LMFDB - Embedded newform 4029.2.a.j.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.12130 q^{2} +1.00000 q^{3} -0.742675 q^{4} +3.71073 q^{5} +1.12130 q^{6} +4.45947 q^{7} -3.07538 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.12130 q^{2} +1.00000 q^{3} -0.742675 q^{4} +3.71073 q^{5} +1.12130 q^{6} +4.45947 q^{7} -3.07538 q^{8} +1.00000 q^{9} +4.16086 q^{10} -0.158152 q^{11} -0.742675 q^{12} -2.56251 q^{13} +5.00042 q^{14} +3.71073 q^{15} -1.96308 q^{16} -1.00000 q^{17} +1.12130 q^{18} +1.14705 q^{19} -2.75587 q^{20} +4.45947 q^{21} -0.177336 q^{22} +5.04685 q^{23} -3.07538 q^{24} +8.76955 q^{25} -2.87335 q^{26} +1.00000 q^{27} -3.31194 q^{28} -3.47521 q^{29} +4.16086 q^{30} -0.702285 q^{31} +3.94954 q^{32} -0.158152 q^{33} -1.12130 q^{34} +16.5479 q^{35} -0.742675 q^{36} +2.30827 q^{37} +1.28619 q^{38} -2.56251 q^{39} -11.4119 q^{40} +2.38203 q^{41} +5.00042 q^{42} +1.01119 q^{43} +0.117455 q^{44} +3.71073 q^{45} +5.65905 q^{46} -8.39528 q^{47} -1.96308 q^{48} +12.8869 q^{49} +9.83334 q^{50} -1.00000 q^{51} +1.90311 q^{52} +8.78325 q^{53} +1.12130 q^{54} -0.586859 q^{55} -13.7145 q^{56} +1.14705 q^{57} -3.89677 q^{58} -2.85056 q^{59} -2.75587 q^{60} +6.58321 q^{61} -0.787476 q^{62} +4.45947 q^{63} +8.35480 q^{64} -9.50879 q^{65} -0.177336 q^{66} -3.64899 q^{67} +0.742675 q^{68} +5.04685 q^{69} +18.5552 q^{70} +3.48609 q^{71} -3.07538 q^{72} -11.0709 q^{73} +2.58827 q^{74} +8.76955 q^{75} -0.851885 q^{76} -0.705272 q^{77} -2.87335 q^{78} -1.00000 q^{79} -7.28448 q^{80} +1.00000 q^{81} +2.67098 q^{82} +16.8587 q^{83} -3.31194 q^{84} -3.71073 q^{85} +1.13385 q^{86} -3.47521 q^{87} +0.486376 q^{88} +5.47921 q^{89} +4.16086 q^{90} -11.4274 q^{91} -3.74817 q^{92} -0.702285 q^{93} -9.41367 q^{94} +4.25639 q^{95} +3.94954 q^{96} -2.52425 q^{97} +14.4501 q^{98} -0.158152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * 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 $

$2$	1.12130	0.792882	0.396441	−	0.918060i	$-0.370245\pi$
$2$	1.12130	0.792882	0.396441	+	0.918060i	$0.370245\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.742675	−0.371338
$5$	3.71073	1.65949	0.829745	−	0.558142i	$-0.188486\pi$
$5$	3.71073	1.65949	0.829745	+	0.558142i	$0.188486\pi$
$6$	1.12130	0.457771
$7$	4.45947	1.68552	0.842760	−	0.538289i	$-0.180929\pi$
$7$	4.45947	1.68552	0.842760	+	0.538289i	$0.180929\pi$
$8$	−3.07538	−1.08731
$9$	1.00000	0.333333
$10$	4.16086	1.31578
$11$	−0.158152	−0.0476845	−0.0238423	−	0.999716i	$-0.507590\pi$
$11$	−0.158152	−0.0476845	−0.0238423	+	0.999716i	$0.507590\pi$
$12$	−0.742675	−0.214392
$13$	−2.56251	−0.710712	−0.355356	−	0.934731i	$-0.615640\pi$
$13$	−2.56251	−0.710712	−0.355356	+	0.934731i	$0.615640\pi$
$14$	5.00042	1.33642
$15$	3.71073	0.958107
$16$	−1.96308	−0.490771
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.12130	0.264294
$19$	1.14705	0.263151	0.131575	−	0.991306i	$-0.457996\pi$
$19$	1.14705	0.263151	0.131575	+	0.991306i	$0.457996\pi$
$20$	−2.75587	−0.616231
$21$	4.45947	0.973136
$22$	−0.177336	−0.0378082
$23$	5.04685	1.05234	0.526170	−	0.850379i	$-0.323628\pi$
$23$	5.04685	1.05234	0.526170	+	0.850379i	$0.323628\pi$
$24$	−3.07538	−0.627758
$25$	8.76955	1.75391
$26$	−2.87335	−0.563511
$27$	1.00000	0.192450
$28$	−3.31194	−0.625897
$29$	−3.47521	−0.645330	−0.322665	−	0.946513i	$-0.604579\pi$
$29$	−3.47521	−0.645330	−0.322665	+	0.946513i	$0.604579\pi$
$30$	4.16086	0.759666
$31$	−0.702285	−0.126134	−0.0630671	−	0.998009i	$-0.520088\pi$
$31$	−0.702285	−0.126134	−0.0630671	+	0.998009i	$0.520088\pi$
$32$	3.94954	0.698186
$33$	−0.158152	−0.0275307
$34$	−1.12130	−0.192302
$35$	16.5479	2.79711
$36$	−0.742675	−0.123779
$37$	2.30827	0.379477	0.189738	−	0.981835i	$-0.439236\pi$
$37$	2.30827	0.379477	0.189738	+	0.981835i	$0.439236\pi$
$38$	1.28619	0.208648
$39$	−2.56251	−0.410330
$40$	−11.4119	−1.80438
$41$	2.38203	0.372010	0.186005	−	0.982549i	$-0.440446\pi$
$41$	2.38203	0.372010	0.186005	+	0.982549i	$0.440446\pi$
$42$	5.00042	0.771582
$43$	1.01119	0.154205	0.0771025	−	0.997023i	$-0.475433\pi$
$43$	1.01119	0.154205	0.0771025	+	0.997023i	$0.475433\pi$
$44$	0.117455	0.0177071
$45$	3.71073	0.553164
$46$	5.65905	0.834382
$47$	−8.39528	−1.22458	−0.612289	−	0.790634i	$-0.709751\pi$
$47$	−8.39528	−1.22458	−0.612289	+	0.790634i	$0.709751\pi$
$48$	−1.96308	−0.283347
$49$	12.8869	1.84098
$50$	9.83334	1.39064
$51$	−1.00000	−0.140028
$52$	1.90311	0.263914
$53$	8.78325	1.20647	0.603236	−	0.797562i	$-0.293878\pi$
$53$	8.78325	1.20647	0.603236	+	0.797562i	$0.293878\pi$
$54$	1.12130	0.152590
$55$	−0.586859	−0.0791320
$56$	−13.7145	−1.83268
$57$	1.14705	0.151930
$58$	−3.89677	−0.511671
$59$	−2.85056	−0.371111	−0.185555	−	0.982634i	$-0.559408\pi$
$59$	−2.85056	−0.371111	−0.185555	+	0.982634i	$0.559408\pi$
$60$	−2.75587	−0.355781
$61$	6.58321	0.842893	0.421447	−	0.906853i	$-0.361522\pi$
$61$	6.58321	0.842893	0.421447	+	0.906853i	$0.361522\pi$
$62$	−0.787476	−0.100010
$63$	4.45947	0.561840
$64$	8.35480	1.04435
$65$	−9.50879	−1.17942
$66$	−0.177336	−0.0218286
$67$	−3.64899	−0.445796	−0.222898	−	0.974842i	$-0.571552\pi$
$67$	−3.64899	−0.445796	−0.222898	+	0.974842i	$0.571552\pi$
$68$	0.742675	0.0900626
$69$	5.04685	0.607569
$70$	18.5552	2.21778
$71$	3.48609	0.413723	0.206862	−	0.978370i	$-0.433675\pi$
$71$	3.48609	0.413723	0.206862	+	0.978370i	$0.433675\pi$
$72$	−3.07538	−0.362436
$73$	−11.0709	−1.29575	−0.647875	−	0.761747i	$-0.724342\pi$
$73$	−11.0709	−1.29575	−0.647875	+	0.761747i	$0.724342\pi$
$74$	2.58827	0.300880
$75$	8.76955	1.01262
$76$	−0.851885	−0.0977179
$77$	−0.705272	−0.0803732
$78$	−2.87335	−0.325343
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−7.28448	−0.814429
$81$	1.00000	0.111111
$82$	2.67098	0.294960
$83$	16.8587	1.85049	0.925243	−	0.379374i	$-0.123861\pi$
$83$	16.8587	1.85049	0.925243	+	0.379374i	$0.123861\pi$
$84$	−3.31194	−0.361362
$85$	−3.71073	−0.402486
$86$	1.13385	0.122266
$87$	−3.47521	−0.372582
$88$	0.486376	0.0518478
$89$	5.47921	0.580795	0.290398	−	0.956906i	$-0.406212\pi$
$89$	5.47921	0.580795	0.290398	+	0.956906i	$0.406212\pi$
$90$	4.16086	0.438594
$91$	−11.4274	−1.19792
$92$	−3.74817	−0.390774
$93$	−0.702285	−0.0728236
$94$	−9.41367	−0.970946
$95$	4.25639	0.436697
$96$	3.94954	0.403098
$97$	−2.52425	−0.256299	−0.128149	−	0.991755i	$-0.540904\pi$
$97$	−2.52425	−0.256299	−0.128149	+	0.991755i	$0.540904\pi$
$98$	14.4501	1.45968
$99$	−0.158152	−0.0158948
$100$	−6.51293	−0.651293
$101$	−6.95721	−0.692268	−0.346134	−	0.938185i	$-0.612506\pi$
$101$	−6.95721	−0.692268	−0.346134	+	0.938185i	$0.612506\pi$
$102$	−1.12130	−0.111026
$103$	−15.3626	−1.51372	−0.756861	−	0.653575i	$-0.773268\pi$
$103$	−15.3626	−1.51372	−0.756861	+	0.653575i	$0.773268\pi$
$104$	7.88068	0.772764
$105$	16.5479	1.61491
$106$	9.84871	0.956591
$107$	−8.63876	−0.835141	−0.417570	−	0.908645i	$-0.637118\pi$
$107$	−8.63876	−0.835141	−0.417570	+	0.908645i	$0.637118\pi$
$108$	−0.742675	−0.0714640
$109$	−7.80312	−0.747403	−0.373702	−	0.927549i	$-0.621912\pi$
$109$	−7.80312	−0.747403	−0.373702	+	0.927549i	$0.621912\pi$
$110$	−0.658047	−0.0627423
$111$	2.30827	0.219091
$112$	−8.75431	−0.827204
$113$	11.8291	1.11279	0.556394	−	0.830919i	$-0.312185\pi$
$113$	11.8291	1.11279	0.556394	+	0.830919i	$0.312185\pi$
$114$	1.28619	0.120463
$115$	18.7275	1.74635
$116$	2.58095	0.239635
$117$	−2.56251	−0.236904
$118$	−3.19634	−0.294247
$119$	−4.45947	−0.408799
$120$	−11.4119	−1.04176
$121$	−10.9750	−0.997726
$122$	7.38178	0.668315
$123$	2.38203	0.214780
$124$	0.521570	0.0468384
$125$	13.9878	1.25111
$126$	5.00042	0.445473
$127$	5.84946	0.519056	0.259528	−	0.965736i	$-0.416433\pi$
$127$	5.84946	0.519056	0.259528	+	0.965736i	$0.416433\pi$
$128$	1.46920	0.129861
$129$	1.01119	0.0890303
$130$	−10.6623	−0.935142
$131$	−7.80260	−0.681716	−0.340858	−	0.940115i	$-0.610718\pi$
$131$	−7.80260	−0.681716	−0.340858	+	0.940115i	$0.610718\pi$
$132$	0.117455	0.0102232
$133$	5.11523	0.443546
$134$	−4.09163	−0.353463
$135$	3.71073	0.319369
$136$	3.07538	0.263711
$137$	−8.95673	−0.765225	−0.382612	−	0.923909i	$-0.624976\pi$
$137$	−8.95673	−0.765225	−0.382612	+	0.923909i	$0.624976\pi$
$138$	5.65905	0.481730
$139$	7.18008	0.609006	0.304503	−	0.952511i	$-0.401510\pi$
$139$	7.18008	0.609006	0.304503	+	0.952511i	$0.401510\pi$
$140$	−12.2897	−1.03867
$141$	−8.39528	−0.707010
$142$	3.90897	0.328034
$143$	0.405265	0.0338900
$144$	−1.96308	−0.163590
$145$	−12.8956	−1.07092
$146$	−12.4138	−1.02738
$147$	12.8869	1.06289
$148$	−1.71429	−0.140914
$149$	−21.6548	−1.77403	−0.887014	−	0.461743i	$-0.847224\pi$
$149$	−21.6548	−1.77403	−0.887014	+	0.461743i	$0.847224\pi$
$150$	9.83334	0.802889
$151$	4.79642	0.390327	0.195164	−	0.980771i	$-0.437476\pi$
$151$	4.79642	0.390327	0.195164	+	0.980771i	$0.437476\pi$
$152$	−3.52760	−0.286126
$153$	−1.00000	−0.0808452
$154$	−0.790825	−0.0637265
$155$	−2.60599	−0.209318
$156$	1.90311	0.152371
$157$	−0.169751	−0.0135476	−0.00677382	−	0.999977i	$-0.502156\pi$
$157$	−0.169751	−0.0135476	−0.00677382	+	0.999977i	$0.502156\pi$
$158$	−1.12130	−0.0892062
$159$	8.78325	0.696557
$160$	14.6557	1.15863
$161$	22.5062	1.77374
$162$	1.12130	0.0880980
$163$	−3.77808	−0.295922	−0.147961	−	0.988993i	$-0.547271\pi$
$163$	−3.77808	−0.295922	−0.147961	+	0.988993i	$0.547271\pi$
$164$	−1.76907	−0.138141
$165$	−0.586859	−0.0456869
$166$	18.9038	1.46722
$167$	−9.93458	−0.768761	−0.384380	−	0.923175i	$-0.625585\pi$
$167$	−9.93458	−0.768761	−0.384380	+	0.923175i	$0.625585\pi$
$168$	−13.7145	−1.05810
$169$	−6.43354	−0.494888
$170$	−4.16086	−0.319124
$171$	1.14705	0.0877170
$172$	−0.750986	−0.0572621
$173$	9.17614	0.697649	0.348824	−	0.937188i	$-0.386581\pi$
$173$	9.17614	0.697649	0.348824	+	0.937188i	$0.386581\pi$
$174$	−3.89677	−0.295413
$175$	39.1075	2.95625
$176$	0.310465	0.0234022
$177$	−2.85056	−0.214261
$178$	6.14387	0.460502
$179$	−20.1008	−1.50241	−0.751203	−	0.660071i	$-0.770526\pi$
$179$	−20.1008	−1.50241	−0.751203	+	0.660071i	$0.770526\pi$
$180$	−2.75587	−0.205410
$181$	4.98393	0.370452	0.185226	−	0.982696i	$-0.440698\pi$
$181$	4.98393	0.370452	0.185226	+	0.982696i	$0.440698\pi$
$182$	−12.8136	−0.949810
$183$	6.58321	0.486645
$184$	−15.5209	−1.14422
$185$	8.56536	0.629738
$186$	−0.787476	−0.0577405
$187$	0.158152	0.0115652
$188$	6.23497	0.454732
$189$	4.45947	0.324379
$190$	4.77271	0.346249
$191$	9.44429	0.683365	0.341682	−	0.939815i	$-0.389003\pi$
$191$	9.44429	0.683365	0.341682	+	0.939815i	$0.389003\pi$
$192$	8.35480	0.602956
$193$	−5.32987	−0.383652	−0.191826	−	0.981429i	$-0.561441\pi$
$193$	−5.32987	−0.383652	−0.191826	+	0.981429i	$0.561441\pi$
$194$	−2.83045	−0.203215
$195$	−9.50879	−0.680939
$196$	−9.57076	−0.683626
$197$	−3.22808	−0.229991	−0.114996	−	0.993366i	$-0.536685\pi$
$197$	−3.22808	−0.229991	−0.114996	+	0.993366i	$0.536685\pi$
$198$	−0.177336	−0.0126027
$199$	1.95300	0.138444	0.0692222	−	0.997601i	$-0.477948\pi$
$199$	1.95300	0.138444	0.0692222	+	0.997601i	$0.477948\pi$
$200$	−26.9696	−1.90704
$201$	−3.64899	−0.257380
$202$	−7.80115	−0.548887
$203$	−15.4976	−1.08772
$204$	0.742675	0.0519977
$205$	8.83907	0.617348
$206$	−17.2262	−1.20020
$207$	5.04685	0.350780
$208$	5.03042	0.348797
$209$	−0.181408	−0.0125482
$210$	18.5552	1.28043
$211$	23.6760	1.62992	0.814962	−	0.579514i	$-0.196757\pi$
$211$	23.6760	1.62992	0.814962	+	0.579514i	$0.196757\pi$
$212$	−6.52311	−0.448009
$213$	3.48609	0.238863
$214$	−9.68668	−0.662168
$215$	3.75226	0.255902
$216$	−3.07538	−0.209253
$217$	−3.13182	−0.212602
$218$	−8.74968	−0.592603
$219$	−11.0709	−0.748102
$220$	0.435845	0.0293847
$221$	2.56251	0.172373
$222$	2.58827	0.173713
$223$	−19.5202	−1.30717	−0.653583	−	0.756854i	$-0.726735\pi$
$223$	−19.5202	−1.30717	−0.653583	+	0.756854i	$0.726735\pi$
$224$	17.6128	1.17681
$225$	8.76955	0.584636
$226$	13.2640	0.882310
$227$	−5.00307	−0.332066	−0.166033	−	0.986120i	$-0.553096\pi$
$227$	−5.00307	−0.332066	−0.166033	+	0.986120i	$0.553096\pi$
$228$	−0.851885	−0.0564174
$229$	−2.15584	−0.142462	−0.0712311	−	0.997460i	$-0.522693\pi$
$229$	−2.15584	−0.142462	−0.0712311	+	0.997460i	$0.522693\pi$
$230$	20.9992	1.38465
$231$	−0.705272	−0.0464035
$232$	10.6876	0.701674
$233$	8.85300	0.579979	0.289990	−	0.957030i	$-0.406348\pi$
$233$	8.85300	0.579979	0.289990	+	0.957030i	$0.406348\pi$
$234$	−2.87335	−0.187837
$235$	−31.1527	−2.03218
$236$	2.11704	0.137807
$237$	−1.00000	−0.0649570
$238$	−5.00042	−0.324129
$239$	−26.5385	−1.71664	−0.858318	−	0.513118i	$-0.828490\pi$
$239$	−26.5385	−1.71664	−0.858318	+	0.513118i	$0.828490\pi$
$240$	−7.28448	−0.470211
$241$	27.2701	1.75662	0.878312	−	0.478088i	$-0.158670\pi$
$241$	27.2701	1.75662	0.878312	+	0.478088i	$0.158670\pi$
$242$	−12.3063	−0.791079
$243$	1.00000	0.0641500
$244$	−4.88919	−0.312998
$245$	47.8197	3.05509
$246$	2.67098	0.170295
$247$	−2.93932	−0.187025
$248$	2.15979	0.137147
$249$	16.8587	1.06838
$250$	15.6846	0.991980
$251$	−30.4441	−1.92162	−0.960808	−	0.277213i	$-0.910589\pi$
$251$	−30.4441	−1.92162	−0.960808	+	0.277213i	$0.910589\pi$
$252$	−3.31194	−0.208632
$253$	−0.798167	−0.0501803
$254$	6.55903	0.411550
$255$	−3.71073	−0.232375
$256$	−15.0622	−0.941386
$257$	13.3020	0.829753	0.414877	−	0.909878i	$-0.363825\pi$
$257$	13.3020	0.829753	0.414877	+	0.909878i	$0.363825\pi$
$258$	1.13385	0.0705905
$259$	10.2936	0.639616
$260$	7.06195	0.437963
$261$	−3.47521	−0.215110
$262$	−8.74910	−0.540521
$263$	5.31980	0.328033	0.164016	−	0.986458i	$-0.447555\pi$
$263$	5.31980	0.328033	0.164016	+	0.986458i	$0.447555\pi$
$264$	0.486376	0.0299343
$265$	32.5923	2.00213
$266$	5.73573	0.351680
$267$	5.47921	0.335322
$268$	2.71002	0.165541
$269$	18.4906	1.12739	0.563696	−	0.825982i	$-0.309379\pi$
$269$	18.4906	1.12739	0.563696	+	0.825982i	$0.309379\pi$
$270$	4.16086	0.253222
$271$	13.0501	0.792735	0.396367	−	0.918092i	$-0.370271\pi$
$271$	13.0501	0.792735	0.396367	+	0.918092i	$0.370271\pi$
$272$	1.96308	0.119029
$273$	−11.4274	−0.691620
$274$	−10.0432	−0.606733
$275$	−1.38692	−0.0836343
$276$	−3.74817	−0.225613
$277$	−13.8332	−0.831157	−0.415578	−	0.909557i	$-0.636421\pi$
$277$	−13.8332	−0.831157	−0.415578	+	0.909557i	$0.636421\pi$
$278$	8.05106	0.482870
$279$	−0.702285	−0.0420447
$280$	−50.8910	−3.04132
$281$	25.2201	1.50450	0.752252	−	0.658876i	$-0.228968\pi$
$281$	25.2201	1.50450	0.752252	+	0.658876i	$0.228968\pi$
$282$	−9.41367	−0.560576
$283$	−1.78639	−0.106190	−0.0530949	−	0.998589i	$-0.516909\pi$
$283$	−1.78639	−0.106190	−0.0530949	+	0.998589i	$0.516909\pi$
$284$	−2.58904	−0.153631
$285$	4.25639	0.252127
$286$	0.454426	0.0268707
$287$	10.6226	0.627031
$288$	3.94954	0.232729
$289$	1.00000	0.0588235
$290$	−14.4599	−0.849113
$291$	−2.52425	−0.147974
$292$	8.22208	0.481161
$293$	−1.92420	−0.112413	−0.0562066	−	0.998419i	$-0.517901\pi$
$293$	−1.92420	−0.112413	−0.0562066	+	0.998419i	$0.517901\pi$
$294$	14.4501	0.842747
$295$	−10.5777	−0.615855
$296$	−7.09879	−0.412609
$297$	−0.158152	−0.00917689
$298$	−24.2816	−1.40660
$299$	−12.9326	−0.747911
$300$	−6.51293	−0.376024
$301$	4.50937	0.259916
$302$	5.37825	0.309484
$303$	−6.95721	−0.399681
$304$	−2.25175	−0.129147
$305$	24.4285	1.39877
$306$	−1.12130	−0.0641007
$307$	7.91336	0.451639	0.225820	−	0.974169i	$-0.427494\pi$
$307$	7.91336	0.451639	0.225820	+	0.974169i	$0.427494\pi$
$308$	0.523788	0.0298456
$309$	−15.3626	−0.873948
$310$	−2.92211	−0.165965
$311$	0.0890828	0.00505142	0.00252571	−	0.999997i	$-0.499196\pi$
$311$	0.0890828	0.00505142	0.00252571	+	0.999997i	$0.499196\pi$
$312$	7.88068	0.446156
$313$	23.8490	1.34802	0.674012	−	0.738721i	$-0.264570\pi$
$313$	23.8490	1.34802	0.674012	+	0.738721i	$0.264570\pi$
$314$	−0.190343	−0.0107417
$315$	16.5479	0.932369
$316$	0.742675	0.0417788
$317$	−16.0934	−0.903894	−0.451947	−	0.892045i	$-0.649270\pi$
$317$	−16.0934	−0.903894	−0.451947	+	0.892045i	$0.649270\pi$
$318$	9.84871	0.552288
$319$	0.549610	0.0307722
$320$	31.0024	1.73309
$321$	−8.63876	−0.482169
$322$	25.2364	1.40637
$323$	−1.14705	−0.0638235
$324$	−0.742675	−0.0412597
$325$	−22.4720	−1.24653
$326$	−4.23638	−0.234632
$327$	−7.80312	−0.431513
$328$	−7.32563	−0.404490
$329$	−37.4385	−2.06405
$330$	−0.658047	−0.0362243
$331$	17.4313	0.958112	0.479056	−	0.877784i	$-0.340979\pi$
$331$	17.4313	0.958112	0.479056	+	0.877784i	$0.340979\pi$
$332$	−12.5206	−0.687155
$333$	2.30827	0.126492
$334$	−11.1397	−0.609537
$335$	−13.5404	−0.739794
$336$	−8.75431	−0.477587
$337$	−0.0442841	−0.00241231	−0.00120615	−	0.999999i	$-0.500384\pi$
$337$	−0.0442841	−0.00241231	−0.00120615	+	0.999999i	$0.500384\pi$
$338$	−7.21396	−0.392388
$339$	11.8291	0.642468
$340$	2.75587	0.149458
$341$	0.111068	0.00601464
$342$	1.28619	0.0695492
$343$	26.2523	1.41749
$344$	−3.10979	−0.167669
$345$	18.7275	1.00825
$346$	10.2892	0.553153
$347$	25.6885	1.37903	0.689514	−	0.724272i	$-0.257824\pi$
$347$	25.6885	1.37903	0.689514	+	0.724272i	$0.257824\pi$
$348$	2.58095	0.138354
$349$	−17.5495	−0.939404	−0.469702	−	0.882825i	$-0.655639\pi$
$349$	−17.5495	−0.939404	−0.469702	+	0.882825i	$0.655639\pi$
$350$	43.8515	2.34396
$351$	−2.56251	−0.136777
$352$	−0.624626	−0.0332927
$353$	−4.29028	−0.228349	−0.114174	−	0.993461i	$-0.536422\pi$
$353$	−4.29028	−0.228349	−0.114174	+	0.993461i	$0.536422\pi$
$354$	−3.19634	−0.169884
$355$	12.9360	0.686570
$356$	−4.06928	−0.215671
$357$	−4.45947	−0.236020
$358$	−22.5391	−1.19123
$359$	−0.201062	−0.0106117	−0.00530583	−	0.999986i	$-0.501689\pi$
$359$	−0.201062	−0.0106117	−0.00530583	+	0.999986i	$0.501689\pi$
$360$	−11.4119	−0.601460
$361$	−17.6843	−0.930752
$362$	5.58850	0.293725
$363$	−10.9750	−0.576037
$364$	8.48687	0.444833
$365$	−41.0811	−2.15028
$366$	7.38178	0.385852
$367$	−12.3741	−0.645921	−0.322961	−	0.946412i	$-0.604678\pi$
$367$	−12.3741	−0.645921	−0.322961	+	0.946412i	$0.604678\pi$
$368$	−9.90737	−0.516458
$369$	2.38203	0.124003
$370$	9.60438	0.499308
$371$	39.1687	2.03354
$372$	0.521570	0.0270421
$373$	9.96093	0.515758	0.257879	−	0.966177i	$-0.416976\pi$
$373$	9.96093	0.515758	0.257879	+	0.966177i	$0.416976\pi$
$374$	0.177336	0.00916983
$375$	13.9878	0.722326
$376$	25.8186	1.33149
$377$	8.90526	0.458644
$378$	5.00042	0.257194
$379$	−12.6556	−0.650076	−0.325038	−	0.945701i	$-0.605377\pi$
$379$	−12.6556	−0.650076	−0.325038	+	0.945701i	$0.605377\pi$
$380$	−3.16112	−0.162162
$381$	5.84946	0.299677
$382$	10.5899	0.541828
$383$	8.16577	0.417251	0.208626	−	0.977996i	$-0.433101\pi$
$383$	8.16577	0.417251	0.208626	+	0.977996i	$0.433101\pi$
$384$	1.46920	0.0749750
$385$	−2.61708	−0.133379
$386$	−5.97641	−0.304191
$387$	1.01119	0.0514017
$388$	1.87470	0.0951734
$389$	−28.2589	−1.43278	−0.716390	−	0.697700i	$-0.754207\pi$
$389$	−28.2589	−1.43278	−0.716390	+	0.697700i	$0.754207\pi$
$390$	−10.6623	−0.539904
$391$	−5.04685	−0.255230
$392$	−39.6319	−2.00172
$393$	−7.80260	−0.393589
$394$	−3.61966	−0.182356
$395$	−3.71073	−0.186707
$396$	0.117455	0.00590235
$397$	19.8805	0.997773	0.498887	−	0.866667i	$-0.333742\pi$
$397$	19.8805	0.997773	0.498887	+	0.866667i	$0.333742\pi$
$398$	2.18991	0.109770
$399$	5.11523	0.256082
$400$	−17.2153	−0.860767
$401$	−1.80066	−0.0899208	−0.0449604	−	0.998989i	$-0.514316\pi$
$401$	−1.80066	−0.0899208	−0.0449604	+	0.998989i	$0.514316\pi$
$402$	−4.09163	−0.204072
$403$	1.79961	0.0896451
$404$	5.16695	0.257065
$405$	3.71073	0.184388
$406$	−17.3775	−0.862432
$407$	−0.365056	−0.0180952
$408$	3.07538	0.152254
$409$	−2.94550	−0.145646	−0.0728228	−	0.997345i	$-0.523201\pi$
$409$	−2.94550	−0.145646	−0.0728228	+	0.997345i	$0.523201\pi$
$410$	9.91130	0.489484
$411$	−8.95673	−0.441803
$412$	11.4094	0.562102
$413$	−12.7120	−0.625515
$414$	5.65905	0.278127
$415$	62.5583	3.07087
$416$	−10.1207	−0.496209
$417$	7.18008	0.351610
$418$	−0.203413	−0.00994926
$419$	33.7989	1.65119	0.825593	−	0.564266i	$-0.190841\pi$
$419$	33.7989	1.65119	0.825593	+	0.564266i	$0.190841\pi$
$420$	−12.2897	−0.599677
$421$	−12.9894	−0.633066	−0.316533	−	0.948582i	$-0.602519\pi$
$421$	−12.9894	−0.633066	−0.316533	+	0.948582i	$0.602519\pi$
$422$	26.5480	1.29234
$423$	−8.39528	−0.408193
$424$	−27.0118	−1.31181
$425$	−8.76955	−0.425386
$426$	3.90897	0.189390
$427$	29.3576	1.42071
$428$	6.41580	0.310119
$429$	0.405265	0.0195664
$430$	4.20742	0.202900
$431$	29.7547	1.43323	0.716617	−	0.697467i	$-0.245690\pi$
$431$	29.7547	1.43323	0.716617	+	0.697467i	$0.245690\pi$
$432$	−1.96308	−0.0944488
$433$	24.6083	1.18260	0.591299	−	0.806453i	$-0.298615\pi$
$433$	24.6083	1.18260	0.591299	+	0.806453i	$0.298615\pi$
$434$	−3.51172	−0.168568
$435$	−12.8956	−0.618296
$436$	5.79518	0.277539
$437$	5.78898	0.276924
$438$	−12.4138	−0.593156
$439$	−22.8851	−1.09225	−0.546124	−	0.837704i	$-0.683897\pi$
$439$	−22.8851	−1.09225	−0.546124	+	0.837704i	$0.683897\pi$
$440$	1.80481	0.0860409
$441$	12.8869	0.613660
$442$	2.87335	0.136672
$443$	0.700315	0.0332730	0.0166365	−	0.999862i	$-0.494704\pi$
$443$	0.700315	0.0332730	0.0166365	+	0.999862i	$0.494704\pi$
$444$	−1.71429	−0.0813567
$445$	20.3319	0.963824
$446$	−21.8881	−1.03643
$447$	−21.6548	−1.02424
$448$	37.2580	1.76027
$449$	−31.2948	−1.47689	−0.738446	−	0.674312i	$-0.764440\pi$
$449$	−31.2948	−1.47689	−0.738446	+	0.674312i	$0.764440\pi$
$450$	9.83334	0.463548
$451$	−0.376722	−0.0177391
$452$	−8.78518	−0.413220
$453$	4.79642	0.225356
$454$	−5.60997	−0.263289
$455$	−42.4042	−1.98794
$456$	−3.52760	−0.165195
$457$	−24.3529	−1.13918	−0.569591	−	0.821928i	$-0.692898\pi$
$457$	−24.3529	−1.13918	−0.569591	+	0.821928i	$0.692898\pi$
$458$	−2.41736	−0.112956
$459$	−1.00000	−0.0466760
$460$	−13.9085	−0.648485
$461$	0.664620	0.0309544	0.0154772	−	0.999880i	$-0.495073\pi$
$461$	0.664620	0.0309544	0.0154772	+	0.999880i	$0.495073\pi$
$462$	−0.790825	−0.0367925
$463$	−37.9241	−1.76248	−0.881240	−	0.472669i	$-0.843291\pi$
$463$	−37.9241	−1.76248	−0.881240	+	0.472669i	$0.843291\pi$
$464$	6.82212	0.316709
$465$	−2.60599	−0.120850
$466$	9.92691	0.459855
$467$	−18.2438	−0.844220	−0.422110	−	0.906545i	$-0.638710\pi$
$467$	−18.2438	−0.844220	−0.422110	+	0.906545i	$0.638710\pi$
$468$	1.90311	0.0879714
$469$	−16.2726	−0.751398
$470$	−34.9316	−1.61128
$471$	−0.169751	−0.00782173
$472$	8.76653	0.403512
$473$	−0.159921	−0.00735319
$474$	−1.12130	−0.0515032
$475$	10.0591	0.461543
$476$	3.31194	0.151802
$477$	8.78325	0.402158
$478$	−29.7578	−1.36109
$479$	−7.11080	−0.324901	−0.162450	−	0.986717i	$-0.551940\pi$
$479$	−7.11080	−0.324901	−0.162450	+	0.986717i	$0.551940\pi$
$480$	14.6557	0.668937
$481$	−5.91496	−0.269699
$482$	30.5781	1.39280
$483$	22.5062	1.02407
$484$	8.15085	0.370493
$485$	−9.36682	−0.425325
$486$	1.12130	0.0508634
$487$	−36.5169	−1.65474	−0.827370	−	0.561657i	$-0.810164\pi$
$487$	−36.5169	−1.65474	−0.827370	+	0.561657i	$0.810164\pi$
$488$	−20.2458	−0.916486
$489$	−3.77808	−0.170851
$490$	53.6205	2.42233
$491$	30.3559	1.36994	0.684971	−	0.728570i	$-0.259815\pi$
$491$	30.3559	1.36994	0.684971	+	0.728570i	$0.259815\pi$
$492$	−1.76907	−0.0797560
$493$	3.47521	0.156516
$494$	−3.29588	−0.148288
$495$	−0.586859	−0.0263773
$496$	1.37864	0.0619029
$497$	15.5461	0.697339
$498$	18.9038	0.847099
$499$	28.1184	1.25875	0.629377	−	0.777100i	$-0.283310\pi$
$499$	28.1184	1.25875	0.629377	+	0.777100i	$0.283310\pi$
$500$	−10.3884	−0.464583
$501$	−9.93458	−0.443844
$502$	−34.1372	−1.52362
$503$	18.2490	0.813683	0.406842	−	0.913499i	$-0.366630\pi$
$503$	18.2490	0.813683	0.406842	+	0.913499i	$0.366630\pi$
$504$	−13.7145	−0.610894
$505$	−25.8163	−1.14881
$506$	−0.894988	−0.0397871
$507$	−6.43354	−0.285724
$508$	−4.34425	−0.192745
$509$	5.26674	0.233444	0.116722	−	0.993165i	$-0.462761\pi$
$509$	5.26674	0.233444	0.116722	+	0.993165i	$0.462761\pi$
$510$	−4.16086	−0.184246
$511$	−49.3703	−2.18401
$512$	−19.8277	−0.876269
$513$	1.14705	0.0506434
$514$	14.9155	0.657897
$515$	−57.0066	−2.51201
$516$	−0.750986	−0.0330603
$517$	1.32773	0.0583934
$518$	11.5423	0.507140
$519$	9.17614	0.402788
$520$	29.2431	1.28239
$521$	−27.0484	−1.18501	−0.592506	−	0.805566i	$-0.701861\pi$
$521$	−27.0484	−1.18501	−0.592506	+	0.805566i	$0.701861\pi$
$522$	−3.89677	−0.170557
$523$	−38.5092	−1.68389	−0.841945	−	0.539563i	$-0.818589\pi$
$523$	−38.5092	−1.68389	−0.841945	+	0.539563i	$0.818589\pi$
$524$	5.79480	0.253147
$525$	39.1075	1.70679
$526$	5.96512	0.260091
$527$	0.702285	0.0305920
$528$	0.310465	0.0135112
$529$	2.47065	0.107419
$530$	36.5459	1.58745
$531$	−2.85056	−0.123704
$532$	−3.79895	−0.164706
$533$	−6.10397	−0.264392
$534$	6.14387	0.265871
$535$	−32.0561	−1.38591
$536$	11.2220	0.484718
$537$	−20.1008	−0.867414
$538$	20.7336	0.893890
$539$	−2.03808	−0.0877862
$540$	−2.75587	−0.118594
$541$	−12.1623	−0.522900	−0.261450	−	0.965217i	$-0.584201\pi$
$541$	−12.1623	−0.522900	−0.261450	+	0.965217i	$0.584201\pi$
$542$	14.6331	0.628545
$543$	4.98393	0.213881
$544$	−3.94954	−0.169335
$545$	−28.9553	−1.24031
$546$	−12.8136	−0.548373
$547$	−25.9762	−1.11066	−0.555332	−	0.831629i	$-0.687409\pi$
$547$	−25.9762	−1.11066	−0.555332	+	0.831629i	$0.687409\pi$
$548$	6.65194	0.284157
$549$	6.58321	0.280964
$550$	−1.55516	−0.0663122
$551$	−3.98623	−0.169819
$552$	−15.5209	−0.660615
$553$	−4.45947	−0.189636
$554$	−15.5112	−0.659009
$555$	8.56536	0.363579
$556$	−5.33247	−0.226147
$557$	1.47137	0.0623440	0.0311720	−	0.999514i	$-0.490076\pi$
$557$	1.47137	0.0623440	0.0311720	+	0.999514i	$0.490076\pi$
$558$	−0.787476	−0.0333365
$559$	−2.59118	−0.109595
$560$	−32.4849	−1.37274
$561$	0.158152	0.00667717
$562$	28.2794	1.19289
$563$	32.5516	1.37189	0.685944	−	0.727655i	$-0.259390\pi$
$563$	32.5516	1.37189	0.685944	+	0.727655i	$0.259390\pi$
$564$	6.23497	0.262540
$565$	43.8946	1.84666
$566$	−2.00309	−0.0841960
$567$	4.45947	0.187280
$568$	−10.7210	−0.449845
$569$	18.8745	0.791258	0.395629	−	0.918410i	$-0.370527\pi$
$569$	18.8745	0.791258	0.395629	+	0.918410i	$0.370527\pi$
$570$	4.77271	0.199907
$571$	−8.80814	−0.368609	−0.184305	−	0.982869i	$-0.559003\pi$
$571$	−8.80814	−0.368609	−0.184305	+	0.982869i	$0.559003\pi$
$572$	−0.300980	−0.0125846
$573$	9.44429	0.394541
$574$	11.9112	0.497162
$575$	44.2585	1.84571
$576$	8.35480	0.348117
$577$	−47.8658	−1.99268	−0.996340	−	0.0854807i	$-0.972757\pi$
$577$	−47.8658	−1.99268	−0.996340	+	0.0854807i	$0.972757\pi$
$578$	1.12130	0.0466401
$579$	−5.32987	−0.221502
$580$	9.57723	0.397673
$581$	75.1810	3.11903
$582$	−2.83045	−0.117326
$583$	−1.38909	−0.0575301
$584$	34.0471	1.40888
$585$	−9.50879	−0.393140
$586$	−2.15762	−0.0891305
$587$	−43.7066	−1.80396	−0.901982	−	0.431774i	$-0.857888\pi$
$587$	−43.7066	−1.80396	−0.901982	+	0.431774i	$0.857888\pi$
$588$	−9.57076	−0.394691
$589$	−0.805555	−0.0331923
$590$	−11.8608	−0.488301
$591$	−3.22808	−0.132785
$592$	−4.53132	−0.186236
$593$	−31.8062	−1.30612	−0.653061	−	0.757305i	$-0.726515\pi$
$593$	−31.8062	−1.30612	−0.653061	+	0.757305i	$0.726515\pi$
$594$	−0.177336	−0.00727619
$595$	−16.5479	−0.678398
$596$	16.0825	0.658763
$597$	1.95300	0.0799309
$598$	−14.5014	−0.593005
$599$	20.5065	0.837873	0.418937	−	0.908015i	$-0.362403\pi$
$599$	20.5065	0.837873	0.418937	+	0.908015i	$0.362403\pi$
$600$	−26.9696	−1.10103
$601$	−6.20475	−0.253097	−0.126548	−	0.991960i	$-0.540390\pi$
$601$	−6.20475	−0.253097	−0.126548	+	0.991960i	$0.540390\pi$
$602$	5.05638	0.206083
$603$	−3.64899	−0.148599
$604$	−3.56218	−0.144943
$605$	−40.7253	−1.65572
$606$	−7.80115	−0.316900
$607$	9.17460	0.372386	0.186193	−	0.982513i	$-0.440385\pi$
$607$	9.17460	0.372386	0.186193	+	0.982513i	$0.440385\pi$
$608$	4.53031	0.183728
$609$	−15.4976	−0.627994
$610$	27.3918	1.10906
$611$	21.5130	0.870322
$612$	0.742675	0.0300209
$613$	4.22333	0.170579	0.0852893	−	0.996356i	$-0.472819\pi$
$613$	4.22333	0.170579	0.0852893	+	0.996356i	$0.472819\pi$
$614$	8.87329	0.358097
$615$	8.83907	0.356426
$616$	2.16898	0.0873906
$617$	3.71126	0.149410	0.0747048	−	0.997206i	$-0.476199\pi$
$617$	3.71126	0.149410	0.0747048	+	0.997206i	$0.476199\pi$
$618$	−17.2262	−0.692938
$619$	−5.36151	−0.215497	−0.107749	−	0.994178i	$-0.534364\pi$
$619$	−5.36151	−0.215497	−0.107749	+	0.994178i	$0.534364\pi$
$620$	1.93541	0.0777278
$621$	5.04685	0.202523
$622$	0.0998890	0.00400518
$623$	24.4344	0.978942
$624$	5.03042	0.201378
$625$	8.05722	0.322289
$626$	26.7420	1.06882
$627$	−0.181408	−0.00724472
$628$	0.126070	0.00503075
$629$	−2.30827	−0.0920366
$630$	18.5552	0.739259
$631$	−40.5538	−1.61442	−0.807211	−	0.590263i	$-0.799024\pi$
$631$	−40.5538	−1.61442	−0.807211	+	0.590263i	$0.799024\pi$
$632$	3.07538	0.122332
$633$	23.6760	0.941038
$634$	−18.0456	−0.716681
$635$	21.7058	0.861368
$636$	−6.52311	−0.258658
$637$	−33.0227	−1.30841
$638$	0.616280	0.0243988
$639$	3.48609	0.137908
$640$	5.45182	0.215502
$641$	−33.4798	−1.32237	−0.661187	−	0.750221i	$-0.729947\pi$
$641$	−33.4798	−1.32237	−0.661187	+	0.750221i	$0.729947\pi$
$642$	−9.68668	−0.382303
$643$	−34.0508	−1.34283	−0.671417	−	0.741080i	$-0.734314\pi$
$643$	−34.0508	−1.34283	−0.671417	+	0.741080i	$0.734314\pi$
$644$	−16.7148	−0.658657
$645$	3.75226	0.147745
$646$	−1.28619	−0.0506045
$647$	−6.40524	−0.251816	−0.125908	−	0.992042i	$-0.540184\pi$
$647$	−6.40524	−0.251816	−0.125908	+	0.992042i	$0.540184\pi$
$648$	−3.07538	−0.120812
$649$	0.450820	0.0176962
$650$	−25.1980	−0.988348
$651$	−3.13182	−0.122746
$652$	2.80589	0.109887
$653$	15.1156	0.591521	0.295760	−	0.955262i	$-0.404427\pi$
$653$	15.1156	0.591521	0.295760	+	0.955262i	$0.404427\pi$
$654$	−8.74968	−0.342139
$655$	−28.9534	−1.13130
$656$	−4.67612	−0.182572
$657$	−11.0709	−0.431917
$658$	−41.9800	−1.63655
$659$	19.3856	0.755157	0.377579	−	0.925978i	$-0.376757\pi$
$659$	19.3856	0.755157	0.377579	+	0.925978i	$0.376757\pi$
$660$	0.435845	0.0169653
$661$	4.79481	0.186496	0.0932482	−	0.995643i	$-0.470275\pi$
$661$	4.79481	0.186496	0.0932482	+	0.995643i	$0.470275\pi$
$662$	19.5458	0.759670
$663$	2.56251	0.0995196
$664$	−51.8469	−2.01205
$665$	18.9812	0.736061
$666$	2.58827	0.100293
$667$	−17.5388	−0.679107
$668$	7.37817	0.285470
$669$	−19.5202	−0.754693
$670$	−15.1830	−0.586569
$671$	−1.04114	−0.0401929
$672$	17.6128	0.679430
$673$	−20.2126	−0.779137	−0.389569	−	0.920997i	$-0.627376\pi$
$673$	−20.2126	−0.779137	−0.389569	+	0.920997i	$0.627376\pi$
$674$	−0.0496559	−0.00191268
$675$	8.76955	0.337540
$676$	4.77804	0.183771
$677$	45.0621	1.73188	0.865939	−	0.500150i	$-0.166722\pi$
$677$	45.0621	1.73188	0.865939	+	0.500150i	$0.166722\pi$
$678$	13.2640	0.509402
$679$	−11.2568	−0.431997
$680$	11.4119	0.437626
$681$	−5.00307	−0.191718
$682$	0.124541	0.00476890
$683$	−31.2164	−1.19446	−0.597230	−	0.802070i	$-0.703732\pi$
$683$	−31.2164	−1.19446	−0.597230	+	0.802070i	$0.703732\pi$
$684$	−0.851885	−0.0325726
$685$	−33.2360	−1.26988
$686$	29.4368	1.12390
$687$	−2.15584	−0.0822506
$688$	−1.98505	−0.0756793
$689$	−22.5072	−0.857455
$690$	20.9992	0.799427
$691$	−7.50716	−0.285586	−0.142793	−	0.989753i	$-0.545608\pi$
$691$	−7.50716	−0.285586	−0.142793	+	0.989753i	$0.545608\pi$
$692$	−6.81489	−0.259063
$693$	−0.705272	−0.0267911
$694$	28.8046	1.09341
$695$	26.6434	1.01064
$696$	10.6876	0.405111
$697$	−2.38203	−0.0902258
$698$	−19.6784	−0.744837
$699$	8.85300	0.334851
$700$	−29.0442	−1.09777
$701$	−20.0640	−0.757809	−0.378904	−	0.925436i	$-0.623699\pi$
$701$	−20.0640	−0.757809	−0.378904	+	0.925436i	$0.623699\pi$
$702$	−2.87335	−0.108448
$703$	2.64769	0.0998597
$704$	−1.32132	−0.0497993
$705$	−31.1527	−1.17328
$706$	−4.81071	−0.181054
$707$	−31.0255	−1.16683
$708$	2.11704	0.0795632
$709$	5.46694	0.205315	0.102658	−	0.994717i	$-0.467265\pi$
$709$	5.46694	0.205315	0.102658	+	0.994717i	$0.467265\pi$
$710$	14.5052	0.544369
$711$	−1.00000	−0.0375029
$712$	−16.8506	−0.631504
$713$	−3.54432	−0.132736
$714$	−5.00042	−0.187136
$715$	1.50383	0.0562401
$716$	14.9284	0.557900
$717$	−26.5385	−0.991100
$718$	−0.225452	−0.00841380
$719$	4.83539	0.180330	0.0901649	−	0.995927i	$-0.471261\pi$
$719$	4.83539	0.180330	0.0901649	+	0.995927i	$0.471261\pi$
$720$	−7.28448	−0.271476
$721$	−68.5091	−2.55141
$722$	−19.8295	−0.737976
$723$	27.2701	1.01419
$724$	−3.70144	−0.137563
$725$	−30.4760	−1.13185
$726$	−12.3063	−0.456730
$727$	−6.41502	−0.237920	−0.118960	−	0.992899i	$-0.537956\pi$
$727$	−6.41502	−0.237920	−0.118960	+	0.992899i	$0.537956\pi$
$728$	35.1436	1.30251
$729$	1.00000	0.0370370
$730$	−46.0645	−1.70492
$731$	−1.01119	−0.0374002
$732$	−4.88919	−0.180710
$733$	7.36227	0.271932	0.135966	−	0.990714i	$-0.456586\pi$
$733$	7.36227	0.271932	0.135966	+	0.990714i	$0.456586\pi$
$734$	−13.8751	−0.512139
$735$	47.8197	1.76386
$736$	19.9327	0.734729
$737$	0.577094	0.0212575
$738$	2.67098	0.0983201
$739$	−52.5695	−1.93380	−0.966900	−	0.255155i	$-0.917874\pi$
$739$	−52.5695	−1.93380	−0.966900	+	0.255155i	$0.917874\pi$
$740$	−6.36129	−0.233845
$741$	−2.93932	−0.107979
$742$	43.9200	1.61235
$743$	13.5077	0.495549	0.247774	−	0.968818i	$-0.420301\pi$
$743$	13.5077	0.495549	0.247774	+	0.968818i	$0.420301\pi$
$744$	2.15979	0.0791817
$745$	−80.3551	−2.94398
$746$	11.1692	0.408935
$747$	16.8587	0.616829
$748$	−0.117455	−0.00429459
$749$	−38.5243	−1.40765
$750$	15.6846	0.572720
$751$	32.2669	1.17743	0.588717	−	0.808339i	$-0.299633\pi$
$751$	32.2669	1.17743	0.588717	+	0.808339i	$0.299633\pi$
$752$	16.4806	0.600987
$753$	−30.4441	−1.10945
$754$	9.98551	0.363651
$755$	17.7982	0.647744
$756$	−3.31194	−0.120454
$757$	−44.4371	−1.61510	−0.807548	−	0.589802i	$-0.799206\pi$
$757$	−44.4371	−1.61510	−0.807548	+	0.589802i	$0.799206\pi$
$758$	−14.1908	−0.515433
$759$	−0.798167	−0.0289716
$760$	−13.0900	−0.474824
$761$	−23.6776	−0.858311	−0.429155	−	0.903231i	$-0.641189\pi$
$761$	−23.6776	−0.858311	−0.429155	+	0.903231i	$0.641189\pi$
$762$	6.55903	0.237608
$763$	−34.7978	−1.25976
$764$	−7.01404	−0.253759
$765$	−3.71073	−0.134162
$766$	9.15632	0.330831
$767$	7.30458	0.263753
$768$	−15.0622	−0.543509
$769$	−11.9802	−0.432017	−0.216009	−	0.976391i	$-0.569304\pi$
$769$	−11.9802	−0.432017	−0.216009	+	0.976391i	$0.569304\pi$
$770$	−2.93454	−0.105754
$771$	13.3020	0.479058
$772$	3.95836	0.142465
$773$	−15.8386	−0.569674	−0.284837	−	0.958576i	$-0.591939\pi$
$773$	−15.8386	−0.569674	−0.284837	+	0.958576i	$0.591939\pi$
$774$	1.13385	0.0407555
$775$	−6.15872	−0.221228
$776$	7.76302	0.278676
$777$	10.2936	0.369282
$778$	−31.6868	−1.13603
$779$	2.73230	0.0978949
$780$	7.06195	0.252858
$781$	−0.551331	−0.0197282
$782$	−5.65905	−0.202367
$783$	−3.47521	−0.124194
$784$	−25.2980	−0.903499
$785$	−0.629902	−0.0224822
$786$	−8.74910	−0.312070
$787$	−22.6533	−0.807501	−0.403751	−	0.914869i	$-0.632294\pi$
$787$	−22.6533	−0.807501	−0.403751	+	0.914869i	$0.632294\pi$
$788$	2.39742	0.0854044
$789$	5.31980	0.189390
$790$	−4.16086	−0.148037
$791$	52.7515	1.87563
$792$	0.486376	0.0172826
$793$	−16.8695	−0.599055
$794$	22.2921	0.791117
$795$	32.5923	1.15593
$796$	−1.45044	−0.0514096
$797$	−0.290963	−0.0103064	−0.00515322	−	0.999987i	$-0.501640\pi$
$797$	−0.290963	−0.0103064	−0.00515322	+	0.999987i	$0.501640\pi$
$798$	5.73573	0.203043
$799$	8.39528	0.297004
$800$	34.6356	1.22456
$801$	5.47921	0.193598
$802$	−2.01909	−0.0712966
$803$	1.75088	0.0617872
$804$	2.71002	0.0955750
$805$	83.5147	2.94351
$806$	2.01791	0.0710780
$807$	18.4906	0.650900
$808$	21.3960	0.752710
$809$	25.1556	0.884423	0.442212	−	0.896911i	$-0.354194\pi$
$809$	25.1556	0.884423	0.442212	+	0.896911i	$0.354194\pi$
$810$	4.16086	0.146198
$811$	22.1471	0.777688	0.388844	−	0.921304i	$-0.372874\pi$
$811$	22.1471	0.777688	0.388844	+	0.921304i	$0.372874\pi$
$812$	11.5097	0.403911
$813$	13.0501	0.457686
$814$	−0.409339	−0.0143473
$815$	−14.0195	−0.491080
$816$	1.96308	0.0687216
$817$	1.15988	0.0405792
$818$	−3.30280	−0.115480
$819$	−11.4274	−0.399307
$820$	−6.56456	−0.229244
$821$	35.5826	1.24184	0.620920	−	0.783874i	$-0.286759\pi$
$821$	35.5826	1.24184	0.620920	+	0.783874i	$0.286759\pi$
$822$	−10.0432	−0.350298
$823$	15.4353	0.538042	0.269021	−	0.963134i	$-0.413300\pi$
$823$	15.4353	0.538042	0.269021	+	0.963134i	$0.413300\pi$
$824$	47.2458	1.64589
$825$	−1.38692	−0.0482863
$826$	−14.2540	−0.495960
$827$	10.3524	0.359989	0.179995	−	0.983668i	$-0.442392\pi$
$827$	10.3524	0.359989	0.179995	+	0.983668i	$0.442392\pi$
$828$	−3.74817	−0.130258
$829$	−18.4343	−0.640249	−0.320124	−	0.947375i	$-0.603725\pi$
$829$	−18.4343	−0.640249	−0.320124	+	0.947375i	$0.603725\pi$
$830$	70.1469	2.43483
$831$	−13.8332	−0.479868
$832$	−21.4093	−0.742232
$833$	−12.8869	−0.446503
$834$	8.05106	0.278785
$835$	−36.8646	−1.27575
$836$	0.134727	0.00465963
$837$	−0.702285	−0.0242745
$838$	37.8989	1.30920
$839$	13.8162	0.476987	0.238493	−	0.971144i	$-0.423346\pi$
$839$	13.8162	0.476987	0.238493	+	0.971144i	$0.423346\pi$
$840$	−50.8910	−1.75591
$841$	−16.9229	−0.583549
$842$	−14.5651	−0.501947
$843$	25.2201	0.868625
$844$	−17.5836	−0.605253
$845$	−23.8732	−0.821262
$846$	−9.41367	−0.323649
$847$	−48.9426	−1.68169
$848$	−17.2423	−0.592101
$849$	−1.78639	−0.0613087
$850$	−9.83334	−0.337281
$851$	11.6495	0.399339
$852$	−2.58904	−0.0886989
$853$	−2.30957	−0.0790781	−0.0395390	−	0.999218i	$-0.512589\pi$
$853$	−2.30957	−0.0790781	−0.0395390	+	0.999218i	$0.512589\pi$
$854$	32.9188	1.12646
$855$	4.25639	0.145566
$856$	26.5674	0.908056
$857$	14.9916	0.512104	0.256052	−	0.966663i	$-0.417578\pi$
$857$	14.9916	0.512104	0.256052	+	0.966663i	$0.417578\pi$
$858$	0.454426	0.0155138
$859$	−18.6557	−0.636524	−0.318262	−	0.948003i	$-0.603099\pi$
$859$	−18.6557	−0.636524	−0.318262	+	0.948003i	$0.603099\pi$
$860$	−2.78671	−0.0950260
$861$	10.6226	0.362017
$862$	33.3641	1.13639
$863$	47.3655	1.61234	0.806169	−	0.591685i	$-0.201537\pi$
$863$	47.3655	1.61234	0.806169	+	0.591685i	$0.201537\pi$
$864$	3.94954	0.134366
$865$	34.0502	1.15774
$866$	27.5934	0.937661
$867$	1.00000	0.0339618
$868$	2.32592	0.0789470
$869$	0.158152	0.00536493
$870$	−14.4599	−0.490236
$871$	9.35058	0.316832
$872$	23.9975	0.812659
$873$	−2.52425	−0.0854329
$874$	6.49121	0.219568
$875$	62.3781	2.10876
$876$	8.22208	0.277798
$877$	21.2344	0.717034	0.358517	−	0.933523i	$-0.383283\pi$
$877$	21.2344	0.717034	0.358517	+	0.933523i	$0.383283\pi$
$878$	−25.6612	−0.866024
$879$	−1.92420	−0.0649018
$880$	1.15205	0.0388357
$881$	57.3446	1.93199	0.965994	−	0.258564i	$-0.0832494\pi$
$881$	57.3446	1.93199	0.965994	+	0.258564i	$0.0832494\pi$
$882$	14.4501	0.486560
$883$	40.6027	1.36639	0.683195	−	0.730236i	$-0.260590\pi$
$883$	40.6027	1.36639	0.683195	+	0.730236i	$0.260590\pi$
$884$	−1.90311	−0.0640086
$885$	−10.5777	−0.355564
$886$	0.785266	0.0263815
$887$	10.1975	0.342397	0.171199	−	0.985237i	$-0.445236\pi$
$887$	10.1975	0.342397	0.171199	+	0.985237i	$0.445236\pi$
$888$	−7.09879	−0.238220
$889$	26.0855	0.874879
$890$	22.7983	0.764199
$891$	−0.158152	−0.00529828
$892$	14.4971	0.485400
$893$	−9.62979	−0.322249
$894$	−24.2816	−0.812098
$895$	−74.5888	−2.49323
$896$	6.55187	0.218883
$897$	−12.9326	−0.431807
$898$	−35.0910	−1.17100
$899$	2.44059	0.0813982
$900$	−6.51293	−0.217098
$901$	−8.78325	−0.292613
$902$	−0.422420	−0.0140650
$903$	4.50937	0.150062
$904$	−36.3789	−1.20994
$905$	18.4940	0.614762
$906$	5.37825	0.178680
$907$	42.2816	1.40394	0.701969	−	0.712207i	$-0.252304\pi$
$907$	42.2816	1.40394	0.701969	+	0.712207i	$0.252304\pi$
$908$	3.71566	0.123309
$909$	−6.95721	−0.230756
$910$	−47.5480	−1.57620
$911$	−11.2822	−0.373798	−0.186899	−	0.982379i	$-0.559844\pi$
$911$	−11.2822	−0.373798	−0.186899	+	0.982379i	$0.559844\pi$
$912$	−2.25175	−0.0745629
$913$	−2.66624	−0.0882395
$914$	−27.3071	−0.903238
$915$	24.4285	0.807582
$916$	1.60109	0.0529016
$917$	−34.7955	−1.14905
$918$	−1.12130	−0.0370086
$919$	36.4528	1.20247	0.601234	−	0.799073i	$-0.294676\pi$
$919$	36.4528	1.20247	0.601234	+	0.799073i	$0.294676\pi$
$920$	−57.5941	−1.89882
$921$	7.91336	0.260754
$922$	0.745241	0.0245432
$923$	−8.93315	−0.294038
$924$	0.523788	0.0172314
$925$	20.2425	0.665568
$926$	−42.5244	−1.39744
$927$	−15.3626	−0.504574
$928$	−13.7255	−0.450561
$929$	−33.2410	−1.09060	−0.545300	−	0.838241i	$-0.683584\pi$
$929$	−33.2410	−1.09060	−0.545300	+	0.838241i	$0.683584\pi$
$930$	−2.92211	−0.0958199
$931$	14.7819	0.484456
$932$	−6.57490	−0.215368
$933$	0.0890828	0.00291644
$934$	−20.4568	−0.669367
$935$	0.586859	0.0191923
$936$	7.88068	0.257588
$937$	13.2822	0.433910	0.216955	−	0.976182i	$-0.430387\pi$
$937$	13.2822	0.433910	0.216955	+	0.976182i	$0.430387\pi$
$938$	−18.2465	−0.595770
$939$	23.8490	0.778281
$940$	23.1363	0.754623
$941$	−53.8138	−1.75428	−0.877140	−	0.480234i	$-0.840552\pi$
$941$	−53.8138	−1.75428	−0.877140	+	0.480234i	$0.840552\pi$
$942$	−0.190343	−0.00620171
$943$	12.0217	0.391481
$944$	5.59588	0.182130
$945$	16.5479	0.538303
$946$	−0.179321	−0.00583021
$947$	26.2291	0.852331	0.426166	−	0.904645i	$-0.359864\pi$
$947$	26.2291	0.852331	0.426166	+	0.904645i	$0.359864\pi$
$948$	0.742675	0.0241210
$949$	28.3693	0.920905
$950$	11.2793	0.365949
$951$	−16.0934	−0.521863
$952$	13.7145	0.444491
$953$	−27.0878	−0.877459	−0.438730	−	0.898619i	$-0.644571\pi$
$953$	−27.0878	−0.877459	−0.438730	+	0.898619i	$0.644571\pi$
$954$	9.84871	0.318864
$955$	35.0452	1.13404
$956$	19.7095	0.637452
$957$	0.549610	0.0177664
$958$	−7.97338	−0.257608
$959$	−39.9422	−1.28980
$960$	31.0024	1.00060
$961$	−30.5068	−0.984090
$962$	−6.63247	−0.213839
$963$	−8.63876	−0.278380
$964$	−20.2529	−0.652301
$965$	−19.7777	−0.636667
$966$	25.2364	0.811967
$967$	−32.3839	−1.04140	−0.520699	−	0.853741i	$-0.674329\pi$
$967$	−32.3839	−1.04140	−0.520699	+	0.853741i	$0.674329\pi$
$968$	33.7522	1.08484
$969$	−1.14705	−0.0368485
$970$	−10.5031	−0.337233
$971$	15.8353	0.508180	0.254090	−	0.967181i	$-0.418224\pi$
$971$	15.8353	0.508180	0.254090	+	0.967181i	$0.418224\pi$
$972$	−0.742675	−0.0238213
$973$	32.0193	1.02649
$974$	−40.9466	−1.31201
$975$	−22.4720	−0.719682
$976$	−12.9234	−0.413667
$977$	40.6162	1.29943	0.649714	−	0.760179i	$-0.274889\pi$
$977$	40.6162	1.29943	0.649714	+	0.760179i	$0.274889\pi$
$978$	−4.23638	−0.135465
$979$	−0.866546	−0.0276949
$980$	−35.5145	−1.13447
$981$	−7.80312	−0.249134
$982$	34.0382	1.08620
$983$	−13.3582	−0.426060	−0.213030	−	0.977046i	$-0.568333\pi$
$983$	−13.3582	−0.426060	−0.213030	+	0.977046i	$0.568333\pi$
$984$	−7.32563	−0.233533
$985$	−11.9785	−0.381668
$986$	3.89677	0.124098
$987$	−37.4385	−1.19168
$988$	2.18296	0.0694493
$989$	5.10332	0.162276
$990$	−0.658047	−0.0209141
$991$	26.7372	0.849334	0.424667	−	0.905350i	$-0.360391\pi$
$991$	26.7372	0.849334	0.424667	+	0.905350i	$0.360391\pi$
$992$	−2.77370	−0.0880651
$993$	17.4313	0.553166
$994$	17.4319	0.552908
$995$	7.24705	0.229747
$996$	−12.5206	−0.396729
$997$	42.8901	1.35834	0.679171	−	0.733980i	$-0.262339\pi$
$997$	42.8901	1.35834	0.679171	+	0.733980i	$0.262339\pi$
$998$	31.5293	0.998043
$999$	2.30827	0.0730303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.16	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.16	✓	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.12130 q^{2} +1.00000 q^{3} -0.742675 q^{4} +3.71073 q^{5} +1.12130 q^{6} +4.45947 q^{7} -3.07538 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.12130 q^{2} +1.00000 q^{3} -0.742675 q^{4} +3.71073 q^{5} +1.12130 q^{6} +4.45947 q^{7} -3.07538 q^{8} +1.00000 q^{9} +4.16086 q^{10} -0.158152 q^{11} -0.742675 q^{12} -2.56251 q^{13} +5.00042 q^{14} +3.71073 q^{15} -1.96308 q^{16} -1.00000 q^{17} +1.12130 q^{18} +1.14705 q^{19} -2.75587 q^{20} +4.45947 q^{21} -0.177336 q^{22} +5.04685 q^{23} -3.07538 q^{24} +8.76955 q^{25} -2.87335 q^{26} +1.00000 q^{27} -3.31194 q^{28} -3.47521 q^{29} +4.16086 q^{30} -0.702285 q^{31} +3.94954 q^{32} -0.158152 q^{33} -1.12130 q^{34} +16.5479 q^{35} -0.742675 q^{36} +2.30827 q^{37} +1.28619 q^{38} -2.56251 q^{39} -11.4119 q^{40} +2.38203 q^{41} +5.00042 q^{42} +1.01119 q^{43} +0.117455 q^{44} +3.71073 q^{45} +5.65905 q^{46} -8.39528 q^{47} -1.96308 q^{48} +12.8869 q^{49} +9.83334 q^{50} -1.00000 q^{51} +1.90311 q^{52} +8.78325 q^{53} +1.12130 q^{54} -0.586859 q^{55} -13.7145 q^{56} +1.14705 q^{57} -3.89677 q^{58} -2.85056 q^{59} -2.75587 q^{60} +6.58321 q^{61} -0.787476 q^{62} +4.45947 q^{63} +8.35480 q^{64} -9.50879 q^{65} -0.177336 q^{66} -3.64899 q^{67} +0.742675 q^{68} +5.04685 q^{69} +18.5552 q^{70} +3.48609 q^{71} -3.07538 q^{72} -11.0709 q^{73} +2.58827 q^{74} +8.76955 q^{75} -0.851885 q^{76} -0.705272 q^{77} -2.87335 q^{78} -1.00000 q^{79} -7.28448 q^{80} +1.00000 q^{81} +2.67098 q^{82} +16.8587 q^{83} -3.31194 q^{84} -3.71073 q^{85} +1.13385 q^{86} -3.47521 q^{87} +0.486376 q^{88} +5.47921 q^{89} +4.16086 q^{90} -11.4274 q^{91} -3.74817 q^{92} -0.702285 q^{93} -9.41367 q^{94} +4.25639 q^{95} +3.94954 q^{96} -2.52425 q^{97} +14.4501 q^{98} -0.158152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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