LMFDB - Embedded newform 4027.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, 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("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50865 q^{2} -1.26179 q^{3} +4.29331 q^{4} -1.32725 q^{5} +3.16538 q^{6} -1.28298 q^{7} -5.75310 q^{8} -1.40789 q^{9} +O(q^{10})$	\(q-2.50865 q^{2} -1.26179 q^{3} +4.29331 q^{4} -1.32725 q^{5} +3.16538 q^{6} -1.28298 q^{7} -5.75310 q^{8} -1.40789 q^{9} +3.32960 q^{10} +0.495698 q^{11} -5.41725 q^{12} -1.46946 q^{13} +3.21853 q^{14} +1.67471 q^{15} +5.84588 q^{16} -0.136396 q^{17} +3.53189 q^{18} -6.52844 q^{19} -5.69830 q^{20} +1.61885 q^{21} -1.24353 q^{22} -5.31274 q^{23} +7.25920 q^{24} -3.23840 q^{25} +3.68636 q^{26} +5.56183 q^{27} -5.50821 q^{28} -0.800090 q^{29} -4.20126 q^{30} -7.02532 q^{31} -3.15904 q^{32} -0.625467 q^{33} +0.342170 q^{34} +1.70283 q^{35} -6.04449 q^{36} +4.87496 q^{37} +16.3775 q^{38} +1.85415 q^{39} +7.63581 q^{40} -1.51408 q^{41} -4.06111 q^{42} -5.37060 q^{43} +2.12818 q^{44} +1.86862 q^{45} +13.3278 q^{46} +3.92264 q^{47} -7.37626 q^{48} -5.35397 q^{49} +8.12401 q^{50} +0.172104 q^{51} -6.30885 q^{52} -11.2735 q^{53} -13.9527 q^{54} -0.657916 q^{55} +7.38109 q^{56} +8.23751 q^{57} +2.00714 q^{58} -14.6776 q^{59} +7.19005 q^{60} -0.888705 q^{61} +17.6241 q^{62} +1.80629 q^{63} -3.76684 q^{64} +1.95034 q^{65} +1.56907 q^{66} -3.05723 q^{67} -0.585592 q^{68} +6.70356 q^{69} -4.27180 q^{70} +8.58849 q^{71} +8.09972 q^{72} +0.232212 q^{73} -12.2295 q^{74} +4.08618 q^{75} -28.0286 q^{76} -0.635968 q^{77} -4.65141 q^{78} -2.17991 q^{79} -7.75895 q^{80} -2.79419 q^{81} +3.79829 q^{82} +1.17038 q^{83} +6.95020 q^{84} +0.181032 q^{85} +13.4729 q^{86} +1.00954 q^{87} -2.85180 q^{88} -3.90114 q^{89} -4.68771 q^{90} +1.88528 q^{91} -22.8092 q^{92} +8.86448 q^{93} -9.84053 q^{94} +8.66487 q^{95} +3.98604 q^{96} -12.1943 q^{97} +13.4312 q^{98} -0.697887 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.50865	−1.77388	−0.886941	−	0.461884i	$-0.847174\pi$
$2$	−2.50865	−1.77388	−0.886941	+	0.461884i	$0.847174\pi$
$3$	−1.26179	−0.728494	−0.364247	−	0.931302i	$-0.618674\pi$
$3$	−1.26179	−0.728494	−0.364247	+	0.931302i	$0.618674\pi$
$4$	4.29331	2.14665
$5$	−1.32725	−0.593565	−0.296782	−	0.954945i	$-0.595914\pi$
$5$	−1.32725	−0.593565	−0.296782	+	0.954945i	$0.595914\pi$
$6$	3.16538	1.29226
$7$	−1.28298	−0.484919	−0.242460	−	0.970162i	$-0.577954\pi$
$7$	−1.28298	−0.484919	−0.242460	+	0.970162i	$0.577954\pi$
$8$	−5.75310	−2.03403
$9$	−1.40789	−0.469296
$10$	3.32960	1.05291
$11$	0.495698	0.149459	0.0747293	−	0.997204i	$-0.476191\pi$
$11$	0.495698	0.149459	0.0747293	+	0.997204i	$0.476191\pi$
$12$	−5.41725	−1.56383
$13$	−1.46946	−0.407555	−0.203778	−	0.979017i	$-0.565322\pi$
$13$	−1.46946	−0.407555	−0.203778	+	0.979017i	$0.565322\pi$
$14$	3.21853	0.860189
$15$	1.67471	0.432409
$16$	5.84588	1.46147
$17$	−0.136396	−0.0330810	−0.0165405	−	0.999863i	$-0.505265\pi$
$17$	−0.136396	−0.0330810	−0.0165405	+	0.999863i	$0.505265\pi$
$18$	3.53189	0.832475
$19$	−6.52844	−1.49773	−0.748863	−	0.662725i	$-0.769400\pi$
$19$	−6.52844	−1.49773	−0.748863	+	0.662725i	$0.769400\pi$
$20$	−5.69830	−1.27418
$21$	1.61885	0.353261
$22$	−1.24353	−0.265122
$23$	−5.31274	−1.10778	−0.553891	−	0.832589i	$-0.686858\pi$
$23$	−5.31274	−1.10778	−0.553891	+	0.832589i	$0.686858\pi$
$24$	7.25920	1.48178
$25$	−3.23840	−0.647681
$26$	3.68636	0.722954
$27$	5.56183	1.07037
$28$	−5.50821	−1.04095
$29$	−0.800090	−0.148573	−0.0742865	−	0.997237i	$-0.523668\pi$
$29$	−0.800090	−0.148573	−0.0742865	+	0.997237i	$0.523668\pi$
$30$	−4.20126	−0.767042
$31$	−7.02532	−1.26179	−0.630893	−	0.775870i	$-0.717311\pi$
$31$	−7.02532	−1.26179	−0.630893	+	0.775870i	$0.717311\pi$
$32$	−3.15904	−0.558445
$33$	−0.625467	−0.108880
$34$	0.342170	0.0586817
$35$	1.70283	0.287831
$36$	−6.04449	−1.00742
$37$	4.87496	0.801438	0.400719	−	0.916201i	$-0.368760\pi$
$37$	4.87496	0.801438	0.400719	+	0.916201i	$0.368760\pi$
$38$	16.3775	2.65679
$39$	1.85415	0.296902
$40$	7.63581	1.20733
$41$	−1.51408	−0.236459	−0.118230	−	0.992986i	$-0.537722\pi$
$41$	−1.51408	−0.236459	−0.118230	+	0.992986i	$0.537722\pi$
$42$	−4.06111	−0.626643
$43$	−5.37060	−0.819010	−0.409505	−	0.912308i	$-0.634298\pi$
$43$	−5.37060	−0.819010	−0.409505	+	0.912308i	$0.634298\pi$
$44$	2.12818	0.320836
$45$	1.86862	0.278557
$46$	13.3278	1.96507
$47$	3.92264	0.572176	0.286088	−	0.958203i	$-0.407645\pi$
$47$	3.92264	0.572176	0.286088	+	0.958203i	$0.407645\pi$
$48$	−7.37626	−1.06467
$49$	−5.35397	−0.764853
$50$	8.12401	1.14891
$51$	0.172104	0.0240993
$52$	−6.30885	−0.874880
$53$	−11.2735	−1.54854	−0.774269	−	0.632856i	$-0.781882\pi$
$53$	−11.2735	−1.54854	−0.774269	+	0.632856i	$0.781882\pi$
$54$	−13.9527	−1.89872
$55$	−0.657916	−0.0887133
$56$	7.38109	0.986339
$57$	8.23751	1.09108
$58$	2.00714	0.263551
$59$	−14.6776	−1.91086	−0.955432	−	0.295211i	$-0.904610\pi$
$59$	−14.6776	−1.91086	−0.955432	+	0.295211i	$0.904610\pi$
$60$	7.19005	0.928232
$61$	−0.888705	−0.113787	−0.0568935	−	0.998380i	$-0.518120\pi$
$61$	−0.888705	−0.113787	−0.0568935	+	0.998380i	$0.518120\pi$
$62$	17.6241	2.23826
$63$	1.80629	0.227571
$64$	−3.76684	−0.470855
$65$	1.95034	0.241910
$66$	1.56907	0.193140
$67$	−3.05723	−0.373500	−0.186750	−	0.982408i	$-0.559795\pi$
$67$	−3.05723	−0.373500	−0.186750	+	0.982408i	$0.559795\pi$
$68$	−0.585592	−0.0710134
$69$	6.70356	0.807014
$70$	−4.27180	−0.510578
$71$	8.58849	1.01927	0.509633	−	0.860392i	$-0.329781\pi$
$71$	8.58849	1.01927	0.509633	+	0.860392i	$0.329781\pi$
$72$	8.09972	0.954561
$73$	0.232212	0.0271784	0.0135892	−	0.999908i	$-0.495674\pi$
$73$	0.232212	0.0271784	0.0135892	+	0.999908i	$0.495674\pi$
$74$	−12.2295	−1.42166
$75$	4.08618	0.471832
$76$	−28.0286	−3.21510
$77$	−0.635968	−0.0724753
$78$	−4.65141	−0.526668
$79$	−2.17991	−0.245259	−0.122629	−	0.992453i	$-0.539133\pi$
$79$	−2.17991	−0.245259	−0.122629	+	0.992453i	$0.539133\pi$
$80$	−7.75895	−0.867477
$81$	−2.79419	−0.310466
$82$	3.79829	0.419451
$83$	1.17038	0.128466	0.0642328	−	0.997935i	$-0.479540\pi$
$83$	1.17038	0.128466	0.0642328	+	0.997935i	$0.479540\pi$
$84$	6.95020	0.758329
$85$	0.181032	0.0196357
$86$	13.4729	1.45283
$87$	1.00954	0.108235
$88$	−2.85180	−0.304003
$89$	−3.90114	−0.413520	−0.206760	−	0.978392i	$-0.566292\pi$
$89$	−3.90114	−0.413520	−0.206760	+	0.978392i	$0.566292\pi$
$90$	−4.68771	−0.494128
$91$	1.88528	0.197631
$92$	−22.8092	−2.37803
$93$	8.86448	0.919204
$94$	−9.84053	−1.01497
$95$	8.66487	0.888997
$96$	3.98604	0.406824
$97$	−12.1943	−1.23814	−0.619072	−	0.785334i	$-0.712491\pi$
$97$	−12.1943	−1.23814	−0.619072	+	0.785334i	$0.712491\pi$
$98$	13.4312	1.35676
$99$	−0.697887	−0.0701403
$100$	−13.9035	−1.39035
$101$	−8.74945	−0.870603	−0.435301	−	0.900285i	$-0.643358\pi$
$101$	−8.74945	−0.870603	−0.435301	+	0.900285i	$0.643358\pi$
$102$	−0.431747	−0.0427493
$103$	9.18930	0.905448	0.452724	−	0.891651i	$-0.350452\pi$
$103$	9.18930	0.905448	0.452724	+	0.891651i	$0.350452\pi$
$104$	8.45395	0.828978
$105$	−2.14861	−0.209683
$106$	28.2813	2.74692
$107$	−5.18893	−0.501633	−0.250817	−	0.968035i	$-0.580699\pi$
$107$	−5.18893	−0.501633	−0.250817	+	0.968035i	$0.580699\pi$
$108$	23.8786	2.29772
$109$	2.50207	0.239655	0.119827	−	0.992795i	$-0.461766\pi$
$109$	2.50207	0.239655	0.119827	+	0.992795i	$0.461766\pi$
$110$	1.65048	0.157367
$111$	−6.15117	−0.583843
$112$	−7.50012	−0.708694
$113$	13.8422	1.30217	0.651084	−	0.759005i	$-0.274314\pi$
$113$	13.8422	1.30217	0.651084	+	0.759005i	$0.274314\pi$
$114$	−20.6650	−1.93545
$115$	7.05134	0.657541
$116$	−3.43503	−0.318935
$117$	2.06884	0.191264
$118$	36.8210	3.38965
$119$	0.174993	0.0160416
$120$	−9.63478	−0.879531
$121$	−10.7543	−0.977662
$122$	2.22945	0.201845
$123$	1.91045	0.172259
$124$	−30.1619	−2.70862
$125$	10.9344	0.978005
$126$	−4.53133	−0.403683
$127$	−20.5289	−1.82164	−0.910821	−	0.412801i	$-0.864550\pi$
$127$	−20.5289	−1.82164	−0.910821	+	0.412801i	$0.864550\pi$
$128$	15.7677	1.39368
$129$	6.77657	0.596644
$130$	−4.89272	−0.429120
$131$	6.92706	0.605220	0.302610	−	0.953114i	$-0.402142\pi$
$131$	6.92706	0.605220	0.302610	+	0.953114i	$0.402142\pi$
$132$	−2.68532	−0.233727
$133$	8.37582	0.726276
$134$	7.66950	0.662544
$135$	−7.38194	−0.635336
$136$	0.784702	0.0672876
$137$	13.9823	1.19459	0.597295	−	0.802022i	$-0.296242\pi$
$137$	13.9823	1.19459	0.597295	+	0.802022i	$0.296242\pi$
$138$	−16.8169	−1.43155
$139$	−8.38431	−0.711148	−0.355574	−	0.934648i	$-0.615715\pi$
$139$	−8.38431	−0.711148	−0.355574	+	0.934648i	$0.615715\pi$
$140$	7.31078	0.617873
$141$	−4.94955	−0.416827
$142$	−21.5455	−1.80806
$143$	−0.728409	−0.0609126
$144$	−8.23034	−0.685861
$145$	1.06192	0.0881877
$146$	−0.582539	−0.0482112
$147$	6.75559	0.557191
$148$	20.9297	1.72041
$149$	−11.0540	−0.905583	−0.452792	−	0.891616i	$-0.649572\pi$
$149$	−11.0540	−0.905583	−0.452792	+	0.891616i	$0.649572\pi$
$150$	−10.2508	−0.836974
$151$	−10.7265	−0.872913	−0.436457	−	0.899725i	$-0.643767\pi$
$151$	−10.7265	−0.872913	−0.436457	+	0.899725i	$0.643767\pi$
$152$	37.5587	3.04642
$153$	0.192031	0.0155248
$154$	1.59542	0.128563
$155$	9.32437	0.748951
$156$	7.96044	0.637345
$157$	−2.88338	−0.230118	−0.115059	−	0.993359i	$-0.536706\pi$
$157$	−2.88338	−0.230118	−0.115059	+	0.993359i	$0.536706\pi$
$158$	5.46862	0.435060
$159$	14.2248	1.12810
$160$	4.19284	0.331473
$161$	6.81612	0.537185
$162$	7.00964	0.550729
$163$	−14.1435	−1.10781	−0.553903	−	0.832581i	$-0.686862\pi$
$163$	−14.1435	−1.10781	−0.553903	+	0.832581i	$0.686862\pi$
$164$	−6.50041	−0.507597
$165$	0.830151	0.0646272
$166$	−2.93606	−0.227883
$167$	−16.9374	−1.31065	−0.655326	−	0.755346i	$-0.727469\pi$
$167$	−16.9374	−1.31065	−0.655326	+	0.755346i	$0.727469\pi$
$168$	−9.31338	−0.718542
$169$	−10.8407	−0.833899
$170$	−0.454146	−0.0348314
$171$	9.19130	0.702876
$172$	−23.0577	−1.75813
$173$	−11.8132	−0.898141	−0.449070	−	0.893496i	$-0.648245\pi$
$173$	−11.8132	−0.898141	−0.449070	+	0.893496i	$0.648245\pi$
$174$	−2.53259	−0.191995
$175$	4.15479	0.314073
$176$	2.89779	0.218429
$177$	18.5201	1.39205
$178$	9.78658	0.733535
$179$	6.23628	0.466121	0.233061	−	0.972462i	$-0.425126\pi$
$179$	6.23628	0.466121	0.233061	+	0.972462i	$0.425126\pi$
$180$	8.02256	0.597966
$181$	2.52235	0.187485	0.0937423	−	0.995596i	$-0.470117\pi$
$181$	2.52235	0.187485	0.0937423	+	0.995596i	$0.470117\pi$
$182$	−4.72951	−0.350574
$183$	1.12136	0.0828932
$184$	30.5647	2.25326
$185$	−6.47029	−0.475705
$186$	−22.2378	−1.63056
$187$	−0.0676114	−0.00494424
$188$	16.8411	1.22826
$189$	−7.13569	−0.519045
$190$	−21.7371	−1.57698
$191$	−14.5806	−1.05501	−0.527506	−	0.849551i	$-0.676873\pi$
$191$	−14.5806	−1.05501	−0.527506	+	0.849551i	$0.676873\pi$
$192$	4.75296	0.343015
$193$	−8.19903	−0.590179	−0.295090	−	0.955470i	$-0.595350\pi$
$193$	−8.19903	−0.590179	−0.295090	+	0.955470i	$0.595350\pi$
$194$	30.5912	2.19632
$195$	−2.46092	−0.176230
$196$	−22.9863	−1.64188
$197$	13.1145	0.934370	0.467185	−	0.884160i	$-0.345268\pi$
$197$	13.1145	0.934370	0.467185	+	0.884160i	$0.345268\pi$
$198$	1.75075	0.124421
$199$	−14.8296	−1.05124	−0.525620	−	0.850719i	$-0.676167\pi$
$199$	−14.8296	−1.05124	−0.525620	+	0.850719i	$0.676167\pi$
$200$	18.6309	1.31740
$201$	3.85758	0.272092
$202$	21.9493	1.54435
$203$	1.02650	0.0720459
$204$	0.738894	0.0517329
$205$	2.00956	0.140354
$206$	−23.0527	−1.60616
$207$	7.47974	0.519878
$208$	−8.59029	−0.595629
$209$	−3.23613	−0.223848
$210$	5.39011	0.371953
$211$	0.665975	0.0458476	0.0229238	−	0.999737i	$-0.492702\pi$
$211$	0.665975	0.0458476	0.0229238	+	0.999737i	$0.492702\pi$
$212$	−48.4007	−3.32418
$213$	−10.8369	−0.742530
$214$	13.0172	0.889838
$215$	7.12814	0.486135
$216$	−31.9977	−2.17717
$217$	9.01332	0.611864
$218$	−6.27681	−0.425119
$219$	−0.293003	−0.0197993
$220$	−2.82463	−0.190437
$221$	0.200429	0.0134823
$222$	15.4311	1.03567
$223$	−18.9018	−1.26576	−0.632878	−	0.774252i	$-0.718126\pi$
$223$	−18.9018	−1.26576	−0.632878	+	0.774252i	$0.718126\pi$
$224$	4.05297	0.270801
$225$	4.55931	0.303954
$226$	−34.7253	−2.30989
$227$	8.09957	0.537587	0.268794	−	0.963198i	$-0.413375\pi$
$227$	8.09957	0.537587	0.268794	+	0.963198i	$0.413375\pi$
$228$	35.3662	2.34218
$229$	−23.3047	−1.54002	−0.770009	−	0.638033i	$-0.779748\pi$
$229$	−23.3047	−1.54002	−0.770009	+	0.638033i	$0.779748\pi$
$230$	−17.6893	−1.16640
$231$	0.802458	0.0527979
$232$	4.60299	0.302201
$233$	−3.87260	−0.253703	−0.126851	−	0.991922i	$-0.540487\pi$
$233$	−3.87260	−0.253703	−0.126851	+	0.991922i	$0.540487\pi$
$234$	−5.18998	−0.339279
$235$	−5.20633	−0.339624
$236$	−63.0156	−4.10196
$237$	2.75059	0.178670
$238$	−0.438996	−0.0284559
$239$	−16.8934	−1.09274	−0.546372	−	0.837543i	$-0.683991\pi$
$239$	−16.8934	−1.09274	−0.546372	+	0.837543i	$0.683991\pi$
$240$	9.79016	0.631952
$241$	−11.1519	−0.718360	−0.359180	−	0.933268i	$-0.616944\pi$
$241$	−11.1519	−0.718360	−0.359180	+	0.933268i	$0.616944\pi$
$242$	26.9787	1.73426
$243$	−13.1598	−0.844201
$244$	−3.81549	−0.244261
$245$	7.10607	0.453990
$246$	−4.79264	−0.305568
$247$	9.59328	0.610406
$248$	40.4174	2.56651
$249$	−1.47677	−0.0935864
$250$	−27.4306	−1.73487
$251$	−21.0799	−1.33055	−0.665277	−	0.746597i	$-0.731686\pi$
$251$	−21.0799	−1.33055	−0.665277	+	0.746597i	$0.731686\pi$
$252$	7.75494	0.488515
$253$	−2.63351	−0.165568
$254$	51.4997	3.23138
$255$	−0.228425	−0.0143045
$256$	−32.0220	−2.00138
$257$	23.6370	1.47444	0.737218	−	0.675655i	$-0.236139\pi$
$257$	23.6370	1.47444	0.737218	+	0.675655i	$0.236139\pi$
$258$	−17.0000	−1.05838
$259$	−6.25445	−0.388633
$260$	8.37343	0.519298
$261$	1.12644	0.0697246
$262$	−17.3775	−1.07359
$263$	5.64893	0.348328	0.174164	−	0.984717i	$-0.444278\pi$
$263$	5.64893	0.348328	0.174164	+	0.984717i	$0.444278\pi$
$264$	3.59837	0.221464
$265$	14.9628	0.919158
$266$	−21.0120	−1.28833
$267$	4.92241	0.301247
$268$	−13.1256	−0.801774
$269$	26.8710	1.63836	0.819178	−	0.573539i	$-0.194430\pi$
$269$	26.8710	1.63836	0.819178	+	0.573539i	$0.194430\pi$
$270$	18.5187	1.12701
$271$	0.0464063	0.00281898	0.00140949	−	0.999999i	$-0.499551\pi$
$271$	0.0464063	0.00281898	0.00140949	+	0.999999i	$0.499551\pi$
$272$	−0.797357	−0.0483468
$273$	−2.37883	−0.143973
$274$	−35.0767	−2.11906
$275$	−1.60527	−0.0968015
$276$	28.7804	1.73238
$277$	−18.6901	−1.12298	−0.561491	−	0.827483i	$-0.689772\pi$
$277$	−18.6901	−1.12298	−0.561491	+	0.827483i	$0.689772\pi$
$278$	21.0333	1.26149
$279$	9.89086	0.592151
$280$	−9.79655	−0.585456
$281$	26.9714	1.60898	0.804488	−	0.593969i	$-0.202440\pi$
$281$	26.9714	1.60898	0.804488	+	0.593969i	$0.202440\pi$
$282$	12.4167	0.739402
$283$	20.2359	1.20290	0.601450	−	0.798910i	$-0.294590\pi$
$283$	20.2359	1.20290	0.601450	+	0.798910i	$0.294590\pi$
$284$	36.8730	2.18801
$285$	−10.9332	−0.647630
$286$	1.82732	0.108052
$287$	1.94253	0.114664
$288$	4.44757	0.262076
$289$	−16.9814	−0.998906
$290$	−2.66398	−0.156434
$291$	15.3866	0.901981
$292$	0.996959	0.0583426
$293$	23.6195	1.37986	0.689932	−	0.723874i	$-0.257640\pi$
$293$	23.6195	1.37986	0.689932	+	0.723874i	$0.257640\pi$
$294$	−16.9474	−0.988391
$295$	19.4809	1.13422
$296$	−28.0461	−1.63015
$297$	2.75699	0.159977
$298$	27.7307	1.60640
$299$	7.80686	0.451483
$300$	17.5432	1.01286
$301$	6.89035	0.397153
$302$	26.9091	1.54844
$303$	11.0400	0.634229
$304$	−38.1644	−2.18888
$305$	1.17954	0.0675400
$306$	−0.481737	−0.0275391
$307$	26.3774	1.50544	0.752719	−	0.658342i	$-0.228742\pi$
$307$	26.3774	1.50544	0.752719	+	0.658342i	$0.228742\pi$
$308$	−2.73041	−0.155579
$309$	−11.5950	−0.659614
$310$	−23.3915	−1.32855
$311$	20.7081	1.17425	0.587124	−	0.809497i	$-0.300260\pi$
$311$	20.7081	1.17425	0.587124	+	0.809497i	$0.300260\pi$
$312$	−10.6671	−0.603906
$313$	21.1800	1.19716	0.598581	−	0.801062i	$-0.295732\pi$
$313$	21.1800	1.19716	0.598581	+	0.801062i	$0.295732\pi$
$314$	7.23337	0.408203
$315$	−2.39739	−0.135078
$316$	−9.35902	−0.526486
$317$	−23.9156	−1.34324	−0.671618	−	0.740898i	$-0.734400\pi$
$317$	−23.9156	−1.34324	−0.671618	+	0.740898i	$0.734400\pi$
$318$	−35.6851	−2.00112
$319$	−0.396603	−0.0222055
$320$	4.99954	0.279483
$321$	6.54734	0.365437
$322$	−17.0992	−0.952902
$323$	0.890455	0.0495463
$324$	−11.9963	−0.666462
$325$	4.75871	0.263966
$326$	35.4811	1.96512
$327$	−3.15709	−0.174587
$328$	8.71065	0.480965
$329$	−5.03266	−0.277459
$330$	−2.08256	−0.114641
$331$	9.33571	0.513137	0.256568	−	0.966526i	$-0.417408\pi$
$331$	9.33571	0.513137	0.256568	+	0.966526i	$0.417408\pi$
$332$	5.02479	0.275771
$333$	−6.86339	−0.376111
$334$	42.4899	2.32494
$335$	4.05771	0.221696
$336$	9.46357	0.516280
$337$	10.0513	0.547527	0.273763	−	0.961797i	$-0.411732\pi$
$337$	10.0513	0.547527	0.273763	+	0.961797i	$0.411732\pi$
$338$	27.1954	1.47924
$339$	−17.4660	−0.948623
$340$	0.777227	0.0421511
$341$	−3.48244	−0.188585
$342$	−23.0577	−1.24682
$343$	15.8498	0.855811
$344$	30.8976	1.66589
$345$	−8.89731	−0.479015
$346$	29.6351	1.59320
$347$	7.22103	0.387645	0.193823	−	0.981037i	$-0.437911\pi$
$347$	7.22103	0.387645	0.193823	+	0.981037i	$0.437911\pi$
$348$	4.33429	0.232342
$349$	1.08094	0.0578614	0.0289307	−	0.999581i	$-0.490790\pi$
$349$	1.08094	0.0578614	0.0289307	+	0.999581i	$0.490790\pi$
$350$	−10.4229	−0.557128
$351$	−8.17289	−0.436236
$352$	−1.56593	−0.0834643
$353$	23.3346	1.24197	0.620987	−	0.783821i	$-0.286732\pi$
$353$	23.3346	1.24197	0.620987	+	0.783821i	$0.286732\pi$
$354$	−46.4603	−2.46934
$355$	−11.3991	−0.605001
$356$	−16.7488	−0.887684
$357$	−0.220805	−0.0116862
$358$	−15.6446	−0.826844
$359$	−36.5990	−1.93162	−0.965811	−	0.259249i	$-0.916525\pi$
$359$	−36.5990	−1.93162	−0.965811	+	0.259249i	$0.916525\pi$
$360$	−10.7504	−0.566594
$361$	23.6205	1.24318
$362$	−6.32768	−0.332575
$363$	13.5696	0.712221
$364$	8.09410	0.424246
$365$	−0.308204	−0.0161321
$366$	−2.81309	−0.147043
$367$	37.7460	1.97032	0.985161	−	0.171631i	$-0.0549036\pi$
$367$	37.7460	1.97032	0.985161	+	0.171631i	$0.0549036\pi$
$368$	−31.0576	−1.61899
$369$	2.13165	0.110969
$370$	16.2317	0.843845
$371$	14.4637	0.750916
$372$	38.0579	1.97321
$373$	−9.80494	−0.507680	−0.253840	−	0.967246i	$-0.581694\pi$
$373$	−9.80494	−0.507680	−0.253840	+	0.967246i	$0.581694\pi$
$374$	0.169613	0.00877049
$375$	−13.7970	−0.712471
$376$	−22.5674	−1.16382
$377$	1.17570	0.0605517
$378$	17.9009	0.920724
$379$	27.5306	1.41415	0.707077	−	0.707137i	$-0.250013\pi$
$379$	27.5306	1.41415	0.707077	+	0.707137i	$0.250013\pi$
$380$	37.2010	1.90837
$381$	25.9031	1.32706
$382$	36.5775	1.87147
$383$	10.5698	0.540091	0.270045	−	0.962848i	$-0.412961\pi$
$383$	10.5698	0.540091	0.270045	+	0.962848i	$0.412961\pi$
$384$	−19.8956	−1.01529
$385$	0.844090	0.0430188
$386$	20.5685	1.04691
$387$	7.56121	0.384358
$388$	−52.3539	−2.65787
$389$	10.7892	0.547034	0.273517	−	0.961867i	$-0.411813\pi$
$389$	10.7892	0.547034	0.273517	+	0.961867i	$0.411813\pi$
$390$	6.17359	0.312612
$391$	0.724639	0.0366466
$392$	30.8019	1.55573
$393$	−8.74049	−0.440899
$394$	−32.8997	−1.65746
$395$	2.89329	0.145577
$396$	−2.99624	−0.150567
$397$	−13.4501	−0.675040	−0.337520	−	0.941318i	$-0.609588\pi$
$397$	−13.4501	−0.675040	−0.337520	+	0.941318i	$0.609588\pi$
$398$	37.2022	1.86478
$399$	−10.5685	−0.529088
$400$	−18.9313	−0.946566
$401$	−34.2202	−1.70887	−0.854437	−	0.519555i	$-0.826098\pi$
$401$	−34.2202	−1.70887	−0.854437	+	0.519555i	$0.826098\pi$
$402$	−9.67729	−0.482660
$403$	10.3234	0.514247
$404$	−37.5641	−1.86888
$405$	3.70859	0.184281
$406$	−2.57511	−0.127801
$407$	2.41651	0.119782
$408$	−0.990129	−0.0490187
$409$	0.282386	0.0139631	0.00698155	−	0.999976i	$-0.497778\pi$
$409$	0.282386	0.0139631	0.00698155	+	0.999976i	$0.497778\pi$
$410$	−5.04128	−0.248971
$411$	−17.6427	−0.870252
$412$	39.4525	1.94368
$413$	18.8310	0.926615
$414$	−18.7640	−0.922201
$415$	−1.55338	−0.0762526
$416$	4.64209	0.227597
$417$	10.5792	0.518067
$418$	8.11831	0.397080
$419$	14.0753	0.687622	0.343811	−	0.939039i	$-0.388282\pi$
$419$	14.0753	0.687622	0.343811	+	0.939039i	$0.388282\pi$
$420$	−9.22466	−0.450117
$421$	4.88820	0.238236	0.119118	−	0.992880i	$-0.461993\pi$
$421$	4.88820	0.238236	0.119118	+	0.992880i	$0.461993\pi$
$422$	−1.67070	−0.0813282
$423$	−5.52264	−0.268520
$424$	64.8577	3.14977
$425$	0.441707	0.0214259
$426$	27.1859	1.31716
$427$	1.14019	0.0551775
$428$	−22.2777	−1.07683
$429$	0.919099	0.0443745
$430$	−17.8820	−0.862346
$431$	−7.94861	−0.382871	−0.191436	−	0.981505i	$-0.561314\pi$
$431$	−7.94861	−0.382871	−0.191436	+	0.981505i	$0.561314\pi$
$432$	32.5137	1.56432
$433$	−1.44879	−0.0696245	−0.0348122	−	0.999394i	$-0.511083\pi$
$433$	−1.44879	−0.0696245	−0.0348122	+	0.999394i	$0.511083\pi$
$434$	−22.6112	−1.08537
$435$	−1.33992	−0.0642442
$436$	10.7422	0.514456
$437$	34.6839	1.65915
$438$	0.735041	0.0351216
$439$	−24.7621	−1.18183	−0.590915	−	0.806734i	$-0.701233\pi$
$439$	−24.7621	−1.18183	−0.590915	+	0.806734i	$0.701233\pi$
$440$	3.78505	0.180445
$441$	7.53779	0.358942
$442$	−0.502806	−0.0239160
$443$	12.1476	0.577148	0.288574	−	0.957458i	$-0.406819\pi$
$443$	12.1476	0.577148	0.288574	+	0.957458i	$0.406819\pi$
$444$	−26.4089	−1.25331
$445$	5.17779	0.245451
$446$	47.4178	2.24530
$447$	13.9479	0.659712
$448$	4.83276	0.228326
$449$	4.83356	0.228110	0.114055	−	0.993474i	$-0.463616\pi$
$449$	4.83356	0.228110	0.114055	+	0.993474i	$0.463616\pi$
$450$	−11.4377	−0.539178
$451$	−0.750526	−0.0353409
$452$	59.4290	2.79531
$453$	13.5346	0.635912
$454$	−20.3190	−0.953616
$455$	−2.50224	−0.117307
$456$	−47.3912	−2.21930
$457$	−10.6289	−0.497197	−0.248599	−	0.968607i	$-0.579970\pi$
$457$	−10.6289	−0.497197	−0.248599	+	0.968607i	$0.579970\pi$
$458$	58.4633	2.73181
$459$	−0.758613	−0.0354090
$460$	30.2736	1.41151
$461$	19.6158	0.913597	0.456799	−	0.889570i	$-0.348996\pi$
$461$	19.6158	0.913597	0.456799	+	0.889570i	$0.348996\pi$
$462$	−2.01308	−0.0936572
$463$	2.58632	0.120196	0.0600981	−	0.998192i	$-0.480859\pi$
$463$	2.58632	0.120196	0.0600981	+	0.998192i	$0.480859\pi$
$464$	−4.67723	−0.217135
$465$	−11.7654	−0.545607
$466$	9.71499	0.450038
$467$	−24.9586	−1.15495	−0.577473	−	0.816410i	$-0.695961\pi$
$467$	−24.9586	−1.15495	−0.577473	+	0.816410i	$0.695961\pi$
$468$	8.88215	0.410577
$469$	3.92235	0.181117
$470$	13.0608	0.602452
$471$	3.63821	0.167640
$472$	84.4418	3.88675
$473$	−2.66220	−0.122408
$474$	−6.90025	−0.316939
$475$	21.1417	0.970048
$476$	0.751300	0.0344358
$477$	15.8719	0.726723
$478$	42.3796	1.93840
$479$	13.0764	0.597475	0.298738	−	0.954335i	$-0.403434\pi$
$479$	13.0764	0.597475	0.298738	+	0.954335i	$0.403434\pi$
$480$	−5.29048	−0.241476
$481$	−7.16356	−0.326630
$482$	27.9763	1.27428
$483$	−8.60050	−0.391336
$484$	−46.1714	−2.09870
$485$	16.1849	0.734918
$486$	33.0133	1.49751
$487$	36.6145	1.65916	0.829581	−	0.558386i	$-0.188579\pi$
$487$	36.6145	1.65916	0.829581	+	0.558386i	$0.188579\pi$
$488$	5.11281	0.231446
$489$	17.8461	0.807031
$490$	−17.8266	−0.805324
$491$	32.0216	1.44511	0.722557	−	0.691312i	$-0.242967\pi$
$491$	32.0216	1.44511	0.722557	+	0.691312i	$0.242967\pi$
$492$	8.20215	0.369781
$493$	0.109129	0.00491494
$494$	−24.0662	−1.08279
$495$	0.926271	0.0416328
$496$	−41.0692	−1.84406
$497$	−11.0188	−0.494262
$498$	3.70469	0.166011
$499$	−36.6685	−1.64151	−0.820754	−	0.571282i	$-0.806446\pi$
$499$	−36.6685	−1.64151	−0.820754	+	0.571282i	$0.806446\pi$
$500$	46.9449	2.09944
$501$	21.3714	0.954803
$502$	52.8821	2.36024
$503$	1.70453	0.0760013	0.0380007	−	0.999278i	$-0.487901\pi$
$503$	1.70453	0.0760013	0.0380007	+	0.999278i	$0.487901\pi$
$504$	−10.3917	−0.462885
$505$	11.6127	0.516759
$506$	6.60656	0.293697
$507$	13.6787	0.607491
$508$	−88.1367	−3.91044
$509$	−32.1356	−1.42439	−0.712193	−	0.701984i	$-0.752298\pi$
$509$	−32.1356	−1.42439	−0.712193	+	0.701984i	$0.752298\pi$
$510$	0.573037	0.0253745
$511$	−0.297923	−0.0131793
$512$	48.7965	2.15652
$513$	−36.3100	−1.60313
$514$	−59.2969	−2.61547
$515$	−12.1965	−0.537442
$516$	29.0939	1.28079
$517$	1.94445	0.0855167
$518$	15.6902	0.689388
$519$	14.9058	0.654291
$520$	−11.2205	−0.492052
$521$	19.6829	0.862322	0.431161	−	0.902275i	$-0.358104\pi$
$521$	19.6829	0.862322	0.431161	+	0.902275i	$0.358104\pi$
$522$	−2.82583	−0.123683
$523$	−2.22306	−0.0972077	−0.0486039	−	0.998818i	$-0.515477\pi$
$523$	−2.22306	−0.0972077	−0.0486039	+	0.998818i	$0.515477\pi$
$524$	29.7400	1.29920
$525$	−5.24247	−0.228800
$526$	−14.1712	−0.617893
$527$	0.958229	0.0417411
$528$	−3.65640	−0.159124
$529$	5.22520	0.227183
$530$	−37.5364	−1.63048
$531$	20.6644	0.896760
$532$	35.9600	1.55906
$533$	2.22488	0.0963703
$534$	−12.3486	−0.534376
$535$	6.88702	0.297752
$536$	17.5885	0.759709
$537$	−7.86887	−0.339567
$538$	−67.4099	−2.90625
$539$	−2.65395	−0.114314
$540$	−31.6929	−1.36385
$541$	32.6995	1.40586	0.702931	−	0.711258i	$-0.251874\pi$
$541$	32.6995	1.40586	0.702931	+	0.711258i	$0.251874\pi$
$542$	−0.116417	−0.00500054
$543$	−3.18267	−0.136581
$544$	0.430882	0.0184739
$545$	−3.32088	−0.142251
$546$	5.96764	0.255392
$547$	24.4758	1.04651	0.523254	−	0.852177i	$-0.324718\pi$
$547$	24.4758	1.04651	0.523254	+	0.852177i	$0.324718\pi$
$548$	60.0303	2.56437
$549$	1.25120	0.0533998
$550$	4.02706	0.171714
$551$	5.22333	0.222521
$552$	−38.5662	−1.64149
$553$	2.79677	0.118931
$554$	46.8870	1.99204
$555$	8.16415	0.346549
$556$	−35.9964	−1.52659
$557$	−28.3326	−1.20049	−0.600246	−	0.799815i	$-0.704931\pi$
$557$	−28.3326	−1.20049	−0.600246	+	0.799815i	$0.704931\pi$
$558$	−24.8127	−1.05040
$559$	7.89189	0.333792
$560$	9.95454	0.420656
$561$	0.0853114	0.00360185
$562$	−67.6616	−2.85413
$563$	−27.5614	−1.16157	−0.580787	−	0.814055i	$-0.697255\pi$
$563$	−27.5614	−1.16157	−0.580787	+	0.814055i	$0.697255\pi$
$564$	−21.2499	−0.894784
$565$	−18.3721	−0.772922
$566$	−50.7648	−2.13380
$567$	3.58488	0.150551
$568$	−49.4104	−2.07322
$569$	−0.370577	−0.0155354	−0.00776770	−	0.999970i	$-0.502473\pi$
$569$	−0.370577	−0.0155354	−0.00776770	+	0.999970i	$0.502473\pi$
$570$	27.4276	1.14882
$571$	21.6690	0.906820	0.453410	−	0.891302i	$-0.350207\pi$
$571$	21.6690	0.906820	0.453410	+	0.891302i	$0.350207\pi$
$572$	−3.12728	−0.130758
$573$	18.3976	0.768570
$574$	−4.87311	−0.203400
$575$	17.2048	0.717490
$576$	5.30328	0.220970
$577$	−17.6870	−0.736318	−0.368159	−	0.929763i	$-0.620012\pi$
$577$	−17.6870	−0.736318	−0.368159	+	0.929763i	$0.620012\pi$
$578$	42.6003	1.77194
$579$	10.3455	0.429942
$580$	4.55915	0.189308
$581$	−1.50156	−0.0622954
$582$	−38.5996	−1.60001
$583$	−5.58827	−0.231442
$584$	−1.33594	−0.0552816
$585$	−2.74586	−0.113528
$586$	−59.2529	−2.44772
$587$	−37.6819	−1.55530	−0.777649	−	0.628699i	$-0.783588\pi$
$587$	−37.6819	−1.55530	−0.777649	+	0.628699i	$0.783588\pi$
$588$	29.0038	1.19610
$589$	45.8644	1.88981
$590$	−48.8707	−2.01197
$591$	−16.5477	−0.680683
$592$	28.4984	1.17128
$593$	15.5305	0.637760	0.318880	−	0.947795i	$-0.396693\pi$
$593$	15.5305	0.637760	0.318880	+	0.947795i	$0.396693\pi$
$594$	−6.91630	−0.283779
$595$	−0.232260	−0.00952173
$596$	−47.4584	−1.94397
$597$	18.7118	0.765823
$598$	−19.5847	−0.800876
$599$	−14.6700	−0.599401	−0.299701	−	0.954033i	$-0.596887\pi$
$599$	−14.6700	−0.599401	−0.299701	+	0.954033i	$0.596887\pi$
$600$	−23.5082	−0.959719
$601$	−17.4163	−0.710428	−0.355214	−	0.934785i	$-0.615592\pi$
$601$	−17.4163	−0.710428	−0.355214	+	0.934785i	$0.615592\pi$
$602$	−17.2855	−0.704503
$603$	4.30423	0.175282
$604$	−46.0523	−1.87384
$605$	14.2736	0.580306
$606$	−27.6954	−1.12505
$607$	33.8151	1.37251	0.686257	−	0.727359i	$-0.259253\pi$
$607$	33.8151	1.37251	0.686257	+	0.727359i	$0.259253\pi$
$608$	20.6236	0.836397
$609$	−1.29522	−0.0524850
$610$	−2.95904	−0.119808
$611$	−5.76417	−0.233193
$612$	0.824447	0.0333263
$613$	−2.85533	−0.115326	−0.0576628	−	0.998336i	$-0.518365\pi$
$613$	−2.85533	−0.115326	−0.0576628	+	0.998336i	$0.518365\pi$
$614$	−66.1716	−2.67047
$615$	−2.53565	−0.102247
$616$	3.65879	0.147417
$617$	20.5677	0.828023	0.414011	−	0.910272i	$-0.364127\pi$
$617$	20.5677	0.828023	0.414011	+	0.910272i	$0.364127\pi$
$618$	29.0876	1.17008
$619$	6.60051	0.265297	0.132649	−	0.991163i	$-0.457652\pi$
$619$	6.60051	0.265297	0.132649	+	0.991163i	$0.457652\pi$
$620$	40.0324	1.60774
$621$	−29.5485	−1.18574
$622$	−51.9492	−2.08297
$623$	5.00506	0.200524
$624$	10.8391	0.433913
$625$	1.67928	0.0671714
$626$	−53.1330	−2.12362
$627$	4.08332	0.163072
$628$	−12.3792	−0.493985
$629$	−0.664927	−0.0265124
$630$	6.01421	0.239612
$631$	8.62745	0.343453	0.171727	−	0.985145i	$-0.445065\pi$
$631$	8.62745	0.343453	0.171727	+	0.985145i	$0.445065\pi$
$632$	12.5412	0.498863
$633$	−0.840320	−0.0333997
$634$	59.9959	2.38274
$635$	27.2470	1.08126
$636$	61.0715	2.42164
$637$	7.86746	0.311720
$638$	0.994936	0.0393899
$639$	−12.0916	−0.478337
$640$	−20.9278	−0.827242
$641$	25.6025	1.01124	0.505619	−	0.862757i	$-0.331264\pi$
$641$	25.6025	1.01124	0.505619	+	0.862757i	$0.331264\pi$
$642$	−16.4250	−0.648242
$643$	28.0412	1.10584	0.552919	−	0.833235i	$-0.313514\pi$
$643$	28.0412	1.10584	0.552919	+	0.833235i	$0.313514\pi$
$644$	29.2637	1.15315
$645$	−8.99421	−0.354147
$646$	−2.23384	−0.0878892
$647$	−5.17910	−0.203611	−0.101806	−	0.994804i	$-0.532462\pi$
$647$	−5.17910	−0.203611	−0.101806	+	0.994804i	$0.532462\pi$
$648$	16.0753	0.631496
$649$	−7.27567	−0.285595
$650$	−11.9379	−0.468244
$651$	−11.3729	−0.445739
$652$	−60.7225	−2.37808
$653$	−23.3641	−0.914309	−0.457154	−	0.889387i	$-0.651131\pi$
$653$	−23.3641	−0.914309	−0.457154	+	0.889387i	$0.651131\pi$
$654$	7.92001	0.309697
$655$	−9.19395	−0.359237
$656$	−8.85112	−0.345578
$657$	−0.326929	−0.0127547
$658$	12.6252	0.492180
$659$	−21.7663	−0.847894	−0.423947	−	0.905687i	$-0.639356\pi$
$659$	−21.7663	−0.847894	−0.423947	+	0.905687i	$0.639356\pi$
$660$	3.56409	0.138732
$661$	21.9263	0.852836	0.426418	−	0.904526i	$-0.359775\pi$
$661$	21.9263	0.852836	0.426418	+	0.904526i	$0.359775\pi$
$662$	−23.4200	−0.910244
$663$	−0.252899	−0.00982180
$664$	−6.73329	−0.261302
$665$	−11.1168	−0.431092
$666$	17.2178	0.667177
$667$	4.25067	0.164587
$668$	−72.7173	−2.81352
$669$	23.8500	0.922096
$670$	−10.1794	−0.393263
$671$	−0.440529	−0.0170065
$672$	−5.11400	−0.197277
$673$	23.0667	0.889156	0.444578	−	0.895740i	$-0.353354\pi$
$673$	23.0667	0.889156	0.444578	+	0.895740i	$0.353354\pi$
$674$	−25.2150	−0.971247
$675$	−18.0114	−0.693261
$676$	−46.5424	−1.79009
$677$	21.7698	0.836680	0.418340	−	0.908291i	$-0.362612\pi$
$677$	21.7698	0.836680	0.418340	+	0.908291i	$0.362612\pi$
$678$	43.8160	1.68274
$679$	15.6450	0.600400
$680$	−1.04150	−0.0399396
$681$	−10.2199	−0.391629
$682$	8.73621	0.334527
$683$	−50.6180	−1.93684	−0.968422	−	0.249319i	$-0.919793\pi$
$683$	−50.6180	−1.93684	−0.968422	+	0.249319i	$0.919793\pi$
$684$	39.4611	1.50883
$685$	−18.5580	−0.709066
$686$	−39.7617	−1.51811
$687$	29.4056	1.12189
$688$	−31.3959	−1.19696
$689$	16.5660	0.631115
$690$	22.3202	0.849715
$691$	−19.3061	−0.734440	−0.367220	−	0.930134i	$-0.619690\pi$
$691$	−19.3061	−0.734440	−0.367220	+	0.930134i	$0.619690\pi$
$692$	−50.7177	−1.92800
$693$	0.895372	0.0340124
$694$	−18.1150	−0.687637
$695$	11.1281	0.422112
$696$	−5.80801	−0.220152
$697$	0.206515	0.00782231
$698$	−2.71170	−0.102639
$699$	4.88641	0.184821
$700$	17.8378	0.674206
$701$	−12.6756	−0.478750	−0.239375	−	0.970927i	$-0.576943\pi$
$701$	−12.6756	−0.478750	−0.239375	+	0.970927i	$0.576943\pi$
$702$	20.5029	0.773831
$703$	−31.8258	−1.20033
$704$	−1.86721	−0.0703733
$705$	6.56930	0.247414
$706$	−58.5382	−2.20311
$707$	11.2253	0.422172
$708$	79.5124	2.98826
$709$	42.0191	1.57806	0.789030	−	0.614355i	$-0.210584\pi$
$709$	42.0191	1.57806	0.789030	+	0.614355i	$0.210584\pi$
$710$	28.5963	1.07320
$711$	3.06907	0.115099
$712$	22.4436	0.841111
$713$	37.3237	1.39778
$714$	0.553921	0.0207300
$715$	0.966782	0.0361556
$716$	26.7743	1.00060
$717$	21.3159	0.796058
$718$	91.8140	3.42647
$719$	22.8713	0.852957	0.426479	−	0.904498i	$-0.359754\pi$
$719$	22.8713	0.852957	0.426479	+	0.904498i	$0.359754\pi$
$720$	10.9237	0.407103
$721$	−11.7896	−0.439069
$722$	−59.2554	−2.20526
$723$	14.0714	0.523321
$724$	10.8292	0.402464
$725$	2.59101	0.0962278
$726$	−34.0414	−1.26340
$727$	−13.3120	−0.493714	−0.246857	−	0.969052i	$-0.579398\pi$
$727$	−13.3120	−0.493714	−0.246857	+	0.969052i	$0.579398\pi$
$728$	−10.8462	−0.401988
$729$	24.9875	0.925462
$730$	0.773175	0.0286165
$731$	0.732531	0.0270936
$732$	4.81434	0.177943
$733$	−26.6587	−0.984663	−0.492331	−	0.870408i	$-0.663855\pi$
$733$	−26.6587	−0.984663	−0.492331	+	0.870408i	$0.663855\pi$
$734$	−94.6913	−3.49512
$735$	−8.96636	−0.330729
$736$	16.7832	0.618635
$737$	−1.51546	−0.0558227
$738$	−5.34756	−0.196847
$739$	8.51309	0.313159	0.156580	−	0.987665i	$-0.449953\pi$
$739$	8.51309	0.313159	0.156580	+	0.987665i	$0.449953\pi$
$740$	−27.7790	−1.02117
$741$	−12.1047	−0.444677
$742$	−36.2842	−1.33204
$743$	−32.0690	−1.17650	−0.588248	−	0.808681i	$-0.700182\pi$
$743$	−32.0690	−1.17650	−0.588248	+	0.808681i	$0.700182\pi$
$744$	−50.9982	−1.86969
$745$	14.6715	0.537522
$746$	24.5971	0.900565
$747$	−1.64776	−0.0602883
$748$	−0.290277	−0.0106136
$749$	6.65728	0.243252
$750$	34.6117	1.26384
$751$	−9.12856	−0.333106	−0.166553	−	0.986033i	$-0.553264\pi$
$751$	−9.12856	−0.333106	−0.166553	+	0.986033i	$0.553264\pi$
$752$	22.9313	0.836218
$753$	26.5984	0.969301
$754$	−2.94942	−0.107411
$755$	14.2368	0.518131
$756$	−30.6357	−1.11421
$757$	4.27777	0.155478	0.0777391	−	0.996974i	$-0.475230\pi$
$757$	4.27777	0.155478	0.0777391	+	0.996974i	$0.475230\pi$
$758$	−69.0646	−2.50854
$759$	3.32294	0.120615
$760$	−49.8499	−1.80824
$761$	−38.6633	−1.40154	−0.700771	−	0.713386i	$-0.747161\pi$
$761$	−38.6633	−1.40154	−0.700771	+	0.713386i	$0.747161\pi$
$762$	−64.9817	−2.35404
$763$	−3.21010	−0.116213
$764$	−62.5988	−2.26475
$765$	−0.254873	−0.00921496
$766$	−26.5159	−0.958057
$767$	21.5682	0.778782
$768$	40.4051	1.45799
$769$	−6.73580	−0.242899	−0.121450	−	0.992598i	$-0.538754\pi$
$769$	−6.73580	−0.242899	−0.121450	+	0.992598i	$0.538754\pi$
$770$	−2.11752	−0.0763102
$771$	−29.8249	−1.07412
$772$	−35.2010	−1.26691
$773$	−21.5244	−0.774180	−0.387090	−	0.922042i	$-0.626520\pi$
$773$	−21.5244	−0.774180	−0.387090	+	0.922042i	$0.626520\pi$
$774$	−18.9684	−0.681805
$775$	22.7508	0.817234
$776$	70.1550	2.51842
$777$	7.89180	0.283117
$778$	−27.0663	−0.970373
$779$	9.88457	0.354151
$780$	−10.5655	−0.378306
$781$	4.25730	0.152338
$782$	−1.81786	−0.0650066
$783$	−4.44996	−0.159029
$784$	−31.2987	−1.11781
$785$	3.82696	0.136590
$786$	21.9268	0.782103
$787$	−54.3757	−1.93829	−0.969143	−	0.246501i	$-0.920719\pi$
$787$	−54.3757	−1.93829	−0.969143	+	0.246501i	$0.920719\pi$
$788$	56.3046	2.00577
$789$	−7.12776	−0.253755
$790$	−7.25823	−0.258236
$791$	−17.7593	−0.631447
$792$	4.01501	0.142667
$793$	1.30592	0.0463745
$794$	33.7415	1.19744
$795$	−18.8799	−0.669602
$796$	−63.6679	−2.25665
$797$	13.2704	0.470061	0.235031	−	0.971988i	$-0.424481\pi$
$797$	13.2704	0.470061	0.235031	+	0.971988i	$0.424481\pi$
$798$	26.5127	0.938539
$799$	−0.535034	−0.0189282
$800$	10.2302	0.361694
$801$	5.49236	0.194063
$802$	85.8463	3.03134
$803$	0.115107	0.00406204
$804$	16.5618	0.584088
$805$	−9.04670	−0.318854
$806$	−25.8979	−0.912213
$807$	−33.9056	−1.19353
$808$	50.3364	1.77083
$809$	49.4542	1.73872	0.869359	−	0.494182i	$-0.164532\pi$
$809$	49.4542	1.73872	0.869359	+	0.494182i	$0.164532\pi$
$810$	−9.30355	−0.326893
$811$	−23.8933	−0.839008	−0.419504	−	0.907753i	$-0.637796\pi$
$811$	−23.8933	−0.839008	−0.419504	+	0.907753i	$0.637796\pi$
$812$	4.40706	0.154658
$813$	−0.0585550	−0.00205361
$814$	−6.06216	−0.212479
$815$	18.7720	0.657555
$816$	1.00610	0.0352204
$817$	35.0616	1.22665
$818$	−0.708407	−0.0247689
$819$	−2.65427	−0.0927475
$820$	8.62767	0.301291
$821$	26.9302	0.939869	0.469935	−	0.882701i	$-0.344277\pi$
$821$	26.9302	0.939869	0.469935	+	0.882701i	$0.344277\pi$
$822$	44.2594	1.54372
$823$	30.1151	1.04975	0.524874	−	0.851180i	$-0.324113\pi$
$823$	30.1151	1.04975	0.524874	+	0.851180i	$0.324113\pi$
$824$	−52.8669	−1.84171
$825$	2.02551	0.0705193
$826$	−47.2404	−1.64370
$827$	18.5221	0.644075	0.322038	−	0.946727i	$-0.395632\pi$
$827$	18.5221	0.644075	0.322038	+	0.946727i	$0.395632\pi$
$828$	32.1128	1.11600
$829$	17.6217	0.612026	0.306013	−	0.952027i	$-0.401005\pi$
$829$	17.6217	0.612026	0.306013	+	0.952027i	$0.401005\pi$
$830$	3.89689	0.135263
$831$	23.5830	0.818086
$832$	5.53522	0.191899
$833$	0.730263	0.0253021
$834$	−26.5396	−0.918990
$835$	22.4801	0.777957
$836$	−13.8937	−0.480524
$837$	−39.0736	−1.35058
$838$	−35.3099	−1.21976
$839$	26.3821	0.910811	0.455406	−	0.890284i	$-0.349494\pi$
$839$	26.3821	0.910811	0.455406	+	0.890284i	$0.349494\pi$
$840$	12.3612	0.426502
$841$	−28.3599	−0.977926
$842$	−12.2628	−0.422603
$843$	−34.0322	−1.17213
$844$	2.85924	0.0984190
$845$	14.3883	0.494973
$846$	13.8544	0.476322
$847$	13.7975	0.474087
$848$	−65.9037	−2.26314
$849$	−25.5335	−0.876306
$850$	−1.10809	−0.0380070
$851$	−25.8994	−0.887819
$852$	−46.5260	−1.59395
$853$	29.4488	1.00831	0.504154	−	0.863614i	$-0.331805\pi$
$853$	29.4488	1.00831	0.504154	+	0.863614i	$0.331805\pi$
$854$	−2.86033	−0.0978784
$855$	−12.1992	−0.417203
$856$	29.8525	1.02034
$857$	24.6962	0.843607	0.421804	−	0.906687i	$-0.361397\pi$
$857$	24.6962	0.843607	0.421804	+	0.906687i	$0.361397\pi$
$858$	−2.30569	−0.0787151
$859$	−22.0870	−0.753598	−0.376799	−	0.926295i	$-0.622975\pi$
$859$	−22.0870	−0.753598	−0.376799	+	0.926295i	$0.622975\pi$
$860$	30.6033	1.04356
$861$	−2.45106	−0.0835319
$862$	19.9403	0.679168
$863$	16.1082	0.548330	0.274165	−	0.961683i	$-0.411598\pi$
$863$	16.1082	0.548330	0.274165	+	0.961683i	$0.411598\pi$
$864$	−17.5700	−0.597745
$865$	15.6791	0.533105
$866$	3.63451	0.123506
$867$	21.4269	0.727697
$868$	38.6969	1.31346
$869$	−1.08058	−0.0366561
$870$	3.36138	0.113962
$871$	4.49247	0.152222
$872$	−14.3947	−0.487465
$873$	17.1682	0.581056
$874$	−87.0096	−2.94314
$875$	−14.0286	−0.474254
$876$	−1.25795	−0.0425023
$877$	−11.5221	−0.389074	−0.194537	−	0.980895i	$-0.562321\pi$
$877$	−11.5221	−0.389074	−0.194537	+	0.980895i	$0.562321\pi$
$878$	62.1194	2.09643
$879$	−29.8028	−1.00522
$880$	−3.84609	−0.129652
$881$	−21.9545	−0.739664	−0.369832	−	0.929099i	$-0.620585\pi$
$881$	−21.9545	−0.739664	−0.369832	+	0.929099i	$0.620585\pi$
$882$	−18.9097	−0.636721
$883$	−4.38186	−0.147461	−0.0737306	−	0.997278i	$-0.523490\pi$
$883$	−4.38186	−0.147461	−0.0737306	+	0.997278i	$0.523490\pi$
$884$	0.860504	0.0289419
$885$	−24.5808	−0.826274
$886$	−30.4739	−1.02379
$887$	32.1308	1.07885	0.539424	−	0.842035i	$-0.318642\pi$
$887$	32.1308	1.07885	0.539424	+	0.842035i	$0.318642\pi$
$888$	35.3883	1.18755
$889$	26.3380	0.883349
$890$	−12.9892	−0.435400
$891$	−1.38507	−0.0464018
$892$	−81.1511	−2.71714
$893$	−25.6087	−0.856963
$894$	−34.9903	−1.17025
$895$	−8.27711	−0.276673
$896$	−20.2296	−0.675825
$897$	−9.85062	−0.328903
$898$	−12.1257	−0.404639
$899$	5.62089	0.187467
$900$	19.5745	0.652484
$901$	1.53767	0.0512272
$902$	1.88280	0.0626905
$903$	−8.69418	−0.289324
$904$	−79.6358	−2.64865
$905$	−3.34779	−0.111284
$906$	−33.9536	−1.12803
$907$	−9.37012	−0.311130	−0.155565	−	0.987826i	$-0.549720\pi$
$907$	−9.37012	−0.311130	−0.155565	+	0.987826i	$0.549720\pi$
$908$	34.7739	1.15401
$909$	12.3182	0.408570
$910$	6.27724	0.208089
$911$	−42.2698	−1.40046	−0.700230	−	0.713917i	$-0.746919\pi$
$911$	−42.2698	−1.40046	−0.700230	+	0.713917i	$0.746919\pi$
$912$	48.1555	1.59459
$913$	0.580154	0.0192003
$914$	26.6641	0.881969
$915$	−1.48833	−0.0492025
$916$	−100.054	−3.30589
$917$	−8.88725	−0.293483
$918$	1.90309	0.0628114
$919$	−12.2737	−0.404873	−0.202436	−	0.979295i	$-0.564886\pi$
$919$	−12.2737	−0.404873	−0.202436	+	0.979295i	$0.564886\pi$
$920$	−40.5671	−1.33746
$921$	−33.2827	−1.09670
$922$	−49.2090	−1.62061
$923$	−12.6205	−0.415407
$924$	3.44520	0.113339
$925$	−15.7871	−0.519076
$926$	−6.48815	−0.213214
$927$	−12.9375	−0.424923
$928$	2.52752	0.0829697
$929$	2.66574	0.0874601	0.0437301	−	0.999043i	$-0.486076\pi$
$929$	2.66574	0.0874601	0.0437301	+	0.999043i	$0.486076\pi$
$930$	29.5152	0.967842
$931$	34.9531	1.14554
$932$	−16.6263	−0.544612
$933$	−26.1292	−0.855433
$934$	62.6123	2.04874
$935$	0.0897374	0.00293473
$936$	−11.9022	−0.389036
$937$	−45.0249	−1.47090	−0.735449	−	0.677580i	$-0.763029\pi$
$937$	−45.0249	−1.47090	−0.735449	+	0.677580i	$0.763029\pi$
$938$	−9.83978	−0.321280
$939$	−26.7246	−0.872126
$940$	−22.3524	−0.729055
$941$	−56.3597	−1.83727	−0.918636	−	0.395104i	$-0.870708\pi$
$941$	−56.3597	−1.83727	−0.918636	+	0.395104i	$0.870708\pi$
$942$	−9.12699	−0.297373
$943$	8.04391	0.261946
$944$	−85.8036	−2.79267
$945$	9.47085	0.308087
$946$	6.67851	0.217137
$947$	−27.2891	−0.886776	−0.443388	−	0.896330i	$-0.646224\pi$
$947$	−27.2891	−0.886776	−0.443388	+	0.896330i	$0.646224\pi$
$948$	11.8091	0.383542
$949$	−0.341227	−0.0110767
$950$	−53.0371	−1.72075
$951$	30.1765	0.978540
$952$	−1.00675	−0.0326291
$953$	−41.6875	−1.35039	−0.675195	−	0.737640i	$-0.735940\pi$
$953$	−41.6875	−1.35039	−0.675195	+	0.737640i	$0.735940\pi$
$954$	−39.8169	−1.28912
$955$	19.3521	0.626218
$956$	−72.5286	−2.34574
$957$	0.500429	0.0161766
$958$	−32.8040	−1.05985
$959$	−17.9390	−0.579279
$960$	−6.30837	−0.203602
$961$	18.3552	0.592102
$962$	17.9708	0.579403
$963$	7.30544	0.235414
$964$	−47.8787	−1.54207
$965$	10.8822	0.350310
$966$	21.5756	0.694184
$967$	6.57891	0.211564	0.105782	−	0.994389i	$-0.466266\pi$
$967$	6.57891	0.211564	0.105782	+	0.994389i	$0.466266\pi$
$968$	61.8705	1.98859
$969$	−1.12357	−0.0360942
$970$	−40.6022	−1.30366
$971$	−20.9415	−0.672044	−0.336022	−	0.941854i	$-0.609082\pi$
$971$	−20.9415	−0.672044	−0.336022	+	0.941854i	$0.609082\pi$
$972$	−56.4991	−1.81221
$973$	10.7569	0.344849
$974$	−91.8529	−2.94316
$975$	−6.00449	−0.192298
$976$	−5.19526	−0.166296
$977$	12.3946	0.396540	0.198270	−	0.980147i	$-0.436468\pi$
$977$	12.3946	0.396540	0.198270	+	0.980147i	$0.436468\pi$
$978$	−44.7697	−1.43158
$979$	−1.93379	−0.0618041
$980$	30.5085	0.974559
$981$	−3.52263	−0.112469
$982$	−80.3308	−2.56346
$983$	−27.8300	−0.887639	−0.443819	−	0.896116i	$-0.646377\pi$
$983$	−27.8300	−0.887639	−0.443819	+	0.896116i	$0.646377\pi$
$984$	−10.9910	−0.350380
$985$	−17.4062	−0.554609
$986$	−0.273767	−0.00871852
$987$	6.35015	0.202128
$988$	41.1869	1.31033
$989$	28.5326	0.907285
$990$	−2.32369	−0.0738516
$991$	36.1478	1.14827	0.574136	−	0.818760i	$-0.305338\pi$
$991$	36.1478	1.14827	0.574136	+	0.818760i	$0.305338\pi$
$992$	22.1933	0.704637
$993$	−11.7797	−0.373817
$994$	27.6423	0.876762
$995$	19.6826	0.623979
$996$	−6.34022	−0.200898
$997$	57.2963	1.81459	0.907296	−	0.420492i	$-0.138142\pi$
$997$	57.2963	1.81459	0.907296	+	0.420492i	$0.138142\pi$
$998$	91.9883	2.91184
$999$	27.1137	0.857838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.11	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.11	✓	174	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50865 q^{2} -1.26179 q^{3} +4.29331 q^{4} -1.32725 q^{5} +3.16538 q^{6} -1.28298 q^{7} -5.75310 q^{8} -1.40789 q^{9} +O(q^{10})\)	\(q-2.50865 q^{2} -1.26179 q^{3} +4.29331 q^{4} -1.32725 q^{5} +3.16538 q^{6} -1.28298 q^{7} -5.75310 q^{8} -1.40789 q^{9} +3.32960 q^{10} +0.495698 q^{11} -5.41725 q^{12} -1.46946 q^{13} +3.21853 q^{14} +1.67471 q^{15} +5.84588 q^{16} -0.136396 q^{17} +3.53189 q^{18} -6.52844 q^{19} -5.69830 q^{20} +1.61885 q^{21} -1.24353 q^{22} -5.31274 q^{23} +7.25920 q^{24} -3.23840 q^{25} +3.68636 q^{26} +5.56183 q^{27} -5.50821 q^{28} -0.800090 q^{29} -4.20126 q^{30} -7.02532 q^{31} -3.15904 q^{32} -0.625467 q^{33} +0.342170 q^{34} +1.70283 q^{35} -6.04449 q^{36} +4.87496 q^{37} +16.3775 q^{38} +1.85415 q^{39} +7.63581 q^{40} -1.51408 q^{41} -4.06111 q^{42} -5.37060 q^{43} +2.12818 q^{44} +1.86862 q^{45} +13.3278 q^{46} +3.92264 q^{47} -7.37626 q^{48} -5.35397 q^{49} +8.12401 q^{50} +0.172104 q^{51} -6.30885 q^{52} -11.2735 q^{53} -13.9527 q^{54} -0.657916 q^{55} +7.38109 q^{56} +8.23751 q^{57} +2.00714 q^{58} -14.6776 q^{59} +7.19005 q^{60} -0.888705 q^{61} +17.6241 q^{62} +1.80629 q^{63} -3.76684 q^{64} +1.95034 q^{65} +1.56907 q^{66} -3.05723 q^{67} -0.585592 q^{68} +6.70356 q^{69} -4.27180 q^{70} +8.58849 q^{71} +8.09972 q^{72} +0.232212 q^{73} -12.2295 q^{74} +4.08618 q^{75} -28.0286 q^{76} -0.635968 q^{77} -4.65141 q^{78} -2.17991 q^{79} -7.75895 q^{80} -2.79419 q^{81} +3.79829 q^{82} +1.17038 q^{83} +6.95020 q^{84} +0.181032 q^{85} +13.4729 q^{86} +1.00954 q^{87} -2.85180 q^{88} -3.90114 q^{89} -4.68771 q^{90} +1.88528 q^{91} -22.8092 q^{92} +8.86448 q^{93} -9.84053 q^{94} +8.66487 q^{95} +3.98604 q^{96} -12.1943 q^{97} +13.4312 q^{98} -0.697887 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

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