LMFDB - Embedded newform 4013.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42541 q^{2} +2.84636 q^{3} +3.88263 q^{4} -0.259504 q^{5} -6.90359 q^{6} +3.45507 q^{7} -4.56617 q^{8} +5.10174 q^{9} +O(q^{10})$	\(q-2.42541 q^{2} +2.84636 q^{3} +3.88263 q^{4} -0.259504 q^{5} -6.90359 q^{6} +3.45507 q^{7} -4.56617 q^{8} +5.10174 q^{9} +0.629405 q^{10} +5.35972 q^{11} +11.0514 q^{12} -1.33016 q^{13} -8.37997 q^{14} -0.738641 q^{15} +3.30958 q^{16} +0.650535 q^{17} -12.3738 q^{18} +4.88293 q^{19} -1.00756 q^{20} +9.83435 q^{21} -12.9995 q^{22} -0.877224 q^{23} -12.9969 q^{24} -4.93266 q^{25} +3.22619 q^{26} +5.98231 q^{27} +13.4148 q^{28} -10.3512 q^{29} +1.79151 q^{30} +6.80627 q^{31} +1.10524 q^{32} +15.2557 q^{33} -1.57782 q^{34} -0.896604 q^{35} +19.8082 q^{36} +2.18527 q^{37} -11.8431 q^{38} -3.78611 q^{39} +1.18494 q^{40} +0.175733 q^{41} -23.8524 q^{42} +4.50741 q^{43} +20.8098 q^{44} -1.32392 q^{45} +2.12763 q^{46} -3.23334 q^{47} +9.42024 q^{48} +4.93748 q^{49} +11.9637 q^{50} +1.85166 q^{51} -5.16453 q^{52} +5.17522 q^{53} -14.5096 q^{54} -1.39087 q^{55} -15.7764 q^{56} +13.8985 q^{57} +25.1058 q^{58} +14.9792 q^{59} -2.86787 q^{60} -0.893095 q^{61} -16.5080 q^{62} +17.6269 q^{63} -9.29981 q^{64} +0.345182 q^{65} -37.0013 q^{66} -0.108474 q^{67} +2.52579 q^{68} -2.49689 q^{69} +2.17464 q^{70} -1.82213 q^{71} -23.2954 q^{72} +9.80122 q^{73} -5.30019 q^{74} -14.0401 q^{75} +18.9586 q^{76} +18.5182 q^{77} +9.18289 q^{78} +6.76142 q^{79} -0.858849 q^{80} +1.72256 q^{81} -0.426225 q^{82} -12.9480 q^{83} +38.1832 q^{84} -0.168817 q^{85} -10.9323 q^{86} -29.4631 q^{87} -24.4734 q^{88} -16.7180 q^{89} +3.21106 q^{90} -4.59579 q^{91} -3.40594 q^{92} +19.3731 q^{93} +7.84220 q^{94} -1.26714 q^{95} +3.14590 q^{96} -11.4640 q^{97} -11.9754 q^{98} +27.3439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * 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 $

$2$	−2.42541	−1.71503	−0.857513	−	0.514462i	$-0.827992\pi$
$2$	−2.42541	−1.71503	−0.857513	+	0.514462i	$0.827992\pi$
$3$	2.84636	1.64334	0.821672	−	0.569960i	$-0.193041\pi$
$3$	2.84636	1.64334	0.821672	+	0.569960i	$0.193041\pi$
$4$	3.88263	1.94132
$5$	−0.259504	−0.116054	−0.0580269	−	0.998315i	$-0.518481\pi$
$5$	−0.259504	−0.116054	−0.0580269	+	0.998315i	$0.518481\pi$
$6$	−6.90359	−2.81838
$7$	3.45507	1.30589	0.652946	−	0.757404i	$-0.273533\pi$
$7$	3.45507	1.30589	0.652946	+	0.757404i	$0.273533\pi$
$8$	−4.56617	−1.61438
$9$	5.10174	1.70058
$10$	0.629405	0.199035
$11$	5.35972	1.61602	0.808008	−	0.589171i	$-0.200546\pi$
$11$	5.35972	1.61602	0.808008	+	0.589171i	$0.200546\pi$
$12$	11.0514	3.19025
$13$	−1.33016	−0.368920	−0.184460	−	0.982840i	$-0.559054\pi$
$13$	−1.33016	−0.368920	−0.184460	+	0.982840i	$0.559054\pi$
$14$	−8.37997	−2.23964
$15$	−0.738641	−0.190716
$16$	3.30958	0.827395
$17$	0.650535	0.157778	0.0788890	−	0.996883i	$-0.474863\pi$
$17$	0.650535	0.157778	0.0788890	+	0.996883i	$0.474863\pi$
$18$	−12.3738	−2.91654
$19$	4.88293	1.12022	0.560110	−	0.828418i	$-0.310759\pi$
$19$	4.88293	1.12022	0.560110	+	0.828418i	$0.310759\pi$
$20$	−1.00756	−0.225297
$21$	9.83435	2.14603
$22$	−12.9995	−2.77151
$23$	−0.877224	−0.182914	−0.0914569	−	0.995809i	$-0.529152\pi$
$23$	−0.877224	−0.182914	−0.0914569	+	0.995809i	$0.529152\pi$
$24$	−12.9969	−2.65299
$25$	−4.93266	−0.986532
$26$	3.22619	0.632708
$27$	5.98231	1.15130
$28$	13.4148	2.53515
$29$	−10.3512	−1.92216	−0.961081	−	0.276267i	$-0.910903\pi$
$29$	−10.3512	−1.92216	−0.961081	+	0.276267i	$0.910903\pi$
$30$	1.79151	0.327084
$31$	6.80627	1.22244	0.611221	−	0.791460i	$-0.290679\pi$
$31$	6.80627	1.22244	0.611221	+	0.791460i	$0.290679\pi$
$32$	1.10524	0.195380
$33$	15.2557	2.65567
$34$	−1.57782	−0.270594
$35$	−0.896604	−0.151554
$36$	19.8082	3.30137
$37$	2.18527	0.359256	0.179628	−	0.983735i	$-0.442511\pi$
$37$	2.18527	0.359256	0.179628	+	0.983735i	$0.442511\pi$
$38$	−11.8431	−1.92121
$39$	−3.78611	−0.606263
$40$	1.18494	0.187355
$41$	0.175733	0.0274448	0.0137224	−	0.999906i	$-0.495632\pi$
$41$	0.175733	0.0274448	0.0137224	+	0.999906i	$0.495632\pi$
$42$	−23.8524	−3.68050
$43$	4.50741	0.687374	0.343687	−	0.939084i	$-0.388324\pi$
$43$	4.50741	0.687374	0.343687	+	0.939084i	$0.388324\pi$
$44$	20.8098	3.13720
$45$	−1.32392	−0.197359
$46$	2.12763	0.313702
$47$	−3.23334	−0.471632	−0.235816	−	0.971798i	$-0.575776\pi$
$47$	−3.23334	−0.471632	−0.235816	+	0.971798i	$0.575776\pi$
$48$	9.42024	1.35969
$49$	4.93748	0.705354
$50$	11.9637	1.69193
$51$	1.85166	0.259284
$52$	−5.16453	−0.716191
$53$	5.17522	0.710871	0.355435	−	0.934701i	$-0.384333\pi$
$53$	5.17522	0.710871	0.355435	+	0.934701i	$0.384333\pi$
$54$	−14.5096	−1.97450
$55$	−1.39087	−0.187545
$56$	−15.7764	−2.10821
$57$	13.8985	1.84091
$58$	25.1058	3.29656
$59$	14.9792	1.95013	0.975066	−	0.221916i	$-0.0712310\pi$
$59$	14.9792	1.95013	0.975066	+	0.221916i	$0.0712310\pi$
$60$	−2.86787	−0.370241
$61$	−0.893095	−0.114349	−0.0571746	−	0.998364i	$-0.518209\pi$
$61$	−0.893095	−0.114349	−0.0571746	+	0.998364i	$0.518209\pi$
$62$	−16.5080	−2.09652
$63$	17.6269	2.22078
$64$	−9.29981	−1.16248
$65$	0.345182	0.0428146
$66$	−37.0013	−4.55455
$67$	−0.108474	−0.0132522	−0.00662608	−	0.999978i	$-0.502109\pi$
$67$	−0.108474	−0.0132522	−0.00662608	+	0.999978i	$0.502109\pi$
$68$	2.52579	0.306297
$69$	−2.49689	−0.300590
$70$	2.17464	0.259919
$71$	−1.82213	−0.216247	−0.108123	−	0.994137i	$-0.534484\pi$
$71$	−1.82213	−0.216247	−0.108123	+	0.994137i	$0.534484\pi$
$72$	−23.2954	−2.74539
$73$	9.80122	1.14715	0.573573	−	0.819154i	$-0.305557\pi$
$73$	9.80122	1.14715	0.573573	+	0.819154i	$0.305557\pi$
$74$	−5.30019	−0.616134
$75$	−14.0401	−1.62121
$76$	18.9586	2.17470
$77$	18.5182	2.11034
$78$	9.18289	1.03976
$79$	6.76142	0.760719	0.380359	−	0.924839i	$-0.375800\pi$
$79$	6.76142	0.760719	0.380359	+	0.924839i	$0.375800\pi$
$80$	−0.858849	−0.0960223
$81$	1.72256	0.191395
$82$	−0.426225	−0.0470686
$83$	−12.9480	−1.42123	−0.710615	−	0.703581i	$-0.751583\pi$
$83$	−12.9480	−1.42123	−0.710615	+	0.703581i	$0.751583\pi$
$84$	38.1832	4.16613
$85$	−0.168817	−0.0183107
$86$	−10.9323	−1.17886
$87$	−29.4631	−3.15877
$88$	−24.4734	−2.60887
$89$	−16.7180	−1.77211	−0.886055	−	0.463580i	$-0.846565\pi$
$89$	−16.7180	−1.77211	−0.886055	+	0.463580i	$0.846565\pi$
$90$	3.21106	0.338476
$91$	−4.59579	−0.481770
$92$	−3.40594	−0.355094
$93$	19.3731	2.00889
$94$	7.84220	0.808861
$95$	−1.26714	−0.130006
$96$	3.14590	0.321077
$97$	−11.4640	−1.16399	−0.581997	−	0.813191i	$-0.697728\pi$
$97$	−11.4640	−1.16399	−0.581997	+	0.813191i	$0.697728\pi$
$98$	−11.9754	−1.20970
$99$	27.3439	2.74817
$100$	−19.1517	−1.91517
$101$	−10.6647	−1.06118	−0.530588	−	0.847630i	$-0.678029\pi$
$101$	−10.6647	−1.06118	−0.530588	+	0.847630i	$0.678029\pi$
$102$	−4.49103	−0.444678
$103$	13.3925	1.31960	0.659802	−	0.751440i	$-0.270640\pi$
$103$	13.3925	1.31960	0.659802	+	0.751440i	$0.270640\pi$
$104$	6.07374	0.595579
$105$	−2.55205	−0.249055
$106$	−12.5520	−1.21916
$107$	−4.94923	−0.478460	−0.239230	−	0.970963i	$-0.576895\pi$
$107$	−4.94923	−0.478460	−0.239230	+	0.970963i	$0.576895\pi$
$108$	23.2271	2.23503
$109$	6.54334	0.626738	0.313369	−	0.949631i	$-0.398542\pi$
$109$	6.54334	0.626738	0.313369	+	0.949631i	$0.398542\pi$
$110$	3.37344	0.321644
$111$	6.22006	0.590382
$112$	11.4348	1.08049
$113$	−10.1398	−0.953870	−0.476935	−	0.878939i	$-0.658252\pi$
$113$	−10.1398	−0.953870	−0.476935	+	0.878939i	$0.658252\pi$
$114$	−33.7097	−3.15721
$115$	0.227643	0.0212278
$116$	−40.1898	−3.73153
$117$	−6.78614	−0.627379
$118$	−36.3309	−3.34453
$119$	2.24764	0.206041
$120$	3.37276	0.307889
$121$	17.7266	1.61151
$122$	2.16613	0.196112
$123$	0.500198	0.0451013
$124$	26.4263	2.37315
$125$	2.57757	0.230545
$126$	−42.7524	−3.80869
$127$	−3.30172	−0.292980	−0.146490	−	0.989212i	$-0.546798\pi$
$127$	−3.30172	−0.292980	−0.146490	+	0.989212i	$0.546798\pi$
$128$	20.3454	1.79830
$129$	12.8297	1.12959
$130$	−0.837210	−0.0734282
$131$	7.57366	0.661713	0.330857	−	0.943681i	$-0.392662\pi$
$131$	7.57366	0.661713	0.330857	+	0.943681i	$0.392662\pi$
$132$	59.2322	5.15550
$133$	16.8708	1.46289
$134$	0.263094	0.0227278
$135$	−1.55244	−0.133612
$136$	−2.97045	−0.254714
$137$	13.9068	1.18814	0.594071	−	0.804413i	$-0.297520\pi$
$137$	13.9068	1.18814	0.594071	+	0.804413i	$0.297520\pi$
$138$	6.05599	0.515521
$139$	−6.73165	−0.570971	−0.285486	−	0.958383i	$-0.592155\pi$
$139$	−6.73165	−0.570971	−0.285486	+	0.958383i	$0.592155\pi$
$140$	−3.48119	−0.294214
$141$	−9.20325	−0.775053
$142$	4.41941	0.370869
$143$	−7.12929	−0.596181
$144$	16.8846	1.40705
$145$	2.68617	0.223074
$146$	−23.7720	−1.96739
$147$	14.0538	1.15914
$148$	8.48461	0.697431
$149$	9.05014	0.741417	0.370708	−	0.928749i	$-0.379115\pi$
$149$	9.05014	0.741417	0.370708	+	0.928749i	$0.379115\pi$
$150$	34.0531	2.78042
$151$	−7.41788	−0.603659	−0.301829	−	0.953362i	$-0.597597\pi$
$151$	−7.41788	−0.603659	−0.301829	+	0.953362i	$0.597597\pi$
$152$	−22.2963	−1.80846
$153$	3.31887	0.268314
$154$	−44.9143	−3.61929
$155$	−1.76626	−0.141869
$156$	−14.7001	−1.17695
$157$	−2.34856	−0.187436	−0.0937178	−	0.995599i	$-0.529875\pi$
$157$	−2.34856	−0.187436	−0.0937178	+	0.995599i	$0.529875\pi$
$158$	−16.3992	−1.30465
$159$	14.7305	1.16821
$160$	−0.286813	−0.0226746
$161$	−3.03087	−0.238866
$162$	−4.17792	−0.328248
$163$	9.73509	0.762511	0.381255	−	0.924470i	$-0.375492\pi$
$163$	9.73509	0.762511	0.381255	+	0.924470i	$0.375492\pi$
$164$	0.682306	0.0532791
$165$	−3.95891	−0.308201
$166$	31.4043	2.43745
$167$	16.2729	1.25923	0.629616	−	0.776906i	$-0.283212\pi$
$167$	16.2729	1.25923	0.629616	+	0.776906i	$0.283212\pi$
$168$	−44.9053	−3.46452
$169$	−11.2307	−0.863898
$170$	0.409450	0.0314034
$171$	24.9114	1.90503
$172$	17.5006	1.33441
$173$	1.75848	0.133695	0.0668475	−	0.997763i	$-0.478706\pi$
$173$	1.75848	0.133695	0.0668475	+	0.997763i	$0.478706\pi$
$174$	71.4602	5.41738
$175$	−17.0427	−1.28830
$176$	17.7384	1.33708
$177$	42.6363	3.20474
$178$	40.5482	3.03922
$179$	−13.1963	−0.986337	−0.493169	−	0.869934i	$-0.664161\pi$
$179$	−13.1963	−0.986337	−0.493169	+	0.869934i	$0.664161\pi$
$180$	−5.14031	−0.383136
$181$	−12.2480	−0.910385	−0.455192	−	0.890393i	$-0.650430\pi$
$181$	−12.2480	−0.910385	−0.455192	+	0.890393i	$0.650430\pi$
$182$	11.1467	0.826249
$183$	−2.54207	−0.187915
$184$	4.00555	0.295293
$185$	−0.567087	−0.0416931
$186$	−46.9877	−3.44531
$187$	3.48669	0.254972
$188$	−12.5539	−0.915586
$189$	20.6693	1.50347
$190$	3.07334	0.222963
$191$	−5.08191	−0.367714	−0.183857	−	0.982953i	$-0.558858\pi$
$191$	−5.08191	−0.367714	−0.183857	+	0.982953i	$0.558858\pi$
$192$	−26.4706	−1.91035
$193$	22.8272	1.64314	0.821569	−	0.570109i	$-0.193099\pi$
$193$	22.8272	1.64314	0.821569	+	0.570109i	$0.193099\pi$
$194$	27.8050	1.99628
$195$	0.982512	0.0703591
$196$	19.1704	1.36932
$197$	−7.29648	−0.519853	−0.259926	−	0.965628i	$-0.583698\pi$
$197$	−7.29648	−0.519853	−0.259926	+	0.965628i	$0.583698\pi$
$198$	−66.3203	−4.71318
$199$	−25.2937	−1.79303	−0.896513	−	0.443018i	$-0.853908\pi$
$199$	−25.2937	−1.79303	−0.896513	+	0.443018i	$0.853908\pi$
$200$	22.5233	1.59264
$201$	−0.308755	−0.0217779
$202$	25.8663	1.81995
$203$	−35.7639	−2.51014
$204$	7.18930	0.503352
$205$	−0.0456034	−0.00318508
$206$	−32.4824	−2.26316
$207$	−4.47537	−0.311060
$208$	−4.40227	−0.305243
$209$	26.1711	1.81029
$210$	6.18979	0.427136
$211$	9.35035	0.643704	0.321852	−	0.946790i	$-0.395695\pi$
$211$	9.35035	0.643704	0.321852	+	0.946790i	$0.395695\pi$
$212$	20.0935	1.38003
$213$	−5.18642	−0.355368
$214$	12.0039	0.820573
$215$	−1.16969	−0.0797723
$216$	−27.3162	−1.85863
$217$	23.5161	1.59638
$218$	−15.8703	−1.07487
$219$	27.8978	1.88516
$220$	−5.40024	−0.364084
$221$	−0.865317	−0.0582075
$222$	−15.0862	−1.01252
$223$	−5.09995	−0.341518	−0.170759	−	0.985313i	$-0.554622\pi$
$223$	−5.09995	−0.341518	−0.170759	+	0.985313i	$0.554622\pi$
$224$	3.81866	0.255145
$225$	−25.1652	−1.67768
$226$	24.5932	1.63591
$227$	−25.3299	−1.68120	−0.840602	−	0.541654i	$-0.817798\pi$
$227$	−25.3299	−1.68120	−0.840602	+	0.541654i	$0.817798\pi$
$228$	53.9630	3.57378
$229$	−18.2929	−1.20883	−0.604414	−	0.796670i	$-0.706593\pi$
$229$	−18.2929	−1.20883	−0.604414	+	0.796670i	$0.706593\pi$
$230$	−0.552129	−0.0364063
$231$	52.7093	3.46802
$232$	47.2651	3.10311
$233$	−4.53979	−0.297411	−0.148706	−	0.988882i	$-0.547511\pi$
$233$	−4.53979	−0.297411	−0.148706	+	0.988882i	$0.547511\pi$
$234$	16.4592	1.07597
$235$	0.839066	0.0547346
$236$	58.1589	3.78582
$237$	19.2454	1.25012
$238$	−5.45146	−0.353366
$239$	−10.4496	−0.675932	−0.337966	−	0.941158i	$-0.609739\pi$
$239$	−10.4496	−0.675932	−0.337966	+	0.941158i	$0.609739\pi$
$240$	−2.44459	−0.157798
$241$	26.5259	1.70868	0.854340	−	0.519714i	$-0.173961\pi$
$241$	26.5259	1.70868	0.854340	+	0.519714i	$0.173961\pi$
$242$	−42.9943	−2.76378
$243$	−13.0439	−0.836768
$244$	−3.46756	−0.221988
$245$	−1.28130	−0.0818591
$246$	−1.21319	−0.0773500
$247$	−6.49508	−0.413272
$248$	−31.0786	−1.97349
$249$	−36.8547	−2.33557
$250$	−6.25167	−0.395390
$251$	12.1842	0.769060	0.384530	−	0.923113i	$-0.374364\pi$
$251$	12.1842	0.769060	0.384530	+	0.923113i	$0.374364\pi$
$252$	68.4387	4.31123
$253$	−4.70167	−0.295592
$254$	8.00804	0.502469
$255$	−0.480512	−0.0300909
$256$	−30.7465	−1.92165
$257$	27.8443	1.73688	0.868440	−	0.495794i	$-0.165123\pi$
$257$	27.8443	1.73688	0.868440	+	0.495794i	$0.165123\pi$
$258$	−31.1173	−1.93728
$259$	7.55026	0.469150
$260$	1.34022	0.0831167
$261$	−52.8090	−3.26879
$262$	−18.3693	−1.13486
$263$	−14.7889	−0.911920	−0.455960	−	0.890000i	$-0.650704\pi$
$263$	−14.7889	−0.911920	−0.455960	+	0.890000i	$0.650704\pi$
$264$	−69.6599	−4.28727
$265$	−1.34299	−0.0824993
$266$	−40.9187	−2.50889
$267$	−47.5855	−2.91219
$268$	−0.421163	−0.0257267
$269$	−26.2903	−1.60295	−0.801475	−	0.598028i	$-0.795951\pi$
$269$	−26.2903	−1.60295	−0.801475	+	0.598028i	$0.795951\pi$
$270$	3.76530	0.229149
$271$	1.16440	0.0707324	0.0353662	−	0.999374i	$-0.488740\pi$
$271$	1.16440	0.0707324	0.0353662	+	0.999374i	$0.488740\pi$
$272$	2.15300	0.130545
$273$	−13.0813	−0.791714
$274$	−33.7299	−2.03770
$275$	−26.4377	−1.59425
$276$	−9.69451	−0.583541
$277$	0.998689	0.0600054	0.0300027	−	0.999550i	$-0.490448\pi$
$277$	0.998689	0.0600054	0.0300027	+	0.999550i	$0.490448\pi$
$278$	16.3270	0.979231
$279$	34.7238	2.07886
$280$	4.09404	0.244666
$281$	−28.1329	−1.67827	−0.839134	−	0.543924i	$-0.816938\pi$
$281$	−28.1329	−1.67827	−0.839134	+	0.543924i	$0.816938\pi$
$282$	22.3217	1.32924
$283$	8.14976	0.484453	0.242227	−	0.970220i	$-0.422122\pi$
$283$	8.14976	0.484453	0.242227	+	0.970220i	$0.422122\pi$
$284$	−7.07465	−0.419803
$285$	−3.60673	−0.213644
$286$	17.2915	1.02247
$287$	0.607168	0.0358400
$288$	5.63863	0.332260
$289$	−16.5768	−0.975106
$290$	−6.51507	−0.382578
$291$	−32.6306	−1.91284
$292$	38.0545	2.22697
$293$	−31.6968	−1.85175	−0.925874	−	0.377832i	$-0.876670\pi$
$293$	−31.6968	−1.85175	−0.925874	+	0.377832i	$0.876670\pi$
$294$	−34.0864	−1.98796
$295$	−3.88718	−0.226320
$296$	−9.97832	−0.579978
$297$	32.0635	1.86051
$298$	−21.9503	−1.27155
$299$	1.16685	0.0674806
$300$	−54.5126	−3.14728
$301$	15.5734	0.897636
$302$	17.9914	1.03529
$303$	−30.3555	−1.74388
$304$	16.1604	0.926864
$305$	0.231762	0.0132707
$306$	−8.04962	−0.460166
$307$	7.61874	0.434824	0.217412	−	0.976080i	$-0.430238\pi$
$307$	7.61874	0.434824	0.217412	+	0.976080i	$0.430238\pi$
$308$	71.8993	4.09684
$309$	38.1199	2.16856
$310$	4.28390	0.243309
$311$	−20.7704	−1.17778	−0.588892	−	0.808212i	$-0.700435\pi$
$311$	−20.7704	−1.17778	−0.588892	+	0.808212i	$0.700435\pi$
$312$	17.2880	0.978741
$313$	15.2763	0.863465	0.431733	−	0.902002i	$-0.357902\pi$
$313$	15.2763	0.863465	0.431733	+	0.902002i	$0.357902\pi$
$314$	5.69623	0.321457
$315$	−4.57424	−0.257729
$316$	26.2521	1.47680
$317$	2.98203	0.167488	0.0837438	−	0.996487i	$-0.473312\pi$
$317$	2.98203	0.167488	0.0837438	+	0.996487i	$0.473312\pi$
$318$	−35.7276	−2.00350
$319$	−55.4793	−3.10624
$320$	2.41334	0.134910
$321$	−14.0873	−0.786275
$322$	7.35110	0.409661
$323$	3.17652	0.176746
$324$	6.68807	0.371559
$325$	6.56123	0.363951
$326$	−23.6116	−1.30773
$327$	18.6247	1.02995
$328$	−0.802425	−0.0443065
$329$	−11.1714	−0.615900
$330$	9.60200	0.528573
$331$	27.2001	1.49505	0.747526	−	0.664233i	$-0.231242\pi$
$331$	27.2001	1.49505	0.747526	+	0.664233i	$0.231242\pi$
$332$	−50.2724	−2.75906
$333$	11.1487	0.610945
$334$	−39.4685	−2.15962
$335$	0.0281494	0.00153796
$336$	32.5475	1.77561
$337$	7.92945	0.431944	0.215972	−	0.976400i	$-0.430708\pi$
$337$	7.92945	0.431944	0.215972	+	0.976400i	$0.430708\pi$
$338$	27.2390	1.48161
$339$	−28.8614	−1.56754
$340$	−0.655453	−0.0355470
$341$	36.4797	1.97549
$342$	−60.4205	−3.26717
$343$	−7.12614	−0.384775
$344$	−20.5816	−1.10968
$345$	0.647954	0.0348847
$346$	−4.26505	−0.229291
$347$	16.0308	0.860578	0.430289	−	0.902691i	$-0.358412\pi$
$347$	16.0308	0.860578	0.430289	+	0.902691i	$0.358412\pi$
$348$	−114.394	−6.13218
$349$	35.0012	1.87357	0.936786	−	0.349903i	$-0.113786\pi$
$349$	35.0012	1.87357	0.936786	+	0.349903i	$0.113786\pi$
$350$	41.3355	2.20948
$351$	−7.95744	−0.424737
$352$	5.92376	0.315737
$353$	12.6403	0.672777	0.336389	−	0.941723i	$-0.390794\pi$
$353$	12.6403	0.672777	0.336389	+	0.941723i	$0.390794\pi$
$354$	−103.411	−5.49621
$355$	0.472850	0.0250963
$356$	−64.9101	−3.44023
$357$	6.39759	0.338596
$358$	32.0065	1.69159
$359$	6.13213	0.323642	0.161821	−	0.986820i	$-0.448263\pi$
$359$	6.13213	0.323642	0.161821	+	0.986820i	$0.448263\pi$
$360$	6.04526	0.318613
$361$	4.84296	0.254893
$362$	29.7064	1.56133
$363$	50.4562	2.64826
$364$	−17.8438	−0.935268
$365$	−2.54346	−0.133131
$366$	6.16557	0.322279
$367$	1.14292	0.0596599	0.0298299	−	0.999555i	$-0.490503\pi$
$367$	1.14292	0.0596599	0.0298299	+	0.999555i	$0.490503\pi$
$368$	−2.90324	−0.151342
$369$	0.896543	0.0466722
$370$	1.37542	0.0715048
$371$	17.8807	0.928321
$372$	75.2185	3.89990
$373$	−19.5383	−1.01165	−0.505827	−	0.862635i	$-0.668813\pi$
$373$	−19.5383	−1.01165	−0.505827	+	0.862635i	$0.668813\pi$
$374$	−8.45666	−0.437284
$375$	7.33667	0.378864
$376$	14.7640	0.761394
$377$	13.7687	0.709124
$378$	−50.1316	−2.57849
$379$	17.2241	0.884743	0.442372	−	0.896832i	$-0.354137\pi$
$379$	17.2241	0.884743	0.442372	+	0.896832i	$0.354137\pi$
$380$	−4.91984	−0.252382
$381$	−9.39787	−0.481468
$382$	12.3257	0.630640
$383$	0.981187	0.0501363	0.0250682	−	0.999686i	$-0.492020\pi$
$383$	0.981187	0.0501363	0.0250682	+	0.999686i	$0.492020\pi$
$384$	57.9103	2.95522
$385$	−4.80555	−0.244913
$386$	−55.3654	−2.81803
$387$	22.9956	1.16893
$388$	−44.5105	−2.25968
$389$	15.5938	0.790636	0.395318	−	0.918544i	$-0.370634\pi$
$389$	15.5938	0.790636	0.395318	+	0.918544i	$0.370634\pi$
$390$	−2.38300	−0.120668
$391$	−0.570665	−0.0288598
$392$	−22.5454	−1.13871
$393$	21.5573	1.08742
$394$	17.6970	0.891561
$395$	−1.75462	−0.0882843
$396$	106.166	5.33506
$397$	−6.59322	−0.330904	−0.165452	−	0.986218i	$-0.552908\pi$
$397$	−6.59322	−0.330904	−0.165452	+	0.986218i	$0.552908\pi$
$398$	61.3478	3.07509
$399$	48.0204	2.40403
$400$	−16.3250	−0.816251
$401$	−8.97263	−0.448072	−0.224036	−	0.974581i	$-0.571923\pi$
$401$	−8.97263	−0.448072	−0.224036	+	0.974581i	$0.571923\pi$
$402$	0.748858	0.0373496
$403$	−9.05343	−0.450984
$404$	−41.4071	−2.06008
$405$	−0.447011	−0.0222122
$406$	86.7424	4.30495
$407$	11.7124	0.580564
$408$	−8.45497	−0.418583
$409$	11.7199	0.579510	0.289755	−	0.957101i	$-0.406426\pi$
$409$	11.7199	0.579510	0.289755	+	0.957101i	$0.406426\pi$
$410$	0.110607	0.00546249
$411$	39.5838	1.95253
$412$	51.9982	2.56177
$413$	51.7543	2.54666
$414$	10.8546	0.533476
$415$	3.36007	0.164939
$416$	−1.47014	−0.0720796
$417$	−19.1607	−0.938302
$418$	−63.4758	−3.10470
$419$	0.960090	0.0469035	0.0234517	−	0.999725i	$-0.492534\pi$
$419$	0.960090	0.0469035	0.0234517	+	0.999725i	$0.492534\pi$
$420$	−9.90869	−0.483495
$421$	−11.5995	−0.565327	−0.282664	−	0.959219i	$-0.591218\pi$
$421$	−11.5995	−0.565327	−0.282664	+	0.959219i	$0.591218\pi$
$422$	−22.6785	−1.10397
$423$	−16.4957	−0.802048
$424$	−23.6309	−1.14762
$425$	−3.20887	−0.155653
$426$	12.5792	0.609465
$427$	−3.08570	−0.149328
$428$	−19.2161	−0.928843
$429$	−20.2925	−0.979731
$430$	2.83699	0.136812
$431$	4.29028	0.206656	0.103328	−	0.994647i	$-0.467051\pi$
$431$	4.29028	0.206656	0.103328	+	0.994647i	$0.467051\pi$
$432$	19.7989	0.952576
$433$	28.6140	1.37510	0.687550	−	0.726137i	$-0.258686\pi$
$433$	28.6140	1.37510	0.687550	+	0.726137i	$0.258686\pi$
$434$	−57.0363	−2.73783
$435$	7.64579	0.366588
$436$	25.4054	1.21670
$437$	−4.28342	−0.204904
$438$	−67.6636	−3.23309
$439$	17.1068	0.816462	0.408231	−	0.912879i	$-0.366146\pi$
$439$	17.1068	0.816462	0.408231	+	0.912879i	$0.366146\pi$
$440$	6.35094	0.302769
$441$	25.1898	1.19951
$442$	2.09875	0.0998274
$443$	−38.9841	−1.85219	−0.926096	−	0.377288i	$-0.876857\pi$
$443$	−38.9841	−1.85219	−0.926096	+	0.377288i	$0.876857\pi$
$444$	24.1502	1.14612
$445$	4.33840	0.205660
$446$	12.3695	0.585712
$447$	25.7599	1.21840
$448$	−32.1315	−1.51807
$449$	−34.3468	−1.62092	−0.810462	−	0.585791i	$-0.800784\pi$
$449$	−34.3468	−1.62092	−0.810462	+	0.585791i	$0.800784\pi$
$450$	61.0359	2.87726
$451$	0.941878	0.0443513
$452$	−39.3690	−1.85176
$453$	−21.1139	−0.992019
$454$	61.4355	2.88331
$455$	1.19263	0.0559112
$456$	−63.4631	−2.97193
$457$	2.97028	0.138944	0.0694718	−	0.997584i	$-0.477869\pi$
$457$	2.97028	0.138944	0.0694718	+	0.997584i	$0.477869\pi$
$458$	44.3678	2.07317
$459$	3.89171	0.181649
$460$	0.883855	0.0412100
$461$	16.3322	0.760665	0.380332	−	0.924850i	$-0.375810\pi$
$461$	16.3322	0.760665	0.380332	+	0.924850i	$0.375810\pi$
$462$	−127.842	−5.94775
$463$	−31.2718	−1.45332	−0.726662	−	0.686995i	$-0.758929\pi$
$463$	−31.2718	−1.45332	−0.726662	+	0.686995i	$0.758929\pi$
$464$	−34.2580	−1.59039
$465$	−5.02739	−0.233140
$466$	11.0109	0.510068
$467$	31.2108	1.44426	0.722131	−	0.691756i	$-0.243163\pi$
$467$	31.2108	1.44426	0.722131	+	0.691756i	$0.243163\pi$
$468$	−26.3481	−1.21794
$469$	−0.374784	−0.0173059
$470$	−2.03508	−0.0938714
$471$	−6.68484	−0.308021
$472$	−68.3977	−3.14826
$473$	24.1585	1.11081
$474$	−46.6781	−2.14399
$475$	−24.0858	−1.10513
$476$	8.72677	0.399991
$477$	26.4026	1.20889
$478$	25.3447	1.15924
$479$	−6.53862	−0.298757	−0.149379	−	0.988780i	$-0.547727\pi$
$479$	−6.53862	−0.298757	−0.149379	+	0.988780i	$0.547727\pi$
$480$	−0.816373	−0.0372622
$481$	−2.90676	−0.132537
$482$	−64.3362	−2.93043
$483$	−8.62692	−0.392539
$484$	68.8259	3.12845
$485$	2.97496	0.135086
$486$	31.6369	1.43508
$487$	20.9601	0.949794	0.474897	−	0.880041i	$-0.342485\pi$
$487$	20.9601	0.949794	0.474897	+	0.880041i	$0.342485\pi$
$488$	4.07802	0.184603
$489$	27.7095	1.25307
$490$	3.10768	0.140390
$491$	−14.4449	−0.651889	−0.325944	−	0.945389i	$-0.605682\pi$
$491$	−14.4449	−0.651889	−0.325944	+	0.945389i	$0.605682\pi$
$492$	1.94209	0.0875560
$493$	−6.73380	−0.303275
$494$	15.7532	0.708772
$495$	−7.09586	−0.318935
$496$	22.5259	1.01144
$497$	−6.29557	−0.282395
$498$	89.3879	4.00557
$499$	14.4707	0.647797	0.323899	−	0.946092i	$-0.395006\pi$
$499$	14.4707	0.647797	0.323899	+	0.946092i	$0.395006\pi$
$500$	10.0077	0.447560
$501$	46.3184	2.06935
$502$	−29.5517	−1.31896
$503$	3.33640	0.148763	0.0743813	−	0.997230i	$-0.476302\pi$
$503$	3.33640	0.148763	0.0743813	+	0.997230i	$0.476302\pi$
$504$	−80.4872	−3.58518
$505$	2.76753	0.123154
$506$	11.4035	0.506948
$507$	−31.9665	−1.41968
$508$	−12.8194	−0.568768
$509$	−29.5329	−1.30902	−0.654512	−	0.756051i	$-0.727126\pi$
$509$	−29.5329	−1.30902	−0.654512	+	0.756051i	$0.727126\pi$
$510$	1.16544	0.0516066
$511$	33.8639	1.49805
$512$	33.8820	1.49739
$513$	29.2112	1.28971
$514$	−67.5340	−2.97880
$515$	−3.47541	−0.153145
$516$	49.8130	2.19290
$517$	−17.3298	−0.762164
$518$	−18.3125	−0.804605
$519$	5.00527	0.219707
$520$	−1.57616	−0.0691192
$521$	28.3489	1.24199	0.620994	−	0.783815i	$-0.286729\pi$
$521$	28.3489	1.24199	0.620994	+	0.783815i	$0.286729\pi$
$522$	128.084	5.60607
$523$	−29.5164	−1.29066	−0.645331	−	0.763903i	$-0.723281\pi$
$523$	−29.5164	−1.29066	−0.645331	+	0.763903i	$0.723281\pi$
$524$	29.4057	1.28460
$525$	−48.5095	−2.11713
$526$	35.8691	1.56397
$527$	4.42772	0.192875
$528$	50.4898	2.19729
$529$	−22.2305	−0.966543
$530$	3.25731	0.141488
$531$	76.4203	3.31636
$532$	65.5033	2.83993
$533$	−0.233753	−0.0101250
$534$	115.415	4.99448
$535$	1.28435	0.0555272
$536$	0.495309	0.0213941
$537$	−37.5613	−1.62089
$538$	63.7650	2.74910
$539$	26.4635	1.13986
$540$	−6.02754	−0.259384
$541$	15.5645	0.669170	0.334585	−	0.942366i	$-0.391404\pi$
$541$	15.5645	0.669170	0.334585	+	0.942366i	$0.391404\pi$
$542$	−2.82416	−0.121308
$543$	−34.8621	−1.49608
$544$	0.718995	0.0308267
$545$	−1.69802	−0.0727353
$546$	31.7275	1.35781
$547$	1.91130	0.0817212	0.0408606	−	0.999165i	$-0.486990\pi$
$547$	1.91130	0.0817212	0.0408606	+	0.999165i	$0.486990\pi$
$548$	53.9952	2.30656
$549$	−4.55634	−0.194460
$550$	64.1223	2.73418
$551$	−50.5439	−2.15324
$552$	11.4012	0.485268
$553$	23.3611	0.993417
$554$	−2.42223	−0.102911
$555$	−1.61413	−0.0685161
$556$	−26.1365	−1.10844
$557$	12.8236	0.543354	0.271677	−	0.962388i	$-0.412422\pi$
$557$	12.8236	0.543354	0.271677	+	0.962388i	$0.412422\pi$
$558$	−84.2197	−3.56530
$559$	−5.99558	−0.253586
$560$	−2.96738	−0.125395
$561$	9.92435	0.419007
$562$	68.2340	2.87828
$563$	38.7812	1.63443	0.817217	−	0.576330i	$-0.195516\pi$
$563$	38.7812	1.63443	0.817217	+	0.576330i	$0.195516\pi$
$564$	−35.7328	−1.50462
$565$	2.63131	0.110700
$566$	−19.7666	−0.830850
$567$	5.95156	0.249942
$568$	8.32014	0.349105
$569$	16.8781	0.707565	0.353783	−	0.935328i	$-0.384895\pi$
$569$	16.8781	0.707565	0.353783	+	0.935328i	$0.384895\pi$
$570$	8.74782	0.366406
$571$	−13.0354	−0.545513	−0.272757	−	0.962083i	$-0.587935\pi$
$571$	−13.0354	−0.545513	−0.272757	+	0.962083i	$0.587935\pi$
$572$	−27.6804	−1.15738
$573$	−14.4649	−0.604281
$574$	−1.47263	−0.0614666
$575$	4.32704	0.180450
$576$	−47.4453	−1.97689
$577$	−35.8026	−1.49048	−0.745241	−	0.666796i	$-0.767665\pi$
$577$	−35.8026	−1.49048	−0.745241	+	0.666796i	$0.767665\pi$
$578$	40.2056	1.67233
$579$	64.9744	2.70024
$580$	10.4294	0.433058
$581$	−44.7363	−1.85597
$582$	79.1428	3.28058
$583$	27.7377	1.14878
$584$	−44.7540	−1.85193
$585$	1.76103	0.0728097
$586$	76.8779	3.17580
$587$	−20.1399	−0.831264	−0.415632	−	0.909533i	$-0.636440\pi$
$587$	−20.1399	−0.831264	−0.415632	+	0.909533i	$0.636440\pi$
$588$	54.5659	2.25026
$589$	33.2345	1.36940
$590$	9.42801	0.388145
$591$	−20.7684	−0.854297
$592$	7.23233	0.297247
$593$	−3.59087	−0.147459	−0.0737297	−	0.997278i	$-0.523490\pi$
$593$	−3.59087	−0.147459	−0.0737297	+	0.997278i	$0.523490\pi$
$594$	−77.7673	−3.19083
$595$	−0.583273	−0.0239119
$596$	35.1384	1.43932
$597$	−71.9950	−2.94656
$598$	−2.83009	−0.115731
$599$	25.2689	1.03246	0.516230	−	0.856450i	$-0.327335\pi$
$599$	25.2689	1.03246	0.516230	+	0.856450i	$0.327335\pi$
$600$	64.1094	2.61726
$601$	25.4671	1.03883	0.519413	−	0.854523i	$-0.326151\pi$
$601$	25.4671	1.03883	0.519413	+	0.854523i	$0.326151\pi$
$602$	−37.7719	−1.53947
$603$	−0.553405	−0.0225364
$604$	−28.8009	−1.17189
$605$	−4.60012	−0.187022
$606$	73.6247	2.99080
$607$	−14.1230	−0.573237	−0.286618	−	0.958045i	$-0.592531\pi$
$607$	−14.1230	−0.573237	−0.286618	+	0.958045i	$0.592531\pi$
$608$	5.39679	0.218869
$609$	−101.797	−4.12502
$610$	−0.562119	−0.0227595
$611$	4.30087	0.173994
$612$	12.8859	0.520883
$613$	4.72368	0.190788	0.0953938	−	0.995440i	$-0.469589\pi$
$613$	4.72368	0.190788	0.0953938	+	0.995440i	$0.469589\pi$
$614$	−18.4786	−0.745735
$615$	−0.129803	−0.00523418
$616$	−84.5571	−3.40690
$617$	42.7353	1.72046	0.860230	−	0.509906i	$-0.170320\pi$
$617$	42.7353	1.72046	0.860230	+	0.509906i	$0.170320\pi$
$618$	−92.4565	−3.71914
$619$	7.11208	0.285859	0.142929	−	0.989733i	$-0.454348\pi$
$619$	7.11208	0.285859	0.142929	+	0.989733i	$0.454348\pi$
$620$	−6.85772	−0.275413
$621$	−5.24783	−0.210588
$622$	50.3769	2.01993
$623$	−57.7620	−2.31418
$624$	−12.5304	−0.501619
$625$	23.9944	0.959776
$626$	−37.0513	−1.48087
$627$	74.4923	2.97494
$628$	−9.11860	−0.363872
$629$	1.42160	0.0566828
$630$	11.0944	0.442013
$631$	−1.58840	−0.0632334	−0.0316167	−	0.999500i	$-0.510066\pi$
$631$	−1.58840	−0.0632334	−0.0316167	+	0.999500i	$0.510066\pi$
$632$	−30.8737	−1.22809
$633$	26.6144	1.05783
$634$	−7.23266	−0.287246
$635$	0.856810	0.0340015
$636$	57.1932	2.26786
$637$	−6.56764	−0.260220
$638$	134.560	5.32729
$639$	−9.29603	−0.367745
$640$	−5.27972	−0.208699
$641$	38.1744	1.50780	0.753899	−	0.656990i	$-0.228171\pi$
$641$	38.1744	1.50780	0.753899	+	0.656990i	$0.228171\pi$
$642$	34.1675	1.34848
$643$	4.67520	0.184372	0.0921859	−	0.995742i	$-0.470615\pi$
$643$	4.67520	0.184372	0.0921859	+	0.995742i	$0.470615\pi$
$644$	−11.7677	−0.463714
$645$	−3.32936	−0.131093
$646$	−7.70437	−0.303124
$647$	30.5657	1.20166	0.600830	−	0.799377i	$-0.294837\pi$
$647$	30.5657	1.20166	0.600830	+	0.799377i	$0.294837\pi$
$648$	−7.86549	−0.308986
$649$	80.2846	3.15144
$650$	−15.9137	−0.624186
$651$	66.9352	2.62340
$652$	37.7978	1.48028
$653$	−12.0726	−0.472438	−0.236219	−	0.971700i	$-0.575908\pi$
$653$	−12.0726	−0.472438	−0.236219	+	0.971700i	$0.575908\pi$
$654$	−45.1725	−1.76639
$655$	−1.96540	−0.0767944
$656$	0.581601	0.0227077
$657$	50.0033	1.95081
$658$	27.0953	1.05628
$659$	19.0343	0.741471	0.370735	−	0.928739i	$-0.379106\pi$
$659$	19.0343	0.741471	0.370735	+	0.928739i	$0.379106\pi$
$660$	−15.3710	−0.598315
$661$	18.5987	0.723404	0.361702	−	0.932294i	$-0.382196\pi$
$661$	18.5987	0.723404	0.361702	+	0.932294i	$0.382196\pi$
$662$	−65.9714	−2.56405
$663$	−2.46300	−0.0956550
$664$	59.1228	2.29441
$665$	−4.37805	−0.169774
$666$	−27.0402	−1.04779
$667$	9.08028	0.351590
$668$	63.1816	2.44457
$669$	−14.5163	−0.561231
$670$	−0.0682739	−0.00263765
$671$	−4.78674	−0.184790
$672$	10.8693	0.419292
$673$	5.70234	0.219809	0.109905	−	0.993942i	$-0.464945\pi$
$673$	5.70234	0.219809	0.109905	+	0.993942i	$0.464945\pi$
$674$	−19.2322	−0.740796
$675$	−29.5087	−1.13579
$676$	−43.6046	−1.67710
$677$	−11.5388	−0.443471	−0.221736	−	0.975107i	$-0.571172\pi$
$677$	−11.5388	−0.443471	−0.221736	+	0.975107i	$0.571172\pi$
$678$	70.0009	2.68837
$679$	−39.6089	−1.52005
$680$	0.770845	0.0295606
$681$	−72.0979	−2.76280
$682$	−88.4784	−3.38801
$683$	−25.4162	−0.972525	−0.486262	−	0.873813i	$-0.661640\pi$
$683$	−25.4162	−0.972525	−0.486262	+	0.873813i	$0.661640\pi$
$684$	96.7220	3.69826
$685$	−3.60889	−0.137888
$686$	17.2838	0.659900
$687$	−52.0681	−1.98652
$688$	14.9176	0.568729
$689$	−6.88387	−0.262255
$690$	−1.57156	−0.0598281
$691$	−8.09173	−0.307824	−0.153912	−	0.988085i	$-0.549187\pi$
$691$	−8.09173	−0.307824	−0.153912	+	0.988085i	$0.549187\pi$
$692$	6.82755	0.259544
$693$	94.4750	3.58881
$694$	−38.8813	−1.47591
$695$	1.74689	0.0662634
$696$	134.533	5.09947
$697$	0.114320	0.00433019
$698$	−84.8924	−3.21323
$699$	−12.9218	−0.488749
$700$	−66.1704	−2.50101
$701$	−0.786185	−0.0296938	−0.0148469	−	0.999890i	$-0.504726\pi$
$701$	−0.786185	−0.0296938	−0.0148469	+	0.999890i	$0.504726\pi$
$702$	19.3001	0.728435
$703$	10.6705	0.402446
$704$	−49.8444	−1.87858
$705$	2.38828	0.0899479
$706$	−30.6580	−1.15383
$707$	−36.8472	−1.38578
$708$	165.541	6.22141
$709$	40.7346	1.52982	0.764910	−	0.644138i	$-0.222784\pi$
$709$	40.7346	1.52982	0.764910	+	0.644138i	$0.222784\pi$
$710$	−1.14686	−0.0430407
$711$	34.4950	1.29366
$712$	76.3374	2.86087
$713$	−5.97062	−0.223602
$714$	−15.5168	−0.580702
$715$	1.85008	0.0691891
$716$	−51.2364	−1.91479
$717$	−29.7434	−1.11079
$718$	−14.8730	−0.555054
$719$	−17.2792	−0.644404	−0.322202	−	0.946671i	$-0.604423\pi$
$719$	−17.2792	−0.644404	−0.322202	+	0.946671i	$0.604423\pi$
$720$	−4.38163	−0.163294
$721$	46.2720	1.72326
$722$	−11.7462	−0.437148
$723$	75.5020	2.80795
$724$	−47.5544	−1.76735
$725$	51.0587	1.89627
$726$	−122.377	−4.54184
$727$	−18.1835	−0.674390	−0.337195	−	0.941435i	$-0.609478\pi$
$727$	−18.1835	−0.674390	−0.337195	+	0.941435i	$0.609478\pi$
$728$	20.9852	0.777762
$729$	−42.2953	−1.56649
$730$	6.16894	0.228323
$731$	2.93223	0.108452
$732$	−9.86992	−0.364803
$733$	0.293819	0.0108525	0.00542623	−	0.999985i	$-0.498273\pi$
$733$	0.293819	0.0108525	0.00542623	+	0.999985i	$0.498273\pi$
$734$	−2.77205	−0.102318
$735$	−3.64703	−0.134523
$736$	−0.969539	−0.0357377
$737$	−0.581388	−0.0214157
$738$	−2.17449	−0.0800440
$739$	−29.6406	−1.09035	−0.545174	−	0.838323i	$-0.683537\pi$
$739$	−29.6406	−1.09035	−0.545174	+	0.838323i	$0.683537\pi$
$740$	−2.20179	−0.0809395
$741$	−18.4873	−0.679148
$742$	−43.3682	−1.59209
$743$	−26.2429	−0.962760	−0.481380	−	0.876512i	$-0.659864\pi$
$743$	−26.2429	−0.962760	−0.481380	+	0.876512i	$0.659864\pi$
$744$	−88.4607	−3.24313
$745$	−2.34855	−0.0860442
$746$	47.3884	1.73501
$747$	−66.0575	−2.41692
$748$	13.5375	0.494981
$749$	−17.0999	−0.624818
$750$	−17.7945	−0.649762
$751$	28.9867	1.05774	0.528870	−	0.848703i	$-0.322616\pi$
$751$	28.9867	1.05774	0.528870	+	0.848703i	$0.322616\pi$
$752$	−10.7010	−0.390225
$753$	34.6806	1.26383
$754$	−33.3948	−1.21617
$755$	1.92497	0.0700569
$756$	80.2513	2.91871
$757$	−37.2287	−1.35310	−0.676549	−	0.736397i	$-0.736526\pi$
$757$	−37.2287	−1.35310	−0.676549	+	0.736397i	$0.736526\pi$
$758$	−41.7756	−1.51736
$759$	−13.3826	−0.485759
$760$	5.78597	0.209879
$761$	−38.2931	−1.38812	−0.694061	−	0.719916i	$-0.744180\pi$
$761$	−38.2931	−1.38812	−0.694061	+	0.719916i	$0.744180\pi$
$762$	22.7937	0.825730
$763$	22.6077	0.818452
$764$	−19.7312	−0.713850
$765$	−0.861259	−0.0311389
$766$	−2.37979	−0.0859851
$767$	−19.9248	−0.719443
$768$	−87.5154	−3.15794
$769$	−11.5978	−0.418226	−0.209113	−	0.977891i	$-0.567058\pi$
$769$	−11.5978	−0.418226	−0.209113	+	0.977891i	$0.567058\pi$
$770$	11.6554	0.420033
$771$	79.2548	2.85429
$772$	88.6297	3.18985
$773$	16.6513	0.598905	0.299453	−	0.954111i	$-0.403196\pi$
$773$	16.6513	0.598905	0.299453	+	0.954111i	$0.403196\pi$
$774$	−55.7740	−2.00475
$775$	−33.5730	−1.20598
$776$	52.3466	1.87913
$777$	21.4907	0.770975
$778$	−37.8214	−1.35596
$779$	0.858090	0.0307443
$780$	3.81473	0.136589
$781$	−9.76609	−0.349458
$782$	1.38410	0.0494953
$783$	−61.9239	−2.21298
$784$	16.3410	0.583606
$785$	0.609461	0.0217526
$786$	−52.2854	−1.86496
$787$	19.2970	0.687863	0.343931	−	0.938995i	$-0.388241\pi$
$787$	19.2970	0.687863	0.343931	+	0.938995i	$0.388241\pi$
$788$	−28.3296	−1.00920
$789$	−42.0944	−1.49860
$790$	4.25567	0.151410
$791$	−35.0336	−1.24565
$792$	−124.857	−4.43660
$793$	1.18796	0.0421857
$794$	15.9913	0.567509
$795$	−3.82263	−0.135575
$796$	−98.2063	−3.48083
$797$	−10.1286	−0.358773	−0.179387	−	0.983779i	$-0.557411\pi$
$797$	−10.1286	−0.358773	−0.179387	+	0.983779i	$0.557411\pi$
$798$	−116.469	−4.12297
$799$	−2.10340	−0.0744131
$800$	−5.45175	−0.192749
$801$	−85.2912	−3.01362
$802$	21.7624	0.768455
$803$	52.5318	1.85381
$804$	−1.19878	−0.0422778
$805$	0.786522	0.0277213
$806$	21.9583	0.773449
$807$	−74.8317	−2.63420
$808$	48.6968	1.71315
$809$	34.9840	1.22997	0.614986	−	0.788538i	$-0.289162\pi$
$809$	34.9840	1.22997	0.614986	+	0.788538i	$0.289162\pi$
$810$	1.08419	0.0380945
$811$	−30.2329	−1.06162	−0.530811	−	0.847490i	$-0.678113\pi$
$811$	−30.2329	−1.06162	−0.530811	+	0.847490i	$0.678113\pi$
$812$	−138.858	−4.87297
$813$	3.31430	0.116238
$814$	−28.4075	−0.995683
$815$	−2.52630	−0.0884923
$816$	6.12820	0.214530
$817$	22.0093	0.770010
$818$	−28.4255	−0.993876
$819$	−23.4466	−0.819289
$820$	−0.177061	−0.00618325
$821$	47.9851	1.67469	0.837345	−	0.546675i	$-0.184107\pi$
$821$	47.9851	1.67469	0.837345	+	0.546675i	$0.184107\pi$
$822$	−96.0072	−3.34864
$823$	−32.1645	−1.12118	−0.560591	−	0.828093i	$-0.689426\pi$
$823$	−32.1645	−1.12118	−0.560591	+	0.828093i	$0.689426\pi$
$824$	−61.1524	−2.13035
$825$	−75.2510	−2.61990
$826$	−125.526	−4.36759
$827$	−22.1703	−0.770937	−0.385469	−	0.922721i	$-0.625960\pi$
$827$	−22.1703	−0.770937	−0.385469	+	0.922721i	$0.625960\pi$
$828$	−17.3762	−0.603866
$829$	−53.2104	−1.84807	−0.924037	−	0.382303i	$-0.875131\pi$
$829$	−53.2104	−1.84807	−0.924037	+	0.382303i	$0.875131\pi$
$830$	−8.14955	−0.282875
$831$	2.84262	0.0986095
$832$	12.3702	0.428861
$833$	3.21201	0.111289
$834$	46.4726	1.60921
$835$	−4.22288	−0.146139
$836$	101.613	3.51435
$837$	40.7172	1.40739
$838$	−2.32862	−0.0804407
$839$	−29.0254	−1.00207	−0.501035	−	0.865427i	$-0.667047\pi$
$839$	−29.0254	−1.00207	−0.501035	+	0.865427i	$0.667047\pi$
$840$	11.6531	0.402070
$841$	78.1465	2.69471
$842$	28.1337	0.969551
$843$	−80.0763	−2.75797
$844$	36.3040	1.24963
$845$	2.91441	0.100259
$846$	40.0089	1.37553
$847$	61.2465	2.10446
$848$	17.1278	0.588171
$849$	23.1971	0.796124
$850$	7.78284	0.266949
$851$	−1.91697	−0.0657130
$852$	−20.1370	−0.689882
$853$	37.8481	1.29589	0.647946	−	0.761686i	$-0.275628\pi$
$853$	37.8481	1.29589	0.647946	+	0.761686i	$0.275628\pi$
$854$	7.48411	0.256101
$855$	−6.46462	−0.221085
$856$	22.5990	0.772419
$857$	43.4319	1.48361	0.741803	−	0.670618i	$-0.233971\pi$
$857$	43.4319	1.48361	0.741803	+	0.670618i	$0.233971\pi$
$858$	49.2177	1.68026
$859$	−49.8686	−1.70149	−0.850747	−	0.525575i	$-0.823850\pi$
$859$	−49.8686	−1.70149	−0.850747	+	0.525575i	$0.823850\pi$
$860$	−4.54148	−0.154863
$861$	1.72822	0.0588975
$862$	−10.4057	−0.354420
$863$	53.8851	1.83427	0.917135	−	0.398577i	$-0.130496\pi$
$863$	53.8851	1.83427	0.917135	+	0.398577i	$0.130496\pi$
$864$	6.61187	0.224940
$865$	−0.456334	−0.0155158
$866$	−69.4008	−2.35833
$867$	−47.1835	−1.60244
$868$	91.3045	3.09908
$869$	36.2393	1.22933
$870$	−18.5442	−0.628708
$871$	0.144287	0.00488899
$872$	−29.8780	−1.01180
$873$	−58.4864	−1.97947
$874$	10.3891	0.351415
$875$	8.90566	0.301066
$876$	108.317	3.65969
$877$	21.4445	0.724129	0.362064	−	0.932153i	$-0.382072\pi$
$877$	21.4445	0.724129	0.362064	+	0.932153i	$0.382072\pi$
$878$	−41.4910	−1.40025
$879$	−90.2205	−3.04306
$880$	−4.60319	−0.155174
$881$	−45.3223	−1.52695	−0.763473	−	0.645840i	$-0.776507\pi$
$881$	−45.3223	−1.52695	−0.763473	+	0.645840i	$0.776507\pi$
$882$	−61.0956	−2.05720
$883$	30.2021	1.01638	0.508191	−	0.861245i	$-0.330314\pi$
$883$	30.2021	1.01638	0.508191	+	0.861245i	$0.330314\pi$
$884$	−3.35971	−0.112999
$885$	−11.0643	−0.371922
$886$	94.5527	3.17656
$887$	−24.8683	−0.834996	−0.417498	−	0.908678i	$-0.637093\pi$
$887$	−24.8683	−0.834996	−0.417498	+	0.908678i	$0.637093\pi$
$888$	−28.4018	−0.953103
$889$	−11.4077	−0.382601
$890$	−10.5224	−0.352713
$891$	9.23243	0.309298
$892$	−19.8012	−0.662994
$893$	−15.7882	−0.528331
$894$	−62.4785	−2.08959
$895$	3.42449	0.114468
$896$	70.2948	2.34838
$897$	3.32127	0.110894
$898$	83.3051	2.77993
$899$	−70.4528	−2.34973
$900$	−97.7071	−3.25690
$901$	3.36666	0.112160
$902$	−2.28444	−0.0760637
$903$	44.3274	1.47512
$904$	46.2999	1.53991
$905$	3.17840	0.105654
$906$	51.2100	1.70134
$907$	−32.7106	−1.08614	−0.543068	−	0.839689i	$-0.682737\pi$
$907$	−32.7106	−1.08614	−0.543068	+	0.839689i	$0.682737\pi$
$908$	−98.3467	−3.26375
$909$	−54.4086	−1.80462
$910$	−2.89262	−0.0958893
$911$	−13.4514	−0.445664	−0.222832	−	0.974857i	$-0.571530\pi$
$911$	−13.4514	−0.445664	−0.222832	+	0.974857i	$0.571530\pi$
$912$	45.9983	1.52316
$913$	−69.3978	−2.29673
$914$	−7.20415	−0.238292
$915$	0.659677	0.0218083
$916$	−71.0246	−2.34672
$917$	26.1675	0.864126
$918$	−9.43900	−0.311533
$919$	19.2362	0.634542	0.317271	−	0.948335i	$-0.397233\pi$
$919$	19.2362	0.634542	0.317271	+	0.948335i	$0.397233\pi$
$920$	−1.03946	−0.0342699
$921$	21.6856	0.714566
$922$	−39.6123	−1.30456
$923$	2.42372	0.0797778
$924$	204.651	6.73253
$925$	−10.7792	−0.354418
$926$	75.8471	2.49249
$927$	68.3252	2.24409
$928$	−11.4405	−0.375552
$929$	21.7856	0.714764	0.357382	−	0.933958i	$-0.383669\pi$
$929$	21.7856	0.714764	0.357382	+	0.933958i	$0.383669\pi$
$930$	12.1935	0.399841
$931$	24.1094	0.790152
$932$	−17.6263	−0.577369
$933$	−59.1200	−1.93550
$934$	−75.6991	−2.47695
$935$	−0.904810	−0.0295905
$936$	30.9866	1.01283
$937$	−6.41809	−0.209670	−0.104835	−	0.994490i	$-0.533431\pi$
$937$	−6.41809	−0.209670	−0.104835	+	0.994490i	$0.533431\pi$
$938$	0.909005	0.0296801
$939$	43.4817	1.41897
$940$	3.25779	0.106257
$941$	−24.8932	−0.811496	−0.405748	−	0.913985i	$-0.632989\pi$
$941$	−24.8932	−0.811496	−0.405748	+	0.913985i	$0.632989\pi$
$942$	16.2135	0.528265
$943$	−0.154157	−0.00502004
$944$	49.5750	1.61353
$945$	−5.36377	−0.174483
$946$	−58.5942	−1.90506
$947$	−14.0718	−0.457271	−0.228635	−	0.973512i	$-0.573426\pi$
$947$	−14.0718	−0.457271	−0.228635	+	0.973512i	$0.573426\pi$
$948$	74.7228	2.42688
$949$	−13.0372	−0.423205
$950$	58.4180	1.89533
$951$	8.48792	0.275240
$952$	−10.2631	−0.332629
$953$	8.71300	0.282242	0.141121	−	0.989992i	$-0.454929\pi$
$953$	8.71300	0.282242	0.141121	+	0.989992i	$0.454929\pi$
$954$	−64.0373	−2.07329
$955$	1.31878	0.0426746
$956$	−40.5722	−1.31220
$957$	−157.914	−5.10463
$958$	15.8589	0.512377
$959$	48.0491	1.55159
$960$	6.86923	0.221703
$961$	15.3253	0.494365
$962$	7.05010	0.227304
$963$	−25.2497	−0.813661
$964$	102.990	3.31709
$965$	−5.92376	−0.190692
$966$	20.9239	0.673214
$967$	−33.1594	−1.06634	−0.533168	−	0.846010i	$-0.678999\pi$
$967$	−33.1594	−1.06634	−0.533168	+	0.846010i	$0.678999\pi$
$968$	−80.9426	−2.60159
$969$	9.04150	0.290455
$970$	−7.21551	−0.231676
$971$	−7.63422	−0.244994	−0.122497	−	0.992469i	$-0.539090\pi$
$971$	−7.63422	−0.244994	−0.122497	+	0.992469i	$0.539090\pi$
$972$	−50.6448	−1.62443
$973$	−23.2583	−0.745627
$974$	−50.8370	−1.62892
$975$	18.6756	0.598098
$976$	−2.95577	−0.0946118
$977$	−55.6597	−1.78071	−0.890356	−	0.455266i	$-0.849544\pi$
$977$	−55.6597	−1.78071	−0.890356	+	0.455266i	$0.849544\pi$
$978$	−67.2071	−2.14905
$979$	−89.6041	−2.86376
$980$	−4.97481	−0.158914
$981$	33.3824	1.06582
$982$	35.0348	1.11801
$983$	28.7880	0.918196	0.459098	−	0.888386i	$-0.348173\pi$
$983$	28.7880	0.918196	0.459098	+	0.888386i	$0.348173\pi$
$984$	−2.28399	−0.0728108
$985$	1.89347	0.0603309
$986$	16.3322	0.520125
$987$	−31.7978	−1.01214
$988$	−25.2180	−0.802292
$989$	−3.95401	−0.125730
$990$	17.2104	0.546982
$991$	−59.8157	−1.90011	−0.950054	−	0.312086i	$-0.898972\pi$
$991$	−59.8157	−1.90011	−0.950054	+	0.312086i	$0.898972\pi$
$992$	7.52254	0.238841
$993$	77.4211	2.45688
$994$	15.2694	0.484315
$995$	6.56383	0.208087
$996$	−143.093	−4.53408
$997$	−36.8728	−1.16777	−0.583887	−	0.811835i	$-0.698469\pi$
$997$	−36.8728	−1.16777	−0.583887	+	0.811835i	$0.698469\pi$
$998$	−35.0974	−1.11099
$999$	13.0730	0.413611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.15	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.15	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42541 q^{2} +2.84636 q^{3} +3.88263 q^{4} -0.259504 q^{5} -6.90359 q^{6} +3.45507 q^{7} -4.56617 q^{8} +5.10174 q^{9} +O(q^{10})\)	\(q-2.42541 q^{2} +2.84636 q^{3} +3.88263 q^{4} -0.259504 q^{5} -6.90359 q^{6} +3.45507 q^{7} -4.56617 q^{8} +5.10174 q^{9} +0.629405 q^{10} +5.35972 q^{11} +11.0514 q^{12} -1.33016 q^{13} -8.37997 q^{14} -0.738641 q^{15} +3.30958 q^{16} +0.650535 q^{17} -12.3738 q^{18} +4.88293 q^{19} -1.00756 q^{20} +9.83435 q^{21} -12.9995 q^{22} -0.877224 q^{23} -12.9969 q^{24} -4.93266 q^{25} +3.22619 q^{26} +5.98231 q^{27} +13.4148 q^{28} -10.3512 q^{29} +1.79151 q^{30} +6.80627 q^{31} +1.10524 q^{32} +15.2557 q^{33} -1.57782 q^{34} -0.896604 q^{35} +19.8082 q^{36} +2.18527 q^{37} -11.8431 q^{38} -3.78611 q^{39} +1.18494 q^{40} +0.175733 q^{41} -23.8524 q^{42} +4.50741 q^{43} +20.8098 q^{44} -1.32392 q^{45} +2.12763 q^{46} -3.23334 q^{47} +9.42024 q^{48} +4.93748 q^{49} +11.9637 q^{50} +1.85166 q^{51} -5.16453 q^{52} +5.17522 q^{53} -14.5096 q^{54} -1.39087 q^{55} -15.7764 q^{56} +13.8985 q^{57} +25.1058 q^{58} +14.9792 q^{59} -2.86787 q^{60} -0.893095 q^{61} -16.5080 q^{62} +17.6269 q^{63} -9.29981 q^{64} +0.345182 q^{65} -37.0013 q^{66} -0.108474 q^{67} +2.52579 q^{68} -2.49689 q^{69} +2.17464 q^{70} -1.82213 q^{71} -23.2954 q^{72} +9.80122 q^{73} -5.30019 q^{74} -14.0401 q^{75} +18.9586 q^{76} +18.5182 q^{77} +9.18289 q^{78} +6.76142 q^{79} -0.858849 q^{80} +1.72256 q^{81} -0.426225 q^{82} -12.9480 q^{83} +38.1832 q^{84} -0.168817 q^{85} -10.9323 q^{86} -29.4631 q^{87} -24.4734 q^{88} -16.7180 q^{89} +3.21106 q^{90} -4.59579 q^{91} -3.40594 q^{92} +19.3731 q^{93} +7.84220 q^{94} -1.26714 q^{95} +3.14590 q^{96} -11.4640 q^{97} -11.9754 q^{98} +27.3439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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