LMFDB - Embedded newform 4034.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.65119 q^{3} +1.00000 q^{4} -2.90851 q^{5} -1.65119 q^{6} +0.175106 q^{7} +1.00000 q^{8} -0.273565 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.65119 q^{3} +1.00000 q^{4} -2.90851 q^{5} -1.65119 q^{6} +0.175106 q^{7} +1.00000 q^{8} -0.273565 q^{9} -2.90851 q^{10} +4.59132 q^{11} -1.65119 q^{12} +2.27470 q^{13} +0.175106 q^{14} +4.80250 q^{15} +1.00000 q^{16} -7.35465 q^{17} -0.273565 q^{18} -1.09879 q^{19} -2.90851 q^{20} -0.289133 q^{21} +4.59132 q^{22} -1.49797 q^{23} -1.65119 q^{24} +3.45941 q^{25} +2.27470 q^{26} +5.40528 q^{27} +0.175106 q^{28} +8.48547 q^{29} +4.80250 q^{30} -5.03714 q^{31} +1.00000 q^{32} -7.58115 q^{33} -7.35465 q^{34} -0.509296 q^{35} -0.273565 q^{36} +6.78262 q^{37} -1.09879 q^{38} -3.75597 q^{39} -2.90851 q^{40} +8.03850 q^{41} -0.289133 q^{42} -4.20919 q^{43} +4.59132 q^{44} +0.795666 q^{45} -1.49797 q^{46} +4.34091 q^{47} -1.65119 q^{48} -6.96934 q^{49} +3.45941 q^{50} +12.1439 q^{51} +2.27470 q^{52} -6.51756 q^{53} +5.40528 q^{54} -13.3539 q^{55} +0.175106 q^{56} +1.81431 q^{57} +8.48547 q^{58} -1.11592 q^{59} +4.80250 q^{60} -5.92414 q^{61} -5.03714 q^{62} -0.0479029 q^{63} +1.00000 q^{64} -6.61599 q^{65} -7.58115 q^{66} -8.49014 q^{67} -7.35465 q^{68} +2.47344 q^{69} -0.509296 q^{70} -12.0430 q^{71} -0.273565 q^{72} +16.0608 q^{73} +6.78262 q^{74} -5.71215 q^{75} -1.09879 q^{76} +0.803967 q^{77} -3.75597 q^{78} -1.02703 q^{79} -2.90851 q^{80} -8.10447 q^{81} +8.03850 q^{82} +12.4052 q^{83} -0.289133 q^{84} +21.3910 q^{85} -4.20919 q^{86} -14.0111 q^{87} +4.59132 q^{88} -16.7546 q^{89} +0.795666 q^{90} +0.398314 q^{91} -1.49797 q^{92} +8.31729 q^{93} +4.34091 q^{94} +3.19583 q^{95} -1.65119 q^{96} -4.23016 q^{97} -6.96934 q^{98} -1.25603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.65119	−0.953316	−0.476658	−	0.879089i	$-0.658152\pi$
$3$	−1.65119	−0.953316	−0.476658	+	0.879089i	$0.658152\pi$
$4$	1.00000	0.500000
$5$	−2.90851	−1.30072	−0.650362	−	0.759625i	$-0.725383\pi$
$5$	−2.90851	−1.30072	−0.650362	+	0.759625i	$0.725383\pi$
$6$	−1.65119	−0.674096
$7$	0.175106	0.0661838	0.0330919	−	0.999452i	$-0.489465\pi$
$7$	0.175106	0.0661838	0.0330919	+	0.999452i	$0.489465\pi$
$8$	1.00000	0.353553
$9$	−0.273565	−0.0911884
$10$	−2.90851	−0.919750
$11$	4.59132	1.38434	0.692168	−	0.721736i	$-0.256656\pi$
$11$	4.59132	1.38434	0.692168	+	0.721736i	$0.256656\pi$
$12$	−1.65119	−0.476658
$13$	2.27470	0.630890	0.315445	−	0.948944i	$-0.397846\pi$
$13$	2.27470	0.630890	0.315445	+	0.948944i	$0.397846\pi$
$14$	0.175106	0.0467990
$15$	4.80250	1.24000
$16$	1.00000	0.250000
$17$	−7.35465	−1.78376	−0.891882	−	0.452267i	$-0.850615\pi$
$17$	−7.35465	−1.78376	−0.891882	+	0.452267i	$0.850615\pi$
$18$	−0.273565	−0.0644799
$19$	−1.09879	−0.252079	−0.126040	−	0.992025i	$-0.540227\pi$
$19$	−1.09879	−0.252079	−0.126040	+	0.992025i	$0.540227\pi$
$20$	−2.90851	−0.650362
$21$	−0.289133	−0.0630941
$22$	4.59132	0.978873
$23$	−1.49797	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$23$	−1.49797	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$24$	−1.65119	−0.337048
$25$	3.45941	0.691882
$26$	2.27470	0.446106
$27$	5.40528	1.04025
$28$	0.175106	0.0330919
$29$	8.48547	1.57571	0.787856	−	0.615859i	$-0.211191\pi$
$29$	8.48547	1.57571	0.787856	+	0.615859i	$0.211191\pi$
$30$	4.80250	0.876813
$31$	−5.03714	−0.904697	−0.452349	−	0.891841i	$-0.649414\pi$
$31$	−5.03714	−0.904697	−0.452349	+	0.891841i	$0.649414\pi$
$32$	1.00000	0.176777
$33$	−7.58115	−1.31971
$34$	−7.35465	−1.26131
$35$	−0.509296	−0.0860868
$36$	−0.273565	−0.0455942
$37$	6.78262	1.11506	0.557528	−	0.830158i	$-0.311750\pi$
$37$	6.78262	1.11506	0.557528	+	0.830158i	$0.311750\pi$
$38$	−1.09879	−0.178247
$39$	−3.75597	−0.601437
$40$	−2.90851	−0.459875
$41$	8.03850	1.25540	0.627701	−	0.778454i	$-0.283996\pi$
$41$	8.03850	1.25540	0.627701	+	0.778454i	$0.283996\pi$
$42$	−0.289133	−0.0446142
$43$	−4.20919	−0.641895	−0.320947	−	0.947097i	$-0.604001\pi$
$43$	−4.20919	−0.641895	−0.320947	+	0.947097i	$0.604001\pi$
$44$	4.59132	0.692168
$45$	0.795666	0.118611
$46$	−1.49797	−0.220864
$47$	4.34091	0.633187	0.316593	−	0.948561i	$-0.397461\pi$
$47$	4.34091	0.633187	0.316593	+	0.948561i	$0.397461\pi$
$48$	−1.65119	−0.238329
$49$	−6.96934	−0.995620
$50$	3.45941	0.489234
$51$	12.1439	1.70049
$52$	2.27470	0.315445
$53$	−6.51756	−0.895255	−0.447628	−	0.894220i	$-0.647731\pi$
$53$	−6.51756	−0.895255	−0.447628	+	0.894220i	$0.647731\pi$
$54$	5.40528	0.735566
$55$	−13.3539	−1.80064
$56$	0.175106	0.0233995
$57$	1.81431	0.240311
$58$	8.48547	1.11420
$59$	−1.11592	−0.145280	−0.0726402	−	0.997358i	$-0.523142\pi$
$59$	−1.11592	−0.145280	−0.0726402	+	0.997358i	$0.523142\pi$
$60$	4.80250	0.620000
$61$	−5.92414	−0.758508	−0.379254	−	0.925293i	$-0.623819\pi$
$61$	−5.92414	−0.758508	−0.379254	+	0.925293i	$0.623819\pi$
$62$	−5.03714	−0.639718
$63$	−0.0479029	−0.00603519
$64$	1.00000	0.125000
$65$	−6.61599	−0.820613
$66$	−7.58115	−0.933176
$67$	−8.49014	−1.03724	−0.518618	−	0.855006i	$-0.673553\pi$
$67$	−8.49014	−1.03724	−0.518618	+	0.855006i	$0.673553\pi$
$68$	−7.35465	−0.891882
$69$	2.47344	0.297767
$70$	−0.509296	−0.0608726
$71$	−12.0430	−1.42924	−0.714620	−	0.699513i	$-0.753400\pi$
$71$	−12.0430	−1.42924	−0.714620	+	0.699513i	$0.753400\pi$
$72$	−0.273565	−0.0322400
$73$	16.0608	1.87978	0.939889	−	0.341479i	$-0.110928\pi$
$73$	16.0608	1.87978	0.939889	+	0.341479i	$0.110928\pi$
$74$	6.78262	0.788464
$75$	−5.71215	−0.659582
$76$	−1.09879	−0.126040
$77$	0.803967	0.0916206
$78$	−3.75597	−0.425280
$79$	−1.02703	−0.115550	−0.0577752	−	0.998330i	$-0.518401\pi$
$79$	−1.02703	−0.115550	−0.0577752	+	0.998330i	$0.518401\pi$
$80$	−2.90851	−0.325181
$81$	−8.10447	−0.900496
$82$	8.03850	0.887704
$83$	12.4052	1.36165	0.680825	−	0.732446i	$-0.261622\pi$
$83$	12.4052	1.36165	0.680825	+	0.732446i	$0.261622\pi$
$84$	−0.289133	−0.0315470
$85$	21.3910	2.32018
$86$	−4.20919	−0.453888
$87$	−14.0111	−1.50215
$88$	4.59132	0.489437
$89$	−16.7546	−1.77599	−0.887993	−	0.459857i	$-0.847901\pi$
$89$	−16.7546	−1.77599	−0.887993	+	0.459857i	$0.847901\pi$
$90$	0.795666	0.0838706
$91$	0.398314	0.0417547
$92$	−1.49797	−0.156174
$93$	8.31729	0.862463
$94$	4.34091	0.447731
$95$	3.19583	0.327885
$96$	−1.65119	−0.168524
$97$	−4.23016	−0.429508	−0.214754	−	0.976668i	$-0.568895\pi$
$97$	−4.23016	−0.429508	−0.214754	+	0.976668i	$0.568895\pi$
$98$	−6.96934	−0.704009
$99$	−1.25603	−0.126235
$100$	3.45941	0.345941
$101$	−11.7156	−1.16575	−0.582875	−	0.812562i	$-0.698072\pi$
$101$	−11.7156	−1.16575	−0.582875	+	0.812562i	$0.698072\pi$
$102$	12.1439	1.20243
$103$	−12.5292	−1.23454	−0.617270	−	0.786751i	$-0.711762\pi$
$103$	−12.5292	−1.23454	−0.617270	+	0.786751i	$0.711762\pi$
$104$	2.27470	0.223053
$105$	0.840946	0.0820679
$106$	−6.51756	−0.633041
$107$	5.95047	0.575253	0.287627	−	0.957743i	$-0.407134\pi$
$107$	5.95047	0.575253	0.287627	+	0.957743i	$0.407134\pi$
$108$	5.40528	0.520124
$109$	7.23191	0.692692	0.346346	−	0.938107i	$-0.387422\pi$
$109$	7.23191	0.692692	0.346346	+	0.938107i	$0.387422\pi$
$110$	−13.3539	−1.27324
$111$	−11.1994	−1.06300
$112$	0.175106	0.0165459
$113$	−12.8456	−1.20841	−0.604206	−	0.796828i	$-0.706510\pi$
$113$	−12.8456	−1.20841	−0.604206	+	0.796828i	$0.706510\pi$
$114$	1.81431	0.169926
$115$	4.35686	0.406279
$116$	8.48547	0.787856
$117$	−0.622280	−0.0575298
$118$	−1.11592	−0.102729
$119$	−1.28784	−0.118056
$120$	4.80250	0.438406
$121$	10.0802	0.916386
$122$	−5.92414	−0.536346
$123$	−13.2731	−1.19680
$124$	−5.03714	−0.452349
$125$	4.48082	0.400777
$126$	−0.0479029	−0.00426753
$127$	−5.15091	−0.457069	−0.228535	−	0.973536i	$-0.573393\pi$
$127$	−5.15091	−0.457069	−0.228535	+	0.973536i	$0.573393\pi$
$128$	1.00000	0.0883883
$129$	6.95017	0.611929
$130$	−6.61599	−0.580261
$131$	−13.8741	−1.21219	−0.606094	−	0.795393i	$-0.707265\pi$
$131$	−13.8741	−1.21219	−0.606094	+	0.795393i	$0.707265\pi$
$132$	−7.58115	−0.659855
$133$	−0.192404	−0.0166836
$134$	−8.49014	−0.733436
$135$	−15.7213	−1.35307
$136$	−7.35465	−0.630656
$137$	−0.197355	−0.0168612	−0.00843060	−	0.999964i	$-0.502684\pi$
$137$	−0.197355	−0.0168612	−0.00843060	+	0.999964i	$0.502684\pi$
$138$	2.47344	0.210553
$139$	−4.35438	−0.369334	−0.184667	−	0.982801i	$-0.559121\pi$
$139$	−4.35438	−0.369334	−0.184667	+	0.982801i	$0.559121\pi$
$140$	−0.509296	−0.0430434
$141$	−7.16767	−0.603627
$142$	−12.0430	−1.01062
$143$	10.4439	0.873363
$144$	−0.273565	−0.0227971
$145$	−24.6800	−2.04957
$146$	16.0608	1.32920
$147$	11.5077	0.949140
$148$	6.78262	0.557528
$149$	9.26838	0.759296	0.379648	−	0.925131i	$-0.376045\pi$
$149$	9.26838	0.759296	0.379648	+	0.925131i	$0.376045\pi$
$150$	−5.71215	−0.466395
$151$	−12.2400	−0.996077	−0.498038	−	0.867155i	$-0.665946\pi$
$151$	−12.2400	−0.996077	−0.498038	+	0.867155i	$0.665946\pi$
$152$	−1.09879	−0.0891235
$153$	2.01198	0.162659
$154$	0.803967	0.0647855
$155$	14.6506	1.17676
$156$	−3.75597	−0.300719
$157$	7.75938	0.619266	0.309633	−	0.950856i	$-0.399794\pi$
$157$	7.75938	0.619266	0.309633	+	0.950856i	$0.399794\pi$
$158$	−1.02703	−0.0817065
$159$	10.7617	0.853461
$160$	−2.90851	−0.229938
$161$	−0.262303	−0.0206724
$162$	−8.10447	−0.636747
$163$	−19.5603	−1.53208	−0.766042	−	0.642790i	$-0.777777\pi$
$163$	−19.5603	−1.53208	−0.766042	+	0.642790i	$0.777777\pi$
$164$	8.03850	0.627701
$165$	22.0498	1.71658
$166$	12.4052	0.962831
$167$	−16.6338	−1.28716	−0.643581	−	0.765378i	$-0.722552\pi$
$167$	−16.6338	−1.28716	−0.643581	+	0.765378i	$0.722552\pi$
$168$	−0.289133	−0.0223071
$169$	−7.82572	−0.601978
$170$	21.3910	1.64062
$171$	0.300590	0.0229867
$172$	−4.20919	−0.320947
$173$	−23.3103	−1.77225	−0.886126	−	0.463444i	$-0.846613\pi$
$173$	−23.3103	−1.77225	−0.886126	+	0.463444i	$0.846613\pi$
$174$	−14.0111	−1.06218
$175$	0.605762	0.0457913
$176$	4.59132	0.346084
$177$	1.84260	0.138498
$178$	−16.7546	−1.25581
$179$	19.2075	1.43564	0.717819	−	0.696230i	$-0.245141\pi$
$179$	19.2075	1.43564	0.717819	+	0.696230i	$0.245141\pi$
$180$	0.795666	0.0593055
$181$	−24.0323	−1.78631	−0.893154	−	0.449750i	$-0.851513\pi$
$181$	−24.0323	−1.78631	−0.893154	+	0.449750i	$0.851513\pi$
$182$	0.398314	0.0295250
$183$	9.78189	0.723098
$184$	−1.49797	−0.110432
$185$	−19.7273	−1.45038
$186$	8.31729	0.609853
$187$	−33.7676	−2.46933
$188$	4.34091	0.316593
$189$	0.946497	0.0688475
$190$	3.19583	0.231850
$191$	−0.318048	−0.0230131	−0.0115066	−	0.999934i	$-0.503663\pi$
$191$	−0.318048	−0.0230131	−0.0115066	+	0.999934i	$0.503663\pi$
$192$	−1.65119	−0.119165
$193$	−14.1977	−1.02197	−0.510985	−	0.859590i	$-0.670719\pi$
$193$	−14.1977	−1.02197	−0.510985	+	0.859590i	$0.670719\pi$
$194$	−4.23016	−0.303708
$195$	10.9243	0.782303
$196$	−6.96934	−0.497810
$197$	8.88794	0.633239	0.316620	−	0.948553i	$-0.397452\pi$
$197$	8.88794	0.633239	0.316620	+	0.948553i	$0.397452\pi$
$198$	−1.25603	−0.0892619
$199$	1.91928	0.136054	0.0680271	−	0.997683i	$-0.478330\pi$
$199$	1.91928	0.136054	0.0680271	+	0.997683i	$0.478330\pi$
$200$	3.45941	0.244617
$201$	14.0189	0.988813
$202$	−11.7156	−0.824310
$203$	1.48586	0.104287
$204$	12.1439	0.850246
$205$	−23.3800	−1.63293
$206$	−12.5292	−0.872952
$207$	0.409793	0.0284826
$208$	2.27470	0.157722
$209$	−5.04489	−0.348962
$210$	0.840946	0.0580308
$211$	−3.45063	−0.237551	−0.118776	−	0.992921i	$-0.537897\pi$
$211$	−3.45063	−0.237551	−0.118776	+	0.992921i	$0.537897\pi$
$212$	−6.51756	−0.447628
$213$	19.8853	1.36252
$214$	5.95047	0.406766
$215$	12.2424	0.834928
$216$	5.40528	0.367783
$217$	−0.882033	−0.0598763
$218$	7.23191	0.489807
$219$	−26.5195	−1.79202
$220$	−13.3539	−0.900319
$221$	−16.7297	−1.12536
$222$	−11.1994	−0.751655
$223$	−5.68461	−0.380669	−0.190335	−	0.981719i	$-0.560957\pi$
$223$	−5.68461	−0.380669	−0.190335	+	0.981719i	$0.560957\pi$
$224$	0.175106	0.0116997
$225$	−0.946374	−0.0630916
$226$	−12.8456	−0.854477
$227$	−19.1381	−1.27024	−0.635120	−	0.772414i	$-0.719049\pi$
$227$	−19.1381	−1.27024	−0.635120	+	0.772414i	$0.719049\pi$
$228$	1.81431	0.120156
$229$	−29.0736	−1.92124	−0.960620	−	0.277865i	$-0.910373\pi$
$229$	−29.0736	−1.92124	−0.960620	+	0.277865i	$0.910373\pi$
$230$	4.35686	0.287283
$231$	−1.32750	−0.0873434
$232$	8.48547	0.557098
$233$	13.9023	0.910773	0.455387	−	0.890294i	$-0.349501\pi$
$233$	13.9023	0.910773	0.455387	+	0.890294i	$0.349501\pi$
$234$	−0.622280	−0.0406797
$235$	−12.6256	−0.823601
$236$	−1.11592	−0.0726402
$237$	1.69583	0.110156
$238$	−1.28784	−0.0834784
$239$	11.5025	0.744035	0.372018	−	0.928226i	$-0.378666\pi$
$239$	11.5025	0.744035	0.372018	+	0.928226i	$0.378666\pi$
$240$	4.80250	0.310000
$241$	12.3351	0.794571	0.397285	−	0.917695i	$-0.369952\pi$
$241$	12.3351	0.794571	0.397285	+	0.917695i	$0.369952\pi$
$242$	10.0802	0.647983
$243$	−2.83382	−0.181790
$244$	−5.92414	−0.379254
$245$	20.2704	1.29503
$246$	−13.2731	−0.846262
$247$	−2.49942	−0.159034
$248$	−5.03714	−0.319859
$249$	−20.4834	−1.29808
$250$	4.48082	0.283392
$251$	−22.2860	−1.40668	−0.703341	−	0.710852i	$-0.748309\pi$
$251$	−22.2860	−1.40668	−0.703341	+	0.710852i	$0.748309\pi$
$252$	−0.0479029	−0.00301760
$253$	−6.87766	−0.432395
$254$	−5.15091	−0.323197
$255$	−35.3207	−2.21187
$256$	1.00000	0.0625000
$257$	14.5519	0.907723	0.453861	−	0.891072i	$-0.350046\pi$
$257$	14.5519	0.907723	0.453861	+	0.891072i	$0.350046\pi$
$258$	6.95017	0.432699
$259$	1.18768	0.0737986
$260$	−6.61599	−0.410306
$261$	−2.32133	−0.143687
$262$	−13.8741	−0.857147
$263$	29.7950	1.83724	0.918619	−	0.395144i	$-0.129305\pi$
$263$	29.7950	1.83724	0.918619	+	0.395144i	$0.129305\pi$
$264$	−7.58115	−0.466588
$265$	18.9564	1.16448
$266$	−0.192404	−0.0117971
$267$	27.6651	1.69308
$268$	−8.49014	−0.518618
$269$	−28.3611	−1.72921	−0.864604	−	0.502453i	$-0.832431\pi$
$269$	−28.3611	−1.72921	−0.864604	+	0.502453i	$0.832431\pi$
$270$	−15.7213	−0.956768
$271$	−25.2576	−1.53429	−0.767145	−	0.641473i	$-0.778323\pi$
$271$	−25.2576	−1.53429	−0.767145	+	0.641473i	$0.778323\pi$
$272$	−7.35465	−0.445941
$273$	−0.657693	−0.0398054
$274$	−0.197355	−0.0119227
$275$	15.8833	0.957796
$276$	2.47344	0.148883
$277$	29.4930	1.77206	0.886030	−	0.463627i	$-0.153452\pi$
$277$	29.4930	1.77206	0.886030	+	0.463627i	$0.153452\pi$
$278$	−4.35438	−0.261158
$279$	1.37799	0.0824979
$280$	−0.509296	−0.0304363
$281$	−8.81833	−0.526057	−0.263029	−	0.964788i	$-0.584721\pi$
$281$	−8.81833	−0.526057	−0.263029	+	0.964788i	$0.584721\pi$
$282$	−7.16767	−0.426829
$283$	12.1847	0.724303	0.362151	−	0.932119i	$-0.382042\pi$
$283$	12.1847	0.724303	0.362151	+	0.932119i	$0.382042\pi$
$284$	−12.0430	−0.714620
$285$	−5.27693	−0.312578
$286$	10.4439	0.617561
$287$	1.40759	0.0830873
$288$	−0.273565	−0.0161200
$289$	37.0909	2.18182
$290$	−24.6800	−1.44926
$291$	6.98481	0.409457
$292$	16.0608	0.939889
$293$	9.53730	0.557175	0.278587	−	0.960411i	$-0.410134\pi$
$293$	9.53730	0.557175	0.278587	+	0.960411i	$0.410134\pi$
$294$	11.5077	0.671144
$295$	3.24566	0.188970
$296$	6.78262	0.394232
$297$	24.8174	1.44005
$298$	9.26838	0.536903
$299$	−3.40744	−0.197057
$300$	−5.71215	−0.329791
$301$	−0.737053	−0.0424830
$302$	−12.2400	−0.704333
$303$	19.3448	1.11133
$304$	−1.09879	−0.0630198
$305$	17.2304	0.986609
$306$	2.01198	0.115017
$307$	−14.6240	−0.834637	−0.417318	−	0.908760i	$-0.637030\pi$
$307$	−14.6240	−0.834637	−0.417318	+	0.908760i	$0.637030\pi$
$308$	0.803967	0.0458103
$309$	20.6882	1.17691
$310$	14.6506	0.832096
$311$	16.6823	0.945966	0.472983	−	0.881071i	$-0.343177\pi$
$311$	16.6823	0.945966	0.472983	+	0.881071i	$0.343177\pi$
$312$	−3.75597	−0.212640
$313$	13.6484	0.771454	0.385727	−	0.922613i	$-0.373951\pi$
$313$	13.6484	0.771454	0.385727	+	0.922613i	$0.373951\pi$
$314$	7.75938	0.437887
$315$	0.139326	0.00785012
$316$	−1.02703	−0.0577752
$317$	11.4124	0.640985	0.320493	−	0.947251i	$-0.396152\pi$
$317$	11.4124	0.640985	0.320493	+	0.947251i	$0.396152\pi$
$318$	10.7617	0.603488
$319$	38.9595	2.18131
$320$	−2.90851	−0.162590
$321$	−9.82536	−0.548398
$322$	−0.262303	−0.0146176
$323$	8.08120	0.449650
$324$	−8.10447	−0.450248
$325$	7.86913	0.436501
$326$	−19.5603	−1.08335
$327$	−11.9413	−0.660354
$328$	8.03850	0.443852
$329$	0.760118	0.0419067
$330$	22.0498	1.21380
$331$	7.99954	0.439694	0.219847	−	0.975534i	$-0.429444\pi$
$331$	7.99954	0.439694	0.219847	+	0.975534i	$0.429444\pi$
$332$	12.4052	0.680825
$333$	−1.85549	−0.101680
$334$	−16.6338	−0.910161
$335$	24.6936	1.34916
$336$	−0.289133	−0.0157735
$337$	−21.2665	−1.15846	−0.579231	−	0.815164i	$-0.696647\pi$
$337$	−21.2665	−1.15846	−0.579231	+	0.815164i	$0.696647\pi$
$338$	−7.82572	−0.425663
$339$	21.2106	1.15200
$340$	21.3910	1.16009
$341$	−23.1271	−1.25241
$342$	0.300590	0.0162541
$343$	−2.44611	−0.132078
$344$	−4.20919	−0.226944
$345$	−7.19400	−0.387312
$346$	−23.3103	−1.25317
$347$	26.9827	1.44851	0.724255	−	0.689532i	$-0.242184\pi$
$347$	26.9827	1.44851	0.724255	+	0.689532i	$0.242184\pi$
$348$	−14.0111	−0.751076
$349$	−8.56707	−0.458585	−0.229292	−	0.973358i	$-0.573641\pi$
$349$	−8.56707	−0.458585	−0.229292	+	0.973358i	$0.573641\pi$
$350$	0.605762	0.0323794
$351$	12.2954	0.656281
$352$	4.59132	0.244718
$353$	34.2908	1.82512	0.912558	−	0.408947i	$-0.134104\pi$
$353$	34.2908	1.82512	0.912558	+	0.408947i	$0.134104\pi$
$354$	1.84260	0.0979330
$355$	35.0271	1.85905
$356$	−16.7546	−0.887993
$357$	2.12647	0.112545
$358$	19.2075	1.01515
$359$	−26.9778	−1.42383	−0.711917	−	0.702263i	$-0.752173\pi$
$359$	−26.9778	−1.42383	−0.711917	+	0.702263i	$0.752173\pi$
$360$	0.795666	0.0419353
$361$	−17.7927	−0.936456
$362$	−24.0323	−1.26311
$363$	−16.6444	−0.873605
$364$	0.398314	0.0208773
$365$	−46.7130	−2.44507
$366$	9.78189	0.511307
$367$	14.0553	0.733679	0.366839	−	0.930284i	$-0.380440\pi$
$367$	14.0553	0.733679	0.366839	+	0.930284i	$0.380440\pi$
$368$	−1.49797	−0.0780871
$369$	−2.19905	−0.114478
$370$	−19.7273	−1.02557
$371$	−1.14126	−0.0592514
$372$	8.31729	0.431231
$373$	−18.3808	−0.951720	−0.475860	−	0.879521i	$-0.657863\pi$
$373$	−18.3808	−0.951720	−0.475860	+	0.879521i	$0.657863\pi$
$374$	−33.7676	−1.74608
$375$	−7.39870	−0.382067
$376$	4.34091	0.223865
$377$	19.3019	0.994100
$378$	0.946497	0.0486825
$379$	21.6927	1.11428	0.557140	−	0.830418i	$-0.311899\pi$
$379$	21.6927	1.11428	0.557140	+	0.830418i	$0.311899\pi$
$380$	3.19583	0.163943
$381$	8.50514	0.435732
$382$	−0.318048	−0.0162727
$383$	33.1914	1.69600	0.848000	−	0.529995i	$-0.177806\pi$
$383$	33.1914	1.69600	0.848000	+	0.529995i	$0.177806\pi$
$384$	−1.65119	−0.0842620
$385$	−2.33834	−0.119173
$386$	−14.1977	−0.722642
$387$	1.15149	0.0585334
$388$	−4.23016	−0.214754
$389$	−3.36586	−0.170656	−0.0853280	−	0.996353i	$-0.527194\pi$
$389$	−3.36586	−0.170656	−0.0853280	+	0.996353i	$0.527194\pi$
$390$	10.9243	0.553172
$391$	11.0170	0.557156
$392$	−6.96934	−0.352005
$393$	22.9089	1.15560
$394$	8.88794	0.447768
$395$	2.98714	0.150299
$396$	−1.25603	−0.0631177
$397$	−17.4776	−0.877177	−0.438589	−	0.898688i	$-0.644521\pi$
$397$	−17.4776	−0.877177	−0.438589	+	0.898688i	$0.644521\pi$
$398$	1.91928	0.0962049
$399$	0.317696	0.0159047
$400$	3.45941	0.172970
$401$	−18.1388	−0.905809	−0.452905	−	0.891559i	$-0.649612\pi$
$401$	−18.1388	−0.905809	−0.452905	+	0.891559i	$0.649612\pi$
$402$	14.0189	0.699197
$403$	−11.4580	−0.570764
$404$	−11.7156	−0.582875
$405$	23.5719	1.17130
$406$	1.48586	0.0737418
$407$	31.1412	1.54361
$408$	12.1439	0.601215
$409$	27.8627	1.37772	0.688860	−	0.724894i	$-0.258111\pi$
$409$	27.8627	1.37772	0.688860	+	0.724894i	$0.258111\pi$
$410$	−23.3800	−1.15466
$411$	0.325872	0.0160741
$412$	−12.5292	−0.617270
$413$	−0.195404	−0.00961521
$414$	0.409793	0.0201402
$415$	−36.0806	−1.77113
$416$	2.27470	0.111527
$417$	7.18992	0.352092
$418$	−5.04489	−0.246754
$419$	15.8362	0.773650	0.386825	−	0.922153i	$-0.373572\pi$
$419$	15.8362	0.773650	0.386825	+	0.922153i	$0.373572\pi$
$420$	0.840946	0.0410340
$421$	10.2605	0.500065	0.250032	−	0.968237i	$-0.419559\pi$
$421$	10.2605	0.500065	0.250032	+	0.968237i	$0.419559\pi$
$422$	−3.45063	−0.167974
$423$	−1.18752	−0.0577393
$424$	−6.51756	−0.316521
$425$	−25.4427	−1.23415
$426$	19.8853	0.963445
$427$	−1.03735	−0.0502009
$428$	5.95047	0.287627
$429$	−17.2449	−0.832591
$430$	12.2424	0.590383
$431$	21.5303	1.03708	0.518538	−	0.855055i	$-0.326476\pi$
$431$	21.5303	1.03708	0.518538	+	0.855055i	$0.326476\pi$
$432$	5.40528	0.260062
$433$	−31.7931	−1.52788	−0.763940	−	0.645288i	$-0.776737\pi$
$433$	−31.7931	−1.52788	−0.763940	+	0.645288i	$0.776737\pi$
$434$	−0.882033	−0.0423389
$435$	40.7515	1.95388
$436$	7.23191	0.346346
$437$	1.64595	0.0787365
$438$	−26.5195	−1.26715
$439$	−32.7947	−1.56521	−0.782603	−	0.622521i	$-0.786108\pi$
$439$	−32.7947	−1.56521	−0.782603	+	0.622521i	$0.786108\pi$
$440$	−13.3539	−0.636622
$441$	1.90657	0.0907890
$442$	−16.7297	−0.795749
$443$	−12.7223	−0.604455	−0.302227	−	0.953236i	$-0.597730\pi$
$443$	−12.7223	−0.604455	−0.302227	+	0.953236i	$0.597730\pi$
$444$	−11.1994	−0.531501
$445$	48.7309	2.31007
$446$	−5.68461	−0.269174
$447$	−15.3039	−0.723849
$448$	0.175106	0.00827297
$449$	2.26696	0.106984	0.0534921	−	0.998568i	$-0.482965\pi$
$449$	2.26696	0.106984	0.0534921	+	0.998568i	$0.482965\pi$
$450$	−0.946374	−0.0446125
$451$	36.9073	1.73790
$452$	−12.8456	−0.604206
$453$	20.2106	0.949576
$454$	−19.1381	−0.898195
$455$	−1.15850	−0.0543113
$456$	1.81431	0.0849628
$457$	−19.2944	−0.902555	−0.451278	−	0.892384i	$-0.649032\pi$
$457$	−19.2944	−0.902555	−0.451278	+	0.892384i	$0.649032\pi$
$458$	−29.0736	−1.35852
$459$	−39.7540	−1.85556
$460$	4.35686	0.203139
$461$	−22.5633	−1.05088	−0.525438	−	0.850832i	$-0.676099\pi$
$461$	−22.5633	−1.05088	−0.525438	+	0.850832i	$0.676099\pi$
$462$	−1.32750	−0.0617611
$463$	34.8397	1.61914	0.809570	−	0.587024i	$-0.199700\pi$
$463$	34.8397	1.61914	0.809570	+	0.587024i	$0.199700\pi$
$464$	8.48547	0.393928
$465$	−24.1909	−1.12183
$466$	13.9023	0.644014
$467$	−11.2153	−0.518980	−0.259490	−	0.965746i	$-0.583554\pi$
$467$	−11.2153	−0.518980	−0.259490	+	0.965746i	$0.583554\pi$
$468$	−0.622280	−0.0287649
$469$	−1.48667	−0.0686482
$470$	−12.6256	−0.582374
$471$	−12.8122	−0.590356
$472$	−1.11592	−0.0513644
$473$	−19.3257	−0.888598
$474$	1.69583	0.0778921
$475$	−3.80116	−0.174409
$476$	−1.28784	−0.0590281
$477$	1.78298	0.0816369
$478$	11.5025	0.526112
$479$	−32.0865	−1.46607	−0.733035	−	0.680191i	$-0.761897\pi$
$479$	−32.0865	−1.46607	−0.733035	+	0.680191i	$0.761897\pi$
$480$	4.80250	0.219203
$481$	15.4285	0.703477
$482$	12.3351	0.561846
$483$	0.433113	0.0197073
$484$	10.0802	0.458193
$485$	12.3035	0.558671
$486$	−2.83382	−0.128545
$487$	40.0306	1.81396	0.906979	−	0.421176i	$-0.138382\pi$
$487$	40.0306	1.81396	0.906979	+	0.421176i	$0.138382\pi$
$488$	−5.92414	−0.268173
$489$	32.2979	1.46056
$490$	20.2704	0.915722
$491$	40.7883	1.84075	0.920376	−	0.391034i	$-0.127883\pi$
$491$	40.7883	1.84075	0.920376	+	0.391034i	$0.127883\pi$
$492$	−13.2731	−0.598398
$493$	−62.4077	−2.81070
$494$	−2.49942	−0.112454
$495$	3.65316	0.164197
$496$	−5.03714	−0.226174
$497$	−2.10880	−0.0945925
$498$	−20.4834	−0.917883
$499$	−13.1717	−0.589645	−0.294822	−	0.955552i	$-0.595260\pi$
$499$	−13.1717	−0.589645	−0.294822	+	0.955552i	$0.595260\pi$
$500$	4.48082	0.200388
$501$	27.4656	1.22707
$502$	−22.2860	−0.994675
$503$	−16.3348	−0.728334	−0.364167	−	0.931334i	$-0.618646\pi$
$503$	−16.3348	−0.728334	−0.364167	+	0.931334i	$0.618646\pi$
$504$	−0.0479029	−0.00213376
$505$	34.0750	1.51632
$506$	−6.87766	−0.305749
$507$	12.9218	0.573876
$508$	−5.15091	−0.228535
$509$	−14.2714	−0.632570	−0.316285	−	0.948664i	$-0.602436\pi$
$509$	−14.2714	−0.632570	−0.316285	+	0.948664i	$0.602436\pi$
$510$	−35.3207	−1.56403
$511$	2.81235	0.124411
$512$	1.00000	0.0441942
$513$	−5.93926	−0.262225
$514$	14.5519	0.641857
$515$	36.4413	1.60580
$516$	6.95017	0.305964
$517$	19.9305	0.876543
$518$	1.18768	0.0521835
$519$	38.4898	1.68952
$520$	−6.61599	−0.290130
$521$	−4.04483	−0.177207	−0.0886036	−	0.996067i	$-0.528240\pi$
$521$	−4.04483	−0.177207	−0.0886036	+	0.996067i	$0.528240\pi$
$522$	−2.32133	−0.101602
$523$	−0.379200	−0.0165813	−0.00829063	−	0.999966i	$-0.502639\pi$
$523$	−0.379200	−0.0165813	−0.00829063	+	0.999966i	$0.502639\pi$
$524$	−13.8741	−0.606094
$525$	−1.00023	−0.0436536
$526$	29.7950	1.29912
$527$	37.0464	1.61377
$528$	−7.58115	−0.329927
$529$	−20.7561	−0.902438
$530$	18.9564	0.823411
$531$	0.305277	0.0132479
$532$	−0.192404	−0.00834178
$533$	18.2852	0.792020
$534$	27.6651	1.19719
$535$	−17.3070	−0.748246
$536$	−8.49014	−0.366718
$537$	−31.7153	−1.36862
$538$	−28.3611	−1.22274
$539$	−31.9985	−1.37827
$540$	−15.7213	−0.676537
$541$	−36.2389	−1.55803	−0.779016	−	0.627005i	$-0.784281\pi$
$541$	−36.2389	−1.55803	−0.779016	+	0.627005i	$0.784281\pi$
$542$	−25.2576	−1.08491
$543$	39.6820	1.70292
$544$	−7.35465	−0.315328
$545$	−21.0341	−0.901000
$546$	−0.657693	−0.0281467
$547$	21.3992	0.914964	0.457482	−	0.889219i	$-0.348751\pi$
$547$	21.3992	0.914964	0.457482	+	0.889219i	$0.348751\pi$
$548$	−0.197355	−0.00843060
$549$	1.62064	0.0691671
$550$	15.8833	0.677264
$551$	−9.32373	−0.397204
$552$	2.47344	0.105276
$553$	−0.179840	−0.00764756
$554$	29.4930	1.25304
$555$	32.5736	1.38267
$556$	−4.35438	−0.184667
$557$	−15.6138	−0.661578	−0.330789	−	0.943705i	$-0.607315\pi$
$557$	−15.6138	−0.661578	−0.330789	+	0.943705i	$0.607315\pi$
$558$	1.37799	0.0583348
$559$	−9.57465	−0.404965
$560$	−0.509296	−0.0215217
$561$	55.7567	2.35405
$562$	−8.81833	−0.371979
$563$	13.5052	0.569178	0.284589	−	0.958650i	$-0.408143\pi$
$563$	13.5052	0.569178	0.284589	+	0.958650i	$0.408143\pi$
$564$	−7.16767	−0.301813
$565$	37.3615	1.57181
$566$	12.1847	0.512159
$567$	−1.41914	−0.0595982
$568$	−12.0430	−0.505312
$569$	41.3132	1.73194	0.865969	−	0.500098i	$-0.166703\pi$
$569$	41.3132	1.73194	0.865969	+	0.500098i	$0.166703\pi$
$570$	−5.27693	−0.221026
$571$	−9.74109	−0.407652	−0.203826	−	0.979007i	$-0.565338\pi$
$571$	−9.74109	−0.407652	−0.203826	+	0.979007i	$0.565338\pi$
$572$	10.4439	0.436681
$573$	0.525158	0.0219388
$574$	1.40759	0.0587516
$575$	−5.18209	−0.216108
$576$	−0.273565	−0.0113986
$577$	−42.2678	−1.75963	−0.879815	−	0.475315i	$-0.842334\pi$
$577$	−42.2678	−1.75963	−0.879815	+	0.475315i	$0.842334\pi$
$578$	37.0909	1.54278
$579$	23.4431	0.974261
$580$	−24.6800	−1.02478
$581$	2.17223	0.0901191
$582$	6.98481	0.289530
$583$	−29.9242	−1.23933
$584$	16.0608	0.664602
$585$	1.80991	0.0748304
$586$	9.53730	0.393982
$587$	17.7079	0.730883	0.365442	−	0.930834i	$-0.380918\pi$
$587$	17.7079	0.730883	0.365442	+	0.930834i	$0.380918\pi$
$588$	11.5077	0.474570
$589$	5.53475	0.228055
$590$	3.24566	0.133622
$591$	−14.6757	−0.603677
$592$	6.78262	0.278764
$593$	19.7357	0.810447	0.405223	−	0.914218i	$-0.367194\pi$
$593$	19.7357	0.810447	0.405223	+	0.914218i	$0.367194\pi$
$594$	24.8174	1.01827
$595$	3.74570	0.153559
$596$	9.26838	0.379648
$597$	−3.16910	−0.129703
$598$	−3.40744	−0.139341
$599$	24.1758	0.987797	0.493898	−	0.869520i	$-0.335572\pi$
$599$	24.1758	0.987797	0.493898	+	0.869520i	$0.335572\pi$
$600$	−5.71215	−0.233197
$601$	−11.4062	−0.465269	−0.232634	−	0.972564i	$-0.574735\pi$
$601$	−11.4062	−0.465269	−0.232634	+	0.972564i	$0.574735\pi$
$602$	−0.737053	−0.0300400
$603$	2.32261	0.0945839
$604$	−12.2400	−0.498038
$605$	−29.3184	−1.19196
$606$	19.3448	0.785828
$607$	14.9158	0.605412	0.302706	−	0.953084i	$-0.402110\pi$
$607$	14.9158	0.605412	0.302706	+	0.953084i	$0.402110\pi$
$608$	−1.09879	−0.0445617
$609$	−2.45343	−0.0994181
$610$	17.2304	0.697638
$611$	9.87428	0.399471
$612$	2.01198	0.0813293
$613$	−6.90356	−0.278832	−0.139416	−	0.990234i	$-0.544523\pi$
$613$	−6.90356	−0.278832	−0.139416	+	0.990234i	$0.544523\pi$
$614$	−14.6240	−0.590177
$615$	38.6049	1.55670
$616$	0.803967	0.0323928
$617$	7.08045	0.285048	0.142524	−	0.989791i	$-0.454478\pi$
$617$	7.08045	0.285048	0.142524	+	0.989791i	$0.454478\pi$
$618$	20.6882	0.832199
$619$	5.05455	0.203159	0.101580	−	0.994827i	$-0.467610\pi$
$619$	5.05455	0.203159	0.101580	+	0.994827i	$0.467610\pi$
$620$	14.6506	0.588381
$621$	−8.09695	−0.324920
$622$	16.6823	0.668899
$623$	−2.93383	−0.117541
$624$	−3.75597	−0.150359
$625$	−30.3295	−1.21318
$626$	13.6484	0.545500
$627$	8.33008	0.332671
$628$	7.75938	0.309633
$629$	−49.8838	−1.98900
$630$	0.139326	0.00555087
$631$	18.2299	0.725723	0.362861	−	0.931843i	$-0.381800\pi$
$631$	18.2299	0.725723	0.362861	+	0.931843i	$0.381800\pi$
$632$	−1.02703	−0.0408532
$633$	5.69765	0.226461
$634$	11.4124	0.453245
$635$	14.9815	0.594521
$636$	10.7617	0.426731
$637$	−15.8532	−0.628126
$638$	38.9595	1.54242
$639$	3.29454	0.130330
$640$	−2.90851	−0.114969
$641$	−16.8500	−0.665537	−0.332768	−	0.943009i	$-0.607983\pi$
$641$	−16.8500	−0.665537	−0.332768	+	0.943009i	$0.607983\pi$
$642$	−9.82536	−0.387776
$643$	9.80221	0.386561	0.193281	−	0.981143i	$-0.438087\pi$
$643$	9.80221	0.386561	0.193281	+	0.981143i	$0.438087\pi$
$644$	−0.262303	−0.0103362
$645$	−20.2146	−0.795950
$646$	8.08120	0.317951
$647$	27.7593	1.09133	0.545666	−	0.838003i	$-0.316277\pi$
$647$	27.7593	1.09133	0.545666	+	0.838003i	$0.316277\pi$
$648$	−8.10447	−0.318374
$649$	−5.12355	−0.201117
$650$	7.86913	0.308653
$651$	1.45641	0.0570810
$652$	−19.5603	−0.766042
$653$	31.2171	1.22162	0.610810	−	0.791777i	$-0.290844\pi$
$653$	31.2171	1.22162	0.610810	+	0.791777i	$0.290844\pi$
$654$	−11.9413	−0.466941
$655$	40.3530	1.57672
$656$	8.03850	0.313851
$657$	−4.39369	−0.171414
$658$	0.760118	0.0296325
$659$	−38.3301	−1.49313	−0.746564	−	0.665313i	$-0.768298\pi$
$659$	−38.3301	−1.49313	−0.746564	+	0.665313i	$0.768298\pi$
$660$	22.0498	0.858289
$661$	−3.48929	−0.135718	−0.0678589	−	0.997695i	$-0.521617\pi$
$661$	−3.48929	−0.135718	−0.0678589	+	0.997695i	$0.521617\pi$
$662$	7.99954	0.310911
$663$	27.6239	1.07282
$664$	12.4052	0.481416
$665$	0.559609	0.0217007
$666$	−1.85549	−0.0718988
$667$	−12.7110	−0.492171
$668$	−16.6338	−0.643581
$669$	9.38637	0.362898
$670$	24.6936	0.953998
$671$	−27.1996	−1.05003
$672$	−0.289133	−0.0111536
$673$	−0.498360	−0.0192104	−0.00960519	−	0.999954i	$-0.503057\pi$
$673$	−0.498360	−0.0192104	−0.00960519	+	0.999954i	$0.503057\pi$
$674$	−21.2665	−0.819156
$675$	18.6991	0.719728
$676$	−7.82572	−0.300989
$677$	−21.3024	−0.818719	−0.409360	−	0.912373i	$-0.634248\pi$
$677$	−21.3024	−0.818719	−0.409360	+	0.912373i	$0.634248\pi$
$678$	21.2106	0.814586
$679$	−0.740726	−0.0284265
$680$	21.3910	0.820309
$681$	31.6007	1.21094
$682$	−23.1271	−0.885584
$683$	−46.0771	−1.76309	−0.881545	−	0.472101i	$-0.843496\pi$
$683$	−46.0771	−1.76309	−0.881545	+	0.472101i	$0.843496\pi$
$684$	0.300590	0.0114934
$685$	0.574009	0.0219318
$686$	−2.44611	−0.0933930
$687$	48.0062	1.83155
$688$	−4.20919	−0.160474
$689$	−14.8255	−0.564807
$690$	−7.19400	−0.273871
$691$	−11.4943	−0.437264	−0.218632	−	0.975807i	$-0.570159\pi$
$691$	−11.4943	−0.437264	−0.218632	+	0.975807i	$0.570159\pi$
$692$	−23.3103	−0.886126
$693$	−0.219938	−0.00835473
$694$	26.9827	1.02425
$695$	12.6647	0.480401
$696$	−14.0111	−0.531091
$697$	−59.1203	−2.23934
$698$	−8.56707	−0.324268
$699$	−22.9554	−0.868255
$700$	0.605762	0.0228957
$701$	20.9213	0.790188	0.395094	−	0.918641i	$-0.370712\pi$
$701$	20.9213	0.790188	0.395094	+	0.918641i	$0.370712\pi$
$702$	12.2954	0.464061
$703$	−7.45266	−0.281083
$704$	4.59132	0.173042
$705$	20.8472	0.785152
$706$	34.2908	1.29055
$707$	−2.05148	−0.0771538
$708$	1.84260	0.0692491
$709$	−3.52199	−0.132271	−0.0661355	−	0.997811i	$-0.521067\pi$
$709$	−3.52199	−0.132271	−0.0661355	+	0.997811i	$0.521067\pi$
$710$	35.0271	1.31454
$711$	0.280961	0.0105369
$712$	−16.7546	−0.627906
$713$	7.54549	0.282581
$714$	2.12647	0.0795813
$715$	−30.3762	−1.13600
$716$	19.2075	0.717819
$717$	−18.9928	−0.709301
$718$	−26.9778	−1.00680
$719$	24.8082	0.925191	0.462596	−	0.886569i	$-0.346918\pi$
$719$	24.8082	0.925191	0.462596	+	0.886569i	$0.346918\pi$
$720$	0.795666	0.0296527
$721$	−2.19394	−0.0817066
$722$	−17.7927	−0.662174
$723$	−20.3675	−0.757477
$724$	−24.0323	−0.893154
$725$	29.3547	1.09021
$726$	−16.6444	−0.617732
$727$	12.1533	0.450740	0.225370	−	0.974273i	$-0.427641\pi$
$727$	12.1533	0.450740	0.225370	+	0.974273i	$0.427641\pi$
$728$	0.398314	0.0147625
$729$	28.9926	1.07380
$730$	−46.7130	−1.72893
$731$	30.9571	1.14499
$732$	9.78189	0.361549
$733$	−7.20867	−0.266258	−0.133129	−	0.991099i	$-0.542503\pi$
$733$	−7.20867	−0.266258	−0.133129	+	0.991099i	$0.542503\pi$
$734$	14.0553	0.518789
$735$	−33.4703	−1.23457
$736$	−1.49797	−0.0552159
$737$	−38.9810	−1.43588
$738$	−2.19905	−0.0809483
$739$	−24.1511	−0.888412	−0.444206	−	0.895925i	$-0.646514\pi$
$739$	−24.1511	−0.888412	−0.444206	+	0.895925i	$0.646514\pi$
$740$	−19.7273	−0.725190
$741$	4.12702	0.151610
$742$	−1.14126	−0.0418971
$743$	−44.3474	−1.62695	−0.813475	−	0.581600i	$-0.802427\pi$
$743$	−44.3474	−1.62695	−0.813475	+	0.581600i	$0.802427\pi$
$744$	8.31729	0.304927
$745$	−26.9572	−0.987634
$746$	−18.3808	−0.672968
$747$	−3.39364	−0.124167
$748$	−33.7676	−1.23466
$749$	1.04196	0.0380724
$750$	−7.39870	−0.270162
$751$	10.2069	0.372455	0.186227	−	0.982507i	$-0.440374\pi$
$751$	10.2069	0.372455	0.186227	+	0.982507i	$0.440374\pi$
$752$	4.34091	0.158297
$753$	36.7985	1.34101
$754$	19.3019	0.702935
$755$	35.6001	1.29562
$756$	0.946497	0.0344238
$757$	38.2621	1.39066	0.695330	−	0.718690i	$-0.255258\pi$
$757$	38.2621	1.39066	0.695330	+	0.718690i	$0.255258\pi$
$758$	21.6927	0.787915
$759$	11.3563	0.412209
$760$	3.19583	0.115925
$761$	−33.7713	−1.22421	−0.612104	−	0.790777i	$-0.709677\pi$
$761$	−33.7713	−1.22421	−0.612104	+	0.790777i	$0.709677\pi$
$762$	8.50514	0.308109
$763$	1.26635	0.0458450
$764$	−0.318048	−0.0115066
$765$	−5.85185	−0.211574
$766$	33.1914	1.19925
$767$	−2.53839	−0.0916559
$768$	−1.65119	−0.0595823
$769$	−42.3699	−1.52790	−0.763949	−	0.645277i	$-0.776742\pi$
$769$	−42.3699	−1.52790	−0.763949	+	0.645277i	$0.776742\pi$
$770$	−2.33834	−0.0842681
$771$	−24.0280	−0.865347
$772$	−14.1977	−0.510985
$773$	−37.8467	−1.36125	−0.680625	−	0.732632i	$-0.738292\pi$
$773$	−37.8467	−1.36125	−0.680625	+	0.732632i	$0.738292\pi$
$774$	1.15149	0.0413893
$775$	−17.4255	−0.625944
$776$	−4.23016	−0.151854
$777$	−1.96108	−0.0703534
$778$	−3.36586	−0.120672
$779$	−8.83261	−0.316461
$780$	10.9243	0.391152
$781$	−55.2932	−1.97855
$782$	11.0170	0.393969
$783$	45.8664	1.63913
$784$	−6.96934	−0.248905
$785$	−22.5682	−0.805494
$786$	22.9089	0.817132
$787$	11.4231	0.407190	0.203595	−	0.979055i	$-0.434737\pi$
$787$	11.4231	0.407190	0.203595	+	0.979055i	$0.434737\pi$
$788$	8.88794	0.316620
$789$	−49.1973	−1.75147
$790$	2.98714	0.106278
$791$	−2.24934	−0.0799773
$792$	−1.25603	−0.0446309
$793$	−13.4757	−0.478535
$794$	−17.4776	−0.620258
$795$	−31.3006	−1.11012
$796$	1.91928	0.0680271
$797$	47.0530	1.66670	0.833351	−	0.552745i	$-0.186420\pi$
$797$	47.0530	1.66670	0.833351	+	0.552745i	$0.186420\pi$
$798$	0.317696	0.0112463
$799$	−31.9259	−1.12946
$800$	3.45941	0.122309
$801$	4.58348	0.161949
$802$	−18.1388	−0.640504
$803$	73.7405	2.60225
$804$	14.0189	0.494407
$805$	0.762911	0.0268891
$806$	−11.4580	−0.403591
$807$	46.8297	1.64848
$808$	−11.7156	−0.412155
$809$	−43.9116	−1.54385	−0.771925	−	0.635714i	$-0.780706\pi$
$809$	−43.9116	−1.54385	−0.771925	+	0.635714i	$0.780706\pi$
$810$	23.5719	0.828232
$811$	20.7404	0.728294	0.364147	−	0.931342i	$-0.381361\pi$
$811$	20.7404	0.728294	0.364147	+	0.931342i	$0.381361\pi$
$812$	1.48586	0.0521433
$813$	41.7052	1.46266
$814$	31.1412	1.09150
$815$	56.8914	1.99282
$816$	12.1439	0.425123
$817$	4.62500	0.161808
$818$	27.8627	0.974195
$819$	−0.108965	−0.00380754
$820$	−23.3800	−0.816466
$821$	37.3140	1.30227	0.651134	−	0.758963i	$-0.274294\pi$
$821$	37.3140	1.30227	0.651134	+	0.758963i	$0.274294\pi$
$822$	0.325872	0.0113661
$823$	−38.4446	−1.34009	−0.670047	−	0.742319i	$-0.733726\pi$
$823$	−38.4446	−1.34009	−0.670047	+	0.742319i	$0.733726\pi$
$824$	−12.5292	−0.436476
$825$	−26.2263	−0.913083
$826$	−0.195404	−0.00679898
$827$	−0.0217812	−0.000757407 0	−0.000378704	−	1.00000i	$-0.500121\pi$
$827$	−0.0217812	−0.000757407 0	−0.000378704		1.00000i	$0.500121\pi$
$828$	0.409793	0.0142413
$829$	−31.3462	−1.08870	−0.544349	−	0.838859i	$-0.683223\pi$
$829$	−31.3462	−1.08870	−0.544349	+	0.838859i	$0.683223\pi$
$830$	−36.0806	−1.25238
$831$	−48.6986	−1.68933
$832$	2.27470	0.0788612
$833$	51.2570	1.77595
$834$	7.18992	0.248966
$835$	48.3795	1.67424
$836$	−5.04489	−0.174481
$837$	−27.2272	−0.941109
$838$	15.8362	0.547053
$839$	24.7931	0.855952	0.427976	−	0.903790i	$-0.359227\pi$
$839$	24.7931	0.855952	0.427976	+	0.903790i	$0.359227\pi$
$840$	0.840946	0.0290154
$841$	43.0032	1.48287
$842$	10.2605	0.353599
$843$	14.5607	0.501499
$844$	−3.45063	−0.118776
$845$	22.7612	0.783007
$846$	−1.18752	−0.0408278
$847$	1.76511	0.0606499
$848$	−6.51756	−0.223814
$849$	−20.1192	−0.690489
$850$	−25.4427	−0.872679
$851$	−10.1602	−0.348286
$852$	19.8853	0.681258
$853$	−1.18860	−0.0406969	−0.0203485	−	0.999793i	$-0.506478\pi$
$853$	−1.18860	−0.0406969	−0.0203485	+	0.999793i	$0.506478\pi$
$854$	−1.03735	−0.0354974
$855$	−0.874268	−0.0298994
$856$	5.95047	0.203383
$857$	29.4590	1.00630	0.503150	−	0.864199i	$-0.332174\pi$
$857$	29.4590	1.00630	0.503150	+	0.864199i	$0.332174\pi$
$858$	−17.2449	−0.588731
$859$	52.0639	1.77640	0.888199	−	0.459459i	$-0.151957\pi$
$859$	52.0639	1.77640	0.888199	+	0.459459i	$0.151957\pi$
$860$	12.2424	0.417464
$861$	−2.32420	−0.0792084
$862$	21.5303	0.733323
$863$	−35.5231	−1.20922	−0.604611	−	0.796521i	$-0.706671\pi$
$863$	−35.5231	−1.20922	−0.604611	+	0.796521i	$0.706671\pi$
$864$	5.40528	0.183892
$865$	67.7983	2.30521
$866$	−31.7931	−1.08037
$867$	−61.2442	−2.07996
$868$	−0.882033	−0.0299381
$869$	−4.71545	−0.159961
$870$	40.7515	1.38160
$871$	−19.3126	−0.654381
$872$	7.23191	0.244904
$873$	1.15723	0.0391662
$874$	1.64595	0.0556751
$875$	0.784618	0.0265249
$876$	−26.5195	−0.896012
$877$	−25.3587	−0.856303	−0.428151	−	0.903707i	$-0.640835\pi$
$877$	−25.3587	−0.856303	−0.428151	+	0.903707i	$0.640835\pi$
$878$	−32.7947	−1.10677
$879$	−15.7479	−0.531164
$880$	−13.3539	−0.450160
$881$	9.02739	0.304141	0.152070	−	0.988370i	$-0.451406\pi$
$881$	9.02739	0.304141	0.152070	+	0.988370i	$0.451406\pi$
$882$	1.90657	0.0641975
$883$	−19.6812	−0.662324	−0.331162	−	0.943574i	$-0.607441\pi$
$883$	−19.6812	−0.662324	−0.331162	+	0.943574i	$0.607441\pi$
$884$	−16.7297	−0.562679
$885$	−5.35921	−0.180148
$886$	−12.7223	−0.427414
$887$	21.8662	0.734194	0.367097	−	0.930183i	$-0.380352\pi$
$887$	21.8662	0.734194	0.367097	+	0.930183i	$0.380352\pi$
$888$	−11.1994	−0.375828
$889$	−0.901955	−0.0302506
$890$	48.7309	1.63346
$891$	−37.2102	−1.24659
$892$	−5.68461	−0.190335
$893$	−4.76974	−0.159613
$894$	−15.3039	−0.511838
$895$	−55.8652	−1.86737
$896$	0.175106	0.00584987
$897$	5.62634	0.187858
$898$	2.26696	0.0756493
$899$	−42.7425	−1.42554
$900$	−0.946374	−0.0315458
$901$	47.9344	1.59692
$902$	36.9073	1.22888
$903$	1.21702	0.0404998
$904$	−12.8456	−0.427238
$905$	69.8982	2.32349
$906$	20.2106	0.671452
$907$	−10.5159	−0.349176	−0.174588	−	0.984642i	$-0.555859\pi$
$907$	−10.5159	−0.349176	−0.174588	+	0.984642i	$0.555859\pi$
$908$	−19.1381	−0.635120
$909$	3.20499	0.106303
$910$	−1.15850	−0.0384039
$911$	11.0532	0.366209	0.183104	−	0.983093i	$-0.441385\pi$
$911$	11.0532	0.366209	0.183104	+	0.983093i	$0.441385\pi$
$912$	1.81431	0.0600778
$913$	56.9563	1.88498
$914$	−19.2944	−0.638203
$915$	−28.4507	−0.940550
$916$	−29.0736	−0.960620
$917$	−2.42944	−0.0802272
$918$	−39.7540	−1.31208
$919$	42.2152	1.39255	0.696275	−	0.717775i	$-0.254839\pi$
$919$	42.2152	1.39255	0.696275	+	0.717775i	$0.254839\pi$
$920$	4.35686	0.143641
$921$	24.1471	0.795673
$922$	−22.5633	−0.743082
$923$	−27.3942	−0.901692
$924$	−1.32750	−0.0436717
$925$	23.4639	0.771487
$926$	34.8397	1.14490
$927$	3.42756	0.112576
$928$	8.48547	0.278549
$929$	19.5889	0.642689	0.321345	−	0.946962i	$-0.395865\pi$
$929$	19.5889	0.642689	0.321345	+	0.946962i	$0.395865\pi$
$930$	−24.1909	−0.793250
$931$	7.65783	0.250975
$932$	13.9023	0.455387
$933$	−27.5457	−0.901805
$934$	−11.2153	−0.366974
$935$	98.2132	3.21191
$936$	−0.622280	−0.0203399
$937$	26.0562	0.851219	0.425609	−	0.904907i	$-0.360060\pi$
$937$	26.0562	0.851219	0.425609	+	0.904907i	$0.360060\pi$
$938$	−1.48667	−0.0485416
$939$	−22.5361	−0.735439
$940$	−12.6256	−0.411800
$941$	2.39100	0.0779444	0.0389722	−	0.999240i	$-0.487592\pi$
$941$	2.39100	0.0779444	0.0389722	+	0.999240i	$0.487592\pi$
$942$	−12.8122	−0.417445
$943$	−12.0414	−0.392123
$944$	−1.11592	−0.0363201
$945$	−2.75289	−0.0895516
$946$	−19.3257	−0.628334
$947$	40.6675	1.32152	0.660758	−	0.750599i	$-0.270235\pi$
$947$	40.6675	1.32152	0.660758	+	0.750599i	$0.270235\pi$
$948$	1.69583	0.0550780
$949$	36.5337	1.18593
$950$	−3.80116	−0.123326
$951$	−18.8441	−0.611062
$952$	−1.28784	−0.0417392
$953$	1.30110	0.0421467	0.0210734	−	0.999778i	$-0.493292\pi$
$953$	1.30110	0.0421467	0.0210734	+	0.999778i	$0.493292\pi$
$954$	1.78298	0.0577260
$955$	0.925043	0.0299337
$956$	11.5025	0.372018
$957$	−64.3297	−2.07948
$958$	−32.0865	−1.03667
$959$	−0.0345581	−0.00111594
$960$	4.80250	0.155000
$961$	−5.62720	−0.181522
$962$	15.4285	0.497434
$963$	−1.62784	−0.0524564
$964$	12.3351	0.397285
$965$	41.2940	1.32930
$966$	0.433113	0.0139352
$967$	46.1056	1.48265	0.741327	−	0.671144i	$-0.234197\pi$
$967$	46.1056	1.48265	0.741327	+	0.671144i	$0.234197\pi$
$968$	10.0802	0.323991
$969$	−13.3436	−0.428659
$970$	12.3035	0.395040
$971$	−11.2565	−0.361237	−0.180619	−	0.983553i	$-0.557810\pi$
$971$	−11.2565	−0.361237	−0.180619	+	0.983553i	$0.557810\pi$
$972$	−2.83382	−0.0908949
$973$	−0.762477	−0.0244439
$974$	40.0306	1.28266
$975$	−12.9934	−0.416123
$976$	−5.92414	−0.189627
$977$	−7.08278	−0.226598	−0.113299	−	0.993561i	$-0.536142\pi$
$977$	−7.08278	−0.226598	−0.113299	+	0.993561i	$0.536142\pi$
$978$	32.2979	1.03277
$979$	−76.9259	−2.45856
$980$	20.2704	0.647513
$981$	−1.97840	−0.0631655
$982$	40.7883	1.30161
$983$	27.4392	0.875173	0.437587	−	0.899176i	$-0.355833\pi$
$983$	27.4392	0.875173	0.437587	+	0.899176i	$0.355833\pi$
$984$	−13.2731	−0.423131
$985$	−25.8506	−0.823669
$986$	−62.4077	−1.98746
$987$	−1.25510	−0.0399503
$988$	−2.49942	−0.0795171
$989$	6.30523	0.200495
$990$	3.65316	0.116105
$991$	−26.5695	−0.844009	−0.422005	−	0.906594i	$-0.638673\pi$
$991$	−26.5695	−0.844009	−0.422005	+	0.906594i	$0.638673\pi$
$992$	−5.03714	−0.159929
$993$	−13.2088	−0.419168
$994$	−2.10880	−0.0668870
$995$	−5.58224	−0.176969
$996$	−20.4834	−0.649041
$997$	−38.9725	−1.23427	−0.617135	−	0.786857i	$-0.711707\pi$
$997$	−38.9725	−1.23427	−0.617135	+	0.786857i	$0.711707\pi$
$998$	−13.1717	−0.416942
$999$	36.6620	1.15993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.12	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.12	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.65119 q^{3} +1.00000 q^{4} -2.90851 q^{5} -1.65119 q^{6} +0.175106 q^{7} +1.00000 q^{8} -0.273565 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.65119 q^{3} +1.00000 q^{4} -2.90851 q^{5} -1.65119 q^{6} +0.175106 q^{7} +1.00000 q^{8} -0.273565 q^{9} -2.90851 q^{10} +4.59132 q^{11} -1.65119 q^{12} +2.27470 q^{13} +0.175106 q^{14} +4.80250 q^{15} +1.00000 q^{16} -7.35465 q^{17} -0.273565 q^{18} -1.09879 q^{19} -2.90851 q^{20} -0.289133 q^{21} +4.59132 q^{22} -1.49797 q^{23} -1.65119 q^{24} +3.45941 q^{25} +2.27470 q^{26} +5.40528 q^{27} +0.175106 q^{28} +8.48547 q^{29} +4.80250 q^{30} -5.03714 q^{31} +1.00000 q^{32} -7.58115 q^{33} -7.35465 q^{34} -0.509296 q^{35} -0.273565 q^{36} +6.78262 q^{37} -1.09879 q^{38} -3.75597 q^{39} -2.90851 q^{40} +8.03850 q^{41} -0.289133 q^{42} -4.20919 q^{43} +4.59132 q^{44} +0.795666 q^{45} -1.49797 q^{46} +4.34091 q^{47} -1.65119 q^{48} -6.96934 q^{49} +3.45941 q^{50} +12.1439 q^{51} +2.27470 q^{52} -6.51756 q^{53} +5.40528 q^{54} -13.3539 q^{55} +0.175106 q^{56} +1.81431 q^{57} +8.48547 q^{58} -1.11592 q^{59} +4.80250 q^{60} -5.92414 q^{61} -5.03714 q^{62} -0.0479029 q^{63} +1.00000 q^{64} -6.61599 q^{65} -7.58115 q^{66} -8.49014 q^{67} -7.35465 q^{68} +2.47344 q^{69} -0.509296 q^{70} -12.0430 q^{71} -0.273565 q^{72} +16.0608 q^{73} +6.78262 q^{74} -5.71215 q^{75} -1.09879 q^{76} +0.803967 q^{77} -3.75597 q^{78} -1.02703 q^{79} -2.90851 q^{80} -8.10447 q^{81} +8.03850 q^{82} +12.4052 q^{83} -0.289133 q^{84} +21.3910 q^{85} -4.20919 q^{86} -14.0111 q^{87} +4.59132 q^{88} -16.7546 q^{89} +0.795666 q^{90} +0.398314 q^{91} -1.49797 q^{92} +8.31729 q^{93} +4.34091 q^{94} +3.19583 q^{95} -1.65119 q^{96} -4.23016 q^{97} -6.96934 q^{98} -1.25603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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