LMFDB - Embedded newform 4033.2.a.d.1.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0358852 q^{2} +0.695499 q^{3} -1.99871 q^{4} -3.90392 q^{5} -0.0249581 q^{6} -3.10806 q^{7} +0.143495 q^{8} -2.51628 q^{9} +O(q^{10})$	\(q-0.0358852 q^{2} +0.695499 q^{3} -1.99871 q^{4} -3.90392 q^{5} -0.0249581 q^{6} -3.10806 q^{7} +0.143495 q^{8} -2.51628 q^{9} +0.140093 q^{10} +6.26055 q^{11} -1.39010 q^{12} -4.52247 q^{13} +0.111534 q^{14} -2.71517 q^{15} +3.99228 q^{16} +1.85452 q^{17} +0.0902973 q^{18} +6.32890 q^{19} +7.80281 q^{20} -2.16166 q^{21} -0.224661 q^{22} +3.00794 q^{23} +0.0998003 q^{24} +10.2406 q^{25} +0.162290 q^{26} -3.83657 q^{27} +6.21213 q^{28} +6.29751 q^{29} +0.0974345 q^{30} -4.55336 q^{31} -0.430253 q^{32} +4.35421 q^{33} -0.0665498 q^{34} +12.1336 q^{35} +5.02932 q^{36} -1.00000 q^{37} -0.227114 q^{38} -3.14537 q^{39} -0.560191 q^{40} +7.26411 q^{41} +0.0775714 q^{42} -4.82003 q^{43} -12.5130 q^{44} +9.82336 q^{45} -0.107941 q^{46} +3.93552 q^{47} +2.77662 q^{48} +2.66006 q^{49} -0.367485 q^{50} +1.28982 q^{51} +9.03911 q^{52} -2.36847 q^{53} +0.137676 q^{54} -24.4407 q^{55} -0.445990 q^{56} +4.40174 q^{57} -0.225987 q^{58} -9.18400 q^{59} +5.42685 q^{60} -11.8993 q^{61} +0.163398 q^{62} +7.82076 q^{63} -7.96911 q^{64} +17.6554 q^{65} -0.156252 q^{66} +2.35117 q^{67} -3.70665 q^{68} +2.09202 q^{69} -0.435418 q^{70} -0.891012 q^{71} -0.361073 q^{72} -6.35087 q^{73} +0.0358852 q^{74} +7.12232 q^{75} -12.6497 q^{76} -19.4582 q^{77} +0.112872 q^{78} -4.87316 q^{79} -15.5855 q^{80} +4.88052 q^{81} -0.260674 q^{82} +16.9643 q^{83} +4.32053 q^{84} -7.23989 q^{85} +0.172968 q^{86} +4.37991 q^{87} +0.898355 q^{88} -8.64600 q^{89} -0.352513 q^{90} +14.0561 q^{91} -6.01201 q^{92} -3.16685 q^{93} -0.141227 q^{94} -24.7075 q^{95} -0.299240 q^{96} -6.40346 q^{97} -0.0954569 q^{98} -15.7533 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−0.0358852	−0.0253747	−0.0126873	−	0.999920i	$-0.504039\pi$
$2$	−0.0358852	−0.0253747	−0.0126873	+	0.999920i	$0.504039\pi$
$3$	0.695499	0.401546	0.200773	−	0.979638i	$-0.435655\pi$
$3$	0.695499	0.401546	0.200773	+	0.979638i	$0.435655\pi$
$4$	−1.99871	−0.999356
$5$	−3.90392	−1.74589	−0.872943	−	0.487822i	$-0.837791\pi$
$5$	−3.90392	−1.74589	−0.872943	+	0.487822i	$0.837791\pi$
$6$	−0.0249581	−0.0101891
$7$	−3.10806	−1.17474	−0.587369	−	0.809319i	$-0.699836\pi$
$7$	−3.10806	−1.17474	−0.587369	+	0.809319i	$0.699836\pi$
$8$	0.143495	0.0507330
$9$	−2.51628	−0.838760
$10$	0.140093	0.0443013
$11$	6.26055	1.88763	0.943814	−	0.330479i	$-0.107210\pi$
$11$	6.26055	1.88763	0.943814	+	0.330479i	$0.107210\pi$
$12$	−1.39010	−0.401288
$13$	−4.52247	−1.25431	−0.627154	−	0.778896i	$-0.715780\pi$
$13$	−4.52247	−1.25431	−0.627154	+	0.778896i	$0.715780\pi$
$14$	0.111534	0.0298086
$15$	−2.71517	−0.701054
$16$	3.99228	0.998069
$17$	1.85452	0.449787	0.224893	−	0.974383i	$-0.427797\pi$
$17$	1.85452	0.449787	0.224893	+	0.974383i	$0.427797\pi$
$18$	0.0902973	0.0212833
$19$	6.32890	1.45195	0.725975	−	0.687721i	$-0.241389\pi$
$19$	6.32890	1.45195	0.725975	+	0.687721i	$0.241389\pi$
$20$	7.80281	1.74476
$21$	−2.16166	−0.471712
$22$	−0.224661	−0.0478979
$23$	3.00794	0.627199	0.313600	−	0.949555i	$-0.398465\pi$
$23$	3.00794	0.627199	0.313600	+	0.949555i	$0.398465\pi$
$24$	0.0998003	0.0203717
$25$	10.2406	2.04812
$26$	0.162290	0.0318276
$27$	−3.83657	−0.738348
$28$	6.21213	1.17398
$29$	6.29751	1.16942	0.584709	−	0.811243i	$-0.301209\pi$
$29$	6.29751	1.16942	0.584709	+	0.811243i	$0.301209\pi$
$30$	0.0974345	0.0177890
$31$	−4.55336	−0.817807	−0.408903	−	0.912578i	$-0.634089\pi$
$31$	−4.55336	−0.817807	−0.408903	+	0.912578i	$0.634089\pi$
$32$	−0.430253	−0.0760587
$33$	4.35421	0.757970
$34$	−0.0665498	−0.0114132
$35$	12.1336	2.05096
$36$	5.02932	0.838220
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−0.227114	−0.0368427
$39$	−3.14537	−0.503663
$40$	−0.560191	−0.0885740
$41$	7.26411	1.13446	0.567232	−	0.823558i	$-0.308014\pi$
$41$	7.26411	1.13446	0.567232	+	0.823558i	$0.308014\pi$
$42$	0.0775714	0.0119695
$43$	−4.82003	−0.735047	−0.367524	−	0.930014i	$-0.619794\pi$
$43$	−4.82003	−0.735047	−0.367524	+	0.930014i	$0.619794\pi$
$44$	−12.5130	−1.88641
$45$	9.82336	1.46438
$46$	−0.107941	−0.0159150
$47$	3.93552	0.574055	0.287028	−	0.957922i	$-0.407333\pi$
$47$	3.93552	0.574055	0.287028	+	0.957922i	$0.407333\pi$
$48$	2.77662	0.400771
$49$	2.66006	0.380009
$50$	−0.367485	−0.0519703
$51$	1.28982	0.180610
$52$	9.03911	1.25350
$53$	−2.36847	−0.325335	−0.162668	−	0.986681i	$-0.552010\pi$
$53$	−2.36847	−0.325335	−0.162668	+	0.986681i	$0.552010\pi$
$54$	0.137676	0.0187353
$55$	−24.4407	−3.29558
$56$	−0.445990	−0.0595980
$57$	4.40174	0.583025
$58$	−0.225987	−0.0296736
$59$	−9.18400	−1.19565	−0.597827	−	0.801625i	$-0.703969\pi$
$59$	−9.18400	−1.19565	−0.597827	+	0.801625i	$0.703969\pi$
$60$	5.42685	0.700603
$61$	−11.8993	−1.52354	−0.761772	−	0.647845i	$-0.775670\pi$
$61$	−11.8993	−1.52354	−0.761772	+	0.647845i	$0.775670\pi$
$62$	0.163398	0.0207516
$63$	7.82076	0.985324
$64$	−7.96911	−0.996139
$65$	17.6554	2.18988
$66$	−0.156252	−0.0192332
$67$	2.35117	0.287241	0.143620	−	0.989633i	$-0.454126\pi$
$67$	2.35117	0.287241	0.143620	+	0.989633i	$0.454126\pi$
$68$	−3.70665	−0.449497
$69$	2.09202	0.251850
$70$	−0.435418	−0.0520424
$71$	−0.891012	−0.105744	−0.0528718	−	0.998601i	$-0.516837\pi$
$71$	−0.891012	−0.105744	−0.0528718	+	0.998601i	$0.516837\pi$
$72$	−0.361073	−0.0425528
$73$	−6.35087	−0.743313	−0.371657	−	0.928370i	$-0.621210\pi$
$73$	−6.35087	−0.743313	−0.371657	+	0.928370i	$0.621210\pi$
$74$	0.0358852	0.00417157
$75$	7.12232	0.822414
$76$	−12.6497	−1.45101
$77$	−19.4582	−2.21747
$78$	0.112872	0.0127803
$79$	−4.87316	−0.548273	−0.274136	−	0.961691i	$-0.588392\pi$
$79$	−4.87316	−0.548273	−0.274136	+	0.961691i	$0.588392\pi$
$80$	−15.5855	−1.74251
$81$	4.88052	0.542280
$82$	−0.260674	−0.0287867
$83$	16.9643	1.86207	0.931036	−	0.364926i	$-0.118906\pi$
$83$	16.9643	1.86207	0.931036	+	0.364926i	$0.118906\pi$
$84$	4.32053	0.471408
$85$	−7.23989	−0.785277
$86$	0.172968	0.0186516
$87$	4.37991	0.469576
$88$	0.898355	0.0957650
$89$	−8.64600	−0.916474	−0.458237	−	0.888830i	$-0.651519\pi$
$89$	−8.64600	−0.916474	−0.458237	+	0.888830i	$0.651519\pi$
$90$	−0.352513	−0.0371582
$91$	14.0561	1.47348
$92$	−6.01201	−0.626796
$93$	−3.16685	−0.328387
$94$	−0.141227	−0.0145665
$95$	−24.7075	−2.53494
$96$	−0.299240	−0.0305411
$97$	−6.40346	−0.650173	−0.325086	−	0.945684i	$-0.605393\pi$
$97$	−6.40346	−0.650173	−0.325086	+	0.945684i	$0.605393\pi$
$98$	−0.0954569	−0.00964260
$99$	−15.7533	−1.58327
$100$	−20.4680	−2.04680
$101$	10.4406	1.03888	0.519439	−	0.854507i	$-0.326141\pi$
$101$	10.4406	1.03888	0.519439	+	0.854507i	$0.326141\pi$
$102$	−0.0462853	−0.00458293
$103$	−13.7407	−1.35391	−0.676955	−	0.736024i	$-0.736701\pi$
$103$	−13.7407	−1.35391	−0.676955	+	0.736024i	$0.736701\pi$
$104$	−0.648950	−0.0636348
$105$	8.43893	0.823555
$106$	0.0849932	0.00825527
$107$	−0.181919	−0.0175868	−0.00879339	−	0.999961i	$-0.502799\pi$
$107$	−0.181919	−0.0175868	−0.00879339	+	0.999961i	$0.502799\pi$
$108$	7.66819	0.737872
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	0.877059	0.0836243
$111$	−0.695499	−0.0660138
$112$	−12.4082	−1.17247
$113$	1.47428	0.138689	0.0693444	−	0.997593i	$-0.477909\pi$
$113$	1.47428	0.138689	0.0693444	+	0.997593i	$0.477909\pi$
$114$	−0.157957	−0.0147941
$115$	−11.7428	−1.09502
$116$	−12.5869	−1.16867
$117$	11.3798	1.05206
$118$	0.329570	0.0303393
$119$	−5.76396	−0.528382
$120$	−0.389612	−0.0355666
$121$	28.1945	2.56314
$122$	0.427007	0.0386594
$123$	5.05218	0.455540
$124$	9.10085	0.817280
$125$	−20.4588	−1.82989
$126$	−0.280650	−0.0250023
$127$	7.17711	0.636866	0.318433	−	0.947945i	$-0.396843\pi$
$127$	7.17711	0.636866	0.318433	+	0.947945i	$0.396843\pi$
$128$	1.14648	0.101335
$129$	−3.35232	−0.295156
$130$	−0.633566	−0.0555674
$131$	8.85720	0.773857	0.386929	−	0.922110i	$-0.373536\pi$
$131$	8.85720	0.773857	0.386929	+	0.922110i	$0.373536\pi$
$132$	−8.70280	−0.757482
$133$	−19.6706	−1.70566
$134$	−0.0843721	−0.00728864
$135$	14.9776	1.28907
$136$	0.266113	0.0228190
$137$	9.90978	0.846649	0.423325	−	0.905978i	$-0.360863\pi$
$137$	9.90978	0.846649	0.423325	+	0.905978i	$0.360863\pi$
$138$	−0.0750726	−0.00639060
$139$	15.8895	1.34773	0.673863	−	0.738856i	$-0.264634\pi$
$139$	15.8895	1.34773	0.673863	+	0.738856i	$0.264634\pi$
$140$	−24.2516	−2.04964
$141$	2.73715	0.230510
$142$	0.0319741	0.00268321
$143$	−28.3131	−2.36766
$144$	−10.0457	−0.837141
$145$	−24.5850	−2.04167
$146$	0.227902	0.0188613
$147$	1.85007	0.152591
$148$	1.99871	0.164293
$149$	−22.3169	−1.82827	−0.914137	−	0.405405i	$-0.867131\pi$
$149$	−22.3169	−1.82827	−0.914137	+	0.405405i	$0.867131\pi$
$150$	−0.255586	−0.0208685
$151$	−5.07641	−0.413112	−0.206556	−	0.978435i	$-0.566226\pi$
$151$	−5.07641	−0.413112	−0.206556	+	0.978435i	$0.566226\pi$
$152$	0.908163	0.0736618
$153$	−4.66649	−0.377263
$154$	0.698261	0.0562675
$155$	17.7759	1.42780
$156$	6.28669	0.503338
$157$	5.19736	0.414795	0.207397	−	0.978257i	$-0.433501\pi$
$157$	5.19736	0.414795	0.207397	+	0.978257i	$0.433501\pi$
$158$	0.174874	0.0139122
$159$	−1.64727	−0.130637
$160$	1.67967	0.132790
$161$	−9.34888	−0.736795
$162$	−0.175138	−0.0137602
$163$	19.3847	1.51833	0.759164	−	0.650899i	$-0.225608\pi$
$163$	19.3847	1.51833	0.759164	+	0.650899i	$0.225608\pi$
$164$	−14.5189	−1.13373
$165$	−16.9985	−1.32333
$166$	−0.608767	−0.0472495
$167$	19.5556	1.51326	0.756628	−	0.653846i	$-0.226845\pi$
$167$	19.5556	1.51326	0.756628	+	0.653846i	$0.226845\pi$
$168$	−0.310186	−0.0239314
$169$	7.45272	0.573286
$170$	0.259805	0.0199261
$171$	−15.9253	−1.21784
$172$	9.63385	0.734574
$173$	−1.53216	−0.116488	−0.0582441	−	0.998302i	$-0.518550\pi$
$173$	−1.53216	−0.116488	−0.0582441	+	0.998302i	$0.518550\pi$
$174$	−0.157174	−0.0119153
$175$	−31.8284	−2.40600
$176$	24.9938	1.88398
$177$	−6.38746	−0.480111
$178$	0.310264	0.0232552
$179$	−6.26887	−0.468557	−0.234279	−	0.972170i	$-0.575273\pi$
$179$	−6.26887	−0.468557	−0.234279	+	0.972170i	$0.575273\pi$
$180$	−19.6341	−1.46344
$181$	−16.9034	−1.25642	−0.628209	−	0.778044i	$-0.716212\pi$
$181$	−16.9034	−1.25642	−0.628209	+	0.778044i	$0.716212\pi$
$182$	−0.504407	−0.0373891
$183$	−8.27592	−0.611774
$184$	0.431624	0.0318197
$185$	3.90392	0.287022
$186$	0.113643	0.00833272
$187$	11.6103	0.849030
$188$	−7.86598	−0.573686
$189$	11.9243	0.867365
$190$	0.886634	0.0643232
$191$	12.9909	0.939989	0.469994	−	0.882669i	$-0.344256\pi$
$191$	12.9909	0.939989	0.469994	+	0.882669i	$0.344256\pi$
$192$	−5.54251	−0.399996
$193$	−15.6094	−1.12359	−0.561795	−	0.827277i	$-0.689889\pi$
$193$	−15.6094	−1.12359	−0.561795	+	0.827277i	$0.689889\pi$
$194$	0.229789	0.0164979
$195$	12.2793	0.879337
$196$	−5.31670	−0.379764
$197$	−5.51839	−0.393169	−0.196584	−	0.980487i	$-0.562985\pi$
$197$	−5.51839	−0.393169	−0.196584	+	0.980487i	$0.562985\pi$
$198$	0.565311	0.0401749
$199$	6.60628	0.468307	0.234154	−	0.972200i	$-0.424768\pi$
$199$	6.60628	0.468307	0.234154	+	0.972200i	$0.424768\pi$
$200$	1.46947	0.103907
$201$	1.63523	0.115341
$202$	−0.374663	−0.0263612
$203$	−19.5731	−1.37376
$204$	−2.57797	−0.180494
$205$	−28.3585	−1.98064
$206$	0.493087	0.0343550
$207$	−7.56883	−0.526070
$208$	−18.0549	−1.25188
$209$	39.6224	2.74074
$210$	−0.302833	−0.0208974
$211$	21.0632	1.45005	0.725026	−	0.688721i	$-0.241828\pi$
$211$	21.0632	1.45005	0.725026	+	0.688721i	$0.241828\pi$
$212$	4.73390	0.325126
$213$	−0.619698	−0.0424610
$214$	0.00652820	0.000446259 0
$215$	18.8170	1.28331
$216$	−0.550527	−0.0374586
$217$	14.1521	0.960709
$218$	0.0358852	0.00243045
$219$	−4.41702	−0.298475
$220$	48.8499	3.29346
$221$	−8.38700	−0.564171
$222$	0.0249581	0.00167508
$223$	20.2254	1.35439	0.677196	−	0.735803i	$-0.263195\pi$
$223$	20.2254	1.35439	0.677196	+	0.735803i	$0.263195\pi$
$224$	1.33725	0.0893490
$225$	−25.7682	−1.71788
$226$	−0.0529049	−0.00351918
$227$	−16.9694	−1.12630	−0.563148	−	0.826356i	$-0.690410\pi$
$227$	−16.9694	−1.12630	−0.563148	+	0.826356i	$0.690410\pi$
$228$	−8.79782	−0.582650
$229$	−19.0192	−1.25682	−0.628412	−	0.777881i	$-0.716295\pi$
$229$	−19.0192	−1.25682	−0.628412	+	0.777881i	$0.716295\pi$
$230$	0.421392	0.0277857
$231$	−13.5332	−0.890416
$232$	0.903658	0.0593281
$233$	−25.2688	−1.65542	−0.827709	−	0.561158i	$-0.810356\pi$
$233$	−25.2688	−1.65542	−0.827709	+	0.561158i	$0.810356\pi$
$234$	−0.408366	−0.0266958
$235$	−15.3640	−1.00223
$236$	18.3562	1.19488
$237$	−3.38927	−0.220157
$238$	0.206841	0.0134075
$239$	4.50912	0.291671	0.145835	−	0.989309i	$-0.453413\pi$
$239$	4.50912	0.291671	0.145835	+	0.989309i	$0.453413\pi$
$240$	−10.8397	−0.699700
$241$	−28.5141	−1.83675	−0.918376	−	0.395708i	$-0.870499\pi$
$241$	−28.5141	−1.83675	−0.918376	+	0.395708i	$0.870499\pi$
$242$	−1.01177	−0.0650387
$243$	14.9041	0.956098
$244$	23.7832	1.52256
$245$	−10.3847	−0.663452
$246$	−0.181299	−0.0115592
$247$	−28.6223	−1.82119
$248$	−0.653382	−0.0414898
$249$	11.7986	0.747709
$250$	0.734169	0.0464329
$251$	1.91385	0.120801	0.0604006	−	0.998174i	$-0.480762\pi$
$251$	1.91385	0.120801	0.0604006	+	0.998174i	$0.480762\pi$
$252$	−15.6315	−0.984689
$253$	18.8314	1.18392
$254$	−0.257552	−0.0161603
$255$	−5.03534	−0.315325
$256$	15.8971	0.993567
$257$	11.3888	0.710415	0.355208	−	0.934787i	$-0.384410\pi$
$257$	11.3888	0.710415	0.355208	+	0.934787i	$0.384410\pi$
$258$	0.120299	0.00748947
$259$	3.10806	0.193126
$260$	−35.2880	−2.18847
$261$	−15.8463	−0.980862
$262$	−0.317842	−0.0196364
$263$	−10.7055	−0.660131	−0.330065	−	0.943958i	$-0.607071\pi$
$263$	−10.7055	−0.660131	−0.330065	+	0.943958i	$0.607071\pi$
$264$	0.624805	0.0384541
$265$	9.24633	0.567998
$266$	0.705885	0.0432806
$267$	−6.01328	−0.368007
$268$	−4.69931	−0.287056
$269$	−11.1466	−0.679621	−0.339810	−	0.940494i	$-0.610363\pi$
$269$	−11.1466	−0.679621	−0.339810	+	0.940494i	$0.610363\pi$
$270$	−0.537476	−0.0327097
$271$	−25.4459	−1.54573	−0.772864	−	0.634572i	$-0.781176\pi$
$271$	−25.4459	−1.54573	−0.772864	+	0.634572i	$0.781176\pi$
$272$	7.40375	0.448918
$273$	9.77602	0.591671
$274$	−0.355614	−0.0214834
$275$	64.1117	3.86608
$276$	−4.18135	−0.251688
$277$	−8.70507	−0.523037	−0.261518	−	0.965198i	$-0.584223\pi$
$277$	−8.70507	−0.523037	−0.261518	+	0.965198i	$0.584223\pi$
$278$	−0.570197	−0.0341981
$279$	11.4575	0.685944
$280$	1.74111	0.104051
$281$	19.4222	1.15863	0.579314	−	0.815104i	$-0.303320\pi$
$281$	19.4222	1.15863	0.579314	+	0.815104i	$0.303320\pi$
$282$	−0.0982233	−0.00584911
$283$	−16.0663	−0.955045	−0.477523	−	0.878619i	$-0.658465\pi$
$283$	−16.0663	−0.955045	−0.477523	+	0.878619i	$0.658465\pi$
$284$	1.78088	0.105676
$285$	−17.1841	−1.01790
$286$	1.01602	0.0600787
$287$	−22.5773	−1.33270
$288$	1.08264	0.0637950
$289$	−13.5608	−0.797692
$290$	0.882236	0.0518067
$291$	−4.45360	−0.261075
$292$	12.6936	0.742834
$293$	0.620867	0.0362715	0.0181357	−	0.999836i	$-0.494227\pi$
$293$	0.620867	0.0362715	0.0181357	+	0.999836i	$0.494227\pi$
$294$	−0.0663902	−0.00387195
$295$	35.8536	2.08748
$296$	−0.143495	−0.00834045
$297$	−24.0190	−1.39373
$298$	0.800848	0.0463919
$299$	−13.6033	−0.786701
$300$	−14.2355	−0.821885
$301$	14.9810	0.863488
$302$	0.182168	0.0104826
$303$	7.26142	0.417158
$304$	25.2667	1.44915
$305$	46.4537	2.65993
$306$	0.167458	0.00957294
$307$	−18.4821	−1.05483	−0.527416	−	0.849607i	$-0.676839\pi$
$307$	−18.4821	−1.05483	−0.527416	+	0.849607i	$0.676839\pi$
$308$	38.8913	2.21604
$309$	−9.55663	−0.543658
$310$	−0.637893	−0.0362299
$311$	23.9828	1.35994	0.679970	−	0.733240i	$-0.261993\pi$
$311$	23.9828	1.35994	0.679970	+	0.733240i	$0.261993\pi$
$312$	−0.451344	−0.0255523
$313$	−28.4813	−1.60986	−0.804930	−	0.593369i	$-0.797797\pi$
$313$	−28.4813	−1.60986	−0.804930	+	0.593369i	$0.797797\pi$
$314$	−0.186508	−0.0105253
$315$	−30.5316	−1.72026
$316$	9.74004	0.547920
$317$	−12.9985	−0.730069	−0.365035	−	0.930994i	$-0.618943\pi$
$317$	−12.9985	−0.730069	−0.365035	+	0.930994i	$0.618943\pi$
$318$	0.0591127	0.00331487
$319$	39.4259	2.20743
$320$	31.1108	1.73914
$321$	−0.126524	−0.00706191
$322$	0.335486	0.0186959
$323$	11.7371	0.653068
$324$	−9.75475	−0.541930
$325$	−46.3127	−2.56897
$326$	−0.695625	−0.0385271
$327$	−0.695499	−0.0384612
$328$	1.04236	0.0575548
$329$	−12.2319	−0.674364
$330$	0.609993	0.0335790
$331$	8.27860	0.455033	0.227516	−	0.973774i	$-0.426939\pi$
$331$	8.27860	0.455033	0.227516	+	0.973774i	$0.426939\pi$
$332$	−33.9067	−1.86087
$333$	2.51628	0.137891
$334$	−0.701756	−0.0383984
$335$	−9.17877	−0.501490
$336$	−8.62992	−0.470801
$337$	−19.2255	−1.04728	−0.523641	−	0.851939i	$-0.675427\pi$
$337$	−19.2255	−1.04728	−0.523641	+	0.851939i	$0.675427\pi$
$338$	−0.267442	−0.0145469
$339$	1.02536	0.0556900
$340$	14.4705	0.784771
$341$	−28.5065	−1.54371
$342$	0.571482	0.0309022
$343$	13.4888	0.728327
$344$	−0.691648	−0.0372911
$345$	−8.16708	−0.439701
$346$	0.0549820	0.00295585
$347$	13.1594	0.706433	0.353217	−	0.935542i	$-0.385088\pi$
$347$	13.1594	0.706433	0.353217	+	0.935542i	$0.385088\pi$
$348$	−8.75418	−0.469273
$349$	3.50908	0.187837	0.0939183	−	0.995580i	$-0.470061\pi$
$349$	3.50908	0.187837	0.0939183	+	0.995580i	$0.470061\pi$
$350$	1.14217	0.0610515
$351$	17.3508	0.926115
$352$	−2.69362	−0.143570
$353$	−27.5838	−1.46814	−0.734070	−	0.679074i	$-0.762382\pi$
$353$	−27.5838	−1.46814	−0.734070	+	0.679074i	$0.762382\pi$
$354$	0.229215	0.0121827
$355$	3.47844	0.184616
$356$	17.2809	0.915884
$357$	−4.00883	−0.212170
$358$	0.224960	0.0118895
$359$	19.2020	1.01345	0.506723	−	0.862109i	$-0.330857\pi$
$359$	19.2020	1.01345	0.506723	+	0.862109i	$0.330857\pi$
$360$	1.40960	0.0742924
$361$	21.0550	1.10816
$362$	0.606581	0.0318812
$363$	19.6092	1.02922
$364$	−28.0941	−1.47253
$365$	24.7933	1.29774
$366$	0.296983	0.0155236
$367$	12.1975	0.636706	0.318353	−	0.947972i	$-0.396870\pi$
$367$	12.1975	0.636706	0.318353	+	0.947972i	$0.396870\pi$
$368$	12.0085	0.625988
$369$	−18.2786	−0.951544
$370$	−0.140093	−0.00728308
$371$	7.36137	0.382183
$372$	6.32963	0.328176
$373$	−19.6126	−1.01550	−0.507752	−	0.861504i	$-0.669523\pi$
$373$	−19.6126	−1.01550	−0.507752	+	0.861504i	$0.669523\pi$
$374$	−0.416638	−0.0215439
$375$	−14.2291	−0.734787
$376$	0.564726	0.0291235
$377$	−28.4803	−1.46681
$378$	−0.427906	−0.0220091
$379$	−0.256703	−0.0131859	−0.00659296	−	0.999978i	$-0.502099\pi$
$379$	−0.256703	−0.0131859	−0.00659296	+	0.999978i	$0.502099\pi$
$380$	49.3832	2.53331
$381$	4.99167	0.255731
$382$	−0.466181	−0.0238519
$383$	−12.8577	−0.656996	−0.328498	−	0.944505i	$-0.606542\pi$
$383$	−12.8577	−0.656996	−0.328498	+	0.944505i	$0.606542\pi$
$384$	0.797375	0.0406909
$385$	75.9632	3.87144
$386$	0.560146	0.0285107
$387$	12.1285	0.616528
$388$	12.7987	0.649754
$389$	1.42581	0.0722913	0.0361456	−	0.999347i	$-0.488492\pi$
$389$	1.42581	0.0722913	0.0361456	+	0.999347i	$0.488492\pi$
$390$	−0.440644	−0.0223129
$391$	5.57829	0.282106
$392$	0.381705	0.0192790
$393$	6.16017	0.310740
$394$	0.198028	0.00997652
$395$	19.0244	0.957222
$396$	31.4863	1.58225
$397$	6.14593	0.308455	0.154228	−	0.988035i	$-0.450711\pi$
$397$	6.14593	0.308455	0.154228	+	0.988035i	$0.450711\pi$
$398$	−0.237068	−0.0118831
$399$	−13.6809	−0.684902
$400$	40.8832	2.04416
$401$	21.9462	1.09594	0.547970	−	0.836498i	$-0.315401\pi$
$401$	21.9462	1.09594	0.547970	+	0.836498i	$0.315401\pi$
$402$	−0.0586807	−0.00292673
$403$	20.5924	1.02578
$404$	−20.8678	−1.03821
$405$	−19.0531	−0.946758
$406$	0.702383	0.0348587
$407$	−6.26055	−0.310324
$408$	0.185082	0.00916290
$409$	−11.9941	−0.593071	−0.296536	−	0.955022i	$-0.595831\pi$
$409$	−11.9941	−0.593071	−0.296536	+	0.955022i	$0.595831\pi$
$410$	1.01765	0.0502582
$411$	6.89224	0.339969
$412$	27.4637	1.35304
$413$	28.5445	1.40458
$414$	0.271609	0.0133489
$415$	−66.2272	−3.25097
$416$	1.94580	0.0954009
$417$	11.0511	0.541175
$418$	−1.42186	−0.0695454
$419$	−35.4890	−1.73375	−0.866876	−	0.498523i	$-0.833876\pi$
$419$	−35.4890	−1.73375	−0.866876	+	0.498523i	$0.833876\pi$
$420$	−16.8670	−0.823025
$421$	−3.49877	−0.170520	−0.0852598	−	0.996359i	$-0.527172\pi$
$421$	−3.49877	−0.170520	−0.0852598	+	0.996359i	$0.527172\pi$
$422$	−0.755858	−0.0367946
$423$	−9.90289	−0.481495
$424$	−0.339863	−0.0165052
$425$	18.9914	0.921216
$426$	0.0222380	0.00107743
$427$	36.9837	1.78976
$428$	0.363604	0.0175755
$429$	−19.6918	−0.950727
$430$	−0.675252	−0.0325635
$431$	2.93412	0.141332	0.0706659	−	0.997500i	$-0.477488\pi$
$431$	2.93412	0.141332	0.0706659	+	0.997500i	$0.477488\pi$
$432$	−15.3166	−0.736922
$433$	0.373579	0.0179531	0.00897654	−	0.999960i	$-0.497143\pi$
$433$	0.373579	0.0179531	0.00897654	+	0.999960i	$0.497143\pi$
$434$	−0.507852	−0.0243777
$435$	−17.0988	−0.819825
$436$	1.99871	0.0957210
$437$	19.0370	0.910662
$438$	0.158506	0.00757370
$439$	28.3657	1.35382	0.676910	−	0.736066i	$-0.263319\pi$
$439$	28.3657	1.35382	0.676910	+	0.736066i	$0.263319\pi$
$440$	−3.50711	−0.167195
$441$	−6.69347	−0.318737
$442$	0.300969	0.0143156
$443$	−25.4610	−1.20969	−0.604843	−	0.796345i	$-0.706764\pi$
$443$	−25.4610	−1.20969	−0.604843	+	0.796345i	$0.706764\pi$
$444$	1.39010	0.0659713
$445$	33.7533	1.60006
$446$	−0.725792	−0.0343672
$447$	−15.5214	−0.734137
$448$	24.7685	1.17020
$449$	−8.90747	−0.420369	−0.210185	−	0.977662i	$-0.567407\pi$
$449$	−8.90747	−0.420369	−0.210185	+	0.977662i	$0.567407\pi$
$450$	0.924697	0.0435906
$451$	45.4774	2.14145
$452$	−2.94667	−0.138600
$453$	−3.53064	−0.165884
$454$	0.608949	0.0285794
$455$	−54.8740	−2.57253
$456$	0.631626	0.0295786
$457$	−30.4406	−1.42395	−0.711976	−	0.702203i	$-0.752200\pi$
$457$	−30.4406	−1.42395	−0.711976	+	0.702203i	$0.752200\pi$
$458$	0.682508	0.0318915
$459$	−7.11499	−0.332099
$460$	23.4704	1.09431
$461$	17.3152	0.806449	0.403224	−	0.915101i	$-0.367889\pi$
$461$	17.3152	0.806449	0.403224	+	0.915101i	$0.367889\pi$
$462$	0.485640	0.0225940
$463$	3.64170	0.169244	0.0846221	−	0.996413i	$-0.473032\pi$
$463$	3.64170	0.169244	0.0846221	+	0.996413i	$0.473032\pi$
$464$	25.1414	1.16716
$465$	12.3631	0.573327
$466$	0.906778	0.0420057
$467$	−22.2326	−1.02880	−0.514401	−	0.857550i	$-0.671986\pi$
$467$	−22.2326	−1.02880	−0.514401	+	0.857550i	$0.671986\pi$
$468$	−22.7450	−1.05139
$469$	−7.30758	−0.337433
$470$	0.551339	0.0254314
$471$	3.61476	0.166559
$472$	−1.31785	−0.0606591
$473$	−30.1760	−1.38749
$474$	0.121625	0.00558641
$475$	64.8117	2.97376
$476$	11.5205	0.528042
$477$	5.95975	0.272878
$478$	−0.161811	−0.00740104
$479$	34.0993	1.55804	0.779019	−	0.627000i	$-0.215717\pi$
$479$	34.0993	1.55804	0.779019	+	0.627000i	$0.215717\pi$
$480$	1.16821	0.0533212
$481$	4.52247	0.206207
$482$	1.02323	0.0466070
$483$	−6.50214	−0.295857
$484$	−56.3527	−2.56149
$485$	24.9986	1.13513
$486$	−0.534836	−0.0242607
$487$	−39.8917	−1.80767	−0.903833	−	0.427886i	$-0.859259\pi$
$487$	−39.8917	−1.80767	−0.903833	+	0.427886i	$0.859259\pi$
$488$	−1.70748	−0.0772939
$489$	13.4821	0.609679
$490$	0.372656	0.0168349
$491$	−14.5434	−0.656335	−0.328167	−	0.944620i	$-0.606431\pi$
$491$	−14.5434	−0.656335	−0.328167	+	0.944620i	$0.606431\pi$
$492$	−10.0979	−0.455247
$493$	11.6789	0.525989
$494$	1.02712	0.0462121
$495$	61.4996	2.76420
$496$	−18.1782	−0.816227
$497$	2.76932	0.124221
$498$	−0.423397	−0.0189729
$499$	36.0285	1.61286	0.806429	−	0.591330i	$-0.201397\pi$
$499$	36.0285	1.61286	0.806429	+	0.591330i	$0.201397\pi$
$500$	40.8913	1.82871
$501$	13.6009	0.607642
$502$	−0.0686789	−0.00306529
$503$	−31.2291	−1.39243	−0.696217	−	0.717831i	$-0.745135\pi$
$503$	−31.2291	−1.39243	−0.696217	+	0.717831i	$0.745135\pi$
$504$	1.12224	0.0499884
$505$	−40.7593	−1.81376
$506$	−0.675768	−0.0300415
$507$	5.18336	0.230201
$508$	−14.3450	−0.636456
$509$	−29.4574	−1.30568	−0.652839	−	0.757497i	$-0.726422\pi$
$509$	−29.4574	−1.30568	−0.652839	+	0.757497i	$0.726422\pi$
$510$	0.180694	0.00800127
$511$	19.7389	0.873198
$512$	−2.86343	−0.126547
$513$	−24.2813	−1.07204
$514$	−0.408690	−0.0180266
$515$	53.6425	2.36377
$516$	6.70033	0.294965
$517$	24.6385	1.08360
$518$	−0.111534	−0.00490050
$519$	−1.06562	−0.0467754
$520$	2.53345	0.111099
$521$	27.7075	1.21389	0.606945	−	0.794744i	$-0.292395\pi$
$521$	27.7075	1.21389	0.606945	+	0.794744i	$0.292395\pi$
$522$	0.568648	0.0248890
$523$	−35.0380	−1.53211	−0.766053	−	0.642777i	$-0.777782\pi$
$523$	−35.0380	−1.53211	−0.766053	+	0.642777i	$0.777782\pi$
$524$	−17.7030	−0.773359
$525$	−22.1366	−0.966121
$526$	0.384170	0.0167506
$527$	−8.44428	−0.367839
$528$	17.3832	0.756506
$529$	−13.9523	−0.606621
$530$	−0.331807	−0.0144128
$531$	23.1095	1.00287
$532$	39.3159	1.70456
$533$	−32.8517	−1.42297
$534$	0.215788	0.00933806
$535$	0.710197	0.0307045
$536$	0.337380	0.0145726
$537$	−4.35999	−0.188147
$538$	0.399998	0.0172451
$539$	16.6535	0.717315
$540$	−29.9360	−1.28824
$541$	0.702438	0.0302002	0.0151001	−	0.999886i	$-0.495193\pi$
$541$	0.702438	0.0302002	0.0151001	+	0.999886i	$0.495193\pi$
$542$	0.913131	0.0392223
$543$	−11.7563	−0.504510
$544$	−0.797912	−0.0342102
$545$	3.90392	0.167226
$546$	−0.350814	−0.0150135
$547$	20.5557	0.878897	0.439448	−	0.898268i	$-0.355174\pi$
$547$	20.5557	0.878897	0.439448	+	0.898268i	$0.355174\pi$
$548$	−19.8068	−0.846104
$549$	29.9419	1.27789
$550$	−2.30066	−0.0981005
$551$	39.8563	1.69794
$552$	0.300194	0.0127771
$553$	15.1461	0.644077
$554$	0.312383	0.0132719
$555$	2.71517	0.115253
$556$	−31.7585	−1.34686
$557$	−29.4945	−1.24972	−0.624861	−	0.780736i	$-0.714845\pi$
$557$	−29.4945	−1.24972	−0.624861	+	0.780736i	$0.714845\pi$
$558$	−0.411156	−0.0174056
$559$	21.7984	0.921975
$560$	48.4408	2.04700
$561$	8.07496	0.340925
$562$	−0.696968	−0.0293998
$563$	−17.5376	−0.739120	−0.369560	−	0.929207i	$-0.620492\pi$
$563$	−17.5376	−0.739120	−0.369560	+	0.929207i	$0.620492\pi$
$564$	−5.47078	−0.230361
$565$	−5.75548	−0.242135
$566$	0.576544	0.0242340
$567$	−15.1690	−0.637036
$568$	−0.127855	−0.00536469
$569$	−39.4602	−1.65426	−0.827128	−	0.562013i	$-0.810027\pi$
$569$	−39.4602	−1.65426	−0.827128	+	0.562013i	$0.810027\pi$
$570$	0.616653	0.0258288
$571$	−43.4916	−1.82007	−0.910033	−	0.414536i	$-0.863944\pi$
$571$	−43.4916	−1.82007	−0.910033	+	0.414536i	$0.863944\pi$
$572$	56.5898	2.36614
$573$	9.03516	0.377449
$574$	0.810192	0.0338168
$575$	30.8031	1.28458
$576$	20.0525	0.835522
$577$	−3.37065	−0.140322	−0.0701610	−	0.997536i	$-0.522351\pi$
$577$	−3.37065	−0.140322	−0.0701610	+	0.997536i	$0.522351\pi$
$578$	0.486631	0.0202412
$579$	−10.8563	−0.451173
$580$	49.1383	2.04036
$581$	−52.7261	−2.18745
$582$	0.159818	0.00662468
$583$	−14.8280	−0.614111
$584$	−0.911315	−0.0377105
$585$	−44.4258	−1.83678
$586$	−0.0222799	−0.000920376 0
$587$	−33.8480	−1.39706	−0.698529	−	0.715582i	$-0.746162\pi$
$587$	−33.8480	−1.39706	−0.698529	+	0.715582i	$0.746162\pi$
$588$	−3.69776	−0.152493
$589$	−28.8177	−1.18741
$590$	−1.28661	−0.0529690
$591$	−3.83803	−0.157875
$592$	−3.99228	−0.164081
$593$	14.7008	0.603689	0.301844	−	0.953357i	$-0.402398\pi$
$593$	14.7008	0.603689	0.301844	+	0.953357i	$0.402398\pi$
$594$	0.861927	0.0353653
$595$	22.5021	0.922494
$596$	44.6051	1.82710
$597$	4.59466	0.188047
$598$	0.488158	0.0199623
$599$	−5.54338	−0.226497	−0.113248	−	0.993567i	$-0.536126\pi$
$599$	−5.54338	−0.226497	−0.113248	+	0.993567i	$0.536126\pi$
$600$	1.02201	0.0417235
$601$	−21.4101	−0.873338	−0.436669	−	0.899622i	$-0.643842\pi$
$601$	−21.4101	−0.873338	−0.436669	+	0.899622i	$0.643842\pi$
$602$	−0.537594	−0.0219107
$603$	−5.91620	−0.240926
$604$	10.1463	0.412846
$605$	−110.069	−4.47494
$606$	−0.260578	−0.0105852
$607$	−7.28684	−0.295764	−0.147882	−	0.989005i	$-0.547246\pi$
$607$	−7.28684	−0.295764	−0.147882	+	0.989005i	$0.547246\pi$
$608$	−2.72303	−0.110433
$609$	−13.6130	−0.551628
$610$	−1.66700	−0.0674949
$611$	−17.7983	−0.720041
$612$	9.32697	0.377021
$613$	−5.31514	−0.214677	−0.107338	−	0.994223i	$-0.534233\pi$
$613$	−5.31514	−0.214677	−0.107338	+	0.994223i	$0.534233\pi$
$614$	0.663235	0.0267660
$615$	−19.7233	−0.795321
$616$	−2.79215	−0.112499
$617$	−37.0035	−1.48970	−0.744852	−	0.667230i	$-0.767480\pi$
$617$	−37.0035	−1.48970	−0.744852	+	0.667230i	$0.767480\pi$
$618$	0.342942	0.0137951
$619$	21.6658	0.870821	0.435410	−	0.900232i	$-0.356603\pi$
$619$	21.6658	0.870821	0.435410	+	0.900232i	$0.356603\pi$
$620$	−35.5290	−1.42688
$621$	−11.5402	−0.463091
$622$	−0.860628	−0.0345080
$623$	26.8723	1.07662
$624$	−12.5572	−0.502690
$625$	28.6667	1.14667
$626$	1.02206	0.0408497
$627$	27.5573	1.10053
$628$	−10.3880	−0.414528
$629$	−1.85452	−0.0739445
$630$	1.09563	0.0436511
$631$	15.0829	0.600441	0.300220	−	0.953870i	$-0.402940\pi$
$631$	15.0829	0.600441	0.300220	+	0.953870i	$0.402940\pi$
$632$	−0.699271	−0.0278155
$633$	14.6495	0.582263
$634$	0.466454	0.0185253
$635$	−28.0189	−1.11189
$636$	3.29242	0.130553
$637$	−12.0301	−0.476648
$638$	−1.41481	−0.0560127
$639$	2.24204	0.0886936
$640$	−4.47576	−0.176920
$641$	29.5716	1.16801	0.584005	−	0.811750i	$-0.301485\pi$
$641$	29.5716	1.16801	0.584005	+	0.811750i	$0.301485\pi$
$642$	0.00454036	0.000179194 0
$643$	−16.3145	−0.643382	−0.321691	−	0.946845i	$-0.604251\pi$
$643$	−16.3145	−0.643382	−0.321691	+	0.946845i	$0.604251\pi$
$644$	18.6857	0.736321
$645$	13.0872	0.515308
$646$	−0.421187	−0.0165714
$647$	−34.4248	−1.35338	−0.676688	−	0.736269i	$-0.736586\pi$
$647$	−34.4248	−1.35338	−0.676688	+	0.736269i	$0.736586\pi$
$648$	0.700328	0.0275115
$649$	−57.4969	−2.25695
$650$	1.66194	0.0651867
$651$	9.84278	0.385769
$652$	−38.7445	−1.51735
$653$	0.0610875	0.00239054	0.00119527	−	0.999999i	$-0.499620\pi$
$653$	0.0610875	0.00239054	0.00119527	+	0.999999i	$0.499620\pi$
$654$	0.0249581	0.000975940 0
$655$	−34.5778	−1.35107
$656$	29.0003	1.13227
$657$	15.9806	0.623462
$658$	0.438943	0.0171118
$659$	−36.6121	−1.42620	−0.713102	−	0.701060i	$-0.752710\pi$
$659$	−36.6121	−1.42620	−0.713102	+	0.701060i	$0.752710\pi$
$660$	33.9750	1.32248
$661$	28.3025	1.10084	0.550419	−	0.834889i	$-0.314468\pi$
$661$	28.3025	1.10084	0.550419	+	0.834889i	$0.314468\pi$
$662$	−0.297079	−0.0115463
$663$	−5.83315	−0.226541
$664$	2.43428	0.0944685
$665$	76.7926	2.97789
$666$	−0.0902973	−0.00349895
$667$	18.9425	0.733458
$668$	−39.0860	−1.51228
$669$	14.0667	0.543851
$670$	0.329382	0.0127251
$671$	−74.4959	−2.87588
$672$	0.930058	0.0358778
$673$	22.6218	0.872008	0.436004	−	0.899945i	$-0.356393\pi$
$673$	22.6218	0.872008	0.436004	+	0.899945i	$0.356393\pi$
$674$	0.689912	0.0265744
$675$	−39.2887	−1.51222
$676$	−14.8958	−0.572917
$677$	−28.8237	−1.10778	−0.553892	−	0.832589i	$-0.686858\pi$
$677$	−28.8237	−1.10778	−0.553892	+	0.832589i	$0.686858\pi$
$678$	−0.0367953	−0.00141312
$679$	19.9024	0.763782
$680$	−1.03889	−0.0398394
$681$	−11.8022	−0.452260
$682$	1.02296	0.0391712
$683$	22.0747	0.844663	0.422332	−	0.906441i	$-0.361212\pi$
$683$	22.0747	0.844663	0.422332	+	0.906441i	$0.361212\pi$
$684$	31.8301	1.21705
$685$	−38.6870	−1.47815
$686$	−0.484048	−0.0184811
$687$	−13.2278	−0.504673
$688$	−19.2429	−0.733628
$689$	10.7114	0.408070
$690$	0.293077	0.0111573
$691$	−34.1599	−1.29950	−0.649752	−	0.760146i	$-0.725127\pi$
$691$	−34.1599	−1.29950	−0.649752	+	0.760146i	$0.725127\pi$
$692$	3.06235	0.116413
$693$	48.9623	1.85992
$694$	−0.472227	−0.0179255
$695$	−62.0312	−2.35298
$696$	0.628493	0.0238230
$697$	13.4714	0.510267
$698$	−0.125924	−0.00476629
$699$	−17.5745	−0.664727
$700$	63.6158	2.40445
$701$	40.3437	1.52376	0.761880	−	0.647718i	$-0.224276\pi$
$701$	40.3437	1.52376	0.761880	+	0.647718i	$0.224276\pi$
$702$	−0.622635	−0.0234999
$703$	−6.32890	−0.238699
$704$	−49.8910	−1.88034
$705$	−10.6856	−0.402444
$706$	0.989852	0.0372536
$707$	−32.4500	−1.22041
$708$	12.7667	0.479802
$709$	−35.9020	−1.34833	−0.674163	−	0.738582i	$-0.735496\pi$
$709$	−35.9020	−1.34833	−0.674163	+	0.738582i	$0.735496\pi$
$710$	−0.124824	−0.00468458
$711$	12.2622	0.459870
$712$	−1.24065	−0.0464955
$713$	−13.6962	−0.512928
$714$	0.143858	0.00538374
$715$	110.532	4.13367
$716$	12.5297	0.468256
$717$	3.13609	0.117119
$718$	−0.689069	−0.0257158
$719$	−18.8206	−0.701891	−0.350945	−	0.936396i	$-0.614140\pi$
$719$	−18.8206	−0.701891	−0.350945	+	0.936396i	$0.614140\pi$
$720$	39.2176	1.46155
$721$	42.7069	1.59049
$722$	−0.755563	−0.0281191
$723$	−19.8315	−0.737542
$724$	33.7850	1.25561
$725$	64.4902	2.39511
$726$	−0.703681	−0.0261161
$727$	2.37184	0.0879667	0.0439834	−	0.999032i	$-0.485995\pi$
$727$	2.37184	0.0879667	0.0439834	+	0.999032i	$0.485995\pi$
$728$	2.01698	0.0747542
$729$	−4.27577	−0.158362
$730$	−0.889712	−0.0329297
$731$	−8.93883	−0.330615
$732$	16.5412	0.611380
$733$	27.3007	1.00838	0.504188	−	0.863594i	$-0.331792\pi$
$733$	27.3007	1.00838	0.504188	+	0.863594i	$0.331792\pi$
$734$	−0.437711	−0.0161562
$735$	−7.22253	−0.266407
$736$	−1.29418	−0.0477040
$737$	14.7196	0.542203
$738$	0.655930	0.0241451
$739$	1.36330	0.0501497	0.0250749	−	0.999686i	$-0.492018\pi$
$739$	1.36330	0.0501497	0.0250749	+	0.999686i	$0.492018\pi$
$740$	−7.80281	−0.286837
$741$	−19.9067	−0.731293
$742$	−0.264164	−0.00969778
$743$	29.1917	1.07094	0.535470	−	0.844554i	$-0.320135\pi$
$743$	29.1917	1.07094	0.535470	+	0.844554i	$0.320135\pi$
$744$	−0.454426	−0.0166601
$745$	87.1235	3.19196
$746$	0.703803	0.0257681
$747$	−42.6869	−1.56183
$748$	−23.2057	−0.848483
$749$	0.565416	0.0206599
$750$	0.510614	0.0186450
$751$	44.3778	1.61937	0.809684	−	0.586866i	$-0.199638\pi$
$751$	44.3778	1.61937	0.809684	+	0.586866i	$0.199638\pi$
$752$	15.7117	0.572947
$753$	1.33108	0.0485073
$754$	1.02202	0.0372198
$755$	19.8179	0.721247
$756$	−23.8332	−0.866807
$757$	45.7708	1.66357	0.831785	−	0.555098i	$-0.187319\pi$
$757$	45.7708	1.66357	0.831785	+	0.555098i	$0.187319\pi$
$758$	0.00921182	0.000334588 0
$759$	13.0972	0.475398
$760$	−3.54540	−0.128605
$761$	8.34828	0.302625	0.151313	−	0.988486i	$-0.451650\pi$
$761$	8.34828	0.302625	0.151313	+	0.988486i	$0.451650\pi$
$762$	−0.179127	−0.00648909
$763$	3.10806	0.112519
$764$	−25.9651	−0.939383
$765$	18.2176	0.658659
$766$	0.461400	0.0166711
$767$	41.5343	1.49972
$768$	11.0564	0.398963
$769$	−23.5362	−0.848737	−0.424369	−	0.905490i	$-0.639504\pi$
$769$	−23.5362	−0.848737	−0.424369	+	0.905490i	$0.639504\pi$
$770$	−2.72596	−0.0982366
$771$	7.92091	0.285265
$772$	31.1987	1.12287
$773$	15.6366	0.562410	0.281205	−	0.959648i	$-0.409266\pi$
$773$	15.6366	0.562410	0.281205	+	0.959648i	$0.409266\pi$
$774$	−0.435235	−0.0156442
$775$	−46.6290	−1.67496
$776$	−0.918862	−0.0329852
$777$	2.16166	0.0775489
$778$	−0.0511654	−0.00183437
$779$	45.9739	1.64718
$780$	−24.5427	−0.878771
$781$	−5.57823	−0.199605
$782$	−0.200178	−0.00715835
$783$	−24.1608	−0.863437
$784$	10.6197	0.379275
$785$	−20.2901	−0.724184
$786$	−0.221059	−0.00788492
$787$	−54.7182	−1.95049	−0.975247	−	0.221118i	$-0.929030\pi$
$787$	−54.7182	−1.95049	−0.975247	+	0.221118i	$0.929030\pi$
$788$	11.0297	0.392916
$789$	−7.44568	−0.265073
$790$	−0.682695	−0.0242892
$791$	−4.58217	−0.162923
$792$	−2.26051	−0.0803239
$793$	53.8140	1.91099
$794$	−0.220548	−0.00782695
$795$	6.43081	0.228077
$796$	−13.2041	−0.468006
$797$	3.94806	0.139847	0.0699237	−	0.997552i	$-0.477724\pi$
$797$	3.94806	0.139847	0.0699237	+	0.997552i	$0.477724\pi$
$798$	0.490942	0.0173792
$799$	7.29850	0.258203
$800$	−4.40604	−0.155777
$801$	21.7558	0.768703
$802$	−0.787543	−0.0278091
$803$	−39.7599	−1.40310
$804$	−3.26836	−0.115266
$805$	36.4973	1.28636
$806$	−0.738963	−0.0260288
$807$	−7.75245	−0.272899
$808$	1.49817	0.0527054
$809$	−34.1292	−1.19992	−0.599960	−	0.800030i	$-0.704817\pi$
$809$	−34.1292	−1.19992	−0.599960	+	0.800030i	$0.704817\pi$
$810$	0.683726	0.0240237
$811$	19.7997	0.695260	0.347630	−	0.937632i	$-0.386987\pi$
$811$	19.7997	0.695260	0.347630	+	0.937632i	$0.386987\pi$
$812$	39.1209	1.37288
$813$	−17.6976	−0.620681
$814$	0.224661	0.00787437
$815$	−75.6764	−2.65083
$816$	5.14930	0.180262
$817$	−30.5055	−1.06725
$818$	0.430412	0.0150490
$819$	−35.3692	−1.23590
$820$	56.6805	1.97937
$821$	−36.1173	−1.26050	−0.630250	−	0.776392i	$-0.717048\pi$
$821$	−36.1173	−1.26050	−0.630250	+	0.776392i	$0.717048\pi$
$822$	−0.247329	−0.00862660
$823$	40.7674	1.42106	0.710531	−	0.703666i	$-0.248455\pi$
$823$	40.7674	1.42106	0.710531	+	0.703666i	$0.248455\pi$
$824$	−1.97171	−0.0686879
$825$	44.5896	1.55241
$826$	−1.02432	−0.0356408
$827$	−43.8381	−1.52440	−0.762201	−	0.647341i	$-0.775881\pi$
$827$	−43.8381	−1.52440	−0.762201	+	0.647341i	$0.775881\pi$
$828$	15.1279	0.525731
$829$	−15.7705	−0.547731	−0.273865	−	0.961768i	$-0.588302\pi$
$829$	−15.7705	−0.547731	−0.273865	+	0.961768i	$0.588302\pi$
$830$	2.37658	0.0824922
$831$	−6.05436	−0.210024
$832$	36.0400	1.24946
$833$	4.93314	0.170923
$834$	−0.396571	−0.0137321
$835$	−76.3434	−2.64197
$836$	−79.1938	−2.73897
$837$	17.4693	0.603826
$838$	1.27353	0.0439934
$839$	−18.6554	−0.644057	−0.322028	−	0.946730i	$-0.604365\pi$
$839$	−18.6554	−0.644057	−0.322028	+	0.946730i	$0.604365\pi$
$840$	1.21094	0.0417814
$841$	10.6586	0.367539
$842$	0.125554	0.00432688
$843$	13.5081	0.465243
$844$	−42.0993	−1.44912
$845$	−29.0948	−1.00089
$846$	0.355367	0.0122178
$847$	−87.6303	−3.01101
$848$	−9.45560	−0.324707
$849$	−11.1741	−0.383495
$850$	−0.681509	−0.0233756
$851$	−3.00794	−0.103111
$852$	1.23860	0.0424337
$853$	−1.04770	−0.0358724	−0.0179362	−	0.999839i	$-0.505710\pi$
$853$	−1.04770	−0.0358724	−0.0179362	+	0.999839i	$0.505710\pi$
$854$	−1.32717	−0.0454147
$855$	62.1711	2.12621
$856$	−0.0261044	−0.000892230 0
$857$	17.1312	0.585192	0.292596	−	0.956236i	$-0.405481\pi$
$857$	17.1312	0.585192	0.292596	+	0.956236i	$0.405481\pi$
$858$	0.706643	0.0241244
$859$	8.20756	0.280038	0.140019	−	0.990149i	$-0.455284\pi$
$859$	8.20756	0.280038	0.140019	+	0.990149i	$0.455284\pi$
$860$	−37.6098	−1.28248
$861$	−15.7025	−0.535140
$862$	−0.105292	−0.00358625
$863$	−24.3392	−0.828516	−0.414258	−	0.910160i	$-0.635959\pi$
$863$	−24.3392	−0.828516	−0.414258	+	0.910160i	$0.635959\pi$
$864$	1.65069	0.0561577
$865$	5.98144	0.203375
$866$	−0.0134060	−0.000455553 0
$867$	−9.43149	−0.320310
$868$	−28.2860	−0.960090
$869$	−30.5086	−1.03493
$870$	0.613594	0.0208028
$871$	−10.6331	−0.360288
$872$	−0.143495	−0.00485934
$873$	16.1129	0.545339
$874$	−0.683146	−0.0231077
$875$	63.5873	2.14964
$876$	8.82836	0.298283
$877$	14.7650	0.498580	0.249290	−	0.968429i	$-0.419803\pi$
$877$	14.7650	0.498580	0.249290	+	0.968429i	$0.419803\pi$
$878$	−1.01791	−0.0343527
$879$	0.431812	0.0145647
$880$	−97.5739	−3.28922
$881$	−8.91632	−0.300399	−0.150199	−	0.988656i	$-0.547992\pi$
$881$	−8.91632	−0.300399	−0.150199	+	0.988656i	$0.547992\pi$
$882$	0.240196	0.00808783
$883$	43.6633	1.46939	0.734693	−	0.678400i	$-0.237326\pi$
$883$	43.6633	1.46939	0.734693	+	0.678400i	$0.237326\pi$
$884$	16.7632	0.563808
$885$	24.9361	0.838219
$886$	0.913671	0.0306954
$887$	22.5380	0.756752	0.378376	−	0.925652i	$-0.376483\pi$
$887$	22.5380	0.756752	0.378376	+	0.925652i	$0.376483\pi$
$888$	−0.0998003	−0.00334908
$889$	−22.3069	−0.748150
$890$	−1.21124	−0.0406010
$891$	30.5547	1.02362
$892$	−40.4247	−1.35352
$893$	24.9075	0.833499
$894$	0.556989	0.0186285
$895$	24.4732	0.818047
$896$	−3.56333	−0.119042
$897$	−9.46110	−0.315897
$898$	0.319646	0.0106667
$899$	−28.6748	−0.956358
$900$	51.5032	1.71677
$901$	−4.39238	−0.146331
$902$	−1.63196	−0.0543385
$903$	10.4192	0.346730
$904$	0.211552	0.00703610
$905$	65.9894	2.19356
$906$	0.126698	0.00420925
$907$	44.2656	1.46981	0.734907	−	0.678168i	$-0.237226\pi$
$907$	44.2656	1.46981	0.734907	+	0.678168i	$0.237226\pi$
$908$	33.9169	1.12557
$909$	−26.2715	−0.871370
$910$	1.96916	0.0652771
$911$	10.0069	0.331543	0.165772	−	0.986164i	$-0.446989\pi$
$911$	10.0069	0.331543	0.165772	+	0.986164i	$0.446989\pi$
$912$	17.5730	0.581899
$913$	106.206	3.51490
$914$	1.09237	0.0361323
$915$	32.3085	1.06809
$916$	38.0139	1.25602
$917$	−27.5288	−0.909080
$918$	0.255323	0.00842691
$919$	55.6311	1.83510	0.917550	−	0.397620i	$-0.130164\pi$
$919$	55.6311	1.83510	0.917550	+	0.397620i	$0.130164\pi$
$920$	−1.68502	−0.0555536
$921$	−12.8543	−0.423564
$922$	−0.621359	−0.0204634
$923$	4.02957	0.132635
$924$	27.0489	0.889843
$925$	−10.2406	−0.336708
$926$	−0.130683	−0.00429452
$927$	34.5754	1.13561
$928$	−2.70952	−0.0889444
$929$	53.8328	1.76620	0.883098	−	0.469189i	$-0.155454\pi$
$929$	53.8328	1.76620	0.883098	+	0.469189i	$0.155454\pi$
$930$	−0.443654	−0.0145480
$931$	16.8353	0.551754
$932$	50.5052	1.65435
$933$	16.6800	0.546079
$934$	0.797821	0.0261055
$935$	−45.3257	−1.48231
$936$	1.63294	0.0533743
$937$	−30.6374	−1.00088	−0.500440	−	0.865771i	$-0.666828\pi$
$937$	−30.6374	−1.00088	−0.500440	+	0.865771i	$0.666828\pi$
$938$	0.262234	0.00856224
$939$	−19.8087	−0.646434
$940$	30.7081	1.00159
$941$	−3.45972	−0.112784	−0.0563919	−	0.998409i	$-0.517960\pi$
$941$	−3.45972	−0.112784	−0.0563919	+	0.998409i	$0.517960\pi$
$942$	−0.129716	−0.00422639
$943$	21.8500	0.711535
$944$	−36.6650	−1.19335
$945$	−46.5515	−1.51432
$946$	1.08287	0.0352072
$947$	26.4932	0.860912	0.430456	−	0.902612i	$-0.358353\pi$
$947$	26.4932	0.860912	0.430456	+	0.902612i	$0.358353\pi$
$948$	6.77418	0.220015
$949$	28.7216	0.932343
$950$	−2.32578	−0.0754582
$951$	−9.04045	−0.293157
$952$	−0.827098	−0.0268064
$953$	38.3694	1.24291	0.621453	−	0.783451i	$-0.286543\pi$
$953$	38.3694	1.24291	0.621453	+	0.783451i	$0.286543\pi$
$954$	−0.213867	−0.00692419
$955$	−50.7154	−1.64111
$956$	−9.01243	−0.291483
$957$	27.4206	0.886384
$958$	−1.22366	−0.0395347
$959$	−30.8002	−0.994591
$960$	21.6375	0.698347
$961$	−10.2670	−0.331192
$962$	−0.162290	−0.00523243
$963$	0.457759	0.0147511
$964$	56.9914	1.83557
$965$	60.9378	1.96166
$966$	0.233330	0.00750728
$967$	−45.5824	−1.46583	−0.732916	−	0.680319i	$-0.761841\pi$
$967$	−45.5824	−1.46583	−0.732916	+	0.680319i	$0.761841\pi$
$968$	4.04576	0.130036
$969$	8.16312	0.262237
$970$	−0.897079	−0.0288035
$971$	−1.28088	−0.0411054	−0.0205527	−	0.999789i	$-0.506543\pi$
$971$	−1.28088	−0.0411054	−0.0205527	+	0.999789i	$0.506543\pi$
$972$	−29.7890	−0.955483
$973$	−49.3855	−1.58323
$974$	1.43152	0.0458689
$975$	−32.2104	−1.03156
$976$	−47.5051	−1.52060
$977$	−2.48348	−0.0794534	−0.0397267	−	0.999211i	$-0.512649\pi$
$977$	−2.48348	−0.0794534	−0.0397267	+	0.999211i	$0.512649\pi$
$978$	−0.483806	−0.0154704
$979$	−54.1287	−1.72996
$980$	20.7560	0.663025
$981$	2.51628	0.0803387
$982$	0.521893	0.0166543
$983$	−20.3960	−0.650532	−0.325266	−	0.945623i	$-0.605454\pi$
$983$	−20.3960	−0.650532	−0.325266	+	0.945623i	$0.605454\pi$
$984$	0.724961	0.0231109
$985$	21.5433	0.686428
$986$	−0.419098	−0.0133468
$987$	−8.50724	−0.270789
$988$	57.2077	1.82002
$989$	−14.4984	−0.461021
$990$	−2.20693	−0.0701407
$991$	−1.39322	−0.0442571	−0.0221286	−	0.999755i	$-0.507044\pi$
$991$	−1.39322	−0.0442571	−0.0221286	+	0.999755i	$0.507044\pi$
$992$	1.95909	0.0622013
$993$	5.75776	0.182717
$994$	−0.0993777	−0.00315207
$995$	−25.7904	−0.817611
$996$	−23.5821	−0.747227
$997$	−30.7049	−0.972435	−0.486217	−	0.873838i	$-0.661624\pi$
$997$	−30.7049	−0.972435	−0.486217	+	0.873838i	$0.661624\pi$
$998$	−1.29289	−0.0409258
$999$	3.83657	0.121384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.41	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.41	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0358852 q^{2} +0.695499 q^{3} -1.99871 q^{4} -3.90392 q^{5} -0.0249581 q^{6} -3.10806 q^{7} +0.143495 q^{8} -2.51628 q^{9} +O(q^{10})\)	\(q-0.0358852 q^{2} +0.695499 q^{3} -1.99871 q^{4} -3.90392 q^{5} -0.0249581 q^{6} -3.10806 q^{7} +0.143495 q^{8} -2.51628 q^{9} +0.140093 q^{10} +6.26055 q^{11} -1.39010 q^{12} -4.52247 q^{13} +0.111534 q^{14} -2.71517 q^{15} +3.99228 q^{16} +1.85452 q^{17} +0.0902973 q^{18} +6.32890 q^{19} +7.80281 q^{20} -2.16166 q^{21} -0.224661 q^{22} +3.00794 q^{23} +0.0998003 q^{24} +10.2406 q^{25} +0.162290 q^{26} -3.83657 q^{27} +6.21213 q^{28} +6.29751 q^{29} +0.0974345 q^{30} -4.55336 q^{31} -0.430253 q^{32} +4.35421 q^{33} -0.0665498 q^{34} +12.1336 q^{35} +5.02932 q^{36} -1.00000 q^{37} -0.227114 q^{38} -3.14537 q^{39} -0.560191 q^{40} +7.26411 q^{41} +0.0775714 q^{42} -4.82003 q^{43} -12.5130 q^{44} +9.82336 q^{45} -0.107941 q^{46} +3.93552 q^{47} +2.77662 q^{48} +2.66006 q^{49} -0.367485 q^{50} +1.28982 q^{51} +9.03911 q^{52} -2.36847 q^{53} +0.137676 q^{54} -24.4407 q^{55} -0.445990 q^{56} +4.40174 q^{57} -0.225987 q^{58} -9.18400 q^{59} +5.42685 q^{60} -11.8993 q^{61} +0.163398 q^{62} +7.82076 q^{63} -7.96911 q^{64} +17.6554 q^{65} -0.156252 q^{66} +2.35117 q^{67} -3.70665 q^{68} +2.09202 q^{69} -0.435418 q^{70} -0.891012 q^{71} -0.361073 q^{72} -6.35087 q^{73} +0.0358852 q^{74} +7.12232 q^{75} -12.6497 q^{76} -19.4582 q^{77} +0.112872 q^{78} -4.87316 q^{79} -15.5855 q^{80} +4.88052 q^{81} -0.260674 q^{82} +16.9643 q^{83} +4.32053 q^{84} -7.23989 q^{85} +0.172968 q^{86} +4.37991 q^{87} +0.898355 q^{88} -8.64600 q^{89} -0.352513 q^{90} +14.0561 q^{91} -6.01201 q^{92} -3.16685 q^{93} -0.141227 q^{94} -24.7075 q^{95} -0.299240 q^{96} -6.40346 q^{97} -0.0954569 q^{98} -15.7533 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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