LMFDB - Embedded newform 8027.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50053 q^{2} +2.23425 q^{3} +4.25264 q^{4} -3.72100 q^{5} -5.58681 q^{6} -1.83421 q^{7} -5.63280 q^{8} +1.99189 q^{9} +O(q^{10})$	\(q-2.50053 q^{2} +2.23425 q^{3} +4.25264 q^{4} -3.72100 q^{5} -5.58681 q^{6} -1.83421 q^{7} -5.63280 q^{8} +1.99189 q^{9} +9.30447 q^{10} -0.837098 q^{11} +9.50148 q^{12} -1.25220 q^{13} +4.58648 q^{14} -8.31365 q^{15} +5.57969 q^{16} -0.557849 q^{17} -4.98077 q^{18} -5.02365 q^{19} -15.8241 q^{20} -4.09808 q^{21} +2.09319 q^{22} -1.00000 q^{23} -12.5851 q^{24} +8.84584 q^{25} +3.13116 q^{26} -2.25238 q^{27} -7.80022 q^{28} -8.80206 q^{29} +20.7885 q^{30} +4.15650 q^{31} -2.68657 q^{32} -1.87029 q^{33} +1.39492 q^{34} +6.82508 q^{35} +8.47078 q^{36} +5.02233 q^{37} +12.5618 q^{38} -2.79773 q^{39} +20.9596 q^{40} -3.70826 q^{41} +10.2474 q^{42} -10.0945 q^{43} -3.55988 q^{44} -7.41181 q^{45} +2.50053 q^{46} -9.03333 q^{47} +12.4664 q^{48} -3.63569 q^{49} -22.1193 q^{50} -1.24637 q^{51} -5.32516 q^{52} -12.9029 q^{53} +5.63214 q^{54} +3.11484 q^{55} +10.3317 q^{56} -11.2241 q^{57} +22.0098 q^{58} +10.1280 q^{59} -35.3550 q^{60} -4.49167 q^{61} -10.3934 q^{62} -3.65353 q^{63} -4.44153 q^{64} +4.65943 q^{65} +4.67671 q^{66} +10.4464 q^{67} -2.37233 q^{68} -2.23425 q^{69} -17.0663 q^{70} +7.31298 q^{71} -11.2199 q^{72} -12.4655 q^{73} -12.5585 q^{74} +19.7638 q^{75} -21.3638 q^{76} +1.53541 q^{77} +6.99580 q^{78} +9.63789 q^{79} -20.7620 q^{80} -11.0080 q^{81} +9.27262 q^{82} +10.1567 q^{83} -17.4277 q^{84} +2.07575 q^{85} +25.2416 q^{86} -19.6660 q^{87} +4.71520 q^{88} -1.95754 q^{89} +18.5334 q^{90} +2.29679 q^{91} -4.25264 q^{92} +9.28667 q^{93} +22.5881 q^{94} +18.6930 q^{95} -6.00248 q^{96} +4.90332 q^{97} +9.09115 q^{98} -1.66740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.50053	−1.76814	−0.884070	−	0.467354i	$-0.845207\pi$
$2$	−2.50053	−1.76814	−0.884070	+	0.467354i	$0.845207\pi$
$3$	2.23425	1.28995	0.644973	−	0.764205i	$-0.276868\pi$
$3$	2.23425	1.28995	0.644973	+	0.764205i	$0.276868\pi$
$4$	4.25264	2.12632
$5$	−3.72100	−1.66408	−0.832041	−	0.554714i	$-0.812827\pi$
$5$	−3.72100	−1.66408	−0.832041	+	0.554714i	$0.812827\pi$
$6$	−5.58681	−2.28081
$7$	−1.83421	−0.693264	−0.346632	−	0.938001i	$-0.612675\pi$
$7$	−1.83421	−0.693264	−0.346632	+	0.938001i	$0.612675\pi$
$8$	−5.63280	−1.99150
$9$	1.99189	0.663962
$10$	9.30447	2.94233
$11$	−0.837098	−0.252395	−0.126197	−	0.992005i	$-0.540277\pi$
$11$	−0.837098	−0.252395	−0.126197	+	0.992005i	$0.540277\pi$
$12$	9.50148	2.74284
$13$	−1.25220	−0.347298	−0.173649	−	0.984808i	$-0.555556\pi$
$13$	−1.25220	−0.347298	−0.173649	+	0.984808i	$0.555556\pi$
$14$	4.58648	1.22579
$15$	−8.31365	−2.14658
$16$	5.57969	1.39492
$17$	−0.557849	−0.135298	−0.0676491	−	0.997709i	$-0.521550\pi$
$17$	−0.557849	−0.135298	−0.0676491	+	0.997709i	$0.521550\pi$
$18$	−4.98077	−1.17398
$19$	−5.02365	−1.15250	−0.576252	−	0.817272i	$-0.695485\pi$
$19$	−5.02365	−1.15250	−0.576252	+	0.817272i	$0.695485\pi$
$20$	−15.8241	−3.53837
$21$	−4.09808	−0.894274
$22$	2.09319	0.446269
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−12.5851	−2.56892
$25$	8.84584	1.76917
$26$	3.13116	0.614071
$27$	−2.25238	−0.433471
$28$	−7.80022	−1.47410
$29$	−8.80206	−1.63450	−0.817251	−	0.576282i	$-0.804503\pi$
$29$	−8.80206	−1.63450	−0.817251	+	0.576282i	$0.804503\pi$
$30$	20.7885	3.79545
$31$	4.15650	0.746529	0.373265	−	0.927725i	$-0.378238\pi$
$31$	4.15650	0.746529	0.373265	+	0.927725i	$0.378238\pi$
$32$	−2.68657	−0.474923
$33$	−1.87029	−0.325576
$34$	1.39492	0.239226
$35$	6.82508	1.15365
$36$	8.47078	1.41180
$37$	5.02233	0.825666	0.412833	−	0.910807i	$-0.364539\pi$
$37$	5.02233	0.825666	0.412833	+	0.910807i	$0.364539\pi$
$38$	12.5618	2.03779
$39$	−2.79773	−0.447995
$40$	20.9596	3.31401
$41$	−3.70826	−0.579133	−0.289567	−	0.957158i	$-0.593511\pi$
$41$	−3.70826	−0.579133	−0.289567	+	0.957158i	$0.593511\pi$
$42$	10.2474	1.58120
$43$	−10.0945	−1.53940	−0.769700	−	0.638406i	$-0.779594\pi$
$43$	−10.0945	−1.53940	−0.769700	+	0.638406i	$0.779594\pi$
$44$	−3.55988	−0.536672
$45$	−7.41181	−1.10489
$46$	2.50053	0.368683
$47$	−9.03333	−1.31765	−0.658823	−	0.752298i	$-0.728946\pi$
$47$	−9.03333	−1.31765	−0.658823	+	0.752298i	$0.728946\pi$
$48$	12.4664	1.79937
$49$	−3.63569	−0.519384
$50$	−22.1193	−3.12814
$51$	−1.24637	−0.174527
$52$	−5.32516	−0.738466
$53$	−12.9029	−1.77234	−0.886172	−	0.463356i	$-0.846645\pi$
$53$	−12.9029	−1.77234	−0.886172	+	0.463356i	$0.846645\pi$
$54$	5.63214	0.766437
$55$	3.11484	0.420005
$56$	10.3317	1.38063
$57$	−11.2241	−1.48667
$58$	22.0098	2.89003
$59$	10.1280	1.31855	0.659274	−	0.751903i	$-0.270864\pi$
$59$	10.1280	1.31855	0.659274	+	0.751903i	$0.270864\pi$
$60$	−35.3550	−4.56431
$61$	−4.49167	−0.575099	−0.287550	−	0.957766i	$-0.592841\pi$
$61$	−4.49167	−0.575099	−0.287550	+	0.957766i	$0.592841\pi$
$62$	−10.3934	−1.31997
$63$	−3.65353	−0.460301
$64$	−4.44153	−0.555191
$65$	4.65943	0.577931
$66$	4.67671	0.575663
$67$	10.4464	1.27624	0.638118	−	0.769939i	$-0.279713\pi$
$67$	10.4464	1.27624	0.638118	+	0.769939i	$0.279713\pi$
$68$	−2.37233	−0.287687
$69$	−2.23425	−0.268972
$70$	−17.0663	−2.03981
$71$	7.31298	0.867891	0.433945	−	0.900939i	$-0.357121\pi$
$71$	7.31298	0.867891	0.433945	+	0.900939i	$0.357121\pi$
$72$	−11.2199	−1.32228
$73$	−12.4655	−1.45898	−0.729489	−	0.683992i	$-0.760242\pi$
$73$	−12.4655	−1.45898	−0.729489	+	0.683992i	$0.760242\pi$
$74$	−12.5585	−1.45989
$75$	19.7638	2.28213
$76$	−21.3638	−2.45060
$77$	1.53541	0.174976
$78$	6.99580	0.792119
$79$	9.63789	1.08435	0.542174	−	0.840266i	$-0.317601\pi$
$79$	9.63789	1.08435	0.542174	+	0.840266i	$0.317601\pi$
$80$	−20.7620	−2.32126
$81$	−11.0080	−1.22312
$82$	9.27262	1.02399
$83$	10.1567	1.11484	0.557421	−	0.830230i	$-0.311791\pi$
$83$	10.1567	1.11484	0.557421	+	0.830230i	$0.311791\pi$
$84$	−17.4277	−1.90151
$85$	2.07575	0.225147
$86$	25.2416	2.72187
$87$	−19.6660	−2.10842
$88$	4.71520	0.502642
$89$	−1.95754	−0.207499	−0.103749	−	0.994603i	$-0.533084\pi$
$89$	−1.95754	−0.207499	−0.103749	+	0.994603i	$0.533084\pi$
$90$	18.5334	1.95360
$91$	2.29679	0.240769
$92$	−4.25264	−0.443369
$93$	9.28667	0.962983
$94$	22.5881	2.32978
$95$	18.6930	1.91786
$96$	−6.00248	−0.612625
$97$	4.90332	0.497857	0.248928	−	0.968522i	$-0.419922\pi$
$97$	4.90332	0.497857	0.248928	+	0.968522i	$0.419922\pi$
$98$	9.09115	0.918345
$99$	−1.66740	−0.167580
$100$	37.6182	3.76182
$101$	−17.8090	−1.77207	−0.886033	−	0.463623i	$-0.846549\pi$
$101$	−17.8090	−1.77207	−0.886033	+	0.463623i	$0.846549\pi$
$102$	3.11660	0.308589
$103$	10.2264	1.00764	0.503820	−	0.863809i	$-0.331928\pi$
$103$	10.2264	1.00764	0.503820	+	0.863809i	$0.331928\pi$
$104$	7.05339	0.691641
$105$	15.2489	1.48815
$106$	32.2640	3.13375
$107$	−0.530277	−0.0512638	−0.0256319	−	0.999671i	$-0.508160\pi$
$107$	−0.530277	−0.0512638	−0.0256319	+	0.999671i	$0.508160\pi$
$108$	−9.57857	−0.921698
$109$	9.00644	0.862661	0.431330	−	0.902194i	$-0.358044\pi$
$109$	9.00644	0.862661	0.431330	+	0.902194i	$0.358044\pi$
$110$	−7.78875	−0.742628
$111$	11.2212	1.06506
$112$	−10.2343	−0.967050
$113$	−13.9447	−1.31181	−0.655903	−	0.754845i	$-0.727712\pi$
$113$	−13.9447	−1.31181	−0.655903	+	0.754845i	$0.727712\pi$
$114$	28.0662	2.62864
$115$	3.72100	0.346985
$116$	−37.4320	−3.47548
$117$	−2.49424	−0.230592
$118$	−25.3253	−2.33138
$119$	1.02321	0.0937974
$120$	46.8291	4.27490
$121$	−10.2993	−0.936297
$122$	11.2315	1.01686
$123$	−8.28520	−0.747051
$124$	17.6761	1.58736
$125$	−14.3104	−1.27996
$126$	9.13575	0.813878
$127$	8.16170	0.724234	0.362117	−	0.932133i	$-0.382054\pi$
$127$	8.16170	0.724234	0.362117	+	0.932133i	$0.382054\pi$
$128$	16.4793	1.45658
$129$	−22.5537	−1.98574
$130$	−11.6510	−1.02186
$131$	−6.00588	−0.524737	−0.262368	−	0.964968i	$-0.584504\pi$
$131$	−6.00588	−0.524737	−0.262368	+	0.964968i	$0.584504\pi$
$132$	−7.95367	−0.692278
$133$	9.21441	0.798991
$134$	−26.1216	−2.25656
$135$	8.38110	0.721331
$136$	3.14225	0.269446
$137$	−2.08748	−0.178345	−0.0891726	−	0.996016i	$-0.528422\pi$
$137$	−2.08748	−0.178345	−0.0891726	+	0.996016i	$0.528422\pi$
$138$	5.58681	0.475581
$139$	−14.0804	−1.19429	−0.597143	−	0.802135i	$-0.703698\pi$
$139$	−14.0804	−1.19429	−0.597143	+	0.802135i	$0.703698\pi$
$140$	29.0246	2.45303
$141$	−20.1827	−1.69969
$142$	−18.2863	−1.53455
$143$	1.04821	0.0876560
$144$	11.1141	0.926175
$145$	32.7525	2.71994
$146$	31.1704	2.57968
$147$	−8.12305	−0.669978
$148$	21.3582	1.75563
$149$	−9.44686	−0.773917	−0.386958	−	0.922097i	$-0.626474\pi$
$149$	−9.44686	−0.773917	−0.386958	+	0.922097i	$0.626474\pi$
$150$	−49.4200	−4.03513
$151$	−2.93003	−0.238443	−0.119221	−	0.992868i	$-0.538040\pi$
$151$	−2.93003	−0.238443	−0.119221	+	0.992868i	$0.538040\pi$
$152$	28.2972	2.29521
$153$	−1.11117	−0.0898329
$154$	−3.83934	−0.309382
$155$	−15.4663	−1.24229
$156$	−11.8977	−0.952582
$157$	11.8860	0.948609	0.474304	−	0.880361i	$-0.342700\pi$
$157$	11.8860	0.948609	0.474304	+	0.880361i	$0.342700\pi$
$158$	−24.0998	−1.91728
$159$	−28.8283	−2.28623
$160$	9.99673	0.790311
$161$	1.83421	0.144556
$162$	27.5259	2.16264
$163$	1.91456	0.149960	0.0749799	−	0.997185i	$-0.476111\pi$
$163$	1.91456	0.149960	0.0749799	+	0.997185i	$0.476111\pi$
$164$	−15.7699	−1.23142
$165$	6.95934	0.541784
$166$	−25.3971	−1.97120
$167$	18.6664	1.44445	0.722224	−	0.691659i	$-0.243120\pi$
$167$	18.6664	1.44445	0.722224	+	0.691659i	$0.243120\pi$
$168$	23.0837	1.78094
$169$	−11.4320	−0.879384
$170$	−5.19048	−0.398092
$171$	−10.0065	−0.765220
$172$	−42.9284	−3.27326
$173$	−9.41295	−0.715654	−0.357827	−	0.933788i	$-0.616482\pi$
$173$	−9.41295	−0.715654	−0.357827	+	0.933788i	$0.616482\pi$
$174$	49.1755	3.72798
$175$	−16.2251	−1.22650
$176$	−4.67075	−0.352071
$177$	22.6284	1.70086
$178$	4.89488	0.366887
$179$	−26.6539	−1.99221	−0.996103	−	0.0881938i	$-0.971891\pi$
$179$	−26.6539	−1.99221	−0.996103	+	0.0881938i	$0.971891\pi$
$180$	−31.5198	−2.34935
$181$	20.3934	1.51583	0.757916	−	0.652353i	$-0.226218\pi$
$181$	20.3934	1.51583	0.757916	+	0.652353i	$0.226218\pi$
$182$	−5.74319	−0.425714
$183$	−10.0355	−0.741847
$184$	5.63280	0.415255
$185$	−18.6881	−1.37397
$186$	−23.2216	−1.70269
$187$	0.466974	0.0341485
$188$	−38.4155	−2.80174
$189$	4.13133	0.300510
$190$	−46.7424	−3.39105
$191$	2.00997	0.145437	0.0727183	−	0.997353i	$-0.476833\pi$
$191$	2.00997	0.145437	0.0727183	+	0.997353i	$0.476833\pi$
$192$	−9.92350	−0.716167
$193$	−19.9241	−1.43417	−0.717086	−	0.696985i	$-0.754524\pi$
$193$	−19.9241	−1.43417	−0.717086	+	0.696985i	$0.754524\pi$
$194$	−12.2609	−0.880281
$195$	10.4104	0.745501
$196$	−15.4613	−1.10438
$197$	−6.96774	−0.496431	−0.248215	−	0.968705i	$-0.579844\pi$
$197$	−6.96774	−0.496431	−0.248215	+	0.968705i	$0.579844\pi$
$198$	4.16939	0.296306
$199$	−6.02338	−0.426986	−0.213493	−	0.976945i	$-0.568484\pi$
$199$	−6.02338	−0.426986	−0.213493	+	0.976945i	$0.568484\pi$
$200$	−49.8268	−3.52329
$201$	23.3400	1.64628
$202$	44.5320	3.13326
$203$	16.1448	1.13314
$204$	−5.30039	−0.371101
$205$	13.7984	0.963725
$206$	−25.5715	−1.78165
$207$	−1.99189	−0.138446
$208$	−6.98688	−0.484453
$209$	4.20529	0.290886
$210$	−38.1304	−2.63125
$211$	21.2667	1.46406	0.732031	−	0.681271i	$-0.238573\pi$
$211$	21.2667	1.46406	0.732031	+	0.681271i	$0.238573\pi$
$212$	−54.8713	−3.76857
$213$	16.3390	1.11953
$214$	1.32597	0.0906416
$215$	37.5617	2.56169
$216$	12.6872	0.863255
$217$	−7.62387	−0.517542
$218$	−22.5209	−1.52531
$219$	−27.8511	−1.88200
$220$	13.2463	0.893066
$221$	0.698537	0.0469887
$222$	−28.0588	−1.88318
$223$	20.9905	1.40563	0.702814	−	0.711374i	$-0.251927\pi$
$223$	20.9905	1.40563	0.702814	+	0.711374i	$0.251927\pi$
$224$	4.92772	0.329247
$225$	17.6199	1.17466
$226$	34.8691	2.31946
$227$	−23.8903	−1.58565	−0.792826	−	0.609447i	$-0.791391\pi$
$227$	−23.8903	−1.58565	−0.792826	+	0.609447i	$0.791391\pi$
$228$	−47.7321	−3.16114
$229$	21.9254	1.44887	0.724436	−	0.689342i	$-0.242100\pi$
$229$	21.9254	1.44887	0.724436	+	0.689342i	$0.242100\pi$
$230$	−9.30447	−0.613518
$231$	3.43049	0.225710
$232$	49.5802	3.25510
$233$	−7.22631	−0.473411	−0.236706	−	0.971581i	$-0.576068\pi$
$233$	−7.22631	−0.473411	−0.236706	+	0.971581i	$0.576068\pi$
$234$	6.23692	0.407720
$235$	33.6130	2.19267
$236$	43.0706	2.80366
$237$	21.5335	1.39875
$238$	−2.55856	−0.165847
$239$	−0.241835	−0.0156430	−0.00782149	−	0.999969i	$-0.502490\pi$
$239$	−0.241835	−0.0156430	−0.00782149	+	0.999969i	$0.502490\pi$
$240$	−46.3876	−2.99431
$241$	−17.3269	−1.11612	−0.558061	−	0.829800i	$-0.688454\pi$
$241$	−17.3269	−1.11612	−0.558061	+	0.829800i	$0.688454\pi$
$242$	25.7536	1.65550
$243$	−17.8376	−1.14428
$244$	−19.1015	−1.22285
$245$	13.5284	0.864298
$246$	20.7174	1.32089
$247$	6.29061	0.400262
$248$	−23.4127	−1.48671
$249$	22.6926	1.43809
$250$	35.7835	2.26314
$251$	29.7492	1.87776	0.938878	−	0.344251i	$-0.111867\pi$
$251$	29.7492	1.87776	0.938878	+	0.344251i	$0.111867\pi$
$252$	−15.5372	−0.978749
$253$	0.837098	0.0526279
$254$	−20.4086	−1.28055
$255$	4.63776	0.290428
$256$	−32.3239	−2.02025
$257$	−20.5116	−1.27948	−0.639739	−	0.768592i	$-0.720958\pi$
$257$	−20.5116	−1.27948	−0.639739	+	0.768592i	$0.720958\pi$
$258$	56.3962	3.51107
$259$	−9.21198	−0.572405
$260$	19.8149	1.22887
$261$	−17.5327	−1.08525
$262$	15.0179	0.927808
$263$	24.1484	1.48905	0.744527	−	0.667592i	$-0.232675\pi$
$263$	24.1484	1.48905	0.744527	+	0.667592i	$0.232675\pi$
$264$	10.5350	0.648382
$265$	48.0115	2.94933
$266$	−23.0409	−1.41273
$267$	−4.37363	−0.267662
$268$	44.4250	2.71369
$269$	18.7472	1.14303	0.571517	−	0.820590i	$-0.306355\pi$
$269$	18.7472	1.14303	0.571517	+	0.820590i	$0.306355\pi$
$270$	−20.9572	−1.27541
$271$	−17.8907	−1.08678	−0.543391	−	0.839480i	$-0.682860\pi$
$271$	−17.8907	−1.08678	−0.543391	+	0.839480i	$0.682860\pi$
$272$	−3.11262	−0.188730
$273$	5.13161	0.310579
$274$	5.21980	0.315339
$275$	−7.40483	−0.446528
$276$	−9.50148	−0.571922
$277$	4.60664	0.276786	0.138393	−	0.990377i	$-0.455806\pi$
$277$	4.60664	0.276786	0.138393	+	0.990377i	$0.455806\pi$
$278$	35.2085	2.11167
$279$	8.27927	0.495667
$280$	−38.4443	−2.29749
$281$	3.26617	0.194843	0.0974217	−	0.995243i	$-0.468940\pi$
$281$	3.26617	0.194843	0.0974217	+	0.995243i	$0.468940\pi$
$282$	50.4675	3.00530
$283$	22.1390	1.31603	0.658014	−	0.753006i	$-0.271397\pi$
$283$	22.1390	1.31603	0.658014	+	0.753006i	$0.271397\pi$
$284$	31.0995	1.84541
$285$	41.7649	2.47394
$286$	−2.62109	−0.154988
$287$	6.80172	0.401493
$288$	−5.35134	−0.315331
$289$	−16.6888	−0.981694
$290$	−81.8985	−4.80924
$291$	10.9553	0.642209
$292$	−53.0114	−3.10226
$293$	−11.4055	−0.666315	−0.333157	−	0.942871i	$-0.608114\pi$
$293$	−11.4055	−0.666315	−0.333157	+	0.942871i	$0.608114\pi$
$294$	20.3119	1.18462
$295$	−37.6861	−2.19417
$296$	−28.2898	−1.64431
$297$	1.88546	0.109406
$298$	23.6221	1.36839
$299$	1.25220	0.0724165
$300$	84.0486	4.85255
$301$	18.5154	1.06721
$302$	7.32664	0.421601
$303$	−39.7899	−2.28587
$304$	−28.0304	−1.60765
$305$	16.7135	0.957012
$306$	2.77852	0.158837
$307$	−19.9930	−1.14106	−0.570532	−	0.821276i	$-0.693263\pi$
$307$	−19.9930	−1.14106	−0.570532	+	0.821276i	$0.693263\pi$
$308$	6.52955	0.372056
$309$	22.8484	1.29980
$310$	38.6740	2.19654
$311$	−17.5458	−0.994932	−0.497466	−	0.867484i	$-0.665736\pi$
$311$	−17.5458	−0.994932	−0.497466	+	0.867484i	$0.665736\pi$
$312$	15.7590	0.892180
$313$	13.9024	0.785807	0.392904	−	0.919580i	$-0.371471\pi$
$313$	13.9024	0.785807	0.392904	+	0.919580i	$0.371471\pi$
$314$	−29.7214	−1.67727
$315$	13.5948	0.765979
$316$	40.9865	2.30567
$317$	5.65379	0.317548	0.158774	−	0.987315i	$-0.449246\pi$
$317$	5.65379	0.317548	0.158774	+	0.987315i	$0.449246\pi$
$318$	72.0859	4.04238
$319$	7.36819	0.412539
$320$	16.5269	0.923883
$321$	−1.18477	−0.0661276
$322$	−4.58648	−0.255595
$323$	2.80244	0.155932
$324$	−46.8133	−2.60074
$325$	−11.0767	−0.614428
$326$	−4.78741	−0.265150
$327$	20.1227	1.11279
$328$	20.8879	1.15334
$329$	16.5690	0.913478
$330$	−17.4020	−0.957951
$331$	10.7456	0.590631	0.295315	−	0.955400i	$-0.404575\pi$
$331$	10.7456	0.590631	0.295315	+	0.955400i	$0.404575\pi$
$332$	43.1928	2.37051
$333$	10.0039	0.548211
$334$	−46.6758	−2.55399
$335$	−38.8712	−2.12376
$336$	−22.8660	−1.24744
$337$	−0.389693	−0.0212279	−0.0106140	−	0.999944i	$-0.503379\pi$
$337$	−0.389693	−0.0212279	−0.0106140	+	0.999944i	$0.503379\pi$
$338$	28.5860	1.55488
$339$	−31.1560	−1.69216
$340$	8.82744	0.478735
$341$	−3.47940	−0.188420
$342$	25.0217	1.35302
$343$	19.5080	1.05334
$344$	56.8604	3.06571
$345$	8.31365	0.447592
$346$	23.5374	1.26538
$347$	22.8198	1.22503	0.612515	−	0.790459i	$-0.290158\pi$
$347$	22.8198	1.22503	0.612515	+	0.790459i	$0.290158\pi$
$348$	−83.6326	−4.48318
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	40.5713	2.16863
$351$	2.82043	0.150543
$352$	2.24892	0.119868
$353$	−9.94388	−0.529259	−0.264630	−	0.964350i	$-0.585250\pi$
$353$	−9.94388	−0.529259	−0.264630	+	0.964350i	$0.585250\pi$
$354$	−56.5830	−3.00736
$355$	−27.2116	−1.44424
$356$	−8.32471	−0.441209
$357$	2.28611	0.120994
$358$	66.6489	3.52250
$359$	15.4977	0.817935	0.408968	−	0.912549i	$-0.365889\pi$
$359$	15.4977	0.817935	0.408968	+	0.912549i	$0.365889\pi$
$360$	41.7492	2.20038
$361$	6.23708	0.328267
$362$	−50.9943	−2.68020
$363$	−23.0112	−1.20777
$364$	9.76743	0.511952
$365$	46.3842	2.42786
$366$	25.0941	1.31169
$367$	−2.67592	−0.139682	−0.0698410	−	0.997558i	$-0.522249\pi$
$367$	−2.67592	−0.139682	−0.0698410	+	0.997558i	$0.522249\pi$
$368$	−5.57969	−0.290861
$369$	−7.38644	−0.384523
$370$	46.7301	2.42938
$371$	23.6665	1.22870
$372$	39.4929	2.04761
$373$	28.0035	1.44997	0.724984	−	0.688766i	$-0.241847\pi$
$373$	28.0035	1.44997	0.724984	+	0.688766i	$0.241847\pi$
$374$	−1.16768	−0.0603794
$375$	−31.9730	−1.65108
$376$	50.8829	2.62409
$377$	11.0219	0.567659
$378$	−10.3305	−0.531344
$379$	25.0214	1.28526	0.642632	−	0.766175i	$-0.277842\pi$
$379$	25.0214	1.28526	0.642632	+	0.766175i	$0.277842\pi$
$380$	79.4947	4.07799
$381$	18.2353	0.934223
$382$	−5.02600	−0.257152
$383$	26.1372	1.33555	0.667775	−	0.744363i	$-0.267247\pi$
$383$	26.1372	1.33555	0.667775	+	0.744363i	$0.267247\pi$
$384$	36.8189	1.87891
$385$	−5.71326	−0.291175
$386$	49.8209	2.53582
$387$	−20.1071	−1.02210
$388$	20.8521	1.05860
$389$	−11.8473	−0.600684	−0.300342	−	0.953832i	$-0.597101\pi$
$389$	−11.8473	−0.600684	−0.300342	+	0.953832i	$0.597101\pi$
$390$	−26.0314	−1.31815
$391$	0.557849	0.0282116
$392$	20.4791	1.03435
$393$	−13.4187	−0.676882
$394$	17.4230	0.877760
$395$	−35.8626	−1.80444
$396$	−7.09088	−0.356330
$397$	−6.60349	−0.331419	−0.165710	−	0.986175i	$-0.552991\pi$
$397$	−6.60349	−0.331419	−0.165710	+	0.986175i	$0.552991\pi$
$398$	15.0616	0.754972
$399$	20.5873	1.03066
$400$	49.3570	2.46785
$401$	19.3919	0.968384	0.484192	−	0.874962i	$-0.339114\pi$
$401$	19.3919	0.968384	0.484192	+	0.874962i	$0.339114\pi$
$402$	−58.3623	−2.91085
$403$	−5.20476	−0.259268
$404$	−75.7355	−3.76798
$405$	40.9609	2.03537
$406$	−40.3705	−2.00355
$407$	−4.20418	−0.208394
$408$	7.02058	0.347570
$409$	28.3690	1.40276	0.701379	−	0.712789i	$-0.252568\pi$
$409$	28.3690	1.40276	0.701379	+	0.712789i	$0.252568\pi$
$410$	−34.5034	−1.70400
$411$	−4.66395	−0.230056
$412$	43.4893	2.14257
$413$	−18.5768	−0.914103
$414$	4.98077	0.244791
$415$	−37.7931	−1.85519
$416$	3.36412	0.164940
$417$	−31.4592	−1.54057
$418$	−10.5154	−0.514327
$419$	32.4032	1.58300	0.791499	−	0.611170i	$-0.209301\pi$
$419$	32.4032	1.58300	0.791499	+	0.611170i	$0.209301\pi$
$420$	64.8483	3.16427
$421$	−13.9906	−0.681859	−0.340930	−	0.940089i	$-0.610742\pi$
$421$	−13.9906	−0.681859	−0.340930	+	0.940089i	$0.610742\pi$
$422$	−53.1781	−2.58867
$423$	−17.9934	−0.874868
$424$	72.6792	3.52962
$425$	−4.93464	−0.239365
$426$	−40.8562	−1.97949
$427$	8.23864	0.398696
$428$	−2.25508	−0.109003
$429$	2.34197	0.113072
$430$	−93.9241	−4.52942
$431$	−38.4530	−1.85222	−0.926108	−	0.377259i	$-0.876867\pi$
$431$	−38.4530	−1.85222	−0.926108	+	0.377259i	$0.876867\pi$
$432$	−12.5676	−0.604658
$433$	−14.0311	−0.674291	−0.337146	−	0.941453i	$-0.609461\pi$
$433$	−14.0311	−0.674291	−0.337146	+	0.941453i	$0.609461\pi$
$434$	19.0637	0.915087
$435$	73.1773	3.50858
$436$	38.3012	1.83429
$437$	5.02365	0.240314
$438$	69.6425	3.32765
$439$	30.9882	1.47899	0.739494	−	0.673163i	$-0.235065\pi$
$439$	30.9882	1.47899	0.739494	+	0.673163i	$0.235065\pi$
$440$	−17.5453	−0.836438
$441$	−7.24189	−0.344852
$442$	−1.74671	−0.0830827
$443$	−7.77684	−0.369489	−0.184744	−	0.982787i	$-0.559146\pi$
$443$	−7.77684	−0.369489	−0.184744	+	0.982787i	$0.559146\pi$
$444$	47.7196	2.26467
$445$	7.28400	0.345295
$446$	−52.4873	−2.48535
$447$	−21.1067	−0.998311
$448$	8.14667	0.384894
$449$	−0.773037	−0.0364819	−0.0182409	−	0.999834i	$-0.505807\pi$
$449$	−0.773037	−0.0364819	−0.0182409	+	0.999834i	$0.505807\pi$
$450$	−44.0591	−2.07696
$451$	3.10418	0.146170
$452$	−59.3018	−2.78932
$453$	−6.54644	−0.307579
$454$	59.7383	2.80366
$455$	−8.54636	−0.400659
$456$	63.2232	2.96070
$457$	4.12162	0.192801	0.0964007	−	0.995343i	$-0.469267\pi$
$457$	4.12162	0.192801	0.0964007	+	0.995343i	$0.469267\pi$
$458$	−54.8251	−2.56181
$459$	1.25649	0.0586478
$460$	15.8241	0.737802
$461$	15.2919	0.712213	0.356106	−	0.934445i	$-0.384104\pi$
$461$	15.2919	0.712213	0.356106	+	0.934445i	$0.384104\pi$
$462$	−8.57805	−0.399087
$463$	−3.33444	−0.154964	−0.0774822	−	0.996994i	$-0.524688\pi$
$463$	−3.33444	−0.154964	−0.0774822	+	0.996994i	$0.524688\pi$
$464$	−49.1128	−2.28000
$465$	−34.5557	−1.60248
$466$	18.0696	0.837058
$467$	18.1664	0.840639	0.420320	−	0.907376i	$-0.361918\pi$
$467$	18.1664	0.840639	0.420320	+	0.907376i	$0.361918\pi$
$468$	−10.6071	−0.490314
$469$	−19.1609	−0.884769
$470$	−84.0503	−3.87695
$471$	26.5564	1.22365
$472$	−57.0488	−2.62588
$473$	8.45010	0.388536
$474$	−53.8451	−2.47319
$475$	−44.4384	−2.03897
$476$	4.35134	0.199443
$477$	−25.7010	−1.17677
$478$	0.604714	0.0276590
$479$	19.5051	0.891212	0.445606	−	0.895229i	$-0.352988\pi$
$479$	19.5051	0.891212	0.445606	+	0.895229i	$0.352988\pi$
$480$	22.3352	1.01946
$481$	−6.28895	−0.286752
$482$	43.3263	1.97346
$483$	4.09808	0.186469
$484$	−43.7991	−1.99087
$485$	−18.2453	−0.828475
$486$	44.6035	2.02326
$487$	−42.4655	−1.92430	−0.962149	−	0.272525i	$-0.912141\pi$
$487$	−42.4655	−1.92430	−0.962149	+	0.272525i	$0.912141\pi$
$488$	25.3007	1.14531
$489$	4.27761	0.193440
$490$	−33.8282	−1.52820
$491$	−32.6450	−1.47325	−0.736623	−	0.676303i	$-0.763581\pi$
$491$	−32.6450	−1.47325	−0.736623	+	0.676303i	$0.763581\pi$
$492$	−35.2340	−1.58847
$493$	4.91022	0.221145
$494$	−15.7299	−0.707720
$495$	6.20441	0.278868
$496$	23.1920	1.04135
$497$	−13.4135	−0.601678
$498$	−56.7436	−2.54274
$499$	21.3716	0.956725	0.478362	−	0.878162i	$-0.341231\pi$
$499$	21.3716	0.956725	0.478362	+	0.878162i	$0.341231\pi$
$500$	−60.8568	−2.72160
$501$	41.7054	1.86326
$502$	−74.3888	−3.32014
$503$	−21.5485	−0.960798	−0.480399	−	0.877050i	$-0.659508\pi$
$503$	−21.5485	−0.960798	−0.480399	+	0.877050i	$0.659508\pi$
$504$	20.5796	0.916688
$505$	66.2674	2.94886
$506$	−2.09319	−0.0930535
$507$	−25.5420	−1.13436
$508$	34.7088	1.53995
$509$	17.6848	0.783867	0.391934	−	0.919994i	$-0.371806\pi$
$509$	17.6848	0.783867	0.391934	+	0.919994i	$0.371806\pi$
$510$	−11.5969	−0.513517
$511$	22.8643	1.01146
$512$	47.8683	2.11550
$513$	11.3152	0.499577
$514$	51.2898	2.26230
$515$	−38.0525	−1.67679
$516$	−95.9128	−4.22233
$517$	7.56178	0.332567
$518$	23.0348	1.01209
$519$	−21.0309	−0.923155
$520$	−26.2456	−1.15095
$521$	−42.0708	−1.84316	−0.921579	−	0.388192i	$-0.873100\pi$
$521$	−42.0708	−1.84316	−0.921579	+	0.388192i	$0.873100\pi$
$522$	43.8410	1.91887
$523$	−24.5808	−1.07484	−0.537421	−	0.843314i	$-0.680601\pi$
$523$	−24.5808	−1.07484	−0.537421	+	0.843314i	$0.680601\pi$
$524$	−25.5409	−1.11576
$525$	−36.2509	−1.58212
$526$	−60.3838	−2.63286
$527$	−2.31870	−0.101004
$528$	−10.4356	−0.454152
$529$	1.00000	0.0434783
$530$	−120.054	−5.21482
$531$	20.1738	0.875467
$532$	39.1856	1.69891
$533$	4.64348	0.201132
$534$	10.9364	0.473264
$535$	1.97316	0.0853071
$536$	−58.8427	−2.54162
$537$	−59.5516	−2.56984
$538$	−46.8778	−2.02105
$539$	3.04343	0.131090
$540$	35.6418	1.53378
$541$	25.3890	1.09156	0.545778	−	0.837929i	$-0.316234\pi$
$541$	25.3890	1.09156	0.545778	+	0.837929i	$0.316234\pi$
$542$	44.7362	1.92158
$543$	45.5641	1.95534
$544$	1.49870	0.0642562
$545$	−33.5130	−1.43554
$546$	−12.8317	−0.549148
$547$	−16.4134	−0.701788	−0.350894	−	0.936415i	$-0.614122\pi$
$547$	−16.4134	−0.701788	−0.350894	+	0.936415i	$0.614122\pi$
$548$	−8.87729	−0.379219
$549$	−8.94690	−0.381844
$550$	18.5160	0.789525
$551$	44.2185	1.88377
$552$	12.5851	0.535657
$553$	−17.6779	−0.751740
$554$	−11.5190	−0.489396
$555$	−41.7539	−1.77235
$556$	−59.8790	−2.53944
$557$	20.4637	0.867076	0.433538	−	0.901135i	$-0.357265\pi$
$557$	20.4637	0.867076	0.433538	+	0.901135i	$0.357265\pi$
$558$	−20.7026	−0.876409
$559$	12.6403	0.534630
$560$	38.0818	1.60925
$561$	1.04334	0.0440498
$562$	−8.16715	−0.344510
$563$	40.6822	1.71455	0.857276	−	0.514857i	$-0.172155\pi$
$563$	40.6822	1.71455	0.857276	+	0.514857i	$0.172155\pi$
$564$	−85.8300	−3.61410
$565$	51.8882	2.18295
$566$	−55.3592	−2.32692
$567$	20.1910	0.847943
$568$	−41.1925	−1.72840
$569$	23.5411	0.986893	0.493446	−	0.869776i	$-0.335737\pi$
$569$	23.5411	0.986893	0.493446	+	0.869776i	$0.335737\pi$
$570$	−104.434	−4.37427
$571$	−34.4447	−1.44147	−0.720734	−	0.693212i	$-0.756195\pi$
$571$	−34.4447	−1.44147	−0.720734	+	0.693212i	$0.756195\pi$
$572$	4.45768	0.186385
$573$	4.49079	0.187605
$574$	−17.0079	−0.709895
$575$	−8.84584	−0.368897
$576$	−8.84702	−0.368626
$577$	5.63823	0.234723	0.117361	−	0.993089i	$-0.462556\pi$
$577$	5.63823	0.234723	0.117361	+	0.993089i	$0.462556\pi$
$578$	41.7308	1.73577
$579$	−44.5156	−1.85000
$580$	139.285	5.78348
$581$	−18.6295	−0.772881
$582$	−27.3939	−1.13552
$583$	10.8010	0.447330
$584$	70.2158	2.90555
$585$	9.28106	0.383725
$586$	28.5197	1.17814
$587$	−9.78380	−0.403821	−0.201910	−	0.979404i	$-0.564715\pi$
$587$	−9.78380	−0.403821	−0.201910	+	0.979404i	$0.564715\pi$
$588$	−34.5444	−1.42459
$589$	−20.8808	−0.860378
$590$	94.2353	3.87961
$591$	−15.5677	−0.640369
$592$	28.0230	1.15174
$593$	33.8365	1.38950	0.694748	−	0.719253i	$-0.255516\pi$
$593$	33.8365	1.38950	0.694748	+	0.719253i	$0.255516\pi$
$594$	−4.71465	−0.193445
$595$	−3.80736	−0.156086
$596$	−40.1741	−1.64560
$597$	−13.4578	−0.550789
$598$	−3.13116	−0.128043
$599$	−6.66274	−0.272232	−0.136116	−	0.990693i	$-0.543462\pi$
$599$	−6.66274	−0.272232	−0.136116	+	0.990693i	$0.543462\pi$
$600$	−111.326	−4.54485
$601$	1.04576	0.0426573	0.0213287	−	0.999773i	$-0.493210\pi$
$601$	1.04576	0.0426573	0.0213287	+	0.999773i	$0.493210\pi$
$602$	−46.2983	−1.88698
$603$	20.8081	0.847373
$604$	−12.4604	−0.507006
$605$	38.3236	1.55807
$606$	99.4958	4.04174
$607$	9.39347	0.381269	0.190635	−	0.981661i	$-0.438945\pi$
$607$	9.39347	0.381269	0.190635	+	0.981661i	$0.438945\pi$
$608$	13.4964	0.547351
$609$	36.0715	1.46169
$610$	−41.7926	−1.69213
$611$	11.3115	0.457616
$612$	−4.72541	−0.191014
$613$	0.362565	0.0146438	0.00732192	−	0.999973i	$-0.497669\pi$
$613$	0.362565	0.0146438	0.00732192	+	0.999973i	$0.497669\pi$
$614$	49.9932	2.01756
$615$	30.8292	1.24315
$616$	−8.64865	−0.348464
$617$	−36.5250	−1.47044	−0.735221	−	0.677828i	$-0.762922\pi$
$617$	−36.5250	−1.47044	−0.735221	+	0.677828i	$0.762922\pi$
$618$	−57.1331	−2.29823
$619$	−43.1200	−1.73314	−0.866570	−	0.499056i	$-0.833680\pi$
$619$	−43.1200	−1.73314	−0.866570	+	0.499056i	$0.833680\pi$
$620$	−65.7728	−2.64150
$621$	2.25238	0.0903849
$622$	43.8738	1.75918
$623$	3.59053	0.143851
$624$	−15.6105	−0.624918
$625$	9.01965	0.360786
$626$	−34.7632	−1.38942
$627$	9.39568	0.375227
$628$	50.5471	2.01705
$629$	−2.80170	−0.111711
$630$	−33.9941	−1.35436
$631$	4.56437	0.181705	0.0908523	−	0.995864i	$-0.471041\pi$
$631$	4.56437	0.181705	0.0908523	+	0.995864i	$0.471041\pi$
$632$	−54.2883	−2.15947
$633$	47.5153	1.88856
$634$	−14.1375	−0.561470
$635$	−30.3697	−1.20518
$636$	−122.596	−4.86126
$637$	4.55261	0.180381
$638$	−18.4244	−0.729428
$639$	14.5666	0.576247
$640$	−61.3195	−2.42387
$641$	10.1232	0.399844	0.199922	−	0.979812i	$-0.435931\pi$
$641$	10.1232	0.399844	0.199922	+	0.979812i	$0.435931\pi$
$642$	2.96256	0.116923
$643$	2.34476	0.0924684	0.0462342	−	0.998931i	$-0.485278\pi$
$643$	2.34476	0.0924684	0.0462342	+	0.998931i	$0.485278\pi$
$644$	7.80022	0.307372
$645$	83.9223	3.30444
$646$	−7.00757	−0.275709
$647$	22.2466	0.874604	0.437302	−	0.899315i	$-0.355934\pi$
$647$	22.2466	0.874604	0.437302	+	0.899315i	$0.355934\pi$
$648$	62.0061	2.43583
$649$	−8.47810	−0.332794
$650$	27.6977	1.08639
$651$	−17.0337	−0.667602
$652$	8.14193	0.318863
$653$	7.41047	0.289994	0.144997	−	0.989432i	$-0.453683\pi$
$653$	7.41047	0.289994	0.144997	+	0.989432i	$0.453683\pi$
$654$	−50.3173	−1.96756
$655$	22.3479	0.873204
$656$	−20.6909	−0.807846
$657$	−24.8299	−0.968707
$658$	−41.4312	−1.61516
$659$	26.5406	1.03387	0.516937	−	0.856024i	$-0.327072\pi$
$659$	26.5406	1.03387	0.516937	+	0.856024i	$0.327072\pi$
$660$	29.5956	1.15201
$661$	−39.6119	−1.54072	−0.770361	−	0.637608i	$-0.779924\pi$
$661$	−39.6119	−1.54072	−0.770361	+	0.637608i	$0.779924\pi$
$662$	−26.8696	−1.04432
$663$	1.56071	0.0606129
$664$	−57.2107	−2.22020
$665$	−34.2868	−1.32959
$666$	−25.0151	−0.969314
$667$	8.80206	0.340817
$668$	79.3815	3.07136
$669$	46.8981	1.81318
$670$	97.1986	3.75511
$671$	3.75997	0.145152
$672$	11.0098	0.424711
$673$	5.12588	0.197588	0.0987942	−	0.995108i	$-0.468501\pi$
$673$	5.12588	0.197588	0.0987942	+	0.995108i	$0.468501\pi$
$674$	0.974439	0.0375340
$675$	−19.9242	−0.766882
$676$	−48.6162	−1.86985
$677$	10.3009	0.395895	0.197948	−	0.980213i	$-0.436572\pi$
$677$	10.3009	0.395895	0.197948	+	0.980213i	$0.436572\pi$
$678$	77.9064	2.99198
$679$	−8.99370	−0.345146
$680$	−11.6923	−0.448379
$681$	−53.3769	−2.04541
$682$	8.70033	0.333153
$683$	−7.42490	−0.284106	−0.142053	−	0.989859i	$-0.545370\pi$
$683$	−7.42490	−0.284106	−0.142053	+	0.989859i	$0.545370\pi$
$684$	−42.5543	−1.62710
$685$	7.76750	0.296781
$686$	−48.7804	−1.86244
$687$	48.9869	1.86897
$688$	−56.3242	−2.14734
$689$	16.1570	0.615531
$690$	−20.7885	−0.791406
$691$	28.0436	1.06683	0.533414	−	0.845854i	$-0.320909\pi$
$691$	28.0436	1.06683	0.533414	+	0.845854i	$0.320909\pi$
$692$	−40.0299	−1.52171
$693$	3.05836	0.116178
$694$	−57.0615	−2.16603
$695$	52.3933	1.98739
$696$	110.775	4.19891
$697$	2.06865	0.0783557
$698$	−2.50053	−0.0946464
$699$	−16.1454	−0.610675
$700$	−68.9995	−2.60794
$701$	−33.1489	−1.25202	−0.626009	−	0.779816i	$-0.715313\pi$
$701$	−33.1489	−1.25202	−0.626009	+	0.779816i	$0.715313\pi$
$702$	−7.05256	−0.266182
$703$	−25.2304	−0.951584
$704$	3.71799	0.140127
$705$	75.1000	2.82843
$706$	24.8650	0.935805
$707$	32.6654	1.22851
$708$	96.2307	3.61657
$709$	−18.4828	−0.694137	−0.347068	−	0.937840i	$-0.612823\pi$
$709$	−18.4828	−0.694137	−0.347068	+	0.937840i	$0.612823\pi$
$710$	68.0433	2.55362
$711$	19.1976	0.719966
$712$	11.0264	0.413232
$713$	−4.15650	−0.155662
$714$	−5.71648	−0.213934
$715$	−3.90040	−0.145867
$716$	−113.350	−4.23607
$717$	−0.540320	−0.0201786
$718$	−38.7523	−1.44622
$719$	40.6637	1.51650	0.758250	−	0.651964i	$-0.226055\pi$
$719$	40.6637	1.51650	0.758250	+	0.651964i	$0.226055\pi$
$720$	−41.3556	−1.54123
$721$	−18.7574	−0.698561
$722$	−15.5960	−0.580423
$723$	−38.7126	−1.43974
$724$	86.7259	3.22314
$725$	−77.8616	−2.89171
$726$	57.5401	2.13551
$727$	32.9747	1.22296	0.611482	−	0.791258i	$-0.290574\pi$
$727$	32.9747	1.22296	0.611482	+	0.791258i	$0.290574\pi$
$728$	−12.9374	−0.479490
$729$	−6.82962	−0.252949
$730$	−115.985	−4.29280
$731$	5.63121	0.208278
$732$	−42.6775	−1.57741
$733$	23.2762	0.859725	0.429863	−	0.902894i	$-0.358562\pi$
$733$	23.2762	0.859725	0.429863	+	0.902894i	$0.358562\pi$
$734$	6.69122	0.246978
$735$	30.2259	1.11490
$736$	2.68657	0.0990283
$737$	−8.74470	−0.322115
$738$	18.4700	0.679890
$739$	38.0870	1.40105	0.700527	−	0.713626i	$-0.252949\pi$
$739$	38.0870	1.40105	0.700527	+	0.713626i	$0.252949\pi$
$740$	−79.4737	−2.92151
$741$	14.0548	0.516317
$742$	−59.1788	−2.17252
$743$	16.7378	0.614050	0.307025	−	0.951701i	$-0.400666\pi$
$743$	16.7378	0.614050	0.307025	+	0.951701i	$0.400666\pi$
$744$	−52.3099	−1.91778
$745$	35.1518	1.28786
$746$	−70.0236	−2.56375
$747$	20.2310	0.740214
$748$	1.98587	0.0726107
$749$	0.972636	0.0355394
$750$	79.9493	2.91934
$751$	20.5396	0.749502	0.374751	−	0.927126i	$-0.377728\pi$
$751$	20.5396	0.749502	0.374751	+	0.927126i	$0.377728\pi$
$752$	−50.4032	−1.83801
$753$	66.4673	2.42220
$754$	−27.5607	−1.00370
$755$	10.9027	0.396788
$756$	17.5691	0.638981
$757$	12.2554	0.445431	0.222715	−	0.974883i	$-0.428508\pi$
$757$	12.2554	0.445431	0.222715	+	0.974883i	$0.428508\pi$
$758$	−62.5668	−2.27253
$759$	1.87029	0.0678872
$760$	−105.294	−3.81941
$761$	−38.5473	−1.39734	−0.698668	−	0.715446i	$-0.746224\pi$
$761$	−38.5473	−1.39734	−0.698668	+	0.715446i	$0.746224\pi$
$762$	−45.5979	−1.65184
$763$	−16.5197	−0.598052
$764$	8.54770	0.309245
$765$	4.13467	0.149489
$766$	−65.3569	−2.36144
$767$	−12.6822	−0.457929
$768$	−72.2198	−2.60601
$769$	−48.8162	−1.76036	−0.880179	−	0.474643i	$-0.842577\pi$
$769$	−48.8162	−1.76036	−0.880179	+	0.474643i	$0.842577\pi$
$770$	14.2862	0.514838
$771$	−45.8281	−1.65046
$772$	−84.7303	−3.04951
$773$	19.6272	0.705940	0.352970	−	0.935635i	$-0.385172\pi$
$773$	19.6272	0.705940	0.352970	+	0.935635i	$0.385172\pi$
$774$	50.2785	1.80722
$775$	36.7677	1.32073
$776$	−27.6194	−0.991480
$777$	−20.5819	−0.738371
$778$	29.6246	1.06209
$779$	18.6290	0.667454
$780$	44.2715	1.58517
$781$	−6.12168	−0.219051
$782$	−1.39492	−0.0498821
$783$	19.8256	0.708509
$784$	−20.2860	−0.724501
$785$	−44.2279	−1.57856
$786$	33.5538	1.19682
$787$	−40.1946	−1.43278	−0.716391	−	0.697699i	$-0.754207\pi$
$787$	−40.1946	−1.43278	−0.716391	+	0.697699i	$0.754207\pi$
$788$	−29.6313	−1.05557
$789$	53.9536	1.92080
$790$	89.6754	3.19051
$791$	25.5774	0.909429
$792$	9.39215	0.333736
$793$	5.62446	0.199731
$794$	16.5122	0.585996
$795$	107.270	3.80447
$796$	−25.6153	−0.907910
$797$	11.8733	0.420574	0.210287	−	0.977640i	$-0.432560\pi$
$797$	11.8733	0.420574	0.210287	+	0.977640i	$0.432560\pi$
$798$	−51.4792	−1.82234
$799$	5.03923	0.178275
$800$	−23.7650	−0.840218
$801$	−3.89919	−0.137771
$802$	−48.4899	−1.71224
$803$	10.4349	0.368238
$804$	99.2567	3.50051
$805$	−6.82508	−0.240552
$806$	13.0147	0.458422
$807$	41.8859	1.47445
$808$	100.315	3.52906
$809$	−39.2394	−1.37958	−0.689791	−	0.724008i	$-0.742298\pi$
$809$	−39.2394	−1.37958	−0.689791	+	0.724008i	$0.742298\pi$
$810$	−102.424	−3.59881
$811$	22.9863	0.807160	0.403580	−	0.914944i	$-0.367766\pi$
$811$	22.9863	0.807160	0.403580	+	0.914944i	$0.367766\pi$
$812$	68.6580	2.40942
$813$	−39.9723	−1.40189
$814$	10.5127	0.368469
$815$	−7.12407	−0.249545
$816$	−6.95438	−0.243452
$817$	50.7113	1.77416
$818$	−70.9375	−2.48027
$819$	4.57495	0.159862
$820$	58.6799	2.04919
$821$	9.62565	0.335938	0.167969	−	0.985792i	$-0.446279\pi$
$821$	9.62565	0.335938	0.167969	+	0.985792i	$0.446279\pi$
$822$	11.6623	0.406771
$823$	29.9009	1.04228	0.521140	−	0.853471i	$-0.325507\pi$
$823$	29.9009	1.04228	0.521140	+	0.853471i	$0.325507\pi$
$824$	−57.6034	−2.00671
$825$	−16.5443	−0.575998
$826$	46.4517	1.61626
$827$	52.2778	1.81788	0.908939	−	0.416929i	$-0.136893\pi$
$827$	52.2778	1.81788	0.908939	+	0.416929i	$0.136893\pi$
$828$	−8.47078	−0.294380
$829$	−26.7023	−0.927408	−0.463704	−	0.885990i	$-0.653480\pi$
$829$	−26.7023	−0.927408	−0.463704	+	0.885990i	$0.653480\pi$
$830$	94.5027	3.28024
$831$	10.2924	0.357039
$832$	5.56168	0.192816
$833$	2.02816	0.0702717
$834$	78.6647	2.72394
$835$	−69.4576	−2.40368
$836$	17.8836	0.618517
$837$	−9.36201	−0.323598
$838$	−81.0251	−2.79896
$839$	−37.8726	−1.30751	−0.653754	−	0.756707i	$-0.726807\pi$
$839$	−37.8726	−1.30751	−0.653754	+	0.756707i	$0.726807\pi$
$840$	−85.8943	−2.96363
$841$	48.4763	1.67160
$842$	34.9838	1.20562
$843$	7.29745	0.251337
$844$	90.4398	3.11307
$845$	42.5385	1.46337
$846$	44.9929	1.54689
$847$	18.8910	0.649101
$848$	−71.9939	−2.47228
$849$	49.4642	1.69761
$850$	12.3392	0.423231
$851$	−5.02233	−0.172163
$852$	69.4841	2.38049
$853$	7.56798	0.259123	0.129561	−	0.991571i	$-0.458643\pi$
$853$	7.56798	0.259123	0.129561	+	0.991571i	$0.458643\pi$
$854$	−20.6010	−0.704950
$855$	37.2344	1.27339
$856$	2.98694	0.102092
$857$	−33.3687	−1.13985	−0.569926	−	0.821696i	$-0.693028\pi$
$857$	−33.3687	−1.13985	−0.569926	+	0.821696i	$0.693028\pi$
$858$	−5.85617	−0.199926
$859$	−27.4503	−0.936592	−0.468296	−	0.883572i	$-0.655132\pi$
$859$	−27.4503	−0.936592	−0.468296	+	0.883572i	$0.655132\pi$
$860$	159.736	5.44697
$861$	15.1968	0.517904
$862$	96.1528	3.27498
$863$	−42.2956	−1.43976	−0.719879	−	0.694100i	$-0.755803\pi$
$863$	−42.2956	−1.43976	−0.719879	+	0.694100i	$0.755803\pi$
$864$	6.05118	0.205865
$865$	35.0256	1.19091
$866$	35.0851	1.19224
$867$	−37.2870	−1.26633
$868$	−32.4216	−1.10046
$869$	−8.06786	−0.273683
$870$	−182.982	−6.20367
$871$	−13.0810	−0.443234
$872$	−50.7315	−1.71798
$873$	9.76686	0.330558
$874$	−12.5618	−0.424909
$875$	26.2481	0.887349
$876$	−118.441	−4.00175
$877$	−25.3352	−0.855508	−0.427754	−	0.903895i	$-0.640695\pi$
$877$	−25.3352	−0.855508	−0.427754	+	0.903895i	$0.640695\pi$
$878$	−77.4870	−2.61506
$879$	−25.4827	−0.859511
$880$	17.3798	0.585874
$881$	−41.6112	−1.40192	−0.700959	−	0.713202i	$-0.747244\pi$
$881$	−41.6112	−1.40192	−0.700959	+	0.713202i	$0.747244\pi$
$882$	18.1085	0.609746
$883$	53.5076	1.80067	0.900337	−	0.435193i	$-0.143320\pi$
$883$	53.5076	1.80067	0.900337	+	0.435193i	$0.143320\pi$
$884$	2.97063	0.0999131
$885$	−84.2004	−2.83037
$886$	19.4462	0.653308
$887$	34.7571	1.16703	0.583515	−	0.812103i	$-0.301677\pi$
$887$	34.7571	1.16703	0.583515	+	0.812103i	$0.301677\pi$
$888$	−63.2065	−2.12107
$889$	−14.9702	−0.502086
$890$	−18.2138	−0.610529
$891$	9.21481	0.308708
$892$	89.2651	2.98882
$893$	45.3803	1.51859
$894$	52.7778	1.76516
$895$	99.1792	3.31519
$896$	−30.2264	−1.00979
$897$	2.79773	0.0934135
$898$	1.93300	0.0645051
$899$	−36.5858	−1.22020
$900$	74.9312	2.49771
$901$	7.19784	0.239795
$902$	−7.76209	−0.258449
$903$	41.3681	1.37664
$904$	78.5477	2.61246
$905$	−75.8839	−2.52247
$906$	16.3696	0.543842
$907$	18.9156	0.628082	0.314041	−	0.949409i	$-0.398317\pi$
$907$	18.9156	0.628082	0.314041	+	0.949409i	$0.398317\pi$
$908$	−101.597	−3.37161
$909$	−35.4736	−1.17658
$910$	21.3704	0.708422
$911$	−13.7060	−0.454101	−0.227051	−	0.973883i	$-0.572908\pi$
$911$	−13.7060	−0.454101	−0.227051	+	0.973883i	$0.572908\pi$
$912$	−62.6270	−2.07379
$913$	−8.50216	−0.281380
$914$	−10.3062	−0.340900
$915$	37.3422	1.23449
$916$	93.2410	3.08077
$917$	11.0160	0.363781
$918$	−3.14188	−0.103698
$919$	5.62628	0.185594	0.0927970	−	0.995685i	$-0.470419\pi$
$919$	5.62628	0.185594	0.0927970	+	0.995685i	$0.470419\pi$
$920$	−20.9596	−0.691019
$921$	−44.6695	−1.47191
$922$	−38.2377	−1.25929
$923$	−9.15730	−0.301416
$924$	14.5887	0.479932
$925$	44.4267	1.46074
$926$	8.33786	0.273999
$927$	20.3699	0.669035
$928$	23.6474	0.776263
$929$	−38.8625	−1.27504	−0.637519	−	0.770435i	$-0.720039\pi$
$929$	−38.8625	−1.27504	−0.637519	+	0.770435i	$0.720039\pi$
$930$	86.4075	2.83341
$931$	18.2644	0.598593
$932$	−30.7309	−1.00662
$933$	−39.2018	−1.28341
$934$	−45.4255	−1.48637
$935$	−1.73761	−0.0568259
$936$	14.0495	0.459224
$937$	−19.8180	−0.647427	−0.323714	−	0.946155i	$-0.604931\pi$
$937$	−19.8180	−0.647427	−0.323714	+	0.946155i	$0.604931\pi$
$938$	47.9124	1.56440
$939$	31.0614	1.01365
$940$	142.944	4.66233
$941$	−21.3134	−0.694796	−0.347398	−	0.937718i	$-0.612935\pi$
$941$	−21.3134	−0.694796	−0.347398	+	0.937718i	$0.612935\pi$
$942$	−66.4051	−2.16359
$943$	3.70826	0.120758
$944$	56.5109	1.83927
$945$	−15.3727	−0.500073
$946$	−21.1297	−0.686986
$947$	38.4697	1.25010	0.625048	−	0.780586i	$-0.285079\pi$
$947$	38.4697	1.25010	0.625048	+	0.780586i	$0.285079\pi$
$948$	91.5742	2.97419
$949$	15.6093	0.506700
$950$	111.120	3.60519
$951$	12.6320	0.409620
$952$	−5.76353	−0.186797
$953$	−12.5905	−0.407847	−0.203924	−	0.978987i	$-0.565369\pi$
$953$	−12.5905	−0.407847	−0.203924	+	0.978987i	$0.565369\pi$
$954$	64.2662	2.08069
$955$	−7.47911	−0.242018
$956$	−1.02844	−0.0332620
$957$	16.4624	0.532154
$958$	−48.7731	−1.57579
$959$	3.82886	0.123640
$960$	36.9253	1.19176
$961$	−13.7235	−0.442694
$962$	15.7257	0.507017
$963$	−1.05625	−0.0340372
$964$	−73.6850	−2.37323
$965$	74.1377	2.38658
$966$	−10.2474	−0.329704
$967$	−33.4993	−1.07726	−0.538632	−	0.842541i	$-0.681059\pi$
$967$	−33.4993	−1.07726	−0.538632	+	0.842541i	$0.681059\pi$
$968$	58.0137	1.86463
$969$	6.26135	0.201144
$970$	45.6228	1.46486
$971$	−23.1645	−0.743386	−0.371693	−	0.928356i	$-0.621223\pi$
$971$	−23.1645	−0.743386	−0.371693	+	0.928356i	$0.621223\pi$
$972$	−75.8570	−2.43312
$973$	25.8264	0.827956
$974$	106.186	3.40243
$975$	−24.7483	−0.792579
$976$	−25.0621	−0.802219
$977$	36.9889	1.18338	0.591690	−	0.806165i	$-0.298461\pi$
$977$	36.9889	1.18338	0.591690	+	0.806165i	$0.298461\pi$
$978$	−10.6963	−0.342029
$979$	1.63865	0.0523715
$980$	57.5315	1.83778
$981$	17.9398	0.572774
$982$	81.6297	2.60491
$983$	−24.4947	−0.781261	−0.390630	−	0.920548i	$-0.627743\pi$
$983$	−24.4947	−0.781261	−0.390630	+	0.920548i	$0.627743\pi$
$984$	46.6689	1.48775
$985$	25.9270	0.826102
$986$	−12.2781	−0.391016
$987$	37.0193	1.17834
$988$	26.7517	0.851086
$989$	10.0945	0.320987
$990$	−15.5143	−0.493077
$991$	−35.1731	−1.11731	−0.558655	−	0.829400i	$-0.688682\pi$
$991$	−35.1731	−1.11731	−0.558655	+	0.829400i	$0.688682\pi$
$992$	−11.1667	−0.354544
$993$	24.0084	0.761882
$994$	33.5408	1.06385
$995$	22.4130	0.710540
$996$	96.5037	3.05784
$997$	−15.8041	−0.500521	−0.250260	−	0.968179i	$-0.580516\pi$
$997$	−15.8041	−0.500521	−0.250260	+	0.968179i	$0.580516\pi$
$998$	−53.4403	−1.69162
$999$	−11.3122	−0.357902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.12	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.12	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50053 q^{2} +2.23425 q^{3} +4.25264 q^{4} -3.72100 q^{5} -5.58681 q^{6} -1.83421 q^{7} -5.63280 q^{8} +1.99189 q^{9} +O(q^{10})\)	\(q-2.50053 q^{2} +2.23425 q^{3} +4.25264 q^{4} -3.72100 q^{5} -5.58681 q^{6} -1.83421 q^{7} -5.63280 q^{8} +1.99189 q^{9} +9.30447 q^{10} -0.837098 q^{11} +9.50148 q^{12} -1.25220 q^{13} +4.58648 q^{14} -8.31365 q^{15} +5.57969 q^{16} -0.557849 q^{17} -4.98077 q^{18} -5.02365 q^{19} -15.8241 q^{20} -4.09808 q^{21} +2.09319 q^{22} -1.00000 q^{23} -12.5851 q^{24} +8.84584 q^{25} +3.13116 q^{26} -2.25238 q^{27} -7.80022 q^{28} -8.80206 q^{29} +20.7885 q^{30} +4.15650 q^{31} -2.68657 q^{32} -1.87029 q^{33} +1.39492 q^{34} +6.82508 q^{35} +8.47078 q^{36} +5.02233 q^{37} +12.5618 q^{38} -2.79773 q^{39} +20.9596 q^{40} -3.70826 q^{41} +10.2474 q^{42} -10.0945 q^{43} -3.55988 q^{44} -7.41181 q^{45} +2.50053 q^{46} -9.03333 q^{47} +12.4664 q^{48} -3.63569 q^{49} -22.1193 q^{50} -1.24637 q^{51} -5.32516 q^{52} -12.9029 q^{53} +5.63214 q^{54} +3.11484 q^{55} +10.3317 q^{56} -11.2241 q^{57} +22.0098 q^{58} +10.1280 q^{59} -35.3550 q^{60} -4.49167 q^{61} -10.3934 q^{62} -3.65353 q^{63} -4.44153 q^{64} +4.65943 q^{65} +4.67671 q^{66} +10.4464 q^{67} -2.37233 q^{68} -2.23425 q^{69} -17.0663 q^{70} +7.31298 q^{71} -11.2199 q^{72} -12.4655 q^{73} -12.5585 q^{74} +19.7638 q^{75} -21.3638 q^{76} +1.53541 q^{77} +6.99580 q^{78} +9.63789 q^{79} -20.7620 q^{80} -11.0080 q^{81} +9.27262 q^{82} +10.1567 q^{83} -17.4277 q^{84} +2.07575 q^{85} +25.2416 q^{86} -19.6660 q^{87} +4.71520 q^{88} -1.95754 q^{89} +18.5334 q^{90} +2.29679 q^{91} -4.25264 q^{92} +9.28667 q^{93} +22.5881 q^{94} +18.6930 q^{95} -6.00248 q^{96} +4.90332 q^{97} +9.09115 q^{98} -1.66740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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