	1.44146	0.720728	−	0.693218i	$-0.243808\pi$
$863$	42.3455	1.44146	0.720728	+	0.693218i	$0.243808\pi$
$864$	−13.4950	−0.459108
$865$	10.7860	0.366733
$866$	−48.4182	−1.64532
$867$	−106.553	−3.61874
$868$	3.29164	0.111725
$869$	11.3230	0.384106
$870$	−32.4601	−1.10050
$871$	−10.2823	−0.348404
$872$	6.04091	0.204571
$873$	−67.9997	−2.30144
$874$	3.51193	0.118793
$875$	−1.00000	−0.0338062
$876$	33.8229	1.14277
$877$	22.9238	0.774081	0.387040	−	0.922063i	$-0.373497\pi$
$877$	22.9238	0.774081	0.387040	+	0.922063i	$0.373497\pi$
$878$	20.7881	0.701566
$879$	21.6766	0.731132
$880$	−4.09025	−0.137882
$881$	−6.95864	−0.234442	−0.117221	−	0.993106i	$-0.537399\pi$
$881$	−6.95864	−0.234442	−0.117221	+	0.993106i	$0.537399\pi$
$882$	−6.95438	−0.234166
$883$	−14.3303	−0.482255	−0.241127	−	0.970493i	$-0.577517\pi$
$883$	−14.3303	−0.482255	−0.241127	+	0.970493i	$0.577517\pi$
$884$	−15.1110	−0.508237
$885$	15.7623	0.529845
$886$	−40.9360	−1.37527
$887$	−19.8043	−0.664964	−0.332482	−	0.943110i	$-0.607886\pi$
$887$	−19.8043	−0.664964	−0.332482	+	0.943110i	$0.607886\pi$
$888$	−12.9338	−0.434031
$889$	−13.9570	−0.468104
$890$	19.1139	0.640700
$891$	−5.13137	−0.171907
$892$	−24.1207	−0.807621
$893$	3.03485	0.101557
$894$	−28.9623	−0.968643
$895$	4.28899	0.143365
$896$	8.51163	0.284353
$897$	−4.31499	−0.144073
$898$	11.1456	0.371934
$899$	15.9731	0.532731
$900$	5.26473	0.175491
$901$	−60.6038	−2.01901
$902$	−9.35579	−0.311514
$903$	9.15995	0.304824
$904$	−10.3354	−0.343749
$905$	13.1150	0.435957
$906$	−71.7447	−2.38356
$907$	−18.9287	−0.628519	−0.314259	−	0.949337i	$-0.601756\pi$
$907$	−18.9287	−0.628519	−0.314259	+	0.949337i	$0.601756\pi$
$908$	12.6369	0.419370
$909$	−44.6499	−1.48095
$910$	−2.62235	−0.0869301
$911$	44.5985	1.47762	0.738808	−	0.673916i	$-0.235389\pi$
$911$	44.5985	1.47762	0.738808	+	0.673916i	$0.235389\pi$
$912$	20.6310	0.683159
$913$	−0.373005	−0.0123447
$914$	5.46871	0.180889
$915$	25.7904	0.852605
$916$	1.39485	0.0460872
$917$	−8.48609	−0.280235
$918$	28.2680	0.932983
$919$	−3.31165	−0.109241	−0.0546207	−	0.998507i	$-0.517395\pi$
$919$	−3.31165	−0.109241	−0.0546207	+	0.998507i	$0.517395\pi$
$920$	−1.29878	−0.0428195
$921$	69.7487	2.29830
$922$	46.7475	1.53955
$923$	13.5904	0.447333
$924$	3.06550	0.100847
$925$	4.45677	0.146538
$926$	9.85710	0.323924
$927$	62.6895	2.05899
$928$	−45.3185	−1.48765
$929$	−56.1318	−1.84162	−0.920812	−	0.390007i	$-0.872472\pi$
$929$	−56.1318	−1.84162	−0.920812	+	0.390007i	$0.872472\pi$
$930$	−11.3170	−0.371098
$931$	1.63633	0.0536286
$932$	2.69838	0.0883884
$933$	−83.4463	−2.73191
$934$	8.00128	0.261810
$935$	6.42718	0.210191
$936$	−5.98964	−0.195777
$937$	−42.1013	−1.37539	−0.687695	−	0.726000i	$-0.741377\pi$
$937$	−42.1013	−1.37539	−0.687695	+	0.726000i	$0.741377\pi$
$938$	13.3113	0.434630
$939$	−14.7441	−0.481157
$940$	2.58699	0.0843782
$941$	−4.00001	−0.130397	−0.0651984	−	0.997872i	$-0.520768\pi$
$941$	−4.00001	−0.130397	−0.0651984	+	0.997872i	$0.520768\pi$
$942$	6.38285	0.207964
$943$	−7.00481	−0.228108
$944$	29.3358	0.954798
$945$	2.01559	0.0655670
$946$	−5.47527	−0.178016
$947$	24.0064	0.780102	0.390051	−	0.920793i	$-0.372457\pi$
$947$	24.0064	0.780102	0.390051	+	0.920793i	$0.372457\pi$
$948$	−48.6842	−1.58119
$949$	13.2595	0.430423
$950$	−3.01496	−0.0978183
$951$	−47.1645	−1.52941
$952$	−8.48703	−0.275066
$953$	−17.9139	−0.580287	−0.290143	−	0.956983i	$-0.593703\pi$
$953$	−17.9139	−0.580287	−0.290143	+	0.956983i	$0.593703\pi$
$954$	55.3700	1.79267
$955$	3.05561	0.0988772
$956$	−30.7093	−0.993208
$957$	14.8757	0.480862
$958$	29.4011	0.949907
$959$	−0.151443	−0.00489035
$960$	6.89217	0.222444
$961$	−25.4311	−0.820359
$962$	11.6872	0.376811
$963$	−26.9651	−0.868939
$964$	−34.3415	−1.10607
$965$	8.51412	0.274079
$966$	5.58611	0.179730
$967$	12.6096	0.405498	0.202749	−	0.979231i	$-0.435012\pi$
$967$	12.6096	0.405498	0.202749	+	0.979231i	$0.435012\pi$
$968$	−11.4700	−0.368658
$969$	−32.4183	−1.04143
$970$	33.1948	1.06582
$971$	16.4188	0.526904	0.263452	−	0.964672i	$-0.415139\pi$
$971$	16.4188	0.526904	0.263452	+	0.964672i	$0.415139\pi$
$972$	30.4971	0.978195
$973$	−6.84428	−0.219418
$974$	68.7888	2.20414
$975$	3.70438	0.118635
$976$	47.9993	1.53642
$977$	7.14891	0.228714	0.114357	−	0.993440i	$-0.463519\pi$
$977$	7.14891	0.228714	0.114357	+	0.993440i	$0.463519\pi$
$978$	19.4648	0.622416
$979$	−8.75944	−0.279953
$980$	1.39485	0.0445569
$981$	20.4493	0.652896
$982$	0.568432	0.0181394
$983$	−24.1763	−0.771104	−0.385552	−	0.922686i	$-0.625989\pi$
$983$	−24.1763	−0.771104	−0.385552	+	0.922686i	$0.625989\pi$
$984$	−17.4518	−0.556343
$985$	−3.12132	−0.0994535
$986$	94.9289	3.02315
$987$	4.82727	0.153654
$988$	−3.24848	−0.103348
$989$	−4.09941	−0.130354
$990$	−5.87213	−0.186628
$991$	−26.0527	−0.827590	−0.413795	−	0.910370i	$-0.635797\pi$
$991$	−26.0527	−0.827590	−0.413795	+	0.910370i	$0.635797\pi$
$992$	−15.7999	−0.501648
$993$	−57.9675	−1.83954
$994$	−17.5939	−0.558044
$995$	−27.5501	−0.873397
$996$	1.60377	0.0508173
$997$	4.43701	0.140521	0.0702607	−	0.997529i	$-0.477617\pi$
$997$	4.43701	0.140521	0.0702607	+	0.997529i	$0.477617\pi$
$998$	−60.9316	−1.92875
$999$	−8.98300	−0.284210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.9	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.9	✓	44	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84251 q^{2} -2.60277 q^{3} +1.39485 q^{4} +1.00000 q^{5} +4.79563 q^{6} -1.00000 q^{7} +1.11499 q^{8} +3.77440 q^{9} +O(q^{10})\)	\(q-1.84251 q^{2} -2.60277 q^{3} +1.39485 q^{4} +1.00000 q^{5} +4.79563 q^{6} -1.00000 q^{7} +1.11499 q^{8} +3.77440 q^{9} -1.84251 q^{10} +0.844378 q^{11} -3.63048 q^{12} -1.42325 q^{13} +1.84251 q^{14} -2.60277 q^{15} -4.84409 q^{16} +7.61174 q^{17} -6.95438 q^{18} +1.63633 q^{19} +1.39485 q^{20} +2.60277 q^{21} -1.55578 q^{22} -1.16483 q^{23} -2.90207 q^{24} +1.00000 q^{25} +2.62235 q^{26} -2.01559 q^{27} -1.39485 q^{28} -6.76868 q^{29} +4.79563 q^{30} -2.35985 q^{31} +6.69531 q^{32} -2.19772 q^{33} -14.0247 q^{34} -1.00000 q^{35} +5.26473 q^{36} +4.45677 q^{37} -3.01496 q^{38} +3.70438 q^{39} +1.11499 q^{40} +6.01358 q^{41} -4.79563 q^{42} +3.51931 q^{43} +1.17778 q^{44} +3.77440 q^{45} +2.14622 q^{46} +1.85467 q^{47} +12.6080 q^{48} +1.00000 q^{49} -1.84251 q^{50} -19.8116 q^{51} -1.98522 q^{52} -7.96189 q^{53} +3.71374 q^{54} +0.844378 q^{55} -1.11499 q^{56} -4.25899 q^{57} +12.4714 q^{58} -6.05599 q^{59} -3.63048 q^{60} -9.90884 q^{61} +4.34805 q^{62} -3.77440 q^{63} -2.64802 q^{64} -1.42325 q^{65} +4.04933 q^{66} +7.22455 q^{67} +10.6172 q^{68} +3.03179 q^{69} +1.84251 q^{70} -9.54885 q^{71} +4.20843 q^{72} -9.31639 q^{73} -8.21165 q^{74} -2.60277 q^{75} +2.28244 q^{76} -0.844378 q^{77} -6.82538 q^{78} +13.4099 q^{79} -4.84409 q^{80} -6.07710 q^{81} -11.0801 q^{82} -0.441751 q^{83} +3.63048 q^{84} +7.61174 q^{85} -6.48438 q^{86} +17.6173 q^{87} +0.941475 q^{88} -10.3738 q^{89} -6.95438 q^{90} +1.42325 q^{91} -1.62477 q^{92} +6.14213 q^{93} -3.41725 q^{94} +1.63633 q^{95} -17.4263 q^{96} -18.0160 q^{97} -1.84251 q^{98} +3.18702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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