LMFDB - Embedded newform 6034.2.a.o.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.09451 q^{3} +1.00000 q^{4} -2.81071 q^{5} +1.09451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.80204 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.09451 q^{3} +1.00000 q^{4} -2.81071 q^{5} +1.09451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.80204 q^{9} +2.81071 q^{10} -3.14149 q^{11} -1.09451 q^{12} -1.81087 q^{13} +1.00000 q^{14} +3.07635 q^{15} +1.00000 q^{16} -1.36053 q^{17} +1.80204 q^{18} +7.68978 q^{19} -2.81071 q^{20} +1.09451 q^{21} +3.14149 q^{22} -4.80831 q^{23} +1.09451 q^{24} +2.90007 q^{25} +1.81087 q^{26} +5.25590 q^{27} -1.00000 q^{28} -7.24448 q^{29} -3.07635 q^{30} +9.25619 q^{31} -1.00000 q^{32} +3.43841 q^{33} +1.36053 q^{34} +2.81071 q^{35} -1.80204 q^{36} -1.58098 q^{37} -7.68978 q^{38} +1.98202 q^{39} +2.81071 q^{40} +1.31343 q^{41} -1.09451 q^{42} +8.85759 q^{43} -3.14149 q^{44} +5.06501 q^{45} +4.80831 q^{46} +4.73841 q^{47} -1.09451 q^{48} +1.00000 q^{49} -2.90007 q^{50} +1.48911 q^{51} -1.81087 q^{52} +1.08452 q^{53} -5.25590 q^{54} +8.82982 q^{55} +1.00000 q^{56} -8.41657 q^{57} +7.24448 q^{58} -0.481656 q^{59} +3.07635 q^{60} -7.80546 q^{61} -9.25619 q^{62} +1.80204 q^{63} +1.00000 q^{64} +5.08981 q^{65} -3.43841 q^{66} +10.9790 q^{67} -1.36053 q^{68} +5.26276 q^{69} -2.81071 q^{70} +0.876158 q^{71} +1.80204 q^{72} -9.59109 q^{73} +1.58098 q^{74} -3.17416 q^{75} +7.68978 q^{76} +3.14149 q^{77} -1.98202 q^{78} +15.1568 q^{79} -2.81071 q^{80} -0.346528 q^{81} -1.31343 q^{82} +10.6776 q^{83} +1.09451 q^{84} +3.82404 q^{85} -8.85759 q^{86} +7.92918 q^{87} +3.14149 q^{88} -9.79354 q^{89} -5.06501 q^{90} +1.81087 q^{91} -4.80831 q^{92} -10.1310 q^{93} -4.73841 q^{94} -21.6137 q^{95} +1.09451 q^{96} +14.7986 q^{97} -1.00000 q^{98} +5.66110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.09451	−0.631918	−0.315959	−	0.948773i	$-0.602326\pi$
$3$	−1.09451	−0.631918	−0.315959	+	0.948773i	$0.602326\pi$
$4$	1.00000	0.500000
$5$	−2.81071	−1.25699	−0.628493	−	0.777815i	$-0.716328\pi$
$5$	−2.81071	−1.25699	−0.628493	+	0.777815i	$0.716328\pi$
$6$	1.09451	0.446833
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−1.80204	−0.600680
$10$	2.81071	0.888823
$11$	−3.14149	−0.947196	−0.473598	−	0.880741i	$-0.657045\pi$
$11$	−3.14149	−0.947196	−0.473598	+	0.880741i	$0.657045\pi$
$12$	−1.09451	−0.315959
$13$	−1.81087	−0.502244	−0.251122	−	0.967955i	$-0.580799\pi$
$13$	−1.81087	−0.502244	−0.251122	+	0.967955i	$0.580799\pi$
$14$	1.00000	0.267261
$15$	3.07635	0.794311
$16$	1.00000	0.250000
$17$	−1.36053	−0.329976	−0.164988	−	0.986296i	$-0.552759\pi$
$17$	−1.36053	−0.329976	−0.164988	+	0.986296i	$0.552759\pi$
$18$	1.80204	0.424745
$19$	7.68978	1.76416	0.882078	−	0.471103i	$-0.156144\pi$
$19$	7.68978	1.76416	0.882078	+	0.471103i	$0.156144\pi$
$20$	−2.81071	−0.628493
$21$	1.09451	0.238842
$22$	3.14149	0.669769
$23$	−4.80831	−1.00260	−0.501301	−	0.865273i	$-0.667145\pi$
$23$	−4.80831	−1.00260	−0.501301	+	0.865273i	$0.667145\pi$
$24$	1.09451	0.223417
$25$	2.90007	0.580013
$26$	1.81087	0.355140
$27$	5.25590	1.01150
$28$	−1.00000	−0.188982
$29$	−7.24448	−1.34527	−0.672633	−	0.739976i	$-0.734837\pi$
$29$	−7.24448	−1.34527	−0.672633	+	0.739976i	$0.734837\pi$
$30$	−3.07635	−0.561663
$31$	9.25619	1.66246	0.831230	−	0.555928i	$-0.187637\pi$
$31$	9.25619	1.66246	0.831230	+	0.555928i	$0.187637\pi$
$32$	−1.00000	−0.176777
$33$	3.43841	0.598550
$34$	1.36053	0.233328
$35$	2.81071	0.475096
$36$	−1.80204	−0.300340
$37$	−1.58098	−0.259911	−0.129955	−	0.991520i	$-0.541483\pi$
$37$	−1.58098	−0.259911	−0.129955	+	0.991520i	$0.541483\pi$
$38$	−7.68978	−1.24745
$39$	1.98202	0.317377
$40$	2.81071	0.444412
$41$	1.31343	0.205123	0.102562	−	0.994727i	$-0.467296\pi$
$41$	1.31343	0.205123	0.102562	+	0.994727i	$0.467296\pi$
$42$	−1.09451	−0.168887
$43$	8.85759	1.35077	0.675385	−	0.737466i	$-0.263978\pi$
$43$	8.85759	1.35077	0.675385	+	0.737466i	$0.263978\pi$
$44$	−3.14149	−0.473598
$45$	5.06501	0.755046
$46$	4.80831	0.708947
$47$	4.73841	0.691168	0.345584	−	0.938388i	$-0.387681\pi$
$47$	4.73841	0.691168	0.345584	+	0.938388i	$0.387681\pi$
$48$	−1.09451	−0.157979
$49$	1.00000	0.142857
$50$	−2.90007	−0.410131
$51$	1.48911	0.208518
$52$	−1.81087	−0.251122
$53$	1.08452	0.148970	0.0744852	−	0.997222i	$-0.476269\pi$
$53$	1.08452	0.148970	0.0744852	+	0.997222i	$0.476269\pi$
$54$	−5.25590	−0.715237
$55$	8.82982	1.19061
$56$	1.00000	0.133631
$57$	−8.41657	−1.11480
$58$	7.24448	0.951247
$59$	−0.481656	−0.0627062	−0.0313531	−	0.999508i	$-0.509982\pi$
$59$	−0.481656	−0.0627062	−0.0313531	+	0.999508i	$0.509982\pi$
$60$	3.07635	0.397156
$61$	−7.80546	−0.999387	−0.499693	−	0.866202i	$-0.666554\pi$
$61$	−7.80546	−0.999387	−0.499693	+	0.866202i	$0.666554\pi$
$62$	−9.25619	−1.17554
$63$	1.80204	0.227036
$64$	1.00000	0.125000
$65$	5.08981	0.631313
$66$	−3.43841	−0.423239
$67$	10.9790	1.34130	0.670648	−	0.741776i	$-0.266016\pi$
$67$	10.9790	1.34130	0.670648	+	0.741776i	$0.266016\pi$
$68$	−1.36053	−0.164988
$69$	5.26276	0.633562
$70$	−2.81071	−0.335944
$71$	0.876158	0.103981	0.0519904	−	0.998648i	$-0.483443\pi$
$71$	0.876158	0.103981	0.0519904	+	0.998648i	$0.483443\pi$
$72$	1.80204	0.212373
$73$	−9.59109	−1.12255	−0.561276	−	0.827629i	$-0.689689\pi$
$73$	−9.59109	−1.12255	−0.561276	+	0.827629i	$0.689689\pi$
$74$	1.58098	0.183785
$75$	−3.17416	−0.366521
$76$	7.68978	0.882078
$77$	3.14149	0.358006
$78$	−1.98202	−0.224419
$79$	15.1568	1.70528	0.852639	−	0.522500i	$-0.175000\pi$
$79$	15.1568	1.70528	0.852639	+	0.522500i	$0.175000\pi$
$80$	−2.81071	−0.314246
$81$	−0.346528	−0.0385031
$82$	−1.31343	−0.145044
$83$	10.6776	1.17202	0.586012	−	0.810303i	$-0.300697\pi$
$83$	10.6776	1.17202	0.586012	+	0.810303i	$0.300697\pi$
$84$	1.09451	0.119421
$85$	3.82404	0.414775
$86$	−8.85759	−0.955138
$87$	7.92918	0.850098
$88$	3.14149	0.334884
$89$	−9.79354	−1.03811	−0.519057	−	0.854740i	$-0.673717\pi$
$89$	−9.79354	−1.03811	−0.519057	+	0.854740i	$0.673717\pi$
$90$	−5.06501	−0.533898
$91$	1.81087	0.189830
$92$	−4.80831	−0.501301
$93$	−10.1310	−1.05054
$94$	−4.73841	−0.488729
$95$	−21.6137	−2.21752
$96$	1.09451	0.111708
$97$	14.7986	1.50257	0.751284	−	0.659979i	$-0.229435\pi$
$97$	14.7986	1.50257	0.751284	+	0.659979i	$0.229435\pi$
$98$	−1.00000	−0.101015
$99$	5.66110	0.568962
$100$	2.90007	0.290007
$101$	−7.94477	−0.790534	−0.395267	−	0.918566i	$-0.629348\pi$
$101$	−7.94477	−0.790534	−0.395267	+	0.918566i	$0.629348\pi$
$102$	−1.48911	−0.147444
$103$	−8.46185	−0.833771	−0.416885	−	0.908959i	$-0.636878\pi$
$103$	−8.46185	−0.833771	−0.416885	+	0.908959i	$0.636878\pi$
$104$	1.81087	0.177570
$105$	−3.07635	−0.300221
$106$	−1.08452	−0.105338
$107$	4.64683	0.449226	0.224613	−	0.974448i	$-0.427888\pi$
$107$	4.64683	0.449226	0.224613	+	0.974448i	$0.427888\pi$
$108$	5.25590	0.505749
$109$	−3.20954	−0.307418	−0.153709	−	0.988116i	$-0.549122\pi$
$109$	−3.20954	−0.307418	−0.153709	+	0.988116i	$0.549122\pi$
$110$	−8.82982	−0.841890
$111$	1.73040	0.164242
$112$	−1.00000	−0.0944911
$113$	10.8600	1.02163	0.510813	−	0.859692i	$-0.329344\pi$
$113$	10.8600	1.02163	0.510813	+	0.859692i	$0.329344\pi$
$114$	8.41657	0.788284
$115$	13.5147	1.26026
$116$	−7.24448	−0.672633
$117$	3.26325	0.301688
$118$	0.481656	0.0443400
$119$	1.36053	0.124719
$120$	−3.07635	−0.280831
$121$	−1.13101	−0.102819
$122$	7.80546	0.706673
$123$	−1.43757	−0.129621
$124$	9.25619	0.831230
$125$	5.90230	0.527917
$126$	−1.80204	−0.160539
$127$	−17.2818	−1.53351	−0.766757	−	0.641938i	$-0.778131\pi$
$127$	−17.2818	−1.53351	−0.766757	+	0.641938i	$0.778131\pi$
$128$	−1.00000	−0.0883883
$129$	−9.69474	−0.853575
$130$	−5.08981	−0.446406
$131$	−15.0633	−1.31609	−0.658043	−	0.752981i	$-0.728615\pi$
$131$	−15.0633	−1.31609	−0.658043	+	0.752981i	$0.728615\pi$
$132$	3.43841	0.299275
$133$	−7.68978	−0.666789
$134$	−10.9790	−0.948439
$135$	−14.7728	−1.27144
$136$	1.36053	0.116664
$137$	20.4563	1.74770	0.873850	−	0.486196i	$-0.161616\pi$
$137$	20.4563	1.74770	0.873850	+	0.486196i	$0.161616\pi$
$138$	−5.26276	−0.447996
$139$	9.16237	0.777142	0.388571	−	0.921419i	$-0.372969\pi$
$139$	9.16237	0.777142	0.388571	+	0.921419i	$0.372969\pi$
$140$	2.81071	0.237548
$141$	−5.18625	−0.436761
$142$	−0.876158	−0.0735255
$143$	5.68882	0.475723
$144$	−1.80204	−0.150170
$145$	20.3621	1.69098
$146$	9.59109	0.793764
$147$	−1.09451	−0.0902739
$148$	−1.58098	−0.129955
$149$	−12.4472	−1.01971	−0.509856	−	0.860259i	$-0.670302\pi$
$149$	−12.4472	−1.01971	−0.509856	+	0.860259i	$0.670302\pi$
$150$	3.17416	0.259169
$151$	−7.91171	−0.643846	−0.321923	−	0.946766i	$-0.604329\pi$
$151$	−7.91171	−0.643846	−0.321923	+	0.946766i	$0.604329\pi$
$152$	−7.68978	−0.623724
$153$	2.45172	0.198210
$154$	−3.14149	−0.253149
$155$	−26.0164	−2.08969
$156$	1.98202	0.158688
$157$	−3.52990	−0.281717	−0.140858	−	0.990030i	$-0.544986\pi$
$157$	−3.52990	−0.281717	−0.140858	+	0.990030i	$0.544986\pi$
$158$	−15.1568	−1.20581
$159$	−1.18702	−0.0941371
$160$	2.81071	0.222206
$161$	4.80831	0.378948
$162$	0.346528	0.0272258
$163$	−2.74807	−0.215246	−0.107623	−	0.994192i	$-0.534324\pi$
$163$	−2.74807	−0.215246	−0.107623	+	0.994192i	$0.534324\pi$
$164$	1.31343	0.102562
$165$	−9.66435	−0.752369
$166$	−10.6776	−0.828746
$167$	−16.7197	−1.29381	−0.646905	−	0.762571i	$-0.723937\pi$
$167$	−16.7197	−1.29381	−0.646905	+	0.762571i	$0.723937\pi$
$168$	−1.09451	−0.0844435
$169$	−9.72077	−0.747751
$170$	−3.82404	−0.293291
$171$	−13.8573	−1.05969
$172$	8.85759	0.675385
$173$	26.0461	1.98025	0.990123	−	0.140200i	$-0.0447745\pi$
$173$	26.0461	1.98025	0.990123	+	0.140200i	$0.0447745\pi$
$174$	−7.92918	−0.601110
$175$	−2.90007	−0.219224
$176$	−3.14149	−0.236799
$177$	0.527178	0.0396252
$178$	9.79354	0.734057
$179$	6.72965	0.502998	0.251499	−	0.967858i	$-0.419076\pi$
$179$	6.72965	0.502998	0.251499	+	0.967858i	$0.419076\pi$
$180$	5.06501	0.377523
$181$	−5.72061	−0.425210	−0.212605	−	0.977138i	$-0.568195\pi$
$181$	−5.72061	−0.425210	−0.212605	+	0.977138i	$0.568195\pi$
$182$	−1.81087	−0.134230
$183$	8.54318	0.631530
$184$	4.80831	0.354473
$185$	4.44366	0.326704
$186$	10.1310	0.742842
$187$	4.27409	0.312552
$188$	4.73841	0.345584
$189$	−5.25590	−0.382310
$190$	21.6137	1.56802
$191$	−14.2019	−1.02761	−0.513806	−	0.857906i	$-0.671765\pi$
$191$	−14.2019	−1.02761	−0.513806	+	0.857906i	$0.671765\pi$
$192$	−1.09451	−0.0789897
$193$	15.8672	1.14214	0.571072	−	0.820900i	$-0.306528\pi$
$193$	15.8672	1.14214	0.571072	+	0.820900i	$0.306528\pi$
$194$	−14.7986	−1.06248
$195$	−5.57086	−0.398938
$196$	1.00000	0.0714286
$197$	2.21134	0.157551	0.0787757	−	0.996892i	$-0.474899\pi$
$197$	2.21134	0.157551	0.0787757	+	0.996892i	$0.474899\pi$
$198$	−5.66110	−0.402317
$199$	10.0916	0.715374	0.357687	−	0.933842i	$-0.383566\pi$
$199$	10.0916	0.715374	0.357687	+	0.933842i	$0.383566\pi$
$200$	−2.90007	−0.205066
$201$	−12.0166	−0.847588
$202$	7.94477	0.558992
$203$	7.24448	0.508463
$204$	1.48911	0.104259
$205$	−3.69166	−0.257837
$206$	8.46185	0.589565
$207$	8.66477	0.602243
$208$	−1.81087	−0.125561
$209$	−24.1574	−1.67100
$210$	3.07635	0.212289
$211$	−10.8458	−0.746658	−0.373329	−	0.927699i	$-0.621784\pi$
$211$	−10.8458	−0.746658	−0.373329	+	0.927699i	$0.621784\pi$
$212$	1.08452	0.0744852
$213$	−0.958967	−0.0657073
$214$	−4.64683	−0.317651
$215$	−24.8961	−1.69790
$216$	−5.25590	−0.357619
$217$	−9.25619	−0.628351
$218$	3.20954	0.217377
$219$	10.4976	0.709360
$220$	8.82982	0.595306
$221$	2.46373	0.165729
$222$	−1.73040	−0.116137
$223$	−10.4097	−0.697087	−0.348543	−	0.937293i	$-0.613324\pi$
$223$	−10.4097	−0.697087	−0.348543	+	0.937293i	$0.613324\pi$
$224$	1.00000	0.0668153
$225$	−5.22604	−0.348402
$226$	−10.8600	−0.722399
$227$	8.76942	0.582047	0.291023	−	0.956716i	$-0.406004\pi$
$227$	8.76942	0.582047	0.291023	+	0.956716i	$0.406004\pi$
$228$	−8.41657	−0.557401
$229$	4.20289	0.277735	0.138867	−	0.990311i	$-0.455654\pi$
$229$	4.20289	0.277735	0.138867	+	0.990311i	$0.455654\pi$
$230$	−13.5147	−0.891136
$231$	−3.43841	−0.226231
$232$	7.24448	0.475624
$233$	5.02737	0.329354	0.164677	−	0.986348i	$-0.447342\pi$
$233$	5.02737	0.329354	0.164677	+	0.986348i	$0.447342\pi$
$234$	−3.26325	−0.213326
$235$	−13.3183	−0.868788
$236$	−0.481656	−0.0313531
$237$	−16.5894	−1.07760
$238$	−1.36053	−0.0881899
$239$	7.71308	0.498918	0.249459	−	0.968385i	$-0.419747\pi$
$239$	7.71308	0.498918	0.249459	+	0.968385i	$0.419747\pi$
$240$	3.07635	0.198578
$241$	8.82661	0.568572	0.284286	−	0.958740i	$-0.408244\pi$
$241$	8.82661	0.568572	0.284286	+	0.958740i	$0.408244\pi$
$242$	1.13101	0.0727044
$243$	−15.3884	−0.987167
$244$	−7.80546	−0.499693
$245$	−2.81071	−0.179569
$246$	1.43757	0.0916558
$247$	−13.9252	−0.886037
$248$	−9.25619	−0.587769
$249$	−11.6868	−0.740622
$250$	−5.90230	−0.373294
$251$	−17.6429	−1.11361	−0.556804	−	0.830644i	$-0.687972\pi$
$251$	−17.6429	−1.11361	−0.556804	+	0.830644i	$0.687972\pi$
$252$	1.80204	0.113518
$253$	15.1053	0.949661
$254$	17.2818	1.08436
$255$	−4.18546	−0.262104
$256$	1.00000	0.0625000
$257$	−32.0616	−1.99995	−0.999973	−	0.00729303i	$-0.997679\pi$
$257$	−32.0616	−1.99995	−0.999973	+	0.00729303i	$0.997679\pi$
$258$	9.69474	0.603568
$259$	1.58098	0.0982370
$260$	5.08981	0.315657
$261$	13.0549	0.808075
$262$	15.0633	0.930613
$263$	21.6086	1.33244	0.666220	−	0.745755i	$-0.267911\pi$
$263$	21.6086	1.33244	0.666220	+	0.745755i	$0.267911\pi$
$264$	−3.43841	−0.211619
$265$	−3.04827	−0.187254
$266$	7.68978	0.471491
$267$	10.7192	0.656002
$268$	10.9790	0.670648
$269$	17.4097	1.06149	0.530744	−	0.847532i	$-0.321913\pi$
$269$	17.4097	1.06149	0.530744	+	0.847532i	$0.321913\pi$
$270$	14.7728	0.899043
$271$	6.62832	0.402642	0.201321	−	0.979525i	$-0.435477\pi$
$271$	6.62832	0.402642	0.201321	+	0.979525i	$0.435477\pi$
$272$	−1.36053	−0.0824941
$273$	−1.98202	−0.119957
$274$	−20.4563	−1.23581
$275$	−9.11054	−0.549386
$276$	5.26276	0.316781
$277$	−10.9097	−0.655498	−0.327749	−	0.944765i	$-0.606290\pi$
$277$	−10.9097	−0.655498	−0.327749	+	0.944765i	$0.606290\pi$
$278$	−9.16237	−0.549523
$279$	−16.6800	−0.998607
$280$	−2.81071	−0.167972
$281$	22.3482	1.33318	0.666590	−	0.745424i	$-0.267753\pi$
$281$	22.3482	1.33318	0.666590	+	0.745424i	$0.267753\pi$
$282$	5.18625	0.308837
$283$	23.7114	1.40950	0.704748	−	0.709458i	$-0.251060\pi$
$283$	23.7114	1.40950	0.704748	+	0.709458i	$0.251060\pi$
$284$	0.876158	0.0519904
$285$	23.6565	1.40129
$286$	−5.68882	−0.336387
$287$	−1.31343	−0.0775293
$288$	1.80204	0.106186
$289$	−15.1490	−0.891116
$290$	−20.3621	−1.19570
$291$	−16.1973	−0.949500
$292$	−9.59109	−0.561276
$293$	15.4160	0.900610	0.450305	−	0.892875i	$-0.351315\pi$
$293$	15.4160	0.900610	0.450305	+	0.892875i	$0.351315\pi$
$294$	1.09451	0.0638333
$295$	1.35379	0.0788208
$296$	1.58098	0.0918923
$297$	−16.5114	−0.958087
$298$	12.4472	0.721046
$299$	8.70721	0.503551
$300$	−3.17416	−0.183260
$301$	−8.85759	−0.510543
$302$	7.91171	0.455268
$303$	8.69565	0.499552
$304$	7.68978	0.441039
$305$	21.9389	1.25621
$306$	−2.45172	−0.140156
$307$	11.7705	0.671775	0.335888	−	0.941902i	$-0.390964\pi$
$307$	11.7705	0.671775	0.335888	+	0.941902i	$0.390964\pi$
$308$	3.14149	0.179003
$309$	9.26160	0.526874
$310$	26.0164	1.47763
$311$	−8.27611	−0.469295	−0.234648	−	0.972080i	$-0.575394\pi$
$311$	−8.27611	−0.469295	−0.234648	+	0.972080i	$0.575394\pi$
$312$	−1.98202	−0.112210
$313$	−31.6761	−1.79044	−0.895220	−	0.445624i	$-0.852982\pi$
$313$	−31.6761	−1.79044	−0.895220	+	0.445624i	$0.852982\pi$
$314$	3.52990	0.199204
$315$	−5.06501	−0.285381
$316$	15.1568	0.852639
$317$	−11.7562	−0.660297	−0.330148	−	0.943929i	$-0.607099\pi$
$317$	−11.7562	−0.660297	−0.330148	+	0.943929i	$0.607099\pi$
$318$	1.18702	0.0665650
$319$	22.7585	1.27423
$320$	−2.81071	−0.157123
$321$	−5.08602	−0.283874
$322$	−4.80831	−0.267957
$323$	−10.4622	−0.582130
$324$	−0.346528	−0.0192515
$325$	−5.25163	−0.291308
$326$	2.74807	0.152202
$327$	3.51288	0.194263
$328$	−1.31343	−0.0725220
$329$	−4.73841	−0.261237
$330$	9.66435	0.532005
$331$	−3.13748	−0.172452	−0.0862259	−	0.996276i	$-0.527481\pi$
$331$	−3.13748	−0.172452	−0.0862259	+	0.996276i	$0.527481\pi$
$332$	10.6776	0.586012
$333$	2.84898	0.156123
$334$	16.7197	0.914861
$335$	−30.8587	−1.68599
$336$	1.09451	0.0597106
$337$	5.45798	0.297315	0.148658	−	0.988889i	$-0.452505\pi$
$337$	5.45798	0.297315	0.148658	+	0.988889i	$0.452505\pi$
$338$	9.72077	0.528740
$339$	−11.8865	−0.645584
$340$	3.82404	0.207388
$341$	−29.0783	−1.57468
$342$	13.8573	0.749317
$343$	−1.00000	−0.0539949
$344$	−8.85759	−0.477569
$345$	−14.7921	−0.796378
$346$	−26.0461	−1.40025
$347$	24.2166	1.30001	0.650007	−	0.759928i	$-0.274766\pi$
$347$	24.2166	1.30001	0.650007	+	0.759928i	$0.274766\pi$
$348$	7.92918	0.425049
$349$	−17.4976	−0.936624	−0.468312	−	0.883563i	$-0.655138\pi$
$349$	−17.4976	−0.936624	−0.468312	+	0.883563i	$0.655138\pi$
$350$	2.90007	0.155015
$351$	−9.51772	−0.508018
$352$	3.14149	0.167442
$353$	−28.0072	−1.49067	−0.745335	−	0.666690i	$-0.767711\pi$
$353$	−28.0072	−1.49067	−0.745335	+	0.666690i	$0.767711\pi$
$354$	−0.527178	−0.0280192
$355$	−2.46262	−0.130702
$356$	−9.79354	−0.519057
$357$	−1.48911	−0.0788123
$358$	−6.72965	−0.355673
$359$	1.35368	0.0714446	0.0357223	−	0.999362i	$-0.488627\pi$
$359$	1.35368	0.0714446	0.0357223	+	0.999362i	$0.488627\pi$
$360$	−5.06501	−0.266949
$361$	40.1327	2.11225
$362$	5.72061	0.300669
$363$	1.23791	0.0649734
$364$	1.81087	0.0949151
$365$	26.9577	1.41103
$366$	−8.54318	−0.446559
$367$	−0.145016	−0.00756976	−0.00378488	−	0.999993i	$-0.501205\pi$
$367$	−0.145016	−0.00756976	−0.00378488	+	0.999993i	$0.501205\pi$
$368$	−4.80831	−0.250651
$369$	−2.36685	−0.123213
$370$	−4.44366	−0.231015
$371$	−1.08452	−0.0563056
$372$	−10.1310	−0.525269
$373$	−24.3753	−1.26210	−0.631052	−	0.775740i	$-0.717377\pi$
$373$	−24.3753	−1.26210	−0.631052	+	0.775740i	$0.717377\pi$
$374$	−4.27409	−0.221008
$375$	−6.46014	−0.333600
$376$	−4.73841	−0.244365
$377$	13.1188	0.675652
$378$	5.25590	0.270334
$379$	11.2444	0.577588	0.288794	−	0.957391i	$-0.406746\pi$
$379$	11.2444	0.577588	0.288794	+	0.957391i	$0.406746\pi$
$380$	−21.6137	−1.10876
$381$	18.9152	0.969054
$382$	14.2019	0.726632
$383$	29.1995	1.49202	0.746012	−	0.665932i	$-0.231966\pi$
$383$	29.1995	1.49202	0.746012	+	0.665932i	$0.231966\pi$
$384$	1.09451	0.0558541
$385$	−8.82982	−0.450009
$386$	−15.8672	−0.807618
$387$	−15.9617	−0.811380
$388$	14.7986	0.751284
$389$	−28.8158	−1.46102	−0.730509	−	0.682903i	$-0.760717\pi$
$389$	−28.8158	−1.46102	−0.730509	+	0.682903i	$0.760717\pi$
$390$	5.57086	0.282092
$391$	6.54184	0.330835
$392$	−1.00000	−0.0505076
$393$	16.4870	0.831657
$394$	−2.21134	−0.111406
$395$	−42.6014	−2.14351
$396$	5.66110	0.284481
$397$	−16.7430	−0.840310	−0.420155	−	0.907452i	$-0.638024\pi$
$397$	−16.7430	−0.840310	−0.420155	+	0.907452i	$0.638024\pi$
$398$	−10.0916	−0.505846
$399$	8.41657	0.421355
$400$	2.90007	0.145003
$401$	8.57885	0.428407	0.214204	−	0.976789i	$-0.431284\pi$
$401$	8.57885	0.428407	0.214204	+	0.976789i	$0.431284\pi$
$402$	12.0166	0.599335
$403$	−16.7617	−0.834960
$404$	−7.94477	−0.395267
$405$	0.973988	0.0483978
$406$	−7.24448	−0.359538
$407$	4.96662	0.246186
$408$	−1.48911	−0.0737222
$409$	−28.1237	−1.39063	−0.695315	−	0.718706i	$-0.744735\pi$
$409$	−28.1237	−1.39063	−0.695315	+	0.718706i	$0.744735\pi$
$410$	3.69166	0.182318
$411$	−22.3897	−1.10440
$412$	−8.46185	−0.416885
$413$	0.481656	0.0237007
$414$	−8.66477	−0.425850
$415$	−30.0117	−1.47322
$416$	1.81087	0.0887850
$417$	−10.0283	−0.491090
$418$	24.1574	1.18158
$419$	−14.1840	−0.692934	−0.346467	−	0.938062i	$-0.612619\pi$
$419$	−14.1840	−0.692934	−0.346467	+	0.938062i	$0.612619\pi$
$420$	−3.07635	−0.150111
$421$	11.0487	0.538482	0.269241	−	0.963073i	$-0.413227\pi$
$421$	11.0487	0.538482	0.269241	+	0.963073i	$0.413227\pi$
$422$	10.8458	0.527967
$423$	−8.53880	−0.415171
$424$	−1.08452	−0.0526690
$425$	−3.94562	−0.191391
$426$	0.958967	0.0464621
$427$	7.80546	0.377733
$428$	4.64683	0.224613
$429$	−6.22649	−0.300618
$430$	24.8961	1.20059
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.25590	0.252874
$433$	−12.0447	−0.578831	−0.289415	−	0.957204i	$-0.593461\pi$
$433$	−12.0447	−0.578831	−0.289415	+	0.957204i	$0.593461\pi$
$434$	9.25619	0.444311
$435$	−22.2866	−1.06856
$436$	−3.20954	−0.153709
$437$	−36.9749	−1.76875
$438$	−10.4976	−0.501593
$439$	−34.2815	−1.63617	−0.818084	−	0.575098i	$-0.804964\pi$
$439$	−34.2815	−1.63617	−0.818084	+	0.575098i	$0.804964\pi$
$440$	−8.82982	−0.420945
$441$	−1.80204	−0.0858115
$442$	−2.46373	−0.117188
$443$	10.4124	0.494707	0.247354	−	0.968925i	$-0.420439\pi$
$443$	10.4124	0.494707	0.247354	+	0.968925i	$0.420439\pi$
$444$	1.73040	0.0821211
$445$	27.5268	1.30489
$446$	10.4097	0.492915
$447$	13.6236	0.644375
$448$	−1.00000	−0.0472456
$449$	7.40036	0.349244	0.174622	−	0.984636i	$-0.444130\pi$
$449$	7.40036	0.349244	0.174622	+	0.984636i	$0.444130\pi$
$450$	5.22604	0.246358
$451$	−4.12613	−0.194292
$452$	10.8600	0.510813
$453$	8.65947	0.406858
$454$	−8.76942	−0.411569
$455$	−5.08981	−0.238614
$456$	8.41657	0.394142
$457$	−9.78764	−0.457846	−0.228923	−	0.973444i	$-0.573520\pi$
$457$	−9.78764	−0.457846	−0.228923	+	0.973444i	$0.573520\pi$
$458$	−4.20289	−0.196388
$459$	−7.15079	−0.333770
$460$	13.5147	0.630128
$461$	9.19878	0.428430	0.214215	−	0.976787i	$-0.431281\pi$
$461$	9.19878	0.428430	0.214215	+	0.976787i	$0.431281\pi$
$462$	3.43841	0.159969
$463$	−8.66471	−0.402683	−0.201342	−	0.979521i	$-0.564530\pi$
$463$	−8.66471	−0.402683	−0.201342	+	0.979521i	$0.564530\pi$
$464$	−7.24448	−0.336317
$465$	28.4753	1.32051
$466$	−5.02737	−0.232888
$467$	−7.24462	−0.335241	−0.167621	−	0.985852i	$-0.553608\pi$
$467$	−7.24462	−0.335241	−0.167621	+	0.985852i	$0.553608\pi$
$468$	3.26325	0.150844
$469$	−10.9790	−0.506962
$470$	13.3183	0.614326
$471$	3.86352	0.178022
$472$	0.481656	0.0221700
$473$	−27.8261	−1.27944
$474$	16.5894	0.761975
$475$	22.3009	1.02323
$476$	1.36053	0.0623597
$477$	−1.95435	−0.0894836
$478$	−7.71308	−0.352788
$479$	10.9184	0.498873	0.249437	−	0.968391i	$-0.419755\pi$
$479$	10.9184	0.498873	0.249437	+	0.968391i	$0.419755\pi$
$480$	−3.07635	−0.140416
$481$	2.86293	0.130539
$482$	−8.82661	−0.402041
$483$	−5.26276	−0.239464
$484$	−1.13101	−0.0514097
$485$	−41.5945	−1.88871
$486$	15.3884	0.698033
$487$	−11.4566	−0.519150	−0.259575	−	0.965723i	$-0.583583\pi$
$487$	−11.4566	−0.519150	−0.259575	+	0.965723i	$0.583583\pi$
$488$	7.80546	0.353337
$489$	3.00780	0.136017
$490$	2.81071	0.126975
$491$	−16.6548	−0.751619	−0.375809	−	0.926697i	$-0.622635\pi$
$491$	−16.6548	−0.751619	−0.375809	+	0.926697i	$0.622635\pi$
$492$	−1.43757	−0.0648105
$493$	9.85632	0.443906
$494$	13.9252	0.626522
$495$	−15.9117	−0.715177
$496$	9.25619	0.415615
$497$	−0.876158	−0.0393011
$498$	11.6868	0.523699
$499$	18.7918	0.841236	0.420618	−	0.907238i	$-0.361813\pi$
$499$	18.7918	0.841236	0.420618	+	0.907238i	$0.361813\pi$
$500$	5.90230	0.263959
$501$	18.2999	0.817581
$502$	17.6429	0.787439
$503$	7.18199	0.320229	0.160115	−	0.987098i	$-0.448814\pi$
$503$	7.18199	0.320229	0.160115	+	0.987098i	$0.448814\pi$
$504$	−1.80204	−0.0802693
$505$	22.3304	0.993690
$506$	−15.1053	−0.671512
$507$	10.6395	0.472517
$508$	−17.2818	−0.766757
$509$	16.8476	0.746756	0.373378	−	0.927679i	$-0.378200\pi$
$509$	16.8476	0.746756	0.373378	+	0.927679i	$0.378200\pi$
$510$	4.18546	0.185335
$511$	9.59109	0.424285
$512$	−1.00000	−0.0441942
$513$	40.4167	1.78444
$514$	32.0616	1.41418
$515$	23.7838	1.04804
$516$	−9.69474	−0.426787
$517$	−14.8857	−0.654672
$518$	−1.58098	−0.0694641
$519$	−28.5078	−1.25135
$520$	−5.08981	−0.223203
$521$	−2.06221	−0.0903469	−0.0451734	−	0.998979i	$-0.514384\pi$
$521$	−2.06221	−0.0903469	−0.0451734	+	0.998979i	$0.514384\pi$
$522$	−13.0549	−0.571395
$523$	−35.4045	−1.54813	−0.774065	−	0.633107i	$-0.781779\pi$
$523$	−35.4045	−1.54813	−0.774065	+	0.633107i	$0.781779\pi$
$524$	−15.0633	−0.658043
$525$	3.17416	0.138532
$526$	−21.6086	−0.942178
$527$	−12.5933	−0.548572
$528$	3.43841	0.149637
$529$	0.119857	0.00521119
$530$	3.04827	0.132408
$531$	0.867963	0.0376664
$532$	−7.68978	−0.333394
$533$	−2.37844	−0.103022
$534$	−10.7192	−0.463863
$535$	−13.0609	−0.564671
$536$	−10.9790	−0.474220
$537$	−7.36570	−0.317853
$538$	−17.4097	−0.750585
$539$	−3.14149	−0.135314
$540$	−14.7728	−0.635719
$541$	−22.1238	−0.951178	−0.475589	−	0.879668i	$-0.657765\pi$
$541$	−22.1238	−0.951178	−0.475589	+	0.879668i	$0.657765\pi$
$542$	−6.62832	−0.284711
$543$	6.26129	0.268698
$544$	1.36053	0.0583321
$545$	9.02107	0.386420
$546$	1.98202	0.0848225
$547$	−3.20639	−0.137095	−0.0685477	−	0.997648i	$-0.521837\pi$
$547$	−3.20639	−0.137095	−0.0685477	+	0.997648i	$0.521837\pi$
$548$	20.4563	0.873850
$549$	14.0658	0.600312
$550$	9.11054	0.388475
$551$	−55.7085	−2.37326
$552$	−5.26276	−0.223998
$553$	−15.1568	−0.644535
$554$	10.9097	0.463507
$555$	−4.86364	−0.206450
$556$	9.16237	0.388571
$557$	24.5406	1.03982	0.519910	−	0.854221i	$-0.325966\pi$
$557$	24.5406	1.03982	0.519910	+	0.854221i	$0.325966\pi$
$558$	16.6800	0.706122
$559$	−16.0399	−0.678415
$560$	2.81071	0.118774
$561$	−4.67805	−0.197507
$562$	−22.3482	−0.942701
$563$	−9.79875	−0.412968	−0.206484	−	0.978450i	$-0.566202\pi$
$563$	−9.79875	−0.412968	−0.206484	+	0.978450i	$0.566202\pi$
$564$	−5.18625	−0.218381
$565$	−30.5244	−1.28417
$566$	−23.7114	−0.996664
$567$	0.346528	0.0145528
$568$	−0.876158	−0.0367628
$569$	25.0678	1.05090	0.525449	−	0.850825i	$-0.323897\pi$
$569$	25.0678	1.05090	0.525449	+	0.850825i	$0.323897\pi$
$570$	−23.6565	−0.990861
$571$	23.6529	0.989845	0.494922	−	0.868937i	$-0.335196\pi$
$571$	23.6529	0.989845	0.494922	+	0.868937i	$0.335196\pi$
$572$	5.68882	0.237862
$573$	15.5442	0.649366
$574$	1.31343	0.0548215
$575$	−13.9444	−0.581523
$576$	−1.80204	−0.0750850
$577$	−12.8266	−0.533978	−0.266989	−	0.963700i	$-0.586029\pi$
$577$	−12.8266	−0.533978	−0.266989	+	0.963700i	$0.586029\pi$
$578$	15.1490	0.630114
$579$	−17.3668	−0.721741
$580$	20.3621	0.845491
$581$	−10.6776	−0.442983
$582$	16.1973	0.671398
$583$	−3.40702	−0.141104
$584$	9.59109	0.396882
$585$	−9.17204	−0.379217
$586$	−15.4160	−0.636827
$587$	16.3498	0.674828	0.337414	−	0.941356i	$-0.390448\pi$
$587$	16.3498	0.674828	0.337414	+	0.941356i	$0.390448\pi$
$588$	−1.09451	−0.0451370
$589$	71.1781	2.93284
$590$	−1.35379	−0.0557347
$591$	−2.42034	−0.0995595
$592$	−1.58098	−0.0649777
$593$	−41.8466	−1.71843	−0.859217	−	0.511611i	$-0.829049\pi$
$593$	−41.8466	−1.71843	−0.859217	+	0.511611i	$0.829049\pi$
$594$	16.5114	0.677470
$595$	−3.82404	−0.156770
$596$	−12.4472	−0.509856
$597$	−11.0454	−0.452057
$598$	−8.70721	−0.356064
$599$	−22.5555	−0.921594	−0.460797	−	0.887506i	$-0.652436\pi$
$599$	−22.5555	−0.921594	−0.460797	+	0.887506i	$0.652436\pi$
$600$	3.17416	0.129585
$601$	−7.15114	−0.291701	−0.145851	−	0.989307i	$-0.546592\pi$
$601$	−7.15114	−0.291701	−0.145851	+	0.989307i	$0.546592\pi$
$602$	8.85759	0.361008
$603$	−19.7846	−0.805690
$604$	−7.91171	−0.321923
$605$	3.17895	0.129243
$606$	−8.69565	−0.353237
$607$	7.32368	0.297259	0.148630	−	0.988893i	$-0.452514\pi$
$607$	7.32368	0.297259	0.148630	+	0.988893i	$0.452514\pi$
$608$	−7.68978	−0.311862
$609$	−7.92918	−0.321307
$610$	−21.9389	−0.888278
$611$	−8.58062	−0.347135
$612$	2.45172	0.0991051
$613$	−15.1562	−0.612152	−0.306076	−	0.952007i	$-0.599016\pi$
$613$	−15.1562	−0.612152	−0.306076	+	0.952007i	$0.599016\pi$
$614$	−11.7705	−0.475017
$615$	4.04057	0.162932
$616$	−3.14149	−0.126574
$617$	7.51837	0.302678	0.151339	−	0.988482i	$-0.451641\pi$
$617$	7.51837	0.302678	0.151339	+	0.988482i	$0.451641\pi$
$618$	−9.26160	−0.372556
$619$	−11.5817	−0.465507	−0.232753	−	0.972536i	$-0.574774\pi$
$619$	−11.5817	−0.465507	−0.232753	+	0.972536i	$0.574774\pi$
$620$	−26.0164	−1.04484
$621$	−25.2720	−1.01413
$622$	8.27611	0.331842
$623$	9.79354	0.392370
$624$	1.98202	0.0793442
$625$	−31.0899	−1.24360
$626$	31.6761	1.26603
$627$	26.4406	1.05594
$628$	−3.52990	−0.140858
$629$	2.15096	0.0857644
$630$	5.06501	0.201795
$631$	−38.1691	−1.51949	−0.759744	−	0.650222i	$-0.774676\pi$
$631$	−38.1691	−1.51949	−0.759744	+	0.650222i	$0.774676\pi$
$632$	−15.1568	−0.602907
$633$	11.8709	0.471826
$634$	11.7562	0.466900
$635$	48.5741	1.92760
$636$	−1.18702	−0.0470685
$637$	−1.81087	−0.0717491
$638$	−22.7585	−0.901018
$639$	−1.57887	−0.0624592
$640$	2.81071	0.111103
$641$	20.4689	0.808474	0.404237	−	0.914654i	$-0.367537\pi$
$641$	20.4689	0.808474	0.404237	+	0.914654i	$0.367537\pi$
$642$	5.08602	0.200729
$643$	0.0544508	0.00214733	0.00107367	−	0.999999i	$-0.499658\pi$
$643$	0.0544508	0.00214733	0.00107367	+	0.999999i	$0.499658\pi$
$644$	4.80831	0.189474
$645$	27.2491	1.07293
$646$	10.4622	0.411628
$647$	−16.1559	−0.635153	−0.317577	−	0.948233i	$-0.602869\pi$
$647$	−16.1559	−0.635153	−0.317577	+	0.948233i	$0.602869\pi$
$648$	0.346528	0.0136129
$649$	1.51312	0.0593951
$650$	5.25163	0.205986
$651$	10.1310	0.397066
$652$	−2.74807	−0.107623
$653$	29.5302	1.15561	0.577803	−	0.816176i	$-0.303910\pi$
$653$	29.5302	1.15561	0.577803	+	0.816176i	$0.303910\pi$
$654$	−3.51288	−0.137365
$655$	42.3385	1.65430
$656$	1.31343	0.0512808
$657$	17.2835	0.674295
$658$	4.73841	0.184722
$659$	0.911920	0.0355234	0.0177617	−	0.999842i	$-0.494346\pi$
$659$	0.911920	0.0355234	0.0177617	+	0.999842i	$0.494346\pi$
$660$	−9.66435	−0.376184
$661$	27.2685	1.06062	0.530312	−	0.847803i	$-0.322075\pi$
$661$	27.2685	1.06062	0.530312	+	0.847803i	$0.322075\pi$
$662$	3.13748	0.121942
$663$	−2.69659	−0.104727
$664$	−10.6776	−0.414373
$665$	21.6137	0.838144
$666$	−2.84898	−0.110396
$667$	34.8337	1.34877
$668$	−16.7197	−0.646905
$669$	11.3936	0.440501
$670$	30.8587	1.19217
$671$	24.5208	0.946615
$672$	−1.09451	−0.0422218
$673$	1.31181	0.0505666	0.0252833	−	0.999680i	$-0.491951\pi$
$673$	1.31181	0.0505666	0.0252833	+	0.999680i	$0.491951\pi$
$674$	−5.45798	−0.210234
$675$	15.2424	0.586682
$676$	−9.72077	−0.373876
$677$	31.6755	1.21739	0.608694	−	0.793405i	$-0.291694\pi$
$677$	31.6755	1.21739	0.608694	+	0.793405i	$0.291694\pi$
$678$	11.8865	0.456497
$679$	−14.7986	−0.567918
$680$	−3.82404	−0.146645
$681$	−9.59824	−0.367805
$682$	29.0783	1.11346
$683$	35.0468	1.34103	0.670515	−	0.741896i	$-0.266073\pi$
$683$	35.0468	1.34103	0.670515	+	0.741896i	$0.266073\pi$
$684$	−13.8573	−0.529847
$685$	−57.4966	−2.19683
$686$	1.00000	0.0381802
$687$	−4.60012	−0.175505
$688$	8.85759	0.337692
$689$	−1.96392	−0.0748195
$690$	14.7921	0.563125
$691$	−9.16982	−0.348837	−0.174418	−	0.984672i	$-0.555804\pi$
$691$	−9.16982	−0.348837	−0.174418	+	0.984672i	$0.555804\pi$
$692$	26.0461	0.990123
$693$	−5.66110	−0.215047
$694$	−24.2166	−0.919248
$695$	−25.7527	−0.976857
$696$	−7.92918	−0.300555
$697$	−1.78696	−0.0676858
$698$	17.4976	0.662293
$699$	−5.50252	−0.208124
$700$	−2.90007	−0.109612
$701$	−30.9682	−1.16965	−0.584827	−	0.811158i	$-0.698838\pi$
$701$	−30.9682	−1.16965	−0.584827	+	0.811158i	$0.698838\pi$
$702$	9.51772	0.359223
$703$	−12.1574	−0.458523
$704$	−3.14149	−0.118400
$705$	14.5770	0.549002
$706$	28.0072	1.05406
$707$	7.94477	0.298794
$708$	0.527178	0.0198126
$709$	23.7361	0.891428	0.445714	−	0.895175i	$-0.352950\pi$
$709$	23.7361	0.891428	0.445714	+	0.895175i	$0.352950\pi$
$710$	2.46262	0.0924206
$711$	−27.3133	−1.02433
$712$	9.79354	0.367028
$713$	−44.5066	−1.66679
$714$	1.48911	0.0557287
$715$	−15.9896	−0.597977
$716$	6.72965	0.251499
$717$	−8.44207	−0.315275
$718$	−1.35368	−0.0505190
$719$	−26.7082	−0.996046	−0.498023	−	0.867164i	$-0.665941\pi$
$719$	−26.7082	−0.996046	−0.498023	+	0.867164i	$0.665941\pi$
$720$	5.06501	0.188762
$721$	8.46185	0.315136
$722$	−40.1327	−1.49359
$723$	−9.66084	−0.359291
$724$	−5.72061	−0.212605
$725$	−21.0095	−0.780273
$726$	−1.23791	−0.0459432
$727$	9.81289	0.363940	0.181970	−	0.983304i	$-0.441753\pi$
$727$	9.81289	0.363940	0.181970	+	0.983304i	$0.441753\pi$
$728$	−1.81087	−0.0671151
$729$	17.8824	0.662311
$730$	−26.9577	−0.997750
$731$	−12.0510	−0.445722
$732$	8.54318	0.315765
$733$	−43.8203	−1.61854	−0.809270	−	0.587438i	$-0.800137\pi$
$733$	−43.8203	−1.61854	−0.809270	+	0.587438i	$0.800137\pi$
$734$	0.145016	0.00535263
$735$	3.07635	0.113473
$736$	4.80831	0.177237
$737$	−34.4904	−1.27047
$738$	2.36685	0.0871250
$739$	20.4900	0.753737	0.376868	−	0.926267i	$-0.377001\pi$
$739$	20.4900	0.753737	0.376868	+	0.926267i	$0.377001\pi$
$740$	4.44366	0.163352
$741$	15.2413	0.559902
$742$	1.08452	0.0398140
$743$	−40.0058	−1.46767	−0.733835	−	0.679328i	$-0.762272\pi$
$743$	−40.0058	−1.46767	−0.733835	+	0.679328i	$0.762272\pi$
$744$	10.1310	0.371421
$745$	34.9854	1.28176
$746$	24.3753	0.892443
$747$	−19.2415	−0.704011
$748$	4.27409	0.156276
$749$	−4.64683	−0.169792
$750$	6.46014	0.235891
$751$	12.9350	0.472005	0.236003	−	0.971752i	$-0.424163\pi$
$751$	12.9350	0.472005	0.236003	+	0.971752i	$0.424163\pi$
$752$	4.73841	0.172792
$753$	19.3103	0.703708
$754$	−13.1188	−0.477758
$755$	22.2375	0.809305
$756$	−5.25590	−0.191155
$757$	3.29759	0.119853	0.0599265	−	0.998203i	$-0.480913\pi$
$757$	3.29759	0.119853	0.0599265	+	0.998203i	$0.480913\pi$
$758$	−11.2444	−0.408416
$759$	−16.5329	−0.600107
$760$	21.6137	0.784012
$761$	−23.0098	−0.834104	−0.417052	−	0.908883i	$-0.636937\pi$
$761$	−23.0098	−0.834104	−0.417052	+	0.908883i	$0.636937\pi$
$762$	−18.9152	−0.685225
$763$	3.20954	0.116193
$764$	−14.2019	−0.513806
$765$	−6.89108	−0.249147
$766$	−29.1995	−1.05502
$767$	0.872213	0.0314938
$768$	−1.09451	−0.0394948
$769$	4.05079	0.146075	0.0730376	−	0.997329i	$-0.476731\pi$
$769$	4.05079	0.146075	0.0730376	+	0.997329i	$0.476731\pi$
$770$	8.82982	0.318204
$771$	35.0918	1.26380
$772$	15.8672	0.571072
$773$	−40.9816	−1.47401	−0.737003	−	0.675890i	$-0.763760\pi$
$773$	−40.9816	−1.47401	−0.737003	+	0.675890i	$0.763760\pi$
$774$	15.9617	0.573732
$775$	26.8436	0.964249
$776$	−14.7986	−0.531238
$777$	−1.73040	−0.0620777
$778$	28.8158	1.03310
$779$	10.1000	0.361869
$780$	−5.57086	−0.199469
$781$	−2.75245	−0.0984902
$782$	−6.54184	−0.233936
$783$	−38.0763	−1.36073
$784$	1.00000	0.0357143
$785$	9.92151	0.354114
$786$	−16.4870	−0.588070
$787$	55.1962	1.96753	0.983767	−	0.179452i	$-0.0574325\pi$
$787$	55.1962	1.96753	0.983767	+	0.179452i	$0.0574325\pi$
$788$	2.21134	0.0787757
$789$	−23.6509	−0.841993
$790$	42.6014	1.51569
$791$	−10.8600	−0.386139
$792$	−5.66110	−0.201158
$793$	14.1346	0.501936
$794$	16.7430	0.594189
$795$	3.33637	0.118329
$796$	10.0916	0.357687
$797$	27.2861	0.966523	0.483261	−	0.875476i	$-0.339452\pi$
$797$	27.2861	0.966523	0.483261	+	0.875476i	$0.339452\pi$
$798$	−8.41657	−0.297943
$799$	−6.44673	−0.228069
$800$	−2.90007	−0.102533
$801$	17.6484	0.623574
$802$	−8.57885	−0.302930
$803$	30.1303	1.06328
$804$	−12.0166	−0.423794
$805$	−13.5147	−0.476332
$806$	16.7617	0.590406
$807$	−19.0551	−0.670772
$808$	7.94477	0.279496
$809$	−12.2541	−0.430833	−0.215416	−	0.976522i	$-0.569111\pi$
$809$	−12.2541	−0.430833	−0.215416	+	0.976522i	$0.569111\pi$
$810$	−0.973988	−0.0342224
$811$	−34.5310	−1.21255	−0.606275	−	0.795255i	$-0.707337\pi$
$811$	−34.5310	−1.21255	−0.606275	+	0.795255i	$0.707337\pi$
$812$	7.24448	0.254232
$813$	−7.25479	−0.254437
$814$	−4.96662	−0.174080
$815$	7.72402	0.270561
$816$	1.48911	0.0521294
$817$	68.1129	2.38297
$818$	28.1237	0.983323
$819$	−3.26325	−0.114027
$820$	−3.69166	−0.128918
$821$	3.31405	0.115661	0.0578306	−	0.998326i	$-0.481582\pi$
$821$	3.31405	0.115661	0.0578306	+	0.998326i	$0.481582\pi$
$822$	22.3897	0.780930
$823$	40.1720	1.40031	0.700154	−	0.713992i	$-0.253115\pi$
$823$	40.1720	1.40031	0.700154	+	0.713992i	$0.253115\pi$
$824$	8.46185	0.294782
$825$	9.97161	0.347167
$826$	−0.481656	−0.0167589
$827$	−20.6302	−0.717384	−0.358692	−	0.933456i	$-0.616777\pi$
$827$	−20.6302	−0.717384	−0.358692	+	0.933456i	$0.616777\pi$
$828$	8.66477	0.301122
$829$	2.09662	0.0728187	0.0364093	−	0.999337i	$-0.488408\pi$
$829$	2.09662	0.0728187	0.0364093	+	0.999337i	$0.488408\pi$
$830$	30.0117	1.04172
$831$	11.9408	0.414220
$832$	−1.81087	−0.0627805
$833$	−1.36053	−0.0471395
$834$	10.0283	0.347253
$835$	46.9942	1.62630
$836$	−24.1574	−0.835501
$837$	48.6496	1.68158
$838$	14.1840	0.489978
$839$	−19.4814	−0.672571	−0.336286	−	0.941760i	$-0.609171\pi$
$839$	−19.4814	−0.672571	−0.336286	+	0.941760i	$0.609171\pi$
$840$	3.07635	0.106144
$841$	23.4826	0.809743
$842$	−11.0487	−0.380764
$843$	−24.4604	−0.842460
$844$	−10.8458	−0.373329
$845$	27.3222	0.939913
$846$	8.53880	0.293570
$847$	1.13101	0.0388621
$848$	1.08452	0.0372426
$849$	−25.9524	−0.890685
$850$	3.94562	0.135334
$851$	7.60182	0.260587
$852$	−0.958967	−0.0328537
$853$	34.1455	1.16912	0.584560	−	0.811350i	$-0.301267\pi$
$853$	34.1455	1.16912	0.584560	+	0.811350i	$0.301267\pi$
$854$	−7.80546	−0.267097
$855$	38.9488	1.33202
$856$	−4.64683	−0.158825
$857$	−26.4892	−0.904852	−0.452426	−	0.891802i	$-0.649441\pi$
$857$	−26.4892	−0.904852	−0.452426	+	0.891802i	$0.649441\pi$
$858$	6.22649	0.212569
$859$	1.13108	0.0385921	0.0192961	−	0.999814i	$-0.493857\pi$
$859$	1.13108	0.0385921	0.0192961	+	0.999814i	$0.493857\pi$
$860$	−24.8961	−0.848949
$861$	1.43757	0.0489921
$862$	1.00000	0.0340601
$863$	−43.1056	−1.46733	−0.733666	−	0.679510i	$-0.762192\pi$
$863$	−43.1056	−1.46733	−0.733666	+	0.679510i	$0.762192\pi$
$864$	−5.25590	−0.178809
$865$	−73.2079	−2.48914
$866$	12.0447	0.409295
$867$	16.5807	0.563112
$868$	−9.25619	−0.314175
$869$	−47.6152	−1.61523
$870$	22.2866	0.755587
$871$	−19.8815	−0.673657
$872$	3.20954	0.108689
$873$	−26.6677	−0.902563
$874$	36.9749	1.25069
$875$	−5.90230	−0.199534
$876$	10.4976	0.354680
$877$	44.1647	1.49134	0.745668	−	0.666318i	$-0.232131\pi$
$877$	44.1647	1.49134	0.745668	+	0.666318i	$0.232131\pi$
$878$	34.2815	1.15695
$879$	−16.8730	−0.569111
$880$	8.82982	0.297653
$881$	25.3224	0.853133	0.426566	−	0.904456i	$-0.359723\pi$
$881$	25.3224	0.853133	0.426566	+	0.904456i	$0.359723\pi$
$882$	1.80204	0.0606779
$883$	−15.4949	−0.521445	−0.260722	−	0.965414i	$-0.583961\pi$
$883$	−15.4949	−0.521445	−0.260722	+	0.965414i	$0.583961\pi$
$884$	2.46373	0.0828643
$885$	−1.48174	−0.0498083
$886$	−10.4124	−0.349811
$887$	27.9796	0.939461	0.469731	−	0.882810i	$-0.344351\pi$
$887$	27.9796	0.939461	0.469731	+	0.882810i	$0.344351\pi$
$888$	−1.73040	−0.0580684
$889$	17.2818	0.579613
$890$	−27.5268	−0.922699
$891$	1.08862	0.0364700
$892$	−10.4097	−0.348543
$893$	36.4373	1.21933
$894$	−13.6236	−0.455642
$895$	−18.9151	−0.632261
$896$	1.00000	0.0334077
$897$	−9.53015	−0.318203
$898$	−7.40036	−0.246953
$899$	−67.0563	−2.23645
$900$	−5.22604	−0.174201
$901$	−1.47552	−0.0491567
$902$	4.12613	0.137385
$903$	9.69474	0.322621
$904$	−10.8600	−0.361200
$905$	16.0790	0.534483
$906$	−8.65947	−0.287692
$907$	−5.49481	−0.182452	−0.0912261	−	0.995830i	$-0.529079\pi$
$907$	−5.49481	−0.182452	−0.0912261	+	0.995830i	$0.529079\pi$
$908$	8.76942	0.291023
$909$	14.3168	0.474858
$910$	5.08981	0.168726
$911$	−12.9031	−0.427499	−0.213749	−	0.976889i	$-0.568568\pi$
$911$	−12.9031	−0.427499	−0.213749	+	0.976889i	$0.568568\pi$
$912$	−8.41657	−0.278700
$913$	−33.5438	−1.11014
$914$	9.78764	0.323746
$915$	−24.0124	−0.793824
$916$	4.20289	0.138867
$917$	15.0633	0.497433
$918$	7.15079	0.236011
$919$	−39.6528	−1.30802	−0.654012	−	0.756484i	$-0.726915\pi$
$919$	−39.6528	−1.30802	−0.654012	+	0.756484i	$0.726915\pi$
$920$	−13.5147	−0.445568
$921$	−12.8829	−0.424507
$922$	−9.19878	−0.302946
$923$	−1.58660	−0.0522237
$924$	−3.43841	−0.113115
$925$	−4.58493	−0.150752
$926$	8.66471	0.284740
$927$	15.2486	0.500830
$928$	7.24448	0.237812
$929$	13.6751	0.448666	0.224333	−	0.974513i	$-0.427980\pi$
$929$	13.6751	0.448666	0.224333	+	0.974513i	$0.427980\pi$
$930$	−28.4753	−0.933742
$931$	7.68978	0.252022
$932$	5.02737	0.164677
$933$	9.05832	0.296556
$934$	7.24462	0.237051
$935$	−12.0132	−0.392874
$936$	−3.26325	−0.106663
$937$	24.9427	0.814842	0.407421	−	0.913240i	$-0.366428\pi$
$937$	24.9427	0.814842	0.407421	+	0.913240i	$0.366428\pi$
$938$	10.9790	0.358476
$939$	34.6699	1.13141
$940$	−13.3183	−0.434394
$941$	−49.7651	−1.62230	−0.811148	−	0.584841i	$-0.801157\pi$
$941$	−49.7651	−1.62230	−0.811148	+	0.584841i	$0.801157\pi$
$942$	−3.86352	−0.125880
$943$	−6.31538	−0.205657
$944$	−0.481656	−0.0156766
$945$	14.7728	0.480559
$946$	27.8261	0.904703
$947$	−39.0796	−1.26992	−0.634958	−	0.772546i	$-0.718983\pi$
$947$	−39.0796	−1.26992	−0.634958	+	0.772546i	$0.718983\pi$
$948$	−16.5894	−0.538798
$949$	17.3682	0.563795
$950$	−22.3009	−0.723536
$951$	12.8674	0.417253
$952$	−1.36053	−0.0440949
$953$	28.5651	0.925314	0.462657	−	0.886537i	$-0.346896\pi$
$953$	28.5651	0.925314	0.462657	+	0.886537i	$0.346896\pi$
$954$	1.95435	0.0632745
$955$	39.9173	1.29169
$956$	7.71308	0.249459
$957$	−24.9095	−0.805209
$958$	−10.9184	−0.352757
$959$	−20.4563	−0.660568
$960$	3.07635	0.0992889
$961$	54.6770	1.76377
$962$	−2.86293	−0.0923047
$963$	−8.37378	−0.269841
$964$	8.82661	0.284286
$965$	−44.5979	−1.43566
$966$	5.26276	0.169327
$967$	−14.7729	−0.475066	−0.237533	−	0.971379i	$-0.576339\pi$
$967$	−14.7729	−0.475066	−0.237533	+	0.971379i	$0.576339\pi$
$968$	1.13101	0.0363522
$969$	11.4510	0.367858
$970$	41.5945	1.33552
$971$	−51.4786	−1.65203	−0.826013	−	0.563652i	$-0.809396\pi$
$971$	−51.4786	−1.65203	−0.826013	+	0.563652i	$0.809396\pi$
$972$	−15.3884	−0.493584
$973$	−9.16237	−0.293732
$974$	11.4566	0.367095
$975$	5.74798	0.184083
$976$	−7.80546	−0.249847
$977$	28.7335	0.919267	0.459634	−	0.888109i	$-0.347981\pi$
$977$	28.7335	0.919267	0.459634	+	0.888109i	$0.347981\pi$
$978$	−3.00780	−0.0961788
$979$	30.7663	0.983297
$980$	−2.81071	−0.0897847
$981$	5.78372	0.184660
$982$	16.6548	0.531475
$983$	46.2001	1.47355	0.736777	−	0.676136i	$-0.236347\pi$
$983$	46.2001	1.47355	0.736777	+	0.676136i	$0.236347\pi$
$984$	1.43757	0.0458279
$985$	−6.21542	−0.198040
$986$	−9.85632	−0.313889
$987$	5.18625	0.165080
$988$	−13.9252	−0.443018
$989$	−42.5900	−1.35428
$990$	15.9117	0.505707
$991$	29.5722	0.939393	0.469696	−	0.882828i	$-0.344363\pi$
$991$	29.5722	0.939393	0.469696	+	0.882828i	$0.344363\pi$
$992$	−9.25619	−0.293884
$993$	3.43402	0.108975
$994$	0.876158	0.0277900
$995$	−28.3645	−0.899215
$996$	−11.6868	−0.370311
$997$	−46.5018	−1.47273	−0.736364	−	0.676586i	$-0.763459\pi$
$997$	−46.5018	−1.47273	−0.736364	+	0.676586i	$0.763459\pi$
$998$	−18.7918	−0.594843
$999$	−8.30944	−0.262899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.9	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.9	✓	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.09451 q^{3} +1.00000 q^{4} -2.81071 q^{5} +1.09451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.80204 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.09451 q^{3} +1.00000 q^{4} -2.81071 q^{5} +1.09451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.80204 q^{9} +2.81071 q^{10} -3.14149 q^{11} -1.09451 q^{12} -1.81087 q^{13} +1.00000 q^{14} +3.07635 q^{15} +1.00000 q^{16} -1.36053 q^{17} +1.80204 q^{18} +7.68978 q^{19} -2.81071 q^{20} +1.09451 q^{21} +3.14149 q^{22} -4.80831 q^{23} +1.09451 q^{24} +2.90007 q^{25} +1.81087 q^{26} +5.25590 q^{27} -1.00000 q^{28} -7.24448 q^{29} -3.07635 q^{30} +9.25619 q^{31} -1.00000 q^{32} +3.43841 q^{33} +1.36053 q^{34} +2.81071 q^{35} -1.80204 q^{36} -1.58098 q^{37} -7.68978 q^{38} +1.98202 q^{39} +2.81071 q^{40} +1.31343 q^{41} -1.09451 q^{42} +8.85759 q^{43} -3.14149 q^{44} +5.06501 q^{45} +4.80831 q^{46} +4.73841 q^{47} -1.09451 q^{48} +1.00000 q^{49} -2.90007 q^{50} +1.48911 q^{51} -1.81087 q^{52} +1.08452 q^{53} -5.25590 q^{54} +8.82982 q^{55} +1.00000 q^{56} -8.41657 q^{57} +7.24448 q^{58} -0.481656 q^{59} +3.07635 q^{60} -7.80546 q^{61} -9.25619 q^{62} +1.80204 q^{63} +1.00000 q^{64} +5.08981 q^{65} -3.43841 q^{66} +10.9790 q^{67} -1.36053 q^{68} +5.26276 q^{69} -2.81071 q^{70} +0.876158 q^{71} +1.80204 q^{72} -9.59109 q^{73} +1.58098 q^{74} -3.17416 q^{75} +7.68978 q^{76} +3.14149 q^{77} -1.98202 q^{78} +15.1568 q^{79} -2.81071 q^{80} -0.346528 q^{81} -1.31343 q^{82} +10.6776 q^{83} +1.09451 q^{84} +3.82404 q^{85} -8.85759 q^{86} +7.92918 q^{87} +3.14149 q^{88} -9.79354 q^{89} -5.06501 q^{90} +1.81087 q^{91} -4.80831 q^{92} -10.1310 q^{93} -4.73841 q^{94} -21.6137 q^{95} +1.09451 q^{96} +14.7986 q^{97} -1.00000 q^{98} +5.66110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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