LMFDB - Embedded newform 6035.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.599472 q^{2} -1.15414 q^{3} -1.64063 q^{4} +1.00000 q^{5} +0.691877 q^{6} -3.77052 q^{7} +2.18246 q^{8} -1.66795 q^{9} +O(q^{10})$	\(q-0.599472 q^{2} -1.15414 q^{3} -1.64063 q^{4} +1.00000 q^{5} +0.691877 q^{6} -3.77052 q^{7} +2.18246 q^{8} -1.66795 q^{9} -0.599472 q^{10} +3.97965 q^{11} +1.89352 q^{12} -4.01546 q^{13} +2.26032 q^{14} -1.15414 q^{15} +1.97294 q^{16} +1.00000 q^{17} +0.999892 q^{18} +2.07028 q^{19} -1.64063 q^{20} +4.35172 q^{21} -2.38569 q^{22} -2.14210 q^{23} -2.51887 q^{24} +1.00000 q^{25} +2.40716 q^{26} +5.38749 q^{27} +6.18604 q^{28} -2.25581 q^{29} +0.691877 q^{30} -8.52400 q^{31} -5.54764 q^{32} -4.59308 q^{33} -0.599472 q^{34} -3.77052 q^{35} +2.73650 q^{36} -3.46178 q^{37} -1.24108 q^{38} +4.63442 q^{39} +2.18246 q^{40} +5.66699 q^{41} -2.60874 q^{42} +1.34229 q^{43} -6.52914 q^{44} -1.66795 q^{45} +1.28413 q^{46} +12.6638 q^{47} -2.27706 q^{48} +7.21684 q^{49} -0.599472 q^{50} -1.15414 q^{51} +6.58790 q^{52} +12.9289 q^{53} -3.22965 q^{54} +3.97965 q^{55} -8.22901 q^{56} -2.38940 q^{57} +1.35230 q^{58} -10.6898 q^{59} +1.89352 q^{60} -9.98641 q^{61} +5.10990 q^{62} +6.28906 q^{63} -0.620226 q^{64} -4.01546 q^{65} +2.75343 q^{66} +10.8583 q^{67} -1.64063 q^{68} +2.47229 q^{69} +2.26032 q^{70} -1.00000 q^{71} -3.64024 q^{72} +8.99056 q^{73} +2.07524 q^{74} -1.15414 q^{75} -3.39658 q^{76} -15.0054 q^{77} -2.77821 q^{78} -9.27589 q^{79} +1.97294 q^{80} -1.21407 q^{81} -3.39720 q^{82} +9.10914 q^{83} -7.13958 q^{84} +1.00000 q^{85} -0.804664 q^{86} +2.60353 q^{87} +8.68542 q^{88} +4.00484 q^{89} +0.999892 q^{90} +15.1404 q^{91} +3.51440 q^{92} +9.83792 q^{93} -7.59158 q^{94} +2.07028 q^{95} +6.40277 q^{96} +17.2324 q^{97} -4.32630 q^{98} -6.63787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.599472	−0.423891	−0.211945	−	0.977281i	$-0.567980\pi$
$2$	−0.599472	−0.423891	−0.211945	+	0.977281i	$0.567980\pi$
$3$	−1.15414	−0.666345	−0.333172	−	0.942866i	$-0.608119\pi$
$3$	−1.15414	−0.666345	−0.333172	+	0.942866i	$0.608119\pi$
$4$	−1.64063	−0.820316
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.691877	0.282458
$7$	−3.77052	−1.42512	−0.712562	−	0.701609i	$-0.752465\pi$
$7$	−3.77052	−1.42512	−0.712562	+	0.701609i	$0.752465\pi$
$8$	2.18246	0.771616
$9$	−1.66795	−0.555985
$10$	−0.599472	−0.189570
$11$	3.97965	1.19991	0.599955	−	0.800034i	$-0.295185\pi$
$11$	3.97965	1.19991	0.599955	+	0.800034i	$0.295185\pi$
$12$	1.89352	0.546614
$13$	−4.01546	−1.11369	−0.556845	−	0.830617i	$-0.687988\pi$
$13$	−4.01546	−1.11369	−0.556845	+	0.830617i	$0.687988\pi$
$14$	2.26032	0.604097
$15$	−1.15414	−0.297998
$16$	1.97294	0.493235
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.999892	0.235677
$19$	2.07028	0.474956	0.237478	−	0.971393i	$-0.423679\pi$
$19$	2.07028	0.474956	0.237478	+	0.971393i	$0.423679\pi$
$20$	−1.64063	−0.366857
$21$	4.35172	0.949624
$22$	−2.38569	−0.508631
$23$	−2.14210	−0.446659	−0.223329	−	0.974743i	$-0.571693\pi$
$23$	−2.14210	−0.446659	−0.223329	+	0.974743i	$0.571693\pi$
$24$	−2.51887	−0.514162
$25$	1.00000	0.200000
$26$	2.40716	0.472083
$27$	5.38749	1.03682
$28$	6.18604	1.16905
$29$	−2.25581	−0.418894	−0.209447	−	0.977820i	$-0.567166\pi$
$29$	−2.25581	−0.418894	−0.209447	+	0.977820i	$0.567166\pi$
$30$	0.691877	0.126319
$31$	−8.52400	−1.53096	−0.765478	−	0.643462i	$-0.777497\pi$
$31$	−8.52400	−1.53096	−0.765478	+	0.643462i	$0.777497\pi$
$32$	−5.54764	−0.980694
$33$	−4.59308	−0.799553
$34$	−0.599472	−0.102809
$35$	−3.77052	−0.637335
$36$	2.73650	0.456083
$37$	−3.46178	−0.569113	−0.284557	−	0.958659i	$-0.591846\pi$
$37$	−3.46178	−0.569113	−0.284557	+	0.958659i	$0.591846\pi$
$38$	−1.24108	−0.201329
$39$	4.63442	0.742101
$40$	2.18246	0.345077
$41$	5.66699	0.885035	0.442517	−	0.896760i	$-0.354086\pi$
$41$	5.66699	0.885035	0.442517	+	0.896760i	$0.354086\pi$
$42$	−2.60874	−0.402537
$43$	1.34229	0.204697	0.102348	−	0.994749i	$-0.467364\pi$
$43$	1.34229	0.204697	0.102348	+	0.994749i	$0.467364\pi$
$44$	−6.52914	−0.984305
$45$	−1.66795	−0.248644
$46$	1.28413	0.189335
$47$	12.6638	1.84720	0.923601	−	0.383356i	$-0.125232\pi$
$47$	12.6638	1.84720	0.923601	+	0.383356i	$0.125232\pi$
$48$	−2.27706	−0.328665
$49$	7.21684	1.03098
$50$	−0.599472	−0.0847782
$51$	−1.15414	−0.161612
$52$	6.58790	0.913578
$53$	12.9289	1.77592	0.887958	−	0.459924i	$-0.152123\pi$
$53$	12.9289	1.77592	0.887958	+	0.459924i	$0.152123\pi$
$54$	−3.22965	−0.439500
$55$	3.97965	0.536616
$56$	−8.22901	−1.09965
$57$	−2.38940	−0.316484
$58$	1.35230	0.177565
$59$	−10.6898	−1.39169	−0.695844	−	0.718193i	$-0.744970\pi$
$59$	−10.6898	−1.39169	−0.695844	+	0.718193i	$0.744970\pi$
$60$	1.89352	0.244453
$61$	−9.98641	−1.27863	−0.639314	−	0.768946i	$-0.720782\pi$
$61$	−9.98641	−1.27863	−0.639314	+	0.768946i	$0.720782\pi$
$62$	5.10990	0.648959
$63$	6.28906	0.792347
$64$	−0.620226	−0.0775282
$65$	−4.01546	−0.498057
$66$	2.75343	0.338923
$67$	10.8583	1.32655	0.663274	−	0.748376i	$-0.269166\pi$
$67$	10.8583	1.32655	0.663274	+	0.748376i	$0.269166\pi$
$68$	−1.64063	−0.198956
$69$	2.47229	0.297629
$70$	2.26032	0.270160
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−3.64024	−0.429007
$73$	8.99056	1.05227	0.526133	−	0.850402i	$-0.323641\pi$
$73$	8.99056	1.05227	0.526133	+	0.850402i	$0.323641\pi$
$74$	2.07524	0.241242
$75$	−1.15414	−0.133269
$76$	−3.39658	−0.389614
$77$	−15.0054	−1.71002
$78$	−2.77821	−0.314570
$79$	−9.27589	−1.04362	−0.521809	−	0.853062i	$-0.674743\pi$
$79$	−9.27589	−1.04362	−0.521809	+	0.853062i	$0.674743\pi$
$80$	1.97294	0.220582
$81$	−1.21407	−0.134896
$82$	−3.39720	−0.375158
$83$	9.10914	0.999858	0.499929	−	0.866066i	$-0.333359\pi$
$83$	9.10914	0.999858	0.499929	+	0.866066i	$0.333359\pi$
$84$	−7.13958	−0.778992
$85$	1.00000	0.108465
$86$	−0.804664	−0.0867691
$87$	2.60353	0.279128
$88$	8.68542	0.925869
$89$	4.00484	0.424513	0.212256	−	0.977214i	$-0.431919\pi$
$89$	4.00484	0.424513	0.212256	+	0.977214i	$0.431919\pi$
$90$	0.999892	0.105398
$91$	15.1404	1.58714
$92$	3.51440	0.366402
$93$	9.83792	1.02014
$94$	−7.59158	−0.783012
$95$	2.07028	0.212407
$96$	6.40277	0.653480
$97$	17.2324	1.74969	0.874844	−	0.484405i	$-0.160964\pi$
$97$	17.2324	1.74969	0.874844	+	0.484405i	$0.160964\pi$
$98$	−4.32630	−0.437022
$99$	−6.63787	−0.667131
$100$	−1.64063	−0.164063
$101$	6.78216	0.674850	0.337425	−	0.941352i	$-0.390444\pi$
$101$	6.78216	0.674850	0.337425	+	0.941352i	$0.390444\pi$
$102$	0.691877	0.0685060
$103$	9.76923	0.962591	0.481295	−	0.876559i	$-0.340166\pi$
$103$	9.76923	0.962591	0.481295	+	0.876559i	$0.340166\pi$
$104$	−8.76358	−0.859340
$105$	4.35172	0.424685
$106$	−7.75050	−0.752795
$107$	−11.8631	−1.14685	−0.573426	−	0.819257i	$-0.694386\pi$
$107$	−11.8631	−1.14685	−0.573426	+	0.819257i	$0.694386\pi$
$108$	−8.83889	−0.850522
$109$	0.768666	0.0736249	0.0368124	−	0.999322i	$-0.488280\pi$
$109$	0.768666	0.0736249	0.0368124	+	0.999322i	$0.488280\pi$
$110$	−2.38569	−0.227467
$111$	3.99539	0.379226
$112$	−7.43902	−0.702921
$113$	−4.76316	−0.448080	−0.224040	−	0.974580i	$-0.571925\pi$
$113$	−4.76316	−0.448080	−0.224040	+	0.974580i	$0.571925\pi$
$114$	1.43238	0.134155
$115$	−2.14210	−0.199752
$116$	3.70096	0.343626
$117$	6.69761	0.619194
$118$	6.40822	0.589924
$119$	−3.77052	−0.345643
$120$	−2.51887	−0.229940
$121$	4.83761	0.439782
$122$	5.98657	0.541999
$123$	−6.54051	−0.589738
$124$	13.9848	1.25587
$125$	1.00000	0.0894427
$126$	−3.77012	−0.335869
$127$	1.55400	0.137895	0.0689476	−	0.997620i	$-0.478036\pi$
$127$	1.55400	0.137895	0.0689476	+	0.997620i	$0.478036\pi$
$128$	11.4671	1.01356
$129$	−1.54919	−0.136399
$130$	2.40716	0.211122
$131$	9.88365	0.863538	0.431769	−	0.901984i	$-0.357889\pi$
$131$	9.88365	0.863538	0.431769	+	0.901984i	$0.357889\pi$
$132$	7.53556	0.655887
$133$	−7.80605	−0.676871
$134$	−6.50923	−0.562312
$135$	5.38749	0.463681
$136$	2.18246	0.187144
$137$	−1.59097	−0.135926	−0.0679631	−	0.997688i	$-0.521650\pi$
$137$	−1.59097	−0.135926	−0.0679631	+	0.997688i	$0.521650\pi$
$138$	−1.48207	−0.126162
$139$	−10.7002	−0.907575	−0.453788	−	0.891110i	$-0.649928\pi$
$139$	−10.7002	−0.907575	−0.453788	+	0.891110i	$0.649928\pi$
$140$	6.18604	0.522816
$141$	−14.6158	−1.23087
$142$	0.599472	0.0503066
$143$	−15.9801	−1.33633
$144$	−3.29078	−0.274231
$145$	−2.25581	−0.187335
$146$	−5.38959	−0.446046
$147$	−8.32926	−0.686986
$148$	5.67951	0.466853
$149$	−17.7439	−1.45364	−0.726820	−	0.686828i	$-0.759003\pi$
$149$	−17.7439	−1.45364	−0.726820	+	0.686828i	$0.759003\pi$
$150$	0.691877	0.0564915
$151$	10.5049	0.854875	0.427437	−	0.904045i	$-0.359416\pi$
$151$	10.5049	0.854875	0.427437	+	0.904045i	$0.359416\pi$
$152$	4.51831	0.366483
$153$	−1.66795	−0.134846
$154$	8.99530	0.724862
$155$	−8.52400	−0.684664
$156$	−7.60338	−0.608758
$157$	7.19126	0.573925	0.286962	−	0.957942i	$-0.407355\pi$
$157$	7.19126	0.573925	0.286962	+	0.957942i	$0.407355\pi$
$158$	5.56064	0.442381
$159$	−14.9218	−1.18337
$160$	−5.54764	−0.438580
$161$	8.07684	0.636544
$162$	0.727800	0.0571814
$163$	14.9412	1.17028	0.585141	−	0.810932i	$-0.301039\pi$
$163$	14.9412	1.17028	0.585141	+	0.810932i	$0.301039\pi$
$164$	−9.29744	−0.726008
$165$	−4.59308	−0.357571
$166$	−5.46068	−0.423831
$167$	−10.5698	−0.817917	−0.408959	−	0.912553i	$-0.634108\pi$
$167$	−10.5698	−0.817917	−0.408959	+	0.912553i	$0.634108\pi$
$168$	9.49745	0.732744
$169$	3.12395	0.240304
$170$	−0.599472	−0.0459774
$171$	−3.45314	−0.264068
$172$	−2.20220	−0.167916
$173$	13.7458	1.04508	0.522538	−	0.852616i	$-0.324985\pi$
$173$	13.7458	1.04508	0.522538	+	0.852616i	$0.324985\pi$
$174$	−1.56075	−0.118320
$175$	−3.77052	−0.285025
$176$	7.85162	0.591838
$177$	12.3375	0.927345
$178$	−2.40079	−0.179947
$179$	−21.3597	−1.59650	−0.798250	−	0.602327i	$-0.794240\pi$
$179$	−21.3597	−1.59650	−0.798250	+	0.602327i	$0.794240\pi$
$180$	2.73650	0.203967
$181$	−8.89696	−0.661306	−0.330653	−	0.943752i	$-0.607269\pi$
$181$	−8.89696	−0.661306	−0.330653	+	0.943752i	$0.607269\pi$
$182$	−9.07625	−0.672776
$183$	11.5257	0.852007
$184$	−4.67505	−0.344649
$185$	−3.46178	−0.254515
$186$	−5.89756	−0.432430
$187$	3.97965	0.291021
$188$	−20.7766	−1.51529
$189$	−20.3136	−1.47760
$190$	−1.24108	−0.0900373
$191$	−9.71312	−0.702817	−0.351408	−	0.936222i	$-0.614297\pi$
$191$	−9.71312	−0.702817	−0.351408	+	0.936222i	$0.614297\pi$
$192$	0.715829	0.0516605
$193$	−7.74764	−0.557687	−0.278844	−	0.960337i	$-0.589951\pi$
$193$	−7.74764	−0.557687	−0.278844	+	0.960337i	$0.589951\pi$
$194$	−10.3304	−0.741677
$195$	4.63442	0.331878
$196$	−11.8402	−0.845727
$197$	−27.3664	−1.94977	−0.974886	−	0.222703i	$-0.928512\pi$
$197$	−27.3664	−1.94977	−0.974886	+	0.222703i	$0.928512\pi$
$198$	3.97922	0.282791
$199$	−11.3457	−0.804275	−0.402137	−	0.915579i	$-0.631733\pi$
$199$	−11.3457	−0.804275	−0.402137	+	0.915579i	$0.631733\pi$
$200$	2.18246	0.154323
$201$	−12.5320	−0.883939
$202$	−4.06572	−0.286063
$203$	8.50560	0.596976
$204$	1.89352	0.132573
$205$	5.66699	0.395800
$206$	−5.85638	−0.408033
$207$	3.57293	0.248335
$208$	−7.92228	−0.549311
$209$	8.23900	0.569904
$210$	−2.60874	−0.180020
$211$	21.4388	1.47591	0.737953	−	0.674852i	$-0.235793\pi$
$211$	21.4388	1.47591	0.737953	+	0.674852i	$0.235793\pi$
$212$	−21.2115	−1.45681
$213$	1.15414	0.0790806
$214$	7.11162	0.486141
$215$	1.34229	0.0915432
$216$	11.7580	0.800028
$217$	32.1399	2.18180
$218$	−0.460794	−0.0312089
$219$	−10.3764	−0.701172
$220$	−6.52914	−0.440195
$221$	−4.01546	−0.270109
$222$	−2.39513	−0.160750
$223$	−19.8068	−1.32636	−0.663182	−	0.748458i	$-0.730794\pi$
$223$	−19.8068	−1.32636	−0.663182	+	0.748458i	$0.730794\pi$
$224$	20.9175	1.39761
$225$	−1.66795	−0.111197
$226$	2.85538	0.189937
$227$	2.43415	0.161560	0.0807802	−	0.996732i	$-0.474259\pi$
$227$	2.43415	0.161560	0.0807802	+	0.996732i	$0.474259\pi$
$228$	3.92013	0.259617
$229$	−12.2600	−0.810165	−0.405082	−	0.914280i	$-0.632757\pi$
$229$	−12.2600	−0.810165	−0.405082	+	0.914280i	$0.632757\pi$
$230$	1.28413	0.0846730
$231$	17.3183	1.13946
$232$	−4.92322	−0.323225
$233$	−22.0465	−1.44431	−0.722157	−	0.691729i	$-0.756849\pi$
$233$	−22.0465	−1.44431	−0.722157	+	0.691729i	$0.756849\pi$
$234$	−4.01503	−0.262471
$235$	12.6638	0.826094
$236$	17.5380	1.14163
$237$	10.7057	0.695410
$238$	2.26032	0.146515
$239$	20.3258	1.31477	0.657384	−	0.753555i	$-0.271663\pi$
$239$	20.3258	1.31477	0.657384	+	0.753555i	$0.271663\pi$
$240$	−2.27706	−0.146983
$241$	4.51760	0.291004	0.145502	−	0.989358i	$-0.453520\pi$
$241$	4.51760	0.291004	0.145502	+	0.989358i	$0.453520\pi$
$242$	−2.90001	−0.186420
$243$	−14.7613	−0.946935
$244$	16.3840	1.04888
$245$	7.21684	0.461067
$246$	3.92086	0.249985
$247$	−8.31315	−0.528953
$248$	−18.6033	−1.18131
$249$	−10.5132	−0.666250
$250$	−0.599472	−0.0379140
$251$	3.53848	0.223347	0.111673	−	0.993745i	$-0.464379\pi$
$251$	3.53848	0.223347	0.111673	+	0.993745i	$0.464379\pi$
$252$	−10.3180	−0.649975
$253$	−8.52481	−0.535950
$254$	−0.931581	−0.0584526
$255$	−1.15414	−0.0722752
$256$	−5.63375	−0.352110
$257$	7.20050	0.449155	0.224578	−	0.974456i	$-0.427900\pi$
$257$	7.20050	0.449155	0.224578	+	0.974456i	$0.427900\pi$
$258$	0.928697	0.0578181
$259$	13.0527	0.811056
$260$	6.58790	0.408564
$261$	3.76259	0.232899
$262$	−5.92497	−0.366046
$263$	−1.16330	−0.0717323	−0.0358661	−	0.999357i	$-0.511419\pi$
$263$	−1.16330	−0.0717323	−0.0358661	+	0.999357i	$0.511419\pi$
$264$	−10.0242	−0.616948
$265$	12.9289	0.794214
$266$	4.67951	0.286919
$267$	−4.62216	−0.282872
$268$	−17.8144	−1.08819
$269$	−13.0758	−0.797243	−0.398622	−	0.917115i	$-0.630511\pi$
$269$	−13.0758	−0.797243	−0.398622	+	0.917115i	$0.630511\pi$
$270$	−3.22965	−0.196550
$271$	15.5863	0.946802	0.473401	−	0.880847i	$-0.343026\pi$
$271$	15.5863	0.946802	0.473401	+	0.880847i	$0.343026\pi$
$272$	1.97294	0.119627
$273$	−17.4742	−1.05759
$274$	0.953745	0.0576179
$275$	3.97965	0.239982
$276$	−4.05612	−0.244150
$277$	21.8036	1.31005	0.655024	−	0.755608i	$-0.272658\pi$
$277$	21.8036	1.31005	0.655024	+	0.755608i	$0.272658\pi$
$278$	6.41445	0.384713
$279$	14.2176	0.851188
$280$	−8.22901	−0.491777
$281$	4.47479	0.266944	0.133472	−	0.991053i	$-0.457387\pi$
$281$	4.47479	0.266944	0.133472	+	0.991053i	$0.457387\pi$
$282$	8.76177	0.521756
$283$	−12.1705	−0.723462	−0.361731	−	0.932283i	$-0.617814\pi$
$283$	−12.1705	−0.723462	−0.361731	+	0.932283i	$0.617814\pi$
$284$	1.64063	0.0973536
$285$	−2.38940	−0.141536
$286$	9.57965	0.566457
$287$	−21.3675	−1.26128
$288$	9.25321	0.545251
$289$	1.00000	0.0588235
$290$	1.35230	0.0794097
$291$	−19.8887	−1.16590
$292$	−14.7502	−0.863191
$293$	−15.9012	−0.928955	−0.464478	−	0.885585i	$-0.653758\pi$
$293$	−15.9012	−0.928955	−0.464478	+	0.885585i	$0.653758\pi$
$294$	4.99316	0.291207
$295$	−10.6898	−0.622382
$296$	−7.55519	−0.439137
$297$	21.4403	1.24409
$298$	10.6370	0.616185
$299$	8.60153	0.497439
$300$	1.89352	0.109323
$301$	−5.06112	−0.291718
$302$	−6.29738	−0.362374
$303$	−7.82758	−0.449683
$304$	4.08455	0.234265
$305$	−9.98641	−0.571820
$306$	0.999892	0.0571600
$307$	−16.2025	−0.924723	−0.462362	−	0.886691i	$-0.652998\pi$
$307$	−16.2025	−0.924723	−0.462362	+	0.886691i	$0.652998\pi$
$308$	24.6183	1.40276
$309$	−11.2751	−0.641417
$310$	5.10990	0.290223
$311$	−4.65488	−0.263954	−0.131977	−	0.991253i	$-0.542133\pi$
$311$	−4.65488	−0.263954	−0.131977	+	0.991253i	$0.542133\pi$
$312$	10.1144	0.572617
$313$	18.4949	1.04539	0.522697	−	0.852518i	$-0.324926\pi$
$313$	18.4949	1.04539	0.522697	+	0.852518i	$0.324926\pi$
$314$	−4.31096	−0.243282
$315$	6.28906	0.354348
$316$	15.2183	0.856098
$317$	−9.75990	−0.548171	−0.274085	−	0.961705i	$-0.588375\pi$
$317$	−9.75990	−0.548171	−0.274085	+	0.961705i	$0.588375\pi$
$318$	8.94518	0.501621
$319$	−8.97735	−0.502635
$320$	−0.620226	−0.0346717
$321$	13.6918	0.764199
$322$	−4.84184	−0.269825
$323$	2.07028	0.115194
$324$	1.99184	0.110658
$325$	−4.01546	−0.222738
$326$	−8.95681	−0.496072
$327$	−0.887151	−0.0490595
$328$	12.3680	0.682907
$329$	−47.7490	−2.63249
$330$	2.75343	0.151571
$331$	−2.48451	−0.136561	−0.0682805	−	0.997666i	$-0.521751\pi$
$331$	−2.48451	−0.136561	−0.0682805	+	0.997666i	$0.521751\pi$
$332$	−14.9448	−0.820200
$333$	5.77409	0.316418
$334$	6.33632	0.346708
$335$	10.8583	0.593251
$336$	8.58569	0.468388
$337$	−5.17260	−0.281770	−0.140885	−	0.990026i	$-0.544995\pi$
$337$	−5.17260	−0.281770	−0.140885	+	0.990026i	$0.544995\pi$
$338$	−1.87272	−0.101863
$339$	5.49736	0.298576
$340$	−1.64063	−0.0889758
$341$	−33.9225	−1.83701
$342$	2.07006	0.111936
$343$	−0.817592	−0.0441458
$344$	2.92949	0.157947
$345$	2.47229	0.133104
$346$	−8.24024	−0.442998
$347$	−6.42768	−0.345056	−0.172528	−	0.985005i	$-0.555194\pi$
$347$	−6.42768	−0.345056	−0.172528	+	0.985005i	$0.555194\pi$
$348$	−4.27144	−0.228973
$349$	20.8868	1.11804	0.559021	−	0.829153i	$-0.311177\pi$
$349$	20.8868	1.11804	0.559021	+	0.829153i	$0.311177\pi$
$350$	2.26032	0.120819
$351$	−21.6333	−1.15470
$352$	−22.0777	−1.17674
$353$	−27.7445	−1.47669	−0.738346	−	0.674423i	$-0.764393\pi$
$353$	−27.7445	−1.47669	−0.738346	+	0.674423i	$0.764393\pi$
$354$	−7.39600	−0.393093
$355$	−1.00000	−0.0530745
$356$	−6.57048	−0.348235
$357$	4.35172	0.230318
$358$	12.8046	0.676742
$359$	−33.7478	−1.78114	−0.890569	−	0.454847i	$-0.849694\pi$
$359$	−33.7478	−1.78114	−0.890569	+	0.454847i	$0.849694\pi$
$360$	−3.64024	−0.191858
$361$	−14.7139	−0.774417
$362$	5.33348	0.280322
$363$	−5.58329	−0.293047
$364$	−24.8398	−1.30196
$365$	8.99056	0.470588
$366$	−6.90936	−0.361158
$367$	19.0396	0.993857	0.496929	−	0.867791i	$-0.334461\pi$
$367$	19.0396	0.993857	0.496929	+	0.867791i	$0.334461\pi$
$368$	−4.22624	−0.220308
$369$	−9.45227	−0.492066
$370$	2.07524	0.107887
$371$	−48.7486	−2.53090
$372$	−16.1404	−0.836841
$373$	7.36513	0.381352	0.190676	−	0.981653i	$-0.438932\pi$
$373$	7.36513	0.381352	0.190676	+	0.981653i	$0.438932\pi$
$374$	−2.38569	−0.123361
$375$	−1.15414	−0.0595997
$376$	27.6382	1.42533
$377$	9.05814	0.466518
$378$	12.1775	0.626341
$379$	10.8146	0.555508	0.277754	−	0.960652i	$-0.410410\pi$
$379$	10.8146	0.555508	0.277754	+	0.960652i	$0.410410\pi$
$380$	−3.39658	−0.174241
$381$	−1.79354	−0.0918858
$382$	5.82275	0.297918
$383$	30.4438	1.55561	0.777803	−	0.628508i	$-0.216334\pi$
$383$	30.4438	1.55561	0.777803	+	0.628508i	$0.216334\pi$
$384$	−13.2347	−0.675379
$385$	−15.0054	−0.764744
$386$	4.64450	0.236399
$387$	−2.23887	−0.113808
$388$	−28.2721	−1.43530
$389$	15.9867	0.810557	0.405278	−	0.914193i	$-0.367175\pi$
$389$	15.9867	0.810557	0.405278	+	0.914193i	$0.367175\pi$
$390$	−2.77821	−0.140680
$391$	−2.14210	−0.108331
$392$	15.7505	0.795518
$393$	−11.4071	−0.575414
$394$	16.4054	0.826491
$395$	−9.27589	−0.466721
$396$	10.8903	0.547259
$397$	−32.5794	−1.63511	−0.817557	−	0.575847i	$-0.804672\pi$
$397$	−32.5794	−1.63511	−0.817557	+	0.575847i	$0.804672\pi$
$398$	6.80143	0.340925
$399$	9.00930	0.451029
$400$	1.97294	0.0986471
$401$	−32.9839	−1.64714	−0.823569	−	0.567217i	$-0.808020\pi$
$401$	−32.9839	−1.64714	−0.823569	+	0.567217i	$0.808020\pi$
$402$	7.51258	0.374694
$403$	34.2278	1.70501
$404$	−11.1270	−0.553591
$405$	−1.21407	−0.0603275
$406$	−5.09887	−0.253053
$407$	−13.7767	−0.682884
$408$	−2.51887	−0.124703
$409$	−33.6948	−1.66610	−0.833050	−	0.553197i	$-0.813408\pi$
$409$	−33.6948	−1.66610	−0.833050	+	0.553197i	$0.813408\pi$
$410$	−3.39720	−0.167776
$411$	1.83621	0.0905736
$412$	−16.0277	−0.789629
$413$	40.3060	1.98333
$414$	−2.14187	−0.105267
$415$	9.10914	0.447150
$416$	22.2764	1.09219
$417$	12.3495	0.604758
$418$	−4.93906	−0.241577
$419$	−11.5603	−0.564758	−0.282379	−	0.959303i	$-0.591124\pi$
$419$	−11.5603	−0.564758	−0.282379	+	0.959303i	$0.591124\pi$
$420$	−7.13958	−0.348376
$421$	−8.60478	−0.419372	−0.209686	−	0.977769i	$-0.567244\pi$
$421$	−8.60478	−0.419372	−0.209686	+	0.977769i	$0.567244\pi$
$422$	−12.8519	−0.625623
$423$	−21.1226	−1.02702
$424$	28.2167	1.37033
$425$	1.00000	0.0485071
$426$	−0.691877	−0.0335215
$427$	37.6540	1.82220
$428$	19.4631	0.940782
$429$	18.4434	0.890454
$430$	−0.804664	−0.0388043
$431$	36.4186	1.75422	0.877110	−	0.480290i	$-0.159468\pi$
$431$	36.4186	1.75422	0.877110	+	0.480290i	$0.159468\pi$
$432$	10.6292	0.511397
$433$	−31.6156	−1.51935	−0.759675	−	0.650302i	$-0.774642\pi$
$433$	−31.6156	−1.51935	−0.759675	+	0.650302i	$0.774642\pi$
$434$	−19.2670	−0.924846
$435$	2.60353	0.124830
$436$	−1.26110	−0.0603957
$437$	−4.43476	−0.212143
$438$	6.22036	0.297220
$439$	−15.2878	−0.729646	−0.364823	−	0.931077i	$-0.618870\pi$
$439$	−15.2878	−0.729646	−0.364823	+	0.931077i	$0.618870\pi$
$440$	8.68542	0.414061
$441$	−12.0374	−0.573207
$442$	2.40716	0.114497
$443$	−13.3436	−0.633973	−0.316987	−	0.948430i	$-0.602671\pi$
$443$	−13.3436	−0.633973	−0.316987	+	0.948430i	$0.602671\pi$
$444$	−6.55497	−0.311085
$445$	4.00484	0.189848
$446$	11.8737	0.562234
$447$	20.4790	0.968625
$448$	2.33857	0.110487
$449$	−25.3777	−1.19765	−0.598824	−	0.800881i	$-0.704365\pi$
$449$	−25.3777	−1.19765	−0.598824	+	0.800881i	$0.704365\pi$
$450$	0.999892	0.0471354
$451$	22.5526	1.06196
$452$	7.81459	0.367567
$453$	−12.1241	−0.569641
$454$	−1.45921	−0.0684840
$455$	15.1404	0.709793
$456$	−5.21478	−0.244204
$457$	7.76458	0.363212	0.181606	−	0.983371i	$-0.441871\pi$
$457$	7.76458	0.363212	0.181606	+	0.983371i	$0.441871\pi$
$458$	7.34954	0.343422
$459$	5.38749	0.251466
$460$	3.51440	0.163860
$461$	2.42916	0.113137	0.0565687	−	0.998399i	$-0.481984\pi$
$461$	2.42916	0.113137	0.0565687	+	0.998399i	$0.481984\pi$
$462$	−10.3819	−0.483008
$463$	−29.3326	−1.36320	−0.681602	−	0.731723i	$-0.738716\pi$
$463$	−29.3326	−1.36320	−0.681602	+	0.731723i	$0.738716\pi$
$464$	−4.45059	−0.206613
$465$	9.83792	0.456223
$466$	13.2163	0.612232
$467$	20.5537	0.951111	0.475555	−	0.879686i	$-0.342247\pi$
$467$	20.5537	0.951111	0.475555	+	0.879686i	$0.342247\pi$
$468$	−10.9883	−0.507935
$469$	−40.9413	−1.89050
$470$	−7.59158	−0.350174
$471$	−8.29974	−0.382432
$472$	−23.3300	−1.07385
$473$	5.34183	0.245618
$474$	−6.41777	−0.294778
$475$	2.07028	0.0949911
$476$	6.18604	0.283537
$477$	−21.5648	−0.987382
$478$	−12.1848	−0.557319
$479$	0.399309	0.0182449	0.00912245	−	0.999958i	$-0.497096\pi$
$479$	0.399309	0.0182449	0.00912245	+	0.999958i	$0.497096\pi$
$480$	6.40277	0.292245
$481$	13.9007	0.633815
$482$	−2.70818	−0.123354
$483$	−9.32183	−0.424158
$484$	−7.93673	−0.360761
$485$	17.2324	0.782484
$486$	8.84896	0.401397
$487$	−38.1569	−1.72906	−0.864528	−	0.502584i	$-0.832383\pi$
$487$	−38.1569	−1.72906	−0.864528	+	0.502584i	$0.832383\pi$
$488$	−21.7949	−0.986610
$489$	−17.2442	−0.779811
$490$	−4.32630	−0.195442
$491$	−19.7837	−0.892828	−0.446414	−	0.894827i	$-0.647299\pi$
$491$	−19.7837	−0.892828	−0.446414	+	0.894827i	$0.647299\pi$
$492$	10.7306	0.483772
$493$	−2.25581	−0.101597
$494$	4.98350	0.224218
$495$	−6.63787	−0.298350
$496$	−16.8174	−0.755122
$497$	3.77052	0.169131
$498$	6.30240	0.282417
$499$	38.5414	1.72535	0.862674	−	0.505760i	$-0.168788\pi$
$499$	38.5414	1.72535	0.862674	+	0.505760i	$0.168788\pi$
$500$	−1.64063	−0.0733713
$501$	12.1991	0.545015
$502$	−2.12122	−0.0946747
$503$	−0.863451	−0.0384994	−0.0192497	−	0.999815i	$-0.506128\pi$
$503$	−0.863451	−0.0384994	−0.0192497	+	0.999815i	$0.506128\pi$
$504$	13.7256	0.611387
$505$	6.78216	0.301802
$506$	5.11039	0.227184
$507$	−3.60548	−0.160125
$508$	−2.54954	−0.113118
$509$	−31.3262	−1.38851	−0.694256	−	0.719728i	$-0.744266\pi$
$509$	−31.3262	−1.38851	−0.694256	+	0.719728i	$0.744266\pi$
$510$	0.691877	0.0306368
$511$	−33.8991	−1.49961
$512$	−19.5569	−0.864301
$513$	11.1536	0.492445
$514$	−4.31650	−0.190393
$515$	9.76923	0.430484
$516$	2.54165	0.111890
$517$	50.3974	2.21647
$518$	−7.82474	−0.343800
$519$	−15.8646	−0.696381
$520$	−8.76358	−0.384309
$521$	22.1683	0.971209	0.485604	−	0.874179i	$-0.338600\pi$
$521$	22.1683	0.971209	0.485604	+	0.874179i	$0.338600\pi$
$522$	−2.25557	−0.0987237
$523$	2.66215	0.116408	0.0582038	−	0.998305i	$-0.481463\pi$
$523$	2.66215	0.116408	0.0582038	+	0.998305i	$0.481463\pi$
$524$	−16.2154	−0.708375
$525$	4.35172	0.189925
$526$	0.697367	0.0304067
$527$	−8.52400	−0.371311
$528$	−9.06189	−0.394368
$529$	−18.4114	−0.800496
$530$	−7.75050	−0.336660
$531$	17.8300	0.773758
$532$	12.8069	0.555248
$533$	−22.7556	−0.985653
$534$	2.77086	0.119907
$535$	−11.8631	−0.512888
$536$	23.6977	1.02359
$537$	24.6521	1.06382
$538$	7.83856	0.337944
$539$	28.7205	1.23708
$540$	−8.83889	−0.380365
$541$	9.15326	0.393529	0.196765	−	0.980451i	$-0.436956\pi$
$541$	9.15326	0.393529	0.196765	+	0.980451i	$0.436956\pi$
$542$	−9.34357	−0.401341
$543$	10.2684	0.440658
$544$	−5.54764	−0.237853
$545$	0.768666	0.0329260
$546$	10.4753	0.448301
$547$	22.2886	0.952994	0.476497	−	0.879176i	$-0.341906\pi$
$547$	22.2886	0.952994	0.476497	+	0.879176i	$0.341906\pi$
$548$	2.61020	0.111502
$549$	16.6569	0.710898
$550$	−2.38569	−0.101726
$551$	−4.67018	−0.198956
$552$	5.39567	0.229655
$553$	34.9749	1.48729
$554$	−13.0706	−0.555318
$555$	3.99539	0.169595
$556$	17.5550	0.744499
$557$	−5.11790	−0.216852	−0.108426	−	0.994105i	$-0.534581\pi$
$557$	−5.11790	−0.216852	−0.108426	+	0.994105i	$0.534581\pi$
$558$	−8.52309	−0.360811
$559$	−5.38990	−0.227969
$560$	−7.43902	−0.314356
$561$	−4.59308	−0.193920
$562$	−2.68252	−0.113155
$563$	36.6498	1.54461	0.772303	−	0.635254i	$-0.219105\pi$
$563$	36.6498	1.54461	0.772303	+	0.635254i	$0.219105\pi$
$564$	23.9792	1.00971
$565$	−4.76316	−0.200387
$566$	7.29589	0.306669
$567$	4.57767	0.192244
$568$	−2.18246	−0.0915739
$569$	1.22972	0.0515527	0.0257764	−	0.999668i	$-0.491794\pi$
$569$	1.22972	0.0515527	0.0257764	+	0.999668i	$0.491794\pi$
$570$	1.43238	0.0599959
$571$	22.4097	0.937815	0.468908	−	0.883247i	$-0.344648\pi$
$571$	22.4097	0.937815	0.468908	+	0.883247i	$0.344648\pi$
$572$	26.2175	1.09621
$573$	11.2103	0.468318
$574$	12.8092	0.534647
$575$	−2.14210	−0.0893318
$576$	1.03451	0.0431045
$577$	3.80541	0.158421	0.0792107	−	0.996858i	$-0.474760\pi$
$577$	3.80541	0.158421	0.0792107	+	0.996858i	$0.474760\pi$
$578$	−0.599472	−0.0249348
$579$	8.94188	0.371612
$580$	3.70096	0.153674
$581$	−34.3462	−1.42492
$582$	11.9227	0.494213
$583$	51.4524	2.13094
$584$	19.6215	0.811945
$585$	6.69761	0.276912
$586$	9.53230	0.393776
$587$	−31.9342	−1.31806	−0.659032	−	0.752115i	$-0.729034\pi$
$587$	−31.9342	−1.31806	−0.659032	+	0.752115i	$0.729034\pi$
$588$	13.6653	0.563546
$589$	−17.6471	−0.727136
$590$	6.40822	0.263822
$591$	31.5847	1.29922
$592$	−6.82989	−0.280707
$593$	−25.0252	−1.02766	−0.513831	−	0.857892i	$-0.671774\pi$
$593$	−25.0252	−1.02766	−0.513831	+	0.857892i	$0.671774\pi$
$594$	−12.8529	−0.527360
$595$	−3.77052	−0.154576
$596$	29.1113	1.19244
$597$	13.0945	0.535924
$598$	−5.15638	−0.210860
$599$	−1.49345	−0.0610207	−0.0305104	−	0.999534i	$-0.509713\pi$
$599$	−1.49345	−0.0610207	−0.0305104	+	0.999534i	$0.509713\pi$
$600$	−2.51887	−0.102832
$601$	−10.2371	−0.417581	−0.208791	−	0.977960i	$-0.566953\pi$
$601$	−10.2371	−0.417581	−0.208791	+	0.977960i	$0.566953\pi$
$602$	3.03400	0.123657
$603$	−18.1111	−0.737541
$604$	−17.2346	−0.701268
$605$	4.83761	0.196677
$606$	4.69242	0.190617
$607$	−11.4750	−0.465757	−0.232878	−	0.972506i	$-0.574814\pi$
$607$	−11.4750	−0.465757	−0.232878	+	0.972506i	$0.574814\pi$
$608$	−11.4852	−0.465786
$609$	−9.81668	−0.397792
$610$	5.98657	0.242389
$611$	−50.8509	−2.05721
$612$	2.73650	0.110616
$613$	−41.0887	−1.65956	−0.829778	−	0.558094i	$-0.811533\pi$
$613$	−41.0887	−1.65956	−0.829778	+	0.558094i	$0.811533\pi$
$614$	9.71293	0.391982
$615$	−6.54051	−0.263739
$616$	−32.7486	−1.31948
$617$	10.4803	0.421922	0.210961	−	0.977494i	$-0.432341\pi$
$617$	10.4803	0.421922	0.210961	+	0.977494i	$0.432341\pi$
$618$	6.75910	0.271891
$619$	−6.00489	−0.241357	−0.120678	−	0.992692i	$-0.538507\pi$
$619$	−6.00489	−0.241357	−0.120678	+	0.992692i	$0.538507\pi$
$620$	13.9848	0.561641
$621$	−11.5405	−0.463106
$622$	2.79047	0.111888
$623$	−15.1003	−0.604983
$624$	9.14344	0.366031
$625$	1.00000	0.0400000
$626$	−11.0872	−0.443133
$627$	−9.50899	−0.379752
$628$	−11.7982	−0.470800
$629$	−3.46178	−0.138030
$630$	−3.77012	−0.150205
$631$	−18.6500	−0.742443	−0.371222	−	0.928544i	$-0.621061\pi$
$631$	−18.6500	−0.742443	−0.371222	+	0.928544i	$0.621061\pi$
$632$	−20.2442	−0.805273
$633$	−24.7434	−0.983462
$634$	5.85079	0.232365
$635$	1.55400	0.0616686
$636$	24.4811	0.970740
$637$	−28.9789	−1.14819
$638$	5.38167	0.213062
$639$	1.66795	0.0659832
$640$	11.4671	0.453277
$641$	−46.5570	−1.83889	−0.919446	−	0.393215i	$-0.871363\pi$
$641$	−46.5570	−1.83889	−0.919446	+	0.393215i	$0.871363\pi$
$642$	−8.20783	−0.323937
$643$	−22.1494	−0.873486	−0.436743	−	0.899586i	$-0.643868\pi$
$643$	−22.1494	−0.873486	−0.436743	+	0.899586i	$0.643868\pi$
$644$	−13.2511	−0.522168
$645$	−1.54919	−0.0609993
$646$	−1.24108	−0.0488296
$647$	0.536547	0.0210938	0.0105469	−	0.999944i	$-0.496643\pi$
$647$	0.536547	0.0210938	0.0105469	+	0.999944i	$0.496643\pi$
$648$	−2.64965	−0.104088
$649$	−42.5415	−1.66990
$650$	2.40716	0.0944166
$651$	−37.0941	−1.45383
$652$	−24.5130	−0.960002
$653$	8.57296	0.335486	0.167743	−	0.985831i	$-0.446352\pi$
$653$	8.57296	0.335486	0.167743	+	0.985831i	$0.446352\pi$
$654$	0.531822	0.0207959
$655$	9.88365	0.386186
$656$	11.1806	0.436530
$657$	−14.9958	−0.585044
$658$	28.6242	1.11589
$659$	16.4597	0.641178	0.320589	−	0.947218i	$-0.396119\pi$
$659$	16.4597	0.641178	0.320589	+	0.947218i	$0.396119\pi$
$660$	7.53556	0.293321
$661$	30.4323	1.18368	0.591840	−	0.806055i	$-0.298402\pi$
$661$	30.4323	1.18368	0.591840	+	0.806055i	$0.298402\pi$
$662$	1.48939	0.0578870
$663$	4.63442	0.179986
$664$	19.8803	0.771506
$665$	−7.80605	−0.302706
$666$	−3.46141	−0.134127
$667$	4.83218	0.187103
$668$	17.3412	0.670951
$669$	22.8599	0.883816
$670$	−6.50923	−0.251474
$671$	−39.7424	−1.53424
$672$	−24.1418	−0.931290
$673$	44.7148	1.72363	0.861814	−	0.507224i	$-0.169328\pi$
$673$	44.7148	1.72363	0.861814	+	0.507224i	$0.169328\pi$
$674$	3.10083	0.119440
$675$	5.38749	0.207364
$676$	−5.12525	−0.197125
$677$	4.44610	0.170877	0.0854387	−	0.996343i	$-0.472771\pi$
$677$	4.44610	0.170877	0.0854387	+	0.996343i	$0.472771\pi$
$678$	−3.29552	−0.126564
$679$	−64.9753	−2.49352
$680$	2.18246	0.0836935
$681$	−2.80936	−0.107655
$682$	20.3356	0.778691
$683$	−40.8546	−1.56326	−0.781628	−	0.623744i	$-0.785611\pi$
$683$	−40.8546	−1.56326	−0.781628	+	0.623744i	$0.785611\pi$
$684$	5.66533	0.216619
$685$	−1.59097	−0.0607880
$686$	0.490124	0.0187130
$687$	14.1498	0.539849
$688$	2.64825	0.100964
$689$	−51.9154	−1.97782
$690$	−1.48207	−0.0564214
$691$	−33.6404	−1.27974	−0.639871	−	0.768482i	$-0.721012\pi$
$691$	−33.6404	−1.27974	−0.639871	+	0.768482i	$0.721012\pi$
$692$	−22.5518	−0.857293
$693$	25.0282	0.950744
$694$	3.85322	0.146266
$695$	−10.7002	−0.405880
$696$	5.68210	0.215380
$697$	5.66699	0.214652
$698$	−12.5210	−0.473928
$699$	25.4448	0.962411
$700$	6.18604	0.233810
$701$	−30.1592	−1.13910	−0.569548	−	0.821958i	$-0.692882\pi$
$701$	−30.1592	−1.13910	−0.569548	+	0.821958i	$0.692882\pi$
$702$	12.9685	0.489466
$703$	−7.16687	−0.270304
$704$	−2.46828	−0.0930268
$705$	−14.6158	−0.550463
$706$	16.6321	0.625956
$707$	−25.5723	−0.961745
$708$	−20.2413	−0.760716
$709$	−5.72105	−0.214858	−0.107429	−	0.994213i	$-0.534262\pi$
$709$	−5.72105	−0.214858	−0.107429	+	0.994213i	$0.534262\pi$
$710$	0.599472	0.0224978
$711$	15.4718	0.580236
$712$	8.74041	0.327561
$713$	18.2593	0.683815
$714$	−2.60874	−0.0976295
$715$	−15.9801	−0.597623
$716$	35.0434	1.30963
$717$	−23.4589	−0.876089
$718$	20.2309	0.755009
$719$	−16.1862	−0.603642	−0.301821	−	0.953365i	$-0.597594\pi$
$719$	−16.1862	−0.603642	−0.301821	+	0.953365i	$0.597594\pi$
$720$	−3.29078	−0.122640
$721$	−36.8351	−1.37181
$722$	8.82059	0.328268
$723$	−5.21396	−0.193909
$724$	14.5967	0.542480
$725$	−2.25581	−0.0837788
$726$	3.34703	0.124220
$727$	−7.42327	−0.275314	−0.137657	−	0.990480i	$-0.543957\pi$
$727$	−7.42327	−0.275314	−0.137657	+	0.990480i	$0.543957\pi$
$728$	33.0433	1.22467
$729$	20.6788	0.765881
$730$	−5.38959	−0.199478
$731$	1.34229	0.0496463
$732$	−18.9095	−0.698915
$733$	8.46639	0.312713	0.156357	−	0.987701i	$-0.450025\pi$
$733$	8.46639	0.312713	0.156357	+	0.987701i	$0.450025\pi$
$734$	−11.4137	−0.421287
$735$	−8.32926	−0.307229
$736$	11.8836	0.438036
$737$	43.2121	1.59174
$738$	5.66638	0.208582
$739$	39.5164	1.45363	0.726817	−	0.686831i	$-0.240999\pi$
$739$	39.5164	1.45363	0.726817	+	0.686831i	$0.240999\pi$
$740$	5.67951	0.208783
$741$	9.59456	0.352465
$742$	29.2234	1.07283
$743$	−12.3365	−0.452582	−0.226291	−	0.974060i	$-0.572660\pi$
$743$	−12.3365	−0.452582	−0.226291	+	0.974060i	$0.572660\pi$
$744$	21.4709	0.787160
$745$	−17.7439	−0.650088
$746$	−4.41519	−0.161652
$747$	−15.1936	−0.555906
$748$	−6.52914	−0.238729
$749$	44.7302	1.63441
$750$	0.691877	0.0252638
$751$	−5.99146	−0.218631	−0.109316	−	0.994007i	$-0.534866\pi$
$751$	−5.99146	−0.218631	−0.109316	+	0.994007i	$0.534866\pi$
$752$	24.9849	0.911105
$753$	−4.08391	−0.148826
$754$	−5.43011	−0.197753
$755$	10.5049	0.382312
$756$	33.3272	1.21210
$757$	−32.4475	−1.17933	−0.589663	−	0.807650i	$-0.700739\pi$
$757$	−32.4475	−1.17933	−0.589663	+	0.807650i	$0.700739\pi$
$758$	−6.48305	−0.235475
$759$	9.83885	0.357128
$760$	4.51831	0.163896
$761$	38.3852	1.39146	0.695730	−	0.718303i	$-0.255081\pi$
$761$	38.3852	1.39146	0.695730	+	0.718303i	$0.255081\pi$
$762$	1.07518	0.0389496
$763$	−2.89827	−0.104925
$764$	15.9357	0.576532
$765$	−1.66795	−0.0603050
$766$	−18.2502	−0.659407
$767$	42.9244	1.54991
$768$	6.50216	0.234626
$769$	−16.0691	−0.579466	−0.289733	−	0.957107i	$-0.593567\pi$
$769$	−16.0691	−0.579466	−0.289733	+	0.957107i	$0.593567\pi$
$770$	8.99530	0.324168
$771$	−8.31041	−0.299292
$772$	12.7110	0.457480
$773$	−22.8423	−0.821579	−0.410790	−	0.911730i	$-0.634747\pi$
$773$	−22.8423	−0.821579	−0.410790	+	0.911730i	$0.634747\pi$
$774$	1.34214	0.0482423
$775$	−8.52400	−0.306191
$776$	37.6091	1.35009
$777$	−15.0647	−0.540443
$778$	−9.58357	−0.343588
$779$	11.7323	0.420352
$780$	−7.60338	−0.272245
$781$	−3.97965	−0.142403
$782$	1.28413	0.0459204
$783$	−12.1532	−0.434319
$784$	14.2384	0.508514
$785$	7.19126	0.256667
$786$	6.83827	0.243913
$787$	−28.0681	−1.00052	−0.500261	−	0.865875i	$-0.666762\pi$
$787$	−28.0681	−1.00052	−0.500261	+	0.865875i	$0.666762\pi$
$788$	44.8982	1.59943
$789$	1.34262	0.0477984
$790$	5.56064	0.197839
$791$	17.9596	0.638569
$792$	−14.4869	−0.514769
$793$	40.1000	1.42399
$794$	19.5305	0.693110
$795$	−14.9218	−0.529220
$796$	18.6141	0.659760
$797$	−20.8089	−0.737090	−0.368545	−	0.929610i	$-0.620144\pi$
$797$	−20.8089	−0.737090	−0.368545	+	0.929610i	$0.620144\pi$
$798$	−5.40083	−0.191187
$799$	12.6638	0.448012
$800$	−5.54764	−0.196139
$801$	−6.67989	−0.236022
$802$	19.7729	0.698207
$803$	35.7793	1.26262
$804$	20.5604	0.725109
$805$	8.07684	0.284671
$806$	−20.5186	−0.722738
$807$	15.0913	0.531239
$808$	14.8018	0.520725
$809$	−40.9142	−1.43847	−0.719233	−	0.694769i	$-0.755506\pi$
$809$	−40.9142	−1.43847	−0.719233	+	0.694769i	$0.755506\pi$
$810$	0.727800	0.0255723
$811$	1.80031	0.0632176	0.0316088	−	0.999500i	$-0.489937\pi$
$811$	1.80031	0.0632176	0.0316088	+	0.999500i	$0.489937\pi$
$812$	−13.9546	−0.489709
$813$	−17.9888	−0.630896
$814$	8.25873	0.289468
$815$	14.9412	0.523366
$816$	−2.27706	−0.0797129
$817$	2.77891	0.0972219
$818$	20.1991	0.706245
$819$	−25.2535	−0.882428
$820$	−9.29744	−0.324681
$821$	36.1986	1.26334	0.631670	−	0.775238i	$-0.282370\pi$
$821$	36.1986	1.26334	0.631670	+	0.775238i	$0.282370\pi$
$822$	−1.10076	−0.0383934
$823$	−19.1159	−0.666340	−0.333170	−	0.942867i	$-0.608118\pi$
$823$	−19.1159	−0.666340	−0.333170	+	0.942867i	$0.608118\pi$
$824$	21.3209	0.742750
$825$	−4.59308	−0.159911
$826$	−24.1623	−0.840715
$827$	48.2902	1.67921	0.839607	−	0.543194i	$-0.182785\pi$
$827$	48.2902	1.67921	0.839607	+	0.543194i	$0.182785\pi$
$828$	−5.86186	−0.203714
$829$	30.7813	1.06908	0.534539	−	0.845144i	$-0.320485\pi$
$829$	30.7813	1.06908	0.534539	+	0.845144i	$0.320485\pi$
$830$	−5.46068	−0.189543
$831$	−25.1644	−0.872944
$832$	2.49049	0.0863423
$833$	7.21684	0.250049
$834$	−7.40319	−0.256352
$835$	−10.5698	−0.365784
$836$	−13.5172	−0.467501
$837$	−45.9230	−1.58733
$838$	6.93009	0.239396
$839$	43.4643	1.50056	0.750278	−	0.661123i	$-0.229920\pi$
$839$	43.4643	1.50056	0.750278	+	0.661123i	$0.229920\pi$
$840$	9.49745	0.327693
$841$	−23.9113	−0.824528
$842$	5.15833	0.177768
$843$	−5.16455	−0.177877
$844$	−35.1731	−1.21071
$845$	3.12395	0.107467
$846$	12.6624	0.435343
$847$	−18.2403	−0.626744
$848$	25.5079	0.875945
$849$	14.0465	0.482075
$850$	−0.599472	−0.0205617
$851$	7.41548	0.254199
$852$	−1.89352	−0.0648711
$853$	−8.52233	−0.291799	−0.145900	−	0.989299i	$-0.546608\pi$
$853$	−8.52233	−0.291799	−0.145900	+	0.989299i	$0.546608\pi$
$854$	−22.5725	−0.772415
$855$	−3.45314	−0.118095
$856$	−25.8908	−0.884930
$857$	0.0724378	0.00247443	0.00123721	−	0.999999i	$-0.499606\pi$
$857$	0.0724378	0.00247443	0.00123721	+	0.999999i	$0.499606\pi$
$858$	−11.0563	−0.377455
$859$	36.9323	1.26011	0.630057	−	0.776549i	$-0.283032\pi$
$859$	36.9323	1.26011	0.630057	+	0.776549i	$0.283032\pi$
$860$	−2.20220	−0.0750944
$861$	24.6611	0.840450
$862$	−21.8319	−0.743598
$863$	54.8315	1.86649	0.933244	−	0.359244i	$-0.116965\pi$
$863$	54.8315	1.86649	0.933244	+	0.359244i	$0.116965\pi$
$864$	−29.8878	−1.01681
$865$	13.7458	0.467372
$866$	18.9527	0.644039
$867$	−1.15414	−0.0391968
$868$	−52.7298	−1.78977
$869$	−36.9148	−1.25225
$870$	−1.56075	−0.0529142
$871$	−43.6010	−1.47736
$872$	1.67758	0.0568101
$873$	−28.7429	−0.972800
$874$	2.65851	0.0899256
$875$	−3.77052	−0.127467
$876$	17.0239	0.575183
$877$	26.1390	0.882651	0.441326	−	0.897347i	$-0.354508\pi$
$877$	26.1390	0.882651	0.441326	+	0.897347i	$0.354508\pi$
$878$	9.16460	0.309290
$879$	18.3522	0.619004
$880$	7.85162	0.264678
$881$	−3.88585	−0.130917	−0.0654587	−	0.997855i	$-0.520851\pi$
$881$	−3.88585	−0.130917	−0.0654587	+	0.997855i	$0.520851\pi$
$882$	7.21606	0.242977
$883$	53.2724	1.79276	0.896379	−	0.443289i	$-0.146188\pi$
$883$	53.2724	1.79276	0.896379	+	0.443289i	$0.146188\pi$
$884$	6.58790	0.221575
$885$	12.3375	0.414721
$886$	7.99912	0.268736
$887$	−55.8193	−1.87423	−0.937114	−	0.349023i	$-0.886514\pi$
$887$	−55.8193	−1.87423	−0.937114	+	0.349023i	$0.886514\pi$
$888$	8.71977	0.292616
$889$	−5.85939	−0.196518
$890$	−2.40079	−0.0804748
$891$	−4.83156	−0.161863
$892$	32.4957	1.08804
$893$	26.2176	0.877339
$894$	−12.2766	−0.410592
$895$	−21.3597	−0.713976
$896$	−43.2369	−1.44444
$897$	−9.92739	−0.331466
$898$	15.2132	0.507672
$899$	19.2286	0.641309
$900$	2.73650	0.0912167
$901$	12.9289	0.430723
$902$	−13.5197	−0.450156
$903$	5.84126	0.194385
$904$	−10.3954	−0.345746
$905$	−8.89696	−0.295745
$906$	7.26808	0.241466
$907$	−7.62110	−0.253054	−0.126527	−	0.991963i	$-0.540383\pi$
$907$	−7.62110	−0.253054	−0.126527	+	0.991963i	$0.540383\pi$
$908$	−3.99355	−0.132531
$909$	−11.3123	−0.375206
$910$	−9.07625	−0.300875
$911$	−5.19950	−0.172267	−0.0861336	−	0.996284i	$-0.527451\pi$
$911$	−5.19950	−0.172267	−0.0861336	+	0.996284i	$0.527451\pi$
$912$	−4.71415	−0.156101
$913$	36.2512	1.19974
$914$	−4.65465	−0.153962
$915$	11.5257	0.381029
$916$	20.1142	0.664591
$917$	−37.2665	−1.23065
$918$	−3.22965	−0.106594
$919$	28.6211	0.944122	0.472061	−	0.881566i	$-0.343510\pi$
$919$	28.6211	0.944122	0.472061	+	0.881566i	$0.343510\pi$
$920$	−4.67505	−0.154132
$921$	18.7000	0.616184
$922$	−1.45622	−0.0479580
$923$	4.01546	0.132171
$924$	−28.4130	−0.934719
$925$	−3.46178	−0.113823
$926$	17.5841	0.577850
$927$	−16.2946	−0.535186
$928$	12.5145	0.410807
$929$	−12.6733	−0.415797	−0.207899	−	0.978150i	$-0.566662\pi$
$929$	−12.6733	−0.415797	−0.207899	+	0.978150i	$0.566662\pi$
$930$	−5.89756	−0.193389
$931$	14.9409	0.489668
$932$	36.1702	1.18479
$933$	5.37240	0.175884
$934$	−12.3214	−0.403167
$935$	3.97965	0.130148
$936$	14.6173	0.477780
$937$	−44.9322	−1.46787	−0.733936	−	0.679219i	$-0.762319\pi$
$937$	−44.9322	−1.46787	−0.733936	+	0.679219i	$0.762319\pi$
$938$	24.5432	0.801364
$939$	−21.3458	−0.696593
$940$	−20.7766	−0.677658
$941$	−22.1033	−0.720546	−0.360273	−	0.932847i	$-0.617316\pi$
$941$	−22.1033	−0.720546	−0.360273	+	0.932847i	$0.617316\pi$
$942$	4.97546	0.162109
$943$	−12.1393	−0.395309
$944$	−21.0903	−0.686430
$945$	−20.3136	−0.660803
$946$	−3.20228	−0.104115
$947$	16.6666	0.541590	0.270795	−	0.962637i	$-0.412713\pi$
$947$	16.6666	0.541590	0.270795	+	0.962637i	$0.412713\pi$
$948$	−17.5641	−0.570456
$949$	−36.1013	−1.17190
$950$	−1.24108	−0.0402659
$951$	11.2643	0.365271
$952$	−8.22901	−0.266704
$953$	50.0757	1.62211	0.811056	−	0.584969i	$-0.198893\pi$
$953$	50.0757	1.62211	0.811056	+	0.584969i	$0.198893\pi$
$954$	12.9275	0.418542
$955$	−9.71312	−0.314309
$956$	−33.3472	−1.07853
$957$	10.3611	0.334928
$958$	−0.239375	−0.00773385
$959$	5.99880	0.193711
$960$	0.715829	0.0231033
$961$	41.6586	1.34383
$962$	−8.33306	−0.268669
$963$	19.7872	0.637633
$964$	−7.41172	−0.238716
$965$	−7.74764	−0.249405
$966$	5.58818	0.179797
$967$	8.14841	0.262035	0.131018	−	0.991380i	$-0.458176\pi$
$967$	8.14841	0.262035	0.131018	+	0.991380i	$0.458176\pi$
$968$	10.5579	0.339343
$969$	−2.38940	−0.0767587
$970$	−10.3304	−0.331688
$971$	16.5793	0.532055	0.266028	−	0.963965i	$-0.414289\pi$
$971$	16.5793	0.532055	0.266028	+	0.963965i	$0.414289\pi$
$972$	24.2178	0.776786
$973$	40.3452	1.29341
$974$	22.8740	0.732931
$975$	4.63442	0.148420
$976$	−19.7026	−0.630665
$977$	−14.0061	−0.448094	−0.224047	−	0.974578i	$-0.571927\pi$
$977$	−14.0061	−0.448094	−0.224047	+	0.974578i	$0.571927\pi$
$978$	10.3374	0.330555
$979$	15.9379	0.509377
$980$	−11.8402	−0.378221
$981$	−1.28210	−0.0409343
$982$	11.8598	0.378462
$983$	−0.163898	−0.00522754	−0.00261377	−	0.999997i	$-0.500832\pi$
$983$	−0.163898	−0.00522754	−0.00261377	+	0.999997i	$0.500832\pi$
$984$	−14.2744	−0.455051
$985$	−27.3664	−0.871965
$986$	1.35230	0.0430660
$987$	55.1092	1.75415
$988$	13.6388	0.433909
$989$	−2.87531	−0.0914296
$990$	3.97922	0.126468
$991$	18.0697	0.574002	0.287001	−	0.957930i	$-0.407342\pi$
$991$	18.0697	0.574002	0.287001	+	0.957930i	$0.407342\pi$
$992$	47.2881	1.50140
$993$	2.86748	0.0909967
$994$	−2.26032	−0.0716931
$995$	−11.3457	−0.359683
$996$	17.2484	0.546536
$997$	−53.8204	−1.70451	−0.852255	−	0.523127i	$-0.824765\pi$
$997$	−53.8204	−1.70451	−0.852255	+	0.523127i	$0.824765\pi$
$998$	−23.1045	−0.731360
$999$	−18.6503	−0.590069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.16	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.16	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-0.599472 q^{2} -1.15414 q^{3} -1.64063 q^{4} +1.00000 q^{5} +0.691877 q^{6} -3.77052 q^{7} +2.18246 q^{8} -1.66795 q^{9} +O(q^{10})\)	\(q-0.599472 q^{2} -1.15414 q^{3} -1.64063 q^{4} +1.00000 q^{5} +0.691877 q^{6} -3.77052 q^{7} +2.18246 q^{8} -1.66795 q^{9} -0.599472 q^{10} +3.97965 q^{11} +1.89352 q^{12} -4.01546 q^{13} +2.26032 q^{14} -1.15414 q^{15} +1.97294 q^{16} +1.00000 q^{17} +0.999892 q^{18} +2.07028 q^{19} -1.64063 q^{20} +4.35172 q^{21} -2.38569 q^{22} -2.14210 q^{23} -2.51887 q^{24} +1.00000 q^{25} +2.40716 q^{26} +5.38749 q^{27} +6.18604 q^{28} -2.25581 q^{29} +0.691877 q^{30} -8.52400 q^{31} -5.54764 q^{32} -4.59308 q^{33} -0.599472 q^{34} -3.77052 q^{35} +2.73650 q^{36} -3.46178 q^{37} -1.24108 q^{38} +4.63442 q^{39} +2.18246 q^{40} +5.66699 q^{41} -2.60874 q^{42} +1.34229 q^{43} -6.52914 q^{44} -1.66795 q^{45} +1.28413 q^{46} +12.6638 q^{47} -2.27706 q^{48} +7.21684 q^{49} -0.599472 q^{50} -1.15414 q^{51} +6.58790 q^{52} +12.9289 q^{53} -3.22965 q^{54} +3.97965 q^{55} -8.22901 q^{56} -2.38940 q^{57} +1.35230 q^{58} -10.6898 q^{59} +1.89352 q^{60} -9.98641 q^{61} +5.10990 q^{62} +6.28906 q^{63} -0.620226 q^{64} -4.01546 q^{65} +2.75343 q^{66} +10.8583 q^{67} -1.64063 q^{68} +2.47229 q^{69} +2.26032 q^{70} -1.00000 q^{71} -3.64024 q^{72} +8.99056 q^{73} +2.07524 q^{74} -1.15414 q^{75} -3.39658 q^{76} -15.0054 q^{77} -2.77821 q^{78} -9.27589 q^{79} +1.97294 q^{80} -1.21407 q^{81} -3.39720 q^{82} +9.10914 q^{83} -7.13958 q^{84} +1.00000 q^{85} -0.804664 q^{86} +2.60353 q^{87} +8.68542 q^{88} +4.00484 q^{89} +0.999892 q^{90} +15.1404 q^{91} +3.51440 q^{92} +9.83792 q^{93} -7.59158 q^{94} +2.07028 q^{95} +6.40277 q^{96} +17.2324 q^{97} -4.32630 q^{98} -6.63787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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